ConnectPP---0.7.2.THM-Prf.s

%------------------------------------------------------------------------------
% File     : ConnectPP---0.7.2
% Problem  : SWW334+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 : n007.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 09:06:31 AM UTC 2026

% Result   : Theorem 59.76s 60.12s
% Output   : Proof 60.10s
% 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_Body__triple__valid__Suc,axiom,
    ! [V_Qa_2,V_pn_2,V_Pa_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_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_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_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2)) ),
    file('theBenchmark.p',fact_Body__triple__valid__Suc) ).

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_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_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_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_Body__triple__valid__0,axiom,
    ! [V_Qa_2,V_pn_2,V_Pa_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_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2)),
    file('theBenchmark.p',fact_Body__triple__valid__0) ).

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_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_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_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_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_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_triple__valid__def2,axiom,
    ! [V_Qa_2,V_c_2,V_Pa_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_Pa_2),V_c_2),V_Qa_2))
    <=> ! [B_Z,B_s] :
          ( hBOOL(hAPP(hAPP(V_Pa_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_Qa_2,B_Z),B_s_H)) ) ) ),
    file('theBenchmark.p',fact_triple__valid__def2) ).

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

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

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

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

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

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

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

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

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

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

fof(fact_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_I8_J,axiom,
    ! [V_fun_2,V_pname_2,V_vname_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_com_Osize_I8_J) ).

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

fof(fact_com_Osize_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_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_nat_Oexhaust,axiom,
    ! [V_y] :
      ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => ~ ! [B_nat] : V_y != hAPP(c_Nat_OSuc,B_nat) ),
    file('theBenchmark.p',fact_nat_Oexhaust) ).

fof(fact_zero__induct,axiom,
    ! [V_k_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,V_k_2))
     => ( ! [B_n] :
            ( hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_OSuc,B_n)))
           => hBOOL(hAPP(V_Pa_2,B_n)) )
       => hBOOL(hAPP(V_Pa_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_Suc__mono,axiom,
    ! [V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ),
    file('theBenchmark.p',fact_Suc__mono) ).

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

fof(fact_evaln_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_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_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_nat__less__cases,axiom,
    ! [V_Pa_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_Pa_2,V_n_2),V_m_2)) )
     => ( ( V_m_2 = V_n_2
         => hBOOL(hAPP(hAPP(V_Pa_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_Pa_2,V_n_2),V_m_2)) )
         => hBOOL(hAPP(hAPP(V_Pa_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_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_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_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_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_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_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_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_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_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_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_not__less0,axiom,
    ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_not__less0) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fof(fact_com_Osimps_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_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_evaln_Oequations_I1_J,axiom,
    ! [V_a2,V_a1] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_a1,V_a2,V_a1),
    file('theBenchmark.p',fact_evaln_Oequations_I1_J) ).

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

fof(fact_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_gr0__conv__Suc,axiom,
    ! [V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
    <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ),
    file('theBenchmark.p',fact_gr0__conv__Suc) ).

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

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

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

fof(fact_WTs__elim__cases_I8_J,axiom,
    ! [V_a_2,V_Pa_2,V_X_2] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_Pa_2,V_a_2)))
     => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_Pa_2))) ),
    file('theBenchmark.p',fact_WTs__elim__cases_I8_J) ).

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

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_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__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_evaln_Oequations_I2_J,axiom,
    ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] : c_Natural_Oevaln(c_Com_Ocom_OAss(V_a1_2,V_a2_2),V_a3_2,V_a4_2,hAPP(hAPP(hAPP(c_Natural_Oupdate,V_a3_2),V_a1_2),hAPP(V_a2_2,V_a3_2))),
    file('theBenchmark.p',fact_evaln_Oequations_I2_J) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fof(fact_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_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_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__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_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_Nats__induct,axiom,
    ! [V_Pa_2,V_x_2,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Nat_Osemiring__1__class_ONats(T_b)))
       => ( ! [B_n] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),B_n)))
         => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ) ),
    file('theBenchmark.p',fact_Nats__induct) ).

fof(fact_Nats__cases,axiom,
    ! [V_x_2,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Nat_Osemiring__1__class_ONats(T_b)))
       => ~ ! [B_n] : V_x_2 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),B_n) ) ),
    file('theBenchmark.p',fact_Nats__cases) ).

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_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_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_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_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_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_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_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_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_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_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_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_WTs__elim__cases_I7_J,axiom,
    ! [V_P] :
      ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P)))
     => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ),
    file('theBenchmark.p',fact_WTs__elim__cases_I7_J) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fof(fact_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_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_a) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_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_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
    ! [V_rx,V_ly,V_lx,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),V_ly)),V_rx) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_lx),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ly),V_rx)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_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_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_nat__mult__less__cancel1,axiom,
    ! [V_n_2,V_m_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_m_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k_2),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ),
    file('theBenchmark.p',fact_nat__mult__less__cancel1) ).

fof(fact_nat__mult__eq__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_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_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_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_split__nat,axiom,
    ! [V_i_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_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_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_ospec,axiom,
    ! [V_x_2,V_Pa_2,V_A_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Option_Oset(T_b,V_A_2)))
         => hBOOL(hAPP(V_Pa_2,B_x)) )
     => ( V_A_2 = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
       => hBOOL(hAPP(V_Pa_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_ospec) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fof(fact_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_Pa_2] :
      ( ! [B_x1] : hBOOL(hAPP(V_Pa_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_Pa_2,hAPP(c_Int_Onat,B_x))) ) ),
    file('theBenchmark.p',fact_all__nat) ).

fof(fact_ex__nat,axiom,
    ! [V_Pa_2] :
      ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
    <=> ? [B_x] :
          ( hBOOL(hAPP(V_Pa_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_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_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_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_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_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_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_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_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_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_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_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_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_xt1_I8_J,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Orderings_Oorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ),
    file('theBenchmark.p',fact_xt1_I8_J) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fof(fact_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_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_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_transfer__nat__int__relations_I2_J,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Int_Onat,V_y_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_transfer__nat__int__relations_I2_J) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fof(fact_transfer__int__nat__quantifiers_I2_J,axiom,
    ! [V_Pa_2] :
      ( ? [B_x] :
          ( hBOOL(hAPP(V_Pa_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_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ),
    file('theBenchmark.p',fact_transfer__int__nat__quantifiers_I2_J) ).

fof(fact_transfer__int__nat__quantifiers_I1_J,axiom,
    ! [V_Pa_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_Pa_2,B_x)) )
    <=> ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ),
    file('theBenchmark.p',fact_transfer__int__nat__quantifiers_I1_J) ).

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

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

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

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

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

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

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

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

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

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

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

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

fof(fact_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_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) ).

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

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_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_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_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_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_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_of__nat__1,axiom,
    ! [T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_of__nat__1) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fof(fact_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_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__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__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__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__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__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_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_y)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) ).

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

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

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

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

fof(fact_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_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_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) ).

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

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

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

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

fof(fact_minus__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_set__mp,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_set__mp) ).

fof(fact_set__rev__mp,axiom,
    ! [V_B_2,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_set__rev__mp) ).

fof(fact_in__mono,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_in__mono) ).

fof(fact_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_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_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_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_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__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__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_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_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_add__mult__distrib2,axiom,
    ! [V_n,V_m,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)),
    file('theBenchmark.p',fact_add__mult__distrib2) ).

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

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

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

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

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

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

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

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

fof(fact_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_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_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__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_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_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_add__gr__0,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) ) ),
    file('theBenchmark.p',fact_add__gr__0) ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

fof(fact_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_rev__predicate1D,axiom,
    ! [V_Qa_2,T_b,V_x_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,V_x_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2))
       => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_rev__predicate1D) ).

fof(fact_predicate1D,axiom,
    ! [V_x_2,V_Qa_2,V_Pa_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2))
     => ( hBOOL(hAPP(V_Pa_2,V_x_2))
       => hBOOL(hAPP(V_Qa_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_predicate1D) ).

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

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

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

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

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

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

fof(fact_Nat__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_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_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_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_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_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_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_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_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_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_Suc__eq__plus1,axiom,
    ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('theBenchmark.p',fact_Suc__eq__plus1) ).

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

fof(fact_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_self__quotient__aux2,axiom,
    ! [V_q,V_r,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_r),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_a),V_q))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ),
    file('theBenchmark.p',fact_self__quotient__aux2) ).

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

fof(fact_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_ex__least__nat__less,axiom,
    ! [V_n_2,V_Pa_2] :
      ( ~ hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
     => ( hBOOL(hAPP(V_Pa_2,V_n_2))
       => ? [B_k] :
            ( hBOOL(hAPP(V_Pa_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_Pa_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_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_I12_J,axiom,
    ! [V_com2,V_com1] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(V_com1,V_com2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com1)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),V_com2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_com_Osize_I12_J) ).

fof(fact_com_Osize_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_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_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_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_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_evaln__elim__cases_I5_J,axiom,
    ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2),V_s_2,V_n_2,V_t_2)
     => ( ( hBOOL(hAPP(V_b_2,V_s_2))
         => ~ c_Natural_Oevaln(V_c1_2,V_s_2,V_n_2,V_t_2) )
       => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2))
           => ~ c_Natural_Oevaln(V_c2_2,V_s_2,V_n_2,V_t_2) ) ) ),
    file('theBenchmark.p',fact_evaln__elim__cases_I5_J) ).

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

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

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

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

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

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

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

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

fof(fact_WTs__elim__cases_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_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_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_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_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_I45_J,axiom,
    ! [V_com2_2,V_com1_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2),
    file('theBenchmark.p',fact_com_Osimps_I45_J) ).

fof(fact_com_Osimps_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_I37_J,axiom,
    ! [V_com_2,V_fun_2,V_loc_2,V_com2_H_2,V_com1_H_2,V_fun_H_2] : c_Com_Ocom_OCond(V_fun_H_2,V_com1_H_2,V_com2_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2),
    file('theBenchmark.p',fact_com_Osimps_I37_J) ).

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

fof(fact_com_Osimps_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_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_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__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_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_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_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_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__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__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__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__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__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__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__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_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_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_WT_Oequations_I3_J,axiom,
    ! [V_a1_2,V_a3_2,V_a2_2] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2)))
    <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ),
    file('theBenchmark.p',fact_WT_Oequations_I3_J) ).

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

fof(fact_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_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_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_evalc_Oequations_I5_J,axiom,
    ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(V_a1_2,V_a3_2,V_a5_2)),V_a2_2),V_a4_2))
    <=> ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2))
          & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) )
        | ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2))
          & hBOOL(hAPP(V_a1_2,V_a2_2)) ) ) ),
    file('theBenchmark.p',fact_evalc_Oequations_I5_J) ).

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

fof(fact_WT_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_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_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_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_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_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_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_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_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_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_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_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_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_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_I57_J,axiom,
    ! [V_com2_2,V_com1_2,V_fun_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2),
    file('theBenchmark.p',fact_com_Osimps_I57_J) ).

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

fof(fact_com_Osimps_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_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_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_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_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_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_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_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_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__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__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__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_mod__pos__neg__trivial,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b) ) ),
    file('theBenchmark.p',fact_mod__pos__neg__trivial) ).

fof(fact_split__zmod,axiom,
    ! [V_k_2,V_n_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,B_j)) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(V_Pa_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_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_z3mod__def,axiom,
    ! [V_k,V_l] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
       => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
       => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) ),
    file('theBenchmark.p',fact_z3mod__def) ).

fof(fact_split__pos__lemma,axiom,
    ! [V_n_2,V_Pa_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_Pa_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_Pa_2,B_i),B_j)) ) ) ),
    file('theBenchmark.p',fact_split__pos__lemma) ).

fof(fact_split__neg__lemma,axiom,
    ! [V_n_2,V_Pa_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_Pa_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_Pa_2,B_i),B_j)) ) ) ),
    file('theBenchmark.p',fact_split__neg__lemma) ).

fof(fact_zmod__zmult2__eq,axiom,
    ! [V_b,V_a,V_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_c)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b)) ),
    file('theBenchmark.p',fact_zmod__zmult2__eq) ).

fof(fact_split__zdiv,axiom,
    ! [V_k_2,V_n_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,B_i)) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(V_Pa_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_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_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_evaln_OWhileFalse,axiom,
    ! [V_n_2,V_c_2,V_s_2,V_b_2] :
      ( ~ hBOOL(hAPP(V_b_2,V_s_2))
     => c_Natural_Oevaln(c_Com_Ocom_OWhile(V_b_2,V_c_2),V_s_2,V_n_2,V_s_2) ),
    file('theBenchmark.p',fact_evaln_OWhileFalse) ).

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

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

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

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

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

fof(fact_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_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__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_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_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_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_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__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__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_evaln_Oequations_I7_J,axiom,
    ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] :
      ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),V_a2_2,V_a4_2,V_a2_2)
    <=> ( hBOOL(hAPP(V_a1_2,V_a2_2))
       => ? [B_s1] :
            ( c_Natural_Oevaln(c_Com_Ocom_OWhile(V_a1_2,V_a3_2),B_s1,V_a4_2,V_a2_2)
            & c_Natural_Oevaln(V_a3_2,V_a2_2,V_a4_2,B_s1) ) ) ),
    file('theBenchmark.p',fact_evaln_Oequations_I7_J) ).

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

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

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

fof(fact_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_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_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_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_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_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_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_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_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_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_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_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_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_mod__1,axiom,
    ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_mod__1) ).

fof(fact_mod__Suc,axiom,
    ! [V_n,V_m] :
      ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) )
      & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n
       => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_mod__Suc) ).

fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom,
    ! [V_y,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y))) ) ),
    file('theBenchmark.p',fact_Divides_Otransfer__nat__int__function__closures_I1_J) ).

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

fof(fact_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_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_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_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_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_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_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_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_Pa_2] :
      ( hBOOL(hAPP(V_Pa_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_Pa_2,B_j)) ) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hBOOL(hAPP(V_Pa_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_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_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_z3div__def,axiom,
    ! [V_k,V_l] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
       => c_SMT_Oz3div(V_k,V_l) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_l))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l))
       => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) ),
    file('theBenchmark.p',fact_z3div__def) ).

fof(fact_zdiv__zminus1__eq__if,axiom,
    ! [V_a,V_b] :
      ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
        & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a)),V_b) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_zdiv__zminus1__eq__if) ).

fof(fact_zdiv__zminus2__eq__if,axiom,
    ! [V_a,V_b] :
      ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b))),c_Groups_Oone__class_Oone(tc_Int_Oint)) )
        & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_zdiv__zminus2__eq__if) ).

fof(fact_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_split__div_H,axiom,
    ! [V_n_2,V_m_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
    <=> ( ? [B_q] :
            ( hBOOL(hAPP(V_Pa_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_Pa_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_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_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_Pa_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_Pa_2,B_x))
           => hBOOL(hAPP(V_Pa_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_Pa_2,B_x))
             => hBOOL(hAPP(V_Pa_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_diffs0__imp__equal,axiom,
    ! [V_n,V_m] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => V_m = V_n ) ),
    file('theBenchmark.p',fact_diffs0__imp__equal) ).

fof(fact_diff__self__eq__0,axiom,
    ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_diff__self__eq__0) ).

fof(fact_minus__nat_Odiff__0,axiom,
    ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m,
    file('theBenchmark.p',fact_minus__nat_Odiff__0) ).

fof(fact_diff__0__eq__0,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    file('theBenchmark.p',fact_diff__0__eq__0) ).

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

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

fof(fact_less__imp__diff__less,axiom,
    ! [V_n,V_k,V_j] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_n)),V_k)) ),
    file('theBenchmark.p',fact_less__imp__diff__less) ).

fof(fact_diff__less__mono2,axiom,
    ! [V_l,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_n)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_l),V_m))) ) ),
    file('theBenchmark.p',fact_diff__less__mono2) ).

fof(fact_mod__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_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_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_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_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_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_Pa_2] :
      ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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__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_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__minus__eq__add,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Ogroup__add(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_diff__minus__eq__add) ).

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

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

fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Ocomm__ring__1(T_a)
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),V_y) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y)) ),
    file('theBenchmark.p',fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J) ).

fof(fact_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_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_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_less__bin__lemma,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_less__bin__lemma) ).

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

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

fof(fact_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_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_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_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_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__add__assoc2,axiom,
    ! [V_i,V_j,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) ),
    file('theBenchmark.p',fact_diff__add__assoc2) ).

fof(fact_add__diff__assoc2,axiom,
    ! [V_i,V_j,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j),V_k)),V_i) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j),V_i)),V_k) ),
    file('theBenchmark.p',fact_add__diff__assoc2) ).

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

fof(fact_le__imp__diff__is__add,axiom,
    ! [V_k_2,V_j_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
     => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2
      <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ),
    file('theBenchmark.p',fact_le__imp__diff__is__add) ).

fof(fact_le__add__diff__inverse2,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),V_n) = V_m ),
    file('theBenchmark.p',fact_le__add__diff__inverse2) ).

fof(fact_le__diff__conv2,axiom,
    ! [V_i_2,V_j_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),V_j_2)) ) ),
    file('theBenchmark.p',fact_le__diff__conv2) ).

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

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

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

fof(fact_le__diff__conv,axiom,
    ! [V_i_2,V_k_2,V_j_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_k_2)),V_i_2))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2))) ),
    file('theBenchmark.p',fact_le__diff__conv) ).

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

fof(fact_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_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__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__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_tsub__eq,axiom,
    ! [V_x,V_y] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x))
     => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ),
    file('theBenchmark.p',fact_tsub__eq) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom,
    ! [V_y,V_x] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_x),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_y)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x),V_y)),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J) ).

fof(fact_le__add__iff2,axiom,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( class_Rings_Oordered__ring(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ),
    file('theBenchmark.p',fact_le__add__iff2) ).

fof(fact_le__add__iff1,axiom,
    ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_b] :
      ( class_Rings_Oordered__ring(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_b_2),V_e_2)),V_d_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ),
    file('theBenchmark.p',fact_le__add__iff1) ).

fof(fact_less__add__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_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_div__le__mono2,axiom,
    ! [V_k,V_n,V_m] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_n)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_k),V_m))) ) ),
    file('theBenchmark.p',fact_div__le__mono2) ).

fof(fact_nat__mult__div__cancel1,axiom,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_m)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_k),V_n)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) ),
    file('theBenchmark.p',fact_nat__mult__div__cancel1) ).

fof(fact_div__mult__self1__is__m,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)),V_n) = V_m ),
    file('theBenchmark.p',fact_div__mult__self1__is__m) ).

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

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

fof(fact_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_Pa_2] :
      ( hBOOL(hAPP(V_Pa_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_Pa_2,B_d)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2))
         => hBOOL(hAPP(V_Pa_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_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
    <=> ~ ( ? [B_d] :
              ( ~ hBOOL(hAPP(V_Pa_2,B_d))
              & V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
          | ( ~ hBOOL(hAPP(V_Pa_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__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_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__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__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__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__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_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_split__div,axiom,
    ! [V_k_2,V_n_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_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_Pa_2,B_i)) ) ) )
        & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ),
    file('theBenchmark.p',fact_split__div) ).

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_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__iff2,axiom,
    ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2)),V_u_2)),V_n_2))) ) ),
    file('theBenchmark.p',fact_nat__less__add__iff2) ).

fof(fact_nat__less__add__iff1,axiom,
    ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_i_2),V_u_2)),V_m_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_j_2),V_u_2)),V_n_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_i_2),V_j_2)),V_u_2)),V_m_2)),V_n_2)) ) ),
    file('theBenchmark.p',fact_nat__less__add__iff1) ).

fof(fact_add__eq__if,axiom,
    ! [V_n,V_m] :
      ( ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_n)) )
      & ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) ),
    file('theBenchmark.p',fact_add__eq__if) ).

fof(fact_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_Pa_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_Pa_2,B_x))
           => hBOOL(hAPP(V_Pa_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_Pa_2,B_x))
             => hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,B_i))
           => hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) )
     => ( hBOOL(hAPP(V_Pa_2,V_i_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2))
         => hBOOL(hAPP(V_Pa_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_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_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_of__int__power,axiom,
    ! [V_n,V_z,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z)),V_n) ),
    file('theBenchmark.p',fact_of__int__power) ).

fof(fact_of__int__number__of__eq,axiom,
    ! [V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Oring__1__class_Oof__int(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v) ),
    file('theBenchmark.p',fact_of__int__number__of__eq) ).

fof(fact_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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__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__of__pos,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ),
    file('theBenchmark.p',fact_abs__of__pos) ).

fof(fact_zero__less__abs__iff,axiom,
    ! [V_a_2,T_b] :
      ( class_Groups_Oordered__ab__group__add__abs(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(c_Groups_Oabs__class_Oabs(T_b),V_a_2)))
      <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_zero__less__abs__iff) ).

fof(fact_abs__not__less__zero,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_abs__not__less__zero) ).

fof(fact_abs__triangle__ineq,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Groups_Oordered__ab__group__add__abs(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)))) ),
    file('theBenchmark.p',fact_abs__triangle__ineq) ).

fof(fact_abs__mult__less,axiom,
    ! [V_d,V_b,V_c,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_d))) ) ) ),
    file('theBenchmark.p',fact_abs__mult__less) ).

fof(fact_abs__triangle__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__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__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__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__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__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_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_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_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_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_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_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_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_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_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_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
    ! [V_n,V_x] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n))) ),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) ).

fof(fact_mult__number__of__left,axiom,
    ! [V_z,V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)),V_z)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w))),V_z) ),
    file('theBenchmark.p',fact_mult__number__of__left) ).

fof(fact_arith__simps_I32_J,axiom,
    ! [V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) ),
    file('theBenchmark.p',fact_arith__simps_I32_J) ).

fof(fact_number__of__mult,axiom,
    ! [V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
    file('theBenchmark.p',fact_number__of__mult) ).

fof(fact_abs__zmult__eq__1,axiom,
    ! [V_n,V_m] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n)) = c_Groups_Oone__class_Oone(tc_Int_Oint)
     => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    file('theBenchmark.p',fact_abs__zmult__eq__1) ).

fof(fact_number__of__diff,axiom,
    ! [V_w,V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_v),V_w)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
    file('theBenchmark.p',fact_number__of__diff) ).

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

fof(fact_number__of__minus,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
    file('theBenchmark.p',fact_number__of__minus) ).

fof(fact_arith__simps_I30_J,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)) ),
    file('theBenchmark.p',fact_arith__simps_I30_J) ).

fof(fact_mult__sgn__abs,axiom,
    ! [V_x,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Osgn__class_Osgn(T_a,V_x)),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_x)) = V_x ),
    file('theBenchmark.p',fact_mult__sgn__abs) ).

fof(fact_abs__sgn,axiom,
    ! [V_k,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_k) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_k),c_Groups_Osgn__class_Osgn(T_a,V_k)) ),
    file('theBenchmark.p',fact_abs__sgn) ).

fof(fact_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__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_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__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__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__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__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_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_number__of__is__id,axiom,
    ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k,
    file('theBenchmark.p',fact_number__of__is__id) ).

fof(fact_less__eq__number__of__int__code,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_less__eq__number__of__int__code) ).

fof(fact_less__number__of__int__code,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_less__number__of__int__code) ).

fof(fact_plus__numeral__code_I9_J,axiom,
    ! [V_w,V_v] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),V_w)),
    file('theBenchmark.p',fact_plus__numeral__code_I9_J) ).

fof(fact_times__numeral__code_I5_J,axiom,
    ! [V_w,V_v] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_v),V_w)),
    file('theBenchmark.p',fact_times__numeral__code_I5_J) ).

fof(fact_minus__numeral__code_I5_J,axiom,
    ! [V_w] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_w)),
    file('theBenchmark.p',fact_minus__numeral__code_I5_J) ).

fof(fact_nat__power__eq__Suc__0__iff,axiom,
    ! [V_m_2,V_x_2] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_x_2),V_m_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> ( V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_nat__power__eq__Suc__0__iff) ).

fof(fact_power__Suc__0,axiom,
    ! [V_n] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_n) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_power__Suc__0) ).

fof(fact_nat__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_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_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_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_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_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_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_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_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_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_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_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_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_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_zero__le__power,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
    file('theBenchmark.p',fact_zero__le__power) ).

fof(fact_power__mono,axiom,
    ! [V_n,V_b,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n))) ) ) ),
    file('theBenchmark.p',fact_power__mono) ).

fof(fact_zero__less__power,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
    file('theBenchmark.p',fact_zero__less__power) ).

fof(fact_power__eq__0__iff,axiom,
    ! [V_n_2,V_a_2,T_b] :
      ( ( class_Rings_Ozero__neq__one(T_b)
        & class_Rings_Ono__zero__divisors(T_b)
        & class_Rings_Omult__zero(T_b)
        & class_Power_Opower(T_b) )
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_b)
      <=> ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_power__eq__0__iff) ).

fof(fact_one__le__power,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
    file('theBenchmark.p',fact_one__le__power) ).

fof(fact_power__0__Suc,axiom,
    ! [V_n,T_a] :
      ( ( class_Rings_Osemiring__0(T_a)
        & class_Power_Opower(T_a) )
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Nat_OSuc,V_n)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_power__0__Suc) ).

fof(fact_power__inject__exp,axiom,
    ! [V_n_2,V_m_2,V_a_2,T_b] :
      ( class_Rings_Olinordered__semidom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_a_2))
       => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_m_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),V_n_2)
        <=> V_m_2 = V_n_2 ) ) ),
    file('theBenchmark.p',fact_power__inject__exp) ).

fof(fact_power__Suc2,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_a) ),
    file('theBenchmark.p',fact_power__Suc2) ).

fof(fact_power__Suc,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Power_Opower(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
    file('theBenchmark.p',fact_power__Suc) ).

fof(fact_power__0,axiom,
    ! [V_a,T_a] :
      ( class_Power_Opower(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_power__0) ).

fof(fact_power__add,axiom,
    ! [V_n,V_m,V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
    file('theBenchmark.p',fact_power__add) ).

fof(fact_abs__power__minus,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n)) = hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
    file('theBenchmark.p',fact_abs__power__minus) ).

fof(fact_power__less__imp__less__base,axiom,
    ! [V_b,V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_power__less__imp__less__base) ).

fof(fact_power__inject__base,axiom,
    ! [V_b,V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
           => V_a = V_b ) ) ) ),
    file('theBenchmark.p',fact_power__inject__base) ).

fof(fact_power__le__imp__le__base,axiom,
    ! [V_b,V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),hAPP(c_Nat_OSuc,V_n))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ),
    file('theBenchmark.p',fact_power__le__imp__le__base) ).

fof(fact_power__gt1__lemma,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)))) ) ),
    file('theBenchmark.p',fact_power__gt1__lemma) ).

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

fof(fact_power__0__left,axiom,
    ! [V_n,T_a] :
      ( ( class_Rings_Osemiring__0(T_a)
        & class_Power_Opower(T_a) )
     => ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Ozero__class_Ozero(T_a) )
        & ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_n) = c_Groups_Oone__class_Oone(T_a) ) ) ),
    file('theBenchmark.p',fact_power__0__left) ).

fof(fact_power__gt1,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Nat_OSuc,V_n)))) ) ),
    file('theBenchmark.p',fact_power__gt1) ).

fof(fact_power__strict__increasing,axiom,
    ! [V_a,V_N,V_n,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ),
    file('theBenchmark.p',fact_power__strict__increasing) ).

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

fof(fact_power__strict__increasing__iff,axiom,
    ! [V_y_2,V_x_2,V_b_2,T_b] :
      ( class_Rings_Olinordered__semidom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),V_b_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_x_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_b_2),V_y_2)))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_power__strict__increasing__iff) ).

fof(fact_zero__le__power__abs,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_n))) ),
    file('theBenchmark.p',fact_zero__le__power__abs) ).

fof(fact_power__increasing,axiom,
    ! [V_a,V_N,V_n,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_N))) ) ) ),
    file('theBenchmark.p',fact_power__increasing) ).

fof(fact_power__minus,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_n) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a))),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)) ),
    file('theBenchmark.p',fact_power__minus) ).

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

fof(fact_power__eq__imp__eq__base,axiom,
    ! [V_b,V_n,V_a,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_b),V_n)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n))
             => V_a = V_b ) ) ) ) ),
    file('theBenchmark.p',fact_power__eq__imp__eq__base) ).

fof(fact_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_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_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_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_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_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_divmod__nat__rel__unique,axiom,
    ! [V_qr_H,V_qr,V_n,V_m] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr))
     => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H))
       => V_qr = V_qr_H ) ),
    file('theBenchmark.p',fact_divmod__nat__rel__unique) ).

fof(fact_divmod__nat__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_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_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_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_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_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_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_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_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_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_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_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_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_divmod__int__rel__0,axiom,
    ! [V_b] :
      ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))) ),
    file('theBenchmark.p',fact_divmod__int__rel__0) ).

fof(fact_self__remainder,axiom,
    ! [V_r,V_q,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_self__remainder) ).

fof(fact_unique__quotient,axiom,
    ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H)))
       => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => V_q = V_q_H ) ) ),
    file('theBenchmark.p',fact_unique__quotient) ).

fof(fact_unique__remainder,axiom,
    ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_H),V_r_H)))
       => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => V_r = V_r_H ) ) ),
    file('theBenchmark.p',fact_unique__remainder) ).

fof(fact_self__quotient,axiom,
    ! [V_r,V_q,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_a),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    file('theBenchmark.p',fact_self__quotient) ).

fof(fact_divmod__int__rel__mod,axiom,
    ! [V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ),
    file('theBenchmark.p',fact_divmod__int__rel__mod) ).

fof(fact_divmod__int__rel__div,axiom,
    ! [V_r,V_q,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)))
     => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ),
    file('theBenchmark.p',fact_divmod__int__rel__div) ).

fof(fact_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_zadd1__lemma,axiom,
    ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_aq),V_ar)))
     => ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_b,V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_bq),V_br)))
       => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
         => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_a),V_b),V_c),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_aq),V_bq)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br)),V_c))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_ar),V_br),V_c)))) ) ) ),
    file('theBenchmark.p',fact_zadd1__lemma) ).

fof(fact_zminus1__lemma,axiom,
    ! [V_r_2,V_q_2,V_b_2,V_a_2] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a_2,V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q_2),V_r_2)))
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a_2),V_b_2),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_q_2)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,V_r_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_b_2),V_r_2))))) ),
    file('theBenchmark.p',fact_zminus1__lemma) ).

fof(fact_divmod__int__relI,axiom,
    ! [V_r,V_q,V_b,V_a] :
      ( V_a = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b),V_q)),V_r)
     => ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) ) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
           => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) ) ) )
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r))) ) ),
    file('theBenchmark.p',fact_divmod__int__relI) ).

fof(fact_same__fstI,axiom,
    ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_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_Pa_2,V_R_2))) ) ),
    file('theBenchmark.p',fact_same__fstI) ).

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_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_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_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_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_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_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_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_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_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_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_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_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_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_negDivAlg__correct,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
       => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ),
    file('theBenchmark.p',fact_negDivAlg__correct) ).

fof(fact_divmod__int__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_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_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_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_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_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_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_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_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__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__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_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_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_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_negateSnd__eq,axiom,
    ! [V_r,V_q] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),V_r)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_q),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_r)),
    file('theBenchmark.p',fact_negateSnd__eq) ).

fof(fact_mod__neg__neg,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
       => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)))) ) ),
    file('theBenchmark.p',fact_mod__neg__neg) ).

fof(fact_divmod__int__rel__neg,axiom,
    ! [V_qr,V_b,V_a] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_b)),V_qr))
     => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ),
    file('theBenchmark.p',fact_divmod__int__rel__neg) ).

fof(fact_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__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_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_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_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_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_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_exI__realizer,axiom,
    ! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(V_Pa_2,V_y_2),V_x_2))
     => hBOOL(hAPP(hAPP(V_Pa_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_conjI__realizer,axiom,
    ! [T_c,T_b,V_q_2,V_Qa_2,V_p_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,V_p_2))
     => ( hBOOL(hAPP(V_Qa_2,V_q_2))
       => ( hBOOL(hAPP(V_Qa_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_Pa_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_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_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_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_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_mod__nat__def,axiom,
    ! [V_n,V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(V_m,V_n)),
    file('theBenchmark.p',fact_mod__nat__def) ).

fof(fact_divmod__nat__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_split__paired__All,axiom,
    ! [T_c,T_b,V_Pa_2] :
      ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
    <=> ! [B_a,B_b] : hBOOL(hAPP(V_Pa_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_fst__conv,axiom,
    ! [V_b,V_a,T_b,T_a] : hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a),V_b)) = V_a,
    file('theBenchmark.p',fact_fst__conv) ).

fof(fact_fst__eqD,axiom,
    ! [V_a,V_y,V_x,T_b,T_a] :
      ( hAPP(c_Product__Type_Ofst(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) = V_a
     => V_x = V_a ),
    file('theBenchmark.p',fact_fst__eqD) ).

fof(fact_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_Pair__fst__snd__eq,axiom,
    ! [T_c,T_b,V_t_2,V_s_2] :
      ( V_s_2 = V_t_2
    <=> ( hAPP(c_Product__Type_Osnd(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Osnd(T_b,T_c),V_t_2)
        & hAPP(c_Product__Type_Ofst(T_b,T_c),V_s_2) = hAPP(c_Product__Type_Ofst(T_b,T_c),V_t_2) ) ),
    file('theBenchmark.p',fact_Pair__fst__snd__eq) ).

fof(fact_prod_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_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_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_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_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_iszero__Numeral0,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ),
    file('theBenchmark.p',fact_iszero__Numeral0) ).

fof(fact_Pls__def,axiom,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    file('theBenchmark.p',fact_Pls__def) ).

fof(fact_rel__simps_I19_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    file('theBenchmark.p',fact_rel__simps_I19_J) ).

fof(fact_rel__simps_I2_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    file('theBenchmark.p',fact_rel__simps_I2_J) ).

fof(fact_add__Pls__right,axiom,
    ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k,
    file('theBenchmark.p',fact_add__Pls__right) ).

fof(fact_add__Pls,axiom,
    ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k,
    file('theBenchmark.p',fact_add__Pls) ).

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

fof(fact_diff__bin__simps_I1_J,axiom,
    ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k,
    file('theBenchmark.p',fact_diff__bin__simps_I1_J) ).

fof(fact_minus__Pls,axiom,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
    file('theBenchmark.p',fact_minus__Pls) ).

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

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

fof(fact_iszero__def,axiom,
    ! [V_z_2,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => ( c_Int_Oiszero(T_b,V_z_2)
      <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_iszero__def) ).

fof(fact_iszero__0,axiom,
    ! [T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ),
    file('theBenchmark.p',fact_iszero__0) ).

fof(fact_not__iszero__1,axiom,
    ! [T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ),
    file('theBenchmark.p',fact_not__iszero__1) ).

fof(fact_number__of__Pls,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_number__of__Pls) ).

fof(fact_semiring__norm_I112_J,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ),
    file('theBenchmark.p',fact_semiring__norm_I112_J) ).

fof(fact_add__numeral__0__right,axiom,
    ! [V_a,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) = V_a ),
    file('theBenchmark.p',fact_add__numeral__0__right) ).

fof(fact_add__numeral__0,axiom,
    ! [V_a,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)),V_a) = V_a ),
    file('theBenchmark.p',fact_add__numeral__0) ).

fof(fact_bin__less__0__simps_I1_J,axiom,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    file('theBenchmark.p',fact_bin__less__0__simps_I1_J) ).

fof(fact_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_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_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_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_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_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_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_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__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__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_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_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_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_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_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_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_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_rel__simps_I51_J,axiom,
    ! [V_l_2,V_k_2] :
      ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2)
    <=> V_k_2 = V_l_2 ),
    file('theBenchmark.p',fact_rel__simps_I51_J) ).

fof(fact_less__eq__int__code_I16_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__eq__int__code_I16_J) ).

fof(fact_rel__simps_I34_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I34_J) ).

fof(fact_rel__simps_I17_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I17_J) ).

fof(fact_less__int__code_I16_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__int__code_I16_J) ).

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

fof(fact_rel__simps_I39_J,axiom,
    ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l),
    file('theBenchmark.p',fact_rel__simps_I39_J) ).

fof(fact_rel__simps_I47_J,axiom,
    ! [V_k_2] :
      ( c_Int_OBit1(V_k_2) = c_Int_OMin
    <=> V_k_2 = c_Int_OMin ),
    file('theBenchmark.p',fact_rel__simps_I47_J) ).

fof(fact_rel__simps_I43_J,axiom,
    ! [V_l_2] :
      ( c_Int_OMin = c_Int_OBit1(V_l_2)
    <=> c_Int_OMin = V_l_2 ),
    file('theBenchmark.p',fact_rel__simps_I43_J) ).

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

fof(fact_succ__pred,axiom,
    ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
    file('theBenchmark.p',fact_succ__pred) ).

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

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_number__of__Bit1,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
    file('theBenchmark.p',fact_number__of__Bit1) ).

fof(fact_mult__numeral__1,axiom,
    ! [V_a,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))),V_a) = V_a ),
    file('theBenchmark.p',fact_mult__numeral__1) ).

fof(fact_mult__numeral__1__right,axiom,
    ! [V_a,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) = V_a ),
    file('theBenchmark.p',fact_mult__numeral__1__right) ).

fof(fact_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_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_rel__simps_I29_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ),
    file('theBenchmark.p',fact_rel__simps_I29_J) ).

fof(fact_rel__simps_I5_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ),
    file('theBenchmark.p',fact_rel__simps_I5_J) ).

fof(fact_one__is__num__one,axiom,
    c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),
    file('theBenchmark.p',fact_one__is__num__one) ).

fof(fact_nat__numeral__1__eq__1,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat),
    file('theBenchmark.p',fact_nat__numeral__1__eq__1) ).

fof(fact_Numeral1__eq1__nat,axiom,
    c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)),
    file('theBenchmark.p',fact_Numeral1__eq1__nat) ).

fof(fact_diff__bin__simps_I4_J,axiom,
    ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),V_l)),
    file('theBenchmark.p',fact_diff__bin__simps_I4_J) ).

fof(fact_minus__Min,axiom,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls),
    file('theBenchmark.p',fact_minus__Min) ).

fof(fact_not__iszero__Numeral1,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ),
    file('theBenchmark.p',fact_not__iszero__Numeral1) ).

fof(fact_numeral__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_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_power3__eq__cube,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a)),V_a) ),
    file('theBenchmark.p',fact_power3__eq__cube) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J) ).

fof(fact_Suc3__eq__add__3,axiom,
    ! [V_n] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_n),
    file('theBenchmark.p',fact_Suc3__eq__add__3) ).

fof(fact_transfer__int__nat__numerals_I4_J,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    file('theBenchmark.p',fact_transfer__int__nat__numerals_I4_J) ).

fof(fact_transfer__nat__int__numerals_I4_J,axiom,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OBit1(c_Int_OPls))) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),
    file('theBenchmark.p',fact_transfer__nat__int__numerals_I4_J) ).

fof(fact_le__special_I2_J,axiom,
    ! [V_y_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ),
    file('theBenchmark.p',fact_le__special_I2_J) ).

fof(fact_le__special_I4_J,axiom,
    ! [V_x_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ),
    file('theBenchmark.p',fact_le__special_I4_J) ).

fof(fact_less__special_I4_J,axiom,
    ! [V_x_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),c_Groups_Oone__class_Oone(T_b)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ),
    file('theBenchmark.p',fact_less__special_I4_J) ).

fof(fact_less__special_I2_J,axiom,
    ! [V_y_2,T_b] :
      ( ( class_Rings_Olinordered__idom(T_b)
        & class_Int_Onumber__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Oone__class_Oone(T_b)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ),
    file('theBenchmark.p',fact_less__special_I2_J) ).

fof(fact_add__special_I3_J,axiom,
    ! [V_v,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_v)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_v),c_Int_OBit1(c_Int_OPls))) ),
    file('theBenchmark.p',fact_add__special_I3_J) ).

fof(fact_add__special_I2_J,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_w)) ),
    file('theBenchmark.p',fact_add__special_I2_J) ).

fof(fact_Suc__diff__eq__diff__pred,axiom,
    ! [V_m,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls)),V_n))
     => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)))) ),
    file('theBenchmark.p',fact_Suc__diff__eq__diff__pred) ).

fof(fact_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_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_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_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_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_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_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_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_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_neg__zdiv__mult__2,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_b),c_Groups_Oone__class_Oone(tc_Int_Oint))),V_a) ),
    file('theBenchmark.p',fact_neg__zdiv__mult__2) ).

fof(fact_pos__zdiv__mult__2,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_b),V_a) ),
    file('theBenchmark.p',fact_pos__zdiv__mult__2) ).

fof(fact_pos__zmod__mult__2,axiom,
    ! [V_b,V_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a))
     => c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_a)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,V_b,V_a))) ),
    file('theBenchmark.p',fact_pos__zmod__mult__2) ).

fof(fact_of__nat__double,axiom,
    ! [V_x,T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x))
       => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_x))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_a),hAPP(c_Int_Onat,V_x))) ) ),
    file('theBenchmark.p',fact_of__nat__double) ).

fof(fact_rel__simps_I48_J,axiom,
    ! [V_l_2,V_k_2] :
      ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2)
    <=> V_k_2 = V_l_2 ),
    file('theBenchmark.p',fact_rel__simps_I48_J) ).

fof(fact_rel__simps_I31_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I31_J) ).

fof(fact_less__eq__int__code_I13_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__eq__int__code_I13_J) ).

fof(fact_less__int__code_I13_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__int__code_I13_J) ).

fof(fact_rel__simps_I14_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I14_J) ).

fof(fact_Bit0__Pls,axiom,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    file('theBenchmark.p',fact_Bit0__Pls) ).

fof(fact_rel__simps_I38_J,axiom,
    ! [V_l_2] :
      ( c_Int_OPls = c_Int_OBit0(V_l_2)
    <=> c_Int_OPls = V_l_2 ),
    file('theBenchmark.p',fact_rel__simps_I38_J) ).

fof(fact_rel__simps_I44_J,axiom,
    ! [V_k_2] :
      ( c_Int_OBit0(V_k_2) = c_Int_OPls
    <=> V_k_2 = c_Int_OPls ),
    file('theBenchmark.p',fact_rel__simps_I44_J) ).

fof(fact_rel__simps_I49_J,axiom,
    ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l),
    file('theBenchmark.p',fact_rel__simps_I49_J) ).

fof(fact_rel__simps_I50_J,axiom,
    ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l),
    file('theBenchmark.p',fact_rel__simps_I50_J) ).

fof(fact_add__Bit0__Bit0,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)),
    file('theBenchmark.p',fact_add__Bit0__Bit0) ).

fof(fact_Bit0__def,axiom,
    ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k),
    file('theBenchmark.p',fact_Bit0__def) ).

fof(fact_mult__Bit0,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(V_k)),V_l) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l)),
    file('theBenchmark.p',fact_mult__Bit0) ).

fof(fact_diff__bin__simps_I7_J,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),V_l)),
    file('theBenchmark.p',fact_diff__bin__simps_I7_J) ).

fof(fact_minus__Bit0,axiom,
    ! [V_k] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(V_k)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_k)),
    file('theBenchmark.p',fact_minus__Bit0) ).

fof(fact_rel__simps_I42_J,axiom,
    ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l),
    file('theBenchmark.p',fact_rel__simps_I42_J) ).

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

fof(fact_bin__less__0__simps_I3_J,axiom,
    ! [V_w_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_w_2)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_bin__less__0__simps_I3_J) ).

fof(fact_rel__simps_I21_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ),
    file('theBenchmark.p',fact_rel__simps_I21_J) ).

fof(fact_rel__simps_I27_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ),
    file('theBenchmark.p',fact_rel__simps_I27_J) ).

fof(fact_rel__simps_I32_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I32_J) ).

fof(fact_less__eq__int__code_I14_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__eq__int__code_I14_J) ).

fof(fact_rel__simps_I10_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ),
    file('theBenchmark.p',fact_rel__simps_I10_J) ).

fof(fact_rel__simps_I4_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ),
    file('theBenchmark.p',fact_rel__simps_I4_J) ).

fof(fact_less__int__code_I15_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__int__code_I15_J) ).

fof(fact_rel__simps_I16_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I16_J) ).

fof(fact_add__Bit0__Bit1,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(V_k)),c_Int_OBit1(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)),
    file('theBenchmark.p',fact_add__Bit0__Bit1) ).

fof(fact_add__Bit1__Bit0,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(V_k)),c_Int_OBit0(V_l)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_l)),
    file('theBenchmark.p',fact_add__Bit1__Bit0) ).

fof(fact_diff__bin__simps_I3_J,axiom,
    ! [V_l] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_l)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),V_l)),
    file('theBenchmark.p',fact_diff__bin__simps_I3_J) ).

fof(fact_diff__bin__simps_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__Bit1,axiom,
    ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)),
    file('theBenchmark.p',fact_succ__Bit1) ).

fof(fact_succ__Bit0,axiom,
    ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k),
    file('theBenchmark.p',fact_succ__Bit0) ).

fof(fact_number__of__Bit0,axiom,
    ! [V_w,T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w))),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w)) ),
    file('theBenchmark.p',fact_number__of__Bit0) ).

fof(fact_rel__simps_I15_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I15_J) ).

fof(fact_less__int__code_I14_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__int__code_I14_J) ).

fof(fact_rel__simps_I33_J,axiom,
    ! [V_l_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ),
    file('theBenchmark.p',fact_rel__simps_I33_J) ).

fof(fact_less__eq__int__code_I15_J,axiom,
    ! [V_k2_2,V_k1_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ),
    file('theBenchmark.p',fact_less__eq__int__code_I15_J) ).

fof(fact_mult__Bit1,axiom,
    ! [V_l,V_k] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(V_k)),V_l) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k),V_l))),V_l),
    file('theBenchmark.p',fact_mult__Bit1) ).

fof(fact_rel__simps_I25_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2)))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ),
    file('theBenchmark.p',fact_rel__simps_I25_J) ).

fof(fact_rel__simps_I11_J,axiom,
    ! [V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ),
    file('theBenchmark.p',fact_rel__simps_I11_J) ).

fof(fact_diff__bin__simps_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,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_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_one__add__one__is__two,axiom,
    ! [T_a] :
      ( class_Int_Onumber__ring(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Oone__class_Oone(T_a)) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))) ),
    file('theBenchmark.p',fact_one__add__one__is__two) ).

fof(fact_zero__eq__power2,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Oring__1__no__zero__divisors(T_b)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_b)
      <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_zero__eq__power2) ).

fof(fact_zero__power2,axiom,
    ! [T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_zero__power2) ).

fof(fact_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_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_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
    ! [V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) ).

fof(fact_power2__eq__square,axiom,
    ! [V_a,T_a] :
      ( class_Groups_Omonoid__mult(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) ),
    file('theBenchmark.p',fact_power2__eq__square) ).

fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J) ).

fof(fact_add__2__eq__Suc,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)),
    file('theBenchmark.p',fact_add__2__eq__Suc) ).

fof(fact_add__2__eq__Suc_H,axiom,
    ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_n)),
    file('theBenchmark.p',fact_add__2__eq__Suc_H) ).

fof(fact_one__power2,axiom,
    ! [T_a] :
      ( class_Rings_Osemiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),c_Groups_Oone__class_Oone(T_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_a) ),
    file('theBenchmark.p',fact_one__power2) ).

fof(fact_power2__minus,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('theBenchmark.p',fact_power2__minus) ).

fof(fact_nat__mult__2__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_abs__power2,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(c_Groups_Oabs__class_Oabs(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('theBenchmark.p',fact_abs__power2) ).

fof(fact_power2__abs,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ),
    file('theBenchmark.p',fact_power2__abs) ).

fof(fact_nat__1__add__1,axiom,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
    file('theBenchmark.p',fact_nat__1__add__1) ).

fof(fact_mod2__Suc__Suc,axiom,
    ! [V_m] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    file('theBenchmark.p',fact_mod2__Suc__Suc) ).

fof(fact_div2__Suc__Suc,axiom,
    ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,V_m))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    file('theBenchmark.p',fact_div2__Suc__Suc) ).

fof(fact_zmod__number__of__Bit0,axiom,
    ! [V_w,V_v] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_v)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))),
    file('theBenchmark.p',fact_zmod__number__of__Bit0) ).

fof(fact_add__self__div__2,axiom,
    ! [V_m] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = V_m,
    file('theBenchmark.p',fact_add__self__div__2) ).

fof(fact_power2__eq__imp__eq,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
           => V_x = V_y ) ) ) ),
    file('theBenchmark.p',fact_power2__eq__imp__eq) ).

fof(fact_power2__le__imp__le,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ),
    file('theBenchmark.p',fact_power2__le__imp__le) ).

fof(fact_zero__le__power2,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    file('theBenchmark.p',fact_zero__le__power2) ).

fof(fact_zero__less__power2,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_zero__less__power2) ).

fof(fact_power2__less__0,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Olinordered__idom(T_a)
     => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_power2__less__0) ).

fof(fact_sum__power2__eq__zero__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Rings_Olinordered__idom(T_b)
     => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_x_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) = c_Groups_Ozero__class_Ozero(T_b)
      <=> ( V_y_2 = c_Groups_Ozero__class_Ozero(T_b)
          & V_x_2 = c_Groups_Ozero__class_Ozero(T_b) ) ) ),
    file('theBenchmark.p',fact_sum__power2__eq__zero__iff) ).

fof(fact_power2__eq__square__number__of,axiom,
    ! [V_w,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Groups_Omonoid__mult(T_b) )
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_w)) ),
    file('theBenchmark.p',fact_power2__eq__square__number__of) ).

fof(fact_less__2__cases,axiom,
    ! [V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
     => ( V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_less__2__cases) ).

fof(fact_nat__2,axiom,
    hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_nat__2) ).

fof(fact_power2__eq__1__iff,axiom,
    ! [V_a_2,T_b] :
      ( class_Rings_Oring__1__no__zero__divisors(T_b)
     => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_a_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = c_Groups_Oone__class_Oone(T_b)
      <=> ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_b),c_Groups_Oone__class_Oone(T_b))
          | V_a_2 = c_Groups_Oone__class_Oone(T_b) ) ) ),
    file('theBenchmark.p',fact_power2__eq__1__iff) ).

fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
    ! [V_n,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)) ),
    file('theBenchmark.p',fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) ).

fof(fact_power__minus__even,axiom,
    ! [V_n,V_a,T_a] :
      ( class_Rings_Oring__1(T_a)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) = hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_n)) ),
    file('theBenchmark.p',fact_power__minus__even) ).

fof(fact_power2__less__imp__less,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Rings_Olinordered__semidom(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ),
    file('theBenchmark.p',fact_power2__less__imp__less) ).

fof(fact_sum__power2__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_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_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_negDivAlg__eqn__1__number__of,axiom,
    ! [V_w] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))))
         => c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w))) ) ) ),
    file('theBenchmark.p',fact_negDivAlg__eqn__1__number__of) ).

fof(fact_negDivAlg__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_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_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_posDivAlg__eqn__1__number__of,axiom,
    ! [V_w] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)),c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)))
         => c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint)) ) ) ),
    file('theBenchmark.p',fact_posDivAlg__eqn__1__number__of) ).

fof(fact_posDivAlg_Osimps,axiom,
    ! [V_b,V_a] :
      ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) )
       => c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) )
       => c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a) ) ),
    file('theBenchmark.p',fact_posDivAlg_Osimps) ).

fof(fact_posDivAlg__eqn,axiom,
    ! [V_a,V_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
         => c_Divides_OposDivAlg(V_a,V_b) = hAPP(c_Divides_Oadjust(V_b),c_Divides_OposDivAlg(V_a,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),V_b))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b))
         => c_Divides_OposDivAlg(V_a,V_b) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a) ) ) ),
    file('theBenchmark.p',fact_posDivAlg__eqn) ).

fof(fact_posDivAlg__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_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_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_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_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_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_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_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_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_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_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_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_accp_Osimps,axiom,
    ! [V_a_2,V_r_2,T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
         => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ),
    file('theBenchmark.p',fact_accp_Osimps) ).

fof(fact_accp_Oequations,axiom,
    ! [V_a_2,V_r_2,T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2))
         => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),B_x)) ) ),
    file('theBenchmark.p',fact_accp_Oequations) ).

fof(fact_accp__downward,axiom,
    ! [V_a_2,V_b_2,V_r_2,T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_b_2))
     => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2))
       => hBOOL(hAPP(c_Wellfounded_Oaccp(T_b,V_r_2),V_a_2)) ) ),
    file('theBenchmark.p',fact_accp__downward) ).

fof(fact_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_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_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__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__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_less__eq__Suc__le__raw,axiom,
    ! [V_n_2] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),
    file('theBenchmark.p',fact_less__eq__Suc__le__raw) ).

fof(fact_nat__number__of__Bit0,axiom,
    ! [V_w_2] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_COMBI(tc_Nat_Onat))),
    file('theBenchmark.p',fact_nat__number__of__Bit0) ).

fof(fact_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_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_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_divide__self__if,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Odivision__ring__inverse__zero(T_a)
     => ( ( V_a != c_Groups_Ozero__class_Ozero(T_a)
         => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) )
        & ( V_a = c_Groups_Ozero__class_Ozero(T_a)
         => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ) ),
    file('theBenchmark.p',fact_divide__self__if) ).

fof(fact_divide__self,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Odivision__ring(T_a)
     => ( V_a != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ),
    file('theBenchmark.p',fact_divide__self) ).

fof(fact_right__inverse__eq,axiom,
    ! [V_a_2,V_b_2,T_b] :
      ( class_Rings_Odivision__ring(T_b)
     => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_b)
       => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_b)
        <=> V_a_2 = V_b_2 ) ) ),
    file('theBenchmark.p',fact_right__inverse__eq) ).

fof(fact_nonzero__minus__divide__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_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_power__number__of__even__number__of,axiom,
    ! [V_w_2,V_v_2,T_b] :
      ( class_Int_Onumber__ring(T_b)
     => hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(V_w_2))) = hAPP(hAPP(c_HOL_OLet(T_b,T_b),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_v_2)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(T_b,T_b,T_b),c_Groups_Otimes__class_Otimes(T_b)),c_COMBI(T_b))) ),
    file('theBenchmark.p',fact_power__number__of__even__number__of) ).

fof(fact_diff__nat__eq__if,axiom,
    ! [V_z_2,V_z_H_2] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_z_2),V_z_H_2)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_Int_Oint),c_If(tc_Nat_Onat)),c_Nat__Numeral_Oneg)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Int_Onat)) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,V_z_2)),hAPP(c_Int_Onat,V_z_H_2)) = hAPP(c_Int_Onat,V_z_2) ) ),
    file('theBenchmark.p',fact_diff__nat__eq__if) ).

fof(fact_semiring__1__class_Oof__nat__code,axiom,
    ! [V_n_2,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),V_n_2) = c_Nat_Osemiring__1__class_Oof__nat__aux(T_b,hAPP(hAPP(c_COMBC(T_b,T_b,T_b),c_Groups_Oplus__class_Oplus(T_b)),c_Groups_Oone__class_Oone(T_b)),V_n_2,c_Groups_Ozero__class_Ozero(T_b)) ),
    file('theBenchmark.p',fact_semiring__1__class_Oof__nat__code) ).

fof(fact_eq__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_eq__number__of__Suc,axiom,
    ! [V_n_2,V_v_2] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2)
    <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ),
    file('theBenchmark.p',fact_eq__number__of__Suc) ).

fof(fact_Suc__eq__number__of,axiom,
    ! [V_v_2,V_n_2] :
      ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)
    <=> hBOOL(hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_HOL_Obool),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),c_fNot),c_Nat__Numeral_Oneg))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Int_Oint),c_fequal),c_Int_Onat)),V_n_2))))) ),
    file('theBenchmark.p',fact_Suc__eq__number__of) ).

fof(fact_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_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_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__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_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_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_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_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_zpower__number__of__odd,axiom,
    ! [V_z_2,V_w_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2)))
       => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_z_2),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_w_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Otimes__class_Otimes(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z_2))),c_COMBI(tc_Int_Oint))) ) ),
    file('theBenchmark.p',fact_zpower__number__of__odd) ).

fof(fact_power__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_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_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_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_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_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_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_predicate2D,axiom,
    ! [V_y_2,V_x_2,V_Qa_2,V_Pa_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_Pa_2),V_Qa_2))
     => ( hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2))
       => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_predicate2D) ).

fof(fact_rev__predicate2D,axiom,
    ! [V_Qa_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(V_Pa_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_Pa_2),V_Qa_2))
       => hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_rev__predicate2D) ).

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_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_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_divide__right__mono__neg,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Fields_Olinordered__field__inverse__zero(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_c))) ) ) ),
    file('theBenchmark.p',fact_divide__right__mono__neg) ).

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

fof(fact_divide__le__0__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Fields_Olinordered__field__inverse__zero(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_a_2),V_b_2)),c_Groups_Ozero__class_Ozero(T_b)))
      <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_b_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),c_Groups_Ozero__class_Ozero(T_b))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),c_Groups_Ozero__class_Ozero(T_b)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),V_a_2)) ) ) ) ),
    file('theBenchmark.p',fact_divide__le__0__iff) ).

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

fof(fact_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_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_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__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__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__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__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__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_frac__eq__eq,axiom,
    ! [V_w_2,V_x_2,V_z_2,V_y_2,T_b] :
      ( class_Fields_Ofield(T_b)
     => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_b)
       => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_b)
         => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_x_2),V_y_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_w_2),V_z_2)
          <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),V_z_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_w_2),V_y_2) ) ) ) ),
    file('theBenchmark.p',fact_frac__eq__eq) ).

fof(fact_mult__divide__mult__cancel__left,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c),V_b)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ),
    file('theBenchmark.p',fact_mult__divide__mult__cancel__left) ).

fof(fact_mult__divide__mult__cancel__right,axiom,
    ! [V_b,V_a,V_c,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => ( V_c != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b),V_c)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_b) ) ),
    file('theBenchmark.p',fact_mult__divide__mult__cancel__right) ).

fof(fact_divide__eq__eq,axiom,
    ! [V_a_2,V_c_2,V_b_2,T_b] :
      ( class_Fields_Ofield__inverse__zero(T_b)
     => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2) = V_a_2
      <=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
           => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
          & ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
           => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) ) ) ) ),
    file('theBenchmark.p',fact_divide__eq__eq) ).

fof(fact_eq__divide__eq,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Fields_Ofield__inverse__zero(T_b)
     => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_b),V_b_2),V_c_2)
      <=> ( ( V_c_2 = c_Groups_Ozero__class_Ozero(T_b)
           => V_a_2 = c_Groups_Ozero__class_Ozero(T_b) )
          & ( V_c_2 != c_Groups_Ozero__class_Ozero(T_b)
           => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_a_2),V_c_2) = V_b_2 ) ) ) ),
    file('theBenchmark.p',fact_eq__divide__eq) ).

fof(fact_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_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__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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_add__frac__eq,axiom,
    ! [V_w,V_x,V_z,V_y,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
       => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ),
    file('theBenchmark.p',fact_add__frac__eq) ).

fof(fact_divide__add__eq__iff,axiom,
    ! [V_y,V_x,V_z,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ),
    file('theBenchmark.p',fact_divide__add__eq__iff) ).

fof(fact_add__frac__num,axiom,
    ! [V_z,V_x,V_y,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ),
    file('theBenchmark.p',fact_add__frac__num) ).

fof(fact_add__divide__eq__iff,axiom,
    ! [V_y,V_x,V_z,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ),
    file('theBenchmark.p',fact_add__divide__eq__iff) ).

fof(fact_add__num__frac,axiom,
    ! [V_x,V_z,V_y,T_a] :
      ( class_Fields_Ofield__inverse__zero(T_a)
     => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_z),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_y) ) ),
    file('theBenchmark.p',fact_add__num__frac) ).

fof(fact_diff__divide__eq__iff,axiom,
    ! [V_y,V_x,V_z,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_y),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_x)),V_y)),V_z) ) ),
    file('theBenchmark.p',fact_diff__divide__eq__iff) ).

fof(fact_divide__diff__eq__iff,axiom,
    ! [V_y,V_x,V_z,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_z)),V_y) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_z),V_y))),V_z) ) ),
    file('theBenchmark.p',fact_divide__diff__eq__iff) ).

fof(fact_diff__frac__eq,axiom,
    ! [V_w,V_x,V_z,V_y,T_a] :
      ( class_Fields_Ofield(T_a)
     => ( V_y != c_Groups_Ozero__class_Ozero(T_a)
       => ( V_z != c_Groups_Ozero__class_Ozero(T_a)
         => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_w),V_z)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_w),V_y))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_y),V_z)) ) ) ),
    file('theBenchmark.p',fact_diff__frac__eq) ).

fof(fact_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_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__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__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_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_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_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_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_negDivAlg_Opinduct,axiom,
    ! [V_Pa_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_Pa_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_Pa_2,B_a),B_b)) ) )
       => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_negDivAlg_Opinduct) ).

fof(fact_posDivAlg_Opinduct,axiom,
    ! [V_Pa_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_Pa_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_Pa_2,B_a),B_b)) ) )
       => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_posDivAlg_Opinduct) ).

fof(fact_nat__case__add__eq__if,axiom,
    ! [V_n_2,V_v_2,V_f_2,V_a_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2)),V_n_2)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,T_b),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,T_b,T_b),hAPP(hAPP(c_COMBC(tc_Int_Oint,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),tc_Int_Oint),c_If(T_b)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(T_b,V_a_2,V_f_2,V_n_2))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,tc_Int_Oint),V_f_2),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Int_Onat)),V_n_2)))),
    file('theBenchmark.p',fact_nat__case__add__eq__if) ).

fof(fact_adjust__def,axiom,
    ! [V_b_2] : c_Divides_Oadjust(V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))),
    file('theBenchmark.p',fact_adjust__def) ).

fof(fact_split__weak__cong,axiom,
    ! [V_c_2,T_d,T_c,T_b,V_q_2,V_p_2] :
      ( V_p_2 = V_q_2
     => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),V_c_2),V_q_2) ),
    file('theBenchmark.p',fact_split__weak__cong) ).

fof(fact_split__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_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_split__eta,axiom,
    ! [V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_d),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,T_d),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),T_d,T_c),V_f_2)),c_Product__Type_OPair(T_b,T_c))) = V_f_2,
    file('theBenchmark.p',fact_split__eta) ).

fof(fact_fst__def,axiom,
    ! [V_p_2,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_b),c_COMBK(T_b,T_c)),V_p_2),
    file('theBenchmark.p',fact_fst__def) ).

fof(fact_snd__def,axiom,
    ! [V_p_2,T_b,T_c] : hAPP(c_Product__Type_Osnd(T_c,T_b),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_b,T_b),hAPP(c_COMBK(tc_fun(T_b,T_b),T_c),c_COMBI(T_b))),V_p_2),
    file('theBenchmark.p',fact_snd__def) ).

fof(fact_nat__case__0,axiom,
    ! [V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2,
    file('theBenchmark.p',fact_nat__case__0) ).

fof(fact_nat__case__Suc,axiom,
    ! [V_nat_2,V_f2_2,V_f1_2,T_b] : c_Nat_Onat_Onat__case(T_b,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2),
    file('theBenchmark.p',fact_nat__case__Suc) ).

fof(fact_prod__case__beta,axiom,
    ! [V_p_2,V_f_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_f_2),V_p_2) = hAPP(hAPP(V_f_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)),
    file('theBenchmark.p',fact_prod__case__beta) ).

fof(fact_split__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__beta,axiom,
    ! [V_z_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_Pa_2),V_z_2) = hAPP(hAPP(V_Pa_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__def,axiom,
    ! [V_p_2,V_c_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_p_2)),hAPP(c_Product__Type_Osnd(T_c,T_d),V_p_2)),
    file('theBenchmark.p',fact_split__def) ).

fof(fact_less__eq__nat_Osimps_I2_J,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2))
    <=> hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ),
    file('theBenchmark.p',fact_less__eq__nat_Osimps_I2_J) ).

fof(fact_diff__Suc,axiom,
    ! [V_n_2,V_m_2] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2)),
    file('theBenchmark.p',fact_diff__Suc) ).

fof(fact_divmod__int__rel__def,axiom,
    ! [V_b_2,V_a_2] : c_Divides_Odivmod__int__rel(V_a_2,V_b_2) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,V_a_2))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_2)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),V_b_2))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),
    file('theBenchmark.p',fact_divmod__int__rel__def) ).

fof(fact_nat__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_divmod__int__pdivmod,axiom,
    ! [V_l_2,V_k_2] :
      ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l_2)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_l_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) )
          & ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) ) ) )
      & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    file('theBenchmark.p',fact_divmod__int__pdivmod) ).

fof(fact_divmod__int__code,axiom,
    ! [V_l_2,V_k_2] :
      ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => ( ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_k_2)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_l_2))),c_Divides_Opdivmod(V_k_2,V_l_2)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_l_2))))),c_Divides_Opdivmod(V_k_2,V_l_2)))) )
          & ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
           => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2) ) ) )
      & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
       => c_Divides_Odivmod__int(V_k_2,V_l_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ) ),
    file('theBenchmark.p',fact_divmod__int__code) ).

fof(fact_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_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_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_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_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_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_splitD_H,axiom,
    ! [V_c_2,V_b_2,V_a_2,V_R_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_d,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_c_2))
     => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ),
    file('theBenchmark.p',fact_splitD_H) ).

fof(fact_apsnd__conv,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_d),V_x_2),V_y_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),hAPP(V_f_2,V_y_2)),
    file('theBenchmark.p',fact_apsnd__conv) ).

fof(fact_fst__apsnd,axiom,
    ! [V_x_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Product__Type_Ofst(T_b,T_c),hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),V_x_2)) = hAPP(c_Product__Type_Ofst(T_b,T_d),V_x_2),
    file('theBenchmark.p',fact_fst__apsnd) ).

fof(fact_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_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_nat__rec__0,axiom,
    ! [V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_f1_2,
    file('theBenchmark.p',fact_nat__rec__0) ).

fof(fact_nat__rec__Suc,axiom,
    ! [V_nat_2,V_f2_2,V_f1_2,T_b] : hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(hAPP(V_f2_2,V_nat_2),hAPP(c_Nat_Onat_Onat__rec(T_b,V_f1_2,V_f2_2),V_nat_2)),
    file('theBenchmark.p',fact_nat__rec__Suc) ).

fof(fact_negateSnd__def,axiom,
    c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)),
    file('theBenchmark.p',fact_negateSnd__def) ).

fof(fact_divmod__nat__if,axiom,
    ! [V_m_2,V_n_2] :
      ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
            | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
       => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Nat_Onat,tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_prod(tc_Nat_Onat,tc_Nat_Onat)),tc_Nat_Onat),c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat)),c_Nat_OSuc)),c_Divides_Odivmod__nat(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2),V_n_2)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2))
          | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
       => c_Divides_Odivmod__nat(V_m_2,V_n_2) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2) ) ),
    file('theBenchmark.p',fact_divmod__nat__if) ).

fof(fact_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_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__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_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_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_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_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_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_le__maxI1,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ),
    file('theBenchmark.p',fact_le__maxI1) ).

fof(fact_le__maxI2,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y))) ),
    file('theBenchmark.p',fact_le__maxI2) ).

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

fof(fact_min__max_Ole__sup__iff,axiom,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),V_y_2)),V_z_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ),
    file('theBenchmark.p',fact_min__max_Ole__sup__iff) ).

fof(fact_min__max_Ole__supI1,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_min__max_Ole__supI1) ).

fof(fact_min__max_Ole__supI2,axiom,
    ! [V_a,V_b,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_min__max_Ole__supI2) ).

fof(fact_min__max_Osup__absorb2,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ),
    file('theBenchmark.p',fact_min__max_Osup__absorb2) ).

fof(fact_min__max_Osup__absorb1,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ),
    file('theBenchmark.p',fact_min__max_Osup__absorb1) ).

fof(fact_min__max_Ole__supI,axiom,
    ! [V_b,V_x,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x)) ) ) ),
    file('theBenchmark.p',fact_min__max_Ole__supI) ).

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

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

fof(fact_min__max_Ole__supE,axiom,
    ! [V_x,V_b,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_x))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ),
    file('theBenchmark.p',fact_min__max_Ole__supE) ).

fof(fact_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_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__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__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_Oless__supI1,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_min__max_Oless__supI1) ).

fof(fact_min__max_Oless__supI2,axiom,
    ! [V_a,V_b,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_min__max_Oless__supI2) ).

fof(fact_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__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_min__max_Oless__infI1,axiom,
    ! [V_b,V_x,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_min__max_Oless__infI1) ).

fof(fact_min__max_Oless__infI2,axiom,
    ! [V_a,V_x,V_b,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_min__max_Oless__infI2) ).

fof(fact_min__less__iff__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_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__add__distrib__left,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a)
     => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),V_z)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_min__add__distrib__left) ).

fof(fact_min__max_Osup_Oidem,axiom,
    ! [V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ),
    file('theBenchmark.p',fact_min__max_Osup_Oidem) ).

fof(fact_min__max_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__max_Osup_Ocommute,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_a) ),
    file('theBenchmark.p',fact_min__max_Osup_Ocommute) ).

fof(fact_min__max_Osup__commute,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x) ),
    file('theBenchmark.p',fact_min__max_Osup__commute) ).

fof(fact_min__max_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__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_Osup__inf__absorb,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)) = V_x ),
    file('theBenchmark.p',fact_min__max_Osup__inf__absorb) ).

fof(fact_min__max_Oinf__sup__absorb,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = V_x ),
    file('theBenchmark.p',fact_min__max_Oinf__sup__absorb) ).

fof(fact_min__max_Osup_Oleft__idem,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_min__max_Osup_Oleft__idem) ).

fof(fact_min__max_Osup__left__idem,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) ),
    file('theBenchmark.p',fact_min__max_Osup__left__idem) ).

fof(fact_min__max_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__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_Osup_Oleft__commute,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_min__max_Osup_Oleft__commute) ).

fof(fact_min__max_Osup__left__commute,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_min__max_Osup__left__commute) ).

fof(fact_min__max_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__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_Osup__inf__distrib1,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_min__max_Osup__inf__distrib1) ).

fof(fact_min__max_Oinf__sup__distrib1,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_min__max_Oinf__sup__distrib1) ).

fof(fact_min__max_Osup_Oassoc,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_min__max_Osup_Oassoc) ).

fof(fact_min__max_Osup__assoc,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_min__max_Osup__assoc) ).

fof(fact_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__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_Osup__inf__distrib2,axiom,
    ! [V_x,V_z,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_z),V_x)) ),
    file('theBenchmark.p',fact_min__max_Osup__inf__distrib2) ).

fof(fact_min__max_Oinf__sup__distrib2,axiom,
    ! [V_x,V_z,V_y,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)),V_x) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_y),V_x)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_z),V_x)) ),
    file('theBenchmark.p',fact_min__max_Oinf__sup__distrib2) ).

fof(fact_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_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_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_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_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_max__0L,axiom,
    ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n,
    file('theBenchmark.p',fact_max__0L) ).

fof(fact_max__0R,axiom,
    ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n,
    file('theBenchmark.p',fact_max__0R) ).

fof(fact_min__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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_code__numeral_Osimps_I3_J,axiom,
    ! [V_code__numeral_H_1] : c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_1) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',fact_code__numeral_Osimps_I3_J) ).

fof(fact_code__numeral_Osimps_I2_J,axiom,
    ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H),
    file('theBenchmark.p',fact_code__numeral_Osimps_I2_J) ).

fof(fact_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_acc_Osimps,axiom,
    ! [V_r_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2)))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_a_2)),V_r_2))
         => hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_acc_Osimps) ).

fof(fact_acc__downward,axiom,
    ! [V_a_2,V_r_2,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),c_Wellfounded_Oacc(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Wellfounded_Oacc(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_acc__downward) ).

fof(fact_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_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_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_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_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_Nitpick_Oint__lcm__def,axiom,
    ! [V_y,V_x] : c_Nitpick_Oint__lcm(V_x,V_y) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Nitpick_Onat__lcm(hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_x)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_y)))),
    file('theBenchmark.p',fact_Nitpick_Oint__lcm__def) ).

fof(fact_Nitpick_Ozero__frac__def,axiom,
    ! [T_a] : c_Nitpick_Ozero__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('theBenchmark.p',fact_Nitpick_Ozero__frac__def) ).

fof(fact_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_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_Oone__frac__def,axiom,
    ! [T_a] : c_Nitpick_Oone__frac(T_a) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('theBenchmark.p',fact_Nitpick_Oone__frac__def) ).

fof(fact_Nitpick_Onumber__of__frac__def,axiom,
    ! [V_n,T_a] : c_Nitpick_Onumber__of__frac(T_a,V_n) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_n),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    file('theBenchmark.p',fact_Nitpick_Onumber__of__frac__def) ).

fof(fact_nat__gcd_Opsimps,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Nitpick_Onat__gcd__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)))
     => ( ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = c_Nitpick_Onat__gcd(V_y_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x_2,V_y_2)) )
        & ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
         => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) ) ),
    file('theBenchmark.p',fact_nat__gcd_Opsimps) ).

fof(fact_norm__frac_Opinduct,axiom,
    ! [V_Pa_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_Pa_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_Pa_2,B_a),B_b)) ) )
       => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_norm__frac_Opinduct) ).

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_nat__gcd_Opinduct,axiom,
    ! [V_Pa_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_Pa_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) )
             => hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y)) ) )
       => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_nat__gcd_Opinduct) ).

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_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_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_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_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_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_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_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_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_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_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_Nitpick_Ouminus__frac__def,axiom,
    ! [V_q,T_a] : c_Nitpick_Ouminus__frac(T_a,V_q) = c_Nitpick_OAbs__Frac(T_a,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_a),V_q))),hAPP(c_Nitpick_Odenom(T_a),V_q))),
    file('theBenchmark.p',fact_Nitpick_Ouminus__frac__def) ).

fof(fact_Nitpick_Oless__frac__def,axiom,
    ! [V_r_2,V_q_2,T_b] :
      ( c_Nitpick_Oless__frac(T_b,V_q_2,V_r_2)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_Nitpick_Oless__frac__def) ).

fof(fact_Nitpick_Oless__eq__frac__def,axiom,
    ! [V_r_2,V_q_2,T_b] :
      ( c_Nitpick_Oless__eq__frac(T_b,V_q_2,V_r_2)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(T_b),c_Nitpick_Oplus__frac(T_b,V_q_2,c_Nitpick_Ouminus__frac(T_b,V_r_2)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    file('theBenchmark.p',fact_Nitpick_Oless__eq__frac__def) ).

fof(fact_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_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_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_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_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_subtract__code__numeral__def,axiom,
    c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',fact_subtract__code__numeral__def) ).

fof(fact_minus__code__numeral__code,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,V_n),V_m),
    file('theBenchmark.p',fact_minus__code__numeral__code) ).

fof(fact_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__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_subset__image__iff,axiom,
    ! [V_A_2,V_f_2,T_c,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2)))
    <=> ? [B_AA] :
          ( V_B_2 = hAPP(c_Set_Oimage(T_c,T_b,V_f_2),B_AA)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),B_AA),V_A_2)) ) ),
    file('theBenchmark.p',fact_subset__image__iff) ).

fof(fact_image__mono,axiom,
    ! [V_f_2,T_c,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2))) ),
    file('theBenchmark.p',fact_image__mono) ).

fof(fact_image__image,axiom,
    ! [V_A_2,V_g_2,T_d,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_A_2)) = hAPP(c_Set_Oimage(T_d,T_b,hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_f_2),V_g_2)),V_A_2),
    file('theBenchmark.p',fact_image__image) ).

fof(fact_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_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_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_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__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_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_The__split,axiom,
    ! [V_Pa_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_Pa_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_Pa_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_code__numeral_Orecs_I2_J,axiom,
    ! [V_code__numeral_2,V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2)) = hAPP(hAPP(V_f2_2,V_code__numeral_2),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,V_code__numeral_2)),
    file('theBenchmark.p',fact_code__numeral_Orecs_I2_J) ).

fof(fact_Random_Osimps,axiom,
    ! [V_size_2,V_g_2,T_b,V_nrandom_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm)),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(V_g_2,V_size_2)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(T_b,V_g_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_size_2))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b))))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(T_b)),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(T_b)),c_Product__Type_Ofst(T_b,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))))))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_nrandom_2),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)))
       => c_Random__Sequence_ORandom(T_b,V_g_2,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)) ) ),
    file('theBenchmark.p',fact_Random_Osimps) ).

fof(fact_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_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_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_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_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_split__paired__The,axiom,
    ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_Pa_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_Pa_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_code__numeral_Orecs_I1_J,axiom,
    ! [V_f2_2,V_f1_2,T_b] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(T_b,V_f1_2,V_f2_2,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = V_f1_2,
    file('theBenchmark.p',fact_code__numeral_Orecs_I1_J) ).

fof(fact_Random__Sequence_Oempty__def,axiom,
    ! [V_size_2,V_nrandom_2,T_b] : c_Random__Sequence_Oempty(T_b,V_nrandom_2,V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(T_b)),
    file('theBenchmark.p',fact_Random__Sequence_Oempty__def) ).

fof(fact_Random__Sequence_Osingle__def,axiom,
    ! [V_size_2,V_nrandom_2,V_x_2,T_b] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(T_b),V_x_2),V_nrandom_2),V_size_2) = hAPP(c_Product__Type_OPair(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(T_b),V_x_2)),
    file('theBenchmark.p',fact_Random__Sequence_Osingle__def) ).

fof(fact_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_transfer__int__nat__set__relations_I4_J,axiom,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( c_Nat__Transfer_Onat__set(V_B_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ),
    file('theBenchmark.p',fact_transfer__int__nat__set__relations_I4_J) ).

fof(fact_transfer__int__nat__set__relations_I5_J,axiom,
    ! [V_B_2,V_A_2] :
      ( c_Nat__Transfer_Onat__set(V_A_2)
     => ( c_Nat__Transfer_Onat__set(V_B_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2))
        <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_B_2))) ) ) ),
    file('theBenchmark.p',fact_transfer__int__nat__set__relations_I5_J) ).

fof(fact_transfer__int__nat__set__relations_I2_J,axiom,
    ! [V_A_2,V_x_2] :
      ( c_Nat__Transfer_Ois__nat(V_x_2)
     => ( c_Nat__Transfer_Onat__set(V_A_2)
       => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2))
        <=> hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,V_x_2)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_transfer__int__nat__set__relations_I2_J) ).

fof(fact_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_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_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_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_exE__realizer,axiom,
    ! [T_d,V_f_2,V_Qa_2,V_p_2,T_b,T_c,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(V_Pa_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_Pa_2,B_y),B_x))
           => hBOOL(hAPP(V_Qa_2,hAPP(hAPP(V_f_2,B_x),B_y))) )
       => hBOOL(hAPP(V_Qa_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_New__DSequence_Opos__not__seq__def,axiom,
    ! [V_i_2,V_xq_2] : hAPP(c_New__DSequence_Opos__not__seq(V_xq_2),V_i_2) = c_Lazy__Sequence_Ohb__not__seq(hAPP(V_xq_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))),V_i_2))),
    file('theBenchmark.p',fact_New__DSequence_Opos__not__seq__def) ).

fof(fact_code__numeral__not__eq__zero,axiom,
    ! [V_i_2] :
      ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),V_i_2)) ),
    file('theBenchmark.p',fact_code__numeral__not__eq__zero) ).

fof(fact_beyond__def,axiom,
    ! [V_l,V_k] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
       => c_Quickcheck_Obeyond(V_k,V_l) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l))
       => c_Quickcheck_Obeyond(V_k,V_l) = V_l ) ),
    file('theBenchmark.p',fact_beyond__def) ).

fof(fact_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_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_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_times__code__numeral__code,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),V_m)),
    file('theBenchmark.p',fact_times__code__numeral__code) ).

fof(fact_beyond__zero,axiom,
    ! [V_k] : c_Quickcheck_Obeyond(V_k,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    file('theBenchmark.p',fact_beyond__zero) ).

fof(fact_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_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_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_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_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_plus__code__numeral__code,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),
    file('theBenchmark.p',fact_plus__code__numeral__code) ).

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

fof(fact_subtract__code__numeral__code,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,V_n)),hAPP(c_Code__Numeral_Oof__nat,V_m)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m)),
    file('theBenchmark.p',fact_subtract__code__numeral__code) ).

fof(fact_code__numeral__decr,axiom,
    ! [V_k] :
      ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_k)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,V_k))) ),
    file('theBenchmark.p',fact_code__numeral__decr) ).

fof(fact_pos__not__random__dseq__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_R_2] : c_New__Random__Sequence_Opos__not__random__dseq(V_R_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2)),
    file('theBenchmark.p',fact_pos__not__random__dseq__def) ).

fof(fact_mod__code__numeral__def,axiom,
    ! [V_m,V_n] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,V_n,V_m) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,V_n),hAPP(c_Code__Numeral_Onat__of,V_m))),
    file('theBenchmark.p',fact_mod__code__numeral__def) ).

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

fof(fact_New__DSequence_Opos__decr__bind__def,axiom,
    ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
      ( ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)) )
      & ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Opos__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_b) ) ),
    file('theBenchmark.p',fact_New__DSequence_Opos__decr__bind__def) ).

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

fof(fact_Code__Numeral_Onat__of__inject,axiom,
    ! [V_l_2,V_k_2] :
      ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2)
    <=> V_k_2 = V_l_2 ),
    file('theBenchmark.p',fact_Code__Numeral_Onat__of__inject) ).

fof(fact_nat__of__inverse,axiom,
    ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x,
    file('theBenchmark.p',fact_nat__of__inverse) ).

fof(fact_of__nat__nat__of,axiom,
    ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k,
    file('theBenchmark.p',fact_of__nat__nat__of) ).

fof(fact_nat__of__of__nat,axiom,
    ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n,
    file('theBenchmark.p',fact_nat__of__of__nat) ).

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

fof(fact_nat__of__number,axiom,
    ! [V_k] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),V_k)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_k),
    file('theBenchmark.p',fact_nat__of__number) ).

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

fof(fact_nat__of__code,axiom,
    ! [V_i] : hAPP(c_Code__Numeral_Onat__of,V_i) = c_Code__Numeral_Onat__of__aux(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    file('theBenchmark.p',fact_nat__of__code) ).

fof(fact_nat__of__aux__def,axiom,
    ! [V_n,V_i] : c_Code__Numeral_Onat__of__aux(V_i,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_i)),V_n),
    file('theBenchmark.p',fact_nat__of__aux__def) ).

fof(fact_Suc__code__numeral__def,axiom,
    ! [V_k] : c_Code__Numeral_OSuc__code__numeral(V_k) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,V_k))),
    file('theBenchmark.p',fact_Suc__code__numeral__def) ).

fof(fact_minus__code__numeral__def,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
    file('theBenchmark.p',fact_minus__code__numeral__def) ).

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

fof(fact_div__code__numeral__def,axiom,
    ! [V_m,V_n] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),V_n),V_m) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_n)),hAPP(c_Code__Numeral_Onat__of,V_m))),
    file('theBenchmark.p',fact_div__code__numeral__def) ).

fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Opos__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    file('theBenchmark.p',fact_New__Random__Sequence_Opos__decr__bind__def) ).

fof(fact_New__DSequence_Opos__empty__def,axiom,
    ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a),
    file('theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).

fof(fact_New__DSequence_Opos__bind__def,axiom,
    ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Opos__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Obind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2),V_i_2)),
    file('theBenchmark.p',fact_New__DSequence_Opos__bind__def) ).

fof(fact_New__DSequence_Oneg__decr__bind__def,axiom,
    ! [V_f_2,V_x_2,T_b,T_c,V_i_2] :
      ( ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)) )
      & ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_New__DSequence_Oneg__decr__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_b) ) ),
    file('theBenchmark.p',fact_New__DSequence_Oneg__decr__bind__def) ).

fof(fact_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_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_pos__empty__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,T_b] : c_New__Random__Sequence_Opos__empty(T_b,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_b),
    file('theBenchmark.p',fact_pos__empty__def) ).

fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : c_New__Random__Sequence_Oneg__decr__bind(T_c,T_b,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    file('theBenchmark.p',fact_New__Random__Sequence_Oneg__decr__bind__def) ).

fof(fact_pos__bind__def,axiom,
    ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_b,T_c] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_c,T_b,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_c,T_b,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_c,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b)))),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_b))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)),
    file('theBenchmark.p',fact_pos__bind__def) ).

fof(fact_New__DSequence_Oneg__bind__def,axiom,
    ! [V_i_2,V_f_2,V_x_2,T_b,T_c] : hAPP(c_New__DSequence_Oneg__bind(T_c,T_b,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_c,T_b,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_c,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_b))),V_f_2),V_i_2)),
    file('theBenchmark.p',fact_New__DSequence_Oneg__bind__def) ).

fof(fact_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_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_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_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_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_power__dvd__imp__le,axiom,
    ! [V_n,V_m,V_i] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_i),V_n)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_i))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ),
    file('theBenchmark.p',fact_power__dvd__imp__le) ).

fof(fact_dvd_Oorder__refl,axiom,
    ! [V_x] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_x),V_x)),
    file('theBenchmark.p',fact_dvd_Oorder__refl) ).

fof(fact_dvd__0__right,axiom,
    ! [V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ),
    file('theBenchmark.p',fact_dvd__0__right) ).

fof(fact_dvd__1__left,axiom,
    ! [V_k] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),V_k)),
    file('theBenchmark.p',fact_dvd__1__left) ).

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

fof(fact_dvd__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__nat,axiom,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n))) ) ),
    file('theBenchmark.p',fact_dvd__diff__nat) ).

fof(fact_dvd__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_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_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_minus__dvd__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Rings_Ocomm__ring__1(T_b)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(T_b),V_x_2)),V_y_2))
      <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_x_2),V_y_2)) ) ),
    file('theBenchmark.p',fact_minus__dvd__iff) ).

fof(fact_dvd__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_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__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_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__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_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_nat__dvd__1__iff__1,axiom,
    ! [V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    <=> V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_nat__dvd__1__iff__1) ).

fof(fact_dvd__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_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__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_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_le__imp__power__dvd,axiom,
    ! [V_a,V_n,V_m,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ),
    file('theBenchmark.p',fact_le__imp__power__dvd) ).

fof(fact_dvd__power__le,axiom,
    ! [V_m,V_n,V_y,V_x,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),V_y))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_m))) ) ) ),
    file('theBenchmark.p',fact_dvd__power__le) ).

fof(fact_power__le__dvd,axiom,
    ! [V_m,V_b,V_n,V_a,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n)),V_b))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_m)),V_b)) ) ) ),
    file('theBenchmark.p',fact_power__le__dvd) ).

fof(fact_div__power,axiom,
    ! [V_n,V_x,V_y,T_a] :
      ( class_Divides_Osemiring__div(T_a)
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_y),V_x))
       => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_x),V_y)),V_n) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_y),V_n)) ) ),
    file('theBenchmark.p',fact_div__power) ).

fof(fact_dvd__1__iff__1,axiom,
    ! [V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    <=> V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    file('theBenchmark.p',fact_dvd__1__iff__1) ).

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

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

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

fof(fact_dvd__diffD1,axiom,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_m))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m))
         => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),V_n)) ) ) ),
    file('theBenchmark.p',fact_dvd__diffD1) ).

fof(fact_unity__coeff__ex,axiom,
    ! [V_l_2,V_Pa_2,T_b] :
      ( ( class_Rings_Osemiring__0(T_b)
        & class_Rings_Odvd(T_b) )
     => ( ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
      <=> ? [B_x] :
            ( hBOOL(hAPP(V_Pa_2,B_x))
            & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_l_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),c_Groups_Ozero__class_Ozero(T_b)))) ) ) ),
    file('theBenchmark.p',fact_unity__coeff__ex) ).

fof(fact_inf__period_I4_J,axiom,
    ! [V_t_2,V_D_2,V_d_2,T_b] :
      ( ( class_Rings_Odvd(T_b)
        & class_Rings_Ocomm__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
       => ! [B_x,B_k] :
            ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
          <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ),
    file('theBenchmark.p',fact_inf__period_I4_J) ).

fof(fact_inf__period_I3_J,axiom,
    ! [V_t_2,V_D_2,V_d_2,T_b] :
      ( ( class_Rings_Odvd(T_b)
        & class_Rings_Ocomm__ring(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),V_D_2))
       => ! [B_x,B_k] :
            ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),B_x),V_t_2)))
          <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),V_d_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_b),B_x),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),B_k),V_D_2))),V_t_2))) ) ) ),
    file('theBenchmark.p',fact_inf__period_I3_J) ).

fof(fact_dvd__eq__mod__eq__0__number__of,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( ( class_Int_Onumber(T_b)
        & class_Divides_Osemiring__div(T_b) )
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_b),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2)))
      <=> c_Divides_Odiv__class_Omod(T_b,hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_y_2),hAPP(c_Int_Onumber__class_Onumber__of(T_b),V_x_2)) = c_Groups_Ozero__class_Ozero(T_b) ) ),
    file('theBenchmark.p',fact_dvd__eq__mod__eq__0__number__of) ).

fof(fact_dvd__div__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_dvd__power,axiom,
    ! [V_x,V_n,T_a] :
      ( class_Rings_Ocomm__semiring__1(T_a)
     => ( ( V_x = c_Groups_Oone__class_Oone(T_a)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) )
       => hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(T_a),V_x),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),V_n))) ) ),
    file('theBenchmark.p',fact_dvd__power) ).

fof(fact_dvd__mult__cancel2,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n_2),V_m_2)),V_m_2))
      <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_dvd__mult__cancel2) ).

fof(fact_dvd__mult__cancel1,axiom,
    ! [V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2)),V_m_2))
      <=> V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_dvd__mult__cancel1) ).

fof(fact_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_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_rp__inv__image__rp,axiom,
    ! [V_f_2,T_c,V_Pa_2,T_b] :
      ( c_FunDef_Oreduction__pair(T_b,V_Pa_2)
     => c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2)) ),
    file('theBenchmark.p',fact_rp__inv__image__rp) ).

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_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_uminus__dvd__conv_I1_J,axiom,
    ! [V_t_2,V_d_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
    <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d_2)),V_t_2)) ),
    file('theBenchmark.p',fact_uminus__dvd__conv_I1_J) ).

fof(fact_uminus__dvd__conv_I2_J,axiom,
    ! [V_t_2,V_d_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),V_t_2))
    <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_d_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_t_2))) ),
    file('theBenchmark.p',fact_uminus__dvd__conv_I2_J) ).

fof(fact_zdvd__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_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_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__reduce,axiom,
    ! [V_m_2,V_n_2,V_k_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_n_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_k_2),V_m_2))))
    <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_k_2),V_n_2)) ),
    file('theBenchmark.p',fact_zdvd__reduce) ).

fof(fact_zdvd__period,axiom,
    ! [V_c_2,V_t_2,V_x_2,V_d_2,V_a_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),V_d_2))
     => ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),V_t_2)))
      <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),V_a_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_c_2),V_d_2))),V_t_2))) ) ),
    file('theBenchmark.p',fact_zdvd__period) ).

fof(fact_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__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_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_int__dvd__iff,axiom,
    ! [V_z_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2)),V_z_2))
    <=> hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_z_2)))) ),
    file('theBenchmark.p',fact_int__dvd__iff) ).

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

fof(fact_dvd_Ostrict__monoI,axiom,
    ! [V_f_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( ! [B_x,B_y] :
            ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_y),B_x))
              & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y)) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) )
       => c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,T_b,hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_f_2) ) ),
    file('theBenchmark.p',fact_dvd_Ostrict__monoI) ).

fof(fact_dvd_OmonoI,axiom,
    ! [V_f_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( ! [B_x,B_y] :
            ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y))) )
       => c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2) ) ),
    file('theBenchmark.p',fact_dvd_OmonoI) ).

fof(fact_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_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_CollectI,axiom,
    ! [T_b,V_a_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,V_a_2))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ),
    file('theBenchmark.p',fact_CollectI) ).

fof(fact_Collect__def,axiom,
    ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2,
    file('theBenchmark.p',fact_Collect__def) ).

fof(fact_CollectE,axiom,
    ! [V_Pa_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
     => hBOOL(hAPP(V_Pa_2,V_a_2)) ),
    file('theBenchmark.p',fact_CollectE) ).

fof(fact_CollectD,axiom,
    ! [V_Pa_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
     => hBOOL(hAPP(V_Pa_2,V_a_2)) ),
    file('theBenchmark.p',fact_CollectD) ).

fof(fact_mem__Collect__eq,axiom,
    ! [V_Pa_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
    <=> hBOOL(hAPP(V_Pa_2,V_a_2)) ),
    file('theBenchmark.p',fact_mem__Collect__eq) ).

fof(fact_Collect__mem__eq,axiom,
    ! [V_A_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)) = V_A_2,
    file('theBenchmark.p',fact_Collect__mem__eq) ).

fof(fact_Collect__neg__eq,axiom,
    ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),
    file('theBenchmark.p',fact_Collect__neg__eq) ).

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_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_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_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_converse__converse,axiom,
    ! [V_r_2,T_b,T_c] : hAPP(c_Relation_Oconverse(T_c,T_b),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)) = V_r_2,
    file('theBenchmark.p',fact_converse__converse) ).

fof(fact_converse__inv__image,axiom,
    ! [V_f_2,V_R_2,T_c,T_b] : hAPP(c_Relation_Oconverse(T_b,T_b),hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),V_R_2),V_f_2)) = hAPP(hAPP(c_Relation_Oinv__image(T_c,T_b),hAPP(c_Relation_Oconverse(T_c,T_c),V_R_2)),V_f_2),
    file('theBenchmark.p',fact_converse__inv__image) ).

fof(fact_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_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom,
    ! [V_Pa_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_Pa_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_Pa_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_Pa_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_Pa_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_Pa_2),c_Int_Onat)))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J) ).

fof(fact_converse__iff,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ),
    file('theBenchmark.p',fact_converse__iff) ).

fof(fact_converseI,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2))) ),
    file('theBenchmark.p',fact_converseI) ).

fof(fact_converseD,axiom,
    ! [V_r_2,V_b_2,V_a_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(c_Relation_Oconverse(T_c,T_b),V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_c,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_c,T_b),V_b_2),V_a_2)),V_r_2)) ),
    file('theBenchmark.p',fact_converseD) ).

fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom,
    ! [V_Pa_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_Pa_2))),
    file('theBenchmark.p',fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J) ).

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_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_Id__on__eqI,axiom,
    ! [V_A_2,T_b,V_b_2,V_a_2] :
      ( V_a_2 = V_b_2
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Relation_OId__on(T_b,V_A_2))) ) ),
    file('theBenchmark.p',fact_Id__on__eqI) ).

fof(fact_Id__on__iff,axiom,
    ! [V_A_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Relation_OId__on(T_b,V_A_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
        & V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_Id__on__iff) ).

fof(fact_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_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_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_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_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_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_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_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_transfer__nat__int__set__cong,axiom,
    ! [V_P_H_2,V_Pa_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_Pa_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_Pa_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_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_Range__Collect__split,axiom,
    ! [V_Pa_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_Pa_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_Pa_2))),
    file('theBenchmark.p',fact_Range__Collect__split) ).

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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_Domain__Collect__split,axiom,
    ! [V_Pa_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_Pa_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_Pa_2)),
    file('theBenchmark.p',fact_Domain__Collect__split) ).

fof(fact_card__less__Suc2,axiom,
    ! [V_i_2,V_M_2] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
     => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),V_i_2)))) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) ),
    file('theBenchmark.p',fact_card__less__Suc2) ).

fof(fact_card__less,axiom,
    ! [V_i_2,V_M_2] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2))
     => hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_M_2))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_OSuc,V_i_2))))) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    file('theBenchmark.p',fact_card__less) ).

fof(fact_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_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_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_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_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_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_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_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_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__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_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_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_pred__comp__rel__comp__eq,axiom,
    ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(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))
       => hBOOL(hAPP(hAPP(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_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_wf__inv__image,axiom,
    ! [V_f_2,T_c,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => c_Wellfounded_Owf(T_c,hAPP(hAPP(c_Relation_Oinv__image(T_b,T_c),V_r_2),V_f_2)) ),
    file('theBenchmark.p',fact_wf__inv__image) ).

fof(fact_wf__lex__prod,axiom,
    ! [V_rb_2,T_c,V_ra_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_ra_2)
     => ( c_Wellfounded_Owf(T_c,V_rb_2)
       => c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Wellfounded_Olex__prod(T_b,T_c,V_ra_2,V_rb_2)) ) ),
    file('theBenchmark.p',fact_wf__lex__prod) ).

fof(fact_wf__measure,axiom,
    ! [V_f_2,T_b] : c_Wellfounded_Owf(T_b,hAPP(c_Wellfounded_Omeasure(T_b),V_f_2)),
    file('theBenchmark.p',fact_wf__measure) ).

fof(fact_wf__comp__self,axiom,
    ! [V_R_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_R_2)
    <=> c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),V_R_2),V_R_2)) ),
    file('theBenchmark.p',fact_wf__comp__self) ).

fof(fact_wf__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_pred__comp_Oequations,axiom,
    ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(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_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__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__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__irrefl,axiom,
    ! [V_a_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ),
    file('theBenchmark.p',fact_wf__irrefl) ).

fof(fact_wf__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__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__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__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__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__acc__iff,axiom,
    ! [V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
    <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Wellfounded_Oacc(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_wf__acc__iff) ).

fof(fact_acc__wfD,axiom,
    ! [V_x_2,V_r_2,T_b] :
      ( c_Wellfounded_Owf(T_b,V_r_2)
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_acc__wfD) ).

fof(fact_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_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_Pa_2,T_b] :
      ( c_FunDef_Oreduction__pair(T_b,V_Pa_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_Pa_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_Pa_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_Pa_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_Pa_2)) ) ),
    file('theBenchmark.p',fact_reduction__pair__def) ).

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_wf__if__measure,axiom,
    ! [T_b,V_g_2,V_f_2,V_Pa_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_Pa_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_Pa_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_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__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_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_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__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_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_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_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_reduction__pair__lemma,axiom,
    ! [V_S_2,V_R_2,V_Pa_2,T_b] :
      ( c_FunDef_Oreduction__pair(T_b,V_Pa_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_Pa_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_Pa_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_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_wf__same__fst,axiom,
    ! [T_b,V_R_2,T_c,V_Pa_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_Pa_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_Pa_2,V_R_2)) ),
    file('theBenchmark.p',fact_wf__same__fst) ).

fof(fact_sup1E,axiom,
    ! [V_x_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2))
     => ( ~ hBOOL(hAPP(V_A_2,V_x_2))
       => hBOOL(hAPP(V_B_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_sup1E) ).

fof(fact_sup1CI,axiom,
    ! [T_b,V_A_2,V_x_2,V_B_2] :
      ( ( ~ hBOOL(hAPP(V_B_2,V_x_2))
       => hBOOL(hAPP(V_A_2,V_x_2)) )
     => hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),V_x_2)) ),
    file('theBenchmark.p',fact_sup1CI) ).

fof(fact_UnCI,axiom,
    ! [V_A_2,V_B_2,V_c_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2)) )
     => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ),
    file('theBenchmark.p',fact_UnCI) ).

fof(fact_UnE,axiom,
    ! [V_B_2,V_A_2,V_c_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_c_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_UnE) ).

fof(fact_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_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_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_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_sup__max,axiom,
    ! [T_b] :
      ( ( class_Orderings_Olinorder(T_b)
        & class_Lattices_Osemilattice__sup(T_b) )
     => c_Lattices_Osemilattice__sup__class_Osup(T_b) = c_Orderings_Oord__class_Omax(T_b) ),
    file('theBenchmark.p',fact_sup__max) ).

fof(fact_sup__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_Oidem,axiom,
    ! [V_a,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ),
    file('theBenchmark.p',fact_sup_Oidem) ).

fof(fact_sup__idem,axiom,
    ! [V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ),
    file('theBenchmark.p',fact_sup__idem) ).

fof(fact_sup_Ocommute,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_a) ),
    file('theBenchmark.p',fact_sup_Ocommute) ).

fof(fact_inf__sup__aci_I5_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ),
    file('theBenchmark.p',fact_inf__sup__aci_I5_J) ).

fof(fact_sup__commute,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_x) ),
    file('theBenchmark.p',fact_sup__commute) ).

fof(fact_sup_Oleft__idem,axiom,
    ! [V_b,V_a,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b) ),
    file('theBenchmark.p',fact_sup_Oleft__idem) ).

fof(fact_inf__sup__aci_I8_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ),
    file('theBenchmark.p',fact_inf__sup__aci_I8_J) ).

fof(fact_sup__left__idem,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) ),
    file('theBenchmark.p',fact_sup__left__idem) ).

fof(fact_sup_Oleft__commute,axiom,
    ! [V_c,V_a,V_b,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_c)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_sup_Oleft__commute) ).

fof(fact_inf__sup__aci_I7_J,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_inf__sup__aci_I7_J) ).

fof(fact_sup__left__commute,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)) ),
    file('theBenchmark.p',fact_sup__left__commute) ).

fof(fact_sup_Oassoc,axiom,
    ! [V_c,V_b,V_a,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b),V_c)) ),
    file('theBenchmark.p',fact_sup_Oassoc) ).

fof(fact_inf__sup__aci_I6_J,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_inf__sup__aci_I6_J) ).

fof(fact_sup__assoc,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),V_z) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)) ),
    file('theBenchmark.p',fact_sup__assoc) ).

fof(fact_sup__apply,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Lattices_Olattice(T_b)
     => hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,T_b)),V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_g_2,V_x_2)) ),
    file('theBenchmark.p',fact_sup__apply) ).

fof(fact_Un__absorb,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_A_2) = V_A_2,
    file('theBenchmark.p',fact_Un__absorb) ).

fof(fact_Un__commute,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2),
    file('theBenchmark.p',fact_Un__commute) ).

fof(fact_Un__left__absorb,axiom,
    ! [V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),
    file('theBenchmark.p',fact_Un__left__absorb) ).

fof(fact_Un__left__commute,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_C_2)),
    file('theBenchmark.p',fact_Un__left__commute) ).

fof(fact_Un__assoc,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_C_2)),
    file('theBenchmark.p',fact_Un__assoc) ).

fof(fact_bex__Un,axiom,
    ! [V_Pa_2,V_B_2,V_A_2,T_b] :
      ( ? [B_x] :
          ( hBOOL(hAPP(V_Pa_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_Pa_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
        | ? [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,B_x)) )
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2))
           => hBOOL(hAPP(V_Pa_2,B_x)) )
        & ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(V_Pa_2,B_x)) ) ) ),
    file('theBenchmark.p',fact_ball__Un) ).

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_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_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_inf__sup__ord_I3_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ),
    file('theBenchmark.p',fact_inf__sup__ord_I3_J) ).

fof(fact_sup__ge1,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ),
    file('theBenchmark.p',fact_sup__ge1) ).

fof(fact_inf__sup__ord_I4_J,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ),
    file('theBenchmark.p',fact_inf__sup__ord_I4_J) ).

fof(fact_sup__ge2,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y))) ),
    file('theBenchmark.p',fact_sup__ge2) ).

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

fof(fact_le__sup__iff,axiom,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( class_Lattices_Osemilattice__sup(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),V_x_2),V_y_2)),V_z_2))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_z_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2)) ) ) ),
    file('theBenchmark.p',fact_le__sup__iff) ).

fof(fact_le__supI1,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_le__supI1) ).

fof(fact_le__supI2,axiom,
    ! [V_a,V_b,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b))) ) ),
    file('theBenchmark.p',fact_le__supI2) ).

fof(fact_sup__absorb2,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ),
    file('theBenchmark.p',fact_sup__absorb2) ).

fof(fact_sup__absorb1,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ),
    file('theBenchmark.p',fact_sup__absorb1) ).

fof(fact_le__supI,axiom,
    ! [V_b,V_x,V_a,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x)) ) ) ),
    file('theBenchmark.p',fact_le__supI) ).

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

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

fof(fact_le__supE,axiom,
    ! [V_x,V_b,V_a,T_a] :
      ( class_Lattices_Osemilattice__sup(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_b)),V_x))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ),
    file('theBenchmark.p',fact_le__supE) ).

fof(fact_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_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_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_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_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_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_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_Collect__disj__eq,axiom,
    ! [V_Qa_2,V_Pa_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_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)),
    file('theBenchmark.p',fact_Collect__disj__eq) ).

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_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_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_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_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_Collect__imp__eq,axiom,
    ! [V_Qa_2,V_Pa_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_Pa_2)),V_Qa_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_Pa_2))),hAPP(c_Set_OCollect(T_b),V_Qa_2)),
    file('theBenchmark.p',fact_Collect__imp__eq) ).

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_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__pred__nat,axiom,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    file('theBenchmark.p',fact_wf__pred__nat) ).

fof(fact_Eps__split,axiom,
    ! [V_Pa_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_Pa_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_Pa_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_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__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_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_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_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_someI__ex,axiom,
    ! [T_b,V_Pa_2] :
      ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
     => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ),
    file('theBenchmark.p',fact_someI__ex) ).

fof(fact_some__eq__ex,axiom,
    ! [T_b,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2)))
    <=> ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1)) ),
    file('theBenchmark.p',fact_some__eq__ex) ).

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__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_someI,axiom,
    ! [T_b,V_x_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,V_x_2))
     => hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ),
    file('theBenchmark.p',fact_someI) ).

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_exE__some,axiom,
    ! [T_b,V_c_2,V_Pa_2] :
      ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
     => ( V_c_2 = c_Hilbert__Choice_OEps(T_b,V_Pa_2)
       => hBOOL(hAPP(V_Pa_2,V_c_2)) ) ),
    file('theBenchmark.p',fact_exE__some) ).

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_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_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_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_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_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_split__paired__Eps,axiom,
    ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_Pa_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_Pa_2)),c_Product__Type_OPair(T_b,T_c)))),
    file('theBenchmark.p',fact_split__paired__Eps) ).

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_hoare__derivs_OBody,axiom,
    ! [V_Procsa_2,V_Qa_2,V_Pa_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_Pa_2)),c_Com_Ocom_OBODY)),V_Qa_2)),V_Procsa_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_Pa_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_Qa_2)),V_Procsa_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_Pa_2)),c_Com_Ocom_OBODY)),V_Qa_2)),V_Procsa_2)) ),
    file('theBenchmark.p',fact_hoare__derivs_OBody) ).

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_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_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_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_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_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_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__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__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_r__r__into__trancl,axiom,
    ! [V_c_2,V_R_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_R_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_R_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2))) ) ),
    file('theBenchmark.p',fact_r__r__into__trancl) ).

fof(fact_trancl__into__trancl2,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_trancl__into__trancl2) ).

fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).

fof(fact_trancl__trans,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_trancl__trans) ).

fof(fact_cut,axiom,
    ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_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_ts_2) ) ),
    file('theBenchmark.p',fact_cut) ).

fof(fact_thin,axiom,
    ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_G_H_2,V_ts_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_ts_2) ) ),
    file('theBenchmark.p',fact_thin) ).

fof(fact_weaken,axiom,
    ! [V_ts_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_ts_2),V_ts_H_2))
       => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ) ),
    file('theBenchmark.p',fact_weaken) ).

fof(fact_asm,axiom,
    ! [V_Ga_2,V_ts_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_Ga_2))
     => c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2) ),
    file('theBenchmark.p',fact_asm) ).

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__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_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__converseI,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ),
    file('theBenchmark.p',fact_trancl__converseI) ).

fof(fact_trancl__converseD,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_b),c_Transitive__Closure_Otrancl(T_b,V_r_2)))) ),
    file('theBenchmark.p',fact_trancl__converseD) ).

fof(fact_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_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_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_Body1,axiom,
    ! [V_pn_2,V_Procsa_2,V_Qa_2,V_Pa_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_Pa_2)),c_Com_Ocom_OBODY)),V_Qa_2)),V_Procsa_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_Pa_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_Qa_2)),V_Procsa_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procsa_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_Pa_2,V_pn_2)),hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(V_Qa_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_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_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_acyclicP__converse,axiom,
    ! [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),c_Predicate_Oconversep(T_b,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_acyclicP__converse) ).

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_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_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_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_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_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__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__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_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_image__is__empty,axiom,
    ! [V_A_2,V_f_2,T_b,T_c] :
      ( hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_image__is__empty) ).

fof(fact_image__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_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_derivs__insertD,axiom,
    ! [V_ts_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_ts_2))
     => ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_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_ts_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_ts_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_ts_2)) ) ),
    file('theBenchmark.p',fact_hoare__derivs_Oinsert) ).

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_image__insert,axiom,
    ! [V_B_2,V_a_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(V_f_2,V_a_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),V_B_2)),
    file('theBenchmark.p',fact_image__insert) ).

fof(fact_image__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_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_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__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__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_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_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_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_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_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_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_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__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_subset__insertI,axiom,
    ! [V_a_2,V_B_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2))),
    file('theBenchmark.p',fact_subset__insertI) ).

fof(fact_subset__insertI2,axiom,
    ! [V_b_2,V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),V_B_2))) ),
    file('theBenchmark.p',fact_subset__insertI2) ).

fof(fact_insert__mono,axiom,
    ! [V_a_2,V_D_2,V_C_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_D_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_C_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_D_2))) ),
    file('theBenchmark.p',fact_insert__mono) ).

fof(fact_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_conversepD,axiom,
    ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
     => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ),
    file('theBenchmark.p',fact_conversepD) ).

fof(fact_conversep_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(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2)) ),
    file('theBenchmark.p',fact_conversep_Ointros) ).

fof(fact_conversep_Oequations,axiom,
    ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2))
    <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ),
    file('theBenchmark.p',fact_conversep_Oequations) ).

fof(fact_conversep__iff,axiom,
    ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
    <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ),
    file('theBenchmark.p',fact_conversep__iff) ).

fof(fact_conversep__conversep,axiom,
    ! [V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Oconversep(T_b,T_c,V_r_2)) = V_r_2,
    file('theBenchmark.p',fact_conversep__conversep) ).

fof(fact_conversep__eq,axiom,
    ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal,
    file('theBenchmark.p',fact_conversep__eq) ).

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_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_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__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_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__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_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_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_conversep__noteq,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot)),c_fequal)),V_x_2),V_y_2))
    <=> V_x_2 != V_y_2 ),
    file('theBenchmark.p',fact_conversep__noteq) ).

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_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_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_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__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__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_Collect__empty__eq,axiom,
    ! [V_Pa_2,T_b] :
      ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ),
    file('theBenchmark.p',fact_Collect__empty__eq) ).

fof(fact_empty__Collect__eq,axiom,
    ! [V_Pa_2,T_b] :
      ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2)
    <=> ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x)) ),
    file('theBenchmark.p',fact_empty__Collect__eq) ).

fof(fact_Collect__conv__if,axiom,
    ! [T_b,V_a_2,V_Pa_2] :
      ( ( ~ hBOOL(hAPP(V_Pa_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_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2] :
      ( ( ~ hBOOL(hAPP(V_Pa_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_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) )
      & ( hBOOL(hAPP(V_Pa_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_Pa_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_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_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_diff__single__insert,axiom,
    ! [V_B_2,V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_diff__single__insert) ).

fof(fact_subset__insert__iff,axiom,
    ! [V_B_2,V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
    <=> ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) )
        & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_subset__insert__iff) ).

fof(fact_insert__Collect,axiom,
    ! [V_Pa_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_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_Pa_2)),
    file('theBenchmark.p',fact_insert__Collect) ).

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_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_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_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_Comp,axiom,
    ! [V_R_2,V_d_2,V_Qa_2,V_c_2,V_Pa_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_Pa_2),V_c_2),V_Qa_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_Qa_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_Pa_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_Pa_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_Pa_2),c_Com_Ocom_OSKIP),V_Pa_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_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_converse__join,axiom,
    ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)),
    file('theBenchmark.p',fact_converse__join) ).

fof(fact_LoopF,axiom,
    ! [V_c_2,V_b_2,V_Pa_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_Pa_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_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_LoopF) ).

fof(fact_converse__pred__comp,axiom,
    ! [V_s_2,V_r_2,T_d,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Opred__comp(T_c,T_d,T_b,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_b,T_d,T_c,c_Predicate_Oconversep(T_d,T_b,V_s_2),c_Predicate_Oconversep(T_c,T_d,V_r_2)),
    file('theBenchmark.p',fact_converse__pred__comp) ).

fof(fact_insert__subset,axiom,
    ! [V_B_2,V_A_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)),V_B_2))
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_insert__subset) ).

fof(fact_subset__insert,axiom,
    ! [V_B_2,V_A_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_B_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ),
    file('theBenchmark.p',fact_subset__insert) ).

fof(fact_insert__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_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_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_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_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_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_Ass,axiom,
    ! [V_a_2,V_X_2,V_Pa_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_Pa_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_Pa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))),
    file('theBenchmark.p',fact_Ass) ).

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_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_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_BodyN,axiom,
    ! [V_Ga_2,V_Qa_2,V_pn_2,V_Pa_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_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_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_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_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_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_BodyN) ).

fof(fact_weak__Body,axiom,
    ! [V_Qa_2,V_pn_2,V_Pa_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_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_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_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_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_conversep__converse__eq,axiom,
    ! [V_y_2,V_x_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(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),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_Relation_Oconverse(T_b,T_c),V_r_2))) ),
    file('theBenchmark.p',fact_conversep__converse__eq) ).

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_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_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_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_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_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_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_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_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_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_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_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_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_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_dvd_OatLeastLessThan__empty__iff2,axiom,
    ! [V_b_2,V_a_2] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2)
    <=> ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_dvd_OatLeastLessThan__empty__iff2) ).

fof(fact_dvd_OgreaterThanAtMost__empty__iff2,axiom,
    ! [V_l_2,V_k_2] :
      ( c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) = c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2)
    <=> ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) ) ),
    file('theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty__iff2) ).

fof(fact_dvd_OatLeastLessThan__empty__iff,axiom,
    ! [V_b_2,V_a_2] :
      ( c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    <=> ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_dvd_OatLeastLessThan__empty__iff) ).

fof(fact_dvd_OgreaterThanAtMost__empty__iff,axiom,
    ! [V_l_2,V_k_2] :
      ( c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    <=> ~ ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k_2),V_l_2)) ) ),
    file('theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty__iff) ).

fof(fact_dvd_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_OatLeastLessThan__empty,axiom,
    ! [V_a_2,V_b_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_b_2),V_a_2))
     => c_SetInterval_Oord_OatLeastLessThan(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_a_2,V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_dvd_OatLeastLessThan__empty) ).

fof(fact_dvd_OgreaterThanAtMost__empty,axiom,
    ! [V_k_2,V_l_2] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_l_2),V_k_2))
     => c_SetInterval_Oord_OgreaterThanAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_Nat_Onat),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_Nat_Onat),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Nat_Onat),c_fNot)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Rings_Odvd__class_Odvd(tc_Nat_Onat)))),V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_dvd_OgreaterThanAtMost__empty) ).

fof(fact_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_card__Diff__singleton__if,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) )
        & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ) ),
    file('theBenchmark.p',fact_card__Diff__singleton__if) ).

fof(fact_card__Diff__singleton,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    file('theBenchmark.p',fact_card__Diff__singleton) ).

fof(fact_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_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_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__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__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__Collect__conjI,axiom,
    ! [V_Qa_2,V_Pa_2,T_b] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_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_Pa_2)),V_Qa_2)))) ),
    file('theBenchmark.p',fact_finite__Collect__conjI) ).

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_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_finite_Oequations_I1_J,axiom,
    ! [T_b] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_finite_Oequations_I1_J) ).

fof(fact_finite__insert,axiom,
    ! [V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    file('theBenchmark.p',fact_finite__insert) ).

fof(fact_finite__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__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__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__subset,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    file('theBenchmark.p',fact_finite__subset) ).

fof(fact_rev__finite__subset,axiom,
    ! [V_A_2,V_B_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    file('theBenchmark.p',fact_rev__finite__subset) ).

fof(fact_finite__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__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,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_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_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_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_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_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_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_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_finite__Collect__disjI,axiom,
    ! [V_Qa_2,V_Pa_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_Pa_2)),V_Qa_2))))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2)))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ),
    file('theBenchmark.p',fact_finite__Collect__disjI) ).

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__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_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_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_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__Collect__bounded__ex,axiom,
    ! [V_Qa_2,T_c,V_Pa_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_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_Pa_2))),V_Qa_2)))))
      <=> ! [B_y] :
            ( hBOOL(hAPP(V_Pa_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_Qa_2),B_y)))) ) ) ),
    file('theBenchmark.p',fact_finite__Collect__bounded__ex) ).

fof(fact_finite__image__set,axiom,
    ! [V_f_2,T_c,V_Pa_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_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_Pa_2))))) ),
    file('theBenchmark.p',fact_finite__image__set) ).

fof(fact_finite__M__bounded__by__nat,axiom,
    ! [V_i_2,V_Pa_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_Pa_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_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__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__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__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_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_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_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__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_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__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_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_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_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_Qa_2,V_Pa_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_Pa_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Qa_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_Pa_2)),V_c0_2)),V_Qa_2)),V_U_2)) ) ) ),
    file('theBenchmark.p',fact_finite__pointwise) ).

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__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_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_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_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__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_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_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_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_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_min__max_Oinf__Sup1__distrib,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_b),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_b,tc_HOL_Obool,T_b)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2))))) ) ) ),
    file('theBenchmark.p',fact_min__max_Oinf__Sup1__distrib) ).

fof(fact_min__max_OInf__le__Sup,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__le__Sup) ).

fof(fact_min__max_OInf__fin_Oin__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oin__idem) ).

fof(fact_min__max_OSup__fin_Oin__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oin__idem) ).

fof(fact_min__max_OInf__fin_Osingleton,axiom,
    ! [V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Osingleton) ).

fof(fact_min__max_OSup__fin_Osingleton,axiom,
    ! [V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = V_x_2 ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Osingleton) ).

fof(fact_min__max_OInf__fin_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oinsert__idem) ).

fof(fact_min__max_OSup__fin_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oinsert__idem) ).

fof(fact_min__max_OInf__fin_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Osubset__idem) ).

fof(fact_min__max_OSup__fin_Osubset__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
           => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Osubset__idem) ).

fof(fact_min__max_Osup__Inf__absorb,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) = V_a_2 ) ) ),
    file('theBenchmark.p',fact_min__max_Osup__Inf__absorb) ).

fof(fact_min__max_Oinf__Sup__absorb,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_a_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) = V_a_2 ) ) ),
    file('theBenchmark.p',fact_min__max_Oinf__Sup__absorb) ).

fof(fact_min__max_OInf__fin_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Ounion__idem) ).

fof(fact_min__max_OSup__fin_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Ounion__idem) ).

fof(fact_min__max_OInf__fin_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oinsert) ).

fof(fact_min__max_OSup__fin_Oinsert,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)) ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oinsert) ).

fof(fact_min__max_OInf__fin_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_Oinsert__remove) ).

fof(fact_min__max_OSup__fin_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) )
          & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = V_x_2 ) ) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_Oinsert__remove) ).

fof(fact_min__max_OInf__fin_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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__trans,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__trans) ).

fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).

fof(fact_converse__rtrancl__into__rtrancl,axiom,
    ! [V_c_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).

fof(fact_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_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__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__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_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_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_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_rtrancl__converseI,axiom,
    ! [V_r_2,V_x_2,V_y_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)))) ),
    file('theBenchmark.p',fact_rtrancl__converseI) ).

fof(fact_rtrancl__converseD,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_x_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_rtrancl__converseD) ).

fof(fact_trancl__reflcl,axiom,
    ! [V_r_2,T_b] : c_Transitive__Closure_Otrancl(T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),c_Relation_OId(T_b))) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
    file('theBenchmark.p',fact_trancl__reflcl) ).

fof(fact_reflcl__trancl,axiom,
    ! [V_r_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(T_b,V_r_2)),c_Relation_OId(T_b)) = c_Transitive__Closure_Ortrancl(T_b,V_r_2),
    file('theBenchmark.p',fact_reflcl__trancl) ).

fof(fact_rtrancl__unfold,axiom,
    ! [V_r_2,T_b] : c_Transitive__Closure_Ortrancl(T_b,V_r_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId(T_b)),hAPP(hAPP(c_Relation_Orel__comp(T_b,T_b,T_b),c_Transitive__Closure_Ortrancl(T_b,V_r_2)),V_r_2)),
    file('theBenchmark.p',fact_rtrancl__unfold) ).

fof(fact_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__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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_greaterThanAtMost__empty,axiom,
    ! [V_k_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_k_2))
       => c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_greaterThanAtMost__empty) ).

fof(fact_greaterThanAtMost__empty__iff2,axiom,
    ! [V_l_2,V_k_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ),
    file('theBenchmark.p',fact_greaterThanAtMost__empty__iff2) ).

fof(fact_greaterThanAtMost__empty__iff,axiom,
    ! [V_l_2,V_k_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_k_2,V_l_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_l_2)) ) ),
    file('theBenchmark.p',fact_greaterThanAtMost__empty__iff) ).

fof(fact_ivl__disj__un_I20_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_l_2,V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I20_J) ).

fof(fact_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_card__Plus__conv__if,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
            & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
       => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) )
       => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ),
    file('theBenchmark.p',fact_card__Plus__conv__if) ).

fof(fact_finite__Plus__iff,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
    <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ),
    file('theBenchmark.p',fact_finite__Plus__iff) ).

fof(fact_finite__Plus,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2))) ) ),
    file('theBenchmark.p',fact_finite__Plus) ).

fof(fact_finite__PlusD_I1_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    file('theBenchmark.p',fact_finite__PlusD_I1_J) ).

fof(fact_finite__PlusD_I2_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2)) ),
    file('theBenchmark.p',fact_finite__PlusD_I2_J) ).

fof(fact_card__Plus,axiom,
    ! [V_B_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_B_2))
       => hAPP(c_Finite__Set_Ocard(tc_sum(T_b,T_c)),c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_c),V_B_2)) ) ),
    file('theBenchmark.p',fact_card__Plus) ).

fof(fact_Plus__eq__empty__conv,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( c_Sum__Type_OPlus(T_b,T_c,V_A_2,V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(T_b,T_c),tc_HOL_Obool))
    <=> ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        & V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_Plus__eq__empty__conv) ).

fof(fact_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_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_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_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,axiom,
    ! [T_b,T_c,V_y_2,V_x_2,V_f_2] :
      ( hAPP(V_f_2,V_x_2) = V_y_2
     => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 ),
    file('theBenchmark.p',fact_fun__upd__idem) ).

fof(fact_fun__upd__other,axiom,
    ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
      ( V_z_2 != V_x_2
     => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) ),
    file('theBenchmark.p',fact_fun__upd__other) ).

fof(fact_fun__upd__twist,axiom,
    ! [V_d_2,V_b_2,V_m_2,T_c,T_b,V_c_2,V_a_2] :
      ( V_a_2 != V_c_2
     => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_m_2),V_a_2),V_b_2)),V_c_2),V_d_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_m_2),V_c_2),V_d_2)),V_a_2),V_b_2) ),
    file('theBenchmark.p',fact_fun__upd__twist) ).

fof(fact_fun__upd__apply,axiom,
    ! [V_y_2,V_f_2,T_c,T_b,V_x_2,V_z_2] :
      ( ( V_z_2 != V_x_2
       => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = hAPP(V_f_2,V_z_2) )
      & ( V_z_2 = V_x_2
       => hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2),V_z_2) = V_y_2 ) ),
    file('theBenchmark.p',fact_fun__upd__apply) ).

fof(fact_fun__upd__same,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,T_b),V_f_2),V_x_2),V_y_2),V_x_2) = V_y_2,
    file('theBenchmark.p',fact_fun__upd__same) ).

fof(fact_fun__upd__upd,axiom,
    ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2)),V_x_2),V_z_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_z_2),
    file('theBenchmark.p',fact_fun__upd__upd) ).

fof(fact_fun__upd__idem__iff,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_c),V_f_2),V_x_2),V_y_2) = V_f_2
    <=> hAPP(V_f_2,V_x_2) = V_y_2 ),
    file('theBenchmark.p',fact_fun__upd__idem__iff) ).

fof(fact_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__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_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_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_transfer__nat__int__sum__prod2_I2_J,axiom,
    ! [V_A_2,V_f_2,T_b] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2)),
    file('theBenchmark.p',fact_transfer__nat__int__sum__prod2_I2_J) ).

fof(fact_of__nat__setprod,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( ( class_Rings_Osemiring__1(T_b)
        & class_Groups_Ocomm__monoid__mult(T_b) )
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_of__nat__setprod) ).

fof(fact_int__setprod,axiom,
    ! [V_A_2,V_f_2,T_b] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,T_b),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_f_2)),V_A_2),
    file('theBenchmark.p',fact_int__setprod) ).

fof(fact_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_setprod__1,axiom,
    ! [V_A_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__mult(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Oone__class_Oone(T_b))),V_A_2) = c_Groups_Oone__class_Oone(T_b) ),
    file('theBenchmark.p',fact_setprod__1) ).

fof(fact_abs__setprod,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( class_Fields_Olinordered__field(T_b)
     => hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),c_Groups_Oabs__class_Oabs(T_b)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_abs__setprod) ).

fof(fact_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_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_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_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__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_map__upd__Some__unfold,axiom,
    ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_b,T_c] :
      ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_b),V_b_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
    <=> ( ( hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
          & V_x_2 != V_a_2 )
        | ( V_b_2 = V_y_2
          & V_x_2 = V_a_2 ) ) ),
    file('theBenchmark.p',fact_map__upd__Some__unfold) ).

fof(fact_map__upd__triv,axiom,
    ! [T_c,V_x_2,T_b,V_k_2,V_t_2] :
      ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
     => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_c,tc_Option_Ooption(T_b)),V_t_2),V_k_2),hAPP(c_Option_Ooption_OSome(T_b),V_x_2)) = V_t_2 ),
    file('theBenchmark.p',fact_map__upd__triv) ).

fof(fact_map__upd__eqD1,axiom,
    ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_c,T_b] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_x_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_n_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))
     => V_x_2 = V_y_2 ),
    file('theBenchmark.p',fact_map__upd__eqD1) ).

fof(fact_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_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_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_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_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_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__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_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_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_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_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_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_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__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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_Collect__conj__eq,axiom,
    ! [V_Qa_2,V_Pa_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_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)),
    file('theBenchmark.p',fact_Collect__conj__eq) ).

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_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_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_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_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__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_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_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_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_Oidem,axiom,
    ! [V_a,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ),
    file('theBenchmark.p',fact_inf_Oidem) ).

fof(fact_inf__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_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__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__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_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__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__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_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__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__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_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__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__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__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_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_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__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__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__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_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_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_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_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_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_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__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__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__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__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_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_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__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__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_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_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_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_inf__sup__ord_I1_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ),
    file('theBenchmark.p',fact_inf__sup__ord_I1_J) ).

fof(fact_inf__le1,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_x)) ),
    file('theBenchmark.p',fact_inf__le1) ).

fof(fact_inf__sup__ord_I2_J,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ),
    file('theBenchmark.p',fact_inf__sup__ord_I2_J) ).

fof(fact_inf__le2,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),V_y)) ),
    file('theBenchmark.p',fact_inf__le2) ).

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

fof(fact_le__inf__iff,axiom,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( class_Lattices_Osemilattice__inf(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),V_y_2),V_z_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_z_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_le__inf__iff) ).

fof(fact_le__infI1,axiom,
    ! [V_b,V_x,V_a,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_le__infI1) ).

fof(fact_le__infI2,axiom,
    ! [V_a,V_x,V_b,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)),V_x)) ) ),
    file('theBenchmark.p',fact_le__infI2) ).

fof(fact_inf__absorb1,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ),
    file('theBenchmark.p',fact_inf__absorb1) ).

fof(fact_inf__absorb2,axiom,
    ! [V_x,V_y,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x))
       => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ),
    file('theBenchmark.p',fact_inf__absorb2) ).

fof(fact_le__infI,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b))) ) ) ),
    file('theBenchmark.p',fact_le__infI) ).

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

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

fof(fact_le__infE,axiom,
    ! [V_b,V_a,V_x,T_a] :
      ( class_Lattices_Osemilattice__inf(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_b)))
       => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a))
           => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ),
    file('theBenchmark.p',fact_le__infE) ).

fof(fact_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_insert__inter__insert,axiom,
    ! [V_B_2,V_A_2,V_a_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_B_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
    file('theBenchmark.p',fact_insert__inter__insert) ).

fof(fact_Inf__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_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_distrib__inf__le,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_y),V_z)))) ),
    file('theBenchmark.p',fact_distrib__inf__le) ).

fof(fact_distrib__sup__le,axiom,
    ! [V_z,V_y,V_x,T_a] :
      ( class_Lattices_Olattice(T_a)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_y),V_z))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_z)))) ),
    file('theBenchmark.p',fact_distrib__sup__le) ).

fof(fact_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_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_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_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_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__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_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_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_Int__Collect,axiom,
    ! [V_Pa_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_Pa_2))))
    <=> ( hBOOL(hAPP(V_Pa_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_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_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_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_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_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_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_if__image__distrib,axiom,
    ! [V_S_2,V_g_2,V_f_2,V_Pa_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_Pa_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_Pa_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_Pa_2))))),
    file('theBenchmark.p',fact_if__image__distrib) ).

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_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_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_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_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_card_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) ) ),
    file('theBenchmark.p',fact_card_Ounion__inter) ).

fof(fact_card__Un__Int,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),V_A_2)),hAPP(c_Finite__Set_Ocard(T_b),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_card__Un__Int) ).

fof(fact_card__Diff__subset__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_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_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_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_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_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__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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_converse__meet,axiom,
    ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)),
    file('theBenchmark.p',fact_converse__meet) ).

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_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_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_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_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_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_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_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_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_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_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_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_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_fold__image__distrib,axiom,
    ! [V_h_2,V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),hAPP(hAPP(c_COMBS(T_b,T_c,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,T_c),T_b),c_Groups_Otimes__class_Otimes(T_c)),V_g_2)),V_h_2)),c_Groups_Oone__class_Oone(T_c)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_h_2),c_Groups_Oone__class_Oone(T_c)),V_A_2)) ) ),
    file('theBenchmark.p',fact_fold__image__distrib) ).

fof(fact_fold__image__insert,axiom,
    ! [V_z_2,V_g_2,V_a_2,V_A_2,T_b,T_c] :
      ( class_Groups_Oab__semigroup__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(V_g_2,V_a_2)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Otimes__class_Otimes(T_c)),V_g_2),V_z_2),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_fold__image__insert) ).

fof(fact_setprod_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_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_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_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_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_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_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_escape,axiom,
    ! [V_Qa_2,V_c_2,V_Ga_2,T_b,V_Pa_2] :
      ( ! [B_Z,B_s] :
          ( hBOOL(hAPP(hAPP(V_Pa_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_Qa_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_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_escape) ).

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__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_Pow__not__empty,axiom,
    ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),
    file('theBenchmark.p',fact_Pow__not__empty) ).

fof(fact_Pow__bottom,axiom,
    ! [V_B_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),hAPP(c_Set_OPow(T_b),V_B_2))),
    file('theBenchmark.p',fact_Pow__bottom) ).

fof(fact_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__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_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_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_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__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_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__def,axiom,
    ! [V_A_2,T_b] : hAPP(c_Set_OPow(T_b),V_A_2) = hAPP(c_Set_OCollect(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),
    file('theBenchmark.p',fact_Pow__def) ).

fof(fact_finite__Pow__iff,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OPow(T_b),V_A_2)))
    <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ),
    file('theBenchmark.p',fact_finite__Pow__iff) ).

fof(fact_Pow__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_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_finite__empty__induct,axiom,
    ! [V_Pa_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(V_Pa_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_Pa_2,B_A))
                 => hBOOL(hAPP(V_Pa_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_Pa_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_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom,
    ! [V_n_2,V_m_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_m_2,V_n_2) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2))),
    file('theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__functions_I2_J) ).

fof(fact_image__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__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_SetInterval_Otransfer__nat__int__set__function__closures,axiom,
    ! [V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2))
     => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ),
    file('theBenchmark.p',fact_SetInterval_Otransfer__nat__int__set__function__closures) ).

fof(fact_card__atLeastAtMost,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_u_2)),V_l_2),
    file('theBenchmark.p',fact_card__atLeastAtMost) ).

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

fof(fact_Powp__mono,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(T_b,V_A_2)),c_Predicate_OPowp(T_b,V_B_2))) ),
    file('theBenchmark.p',fact_Powp__mono) ).

fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
    ! [V_u_2,V_l_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_l_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,V_l_2,V_u_2),
    file('theBenchmark.p',fact_atLeastPlusOneAtMost__greaterThanAtMost__int) ).

fof(fact_Int__atLeastAtMost,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__atLeastAtMost) ).

fof(fact_atLeastatMost__psubset__iff,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)))
      <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_d_2))
          & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_b_2),V_d_2))
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_a_2)) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a_2),V_b_2)) ) ) ) ),
    file('theBenchmark.p',fact_atLeastatMost__psubset__iff) ).

fof(fact_ivl__disj__un_I22_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I22_J) ).

fof(fact_ivl__disj__int_I16_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I16_J) ).

fof(fact_ivl__disj__int_I13_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I13_J) ).

fof(fact_ivl__disj__int_I12_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_m_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I12_J) ).

fof(fact_simp__from__to,axiom,
    ! [V_i_2,V_j_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),V_i_2),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2))
       => c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_i_2,V_j_2) = c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_simp__from__to) ).

fof(fact_card__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_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_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_ex__nat__less,axiom,
    ! [V_Pa_2,V_n_2] :
      ( ? [B_m] :
          ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_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_Pa_2,B_x)) ) ),
    file('theBenchmark.p',fact_all__nat__less) ).

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_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_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_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_I6_J,axiom,
    ! [V_t_2,V_B_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ! [B_x] :
          ( ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xb] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
                 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ),
    file('theBenchmark.p',fact_bset_I6_J) ).

fof(fact_aset_I8_J,axiom,
    ! [V_t_2,V_A_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ! [B_x] :
          ( ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xb] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
                 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ),
    file('theBenchmark.p',fact_aset_I8_J) ).

fof(fact_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_periodic__finite__ex,axiom,
    ! [V_Pa_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_Pa_2,B_x))
          <=> hBOOL(hAPP(V_Pa_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_Pa_2,B_x1))
        <=> ? [B_x] :
              ( hBOOL(hAPP(V_Pa_2,B_x))
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_d_2))) ) ) ) ),
    file('theBenchmark.p',fact_periodic__finite__ex) ).

fof(fact_bset_I5_J,axiom,
    ! [V_t_2,V_B_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ! [B_x] :
          ( ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xb] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2))
                 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2)),V_t_2)) ) ) ),
    file('theBenchmark.p',fact_bset_I5_J) ).

fof(fact_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_aset_I7_J,axiom,
    ! [V_t_2,V_A_2,V_D_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2))
     => ! [B_x] :
          ( ! [B_xa] :
              ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_D_2)))
             => ! [B_xb] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2))
                 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) )
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2))) ) ) ),
    file('theBenchmark.p',fact_aset_I7_J) ).

fof(fact_image__minus__const__atLeastLessThan__nat,axiom,
    ! [V_x_2,V_y_2,V_c_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
       => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
           => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2))
           => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2))
       => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2)) ) ),
    file('theBenchmark.p',fact_image__minus__const__atLeastLessThan__nat) ).

fof(fact_finite__atLeastLessThan,axiom,
    ! [V_u_2,V_l_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2))),
    file('theBenchmark.p',fact_finite__atLeastLessThan) ).

fof(fact_atLeastLessThan__eq__iff,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
         => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
          <=> ( V_b_2 = V_d_2
              & V_a_2 = V_c_2 ) ) ) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__eq__iff) ).

fof(fact_atLeastLessThan__inj_I1_J,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
           => V_a_2 = V_c_2 ) ) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__inj_I1_J) ).

fof(fact_atLeastLessThan__inj_I2_J,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_c_2),V_d_2))
           => V_b_2 = V_d_2 ) ) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__inj_I2_J) ).

fof(fact_all__nat__less__eq,axiom,
    ! [V_Pa_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_Pa_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_Pa_2,B_x)) ) ),
    file('theBenchmark.p',fact_all__nat__less__eq) ).

fof(fact_ex__nat__less__eq,axiom,
    ! [V_Pa_2,V_n_2] :
      ( ? [B_m] :
          ( hBOOL(hAPP(V_Pa_2,B_m))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) )
    <=> ? [B_x] :
          ( hBOOL(hAPP(V_Pa_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2))) ) ),
    file('theBenchmark.p',fact_ex__nat__less__eq) ).

fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),hAPP(c_Nat_OSuc,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_l_2,V_u_2),
    file('theBenchmark.p',fact_atLeastLessThanSuc__atLeastAtMost) ).

fof(fact_atLeastLessThan0,axiom,
    ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('theBenchmark.p',fact_atLeastLessThan0) ).

fof(fact_card__atLeastLessThan,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_l_2),V_u_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_u_2),V_l_2),
    file('theBenchmark.p',fact_card__atLeastLessThan) ).

fof(fact_image__Suc__atLeastLessThan,axiom,
    ! [V_j_2,V_i_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_i_2)),hAPP(c_Nat_OSuc,V_j_2)),
    file('theBenchmark.p',fact_image__Suc__atLeastLessThan) ).

fof(fact_atLeastLessThan__empty,axiom,
    ! [V_a_2,V_b_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2))
       => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__empty) ).

fof(fact_atLeastLessThan__empty__iff,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__empty__iff) ).

fof(fact_atLeastLessThan__empty__iff2,axiom,
    ! [V_b_2,V_a_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)
      <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_a_2),V_b_2)) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__empty__iff2) ).

fof(fact_atLeastLessThan__subset__iff,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)))
       => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_d_2))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_c_2),V_a_2)) )
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_b_2),V_a_2)) ) ) ),
    file('theBenchmark.p',fact_atLeastLessThan__subset__iff) ).

fof(fact_ivl__disj__un_I17_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I17_J) ).

fof(fact_ivl__diff,axiom,
    ! [V_m_2,V_n_2,V_i_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_i_2),V_n_2))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_i_2),V_n_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_n_2),V_m_2) ) ),
    file('theBenchmark.p',fact_ivl__diff) ).

fof(fact_ivl__disj__int_I11_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I11_J) ).

fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom,
    ! [V_u_2,V_l_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_l_2)),V_u_2) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_l_2,V_u_2),
    file('theBenchmark.p',fact_atLeastSucLessThan__greaterThanLessThan) ).

fof(fact_image__add__atLeastLessThan,axiom,
    ! [V_j_2,V_i_2,V_k_2] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_k_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),V_k_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)),
    file('theBenchmark.p',fact_image__add__atLeastLessThan) ).

fof(fact_atLeastLessThan__singleton,axiom,
    ! [V_m_2] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_m_2),hAPP(c_Nat_OSuc,V_m_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),V_m_2),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('theBenchmark.p',fact_atLeastLessThan__singleton) ).

fof(fact_ivl__disj__un_I21_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_l_2),V_m_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_m_2),V_u_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_l_2,V_u_2) ) ) ),
    file('theBenchmark.p',fact_ivl__disj__un_I21_J) ).

fof(fact_atLeastLessThan__add__Un,axiom,
    ! [V_k_2,V_j_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2))
     => hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_i_2),V_j_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_j_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),V_k_2))) ),
    file('theBenchmark.p',fact_atLeastLessThan__add__Un) ).

fof(fact_ivl__disj__int_I15_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_l_2),V_m_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_m_2,V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I15_J) ).

fof(fact_Int__atLeastLessThan,axiom,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_b_2),V_d_2)) ),
    file('theBenchmark.p',fact_Int__atLeastLessThan) ).

fof(fact_subset__card__intvl__is__intvl,axiom,
    ! [V_k_2,V_A_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2)))))
     => V_A_2 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_k_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),V_A_2))) ),
    file('theBenchmark.p',fact_subset__card__intvl__is__intvl) ).

fof(fact_ivl__disj__int_I9_J,axiom,
    ! [V_u_2,V_m_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_m_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_b,V_m_2),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I9_J) ).

fof(fact_image__uminus__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_setsum__commute,axiom,
    ! [V_A_2,V_B_2,V_f_2,T_d,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),V_f_2)),V_B_2)),V_A_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_c,T_b),tc_fun(tc_fun(T_c,tc_HOL_Obool),T_b),T_d),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b)),hAPP(c_COMBC(T_c,T_d,T_b),V_f_2))),V_A_2)),V_B_2) ),
    file('theBenchmark.p',fact_setsum__commute) ).

fof(fact_of__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_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_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_of__nat__setsum,axiom,
    ! [V_A_2,V_f_2,T_c,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,tc_Nat_Onat),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,T_b,T_c),c_Nat_Osemiring__1__class_Oof__nat(T_b)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_of__nat__setsum) ).

fof(fact_setsum__product,axiom,
    ! [V_B_2,V_g_2,T_d,V_A_2,V_f_2,T_c,T_b] :
      ( class_Rings_Osemiring__0(T_b)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b),V_g_2),V_B_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_HOL_Obool),T_b),hAPP(hAPP(c_COMBB(tc_fun(T_d,T_b),tc_fun(tc_fun(T_d,tc_HOL_Obool),T_b),T_c),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_d,T_b)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,T_b),tc_fun(T_d,T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,T_b),tc_fun(tc_fun(T_d,T_b),tc_fun(T_d,T_b)),T_c),c_COMBB(T_b,T_b,T_d)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2))),V_g_2))),V_B_2)),V_A_2) ),
    file('theBenchmark.p',fact_setsum__product) ).

fof(fact_setsum__left__distrib,axiom,
    ! [V_r_2,V_A_2,V_f_2,T_c,T_b] :
      ( class_Rings_Osemiring__0(T_b)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),V_r_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_r_2)),V_A_2) ),
    file('theBenchmark.p',fact_setsum__left__distrib) ).

fof(fact_setsum__right__distrib,axiom,
    ! [V_A_2,V_f_2,T_c,V_r_2,T_b] :
      ( class_Rings_Osemiring__0(T_b)
     => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_r_2)),V_f_2)),V_A_2) ),
    file('theBenchmark.p',fact_setsum__right__distrib) ).

fof(fact_setsum__addf,axiom,
    ! [V_A_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),V_A_2)) ),
    file('theBenchmark.p',fact_setsum__addf) ).

fof(fact_setsum__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_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__infinite,axiom,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ),
    file('theBenchmark.p',fact_setsum__infinite) ).

fof(fact_setsum_Oinfinite,axiom,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) ) ),
    file('theBenchmark.p',fact_setsum_Oinfinite) ).

fof(fact_setsum__empty,axiom,
    ! [V_f_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ),
    file('theBenchmark.p',fact_setsum__empty) ).

fof(fact_setsum_Oempty,axiom,
    ! [V_g_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),V_g_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(T_b) ),
    file('theBenchmark.p',fact_setsum_Oempty) ).

fof(fact_setsum_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_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_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_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__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__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_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_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_setsum__constant,axiom,
    ! [V_A_2,V_y_2,T_c,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_y_2)),V_A_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Finite__Set_Ocard(T_c),V_A_2))),V_y_2) ),
    file('theBenchmark.p',fact_setsum__constant) ).

fof(fact_setsum__lessThan__Suc,axiom,
    ! [V_n_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,V_n_2)) ),
    file('theBenchmark.p',fact_setsum__lessThan__Suc) ).

fof(fact_setsum__atMost__Suc,axiom,
    ! [V_n_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2))),hAPP(V_f_2,hAPP(c_Nat_OSuc,V_n_2))) ),
    file('theBenchmark.p',fact_setsum__atMost__Suc) ).

fof(fact_setsum_Oinsert,axiom,
    ! [V_g_2,V_x_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_g_2,V_x_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_setsum_Oinsert) ).

fof(fact_setsum__insert,axiom,
    ! [V_f_2,V_a_2,V_F_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_F_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_F_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_a_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_F_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__insert) ).

fof(fact_setsum__Un__Int,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__Un__Int) ).

fof(fact_setsum__diff,axiom,
    ! [V_f_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Oab__group__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2)) ) ) ),
    file('theBenchmark.p',fact_setsum__diff) ).

fof(fact_setsum_Oeq__fold,axiom,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) ) ),
    file('theBenchmark.p',fact_setsum_Oeq__fold) ).

fof(fact_setsum_OF__eq,axiom,
    ! [V_g_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = c_Groups_Ozero__class_Ozero(T_c) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_c,T_b,c_Groups_Oplus__class_Oplus(T_c)),V_g_2),c_Groups_Ozero__class_Ozero(T_c)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_setsum_OF__eq) ).

fof(fact_setsum__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_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_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__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_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_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__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_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_Pa_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_Pa_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_Pa_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_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_setsum__cases,axiom,
    ! [V_g_2,V_f_2,V_Pa_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_Pa_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_Pa_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_Pa_2))))) ) ),
    file('theBenchmark.p',fact_setsum__cases) ).

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_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__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__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_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_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_setsum__bounded,axiom,
    ! [V_K_2,V_f_2,V_A_2,T_b,T_c] :
      ( ( class_Rings_Osemiring__1(T_c)
        & class_Groups_Oordered__ab__semigroup__add(T_c) )
     => ( ! [B_i] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_i),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_i)),V_K_2)) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_c),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_c),hAPP(c_Finite__Set_Ocard(T_b),V_A_2))),V_K_2))) ) ),
    file('theBenchmark.p',fact_setsum__bounded) ).

fof(fact_setsum_Ounion__inter__neutral,axiom,
    ! [V_g_2,V_B_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
               => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_setsum_Ounion__inter__neutral) ).

fof(fact_setsum__Un__zero,axiom,
    ! [V_f_2,V_T_2,V_S_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)))
               => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_S_2),V_T_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_S_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_T_2)) ) ) ) ),
    file('theBenchmark.p',fact_setsum__Un__zero) ).

fof(fact_setsum__mono3,axiom,
    ! [V_f_2,V_A_2,V_B_2,T_b,T_c] :
      ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
        & class_Groups_Ocomm__monoid__add(T_c) )
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_A_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),V_B_2))) ) ) ) ),
    file('theBenchmark.p',fact_setsum__mono3) ).

fof(fact_setsum__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_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_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_sum__diff__distrib,axiom,
    ! [V_n_2,V_Pa_2,V_Qa_2] :
      ( ! [B_x] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(V_Qa_2,B_x)),hAPP(V_Pa_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_Pa_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_Qa_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_Pa_2)),V_Qa_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_finite__subset__induct,axiom,
    ! [V_Pa_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_Pa_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_Pa_2,B_F))
                     => hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F))) ) ) ) )
           => hBOOL(hAPP(V_Pa_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_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_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_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_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_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_Image__Un,axiom,
    ! [V_B_2,V_A_2,V_R_2,T_b,T_c] : hAPP(c_Relation_OImage(T_c,T_b,V_R_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_A_2)),hAPP(c_Relation_OImage(T_c,T_b,V_R_2),V_B_2)),
    file('theBenchmark.p',fact_Image__Un) ).

fof(fact_Image__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_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_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_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_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_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_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_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_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_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__atLeastAtMostR2,axiom,
    ! [V_d_2,V_c_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_d_2) ),
    file('theBenchmark.p',fact_Int__atLeastAtMostR2) ).

fof(fact_Int__atLeastAtMostL2,axiom,
    ! [V_c_2,V_b_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_b,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_b,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_a_2),V_c_2),V_b_2) ),
    file('theBenchmark.p',fact_Int__atLeastAtMostL2) ).

fof(fact_ivl__disj__int_I6_J,axiom,
    ! [V_u_2,V_l_2,T_b] :
      ( class_Orderings_Oorder(T_b)
     => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_b,V_l_2,V_u_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_b),V_u_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_ivl__disj__int_I6_J) ).

fof(fact_image__uminus__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_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_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_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_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_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_minus,axiom,
    ! [V_y_2,V_x_2] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_y_2),V_x_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_minus) ).

fof(fact_Zero__int__def,axiom,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_Zero__int__def) ).

fof(fact_int__def,axiom,
    ! [V_m_2] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_m_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_int__def) ).

fof(fact_add,axiom,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_u_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y_2),V_v_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_add) ).

fof(fact_nat,axiom,
    ! [V_y_2,V_x_2] : hAPP(c_Int_Onat,hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_y_2),
    file('theBenchmark.p',fact_nat) ).

fof(fact_less,axiom,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ),
    file('theBenchmark.p',fact_less) ).

fof(fact_le,axiom,
    ! [V_v_2,V_u_2,V_y_2,V_x_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))),hAPP(c_Int_OAbs__Integ,hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Int_Ointrel),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),V_u_2),V_v_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))))))
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_x_2),V_v_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_u_2),V_y_2))) ),
    file('theBenchmark.p',fact_le) ).

fof(fact_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_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_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_greaterThan__eq__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_greaterThan__eq__iff) ).

fof(fact_greaterThan__iff,axiom,
    ! [V_k_2,V_i_2,T_b] :
      ( class_Orderings_Oord(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_k_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_greaterThan__iff) ).

fof(fact_greaterThan__subset__iff,axiom,
    ! [V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_x_2)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_y_2)))
      <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_y_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_greaterThan__subset__iff) ).

fof(fact_Compl__greaterThan,axiom,
    ! [V_k_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2) ),
    file('theBenchmark.p',fact_Compl__greaterThan) ).

fof(fact_Compl__atMost,axiom,
    ! [V_k_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_b),V_k_2)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_b),V_k_2) ),
    file('theBenchmark.p',fact_Compl__atMost) ).

fof(fact_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_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_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_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_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_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_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_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_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_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_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_dom__if,axiom,
    ! [V_g_2,V_f_2,V_Pa_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_Pa_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_Pa_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_Pa_2)))),
    file('theBenchmark.p',fact_dom__if) ).

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_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_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_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_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_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_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_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_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_equiv__class__eq,axiom,
    ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
       => hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_equiv__class__eq) ).

fof(fact_eq__equiv__class,axiom,
    ! [V_A_2,V_b_2,V_a_2,V_r_2,T_b] :
      ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
     => ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ) ),
    file('theBenchmark.p',fact_eq__equiv__class) ).

fof(fact_eq__equiv__class__iff,axiom,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
         => ( hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
          <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ) ),
    file('theBenchmark.p',fact_eq__equiv__class__iff) ).

fof(fact_equiv__class__eq__iff,axiom,
    ! [V_y_2,V_x_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
      <=> ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2))
          & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
          & hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_y_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))) ) ) ),
    file('theBenchmark.p',fact_equiv__class__eq__iff) ).

fof(fact_equiv__class__subset,axiom,
    ! [V_b_2,V_a_2,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_equiv__class__subset) ).

fof(fact_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_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_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_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_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_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_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_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__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_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__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__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_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__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__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_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__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_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_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_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_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__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_eq__card__imp__inj__on,axiom,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2)
       => c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2) ) ),
    file('theBenchmark.p',fact_eq__card__imp__inj__on) ).

fof(fact_inj__on__iff__eq__card,axiom,
    ! [V_f_2,T_c,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
      <=> hAPP(c_Finite__Set_Ocard(T_c),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)) = hAPP(c_Finite__Set_Ocard(T_b),V_A_2) ) ),
    file('theBenchmark.p',fact_inj__on__iff__eq__card) ).

fof(fact_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_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_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_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_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__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__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_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_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_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_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_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_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__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_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_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_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_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_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_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_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_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_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_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_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__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_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_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_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_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_ball__UN,axiom,
    ! [V_Pa_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_Pa_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_Pa_2,B_xa)) ) ) ),
    file('theBenchmark.p',fact_ball__UN) ).

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_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_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_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_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_UN__simps_I5_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)),
    file('theBenchmark.p',fact_UN__simps_I5_J) ).

fof(fact_UN__simps_I4_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2),
    file('theBenchmark.p',fact_UN__simps_I4_J) ).

fof(fact_UN__extend__simps_I5_J,axiom,
    ! [V_B_2,V_C_2,T_c,V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)),
    file('theBenchmark.p',fact_UN__extend__simps_I5_J) ).

fof(fact_Int__UN__distrib,axiom,
    ! [V_A_2,V_I_2,T_c,V_B_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_B_2)),V_A_2)),
    file('theBenchmark.p',fact_Int__UN__distrib) ).

fof(fact_UN__extend__simps_I4_J,axiom,
    ! [V_B_2,V_A_2,V_C_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)),
    file('theBenchmark.p',fact_UN__extend__simps_I4_J) ).

fof(fact_Int__UN__distrib2,axiom,
    ! [V_B_2,V_J_2,T_d,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),T_c),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_J_2)),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool))),T_c),c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2))),V_B_2))),
    file('theBenchmark.p',fact_Int__UN__distrib2) ).

fof(fact_SUPR__apply,axiom,
    ! [V_x_2,V_f_2,V_A_2,T_d,T_c,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,T_b)),V_A_2),V_f_2),V_x_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,T_b),V_A_2),hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_f_2),V_x_2)) ),
    file('theBenchmark.p',fact_SUPR__apply) ).

fof(fact_UN__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_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_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__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__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__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__extend__simps_I2_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = V_B_2 ) ),
    file('theBenchmark.p',fact_UN__extend__simps_I2_J) ).

fof(fact_UN__extend__simps_I3_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) ),
    file('theBenchmark.p',fact_UN__extend__simps_I3_J) ).

fof(fact_UN__simps_I2_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_UN__simps_I2_J) ).

fof(fact_UN__simps_I3_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_UN__simps_I3_J) ).

fof(fact_UN__insert,axiom,
    ! [V_B_2,V_A_2,V_a_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(T_c),V_a_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_B_2,V_a_2)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),
    file('theBenchmark.p',fact_UN__insert) ).

fof(fact_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_UN__equiv__class,axiom,
    ! [V_a_2,V_f_2,T_c,V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => ( c_Equiv__Relations_Ocongruent(T_b,tc_fun(T_c,tc_HOL_Obool),V_r_2,V_f_2)
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),V_f_2) = hAPP(V_f_2,V_a_2) ) ) ),
    file('theBenchmark.p',fact_UN__equiv__class) ).

fof(fact_SUP2__I,axiom,
    ! [T_d,T_c,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2))
       => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_fun(T_d,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ),
    file('theBenchmark.p',fact_SUP2__I) ).

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

fof(fact_Rep__Integ__inverse,axiom,
    ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2,
    file('theBenchmark.p',fact_Rep__Integ__inverse) ).

fof(fact_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_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_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_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_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_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_fold1Set_Ointros,axiom,
    ! [V_x_2,V_A_2,V_a_2,V_f_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,V_a_2,V_A_2),V_x_2))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),V_x_2)) ) ),
    file('theBenchmark.p',fact_fold1Set_Ointros) ).

fof(fact_ran__restrictD,axiom,
    ! [V_A_2,V_m_2,T_c,V_y_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),c_Map_Oran(T_c,T_b,c_Map_Orestrict__map(T_c,T_b,V_m_2,V_A_2))))
     => ? [B_x] :
          ( hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_b),V_y_2)
          & hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_ran__restrictD) ).

fof(fact_compl__unique,axiom,
    ! [V_y,V_x,T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a)
       => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a)
         => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ),
    file('theBenchmark.p',fact_compl__unique) ).

fof(fact_UNIV__I,axiom,
    ! [V_x_2,T_b] : hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_UNIV__I) ).

fof(fact_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_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_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_injD,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
       => V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_injD) ).

fof(fact_inj__eq,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2)
      <=> V_x_2 = V_y_2 ) ),
    file('theBenchmark.p',fact_inj__eq) ).

fof(fact_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_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_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__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__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_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__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__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_fold1Set__nonempty,axiom,
    ! [V_x_2,V_A_2,V_f_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2),V_x_2))
     => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ),
    file('theBenchmark.p',fact_fold1Set__nonempty) ).

fof(fact_empty__fold1SetE,axiom,
    ! [V_x_2,V_f_2,T_b] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))),V_x_2)),
    file('theBenchmark.p',fact_empty__fold1SetE) ).

fof(fact_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_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_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_inj__image__eq__iff,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => ( hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2) = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_B_2)
      <=> V_A_2 = V_B_2 ) ),
    file('theBenchmark.p',fact_inj__image__eq__iff) ).

fof(fact_Compl__UNIV__eq,axiom,
    ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__UNIV__eq) ).

fof(fact_Compl__empty__eq,axiom,
    ! [T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__empty__eq) ).

fof(fact_finite__compl,axiom,
    ! [V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)))
      <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_finite__compl) ).

fof(fact_Compl__partition2,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__partition2) ).

fof(fact_Compl__partition,axiom,
    ! [V_A_2,T_b] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Compl__partition) ).

fof(fact_Compl__eq__Diff__UNIV,axiom,
    ! [V_A_2,T_b] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_A_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_A_2),
    file('theBenchmark.p',fact_Compl__eq__Diff__UNIV) ).

fof(fact_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_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_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_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_finite__Collect__not,axiom,
    ! [V_Pa_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_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_Pa_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_SUP__UN__eq,axiom,
    ! [V_x_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_COMBC(T_c,tc_fun(T_c,tc_HOL_Obool),tc_HOL_Obool),c_member(T_c))),V_r_2)),V_x_2))
    <=> hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_r_2))) ),
    file('theBenchmark.p',fact_SUP__UN__eq) ).

fof(fact_finite__range__imageI,axiom,
    ! [V_f_2,T_d,V_g_2,T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_c,T_b,V_g_2),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)))))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(T_d),hAPP(c_Set_Oimage(T_c,T_d,hAPP(hAPP(c_COMBB(T_b,T_d,T_c),V_f_2),V_g_2)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))))) ),
    file('theBenchmark.p',fact_finite__range__imageI) ).

fof(fact_nat__of,axiom,
    ! [V_x_2] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,V_x_2)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    file('theBenchmark.p',fact_nat__of) ).

fof(fact_the__inv__f__f,axiom,
    ! [V_x_2,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => hAPP(c_Fun_Othe__inv__into(T_b,T_c,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_f_2),hAPP(V_f_2,V_x_2)) = V_x_2 ),
    file('theBenchmark.p',fact_the__inv__f__f) ).

fof(fact_finite__fun__UNIVD1,axiom,
    ! [T_c,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,T_c)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,T_c),tc_HOL_Obool))))
     => ( hAPP(c_Finite__Set_Ocard(T_c),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_finite__fun__UNIVD1) ).

fof(fact_inj__of__nat,axiom,
    ! [T_b] :
      ( class_Nat_Osemiring__char__0(T_b)
     => c_Fun_Oinj__on(tc_Nat_Onat,T_b,c_Nat_Osemiring__1__class_Oof__nat(T_b),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_inj__of__nat) ).

fof(fact_dom__const,axiom,
    ! [V_f_2,T_c,T_b] : c_Map_Odom(T_b,T_c,hAPP(hAPP(c_COMBB(T_c,tc_Option_Ooption(T_c),T_b),c_Option_Ooption_OSome(T_c)),V_f_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_dom__const) ).

fof(fact_atLeast__0,axiom,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),
    file('theBenchmark.p',fact_atLeast__0) ).

fof(fact_inj__fun,axiom,
    ! [T_d,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))
     => c_Fun_Oinj__on(T_b,tc_fun(T_d,T_c),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_d,T_c),T_b),c_COMBK(T_c,T_d)),V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) ),
    file('theBenchmark.p',fact_inj__fun) ).

fof(fact_compl__bot__eq,axiom,
    ! [T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ),
    file('theBenchmark.p',fact_compl__bot__eq) ).

fof(fact_compl__top__eq,axiom,
    ! [T_a] :
      ( class_Lattices_Oboolean__algebra(T_a)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ),
    file('theBenchmark.p',fact_compl__top__eq) ).

fof(fact_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__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_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_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_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_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_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_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_equivp__transp,axiom,
    ! [V_z_2,V_y_2,V_x_2,V_R_2,T_b] :
      ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
     => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
       => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2))
         => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ),
    file('theBenchmark.p',fact_equivp__transp) ).

fof(fact_equivp__symp,axiom,
    ! [V_y_2,V_x_2,V_R_2,T_b] :
      ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
     => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2))
       => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ),
    file('theBenchmark.p',fact_equivp__symp) ).

fof(fact_equivp__reflp,axiom,
    ! [V_x_2,V_R_2,T_b] :
      ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
     => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ),
    file('theBenchmark.p',fact_equivp__reflp) ).

fof(fact_equivp__def,axiom,
    ! [V_R_2,T_b] :
      ( c_Equiv__Relations_Oequivp(T_b,V_R_2)
    <=> ! [B_x,B_y] :
          ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y))
        <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ),
    file('theBenchmark.p',fact_equivp__def) ).

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

fof(fact_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__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_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__code__numeral,axiom,
    c_Typedef_Otype__definition(tc_Code__Numeral_Ocode__numeral,tc_Nat_Onat,c_Code__Numeral_Onat__of,c_Code__Numeral_Oof__nat,c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    file('theBenchmark.p',fact_type__definition__code__numeral) ).

fof(fact_type__definition_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_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_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_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_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_vimageI,axiom,
    ! [T_c,V_B_2,T_b,V_b_2,V_a_2,V_f_2] :
      ( hAPP(V_f_2,V_a_2) = V_b_2
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),V_B_2))
       => hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),hAPP(c_Set_Ovimage(T_c,T_b,V_f_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_vimageI) ).

fof(fact_vimage__Diff,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
    file('theBenchmark.p',fact_vimage__Diff) ).

fof(fact_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_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_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_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_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__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__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__Collect__eq,axiom,
    ! [V_Pa_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_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_Pa_2),V_f_2)),
    file('theBenchmark.p',fact_vimage__Collect__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__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__Int,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),V_B_2)),
    file('theBenchmark.p',fact_vimage__Int) ).

fof(fact_vimage__empty,axiom,
    ! [V_f_2,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,T_c,V_f_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_vimage__empty) ).

fof(fact_vimage__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__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_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_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_rel__pow__imp__rtrancl,axiom,
    ! [V_R_2,V_n_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ),
    file('theBenchmark.p',fact_rel__pow__imp__rtrancl) ).

fof(fact_rtrancl__power,axiom,
    ! [V_R_2,V_p_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
    <=> ? [B_n] : hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),V_p_2),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),B_n),V_R_2))) ),
    file('theBenchmark.p',fact_rtrancl__power) ).

fof(fact_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_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__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_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_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_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_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_rel__pow__Suc__I,axiom,
    ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),V_R_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ),
    file('theBenchmark.p',fact_rel__pow__Suc__I) ).

fof(fact_rel__pow__Suc__I2,axiom,
    ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_R_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2))) ) ),
    file('theBenchmark.p',fact_rel__pow__Suc__I2) ).

fof(fact_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_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_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_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_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_conseq2,axiom,
    ! [V_Qa_2,V_Q_H_2,V_c_2,V_Pa_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_Pa_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_Qa_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_Pa_2),V_c_2),V_Qa_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_Pa_2,V_Qa_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_Qa_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_Pa_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_Pa_2),V_c_2),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_conseq1) ).

fof(fact_insert__fold1SetE,axiom,
    ! [V_x_2,V_X_2,V_a_2,V_f_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2)),V_x_2))
     => ~ ! [B_a,B_A] :
            ( hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A)
           => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_x_2))
             => hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A)) ) ) ),
    file('theBenchmark.p',fact_insert__fold1SetE) ).

fof(fact_fold1Set_Oequations,axiom,
    ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2)),V_a3_2))
    <=> ? [B_a,B_A] :
          ( ~ hBOOL(hAPP(hAPP(c_member(T_b),B_a),B_A))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_b,V_f_2,B_a,B_A),V_a3_2))
          & hAPP(hAPP(c_Set_Oinsert(T_b),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_A) ) ),
    file('theBenchmark.p',fact_fold1Set_Oequations) ).

fof(fact_image__split__eq__Sigma,axiom,
    ! [V_A_2,V_g_2,V_f_2,T_c,T_b,T_d] : hAPP(c_Set_Oimage(T_d,tc_prod(T_b,T_c),hAPP(hAPP(c_COMBS(T_d,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),T_d),c_Product__Type_OPair(T_b,T_c)),V_f_2)),V_g_2)),V_A_2) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_Oimage(T_d,T_b,V_f_2),V_A_2)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),c_Set_Oimage(T_d,T_c,V_g_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_d,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_d,tc_HOL_Obool),T_b),c_Set_Ovimage(T_d,T_b,V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),V_A_2))),
    file('theBenchmark.p',fact_image__split__eq__Sigma) ).

fof(fact_fold1__Un,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Groups_Oab__semigroup__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
               => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ) ),
    file('theBenchmark.p',fact_fold1__Un) ).

fof(fact_SigmaI,axiom,
    ! [V_B_2,V_b_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_c),V_b_2),hAPP(V_B_2,V_a_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2))) ) ),
    file('theBenchmark.p',fact_SigmaI) ).

fof(fact_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_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,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_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_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_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_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_Times__empty,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] :
      ( hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))
    <=> ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))
        | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_Times__empty) ).

fof(fact_Sigma__empty2,axiom,
    ! [V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),
    file('theBenchmark.p',fact_Sigma__empty2) ).

fof(fact_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__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_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_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_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_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_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_equiv__type,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Equiv__Relations_Oequiv(T_b,V_A_2,V_r_2)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ),
    file('theBenchmark.p',fact_equiv__type) ).

fof(fact_Sigma__Int__distrib1,axiom,
    ! [V_C_2,V_J_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_J_2)),V_C_2) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_C_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_J_2),V_C_2)),
    file('theBenchmark.p',fact_Sigma__Int__distrib1) ).

fof(fact_Times__Int__distrib1,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_B_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_C_2))),
    file('theBenchmark.p',fact_Times__Int__distrib1) ).

fof(fact_Sigma__Int__distrib2,axiom,
    ! [V_B_2,V_A_2,V_I_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_I_2),V_B_2)),
    file('theBenchmark.p',fact_Sigma__Int__distrib2) ).

fof(fact_Id__on__subset__Times,axiom,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),c_Relation_OId__on(T_b,V_A_2)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))),
    file('theBenchmark.p',fact_Id__on__subset__Times) ).

fof(fact_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_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_Collect__split,axiom,
    ! [V_Qa_2,V_Pa_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_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Qa_2))),
    file('theBenchmark.p',fact_Collect__split) ).

fof(fact_SetCompr__Sigma__eq,axiom,
    ! [V_Qa_2,V_Pa_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_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_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_Qa_2)),
    file('theBenchmark.p',fact_SetCompr__Sigma__eq) ).

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_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_fold1__def,axiom,
    ! [V_A_2,V_f_2,T_b] : hAPP(c_Finite__Set_Ofold1(T_b,V_f_2),V_A_2) = c_HOL_OThe(T_b,c_Finite__Set_Ofold1Set(T_b,V_f_2,V_A_2)),
    file('theBenchmark.p',fact_fold1__def) ).

fof(fact_Sup__fin_OF__eq,axiom,
    ! [V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olattice__class_OSup__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__sup__class_Osup(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_Sup__fin_OF__eq) ).

fof(fact_Inf__fin_OF__eq,axiom,
    ! [V_A_2,T_b] :
      ( class_Lattices_Olattice(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olattice__class_OInf__fin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_Inf__fin_OF__eq) ).

fof(fact_Min_OF__eq,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olinorder__class_OMin(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_Min_OF__eq) ).

fof(fact_Max_OF__eq,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olinorder__class_OMax(T_b,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_Max_OF__eq) ).

fof(fact_min__max_OInf__fin_OF__eq,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_min__max_OInf__fin_OF__eq) ).

fof(fact_min__max_OSup__fin_OF__eq,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2) = hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omax(T_b)),V_A_2) ) ),
    file('theBenchmark.p',fact_min__max_OSup__fin_OF__eq) ).

fof(fact_insert__times__insert,axiom,
    ! [V_B_2,V_b_2,V_A_2,V_a_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Set_Oinsert(T_c),V_b_2),V_B_2)))),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),V_A_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),V_B_2)))),
    file('theBenchmark.p',fact_insert__times__insert) ).

fof(fact_finite__equiv__class,axiom,
    ! [V_X_2,V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
       => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2)))
         => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_X_2)) ) ) ),
    file('theBenchmark.p',fact_finite__equiv__class) ).

fof(fact_UN__Times__distrib,axiom,
    ! [V_F_2,V_E_2,V_B_2,V_A_2,T_c,T_b,T_e,T_d] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(T_d,T_e),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(T_d,T_e),V_A_2),hAPP(c_COMBK(tc_fun(T_e,tc_HOL_Obool),T_d),V_B_2))),hAPP(c_Product__Type_Oprod_Oprod__case(T_d,T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_fun(T_e,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),tc_fun(T_e,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_d),c_COMBB(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),T_e)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_d),c_Product__Type_OSigma(T_b,T_c)),V_E_2))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),T_e),c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b)),V_F_2)))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_E_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_e,tc_fun(T_c,tc_HOL_Obool)),V_B_2),V_F_2))),
    file('theBenchmark.p',fact_UN__Times__distrib) ).

fof(fact_Sigma__def,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),V_A_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_b),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),V_B_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),T_c),c_Set_Oinsert(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_Sigma__def) ).

fof(fact_fold1__belowI,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Lattices_Osemilattice__inf(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)),V_a_2)) ) ) ),
    file('theBenchmark.p',fact_fold1__belowI) ).

fof(fact_finite__quotient,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2))))
       => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(T_b),V_A_2),V_r_2))) ) ),
    file('theBenchmark.p',fact_finite__quotient) ).

fof(fact_below__fold1__iff,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Osemilattice__inf(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Lattices_Osemilattice__inf__class_Oinf(T_b)),V_A_2)))
          <=> ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ),
    file('theBenchmark.p',fact_below__fold1__iff) ).

fof(fact_min__max_Ofold1__belowI,axiom,
    ! [V_a_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_a_2)) ) ) ),
    file('theBenchmark.p',fact_min__max_Ofold1__belowI) ).

fof(fact_fold1__insert__idem,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_b)
     => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_fold1__insert__idem) ).

fof(fact_fold1__below__iff,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
          <=> ? [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_x_2))
                & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_fold1__below__iff) ).

fof(fact_min__max_Obelow__fold1__iff,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
          <=> ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),B_x)) ) ) ) ) ),
    file('theBenchmark.p',fact_min__max_Obelow__fold1__iff) ).

fof(fact_fold1__Un2,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
           => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
             => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_A_2)),hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),V_B_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_fold1__Un2) ).

fof(fact_fold1__strict__below__iff,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)),V_x_2))
          <=> ? [B_x] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),B_x),V_x_2))
                & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ) ) ),
    file('theBenchmark.p',fact_fold1__strict__below__iff) ).

fof(fact_strict__below__fold1__iff,axiom,
    ! [V_x_2,V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),hAPP(c_Finite__Set_Ofold1(T_b,c_Orderings_Oord__class_Omin(T_b)),V_A_2)))
          <=> ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),V_x_2),B_x)) ) ) ) ) ),
    file('theBenchmark.p',fact_strict__below__fold1__iff) ).

fof(fact_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_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_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_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_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_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_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_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_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_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_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_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_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_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__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_map__pair__simp,axiom,
    ! [V_b_2,V_a_2,V_g_2,V_f_2,T_c,T_e,T_b,T_d] : hAPP(c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),V_a_2),V_b_2)) = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,V_a_2)),hAPP(V_g_2,V_b_2)),
    file('theBenchmark.p',fact_map__pair__simp) ).

fof(fact_map__pair__ident,axiom,
    ! [V_z_2,T_c,T_b] : hAPP(c_Product__Type_Omap__pair(T_b,T_b,T_c,T_c,c_COMBI(T_b),c_COMBI(T_c)),V_z_2) = V_z_2,
    file('theBenchmark.p',fact_map__pair__ident) ).

fof(fact_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_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_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_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_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__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_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_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_prod__fun__imageE,axiom,
    ! [V_R_2,V_g_2,V_f_2,T_e,T_d,V_c_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_d,T_e),tc_prod(T_b,T_c),c_Product__Type_Omap__pair(T_d,T_b,T_e,T_c,V_f_2,V_g_2)),V_R_2)))
     => ~ ! [B_x,B_y] :
            ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_d,T_e)),hAPP(hAPP(c_Product__Type_OPair(T_d,T_e),B_x),B_y)),V_R_2)) ) ),
    file('theBenchmark.p',fact_prod__fun__imageE) ).

fof(fact_refl__on__def,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),hAPP(hAPP(c_Product__Type_OSigma(T_b,T_b),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_b),V_A_2)))) ) ),
    file('theBenchmark.p',fact_refl__on__def) ).

fof(fact_refl__on__Id__on,axiom,
    ! [V_A_2,T_b] : c_Relation_Orefl__on(T_b,V_A_2,c_Relation_OId__on(T_b,V_A_2)),
    file('theBenchmark.p',fact_refl__on__Id__on) ).

fof(fact_refl__on__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_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_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__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_refl__on__Int,axiom,
    ! [V_s_2,V_B_2,V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
     => ( c_Relation_Orefl__on(T_b,V_B_2,V_s_2)
       => c_Relation_Orefl__on(T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2)) ) ),
    file('theBenchmark.p',fact_refl__on__Int) ).

fof(fact_refl__onD,axiom,
    ! [V_a_2,V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_a_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_refl__onD) ).

fof(fact_refl__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__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__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_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_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_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_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_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_Pa_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_Pa_2,hAPP(c_Int_ORep__Integ,B_x)))
       => hBOOL(hAPP(V_Pa_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_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_fun__left__comm__idem_Ofun__left__idem,axiom,
    ! [V_z_2,V_x_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm__idem(T_b,T_c,V_f_2)
     => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) = hAPP(hAPP(V_f_2,V_x_2),V_z_2) ),
    file('theBenchmark.p',fact_fun__left__comm__idem_Ofun__left__idem) ).

fof(fact_fun__left__comm__idem_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,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_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__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_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_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_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_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__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_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__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__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__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__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__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_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_Abs__Integ__induct,axiom,
    ! [V_x_2,V_Pa_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_Pa_2,hAPP(c_Int_OAbs__Integ,B_y))) )
     => hBOOL(hAPP(V_Pa_2,V_x_2)) ),
    file('theBenchmark.p',fact_Abs__Integ__induct) ).

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_ball__empty,axiom,
    ! [V_Pa_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_Pa_2,B_x)) ),
    file('theBenchmark.p',fact_ball__empty) ).

fof(fact_congruent__def,axiom,
    ! [V_f_2,V_r_2,T_c,T_b] :
      ( c_Equiv__Relations_Ocongruent(T_b,T_c,V_r_2,V_f_2)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),V_r_2))
         => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_b,T_c),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBB(T_c,tc_HOL_Obool,T_b)),hAPP(hAPP(c_COMBB(T_c,tc_fun(T_c,tc_HOL_Obool),T_b),c_fequal),V_f_2))),V_f_2)),B_x)) ) ),
    file('theBenchmark.p',fact_congruent__def) ).

fof(fact_Abs__Integ__cases,axiom,
    ! [V_x_2] :
      ~ ! [B_y] :
          ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y)
         => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ),
    file('theBenchmark.p',fact_Abs__Integ__cases) ).

fof(fact_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_triples__valid__Suc,axiom,
    ! [V_n_2,V_ts_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_b)),B_x),V_ts_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_ts_2))
         => c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,B_x) ) ),
    file('theBenchmark.p',fact_triples__valid__Suc) ).

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_hoare__valids__def,axiom,
    ! [V_ts_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_ts_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_ts_2))
             => c_Hoare__Mirabelle_Otriple__valid(T_b,B_n,B_x) ) ) ),
    file('theBenchmark.p',fact_hoare__valids__def) ).

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_vimage__Times,axiom,
    ! [V_B_2,V_A_2,V_f_2,T_d,T_c,T_b] : hAPP(c_Set_Ovimage(T_b,tc_prod(T_c,T_d),V_f_2),hAPP(hAPP(c_Product__Type_OSigma(T_c,T_d),V_A_2),hAPP(c_COMBK(tc_fun(T_d,tc_HOL_Obool),T_c),V_B_2))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_Ovimage(T_b,T_c,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_c,T_b,c_Product__Type_Ofst(T_c,T_d)),V_f_2)),V_A_2)),hAPP(c_Set_Ovimage(T_b,T_d,hAPP(c_Fun_Ocomp(tc_prod(T_c,T_d),T_d,T_b,c_Product__Type_Osnd(T_c,T_d)),V_f_2)),V_B_2)),
    file('theBenchmark.p',fact_vimage__Times) ).

fof(fact_setsum__SucD,axiom,
    ! [V_n_2,V_A_2,V_f_2,T_b] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,V_n_2)
     => ? [B_x] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_setsum__SucD) ).

fof(fact_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_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_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_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_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_id__o,axiom,
    ! [V_g_2,T_b,T_c] : hAPP(c_Fun_Ocomp(T_c,T_c,T_b,c_Fun_Oid(T_c)),V_g_2) = V_g_2,
    file('theBenchmark.p',fact_id__o) ).

fof(fact_o__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_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_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_apfst__compose,axiom,
    ! [V_x_2,V_g_2,T_e,V_f_2,T_c,T_b,T_d] : hAPP(c_Product__Type_Oapfst(T_d,T_b,T_c,V_f_2),hAPP(c_Product__Type_Oapfst(T_e,T_d,T_c,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapfst(T_e,T_b,T_c,hAPP(c_Fun_Ocomp(T_d,T_b,T_e,V_f_2),V_g_2)),V_x_2),
    file('theBenchmark.p',fact_apfst__compose) ).

fof(fact_apsnd__compose,axiom,
    ! [V_x_2,V_g_2,T_e,V_f_2,T_b,T_c,T_d] : hAPP(c_Product__Type_Oapsnd(T_d,T_c,T_b,V_f_2),hAPP(c_Product__Type_Oapsnd(T_e,T_d,T_b,V_g_2),V_x_2)) = hAPP(c_Product__Type_Oapsnd(T_e,T_c,T_b,hAPP(c_Fun_Ocomp(T_d,T_c,T_e,V_f_2),V_g_2)),V_x_2),
    file('theBenchmark.p',fact_apsnd__compose) ).

fof(fact_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__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__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__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__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_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_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_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_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_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_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_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_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,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_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_setsum_Oreindex,axiom,
    ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_setsum_Oreindex) ).

fof(fact_setprod_Oreindex,axiom,
    ! [V_g_2,V_h_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__mult(T_c)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2)
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_g_2),hAPP(c_Set_Oimage(T_b,T_b,V_h_2),V_A_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,T_c,T_b,V_g_2),V_h_2)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_setprod_Oreindex) ).

fof(fact_the__inv__into__comp,axiom,
    ! [V_x_2,V_A_2,V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))
     => ( c_Fun_Oinj__on(T_d,T_b,V_g_2,V_A_2)
       => ( hBOOL(hAPP(hAPP(c_member(T_c),V_x_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2))))
         => hAPP(c_Fun_Othe__inv__into(T_d,T_c,V_A_2,hAPP(c_Fun_Ocomp(T_b,T_c,T_d,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_b,T_d,T_c,c_Fun_Othe__inv__into(T_d,T_b,V_A_2,V_g_2)),c_Fun_Othe__inv__into(T_b,T_c,hAPP(c_Set_Oimage(T_d,T_b,V_g_2),V_A_2),V_f_2)),V_x_2) ) ) ),
    file('theBenchmark.p',fact_the__inv__into__comp) ).

fof(fact_fold__image__reindex,axiom,
    ! [V_z_2,V_g_2,V_h_2,T_c,V_A_2,T_b,T_d] :
      ( class_Groups_Oab__semigroup__mult(T_d)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( c_Fun_Oinj__on(T_b,T_c,V_h_2,V_A_2)
         => hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_c,c_Groups_Otimes__class_Otimes(T_d)),V_g_2),V_z_2),hAPP(c_Set_Oimage(T_b,T_c,V_h_2),V_A_2)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_d,T_b,c_Groups_Otimes__class_Otimes(T_d)),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_g_2),V_h_2)),V_z_2),V_A_2) ) ) ),
    file('theBenchmark.p',fact_fold__image__reindex) ).

fof(fact_Nitpick_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_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_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_split__comp,axiom,
    ! [V_x_2,V_g_2,V_f_2,T_e,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),hAPP(c_Fun_Ocomp(T_e,tc_fun(T_d,T_b),T_c,V_f_2),V_g_2)),V_x_2) = hAPP(hAPP(V_f_2,hAPP(V_g_2,hAPP(c_Product__Type_Ofst(T_c,T_d),V_x_2))),hAPP(c_Product__Type_Osnd(T_c,T_d),V_x_2)),
    file('theBenchmark.p',fact_split__comp) ).

fof(fact_number__of__code__numeral__def,axiom,
    c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Code__Numeral_Ocode__numeral,tc_Int_Oint,c_Code__Numeral_Oof__nat),c_Int_Onat),
    file('theBenchmark.p',fact_number__of__code__numeral__def) ).

fof(fact_int__of__def,axiom,
    c_Code__Numeral_Oint__of = hAPP(c_Fun_Ocomp(tc_Nat_Onat,tc_Int_Oint,tc_Code__Numeral_Ocode__numeral,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),c_Code__Numeral_Onat__of),
    file('theBenchmark.p',fact_int__of__def) ).

fof(fact_Loop__sound__lemma,axiom,
    ! [V_c_2,V_b_2,V_Pa_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_Pa_2,V_b_2)),V_c_2),V_Pa_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_Pa_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_Loop__sound__lemma) ).

fof(fact_hoare__derivs_OIf,axiom,
    ! [V_d_2,V_Qa_2,V_c_2,V_b_2,V_Pa_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_Pa_2,V_b_2)),V_c_2),V_Qa_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_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Qa_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_Pa_2),c_Com_Ocom_OCond(V_b_2,V_c_2,V_d_2)),V_Qa_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ) ),
    file('theBenchmark.p',fact_hoare__derivs_OIf) ).

fof(fact_peek__and__def,axiom,
    ! [V_s_2,V_Z_2,V_p_2,V_Pa_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_p_2),V_Z_2),V_s_2))
    <=> ( hBOOL(hAPP(V_p_2,V_s_2))
        & hBOOL(hAPP(hAPP(V_Pa_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_Pa_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_Pa_2,V_b_2)),V_c_2),V_Pa_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_Pa_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)))) ),
    file('theBenchmark.p',fact_Loop) ).

fof(fact_folding_Oremove,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(V_F_2,V_A_2) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ) ),
    file('theBenchmark.p',fact_folding_Oremove) ).

fof(fact_folding__image_Oreindex,axiom,
    ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => ( c_Fun_Oinj__on(T_c,T_c,V_h_2,V_A_2)
         => hAPP(hAPP(V_F_2,V_g_2),hAPP(c_Set_Oimage(T_c,T_c,V_h_2),V_A_2)) = hAPP(hAPP(V_F_2,hAPP(c_Fun_Ocomp(T_c,T_b,T_c,V_g_2),V_h_2)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_folding__image_Oreindex) ).

fof(fact_folding_Ocommute__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_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__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__image_Odistrib,axiom,
    ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => hAPP(hAPP(V_F_2,hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)),V_h_2)),V_A_2) = hAPP(hAPP(V_f_2,hAPP(hAPP(V_F_2,V_g_2),V_A_2)),hAPP(hAPP(V_F_2,V_h_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_folding__image_Odistrib) ).

fof(fact_folding_Ocommute__comp_H,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_folding_Ocommute__comp_H) ).

fof(fact_folding_Ocommute__left__comp_H,axiom,
    ! [V_g_2,V_x_2,T_d,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_f_2,V_x_2)),V_g_2)) ) ),
    file('theBenchmark.p',fact_folding_Ocommute__left__comp_H) ).

fof(fact_folding_Ocommute__comp_H_H,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_B_2)),hAPP(V_F_2,V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
    file('theBenchmark.p',fact_folding_Ocommute__comp_H_H) ).

fof(fact_folding_Ocommute__left__comp_H_H,axiom,
    ! [V_g_2,T_d,V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),V_g_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_A_2)),hAPP(c_Fun_Ocomp(T_c,T_c,T_d,hAPP(V_F_2,V_B_2)),V_g_2)) ) ) ),
    file('theBenchmark.p',fact_folding_Ocommute__left__comp_H_H) ).

fof(fact_folding_Oempty,axiom,
    ! [V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = c_Fun_Oid(T_c) ),
    file('theBenchmark.p',fact_folding_Oempty) ).

fof(fact_folding__image_Oeq__fold,axiom,
    ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__image(T_b,T_c,V_f_2,V_z_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_c),V_A_2))
       => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2),V_z_2),V_A_2) ) ),
    file('theBenchmark.p',fact_folding__image_Oeq__fold) ).

fof(fact_folding_Oinsert,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ) ),
    file('theBenchmark.p',fact_folding_Oinsert) ).

fof(fact_folding_Ounion__inter,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
    file('theBenchmark.p',fact_folding_Ounion__inter) ).

fof(fact_folding_Oinsert__remove,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))),hAPP(V_f_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_folding_Oinsert__remove) ).

fof(fact_folding_Ounion,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
           => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ) ),
    file('theBenchmark.p',fact_folding_Ounion) ).

fof(fact_setsum__reindex__nonzero,axiom,
    ! [T_c,V_h_2,V_f_2,V_S_2,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__add(T_d)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_S_2))
       => ( ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_S_2))
             => ! [B_y] :
                  ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),V_S_2))
                 => ( B_x != B_y
                   => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y)
                     => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_d) ) ) ) )
         => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_c,T_d),V_h_2),hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_S_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_d),hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2)),V_S_2) ) ) ),
    file('theBenchmark.p',fact_setsum__reindex__nonzero) ).

fof(fact_Random__Sequence_Omap__def,axiom,
    ! [V_Pa_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_Pa_2) = c_Random__Sequence_Obind(T_c,T_b,V_Pa_2,hAPP(c_Fun_Ocomp(T_b,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(T_b)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),T_c,c_Random__Sequence_Osingle(T_b)),V_f_2)),
    file('theBenchmark.p',fact_Random__Sequence_Omap__def) ).

fof(fact_folding__idem_Ounion__idem,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2))
         => hAPP(V_F_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) ) ) ),
    file('theBenchmark.p',fact_folding__idem_Ounion__idem) ).

fof(fact_folding__idem_Osubset__comp__idem,axiom,
    ! [V_B_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2))
         => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_F_2,V_B_2)) = hAPP(V_F_2,V_A_2) ) ) ),
    file('theBenchmark.p',fact_folding__idem_Osubset__comp__idem) ).

fof(fact_folding__idem_Oidem__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_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_Oin__comp__idem,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) = hAPP(V_F_2,V_A_2) ) ) ),
    file('theBenchmark.p',fact_folding__idem_Oin__comp__idem) ).

fof(fact_folding__idem_Oinsert__idem,axiom,
    ! [V_x_2,V_A_2,V_F_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofolding__idem(T_b,T_c,V_f_2,V_F_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_F_2,V_A_2)),hAPP(V_f_2,V_x_2)) ) ),
    file('theBenchmark.p',fact_folding__idem_Oinsert__idem) ).

fof(fact_strong__setprod__reindex__cong,axiom,
    ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_c,T_b,T_d] :
      ( class_Groups_Ocomm__monoid__mult(T_d)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,V_A_2)
       => ( V_B_2 = hAPP(c_Set_Oimage(T_b,T_c,V_f_2),V_A_2)
         => ( ! [B_x] :
                ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
               => hAPP(V_g_2,B_x) = hAPP(hAPP(c_Fun_Ocomp(T_c,T_d,T_b,V_h_2),V_f_2),B_x) )
           => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_c,T_d),V_h_2),V_B_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_d),V_g_2),V_A_2) ) ) ) ),
    file('theBenchmark.p',fact_strong__setprod__reindex__cong) ).

fof(fact_pos__map__def,axiom,
    ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_Pa_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_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_neg__map__def,axiom,
    ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_Pa_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_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__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_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_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_rtrancl__Un__separatorE,axiom,
    ! [V_Qa_2,V_Pa_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_Pa_2),V_Qa_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_Pa_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_Qa_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_Pa_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__Un__separatorE) ).

fof(fact_rtrancl__Un__separator__converseE,axiom,
    ! [V_Qa_2,V_Pa_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_Pa_2),V_Qa_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_Pa_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_Qa_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_Pa_2))) ) ),
    file('theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).

fof(fact_rel__pow__Suc__E,axiom,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
     => ~ ! [B_y] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),V_R_2)) ) ),
    file('theBenchmark.p',fact_rel__pow__Suc__E) ).

fof(fact_rel__pow__Suc__E2,axiom,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
     => ~ ! [B_y] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2))
           => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2))) ) ),
    file('theBenchmark.p',fact_rel__pow__Suc__E2) ).

fof(fact_rel__pow__Suc__D2,axiom,
    ! [V_R_2,V_n_2,V_z_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),hAPP(c_Nat_OSuc,V_n_2)),V_R_2)))
     => ? [B_y] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_y),V_z_2)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(T_b,T_b),tc_HOL_Obool),V_n_2),V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_y)),V_R_2)) ) ),
    file('theBenchmark.p',fact_rel__pow__Suc__D2) ).

fof(fact_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_tranclD2,axiom,
    ! [V_R_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
     => ? [B_z] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),V_R_2))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),c_Transitive__Closure_Ortrancl(T_b,V_R_2))) ) ),
    file('theBenchmark.p',fact_tranclD2) ).

fof(fact_tranclD,axiom,
    ! [V_R_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Otrancl(T_b,V_R_2)))
     => ? [B_z] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_z),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_R_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),B_z)),V_R_2)) ) ),
    file('theBenchmark.p',fact_tranclD) ).

fof(fact_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_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_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_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__empty,axiom,
    ! [V_z_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_Finite__Set_Ofold(T_c,T_b,V_f_2),V_z_2),c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool))) = V_z_2,
    file('theBenchmark.p',fact_fold__empty) ).

fof(fact_fold__image__def,axiom,
    ! [V_g_2,V_f_2,T_c,T_b] : hAPP(c_Finite__Set_Ofold__image(T_b,T_c,V_f_2),V_g_2) = c_Finite__Set_Ofold(T_c,T_b,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),V_f_2),V_g_2)),
    file('theBenchmark.p',fact_fold__image__def) ).

fof(fact_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_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_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_fun__left__comm_Ofold__rec,axiom,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__rec) ).

fof(fact_fun__left__comm_Ofold__insert__remove,axiom,
    ! [V_x_2,V_z_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))))) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__insert__remove) ).

fof(fact_fun__left__comm_Ofold__graph__determ,axiom,
    ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_x_2))
       => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
         => V_y_2 = V_x_2 ) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__determ) ).

fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom,
    ! [V_g_2,T_d,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => c_Finite__Set_Ofun__left__comm(T_d,T_c,hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,T_c),T_d),V_f_2),V_g_2)) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofun__left__comm__apply) ).

fof(fact_fun__left__comm_Ofun__left__comm,axiom,
    ! [V_z_2,V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(V_f_2,V_y_2),V_z_2)) = hAPP(hAPP(V_f_2,V_y_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofun__left__comm) ).

fof(fact_fun__left__comm,axiom,
    ! [T_b] :
      ( class_Groups_Oab__semigroup__mult(T_b)
     => c_Finite__Set_Ofun__left__comm(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b)) ),
    file('theBenchmark.p',fact_fun__left__comm) ).

fof(fact_fun__left__comm_Ofun__comp__comm,axiom,
    ! [V_y_2,V_x_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)) = hAPP(c_Fun_Ocomp(T_c,T_c,T_c,hAPP(V_f_2,V_y_2)),hAPP(V_f_2,V_x_2)) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofun__comp__comm) ).

fof(fact_fun__left__comm_Ofold__fun__comm,axiom,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__fun__comm) ).

fof(fact_fun__left__comm_Ofold__equality,axiom,
    ! [V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
       => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2) = V_y_2 ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__equality) ).

fof(fact_fun__left__comm_Ofold__graph__fold,axiom,
    ! [V_z_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2))) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__fold) ).

fof(fact_fun__left__comm_Ofold__insert,axiom,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(V_f_2,V_x_2),hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),V_A_2)) ) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__insert) ).

fof(fact_fun__left__comm_Ofold__insert2,axiom,
    ! [V_z_2,V_x_2,V_A_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
         => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_z_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),hAPP(hAPP(V_f_2,V_x_2),V_z_2)),V_A_2) ) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__insert2) ).

fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom,
    ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,V_A_2),V_y_2))
       => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
         => ? [B_y_H] :
              ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_b,T_c,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))),B_y_H))
              & V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) ) ) ) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__graph__insertE__aux) ).

fof(fact_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__D,axiom,
    ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => ( hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ),
    file('theBenchmark.p',fact_INT__D) ).

fof(fact_INT__E,axiom,
    ! [V_a_2,V_B_2,V_A_2,T_c,V_b_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2)))
       => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_a_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_INT__E) ).

fof(fact_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_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_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__lower,axiom,
    ! [V_B_2,T_c,V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),hAPP(V_B_2,V_a_2))) ),
    file('theBenchmark.p',fact_INT__lower) ).

fof(fact_INT__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_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_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_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_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_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__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__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_Image__INT__subset,axiom,
    ! [V_B_2,V_A_2,T_d,V_r_2,T_c,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Relation_OImage(T_c,T_b,V_r_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_d),c_Relation_OImage(T_c,T_b,V_r_2)),V_B_2)))),
    file('theBenchmark.p',fact_Image__INT__subset) ).

fof(fact_Pow__INT__eq,axiom,
    ! [V_B_2,V_A_2,T_c,T_b] : hAPP(c_Set_OPow(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),T_c),c_Set_OPow(T_b)),V_B_2)),
    file('theBenchmark.p',fact_Pow__INT__eq) ).

fof(fact_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_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_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_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__subset__iff,axiom,
    ! [V_A_2,V_I_2,T_c,V_B_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_I_2),V_A_2)))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_I_2))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(V_A_2,B_x))) ) ),
    file('theBenchmark.p',fact_INT__subset__iff) ).

fof(fact_INT__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_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_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_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_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_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__extend__simps_I9_J,axiom,
    ! [V_C_2,V_B_2,T_d,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_c,tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_d,tc_HOL_Obool),tc_fun(tc_fun(T_d,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_c),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_d,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2),
    file('theBenchmark.p',fact_INT__extend__simps_I9_J) ).

fof(fact_INT__simps_I9_J,axiom,
    ! [V_C_2,V_B_2,V_A_2,T_d,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_d,tc_fun(T_c,tc_HOL_Obool)),V_A_2),V_B_2)),V_C_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_d,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBC(T_d,tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool)),T_d),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_c,tc_fun(T_b,tc_HOL_Obool))),V_B_2)),V_C_2)),
    file('theBenchmark.p',fact_INT__simps_I9_J) ).

fof(fact_UN__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_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_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_Collect__ball__eq,axiom,
    ! [V_Pa_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_Pa_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_Pa_2))),
    file('theBenchmark.p',fact_Collect__ball__eq) ).

fof(fact_INFI__bool__eq,axiom,
    ! [T_b] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_HOL_Obool) = c_Set_OBall(T_b),
    file('theBenchmark.p',fact_INFI__bool__eq) ).

fof(fact_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_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_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_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__extend__simps_I3_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))),V_B_2) ) ),
    file('theBenchmark.p',fact_INT__extend__simps_I3_J) ).

fof(fact_INT__simps_I3_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_INT__simps_I3_J) ).

fof(fact_INT__extend__simps_I4_J,axiom,
    ! [V_B_2,V_A_2,T_c,T_b,V_C_2] :
      ( ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2)),V_B_2)) )
      & ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
       => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_c,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_c,tc_HOL_Obool)),V_C_2),V_B_2)) = V_A_2 ) ),
    file('theBenchmark.p',fact_INT__extend__simps_I4_J) ).

fof(fact_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_Sup__Inf,axiom,
    ! [V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(T_b)))))) ),
    file('theBenchmark.p',fact_Sup__Inf) ).

fof(fact_Inf__Sup,axiom,
    ! [V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => c_Complete__Lattice_OInf__class_OInf(T_b,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_b,hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OAll(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBS(T_b,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fimplies),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),c_Orderings_Oord__class_Oless__eq(T_b))))) ),
    file('theBenchmark.p',fact_Inf__Sup) ).

fof(fact_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_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_Sigma__Union,axiom,
    ! [V_B_2,V_X_2,T_c,T_b] : hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_X_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),V_X_2),hAPP(hAPP(c_COMBC(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool)),tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool)),c_Product__Type_OSigma(T_b,T_c)),V_B_2)),
    file('theBenchmark.p',fact_Sigma__Union) ).

fof(fact_image__Union,axiom,
    ! [V_S_2,V_f_2,T_b,T_c] : hAPP(c_Set_Oimage(T_c,T_b,V_f_2),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_c,tc_HOL_Obool),V_S_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(T_c,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),V_S_2),c_Set_Oimage(T_c,T_b,V_f_2)),
    file('theBenchmark.p',fact_image__Union) ).

fof(fact_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_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_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_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_Union__mono,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_B_2))) ),
    file('theBenchmark.p',fact_Union__mono) ).

fof(fact_Union__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__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_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_Union__disjoint,axiom,
    ! [V_A_2,V_C_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),V_C_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),B_x),V_C_2))
         => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),B_x),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    file('theBenchmark.p',fact_Union__disjoint) ).

fof(fact_Sup__le__iff,axiom,
    ! [V_b_2,V_A_2,T_b] :
      ( class_Complete__Lattice_Ocomplete__lattice(T_b)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Complete__Lattice_OSup__class_OSup(T_b,V_A_2)),V_b_2))
      <=> ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),B_x),V_b_2)) ) ) ),
    file('theBenchmark.p',fact_Sup__le__iff) ).

fof(fact_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_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_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_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__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_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_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_Union__UNIV,axiom,
    ! [T_b] : c_Complete__Lattice_OSup__class_OSup(tc_fun(T_b,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_Union__UNIV) ).

fof(fact_Union__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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_Qa_2,V_Pa_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_Pa_2,B_x))
             => hBOOL(hAPP(V_Qa_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_Pa_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_Qa_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_setprod__pos,axiom,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( class_Rings_Olinordered__semidom(T_c)
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),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__pos) ).

fof(fact_map__add__upd,axiom,
    ! [V_y_2,V_x_2,V_g_2,V_f_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_f_2,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_g_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__add(T_b,T_c,V_f_2,V_g_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),
    file('theBenchmark.p',fact_map__add__upd) ).

fof(fact_dom__map__add,axiom,
    ! [V_n_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m_2,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),c_Map_Odom(T_b,T_c,V_n_2)),c_Map_Odom(T_b,T_c,V_m_2)),
    file('theBenchmark.p',fact_dom__map__add) ).

fof(fact_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__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__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__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_I2_J,axiom,
    ! [V_l2_2,V_l1_2,T_c,V_m_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l1_2)))
     => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ),
    file('theBenchmark.p',fact_map__add__dom__app__simps_I2_J) ).

fof(fact_map__add__dom__app__simps_I3_J,axiom,
    ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
     => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l1_2,V_m_2) ),
    file('theBenchmark.p',fact_map__add__dom__app__simps_I3_J) ).

fof(fact_map__add__dom__app__simps_I1_J,axiom,
    ! [V_l1_2,V_l2_2,T_c,V_m_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_m_2),c_Map_Odom(T_b,T_c,V_l2_2)))
     => hAPP(c_Map_Omap__add(T_b,T_c,V_l1_2,V_l2_2),V_m_2) = hAPP(V_l2_2,V_m_2) ),
    file('theBenchmark.p',fact_map__add__dom__app__simps_I1_J) ).

fof(fact_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_setprod__nonneg,axiom,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( class_Rings_Olinordered__semidom(T_c)
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),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),c_Groups_Ozero__class_Ozero(T_c)),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__nonneg) ).

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_Pa_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_Pa_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_Pa_2,B_f),B_d),B_i)) ) )
       => hBOOL(hAPP(hAPP(hAPP(V_Pa_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_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_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_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_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_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_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_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_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_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_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__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__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__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__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_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__idem,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => c_List_Oremove1(T_b,V_x_2,V_xs_2) = V_xs_2 ),
    file('theBenchmark.p',fact_remove1__idem) ).

fof(fact_notin__set__remove1,axiom,
    ! [V_y_2,V_xs_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_y_2,V_xs_2)))) ),
    file('theBenchmark.p',fact_notin__set__remove1) ).

fof(fact_in__set__remove1,axiom,
    ! [V_xs_2,T_b,V_b_2,V_a_2] :
      ( V_a_2 != V_b_2
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),c_List_Oremove1(T_b,V_b_2,V_xs_2))))
      <=> hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    file('theBenchmark.p',fact_in__set__remove1) ).

fof(fact_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_zip__same,axiom,
    ! [V_xs_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_xs_2))))
    <=> ( V_a_2 = V_b_2
        & hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    file('theBenchmark.p',fact_zip__same) ).

fof(fact_set__zip__leftD,axiom,
    ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_set__zip__leftD) ).

fof(fact_set__zip__rightD,axiom,
    ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
     => hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ),
    file('theBenchmark.p',fact_set__zip__rightD) ).

fof(fact_in__set__zipE,axiom,
    ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_x_2),V_y_2)),hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))))
     => ~ ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
         => ~ hBOOL(hAPP(hAPP(c_member(T_c),V_y_2),hAPP(c_List_Oset(T_c),V_ys_2))) ) ),
    file('theBenchmark.p',fact_in__set__zipE) ).

fof(fact_zip__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_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_neq__if__length__neq,axiom,
    ! [V_ys,V_xs,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)
     => V_xs != V_ys ),
    file('theBenchmark.p',fact_neq__if__length__neq) ).

fof(fact_length__insort,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)) ),
    file('theBenchmark.p',fact_length__insort) ).

fof(fact_insort__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_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_lexn__length,axiom,
    ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = V_n_2 ) ),
    file('theBenchmark.p',fact_lexn__length) ).

fof(fact_length__map,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2),
    file('theBenchmark.p',fact_length__map) ).

fof(fact_map__eq__imp__length__eq,axiom,
    ! [V_ys_2,V_g_2,T_d,V_xs_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = hAPP(hAPP(c_List_Omap(T_d,T_b),V_g_2),V_ys_2)
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_d)),V_ys_2) ),
    file('theBenchmark.p',fact_map__eq__imp__length__eq) ).

fof(fact_remove1__insort,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2)) = V_xs_2 ),
    file('theBenchmark.p',fact_remove1__insort) ).

fof(fact_card__length,axiom,
    ! [V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
    file('theBenchmark.p',fact_card__length) ).

fof(fact_card__distinct,axiom,
    ! [V_xs_2,T_b] :
      ( hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
     => hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_card__distinct) ).

fof(fact_distinct__card,axiom,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ),
    file('theBenchmark.p',fact_distinct__card) ).

fof(fact_map__of__zip__inject,axiom,
    ! [V_zs_2,V_xs_2,T_c,V_ys_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_zs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2)
       => ( hBOOL(hAPP(c_List_Odistinct(T_c),V_xs_2))
         => ( c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_ys_2)) = c_Map_Omap__of(T_c,T_b,hAPP(hAPP(c_List_Ozip(T_c,T_b),V_xs_2),V_zs_2))
           => V_ys_2 = V_zs_2 ) ) ) ),
    file('theBenchmark.p',fact_map__of__zip__inject) ).

fof(fact_map__fst__zip,axiom,
    ! [V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_xs_2 ),
    file('theBenchmark.p',fact_map__fst__zip) ).

fof(fact_map__snd__zip,axiom,
    ! [V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = V_ys_2 ),
    file('theBenchmark.p',fact_map__snd__zip) ).

fof(fact_distinct__insort,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),V_xs_2)))
      <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
          & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ) ),
    file('theBenchmark.p',fact_distinct__insort) ).

fof(fact_length__pos__if__in__set,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
    file('theBenchmark.p',fact_length__pos__if__in__set) ).

fof(fact_zip__eq__conv,axiom,
    ! [V_zs_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => ( hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2) = V_zs_2
      <=> ( hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_c),c_Product__Type_Osnd(T_b,T_c)),V_zs_2) = V_ys_2
          & hAPP(hAPP(c_List_Omap(tc_prod(T_b,T_c),T_b),c_Product__Type_Ofst(T_b,T_c)),V_zs_2) = V_xs_2 ) ) ),
    file('theBenchmark.p',fact_zip__eq__conv) ).

fof(fact_lenlex__conv,axiom,
    ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_Nat_Onat),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBC(tc_List_Olist(T_b),tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(tc_List_Olist(T_b),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b))))),c_List_Olex(T_b,V_r_2)))))),
    file('theBenchmark.p',fact_lenlex__conv) ).

fof(fact_lenlex__def,axiom,
    ! [V_r_2,T_b] : c_List_Olenlex(T_b,V_r_2) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(T_b)),tc_List_Olist(T_b)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(T_b),c_Wellfounded_Oless__than,c_List_Olex(T_b,V_r_2))),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(T_b),tc_prod(tc_Nat_Onat,tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(T_b))),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_COMBI(tc_List_Olist(T_b)))),
    file('theBenchmark.p',fact_lenlex__def) ).

fof(fact_finite__lists__length__eq,axiom,
    ! [V_n_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ),
    file('theBenchmark.p',fact_finite__lists__length__eq) ).

fof(fact_list__eq__iff__zip__eq,axiom,
    ! [T_b,V_ys_2,V_xs_2] :
      ( V_xs_2 = V_ys_2
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),c_fequal),B_x)) )
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ),
    file('theBenchmark.p',fact_list__eq__iff__zip__eq) ).

fof(fact_map__of__zip__is__None,axiom,
    ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => ( hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),V_x_2) = c_Option_Ooption_ONone(T_c)
      <=> ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    file('theBenchmark.p',fact_map__of__zip__is__None) ).

fof(fact_map__of__zip__is__Some,axiom,
    ! [V_x_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      <=> ? [B_y] : hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),V_x_2) = hAPP(c_Option_Ooption_OSome(T_c),B_y) ) ),
    file('theBenchmark.p',fact_map__of__zip__is__Some) ).

fof(fact_length__remove1,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremove1(T_b,V_x_2,V_xs_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    file('theBenchmark.p',fact_length__remove1) ).

fof(fact_dom__map__of__zip,axiom,
    ! [V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
       => c_Map_Odom(T_b,T_c,c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2))) = hAPP(c_List_Oset(T_b),V_xs_2) ) ),
    file('theBenchmark.p',fact_dom__map__of__zip) ).

fof(fact_finite__lists__length__le,axiom,
    ! [V_n_2,V_A_2,T_b] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
     => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(T_b)),hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_n_2))))) ),
    file('theBenchmark.p',fact_finite__lists__length__le) ).

fof(fact_Nitpick_Ocard_H__def,axiom,
    ! [V_A_2,T_b] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Nitpick_Ocard_H(T_b,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => c_Nitpick_Ocard_H(T_b,V_A_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b)))) ) ),
    file('theBenchmark.p',fact_Nitpick_Ocard_H__def) ).

fof(fact_listrel__iff__zip,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
    <=> ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),B_x),hAPP(c_List_Oset(tc_prod(T_b,T_b)),hAPP(hAPP(c_List_Ozip(T_b,T_b),V_xs_2),V_ys_2))))
           => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_b,tc_HOL_Obool),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2)),B_x)) )
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ) ),
    file('theBenchmark.p',fact_listrel__iff__zip) ).

fof(fact_listrel__rtrancl__refl,axiom,
    ! [V_r_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_xs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))),
    file('theBenchmark.p',fact_listrel__rtrancl__refl) ).

fof(fact_listrel__eq__len,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ),
    file('theBenchmark.p',fact_listrel__eq__len) ).

fof(fact_listrel__rtrancl__trans,axiom,
    ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_zs_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ) ),
    file('theBenchmark.p',fact_listrel__rtrancl__trans) ).

fof(fact_listrel__mono,axiom,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_List_Olistrel(T_b,V_s_2))) ),
    file('theBenchmark.p',fact_listrel__mono) ).

fof(fact_listrelp__listrel__eq,axiom,
    ! [V_xa_2,V_x_2,V_r_2,T_b] :
      ( c_List_Olistrelp(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_b),c_COMBC(T_b,tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_b,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_b),tc_fun(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_b,T_b)))),c_Product__Type_OPair(T_b,T_b)))),V_r_2),V_x_2,V_xa_2)
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_xa_2)),c_List_Olistrel(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_listrelp__listrel__eq) ).

fof(fact_lexn_Osimps_I2_J,axiom,
    ! [V_n_2,V_r_2,T_b] : hAPP(c_List_Olexn(T_b,V_r_2),hAPP(c_Nat_OSuc,V_n_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(T_b,tc_List_Olist(T_b)),tc_prod(T_b,tc_List_Olist(T_b))),tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_Product__Type_Omap__pair(tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),tc_prod(T_b,tc_List_Olist(T_b)),tc_List_Olist(T_b),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),c_Wellfounded_Olex__prod(T_b,tc_List_Olist(T_b),V_r_2,hAPP(c_List_Olexn(T_b,V_r_2),V_n_2)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2))))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),hAPP(c_Nat_OSuc,V_n_2)))))),
    file('theBenchmark.p',fact_lexn_Osimps_I2_J) ).

fof(fact_impossible__Cons,axiom,
    ! [V_x,V_ys,V_xs,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)))
     => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ),
    file('theBenchmark.p',fact_impossible__Cons) ).

fof(fact_set__ConsD,axiom,
    ! [V_xs_2,V_x_2,V_y_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2))))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)))
        | V_y_2 = V_x_2 ) ),
    file('theBenchmark.p',fact_set__ConsD) ).

fof(fact_zip__Cons__Cons,axiom,
    ! [V_ys,V_y,V_xs,V_x,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),
    file('theBenchmark.p',fact_zip__Cons__Cons) ).

fof(fact_set__subset__Cons,axiom,
    ! [V_x_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))),
    file('theBenchmark.p',fact_set__subset__Cons) ).

fof(fact_List_Oset_Osimps_I2_J,axiom,
    ! [V_xs_2,V_x_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)),
    file('theBenchmark.p',fact_List_Oset_Osimps_I2_J) ).

fof(fact_foldr_Osimps_I2_J,axiom,
    ! [V_a_2,V_xs_2,V_x_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2),V_a_2) = hAPP(hAPP(V_f_2,V_x_2),c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2)),
    file('theBenchmark.p',fact_foldr_Osimps_I2_J) ).

fof(fact_not__Cons__self,axiom,
    ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),
    file('theBenchmark.p',fact_not__Cons__self) ).

fof(fact_not__Cons__self2,axiom,
    ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs,
    file('theBenchmark.p',fact_not__Cons__self2) ).

fof(fact_list_Oinject,axiom,
    ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_b] :
      ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_H_2),V_list_H_2)
    <=> ( V_list_2 = V_list_H_2
        & V_a_2 = V_a_H_2 ) ),
    file('theBenchmark.p',fact_list_Oinject) ).

fof(fact_listrelp_Oequations_I2_J,axiom,
    ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_b] :
      ( c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a1_2),V_a3_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a4_2))
    <=> ( c_List_Olistrelp(T_b,V_r_2,V_a3_2,V_a4_2)
        & hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ),
    file('theBenchmark.p',fact_listrelp_Oequations_I2_J) ).

fof(fact_listrelp_OCons,axiom,
    ! [V_ys_2,V_xs_2,T_b,V_y_2,V_x_2,V_r_2] :
      ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2))
     => ( c_List_Olistrelp(T_b,V_r_2,V_xs_2,V_ys_2)
       => c_List_Olistrelp(T_b,V_r_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ),
    file('theBenchmark.p',fact_listrelp_OCons) ).

fof(fact_map_Osimps_I2_J,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),hAPP(V_f_2,V_x_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_map_Osimps_I2_J) ).

fof(fact_remove1_Osimps_I2_J,axiom,
    ! [V_xs,T_a,V_y,V_x] :
      ( ( V_x != V_y
       => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Oremove1(T_a,V_x,V_xs)) )
      & ( V_x = V_y
       => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) ),
    file('theBenchmark.p',fact_remove1_Osimps_I2_J) ).

fof(fact_insort__key_Osimps_I2_J,axiom,
    ! [V_ys_2,T_c,V_y_2,V_x_2,V_f_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_ys_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2)))
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) = hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_y_2),V_ys_2)) ) ) ),
    file('theBenchmark.p',fact_insort__key_Osimps_I2_J) ).

fof(fact_distinct_Osimps_I2_J,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)))
    <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
        & ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    file('theBenchmark.p',fact_distinct_Osimps_I2_J) ).

fof(fact_map__of__Cons__code_I2_J,axiom,
    ! [V_ps,V_v,T_c,T_b,V_k,V_l] :
      ( ( V_l != V_k
       => hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(c_Map_Omap__of(T_b,T_c,V_ps),V_k) )
      & ( V_l = V_k
       => hAPP(c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_l),V_v)),V_ps)),V_k) = hAPP(c_Option_Ooption_OSome(T_c),V_v) ) ),
    file('theBenchmark.p',fact_map__of__Cons__code_I2_J) ).

fof(fact_list_Osize_I4_J,axiom,
    ! [V_list,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),V_list)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_list)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_list_Osize_I4_J) ).

fof(fact_listrel_OCons,axiom,
    ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_listrel_OCons) ).

fof(fact_map__of_Osimps_I2_J,axiom,
    ! [V_ps_2,V_p_2,T_c,T_b] : c_Map_Omap__of(T_b,T_c,hAPP(hAPP(c_List_Olist_OCons(tc_prod(T_b,T_c)),V_p_2),V_ps_2)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__of(T_b,T_c,V_ps_2)),hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Option_Ooption_OSome(T_c),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2))),
    file('theBenchmark.p',fact_map__of_Osimps_I2_J) ).

fof(fact_Cons__in__lex,axiom,
    ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olex(T_b,V_r_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olex(T_b,V_r_2)))
          & V_x_2 = V_y_2 )
        | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ),
    file('theBenchmark.p',fact_Cons__in__lex) ).

fof(fact_listrel__Cons,axiom,
    ! [V_xs_2,V_x_2,V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = c_List_Oset__Cons(T_b,hAPP(c_Relation_OImage(T_b,T_b,V_r_2),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),V_xs_2),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))))),
    file('theBenchmark.p',fact_listrel__Cons) ).

fof(fact_set__Cons__def,axiom,
    ! [V_XS_2,V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,V_XS_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(T_b)),c_HOL_OEx(T_b)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_HOL_Obool),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool,T_b),c_HOL_OEx(tc_List_Olist(T_b)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBS(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(T_b,tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(T_b)),hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_fun(tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b))),tc_fun(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),tc_List_Olist(T_b)),c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),tc_List_Olist(T_b)),c_COMBB(tc_List_Olist(T_b),tc_HOL_Obool,tc_List_Olist(T_b))),c_fequal))),c_List_Olist_OCons(T_b)))))),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),T_b),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),T_b),c_fconj),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_A_2)))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(T_b))),V_XS_2)))))),
    file('theBenchmark.p',fact_set__Cons__def) ).

fof(fact_listrel__Cons2,axiom,
    ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel(T_b,V_r_2)))
     => ~ ! [B_x,B_xs] :
            ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_xs)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),V_y_2)),V_r_2))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),B_xs),V_ys_2)),c_List_Olistrel(T_b,V_r_2))) ) ) ),
    file('theBenchmark.p',fact_listrel__Cons2) ).

fof(fact_listrel__Cons1,axiom,
    ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
     => ~ ! [B_y,B_ys] :
            ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_ys)
           => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_y_2),B_y)),V_r_2))
             => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_ys_2),B_ys)),c_List_Olistrel(T_b,V_r_2))) ) ) ),
    file('theBenchmark.p',fact_listrel__Cons1) ).

fof(fact_length__sublist,axiom,
    ! [V_I_2,V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Osublist(T_b,V_xs_2,V_I_2)) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),V_I_2)))),
    file('theBenchmark.p',fact_length__sublist) ).

fof(fact_pick_Osimps,axiom,
    ! [V_xs,V_x,T_a,V_i] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
       => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Random_Opick(T_a,V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_a),V_x)))
       => hAPP(c_Random_Opick(T_a,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_a)),V_x),V_xs)),V_i) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_a),V_x) ) ),
    file('theBenchmark.p',fact_pick_Osimps) ).

fof(fact_distinct__sublistI,axiom,
    ! [V_I_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))) ),
    file('theBenchmark.p',fact_distinct__sublistI) ).

fof(fact_in__set__sublistD,axiom,
    ! [V_I_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_in__set__sublistD) ).

fof(fact_notin__set__sublistI,axiom,
    ! [V_I_2,V_xs_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2)))) ),
    file('theBenchmark.p',fact_notin__set__sublistI) ).

fof(fact_set__sublist__subset,axiom,
    ! [V_I_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),c_List_Osublist(T_b,V_xs_2,V_I_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    file('theBenchmark.p',fact_set__sublist__subset) ).

fof(fact_select__weight__cons__zero,axiom,
    ! [V_xs_2,V_x_2,T_b] : c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),V_x_2)),V_xs_2)) = c_Random_Oselect__weight(T_b,V_xs_2),
    file('theBenchmark.p',fact_select__weight__cons__zero) ).

fof(fact_pick__member,axiom,
    ! [V_xs_2,T_b,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i_2),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Random_Opick(T_b,V_xs_2),V_i_2)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ),
    file('theBenchmark.p',fact_pick__member) ).

fof(fact_listsum__simps_I2_J,axiom,
    ! [V_xs,V_x,T_a] :
      ( class_Groups_Omonoid__add(T_a)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs)) ),
    file('theBenchmark.p',fact_listsum__simps_I2_J) ).

fof(fact_listsum__addf,axiom,
    ! [V_xs_2,V_g_2,V_f_2,T_c,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBS(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Oplus__class_Oplus(T_b)),V_f_2)),V_g_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_g_2),V_xs_2))) ),
    file('theBenchmark.p',fact_listsum__addf) ).

fof(fact_listsum__const__mult,axiom,
    ! [V_xs_2,V_f_2,V_c_2,T_c,T_b] :
      ( class_Rings_Osemiring__0(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBB(T_b,T_b,T_c),hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) ),
    file('theBenchmark.p',fact_listsum__const__mult) ).

fof(fact_listsum__mult__const,axiom,
    ! [V_xs_2,V_c_2,V_f_2,T_c,T_b] :
      ( class_Rings_Osemiring__0(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(hAPP(c_COMBC(T_c,T_b,T_b),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_b,T_b),T_c),c_Groups_Otimes__class_Otimes(T_b)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))),V_c_2) ),
    file('theBenchmark.p',fact_listsum__mult__const) ).

fof(fact_listsum__0,axiom,
    ! [V_xs_2,T_c,T_b] :
      ( class_Groups_Omonoid__add(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),c_Groups_Ozero__class_Ozero(T_b))),V_xs_2)) = c_Groups_Ozero__class_Ozero(T_b) ),
    file('theBenchmark.p',fact_listsum__0) ).

fof(fact_listsum__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__abs,axiom,
    ! [V_xs_2,T_b] :
      ( class_Groups_Oordered__ab__group__add__abs(T_b)
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(c_Groups_Oabs__class_Oabs(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_b,T_b),c_Groups_Oabs__class_Oabs(T_b)),V_xs_2)))) ),
    file('theBenchmark.p',fact_listsum__abs) ).

fof(fact_uminus__listsum__map,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] :
      ( class_Groups_Oab__group__add(T_b)
     => hAPP(c_Groups_Ouminus__class_Ouminus(T_b),hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_Fun_Ocomp(T_b,T_b,T_c,c_Groups_Ouminus__class_Ouminus(T_b)),V_f_2)),V_xs_2)) ),
    file('theBenchmark.p',fact_uminus__listsum__map) ).

fof(fact_distinct__listsum__conv__Setsum,axiom,
    ! [V_xs_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
       => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),V_xs_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_b),c_COMBI(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) ) ),
    file('theBenchmark.p',fact_distinct__listsum__conv__Setsum) ).

fof(fact_select__weight__def,axiom,
    ! [V_xs_2,T_b] : c_Random_Oselect__weight(T_b,V_xs_2) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_Code__Numeral_Ocode__numeral,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Orange(hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))),hAPP(hAPP(c_COMBB(T_b,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(T_b,V_xs_2))),
    file('theBenchmark.p',fact_select__weight__def) ).

fof(fact_listsum__distinct__conv__setsum__set,axiom,
    ! [V_f_2,V_xs_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
       => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_b,T_c),V_f_2),hAPP(c_List_Oset(T_b),V_xs_2)) ) ),
    file('theBenchmark.p',fact_listsum__distinct__conv__setsum__set) ).

fof(fact_setsum__set__upto__conv__listsum__int,axiom,
    ! [V_j_2,V_i_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_i_2,V_j_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_i_2,V_j_2))) ),
    file('theBenchmark.p',fact_setsum__set__upto__conv__listsum__int) ).

fof(fact_interv__listsum__conv__setsum__set__int,axiom,
    ! [V_l_2,V_k_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Int_Oint,T_b),V_f_2),c_List_Oupto(V_k_2,V_l_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,T_b),V_f_2),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(V_k_2,V_l_2))) ),
    file('theBenchmark.p',fact_interv__listsum__conv__setsum__set__int) ).

fof(fact_listsum__triv,axiom,
    ! [V_xs_2,V_r_2,T_c,T_b] :
      ( class_Rings_Osemiring__1(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),hAPP(c_COMBK(T_b,T_c),V_r_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_xs_2))),V_r_2) ),
    file('theBenchmark.p',fact_listsum__triv) ).

fof(fact_listsum__map__remove1,axiom,
    ! [V_f_2,V_xs_2,V_x_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_c),hAPP(V_f_2,V_x_2)),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_List_Oremove1(T_b,V_x_2,V_xs_2)))) ) ),
    file('theBenchmark.p',fact_listsum__map__remove1) ).

fof(fact_select__weight__member,axiom,
    ! [V_s_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Code__Numeral_Ocode__numeral),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2))))
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,T_b),T_b),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,T_b)),V_xs_2)))) ),
    file('theBenchmark.p',fact_select__weight__member) ).

fof(fact_Nitpick_Osetsum_H__def,axiom,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( class_Groups_Ocomm__monoid__add(T_c)
     => ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_c) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
         => c_Nitpick_Osetsum_H(T_b,T_c,V_f_2,V_A_2) = hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),c_Hilbert__Choice_OEps(tc_List_Olist(T_b),hAPP(hAPP(c_COMBS(tc_List_Olist(T_b),tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(T_b)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_fequal),c_List_Oset(T_b))),V_A_2))),c_List_Odistinct(T_b))))) ) ) ),
    file('theBenchmark.p',fact_Nitpick_Osetsum_H__def) ).

fof(fact_insort__insert__insort__key,axiom,
    ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
       => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2) ) ),
    file('theBenchmark.p',fact_insort__insert__insort__key) ).

fof(fact_listsum__eq__0__nat__iff__nat,axiom,
    ! [V_ns_2] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2)))
         => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_listsum__eq__0__nat__iff__nat) ).

fof(fact_distinct__insort__insert,axiom,
    ! [V_x_2,V_f_2,V_xs_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
       => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_c,V_f_2,V_x_2,V_xs_2))) ) ),
    file('theBenchmark.p',fact_distinct__insort__insert) ).

fof(fact_insort__insert__triv,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = V_xs_2 ) ),
    file('theBenchmark.p',fact_insort__insert__triv) ).

fof(fact_set__insort__insert,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2)) = hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_set__insort__insert) ).

fof(fact_insort__insert__key__triv,axiom,
    ! [V_xs_2,T_c,V_x_2,V_f_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_x_2)),hAPP(c_Set_Oimage(T_c,T_b,V_f_2),hAPP(c_List_Oset(T_c),V_xs_2))))
       => c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ),
    file('theBenchmark.p',fact_insort__insert__key__triv) ).

fof(fact_insort__insert__insort,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_b,c_COMBI(T_b),V_x_2,V_xs_2) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_x_2),V_xs_2) ) ),
    file('theBenchmark.p',fact_insort__insert__insort) ).

fof(fact_lexord__cons__cons,axiom,
    ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2))),c_List_Olexord(T_b,V_r_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2)))
          & V_a_2 = V_b_2 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2)) ) ),
    file('theBenchmark.p',fact_lexord__cons__cons) ).

fof(fact_set__zip,axiom,
    ! [V_ys_2,V_xs_2,T_c,T_b] : hAPP(c_List_Oset(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)) = hAPP(c_Set_OCollect(tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(T_b,T_c)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBS(tc_Nat_Onat,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_Nat_Onat,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_prod(T_b,T_c)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(tc_prod(T_b,T_c),tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(T_b,T_c)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(T_b,T_c)),c_COMBB(tc_prod(T_b,T_c),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,T_c,tc_prod(T_b,T_c)),hAPP(hAPP(c_COMBB(T_b,tc_fun(T_c,tc_prod(T_b,T_c)),tc_Nat_Onat),c_Product__Type_OPair(T_b,T_c)),hAPP(c_List_Onth(T_b),V_xs_2))),hAPP(c_List_Onth(T_c),V_ys_2)))))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))))),
    file('theBenchmark.p',fact_set__zip) ).

fof(fact_nth__zip,axiom,
    ! [V_ys,T_b,V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)))
       => hAPP(hAPP(c_List_Onth(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i) = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_b),V_ys),V_i)) ) ),
    file('theBenchmark.p',fact_nth__zip) ).

fof(fact_nth__map,axiom,
    ! [V_f_2,T_c,V_xs_2,T_b,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
     => hAPP(hAPP(c_List_Onth(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)),V_n_2) = hAPP(V_f_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_n_2)) ),
    file('theBenchmark.p',fact_nth__map) ).

fof(fact_elem__le__listsum__nat,axiom,
    ! [V_ns,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns)))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns))) ),
    file('theBenchmark.p',fact_elem__le__listsum__nat) ).

fof(fact_nth_Osimps,axiom,
    ! [V_n_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_n_2) = c_Nat_Onat_Onat__case(T_b,V_x_2,hAPP(c_List_Onth(T_b),V_xs_2),V_n_2),
    file('theBenchmark.p',fact_nth_Osimps) ).

fof(fact_nth__Cons__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_all__set__conv__all__nth,axiom,
    ! [V_Pa_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_Pa_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_Pa_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_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_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_listsum__update__nat,axiom,
    ! [V_n,V_ns,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),V_ns)))
     => hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,V_ns),V_k),V_n)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns)),V_n)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),V_ns),V_k)) ),
    file('theBenchmark.p',fact_listsum__update__nat) ).

fof(fact_select__weigth__select,axiom,
    ! [T_b,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_b)
     => c_Random_Oselect__weight(T_b,hAPP(hAPP(c_List_Omap(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,T_b)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,T_b),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),V_xs_2)) = c_Random_Oselect(T_b,V_xs_2) ),
    file('theBenchmark.p',fact_select__weigth__select) ).

fof(fact_listrel__Nil2,axiom,
    ! [V_r_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2)))
     => V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_listrel__Nil2) ).

fof(fact_listrel__Nil1,axiom,
    ! [V_r_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel(T_b,V_r_2)))
     => V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_listrel__Nil1) ).

fof(fact_list__update__id,axiom,
    ! [V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)) = V_xs,
    file('theBenchmark.p',fact_list__update__id) ).

fof(fact_nth__list__update__neq,axiom,
    ! [V_x,V_xs,T_a,V_j,V_i] :
      ( V_i != V_j
     => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) ),
    file('theBenchmark.p',fact_nth__list__update__neq) ).

fof(fact_list__update__beyond,axiom,
    ! [V_x,V_i,V_xs,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_i))
     => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ),
    file('theBenchmark.p',fact_list__update__beyond) ).

fof(fact_take__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_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_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_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_take__Cons,axiom,
    ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Otake(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otake(T_b)),V_xs_2)),V_n_2),
    file('theBenchmark.p',fact_take__Cons) ).

fof(fact_Nil__is__map__conv,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] :
      ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)
    <=> V_xs_2 = c_List_Olist_ONil(T_c) ),
    file('theBenchmark.p',fact_Nil__is__map__conv) ).

fof(fact_map_Osimps_I1_J,axiom,
    ! [V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olist_ONil(T_c)) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_map_Osimps_I1_J) ).

fof(fact_map__update,axiom,
    ! [V_y_2,V_k_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olist__update(T_c,V_xs_2),V_k_2),V_y_2)) = hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),V_k_2),hAPP(V_f_2,V_y_2)),
    file('theBenchmark.p',fact_map__update) ).

fof(fact_map__is__Nil__conv,axiom,
    ! [V_xs_2,V_f_2,T_b,T_c] :
      ( hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2) = c_List_Olist_ONil(T_b)
    <=> V_xs_2 = c_List_Olist_ONil(T_c) ),
    file('theBenchmark.p',fact_map__is__Nil__conv) ).

fof(fact_zip__update,axiom,
    ! [V_y,V_ys,V_x,V_i,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),V_y)) = hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)),
    file('theBenchmark.p',fact_zip__update) ).

fof(fact_update__zip,axiom,
    ! [V_xy,V_i,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Olist__update(tc_prod(T_a,T_b),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)),V_i),V_xy) = hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),hAPP(c_Product__Type_Ofst(T_a,T_b),V_xy))),hAPP(hAPP(c_List_Olist__update(T_b,V_ys),V_i),hAPP(c_Product__Type_Osnd(T_a,T_b),V_xy))),
    file('theBenchmark.p',fact_update__zip) ).

fof(fact_sublist__nil,axiom,
    ! [V_A_2,T_b] : c_List_Osublist(T_b,c_List_Olist_ONil(T_b),V_A_2) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_sublist__nil) ).

fof(fact_sublist__empty,axiom,
    ! [V_xs_2,T_b] : c_List_Osublist(T_b,V_xs_2,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_sublist__empty) ).

fof(fact_insort__key_Osimps_I1_J,axiom,
    ! [V_x_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_x_2),c_List_Olist_ONil(T_b)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ),
    file('theBenchmark.p',fact_insort__key_Osimps_I1_J) ).

fof(fact_list__update_Osimps_I2_J,axiom,
    ! [V_v_2,V_i_2,V_xs_2,V_x_2,T_b] : hAPP(hAPP(c_List_Olist__update(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),V_i_2),V_v_2) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_v_2),V_xs_2),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_Nat_Onat),hAPP(c_List_Olist_OCons(T_b),V_x_2)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,T_b,tc_List_Olist(T_b)),c_List_Olist__update(T_b,V_xs_2)),V_v_2)),V_i_2),
    file('theBenchmark.p',fact_list__update_Osimps_I2_J) ).

fof(fact_list__update__code_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_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_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_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_list__update__nonempty,axiom,
    ! [V_x_2,V_k_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_b)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_list__update__nonempty) ).

fof(fact_list__update_Osimps_I1_J,axiom,
    ! [V_v,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_v) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_list__update_Osimps_I1_J) ).

fof(fact_list__update__code_I1_J,axiom,
    ! [V_y,V_i,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,c_List_Olist_ONil(T_a)),V_i),V_y) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_list__update__code_I1_J) ).

fof(fact_list__update__overwrite,axiom,
    ! [V_y,V_x,V_i,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i),V_y) = hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_y),
    file('theBenchmark.p',fact_list__update__overwrite) ).

fof(fact_list__update__swap,axiom,
    ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] :
      ( V_i != V_i_H
     => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i_H),V_x_H) = hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i_H),V_x_H)),V_i),V_x) ),
    file('theBenchmark.p',fact_list__update__swap) ).

fof(fact_remove1_Osimps_I1_J,axiom,
    ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_remove1_Osimps_I1_J) ).

fof(fact_distinct_Osimps_I1_J,axiom,
    ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))),
    file('theBenchmark.p',fact_distinct_Osimps_I1_J) ).

fof(fact_insort__not__Nil,axiom,
    ! [V_xs_2,V_a_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_c,V_f_2),V_a_2),V_xs_2) != c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_insort__not__Nil) ).

fof(fact_listrelp_ONil,axiom,
    ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)),
    file('theBenchmark.p',fact_listrelp_ONil) ).

fof(fact_listrelp_Oequations_I1_J,axiom,
    ! [V_r_2,T_b] : c_List_Olistrelp(T_b,V_r_2,c_List_Olist_ONil(T_b),c_List_Olist_ONil(T_b)),
    file('theBenchmark.p',fact_listrelp_Oequations_I1_J) ).

fof(fact_List_Oset_Osimps_I1_J,axiom,
    ! [T_b] : hAPP(c_List_Oset(T_b),c_List_Olist_ONil(T_b)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)),
    file('theBenchmark.p',fact_List_Oset_Osimps_I1_J) ).

fof(fact_set__empty2,axiom,
    ! [V_xs_2,T_b] :
      ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_List_Oset(T_b),V_xs_2)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_set__empty2) ).

fof(fact_set__empty,axiom,
    ! [V_xs_2,T_b] :
      ( hAPP(c_List_Oset(T_b),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_set__empty) ).

fof(fact_listsum__simps_I1_J,axiom,
    ! [T_a] :
      ( class_Groups_Omonoid__add(T_a)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ),
    file('theBenchmark.p',fact_listsum__simps_I1_J) ).

fof(fact_length__greater__0__conv,axiom,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
    <=> V_xs_2 != c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_length__greater__0__conv) ).

fof(fact_set__update__subsetI,axiom,
    ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_A_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2))
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),V_A_2)) ) ),
    file('theBenchmark.p',fact_set__update__subsetI) ).

fof(fact_take__1__Cons,axiom,
    ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Otake(T_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)),
    file('theBenchmark.p',fact_take__1__Cons) ).

fof(fact_set__update__subset__insert,axiom,
    ! [V_x_2,V_i_2,V_xs_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2))),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))),
    file('theBenchmark.p',fact_set__update__subset__insert) ).

fof(fact_nth__list__update,axiom,
    ! [V_x,V_j,V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => ( ( V_i != V_j
         => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j) )
        & ( V_i = V_j
         => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_j) = V_x ) ) ),
    file('theBenchmark.p',fact_nth__list__update) ).

fof(fact_list__update__same__conv,axiom,
    ! [V_x_2,V_xs_2,T_b,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
     => ( hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_x_2) = V_xs_2
      <=> hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2) = V_x_2 ) ),
    file('theBenchmark.p',fact_list__update__same__conv) ).

fof(fact_nth__list__update__eq,axiom,
    ! [V_x,V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_i) = V_x ),
    file('theBenchmark.p',fact_nth__list__update__eq) ).

fof(fact_listrel_ONil,axiom,
    ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olist_ONil(T_b))),c_List_Olistrel(T_b,V_r_2))),
    file('theBenchmark.p',fact_listrel_ONil) ).

fof(fact_lexord__Nil__right,axiom,
    ! [V_r_2,V_x_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olexord(T_b,V_r_2))),
    file('theBenchmark.p',fact_lexord__Nil__right) ).

fof(fact_Nil__notin__lex,axiom,
    ! [V_r_2,V_ys_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_ys_2)),c_List_Olex(T_b,V_r_2))),
    file('theBenchmark.p',fact_Nil__notin__lex) ).

fof(fact_Nil2__notin__lex,axiom,
    ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olex(T_b,V_r_2))),
    file('theBenchmark.p',fact_Nil2__notin__lex) ).

fof(fact_set__update__memI,axiom,
    ! [V_x_2,V_xs_2,T_b,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_n_2),V_x_2)))) ),
    file('theBenchmark.p',fact_set__update__memI) ).

fof(fact_upto_Osimps,axiom,
    ! [V_j,V_i] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
       => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j))
       => c_List_Oupto(V_i,V_j) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j)) ) ),
    file('theBenchmark.p',fact_upto_Osimps) ).

fof(fact_sublist__singleton,axiom,
    ! [V_x_2,T_b,V_A_2] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
       => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = c_List_Olist_ONil(T_b) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2))
       => c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)),V_A_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)) ) ),
    file('theBenchmark.p',fact_sublist__singleton) ).

fof(fact_take__Cons_H,axiom,
    ! [V_xs,V_x,T_a,V_n] :
      ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)) )
      & ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) ),
    file('theBenchmark.p',fact_take__Cons_H) ).

fof(fact_upto__rec__number__of,axiom,
    ! [V_n,V_m] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = c_List_Olist_ONil(tc_Int_Oint) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)))
       => c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_m)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_n))) ) ),
    file('theBenchmark.p',fact_upto__rec__number__of) ).

fof(fact_select,axiom,
    ! [V_s_2,T_b,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_Product__Type_Ofst(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(T_b,V_xs_2),V_s_2))),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_select) ).

fof(fact_listrel__Nil,axiom,
    ! [V_r_2,T_b] : hAPP(c_Relation_OImage(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Olistrel(T_b,V_r_2)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),
    file('theBenchmark.p',fact_listrel__Nil) ).

fof(fact_set__Cons__sing__Nil,axiom,
    ! [V_A_2,T_b] : c_List_Oset__Cons(T_b,V_A_2,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(T_b,tc_List_Olist(T_b),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))),V_A_2),
    file('theBenchmark.p',fact_set__Cons__sing__Nil) ).

fof(fact_take__Cons__number__of,axiom,
    ! [V_xs,V_x,T_a,V_v] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs)) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) ),
    file('theBenchmark.p',fact_take__Cons__number__of) ).

fof(fact_distinct__list__update,axiom,
    ! [V_i_2,V_a_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(hAPP(c_Set_Oinsert(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_i_2)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))))
       => hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),V_i_2),V_a_2))) ) ),
    file('theBenchmark.p',fact_distinct__list__update) ).

fof(fact_upto_Opsimps,axiom,
    ! [V_j_2,V_i_2] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_List_Oupto__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_i_2),V_j_2)))
     => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
         => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2))
         => c_List_Oupto(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),V_i_2),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_j_2)) ) ) ),
    file('theBenchmark.p',fact_upto_Opsimps) ).

fof(fact_anamorph_Osimps,axiom,
    ! [V_x_2,V_f_2,T_b,T_c,V_k_2] :
      ( ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2,V_k_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(T_b,T_c),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_prod(tc_List_Olist(T_b),T_c)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),c_COMBB(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c),T_c)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),tc_fun(tc_prod(tc_List_Olist(T_b),T_c),tc_prod(tc_List_Olist(T_b),T_c)),T_b),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_b),T_c,tc_prod(tc_List_Olist(T_b),T_c))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c))),T_b),hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(T_c,tc_prod(tc_List_Olist(T_b),T_c)),tc_List_Olist(T_b)),c_Product__Type_OPair(tc_List_Olist(T_b),T_c))),c_List_Olist_OCons(T_b))))),c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(V_f_2,V_x_2)) )
      & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
       => hAPP(c_Lazy__Sequence_Oanamorph(T_c,T_b,V_f_2,V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),T_c),c_List_Olist_ONil(T_b)),V_x_2) ) ),
    file('theBenchmark.p',fact_anamorph_Osimps) ).

fof(fact_listset_Osimps_I1_J,axiom,
    ! [T_b] : c_List_Olistset(T_b,c_List_Olist_ONil(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),
    file('theBenchmark.p',fact_listset_Osimps_I1_J) ).

fof(fact_zip__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_Pa_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_Pa_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_Pa_2,B_i),B_j)) ) )
       => hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2)) ) ),
    file('theBenchmark.p',fact_upto_Opinduct) ).

fof(fact_map__upd__upds__conv__if,axiom,
    ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_c,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2))))
       => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),V_xs_2,V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2))))
       => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_f_2),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),V_y_2)),V_xs_2,V_ys_2) = c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2) ) ),
    file('theBenchmark.p',fact_map__upd__upds__conv__if) ).

fof(fact_map__upds__Nil1,axiom,
    ! [V_bs_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,c_List_Olist_ONil(T_b),V_bs_2) = V_m_2,
    file('theBenchmark.p',fact_map__upds__Nil1) ).

fof(fact_map__upds__Nil2,axiom,
    ! [V_as_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_as_2,c_List_Olist_ONil(T_c)) = V_m_2,
    file('theBenchmark.p',fact_map__upds__Nil2) ).

fof(fact_map__upds__apply__nontin,axiom,
    ! [V_ys_2,V_f_2,T_c,V_xs_2,V_x_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
     => hAPP(c_Map_Omap__upds(T_b,T_c,V_f_2,V_xs_2,V_ys_2),V_x_2) = hAPP(V_f_2,V_x_2) ),
    file('theBenchmark.p',fact_map__upds__apply__nontin) ).

fof(fact_map__add__upds,axiom,
    ! [V_ys_2,V_xs_2,V_m2_2,V_m1_2,T_c,T_b] : c_Map_Omap__add(T_b,T_c,V_m1_2,c_Map_Omap__upds(T_b,T_c,V_m2_2,V_xs_2,V_ys_2)) = c_Map_Omap__upds(T_b,T_c,c_Map_Omap__add(T_b,T_c,V_m1_2,V_m2_2),V_xs_2,V_ys_2),
    file('theBenchmark.p',fact_map__add__upds) ).

fof(fact_map__upds__Cons,axiom,
    ! [V_bs_2,V_b_2,V_as_2,V_a_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_as_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_b_2),V_bs_2)) = c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)),V_as_2,V_bs_2),
    file('theBenchmark.p',fact_map__upds__Cons) ).

fof(fact_map__upds__list__update2__drop,axiom,
    ! [V_y_2,V_m_2,V_ys_2,T_c,V_i_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_i_2))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
       => c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,hAPP(hAPP(c_List_Olist__update(T_c,V_ys_2),V_i_2),V_y_2)) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ) ),
    file('theBenchmark.p',fact_map__upds__list__update2__drop) ).

fof(fact_map__upds__twist,axiom,
    ! [V_bs_2,V_b_2,V_m_2,T_c,V_as_2,V_a_2,T_b] :
      ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_as_2)))
     => c_Map_Omap__upds(T_b,T_c,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),V_m_2),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)),V_as_2,V_bs_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_m_2,V_as_2,V_bs_2)),V_a_2),hAPP(c_Option_Ooption_OSome(T_c),V_b_2)) ),
    file('theBenchmark.p',fact_map__upds__twist) ).

fof(fact_restrict__map__upds,axiom,
    ! [V_m_2,V_D_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),V_D_2))
       => c_Map_Orestrict__map(T_b,T_c,c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2),V_D_2) = c_Map_Omap__upds(T_b,T_c,c_Map_Orestrict__map(T_b,T_c,V_m_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_D_2),hAPP(c_List_Oset(T_b),V_xs_2))),V_xs_2,V_ys_2) ) ),
    file('theBenchmark.p',fact_restrict__map__upds) ).

fof(fact_dom__map__upds,axiom,
    ! [V_ys_2,V_xs_2,V_m_2,T_c,T_b] : c_Map_Odom(T_b,T_c,c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)),V_xs_2))),c_Map_Odom(T_b,T_c,V_m_2)),
    file('theBenchmark.p',fact_dom__map__upds) ).

fof(fact_map__upds__append1,axiom,
    ! [V_x_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)))
     => c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))),V_ys_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,tc_Option_Ooption(T_c)),c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2)),V_x_2),hAPP(c_Option_Ooption_OSome(T_c),hAPP(hAPP(c_List_Onth(T_c),V_ys_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))) ),
    file('theBenchmark.p',fact_map__upds__append1) ).

fof(fact_sublist__Cons,axiom,
    ! [V_A_2,V_l_2,V_x_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(hAPP(c_If(tc_List_Olist(T_b)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))),c_List_Olist_ONil(T_b))),c_List_Osublist(T_b,V_l_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),c_Nat_OSuc)),V_A_2)))),
    file('theBenchmark.p',fact_sublist__Cons) ).

fof(fact_append1__eq__conv,axiom,
    ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b)))
    <=> ( V_x_2 = V_y_2
        & V_xs_2 = V_ys_2 ) ),
    file('theBenchmark.p',fact_append1__eq__conv) ).

fof(fact_Cons__eq__append__conv,axiom,
    ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_b] :
      ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2)
    <=> ( ? [B_ys_H] :
            ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2)
            & hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) = V_ys_2 )
        | ( hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) = V_zs_2
          & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ),
    file('theBenchmark.p',fact_Cons__eq__append__conv) ).

fof(fact_append__eq__Cons__conv,axiom,
    ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_zs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
    <=> ( ? [B_ys_H] :
            ( hAPP(hAPP(c_List_Oappend(T_b),B_ys_H),V_zs_2) = V_xs_2
            & V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),B_ys_H) )
        | ( V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
          & V_ys_2 = c_List_Olist_ONil(T_b) ) ) ),
    file('theBenchmark.p',fact_append__eq__Cons__conv) ).

fof(fact_fun__upds__append__drop,axiom,
    ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => c_Map_Omap__upds(T_b,T_c,V_m_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_zs_2),V_ys_2) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ),
    file('theBenchmark.p',fact_fun__upds__append__drop) ).

fof(fact_fun__upds__append2__drop,axiom,
    ! [V_zs_2,V_m_2,V_ys_2,T_c,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_c)),V_ys_2)
     => c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,hAPP(hAPP(c_List_Oappend(T_c),V_ys_2),V_zs_2)) = c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) ),
    file('theBenchmark.p',fact_fun__upds__append2__drop) ).

fof(fact_list__update__length,axiom,
    ! [V_y,V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_y) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)),
    file('theBenchmark.p',fact_list__update__length) ).

fof(fact_nth__append__length,axiom,
    ! [V_ys,V_x,V_xs,T_a] : hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = V_x,
    file('theBenchmark.p',fact_nth__append__length) ).

fof(fact_Cons__eq__appendI,axiom,
    ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] :
      ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys
     => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs)
       => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ),
    file('theBenchmark.p',fact_Cons__eq__appendI) ).

fof(fact_append__Cons,axiom,
    ! [V_ys,V_xs,V_x,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_ys) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),
    file('theBenchmark.p',fact_append__Cons) ).

fof(fact_take__append,axiom,
    ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)),
    file('theBenchmark.p',fact_take__append) ).

fof(fact_list__update__append1,axiom,
    ! [V_x,V_ys,V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_i),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x)),V_ys) ),
    file('theBenchmark.p',fact_list__update__append1) ).

fof(fact_remove1__append,axiom,
    ! [V_ys_2,V_xs_2,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oremove1(T_b,V_x_2,V_ys_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_Oremove1(T_b,V_x_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Oremove1(T_b,V_x_2,V_xs_2)),V_ys_2) ) ),
    file('theBenchmark.p',fact_remove1__append) ).

fof(fact_length__append,axiom,
    ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)),
    file('theBenchmark.p',fact_length__append) ).

fof(fact_zip__append,axiom,
    ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_us)
     => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_vs)
       => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),hAPP(hAPP(c_List_Oappend(T_b),V_us),V_vs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_us)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),V_vs)) ) ),
    file('theBenchmark.p',fact_zip__append) ).

fof(fact_map__append,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_ys_2)),
    file('theBenchmark.p',fact_map__append) ).

fof(fact_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_ts_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_ts_2)
    <=> ? [B_us] :
          ( ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_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_ts_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_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_eq__Nil__appendI,axiom,
    ! [T_a,V_ys,V_xs] :
      ( V_xs = V_ys
     => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ),
    file('theBenchmark.p',fact_eq__Nil__appendI) ).

fof(fact_append__self__conv2,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_ys_2
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_append__self__conv2) ).

fof(fact_append__self__conv,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_xs_2
    <=> V_ys_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_append__self__conv) ).

fof(fact_append__is__Nil__conv,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_b)
    <=> ( V_ys_2 = c_List_Olist_ONil(T_b)
        & V_xs_2 = c_List_Olist_ONil(T_b) ) ),
    file('theBenchmark.p',fact_append__is__Nil__conv) ).

fof(fact_self__append__conv2,axiom,
    ! [V_xs_2,T_b,V_ys_2] :
      ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_self__append__conv2) ).

fof(fact_self__append__conv,axiom,
    ! [V_ys_2,T_b,V_xs_2] :
      ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
    <=> V_ys_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_self__append__conv) ).

fof(fact_append__Nil2,axiom,
    ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs,
    file('theBenchmark.p',fact_append__Nil2) ).

fof(fact_Nil__is__append__conv,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( c_List_Olist_ONil(T_b) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)
    <=> ( V_ys_2 = c_List_Olist_ONil(T_b)
        & V_xs_2 = c_List_Olist_ONil(T_b) ) ),
    file('theBenchmark.p',fact_Nil__is__append__conv) ).

fof(fact_append__Nil,axiom,
    ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys,
    file('theBenchmark.p',fact_append__Nil) ).

fof(fact_lexord__append__leftI,axiom,
    ! [V_x_2,V_r_2,V_v_2,V_u_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_lexord__append__leftI) ).

fof(fact_distinct__append,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)))
    <=> ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        & hBOOL(hAPP(c_List_Odistinct(T_b),V_ys_2))
        & hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ) ),
    file('theBenchmark.p',fact_distinct__append) ).

fof(fact_nth__append,axiom,
    ! [V_ys,V_xs,T_a,V_n] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
       => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
       => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ) ),
    file('theBenchmark.p',fact_nth__append) ).

fof(fact_list__update__append,axiom,
    ! [V_x,V_ys,V_xs,T_a,V_n] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
       => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist__update(T_a,V_ys),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_x)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
       => hAPP(hAPP(c_List_Olist__update(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_n),V_x) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_n),V_x)),V_ys) ) ),
    file('theBenchmark.p',fact_list__update__append) ).

fof(fact_sublist__append,axiom,
    ! [V_A_2,V_l_H_2,V_l_2,T_b] : c_List_Osublist(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_l_2),V_l_H_2),V_A_2) = hAPP(hAPP(c_List_Oappend(T_b),c_List_Osublist(T_b,V_l_2,V_A_2)),c_List_Osublist(T_b,V_l_H_2,hAPP(c_Set_OCollect(tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_Nat_Onat),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_l_2)))),V_A_2)))),
    file('theBenchmark.p',fact_sublist__append) ).

fof(fact_lexord__append__left__rightI,axiom,
    ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_a_2),V_b_2)),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_x_2))),hAPP(hAPP(c_List_Oappend(T_b),V_u_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_b_2),V_y_2)))),c_List_Olexord(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_lexord__append__left__rightI) ).

fof(fact_take__Suc__conv__app__nth,axiom,
    ! [V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),c_List_Olist_ONil(T_a))) ),
    file('theBenchmark.p',fact_take__Suc__conv__app__nth) ).

fof(fact_snoc__listrel1__snoc__iff,axiom,
    ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b)))),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),c_List_Olist_ONil(T_b))))),c_List_Olistrel1(T_b,V_r_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
          & V_xs_2 = V_ys_2 )
        | ( V_x_2 = V_y_2
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ),
    file('theBenchmark.p',fact_snoc__listrel1__snoc__iff) ).

fof(fact_lexord__append__leftD,axiom,
    ! [V_r_2,V_v_2,V_u_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_u_2)),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_v_2))),c_List_Olexord(T_b,V_r_2)))
     => ( ! [B_a] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_a)),V_r_2))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_u_2),V_v_2)),c_List_Olexord(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_lexord__append__leftD) ).

fof(fact_Cons__acc__listrel1I,axiom,
    ! [V_xs_2,V_r_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Wellfounded_Oacc(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
       => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ),
    file('theBenchmark.p',fact_Cons__acc__listrel1I) ).

fof(fact_listrel1__converse,axiom,
    ! [V_r_2,T_b] : c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2)) = hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)),
    file('theBenchmark.p',fact_listrel1__converse) ).

fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom,
    ! [V_r_2,T_b] : c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)),
    file('theBenchmark.p',fact_listrel__rtrancl__eq__rtrancl__listrel1) ).

fof(fact_listrel1__mono,axiom,
    ! [V_s_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_s_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel1(T_b,V_s_2))) ),
    file('theBenchmark.p',fact_listrel1__mono) ).

fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom,
    ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))),
    file('theBenchmark.p',fact_listrel1__rtrancl__subset__rtrancl__listrel1) ).

fof(fact_listrel__subset__rtrancl__listrel1,axiom,
    ! [V_r_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel(T_b,V_r_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))),
    file('theBenchmark.p',fact_listrel__subset__rtrancl__listrel1) ).

fof(fact_rtrancl__listrel1__ConsI1,axiom,
    ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ),
    file('theBenchmark.p',fact_rtrancl__listrel1__ConsI1) ).

fof(fact_listrel1I2,axiom,
    ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_listrel1I2) ).

fof(fact_rtrancl__listrel1__eq__len,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_x_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_y_2) ),
    file('theBenchmark.p',fact_rtrancl__listrel1__eq__len) ).

fof(fact_listrel1__eq__len,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) ),
    file('theBenchmark.p',fact_listrel1__eq__len) ).

fof(fact_not__Nil__listrel1,axiom,
    ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xs_2)),c_List_Olistrel1(T_b,V_r_2))),
    file('theBenchmark.p',fact_not__Nil__listrel1) ).

fof(fact_not__listrel1__Nil,axiom,
    ! [V_r_2,V_xs_2,T_b] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),c_List_Olist_ONil(T_b))),c_List_Olistrel1(T_b,V_r_2))),
    file('theBenchmark.p',fact_not__listrel1__Nil) ).

fof(fact_append__listrel1I,axiom,
    ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_us_2),V_vs_2)),c_List_Olistrel1(T_b,V_r_2)))
          & V_xs_2 = V_ys_2 )
        | ( V_us_2 = V_vs_2
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) )
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_us_2)),hAPP(hAPP(c_List_Oappend(T_b),V_ys_2),V_vs_2))),c_List_Olistrel1(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_append__listrel1I) ).

fof(fact_in__listrel1__converse,axiom,
    ! [V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olistrel1(T_b,hAPP(c_Relation_Oconverse(T_b,T_b),V_r_2))))
    <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olistrel1(T_b,V_r_2)))) ),
    file('theBenchmark.p',fact_in__listrel1__converse) ).

fof(fact_rtrancl__listrel1__if__listrel,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ),
    file('theBenchmark.p',fact_rtrancl__listrel1__if__listrel) ).

fof(fact_listrel__reflcl__if__listrel1,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel(T_b,c_Transitive__Closure_Ortrancl(T_b,V_r_2)))) ),
    file('theBenchmark.p',fact_listrel__reflcl__if__listrel1) ).

fof(fact_listrel1I1,axiom,
    ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_xs_2))),c_List_Olistrel1(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_listrel1I1) ).

fof(fact_Cons__listrel1__Cons,axiom,
    ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_List_Olistrel1(T_b,V_r_2)))
    <=> ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
          & V_x_2 = V_y_2 )
        | ( V_xs_2 = V_ys_2
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2)) ) ) ),
    file('theBenchmark.p',fact_Cons__listrel1__Cons) ).

fof(fact_listrel1__subset__listrel,axiom,
    ! [V_r_H_2,V_r_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(T_b,T_b),tc_HOL_Obool)),V_r_2),V_r_H_2))
     => ( c_Relation_Orefl__on(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)),V_r_H_2)
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b)),tc_HOL_Obool)),c_List_Olistrel1(T_b,V_r_2)),c_List_Olistrel(T_b,V_r_H_2))) ) ),
    file('theBenchmark.p',fact_listrel1__subset__listrel) ).

fof(fact_listrel1I,axiom,
    ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),V_r_2))
     => ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_vs_2))
       => ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_b),V_us_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_vs_2))
         => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2))) ) ) ),
    file('theBenchmark.p',fact_listrel1I) ).

fof(fact_rtrancl__listrel1__ConsI2,axiom,
    ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),V_x_2),V_y_2)),c_Transitive__Closure_Ortrancl(T_b,V_r_2)))
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
       => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2))),c_Transitive__Closure_Ortrancl(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ) ),
    file('theBenchmark.p',fact_rtrancl__listrel1__ConsI2) ).

fof(fact_listrel1__iff__update,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
    <=> ? [B_y,B_n] :
          ( V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_b,V_xs_2),B_n),B_y)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_n)),B_y)),V_r_2)) ) ),
    file('theBenchmark.p',fact_listrel1__iff__update) ).

fof(fact_listrel1E,axiom,
    ! [V_r_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_xs_2),V_ys_2)),c_List_Olistrel1(T_b,V_r_2)))
     => ~ ! [B_x,B_y] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_y)),V_r_2))
           => ! [B_us,B_vs] :
                ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_x),B_vs))
               => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),hAPP(hAPP(c_List_Olist_OCons(T_b),B_y),B_vs)) ) ) ),
    file('theBenchmark.p',fact_listrel1E) ).

fof(fact_rotate1__def,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Orotate1(T_b),V_xs_2) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)))),V_xs_2),
    file('theBenchmark.p',fact_rotate1__def) ).

fof(fact_upd__conv__take__nth__drop,axiom,
    ! [V_a,V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_a) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ),
    file('theBenchmark.p',fact_upd__conv__take__nth__drop) ).

fof(fact_drop__append,axiom,
    ! [V_ys,V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_ys)),
    file('theBenchmark.p',fact_drop__append) ).

fof(fact_drop__Nil,axiom,
    ! [V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_drop__Nil) ).

fof(fact_rotate1__is__Nil__conv,axiom,
    ! [V_xs_2,T_b] :
      ( hAPP(c_List_Orotate1(T_b),V_xs_2) = c_List_Olist_ONil(T_b)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_rotate1__is__Nil__conv) ).

fof(fact_drop__take,axiom,
    ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Otake(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),
    file('theBenchmark.p',fact_drop__take) ).

fof(fact_take__drop,axiom,
    ! [V_xs,V_m,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(hAPP(c_List_Odrop(T_a),V_m),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_m),hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m)),V_xs)),
    file('theBenchmark.p',fact_take__drop) ).

fof(fact_in__set__dropD,axiom,
    ! [V_xs_2,V_n_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_in__set__dropD) ).

fof(fact_set__rotate1,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
    file('theBenchmark.p',fact_set__rotate1) ).

fof(fact_set__drop__subset,axiom,
    ! [V_xs_2,V_n_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    file('theBenchmark.p',fact_set__drop__subset) ).

fof(fact_distinct1__rotate,axiom,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate1(T_b),V_xs_2)))
    <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_distinct1__rotate) ).

fof(fact_distinct__drop,axiom,
    ! [V_i,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ),
    file('theBenchmark.p',fact_distinct__drop) ).

fof(fact_drop__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__rotate1,axiom,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate1(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
    file('theBenchmark.p',fact_length__rotate1) ).

fof(fact_length__drop,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n),
    file('theBenchmark.p',fact_length__drop) ).

fof(fact_drop__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_drop__all,axiom,
    ! [V_n,V_xs,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n))
     => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_drop__all) ).

fof(fact_drop__eq__Nil,axiom,
    ! [V_xs_2,V_n_2,T_b] :
      ( hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
    <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_n_2)) ),
    file('theBenchmark.p',fact_drop__eq__Nil) ).

fof(fact_set__drop__subset__set__drop,axiom,
    ! [V_xs_2,T_b,V_m_2,V_n_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_m_2),V_xs_2))),hAPP(c_List_Oset(T_b),hAPP(hAPP(c_List_Odrop(T_b),V_n_2),V_xs_2)))) ),
    file('theBenchmark.p',fact_set__drop__subset__set__drop) ).

fof(fact_append__take__drop__id,axiom,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = V_xs,
    file('theBenchmark.p',fact_append__take__drop__id) ).

fof(fact_append__eq__conv__conj,axiom,
    ! [V_zs_2,V_ys_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2) = V_zs_2
    <=> ( V_ys_2 = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2)
        & V_xs_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),V_zs_2) ) ),
    file('theBenchmark.p',fact_append__eq__conv__conj) ).

fof(fact_drop__Cons,axiom,
    ! [V_xs_2,V_x_2,V_n_2,T_b] : hAPP(hAPP(c_List_Odrop(T_b),V_n_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_Nat_Onat_Onat__case(tc_List_Olist(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Odrop(T_b)),V_xs_2),V_n_2),
    file('theBenchmark.p',fact_drop__Cons) ).

fof(fact_drop__Cons_H,axiom,
    ! [V_xs,V_x,T_a,V_n] :
      ( ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) )
      & ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ) ),
    file('theBenchmark.p',fact_drop__Cons_H) ).

fof(fact_nth__drop,axiom,
    ! [V_xs,T_a,V_i,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),V_i) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_i)) ),
    file('theBenchmark.p',fact_nth__drop) ).

fof(fact_append__eq__append__conv__if,axiom,
    ! [V_ys_092_060_094isub_0622_2,V_ys_092_060_094isub_0621_2,V_xs_092_060_094isub_0622_2,V_xs_092_060_094isub_0621_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_092_060_094isub_0621_2),V_xs_092_060_094isub_0622_2) = hAPP(hAPP(c_List_Oappend(T_b),V_ys_092_060_094isub_0621_2),V_ys_092_060_094isub_0622_2)
    <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)))
         => ( hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2)),V_xs_092_060_094isub_0622_2) = V_ys_092_060_094isub_0622_2
            & hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)),V_xs_092_060_094isub_0621_2) = V_ys_092_060_094isub_0621_2 ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_092_060_094isub_0621_2)))
         => ( V_xs_092_060_094isub_0622_2 = hAPP(hAPP(c_List_Oappend(T_b),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2)),V_ys_092_060_094isub_0622_2)
            & V_xs_092_060_094isub_0621_2 = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_092_060_094isub_0621_2)),V_ys_092_060_094isub_0621_2) ) ) ) ),
    file('theBenchmark.p',fact_append__eq__append__conv__if) ).

fof(fact_nth__drop_H,axiom,
    ! [V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs) ),
    file('theBenchmark.p',fact_nth__drop_H) ).

fof(fact_rotate__simps,axiom,
    ! [V_xs,V_x,T_b,T_a] :
      ( hAPP(c_List_Orotate1(T_b),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),V_xs)) = hAPP(hAPP(c_List_Oappend(T_b),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x),c_List_Olist_ONil(T_b)))
      & hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ),
    file('theBenchmark.p',fact_rotate__simps) ).

fof(fact_drop__Cons__number__of,axiom,
    ! [V_xs,V_x,T_a,V_v] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
       => hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ) ),
    file('theBenchmark.p',fact_drop__Cons__number__of) ).

fof(fact_take__add,axiom,
    ! [V_xs,T_a,V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_j)),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_j),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ),
    file('theBenchmark.p',fact_take__add) ).

fof(fact_rotate1__length01,axiom,
    ! [V_xs,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
     => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ),
    file('theBenchmark.p',fact_rotate1__length01) ).

fof(fact_zip__append1,axiom,
    ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)),V_zs) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_ys),hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_zs))),
    file('theBenchmark.p',fact_zip__append1) ).

fof(fact_zip__append2,axiom,
    ! [V_zs,V_ys,V_xs,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),hAPP(hAPP(c_List_Oappend(T_b),V_ys),V_zs)) = hAPP(hAPP(c_List_Oappend(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_ys)),hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)),V_xs)),V_zs)),
    file('theBenchmark.p',fact_zip__append2) ).

fof(fact_id__take__nth__drop,axiom,
    ! [V_xs,T_a,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => V_xs = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_i)),V_xs))) ),
    file('theBenchmark.p',fact_id__take__nth__drop) ).

fof(fact_take__hd__drop,axiom,
    ! [V_xs,T_a,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs))),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) ),
    file('theBenchmark.p',fact_take__hd__drop) ).

fof(fact_hd__drop__conv__nth,axiom,
    ! [V_n,T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
       => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) ) ),
    file('theBenchmark.p',fact_hd__drop__conv__nth) ).

fof(fact_hd__append2,axiom,
    ! [V_ys,T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) ),
    file('theBenchmark.p',fact_hd__append2) ).

fof(fact_hd__append,axiom,
    ! [V_ys,T_a,V_xs] :
      ( ( V_xs != c_List_Olist_ONil(T_a)
       => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_xs) )
      & ( V_xs = c_List_Olist_ONil(T_a)
       => hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(c_List_Ohd(T_a),V_ys) ) ),
    file('theBenchmark.p',fact_hd__append) ).

fof(fact_hd_Osimps,axiom,
    ! [V_xs,V_x,T_a] : hAPP(c_List_Ohd(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x,
    file('theBenchmark.p',fact_hd_Osimps) ).

fof(fact_hd__map,axiom,
    ! [V_f_2,T_c,T_b,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_b)
     => hAPP(c_List_Ohd(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,hAPP(c_List_Ohd(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_hd__map) ).

fof(fact_hd__in__set,axiom,
    ! [T_b,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_hd__in__set) ).

fof(fact_hd__conv__nth,axiom,
    ! [T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(c_List_Ohd(T_a),V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    file('theBenchmark.p',fact_hd__conv__nth) ).

fof(fact_rotate1__hd__tl,axiom,
    ! [T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(c_List_Orotate1(T_a),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),c_List_Olist_ONil(T_a))) ),
    file('theBenchmark.p',fact_rotate1__hd__tl) ).

fof(fact_hd__rotate__conv__nth,axiom,
    ! [V_n,T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(hAPP(c_List_Onth(T_a),V_xs),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))) ),
    file('theBenchmark.p',fact_hd__rotate__conv__nth) ).

fof(fact_drop__Suc,axiom,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)),
    file('theBenchmark.p',fact_drop__Suc) ).

fof(fact_drop__tl,axiom,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),
    file('theBenchmark.p',fact_drop__tl) ).

fof(fact_tl__drop,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)),
    file('theBenchmark.p',fact_tl__drop) ).

fof(fact_tl_Osimps_I1_J,axiom,
    ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_tl_Osimps_I1_J) ).

fof(fact_rotate__is__Nil__conv,axiom,
    ! [V_xs_2,V_n_2,T_b] :
      ( hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2) = c_List_Olist_ONil(T_b)
    <=> V_xs_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_rotate__is__Nil__conv) ).

fof(fact_take__tl,axiom,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)),
    file('theBenchmark.p',fact_take__tl) ).

fof(fact_set__rotate,axiom,
    ! [V_xs_2,V_n_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
    file('theBenchmark.p',fact_set__rotate) ).

fof(fact_distinct__rotate,axiom,
    ! [V_xs_2,V_n_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orotate(T_b,V_n_2),V_xs_2)))
    <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_distinct__rotate) ).

fof(fact_distinct__tl,axiom,
    ! [V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ),
    file('theBenchmark.p',fact_distinct__tl) ).

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

fof(fact_rotate__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_n_2,T_b] : hAPP(c_List_Orotate(T_b,V_n_2),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orotate(T_c,V_n_2),V_xs_2)),
    file('theBenchmark.p',fact_rotate__map) ).

fof(fact_map__tl,axiom,
    ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Otl(T_c),V_xs_2)) = hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_map__tl) ).

fof(fact_length__rotate,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orotate(T_a,V_n),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
    file('theBenchmark.p',fact_length__rotate) ).

fof(fact_rotate__conv__mod,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(c_List_Orotate(T_a,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs),
    file('theBenchmark.p',fact_rotate__conv__mod) ).

fof(fact_tl_Osimps_I2_J,axiom,
    ! [V_xs,V_x,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs,
    file('theBenchmark.p',fact_tl_Osimps_I2_J) ).

fof(fact_tl__append2,axiom,
    ! [V_ys,T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),V_ys) ),
    file('theBenchmark.p',fact_tl__append2) ).

fof(fact_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_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_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_tl__append,axiom,
    ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,hAPP(c_List_Otl(T_b),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b)),V_ys_2))),V_xs_2),
    file('theBenchmark.p',fact_tl__append) ).

fof(fact_rotate0,axiom,
    ! [T_b] : c_List_Orotate(T_b,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_b)),
    file('theBenchmark.p',fact_rotate0) ).

fof(fact_rotate__add,axiom,
    ! [V_n_2,V_m_2,T_b] : c_List_Orotate(T_b,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2)) = hAPP(c_Fun_Ocomp(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orotate(T_b,V_m_2)),c_List_Orotate(T_b,V_n_2)),
    file('theBenchmark.p',fact_rotate__add) ).

fof(fact_rotate__id,axiom,
    ! [V_xs,T_a,V_n] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
     => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ),
    file('theBenchmark.p',fact_rotate__id) ).

fof(fact_rotate__length01,axiom,
    ! [V_n,V_xs,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
     => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ),
    file('theBenchmark.p',fact_rotate__length01) ).

fof(fact_length__tl,axiom,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('theBenchmark.p',fact_length__tl) ).

fof(fact_tl__take,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(T_a),V_xs)),
    file('theBenchmark.p',fact_tl__take) ).

fof(fact_take__Suc,axiom,
    ! [V_n,T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs))) ),
    file('theBenchmark.p',fact_take__Suc) ).

fof(fact_rotate__drop__take,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(hAPP(c_List_Odrop(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)),hAPP(hAPP(c_List_Otake(T_a),c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),V_xs)),
    file('theBenchmark.p',fact_rotate__drop__take) ).

fof(fact_fold1__set,axiom,
    ! [V_xs_2,T_b] :
      ( class_Lattices_Oab__semigroup__idem__mult(T_b)
     => ( V_xs_2 != c_List_Olist_ONil(T_b)
       => hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Otl(T_b),V_xs_2)) ) ),
    file('theBenchmark.p',fact_fold1__set) ).

fof(fact_list_Osize_I2_J,axiom,
    ! [V_list_2,V_a_2,V_fa_2,T_b] : c_List_Olist_Olist__size(T_b,V_fa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a_2),V_list_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),c_List_Olist_Olist__size(T_b,V_fa_2,V_list_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    file('theBenchmark.p',fact_list_Osize_I2_J) ).

fof(fact_foldl__append,axiom,
    ! [V_ys_2,V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Oappend(T_c),V_xs_2),V_ys_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2)),V_ys_2),
    file('theBenchmark.p',fact_foldl__append) ).

fof(fact_foldl__Cons,axiom,
    ! [V_xs_2,V_x_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),hAPP(hAPP(c_List_Olist_OCons(T_c),V_x_2),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,hAPP(hAPP(V_f_2,V_a_2),V_x_2)),V_xs_2),
    file('theBenchmark.p',fact_foldl__Cons) ).

fof(fact_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__accI,axiom,
    ! [V_r_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2))))
     => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2)))) ),
    file('theBenchmark.p',fact_lists__accI) ).

fof(fact_lists_ONil,axiom,
    ! [V_A_2,T_b] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_List_Olists(T_b,V_A_2))),
    file('theBenchmark.p',fact_lists_ONil) ).

fof(fact_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_listrel__refl__on,axiom,
    ! [V_r_2,V_A_2,T_b] :
      ( c_Relation_Orefl__on(T_b,V_A_2,V_r_2)
     => c_Relation_Orefl__on(tc_List_Olist(T_b),c_List_Olists(T_b,V_A_2),c_List_Olistrel(T_b,V_r_2)) ),
    file('theBenchmark.p',fact_listrel__refl__on) ).

fof(fact_lists__UNIV,axiom,
    ! [T_b] : c_List_Olists(T_b,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),
    file('theBenchmark.p',fact_lists__UNIV) ).

fof(fact_lists__mono,axiom,
    ! [V_B_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2))
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool)),c_List_Olists(T_b,V_A_2)),c_List_Olists(T_b,V_B_2))) ),
    file('theBenchmark.p',fact_lists__mono) ).

fof(fact_append__in__lists__conv,axiom,
    ! [V_A_2,V_ys_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)),c_List_Olists(T_b,V_A_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),c_List_Olists(T_b,V_A_2)))
        & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2))) ) ),
    file('theBenchmark.p',fact_append__in__lists__conv) ).

fof(fact_Cons__in__lists__iff,axiom,
    ! [V_A_2,V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)),c_List_Olists(T_b,V_A_2)))
    <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) ) ),
    file('theBenchmark.p',fact_Cons__in__lists__iff) ).

fof(fact_in__lists__conv__set,axiom,
    ! [V_A_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,V_A_2)))
    <=> ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ),
    file('theBenchmark.p',fact_in__lists__conv__set) ).

fof(fact_lists__eq__set,axiom,
    ! [V_A_2,T_b] : c_List_Olists(T_b,V_A_2) = hAPP(c_Set_OCollect(tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(T_b)),c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool))),c_List_Oset(T_b))),V_A_2)),
    file('theBenchmark.p',fact_lists__eq__set) ).

fof(fact_lists__empty,axiom,
    ! [T_b] : c_List_Olists(T_b,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(T_b),tc_HOL_Obool))),
    file('theBenchmark.p',fact_lists__empty) ).

fof(fact_lists__accD,axiom,
    ! [V_r_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_List_Olists(T_b,c_Wellfounded_Oacc(T_b,V_r_2))))
     => hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_xs_2),c_Wellfounded_Oacc(tc_List_Olist(T_b),c_List_Olistrel1(T_b,V_r_2)))) ),
    file('theBenchmark.p',fact_lists__accD) ).

fof(fact_lexord__append__rightI,axiom,
    ! [V_r_2,V_x_2,T_b,V_y_2] :
      ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_b),B_z)
     => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),hAPP(hAPP(c_List_Oappend(T_b),V_x_2),V_y_2))),c_List_Olexord(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_lexord__append__rightI) ).

fof(fact_lexord__Nil__left,axiom,
    ! [V_r_2,V_y_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_y_2)),c_List_Olexord(T_b,V_r_2)))
    <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_x) ),
    file('theBenchmark.p',fact_lexord__Nil__left) ).

fof(fact_last__list__update,axiom,
    ! [V_x,V_k,T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => ( ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
         => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Olast(T_a,V_xs) )
        & ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
         => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) ) ),
    file('theBenchmark.p',fact_last__list__update) ).

fof(fact_listsum__mono,axiom,
    ! [V_g_2,V_f_2,V_xs_2,T_b,T_c] :
      ( ( class_Groups_Oordered__ab__semigroup__add(T_c)
        & class_Groups_Omonoid__add(T_c) )
     => ( ! [B_x] :
            ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
       => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))),hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_g_2),V_xs_2)))) ) ),
    file('theBenchmark.p',fact_listsum__mono) ).

fof(fact_last_Osimps,axiom,
    ! [V_x,T_a,V_xs] :
      ( ( V_xs != c_List_Olist_ONil(T_a)
       => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) )
      & ( V_xs = c_List_Olist_ONil(T_a)
       => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ),
    file('theBenchmark.p',fact_last_Osimps) ).

fof(fact_last__ConsR,axiom,
    ! [V_x,T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ),
    file('theBenchmark.p',fact_last__ConsR) ).

fof(fact_last__ConsL,axiom,
    ! [V_x,T_a,V_xs] :
      ( V_xs = c_List_Olist_ONil(T_a)
     => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ),
    file('theBenchmark.p',fact_last__ConsL) ).

fof(fact_last__append,axiom,
    ! [V_xs,T_a,V_ys] :
      ( ( V_ys != c_List_Olist_ONil(T_a)
       => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) )
      & ( V_ys = c_List_Olist_ONil(T_a)
       => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ),
    file('theBenchmark.p',fact_last__append) ).

fof(fact_last__appendR,axiom,
    ! [V_xs,T_a,V_ys] :
      ( V_ys != c_List_Olist_ONil(T_a)
     => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ),
    file('theBenchmark.p',fact_last__appendR) ).

fof(fact_last__appendL,axiom,
    ! [V_xs,T_a,V_ys] :
      ( V_ys = c_List_Olist_ONil(T_a)
     => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ),
    file('theBenchmark.p',fact_last__appendL) ).

fof(fact_last__map,axiom,
    ! [V_f_2,T_c,T_b,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_b)
     => c_List_Olast(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)) = hAPP(V_f_2,c_List_Olast(T_b,V_xs_2)) ),
    file('theBenchmark.p',fact_last__map) ).

fof(fact_last__in__set,axiom,
    ! [T_b,V_as_2] :
      ( V_as_2 != c_List_Olist_ONil(T_b)
     => hBOOL(hAPP(hAPP(c_member(T_b),c_List_Olast(T_b,V_as_2)),hAPP(c_List_Oset(T_b),V_as_2))) ),
    file('theBenchmark.p',fact_last__in__set) ).

fof(fact_last__snoc,axiom,
    ! [V_x,V_xs,T_a] : c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_x,
    file('theBenchmark.p',fact_last__snoc) ).

fof(fact_last__drop,axiom,
    ! [V_xs,T_a,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ),
    file('theBenchmark.p',fact_last__drop) ).

fof(fact_last__conv__nth,axiom,
    ! [T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => c_List_Olast(T_a,V_xs) = hAPP(hAPP(c_List_Onth(T_a),V_xs),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    file('theBenchmark.p',fact_last__conv__nth) ).

fof(fact_lexord__linear,axiom,
    ! [V_y_2,V_x_2,V_r_2,T_b] :
      ( ! [B_a,B_b] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_b),B_a)),V_r_2))
          | B_a = B_b
          | hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_a),B_b)),V_r_2)) )
     => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_x_2)),c_List_Olexord(T_b,V_r_2)))
        | V_x_2 = V_y_2
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_x_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ) ),
    file('theBenchmark.p',fact_lexord__linear) ).

fof(fact_lexord__irreflexive,axiom,
    ! [V_y_2,V_r_2,T_b] :
      ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_b),B_x),B_x)),V_r_2))
     => ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),V_y_2),V_y_2)),c_List_Olexord(T_b,V_r_2))) ),
    file('theBenchmark.p',fact_lexord__irreflexive) ).

fof(fact_lists_Osimps,axiom,
    ! [V_A_2,V_a_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_a_2),c_List_Olists(T_b,V_A_2)))
    <=> ( ? [B_a,B_l] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),B_l),c_List_Olists(T_b,V_A_2)))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_a),V_A_2))
            & V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_b),B_a),B_l) )
        | V_a_2 = c_List_Olist_ONil(T_b) ) ),
    file('theBenchmark.p',fact_lists_Osimps) ).

fof(fact_list__size__pointwise,axiom,
    ! [V_g_2,V_f_2,V_xs_2,T_b] :
      ( ! [B_x] :
          ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2)))
         => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) )
     => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(T_b,V_f_2,V_xs_2)),c_List_Olist_Olist__size(T_b,V_g_2,V_xs_2))) ),
    file('theBenchmark.p',fact_list__size__pointwise) ).

fof(fact_butlast__take,axiom,
    ! [V_xs,T_a,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs) ),
    file('theBenchmark.p',fact_butlast__take) ).

fof(fact_nth__take__lemma,axiom,
    ! [V_ys,V_xs,T_a,V_k] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)))
       => ( ! [B_i] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k))
             => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) )
         => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ),
    file('theBenchmark.p',fact_nth__take__lemma) ).

fof(fact_map__butlast,axiom,
    ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Obutlast(T_c,V_xs_2)) = c_List_Obutlast(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_map__butlast) ).

fof(fact_butlast__append,axiom,
    ! [V_xs,T_a,V_ys] :
      ( ( V_ys != c_List_Olist_ONil(T_a)
       => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Obutlast(T_a,V_ys)) )
      & ( V_ys = c_List_Olist_ONil(T_a)
       => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) ),
    file('theBenchmark.p',fact_butlast__append) ).

fof(fact_butlast_Osimps_I2_J,axiom,
    ! [V_x,T_a,V_xs] :
      ( ( V_xs != c_List_Olist_ONil(T_a)
       => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Obutlast(T_a,V_xs)) )
      & ( V_xs = c_List_Olist_ONil(T_a)
       => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) ),
    file('theBenchmark.p',fact_butlast_Osimps_I2_J) ).

fof(fact_in__set__butlastD,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2))))
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    file('theBenchmark.p',fact_in__set__butlastD) ).

fof(fact_distinct__butlast,axiom,
    ! [T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
       => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ),
    file('theBenchmark.p',fact_distinct__butlast) ).

fof(fact_butlast_Osimps_I1_J,axiom,
    ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_butlast_Osimps_I1_J) ).

fof(fact_butlast__drop,axiom,
    ! [V_xs,V_n,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)),
    file('theBenchmark.p',fact_butlast__drop) ).

fof(fact_drop__butlast,axiom,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = c_List_Obutlast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),
    file('theBenchmark.p',fact_drop__butlast) ).

fof(fact_in__set__butlast__appendI,axiom,
    ! [V_ys_2,V_xs_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_ys_2))))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,V_xs_2)))) )
     => hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_Obutlast(T_b,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2))))) ),
    file('theBenchmark.p',fact_in__set__butlast__appendI) ).

fof(fact_butlast__snoc,axiom,
    ! [V_x,V_xs,T_a] : c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a)))) = V_xs,
    file('theBenchmark.p',fact_butlast__snoc) ).

fof(fact_take__butlast,axiom,
    ! [V_xs,T_a,V_n] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
     => hAPP(hAPP(c_List_Otake(T_a),V_n),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) ),
    file('theBenchmark.p',fact_take__butlast) ).

fof(fact_length__butlast,axiom,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Obutlast(T_a,V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    file('theBenchmark.p',fact_length__butlast) ).

fof(fact_butlast__conv__take,axiom,
    ! [V_xs,T_a] : c_List_Obutlast(T_a,V_xs) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),V_xs),
    file('theBenchmark.p',fact_butlast__conv__take) ).

fof(fact_butlast__list__update,axiom,
    ! [V_x,V_xs,T_a,V_k] :
      ( ( V_k != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
       => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = hAPP(hAPP(c_List_Olist__update(T_a,c_List_Obutlast(T_a,V_xs)),V_k),V_x) )
      & ( V_k = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
       => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = c_List_Obutlast(T_a,V_xs) ) ),
    file('theBenchmark.p',fact_butlast__list__update) ).

fof(fact_append__butlast__last__id,axiom,
    ! [T_a,V_xs] :
      ( V_xs != c_List_Olist_ONil(T_a)
     => hAPP(hAPP(c_List_Oappend(T_a),c_List_Obutlast(T_a,V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),c_List_Olast(T_a,V_xs)),c_List_Olist_ONil(T_a))) = V_xs ),
    file('theBenchmark.p',fact_append__butlast__last__id) ).

fof(fact_snoc__eq__iff__butlast,axiom,
    ! [V_ys_2,V_x_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Olist_ONil(T_b))) = V_ys_2
    <=> ( c_List_Olast(T_b,V_ys_2) = V_x_2
        & c_List_Obutlast(T_b,V_ys_2) = V_xs_2
        & V_ys_2 != c_List_Olist_ONil(T_b) ) ),
    file('theBenchmark.p',fact_snoc__eq__iff__butlast) ).

fof(fact_transpose__aux__max,axiom,
    ! [V_xss_2,T_c,V_xs_2,T_b] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c))),V_xss_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)),c_List_Ofoldr(tc_List_Olist(T_c),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(T_c)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(T_c)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(T_c),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_c)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_c),tc_List_Olist(T_c),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_c)))),V_xss_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    file('theBenchmark.p',fact_transpose__aux__max) ).

fof(fact_partition__set,axiom,
    ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
      ( c_List_Opartition(T_b,V_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2,T_b] :
      ( hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2,B_x)) ) ),
    file('theBenchmark.p',fact_filter__empty__conv) ).

fof(fact_filter__id__conv,axiom,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_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_Pa_2,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
       => hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_xs_2) ) ),
    file('theBenchmark.p',fact_filter__insort__triv) ).

fof(fact_distinct__filter,axiom,
    ! [V_Pa_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_Pa_2),V_xs_2))) ),
    file('theBenchmark.p',fact_distinct__filter) ).

fof(fact_filter__remove1,axiom,
    ! [V_xs_2,V_x_2,V_Qa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Qa_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_Qa_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_Pa_2] :
      ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
     => c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) ),
    file('theBenchmark.p',fact_remove1__filter__not) ).

fof(fact_filter__filter,axiom,
    ! [V_xs_2,V_Qa_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Ofilter(T_b,V_Qa_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_Qa_2)),V_Pa_2)),V_xs_2),
    file('theBenchmark.p',fact_filter__filter) ).

fof(fact_partition__filter1,axiom,
    ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2),
    file('theBenchmark.p',fact_partition__filter1) ).

fof(fact_sum__length__filter__compl,axiom,
    ! [V_xs_2,V_Pa_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_Pa_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_Pa_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_Pa_2] :
      ( ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
       => hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) )
      & ( hBOOL(hAPP(V_Pa_2,V_x_2))
       => hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_xs_2)) ) ),
    file('theBenchmark.p',fact_filter_Osimps_I2_J) ).

fof(fact_filter__append,axiom,
    ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2)),
    file('theBenchmark.p',fact_filter__append) ).

fof(fact_partition__filter__conv,axiom,
    ! [V_xs_2,V_f_2,T_b] : c_List_Opartition(T_b,V_f_2,V_xs_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_b),tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_f_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,T_b,c_fNot),V_f_2)),V_xs_2)),
    file('theBenchmark.p',fact_partition__filter__conv) ).

fof(fact_filter__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_f_2)),V_xs_2)),
    file('theBenchmark.p',fact_filter__map) ).

fof(fact_partition__filter2,axiom,
    ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_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_Pa_2)),V_xs_2),
    file('theBenchmark.p',fact_partition__filter2) ).

fof(fact_set__filter,axiom,
    ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2)),
    file('theBenchmark.p',fact_set__filter) ).

fof(fact_length__filter__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_f_2)),V_xs_2)),
    file('theBenchmark.p',fact_length__filter__map) ).

fof(fact_length__filter__less,axiom,
    ! [V_Pa_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_Pa_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_Pa_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_Pa_2,T_b] :
      ( c_List_Opartition(T_b,V_Pa_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_Pa_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_Pa_2,B_x)) ) ) ),
    file('theBenchmark.p',fact_partition__P) ).

fof(fact_partition_Osimps_I1_J,axiom,
    ! [V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_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_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_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_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_sublist__shift__lemma__Suc,axiom,
    ! [V_is_2,V_xs_2,V_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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__filter,axiom,
    ! [V_Pa_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_Pa_2),V_xs_2))) ) ),
    file('theBenchmark.p',fact_sorted__filter) ).

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_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_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__Suc,axiom,
    ! [V_j,V_i] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
       => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
       => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ) ),
    file('theBenchmark.p',fact_upt__Suc) ).

fof(fact_upt__Suc__append,axiom,
    ! [V_j,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
     => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(V_i,V_j)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_j),c_List_Olist_ONil(tc_Nat_Onat))) ),
    file('theBenchmark.p',fact_upt__Suc__append) ).

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

fof(fact_sorted__many__eq,axiom,
    ! [V_zs_2,V_y_2,V_x_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2)))
      <=> ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_zs_2))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_x_2),V_y_2)) ) ) ),
    file('theBenchmark.p',fact_sorted__many__eq) ).

fof(fact_sorted__many,axiom,
    ! [V_zs,V_y,V_x,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y))
       => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))
         => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs))) ) ) ),
    file('theBenchmark.p',fact_sorted__many) ).

fof(fact_take__upt,axiom,
    ! [V_n,V_m,V_i] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)),V_n))
     => hAPP(hAPP(c_List_Otake(tc_Nat_Onat),V_m),c_List_Oupt(V_i,V_n)) = c_List_Oupt(V_i,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)) ),
    file('theBenchmark.p',fact_take__upt) ).

fof(fact_upt__eq__Nil__conv,axiom,
    ! [V_j_2,V_i_2] :
      ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat)
    <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2))
        | V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    file('theBenchmark.p',fact_upt__eq__Nil__conv) ).

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

fof(fact_sorted__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_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,hAPP(c_List_Otl(T_a),V_xs)) ) ),
    file('theBenchmark.p',fact_sorted__tl) ).

fof(fact_sorted__insort__key,axiom,
    ! [V_xs_2,V_x_2,V_f_2,T_c,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_c,T_b,V_f_2),V_x_2),V_xs_2)))
      <=> c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) ) ),
    file('theBenchmark.p',fact_sorted__insort__key) ).

fof(fact_sorted__map__remove1,axiom,
    ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
       => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremove1(T_c,V_x_2,V_xs_2))) ) ),
    file('theBenchmark.p',fact_sorted__map__remove1) ).

fof(fact_map__Suc__upt,axiom,
    ! [V_n_2,V_m_2] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(V_m_2,V_n_2)) = c_List_Oupt(hAPP(c_Nat_OSuc,V_m_2),hAPP(c_Nat_OSuc,V_n_2)),
    file('theBenchmark.p',fact_map__Suc__upt) ).

fof(fact_sorted__insort__insert__key,axiom,
    ! [V_x_2,V_xs_2,V_f_2,T_c,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2))
       => c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Olinorder__class_Oinsort__insert__key(T_c,T_b,V_f_2,V_x_2,V_xs_2))) ) ),
    file('theBenchmark.p',fact_sorted__insort__insert__key) ).

fof(fact_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_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_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_Pa_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_Pa_2,V_x_2))
         => hAPP(c_List_Ofilter(T_c,V_Pa_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_Pa_2),V_xs_2)) ) ) ),
    file('theBenchmark.p',fact_filter__insort) ).

fof(fact_map__nth,axiom,
    ! [V_xs_2,T_b] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),hAPP(c_List_Onth(T_b),V_xs_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) = V_xs_2,
    file('theBenchmark.p',fact_map__nth) ).

fof(fact_atLeastAtMost__upt,axiom,
    ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_n_2,hAPP(c_Nat_OSuc,V_m_2))),
    file('theBenchmark.p',fact_atLeastAtMost__upt) ).

fof(fact_atLeast__upt,axiom,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)),
    file('theBenchmark.p',fact_atLeast__upt) ).

fof(fact_setsum__set__upt__conv__listsum__nat,axiom,
    ! [V_n_2,V_m_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) = hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) ),
    file('theBenchmark.p',fact_setsum__set__upt__conv__listsum__nat) ).

fof(fact_interv__listsum__conv__setsum__set__nat,axiom,
    ! [V_n_2,V_m_2,V_f_2,T_b] :
      ( class_Groups_Ocomm__monoid__add(T_b)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_f_2),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(V_m_2,V_n_2))) ),
    file('theBenchmark.p',fact_interv__listsum__conv__setsum__set__nat) ).

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

fof(fact_greaterThanAtMost__upt,axiom,
    ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),hAPP(c_Nat_OSuc,V_m_2))),
    file('theBenchmark.p',fact_greaterThanAtMost__upt) ).

fof(fact_sorted_Oequations_I2_J,axiom,
    ! [V_a1_2,V_a2_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_a2_2),V_a1_2))
      <=> ( c_List_Olinorder__class_Osorted(T_b,V_a1_2)
          & ! [B_x] :
              ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_a1_2)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),V_a2_2),B_x)) ) ) ) ),
    file('theBenchmark.p',fact_sorted_Oequations_I2_J) ).

fof(fact_greaterThanLessThan__upt,axiom,
    ! [V_m_2,V_n_2] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,V_n_2,V_m_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,V_n_2),V_m_2)),
    file('theBenchmark.p',fact_greaterThanLessThan__upt) ).

fof(fact_nth__map__upt,axiom,
    ! [V_f_2,T_b,V_m_2,V_n_2,V_i_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n_2),V_m_2)))
     => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_b),V_f_2),c_List_Oupt(V_m_2,V_n_2))),V_i_2) = hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_i_2)) ),
    file('theBenchmark.p',fact_nth__map__upt) ).

fof(fact_sorted__list__of__set,axiom,
    ! [V_A_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2))
       => ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)))
          & c_List_Olinorder__class_Osorted(T_b,c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2))
          & hAPP(c_List_Oset(T_b),c_List_Olinorder__class_Osorted__list__of__set(T_b,V_A_2)) = V_A_2 ) ) ),
    file('theBenchmark.p',fact_sorted__list__of__set) ).

fof(fact_atMost__upto,axiom,
    ! [V_n_2] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_n_2) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2))),
    file('theBenchmark.p',fact_atMost__upto) ).

fof(fact_insort__remove1,axiom,
    ! [V_xs_2,V_a_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
         => hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(T_b,T_b,c_COMBI(T_b)),V_a_2),c_List_Oremove1(T_b,V_a_2,V_xs_2)) = V_xs_2 ) ) ),
    file('theBenchmark.p',fact_insort__remove1) ).

fof(fact_sorted__nth__mono,axiom,
    ! [V_j,V_i,V_xs,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,V_xs)
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j))
         => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)))
           => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),V_j))) ) ) ) ),
    file('theBenchmark.p',fact_sorted__nth__mono) ).

fof(fact_sorted__equals__nth__mono,axiom,
    ! [V_xs_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
      <=> ! [B_j] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
           => ! [B_i] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j))
               => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_i)),hAPP(hAPP(c_List_Onth(T_b),V_xs_2),B_j))) ) ) ) ),
    file('theBenchmark.p',fact_sorted__equals__nth__mono) ).

fof(fact_map__sorted__distinct__set__unique,axiom,
    ! [V_ys_2,V_xs_2,V_f_2,T_b,T_c] :
      ( class_Orderings_Olinorder(T_c)
     => ( c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(T_b),V_xs_2)),hAPP(c_List_Oset(T_b),V_ys_2)))
       => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2))
         => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_xs_2)))
           => ( c_List_Olinorder__class_Osorted(T_c,hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2))
             => ( hBOOL(hAPP(c_List_Odistinct(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),V_ys_2)))
               => ( hAPP(c_List_Oset(T_b),V_xs_2) = hAPP(c_List_Oset(T_b),V_ys_2)
                 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ),
    file('theBenchmark.p',fact_map__sorted__distinct__set__unique) ).

fof(fact_sublist__shift__lemma,axiom,
    ! [V_i_2,V_xs_2,V_A_2,T_b] : hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(V_i_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))))) = hAPP(hAPP(c_List_Omap(tc_prod(T_b,tc_Nat_Onat),T_b),c_Product__Type_Ofst(T_b,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(T_b,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),tc_prod(T_b,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(T_b,tc_Nat_Onat),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_prod(T_b,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(T_b,tc_Nat_Onat))),V_i_2))),V_A_2)),hAPP(hAPP(c_List_Ozip(T_b,tc_Nat_Onat),V_xs_2),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))))),
    file('theBenchmark.p',fact_sublist__shift__lemma) ).

fof(fact_transpose__rectangle,axiom,
    ! [V_n_2,T_b,V_xs_2] :
      ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_b))
       => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
     => ( ! [B_i] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
           => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),B_i)) = V_n_2 )
       => c_List_Otranspose(T_b,V_xs_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(T_b)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,T_b),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(T_b)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,T_b)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_Nat_Onat,T_b),tc_Nat_Onat),c_List_Onth(T_b)),hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_n_2)) ) ),
    file('theBenchmark.p',fact_transpose__rectangle) ).

fof(fact_transpose_Opsimps_I2_J,axiom,
    ! [V_xss_2,T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)))
     => c_List_Otranspose(T_b,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_b)),c_List_Olist_ONil(T_b)),V_xss_2)) = c_List_Otranspose(T_b,V_xss_2) ),
    file('theBenchmark.p',fact_transpose_Opsimps_I2_J) ).

fof(fact_transpose_Opsimps_I1_J,axiom,
    ! [T_b] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(T_b)),c_List_Otranspose__rel(T_b)),c_List_Olist_ONil(tc_List_Olist(T_b))))
     => c_List_Otranspose(T_b,c_List_Olist_ONil(tc_List_Olist(T_b))) = c_List_Olist_ONil(tc_List_Olist(T_b)) ),
    file('theBenchmark.p',fact_transpose_Opsimps_I1_J) ).

fof(fact_transpose__column,axiom,
    ! [V_i_2,V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
       => hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_Nat_Onat,T_b),c_List_Onth(T_b)),V_i_2)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2) ) ),
    file('theBenchmark.p',fact_transpose__column) ).

fof(fact_transpose__aux__filter__head,axiom,
    ! [V_xss_2,T_b] : c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,c_List_Olist_ONil(T_b),hAPP(hAPP(c_COMBB(tc_List_Olist(T_b),tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),c_COMBK(tc_List_Olist(T_b),tc_List_Olist(T_b))),hAPP(hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),T_b),c_List_Ohd(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)),
    file('theBenchmark.p',fact_transpose__aux__filter__head) ).

fof(fact_inj__on__rev,axiom,
    ! [V_A_2,T_b] : c_Fun_Oinj__on(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Orev(T_b),V_A_2),
    file('theBenchmark.p',fact_inj__on__rev) ).

fof(fact_filter__concat,axiom,
    ! [V_xs_2,V_p_2,T_b] : hAPP(c_List_Ofilter(T_b,V_p_2),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Ofilter(T_b,V_p_2)),V_xs_2)),
    file('theBenchmark.p',fact_filter__concat) ).

fof(fact_length__concat,axiom,
    ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oconcat(T_b,V_xss_2)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xss_2)),
    file('theBenchmark.p',fact_length__concat) ).

fof(fact_rev_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__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__concat,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),c_List_Oconcat(T_b,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Orev(T_b)),hAPP(c_List_Orev(tc_List_Olist(T_b)),V_xs_2))),
    file('theBenchmark.p',fact_rev__concat) ).

fof(fact_rev__map,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] : hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2)),
    file('theBenchmark.p',fact_rev__map) ).

fof(fact_map__concat,axiom,
    ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oconcat(T_c,V_xs_2)) = c_List_Oconcat(T_b,hAPP(hAPP(c_List_Omap(tc_List_Olist(T_c),tc_List_Olist(T_b)),hAPP(c_List_Omap(T_c,T_b),V_f_2)),V_xs_2)),
    file('theBenchmark.p',fact_map__concat) ).

fof(fact_rev__foldl__cons,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),T_b,hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)),c_List_Olist_ONil(T_b)),V_xs_2),
    file('theBenchmark.p',fact_rev__foldl__cons) ).

fof(fact_concat__conv__foldl,axiom,
    ! [V_xss_2,T_b] : c_List_Oconcat(T_b,V_xss_2) = hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),c_List_Olist_ONil(T_b)),V_xss_2),
    file('theBenchmark.p',fact_concat__conv__foldl) ).

fof(fact_foldl__conv__concat,axiom,
    ! [V_xss_2,V_xs_2,T_b] : hAPP(c_List_Ofoldl(tc_List_Olist(T_b),tc_List_Olist(T_b),c_List_Oappend(T_b),V_xs_2),V_xss_2) = hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),c_List_Oconcat(T_b,V_xss_2)),
    file('theBenchmark.p',fact_foldl__conv__concat) ).

fof(fact_rev__append,axiom,
    ! [V_ys,V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Orev(T_a),V_ys)),hAPP(c_List_Orev(T_a),V_xs)),
    file('theBenchmark.p',fact_rev__append) ).

fof(fact_concat__append,axiom,
    ! [V_ys,V_xs,T_a] : c_List_Oconcat(T_a,hAPP(hAPP(c_List_Oappend(tc_List_Olist(T_a)),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oconcat(T_a,V_xs)),c_List_Oconcat(T_a,V_ys)),
    file('theBenchmark.p',fact_concat__append) ).

fof(fact_distinct__rev,axiom,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Orev(T_b),V_xs_2)))
    <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_distinct__rev) ).

fof(fact_set__concat,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oconcat(T_b,V_xs_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xs_2)),c_List_Oset(T_b)),
    file('theBenchmark.p',fact_set__concat) ).

fof(fact_length__rev,axiom,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs),
    file('theBenchmark.p',fact_length__rev) ).

fof(fact_listsum__rev,axiom,
    ! [V_xs,T_a] :
      ( class_Groups_Ocomm__monoid__add(T_a)
     => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Omonoid__add__class_Olistsum(T_a),V_xs) ),
    file('theBenchmark.p',fact_listsum__rev) ).

fof(fact_rev__is__rev__conv,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( hAPP(c_List_Orev(T_b),V_xs_2) = hAPP(c_List_Orev(T_b),V_ys_2)
    <=> V_xs_2 = V_ys_2 ),
    file('theBenchmark.p',fact_rev__is__rev__conv) ).

fof(fact_rev__swap,axiom,
    ! [V_ys_2,V_xs_2,T_b] :
      ( hAPP(c_List_Orev(T_b),V_xs_2) = V_ys_2
    <=> V_xs_2 = hAPP(c_List_Orev(T_b),V_ys_2) ),
    file('theBenchmark.p',fact_rev__swap) ).

fof(fact_rev__rev__ident,axiom,
    ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs,
    file('theBenchmark.p',fact_rev__rev__ident) ).

fof(fact_foldr__foldl,axiom,
    ! [V_a_2,V_xs_2,V_f_2,T_b,T_c] : c_List_Ofoldr(T_c,T_b,V_f_2,V_xs_2,V_a_2) = hAPP(c_List_Ofoldl(T_b,T_c,hAPP(c_COMBC(T_c,T_b,T_b),V_f_2),V_a_2),hAPP(c_List_Orev(T_c),V_xs_2)),
    file('theBenchmark.p',fact_foldr__foldl) ).

fof(fact_foldl__foldr,axiom,
    ! [V_xs_2,V_a_2,V_f_2,T_c,T_b] : hAPP(c_List_Ofoldl(T_b,T_c,V_f_2,V_a_2),V_xs_2) = c_List_Ofoldr(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_b),V_f_2),hAPP(c_List_Orev(T_c),V_xs_2),V_a_2),
    file('theBenchmark.p',fact_foldl__foldr) ).

fof(fact_set__rev,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
    file('theBenchmark.p',fact_set__rev) ).

fof(fact_zip__rev,axiom,
    ! [V_ys,T_b,V_xs,T_a] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys)
     => hAPP(hAPP(c_List_Ozip(T_a,T_b),hAPP(c_List_Orev(T_a),V_xs)),hAPP(c_List_Orev(T_b),V_ys)) = hAPP(c_List_Orev(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys)) ),
    file('theBenchmark.p',fact_zip__rev) ).

fof(fact_rev__filter,axiom,
    ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_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(fact_transpose__column__length,axiom,
    ! [V_i_2,V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
       => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2)) ) ),
    file('theBenchmark.p',fact_transpose__column__length) ).

fof(fact_transpose__aux__filter__tail,axiom,
    ! [V_xss_2,T_b] : c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otl(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)),
    file('theBenchmark.p',fact_transpose__aux__filter__tail) ).

fof(fact_nth__nth__transpose__sorted,axiom,
    ! [V_j_2,V_i_2,V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
     => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
       => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2))))
         => hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_j_2)),V_i_2) ) ) ),
    file('theBenchmark.p',fact_nth__nth__transpose__sorted) ).

fof(fact_transpose__transpose,axiom,
    ! [V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2)))
     => c_List_Otranspose(T_b,c_List_Otranspose(T_b,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b))),V_xs_2) ),
    file('theBenchmark.p',fact_transpose__transpose) ).

fof(fact_transfer__nat__int__list__functions_I2_J,axiom,
    c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
    file('theBenchmark.p',fact_transfer__nat__int__list__functions_I2_J) ).

fof(fact_takeWhile__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_takeWhile__map) ).

fof(fact_return__list__def,axiom,
    ! [V_l_2] : c_List_Oreturn__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),V_l_2),
    file('theBenchmark.p',fact_return__list__def) ).

fof(fact_zip__takeWhile__snd,axiom,
    ! [V_ys_2,V_Pa_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_Pa_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),
    file('theBenchmark.p',fact_zip__takeWhile__snd) ).

fof(fact_zip__takeWhile__fst,axiom,
    ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),
    file('theBenchmark.p',fact_zip__takeWhile__fst) ).

fof(fact_set__takeWhileD,axiom,
    ! [V_xs_2,V_Pa_2,V_x_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))
     => ( hBOOL(hAPP(V_Pa_2,V_x_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    file('theBenchmark.p',fact_set__takeWhileD) ).

fof(fact_takeWhile__eq__all__conv,axiom,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( c_List_OtakeWhile(T_b,V_Pa_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_Pa_2,B_x)) ) ),
    file('theBenchmark.p',fact_takeWhile__eq__all__conv) ).

fof(fact_length__takeWhile__le,axiom,
    ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
    file('theBenchmark.p',fact_length__takeWhile__le) ).

fof(fact_takeWhile__eq__take,axiom,
    ! [V_xs_2,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2),
    file('theBenchmark.p',fact_takeWhile__eq__take) ).

fof(fact_distinct__takeWhile,axiom,
    ! [V_Pa_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))) ),
    file('theBenchmark.p',fact_distinct__takeWhile) ).

fof(fact_takeWhile__tail,axiom,
    ! [V_l_2,V_xs_2,T_b,V_x_2,V_Pa_2] :
      ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
     => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ),
    file('theBenchmark.p',fact_takeWhile__tail) ).

fof(fact_takeWhile_Osimps_I2_J,axiom,
    ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
      ( ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
       => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b) )
      & ( hBOOL(hAPP(V_Pa_2,V_x_2))
       => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) ),
    file('theBenchmark.p',fact_takeWhile_Osimps_I2_J) ).

fof(fact_sorted__takeWhile,axiom,
    ! [V_Pa_2,V_xs_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
       => c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)) ) ),
    file('theBenchmark.p',fact_sorted__takeWhile) ).

fof(fact_takeWhile_Osimps_I1_J,axiom,
    ! [V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_takeWhile_Osimps_I1_J) ).

fof(fact_takeWhile__append1,axiom,
    ! [V_ys_2,V_Pa_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_Pa_2,V_x_2))
       => c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) ) ),
    file('theBenchmark.p',fact_takeWhile__append1) ).

fof(fact_nth__length__takeWhile,axiom,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
     => ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))) ),
    file('theBenchmark.p',fact_nth__length__takeWhile) ).

fof(fact_takeWhile__nth,axiom,
    ! [V_xs_2,V_Pa_2,T_b,V_j_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))))
     => hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2) ),
    file('theBenchmark.p',fact_takeWhile__nth) ).

fof(fact_map__upds__def,axiom,
    ! [V_ys_2,V_xs_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) = c_Map_Omap__add(T_b,T_c,V_m_2,c_Map_Omap__of(T_b,T_c,hAPP(c_List_Orev(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))),
    file('theBenchmark.p',fact_map__upds__def) ).

fof(fact_takeWhile__not__last,axiom,
    ! [T_b,V_xs_2] :
      ( V_xs_2 != c_List_Olist_ONil(T_b)
     => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
       => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),c_List_Olast(T_b,V_xs_2))),V_xs_2) = c_List_Obutlast(T_b,V_xs_2) ) ),
    file('theBenchmark.p',fact_takeWhile__not__last) ).

fof(fact_filter__equals__takeWhile__sorted__rev,axiom,
    ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
       => hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2),V_xs_2) ) ),
    file('theBenchmark.p',fact_filter__equals__takeWhile__sorted__rev) ).

fof(fact_transfer__nat__int__list__return__embed,axiom,
    ! [V_l] :
      ( c_List_Onat__list(V_l)
     => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ),
    file('theBenchmark.p',fact_transfer__nat__int__list__return__embed) ).

fof(fact_length__remdups__concat,axiom,
    ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,c_List_Oconcat(T_b,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)),c_List_Oset(T_b))),
    file('theBenchmark.p',fact_length__remdups__concat) ).

fof(fact_distinct__remdups,axiom,
    ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))),
    file('theBenchmark.p',fact_distinct__remdups) ).

fof(fact_length__remdups__leq,axiom,
    ! [V_xs,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),
    file('theBenchmark.p',fact_length__remdups__leq) ).

fof(fact_remdups__map__remdups,axiom,
    ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremdups(T_c,V_xs_2))) = c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_remdups__map__remdups) ).

fof(fact_embed__list__def,axiom,
    ! [V_l_2] : c_List_Oembed__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_l_2),
    file('theBenchmark.p',fact_embed__list__def) ).

fof(fact_set__remdups,axiom,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
    file('theBenchmark.p',fact_set__remdups) ).

fof(fact_remdups_Osimps_I1_J,axiom,
    ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    file('theBenchmark.p',fact_remdups_Osimps_I1_J) ).

fof(fact_remdups__eq__nil__right__iff,axiom,
    ! [V_x_2,T_b] :
      ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
    <=> V_x_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_remdups__eq__nil__right__iff) ).

fof(fact_remdups__eq__nil__iff,axiom,
    ! [V_x_2,T_b] :
      ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
    <=> V_x_2 = c_List_Olist_ONil(T_b) ),
    file('theBenchmark.p',fact_remdups__eq__nil__iff) ).

fof(fact_sorted__remdups,axiom,
    ! [V_l,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( c_List_Olinorder__class_Osorted(T_a,V_l)
       => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ),
    file('theBenchmark.p',fact_sorted__remdups) ).

fof(fact_remove1__remdups,axiom,
    ! [V_x,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => c_List_Oremove1(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oremove1(T_a,V_x,V_xs)) ),
    file('theBenchmark.p',fact_remove1__remdups) ).

fof(fact_distinct__remdups__id,axiom,
    ! [V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => c_List_Oremdups(T_a,V_xs) = V_xs ),
    file('theBenchmark.p',fact_distinct__remdups__id) ).

fof(fact_remdups__id__iff__distinct,axiom,
    ! [V_xs_2,T_b] :
      ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
    <=> hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    file('theBenchmark.p',fact_remdups__id__iff__distinct) ).

fof(fact_length__remdups__eq,axiom,
    ! [V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
    <=> c_List_Oremdups(T_b,V_xs_2) = V_xs_2 ),
    file('theBenchmark.p',fact_length__remdups__eq) ).

fof(fact_remdups__remdups,axiom,
    ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs),
    file('theBenchmark.p',fact_remdups__remdups) ).

fof(fact_remdups__filter,axiom,
    ! [V_xs_2,V_Pa_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oremdups(T_b,V_xs_2)),
    file('theBenchmark.p',fact_remdups__filter) ).

fof(fact_remdups_Osimps_I2_J,axiom,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oremdups(T_b,V_xs_2)) )
      & ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Oremdups(T_b,V_xs_2) ) ),
    file('theBenchmark.p',fact_remdups_Osimps_I2_J) ).

fof(fact_length__remdups__card__conv,axiom,
    ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)),
    file('theBenchmark.p',fact_length__remdups__card__conv) ).

fof(fact_fun__left__comm_Ofold__set__remdups,axiom,
    ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
      ( c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2)
     => hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),c_List_Oremdups(T_b,V_xs_2)) ),
    file('theBenchmark.p',fact_fun__left__comm_Ofold__set__remdups) ).

fof(fact_transfer__nat__int__list__functions_I1_J,axiom,
    ! [V_m,V_l] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),V_l),V_m) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(V_l)),c_List_Oembed__list(V_m))),
    file('theBenchmark.p',fact_transfer__nat__int__list__functions_I1_J) ).

fof(fact_takeWhile__neq__rev,axiom,
    ! [V_x_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Orev(T_b),hAPP(c_List_Otl(T_b),c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ),
    file('theBenchmark.p',fact_takeWhile__neq__rev) ).

fof(fact_dropWhile__neq__rev,axiom,
    ! [V_x_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
       => c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Orev(T_b),c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2))) ) ),
    file('theBenchmark.p',fact_dropWhile__neq__rev) ).

fof(fact_dropWhile__map,axiom,
    ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OdropWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)),
    file('theBenchmark.p',fact_dropWhile__map) ).

fof(fact_takeWhile__dropWhile__id,axiom,
    ! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) = V_xs_2,
    file('theBenchmark.p',fact_takeWhile__dropWhile__id) ).

fof(fact_length__dropWhile__le,axiom,
    ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
    file('theBenchmark.p',fact_length__dropWhile__le) ).

fof(fact_distinct__dropWhile,axiom,
    ! [V_Pa_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))) ),
    file('theBenchmark.p',fact_distinct__dropWhile) ).

fof(fact_dropWhile_Osimps_I2_J,axiom,
    ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
      ( ( ~ hBOOL(hAPP(V_Pa_2,V_x_2))
       => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2) )
      & ( hBOOL(hAPP(V_Pa_2,V_x_2))
       => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) ) ),
    file('theBenchmark.p',fact_dropWhile_Osimps_I2_J) ).

fof(fact_sorted__dropWhile,axiom,
    ! [V_Pa_2,V_xs_2,T_b] :
      ( class_Orderings_Olinorder(T_b)
     => ( c_List_Olinorder__class_Osorted(T_b,V_xs_2)
       => c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) ) ),
    file('theBenchmark.p',fact_sorted__dropWhile) ).

fof(fact_dropWhile_Osimps_I1_J,axiom,
    ! [V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
    file('theBenchmark.p',fact_dropWhile_Osimps_I1_J) ).

fof(fact_hd__dropWhile,axiom,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) != c_List_Olist_ONil(T_b)
     => ~ hBOOL(hAPP(V_Pa_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) ),
    file('theBenchmark.p',fact_hd__dropWhile) ).

fof(fact_dropWhile__eq__Nil__conv,axiom,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( c_List_OdropWhile(T_b,V_Pa_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_Pa_2,B_x)) ) ),
    file('theBenchmark.p',fact_dropWhile__eq__Nil__conv) ).

fof(fact_dropWhile__append1,axiom,
    ! [V_ys_2,V_Pa_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_Pa_2,V_x_2))
       => c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) ) ),
    file('theBenchmark.p',fact_dropWhile__append1) ).

fof(fact_dropWhile__eq__Cons__conv,axiom,
    ! [V_ys_2,V_y_2,V_xs_2,V_Pa_2,T_b] :
      ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
    <=> ( ~ hBOOL(hAPP(V_Pa_2,V_y_2))
        & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) ) ),
    file('theBenchmark.p',fact_dropWhile__eq__Cons__conv) ).

fof(fact_dropWhile__eq__drop,axiom,
    ! [V_xs_2,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2),
    file('theBenchmark.p',fact_dropWhile__eq__drop) ).

fof(fact_dropWhile__nth,axiom,
    ! [V_xs_2,V_Pa_2,T_b,V_j_2] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))))
     => hAPP(hAPP(c_List_Onth(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) ),
    file('theBenchmark.p',fact_dropWhile__nth) ).

fof(fact_listsum__map__filter,axiom,
    ! [V_f_2,V_Pa_2,V_xs_2,T_b,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(V_Pa_2,B_x))
             => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_c) ) )
       => hAPP(c_List_Omonoid__add__class_Olistsum(T_c),hAPP(hAPP(c_List_Omap(T_b,T_c),V_f_2),hAPP(c_List_Ofilter(T_b,V_Pa_2),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)) ) ),
    file('theBenchmark.p',fact_listsum__map__filter) ).

fof(fact_sorted__nth__monoI,axiom,
    ! [V_xs,T_a] :
      ( class_Orderings_Olinorder(T_a)
     => ( ! [B_i,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_a)),V_xs)))
             => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_j))) ) )
       => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ),
    file('theBenchmark.p',fact_sorted__nth__monoI) ).

fof(fact_n__lists_Osimps_I2_J,axiom,
    ! [V_xs_2,V_n_2,T_b] : c_Enum_On__lists(T_b,hAPP(c_Nat_OSuc,V_n_2),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))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_List_Omap(T_b,tc_List_Olist(T_b))),hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),V_xs_2)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))),
    file('theBenchmark.p',fact_n__lists_Osimps_I2_J) ).

fof(fact_sublists__powset,axiom,
    ! [V_xs_2,T_b] : hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_Osublists(T_b,V_xs_2))) = hAPP(c_Set_OPow(T_b),hAPP(c_List_Oset(T_b),V_xs_2)),
    file('theBenchmark.p',fact_sublists__powset) ).

fof(fact_distinct__n__lists,axiom,
    ! [V_n,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs))
     => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ),
    file('theBenchmark.p',fact_distinct__n__lists) ).

fof(fact_distinct__set__sublists,axiom,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
     => hBOOL(hAPP(c_List_Odistinct(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),c_List_Oset(T_b)),c_Enum_Osublists(T_b,V_xs_2)))) ),
    file('theBenchmark.p',fact_distinct__set__sublists) ).

fof(fact_length__n__lists,axiom,
    ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_On__lists(T_a,V_n,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),V_n),
    file('theBenchmark.p',fact_length__n__lists) ).

fof(fact_length__n__lists__elem,axiom,
    ! [V_xs_2,V_n_2,V_ys_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))))
     => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2 ),
    file('theBenchmark.p',fact_length__n__lists__elem) ).

fof(fact_sublists_Osimps_I1_J,axiom,
    ! [T_a] : c_Enum_Osublists(T_a,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))),
    file('theBenchmark.p',fact_sublists_Osimps_I1_J) ).

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_Qa_2,V_Pa_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_Pa_2),V_Qa_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Qa_2,V_R_2)),
    file('theBenchmark.p',help_c__COMBB__1) ).

fof(help_c__COMBC__1,axiom,
    ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Qa_2),
    file('theBenchmark.p',help_c__COMBC__1) ).

fof(help_c__COMBS__1,axiom,
    ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Qa_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_Pa_2] :
      ( ~ hBOOL(V_Pa_2)
      | ~ hBOOL(hAPP(c_fNot,V_Pa_2)) ),
    file('theBenchmark.p',help_c__fNot__1) ).

fof(help_c__fNot__2,axiom,
    ! [V_Pa_2] :
      ( hBOOL(hAPP(c_fNot,V_Pa_2))
      | ~ ~ hBOOL(V_Pa_2) ),
    file('theBenchmark.p',help_c__fNot__2) ).

fof(help_c__fconj__1,axiom,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2))
      | ~ hBOOL(V_Qa_2)
      | ~ hBOOL(V_Pa_2) ),
    file('theBenchmark.p',help_c__fconj__1) ).

fof(help_c__fconj__2,axiom,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(V_Pa_2)
      | ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) ),
    file('theBenchmark.p',help_c__fconj__2) ).

fof(help_c__fconj__3,axiom,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(V_Qa_2)
      | ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) ),
    file('theBenchmark.p',help_c__fconj__3) ).

fof(help_c__fdisj__1,axiom,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2))
      | ~ hBOOL(V_Pa_2) ),
    file('theBenchmark.p',help_c__fdisj__1) ).

fof(help_c__fdisj__2,axiom,
    ! [V_Pa_2,V_Qa_2] :
      ( hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2))
      | ~ hBOOL(V_Qa_2) ),
    file('theBenchmark.p',help_c__fdisj__2) ).

fof(help_c__fdisj__3,axiom,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(V_Qa_2)
      | hBOOL(V_Pa_2)
      | ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ),
    file('theBenchmark.p',help_c__fdisj__3) ).

fof(help_c__fimplies__1,axiom,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2))
      | hBOOL(V_Pa_2) ),
    file('theBenchmark.p',help_c__fimplies__1) ).

fof(help_c__fimplies__2,axiom,
    ! [V_Pa_2,V_Qa_2] :
      ( hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2))
      | ~ hBOOL(V_Qa_2) ),
    file('theBenchmark.p',help_c__fimplies__2) ).

fof(help_c__fimplies__3,axiom,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(V_Qa_2)
      | ~ hBOOL(V_Pa_2)
      | ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ),
    file('theBenchmark.p',help_c__fimplies__3) ).

fof(conj_0,hypothesis,
    hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs)),
    file('theBenchmark.p',conj_0) ).

fof(conj_1,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_na,B_x) ),
    file('theBenchmark.p',conj_1) ).

fof(conj_2,hypothesis,
    ! [B_x] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
     => c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Com_Ocom_OBODY,B_x)),v_Q(B_x))) ),
    file('theBenchmark.p',conj_2) ).

fof(conj_3,hypothesis,
    ! [B_x] :
      ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs))
     => c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x))) ),
    file('theBenchmark.p',conj_3) ).

fof(conj_4,conjecture,
    c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))),
    file('theBenchmark.p',conj_4) ).

fof(f_1_1,plain,
    ! [V_g_2,V_f_2] :
      ( V_f_2 = V_g_2
      | ? [B_x] : hAPP(V_f_2,B_x) != hAPP(V_g_2,B_x) ),
    inference(fof_nnf,[status(thm)],[fact_ext]) ).

fof(f_1_2,plain,
    ! [U_2,U_1] :
      ( U_1 = U_2
      | ? [U_0] : hAPP(U_1,U_0) != hAPP(U_2,U_0) ),
    inference(variable_rename,[status(thm)],[f_1_1]) ).

fof(f_1_3,plain,
    ! [U_2,U_1] :
      ( U_1 = U_2
      | hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_2,U_1))],[f_1_2]) ).

fof(f_1_4,plain,
    ! [U_1,U_2] :
      ( U_1 = U_2
      | hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
    inference(definitional_conversion,[status(esa)],[f_1_3]) ).

cnf(f_1_5,plain,
    ( U_1 = U_2
    | hAPP(U_1,sK1(U_2,U_1)) != hAPP(U_2,sK1(U_2,U_1)) ),
    inference(clausify,[status(thm)],[f_1_4]) ).

fof(f_2_1,plain,
    ! [V_Qa_2,V_pn_2,V_Pa_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_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_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_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_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_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2))
        | ~ c_Hoare__Mirabelle_Otriple__valid(T_b,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_b),V_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Body__triple__valid__Suc]) ).

fof(f_2_2,plain,
    ! [U_7,U_6,U_5,U_4,U_3] :
      ( ( c_Hoare__Mirabelle_Otriple__valid(U_3,U_4,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_3),U_5),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_6))),U_7))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_3,hAPP(c_Nat_OSuc,U_4),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_3),U_5),hAPP(c_Com_Ocom_OBODY,U_6)),U_7)) )
      & ( c_Hoare__Mirabelle_Otriple__valid(U_3,hAPP(c_Nat_OSuc,U_4),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_3),U_5),hAPP(c_Com_Ocom_OBODY,U_6)),U_7))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_3,U_4,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_3),U_5),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_6))),U_7)) ) ),
    inference(variable_rename,[status(thm)],[f_2_1]) ).

fof(f_2_3,plain,
    ( ! [U_17,U_15,U_13,U_11,U_9] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_9,U_11,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9),U_13),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_15))),U_17))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_9,hAPP(c_Nat_OSuc,U_11),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9),U_13),hAPP(c_Com_Ocom_OBODY,U_15)),U_17)) )
    & ! [U_16,U_14,U_12,U_10,U_8] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_8,hAPP(c_Nat_OSuc,U_10),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8),U_12),hAPP(c_Com_Ocom_OBODY,U_14)),U_16))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_8,U_10,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8),U_12),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_14))),U_16)) ) ),
    inference(miniscope,[status(thm)],[f_2_2]) ).

fof(f_2_4,plain,
    ( ! [U_11,U_9,U_13,U_15,U_17] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_9,U_11,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9),U_13),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_15))),U_17))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_9,hAPP(c_Nat_OSuc,U_11),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9),U_13),hAPP(c_Com_Ocom_OBODY,U_15)),U_17)) )
    & ! [U_10,U_14,U_8,U_12,U_16] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_8,hAPP(c_Nat_OSuc,U_10),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8),U_12),hAPP(c_Com_Ocom_OBODY,U_14)),U_16))
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_8,U_10,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8),U_12),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_14))),U_16)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2_3]) ).

cnf(f_2_5,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_8,hAPP(c_Nat_OSuc,U_10),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8),U_12),hAPP(c_Com_Ocom_OBODY,U_14)),U_16))
    | ~ c_Hoare__Mirabelle_Otriple__valid(U_8,U_10,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8),U_12),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_14))),U_16)) ),
    inference(clausify,[status(thm)],[f_2_4]) ).

cnf(f_2_6,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_9,U_11,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9),U_13),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_15))),U_17))
    | ~ c_Hoare__Mirabelle_Otriple__valid(U_9,hAPP(c_Nat_OSuc,U_11),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9),U_13),hAPP(c_Com_Ocom_OBODY,U_15)),U_17)) ),
    inference(clausify,[status(thm)],[f_2_4]) ).

fof(f_3_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_3_2,plain,
    ! [U_24,U_23,U_22,U_21,U_20,U_19,U_18] :
      ( ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_18),U_19),U_20),U_21) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_18),U_22),U_23),U_24)
        | U_21 != U_24
        | U_20 != U_23
        | U_19 != U_22 )
      & ( ( U_21 = U_24
          & U_20 = U_23
          & U_19 = U_22 )
        | hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_18),U_19),U_20),U_21) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_18),U_22),U_23),U_24) ) ),
    inference(variable_rename,[status(thm)],[f_3_1]) ).

fof(f_3_3,plain,
    ( ! [U_38,U_36,U_34,U_32,U_30,U_28] :
        ( ! [U_26] : hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_26),U_28),U_30),U_32) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_26),U_34),U_36),U_38)
        | U_32 != U_38
        | U_30 != U_36
        | U_28 != U_34 )
    & ! [U_37,U_35,U_33,U_31,U_29,U_27] :
        ( ! [U_25] : hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_25),U_27),U_29),U_31) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_25),U_33),U_35),U_37)
        | ( U_31 = U_37
          & U_29 = U_35
          & U_27 = U_33 ) ) ),
    inference(miniscope,[status(thm)],[f_3_2]) ).

fof(f_3_4,plain,
    ( ! [U_27,U_31,U_29,U_33,U_35,U_37] :
        ( U_31 = U_37
        | ~ sP0(U_27,U_31,U_29,U_33,U_35,U_37) )
    & ! [U_27,U_31,U_29,U_33,U_35,U_37] :
        ( U_29 = U_35
        | ~ sP0(U_27,U_31,U_29,U_33,U_35,U_37) )
    & ! [U_27,U_31,U_29,U_33,U_35,U_37] :
        ( U_27 = U_33
        | ~ sP0(U_27,U_31,U_29,U_33,U_35,U_37) )
    & ! [U_26,U_32,U_28,U_38,U_30,U_34,U_36] :
        ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_26),U_28),U_30),U_32) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_26),U_34),U_36),U_38)
        | U_32 != U_38
        | U_30 != U_36
        | U_28 != U_34 )
    & ! [U_27,U_31,U_25,U_29,U_33,U_35,U_37] :
        ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_25),U_27),U_29),U_31) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_25),U_33),U_35),U_37)
        | sP0(U_27,U_31,U_29,U_33,U_35,U_37) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP0])],[f_3_3]) ).

cnf(f_3_5,plain,
    ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_25),U_27),U_29),U_31) != hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_25),U_33),U_35),U_37)
    | sP0(U_27,U_31,U_29,U_33,U_35,U_37) ),
    inference(clausify,[status(thm)],[f_3_4]) ).

cnf(f_3_6,plain,
    ( hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_26),U_28),U_30),U_32) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_26),U_34),U_36),U_38)
    | U_32 != U_38
    | U_30 != U_36
    | U_28 != U_34 ),
    inference(clausify,[status(thm)],[f_3_4]) ).

cnf(f_3_7,plain,
    ( U_27 = U_33
    | ~ sP0(U_27,U_31,U_29,U_33,U_35,U_37) ),
    inference(clausify,[status(thm)],[f_3_4]) ).

cnf(f_3_8,plain,
    ( U_29 = U_35
    | ~ sP0(U_27,U_31,U_29,U_33,U_35,U_37) ),
    inference(clausify,[status(thm)],[f_3_4]) ).

cnf(f_3_9,plain,
    ( U_31 = U_37
    | ~ sP0(U_27,U_31,U_29,U_33,U_35,U_37) ),
    inference(clausify,[status(thm)],[f_3_4]) ).

fof(f_4_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_4_2,plain,
    ! [U_41,U_40,U_39] :
      ( c_Hoare__Mirabelle_Otriple__valid(U_39,U_40,U_41)
      | ~ c_Hoare__Mirabelle_Otriple__valid(U_39,hAPP(c_Nat_OSuc,U_40),U_41) ),
    inference(variable_rename,[status(thm)],[f_4_1]) ).

fof(f_4_3,plain,
    ! [U_39,U_41,U_40] :
      ( c_Hoare__Mirabelle_Otriple__valid(U_39,U_40,U_41)
      | ~ c_Hoare__Mirabelle_Otriple__valid(U_39,hAPP(c_Nat_OSuc,U_40),U_41) ),
    inference(definitional_conversion,[status(esa)],[f_4_2]) ).

cnf(f_4_4,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_39,U_40,U_41)
    | ~ c_Hoare__Mirabelle_Otriple__valid(U_39,hAPP(c_Nat_OSuc,U_40),U_41) ),
    inference(clausify,[status(thm)],[f_4_3]) ).

fof(f_5_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_5_2,plain,
    ! [U_45,U_44,U_43,U_42] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_44),U_45),U_43))
        & ~ hBOOL(hAPP(hAPP(c_member(U_44),U_45),U_42)) )
      | ( hBOOL(hAPP(hAPP(c_member(U_44),U_45),U_43))
        & hBOOL(hAPP(hAPP(c_member(U_44),U_45),U_42)) )
      | U_42 != U_43 ),
    inference(variable_rename,[status(thm)],[f_5_1]) ).

fof(f_5_3,plain,
    ( ! [U_43,U_42,U_45,U_44] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_44),U_45),U_43))
        | ~ sP2(U_43,U_42,U_45,U_44) )
    & ! [U_43,U_42,U_45,U_44] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_44),U_45),U_42))
        | ~ sP2(U_43,U_42,U_45,U_44) )
    & ! [U_43,U_42,U_45,U_44] :
        ( hBOOL(hAPP(hAPP(c_member(U_44),U_45),U_43))
        | ~ sP1(U_43,U_42,U_45,U_44) )
    & ! [U_43,U_42,U_45,U_44] :
        ( hBOOL(hAPP(hAPP(c_member(U_44),U_45),U_42))
        | ~ sP1(U_43,U_42,U_45,U_44) )
    & ! [U_43,U_42,U_45,U_44] :
        ( sP2(U_43,U_42,U_45,U_44)
        | sP1(U_43,U_42,U_45,U_44)
        | U_42 != U_43 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1,sP2])],[f_5_2]) ).

cnf(f_5_4,plain,
    ( sP2(U_43,U_42,U_45,U_44)
    | sP1(U_43,U_42,U_45,U_44)
    | U_42 != U_43 ),
    inference(clausify,[status(thm)],[f_5_3]) ).

cnf(f_5_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_44),U_45),U_42))
    | ~ sP1(U_43,U_42,U_45,U_44) ),
    inference(clausify,[status(thm)],[f_5_3]) ).

cnf(f_5_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_44),U_45),U_43))
    | ~ sP1(U_43,U_42,U_45,U_44) ),
    inference(clausify,[status(thm)],[f_5_3]) ).

cnf(f_5_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_44),U_45),U_42))
    | ~ sP2(U_43,U_42,U_45,U_44) ),
    inference(clausify,[status(thm)],[f_5_3]) ).

cnf(f_5_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_44),U_45),U_43))
    | ~ sP2(U_43,U_42,U_45,U_44) ),
    inference(clausify,[status(thm)],[f_5_3]) ).

fof(f_6_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_6_2,plain,
    ! [U_51,U_50,U_49,U_48,U_47,U_46] : c_Hoare__Mirabelle_Otriple_Otriple__rec(U_46,U_47,U_48,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_46),U_49),U_50),U_51)) = hAPP(hAPP(hAPP(U_48,U_49),U_50),U_51),
    inference(variable_rename,[status(thm)],[f_6_1]) ).

fof(f_6_3,plain,
    ! [U_49,U_47,U_48,U_46,U_50,U_51] : c_Hoare__Mirabelle_Otriple_Otriple__rec(U_46,U_47,U_48,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_46),U_49),U_50),U_51)) = hAPP(hAPP(hAPP(U_48,U_49),U_50),U_51),
    inference(definitional_conversion,[status(esa)],[f_6_2]) ).

cnf(f_6_4,plain,
    c_Hoare__Mirabelle_Otriple_Otriple__rec(U_46,U_47,U_48,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_46),U_49),U_50),U_51)) = hAPP(hAPP(hAPP(U_48,U_49),U_50),U_51),
    inference(clausify,[status(thm)],[f_6_3]) ).

fof(f_7_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_7_2,plain,
    ! [U_57,U_56,U_55,U_54,U_53,U_52] : c_Hoare__Mirabelle_Otriple_Otriple__case(U_52,U_53,U_54,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_52),U_55),U_56),U_57)) = hAPP(hAPP(hAPP(U_54,U_55),U_56),U_57),
    inference(variable_rename,[status(thm)],[f_7_1]) ).

fof(f_7_3,plain,
    ! [U_53,U_52,U_54,U_55,U_56,U_57] : c_Hoare__Mirabelle_Otriple_Otriple__case(U_52,U_53,U_54,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_52),U_55),U_56),U_57)) = hAPP(hAPP(hAPP(U_54,U_55),U_56),U_57),
    inference(definitional_conversion,[status(esa)],[f_7_2]) ).

cnf(f_7_4,plain,
    c_Hoare__Mirabelle_Otriple_Otriple__case(U_52,U_53,U_54,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_52),U_55),U_56),U_57)) = hAPP(hAPP(hAPP(U_54,U_55),U_56),U_57),
    inference(clausify,[status(thm)],[f_7_3]) ).

fof(f_8_1,plain,
    ! [V_Qa_2,V_pn_2,V_Pa_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_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_2)),
    inference(fof_nnf,[status(thm)],[fact_Body__triple__valid__0]) ).

fof(f_8_2,plain,
    ! [U_61,U_60,U_59,U_58] : c_Hoare__Mirabelle_Otriple__valid(U_58,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_58),U_59),hAPP(c_Com_Ocom_OBODY,U_60)),U_61)),
    inference(variable_rename,[status(thm)],[f_8_1]) ).

fof(f_8_3,plain,
    ! [U_58,U_59,U_60,U_61] : c_Hoare__Mirabelle_Otriple__valid(U_58,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_58),U_59),hAPP(c_Com_Ocom_OBODY,U_60)),U_61)),
    inference(definitional_conversion,[status(esa)],[f_8_2]) ).

cnf(f_8_4,plain,
    c_Hoare__Mirabelle_Otriple__valid(U_58,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_58),U_59),hAPP(c_Com_Ocom_OBODY,U_60)),U_61)),
    inference(clausify,[status(thm)],[f_8_3]) ).

fof(f_9_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_9_2,plain,
    ! [U_65,U_64,U_63,U_62] :
      ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_62),U_63,hAPP(c_Nat_OSuc,U_64),U_65)
      | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_62)),U_63,U_64,U_65) ),
    inference(variable_rename,[status(thm)],[f_9_1]) ).

fof(f_9_3,plain,
    ! [U_62,U_63,U_64,U_65] :
      ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_62),U_63,hAPP(c_Nat_OSuc,U_64),U_65)
      | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_62)),U_63,U_64,U_65) ),
    inference(definitional_conversion,[status(esa)],[f_9_2]) ).

cnf(f_9_4,plain,
    ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_62),U_63,hAPP(c_Nat_OSuc,U_64),U_65)
    | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_62)),U_63,U_64,U_65) ),
    inference(clausify,[status(thm)],[f_9_3]) ).

fof(f_10_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_10_2,plain,
    ! [U_67,U_66] :
      ( ( hAPP(c_Com_Ocom_OBODY,U_66) = hAPP(c_Com_Ocom_OBODY,U_67)
        | U_66 != U_67 )
      & ( U_66 = U_67
        | hAPP(c_Com_Ocom_OBODY,U_66) != hAPP(c_Com_Ocom_OBODY,U_67) ) ),
    inference(variable_rename,[status(thm)],[f_10_1]) ).

fof(f_10_3,plain,
    ( ! [U_71,U_69] :
        ( hAPP(c_Com_Ocom_OBODY,U_69) = hAPP(c_Com_Ocom_OBODY,U_71)
        | U_69 != U_71 )
    & ! [U_70,U_68] :
        ( U_68 = U_70
        | hAPP(c_Com_Ocom_OBODY,U_68) != hAPP(c_Com_Ocom_OBODY,U_70) ) ),
    inference(miniscope,[status(thm)],[f_10_2]) ).

fof(f_10_4,plain,
    ( ! [U_71,U_69] :
        ( hAPP(c_Com_Ocom_OBODY,U_69) = hAPP(c_Com_Ocom_OBODY,U_71)
        | U_69 != U_71 )
    & ! [U_70,U_68] :
        ( U_68 = U_70
        | hAPP(c_Com_Ocom_OBODY,U_68) != hAPP(c_Com_Ocom_OBODY,U_70) ) ),
    inference(definitional_conversion,[status(esa)],[f_10_3]) ).

cnf(f_10_5,plain,
    ( U_68 = U_70
    | hAPP(c_Com_Ocom_OBODY,U_68) != hAPP(c_Com_Ocom_OBODY,U_70) ),
    inference(clausify,[status(thm)],[f_10_4]) ).

cnf(f_10_6,plain,
    ( hAPP(c_Com_Ocom_OBODY,U_69) = hAPP(c_Com_Ocom_OBODY,U_71)
    | U_69 != U_71 ),
    inference(clausify,[status(thm)],[f_10_4]) ).

fof(f_11_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_11_2,plain,
    ! [U_75,U_74,U_73,U_72] :
      ( ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_72),U_73,hAPP(c_Nat_OSuc,U_74),U_75)
        | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_72)),U_73,U_74,U_75) )
      & ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_72)),U_73,U_74,U_75)
        | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_72),U_73,hAPP(c_Nat_OSuc,U_74),U_75) ) ),
    inference(variable_rename,[status(thm)],[f_11_1]) ).

fof(f_11_3,plain,
    ( ! [U_83,U_81,U_79,U_77] :
        ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_77),U_79,hAPP(c_Nat_OSuc,U_81),U_83)
        | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_77)),U_79,U_81,U_83) )
    & ! [U_82,U_80,U_78,U_76] :
        ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_76)),U_78,U_80,U_82)
        | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_76),U_78,hAPP(c_Nat_OSuc,U_80),U_82) ) ),
    inference(miniscope,[status(thm)],[f_11_2]) ).

fof(f_11_4,plain,
    ( ! [U_81,U_77,U_79,U_83] :
        ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_77),U_79,hAPP(c_Nat_OSuc,U_81),U_83)
        | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_77)),U_79,U_81,U_83) )
    & ! [U_78,U_82,U_76,U_80] :
        ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_76)),U_78,U_80,U_82)
        | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_76),U_78,hAPP(c_Nat_OSuc,U_80),U_82) ) ),
    inference(definitional_conversion,[status(esa)],[f_11_3]) ).

cnf(f_11_5,plain,
    ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_76)),U_78,U_80,U_82)
    | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_76),U_78,hAPP(c_Nat_OSuc,U_80),U_82) ),
    inference(clausify,[status(thm)],[f_11_4]) ).

cnf(f_11_6,plain,
    ( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_77),U_79,hAPP(c_Nat_OSuc,U_81),U_83)
    | ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_77)),U_79,U_81,U_83) ),
    inference(clausify,[status(thm)],[f_11_4]) ).

fof(f_12_1,plain,
    ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n),
    inference(fof_nnf,[status(thm)],[fact_n__not__Suc__n]) ).

fof(f_12_2,plain,
    ! [U_84] : U_84 != hAPP(c_Nat_OSuc,U_84),
    inference(variable_rename,[status(thm)],[f_12_1]) ).

fof(f_12_3,plain,
    ! [U_84] : U_84 != hAPP(c_Nat_OSuc,U_84),
    inference(definitional_conversion,[status(esa)],[f_12_2]) ).

cnf(f_12_4,plain,
    U_84 != hAPP(c_Nat_OSuc,U_84),
    inference(clausify,[status(thm)],[f_12_3]) ).

fof(f_13_1,plain,
    ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n,
    inference(fof_nnf,[status(thm)],[fact_Suc__n__not__n]) ).

fof(f_13_2,plain,
    ! [U_85] : hAPP(c_Nat_OSuc,U_85) != U_85,
    inference(variable_rename,[status(thm)],[f_13_1]) ).

fof(f_13_3,plain,
    ! [U_85] : hAPP(c_Nat_OSuc,U_85) != U_85,
    inference(definitional_conversion,[status(esa)],[f_13_2]) ).

cnf(f_13_4,plain,
    hAPP(c_Nat_OSuc,U_85) != U_85,
    inference(clausify,[status(thm)],[f_13_3]) ).

fof(f_14_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_14_2,plain,
    ! [U_87,U_86] :
      ( ( hAPP(c_Nat_OSuc,U_86) = hAPP(c_Nat_OSuc,U_87)
        | U_86 != U_87 )
      & ( U_86 = U_87
        | hAPP(c_Nat_OSuc,U_86) != hAPP(c_Nat_OSuc,U_87) ) ),
    inference(variable_rename,[status(thm)],[f_14_1]) ).

fof(f_14_3,plain,
    ( ! [U_91,U_89] :
        ( hAPP(c_Nat_OSuc,U_89) = hAPP(c_Nat_OSuc,U_91)
        | U_89 != U_91 )
    & ! [U_90,U_88] :
        ( U_88 = U_90
        | hAPP(c_Nat_OSuc,U_88) != hAPP(c_Nat_OSuc,U_90) ) ),
    inference(miniscope,[status(thm)],[f_14_2]) ).

fof(f_14_4,plain,
    ( ! [U_89,U_91] :
        ( hAPP(c_Nat_OSuc,U_89) = hAPP(c_Nat_OSuc,U_91)
        | U_89 != U_91 )
    & ! [U_90,U_88] :
        ( U_88 = U_90
        | hAPP(c_Nat_OSuc,U_88) != hAPP(c_Nat_OSuc,U_90) ) ),
    inference(definitional_conversion,[status(esa)],[f_14_3]) ).

cnf(f_14_5,plain,
    ( U_88 = U_90
    | hAPP(c_Nat_OSuc,U_88) != hAPP(c_Nat_OSuc,U_90) ),
    inference(clausify,[status(thm)],[f_14_4]) ).

cnf(f_14_6,plain,
    ( hAPP(c_Nat_OSuc,U_89) = hAPP(c_Nat_OSuc,U_91)
    | U_89 != U_91 ),
    inference(clausify,[status(thm)],[f_14_4]) ).

fof(f_15_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_15_2,plain,
    ! [U_93,U_92] :
      ( U_92 = U_93
      | hAPP(c_Nat_OSuc,U_92) != hAPP(c_Nat_OSuc,U_93) ),
    inference(variable_rename,[status(thm)],[f_15_1]) ).

fof(f_15_3,plain,
    ! [U_93,U_92] :
      ( U_92 = U_93
      | hAPP(c_Nat_OSuc,U_92) != hAPP(c_Nat_OSuc,U_93) ),
    inference(definitional_conversion,[status(esa)],[f_15_2]) ).

cnf(f_15_4,plain,
    ( U_92 = U_93
    | hAPP(c_Nat_OSuc,U_92) != hAPP(c_Nat_OSuc,U_93) ),
    inference(clausify,[status(thm)],[f_15_3]) ).

fof(f_16_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_16_2,plain,
    ! [U_97,U_96,U_95,U_94] :
      ( c_Natural_Oevaln(U_94,U_95,hAPP(c_Nat_OSuc,U_96),U_97)
      | ~ c_Natural_Oevaln(U_94,U_95,U_96,U_97) ),
    inference(variable_rename,[status(thm)],[f_16_1]) ).

fof(f_16_3,plain,
    ! [U_94,U_95,U_96,U_97] :
      ( c_Natural_Oevaln(U_94,U_95,hAPP(c_Nat_OSuc,U_96),U_97)
      | ~ c_Natural_Oevaln(U_94,U_95,U_96,U_97) ),
    inference(definitional_conversion,[status(esa)],[f_16_2]) ).

cnf(f_16_4,plain,
    ( c_Natural_Oevaln(U_94,U_95,hAPP(c_Nat_OSuc,U_96),U_97)
    | ~ c_Natural_Oevaln(U_94,U_95,U_96,U_97) ),
    inference(clausify,[status(thm)],[f_16_3]) ).

fof(f_17_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_17_2,plain,
    ! [U_98] : hAPP(c_Nat_OSuc,U_98) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_17_1]) ).

fof(f_17_3,plain,
    ! [U_98] : hAPP(c_Nat_OSuc,U_98) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_17_2]) ).

cnf(f_17_4,plain,
    hAPP(c_Nat_OSuc,U_98) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_17_3]) ).

fof(f_18_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_18_2,plain,
    ! [U_99] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_99),
    inference(variable_rename,[status(thm)],[f_18_1]) ).

fof(f_18_3,plain,
    ! [U_99] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_99),
    inference(definitional_conversion,[status(esa)],[f_18_2]) ).

cnf(f_18_4,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_99),
    inference(clausify,[status(thm)],[f_18_3]) ).

fof(f_19_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_19_2,plain,
    ! [U_100] : hAPP(c_Nat_OSuc,U_100) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_19_1]) ).

fof(f_19_3,plain,
    ! [U_100] : hAPP(c_Nat_OSuc,U_100) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_19_2]) ).

cnf(f_19_4,plain,
    hAPP(c_Nat_OSuc,U_100) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_19_3]) ).

fof(f_20_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_20_2,plain,
    ! [U_101] : hAPP(c_Nat_OSuc,U_101) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_20_1]) ).

fof(f_20_3,plain,
    ! [U_101] : hAPP(c_Nat_OSuc,U_101) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_20_2]) ).

cnf(f_20_4,plain,
    hAPP(c_Nat_OSuc,U_101) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_20_3]) ).

fof(f_21_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_21_2,plain,
    ! [U_102] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_102),
    inference(variable_rename,[status(thm)],[f_21_1]) ).

fof(f_21_3,plain,
    ! [U_102] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_102),
    inference(definitional_conversion,[status(esa)],[f_21_2]) ).

cnf(f_21_4,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_102),
    inference(clausify,[status(thm)],[f_21_3]) ).

fof(f_22_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_22_2,plain,
    ! [U_103] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_103),
    inference(variable_rename,[status(thm)],[f_22_1]) ).

fof(f_22_3,plain,
    ! [U_103] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_103),
    inference(definitional_conversion,[status(esa)],[f_22_2]) ).

cnf(f_22_4,plain,
    c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,U_103),
    inference(clausify,[status(thm)],[f_22_3]) ).

fof(f_23_1,plain,
    ! [V_Qa_2,V_c_2,V_Pa_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_Pa_2),V_c_2),V_Qa_2))
        | ? [B_Z,B_s] :
            ( ? [B_s_H] :
                ( ~ hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H))
                & c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H) )
            & hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) ) )
      & ( ! [B_Z,B_s] :
            ( ! [B_s_H] :
                ( hBOOL(hAPP(hAPP(V_Qa_2,B_Z),B_s_H))
                | ~ c_Natural_Oevaln(V_c_2,B_s,V_n_2,B_s_H) )
            | ~ hBOOL(hAPP(hAPP(V_Pa_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_Pa_2),V_c_2),V_Qa_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_triple__valid__def2]) ).

fof(f_23_2,plain,
    ! [U_114,U_113,U_112,U_111,U_110] :
      ( ( c_Hoare__Mirabelle_Otriple__valid(U_110,U_111,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_110),U_112),U_113),U_114))
        | ? [U_109,U_108] :
            ( ? [U_107] :
                ( ~ hBOOL(hAPP(hAPP(U_114,U_109),U_107))
                & c_Natural_Oevaln(U_113,U_108,U_111,U_107) )
            & hBOOL(hAPP(hAPP(U_112,U_109),U_108)) ) )
      & ( ! [U_106,U_105] :
            ( ! [U_104] :
                ( hBOOL(hAPP(hAPP(U_114,U_106),U_104))
                | ~ c_Natural_Oevaln(U_113,U_105,U_111,U_104) )
            | ~ hBOOL(hAPP(hAPP(U_112,U_106),U_105)) )
        | ~ c_Hoare__Mirabelle_Otriple__valid(U_110,U_111,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_110),U_112),U_113),U_114)) ) ),
    inference(variable_rename,[status(thm)],[f_23_1]) ).

fof(f_23_3,plain,
    ( ! [U_124,U_122,U_120,U_118] :
        ( ! [U_116] : c_Hoare__Mirabelle_Otriple__valid(U_116,U_118,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_116),U_120),U_122),U_124))
        | ? [U_109,U_108] :
            ( ? [U_107] :
                ( ~ hBOOL(hAPP(hAPP(U_124,U_109),U_107))
                & c_Natural_Oevaln(U_122,U_108,U_118,U_107) )
            & hBOOL(hAPP(hAPP(U_120,U_109),U_108)) ) )
    & ! [U_123,U_121,U_119,U_117] :
        ( ! [U_115] : ~ c_Hoare__Mirabelle_Otriple__valid(U_115,U_117,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_115),U_119),U_121),U_123))
        | ! [U_106,U_105] :
            ( ! [U_104] :
                ( hBOOL(hAPP(hAPP(U_123,U_106),U_104))
                | ~ c_Natural_Oevaln(U_121,U_105,U_117,U_104) )
            | ~ hBOOL(hAPP(hAPP(U_119,U_106),U_105)) ) ) ),
    inference(miniscope,[status(thm)],[f_23_2]) ).

fof(f_23_4,plain,
    ( ! [U_124,U_122,U_120,U_118] :
        ( ! [U_116] : c_Hoare__Mirabelle_Otriple__valid(U_116,U_118,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_116),U_120),U_122),U_124))
        | ? [U_108] :
            ( ? [U_107] :
                ( ~ hBOOL(hAPP(hAPP(U_124,sK2(U_124,U_122,U_120,U_118)),U_107))
                & c_Natural_Oevaln(U_122,U_108,U_118,U_107) )
            & hBOOL(hAPP(hAPP(U_120,sK2(U_124,U_122,U_120,U_118)),U_108)) ) )
    & ! [U_123,U_121,U_119,U_117] :
        ( ! [U_115] : ~ c_Hoare__Mirabelle_Otriple__valid(U_115,U_117,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_115),U_119),U_121),U_123))
        | ! [U_106,U_105] :
            ( ! [U_104] :
                ( hBOOL(hAPP(hAPP(U_123,U_106),U_104))
                | ~ c_Natural_Oevaln(U_121,U_105,U_117,U_104) )
            | ~ hBOOL(hAPP(hAPP(U_119,U_106),U_105)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_109,sK2(U_124,U_122,U_120,U_118))],[f_23_3]) ).

fof(f_23_5,plain,
    ( ! [U_124,U_122,U_120,U_118] :
        ( ! [U_116] : c_Hoare__Mirabelle_Otriple__valid(U_116,U_118,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_116),U_120),U_122),U_124))
        | ( ? [U_107] :
              ( ~ hBOOL(hAPP(hAPP(U_124,sK2(U_124,U_122,U_120,U_118)),U_107))
              & c_Natural_Oevaln(U_122,sK3(U_124,U_122,U_120,U_118),U_118,U_107) )
          & hBOOL(hAPP(hAPP(U_120,sK2(U_124,U_122,U_120,U_118)),sK3(U_124,U_122,U_120,U_118))) ) )
    & ! [U_123,U_121,U_119,U_117] :
        ( ! [U_115] : ~ c_Hoare__Mirabelle_Otriple__valid(U_115,U_117,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_115),U_119),U_121),U_123))
        | ! [U_106,U_105] :
            ( ! [U_104] :
                ( hBOOL(hAPP(hAPP(U_123,U_106),U_104))
                | ~ c_Natural_Oevaln(U_121,U_105,U_117,U_104) )
            | ~ hBOOL(hAPP(hAPP(U_119,U_106),U_105)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_108,sK3(U_124,U_122,U_120,U_118))],[f_23_4]) ).

fof(f_23_6,plain,
    ( ! [U_124,U_122,U_120,U_118] :
        ( ! [U_116] : c_Hoare__Mirabelle_Otriple__valid(U_116,U_118,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_116),U_120),U_122),U_124))
        | ( ~ hBOOL(hAPP(hAPP(U_124,sK2(U_124,U_122,U_120,U_118)),sK4(U_124,U_122,U_120,U_118)))
          & c_Natural_Oevaln(U_122,sK3(U_124,U_122,U_120,U_118),U_118,sK4(U_124,U_122,U_120,U_118))
          & hBOOL(hAPP(hAPP(U_120,sK2(U_124,U_122,U_120,U_118)),sK3(U_124,U_122,U_120,U_118))) ) )
    & ! [U_123,U_121,U_119,U_117] :
        ( ! [U_115] : ~ c_Hoare__Mirabelle_Otriple__valid(U_115,U_117,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_115),U_119),U_121),U_123))
        | ! [U_106,U_105] :
            ( ! [U_104] :
                ( hBOOL(hAPP(hAPP(U_123,U_106),U_104))
                | ~ c_Natural_Oevaln(U_121,U_105,U_117,U_104) )
            | ~ hBOOL(hAPP(hAPP(U_119,U_106),U_105)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_107,sK4(U_124,U_122,U_120,U_118))],[f_23_5]) ).

fof(f_23_7,plain,
    ( ! [U_122,U_124,U_120,U_118] :
        ( ~ hBOOL(hAPP(hAPP(U_124,sK2(U_124,U_122,U_120,U_118)),sK4(U_124,U_122,U_120,U_118)))
        | ~ sP3(U_122,U_124,U_120,U_118) )
    & ! [U_122,U_124,U_120,U_118] :
        ( c_Natural_Oevaln(U_122,sK3(U_124,U_122,U_120,U_118),U_118,sK4(U_124,U_122,U_120,U_118))
        | ~ sP3(U_122,U_124,U_120,U_118) )
    & ! [U_122,U_124,U_120,U_118] :
        ( hBOOL(hAPP(hAPP(U_120,sK2(U_124,U_122,U_120,U_118)),sK3(U_124,U_122,U_120,U_118)))
        | ~ sP3(U_122,U_124,U_120,U_118) )
    & ! [U_122,U_124,U_116,U_120,U_118] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_116,U_118,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_116),U_120),U_122),U_124))
        | sP3(U_122,U_124,U_120,U_118) )
    & ! [U_121,U_105,U_123,U_104,U_106,U_117,U_115,U_119] :
        ( ~ c_Hoare__Mirabelle_Otriple__valid(U_115,U_117,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_115),U_119),U_121),U_123))
        | hBOOL(hAPP(hAPP(U_123,U_106),U_104))
        | ~ c_Natural_Oevaln(U_121,U_105,U_117,U_104)
        | ~ hBOOL(hAPP(hAPP(U_119,U_106),U_105)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP3])],[f_23_6]) ).

cnf(f_23_8,plain,
    ( ~ c_Hoare__Mirabelle_Otriple__valid(U_115,U_117,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_115),U_119),U_121),U_123))
    | hBOOL(hAPP(hAPP(U_123,U_106),U_104))
    | ~ c_Natural_Oevaln(U_121,U_105,U_117,U_104)
    | ~ hBOOL(hAPP(hAPP(U_119,U_106),U_105)) ),
    inference(clausify,[status(thm)],[f_23_7]) ).

cnf(f_23_9,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_116,U_118,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_116),U_120),U_122),U_124))
    | sP3(U_122,U_124,U_120,U_118) ),
    inference(clausify,[status(thm)],[f_23_7]) ).

cnf(f_23_10,plain,
    ( hBOOL(hAPP(hAPP(U_120,sK2(U_124,U_122,U_120,U_118)),sK3(U_124,U_122,U_120,U_118)))
    | ~ sP3(U_122,U_124,U_120,U_118) ),
    inference(clausify,[status(thm)],[f_23_7]) ).

cnf(f_23_11,plain,
    ( c_Natural_Oevaln(U_122,sK3(U_124,U_122,U_120,U_118),U_118,sK4(U_124,U_122,U_120,U_118))
    | ~ sP3(U_122,U_124,U_120,U_118) ),
    inference(clausify,[status(thm)],[f_23_7]) ).

cnf(f_23_12,plain,
    ( ~ hBOOL(hAPP(hAPP(U_124,sK2(U_124,U_122,U_120,U_118)),sK4(U_124,U_122,U_120,U_118)))
    | ~ sP3(U_122,U_124,U_120,U_118) ),
    inference(clausify,[status(thm)],[f_23_7]) ).

fof(f_24_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_24_2,plain,
    ! [U_128,U_127,U_126,U_125] :
      ( hBOOL(hAPP(hAPP(c_member(U_127),U_125),U_128))
      | ~ hBOOL(hAPP(hAPP(c_member(U_127),U_126),U_128))
      | U_125 != U_126 ),
    inference(variable_rename,[status(thm)],[f_24_1]) ).

fof(f_24_3,plain,
    ! [U_127,U_128,U_126,U_125] :
      ( hBOOL(hAPP(hAPP(c_member(U_127),U_125),U_128))
      | ~ hBOOL(hAPP(hAPP(c_member(U_127),U_126),U_128))
      | U_125 != U_126 ),
    inference(definitional_conversion,[status(esa)],[f_24_2]) ).

cnf(f_24_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_127),U_125),U_128))
    | ~ hBOOL(hAPP(hAPP(c_member(U_127),U_126),U_128))
    | U_125 != U_126 ),
    inference(clausify,[status(thm)],[f_24_3]) ).

fof(f_25_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_25_2,plain,
    ! [U_132,U_131,U_130,U_129] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_131),U_129),U_132))
          | ~ hBOOL(hAPP(hAPP(c_member(U_131),U_130),U_132)) )
        & ( hBOOL(hAPP(hAPP(c_member(U_131),U_130),U_132))
          | ~ hBOOL(hAPP(hAPP(c_member(U_131),U_129),U_132)) ) )
      | U_129 != U_130 ),
    inference(variable_rename,[status(thm)],[f_25_1]) ).

fof(f_25_3,plain,
    ( ! [U_130,U_129,U_131,U_132] :
        ( hBOOL(hAPP(hAPP(c_member(U_131),U_129),U_132))
        | ~ hBOOL(hAPP(hAPP(c_member(U_131),U_130),U_132))
        | ~ sP4(U_130,U_129,U_131,U_132) )
    & ! [U_130,U_129,U_131,U_132] :
        ( hBOOL(hAPP(hAPP(c_member(U_131),U_130),U_132))
        | ~ hBOOL(hAPP(hAPP(c_member(U_131),U_129),U_132))
        | ~ sP4(U_130,U_129,U_131,U_132) )
    & ! [U_130,U_129,U_131,U_132] :
        ( sP4(U_130,U_129,U_131,U_132)
        | U_129 != U_130 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP4])],[f_25_2]) ).

cnf(f_25_4,plain,
    ( sP4(U_130,U_129,U_131,U_132)
    | U_129 != U_130 ),
    inference(clausify,[status(thm)],[f_25_3]) ).

cnf(f_25_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_131),U_130),U_132))
    | ~ hBOOL(hAPP(hAPP(c_member(U_131),U_129),U_132))
    | ~ sP4(U_130,U_129,U_131,U_132) ),
    inference(clausify,[status(thm)],[f_25_3]) ).

cnf(f_25_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_131),U_129),U_132))
    | ~ hBOOL(hAPP(hAPP(c_member(U_131),U_130),U_132))
    | ~ sP4(U_130,U_129,U_131,U_132) ),
    inference(clausify,[status(thm)],[f_25_3]) ).

fof(f_26_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_26_2,plain,
    ! [U_136,U_135,U_134,U_133] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_135),U_136),U_133))
          | ~ hBOOL(hAPP(hAPP(c_member(U_135),U_136),U_134)) )
        & ( hBOOL(hAPP(hAPP(c_member(U_135),U_136),U_134))
          | ~ hBOOL(hAPP(hAPP(c_member(U_135),U_136),U_133)) ) )
      | U_133 != U_134 ),
    inference(variable_rename,[status(thm)],[f_26_1]) ).

fof(f_26_3,plain,
    ( ! [U_133,U_134,U_135,U_136] :
        ( hBOOL(hAPP(hAPP(c_member(U_135),U_136),U_133))
        | ~ hBOOL(hAPP(hAPP(c_member(U_135),U_136),U_134))
        | ~ sP5(U_133,U_134,U_135,U_136) )
    & ! [U_133,U_134,U_135,U_136] :
        ( hBOOL(hAPP(hAPP(c_member(U_135),U_136),U_134))
        | ~ hBOOL(hAPP(hAPP(c_member(U_135),U_136),U_133))
        | ~ sP5(U_133,U_134,U_135,U_136) )
    & ! [U_133,U_134,U_135,U_136] :
        ( sP5(U_133,U_134,U_135,U_136)
        | U_133 != U_134 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP5])],[f_26_2]) ).

cnf(f_26_4,plain,
    ( sP5(U_133,U_134,U_135,U_136)
    | U_133 != U_134 ),
    inference(clausify,[status(thm)],[f_26_3]) ).

cnf(f_26_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_135),U_136),U_134))
    | ~ hBOOL(hAPP(hAPP(c_member(U_135),U_136),U_133))
    | ~ sP5(U_133,U_134,U_135,U_136) ),
    inference(clausify,[status(thm)],[f_26_3]) ).

cnf(f_26_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_135),U_136),U_133))
    | ~ hBOOL(hAPP(hAPP(c_member(U_135),U_136),U_134))
    | ~ sP5(U_133,U_134,U_135,U_136) ),
    inference(clausify,[status(thm)],[f_26_3]) ).

fof(f_27_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_27_2,plain,
    ! [U_139,U_138,U_137] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_137),U_138),U_139))
        | ~ hBOOL(hAPP(U_139,U_138)) )
      & ( hBOOL(hAPP(U_139,U_138))
        | ~ hBOOL(hAPP(hAPP(c_member(U_137),U_138),U_139)) ) ),
    inference(variable_rename,[status(thm)],[f_27_1]) ).

fof(f_27_3,plain,
    ( ! [U_145,U_143] :
        ( ! [U_141] : hBOOL(hAPP(hAPP(c_member(U_141),U_143),U_145))
        | ~ hBOOL(hAPP(U_145,U_143)) )
    & ! [U_144,U_142] :
        ( ! [U_140] : ~ hBOOL(hAPP(hAPP(c_member(U_140),U_142),U_144))
        | hBOOL(hAPP(U_144,U_142)) ) ),
    inference(miniscope,[status(thm)],[f_27_2]) ).

fof(f_27_4,plain,
    ( ! [U_145,U_141,U_143] :
        ( hBOOL(hAPP(hAPP(c_member(U_141),U_143),U_145))
        | ~ hBOOL(hAPP(U_145,U_143)) )
    & ! [U_142,U_140,U_144] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_140),U_142),U_144))
        | hBOOL(hAPP(U_144,U_142)) ) ),
    inference(definitional_conversion,[status(esa)],[f_27_3]) ).

cnf(f_27_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_140),U_142),U_144))
    | hBOOL(hAPP(U_144,U_142)) ),
    inference(clausify,[status(thm)],[f_27_4]) ).

cnf(f_27_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_141),U_143),U_145))
    | ~ hBOOL(hAPP(U_145,U_143)) ),
    inference(clausify,[status(thm)],[f_27_4]) ).

fof(f_28_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_28_2,plain,
    ! [U_150,U_149,U_148,U_147,U_146] : c_Hoare__Mirabelle_Otriple_Otriple__size(U_146,U_147,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_146),U_148),U_149),U_150)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_28_1]) ).

fof(f_28_3,plain,
    ! [U_146,U_147,U_148,U_149,U_150] : c_Hoare__Mirabelle_Otriple_Otriple__size(U_146,U_147,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_146),U_148),U_149),U_150)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_28_2]) ).

cnf(f_28_4,plain,
    c_Hoare__Mirabelle_Otriple_Otriple__size(U_146,U_147,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_146),U_148),U_149),U_150)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_28_3]) ).

fof(f_29_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_29_2,plain,
    ! [U_154,U_153,U_152,U_151] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(U_151)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_151),U_152),U_153),U_154)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_29_1]) ).

fof(f_29_3,plain,
    ! [U_151,U_152,U_153,U_154] : hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(U_151)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_151),U_152),U_153),U_154)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_29_2]) ).

cnf(f_29_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Hoare__Mirabelle_Otriple(U_151)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_151),U_152),U_153),U_154)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_29_3]) ).

fof(f_30_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_30_2,plain,
    ! [U_159,U_158,U_157,U_156] :
      ( ? [U_155] :
          ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_156)),U_157,U_155,U_159)
          & U_158 = hAPP(c_Nat_OSuc,U_155) )
      | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_156),U_157,U_158,U_159) ),
    inference(variable_rename,[status(thm)],[f_30_1]) ).

fof(f_30_3,plain,
    ! [U_159,U_158,U_157,U_156] :
      ( ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_156)),U_157,sK5(U_159,U_158,U_157,U_156),U_159)
        & U_158 = hAPP(c_Nat_OSuc,sK5(U_159,U_158,U_157,U_156)) )
      | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_156),U_157,U_158,U_159) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_155,sK5(U_159,U_158,U_157,U_156))],[f_30_2]) ).

fof(f_30_4,plain,
    ( ! [U_156,U_157,U_158,U_159] :
        ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_156)),U_157,sK5(U_159,U_158,U_157,U_156),U_159)
        | ~ sP6(U_156,U_157,U_158,U_159) )
    & ! [U_156,U_157,U_158,U_159] :
        ( U_158 = hAPP(c_Nat_OSuc,sK5(U_159,U_158,U_157,U_156))
        | ~ sP6(U_156,U_157,U_158,U_159) )
    & ! [U_156,U_157,U_158,U_159] :
        ( sP6(U_156,U_157,U_158,U_159)
        | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_156),U_157,U_158,U_159) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP6])],[f_30_3]) ).

cnf(f_30_5,plain,
    ( sP6(U_156,U_157,U_158,U_159)
    | ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,U_156),U_157,U_158,U_159) ),
    inference(clausify,[status(thm)],[f_30_4]) ).

cnf(f_30_6,plain,
    ( U_158 = hAPP(c_Nat_OSuc,sK5(U_159,U_158,U_157,U_156))
    | ~ sP6(U_156,U_157,U_158,U_159) ),
    inference(clausify,[status(thm)],[f_30_4]) ).

cnf(f_30_7,plain,
    ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_156)),U_157,sK5(U_159,U_158,U_157,U_156),U_159)
    | ~ sP6(U_156,U_157,U_158,U_159) ),
    inference(clausify,[status(thm)],[f_30_4]) ).

fof(f_31_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_31_2,plain,
    ! [U_162,U_161,U_160] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_160)),U_161),U_162))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_160))),U_161),U_162)) ),
    inference(variable_rename,[status(thm)],[f_31_1]) ).

fof(f_31_3,plain,
    ! [U_162,U_161,U_160] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_160)),U_161),U_162))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_160))),U_161),U_162)) ),
    inference(definitional_conversion,[status(esa)],[f_31_2]) ).

cnf(f_31_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_160)),U_161),U_162))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_160))),U_161),U_162)) ),
    inference(clausify,[status(thm)],[f_31_3]) ).

fof(f_32_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_32_2,plain,
    ! [U_165,U_164,U_163] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_163))),U_164),U_165))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_163)),U_164),U_165)) ),
    inference(variable_rename,[status(thm)],[f_32_1]) ).

fof(f_32_3,plain,
    ! [U_163,U_164,U_165] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_163))),U_164),U_165))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_163)),U_164),U_165)) ),
    inference(definitional_conversion,[status(esa)],[f_32_2]) ).

cnf(f_32_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_163))),U_164),U_165))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_163)),U_164),U_165)) ),
    inference(clausify,[status(thm)],[f_32_3]) ).

fof(f_33_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_33_2,plain,
    ! [U_168,U_167,U_166] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_166)),U_167),U_168))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_166))),U_167),U_168)) )
      & ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_166))),U_167),U_168))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_166)),U_167),U_168)) ) ),
    inference(variable_rename,[status(thm)],[f_33_1]) ).

fof(f_33_3,plain,
    ( ! [U_174,U_172,U_170] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_170)),U_172),U_174))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_170))),U_172),U_174)) )
    & ! [U_173,U_171,U_169] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_169))),U_171),U_173))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_169)),U_171),U_173)) ) ),
    inference(miniscope,[status(thm)],[f_33_2]) ).

fof(f_33_4,plain,
    ( ! [U_170,U_172,U_174] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_170)),U_172),U_174))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_170))),U_172),U_174)) )
    & ! [U_171,U_173,U_169] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_169))),U_171),U_173))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_169)),U_171),U_173)) ) ),
    inference(definitional_conversion,[status(esa)],[f_33_3]) ).

cnf(f_33_5,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_169))),U_171),U_173))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_169)),U_171),U_173)) ),
    inference(clausify,[status(thm)],[f_33_4]) ).

cnf(f_33_6,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,U_170)),U_172),U_174))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_170))),U_172),U_174)) ),
    inference(clausify,[status(thm)],[f_33_4]) ).

fof(f_34_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_34_2,plain,
    ! [U_175] :
      ( hBOOL(hAPP(hAPP(c_member(U_175),c_Groups_Ozero__class_Ozero(U_175)),c_Nat_Osemiring__1__class_ONats(U_175)))
      | ~ class_Rings_Osemiring__1(U_175) ),
    inference(variable_rename,[status(thm)],[f_34_1]) ).

fof(f_34_3,plain,
    ! [U_175] :
      ( hBOOL(hAPP(hAPP(c_member(U_175),c_Groups_Ozero__class_Ozero(U_175)),c_Nat_Osemiring__1__class_ONats(U_175)))
      | ~ class_Rings_Osemiring__1(U_175) ),
    inference(definitional_conversion,[status(esa)],[f_34_2]) ).

cnf(f_34_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_175),c_Groups_Ozero__class_Ozero(U_175)),c_Nat_Osemiring__1__class_ONats(U_175)))
    | ~ class_Rings_Osemiring__1(U_175) ),
    inference(clausify,[status(thm)],[f_34_3]) ).

fof(f_35_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_35_2,plain,
    ! [U_176] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,U_176)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_35_1]) ).

fof(f_35_3,plain,
    ! [U_176] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,U_176)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_35_2]) ).

cnf(f_35_4,plain,
    c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,U_176)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_35_3]) ).

fof(f_36_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_36_2,plain,
    ! [U_177] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,U_177)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_36_1]) ).

fof(f_36_3,plain,
    ! [U_177] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,U_177)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_36_2]) ).

cnf(f_36_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),hAPP(c_Com_Ocom_OBODY,U_177)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_36_3]) ).

fof(f_37_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_37_2,plain,
    ! [U_179,U_178] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_178) = U_179
          | U_179 != c_Groups_Ozero__class_Ozero(U_178) )
        & ( U_179 = c_Groups_Ozero__class_Ozero(U_178)
          | c_Groups_Ozero__class_Ozero(U_178) != U_179 ) )
      | ~ class_Groups_Ozero(U_178) ),
    inference(variable_rename,[status(thm)],[f_37_1]) ).

fof(f_37_3,plain,
    ( ! [U_178,U_179] :
        ( c_Groups_Ozero__class_Ozero(U_178) = U_179
        | U_179 != c_Groups_Ozero__class_Ozero(U_178)
        | ~ sP7(U_178,U_179) )
    & ! [U_178,U_179] :
        ( U_179 = c_Groups_Ozero__class_Ozero(U_178)
        | c_Groups_Ozero__class_Ozero(U_178) != U_179
        | ~ sP7(U_178,U_179) )
    & ! [U_178,U_179] :
        ( sP7(U_178,U_179)
        | ~ class_Groups_Ozero(U_178) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP7])],[f_37_2]) ).

cnf(f_37_4,plain,
    ( sP7(U_178,U_179)
    | ~ class_Groups_Ozero(U_178) ),
    inference(clausify,[status(thm)],[f_37_3]) ).

cnf(f_37_5,plain,
    ( U_179 = c_Groups_Ozero__class_Ozero(U_178)
    | c_Groups_Ozero__class_Ozero(U_178) != U_179
    | ~ sP7(U_178,U_179) ),
    inference(clausify,[status(thm)],[f_37_3]) ).

cnf(f_37_6,plain,
    ( c_Groups_Ozero__class_Ozero(U_178) = U_179
    | U_179 != c_Groups_Ozero__class_Ozero(U_178)
    | ~ sP7(U_178,U_179) ),
    inference(clausify,[status(thm)],[f_37_3]) ).

fof(f_38_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_38_2,plain,
    ! [U_182,U_181,U_180] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_180),U_181),hAPP(c_fequal,U_182)))
        | U_181 != U_182 )
      & ( U_181 = U_182
        | ~ hBOOL(hAPP(hAPP(c_member(U_180),U_181),hAPP(c_fequal,U_182))) ) ),
    inference(variable_rename,[status(thm)],[f_38_1]) ).

fof(f_38_3,plain,
    ( ! [U_188,U_186] :
        ( ! [U_184] : hBOOL(hAPP(hAPP(c_member(U_184),U_186),hAPP(c_fequal,U_188)))
        | U_186 != U_188 )
    & ! [U_187,U_185] :
        ( ! [U_183] : ~ hBOOL(hAPP(hAPP(c_member(U_183),U_185),hAPP(c_fequal,U_187)))
        | U_185 = U_187 ) ),
    inference(miniscope,[status(thm)],[f_38_2]) ).

fof(f_38_4,plain,
    ( ! [U_188,U_184,U_186] :
        ( hBOOL(hAPP(hAPP(c_member(U_184),U_186),hAPP(c_fequal,U_188)))
        | U_186 != U_188 )
    & ! [U_185,U_187,U_183] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_183),U_185),hAPP(c_fequal,U_187)))
        | U_185 = U_187 ) ),
    inference(definitional_conversion,[status(esa)],[f_38_3]) ).

cnf(f_38_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_183),U_185),hAPP(c_fequal,U_187)))
    | U_185 = U_187 ),
    inference(clausify,[status(thm)],[f_38_4]) ).

cnf(f_38_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_184),U_186),hAPP(c_fequal,U_188)))
    | U_186 != U_188 ),
    inference(clausify,[status(thm)],[f_38_4]) ).

fof(f_39_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_39_2,plain,
    ! [U_192,U_191,U_190,U_189] :
      ( U_192 = U_191
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_189),U_190),U_192))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_189),U_190),U_191)) ),
    inference(variable_rename,[status(thm)],[f_39_1]) ).

fof(f_39_3,plain,
    ! [U_192,U_191,U_189,U_190] :
      ( U_192 = U_191
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_189),U_190),U_192))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_189),U_190),U_191)) ),
    inference(definitional_conversion,[status(esa)],[f_39_2]) ).

cnf(f_39_4,plain,
    ( U_192 = U_191
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_189),U_190),U_192))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_189),U_190),U_191)) ),
    inference(clausify,[status(thm)],[f_39_3]) ).

fof(f_40_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_40_2,plain,
    ! [U_196,U_195,U_194,U_193] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_193),U_194),U_196))
      | ~ c_Natural_Oevaln(U_193,U_194,U_195,U_196) ),
    inference(variable_rename,[status(thm)],[f_40_1]) ).

fof(f_40_3,plain,
    ! [U_195,U_196,U_194,U_193] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_193),U_194),U_196))
      | ~ c_Natural_Oevaln(U_193,U_194,U_195,U_196) ),
    inference(definitional_conversion,[status(esa)],[f_40_2]) ).

cnf(f_40_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_193),U_194),U_196))
    | ~ c_Natural_Oevaln(U_193,U_194,U_195,U_196) ),
    inference(clausify,[status(thm)],[f_40_3]) ).

fof(f_41_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_41_2,plain,
    ! [U_201,U_200,U_199] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_199),U_200),U_201))
        | ! [U_198] : ~ c_Natural_Oevaln(U_199,U_200,U_198,U_201) )
      & ( ? [U_197] : c_Natural_Oevaln(U_199,U_200,U_197,U_201)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_199),U_200),U_201)) ) ),
    inference(variable_rename,[status(thm)],[f_41_1]) ).

fof(f_41_3,plain,
    ( ! [U_207,U_205,U_203] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_203),U_205),U_207))
        | ! [U_198] : ~ c_Natural_Oevaln(U_203,U_205,U_198,U_207) )
    & ! [U_206,U_204,U_202] :
        ( ? [U_197] : c_Natural_Oevaln(U_202,U_204,U_197,U_206)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_202),U_204),U_206)) ) ),
    inference(miniscope,[status(thm)],[f_41_2]) ).

fof(f_41_4,plain,
    ( ! [U_207,U_205,U_203] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_203),U_205),U_207))
        | ! [U_198] : ~ c_Natural_Oevaln(U_203,U_205,U_198,U_207) )
    & ! [U_206,U_204,U_202] :
        ( c_Natural_Oevaln(U_202,U_204,sK6(U_206,U_204,U_202),U_206)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_202),U_204),U_206)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_197,sK6(U_206,U_204,U_202))],[f_41_3]) ).

fof(f_41_5,plain,
    ( ! [U_198,U_205,U_203,U_207] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_203),U_205),U_207))
        | ~ c_Natural_Oevaln(U_203,U_205,U_198,U_207) )
    & ! [U_206,U_204,U_202] :
        ( c_Natural_Oevaln(U_202,U_204,sK6(U_206,U_204,U_202),U_206)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_202),U_204),U_206)) ) ),
    inference(definitional_conversion,[status(esa)],[f_41_4]) ).

cnf(f_41_6,plain,
    ( c_Natural_Oevaln(U_202,U_204,sK6(U_206,U_204,U_202),U_206)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_202),U_204),U_206)) ),
    inference(clausify,[status(thm)],[f_41_5]) ).

cnf(f_41_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_203),U_205),U_207))
    | ~ c_Natural_Oevaln(U_203,U_205,U_198,U_207) ),
    inference(clausify,[status(thm)],[f_41_5]) ).

fof(f_42_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_42_2,plain,
    ! [U_211,U_210,U_209,U_208] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_208,U_209,hAPP(c_Nat_OSuc,U_210),U_211) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_208,U_209,U_210,hAPP(U_209,U_211))
      | ~ class_Rings_Osemiring__1(U_208) ),
    inference(variable_rename,[status(thm)],[f_42_1]) ).

fof(f_42_3,plain,
    ! [U_208,U_210,U_209,U_211] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_208,U_209,hAPP(c_Nat_OSuc,U_210),U_211) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_208,U_209,U_210,hAPP(U_209,U_211))
      | ~ class_Rings_Osemiring__1(U_208) ),
    inference(definitional_conversion,[status(esa)],[f_42_2]) ).

cnf(f_42_4,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_208,U_209,hAPP(c_Nat_OSuc,U_210),U_211) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_208,U_209,U_210,hAPP(U_209,U_211))
    | ~ class_Rings_Osemiring__1(U_208) ),
    inference(clausify,[status(thm)],[f_42_3]) ).

fof(f_43_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_43_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_43_1]) ).

cnf(f_43_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_43_2]) ).

fof(f_44_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_44_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_44_1]) ).

cnf(f_44_3,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_44_2]) ).

fof(f_45_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_45_2,plain,
    ! [U_214,U_213,U_212] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_212,U_213,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_214) = U_214
      | ~ class_Rings_Osemiring__1(U_212) ),
    inference(variable_rename,[status(thm)],[f_45_1]) ).

fof(f_45_3,plain,
    ! [U_212,U_213,U_214] :
      ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_212,U_213,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_214) = U_214
      | ~ class_Rings_Osemiring__1(U_212) ),
    inference(definitional_conversion,[status(esa)],[f_45_2]) ).

cnf(f_45_4,plain,
    ( c_Nat_Osemiring__1__class_Oof__nat__aux(U_212,U_213,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_214) = U_214
    | ~ class_Rings_Osemiring__1(U_212) ),
    inference(clausify,[status(thm)],[f_45_3]) ).

fof(f_46_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_46_2,plain,
    ! [U_218,U_217,U_216] :
      ( ? [U_215] : c_Natural_Oevaln(U_216,U_217,U_215,U_218)
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_216),U_217),U_218)) ),
    inference(variable_rename,[status(thm)],[f_46_1]) ).

fof(f_46_3,plain,
    ! [U_218,U_217,U_216] :
      ( c_Natural_Oevaln(U_216,U_217,sK7(U_218,U_217,U_216),U_218)
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_216),U_217),U_218)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_215,sK7(U_218,U_217,U_216))],[f_46_2]) ).

fof(f_46_4,plain,
    ! [U_216,U_217,U_218] :
      ( c_Natural_Oevaln(U_216,U_217,sK7(U_218,U_217,U_216),U_218)
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_216),U_217),U_218)) ),
    inference(definitional_conversion,[status(esa)],[f_46_3]) ).

cnf(f_46_5,plain,
    ( c_Natural_Oevaln(U_216,U_217,sK7(U_218,U_217,U_216),U_218)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_216),U_217),U_218)) ),
    inference(clausify,[status(thm)],[f_46_4]) ).

fof(f_47_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_47_2,plain,
    ! [U_221,U_220,U_219] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(U_219,U_220,U_221)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_47_1]) ).

fof(f_47_3,plain,
    ! [U_221,U_220,U_219] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(U_219,U_220,U_221)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_47_2]) ).

cnf(f_47_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(U_219,U_220,U_221)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_47_3]) ).

fof(f_48_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_48_2,plain,
    ! [U_224,U_223,U_222] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(U_222,U_223,U_224)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_48_1]) ).

fof(f_48_3,plain,
    ! [U_223,U_224,U_222] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(U_222,U_223,U_224)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_48_2]) ).

cnf(f_48_4,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(U_222,U_223,U_224)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_48_3]) ).

fof(f_49_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_49_2,plain,
    ! [U_226,U_225] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(U_225,U_226)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_49_1]) ).

fof(f_49_3,plain,
    ! [U_225,U_226] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(U_225,U_226)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_49_2]) ).

cnf(f_49_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OAss(U_225,U_226)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_49_3]) ).

fof(f_50_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_50_2,plain,
    ! [U_228,U_227] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(U_227,U_228)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_50_1]) ).

fof(f_50_3,plain,
    ! [U_227,U_228] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(U_227,U_228)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_50_2]) ).

cnf(f_50_4,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OAss(U_227,U_228)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_50_3]) ).

fof(f_51_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_51_2,plain,
    ! [U_229] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_229))),
    inference(variable_rename,[status(thm)],[f_51_1]) ).

fof(f_51_3,plain,
    ! [U_229] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Nat_OSuc,U_229))),
    inference(definitional_conversion,[status(esa)],[f_51_2]) ).

cnf(f_51_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_229))),
    inference(clausify,[status(thm)],[f_51_3]) ).

fof(f_52_1,plain,
    ! [V_y] :
      ( ? [B_nat] : V_y = hAPP(c_Nat_OSuc,B_nat)
      | V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(fof_nnf,[status(thm)],[fact_nat_Oexhaust]) ).

fof(f_52_2,plain,
    ! [U_231] :
      ( ? [U_230] : U_231 = hAPP(c_Nat_OSuc,U_230)
      | U_231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_52_1]) ).

fof(f_52_3,plain,
    ! [U_231] :
      ( U_231 = hAPP(c_Nat_OSuc,sK8(U_231))
      | U_231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK8]),skolemize(U_230,sK8(U_231))],[f_52_2]) ).

fof(f_52_4,plain,
    ! [U_231] :
      ( U_231 = hAPP(c_Nat_OSuc,sK8(U_231))
      | U_231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_52_3]) ).

cnf(f_52_5,plain,
    ( U_231 = hAPP(c_Nat_OSuc,sK8(U_231))
    | U_231 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_52_4]) ).

fof(f_53_1,plain,
    ! [V_k_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ? [B_n] :
          ( ~ hBOOL(hAPP(V_Pa_2,B_n))
          & hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_OSuc,B_n))) )
      | ~ hBOOL(hAPP(V_Pa_2,V_k_2)) ),
    inference(fof_nnf,[status(thm)],[fact_zero__induct]) ).

fof(f_53_2,plain,
    ! [U_234,U_233] :
      ( hBOOL(hAPP(U_233,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ? [U_232] :
          ( ~ hBOOL(hAPP(U_233,U_232))
          & hBOOL(hAPP(U_233,hAPP(c_Nat_OSuc,U_232))) )
      | ~ hBOOL(hAPP(U_233,U_234)) ),
    inference(variable_rename,[status(thm)],[f_53_1]) ).

fof(f_53_3,plain,
    ! [U_234,U_233] :
      ( hBOOL(hAPP(U_233,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ( ~ hBOOL(hAPP(U_233,sK9(U_234,U_233)))
        & hBOOL(hAPP(U_233,hAPP(c_Nat_OSuc,sK9(U_234,U_233)))) )
      | ~ hBOOL(hAPP(U_233,U_234)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK9]),skolemize(U_232,sK9(U_234,U_233))],[f_53_2]) ).

fof(f_53_4,plain,
    ( ! [U_233,U_234] :
        ( ~ hBOOL(hAPP(U_233,sK9(U_234,U_233)))
        | ~ sP8(U_233,U_234) )
    & ! [U_233,U_234] :
        ( hBOOL(hAPP(U_233,hAPP(c_Nat_OSuc,sK9(U_234,U_233))))
        | ~ sP8(U_233,U_234) )
    & ! [U_233,U_234] :
        ( hBOOL(hAPP(U_233,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | sP8(U_233,U_234)
        | ~ hBOOL(hAPP(U_233,U_234)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP8])],[f_53_3]) ).

cnf(f_53_5,plain,
    ( hBOOL(hAPP(U_233,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | sP8(U_233,U_234)
    | ~ hBOOL(hAPP(U_233,U_234)) ),
    inference(clausify,[status(thm)],[f_53_4]) ).

cnf(f_53_6,plain,
    ( hBOOL(hAPP(U_233,hAPP(c_Nat_OSuc,sK9(U_234,U_233))))
    | ~ sP8(U_233,U_234) ),
    inference(clausify,[status(thm)],[f_53_4]) ).

cnf(f_53_7,plain,
    ( ~ hBOOL(hAPP(U_233,sK9(U_234,U_233)))
    | ~ sP8(U_233,U_234) ),
    inference(clausify,[status(thm)],[f_53_4]) ).

fof(f_54_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_54_2,plain,
    ! [U_235] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_235),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_54_1]) ).

fof(f_54_3,plain,
    ! [U_235] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_235),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_54_2]) ).

cnf(f_54_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_235),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_54_3]) ).

fof(f_55_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_55_2,plain,
    ! [U_237,U_236] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_236)),hAPP(c_Nat_OSuc,U_237)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_236),U_237)) ),
    inference(variable_rename,[status(thm)],[f_55_1]) ).

fof(f_55_3,plain,
    ! [U_236,U_237] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_236)),hAPP(c_Nat_OSuc,U_237)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_236),U_237)) ),
    inference(definitional_conversion,[status(esa)],[f_55_2]) ).

cnf(f_55_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_236)),hAPP(c_Nat_OSuc,U_237)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_236),U_237)) ),
    inference(clausify,[status(thm)],[f_55_3]) ).

fof(f_56_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_56_2,plain,
    ! [U_238] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_238),hAPP(c_Nat_OSuc,U_238))),
    inference(variable_rename,[status(thm)],[f_56_1]) ).

fof(f_56_3,plain,
    ! [U_238] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_238),hAPP(c_Nat_OSuc,U_238))),
    inference(definitional_conversion,[status(esa)],[f_56_2]) ).

cnf(f_56_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_238),hAPP(c_Nat_OSuc,U_238))),
    inference(clausify,[status(thm)],[f_56_3]) ).

fof(f_57_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_57_2,plain,
    ! [U_240,U_239] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_239,U_240,U_239),
    inference(variable_rename,[status(thm)],[f_57_1]) ).

fof(f_57_3,plain,
    ! [U_239,U_240] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_239,U_240,U_239),
    inference(definitional_conversion,[status(esa)],[f_57_2]) ).

cnf(f_57_4,plain,
    c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_239,U_240,U_239),
    inference(clausify,[status(thm)],[f_57_3]) ).

fof(f_58_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_58_2,plain,
    ! [U_243,U_242,U_241] :
      ( U_243 = U_241
      | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_241,U_242,U_243) ),
    inference(variable_rename,[status(thm)],[f_58_1]) ).

fof(f_58_3,plain,
    ! [U_243,U_241,U_242] :
      ( U_243 = U_241
      | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_241,U_242,U_243) ),
    inference(definitional_conversion,[status(esa)],[f_58_2]) ).

cnf(f_58_4,plain,
    ( U_243 = U_241
    | ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_241,U_242,U_243) ),
    inference(clausify,[status(thm)],[f_58_3]) ).

fof(f_59_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_59_2,plain,
    ! [U_245,U_244] :
      ( U_245 = U_244
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_244),U_245)) ),
    inference(variable_rename,[status(thm)],[f_59_1]) ).

fof(f_59_3,plain,
    ! [U_244,U_245] :
      ( U_245 = U_244
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_244),U_245)) ),
    inference(definitional_conversion,[status(esa)],[f_59_2]) ).

cnf(f_59_4,plain,
    ( U_245 = U_244
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_244),U_245)) ),
    inference(clausify,[status(thm)],[f_59_3]) ).

fof(f_60_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_60_2,plain,
    ! [U_246] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_246),U_246)),
    inference(variable_rename,[status(thm)],[f_60_1]) ).

fof(f_60_3,plain,
    ! [U_246] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_246),U_246)),
    inference(definitional_conversion,[status(esa)],[f_60_2]) ).

cnf(f_60_4,plain,
    hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_246),U_246)),
    inference(clausify,[status(thm)],[f_60_3]) ).

fof(f_61_1,plain,
    ! [V_Pa_2,V_n_2,V_m_2] :
      ( hBOOL(hAPP(hAPP(V_Pa_2,V_n_2),V_m_2))
      | ( ~ hBOOL(hAPP(hAPP(V_Pa_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_Pa_2,V_n_2),V_m_2))
        & V_m_2 = V_n_2 )
      | ( ~ hBOOL(hAPP(hAPP(V_Pa_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_61_2,plain,
    ! [U_249,U_248,U_247] :
      ( hBOOL(hAPP(hAPP(U_249,U_248),U_247))
      | ( ~ hBOOL(hAPP(hAPP(U_249,U_248),U_247))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_248),U_247)) )
      | ( ~ hBOOL(hAPP(hAPP(U_249,U_248),U_247))
        & U_247 = U_248 )
      | ( ~ hBOOL(hAPP(hAPP(U_249,U_248),U_247))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_247),U_248)) ) ),
    inference(variable_rename,[status(thm)],[f_61_1]) ).

fof(f_61_3,plain,
    ( ! [U_248,U_247,U_249] :
        ( ~ hBOOL(hAPP(hAPP(U_249,U_248),U_247))
        | ~ sP11(U_248,U_247,U_249) )
    & ! [U_248,U_247,U_249] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_248),U_247))
        | ~ sP11(U_248,U_247,U_249) )
    & ! [U_248,U_247,U_249] :
        ( ~ hBOOL(hAPP(hAPP(U_249,U_248),U_247))
        | ~ sP10(U_248,U_247,U_249) )
    & ! [U_248,U_247,U_249] :
        ( U_247 = U_248
        | ~ sP10(U_248,U_247,U_249) )
    & ! [U_248,U_247,U_249] :
        ( ~ hBOOL(hAPP(hAPP(U_249,U_248),U_247))
        | ~ sP9(U_248,U_247,U_249) )
    & ! [U_248,U_247,U_249] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_247),U_248))
        | ~ sP9(U_248,U_247,U_249) )
    & ! [U_248,U_247,U_249] :
        ( hBOOL(hAPP(hAPP(U_249,U_248),U_247))
        | sP11(U_248,U_247,U_249)
        | sP10(U_248,U_247,U_249)
        | sP9(U_248,U_247,U_249) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP9,sP10,sP11])],[f_61_2]) ).

cnf(f_61_4,plain,
    ( hBOOL(hAPP(hAPP(U_249,U_248),U_247))
    | sP11(U_248,U_247,U_249)
    | sP10(U_248,U_247,U_249)
    | sP9(U_248,U_247,U_249) ),
    inference(clausify,[status(thm)],[f_61_3]) ).

cnf(f_61_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_247),U_248))
    | ~ sP9(U_248,U_247,U_249) ),
    inference(clausify,[status(thm)],[f_61_3]) ).

cnf(f_61_6,plain,
    ( ~ hBOOL(hAPP(hAPP(U_249,U_248),U_247))
    | ~ sP9(U_248,U_247,U_249) ),
    inference(clausify,[status(thm)],[f_61_3]) ).

cnf(f_61_7,plain,
    ( U_247 = U_248
    | ~ sP10(U_248,U_247,U_249) ),
    inference(clausify,[status(thm)],[f_61_3]) ).

cnf(f_61_8,plain,
    ( ~ hBOOL(hAPP(hAPP(U_249,U_248),U_247))
    | ~ sP10(U_248,U_247,U_249) ),
    inference(clausify,[status(thm)],[f_61_3]) ).

cnf(f_61_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_248),U_247))
    | ~ sP11(U_248,U_247,U_249) ),
    inference(clausify,[status(thm)],[f_61_3]) ).

cnf(f_61_10,plain,
    ( ~ hBOOL(hAPP(hAPP(U_249,U_248),U_247))
    | ~ sP11(U_248,U_247,U_249) ),
    inference(clausify,[status(thm)],[f_61_3]) ).

fof(f_62_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_62_2,plain,
    ! [U_251,U_250] :
      ( U_250 != U_251
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_250),U_251)) ),
    inference(variable_rename,[status(thm)],[f_62_1]) ).

fof(f_62_3,plain,
    ! [U_251,U_250] :
      ( U_250 != U_251
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_250),U_251)) ),
    inference(definitional_conversion,[status(esa)],[f_62_2]) ).

cnf(f_62_4,plain,
    ( U_250 != U_251
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_250),U_251)) ),
    inference(clausify,[status(thm)],[f_62_3]) ).

fof(f_63_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_63_2,plain,
    ! [U_253,U_252] :
      ( U_253 != U_252
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_252),U_253)) ),
    inference(variable_rename,[status(thm)],[f_63_1]) ).

fof(f_63_3,plain,
    ! [U_253,U_252] :
      ( U_253 != U_252
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_252),U_253)) ),
    inference(definitional_conversion,[status(esa)],[f_63_2]) ).

cnf(f_63_4,plain,
    ( U_253 != U_252
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_252),U_253)) ),
    inference(clausify,[status(thm)],[f_63_3]) ).

fof(f_64_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_64_2,plain,
    ! [U_254] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_254),U_254)),
    inference(variable_rename,[status(thm)],[f_64_1]) ).

fof(f_64_3,plain,
    ! [U_254] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_254),U_254)),
    inference(definitional_conversion,[status(esa)],[f_64_2]) ).

cnf(f_64_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_254),U_254)),
    inference(clausify,[status(thm)],[f_64_3]) ).

fof(f_65_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_65_2,plain,
    ! [U_256,U_255] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_256),U_255))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_255),U_256))
      | U_255 = U_256 ),
    inference(variable_rename,[status(thm)],[f_65_1]) ).

fof(f_65_3,plain,
    ! [U_255,U_256] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_256),U_255))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_255),U_256))
      | U_255 = U_256 ),
    inference(definitional_conversion,[status(esa)],[f_65_2]) ).

cnf(f_65_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_256),U_255))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_255),U_256))
    | U_255 = U_256 ),
    inference(clausify,[status(thm)],[f_65_3]) ).

fof(f_66_1,plain,
    ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_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_66_2,plain,
    ! [U_262,U_261,U_260,U_259,U_258,U_257] :
      ( ( c_Com_Ocom_OCall(U_257,U_258,U_259) = c_Com_Ocom_OCall(U_260,U_261,U_262)
        | U_259 != U_262
        | U_258 != U_261
        | U_257 != U_260 )
      & ( ( U_259 = U_262
          & U_258 = U_261
          & U_257 = U_260 )
        | c_Com_Ocom_OCall(U_257,U_258,U_259) != c_Com_Ocom_OCall(U_260,U_261,U_262) ) ),
    inference(variable_rename,[status(thm)],[f_66_1]) ).

fof(f_66_3,plain,
    ( ! [U_274,U_272,U_270,U_268,U_266,U_264] :
        ( c_Com_Ocom_OCall(U_264,U_266,U_268) = c_Com_Ocom_OCall(U_270,U_272,U_274)
        | U_268 != U_274
        | U_266 != U_272
        | U_264 != U_270 )
    & ! [U_273,U_271,U_269,U_267,U_265,U_263] :
        ( ( U_267 = U_273
          & U_265 = U_271
          & U_263 = U_269 )
        | c_Com_Ocom_OCall(U_263,U_265,U_267) != c_Com_Ocom_OCall(U_269,U_271,U_273) ) ),
    inference(miniscope,[status(thm)],[f_66_2]) ).

fof(f_66_4,plain,
    ( ! [U_269,U_273,U_263,U_267,U_265,U_271] :
        ( U_267 = U_273
        | ~ sP12(U_269,U_273,U_263,U_267,U_265,U_271) )
    & ! [U_269,U_273,U_263,U_267,U_265,U_271] :
        ( U_265 = U_271
        | ~ sP12(U_269,U_273,U_263,U_267,U_265,U_271) )
    & ! [U_269,U_273,U_263,U_267,U_265,U_271] :
        ( U_263 = U_269
        | ~ sP12(U_269,U_273,U_263,U_267,U_265,U_271) )
    & ! [U_266,U_270,U_264,U_268,U_272,U_274] :
        ( c_Com_Ocom_OCall(U_264,U_266,U_268) = c_Com_Ocom_OCall(U_270,U_272,U_274)
        | U_268 != U_274
        | U_266 != U_272
        | U_264 != U_270 )
    & ! [U_269,U_273,U_263,U_267,U_265,U_271] :
        ( sP12(U_269,U_273,U_263,U_267,U_265,U_271)
        | c_Com_Ocom_OCall(U_263,U_265,U_267) != c_Com_Ocom_OCall(U_269,U_271,U_273) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP12])],[f_66_3]) ).

cnf(f_66_5,plain,
    ( sP12(U_269,U_273,U_263,U_267,U_265,U_271)
    | c_Com_Ocom_OCall(U_263,U_265,U_267) != c_Com_Ocom_OCall(U_269,U_271,U_273) ),
    inference(clausify,[status(thm)],[f_66_4]) ).

cnf(f_66_6,plain,
    ( c_Com_Ocom_OCall(U_264,U_266,U_268) = c_Com_Ocom_OCall(U_270,U_272,U_274)
    | U_268 != U_274
    | U_266 != U_272
    | U_264 != U_270 ),
    inference(clausify,[status(thm)],[f_66_4]) ).

cnf(f_66_7,plain,
    ( U_263 = U_269
    | ~ sP12(U_269,U_273,U_263,U_267,U_265,U_271) ),
    inference(clausify,[status(thm)],[f_66_4]) ).

cnf(f_66_8,plain,
    ( U_265 = U_271
    | ~ sP12(U_269,U_273,U_263,U_267,U_265,U_271) ),
    inference(clausify,[status(thm)],[f_66_4]) ).

cnf(f_66_9,plain,
    ( U_267 = U_273
    | ~ sP12(U_269,U_273,U_263,U_267,U_265,U_271) ),
    inference(clausify,[status(thm)],[f_66_4]) ).

fof(f_67_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_67_2,plain,
    ! [U_278,U_277,U_276,U_275] :
      ( ( c_Com_Ocom_OAss(U_275,U_276) = c_Com_Ocom_OAss(U_277,U_278)
        | U_276 != U_278
        | U_275 != U_277 )
      & ( ( U_276 = U_278
          & U_275 = U_277 )
        | c_Com_Ocom_OAss(U_275,U_276) != c_Com_Ocom_OAss(U_277,U_278) ) ),
    inference(variable_rename,[status(thm)],[f_67_1]) ).

fof(f_67_3,plain,
    ( ! [U_286,U_284,U_282,U_280] :
        ( c_Com_Ocom_OAss(U_280,U_282) = c_Com_Ocom_OAss(U_284,U_286)
        | U_282 != U_286
        | U_280 != U_284 )
    & ! [U_285,U_283,U_281,U_279] :
        ( ( U_281 = U_285
          & U_279 = U_283 )
        | c_Com_Ocom_OAss(U_279,U_281) != c_Com_Ocom_OAss(U_283,U_285) ) ),
    inference(miniscope,[status(thm)],[f_67_2]) ).

fof(f_67_4,plain,
    ( ! [U_281,U_279,U_285,U_283] :
        ( U_281 = U_285
        | ~ sP13(U_281,U_279,U_285,U_283) )
    & ! [U_281,U_279,U_285,U_283] :
        ( U_279 = U_283
        | ~ sP13(U_281,U_279,U_285,U_283) )
    & ! [U_286,U_282,U_284,U_280] :
        ( c_Com_Ocom_OAss(U_280,U_282) = c_Com_Ocom_OAss(U_284,U_286)
        | U_282 != U_286
        | U_280 != U_284 )
    & ! [U_281,U_279,U_285,U_283] :
        ( sP13(U_281,U_279,U_285,U_283)
        | c_Com_Ocom_OAss(U_279,U_281) != c_Com_Ocom_OAss(U_283,U_285) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP13])],[f_67_3]) ).

cnf(f_67_5,plain,
    ( sP13(U_281,U_279,U_285,U_283)
    | c_Com_Ocom_OAss(U_279,U_281) != c_Com_Ocom_OAss(U_283,U_285) ),
    inference(clausify,[status(thm)],[f_67_4]) ).

cnf(f_67_6,plain,
    ( c_Com_Ocom_OAss(U_280,U_282) = c_Com_Ocom_OAss(U_284,U_286)
    | U_282 != U_286
    | U_280 != U_284 ),
    inference(clausify,[status(thm)],[f_67_4]) ).

cnf(f_67_7,plain,
    ( U_279 = U_283
    | ~ sP13(U_281,U_279,U_285,U_283) ),
    inference(clausify,[status(thm)],[f_67_4]) ).

cnf(f_67_8,plain,
    ( U_281 = U_285
    | ~ sP13(U_281,U_279,U_285,U_283) ),
    inference(clausify,[status(thm)],[f_67_4]) ).

fof(f_68_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_68_2,plain,
    ! [U_288,U_287] :
      ( ( U_287 != U_288
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_288),U_287))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_287),U_288)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_288),U_287))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_287),U_288))
        | U_287 = U_288 ) ),
    inference(variable_rename,[status(thm)],[f_68_1]) ).

fof(f_68_3,plain,
    ( ! [U_292,U_290] :
        ( U_290 != U_292
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_292),U_290))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_290),U_292)) ) )
    & ! [U_291,U_289] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_291),U_289))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_289),U_291))
        | U_289 = U_291 ) ),
    inference(miniscope,[status(thm)],[f_68_2]) ).

fof(f_68_4,plain,
    ( ! [U_292,U_290] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_292),U_290))
        | ~ sP14(U_292,U_290) )
    & ! [U_292,U_290] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_290),U_292))
        | ~ sP14(U_292,U_290) )
    & ! [U_292,U_290] :
        ( U_290 != U_292
        | sP14(U_292,U_290) )
    & ! [U_291,U_289] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_291),U_289))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_289),U_291))
        | U_289 = U_291 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP14])],[f_68_3]) ).

cnf(f_68_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_291),U_289))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_289),U_291))
    | U_289 = U_291 ),
    inference(clausify,[status(thm)],[f_68_4]) ).

cnf(f_68_6,plain,
    ( U_290 != U_292
    | sP14(U_292,U_290) ),
    inference(clausify,[status(thm)],[f_68_4]) ).

cnf(f_68_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_290),U_292))
    | ~ sP14(U_292,U_290) ),
    inference(clausify,[status(thm)],[f_68_4]) ).

cnf(f_68_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_292),U_290))
    | ~ sP14(U_292,U_290) ),
    inference(clausify,[status(thm)],[f_68_4]) ).

fof(f_69_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_69_2,plain,
    ! [U_297,U_296,U_295,U_294,U_293] : c_Com_Ocom_OCall(U_293,U_294,U_295) != c_Com_Ocom_OAss(U_296,U_297),
    inference(variable_rename,[status(thm)],[f_69_1]) ).

fof(f_69_3,plain,
    ! [U_294,U_297,U_293,U_295,U_296] : c_Com_Ocom_OCall(U_293,U_294,U_295) != c_Com_Ocom_OAss(U_296,U_297),
    inference(definitional_conversion,[status(esa)],[f_69_2]) ).

cnf(f_69_4,plain,
    c_Com_Ocom_OCall(U_293,U_294,U_295) != c_Com_Ocom_OAss(U_296,U_297),
    inference(clausify,[status(thm)],[f_69_3]) ).

fof(f_70_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_70_2,plain,
    ! [U_300,U_299,U_298] : c_Com_Ocom_OCall(U_298,U_299,U_300) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_70_1]) ).

fof(f_70_3,plain,
    ! [U_299,U_298,U_300] : c_Com_Ocom_OCall(U_298,U_299,U_300) != c_Com_Ocom_OSKIP,
    inference(definitional_conversion,[status(esa)],[f_70_2]) ).

cnf(f_70_4,plain,
    c_Com_Ocom_OCall(U_298,U_299,U_300) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_70_3]) ).

fof(f_71_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_71_2,plain,
    ! [U_305,U_304,U_303,U_302,U_301] : c_Com_Ocom_OAss(U_301,U_302) != c_Com_Ocom_OCall(U_303,U_304,U_305),
    inference(variable_rename,[status(thm)],[f_71_1]) ).

fof(f_71_3,plain,
    ! [U_301,U_302,U_303,U_304,U_305] : c_Com_Ocom_OAss(U_301,U_302) != c_Com_Ocom_OCall(U_303,U_304,U_305),
    inference(definitional_conversion,[status(esa)],[f_71_2]) ).

cnf(f_71_4,plain,
    c_Com_Ocom_OAss(U_301,U_302) != c_Com_Ocom_OCall(U_303,U_304,U_305),
    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_307,U_306] : c_Com_Ocom_OAss(U_306,U_307) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_72_1]) ).

fof(f_72_3,plain,
    ! [U_306,U_307] : c_Com_Ocom_OAss(U_306,U_307) != c_Com_Ocom_OSKIP,
    inference(definitional_conversion,[status(esa)],[f_72_2]) ).

cnf(f_72_4,plain,
    c_Com_Ocom_OAss(U_306,U_307) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_72_3]) ).

fof(f_73_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_73_2,plain,
    ! [U_308] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_308),U_308)),
    inference(variable_rename,[status(thm)],[f_73_1]) ).

fof(f_73_3,plain,
    ! [U_308] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_308),U_308)),
    inference(definitional_conversion,[status(esa)],[f_73_2]) ).

cnf(f_73_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_308),U_308)),
    inference(clausify,[status(thm)],[f_73_3]) ).

fof(f_74_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_74_2,plain,
    ! [U_311,U_310,U_309] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(U_309,U_310,U_311),
    inference(variable_rename,[status(thm)],[f_74_1]) ).

fof(f_74_3,plain,
    ! [U_310,U_309,U_311] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(U_309,U_310,U_311),
    inference(definitional_conversion,[status(esa)],[f_74_2]) ).

cnf(f_74_4,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(U_309,U_310,U_311),
    inference(clausify,[status(thm)],[f_74_3]) ).

fof(f_75_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_75_2,plain,
    ! [U_313,U_312] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(U_312,U_313),
    inference(variable_rename,[status(thm)],[f_75_1]) ).

fof(f_75_3,plain,
    ! [U_312,U_313] : c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(U_312,U_313),
    inference(definitional_conversion,[status(esa)],[f_75_2]) ).

cnf(f_75_4,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OAss(U_312,U_313),
    inference(clausify,[status(thm)],[f_75_3]) ).

fof(f_76_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_76_2,plain,
    ! [U_314] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_314),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_76_1]) ).

fof(f_76_3,plain,
    ! [U_314] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_314),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_76_2]) ).

cnf(f_76_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_314),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_76_3]) ).

fof(f_77_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_77_2,plain,
    ! [U_315] :
      ( ( U_315 != 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_315)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_315))
        | U_315 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_77_1]) ).

fof(f_77_3,plain,
    ( ! [U_317] :
        ( U_317 != 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_317)) )
    & ! [U_316] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_316))
        | U_316 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_77_2]) ).

fof(f_77_4,plain,
    ( ! [U_317] :
        ( U_317 != 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_317)) )
    & ! [U_316] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_316))
        | U_316 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_77_3]) ).

cnf(f_77_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_316))
    | U_316 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_77_4]) ).

cnf(f_77_6,plain,
    ( U_317 != 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_317)) ),
    inference(clausify,[status(thm)],[f_77_4]) ).

fof(f_78_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_78_2,plain,
    ! [U_318] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_318),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_78_1]) ).

fof(f_78_3,plain,
    ! [U_318] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_318),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_78_2]) ).

cnf(f_78_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_318),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_78_3]) ).

fof(f_79_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_79_2,plain,
    ! [U_320,U_319] :
      ( U_320 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_319),U_320)) ),
    inference(variable_rename,[status(thm)],[f_79_1]) ).

fof(f_79_3,plain,
    ! [U_320] :
      ( ! [U_319] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_319),U_320))
      | U_320 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(miniscope,[status(thm)],[f_79_2]) ).

fof(f_79_4,plain,
    ! [U_319,U_320] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_319),U_320))
      | U_320 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_79_3]) ).

cnf(f_79_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_319),U_320))
    | U_320 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_79_4]) ).

fof(f_80_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_80_2,plain,
    ! [U_321] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_321))
      | U_321 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_80_1]) ).

fof(f_80_3,plain,
    ! [U_321] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_321))
      | U_321 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_80_2]) ).

cnf(f_80_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_321))
    | U_321 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_80_3]) ).

fof(f_81_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_81_2,plain,
    ! [U_323,U_322] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_322),U_323))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_322)),hAPP(c_Nat_OSuc,U_323))) ),
    inference(variable_rename,[status(thm)],[f_81_1]) ).

fof(f_81_3,plain,
    ! [U_322,U_323] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_322),U_323))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_322)),hAPP(c_Nat_OSuc,U_323))) ),
    inference(definitional_conversion,[status(esa)],[f_81_2]) ).

cnf(f_81_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_322),U_323))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_322)),hAPP(c_Nat_OSuc,U_323))) ),
    inference(clausify,[status(thm)],[f_81_3]) ).

fof(f_82_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_82_2,plain,
    ! [U_325,U_324] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_324),U_325))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_324)),U_325)) ),
    inference(variable_rename,[status(thm)],[f_82_1]) ).

fof(f_82_3,plain,
    ! [U_324,U_325] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_324),U_325))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_324)),U_325)) ),
    inference(definitional_conversion,[status(esa)],[f_82_2]) ).

cnf(f_82_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_324),U_325))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_324)),U_325)) ),
    inference(clausify,[status(thm)],[f_82_3]) ).

fof(f_83_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_83_2,plain,
    ! [U_327,U_326] :
      ( U_326 = U_327
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_326),U_327))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_326),hAPP(c_Nat_OSuc,U_327))) ),
    inference(variable_rename,[status(thm)],[f_83_1]) ).

fof(f_83_3,plain,
    ! [U_326,U_327] :
      ( U_326 = U_327
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_326),U_327))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_326),hAPP(c_Nat_OSuc,U_327))) ),
    inference(definitional_conversion,[status(esa)],[f_83_2]) ).

cnf(f_83_4,plain,
    ( U_326 = U_327
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_326),U_327))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_326),hAPP(c_Nat_OSuc,U_327))) ),
    inference(clausify,[status(thm)],[f_83_3]) ).

fof(f_84_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_84_2,plain,
    ! [U_330,U_329,U_328] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_328)),U_330))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_329),U_330))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_328),U_329)) ),
    inference(variable_rename,[status(thm)],[f_84_1]) ).

fof(f_84_3,plain,
    ! [U_328,U_329,U_330] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_328)),U_330))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_329),U_330))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_328),U_329)) ),
    inference(definitional_conversion,[status(esa)],[f_84_2]) ).

cnf(f_84_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_328)),U_330))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_329),U_330))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_328),U_329)) ),
    inference(clausify,[status(thm)],[f_84_3]) ).

fof(f_85_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_85_2,plain,
    ! [U_332,U_331] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_331)),U_332))
      | hAPP(c_Nat_OSuc,U_331) = U_332
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_331),U_332)) ),
    inference(variable_rename,[status(thm)],[f_85_1]) ).

fof(f_85_3,plain,
    ! [U_331,U_332] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_331)),U_332))
      | hAPP(c_Nat_OSuc,U_331) = U_332
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_331),U_332)) ),
    inference(definitional_conversion,[status(esa)],[f_85_2]) ).

cnf(f_85_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_331)),U_332))
    | hAPP(c_Nat_OSuc,U_331) = U_332
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_331),U_332)) ),
    inference(clausify,[status(thm)],[f_85_3]) ).

fof(f_86_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_86_2,plain,
    ! [U_334,U_333] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_333),hAPP(c_Nat_OSuc,U_334)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_333),U_334)) ),
    inference(variable_rename,[status(thm)],[f_86_1]) ).

fof(f_86_3,plain,
    ! [U_334,U_333] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_333),hAPP(c_Nat_OSuc,U_334)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_333),U_334)) ),
    inference(definitional_conversion,[status(esa)],[f_86_2]) ).

cnf(f_86_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_333),hAPP(c_Nat_OSuc,U_334)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_333),U_334)) ),
    inference(clausify,[status(thm)],[f_86_3]) ).

fof(f_87_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_87_2,plain,
    ! [U_336,U_335] :
      ( U_336 = U_335
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_335),hAPP(c_Nat_OSuc,U_336)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_335),U_336)) ),
    inference(variable_rename,[status(thm)],[f_87_1]) ).

fof(f_87_3,plain,
    ! [U_335,U_336] :
      ( U_336 = U_335
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_335),hAPP(c_Nat_OSuc,U_336)))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_335),U_336)) ),
    inference(definitional_conversion,[status(esa)],[f_87_2]) ).

cnf(f_87_4,plain,
    ( U_336 = U_335
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_335),hAPP(c_Nat_OSuc,U_336)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_335),U_336)) ),
    inference(clausify,[status(thm)],[f_87_3]) ).

fof(f_88_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_88_2,plain,
    ! [U_338,U_337] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_337),hAPP(c_Nat_OSuc,U_338)))
          | U_337 != U_338 )
        & ( U_337 = U_338
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_337),hAPP(c_Nat_OSuc,U_338))) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_337),U_338)) ),
    inference(variable_rename,[status(thm)],[f_88_1]) ).

fof(f_88_3,plain,
    ( ! [U_338,U_337] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_337),hAPP(c_Nat_OSuc,U_338)))
        | U_337 != U_338
        | ~ sP15(U_338,U_337) )
    & ! [U_338,U_337] :
        ( U_337 = U_338
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_337),hAPP(c_Nat_OSuc,U_338)))
        | ~ sP15(U_338,U_337) )
    & ! [U_338,U_337] :
        ( sP15(U_338,U_337)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_337),U_338)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP15])],[f_88_2]) ).

cnf(f_88_4,plain,
    ( sP15(U_338,U_337)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_337),U_338)) ),
    inference(clausify,[status(thm)],[f_88_3]) ).

cnf(f_88_5,plain,
    ( U_337 = U_338
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_337),hAPP(c_Nat_OSuc,U_338)))
    | ~ sP15(U_338,U_337) ),
    inference(clausify,[status(thm)],[f_88_3]) ).

cnf(f_88_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_337),hAPP(c_Nat_OSuc,U_338)))
    | U_337 != U_338
    | ~ sP15(U_338,U_337) ),
    inference(clausify,[status(thm)],[f_88_3]) ).

fof(f_89_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_89_2,plain,
    ! [U_340,U_339] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_339)),hAPP(c_Nat_OSuc,U_340)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_339),U_340)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_339),U_340))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_339)),hAPP(c_Nat_OSuc,U_340))) ) ),
    inference(variable_rename,[status(thm)],[f_89_1]) ).

fof(f_89_3,plain,
    ( ! [U_344,U_342] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_342)),hAPP(c_Nat_OSuc,U_344)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_342),U_344)) )
    & ! [U_343,U_341] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_341),U_343))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_341)),hAPP(c_Nat_OSuc,U_343))) ) ),
    inference(miniscope,[status(thm)],[f_89_2]) ).

fof(f_89_4,plain,
    ( ! [U_342,U_344] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_342)),hAPP(c_Nat_OSuc,U_344)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_342),U_344)) )
    & ! [U_341,U_343] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_341),U_343))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_341)),hAPP(c_Nat_OSuc,U_343))) ) ),
    inference(definitional_conversion,[status(esa)],[f_89_3]) ).

cnf(f_89_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_341),U_343))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_341)),hAPP(c_Nat_OSuc,U_343))) ),
    inference(clausify,[status(thm)],[f_89_4]) ).

cnf(f_89_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_342)),hAPP(c_Nat_OSuc,U_344)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_342),U_344)) ),
    inference(clausify,[status(thm)],[f_89_4]) ).

fof(f_90_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_90_2,plain,
    ! [U_346,U_345] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_345),hAPP(c_Nat_OSuc,U_346)))
        | ( U_345 != U_346
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_345),U_346)) ) )
      & ( U_345 = U_346
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_345),U_346))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_345),hAPP(c_Nat_OSuc,U_346))) ) ),
    inference(variable_rename,[status(thm)],[f_90_1]) ).

fof(f_90_3,plain,
    ( ! [U_350,U_348] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_348),hAPP(c_Nat_OSuc,U_350)))
        | ( U_348 != U_350
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_348),U_350)) ) )
    & ! [U_349,U_347] :
        ( U_347 = U_349
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_347),U_349))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_347),hAPP(c_Nat_OSuc,U_349))) ) ),
    inference(miniscope,[status(thm)],[f_90_2]) ).

fof(f_90_4,plain,
    ( ! [U_350,U_348] :
        ( U_348 != U_350
        | ~ sP16(U_350,U_348) )
    & ! [U_350,U_348] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_348),U_350))
        | ~ sP16(U_350,U_348) )
    & ! [U_350,U_348] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_348),hAPP(c_Nat_OSuc,U_350)))
        | sP16(U_350,U_348) )
    & ! [U_349,U_347] :
        ( U_347 = U_349
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_347),U_349))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_347),hAPP(c_Nat_OSuc,U_349))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP16])],[f_90_3]) ).

cnf(f_90_5,plain,
    ( U_347 = U_349
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_347),U_349))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_347),hAPP(c_Nat_OSuc,U_349))) ),
    inference(clausify,[status(thm)],[f_90_4]) ).

cnf(f_90_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_348),hAPP(c_Nat_OSuc,U_350)))
    | sP16(U_350,U_348) ),
    inference(clausify,[status(thm)],[f_90_4]) ).

cnf(f_90_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_348),U_350))
    | ~ sP16(U_350,U_348) ),
    inference(clausify,[status(thm)],[f_90_4]) ).

cnf(f_90_8,plain,
    ( U_348 != U_350
    | ~ sP16(U_350,U_348) ),
    inference(clausify,[status(thm)],[f_90_4]) ).

fof(f_91_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_91_2,plain,
    ! [U_352,U_351] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_351),U_352))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_352),hAPP(c_Nat_OSuc,U_351))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_352),hAPP(c_Nat_OSuc,U_351)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_351),U_352)) ) ),
    inference(variable_rename,[status(thm)],[f_91_1]) ).

fof(f_91_3,plain,
    ( ! [U_356,U_354] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_354),U_356))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_356),hAPP(c_Nat_OSuc,U_354))) )
    & ! [U_355,U_353] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_355),hAPP(c_Nat_OSuc,U_353)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_353),U_355)) ) ),
    inference(miniscope,[status(thm)],[f_91_2]) ).

fof(f_91_4,plain,
    ( ! [U_354,U_356] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_354),U_356))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_356),hAPP(c_Nat_OSuc,U_354))) )
    & ! [U_355,U_353] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_355),hAPP(c_Nat_OSuc,U_353)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_353),U_355)) ) ),
    inference(definitional_conversion,[status(esa)],[f_91_3]) ).

cnf(f_91_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_355),hAPP(c_Nat_OSuc,U_353)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_353),U_355)) ),
    inference(clausify,[status(thm)],[f_91_4]) ).

cnf(f_91_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_354),U_356))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_356),hAPP(c_Nat_OSuc,U_354))) ),
    inference(clausify,[status(thm)],[f_91_4]) ).

fof(f_92_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_92_2,plain,
    ! [U_359,U_358,U_357] : c_Com_Ocom_OAss(U_357,U_358) != hAPP(c_Com_Ocom_OBODY,U_359),
    inference(variable_rename,[status(thm)],[f_92_1]) ).

fof(f_92_3,plain,
    ! [U_357,U_358,U_359] : c_Com_Ocom_OAss(U_357,U_358) != hAPP(c_Com_Ocom_OBODY,U_359),
    inference(definitional_conversion,[status(esa)],[f_92_2]) ).

cnf(f_92_4,plain,
    c_Com_Ocom_OAss(U_357,U_358) != hAPP(c_Com_Ocom_OBODY,U_359),
    inference(clausify,[status(thm)],[f_92_3]) ).

fof(f_93_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_93_2,plain,
    ! [U_362,U_361,U_360] : hAPP(c_Com_Ocom_OBODY,U_360) != c_Com_Ocom_OAss(U_361,U_362),
    inference(variable_rename,[status(thm)],[f_93_1]) ).

fof(f_93_3,plain,
    ! [U_360,U_361,U_362] : hAPP(c_Com_Ocom_OBODY,U_360) != c_Com_Ocom_OAss(U_361,U_362),
    inference(definitional_conversion,[status(esa)],[f_93_2]) ).

cnf(f_93_4,plain,
    hAPP(c_Com_Ocom_OBODY,U_360) != c_Com_Ocom_OAss(U_361,U_362),
    inference(clausify,[status(thm)],[f_93_3]) ).

fof(f_94_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_94_2,plain,
    ! [U_366,U_365,U_364,U_363] : c_Com_Ocom_OCall(U_363,U_364,U_365) != hAPP(c_Com_Ocom_OBODY,U_366),
    inference(variable_rename,[status(thm)],[f_94_1]) ).

fof(f_94_3,plain,
    ! [U_364,U_363,U_365,U_366] : c_Com_Ocom_OCall(U_363,U_364,U_365) != hAPP(c_Com_Ocom_OBODY,U_366),
    inference(definitional_conversion,[status(esa)],[f_94_2]) ).

cnf(f_94_4,plain,
    c_Com_Ocom_OCall(U_363,U_364,U_365) != hAPP(c_Com_Ocom_OBODY,U_366),
    inference(clausify,[status(thm)],[f_94_3]) ).

fof(f_95_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_95_2,plain,
    ! [U_370,U_369,U_368,U_367] : hAPP(c_Com_Ocom_OBODY,U_367) != c_Com_Ocom_OCall(U_368,U_369,U_370),
    inference(variable_rename,[status(thm)],[f_95_1]) ).

fof(f_95_3,plain,
    ! [U_367,U_368,U_369,U_370] : hAPP(c_Com_Ocom_OBODY,U_367) != c_Com_Ocom_OCall(U_368,U_369,U_370),
    inference(definitional_conversion,[status(esa)],[f_95_2]) ).

cnf(f_95_4,plain,
    hAPP(c_Com_Ocom_OBODY,U_367) != c_Com_Ocom_OCall(U_368,U_369,U_370),
    inference(clausify,[status(thm)],[f_95_3]) ).

fof(f_96_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_96_2,plain,
    ! [U_372,U_371] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_371,U_372,U_371),
    inference(variable_rename,[status(thm)],[f_96_1]) ).

fof(f_96_3,plain,
    ! [U_371,U_372] : c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_371,U_372,U_371),
    inference(definitional_conversion,[status(esa)],[f_96_2]) ).

cnf(f_96_4,plain,
    c_Natural_Oevaln(c_Com_Ocom_OSKIP,U_371,U_372,U_371),
    inference(clausify,[status(thm)],[f_96_3]) ).

fof(f_97_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_97_2,plain,
    ! [U_373] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_373),U_373)),
    inference(variable_rename,[status(thm)],[f_97_1]) ).

fof(f_97_3,plain,
    ! [U_373] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_373),U_373)),
    inference(definitional_conversion,[status(esa)],[f_97_2]) ).

cnf(f_97_4,plain,
    hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),U_373),U_373)),
    inference(clausify,[status(thm)],[f_97_3]) ).

fof(f_98_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_98_2,plain,
    ! [U_374] : hAPP(c_Com_Ocom_OBODY,U_374) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_98_1]) ).

fof(f_98_3,plain,
    ! [U_374] : hAPP(c_Com_Ocom_OBODY,U_374) != c_Com_Ocom_OSKIP,
    inference(definitional_conversion,[status(esa)],[f_98_2]) ).

cnf(f_98_4,plain,
    hAPP(c_Com_Ocom_OBODY,U_374) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_98_3]) ).

fof(f_99_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_99_2,plain,
    ! [U_375] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,U_375),
    inference(variable_rename,[status(thm)],[f_99_1]) ).

fof(f_99_3,plain,
    ! [U_375] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,U_375),
    inference(definitional_conversion,[status(esa)],[f_99_2]) ).

cnf(f_99_4,plain,
    c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,U_375),
    inference(clausify,[status(thm)],[f_99_3]) ).

fof(f_100_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_100_2,plain,
    ! [U_378] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_378))
        | ! [U_377] : U_378 != hAPP(c_Nat_OSuc,U_377) )
      & ( ? [U_376] : U_378 = hAPP(c_Nat_OSuc,U_376)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_378)) ) ),
    inference(variable_rename,[status(thm)],[f_100_1]) ).

fof(f_100_3,plain,
    ( ! [U_380] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_380))
        | ! [U_377] : U_380 != hAPP(c_Nat_OSuc,U_377) )
    & ! [U_379] :
        ( ? [U_376] : U_379 = hAPP(c_Nat_OSuc,U_376)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_379)) ) ),
    inference(miniscope,[status(thm)],[f_100_2]) ).

fof(f_100_4,plain,
    ( ! [U_380] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_380))
        | ! [U_377] : U_380 != hAPP(c_Nat_OSuc,U_377) )
    & ! [U_379] :
        ( U_379 = hAPP(c_Nat_OSuc,sK10(U_379))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_379)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(U_376,sK10(U_379))],[f_100_3]) ).

fof(f_100_5,plain,
    ( ! [U_377,U_380] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_380))
        | U_380 != hAPP(c_Nat_OSuc,U_377) )
    & ! [U_379] :
        ( U_379 = hAPP(c_Nat_OSuc,sK10(U_379))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_379)) ) ),
    inference(definitional_conversion,[status(esa)],[f_100_4]) ).

cnf(f_100_6,plain,
    ( U_379 = hAPP(c_Nat_OSuc,sK10(U_379))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_379)) ),
    inference(clausify,[status(thm)],[f_100_5]) ).

cnf(f_100_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_380))
    | U_380 != hAPP(c_Nat_OSuc,U_377) ),
    inference(clausify,[status(thm)],[f_100_5]) ).

fof(f_101_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_101_2,plain,
    ! [U_381] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_381),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_381 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_381 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_381),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(variable_rename,[status(thm)],[f_101_1]) ).

fof(f_101_3,plain,
    ( ! [U_383] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_383),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_383 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_382] :
        ( U_382 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_382),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(miniscope,[status(thm)],[f_101_2]) ).

fof(f_101_4,plain,
    ( ! [U_383] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_383),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_383 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_382] :
        ( U_382 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_382),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_101_3]) ).

cnf(f_101_5,plain,
    ( U_382 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_382),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ),
    inference(clausify,[status(thm)],[f_101_4]) ).

cnf(f_101_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_383),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | U_383 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_101_4]) ).

fof(f_102_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_102_2,plain,
    ! [U_387,U_386] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_386),hAPP(c_Nat_OSuc,U_387)))
        | ( ! [U_385] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_385),U_387))
              | U_386 != hAPP(c_Nat_OSuc,U_385) )
          & U_386 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ? [U_384] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_384),U_387))
            & U_386 = hAPP(c_Nat_OSuc,U_384) )
        | U_386 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_386),hAPP(c_Nat_OSuc,U_387))) ) ),
    inference(variable_rename,[status(thm)],[f_102_1]) ).

fof(f_102_3,plain,
    ( ! [U_391,U_389] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_389),hAPP(c_Nat_OSuc,U_391)))
        | ( ! [U_385] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_385),U_391))
              | U_389 != hAPP(c_Nat_OSuc,U_385) )
          & U_389 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_390,U_388] :
        ( ? [U_384] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_384),U_390))
            & U_388 = hAPP(c_Nat_OSuc,U_384) )
        | U_388 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_388),hAPP(c_Nat_OSuc,U_390))) ) ),
    inference(miniscope,[status(thm)],[f_102_2]) ).

fof(f_102_4,plain,
    ( ! [U_391,U_389] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_389),hAPP(c_Nat_OSuc,U_391)))
        | ( ! [U_385] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_385),U_391))
              | U_389 != hAPP(c_Nat_OSuc,U_385) )
          & U_389 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_390,U_388] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK11(U_390,U_388)),U_390))
          & U_388 = hAPP(c_Nat_OSuc,sK11(U_390,U_388)) )
        | U_388 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_388),hAPP(c_Nat_OSuc,U_390))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK11]),skolemize(U_384,sK11(U_390,U_388))],[f_102_3]) ).

fof(f_102_5,plain,
    ( ! [U_385,U_391,U_389] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_385),U_391))
        | U_389 != hAPP(c_Nat_OSuc,U_385)
        | ~ sP18(U_385,U_391,U_389) )
    & ! [U_385,U_391,U_389] :
        ( U_389 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP18(U_385,U_391,U_389) )
    & ! [U_388,U_390] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK11(U_390,U_388)),U_390))
        | ~ sP17(U_388,U_390) )
    & ! [U_388,U_390] :
        ( U_388 = hAPP(c_Nat_OSuc,sK11(U_390,U_388))
        | ~ sP17(U_388,U_390) )
    & ! [U_385,U_391,U_389] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_389),hAPP(c_Nat_OSuc,U_391)))
        | sP18(U_385,U_391,U_389) )
    & ! [U_388,U_390] :
        ( sP17(U_388,U_390)
        | U_388 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_388),hAPP(c_Nat_OSuc,U_390))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP17,sP18])],[f_102_4]) ).

cnf(f_102_6,plain,
    ( sP17(U_388,U_390)
    | U_388 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_388),hAPP(c_Nat_OSuc,U_390))) ),
    inference(clausify,[status(thm)],[f_102_5]) ).

cnf(f_102_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_389),hAPP(c_Nat_OSuc,U_391)))
    | sP18(U_385,U_391,U_389) ),
    inference(clausify,[status(thm)],[f_102_5]) ).

cnf(f_102_8,plain,
    ( U_388 = hAPP(c_Nat_OSuc,sK11(U_390,U_388))
    | ~ sP17(U_388,U_390) ),
    inference(clausify,[status(thm)],[f_102_5]) ).

cnf(f_102_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK11(U_390,U_388)),U_390))
    | ~ sP17(U_388,U_390) ),
    inference(clausify,[status(thm)],[f_102_5]) ).

cnf(f_102_10,plain,
    ( U_389 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP18(U_385,U_391,U_389) ),
    inference(clausify,[status(thm)],[f_102_5]) ).

cnf(f_102_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_385),U_391))
    | U_389 != hAPP(c_Nat_OSuc,U_385)
    | ~ sP18(U_385,U_391,U_389) ),
    inference(clausify,[status(thm)],[f_102_5]) ).

fof(f_103_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_103_2,plain,
    ! [U_393,U_392] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_392),c_Groups_Ozero__class_Ozero(U_392)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_392),U_393)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_393)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_393))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_392),c_Groups_Ozero__class_Ozero(U_392)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_392),U_393))) ) )
      | ~ class_Rings_Olinordered__semidom(U_392) ),
    inference(variable_rename,[status(thm)],[f_103_1]) ).

fof(f_103_3,plain,
    ( ! [U_393,U_392] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_392),c_Groups_Ozero__class_Ozero(U_392)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_392),U_393)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_393))
        | ~ sP19(U_393,U_392) )
    & ! [U_393,U_392] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_393))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_392),c_Groups_Ozero__class_Ozero(U_392)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_392),U_393)))
        | ~ sP19(U_393,U_392) )
    & ! [U_393,U_392] :
        ( sP19(U_393,U_392)
        | ~ class_Rings_Olinordered__semidom(U_392) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP19])],[f_103_2]) ).

cnf(f_103_4,plain,
    ( sP19(U_393,U_392)
    | ~ class_Rings_Olinordered__semidom(U_392) ),
    inference(clausify,[status(thm)],[f_103_3]) ).

cnf(f_103_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_393))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_392),c_Groups_Ozero__class_Ozero(U_392)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_392),U_393)))
    | ~ sP19(U_393,U_392) ),
    inference(clausify,[status(thm)],[f_103_3]) ).

cnf(f_103_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_392),c_Groups_Ozero__class_Ozero(U_392)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_392),U_393)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_393))
    | ~ sP19(U_393,U_392) ),
    inference(clausify,[status(thm)],[f_103_3]) ).

fof(f_104_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_104_2,plain,
    ! [U_395] :
      ( ? [U_394] : U_395 = hAPP(c_Nat_OSuc,U_394)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_395)) ),
    inference(variable_rename,[status(thm)],[f_104_1]) ).

fof(f_104_3,plain,
    ! [U_395] :
      ( U_395 = hAPP(c_Nat_OSuc,sK12(U_395))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_395)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK12]),skolemize(U_394,sK12(U_395))],[f_104_2]) ).

fof(f_104_4,plain,
    ! [U_395] :
      ( U_395 = hAPP(c_Nat_OSuc,sK12(U_395))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_395)) ),
    inference(definitional_conversion,[status(esa)],[f_104_3]) ).

cnf(f_104_5,plain,
    ( U_395 = hAPP(c_Nat_OSuc,sK12(U_395))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_395)) ),
    inference(clausify,[status(thm)],[f_104_4]) ).

fof(f_105_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_105_2,plain,
    ! [U_400,U_399,U_398,U_397] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_397),hAPP(U_398,U_399)),hAPP(U_398,U_400)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_399),U_400))
      | ? [U_396] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_397),hAPP(U_398,U_396)),hAPP(U_398,hAPP(c_Nat_OSuc,U_396))))
      | ~ class_Orderings_Oorder(U_397) ),
    inference(variable_rename,[status(thm)],[f_105_1]) ).

fof(f_105_3,plain,
    ! [U_400,U_399,U_398,U_397] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_397),hAPP(U_398,U_399)),hAPP(U_398,U_400)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_399),U_400))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_397),hAPP(U_398,sK13(U_400,U_399,U_398,U_397))),hAPP(U_398,hAPP(c_Nat_OSuc,sK13(U_400,U_399,U_398,U_397)))))
      | ~ class_Orderings_Oorder(U_397) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK13]),skolemize(U_396,sK13(U_400,U_399,U_398,U_397))],[f_105_2]) ).

fof(f_105_4,plain,
    ! [U_397,U_398,U_399,U_400] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_397),hAPP(U_398,U_399)),hAPP(U_398,U_400)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_399),U_400))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_397),hAPP(U_398,sK13(U_400,U_399,U_398,U_397))),hAPP(U_398,hAPP(c_Nat_OSuc,sK13(U_400,U_399,U_398,U_397)))))
      | ~ class_Orderings_Oorder(U_397) ),
    inference(definitional_conversion,[status(esa)],[f_105_3]) ).

cnf(f_105_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_397),hAPP(U_398,U_399)),hAPP(U_398,U_400)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_399),U_400))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_397),hAPP(U_398,sK13(U_400,U_399,U_398,U_397))),hAPP(U_398,hAPP(c_Nat_OSuc,sK13(U_400,U_399,U_398,U_397)))))
    | ~ class_Orderings_Oorder(U_397) ),
    inference(clausify,[status(thm)],[f_105_4]) ).

fof(f_106_1,plain,
    ! [V_m_2,V_n_2,V_f_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_m_2)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,V_n_2)),hAPP(V_f_2,V_m_2))) ) )
      | ? [B_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n))))
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_lift__Suc__mono__less__iff]) ).

fof(f_106_2,plain,
    ! [U_405,U_404,U_403,U_402] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_402),hAPP(U_403,U_404)),hAPP(U_403,U_405)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_404),U_405)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_404),U_405))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_402),hAPP(U_403,U_404)),hAPP(U_403,U_405))) ) )
      | ? [U_401] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_402),hAPP(U_403,U_401)),hAPP(U_403,hAPP(c_Nat_OSuc,U_401))))
      | ~ class_Orderings_Oorder(U_402) ),
    inference(variable_rename,[status(thm)],[f_106_1]) ).

fof(f_106_3,plain,
    ! [U_405,U_404,U_403,U_402] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_402),hAPP(U_403,U_404)),hAPP(U_403,U_405)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_404),U_405)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_404),U_405))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_402),hAPP(U_403,U_404)),hAPP(U_403,U_405))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_402),hAPP(U_403,sK14(U_405,U_404,U_403,U_402))),hAPP(U_403,hAPP(c_Nat_OSuc,sK14(U_405,U_404,U_403,U_402)))))
      | ~ class_Orderings_Oorder(U_402) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK14]),skolemize(U_401,sK14(U_405,U_404,U_403,U_402))],[f_106_2]) ).

fof(f_106_4,plain,
    ( ! [U_403,U_402,U_404,U_405] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_402),hAPP(U_403,U_404)),hAPP(U_403,U_405)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_404),U_405))
        | ~ sP20(U_403,U_402,U_404,U_405) )
    & ! [U_403,U_402,U_404,U_405] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_404),U_405))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_402),hAPP(U_403,U_404)),hAPP(U_403,U_405)))
        | ~ sP20(U_403,U_402,U_404,U_405) )
    & ! [U_403,U_402,U_404,U_405] :
        ( sP20(U_403,U_402,U_404,U_405)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_402),hAPP(U_403,sK14(U_405,U_404,U_403,U_402))),hAPP(U_403,hAPP(c_Nat_OSuc,sK14(U_405,U_404,U_403,U_402)))))
        | ~ class_Orderings_Oorder(U_402) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP20])],[f_106_3]) ).

cnf(f_106_5,plain,
    ( sP20(U_403,U_402,U_404,U_405)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_402),hAPP(U_403,sK14(U_405,U_404,U_403,U_402))),hAPP(U_403,hAPP(c_Nat_OSuc,sK14(U_405,U_404,U_403,U_402)))))
    | ~ class_Orderings_Oorder(U_402) ),
    inference(clausify,[status(thm)],[f_106_4]) ).

cnf(f_106_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_404),U_405))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_402),hAPP(U_403,U_404)),hAPP(U_403,U_405)))
    | ~ sP20(U_403,U_402,U_404,U_405) ),
    inference(clausify,[status(thm)],[f_106_4]) ).

cnf(f_106_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_402),hAPP(U_403,U_404)),hAPP(U_403,U_405)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_404),U_405))
    | ~ sP20(U_403,U_402,U_404,U_405) ),
    inference(clausify,[status(thm)],[f_106_4]) ).

fof(f_107_1,plain,
    ! [V_a_2,V_Pa_2,V_X_2] :
      ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_Pa_2)))
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_Pa_2,V_a_2))) ),
    inference(fof_nnf,[status(thm)],[fact_WTs__elim__cases_I8_J]) ).

fof(f_107_2,plain,
    ! [U_408,U_407,U_406] :
      ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_407)))
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_406,U_407,U_408))) ),
    inference(variable_rename,[status(thm)],[f_107_1]) ).

fof(f_107_3,plain,
    ! [U_408,U_407] :
      ( ! [U_406] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_406,U_407,U_408)))
      | hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_407))) ),
    inference(miniscope,[status(thm)],[f_107_2]) ).

fof(f_107_4,plain,
    ! [U_407,U_408,U_406] :
      ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_406,U_407,U_408)))
      | hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_407))) ),
    inference(definitional_conversion,[status(esa)],[f_107_3]) ).

cnf(f_107_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_406,U_407,U_408)))
    | hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_407))) ),
    inference(clausify,[status(thm)],[f_107_4]) ).

fof(f_108_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_108_2,plain,
    ! [U_412,U_411,U_410,U_409] :
      ( U_412 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_411),U_409),hAPP(U_410,U_411))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_409,U_410)),U_411),U_412)) ),
    inference(variable_rename,[status(thm)],[f_108_1]) ).

fof(f_108_3,plain,
    ! [U_409,U_410,U_411,U_412] :
      ( U_412 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_411),U_409),hAPP(U_410,U_411))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_409,U_410)),U_411),U_412)) ),
    inference(definitional_conversion,[status(esa)],[f_108_2]) ).

cnf(f_108_4,plain,
    ( U_412 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_411),U_409),hAPP(U_410,U_411))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_409,U_410)),U_411),U_412)) ),
    inference(clausify,[status(thm)],[f_108_3]) ).

fof(f_109_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_109_2,plain,
    ! [U_415,U_414,U_413] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_413,U_414)),U_415),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_415),U_413),hAPP(U_414,U_415)))),
    inference(variable_rename,[status(thm)],[f_109_1]) ).

fof(f_109_3,plain,
    ! [U_413,U_414,U_415] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_413,U_414)),U_415),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_415),U_413),hAPP(U_414,U_415)))),
    inference(definitional_conversion,[status(esa)],[f_109_2]) ).

cnf(f_109_4,plain,
    hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_413,U_414)),U_415),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_415),U_413),hAPP(U_414,U_415)))),
    inference(clausify,[status(thm)],[f_109_3]) ).

fof(f_110_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_110_2,plain,
    ! [U_419,U_418,U_417,U_416] : c_Natural_Oevaln(c_Com_Ocom_OAss(U_416,U_417),U_418,U_419,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_418),U_416),hAPP(U_417,U_418))),
    inference(variable_rename,[status(thm)],[f_110_1]) ).

fof(f_110_3,plain,
    ! [U_416,U_417,U_418,U_419] : c_Natural_Oevaln(c_Com_Ocom_OAss(U_416,U_417),U_418,U_419,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_418),U_416),hAPP(U_417,U_418))),
    inference(definitional_conversion,[status(esa)],[f_110_2]) ).

cnf(f_110_4,plain,
    c_Natural_Oevaln(c_Com_Ocom_OAss(U_416,U_417),U_418,U_419,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_418),U_416),hAPP(U_417,U_418))),
    inference(clausify,[status(thm)],[f_110_3]) ).

fof(f_111_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_111_2,plain,
    ! [U_424,U_423,U_422,U_421,U_420] :
      ( U_424 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_422),U_420),hAPP(U_421,U_422))
      | ~ c_Natural_Oevaln(c_Com_Ocom_OAss(U_420,U_421),U_422,U_423,U_424) ),
    inference(variable_rename,[status(thm)],[f_111_1]) ).

fof(f_111_3,plain,
    ! [U_420,U_421,U_422,U_423,U_424] :
      ( U_424 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_422),U_420),hAPP(U_421,U_422))
      | ~ c_Natural_Oevaln(c_Com_Ocom_OAss(U_420,U_421),U_422,U_423,U_424) ),
    inference(definitional_conversion,[status(esa)],[f_111_2]) ).

cnf(f_111_4,plain,
    ( U_424 = hAPP(hAPP(hAPP(c_Natural_Oupdate,U_422),U_420),hAPP(U_421,U_422))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OAss(U_420,U_421),U_422,U_423,U_424) ),
    inference(clausify,[status(thm)],[f_111_3]) ).

fof(f_112_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_112_2,plain,
    ! [U_426,U_425] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_425),U_426),U_426))
      | ~ class_Orderings_Opreorder(U_425) ),
    inference(variable_rename,[status(thm)],[f_112_1]) ).

fof(f_112_3,plain,
    ! [U_425,U_426] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_425),U_426),U_426))
      | ~ class_Orderings_Opreorder(U_425) ),
    inference(definitional_conversion,[status(esa)],[f_112_2]) ).

cnf(f_112_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_425),U_426),U_426))
    | ~ class_Orderings_Opreorder(U_425) ),
    inference(clausify,[status(thm)],[f_112_3]) ).

fof(f_113_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_113_2,plain,
    ! [U_429,U_428,U_427] :
      ( ( ( U_428 != U_429
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_427),U_429),U_428))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_427),U_428),U_429)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_427),U_429),U_428))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_427),U_428),U_429))
          | U_428 = U_429 ) )
      | ~ class_Orderings_Olinorder(U_427) ),
    inference(variable_rename,[status(thm)],[f_113_1]) ).

fof(f_113_3,plain,
    ( ! [U_427,U_428,U_429] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_427),U_429),U_428))
        | ~ sP21(U_427,U_428,U_429) )
    & ! [U_427,U_428,U_429] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_427),U_428),U_429))
        | ~ sP21(U_427,U_428,U_429) )
    & ! [U_427,U_428,U_429] :
        ( U_428 != U_429
        | sP21(U_427,U_428,U_429)
        | ~ sP22(U_427,U_428,U_429) )
    & ! [U_427,U_428,U_429] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_427),U_429),U_428))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_427),U_428),U_429))
        | U_428 = U_429
        | ~ sP22(U_427,U_428,U_429) )
    & ! [U_427,U_428,U_429] :
        ( sP22(U_427,U_428,U_429)
        | ~ class_Orderings_Olinorder(U_427) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP21,sP22])],[f_113_2]) ).

cnf(f_113_4,plain,
    ( sP22(U_427,U_428,U_429)
    | ~ class_Orderings_Olinorder(U_427) ),
    inference(clausify,[status(thm)],[f_113_3]) ).

cnf(f_113_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_427),U_429),U_428))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_427),U_428),U_429))
    | U_428 = U_429
    | ~ sP22(U_427,U_428,U_429) ),
    inference(clausify,[status(thm)],[f_113_3]) ).

cnf(f_113_6,plain,
    ( U_428 != U_429
    | sP21(U_427,U_428,U_429)
    | ~ sP22(U_427,U_428,U_429) ),
    inference(clausify,[status(thm)],[f_113_3]) ).

cnf(f_113_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_427),U_428),U_429))
    | ~ sP21(U_427,U_428,U_429) ),
    inference(clausify,[status(thm)],[f_113_3]) ).

cnf(f_113_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_427),U_429),U_428))
    | ~ sP21(U_427,U_428,U_429) ),
    inference(clausify,[status(thm)],[f_113_3]) ).

fof(f_114_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_114_2,plain,
    ! [U_432,U_431,U_430] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_430),U_431),U_432))
          | ( U_431 != U_432
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_430),U_432),U_431)) ) )
        & ( U_431 = U_432
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_430),U_432),U_431))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_430),U_431),U_432)) ) )
      | ~ class_Orderings_Olinorder(U_430) ),
    inference(variable_rename,[status(thm)],[f_114_1]) ).

fof(f_114_3,plain,
    ( ! [U_432,U_431,U_430] :
        ( U_431 != U_432
        | ~ sP23(U_432,U_431,U_430) )
    & ! [U_432,U_431,U_430] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_430),U_432),U_431))
        | ~ sP23(U_432,U_431,U_430) )
    & ! [U_432,U_431,U_430] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_430),U_431),U_432))
        | sP23(U_432,U_431,U_430)
        | ~ sP24(U_432,U_431,U_430) )
    & ! [U_432,U_431,U_430] :
        ( U_431 = U_432
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_430),U_432),U_431))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_430),U_431),U_432))
        | ~ sP24(U_432,U_431,U_430) )
    & ! [U_432,U_431,U_430] :
        ( sP24(U_432,U_431,U_430)
        | ~ class_Orderings_Olinorder(U_430) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP23,sP24])],[f_114_2]) ).

cnf(f_114_4,plain,
    ( sP24(U_432,U_431,U_430)
    | ~ class_Orderings_Olinorder(U_430) ),
    inference(clausify,[status(thm)],[f_114_3]) ).

cnf(f_114_5,plain,
    ( U_431 = U_432
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_430),U_432),U_431))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_430),U_431),U_432))
    | ~ sP24(U_432,U_431,U_430) ),
    inference(clausify,[status(thm)],[f_114_3]) ).

cnf(f_114_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_430),U_431),U_432))
    | sP23(U_432,U_431,U_430)
    | ~ sP24(U_432,U_431,U_430) ),
    inference(clausify,[status(thm)],[f_114_3]) ).

cnf(f_114_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_430),U_432),U_431))
    | ~ sP23(U_432,U_431,U_430) ),
    inference(clausify,[status(thm)],[f_114_3]) ).

cnf(f_114_8,plain,
    ( U_431 != U_432
    | ~ sP23(U_432,U_431,U_430) ),
    inference(clausify,[status(thm)],[f_114_3]) ).

fof(f_115_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_115_2,plain,
    ! [U_435,U_434,U_433] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_433),U_434) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_433),U_435)
          | U_434 != U_435 )
        & ( U_434 = U_435
          | hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_433),U_434) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_433),U_435) ) )
      | ~ class_Nat_Osemiring__char__0(U_433) ),
    inference(variable_rename,[status(thm)],[f_115_1]) ).

fof(f_115_3,plain,
    ( ! [U_433,U_435,U_434] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_433),U_434) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_433),U_435)
        | U_434 != U_435
        | ~ sP25(U_433,U_435,U_434) )
    & ! [U_433,U_435,U_434] :
        ( U_434 = U_435
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_433),U_434) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_433),U_435)
        | ~ sP25(U_433,U_435,U_434) )
    & ! [U_433,U_435,U_434] :
        ( sP25(U_433,U_435,U_434)
        | ~ class_Nat_Osemiring__char__0(U_433) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP25])],[f_115_2]) ).

cnf(f_115_4,plain,
    ( sP25(U_433,U_435,U_434)
    | ~ class_Nat_Osemiring__char__0(U_433) ),
    inference(clausify,[status(thm)],[f_115_3]) ).

cnf(f_115_5,plain,
    ( U_434 = U_435
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_433),U_434) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_433),U_435)
    | ~ sP25(U_433,U_435,U_434) ),
    inference(clausify,[status(thm)],[f_115_3]) ).

cnf(f_115_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_433),U_434) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_433),U_435)
    | U_434 != U_435
    | ~ sP25(U_433,U_435,U_434) ),
    inference(clausify,[status(thm)],[f_115_3]) ).

fof(f_116_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_116_2,plain,
    ! [U_439,U_438,U_437,U_436] :
      ( hBOOL(hAPP(hAPP(c_member(U_436),U_439),U_438))
      | ~ hBOOL(hAPP(hAPP(c_member(U_436),U_439),U_437))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_436,tc_HOL_Obool)),U_437),U_438)) ),
    inference(variable_rename,[status(thm)],[f_116_1]) ).

fof(f_116_3,plain,
    ! [U_437,U_438,U_436,U_439] :
      ( hBOOL(hAPP(hAPP(c_member(U_436),U_439),U_438))
      | ~ hBOOL(hAPP(hAPP(c_member(U_436),U_439),U_437))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_436,tc_HOL_Obool)),U_437),U_438)) ),
    inference(definitional_conversion,[status(esa)],[f_116_2]) ).

cnf(f_116_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_436),U_439),U_438))
    | ~ hBOOL(hAPP(hAPP(c_member(U_436),U_439),U_437))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_436,tc_HOL_Obool)),U_437),U_438)) ),
    inference(clausify,[status(thm)],[f_116_3]) ).

fof(f_117_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_117_2,plain,
    ! [U_441,U_440] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(U_440,U_441))),
    inference(variable_rename,[status(thm)],[f_117_1]) ).

fof(f_117_3,plain,
    ! [U_441,U_440] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(U_440,U_441))),
    inference(definitional_conversion,[status(esa)],[f_117_2]) ).

cnf(f_117_4,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(U_440,U_441))),
    inference(clausify,[status(thm)],[f_117_3]) ).

fof(f_118_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_118_2,plain,
    ! [U_443,U_442] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(U_442,U_443))),
    inference(variable_rename,[status(thm)],[f_118_1]) ).

fof(f_118_3,plain,
    ! [U_442,U_443] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(U_442,U_443))),
    inference(definitional_conversion,[status(esa)],[f_118_2]) ).

cnf(f_118_4,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OAss(U_442,U_443))),
    inference(clausify,[status(thm)],[f_118_3]) ).

fof(f_119_1,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(fof_nnf,[status(thm)],[fact_WT_OSkip]) ).

fof(f_119_2,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(definitional_conversion,[status(esa)],[f_119_1]) ).

cnf(f_119_3,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(clausify,[status(thm)],[f_119_2]) ).

fof(f_120_1,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(fof_nnf,[status(thm)],[fact_WT_Oequations_I1_J]) ).

fof(f_120_2,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(definitional_conversion,[status(esa)],[f_120_1]) ).

cnf(f_120_3,plain,
    hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)),
    inference(clausify,[status(thm)],[f_120_2]) ).

fof(f_121_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_121_2,plain,
    ! [U_445,U_444] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_444),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_444),U_445)),c_Groups_Ozero__class_Ozero(U_444)))
      | ~ class_Rings_Olinordered__semidom(U_444) ),
    inference(variable_rename,[status(thm)],[f_121_1]) ).

fof(f_121_3,plain,
    ! [U_445,U_444] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_444),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_444),U_445)),c_Groups_Ozero__class_Ozero(U_444)))
      | ~ class_Rings_Olinordered__semidom(U_444) ),
    inference(definitional_conversion,[status(esa)],[f_121_2]) ).

cnf(f_121_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_444),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_444),U_445)),c_Groups_Ozero__class_Ozero(U_444)))
    | ~ class_Rings_Olinordered__semidom(U_444) ),
    inference(clausify,[status(thm)],[f_121_3]) ).

fof(f_122_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_122_2,plain,
    ! [U_446] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_446),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_446)
      | ~ class_Rings_Osemiring__1(U_446) ),
    inference(variable_rename,[status(thm)],[f_122_1]) ).

fof(f_122_3,plain,
    ! [U_446] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_446),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_446)
      | ~ class_Rings_Osemiring__1(U_446) ),
    inference(definitional_conversion,[status(esa)],[f_122_2]) ).

cnf(f_122_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_446),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(U_446)
    | ~ class_Rings_Osemiring__1(U_446) ),
    inference(clausify,[status(thm)],[f_122_3]) ).

fof(f_123_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_123_2,plain,
    ! [U_449,U_448,U_447] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_447),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_447),U_448)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_447),U_449)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_448),U_449)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_448),U_449))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_447),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_447),U_448)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_447),U_449))) ) )
      | ~ class_Rings_Olinordered__semidom(U_447) ),
    inference(variable_rename,[status(thm)],[f_123_1]) ).

fof(f_123_3,plain,
    ( ! [U_447,U_448,U_449] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_447),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_447),U_448)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_447),U_449)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_448),U_449))
        | ~ sP26(U_447,U_448,U_449) )
    & ! [U_447,U_448,U_449] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_448),U_449))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_447),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_447),U_448)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_447),U_449)))
        | ~ sP26(U_447,U_448,U_449) )
    & ! [U_447,U_448,U_449] :
        ( sP26(U_447,U_448,U_449)
        | ~ class_Rings_Olinordered__semidom(U_447) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP26])],[f_123_2]) ).

cnf(f_123_4,plain,
    ( sP26(U_447,U_448,U_449)
    | ~ class_Rings_Olinordered__semidom(U_447) ),
    inference(clausify,[status(thm)],[f_123_3]) ).

cnf(f_123_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_448),U_449))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_447),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_447),U_448)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_447),U_449)))
    | ~ sP26(U_447,U_448,U_449) ),
    inference(clausify,[status(thm)],[f_123_3]) ).

cnf(f_123_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_447),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_447),U_448)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_447),U_449)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_448),U_449))
    | ~ sP26(U_447,U_448,U_449) ),
    inference(clausify,[status(thm)],[f_123_3]) ).

fof(f_124_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_124_2,plain,
    ! [U_452,U_451,U_450] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_450),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_450),U_451)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_450),U_452)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_451),U_452))
      | ~ class_Rings_Olinordered__semidom(U_450) ),
    inference(variable_rename,[status(thm)],[f_124_1]) ).

fof(f_124_3,plain,
    ! [U_451,U_450,U_452] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_450),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_450),U_451)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_450),U_452)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_451),U_452))
      | ~ class_Rings_Olinordered__semidom(U_450) ),
    inference(definitional_conversion,[status(esa)],[f_124_2]) ).

cnf(f_124_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_450),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_450),U_451)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_450),U_452)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_451),U_452))
    | ~ class_Rings_Olinordered__semidom(U_450) ),
    inference(clausify,[status(thm)],[f_124_3]) ).

fof(f_125_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_125_2,plain,
    ! [U_455,U_454,U_453] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_454),U_455))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_453),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_453),U_454)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_453),U_455)))
      | ~ class_Rings_Olinordered__semidom(U_453) ),
    inference(variable_rename,[status(thm)],[f_125_1]) ).

fof(f_125_3,plain,
    ! [U_453,U_454,U_455] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_454),U_455))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_453),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_453),U_454)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_453),U_455)))
      | ~ class_Rings_Olinordered__semidom(U_453) ),
    inference(definitional_conversion,[status(esa)],[f_125_2]) ).

cnf(f_125_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_454),U_455))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_453),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_453),U_454)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_453),U_455)))
    | ~ class_Rings_Olinordered__semidom(U_453) ),
    inference(clausify,[status(thm)],[f_125_3]) ).

fof(f_126_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_126_2,plain,
    ! [U_457,U_456] :
      ( hBOOL(hAPP(hAPP(c_member(U_456),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_456),U_457)),c_Nat_Osemiring__1__class_ONats(U_456)))
      | ~ class_Rings_Osemiring__1(U_456) ),
    inference(variable_rename,[status(thm)],[f_126_1]) ).

fof(f_126_3,plain,
    ! [U_456,U_457] :
      ( hBOOL(hAPP(hAPP(c_member(U_456),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_456),U_457)),c_Nat_Osemiring__1__class_ONats(U_456)))
      | ~ class_Rings_Osemiring__1(U_456) ),
    inference(definitional_conversion,[status(esa)],[f_126_2]) ).

cnf(f_126_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_456),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_456),U_457)),c_Nat_Osemiring__1__class_ONats(U_456)))
    | ~ class_Rings_Osemiring__1(U_456) ),
    inference(clausify,[status(thm)],[f_126_3]) ).

fof(f_127_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_127_2,plain,
    ! [U_461,U_460,U_459,U_458] : c_Natural_Oevaln(c_Com_Ocom_OAss(U_458,U_459),U_460,U_461,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_460),U_458),hAPP(U_459,U_460))),
    inference(variable_rename,[status(thm)],[f_127_1]) ).

fof(f_127_3,plain,
    ! [U_458,U_459,U_460,U_461] : c_Natural_Oevaln(c_Com_Ocom_OAss(U_458,U_459),U_460,U_461,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_460),U_458),hAPP(U_459,U_460))),
    inference(definitional_conversion,[status(esa)],[f_127_2]) ).

cnf(f_127_4,plain,
    c_Natural_Oevaln(c_Com_Ocom_OAss(U_458,U_459),U_460,U_461,hAPP(hAPP(hAPP(c_Natural_Oupdate,U_460),U_458),hAPP(U_459,U_460))),
    inference(clausify,[status(thm)],[f_127_3]) ).

fof(f_128_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_128_2,plain,
    ! [U_464,U_463,U_462] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_462,U_463)),U_464),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_464),U_462),hAPP(U_463,U_464)))),
    inference(variable_rename,[status(thm)],[f_128_1]) ).

fof(f_128_3,plain,
    ! [U_462,U_463,U_464] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_462,U_463)),U_464),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_464),U_462),hAPP(U_463,U_464)))),
    inference(definitional_conversion,[status(esa)],[f_128_2]) ).

cnf(f_128_4,plain,
    hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OAss(U_462,U_463)),U_464),hAPP(hAPP(hAPP(c_Natural_Oupdate,U_464),U_462),hAPP(U_463,U_464)))),
    inference(clausify,[status(thm)],[f_128_3]) ).

fof(f_129_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_129_2,plain,
    ! [U_467,U_466,U_465] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_466,U_465,U_467)))
      | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_465))) ),
    inference(variable_rename,[status(thm)],[f_129_1]) ).

fof(f_129_3,plain,
    ! [U_465,U_466,U_467] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_466,U_465,U_467)))
      | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_465))) ),
    inference(definitional_conversion,[status(esa)],[f_129_2]) ).

cnf(f_129_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_466,U_465,U_467)))
    | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_465))) ),
    inference(clausify,[status(thm)],[f_129_3]) ).

fof(f_130_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_130_2,plain,
    ! [U_470,U_469,U_468] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_468,U_469,U_470)))
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_469))) )
      & ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_469)))
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_468,U_469,U_470))) ) ),
    inference(variable_rename,[status(thm)],[f_130_1]) ).

fof(f_130_3,plain,
    ( ! [U_476,U_474] :
        ( ! [U_472] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_472,U_474,U_476)))
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_474))) )
    & ! [U_475,U_473] :
        ( ! [U_471] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_471,U_473,U_475)))
        | hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_473))) ) ),
    inference(miniscope,[status(thm)],[f_130_2]) ).

fof(f_130_4,plain,
    ( ! [U_476,U_472,U_474] :
        ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_472,U_474,U_476)))
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_474))) )
    & ! [U_471,U_475,U_473] :
        ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_471,U_473,U_475)))
        | hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_473))) ) ),
    inference(definitional_conversion,[status(esa)],[f_130_3]) ).

cnf(f_130_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_471,U_473,U_475)))
    | hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_473))) ),
    inference(clausify,[status(thm)],[f_130_4]) ).

cnf(f_130_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(U_472,U_474,U_476)))
    | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_474))) ),
    inference(clausify,[status(thm)],[f_130_4]) ).

fof(f_131_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_131_2,plain,
    ! [U_479,U_478,U_477] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_477),U_479),U_478))
      | U_478 = U_479
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_477),U_478),U_479))
      | ~ class_Orderings_Olinorder(U_477) ),
    inference(variable_rename,[status(thm)],[f_131_1]) ).

fof(f_131_3,plain,
    ! [U_477,U_478,U_479] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_477),U_479),U_478))
      | U_478 = U_479
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_477),U_478),U_479))
      | ~ class_Orderings_Olinorder(U_477) ),
    inference(definitional_conversion,[status(esa)],[f_131_2]) ).

cnf(f_131_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_477),U_479),U_478))
    | U_478 = U_479
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_477),U_478),U_479))
    | ~ class_Orderings_Olinorder(U_477) ),
    inference(clausify,[status(thm)],[f_131_3]) ).

fof(f_132_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_132_2,plain,
    ! [U_482,U_481,U_480] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_480),U_482),U_481))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_480),U_481),U_482))
      | ~ class_Orderings_Opreorder(U_480) ),
    inference(variable_rename,[status(thm)],[f_132_1]) ).

fof(f_132_3,plain,
    ! [U_482,U_480,U_481] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_480),U_482),U_481))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_480),U_481),U_482))
      | ~ class_Orderings_Opreorder(U_480) ),
    inference(definitional_conversion,[status(esa)],[f_132_2]) ).

cnf(f_132_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_480),U_482),U_481))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_480),U_481),U_482))
    | ~ class_Orderings_Opreorder(U_480) ),
    inference(clausify,[status(thm)],[f_132_3]) ).

fof(f_133_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_133_2,plain,
    ! [U_486,U_485,U_484,U_483] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_483),U_486),U_485))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_483),U_486),U_484))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_483),U_484),U_485))
      | ~ class_Orderings_Oorder(U_483) ),
    inference(variable_rename,[status(thm)],[f_133_1]) ).

fof(f_133_3,plain,
    ! [U_483,U_484,U_485,U_486] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_483),U_486),U_485))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_483),U_486),U_484))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_483),U_484),U_485))
      | ~ class_Orderings_Oorder(U_483) ),
    inference(definitional_conversion,[status(esa)],[f_133_2]) ).

cnf(f_133_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_483),U_486),U_485))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_483),U_486),U_484))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_483),U_484),U_485))
    | ~ class_Orderings_Oorder(U_483) ),
    inference(clausify,[status(thm)],[f_133_3]) ).

fof(f_134_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_134_2,plain,
    ! [U_490,U_489,U_488,U_487] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_487),U_488),U_490))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_487),U_489),U_490))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_487),U_488),U_489))
      | ~ class_Orderings_Opreorder(U_487) ),
    inference(variable_rename,[status(thm)],[f_134_1]) ).

fof(f_134_3,plain,
    ! [U_488,U_487,U_489,U_490] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_487),U_488),U_490))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_487),U_489),U_490))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_487),U_488),U_489))
      | ~ class_Orderings_Opreorder(U_487) ),
    inference(definitional_conversion,[status(esa)],[f_134_2]) ).

cnf(f_134_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_487),U_488),U_490))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_487),U_489),U_490))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_487),U_488),U_489))
    | ~ class_Orderings_Opreorder(U_487) ),
    inference(clausify,[status(thm)],[f_134_3]) ).

fof(f_135_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_135_2,plain,
    ! [U_494,U_493,U_492,U_491] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_491),U_494),U_493))
      | U_492 != U_494
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_491),U_492),U_493))
      | ~ class_Orderings_Oorder(U_491) ),
    inference(variable_rename,[status(thm)],[f_135_1]) ).

fof(f_135_3,plain,
    ! [U_492,U_493,U_491,U_494] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_491),U_494),U_493))
      | U_492 != U_494
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_491),U_492),U_493))
      | ~ class_Orderings_Oorder(U_491) ),
    inference(definitional_conversion,[status(esa)],[f_135_2]) ).

cnf(f_135_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_491),U_494),U_493))
    | U_492 != U_494
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_491),U_492),U_493))
    | ~ class_Orderings_Oorder(U_491) ),
    inference(clausify,[status(thm)],[f_135_3]) ).

fof(f_136_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_136_2,plain,
    ! [U_498,U_497,U_496,U_495] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_495),U_496),U_498))
      | U_497 != U_498
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_495),U_496),U_497))
      | ~ class_Orderings_Oord(U_495) ),
    inference(variable_rename,[status(thm)],[f_136_1]) ).

fof(f_136_3,plain,
    ! [U_498,U_496,U_497,U_495] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_495),U_496),U_498))
      | U_497 != U_498
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_495),U_496),U_497))
      | ~ class_Orderings_Oord(U_495) ),
    inference(definitional_conversion,[status(esa)],[f_136_2]) ).

cnf(f_136_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_495),U_496),U_498))
    | U_497 != U_498
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_495),U_496),U_497))
    | ~ class_Orderings_Oord(U_495) ),
    inference(clausify,[status(thm)],[f_136_3]) ).

fof(f_137_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_137_2,plain,
    ! [U_502,U_501,U_500,U_499] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_499),U_502),U_500))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_499),U_502),U_501))
      | U_500 != U_501
      | ~ class_Orderings_Oorder(U_499) ),
    inference(variable_rename,[status(thm)],[f_137_1]) ).

fof(f_137_3,plain,
    ! [U_502,U_501,U_500,U_499] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_499),U_502),U_500))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_499),U_502),U_501))
      | U_500 != U_501
      | ~ class_Orderings_Oorder(U_499) ),
    inference(definitional_conversion,[status(esa)],[f_137_2]) ).

cnf(f_137_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_499),U_502),U_500))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_499),U_502),U_501))
    | U_500 != U_501
    | ~ class_Orderings_Oorder(U_499) ),
    inference(clausify,[status(thm)],[f_137_3]) ).

fof(f_138_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_138_2,plain,
    ! [U_506,U_505,U_504,U_503] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_503),U_504),U_506))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_503),U_505),U_506))
      | U_504 != U_505
      | ~ class_Orderings_Oord(U_503) ),
    inference(variable_rename,[status(thm)],[f_138_1]) ).

fof(f_138_3,plain,
    ! [U_505,U_503,U_504,U_506] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_503),U_504),U_506))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_503),U_505),U_506))
      | U_504 != U_505
      | ~ class_Orderings_Oord(U_503) ),
    inference(definitional_conversion,[status(esa)],[f_138_2]) ).

cnf(f_138_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_503),U_504),U_506))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_503),U_505),U_506))
    | U_504 != U_505
    | ~ class_Orderings_Oord(U_503) ),
    inference(clausify,[status(thm)],[f_138_3]) ).

fof(f_139_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_139_2,plain,
    ! [U_509,U_508,U_507] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_507),U_509),U_508))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_507),U_508),U_509))
      | ~ class_Orderings_Oorder(U_507) ),
    inference(variable_rename,[status(thm)],[f_139_1]) ).

fof(f_139_3,plain,
    ! [U_508,U_509,U_507] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_507),U_509),U_508))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_507),U_508),U_509))
      | ~ class_Orderings_Oorder(U_507) ),
    inference(definitional_conversion,[status(esa)],[f_139_2]) ).

cnf(f_139_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_507),U_509),U_508))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_507),U_508),U_509))
    | ~ class_Orderings_Oorder(U_507) ),
    inference(clausify,[status(thm)],[f_139_3]) ).

fof(f_140_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_140_2,plain,
    ! [U_512,U_511,U_510] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_510),U_512),U_511))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_510),U_511),U_512))
      | ~ class_Orderings_Opreorder(U_510) ),
    inference(variable_rename,[status(thm)],[f_140_1]) ).

fof(f_140_3,plain,
    ! [U_510,U_511,U_512] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_510),U_512),U_511))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_510),U_511),U_512))
      | ~ class_Orderings_Opreorder(U_510) ),
    inference(definitional_conversion,[status(esa)],[f_140_2]) ).

cnf(f_140_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_510),U_512),U_511))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_510),U_511),U_512))
    | ~ class_Orderings_Opreorder(U_510) ),
    inference(clausify,[status(thm)],[f_140_3]) ).

fof(f_141_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_141_2,plain,
    ! [U_515,U_514,U_513] :
      ( U_515 != U_514
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_513),U_514),U_515))
      | ~ class_Orderings_Oorder(U_513) ),
    inference(variable_rename,[status(thm)],[f_141_1]) ).

fof(f_141_3,plain,
    ! [U_513,U_514,U_515] :
      ( U_515 != U_514
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_513),U_514),U_515))
      | ~ class_Orderings_Oorder(U_513) ),
    inference(definitional_conversion,[status(esa)],[f_141_2]) ).

cnf(f_141_4,plain,
    ( U_515 != U_514
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_513),U_514),U_515))
    | ~ class_Orderings_Oorder(U_513) ),
    inference(clausify,[status(thm)],[f_141_3]) ).

fof(f_142_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_142_2,plain,
    ! [U_518,U_517,U_516] :
      ( U_517 != U_518
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_516),U_517),U_518))
      | ~ class_Orderings_Oorder(U_516) ),
    inference(variable_rename,[status(thm)],[f_142_1]) ).

fof(f_142_3,plain,
    ! [U_516,U_517,U_518] :
      ( U_517 != U_518
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_516),U_517),U_518))
      | ~ class_Orderings_Oorder(U_516) ),
    inference(definitional_conversion,[status(esa)],[f_142_2]) ).

cnf(f_142_4,plain,
    ( U_517 != U_518
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_516),U_517),U_518))
    | ~ class_Orderings_Oorder(U_516) ),
    inference(clausify,[status(thm)],[f_142_3]) ).

fof(f_143_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_143_2,plain,
    ! [U_521,U_520,U_519] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_519),U_521),U_520))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_519),U_520),U_521))
      | ~ class_Orderings_Opreorder(U_519) ),
    inference(variable_rename,[status(thm)],[f_143_1]) ).

fof(f_143_3,plain,
    ! [U_519,U_520,U_521] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_519),U_521),U_520))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_519),U_520),U_521))
      | ~ class_Orderings_Opreorder(U_519) ),
    inference(definitional_conversion,[status(esa)],[f_143_2]) ).

cnf(f_143_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_519),U_521),U_520))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_519),U_520),U_521))
    | ~ class_Orderings_Opreorder(U_519) ),
    inference(clausify,[status(thm)],[f_143_3]) ).

fof(f_144_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_144_2,plain,
    ! [U_524,U_523,U_522] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_522),U_524),U_523))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_522),U_523),U_524))
      | ~ class_Orderings_Opreorder(U_522) ),
    inference(variable_rename,[status(thm)],[f_144_1]) ).

fof(f_144_3,plain,
    ! [U_522,U_523,U_524] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_522),U_524),U_523))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_522),U_523),U_524))
      | ~ class_Orderings_Opreorder(U_522) ),
    inference(definitional_conversion,[status(esa)],[f_144_2]) ).

cnf(f_144_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_522),U_524),U_523))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_522),U_523),U_524))
    | ~ class_Orderings_Opreorder(U_522) ),
    inference(clausify,[status(thm)],[f_144_3]) ).

fof(f_145_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_145_2,plain,
    ! [U_527,U_526,U_525] :
      ( U_526 != U_527
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_525),U_526),U_527))
      | ~ class_Orderings_Oorder(U_525) ),
    inference(variable_rename,[status(thm)],[f_145_1]) ).

fof(f_145_3,plain,
    ! [U_526,U_525,U_527] :
      ( U_526 != U_527
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_525),U_526),U_527))
      | ~ class_Orderings_Oorder(U_525) ),
    inference(definitional_conversion,[status(esa)],[f_145_2]) ).

cnf(f_145_4,plain,
    ( U_526 != U_527
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_525),U_526),U_527))
    | ~ class_Orderings_Oorder(U_525) ),
    inference(clausify,[status(thm)],[f_145_3]) ).

fof(f_146_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_146_2,plain,
    ! [U_530,U_529,U_528] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_528),U_530),U_529))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_528),U_529),U_530))
      | U_529 = U_530
      | ~ class_Orderings_Olinorder(U_528) ),
    inference(variable_rename,[status(thm)],[f_146_1]) ).

fof(f_146_3,plain,
    ! [U_528,U_529,U_530] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_528),U_530),U_529))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_528),U_529),U_530))
      | U_529 = U_530
      | ~ class_Orderings_Olinorder(U_528) ),
    inference(definitional_conversion,[status(esa)],[f_146_2]) ).

cnf(f_146_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_528),U_530),U_529))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_528),U_529),U_530))
    | U_529 = U_530
    | ~ class_Orderings_Olinorder(U_528) ),
    inference(clausify,[status(thm)],[f_146_3]) ).

fof(f_147_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_147_2,plain,
    ! [U_533,U_532,U_531] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_531),U_533),U_532))
          | U_533 != U_532 )
        & ( U_533 = U_532
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_531),U_533),U_532)) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_531),U_532),U_533))
      | ~ class_Orderings_Olinorder(U_531) ),
    inference(variable_rename,[status(thm)],[f_147_1]) ).

fof(f_147_3,plain,
    ( ! [U_532,U_531,U_533] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_531),U_533),U_532))
        | U_533 != U_532
        | ~ sP27(U_532,U_531,U_533) )
    & ! [U_532,U_531,U_533] :
        ( U_533 = U_532
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_531),U_533),U_532))
        | ~ sP27(U_532,U_531,U_533) )
    & ! [U_532,U_531,U_533] :
        ( sP27(U_532,U_531,U_533)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_531),U_532),U_533))
        | ~ class_Orderings_Olinorder(U_531) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP27])],[f_147_2]) ).

cnf(f_147_4,plain,
    ( sP27(U_532,U_531,U_533)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_531),U_532),U_533))
    | ~ class_Orderings_Olinorder(U_531) ),
    inference(clausify,[status(thm)],[f_147_3]) ).

cnf(f_147_5,plain,
    ( U_533 = U_532
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_531),U_533),U_532))
    | ~ sP27(U_532,U_531,U_533) ),
    inference(clausify,[status(thm)],[f_147_3]) ).

cnf(f_147_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_531),U_533),U_532))
    | U_533 != U_532
    | ~ sP27(U_532,U_531,U_533) ),
    inference(clausify,[status(thm)],[f_147_3]) ).

fof(f_148_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_148_2,plain,
    ! [U_536,U_535,U_534] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_534),U_536),U_535))
      | U_535 = U_536
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_534),U_535),U_536))
      | ~ class_Orderings_Olinorder(U_534) ),
    inference(variable_rename,[status(thm)],[f_148_1]) ).

fof(f_148_3,plain,
    ! [U_536,U_535,U_534] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_534),U_536),U_535))
      | U_535 = U_536
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_534),U_535),U_536))
      | ~ class_Orderings_Olinorder(U_534) ),
    inference(definitional_conversion,[status(esa)],[f_148_2]) ).

cnf(f_148_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_534),U_536),U_535))
    | U_535 = U_536
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_534),U_535),U_536))
    | ~ class_Orderings_Olinorder(U_534) ),
    inference(clausify,[status(thm)],[f_148_3]) ).

fof(f_149_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_149_2,plain,
    ! [U_537] :
      ( ( 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_537)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_537)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_537))
        | ~ 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_537))) ) ),
    inference(variable_rename,[status(thm)],[f_149_1]) ).

fof(f_149_3,plain,
    ( ! [U_539] :
        ( 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_539)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_539)) )
    & ! [U_538] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_538))
        | ~ 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_538))) ) ),
    inference(miniscope,[status(thm)],[f_149_2]) ).

fof(f_149_4,plain,
    ( ! [U_539] :
        ( 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_539)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_539)) )
    & ! [U_538] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_538))
        | ~ 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_538))) ) ),
    inference(definitional_conversion,[status(esa)],[f_149_3]) ).

cnf(f_149_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_538))
    | ~ 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_538))) ),
    inference(clausify,[status(thm)],[f_149_4]) ).

cnf(f_149_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_539)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_539)) ),
    inference(clausify,[status(thm)],[f_149_4]) ).

fof(f_150_1,plain,
    ! [V_Pa_2,V_x_2,T_b] :
      ( hBOOL(hAPP(V_Pa_2,V_x_2))
      | ? [B_n] : ~ hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),B_n)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Nats__induct]) ).

fof(f_150_2,plain,
    ! [U_543,U_542,U_541] :
      ( hBOOL(hAPP(U_543,U_542))
      | ? [U_540] : ~ hBOOL(hAPP(U_543,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_541),U_540)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_541),U_542),c_Nat_Osemiring__1__class_ONats(U_541)))
      | ~ class_Rings_Osemiring__1(U_541) ),
    inference(variable_rename,[status(thm)],[f_150_1]) ).

fof(f_150_3,plain,
    ! [U_543,U_542,U_541] :
      ( hBOOL(hAPP(U_543,U_542))
      | ~ hBOOL(hAPP(U_543,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_541),sK15(U_543,U_542,U_541))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_541),U_542),c_Nat_Osemiring__1__class_ONats(U_541)))
      | ~ class_Rings_Osemiring__1(U_541) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK15]),skolemize(U_540,sK15(U_543,U_542,U_541))],[f_150_2]) ).

fof(f_150_4,plain,
    ! [U_541,U_542,U_543] :
      ( hBOOL(hAPP(U_543,U_542))
      | ~ hBOOL(hAPP(U_543,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_541),sK15(U_543,U_542,U_541))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_541),U_542),c_Nat_Osemiring__1__class_ONats(U_541)))
      | ~ class_Rings_Osemiring__1(U_541) ),
    inference(definitional_conversion,[status(esa)],[f_150_3]) ).

cnf(f_150_5,plain,
    ( hBOOL(hAPP(U_543,U_542))
    | ~ hBOOL(hAPP(U_543,hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_541),sK15(U_543,U_542,U_541))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_541),U_542),c_Nat_Osemiring__1__class_ONats(U_541)))
    | ~ class_Rings_Osemiring__1(U_541) ),
    inference(clausify,[status(thm)],[f_150_4]) ).

fof(f_151_1,plain,
    ! [V_x_2,T_b] :
      ( ? [B_n] : V_x_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(T_b),B_n)
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),c_Nat_Osemiring__1__class_ONats(T_b)))
      | ~ class_Rings_Osemiring__1(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_Nats__cases]) ).

fof(f_151_2,plain,
    ! [U_546,U_545] :
      ( ? [U_544] : U_546 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_545),U_544)
      | ~ hBOOL(hAPP(hAPP(c_member(U_545),U_546),c_Nat_Osemiring__1__class_ONats(U_545)))
      | ~ class_Rings_Osemiring__1(U_545) ),
    inference(variable_rename,[status(thm)],[f_151_1]) ).

fof(f_151_3,plain,
    ! [U_546,U_545] :
      ( U_546 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_545),sK16(U_546,U_545))
      | ~ hBOOL(hAPP(hAPP(c_member(U_545),U_546),c_Nat_Osemiring__1__class_ONats(U_545)))
      | ~ class_Rings_Osemiring__1(U_545) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK16]),skolemize(U_544,sK16(U_546,U_545))],[f_151_2]) ).

fof(f_151_4,plain,
    ! [U_545,U_546] :
      ( U_546 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_545),sK16(U_546,U_545))
      | ~ hBOOL(hAPP(hAPP(c_member(U_545),U_546),c_Nat_Osemiring__1__class_ONats(U_545)))
      | ~ class_Rings_Osemiring__1(U_545) ),
    inference(definitional_conversion,[status(esa)],[f_151_3]) ).

cnf(f_151_5,plain,
    ( U_546 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_545),sK16(U_546,U_545))
    | ~ hBOOL(hAPP(hAPP(c_member(U_545),U_546),c_Nat_Osemiring__1__class_ONats(U_545)))
    | ~ class_Rings_Osemiring__1(U_545) ),
    inference(clausify,[status(thm)],[f_151_4]) ).

fof(f_152_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_152_2,plain,
    ! [U_547] :
      ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_547)))
      | hAPP(c_Com_Obody,U_547) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
    inference(variable_rename,[status(thm)],[f_152_1]) ).

fof(f_152_3,plain,
    ! [U_547] :
      ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_547)))
      | hAPP(c_Com_Obody,U_547) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
    inference(definitional_conversion,[status(esa)],[f_152_2]) ).

cnf(f_152_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_547)))
    | hAPP(c_Com_Obody,U_547) = c_Option_Ooption_ONone(tc_Com_Ocom) ),
    inference(clausify,[status(thm)],[f_152_3]) ).

fof(f_153_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_153_2,plain,
    ! [U_549,U_548] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_548)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_549)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_548),U_549)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_548),U_549))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_548)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_549))) ) ),
    inference(variable_rename,[status(thm)],[f_153_1]) ).

fof(f_153_3,plain,
    ( ! [U_553,U_551] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_551)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_553)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_551),U_553)) )
    & ! [U_552,U_550] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_550),U_552))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_550)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_552))) ) ),
    inference(miniscope,[status(thm)],[f_153_2]) ).

fof(f_153_4,plain,
    ( ! [U_551,U_553] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_551)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_553)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_551),U_553)) )
    & ! [U_552,U_550] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_550),U_552))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_550)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_552))) ) ),
    inference(definitional_conversion,[status(esa)],[f_153_3]) ).

cnf(f_153_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_550),U_552))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_550)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_552))) ),
    inference(clausify,[status(thm)],[f_153_4]) ).

cnf(f_153_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_551)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_553)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_551),U_553)) ),
    inference(clausify,[status(thm)],[f_153_4]) ).

fof(f_154_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_154_2,plain,
    ! [U_555,U_554] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_554)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_555)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_554),U_555)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_554),U_555))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_554)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_555))) ) ),
    inference(variable_rename,[status(thm)],[f_154_1]) ).

fof(f_154_3,plain,
    ( ! [U_559,U_557] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_557)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_559)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_557),U_559)) )
    & ! [U_558,U_556] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_556),U_558))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_556)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_558))) ) ),
    inference(miniscope,[status(thm)],[f_154_2]) ).

fof(f_154_4,plain,
    ( ! [U_557,U_559] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_557)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_559)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_557),U_559)) )
    & ! [U_558,U_556] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_556),U_558))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_556)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_558))) ) ),
    inference(definitional_conversion,[status(esa)],[f_154_3]) ).

cnf(f_154_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_556),U_558))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_556)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_558))) ),
    inference(clausify,[status(thm)],[f_154_4]) ).

cnf(f_154_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_557)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_559)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_557),U_559)) ),
    inference(clausify,[status(thm)],[f_154_4]) ).

fof(f_155_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_155_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_155_1]) ).

cnf(f_155_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_155_2]) ).

fof(f_156_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_156_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_156_1]) ).

cnf(f_156_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_156_2]) ).

fof(f_157_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_157_2,plain,
    ! [U_560] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_560) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_560 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_560 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_560) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_157_1]) ).

fof(f_157_3,plain,
    ( ! [U_562] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_562) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_562 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_561] :
        ( U_561 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_561) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_157_2]) ).

fof(f_157_4,plain,
    ( ! [U_562] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_562) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_562 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_561] :
        ( U_561 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_561) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa)],[f_157_3]) ).

cnf(f_157_5,plain,
    ( U_561 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_561) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_157_4]) ).

cnf(f_157_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_562) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_562 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_157_4]) ).

fof(f_158_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_158_2,plain,
    ! [U_565] :
      ( ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_565)))
        | ! [U_564] : hAPP(c_Com_Obody,U_565) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_564) )
      & ( ? [U_563] : hAPP(c_Com_Obody,U_565) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_563)
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_565))) ) ),
    inference(variable_rename,[status(thm)],[f_158_1]) ).

fof(f_158_3,plain,
    ( ! [U_567] :
        ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_567)))
        | ! [U_564] : hAPP(c_Com_Obody,U_567) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_564) )
    & ! [U_566] :
        ( ? [U_563] : hAPP(c_Com_Obody,U_566) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_563)
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_566))) ) ),
    inference(miniscope,[status(thm)],[f_158_2]) ).

fof(f_158_4,plain,
    ( ! [U_567] :
        ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_567)))
        | ! [U_564] : hAPP(c_Com_Obody,U_567) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_564) )
    & ! [U_566] :
        ( hAPP(c_Com_Obody,U_566) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK17(U_566))
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_566))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK17]),skolemize(U_563,sK17(U_566))],[f_158_3]) ).

fof(f_158_5,plain,
    ( ! [U_564,U_567] :
        ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_567)))
        | hAPP(c_Com_Obody,U_567) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_564) )
    & ! [U_566] :
        ( hAPP(c_Com_Obody,U_566) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK17(U_566))
        | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_566))) ) ),
    inference(definitional_conversion,[status(esa)],[f_158_4]) ).

cnf(f_158_6,plain,
    ( hAPP(c_Com_Obody,U_566) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK17(U_566))
    | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_566))) ),
    inference(clausify,[status(thm)],[f_158_5]) ).

cnf(f_158_7,plain,
    ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_567)))
    | hAPP(c_Com_Obody,U_567) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_564) ),
    inference(clausify,[status(thm)],[f_158_5]) ).

fof(f_159_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_159_2,plain,
    ! [U_570,U_569,U_568] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_568),U_570),U_569))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_568),U_569),U_570))
      | U_569 = U_570
      | ~ class_Rings_Olinordered__idom(U_568) ),
    inference(variable_rename,[status(thm)],[f_159_1]) ).

fof(f_159_3,plain,
    ! [U_568,U_569,U_570] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_568),U_570),U_569))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_568),U_569),U_570))
      | U_569 = U_570
      | ~ class_Rings_Olinordered__idom(U_568) ),
    inference(definitional_conversion,[status(esa)],[f_159_2]) ).

cnf(f_159_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_568),U_570),U_569))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_568),U_569),U_570))
    | U_569 = U_570
    | ~ class_Rings_Olinordered__idom(U_568) ),
    inference(clausify,[status(thm)],[f_159_3]) ).

fof(f_160_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_160_2,plain,
    ! [U_571] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_571)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_160_1]) ).

fof(f_160_3,plain,
    ! [U_571] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_571)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_160_2]) ).

cnf(f_160_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_571)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_160_3]) ).

fof(f_161_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_161_2,plain,
    ! [U_573,U_572] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_573),U_572))
      | U_572 = U_573
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_572),U_573)) ),
    inference(variable_rename,[status(thm)],[f_161_1]) ).

fof(f_161_3,plain,
    ! [U_572,U_573] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_573),U_572))
      | U_572 = U_573
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_572),U_573)) ),
    inference(definitional_conversion,[status(esa)],[f_161_2]) ).

cnf(f_161_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_573),U_572))
    | U_572 = U_573
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_572),U_573)) ),
    inference(clausify,[status(thm)],[f_161_3]) ).

fof(f_162_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_162_2,plain,
    ! [U_577,U_576,U_575,U_574] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_574,tc_HOL_Obool)),U_575),U_577))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_574,tc_HOL_Obool)),U_576),U_577))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_574,tc_HOL_Obool)),U_575),U_576)) ),
    inference(variable_rename,[status(thm)],[f_162_1]) ).

fof(f_162_3,plain,
    ! [U_574,U_575,U_576,U_577] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_574,tc_HOL_Obool)),U_575),U_577))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_574,tc_HOL_Obool)),U_576),U_577))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_574,tc_HOL_Obool)),U_575),U_576)) ),
    inference(definitional_conversion,[status(esa)],[f_162_2]) ).

cnf(f_162_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_574,tc_HOL_Obool)),U_575),U_577))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_574,tc_HOL_Obool)),U_576),U_577))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_574,tc_HOL_Obool)),U_575),U_576)) ),
    inference(clausify,[status(thm)],[f_162_3]) ).

fof(f_163_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_163_2,plain,
    ! [U_579,U_578] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_578) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_579)
        | U_578 != U_579 )
      & ( U_578 = U_579
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_578) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_579) ) ),
    inference(variable_rename,[status(thm)],[f_163_1]) ).

fof(f_163_3,plain,
    ( ! [U_583,U_581] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_581) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_583)
        | U_581 != U_583 )
    & ! [U_582,U_580] :
        ( U_580 = U_582
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_580) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_582) ) ),
    inference(miniscope,[status(thm)],[f_163_2]) ).

fof(f_163_4,plain,
    ( ! [U_581,U_583] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_581) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_583)
        | U_581 != U_583 )
    & ! [U_580,U_582] :
        ( U_580 = U_582
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_580) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_582) ) ),
    inference(definitional_conversion,[status(esa)],[f_163_3]) ).

cnf(f_163_5,plain,
    ( U_580 = U_582
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_580) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_582) ),
    inference(clausify,[status(thm)],[f_163_4]) ).

cnf(f_163_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_581) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_583)
    | U_581 != U_583 ),
    inference(clausify,[status(thm)],[f_163_4]) ).

fof(f_164_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_164_2,plain,
    ! [U_585,U_584] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_584) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_585)
        | U_584 != U_585 )
      & ( U_584 = U_585
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_584) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_585) ) ),
    inference(variable_rename,[status(thm)],[f_164_1]) ).

fof(f_164_3,plain,
    ( ! [U_589,U_587] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_587) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_589)
        | U_587 != U_589 )
    & ! [U_588,U_586] :
        ( U_586 = U_588
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_586) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_588) ) ),
    inference(miniscope,[status(thm)],[f_164_2]) ).

fof(f_164_4,plain,
    ( ! [U_587,U_589] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_587) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_589)
        | U_587 != U_589 )
    & ! [U_588,U_586] :
        ( U_586 = U_588
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_586) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_588) ) ),
    inference(definitional_conversion,[status(esa)],[f_164_3]) ).

cnf(f_164_5,plain,
    ( U_586 = U_588
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_586) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_588) ),
    inference(clausify,[status(thm)],[f_164_4]) ).

cnf(f_164_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_587) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_589)
    | U_587 != U_589 ),
    inference(clausify,[status(thm)],[f_164_4]) ).

fof(f_165_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_165_2,plain,
    ! [U_591,U_590] :
      ( hBOOL(hAPP(c_Com_OWT,U_591))
      | hAPP(c_Com_Obody,U_590) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_591)
      | ~ c_Com_OWT__bodies ),
    inference(variable_rename,[status(thm)],[f_165_1]) ).

fof(f_165_3,plain,
    ( ! [U_591] :
        ( ! [U_590] : hAPP(c_Com_Obody,U_590) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_591)
        | hBOOL(hAPP(c_Com_OWT,U_591)) )
    | ~ c_Com_OWT__bodies ),
    inference(miniscope,[status(thm)],[f_165_2]) ).

fof(f_165_4,plain,
    ! [U_590,U_591] :
      ( hAPP(c_Com_Obody,U_590) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_591)
      | hBOOL(hAPP(c_Com_OWT,U_591))
      | ~ c_Com_OWT__bodies ),
    inference(definitional_conversion,[status(esa)],[f_165_3]) ).

cnf(f_165_5,plain,
    ( hAPP(c_Com_Obody,U_590) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_591)
    | hBOOL(hAPP(c_Com_OWT,U_591))
    | ~ c_Com_OWT__bodies ),
    inference(clausify,[status(thm)],[f_165_4]) ).

fof(f_166_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_166_2,plain,
    ! [U_593] :
      ( ? [U_592] : hAPP(c_Com_Obody,U_593) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),U_592)
      | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_593))) ),
    inference(variable_rename,[status(thm)],[f_166_1]) ).

fof(f_166_3,plain,
    ! [U_593] :
      ( hAPP(c_Com_Obody,U_593) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK18(U_593))
      | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_593))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK18]),skolemize(U_592,sK18(U_593))],[f_166_2]) ).

fof(f_166_4,plain,
    ! [U_593] :
      ( hAPP(c_Com_Obody,U_593) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK18(U_593))
      | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_593))) ),
    inference(definitional_conversion,[status(esa)],[f_166_3]) ).

cnf(f_166_5,plain,
    ( hAPP(c_Com_Obody,U_593) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),sK18(U_593))
    | ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,U_593))) ),
    inference(clausify,[status(thm)],[f_166_4]) ).

fof(f_167_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_167_2,plain,
    ! [U_595,U_594] : hAPP(c_Option_Othe(U_594),hAPP(c_Option_Ooption_OSome(U_594),U_595)) = U_595,
    inference(variable_rename,[status(thm)],[f_167_1]) ).

fof(f_167_3,plain,
    ! [U_594,U_595] : hAPP(c_Option_Othe(U_594),hAPP(c_Option_Ooption_OSome(U_594),U_595)) = U_595,
    inference(definitional_conversion,[status(esa)],[f_167_2]) ).

cnf(f_167_4,plain,
    hAPP(c_Option_Othe(U_594),hAPP(c_Option_Ooption_OSome(U_594),U_595)) = U_595,
    inference(clausify,[status(thm)],[f_167_3]) ).

fof(f_168_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_168_2,plain,
    ! [U_597,U_596] : c_Option_Ooption_ONone(U_596) != hAPP(c_Option_Ooption_OSome(U_596),U_597),
    inference(variable_rename,[status(thm)],[f_168_1]) ).

fof(f_168_3,plain,
    ! [U_596,U_597] : c_Option_Ooption_ONone(U_596) != hAPP(c_Option_Ooption_OSome(U_596),U_597),
    inference(definitional_conversion,[status(esa)],[f_168_2]) ).

cnf(f_168_4,plain,
    c_Option_Ooption_ONone(U_596) != hAPP(c_Option_Ooption_OSome(U_596),U_597),
    inference(clausify,[status(thm)],[f_168_3]) ).

fof(f_169_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_169_2,plain,
    ! [U_599,U_598] : hAPP(c_Option_Ooption_OSome(U_598),U_599) != c_Option_Ooption_ONone(U_598),
    inference(variable_rename,[status(thm)],[f_169_1]) ).

fof(f_169_3,plain,
    ! [U_598,U_599] : hAPP(c_Option_Ooption_OSome(U_598),U_599) != c_Option_Ooption_ONone(U_598),
    inference(definitional_conversion,[status(esa)],[f_169_2]) ).

cnf(f_169_4,plain,
    hAPP(c_Option_Ooption_OSome(U_598),U_599) != c_Option_Ooption_ONone(U_598),
    inference(clausify,[status(thm)],[f_169_3]) ).

fof(f_170_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_170_2,plain,
    ! [U_603,U_602] :
      ( ( ! [U_601] : U_602 != hAPP(c_Option_Ooption_OSome(U_603),U_601)
        | U_602 != c_Option_Ooption_ONone(U_603) )
      & ( U_602 = c_Option_Ooption_ONone(U_603)
        | ? [U_600] : U_602 = hAPP(c_Option_Ooption_OSome(U_603),U_600) ) ),
    inference(variable_rename,[status(thm)],[f_170_1]) ).

fof(f_170_3,plain,
    ( ! [U_607,U_605] :
        ( ! [U_601] : U_605 != hAPP(c_Option_Ooption_OSome(U_607),U_601)
        | U_605 != c_Option_Ooption_ONone(U_607) )
    & ! [U_606,U_604] :
        ( U_604 = c_Option_Ooption_ONone(U_606)
        | ? [U_600] : U_604 = hAPP(c_Option_Ooption_OSome(U_606),U_600) ) ),
    inference(miniscope,[status(thm)],[f_170_2]) ).

fof(f_170_4,plain,
    ( ! [U_607,U_605] :
        ( ! [U_601] : U_605 != hAPP(c_Option_Ooption_OSome(U_607),U_601)
        | U_605 != c_Option_Ooption_ONone(U_607) )
    & ! [U_606,U_604] :
        ( U_604 = c_Option_Ooption_ONone(U_606)
        | U_604 = hAPP(c_Option_Ooption_OSome(U_606),sK19(U_606,U_604)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK19]),skolemize(U_600,sK19(U_606,U_604))],[f_170_3]) ).

fof(f_170_5,plain,
    ( ! [U_601,U_605,U_607] :
        ( U_605 != hAPP(c_Option_Ooption_OSome(U_607),U_601)
        | U_605 != c_Option_Ooption_ONone(U_607) )
    & ! [U_604,U_606] :
        ( U_604 = c_Option_Ooption_ONone(U_606)
        | U_604 = hAPP(c_Option_Ooption_OSome(U_606),sK19(U_606,U_604)) ) ),
    inference(definitional_conversion,[status(esa)],[f_170_4]) ).

cnf(f_170_6,plain,
    ( U_604 = c_Option_Ooption_ONone(U_606)
    | U_604 = hAPP(c_Option_Ooption_OSome(U_606),sK19(U_606,U_604)) ),
    inference(clausify,[status(thm)],[f_170_5]) ).

cnf(f_170_7,plain,
    ( U_605 != hAPP(c_Option_Ooption_OSome(U_607),U_601)
    | U_605 != c_Option_Ooption_ONone(U_607) ),
    inference(clausify,[status(thm)],[f_170_5]) ).

fof(f_171_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_171_2,plain,
    ! [U_611,U_610] :
      ( ( U_610 != c_Option_Ooption_ONone(U_611)
        | ! [U_609] : U_610 != hAPP(c_Option_Ooption_OSome(U_611),U_609) )
      & ( ? [U_608] : U_610 = hAPP(c_Option_Ooption_OSome(U_611),U_608)
        | U_610 = c_Option_Ooption_ONone(U_611) ) ),
    inference(variable_rename,[status(thm)],[f_171_1]) ).

fof(f_171_3,plain,
    ( ! [U_615,U_613] :
        ( U_613 != c_Option_Ooption_ONone(U_615)
        | ! [U_609] : U_613 != hAPP(c_Option_Ooption_OSome(U_615),U_609) )
    & ! [U_614,U_612] :
        ( ? [U_608] : U_612 = hAPP(c_Option_Ooption_OSome(U_614),U_608)
        | U_612 = c_Option_Ooption_ONone(U_614) ) ),
    inference(miniscope,[status(thm)],[f_171_2]) ).

fof(f_171_4,plain,
    ( ! [U_615,U_613] :
        ( U_613 != c_Option_Ooption_ONone(U_615)
        | ! [U_609] : U_613 != hAPP(c_Option_Ooption_OSome(U_615),U_609) )
    & ! [U_614,U_612] :
        ( U_612 = hAPP(c_Option_Ooption_OSome(U_614),sK20(U_614,U_612))
        | U_612 = c_Option_Ooption_ONone(U_614) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK20]),skolemize(U_608,sK20(U_614,U_612))],[f_171_3]) ).

fof(f_171_5,plain,
    ( ! [U_609,U_613,U_615] :
        ( U_613 != c_Option_Ooption_ONone(U_615)
        | U_613 != hAPP(c_Option_Ooption_OSome(U_615),U_609) )
    & ! [U_614,U_612] :
        ( U_612 = hAPP(c_Option_Ooption_OSome(U_614),sK20(U_614,U_612))
        | U_612 = c_Option_Ooption_ONone(U_614) ) ),
    inference(definitional_conversion,[status(esa)],[f_171_4]) ).

cnf(f_171_6,plain,
    ( U_612 = hAPP(c_Option_Ooption_OSome(U_614),sK20(U_614,U_612))
    | U_612 = c_Option_Ooption_ONone(U_614) ),
    inference(clausify,[status(thm)],[f_171_5]) ).

cnf(f_171_7,plain,
    ( U_613 != c_Option_Ooption_ONone(U_615)
    | U_613 != hAPP(c_Option_Ooption_OSome(U_615),U_609) ),
    inference(clausify,[status(thm)],[f_171_5]) ).

fof(f_172_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_172_2,plain,
    ! [U_617] :
      ( ? [U_616] :
          ( U_617 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_616)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_616)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_617)) ),
    inference(variable_rename,[status(thm)],[f_172_1]) ).

fof(f_172_3,plain,
    ! [U_617] :
      ( ( U_617 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK21(U_617))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK21(U_617))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_617)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK21]),skolemize(U_616,sK21(U_617))],[f_172_2]) ).

fof(f_172_4,plain,
    ( ! [U_617] :
        ( U_617 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK21(U_617))
        | ~ sP28(U_617) )
    & ! [U_617] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK21(U_617)))
        | ~ sP28(U_617) )
    & ! [U_617] :
        ( sP28(U_617)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_617)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP28])],[f_172_3]) ).

cnf(f_172_5,plain,
    ( sP28(U_617)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_617)) ),
    inference(clausify,[status(thm)],[f_172_4]) ).

cnf(f_172_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK21(U_617)))
    | ~ sP28(U_617) ),
    inference(clausify,[status(thm)],[f_172_4]) ).

cnf(f_172_7,plain,
    ( U_617 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK21(U_617))
    | ~ sP28(U_617) ),
    inference(clausify,[status(thm)],[f_172_4]) ).

fof(f_173_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_173_2,plain,
    ! [U_619,U_618] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_618),c_Groups_Ozero__class_Ozero(U_618)),hAPP(c_Int_Oring__1__class_Oof__int(U_618),U_619)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_619)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_619))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_618),c_Groups_Ozero__class_Ozero(U_618)),hAPP(c_Int_Oring__1__class_Oof__int(U_618),U_619))) ) )
      | ~ class_Rings_Olinordered__idom(U_618) ),
    inference(variable_rename,[status(thm)],[f_173_1]) ).

fof(f_173_3,plain,
    ( ! [U_619,U_618] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_618),c_Groups_Ozero__class_Ozero(U_618)),hAPP(c_Int_Oring__1__class_Oof__int(U_618),U_619)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_619))
        | ~ sP29(U_619,U_618) )
    & ! [U_619,U_618] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_619))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_618),c_Groups_Ozero__class_Ozero(U_618)),hAPP(c_Int_Oring__1__class_Oof__int(U_618),U_619)))
        | ~ sP29(U_619,U_618) )
    & ! [U_619,U_618] :
        ( sP29(U_619,U_618)
        | ~ class_Rings_Olinordered__idom(U_618) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP29])],[f_173_2]) ).

cnf(f_173_4,plain,
    ( sP29(U_619,U_618)
    | ~ class_Rings_Olinordered__idom(U_618) ),
    inference(clausify,[status(thm)],[f_173_3]) ).

cnf(f_173_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_619))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_618),c_Groups_Ozero__class_Ozero(U_618)),hAPP(c_Int_Oring__1__class_Oof__int(U_618),U_619)))
    | ~ sP29(U_619,U_618) ),
    inference(clausify,[status(thm)],[f_173_3]) ).

cnf(f_173_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_618),c_Groups_Ozero__class_Ozero(U_618)),hAPP(c_Int_Oring__1__class_Oof__int(U_618),U_619)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_619))
    | ~ sP29(U_619,U_618) ),
    inference(clausify,[status(thm)],[f_173_3]) ).

fof(f_174_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_174_2,plain,
    ! [U_621,U_620] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_620),hAPP(c_Int_Oring__1__class_Oof__int(U_620),U_621)),c_Groups_Ozero__class_Ozero(U_620)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_621),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_621),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_620),hAPP(c_Int_Oring__1__class_Oof__int(U_620),U_621)),c_Groups_Ozero__class_Ozero(U_620))) ) )
      | ~ class_Rings_Olinordered__idom(U_620) ),
    inference(variable_rename,[status(thm)],[f_174_1]) ).

fof(f_174_3,plain,
    ( ! [U_621,U_620] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_620),hAPP(c_Int_Oring__1__class_Oof__int(U_620),U_621)),c_Groups_Ozero__class_Ozero(U_620)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_621),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP30(U_621,U_620) )
    & ! [U_621,U_620] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_621),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_620),hAPP(c_Int_Oring__1__class_Oof__int(U_620),U_621)),c_Groups_Ozero__class_Ozero(U_620)))
        | ~ sP30(U_621,U_620) )
    & ! [U_621,U_620] :
        ( sP30(U_621,U_620)
        | ~ class_Rings_Olinordered__idom(U_620) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP30])],[f_174_2]) ).

cnf(f_174_4,plain,
    ( sP30(U_621,U_620)
    | ~ class_Rings_Olinordered__idom(U_620) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_621),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_620),hAPP(c_Int_Oring__1__class_Oof__int(U_620),U_621)),c_Groups_Ozero__class_Ozero(U_620)))
    | ~ sP30(U_621,U_620) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

cnf(f_174_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_620),hAPP(c_Int_Oring__1__class_Oof__int(U_620),U_621)),c_Groups_Ozero__class_Ozero(U_620)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_621),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP30(U_621,U_620) ),
    inference(clausify,[status(thm)],[f_174_3]) ).

fof(f_175_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_175_2,plain,
    ! [U_624,U_623,U_622] :
      ( 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_624)),U_622)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_624)),U_623)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_624))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_622),U_623)) ),
    inference(variable_rename,[status(thm)],[f_175_1]) ).

fof(f_175_3,plain,
    ! [U_622,U_624,U_623] :
      ( 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_624)),U_622)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_624)),U_623)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_624))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_622),U_623)) ),
    inference(definitional_conversion,[status(esa)],[f_175_2]) ).

cnf(f_175_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_624)),U_622)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_624)),U_623)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_624))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_622),U_623)) ),
    inference(clausify,[status(thm)],[f_175_3]) ).

fof(f_176_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_176_2,plain,
    ! [U_627,U_626,U_625] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_625),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_626),U_627)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_625),hAPP(c_Int_Oring__1__class_Oof__int(U_625),U_626)),hAPP(c_Int_Oring__1__class_Oof__int(U_625),U_627))
      | ~ class_Rings_Oring__1(U_625) ),
    inference(variable_rename,[status(thm)],[f_176_1]) ).

fof(f_176_3,plain,
    ! [U_625,U_626,U_627] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_625),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_626),U_627)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_625),hAPP(c_Int_Oring__1__class_Oof__int(U_625),U_626)),hAPP(c_Int_Oring__1__class_Oof__int(U_625),U_627))
      | ~ class_Rings_Oring__1(U_625) ),
    inference(definitional_conversion,[status(esa)],[f_176_2]) ).

cnf(f_176_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_625),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_626),U_627)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_625),hAPP(c_Int_Oring__1__class_Oof__int(U_625),U_626)),hAPP(c_Int_Oring__1__class_Oof__int(U_625),U_627))
    | ~ class_Rings_Oring__1(U_625) ),
    inference(clausify,[status(thm)],[f_176_3]) ).

fof(f_177_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_177_2,plain,
    ! [U_629,U_628] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_628),U_629) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_629),U_628),
    inference(variable_rename,[status(thm)],[f_177_1]) ).

fof(f_177_3,plain,
    ! [U_629,U_628] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_628),U_629) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_629),U_628),
    inference(definitional_conversion,[status(esa)],[f_177_2]) ).

cnf(f_177_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_628),U_629) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_629),U_628),
    inference(clausify,[status(thm)],[f_177_3]) ).

fof(f_178_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_178_2,plain,
    ! [U_632,U_631,U_630] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_630),U_631) = hAPP(c_Int_Oring__1__class_Oof__int(U_630),U_632)
          | U_631 != U_632 )
        & ( U_631 = U_632
          | hAPP(c_Int_Oring__1__class_Oof__int(U_630),U_631) != hAPP(c_Int_Oring__1__class_Oof__int(U_630),U_632) ) )
      | ~ class_Int_Oring__char__0(U_630) ),
    inference(variable_rename,[status(thm)],[f_178_1]) ).

fof(f_178_3,plain,
    ( ! [U_630,U_631,U_632] :
        ( hAPP(c_Int_Oring__1__class_Oof__int(U_630),U_631) = hAPP(c_Int_Oring__1__class_Oof__int(U_630),U_632)
        | U_631 != U_632
        | ~ sP31(U_630,U_631,U_632) )
    & ! [U_630,U_631,U_632] :
        ( U_631 = U_632
        | hAPP(c_Int_Oring__1__class_Oof__int(U_630),U_631) != hAPP(c_Int_Oring__1__class_Oof__int(U_630),U_632)
        | ~ sP31(U_630,U_631,U_632) )
    & ! [U_630,U_631,U_632] :
        ( sP31(U_630,U_631,U_632)
        | ~ class_Int_Oring__char__0(U_630) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP31])],[f_178_2]) ).

cnf(f_178_4,plain,
    ( sP31(U_630,U_631,U_632)
    | ~ class_Int_Oring__char__0(U_630) ),
    inference(clausify,[status(thm)],[f_178_3]) ).

cnf(f_178_5,plain,
    ( U_631 = U_632
    | hAPP(c_Int_Oring__1__class_Oof__int(U_630),U_631) != hAPP(c_Int_Oring__1__class_Oof__int(U_630),U_632)
    | ~ sP31(U_630,U_631,U_632) ),
    inference(clausify,[status(thm)],[f_178_3]) ).

cnf(f_178_6,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_630),U_631) = hAPP(c_Int_Oring__1__class_Oof__int(U_630),U_632)
    | U_631 != U_632
    | ~ sP31(U_630,U_631,U_632) ),
    inference(clausify,[status(thm)],[f_178_3]) ).

fof(f_179_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_179_2,plain,
    ! [U_635,U_634,U_633] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_633),U_634)),U_635) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_633),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_634),U_635)),
    inference(variable_rename,[status(thm)],[f_179_1]) ).

fof(f_179_3,plain,
    ! [U_634,U_633,U_635] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_633),U_634)),U_635) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_633),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_634),U_635)),
    inference(definitional_conversion,[status(esa)],[f_179_2]) ).

cnf(f_179_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_633),U_634)),U_635) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_633),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_634),U_635)),
    inference(clausify,[status(thm)],[f_179_3]) ).

fof(f_180_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_180_2,plain,
    ! [U_639,U_638,U_637,U_636] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_636),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_636),U_637),U_638)),U_639) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_636),U_637),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_636),U_638),U_639))
      | ~ class_Groups_Oab__semigroup__mult(U_636) ),
    inference(variable_rename,[status(thm)],[f_180_1]) ).

fof(f_180_3,plain,
    ! [U_636,U_637,U_638,U_639] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_636),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_636),U_637),U_638)),U_639) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_636),U_637),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_636),U_638),U_639))
      | ~ class_Groups_Oab__semigroup__mult(U_636) ),
    inference(definitional_conversion,[status(esa)],[f_180_2]) ).

cnf(f_180_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_636),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_636),U_637),U_638)),U_639) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_636),U_637),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_636),U_638),U_639))
    | ~ class_Groups_Oab__semigroup__mult(U_636) ),
    inference(clausify,[status(thm)],[f_180_3]) ).

fof(f_181_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_181_2,plain,
    ! [U_642,U_641,U_640] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_640),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_641),U_642)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_640),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_640),U_641)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_640),U_642))
      | ~ class_Rings_Osemiring__1(U_640) ),
    inference(variable_rename,[status(thm)],[f_181_1]) ).

fof(f_181_3,plain,
    ! [U_640,U_641,U_642] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_640),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_641),U_642)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_640),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_640),U_641)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_640),U_642))
      | ~ class_Rings_Osemiring__1(U_640) ),
    inference(definitional_conversion,[status(esa)],[f_181_2]) ).

cnf(f_181_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_640),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_641),U_642)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_640),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_640),U_641)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_640),U_642))
    | ~ class_Rings_Osemiring__1(U_640) ),
    inference(clausify,[status(thm)],[f_181_3]) ).

fof(f_182_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_182_2,plain,
    ! [U_645,U_644,U_643] :
      ( U_645 = c_Groups_Ozero__class_Ozero(U_643)
      | U_644 = c_Groups_Ozero__class_Ozero(U_643)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_643),U_644),U_645) != c_Groups_Ozero__class_Ozero(U_643)
      | ~ class_Rings_Ono__zero__divisors(U_643) ),
    inference(variable_rename,[status(thm)],[f_182_1]) ).

fof(f_182_3,plain,
    ! [U_643,U_644,U_645] :
      ( U_645 = c_Groups_Ozero__class_Ozero(U_643)
      | U_644 = c_Groups_Ozero__class_Ozero(U_643)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_643),U_644),U_645) != c_Groups_Ozero__class_Ozero(U_643)
      | ~ class_Rings_Ono__zero__divisors(U_643) ),
    inference(definitional_conversion,[status(esa)],[f_182_2]) ).

cnf(f_182_4,plain,
    ( U_645 = c_Groups_Ozero__class_Ozero(U_643)
    | U_644 = c_Groups_Ozero__class_Ozero(U_643)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_643),U_644),U_645) != c_Groups_Ozero__class_Ozero(U_643)
    | ~ class_Rings_Ono__zero__divisors(U_643) ),
    inference(clausify,[status(thm)],[f_182_3]) ).

fof(f_183_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_183_2,plain,
    ! [U_648,U_647,U_646] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_646),U_647),U_648) != c_Groups_Ozero__class_Ozero(U_646)
      | U_648 = c_Groups_Ozero__class_Ozero(U_646)
      | U_647 = c_Groups_Ozero__class_Ozero(U_646)
      | ~ class_Rings_Ono__zero__divisors(U_646) ),
    inference(variable_rename,[status(thm)],[f_183_1]) ).

fof(f_183_3,plain,
    ! [U_647,U_646,U_648] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_646),U_647),U_648) != c_Groups_Ozero__class_Ozero(U_646)
      | U_648 = c_Groups_Ozero__class_Ozero(U_646)
      | U_647 = c_Groups_Ozero__class_Ozero(U_646)
      | ~ class_Rings_Ono__zero__divisors(U_646) ),
    inference(definitional_conversion,[status(esa)],[f_183_2]) ).

cnf(f_183_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_646),U_647),U_648) != c_Groups_Ozero__class_Ozero(U_646)
    | U_648 = c_Groups_Ozero__class_Ozero(U_646)
    | U_647 = c_Groups_Ozero__class_Ozero(U_646)
    | ~ class_Rings_Ono__zero__divisors(U_646) ),
    inference(clausify,[status(thm)],[f_183_3]) ).

fof(f_184_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_184_2,plain,
    ! [U_651,U_650,U_649] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_649),U_650),U_651) = c_Groups_Ozero__class_Ozero(U_649)
          | ( U_651 != c_Groups_Ozero__class_Ozero(U_649)
            & U_650 != c_Groups_Ozero__class_Ozero(U_649) ) )
        & ( U_651 = c_Groups_Ozero__class_Ozero(U_649)
          | U_650 = c_Groups_Ozero__class_Ozero(U_649)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_649),U_650),U_651) != c_Groups_Ozero__class_Ozero(U_649) ) )
      | ~ class_Rings_Oring__no__zero__divisors(U_649) ),
    inference(variable_rename,[status(thm)],[f_184_1]) ).

fof(f_184_3,plain,
    ( ! [U_649,U_650,U_651] :
        ( U_651 != c_Groups_Ozero__class_Ozero(U_649)
        | ~ sP32(U_649,U_650,U_651) )
    & ! [U_649,U_650,U_651] :
        ( U_650 != c_Groups_Ozero__class_Ozero(U_649)
        | ~ sP32(U_649,U_650,U_651) )
    & ! [U_649,U_650,U_651] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_649),U_650),U_651) = c_Groups_Ozero__class_Ozero(U_649)
        | sP32(U_649,U_650,U_651)
        | ~ sP33(U_649,U_650,U_651) )
    & ! [U_649,U_650,U_651] :
        ( U_651 = c_Groups_Ozero__class_Ozero(U_649)
        | U_650 = c_Groups_Ozero__class_Ozero(U_649)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_649),U_650),U_651) != c_Groups_Ozero__class_Ozero(U_649)
        | ~ sP33(U_649,U_650,U_651) )
    & ! [U_649,U_650,U_651] :
        ( sP33(U_649,U_650,U_651)
        | ~ class_Rings_Oring__no__zero__divisors(U_649) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP32,sP33])],[f_184_2]) ).

cnf(f_184_4,plain,
    ( sP33(U_649,U_650,U_651)
    | ~ class_Rings_Oring__no__zero__divisors(U_649) ),
    inference(clausify,[status(thm)],[f_184_3]) ).

cnf(f_184_5,plain,
    ( U_651 = c_Groups_Ozero__class_Ozero(U_649)
    | U_650 = c_Groups_Ozero__class_Ozero(U_649)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_649),U_650),U_651) != c_Groups_Ozero__class_Ozero(U_649)
    | ~ sP33(U_649,U_650,U_651) ),
    inference(clausify,[status(thm)],[f_184_3]) ).

cnf(f_184_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_649),U_650),U_651) = c_Groups_Ozero__class_Ozero(U_649)
    | sP32(U_649,U_650,U_651)
    | ~ sP33(U_649,U_650,U_651) ),
    inference(clausify,[status(thm)],[f_184_3]) ).

cnf(f_184_7,plain,
    ( U_650 != c_Groups_Ozero__class_Ozero(U_649)
    | ~ sP32(U_649,U_650,U_651) ),
    inference(clausify,[status(thm)],[f_184_3]) ).

cnf(f_184_8,plain,
    ( U_651 != c_Groups_Ozero__class_Ozero(U_649)
    | ~ sP32(U_649,U_650,U_651) ),
    inference(clausify,[status(thm)],[f_184_3]) ).

fof(f_185_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_185_2,plain,
    ! [U_653,U_652] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_652),U_653),c_Groups_Ozero__class_Ozero(U_652)) = c_Groups_Ozero__class_Ozero(U_652)
      | ~ class_Rings_Omult__zero(U_652) ),
    inference(variable_rename,[status(thm)],[f_185_1]) ).

fof(f_185_3,plain,
    ! [U_652,U_653] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_652),U_653),c_Groups_Ozero__class_Ozero(U_652)) = c_Groups_Ozero__class_Ozero(U_652)
      | ~ class_Rings_Omult__zero(U_652) ),
    inference(definitional_conversion,[status(esa)],[f_185_2]) ).

cnf(f_185_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_652),U_653),c_Groups_Ozero__class_Ozero(U_652)) = c_Groups_Ozero__class_Ozero(U_652)
    | ~ class_Rings_Omult__zero(U_652) ),
    inference(clausify,[status(thm)],[f_185_3]) ).

fof(f_186_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_186_2,plain,
    ! [U_655,U_654] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_654),c_Groups_Ozero__class_Ozero(U_654)),U_655) = c_Groups_Ozero__class_Ozero(U_654)
      | ~ class_Rings_Omult__zero(U_654) ),
    inference(variable_rename,[status(thm)],[f_186_1]) ).

fof(f_186_3,plain,
    ! [U_655,U_654] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_654),c_Groups_Ozero__class_Ozero(U_654)),U_655) = c_Groups_Ozero__class_Ozero(U_654)
      | ~ class_Rings_Omult__zero(U_654) ),
    inference(definitional_conversion,[status(esa)],[f_186_2]) ).

cnf(f_186_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_654),c_Groups_Ozero__class_Ozero(U_654)),U_655) = c_Groups_Ozero__class_Ozero(U_654)
    | ~ class_Rings_Omult__zero(U_654) ),
    inference(clausify,[status(thm)],[f_186_3]) ).

fof(f_187_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_187_2,plain,
    ! [U_656] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_656)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_656),
    inference(variable_rename,[status(thm)],[f_187_1]) ).

fof(f_187_3,plain,
    ! [U_656] : hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_656)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_656),
    inference(definitional_conversion,[status(esa)],[f_187_2]) ).

cnf(f_187_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_656)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_656),
    inference(clausify,[status(thm)],[f_187_3]) ).

fof(f_188_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_188_2,plain,
    ! [U_660,U_659,U_658,U_657] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_657),U_660),U_659)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_657),U_660),U_658)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_657),U_660),c_Groups_Ozero__class_Ozero(U_657)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_657),U_658),U_659))
      | ~ class_Rings_Olinordered__ring__strict(U_657) ),
    inference(variable_rename,[status(thm)],[f_188_1]) ).

fof(f_188_3,plain,
    ! [U_657,U_658,U_659,U_660] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_657),U_660),U_659)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_657),U_660),U_658)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_657),U_660),c_Groups_Ozero__class_Ozero(U_657)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_657),U_658),U_659))
      | ~ class_Rings_Olinordered__ring__strict(U_657) ),
    inference(definitional_conversion,[status(esa)],[f_188_2]) ).

cnf(f_188_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_657),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_657),U_660),U_659)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_657),U_660),U_658)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_657),U_660),c_Groups_Ozero__class_Ozero(U_657)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_657),U_658),U_659))
    | ~ class_Rings_Olinordered__ring__strict(U_657) ),
    inference(clausify,[status(thm)],[f_188_3]) ).

fof(f_189_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_189_2,plain,
    ! [U_664,U_663,U_662,U_661] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_661),U_663),U_664)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_661),U_662),U_664)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_661),U_664),c_Groups_Ozero__class_Ozero(U_661)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_661),U_662),U_663))
      | ~ class_Rings_Olinordered__ring__strict(U_661) ),
    inference(variable_rename,[status(thm)],[f_189_1]) ).

fof(f_189_3,plain,
    ! [U_661,U_662,U_663,U_664] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_661),U_663),U_664)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_661),U_662),U_664)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_661),U_664),c_Groups_Ozero__class_Ozero(U_661)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_661),U_662),U_663))
      | ~ class_Rings_Olinordered__ring__strict(U_661) ),
    inference(definitional_conversion,[status(esa)],[f_189_2]) ).

cnf(f_189_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_661),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_661),U_663),U_664)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_661),U_662),U_664)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_661),U_664),c_Groups_Ozero__class_Ozero(U_661)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_661),U_662),U_663))
    | ~ class_Rings_Olinordered__ring__strict(U_661) ),
    inference(clausify,[status(thm)],[f_189_3]) ).

fof(f_190_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_190_2,plain,
    ! [U_668,U_667,U_666,U_665] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_665),U_668),U_666)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_665),U_668),U_667)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_665),c_Groups_Ozero__class_Ozero(U_665)),U_668))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_665),U_666),U_667))
      | ~ class_Rings_Olinordered__comm__semiring__strict(U_665) ),
    inference(variable_rename,[status(thm)],[f_190_1]) ).

fof(f_190_3,plain,
    ! [U_665,U_666,U_667,U_668] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_665),U_668),U_666)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_665),U_668),U_667)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_665),c_Groups_Ozero__class_Ozero(U_665)),U_668))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_665),U_666),U_667))
      | ~ class_Rings_Olinordered__comm__semiring__strict(U_665) ),
    inference(definitional_conversion,[status(esa)],[f_190_2]) ).

cnf(f_190_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_665),U_668),U_666)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_665),U_668),U_667)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_665),c_Groups_Ozero__class_Ozero(U_665)),U_668))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_665),U_666),U_667))
    | ~ class_Rings_Olinordered__comm__semiring__strict(U_665) ),
    inference(clausify,[status(thm)],[f_190_3]) ).

fof(f_191_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_191_2,plain,
    ! [U_672,U_671,U_670,U_669] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_669),U_672),U_670)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_669),U_672),U_671)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_669),c_Groups_Ozero__class_Ozero(U_669)),U_672))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_669),U_670),U_671))
      | ~ class_Rings_Olinordered__semiring__strict(U_669) ),
    inference(variable_rename,[status(thm)],[f_191_1]) ).

fof(f_191_3,plain,
    ! [U_669,U_670,U_671,U_672] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_669),U_672),U_670)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_669),U_672),U_671)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_669),c_Groups_Ozero__class_Ozero(U_669)),U_672))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_669),U_670),U_671))
      | ~ class_Rings_Olinordered__semiring__strict(U_669) ),
    inference(definitional_conversion,[status(esa)],[f_191_2]) ).

cnf(f_191_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_669),U_672),U_670)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_669),U_672),U_671)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_669),c_Groups_Ozero__class_Ozero(U_669)),U_672))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_669),U_670),U_671))
    | ~ class_Rings_Olinordered__semiring__strict(U_669) ),
    inference(clausify,[status(thm)],[f_191_3]) ).

fof(f_192_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_192_2,plain,
    ! [U_676,U_675,U_674,U_673] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_673),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_673),U_674),U_676)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_673),U_675),U_676)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_673),c_Groups_Ozero__class_Ozero(U_673)),U_676))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_673),U_674),U_675))
      | ~ class_Rings_Olinordered__semiring__strict(U_673) ),
    inference(variable_rename,[status(thm)],[f_192_1]) ).

fof(f_192_3,plain,
    ! [U_673,U_674,U_675,U_676] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_673),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_673),U_674),U_676)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_673),U_675),U_676)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_673),c_Groups_Ozero__class_Ozero(U_673)),U_676))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_673),U_674),U_675))
      | ~ class_Rings_Olinordered__semiring__strict(U_673) ),
    inference(definitional_conversion,[status(esa)],[f_192_2]) ).

cnf(f_192_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_673),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_673),U_674),U_676)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_673),U_675),U_676)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_673),c_Groups_Ozero__class_Ozero(U_673)),U_676))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_673),U_674),U_675))
    | ~ class_Rings_Olinordered__semiring__strict(U_673) ),
    inference(clausify,[status(thm)],[f_192_3]) ).

fof(f_193_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_193_2,plain,
    ! [U_679,U_678,U_677] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_677),c_Groups_Ozero__class_Ozero(U_677)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_677),U_678),U_679)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_677),U_679),c_Groups_Ozero__class_Ozero(U_677)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_677),U_678),c_Groups_Ozero__class_Ozero(U_677)))
      | ~ class_Rings_Olinordered__ring__strict(U_677) ),
    inference(variable_rename,[status(thm)],[f_193_1]) ).

fof(f_193_3,plain,
    ! [U_678,U_677,U_679] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_677),c_Groups_Ozero__class_Ozero(U_677)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_677),U_678),U_679)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_677),U_679),c_Groups_Ozero__class_Ozero(U_677)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_677),U_678),c_Groups_Ozero__class_Ozero(U_677)))
      | ~ class_Rings_Olinordered__ring__strict(U_677) ),
    inference(definitional_conversion,[status(esa)],[f_193_2]) ).

cnf(f_193_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_677),c_Groups_Ozero__class_Ozero(U_677)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_677),U_678),U_679)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_677),U_679),c_Groups_Ozero__class_Ozero(U_677)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_677),U_678),c_Groups_Ozero__class_Ozero(U_677)))
    | ~ class_Rings_Olinordered__ring__strict(U_677) ),
    inference(clausify,[status(thm)],[f_193_3]) ).

fof(f_194_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_194_2,plain,
    ! [U_682,U_681,U_680] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_680),U_681),U_682)),c_Groups_Ozero__class_Ozero(U_680)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_680),c_Groups_Ozero__class_Ozero(U_680)),U_682))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_680),U_681),c_Groups_Ozero__class_Ozero(U_680)))
      | ~ class_Rings_Olinordered__semiring__strict(U_680) ),
    inference(variable_rename,[status(thm)],[f_194_1]) ).

fof(f_194_3,plain,
    ! [U_680,U_681,U_682] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_680),U_681),U_682)),c_Groups_Ozero__class_Ozero(U_680)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_680),c_Groups_Ozero__class_Ozero(U_680)),U_682))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_680),U_681),c_Groups_Ozero__class_Ozero(U_680)))
      | ~ class_Rings_Olinordered__semiring__strict(U_680) ),
    inference(definitional_conversion,[status(esa)],[f_194_2]) ).

cnf(f_194_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_680),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_680),U_681),U_682)),c_Groups_Ozero__class_Ozero(U_680)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_680),c_Groups_Ozero__class_Ozero(U_680)),U_682))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_680),U_681),c_Groups_Ozero__class_Ozero(U_680)))
    | ~ class_Rings_Olinordered__semiring__strict(U_680) ),
    inference(clausify,[status(thm)],[f_194_3]) ).

fof(f_195_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_195_2,plain,
    ! [U_686,U_685,U_684,U_683] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_683),U_684),U_685)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_683),U_684),U_686)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_683),U_686),U_685)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_683),U_686),U_685))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_683),U_684),U_685)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_683),U_684),U_686))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_683),U_684),c_Groups_Ozero__class_Ozero(U_683)))
      | ~ class_Rings_Olinordered__ring__strict(U_683) ),
    inference(variable_rename,[status(thm)],[f_195_1]) ).

fof(f_195_3,plain,
    ( ! [U_685,U_683,U_684,U_686] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_683),U_684),U_685)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_683),U_684),U_686)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_683),U_686),U_685))
        | ~ sP34(U_685,U_683,U_684,U_686) )
    & ! [U_685,U_683,U_684,U_686] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_683),U_686),U_685))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_683),U_684),U_685)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_683),U_684),U_686)))
        | ~ sP34(U_685,U_683,U_684,U_686) )
    & ! [U_685,U_683,U_684,U_686] :
        ( sP34(U_685,U_683,U_684,U_686)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_683),U_684),c_Groups_Ozero__class_Ozero(U_683)))
        | ~ class_Rings_Olinordered__ring__strict(U_683) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP34])],[f_195_2]) ).

cnf(f_195_4,plain,
    ( sP34(U_685,U_683,U_684,U_686)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_683),U_684),c_Groups_Ozero__class_Ozero(U_683)))
    | ~ class_Rings_Olinordered__ring__strict(U_683) ),
    inference(clausify,[status(thm)],[f_195_3]) ).

cnf(f_195_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_683),U_686),U_685))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_683),U_684),U_685)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_683),U_684),U_686)))
    | ~ sP34(U_685,U_683,U_684,U_686) ),
    inference(clausify,[status(thm)],[f_195_3]) ).

cnf(f_195_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_683),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_683),U_684),U_685)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_683),U_684),U_686)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_683),U_686),U_685))
    | ~ sP34(U_685,U_683,U_684,U_686) ),
    inference(clausify,[status(thm)],[f_195_3]) ).

fof(f_196_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_196_2,plain,
    ! [U_689,U_688,U_687] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_687),c_Groups_Ozero__class_Ozero(U_687)),U_688))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_687),c_Groups_Ozero__class_Ozero(U_687)),U_689))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_687),c_Groups_Ozero__class_Ozero(U_687)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_687),U_688),U_689)))
      | ~ class_Rings_Olinordered__semiring__strict(U_687) ),
    inference(variable_rename,[status(thm)],[f_196_1]) ).

fof(f_196_3,plain,
    ! [U_689,U_687,U_688] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_687),c_Groups_Ozero__class_Ozero(U_687)),U_688))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_687),c_Groups_Ozero__class_Ozero(U_687)),U_689))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_687),c_Groups_Ozero__class_Ozero(U_687)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_687),U_688),U_689)))
      | ~ class_Rings_Olinordered__semiring__strict(U_687) ),
    inference(definitional_conversion,[status(esa)],[f_196_2]) ).

cnf(f_196_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_687),c_Groups_Ozero__class_Ozero(U_687)),U_688))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_687),c_Groups_Ozero__class_Ozero(U_687)),U_689))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_687),c_Groups_Ozero__class_Ozero(U_687)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_687),U_688),U_689)))
    | ~ class_Rings_Olinordered__semiring__strict(U_687) ),
    inference(clausify,[status(thm)],[f_196_3]) ).

fof(f_197_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_197_2,plain,
    ! [U_692,U_691,U_690] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_690),c_Groups_Ozero__class_Ozero(U_690)),U_692))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_690),c_Groups_Ozero__class_Ozero(U_690)),U_691))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_690),c_Groups_Ozero__class_Ozero(U_690)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_690),U_691),U_692)))
      | ~ class_Rings_Olinordered__semiring__strict(U_690) ),
    inference(variable_rename,[status(thm)],[f_197_1]) ).

fof(f_197_3,plain,
    ! [U_692,U_691,U_690] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_690),c_Groups_Ozero__class_Ozero(U_690)),U_692))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_690),c_Groups_Ozero__class_Ozero(U_690)),U_691))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_690),c_Groups_Ozero__class_Ozero(U_690)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_690),U_691),U_692)))
      | ~ class_Rings_Olinordered__semiring__strict(U_690) ),
    inference(definitional_conversion,[status(esa)],[f_197_2]) ).

cnf(f_197_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_690),c_Groups_Ozero__class_Ozero(U_690)),U_692))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_690),c_Groups_Ozero__class_Ozero(U_690)),U_691))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_690),c_Groups_Ozero__class_Ozero(U_690)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_690),U_691),U_692)))
    | ~ class_Rings_Olinordered__semiring__strict(U_690) ),
    inference(clausify,[status(thm)],[f_197_3]) ).

fof(f_198_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_198_2,plain,
    ! [U_695,U_694,U_693] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_693),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_695),U_694)),c_Groups_Ozero__class_Ozero(U_693)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_693),U_695),c_Groups_Ozero__class_Ozero(U_693)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_693),c_Groups_Ozero__class_Ozero(U_693)),U_694))
      | ~ class_Rings_Olinordered__semiring__strict(U_693) ),
    inference(variable_rename,[status(thm)],[f_198_1]) ).

fof(f_198_3,plain,
    ! [U_693,U_694,U_695] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_693),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_695),U_694)),c_Groups_Ozero__class_Ozero(U_693)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_693),U_695),c_Groups_Ozero__class_Ozero(U_693)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_693),c_Groups_Ozero__class_Ozero(U_693)),U_694))
      | ~ class_Rings_Olinordered__semiring__strict(U_693) ),
    inference(definitional_conversion,[status(esa)],[f_198_2]) ).

cnf(f_198_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_693),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_693),U_695),U_694)),c_Groups_Ozero__class_Ozero(U_693)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_693),U_695),c_Groups_Ozero__class_Ozero(U_693)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_693),c_Groups_Ozero__class_Ozero(U_693)),U_694))
    | ~ class_Rings_Olinordered__semiring__strict(U_693) ),
    inference(clausify,[status(thm)],[f_198_3]) ).

fof(f_199_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_199_2,plain,
    ! [U_698,U_697,U_696] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_696),U_697),U_698)),c_Groups_Ozero__class_Ozero(U_696)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_696),U_698),c_Groups_Ozero__class_Ozero(U_696)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_696),c_Groups_Ozero__class_Ozero(U_696)),U_697))
      | ~ class_Rings_Olinordered__semiring__strict(U_696) ),
    inference(variable_rename,[status(thm)],[f_199_1]) ).

fof(f_199_3,plain,
    ! [U_696,U_697,U_698] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_696),U_697),U_698)),c_Groups_Ozero__class_Ozero(U_696)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_696),U_698),c_Groups_Ozero__class_Ozero(U_696)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_696),c_Groups_Ozero__class_Ozero(U_696)),U_697))
      | ~ class_Rings_Olinordered__semiring__strict(U_696) ),
    inference(definitional_conversion,[status(esa)],[f_199_2]) ).

cnf(f_199_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_696),U_697),U_698)),c_Groups_Ozero__class_Ozero(U_696)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_696),U_698),c_Groups_Ozero__class_Ozero(U_696)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_696),c_Groups_Ozero__class_Ozero(U_696)),U_697))
    | ~ class_Rings_Olinordered__semiring__strict(U_696) ),
    inference(clausify,[status(thm)],[f_199_3]) ).

fof(f_200_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_200_2,plain,
    ! [U_701,U_700,U_699] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_699),c_Groups_Ozero__class_Ozero(U_699)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_699),U_700),U_701)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_699),c_Groups_Ozero__class_Ozero(U_699)),U_701))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_699),c_Groups_Ozero__class_Ozero(U_699)),U_700))
      | ~ class_Rings_Olinordered__semiring__strict(U_699) ),
    inference(variable_rename,[status(thm)],[f_200_1]) ).

fof(f_200_3,plain,
    ! [U_700,U_699,U_701] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_699),c_Groups_Ozero__class_Ozero(U_699)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_699),U_700),U_701)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_699),c_Groups_Ozero__class_Ozero(U_699)),U_701))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_699),c_Groups_Ozero__class_Ozero(U_699)),U_700))
      | ~ class_Rings_Olinordered__semiring__strict(U_699) ),
    inference(definitional_conversion,[status(esa)],[f_200_2]) ).

cnf(f_200_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_699),c_Groups_Ozero__class_Ozero(U_699)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_699),U_700),U_701)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_699),c_Groups_Ozero__class_Ozero(U_699)),U_701))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_699),c_Groups_Ozero__class_Ozero(U_699)),U_700))
    | ~ class_Rings_Olinordered__semiring__strict(U_699) ),
    inference(clausify,[status(thm)],[f_200_3]) ).

fof(f_201_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_201_2,plain,
    ! [U_705,U_704,U_703,U_702] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_702),U_703),U_704)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_702),U_703),U_705)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_702),U_704),U_705)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_702),U_704),U_705))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_702),U_703),U_704)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_702),U_703),U_705))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_702),c_Groups_Ozero__class_Ozero(U_702)),U_703))
      | ~ class_Rings_Olinordered__ring__strict(U_702) ),
    inference(variable_rename,[status(thm)],[f_201_1]) ).

fof(f_201_3,plain,
    ( ! [U_704,U_705,U_702,U_703] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_702),U_703),U_704)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_702),U_703),U_705)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_702),U_704),U_705))
        | ~ sP35(U_704,U_705,U_702,U_703) )
    & ! [U_704,U_705,U_702,U_703] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_702),U_704),U_705))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_702),U_703),U_704)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_702),U_703),U_705)))
        | ~ sP35(U_704,U_705,U_702,U_703) )
    & ! [U_704,U_705,U_702,U_703] :
        ( sP35(U_704,U_705,U_702,U_703)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_702),c_Groups_Ozero__class_Ozero(U_702)),U_703))
        | ~ class_Rings_Olinordered__ring__strict(U_702) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP35])],[f_201_2]) ).

cnf(f_201_4,plain,
    ( sP35(U_704,U_705,U_702,U_703)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_702),c_Groups_Ozero__class_Ozero(U_702)),U_703))
    | ~ class_Rings_Olinordered__ring__strict(U_702) ),
    inference(clausify,[status(thm)],[f_201_3]) ).

cnf(f_201_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_702),U_704),U_705))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_702),U_703),U_704)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_702),U_703),U_705)))
    | ~ sP35(U_704,U_705,U_702,U_703) ),
    inference(clausify,[status(thm)],[f_201_3]) ).

cnf(f_201_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_702),U_703),U_704)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_702),U_703),U_705)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_702),U_704),U_705))
    | ~ sP35(U_704,U_705,U_702,U_703) ),
    inference(clausify,[status(thm)],[f_201_3]) ).

fof(f_202_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_202_2,plain,
    ! [U_709,U_708,U_707,U_706] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_706),U_707),U_708)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_706),U_707),U_709)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),U_709),U_708))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),U_707),c_Groups_Ozero__class_Ozero(U_706))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),U_708),U_709))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),c_Groups_Ozero__class_Ozero(U_706)),U_707)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),U_709),U_708))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),U_707),c_Groups_Ozero__class_Ozero(U_706))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),U_708),U_709))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),c_Groups_Ozero__class_Ozero(U_706)),U_707)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_706),U_707),U_708)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_706),U_707),U_709))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_706) ),
    inference(variable_rename,[status(thm)],[f_202_1]) ).

fof(f_202_3,plain,
    ( ! [U_706,U_707,U_708,U_709] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),U_709),U_708))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),U_707),c_Groups_Ozero__class_Ozero(U_706)))
        | ~ sP38(U_706,U_707,U_708,U_709) )
    & ! [U_706,U_707,U_708,U_709] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),U_708),U_709))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),c_Groups_Ozero__class_Ozero(U_706)),U_707))
        | ~ sP38(U_706,U_707,U_708,U_709) )
    & ! [U_706,U_707,U_708,U_709] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),U_709),U_708))
        | ~ sP37(U_706,U_707,U_708,U_709) )
    & ! [U_706,U_707,U_708,U_709] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),U_707),c_Groups_Ozero__class_Ozero(U_706)))
        | ~ sP37(U_706,U_707,U_708,U_709) )
    & ! [U_706,U_707,U_708,U_709] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),U_708),U_709))
        | ~ sP36(U_706,U_707,U_708,U_709) )
    & ! [U_706,U_707,U_708,U_709] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),c_Groups_Ozero__class_Ozero(U_706)),U_707))
        | ~ sP36(U_706,U_707,U_708,U_709) )
    & ! [U_706,U_707,U_708,U_709] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_706),U_707),U_708)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_706),U_707),U_709)))
        | sP38(U_706,U_707,U_708,U_709)
        | ~ sP39(U_706,U_707,U_708,U_709) )
    & ! [U_706,U_707,U_708,U_709] :
        ( sP37(U_706,U_707,U_708,U_709)
        | sP36(U_706,U_707,U_708,U_709)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_706),U_707),U_708)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_706),U_707),U_709)))
        | ~ sP39(U_706,U_707,U_708,U_709) )
    & ! [U_706,U_707,U_708,U_709] :
        ( sP39(U_706,U_707,U_708,U_709)
        | ~ class_Rings_Olinordered__ring__strict(U_706) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP36,sP37,sP38,sP39])],[f_202_2]) ).

cnf(f_202_4,plain,
    ( sP39(U_706,U_707,U_708,U_709)
    | ~ class_Rings_Olinordered__ring__strict(U_706) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

cnf(f_202_5,plain,
    ( sP37(U_706,U_707,U_708,U_709)
    | sP36(U_706,U_707,U_708,U_709)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_706),U_707),U_708)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_706),U_707),U_709)))
    | ~ sP39(U_706,U_707,U_708,U_709) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

cnf(f_202_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_706),U_707),U_708)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_706),U_707),U_709)))
    | sP38(U_706,U_707,U_708,U_709)
    | ~ sP39(U_706,U_707,U_708,U_709) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

cnf(f_202_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),c_Groups_Ozero__class_Ozero(U_706)),U_707))
    | ~ sP36(U_706,U_707,U_708,U_709) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

cnf(f_202_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),U_708),U_709))
    | ~ sP36(U_706,U_707,U_708,U_709) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

cnf(f_202_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),U_707),c_Groups_Ozero__class_Ozero(U_706)))
    | ~ sP37(U_706,U_707,U_708,U_709) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

cnf(f_202_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),U_709),U_708))
    | ~ sP37(U_706,U_707,U_708,U_709) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

cnf(f_202_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),U_708),U_709))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),c_Groups_Ozero__class_Ozero(U_706)),U_707))
    | ~ sP38(U_706,U_707,U_708,U_709) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

cnf(f_202_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),U_709),U_708))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_706),U_707),c_Groups_Ozero__class_Ozero(U_706)))
    | ~ sP38(U_706,U_707,U_708,U_709) ),
    inference(clausify,[status(thm)],[f_202_3]) ).

fof(f_203_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_203_2,plain,
    ! [U_713,U_712,U_711,U_710] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_710),U_711),U_712)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_710),U_713),U_712)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),U_713),U_711))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),U_712),c_Groups_Ozero__class_Ozero(U_710))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),U_711),U_713))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),c_Groups_Ozero__class_Ozero(U_710)),U_712)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),U_713),U_711))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),U_712),c_Groups_Ozero__class_Ozero(U_710))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),U_711),U_713))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),c_Groups_Ozero__class_Ozero(U_710)),U_712)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_710),U_711),U_712)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_710),U_713),U_712))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_710) ),
    inference(variable_rename,[status(thm)],[f_203_1]) ).

fof(f_203_3,plain,
    ( ! [U_712,U_713,U_711,U_710] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),U_713),U_711))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),U_712),c_Groups_Ozero__class_Ozero(U_710)))
        | ~ sP42(U_712,U_713,U_711,U_710) )
    & ! [U_712,U_713,U_711,U_710] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),U_711),U_713))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),c_Groups_Ozero__class_Ozero(U_710)),U_712))
        | ~ sP42(U_712,U_713,U_711,U_710) )
    & ! [U_712,U_713,U_711,U_710] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),U_713),U_711))
        | ~ sP41(U_712,U_713,U_711,U_710) )
    & ! [U_712,U_713,U_711,U_710] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),U_712),c_Groups_Ozero__class_Ozero(U_710)))
        | ~ sP41(U_712,U_713,U_711,U_710) )
    & ! [U_712,U_713,U_711,U_710] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),U_711),U_713))
        | ~ sP40(U_712,U_713,U_711,U_710) )
    & ! [U_712,U_713,U_711,U_710] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),c_Groups_Ozero__class_Ozero(U_710)),U_712))
        | ~ sP40(U_712,U_713,U_711,U_710) )
    & ! [U_712,U_713,U_711,U_710] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_710),U_711),U_712)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_710),U_713),U_712)))
        | sP42(U_712,U_713,U_711,U_710)
        | ~ sP43(U_712,U_713,U_711,U_710) )
    & ! [U_712,U_713,U_711,U_710] :
        ( sP41(U_712,U_713,U_711,U_710)
        | sP40(U_712,U_713,U_711,U_710)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_710),U_711),U_712)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_710),U_713),U_712)))
        | ~ sP43(U_712,U_713,U_711,U_710) )
    & ! [U_712,U_713,U_711,U_710] :
        ( sP43(U_712,U_713,U_711,U_710)
        | ~ class_Rings_Olinordered__ring__strict(U_710) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP40,sP41,sP42,sP43])],[f_203_2]) ).

cnf(f_203_4,plain,
    ( sP43(U_712,U_713,U_711,U_710)
    | ~ class_Rings_Olinordered__ring__strict(U_710) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_5,plain,
    ( sP41(U_712,U_713,U_711,U_710)
    | sP40(U_712,U_713,U_711,U_710)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_710),U_711),U_712)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_710),U_713),U_712)))
    | ~ sP43(U_712,U_713,U_711,U_710) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_710),U_711),U_712)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_710),U_713),U_712)))
    | sP42(U_712,U_713,U_711,U_710)
    | ~ sP43(U_712,U_713,U_711,U_710) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),c_Groups_Ozero__class_Ozero(U_710)),U_712))
    | ~ sP40(U_712,U_713,U_711,U_710) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),U_711),U_713))
    | ~ sP40(U_712,U_713,U_711,U_710) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),U_712),c_Groups_Ozero__class_Ozero(U_710)))
    | ~ sP41(U_712,U_713,U_711,U_710) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),U_713),U_711))
    | ~ sP41(U_712,U_713,U_711,U_710) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),U_711),U_713))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),c_Groups_Ozero__class_Ozero(U_710)),U_712))
    | ~ sP42(U_712,U_713,U_711,U_710) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

cnf(f_203_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),U_713),U_711))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_710),U_712),c_Groups_Ozero__class_Ozero(U_710)))
    | ~ sP42(U_712,U_713,U_711,U_710) ),
    inference(clausify,[status(thm)],[f_203_3]) ).

fof(f_204_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_204_2,plain,
    ! [U_715,U_714] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_714),U_715),U_715)),c_Groups_Ozero__class_Ozero(U_714)))
      | ~ class_Rings_Olinordered__ring(U_714) ),
    inference(variable_rename,[status(thm)],[f_204_1]) ).

fof(f_204_3,plain,
    ! [U_715,U_714] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_714),U_715),U_715)),c_Groups_Ozero__class_Ozero(U_714)))
      | ~ class_Rings_Olinordered__ring(U_714) ),
    inference(definitional_conversion,[status(esa)],[f_204_2]) ).

cnf(f_204_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_714),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_714),U_715),U_715)),c_Groups_Ozero__class_Ozero(U_714)))
    | ~ class_Rings_Olinordered__ring(U_714) ),
    inference(clausify,[status(thm)],[f_204_3]) ).

fof(f_205_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_205_2,plain,
    ! [U_718,U_717,U_716] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_718),U_716)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_718),U_717)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_718))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_716),U_717)) ),
    inference(variable_rename,[status(thm)],[f_205_1]) ).

fof(f_205_3,plain,
    ! [U_717,U_718,U_716] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_718),U_716)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_718),U_717)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_718))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_716),U_717)) ),
    inference(definitional_conversion,[status(esa)],[f_205_2]) ).

cnf(f_205_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_718),U_716)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_718),U_717)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_718))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_716),U_717)) ),
    inference(clausify,[status(thm)],[f_205_3]) ).

fof(f_206_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_206_2,plain,
    ! [U_720,U_719] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_719),U_720) = c_Groups_Ozero__class_Ozero(U_719)
          | U_720 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( U_720 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
          | hAPP(c_Int_Oring__1__class_Oof__int(U_719),U_720) != c_Groups_Ozero__class_Ozero(U_719) ) )
      | ~ class_Int_Oring__char__0(U_719) ),
    inference(variable_rename,[status(thm)],[f_206_1]) ).

fof(f_206_3,plain,
    ( ! [U_719,U_720] :
        ( hAPP(c_Int_Oring__1__class_Oof__int(U_719),U_720) = c_Groups_Ozero__class_Ozero(U_719)
        | U_720 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP44(U_719,U_720) )
    & ! [U_719,U_720] :
        ( U_720 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(c_Int_Oring__1__class_Oof__int(U_719),U_720) != c_Groups_Ozero__class_Ozero(U_719)
        | ~ sP44(U_719,U_720) )
    & ! [U_719,U_720] :
        ( sP44(U_719,U_720)
        | ~ class_Int_Oring__char__0(U_719) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP44])],[f_206_2]) ).

cnf(f_206_4,plain,
    ( sP44(U_719,U_720)
    | ~ class_Int_Oring__char__0(U_719) ),
    inference(clausify,[status(thm)],[f_206_3]) ).

cnf(f_206_5,plain,
    ( U_720 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(c_Int_Oring__1__class_Oof__int(U_719),U_720) != c_Groups_Ozero__class_Ozero(U_719)
    | ~ sP44(U_719,U_720) ),
    inference(clausify,[status(thm)],[f_206_3]) ).

cnf(f_206_6,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_719),U_720) = c_Groups_Ozero__class_Ozero(U_719)
    | U_720 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP44(U_719,U_720) ),
    inference(clausify,[status(thm)],[f_206_3]) ).

fof(f_207_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_207_2,plain,
    ! [U_722,U_721] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_721) = hAPP(c_Int_Oring__1__class_Oof__int(U_721),U_722)
          | U_722 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( U_722 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
          | c_Groups_Ozero__class_Ozero(U_721) != hAPP(c_Int_Oring__1__class_Oof__int(U_721),U_722) ) )
      | ~ class_Int_Oring__char__0(U_721) ),
    inference(variable_rename,[status(thm)],[f_207_1]) ).

fof(f_207_3,plain,
    ( ! [U_722,U_721] :
        ( c_Groups_Ozero__class_Ozero(U_721) = hAPP(c_Int_Oring__1__class_Oof__int(U_721),U_722)
        | U_722 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP45(U_722,U_721) )
    & ! [U_722,U_721] :
        ( U_722 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Groups_Ozero__class_Ozero(U_721) != hAPP(c_Int_Oring__1__class_Oof__int(U_721),U_722)
        | ~ sP45(U_722,U_721) )
    & ! [U_722,U_721] :
        ( sP45(U_722,U_721)
        | ~ class_Int_Oring__char__0(U_721) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP45])],[f_207_2]) ).

cnf(f_207_4,plain,
    ( sP45(U_722,U_721)
    | ~ class_Int_Oring__char__0(U_721) ),
    inference(clausify,[status(thm)],[f_207_3]) ).

cnf(f_207_5,plain,
    ( U_722 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Groups_Ozero__class_Ozero(U_721) != hAPP(c_Int_Oring__1__class_Oof__int(U_721),U_722)
    | ~ sP45(U_722,U_721) ),
    inference(clausify,[status(thm)],[f_207_3]) ).

cnf(f_207_6,plain,
    ( c_Groups_Ozero__class_Ozero(U_721) = hAPP(c_Int_Oring__1__class_Oof__int(U_721),U_722)
    | U_722 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP45(U_722,U_721) ),
    inference(clausify,[status(thm)],[f_207_3]) ).

fof(f_208_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_208_2,plain,
    ! [U_723] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_723),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_723)
      | ~ class_Rings_Oring__1(U_723) ),
    inference(variable_rename,[status(thm)],[f_208_1]) ).

fof(f_208_3,plain,
    ! [U_723] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_723),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_723)
      | ~ class_Rings_Oring__1(U_723) ),
    inference(definitional_conversion,[status(esa)],[f_208_2]) ).

cnf(f_208_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_723),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(U_723)
    | ~ class_Rings_Oring__1(U_723) ),
    inference(clausify,[status(thm)],[f_208_3]) ).

fof(f_209_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_209_2,plain,
    ! [U_726,U_725,U_724] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_724),hAPP(c_Int_Oring__1__class_Oof__int(U_724),U_725)),hAPP(c_Int_Oring__1__class_Oof__int(U_724),U_726)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_725),U_726)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_725),U_726))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_724),hAPP(c_Int_Oring__1__class_Oof__int(U_724),U_725)),hAPP(c_Int_Oring__1__class_Oof__int(U_724),U_726))) ) )
      | ~ class_Rings_Olinordered__idom(U_724) ),
    inference(variable_rename,[status(thm)],[f_209_1]) ).

fof(f_209_3,plain,
    ( ! [U_725,U_724,U_726] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_724),hAPP(c_Int_Oring__1__class_Oof__int(U_724),U_725)),hAPP(c_Int_Oring__1__class_Oof__int(U_724),U_726)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_725),U_726))
        | ~ sP46(U_725,U_724,U_726) )
    & ! [U_725,U_724,U_726] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_725),U_726))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_724),hAPP(c_Int_Oring__1__class_Oof__int(U_724),U_725)),hAPP(c_Int_Oring__1__class_Oof__int(U_724),U_726)))
        | ~ sP46(U_725,U_724,U_726) )
    & ! [U_725,U_724,U_726] :
        ( sP46(U_725,U_724,U_726)
        | ~ class_Rings_Olinordered__idom(U_724) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP46])],[f_209_2]) ).

cnf(f_209_4,plain,
    ( sP46(U_725,U_724,U_726)
    | ~ class_Rings_Olinordered__idom(U_724) ),
    inference(clausify,[status(thm)],[f_209_3]) ).

cnf(f_209_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_725),U_726))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_724),hAPP(c_Int_Oring__1__class_Oof__int(U_724),U_725)),hAPP(c_Int_Oring__1__class_Oof__int(U_724),U_726)))
    | ~ sP46(U_725,U_724,U_726) ),
    inference(clausify,[status(thm)],[f_209_3]) ).

cnf(f_209_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_724),hAPP(c_Int_Oring__1__class_Oof__int(U_724),U_725)),hAPP(c_Int_Oring__1__class_Oof__int(U_724),U_726)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_725),U_726))
    | ~ sP46(U_725,U_724,U_726) ),
    inference(clausify,[status(thm)],[f_209_3]) ).

fof(f_210_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_210_2,plain,
    ! [U_729,U_728,U_727] :
      ( hBOOL(hAPP(hAPP(c_member(U_727),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_727),U_728),U_729)),c_Nat_Osemiring__1__class_ONats(U_727)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_727),U_729),c_Nat_Osemiring__1__class_ONats(U_727)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_727),U_728),c_Nat_Osemiring__1__class_ONats(U_727)))
      | ~ class_Rings_Osemiring__1(U_727) ),
    inference(variable_rename,[status(thm)],[f_210_1]) ).

fof(f_210_3,plain,
    ! [U_727,U_728,U_729] :
      ( hBOOL(hAPP(hAPP(c_member(U_727),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_727),U_728),U_729)),c_Nat_Osemiring__1__class_ONats(U_727)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_727),U_729),c_Nat_Osemiring__1__class_ONats(U_727)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_727),U_728),c_Nat_Osemiring__1__class_ONats(U_727)))
      | ~ class_Rings_Osemiring__1(U_727) ),
    inference(definitional_conversion,[status(esa)],[f_210_2]) ).

cnf(f_210_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_727),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_727),U_728),U_729)),c_Nat_Osemiring__1__class_ONats(U_727)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_727),U_729),c_Nat_Osemiring__1__class_ONats(U_727)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_727),U_728),c_Nat_Osemiring__1__class_ONats(U_727)))
    | ~ class_Rings_Osemiring__1(U_727) ),
    inference(clausify,[status(thm)],[f_210_3]) ).

fof(f_211_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_211_2,plain,
    ! [U_731,U_730] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_730),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_731)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_730),U_731)
      | ~ class_Rings_Oring__1(U_730) ),
    inference(variable_rename,[status(thm)],[f_211_1]) ).

fof(f_211_3,plain,
    ! [U_730,U_731] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_730),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_731)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_730),U_731)
      | ~ class_Rings_Oring__1(U_730) ),
    inference(definitional_conversion,[status(esa)],[f_211_2]) ).

cnf(f_211_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_730),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_731)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_730),U_731)
    | ~ class_Rings_Oring__1(U_730) ),
    inference(clausify,[status(thm)],[f_211_3]) ).

fof(f_212_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_212_2,plain,
    ! [U_734,U_733,U_732] :
      ( ( hAPP(c_Option_Ooption_OSome(U_732),U_733) = hAPP(c_Option_Ooption_OSome(U_732),U_734)
        | U_733 != U_734 )
      & ( U_733 = U_734
        | hAPP(c_Option_Ooption_OSome(U_732),U_733) != hAPP(c_Option_Ooption_OSome(U_732),U_734) ) ),
    inference(variable_rename,[status(thm)],[f_212_1]) ).

fof(f_212_3,plain,
    ( ! [U_740,U_738] :
        ( ! [U_736] : hAPP(c_Option_Ooption_OSome(U_736),U_738) = hAPP(c_Option_Ooption_OSome(U_736),U_740)
        | U_738 != U_740 )
    & ! [U_739,U_737] :
        ( ! [U_735] : hAPP(c_Option_Ooption_OSome(U_735),U_737) != hAPP(c_Option_Ooption_OSome(U_735),U_739)
        | U_737 = U_739 ) ),
    inference(miniscope,[status(thm)],[f_212_2]) ).

fof(f_212_4,plain,
    ( ! [U_740,U_736,U_738] :
        ( hAPP(c_Option_Ooption_OSome(U_736),U_738) = hAPP(c_Option_Ooption_OSome(U_736),U_740)
        | U_738 != U_740 )
    & ! [U_739,U_737,U_735] :
        ( hAPP(c_Option_Ooption_OSome(U_735),U_737) != hAPP(c_Option_Ooption_OSome(U_735),U_739)
        | U_737 = U_739 ) ),
    inference(definitional_conversion,[status(esa)],[f_212_3]) ).

cnf(f_212_5,plain,
    ( hAPP(c_Option_Ooption_OSome(U_735),U_737) != hAPP(c_Option_Ooption_OSome(U_735),U_739)
    | U_737 = U_739 ),
    inference(clausify,[status(thm)],[f_212_4]) ).

cnf(f_212_6,plain,
    ( hAPP(c_Option_Ooption_OSome(U_736),U_738) = hAPP(c_Option_Ooption_OSome(U_736),U_740)
    | U_738 != U_740 ),
    inference(clausify,[status(thm)],[f_212_4]) ).

fof(f_213_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_213_2,plain,
    ! [U_742,U_741] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_741),U_742),c_Groups_Ozero__class_Ozero(U_741)) = c_Groups_Ozero__class_Ozero(U_741)
      | ~ class_Rings_Ocomm__semiring__1(U_741) ),
    inference(variable_rename,[status(thm)],[f_213_1]) ).

fof(f_213_3,plain,
    ! [U_741,U_742] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_741),U_742),c_Groups_Ozero__class_Ozero(U_741)) = c_Groups_Ozero__class_Ozero(U_741)
      | ~ class_Rings_Ocomm__semiring__1(U_741) ),
    inference(definitional_conversion,[status(esa)],[f_213_2]) ).

cnf(f_213_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_741),U_742),c_Groups_Ozero__class_Ozero(U_741)) = c_Groups_Ozero__class_Ozero(U_741)
    | ~ class_Rings_Ocomm__semiring__1(U_741) ),
    inference(clausify,[status(thm)],[f_213_3]) ).

fof(f_214_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_214_2,plain,
    ! [U_744,U_743] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_743),c_Groups_Ozero__class_Ozero(U_743)),U_744) = c_Groups_Ozero__class_Ozero(U_743)
      | ~ class_Rings_Ocomm__semiring__1(U_743) ),
    inference(variable_rename,[status(thm)],[f_214_1]) ).

fof(f_214_3,plain,
    ! [U_743,U_744] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_743),c_Groups_Ozero__class_Ozero(U_743)),U_744) = c_Groups_Ozero__class_Ozero(U_743)
      | ~ class_Rings_Ocomm__semiring__1(U_743) ),
    inference(definitional_conversion,[status(esa)],[f_214_2]) ).

cnf(f_214_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_743),c_Groups_Ozero__class_Ozero(U_743)),U_744) = c_Groups_Ozero__class_Ozero(U_743)
    | ~ class_Rings_Ocomm__semiring__1(U_743) ),
    inference(clausify,[status(thm)],[f_214_3]) ).

fof(f_215_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_215_2,plain,
    ! [U_747,U_746,U_745] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_745),U_746),c_Option_Oset(U_745,U_747)))
        | U_747 != hAPP(c_Option_Ooption_OSome(U_745),U_746) )
      & ( U_747 = hAPP(c_Option_Ooption_OSome(U_745),U_746)
        | ~ hBOOL(hAPP(hAPP(c_member(U_745),U_746),c_Option_Oset(U_745,U_747))) ) ),
    inference(variable_rename,[status(thm)],[f_215_1]) ).

fof(f_215_3,plain,
    ( ! [U_753,U_751,U_749] :
        ( hBOOL(hAPP(hAPP(c_member(U_749),U_751),c_Option_Oset(U_749,U_753)))
        | U_753 != hAPP(c_Option_Ooption_OSome(U_749),U_751) )
    & ! [U_752,U_750,U_748] :
        ( U_752 = hAPP(c_Option_Ooption_OSome(U_748),U_750)
        | ~ hBOOL(hAPP(hAPP(c_member(U_748),U_750),c_Option_Oset(U_748,U_752))) ) ),
    inference(miniscope,[status(thm)],[f_215_2]) ).

fof(f_215_4,plain,
    ( ! [U_749,U_751,U_753] :
        ( hBOOL(hAPP(hAPP(c_member(U_749),U_751),c_Option_Oset(U_749,U_753)))
        | U_753 != hAPP(c_Option_Ooption_OSome(U_749),U_751) )
    & ! [U_750,U_752,U_748] :
        ( U_752 = hAPP(c_Option_Ooption_OSome(U_748),U_750)
        | ~ hBOOL(hAPP(hAPP(c_member(U_748),U_750),c_Option_Oset(U_748,U_752))) ) ),
    inference(definitional_conversion,[status(esa)],[f_215_3]) ).

cnf(f_215_5,plain,
    ( U_752 = hAPP(c_Option_Ooption_OSome(U_748),U_750)
    | ~ hBOOL(hAPP(hAPP(c_member(U_748),U_750),c_Option_Oset(U_748,U_752))) ),
    inference(clausify,[status(thm)],[f_215_4]) ).

cnf(f_215_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_749),U_751),c_Option_Oset(U_749,U_753)))
    | U_753 != hAPP(c_Option_Ooption_OSome(U_749),U_751) ),
    inference(clausify,[status(thm)],[f_215_4]) ).

fof(f_216_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_216_2,plain,
    ! [U_758,U_757,U_756,U_755,U_754] : hAPP(c_Option_Ooption_Ooption__case(U_754,U_755,U_756,U_757),hAPP(c_Option_Ooption_OSome(U_755),U_758)) = hAPP(U_757,U_758),
    inference(variable_rename,[status(thm)],[f_216_1]) ).

fof(f_216_3,plain,
    ! [U_755,U_754,U_756,U_757,U_758] : hAPP(c_Option_Ooption_Ooption__case(U_754,U_755,U_756,U_757),hAPP(c_Option_Ooption_OSome(U_755),U_758)) = hAPP(U_757,U_758),
    inference(definitional_conversion,[status(esa)],[f_216_2]) ).

cnf(f_216_4,plain,
    hAPP(c_Option_Ooption_Ooption__case(U_754,U_755,U_756,U_757),hAPP(c_Option_Ooption_OSome(U_755),U_758)) = hAPP(U_757,U_758),
    inference(clausify,[status(thm)],[f_216_3]) ).

fof(f_217_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_217_2,plain,
    ! [U_763,U_762,U_761,U_760,U_759] : c_Option_Ooption_Ooption__rec(U_759,U_760,U_761,U_762,hAPP(c_Option_Ooption_OSome(U_760),U_763)) = hAPP(U_762,U_763),
    inference(variable_rename,[status(thm)],[f_217_1]) ).

fof(f_217_3,plain,
    ! [U_760,U_759,U_761,U_762,U_763] : c_Option_Ooption_Ooption__rec(U_759,U_760,U_761,U_762,hAPP(c_Option_Ooption_OSome(U_760),U_763)) = hAPP(U_762,U_763),
    inference(definitional_conversion,[status(esa)],[f_217_2]) ).

cnf(f_217_4,plain,
    c_Option_Ooption_Ooption__rec(U_759,U_760,U_761,U_762,hAPP(c_Option_Ooption_OSome(U_760),U_763)) = hAPP(U_762,U_763),
    inference(clausify,[status(thm)],[f_217_3]) ).

fof(f_218_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_218_2,plain,
    ! [U_767,U_766,U_765,U_764] : hAPP(c_Option_Ooption_Ooption__case(U_764,U_765,U_766,U_767),c_Option_Ooption_ONone(U_765)) = U_766,
    inference(variable_rename,[status(thm)],[f_218_1]) ).

fof(f_218_3,plain,
    ! [U_764,U_765,U_766,U_767] : hAPP(c_Option_Ooption_Ooption__case(U_764,U_765,U_766,U_767),c_Option_Ooption_ONone(U_765)) = U_766,
    inference(definitional_conversion,[status(esa)],[f_218_2]) ).

cnf(f_218_4,plain,
    hAPP(c_Option_Ooption_Ooption__case(U_764,U_765,U_766,U_767),c_Option_Ooption_ONone(U_765)) = U_766,
    inference(clausify,[status(thm)],[f_218_3]) ).

fof(f_219_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_219_2,plain,
    ! [U_771,U_770,U_769,U_768] : c_Option_Ooption_Ooption__rec(U_768,U_769,U_770,U_771,c_Option_Ooption_ONone(U_769)) = U_770,
    inference(variable_rename,[status(thm)],[f_219_1]) ).

fof(f_219_3,plain,
    ! [U_769,U_768,U_770,U_771] : c_Option_Ooption_Ooption__rec(U_768,U_769,U_770,U_771,c_Option_Ooption_ONone(U_769)) = U_770,
    inference(definitional_conversion,[status(esa)],[f_219_2]) ).

cnf(f_219_4,plain,
    c_Option_Ooption_Ooption__rec(U_768,U_769,U_770,U_771,c_Option_Ooption_ONone(U_769)) = U_770,
    inference(clausify,[status(thm)],[f_219_3]) ).

fof(f_220_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_220_2,plain,
    ! [U_773,U_772] : ~ c_Option_Ois__none(U_772,hAPP(c_Option_Ooption_OSome(U_772),U_773)),
    inference(variable_rename,[status(thm)],[f_220_1]) ).

fof(f_220_3,plain,
    ! [U_772,U_773] : ~ c_Option_Ois__none(U_772,hAPP(c_Option_Ooption_OSome(U_772),U_773)),
    inference(definitional_conversion,[status(esa)],[f_220_2]) ).

cnf(f_220_4,plain,
    ~ c_Option_Ois__none(U_772,hAPP(c_Option_Ooption_OSome(U_772),U_773)),
    inference(clausify,[status(thm)],[f_220_3]) ).

fof(f_221_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_221_2,plain,
    ! [U_775,U_774] :
      ( ( c_Option_Ois__none(U_774,U_775)
        | U_775 != c_Option_Ooption_ONone(U_774) )
      & ( U_775 = c_Option_Ooption_ONone(U_774)
        | ~ c_Option_Ois__none(U_774,U_775) ) ),
    inference(variable_rename,[status(thm)],[f_221_1]) ).

fof(f_221_3,plain,
    ( ! [U_779,U_777] :
        ( c_Option_Ois__none(U_777,U_779)
        | U_779 != c_Option_Ooption_ONone(U_777) )
    & ! [U_778,U_776] :
        ( U_778 = c_Option_Ooption_ONone(U_776)
        | ~ c_Option_Ois__none(U_776,U_778) ) ),
    inference(miniscope,[status(thm)],[f_221_2]) ).

fof(f_221_4,plain,
    ( ! [U_777,U_779] :
        ( c_Option_Ois__none(U_777,U_779)
        | U_779 != c_Option_Ooption_ONone(U_777) )
    & ! [U_778,U_776] :
        ( U_778 = c_Option_Ooption_ONone(U_776)
        | ~ c_Option_Ois__none(U_776,U_778) ) ),
    inference(definitional_conversion,[status(esa)],[f_221_3]) ).

cnf(f_221_5,plain,
    ( U_778 = c_Option_Ooption_ONone(U_776)
    | ~ c_Option_Ois__none(U_776,U_778) ),
    inference(clausify,[status(thm)],[f_221_4]) ).

cnf(f_221_6,plain,
    ( c_Option_Ois__none(U_777,U_779)
    | U_779 != c_Option_Ooption_ONone(U_777) ),
    inference(clausify,[status(thm)],[f_221_4]) ).

fof(f_222_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_222_2,plain,
    ! [U_780] : c_Option_Ois__none(U_780,c_Option_Ooption_ONone(U_780)),
    inference(variable_rename,[status(thm)],[f_222_1]) ).

fof(f_222_3,plain,
    ! [U_780] : c_Option_Ois__none(U_780,c_Option_Ooption_ONone(U_780)),
    inference(definitional_conversion,[status(esa)],[f_222_2]) ).

cnf(f_222_4,plain,
    c_Option_Ois__none(U_780,c_Option_Ooption_ONone(U_780)),
    inference(clausify,[status(thm)],[f_222_3]) ).

fof(f_223_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_223_2,plain,
    ! [U_781] : 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_781)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_223_1]) ).

fof(f_223_3,plain,
    ! [U_781] : 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_781)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_223_2]) ).

cnf(f_223_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_781)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_223_3]) ).

fof(f_224_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_224_2,plain,
    ! [U_783,U_782] : 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_782)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_783))),
    inference(variable_rename,[status(thm)],[f_224_1]) ).

fof(f_224_3,plain,
    ! [U_782,U_783] : 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_782)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_783))),
    inference(definitional_conversion,[status(esa)],[f_224_2]) ).

cnf(f_224_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_782)))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_783))),
    inference(clausify,[status(thm)],[f_224_3]) ).

fof(f_225_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_225_2,plain,
    ! [U_785,U_784] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_784),U_785) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_785),U_784),
    inference(variable_rename,[status(thm)],[f_225_1]) ).

fof(f_225_3,plain,
    ! [U_784,U_785] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_784),U_785) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_785),U_784),
    inference(definitional_conversion,[status(esa)],[f_225_2]) ).

cnf(f_225_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_784),U_785) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_785),U_784),
    inference(clausify,[status(thm)],[f_225_3]) ).

fof(f_226_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_226_2,plain,
    ! [U_788,U_787,U_786] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_786),U_787)),U_788) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_786),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_787),U_788)),
    inference(variable_rename,[status(thm)],[f_226_1]) ).

fof(f_226_3,plain,
    ! [U_788,U_786,U_787] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_786),U_787)),U_788) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_786),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_787),U_788)),
    inference(definitional_conversion,[status(esa)],[f_226_2]) ).

cnf(f_226_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_786),U_787)),U_788) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_786),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_787),U_788)),
    inference(clausify,[status(thm)],[f_226_3]) ).

fof(f_227_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_227_2,plain,
    ! [U_791,U_790,U_789] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_789),U_790) = hAPP(c_Groups_Ouminus__class_Ouminus(U_789),U_791)
          | U_790 != U_791 )
        & ( U_790 = U_791
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_789),U_790) != hAPP(c_Groups_Ouminus__class_Ouminus(U_789),U_791) ) )
      | ~ class_Groups_Ogroup__add(U_789) ),
    inference(variable_rename,[status(thm)],[f_227_1]) ).

fof(f_227_3,plain,
    ( ! [U_790,U_791,U_789] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(U_789),U_790) = hAPP(c_Groups_Ouminus__class_Ouminus(U_789),U_791)
        | U_790 != U_791
        | ~ sP47(U_790,U_791,U_789) )
    & ! [U_790,U_791,U_789] :
        ( U_790 = U_791
        | hAPP(c_Groups_Ouminus__class_Ouminus(U_789),U_790) != hAPP(c_Groups_Ouminus__class_Ouminus(U_789),U_791)
        | ~ sP47(U_790,U_791,U_789) )
    & ! [U_790,U_791,U_789] :
        ( sP47(U_790,U_791,U_789)
        | ~ class_Groups_Ogroup__add(U_789) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP47])],[f_227_2]) ).

cnf(f_227_4,plain,
    ( sP47(U_790,U_791,U_789)
    | ~ class_Groups_Ogroup__add(U_789) ),
    inference(clausify,[status(thm)],[f_227_3]) ).

cnf(f_227_5,plain,
    ( U_790 = U_791
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_789),U_790) != hAPP(c_Groups_Ouminus__class_Ouminus(U_789),U_791)
    | ~ sP47(U_790,U_791,U_789) ),
    inference(clausify,[status(thm)],[f_227_3]) ).

cnf(f_227_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_789),U_790) = hAPP(c_Groups_Ouminus__class_Ouminus(U_789),U_791)
    | U_790 != U_791
    | ~ sP47(U_790,U_791,U_789) ),
    inference(clausify,[status(thm)],[f_227_3]) ).

fof(f_228_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_228_2,plain,
    ! [U_794,U_793,U_792] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_792),U_793) = U_794
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_792),U_794) != U_793 )
        & ( hAPP(c_Groups_Ouminus__class_Ouminus(U_792),U_794) = U_793
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_792),U_793) != U_794 ) )
      | ~ class_Groups_Ogroup__add(U_792) ),
    inference(variable_rename,[status(thm)],[f_228_1]) ).

fof(f_228_3,plain,
    ( ! [U_793,U_794,U_792] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(U_792),U_793) = U_794
        | hAPP(c_Groups_Ouminus__class_Ouminus(U_792),U_794) != U_793
        | ~ sP48(U_793,U_794,U_792) )
    & ! [U_793,U_794,U_792] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(U_792),U_794) = U_793
        | hAPP(c_Groups_Ouminus__class_Ouminus(U_792),U_793) != U_794
        | ~ sP48(U_793,U_794,U_792) )
    & ! [U_793,U_794,U_792] :
        ( sP48(U_793,U_794,U_792)
        | ~ class_Groups_Ogroup__add(U_792) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP48])],[f_228_2]) ).

cnf(f_228_4,plain,
    ( sP48(U_793,U_794,U_792)
    | ~ class_Groups_Ogroup__add(U_792) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

cnf(f_228_5,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_792),U_794) = U_793
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_792),U_793) != U_794
    | ~ sP48(U_793,U_794,U_792) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

cnf(f_228_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_792),U_793) = U_794
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_792),U_794) != U_793
    | ~ sP48(U_793,U_794,U_792) ),
    inference(clausify,[status(thm)],[f_228_3]) ).

fof(f_229_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_229_2,plain,
    ! [U_797,U_796,U_795] :
      ( ( ( U_796 = hAPP(c_Groups_Ouminus__class_Ouminus(U_795),U_797)
          | U_797 != hAPP(c_Groups_Ouminus__class_Ouminus(U_795),U_796) )
        & ( U_797 = hAPP(c_Groups_Ouminus__class_Ouminus(U_795),U_796)
          | U_796 != hAPP(c_Groups_Ouminus__class_Ouminus(U_795),U_797) ) )
      | ~ class_Groups_Ogroup__add(U_795) ),
    inference(variable_rename,[status(thm)],[f_229_1]) ).

fof(f_229_3,plain,
    ( ! [U_797,U_796,U_795] :
        ( U_796 = hAPP(c_Groups_Ouminus__class_Ouminus(U_795),U_797)
        | U_797 != hAPP(c_Groups_Ouminus__class_Ouminus(U_795),U_796)
        | ~ sP49(U_797,U_796,U_795) )
    & ! [U_797,U_796,U_795] :
        ( U_797 = hAPP(c_Groups_Ouminus__class_Ouminus(U_795),U_796)
        | U_796 != hAPP(c_Groups_Ouminus__class_Ouminus(U_795),U_797)
        | ~ sP49(U_797,U_796,U_795) )
    & ! [U_797,U_796,U_795] :
        ( sP49(U_797,U_796,U_795)
        | ~ class_Groups_Ogroup__add(U_795) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP49])],[f_229_2]) ).

cnf(f_229_4,plain,
    ( sP49(U_797,U_796,U_795)
    | ~ class_Groups_Ogroup__add(U_795) ),
    inference(clausify,[status(thm)],[f_229_3]) ).

cnf(f_229_5,plain,
    ( U_797 = hAPP(c_Groups_Ouminus__class_Ouminus(U_795),U_796)
    | U_796 != hAPP(c_Groups_Ouminus__class_Ouminus(U_795),U_797)
    | ~ sP49(U_797,U_796,U_795) ),
    inference(clausify,[status(thm)],[f_229_3]) ).

cnf(f_229_6,plain,
    ( U_796 = hAPP(c_Groups_Ouminus__class_Ouminus(U_795),U_797)
    | U_797 != hAPP(c_Groups_Ouminus__class_Ouminus(U_795),U_796)
    | ~ sP49(U_797,U_796,U_795) ),
    inference(clausify,[status(thm)],[f_229_3]) ).

fof(f_230_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_230_2,plain,
    ! [U_799,U_798] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_798),hAPP(c_Groups_Ouminus__class_Ouminus(U_798),U_799)) = U_799
      | ~ class_Groups_Ogroup__add(U_798) ),
    inference(variable_rename,[status(thm)],[f_230_1]) ).

fof(f_230_3,plain,
    ! [U_799,U_798] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_798),hAPP(c_Groups_Ouminus__class_Ouminus(U_798),U_799)) = U_799
      | ~ class_Groups_Ogroup__add(U_798) ),
    inference(definitional_conversion,[status(esa)],[f_230_2]) ).

cnf(f_230_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_798),hAPP(c_Groups_Ouminus__class_Ouminus(U_798),U_799)) = U_799
    | ~ class_Groups_Ogroup__add(U_798) ),
    inference(clausify,[status(thm)],[f_230_3]) ).

fof(f_231_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_231_2,plain,
    ! [U_800] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_800)) = U_800,
    inference(variable_rename,[status(thm)],[f_231_1]) ).

fof(f_231_3,plain,
    ! [U_800] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_800)) = U_800,
    inference(definitional_conversion,[status(esa)],[f_231_2]) ).

cnf(f_231_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_800)) = U_800,
    inference(clausify,[status(thm)],[f_231_3]) ).

fof(f_232_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_232_2,plain,
    ! [U_802,U_801] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_801),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_802)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_801),hAPP(c_Int_Oring__1__class_Oof__int(U_801),U_802))
      | ~ class_Rings_Oring__1(U_801) ),
    inference(variable_rename,[status(thm)],[f_232_1]) ).

fof(f_232_3,plain,
    ! [U_801,U_802] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_801),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_802)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_801),hAPP(c_Int_Oring__1__class_Oof__int(U_801),U_802))
      | ~ class_Rings_Oring__1(U_801) ),
    inference(definitional_conversion,[status(esa)],[f_232_2]) ).

cnf(f_232_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_801),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_802)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_801),hAPP(c_Int_Oring__1__class_Oof__int(U_801),U_802))
    | ~ class_Rings_Oring__1(U_801) ),
    inference(clausify,[status(thm)],[f_232_3]) ).

fof(f_233_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_233_2,plain,
    ! [U_803] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_803),c_Groups_Ozero__class_Ozero(U_803)) = c_Groups_Ozero__class_Ozero(U_803)
      | ~ class_Groups_Ogroup__add(U_803) ),
    inference(variable_rename,[status(thm)],[f_233_1]) ).

fof(f_233_3,plain,
    ! [U_803] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_803),c_Groups_Ozero__class_Ozero(U_803)) = c_Groups_Ozero__class_Ozero(U_803)
      | ~ class_Groups_Ogroup__add(U_803) ),
    inference(definitional_conversion,[status(esa)],[f_233_2]) ).

cnf(f_233_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_803),c_Groups_Ozero__class_Ozero(U_803)) = c_Groups_Ozero__class_Ozero(U_803)
    | ~ class_Groups_Ogroup__add(U_803) ),
    inference(clausify,[status(thm)],[f_233_3]) ).

fof(f_234_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_234_2,plain,
    ! [U_805,U_804] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_804) = hAPP(c_Groups_Ouminus__class_Ouminus(U_804),U_805)
          | c_Groups_Ozero__class_Ozero(U_804) != U_805 )
        & ( c_Groups_Ozero__class_Ozero(U_804) = U_805
          | c_Groups_Ozero__class_Ozero(U_804) != hAPP(c_Groups_Ouminus__class_Ouminus(U_804),U_805) ) )
      | ~ class_Groups_Ogroup__add(U_804) ),
    inference(variable_rename,[status(thm)],[f_234_1]) ).

fof(f_234_3,plain,
    ( ! [U_804,U_805] :
        ( c_Groups_Ozero__class_Ozero(U_804) = hAPP(c_Groups_Ouminus__class_Ouminus(U_804),U_805)
        | c_Groups_Ozero__class_Ozero(U_804) != U_805
        | ~ sP50(U_804,U_805) )
    & ! [U_804,U_805] :
        ( c_Groups_Ozero__class_Ozero(U_804) = U_805
        | c_Groups_Ozero__class_Ozero(U_804) != hAPP(c_Groups_Ouminus__class_Ouminus(U_804),U_805)
        | ~ sP50(U_804,U_805) )
    & ! [U_804,U_805] :
        ( sP50(U_804,U_805)
        | ~ class_Groups_Ogroup__add(U_804) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP50])],[f_234_2]) ).

cnf(f_234_4,plain,
    ( sP50(U_804,U_805)
    | ~ class_Groups_Ogroup__add(U_804) ),
    inference(clausify,[status(thm)],[f_234_3]) ).

cnf(f_234_5,plain,
    ( c_Groups_Ozero__class_Ozero(U_804) = U_805
    | c_Groups_Ozero__class_Ozero(U_804) != hAPP(c_Groups_Ouminus__class_Ouminus(U_804),U_805)
    | ~ sP50(U_804,U_805) ),
    inference(clausify,[status(thm)],[f_234_3]) ).

cnf(f_234_6,plain,
    ( c_Groups_Ozero__class_Ozero(U_804) = hAPP(c_Groups_Ouminus__class_Ouminus(U_804),U_805)
    | c_Groups_Ozero__class_Ozero(U_804) != U_805
    | ~ sP50(U_804,U_805) ),
    inference(clausify,[status(thm)],[f_234_3]) ).

fof(f_235_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_235_2,plain,
    ! [U_807,U_806] :
      ( ( ( U_807 = hAPP(c_Groups_Ouminus__class_Ouminus(U_806),U_807)
          | U_807 != c_Groups_Ozero__class_Ozero(U_806) )
        & ( U_807 = c_Groups_Ozero__class_Ozero(U_806)
          | U_807 != hAPP(c_Groups_Ouminus__class_Ouminus(U_806),U_807) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_806) ),
    inference(variable_rename,[status(thm)],[f_235_1]) ).

fof(f_235_3,plain,
    ( ! [U_807,U_806] :
        ( U_807 = hAPP(c_Groups_Ouminus__class_Ouminus(U_806),U_807)
        | U_807 != c_Groups_Ozero__class_Ozero(U_806)
        | ~ sP51(U_807,U_806) )
    & ! [U_807,U_806] :
        ( U_807 = c_Groups_Ozero__class_Ozero(U_806)
        | U_807 != hAPP(c_Groups_Ouminus__class_Ouminus(U_806),U_807)
        | ~ sP51(U_807,U_806) )
    & ! [U_807,U_806] :
        ( sP51(U_807,U_806)
        | ~ class_Groups_Olinordered__ab__group__add(U_806) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP51])],[f_235_2]) ).

cnf(f_235_4,plain,
    ( sP51(U_807,U_806)
    | ~ class_Groups_Olinordered__ab__group__add(U_806) ),
    inference(clausify,[status(thm)],[f_235_3]) ).

cnf(f_235_5,plain,
    ( U_807 = c_Groups_Ozero__class_Ozero(U_806)
    | U_807 != hAPP(c_Groups_Ouminus__class_Ouminus(U_806),U_807)
    | ~ sP51(U_807,U_806) ),
    inference(clausify,[status(thm)],[f_235_3]) ).

cnf(f_235_6,plain,
    ( U_807 = hAPP(c_Groups_Ouminus__class_Ouminus(U_806),U_807)
    | U_807 != c_Groups_Ozero__class_Ozero(U_806)
    | ~ sP51(U_807,U_806) ),
    inference(clausify,[status(thm)],[f_235_3]) ).

fof(f_236_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_236_2,plain,
    ! [U_809,U_808] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_808),U_809) = c_Groups_Ozero__class_Ozero(U_808)
          | U_809 != c_Groups_Ozero__class_Ozero(U_808) )
        & ( U_809 = c_Groups_Ozero__class_Ozero(U_808)
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_808),U_809) != c_Groups_Ozero__class_Ozero(U_808) ) )
      | ~ class_Groups_Ogroup__add(U_808) ),
    inference(variable_rename,[status(thm)],[f_236_1]) ).

fof(f_236_3,plain,
    ( ! [U_809,U_808] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(U_808),U_809) = c_Groups_Ozero__class_Ozero(U_808)
        | U_809 != c_Groups_Ozero__class_Ozero(U_808)
        | ~ sP52(U_809,U_808) )
    & ! [U_809,U_808] :
        ( U_809 = c_Groups_Ozero__class_Ozero(U_808)
        | hAPP(c_Groups_Ouminus__class_Ouminus(U_808),U_809) != c_Groups_Ozero__class_Ozero(U_808)
        | ~ sP52(U_809,U_808) )
    & ! [U_809,U_808] :
        ( sP52(U_809,U_808)
        | ~ class_Groups_Ogroup__add(U_808) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP52])],[f_236_2]) ).

cnf(f_236_4,plain,
    ( sP52(U_809,U_808)
    | ~ class_Groups_Ogroup__add(U_808) ),
    inference(clausify,[status(thm)],[f_236_3]) ).

cnf(f_236_5,plain,
    ( U_809 = c_Groups_Ozero__class_Ozero(U_808)
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_808),U_809) != c_Groups_Ozero__class_Ozero(U_808)
    | ~ sP52(U_809,U_808) ),
    inference(clausify,[status(thm)],[f_236_3]) ).

cnf(f_236_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_808),U_809) = c_Groups_Ozero__class_Ozero(U_808)
    | U_809 != c_Groups_Ozero__class_Ozero(U_808)
    | ~ sP52(U_809,U_808) ),
    inference(clausify,[status(thm)],[f_236_3]) ).

fof(f_237_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_237_2,plain,
    ! [U_811,U_810] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_810),U_811) = U_811
          | U_811 != c_Groups_Ozero__class_Ozero(U_810) )
        & ( U_811 = c_Groups_Ozero__class_Ozero(U_810)
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_810),U_811) != U_811 ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_810) ),
    inference(variable_rename,[status(thm)],[f_237_1]) ).

fof(f_237_3,plain,
    ( ! [U_811,U_810] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(U_810),U_811) = U_811
        | U_811 != c_Groups_Ozero__class_Ozero(U_810)
        | ~ sP53(U_811,U_810) )
    & ! [U_811,U_810] :
        ( U_811 = c_Groups_Ozero__class_Ozero(U_810)
        | hAPP(c_Groups_Ouminus__class_Ouminus(U_810),U_811) != U_811
        | ~ sP53(U_811,U_810) )
    & ! [U_811,U_810] :
        ( sP53(U_811,U_810)
        | ~ class_Groups_Olinordered__ab__group__add(U_810) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP53])],[f_237_2]) ).

cnf(f_237_4,plain,
    ( sP53(U_811,U_810)
    | ~ class_Groups_Olinordered__ab__group__add(U_810) ),
    inference(clausify,[status(thm)],[f_237_3]) ).

cnf(f_237_5,plain,
    ( U_811 = c_Groups_Ozero__class_Ozero(U_810)
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_810),U_811) != U_811
    | ~ sP53(U_811,U_810) ),
    inference(clausify,[status(thm)],[f_237_3]) ).

cnf(f_237_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_810),U_811) = U_811
    | U_811 != c_Groups_Ozero__class_Ozero(U_810)
    | ~ sP53(U_811,U_810) ),
    inference(clausify,[status(thm)],[f_237_3]) ).

fof(f_238_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_238_2,plain,
    ! [U_814,U_813,U_812] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_812),hAPP(c_Groups_Ouminus__class_Ouminus(U_812),U_813)),hAPP(c_Groups_Ouminus__class_Ouminus(U_812),U_814)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_812),U_814),U_813)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_812),U_814),U_813))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_812),hAPP(c_Groups_Ouminus__class_Ouminus(U_812),U_813)),hAPP(c_Groups_Ouminus__class_Ouminus(U_812),U_814))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_812) ),
    inference(variable_rename,[status(thm)],[f_238_1]) ).

fof(f_238_3,plain,
    ( ! [U_813,U_814,U_812] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_812),hAPP(c_Groups_Ouminus__class_Ouminus(U_812),U_813)),hAPP(c_Groups_Ouminus__class_Ouminus(U_812),U_814)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_812),U_814),U_813))
        | ~ sP54(U_813,U_814,U_812) )
    & ! [U_813,U_814,U_812] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_812),U_814),U_813))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_812),hAPP(c_Groups_Ouminus__class_Ouminus(U_812),U_813)),hAPP(c_Groups_Ouminus__class_Ouminus(U_812),U_814)))
        | ~ sP54(U_813,U_814,U_812) )
    & ! [U_813,U_814,U_812] :
        ( sP54(U_813,U_814,U_812)
        | ~ class_Groups_Oordered__ab__group__add(U_812) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP54])],[f_238_2]) ).

cnf(f_238_4,plain,
    ( sP54(U_813,U_814,U_812)
    | ~ class_Groups_Oordered__ab__group__add(U_812) ),
    inference(clausify,[status(thm)],[f_238_3]) ).

cnf(f_238_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_812),U_814),U_813))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_812),hAPP(c_Groups_Ouminus__class_Ouminus(U_812),U_813)),hAPP(c_Groups_Ouminus__class_Ouminus(U_812),U_814)))
    | ~ sP54(U_813,U_814,U_812) ),
    inference(clausify,[status(thm)],[f_238_3]) ).

cnf(f_238_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_812),hAPP(c_Groups_Ouminus__class_Ouminus(U_812),U_813)),hAPP(c_Groups_Ouminus__class_Ouminus(U_812),U_814)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_812),U_814),U_813))
    | ~ sP54(U_813,U_814,U_812) ),
    inference(clausify,[status(thm)],[f_238_3]) ).

fof(f_239_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_239_2,plain,
    ! [U_817,U_816,U_815] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_815),hAPP(c_Groups_Ouminus__class_Ouminus(U_815),U_816)),U_817))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_815),hAPP(c_Groups_Ouminus__class_Ouminus(U_815),U_817)),U_816)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_815),hAPP(c_Groups_Ouminus__class_Ouminus(U_815),U_817)),U_816))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_815),hAPP(c_Groups_Ouminus__class_Ouminus(U_815),U_816)),U_817)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_815) ),
    inference(variable_rename,[status(thm)],[f_239_1]) ).

fof(f_239_3,plain,
    ( ! [U_816,U_817,U_815] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_815),hAPP(c_Groups_Ouminus__class_Ouminus(U_815),U_816)),U_817))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_815),hAPP(c_Groups_Ouminus__class_Ouminus(U_815),U_817)),U_816))
        | ~ sP55(U_816,U_817,U_815) )
    & ! [U_816,U_817,U_815] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_815),hAPP(c_Groups_Ouminus__class_Ouminus(U_815),U_817)),U_816))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_815),hAPP(c_Groups_Ouminus__class_Ouminus(U_815),U_816)),U_817))
        | ~ sP55(U_816,U_817,U_815) )
    & ! [U_816,U_817,U_815] :
        ( sP55(U_816,U_817,U_815)
        | ~ class_Groups_Oordered__ab__group__add(U_815) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP55])],[f_239_2]) ).

cnf(f_239_4,plain,
    ( sP55(U_816,U_817,U_815)
    | ~ class_Groups_Oordered__ab__group__add(U_815) ),
    inference(clausify,[status(thm)],[f_239_3]) ).

cnf(f_239_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_815),hAPP(c_Groups_Ouminus__class_Ouminus(U_815),U_817)),U_816))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_815),hAPP(c_Groups_Ouminus__class_Ouminus(U_815),U_816)),U_817))
    | ~ sP55(U_816,U_817,U_815) ),
    inference(clausify,[status(thm)],[f_239_3]) ).

cnf(f_239_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_815),hAPP(c_Groups_Ouminus__class_Ouminus(U_815),U_816)),U_817))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_815),hAPP(c_Groups_Ouminus__class_Ouminus(U_815),U_817)),U_816))
    | ~ sP55(U_816,U_817,U_815) ),
    inference(clausify,[status(thm)],[f_239_3]) ).

fof(f_240_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_240_2,plain,
    ! [U_820,U_819,U_818] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_818),U_819),hAPP(c_Groups_Ouminus__class_Ouminus(U_818),U_820)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_818),U_820),hAPP(c_Groups_Ouminus__class_Ouminus(U_818),U_819))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_818),U_820),hAPP(c_Groups_Ouminus__class_Ouminus(U_818),U_819)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_818),U_819),hAPP(c_Groups_Ouminus__class_Ouminus(U_818),U_820))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_818) ),
    inference(variable_rename,[status(thm)],[f_240_1]) ).

fof(f_240_3,plain,
    ( ! [U_819,U_820,U_818] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_818),U_819),hAPP(c_Groups_Ouminus__class_Ouminus(U_818),U_820)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_818),U_820),hAPP(c_Groups_Ouminus__class_Ouminus(U_818),U_819)))
        | ~ sP56(U_819,U_820,U_818) )
    & ! [U_819,U_820,U_818] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_818),U_820),hAPP(c_Groups_Ouminus__class_Ouminus(U_818),U_819)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_818),U_819),hAPP(c_Groups_Ouminus__class_Ouminus(U_818),U_820)))
        | ~ sP56(U_819,U_820,U_818) )
    & ! [U_819,U_820,U_818] :
        ( sP56(U_819,U_820,U_818)
        | ~ class_Groups_Oordered__ab__group__add(U_818) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP56])],[f_240_2]) ).

cnf(f_240_4,plain,
    ( sP56(U_819,U_820,U_818)
    | ~ class_Groups_Oordered__ab__group__add(U_818) ),
    inference(clausify,[status(thm)],[f_240_3]) ).

cnf(f_240_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_818),U_820),hAPP(c_Groups_Ouminus__class_Ouminus(U_818),U_819)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_818),U_819),hAPP(c_Groups_Ouminus__class_Ouminus(U_818),U_820)))
    | ~ sP56(U_819,U_820,U_818) ),
    inference(clausify,[status(thm)],[f_240_3]) ).

cnf(f_240_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_818),U_819),hAPP(c_Groups_Ouminus__class_Ouminus(U_818),U_820)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_818),U_820),hAPP(c_Groups_Ouminus__class_Ouminus(U_818),U_819)))
    | ~ sP56(U_819,U_820,U_818) ),
    inference(clausify,[status(thm)],[f_240_3]) ).

fof(f_241_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_241_2,plain,
    ! [U_823,U_822,U_821] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_821),U_822),U_822) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_821),U_823),U_823)
          | ( U_822 != hAPP(c_Groups_Ouminus__class_Ouminus(U_821),U_823)
            & U_822 != U_823 ) )
        & ( U_822 = hAPP(c_Groups_Ouminus__class_Ouminus(U_821),U_823)
          | U_822 = U_823
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_821),U_822),U_822) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_821),U_823),U_823) ) )
      | ~ class_Rings_Oidom(U_821) ),
    inference(variable_rename,[status(thm)],[f_241_1]) ).

fof(f_241_3,plain,
    ( ! [U_821,U_822,U_823] :
        ( U_822 != hAPP(c_Groups_Ouminus__class_Ouminus(U_821),U_823)
        | ~ sP57(U_821,U_822,U_823) )
    & ! [U_821,U_822,U_823] :
        ( U_822 != U_823
        | ~ sP57(U_821,U_822,U_823) )
    & ! [U_821,U_822,U_823] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_821),U_822),U_822) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_821),U_823),U_823)
        | sP57(U_821,U_822,U_823)
        | ~ sP58(U_821,U_822,U_823) )
    & ! [U_821,U_822,U_823] :
        ( U_822 = hAPP(c_Groups_Ouminus__class_Ouminus(U_821),U_823)
        | U_822 = U_823
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_821),U_822),U_822) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_821),U_823),U_823)
        | ~ sP58(U_821,U_822,U_823) )
    & ! [U_821,U_822,U_823] :
        ( sP58(U_821,U_822,U_823)
        | ~ class_Rings_Oidom(U_821) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP57,sP58])],[f_241_2]) ).

cnf(f_241_4,plain,
    ( sP58(U_821,U_822,U_823)
    | ~ class_Rings_Oidom(U_821) ),
    inference(clausify,[status(thm)],[f_241_3]) ).

cnf(f_241_5,plain,
    ( U_822 = hAPP(c_Groups_Ouminus__class_Ouminus(U_821),U_823)
    | U_822 = U_823
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_821),U_822),U_822) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_821),U_823),U_823)
    | ~ sP58(U_821,U_822,U_823) ),
    inference(clausify,[status(thm)],[f_241_3]) ).

cnf(f_241_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_821),U_822),U_822) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_821),U_823),U_823)
    | sP57(U_821,U_822,U_823)
    | ~ sP58(U_821,U_822,U_823) ),
    inference(clausify,[status(thm)],[f_241_3]) ).

cnf(f_241_7,plain,
    ( U_822 != U_823
    | ~ sP57(U_821,U_822,U_823) ),
    inference(clausify,[status(thm)],[f_241_3]) ).

cnf(f_241_8,plain,
    ( U_822 != hAPP(c_Groups_Ouminus__class_Ouminus(U_821),U_823)
    | ~ sP57(U_821,U_822,U_823) ),
    inference(clausify,[status(thm)],[f_241_3]) ).

fof(f_242_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_242_2,plain,
    ! [U_826,U_825,U_824] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_824),hAPP(c_Groups_Ouminus__class_Ouminus(U_824),U_825)),hAPP(c_Groups_Ouminus__class_Ouminus(U_824),U_826)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_824),U_825),U_826)
      | ~ class_Rings_Oring(U_824) ),
    inference(variable_rename,[status(thm)],[f_242_1]) ).

fof(f_242_3,plain,
    ! [U_826,U_825,U_824] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_824),hAPP(c_Groups_Ouminus__class_Ouminus(U_824),U_825)),hAPP(c_Groups_Ouminus__class_Ouminus(U_824),U_826)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_824),U_825),U_826)
      | ~ class_Rings_Oring(U_824) ),
    inference(definitional_conversion,[status(esa)],[f_242_2]) ).

cnf(f_242_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_824),hAPP(c_Groups_Ouminus__class_Ouminus(U_824),U_825)),hAPP(c_Groups_Ouminus__class_Ouminus(U_824),U_826)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_824),U_825),U_826)
    | ~ class_Rings_Oring(U_824) ),
    inference(clausify,[status(thm)],[f_242_3]) ).

fof(f_243_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_243_2,plain,
    ! [U_829,U_828,U_827] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_827),hAPP(c_Groups_Ouminus__class_Ouminus(U_827),U_828)),U_829) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_827),U_828),hAPP(c_Groups_Ouminus__class_Ouminus(U_827),U_829))
      | ~ class_Rings_Oring(U_827) ),
    inference(variable_rename,[status(thm)],[f_243_1]) ).

fof(f_243_3,plain,
    ! [U_828,U_827,U_829] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_827),hAPP(c_Groups_Ouminus__class_Ouminus(U_827),U_828)),U_829) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_827),U_828),hAPP(c_Groups_Ouminus__class_Ouminus(U_827),U_829))
      | ~ class_Rings_Oring(U_827) ),
    inference(definitional_conversion,[status(esa)],[f_243_2]) ).

cnf(f_243_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_827),hAPP(c_Groups_Ouminus__class_Ouminus(U_827),U_828)),U_829) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_827),U_828),hAPP(c_Groups_Ouminus__class_Ouminus(U_827),U_829))
    | ~ class_Rings_Oring(U_827) ),
    inference(clausify,[status(thm)],[f_243_3]) ).

fof(f_244_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_244_2,plain,
    ! [U_832,U_831,U_830] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_830),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_830),U_831),U_832)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_830),hAPP(c_Groups_Ouminus__class_Ouminus(U_830),U_831)),U_832)
      | ~ class_Rings_Oring(U_830) ),
    inference(variable_rename,[status(thm)],[f_244_1]) ).

fof(f_244_3,plain,
    ! [U_830,U_831,U_832] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_830),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_830),U_831),U_832)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_830),hAPP(c_Groups_Ouminus__class_Ouminus(U_830),U_831)),U_832)
      | ~ class_Rings_Oring(U_830) ),
    inference(definitional_conversion,[status(esa)],[f_244_2]) ).

cnf(f_244_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_830),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_830),U_831),U_832)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_830),hAPP(c_Groups_Ouminus__class_Ouminus(U_830),U_831)),U_832)
    | ~ class_Rings_Oring(U_830) ),
    inference(clausify,[status(thm)],[f_244_3]) ).

fof(f_245_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_245_2,plain,
    ! [U_835,U_834,U_833] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_833),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_833),U_834),U_835)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_833),U_834),hAPP(c_Groups_Ouminus__class_Ouminus(U_833),U_835))
      | ~ class_Rings_Oring(U_833) ),
    inference(variable_rename,[status(thm)],[f_245_1]) ).

fof(f_245_3,plain,
    ! [U_833,U_834,U_835] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_833),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_833),U_834),U_835)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_833),U_834),hAPP(c_Groups_Ouminus__class_Ouminus(U_833),U_835))
      | ~ class_Rings_Oring(U_833) ),
    inference(definitional_conversion,[status(esa)],[f_245_2]) ).

cnf(f_245_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_833),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_833),U_834),U_835)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_833),U_834),hAPP(c_Groups_Ouminus__class_Ouminus(U_833),U_835))
    | ~ class_Rings_Oring(U_833) ),
    inference(clausify,[status(thm)],[f_245_3]) ).

fof(f_246_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_246_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_246_1]) ).

cnf(f_246_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_246_2]) ).

fof(f_247_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_247_2,plain,
    ! [U_836] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_836) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_247_1]) ).

fof(f_247_3,plain,
    ! [U_836] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_836) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_247_2]) ).

cnf(f_247_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_836) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_247_3]) ).

fof(f_248_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_248_2,plain,
    ! [U_837] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_837),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_248_1]) ).

fof(f_248_3,plain,
    ! [U_837] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_837),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_248_2]) ).

cnf(f_248_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_837),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_248_3]) ).

fof(f_249_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_249_2,plain,
    ! [U_839,U_838] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_838),U_839) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( U_839 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_838 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_839 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_838 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_838),U_839) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_249_1]) ).

fof(f_249_3,plain,
    ( ! [U_843,U_841] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_841),U_843) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( U_843 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_841 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_842,U_840] :
        ( U_842 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_840 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_840),U_842) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_249_2]) ).

fof(f_249_4,plain,
    ( ! [U_843,U_841] :
        ( U_843 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP59(U_843,U_841) )
    & ! [U_843,U_841] :
        ( U_841 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP59(U_843,U_841) )
    & ! [U_843,U_841] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_841),U_843) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP59(U_843,U_841) )
    & ! [U_842,U_840] :
        ( U_842 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_840 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_840),U_842) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP59])],[f_249_3]) ).

cnf(f_249_5,plain,
    ( U_842 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_840 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_840),U_842) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_249_4]) ).

cnf(f_249_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_841),U_843) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP59(U_843,U_841) ),
    inference(clausify,[status(thm)],[f_249_4]) ).

cnf(f_249_7,plain,
    ( U_841 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP59(U_843,U_841) ),
    inference(clausify,[status(thm)],[f_249_4]) ).

cnf(f_249_8,plain,
    ( U_843 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP59(U_843,U_841) ),
    inference(clausify,[status(thm)],[f_249_4]) ).

fof(f_250_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_250_2,plain,
    ! [U_846,U_845,U_844] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_844),U_845) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_844),U_846)
        | ( U_844 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_845 != U_846 ) )
      & ( U_844 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_845 = U_846
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_844),U_845) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_844),U_846) ) ),
    inference(variable_rename,[status(thm)],[f_250_1]) ).

fof(f_250_3,plain,
    ( ! [U_852,U_850,U_848] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_848),U_850) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_848),U_852)
        | ( U_848 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_850 != U_852 ) )
    & ! [U_851,U_849,U_847] :
        ( U_847 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_849 = U_851
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_847),U_849) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_847),U_851) ) ),
    inference(miniscope,[status(thm)],[f_250_2]) ).

fof(f_250_4,plain,
    ( ! [U_852,U_850,U_848] :
        ( U_848 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP60(U_852,U_850,U_848) )
    & ! [U_852,U_850,U_848] :
        ( U_850 != U_852
        | ~ sP60(U_852,U_850,U_848) )
    & ! [U_852,U_850,U_848] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_848),U_850) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_848),U_852)
        | sP60(U_852,U_850,U_848) )
    & ! [U_849,U_847,U_851] :
        ( U_847 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_849 = U_851
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_847),U_849) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_847),U_851) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP60])],[f_250_3]) ).

cnf(f_250_5,plain,
    ( U_847 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_849 = U_851
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_847),U_849) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_847),U_851) ),
    inference(clausify,[status(thm)],[f_250_4]) ).

cnf(f_250_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_848),U_850) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_848),U_852)
    | sP60(U_852,U_850,U_848) ),
    inference(clausify,[status(thm)],[f_250_4]) ).

cnf(f_250_7,plain,
    ( U_850 != U_852
    | ~ sP60(U_852,U_850,U_848) ),
    inference(clausify,[status(thm)],[f_250_4]) ).

cnf(f_250_8,plain,
    ( U_848 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP60(U_852,U_850,U_848) ),
    inference(clausify,[status(thm)],[f_250_4]) ).

fof(f_251_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_251_2,plain,
    ! [U_855,U_854,U_853] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_853),U_854) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_855),U_854)
        | ( U_854 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_853 != U_855 ) )
      & ( U_854 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_853 = U_855
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_853),U_854) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_855),U_854) ) ),
    inference(variable_rename,[status(thm)],[f_251_1]) ).

fof(f_251_3,plain,
    ( ! [U_861,U_859,U_857] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_857),U_859) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_861),U_859)
        | ( U_859 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_857 != U_861 ) )
    & ! [U_860,U_858,U_856] :
        ( U_858 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_856 = U_860
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_856),U_858) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_860),U_858) ) ),
    inference(miniscope,[status(thm)],[f_251_2]) ).

fof(f_251_4,plain,
    ( ! [U_861,U_859,U_857] :
        ( U_859 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP61(U_861,U_859,U_857) )
    & ! [U_861,U_859,U_857] :
        ( U_857 != U_861
        | ~ sP61(U_861,U_859,U_857) )
    & ! [U_861,U_859,U_857] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_857),U_859) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_861),U_859)
        | sP61(U_861,U_859,U_857) )
    & ! [U_858,U_856,U_860] :
        ( U_858 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_856 = U_860
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_856),U_858) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_860),U_858) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP61])],[f_251_3]) ).

cnf(f_251_5,plain,
    ( U_858 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_856 = U_860
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_856),U_858) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_860),U_858) ),
    inference(clausify,[status(thm)],[f_251_4]) ).

cnf(f_251_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_857),U_859) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_861),U_859)
    | sP61(U_861,U_859,U_857) ),
    inference(clausify,[status(thm)],[f_251_4]) ).

cnf(f_251_7,plain,
    ( U_857 != U_861
    | ~ sP61(U_861,U_859,U_857) ),
    inference(clausify,[status(thm)],[f_251_4]) ).

cnf(f_251_8,plain,
    ( U_859 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP61(U_861,U_859,U_857) ),
    inference(clausify,[status(thm)],[f_251_4]) ).

fof(f_252_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_252_2,plain,
    ! [U_863,U_862] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_862)),U_863) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_862),U_863)),
    inference(variable_rename,[status(thm)],[f_252_1]) ).

fof(f_252_3,plain,
    ! [U_863,U_862] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_862)),U_863) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_862),U_863)),
    inference(definitional_conversion,[status(esa)],[f_252_2]) ).

cnf(f_252_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_862)),U_863) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_862),U_863)),
    inference(clausify,[status(thm)],[f_252_3]) ).

fof(f_253_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_253_2,plain,
    ! [U_866,U_865,U_864] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_864)),U_865) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_864)),U_866)
        | U_865 != U_866 )
      & ( U_865 = U_866
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_864)),U_865) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_864)),U_866) ) ),
    inference(variable_rename,[status(thm)],[f_253_1]) ).

fof(f_253_3,plain,
    ( ! [U_872,U_870] :
        ( ! [U_868] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_868)),U_870) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_868)),U_872)
        | U_870 != U_872 )
    & ! [U_871,U_869] :
        ( ! [U_867] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_867)),U_869) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_867)),U_871)
        | U_869 = U_871 ) ),
    inference(miniscope,[status(thm)],[f_253_2]) ).

fof(f_253_4,plain,
    ( ! [U_872,U_868,U_870] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_868)),U_870) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_868)),U_872)
        | U_870 != U_872 )
    & ! [U_869,U_871,U_867] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_867)),U_869) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_867)),U_871)
        | U_869 = U_871 ) ),
    inference(definitional_conversion,[status(esa)],[f_253_3]) ).

cnf(f_253_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_867)),U_869) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_867)),U_871)
    | U_869 = U_871 ),
    inference(clausify,[status(thm)],[f_253_4]) ).

cnf(f_253_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_868)),U_870) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_868)),U_872)
    | U_870 != U_872 ),
    inference(clausify,[status(thm)],[f_253_4]) ).

fof(f_254_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_254_2,plain,
    ! [U_874,U_873] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_873),U_874),hAPP(c_Groups_Ouminus__class_Ouminus(U_873),U_874)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_873),U_874),c_Groups_Ozero__class_Ozero(U_873))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_873),U_874),c_Groups_Ozero__class_Ozero(U_873)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_873),U_874),hAPP(c_Groups_Ouminus__class_Ouminus(U_873),U_874))) ) )
      | ~ class_Rings_Olinordered__idom(U_873) ),
    inference(variable_rename,[status(thm)],[f_254_1]) ).

fof(f_254_3,plain,
    ( ! [U_873,U_874] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_873),U_874),hAPP(c_Groups_Ouminus__class_Ouminus(U_873),U_874)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_873),U_874),c_Groups_Ozero__class_Ozero(U_873)))
        | ~ sP62(U_873,U_874) )
    & ! [U_873,U_874] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_873),U_874),c_Groups_Ozero__class_Ozero(U_873)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_873),U_874),hAPP(c_Groups_Ouminus__class_Ouminus(U_873),U_874)))
        | ~ sP62(U_873,U_874) )
    & ! [U_873,U_874] :
        ( sP62(U_873,U_874)
        | ~ class_Rings_Olinordered__idom(U_873) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP62])],[f_254_2]) ).

cnf(f_254_4,plain,
    ( sP62(U_873,U_874)
    | ~ class_Rings_Olinordered__idom(U_873) ),
    inference(clausify,[status(thm)],[f_254_3]) ).

cnf(f_254_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_873),U_874),c_Groups_Ozero__class_Ozero(U_873)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_873),U_874),hAPP(c_Groups_Ouminus__class_Ouminus(U_873),U_874)))
    | ~ sP62(U_873,U_874) ),
    inference(clausify,[status(thm)],[f_254_3]) ).

cnf(f_254_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_873),U_874),hAPP(c_Groups_Ouminus__class_Ouminus(U_873),U_874)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_873),U_874),c_Groups_Ozero__class_Ozero(U_873)))
    | ~ sP62(U_873,U_874) ),
    inference(clausify,[status(thm)],[f_254_3]) ).

fof(f_255_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_255_2,plain,
    ! [U_876,U_875] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_875),hAPP(c_Groups_Ouminus__class_Ouminus(U_875),U_876)),U_876))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_875),c_Groups_Ozero__class_Ozero(U_875)),U_876)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_875),c_Groups_Ozero__class_Ozero(U_875)),U_876))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_875),hAPP(c_Groups_Ouminus__class_Ouminus(U_875),U_876)),U_876)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_875) ),
    inference(variable_rename,[status(thm)],[f_255_1]) ).

fof(f_255_3,plain,
    ( ! [U_876,U_875] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_875),hAPP(c_Groups_Ouminus__class_Ouminus(U_875),U_876)),U_876))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_875),c_Groups_Ozero__class_Ozero(U_875)),U_876))
        | ~ sP63(U_876,U_875) )
    & ! [U_876,U_875] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_875),c_Groups_Ozero__class_Ozero(U_875)),U_876))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_875),hAPP(c_Groups_Ouminus__class_Ouminus(U_875),U_876)),U_876))
        | ~ sP63(U_876,U_875) )
    & ! [U_876,U_875] :
        ( sP63(U_876,U_875)
        | ~ class_Groups_Olinordered__ab__group__add(U_875) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP63])],[f_255_2]) ).

cnf(f_255_4,plain,
    ( sP63(U_876,U_875)
    | ~ class_Groups_Olinordered__ab__group__add(U_875) ),
    inference(clausify,[status(thm)],[f_255_3]) ).

cnf(f_255_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_875),c_Groups_Ozero__class_Ozero(U_875)),U_876))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_875),hAPP(c_Groups_Ouminus__class_Ouminus(U_875),U_876)),U_876))
    | ~ sP63(U_876,U_875) ),
    inference(clausify,[status(thm)],[f_255_3]) ).

cnf(f_255_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_875),hAPP(c_Groups_Ouminus__class_Ouminus(U_875),U_876)),U_876))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_875),c_Groups_Ozero__class_Ozero(U_875)),U_876))
    | ~ sP63(U_876,U_875) ),
    inference(clausify,[status(thm)],[f_255_3]) ).

fof(f_256_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_256_2,plain,
    ! [U_878,U_877] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_877),hAPP(c_Groups_Ouminus__class_Ouminus(U_877),U_878)),c_Groups_Ozero__class_Ozero(U_877)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_877),c_Groups_Ozero__class_Ozero(U_877)),U_878)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_877),c_Groups_Ozero__class_Ozero(U_877)),U_878))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_877),hAPP(c_Groups_Ouminus__class_Ouminus(U_877),U_878)),c_Groups_Ozero__class_Ozero(U_877))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_877) ),
    inference(variable_rename,[status(thm)],[f_256_1]) ).

fof(f_256_3,plain,
    ( ! [U_878,U_877] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_877),hAPP(c_Groups_Ouminus__class_Ouminus(U_877),U_878)),c_Groups_Ozero__class_Ozero(U_877)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_877),c_Groups_Ozero__class_Ozero(U_877)),U_878))
        | ~ sP64(U_878,U_877) )
    & ! [U_878,U_877] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_877),c_Groups_Ozero__class_Ozero(U_877)),U_878))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_877),hAPP(c_Groups_Ouminus__class_Ouminus(U_877),U_878)),c_Groups_Ozero__class_Ozero(U_877)))
        | ~ sP64(U_878,U_877) )
    & ! [U_878,U_877] :
        ( sP64(U_878,U_877)
        | ~ class_Groups_Oordered__ab__group__add(U_877) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP64])],[f_256_2]) ).

cnf(f_256_4,plain,
    ( sP64(U_878,U_877)
    | ~ class_Groups_Oordered__ab__group__add(U_877) ),
    inference(clausify,[status(thm)],[f_256_3]) ).

cnf(f_256_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_877),c_Groups_Ozero__class_Ozero(U_877)),U_878))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_877),hAPP(c_Groups_Ouminus__class_Ouminus(U_877),U_878)),c_Groups_Ozero__class_Ozero(U_877)))
    | ~ sP64(U_878,U_877) ),
    inference(clausify,[status(thm)],[f_256_3]) ).

cnf(f_256_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_877),hAPP(c_Groups_Ouminus__class_Ouminus(U_877),U_878)),c_Groups_Ozero__class_Ozero(U_877)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_877),c_Groups_Ozero__class_Ozero(U_877)),U_878))
    | ~ sP64(U_878,U_877) ),
    inference(clausify,[status(thm)],[f_256_3]) ).

fof(f_257_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_257_2,plain,
    ! [U_880,U_879] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_879),c_Groups_Ozero__class_Ozero(U_879)),hAPP(c_Groups_Ouminus__class_Ouminus(U_879),U_880)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_879),U_880),c_Groups_Ozero__class_Ozero(U_879))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_879),U_880),c_Groups_Ozero__class_Ozero(U_879)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_879),c_Groups_Ozero__class_Ozero(U_879)),hAPP(c_Groups_Ouminus__class_Ouminus(U_879),U_880))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_879) ),
    inference(variable_rename,[status(thm)],[f_257_1]) ).

fof(f_257_3,plain,
    ( ! [U_880,U_879] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_879),c_Groups_Ozero__class_Ozero(U_879)),hAPP(c_Groups_Ouminus__class_Ouminus(U_879),U_880)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_879),U_880),c_Groups_Ozero__class_Ozero(U_879)))
        | ~ sP65(U_880,U_879) )
    & ! [U_880,U_879] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_879),U_880),c_Groups_Ozero__class_Ozero(U_879)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_879),c_Groups_Ozero__class_Ozero(U_879)),hAPP(c_Groups_Ouminus__class_Ouminus(U_879),U_880)))
        | ~ sP65(U_880,U_879) )
    & ! [U_880,U_879] :
        ( sP65(U_880,U_879)
        | ~ class_Groups_Oordered__ab__group__add(U_879) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP65])],[f_257_2]) ).

cnf(f_257_4,plain,
    ( sP65(U_880,U_879)
    | ~ class_Groups_Oordered__ab__group__add(U_879) ),
    inference(clausify,[status(thm)],[f_257_3]) ).

cnf(f_257_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_879),U_880),c_Groups_Ozero__class_Ozero(U_879)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_879),c_Groups_Ozero__class_Ozero(U_879)),hAPP(c_Groups_Ouminus__class_Ouminus(U_879),U_880)))
    | ~ sP65(U_880,U_879) ),
    inference(clausify,[status(thm)],[f_257_3]) ).

cnf(f_257_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_879),c_Groups_Ozero__class_Ozero(U_879)),hAPP(c_Groups_Ouminus__class_Ouminus(U_879),U_880)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_879),U_880),c_Groups_Ozero__class_Ozero(U_879)))
    | ~ sP65(U_880,U_879) ),
    inference(clausify,[status(thm)],[f_257_3]) ).

fof(f_258_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_258_2,plain,
    ! [U_882,U_881] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_881)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_882)
        | U_882 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_881 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( U_882 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_881 = 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_881)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_882) ) ),
    inference(variable_rename,[status(thm)],[f_258_1]) ).

fof(f_258_3,plain,
    ( ! [U_886,U_884] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_884)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_886)
        | U_886 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_884 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_885,U_883] :
        ( ( U_885 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_883 = 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_883)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_885) ) ),
    inference(miniscope,[status(thm)],[f_258_2]) ).

fof(f_258_4,plain,
    ( ! [U_883,U_885] :
        ( U_885 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP66(U_883,U_885) )
    & ! [U_883,U_885] :
        ( U_883 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP66(U_883,U_885) )
    & ! [U_886,U_884] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_884)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_886)
        | U_886 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_884 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_883,U_885] :
        ( sP66(U_883,U_885)
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_883)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_885) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP66])],[f_258_3]) ).

cnf(f_258_5,plain,
    ( sP66(U_883,U_885)
    | hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_883)) != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_885) ),
    inference(clausify,[status(thm)],[f_258_4]) ).

cnf(f_258_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_884)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_886)
    | U_886 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_884 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_258_4]) ).

cnf(f_258_7,plain,
    ( U_883 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP66(U_883,U_885) ),
    inference(clausify,[status(thm)],[f_258_4]) ).

cnf(f_258_8,plain,
    ( U_885 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP66(U_883,U_885) ),
    inference(clausify,[status(thm)],[f_258_4]) ).

fof(f_259_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_259_2,plain,
    ! [U_888,U_887] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_887)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_888)))),
    inference(variable_rename,[status(thm)],[f_259_1]) ).

fof(f_259_3,plain,
    ! [U_887,U_888] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_887)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_888)))),
    inference(definitional_conversion,[status(esa)],[f_259_2]) ).

cnf(f_259_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_887)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_888)))),
    inference(clausify,[status(thm)],[f_259_3]) ).

fof(f_260_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_260_2,plain,
    ! [U_890,U_889] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_889),U_890) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_890 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_889 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( ( U_890 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_889 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_889),U_890) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_260_1]) ).

fof(f_260_3,plain,
    ( ! [U_894,U_892] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_892),U_894) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_894 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_892 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_893,U_891] :
        ( ( U_893 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_891 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_891),U_893) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_260_2]) ).

fof(f_260_4,plain,
    ( ! [U_893,U_891] :
        ( U_893 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP67(U_893,U_891) )
    & ! [U_893,U_891] :
        ( U_891 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP67(U_893,U_891) )
    & ! [U_892,U_894] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_892),U_894) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_894 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_892 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_893,U_891] :
        ( sP67(U_893,U_891)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_891),U_893) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP67])],[f_260_3]) ).

cnf(f_260_5,plain,
    ( sP67(U_893,U_891)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_891),U_893) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_260_4]) ).

cnf(f_260_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_892),U_894) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_894 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_892 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_260_4]) ).

cnf(f_260_7,plain,
    ( U_891 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP67(U_893,U_891) ),
    inference(clausify,[status(thm)],[f_260_4]) ).

cnf(f_260_8,plain,
    ( U_893 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP67(U_893,U_891) ),
    inference(clausify,[status(thm)],[f_260_4]) ).

fof(f_261_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_261_2,plain,
    ! [U_896,U_895] :
      ( ( 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_895),U_896)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_896))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_895)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_896))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_895)) )
        | ~ 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_895),U_896))) ) ),
    inference(variable_rename,[status(thm)],[f_261_1]) ).

fof(f_261_3,plain,
    ( ! [U_900,U_898] :
        ( 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_898),U_900)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_900))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_898)) )
    & ! [U_899,U_897] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_899))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_897)) )
        | ~ 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_897),U_899))) ) ),
    inference(miniscope,[status(thm)],[f_261_2]) ).

fof(f_261_4,plain,
    ( ! [U_899,U_897] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_899))
        | ~ sP68(U_899,U_897) )
    & ! [U_899,U_897] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_897))
        | ~ sP68(U_899,U_897) )
    & ! [U_900,U_898] :
        ( 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_898),U_900)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_900))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_898)) )
    & ! [U_899,U_897] :
        ( sP68(U_899,U_897)
        | ~ 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_897),U_899))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP68])],[f_261_3]) ).

cnf(f_261_5,plain,
    ( sP68(U_899,U_897)
    | ~ 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_897),U_899))) ),
    inference(clausify,[status(thm)],[f_261_4]) ).

cnf(f_261_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_898),U_900)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_900))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_898)) ),
    inference(clausify,[status(thm)],[f_261_4]) ).

cnf(f_261_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_897))
    | ~ sP68(U_899,U_897) ),
    inference(clausify,[status(thm)],[f_261_4]) ).

cnf(f_261_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_899))
    | ~ sP68(U_899,U_897) ),
    inference(clausify,[status(thm)],[f_261_4]) ).

fof(f_262_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_262_2,plain,
    ! [U_903,U_902,U_901] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_901),U_902)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_901),U_903)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_902),U_903))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_901)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_902),U_903))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_901)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_901),U_902)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_901),U_903))) ) ),
    inference(variable_rename,[status(thm)],[f_262_1]) ).

fof(f_262_3,plain,
    ( ! [U_909,U_907,U_905] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_905),U_907)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_905),U_909)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_907),U_909))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_905)) )
    & ! [U_908,U_906,U_904] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_906),U_908))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_904)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_904),U_906)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_904),U_908))) ) ),
    inference(miniscope,[status(thm)],[f_262_2]) ).

fof(f_262_4,plain,
    ( ! [U_906,U_904,U_908] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_906),U_908))
        | ~ sP69(U_906,U_904,U_908) )
    & ! [U_906,U_904,U_908] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_904))
        | ~ sP69(U_906,U_904,U_908) )
    & ! [U_907,U_909,U_905] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_905),U_907)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_905),U_909)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_907),U_909))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_905)) )
    & ! [U_906,U_904,U_908] :
        ( sP69(U_906,U_904,U_908)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_904),U_906)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_904),U_908))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP69])],[f_262_3]) ).

cnf(f_262_5,plain,
    ( sP69(U_906,U_904,U_908)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_904),U_906)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_904),U_908))) ),
    inference(clausify,[status(thm)],[f_262_4]) ).

cnf(f_262_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_905),U_907)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_905),U_909)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_907),U_909))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_905)) ),
    inference(clausify,[status(thm)],[f_262_4]) ).

cnf(f_262_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_904))
    | ~ sP69(U_906,U_904,U_908) ),
    inference(clausify,[status(thm)],[f_262_4]) ).

cnf(f_262_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_906),U_908))
    | ~ sP69(U_906,U_904,U_908) ),
    inference(clausify,[status(thm)],[f_262_4]) ).

fof(f_263_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_263_2,plain,
    ! [U_912,U_911,U_910] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_910),U_911)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_912),U_911)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_910),U_912))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_911)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_910),U_912))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_911)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_910),U_911)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_912),U_911))) ) ),
    inference(variable_rename,[status(thm)],[f_263_1]) ).

fof(f_263_3,plain,
    ( ! [U_918,U_916,U_914] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_914),U_916)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_918),U_916)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_914),U_918))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_916)) )
    & ! [U_917,U_915,U_913] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_913),U_917))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_915)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_913),U_915)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_917),U_915))) ) ),
    inference(miniscope,[status(thm)],[f_263_2]) ).

fof(f_263_4,plain,
    ( ! [U_917,U_915,U_913] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_913),U_917))
        | ~ sP70(U_917,U_915,U_913) )
    & ! [U_917,U_915,U_913] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_915))
        | ~ sP70(U_917,U_915,U_913) )
    & ! [U_914,U_916,U_918] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_914),U_916)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_918),U_916)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_914),U_918))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_916)) )
    & ! [U_917,U_915,U_913] :
        ( sP70(U_917,U_915,U_913)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_913),U_915)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_917),U_915))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP70])],[f_263_3]) ).

cnf(f_263_5,plain,
    ( sP70(U_917,U_915,U_913)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_913),U_915)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_917),U_915))) ),
    inference(clausify,[status(thm)],[f_263_4]) ).

cnf(f_263_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_914),U_916)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_918),U_916)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_914),U_918))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_916)) ),
    inference(clausify,[status(thm)],[f_263_4]) ).

cnf(f_263_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_915))
    | ~ sP70(U_917,U_915,U_913) ),
    inference(clausify,[status(thm)],[f_263_4]) ).

cnf(f_263_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_913),U_917))
    | ~ sP70(U_917,U_915,U_913) ),
    inference(clausify,[status(thm)],[f_263_4]) ).

fof(f_264_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_264_2,plain,
    ! [U_921,U_920,U_919] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_919),U_921)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_920),U_921)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_921))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_919),U_920)) ),
    inference(variable_rename,[status(thm)],[f_264_1]) ).

fof(f_264_3,plain,
    ! [U_920,U_919,U_921] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_919),U_921)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_920),U_921)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_921))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_919),U_920)) ),
    inference(definitional_conversion,[status(esa)],[f_264_2]) ).

cnf(f_264_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_919),U_921)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_920),U_921)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_921))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_919),U_920)) ),
    inference(clausify,[status(thm)],[f_264_3]) ).

fof(f_265_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_265_2,plain,
    ! [U_924,U_923,U_922] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_924),U_922)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_924),U_923)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_924))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_922),U_923)) ),
    inference(variable_rename,[status(thm)],[f_265_1]) ).

fof(f_265_3,plain,
    ! [U_922,U_923,U_924] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_924),U_922)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_924),U_923)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_924))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_922),U_923)) ),
    inference(definitional_conversion,[status(esa)],[f_265_2]) ).

cnf(f_265_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_924),U_922)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_924),U_923)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_924))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_922),U_923)) ),
    inference(clausify,[status(thm)],[f_265_3]) ).

fof(f_266_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_266_2,plain,
    ! [U_927,U_926,U_925] :
      ( ( 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_925)),U_926)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_925)),U_927)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_926),U_927)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_926),U_927))
        | ~ 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_925)),U_926)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_925)),U_927))) ) ),
    inference(variable_rename,[status(thm)],[f_266_1]) ).

fof(f_266_3,plain,
    ( ! [U_933,U_931] :
        ( ! [U_929] : 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_929)),U_931)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_929)),U_933)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_931),U_933)) )
    & ! [U_932,U_930] :
        ( ! [U_928] : ~ 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_928)),U_930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_928)),U_932)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_930),U_932)) ) ),
    inference(miniscope,[status(thm)],[f_266_2]) ).

fof(f_266_4,plain,
    ( ! [U_933,U_929,U_931] :
        ( 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_929)),U_931)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_929)),U_933)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_931),U_933)) )
    & ! [U_930,U_928,U_932] :
        ( ~ 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_928)),U_930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_928)),U_932)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_930),U_932)) ) ),
    inference(definitional_conversion,[status(esa)],[f_266_3]) ).

cnf(f_266_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_928)),U_930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_928)),U_932)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_930),U_932)) ),
    inference(clausify,[status(thm)],[f_266_4]) ).

cnf(f_266_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_929)),U_931)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_929)),U_933)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_931),U_933)) ),
    inference(clausify,[status(thm)],[f_266_4]) ).

fof(f_267_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_267_2,plain,
    ! [U_935,U_934] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_934)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_935)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_934),U_935)),
    inference(variable_rename,[status(thm)],[f_267_1]) ).

fof(f_267_3,plain,
    ! [U_935,U_934] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_934)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_935)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_934),U_935)),
    inference(definitional_conversion,[status(esa)],[f_267_2]) ).

cnf(f_267_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_934)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_935)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_934),U_935)),
    inference(clausify,[status(thm)],[f_267_3]) ).

fof(f_268_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_268_2,plain,
    ! [U_937,U_936] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_936)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_937)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_936),U_937)),
    inference(variable_rename,[status(thm)],[f_268_1]) ).

fof(f_268_3,plain,
    ! [U_936,U_937] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_936)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_937)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_936),U_937)),
    inference(definitional_conversion,[status(esa)],[f_268_2]) ).

cnf(f_268_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_936)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_937)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_936),U_937)),
    inference(clausify,[status(thm)],[f_268_3]) ).

fof(f_269_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_269_2,plain,
    ! [U_939,U_938] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_938),U_939)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_938)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_939)),
    inference(variable_rename,[status(thm)],[f_269_1]) ).

fof(f_269_3,plain,
    ! [U_939,U_938] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_938),U_939)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_938)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_939)),
    inference(definitional_conversion,[status(esa)],[f_269_2]) ).

cnf(f_269_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_938),U_939)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_938)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_939)),
    inference(clausify,[status(thm)],[f_269_3]) ).

fof(f_270_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_270_2,plain,
    ! [U_941,U_940] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_940),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_941),U_940)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_941))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_940)) ),
    inference(variable_rename,[status(thm)],[f_270_1]) ).

fof(f_270_3,plain,
    ! [U_940,U_941] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_940),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_941),U_940)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_941))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_940)) ),
    inference(definitional_conversion,[status(esa)],[f_270_2]) ).

cnf(f_270_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_940),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_941),U_940)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_941))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_940)) ),
    inference(clausify,[status(thm)],[f_270_3]) ).

fof(f_271_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_271_2,plain,
    ! [U_943,U_942] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_942),U_943)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_943))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_942)) ),
    inference(variable_rename,[status(thm)],[f_271_1]) ).

fof(f_271_3,plain,
    ! [U_942,U_943] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_942),U_943)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_943))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_942)) ),
    inference(definitional_conversion,[status(esa)],[f_271_2]) ).

cnf(f_271_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_942),U_943)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_943))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_942)) ),
    inference(clausify,[status(thm)],[f_271_3]) ).

fof(f_272_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_272_2,plain,
    ! [U_945,U_944] :
      ( 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_945),U_944)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_945))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_944)) ),
    inference(variable_rename,[status(thm)],[f_272_1]) ).

fof(f_272_3,plain,
    ! [U_944,U_945] :
      ( 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_945),U_944)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_945))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_944)) ),
    inference(definitional_conversion,[status(esa)],[f_272_2]) ).

cnf(f_272_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_945),U_944)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_945))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_944)) ),
    inference(clausify,[status(thm)],[f_272_3]) ).

fof(f_273_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_273_2,plain,
    ! [U_948,U_947,U_946] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_946),U_947),U_948) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_946),U_948),U_947)
      | ~ class_Rings_Ocomm__semiring__1(U_946) ),
    inference(variable_rename,[status(thm)],[f_273_1]) ).

fof(f_273_3,plain,
    ! [U_946,U_947,U_948] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_946),U_947),U_948) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_946),U_948),U_947)
      | ~ class_Rings_Ocomm__semiring__1(U_946) ),
    inference(definitional_conversion,[status(esa)],[f_273_2]) ).

cnf(f_273_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_946),U_947),U_948) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_946),U_948),U_947)
    | ~ class_Rings_Ocomm__semiring__1(U_946) ),
    inference(clausify,[status(thm)],[f_273_3]) ).

fof(f_274_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_274_2,plain,
    ! [U_952,U_951,U_950,U_949] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_949),U_950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_949),U_951),U_952)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_949),U_951),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_949),U_950),U_952))
      | ~ class_Rings_Ocomm__semiring__1(U_949) ),
    inference(variable_rename,[status(thm)],[f_274_1]) ).

fof(f_274_3,plain,
    ! [U_949,U_950,U_951,U_952] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_949),U_950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_949),U_951),U_952)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_949),U_951),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_949),U_950),U_952))
      | ~ class_Rings_Ocomm__semiring__1(U_949) ),
    inference(definitional_conversion,[status(esa)],[f_274_2]) ).

cnf(f_274_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_949),U_950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_949),U_951),U_952)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_949),U_951),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_949),U_950),U_952))
    | ~ class_Rings_Ocomm__semiring__1(U_949) ),
    inference(clausify,[status(thm)],[f_274_3]) ).

fof(f_275_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_275_2,plain,
    ! [U_956,U_955,U_954,U_953] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_953),U_954),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_953),U_955),U_956)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_953),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_953),U_954),U_955)),U_956)
      | ~ class_Rings_Ocomm__semiring__1(U_953) ),
    inference(variable_rename,[status(thm)],[f_275_1]) ).

fof(f_275_3,plain,
    ! [U_953,U_954,U_955,U_956] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_953),U_954),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_953),U_955),U_956)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_953),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_953),U_954),U_955)),U_956)
      | ~ class_Rings_Ocomm__semiring__1(U_953) ),
    inference(definitional_conversion,[status(esa)],[f_275_2]) ).

cnf(f_275_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_953),U_954),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_953),U_955),U_956)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_953),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_953),U_954),U_955)),U_956)
    | ~ class_Rings_Ocomm__semiring__1(U_953) ),
    inference(clausify,[status(thm)],[f_275_3]) ).

fof(f_276_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_276_2,plain,
    ! [U_960,U_959,U_958,U_957] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_957),U_958),U_959)),U_960) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_957),U_958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_957),U_959),U_960))
      | ~ class_Rings_Ocomm__semiring__1(U_957) ),
    inference(variable_rename,[status(thm)],[f_276_1]) ).

fof(f_276_3,plain,
    ! [U_957,U_958,U_959,U_960] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_957),U_958),U_959)),U_960) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_957),U_958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_957),U_959),U_960))
      | ~ class_Rings_Ocomm__semiring__1(U_957) ),
    inference(definitional_conversion,[status(esa)],[f_276_2]) ).

cnf(f_276_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_957),U_958),U_959)),U_960) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_957),U_958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_957),U_959),U_960))
    | ~ class_Rings_Ocomm__semiring__1(U_957) ),
    inference(clausify,[status(thm)],[f_276_3]) ).

fof(f_277_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_277_2,plain,
    ! [U_964,U_963,U_962,U_961] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_961),U_962),U_963)),U_964) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_961),U_962),U_964)),U_963)
      | ~ class_Rings_Ocomm__semiring__1(U_961) ),
    inference(variable_rename,[status(thm)],[f_277_1]) ).

fof(f_277_3,plain,
    ! [U_961,U_962,U_963,U_964] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_961),U_962),U_963)),U_964) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_961),U_962),U_964)),U_963)
      | ~ class_Rings_Ocomm__semiring__1(U_961) ),
    inference(definitional_conversion,[status(esa)],[f_277_2]) ).

cnf(f_277_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_961),U_962),U_963)),U_964) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_961),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_961),U_962),U_964)),U_963)
    | ~ class_Rings_Ocomm__semiring__1(U_961) ),
    inference(clausify,[status(thm)],[f_277_3]) ).

fof(f_278_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_278_2,plain,
    ! [U_969,U_968,U_967,U_966,U_965] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_965),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_965),U_966),U_967)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_965),U_968),U_969)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_965),U_966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_965),U_967),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_965),U_968),U_969)))
      | ~ class_Rings_Ocomm__semiring__1(U_965) ),
    inference(variable_rename,[status(thm)],[f_278_1]) ).

fof(f_278_3,plain,
    ! [U_965,U_966,U_967,U_968,U_969] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_965),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_965),U_966),U_967)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_965),U_968),U_969)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_965),U_966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_965),U_967),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_965),U_968),U_969)))
      | ~ class_Rings_Ocomm__semiring__1(U_965) ),
    inference(definitional_conversion,[status(esa)],[f_278_2]) ).

cnf(f_278_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_965),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_965),U_966),U_967)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_965),U_968),U_969)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_965),U_966),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_965),U_967),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_965),U_968),U_969)))
    | ~ class_Rings_Ocomm__semiring__1(U_965) ),
    inference(clausify,[status(thm)],[f_278_3]) ).

fof(f_279_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_279_2,plain,
    ! [U_974,U_973,U_972,U_971,U_970] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_970),U_971),U_972)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_970),U_973),U_974)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_970),U_973),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_970),U_971),U_972)),U_974))
      | ~ class_Rings_Ocomm__semiring__1(U_970) ),
    inference(variable_rename,[status(thm)],[f_279_1]) ).

fof(f_279_3,plain,
    ! [U_970,U_971,U_972,U_973,U_974] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_970),U_971),U_972)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_970),U_973),U_974)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_970),U_973),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_970),U_971),U_972)),U_974))
      | ~ class_Rings_Ocomm__semiring__1(U_970) ),
    inference(definitional_conversion,[status(esa)],[f_279_2]) ).

cnf(f_279_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_970),U_971),U_972)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_970),U_973),U_974)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_970),U_973),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_970),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_970),U_971),U_972)),U_974))
    | ~ class_Rings_Ocomm__semiring__1(U_970) ),
    inference(clausify,[status(thm)],[f_279_3]) ).

fof(f_280_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_280_2,plain,
    ! [U_979,U_978,U_977,U_976,U_975] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),U_976),U_977)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),U_978),U_979)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),U_976),U_978)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),U_977),U_979))
      | ~ class_Rings_Ocomm__semiring__1(U_975) ),
    inference(variable_rename,[status(thm)],[f_280_1]) ).

fof(f_280_3,plain,
    ! [U_975,U_976,U_977,U_978,U_979] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),U_976),U_977)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),U_978),U_979)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),U_976),U_978)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),U_977),U_979))
      | ~ class_Rings_Ocomm__semiring__1(U_975) ),
    inference(definitional_conversion,[status(esa)],[f_280_2]) ).

cnf(f_280_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),U_976),U_977)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),U_978),U_979)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),U_976),U_978)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_975),U_977),U_979))
    | ~ class_Rings_Ocomm__semiring__1(U_975) ),
    inference(clausify,[status(thm)],[f_280_3]) ).

fof(f_281_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_281_2,plain,
    ! [U_982,U_981,U_980] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_980),U_981) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_980),U_982)
          | U_981 != U_982 )
        & ( U_981 = U_982
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_980),U_981) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_980),U_982) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_980)) ),
    inference(variable_rename,[status(thm)],[f_281_1]) ).

fof(f_281_3,plain,
    ( ! [U_980,U_981,U_982] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_980),U_981) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_980),U_982)
        | U_981 != U_982
        | ~ sP71(U_980,U_981,U_982) )
    & ! [U_980,U_981,U_982] :
        ( U_981 = U_982
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_980),U_981) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_980),U_982)
        | ~ sP71(U_980,U_981,U_982) )
    & ! [U_980,U_981,U_982] :
        ( sP71(U_980,U_981,U_982)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_980)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP71])],[f_281_2]) ).

cnf(f_281_4,plain,
    ( sP71(U_980,U_981,U_982)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_980)) ),
    inference(clausify,[status(thm)],[f_281_3]) ).

cnf(f_281_5,plain,
    ( U_981 = U_982
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_980),U_981) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_980),U_982)
    | ~ sP71(U_980,U_981,U_982) ),
    inference(clausify,[status(thm)],[f_281_3]) ).

cnf(f_281_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_980),U_981) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_980),U_982)
    | U_981 != U_982
    | ~ sP71(U_980,U_981,U_982) ),
    inference(clausify,[status(thm)],[f_281_3]) ).

fof(f_282_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_282_2,plain,
    ! [U_985,U_984,U_983] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_983),U_984)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_983),U_985)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_984),U_985)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_984),U_985))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_983),U_984)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_983),U_985))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_983)) ),
    inference(variable_rename,[status(thm)],[f_282_1]) ).

fof(f_282_3,plain,
    ( ! [U_983,U_984,U_985] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_983),U_984)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_983),U_985)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_984),U_985))
        | ~ sP72(U_983,U_984,U_985) )
    & ! [U_983,U_984,U_985] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_984),U_985))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_983),U_984)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_983),U_985)))
        | ~ sP72(U_983,U_984,U_985) )
    & ! [U_983,U_984,U_985] :
        ( sP72(U_983,U_984,U_985)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_983)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP72])],[f_282_2]) ).

cnf(f_282_4,plain,
    ( sP72(U_983,U_984,U_985)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_983)) ),
    inference(clausify,[status(thm)],[f_282_3]) ).

cnf(f_282_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_984),U_985))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_983),U_984)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_983),U_985)))
    | ~ sP72(U_983,U_984,U_985) ),
    inference(clausify,[status(thm)],[f_282_3]) ).

cnf(f_282_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_983),U_984)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_983),U_985)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_984),U_985))
    | ~ sP72(U_983,U_984,U_985) ),
    inference(clausify,[status(thm)],[f_282_3]) ).

fof(f_283_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_283_2,plain,
    ! [U_988,U_987,U_986] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_986),U_987) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_986),U_988)
        | ( U_987 != U_988
          & U_986 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_987 = U_988
        | U_986 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_986),U_987) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_986),U_988) ) ),
    inference(variable_rename,[status(thm)],[f_283_1]) ).

fof(f_283_3,plain,
    ( ! [U_994,U_992,U_990] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_990),U_992) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_990),U_994)
        | ( U_992 != U_994
          & U_990 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_993,U_991,U_989] :
        ( U_991 = U_993
        | U_989 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_989),U_991) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_989),U_993) ) ),
    inference(miniscope,[status(thm)],[f_283_2]) ).

fof(f_283_4,plain,
    ( ! [U_994,U_992,U_990] :
        ( U_992 != U_994
        | ~ sP73(U_994,U_992,U_990) )
    & ! [U_994,U_992,U_990] :
        ( U_990 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP73(U_994,U_992,U_990) )
    & ! [U_994,U_992,U_990] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_990),U_992) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_990),U_994)
        | sP73(U_994,U_992,U_990) )
    & ! [U_991,U_993,U_989] :
        ( U_991 = U_993
        | U_989 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_989),U_991) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_989),U_993) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP73])],[f_283_3]) ).

cnf(f_283_5,plain,
    ( U_991 = U_993
    | U_989 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_989),U_991) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_989),U_993) ),
    inference(clausify,[status(thm)],[f_283_4]) ).

cnf(f_283_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_990),U_992) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_990),U_994)
    | sP73(U_994,U_992,U_990) ),
    inference(clausify,[status(thm)],[f_283_4]) ).

cnf(f_283_7,plain,
    ( U_990 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP73(U_994,U_992,U_990) ),
    inference(clausify,[status(thm)],[f_283_4]) ).

cnf(f_283_8,plain,
    ( U_992 != U_994
    | ~ sP73(U_994,U_992,U_990) ),
    inference(clausify,[status(thm)],[f_283_4]) ).

fof(f_284_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_284_2,plain,
    ! [U_996] :
      ( ? [U_995] : U_996 = 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_995)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_996),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_284_1]) ).

fof(f_284_3,plain,
    ! [U_996] :
      ( U_996 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK22(U_996))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_996),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK22]),skolemize(U_995,sK22(U_996))],[f_284_2]) ).

fof(f_284_4,plain,
    ! [U_996] :
      ( U_996 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK22(U_996))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_996),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_284_3]) ).

cnf(f_284_5,plain,
    ( U_996 = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK22(U_996))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_996),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_284_4]) ).

fof(f_285_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_285_2,plain,
    ! [U_998,U_997] :
      ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_997),U_998) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_997),hAPP(c_Int_Onat,U_998))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_998),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hAPP(c_Int_Oring__1__class_Oof__int(U_997),U_998) = hAPP(c_Groups_Ouminus__class_Ouminus(U_997),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_997),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_998))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_998),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ class_Rings_Oring__1(U_997) ),
    inference(variable_rename,[status(thm)],[f_285_1]) ).

fof(f_285_3,plain,
    ( ! [U_997,U_998] :
        ( hAPP(c_Int_Oring__1__class_Oof__int(U_997),U_998) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_997),hAPP(c_Int_Onat,U_998))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_998),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP74(U_997,U_998) )
    & ! [U_997,U_998] :
        ( hAPP(c_Int_Oring__1__class_Oof__int(U_997),U_998) = hAPP(c_Groups_Ouminus__class_Ouminus(U_997),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_997),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_998))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_998),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP74(U_997,U_998) )
    & ! [U_997,U_998] :
        ( sP74(U_997,U_998)
        | ~ class_Rings_Oring__1(U_997) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP74])],[f_285_2]) ).

cnf(f_285_4,plain,
    ( sP74(U_997,U_998)
    | ~ class_Rings_Oring__1(U_997) ),
    inference(clausify,[status(thm)],[f_285_3]) ).

cnf(f_285_5,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_997),U_998) = hAPP(c_Groups_Ouminus__class_Ouminus(U_997),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_997),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_998))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_998),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP74(U_997,U_998) ),
    inference(clausify,[status(thm)],[f_285_3]) ).

cnf(f_285_6,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_997),U_998) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_997),hAPP(c_Int_Onat,U_998))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_998),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP74(U_997,U_998) ),
    inference(clausify,[status(thm)],[f_285_3]) ).

fof(f_286_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_286_2,plain,
    ! [U_999] : ~ 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_999))))),
    inference(variable_rename,[status(thm)],[f_286_1]) ).

fof(f_286_3,plain,
    ! [U_999] : ~ 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_999))))),
    inference(definitional_conversion,[status(esa)],[f_286_2]) ).

cnf(f_286_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_999))))),
    inference(clausify,[status(thm)],[f_286_3]) ).

fof(f_287_1,plain,
    ! [V_i_2,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2)))
        | ( ~ hBOOL(hAPP(V_Pa_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_Pa_2,B_n))
            & V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) )
      & ( ( ( hBOOL(hAPP(V_Pa_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_Pa_2,B_n))
              | V_i_2 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) )
        | ~ hBOOL(hAPP(V_Pa_2,hAPP(c_Int_Onat,V_i_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__nat]) ).

fof(f_287_2,plain,
    ! [U_1003,U_1002] :
      ( ( hBOOL(hAPP(U_1002,hAPP(c_Int_Onat,U_1003)))
        | ( ~ hBOOL(hAPP(U_1002,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1003),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ? [U_1001] :
            ( ~ hBOOL(hAPP(U_1002,U_1001))
            & U_1003 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1001) ) )
      & ( ( ( hBOOL(hAPP(U_1002,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1003),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ! [U_1000] :
              ( hBOOL(hAPP(U_1002,U_1000))
              | U_1003 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1000) ) )
        | ~ hBOOL(hAPP(U_1002,hAPP(c_Int_Onat,U_1003))) ) ),
    inference(variable_rename,[status(thm)],[f_287_1]) ).

fof(f_287_3,plain,
    ( ! [U_1007,U_1005] :
        ( hBOOL(hAPP(U_1005,hAPP(c_Int_Onat,U_1007)))
        | ( ~ hBOOL(hAPP(U_1005,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1007),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ? [U_1001] :
            ( ~ hBOOL(hAPP(U_1005,U_1001))
            & U_1007 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1001) ) )
    & ! [U_1006,U_1004] :
        ( ( ( hBOOL(hAPP(U_1004,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1006),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ! [U_1000] :
              ( hBOOL(hAPP(U_1004,U_1000))
              | U_1006 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1000) ) )
        | ~ hBOOL(hAPP(U_1004,hAPP(c_Int_Onat,U_1006))) ) ),
    inference(miniscope,[status(thm)],[f_287_2]) ).

fof(f_287_4,plain,
    ( ! [U_1007,U_1005] :
        ( hBOOL(hAPP(U_1005,hAPP(c_Int_Onat,U_1007)))
        | ( ~ hBOOL(hAPP(U_1005,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1007),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_1005,sK23(U_1007,U_1005)))
          & U_1007 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK23(U_1007,U_1005)) ) )
    & ! [U_1006,U_1004] :
        ( ( ( hBOOL(hAPP(U_1004,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1006),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ! [U_1000] :
              ( hBOOL(hAPP(U_1004,U_1000))
              | U_1006 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1000) ) )
        | ~ hBOOL(hAPP(U_1004,hAPP(c_Int_Onat,U_1006))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK23]),skolemize(U_1001,sK23(U_1007,U_1005))],[f_287_3]) ).

fof(f_287_5,plain,
    ( ! [U_1005,U_1007] :
        ( ~ hBOOL(hAPP(U_1005,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP77(U_1005,U_1007) )
    & ! [U_1005,U_1007] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1007),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP77(U_1005,U_1007) )
    & ! [U_1005,U_1007] :
        ( ~ hBOOL(hAPP(U_1005,sK23(U_1007,U_1005)))
        | ~ sP76(U_1005,U_1007) )
    & ! [U_1005,U_1007] :
        ( U_1007 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK23(U_1007,U_1005))
        | ~ sP76(U_1005,U_1007) )
    & ! [U_1000,U_1004,U_1006] :
        ( hBOOL(hAPP(U_1004,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1006),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP75(U_1000,U_1004,U_1006) )
    & ! [U_1000,U_1004,U_1006] :
        ( hBOOL(hAPP(U_1004,U_1000))
        | U_1006 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1000)
        | ~ sP75(U_1000,U_1004,U_1006) )
    & ! [U_1005,U_1007] :
        ( hBOOL(hAPP(U_1005,hAPP(c_Int_Onat,U_1007)))
        | sP77(U_1005,U_1007)
        | sP76(U_1005,U_1007) )
    & ! [U_1000,U_1004,U_1006] :
        ( sP75(U_1000,U_1004,U_1006)
        | ~ hBOOL(hAPP(U_1004,hAPP(c_Int_Onat,U_1006))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP75,sP76,sP77])],[f_287_4]) ).

cnf(f_287_6,plain,
    ( sP75(U_1000,U_1004,U_1006)
    | ~ hBOOL(hAPP(U_1004,hAPP(c_Int_Onat,U_1006))) ),
    inference(clausify,[status(thm)],[f_287_5]) ).

cnf(f_287_7,plain,
    ( hBOOL(hAPP(U_1005,hAPP(c_Int_Onat,U_1007)))
    | sP77(U_1005,U_1007)
    | sP76(U_1005,U_1007) ),
    inference(clausify,[status(thm)],[f_287_5]) ).

cnf(f_287_8,plain,
    ( hBOOL(hAPP(U_1004,U_1000))
    | U_1006 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1000)
    | ~ sP75(U_1000,U_1004,U_1006) ),
    inference(clausify,[status(thm)],[f_287_5]) ).

cnf(f_287_9,plain,
    ( hBOOL(hAPP(U_1004,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1006),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP75(U_1000,U_1004,U_1006) ),
    inference(clausify,[status(thm)],[f_287_5]) ).

cnf(f_287_10,plain,
    ( U_1007 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK23(U_1007,U_1005))
    | ~ sP76(U_1005,U_1007) ),
    inference(clausify,[status(thm)],[f_287_5]) ).

cnf(f_287_11,plain,
    ( ~ hBOOL(hAPP(U_1005,sK23(U_1007,U_1005)))
    | ~ sP76(U_1005,U_1007) ),
    inference(clausify,[status(thm)],[f_287_5]) ).

cnf(f_287_12,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1007),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP77(U_1005,U_1007) ),
    inference(clausify,[status(thm)],[f_287_5]) ).

cnf(f_287_13,plain,
    ( ~ hBOOL(hAPP(U_1005,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP77(U_1005,U_1007) ),
    inference(clausify,[status(thm)],[f_287_5]) ).

fof(f_288_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_288_2,plain,
    ! [U_1008] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1008)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1008)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1008))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1008))) ) ),
    inference(variable_rename,[status(thm)],[f_288_1]) ).

fof(f_288_3,plain,
    ( ! [U_1010] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1010)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1010)) )
    & ! [U_1009] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1009))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1009))) ) ),
    inference(miniscope,[status(thm)],[f_288_2]) ).

fof(f_288_4,plain,
    ( ! [U_1010] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1010)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1010)) )
    & ! [U_1009] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1009))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1009))) ) ),
    inference(definitional_conversion,[status(esa)],[f_288_3]) ).

cnf(f_288_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1009))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(c_Int_Onat,U_1009))) ),
    inference(clausify,[status(thm)],[f_288_4]) ).

cnf(f_288_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_1010)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1010)) ),
    inference(clausify,[status(thm)],[f_288_4]) ).

fof(f_289_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_289_2,plain,
    ! [U_1011] : 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_1011))))),
    inference(variable_rename,[status(thm)],[f_289_1]) ).

fof(f_289_3,plain,
    ! [U_1011] : 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_1011))))),
    inference(definitional_conversion,[status(esa)],[f_289_2]) ).

cnf(f_289_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_1011))))),
    inference(clausify,[status(thm)],[f_289_3]) ).

fof(f_290_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_290_2,plain,
    ! [U_1013,U_1012] : c_Option_Ooption_Ooption__size(U_1012,U_1013,c_Option_Ooption_ONone(U_1012)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_290_1]) ).

fof(f_290_3,plain,
    ! [U_1012,U_1013] : c_Option_Ooption_Ooption__size(U_1012,U_1013,c_Option_Ooption_ONone(U_1012)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_290_2]) ).

cnf(f_290_4,plain,
    c_Option_Ooption_Ooption__size(U_1012,U_1013,c_Option_Ooption_ONone(U_1012)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_290_3]) ).

fof(f_291_1,plain,
    ! [V_x_2,V_Pa_2,V_A_2,T_b] :
      ( hBOOL(hAPP(V_Pa_2,V_x_2))
      | V_A_2 != hAPP(c_Option_Ooption_OSome(T_b),V_x_2)
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_Pa_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),c_Option_Oset(T_b,V_A_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_ospec]) ).

fof(f_291_2,plain,
    ! [U_1018,U_1017,U_1016,U_1015] :
      ( hBOOL(hAPP(U_1017,U_1018))
      | U_1016 != hAPP(c_Option_Ooption_OSome(U_1015),U_1018)
      | ? [U_1014] :
          ( ~ hBOOL(hAPP(U_1017,U_1014))
          & hBOOL(hAPP(hAPP(c_member(U_1015),U_1014),c_Option_Oset(U_1015,U_1016))) ) ),
    inference(variable_rename,[status(thm)],[f_291_1]) ).

fof(f_291_3,plain,
    ! [U_1018,U_1017,U_1016,U_1015] :
      ( hBOOL(hAPP(U_1017,U_1018))
      | U_1016 != hAPP(c_Option_Ooption_OSome(U_1015),U_1018)
      | ( ~ hBOOL(hAPP(U_1017,sK24(U_1018,U_1017,U_1016,U_1015)))
        & hBOOL(hAPP(hAPP(c_member(U_1015),sK24(U_1018,U_1017,U_1016,U_1015)),c_Option_Oset(U_1015,U_1016))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK24]),skolemize(U_1014,sK24(U_1018,U_1017,U_1016,U_1015))],[f_291_2]) ).

fof(f_291_4,plain,
    ( ! [U_1015,U_1016,U_1017,U_1018] :
        ( ~ hBOOL(hAPP(U_1017,sK24(U_1018,U_1017,U_1016,U_1015)))
        | ~ sP78(U_1015,U_1016,U_1017,U_1018) )
    & ! [U_1015,U_1016,U_1017,U_1018] :
        ( hBOOL(hAPP(hAPP(c_member(U_1015),sK24(U_1018,U_1017,U_1016,U_1015)),c_Option_Oset(U_1015,U_1016)))
        | ~ sP78(U_1015,U_1016,U_1017,U_1018) )
    & ! [U_1015,U_1016,U_1017,U_1018] :
        ( hBOOL(hAPP(U_1017,U_1018))
        | U_1016 != hAPP(c_Option_Ooption_OSome(U_1015),U_1018)
        | sP78(U_1015,U_1016,U_1017,U_1018) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP78])],[f_291_3]) ).

cnf(f_291_5,plain,
    ( hBOOL(hAPP(U_1017,U_1018))
    | U_1016 != hAPP(c_Option_Ooption_OSome(U_1015),U_1018)
    | sP78(U_1015,U_1016,U_1017,U_1018) ),
    inference(clausify,[status(thm)],[f_291_4]) ).

cnf(f_291_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1015),sK24(U_1018,U_1017,U_1016,U_1015)),c_Option_Oset(U_1015,U_1016)))
    | ~ sP78(U_1015,U_1016,U_1017,U_1018) ),
    inference(clausify,[status(thm)],[f_291_4]) ).

cnf(f_291_7,plain,
    ( ~ hBOOL(hAPP(U_1017,sK24(U_1018,U_1017,U_1016,U_1015)))
    | ~ sP78(U_1015,U_1016,U_1017,U_1018) ),
    inference(clausify,[status(thm)],[f_291_4]) ).

fof(f_292_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_292_2,plain,
    ! [U_1020,U_1019] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1019),U_1020),U_1020))
      | ~ class_Orderings_Opreorder(U_1019) ),
    inference(variable_rename,[status(thm)],[f_292_1]) ).

fof(f_292_3,plain,
    ! [U_1020,U_1019] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1019),U_1020),U_1020))
      | ~ class_Orderings_Opreorder(U_1019) ),
    inference(definitional_conversion,[status(esa)],[f_292_2]) ).

cnf(f_292_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1019),U_1020),U_1020))
    | ~ class_Orderings_Opreorder(U_1019) ),
    inference(clausify,[status(thm)],[f_292_3]) ).

fof(f_293_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_293_2,plain,
    ! [U_1023,U_1022,U_1021] :
      ( hBOOL(hAPP(hAPP(c_member(U_1021),U_1022),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1021,tc_HOL_Obool)),U_1023)))
      | hBOOL(hAPP(hAPP(c_member(U_1021),U_1022),U_1023)) ),
    inference(variable_rename,[status(thm)],[f_293_1]) ).

fof(f_293_3,plain,
    ! [U_1021,U_1022,U_1023] :
      ( hBOOL(hAPP(hAPP(c_member(U_1021),U_1022),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1021,tc_HOL_Obool)),U_1023)))
      | hBOOL(hAPP(hAPP(c_member(U_1021),U_1022),U_1023)) ),
    inference(definitional_conversion,[status(esa)],[f_293_2]) ).

cnf(f_293_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1021),U_1022),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1021,tc_HOL_Obool)),U_1023)))
    | hBOOL(hAPP(hAPP(c_member(U_1021),U_1022),U_1023)) ),
    inference(clausify,[status(thm)],[f_293_3]) ).

fof(f_294_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_294_2,plain,
    ! [U_1025,U_1024] : 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_1024))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1025))),
    inference(variable_rename,[status(thm)],[f_294_1]) ).

fof(f_294_3,plain,
    ! [U_1024,U_1025] : 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_1024))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1025))),
    inference(definitional_conversion,[status(esa)],[f_294_2]) ).

cnf(f_294_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_1024))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1025))),
    inference(clausify,[status(thm)],[f_294_3]) ).

fof(f_295_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_295_2,plain,
    ! [U_1026] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1026),U_1026)),
    inference(variable_rename,[status(thm)],[f_295_1]) ).

fof(f_295_3,plain,
    ! [U_1026] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1026),U_1026)),
    inference(definitional_conversion,[status(esa)],[f_295_2]) ).

cnf(f_295_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1026),U_1026)),
    inference(clausify,[status(thm)],[f_295_3]) ).

fof(f_296_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_296_2,plain,
    ! [U_1028,U_1027] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1028),U_1027))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1027),U_1028)) ),
    inference(variable_rename,[status(thm)],[f_296_1]) ).

fof(f_296_3,plain,
    ! [U_1027,U_1028] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1028),U_1027))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1027),U_1028)) ),
    inference(definitional_conversion,[status(esa)],[f_296_2]) ).

cnf(f_296_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1028),U_1027))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1027),U_1028)) ),
    inference(clausify,[status(thm)],[f_296_3]) ).

fof(f_297_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_297_2,plain,
    ! [U_1031,U_1030,U_1029] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1029),U_1031))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1030),U_1031))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1029),U_1030)) ),
    inference(variable_rename,[status(thm)],[f_297_1]) ).

fof(f_297_3,plain,
    ! [U_1029,U_1030,U_1031] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1029),U_1031))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1030),U_1031))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1029),U_1030)) ),
    inference(definitional_conversion,[status(esa)],[f_297_2]) ).

cnf(f_297_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1029),U_1031))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1030),U_1031))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1029),U_1030)) ),
    inference(clausify,[status(thm)],[f_297_3]) ).

fof(f_298_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_298_2,plain,
    ! [U_1033,U_1032] :
      ( U_1032 = U_1033
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1033),U_1032))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1032),U_1033)) ),
    inference(variable_rename,[status(thm)],[f_298_1]) ).

fof(f_298_3,plain,
    ! [U_1032,U_1033] :
      ( U_1032 = U_1033
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1033),U_1032))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1032),U_1033)) ),
    inference(definitional_conversion,[status(esa)],[f_298_2]) ).

cnf(f_298_4,plain,
    ( U_1032 = U_1033
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1033),U_1032))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1032),U_1033)) ),
    inference(clausify,[status(thm)],[f_298_3]) ).

fof(f_299_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_299_2,plain,
    ! [U_1039,U_1038,U_1037,U_1036] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1037,U_1036)),U_1038),U_1039))
          | ? [U_1035] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1036),hAPP(U_1038,U_1035)),hAPP(U_1039,U_1035))) )
        & ( ! [U_1034] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1036),hAPP(U_1038,U_1034)),hAPP(U_1039,U_1034)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1037,U_1036)),U_1038),U_1039)) ) )
      | ~ class_Orderings_Oord(U_1036) ),
    inference(variable_rename,[status(thm)],[f_299_1]) ).

fof(f_299_3,plain,
    ! [U_1039,U_1038,U_1037,U_1036] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1037,U_1036)),U_1038),U_1039))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1036),hAPP(U_1038,sK25(U_1039,U_1038,U_1037,U_1036))),hAPP(U_1039,sK25(U_1039,U_1038,U_1037,U_1036)))) )
        & ( ! [U_1034] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1036),hAPP(U_1038,U_1034)),hAPP(U_1039,U_1034)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1037,U_1036)),U_1038),U_1039)) ) )
      | ~ class_Orderings_Oord(U_1036) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK25]),skolemize(U_1035,sK25(U_1039,U_1038,U_1037,U_1036))],[f_299_2]) ).

fof(f_299_4,plain,
    ( ! [U_1034,U_1036,U_1037,U_1038,U_1039] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1037,U_1036)),U_1038),U_1039))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1036),hAPP(U_1038,sK25(U_1039,U_1038,U_1037,U_1036))),hAPP(U_1039,sK25(U_1039,U_1038,U_1037,U_1036))))
        | ~ sP79(U_1034,U_1036,U_1037,U_1038,U_1039) )
    & ! [U_1034,U_1036,U_1037,U_1038,U_1039] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1036),hAPP(U_1038,U_1034)),hAPP(U_1039,U_1034)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1037,U_1036)),U_1038),U_1039))
        | ~ sP79(U_1034,U_1036,U_1037,U_1038,U_1039) )
    & ! [U_1034,U_1036,U_1037,U_1038,U_1039] :
        ( sP79(U_1034,U_1036,U_1037,U_1038,U_1039)
        | ~ class_Orderings_Oord(U_1036) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP79])],[f_299_3]) ).

cnf(f_299_5,plain,
    ( sP79(U_1034,U_1036,U_1037,U_1038,U_1039)
    | ~ class_Orderings_Oord(U_1036) ),
    inference(clausify,[status(thm)],[f_299_4]) ).

cnf(f_299_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1036),hAPP(U_1038,U_1034)),hAPP(U_1039,U_1034)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1037,U_1036)),U_1038),U_1039))
    | ~ sP79(U_1034,U_1036,U_1037,U_1038,U_1039) ),
    inference(clausify,[status(thm)],[f_299_4]) ).

cnf(f_299_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1037,U_1036)),U_1038),U_1039))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1036),hAPP(U_1038,sK25(U_1039,U_1038,U_1037,U_1036))),hAPP(U_1039,sK25(U_1039,U_1038,U_1037,U_1036))))
    | ~ sP79(U_1034,U_1036,U_1037,U_1038,U_1039) ),
    inference(clausify,[status(thm)],[f_299_4]) ).

fof(f_300_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_300_2,plain,
    ! [U_1042,U_1041,U_1040] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1040),U_1042),U_1041))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1040),U_1041),U_1042))
      | ~ class_Orderings_Olinorder(U_1040) ),
    inference(variable_rename,[status(thm)],[f_300_1]) ).

fof(f_300_3,plain,
    ! [U_1041,U_1042,U_1040] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1040),U_1042),U_1041))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1040),U_1041),U_1042))
      | ~ class_Orderings_Olinorder(U_1040) ),
    inference(definitional_conversion,[status(esa)],[f_300_2]) ).

cnf(f_300_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1040),U_1042),U_1041))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1040),U_1041),U_1042))
    | ~ class_Orderings_Olinorder(U_1040) ),
    inference(clausify,[status(thm)],[f_300_3]) ).

fof(f_301_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_301_2,plain,
    ! [U_1045,U_1044,U_1043] :
      ( ( ( U_1044 = U_1045
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1043),U_1045),U_1044))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1043),U_1044),U_1045)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1043),U_1045),U_1044))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1043),U_1044),U_1045)) )
          | U_1044 != U_1045 ) )
      | ~ class_Orderings_Oorder(U_1043) ),
    inference(variable_rename,[status(thm)],[f_301_1]) ).

fof(f_301_3,plain,
    ( ! [U_1043,U_1044,U_1045] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1043),U_1045),U_1044))
        | ~ sP80(U_1043,U_1044,U_1045) )
    & ! [U_1043,U_1044,U_1045] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1043),U_1044),U_1045))
        | ~ sP80(U_1043,U_1044,U_1045) )
    & ! [U_1043,U_1044,U_1045] :
        ( U_1044 = U_1045
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1043),U_1045),U_1044))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1043),U_1044),U_1045))
        | ~ sP81(U_1043,U_1044,U_1045) )
    & ! [U_1043,U_1044,U_1045] :
        ( sP80(U_1043,U_1044,U_1045)
        | U_1044 != U_1045
        | ~ sP81(U_1043,U_1044,U_1045) )
    & ! [U_1043,U_1044,U_1045] :
        ( sP81(U_1043,U_1044,U_1045)
        | ~ class_Orderings_Oorder(U_1043) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP80,sP81])],[f_301_2]) ).

cnf(f_301_4,plain,
    ( sP81(U_1043,U_1044,U_1045)
    | ~ class_Orderings_Oorder(U_1043) ),
    inference(clausify,[status(thm)],[f_301_3]) ).

cnf(f_301_5,plain,
    ( sP80(U_1043,U_1044,U_1045)
    | U_1044 != U_1045
    | ~ sP81(U_1043,U_1044,U_1045) ),
    inference(clausify,[status(thm)],[f_301_3]) ).

cnf(f_301_6,plain,
    ( U_1044 = U_1045
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1043),U_1045),U_1044))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1043),U_1044),U_1045))
    | ~ sP81(U_1043,U_1044,U_1045) ),
    inference(clausify,[status(thm)],[f_301_3]) ).

cnf(f_301_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1043),U_1044),U_1045))
    | ~ sP80(U_1043,U_1044,U_1045) ),
    inference(clausify,[status(thm)],[f_301_3]) ).

cnf(f_301_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1043),U_1045),U_1044))
    | ~ sP80(U_1043,U_1044,U_1045) ),
    inference(clausify,[status(thm)],[f_301_3]) ).

fof(f_302_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_302_2,plain,
    ! [U_1048,U_1047,U_1046] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1046),U_1047),U_1048))
      | U_1047 != U_1048
      | ~ class_Orderings_Opreorder(U_1046) ),
    inference(variable_rename,[status(thm)],[f_302_1]) ).

fof(f_302_3,plain,
    ! [U_1046,U_1048,U_1047] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1046),U_1047),U_1048))
      | U_1047 != U_1048
      | ~ class_Orderings_Opreorder(U_1046) ),
    inference(definitional_conversion,[status(esa)],[f_302_2]) ).

cnf(f_302_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1046),U_1047),U_1048))
    | U_1047 != U_1048
    | ~ class_Orderings_Opreorder(U_1046) ),
    inference(clausify,[status(thm)],[f_302_3]) ).

fof(f_303_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_303_2,plain,
    ! [U_1053,U_1052,U_1051,U_1050,U_1049] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1049),hAPP(U_1051,U_1053)),hAPP(U_1052,U_1053)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1050,U_1049)),U_1051),U_1052))
      | ~ class_Orderings_Oord(U_1049) ),
    inference(variable_rename,[status(thm)],[f_303_1]) ).

fof(f_303_3,plain,
    ! [U_1049,U_1051,U_1050,U_1052,U_1053] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1049),hAPP(U_1051,U_1053)),hAPP(U_1052,U_1053)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1050,U_1049)),U_1051),U_1052))
      | ~ class_Orderings_Oord(U_1049) ),
    inference(definitional_conversion,[status(esa)],[f_303_2]) ).

cnf(f_303_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1049),hAPP(U_1051,U_1053)),hAPP(U_1052,U_1053)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1050,U_1049)),U_1051),U_1052))
    | ~ class_Orderings_Oord(U_1049) ),
    inference(clausify,[status(thm)],[f_303_3]) ).

fof(f_304_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_304_2,plain,
    ! [U_1056,U_1055,U_1054] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1054),U_1056),U_1055))
          | U_1056 != U_1055 )
        & ( U_1056 = U_1055
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1054),U_1056),U_1055)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1054),U_1055),U_1056))
      | ~ class_Orderings_Oorder(U_1054) ),
    inference(variable_rename,[status(thm)],[f_304_1]) ).

fof(f_304_3,plain,
    ( ! [U_1054,U_1055,U_1056] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1054),U_1056),U_1055))
        | U_1056 != U_1055
        | ~ sP82(U_1054,U_1055,U_1056) )
    & ! [U_1054,U_1055,U_1056] :
        ( U_1056 = U_1055
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1054),U_1056),U_1055))
        | ~ sP82(U_1054,U_1055,U_1056) )
    & ! [U_1054,U_1055,U_1056] :
        ( sP82(U_1054,U_1055,U_1056)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1054),U_1055),U_1056))
        | ~ class_Orderings_Oorder(U_1054) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP82])],[f_304_2]) ).

cnf(f_304_4,plain,
    ( sP82(U_1054,U_1055,U_1056)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1054),U_1055),U_1056))
    | ~ class_Orderings_Oorder(U_1054) ),
    inference(clausify,[status(thm)],[f_304_3]) ).

cnf(f_304_5,plain,
    ( U_1056 = U_1055
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1054),U_1056),U_1055))
    | ~ sP82(U_1054,U_1055,U_1056) ),
    inference(clausify,[status(thm)],[f_304_3]) ).

cnf(f_304_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1054),U_1056),U_1055))
    | U_1056 != U_1055
    | ~ sP82(U_1054,U_1055,U_1056) ),
    inference(clausify,[status(thm)],[f_304_3]) ).

fof(f_305_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_305_2,plain,
    ! [U_1060,U_1059,U_1058,U_1057] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1057),U_1058),U_1060))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1057),U_1059),U_1060))
      | U_1058 != U_1059
      | ~ class_Orderings_Oord(U_1057) ),
    inference(variable_rename,[status(thm)],[f_305_1]) ).

fof(f_305_3,plain,
    ! [U_1059,U_1058,U_1057,U_1060] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1057),U_1058),U_1060))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1057),U_1059),U_1060))
      | U_1058 != U_1059
      | ~ class_Orderings_Oord(U_1057) ),
    inference(definitional_conversion,[status(esa)],[f_305_2]) ).

cnf(f_305_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1057),U_1058),U_1060))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1057),U_1059),U_1060))
    | U_1058 != U_1059
    | ~ class_Orderings_Oord(U_1057) ),
    inference(clausify,[status(thm)],[f_305_3]) ).

fof(f_306_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_306_2,plain,
    ! [U_1064,U_1063,U_1062,U_1061] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1061),U_1064),U_1062))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1061),U_1064),U_1063))
      | U_1062 != U_1063
      | ~ class_Orderings_Oorder(U_1061) ),
    inference(variable_rename,[status(thm)],[f_306_1]) ).

fof(f_306_3,plain,
    ! [U_1062,U_1061,U_1063,U_1064] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1061),U_1064),U_1062))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1061),U_1064),U_1063))
      | U_1062 != U_1063
      | ~ class_Orderings_Oorder(U_1061) ),
    inference(definitional_conversion,[status(esa)],[f_306_2]) ).

cnf(f_306_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1061),U_1064),U_1062))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1061),U_1064),U_1063))
    | U_1062 != U_1063
    | ~ class_Orderings_Oorder(U_1061) ),
    inference(clausify,[status(thm)],[f_306_3]) ).

fof(f_307_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_307_2,plain,
    ! [U_1068,U_1067,U_1066,U_1065] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1065),U_1066),U_1068))
      | U_1067 != U_1068
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1065),U_1066),U_1067))
      | ~ class_Orderings_Oord(U_1065) ),
    inference(variable_rename,[status(thm)],[f_307_1]) ).

fof(f_307_3,plain,
    ! [U_1068,U_1066,U_1067,U_1065] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1065),U_1066),U_1068))
      | U_1067 != U_1068
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1065),U_1066),U_1067))
      | ~ class_Orderings_Oord(U_1065) ),
    inference(definitional_conversion,[status(esa)],[f_307_2]) ).

cnf(f_307_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1065),U_1066),U_1068))
    | U_1067 != U_1068
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1065),U_1066),U_1067))
    | ~ class_Orderings_Oord(U_1065) ),
    inference(clausify,[status(thm)],[f_307_3]) ).

fof(f_308_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_308_2,plain,
    ! [U_1072,U_1071,U_1070,U_1069] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1069),U_1072),U_1071))
      | U_1070 != U_1072
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1069),U_1070),U_1071))
      | ~ class_Orderings_Oorder(U_1069) ),
    inference(variable_rename,[status(thm)],[f_308_1]) ).

fof(f_308_3,plain,
    ! [U_1070,U_1071,U_1069,U_1072] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1069),U_1072),U_1071))
      | U_1070 != U_1072
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1069),U_1070),U_1071))
      | ~ class_Orderings_Oorder(U_1069) ),
    inference(definitional_conversion,[status(esa)],[f_308_2]) ).

cnf(f_308_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1069),U_1072),U_1071))
    | U_1070 != U_1072
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1069),U_1070),U_1071))
    | ~ class_Orderings_Oorder(U_1069) ),
    inference(clausify,[status(thm)],[f_308_3]) ).

fof(f_309_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_309_2,plain,
    ! [U_1075,U_1074,U_1073] :
      ( U_1074 = U_1075
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1073),U_1075),U_1074))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1073),U_1074),U_1075))
      | ~ class_Orderings_Oorder(U_1073) ),
    inference(variable_rename,[status(thm)],[f_309_1]) ).

fof(f_309_3,plain,
    ! [U_1075,U_1073,U_1074] :
      ( U_1074 = U_1075
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1073),U_1075),U_1074))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1073),U_1074),U_1075))
      | ~ class_Orderings_Oorder(U_1073) ),
    inference(definitional_conversion,[status(esa)],[f_309_2]) ).

cnf(f_309_4,plain,
    ( U_1074 = U_1075
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1073),U_1075),U_1074))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1073),U_1074),U_1075))
    | ~ class_Orderings_Oorder(U_1073) ),
    inference(clausify,[status(thm)],[f_309_3]) ).

fof(f_310_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_310_2,plain,
    ! [U_1079,U_1078,U_1077,U_1076] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1076),U_1077),U_1079))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1076),U_1078),U_1079))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1076),U_1077),U_1078))
      | ~ class_Orderings_Opreorder(U_1076) ),
    inference(variable_rename,[status(thm)],[f_310_1]) ).

fof(f_310_3,plain,
    ! [U_1077,U_1076,U_1078,U_1079] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1076),U_1077),U_1079))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1076),U_1078),U_1079))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1076),U_1077),U_1078))
      | ~ class_Orderings_Opreorder(U_1076) ),
    inference(definitional_conversion,[status(esa)],[f_310_2]) ).

cnf(f_310_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1076),U_1077),U_1079))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1076),U_1078),U_1079))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1076),U_1077),U_1078))
    | ~ class_Orderings_Opreorder(U_1076) ),
    inference(clausify,[status(thm)],[f_310_3]) ).

fof(f_311_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_311_2,plain,
    ! [U_1082,U_1081,U_1080] :
      ( U_1082 = U_1081
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1080),U_1082),U_1081))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1080),U_1081),U_1082))
      | ~ class_Orderings_Oorder(U_1080) ),
    inference(variable_rename,[status(thm)],[f_311_1]) ).

fof(f_311_3,plain,
    ! [U_1082,U_1080,U_1081] :
      ( U_1082 = U_1081
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1080),U_1082),U_1081))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1080),U_1081),U_1082))
      | ~ class_Orderings_Oorder(U_1080) ),
    inference(definitional_conversion,[status(esa)],[f_311_2]) ).

cnf(f_311_4,plain,
    ( U_1082 = U_1081
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1080),U_1082),U_1081))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1080),U_1081),U_1082))
    | ~ class_Orderings_Oorder(U_1080) ),
    inference(clausify,[status(thm)],[f_311_3]) ).

fof(f_312_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_312_2,plain,
    ! [U_1086,U_1085,U_1084,U_1083] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1083),U_1086),U_1085))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1083),U_1086),U_1084))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1083),U_1084),U_1085))
      | ~ class_Orderings_Oorder(U_1083) ),
    inference(variable_rename,[status(thm)],[f_312_1]) ).

fof(f_312_3,plain,
    ! [U_1084,U_1083,U_1085,U_1086] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1083),U_1086),U_1085))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1083),U_1086),U_1084))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1083),U_1084),U_1085))
      | ~ class_Orderings_Oorder(U_1083) ),
    inference(definitional_conversion,[status(esa)],[f_312_2]) ).

cnf(f_312_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1083),U_1086),U_1085))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1083),U_1086),U_1084))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1083),U_1084),U_1085))
    | ~ class_Orderings_Oorder(U_1083) ),
    inference(clausify,[status(thm)],[f_312_3]) ).

fof(f_313_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_313_2,plain,
    ! [U_1091,U_1090,U_1089,U_1088,U_1087] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),hAPP(U_1089,U_1091)),hAPP(U_1090,U_1091)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1088,U_1087)),U_1089),U_1090))
      | ~ class_Orderings_Oord(U_1087) ),
    inference(variable_rename,[status(thm)],[f_313_1]) ).

fof(f_313_3,plain,
    ! [U_1087,U_1088,U_1089,U_1090,U_1091] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),hAPP(U_1089,U_1091)),hAPP(U_1090,U_1091)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1088,U_1087)),U_1089),U_1090))
      | ~ class_Orderings_Oord(U_1087) ),
    inference(definitional_conversion,[status(esa)],[f_313_2]) ).

cnf(f_313_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1087),hAPP(U_1089,U_1091)),hAPP(U_1090,U_1091)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1088,U_1087)),U_1089),U_1090))
    | ~ class_Orderings_Oord(U_1087) ),
    inference(clausify,[status(thm)],[f_313_3]) ).

fof(f_314_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_314_2,plain,
    ! [U_1094,U_1093,U_1092] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1092),U_1094),U_1093))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1092),U_1093),U_1094))
      | ~ class_Orderings_Olinorder(U_1092) ),
    inference(variable_rename,[status(thm)],[f_314_1]) ).

fof(f_314_3,plain,
    ! [U_1093,U_1092,U_1094] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1092),U_1094),U_1093))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1092),U_1093),U_1094))
      | ~ class_Orderings_Olinorder(U_1092) ),
    inference(definitional_conversion,[status(esa)],[f_314_2]) ).

cnf(f_314_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1092),U_1094),U_1093))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1092),U_1093),U_1094))
    | ~ class_Orderings_Olinorder(U_1092) ),
    inference(clausify,[status(thm)],[f_314_3]) ).

fof(f_315_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_315_2,plain,
    ! [U_1096,U_1095] :
      ( ( ( hAPP(c_Int_Onat,U_1095) = hAPP(c_Int_Onat,U_1096)
          | U_1095 != U_1096 )
        & ( U_1095 = U_1096
          | hAPP(c_Int_Onat,U_1095) != hAPP(c_Int_Onat,U_1096) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1096))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1095)) ),
    inference(variable_rename,[status(thm)],[f_315_1]) ).

fof(f_315_3,plain,
    ( ! [U_1095,U_1096] :
        ( hAPP(c_Int_Onat,U_1095) = hAPP(c_Int_Onat,U_1096)
        | U_1095 != U_1096
        | ~ sP83(U_1095,U_1096) )
    & ! [U_1095,U_1096] :
        ( U_1095 = U_1096
        | hAPP(c_Int_Onat,U_1095) != hAPP(c_Int_Onat,U_1096)
        | ~ sP83(U_1095,U_1096) )
    & ! [U_1095,U_1096] :
        ( sP83(U_1095,U_1096)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1096))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1095)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP83])],[f_315_2]) ).

cnf(f_315_4,plain,
    ( sP83(U_1095,U_1096)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1096))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1095)) ),
    inference(clausify,[status(thm)],[f_315_3]) ).

cnf(f_315_5,plain,
    ( U_1095 = U_1096
    | hAPP(c_Int_Onat,U_1095) != hAPP(c_Int_Onat,U_1096)
    | ~ sP83(U_1095,U_1096) ),
    inference(clausify,[status(thm)],[f_315_3]) ).

cnf(f_315_6,plain,
    ( hAPP(c_Int_Onat,U_1095) = hAPP(c_Int_Onat,U_1096)
    | U_1095 != U_1096
    | ~ sP83(U_1095,U_1096) ),
    inference(clausify,[status(thm)],[f_315_3]) ).

fof(f_316_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_316_2,plain,
    ! [U_1098,U_1097] :
      ( ( ( hAPP(c_Int_Onat,U_1097) = hAPP(c_Int_Onat,U_1098)
          | U_1097 != U_1098 )
        & ( U_1097 = U_1098
          | hAPP(c_Int_Onat,U_1097) != hAPP(c_Int_Onat,U_1098) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1098))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1097)) ),
    inference(variable_rename,[status(thm)],[f_316_1]) ).

fof(f_316_3,plain,
    ( ! [U_1098,U_1097] :
        ( hAPP(c_Int_Onat,U_1097) = hAPP(c_Int_Onat,U_1098)
        | U_1097 != U_1098
        | ~ sP84(U_1098,U_1097) )
    & ! [U_1098,U_1097] :
        ( U_1097 = U_1098
        | hAPP(c_Int_Onat,U_1097) != hAPP(c_Int_Onat,U_1098)
        | ~ sP84(U_1098,U_1097) )
    & ! [U_1098,U_1097] :
        ( sP84(U_1098,U_1097)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1098))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1097)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP84])],[f_316_2]) ).

cnf(f_316_4,plain,
    ( sP84(U_1098,U_1097)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1098))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1097)) ),
    inference(clausify,[status(thm)],[f_316_3]) ).

cnf(f_316_5,plain,
    ( U_1097 = U_1098
    | hAPP(c_Int_Onat,U_1097) != hAPP(c_Int_Onat,U_1098)
    | ~ sP84(U_1098,U_1097) ),
    inference(clausify,[status(thm)],[f_316_3]) ).

cnf(f_316_6,plain,
    ( hAPP(c_Int_Onat,U_1097) = hAPP(c_Int_Onat,U_1098)
    | U_1097 != U_1098
    | ~ sP84(U_1098,U_1097) ),
    inference(clausify,[status(thm)],[f_316_3]) ).

fof(f_317_1,plain,
    ! [V_Pa_2] :
      ( ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,B_x1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_all__nat]) ).

fof(f_317_2,plain,
    ! [U_1103] :
      ( ( ! [U_1102] : hBOOL(hAPP(U_1103,U_1102))
        | ? [U_1101] :
            ( ~ hBOOL(hAPP(U_1103,hAPP(c_Int_Onat,U_1101)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1101)) ) )
      & ( ! [U_1100] :
            ( hBOOL(hAPP(U_1103,hAPP(c_Int_Onat,U_1100)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1100)) )
        | ? [U_1099] : ~ hBOOL(hAPP(U_1103,U_1099)) ) ),
    inference(variable_rename,[status(thm)],[f_317_1]) ).

fof(f_317_3,plain,
    ( ! [U_1105] :
        ( ! [U_1102] : hBOOL(hAPP(U_1105,U_1102))
        | ? [U_1101] :
            ( ~ hBOOL(hAPP(U_1105,hAPP(c_Int_Onat,U_1101)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1101)) ) )
    & ! [U_1104] :
        ( ! [U_1100] :
            ( hBOOL(hAPP(U_1104,hAPP(c_Int_Onat,U_1100)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1100)) )
        | ? [U_1099] : ~ hBOOL(hAPP(U_1104,U_1099)) ) ),
    inference(miniscope,[status(thm)],[f_317_2]) ).

fof(f_317_4,plain,
    ( ! [U_1105] :
        ( ! [U_1102] : hBOOL(hAPP(U_1105,U_1102))
        | ? [U_1101] :
            ( ~ hBOOL(hAPP(U_1105,hAPP(c_Int_Onat,U_1101)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1101)) ) )
    & ! [U_1104] :
        ( ! [U_1100] :
            ( hBOOL(hAPP(U_1104,hAPP(c_Int_Onat,U_1100)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1100)) )
        | ~ hBOOL(hAPP(U_1104,sK26(U_1104))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK26]),skolemize(U_1099,sK26(U_1104))],[f_317_3]) ).

fof(f_317_5,plain,
    ( ! [U_1105] :
        ( ! [U_1102] : hBOOL(hAPP(U_1105,U_1102))
        | ( ~ hBOOL(hAPP(U_1105,hAPP(c_Int_Onat,sK27(U_1105))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK27(U_1105))) ) )
    & ! [U_1104] :
        ( ! [U_1100] :
            ( hBOOL(hAPP(U_1104,hAPP(c_Int_Onat,U_1100)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1100)) )
        | ~ hBOOL(hAPP(U_1104,sK26(U_1104))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK27]),skolemize(U_1101,sK27(U_1105))],[f_317_4]) ).

fof(f_317_6,plain,
    ( ! [U_1105] :
        ( ~ hBOOL(hAPP(U_1105,hAPP(c_Int_Onat,sK27(U_1105))))
        | ~ sP85(U_1105) )
    & ! [U_1105] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK27(U_1105)))
        | ~ sP85(U_1105) )
    & ! [U_1102,U_1105] :
        ( hBOOL(hAPP(U_1105,U_1102))
        | sP85(U_1105) )
    & ! [U_1100,U_1104] :
        ( hBOOL(hAPP(U_1104,hAPP(c_Int_Onat,U_1100)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1100))
        | ~ hBOOL(hAPP(U_1104,sK26(U_1104))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP85])],[f_317_5]) ).

cnf(f_317_7,plain,
    ( hBOOL(hAPP(U_1104,hAPP(c_Int_Onat,U_1100)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1100))
    | ~ hBOOL(hAPP(U_1104,sK26(U_1104))) ),
    inference(clausify,[status(thm)],[f_317_6]) ).

cnf(f_317_8,plain,
    ( hBOOL(hAPP(U_1105,U_1102))
    | sP85(U_1105) ),
    inference(clausify,[status(thm)],[f_317_6]) ).

cnf(f_317_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK27(U_1105)))
    | ~ sP85(U_1105) ),
    inference(clausify,[status(thm)],[f_317_6]) ).

cnf(f_317_10,plain,
    ( ~ hBOOL(hAPP(U_1105,hAPP(c_Int_Onat,sK27(U_1105))))
    | ~ sP85(U_1105) ),
    inference(clausify,[status(thm)],[f_317_6]) ).

fof(f_318_1,plain,
    ! [V_Pa_2] :
      ( ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,B_x1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_ex__nat]) ).

fof(f_318_2,plain,
    ! [U_1110] :
      ( ( ? [U_1109] : hBOOL(hAPP(U_1110,U_1109))
        | ! [U_1108] :
            ( ~ hBOOL(hAPP(U_1110,hAPP(c_Int_Onat,U_1108)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1108)) ) )
      & ( ? [U_1107] :
            ( hBOOL(hAPP(U_1110,hAPP(c_Int_Onat,U_1107)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1107)) )
        | ! [U_1106] : ~ hBOOL(hAPP(U_1110,U_1106)) ) ),
    inference(variable_rename,[status(thm)],[f_318_1]) ).

fof(f_318_3,plain,
    ( ! [U_1112] :
        ( ? [U_1109] : hBOOL(hAPP(U_1112,U_1109))
        | ! [U_1108] :
            ( ~ hBOOL(hAPP(U_1112,hAPP(c_Int_Onat,U_1108)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1108)) ) )
    & ! [U_1111] :
        ( ? [U_1107] :
            ( hBOOL(hAPP(U_1111,hAPP(c_Int_Onat,U_1107)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1107)) )
        | ! [U_1106] : ~ hBOOL(hAPP(U_1111,U_1106)) ) ),
    inference(miniscope,[status(thm)],[f_318_2]) ).

fof(f_318_4,plain,
    ( ! [U_1112] :
        ( ? [U_1109] : hBOOL(hAPP(U_1112,U_1109))
        | ! [U_1108] :
            ( ~ hBOOL(hAPP(U_1112,hAPP(c_Int_Onat,U_1108)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1108)) ) )
    & ! [U_1111] :
        ( ( hBOOL(hAPP(U_1111,hAPP(c_Int_Onat,sK28(U_1111))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK28(U_1111))) )
        | ! [U_1106] : ~ hBOOL(hAPP(U_1111,U_1106)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK28]),skolemize(U_1107,sK28(U_1111))],[f_318_3]) ).

fof(f_318_5,plain,
    ( ! [U_1112] :
        ( hBOOL(hAPP(U_1112,sK29(U_1112)))
        | ! [U_1108] :
            ( ~ hBOOL(hAPP(U_1112,hAPP(c_Int_Onat,U_1108)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1108)) ) )
    & ! [U_1111] :
        ( ( hBOOL(hAPP(U_1111,hAPP(c_Int_Onat,sK28(U_1111))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK28(U_1111))) )
        | ! [U_1106] : ~ hBOOL(hAPP(U_1111,U_1106)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK29]),skolemize(U_1109,sK29(U_1112))],[f_318_4]) ).

fof(f_318_6,plain,
    ( ! [U_1111] :
        ( hBOOL(hAPP(U_1111,hAPP(c_Int_Onat,sK28(U_1111))))
        | ~ sP86(U_1111) )
    & ! [U_1111] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK28(U_1111)))
        | ~ sP86(U_1111) )
    & ! [U_1108,U_1112] :
        ( hBOOL(hAPP(U_1112,sK29(U_1112)))
        | ~ hBOOL(hAPP(U_1112,hAPP(c_Int_Onat,U_1108)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1108)) )
    & ! [U_1106,U_1111] :
        ( sP86(U_1111)
        | ~ hBOOL(hAPP(U_1111,U_1106)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP86])],[f_318_5]) ).

cnf(f_318_7,plain,
    ( sP86(U_1111)
    | ~ hBOOL(hAPP(U_1111,U_1106)) ),
    inference(clausify,[status(thm)],[f_318_6]) ).

cnf(f_318_8,plain,
    ( hBOOL(hAPP(U_1112,sK29(U_1112)))
    | ~ hBOOL(hAPP(U_1112,hAPP(c_Int_Onat,U_1108)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1108)) ),
    inference(clausify,[status(thm)],[f_318_6]) ).

cnf(f_318_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK28(U_1111)))
    | ~ sP86(U_1111) ),
    inference(clausify,[status(thm)],[f_318_6]) ).

cnf(f_318_10,plain,
    ( hBOOL(hAPP(U_1111,hAPP(c_Int_Onat,sK28(U_1111))))
    | ~ sP86(U_1111) ),
    inference(clausify,[status(thm)],[f_318_6]) ).

fof(f_319_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_319_2,plain,
    ! [U_1113] :
      ( hAPP(c_Int_Onat,U_1113) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1113)) ),
    inference(variable_rename,[status(thm)],[f_319_1]) ).

fof(f_319_3,plain,
    ! [U_1113] :
      ( hAPP(c_Int_Onat,U_1113) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1113)) ),
    inference(definitional_conversion,[status(esa)],[f_319_2]) ).

cnf(f_319_4,plain,
    ( hAPP(c_Int_Onat,U_1113) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1113)) ),
    inference(clausify,[status(thm)],[f_319_3]) ).

fof(f_320_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_320_2,plain,
    ! [U_1116,U_1115,U_1114] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1114),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1114),U_1115)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1114),U_1116)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1115),U_1116)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1115),U_1116))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1114),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1114),U_1115)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1114),U_1116))) ) )
      | ~ class_Rings_Olinordered__semidom(U_1114) ),
    inference(variable_rename,[status(thm)],[f_320_1]) ).

fof(f_320_3,plain,
    ( ! [U_1115,U_1114,U_1116] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1114),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1114),U_1115)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1114),U_1116)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1115),U_1116))
        | ~ sP87(U_1115,U_1114,U_1116) )
    & ! [U_1115,U_1114,U_1116] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1115),U_1116))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1114),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1114),U_1115)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1114),U_1116)))
        | ~ sP87(U_1115,U_1114,U_1116) )
    & ! [U_1115,U_1114,U_1116] :
        ( sP87(U_1115,U_1114,U_1116)
        | ~ class_Rings_Olinordered__semidom(U_1114) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP87])],[f_320_2]) ).

cnf(f_320_4,plain,
    ( sP87(U_1115,U_1114,U_1116)
    | ~ class_Rings_Olinordered__semidom(U_1114) ),
    inference(clausify,[status(thm)],[f_320_3]) ).

cnf(f_320_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1115),U_1116))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1114),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1114),U_1115)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1114),U_1116)))
    | ~ sP87(U_1115,U_1114,U_1116) ),
    inference(clausify,[status(thm)],[f_320_3]) ).

cnf(f_320_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1114),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1114),U_1115)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1114),U_1116)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1115),U_1116))
    | ~ sP87(U_1115,U_1114,U_1116) ),
    inference(clausify,[status(thm)],[f_320_3]) ).

fof(f_321_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_321_2,plain,
    ! [U_1117] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1117)) = U_1117
      | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1117)) ),
    inference(variable_rename,[status(thm)],[f_321_1]) ).

fof(f_321_3,plain,
    ! [U_1117] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1117)) = U_1117
      | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1117)) ),
    inference(definitional_conversion,[status(esa)],[f_321_2]) ).

cnf(f_321_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1117)) = U_1117
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1117)) ),
    inference(clausify,[status(thm)],[f_321_3]) ).

fof(f_322_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_322_2,plain,
    ! [U_1118] :
      ( ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1118))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1118)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1118))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1118)) ) ),
    inference(variable_rename,[status(thm)],[f_322_1]) ).

fof(f_322_3,plain,
    ( ! [U_1120] :
        ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1120))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1120)) )
    & ! [U_1119] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1119))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1119)) ) ),
    inference(miniscope,[status(thm)],[f_322_2]) ).

fof(f_322_4,plain,
    ( ! [U_1120] :
        ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1120))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1120)) )
    & ! [U_1119] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1119))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1119)) ) ),
    inference(definitional_conversion,[status(esa)],[f_322_3]) ).

cnf(f_322_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1119))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1119)) ),
    inference(clausify,[status(thm)],[f_322_4]) ).

cnf(f_322_6,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1120))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1120)) ),
    inference(clausify,[status(thm)],[f_322_4]) ).

fof(f_323_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_323_2,plain,
    ! [U_1123,U_1122,U_1121] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1121),hAPP(c_Int_Oring__1__class_Oof__int(U_1121),U_1122)),hAPP(c_Int_Oring__1__class_Oof__int(U_1121),U_1123)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1122),U_1123)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1122),U_1123))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1121),hAPP(c_Int_Oring__1__class_Oof__int(U_1121),U_1122)),hAPP(c_Int_Oring__1__class_Oof__int(U_1121),U_1123))) ) )
      | ~ class_Rings_Olinordered__idom(U_1121) ),
    inference(variable_rename,[status(thm)],[f_323_1]) ).

fof(f_323_3,plain,
    ( ! [U_1122,U_1121,U_1123] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1121),hAPP(c_Int_Oring__1__class_Oof__int(U_1121),U_1122)),hAPP(c_Int_Oring__1__class_Oof__int(U_1121),U_1123)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1122),U_1123))
        | ~ sP88(U_1122,U_1121,U_1123) )
    & ! [U_1122,U_1121,U_1123] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1122),U_1123))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1121),hAPP(c_Int_Oring__1__class_Oof__int(U_1121),U_1122)),hAPP(c_Int_Oring__1__class_Oof__int(U_1121),U_1123)))
        | ~ sP88(U_1122,U_1121,U_1123) )
    & ! [U_1122,U_1121,U_1123] :
        ( sP88(U_1122,U_1121,U_1123)
        | ~ class_Rings_Olinordered__idom(U_1121) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP88])],[f_323_2]) ).

cnf(f_323_4,plain,
    ( sP88(U_1122,U_1121,U_1123)
    | ~ class_Rings_Olinordered__idom(U_1121) ),
    inference(clausify,[status(thm)],[f_323_3]) ).

cnf(f_323_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1122),U_1123))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1121),hAPP(c_Int_Oring__1__class_Oof__int(U_1121),U_1122)),hAPP(c_Int_Oring__1__class_Oof__int(U_1121),U_1123)))
    | ~ sP88(U_1122,U_1121,U_1123) ),
    inference(clausify,[status(thm)],[f_323_3]) ).

cnf(f_323_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1121),hAPP(c_Int_Oring__1__class_Oof__int(U_1121),U_1122)),hAPP(c_Int_Oring__1__class_Oof__int(U_1121),U_1123)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1122),U_1123))
    | ~ sP88(U_1122,U_1121,U_1123) ),
    inference(clausify,[status(thm)],[f_323_3]) ).

fof(f_324_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_324_2,plain,
    ! [U_1124] :
      ( hAPP(c_Int_Onat,U_1124) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1124),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_324_1]) ).

fof(f_324_3,plain,
    ! [U_1124] :
      ( hAPP(c_Int_Onat,U_1124) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1124),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_324_2]) ).

cnf(f_324_4,plain,
    ( hAPP(c_Int_Onat,U_1124) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1124),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_324_3]) ).

fof(f_325_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_325_2,plain,
    ! [U_1125] :
      ( ( hAPP(c_Int_Onat,U_1125) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1125),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1125),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onat,U_1125) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_325_1]) ).

fof(f_325_3,plain,
    ( ! [U_1127] :
        ( hAPP(c_Int_Onat,U_1127) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1127),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_1126] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1126),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onat,U_1126) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_325_2]) ).

fof(f_325_4,plain,
    ( ! [U_1127] :
        ( hAPP(c_Int_Onat,U_1127) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1127),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_1126] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1126),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hAPP(c_Int_Onat,U_1126) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_325_3]) ).

cnf(f_325_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1126),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hAPP(c_Int_Onat,U_1126) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_325_4]) ).

cnf(f_325_6,plain,
    ( hAPP(c_Int_Onat,U_1127) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1127),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_325_4]) ).

fof(f_326_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_326_2,plain,
    ! [U_1128] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1128)) = 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_1128)) )
      & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1128)) = U_1128
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1128)) ) ),
    inference(variable_rename,[status(thm)],[f_326_1]) ).

fof(f_326_3,plain,
    ( ! [U_1130] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1130)) = 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_1130)) )
    & ! [U_1129] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1129)) = U_1129
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1129)) ) ),
    inference(miniscope,[status(thm)],[f_326_2]) ).

fof(f_326_4,plain,
    ( ! [U_1130] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1130)) = 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_1130)) )
    & ! [U_1129] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1129)) = U_1129
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1129)) ) ),
    inference(definitional_conversion,[status(esa)],[f_326_3]) ).

cnf(f_326_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1129)) = U_1129
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1129)) ),
    inference(clausify,[status(thm)],[f_326_4]) ).

cnf(f_326_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1130)) = 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_1130)) ),
    inference(clausify,[status(thm)],[f_326_4]) ).

fof(f_327_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_327_2,plain,
    ! [U_1132,U_1131] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1131) = U_1132
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1132))
        | U_1131 != hAPP(c_Int_Onat,U_1132) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1132))
          & U_1131 = hAPP(c_Int_Onat,U_1132) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1131) != U_1132 ) ),
    inference(variable_rename,[status(thm)],[f_327_1]) ).

fof(f_327_3,plain,
    ( ! [U_1136,U_1134] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1134) = U_1136
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1136))
        | U_1134 != hAPP(c_Int_Onat,U_1136) )
    & ! [U_1135,U_1133] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1135))
          & U_1133 = hAPP(c_Int_Onat,U_1135) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1133) != U_1135 ) ),
    inference(miniscope,[status(thm)],[f_327_2]) ).

fof(f_327_4,plain,
    ( ! [U_1135,U_1133] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1135))
        | ~ sP89(U_1135,U_1133) )
    & ! [U_1135,U_1133] :
        ( U_1133 = hAPP(c_Int_Onat,U_1135)
        | ~ sP89(U_1135,U_1133) )
    & ! [U_1136,U_1134] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1134) = U_1136
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1136))
        | U_1134 != hAPP(c_Int_Onat,U_1136) )
    & ! [U_1135,U_1133] :
        ( sP89(U_1135,U_1133)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1133) != U_1135 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP89])],[f_327_3]) ).

cnf(f_327_5,plain,
    ( sP89(U_1135,U_1133)
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1133) != U_1135 ),
    inference(clausify,[status(thm)],[f_327_4]) ).

cnf(f_327_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1134) = U_1136
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1136))
    | U_1134 != hAPP(c_Int_Onat,U_1136) ),
    inference(clausify,[status(thm)],[f_327_4]) ).

cnf(f_327_7,plain,
    ( U_1133 = hAPP(c_Int_Onat,U_1135)
    | ~ sP89(U_1135,U_1133) ),
    inference(clausify,[status(thm)],[f_327_4]) ).

cnf(f_327_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1135))
    | ~ sP89(U_1135,U_1133) ),
    inference(clausify,[status(thm)],[f_327_4]) ).

fof(f_328_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_328_2,plain,
    ! [U_1137] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1137)) = U_1137
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1137)) ),
    inference(variable_rename,[status(thm)],[f_328_1]) ).

fof(f_328_3,plain,
    ! [U_1137] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1137)) = U_1137
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1137)) ),
    inference(definitional_conversion,[status(esa)],[f_328_2]) ).

cnf(f_328_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,U_1137)) = U_1137
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1137)) ),
    inference(clausify,[status(thm)],[f_328_3]) ).

fof(f_329_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_329_2,plain,
    ! [U_1140,U_1139,U_1138] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_1138),U_1139),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1138,tc_HOL_Obool)),U_1140)))
        | hBOOL(hAPP(hAPP(c_member(U_1138),U_1139),U_1140)) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(U_1138),U_1139),U_1140))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1138),U_1139),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1138,tc_HOL_Obool)),U_1140))) ) ),
    inference(variable_rename,[status(thm)],[f_329_1]) ).

fof(f_329_3,plain,
    ( ! [U_1146,U_1144,U_1142] :
        ( hBOOL(hAPP(hAPP(c_member(U_1142),U_1144),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1142,tc_HOL_Obool)),U_1146)))
        | hBOOL(hAPP(hAPP(c_member(U_1142),U_1144),U_1146)) )
    & ! [U_1145,U_1143,U_1141] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_1141),U_1143),U_1145))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1141),U_1143),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1141,tc_HOL_Obool)),U_1145))) ) ),
    inference(miniscope,[status(thm)],[f_329_2]) ).

fof(f_329_4,plain,
    ( ! [U_1142,U_1144,U_1146] :
        ( hBOOL(hAPP(hAPP(c_member(U_1142),U_1144),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1142,tc_HOL_Obool)),U_1146)))
        | hBOOL(hAPP(hAPP(c_member(U_1142),U_1144),U_1146)) )
    & ! [U_1143,U_1145,U_1141] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_1141),U_1143),U_1145))
        | ~ hBOOL(hAPP(hAPP(c_member(U_1141),U_1143),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1141,tc_HOL_Obool)),U_1145))) ) ),
    inference(definitional_conversion,[status(esa)],[f_329_3]) ).

cnf(f_329_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_1141),U_1143),U_1145))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1141),U_1143),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1141,tc_HOL_Obool)),U_1145))) ),
    inference(clausify,[status(thm)],[f_329_4]) ).

cnf(f_329_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1142),U_1144),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1142,tc_HOL_Obool)),U_1146)))
    | hBOOL(hAPP(hAPP(c_member(U_1142),U_1144),U_1146)) ),
    inference(clausify,[status(thm)],[f_329_4]) ).

fof(f_330_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_330_2,plain,
    ! [U_1149,U_1148,U_1147] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_1147),U_1148),U_1149))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1147),U_1148),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1147,tc_HOL_Obool)),U_1149))) ),
    inference(variable_rename,[status(thm)],[f_330_1]) ).

fof(f_330_3,plain,
    ! [U_1148,U_1147,U_1149] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_1147),U_1148),U_1149))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1147),U_1148),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1147,tc_HOL_Obool)),U_1149))) ),
    inference(definitional_conversion,[status(esa)],[f_330_2]) ).

cnf(f_330_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_1147),U_1148),U_1149))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1147),U_1148),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1147,tc_HOL_Obool)),U_1149))) ),
    inference(clausify,[status(thm)],[f_330_3]) ).

fof(f_331_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_331_2,plain,
    ! [U_1152,U_1151,U_1150] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_1150),U_1151),U_1152))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1150),U_1151),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1150,tc_HOL_Obool)),U_1152))) ),
    inference(variable_rename,[status(thm)],[f_331_1]) ).

fof(f_331_3,plain,
    ! [U_1150,U_1151,U_1152] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_1150),U_1151),U_1152))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1150),U_1151),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1150,tc_HOL_Obool)),U_1152))) ),
    inference(definitional_conversion,[status(esa)],[f_331_2]) ).

cnf(f_331_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_1150),U_1151),U_1152))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1150),U_1151),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1150,tc_HOL_Obool)),U_1152))) ),
    inference(clausify,[status(thm)],[f_331_3]) ).

fof(f_332_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_332_2,plain,
    ! [U_1153] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1153)) = U_1153,
    inference(variable_rename,[status(thm)],[f_332_1]) ).

fof(f_332_3,plain,
    ! [U_1153] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1153)) = U_1153,
    inference(definitional_conversion,[status(esa)],[f_332_2]) ).

cnf(f_332_4,plain,
    hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1153)) = U_1153,
    inference(clausify,[status(thm)],[f_332_3]) ).

fof(f_333_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_333_2,plain,
    ! [U_1157,U_1156,U_1155,U_1154] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1154),U_1157),U_1156))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1154),U_1157),U_1155))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1154),U_1155),U_1156))
      | ~ class_Orderings_Oorder(U_1154) ),
    inference(variable_rename,[status(thm)],[f_333_1]) ).

fof(f_333_3,plain,
    ! [U_1154,U_1155,U_1156,U_1157] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1154),U_1157),U_1156))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1154),U_1157),U_1155))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1154),U_1155),U_1156))
      | ~ class_Orderings_Oorder(U_1154) ),
    inference(definitional_conversion,[status(esa)],[f_333_2]) ).

cnf(f_333_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1154),U_1157),U_1156))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1154),U_1157),U_1155))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1154),U_1155),U_1156))
    | ~ class_Orderings_Oorder(U_1154) ),
    inference(clausify,[status(thm)],[f_333_3]) ).

fof(f_334_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_334_2,plain,
    ! [U_1161,U_1160,U_1159,U_1158] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1158),U_1159),U_1161))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1158),U_1160),U_1161))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1158),U_1159),U_1160))
      | ~ class_Orderings_Opreorder(U_1158) ),
    inference(variable_rename,[status(thm)],[f_334_1]) ).

fof(f_334_3,plain,
    ! [U_1158,U_1159,U_1160,U_1161] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1158),U_1159),U_1161))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1158),U_1160),U_1161))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1158),U_1159),U_1160))
      | ~ class_Orderings_Opreorder(U_1158) ),
    inference(definitional_conversion,[status(esa)],[f_334_2]) ).

cnf(f_334_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1158),U_1159),U_1161))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1158),U_1160),U_1161))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1158),U_1159),U_1160))
    | ~ class_Orderings_Opreorder(U_1158) ),
    inference(clausify,[status(thm)],[f_334_3]) ).

fof(f_335_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_335_2,plain,
    ! [U_1165,U_1164,U_1163,U_1162] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1162),U_1165),U_1164))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1162),U_1165),U_1163))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1162),U_1163),U_1164))
      | ~ class_Orderings_Oorder(U_1162) ),
    inference(variable_rename,[status(thm)],[f_335_1]) ).

fof(f_335_3,plain,
    ! [U_1163,U_1162,U_1164,U_1165] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1162),U_1165),U_1164))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1162),U_1165),U_1163))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1162),U_1163),U_1164))
      | ~ class_Orderings_Oorder(U_1162) ),
    inference(definitional_conversion,[status(esa)],[f_335_2]) ).

cnf(f_335_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1162),U_1165),U_1164))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1162),U_1165),U_1163))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1162),U_1163),U_1164))
    | ~ class_Orderings_Oorder(U_1162) ),
    inference(clausify,[status(thm)],[f_335_3]) ).

fof(f_336_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_336_2,plain,
    ! [U_1169,U_1168,U_1167,U_1166] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1166),U_1167),U_1169))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1166),U_1168),U_1169))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1166),U_1167),U_1168))
      | ~ class_Orderings_Opreorder(U_1166) ),
    inference(variable_rename,[status(thm)],[f_336_1]) ).

fof(f_336_3,plain,
    ! [U_1166,U_1167,U_1168,U_1169] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1166),U_1167),U_1169))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1166),U_1168),U_1169))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1166),U_1167),U_1168))
      | ~ class_Orderings_Opreorder(U_1166) ),
    inference(definitional_conversion,[status(esa)],[f_336_2]) ).

cnf(f_336_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1166),U_1167),U_1169))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1166),U_1168),U_1169))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1166),U_1167),U_1168))
    | ~ class_Orderings_Opreorder(U_1166) ),
    inference(clausify,[status(thm)],[f_336_3]) ).

fof(f_337_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_337_2,plain,
    ! [U_1172,U_1171,U_1170] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1170),U_1171),U_1172))
      | U_1172 = U_1171
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1170),U_1171),U_1172))
      | ~ class_Orderings_Oorder(U_1170) ),
    inference(variable_rename,[status(thm)],[f_337_1]) ).

fof(f_337_3,plain,
    ! [U_1170,U_1171,U_1172] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1170),U_1171),U_1172))
      | U_1172 = U_1171
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1170),U_1171),U_1172))
      | ~ class_Orderings_Oorder(U_1170) ),
    inference(definitional_conversion,[status(esa)],[f_337_2]) ).

cnf(f_337_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1170),U_1171),U_1172))
    | U_1172 = U_1171
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1170),U_1171),U_1172))
    | ~ class_Orderings_Oorder(U_1170) ),
    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),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_338_2,plain,
    ! [U_1175,U_1174,U_1173] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1173),U_1174),U_1175))
      | U_1174 = U_1175
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1173),U_1174),U_1175))
      | ~ class_Orderings_Oorder(U_1173) ),
    inference(variable_rename,[status(thm)],[f_338_1]) ).

fof(f_338_3,plain,
    ! [U_1173,U_1174,U_1175] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1173),U_1174),U_1175))
      | U_1174 = U_1175
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1173),U_1174),U_1175))
      | ~ class_Orderings_Oorder(U_1173) ),
    inference(definitional_conversion,[status(esa)],[f_338_2]) ).

cnf(f_338_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1173),U_1174),U_1175))
    | U_1174 = U_1175
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1173),U_1174),U_1175))
    | ~ class_Orderings_Oorder(U_1173) ),
    inference(clausify,[status(thm)],[f_338_3]) ).

fof(f_339_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_339_2,plain,
    ! [U_1178,U_1177,U_1176] :
      ( U_1177 = U_1178
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1176),U_1177),U_1178))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1176),U_1177),U_1178))
      | ~ class_Orderings_Oorder(U_1176) ),
    inference(variable_rename,[status(thm)],[f_339_1]) ).

fof(f_339_3,plain,
    ! [U_1176,U_1177,U_1178] :
      ( U_1177 = U_1178
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1176),U_1177),U_1178))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1176),U_1177),U_1178))
      | ~ class_Orderings_Oorder(U_1176) ),
    inference(definitional_conversion,[status(esa)],[f_339_2]) ).

cnf(f_339_4,plain,
    ( U_1177 = U_1178
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1176),U_1177),U_1178))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1176),U_1177),U_1178))
    | ~ class_Orderings_Oorder(U_1176) ),
    inference(clausify,[status(thm)],[f_339_3]) ).

fof(f_340_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_340_2,plain,
    ! [U_1181,U_1180,U_1179] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1179),U_1180),U_1181))
          | U_1180 != U_1181 )
        & ( U_1180 = U_1181
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1179),U_1180),U_1181)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1179),U_1180),U_1181))
      | ~ class_Orderings_Olinorder(U_1179) ),
    inference(variable_rename,[status(thm)],[f_340_1]) ).

fof(f_340_3,plain,
    ( ! [U_1179,U_1180,U_1181] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1179),U_1180),U_1181))
        | U_1180 != U_1181
        | ~ sP90(U_1179,U_1180,U_1181) )
    & ! [U_1179,U_1180,U_1181] :
        ( U_1180 = U_1181
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1179),U_1180),U_1181))
        | ~ sP90(U_1179,U_1180,U_1181) )
    & ! [U_1179,U_1180,U_1181] :
        ( sP90(U_1179,U_1180,U_1181)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1179),U_1180),U_1181))
        | ~ class_Orderings_Olinorder(U_1179) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP90])],[f_340_2]) ).

cnf(f_340_4,plain,
    ( sP90(U_1179,U_1180,U_1181)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1179),U_1180),U_1181))
    | ~ class_Orderings_Olinorder(U_1179) ),
    inference(clausify,[status(thm)],[f_340_3]) ).

cnf(f_340_5,plain,
    ( U_1180 = U_1181
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1179),U_1180),U_1181))
    | ~ sP90(U_1179,U_1180,U_1181) ),
    inference(clausify,[status(thm)],[f_340_3]) ).

cnf(f_340_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1179),U_1180),U_1181))
    | U_1180 != U_1181
    | ~ sP90(U_1179,U_1180,U_1181) ),
    inference(clausify,[status(thm)],[f_340_3]) ).

fof(f_341_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_341_2,plain,
    ! [U_1184,U_1183,U_1182] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1182),U_1183),U_1184))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1182),U_1183),U_1184))
      | ~ class_Orderings_Opreorder(U_1182) ),
    inference(variable_rename,[status(thm)],[f_341_1]) ).

fof(f_341_3,plain,
    ! [U_1183,U_1184,U_1182] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1182),U_1183),U_1184))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1182),U_1183),U_1184))
      | ~ class_Orderings_Opreorder(U_1182) ),
    inference(definitional_conversion,[status(esa)],[f_341_2]) ).

cnf(f_341_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1182),U_1183),U_1184))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1182),U_1183),U_1184))
    | ~ class_Orderings_Opreorder(U_1182) ),
    inference(clausify,[status(thm)],[f_341_3]) ).

fof(f_342_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_342_2,plain,
    ! [U_1187,U_1186,U_1185] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1185),U_1187),U_1186))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1185),U_1186),U_1187))
      | ~ class_Orderings_Olinorder(U_1185) ),
    inference(variable_rename,[status(thm)],[f_342_1]) ).

fof(f_342_3,plain,
    ! [U_1185,U_1186,U_1187] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1185),U_1187),U_1186))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1185),U_1186),U_1187))
      | ~ class_Orderings_Olinorder(U_1185) ),
    inference(definitional_conversion,[status(esa)],[f_342_2]) ).

cnf(f_342_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1185),U_1187),U_1186))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1185),U_1186),U_1187))
    | ~ class_Orderings_Olinorder(U_1185) ),
    inference(clausify,[status(thm)],[f_342_3]) ).

fof(f_343_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_343_2,plain,
    ! [U_1190,U_1189,U_1188] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1188),U_1190),U_1189))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1188),U_1190),U_1189))
      | U_1189 = U_1190
      | ~ class_Orderings_Oorder(U_1188) ),
    inference(variable_rename,[status(thm)],[f_343_1]) ).

fof(f_343_3,plain,
    ! [U_1188,U_1189,U_1190] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1188),U_1190),U_1189))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1188),U_1190),U_1189))
      | U_1189 = U_1190
      | ~ class_Orderings_Oorder(U_1188) ),
    inference(definitional_conversion,[status(esa)],[f_343_2]) ).

cnf(f_343_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1188),U_1190),U_1189))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1188),U_1190),U_1189))
    | U_1189 = U_1190
    | ~ class_Orderings_Oorder(U_1188) ),
    inference(clausify,[status(thm)],[f_343_3]) ).

fof(f_344_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_344_2,plain,
    ! [U_1193,U_1192,U_1191] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1191),U_1192),U_1193))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1191),U_1192),U_1193))
      | U_1192 = U_1193
      | ~ class_Orderings_Oorder(U_1191) ),
    inference(variable_rename,[status(thm)],[f_344_1]) ).

fof(f_344_3,plain,
    ! [U_1192,U_1191,U_1193] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1191),U_1192),U_1193))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1191),U_1192),U_1193))
      | U_1192 = U_1193
      | ~ class_Orderings_Oorder(U_1191) ),
    inference(definitional_conversion,[status(esa)],[f_344_2]) ).

cnf(f_344_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1191),U_1192),U_1193))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1191),U_1192),U_1193))
    | U_1192 = U_1193
    | ~ class_Orderings_Oorder(U_1191) ),
    inference(clausify,[status(thm)],[f_344_3]) ).

fof(f_345_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_345_2,plain,
    ! [U_1196,U_1195,U_1194] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1194),U_1195),U_1196))
          | U_1195 != U_1196 )
        & ( U_1195 = U_1196
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1194),U_1195),U_1196)) ) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1194),U_1195),U_1196))
      | ~ class_Orderings_Olinorder(U_1194) ),
    inference(variable_rename,[status(thm)],[f_345_1]) ).

fof(f_345_3,plain,
    ( ! [U_1194,U_1195,U_1196] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1194),U_1195),U_1196))
        | U_1195 != U_1196
        | ~ sP91(U_1194,U_1195,U_1196) )
    & ! [U_1194,U_1195,U_1196] :
        ( U_1195 = U_1196
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1194),U_1195),U_1196))
        | ~ sP91(U_1194,U_1195,U_1196) )
    & ! [U_1194,U_1195,U_1196] :
        ( sP91(U_1194,U_1195,U_1196)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1194),U_1195),U_1196))
        | ~ class_Orderings_Olinorder(U_1194) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP91])],[f_345_2]) ).

cnf(f_345_4,plain,
    ( sP91(U_1194,U_1195,U_1196)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1194),U_1195),U_1196))
    | ~ class_Orderings_Olinorder(U_1194) ),
    inference(clausify,[status(thm)],[f_345_3]) ).

cnf(f_345_5,plain,
    ( U_1195 = U_1196
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1194),U_1195),U_1196))
    | ~ sP91(U_1194,U_1195,U_1196) ),
    inference(clausify,[status(thm)],[f_345_3]) ).

cnf(f_345_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1194),U_1195),U_1196))
    | U_1195 != U_1196
    | ~ sP91(U_1194,U_1195,U_1196) ),
    inference(clausify,[status(thm)],[f_345_3]) ).

fof(f_346_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_346_2,plain,
    ! [U_1199,U_1198,U_1197] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1197),U_1199),U_1198))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1197),U_1198),U_1199))
      | ~ class_Orderings_Olinorder(U_1197) ),
    inference(variable_rename,[status(thm)],[f_346_1]) ).

fof(f_346_3,plain,
    ! [U_1199,U_1198,U_1197] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1197),U_1199),U_1198))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1197),U_1198),U_1199))
      | ~ class_Orderings_Olinorder(U_1197) ),
    inference(definitional_conversion,[status(esa)],[f_346_2]) ).

cnf(f_346_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1197),U_1199),U_1198))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1197),U_1198),U_1199))
    | ~ class_Orderings_Olinorder(U_1197) ),
    inference(clausify,[status(thm)],[f_346_3]) ).

fof(f_347_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_347_2,plain,
    ! [U_1202,U_1201,U_1200] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1200),U_1202),U_1201))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1200),U_1201),U_1202))
      | ~ class_Orderings_Olinorder(U_1200) ),
    inference(variable_rename,[status(thm)],[f_347_1]) ).

fof(f_347_3,plain,
    ! [U_1200,U_1201,U_1202] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1200),U_1202),U_1201))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1200),U_1201),U_1202))
      | ~ class_Orderings_Olinorder(U_1200) ),
    inference(definitional_conversion,[status(esa)],[f_347_2]) ).

cnf(f_347_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1200),U_1202),U_1201))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1200),U_1201),U_1202))
    | ~ class_Orderings_Olinorder(U_1200) ),
    inference(clausify,[status(thm)],[f_347_3]) ).

fof(f_348_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_348_2,plain,
    ! [U_1205,U_1204,U_1203] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1203),U_1204),U_1205))
          | ( U_1204 != U_1205
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1203),U_1204),U_1205)) ) )
        & ( U_1204 = U_1205
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1203),U_1204),U_1205))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1203),U_1204),U_1205)) ) )
      | ~ class_Orderings_Oorder(U_1203) ),
    inference(variable_rename,[status(thm)],[f_348_1]) ).

fof(f_348_3,plain,
    ( ! [U_1203,U_1204,U_1205] :
        ( U_1204 != U_1205
        | ~ sP92(U_1203,U_1204,U_1205) )
    & ! [U_1203,U_1204,U_1205] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1203),U_1204),U_1205))
        | ~ sP92(U_1203,U_1204,U_1205) )
    & ! [U_1203,U_1204,U_1205] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1203),U_1204),U_1205))
        | sP92(U_1203,U_1204,U_1205)
        | ~ sP93(U_1203,U_1204,U_1205) )
    & ! [U_1203,U_1204,U_1205] :
        ( U_1204 = U_1205
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1203),U_1204),U_1205))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1203),U_1204),U_1205))
        | ~ sP93(U_1203,U_1204,U_1205) )
    & ! [U_1203,U_1204,U_1205] :
        ( sP93(U_1203,U_1204,U_1205)
        | ~ class_Orderings_Oorder(U_1203) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP92,sP93])],[f_348_2]) ).

cnf(f_348_4,plain,
    ( sP93(U_1203,U_1204,U_1205)
    | ~ class_Orderings_Oorder(U_1203) ),
    inference(clausify,[status(thm)],[f_348_3]) ).

cnf(f_348_5,plain,
    ( U_1204 = U_1205
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1203),U_1204),U_1205))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1203),U_1204),U_1205))
    | ~ sP93(U_1203,U_1204,U_1205) ),
    inference(clausify,[status(thm)],[f_348_3]) ).

cnf(f_348_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1203),U_1204),U_1205))
    | sP92(U_1203,U_1204,U_1205)
    | ~ sP93(U_1203,U_1204,U_1205) ),
    inference(clausify,[status(thm)],[f_348_3]) ).

cnf(f_348_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1203),U_1204),U_1205))
    | ~ sP92(U_1203,U_1204,U_1205) ),
    inference(clausify,[status(thm)],[f_348_3]) ).

cnf(f_348_8,plain,
    ( U_1204 != U_1205
    | ~ sP92(U_1203,U_1204,U_1205) ),
    inference(clausify,[status(thm)],[f_348_3]) ).

fof(f_349_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_349_2,plain,
    ! [U_1208,U_1207,U_1206] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1206),U_1207),U_1208))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1206),U_1208),U_1207))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1206),U_1207),U_1208)) )
        & ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1206),U_1208),U_1207))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1206),U_1207),U_1208)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1206),U_1207),U_1208)) ) )
      | ~ class_Orderings_Opreorder(U_1206) ),
    inference(variable_rename,[status(thm)],[f_349_1]) ).

fof(f_349_3,plain,
    ( ! [U_1207,U_1206,U_1208] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1206),U_1208),U_1207))
        | ~ sP94(U_1207,U_1206,U_1208) )
    & ! [U_1207,U_1206,U_1208] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1206),U_1207),U_1208))
        | ~ sP94(U_1207,U_1206,U_1208) )
    & ! [U_1207,U_1206,U_1208] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1206),U_1207),U_1208))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1206),U_1208),U_1207))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1206),U_1207),U_1208))
        | ~ sP95(U_1207,U_1206,U_1208) )
    & ! [U_1207,U_1206,U_1208] :
        ( sP94(U_1207,U_1206,U_1208)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1206),U_1207),U_1208))
        | ~ sP95(U_1207,U_1206,U_1208) )
    & ! [U_1207,U_1206,U_1208] :
        ( sP95(U_1207,U_1206,U_1208)
        | ~ class_Orderings_Opreorder(U_1206) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP94,sP95])],[f_349_2]) ).

cnf(f_349_4,plain,
    ( sP95(U_1207,U_1206,U_1208)
    | ~ class_Orderings_Opreorder(U_1206) ),
    inference(clausify,[status(thm)],[f_349_3]) ).

cnf(f_349_5,plain,
    ( sP94(U_1207,U_1206,U_1208)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1206),U_1207),U_1208))
    | ~ sP95(U_1207,U_1206,U_1208) ),
    inference(clausify,[status(thm)],[f_349_3]) ).

cnf(f_349_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1206),U_1207),U_1208))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1206),U_1208),U_1207))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1206),U_1207),U_1208))
    | ~ sP95(U_1207,U_1206,U_1208) ),
    inference(clausify,[status(thm)],[f_349_3]) ).

cnf(f_349_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1206),U_1207),U_1208))
    | ~ sP94(U_1207,U_1206,U_1208) ),
    inference(clausify,[status(thm)],[f_349_3]) ).

cnf(f_349_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1206),U_1208),U_1207))
    | ~ sP94(U_1207,U_1206,U_1208) ),
    inference(clausify,[status(thm)],[f_349_3]) ).

fof(f_350_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_350_2,plain,
    ! [U_1211,U_1210,U_1209] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1209),U_1210),U_1211))
          | U_1210 = U_1211
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1209),U_1210),U_1211)) )
        & ( ( U_1210 != U_1211
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1209),U_1210),U_1211)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1209),U_1210),U_1211)) ) )
      | ~ class_Orderings_Oorder(U_1209) ),
    inference(variable_rename,[status(thm)],[f_350_1]) ).

fof(f_350_3,plain,
    ( ! [U_1210,U_1209,U_1211] :
        ( U_1210 != U_1211
        | ~ sP96(U_1210,U_1209,U_1211) )
    & ! [U_1210,U_1209,U_1211] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1209),U_1210),U_1211))
        | ~ sP96(U_1210,U_1209,U_1211) )
    & ! [U_1210,U_1209,U_1211] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1209),U_1210),U_1211))
        | U_1210 = U_1211
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1209),U_1210),U_1211))
        | ~ sP97(U_1210,U_1209,U_1211) )
    & ! [U_1210,U_1209,U_1211] :
        ( sP96(U_1210,U_1209,U_1211)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1209),U_1210),U_1211))
        | ~ sP97(U_1210,U_1209,U_1211) )
    & ! [U_1210,U_1209,U_1211] :
        ( sP97(U_1210,U_1209,U_1211)
        | ~ class_Orderings_Oorder(U_1209) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP96,sP97])],[f_350_2]) ).

cnf(f_350_4,plain,
    ( sP97(U_1210,U_1209,U_1211)
    | ~ class_Orderings_Oorder(U_1209) ),
    inference(clausify,[status(thm)],[f_350_3]) ).

cnf(f_350_5,plain,
    ( sP96(U_1210,U_1209,U_1211)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1209),U_1210),U_1211))
    | ~ sP97(U_1210,U_1209,U_1211) ),
    inference(clausify,[status(thm)],[f_350_3]) ).

cnf(f_350_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1209),U_1210),U_1211))
    | U_1210 = U_1211
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1209),U_1210),U_1211))
    | ~ sP97(U_1210,U_1209,U_1211) ),
    inference(clausify,[status(thm)],[f_350_3]) ).

cnf(f_350_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1209),U_1210),U_1211))
    | ~ sP96(U_1210,U_1209,U_1211) ),
    inference(clausify,[status(thm)],[f_350_3]) ).

cnf(f_350_8,plain,
    ( U_1210 != U_1211
    | ~ sP96(U_1210,U_1209,U_1211) ),
    inference(clausify,[status(thm)],[f_350_3]) ).

fof(f_351_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_351_2,plain,
    ! [U_1214,U_1213,U_1212] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1212),U_1214),U_1213))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1212),U_1213),U_1214))
      | ~ class_Orderings_Olinorder(U_1212) ),
    inference(variable_rename,[status(thm)],[f_351_1]) ).

fof(f_351_3,plain,
    ! [U_1213,U_1212,U_1214] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1212),U_1214),U_1213))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1212),U_1213),U_1214))
      | ~ class_Orderings_Olinorder(U_1212) ),
    inference(definitional_conversion,[status(esa)],[f_351_2]) ).

cnf(f_351_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1212),U_1214),U_1213))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1212),U_1213),U_1214))
    | ~ class_Orderings_Olinorder(U_1212) ),
    inference(clausify,[status(thm)],[f_351_3]) ).

fof(f_352_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_352_2,plain,
    ! [U_1217,U_1216,U_1215] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1215),U_1216),U_1217))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1215),U_1217),U_1216)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1215),U_1217),U_1216))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1215),U_1216),U_1217)) ) )
      | ~ class_Orderings_Olinorder(U_1215) ),
    inference(variable_rename,[status(thm)],[f_352_1]) ).

fof(f_352_3,plain,
    ( ! [U_1215,U_1216,U_1217] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1215),U_1216),U_1217))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1215),U_1217),U_1216))
        | ~ sP98(U_1215,U_1216,U_1217) )
    & ! [U_1215,U_1216,U_1217] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1215),U_1217),U_1216))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1215),U_1216),U_1217))
        | ~ sP98(U_1215,U_1216,U_1217) )
    & ! [U_1215,U_1216,U_1217] :
        ( sP98(U_1215,U_1216,U_1217)
        | ~ class_Orderings_Olinorder(U_1215) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP98])],[f_352_2]) ).

cnf(f_352_4,plain,
    ( sP98(U_1215,U_1216,U_1217)
    | ~ class_Orderings_Olinorder(U_1215) ),
    inference(clausify,[status(thm)],[f_352_3]) ).

cnf(f_352_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1215),U_1217),U_1216))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1215),U_1216),U_1217))
    | ~ sP98(U_1215,U_1216,U_1217) ),
    inference(clausify,[status(thm)],[f_352_3]) ).

cnf(f_352_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1215),U_1216),U_1217))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1215),U_1217),U_1216))
    | ~ sP98(U_1215,U_1216,U_1217) ),
    inference(clausify,[status(thm)],[f_352_3]) ).

fof(f_353_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_353_2,plain,
    ! [U_1220,U_1219,U_1218] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1218),U_1219),U_1220))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1218),U_1220),U_1219)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1218),U_1220),U_1219))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1218),U_1219),U_1220)) ) )
      | ~ class_Orderings_Olinorder(U_1218) ),
    inference(variable_rename,[status(thm)],[f_353_1]) ).

fof(f_353_3,plain,
    ( ! [U_1220,U_1218,U_1219] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1218),U_1219),U_1220))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1218),U_1220),U_1219))
        | ~ sP99(U_1220,U_1218,U_1219) )
    & ! [U_1220,U_1218,U_1219] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1218),U_1220),U_1219))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1218),U_1219),U_1220))
        | ~ sP99(U_1220,U_1218,U_1219) )
    & ! [U_1220,U_1218,U_1219] :
        ( sP99(U_1220,U_1218,U_1219)
        | ~ class_Orderings_Olinorder(U_1218) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP99])],[f_353_2]) ).

cnf(f_353_4,plain,
    ( sP99(U_1220,U_1218,U_1219)
    | ~ class_Orderings_Olinorder(U_1218) ),
    inference(clausify,[status(thm)],[f_353_3]) ).

cnf(f_353_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1218),U_1220),U_1219))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1218),U_1219),U_1220))
    | ~ sP99(U_1220,U_1218,U_1219) ),
    inference(clausify,[status(thm)],[f_353_3]) ).

cnf(f_353_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1218),U_1219),U_1220))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1218),U_1220),U_1219))
    | ~ sP99(U_1220,U_1218,U_1219) ),
    inference(clausify,[status(thm)],[f_353_3]) ).

fof(f_354_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_354_2,plain,
    ! [U_1223,U_1222,U_1221] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1221),U_1222),hAPP(c_Groups_Ouminus__class_Ouminus(U_1221),U_1223)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1221),U_1223),hAPP(c_Groups_Ouminus__class_Ouminus(U_1221),U_1222))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1221),U_1223),hAPP(c_Groups_Ouminus__class_Ouminus(U_1221),U_1222)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1221),U_1222),hAPP(c_Groups_Ouminus__class_Ouminus(U_1221),U_1223))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1221) ),
    inference(variable_rename,[status(thm)],[f_354_1]) ).

fof(f_354_3,plain,
    ( ! [U_1222,U_1223,U_1221] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1221),U_1222),hAPP(c_Groups_Ouminus__class_Ouminus(U_1221),U_1223)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1221),U_1223),hAPP(c_Groups_Ouminus__class_Ouminus(U_1221),U_1222)))
        | ~ sP100(U_1222,U_1223,U_1221) )
    & ! [U_1222,U_1223,U_1221] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1221),U_1223),hAPP(c_Groups_Ouminus__class_Ouminus(U_1221),U_1222)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1221),U_1222),hAPP(c_Groups_Ouminus__class_Ouminus(U_1221),U_1223)))
        | ~ sP100(U_1222,U_1223,U_1221) )
    & ! [U_1222,U_1223,U_1221] :
        ( sP100(U_1222,U_1223,U_1221)
        | ~ class_Groups_Oordered__ab__group__add(U_1221) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP100])],[f_354_2]) ).

cnf(f_354_4,plain,
    ( sP100(U_1222,U_1223,U_1221)
    | ~ class_Groups_Oordered__ab__group__add(U_1221) ),
    inference(clausify,[status(thm)],[f_354_3]) ).

cnf(f_354_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1221),U_1223),hAPP(c_Groups_Ouminus__class_Ouminus(U_1221),U_1222)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1221),U_1222),hAPP(c_Groups_Ouminus__class_Ouminus(U_1221),U_1223)))
    | ~ sP100(U_1222,U_1223,U_1221) ),
    inference(clausify,[status(thm)],[f_354_3]) ).

cnf(f_354_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1221),U_1222),hAPP(c_Groups_Ouminus__class_Ouminus(U_1221),U_1223)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1221),U_1223),hAPP(c_Groups_Ouminus__class_Ouminus(U_1221),U_1222)))
    | ~ sP100(U_1222,U_1223,U_1221) ),
    inference(clausify,[status(thm)],[f_354_3]) ).

fof(f_355_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_355_2,plain,
    ! [U_1226,U_1225,U_1224] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1224),hAPP(c_Groups_Ouminus__class_Ouminus(U_1224),U_1225)),U_1226))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1224),hAPP(c_Groups_Ouminus__class_Ouminus(U_1224),U_1226)),U_1225)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1224),hAPP(c_Groups_Ouminus__class_Ouminus(U_1224),U_1226)),U_1225))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1224),hAPP(c_Groups_Ouminus__class_Ouminus(U_1224),U_1225)),U_1226)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1224) ),
    inference(variable_rename,[status(thm)],[f_355_1]) ).

fof(f_355_3,plain,
    ( ! [U_1225,U_1224,U_1226] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1224),hAPP(c_Groups_Ouminus__class_Ouminus(U_1224),U_1225)),U_1226))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1224),hAPP(c_Groups_Ouminus__class_Ouminus(U_1224),U_1226)),U_1225))
        | ~ sP101(U_1225,U_1224,U_1226) )
    & ! [U_1225,U_1224,U_1226] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1224),hAPP(c_Groups_Ouminus__class_Ouminus(U_1224),U_1226)),U_1225))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1224),hAPP(c_Groups_Ouminus__class_Ouminus(U_1224),U_1225)),U_1226))
        | ~ sP101(U_1225,U_1224,U_1226) )
    & ! [U_1225,U_1224,U_1226] :
        ( sP101(U_1225,U_1224,U_1226)
        | ~ class_Groups_Oordered__ab__group__add(U_1224) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP101])],[f_355_2]) ).

cnf(f_355_4,plain,
    ( sP101(U_1225,U_1224,U_1226)
    | ~ class_Groups_Oordered__ab__group__add(U_1224) ),
    inference(clausify,[status(thm)],[f_355_3]) ).

cnf(f_355_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1224),hAPP(c_Groups_Ouminus__class_Ouminus(U_1224),U_1226)),U_1225))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1224),hAPP(c_Groups_Ouminus__class_Ouminus(U_1224),U_1225)),U_1226))
    | ~ sP101(U_1225,U_1224,U_1226) ),
    inference(clausify,[status(thm)],[f_355_3]) ).

cnf(f_355_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1224),hAPP(c_Groups_Ouminus__class_Ouminus(U_1224),U_1225)),U_1226))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1224),hAPP(c_Groups_Ouminus__class_Ouminus(U_1224),U_1226)),U_1225))
    | ~ sP101(U_1225,U_1224,U_1226) ),
    inference(clausify,[status(thm)],[f_355_3]) ).

fof(f_356_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_356_2,plain,
    ! [U_1229,U_1228,U_1227] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1227),hAPP(c_Groups_Ouminus__class_Ouminus(U_1227),U_1228)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1227),U_1229)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1227),U_1229),U_1228)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1227),U_1229),U_1228))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1227),hAPP(c_Groups_Ouminus__class_Ouminus(U_1227),U_1228)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1227),U_1229))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1227) ),
    inference(variable_rename,[status(thm)],[f_356_1]) ).

fof(f_356_3,plain,
    ( ! [U_1228,U_1227,U_1229] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1227),hAPP(c_Groups_Ouminus__class_Ouminus(U_1227),U_1228)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1227),U_1229)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1227),U_1229),U_1228))
        | ~ sP102(U_1228,U_1227,U_1229) )
    & ! [U_1228,U_1227,U_1229] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1227),U_1229),U_1228))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1227),hAPP(c_Groups_Ouminus__class_Ouminus(U_1227),U_1228)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1227),U_1229)))
        | ~ sP102(U_1228,U_1227,U_1229) )
    & ! [U_1228,U_1227,U_1229] :
        ( sP102(U_1228,U_1227,U_1229)
        | ~ class_Groups_Oordered__ab__group__add(U_1227) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP102])],[f_356_2]) ).

cnf(f_356_4,plain,
    ( sP102(U_1228,U_1227,U_1229)
    | ~ class_Groups_Oordered__ab__group__add(U_1227) ),
    inference(clausify,[status(thm)],[f_356_3]) ).

cnf(f_356_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1227),U_1229),U_1228))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1227),hAPP(c_Groups_Ouminus__class_Ouminus(U_1227),U_1228)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1227),U_1229)))
    | ~ sP102(U_1228,U_1227,U_1229) ),
    inference(clausify,[status(thm)],[f_356_3]) ).

cnf(f_356_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1227),hAPP(c_Groups_Ouminus__class_Ouminus(U_1227),U_1228)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1227),U_1229)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1227),U_1229),U_1228))
    | ~ sP102(U_1228,U_1227,U_1229) ),
    inference(clausify,[status(thm)],[f_356_3]) ).

fof(f_357_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_357_2,plain,
    ! [U_1232,U_1231,U_1230] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1230),hAPP(c_Groups_Ouminus__class_Ouminus(U_1230),U_1232)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1230),U_1231)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1230),U_1231),U_1232))
      | ~ class_Groups_Oordered__ab__group__add(U_1230) ),
    inference(variable_rename,[status(thm)],[f_357_1]) ).

fof(f_357_3,plain,
    ! [U_1232,U_1231,U_1230] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1230),hAPP(c_Groups_Ouminus__class_Ouminus(U_1230),U_1232)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1230),U_1231)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1230),U_1231),U_1232))
      | ~ class_Groups_Oordered__ab__group__add(U_1230) ),
    inference(definitional_conversion,[status(esa)],[f_357_2]) ).

cnf(f_357_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1230),hAPP(c_Groups_Ouminus__class_Ouminus(U_1230),U_1232)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1230),U_1231)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1230),U_1231),U_1232))
    | ~ class_Groups_Oordered__ab__group__add(U_1230) ),
    inference(clausify,[status(thm)],[f_357_3]) ).

fof(f_358_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_358_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_358_1]) ).

cnf(f_358_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_358_2]) ).

fof(f_359_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_359_2,plain,
    ! [U_1234,U_1233] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1233),U_1234))
        | U_1233 = U_1234
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1233),U_1234)) )
      & ( ( U_1233 != U_1234
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1233),U_1234)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1233),U_1234)) ) ),
    inference(variable_rename,[status(thm)],[f_359_1]) ).

fof(f_359_3,plain,
    ( ! [U_1238,U_1236] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1236),U_1238))
        | U_1236 = U_1238
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1236),U_1238)) )
    & ! [U_1237,U_1235] :
        ( ( U_1235 != U_1237
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1235),U_1237)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1235),U_1237)) ) ),
    inference(miniscope,[status(thm)],[f_359_2]) ).

fof(f_359_4,plain,
    ( ! [U_1237,U_1235] :
        ( U_1235 != U_1237
        | ~ sP103(U_1237,U_1235) )
    & ! [U_1237,U_1235] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1235),U_1237))
        | ~ sP103(U_1237,U_1235) )
    & ! [U_1238,U_1236] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1236),U_1238))
        | U_1236 = U_1238
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1236),U_1238)) )
    & ! [U_1237,U_1235] :
        ( sP103(U_1237,U_1235)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1235),U_1237)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP103])],[f_359_3]) ).

cnf(f_359_5,plain,
    ( sP103(U_1237,U_1235)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1235),U_1237)) ),
    inference(clausify,[status(thm)],[f_359_4]) ).

cnf(f_359_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1236),U_1238))
    | U_1236 = U_1238
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1236),U_1238)) ),
    inference(clausify,[status(thm)],[f_359_4]) ).

cnf(f_359_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1235),U_1237))
    | ~ sP103(U_1237,U_1235) ),
    inference(clausify,[status(thm)],[f_359_4]) ).

cnf(f_359_8,plain,
    ( U_1235 != U_1237
    | ~ sP103(U_1237,U_1235) ),
    inference(clausify,[status(thm)],[f_359_4]) ).

fof(f_360_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_360_2,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_360_1]) ).

cnf(f_360_3,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_360_2]) ).

fof(f_361_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_361_2,plain,
    ! [U_1239] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1239))),
    inference(variable_rename,[status(thm)],[f_361_1]) ).

fof(f_361_3,plain,
    ! [U_1239] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1239))),
    inference(definitional_conversion,[status(esa)],[f_361_2]) ).

cnf(f_361_4,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1239))),
    inference(clausify,[status(thm)],[f_361_3]) ).

fof(f_362_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_362_2,plain,
    ! [U_1241,U_1240] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1240)),hAPP(c_Int_Onat,U_1241)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1240),U_1241)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1240),U_1241))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1240)),hAPP(c_Int_Onat,U_1241))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1241))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1240)) ),
    inference(variable_rename,[status(thm)],[f_362_1]) ).

fof(f_362_3,plain,
    ( ! [U_1241,U_1240] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1240)),hAPP(c_Int_Onat,U_1241)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1240),U_1241))
        | ~ sP104(U_1241,U_1240) )
    & ! [U_1241,U_1240] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1240),U_1241))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1240)),hAPP(c_Int_Onat,U_1241)))
        | ~ sP104(U_1241,U_1240) )
    & ! [U_1241,U_1240] :
        ( sP104(U_1241,U_1240)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1241))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1240)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP104])],[f_362_2]) ).

cnf(f_362_4,plain,
    ( sP104(U_1241,U_1240)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1241))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1240)) ),
    inference(clausify,[status(thm)],[f_362_3]) ).

cnf(f_362_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1240),U_1241))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1240)),hAPP(c_Int_Onat,U_1241)))
    | ~ sP104(U_1241,U_1240) ),
    inference(clausify,[status(thm)],[f_362_3]) ).

cnf(f_362_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1240)),hAPP(c_Int_Onat,U_1241)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1240),U_1241))
    | ~ sP104(U_1241,U_1240) ),
    inference(clausify,[status(thm)],[f_362_3]) ).

fof(f_363_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_363_2,plain,
    ! [U_1243,U_1242] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1242)),hAPP(c_Int_Onat,U_1243)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1242),U_1243)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1242),U_1243))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1242)),hAPP(c_Int_Onat,U_1243))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1242)) ),
    inference(variable_rename,[status(thm)],[f_363_1]) ).

fof(f_363_3,plain,
    ( ! [U_1243,U_1242] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1242)),hAPP(c_Int_Onat,U_1243)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1242),U_1243))
        | ~ sP105(U_1243,U_1242) )
    & ! [U_1243,U_1242] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1242),U_1243))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1242)),hAPP(c_Int_Onat,U_1243)))
        | ~ sP105(U_1243,U_1242) )
    & ! [U_1243,U_1242] :
        ( sP105(U_1243,U_1242)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1242)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP105])],[f_363_2]) ).

cnf(f_363_4,plain,
    ( sP105(U_1243,U_1242)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1242)) ),
    inference(clausify,[status(thm)],[f_363_3]) ).

cnf(f_363_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1242),U_1243))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1242)),hAPP(c_Int_Onat,U_1243)))
    | ~ sP105(U_1243,U_1242) ),
    inference(clausify,[status(thm)],[f_363_3]) ).

cnf(f_363_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1242)),hAPP(c_Int_Onat,U_1243)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1242),U_1243))
    | ~ sP105(U_1243,U_1242) ),
    inference(clausify,[status(thm)],[f_363_3]) ).

fof(f_364_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_364_2,plain,
    ! [U_1245,U_1244] :
      ( ( U_1244 = hAPP(c_Int_Onat,U_1245)
        | ( U_1244 != 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_1245)) )
        | ( U_1245 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1244)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1245)) ) )
      & ( ( ( U_1244 = 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_1245)) )
          & ( U_1245 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1244)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1245)) ) )
        | U_1244 != hAPP(c_Int_Onat,U_1245) ) ),
    inference(variable_rename,[status(thm)],[f_364_1]) ).

fof(f_364_3,plain,
    ( ! [U_1249,U_1247] :
        ( U_1247 = hAPP(c_Int_Onat,U_1249)
        | ( U_1247 != 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_1249)) )
        | ( U_1249 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1247)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1249)) ) )
    & ! [U_1248,U_1246] :
        ( ( ( U_1246 = 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_1248)) )
          & ( U_1248 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1246)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1248)) ) )
        | U_1246 != hAPP(c_Int_Onat,U_1248) ) ),
    inference(miniscope,[status(thm)],[f_364_2]) ).

fof(f_364_4,plain,
    ( ! [U_1247,U_1249] :
        ( U_1247 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP108(U_1247,U_1249) )
    & ! [U_1247,U_1249] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1249))
        | ~ sP108(U_1247,U_1249) )
    & ! [U_1247,U_1249] :
        ( U_1249 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1247)
        | ~ sP107(U_1247,U_1249) )
    & ! [U_1247,U_1249] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1249))
        | ~ sP107(U_1247,U_1249) )
    & ! [U_1248,U_1246] :
        ( U_1246 = 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_1248))
        | ~ sP106(U_1248,U_1246) )
    & ! [U_1248,U_1246] :
        ( U_1248 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1246)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1248))
        | ~ sP106(U_1248,U_1246) )
    & ! [U_1247,U_1249] :
        ( U_1247 = hAPP(c_Int_Onat,U_1249)
        | sP108(U_1247,U_1249)
        | sP107(U_1247,U_1249) )
    & ! [U_1248,U_1246] :
        ( sP106(U_1248,U_1246)
        | U_1246 != hAPP(c_Int_Onat,U_1248) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP106,sP107,sP108])],[f_364_3]) ).

cnf(f_364_5,plain,
    ( sP106(U_1248,U_1246)
    | U_1246 != hAPP(c_Int_Onat,U_1248) ),
    inference(clausify,[status(thm)],[f_364_4]) ).

cnf(f_364_6,plain,
    ( U_1247 = hAPP(c_Int_Onat,U_1249)
    | sP108(U_1247,U_1249)
    | sP107(U_1247,U_1249) ),
    inference(clausify,[status(thm)],[f_364_4]) ).

cnf(f_364_7,plain,
    ( U_1248 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1246)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1248))
    | ~ sP106(U_1248,U_1246) ),
    inference(clausify,[status(thm)],[f_364_4]) ).

cnf(f_364_8,plain,
    ( U_1246 = 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_1248))
    | ~ sP106(U_1248,U_1246) ),
    inference(clausify,[status(thm)],[f_364_4]) ).

cnf(f_364_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1249))
    | ~ sP107(U_1247,U_1249) ),
    inference(clausify,[status(thm)],[f_364_4]) ).

cnf(f_364_10,plain,
    ( U_1249 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1247)
    | ~ sP107(U_1247,U_1249) ),
    inference(clausify,[status(thm)],[f_364_4]) ).

cnf(f_364_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1249))
    | ~ sP108(U_1247,U_1249) ),
    inference(clausify,[status(thm)],[f_364_4]) ).

cnf(f_364_12,plain,
    ( U_1247 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP108(U_1247,U_1249) ),
    inference(clausify,[status(thm)],[f_364_4]) ).

fof(f_365_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_365_2,plain,
    ! [U_1251,U_1250] :
      ( ( hAPP(c_Int_Onat,U_1250) = U_1251
        | ( U_1251 != 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_1250)) )
        | ( U_1250 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1251)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1250)) ) )
      & ( ( ( U_1251 = 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_1250)) )
          & ( U_1250 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1251)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1250)) ) )
        | hAPP(c_Int_Onat,U_1250) != U_1251 ) ),
    inference(variable_rename,[status(thm)],[f_365_1]) ).

fof(f_365_3,plain,
    ( ! [U_1255,U_1253] :
        ( hAPP(c_Int_Onat,U_1253) = U_1255
        | ( U_1255 != 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_1253)) )
        | ( U_1253 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1255)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1253)) ) )
    & ! [U_1254,U_1252] :
        ( ( ( U_1254 = 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_1252)) )
          & ( U_1252 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1254)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1252)) ) )
        | hAPP(c_Int_Onat,U_1252) != U_1254 ) ),
    inference(miniscope,[status(thm)],[f_365_2]) ).

fof(f_365_4,plain,
    ( ! [U_1255,U_1253] :
        ( U_1255 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP111(U_1255,U_1253) )
    & ! [U_1255,U_1253] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1253))
        | ~ sP111(U_1255,U_1253) )
    & ! [U_1255,U_1253] :
        ( U_1253 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1255)
        | ~ sP110(U_1255,U_1253) )
    & ! [U_1255,U_1253] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1253))
        | ~ sP110(U_1255,U_1253) )
    & ! [U_1254,U_1252] :
        ( U_1254 = 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_1252))
        | ~ sP109(U_1254,U_1252) )
    & ! [U_1254,U_1252] :
        ( U_1252 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1254)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1252))
        | ~ sP109(U_1254,U_1252) )
    & ! [U_1255,U_1253] :
        ( hAPP(c_Int_Onat,U_1253) = U_1255
        | sP111(U_1255,U_1253)
        | sP110(U_1255,U_1253) )
    & ! [U_1254,U_1252] :
        ( sP109(U_1254,U_1252)
        | hAPP(c_Int_Onat,U_1252) != U_1254 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP109,sP110,sP111])],[f_365_3]) ).

cnf(f_365_5,plain,
    ( sP109(U_1254,U_1252)
    | hAPP(c_Int_Onat,U_1252) != U_1254 ),
    inference(clausify,[status(thm)],[f_365_4]) ).

cnf(f_365_6,plain,
    ( hAPP(c_Int_Onat,U_1253) = U_1255
    | sP111(U_1255,U_1253)
    | sP110(U_1255,U_1253) ),
    inference(clausify,[status(thm)],[f_365_4]) ).

cnf(f_365_7,plain,
    ( U_1252 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1254)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1252))
    | ~ sP109(U_1254,U_1252) ),
    inference(clausify,[status(thm)],[f_365_4]) ).

cnf(f_365_8,plain,
    ( U_1254 = 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_1252))
    | ~ sP109(U_1254,U_1252) ),
    inference(clausify,[status(thm)],[f_365_4]) ).

cnf(f_365_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1253))
    | ~ sP110(U_1255,U_1253) ),
    inference(clausify,[status(thm)],[f_365_4]) ).

cnf(f_365_10,plain,
    ( U_1253 != hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1255)
    | ~ sP110(U_1255,U_1253) ),
    inference(clausify,[status(thm)],[f_365_4]) ).

cnf(f_365_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1253))
    | ~ sP111(U_1255,U_1253) ),
    inference(clausify,[status(thm)],[f_365_4]) ).

cnf(f_365_12,plain,
    ( U_1255 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP111(U_1255,U_1253) ),
    inference(clausify,[status(thm)],[f_365_4]) ).

fof(f_366_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_366_2,plain,
    ! [U_1257,U_1256] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1256),U_1257)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_1256)),hAPP(c_Int_Onat,U_1257))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1256)) ),
    inference(variable_rename,[status(thm)],[f_366_1]) ).

fof(f_366_3,plain,
    ! [U_1257,U_1256] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1256),U_1257)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_1256)),hAPP(c_Int_Onat,U_1257))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1256)) ),
    inference(definitional_conversion,[status(esa)],[f_366_2]) ).

cnf(f_366_4,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1256),U_1257)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_1256)),hAPP(c_Int_Onat,U_1257))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1256)) ),
    inference(clausify,[status(thm)],[f_366_3]) ).

fof(f_367_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_367_2,plain,
    ! [U_1259,U_1258] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_1258)),hAPP(c_Int_Onat,U_1259)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1258),U_1259))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1259))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1258)) ),
    inference(variable_rename,[status(thm)],[f_367_1]) ).

fof(f_367_3,plain,
    ! [U_1259,U_1258] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_1258)),hAPP(c_Int_Onat,U_1259)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1258),U_1259))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1259))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1258)) ),
    inference(definitional_conversion,[status(esa)],[f_367_2]) ).

cnf(f_367_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,U_1258)),hAPP(c_Int_Onat,U_1259)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1258),U_1259))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1259))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1258)) ),
    inference(clausify,[status(thm)],[f_367_3]) ).

fof(f_368_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_368_2,plain,
    ! [U_1261,U_1260] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1260),hAPP(c_Int_Onat,U_1261)) = hAPP(c_Int_Oring__1__class_Oof__int(U_1260),U_1261)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1261))
      | ~ class_Rings_Oring__1(U_1260) ),
    inference(variable_rename,[status(thm)],[f_368_1]) ).

fof(f_368_3,plain,
    ! [U_1260,U_1261] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1260),hAPP(c_Int_Onat,U_1261)) = hAPP(c_Int_Oring__1__class_Oof__int(U_1260),U_1261)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1261))
      | ~ class_Rings_Oring__1(U_1260) ),
    inference(definitional_conversion,[status(esa)],[f_368_2]) ).

cnf(f_368_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1260),hAPP(c_Int_Onat,U_1261)) = hAPP(c_Int_Oring__1__class_Oof__int(U_1260),U_1261)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1261))
    | ~ class_Rings_Oring__1(U_1260) ),
    inference(clausify,[status(thm)],[f_368_3]) ).

fof(f_369_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_369_2,plain,
    ! [U_1263,U_1262] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1262),hAPP(c_Int_Oring__1__class_Oof__int(U_1262),U_1263)),c_Groups_Ozero__class_Ozero(U_1262)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1263),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1263),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1262),hAPP(c_Int_Oring__1__class_Oof__int(U_1262),U_1263)),c_Groups_Ozero__class_Ozero(U_1262))) ) )
      | ~ class_Rings_Olinordered__idom(U_1262) ),
    inference(variable_rename,[status(thm)],[f_369_1]) ).

fof(f_369_3,plain,
    ( ! [U_1263,U_1262] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1262),hAPP(c_Int_Oring__1__class_Oof__int(U_1262),U_1263)),c_Groups_Ozero__class_Ozero(U_1262)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1263),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP112(U_1263,U_1262) )
    & ! [U_1263,U_1262] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1263),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1262),hAPP(c_Int_Oring__1__class_Oof__int(U_1262),U_1263)),c_Groups_Ozero__class_Ozero(U_1262)))
        | ~ sP112(U_1263,U_1262) )
    & ! [U_1263,U_1262] :
        ( sP112(U_1263,U_1262)
        | ~ class_Rings_Olinordered__idom(U_1262) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP112])],[f_369_2]) ).

cnf(f_369_4,plain,
    ( sP112(U_1263,U_1262)
    | ~ class_Rings_Olinordered__idom(U_1262) ),
    inference(clausify,[status(thm)],[f_369_3]) ).

cnf(f_369_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1263),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1262),hAPP(c_Int_Oring__1__class_Oof__int(U_1262),U_1263)),c_Groups_Ozero__class_Ozero(U_1262)))
    | ~ sP112(U_1263,U_1262) ),
    inference(clausify,[status(thm)],[f_369_3]) ).

cnf(f_369_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1262),hAPP(c_Int_Oring__1__class_Oof__int(U_1262),U_1263)),c_Groups_Ozero__class_Ozero(U_1262)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1263),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP112(U_1263,U_1262) ),
    inference(clausify,[status(thm)],[f_369_3]) ).

fof(f_370_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_370_2,plain,
    ! [U_1265,U_1264] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1264),c_Groups_Ozero__class_Ozero(U_1264)),hAPP(c_Int_Oring__1__class_Oof__int(U_1264),U_1265)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1265)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1265))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1264),c_Groups_Ozero__class_Ozero(U_1264)),hAPP(c_Int_Oring__1__class_Oof__int(U_1264),U_1265))) ) )
      | ~ class_Rings_Olinordered__idom(U_1264) ),
    inference(variable_rename,[status(thm)],[f_370_1]) ).

fof(f_370_3,plain,
    ( ! [U_1264,U_1265] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1264),c_Groups_Ozero__class_Ozero(U_1264)),hAPP(c_Int_Oring__1__class_Oof__int(U_1264),U_1265)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1265))
        | ~ sP113(U_1264,U_1265) )
    & ! [U_1264,U_1265] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1265))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1264),c_Groups_Ozero__class_Ozero(U_1264)),hAPP(c_Int_Oring__1__class_Oof__int(U_1264),U_1265)))
        | ~ sP113(U_1264,U_1265) )
    & ! [U_1264,U_1265] :
        ( sP113(U_1264,U_1265)
        | ~ class_Rings_Olinordered__idom(U_1264) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP113])],[f_370_2]) ).

cnf(f_370_4,plain,
    ( sP113(U_1264,U_1265)
    | ~ class_Rings_Olinordered__idom(U_1264) ),
    inference(clausify,[status(thm)],[f_370_3]) ).

cnf(f_370_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1265))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1264),c_Groups_Ozero__class_Ozero(U_1264)),hAPP(c_Int_Oring__1__class_Oof__int(U_1264),U_1265)))
    | ~ sP113(U_1264,U_1265) ),
    inference(clausify,[status(thm)],[f_370_3]) ).

cnf(f_370_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1264),c_Groups_Ozero__class_Ozero(U_1264)),hAPP(c_Int_Oring__1__class_Oof__int(U_1264),U_1265)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1265))
    | ~ sP113(U_1264,U_1265) ),
    inference(clausify,[status(thm)],[f_370_3]) ).

fof(f_371_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_371_2,plain,
    ! [U_1267,U_1266] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1266)),U_1267))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1266),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1267))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1266),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1267)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1266)),U_1267)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1266)) ),
    inference(variable_rename,[status(thm)],[f_371_1]) ).

fof(f_371_3,plain,
    ( ! [U_1267,U_1266] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1266)),U_1267))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1266),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1267)))
        | ~ sP114(U_1267,U_1266) )
    & ! [U_1267,U_1266] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1266),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1267)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1266)),U_1267))
        | ~ sP114(U_1267,U_1266) )
    & ! [U_1267,U_1266] :
        ( sP114(U_1267,U_1266)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1266)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP114])],[f_371_2]) ).

cnf(f_371_4,plain,
    ( sP114(U_1267,U_1266)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1266)) ),
    inference(clausify,[status(thm)],[f_371_3]) ).

cnf(f_371_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1266),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1267)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1266)),U_1267))
    | ~ sP114(U_1267,U_1266) ),
    inference(clausify,[status(thm)],[f_371_3]) ).

cnf(f_371_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1266)),U_1267))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1266),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1267)))
    | ~ sP114(U_1267,U_1266) ),
    inference(clausify,[status(thm)],[f_371_3]) ).

fof(f_372_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_372_2,plain,
    ! [U_1269,U_1268] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1268),U_1269)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1268))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1269)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1268),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_372_1]) ).

fof(f_372_3,plain,
    ! [U_1269,U_1268] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1268),U_1269)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1268))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1269)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1268),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_372_2]) ).

cnf(f_372_4,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1268),U_1269)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1268))),hAPP(c_Int_Onat,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_1269)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_1268),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_372_3]) ).

fof(f_373_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_373_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_373_1]) ).

cnf(f_373_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_373_2]) ).

fof(f_374_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_374_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_374_1]) ).

cnf(f_374_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_374_2]) ).

fof(f_375_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_375_2,plain,
    ! [U_1272,U_1271,U_1270] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1270),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1270),U_1271),U_1272)),c_Groups_Ozero__class_Ozero(U_1270)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1270),c_Groups_Ozero__class_Ozero(U_1270)),U_1272))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1270),U_1271),c_Groups_Ozero__class_Ozero(U_1270))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1270),U_1272),c_Groups_Ozero__class_Ozero(U_1270)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1270),c_Groups_Ozero__class_Ozero(U_1270)),U_1271)) ) )
      | ~ class_Rings_Oordered__cancel__semiring(U_1270) ),
    inference(variable_rename,[status(thm)],[f_375_1]) ).

fof(f_375_3,plain,
    ( ! [U_1270,U_1271,U_1272] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1270),c_Groups_Ozero__class_Ozero(U_1270)),U_1272))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1270),U_1271),c_Groups_Ozero__class_Ozero(U_1270)))
        | ~ sP115(U_1270,U_1271,U_1272) )
    & ! [U_1270,U_1271,U_1272] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1270),U_1272),c_Groups_Ozero__class_Ozero(U_1270)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1270),c_Groups_Ozero__class_Ozero(U_1270)),U_1271))
        | ~ sP115(U_1270,U_1271,U_1272) )
    & ! [U_1270,U_1271,U_1272] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1270),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1270),U_1271),U_1272)),c_Groups_Ozero__class_Ozero(U_1270)))
        | sP115(U_1270,U_1271,U_1272)
        | ~ class_Rings_Oordered__cancel__semiring(U_1270) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP115])],[f_375_2]) ).

cnf(f_375_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1270),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1270),U_1271),U_1272)),c_Groups_Ozero__class_Ozero(U_1270)))
    | sP115(U_1270,U_1271,U_1272)
    | ~ class_Rings_Oordered__cancel__semiring(U_1270) ),
    inference(clausify,[status(thm)],[f_375_3]) ).

cnf(f_375_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1270),U_1272),c_Groups_Ozero__class_Ozero(U_1270)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1270),c_Groups_Ozero__class_Ozero(U_1270)),U_1271))
    | ~ sP115(U_1270,U_1271,U_1272) ),
    inference(clausify,[status(thm)],[f_375_3]) ).

cnf(f_375_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1270),c_Groups_Ozero__class_Ozero(U_1270)),U_1272))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1270),U_1271),c_Groups_Ozero__class_Ozero(U_1270)))
    | ~ sP115(U_1270,U_1271,U_1272) ),
    inference(clausify,[status(thm)],[f_375_3]) ).

fof(f_376_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_376_2,plain,
    ! [U_1275,U_1274,U_1273] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1273),c_Groups_Ozero__class_Ozero(U_1273)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1273),U_1274),U_1275)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1273),U_1275),c_Groups_Ozero__class_Ozero(U_1273)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1273),U_1274),c_Groups_Ozero__class_Ozero(U_1273))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1273),c_Groups_Ozero__class_Ozero(U_1273)),U_1275))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1273),c_Groups_Ozero__class_Ozero(U_1273)),U_1274)) ) )
      | ~ class_Rings_Oordered__ring(U_1273) ),
    inference(variable_rename,[status(thm)],[f_376_1]) ).

fof(f_376_3,plain,
    ( ! [U_1275,U_1274,U_1273] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1273),U_1275),c_Groups_Ozero__class_Ozero(U_1273)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1273),U_1274),c_Groups_Ozero__class_Ozero(U_1273)))
        | ~ sP116(U_1275,U_1274,U_1273) )
    & ! [U_1275,U_1274,U_1273] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1273),c_Groups_Ozero__class_Ozero(U_1273)),U_1275))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1273),c_Groups_Ozero__class_Ozero(U_1273)),U_1274))
        | ~ sP116(U_1275,U_1274,U_1273) )
    & ! [U_1275,U_1274,U_1273] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1273),c_Groups_Ozero__class_Ozero(U_1273)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1273),U_1274),U_1275)))
        | sP116(U_1275,U_1274,U_1273)
        | ~ class_Rings_Oordered__ring(U_1273) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP116])],[f_376_2]) ).

cnf(f_376_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1273),c_Groups_Ozero__class_Ozero(U_1273)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1273),U_1274),U_1275)))
    | sP116(U_1275,U_1274,U_1273)
    | ~ class_Rings_Oordered__ring(U_1273) ),
    inference(clausify,[status(thm)],[f_376_3]) ).

cnf(f_376_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1273),c_Groups_Ozero__class_Ozero(U_1273)),U_1275))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1273),c_Groups_Ozero__class_Ozero(U_1273)),U_1274))
    | ~ sP116(U_1275,U_1274,U_1273) ),
    inference(clausify,[status(thm)],[f_376_3]) ).

cnf(f_376_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1273),U_1275),c_Groups_Ozero__class_Ozero(U_1273)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1273),U_1274),c_Groups_Ozero__class_Ozero(U_1273)))
    | ~ sP116(U_1275,U_1274,U_1273) ),
    inference(clausify,[status(thm)],[f_376_3]) ).

fof(f_377_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_377_2,plain,
    ! [U_1280,U_1279,U_1278,U_1277,U_1276] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1276),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1276),U_1277),U_1279)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1276),U_1278),U_1280)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1276),c_Groups_Ozero__class_Ozero(U_1276)),U_1279))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1276),c_Groups_Ozero__class_Ozero(U_1276)),U_1278))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1276),U_1279),U_1280))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1276),U_1277),U_1278))
      | ~ class_Rings_Oordered__semiring(U_1276) ),
    inference(variable_rename,[status(thm)],[f_377_1]) ).

fof(f_377_3,plain,
    ! [U_1279,U_1278,U_1276,U_1277,U_1280] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1276),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1276),U_1277),U_1279)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1276),U_1278),U_1280)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1276),c_Groups_Ozero__class_Ozero(U_1276)),U_1279))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1276),c_Groups_Ozero__class_Ozero(U_1276)),U_1278))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1276),U_1279),U_1280))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1276),U_1277),U_1278))
      | ~ class_Rings_Oordered__semiring(U_1276) ),
    inference(definitional_conversion,[status(esa)],[f_377_2]) ).

cnf(f_377_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1276),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1276),U_1277),U_1279)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1276),U_1278),U_1280)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1276),c_Groups_Ozero__class_Ozero(U_1276)),U_1279))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1276),c_Groups_Ozero__class_Ozero(U_1276)),U_1278))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1276),U_1279),U_1280))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1276),U_1277),U_1278))
    | ~ class_Rings_Oordered__semiring(U_1276) ),
    inference(clausify,[status(thm)],[f_377_3]) ).

fof(f_378_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_378_2,plain,
    ! [U_1285,U_1284,U_1283,U_1282,U_1281] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1281),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1281),U_1282),U_1284)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1281),U_1283),U_1285)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1281),c_Groups_Ozero__class_Ozero(U_1281)),U_1284))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1281),c_Groups_Ozero__class_Ozero(U_1281)),U_1282))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1281),U_1284),U_1285))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1281),U_1282),U_1283))
      | ~ class_Rings_Oordered__semiring(U_1281) ),
    inference(variable_rename,[status(thm)],[f_378_1]) ).

fof(f_378_3,plain,
    ! [U_1282,U_1285,U_1281,U_1283,U_1284] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1281),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1281),U_1282),U_1284)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1281),U_1283),U_1285)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1281),c_Groups_Ozero__class_Ozero(U_1281)),U_1284))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1281),c_Groups_Ozero__class_Ozero(U_1281)),U_1282))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1281),U_1284),U_1285))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1281),U_1282),U_1283))
      | ~ class_Rings_Oordered__semiring(U_1281) ),
    inference(definitional_conversion,[status(esa)],[f_378_2]) ).

cnf(f_378_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1281),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1281),U_1282),U_1284)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1281),U_1283),U_1285)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1281),c_Groups_Ozero__class_Ozero(U_1281)),U_1284))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1281),c_Groups_Ozero__class_Ozero(U_1281)),U_1282))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1281),U_1284),U_1285))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1281),U_1282),U_1283))
    | ~ class_Rings_Oordered__semiring(U_1281) ),
    inference(clausify,[status(thm)],[f_378_3]) ).

fof(f_379_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_379_2,plain,
    ! [U_1289,U_1288,U_1287,U_1286] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1286),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1286),U_1289),U_1288)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1286),U_1289),U_1287)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1286),U_1289),c_Groups_Ozero__class_Ozero(U_1286)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1286),U_1287),U_1288))
      | ~ class_Rings_Oordered__ring(U_1286) ),
    inference(variable_rename,[status(thm)],[f_379_1]) ).

fof(f_379_3,plain,
    ! [U_1288,U_1286,U_1289,U_1287] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1286),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1286),U_1289),U_1288)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1286),U_1289),U_1287)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1286),U_1289),c_Groups_Ozero__class_Ozero(U_1286)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1286),U_1287),U_1288))
      | ~ class_Rings_Oordered__ring(U_1286) ),
    inference(definitional_conversion,[status(esa)],[f_379_2]) ).

cnf(f_379_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1286),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1286),U_1289),U_1288)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1286),U_1289),U_1287)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1286),U_1289),c_Groups_Ozero__class_Ozero(U_1286)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1286),U_1287),U_1288))
    | ~ class_Rings_Oordered__ring(U_1286) ),
    inference(clausify,[status(thm)],[f_379_3]) ).

fof(f_380_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_380_2,plain,
    ! [U_1293,U_1292,U_1291,U_1290] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1290),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1290),U_1292),U_1293)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1290),U_1291),U_1293)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1290),U_1293),c_Groups_Ozero__class_Ozero(U_1290)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1290),U_1291),U_1292))
      | ~ class_Rings_Oordered__ring(U_1290) ),
    inference(variable_rename,[status(thm)],[f_380_1]) ).

fof(f_380_3,plain,
    ! [U_1290,U_1291,U_1292,U_1293] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1290),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1290),U_1292),U_1293)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1290),U_1291),U_1293)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1290),U_1293),c_Groups_Ozero__class_Ozero(U_1290)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1290),U_1291),U_1292))
      | ~ class_Rings_Oordered__ring(U_1290) ),
    inference(definitional_conversion,[status(esa)],[f_380_2]) ).

cnf(f_380_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1290),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1290),U_1292),U_1293)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1290),U_1291),U_1293)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1290),U_1293),c_Groups_Ozero__class_Ozero(U_1290)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1290),U_1291),U_1292))
    | ~ class_Rings_Oordered__ring(U_1290) ),
    inference(clausify,[status(thm)],[f_380_3]) ).

fof(f_381_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_381_2,plain,
    ! [U_1297,U_1296,U_1295,U_1294] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1294),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1294),U_1297),U_1295)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1294),U_1297),U_1296)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1294),c_Groups_Ozero__class_Ozero(U_1294)),U_1297))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1294),U_1295),U_1296))
      | ~ class_Rings_Oordered__comm__semiring(U_1294) ),
    inference(variable_rename,[status(thm)],[f_381_1]) ).

fof(f_381_3,plain,
    ! [U_1294,U_1295,U_1296,U_1297] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1294),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1294),U_1297),U_1295)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1294),U_1297),U_1296)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1294),c_Groups_Ozero__class_Ozero(U_1294)),U_1297))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1294),U_1295),U_1296))
      | ~ class_Rings_Oordered__comm__semiring(U_1294) ),
    inference(definitional_conversion,[status(esa)],[f_381_2]) ).

cnf(f_381_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1294),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1294),U_1297),U_1295)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1294),U_1297),U_1296)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1294),c_Groups_Ozero__class_Ozero(U_1294)),U_1297))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1294),U_1295),U_1296))
    | ~ class_Rings_Oordered__comm__semiring(U_1294) ),
    inference(clausify,[status(thm)],[f_381_3]) ).

fof(f_382_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_382_2,plain,
    ! [U_1301,U_1300,U_1299,U_1298] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1298),U_1301),U_1299)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1298),U_1301),U_1300)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1298),c_Groups_Ozero__class_Ozero(U_1298)),U_1301))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1298),U_1299),U_1300))
      | ~ class_Rings_Oordered__semiring(U_1298) ),
    inference(variable_rename,[status(thm)],[f_382_1]) ).

fof(f_382_3,plain,
    ! [U_1298,U_1299,U_1300,U_1301] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1298),U_1301),U_1299)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1298),U_1301),U_1300)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1298),c_Groups_Ozero__class_Ozero(U_1298)),U_1301))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1298),U_1299),U_1300))
      | ~ class_Rings_Oordered__semiring(U_1298) ),
    inference(definitional_conversion,[status(esa)],[f_382_2]) ).

cnf(f_382_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1298),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1298),U_1301),U_1299)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1298),U_1301),U_1300)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1298),c_Groups_Ozero__class_Ozero(U_1298)),U_1301))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1298),U_1299),U_1300))
    | ~ class_Rings_Oordered__semiring(U_1298) ),
    inference(clausify,[status(thm)],[f_382_3]) ).

fof(f_383_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_383_2,plain,
    ! [U_1305,U_1304,U_1303,U_1302] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1302),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1302),U_1303),U_1305)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1302),U_1304),U_1305)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1302),c_Groups_Ozero__class_Ozero(U_1302)),U_1305))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1302),U_1303),U_1304))
      | ~ class_Rings_Oordered__semiring(U_1302) ),
    inference(variable_rename,[status(thm)],[f_383_1]) ).

fof(f_383_3,plain,
    ! [U_1302,U_1303,U_1304,U_1305] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1302),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1302),U_1303),U_1305)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1302),U_1304),U_1305)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1302),c_Groups_Ozero__class_Ozero(U_1302)),U_1305))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1302),U_1303),U_1304))
      | ~ class_Rings_Oordered__semiring(U_1302) ),
    inference(definitional_conversion,[status(esa)],[f_383_2]) ).

cnf(f_383_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1302),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1302),U_1303),U_1305)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1302),U_1304),U_1305)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1302),c_Groups_Ozero__class_Ozero(U_1302)),U_1305))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1302),U_1303),U_1304))
    | ~ class_Rings_Oordered__semiring(U_1302) ),
    inference(clausify,[status(thm)],[f_383_3]) ).

fof(f_384_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_384_2,plain,
    ! [U_1308,U_1307,U_1306] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1306),c_Groups_Ozero__class_Ozero(U_1306)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1306),U_1307),U_1308)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1306),U_1308),c_Groups_Ozero__class_Ozero(U_1306)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1306),U_1307),c_Groups_Ozero__class_Ozero(U_1306)))
      | ~ class_Rings_Oordered__ring(U_1306) ),
    inference(variable_rename,[status(thm)],[f_384_1]) ).

fof(f_384_3,plain,
    ! [U_1307,U_1306,U_1308] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1306),c_Groups_Ozero__class_Ozero(U_1306)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1306),U_1307),U_1308)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1306),U_1308),c_Groups_Ozero__class_Ozero(U_1306)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1306),U_1307),c_Groups_Ozero__class_Ozero(U_1306)))
      | ~ class_Rings_Oordered__ring(U_1306) ),
    inference(definitional_conversion,[status(esa)],[f_384_2]) ).

cnf(f_384_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1306),c_Groups_Ozero__class_Ozero(U_1306)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1306),U_1307),U_1308)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1306),U_1308),c_Groups_Ozero__class_Ozero(U_1306)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1306),U_1307),c_Groups_Ozero__class_Ozero(U_1306)))
    | ~ class_Rings_Oordered__ring(U_1306) ),
    inference(clausify,[status(thm)],[f_384_3]) ).

fof(f_385_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_385_2,plain,
    ! [U_1311,U_1310,U_1309] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1309),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1309),U_1310),U_1311)),c_Groups_Ozero__class_Ozero(U_1309)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1309),c_Groups_Ozero__class_Ozero(U_1309)),U_1311))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1309),U_1310),c_Groups_Ozero__class_Ozero(U_1309)))
      | ~ class_Rings_Oordered__cancel__semiring(U_1309) ),
    inference(variable_rename,[status(thm)],[f_385_1]) ).

fof(f_385_3,plain,
    ! [U_1309,U_1310,U_1311] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1309),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1309),U_1310),U_1311)),c_Groups_Ozero__class_Ozero(U_1309)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1309),c_Groups_Ozero__class_Ozero(U_1309)),U_1311))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1309),U_1310),c_Groups_Ozero__class_Ozero(U_1309)))
      | ~ class_Rings_Oordered__cancel__semiring(U_1309) ),
    inference(definitional_conversion,[status(esa)],[f_385_2]) ).

cnf(f_385_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1309),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1309),U_1310),U_1311)),c_Groups_Ozero__class_Ozero(U_1309)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1309),c_Groups_Ozero__class_Ozero(U_1309)),U_1311))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1309),U_1310),c_Groups_Ozero__class_Ozero(U_1309)))
    | ~ class_Rings_Oordered__cancel__semiring(U_1309) ),
    inference(clausify,[status(thm)],[f_385_3]) ).

fof(f_386_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_386_2,plain,
    ! [U_1314,U_1313,U_1312] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1312),U_1314),U_1313)),c_Groups_Ozero__class_Ozero(U_1312)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1312),U_1314),c_Groups_Ozero__class_Ozero(U_1312)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1312),c_Groups_Ozero__class_Ozero(U_1312)),U_1313))
      | ~ class_Rings_Oordered__cancel__semiring(U_1312) ),
    inference(variable_rename,[status(thm)],[f_386_1]) ).

fof(f_386_3,plain,
    ! [U_1312,U_1313,U_1314] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1312),U_1314),U_1313)),c_Groups_Ozero__class_Ozero(U_1312)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1312),U_1314),c_Groups_Ozero__class_Ozero(U_1312)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1312),c_Groups_Ozero__class_Ozero(U_1312)),U_1313))
      | ~ class_Rings_Oordered__cancel__semiring(U_1312) ),
    inference(definitional_conversion,[status(esa)],[f_386_2]) ).

cnf(f_386_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1312),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1312),U_1314),U_1313)),c_Groups_Ozero__class_Ozero(U_1312)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1312),U_1314),c_Groups_Ozero__class_Ozero(U_1312)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1312),c_Groups_Ozero__class_Ozero(U_1312)),U_1313))
    | ~ class_Rings_Oordered__cancel__semiring(U_1312) ),
    inference(clausify,[status(thm)],[f_386_3]) ).

fof(f_387_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_387_2,plain,
    ! [U_1317,U_1316,U_1315] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1315),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1315),U_1316),U_1317)),c_Groups_Ozero__class_Ozero(U_1315)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1315),U_1317),c_Groups_Ozero__class_Ozero(U_1315)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1315),c_Groups_Ozero__class_Ozero(U_1315)),U_1316))
      | ~ class_Rings_Oordered__cancel__semiring(U_1315) ),
    inference(variable_rename,[status(thm)],[f_387_1]) ).

fof(f_387_3,plain,
    ! [U_1315,U_1316,U_1317] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1315),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1315),U_1316),U_1317)),c_Groups_Ozero__class_Ozero(U_1315)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1315),U_1317),c_Groups_Ozero__class_Ozero(U_1315)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1315),c_Groups_Ozero__class_Ozero(U_1315)),U_1316))
      | ~ class_Rings_Oordered__cancel__semiring(U_1315) ),
    inference(definitional_conversion,[status(esa)],[f_387_2]) ).

cnf(f_387_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1315),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1315),U_1316),U_1317)),c_Groups_Ozero__class_Ozero(U_1315)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1315),U_1317),c_Groups_Ozero__class_Ozero(U_1315)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1315),c_Groups_Ozero__class_Ozero(U_1315)),U_1316))
    | ~ class_Rings_Oordered__cancel__semiring(U_1315) ),
    inference(clausify,[status(thm)],[f_387_3]) ).

fof(f_388_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_388_2,plain,
    ! [U_1320,U_1319,U_1318] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1318),c_Groups_Ozero__class_Ozero(U_1318)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1318),U_1319),U_1320)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1318),c_Groups_Ozero__class_Ozero(U_1318)),U_1320))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1318),c_Groups_Ozero__class_Ozero(U_1318)),U_1319))
      | ~ class_Rings_Oordered__cancel__semiring(U_1318) ),
    inference(variable_rename,[status(thm)],[f_388_1]) ).

fof(f_388_3,plain,
    ! [U_1319,U_1318,U_1320] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1318),c_Groups_Ozero__class_Ozero(U_1318)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1318),U_1319),U_1320)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1318),c_Groups_Ozero__class_Ozero(U_1318)),U_1320))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1318),c_Groups_Ozero__class_Ozero(U_1318)),U_1319))
      | ~ class_Rings_Oordered__cancel__semiring(U_1318) ),
    inference(definitional_conversion,[status(esa)],[f_388_2]) ).

cnf(f_388_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1318),c_Groups_Ozero__class_Ozero(U_1318)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1318),U_1319),U_1320)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1318),c_Groups_Ozero__class_Ozero(U_1318)),U_1320))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1318),c_Groups_Ozero__class_Ozero(U_1318)),U_1319))
    | ~ class_Rings_Oordered__cancel__semiring(U_1318) ),
    inference(clausify,[status(thm)],[f_388_3]) ).

fof(f_389_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_389_2,plain,
    ! [U_1323,U_1322,U_1321] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1321),U_1322),U_1323)),c_Groups_Ozero__class_Ozero(U_1321)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),c_Groups_Ozero__class_Ozero(U_1321)),U_1323))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),U_1322),c_Groups_Ozero__class_Ozero(U_1321))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),U_1323),c_Groups_Ozero__class_Ozero(U_1321)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),c_Groups_Ozero__class_Ozero(U_1321)),U_1322)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),c_Groups_Ozero__class_Ozero(U_1321)),U_1323))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),U_1322),c_Groups_Ozero__class_Ozero(U_1321))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),U_1323),c_Groups_Ozero__class_Ozero(U_1321)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),c_Groups_Ozero__class_Ozero(U_1321)),U_1322)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1321),U_1322),U_1323)),c_Groups_Ozero__class_Ozero(U_1321))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_1321) ),
    inference(variable_rename,[status(thm)],[f_389_1]) ).

fof(f_389_3,plain,
    ( ! [U_1321,U_1322,U_1323] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),c_Groups_Ozero__class_Ozero(U_1321)),U_1323))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),U_1322),c_Groups_Ozero__class_Ozero(U_1321)))
        | ~ sP119(U_1321,U_1322,U_1323) )
    & ! [U_1321,U_1322,U_1323] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),U_1323),c_Groups_Ozero__class_Ozero(U_1321)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),c_Groups_Ozero__class_Ozero(U_1321)),U_1322))
        | ~ sP119(U_1321,U_1322,U_1323) )
    & ! [U_1321,U_1322,U_1323] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),c_Groups_Ozero__class_Ozero(U_1321)),U_1323))
        | ~ sP118(U_1321,U_1322,U_1323) )
    & ! [U_1321,U_1322,U_1323] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),U_1322),c_Groups_Ozero__class_Ozero(U_1321)))
        | ~ sP118(U_1321,U_1322,U_1323) )
    & ! [U_1321,U_1322,U_1323] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),U_1323),c_Groups_Ozero__class_Ozero(U_1321)))
        | ~ sP117(U_1321,U_1322,U_1323) )
    & ! [U_1321,U_1322,U_1323] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),c_Groups_Ozero__class_Ozero(U_1321)),U_1322))
        | ~ sP117(U_1321,U_1322,U_1323) )
    & ! [U_1321,U_1322,U_1323] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1321),U_1322),U_1323)),c_Groups_Ozero__class_Ozero(U_1321)))
        | sP119(U_1321,U_1322,U_1323)
        | ~ sP120(U_1321,U_1322,U_1323) )
    & ! [U_1321,U_1322,U_1323] :
        ( sP118(U_1321,U_1322,U_1323)
        | sP117(U_1321,U_1322,U_1323)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1321),U_1322),U_1323)),c_Groups_Ozero__class_Ozero(U_1321)))
        | ~ sP120(U_1321,U_1322,U_1323) )
    & ! [U_1321,U_1322,U_1323] :
        ( sP120(U_1321,U_1322,U_1323)
        | ~ class_Rings_Olinordered__ring__strict(U_1321) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP117,sP118,sP119,sP120])],[f_389_2]) ).

cnf(f_389_4,plain,
    ( sP120(U_1321,U_1322,U_1323)
    | ~ class_Rings_Olinordered__ring__strict(U_1321) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

cnf(f_389_5,plain,
    ( sP118(U_1321,U_1322,U_1323)
    | sP117(U_1321,U_1322,U_1323)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1321),U_1322),U_1323)),c_Groups_Ozero__class_Ozero(U_1321)))
    | ~ sP120(U_1321,U_1322,U_1323) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

cnf(f_389_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1321),U_1322),U_1323)),c_Groups_Ozero__class_Ozero(U_1321)))
    | sP119(U_1321,U_1322,U_1323)
    | ~ sP120(U_1321,U_1322,U_1323) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

cnf(f_389_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),c_Groups_Ozero__class_Ozero(U_1321)),U_1322))
    | ~ sP117(U_1321,U_1322,U_1323) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

cnf(f_389_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),U_1323),c_Groups_Ozero__class_Ozero(U_1321)))
    | ~ sP117(U_1321,U_1322,U_1323) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

cnf(f_389_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),U_1322),c_Groups_Ozero__class_Ozero(U_1321)))
    | ~ sP118(U_1321,U_1322,U_1323) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

cnf(f_389_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),c_Groups_Ozero__class_Ozero(U_1321)),U_1323))
    | ~ sP118(U_1321,U_1322,U_1323) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

cnf(f_389_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),U_1323),c_Groups_Ozero__class_Ozero(U_1321)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),c_Groups_Ozero__class_Ozero(U_1321)),U_1322))
    | ~ sP119(U_1321,U_1322,U_1323) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

cnf(f_389_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),c_Groups_Ozero__class_Ozero(U_1321)),U_1323))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1321),U_1322),c_Groups_Ozero__class_Ozero(U_1321)))
    | ~ sP119(U_1321,U_1322,U_1323) ),
    inference(clausify,[status(thm)],[f_389_3]) ).

fof(f_390_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_390_2,plain,
    ! [U_1326,U_1325,U_1324] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),c_Groups_Ozero__class_Ozero(U_1324)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1324),U_1325),U_1326)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),U_1326),c_Groups_Ozero__class_Ozero(U_1324)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),U_1325),c_Groups_Ozero__class_Ozero(U_1324))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),c_Groups_Ozero__class_Ozero(U_1324)),U_1326))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),c_Groups_Ozero__class_Ozero(U_1324)),U_1325)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),U_1326),c_Groups_Ozero__class_Ozero(U_1324)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),U_1325),c_Groups_Ozero__class_Ozero(U_1324))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),c_Groups_Ozero__class_Ozero(U_1324)),U_1326))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),c_Groups_Ozero__class_Ozero(U_1324)),U_1325)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),c_Groups_Ozero__class_Ozero(U_1324)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1324),U_1325),U_1326))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_1324) ),
    inference(variable_rename,[status(thm)],[f_390_1]) ).

fof(f_390_3,plain,
    ( ! [U_1324,U_1326,U_1325] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),U_1326),c_Groups_Ozero__class_Ozero(U_1324)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),U_1325),c_Groups_Ozero__class_Ozero(U_1324)))
        | ~ sP123(U_1324,U_1326,U_1325) )
    & ! [U_1324,U_1326,U_1325] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),c_Groups_Ozero__class_Ozero(U_1324)),U_1326))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),c_Groups_Ozero__class_Ozero(U_1324)),U_1325))
        | ~ sP123(U_1324,U_1326,U_1325) )
    & ! [U_1324,U_1326,U_1325] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),U_1326),c_Groups_Ozero__class_Ozero(U_1324)))
        | ~ sP122(U_1324,U_1326,U_1325) )
    & ! [U_1324,U_1326,U_1325] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),U_1325),c_Groups_Ozero__class_Ozero(U_1324)))
        | ~ sP122(U_1324,U_1326,U_1325) )
    & ! [U_1324,U_1326,U_1325] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),c_Groups_Ozero__class_Ozero(U_1324)),U_1326))
        | ~ sP121(U_1324,U_1326,U_1325) )
    & ! [U_1324,U_1326,U_1325] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),c_Groups_Ozero__class_Ozero(U_1324)),U_1325))
        | ~ sP121(U_1324,U_1326,U_1325) )
    & ! [U_1324,U_1326,U_1325] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),c_Groups_Ozero__class_Ozero(U_1324)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1324),U_1325),U_1326)))
        | sP123(U_1324,U_1326,U_1325)
        | ~ sP124(U_1324,U_1326,U_1325) )
    & ! [U_1324,U_1326,U_1325] :
        ( sP122(U_1324,U_1326,U_1325)
        | sP121(U_1324,U_1326,U_1325)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),c_Groups_Ozero__class_Ozero(U_1324)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1324),U_1325),U_1326)))
        | ~ sP124(U_1324,U_1326,U_1325) )
    & ! [U_1324,U_1326,U_1325] :
        ( sP124(U_1324,U_1326,U_1325)
        | ~ class_Rings_Olinordered__ring__strict(U_1324) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP121,sP122,sP123,sP124])],[f_390_2]) ).

cnf(f_390_4,plain,
    ( sP124(U_1324,U_1326,U_1325)
    | ~ class_Rings_Olinordered__ring__strict(U_1324) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

cnf(f_390_5,plain,
    ( sP122(U_1324,U_1326,U_1325)
    | sP121(U_1324,U_1326,U_1325)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),c_Groups_Ozero__class_Ozero(U_1324)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1324),U_1325),U_1326)))
    | ~ sP124(U_1324,U_1326,U_1325) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

cnf(f_390_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),c_Groups_Ozero__class_Ozero(U_1324)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1324),U_1325),U_1326)))
    | sP123(U_1324,U_1326,U_1325)
    | ~ sP124(U_1324,U_1326,U_1325) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

cnf(f_390_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),c_Groups_Ozero__class_Ozero(U_1324)),U_1325))
    | ~ sP121(U_1324,U_1326,U_1325) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

cnf(f_390_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),c_Groups_Ozero__class_Ozero(U_1324)),U_1326))
    | ~ sP121(U_1324,U_1326,U_1325) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

cnf(f_390_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),U_1325),c_Groups_Ozero__class_Ozero(U_1324)))
    | ~ sP122(U_1324,U_1326,U_1325) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

cnf(f_390_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),U_1326),c_Groups_Ozero__class_Ozero(U_1324)))
    | ~ sP122(U_1324,U_1326,U_1325) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

cnf(f_390_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),c_Groups_Ozero__class_Ozero(U_1324)),U_1326))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),c_Groups_Ozero__class_Ozero(U_1324)),U_1325))
    | ~ sP123(U_1324,U_1326,U_1325) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

cnf(f_390_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),U_1326),c_Groups_Ozero__class_Ozero(U_1324)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1324),U_1325),c_Groups_Ozero__class_Ozero(U_1324)))
    | ~ sP123(U_1324,U_1326,U_1325) ),
    inference(clausify,[status(thm)],[f_390_3]) ).

fof(f_391_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_391_2,plain,
    ! [U_1328,U_1327] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1327),c_Groups_Ozero__class_Ozero(U_1327)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1327),U_1328),U_1328)))
      | ~ class_Rings_Olinordered__ring(U_1327) ),
    inference(variable_rename,[status(thm)],[f_391_1]) ).

fof(f_391_3,plain,
    ! [U_1328,U_1327] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1327),c_Groups_Ozero__class_Ozero(U_1327)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1327),U_1328),U_1328)))
      | ~ class_Rings_Olinordered__ring(U_1327) ),
    inference(definitional_conversion,[status(esa)],[f_391_2]) ).

cnf(f_391_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1327),c_Groups_Ozero__class_Ozero(U_1327)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1327),U_1328),U_1328)))
    | ~ class_Rings_Olinordered__ring(U_1327) ),
    inference(clausify,[status(thm)],[f_391_3]) ).

fof(f_392_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_392_2,plain,
    ! [U_1330,U_1329] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1329),c_Groups_Ozero__class_Ozero(U_1329)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1329),U_1330)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1329),U_1330),c_Groups_Ozero__class_Ozero(U_1329))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1329),U_1330),c_Groups_Ozero__class_Ozero(U_1329)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1329),c_Groups_Ozero__class_Ozero(U_1329)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1329),U_1330))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1329) ),
    inference(variable_rename,[status(thm)],[f_392_1]) ).

fof(f_392_3,plain,
    ( ! [U_1329,U_1330] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1329),c_Groups_Ozero__class_Ozero(U_1329)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1329),U_1330)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1329),U_1330),c_Groups_Ozero__class_Ozero(U_1329)))
        | ~ sP125(U_1329,U_1330) )
    & ! [U_1329,U_1330] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1329),U_1330),c_Groups_Ozero__class_Ozero(U_1329)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1329),c_Groups_Ozero__class_Ozero(U_1329)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1329),U_1330)))
        | ~ sP125(U_1329,U_1330) )
    & ! [U_1329,U_1330] :
        ( sP125(U_1329,U_1330)
        | ~ class_Groups_Oordered__ab__group__add(U_1329) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP125])],[f_392_2]) ).

cnf(f_392_4,plain,
    ( sP125(U_1329,U_1330)
    | ~ class_Groups_Oordered__ab__group__add(U_1329) ),
    inference(clausify,[status(thm)],[f_392_3]) ).

cnf(f_392_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1329),U_1330),c_Groups_Ozero__class_Ozero(U_1329)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1329),c_Groups_Ozero__class_Ozero(U_1329)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1329),U_1330)))
    | ~ sP125(U_1329,U_1330) ),
    inference(clausify,[status(thm)],[f_392_3]) ).

cnf(f_392_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1329),c_Groups_Ozero__class_Ozero(U_1329)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1329),U_1330)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1329),U_1330),c_Groups_Ozero__class_Ozero(U_1329)))
    | ~ sP125(U_1329,U_1330) ),
    inference(clausify,[status(thm)],[f_392_3]) ).

fof(f_393_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_393_2,plain,
    ! [U_1332,U_1331] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1331),U_1332),hAPP(c_Groups_Ouminus__class_Ouminus(U_1331),U_1332)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1331),U_1332),c_Groups_Ozero__class_Ozero(U_1331))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1331),U_1332),c_Groups_Ozero__class_Ozero(U_1331)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1331),U_1332),hAPP(c_Groups_Ouminus__class_Ouminus(U_1331),U_1332))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1331) ),
    inference(variable_rename,[status(thm)],[f_393_1]) ).

fof(f_393_3,plain,
    ( ! [U_1332,U_1331] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1331),U_1332),hAPP(c_Groups_Ouminus__class_Ouminus(U_1331),U_1332)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1331),U_1332),c_Groups_Ozero__class_Ozero(U_1331)))
        | ~ sP126(U_1332,U_1331) )
    & ! [U_1332,U_1331] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1331),U_1332),c_Groups_Ozero__class_Ozero(U_1331)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1331),U_1332),hAPP(c_Groups_Ouminus__class_Ouminus(U_1331),U_1332)))
        | ~ sP126(U_1332,U_1331) )
    & ! [U_1332,U_1331] :
        ( sP126(U_1332,U_1331)
        | ~ class_Groups_Olinordered__ab__group__add(U_1331) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP126])],[f_393_2]) ).

cnf(f_393_4,plain,
    ( sP126(U_1332,U_1331)
    | ~ class_Groups_Olinordered__ab__group__add(U_1331) ),
    inference(clausify,[status(thm)],[f_393_3]) ).

cnf(f_393_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1331),U_1332),c_Groups_Ozero__class_Ozero(U_1331)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1331),U_1332),hAPP(c_Groups_Ouminus__class_Ouminus(U_1331),U_1332)))
    | ~ sP126(U_1332,U_1331) ),
    inference(clausify,[status(thm)],[f_393_3]) ).

cnf(f_393_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1331),U_1332),hAPP(c_Groups_Ouminus__class_Ouminus(U_1331),U_1332)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1331),U_1332),c_Groups_Ozero__class_Ozero(U_1331)))
    | ~ sP126(U_1332,U_1331) ),
    inference(clausify,[status(thm)],[f_393_3]) ).

fof(f_394_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_394_2,plain,
    ! [U_1334,U_1333] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1333),hAPP(c_Groups_Ouminus__class_Ouminus(U_1333),U_1334)),c_Groups_Ozero__class_Ozero(U_1333)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1333),c_Groups_Ozero__class_Ozero(U_1333)),U_1334)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1333),c_Groups_Ozero__class_Ozero(U_1333)),U_1334))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1333),hAPP(c_Groups_Ouminus__class_Ouminus(U_1333),U_1334)),c_Groups_Ozero__class_Ozero(U_1333))) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_1333) ),
    inference(variable_rename,[status(thm)],[f_394_1]) ).

fof(f_394_3,plain,
    ( ! [U_1334,U_1333] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1333),hAPP(c_Groups_Ouminus__class_Ouminus(U_1333),U_1334)),c_Groups_Ozero__class_Ozero(U_1333)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1333),c_Groups_Ozero__class_Ozero(U_1333)),U_1334))
        | ~ sP127(U_1334,U_1333) )
    & ! [U_1334,U_1333] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1333),c_Groups_Ozero__class_Ozero(U_1333)),U_1334))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1333),hAPP(c_Groups_Ouminus__class_Ouminus(U_1333),U_1334)),c_Groups_Ozero__class_Ozero(U_1333)))
        | ~ sP127(U_1334,U_1333) )
    & ! [U_1334,U_1333] :
        ( sP127(U_1334,U_1333)
        | ~ class_Groups_Oordered__ab__group__add(U_1333) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP127])],[f_394_2]) ).

cnf(f_394_4,plain,
    ( sP127(U_1334,U_1333)
    | ~ class_Groups_Oordered__ab__group__add(U_1333) ),
    inference(clausify,[status(thm)],[f_394_3]) ).

cnf(f_394_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1333),c_Groups_Ozero__class_Ozero(U_1333)),U_1334))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1333),hAPP(c_Groups_Ouminus__class_Ouminus(U_1333),U_1334)),c_Groups_Ozero__class_Ozero(U_1333)))
    | ~ sP127(U_1334,U_1333) ),
    inference(clausify,[status(thm)],[f_394_3]) ).

cnf(f_394_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1333),hAPP(c_Groups_Ouminus__class_Ouminus(U_1333),U_1334)),c_Groups_Ozero__class_Ozero(U_1333)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1333),c_Groups_Ozero__class_Ozero(U_1333)),U_1334))
    | ~ sP127(U_1334,U_1333) ),
    inference(clausify,[status(thm)],[f_394_3]) ).

fof(f_395_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_395_2,plain,
    ! [U_1336,U_1335] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1335),hAPP(c_Groups_Ouminus__class_Ouminus(U_1335),U_1336)),U_1336))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1335),c_Groups_Ozero__class_Ozero(U_1335)),U_1336)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1335),c_Groups_Ozero__class_Ozero(U_1335)),U_1336))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1335),hAPP(c_Groups_Ouminus__class_Ouminus(U_1335),U_1336)),U_1336)) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1335) ),
    inference(variable_rename,[status(thm)],[f_395_1]) ).

fof(f_395_3,plain,
    ( ! [U_1335,U_1336] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1335),hAPP(c_Groups_Ouminus__class_Ouminus(U_1335),U_1336)),U_1336))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1335),c_Groups_Ozero__class_Ozero(U_1335)),U_1336))
        | ~ sP128(U_1335,U_1336) )
    & ! [U_1335,U_1336] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1335),c_Groups_Ozero__class_Ozero(U_1335)),U_1336))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1335),hAPP(c_Groups_Ouminus__class_Ouminus(U_1335),U_1336)),U_1336))
        | ~ sP128(U_1335,U_1336) )
    & ! [U_1335,U_1336] :
        ( sP128(U_1335,U_1336)
        | ~ class_Groups_Olinordered__ab__group__add(U_1335) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP128])],[f_395_2]) ).

cnf(f_395_4,plain,
    ( sP128(U_1335,U_1336)
    | ~ class_Groups_Olinordered__ab__group__add(U_1335) ),
    inference(clausify,[status(thm)],[f_395_3]) ).

cnf(f_395_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1335),c_Groups_Ozero__class_Ozero(U_1335)),U_1336))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1335),hAPP(c_Groups_Ouminus__class_Ouminus(U_1335),U_1336)),U_1336))
    | ~ sP128(U_1335,U_1336) ),
    inference(clausify,[status(thm)],[f_395_3]) ).

cnf(f_395_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1335),hAPP(c_Groups_Ouminus__class_Ouminus(U_1335),U_1336)),U_1336))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1335),c_Groups_Ozero__class_Ozero(U_1335)),U_1336))
    | ~ sP128(U_1335,U_1336) ),
    inference(clausify,[status(thm)],[f_395_3]) ).

fof(f_396_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_396_2,plain,
    ! [U_1338,U_1337] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1337),c_Groups_Ozero__class_Ozero(U_1337)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1337),U_1338)))
      | ~ class_Rings_Olinordered__semidom(U_1337) ),
    inference(variable_rename,[status(thm)],[f_396_1]) ).

fof(f_396_3,plain,
    ! [U_1337,U_1338] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1337),c_Groups_Ozero__class_Ozero(U_1337)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1337),U_1338)))
      | ~ class_Rings_Olinordered__semidom(U_1337) ),
    inference(definitional_conversion,[status(esa)],[f_396_2]) ).

cnf(f_396_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1337),c_Groups_Ozero__class_Ozero(U_1337)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1337),U_1338)))
    | ~ class_Rings_Olinordered__semidom(U_1337) ),
    inference(clausify,[status(thm)],[f_396_3]) ).

fof(f_397_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_397_2,plain,
    ! [U_1340,U_1339] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1339),c_Groups_Ozero__class_Ozero(U_1339)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1339),U_1340)))
      | ~ class_Rings_Olinordered__semidom(U_1339) ),
    inference(variable_rename,[status(thm)],[f_397_1]) ).

fof(f_397_3,plain,
    ! [U_1339,U_1340] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1339),c_Groups_Ozero__class_Ozero(U_1339)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1339),U_1340)))
      | ~ class_Rings_Olinordered__semidom(U_1339) ),
    inference(definitional_conversion,[status(esa)],[f_397_2]) ).

cnf(f_397_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1339),c_Groups_Ozero__class_Ozero(U_1339)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1339),U_1340)))
    | ~ class_Rings_Olinordered__semidom(U_1339) ),
    inference(clausify,[status(thm)],[f_397_3]) ).

fof(f_398_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_398_2,plain,
    ! [U_1341] : 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_1341))),
    inference(variable_rename,[status(thm)],[f_398_1]) ).

fof(f_398_3,plain,
    ! [U_1341] : 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_1341))),
    inference(definitional_conversion,[status(esa)],[f_398_2]) ).

cnf(f_398_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_1341))),
    inference(clausify,[status(thm)],[f_398_3]) ).

fof(f_399_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_399_2,plain,
    ! [U_1342] : 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_1342))),
    inference(variable_rename,[status(thm)],[f_399_1]) ).

fof(f_399_3,plain,
    ! [U_1342] : 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_1342))),
    inference(definitional_conversion,[status(esa)],[f_399_2]) ).

cnf(f_399_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_1342))),
    inference(clausify,[status(thm)],[f_399_3]) ).

fof(f_400_1,plain,
    ! [V_Pa_2] :
      ( ( ? [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) )
      & ( ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x)))
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_400_2,plain,
    ! [U_1347] :
      ( ( ? [U_1346] :
            ( hBOOL(hAPP(U_1347,U_1346))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1346)) )
        | ! [U_1345] : ~ hBOOL(hAPP(U_1347,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1345))) )
      & ( ? [U_1344] : hBOOL(hAPP(U_1347,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1344)))
        | ! [U_1343] :
            ( ~ hBOOL(hAPP(U_1347,U_1343))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1343)) ) ) ),
    inference(variable_rename,[status(thm)],[f_400_1]) ).

fof(f_400_3,plain,
    ( ! [U_1349] :
        ( ? [U_1346] :
            ( hBOOL(hAPP(U_1349,U_1346))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1346)) )
        | ! [U_1345] : ~ hBOOL(hAPP(U_1349,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1345))) )
    & ! [U_1348] :
        ( ? [U_1344] : hBOOL(hAPP(U_1348,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1344)))
        | ! [U_1343] :
            ( ~ hBOOL(hAPP(U_1348,U_1343))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1343)) ) ) ),
    inference(miniscope,[status(thm)],[f_400_2]) ).

fof(f_400_4,plain,
    ( ! [U_1349] :
        ( ? [U_1346] :
            ( hBOOL(hAPP(U_1349,U_1346))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1346)) )
        | ! [U_1345] : ~ hBOOL(hAPP(U_1349,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1345))) )
    & ! [U_1348] :
        ( hBOOL(hAPP(U_1348,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK30(U_1348))))
        | ! [U_1343] :
            ( ~ hBOOL(hAPP(U_1348,U_1343))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1343)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK30]),skolemize(U_1344,sK30(U_1348))],[f_400_3]) ).

fof(f_400_5,plain,
    ( ! [U_1349] :
        ( ( hBOOL(hAPP(U_1349,sK31(U_1349)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK31(U_1349))) )
        | ! [U_1345] : ~ hBOOL(hAPP(U_1349,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1345))) )
    & ! [U_1348] :
        ( hBOOL(hAPP(U_1348,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK30(U_1348))))
        | ! [U_1343] :
            ( ~ hBOOL(hAPP(U_1348,U_1343))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1343)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(U_1346,sK31(U_1349))],[f_400_4]) ).

fof(f_400_6,plain,
    ( ! [U_1349] :
        ( hBOOL(hAPP(U_1349,sK31(U_1349)))
        | ~ sP129(U_1349) )
    & ! [U_1349] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK31(U_1349)))
        | ~ sP129(U_1349) )
    & ! [U_1345,U_1349] :
        ( sP129(U_1349)
        | ~ hBOOL(hAPP(U_1349,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1345))) )
    & ! [U_1348,U_1343] :
        ( hBOOL(hAPP(U_1348,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK30(U_1348))))
        | ~ hBOOL(hAPP(U_1348,U_1343))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1343)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP129])],[f_400_5]) ).

cnf(f_400_7,plain,
    ( hBOOL(hAPP(U_1348,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK30(U_1348))))
    | ~ hBOOL(hAPP(U_1348,U_1343))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1343)) ),
    inference(clausify,[status(thm)],[f_400_6]) ).

cnf(f_400_8,plain,
    ( sP129(U_1349)
    | ~ hBOOL(hAPP(U_1349,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1345))) ),
    inference(clausify,[status(thm)],[f_400_6]) ).

cnf(f_400_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK31(U_1349)))
    | ~ sP129(U_1349) ),
    inference(clausify,[status(thm)],[f_400_6]) ).

cnf(f_400_10,plain,
    ( hBOOL(hAPP(U_1349,sK31(U_1349)))
    | ~ sP129(U_1349) ),
    inference(clausify,[status(thm)],[f_400_6]) ).

fof(f_401_1,plain,
    ! [V_Pa_2] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) )
      & ( ! [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x)))
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_401_2,plain,
    ! [U_1354] :
      ( ( ! [U_1353] :
            ( hBOOL(hAPP(U_1354,U_1353))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1353)) )
        | ? [U_1352] : ~ hBOOL(hAPP(U_1354,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1352))) )
      & ( ! [U_1351] : hBOOL(hAPP(U_1354,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1351)))
        | ? [U_1350] :
            ( ~ hBOOL(hAPP(U_1354,U_1350))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1350)) ) ) ),
    inference(variable_rename,[status(thm)],[f_401_1]) ).

fof(f_401_3,plain,
    ( ! [U_1356] :
        ( ! [U_1353] :
            ( hBOOL(hAPP(U_1356,U_1353))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1353)) )
        | ? [U_1352] : ~ hBOOL(hAPP(U_1356,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1352))) )
    & ! [U_1355] :
        ( ! [U_1351] : hBOOL(hAPP(U_1355,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1351)))
        | ? [U_1350] :
            ( ~ hBOOL(hAPP(U_1355,U_1350))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1350)) ) ) ),
    inference(miniscope,[status(thm)],[f_401_2]) ).

fof(f_401_4,plain,
    ( ! [U_1356] :
        ( ! [U_1353] :
            ( hBOOL(hAPP(U_1356,U_1353))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1353)) )
        | ? [U_1352] : ~ hBOOL(hAPP(U_1356,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1352))) )
    & ! [U_1355] :
        ( ! [U_1351] : hBOOL(hAPP(U_1355,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1351)))
        | ( ~ hBOOL(hAPP(U_1355,sK32(U_1355)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK32(U_1355))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK32]),skolemize(U_1350,sK32(U_1355))],[f_401_3]) ).

fof(f_401_5,plain,
    ( ! [U_1356] :
        ( ! [U_1353] :
            ( hBOOL(hAPP(U_1356,U_1353))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1353)) )
        | ~ hBOOL(hAPP(U_1356,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK33(U_1356)))) )
    & ! [U_1355] :
        ( ! [U_1351] : hBOOL(hAPP(U_1355,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1351)))
        | ( ~ hBOOL(hAPP(U_1355,sK32(U_1355)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK32(U_1355))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK33]),skolemize(U_1352,sK33(U_1356))],[f_401_4]) ).

fof(f_401_6,plain,
    ( ! [U_1355] :
        ( ~ hBOOL(hAPP(U_1355,sK32(U_1355)))
        | ~ sP130(U_1355) )
    & ! [U_1355] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK32(U_1355)))
        | ~ sP130(U_1355) )
    & ! [U_1353,U_1356] :
        ( hBOOL(hAPP(U_1356,U_1353))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1353))
        | ~ hBOOL(hAPP(U_1356,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK33(U_1356)))) )
    & ! [U_1351,U_1355] :
        ( hBOOL(hAPP(U_1355,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1351)))
        | sP130(U_1355) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP130])],[f_401_5]) ).

cnf(f_401_7,plain,
    ( hBOOL(hAPP(U_1355,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1351)))
    | sP130(U_1355) ),
    inference(clausify,[status(thm)],[f_401_6]) ).

cnf(f_401_8,plain,
    ( hBOOL(hAPP(U_1356,U_1353))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1353))
    | ~ hBOOL(hAPP(U_1356,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK33(U_1356)))) ),
    inference(clausify,[status(thm)],[f_401_6]) ).

cnf(f_401_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK32(U_1355)))
    | ~ sP130(U_1355) ),
    inference(clausify,[status(thm)],[f_401_6]) ).

cnf(f_401_10,plain,
    ( ~ hBOOL(hAPP(U_1355,sK32(U_1355)))
    | ~ sP130(U_1355) ),
    inference(clausify,[status(thm)],[f_401_6]) ).

fof(f_402_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_402_2,plain,
    ! [U_1358,U_1357] :
      ( 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_1357),U_1358)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1358))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1357)) ),
    inference(variable_rename,[status(thm)],[f_402_1]) ).

fof(f_402_3,plain,
    ! [U_1357,U_1358] :
      ( 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_1357),U_1358)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1358))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1357)) ),
    inference(definitional_conversion,[status(esa)],[f_402_2]) ).

cnf(f_402_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_1357),U_1358)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1358))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1357)) ),
    inference(clausify,[status(thm)],[f_402_3]) ).

fof(f_403_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_403_2,plain,
    ! [U_1359] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1359))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1359),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1359),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1359)) ) ),
    inference(variable_rename,[status(thm)],[f_403_1]) ).

fof(f_403_3,plain,
    ( ! [U_1361] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1361))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1361),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_1360] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1360),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1360)) ) ),
    inference(miniscope,[status(thm)],[f_403_2]) ).

fof(f_403_4,plain,
    ( ! [U_1361] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1361))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1361),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_1360] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1360),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1360)) ) ),
    inference(definitional_conversion,[status(esa)],[f_403_3]) ).

cnf(f_403_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1360),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1360)) ),
    inference(clausify,[status(thm)],[f_403_4]) ).

cnf(f_403_6,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,U_1361))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1361),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_403_4]) ).

fof(f_404_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_404_2,plain,
    ! [U_1363,U_1362] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1362)),hAPP(c_Int_Onat,U_1363)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1362),U_1363))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1363)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1362),U_1363))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1363)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1362)),hAPP(c_Int_Onat,U_1363))) ) ),
    inference(variable_rename,[status(thm)],[f_404_1]) ).

fof(f_404_3,plain,
    ( ! [U_1367,U_1365] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1365)),hAPP(c_Int_Onat,U_1367)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1365),U_1367))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1367)) )
    & ! [U_1366,U_1364] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1364),U_1366))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1366)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1364)),hAPP(c_Int_Onat,U_1366))) ) ),
    inference(miniscope,[status(thm)],[f_404_2]) ).

fof(f_404_4,plain,
    ( ! [U_1366,U_1364] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1364),U_1366))
        | ~ sP131(U_1366,U_1364) )
    & ! [U_1366,U_1364] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1366))
        | ~ sP131(U_1366,U_1364) )
    & ! [U_1367,U_1365] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1365)),hAPP(c_Int_Onat,U_1367)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1365),U_1367))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1367)) )
    & ! [U_1366,U_1364] :
        ( sP131(U_1366,U_1364)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1364)),hAPP(c_Int_Onat,U_1366))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP131])],[f_404_3]) ).

cnf(f_404_5,plain,
    ( sP131(U_1366,U_1364)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1364)),hAPP(c_Int_Onat,U_1366))) ),
    inference(clausify,[status(thm)],[f_404_4]) ).

cnf(f_404_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1365)),hAPP(c_Int_Onat,U_1367)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1365),U_1367))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1367)) ),
    inference(clausify,[status(thm)],[f_404_4]) ).

cnf(f_404_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1366))
    | ~ sP131(U_1366,U_1364) ),
    inference(clausify,[status(thm)],[f_404_4]) ).

cnf(f_404_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1364),U_1366))
    | ~ sP131(U_1366,U_1364) ),
    inference(clausify,[status(thm)],[f_404_4]) ).

fof(f_405_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_405_2,plain,
    ! [U_1369,U_1368] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1369)),hAPP(c_Int_Onat,U_1368)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1369),U_1368)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1369),U_1368))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1369)),hAPP(c_Int_Onat,U_1368))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1368)) ),
    inference(variable_rename,[status(thm)],[f_405_1]) ).

fof(f_405_3,plain,
    ( ! [U_1368,U_1369] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1369)),hAPP(c_Int_Onat,U_1368)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1369),U_1368))
        | ~ sP132(U_1368,U_1369) )
    & ! [U_1368,U_1369] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1369),U_1368))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1369)),hAPP(c_Int_Onat,U_1368)))
        | ~ sP132(U_1368,U_1369) )
    & ! [U_1368,U_1369] :
        ( sP132(U_1368,U_1369)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1368)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP132])],[f_405_2]) ).

cnf(f_405_4,plain,
    ( sP132(U_1368,U_1369)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1368)) ),
    inference(clausify,[status(thm)],[f_405_3]) ).

cnf(f_405_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1369),U_1368))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1369)),hAPP(c_Int_Onat,U_1368)))
    | ~ sP132(U_1368,U_1369) ),
    inference(clausify,[status(thm)],[f_405_3]) ).

cnf(f_405_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,U_1369)),hAPP(c_Int_Onat,U_1368)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_1369),U_1368))
    | ~ sP132(U_1368,U_1369) ),
    inference(clausify,[status(thm)],[f_405_3]) ).

fof(f_406_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_406_2,plain,
    ! [U_1371,U_1370] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1370),hAPP(c_Int_Onat,U_1371)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1370)),U_1371)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1370)),U_1371))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1370),hAPP(c_Int_Onat,U_1371))) ) ),
    inference(variable_rename,[status(thm)],[f_406_1]) ).

fof(f_406_3,plain,
    ( ! [U_1375,U_1373] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1373),hAPP(c_Int_Onat,U_1375)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1373)),U_1375)) )
    & ! [U_1374,U_1372] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1372)),U_1374))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1372),hAPP(c_Int_Onat,U_1374))) ) ),
    inference(miniscope,[status(thm)],[f_406_2]) ).

fof(f_406_4,plain,
    ( ! [U_1373,U_1375] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1373),hAPP(c_Int_Onat,U_1375)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1373)),U_1375)) )
    & ! [U_1374,U_1372] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1372)),U_1374))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1372),hAPP(c_Int_Onat,U_1374))) ) ),
    inference(definitional_conversion,[status(esa)],[f_406_3]) ).

cnf(f_406_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_1372)),U_1374))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1372),hAPP(c_Int_Onat,U_1374))) ),
    inference(clausify,[status(thm)],[f_406_4]) ).

cnf(f_406_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1373),hAPP(c_Int_Onat,U_1375)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1373)),U_1375)) ),
    inference(clausify,[status(thm)],[f_406_4]) ).

fof(f_407_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_407_2,plain,
    ! [U_1376] : 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_1376))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_407_1]) ).

fof(f_407_3,plain,
    ! [U_1376] : 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_1376))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_407_2]) ).

cnf(f_407_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_1376))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_407_3]) ).

fof(f_408_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_408_2,plain,
    ! [U_1380,U_1379,U_1378,U_1377] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1377),U_1379),U_1380))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1377),c_Groups_Ozero__class_Ozero(U_1377)),U_1378))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1377),U_1378),U_1379)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1377),U_1378),U_1380)))
      | ~ class_Rings_Olinordered__semiring__strict(U_1377) ),
    inference(variable_rename,[status(thm)],[f_408_1]) ).

fof(f_408_3,plain,
    ! [U_1377,U_1378,U_1379,U_1380] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1377),U_1379),U_1380))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1377),c_Groups_Ozero__class_Ozero(U_1377)),U_1378))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1377),U_1378),U_1379)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1377),U_1378),U_1380)))
      | ~ class_Rings_Olinordered__semiring__strict(U_1377) ),
    inference(definitional_conversion,[status(esa)],[f_408_2]) ).

cnf(f_408_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1377),U_1379),U_1380))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1377),c_Groups_Ozero__class_Ozero(U_1377)),U_1378))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1377),U_1378),U_1379)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1377),U_1378),U_1380)))
    | ~ class_Rings_Olinordered__semiring__strict(U_1377) ),
    inference(clausify,[status(thm)],[f_408_3]) ).

fof(f_409_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_409_2,plain,
    ! [U_1384,U_1383,U_1382,U_1381] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1381),U_1382),U_1384))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1381),c_Groups_Ozero__class_Ozero(U_1381)),U_1383))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1381),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1381),U_1382),U_1383)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1381),U_1384),U_1383)))
      | ~ class_Rings_Olinordered__semiring__strict(U_1381) ),
    inference(variable_rename,[status(thm)],[f_409_1]) ).

fof(f_409_3,plain,
    ! [U_1381,U_1382,U_1383,U_1384] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1381),U_1382),U_1384))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1381),c_Groups_Ozero__class_Ozero(U_1381)),U_1383))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1381),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1381),U_1382),U_1383)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1381),U_1384),U_1383)))
      | ~ class_Rings_Olinordered__semiring__strict(U_1381) ),
    inference(definitional_conversion,[status(esa)],[f_409_2]) ).

cnf(f_409_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1381),U_1382),U_1384))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1381),c_Groups_Ozero__class_Ozero(U_1381)),U_1383))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1381),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1381),U_1382),U_1383)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1381),U_1384),U_1383)))
    | ~ class_Rings_Olinordered__semiring__strict(U_1381) ),
    inference(clausify,[status(thm)],[f_409_3]) ).

fof(f_410_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_410_2,plain,
    ! [U_1388,U_1387,U_1386,U_1385] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1385),U_1387),U_1388))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1385),c_Groups_Ozero__class_Ozero(U_1385)),U_1386))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1385),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1385),U_1386),U_1387)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1385),U_1386),U_1388)))
      | ~ class_Rings_Olinordered__semiring__strict(U_1385) ),
    inference(variable_rename,[status(thm)],[f_410_1]) ).

fof(f_410_3,plain,
    ! [U_1385,U_1386,U_1387,U_1388] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1385),U_1387),U_1388))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1385),c_Groups_Ozero__class_Ozero(U_1385)),U_1386))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1385),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1385),U_1386),U_1387)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1385),U_1386),U_1388)))
      | ~ class_Rings_Olinordered__semiring__strict(U_1385) ),
    inference(definitional_conversion,[status(esa)],[f_410_2]) ).

cnf(f_410_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1385),U_1387),U_1388))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1385),c_Groups_Ozero__class_Ozero(U_1385)),U_1386))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1385),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1385),U_1386),U_1387)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1385),U_1386),U_1388)))
    | ~ class_Rings_Olinordered__semiring__strict(U_1385) ),
    inference(clausify,[status(thm)],[f_410_3]) ).

fof(f_411_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_411_2,plain,
    ! [U_1392,U_1391,U_1390,U_1389] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1389),U_1391),U_1392))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1389),c_Groups_Ozero__class_Ozero(U_1389)),U_1390))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1389),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1389),U_1390),U_1391)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1389),U_1390),U_1392)))
      | ~ class_Rings_Olinordered__semiring(U_1389) ),
    inference(variable_rename,[status(thm)],[f_411_1]) ).

fof(f_411_3,plain,
    ! [U_1389,U_1390,U_1391,U_1392] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1389),U_1391),U_1392))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1389),c_Groups_Ozero__class_Ozero(U_1389)),U_1390))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1389),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1389),U_1390),U_1391)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1389),U_1390),U_1392)))
      | ~ class_Rings_Olinordered__semiring(U_1389) ),
    inference(definitional_conversion,[status(esa)],[f_411_2]) ).

cnf(f_411_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1389),U_1391),U_1392))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1389),c_Groups_Ozero__class_Ozero(U_1389)),U_1390))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1389),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1389),U_1390),U_1391)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1389),U_1390),U_1392)))
    | ~ class_Rings_Olinordered__semiring(U_1389) ),
    inference(clausify,[status(thm)],[f_411_3]) ).

fof(f_412_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_412_2,plain,
    ! [U_1396,U_1395,U_1394,U_1393] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1393),U_1394),U_1396))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1393),c_Groups_Ozero__class_Ozero(U_1393)),U_1395))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1393),U_1394),U_1395)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1393),U_1396),U_1395)))
      | ~ class_Rings_Olinordered__semiring__strict(U_1393) ),
    inference(variable_rename,[status(thm)],[f_412_1]) ).

fof(f_412_3,plain,
    ! [U_1393,U_1394,U_1395,U_1396] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1393),U_1394),U_1396))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1393),c_Groups_Ozero__class_Ozero(U_1393)),U_1395))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1393),U_1394),U_1395)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1393),U_1396),U_1395)))
      | ~ class_Rings_Olinordered__semiring__strict(U_1393) ),
    inference(definitional_conversion,[status(esa)],[f_412_2]) ).

cnf(f_412_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1393),U_1394),U_1396))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1393),c_Groups_Ozero__class_Ozero(U_1393)),U_1395))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1393),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1393),U_1394),U_1395)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1393),U_1396),U_1395)))
    | ~ class_Rings_Olinordered__semiring__strict(U_1393) ),
    inference(clausify,[status(thm)],[f_412_3]) ).

fof(f_413_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_413_2,plain,
    ! [U_1400,U_1399,U_1398,U_1397] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1397),U_1398),U_1400))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1397),c_Groups_Ozero__class_Ozero(U_1397)),U_1399))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1397),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1397),U_1398),U_1399)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1397),U_1400),U_1399)))
      | ~ class_Rings_Olinordered__semiring(U_1397) ),
    inference(variable_rename,[status(thm)],[f_413_1]) ).

fof(f_413_3,plain,
    ! [U_1397,U_1398,U_1399,U_1400] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1397),U_1398),U_1400))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1397),c_Groups_Ozero__class_Ozero(U_1397)),U_1399))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1397),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1397),U_1398),U_1399)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1397),U_1400),U_1399)))
      | ~ class_Rings_Olinordered__semiring(U_1397) ),
    inference(definitional_conversion,[status(esa)],[f_413_2]) ).

cnf(f_413_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1397),U_1398),U_1400))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1397),c_Groups_Ozero__class_Ozero(U_1397)),U_1399))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1397),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1397),U_1398),U_1399)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1397),U_1400),U_1399)))
    | ~ class_Rings_Olinordered__semiring(U_1397) ),
    inference(clausify,[status(thm)],[f_413_3]) ).

fof(f_414_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_414_2,plain,
    ! [U_1405,U_1404,U_1403,U_1402,U_1401] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1401),U_1402),U_1404)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1401),U_1403),U_1405)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1401),c_Groups_Ozero__class_Ozero(U_1401)),U_1404))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1401),c_Groups_Ozero__class_Ozero(U_1401)),U_1402))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1401),U_1404),U_1405))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1401),U_1402),U_1403))
      | ~ class_Rings_Olinordered__semiring__strict(U_1401) ),
    inference(variable_rename,[status(thm)],[f_414_1]) ).

fof(f_414_3,plain,
    ! [U_1401,U_1402,U_1403,U_1404,U_1405] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1401),U_1402),U_1404)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1401),U_1403),U_1405)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1401),c_Groups_Ozero__class_Ozero(U_1401)),U_1404))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1401),c_Groups_Ozero__class_Ozero(U_1401)),U_1402))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1401),U_1404),U_1405))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1401),U_1402),U_1403))
      | ~ class_Rings_Olinordered__semiring__strict(U_1401) ),
    inference(definitional_conversion,[status(esa)],[f_414_2]) ).

cnf(f_414_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1401),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1401),U_1402),U_1404)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1401),U_1403),U_1405)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1401),c_Groups_Ozero__class_Ozero(U_1401)),U_1404))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1401),c_Groups_Ozero__class_Ozero(U_1401)),U_1402))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1401),U_1404),U_1405))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1401),U_1402),U_1403))
    | ~ class_Rings_Olinordered__semiring__strict(U_1401) ),
    inference(clausify,[status(thm)],[f_414_3]) ).

fof(f_415_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_415_2,plain,
    ! [U_1410,U_1409,U_1408,U_1407,U_1406] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1406),U_1407),U_1409)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1406),U_1408),U_1410)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1406),c_Groups_Ozero__class_Ozero(U_1406)),U_1409))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1406),c_Groups_Ozero__class_Ozero(U_1406)),U_1407))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1406),U_1409),U_1410))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1406),U_1407),U_1408))
      | ~ class_Rings_Olinordered__semiring__strict(U_1406) ),
    inference(variable_rename,[status(thm)],[f_415_1]) ).

fof(f_415_3,plain,
    ! [U_1408,U_1406,U_1409,U_1407,U_1410] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1406),U_1407),U_1409)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1406),U_1408),U_1410)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1406),c_Groups_Ozero__class_Ozero(U_1406)),U_1409))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1406),c_Groups_Ozero__class_Ozero(U_1406)),U_1407))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1406),U_1409),U_1410))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1406),U_1407),U_1408))
      | ~ class_Rings_Olinordered__semiring__strict(U_1406) ),
    inference(definitional_conversion,[status(esa)],[f_415_2]) ).

cnf(f_415_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1406),U_1407),U_1409)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1406),U_1408),U_1410)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1406),c_Groups_Ozero__class_Ozero(U_1406)),U_1409))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1406),c_Groups_Ozero__class_Ozero(U_1406)),U_1407))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1406),U_1409),U_1410))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1406),U_1407),U_1408))
    | ~ class_Rings_Olinordered__semiring__strict(U_1406) ),
    inference(clausify,[status(thm)],[f_415_3]) ).

fof(f_416_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_416_2,plain,
    ! [U_1415,U_1414,U_1413,U_1412,U_1411] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1411),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1411),U_1412),U_1414)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1411),U_1413),U_1415)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1411),c_Groups_Ozero__class_Ozero(U_1411)),U_1414))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1411),c_Groups_Ozero__class_Ozero(U_1411)),U_1412))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1411),U_1414),U_1415))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1411),U_1412),U_1413))
      | ~ class_Rings_Olinordered__semiring__strict(U_1411) ),
    inference(variable_rename,[status(thm)],[f_416_1]) ).

fof(f_416_3,plain,
    ! [U_1412,U_1413,U_1411,U_1414,U_1415] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1411),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1411),U_1412),U_1414)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1411),U_1413),U_1415)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1411),c_Groups_Ozero__class_Ozero(U_1411)),U_1414))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1411),c_Groups_Ozero__class_Ozero(U_1411)),U_1412))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1411),U_1414),U_1415))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1411),U_1412),U_1413))
      | ~ class_Rings_Olinordered__semiring__strict(U_1411) ),
    inference(definitional_conversion,[status(esa)],[f_416_2]) ).

cnf(f_416_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1411),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1411),U_1412),U_1414)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1411),U_1413),U_1415)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1411),c_Groups_Ozero__class_Ozero(U_1411)),U_1414))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1411),c_Groups_Ozero__class_Ozero(U_1411)),U_1412))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1411),U_1414),U_1415))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1411),U_1412),U_1413))
    | ~ class_Rings_Olinordered__semiring__strict(U_1411) ),
    inference(clausify,[status(thm)],[f_416_3]) ).

fof(f_417_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_417_2,plain,
    ! [U_1420,U_1419,U_1418,U_1417,U_1416] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1416),U_1417),U_1419)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1416),U_1418),U_1420)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1416),c_Groups_Ozero__class_Ozero(U_1416)),U_1419))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1416),c_Groups_Ozero__class_Ozero(U_1416)),U_1418))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1416),U_1419),U_1420))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1416),U_1417),U_1418))
      | ~ class_Rings_Olinordered__semiring__strict(U_1416) ),
    inference(variable_rename,[status(thm)],[f_417_1]) ).

fof(f_417_3,plain,
    ! [U_1418,U_1416,U_1417,U_1419,U_1420] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1416),U_1417),U_1419)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1416),U_1418),U_1420)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1416),c_Groups_Ozero__class_Ozero(U_1416)),U_1419))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1416),c_Groups_Ozero__class_Ozero(U_1416)),U_1418))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1416),U_1419),U_1420))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1416),U_1417),U_1418))
      | ~ class_Rings_Olinordered__semiring__strict(U_1416) ),
    inference(definitional_conversion,[status(esa)],[f_417_2]) ).

cnf(f_417_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1416),U_1417),U_1419)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1416),U_1418),U_1420)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1416),c_Groups_Ozero__class_Ozero(U_1416)),U_1419))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1416),c_Groups_Ozero__class_Ozero(U_1416)),U_1418))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1416),U_1419),U_1420))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1416),U_1417),U_1418))
    | ~ class_Rings_Olinordered__semiring__strict(U_1416) ),
    inference(clausify,[status(thm)],[f_417_3]) ).

fof(f_418_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_418_2,plain,
    ! [U_1424,U_1423,U_1422,U_1421] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1421),U_1422),U_1423)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1421),U_1422),U_1424)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),U_1424),U_1423)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),U_1424),U_1423))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1421),U_1422),U_1423)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1421),U_1422),U_1424))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1421),U_1422),c_Groups_Ozero__class_Ozero(U_1421)))
      | ~ class_Rings_Olinordered__ring__strict(U_1421) ),
    inference(variable_rename,[status(thm)],[f_418_1]) ).

fof(f_418_3,plain,
    ( ! [U_1424,U_1422,U_1421,U_1423] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1421),U_1422),U_1423)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1421),U_1422),U_1424)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),U_1424),U_1423))
        | ~ sP133(U_1424,U_1422,U_1421,U_1423) )
    & ! [U_1424,U_1422,U_1421,U_1423] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),U_1424),U_1423))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1421),U_1422),U_1423)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1421),U_1422),U_1424)))
        | ~ sP133(U_1424,U_1422,U_1421,U_1423) )
    & ! [U_1424,U_1422,U_1421,U_1423] :
        ( sP133(U_1424,U_1422,U_1421,U_1423)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1421),U_1422),c_Groups_Ozero__class_Ozero(U_1421)))
        | ~ class_Rings_Olinordered__ring__strict(U_1421) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP133])],[f_418_2]) ).

cnf(f_418_4,plain,
    ( sP133(U_1424,U_1422,U_1421,U_1423)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1421),U_1422),c_Groups_Ozero__class_Ozero(U_1421)))
    | ~ class_Rings_Olinordered__ring__strict(U_1421) ),
    inference(clausify,[status(thm)],[f_418_3]) ).

cnf(f_418_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),U_1424),U_1423))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1421),U_1422),U_1423)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1421),U_1422),U_1424)))
    | ~ sP133(U_1424,U_1422,U_1421,U_1423) ),
    inference(clausify,[status(thm)],[f_418_3]) ).

cnf(f_418_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1421),U_1422),U_1423)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1421),U_1422),U_1424)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1421),U_1424),U_1423))
    | ~ sP133(U_1424,U_1422,U_1421,U_1423) ),
    inference(clausify,[status(thm)],[f_418_3]) ).

fof(f_419_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_419_2,plain,
    ! [U_1428,U_1427,U_1426,U_1425] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1425),U_1426),U_1427)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1425),U_1426),U_1428)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1425),U_1427),U_1428)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1425),U_1427),U_1428))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1425),U_1426),U_1427)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1425),U_1426),U_1428))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1425),c_Groups_Ozero__class_Ozero(U_1425)),U_1426))
      | ~ class_Rings_Olinordered__ring__strict(U_1425) ),
    inference(variable_rename,[status(thm)],[f_419_1]) ).

fof(f_419_3,plain,
    ( ! [U_1426,U_1425,U_1427,U_1428] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1425),U_1426),U_1427)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1425),U_1426),U_1428)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1425),U_1427),U_1428))
        | ~ sP134(U_1426,U_1425,U_1427,U_1428) )
    & ! [U_1426,U_1425,U_1427,U_1428] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1425),U_1427),U_1428))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1425),U_1426),U_1427)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1425),U_1426),U_1428)))
        | ~ sP134(U_1426,U_1425,U_1427,U_1428) )
    & ! [U_1426,U_1425,U_1427,U_1428] :
        ( sP134(U_1426,U_1425,U_1427,U_1428)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1425),c_Groups_Ozero__class_Ozero(U_1425)),U_1426))
        | ~ class_Rings_Olinordered__ring__strict(U_1425) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP134])],[f_419_2]) ).

cnf(f_419_4,plain,
    ( sP134(U_1426,U_1425,U_1427,U_1428)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1425),c_Groups_Ozero__class_Ozero(U_1425)),U_1426))
    | ~ class_Rings_Olinordered__ring__strict(U_1425) ),
    inference(clausify,[status(thm)],[f_419_3]) ).

cnf(f_419_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1425),U_1427),U_1428))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1425),U_1426),U_1427)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1425),U_1426),U_1428)))
    | ~ sP134(U_1426,U_1425,U_1427,U_1428) ),
    inference(clausify,[status(thm)],[f_419_3]) ).

cnf(f_419_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1425),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1425),U_1426),U_1427)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1425),U_1426),U_1428)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1425),U_1427),U_1428))
    | ~ sP134(U_1426,U_1425,U_1427,U_1428) ),
    inference(clausify,[status(thm)],[f_419_3]) ).

fof(f_420_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_420_2,plain,
    ! [U_1429] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1429)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | U_1429 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_1429 = 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_1429)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_420_1]) ).

fof(f_420_3,plain,
    ( ! [U_1431] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1431)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | U_1431 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1430] :
        ( U_1430 = 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_1430)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_420_2]) ).

fof(f_420_4,plain,
    ( ! [U_1431] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1431)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | U_1431 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1430] :
        ( U_1430 = 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_1430)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_420_3]) ).

cnf(f_420_5,plain,
    ( U_1430 = 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_1430)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_420_4]) ).

cnf(f_420_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_1431)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_1431 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_420_4]) ).

fof(f_421_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_421_2,plain,
    ! [U_1433,U_1432] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1432)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1433))))
        | U_1433 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1432 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( U_1433 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_1432 = 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_1432)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1433)))) ) ),
    inference(variable_rename,[status(thm)],[f_421_1]) ).

fof(f_421_3,plain,
    ( ! [U_1437,U_1435] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1435)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1437))))
        | U_1437 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1435 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1436,U_1434] :
        ( ( U_1436 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_1434 = 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_1434)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1436)))) ) ),
    inference(miniscope,[status(thm)],[f_421_2]) ).

fof(f_421_4,plain,
    ( ! [U_1436,U_1434] :
        ( U_1436 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP135(U_1436,U_1434) )
    & ! [U_1436,U_1434] :
        ( U_1434 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP135(U_1436,U_1434) )
    & ! [U_1437,U_1435] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1435)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1437))))
        | U_1437 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1435 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1436,U_1434] :
        ( sP135(U_1436,U_1434)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1434)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1436)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP135])],[f_421_3]) ).

cnf(f_421_5,plain,
    ( sP135(U_1436,U_1434)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1434)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1436)))) ),
    inference(clausify,[status(thm)],[f_421_4]) ).

cnf(f_421_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_1435)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_1437))))
    | U_1437 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_1435 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_421_4]) ).

cnf(f_421_7,plain,
    ( U_1434 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP135(U_1436,U_1434) ),
    inference(clausify,[status(thm)],[f_421_4]) ).

cnf(f_421_8,plain,
    ( U_1436 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP135(U_1436,U_1434) ),
    inference(clausify,[status(thm)],[f_421_4]) ).

fof(f_422_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_422_2,plain,
    ! [U_1438] : 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_1438))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_422_1]) ).

fof(f_422_3,plain,
    ! [U_1438] : 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_1438))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_422_2]) ).

cnf(f_422_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_1438))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_422_3]) ).

fof(f_423_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_423_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_423_1]) ).

cnf(f_423_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_423_2]) ).

fof(f_424_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_424_2,plain,
    ! [U_1440,U_1439] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_1439)),hAPP(c_Option_Ooption_OSome(U_1439),U_1440)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_424_1]) ).

fof(f_424_3,plain,
    ! [U_1440,U_1439] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_1439)),hAPP(c_Option_Ooption_OSome(U_1439),U_1440)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_424_2]) ).

cnf(f_424_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_1439)),hAPP(c_Option_Ooption_OSome(U_1439),U_1440)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_424_3]) ).

fof(f_425_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_425_2,plain,
    ! [U_1441] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_1441)),c_Option_Ooption_ONone(U_1441)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_425_1]) ).

fof(f_425_3,plain,
    ! [U_1441] : hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_1441)),c_Option_Ooption_ONone(U_1441)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_425_2]) ).

cnf(f_425_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Option_Ooption(U_1441)),c_Option_Ooption_ONone(U_1441)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_425_3]) ).

fof(f_426_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_426_2,plain,
    ! [U_1444,U_1443,U_1442] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1442),hAPP(c_Groups_Ouminus__class_Ouminus(U_1442),U_1444)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1442),U_1443)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1442),U_1443),U_1444))
      | ~ class_Lattices_Oboolean__algebra(U_1442) ),
    inference(variable_rename,[status(thm)],[f_426_1]) ).

fof(f_426_3,plain,
    ! [U_1442,U_1443,U_1444] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1442),hAPP(c_Groups_Ouminus__class_Ouminus(U_1442),U_1444)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1442),U_1443)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1442),U_1443),U_1444))
      | ~ class_Lattices_Oboolean__algebra(U_1442) ),
    inference(definitional_conversion,[status(esa)],[f_426_2]) ).

cnf(f_426_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1442),hAPP(c_Groups_Ouminus__class_Ouminus(U_1442),U_1444)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1442),U_1443)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1442),U_1443),U_1444))
    | ~ class_Lattices_Oboolean__algebra(U_1442) ),
    inference(clausify,[status(thm)],[f_426_3]) ).

fof(f_427_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_427_2,plain,
    ! [U_1447,U_1446,U_1445] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1445),hAPP(c_Groups_Ouminus__class_Ouminus(U_1445),U_1446)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1445),U_1447)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1445),U_1447),U_1446)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1445),U_1447),U_1446))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1445),hAPP(c_Groups_Ouminus__class_Ouminus(U_1445),U_1446)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1445),U_1447))) ) )
      | ~ class_Lattices_Oboolean__algebra(U_1445) ),
    inference(variable_rename,[status(thm)],[f_427_1]) ).

fof(f_427_3,plain,
    ( ! [U_1445,U_1446,U_1447] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1445),hAPP(c_Groups_Ouminus__class_Ouminus(U_1445),U_1446)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1445),U_1447)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1445),U_1447),U_1446))
        | ~ sP136(U_1445,U_1446,U_1447) )
    & ! [U_1445,U_1446,U_1447] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1445),U_1447),U_1446))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1445),hAPP(c_Groups_Ouminus__class_Ouminus(U_1445),U_1446)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1445),U_1447)))
        | ~ sP136(U_1445,U_1446,U_1447) )
    & ! [U_1445,U_1446,U_1447] :
        ( sP136(U_1445,U_1446,U_1447)
        | ~ class_Lattices_Oboolean__algebra(U_1445) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP136])],[f_427_2]) ).

cnf(f_427_4,plain,
    ( sP136(U_1445,U_1446,U_1447)
    | ~ class_Lattices_Oboolean__algebra(U_1445) ),
    inference(clausify,[status(thm)],[f_427_3]) ).

cnf(f_427_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1445),U_1447),U_1446))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1445),hAPP(c_Groups_Ouminus__class_Ouminus(U_1445),U_1446)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1445),U_1447)))
    | ~ sP136(U_1445,U_1446,U_1447) ),
    inference(clausify,[status(thm)],[f_427_3]) ).

cnf(f_427_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1445),hAPP(c_Groups_Ouminus__class_Ouminus(U_1445),U_1446)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1445),U_1447)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1445),U_1447),U_1446))
    | ~ sP136(U_1445,U_1446,U_1447) ),
    inference(clausify,[status(thm)],[f_427_3]) ).

fof(f_428_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_428_2,plain,
    ! [U_1448] :
      ( ( 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_1448)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1448)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1448))
        | ~ 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_1448))) ) ),
    inference(variable_rename,[status(thm)],[f_428_1]) ).

fof(f_428_3,plain,
    ( ! [U_1450] :
        ( 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_1450)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1450)) )
    & ! [U_1449] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1449))
        | ~ 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_1449))) ) ),
    inference(miniscope,[status(thm)],[f_428_2]) ).

fof(f_428_4,plain,
    ( ! [U_1450] :
        ( 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_1450)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1450)) )
    & ! [U_1449] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1449))
        | ~ 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_1449))) ) ),
    inference(definitional_conversion,[status(esa)],[f_428_3]) ).

cnf(f_428_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1449))
    | ~ 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_1449))) ),
    inference(clausify,[status(thm)],[f_428_4]) ).

cnf(f_428_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_1450)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1450)) ),
    inference(clausify,[status(thm)],[f_428_4]) ).

fof(f_429_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_429_2,plain,
    ! [U_1453,U_1452,U_1451] : c_Option_Ooption_Ooption__size(U_1451,U_1452,hAPP(c_Option_Ooption_OSome(U_1451),U_1453)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_1452,U_1453)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_429_1]) ).

fof(f_429_3,plain,
    ! [U_1453,U_1452,U_1451] : c_Option_Ooption_Ooption__size(U_1451,U_1452,hAPP(c_Option_Ooption_OSome(U_1451),U_1453)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_1452,U_1453)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_429_2]) ).

cnf(f_429_4,plain,
    c_Option_Ooption_Ooption__size(U_1451,U_1452,hAPP(c_Option_Ooption_OSome(U_1451),U_1453)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_1452,U_1453)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_429_3]) ).

fof(f_430_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_430_2,plain,
    c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_430_1]) ).

cnf(f_430_3,plain,
    c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_430_2]) ).

fof(f_431_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_431_2,plain,
    c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_431_1]) ).

cnf(f_431_3,plain,
    c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_431_2]) ).

fof(f_432_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_432_2,plain,
    ! [U_1455,U_1454] :
      ( 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_1454,U_1455)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1455))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1454)) ),
    inference(variable_rename,[status(thm)],[f_432_1]) ).

fof(f_432_3,plain,
    ! [U_1454,U_1455] :
      ( 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_1454,U_1455)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1455))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1454)) ),
    inference(definitional_conversion,[status(esa)],[f_432_2]) ).

cnf(f_432_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_1454,U_1455)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1455))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_1454)) ),
    inference(clausify,[status(thm)],[f_432_3]) ).

fof(f_433_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_433_2,plain,
    ! [U_1459,U_1458,U_1457,U_1456] :
      ( hBOOL(hAPP(hAPP(c_member(U_1456),U_1459),U_1458))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1456),U_1459),U_1457))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1456,tc_HOL_Obool)),U_1457),U_1458)) ),
    inference(variable_rename,[status(thm)],[f_433_1]) ).

fof(f_433_3,plain,
    ! [U_1456,U_1457,U_1458,U_1459] :
      ( hBOOL(hAPP(hAPP(c_member(U_1456),U_1459),U_1458))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1456),U_1459),U_1457))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1456,tc_HOL_Obool)),U_1457),U_1458)) ),
    inference(definitional_conversion,[status(esa)],[f_433_2]) ).

cnf(f_433_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1456),U_1459),U_1458))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1456),U_1459),U_1457))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1456,tc_HOL_Obool)),U_1457),U_1458)) ),
    inference(clausify,[status(thm)],[f_433_3]) ).

fof(f_434_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_434_2,plain,
    ! [U_1460] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1460)),
    inference(variable_rename,[status(thm)],[f_434_1]) ).

fof(f_434_3,plain,
    ! [U_1460] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1460)),
    inference(definitional_conversion,[status(esa)],[f_434_2]) ).

cnf(f_434_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1460)),
    inference(clausify,[status(thm)],[f_434_3]) ).

fof(f_435_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_435_2,plain,
    ! [U_1463,U_1462,U_1461] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1461,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1461,tc_HOL_Obool)),U_1463)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1461,tc_HOL_Obool)),U_1462)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1461,tc_HOL_Obool)),U_1462),U_1463)) ),
    inference(variable_rename,[status(thm)],[f_435_1]) ).

fof(f_435_3,plain,
    ! [U_1461,U_1462,U_1463] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1461,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1461,tc_HOL_Obool)),U_1463)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1461,tc_HOL_Obool)),U_1462)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1461,tc_HOL_Obool)),U_1462),U_1463)) ),
    inference(definitional_conversion,[status(esa)],[f_435_2]) ).

cnf(f_435_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1461,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1461,tc_HOL_Obool)),U_1463)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1461,tc_HOL_Obool)),U_1462)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1461,tc_HOL_Obool)),U_1462),U_1463)) ),
    inference(clausify,[status(thm)],[f_435_3]) ).

fof(f_436_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_436_2,plain,
    ! [U_1466,U_1465,U_1464] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1464,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1464,tc_HOL_Obool)),U_1465)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1464,tc_HOL_Obool)),U_1466)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1464,tc_HOL_Obool)),U_1466),U_1465)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1464,tc_HOL_Obool)),U_1466),U_1465))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1464,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1464,tc_HOL_Obool)),U_1465)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1464,tc_HOL_Obool)),U_1466))) ) ),
    inference(variable_rename,[status(thm)],[f_436_1]) ).

fof(f_436_3,plain,
    ( ! [U_1472,U_1470,U_1468] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1468,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1468,tc_HOL_Obool)),U_1470)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1468,tc_HOL_Obool)),U_1472)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1468,tc_HOL_Obool)),U_1472),U_1470)) )
    & ! [U_1471,U_1469,U_1467] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1467,tc_HOL_Obool)),U_1471),U_1469))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1467,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1467,tc_HOL_Obool)),U_1469)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1467,tc_HOL_Obool)),U_1471))) ) ),
    inference(miniscope,[status(thm)],[f_436_2]) ).

fof(f_436_4,plain,
    ( ! [U_1468,U_1470,U_1472] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1468,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1468,tc_HOL_Obool)),U_1470)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1468,tc_HOL_Obool)),U_1472)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1468,tc_HOL_Obool)),U_1472),U_1470)) )
    & ! [U_1469,U_1467,U_1471] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1467,tc_HOL_Obool)),U_1471),U_1469))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1467,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1467,tc_HOL_Obool)),U_1469)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1467,tc_HOL_Obool)),U_1471))) ) ),
    inference(definitional_conversion,[status(esa)],[f_436_3]) ).

cnf(f_436_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1467,tc_HOL_Obool)),U_1471),U_1469))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1467,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1467,tc_HOL_Obool)),U_1469)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1467,tc_HOL_Obool)),U_1471))) ),
    inference(clausify,[status(thm)],[f_436_4]) ).

cnf(f_436_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1468,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1468,tc_HOL_Obool)),U_1470)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1468,tc_HOL_Obool)),U_1472)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1468,tc_HOL_Obool)),U_1472),U_1470)) ),
    inference(clausify,[status(thm)],[f_436_4]) ).

fof(f_437_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_437_2,plain,
    ! [U_1475,U_1474,U_1473] :
      ( ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1473,tc_HOL_Obool)),U_1474) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1473,tc_HOL_Obool)),U_1475)
        | U_1474 != U_1475 )
      & ( U_1474 = U_1475
        | hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1473,tc_HOL_Obool)),U_1474) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1473,tc_HOL_Obool)),U_1475) ) ),
    inference(variable_rename,[status(thm)],[f_437_1]) ).

fof(f_437_3,plain,
    ( ! [U_1481,U_1479] :
        ( ! [U_1477] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1477,tc_HOL_Obool)),U_1479) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1477,tc_HOL_Obool)),U_1481)
        | U_1479 != U_1481 )
    & ! [U_1480,U_1478] :
        ( ! [U_1476] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1476,tc_HOL_Obool)),U_1478) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1476,tc_HOL_Obool)),U_1480)
        | U_1478 = U_1480 ) ),
    inference(miniscope,[status(thm)],[f_437_2]) ).

fof(f_437_4,plain,
    ( ! [U_1481,U_1477,U_1479] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1477,tc_HOL_Obool)),U_1479) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1477,tc_HOL_Obool)),U_1481)
        | U_1479 != U_1481 )
    & ! [U_1476,U_1478,U_1480] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1476,tc_HOL_Obool)),U_1478) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1476,tc_HOL_Obool)),U_1480)
        | U_1478 = U_1480 ) ),
    inference(definitional_conversion,[status(esa)],[f_437_3]) ).

cnf(f_437_5,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1476,tc_HOL_Obool)),U_1478) != hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1476,tc_HOL_Obool)),U_1480)
    | U_1478 = U_1480 ),
    inference(clausify,[status(thm)],[f_437_4]) ).

cnf(f_437_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1477,tc_HOL_Obool)),U_1479) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1477,tc_HOL_Obool)),U_1481)
    | U_1479 != U_1481 ),
    inference(clausify,[status(thm)],[f_437_4]) ).

fof(f_438_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_438_2,plain,
    ! [U_1483,U_1482] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1482,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1482,tc_HOL_Obool)),U_1483)) = U_1483,
    inference(variable_rename,[status(thm)],[f_438_1]) ).

fof(f_438_3,plain,
    ! [U_1482,U_1483] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1482,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1482,tc_HOL_Obool)),U_1483)) = U_1483,
    inference(definitional_conversion,[status(esa)],[f_438_2]) ).

cnf(f_438_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1482,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_1482,tc_HOL_Obool)),U_1483)) = U_1483,
    inference(clausify,[status(thm)],[f_438_3]) ).

fof(f_439_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_439_2,plain,
    ! [U_1484] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1484),U_1484)),
    inference(variable_rename,[status(thm)],[f_439_1]) ).

fof(f_439_3,plain,
    ! [U_1484] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1484),U_1484)),
    inference(definitional_conversion,[status(esa)],[f_439_2]) ).

cnf(f_439_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1484),U_1484)),
    inference(clausify,[status(thm)],[f_439_3]) ).

fof(f_440_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_440_2,plain,
    ! [U_1486,U_1485] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1485),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1486),U_1485))),
    inference(variable_rename,[status(thm)],[f_440_1]) ).

fof(f_440_3,plain,
    ! [U_1485,U_1486] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1485),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1486),U_1485))),
    inference(definitional_conversion,[status(esa)],[f_440_2]) ).

cnf(f_440_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1485),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1486),U_1485))),
    inference(clausify,[status(thm)],[f_440_3]) ).

fof(f_441_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_441_2,plain,
    ! [U_1488,U_1487] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1487),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1487),U_1488))),
    inference(variable_rename,[status(thm)],[f_441_1]) ).

fof(f_441_3,plain,
    ! [U_1487,U_1488] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1487),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1487),U_1488))),
    inference(definitional_conversion,[status(esa)],[f_441_2]) ).

cnf(f_441_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1487),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1487),U_1488))),
    inference(clausify,[status(thm)],[f_441_3]) ).

fof(f_442_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_442_2,plain,
    ! [U_1492,U_1491] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1491),U_1492))
        | ! [U_1490] : U_1492 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1491),U_1490) )
      & ( ? [U_1489] : U_1492 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1491),U_1489)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1491),U_1492)) ) ),
    inference(variable_rename,[status(thm)],[f_442_1]) ).

fof(f_442_3,plain,
    ( ! [U_1496,U_1494] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1494),U_1496))
        | ! [U_1490] : U_1496 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1494),U_1490) )
    & ! [U_1495,U_1493] :
        ( ? [U_1489] : U_1495 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1493),U_1489)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1493),U_1495)) ) ),
    inference(miniscope,[status(thm)],[f_442_2]) ).

fof(f_442_4,plain,
    ( ! [U_1496,U_1494] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1494),U_1496))
        | ! [U_1490] : U_1496 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1494),U_1490) )
    & ! [U_1495,U_1493] :
        ( U_1495 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1493),sK34(U_1495,U_1493))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1493),U_1495)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK34]),skolemize(U_1489,sK34(U_1495,U_1493))],[f_442_3]) ).

fof(f_442_5,plain,
    ( ! [U_1490,U_1494,U_1496] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1494),U_1496))
        | U_1496 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1494),U_1490) )
    & ! [U_1495,U_1493] :
        ( U_1495 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1493),sK34(U_1495,U_1493))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1493),U_1495)) ) ),
    inference(definitional_conversion,[status(esa)],[f_442_4]) ).

cnf(f_442_6,plain,
    ( U_1495 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1493),sK34(U_1495,U_1493))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1493),U_1495)) ),
    inference(clausify,[status(thm)],[f_442_5]) ).

cnf(f_442_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1494),U_1496))
    | U_1496 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1494),U_1490) ),
    inference(clausify,[status(thm)],[f_442_5]) ).

fof(f_443_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_443_2,plain,
    ! [U_1498,U_1497] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1498),U_1497))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1497),U_1498)) ),
    inference(variable_rename,[status(thm)],[f_443_1]) ).

fof(f_443_3,plain,
    ! [U_1498,U_1497] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1498),U_1497))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1497),U_1498)) ),
    inference(definitional_conversion,[status(esa)],[f_443_2]) ).

cnf(f_443_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1498),U_1497))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1497),U_1498)) ),
    inference(clausify,[status(thm)],[f_443_3]) ).

fof(f_444_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_444_2,plain,
    ! [U_1501,U_1500,U_1499] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1499),U_1500)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1499),U_1501)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1500),U_1501)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1500),U_1501))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1499),U_1500)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1499),U_1501))) ) ),
    inference(variable_rename,[status(thm)],[f_444_1]) ).

fof(f_444_3,plain,
    ( ! [U_1507,U_1505] :
        ( ! [U_1503] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1503),U_1505)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1503),U_1507)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1505),U_1507)) )
    & ! [U_1506,U_1504] :
        ( ! [U_1502] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1502),U_1504)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1502),U_1506)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1504),U_1506)) ) ),
    inference(miniscope,[status(thm)],[f_444_2]) ).

fof(f_444_4,plain,
    ( ! [U_1507,U_1503,U_1505] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1503),U_1505)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1503),U_1507)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1505),U_1507)) )
    & ! [U_1504,U_1502,U_1506] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1502),U_1504)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1502),U_1506)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1504),U_1506)) ) ),
    inference(definitional_conversion,[status(esa)],[f_444_3]) ).

cnf(f_444_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_1502),U_1504)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1502),U_1506)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1504),U_1506)) ),
    inference(clausify,[status(thm)],[f_444_4]) ).

cnf(f_444_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_1503),U_1505)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1503),U_1507)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1505),U_1507)) ),
    inference(clausify,[status(thm)],[f_444_4]) ).

fof(f_445_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_445_2,plain,
    ! [U_1509,U_1508] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1508),U_1509))
      | U_1508 != U_1509 ),
    inference(variable_rename,[status(thm)],[f_445_1]) ).

fof(f_445_3,plain,
    ! [U_1509,U_1508] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1508),U_1509))
      | U_1508 != U_1509 ),
    inference(definitional_conversion,[status(esa)],[f_445_2]) ).

cnf(f_445_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1508),U_1509))
    | U_1508 != U_1509 ),
    inference(clausify,[status(thm)],[f_445_3]) ).

fof(f_446_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_446_2,plain,
    ! [U_1512,U_1511,U_1510] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1510),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1511),U_1512)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1510),U_1511)) ),
    inference(variable_rename,[status(thm)],[f_446_1]) ).

fof(f_446_3,plain,
    ! [U_1510,U_1511,U_1512] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1510),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1511),U_1512)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1510),U_1511)) ),
    inference(definitional_conversion,[status(esa)],[f_446_2]) ).

cnf(f_446_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1510),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1511),U_1512)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1510),U_1511)) ),
    inference(clausify,[status(thm)],[f_446_3]) ).

fof(f_447_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_447_2,plain,
    ! [U_1515,U_1514,U_1513] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1513),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1515),U_1514)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1513),U_1514)) ),
    inference(variable_rename,[status(thm)],[f_447_1]) ).

fof(f_447_3,plain,
    ! [U_1513,U_1514,U_1515] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1513),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1515),U_1514)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1513),U_1514)) ),
    inference(definitional_conversion,[status(esa)],[f_447_2]) ).

cnf(f_447_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1513),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1515),U_1514)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1513),U_1514)) ),
    inference(clausify,[status(thm)],[f_447_3]) ).

fof(f_448_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_448_2,plain,
    ! [U_1518,U_1517,U_1516] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1516),U_1518)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1517),U_1518)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1516),U_1517)) ),
    inference(variable_rename,[status(thm)],[f_448_1]) ).

fof(f_448_3,plain,
    ! [U_1516,U_1517,U_1518] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1516),U_1518)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1517),U_1518)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1516),U_1517)) ),
    inference(definitional_conversion,[status(esa)],[f_448_2]) ).

cnf(f_448_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_1516),U_1518)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1517),U_1518)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1516),U_1517)) ),
    inference(clausify,[status(thm)],[f_448_3]) ).

fof(f_449_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_449_2,plain,
    ! [U_1521,U_1520,U_1519] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1519),U_1521))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1520),U_1521))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1519),U_1520)) ),
    inference(variable_rename,[status(thm)],[f_449_1]) ).

fof(f_449_3,plain,
    ! [U_1519,U_1520,U_1521] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1519),U_1521))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1520),U_1521))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1519),U_1520)) ),
    inference(definitional_conversion,[status(esa)],[f_449_2]) ).

cnf(f_449_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1519),U_1521))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1520),U_1521))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1519),U_1520)) ),
    inference(clausify,[status(thm)],[f_449_3]) ).

fof(f_450_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_450_2,plain,
    ! [U_1523,U_1522] :
      ( U_1522 = U_1523
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1523),U_1522))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1522),U_1523)) ),
    inference(variable_rename,[status(thm)],[f_450_1]) ).

fof(f_450_3,plain,
    ! [U_1522,U_1523] :
      ( U_1522 = U_1523
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1523),U_1522))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1522),U_1523)) ),
    inference(definitional_conversion,[status(esa)],[f_450_2]) ).

cnf(f_450_4,plain,
    ( U_1522 = U_1523
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1523),U_1522))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1522),U_1523)) ),
    inference(clausify,[status(thm)],[f_450_3]) ).

fof(f_451_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_451_2,plain,
    ! [U_1527,U_1526,U_1525,U_1524] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1524),U_1526)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1525),U_1527)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1526),U_1527))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1524),U_1525)) ),
    inference(variable_rename,[status(thm)],[f_451_1]) ).

fof(f_451_3,plain,
    ! [U_1524,U_1525,U_1526,U_1527] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1524),U_1526)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1525),U_1527)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1526),U_1527))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1524),U_1525)) ),
    inference(definitional_conversion,[status(esa)],[f_451_2]) ).

cnf(f_451_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_1524),U_1526)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1525),U_1527)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1526),U_1527))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1524),U_1525)) ),
    inference(clausify,[status(thm)],[f_451_3]) ).

fof(f_452_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_452_2,plain,
    ! [U_1530,U_1529,U_1528] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1529),U_1530))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1528),U_1529)),U_1530)) ),
    inference(variable_rename,[status(thm)],[f_452_1]) ).

fof(f_452_3,plain,
    ! [U_1530,U_1529] :
      ( ! [U_1528] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1528),U_1529)),U_1530))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1529),U_1530)) ),
    inference(miniscope,[status(thm)],[f_452_2]) ).

fof(f_452_4,plain,
    ! [U_1529,U_1528,U_1530] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1528),U_1529)),U_1530))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1529),U_1530)) ),
    inference(definitional_conversion,[status(esa)],[f_452_3]) ).

cnf(f_452_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_1528),U_1529)),U_1530))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1529),U_1530)) ),
    inference(clausify,[status(thm)],[f_452_4]) ).

fof(f_453_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_453_2,plain,
    ! [U_1533,U_1532,U_1531] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1531),U_1533))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1531),U_1532)),U_1533)) ),
    inference(variable_rename,[status(thm)],[f_453_1]) ).

fof(f_453_3,plain,
    ! [U_1531,U_1532,U_1533] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1531),U_1533))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1531),U_1532)),U_1533)) ),
    inference(definitional_conversion,[status(esa)],[f_453_2]) ).

cnf(f_453_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1531),U_1533))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1531),U_1532)),U_1533)) ),
    inference(clausify,[status(thm)],[f_453_3]) ).

fof(f_454_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_454_2,plain,
    ! [U_1536,U_1535,U_1534] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1535),U_1536))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1534),U_1536)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1534),U_1535)),U_1536)) ),
    inference(variable_rename,[status(thm)],[f_454_1]) ).

fof(f_454_3,plain,
    ( ! [U_1534,U_1535,U_1536] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1535),U_1536))
        | ~ sP137(U_1534,U_1535,U_1536) )
    & ! [U_1534,U_1535,U_1536] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1534),U_1536))
        | ~ sP137(U_1534,U_1535,U_1536) )
    & ! [U_1534,U_1535,U_1536] :
        ( sP137(U_1534,U_1535,U_1536)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1534),U_1535)),U_1536)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP137])],[f_454_2]) ).

cnf(f_454_4,plain,
    ( sP137(U_1534,U_1535,U_1536)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1534),U_1535)),U_1536)) ),
    inference(clausify,[status(thm)],[f_454_3]) ).

cnf(f_454_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1534),U_1536))
    | ~ sP137(U_1534,U_1535,U_1536) ),
    inference(clausify,[status(thm)],[f_454_3]) ).

cnf(f_454_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1535),U_1536))
    | ~ sP137(U_1534,U_1535,U_1536) ),
    inference(clausify,[status(thm)],[f_454_3]) ).

fof(f_455_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_455_2,plain,
    ! [U_1538,U_1537] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1537),U_1538),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1537),U_1538),c_Groups_Oone__class_Oone(U_1537))))
      | ~ class_Rings_Olinordered__semidom(U_1537) ),
    inference(variable_rename,[status(thm)],[f_455_1]) ).

fof(f_455_3,plain,
    ! [U_1537,U_1538] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1537),U_1538),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1537),U_1538),c_Groups_Oone__class_Oone(U_1537))))
      | ~ class_Rings_Olinordered__semidom(U_1537) ),
    inference(definitional_conversion,[status(esa)],[f_455_2]) ).

cnf(f_455_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1537),U_1538),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1537),U_1538),c_Groups_Oone__class_Oone(U_1537))))
    | ~ class_Rings_Olinordered__semidom(U_1537) ),
    inference(clausify,[status(thm)],[f_455_3]) ).

fof(f_456_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_456_2,plain,
    ! [U_1542,U_1541,U_1540,U_1539] :
      ( U_1540 = U_1542
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1539),U_1540),U_1541) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1539),U_1542),U_1541)
      | ~ class_Groups_Ocancel__semigroup__add(U_1539) ),
    inference(variable_rename,[status(thm)],[f_456_1]) ).

fof(f_456_3,plain,
    ! [U_1539,U_1540,U_1541,U_1542] :
      ( U_1540 = U_1542
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1539),U_1540),U_1541) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1539),U_1542),U_1541)
      | ~ class_Groups_Ocancel__semigroup__add(U_1539) ),
    inference(definitional_conversion,[status(esa)],[f_456_2]) ).

cnf(f_456_4,plain,
    ( U_1540 = U_1542
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1539),U_1540),U_1541) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1539),U_1542),U_1541)
    | ~ class_Groups_Ocancel__semigroup__add(U_1539) ),
    inference(clausify,[status(thm)],[f_456_3]) ).

fof(f_457_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_457_2,plain,
    ! [U_1546,U_1545,U_1544,U_1543] :
      ( U_1545 = U_1546
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1543),U_1544),U_1545) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1543),U_1544),U_1546)
      | ~ class_Groups_Ocancel__ab__semigroup__add(U_1543) ),
    inference(variable_rename,[status(thm)],[f_457_1]) ).

fof(f_457_3,plain,
    ! [U_1543,U_1544,U_1545,U_1546] :
      ( U_1545 = U_1546
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1543),U_1544),U_1545) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1543),U_1544),U_1546)
      | ~ class_Groups_Ocancel__ab__semigroup__add(U_1543) ),
    inference(definitional_conversion,[status(esa)],[f_457_2]) ).

cnf(f_457_4,plain,
    ( U_1545 = U_1546
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1543),U_1544),U_1545) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1543),U_1544),U_1546)
    | ~ class_Groups_Ocancel__ab__semigroup__add(U_1543) ),
    inference(clausify,[status(thm)],[f_457_3]) ).

fof(f_458_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_458_2,plain,
    ! [U_1550,U_1549,U_1548,U_1547] :
      ( U_1549 = U_1550
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1547),U_1548),U_1549) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1547),U_1548),U_1550)
      | ~ class_Groups_Ocancel__semigroup__add(U_1547) ),
    inference(variable_rename,[status(thm)],[f_458_1]) ).

fof(f_458_3,plain,
    ! [U_1548,U_1547,U_1549,U_1550] :
      ( U_1549 = U_1550
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1547),U_1548),U_1549) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1547),U_1548),U_1550)
      | ~ class_Groups_Ocancel__semigroup__add(U_1547) ),
    inference(definitional_conversion,[status(esa)],[f_458_2]) ).

cnf(f_458_4,plain,
    ( U_1549 = U_1550
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1547),U_1548),U_1549) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1547),U_1548),U_1550)
    | ~ class_Groups_Ocancel__semigroup__add(U_1547) ),
    inference(clausify,[status(thm)],[f_458_3]) ).

fof(f_459_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_459_2,plain,
    ! [U_1554,U_1553,U_1552,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)
          | U_1552 != U_1554 )
        & ( U_1552 = U_1554
          | 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_Ocancel__semigroup__add(U_1551) ),
    inference(variable_rename,[status(thm)],[f_459_1]) ).

fof(f_459_3,plain,
    ( ! [U_1551,U_1552,U_1553,U_1554] :
        ( 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)
        | U_1552 != U_1554
        | ~ sP138(U_1551,U_1552,U_1553,U_1554) )
    & ! [U_1551,U_1552,U_1553,U_1554] :
        ( U_1552 = U_1554
        | 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)
        | ~ sP138(U_1551,U_1552,U_1553,U_1554) )
    & ! [U_1551,U_1552,U_1553,U_1554] :
        ( sP138(U_1551,U_1552,U_1553,U_1554)
        | ~ class_Groups_Ocancel__semigroup__add(U_1551) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP138])],[f_459_2]) ).

cnf(f_459_4,plain,
    ( sP138(U_1551,U_1552,U_1553,U_1554)
    | ~ class_Groups_Ocancel__semigroup__add(U_1551) ),
    inference(clausify,[status(thm)],[f_459_3]) ).

cnf(f_459_5,plain,
    ( U_1552 = U_1554
    | 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)
    | ~ sP138(U_1551,U_1552,U_1553,U_1554) ),
    inference(clausify,[status(thm)],[f_459_3]) ).

cnf(f_459_6,plain,
    ( 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)
    | U_1552 != U_1554
    | ~ sP138(U_1551,U_1552,U_1553,U_1554) ),
    inference(clausify,[status(thm)],[f_459_3]) ).

fof(f_460_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_460_2,plain,
    ! [U_1558,U_1557,U_1556,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)
          | U_1557 != U_1558 )
        & ( U_1557 = U_1558
          | 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_Ocancel__semigroup__add(U_1555) ),
    inference(variable_rename,[status(thm)],[f_460_1]) ).

fof(f_460_3,plain,
    ( ! [U_1558,U_1557,U_1555,U_1556] :
        ( 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)
        | U_1557 != U_1558
        | ~ sP139(U_1558,U_1557,U_1555,U_1556) )
    & ! [U_1558,U_1557,U_1555,U_1556] :
        ( U_1557 = U_1558
        | 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)
        | ~ sP139(U_1558,U_1557,U_1555,U_1556) )
    & ! [U_1558,U_1557,U_1555,U_1556] :
        ( sP139(U_1558,U_1557,U_1555,U_1556)
        | ~ class_Groups_Ocancel__semigroup__add(U_1555) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP139])],[f_460_2]) ).

cnf(f_460_4,plain,
    ( sP139(U_1558,U_1557,U_1555,U_1556)
    | ~ class_Groups_Ocancel__semigroup__add(U_1555) ),
    inference(clausify,[status(thm)],[f_460_3]) ).

cnf(f_460_5,plain,
    ( U_1557 = U_1558
    | 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)
    | ~ sP139(U_1558,U_1557,U_1555,U_1556) ),
    inference(clausify,[status(thm)],[f_460_3]) ).

cnf(f_460_6,plain,
    ( 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)
    | U_1557 != U_1558
    | ~ sP139(U_1558,U_1557,U_1555,U_1556) ),
    inference(clausify,[status(thm)],[f_460_3]) ).

fof(f_461_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_461_2,plain,
    ! [U_1562,U_1561,U_1560,U_1559] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1559),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1559),U_1560),U_1561)),U_1562) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1559),U_1560),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1559),U_1561),U_1562))
      | ~ class_Groups_Oab__semigroup__add(U_1559) ),
    inference(variable_rename,[status(thm)],[f_461_1]) ).

fof(f_461_3,plain,
    ! [U_1561,U_1559,U_1560,U_1562] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1559),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1559),U_1560),U_1561)),U_1562) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1559),U_1560),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1559),U_1561),U_1562))
      | ~ class_Groups_Oab__semigroup__add(U_1559) ),
    inference(definitional_conversion,[status(esa)],[f_461_2]) ).

cnf(f_461_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1559),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1559),U_1560),U_1561)),U_1562) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1559),U_1560),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1559),U_1561),U_1562))
    | ~ class_Groups_Oab__semigroup__add(U_1559) ),
    inference(clausify,[status(thm)],[f_461_3]) ).

fof(f_462_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_462_2,plain,
    ! [U_1564,U_1563] :
      ( ( ( c_Groups_Oone__class_Oone(U_1563) = U_1564
          | U_1564 != c_Groups_Oone__class_Oone(U_1563) )
        & ( U_1564 = c_Groups_Oone__class_Oone(U_1563)
          | c_Groups_Oone__class_Oone(U_1563) != U_1564 ) )
      | ~ class_Groups_Oone(U_1563) ),
    inference(variable_rename,[status(thm)],[f_462_1]) ).

fof(f_462_3,plain,
    ( ! [U_1564,U_1563] :
        ( c_Groups_Oone__class_Oone(U_1563) = U_1564
        | U_1564 != c_Groups_Oone__class_Oone(U_1563)
        | ~ sP140(U_1564,U_1563) )
    & ! [U_1564,U_1563] :
        ( U_1564 = c_Groups_Oone__class_Oone(U_1563)
        | c_Groups_Oone__class_Oone(U_1563) != U_1564
        | ~ sP140(U_1564,U_1563) )
    & ! [U_1564,U_1563] :
        ( sP140(U_1564,U_1563)
        | ~ class_Groups_Oone(U_1563) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP140])],[f_462_2]) ).

cnf(f_462_4,plain,
    ( sP140(U_1564,U_1563)
    | ~ class_Groups_Oone(U_1563) ),
    inference(clausify,[status(thm)],[f_462_3]) ).

cnf(f_462_5,plain,
    ( U_1564 = c_Groups_Oone__class_Oone(U_1563)
    | c_Groups_Oone__class_Oone(U_1563) != U_1564
    | ~ sP140(U_1564,U_1563) ),
    inference(clausify,[status(thm)],[f_462_3]) ).

cnf(f_462_6,plain,
    ( c_Groups_Oone__class_Oone(U_1563) = U_1564
    | U_1564 != c_Groups_Oone__class_Oone(U_1563)
    | ~ sP140(U_1564,U_1563) ),
    inference(clausify,[status(thm)],[f_462_3]) ).

fof(f_463_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_463_2,plain,
    ! [U_1567,U_1566,U_1565] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1565),U_1566) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1567),U_1566)
        | U_1565 != U_1567 )
      & ( U_1565 = U_1567
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1565),U_1566) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1567),U_1566) ) ),
    inference(variable_rename,[status(thm)],[f_463_1]) ).

fof(f_463_3,plain,
    ( ! [U_1573,U_1571,U_1569] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1569),U_1571) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1573),U_1571)
        | U_1569 != U_1573 )
    & ! [U_1572,U_1570,U_1568] :
        ( U_1568 = U_1572
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1568),U_1570) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1572),U_1570) ) ),
    inference(miniscope,[status(thm)],[f_463_2]) ).

fof(f_463_4,plain,
    ( ! [U_1569,U_1571,U_1573] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1569),U_1571) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1573),U_1571)
        | U_1569 != U_1573 )
    & ! [U_1568,U_1572,U_1570] :
        ( U_1568 = U_1572
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1568),U_1570) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1572),U_1570) ) ),
    inference(definitional_conversion,[status(esa)],[f_463_3]) ).

cnf(f_463_5,plain,
    ( U_1568 = U_1572
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1568),U_1570) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1572),U_1570) ),
    inference(clausify,[status(thm)],[f_463_4]) ).

cnf(f_463_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1569),U_1571) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1573),U_1571)
    | U_1569 != U_1573 ),
    inference(clausify,[status(thm)],[f_463_4]) ).

fof(f_464_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_464_2,plain,
    ! [U_1576,U_1575,U_1574] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1574),U_1575) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1574),U_1576)
        | U_1575 != U_1576 )
      & ( U_1575 = U_1576
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1574),U_1575) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1574),U_1576) ) ),
    inference(variable_rename,[status(thm)],[f_464_1]) ).

fof(f_464_3,plain,
    ( ! [U_1582,U_1580] :
        ( ! [U_1578] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1578),U_1580) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1578),U_1582)
        | U_1580 != U_1582 )
    & ! [U_1581,U_1579] :
        ( ! [U_1577] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1577),U_1579) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1577),U_1581)
        | U_1579 = U_1581 ) ),
    inference(miniscope,[status(thm)],[f_464_2]) ).

fof(f_464_4,plain,
    ( ! [U_1582,U_1578,U_1580] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1578),U_1580) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1578),U_1582)
        | U_1580 != U_1582 )
    & ! [U_1579,U_1581,U_1577] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1577),U_1579) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1577),U_1581)
        | U_1579 = U_1581 ) ),
    inference(definitional_conversion,[status(esa)],[f_464_3]) ).

cnf(f_464_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1577),U_1579) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1577),U_1581)
    | U_1579 = U_1581 ),
    inference(clausify,[status(thm)],[f_464_4]) ).

cnf(f_464_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1578),U_1580) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1578),U_1582)
    | U_1580 != U_1582 ),
    inference(clausify,[status(thm)],[f_464_4]) ).

fof(f_465_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_465_2,plain,
    ! [U_1585,U_1584,U_1583] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1583),U_1584)),U_1585) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1583),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1584),U_1585)),
    inference(variable_rename,[status(thm)],[f_465_1]) ).

fof(f_465_3,plain,
    ! [U_1583,U_1584,U_1585] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1583),U_1584)),U_1585) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1583),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1584),U_1585)),
    inference(definitional_conversion,[status(esa)],[f_465_2]) ).

cnf(f_465_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1583),U_1584)),U_1585) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1583),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1584),U_1585)),
    inference(clausify,[status(thm)],[f_465_3]) ).

fof(f_466_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_466_2,plain,
    ! [U_1588,U_1587,U_1586] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1586),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1587),U_1588)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1587),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1586),U_1588)),
    inference(variable_rename,[status(thm)],[f_466_1]) ).

fof(f_466_3,plain,
    ! [U_1586,U_1587,U_1588] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1586),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1587),U_1588)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1587),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1586),U_1588)),
    inference(definitional_conversion,[status(esa)],[f_466_2]) ).

cnf(f_466_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1586),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1587),U_1588)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1587),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1586),U_1588)),
    inference(clausify,[status(thm)],[f_466_3]) ).

fof(f_467_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_467_2,plain,
    ! [U_1590,U_1589] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1589),U_1590) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1590),U_1589),
    inference(variable_rename,[status(thm)],[f_467_1]) ).

fof(f_467_3,plain,
    ! [U_1589,U_1590] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1589),U_1590) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1590),U_1589),
    inference(definitional_conversion,[status(esa)],[f_467_2]) ).

cnf(f_467_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1589),U_1590) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1590),U_1589),
    inference(clausify,[status(thm)],[f_467_3]) ).

fof(f_468_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_468_2,plain,
    ! [U_1595,U_1594,U_1593,U_1592,U_1591] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1591),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1591),U_1592),U_1593)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1591),U_1594),U_1595)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1591),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1591),U_1592),U_1594)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1591),U_1593),U_1595))
      | ~ class_Rings_Ocomm__semiring__1(U_1591) ),
    inference(variable_rename,[status(thm)],[f_468_1]) ).

fof(f_468_3,plain,
    ! [U_1591,U_1592,U_1593,U_1594,U_1595] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1591),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1591),U_1592),U_1593)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1591),U_1594),U_1595)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1591),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1591),U_1592),U_1594)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1591),U_1593),U_1595))
      | ~ class_Rings_Ocomm__semiring__1(U_1591) ),
    inference(definitional_conversion,[status(esa)],[f_468_2]) ).

cnf(f_468_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1591),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1591),U_1592),U_1593)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1591),U_1594),U_1595)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1591),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1591),U_1592),U_1594)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1591),U_1593),U_1595))
    | ~ class_Rings_Ocomm__semiring__1(U_1591) ),
    inference(clausify,[status(thm)],[f_468_3]) ).

fof(f_469_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_469_2,plain,
    ! [U_1599,U_1598,U_1597,U_1596] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1596),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1596),U_1597),U_1598)),U_1599) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1596),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1596),U_1597),U_1599)),U_1598)
      | ~ class_Rings_Ocomm__semiring__1(U_1596) ),
    inference(variable_rename,[status(thm)],[f_469_1]) ).

fof(f_469_3,plain,
    ! [U_1596,U_1597,U_1598,U_1599] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1596),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1596),U_1597),U_1598)),U_1599) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1596),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1596),U_1597),U_1599)),U_1598)
      | ~ class_Rings_Ocomm__semiring__1(U_1596) ),
    inference(definitional_conversion,[status(esa)],[f_469_2]) ).

cnf(f_469_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1596),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1596),U_1597),U_1598)),U_1599) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1596),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1596),U_1597),U_1599)),U_1598)
    | ~ class_Rings_Ocomm__semiring__1(U_1596) ),
    inference(clausify,[status(thm)],[f_469_3]) ).

fof(f_470_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_470_2,plain,
    ! [U_1603,U_1602,U_1601,U_1600] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1600),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1600),U_1601),U_1602)),U_1603) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1600),U_1601),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1600),U_1602),U_1603))
      | ~ class_Rings_Ocomm__semiring__1(U_1600) ),
    inference(variable_rename,[status(thm)],[f_470_1]) ).

fof(f_470_3,plain,
    ! [U_1600,U_1601,U_1602,U_1603] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1600),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1600),U_1601),U_1602)),U_1603) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1600),U_1601),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1600),U_1602),U_1603))
      | ~ class_Rings_Ocomm__semiring__1(U_1600) ),
    inference(definitional_conversion,[status(esa)],[f_470_2]) ).

cnf(f_470_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1600),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1600),U_1601),U_1602)),U_1603) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1600),U_1601),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1600),U_1602),U_1603))
    | ~ class_Rings_Ocomm__semiring__1(U_1600) ),
    inference(clausify,[status(thm)],[f_470_3]) ).

fof(f_471_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_471_2,plain,
    ! [U_1607,U_1606,U_1605,U_1604] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),U_1605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),U_1606),U_1607)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),U_1605),U_1606)),U_1607)
      | ~ class_Rings_Ocomm__semiring__1(U_1604) ),
    inference(variable_rename,[status(thm)],[f_471_1]) ).

fof(f_471_3,plain,
    ! [U_1604,U_1605,U_1606,U_1607] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),U_1605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),U_1606),U_1607)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),U_1605),U_1606)),U_1607)
      | ~ class_Rings_Ocomm__semiring__1(U_1604) ),
    inference(definitional_conversion,[status(esa)],[f_471_2]) ).

cnf(f_471_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),U_1605),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),U_1606),U_1607)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1604),U_1605),U_1606)),U_1607)
    | ~ class_Rings_Ocomm__semiring__1(U_1604) ),
    inference(clausify,[status(thm)],[f_471_3]) ).

fof(f_472_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_472_2,plain,
    ! [U_1611,U_1610,U_1609,U_1608] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1608),U_1609),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1608),U_1610),U_1611)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1608),U_1610),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1608),U_1609),U_1611))
      | ~ class_Rings_Ocomm__semiring__1(U_1608) ),
    inference(variable_rename,[status(thm)],[f_472_1]) ).

fof(f_472_3,plain,
    ! [U_1608,U_1609,U_1610,U_1611] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1608),U_1609),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1608),U_1610),U_1611)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1608),U_1610),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1608),U_1609),U_1611))
      | ~ class_Rings_Ocomm__semiring__1(U_1608) ),
    inference(definitional_conversion,[status(esa)],[f_472_2]) ).

cnf(f_472_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1608),U_1609),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1608),U_1610),U_1611)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1608),U_1610),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1608),U_1609),U_1611))
    | ~ class_Rings_Ocomm__semiring__1(U_1608) ),
    inference(clausify,[status(thm)],[f_472_3]) ).

fof(f_473_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_473_2,plain,
    ! [U_1614,U_1613,U_1612] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1612),U_1613),U_1614) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1612),U_1614),U_1613)
      | ~ class_Rings_Ocomm__semiring__1(U_1612) ),
    inference(variable_rename,[status(thm)],[f_473_1]) ).

fof(f_473_3,plain,
    ! [U_1612,U_1613,U_1614] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1612),U_1613),U_1614) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1612),U_1614),U_1613)
      | ~ class_Rings_Ocomm__semiring__1(U_1612) ),
    inference(definitional_conversion,[status(esa)],[f_473_2]) ).

cnf(f_473_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1612),U_1613),U_1614) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1612),U_1614),U_1613)
    | ~ class_Rings_Ocomm__semiring__1(U_1612) ),
    inference(clausify,[status(thm)],[f_473_3]) ).

fof(f_474_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_474_2,plain,
    ! [U_1617,U_1616,U_1615] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1615),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1615),U_1616),U_1617)),U_1617) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1615),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1615),U_1616),c_Groups_Oone__class_Oone(U_1615))),U_1617)
      | ~ class_Rings_Ocomm__semiring__1(U_1615) ),
    inference(variable_rename,[status(thm)],[f_474_1]) ).

fof(f_474_3,plain,
    ! [U_1615,U_1616,U_1617] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1615),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1615),U_1616),U_1617)),U_1617) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1615),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1615),U_1616),c_Groups_Oone__class_Oone(U_1615))),U_1617)
      | ~ class_Rings_Ocomm__semiring__1(U_1615) ),
    inference(definitional_conversion,[status(esa)],[f_474_2]) ).

cnf(f_474_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1615),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1615),U_1616),U_1617)),U_1617) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1615),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1615),U_1616),c_Groups_Oone__class_Oone(U_1615))),U_1617)
    | ~ class_Rings_Ocomm__semiring__1(U_1615) ),
    inference(clausify,[status(thm)],[f_474_3]) ).

fof(f_475_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_475_2,plain,
    ! [U_1620,U_1619,U_1618] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1618),U_1619),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1618),U_1620),U_1619)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1618),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1618),U_1620),c_Groups_Oone__class_Oone(U_1618))),U_1619)
      | ~ class_Rings_Ocomm__semiring__1(U_1618) ),
    inference(variable_rename,[status(thm)],[f_475_1]) ).

fof(f_475_3,plain,
    ! [U_1618,U_1619,U_1620] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1618),U_1619),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1618),U_1620),U_1619)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1618),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1618),U_1620),c_Groups_Oone__class_Oone(U_1618))),U_1619)
      | ~ class_Rings_Ocomm__semiring__1(U_1618) ),
    inference(definitional_conversion,[status(esa)],[f_475_2]) ).

cnf(f_475_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1618),U_1619),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1618),U_1620),U_1619)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1618),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1618),U_1620),c_Groups_Oone__class_Oone(U_1618))),U_1619)
    | ~ class_Rings_Ocomm__semiring__1(U_1618) ),
    inference(clausify,[status(thm)],[f_475_3]) ).

fof(f_476_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_476_2,plain,
    ! [U_1622,U_1621] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1621),U_1622),U_1622) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1621),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1621),c_Groups_Oone__class_Oone(U_1621)),c_Groups_Oone__class_Oone(U_1621))),U_1622)
      | ~ class_Rings_Ocomm__semiring__1(U_1621) ),
    inference(variable_rename,[status(thm)],[f_476_1]) ).

fof(f_476_3,plain,
    ! [U_1621,U_1622] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1621),U_1622),U_1622) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1621),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1621),c_Groups_Oone__class_Oone(U_1621)),c_Groups_Oone__class_Oone(U_1621))),U_1622)
      | ~ class_Rings_Ocomm__semiring__1(U_1621) ),
    inference(definitional_conversion,[status(esa)],[f_476_2]) ).

cnf(f_476_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1621),U_1622),U_1622) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1621),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1621),c_Groups_Oone__class_Oone(U_1621)),c_Groups_Oone__class_Oone(U_1621))),U_1622)
    | ~ class_Rings_Ocomm__semiring__1(U_1621) ),
    inference(clausify,[status(thm)],[f_476_3]) ).

fof(f_477_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_477_2,plain,
    ! [U_1625,U_1624,U_1623] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1623),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1624),U_1625)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1623),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1623),U_1624)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1623),U_1625))
      | ~ class_Rings_Osemiring__1(U_1623) ),
    inference(variable_rename,[status(thm)],[f_477_1]) ).

fof(f_477_3,plain,
    ! [U_1623,U_1624,U_1625] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1623),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1624),U_1625)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1623),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1623),U_1624)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1623),U_1625))
      | ~ class_Rings_Osemiring__1(U_1623) ),
    inference(definitional_conversion,[status(esa)],[f_477_2]) ).

cnf(f_477_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1623),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1624),U_1625)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1623),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1623),U_1624)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1623),U_1625))
    | ~ class_Rings_Osemiring__1(U_1623) ),
    inference(clausify,[status(thm)],[f_477_3]) ).

fof(f_478_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_478_2,plain,
    ! [U_1626] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1626),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1626)
      | ~ class_Rings_Osemiring__1(U_1626) ),
    inference(variable_rename,[status(thm)],[f_478_1]) ).

fof(f_478_3,plain,
    ! [U_1626] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1626),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1626)
      | ~ class_Rings_Osemiring__1(U_1626) ),
    inference(definitional_conversion,[status(esa)],[f_478_2]) ).

cnf(f_478_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1626),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_1626)
    | ~ class_Rings_Osemiring__1(U_1626) ),
    inference(clausify,[status(thm)],[f_478_3]) ).

fof(f_479_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_479_2,plain,
    ! [U_1629,U_1628,U_1627] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_1627),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1628),U_1629)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1627),hAPP(c_Int_Oring__1__class_Oof__int(U_1627),U_1628)),hAPP(c_Int_Oring__1__class_Oof__int(U_1627),U_1629))
      | ~ class_Rings_Oring__1(U_1627) ),
    inference(variable_rename,[status(thm)],[f_479_1]) ).

fof(f_479_3,plain,
    ! [U_1627,U_1628,U_1629] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_1627),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1628),U_1629)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1627),hAPP(c_Int_Oring__1__class_Oof__int(U_1627),U_1628)),hAPP(c_Int_Oring__1__class_Oof__int(U_1627),U_1629))
      | ~ class_Rings_Oring__1(U_1627) ),
    inference(definitional_conversion,[status(esa)],[f_479_2]) ).

cnf(f_479_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_1627),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_1628),U_1629)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1627),hAPP(c_Int_Oring__1__class_Oof__int(U_1627),U_1628)),hAPP(c_Int_Oring__1__class_Oof__int(U_1627),U_1629))
    | ~ class_Rings_Oring__1(U_1627) ),
    inference(clausify,[status(thm)],[f_479_3]) ).

fof(f_480_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_480_2,plain,
    ! [U_1630] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_1630),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_1630)
      | ~ class_Rings_Oring__1(U_1630) ),
    inference(variable_rename,[status(thm)],[f_480_1]) ).

fof(f_480_3,plain,
    ! [U_1630] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_1630),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_1630)
      | ~ class_Rings_Oring__1(U_1630) ),
    inference(definitional_conversion,[status(esa)],[f_480_2]) ).

cnf(f_480_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_1630),c_Groups_Oone__class_Oone(tc_Int_Oint)) = c_Groups_Oone__class_Oone(U_1630)
    | ~ class_Rings_Oring__1(U_1630) ),
    inference(clausify,[status(thm)],[f_480_3]) ).

fof(f_481_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_481_2,plain,
    ! [U_1631] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1631),c_Groups_Ozero__class_Ozero(U_1631)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1631),c_Groups_Oone__class_Oone(U_1631)),c_Groups_Oone__class_Oone(U_1631))))
      | ~ class_Rings_Olinordered__semidom(U_1631) ),
    inference(variable_rename,[status(thm)],[f_481_1]) ).

fof(f_481_3,plain,
    ! [U_1631] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1631),c_Groups_Ozero__class_Ozero(U_1631)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1631),c_Groups_Oone__class_Oone(U_1631)),c_Groups_Oone__class_Oone(U_1631))))
      | ~ class_Rings_Olinordered__semidom(U_1631) ),
    inference(definitional_conversion,[status(esa)],[f_481_2]) ).

cnf(f_481_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1631),c_Groups_Ozero__class_Ozero(U_1631)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1631),c_Groups_Oone__class_Oone(U_1631)),c_Groups_Oone__class_Oone(U_1631))))
    | ~ class_Rings_Olinordered__semidom(U_1631) ),
    inference(clausify,[status(thm)],[f_481_3]) ).

fof(f_482_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_482_2,plain,
    ! [U_1633,U_1632] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1632),hAPP(c_Nat_OSuc,U_1633)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1632),c_Groups_Oone__class_Oone(U_1632)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1632),U_1633))
      | ~ class_Rings_Osemiring__1(U_1632) ),
    inference(variable_rename,[status(thm)],[f_482_1]) ).

fof(f_482_3,plain,
    ! [U_1632,U_1633] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1632),hAPP(c_Nat_OSuc,U_1633)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1632),c_Groups_Oone__class_Oone(U_1632)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1632),U_1633))
      | ~ class_Rings_Osemiring__1(U_1632) ),
    inference(definitional_conversion,[status(esa)],[f_482_2]) ).

cnf(f_482_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1632),hAPP(c_Nat_OSuc,U_1633)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1632),c_Groups_Oone__class_Oone(U_1632)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_1632),U_1633))
    | ~ class_Rings_Osemiring__1(U_1632) ),
    inference(clausify,[status(thm)],[f_482_3]) ).

fof(f_483_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_483_2,plain,
    ! [U_1637,U_1636,U_1635,U_1634] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1634),U_1636),U_1637))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1634),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1634),U_1635),U_1636)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1634),U_1635),U_1637)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1634) ),
    inference(variable_rename,[status(thm)],[f_483_1]) ).

fof(f_483_3,plain,
    ! [U_1634,U_1635,U_1636,U_1637] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1634),U_1636),U_1637))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1634),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1634),U_1635),U_1636)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1634),U_1635),U_1637)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1634) ),
    inference(definitional_conversion,[status(esa)],[f_483_2]) ).

cnf(f_483_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1634),U_1636),U_1637))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1634),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1634),U_1635),U_1636)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1634),U_1635),U_1637)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1634) ),
    inference(clausify,[status(thm)],[f_483_3]) ).

fof(f_484_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_484_2,plain,
    ! [U_1641,U_1640,U_1639,U_1638] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1638),U_1639),U_1641))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1638),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1638),U_1639),U_1640)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1638),U_1641),U_1640)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1638) ),
    inference(variable_rename,[status(thm)],[f_484_1]) ).

fof(f_484_3,plain,
    ! [U_1638,U_1639,U_1640,U_1641] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1638),U_1639),U_1641))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1638),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1638),U_1639),U_1640)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1638),U_1641),U_1640)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1638) ),
    inference(definitional_conversion,[status(esa)],[f_484_2]) ).

cnf(f_484_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1638),U_1639),U_1641))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1638),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1638),U_1639),U_1640)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1638),U_1641),U_1640)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1638) ),
    inference(clausify,[status(thm)],[f_484_3]) ).

fof(f_485_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_485_2,plain,
    ! [U_1646,U_1645,U_1644,U_1643,U_1642] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1642),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1642),U_1643),U_1645)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1642),U_1644),U_1646)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1642),U_1645),U_1646))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1642),U_1643),U_1644))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_1642) ),
    inference(variable_rename,[status(thm)],[f_485_1]) ).

fof(f_485_3,plain,
    ! [U_1642,U_1643,U_1644,U_1645,U_1646] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1642),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1642),U_1643),U_1645)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1642),U_1644),U_1646)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1642),U_1645),U_1646))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1642),U_1643),U_1644))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_1642) ),
    inference(definitional_conversion,[status(esa)],[f_485_2]) ).

cnf(f_485_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1642),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1642),U_1643),U_1645)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1642),U_1644),U_1646)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1642),U_1645),U_1646))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1642),U_1643),U_1644))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_1642) ),
    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__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_486_2,plain,
    ! [U_1650,U_1649,U_1648,U_1647] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1647),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1647),U_1650),U_1648)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1647),U_1650),U_1649)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1647),U_1648),U_1649))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_1647) ),
    inference(variable_rename,[status(thm)],[f_486_1]) ).

fof(f_486_3,plain,
    ! [U_1647,U_1648,U_1649,U_1650] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1647),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1647),U_1650),U_1648)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1647),U_1650),U_1649)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1647),U_1648),U_1649))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_1647) ),
    inference(definitional_conversion,[status(esa)],[f_486_2]) ).

cnf(f_486_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1647),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1647),U_1650),U_1648)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1647),U_1650),U_1649)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1647),U_1648),U_1649))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_1647) ),
    inference(clausify,[status(thm)],[f_486_3]) ).

fof(f_487_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_487_2,plain,
    ! [U_1654,U_1653,U_1652,U_1651] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1651),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1651),U_1652),U_1654)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1651),U_1653),U_1654)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1651),U_1652),U_1653))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_1651) ),
    inference(variable_rename,[status(thm)],[f_487_1]) ).

fof(f_487_3,plain,
    ! [U_1651,U_1652,U_1653,U_1654] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1651),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1651),U_1652),U_1654)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1651),U_1653),U_1654)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1651),U_1652),U_1653))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_1651) ),
    inference(definitional_conversion,[status(esa)],[f_487_2]) ).

cnf(f_487_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1651),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1651),U_1652),U_1654)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1651),U_1653),U_1654)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1651),U_1652),U_1653))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_1651) ),
    inference(clausify,[status(thm)],[f_487_3]) ).

fof(f_488_1,plain,
    ! [V_b_2,V_a_2,V_c_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__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_488_2,plain,
    ! [U_1658,U_1657,U_1656,U_1655] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1655),U_1656),U_1657)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1655),U_1656),U_1658)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1655),U_1657),U_1658)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1655),U_1657),U_1658))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1655),U_1656),U_1657)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1655),U_1656),U_1658))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1655) ),
    inference(variable_rename,[status(thm)],[f_488_1]) ).

fof(f_488_3,plain,
    ( ! [U_1656,U_1655,U_1657,U_1658] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1655),U_1656),U_1657)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1655),U_1656),U_1658)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1655),U_1657),U_1658))
        | ~ sP141(U_1656,U_1655,U_1657,U_1658) )
    & ! [U_1656,U_1655,U_1657,U_1658] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1655),U_1657),U_1658))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1655),U_1656),U_1657)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1655),U_1656),U_1658)))
        | ~ sP141(U_1656,U_1655,U_1657,U_1658) )
    & ! [U_1656,U_1655,U_1657,U_1658] :
        ( sP141(U_1656,U_1655,U_1657,U_1658)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1655) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP141])],[f_488_2]) ).

cnf(f_488_4,plain,
    ( sP141(U_1656,U_1655,U_1657,U_1658)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1655) ),
    inference(clausify,[status(thm)],[f_488_3]) ).

cnf(f_488_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1655),U_1657),U_1658))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1655),U_1656),U_1657)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1655),U_1656),U_1658)))
    | ~ sP141(U_1656,U_1655,U_1657,U_1658) ),
    inference(clausify,[status(thm)],[f_488_3]) ).

cnf(f_488_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1655),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1655),U_1656),U_1657)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1655),U_1656),U_1658)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1655),U_1657),U_1658))
    | ~ sP141(U_1656,U_1655,U_1657,U_1658) ),
    inference(clausify,[status(thm)],[f_488_3]) ).

fof(f_489_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_489_2,plain,
    ! [U_1662,U_1661,U_1660,U_1659] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1659),U_1660),U_1661)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1659),U_1662),U_1661)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1659),U_1660),U_1662)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1659),U_1660),U_1662))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1659),U_1660),U_1661)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1659),U_1662),U_1661))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1659) ),
    inference(variable_rename,[status(thm)],[f_489_1]) ).

fof(f_489_3,plain,
    ( ! [U_1660,U_1661,U_1659,U_1662] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1659),U_1660),U_1661)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1659),U_1662),U_1661)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1659),U_1660),U_1662))
        | ~ sP142(U_1660,U_1661,U_1659,U_1662) )
    & ! [U_1660,U_1661,U_1659,U_1662] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1659),U_1660),U_1662))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1659),U_1660),U_1661)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1659),U_1662),U_1661)))
        | ~ sP142(U_1660,U_1661,U_1659,U_1662) )
    & ! [U_1660,U_1661,U_1659,U_1662] :
        ( sP142(U_1660,U_1661,U_1659,U_1662)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1659) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP142])],[f_489_2]) ).

cnf(f_489_4,plain,
    ( sP142(U_1660,U_1661,U_1659,U_1662)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1659) ),
    inference(clausify,[status(thm)],[f_489_3]) ).

cnf(f_489_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1659),U_1660),U_1662))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1659),U_1660),U_1661)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1659),U_1662),U_1661)))
    | ~ sP142(U_1660,U_1661,U_1659,U_1662) ),
    inference(clausify,[status(thm)],[f_489_3]) ).

cnf(f_489_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1659),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1659),U_1660),U_1661)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1659),U_1662),U_1661)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1659),U_1660),U_1662))
    | ~ sP142(U_1660,U_1661,U_1659,U_1662) ),
    inference(clausify,[status(thm)],[f_489_3]) ).

fof(f_490_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_490_2,plain,
    ! [U_1664,U_1663] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1663),c_Groups_Ozero__class_Ozero(U_1663)),U_1664) = U_1664
      | ~ class_Rings_Ocomm__semiring__1(U_1663) ),
    inference(variable_rename,[status(thm)],[f_490_1]) ).

fof(f_490_3,plain,
    ! [U_1664,U_1663] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1663),c_Groups_Ozero__class_Ozero(U_1663)),U_1664) = U_1664
      | ~ class_Rings_Ocomm__semiring__1(U_1663) ),
    inference(definitional_conversion,[status(esa)],[f_490_2]) ).

cnf(f_490_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1663),c_Groups_Ozero__class_Ozero(U_1663)),U_1664) = U_1664
    | ~ class_Rings_Ocomm__semiring__1(U_1663) ),
    inference(clausify,[status(thm)],[f_490_3]) ).

fof(f_491_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_491_2,plain,
    ! [U_1666,U_1665] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1665),U_1666),c_Groups_Ozero__class_Ozero(U_1665)) = U_1666
      | ~ class_Rings_Ocomm__semiring__1(U_1665) ),
    inference(variable_rename,[status(thm)],[f_491_1]) ).

fof(f_491_3,plain,
    ! [U_1666,U_1665] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1665),U_1666),c_Groups_Ozero__class_Ozero(U_1665)) = U_1666
      | ~ class_Rings_Ocomm__semiring__1(U_1665) ),
    inference(definitional_conversion,[status(esa)],[f_491_2]) ).

cnf(f_491_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1665),U_1666),c_Groups_Ozero__class_Ozero(U_1665)) = U_1666
    | ~ class_Rings_Ocomm__semiring__1(U_1665) ),
    inference(clausify,[status(thm)],[f_491_3]) ).

fof(f_492_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_492_2,plain,
    ! [U_1669,U_1668,U_1667] :
      ( ( ( U_1668 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1667),U_1668),U_1669)
          | U_1669 != c_Groups_Ozero__class_Ozero(U_1667) )
        & ( U_1669 = c_Groups_Ozero__class_Ozero(U_1667)
          | U_1668 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1667),U_1668),U_1669) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1667) ),
    inference(variable_rename,[status(thm)],[f_492_1]) ).

fof(f_492_3,plain,
    ( ! [U_1667,U_1668,U_1669] :
        ( U_1668 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1667),U_1668),U_1669)
        | U_1669 != c_Groups_Ozero__class_Ozero(U_1667)
        | ~ sP143(U_1667,U_1668,U_1669) )
    & ! [U_1667,U_1668,U_1669] :
        ( U_1669 = c_Groups_Ozero__class_Ozero(U_1667)
        | U_1668 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1667),U_1668),U_1669)
        | ~ sP143(U_1667,U_1668,U_1669) )
    & ! [U_1667,U_1668,U_1669] :
        ( sP143(U_1667,U_1668,U_1669)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1667) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP143])],[f_492_2]) ).

cnf(f_492_4,plain,
    ( sP143(U_1667,U_1668,U_1669)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1667) ),
    inference(clausify,[status(thm)],[f_492_3]) ).

cnf(f_492_5,plain,
    ( U_1669 = c_Groups_Ozero__class_Ozero(U_1667)
    | U_1668 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1667),U_1668),U_1669)
    | ~ sP143(U_1667,U_1668,U_1669) ),
    inference(clausify,[status(thm)],[f_492_3]) ).

cnf(f_492_6,plain,
    ( U_1668 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1667),U_1668),U_1669)
    | U_1669 != c_Groups_Ozero__class_Ozero(U_1667)
    | ~ sP143(U_1667,U_1668,U_1669) ),
    inference(clausify,[status(thm)],[f_492_3]) ).

fof(f_493_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_493_2,plain,
    ! [U_1671,U_1670] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1670),U_1671),U_1671) = c_Groups_Ozero__class_Ozero(U_1670)
          | U_1671 != c_Groups_Ozero__class_Ozero(U_1670) )
        & ( U_1671 = c_Groups_Ozero__class_Ozero(U_1670)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1670),U_1671),U_1671) != c_Groups_Ozero__class_Ozero(U_1670) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1670) ),
    inference(variable_rename,[status(thm)],[f_493_1]) ).

fof(f_493_3,plain,
    ( ! [U_1671,U_1670] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1670),U_1671),U_1671) = c_Groups_Ozero__class_Ozero(U_1670)
        | U_1671 != c_Groups_Ozero__class_Ozero(U_1670)
        | ~ sP144(U_1671,U_1670) )
    & ! [U_1671,U_1670] :
        ( U_1671 = c_Groups_Ozero__class_Ozero(U_1670)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1670),U_1671),U_1671) != c_Groups_Ozero__class_Ozero(U_1670)
        | ~ sP144(U_1671,U_1670) )
    & ! [U_1671,U_1670] :
        ( sP144(U_1671,U_1670)
        | ~ class_Groups_Olinordered__ab__group__add(U_1670) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP144])],[f_493_2]) ).

cnf(f_493_4,plain,
    ( sP144(U_1671,U_1670)
    | ~ class_Groups_Olinordered__ab__group__add(U_1670) ),
    inference(clausify,[status(thm)],[f_493_3]) ).

cnf(f_493_5,plain,
    ( U_1671 = c_Groups_Ozero__class_Ozero(U_1670)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1670),U_1671),U_1671) != c_Groups_Ozero__class_Ozero(U_1670)
    | ~ sP144(U_1671,U_1670) ),
    inference(clausify,[status(thm)],[f_493_3]) ).

cnf(f_493_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1670),U_1671),U_1671) = c_Groups_Ozero__class_Ozero(U_1670)
    | U_1671 != c_Groups_Ozero__class_Ozero(U_1670)
    | ~ sP144(U_1671,U_1670) ),
    inference(clausify,[status(thm)],[f_493_3]) ).

fof(f_494_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_494_2,plain,
    ! [U_1673,U_1672] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1672),c_Groups_Ozero__class_Ozero(U_1672)),U_1673) = U_1673
      | ~ class_Groups_Omonoid__add(U_1672) ),
    inference(variable_rename,[status(thm)],[f_494_1]) ).

fof(f_494_3,plain,
    ! [U_1672,U_1673] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1672),c_Groups_Ozero__class_Ozero(U_1672)),U_1673) = U_1673
      | ~ class_Groups_Omonoid__add(U_1672) ),
    inference(definitional_conversion,[status(esa)],[f_494_2]) ).

cnf(f_494_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1672),c_Groups_Ozero__class_Ozero(U_1672)),U_1673) = U_1673
    | ~ class_Groups_Omonoid__add(U_1672) ),
    inference(clausify,[status(thm)],[f_494_3]) ).

fof(f_495_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_495_2,plain,
    ! [U_1675,U_1674] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1674),c_Groups_Ozero__class_Ozero(U_1674)),U_1675) = U_1675
      | ~ class_Groups_Ocomm__monoid__add(U_1674) ),
    inference(variable_rename,[status(thm)],[f_495_1]) ).

fof(f_495_3,plain,
    ! [U_1674,U_1675] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1674),c_Groups_Ozero__class_Ozero(U_1674)),U_1675) = U_1675
      | ~ class_Groups_Ocomm__monoid__add(U_1674) ),
    inference(definitional_conversion,[status(esa)],[f_495_2]) ).

cnf(f_495_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1674),c_Groups_Ozero__class_Ozero(U_1674)),U_1675) = U_1675
    | ~ class_Groups_Ocomm__monoid__add(U_1674) ),
    inference(clausify,[status(thm)],[f_495_3]) ).

fof(f_496_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_496_2,plain,
    ! [U_1677,U_1676] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_1676) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1676),U_1677),U_1677)
          | U_1677 != c_Groups_Ozero__class_Ozero(U_1676) )
        & ( U_1677 = c_Groups_Ozero__class_Ozero(U_1676)
          | c_Groups_Ozero__class_Ozero(U_1676) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1676),U_1677),U_1677) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1676) ),
    inference(variable_rename,[status(thm)],[f_496_1]) ).

fof(f_496_3,plain,
    ( ! [U_1676,U_1677] :
        ( c_Groups_Ozero__class_Ozero(U_1676) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1676),U_1677),U_1677)
        | U_1677 != c_Groups_Ozero__class_Ozero(U_1676)
        | ~ sP145(U_1676,U_1677) )
    & ! [U_1676,U_1677] :
        ( U_1677 = c_Groups_Ozero__class_Ozero(U_1676)
        | c_Groups_Ozero__class_Ozero(U_1676) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1676),U_1677),U_1677)
        | ~ sP145(U_1676,U_1677) )
    & ! [U_1676,U_1677] :
        ( sP145(U_1676,U_1677)
        | ~ class_Groups_Olinordered__ab__group__add(U_1676) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP145])],[f_496_2]) ).

cnf(f_496_4,plain,
    ( sP145(U_1676,U_1677)
    | ~ class_Groups_Olinordered__ab__group__add(U_1676) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

cnf(f_496_5,plain,
    ( U_1677 = c_Groups_Ozero__class_Ozero(U_1676)
    | c_Groups_Ozero__class_Ozero(U_1676) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1676),U_1677),U_1677)
    | ~ sP145(U_1676,U_1677) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

cnf(f_496_6,plain,
    ( c_Groups_Ozero__class_Ozero(U_1676) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1676),U_1677),U_1677)
    | U_1677 != c_Groups_Ozero__class_Ozero(U_1676)
    | ~ sP145(U_1676,U_1677) ),
    inference(clausify,[status(thm)],[f_496_3]) ).

fof(f_497_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_497_2,plain,
    ! [U_1679,U_1678] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1678),U_1679),c_Groups_Ozero__class_Ozero(U_1678)) = U_1679
      | ~ class_Groups_Omonoid__add(U_1678) ),
    inference(variable_rename,[status(thm)],[f_497_1]) ).

fof(f_497_3,plain,
    ! [U_1679,U_1678] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1678),U_1679),c_Groups_Ozero__class_Ozero(U_1678)) = U_1679
      | ~ class_Groups_Omonoid__add(U_1678) ),
    inference(definitional_conversion,[status(esa)],[f_497_2]) ).

cnf(f_497_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1678),U_1679),c_Groups_Ozero__class_Ozero(U_1678)) = U_1679
    | ~ class_Groups_Omonoid__add(U_1678) ),
    inference(clausify,[status(thm)],[f_497_3]) ).

fof(f_498_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_498_2,plain,
    ! [U_1681,U_1680] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1680),U_1681),c_Groups_Ozero__class_Ozero(U_1680)) = U_1681
      | ~ class_Groups_Ocomm__monoid__add(U_1680) ),
    inference(variable_rename,[status(thm)],[f_498_1]) ).

fof(f_498_3,plain,
    ! [U_1680,U_1681] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1680),U_1681),c_Groups_Ozero__class_Ozero(U_1680)) = U_1681
      | ~ class_Groups_Ocomm__monoid__add(U_1680) ),
    inference(definitional_conversion,[status(esa)],[f_498_2]) ).

cnf(f_498_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1680),U_1681),c_Groups_Ozero__class_Ozero(U_1680)) = U_1681
    | ~ class_Groups_Ocomm__monoid__add(U_1680) ),
    inference(clausify,[status(thm)],[f_498_3]) ).

fof(f_499_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_499_2,plain,
    ! [U_1685,U_1684,U_1683,U_1682] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1682),U_1684),U_1685))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1682),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1682),U_1683),U_1684)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1682),U_1683),U_1685)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1682) ),
    inference(variable_rename,[status(thm)],[f_499_1]) ).

fof(f_499_3,plain,
    ! [U_1682,U_1683,U_1684,U_1685] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1682),U_1684),U_1685))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1682),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1682),U_1683),U_1684)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1682),U_1683),U_1685)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1682) ),
    inference(definitional_conversion,[status(esa)],[f_499_2]) ).

cnf(f_499_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1682),U_1684),U_1685))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1682),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1682),U_1683),U_1684)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1682),U_1683),U_1685)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1682) ),
    inference(clausify,[status(thm)],[f_499_3]) ).

fof(f_500_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_500_2,plain,
    ! [U_1689,U_1688,U_1687,U_1686] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1686),U_1687),U_1689))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1686),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1686),U_1687),U_1688)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1686),U_1689),U_1688)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1686) ),
    inference(variable_rename,[status(thm)],[f_500_1]) ).

fof(f_500_3,plain,
    ! [U_1686,U_1687,U_1688,U_1689] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1686),U_1687),U_1689))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1686),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1686),U_1687),U_1688)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1686),U_1689),U_1688)))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1686) ),
    inference(definitional_conversion,[status(esa)],[f_500_2]) ).

cnf(f_500_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1686),U_1687),U_1689))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1686),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1686),U_1687),U_1688)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1686),U_1689),U_1688)))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1686) ),
    inference(clausify,[status(thm)],[f_500_3]) ).

fof(f_501_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_501_2,plain,
    ! [U_1694,U_1693,U_1692,U_1691,U_1690] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1690),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1690),U_1691),U_1693)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1690),U_1692),U_1694)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1690),U_1693),U_1694))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1690),U_1691),U_1692))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1690) ),
    inference(variable_rename,[status(thm)],[f_501_1]) ).

fof(f_501_3,plain,
    ! [U_1690,U_1691,U_1692,U_1693,U_1694] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1690),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1690),U_1691),U_1693)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1690),U_1692),U_1694)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1690),U_1693),U_1694))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1690),U_1691),U_1692))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1690) ),
    inference(definitional_conversion,[status(esa)],[f_501_2]) ).

cnf(f_501_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1690),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1690),U_1691),U_1693)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1690),U_1692),U_1694)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1690),U_1693),U_1694))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1690),U_1691),U_1692))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1690) ),
    inference(clausify,[status(thm)],[f_501_3]) ).

fof(f_502_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_502_2,plain,
    ! [U_1698,U_1697,U_1696,U_1695] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1695),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1695),U_1698),U_1696)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1695),U_1698),U_1697)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1695),U_1696),U_1697))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1695) ),
    inference(variable_rename,[status(thm)],[f_502_1]) ).

fof(f_502_3,plain,
    ! [U_1695,U_1696,U_1697,U_1698] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1695),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1695),U_1698),U_1696)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1695),U_1698),U_1697)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1695),U_1696),U_1697))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1695) ),
    inference(definitional_conversion,[status(esa)],[f_502_2]) ).

cnf(f_502_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1695),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1695),U_1698),U_1696)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1695),U_1698),U_1697)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1695),U_1696),U_1697))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1695) ),
    inference(clausify,[status(thm)],[f_502_3]) ).

fof(f_503_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_503_2,plain,
    ! [U_1702,U_1701,U_1700,U_1699] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1699),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1699),U_1700),U_1702)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1699),U_1701),U_1702)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1699),U_1700),U_1701))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1699) ),
    inference(variable_rename,[status(thm)],[f_503_1]) ).

fof(f_503_3,plain,
    ! [U_1699,U_1700,U_1701,U_1702] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1699),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1699),U_1700),U_1702)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1699),U_1701),U_1702)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1699),U_1700),U_1701))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1699) ),
    inference(definitional_conversion,[status(esa)],[f_503_2]) ).

cnf(f_503_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1699),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1699),U_1700),U_1702)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1699),U_1701),U_1702)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1699),U_1700),U_1701))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1699) ),
    inference(clausify,[status(thm)],[f_503_3]) ).

fof(f_504_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_504_2,plain,
    ! [U_1706,U_1705,U_1704,U_1703] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1703),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1703),U_1704),U_1705)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1703),U_1704),U_1706)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1703),U_1705),U_1706)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1703),U_1705),U_1706))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1703),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1703),U_1704),U_1705)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1703),U_1704),U_1706))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1703) ),
    inference(variable_rename,[status(thm)],[f_504_1]) ).

fof(f_504_3,plain,
    ( ! [U_1704,U_1703,U_1705,U_1706] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1703),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1703),U_1704),U_1705)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1703),U_1704),U_1706)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1703),U_1705),U_1706))
        | ~ sP146(U_1704,U_1703,U_1705,U_1706) )
    & ! [U_1704,U_1703,U_1705,U_1706] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1703),U_1705),U_1706))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1703),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1703),U_1704),U_1705)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1703),U_1704),U_1706)))
        | ~ sP146(U_1704,U_1703,U_1705,U_1706) )
    & ! [U_1704,U_1703,U_1705,U_1706] :
        ( sP146(U_1704,U_1703,U_1705,U_1706)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1703) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP146])],[f_504_2]) ).

cnf(f_504_4,plain,
    ( sP146(U_1704,U_1703,U_1705,U_1706)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1703) ),
    inference(clausify,[status(thm)],[f_504_3]) ).

cnf(f_504_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1703),U_1705),U_1706))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1703),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1703),U_1704),U_1705)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1703),U_1704),U_1706)))
    | ~ sP146(U_1704,U_1703,U_1705,U_1706) ),
    inference(clausify,[status(thm)],[f_504_3]) ).

cnf(f_504_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1703),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1703),U_1704),U_1705)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1703),U_1704),U_1706)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1703),U_1705),U_1706))
    | ~ sP146(U_1704,U_1703,U_1705,U_1706) ),
    inference(clausify,[status(thm)],[f_504_3]) ).

fof(f_505_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_505_2,plain,
    ! [U_1710,U_1709,U_1708,U_1707] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1707),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1707),U_1708),U_1709)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1707),U_1710),U_1709)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1707),U_1708),U_1710)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1707),U_1708),U_1710))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1707),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1707),U_1708),U_1709)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1707),U_1710),U_1709))) ) )
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1707) ),
    inference(variable_rename,[status(thm)],[f_505_1]) ).

fof(f_505_3,plain,
    ( ! [U_1708,U_1709,U_1710,U_1707] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1707),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1707),U_1708),U_1709)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1707),U_1710),U_1709)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1707),U_1708),U_1710))
        | ~ sP147(U_1708,U_1709,U_1710,U_1707) )
    & ! [U_1708,U_1709,U_1710,U_1707] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1707),U_1708),U_1710))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1707),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1707),U_1708),U_1709)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1707),U_1710),U_1709)))
        | ~ sP147(U_1708,U_1709,U_1710,U_1707) )
    & ! [U_1708,U_1709,U_1710,U_1707] :
        ( sP147(U_1708,U_1709,U_1710,U_1707)
        | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1707) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP147])],[f_505_2]) ).

cnf(f_505_4,plain,
    ( sP147(U_1708,U_1709,U_1710,U_1707)
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_1707) ),
    inference(clausify,[status(thm)],[f_505_3]) ).

cnf(f_505_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1707),U_1708),U_1710))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1707),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1707),U_1708),U_1709)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1707),U_1710),U_1709)))
    | ~ sP147(U_1708,U_1709,U_1710,U_1707) ),
    inference(clausify,[status(thm)],[f_505_3]) ).

cnf(f_505_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1707),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1707),U_1708),U_1709)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1707),U_1710),U_1709)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1707),U_1708),U_1710))
    | ~ sP147(U_1708,U_1709,U_1710,U_1707) ),
    inference(clausify,[status(thm)],[f_505_3]) ).

fof(f_506_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_506_2,plain,
    ! [U_1714,U_1713,U_1712,U_1711] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1711),U_1712),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1711),U_1713),U_1714)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1711),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1711),U_1712),U_1713)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1711),U_1712),U_1714))
      | ~ class_Rings_Ocomm__semiring__1(U_1711) ),
    inference(variable_rename,[status(thm)],[f_506_1]) ).

fof(f_506_3,plain,
    ! [U_1713,U_1711,U_1712,U_1714] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1711),U_1712),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1711),U_1713),U_1714)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1711),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1711),U_1712),U_1713)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1711),U_1712),U_1714))
      | ~ class_Rings_Ocomm__semiring__1(U_1711) ),
    inference(definitional_conversion,[status(esa)],[f_506_2]) ).

cnf(f_506_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1711),U_1712),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1711),U_1713),U_1714)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1711),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1711),U_1712),U_1713)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1711),U_1712),U_1714))
    | ~ class_Rings_Ocomm__semiring__1(U_1711) ),
    inference(clausify,[status(thm)],[f_506_3]) ).

fof(f_507_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_507_2,plain,
    ! [U_1719,U_1718,U_1717,U_1716,U_1715] :
      ( ( ( ( U_1718 != U_1719
            & U_1716 != U_1717 )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1716),U_1718)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1717),U_1719)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1716),U_1719)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1717),U_1718)) )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1716),U_1718)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1717),U_1719)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1716),U_1719)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1717),U_1718))
          | U_1718 = U_1719
          | U_1716 = U_1717 ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1715) ),
    inference(variable_rename,[status(thm)],[f_507_1]) ).

fof(f_507_3,plain,
    ( ! [U_1716,U_1717,U_1718,U_1719] :
        ( U_1718 != U_1719
        | ~ sP148(U_1716,U_1717,U_1718,U_1719) )
    & ! [U_1716,U_1717,U_1718,U_1719] :
        ( U_1716 != U_1717
        | ~ sP148(U_1716,U_1717,U_1718,U_1719) )
    & ! [U_1715,U_1716,U_1717,U_1718,U_1719] :
        ( sP148(U_1716,U_1717,U_1718,U_1719)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1716),U_1718)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1717),U_1719)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1716),U_1719)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1717),U_1718))
        | ~ sP149(U_1715,U_1716,U_1717,U_1718,U_1719) )
    & ! [U_1715,U_1716,U_1717,U_1718,U_1719] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1716),U_1718)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1717),U_1719)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1716),U_1719)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1717),U_1718))
        | U_1718 = U_1719
        | U_1716 = U_1717
        | ~ sP149(U_1715,U_1716,U_1717,U_1718,U_1719) )
    & ! [U_1715,U_1716,U_1717,U_1718,U_1719] :
        ( sP149(U_1715,U_1716,U_1717,U_1718,U_1719)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1715) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP148,sP149])],[f_507_2]) ).

cnf(f_507_4,plain,
    ( sP149(U_1715,U_1716,U_1717,U_1718,U_1719)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1715) ),
    inference(clausify,[status(thm)],[f_507_3]) ).

cnf(f_507_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1716),U_1718)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1717),U_1719)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1716),U_1719)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1717),U_1718))
    | U_1718 = U_1719
    | U_1716 = U_1717
    | ~ sP149(U_1715,U_1716,U_1717,U_1718,U_1719) ),
    inference(clausify,[status(thm)],[f_507_3]) ).

cnf(f_507_6,plain,
    ( sP148(U_1716,U_1717,U_1718,U_1719)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1716),U_1718)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1717),U_1719)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1715),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1716),U_1719)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1715),U_1717),U_1718))
    | ~ sP149(U_1715,U_1716,U_1717,U_1718,U_1719) ),
    inference(clausify,[status(thm)],[f_507_3]) ).

cnf(f_507_7,plain,
    ( U_1716 != U_1717
    | ~ sP148(U_1716,U_1717,U_1718,U_1719) ),
    inference(clausify,[status(thm)],[f_507_3]) ).

cnf(f_507_8,plain,
    ( U_1718 != U_1719
    | ~ sP148(U_1716,U_1717,U_1718,U_1719) ),
    inference(clausify,[status(thm)],[f_507_3]) ).

fof(f_508_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_508_2,plain,
    ! [U_1723,U_1722,U_1721,U_1720] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1720),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1720),U_1721),U_1722)),U_1723) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1720),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1720),U_1721),U_1723)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1720),U_1722),U_1723))
      | ~ class_Rings_Ocomm__semiring__1(U_1720) ),
    inference(variable_rename,[status(thm)],[f_508_1]) ).

fof(f_508_3,plain,
    ! [U_1720,U_1721,U_1723,U_1722] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1720),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1720),U_1721),U_1722)),U_1723) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1720),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1720),U_1721),U_1723)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1720),U_1722),U_1723))
      | ~ class_Rings_Ocomm__semiring__1(U_1720) ),
    inference(definitional_conversion,[status(esa)],[f_508_2]) ).

cnf(f_508_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1720),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1720),U_1721),U_1722)),U_1723) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1720),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1720),U_1721),U_1723)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1720),U_1722),U_1723))
    | ~ class_Rings_Ocomm__semiring__1(U_1720) ),
    inference(clausify,[status(thm)],[f_508_3]) ).

fof(f_509_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_509_2,plain,
    ! [U_1727,U_1726,U_1725,U_1724] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1724),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1724),U_1725),U_1726)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1724),U_1727),U_1726)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1724),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1724),U_1725),U_1727)),U_1726)
      | ~ class_Rings_Ocomm__semiring__1(U_1724) ),
    inference(variable_rename,[status(thm)],[f_509_1]) ).

fof(f_509_3,plain,
    ! [U_1727,U_1724,U_1725,U_1726] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1724),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1724),U_1725),U_1726)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1724),U_1727),U_1726)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1724),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1724),U_1725),U_1727)),U_1726)
      | ~ class_Rings_Ocomm__semiring__1(U_1724) ),
    inference(definitional_conversion,[status(esa)],[f_509_2]) ).

cnf(f_509_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1724),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1724),U_1725),U_1726)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1724),U_1727),U_1726)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1724),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1724),U_1725),U_1727)),U_1726)
    | ~ class_Rings_Ocomm__semiring__1(U_1724) ),
    inference(clausify,[status(thm)],[f_509_3]) ).

fof(f_510_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_510_2,plain,
    ! [U_1732,U_1731,U_1730,U_1729,U_1728] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1728),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1729),U_1730)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1731),U_1732)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1728),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1729),U_1732)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1731),U_1730))
          | ( U_1730 != U_1732
            & U_1729 != U_1731 ) )
        & ( U_1730 = U_1732
          | U_1729 = U_1731
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1728),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1729),U_1730)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1731),U_1732)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1728),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1729),U_1732)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1731),U_1730)) ) )
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1728) ),
    inference(variable_rename,[status(thm)],[f_510_1]) ).

fof(f_510_3,plain,
    ( ! [U_1729,U_1730,U_1731,U_1732] :
        ( U_1730 != U_1732
        | ~ sP150(U_1729,U_1730,U_1731,U_1732) )
    & ! [U_1729,U_1730,U_1731,U_1732] :
        ( U_1729 != U_1731
        | ~ sP150(U_1729,U_1730,U_1731,U_1732) )
    & ! [U_1728,U_1729,U_1730,U_1731,U_1732] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1728),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1729),U_1730)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1731),U_1732)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1728),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1729),U_1732)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1731),U_1730))
        | sP150(U_1729,U_1730,U_1731,U_1732)
        | ~ sP151(U_1728,U_1729,U_1730,U_1731,U_1732) )
    & ! [U_1728,U_1729,U_1730,U_1731,U_1732] :
        ( U_1730 = U_1732
        | U_1729 = U_1731
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1728),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1729),U_1730)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1731),U_1732)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1728),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1729),U_1732)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1731),U_1730))
        | ~ sP151(U_1728,U_1729,U_1730,U_1731,U_1732) )
    & ! [U_1728,U_1729,U_1730,U_1731,U_1732] :
        ( sP151(U_1728,U_1729,U_1730,U_1731,U_1732)
        | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1728) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP150,sP151])],[f_510_2]) ).

cnf(f_510_4,plain,
    ( sP151(U_1728,U_1729,U_1730,U_1731,U_1732)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1728) ),
    inference(clausify,[status(thm)],[f_510_3]) ).

cnf(f_510_5,plain,
    ( U_1730 = U_1732
    | U_1729 = U_1731
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1728),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1729),U_1730)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1731),U_1732)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1728),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1729),U_1732)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1731),U_1730))
    | ~ sP151(U_1728,U_1729,U_1730,U_1731,U_1732) ),
    inference(clausify,[status(thm)],[f_510_3]) ).

cnf(f_510_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1728),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1729),U_1730)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1731),U_1732)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1728),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1729),U_1732)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1728),U_1731),U_1730))
    | sP150(U_1729,U_1730,U_1731,U_1732)
    | ~ sP151(U_1728,U_1729,U_1730,U_1731,U_1732) ),
    inference(clausify,[status(thm)],[f_510_3]) ).

cnf(f_510_7,plain,
    ( U_1729 != U_1731
    | ~ sP150(U_1729,U_1730,U_1731,U_1732) ),
    inference(clausify,[status(thm)],[f_510_3]) ).

cnf(f_510_8,plain,
    ( U_1730 != U_1732
    | ~ sP150(U_1729,U_1730,U_1731,U_1732) ),
    inference(clausify,[status(thm)],[f_510_3]) ).

fof(f_511_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_511_2,plain,
    ! [U_1737,U_1736,U_1735,U_1734,U_1733] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),U_1734),U_1735)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),U_1736),U_1735)),U_1737)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1733),U_1734),U_1736)),U_1735)),U_1737)
      | ~ class_Rings_Osemiring(U_1733) ),
    inference(variable_rename,[status(thm)],[f_511_1]) ).

fof(f_511_3,plain,
    ! [U_1736,U_1734,U_1735,U_1733,U_1737] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),U_1734),U_1735)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),U_1736),U_1735)),U_1737)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1733),U_1734),U_1736)),U_1735)),U_1737)
      | ~ class_Rings_Osemiring(U_1733) ),
    inference(definitional_conversion,[status(esa)],[f_511_2]) ).

cnf(f_511_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),U_1734),U_1735)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),U_1736),U_1735)),U_1737)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1733),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1733),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1733),U_1734),U_1736)),U_1735)),U_1737)
    | ~ class_Rings_Osemiring(U_1733) ),
    inference(clausify,[status(thm)],[f_511_3]) ).

fof(f_512_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_512_2,plain,
    ! [U_1741,U_1740,U_1739,U_1738] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1738),U_1739),U_1740)),U_1741) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),U_1739),U_1741)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),U_1740),U_1741))
      | ~ class_Rings_Ocomm__semiring(U_1738) ),
    inference(variable_rename,[status(thm)],[f_512_1]) ).

fof(f_512_3,plain,
    ! [U_1738,U_1739,U_1740,U_1741] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1738),U_1739),U_1740)),U_1741) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),U_1739),U_1741)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),U_1740),U_1741))
      | ~ class_Rings_Ocomm__semiring(U_1738) ),
    inference(definitional_conversion,[status(esa)],[f_512_2]) ).

cnf(f_512_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1738),U_1739),U_1740)),U_1741) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1738),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),U_1739),U_1741)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1738),U_1740),U_1741))
    | ~ class_Rings_Ocomm__semiring(U_1738) ),
    inference(clausify,[status(thm)],[f_512_3]) ).

fof(f_513_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_513_2,plain,
    ! [U_1742] :
      ( c_Groups_Oone__class_Oone(U_1742) != c_Groups_Ozero__class_Ozero(U_1742)
      | ~ class_Rings_Ozero__neq__one(U_1742) ),
    inference(variable_rename,[status(thm)],[f_513_1]) ).

fof(f_513_3,plain,
    ! [U_1742] :
      ( c_Groups_Oone__class_Oone(U_1742) != c_Groups_Ozero__class_Ozero(U_1742)
      | ~ class_Rings_Ozero__neq__one(U_1742) ),
    inference(definitional_conversion,[status(esa)],[f_513_2]) ).

cnf(f_513_4,plain,
    ( c_Groups_Oone__class_Oone(U_1742) != c_Groups_Ozero__class_Ozero(U_1742)
    | ~ class_Rings_Ozero__neq__one(U_1742) ),
    inference(clausify,[status(thm)],[f_513_3]) ).

fof(f_514_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_514_2,plain,
    ! [U_1743] :
      ( c_Groups_Ozero__class_Ozero(U_1743) != c_Groups_Oone__class_Oone(U_1743)
      | ~ class_Rings_Ozero__neq__one(U_1743) ),
    inference(variable_rename,[status(thm)],[f_514_1]) ).

fof(f_514_3,plain,
    ! [U_1743] :
      ( c_Groups_Ozero__class_Ozero(U_1743) != c_Groups_Oone__class_Oone(U_1743)
      | ~ class_Rings_Ozero__neq__one(U_1743) ),
    inference(definitional_conversion,[status(esa)],[f_514_2]) ).

cnf(f_514_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_1743) != c_Groups_Oone__class_Oone(U_1743)
    | ~ class_Rings_Ozero__neq__one(U_1743) ),
    inference(clausify,[status(thm)],[f_514_3]) ).

fof(f_515_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_515_2,plain,
    ! [U_1745,U_1744] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1744),c_Groups_Oone__class_Oone(U_1744)),U_1745) = U_1745
      | ~ class_Rings_Ocomm__semiring__1(U_1744) ),
    inference(variable_rename,[status(thm)],[f_515_1]) ).

fof(f_515_3,plain,
    ! [U_1744,U_1745] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1744),c_Groups_Oone__class_Oone(U_1744)),U_1745) = U_1745
      | ~ class_Rings_Ocomm__semiring__1(U_1744) ),
    inference(definitional_conversion,[status(esa)],[f_515_2]) ).

cnf(f_515_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1744),c_Groups_Oone__class_Oone(U_1744)),U_1745) = U_1745
    | ~ class_Rings_Ocomm__semiring__1(U_1744) ),
    inference(clausify,[status(thm)],[f_515_3]) ).

fof(f_516_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_516_2,plain,
    ! [U_1747,U_1746] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1746),U_1747),c_Groups_Oone__class_Oone(U_1746)) = U_1747
      | ~ class_Rings_Ocomm__semiring__1(U_1746) ),
    inference(variable_rename,[status(thm)],[f_516_1]) ).

fof(f_516_3,plain,
    ! [U_1746,U_1747] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1746),U_1747),c_Groups_Oone__class_Oone(U_1746)) = U_1747
      | ~ class_Rings_Ocomm__semiring__1(U_1746) ),
    inference(definitional_conversion,[status(esa)],[f_516_2]) ).

cnf(f_516_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1746),U_1747),c_Groups_Oone__class_Oone(U_1746)) = U_1747
    | ~ class_Rings_Ocomm__semiring__1(U_1746) ),
    inference(clausify,[status(thm)],[f_516_3]) ).

fof(f_517_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_517_2,plain,
    ! [U_1749,U_1748] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1748),U_1749),c_Groups_Oone__class_Oone(U_1748)) = U_1749
      | ~ class_Groups_Ocomm__monoid__mult(U_1748) ),
    inference(variable_rename,[status(thm)],[f_517_1]) ).

fof(f_517_3,plain,
    ! [U_1748,U_1749] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1748),U_1749),c_Groups_Oone__class_Oone(U_1748)) = U_1749
      | ~ class_Groups_Ocomm__monoid__mult(U_1748) ),
    inference(definitional_conversion,[status(esa)],[f_517_2]) ).

cnf(f_517_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1748),U_1749),c_Groups_Oone__class_Oone(U_1748)) = U_1749
    | ~ class_Groups_Ocomm__monoid__mult(U_1748) ),
    inference(clausify,[status(thm)],[f_517_3]) ).

fof(f_518_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_518_2,plain,
    ! [U_1751,U_1750] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1750),U_1751),c_Groups_Oone__class_Oone(U_1750)) = U_1751
      | ~ class_Groups_Omonoid__mult(U_1750) ),
    inference(variable_rename,[status(thm)],[f_518_1]) ).

fof(f_518_3,plain,
    ! [U_1750,U_1751] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1750),U_1751),c_Groups_Oone__class_Oone(U_1750)) = U_1751
      | ~ class_Groups_Omonoid__mult(U_1750) ),
    inference(definitional_conversion,[status(esa)],[f_518_2]) ).

cnf(f_518_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1750),U_1751),c_Groups_Oone__class_Oone(U_1750)) = U_1751
    | ~ class_Groups_Omonoid__mult(U_1750) ),
    inference(clausify,[status(thm)],[f_518_3]) ).

fof(f_519_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_519_2,plain,
    ! [U_1753,U_1752] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1752),c_Groups_Oone__class_Oone(U_1752)),U_1753) = U_1753
      | ~ class_Groups_Ocomm__monoid__mult(U_1752) ),
    inference(variable_rename,[status(thm)],[f_519_1]) ).

fof(f_519_3,plain,
    ! [U_1752,U_1753] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1752),c_Groups_Oone__class_Oone(U_1752)),U_1753) = U_1753
      | ~ class_Groups_Ocomm__monoid__mult(U_1752) ),
    inference(definitional_conversion,[status(esa)],[f_519_2]) ).

cnf(f_519_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1752),c_Groups_Oone__class_Oone(U_1752)),U_1753) = U_1753
    | ~ class_Groups_Ocomm__monoid__mult(U_1752) ),
    inference(clausify,[status(thm)],[f_519_3]) ).

fof(f_520_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_520_2,plain,
    ! [U_1755,U_1754] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1754),c_Groups_Oone__class_Oone(U_1754)),U_1755) = U_1755
      | ~ class_Groups_Omonoid__mult(U_1754) ),
    inference(variable_rename,[status(thm)],[f_520_1]) ).

fof(f_520_3,plain,
    ! [U_1754,U_1755] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1754),c_Groups_Oone__class_Oone(U_1754)),U_1755) = U_1755
      | ~ class_Groups_Omonoid__mult(U_1754) ),
    inference(definitional_conversion,[status(esa)],[f_520_2]) ).

cnf(f_520_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1754),c_Groups_Oone__class_Oone(U_1754)),U_1755) = U_1755
    | ~ class_Groups_Omonoid__mult(U_1754) ),
    inference(clausify,[status(thm)],[f_520_3]) ).

fof(f_521_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_521_2,plain,
    ! [U_1758,U_1757,U_1756] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1756),hAPP(c_Groups_Ouminus__class_Ouminus(U_1756),U_1757)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1756),U_1757),U_1758)) = U_1758
      | ~ class_Groups_Ogroup__add(U_1756) ),
    inference(variable_rename,[status(thm)],[f_521_1]) ).

fof(f_521_3,plain,
    ! [U_1756,U_1757,U_1758] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1756),hAPP(c_Groups_Ouminus__class_Ouminus(U_1756),U_1757)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1756),U_1757),U_1758)) = U_1758
      | ~ class_Groups_Ogroup__add(U_1756) ),
    inference(definitional_conversion,[status(esa)],[f_521_2]) ).

cnf(f_521_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1756),hAPP(c_Groups_Ouminus__class_Ouminus(U_1756),U_1757)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1756),U_1757),U_1758)) = U_1758
    | ~ class_Groups_Ogroup__add(U_1756) ),
    inference(clausify,[status(thm)],[f_521_3]) ).

fof(f_522_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_522_2,plain,
    ! [U_1761,U_1760,U_1759] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1759),U_1760),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1759),hAPP(c_Groups_Ouminus__class_Ouminus(U_1759),U_1760)),U_1761)) = U_1761
      | ~ class_Groups_Ogroup__add(U_1759) ),
    inference(variable_rename,[status(thm)],[f_522_1]) ).

fof(f_522_3,plain,
    ! [U_1759,U_1760,U_1761] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1759),U_1760),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1759),hAPP(c_Groups_Ouminus__class_Ouminus(U_1759),U_1760)),U_1761)) = U_1761
      | ~ class_Groups_Ogroup__add(U_1759) ),
    inference(definitional_conversion,[status(esa)],[f_522_2]) ).

cnf(f_522_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1759),U_1760),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1759),hAPP(c_Groups_Ouminus__class_Ouminus(U_1759),U_1760)),U_1761)) = U_1761
    | ~ class_Groups_Ogroup__add(U_1759) ),
    inference(clausify,[status(thm)],[f_522_3]) ).

fof(f_523_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_523_2,plain,
    ! [U_1764,U_1763,U_1762] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1762),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1762),U_1763),U_1764)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1762),hAPP(c_Groups_Ouminus__class_Ouminus(U_1762),U_1764)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1762),U_1763))
      | ~ class_Groups_Ogroup__add(U_1762) ),
    inference(variable_rename,[status(thm)],[f_523_1]) ).

fof(f_523_3,plain,
    ! [U_1762,U_1763,U_1764] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1762),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1762),U_1763),U_1764)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1762),hAPP(c_Groups_Ouminus__class_Ouminus(U_1762),U_1764)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1762),U_1763))
      | ~ class_Groups_Ogroup__add(U_1762) ),
    inference(definitional_conversion,[status(esa)],[f_523_2]) ).

cnf(f_523_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1762),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1762),U_1763),U_1764)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1762),hAPP(c_Groups_Ouminus__class_Ouminus(U_1762),U_1764)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1762),U_1763))
    | ~ class_Groups_Ogroup__add(U_1762) ),
    inference(clausify,[status(thm)],[f_523_3]) ).

fof(f_524_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_524_2,plain,
    ! [U_1767,U_1766,U_1765] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1765),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1765),U_1766),U_1767)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1765),hAPP(c_Groups_Ouminus__class_Ouminus(U_1765),U_1766)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1765),U_1767))
      | ~ class_Groups_Oab__group__add(U_1765) ),
    inference(variable_rename,[status(thm)],[f_524_1]) ).

fof(f_524_3,plain,
    ! [U_1765,U_1766,U_1767] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1765),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1765),U_1766),U_1767)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1765),hAPP(c_Groups_Ouminus__class_Ouminus(U_1765),U_1766)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1765),U_1767))
      | ~ class_Groups_Oab__group__add(U_1765) ),
    inference(definitional_conversion,[status(esa)],[f_524_2]) ).

cnf(f_524_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_1765),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1765),U_1766),U_1767)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1765),hAPP(c_Groups_Ouminus__class_Ouminus(U_1765),U_1766)),hAPP(c_Groups_Ouminus__class_Ouminus(U_1765),U_1767))
    | ~ class_Groups_Oab__group__add(U_1765) ),
    inference(clausify,[status(thm)],[f_524_3]) ).

fof(f_525_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_525_2,plain,
    ! [U_1771,U_1770,U_1769,U_1768] :
      ( hBOOL(hAPP(hAPP(c_member(U_1768),U_1771),U_1770))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1768),U_1771),U_1769))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1768,tc_HOL_Obool)),U_1769),U_1770)) ),
    inference(variable_rename,[status(thm)],[f_525_1]) ).

fof(f_525_3,plain,
    ! [U_1768,U_1769,U_1770,U_1771] :
      ( hBOOL(hAPP(hAPP(c_member(U_1768),U_1771),U_1770))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1768),U_1771),U_1769))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1768,tc_HOL_Obool)),U_1769),U_1770)) ),
    inference(definitional_conversion,[status(esa)],[f_525_2]) ).

cnf(f_525_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1768),U_1771),U_1770))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1768),U_1771),U_1769))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1768,tc_HOL_Obool)),U_1769),U_1770)) ),
    inference(clausify,[status(thm)],[f_525_3]) ).

fof(f_526_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_526_2,plain,
    ! [U_1775,U_1774,U_1773,U_1772] :
      ( hBOOL(hAPP(hAPP(c_member(U_1772),U_1773),U_1775))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1772,tc_HOL_Obool)),U_1774),U_1775))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1772),U_1773),U_1774)) ),
    inference(variable_rename,[status(thm)],[f_526_1]) ).

fof(f_526_3,plain,
    ! [U_1772,U_1773,U_1774,U_1775] :
      ( hBOOL(hAPP(hAPP(c_member(U_1772),U_1773),U_1775))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1772,tc_HOL_Obool)),U_1774),U_1775))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1772),U_1773),U_1774)) ),
    inference(definitional_conversion,[status(esa)],[f_526_2]) ).

cnf(f_526_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1772),U_1773),U_1775))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1772,tc_HOL_Obool)),U_1774),U_1775))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1772),U_1773),U_1774)) ),
    inference(clausify,[status(thm)],[f_526_3]) ).

fof(f_527_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_527_2,plain,
    ! [U_1779,U_1778,U_1777,U_1776] :
      ( hBOOL(hAPP(hAPP(c_member(U_1776),U_1779),U_1778))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1776),U_1779),U_1777))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1776,tc_HOL_Obool)),U_1777),U_1778)) ),
    inference(variable_rename,[status(thm)],[f_527_1]) ).

fof(f_527_3,plain,
    ! [U_1776,U_1777,U_1778,U_1779] :
      ( hBOOL(hAPP(hAPP(c_member(U_1776),U_1779),U_1778))
      | ~ hBOOL(hAPP(hAPP(c_member(U_1776),U_1779),U_1777))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1776,tc_HOL_Obool)),U_1777),U_1778)) ),
    inference(definitional_conversion,[status(esa)],[f_527_2]) ).

cnf(f_527_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_1776),U_1779),U_1778))
    | ~ hBOOL(hAPP(hAPP(c_member(U_1776),U_1779),U_1777))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1776,tc_HOL_Obool)),U_1777),U_1778)) ),
    inference(clausify,[status(thm)],[f_527_3]) ).

fof(f_528_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_528_2,plain,
    ! [U_1780] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1780) = U_1780,
    inference(variable_rename,[status(thm)],[f_528_1]) ).

fof(f_528_3,plain,
    ! [U_1780] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1780) = U_1780,
    inference(definitional_conversion,[status(esa)],[f_528_2]) ).

cnf(f_528_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1780) = U_1780,
    inference(clausify,[status(thm)],[f_528_3]) ).

fof(f_529_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_529_2,plain,
    ! [U_1781] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1781),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1781,
    inference(variable_rename,[status(thm)],[f_529_1]) ).

fof(f_529_3,plain,
    ! [U_1781] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1781),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1781,
    inference(definitional_conversion,[status(esa)],[f_529_2]) ).

cnf(f_529_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1781),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_1781,
    inference(clausify,[status(thm)],[f_529_3]) ).

fof(f_530_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_530_2,plain,
    ! [U_1783,U_1782] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1782),U_1783) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1783 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1782 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( U_1783 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_1782 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1782),U_1783) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_530_1]) ).

fof(f_530_3,plain,
    ( ! [U_1787,U_1785] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1785),U_1787) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1787 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1785 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1786,U_1784] :
        ( ( U_1786 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_1784 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1784),U_1786) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_530_2]) ).

fof(f_530_4,plain,
    ( ! [U_1786,U_1784] :
        ( U_1786 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP152(U_1786,U_1784) )
    & ! [U_1786,U_1784] :
        ( U_1784 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP152(U_1786,U_1784) )
    & ! [U_1787,U_1785] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1785),U_1787) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1787 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_1785 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1786,U_1784] :
        ( sP152(U_1786,U_1784)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1784),U_1786) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP152])],[f_530_3]) ).

cnf(f_530_5,plain,
    ( sP152(U_1786,U_1784)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1784),U_1786) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_530_4]) ).

cnf(f_530_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1785),U_1787) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_1787 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_1785 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_530_4]) ).

cnf(f_530_7,plain,
    ( U_1784 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP152(U_1786,U_1784) ),
    inference(clausify,[status(thm)],[f_530_4]) ).

cnf(f_530_8,plain,
    ( U_1786 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP152(U_1786,U_1784) ),
    inference(clausify,[status(thm)],[f_530_4]) ).

fof(f_531_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_531_2,plain,
    ! [U_1789,U_1788] :
      ( U_1789 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1788),U_1789) != U_1788 ),
    inference(variable_rename,[status(thm)],[f_531_1]) ).

fof(f_531_3,plain,
    ! [U_1789] :
      ( ! [U_1788] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1788),U_1789) != U_1788
      | U_1789 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(miniscope,[status(thm)],[f_531_2]) ).

fof(f_531_4,plain,
    ! [U_1789,U_1788] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1788),U_1789) != U_1788
      | U_1789 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_531_3]) ).

cnf(f_531_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1788),U_1789) != U_1788
    | U_1789 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_531_4]) ).

fof(f_532_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_532_2,plain,
    ! [U_1791,U_1790] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1790)),U_1791) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1790),hAPP(c_Nat_OSuc,U_1791)),
    inference(variable_rename,[status(thm)],[f_532_1]) ).

fof(f_532_3,plain,
    ! [U_1790,U_1791] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1790)),U_1791) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1790),hAPP(c_Nat_OSuc,U_1791)),
    inference(definitional_conversion,[status(esa)],[f_532_2]) ).

cnf(f_532_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1790)),U_1791) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1790),hAPP(c_Nat_OSuc,U_1791)),
    inference(clausify,[status(thm)],[f_532_3]) ).

fof(f_533_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_533_2,plain,
    ! [U_1793,U_1792] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1792)),U_1793) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1792),U_1793)),
    inference(variable_rename,[status(thm)],[f_533_1]) ).

fof(f_533_3,plain,
    ! [U_1792,U_1793] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1792)),U_1793) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1792),U_1793)),
    inference(definitional_conversion,[status(esa)],[f_533_2]) ).

cnf(f_533_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1792)),U_1793) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1792),U_1793)),
    inference(clausify,[status(thm)],[f_533_3]) ).

fof(f_534_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_534_2,plain,
    ! [U_1795,U_1794] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1794),hAPP(c_Nat_OSuc,U_1795)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1794),U_1795)),
    inference(variable_rename,[status(thm)],[f_534_1]) ).

fof(f_534_3,plain,
    ! [U_1794,U_1795] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1794),hAPP(c_Nat_OSuc,U_1795)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1794),U_1795)),
    inference(definitional_conversion,[status(esa)],[f_534_2]) ).

cnf(f_534_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1794),hAPP(c_Nat_OSuc,U_1795)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1794),U_1795)),
    inference(clausify,[status(thm)],[f_534_3]) ).

fof(f_535_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_535_2,plain,
    ! [U_1798,U_1797,U_1796] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1796),U_1798))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1796),U_1797)),U_1798)) ),
    inference(variable_rename,[status(thm)],[f_535_1]) ).

fof(f_535_3,plain,
    ! [U_1796,U_1797,U_1798] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1796),U_1798))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1796),U_1797)),U_1798)) ),
    inference(definitional_conversion,[status(esa)],[f_535_2]) ).

cnf(f_535_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1796),U_1798))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1796),U_1797)),U_1798)) ),
    inference(clausify,[status(thm)],[f_535_3]) ).

fof(f_536_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_536_2,plain,
    ! [U_1802,U_1801,U_1800,U_1799] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1801),U_1802))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1801),U_1800) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1799),U_1802)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1799),U_1800)) ),
    inference(variable_rename,[status(thm)],[f_536_1]) ).

fof(f_536_3,plain,
    ! [U_1799,U_1800,U_1801,U_1802] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1801),U_1802))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1801),U_1800) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1799),U_1802)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1799),U_1800)) ),
    inference(definitional_conversion,[status(esa)],[f_536_2]) ).

cnf(f_536_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1801),U_1802))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1801),U_1800) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1799),U_1802)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1799),U_1800)) ),
    inference(clausify,[status(thm)],[f_536_3]) ).

fof(f_537_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_537_2,plain,
    ! [U_1806,U_1805,U_1804,U_1803] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1803),U_1805)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1804),U_1806)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1805),U_1806))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1803),U_1804)) ),
    inference(variable_rename,[status(thm)],[f_537_1]) ).

fof(f_537_3,plain,
    ! [U_1803,U_1804,U_1805,U_1806] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1803),U_1805)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1804),U_1806)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1805),U_1806))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1803),U_1804)) ),
    inference(definitional_conversion,[status(esa)],[f_537_2]) ).

cnf(f_537_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1803),U_1805)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1804),U_1806)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1805),U_1806))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1803),U_1804)) ),
    inference(clausify,[status(thm)],[f_537_3]) ).

fof(f_538_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_538_2,plain,
    ! [U_1809,U_1808,U_1807] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1807),U_1809)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1808),U_1809)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1807),U_1808)) ),
    inference(variable_rename,[status(thm)],[f_538_1]) ).

fof(f_538_3,plain,
    ! [U_1807,U_1808,U_1809] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1807),U_1809)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1808),U_1809)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1807),U_1808)) ),
    inference(definitional_conversion,[status(esa)],[f_538_2]) ).

cnf(f_538_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1807),U_1809)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1808),U_1809)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1807),U_1808)) ),
    inference(clausify,[status(thm)],[f_538_3]) ).

fof(f_539_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_539_2,plain,
    ! [U_1812,U_1811,U_1810] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1810),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1812),U_1811)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1810),U_1811)) ),
    inference(variable_rename,[status(thm)],[f_539_1]) ).

fof(f_539_3,plain,
    ! [U_1810,U_1811,U_1812] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1810),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1812),U_1811)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1810),U_1811)) ),
    inference(definitional_conversion,[status(esa)],[f_539_2]) ).

cnf(f_539_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1810),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1812),U_1811)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1810),U_1811)) ),
    inference(clausify,[status(thm)],[f_539_3]) ).

fof(f_540_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_540_2,plain,
    ! [U_1815,U_1814,U_1813] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1813),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1814),U_1815)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1813),U_1814)) ),
    inference(variable_rename,[status(thm)],[f_540_1]) ).

fof(f_540_3,plain,
    ! [U_1813,U_1814,U_1815] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1813),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1814),U_1815)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1813),U_1814)) ),
    inference(definitional_conversion,[status(esa)],[f_540_2]) ).

cnf(f_540_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1813),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1814),U_1815)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1813),U_1814)) ),
    inference(clausify,[status(thm)],[f_540_3]) ).

fof(f_541_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_541_2,plain,
    ! [U_1818,U_1817,U_1816] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1816),U_1817)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1816),U_1818)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1817),U_1818)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1817),U_1818))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1816),U_1817)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1816),U_1818))) ) ),
    inference(variable_rename,[status(thm)],[f_541_1]) ).

fof(f_541_3,plain,
    ( ! [U_1824,U_1822] :
        ( ! [U_1820] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1820),U_1822)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1820),U_1824)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1822),U_1824)) )
    & ! [U_1823,U_1821] :
        ( ! [U_1819] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1819),U_1821)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1819),U_1823)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1821),U_1823)) ) ),
    inference(miniscope,[status(thm)],[f_541_2]) ).

fof(f_541_4,plain,
    ( ! [U_1824,U_1820,U_1822] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1820),U_1822)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1820),U_1824)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1822),U_1824)) )
    & ! [U_1821,U_1819,U_1823] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1819),U_1821)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1819),U_1823)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1821),U_1823)) ) ),
    inference(definitional_conversion,[status(esa)],[f_541_3]) ).

cnf(f_541_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1819),U_1821)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1819),U_1823)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1821),U_1823)) ),
    inference(clausify,[status(thm)],[f_541_4]) ).

cnf(f_541_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1820),U_1822)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1820),U_1824)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1822),U_1824)) ),
    inference(clausify,[status(thm)],[f_541_4]) ).

fof(f_542_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_542_2,plain,
    ! [U_1826,U_1825] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1825),U_1826)),U_1826)),
    inference(variable_rename,[status(thm)],[f_542_1]) ).

fof(f_542_3,plain,
    ! [U_1826,U_1825] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1825),U_1826)),U_1826)),
    inference(definitional_conversion,[status(esa)],[f_542_2]) ).

cnf(f_542_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1825),U_1826)),U_1826)),
    inference(clausify,[status(thm)],[f_542_3]) ).

fof(f_543_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_543_2,plain,
    ! [U_1828,U_1827] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1827),U_1828)),U_1827)),
    inference(variable_rename,[status(thm)],[f_543_1]) ).

fof(f_543_3,plain,
    ! [U_1827,U_1828] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1827),U_1828)),U_1827)),
    inference(definitional_conversion,[status(esa)],[f_543_2]) ).

cnf(f_543_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1827),U_1828)),U_1827)),
    inference(clausify,[status(thm)],[f_543_3]) ).

fof(f_544_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_544_2,plain,
    ! [U_1829] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1829)),
    inference(variable_rename,[status(thm)],[f_544_1]) ).

fof(f_544_3,plain,
    ! [U_1829] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1829)),
    inference(definitional_conversion,[status(esa)],[f_544_2]) ).

cnf(f_544_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_1829)),
    inference(clausify,[status(thm)],[f_544_3]) ).

fof(f_545_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_545_2,plain,
    ! [U_1830] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1830),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_1830 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( U_1830 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1830),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[f_545_1]) ).

fof(f_545_3,plain,
    ( ! [U_1832] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1832),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_1832 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1831] :
        ( U_1831 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1831),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(miniscope,[status(thm)],[f_545_2]) ).

fof(f_545_4,plain,
    ( ! [U_1832] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1832),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_1832 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_1831] :
        ( U_1831 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1831),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(definitional_conversion,[status(esa)],[f_545_3]) ).

cnf(f_545_5,plain,
    ( U_1831 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1831),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_545_4]) ).

cnf(f_545_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1832),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_1832 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_545_4]) ).

fof(f_546_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_546_2,plain,
    ! [U_1834,U_1833] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1833),U_1834))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1833)),U_1834)) ),
    inference(variable_rename,[status(thm)],[f_546_1]) ).

fof(f_546_3,plain,
    ! [U_1833,U_1834] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1833),U_1834))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1833)),U_1834)) ),
    inference(definitional_conversion,[status(esa)],[f_546_2]) ).

cnf(f_546_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1833),U_1834))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1833)),U_1834)) ),
    inference(clausify,[status(thm)],[f_546_3]) ).

fof(f_547_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_547_2,plain,
    ! [U_1836,U_1835] :
      ( U_1835 = hAPP(c_Nat_OSuc,U_1836)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1835),U_1836))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1835),hAPP(c_Nat_OSuc,U_1836))) ),
    inference(variable_rename,[status(thm)],[f_547_1]) ).

fof(f_547_3,plain,
    ! [U_1835,U_1836] :
      ( U_1835 = hAPP(c_Nat_OSuc,U_1836)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1835),U_1836))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1835),hAPP(c_Nat_OSuc,U_1836))) ),
    inference(definitional_conversion,[status(esa)],[f_547_2]) ).

cnf(f_547_4,plain,
    ( U_1835 = hAPP(c_Nat_OSuc,U_1836)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1835),U_1836))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1835),hAPP(c_Nat_OSuc,U_1836))) ),
    inference(clausify,[status(thm)],[f_547_3]) ).

fof(f_548_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_548_2,plain,
    ! [U_1838,U_1837] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1837),hAPP(c_Nat_OSuc,U_1838)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1837),U_1838)) ),
    inference(variable_rename,[status(thm)],[f_548_1]) ).

fof(f_548_3,plain,
    ! [U_1838,U_1837] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1837),hAPP(c_Nat_OSuc,U_1838)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1837),U_1838)) ),
    inference(definitional_conversion,[status(esa)],[f_548_2]) ).

cnf(f_548_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1837),hAPP(c_Nat_OSuc,U_1838)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1837),U_1838)) ),
    inference(clausify,[status(thm)],[f_548_3]) ).

fof(f_549_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_549_2,plain,
    ! [U_1840,U_1839] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1839)),hAPP(c_Nat_OSuc,U_1840)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1839),U_1840)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1839),U_1840))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1839)),hAPP(c_Nat_OSuc,U_1840))) ) ),
    inference(variable_rename,[status(thm)],[f_549_1]) ).

fof(f_549_3,plain,
    ( ! [U_1844,U_1842] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1842)),hAPP(c_Nat_OSuc,U_1844)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1842),U_1844)) )
    & ! [U_1843,U_1841] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1841),U_1843))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1841)),hAPP(c_Nat_OSuc,U_1843))) ) ),
    inference(miniscope,[status(thm)],[f_549_2]) ).

fof(f_549_4,plain,
    ( ! [U_1842,U_1844] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1842)),hAPP(c_Nat_OSuc,U_1844)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1842),U_1844)) )
    & ! [U_1843,U_1841] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1841),U_1843))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1841)),hAPP(c_Nat_OSuc,U_1843))) ) ),
    inference(definitional_conversion,[status(esa)],[f_549_3]) ).

cnf(f_549_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1841),U_1843))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1841)),hAPP(c_Nat_OSuc,U_1843))) ),
    inference(clausify,[status(thm)],[f_549_4]) ).

cnf(f_549_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1842)),hAPP(c_Nat_OSuc,U_1844)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1842),U_1844)) ),
    inference(clausify,[status(thm)],[f_549_4]) ).

fof(f_550_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_550_2,plain,
    ! [U_1846,U_1845] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1845),hAPP(c_Nat_OSuc,U_1846)))
        | ( U_1845 != hAPP(c_Nat_OSuc,U_1846)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1845),U_1846)) ) )
      & ( U_1845 = hAPP(c_Nat_OSuc,U_1846)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1845),U_1846))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1845),hAPP(c_Nat_OSuc,U_1846))) ) ),
    inference(variable_rename,[status(thm)],[f_550_1]) ).

fof(f_550_3,plain,
    ( ! [U_1850,U_1848] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1848),hAPP(c_Nat_OSuc,U_1850)))
        | ( U_1848 != hAPP(c_Nat_OSuc,U_1850)
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1848),U_1850)) ) )
    & ! [U_1849,U_1847] :
        ( U_1847 = hAPP(c_Nat_OSuc,U_1849)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1847),U_1849))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1847),hAPP(c_Nat_OSuc,U_1849))) ) ),
    inference(miniscope,[status(thm)],[f_550_2]) ).

fof(f_550_4,plain,
    ( ! [U_1850,U_1848] :
        ( U_1848 != hAPP(c_Nat_OSuc,U_1850)
        | ~ sP153(U_1850,U_1848) )
    & ! [U_1850,U_1848] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1848),U_1850))
        | ~ sP153(U_1850,U_1848) )
    & ! [U_1850,U_1848] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1848),hAPP(c_Nat_OSuc,U_1850)))
        | sP153(U_1850,U_1848) )
    & ! [U_1849,U_1847] :
        ( U_1847 = hAPP(c_Nat_OSuc,U_1849)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1847),U_1849))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1847),hAPP(c_Nat_OSuc,U_1849))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP153])],[f_550_3]) ).

cnf(f_550_5,plain,
    ( U_1847 = hAPP(c_Nat_OSuc,U_1849)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1847),U_1849))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1847),hAPP(c_Nat_OSuc,U_1849))) ),
    inference(clausify,[status(thm)],[f_550_4]) ).

cnf(f_550_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1848),hAPP(c_Nat_OSuc,U_1850)))
    | sP153(U_1850,U_1848) ),
    inference(clausify,[status(thm)],[f_550_4]) ).

cnf(f_550_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1848),U_1850))
    | ~ sP153(U_1850,U_1848) ),
    inference(clausify,[status(thm)],[f_550_4]) ).

cnf(f_550_8,plain,
    ( U_1848 != hAPP(c_Nat_OSuc,U_1850)
    | ~ sP153(U_1850,U_1848) ),
    inference(clausify,[status(thm)],[f_550_4]) ).

fof(f_551_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_551_2,plain,
    ! [U_1852,U_1851] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1851),U_1852))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1852)),U_1851)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1852)),U_1851))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1851),U_1852)) ) ),
    inference(variable_rename,[status(thm)],[f_551_1]) ).

fof(f_551_3,plain,
    ( ! [U_1856,U_1854] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1854),U_1856))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1856)),U_1854)) )
    & ! [U_1855,U_1853] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1855)),U_1853))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1853),U_1855)) ) ),
    inference(miniscope,[status(thm)],[f_551_2]) ).

fof(f_551_4,plain,
    ( ! [U_1854,U_1856] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1854),U_1856))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1856)),U_1854)) )
    & ! [U_1855,U_1853] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1855)),U_1853))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1853),U_1855)) ) ),
    inference(definitional_conversion,[status(esa)],[f_551_3]) ).

cnf(f_551_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1855)),U_1853))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1853),U_1855)) ),
    inference(clausify,[status(thm)],[f_551_4]) ).

cnf(f_551_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1854),U_1856))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1856)),U_1854)) ),
    inference(clausify,[status(thm)],[f_551_4]) ).

fof(f_552_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_552_2,plain,
    ! [U_1857] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1857)),U_1857)),
    inference(variable_rename,[status(thm)],[f_552_1]) ).

fof(f_552_3,plain,
    ! [U_1857] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1857)),U_1857)),
    inference(definitional_conversion,[status(esa)],[f_552_2]) ).

cnf(f_552_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_1857)),U_1857)),
    inference(clausify,[status(thm)],[f_552_3]) ).

fof(f_553_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_553_2,plain,
    ! [U_1859,U_1858] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1858),U_1859))
      | ( U_1858 != U_1859
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1858),U_1859)) ) ),
    inference(variable_rename,[status(thm)],[f_553_1]) ).

fof(f_553_3,plain,
    ( ! [U_1858,U_1859] :
        ( U_1858 != U_1859
        | ~ sP154(U_1858,U_1859) )
    & ! [U_1858,U_1859] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1858),U_1859))
        | ~ sP154(U_1858,U_1859) )
    & ! [U_1858,U_1859] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1858),U_1859))
        | sP154(U_1858,U_1859) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP154])],[f_553_2]) ).

cnf(f_553_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1858),U_1859))
    | sP154(U_1858,U_1859) ),
    inference(clausify,[status(thm)],[f_553_3]) ).

cnf(f_553_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1858),U_1859))
    | ~ sP154(U_1858,U_1859) ),
    inference(clausify,[status(thm)],[f_553_3]) ).

cnf(f_553_6,plain,
    ( U_1858 != U_1859
    | ~ sP154(U_1858,U_1859) ),
    inference(clausify,[status(thm)],[f_553_3]) ).

fof(f_554_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_554_2,plain,
    ! [U_1861,U_1860] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1860),U_1861))
      | U_1860 = U_1861
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1860),U_1861)) ),
    inference(variable_rename,[status(thm)],[f_554_1]) ).

fof(f_554_3,plain,
    ! [U_1861,U_1860] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1860),U_1861))
      | U_1860 = U_1861
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1860),U_1861)) ),
    inference(definitional_conversion,[status(esa)],[f_554_2]) ).

cnf(f_554_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1860),U_1861))
    | U_1860 = U_1861
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1860),U_1861)) ),
    inference(clausify,[status(thm)],[f_554_3]) ).

fof(f_555_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_555_2,plain,
    ! [U_1863,U_1862] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1862),U_1863))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1862),U_1863)) ),
    inference(variable_rename,[status(thm)],[f_555_1]) ).

fof(f_555_3,plain,
    ! [U_1862,U_1863] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1862),U_1863))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1862),U_1863)) ),
    inference(definitional_conversion,[status(esa)],[f_555_2]) ).

cnf(f_555_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1862),U_1863))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1862),U_1863)) ),
    inference(clausify,[status(thm)],[f_555_3]) ).

fof(f_556_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_556_2,plain,
    ! [U_1865,U_1864] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1864),U_1865))
        | ( U_1864 != U_1865
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1864),U_1865)) ) )
      & ( U_1864 = U_1865
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1864),U_1865))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1864),U_1865)) ) ),
    inference(variable_rename,[status(thm)],[f_556_1]) ).

fof(f_556_3,plain,
    ( ! [U_1869,U_1867] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1867),U_1869))
        | ( U_1867 != U_1869
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1867),U_1869)) ) )
    & ! [U_1868,U_1866] :
        ( U_1866 = U_1868
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1866),U_1868))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1866),U_1868)) ) ),
    inference(miniscope,[status(thm)],[f_556_2]) ).

fof(f_556_4,plain,
    ( ! [U_1867,U_1869] :
        ( U_1867 != U_1869
        | ~ sP155(U_1867,U_1869) )
    & ! [U_1867,U_1869] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1867),U_1869))
        | ~ sP155(U_1867,U_1869) )
    & ! [U_1867,U_1869] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1867),U_1869))
        | sP155(U_1867,U_1869) )
    & ! [U_1868,U_1866] :
        ( U_1866 = U_1868
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1866),U_1868))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1866),U_1868)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP155])],[f_556_3]) ).

cnf(f_556_5,plain,
    ( U_1866 = U_1868
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1866),U_1868))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1866),U_1868)) ),
    inference(clausify,[status(thm)],[f_556_4]) ).

cnf(f_556_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1867),U_1869))
    | sP155(U_1867,U_1869) ),
    inference(clausify,[status(thm)],[f_556_4]) ).

cnf(f_556_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1867),U_1869))
    | ~ sP155(U_1867,U_1869) ),
    inference(clausify,[status(thm)],[f_556_4]) ).

cnf(f_556_8,plain,
    ( U_1867 != U_1869
    | ~ sP155(U_1867,U_1869) ),
    inference(clausify,[status(thm)],[f_556_4]) ).

fof(f_557_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_557_2,plain,
    ! [U_1871,U_1870] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1870),U_1871))
        | U_1870 = U_1871
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1870),U_1871)) )
      & ( ( U_1870 != U_1871
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1870),U_1871)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1870),U_1871)) ) ),
    inference(variable_rename,[status(thm)],[f_557_1]) ).

fof(f_557_3,plain,
    ( ! [U_1875,U_1873] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1873),U_1875))
        | U_1873 = U_1875
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1873),U_1875)) )
    & ! [U_1874,U_1872] :
        ( ( U_1872 != U_1874
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1872),U_1874)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1872),U_1874)) ) ),
    inference(miniscope,[status(thm)],[f_557_2]) ).

fof(f_557_4,plain,
    ( ! [U_1874,U_1872] :
        ( U_1872 != U_1874
        | ~ sP156(U_1874,U_1872) )
    & ! [U_1874,U_1872] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1872),U_1874))
        | ~ sP156(U_1874,U_1872) )
    & ! [U_1873,U_1875] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1873),U_1875))
        | U_1873 = U_1875
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1873),U_1875)) )
    & ! [U_1874,U_1872] :
        ( sP156(U_1874,U_1872)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1872),U_1874)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP156])],[f_557_3]) ).

cnf(f_557_5,plain,
    ( sP156(U_1874,U_1872)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1872),U_1874)) ),
    inference(clausify,[status(thm)],[f_557_4]) ).

cnf(f_557_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_1873),U_1875))
    | U_1873 = U_1875
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1873),U_1875)) ),
    inference(clausify,[status(thm)],[f_557_4]) ).

cnf(f_557_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1872),U_1874))
    | ~ sP156(U_1874,U_1872) ),
    inference(clausify,[status(thm)],[f_557_4]) ).

cnf(f_557_8,plain,
    ( U_1872 != U_1874
    | ~ sP156(U_1874,U_1872) ),
    inference(clausify,[status(thm)],[f_557_4]) ).

fof(f_558_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_558_2,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_558_1]) ).

cnf(f_558_3,plain,
    c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_558_2]) ).

fof(f_559_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_559_2,plain,
    ! [U_1878,U_1877,U_1876] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1876),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1877),U_1878)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1876),U_1877)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1876),U_1878)),
    inference(variable_rename,[status(thm)],[f_559_1]) ).

fof(f_559_3,plain,
    ! [U_1877,U_1876,U_1878] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1876),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1877),U_1878)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1876),U_1877)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1876),U_1878)),
    inference(definitional_conversion,[status(esa)],[f_559_2]) ).

cnf(f_559_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1876),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1877),U_1878)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1876),U_1877)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1876),U_1878)),
    inference(clausify,[status(thm)],[f_559_3]) ).

fof(f_560_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_560_2,plain,
    ! [U_1881,U_1880,U_1879] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1879),U_1880)),U_1881) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1879),U_1881)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1880),U_1881)),
    inference(variable_rename,[status(thm)],[f_560_1]) ).

fof(f_560_3,plain,
    ! [U_1879,U_1880,U_1881] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1879),U_1880)),U_1881) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1879),U_1881)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1880),U_1881)),
    inference(definitional_conversion,[status(esa)],[f_560_2]) ).

cnf(f_560_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_1879),U_1880)),U_1881) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1879),U_1881)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1880),U_1881)),
    inference(clausify,[status(thm)],[f_560_3]) ).

fof(f_561_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_561_2,plain,
    ! [U_1885,U_1884,U_1883,U_1882] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1882),U_1883)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1884),U_1883)),U_1885)) = 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_1882),U_1884)),U_1883)),U_1885),
    inference(variable_rename,[status(thm)],[f_561_1]) ).

fof(f_561_3,plain,
    ! [U_1882,U_1883,U_1884,U_1885] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1882),U_1883)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1884),U_1883)),U_1885)) = 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_1882),U_1884)),U_1883)),U_1885),
    inference(definitional_conversion,[status(esa)],[f_561_2]) ).

cnf(f_561_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1882),U_1883)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1884),U_1883)),U_1885)) = 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_1882),U_1884)),U_1883)),U_1885),
    inference(clausify,[status(thm)],[f_561_3]) ).

fof(f_562_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_562_2,plain,
    ! [U_1886] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1886),U_1886))),
    inference(variable_rename,[status(thm)],[f_562_1]) ).

fof(f_562_3,plain,
    ! [U_1886] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1886),U_1886))),
    inference(definitional_conversion,[status(esa)],[f_562_2]) ).

cnf(f_562_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1886),U_1886))),
    inference(clausify,[status(thm)],[f_562_3]) ).

fof(f_563_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_563_2,plain,
    ! [U_1887] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1887),U_1887)))),
    inference(variable_rename,[status(thm)],[f_563_1]) ).

fof(f_563_3,plain,
    ! [U_1887] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1887),U_1887)))),
    inference(definitional_conversion,[status(esa)],[f_563_2]) ).

cnf(f_563_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1887),U_1887)))),
    inference(clausify,[status(thm)],[f_563_3]) ).

fof(f_564_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_564_2,plain,
    ! [U_1890,U_1889,U_1888] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1888),U_1890)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1889),U_1890)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1888),U_1889)) ),
    inference(variable_rename,[status(thm)],[f_564_1]) ).

fof(f_564_3,plain,
    ! [U_1888,U_1889,U_1890] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1888),U_1890)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1889),U_1890)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1888),U_1889)) ),
    inference(definitional_conversion,[status(esa)],[f_564_2]) ).

cnf(f_564_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_1888),U_1890)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1889),U_1890)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1888),U_1889)) ),
    inference(clausify,[status(thm)],[f_564_3]) ).

fof(f_565_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_565_2,plain,
    ! [U_1893,U_1892,U_1891] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1893),U_1891)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1893),U_1892)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1891),U_1892)) ),
    inference(variable_rename,[status(thm)],[f_565_1]) ).

fof(f_565_3,plain,
    ! [U_1891,U_1892,U_1893] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1893),U_1891)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1893),U_1892)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1891),U_1892)) ),
    inference(definitional_conversion,[status(esa)],[f_565_2]) ).

cnf(f_565_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_1893),U_1891)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1893),U_1892)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1891),U_1892)) ),
    inference(clausify,[status(thm)],[f_565_3]) ).

fof(f_566_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_566_2,plain,
    ! [U_1897,U_1896,U_1895,U_1894] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1894),U_1896)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1895),U_1897)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1896),U_1897))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1894),U_1895)) ),
    inference(variable_rename,[status(thm)],[f_566_1]) ).

fof(f_566_3,plain,
    ! [U_1894,U_1895,U_1896,U_1897] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1894),U_1896)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1895),U_1897)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1896),U_1897))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1894),U_1895)) ),
    inference(definitional_conversion,[status(esa)],[f_566_2]) ).

cnf(f_566_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_1894),U_1896)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_1895),U_1897)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1896),U_1897))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1894),U_1895)) ),
    inference(clausify,[status(thm)],[f_566_3]) ).

fof(f_567_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_567_2,plain,
    ! [U_1898] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1898),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_1898,
    inference(variable_rename,[status(thm)],[f_567_1]) ).

fof(f_567_3,plain,
    ! [U_1898] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1898),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_1898,
    inference(definitional_conversion,[status(esa)],[f_567_2]) ).

cnf(f_567_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_1898),c_Groups_Oone__class_Oone(tc_Int_Oint)) = U_1898,
    inference(clausify,[status(thm)],[f_567_3]) ).

fof(f_568_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_568_2,plain,
    ! [U_1899] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1899) = U_1899,
    inference(variable_rename,[status(thm)],[f_568_1]) ).

fof(f_568_3,plain,
    ! [U_1899] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1899) = U_1899,
    inference(definitional_conversion,[status(esa)],[f_568_2]) ).

cnf(f_568_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_1899) = U_1899,
    inference(clausify,[status(thm)],[f_568_3]) ).

fof(f_569_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_569_2,plain,
    ! [U_1903,U_1902,U_1901,U_1900] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1901,U_1900)),U_1902),U_1903))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1901,U_1900)),U_1903),U_1902))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1901,U_1900)),U_1902),U_1903)) )
        & ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1901,U_1900)),U_1903),U_1902))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1901,U_1900)),U_1902),U_1903)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1901,U_1900)),U_1902),U_1903)) ) )
      | ~ class_Orderings_Oord(U_1900) ),
    inference(variable_rename,[status(thm)],[f_569_1]) ).

fof(f_569_3,plain,
    ( ! [U_1900,U_1901,U_1902,U_1903] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1901,U_1900)),U_1903),U_1902))
        | ~ sP157(U_1900,U_1901,U_1902,U_1903) )
    & ! [U_1900,U_1901,U_1902,U_1903] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1901,U_1900)),U_1902),U_1903))
        | ~ sP157(U_1900,U_1901,U_1902,U_1903) )
    & ! [U_1900,U_1901,U_1902,U_1903] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1901,U_1900)),U_1902),U_1903))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1901,U_1900)),U_1903),U_1902))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1901,U_1900)),U_1902),U_1903))
        | ~ sP158(U_1900,U_1901,U_1902,U_1903) )
    & ! [U_1900,U_1901,U_1902,U_1903] :
        ( sP157(U_1900,U_1901,U_1902,U_1903)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1901,U_1900)),U_1902),U_1903))
        | ~ sP158(U_1900,U_1901,U_1902,U_1903) )
    & ! [U_1900,U_1901,U_1902,U_1903] :
        ( sP158(U_1900,U_1901,U_1902,U_1903)
        | ~ class_Orderings_Oord(U_1900) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP157,sP158])],[f_569_2]) ).

cnf(f_569_4,plain,
    ( sP158(U_1900,U_1901,U_1902,U_1903)
    | ~ class_Orderings_Oord(U_1900) ),
    inference(clausify,[status(thm)],[f_569_3]) ).

cnf(f_569_5,plain,
    ( sP157(U_1900,U_1901,U_1902,U_1903)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1901,U_1900)),U_1902),U_1903))
    | ~ sP158(U_1900,U_1901,U_1902,U_1903) ),
    inference(clausify,[status(thm)],[f_569_3]) ).

cnf(f_569_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1901,U_1900)),U_1902),U_1903))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1901,U_1900)),U_1903),U_1902))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1901,U_1900)),U_1902),U_1903))
    | ~ sP158(U_1900,U_1901,U_1902,U_1903) ),
    inference(clausify,[status(thm)],[f_569_3]) ).

cnf(f_569_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1901,U_1900)),U_1902),U_1903))
    | ~ sP157(U_1900,U_1901,U_1902,U_1903) ),
    inference(clausify,[status(thm)],[f_569_3]) ).

cnf(f_569_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1901,U_1900)),U_1903),U_1902))
    | ~ sP157(U_1900,U_1901,U_1902,U_1903) ),
    inference(clausify,[status(thm)],[f_569_3]) ).

fof(f_570_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_570_2,plain,
    ! [U_1908,U_1907,U_1906,U_1905,U_1904] :
      ( c_Natural_Oevaln(U_1904,U_1905,U_1908,U_1907)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1906),U_1908))
      | ~ c_Natural_Oevaln(U_1904,U_1905,U_1906,U_1907) ),
    inference(variable_rename,[status(thm)],[f_570_1]) ).

fof(f_570_3,plain,
    ! [U_1906,U_1907,U_1908,U_1905,U_1904] :
      ( c_Natural_Oevaln(U_1904,U_1905,U_1908,U_1907)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1906),U_1908))
      | ~ c_Natural_Oevaln(U_1904,U_1905,U_1906,U_1907) ),
    inference(definitional_conversion,[status(esa)],[f_570_2]) ).

cnf(f_570_4,plain,
    ( c_Natural_Oevaln(U_1904,U_1905,U_1908,U_1907)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_1906),U_1908))
    | ~ c_Natural_Oevaln(U_1904,U_1905,U_1906,U_1907) ),
    inference(clausify,[status(thm)],[f_570_3]) ).

fof(f_571_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_571_2,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_571_1]) ).

cnf(f_571_3,plain,
    ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_571_2]) ).

fof(f_572_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_572_2,plain,
    ! [U_1912,U_1911,U_1910,U_1909] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1909,tc_HOL_Obool)),U_1910),U_1912))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1909,tc_HOL_Obool)),U_1911),U_1912))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1909,tc_HOL_Obool)),U_1910),U_1911)) ),
    inference(variable_rename,[status(thm)],[f_572_1]) ).

fof(f_572_3,plain,
    ! [U_1909,U_1910,U_1911,U_1912] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1909,tc_HOL_Obool)),U_1910),U_1912))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1909,tc_HOL_Obool)),U_1911),U_1912))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1909,tc_HOL_Obool)),U_1910),U_1911)) ),
    inference(definitional_conversion,[status(esa)],[f_572_2]) ).

cnf(f_572_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1909,tc_HOL_Obool)),U_1910),U_1912))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1909,tc_HOL_Obool)),U_1911),U_1912))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1909,tc_HOL_Obool)),U_1910),U_1911)) ),
    inference(clausify,[status(thm)],[f_572_3]) ).

fof(f_573_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_573_2,plain,
    ! [U_1916,U_1915,U_1914,U_1913] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1913,tc_HOL_Obool)),U_1914),U_1916))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1913,tc_HOL_Obool)),U_1915),U_1916))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1913,tc_HOL_Obool)),U_1914),U_1915)) ),
    inference(variable_rename,[status(thm)],[f_573_1]) ).

fof(f_573_3,plain,
    ! [U_1913,U_1914,U_1915,U_1916] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1913,tc_HOL_Obool)),U_1914),U_1916))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1913,tc_HOL_Obool)),U_1915),U_1916))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1913,tc_HOL_Obool)),U_1914),U_1915)) ),
    inference(definitional_conversion,[status(esa)],[f_573_2]) ).

cnf(f_573_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1913,tc_HOL_Obool)),U_1914),U_1916))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1913,tc_HOL_Obool)),U_1915),U_1916))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1913,tc_HOL_Obool)),U_1914),U_1915)) ),
    inference(clausify,[status(thm)],[f_573_3]) ).

fof(f_574_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_574_2,plain,
    ! [U_1919,U_1918,U_1917] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1917,tc_HOL_Obool)),U_1918),U_1919))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1917,tc_HOL_Obool)),U_1918),U_1919)) ),
    inference(variable_rename,[status(thm)],[f_574_1]) ).

fof(f_574_3,plain,
    ! [U_1918,U_1917,U_1919] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1917,tc_HOL_Obool)),U_1918),U_1919))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1917,tc_HOL_Obool)),U_1918),U_1919)) ),
    inference(definitional_conversion,[status(esa)],[f_574_2]) ).

cnf(f_574_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1917,tc_HOL_Obool)),U_1918),U_1919))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1917,tc_HOL_Obool)),U_1918),U_1919)) ),
    inference(clausify,[status(thm)],[f_574_3]) ).

fof(f_575_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_575_2,plain,
    ! [U_1922,U_1921,U_1920] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1920,tc_HOL_Obool)),U_1921),U_1922))
        | ( U_1921 != U_1922
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1920,tc_HOL_Obool)),U_1921),U_1922)) ) )
      & ( U_1921 = U_1922
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1920,tc_HOL_Obool)),U_1921),U_1922))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1920,tc_HOL_Obool)),U_1921),U_1922)) ) ),
    inference(variable_rename,[status(thm)],[f_575_1]) ).

fof(f_575_3,plain,
    ( ! [U_1928,U_1926,U_1924] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1924,tc_HOL_Obool)),U_1926),U_1928))
        | ( U_1926 != U_1928
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1924,tc_HOL_Obool)),U_1926),U_1928)) ) )
    & ! [U_1927,U_1925,U_1923] :
        ( U_1925 = U_1927
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1923,tc_HOL_Obool)),U_1925),U_1927))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1923,tc_HOL_Obool)),U_1925),U_1927)) ) ),
    inference(miniscope,[status(thm)],[f_575_2]) ).

fof(f_575_4,plain,
    ( ! [U_1926,U_1924,U_1928] :
        ( U_1926 != U_1928
        | ~ sP159(U_1926,U_1924,U_1928) )
    & ! [U_1926,U_1924,U_1928] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1924,tc_HOL_Obool)),U_1926),U_1928))
        | ~ sP159(U_1926,U_1924,U_1928) )
    & ! [U_1926,U_1924,U_1928] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1924,tc_HOL_Obool)),U_1926),U_1928))
        | sP159(U_1926,U_1924,U_1928) )
    & ! [U_1925,U_1923,U_1927] :
        ( U_1925 = U_1927
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1923,tc_HOL_Obool)),U_1925),U_1927))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1923,tc_HOL_Obool)),U_1925),U_1927)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP159])],[f_575_3]) ).

cnf(f_575_5,plain,
    ( U_1925 = U_1927
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1923,tc_HOL_Obool)),U_1925),U_1927))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1923,tc_HOL_Obool)),U_1925),U_1927)) ),
    inference(clausify,[status(thm)],[f_575_4]) ).

cnf(f_575_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1924,tc_HOL_Obool)),U_1926),U_1928))
    | sP159(U_1926,U_1924,U_1928) ),
    inference(clausify,[status(thm)],[f_575_4]) ).

cnf(f_575_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1924,tc_HOL_Obool)),U_1926),U_1928))
    | ~ sP159(U_1926,U_1924,U_1928) ),
    inference(clausify,[status(thm)],[f_575_4]) ).

cnf(f_575_8,plain,
    ( U_1926 != U_1928
    | ~ sP159(U_1926,U_1924,U_1928) ),
    inference(clausify,[status(thm)],[f_575_4]) ).

fof(f_576_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_576_2,plain,
    ! [U_1931,U_1930,U_1929] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1929,tc_HOL_Obool)),U_1930),U_1931))
        | U_1930 = U_1931
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1929,tc_HOL_Obool)),U_1930),U_1931)) )
      & ( ( U_1930 != U_1931
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1929,tc_HOL_Obool)),U_1930),U_1931)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1929,tc_HOL_Obool)),U_1930),U_1931)) ) ),
    inference(variable_rename,[status(thm)],[f_576_1]) ).

fof(f_576_3,plain,
    ( ! [U_1937,U_1935,U_1933] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1933,tc_HOL_Obool)),U_1935),U_1937))
        | U_1935 = U_1937
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1933,tc_HOL_Obool)),U_1935),U_1937)) )
    & ! [U_1936,U_1934,U_1932] :
        ( ( U_1934 != U_1936
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1932,tc_HOL_Obool)),U_1934),U_1936)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1932,tc_HOL_Obool)),U_1934),U_1936)) ) ),
    inference(miniscope,[status(thm)],[f_576_2]) ).

fof(f_576_4,plain,
    ( ! [U_1934,U_1932,U_1936] :
        ( U_1934 != U_1936
        | ~ sP160(U_1934,U_1932,U_1936) )
    & ! [U_1934,U_1932,U_1936] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1932,tc_HOL_Obool)),U_1934),U_1936))
        | ~ sP160(U_1934,U_1932,U_1936) )
    & ! [U_1935,U_1933,U_1937] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1933,tc_HOL_Obool)),U_1935),U_1937))
        | U_1935 = U_1937
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1933,tc_HOL_Obool)),U_1935),U_1937)) )
    & ! [U_1934,U_1932,U_1936] :
        ( sP160(U_1934,U_1932,U_1936)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1932,tc_HOL_Obool)),U_1934),U_1936)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP160])],[f_576_3]) ).

cnf(f_576_5,plain,
    ( sP160(U_1934,U_1932,U_1936)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1932,tc_HOL_Obool)),U_1934),U_1936)) ),
    inference(clausify,[status(thm)],[f_576_4]) ).

cnf(f_576_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_1933,tc_HOL_Obool)),U_1935),U_1937))
    | U_1935 = U_1937
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1933,tc_HOL_Obool)),U_1935),U_1937)) ),
    inference(clausify,[status(thm)],[f_576_4]) ).

cnf(f_576_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_1932,tc_HOL_Obool)),U_1934),U_1936))
    | ~ sP160(U_1934,U_1932,U_1936) ),
    inference(clausify,[status(thm)],[f_576_4]) ).

cnf(f_576_8,plain,
    ( U_1934 != U_1936
    | ~ sP160(U_1934,U_1932,U_1936) ),
    inference(clausify,[status(thm)],[f_576_4]) ).

fof(f_577_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_577_2,plain,
    ! [U_1943,U_1942,U_1941,U_1940,U_1939,U_1938] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1938),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1938),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1938),U_1942),U_1939)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1938),U_1943),U_1941))),U_1940))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1938),U_1942),U_1943) != c_Groups_Oone__class_Oone(U_1938)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1938),c_Groups_Ozero__class_Ozero(U_1938)),U_1943))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1938),c_Groups_Ozero__class_Ozero(U_1938)),U_1942))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1938),U_1941),U_1940))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1938),U_1939),U_1940))
      | ~ class_Rings_Olinordered__semiring__1(U_1938) ),
    inference(variable_rename,[status(thm)],[f_577_1]) ).

fof(f_577_3,plain,
    ! [U_1938,U_1939,U_1940,U_1941,U_1942,U_1943] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1938),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1938),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1938),U_1942),U_1939)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1938),U_1943),U_1941))),U_1940))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1938),U_1942),U_1943) != c_Groups_Oone__class_Oone(U_1938)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1938),c_Groups_Ozero__class_Ozero(U_1938)),U_1943))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1938),c_Groups_Ozero__class_Ozero(U_1938)),U_1942))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1938),U_1941),U_1940))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1938),U_1939),U_1940))
      | ~ class_Rings_Olinordered__semiring__1(U_1938) ),
    inference(definitional_conversion,[status(esa)],[f_577_2]) ).

cnf(f_577_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1938),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1938),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1938),U_1942),U_1939)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1938),U_1943),U_1941))),U_1940))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1938),U_1942),U_1943) != c_Groups_Oone__class_Oone(U_1938)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1938),c_Groups_Ozero__class_Ozero(U_1938)),U_1943))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1938),c_Groups_Ozero__class_Ozero(U_1938)),U_1942))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1938),U_1941),U_1940))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1938),U_1939),U_1940))
    | ~ class_Rings_Olinordered__semiring__1(U_1938) ),
    inference(clausify,[status(thm)],[f_577_3]) ).

fof(f_578_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_578_2,plain,
    ! [U_1949,U_1948,U_1947,U_1946,U_1945,U_1944] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1944),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1944),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1944),U_1948),U_1945)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1944),U_1949),U_1947))),U_1946))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1944),U_1948),U_1949) != c_Groups_Oone__class_Oone(U_1944)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1944),c_Groups_Ozero__class_Ozero(U_1944)),U_1949))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1944),c_Groups_Ozero__class_Ozero(U_1944)),U_1948))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1944),U_1947),U_1946))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1944),U_1945),U_1946))
      | ~ class_Rings_Olinordered__semiring__1__strict(U_1944) ),
    inference(variable_rename,[status(thm)],[f_578_1]) ).

fof(f_578_3,plain,
    ! [U_1947,U_1946,U_1948,U_1944,U_1945,U_1949] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1944),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1944),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1944),U_1948),U_1945)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1944),U_1949),U_1947))),U_1946))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1944),U_1948),U_1949) != c_Groups_Oone__class_Oone(U_1944)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1944),c_Groups_Ozero__class_Ozero(U_1944)),U_1949))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1944),c_Groups_Ozero__class_Ozero(U_1944)),U_1948))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1944),U_1947),U_1946))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1944),U_1945),U_1946))
      | ~ class_Rings_Olinordered__semiring__1__strict(U_1944) ),
    inference(definitional_conversion,[status(esa)],[f_578_2]) ).

cnf(f_578_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1944),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1944),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1944),U_1948),U_1945)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1944),U_1949),U_1947))),U_1946))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1944),U_1948),U_1949) != c_Groups_Oone__class_Oone(U_1944)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1944),c_Groups_Ozero__class_Ozero(U_1944)),U_1949))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1944),c_Groups_Ozero__class_Ozero(U_1944)),U_1948))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1944),U_1947),U_1946))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1944),U_1945),U_1946))
    | ~ class_Rings_Olinordered__semiring__1__strict(U_1944) ),
    inference(clausify,[status(thm)],[f_578_3]) ).

fof(f_579_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_579_2,plain,
    ! [U_1952,U_1951,U_1950] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1950),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1950),U_1951),U_1952)),c_Groups_Ozero__class_Ozero(U_1950)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1950),U_1952),c_Groups_Ozero__class_Ozero(U_1950)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1950),U_1951),c_Groups_Ozero__class_Ozero(U_1950)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1950) ),
    inference(variable_rename,[status(thm)],[f_579_1]) ).

fof(f_579_3,plain,
    ! [U_1951,U_1950,U_1952] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1950),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1950),U_1951),U_1952)),c_Groups_Ozero__class_Ozero(U_1950)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1950),U_1952),c_Groups_Ozero__class_Ozero(U_1950)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1950),U_1951),c_Groups_Ozero__class_Ozero(U_1950)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1950) ),
    inference(definitional_conversion,[status(esa)],[f_579_2]) ).

cnf(f_579_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1950),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1950),U_1951),U_1952)),c_Groups_Ozero__class_Ozero(U_1950)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1950),U_1952),c_Groups_Ozero__class_Ozero(U_1950)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1950),U_1951),c_Groups_Ozero__class_Ozero(U_1950)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_1950) ),
    inference(clausify,[status(thm)],[f_579_3]) ).

fof(f_580_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_580_2,plain,
    ! [U_1956,U_1955,U_1954,U_1953] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1953),U_1955),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1953),U_1956),U_1954)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1953),U_1955),U_1956))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1953),c_Groups_Ozero__class_Ozero(U_1953)),U_1954))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1953) ),
    inference(variable_rename,[status(thm)],[f_580_1]) ).

fof(f_580_3,plain,
    ! [U_1954,U_1953,U_1955,U_1956] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1953),U_1955),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1953),U_1956),U_1954)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1953),U_1955),U_1956))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1953),c_Groups_Ozero__class_Ozero(U_1953)),U_1954))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1953) ),
    inference(definitional_conversion,[status(esa)],[f_580_2]) ).

cnf(f_580_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1953),U_1955),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1953),U_1956),U_1954)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1953),U_1955),U_1956))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1953),c_Groups_Ozero__class_Ozero(U_1953)),U_1954))
    | ~ class_Groups_Oordered__comm__monoid__add(U_1953) ),
    inference(clausify,[status(thm)],[f_580_3]) ).

fof(f_581_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_581_2,plain,
    ! [U_1960,U_1959,U_1958,U_1957] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1957),U_1959),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1957),U_1958),U_1960)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1957),U_1959),U_1960))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1957),c_Groups_Ozero__class_Ozero(U_1957)),U_1958))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1957) ),
    inference(variable_rename,[status(thm)],[f_581_1]) ).

fof(f_581_3,plain,
    ! [U_1958,U_1957,U_1959,U_1960] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1957),U_1959),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1957),U_1958),U_1960)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1957),U_1959),U_1960))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1957),c_Groups_Ozero__class_Ozero(U_1957)),U_1958))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1957) ),
    inference(definitional_conversion,[status(esa)],[f_581_2]) ).

cnf(f_581_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1957),U_1959),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1957),U_1958),U_1960)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1957),U_1959),U_1960))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1957),c_Groups_Ozero__class_Ozero(U_1957)),U_1958))
    | ~ class_Groups_Oordered__comm__monoid__add(U_1957) ),
    inference(clausify,[status(thm)],[f_581_3]) ).

fof(f_582_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_582_2,plain,
    ! [U_1963,U_1962,U_1961] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1961),U_1962),U_1963) = c_Groups_Ozero__class_Ozero(U_1961)
          | U_1963 != c_Groups_Ozero__class_Ozero(U_1961)
          | U_1962 != c_Groups_Ozero__class_Ozero(U_1961) )
        & ( ( U_1963 = c_Groups_Ozero__class_Ozero(U_1961)
            & U_1962 = c_Groups_Ozero__class_Ozero(U_1961) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1961),U_1962),U_1963) != c_Groups_Ozero__class_Ozero(U_1961) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1961),c_Groups_Ozero__class_Ozero(U_1961)),U_1963))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1961),c_Groups_Ozero__class_Ozero(U_1961)),U_1962))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1961) ),
    inference(variable_rename,[status(thm)],[f_582_1]) ).

fof(f_582_3,plain,
    ( ! [U_1961,U_1962,U_1963] :
        ( U_1963 = c_Groups_Ozero__class_Ozero(U_1961)
        | ~ sP161(U_1961,U_1962,U_1963) )
    & ! [U_1961,U_1962,U_1963] :
        ( U_1962 = c_Groups_Ozero__class_Ozero(U_1961)
        | ~ sP161(U_1961,U_1962,U_1963) )
    & ! [U_1961,U_1962,U_1963] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1961),U_1962),U_1963) = c_Groups_Ozero__class_Ozero(U_1961)
        | U_1963 != c_Groups_Ozero__class_Ozero(U_1961)
        | U_1962 != c_Groups_Ozero__class_Ozero(U_1961)
        | ~ sP162(U_1961,U_1962,U_1963) )
    & ! [U_1961,U_1962,U_1963] :
        ( sP161(U_1961,U_1962,U_1963)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1961),U_1962),U_1963) != c_Groups_Ozero__class_Ozero(U_1961)
        | ~ sP162(U_1961,U_1962,U_1963) )
    & ! [U_1961,U_1962,U_1963] :
        ( sP162(U_1961,U_1962,U_1963)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1961),c_Groups_Ozero__class_Ozero(U_1961)),U_1963))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1961),c_Groups_Ozero__class_Ozero(U_1961)),U_1962))
        | ~ class_Groups_Oordered__comm__monoid__add(U_1961) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP161,sP162])],[f_582_2]) ).

cnf(f_582_4,plain,
    ( sP162(U_1961,U_1962,U_1963)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1961),c_Groups_Ozero__class_Ozero(U_1961)),U_1963))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1961),c_Groups_Ozero__class_Ozero(U_1961)),U_1962))
    | ~ class_Groups_Oordered__comm__monoid__add(U_1961) ),
    inference(clausify,[status(thm)],[f_582_3]) ).

cnf(f_582_5,plain,
    ( sP161(U_1961,U_1962,U_1963)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1961),U_1962),U_1963) != c_Groups_Ozero__class_Ozero(U_1961)
    | ~ sP162(U_1961,U_1962,U_1963) ),
    inference(clausify,[status(thm)],[f_582_3]) ).

cnf(f_582_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1961),U_1962),U_1963) = c_Groups_Ozero__class_Ozero(U_1961)
    | U_1963 != c_Groups_Ozero__class_Ozero(U_1961)
    | U_1962 != c_Groups_Ozero__class_Ozero(U_1961)
    | ~ sP162(U_1961,U_1962,U_1963) ),
    inference(clausify,[status(thm)],[f_582_3]) ).

cnf(f_582_7,plain,
    ( U_1962 = c_Groups_Ozero__class_Ozero(U_1961)
    | ~ sP161(U_1961,U_1962,U_1963) ),
    inference(clausify,[status(thm)],[f_582_3]) ).

cnf(f_582_8,plain,
    ( U_1963 = c_Groups_Ozero__class_Ozero(U_1961)
    | ~ sP161(U_1961,U_1962,U_1963) ),
    inference(clausify,[status(thm)],[f_582_3]) ).

fof(f_583_1,plain,
    ! [V_b,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__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_583_2,plain,
    ! [U_1966,U_1965,U_1964] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1964),c_Groups_Ozero__class_Ozero(U_1964)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1964),U_1965),U_1966)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1964),c_Groups_Ozero__class_Ozero(U_1964)),U_1966))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1964),c_Groups_Ozero__class_Ozero(U_1964)),U_1965))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1964) ),
    inference(variable_rename,[status(thm)],[f_583_1]) ).

fof(f_583_3,plain,
    ! [U_1965,U_1966,U_1964] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1964),c_Groups_Ozero__class_Ozero(U_1964)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1964),U_1965),U_1966)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1964),c_Groups_Ozero__class_Ozero(U_1964)),U_1966))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1964),c_Groups_Ozero__class_Ozero(U_1964)),U_1965))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1964) ),
    inference(definitional_conversion,[status(esa)],[f_583_2]) ).

cnf(f_583_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1964),c_Groups_Ozero__class_Ozero(U_1964)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1964),U_1965),U_1966)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1964),c_Groups_Ozero__class_Ozero(U_1964)),U_1966))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1964),c_Groups_Ozero__class_Ozero(U_1964)),U_1965))
    | ~ class_Groups_Oordered__comm__monoid__add(U_1964) ),
    inference(clausify,[status(thm)],[f_583_3]) ).

fof(f_584_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_584_2,plain,
    ! [U_1968,U_1967] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1967),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1967),U_1968),U_1968)),c_Groups_Ozero__class_Ozero(U_1967)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1967),U_1968),c_Groups_Ozero__class_Ozero(U_1967))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1967),U_1968),c_Groups_Ozero__class_Ozero(U_1967)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1967),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1967),U_1968),U_1968)),c_Groups_Ozero__class_Ozero(U_1967))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1967) ),
    inference(variable_rename,[status(thm)],[f_584_1]) ).

fof(f_584_3,plain,
    ( ! [U_1968,U_1967] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1967),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1967),U_1968),U_1968)),c_Groups_Ozero__class_Ozero(U_1967)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1967),U_1968),c_Groups_Ozero__class_Ozero(U_1967)))
        | ~ sP163(U_1968,U_1967) )
    & ! [U_1968,U_1967] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1967),U_1968),c_Groups_Ozero__class_Ozero(U_1967)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1967),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1967),U_1968),U_1968)),c_Groups_Ozero__class_Ozero(U_1967)))
        | ~ sP163(U_1968,U_1967) )
    & ! [U_1968,U_1967] :
        ( sP163(U_1968,U_1967)
        | ~ class_Groups_Olinordered__ab__group__add(U_1967) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP163])],[f_584_2]) ).

cnf(f_584_4,plain,
    ( sP163(U_1968,U_1967)
    | ~ class_Groups_Olinordered__ab__group__add(U_1967) ),
    inference(clausify,[status(thm)],[f_584_3]) ).

cnf(f_584_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1967),U_1968),c_Groups_Ozero__class_Ozero(U_1967)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1967),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1967),U_1968),U_1968)),c_Groups_Ozero__class_Ozero(U_1967)))
    | ~ sP163(U_1968,U_1967) ),
    inference(clausify,[status(thm)],[f_584_3]) ).

cnf(f_584_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1967),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1967),U_1968),U_1968)),c_Groups_Ozero__class_Ozero(U_1967)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1967),U_1968),c_Groups_Ozero__class_Ozero(U_1967)))
    | ~ sP163(U_1968,U_1967) ),
    inference(clausify,[status(thm)],[f_584_3]) ).

fof(f_585_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_585_2,plain,
    ! [U_1970,U_1969] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1969),c_Groups_Ozero__class_Ozero(U_1969)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1969),U_1970),U_1970)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1969),c_Groups_Ozero__class_Ozero(U_1969)),U_1970)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1969),c_Groups_Ozero__class_Ozero(U_1969)),U_1970))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1969),c_Groups_Ozero__class_Ozero(U_1969)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1969),U_1970),U_1970))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1969) ),
    inference(variable_rename,[status(thm)],[f_585_1]) ).

fof(f_585_3,plain,
    ( ! [U_1970,U_1969] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1969),c_Groups_Ozero__class_Ozero(U_1969)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1969),U_1970),U_1970)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1969),c_Groups_Ozero__class_Ozero(U_1969)),U_1970))
        | ~ sP164(U_1970,U_1969) )
    & ! [U_1970,U_1969] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1969),c_Groups_Ozero__class_Ozero(U_1969)),U_1970))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1969),c_Groups_Ozero__class_Ozero(U_1969)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1969),U_1970),U_1970)))
        | ~ sP164(U_1970,U_1969) )
    & ! [U_1970,U_1969] :
        ( sP164(U_1970,U_1969)
        | ~ class_Groups_Olinordered__ab__group__add(U_1969) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP164])],[f_585_2]) ).

cnf(f_585_4,plain,
    ( sP164(U_1970,U_1969)
    | ~ class_Groups_Olinordered__ab__group__add(U_1969) ),
    inference(clausify,[status(thm)],[f_585_3]) ).

cnf(f_585_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1969),c_Groups_Ozero__class_Ozero(U_1969)),U_1970))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1969),c_Groups_Ozero__class_Ozero(U_1969)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1969),U_1970),U_1970)))
    | ~ sP164(U_1970,U_1969) ),
    inference(clausify,[status(thm)],[f_585_3]) ).

cnf(f_585_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1969),c_Groups_Ozero__class_Ozero(U_1969)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1969),U_1970),U_1970)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1969),c_Groups_Ozero__class_Ozero(U_1969)),U_1970))
    | ~ sP164(U_1970,U_1969) ),
    inference(clausify,[status(thm)],[f_585_3]) ).

fof(f_586_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_586_2,plain,
    ! [U_1975,U_1974,U_1973,U_1972,U_1971] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1971),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1971),U_1972),U_1974)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1971),U_1973),U_1975)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1971),U_1974),U_1975))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1971),U_1972),U_1973))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1971) ),
    inference(variable_rename,[status(thm)],[f_586_1]) ).

fof(f_586_3,plain,
    ! [U_1971,U_1972,U_1973,U_1974,U_1975] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1971),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1971),U_1972),U_1974)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1971),U_1973),U_1975)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1971),U_1974),U_1975))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1971),U_1972),U_1973))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1971) ),
    inference(definitional_conversion,[status(esa)],[f_586_2]) ).

cnf(f_586_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1971),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1971),U_1972),U_1974)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1971),U_1973),U_1975)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1971),U_1974),U_1975))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1971),U_1972),U_1973))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1971) ),
    inference(clausify,[status(thm)],[f_586_3]) ).

fof(f_587_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_587_2,plain,
    ! [U_1980,U_1979,U_1978,U_1977,U_1976] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1976),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1976),U_1977),U_1979)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1976),U_1978),U_1980)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1976),U_1979),U_1980))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1976),U_1977),U_1978))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1976) ),
    inference(variable_rename,[status(thm)],[f_587_1]) ).

fof(f_587_3,plain,
    ! [U_1976,U_1977,U_1978,U_1979,U_1980] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1976),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1976),U_1977),U_1979)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1976),U_1978),U_1980)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1976),U_1979),U_1980))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1976),U_1977),U_1978))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1976) ),
    inference(definitional_conversion,[status(esa)],[f_587_2]) ).

cnf(f_587_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1976),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1976),U_1977),U_1979)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1976),U_1978),U_1980)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_1976),U_1979),U_1980))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1976),U_1977),U_1978))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_1976) ),
    inference(clausify,[status(thm)],[f_587_3]) ).

fof(f_588_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_588_2,plain,
    ! [U_1982,U_1981] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1981),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1981),U_1982),U_1982)),c_Groups_Ozero__class_Ozero(U_1981)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1981),U_1982),c_Groups_Ozero__class_Ozero(U_1981))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1981),U_1982),c_Groups_Ozero__class_Ozero(U_1981)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1981),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1981),U_1982),U_1982)),c_Groups_Ozero__class_Ozero(U_1981))) ) )
      | ~ class_Rings_Olinordered__idom(U_1981) ),
    inference(variable_rename,[status(thm)],[f_588_1]) ).

fof(f_588_3,plain,
    ( ! [U_1982,U_1981] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1981),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1981),U_1982),U_1982)),c_Groups_Ozero__class_Ozero(U_1981)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1981),U_1982),c_Groups_Ozero__class_Ozero(U_1981)))
        | ~ sP165(U_1982,U_1981) )
    & ! [U_1982,U_1981] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1981),U_1982),c_Groups_Ozero__class_Ozero(U_1981)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1981),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1981),U_1982),U_1982)),c_Groups_Ozero__class_Ozero(U_1981)))
        | ~ sP165(U_1982,U_1981) )
    & ! [U_1982,U_1981] :
        ( sP165(U_1982,U_1981)
        | ~ class_Rings_Olinordered__idom(U_1981) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP165])],[f_588_2]) ).

cnf(f_588_4,plain,
    ( sP165(U_1982,U_1981)
    | ~ class_Rings_Olinordered__idom(U_1981) ),
    inference(clausify,[status(thm)],[f_588_3]) ).

cnf(f_588_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1981),U_1982),c_Groups_Ozero__class_Ozero(U_1981)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1981),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1981),U_1982),U_1982)),c_Groups_Ozero__class_Ozero(U_1981)))
    | ~ sP165(U_1982,U_1981) ),
    inference(clausify,[status(thm)],[f_588_3]) ).

cnf(f_588_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1981),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1981),U_1982),U_1982)),c_Groups_Ozero__class_Ozero(U_1981)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1981),U_1982),c_Groups_Ozero__class_Ozero(U_1981)))
    | ~ sP165(U_1982,U_1981) ),
    inference(clausify,[status(thm)],[f_588_3]) ).

fof(f_589_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_589_2,plain,
    ! [U_1986,U_1985,U_1984,U_1983] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1983),U_1985),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1983),U_1984),U_1986)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1983),U_1985),U_1986))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1983),c_Groups_Ozero__class_Ozero(U_1983)),U_1984))
      | ~ class_Rings_Olinordered__semidom(U_1983) ),
    inference(variable_rename,[status(thm)],[f_589_1]) ).

fof(f_589_3,plain,
    ! [U_1984,U_1983,U_1985,U_1986] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1983),U_1985),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1983),U_1984),U_1986)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1983),U_1985),U_1986))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1983),c_Groups_Ozero__class_Ozero(U_1983)),U_1984))
      | ~ class_Rings_Olinordered__semidom(U_1983) ),
    inference(definitional_conversion,[status(esa)],[f_589_2]) ).

cnf(f_589_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1983),U_1985),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1983),U_1984),U_1986)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1983),U_1985),U_1986))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1983),c_Groups_Ozero__class_Ozero(U_1983)),U_1984))
    | ~ class_Rings_Olinordered__semidom(U_1983) ),
    inference(clausify,[status(thm)],[f_589_3]) ).

fof(f_590_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_590_2,plain,
    ! [U_1989,U_1988,U_1987] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1987),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1987),U_1988),U_1989)),c_Groups_Ozero__class_Ozero(U_1987)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1987),U_1989),c_Groups_Ozero__class_Ozero(U_1987)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1987),U_1988),c_Groups_Ozero__class_Ozero(U_1987)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1987) ),
    inference(variable_rename,[status(thm)],[f_590_1]) ).

fof(f_590_3,plain,
    ! [U_1987,U_1988,U_1989] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1987),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1987),U_1988),U_1989)),c_Groups_Ozero__class_Ozero(U_1987)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1987),U_1989),c_Groups_Ozero__class_Ozero(U_1987)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1987),U_1988),c_Groups_Ozero__class_Ozero(U_1987)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1987) ),
    inference(definitional_conversion,[status(esa)],[f_590_2]) ).

cnf(f_590_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1987),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1987),U_1988),U_1989)),c_Groups_Ozero__class_Ozero(U_1987)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1987),U_1989),c_Groups_Ozero__class_Ozero(U_1987)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1987),U_1988),c_Groups_Ozero__class_Ozero(U_1987)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_1987) ),
    inference(clausify,[status(thm)],[f_590_3]) ).

fof(f_591_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_591_2,plain,
    ! [U_1992,U_1991,U_1990] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1990),c_Groups_Ozero__class_Ozero(U_1990)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1990),U_1991),U_1992)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1990),c_Groups_Ozero__class_Ozero(U_1990)),U_1992))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1990),c_Groups_Ozero__class_Ozero(U_1990)),U_1991))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1990) ),
    inference(variable_rename,[status(thm)],[f_591_1]) ).

fof(f_591_3,plain,
    ! [U_1991,U_1990,U_1992] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1990),c_Groups_Ozero__class_Ozero(U_1990)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1990),U_1991),U_1992)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1990),c_Groups_Ozero__class_Ozero(U_1990)),U_1992))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1990),c_Groups_Ozero__class_Ozero(U_1990)),U_1991))
      | ~ class_Groups_Oordered__comm__monoid__add(U_1990) ),
    inference(definitional_conversion,[status(esa)],[f_591_2]) ).

cnf(f_591_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1990),c_Groups_Ozero__class_Ozero(U_1990)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1990),U_1991),U_1992)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1990),c_Groups_Ozero__class_Ozero(U_1990)),U_1992))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1990),c_Groups_Ozero__class_Ozero(U_1990)),U_1991))
    | ~ class_Groups_Oordered__comm__monoid__add(U_1990) ),
    inference(clausify,[status(thm)],[f_591_3]) ).

fof(f_592_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_592_2,plain,
    ! [U_1994,U_1993] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1993),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1993),U_1994),U_1994)),c_Groups_Ozero__class_Ozero(U_1993)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1993),U_1994),c_Groups_Ozero__class_Ozero(U_1993))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1993),U_1994),c_Groups_Ozero__class_Ozero(U_1993)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1993),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1993),U_1994),U_1994)),c_Groups_Ozero__class_Ozero(U_1993))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1993) ),
    inference(variable_rename,[status(thm)],[f_592_1]) ).

fof(f_592_3,plain,
    ( ! [U_1994,U_1993] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1993),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1993),U_1994),U_1994)),c_Groups_Ozero__class_Ozero(U_1993)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1993),U_1994),c_Groups_Ozero__class_Ozero(U_1993)))
        | ~ sP166(U_1994,U_1993) )
    & ! [U_1994,U_1993] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1993),U_1994),c_Groups_Ozero__class_Ozero(U_1993)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1993),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1993),U_1994),U_1994)),c_Groups_Ozero__class_Ozero(U_1993)))
        | ~ sP166(U_1994,U_1993) )
    & ! [U_1994,U_1993] :
        ( sP166(U_1994,U_1993)
        | ~ class_Groups_Olinordered__ab__group__add(U_1993) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP166])],[f_592_2]) ).

cnf(f_592_4,plain,
    ( sP166(U_1994,U_1993)
    | ~ class_Groups_Olinordered__ab__group__add(U_1993) ),
    inference(clausify,[status(thm)],[f_592_3]) ).

cnf(f_592_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1993),U_1994),c_Groups_Ozero__class_Ozero(U_1993)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1993),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1993),U_1994),U_1994)),c_Groups_Ozero__class_Ozero(U_1993)))
    | ~ sP166(U_1994,U_1993) ),
    inference(clausify,[status(thm)],[f_592_3]) ).

cnf(f_592_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1993),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1993),U_1994),U_1994)),c_Groups_Ozero__class_Ozero(U_1993)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1993),U_1994),c_Groups_Ozero__class_Ozero(U_1993)))
    | ~ sP166(U_1994,U_1993) ),
    inference(clausify,[status(thm)],[f_592_3]) ).

fof(f_593_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_593_2,plain,
    ! [U_1996,U_1995] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),c_Groups_Ozero__class_Ozero(U_1995)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1995),U_1996),U_1996)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),c_Groups_Ozero__class_Ozero(U_1995)),U_1996)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),c_Groups_Ozero__class_Ozero(U_1995)),U_1996))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),c_Groups_Ozero__class_Ozero(U_1995)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1995),U_1996),U_1996))) ) )
      | ~ class_Groups_Olinordered__ab__group__add(U_1995) ),
    inference(variable_rename,[status(thm)],[f_593_1]) ).

fof(f_593_3,plain,
    ( ! [U_1996,U_1995] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),c_Groups_Ozero__class_Ozero(U_1995)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1995),U_1996),U_1996)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),c_Groups_Ozero__class_Ozero(U_1995)),U_1996))
        | ~ sP167(U_1996,U_1995) )
    & ! [U_1996,U_1995] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),c_Groups_Ozero__class_Ozero(U_1995)),U_1996))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),c_Groups_Ozero__class_Ozero(U_1995)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1995),U_1996),U_1996)))
        | ~ sP167(U_1996,U_1995) )
    & ! [U_1996,U_1995] :
        ( sP167(U_1996,U_1995)
        | ~ class_Groups_Olinordered__ab__group__add(U_1995) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP167])],[f_593_2]) ).

cnf(f_593_4,plain,
    ( sP167(U_1996,U_1995)
    | ~ class_Groups_Olinordered__ab__group__add(U_1995) ),
    inference(clausify,[status(thm)],[f_593_3]) ).

cnf(f_593_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),c_Groups_Ozero__class_Ozero(U_1995)),U_1996))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),c_Groups_Ozero__class_Ozero(U_1995)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1995),U_1996),U_1996)))
    | ~ sP167(U_1996,U_1995) ),
    inference(clausify,[status(thm)],[f_593_3]) ).

cnf(f_593_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),c_Groups_Ozero__class_Ozero(U_1995)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1995),U_1996),U_1996)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_1995),c_Groups_Ozero__class_Ozero(U_1995)),U_1996))
    | ~ sP167(U_1996,U_1995) ),
    inference(clausify,[status(thm)],[f_593_3]) ).

fof(f_594_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_594_2,plain,
    ! [U_2002,U_2001,U_2000,U_1999,U_1998,U_1997] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1997),U_1999),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1997),U_1998),U_2001)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1997),U_2000),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1997),U_1998),U_2002))
      | U_2001 = U_2002
      | U_1999 != U_2000
      | U_1998 = c_Groups_Ozero__class_Ozero(U_1997)
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1997) ),
    inference(variable_rename,[status(thm)],[f_594_1]) ).

fof(f_594_3,plain,
    ! [U_1998,U_1999,U_1997,U_2000,U_2001,U_2002] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1997),U_1999),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1997),U_1998),U_2001)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1997),U_2000),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1997),U_1998),U_2002))
      | U_2001 = U_2002
      | U_1999 != U_2000
      | U_1998 = c_Groups_Ozero__class_Ozero(U_1997)
      | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1997) ),
    inference(definitional_conversion,[status(esa)],[f_594_2]) ).

cnf(f_594_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1997),U_1999),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1997),U_1998),U_2001)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_1997),U_2000),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_1997),U_1998),U_2002))
    | U_2001 = U_2002
    | U_1999 != U_2000
    | U_1998 = c_Groups_Ozero__class_Ozero(U_1997)
    | ~ class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(U_1997) ),
    inference(clausify,[status(thm)],[f_594_3]) ).

fof(f_595_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_595_2,plain,
    ! [U_2005,U_2004,U_2003] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2003),U_2004),U_2004)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2003),U_2005),U_2005)) = c_Groups_Ozero__class_Ozero(U_2003)
          | U_2005 != c_Groups_Ozero__class_Ozero(U_2003)
          | U_2004 != c_Groups_Ozero__class_Ozero(U_2003) )
        & ( ( U_2005 = c_Groups_Ozero__class_Ozero(U_2003)
            & U_2004 = c_Groups_Ozero__class_Ozero(U_2003) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2003),U_2004),U_2004)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2003),U_2005),U_2005)) != c_Groups_Ozero__class_Ozero(U_2003) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_2003) ),
    inference(variable_rename,[status(thm)],[f_595_1]) ).

fof(f_595_3,plain,
    ( ! [U_2003,U_2004,U_2005] :
        ( U_2005 = c_Groups_Ozero__class_Ozero(U_2003)
        | ~ sP168(U_2003,U_2004,U_2005) )
    & ! [U_2003,U_2004,U_2005] :
        ( U_2004 = c_Groups_Ozero__class_Ozero(U_2003)
        | ~ sP168(U_2003,U_2004,U_2005) )
    & ! [U_2003,U_2004,U_2005] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2003),U_2004),U_2004)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2003),U_2005),U_2005)) = c_Groups_Ozero__class_Ozero(U_2003)
        | U_2005 != c_Groups_Ozero__class_Ozero(U_2003)
        | U_2004 != c_Groups_Ozero__class_Ozero(U_2003)
        | ~ sP169(U_2003,U_2004,U_2005) )
    & ! [U_2003,U_2004,U_2005] :
        ( sP168(U_2003,U_2004,U_2005)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2003),U_2004),U_2004)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2003),U_2005),U_2005)) != c_Groups_Ozero__class_Ozero(U_2003)
        | ~ sP169(U_2003,U_2004,U_2005) )
    & ! [U_2003,U_2004,U_2005] :
        ( sP169(U_2003,U_2004,U_2005)
        | ~ class_Rings_Olinordered__ring__strict(U_2003) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP168,sP169])],[f_595_2]) ).

cnf(f_595_4,plain,
    ( sP169(U_2003,U_2004,U_2005)
    | ~ class_Rings_Olinordered__ring__strict(U_2003) ),
    inference(clausify,[status(thm)],[f_595_3]) ).

cnf(f_595_5,plain,
    ( sP168(U_2003,U_2004,U_2005)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2003),U_2004),U_2004)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2003),U_2005),U_2005)) != c_Groups_Ozero__class_Ozero(U_2003)
    | ~ sP169(U_2003,U_2004,U_2005) ),
    inference(clausify,[status(thm)],[f_595_3]) ).

cnf(f_595_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2003),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2003),U_2004),U_2004)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2003),U_2005),U_2005)) = c_Groups_Ozero__class_Ozero(U_2003)
    | U_2005 != c_Groups_Ozero__class_Ozero(U_2003)
    | U_2004 != c_Groups_Ozero__class_Ozero(U_2003)
    | ~ sP169(U_2003,U_2004,U_2005) ),
    inference(clausify,[status(thm)],[f_595_3]) ).

cnf(f_595_7,plain,
    ( U_2004 = c_Groups_Ozero__class_Ozero(U_2003)
    | ~ sP168(U_2003,U_2004,U_2005) ),
    inference(clausify,[status(thm)],[f_595_3]) ).

cnf(f_595_8,plain,
    ( U_2005 = c_Groups_Ozero__class_Ozero(U_2003)
    | ~ sP168(U_2003,U_2004,U_2005) ),
    inference(clausify,[status(thm)],[f_595_3]) ).

fof(f_596_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_596_2,plain,
    ! [U_2008,U_2007,U_2006] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2006),U_2007) = U_2008
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2006),U_2007),U_2008) != c_Groups_Ozero__class_Ozero(U_2006)
      | ~ class_Groups_Ogroup__add(U_2006) ),
    inference(variable_rename,[status(thm)],[f_596_1]) ).

fof(f_596_3,plain,
    ! [U_2007,U_2008,U_2006] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2006),U_2007) = U_2008
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2006),U_2007),U_2008) != c_Groups_Ozero__class_Ozero(U_2006)
      | ~ class_Groups_Ogroup__add(U_2006) ),
    inference(definitional_conversion,[status(esa)],[f_596_2]) ).

cnf(f_596_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2006),U_2007) = U_2008
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2006),U_2007),U_2008) != c_Groups_Ozero__class_Ozero(U_2006)
    | ~ class_Groups_Ogroup__add(U_2006) ),
    inference(clausify,[status(thm)],[f_596_3]) ).

fof(f_597_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_597_2,plain,
    ! [U_2010,U_2009] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2009),hAPP(c_Groups_Ouminus__class_Ouminus(U_2009),U_2010)),U_2010) = c_Groups_Ozero__class_Ozero(U_2009)
      | ~ class_Groups_Oab__group__add(U_2009) ),
    inference(variable_rename,[status(thm)],[f_597_1]) ).

fof(f_597_3,plain,
    ! [U_2010,U_2009] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2009),hAPP(c_Groups_Ouminus__class_Ouminus(U_2009),U_2010)),U_2010) = c_Groups_Ozero__class_Ozero(U_2009)
      | ~ class_Groups_Oab__group__add(U_2009) ),
    inference(definitional_conversion,[status(esa)],[f_597_2]) ).

cnf(f_597_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2009),hAPP(c_Groups_Ouminus__class_Ouminus(U_2009),U_2010)),U_2010) = c_Groups_Ozero__class_Ozero(U_2009)
    | ~ class_Groups_Oab__group__add(U_2009) ),
    inference(clausify,[status(thm)],[f_597_3]) ).

fof(f_598_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_598_2,plain,
    ! [U_2012,U_2011] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2011),hAPP(c_Groups_Ouminus__class_Ouminus(U_2011),U_2012)),U_2012) = c_Groups_Ozero__class_Ozero(U_2011)
      | ~ class_Groups_Ogroup__add(U_2011) ),
    inference(variable_rename,[status(thm)],[f_598_1]) ).

fof(f_598_3,plain,
    ! [U_2011,U_2012] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2011),hAPP(c_Groups_Ouminus__class_Ouminus(U_2011),U_2012)),U_2012) = c_Groups_Ozero__class_Ozero(U_2011)
      | ~ class_Groups_Ogroup__add(U_2011) ),
    inference(definitional_conversion,[status(esa)],[f_598_2]) ).

cnf(f_598_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2011),hAPP(c_Groups_Ouminus__class_Ouminus(U_2011),U_2012)),U_2012) = c_Groups_Ozero__class_Ozero(U_2011)
    | ~ class_Groups_Ogroup__add(U_2011) ),
    inference(clausify,[status(thm)],[f_598_3]) ).

fof(f_599_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_599_2,plain,
    ! [U_2015,U_2014,U_2013] :
      ( ( ( U_2014 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2013),U_2015)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2013),U_2014),U_2015) != c_Groups_Ozero__class_Ozero(U_2013) )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2013),U_2014),U_2015) = c_Groups_Ozero__class_Ozero(U_2013)
          | U_2014 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2013),U_2015) ) )
      | ~ class_Groups_Ogroup__add(U_2013) ),
    inference(variable_rename,[status(thm)],[f_599_1]) ).

fof(f_599_3,plain,
    ( ! [U_2013,U_2014,U_2015] :
        ( U_2014 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2013),U_2015)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2013),U_2014),U_2015) != c_Groups_Ozero__class_Ozero(U_2013)
        | ~ sP170(U_2013,U_2014,U_2015) )
    & ! [U_2013,U_2014,U_2015] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2013),U_2014),U_2015) = c_Groups_Ozero__class_Ozero(U_2013)
        | U_2014 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2013),U_2015)
        | ~ sP170(U_2013,U_2014,U_2015) )
    & ! [U_2013,U_2014,U_2015] :
        ( sP170(U_2013,U_2014,U_2015)
        | ~ class_Groups_Ogroup__add(U_2013) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP170])],[f_599_2]) ).

cnf(f_599_4,plain,
    ( sP170(U_2013,U_2014,U_2015)
    | ~ class_Groups_Ogroup__add(U_2013) ),
    inference(clausify,[status(thm)],[f_599_3]) ).

cnf(f_599_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2013),U_2014),U_2015) = c_Groups_Ozero__class_Ozero(U_2013)
    | U_2014 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2013),U_2015)
    | ~ sP170(U_2013,U_2014,U_2015) ),
    inference(clausify,[status(thm)],[f_599_3]) ).

cnf(f_599_6,plain,
    ( U_2014 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2013),U_2015)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2013),U_2014),U_2015) != c_Groups_Ozero__class_Ozero(U_2013)
    | ~ sP170(U_2013,U_2014,U_2015) ),
    inference(clausify,[status(thm)],[f_599_3]) ).

fof(f_600_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_600_2,plain,
    ! [U_2017,U_2016] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2016),U_2017),hAPP(c_Groups_Ouminus__class_Ouminus(U_2016),U_2017)) = c_Groups_Ozero__class_Ozero(U_2016)
      | ~ class_Groups_Ogroup__add(U_2016) ),
    inference(variable_rename,[status(thm)],[f_600_1]) ).

fof(f_600_3,plain,
    ! [U_2017,U_2016] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2016),U_2017),hAPP(c_Groups_Ouminus__class_Ouminus(U_2016),U_2017)) = c_Groups_Ozero__class_Ozero(U_2016)
      | ~ class_Groups_Ogroup__add(U_2016) ),
    inference(definitional_conversion,[status(esa)],[f_600_2]) ).

cnf(f_600_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2016),U_2017),hAPP(c_Groups_Ouminus__class_Ouminus(U_2016),U_2017)) = c_Groups_Ozero__class_Ozero(U_2016)
    | ~ class_Groups_Ogroup__add(U_2016) ),
    inference(clausify,[status(thm)],[f_600_3]) ).

fof(f_601_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_601_2,plain,
    ! [U_2018] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2018),c_Groups_Oone__class_Oone(U_2018)),c_Groups_Ozero__class_Ozero(U_2018)))
      | ~ class_Rings_Olinordered__semidom(U_2018) ),
    inference(variable_rename,[status(thm)],[f_601_1]) ).

fof(f_601_3,plain,
    ! [U_2018] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2018),c_Groups_Oone__class_Oone(U_2018)),c_Groups_Ozero__class_Ozero(U_2018)))
      | ~ class_Rings_Olinordered__semidom(U_2018) ),
    inference(definitional_conversion,[status(esa)],[f_601_2]) ).

cnf(f_601_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2018),c_Groups_Oone__class_Oone(U_2018)),c_Groups_Ozero__class_Ozero(U_2018)))
    | ~ class_Rings_Olinordered__semidom(U_2018) ),
    inference(clausify,[status(thm)],[f_601_3]) ).

fof(f_602_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_602_2,plain,
    ! [U_2019] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2019),c_Groups_Ozero__class_Ozero(U_2019)),c_Groups_Oone__class_Oone(U_2019)))
      | ~ class_Rings_Olinordered__semidom(U_2019) ),
    inference(variable_rename,[status(thm)],[f_602_1]) ).

fof(f_602_3,plain,
    ! [U_2019] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2019),c_Groups_Ozero__class_Ozero(U_2019)),c_Groups_Oone__class_Oone(U_2019)))
      | ~ class_Rings_Olinordered__semidom(U_2019) ),
    inference(definitional_conversion,[status(esa)],[f_602_2]) ).

cnf(f_602_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2019),c_Groups_Ozero__class_Ozero(U_2019)),c_Groups_Oone__class_Oone(U_2019)))
    | ~ class_Rings_Olinordered__semidom(U_2019) ),
    inference(clausify,[status(thm)],[f_602_3]) ).

fof(f_603_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_603_2,plain,
    ! [U_2020] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2020),c_Groups_Oone__class_Oone(U_2020)),c_Groups_Ozero__class_Ozero(U_2020)))
      | ~ class_Rings_Olinordered__semidom(U_2020) ),
    inference(variable_rename,[status(thm)],[f_603_1]) ).

fof(f_603_3,plain,
    ! [U_2020] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2020),c_Groups_Oone__class_Oone(U_2020)),c_Groups_Ozero__class_Ozero(U_2020)))
      | ~ class_Rings_Olinordered__semidom(U_2020) ),
    inference(definitional_conversion,[status(esa)],[f_603_2]) ).

cnf(f_603_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2020),c_Groups_Oone__class_Oone(U_2020)),c_Groups_Ozero__class_Ozero(U_2020)))
    | ~ class_Rings_Olinordered__semidom(U_2020) ),
    inference(clausify,[status(thm)],[f_603_3]) ).

fof(f_604_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_604_2,plain,
    ! [U_2021] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2021),c_Groups_Ozero__class_Ozero(U_2021)),c_Groups_Oone__class_Oone(U_2021)))
      | ~ class_Rings_Olinordered__semidom(U_2021) ),
    inference(variable_rename,[status(thm)],[f_604_1]) ).

fof(f_604_3,plain,
    ! [U_2021] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2021),c_Groups_Ozero__class_Ozero(U_2021)),c_Groups_Oone__class_Oone(U_2021)))
      | ~ class_Rings_Olinordered__semidom(U_2021) ),
    inference(definitional_conversion,[status(esa)],[f_604_2]) ).

cnf(f_604_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2021),c_Groups_Ozero__class_Ozero(U_2021)),c_Groups_Oone__class_Oone(U_2021)))
    | ~ class_Rings_Olinordered__semidom(U_2021) ),
    inference(clausify,[status(thm)],[f_604_3]) ).

fof(f_605_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_605_2,plain,
    ! [U_2024,U_2023,U_2022] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2022),c_Groups_Oone__class_Oone(U_2022)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2022),U_2023),U_2024)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2022),c_Groups_Oone__class_Oone(U_2022)),U_2024))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2022),c_Groups_Oone__class_Oone(U_2022)),U_2023))
      | ~ class_Rings_Olinordered__semidom(U_2022) ),
    inference(variable_rename,[status(thm)],[f_605_1]) ).

fof(f_605_3,plain,
    ! [U_2022,U_2023,U_2024] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2022),c_Groups_Oone__class_Oone(U_2022)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2022),U_2023),U_2024)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2022),c_Groups_Oone__class_Oone(U_2022)),U_2024))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2022),c_Groups_Oone__class_Oone(U_2022)),U_2023))
      | ~ class_Rings_Olinordered__semidom(U_2022) ),
    inference(definitional_conversion,[status(esa)],[f_605_2]) ).

cnf(f_605_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2022),c_Groups_Oone__class_Oone(U_2022)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2022),U_2023),U_2024)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2022),c_Groups_Oone__class_Oone(U_2022)),U_2024))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2022),c_Groups_Oone__class_Oone(U_2022)),U_2023))
    | ~ class_Rings_Olinordered__semidom(U_2022) ),
    inference(clausify,[status(thm)],[f_605_3]) ).

fof(f_606_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_606_2,plain,
    ! [U_2026,U_2025] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2025),U_2026) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2025),hAPP(c_Groups_Ouminus__class_Ouminus(U_2025),c_Groups_Oone__class_Oone(U_2025))),U_2026)
      | ~ class_Rings_Ocomm__ring__1(U_2025) ),
    inference(variable_rename,[status(thm)],[f_606_1]) ).

fof(f_606_3,plain,
    ! [U_2026,U_2025] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2025),U_2026) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2025),hAPP(c_Groups_Ouminus__class_Ouminus(U_2025),c_Groups_Oone__class_Oone(U_2025))),U_2026)
      | ~ class_Rings_Ocomm__ring__1(U_2025) ),
    inference(definitional_conversion,[status(esa)],[f_606_2]) ).

cnf(f_606_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2025),U_2026) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2025),hAPP(c_Groups_Ouminus__class_Ouminus(U_2025),c_Groups_Oone__class_Oone(U_2025))),U_2026)
    | ~ class_Rings_Ocomm__ring__1(U_2025) ),
    inference(clausify,[status(thm)],[f_606_3]) ).

fof(f_607_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_607_2,plain,
    ! [U_2028,U_2027] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2027),U_2028),U_2028) = c_Groups_Oone__class_Oone(U_2027)
          | ( U_2028 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2027),c_Groups_Oone__class_Oone(U_2027))
            & U_2028 != c_Groups_Oone__class_Oone(U_2027) ) )
        & ( U_2028 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2027),c_Groups_Oone__class_Oone(U_2027))
          | U_2028 = c_Groups_Oone__class_Oone(U_2027)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2027),U_2028),U_2028) != c_Groups_Oone__class_Oone(U_2027) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(U_2027) ),
    inference(variable_rename,[status(thm)],[f_607_1]) ).

fof(f_607_3,plain,
    ( ! [U_2028,U_2027] :
        ( U_2028 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2027),c_Groups_Oone__class_Oone(U_2027))
        | ~ sP171(U_2028,U_2027) )
    & ! [U_2028,U_2027] :
        ( U_2028 != c_Groups_Oone__class_Oone(U_2027)
        | ~ sP171(U_2028,U_2027) )
    & ! [U_2028,U_2027] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2027),U_2028),U_2028) = c_Groups_Oone__class_Oone(U_2027)
        | sP171(U_2028,U_2027)
        | ~ sP172(U_2028,U_2027) )
    & ! [U_2028,U_2027] :
        ( U_2028 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2027),c_Groups_Oone__class_Oone(U_2027))
        | U_2028 = c_Groups_Oone__class_Oone(U_2027)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2027),U_2028),U_2028) != c_Groups_Oone__class_Oone(U_2027)
        | ~ sP172(U_2028,U_2027) )
    & ! [U_2028,U_2027] :
        ( sP172(U_2028,U_2027)
        | ~ class_Rings_Oring__1__no__zero__divisors(U_2027) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP171,sP172])],[f_607_2]) ).

cnf(f_607_4,plain,
    ( sP172(U_2028,U_2027)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_2027) ),
    inference(clausify,[status(thm)],[f_607_3]) ).

cnf(f_607_5,plain,
    ( U_2028 = hAPP(c_Groups_Ouminus__class_Ouminus(U_2027),c_Groups_Oone__class_Oone(U_2027))
    | U_2028 = c_Groups_Oone__class_Oone(U_2027)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2027),U_2028),U_2028) != c_Groups_Oone__class_Oone(U_2027)
    | ~ sP172(U_2028,U_2027) ),
    inference(clausify,[status(thm)],[f_607_3]) ).

cnf(f_607_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2027),U_2028),U_2028) = c_Groups_Oone__class_Oone(U_2027)
    | sP171(U_2028,U_2027)
    | ~ sP172(U_2028,U_2027) ),
    inference(clausify,[status(thm)],[f_607_3]) ).

cnf(f_607_7,plain,
    ( U_2028 != c_Groups_Oone__class_Oone(U_2027)
    | ~ sP171(U_2028,U_2027) ),
    inference(clausify,[status(thm)],[f_607_3]) ).

cnf(f_607_8,plain,
    ( U_2028 != hAPP(c_Groups_Ouminus__class_Ouminus(U_2027),c_Groups_Oone__class_Oone(U_2027))
    | ~ sP171(U_2028,U_2027) ),
    inference(clausify,[status(thm)],[f_607_3]) ).

fof(f_608_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_608_2,plain,
    ! [U_2030,U_2029] :
      ( ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2029),U_2030)
        | ( ( U_2030 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_2029 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_2030 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_2029 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( U_2030 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_2029 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_2030 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2029 = 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_2029),U_2030) ) ),
    inference(variable_rename,[status(thm)],[f_608_1]) ).

fof(f_608_3,plain,
    ( ! [U_2034,U_2032] :
        ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2032),U_2034)
        | ( ( U_2034 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_2032 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_2034 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_2032 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
    & ! [U_2033,U_2031] :
        ( ( U_2033 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_2031 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_2033 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2031 = 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_2031),U_2033) ) ),
    inference(miniscope,[status(thm)],[f_608_2]) ).

fof(f_608_4,plain,
    ( ! [U_2034,U_2032] :
        ( U_2034 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2032 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP175(U_2034,U_2032) )
    & ! [U_2034,U_2032] :
        ( U_2034 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2032 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP175(U_2034,U_2032) )
    & ! [U_2031,U_2033] :
        ( U_2033 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP174(U_2031,U_2033) )
    & ! [U_2031,U_2033] :
        ( U_2031 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP174(U_2031,U_2033) )
    & ! [U_2031,U_2033] :
        ( U_2033 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP173(U_2031,U_2033) )
    & ! [U_2031,U_2033] :
        ( U_2031 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP173(U_2031,U_2033) )
    & ! [U_2034,U_2032] :
        ( hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2032),U_2034)
        | sP175(U_2034,U_2032) )
    & ! [U_2031,U_2033] :
        ( sP174(U_2031,U_2033)
        | sP173(U_2031,U_2033)
        | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2031),U_2033) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP173,sP174,sP175])],[f_608_3]) ).

cnf(f_608_5,plain,
    ( sP174(U_2031,U_2033)
    | sP173(U_2031,U_2033)
    | hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2031),U_2033) ),
    inference(clausify,[status(thm)],[f_608_4]) ).

cnf(f_608_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_2032),U_2034)
    | sP175(U_2034,U_2032) ),
    inference(clausify,[status(thm)],[f_608_4]) ).

cnf(f_608_7,plain,
    ( U_2031 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP173(U_2031,U_2033) ),
    inference(clausify,[status(thm)],[f_608_4]) ).

cnf(f_608_8,plain,
    ( U_2033 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP173(U_2031,U_2033) ),
    inference(clausify,[status(thm)],[f_608_4]) ).

cnf(f_608_9,plain,
    ( U_2031 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP174(U_2031,U_2033) ),
    inference(clausify,[status(thm)],[f_608_4]) ).

cnf(f_608_10,plain,
    ( U_2033 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP174(U_2031,U_2033) ),
    inference(clausify,[status(thm)],[f_608_4]) ).

cnf(f_608_11,plain,
    ( U_2034 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2032 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP175(U_2034,U_2032) ),
    inference(clausify,[status(thm)],[f_608_4]) ).

cnf(f_608_12,plain,
    ( U_2034 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_2032 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP175(U_2034,U_2032) ),
    inference(clausify,[status(thm)],[f_608_4]) ).

fof(f_609_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_609_2,plain,
    ! [U_2036,U_2035] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2035),U_2036) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( ( U_2036 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_2035 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_2036 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_2035 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
      & ( ( U_2036 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_2035 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_2036 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2035 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2035),U_2036) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_609_1]) ).

fof(f_609_3,plain,
    ( ! [U_2040,U_2038] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2038),U_2040) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( ( U_2040 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            | U_2038 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( U_2040 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_2038 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) )
    & ! [U_2039,U_2037] :
        ( ( U_2039 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_2037 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( U_2039 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_2037 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2037),U_2039) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_609_2]) ).

fof(f_609_4,plain,
    ( ! [U_2040,U_2038] :
        ( U_2040 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_2038 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP178(U_2040,U_2038) )
    & ! [U_2040,U_2038] :
        ( U_2040 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_2038 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP178(U_2040,U_2038) )
    & ! [U_2037,U_2039] :
        ( U_2039 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP177(U_2037,U_2039) )
    & ! [U_2037,U_2039] :
        ( U_2037 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP177(U_2037,U_2039) )
    & ! [U_2037,U_2039] :
        ( U_2039 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP176(U_2037,U_2039) )
    & ! [U_2037,U_2039] :
        ( U_2037 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP176(U_2037,U_2039) )
    & ! [U_2040,U_2038] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2038),U_2040) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | sP178(U_2040,U_2038) )
    & ! [U_2037,U_2039] :
        ( sP177(U_2037,U_2039)
        | sP176(U_2037,U_2039)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2037),U_2039) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP176,sP177,sP178])],[f_609_3]) ).

cnf(f_609_5,plain,
    ( sP177(U_2037,U_2039)
    | sP176(U_2037,U_2039)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2037),U_2039) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_609_4]) ).

cnf(f_609_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2038),U_2040) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | sP178(U_2040,U_2038) ),
    inference(clausify,[status(thm)],[f_609_4]) ).

cnf(f_609_7,plain,
    ( U_2037 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP176(U_2037,U_2039) ),
    inference(clausify,[status(thm)],[f_609_4]) ).

cnf(f_609_8,plain,
    ( U_2039 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP176(U_2037,U_2039) ),
    inference(clausify,[status(thm)],[f_609_4]) ).

cnf(f_609_9,plain,
    ( U_2037 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP177(U_2037,U_2039) ),
    inference(clausify,[status(thm)],[f_609_4]) ).

cnf(f_609_10,plain,
    ( U_2039 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP177(U_2037,U_2039) ),
    inference(clausify,[status(thm)],[f_609_4]) ).

cnf(f_609_11,plain,
    ( U_2040 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2038 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP178(U_2040,U_2038) ),
    inference(clausify,[status(thm)],[f_609_4]) ).

cnf(f_609_12,plain,
    ( U_2040 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_2038 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP178(U_2040,U_2038) ),
    inference(clausify,[status(thm)],[f_609_4]) ).

fof(f_610_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_610_2,plain,
    ! [U_2042,U_2041] :
      ( ( 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_2041),U_2042)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2042))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2041)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2042))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2041))
        | ~ 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_2041),U_2042))) ) ),
    inference(variable_rename,[status(thm)],[f_610_1]) ).

fof(f_610_3,plain,
    ( ! [U_2046,U_2044] :
        ( 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_2044),U_2046)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2046))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2044)) ) )
    & ! [U_2045,U_2043] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2045))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2043))
        | ~ 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_2043),U_2045))) ) ),
    inference(miniscope,[status(thm)],[f_610_2]) ).

fof(f_610_4,plain,
    ( ! [U_2044,U_2046] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2046))
        | ~ sP179(U_2044,U_2046) )
    & ! [U_2044,U_2046] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2044))
        | ~ sP179(U_2044,U_2046) )
    & ! [U_2044,U_2046] :
        ( 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_2044),U_2046)))
        | sP179(U_2044,U_2046) )
    & ! [U_2045,U_2043] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2045))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2043))
        | ~ 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_2043),U_2045))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP179])],[f_610_3]) ).

cnf(f_610_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2045))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2043))
    | ~ 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_2043),U_2045))) ),
    inference(clausify,[status(thm)],[f_610_4]) ).

cnf(f_610_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_2044),U_2046)))
    | sP179(U_2044,U_2046) ),
    inference(clausify,[status(thm)],[f_610_4]) ).

cnf(f_610_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2044))
    | ~ sP179(U_2044,U_2046) ),
    inference(clausify,[status(thm)],[f_610_4]) ).

cnf(f_610_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2046))
    | ~ sP179(U_2044,U_2046) ),
    inference(clausify,[status(thm)],[f_610_4]) ).

fof(f_611_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_611_2,plain,
    ! [U_2048,U_2047] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2047),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2047),U_2048)))),
    inference(variable_rename,[status(thm)],[f_611_1]) ).

fof(f_611_3,plain,
    ! [U_2047,U_2048] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2047),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2047),U_2048)))),
    inference(definitional_conversion,[status(esa)],[f_611_2]) ).

cnf(f_611_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2047),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2047),U_2048)))),
    inference(clausify,[status(thm)],[f_611_3]) ).

fof(f_612_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_612_2,plain,
    ! [U_2050,U_2049] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2049),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2050),U_2049)))),
    inference(variable_rename,[status(thm)],[f_612_1]) ).

fof(f_612_3,plain,
    ! [U_2050,U_2049] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2049),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2050),U_2049)))),
    inference(definitional_conversion,[status(esa)],[f_612_2]) ).

cnf(f_612_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2049),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2050),U_2049)))),
    inference(clausify,[status(thm)],[f_612_3]) ).

fof(f_613_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_613_2,plain,
    ! [U_2054,U_2053] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2053),U_2054))
        | ! [U_2052] : U_2054 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2053),U_2052)) )
      & ( ? [U_2051] : U_2054 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2053),U_2051))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2053),U_2054)) ) ),
    inference(variable_rename,[status(thm)],[f_613_1]) ).

fof(f_613_3,plain,
    ( ! [U_2058,U_2056] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2056),U_2058))
        | ! [U_2052] : U_2058 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2056),U_2052)) )
    & ! [U_2057,U_2055] :
        ( ? [U_2051] : U_2057 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2055),U_2051))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2055),U_2057)) ) ),
    inference(miniscope,[status(thm)],[f_613_2]) ).

fof(f_613_4,plain,
    ( ! [U_2058,U_2056] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2056),U_2058))
        | ! [U_2052] : U_2058 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2056),U_2052)) )
    & ! [U_2057,U_2055] :
        ( U_2057 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2055),sK35(U_2057,U_2055)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2055),U_2057)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK35]),skolemize(U_2051,sK35(U_2057,U_2055))],[f_613_3]) ).

fof(f_613_5,plain,
    ( ! [U_2056,U_2058,U_2052] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2056),U_2058))
        | U_2058 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2056),U_2052)) )
    & ! [U_2055,U_2057] :
        ( U_2057 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2055),sK35(U_2057,U_2055)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2055),U_2057)) ) ),
    inference(definitional_conversion,[status(esa)],[f_613_4]) ).

cnf(f_613_6,plain,
    ( U_2057 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2055),sK35(U_2057,U_2055)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2055),U_2057)) ),
    inference(clausify,[status(thm)],[f_613_5]) ).

cnf(f_613_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2056),U_2058))
    | U_2058 != hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2056),U_2052)) ),
    inference(clausify,[status(thm)],[f_613_5]) ).

fof(f_614_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_614_2,plain,
    ! [U_2060,U_2059] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2059),hAPP(c_Nat_OSuc,U_2060)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2059),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2059),U_2060)),
    inference(variable_rename,[status(thm)],[f_614_1]) ).

fof(f_614_3,plain,
    ! [U_2059,U_2060] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2059),hAPP(c_Nat_OSuc,U_2060)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2059),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2059),U_2060)),
    inference(definitional_conversion,[status(esa)],[f_614_2]) ).

cnf(f_614_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2059),hAPP(c_Nat_OSuc,U_2060)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2059),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2059),U_2060)),
    inference(clausify,[status(thm)],[f_614_3]) ).

fof(f_615_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_615_2,plain,
    ! [U_2062,U_2061] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2061)),U_2062) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2062),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2061),U_2062)),
    inference(variable_rename,[status(thm)],[f_615_1]) ).

fof(f_615_3,plain,
    ! [U_2061,U_2062] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2061)),U_2062) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2062),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2061),U_2062)),
    inference(definitional_conversion,[status(esa)],[f_615_2]) ).

cnf(f_615_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2061)),U_2062) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2062),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2061),U_2062)),
    inference(clausify,[status(thm)],[f_615_3]) ).

fof(f_616_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_616_2,plain,
    ! [U_2064,U_2063] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2063),U_2064))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2063)),U_2064)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2063)),U_2064))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2063),U_2064)) ) ),
    inference(variable_rename,[status(thm)],[f_616_1]) ).

fof(f_616_3,plain,
    ( ! [U_2068,U_2066] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2066),U_2068))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2066)),U_2068)) )
    & ! [U_2067,U_2065] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2065)),U_2067))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2065),U_2067)) ) ),
    inference(miniscope,[status(thm)],[f_616_2]) ).

fof(f_616_4,plain,
    ( ! [U_2066,U_2068] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2066),U_2068))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2066)),U_2068)) )
    & ! [U_2067,U_2065] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2065)),U_2067))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2065),U_2067)) ) ),
    inference(definitional_conversion,[status(esa)],[f_616_3]) ).

cnf(f_616_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2065)),U_2067))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2065),U_2067)) ),
    inference(clausify,[status(thm)],[f_616_4]) ).

cnf(f_616_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2066),U_2068))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2066)),U_2068)) ),
    inference(clausify,[status(thm)],[f_616_4]) ).

fof(f_617_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(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_617_2,plain,
    ! [U_2070,U_2069] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2069),hAPP(c_Nat_OSuc,U_2070)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2069),U_2070)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2069),U_2070))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2069),hAPP(c_Nat_OSuc,U_2070))) ) ),
    inference(variable_rename,[status(thm)],[f_617_1]) ).

fof(f_617_3,plain,
    ( ! [U_2074,U_2072] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2072),hAPP(c_Nat_OSuc,U_2074)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2072),U_2074)) )
    & ! [U_2073,U_2071] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2071),U_2073))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2071),hAPP(c_Nat_OSuc,U_2073))) ) ),
    inference(miniscope,[status(thm)],[f_617_2]) ).

fof(f_617_4,plain,
    ( ! [U_2072,U_2074] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2072),hAPP(c_Nat_OSuc,U_2074)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2072),U_2074)) )
    & ! [U_2073,U_2071] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2071),U_2073))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2071),hAPP(c_Nat_OSuc,U_2073))) ) ),
    inference(definitional_conversion,[status(esa)],[f_617_3]) ).

cnf(f_617_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2071),U_2073))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2071),hAPP(c_Nat_OSuc,U_2073))) ),
    inference(clausify,[status(thm)],[f_617_4]) ).

cnf(f_617_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2072),hAPP(c_Nat_OSuc,U_2074)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2072),U_2074)) ),
    inference(clausify,[status(thm)],[f_617_4]) ).

fof(f_618_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_618_2,plain,
    ! [U_2076,U_2075] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2075)),U_2076))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2075),U_2076)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2075),U_2076))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2075)),U_2076)) ) ),
    inference(variable_rename,[status(thm)],[f_618_1]) ).

fof(f_618_3,plain,
    ( ! [U_2080,U_2078] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2078)),U_2080))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2078),U_2080)) )
    & ! [U_2079,U_2077] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2077),U_2079))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2077)),U_2079)) ) ),
    inference(miniscope,[status(thm)],[f_618_2]) ).

fof(f_618_4,plain,
    ( ! [U_2078,U_2080] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2078)),U_2080))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2078),U_2080)) )
    & ! [U_2079,U_2077] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2077),U_2079))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2077)),U_2079)) ) ),
    inference(definitional_conversion,[status(esa)],[f_618_3]) ).

cnf(f_618_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2077),U_2079))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2077)),U_2079)) ),
    inference(clausify,[status(thm)],[f_618_4]) ).

cnf(f_618_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2078)),U_2080))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2078),U_2080)) ),
    inference(clausify,[status(thm)],[f_618_4]) ).

fof(f_619_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_619_2,plain,
    ! [U_2082,U_2081] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2081),hAPP(c_Nat_OSuc,U_2082)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2081),U_2082)) ),
    inference(variable_rename,[status(thm)],[f_619_1]) ).

fof(f_619_3,plain,
    ! [U_2082,U_2081] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2081),hAPP(c_Nat_OSuc,U_2082)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2081),U_2082)) ),
    inference(definitional_conversion,[status(esa)],[f_619_2]) ).

cnf(f_619_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2081),hAPP(c_Nat_OSuc,U_2082)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2081),U_2082)) ),
    inference(clausify,[status(thm)],[f_619_3]) ).

fof(f_620_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_620_2,plain,
    ! [U_2084,U_2083] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2083)),U_2084))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2083),U_2084)) ),
    inference(variable_rename,[status(thm)],[f_620_1]) ).

fof(f_620_3,plain,
    ! [U_2083,U_2084] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2083)),U_2084))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2083),U_2084)) ),
    inference(definitional_conversion,[status(esa)],[f_620_2]) ).

cnf(f_620_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2083)),U_2084))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2083),U_2084)) ),
    inference(clausify,[status(thm)],[f_620_3]) ).

fof(f_621_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_621_2,plain,
    ! [U_2086,U_2085] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2086),hAPP(c_Nat_OSuc,U_2085)))
          | U_2086 != U_2085 )
        & ( U_2086 = U_2085
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2086),hAPP(c_Nat_OSuc,U_2085))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2085),U_2086)) ),
    inference(variable_rename,[status(thm)],[f_621_1]) ).

fof(f_621_3,plain,
    ( ! [U_2085,U_2086] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2086),hAPP(c_Nat_OSuc,U_2085)))
        | U_2086 != U_2085
        | ~ sP180(U_2085,U_2086) )
    & ! [U_2085,U_2086] :
        ( U_2086 = U_2085
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2086),hAPP(c_Nat_OSuc,U_2085)))
        | ~ sP180(U_2085,U_2086) )
    & ! [U_2085,U_2086] :
        ( sP180(U_2085,U_2086)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2085),U_2086)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP180])],[f_621_2]) ).

cnf(f_621_4,plain,
    ( sP180(U_2085,U_2086)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2085),U_2086)) ),
    inference(clausify,[status(thm)],[f_621_3]) ).

cnf(f_621_5,plain,
    ( U_2086 = U_2085
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2086),hAPP(c_Nat_OSuc,U_2085)))
    | ~ sP180(U_2085,U_2086) ),
    inference(clausify,[status(thm)],[f_621_3]) ).

cnf(f_621_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2086),hAPP(c_Nat_OSuc,U_2085)))
    | U_2086 != U_2085
    | ~ sP180(U_2085,U_2086) ),
    inference(clausify,[status(thm)],[f_621_3]) ).

fof(f_622_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_622_2,plain,
    ! [U_2088,U_2087] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2087),U_2088))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2087)),U_2088)) ),
    inference(variable_rename,[status(thm)],[f_622_1]) ).

fof(f_622_3,plain,
    ! [U_2088,U_2087] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2087),U_2088))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2087)),U_2088)) ),
    inference(definitional_conversion,[status(esa)],[f_622_2]) ).

cnf(f_622_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2087),U_2088))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2087)),U_2088)) ),
    inference(clausify,[status(thm)],[f_622_3]) ).

fof(f_623_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_623_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_623_1]) ).

cnf(f_623_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_623_2]) ).

fof(f_624_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_624_2,plain,
    ! [U_2091,U_2090,U_2089] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2089)),U_2090)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2089)),U_2091)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2090),U_2091)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2090),U_2091))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2089)),U_2090)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2089)),U_2091))) ) ),
    inference(variable_rename,[status(thm)],[f_624_1]) ).

fof(f_624_3,plain,
    ( ! [U_2097,U_2095] :
        ( ! [U_2093] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2093)),U_2095)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2093)),U_2097)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2095),U_2097)) )
    & ! [U_2096,U_2094] :
        ( ! [U_2092] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2092)),U_2094)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2092)),U_2096)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2094),U_2096)) ) ),
    inference(miniscope,[status(thm)],[f_624_2]) ).

fof(f_624_4,plain,
    ( ! [U_2093,U_2095,U_2097] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2093)),U_2095)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2093)),U_2097)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2095),U_2097)) )
    & ! [U_2094,U_2096,U_2092] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2092)),U_2094)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2092)),U_2096)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2094),U_2096)) ) ),
    inference(definitional_conversion,[status(esa)],[f_624_3]) ).

cnf(f_624_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2092)),U_2094)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2092)),U_2096)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2094),U_2096)) ),
    inference(clausify,[status(thm)],[f_624_4]) ).

cnf(f_624_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2093)),U_2095)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2093)),U_2097)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2095),U_2097)) ),
    inference(clausify,[status(thm)],[f_624_4]) ).

fof(f_625_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_625_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_625_1]) ).

cnf(f_625_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_625_2]) ).

fof(f_626_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_626_2,plain,
    ! [U_2099,U_2098] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2098)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2099)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2098),U_2099)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2098),U_2099))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2098)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2099))) ) ),
    inference(variable_rename,[status(thm)],[f_626_1]) ).

fof(f_626_3,plain,
    ( ! [U_2103,U_2101] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2101)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2103)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2101),U_2103)) )
    & ! [U_2102,U_2100] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2100),U_2102))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2100)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2102))) ) ),
    inference(miniscope,[status(thm)],[f_626_2]) ).

fof(f_626_4,plain,
    ( ! [U_2103,U_2101] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2101)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2103)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2101),U_2103)) )
    & ! [U_2102,U_2100] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2100),U_2102))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2100)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2102))) ) ),
    inference(definitional_conversion,[status(esa)],[f_626_3]) ).

cnf(f_626_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2100),U_2102))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2100)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2102))) ),
    inference(clausify,[status(thm)],[f_626_4]) ).

cnf(f_626_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_2101)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2103)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2101),U_2103)) ),
    inference(clausify,[status(thm)],[f_626_4]) ).

fof(f_627_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_627_2,plain,
    ! [U_2105,U_2104] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2104)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2105)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2104),U_2105)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2104),U_2105))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2104)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2105))) ) ),
    inference(variable_rename,[status(thm)],[f_627_1]) ).

fof(f_627_3,plain,
    ( ! [U_2109,U_2107] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2107)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2109)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2107),U_2109)) )
    & ! [U_2108,U_2106] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2106),U_2108))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2106)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2108))) ) ),
    inference(miniscope,[status(thm)],[f_627_2]) ).

fof(f_627_4,plain,
    ( ! [U_2109,U_2107] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2107)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2109)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2107),U_2109)) )
    & ! [U_2106,U_2108] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2106),U_2108))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2106)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2108))) ) ),
    inference(definitional_conversion,[status(esa)],[f_627_3]) ).

cnf(f_627_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2106),U_2108))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2106)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2108))) ),
    inference(clausify,[status(thm)],[f_627_4]) ).

cnf(f_627_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_2107)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2109)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2107),U_2109)) ),
    inference(clausify,[status(thm)],[f_627_4]) ).

fof(f_628_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_628_2,plain,
    ! [U_2112,U_2111,U_2110] :
      ( hBOOL(hAPP(hAPP(c_member(U_2110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2110),U_2111),U_2112)),c_Nat_Osemiring__1__class_ONats(U_2110)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2110),U_2112),c_Nat_Osemiring__1__class_ONats(U_2110)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2110),U_2111),c_Nat_Osemiring__1__class_ONats(U_2110)))
      | ~ class_Rings_Osemiring__1(U_2110) ),
    inference(variable_rename,[status(thm)],[f_628_1]) ).

fof(f_628_3,plain,
    ! [U_2110,U_2111,U_2112] :
      ( hBOOL(hAPP(hAPP(c_member(U_2110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2110),U_2111),U_2112)),c_Nat_Osemiring__1__class_ONats(U_2110)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2110),U_2112),c_Nat_Osemiring__1__class_ONats(U_2110)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2110),U_2111),c_Nat_Osemiring__1__class_ONats(U_2110)))
      | ~ class_Rings_Osemiring__1(U_2110) ),
    inference(definitional_conversion,[status(esa)],[f_628_2]) ).

cnf(f_628_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2110),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2110),U_2111),U_2112)),c_Nat_Osemiring__1__class_ONats(U_2110)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2110),U_2112),c_Nat_Osemiring__1__class_ONats(U_2110)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2110),U_2111),c_Nat_Osemiring__1__class_ONats(U_2110)))
    | ~ class_Rings_Osemiring__1(U_2110) ),
    inference(clausify,[status(thm)],[f_628_3]) ).

fof(f_629_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_629_2,plain,
    ! [U_2113] :
      ( hBOOL(hAPP(hAPP(c_member(U_2113),c_Groups_Oone__class_Oone(U_2113)),c_Nat_Osemiring__1__class_ONats(U_2113)))
      | ~ class_Rings_Osemiring__1(U_2113) ),
    inference(variable_rename,[status(thm)],[f_629_1]) ).

fof(f_629_3,plain,
    ! [U_2113] :
      ( hBOOL(hAPP(hAPP(c_member(U_2113),c_Groups_Oone__class_Oone(U_2113)),c_Nat_Osemiring__1__class_ONats(U_2113)))
      | ~ class_Rings_Osemiring__1(U_2113) ),
    inference(definitional_conversion,[status(esa)],[f_629_2]) ).

cnf(f_629_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2113),c_Groups_Oone__class_Oone(U_2113)),c_Nat_Osemiring__1__class_ONats(U_2113)))
    | ~ class_Rings_Osemiring__1(U_2113) ),
    inference(clausify,[status(thm)],[f_629_3]) ).

fof(f_630_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_630_2,plain,
    ! [U_2116,U_2115,U_2114] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2114),c_Groups_Ozero__class_Ozero(U_2114)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2114),U_2115),U_2116)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2114),c_Groups_Ozero__class_Ozero(U_2114)),U_2116))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2114),c_Groups_Ozero__class_Ozero(U_2114)),U_2115))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2114) ),
    inference(variable_rename,[status(thm)],[f_630_1]) ).

fof(f_630_3,plain,
    ! [U_2114,U_2115,U_2116] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2114),c_Groups_Ozero__class_Ozero(U_2114)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2114),U_2115),U_2116)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2114),c_Groups_Ozero__class_Ozero(U_2114)),U_2116))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2114),c_Groups_Ozero__class_Ozero(U_2114)),U_2115))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2114) ),
    inference(definitional_conversion,[status(esa)],[f_630_2]) ).

cnf(f_630_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2114),c_Groups_Ozero__class_Ozero(U_2114)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2114),U_2115),U_2116)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2114),c_Groups_Ozero__class_Ozero(U_2114)),U_2116))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2114),c_Groups_Ozero__class_Ozero(U_2114)),U_2115))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2114) ),
    inference(clausify,[status(thm)],[f_630_3]) ).

fof(f_631_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_631_2,plain,
    ! [U_2119,U_2118,U_2117] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),c_Groups_Ozero__class_Ozero(U_2117)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2117),U_2118),U_2119)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),c_Groups_Ozero__class_Ozero(U_2117)),U_2119))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2117),c_Groups_Ozero__class_Ozero(U_2117)),U_2118))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2117) ),
    inference(variable_rename,[status(thm)],[f_631_1]) ).

fof(f_631_3,plain,
    ! [U_2117,U_2118,U_2119] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),c_Groups_Ozero__class_Ozero(U_2117)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2117),U_2118),U_2119)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),c_Groups_Ozero__class_Ozero(U_2117)),U_2119))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2117),c_Groups_Ozero__class_Ozero(U_2117)),U_2118))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2117) ),
    inference(definitional_conversion,[status(esa)],[f_631_2]) ).

cnf(f_631_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),c_Groups_Ozero__class_Ozero(U_2117)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2117),U_2118),U_2119)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2117),c_Groups_Ozero__class_Ozero(U_2117)),U_2119))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2117),c_Groups_Ozero__class_Ozero(U_2117)),U_2118))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2117) ),
    inference(clausify,[status(thm)],[f_631_3]) ).

fof(f_632_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_632_2,plain,
    ! [U_2123,U_2122,U_2121,U_2120] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2120),U_2122),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2120),U_2121),U_2123)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2120),U_2122),U_2123))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2120),c_Groups_Ozero__class_Ozero(U_2120)),U_2121))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2120) ),
    inference(variable_rename,[status(thm)],[f_632_1]) ).

fof(f_632_3,plain,
    ! [U_2120,U_2121,U_2122,U_2123] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2120),U_2122),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2120),U_2121),U_2123)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2120),U_2122),U_2123))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2120),c_Groups_Ozero__class_Ozero(U_2120)),U_2121))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2120) ),
    inference(definitional_conversion,[status(esa)],[f_632_2]) ).

cnf(f_632_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2120),U_2122),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2120),U_2121),U_2123)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2120),U_2122),U_2123))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2120),c_Groups_Ozero__class_Ozero(U_2120)),U_2121))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2120) ),
    inference(clausify,[status(thm)],[f_632_3]) ).

fof(f_633_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_633_2,plain,
    ! [U_2127,U_2126,U_2125,U_2124] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2124),U_2126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2124),U_2125),U_2127)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2124),U_2126),U_2127))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2124),c_Groups_Ozero__class_Ozero(U_2124)),U_2125))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2124) ),
    inference(variable_rename,[status(thm)],[f_633_1]) ).

fof(f_633_3,plain,
    ! [U_2124,U_2125,U_2126,U_2127] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2124),U_2126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2124),U_2125),U_2127)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2124),U_2126),U_2127))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2124),c_Groups_Ozero__class_Ozero(U_2124)),U_2125))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2124) ),
    inference(definitional_conversion,[status(esa)],[f_633_2]) ).

cnf(f_633_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2124),U_2126),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2124),U_2125),U_2127)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2124),U_2126),U_2127))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2124),c_Groups_Ozero__class_Ozero(U_2124)),U_2125))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2124) ),
    inference(clausify,[status(thm)],[f_633_3]) ).

fof(f_634_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_634_2,plain,
    ! [U_2130,U_2129,U_2128] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2128),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2128),U_2129),U_2130)),c_Groups_Ozero__class_Ozero(U_2128)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2128),U_2130),c_Groups_Ozero__class_Ozero(U_2128)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2128),U_2129),c_Groups_Ozero__class_Ozero(U_2128)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2128) ),
    inference(variable_rename,[status(thm)],[f_634_1]) ).

fof(f_634_3,plain,
    ! [U_2128,U_2129,U_2130] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2128),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2128),U_2129),U_2130)),c_Groups_Ozero__class_Ozero(U_2128)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2128),U_2130),c_Groups_Ozero__class_Ozero(U_2128)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2128),U_2129),c_Groups_Ozero__class_Ozero(U_2128)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2128) ),
    inference(definitional_conversion,[status(esa)],[f_634_2]) ).

cnf(f_634_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2128),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2128),U_2129),U_2130)),c_Groups_Ozero__class_Ozero(U_2128)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2128),U_2130),c_Groups_Ozero__class_Ozero(U_2128)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2128),U_2129),c_Groups_Ozero__class_Ozero(U_2128)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2128) ),
    inference(clausify,[status(thm)],[f_634_3]) ).

fof(f_635_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_635_2,plain,
    ! [U_2133,U_2132,U_2131] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2131),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2131),U_2132),U_2133)),c_Groups_Ozero__class_Ozero(U_2131)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2131),U_2133),c_Groups_Ozero__class_Ozero(U_2131)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2131),U_2132),c_Groups_Ozero__class_Ozero(U_2131)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2131) ),
    inference(variable_rename,[status(thm)],[f_635_1]) ).

fof(f_635_3,plain,
    ! [U_2131,U_2132,U_2133] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2131),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2131),U_2132),U_2133)),c_Groups_Ozero__class_Ozero(U_2131)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2131),U_2133),c_Groups_Ozero__class_Ozero(U_2131)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2131),U_2132),c_Groups_Ozero__class_Ozero(U_2131)))
      | ~ class_Groups_Oordered__comm__monoid__add(U_2131) ),
    inference(definitional_conversion,[status(esa)],[f_635_2]) ).

cnf(f_635_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2131),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2131),U_2132),U_2133)),c_Groups_Ozero__class_Ozero(U_2131)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2131),U_2133),c_Groups_Ozero__class_Ozero(U_2131)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2131),U_2132),c_Groups_Ozero__class_Ozero(U_2131)))
    | ~ class_Groups_Oordered__comm__monoid__add(U_2131) ),
    inference(clausify,[status(thm)],[f_635_3]) ).

fof(f_636_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_636_2,plain,
    ! [U_2136,U_2135,U_2134] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2134),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2134),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2134),U_2135),U_2135)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2134),U_2136),U_2136))),c_Groups_Ozero__class_Ozero(U_2134)))
          | U_2136 != c_Groups_Ozero__class_Ozero(U_2134)
          | U_2135 != c_Groups_Ozero__class_Ozero(U_2134) )
        & ( ( U_2136 = c_Groups_Ozero__class_Ozero(U_2134)
            & U_2135 = c_Groups_Ozero__class_Ozero(U_2134) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2134),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2134),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2134),U_2135),U_2135)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2134),U_2136),U_2136))),c_Groups_Ozero__class_Ozero(U_2134))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_2134) ),
    inference(variable_rename,[status(thm)],[f_636_1]) ).

fof(f_636_3,plain,
    ( ! [U_2134,U_2135,U_2136] :
        ( U_2136 = c_Groups_Ozero__class_Ozero(U_2134)
        | ~ sP181(U_2134,U_2135,U_2136) )
    & ! [U_2134,U_2135,U_2136] :
        ( U_2135 = c_Groups_Ozero__class_Ozero(U_2134)
        | ~ sP181(U_2134,U_2135,U_2136) )
    & ! [U_2134,U_2135,U_2136] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2134),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2134),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2134),U_2135),U_2135)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2134),U_2136),U_2136))),c_Groups_Ozero__class_Ozero(U_2134)))
        | U_2136 != c_Groups_Ozero__class_Ozero(U_2134)
        | U_2135 != c_Groups_Ozero__class_Ozero(U_2134)
        | ~ sP182(U_2134,U_2135,U_2136) )
    & ! [U_2134,U_2135,U_2136] :
        ( sP181(U_2134,U_2135,U_2136)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2134),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2134),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2134),U_2135),U_2135)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2134),U_2136),U_2136))),c_Groups_Ozero__class_Ozero(U_2134)))
        | ~ sP182(U_2134,U_2135,U_2136) )
    & ! [U_2134,U_2135,U_2136] :
        ( sP182(U_2134,U_2135,U_2136)
        | ~ class_Rings_Olinordered__ring__strict(U_2134) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP181,sP182])],[f_636_2]) ).

cnf(f_636_4,plain,
    ( sP182(U_2134,U_2135,U_2136)
    | ~ class_Rings_Olinordered__ring__strict(U_2134) ),
    inference(clausify,[status(thm)],[f_636_3]) ).

cnf(f_636_5,plain,
    ( sP181(U_2134,U_2135,U_2136)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2134),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2134),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2134),U_2135),U_2135)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2134),U_2136),U_2136))),c_Groups_Ozero__class_Ozero(U_2134)))
    | ~ sP182(U_2134,U_2135,U_2136) ),
    inference(clausify,[status(thm)],[f_636_3]) ).

cnf(f_636_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2134),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2134),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2134),U_2135),U_2135)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2134),U_2136),U_2136))),c_Groups_Ozero__class_Ozero(U_2134)))
    | U_2136 != c_Groups_Ozero__class_Ozero(U_2134)
    | U_2135 != c_Groups_Ozero__class_Ozero(U_2134)
    | ~ sP182(U_2134,U_2135,U_2136) ),
    inference(clausify,[status(thm)],[f_636_3]) ).

cnf(f_636_7,plain,
    ( U_2135 = c_Groups_Ozero__class_Ozero(U_2134)
    | ~ sP181(U_2134,U_2135,U_2136) ),
    inference(clausify,[status(thm)],[f_636_3]) ).

cnf(f_636_8,plain,
    ( U_2136 = c_Groups_Ozero__class_Ozero(U_2134)
    | ~ sP181(U_2134,U_2135,U_2136) ),
    inference(clausify,[status(thm)],[f_636_3]) ).

fof(f_637_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_637_2,plain,
    ! [U_2139,U_2138,U_2137] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2137),c_Groups_Ozero__class_Ozero(U_2137)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2137),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2137),U_2138),U_2138)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2137),U_2139),U_2139))))
      | ~ class_Rings_Olinordered__ring(U_2137) ),
    inference(variable_rename,[status(thm)],[f_637_1]) ).

fof(f_637_3,plain,
    ! [U_2139,U_2138,U_2137] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2137),c_Groups_Ozero__class_Ozero(U_2137)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2137),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2137),U_2138),U_2138)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2137),U_2139),U_2139))))
      | ~ class_Rings_Olinordered__ring(U_2137) ),
    inference(definitional_conversion,[status(esa)],[f_637_2]) ).

cnf(f_637_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2137),c_Groups_Ozero__class_Ozero(U_2137)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2137),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2137),U_2138),U_2138)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2137),U_2139),U_2139))))
    | ~ class_Rings_Olinordered__ring(U_2137) ),
    inference(clausify,[status(thm)],[f_637_3]) ).

fof(f_638_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_638_2,plain,
    ! [U_2142,U_2141,U_2140] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2140),U_2141),U_2141)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2140),U_2142),U_2142))),c_Groups_Ozero__class_Ozero(U_2140)))
      | ~ class_Rings_Olinordered__ring(U_2140) ),
    inference(variable_rename,[status(thm)],[f_638_1]) ).

fof(f_638_3,plain,
    ! [U_2140,U_2141,U_2142] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2140),U_2141),U_2141)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2140),U_2142),U_2142))),c_Groups_Ozero__class_Ozero(U_2140)))
      | ~ class_Rings_Olinordered__ring(U_2140) ),
    inference(definitional_conversion,[status(esa)],[f_638_2]) ).

cnf(f_638_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2140),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2140),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2140),U_2141),U_2141)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2140),U_2142),U_2142))),c_Groups_Ozero__class_Ozero(U_2140)))
    | ~ class_Rings_Olinordered__ring(U_2140) ),
    inference(clausify,[status(thm)],[f_638_3]) ).

fof(f_639_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_639_2,plain,
    ! [U_2145,U_2144,U_2143] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2143),c_Groups_Ozero__class_Ozero(U_2143)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2143),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2143),U_2144),U_2144)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2143),U_2145),U_2145))))
          | ( U_2145 = c_Groups_Ozero__class_Ozero(U_2143)
            & U_2144 = c_Groups_Ozero__class_Ozero(U_2143) ) )
        & ( U_2145 != c_Groups_Ozero__class_Ozero(U_2143)
          | U_2144 != c_Groups_Ozero__class_Ozero(U_2143)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2143),c_Groups_Ozero__class_Ozero(U_2143)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2143),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2143),U_2144),U_2144)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2143),U_2145),U_2145)))) ) )
      | ~ class_Rings_Olinordered__ring__strict(U_2143) ),
    inference(variable_rename,[status(thm)],[f_639_1]) ).

fof(f_639_3,plain,
    ( ! [U_2143,U_2144,U_2145] :
        ( U_2145 = c_Groups_Ozero__class_Ozero(U_2143)
        | ~ sP183(U_2143,U_2144,U_2145) )
    & ! [U_2143,U_2144,U_2145] :
        ( U_2144 = c_Groups_Ozero__class_Ozero(U_2143)
        | ~ sP183(U_2143,U_2144,U_2145) )
    & ! [U_2143,U_2144,U_2145] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2143),c_Groups_Ozero__class_Ozero(U_2143)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2143),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2143),U_2144),U_2144)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2143),U_2145),U_2145))))
        | sP183(U_2143,U_2144,U_2145)
        | ~ sP184(U_2143,U_2144,U_2145) )
    & ! [U_2143,U_2144,U_2145] :
        ( U_2145 != c_Groups_Ozero__class_Ozero(U_2143)
        | U_2144 != c_Groups_Ozero__class_Ozero(U_2143)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2143),c_Groups_Ozero__class_Ozero(U_2143)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2143),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2143),U_2144),U_2144)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2143),U_2145),U_2145))))
        | ~ sP184(U_2143,U_2144,U_2145) )
    & ! [U_2143,U_2144,U_2145] :
        ( sP184(U_2143,U_2144,U_2145)
        | ~ class_Rings_Olinordered__ring__strict(U_2143) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP183,sP184])],[f_639_2]) ).

cnf(f_639_4,plain,
    ( sP184(U_2143,U_2144,U_2145)
    | ~ class_Rings_Olinordered__ring__strict(U_2143) ),
    inference(clausify,[status(thm)],[f_639_3]) ).

cnf(f_639_5,plain,
    ( U_2145 != c_Groups_Ozero__class_Ozero(U_2143)
    | U_2144 != c_Groups_Ozero__class_Ozero(U_2143)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2143),c_Groups_Ozero__class_Ozero(U_2143)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2143),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2143),U_2144),U_2144)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2143),U_2145),U_2145))))
    | ~ sP184(U_2143,U_2144,U_2145) ),
    inference(clausify,[status(thm)],[f_639_3]) ).

cnf(f_639_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2143),c_Groups_Ozero__class_Ozero(U_2143)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2143),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2143),U_2144),U_2144)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2143),U_2145),U_2145))))
    | sP183(U_2143,U_2144,U_2145)
    | ~ sP184(U_2143,U_2144,U_2145) ),
    inference(clausify,[status(thm)],[f_639_3]) ).

cnf(f_639_7,plain,
    ( U_2144 = c_Groups_Ozero__class_Ozero(U_2143)
    | ~ sP183(U_2143,U_2144,U_2145) ),
    inference(clausify,[status(thm)],[f_639_3]) ).

cnf(f_639_8,plain,
    ( U_2145 = c_Groups_Ozero__class_Ozero(U_2143)
    | ~ sP183(U_2143,U_2144,U_2145) ),
    inference(clausify,[status(thm)],[f_639_3]) ).

fof(f_640_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_640_2,plain,
    ! [U_2148,U_2147,U_2146] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2146),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2146),U_2148),U_2147)),U_2147))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2146),U_2148),c_Groups_Oone__class_Oone(U_2146)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2146),c_Groups_Ozero__class_Ozero(U_2146)),U_2148))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2146),c_Groups_Ozero__class_Ozero(U_2146)),U_2147))
      | ~ class_Rings_Olinordered__idom(U_2146) ),
    inference(variable_rename,[status(thm)],[f_640_1]) ).

fof(f_640_3,plain,
    ! [U_2148,U_2147,U_2146] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2146),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2146),U_2148),U_2147)),U_2147))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2146),U_2148),c_Groups_Oone__class_Oone(U_2146)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2146),c_Groups_Ozero__class_Ozero(U_2146)),U_2148))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2146),c_Groups_Ozero__class_Ozero(U_2146)),U_2147))
      | ~ class_Rings_Olinordered__idom(U_2146) ),
    inference(definitional_conversion,[status(esa)],[f_640_2]) ).

cnf(f_640_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2146),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2146),U_2148),U_2147)),U_2147))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2146),U_2148),c_Groups_Oone__class_Oone(U_2146)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2146),c_Groups_Ozero__class_Ozero(U_2146)),U_2148))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2146),c_Groups_Ozero__class_Ozero(U_2146)),U_2147))
    | ~ class_Rings_Olinordered__idom(U_2146) ),
    inference(clausify,[status(thm)],[f_640_3]) ).

fof(f_641_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_641_2,plain,
    ! [U_2151,U_2150,U_2149] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2149),U_2150),U_2151)),U_2150))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2149),U_2151),c_Groups_Oone__class_Oone(U_2149)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2149),c_Groups_Ozero__class_Ozero(U_2149)),U_2151))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2149),c_Groups_Ozero__class_Ozero(U_2149)),U_2150))
      | ~ class_Rings_Olinordered__idom(U_2149) ),
    inference(variable_rename,[status(thm)],[f_641_1]) ).

fof(f_641_3,plain,
    ! [U_2151,U_2150,U_2149] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2149),U_2150),U_2151)),U_2150))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2149),U_2151),c_Groups_Oone__class_Oone(U_2149)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2149),c_Groups_Ozero__class_Ozero(U_2149)),U_2151))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2149),c_Groups_Ozero__class_Ozero(U_2149)),U_2150))
      | ~ class_Rings_Olinordered__idom(U_2149) ),
    inference(definitional_conversion,[status(esa)],[f_641_2]) ).

cnf(f_641_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2149),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2149),U_2150),U_2151)),U_2150))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2149),U_2151),c_Groups_Oone__class_Oone(U_2149)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2149),c_Groups_Ozero__class_Ozero(U_2149)),U_2151))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_2149),c_Groups_Ozero__class_Ozero(U_2149)),U_2150))
    | ~ class_Rings_Olinordered__idom(U_2149) ),
    inference(clausify,[status(thm)],[f_641_3]) ).

fof(f_642_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_642_2,plain,
    ! [U_2153,U_2152] :
      ( ( 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_2152),U_2153)))
        | ~ 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_2153))
        | ~ 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_2152)) )
      & ( ( 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_2153))
          & 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_2152)) )
        | ~ 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_2152),U_2153))) ) ),
    inference(variable_rename,[status(thm)],[f_642_1]) ).

fof(f_642_3,plain,
    ( ! [U_2157,U_2155] :
        ( 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_2155),U_2157)))
        | ~ 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_2157))
        | ~ 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_2155)) )
    & ! [U_2156,U_2154] :
        ( ( 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_2156))
          & 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_2154)) )
        | ~ 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_2154),U_2156))) ) ),
    inference(miniscope,[status(thm)],[f_642_2]) ).

fof(f_642_4,plain,
    ( ! [U_2154,U_2156] :
        ( 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_2156))
        | ~ sP185(U_2154,U_2156) )
    & ! [U_2154,U_2156] :
        ( 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_2154))
        | ~ sP185(U_2154,U_2156) )
    & ! [U_2157,U_2155] :
        ( 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_2155),U_2157)))
        | ~ 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_2157))
        | ~ 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_2155)) )
    & ! [U_2154,U_2156] :
        ( sP185(U_2154,U_2156)
        | ~ 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_2154),U_2156))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP185])],[f_642_3]) ).

cnf(f_642_5,plain,
    ( sP185(U_2154,U_2156)
    | ~ 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_2154),U_2156))) ),
    inference(clausify,[status(thm)],[f_642_4]) ).

cnf(f_642_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_2155),U_2157)))
    | ~ 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_2157))
    | ~ 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_2155)) ),
    inference(clausify,[status(thm)],[f_642_4]) ).

cnf(f_642_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_2154))
    | ~ sP185(U_2154,U_2156) ),
    inference(clausify,[status(thm)],[f_642_4]) ).

cnf(f_642_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_2156))
    | ~ sP185(U_2154,U_2156) ),
    inference(clausify,[status(thm)],[f_642_4]) ).

fof(f_643_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_643_2,plain,
    ! [U_2160,U_2159,U_2158] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2158),U_2159)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2158),U_2160)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2159),U_2160))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2158)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2159),U_2160))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2158))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2158),U_2159)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2158),U_2160))) ) ),
    inference(variable_rename,[status(thm)],[f_643_1]) ).

fof(f_643_3,plain,
    ( ! [U_2166,U_2164,U_2162] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2162),U_2164)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2162),U_2166)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2164),U_2166))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2162)) ) )
    & ! [U_2165,U_2163,U_2161] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2163),U_2165))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2161))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2161),U_2163)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2161),U_2165))) ) ),
    inference(miniscope,[status(thm)],[f_643_2]) ).

fof(f_643_4,plain,
    ( ! [U_2162,U_2166,U_2164] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2164),U_2166))
        | ~ sP186(U_2162,U_2166,U_2164) )
    & ! [U_2162,U_2166,U_2164] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2162))
        | ~ sP186(U_2162,U_2166,U_2164) )
    & ! [U_2162,U_2166,U_2164] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2162),U_2164)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2162),U_2166)))
        | sP186(U_2162,U_2166,U_2164) )
    & ! [U_2161,U_2165,U_2163] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2163),U_2165))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2161))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2161),U_2163)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2161),U_2165))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP186])],[f_643_3]) ).

cnf(f_643_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2163),U_2165))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2161))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2161),U_2163)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2161),U_2165))) ),
    inference(clausify,[status(thm)],[f_643_4]) ).

cnf(f_643_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_2162),U_2164)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2162),U_2166)))
    | sP186(U_2162,U_2166,U_2164) ),
    inference(clausify,[status(thm)],[f_643_4]) ).

cnf(f_643_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2162))
    | ~ sP186(U_2162,U_2166,U_2164) ),
    inference(clausify,[status(thm)],[f_643_4]) ).

cnf(f_643_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2164),U_2166))
    | ~ sP186(U_2162,U_2166,U_2164) ),
    inference(clausify,[status(thm)],[f_643_4]) ).

fof(f_644_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_644_2,plain,
    ! [U_2169,U_2168,U_2167] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2167),U_2168)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2169),U_2168)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2167),U_2169))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2168)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2167),U_2169))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2168))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2167),U_2168)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2169),U_2168))) ) ),
    inference(variable_rename,[status(thm)],[f_644_1]) ).

fof(f_644_3,plain,
    ( ! [U_2175,U_2173,U_2171] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2171),U_2173)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2175),U_2173)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2171),U_2175))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2173)) ) )
    & ! [U_2174,U_2172,U_2170] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2170),U_2174))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2172))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2170),U_2172)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2174),U_2172))) ) ),
    inference(miniscope,[status(thm)],[f_644_2]) ).

fof(f_644_4,plain,
    ( ! [U_2175,U_2173,U_2171] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2171),U_2175))
        | ~ sP187(U_2175,U_2173,U_2171) )
    & ! [U_2175,U_2173,U_2171] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2173))
        | ~ sP187(U_2175,U_2173,U_2171) )
    & ! [U_2175,U_2173,U_2171] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2171),U_2173)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2175),U_2173)))
        | sP187(U_2175,U_2173,U_2171) )
    & ! [U_2170,U_2172,U_2174] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2170),U_2174))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2172))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2170),U_2172)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2174),U_2172))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP187])],[f_644_3]) ).

cnf(f_644_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2170),U_2174))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2172))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2170),U_2172)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2174),U_2172))) ),
    inference(clausify,[status(thm)],[f_644_4]) ).

cnf(f_644_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_2171),U_2173)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2175),U_2173)))
    | sP187(U_2175,U_2173,U_2171) ),
    inference(clausify,[status(thm)],[f_644_4]) ).

cnf(f_644_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2173))
    | ~ sP187(U_2175,U_2173,U_2171) ),
    inference(clausify,[status(thm)],[f_644_4]) ).

cnf(f_644_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2171),U_2175))
    | ~ sP187(U_2175,U_2173,U_2171) ),
    inference(clausify,[status(thm)],[f_644_4]) ).

fof(f_645_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_645_2,plain,
    ! [U_2178,U_2177,U_2176] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2176),U_2177)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2176),U_2178)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2177),U_2178)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2177),U_2178))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2176),U_2177)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2176),U_2178))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2176)) ),
    inference(variable_rename,[status(thm)],[f_645_1]) ).

fof(f_645_3,plain,
    ( ! [U_2176,U_2177,U_2178] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2176),U_2177)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2176),U_2178)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2177),U_2178))
        | ~ sP188(U_2176,U_2177,U_2178) )
    & ! [U_2176,U_2177,U_2178] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2177),U_2178))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2176),U_2177)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2176),U_2178)))
        | ~ sP188(U_2176,U_2177,U_2178) )
    & ! [U_2176,U_2177,U_2178] :
        ( sP188(U_2176,U_2177,U_2178)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2176)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP188])],[f_645_2]) ).

cnf(f_645_4,plain,
    ( sP188(U_2176,U_2177,U_2178)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_2176)) ),
    inference(clausify,[status(thm)],[f_645_3]) ).

cnf(f_645_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2177),U_2178))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2176),U_2177)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2176),U_2178)))
    | ~ sP188(U_2176,U_2177,U_2178) ),
    inference(clausify,[status(thm)],[f_645_3]) ).

cnf(f_645_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_2176),U_2177)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2176),U_2178)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2177),U_2178))
    | ~ sP188(U_2176,U_2177,U_2178) ),
    inference(clausify,[status(thm)],[f_645_3]) ).

fof(f_646_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_646_2,plain,
    ! [U_2180,U_2179] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2179)),hAPP(c_Int_Onat,U_2180)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2179),U_2180)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2179),U_2180))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2179)),hAPP(c_Int_Onat,U_2180))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2180))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2179)) ),
    inference(variable_rename,[status(thm)],[f_646_1]) ).

fof(f_646_3,plain,
    ( ! [U_2179,U_2180] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2179)),hAPP(c_Int_Onat,U_2180)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2179),U_2180))
        | ~ sP189(U_2179,U_2180) )
    & ! [U_2179,U_2180] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2179),U_2180))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2179)),hAPP(c_Int_Onat,U_2180)))
        | ~ sP189(U_2179,U_2180) )
    & ! [U_2179,U_2180] :
        ( sP189(U_2179,U_2180)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2180))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2179)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP189])],[f_646_2]) ).

cnf(f_646_4,plain,
    ( sP189(U_2179,U_2180)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2180))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2179)) ),
    inference(clausify,[status(thm)],[f_646_3]) ).

cnf(f_646_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2179),U_2180))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2179)),hAPP(c_Int_Onat,U_2180)))
    | ~ sP189(U_2179,U_2180) ),
    inference(clausify,[status(thm)],[f_646_3]) ).

cnf(f_646_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2179)),hAPP(c_Int_Onat,U_2180)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2179),U_2180))
    | ~ sP189(U_2179,U_2180) ),
    inference(clausify,[status(thm)],[f_646_3]) ).

fof(f_647_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_647_2,plain,
    ! [U_2181] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2181))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2181)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2181))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2181)) ) ),
    inference(variable_rename,[status(thm)],[f_647_1]) ).

fof(f_647_3,plain,
    ( ! [U_2183] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2183))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2183)) )
    & ! [U_2182] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2182))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2182)) ) ),
    inference(miniscope,[status(thm)],[f_647_2]) ).

fof(f_647_4,plain,
    ( ! [U_2183] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2183))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2183)) )
    & ! [U_2182] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2182))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2182)) ) ),
    inference(definitional_conversion,[status(esa)],[f_647_3]) ).

cnf(f_647_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2182))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2182)) ),
    inference(clausify,[status(thm)],[f_647_4]) ).

cnf(f_647_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2183))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2183)) ),
    inference(clausify,[status(thm)],[f_647_4]) ).

fof(f_648_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_648_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_648_1]) ).

cnf(f_648_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_648_2]) ).

fof(f_649_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_649_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_649_1]) ).

cnf(f_649_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_649_2]) ).

fof(f_650_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_650_2,plain,
    ! [U_2185,U_2184] :
      ( ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2184),U_2185) = c_Groups_Oone__class_Oone(tc_Int_Oint)
          | U_2185 != c_Groups_Oone__class_Oone(tc_Int_Oint)
          | U_2184 != c_Groups_Oone__class_Oone(tc_Int_Oint) )
        & ( ( U_2185 = c_Groups_Oone__class_Oone(tc_Int_Oint)
            & U_2184 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2184),U_2185) != 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_2184)) ),
    inference(variable_rename,[status(thm)],[f_650_1]) ).

fof(f_650_3,plain,
    ( ! [U_2184,U_2185] :
        ( U_2185 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP190(U_2184,U_2185) )
    & ! [U_2184,U_2185] :
        ( U_2184 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP190(U_2184,U_2185) )
    & ! [U_2184,U_2185] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2184),U_2185) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | U_2185 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | U_2184 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP191(U_2184,U_2185) )
    & ! [U_2184,U_2185] :
        ( sP190(U_2184,U_2185)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2184),U_2185) != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP191(U_2184,U_2185) )
    & ! [U_2184,U_2185] :
        ( sP191(U_2184,U_2185)
        | ~ 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,[sP190,sP191])],[f_650_2]) ).

cnf(f_650_4,plain,
    ( sP191(U_2184,U_2185)
    | ~ 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_650_3]) ).

cnf(f_650_5,plain,
    ( sP190(U_2184,U_2185)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2184),U_2185) != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP191(U_2184,U_2185) ),
    inference(clausify,[status(thm)],[f_650_3]) ).

cnf(f_650_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2184),U_2185) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_2185 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_2184 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP191(U_2184,U_2185) ),
    inference(clausify,[status(thm)],[f_650_3]) ).

cnf(f_650_7,plain,
    ( U_2184 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP190(U_2184,U_2185) ),
    inference(clausify,[status(thm)],[f_650_3]) ).

cnf(f_650_8,plain,
    ( U_2185 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP190(U_2184,U_2185) ),
    inference(clausify,[status(thm)],[f_650_3]) ).

fof(f_651_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_651_2,plain,
    ! [U_2187,U_2186] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2186),U_2187),U_2187) = U_2187
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_2186) ),
    inference(variable_rename,[status(thm)],[f_651_1]) ).

fof(f_651_3,plain,
    ! [U_2186,U_2187] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2186),U_2187),U_2187) = U_2187
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_2186) ),
    inference(definitional_conversion,[status(esa)],[f_651_2]) ).

cnf(f_651_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2186),U_2187),U_2187) = U_2187
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_2186) ),
    inference(clausify,[status(thm)],[f_651_3]) ).

fof(f_652_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_652_2,plain,
    ! [U_2189,U_2188] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2188),U_2189),U_2189) = U_2189
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_2188) ),
    inference(variable_rename,[status(thm)],[f_652_1]) ).

fof(f_652_3,plain,
    ! [U_2188,U_2189] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2188),U_2189),U_2189) = U_2189
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_2188) ),
    inference(definitional_conversion,[status(esa)],[f_652_2]) ).

cnf(f_652_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2188),U_2189),U_2189) = U_2189
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_2188) ),
    inference(clausify,[status(thm)],[f_652_3]) ).

fof(f_653_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_653_2,plain,
    ! [U_2192,U_2191,U_2190] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),U_2191),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),U_2191),U_2192)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),U_2191),U_2192)
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_2190) ),
    inference(variable_rename,[status(thm)],[f_653_1]) ).

fof(f_653_3,plain,
    ! [U_2191,U_2190,U_2192] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),U_2191),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),U_2191),U_2192)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),U_2191),U_2192)
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_2190) ),
    inference(definitional_conversion,[status(esa)],[f_653_2]) ).

cnf(f_653_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),U_2191),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),U_2191),U_2192)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2190),U_2191),U_2192)
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_2190) ),
    inference(clausify,[status(thm)],[f_653_3]) ).

fof(f_654_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_654_2,plain,
    ! [U_2194,U_2193] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2193),hAPP(c_Groups_Ouminus__class_Ouminus(U_2193),U_2194)) = U_2194
      | ~ class_Lattices_Oboolean__algebra(U_2193) ),
    inference(variable_rename,[status(thm)],[f_654_1]) ).

fof(f_654_3,plain,
    ! [U_2193,U_2194] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2193),hAPP(c_Groups_Ouminus__class_Ouminus(U_2193),U_2194)) = U_2194
      | ~ class_Lattices_Oboolean__algebra(U_2193) ),
    inference(definitional_conversion,[status(esa)],[f_654_2]) ).

cnf(f_654_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2193),hAPP(c_Groups_Ouminus__class_Ouminus(U_2193),U_2194)) = U_2194
    | ~ class_Lattices_Oboolean__algebra(U_2193) ),
    inference(clausify,[status(thm)],[f_654_3]) ).

fof(f_655_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_655_2,plain,
    ! [U_2198,U_2197,U_2196,U_2195] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2196,U_2195)),U_2197),U_2198) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2195),hAPP(U_2197,U_2198))
      | ~ class_Groups_Ouminus(U_2195) ),
    inference(variable_rename,[status(thm)],[f_655_1]) ).

fof(f_655_3,plain,
    ! [U_2195,U_2196,U_2197,U_2198] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2196,U_2195)),U_2197),U_2198) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2195),hAPP(U_2197,U_2198))
      | ~ class_Groups_Ouminus(U_2195) ),
    inference(definitional_conversion,[status(esa)],[f_655_2]) ).

cnf(f_655_4,plain,
    ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_2196,U_2195)),U_2197),U_2198) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2195),hAPP(U_2197,U_2198))
    | ~ class_Groups_Ouminus(U_2195) ),
    inference(clausify,[status(thm)],[f_655_3]) ).

fof(f_656_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_656_2,plain,
    ! [U_2201,U_2200,U_2199] :
      ( ( ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2199),U_2200) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2199),U_2201)
          | U_2200 != U_2201 )
        & ( U_2200 = U_2201
          | hAPP(c_Groups_Ouminus__class_Ouminus(U_2199),U_2200) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2199),U_2201) ) )
      | ~ class_Lattices_Oboolean__algebra(U_2199) ),
    inference(variable_rename,[status(thm)],[f_656_1]) ).

fof(f_656_3,plain,
    ( ! [U_2199,U_2200,U_2201] :
        ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2199),U_2200) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2199),U_2201)
        | U_2200 != U_2201
        | ~ sP192(U_2199,U_2200,U_2201) )
    & ! [U_2199,U_2200,U_2201] :
        ( U_2200 = U_2201
        | hAPP(c_Groups_Ouminus__class_Ouminus(U_2199),U_2200) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2199),U_2201)
        | ~ sP192(U_2199,U_2200,U_2201) )
    & ! [U_2199,U_2200,U_2201] :
        ( sP192(U_2199,U_2200,U_2201)
        | ~ class_Lattices_Oboolean__algebra(U_2199) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP192])],[f_656_2]) ).

cnf(f_656_4,plain,
    ( sP192(U_2199,U_2200,U_2201)
    | ~ class_Lattices_Oboolean__algebra(U_2199) ),
    inference(clausify,[status(thm)],[f_656_3]) ).

cnf(f_656_5,plain,
    ( U_2200 = U_2201
    | hAPP(c_Groups_Ouminus__class_Ouminus(U_2199),U_2200) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2199),U_2201)
    | ~ sP192(U_2199,U_2200,U_2201) ),
    inference(clausify,[status(thm)],[f_656_3]) ).

cnf(f_656_6,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_2199),U_2200) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2199),U_2201)
    | U_2200 != U_2201
    | ~ sP192(U_2199,U_2200,U_2201) ),
    inference(clausify,[status(thm)],[f_656_3]) ).

fof(f_657_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_657_2,plain,
    ! [U_2203,U_2202] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2202)),hAPP(c_Int_Onat,U_2203)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2202),U_2203)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2202),U_2203))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2202)),hAPP(c_Int_Onat,U_2203))) ) )
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2203))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2202)) ) ),
    inference(variable_rename,[status(thm)],[f_657_1]) ).

fof(f_657_3,plain,
    ( ! [U_2202,U_2203] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2202)),hAPP(c_Int_Onat,U_2203)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2202),U_2203))
        | ~ sP194(U_2202,U_2203) )
    & ! [U_2202,U_2203] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2202),U_2203))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2202)),hAPP(c_Int_Onat,U_2203)))
        | ~ sP194(U_2202,U_2203) )
    & ! [U_2202,U_2203] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2203))
        | ~ sP193(U_2202,U_2203) )
    & ! [U_2202,U_2203] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2202))
        | ~ sP193(U_2202,U_2203) )
    & ! [U_2202,U_2203] :
        ( sP194(U_2202,U_2203)
        | sP193(U_2202,U_2203) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP193,sP194])],[f_657_2]) ).

cnf(f_657_4,plain,
    ( sP194(U_2202,U_2203)
    | sP193(U_2202,U_2203) ),
    inference(clausify,[status(thm)],[f_657_3]) ).

cnf(f_657_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2202))
    | ~ sP193(U_2202,U_2203) ),
    inference(clausify,[status(thm)],[f_657_3]) ).

cnf(f_657_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2203))
    | ~ sP193(U_2202,U_2203) ),
    inference(clausify,[status(thm)],[f_657_3]) ).

cnf(f_657_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2202),U_2203))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2202)),hAPP(c_Int_Onat,U_2203)))
    | ~ sP194(U_2202,U_2203) ),
    inference(clausify,[status(thm)],[f_657_3]) ).

cnf(f_657_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onat,U_2202)),hAPP(c_Int_Onat,U_2203)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2202),U_2203))
    | ~ sP194(U_2202,U_2203) ),
    inference(clausify,[status(thm)],[f_657_3]) ).

fof(f_658_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_658_2,plain,
    ! [U_2205,U_2204] : c_Int_Onat__aux(U_2204,U_2205) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2204)),U_2205),
    inference(variable_rename,[status(thm)],[f_658_1]) ).

fof(f_658_3,plain,
    ! [U_2204,U_2205] : c_Int_Onat__aux(U_2204,U_2205) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2204)),U_2205),
    inference(definitional_conversion,[status(esa)],[f_658_2]) ).

cnf(f_658_4,plain,
    c_Int_Onat__aux(U_2204,U_2205) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2204)),U_2205),
    inference(clausify,[status(thm)],[f_658_3]) ).

fof(f_659_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_659_2,plain,
    ! [U_2206] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_2206)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_2206)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_659_1]) ).

fof(f_659_3,plain,
    ! [U_2206] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_2206)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_2206)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_659_2]) ).

cnf(f_659_4,plain,
    c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,U_2206)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(U_2206)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_659_3]) ).

fof(f_660_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_660_2,plain,
    ! [U_2207] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2207)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_2207)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_660_1]) ).

fof(f_660_3,plain,
    ! [U_2207] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2207)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_2207)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_660_2]) ).

cnf(f_660_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_2207)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_2207)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_660_3]) ).

fof(f_661_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_661_2,plain,
    ! [U_2210,U_2209,U_2208] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2208),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2210),U_2209)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2208),U_2209)) ),
    inference(variable_rename,[status(thm)],[f_661_1]) ).

fof(f_661_3,plain,
    ! [U_2208,U_2209,U_2210] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2208),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2210),U_2209)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2208),U_2209)) ),
    inference(definitional_conversion,[status(esa)],[f_661_2]) ).

cnf(f_661_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2208),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2210),U_2209)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2208),U_2209)) ),
    inference(clausify,[status(thm)],[f_661_3]) ).

fof(f_662_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_662_2,plain,
    ! [U_2213,U_2212,U_2211] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2211),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2212),U_2213)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2211),U_2212)) ),
    inference(variable_rename,[status(thm)],[f_662_1]) ).

fof(f_662_3,plain,
    ! [U_2211,U_2212,U_2213] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2211),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2212),U_2213)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2211),U_2212)) ),
    inference(definitional_conversion,[status(esa)],[f_662_2]) ).

cnf(f_662_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2211),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2212),U_2213)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2211),U_2212)) ),
    inference(clausify,[status(thm)],[f_662_3]) ).

fof(f_663_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_663_2,plain,
    ! [U_2215,U_2214] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2214),U_2215))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2214),U_2215)) ),
    inference(variable_rename,[status(thm)],[f_663_1]) ).

fof(f_663_3,plain,
    ! [U_2214,U_2215] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2214),U_2215))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2214),U_2215)) ),
    inference(definitional_conversion,[status(esa)],[f_663_2]) ).

cnf(f_663_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2214),U_2215))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2214),U_2215)) ),
    inference(clausify,[status(thm)],[f_663_3]) ).

fof(f_664_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_664_2,plain,
    ! [U_2218,U_2217,U_2216] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2216),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2217),U_2218)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2216),U_2217)) ),
    inference(variable_rename,[status(thm)],[f_664_1]) ).

fof(f_664_3,plain,
    ! [U_2216,U_2217,U_2218] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2216),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2217),U_2218)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2216),U_2217)) ),
    inference(definitional_conversion,[status(esa)],[f_664_2]) ).

cnf(f_664_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2216),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2217),U_2218)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2216),U_2217)) ),
    inference(clausify,[status(thm)],[f_664_3]) ).

fof(f_665_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_665_2,plain,
    ! [U_2221,U_2220,U_2219] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2219),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2221),U_2220)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2219),U_2220)) ),
    inference(variable_rename,[status(thm)],[f_665_1]) ).

fof(f_665_3,plain,
    ! [U_2219,U_2220,U_2221] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2219),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2221),U_2220)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2219),U_2220)) ),
    inference(definitional_conversion,[status(esa)],[f_665_2]) ).

cnf(f_665_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2219),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2221),U_2220)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2219),U_2220)) ),
    inference(clausify,[status(thm)],[f_665_3]) ).

fof(f_666_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_666_2,plain,
    ! [U_2223,U_2222] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),c_Groups_Oone__class_Oone(U_2222)),U_2223)),U_2223)),c_Groups_Ozero__class_Ozero(U_2222)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2222),U_2223),c_Groups_Ozero__class_Ozero(U_2222))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2222),U_2223),c_Groups_Ozero__class_Ozero(U_2222)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),c_Groups_Oone__class_Oone(U_2222)),U_2223)),U_2223)),c_Groups_Ozero__class_Ozero(U_2222))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_2222),U_2223),c_Int_Oring__1__class_OInts(U_2222)))
      | ~ class_Rings_Olinordered__idom(U_2222) ),
    inference(variable_rename,[status(thm)],[f_666_1]) ).

fof(f_666_3,plain,
    ( ! [U_2222,U_2223] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),c_Groups_Oone__class_Oone(U_2222)),U_2223)),U_2223)),c_Groups_Ozero__class_Ozero(U_2222)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2222),U_2223),c_Groups_Ozero__class_Ozero(U_2222)))
        | ~ sP195(U_2222,U_2223) )
    & ! [U_2222,U_2223] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2222),U_2223),c_Groups_Ozero__class_Ozero(U_2222)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),c_Groups_Oone__class_Oone(U_2222)),U_2223)),U_2223)),c_Groups_Ozero__class_Ozero(U_2222)))
        | ~ sP195(U_2222,U_2223) )
    & ! [U_2222,U_2223] :
        ( sP195(U_2222,U_2223)
        | ~ hBOOL(hAPP(hAPP(c_member(U_2222),U_2223),c_Int_Oring__1__class_OInts(U_2222)))
        | ~ class_Rings_Olinordered__idom(U_2222) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP195])],[f_666_2]) ).

cnf(f_666_4,plain,
    ( sP195(U_2222,U_2223)
    | ~ hBOOL(hAPP(hAPP(c_member(U_2222),U_2223),c_Int_Oring__1__class_OInts(U_2222)))
    | ~ class_Rings_Olinordered__idom(U_2222) ),
    inference(clausify,[status(thm)],[f_666_3]) ).

cnf(f_666_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2222),U_2223),c_Groups_Ozero__class_Ozero(U_2222)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),c_Groups_Oone__class_Oone(U_2222)),U_2223)),U_2223)),c_Groups_Ozero__class_Ozero(U_2222)))
    | ~ sP195(U_2222,U_2223) ),
    inference(clausify,[status(thm)],[f_666_3]) ).

cnf(f_666_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2222),c_Groups_Oone__class_Oone(U_2222)),U_2223)),U_2223)),c_Groups_Ozero__class_Ozero(U_2222)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2222),U_2223),c_Groups_Ozero__class_Ozero(U_2222)))
    | ~ sP195(U_2222,U_2223) ),
    inference(clausify,[status(thm)],[f_666_3]) ).

fof(f_667_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_667_2,plain,
    ! [U_2225,U_2224] :
      ( ( ( c_Groups_Osgn__class_Osgn(U_2224,U_2225) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2224),c_Groups_Oone__class_Oone(U_2224))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2224),U_2225),c_Groups_Ozero__class_Ozero(U_2224))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2224),U_2225),c_Groups_Ozero__class_Ozero(U_2224)))
          | c_Groups_Osgn__class_Osgn(U_2224,U_2225) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2224),c_Groups_Oone__class_Oone(U_2224)) ) )
      | ~ class_Rings_Olinordered__idom(U_2224) ),
    inference(variable_rename,[status(thm)],[f_667_1]) ).

fof(f_667_3,plain,
    ( ! [U_2224,U_2225] :
        ( c_Groups_Osgn__class_Osgn(U_2224,U_2225) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2224),c_Groups_Oone__class_Oone(U_2224))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2224),U_2225),c_Groups_Ozero__class_Ozero(U_2224)))
        | ~ sP196(U_2224,U_2225) )
    & ! [U_2224,U_2225] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2224),U_2225),c_Groups_Ozero__class_Ozero(U_2224)))
        | c_Groups_Osgn__class_Osgn(U_2224,U_2225) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2224),c_Groups_Oone__class_Oone(U_2224))
        | ~ sP196(U_2224,U_2225) )
    & ! [U_2224,U_2225] :
        ( sP196(U_2224,U_2225)
        | ~ class_Rings_Olinordered__idom(U_2224) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP196])],[f_667_2]) ).

cnf(f_667_4,plain,
    ( sP196(U_2224,U_2225)
    | ~ class_Rings_Olinordered__idom(U_2224) ),
    inference(clausify,[status(thm)],[f_667_3]) ).

cnf(f_667_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2224),U_2225),c_Groups_Ozero__class_Ozero(U_2224)))
    | c_Groups_Osgn__class_Osgn(U_2224,U_2225) != hAPP(c_Groups_Ouminus__class_Ouminus(U_2224),c_Groups_Oone__class_Oone(U_2224))
    | ~ sP196(U_2224,U_2225) ),
    inference(clausify,[status(thm)],[f_667_3]) ).

cnf(f_667_6,plain,
    ( c_Groups_Osgn__class_Osgn(U_2224,U_2225) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2224),c_Groups_Oone__class_Oone(U_2224))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2224),U_2225),c_Groups_Ozero__class_Ozero(U_2224)))
    | ~ sP196(U_2224,U_2225) ),
    inference(clausify,[status(thm)],[f_667_3]) ).

fof(f_668_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_668_2,plain,
    ! [U_2228,U_2227,U_2226] :
      ( U_2227 = U_2228
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2226,tc_HOL_Obool)),U_2228),U_2227))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2226,tc_HOL_Obool)),U_2227),U_2228)) ),
    inference(variable_rename,[status(thm)],[f_668_1]) ).

fof(f_668_3,plain,
    ! [U_2228,U_2226,U_2227] :
      ( U_2227 = U_2228
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2226,tc_HOL_Obool)),U_2228),U_2227))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2226,tc_HOL_Obool)),U_2227),U_2228)) ),
    inference(definitional_conversion,[status(esa)],[f_668_2]) ).

cnf(f_668_4,plain,
    ( U_2227 = U_2228
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2226,tc_HOL_Obool)),U_2228),U_2227))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2226,tc_HOL_Obool)),U_2227),U_2228)) ),
    inference(clausify,[status(thm)],[f_668_3]) ).

fof(f_669_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_669_2,plain,
    ! [U_2230,U_2229] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2229,tc_HOL_Obool)),U_2230),U_2230)),
    inference(variable_rename,[status(thm)],[f_669_1]) ).

fof(f_669_3,plain,
    ! [U_2230,U_2229] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2229,tc_HOL_Obool)),U_2230),U_2230)),
    inference(definitional_conversion,[status(esa)],[f_669_2]) ).

cnf(f_669_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2229,tc_HOL_Obool)),U_2230),U_2230)),
    inference(clausify,[status(thm)],[f_669_3]) ).

fof(f_670_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_670_2,plain,
    ! [U_2233,U_2232,U_2231] :
      ( ( U_2231 = U_2232
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2233,tc_HOL_Obool)),U_2232),U_2231))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2233,tc_HOL_Obool)),U_2231),U_2232)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2233,tc_HOL_Obool)),U_2232),U_2231))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2233,tc_HOL_Obool)),U_2231),U_2232)) )
        | U_2231 != U_2232 ) ),
    inference(variable_rename,[status(thm)],[f_670_1]) ).

fof(f_670_3,plain,
    ( ! [U_2239,U_2237,U_2235] :
        ( U_2235 = U_2237
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2239,tc_HOL_Obool)),U_2237),U_2235))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2239,tc_HOL_Obool)),U_2235),U_2237)) )
    & ! [U_2238,U_2236,U_2234] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2238,tc_HOL_Obool)),U_2236),U_2234))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2238,tc_HOL_Obool)),U_2234),U_2236)) )
        | U_2234 != U_2236 ) ),
    inference(miniscope,[status(thm)],[f_670_2]) ).

fof(f_670_4,plain,
    ( ! [U_2236,U_2234,U_2238] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2238,tc_HOL_Obool)),U_2236),U_2234))
        | ~ sP197(U_2236,U_2234,U_2238) )
    & ! [U_2236,U_2234,U_2238] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2238,tc_HOL_Obool)),U_2234),U_2236))
        | ~ sP197(U_2236,U_2234,U_2238) )
    & ! [U_2237,U_2235,U_2239] :
        ( U_2235 = U_2237
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2239,tc_HOL_Obool)),U_2237),U_2235))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2239,tc_HOL_Obool)),U_2235),U_2237)) )
    & ! [U_2236,U_2234,U_2238] :
        ( sP197(U_2236,U_2234,U_2238)
        | U_2234 != U_2236 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP197])],[f_670_3]) ).

cnf(f_670_5,plain,
    ( sP197(U_2236,U_2234,U_2238)
    | U_2234 != U_2236 ),
    inference(clausify,[status(thm)],[f_670_4]) ).

cnf(f_670_6,plain,
    ( U_2235 = U_2237
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2239,tc_HOL_Obool)),U_2237),U_2235))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2239,tc_HOL_Obool)),U_2235),U_2237)) ),
    inference(clausify,[status(thm)],[f_670_4]) ).

cnf(f_670_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2238,tc_HOL_Obool)),U_2234),U_2236))
    | ~ sP197(U_2236,U_2234,U_2238) ),
    inference(clausify,[status(thm)],[f_670_4]) ).

cnf(f_670_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2238,tc_HOL_Obool)),U_2236),U_2234))
    | ~ sP197(U_2236,U_2234,U_2238) ),
    inference(clausify,[status(thm)],[f_670_4]) ).

fof(f_671_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_671_2,plain,
    ! [U_2242,U_2241,U_2240] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2242,tc_HOL_Obool)),U_2240),U_2241))
      | U_2240 != U_2241 ),
    inference(variable_rename,[status(thm)],[f_671_1]) ).

fof(f_671_3,plain,
    ! [U_2241,U_2240,U_2242] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2242,tc_HOL_Obool)),U_2240),U_2241))
      | U_2240 != U_2241 ),
    inference(definitional_conversion,[status(esa)],[f_671_2]) ).

cnf(f_671_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2242,tc_HOL_Obool)),U_2240),U_2241))
    | U_2240 != U_2241 ),
    inference(clausify,[status(thm)],[f_671_3]) ).

fof(f_672_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_672_2,plain,
    ! [U_2245,U_2244,U_2243] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2245,tc_HOL_Obool)),U_2244),U_2243))
      | U_2243 != U_2244 ),
    inference(variable_rename,[status(thm)],[f_672_1]) ).

fof(f_672_3,plain,
    ! [U_2243,U_2244,U_2245] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2245,tc_HOL_Obool)),U_2244),U_2243))
      | U_2243 != U_2244 ),
    inference(definitional_conversion,[status(esa)],[f_672_2]) ).

cnf(f_672_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2245,tc_HOL_Obool)),U_2244),U_2243))
    | U_2243 != U_2244 ),
    inference(clausify,[status(thm)],[f_672_3]) ).

fof(f_673_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_673_2,plain,
    ! [U_2249,U_2248,U_2247,U_2246] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2246,tc_HOL_Obool)),U_2247),U_2249))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2246,tc_HOL_Obool)),U_2248),U_2249))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2246,tc_HOL_Obool)),U_2247),U_2248)) ),
    inference(variable_rename,[status(thm)],[f_673_1]) ).

fof(f_673_3,plain,
    ! [U_2246,U_2247,U_2248,U_2249] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2246,tc_HOL_Obool)),U_2247),U_2249))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2246,tc_HOL_Obool)),U_2248),U_2249))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2246,tc_HOL_Obool)),U_2247),U_2248)) ),
    inference(definitional_conversion,[status(esa)],[f_673_2]) ).

cnf(f_673_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2246,tc_HOL_Obool)),U_2247),U_2249))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2246,tc_HOL_Obool)),U_2248),U_2249))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2246,tc_HOL_Obool)),U_2247),U_2248)) ),
    inference(clausify,[status(thm)],[f_673_3]) ).

fof(f_674_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_674_2,plain,
    ! [U_2252,U_2251,U_2250] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2252,tc_HOL_Obool)),U_2251),U_2250))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2252,tc_HOL_Obool)),U_2250),U_2251)) )
      | U_2250 != U_2251 ),
    inference(variable_rename,[status(thm)],[f_674_1]) ).

fof(f_674_3,plain,
    ( ! [U_2250,U_2251,U_2252] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2252,tc_HOL_Obool)),U_2251),U_2250))
        | ~ sP198(U_2250,U_2251,U_2252) )
    & ! [U_2250,U_2251,U_2252] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2252,tc_HOL_Obool)),U_2250),U_2251))
        | ~ sP198(U_2250,U_2251,U_2252) )
    & ! [U_2250,U_2251,U_2252] :
        ( sP198(U_2250,U_2251,U_2252)
        | U_2250 != U_2251 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP198])],[f_674_2]) ).

cnf(f_674_4,plain,
    ( sP198(U_2250,U_2251,U_2252)
    | U_2250 != U_2251 ),
    inference(clausify,[status(thm)],[f_674_3]) ).

cnf(f_674_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2252,tc_HOL_Obool)),U_2250),U_2251))
    | ~ sP198(U_2250,U_2251,U_2252) ),
    inference(clausify,[status(thm)],[f_674_3]) ).

cnf(f_674_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2252,tc_HOL_Obool)),U_2251),U_2250))
    | ~ sP198(U_2250,U_2251,U_2252) ),
    inference(clausify,[status(thm)],[f_674_3]) ).

fof(f_675_1,plain,
    ! [V_Qa_2,T_b,V_x_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Qa_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2))
      | ~ hBOOL(hAPP(V_Pa_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rev__predicate1D]) ).

fof(f_675_2,plain,
    ! [U_2256,U_2255,U_2254,U_2253] :
      ( hBOOL(hAPP(U_2256,U_2254))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2255,tc_HOL_Obool)),U_2253),U_2256))
      | ~ hBOOL(hAPP(U_2253,U_2254)) ),
    inference(variable_rename,[status(thm)],[f_675_1]) ).

fof(f_675_3,plain,
    ! [U_2255,U_2253,U_2254,U_2256] :
      ( hBOOL(hAPP(U_2256,U_2254))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2255,tc_HOL_Obool)),U_2253),U_2256))
      | ~ hBOOL(hAPP(U_2253,U_2254)) ),
    inference(definitional_conversion,[status(esa)],[f_675_2]) ).

cnf(f_675_4,plain,
    ( hBOOL(hAPP(U_2256,U_2254))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2255,tc_HOL_Obool)),U_2253),U_2256))
    | ~ hBOOL(hAPP(U_2253,U_2254)) ),
    inference(clausify,[status(thm)],[f_675_3]) ).

fof(f_676_1,plain,
    ! [V_x_2,V_Qa_2,V_Pa_2,T_b] :
      ( hBOOL(hAPP(V_Qa_2,V_x_2))
      | ~ hBOOL(hAPP(V_Pa_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_Pa_2),V_Qa_2)) ),
    inference(fof_nnf,[status(thm)],[fact_predicate1D]) ).

fof(f_676_2,plain,
    ! [U_2260,U_2259,U_2258,U_2257] :
      ( hBOOL(hAPP(U_2259,U_2260))
      | ~ hBOOL(hAPP(U_2258,U_2260))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2257,tc_HOL_Obool)),U_2258),U_2259)) ),
    inference(variable_rename,[status(thm)],[f_676_1]) ).

fof(f_676_3,plain,
    ! [U_2260,U_2259,U_2258] :
      ( ! [U_2257] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2257,tc_HOL_Obool)),U_2258),U_2259))
      | hBOOL(hAPP(U_2259,U_2260))
      | ~ hBOOL(hAPP(U_2258,U_2260)) ),
    inference(miniscope,[status(thm)],[f_676_2]) ).

fof(f_676_4,plain,
    ! [U_2257,U_2258,U_2259,U_2260] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2257,tc_HOL_Obool)),U_2258),U_2259))
      | hBOOL(hAPP(U_2259,U_2260))
      | ~ hBOOL(hAPP(U_2258,U_2260)) ),
    inference(definitional_conversion,[status(esa)],[f_676_3]) ).

cnf(f_676_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_2257,tc_HOL_Obool)),U_2258),U_2259))
    | hBOOL(hAPP(U_2259,U_2260))
    | ~ hBOOL(hAPP(U_2258,U_2260)) ),
    inference(clausify,[status(thm)],[f_676_4]) ).

fof(f_677_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_677_2,plain,
    ! [U_2263,U_2262,U_2261] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2261),U_2262)),U_2263) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2261),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2262),U_2263)),
    inference(variable_rename,[status(thm)],[f_677_1]) ).

fof(f_677_3,plain,
    ! [U_2261,U_2262,U_2263] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2261),U_2262)),U_2263) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2261),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2262),U_2263)),
    inference(definitional_conversion,[status(esa)],[f_677_2]) ).

cnf(f_677_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2261),U_2262)),U_2263) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2261),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2262),U_2263)),
    inference(clausify,[status(thm)],[f_677_3]) ).

fof(f_678_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_678_2,plain,
    ! [U_2266,U_2265,U_2264] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2264),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2265),U_2266)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2265),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2264),U_2266)),
    inference(variable_rename,[status(thm)],[f_678_1]) ).

fof(f_678_3,plain,
    ! [U_2264,U_2265,U_2266] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2264),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2265),U_2266)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2265),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2264),U_2266)),
    inference(definitional_conversion,[status(esa)],[f_678_2]) ).

cnf(f_678_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2264),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2265),U_2266)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2265),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2264),U_2266)),
    inference(clausify,[status(thm)],[f_678_3]) ).

fof(f_679_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_679_2,plain,
    ! [U_2268,U_2267] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2267),U_2268) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2268),U_2267),
    inference(variable_rename,[status(thm)],[f_679_1]) ).

fof(f_679_3,plain,
    ! [U_2267,U_2268] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2267),U_2268) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2268),U_2267),
    inference(definitional_conversion,[status(esa)],[f_679_2]) ).

cnf(f_679_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2267),U_2268) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2268),U_2267),
    inference(clausify,[status(thm)],[f_679_3]) ).

fof(f_680_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_680_2,plain,
    ! [U_2270,U_2269] :
      ( c_Groups_Osgn__class_Osgn(U_2269,c_Groups_Osgn__class_Osgn(U_2269,U_2270)) = c_Groups_Osgn__class_Osgn(U_2269,U_2270)
      | ~ class_Rings_Olinordered__idom(U_2269) ),
    inference(variable_rename,[status(thm)],[f_680_1]) ).

fof(f_680_3,plain,
    ! [U_2269,U_2270] :
      ( c_Groups_Osgn__class_Osgn(U_2269,c_Groups_Osgn__class_Osgn(U_2269,U_2270)) = c_Groups_Osgn__class_Osgn(U_2269,U_2270)
      | ~ class_Rings_Olinordered__idom(U_2269) ),
    inference(definitional_conversion,[status(esa)],[f_680_2]) ).

cnf(f_680_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_2269,c_Groups_Osgn__class_Osgn(U_2269,U_2270)) = c_Groups_Osgn__class_Osgn(U_2269,U_2270)
    | ~ class_Rings_Olinordered__idom(U_2269) ),
    inference(clausify,[status(thm)],[f_680_3]) ).

fof(f_681_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_681_2,plain,
    ! [U_2271] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_2271) = U_2271,
    inference(variable_rename,[status(thm)],[f_681_1]) ).

fof(f_681_3,plain,
    ! [U_2271] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_2271) = U_2271,
    inference(definitional_conversion,[status(esa)],[f_681_2]) ).

cnf(f_681_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),U_2271) = U_2271,
    inference(clausify,[status(thm)],[f_681_3]) ).

fof(f_682_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_682_2,plain,
    ! [U_2272] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2272),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_2272,
    inference(variable_rename,[status(thm)],[f_682_1]) ).

fof(f_682_3,plain,
    ! [U_2272] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2272),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_2272,
    inference(definitional_conversion,[status(esa)],[f_682_2]) ).

cnf(f_682_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2272),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_2272,
    inference(clausify,[status(thm)],[f_682_3]) ).

fof(f_683_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_683_2,plain,
    ! [U_2273] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2273) = U_2273,
    inference(variable_rename,[status(thm)],[f_683_1]) ).

fof(f_683_3,plain,
    ! [U_2273] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2273) = U_2273,
    inference(definitional_conversion,[status(esa)],[f_683_2]) ).

cnf(f_683_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2273) = U_2273,
    inference(clausify,[status(thm)],[f_683_3]) ).

fof(f_684_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_684_2,plain,
    ! [U_2276,U_2275,U_2274] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2276),U_2274)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2276),U_2275)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2274),U_2275)) ),
    inference(variable_rename,[status(thm)],[f_684_1]) ).

fof(f_684_3,plain,
    ! [U_2274,U_2275,U_2276] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2276),U_2274)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2276),U_2275)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2274),U_2275)) ),
    inference(definitional_conversion,[status(esa)],[f_684_2]) ).

cnf(f_684_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_2276),U_2274)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2276),U_2275)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2274),U_2275)) ),
    inference(clausify,[status(thm)],[f_684_3]) ).

fof(f_685_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_685_2,plain,
    ! [U_2279,U_2278,U_2277] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2277),U_2279)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2278),U_2279)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2277),U_2278)) ),
    inference(variable_rename,[status(thm)],[f_685_1]) ).

fof(f_685_3,plain,
    ! [U_2277,U_2278,U_2279] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2277),U_2279)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2278),U_2279)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2277),U_2278)) ),
    inference(definitional_conversion,[status(esa)],[f_685_2]) ).

cnf(f_685_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2277),U_2279)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2278),U_2279)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2277),U_2278)) ),
    inference(clausify,[status(thm)],[f_685_3]) ).

fof(f_686_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_686_2,plain,
    ! [U_2282,U_2281,U_2280] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2280),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2281),U_2282)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2280),U_2281)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2280),U_2282)),
    inference(variable_rename,[status(thm)],[f_686_1]) ).

fof(f_686_3,plain,
    ! [U_2280,U_2281,U_2282] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2280),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2281),U_2282)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2280),U_2281)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2280),U_2282)),
    inference(definitional_conversion,[status(esa)],[f_686_2]) ).

cnf(f_686_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2280),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2281),U_2282)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2280),U_2281)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2280),U_2282)),
    inference(clausify,[status(thm)],[f_686_3]) ).

fof(f_687_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_687_2,plain,
    ! [U_2285,U_2284,U_2283] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2283),U_2284)),U_2285) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2283),U_2285)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2284),U_2285)),
    inference(variable_rename,[status(thm)],[f_687_1]) ).

fof(f_687_3,plain,
    ! [U_2283,U_2284,U_2285] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2283),U_2284)),U_2285) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2283),U_2285)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2284),U_2285)),
    inference(definitional_conversion,[status(esa)],[f_687_2]) ).

cnf(f_687_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2283),U_2284)),U_2285) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2283),U_2285)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2284),U_2285)),
    inference(clausify,[status(thm)],[f_687_3]) ).

fof(f_688_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_688_2,plain,
    ! [U_2287,U_2286] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2286),U_2287)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2286)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2287)),
    inference(variable_rename,[status(thm)],[f_688_1]) ).

fof(f_688_3,plain,
    ! [U_2286,U_2287] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2286),U_2287)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2286)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2287)),
    inference(definitional_conversion,[status(esa)],[f_688_2]) ).

cnf(f_688_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2286),U_2287)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2286)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2287)),
    inference(clausify,[status(thm)],[f_688_3]) ).

fof(f_689_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_689_2,plain,
    ! [U_2289,U_2288] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2288),U_2289) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2289 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2288 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( U_2289 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_2288 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2288),U_2289) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_689_1]) ).

fof(f_689_3,plain,
    ( ! [U_2293,U_2291] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2291),U_2293) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2293 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2291 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_2292,U_2290] :
        ( ( U_2292 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_2290 = c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2290),U_2292) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_689_2]) ).

fof(f_689_4,plain,
    ( ! [U_2292,U_2290] :
        ( U_2292 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP199(U_2292,U_2290) )
    & ! [U_2292,U_2290] :
        ( U_2290 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP199(U_2292,U_2290) )
    & ! [U_2293,U_2291] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2291),U_2293) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2293 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2291 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_2292,U_2290] :
        ( sP199(U_2292,U_2290)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2290),U_2292) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP199])],[f_689_3]) ).

cnf(f_689_5,plain,
    ( sP199(U_2292,U_2290)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2290),U_2292) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_689_4]) ).

cnf(f_689_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2291),U_2293) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_2293 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_2291 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_689_4]) ).

cnf(f_689_7,plain,
    ( U_2290 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP199(U_2292,U_2290) ),
    inference(clausify,[status(thm)],[f_689_4]) ).

cnf(f_689_8,plain,
    ( U_2292 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP199(U_2292,U_2290) ),
    inference(clausify,[status(thm)],[f_689_4]) ).

fof(f_690_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_690_2,plain,
    ! [U_2294] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2294),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2294,
    inference(variable_rename,[status(thm)],[f_690_1]) ).

fof(f_690_3,plain,
    ! [U_2294] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2294),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2294,
    inference(definitional_conversion,[status(esa)],[f_690_2]) ).

cnf(f_690_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2294),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_2294,
    inference(clausify,[status(thm)],[f_690_3]) ).

fof(f_691_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_691_2,plain,
    ! [U_2296,U_2295] :
      ( ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2295),U_2296)
        | U_2296 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2295 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( ( U_2296 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_2295 = 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_2295),U_2296) ) ),
    inference(variable_rename,[status(thm)],[f_691_1]) ).

fof(f_691_3,plain,
    ( ! [U_2300,U_2298] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2298),U_2300)
        | U_2300 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2298 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_2299,U_2297] :
        ( ( U_2299 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          & U_2297 = 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_2297),U_2299) ) ),
    inference(miniscope,[status(thm)],[f_691_2]) ).

fof(f_691_4,plain,
    ( ! [U_2299,U_2297] :
        ( U_2299 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP200(U_2299,U_2297) )
    & ! [U_2299,U_2297] :
        ( U_2297 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP200(U_2299,U_2297) )
    & ! [U_2300,U_2298] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2298),U_2300)
        | U_2300 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_2298 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_2299,U_2297] :
        ( sP200(U_2299,U_2297)
        | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2297),U_2299) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP200])],[f_691_3]) ).

cnf(f_691_5,plain,
    ( sP200(U_2299,U_2297)
    | c_Groups_Oone__class_Oone(tc_Nat_Onat) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2297),U_2299) ),
    inference(clausify,[status(thm)],[f_691_4]) ).

cnf(f_691_6,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2298),U_2300)
    | U_2300 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_2298 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_691_4]) ).

cnf(f_691_7,plain,
    ( U_2297 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP200(U_2299,U_2297) ),
    inference(clausify,[status(thm)],[f_691_4]) ).

cnf(f_691_8,plain,
    ( U_2299 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP200(U_2299,U_2297) ),
    inference(clausify,[status(thm)],[f_691_4]) ).

fof(f_692_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_692_2,plain,
    ! [U_2301] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2301) = U_2301,
    inference(variable_rename,[status(thm)],[f_692_1]) ).

fof(f_692_3,plain,
    ! [U_2301] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2301) = U_2301,
    inference(definitional_conversion,[status(esa)],[f_692_2]) ).

cnf(f_692_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2301) = U_2301,
    inference(clausify,[status(thm)],[f_692_3]) ).

fof(f_693_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_693_2,plain,
    ! [U_2302] :
      ( c_Groups_Osgn__class_Osgn(U_2302,c_Groups_Ozero__class_Ozero(U_2302)) = c_Groups_Ozero__class_Ozero(U_2302)
      | ~ class_Groups_Osgn__if(U_2302) ),
    inference(variable_rename,[status(thm)],[f_693_1]) ).

fof(f_693_3,plain,
    ! [U_2302] :
      ( c_Groups_Osgn__class_Osgn(U_2302,c_Groups_Ozero__class_Ozero(U_2302)) = c_Groups_Ozero__class_Ozero(U_2302)
      | ~ class_Groups_Osgn__if(U_2302) ),
    inference(definitional_conversion,[status(esa)],[f_693_2]) ).

cnf(f_693_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_2302,c_Groups_Ozero__class_Ozero(U_2302)) = c_Groups_Ozero__class_Ozero(U_2302)
    | ~ class_Groups_Osgn__if(U_2302) ),
    inference(clausify,[status(thm)],[f_693_3]) ).

fof(f_694_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_694_2,plain,
    ! [U_2304,U_2303] :
      ( ( ( c_Groups_Osgn__class_Osgn(U_2303,U_2304) = c_Groups_Ozero__class_Ozero(U_2303)
          | U_2304 != c_Groups_Ozero__class_Ozero(U_2303) )
        & ( U_2304 = c_Groups_Ozero__class_Ozero(U_2303)
          | c_Groups_Osgn__class_Osgn(U_2303,U_2304) != c_Groups_Ozero__class_Ozero(U_2303) ) )
      | ~ class_Rings_Olinordered__idom(U_2303) ),
    inference(variable_rename,[status(thm)],[f_694_1]) ).

fof(f_694_3,plain,
    ( ! [U_2303,U_2304] :
        ( c_Groups_Osgn__class_Osgn(U_2303,U_2304) = c_Groups_Ozero__class_Ozero(U_2303)
        | U_2304 != c_Groups_Ozero__class_Ozero(U_2303)
        | ~ sP201(U_2303,U_2304) )
    & ! [U_2303,U_2304] :
        ( U_2304 = c_Groups_Ozero__class_Ozero(U_2303)
        | c_Groups_Osgn__class_Osgn(U_2303,U_2304) != c_Groups_Ozero__class_Ozero(U_2303)
        | ~ sP201(U_2303,U_2304) )
    & ! [U_2303,U_2304] :
        ( sP201(U_2303,U_2304)
        | ~ class_Rings_Olinordered__idom(U_2303) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP201])],[f_694_2]) ).

cnf(f_694_4,plain,
    ( sP201(U_2303,U_2304)
    | ~ class_Rings_Olinordered__idom(U_2303) ),
    inference(clausify,[status(thm)],[f_694_3]) ).

cnf(f_694_5,plain,
    ( U_2304 = c_Groups_Ozero__class_Ozero(U_2303)
    | c_Groups_Osgn__class_Osgn(U_2303,U_2304) != c_Groups_Ozero__class_Ozero(U_2303)
    | ~ sP201(U_2303,U_2304) ),
    inference(clausify,[status(thm)],[f_694_3]) ).

cnf(f_694_6,plain,
    ( c_Groups_Osgn__class_Osgn(U_2303,U_2304) = c_Groups_Ozero__class_Ozero(U_2303)
    | U_2304 != c_Groups_Ozero__class_Ozero(U_2303)
    | ~ sP201(U_2303,U_2304) ),
    inference(clausify,[status(thm)],[f_694_3]) ).

fof(f_695_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_695_2,plain,
    ! [U_2307,U_2306,U_2305] :
      ( c_Groups_Osgn__class_Osgn(U_2305,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2305),U_2306),U_2307)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2305),c_Groups_Osgn__class_Osgn(U_2305,U_2306)),c_Groups_Osgn__class_Osgn(U_2305,U_2307))
      | ~ class_Rings_Olinordered__idom(U_2305) ),
    inference(variable_rename,[status(thm)],[f_695_1]) ).

fof(f_695_3,plain,
    ! [U_2306,U_2305,U_2307] :
      ( c_Groups_Osgn__class_Osgn(U_2305,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2305),U_2306),U_2307)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2305),c_Groups_Osgn__class_Osgn(U_2305,U_2306)),c_Groups_Osgn__class_Osgn(U_2305,U_2307))
      | ~ class_Rings_Olinordered__idom(U_2305) ),
    inference(definitional_conversion,[status(esa)],[f_695_2]) ).

cnf(f_695_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_2305,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2305),U_2306),U_2307)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2305),c_Groups_Osgn__class_Osgn(U_2305,U_2306)),c_Groups_Osgn__class_Osgn(U_2305,U_2307))
    | ~ class_Rings_Olinordered__idom(U_2305) ),
    inference(clausify,[status(thm)],[f_695_3]) ).

fof(f_696_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_696_2,plain,
    ! [U_2309,U_2308] :
      ( 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_2308),U_2309)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2309))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2308)) ),
    inference(variable_rename,[status(thm)],[f_696_1]) ).

fof(f_696_3,plain,
    ! [U_2308,U_2309] :
      ( 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_2308),U_2309)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2309))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2308)) ),
    inference(definitional_conversion,[status(esa)],[f_696_2]) ).

cnf(f_696_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_2308),U_2309)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2309))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2308)) ),
    inference(clausify,[status(thm)],[f_696_3]) ).

fof(f_697_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_697_2,plain,
    ! [U_2313,U_2312,U_2311,U_2310] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2310),U_2312)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2311),U_2313)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2312),U_2313))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2310),U_2311)) ),
    inference(variable_rename,[status(thm)],[f_697_1]) ).

fof(f_697_3,plain,
    ! [U_2310,U_2311,U_2312,U_2313] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2310),U_2312)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2311),U_2313)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2312),U_2313))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2310),U_2311)) ),
    inference(definitional_conversion,[status(esa)],[f_697_2]) ).

cnf(f_697_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2310),U_2312)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2311),U_2313)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2312),U_2313))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2310),U_2311)) ),
    inference(clausify,[status(thm)],[f_697_3]) ).

fof(f_698_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_698_2,plain,
    ! [U_2314] : 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_2314)),U_2314) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_698_1]) ).

fof(f_698_3,plain,
    ! [U_2314] : 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_2314)),U_2314) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_698_2]) ).

cnf(f_698_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_2314)),U_2314) != c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_698_3]) ).

fof(f_699_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_699_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_699_1]) ).

cnf(f_699_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_699_2]) ).

fof(f_700_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_700_2,plain,
    ! [U_2316,U_2315] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2315)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2316)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2315),U_2316)),
    inference(variable_rename,[status(thm)],[f_700_1]) ).

fof(f_700_3,plain,
    ! [U_2315,U_2316] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2315)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2316)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2315),U_2316)),
    inference(definitional_conversion,[status(esa)],[f_700_2]) ).

cnf(f_700_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2315)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2316)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2315),U_2316)),
    inference(clausify,[status(thm)],[f_700_3]) ).

fof(f_701_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_701_2,plain,
    ! [U_2318,U_2317] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2317)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2318)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2317),U_2318)),
    inference(variable_rename,[status(thm)],[f_701_1]) ).

fof(f_701_3,plain,
    ! [U_2317,U_2318] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2317)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2318)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2317),U_2318)),
    inference(definitional_conversion,[status(esa)],[f_701_2]) ).

cnf(f_701_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2317)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2318)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2317),U_2318)),
    inference(clausify,[status(thm)],[f_701_3]) ).

fof(f_702_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_702_2,plain,
    ! [U_2321,U_2320,U_2319] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2319)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2320)),U_2321)) = 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_2319),U_2320))),U_2321),
    inference(variable_rename,[status(thm)],[f_702_1]) ).

fof(f_702_3,plain,
    ! [U_2319,U_2320,U_2321] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2319)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2320)),U_2321)) = 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_2319),U_2320))),U_2321),
    inference(definitional_conversion,[status(esa)],[f_702_2]) ).

cnf(f_702_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2319)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2320)),U_2321)) = 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_2319),U_2320))),U_2321),
    inference(clausify,[status(thm)],[f_702_3]) ).

fof(f_703_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_703_2,plain,
    ! [U_2325,U_2324] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2324),U_2325))
        | ! [U_2323] : U_2325 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2324),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2323)) )
      & ( ? [U_2322] : U_2325 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2324),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2322))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2324),U_2325)) ) ),
    inference(variable_rename,[status(thm)],[f_703_1]) ).

fof(f_703_3,plain,
    ( ! [U_2329,U_2327] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2327),U_2329))
        | ! [U_2323] : U_2329 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2327),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2323)) )
    & ! [U_2328,U_2326] :
        ( ? [U_2322] : U_2328 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2326),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2322))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2326),U_2328)) ) ),
    inference(miniscope,[status(thm)],[f_703_2]) ).

fof(f_703_4,plain,
    ( ! [U_2329,U_2327] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2327),U_2329))
        | ! [U_2323] : U_2329 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2327),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2323)) )
    & ! [U_2328,U_2326] :
        ( U_2328 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2326),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK36(U_2328,U_2326)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2326),U_2328)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK36]),skolemize(U_2322,sK36(U_2328,U_2326))],[f_703_3]) ).

fof(f_703_5,plain,
    ( ! [U_2329,U_2323,U_2327] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2327),U_2329))
        | U_2329 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2327),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2323)) )
    & ! [U_2328,U_2326] :
        ( U_2328 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2326),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK36(U_2328,U_2326)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2326),U_2328)) ) ),
    inference(definitional_conversion,[status(esa)],[f_703_4]) ).

cnf(f_703_6,plain,
    ( U_2328 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2326),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),sK36(U_2328,U_2326)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2326),U_2328)) ),
    inference(clausify,[status(thm)],[f_703_5]) ).

cnf(f_703_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2327),U_2329))
    | U_2329 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2327),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_2323)) ),
    inference(clausify,[status(thm)],[f_703_5]) ).

fof(f_704_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_704_2,plain,
    ! [U_2331,U_2330] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2330),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2331),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ( U_2330 != U_2331
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2330),U_2331)) ) )
      & ( U_2330 = U_2331
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2330),U_2331))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2330),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2331),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[f_704_1]) ).

fof(f_704_3,plain,
    ( ! [U_2335,U_2333] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2333),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2335),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ( U_2333 != U_2335
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2333),U_2335)) ) )
    & ! [U_2334,U_2332] :
        ( U_2332 = U_2334
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2332),U_2334))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2332),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2334),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(miniscope,[status(thm)],[f_704_2]) ).

fof(f_704_4,plain,
    ( ! [U_2335,U_2333] :
        ( U_2333 != U_2335
        | ~ sP202(U_2335,U_2333) )
    & ! [U_2335,U_2333] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2333),U_2335))
        | ~ sP202(U_2335,U_2333) )
    & ! [U_2335,U_2333] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2333),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2335),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | sP202(U_2335,U_2333) )
    & ! [U_2334,U_2332] :
        ( U_2332 = U_2334
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2332),U_2334))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2332),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2334),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP202])],[f_704_3]) ).

cnf(f_704_5,plain,
    ( U_2332 = U_2334
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2332),U_2334))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2332),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2334),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_704_4]) ).

cnf(f_704_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2333),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2335),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | sP202(U_2335,U_2333) ),
    inference(clausify,[status(thm)],[f_704_4]) ).

cnf(f_704_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2333),U_2335))
    | ~ sP202(U_2335,U_2333) ),
    inference(clausify,[status(thm)],[f_704_4]) ).

cnf(f_704_8,plain,
    ( U_2333 != U_2335
    | ~ sP202(U_2335,U_2333) ),
    inference(clausify,[status(thm)],[f_704_4]) ).

fof(f_705_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_705_2,plain,
    ! [U_2336] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2336)),U_2336) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_705_1]) ).

fof(f_705_3,plain,
    ! [U_2336] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2336)),U_2336) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_705_2]) ).

cnf(f_705_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2336)),U_2336) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_705_3]) ).

fof(f_706_1,plain,
    ! [V_n] : hAPP(c_Nat_OSuc,V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_Suc__eq__plus1]) ).

fof(f_706_2,plain,
    ! [U_2337] : hAPP(c_Nat_OSuc,U_2337) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2337),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_706_1]) ).

fof(f_706_3,plain,
    ! [U_2337] : hAPP(c_Nat_OSuc,U_2337) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2337),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_706_2]) ).

cnf(f_706_4,plain,
    hAPP(c_Nat_OSuc,U_2337) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2337),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_706_3]) ).

fof(f_707_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_707_2,plain,
    ! [U_2338] : hAPP(c_Nat_OSuc,U_2338) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2338),
    inference(variable_rename,[status(thm)],[f_707_1]) ).

fof(f_707_3,plain,
    ! [U_2338] : hAPP(c_Nat_OSuc,U_2338) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2338),
    inference(definitional_conversion,[status(esa)],[f_707_2]) ).

cnf(f_707_4,plain,
    hAPP(c_Nat_OSuc,U_2338) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_2338),
    inference(clausify,[status(thm)],[f_707_3]) ).

fof(f_708_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_708_2,plain,
    ! [U_2340,U_2339] :
      ( U_2339 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | U_2340 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | U_2339 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2339),U_2340) ),
    inference(variable_rename,[status(thm)],[f_708_1]) ).

fof(f_708_3,plain,
    ! [U_2339,U_2340] :
      ( U_2339 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | U_2340 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
      | U_2339 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2339),U_2340) ),
    inference(definitional_conversion,[status(esa)],[f_708_2]) ).

cnf(f_708_4,plain,
    ( U_2339 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_2340 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_2339 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_2339),U_2340) ),
    inference(clausify,[status(thm)],[f_708_3]) ).

fof(f_709_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_709_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_709_1]) ).

cnf(f_709_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_709_2]) ).

fof(f_710_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_710_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_710_1]) ).

cnf(f_710_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_710_2]) ).

fof(f_711_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_711_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_711_1]) ).

cnf(f_711_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_711_2]) ).

fof(f_712_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_712_2,plain,
    ! [U_2341] :
      ( hBOOL(hAPP(hAPP(c_member(U_2341),c_Groups_Ozero__class_Ozero(U_2341)),c_Int_Oring__1__class_OInts(U_2341)))
      | ~ class_Rings_Oring__1(U_2341) ),
    inference(variable_rename,[status(thm)],[f_712_1]) ).

fof(f_712_3,plain,
    ! [U_2341] :
      ( hBOOL(hAPP(hAPP(c_member(U_2341),c_Groups_Ozero__class_Ozero(U_2341)),c_Int_Oring__1__class_OInts(U_2341)))
      | ~ class_Rings_Oring__1(U_2341) ),
    inference(definitional_conversion,[status(esa)],[f_712_2]) ).

cnf(f_712_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2341),c_Groups_Ozero__class_Ozero(U_2341)),c_Int_Oring__1__class_OInts(U_2341)))
    | ~ class_Rings_Oring__1(U_2341) ),
    inference(clausify,[status(thm)],[f_712_3]) ).

fof(f_713_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_713_2,plain,
    ! [U_2344,U_2343,U_2342] :
      ( hBOOL(hAPP(hAPP(c_member(U_2342),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2342),U_2343),U_2344)),c_Int_Oring__1__class_OInts(U_2342)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2342),U_2344),c_Int_Oring__1__class_OInts(U_2342)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2342),U_2343),c_Int_Oring__1__class_OInts(U_2342)))
      | ~ class_Rings_Oring__1(U_2342) ),
    inference(variable_rename,[status(thm)],[f_713_1]) ).

fof(f_713_3,plain,
    ! [U_2342,U_2343,U_2344] :
      ( hBOOL(hAPP(hAPP(c_member(U_2342),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2342),U_2343),U_2344)),c_Int_Oring__1__class_OInts(U_2342)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2342),U_2344),c_Int_Oring__1__class_OInts(U_2342)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2342),U_2343),c_Int_Oring__1__class_OInts(U_2342)))
      | ~ class_Rings_Oring__1(U_2342) ),
    inference(definitional_conversion,[status(esa)],[f_713_2]) ).

cnf(f_713_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2342),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2342),U_2343),U_2344)),c_Int_Oring__1__class_OInts(U_2342)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2342),U_2344),c_Int_Oring__1__class_OInts(U_2342)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2342),U_2343),c_Int_Oring__1__class_OInts(U_2342)))
    | ~ class_Rings_Oring__1(U_2342) ),
    inference(clausify,[status(thm)],[f_713_3]) ).

fof(f_714_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_714_2,plain,
    ! [U_2347,U_2346,U_2345] :
      ( hBOOL(hAPP(hAPP(c_member(U_2345),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2345),U_2346),U_2347)),c_Int_Oring__1__class_OInts(U_2345)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2345),U_2347),c_Int_Oring__1__class_OInts(U_2345)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2345),U_2346),c_Int_Oring__1__class_OInts(U_2345)))
      | ~ class_Rings_Oring__1(U_2345) ),
    inference(variable_rename,[status(thm)],[f_714_1]) ).

fof(f_714_3,plain,
    ! [U_2345,U_2346,U_2347] :
      ( hBOOL(hAPP(hAPP(c_member(U_2345),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2345),U_2346),U_2347)),c_Int_Oring__1__class_OInts(U_2345)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2345),U_2347),c_Int_Oring__1__class_OInts(U_2345)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2345),U_2346),c_Int_Oring__1__class_OInts(U_2345)))
      | ~ class_Rings_Oring__1(U_2345) ),
    inference(definitional_conversion,[status(esa)],[f_714_2]) ).

cnf(f_714_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2345),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2345),U_2346),U_2347)),c_Int_Oring__1__class_OInts(U_2345)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2345),U_2347),c_Int_Oring__1__class_OInts(U_2345)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2345),U_2346),c_Int_Oring__1__class_OInts(U_2345)))
    | ~ class_Rings_Oring__1(U_2345) ),
    inference(clausify,[status(thm)],[f_714_3]) ).

fof(f_715_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_715_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_715_1]) ).

cnf(f_715_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_715_2]) ).

fof(f_716_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_716_2,plain,
    ! [U_2348] :
      ( hBOOL(hAPP(hAPP(c_member(U_2348),c_Groups_Oone__class_Oone(U_2348)),c_Int_Oring__1__class_OInts(U_2348)))
      | ~ class_Rings_Oring__1(U_2348) ),
    inference(variable_rename,[status(thm)],[f_716_1]) ).

fof(f_716_3,plain,
    ! [U_2348] :
      ( hBOOL(hAPP(hAPP(c_member(U_2348),c_Groups_Oone__class_Oone(U_2348)),c_Int_Oring__1__class_OInts(U_2348)))
      | ~ class_Rings_Oring__1(U_2348) ),
    inference(definitional_conversion,[status(esa)],[f_716_2]) ).

cnf(f_716_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2348),c_Groups_Oone__class_Oone(U_2348)),c_Int_Oring__1__class_OInts(U_2348)))
    | ~ class_Rings_Oring__1(U_2348) ),
    inference(clausify,[status(thm)],[f_716_3]) ).

fof(f_717_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_717_2,plain,
    ! [U_2350,U_2349] :
      ( hBOOL(hAPP(hAPP(c_member(U_2349),hAPP(c_Groups_Ouminus__class_Ouminus(U_2349),U_2350)),c_Int_Oring__1__class_OInts(U_2349)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2349),U_2350),c_Int_Oring__1__class_OInts(U_2349)))
      | ~ class_Rings_Oring__1(U_2349) ),
    inference(variable_rename,[status(thm)],[f_717_1]) ).

fof(f_717_3,plain,
    ! [U_2349,U_2350] :
      ( hBOOL(hAPP(hAPP(c_member(U_2349),hAPP(c_Groups_Ouminus__class_Ouminus(U_2349),U_2350)),c_Int_Oring__1__class_OInts(U_2349)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_2349),U_2350),c_Int_Oring__1__class_OInts(U_2349)))
      | ~ class_Rings_Oring__1(U_2349) ),
    inference(definitional_conversion,[status(esa)],[f_717_2]) ).

cnf(f_717_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2349),hAPP(c_Groups_Ouminus__class_Ouminus(U_2349),U_2350)),c_Int_Oring__1__class_OInts(U_2349)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_2349),U_2350),c_Int_Oring__1__class_OInts(U_2349)))
    | ~ class_Rings_Oring__1(U_2349) ),
    inference(clausify,[status(thm)],[f_717_3]) ).

fof(f_718_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_718_2,plain,
    ! [U_2352,U_2351] :
      ( hBOOL(hAPP(hAPP(c_member(U_2351),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2351),U_2352)),c_Int_Oring__1__class_OInts(U_2351)))
      | ~ class_Rings_Oring__1(U_2351) ),
    inference(variable_rename,[status(thm)],[f_718_1]) ).

fof(f_718_3,plain,
    ! [U_2351,U_2352] :
      ( hBOOL(hAPP(hAPP(c_member(U_2351),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2351),U_2352)),c_Int_Oring__1__class_OInts(U_2351)))
      | ~ class_Rings_Oring__1(U_2351) ),
    inference(definitional_conversion,[status(esa)],[f_718_2]) ).

cnf(f_718_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2351),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_2351),U_2352)),c_Int_Oring__1__class_OInts(U_2351)))
    | ~ class_Rings_Oring__1(U_2351) ),
    inference(clausify,[status(thm)],[f_718_3]) ).

fof(f_719_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_719_2,plain,
    ! [U_2354,U_2353] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2353),c_Groups_Osgn__class_Osgn(U_2353,U_2354)),c_Groups_Ozero__class_Ozero(U_2353)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2353),U_2354),c_Groups_Ozero__class_Ozero(U_2353))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2353),U_2354),c_Groups_Ozero__class_Ozero(U_2353)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2353),c_Groups_Osgn__class_Osgn(U_2353,U_2354)),c_Groups_Ozero__class_Ozero(U_2353))) ) )
      | ~ class_Rings_Olinordered__idom(U_2353) ),
    inference(variable_rename,[status(thm)],[f_719_1]) ).

fof(f_719_3,plain,
    ( ! [U_2353,U_2354] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2353),c_Groups_Osgn__class_Osgn(U_2353,U_2354)),c_Groups_Ozero__class_Ozero(U_2353)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2353),U_2354),c_Groups_Ozero__class_Ozero(U_2353)))
        | ~ sP203(U_2353,U_2354) )
    & ! [U_2353,U_2354] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2353),U_2354),c_Groups_Ozero__class_Ozero(U_2353)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2353),c_Groups_Osgn__class_Osgn(U_2353,U_2354)),c_Groups_Ozero__class_Ozero(U_2353)))
        | ~ sP203(U_2353,U_2354) )
    & ! [U_2353,U_2354] :
        ( sP203(U_2353,U_2354)
        | ~ class_Rings_Olinordered__idom(U_2353) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP203])],[f_719_2]) ).

cnf(f_719_4,plain,
    ( sP203(U_2353,U_2354)
    | ~ class_Rings_Olinordered__idom(U_2353) ),
    inference(clausify,[status(thm)],[f_719_3]) ).

cnf(f_719_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2353),U_2354),c_Groups_Ozero__class_Ozero(U_2353)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2353),c_Groups_Osgn__class_Osgn(U_2353,U_2354)),c_Groups_Ozero__class_Ozero(U_2353)))
    | ~ sP203(U_2353,U_2354) ),
    inference(clausify,[status(thm)],[f_719_3]) ).

cnf(f_719_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2353),c_Groups_Osgn__class_Osgn(U_2353,U_2354)),c_Groups_Ozero__class_Ozero(U_2353)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2353),U_2354),c_Groups_Ozero__class_Ozero(U_2353)))
    | ~ sP203(U_2353,U_2354) ),
    inference(clausify,[status(thm)],[f_719_3]) ).

fof(f_720_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_720_2,plain,
    ! [U_2356,U_2355] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2355),c_Groups_Ozero__class_Ozero(U_2355)),c_Groups_Osgn__class_Osgn(U_2355,U_2356)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2355),c_Groups_Ozero__class_Ozero(U_2355)),U_2356)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2355),c_Groups_Ozero__class_Ozero(U_2355)),U_2356))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2355),c_Groups_Ozero__class_Ozero(U_2355)),c_Groups_Osgn__class_Osgn(U_2355,U_2356))) ) )
      | ~ class_Rings_Olinordered__idom(U_2355) ),
    inference(variable_rename,[status(thm)],[f_720_1]) ).

fof(f_720_3,plain,
    ( ! [U_2355,U_2356] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2355),c_Groups_Ozero__class_Ozero(U_2355)),c_Groups_Osgn__class_Osgn(U_2355,U_2356)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2355),c_Groups_Ozero__class_Ozero(U_2355)),U_2356))
        | ~ sP204(U_2355,U_2356) )
    & ! [U_2355,U_2356] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2355),c_Groups_Ozero__class_Ozero(U_2355)),U_2356))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2355),c_Groups_Ozero__class_Ozero(U_2355)),c_Groups_Osgn__class_Osgn(U_2355,U_2356)))
        | ~ sP204(U_2355,U_2356) )
    & ! [U_2355,U_2356] :
        ( sP204(U_2355,U_2356)
        | ~ class_Rings_Olinordered__idom(U_2355) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP204])],[f_720_2]) ).

cnf(f_720_4,plain,
    ( sP204(U_2355,U_2356)
    | ~ class_Rings_Olinordered__idom(U_2355) ),
    inference(clausify,[status(thm)],[f_720_3]) ).

cnf(f_720_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2355),c_Groups_Ozero__class_Ozero(U_2355)),U_2356))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2355),c_Groups_Ozero__class_Ozero(U_2355)),c_Groups_Osgn__class_Osgn(U_2355,U_2356)))
    | ~ sP204(U_2355,U_2356) ),
    inference(clausify,[status(thm)],[f_720_3]) ).

cnf(f_720_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2355),c_Groups_Ozero__class_Ozero(U_2355)),c_Groups_Osgn__class_Osgn(U_2355,U_2356)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2355),c_Groups_Ozero__class_Ozero(U_2355)),U_2356))
    | ~ sP204(U_2355,U_2356) ),
    inference(clausify,[status(thm)],[f_720_3]) ).

fof(f_721_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_721_2,plain,
    ! [U_2360,U_2359] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2359),U_2360))
        | ! [U_2358] : U_2360 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2359),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2358))) )
      & ( ? [U_2357] : U_2360 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2359),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2357)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2359),U_2360)) ) ),
    inference(variable_rename,[status(thm)],[f_721_1]) ).

fof(f_721_3,plain,
    ( ! [U_2364,U_2362] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2362),U_2364))
        | ! [U_2358] : U_2364 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2362),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2358))) )
    & ! [U_2363,U_2361] :
        ( ? [U_2357] : U_2363 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2361),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2357)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2361),U_2363)) ) ),
    inference(miniscope,[status(thm)],[f_721_2]) ).

fof(f_721_4,plain,
    ( ! [U_2364,U_2362] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2362),U_2364))
        | ! [U_2358] : U_2364 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2362),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2358))) )
    & ! [U_2363,U_2361] :
        ( U_2363 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2361),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK37(U_2363,U_2361))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2361),U_2363)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK37]),skolemize(U_2357,sK37(U_2363,U_2361))],[f_721_3]) ).

fof(f_721_5,plain,
    ( ! [U_2362,U_2364,U_2358] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2362),U_2364))
        | U_2364 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2362),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2358))) )
    & ! [U_2363,U_2361] :
        ( U_2363 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2361),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK37(U_2363,U_2361))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2361),U_2363)) ) ),
    inference(definitional_conversion,[status(esa)],[f_721_4]) ).

cnf(f_721_6,plain,
    ( U_2363 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2361),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,sK37(U_2363,U_2361))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2361),U_2363)) ),
    inference(clausify,[status(thm)],[f_721_5]) ).

cnf(f_721_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2362),U_2364))
    | U_2364 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2362),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2358))) ),
    inference(clausify,[status(thm)],[f_721_5]) ).

fof(f_722_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_722_2,plain,
    ! [U_2365] :
      ( ( 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_2365)),U_2365)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2365),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2365),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_2365)),U_2365)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_722_1]) ).

fof(f_722_3,plain,
    ( ! [U_2367] :
        ( 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_2367)),U_2367)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2367),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_2366] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2366),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_2366)),U_2366)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_722_2]) ).

fof(f_722_4,plain,
    ( ! [U_2367] :
        ( 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_2367)),U_2367)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2367),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_2366] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2366),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_2366)),U_2366)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_722_3]) ).

cnf(f_722_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2366),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_2366)),U_2366)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_722_4]) ).

cnf(f_722_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_2367)),U_2367)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2367),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_722_4]) ).

fof(f_723_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_723_2,plain,
    ! [U_2369,U_2368] :
      ( hBOOL(hAPP(hAPP(c_member(U_2368),hAPP(c_Int_Oring__1__class_Oof__int(U_2368),U_2369)),c_Int_Oring__1__class_OInts(U_2368)))
      | ~ class_Rings_Oring__1(U_2368) ),
    inference(variable_rename,[status(thm)],[f_723_1]) ).

fof(f_723_3,plain,
    ! [U_2368,U_2369] :
      ( hBOOL(hAPP(hAPP(c_member(U_2368),hAPP(c_Int_Oring__1__class_Oof__int(U_2368),U_2369)),c_Int_Oring__1__class_OInts(U_2368)))
      | ~ class_Rings_Oring__1(U_2368) ),
    inference(definitional_conversion,[status(esa)],[f_723_2]) ).

cnf(f_723_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_2368),hAPP(c_Int_Oring__1__class_Oof__int(U_2368),U_2369)),c_Int_Oring__1__class_OInts(U_2368)))
    | ~ class_Rings_Oring__1(U_2368) ),
    inference(clausify,[status(thm)],[f_723_3]) ).

fof(f_724_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_724_2,plain,
    ! [U_2371,U_2370] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2370),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2371),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2370),U_2371)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2370),U_2371))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2370),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2371),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[f_724_1]) ).

fof(f_724_3,plain,
    ( ! [U_2375,U_2373] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2373),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2375),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2373),U_2375)) )
    & ! [U_2374,U_2372] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2372),U_2374))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2372),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2374),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(miniscope,[status(thm)],[f_724_2]) ).

fof(f_724_4,plain,
    ( ! [U_2373,U_2375] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2373),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2375),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2373),U_2375)) )
    & ! [U_2374,U_2372] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2372),U_2374))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2372),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2374),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_724_3]) ).

cnf(f_724_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2372),U_2374))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2372),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2374),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_724_4]) ).

cnf(f_724_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2373),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2375),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2373),U_2375)) ),
    inference(clausify,[status(thm)],[f_724_4]) ).

fof(f_725_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_725_2,plain,
    ! [U_2377,U_2376] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2376),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2377))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2376),U_2377)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2376),U_2377))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2376),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2377)) ) ),
    inference(variable_rename,[status(thm)],[f_725_1]) ).

fof(f_725_3,plain,
    ( ! [U_2381,U_2379] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2379),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2381))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2379),U_2381)) )
    & ! [U_2380,U_2378] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2378),U_2380))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2378),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2380)) ) ),
    inference(miniscope,[status(thm)],[f_725_2]) ).

fof(f_725_4,plain,
    ( ! [U_2381,U_2379] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2379),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2381))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2379),U_2381)) )
    & ! [U_2378,U_2380] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2378),U_2380))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2378),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2380)) ) ),
    inference(definitional_conversion,[status(esa)],[f_725_3]) ).

cnf(f_725_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2378),U_2380))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2378),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2380)) ),
    inference(clausify,[status(thm)],[f_725_4]) ).

cnf(f_725_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_2379),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2381))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2379),U_2381)) ),
    inference(clausify,[status(thm)],[f_725_4]) ).

fof(f_726_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_726_2,plain,
    ! [U_2383,U_2382] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2382),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2383))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2382),U_2383)) ),
    inference(variable_rename,[status(thm)],[f_726_1]) ).

fof(f_726_3,plain,
    ! [U_2383,U_2382] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2382),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2383))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2382),U_2383)) ),
    inference(definitional_conversion,[status(esa)],[f_726_2]) ).

cnf(f_726_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_2382),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_2383))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2382),U_2383)) ),
    inference(clausify,[status(thm)],[f_726_3]) ).

fof(f_727_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_727_2,plain,
    ! [U_2384] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2384)) = 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_2384)),
    inference(variable_rename,[status(thm)],[f_727_1]) ).

fof(f_727_3,plain,
    ! [U_2384] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2384)) = 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_2384)),
    inference(definitional_conversion,[status(esa)],[f_727_2]) ).

cnf(f_727_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Nat_OSuc,U_2384)) = 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_2384)),
    inference(clausify,[status(thm)],[f_727_3]) ).

fof(f_728_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_728_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_728_1]) ).

cnf(f_728_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_728_2]) ).

fof(f_729_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_729_2,plain,
    ! [U_2386,U_2385] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2385),U_2386)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2385)),hAPP(c_Int_Onat,U_2386))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2386))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2385)) ),
    inference(variable_rename,[status(thm)],[f_729_1]) ).

fof(f_729_3,plain,
    ! [U_2385,U_2386] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2385),U_2386)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2385)),hAPP(c_Int_Onat,U_2386))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2386))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2385)) ),
    inference(definitional_conversion,[status(esa)],[f_729_2]) ).

cnf(f_729_4,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2385),U_2386)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2385)),hAPP(c_Int_Onat,U_2386))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2386))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2385)) ),
    inference(clausify,[status(thm)],[f_729_3]) ).

fof(f_730_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_730_2,plain,
    ! [U_2388,U_2387] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2387)),hAPP(c_Int_Onat,U_2388)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2387),U_2388))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2388))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2387)) ),
    inference(variable_rename,[status(thm)],[f_730_1]) ).

fof(f_730_3,plain,
    ! [U_2387,U_2388] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2387)),hAPP(c_Int_Onat,U_2388)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2387),U_2388))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2388))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2387)) ),
    inference(definitional_conversion,[status(esa)],[f_730_2]) ).

cnf(f_730_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onat,U_2387)),hAPP(c_Int_Onat,U_2388)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2387),U_2388))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2388))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2387)) ),
    inference(clausify,[status(thm)],[f_730_3]) ).

fof(f_731_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_731_2,plain,
    ! [U_2389] :
      ( 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_2389)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2389)) ),
    inference(variable_rename,[status(thm)],[f_731_1]) ).

fof(f_731_3,plain,
    ! [U_2389] :
      ( 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_2389)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2389)) ),
    inference(definitional_conversion,[status(esa)],[f_731_2]) ).

cnf(f_731_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_2389)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2389)) ),
    inference(clausify,[status(thm)],[f_731_3]) ).

fof(f_732_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_732_2,plain,
    ! [U_2391,U_2390] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2390),U_2391),U_2391) = c_Groups_Ozero__class_Ozero(U_2390)
          | U_2391 != c_Groups_Ozero__class_Ozero(U_2390) )
        & ( U_2391 = c_Groups_Ozero__class_Ozero(U_2390)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2390),U_2391),U_2391) != c_Groups_Ozero__class_Ozero(U_2390) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_2390),U_2391),c_Int_Oring__1__class_OInts(U_2390)))
      | ~ class_Int_Oring__char__0(U_2390) ),
    inference(variable_rename,[status(thm)],[f_732_1]) ).

fof(f_732_3,plain,
    ( ! [U_2390,U_2391] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2390),U_2391),U_2391) = c_Groups_Ozero__class_Ozero(U_2390)
        | U_2391 != c_Groups_Ozero__class_Ozero(U_2390)
        | ~ sP205(U_2390,U_2391) )
    & ! [U_2390,U_2391] :
        ( U_2391 = c_Groups_Ozero__class_Ozero(U_2390)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2390),U_2391),U_2391) != c_Groups_Ozero__class_Ozero(U_2390)
        | ~ sP205(U_2390,U_2391) )
    & ! [U_2390,U_2391] :
        ( sP205(U_2390,U_2391)
        | ~ hBOOL(hAPP(hAPP(c_member(U_2390),U_2391),c_Int_Oring__1__class_OInts(U_2390)))
        | ~ class_Int_Oring__char__0(U_2390) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP205])],[f_732_2]) ).

cnf(f_732_4,plain,
    ( sP205(U_2390,U_2391)
    | ~ hBOOL(hAPP(hAPP(c_member(U_2390),U_2391),c_Int_Oring__1__class_OInts(U_2390)))
    | ~ class_Int_Oring__char__0(U_2390) ),
    inference(clausify,[status(thm)],[f_732_3]) ).

cnf(f_732_5,plain,
    ( U_2391 = c_Groups_Ozero__class_Ozero(U_2390)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2390),U_2391),U_2391) != c_Groups_Ozero__class_Ozero(U_2390)
    | ~ sP205(U_2390,U_2391) ),
    inference(clausify,[status(thm)],[f_732_3]) ).

cnf(f_732_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2390),U_2391),U_2391) = c_Groups_Ozero__class_Ozero(U_2390)
    | U_2391 != c_Groups_Ozero__class_Ozero(U_2390)
    | ~ sP205(U_2390,U_2391) ),
    inference(clausify,[status(thm)],[f_732_3]) ).

fof(f_733_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_733_2,plain,
    ! [U_2393,U_2392] :
      ( c_Groups_Osgn__class_Osgn(U_2392,U_2393) = c_Groups_Oone__class_Oone(U_2392)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2392),c_Groups_Ozero__class_Ozero(U_2392)),U_2393))
      | ~ class_Rings_Olinordered__idom(U_2392) ),
    inference(variable_rename,[status(thm)],[f_733_1]) ).

fof(f_733_3,plain,
    ! [U_2393,U_2392] :
      ( c_Groups_Osgn__class_Osgn(U_2392,U_2393) = c_Groups_Oone__class_Oone(U_2392)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2392),c_Groups_Ozero__class_Ozero(U_2392)),U_2393))
      | ~ class_Rings_Olinordered__idom(U_2392) ),
    inference(definitional_conversion,[status(esa)],[f_733_2]) ).

cnf(f_733_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_2392,U_2393) = c_Groups_Oone__class_Oone(U_2392)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2392),c_Groups_Ozero__class_Ozero(U_2392)),U_2393))
    | ~ class_Rings_Olinordered__idom(U_2392) ),
    inference(clausify,[status(thm)],[f_733_3]) ).

fof(f_734_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_734_2,plain,
    ! [U_2395,U_2394] :
      ( ( ( c_Groups_Osgn__class_Osgn(U_2394,U_2395) = c_Groups_Oone__class_Oone(U_2394)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2394),c_Groups_Ozero__class_Ozero(U_2394)),U_2395)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2394),c_Groups_Ozero__class_Ozero(U_2394)),U_2395))
          | c_Groups_Osgn__class_Osgn(U_2394,U_2395) != c_Groups_Oone__class_Oone(U_2394) ) )
      | ~ class_Rings_Olinordered__idom(U_2394) ),
    inference(variable_rename,[status(thm)],[f_734_1]) ).

fof(f_734_3,plain,
    ( ! [U_2395,U_2394] :
        ( c_Groups_Osgn__class_Osgn(U_2394,U_2395) = c_Groups_Oone__class_Oone(U_2394)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2394),c_Groups_Ozero__class_Ozero(U_2394)),U_2395))
        | ~ sP206(U_2395,U_2394) )
    & ! [U_2395,U_2394] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2394),c_Groups_Ozero__class_Ozero(U_2394)),U_2395))
        | c_Groups_Osgn__class_Osgn(U_2394,U_2395) != c_Groups_Oone__class_Oone(U_2394)
        | ~ sP206(U_2395,U_2394) )
    & ! [U_2395,U_2394] :
        ( sP206(U_2395,U_2394)
        | ~ class_Rings_Olinordered__idom(U_2394) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP206])],[f_734_2]) ).

cnf(f_734_4,plain,
    ( sP206(U_2395,U_2394)
    | ~ class_Rings_Olinordered__idom(U_2394) ),
    inference(clausify,[status(thm)],[f_734_3]) ).

cnf(f_734_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2394),c_Groups_Ozero__class_Ozero(U_2394)),U_2395))
    | c_Groups_Osgn__class_Osgn(U_2394,U_2395) != c_Groups_Oone__class_Oone(U_2394)
    | ~ sP206(U_2395,U_2394) ),
    inference(clausify,[status(thm)],[f_734_3]) ).

cnf(f_734_6,plain,
    ( c_Groups_Osgn__class_Osgn(U_2394,U_2395) = c_Groups_Oone__class_Oone(U_2394)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2394),c_Groups_Ozero__class_Ozero(U_2394)),U_2395))
    | ~ sP206(U_2395,U_2394) ),
    inference(clausify,[status(thm)],[f_734_3]) ).

fof(f_735_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_735_2,plain,
    ! [U_2396] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_2396)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2396))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2396)) ),
    inference(variable_rename,[status(thm)],[f_735_1]) ).

fof(f_735_3,plain,
    ! [U_2396] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_2396)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2396))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2396)) ),
    inference(definitional_conversion,[status(esa)],[f_735_2]) ).

cnf(f_735_4,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onat,U_2396)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2396))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2396)) ),
    inference(clausify,[status(thm)],[f_735_3]) ).

fof(f_736_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_736_2,plain,
    ! [U_2398,U_2397] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2397),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2397),c_Groups_Oone__class_Oone(U_2397)),U_2398)),U_2398) != c_Groups_Ozero__class_Ozero(U_2397)
      | ~ hBOOL(hAPP(hAPP(c_member(U_2397),U_2398),c_Int_Oring__1__class_OInts(U_2397)))
      | ~ class_Int_Oring__char__0(U_2397) ),
    inference(variable_rename,[status(thm)],[f_736_1]) ).

fof(f_736_3,plain,
    ! [U_2397,U_2398] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2397),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2397),c_Groups_Oone__class_Oone(U_2397)),U_2398)),U_2398) != c_Groups_Ozero__class_Ozero(U_2397)
      | ~ hBOOL(hAPP(hAPP(c_member(U_2397),U_2398),c_Int_Oring__1__class_OInts(U_2397)))
      | ~ class_Int_Oring__char__0(U_2397) ),
    inference(definitional_conversion,[status(esa)],[f_736_2]) ).

cnf(f_736_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2397),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2397),c_Groups_Oone__class_Oone(U_2397)),U_2398)),U_2398) != c_Groups_Ozero__class_Ozero(U_2397)
    | ~ hBOOL(hAPP(hAPP(c_member(U_2397),U_2398),c_Int_Oring__1__class_OInts(U_2397)))
    | ~ class_Int_Oring__char__0(U_2397) ),
    inference(clausify,[status(thm)],[f_736_3]) ).

fof(f_737_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_737_2,plain,
    ! [U_2399] :
      ( ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2399) = 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_2399)) )
          & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2399) = 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_2399)) ) )
        | U_2399 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2399) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_2399 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_737_1]) ).

fof(f_737_3,plain,
    ( ! [U_2401] :
        ( ( ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2401) = 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_2401)) )
          & ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2401) = 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_2401)) ) )
        | U_2401 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_2400] :
        ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2400) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_2400 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_737_2]) ).

fof(f_737_4,plain,
    ( ! [U_2401] :
        ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2401) = 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_2401))
        | ~ sP207(U_2401) )
    & ! [U_2401] :
        ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2401) = 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_2401))
        | ~ sP207(U_2401) )
    & ! [U_2401] :
        ( sP207(U_2401)
        | U_2401 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_2400] :
        ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2400) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_2400 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP207])],[f_737_3]) ).

cnf(f_737_5,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2400) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_2400 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_737_4]) ).

cnf(f_737_6,plain,
    ( sP207(U_2401)
    | U_2401 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_737_4]) ).

cnf(f_737_7,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2401) = 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_2401))
    | ~ sP207(U_2401) ),
    inference(clausify,[status(thm)],[f_737_4]) ).

cnf(f_737_8,plain,
    ( c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_2401) = 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_2401))
    | ~ sP207(U_2401) ),
    inference(clausify,[status(thm)],[f_737_4]) ).

fof(f_738_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_738_2,plain,
    ! [U_2403,U_2402] :
      ( ( ( ( ( c_Groups_Osgn__class_Osgn(U_2402,U_2403) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2402),c_Groups_Oone__class_Oone(U_2402))
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2402),c_Groups_Ozero__class_Ozero(U_2402)),U_2403)) )
            & ( c_Groups_Osgn__class_Osgn(U_2402,U_2403) = c_Groups_Oone__class_Oone(U_2402)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2402),c_Groups_Ozero__class_Ozero(U_2402)),U_2403)) ) )
          | U_2403 = c_Groups_Ozero__class_Ozero(U_2402) )
        & ( c_Groups_Osgn__class_Osgn(U_2402,U_2403) = c_Groups_Ozero__class_Ozero(U_2402)
          | U_2403 != c_Groups_Ozero__class_Ozero(U_2402) ) )
      | ~ class_Groups_Osgn__if(U_2402) ),
    inference(variable_rename,[status(thm)],[f_738_1]) ).

fof(f_738_3,plain,
    ( ! [U_2402,U_2403] :
        ( c_Groups_Osgn__class_Osgn(U_2402,U_2403) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2402),c_Groups_Oone__class_Oone(U_2402))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2402),c_Groups_Ozero__class_Ozero(U_2402)),U_2403))
        | ~ sP208(U_2402,U_2403) )
    & ! [U_2402,U_2403] :
        ( c_Groups_Osgn__class_Osgn(U_2402,U_2403) = c_Groups_Oone__class_Oone(U_2402)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2402),c_Groups_Ozero__class_Ozero(U_2402)),U_2403))
        | ~ sP208(U_2402,U_2403) )
    & ! [U_2402,U_2403] :
        ( sP208(U_2402,U_2403)
        | U_2403 = c_Groups_Ozero__class_Ozero(U_2402)
        | ~ sP209(U_2402,U_2403) )
    & ! [U_2402,U_2403] :
        ( c_Groups_Osgn__class_Osgn(U_2402,U_2403) = c_Groups_Ozero__class_Ozero(U_2402)
        | U_2403 != c_Groups_Ozero__class_Ozero(U_2402)
        | ~ sP209(U_2402,U_2403) )
    & ! [U_2402,U_2403] :
        ( sP209(U_2402,U_2403)
        | ~ class_Groups_Osgn__if(U_2402) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP208,sP209])],[f_738_2]) ).

cnf(f_738_4,plain,
    ( sP209(U_2402,U_2403)
    | ~ class_Groups_Osgn__if(U_2402) ),
    inference(clausify,[status(thm)],[f_738_3]) ).

cnf(f_738_5,plain,
    ( c_Groups_Osgn__class_Osgn(U_2402,U_2403) = c_Groups_Ozero__class_Ozero(U_2402)
    | U_2403 != c_Groups_Ozero__class_Ozero(U_2402)
    | ~ sP209(U_2402,U_2403) ),
    inference(clausify,[status(thm)],[f_738_3]) ).

cnf(f_738_6,plain,
    ( sP208(U_2402,U_2403)
    | U_2403 = c_Groups_Ozero__class_Ozero(U_2402)
    | ~ sP209(U_2402,U_2403) ),
    inference(clausify,[status(thm)],[f_738_3]) ).

cnf(f_738_7,plain,
    ( c_Groups_Osgn__class_Osgn(U_2402,U_2403) = c_Groups_Oone__class_Oone(U_2402)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2402),c_Groups_Ozero__class_Ozero(U_2402)),U_2403))
    | ~ sP208(U_2402,U_2403) ),
    inference(clausify,[status(thm)],[f_738_3]) ).

cnf(f_738_8,plain,
    ( c_Groups_Osgn__class_Osgn(U_2402,U_2403) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2402),c_Groups_Oone__class_Oone(U_2402))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2402),c_Groups_Ozero__class_Ozero(U_2402)),U_2403))
    | ~ sP208(U_2402,U_2403) ),
    inference(clausify,[status(thm)],[f_738_3]) ).

fof(f_739_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_739_2,plain,
    ! [U_2405,U_2404] :
      ( c_Groups_Osgn__class_Osgn(U_2404,U_2405) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2404),c_Groups_Oone__class_Oone(U_2404))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2404),U_2405),c_Groups_Ozero__class_Ozero(U_2404)))
      | ~ class_Rings_Olinordered__idom(U_2404) ),
    inference(variable_rename,[status(thm)],[f_739_1]) ).

fof(f_739_3,plain,
    ! [U_2405,U_2404] :
      ( c_Groups_Osgn__class_Osgn(U_2404,U_2405) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2404),c_Groups_Oone__class_Oone(U_2404))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2404),U_2405),c_Groups_Ozero__class_Ozero(U_2404)))
      | ~ class_Rings_Olinordered__idom(U_2404) ),
    inference(definitional_conversion,[status(esa)],[f_739_2]) ).

cnf(f_739_4,plain,
    ( c_Groups_Osgn__class_Osgn(U_2404,U_2405) = hAPP(c_Groups_Ouminus__class_Ouminus(U_2404),c_Groups_Oone__class_Oone(U_2404))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_2404),U_2405),c_Groups_Ozero__class_Ozero(U_2404)))
    | ~ class_Rings_Olinordered__idom(U_2404) ),
    inference(clausify,[status(thm)],[f_739_3]) ).

fof(f_740_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_740_2,plain,
    ! [U_2408,U_2407,U_2406] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2408),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_2407))
      | U_2406 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2406),U_2408))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2406)) ),
    inference(variable_rename,[status(thm)],[f_740_1]) ).

fof(f_740_3,plain,
    ! [U_2407,U_2408,U_2406] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2408),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_2407))
      | U_2406 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2406),U_2408))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2406)) ),
    inference(definitional_conversion,[status(esa)],[f_740_2]) ).

cnf(f_740_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2408),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_2407))
    | U_2406 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2407),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2406),U_2408))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2406)) ),
    inference(clausify,[status(thm)],[f_740_3]) ).

fof(f_741_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_741_2,plain,
    ! [U_2411,U_2410,U_2409] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2411))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2410),U_2409))
      | U_2409 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2409),U_2411))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2409)) ),
    inference(variable_rename,[status(thm)],[f_741_1]) ).

fof(f_741_3,plain,
    ! [U_2409,U_2410,U_2411] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2411))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2410),U_2409))
      | U_2409 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2409),U_2411))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2409)) ),
    inference(definitional_conversion,[status(esa)],[f_741_2]) ).

cnf(f_741_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_2411))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2410),U_2409))
    | U_2409 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2410),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2409),U_2411))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2409)) ),
    inference(clausify,[status(thm)],[f_741_3]) ).

fof(f_742_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_742_2,plain,
    ! [U_2417,U_2416,U_2415,U_2414,U_2413,U_2412] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2416),U_2413))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2415),U_2412))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2415))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2417))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2414),U_2412))
      | ~ 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_2415),U_2416)),U_2417)),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_2412),U_2413)),U_2414) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2415),U_2416)),U_2417) ),
    inference(variable_rename,[status(thm)],[f_742_1]) ).

fof(f_742_3,plain,
    ! [U_2413,U_2412,U_2414,U_2415,U_2416,U_2417] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2416),U_2413))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2415),U_2412))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2415))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2417))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2414),U_2412))
      | ~ 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_2415),U_2416)),U_2417)),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_2412),U_2413)),U_2414) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2415),U_2416)),U_2417) ),
    inference(definitional_conversion,[status(esa)],[f_742_2]) ).

cnf(f_742_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2416),U_2413))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2415),U_2412))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2415))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2417))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2414),U_2412))
    | ~ 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_2415),U_2416)),U_2417)),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_2412),U_2413)),U_2414) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2415),U_2416)),U_2417) ),
    inference(clausify,[status(thm)],[f_742_3]) ).

fof(f_743_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_743_2,plain,
    ! [U_2422,U_2421,U_2420,U_2419,U_2418] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2421),U_2419))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2418),U_2420))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2418),U_2422))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2422),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_2418),U_2419)),U_2420)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2418),U_2421)),U_2422))) ),
    inference(variable_rename,[status(thm)],[f_743_1]) ).

fof(f_743_3,plain,
    ! [U_2419,U_2420,U_2418,U_2421,U_2422] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2421),U_2419))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2418),U_2420))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2418),U_2422))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2422),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_2418),U_2419)),U_2420)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2418),U_2421)),U_2422))) ),
    inference(definitional_conversion,[status(esa)],[f_743_2]) ).

cnf(f_743_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2421),U_2419))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2418),U_2420))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2418),U_2422))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2422),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_2418),U_2419)),U_2420)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2418),U_2421)),U_2422))) ),
    inference(clausify,[status(thm)],[f_743_3]) ).

fof(f_744_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_744_2,plain,
    ! [U_2428,U_2427,U_2426,U_2425,U_2424,U_2423] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2424),U_2427))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2426),U_2423))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2426))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2425))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2428),U_2426))
      | ~ 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_2426),U_2427)),U_2428)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2423),U_2424)),U_2425) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2426),U_2427)),U_2428) ),
    inference(variable_rename,[status(thm)],[f_744_1]) ).

fof(f_744_3,plain,
    ! [U_2424,U_2423,U_2425,U_2426,U_2427,U_2428] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2424),U_2427))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2426),U_2423))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2426))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2425))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2428),U_2426))
      | ~ 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_2426),U_2427)),U_2428)))
      | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2423),U_2424)),U_2425) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2426),U_2427)),U_2428) ),
    inference(definitional_conversion,[status(esa)],[f_744_2]) ).

cnf(f_744_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2424),U_2427))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2426),U_2423))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2426))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2425))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2428),U_2426))
    | ~ 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_2426),U_2427)),U_2428)))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2423),U_2424)),U_2425) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2426),U_2427)),U_2428) ),
    inference(clausify,[status(thm)],[f_744_3]) ).

fof(f_745_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_745_2,plain,
    ! [U_2433,U_2432,U_2431,U_2430,U_2429] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2430),U_2432))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2433),U_2429))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2431),U_2429))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2431))
      | ~ 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_2429),U_2430)),U_2431)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2429),U_2432)),U_2433))) ),
    inference(variable_rename,[status(thm)],[f_745_1]) ).

fof(f_745_3,plain,
    ! [U_2430,U_2431,U_2432,U_2429,U_2433] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2430),U_2432))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2433),U_2429))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2431),U_2429))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2431))
      | ~ 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_2429),U_2430)),U_2431)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2429),U_2432)),U_2433))) ),
    inference(definitional_conversion,[status(esa)],[f_745_2]) ).

cnf(f_745_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2430),U_2432))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2433),U_2429))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2431),U_2429))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2431))
    | ~ 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_2429),U_2430)),U_2431)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2429),U_2432)),U_2433))) ),
    inference(clausify,[status(thm)],[f_745_3]) ).

fof(f_746_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_746_2,plain,
    ! [U_2436,U_2435,U_2434] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2435),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_2434))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2436))
      | ~ 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_2434),U_2435)),U_2436)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_746_1]) ).

fof(f_746_3,plain,
    ! [U_2434,U_2436,U_2435] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2435),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_2434))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2436))
      | ~ 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_2434),U_2435)),U_2436)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_746_2]) ).

cnf(f_746_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2435),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_2434))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2436))
    | ~ 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_2434),U_2435)),U_2436)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_746_3]) ).

fof(f_747_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_747_2,plain,
    ! [U_2439,U_2438,U_2437] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2438))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2437))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2439),U_2437))
      | ~ 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_2437),U_2438)),U_2439))) ),
    inference(variable_rename,[status(thm)],[f_747_1]) ).

fof(f_747_3,plain,
    ! [U_2439,U_2437,U_2438] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2438))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2437))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2439),U_2437))
      | ~ 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_2437),U_2438)),U_2439))) ),
    inference(definitional_conversion,[status(esa)],[f_747_2]) ).

cnf(f_747_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2438))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2437))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2439),U_2437))
    | ~ 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_2437),U_2438)),U_2439))) ),
    inference(clausify,[status(thm)],[f_747_3]) ).

fof(f_748_1,plain,
    ! [V_n_2,V_Pa_2] :
      ( ? [B_k] :
          ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,V_n_2))
      | hBOOL(hAPP(V_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(fof_nnf,[status(thm)],[fact_ex__least__nat__less]) ).

fof(f_748_2,plain,
    ! [U_2443,U_2442] :
      ( ? [U_2441] :
          ( hBOOL(hAPP(U_2442,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_2441),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          & ! [U_2440] :
              ( ~ hBOOL(hAPP(U_2442,U_2440))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2440),U_2441)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_2441),U_2443)) )
      | ~ hBOOL(hAPP(U_2442,U_2443))
      | hBOOL(hAPP(U_2442,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[f_748_1]) ).

fof(f_748_3,plain,
    ! [U_2443,U_2442] :
      ( ( hBOOL(hAPP(U_2442,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK38(U_2443,U_2442)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        & ! [U_2440] :
            ( ~ hBOOL(hAPP(U_2442,U_2440))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2440),sK38(U_2443,U_2442))) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK38(U_2443,U_2442)),U_2443)) )
      | ~ hBOOL(hAPP(U_2442,U_2443))
      | hBOOL(hAPP(U_2442,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK38]),skolemize(U_2441,sK38(U_2443,U_2442))],[f_748_2]) ).

fof(f_748_4,plain,
    ( ! [U_2440,U_2442,U_2443] :
        ( hBOOL(hAPP(U_2442,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK38(U_2443,U_2442)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ sP210(U_2440,U_2442,U_2443) )
    & ! [U_2440,U_2442,U_2443] :
        ( ~ hBOOL(hAPP(U_2442,U_2440))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2440),sK38(U_2443,U_2442)))
        | ~ sP210(U_2440,U_2442,U_2443) )
    & ! [U_2440,U_2442,U_2443] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK38(U_2443,U_2442)),U_2443))
        | ~ sP210(U_2440,U_2442,U_2443) )
    & ! [U_2440,U_2442,U_2443] :
        ( sP210(U_2440,U_2442,U_2443)
        | ~ hBOOL(hAPP(U_2442,U_2443))
        | hBOOL(hAPP(U_2442,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP210])],[f_748_3]) ).

cnf(f_748_5,plain,
    ( sP210(U_2440,U_2442,U_2443)
    | ~ hBOOL(hAPP(U_2442,U_2443))
    | hBOOL(hAPP(U_2442,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_748_4]) ).

cnf(f_748_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK38(U_2443,U_2442)),U_2443))
    | ~ sP210(U_2440,U_2442,U_2443) ),
    inference(clausify,[status(thm)],[f_748_4]) ).

cnf(f_748_7,plain,
    ( ~ hBOOL(hAPP(U_2442,U_2440))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_2440),sK38(U_2443,U_2442)))
    | ~ sP210(U_2440,U_2442,U_2443) ),
    inference(clausify,[status(thm)],[f_748_4]) ).

cnf(f_748_8,plain,
    ( hBOOL(hAPP(U_2442,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK38(U_2443,U_2442)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ sP210(U_2440,U_2442,U_2443) ),
    inference(clausify,[status(thm)],[f_748_4]) ).

fof(f_749_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_749_2,plain,
    ! [U_2445,U_2444] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(U_2444,U_2445)) = 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_2444)),c_Com_Ocom_Ocom__size(U_2445))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_749_1]) ).

fof(f_749_3,plain,
    ! [U_2445,U_2444] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(U_2444,U_2445)) = 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_2444)),c_Com_Ocom_Ocom__size(U_2445))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_749_2]) ).

cnf(f_749_4,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OSemi(U_2444,U_2445)) = 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_2444)),c_Com_Ocom_Ocom__size(U_2445))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_749_3]) ).

fof(f_750_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_750_2,plain,
    ! [U_2447,U_2446] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(U_2446,U_2447)) = 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_2446)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_2447))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_750_1]) ).

fof(f_750_3,plain,
    ! [U_2446,U_2447] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(U_2446,U_2447)) = 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_2446)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_2447))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_750_2]) ).

cnf(f_750_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSemi(U_2446,U_2447)) = 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_2446)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_2447))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_750_3]) ).

fof(f_751_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_751_2,plain,
    ! [U_2450,U_2449,U_2448] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(U_2448,U_2449,U_2450)) = 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_2449)),c_Com_Ocom_Ocom__size(U_2450))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_751_1]) ).

fof(f_751_3,plain,
    ! [U_2448,U_2449,U_2450] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(U_2448,U_2449,U_2450)) = 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_2449)),c_Com_Ocom_Ocom__size(U_2450))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_751_2]) ).

cnf(f_751_4,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OCond(U_2448,U_2449,U_2450)) = 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_2449)),c_Com_Ocom_Ocom__size(U_2450))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_751_3]) ).

fof(f_752_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_752_2,plain,
    ! [U_2453,U_2452,U_2451] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(U_2451,U_2452,U_2453)) = 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_2452)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_2453))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_752_1]) ).

fof(f_752_3,plain,
    ! [U_2451,U_2452,U_2453] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(U_2451,U_2452,U_2453)) = 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_2452)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_2453))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_752_2]) ).

cnf(f_752_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCond(U_2451,U_2452,U_2453)) = 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_2452)),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_2453))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_752_3]) ).

fof(f_753_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_753_2,plain,
    ! [U_2456,U_2455,U_2454] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(U_2454,U_2455,U_2456)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_2456)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_753_1]) ).

fof(f_753_3,plain,
    ! [U_2454,U_2455,U_2456] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(U_2454,U_2455,U_2456)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_2456)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_753_2]) ).

cnf(f_753_4,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OLocal(U_2454,U_2455,U_2456)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_2456)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_753_3]) ).

fof(f_754_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_754_2,plain,
    ! [U_2459,U_2458,U_2457] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(U_2457,U_2458,U_2459)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_2459)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_754_1]) ).

fof(f_754_3,plain,
    ! [U_2457,U_2458,U_2459] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(U_2457,U_2458,U_2459)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_2459)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_754_2]) ).

cnf(f_754_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OLocal(U_2457,U_2458,U_2459)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_2459)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_754_3]) ).

fof(f_755_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_755_2,plain,
    ! [U_2463,U_2462,U_2461,U_2460] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2460,U_2461) = U_2463
      | U_2461 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2463),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2461),U_2463)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2461)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2463),U_2461))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2463)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2461)) )
      | U_2460 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2461),U_2462)),U_2463) ),
    inference(variable_rename,[status(thm)],[f_755_1]) ).

fof(f_755_3,plain,
    ( ! [U_2461,U_2463] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2463),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2461),U_2463))
        | ~ sP212(U_2461,U_2463) )
    & ! [U_2461,U_2463] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2461))
        | ~ sP212(U_2461,U_2463) )
    & ! [U_2461,U_2463] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2463),U_2461))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2463))
        | ~ sP211(U_2461,U_2463) )
    & ! [U_2461,U_2463] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2461))
        | ~ sP211(U_2461,U_2463) )
    & ! [U_2460,U_2461,U_2462,U_2463] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2460,U_2461) = U_2463
        | U_2461 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | sP212(U_2461,U_2463)
        | sP211(U_2461,U_2463)
        | U_2460 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2461),U_2462)),U_2463) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP211,sP212])],[f_755_2]) ).

cnf(f_755_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2460,U_2461) = U_2463
    | U_2461 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | sP212(U_2461,U_2463)
    | sP211(U_2461,U_2463)
    | U_2460 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2461),U_2462)),U_2463) ),
    inference(clausify,[status(thm)],[f_755_3]) ).

cnf(f_755_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2461))
    | ~ sP211(U_2461,U_2463) ),
    inference(clausify,[status(thm)],[f_755_3]) ).

cnf(f_755_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2463),U_2461))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2463))
    | ~ sP211(U_2461,U_2463) ),
    inference(clausify,[status(thm)],[f_755_3]) ).

cnf(f_755_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2461))
    | ~ sP212(U_2461,U_2463) ),
    inference(clausify,[status(thm)],[f_755_3]) ).

cnf(f_755_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2463),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2461),U_2463))
    | ~ sP212(U_2461,U_2463) ),
    inference(clausify,[status(thm)],[f_755_3]) ).

fof(f_756_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_756_2,plain,
    ! [U_2467,U_2466,U_2465,U_2464] :
      ( 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_2465),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2467,U_2464))),U_2466)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2466),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2465),U_2466))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2464)) ),
    inference(variable_rename,[status(thm)],[f_756_1]) ).

fof(f_756_3,plain,
    ! [U_2464,U_2466,U_2467,U_2465] :
      ( 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_2465),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2467,U_2464))),U_2466)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2466),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2465),U_2466))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2464)) ),
    inference(definitional_conversion,[status(esa)],[f_756_2]) ).

cnf(f_756_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_2465),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2467,U_2464))),U_2466)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2466),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2465),U_2466))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2464)) ),
    inference(clausify,[status(thm)],[f_756_3]) ).

fof(f_757_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_757_2,plain,
    ! [U_2473,U_2472,U_2471,U_2470,U_2469,U_2468] :
      ( ( c_Natural_Oevaln(U_2470,U_2471,U_2472,U_2473)
        & ~ hBOOL(hAPP(U_2468,U_2471)) )
      | ( c_Natural_Oevaln(U_2469,U_2471,U_2472,U_2473)
        & hBOOL(hAPP(U_2468,U_2471)) )
      | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_2468,U_2469,U_2470),U_2471,U_2472,U_2473) ),
    inference(variable_rename,[status(thm)],[f_757_1]) ).

fof(f_757_3,plain,
    ( ! [U_2472,U_2473,U_2468,U_2470,U_2471] :
        ( c_Natural_Oevaln(U_2470,U_2471,U_2472,U_2473)
        | ~ sP214(U_2472,U_2473,U_2468,U_2470,U_2471) )
    & ! [U_2472,U_2473,U_2468,U_2470,U_2471] :
        ( ~ hBOOL(hAPP(U_2468,U_2471))
        | ~ sP214(U_2472,U_2473,U_2468,U_2470,U_2471) )
    & ! [U_2472,U_2473,U_2468,U_2469,U_2471] :
        ( c_Natural_Oevaln(U_2469,U_2471,U_2472,U_2473)
        | ~ sP213(U_2472,U_2473,U_2468,U_2469,U_2471) )
    & ! [U_2472,U_2473,U_2468,U_2469,U_2471] :
        ( hBOOL(hAPP(U_2468,U_2471))
        | ~ sP213(U_2472,U_2473,U_2468,U_2469,U_2471) )
    & ! [U_2472,U_2473,U_2468,U_2469,U_2470,U_2471] :
        ( sP214(U_2472,U_2473,U_2468,U_2470,U_2471)
        | sP213(U_2472,U_2473,U_2468,U_2469,U_2471)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_2468,U_2469,U_2470),U_2471,U_2472,U_2473) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP213,sP214])],[f_757_2]) ).

cnf(f_757_4,plain,
    ( sP214(U_2472,U_2473,U_2468,U_2470,U_2471)
    | sP213(U_2472,U_2473,U_2468,U_2469,U_2471)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_2468,U_2469,U_2470),U_2471,U_2472,U_2473) ),
    inference(clausify,[status(thm)],[f_757_3]) ).

cnf(f_757_5,plain,
    ( hBOOL(hAPP(U_2468,U_2471))
    | ~ sP213(U_2472,U_2473,U_2468,U_2469,U_2471) ),
    inference(clausify,[status(thm)],[f_757_3]) ).

cnf(f_757_6,plain,
    ( c_Natural_Oevaln(U_2469,U_2471,U_2472,U_2473)
    | ~ sP213(U_2472,U_2473,U_2468,U_2469,U_2471) ),
    inference(clausify,[status(thm)],[f_757_3]) ).

cnf(f_757_7,plain,
    ( ~ hBOOL(hAPP(U_2468,U_2471))
    | ~ sP214(U_2472,U_2473,U_2468,U_2470,U_2471) ),
    inference(clausify,[status(thm)],[f_757_3]) ).

cnf(f_757_8,plain,
    ( c_Natural_Oevaln(U_2470,U_2471,U_2472,U_2473)
    | ~ sP214(U_2472,U_2473,U_2468,U_2470,U_2471) ),
    inference(clausify,[status(thm)],[f_757_3]) ).

fof(f_758_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_758_2,plain,
    ! [U_2479,U_2478,U_2477,U_2476,U_2475,U_2474] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_2474,U_2476,U_2479),U_2475,U_2477,U_2478)
      | ~ c_Natural_Oevaln(U_2476,U_2475,U_2477,U_2478)
      | ~ hBOOL(hAPP(U_2474,U_2475)) ),
    inference(variable_rename,[status(thm)],[f_758_1]) ).

fof(f_758_3,plain,
    ! [U_2479,U_2474,U_2478,U_2477,U_2475,U_2476] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_2474,U_2476,U_2479),U_2475,U_2477,U_2478)
      | ~ c_Natural_Oevaln(U_2476,U_2475,U_2477,U_2478)
      | ~ hBOOL(hAPP(U_2474,U_2475)) ),
    inference(definitional_conversion,[status(esa)],[f_758_2]) ).

cnf(f_758_4,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_2474,U_2476,U_2479),U_2475,U_2477,U_2478)
    | ~ c_Natural_Oevaln(U_2476,U_2475,U_2477,U_2478)
    | ~ hBOOL(hAPP(U_2474,U_2475)) ),
    inference(clausify,[status(thm)],[f_758_3]) ).

fof(f_759_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_759_2,plain,
    ! [U_2485,U_2484,U_2483,U_2482,U_2481,U_2480] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_2480,U_2485,U_2482),U_2481,U_2483,U_2484)
      | ~ c_Natural_Oevaln(U_2482,U_2481,U_2483,U_2484)
      | hBOOL(hAPP(U_2480,U_2481)) ),
    inference(variable_rename,[status(thm)],[f_759_1]) ).

fof(f_759_3,plain,
    ! [U_2484,U_2480,U_2483,U_2482,U_2481,U_2485] :
      ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_2480,U_2485,U_2482),U_2481,U_2483,U_2484)
      | ~ c_Natural_Oevaln(U_2482,U_2481,U_2483,U_2484)
      | hBOOL(hAPP(U_2480,U_2481)) ),
    inference(definitional_conversion,[status(esa)],[f_759_2]) ).

cnf(f_759_4,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_2480,U_2485,U_2482),U_2481,U_2483,U_2484)
    | ~ c_Natural_Oevaln(U_2482,U_2481,U_2483,U_2484)
    | hBOOL(hAPP(U_2480,U_2481)) ),
    inference(clausify,[status(thm)],[f_759_3]) ).

fof(f_760_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_760_2,plain,
    ! [U_2490,U_2489,U_2488,U_2487,U_2486] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2486,U_2490,U_2488)),U_2487),U_2489))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2488),U_2487),U_2489))
      | hBOOL(hAPP(U_2486,U_2487)) ),
    inference(variable_rename,[status(thm)],[f_760_1]) ).

fof(f_760_3,plain,
    ! [U_2487,U_2486,U_2488,U_2489,U_2490] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2486,U_2490,U_2488)),U_2487),U_2489))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2488),U_2487),U_2489))
      | hBOOL(hAPP(U_2486,U_2487)) ),
    inference(definitional_conversion,[status(esa)],[f_760_2]) ).

cnf(f_760_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2486,U_2490,U_2488)),U_2487),U_2489))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2488),U_2487),U_2489))
    | hBOOL(hAPP(U_2486,U_2487)) ),
    inference(clausify,[status(thm)],[f_760_3]) ).

fof(f_761_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_761_2,plain,
    ! [U_2495,U_2494,U_2493,U_2492,U_2491] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2491,U_2493,U_2495)),U_2492),U_2494))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2493),U_2492),U_2494))
      | ~ hBOOL(hAPP(U_2491,U_2492)) ),
    inference(variable_rename,[status(thm)],[f_761_1]) ).

fof(f_761_3,plain,
    ! [U_2492,U_2491,U_2493,U_2494,U_2495] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2491,U_2493,U_2495)),U_2492),U_2494))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2493),U_2492),U_2494))
      | ~ hBOOL(hAPP(U_2491,U_2492)) ),
    inference(definitional_conversion,[status(esa)],[f_761_2]) ).

cnf(f_761_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2491,U_2493,U_2495)),U_2492),U_2494))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2493),U_2492),U_2494))
    | ~ hBOOL(hAPP(U_2491,U_2492)) ),
    inference(clausify,[status(thm)],[f_761_3]) ).

fof(f_762_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_762_2,plain,
    ! [U_2500,U_2499,U_2498,U_2497,U_2496] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2498),U_2499),U_2500))
        & ~ hBOOL(hAPP(U_2496,U_2499)) )
      | ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2497),U_2499),U_2500))
        & hBOOL(hAPP(U_2496,U_2499)) )
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2496,U_2497,U_2498)),U_2499),U_2500)) ),
    inference(variable_rename,[status(thm)],[f_762_1]) ).

fof(f_762_3,plain,
    ( ! [U_2496,U_2498,U_2499,U_2500] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2498),U_2499),U_2500))
        | ~ sP216(U_2496,U_2498,U_2499,U_2500) )
    & ! [U_2496,U_2498,U_2499,U_2500] :
        ( ~ hBOOL(hAPP(U_2496,U_2499))
        | ~ sP216(U_2496,U_2498,U_2499,U_2500) )
    & ! [U_2497,U_2496,U_2499,U_2500] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2497),U_2499),U_2500))
        | ~ sP215(U_2497,U_2496,U_2499,U_2500) )
    & ! [U_2497,U_2496,U_2499,U_2500] :
        ( hBOOL(hAPP(U_2496,U_2499))
        | ~ sP215(U_2497,U_2496,U_2499,U_2500) )
    & ! [U_2497,U_2496,U_2498,U_2499,U_2500] :
        ( sP216(U_2496,U_2498,U_2499,U_2500)
        | sP215(U_2497,U_2496,U_2499,U_2500)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2496,U_2497,U_2498)),U_2499),U_2500)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP215,sP216])],[f_762_2]) ).

cnf(f_762_4,plain,
    ( sP216(U_2496,U_2498,U_2499,U_2500)
    | sP215(U_2497,U_2496,U_2499,U_2500)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2496,U_2497,U_2498)),U_2499),U_2500)) ),
    inference(clausify,[status(thm)],[f_762_3]) ).

cnf(f_762_5,plain,
    ( hBOOL(hAPP(U_2496,U_2499))
    | ~ sP215(U_2497,U_2496,U_2499,U_2500) ),
    inference(clausify,[status(thm)],[f_762_3]) ).

cnf(f_762_6,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2497),U_2499),U_2500))
    | ~ sP215(U_2497,U_2496,U_2499,U_2500) ),
    inference(clausify,[status(thm)],[f_762_3]) ).

cnf(f_762_7,plain,
    ( ~ hBOOL(hAPP(U_2496,U_2499))
    | ~ sP216(U_2496,U_2498,U_2499,U_2500) ),
    inference(clausify,[status(thm)],[f_762_3]) ).

cnf(f_762_8,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2498),U_2499),U_2500))
    | ~ sP216(U_2496,U_2498,U_2499,U_2500) ),
    inference(clausify,[status(thm)],[f_762_3]) ).

fof(f_763_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_763_2,plain,
    ! [U_2506,U_2505,U_2504,U_2503,U_2502,U_2501] :
      ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_2501,U_2505),U_2502,U_2503,U_2506)
      | ~ c_Natural_Oevaln(U_2505,U_2504,U_2503,U_2506)
      | ~ c_Natural_Oevaln(U_2501,U_2502,U_2503,U_2504) ),
    inference(variable_rename,[status(thm)],[f_763_1]) ).

fof(f_763_3,plain,
    ! [U_2503,U_2502,U_2501,U_2504,U_2505,U_2506] :
      ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_2501,U_2505),U_2502,U_2503,U_2506)
      | ~ c_Natural_Oevaln(U_2505,U_2504,U_2503,U_2506)
      | ~ c_Natural_Oevaln(U_2501,U_2502,U_2503,U_2504) ),
    inference(definitional_conversion,[status(esa)],[f_763_2]) ).

cnf(f_763_4,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_2501,U_2505),U_2502,U_2503,U_2506)
    | ~ c_Natural_Oevaln(U_2505,U_2504,U_2503,U_2506)
    | ~ c_Natural_Oevaln(U_2501,U_2502,U_2503,U_2504) ),
    inference(clausify,[status(thm)],[f_763_3]) ).

fof(f_764_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_764_2,plain,
    ! [U_2511,U_2510,U_2509,U_2508,U_2507] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_2507,U_2510)),U_2508),U_2511))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2510),U_2509),U_2511))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2507),U_2508),U_2509)) ),
    inference(variable_rename,[status(thm)],[f_764_1]) ).

fof(f_764_3,plain,
    ! [U_2509,U_2508,U_2507,U_2510,U_2511] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_2507,U_2510)),U_2508),U_2511))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2510),U_2509),U_2511))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2507),U_2508),U_2509)) ),
    inference(definitional_conversion,[status(esa)],[f_764_2]) ).

cnf(f_764_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_2507,U_2510)),U_2508),U_2511))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2510),U_2509),U_2511))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2507),U_2508),U_2509)) ),
    inference(clausify,[status(thm)],[f_764_3]) ).

fof(f_765_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_765_2,plain,
    ! [U_2514,U_2513,U_2512] :
      ( ( hBOOL(hAPP(c_Com_OWT,U_2514))
        & hBOOL(hAPP(c_Com_OWT,U_2513)) )
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_2512,U_2513,U_2514))) ),
    inference(variable_rename,[status(thm)],[f_765_1]) ).

fof(f_765_3,plain,
    ! [U_2514,U_2513] :
      ( ! [U_2512] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_2512,U_2513,U_2514)))
      | ( hBOOL(hAPP(c_Com_OWT,U_2514))
        & hBOOL(hAPP(c_Com_OWT,U_2513)) ) ),
    inference(miniscope,[status(thm)],[f_765_2]) ).

fof(f_765_4,plain,
    ( ! [U_2513,U_2514] :
        ( hBOOL(hAPP(c_Com_OWT,U_2514))
        | ~ sP217(U_2513,U_2514) )
    & ! [U_2513,U_2514] :
        ( hBOOL(hAPP(c_Com_OWT,U_2513))
        | ~ sP217(U_2513,U_2514) )
    & ! [U_2512,U_2513,U_2514] :
        ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_2512,U_2513,U_2514)))
        | sP217(U_2513,U_2514) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP217])],[f_765_3]) ).

cnf(f_765_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_2512,U_2513,U_2514)))
    | sP217(U_2513,U_2514) ),
    inference(clausify,[status(thm)],[f_765_4]) ).

cnf(f_765_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_2513))
    | ~ sP217(U_2513,U_2514) ),
    inference(clausify,[status(thm)],[f_765_4]) ).

cnf(f_765_7,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_2514))
    | ~ sP217(U_2513,U_2514) ),
    inference(clausify,[status(thm)],[f_765_4]) ).

fof(f_766_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_766_2,plain,
    ! [U_2517,U_2516,U_2515] :
      ( hBOOL(hAPP(c_Com_OWT,U_2517))
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_2515,U_2516,U_2517))) ),
    inference(variable_rename,[status(thm)],[f_766_1]) ).

fof(f_766_3,plain,
    ! [U_2517] :
      ( ! [U_2516,U_2515] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_2515,U_2516,U_2517)))
      | hBOOL(hAPP(c_Com_OWT,U_2517)) ),
    inference(miniscope,[status(thm)],[f_766_2]) ).

fof(f_766_4,plain,
    ! [U_2516,U_2517,U_2515] :
      ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_2515,U_2516,U_2517)))
      | hBOOL(hAPP(c_Com_OWT,U_2517)) ),
    inference(definitional_conversion,[status(esa)],[f_766_3]) ).

cnf(f_766_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_2515,U_2516,U_2517)))
    | hBOOL(hAPP(c_Com_OWT,U_2517)) ),
    inference(clausify,[status(thm)],[f_766_4]) ).

fof(f_767_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_767_2,plain,
    ! [U_2519,U_2518] :
      ( ( hBOOL(hAPP(c_Com_OWT,U_2519))
        & hBOOL(hAPP(c_Com_OWT,U_2518)) )
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_2518,U_2519))) ),
    inference(variable_rename,[status(thm)],[f_767_1]) ).

fof(f_767_3,plain,
    ( ! [U_2518,U_2519] :
        ( hBOOL(hAPP(c_Com_OWT,U_2519))
        | ~ sP218(U_2518,U_2519) )
    & ! [U_2518,U_2519] :
        ( hBOOL(hAPP(c_Com_OWT,U_2518))
        | ~ sP218(U_2518,U_2519) )
    & ! [U_2518,U_2519] :
        ( sP218(U_2518,U_2519)
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_2518,U_2519))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP218])],[f_767_2]) ).

cnf(f_767_4,plain,
    ( sP218(U_2518,U_2519)
    | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_2518,U_2519))) ),
    inference(clausify,[status(thm)],[f_767_3]) ).

cnf(f_767_5,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_2518))
    | ~ sP218(U_2518,U_2519) ),
    inference(clausify,[status(thm)],[f_767_3]) ).

cnf(f_767_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_2519))
    | ~ sP218(U_2518,U_2519) ),
    inference(clausify,[status(thm)],[f_767_3]) ).

fof(f_768_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_768_2,plain,
    ! [U_2522,U_2521,U_2520] :
      ( c_Divides_Odiv__class_Omod(U_2520,c_Divides_Odiv__class_Omod(U_2520,U_2521,U_2522),U_2522) = c_Divides_Odiv__class_Omod(U_2520,U_2521,U_2522)
      | ~ class_Divides_Osemiring__div(U_2520) ),
    inference(variable_rename,[status(thm)],[f_768_1]) ).

fof(f_768_3,plain,
    ! [U_2522,U_2520,U_2521] :
      ( c_Divides_Odiv__class_Omod(U_2520,c_Divides_Odiv__class_Omod(U_2520,U_2521,U_2522),U_2522) = c_Divides_Odiv__class_Omod(U_2520,U_2521,U_2522)
      | ~ class_Divides_Osemiring__div(U_2520) ),
    inference(definitional_conversion,[status(esa)],[f_768_2]) ).

cnf(f_768_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2520,c_Divides_Odiv__class_Omod(U_2520,U_2521,U_2522),U_2522) = c_Divides_Odiv__class_Omod(U_2520,U_2521,U_2522)
    | ~ class_Divides_Osemiring__div(U_2520) ),
    inference(clausify,[status(thm)],[f_768_3]) ).

fof(f_769_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_769_2,plain,
    ! [U_2527,U_2526,U_2525,U_2524,U_2523] : c_Com_Ocom_OSemi(U_2523,U_2524) != c_Com_Ocom_OCond(U_2525,U_2526,U_2527),
    inference(variable_rename,[status(thm)],[f_769_1]) ).

fof(f_769_3,plain,
    ! [U_2523,U_2524,U_2525,U_2526,U_2527] : c_Com_Ocom_OSemi(U_2523,U_2524) != c_Com_Ocom_OCond(U_2525,U_2526,U_2527),
    inference(definitional_conversion,[status(esa)],[f_769_2]) ).

cnf(f_769_4,plain,
    c_Com_Ocom_OSemi(U_2523,U_2524) != c_Com_Ocom_OCond(U_2525,U_2526,U_2527),
    inference(clausify,[status(thm)],[f_769_3]) ).

fof(f_770_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_770_2,plain,
    ! [U_2532,U_2531,U_2530,U_2529,U_2528] : c_Com_Ocom_OSemi(U_2528,U_2529) != c_Com_Ocom_OLocal(U_2530,U_2531,U_2532),
    inference(variable_rename,[status(thm)],[f_770_1]) ).

fof(f_770_3,plain,
    ! [U_2528,U_2529,U_2530,U_2531,U_2532] : c_Com_Ocom_OSemi(U_2528,U_2529) != c_Com_Ocom_OLocal(U_2530,U_2531,U_2532),
    inference(definitional_conversion,[status(esa)],[f_770_2]) ).

cnf(f_770_4,plain,
    c_Com_Ocom_OSemi(U_2528,U_2529) != c_Com_Ocom_OLocal(U_2530,U_2531,U_2532),
    inference(clausify,[status(thm)],[f_770_3]) ).

fof(f_771_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_771_2,plain,
    ! [U_2537,U_2536,U_2535,U_2534,U_2533] : c_Com_Ocom_OCond(U_2533,U_2534,U_2535) != c_Com_Ocom_OSemi(U_2536,U_2537),
    inference(variable_rename,[status(thm)],[f_771_1]) ).

fof(f_771_3,plain,
    ! [U_2534,U_2533,U_2535,U_2536,U_2537] : c_Com_Ocom_OCond(U_2533,U_2534,U_2535) != c_Com_Ocom_OSemi(U_2536,U_2537),
    inference(definitional_conversion,[status(esa)],[f_771_2]) ).

cnf(f_771_4,plain,
    c_Com_Ocom_OCond(U_2533,U_2534,U_2535) != c_Com_Ocom_OSemi(U_2536,U_2537),
    inference(clausify,[status(thm)],[f_771_3]) ).

fof(f_772_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_772_2,plain,
    ! [U_2542,U_2541,U_2540,U_2539,U_2538] : c_Com_Ocom_OLocal(U_2538,U_2539,U_2540) != c_Com_Ocom_OSemi(U_2541,U_2542),
    inference(variable_rename,[status(thm)],[f_772_1]) ).

fof(f_772_3,plain,
    ! [U_2539,U_2538,U_2540,U_2541,U_2542] : c_Com_Ocom_OLocal(U_2538,U_2539,U_2540) != c_Com_Ocom_OSemi(U_2541,U_2542),
    inference(definitional_conversion,[status(esa)],[f_772_2]) ).

cnf(f_772_4,plain,
    c_Com_Ocom_OLocal(U_2538,U_2539,U_2540) != c_Com_Ocom_OSemi(U_2541,U_2542),
    inference(clausify,[status(thm)],[f_772_3]) ).

fof(f_773_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_773_2,plain,
    ! [U_2548,U_2547,U_2546,U_2545,U_2544,U_2543] : c_Com_Ocom_OCond(U_2543,U_2544,U_2545) != c_Com_Ocom_OLocal(U_2546,U_2547,U_2548),
    inference(variable_rename,[status(thm)],[f_773_1]) ).

fof(f_773_3,plain,
    ! [U_2544,U_2543,U_2545,U_2546,U_2547,U_2548] : c_Com_Ocom_OCond(U_2543,U_2544,U_2545) != c_Com_Ocom_OLocal(U_2546,U_2547,U_2548),
    inference(definitional_conversion,[status(esa)],[f_773_2]) ).

cnf(f_773_4,plain,
    c_Com_Ocom_OCond(U_2543,U_2544,U_2545) != c_Com_Ocom_OLocal(U_2546,U_2547,U_2548),
    inference(clausify,[status(thm)],[f_773_3]) ).

fof(f_774_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_774_2,plain,
    ! [U_2554,U_2553,U_2552,U_2551,U_2550,U_2549] : c_Com_Ocom_OLocal(U_2549,U_2550,U_2551) != c_Com_Ocom_OCond(U_2552,U_2553,U_2554),
    inference(variable_rename,[status(thm)],[f_774_1]) ).

fof(f_774_3,plain,
    ! [U_2550,U_2549,U_2551,U_2552,U_2553,U_2554] : c_Com_Ocom_OLocal(U_2549,U_2550,U_2551) != c_Com_Ocom_OCond(U_2552,U_2553,U_2554),
    inference(definitional_conversion,[status(esa)],[f_774_2]) ).

cnf(f_774_4,plain,
    c_Com_Ocom_OLocal(U_2549,U_2550,U_2551) != c_Com_Ocom_OCond(U_2552,U_2553,U_2554),
    inference(clausify,[status(thm)],[f_774_3]) ).

fof(f_775_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_775_2,plain,
    ! [U_2558,U_2557,U_2556,U_2555] :
      ( ( c_Com_Ocom_OSemi(U_2555,U_2556) = c_Com_Ocom_OSemi(U_2557,U_2558)
        | U_2556 != U_2558
        | U_2555 != U_2557 )
      & ( ( U_2556 = U_2558
          & U_2555 = U_2557 )
        | c_Com_Ocom_OSemi(U_2555,U_2556) != c_Com_Ocom_OSemi(U_2557,U_2558) ) ),
    inference(variable_rename,[status(thm)],[f_775_1]) ).

fof(f_775_3,plain,
    ( ! [U_2566,U_2564,U_2562,U_2560] :
        ( c_Com_Ocom_OSemi(U_2560,U_2562) = c_Com_Ocom_OSemi(U_2564,U_2566)
        | U_2562 != U_2566
        | U_2560 != U_2564 )
    & ! [U_2565,U_2563,U_2561,U_2559] :
        ( ( U_2561 = U_2565
          & U_2559 = U_2563 )
        | c_Com_Ocom_OSemi(U_2559,U_2561) != c_Com_Ocom_OSemi(U_2563,U_2565) ) ),
    inference(miniscope,[status(thm)],[f_775_2]) ).

fof(f_775_4,plain,
    ( ! [U_2561,U_2559,U_2563,U_2565] :
        ( U_2561 = U_2565
        | ~ sP219(U_2561,U_2559,U_2563,U_2565) )
    & ! [U_2561,U_2559,U_2563,U_2565] :
        ( U_2559 = U_2563
        | ~ sP219(U_2561,U_2559,U_2563,U_2565) )
    & ! [U_2560,U_2562,U_2566,U_2564] :
        ( c_Com_Ocom_OSemi(U_2560,U_2562) = c_Com_Ocom_OSemi(U_2564,U_2566)
        | U_2562 != U_2566
        | U_2560 != U_2564 )
    & ! [U_2561,U_2559,U_2563,U_2565] :
        ( sP219(U_2561,U_2559,U_2563,U_2565)
        | c_Com_Ocom_OSemi(U_2559,U_2561) != c_Com_Ocom_OSemi(U_2563,U_2565) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP219])],[f_775_3]) ).

cnf(f_775_5,plain,
    ( sP219(U_2561,U_2559,U_2563,U_2565)
    | c_Com_Ocom_OSemi(U_2559,U_2561) != c_Com_Ocom_OSemi(U_2563,U_2565) ),
    inference(clausify,[status(thm)],[f_775_4]) ).

cnf(f_775_6,plain,
    ( c_Com_Ocom_OSemi(U_2560,U_2562) = c_Com_Ocom_OSemi(U_2564,U_2566)
    | U_2562 != U_2566
    | U_2560 != U_2564 ),
    inference(clausify,[status(thm)],[f_775_4]) ).

cnf(f_775_7,plain,
    ( U_2559 = U_2563
    | ~ sP219(U_2561,U_2559,U_2563,U_2565) ),
    inference(clausify,[status(thm)],[f_775_4]) ).

cnf(f_775_8,plain,
    ( U_2561 = U_2565
    | ~ sP219(U_2561,U_2559,U_2563,U_2565) ),
    inference(clausify,[status(thm)],[f_775_4]) ).

fof(f_776_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_776_2,plain,
    ! [U_2572,U_2571,U_2570,U_2569,U_2568,U_2567] :
      ( ( c_Com_Ocom_OCond(U_2567,U_2568,U_2569) = c_Com_Ocom_OCond(U_2570,U_2571,U_2572)
        | U_2569 != U_2572
        | U_2568 != U_2571
        | U_2567 != U_2570 )
      & ( ( U_2569 = U_2572
          & U_2568 = U_2571
          & U_2567 = U_2570 )
        | c_Com_Ocom_OCond(U_2567,U_2568,U_2569) != c_Com_Ocom_OCond(U_2570,U_2571,U_2572) ) ),
    inference(variable_rename,[status(thm)],[f_776_1]) ).

fof(f_776_3,plain,
    ( ! [U_2584,U_2582,U_2580,U_2578,U_2576,U_2574] :
        ( c_Com_Ocom_OCond(U_2574,U_2576,U_2578) = c_Com_Ocom_OCond(U_2580,U_2582,U_2584)
        | U_2578 != U_2584
        | U_2576 != U_2582
        | U_2574 != U_2580 )
    & ! [U_2583,U_2581,U_2579,U_2577,U_2575,U_2573] :
        ( ( U_2577 = U_2583
          & U_2575 = U_2581
          & U_2573 = U_2579 )
        | c_Com_Ocom_OCond(U_2573,U_2575,U_2577) != c_Com_Ocom_OCond(U_2579,U_2581,U_2583) ) ),
    inference(miniscope,[status(thm)],[f_776_2]) ).

fof(f_776_4,plain,
    ( ! [U_2573,U_2577,U_2579,U_2575,U_2581,U_2583] :
        ( U_2577 = U_2583
        | ~ sP220(U_2573,U_2577,U_2579,U_2575,U_2581,U_2583) )
    & ! [U_2573,U_2577,U_2579,U_2575,U_2581,U_2583] :
        ( U_2575 = U_2581
        | ~ sP220(U_2573,U_2577,U_2579,U_2575,U_2581,U_2583) )
    & ! [U_2573,U_2577,U_2579,U_2575,U_2581,U_2583] :
        ( U_2573 = U_2579
        | ~ sP220(U_2573,U_2577,U_2579,U_2575,U_2581,U_2583) )
    & ! [U_2584,U_2574,U_2578,U_2576,U_2580,U_2582] :
        ( c_Com_Ocom_OCond(U_2574,U_2576,U_2578) = c_Com_Ocom_OCond(U_2580,U_2582,U_2584)
        | U_2578 != U_2584
        | U_2576 != U_2582
        | U_2574 != U_2580 )
    & ! [U_2573,U_2577,U_2579,U_2575,U_2581,U_2583] :
        ( sP220(U_2573,U_2577,U_2579,U_2575,U_2581,U_2583)
        | c_Com_Ocom_OCond(U_2573,U_2575,U_2577) != c_Com_Ocom_OCond(U_2579,U_2581,U_2583) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP220])],[f_776_3]) ).

cnf(f_776_5,plain,
    ( sP220(U_2573,U_2577,U_2579,U_2575,U_2581,U_2583)
    | c_Com_Ocom_OCond(U_2573,U_2575,U_2577) != c_Com_Ocom_OCond(U_2579,U_2581,U_2583) ),
    inference(clausify,[status(thm)],[f_776_4]) ).

cnf(f_776_6,plain,
    ( c_Com_Ocom_OCond(U_2574,U_2576,U_2578) = c_Com_Ocom_OCond(U_2580,U_2582,U_2584)
    | U_2578 != U_2584
    | U_2576 != U_2582
    | U_2574 != U_2580 ),
    inference(clausify,[status(thm)],[f_776_4]) ).

cnf(f_776_7,plain,
    ( U_2573 = U_2579
    | ~ sP220(U_2573,U_2577,U_2579,U_2575,U_2581,U_2583) ),
    inference(clausify,[status(thm)],[f_776_4]) ).

cnf(f_776_8,plain,
    ( U_2575 = U_2581
    | ~ sP220(U_2573,U_2577,U_2579,U_2575,U_2581,U_2583) ),
    inference(clausify,[status(thm)],[f_776_4]) ).

cnf(f_776_9,plain,
    ( U_2577 = U_2583
    | ~ sP220(U_2573,U_2577,U_2579,U_2575,U_2581,U_2583) ),
    inference(clausify,[status(thm)],[f_776_4]) ).

fof(f_777_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_777_2,plain,
    ! [U_2590,U_2589,U_2588,U_2587,U_2586,U_2585] :
      ( ( c_Com_Ocom_OLocal(U_2585,U_2586,U_2587) = c_Com_Ocom_OLocal(U_2588,U_2589,U_2590)
        | U_2587 != U_2590
        | U_2586 != U_2589
        | U_2585 != U_2588 )
      & ( ( U_2587 = U_2590
          & U_2586 = U_2589
          & U_2585 = U_2588 )
        | c_Com_Ocom_OLocal(U_2585,U_2586,U_2587) != c_Com_Ocom_OLocal(U_2588,U_2589,U_2590) ) ),
    inference(variable_rename,[status(thm)],[f_777_1]) ).

fof(f_777_3,plain,
    ( ! [U_2602,U_2600,U_2598,U_2596,U_2594,U_2592] :
        ( c_Com_Ocom_OLocal(U_2592,U_2594,U_2596) = c_Com_Ocom_OLocal(U_2598,U_2600,U_2602)
        | U_2596 != U_2602
        | U_2594 != U_2600
        | U_2592 != U_2598 )
    & ! [U_2601,U_2599,U_2597,U_2595,U_2593,U_2591] :
        ( ( U_2595 = U_2601
          & U_2593 = U_2599
          & U_2591 = U_2597 )
        | c_Com_Ocom_OLocal(U_2591,U_2593,U_2595) != c_Com_Ocom_OLocal(U_2597,U_2599,U_2601) ) ),
    inference(miniscope,[status(thm)],[f_777_2]) ).

fof(f_777_4,plain,
    ( ! [U_2595,U_2599,U_2591,U_2601,U_2593,U_2597] :
        ( U_2595 = U_2601
        | ~ sP221(U_2595,U_2599,U_2591,U_2601,U_2593,U_2597) )
    & ! [U_2595,U_2599,U_2591,U_2601,U_2593,U_2597] :
        ( U_2593 = U_2599
        | ~ sP221(U_2595,U_2599,U_2591,U_2601,U_2593,U_2597) )
    & ! [U_2595,U_2599,U_2591,U_2601,U_2593,U_2597] :
        ( U_2591 = U_2597
        | ~ sP221(U_2595,U_2599,U_2591,U_2601,U_2593,U_2597) )
    & ! [U_2592,U_2594,U_2600,U_2598,U_2596,U_2602] :
        ( c_Com_Ocom_OLocal(U_2592,U_2594,U_2596) = c_Com_Ocom_OLocal(U_2598,U_2600,U_2602)
        | U_2596 != U_2602
        | U_2594 != U_2600
        | U_2592 != U_2598 )
    & ! [U_2595,U_2599,U_2591,U_2601,U_2593,U_2597] :
        ( sP221(U_2595,U_2599,U_2591,U_2601,U_2593,U_2597)
        | c_Com_Ocom_OLocal(U_2591,U_2593,U_2595) != c_Com_Ocom_OLocal(U_2597,U_2599,U_2601) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP221])],[f_777_3]) ).

cnf(f_777_5,plain,
    ( sP221(U_2595,U_2599,U_2591,U_2601,U_2593,U_2597)
    | c_Com_Ocom_OLocal(U_2591,U_2593,U_2595) != c_Com_Ocom_OLocal(U_2597,U_2599,U_2601) ),
    inference(clausify,[status(thm)],[f_777_4]) ).

cnf(f_777_6,plain,
    ( c_Com_Ocom_OLocal(U_2592,U_2594,U_2596) = c_Com_Ocom_OLocal(U_2598,U_2600,U_2602)
    | U_2596 != U_2602
    | U_2594 != U_2600
    | U_2592 != U_2598 ),
    inference(clausify,[status(thm)],[f_777_4]) ).

cnf(f_777_7,plain,
    ( U_2591 = U_2597
    | ~ sP221(U_2595,U_2599,U_2591,U_2601,U_2593,U_2597) ),
    inference(clausify,[status(thm)],[f_777_4]) ).

cnf(f_777_8,plain,
    ( U_2593 = U_2599
    | ~ sP221(U_2595,U_2599,U_2591,U_2601,U_2593,U_2597) ),
    inference(clausify,[status(thm)],[f_777_4]) ).

cnf(f_777_9,plain,
    ( U_2595 = U_2601
    | ~ sP221(U_2595,U_2599,U_2591,U_2601,U_2593,U_2597) ),
    inference(clausify,[status(thm)],[f_777_4]) ).

fof(f_778_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_778_2,plain,
    ! [U_2604,U_2603] :
      ( c_Divides_Odiv__class_Omod(U_2603,c_Groups_Ozero__class_Ozero(U_2603),U_2604) = c_Groups_Ozero__class_Ozero(U_2603)
      | ~ class_Divides_Osemiring__div(U_2603) ),
    inference(variable_rename,[status(thm)],[f_778_1]) ).

fof(f_778_3,plain,
    ! [U_2604,U_2603] :
      ( c_Divides_Odiv__class_Omod(U_2603,c_Groups_Ozero__class_Ozero(U_2603),U_2604) = c_Groups_Ozero__class_Ozero(U_2603)
      | ~ class_Divides_Osemiring__div(U_2603) ),
    inference(definitional_conversion,[status(esa)],[f_778_2]) ).

cnf(f_778_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2603,c_Groups_Ozero__class_Ozero(U_2603),U_2604) = c_Groups_Ozero__class_Ozero(U_2603)
    | ~ class_Divides_Osemiring__div(U_2603) ),
    inference(clausify,[status(thm)],[f_778_3]) ).

fof(f_779_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_779_2,plain,
    ! [U_2606,U_2605] :
      ( c_Divides_Odiv__class_Omod(U_2605,U_2606,c_Groups_Ozero__class_Ozero(U_2605)) = U_2606
      | ~ class_Divides_Osemiring__div(U_2605) ),
    inference(variable_rename,[status(thm)],[f_779_1]) ).

fof(f_779_3,plain,
    ! [U_2605,U_2606] :
      ( c_Divides_Odiv__class_Omod(U_2605,U_2606,c_Groups_Ozero__class_Ozero(U_2605)) = U_2606
      | ~ class_Divides_Osemiring__div(U_2605) ),
    inference(definitional_conversion,[status(esa)],[f_779_2]) ).

cnf(f_779_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2605,U_2606,c_Groups_Ozero__class_Ozero(U_2605)) = U_2606
    | ~ class_Divides_Osemiring__div(U_2605) ),
    inference(clausify,[status(thm)],[f_779_3]) ).

fof(f_780_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_780_2,plain,
    ! [U_2608,U_2607] :
      ( c_Divides_Odiv__class_Omod(U_2607,U_2608,U_2608) = c_Groups_Ozero__class_Ozero(U_2607)
      | ~ class_Divides_Osemiring__div(U_2607) ),
    inference(variable_rename,[status(thm)],[f_780_1]) ).

fof(f_780_3,plain,
    ! [U_2607,U_2608] :
      ( c_Divides_Odiv__class_Omod(U_2607,U_2608,U_2608) = c_Groups_Ozero__class_Ozero(U_2607)
      | ~ class_Divides_Osemiring__div(U_2607) ),
    inference(definitional_conversion,[status(esa)],[f_780_2]) ).

cnf(f_780_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2607,U_2608,U_2608) = c_Groups_Ozero__class_Ozero(U_2607)
    | ~ class_Divides_Osemiring__div(U_2607) ),
    inference(clausify,[status(thm)],[f_780_3]) ).

fof(f_781_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_781_2,plain,
    ! [U_2614,U_2613,U_2612,U_2611,U_2610,U_2609] :
      ( c_Divides_Odiv__class_Omod(U_2609,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2609),U_2610),U_2613),U_2611) = c_Divides_Odiv__class_Omod(U_2609,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2609),U_2612),U_2614),U_2611)
      | c_Divides_Odiv__class_Omod(U_2609,U_2613,U_2611) != c_Divides_Odiv__class_Omod(U_2609,U_2614,U_2611)
      | c_Divides_Odiv__class_Omod(U_2609,U_2610,U_2611) != c_Divides_Odiv__class_Omod(U_2609,U_2612,U_2611)
      | ~ class_Divides_Osemiring__div(U_2609) ),
    inference(variable_rename,[status(thm)],[f_781_1]) ).

fof(f_781_3,plain,
    ! [U_2609,U_2610,U_2611,U_2612,U_2613,U_2614] :
      ( c_Divides_Odiv__class_Omod(U_2609,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2609),U_2610),U_2613),U_2611) = c_Divides_Odiv__class_Omod(U_2609,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2609),U_2612),U_2614),U_2611)
      | c_Divides_Odiv__class_Omod(U_2609,U_2613,U_2611) != c_Divides_Odiv__class_Omod(U_2609,U_2614,U_2611)
      | c_Divides_Odiv__class_Omod(U_2609,U_2610,U_2611) != c_Divides_Odiv__class_Omod(U_2609,U_2612,U_2611)
      | ~ class_Divides_Osemiring__div(U_2609) ),
    inference(definitional_conversion,[status(esa)],[f_781_2]) ).

cnf(f_781_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2609,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2609),U_2610),U_2613),U_2611) = c_Divides_Odiv__class_Omod(U_2609,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2609),U_2612),U_2614),U_2611)
    | c_Divides_Odiv__class_Omod(U_2609,U_2613,U_2611) != c_Divides_Odiv__class_Omod(U_2609,U_2614,U_2611)
    | c_Divides_Odiv__class_Omod(U_2609,U_2610,U_2611) != c_Divides_Odiv__class_Omod(U_2609,U_2612,U_2611)
    | ~ class_Divides_Osemiring__div(U_2609) ),
    inference(clausify,[status(thm)],[f_781_3]) ).

fof(f_782_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_782_2,plain,
    ! [U_2618,U_2617,U_2616,U_2615] :
      ( c_Divides_Odiv__class_Omod(U_2615,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2615),c_Divides_Odiv__class_Omod(U_2615,U_2616,U_2617)),U_2618),U_2617) = c_Divides_Odiv__class_Omod(U_2615,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2615),U_2616),U_2618),U_2617)
      | ~ class_Divides_Osemiring__div(U_2615) ),
    inference(variable_rename,[status(thm)],[f_782_1]) ).

fof(f_782_3,plain,
    ! [U_2615,U_2617,U_2616,U_2618] :
      ( c_Divides_Odiv__class_Omod(U_2615,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2615),c_Divides_Odiv__class_Omod(U_2615,U_2616,U_2617)),U_2618),U_2617) = c_Divides_Odiv__class_Omod(U_2615,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2615),U_2616),U_2618),U_2617)
      | ~ class_Divides_Osemiring__div(U_2615) ),
    inference(definitional_conversion,[status(esa)],[f_782_2]) ).

cnf(f_782_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2615,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2615),c_Divides_Odiv__class_Omod(U_2615,U_2616,U_2617)),U_2618),U_2617) = c_Divides_Odiv__class_Omod(U_2615,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2615),U_2616),U_2618),U_2617)
    | ~ class_Divides_Osemiring__div(U_2615) ),
    inference(clausify,[status(thm)],[f_782_3]) ).

fof(f_783_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_783_2,plain,
    ! [U_2622,U_2621,U_2620,U_2619] :
      ( c_Divides_Odiv__class_Omod(U_2619,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2619),U_2620),c_Divides_Odiv__class_Omod(U_2619,U_2621,U_2622)),U_2622) = c_Divides_Odiv__class_Omod(U_2619,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2619),U_2620),U_2621),U_2622)
      | ~ class_Divides_Osemiring__div(U_2619) ),
    inference(variable_rename,[status(thm)],[f_783_1]) ).

fof(f_783_3,plain,
    ! [U_2619,U_2620,U_2621,U_2622] :
      ( c_Divides_Odiv__class_Omod(U_2619,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2619),U_2620),c_Divides_Odiv__class_Omod(U_2619,U_2621,U_2622)),U_2622) = c_Divides_Odiv__class_Omod(U_2619,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2619),U_2620),U_2621),U_2622)
      | ~ class_Divides_Osemiring__div(U_2619) ),
    inference(definitional_conversion,[status(esa)],[f_783_2]) ).

cnf(f_783_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2619,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2619),U_2620),c_Divides_Odiv__class_Omod(U_2619,U_2621,U_2622)),U_2622) = c_Divides_Odiv__class_Omod(U_2619,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2619),U_2620),U_2621),U_2622)
    | ~ class_Divides_Osemiring__div(U_2619) ),
    inference(clausify,[status(thm)],[f_783_3]) ).

fof(f_784_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_784_2,plain,
    ! [U_2626,U_2625,U_2624,U_2623] :
      ( c_Divides_Odiv__class_Omod(U_2623,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2623),U_2624),U_2625),U_2626) = c_Divides_Odiv__class_Omod(U_2623,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2623),c_Divides_Odiv__class_Omod(U_2623,U_2624,U_2626)),c_Divides_Odiv__class_Omod(U_2623,U_2625,U_2626)),U_2626)
      | ~ class_Divides_Osemiring__div(U_2623) ),
    inference(variable_rename,[status(thm)],[f_784_1]) ).

fof(f_784_3,plain,
    ! [U_2623,U_2624,U_2625,U_2626] :
      ( c_Divides_Odiv__class_Omod(U_2623,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2623),U_2624),U_2625),U_2626) = c_Divides_Odiv__class_Omod(U_2623,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2623),c_Divides_Odiv__class_Omod(U_2623,U_2624,U_2626)),c_Divides_Odiv__class_Omod(U_2623,U_2625,U_2626)),U_2626)
      | ~ class_Divides_Osemiring__div(U_2623) ),
    inference(definitional_conversion,[status(esa)],[f_784_2]) ).

cnf(f_784_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2623,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2623),U_2624),U_2625),U_2626) = c_Divides_Odiv__class_Omod(U_2623,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2623),c_Divides_Odiv__class_Omod(U_2623,U_2624,U_2626)),c_Divides_Odiv__class_Omod(U_2623,U_2625,U_2626)),U_2626)
    | ~ class_Divides_Osemiring__div(U_2623) ),
    inference(clausify,[status(thm)],[f_784_3]) ).

fof(f_785_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_785_2,plain,
    ! [U_2630,U_2629,U_2628,U_2627] :
      ( c_Divides_Odiv__class_Omod(U_2627,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2627),U_2628),U_2629),U_2630) = c_Divides_Odiv__class_Omod(U_2627,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2627),c_Divides_Odiv__class_Omod(U_2627,U_2628,U_2630)),U_2629),U_2630)
      | ~ class_Divides_Osemiring__div(U_2627) ),
    inference(variable_rename,[status(thm)],[f_785_1]) ).

fof(f_785_3,plain,
    ! [U_2627,U_2628,U_2629,U_2630] :
      ( c_Divides_Odiv__class_Omod(U_2627,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2627),U_2628),U_2629),U_2630) = c_Divides_Odiv__class_Omod(U_2627,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2627),c_Divides_Odiv__class_Omod(U_2627,U_2628,U_2630)),U_2629),U_2630)
      | ~ class_Divides_Osemiring__div(U_2627) ),
    inference(definitional_conversion,[status(esa)],[f_785_2]) ).

cnf(f_785_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2627,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2627),U_2628),U_2629),U_2630) = c_Divides_Odiv__class_Omod(U_2627,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2627),c_Divides_Odiv__class_Omod(U_2627,U_2628,U_2630)),U_2629),U_2630)
    | ~ class_Divides_Osemiring__div(U_2627) ),
    inference(clausify,[status(thm)],[f_785_3]) ).

fof(f_786_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_786_2,plain,
    ! [U_2634,U_2633,U_2632,U_2631] :
      ( c_Divides_Odiv__class_Omod(U_2631,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2631),U_2632),U_2633),U_2634) = c_Divides_Odiv__class_Omod(U_2631,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2631),U_2632),c_Divides_Odiv__class_Omod(U_2631,U_2633,U_2634)),U_2634)
      | ~ class_Divides_Osemiring__div(U_2631) ),
    inference(variable_rename,[status(thm)],[f_786_1]) ).

fof(f_786_3,plain,
    ! [U_2631,U_2632,U_2633,U_2634] :
      ( c_Divides_Odiv__class_Omod(U_2631,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2631),U_2632),U_2633),U_2634) = c_Divides_Odiv__class_Omod(U_2631,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2631),U_2632),c_Divides_Odiv__class_Omod(U_2631,U_2633,U_2634)),U_2634)
      | ~ class_Divides_Osemiring__div(U_2631) ),
    inference(definitional_conversion,[status(esa)],[f_786_2]) ).

cnf(f_786_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2631,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2631),U_2632),U_2633),U_2634) = c_Divides_Odiv__class_Omod(U_2631,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2631),U_2632),c_Divides_Odiv__class_Omod(U_2631,U_2633,U_2634)),U_2634)
    | ~ class_Divides_Osemiring__div(U_2631) ),
    inference(clausify,[status(thm)],[f_786_3]) ).

fof(f_787_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_787_2,plain,
    ! [U_2637,U_2636,U_2635] :
      ( c_Divides_Odiv__class_Omod(U_2635,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2635),U_2636),U_2637),U_2636) = c_Divides_Odiv__class_Omod(U_2635,U_2637,U_2636)
      | ~ class_Divides_Osemiring__div(U_2635) ),
    inference(variable_rename,[status(thm)],[f_787_1]) ).

fof(f_787_3,plain,
    ! [U_2635,U_2636,U_2637] :
      ( c_Divides_Odiv__class_Omod(U_2635,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2635),U_2636),U_2637),U_2636) = c_Divides_Odiv__class_Omod(U_2635,U_2637,U_2636)
      | ~ class_Divides_Osemiring__div(U_2635) ),
    inference(definitional_conversion,[status(esa)],[f_787_2]) ).

cnf(f_787_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2635,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2635),U_2636),U_2637),U_2636) = c_Divides_Odiv__class_Omod(U_2635,U_2637,U_2636)
    | ~ class_Divides_Osemiring__div(U_2635) ),
    inference(clausify,[status(thm)],[f_787_3]) ).

fof(f_788_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_788_2,plain,
    ! [U_2640,U_2639,U_2638] :
      ( c_Divides_Odiv__class_Omod(U_2638,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2638),U_2639),U_2640),U_2640) = c_Divides_Odiv__class_Omod(U_2638,U_2639,U_2640)
      | ~ class_Divides_Osemiring__div(U_2638) ),
    inference(variable_rename,[status(thm)],[f_788_1]) ).

fof(f_788_3,plain,
    ! [U_2638,U_2639,U_2640] :
      ( c_Divides_Odiv__class_Omod(U_2638,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2638),U_2639),U_2640),U_2640) = c_Divides_Odiv__class_Omod(U_2638,U_2639,U_2640)
      | ~ class_Divides_Osemiring__div(U_2638) ),
    inference(definitional_conversion,[status(esa)],[f_788_2]) ).

cnf(f_788_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2638,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2638),U_2639),U_2640),U_2640) = c_Divides_Odiv__class_Omod(U_2638,U_2639,U_2640)
    | ~ class_Divides_Osemiring__div(U_2638) ),
    inference(clausify,[status(thm)],[f_788_3]) ).

fof(f_789_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_789_2,plain,
    ! [U_2644,U_2643,U_2642,U_2641] :
      ( c_Divides_Odiv__class_Omod(U_2641,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2641),U_2642),U_2643),U_2644) = c_Divides_Odiv__class_Omod(U_2641,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2641),U_2642),c_Divides_Odiv__class_Omod(U_2641,U_2643,U_2644)),U_2644)
      | ~ class_Divides_Osemiring__div(U_2641) ),
    inference(variable_rename,[status(thm)],[f_789_1]) ).

fof(f_789_3,plain,
    ! [U_2641,U_2642,U_2643,U_2644] :
      ( c_Divides_Odiv__class_Omod(U_2641,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2641),U_2642),U_2643),U_2644) = c_Divides_Odiv__class_Omod(U_2641,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2641),U_2642),c_Divides_Odiv__class_Omod(U_2641,U_2643,U_2644)),U_2644)
      | ~ class_Divides_Osemiring__div(U_2641) ),
    inference(definitional_conversion,[status(esa)],[f_789_2]) ).

cnf(f_789_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2641,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2641),U_2642),U_2643),U_2644) = c_Divides_Odiv__class_Omod(U_2641,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2641),U_2642),c_Divides_Odiv__class_Omod(U_2641,U_2643,U_2644)),U_2644)
    | ~ class_Divides_Osemiring__div(U_2641) ),
    inference(clausify,[status(thm)],[f_789_3]) ).

fof(f_790_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_790_2,plain,
    ! [U_2648,U_2647,U_2646,U_2645] :
      ( c_Divides_Odiv__class_Omod(U_2645,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2645),U_2646),U_2647),U_2648) = c_Divides_Odiv__class_Omod(U_2645,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2645),c_Divides_Odiv__class_Omod(U_2645,U_2646,U_2648)),U_2647),U_2648)
      | ~ class_Divides_Osemiring__div(U_2645) ),
    inference(variable_rename,[status(thm)],[f_790_1]) ).

fof(f_790_3,plain,
    ! [U_2645,U_2646,U_2647,U_2648] :
      ( c_Divides_Odiv__class_Omod(U_2645,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2645),U_2646),U_2647),U_2648) = c_Divides_Odiv__class_Omod(U_2645,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2645),c_Divides_Odiv__class_Omod(U_2645,U_2646,U_2648)),U_2647),U_2648)
      | ~ class_Divides_Osemiring__div(U_2645) ),
    inference(definitional_conversion,[status(esa)],[f_790_2]) ).

cnf(f_790_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2645,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2645),U_2646),U_2647),U_2648) = c_Divides_Odiv__class_Omod(U_2645,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2645),c_Divides_Odiv__class_Omod(U_2645,U_2646,U_2648)),U_2647),U_2648)
    | ~ class_Divides_Osemiring__div(U_2645) ),
    inference(clausify,[status(thm)],[f_790_3]) ).

fof(f_791_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_791_2,plain,
    ! [U_2652,U_2651,U_2650,U_2649] :
      ( c_Divides_Odiv__class_Omod(U_2649,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2649),U_2650),U_2651),U_2652) = c_Divides_Odiv__class_Omod(U_2649,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2649),c_Divides_Odiv__class_Omod(U_2649,U_2650,U_2652)),c_Divides_Odiv__class_Omod(U_2649,U_2651,U_2652)),U_2652)
      | ~ class_Divides_Osemiring__div(U_2649) ),
    inference(variable_rename,[status(thm)],[f_791_1]) ).

fof(f_791_3,plain,
    ! [U_2649,U_2650,U_2651,U_2652] :
      ( c_Divides_Odiv__class_Omod(U_2649,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2649),U_2650),U_2651),U_2652) = c_Divides_Odiv__class_Omod(U_2649,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2649),c_Divides_Odiv__class_Omod(U_2649,U_2650,U_2652)),c_Divides_Odiv__class_Omod(U_2649,U_2651,U_2652)),U_2652)
      | ~ class_Divides_Osemiring__div(U_2649) ),
    inference(definitional_conversion,[status(esa)],[f_791_2]) ).

cnf(f_791_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2649,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2649),U_2650),U_2651),U_2652) = c_Divides_Odiv__class_Omod(U_2649,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2649),c_Divides_Odiv__class_Omod(U_2649,U_2650,U_2652)),c_Divides_Odiv__class_Omod(U_2649,U_2651,U_2652)),U_2652)
    | ~ class_Divides_Osemiring__div(U_2649) ),
    inference(clausify,[status(thm)],[f_791_3]) ).

fof(f_792_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_792_2,plain,
    ! [U_2656,U_2655,U_2654,U_2653] :
      ( c_Divides_Odiv__class_Omod(U_2653,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2653),U_2654),U_2655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2653),U_2654),U_2656)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2653),U_2654),c_Divides_Odiv__class_Omod(U_2653,U_2655,U_2656))
      | ~ class_Divides_Osemiring__div(U_2653) ),
    inference(variable_rename,[status(thm)],[f_792_1]) ).

fof(f_792_3,plain,
    ! [U_2653,U_2654,U_2655,U_2656] :
      ( c_Divides_Odiv__class_Omod(U_2653,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2653),U_2654),U_2655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2653),U_2654),U_2656)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2653),U_2654),c_Divides_Odiv__class_Omod(U_2653,U_2655,U_2656))
      | ~ class_Divides_Osemiring__div(U_2653) ),
    inference(definitional_conversion,[status(esa)],[f_792_2]) ).

cnf(f_792_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2653,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2653),U_2654),U_2655),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2653),U_2654),U_2656)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2653),U_2654),c_Divides_Odiv__class_Omod(U_2653,U_2655,U_2656))
    | ~ class_Divides_Osemiring__div(U_2653) ),
    inference(clausify,[status(thm)],[f_792_3]) ).

fof(f_793_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_793_2,plain,
    ! [U_2660,U_2659,U_2658,U_2657] :
      ( c_Divides_Odiv__class_Omod(U_2657,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2657),U_2658),U_2659),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2657),U_2660),U_2659)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2657),c_Divides_Odiv__class_Omod(U_2657,U_2658,U_2660)),U_2659)
      | ~ class_Divides_Osemiring__div(U_2657) ),
    inference(variable_rename,[status(thm)],[f_793_1]) ).

fof(f_793_3,plain,
    ! [U_2657,U_2658,U_2659,U_2660] :
      ( c_Divides_Odiv__class_Omod(U_2657,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2657),U_2658),U_2659),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2657),U_2660),U_2659)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2657),c_Divides_Odiv__class_Omod(U_2657,U_2658,U_2660)),U_2659)
      | ~ class_Divides_Osemiring__div(U_2657) ),
    inference(definitional_conversion,[status(esa)],[f_793_2]) ).

cnf(f_793_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2657,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2657),U_2658),U_2659),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2657),U_2660),U_2659)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2657),c_Divides_Odiv__class_Omod(U_2657,U_2658,U_2660)),U_2659)
    | ~ class_Divides_Osemiring__div(U_2657) ),
    inference(clausify,[status(thm)],[f_793_3]) ).

fof(f_794_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_794_2,plain,
    ! [U_2664,U_2663,U_2662,U_2661] :
      ( c_Divides_Odiv__class_Omod(U_2661,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2661),c_Divides_Odiv__class_Omod(U_2661,U_2662,U_2663)),U_2664),U_2663) = c_Divides_Odiv__class_Omod(U_2661,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2661),U_2662),U_2664),U_2663)
      | ~ class_Divides_Osemiring__div(U_2661) ),
    inference(variable_rename,[status(thm)],[f_794_1]) ).

fof(f_794_3,plain,
    ! [U_2661,U_2662,U_2663,U_2664] :
      ( c_Divides_Odiv__class_Omod(U_2661,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2661),c_Divides_Odiv__class_Omod(U_2661,U_2662,U_2663)),U_2664),U_2663) = c_Divides_Odiv__class_Omod(U_2661,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2661),U_2662),U_2664),U_2663)
      | ~ class_Divides_Osemiring__div(U_2661) ),
    inference(definitional_conversion,[status(esa)],[f_794_2]) ).

cnf(f_794_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2661,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2661),c_Divides_Odiv__class_Omod(U_2661,U_2662,U_2663)),U_2664),U_2663) = c_Divides_Odiv__class_Omod(U_2661,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2661),U_2662),U_2664),U_2663)
    | ~ class_Divides_Osemiring__div(U_2661) ),
    inference(clausify,[status(thm)],[f_794_3]) ).

fof(f_795_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_795_2,plain,
    ! [U_2670,U_2669,U_2668,U_2667,U_2666,U_2665] :
      ( c_Divides_Odiv__class_Omod(U_2665,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2665),U_2666),U_2669),U_2667) = c_Divides_Odiv__class_Omod(U_2665,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2665),U_2668),U_2670),U_2667)
      | c_Divides_Odiv__class_Omod(U_2665,U_2669,U_2667) != c_Divides_Odiv__class_Omod(U_2665,U_2670,U_2667)
      | c_Divides_Odiv__class_Omod(U_2665,U_2666,U_2667) != c_Divides_Odiv__class_Omod(U_2665,U_2668,U_2667)
      | ~ class_Divides_Osemiring__div(U_2665) ),
    inference(variable_rename,[status(thm)],[f_795_1]) ).

fof(f_795_3,plain,
    ! [U_2665,U_2666,U_2667,U_2668,U_2669,U_2670] :
      ( c_Divides_Odiv__class_Omod(U_2665,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2665),U_2666),U_2669),U_2667) = c_Divides_Odiv__class_Omod(U_2665,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2665),U_2668),U_2670),U_2667)
      | c_Divides_Odiv__class_Omod(U_2665,U_2669,U_2667) != c_Divides_Odiv__class_Omod(U_2665,U_2670,U_2667)
      | c_Divides_Odiv__class_Omod(U_2665,U_2666,U_2667) != c_Divides_Odiv__class_Omod(U_2665,U_2668,U_2667)
      | ~ class_Divides_Osemiring__div(U_2665) ),
    inference(definitional_conversion,[status(esa)],[f_795_2]) ).

cnf(f_795_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2665,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2665),U_2666),U_2669),U_2667) = c_Divides_Odiv__class_Omod(U_2665,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2665),U_2668),U_2670),U_2667)
    | c_Divides_Odiv__class_Omod(U_2665,U_2669,U_2667) != c_Divides_Odiv__class_Omod(U_2665,U_2670,U_2667)
    | c_Divides_Odiv__class_Omod(U_2665,U_2666,U_2667) != c_Divides_Odiv__class_Omod(U_2665,U_2668,U_2667)
    | ~ class_Divides_Osemiring__div(U_2665) ),
    inference(clausify,[status(thm)],[f_795_3]) ).

fof(f_796_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_796_2,plain,
    ! [U_2673,U_2672,U_2671] :
      ( c_Divides_Odiv__class_Omod(U_2671,hAPP(c_Groups_Ouminus__class_Ouminus(U_2671),U_2672),U_2673) = c_Divides_Odiv__class_Omod(U_2671,hAPP(c_Groups_Ouminus__class_Ouminus(U_2671),c_Divides_Odiv__class_Omod(U_2671,U_2672,U_2673)),U_2673)
      | ~ class_Divides_Oring__div(U_2671) ),
    inference(variable_rename,[status(thm)],[f_796_1]) ).

fof(f_796_3,plain,
    ! [U_2671,U_2672,U_2673] :
      ( c_Divides_Odiv__class_Omod(U_2671,hAPP(c_Groups_Ouminus__class_Ouminus(U_2671),U_2672),U_2673) = c_Divides_Odiv__class_Omod(U_2671,hAPP(c_Groups_Ouminus__class_Ouminus(U_2671),c_Divides_Odiv__class_Omod(U_2671,U_2672,U_2673)),U_2673)
      | ~ class_Divides_Oring__div(U_2671) ),
    inference(definitional_conversion,[status(esa)],[f_796_2]) ).

cnf(f_796_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2671,hAPP(c_Groups_Ouminus__class_Ouminus(U_2671),U_2672),U_2673) = c_Divides_Odiv__class_Omod(U_2671,hAPP(c_Groups_Ouminus__class_Ouminus(U_2671),c_Divides_Odiv__class_Omod(U_2671,U_2672,U_2673)),U_2673)
    | ~ class_Divides_Oring__div(U_2671) ),
    inference(clausify,[status(thm)],[f_796_3]) ).

fof(f_797_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_797_2,plain,
    ! [U_2677,U_2676,U_2675,U_2674] :
      ( c_Divides_Odiv__class_Omod(U_2674,hAPP(c_Groups_Ouminus__class_Ouminus(U_2674),U_2675),U_2676) = c_Divides_Odiv__class_Omod(U_2674,hAPP(c_Groups_Ouminus__class_Ouminus(U_2674),U_2677),U_2676)
      | c_Divides_Odiv__class_Omod(U_2674,U_2675,U_2676) != c_Divides_Odiv__class_Omod(U_2674,U_2677,U_2676)
      | ~ class_Divides_Oring__div(U_2674) ),
    inference(variable_rename,[status(thm)],[f_797_1]) ).

fof(f_797_3,plain,
    ! [U_2674,U_2675,U_2676,U_2677] :
      ( c_Divides_Odiv__class_Omod(U_2674,hAPP(c_Groups_Ouminus__class_Ouminus(U_2674),U_2675),U_2676) = c_Divides_Odiv__class_Omod(U_2674,hAPP(c_Groups_Ouminus__class_Ouminus(U_2674),U_2677),U_2676)
      | c_Divides_Odiv__class_Omod(U_2674,U_2675,U_2676) != c_Divides_Odiv__class_Omod(U_2674,U_2677,U_2676)
      | ~ class_Divides_Oring__div(U_2674) ),
    inference(definitional_conversion,[status(esa)],[f_797_2]) ).

cnf(f_797_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2674,hAPP(c_Groups_Ouminus__class_Ouminus(U_2674),U_2675),U_2676) = c_Divides_Odiv__class_Omod(U_2674,hAPP(c_Groups_Ouminus__class_Ouminus(U_2674),U_2677),U_2676)
    | c_Divides_Odiv__class_Omod(U_2674,U_2675,U_2676) != c_Divides_Odiv__class_Omod(U_2674,U_2677,U_2676)
    | ~ class_Divides_Oring__div(U_2674) ),
    inference(clausify,[status(thm)],[f_797_3]) ).

fof(f_798_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_798_2,plain,
    ! [U_2678] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2678) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_798_1]) ).

fof(f_798_3,plain,
    ! [U_2678] : c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2678) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_798_2]) ).

cnf(f_798_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_2678) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_798_3]) ).

fof(f_799_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_799_2,plain,
    ! [U_2679] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2679,U_2679) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_799_1]) ).

fof(f_799_3,plain,
    ! [U_2679] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2679,U_2679) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_799_2]) ).

cnf(f_799_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2679,U_2679) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_799_3]) ).

fof(f_800_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_800_2,plain,
    ! [U_2682,U_2681,U_2680] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2680),U_2681),U_2682) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2680),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2681,U_2682)),U_2682),
    inference(variable_rename,[status(thm)],[f_800_1]) ).

fof(f_800_3,plain,
    ! [U_2680,U_2681,U_2682] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2680),U_2681),U_2682) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2680),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2681,U_2682)),U_2682),
    inference(definitional_conversion,[status(esa)],[f_800_2]) ).

cnf(f_800_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2680),U_2681),U_2682) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2680),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2681,U_2682)),U_2682),
    inference(clausify,[status(thm)],[f_800_3]) ).

fof(f_801_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_801_2,plain,
    ! [U_2685,U_2684,U_2683] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2683),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2684,U_2685)),U_2685) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2683),U_2684),U_2685),
    inference(variable_rename,[status(thm)],[f_801_1]) ).

fof(f_801_3,plain,
    ! [U_2683,U_2684,U_2685] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2683),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2684,U_2685)),U_2685) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2683),U_2684),U_2685),
    inference(definitional_conversion,[status(esa)],[f_801_2]) ).

cnf(f_801_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2683),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2684,U_2685)),U_2685) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2683),U_2684),U_2685),
    inference(clausify,[status(thm)],[f_801_3]) ).

fof(f_802_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_802_2,plain,
    ! [U_2687,U_2686] : 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_2686,U_2687)),U_2687) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2686),U_2687),
    inference(variable_rename,[status(thm)],[f_802_1]) ).

fof(f_802_3,plain,
    ! [U_2686,U_2687] : 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_2686,U_2687)),U_2687) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2686),U_2687),
    inference(definitional_conversion,[status(esa)],[f_802_2]) ).

cnf(f_802_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_2686,U_2687)),U_2687) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2686),U_2687),
    inference(clausify,[status(thm)],[f_802_3]) ).

fof(f_803_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_803_2,plain,
    ! [U_2689,U_2688] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2688),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2689)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2688,U_2689)),
    inference(variable_rename,[status(thm)],[f_803_1]) ).

fof(f_803_3,plain,
    ! [U_2688,U_2689] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2688),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2689)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2688,U_2689)),
    inference(definitional_conversion,[status(esa)],[f_803_2]) ).

cnf(f_803_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2688),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2689)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2688,U_2689)),
    inference(clausify,[status(thm)],[f_803_3]) ).

fof(f_804_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_804_2,plain,
    ! [U_2691,U_2690] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2690,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2691)) = 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_2690),U_2691)),
    inference(variable_rename,[status(thm)],[f_804_1]) ).

fof(f_804_3,plain,
    ! [U_2690,U_2691] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2690,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2691)) = 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_2690),U_2691)),
    inference(definitional_conversion,[status(esa)],[f_804_2]) ).

cnf(f_804_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2690,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2691)) = 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_2690),U_2691)),
    inference(clausify,[status(thm)],[f_804_3]) ).

fof(f_805_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_805_2,plain,
    ! [U_2694,U_2693,U_2692] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_2692,U_2693,U_2694)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_2694)) )
      & ( hBOOL(hAPP(c_Com_OWT,U_2694))
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_2692,U_2693,U_2694))) ) ),
    inference(variable_rename,[status(thm)],[f_805_1]) ).

fof(f_805_3,plain,
    ( ! [U_2700] :
        ( ! [U_2698,U_2696] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_2696,U_2698,U_2700)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_2700)) )
    & ! [U_2699] :
        ( ! [U_2697,U_2695] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_2695,U_2697,U_2699)))
        | hBOOL(hAPP(c_Com_OWT,U_2699)) ) ),
    inference(miniscope,[status(thm)],[f_805_2]) ).

fof(f_805_4,plain,
    ( ! [U_2696,U_2700,U_2698] :
        ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_2696,U_2698,U_2700)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_2700)) )
    & ! [U_2699,U_2697,U_2695] :
        ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_2695,U_2697,U_2699)))
        | hBOOL(hAPP(c_Com_OWT,U_2699)) ) ),
    inference(definitional_conversion,[status(esa)],[f_805_3]) ).

cnf(f_805_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_2695,U_2697,U_2699)))
    | hBOOL(hAPP(c_Com_OWT,U_2699)) ),
    inference(clausify,[status(thm)],[f_805_4]) ).

cnf(f_805_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_2696,U_2698,U_2700)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_2700)) ),
    inference(clausify,[status(thm)],[f_805_4]) ).

fof(f_806_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_806_2,plain,
    ! [U_2703,U_2702,U_2701] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_2702,U_2703,U_2701)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_2701)) ),
    inference(variable_rename,[status(thm)],[f_806_1]) ).

fof(f_806_3,plain,
    ! [U_2701,U_2702,U_2703] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_2702,U_2703,U_2701)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_2701)) ),
    inference(definitional_conversion,[status(esa)],[f_806_2]) ).

cnf(f_806_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(U_2702,U_2703,U_2701)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_2701)) ),
    inference(clausify,[status(thm)],[f_806_3]) ).

fof(f_807_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_807_2,plain,
    ! [U_2709,U_2708,U_2707,U_2706,U_2705,U_2704] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_2704,U_2705,U_2706),U_2707,U_2708,U_2709)
        | ( ( ~ c_Natural_Oevaln(U_2706,U_2707,U_2708,U_2709)
            | hBOOL(hAPP(U_2704,U_2707)) )
          & ( ~ c_Natural_Oevaln(U_2705,U_2707,U_2708,U_2709)
            | ~ hBOOL(hAPP(U_2704,U_2707)) ) ) )
      & ( ( c_Natural_Oevaln(U_2706,U_2707,U_2708,U_2709)
          & ~ hBOOL(hAPP(U_2704,U_2707)) )
        | ( c_Natural_Oevaln(U_2705,U_2707,U_2708,U_2709)
          & hBOOL(hAPP(U_2704,U_2707)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_2704,U_2705,U_2706),U_2707,U_2708,U_2709) ) ),
    inference(variable_rename,[status(thm)],[f_807_1]) ).

fof(f_807_3,plain,
    ( ! [U_2721,U_2719,U_2717,U_2715,U_2713,U_2711] :
        ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_2711,U_2713,U_2715),U_2717,U_2719,U_2721)
        | ( ( ~ c_Natural_Oevaln(U_2715,U_2717,U_2719,U_2721)
            | hBOOL(hAPP(U_2711,U_2717)) )
          & ( ~ c_Natural_Oevaln(U_2713,U_2717,U_2719,U_2721)
            | ~ hBOOL(hAPP(U_2711,U_2717)) ) ) )
    & ! [U_2720,U_2718,U_2716,U_2714,U_2712,U_2710] :
        ( ( c_Natural_Oevaln(U_2714,U_2716,U_2718,U_2720)
          & ~ hBOOL(hAPP(U_2710,U_2716)) )
        | ( c_Natural_Oevaln(U_2712,U_2716,U_2718,U_2720)
          & hBOOL(hAPP(U_2710,U_2716)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_2710,U_2712,U_2714),U_2716,U_2718,U_2720) ) ),
    inference(miniscope,[status(thm)],[f_807_2]) ).

fof(f_807_4,plain,
    ( ! [U_2719,U_2717,U_2713,U_2715,U_2711,U_2721] :
        ( ~ c_Natural_Oevaln(U_2715,U_2717,U_2719,U_2721)
        | hBOOL(hAPP(U_2711,U_2717))
        | ~ sP224(U_2719,U_2717,U_2713,U_2715,U_2711,U_2721) )
    & ! [U_2719,U_2717,U_2713,U_2715,U_2711,U_2721] :
        ( ~ c_Natural_Oevaln(U_2713,U_2717,U_2719,U_2721)
        | ~ hBOOL(hAPP(U_2711,U_2717))
        | ~ sP224(U_2719,U_2717,U_2713,U_2715,U_2711,U_2721) )
    & ! [U_2714,U_2718,U_2720,U_2710,U_2716] :
        ( c_Natural_Oevaln(U_2714,U_2716,U_2718,U_2720)
        | ~ sP223(U_2714,U_2718,U_2720,U_2710,U_2716) )
    & ! [U_2714,U_2718,U_2720,U_2710,U_2716] :
        ( ~ hBOOL(hAPP(U_2710,U_2716))
        | ~ sP223(U_2714,U_2718,U_2720,U_2710,U_2716) )
    & ! [U_2718,U_2712,U_2720,U_2710,U_2716] :
        ( c_Natural_Oevaln(U_2712,U_2716,U_2718,U_2720)
        | ~ sP222(U_2718,U_2712,U_2720,U_2710,U_2716) )
    & ! [U_2718,U_2712,U_2720,U_2710,U_2716] :
        ( hBOOL(hAPP(U_2710,U_2716))
        | ~ sP222(U_2718,U_2712,U_2720,U_2710,U_2716) )
    & ! [U_2719,U_2717,U_2713,U_2715,U_2711,U_2721] :
        ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_2711,U_2713,U_2715),U_2717,U_2719,U_2721)
        | sP224(U_2719,U_2717,U_2713,U_2715,U_2711,U_2721) )
    & ! [U_2714,U_2718,U_2712,U_2720,U_2710,U_2716] :
        ( sP223(U_2714,U_2718,U_2720,U_2710,U_2716)
        | sP222(U_2718,U_2712,U_2720,U_2710,U_2716)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_2710,U_2712,U_2714),U_2716,U_2718,U_2720) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP222,sP223,sP224])],[f_807_3]) ).

cnf(f_807_5,plain,
    ( sP223(U_2714,U_2718,U_2720,U_2710,U_2716)
    | sP222(U_2718,U_2712,U_2720,U_2710,U_2716)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_2710,U_2712,U_2714),U_2716,U_2718,U_2720) ),
    inference(clausify,[status(thm)],[f_807_4]) ).

cnf(f_807_6,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_2711,U_2713,U_2715),U_2717,U_2719,U_2721)
    | sP224(U_2719,U_2717,U_2713,U_2715,U_2711,U_2721) ),
    inference(clausify,[status(thm)],[f_807_4]) ).

cnf(f_807_7,plain,
    ( hBOOL(hAPP(U_2710,U_2716))
    | ~ sP222(U_2718,U_2712,U_2720,U_2710,U_2716) ),
    inference(clausify,[status(thm)],[f_807_4]) ).

cnf(f_807_8,plain,
    ( c_Natural_Oevaln(U_2712,U_2716,U_2718,U_2720)
    | ~ sP222(U_2718,U_2712,U_2720,U_2710,U_2716) ),
    inference(clausify,[status(thm)],[f_807_4]) ).

cnf(f_807_9,plain,
    ( ~ hBOOL(hAPP(U_2710,U_2716))
    | ~ sP223(U_2714,U_2718,U_2720,U_2710,U_2716) ),
    inference(clausify,[status(thm)],[f_807_4]) ).

cnf(f_807_10,plain,
    ( c_Natural_Oevaln(U_2714,U_2716,U_2718,U_2720)
    | ~ sP223(U_2714,U_2718,U_2720,U_2710,U_2716) ),
    inference(clausify,[status(thm)],[f_807_4]) ).

cnf(f_807_11,plain,
    ( ~ c_Natural_Oevaln(U_2713,U_2717,U_2719,U_2721)
    | ~ hBOOL(hAPP(U_2711,U_2717))
    | ~ sP224(U_2719,U_2717,U_2713,U_2715,U_2711,U_2721) ),
    inference(clausify,[status(thm)],[f_807_4]) ).

cnf(f_807_12,plain,
    ( ~ c_Natural_Oevaln(U_2715,U_2717,U_2719,U_2721)
    | hBOOL(hAPP(U_2711,U_2717))
    | ~ sP224(U_2719,U_2717,U_2713,U_2715,U_2711,U_2721) ),
    inference(clausify,[status(thm)],[f_807_4]) ).

fof(f_808_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_808_2,plain,
    ! [U_2727,U_2726,U_2725,U_2724,U_2723,U_2722] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_2722,U_2723,U_2724),U_2725,U_2726,U_2727)
        | ( ( ~ c_Natural_Oevaln(U_2724,U_2725,U_2726,U_2727)
            | hBOOL(hAPP(U_2722,U_2725)) )
          & ( ~ c_Natural_Oevaln(U_2723,U_2725,U_2726,U_2727)
            | ~ hBOOL(hAPP(U_2722,U_2725)) ) ) )
      & ( ( c_Natural_Oevaln(U_2724,U_2725,U_2726,U_2727)
          & ~ hBOOL(hAPP(U_2722,U_2725)) )
        | ( c_Natural_Oevaln(U_2723,U_2725,U_2726,U_2727)
          & hBOOL(hAPP(U_2722,U_2725)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_2722,U_2723,U_2724),U_2725,U_2726,U_2727) ) ),
    inference(variable_rename,[status(thm)],[f_808_1]) ).

fof(f_808_3,plain,
    ( ! [U_2739,U_2737,U_2735,U_2733,U_2731,U_2729] :
        ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_2729,U_2731,U_2733),U_2735,U_2737,U_2739)
        | ( ( ~ c_Natural_Oevaln(U_2733,U_2735,U_2737,U_2739)
            | hBOOL(hAPP(U_2729,U_2735)) )
          & ( ~ c_Natural_Oevaln(U_2731,U_2735,U_2737,U_2739)
            | ~ hBOOL(hAPP(U_2729,U_2735)) ) ) )
    & ! [U_2738,U_2736,U_2734,U_2732,U_2730,U_2728] :
        ( ( c_Natural_Oevaln(U_2732,U_2734,U_2736,U_2738)
          & ~ hBOOL(hAPP(U_2728,U_2734)) )
        | ( c_Natural_Oevaln(U_2730,U_2734,U_2736,U_2738)
          & hBOOL(hAPP(U_2728,U_2734)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_2728,U_2730,U_2732),U_2734,U_2736,U_2738) ) ),
    inference(miniscope,[status(thm)],[f_808_2]) ).

fof(f_808_4,plain,
    ( ! [U_2735,U_2733,U_2731,U_2729,U_2737,U_2739] :
        ( ~ c_Natural_Oevaln(U_2733,U_2735,U_2737,U_2739)
        | hBOOL(hAPP(U_2729,U_2735))
        | ~ sP227(U_2735,U_2733,U_2731,U_2729,U_2737,U_2739) )
    & ! [U_2735,U_2733,U_2731,U_2729,U_2737,U_2739] :
        ( ~ c_Natural_Oevaln(U_2731,U_2735,U_2737,U_2739)
        | ~ hBOOL(hAPP(U_2729,U_2735))
        | ~ sP227(U_2735,U_2733,U_2731,U_2729,U_2737,U_2739) )
    & ! [U_2734,U_2728,U_2732,U_2736,U_2738] :
        ( c_Natural_Oevaln(U_2732,U_2734,U_2736,U_2738)
        | ~ sP226(U_2734,U_2728,U_2732,U_2736,U_2738) )
    & ! [U_2734,U_2728,U_2732,U_2736,U_2738] :
        ( ~ hBOOL(hAPP(U_2728,U_2734))
        | ~ sP226(U_2734,U_2728,U_2732,U_2736,U_2738) )
    & ! [U_2734,U_2728,U_2736,U_2730,U_2738] :
        ( c_Natural_Oevaln(U_2730,U_2734,U_2736,U_2738)
        | ~ sP225(U_2734,U_2728,U_2736,U_2730,U_2738) )
    & ! [U_2734,U_2728,U_2736,U_2730,U_2738] :
        ( hBOOL(hAPP(U_2728,U_2734))
        | ~ sP225(U_2734,U_2728,U_2736,U_2730,U_2738) )
    & ! [U_2735,U_2733,U_2731,U_2729,U_2737,U_2739] :
        ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_2729,U_2731,U_2733),U_2735,U_2737,U_2739)
        | sP227(U_2735,U_2733,U_2731,U_2729,U_2737,U_2739) )
    & ! [U_2734,U_2728,U_2732,U_2736,U_2730,U_2738] :
        ( sP226(U_2734,U_2728,U_2732,U_2736,U_2738)
        | sP225(U_2734,U_2728,U_2736,U_2730,U_2738)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_2728,U_2730,U_2732),U_2734,U_2736,U_2738) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP225,sP226,sP227])],[f_808_3]) ).

cnf(f_808_5,plain,
    ( sP226(U_2734,U_2728,U_2732,U_2736,U_2738)
    | sP225(U_2734,U_2728,U_2736,U_2730,U_2738)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OCond(U_2728,U_2730,U_2732),U_2734,U_2736,U_2738) ),
    inference(clausify,[status(thm)],[f_808_4]) ).

cnf(f_808_6,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OCond(U_2729,U_2731,U_2733),U_2735,U_2737,U_2739)
    | sP227(U_2735,U_2733,U_2731,U_2729,U_2737,U_2739) ),
    inference(clausify,[status(thm)],[f_808_4]) ).

cnf(f_808_7,plain,
    ( hBOOL(hAPP(U_2728,U_2734))
    | ~ sP225(U_2734,U_2728,U_2736,U_2730,U_2738) ),
    inference(clausify,[status(thm)],[f_808_4]) ).

cnf(f_808_8,plain,
    ( c_Natural_Oevaln(U_2730,U_2734,U_2736,U_2738)
    | ~ sP225(U_2734,U_2728,U_2736,U_2730,U_2738) ),
    inference(clausify,[status(thm)],[f_808_4]) ).

cnf(f_808_9,plain,
    ( ~ hBOOL(hAPP(U_2728,U_2734))
    | ~ sP226(U_2734,U_2728,U_2732,U_2736,U_2738) ),
    inference(clausify,[status(thm)],[f_808_4]) ).

cnf(f_808_10,plain,
    ( c_Natural_Oevaln(U_2732,U_2734,U_2736,U_2738)
    | ~ sP226(U_2734,U_2728,U_2732,U_2736,U_2738) ),
    inference(clausify,[status(thm)],[f_808_4]) ).

cnf(f_808_11,plain,
    ( ~ c_Natural_Oevaln(U_2731,U_2735,U_2737,U_2739)
    | ~ hBOOL(hAPP(U_2729,U_2735))
    | ~ sP227(U_2735,U_2733,U_2731,U_2729,U_2737,U_2739) ),
    inference(clausify,[status(thm)],[f_808_4]) ).

cnf(f_808_12,plain,
    ( ~ c_Natural_Oevaln(U_2733,U_2735,U_2737,U_2739)
    | hBOOL(hAPP(U_2729,U_2735))
    | ~ sP227(U_2735,U_2733,U_2731,U_2729,U_2737,U_2739) ),
    inference(clausify,[status(thm)],[f_808_4]) ).

fof(f_809_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_809_2,plain,
    ! [U_2743,U_2742,U_2741,U_2740] : hAPP(c_Com_Ocom_OBODY,U_2740) != c_Com_Ocom_OLocal(U_2741,U_2742,U_2743),
    inference(variable_rename,[status(thm)],[f_809_1]) ).

fof(f_809_3,plain,
    ! [U_2740,U_2743,U_2741,U_2742] : hAPP(c_Com_Ocom_OBODY,U_2740) != c_Com_Ocom_OLocal(U_2741,U_2742,U_2743),
    inference(definitional_conversion,[status(esa)],[f_809_2]) ).

cnf(f_809_4,plain,
    hAPP(c_Com_Ocom_OBODY,U_2740) != c_Com_Ocom_OLocal(U_2741,U_2742,U_2743),
    inference(clausify,[status(thm)],[f_809_3]) ).

fof(f_810_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_810_2,plain,
    ! [U_2747,U_2746,U_2745,U_2744] : c_Com_Ocom_OLocal(U_2744,U_2745,U_2746) != hAPP(c_Com_Ocom_OBODY,U_2747),
    inference(variable_rename,[status(thm)],[f_810_1]) ).

fof(f_810_3,plain,
    ! [U_2746,U_2744,U_2745,U_2747] : c_Com_Ocom_OLocal(U_2744,U_2745,U_2746) != hAPP(c_Com_Ocom_OBODY,U_2747),
    inference(definitional_conversion,[status(esa)],[f_810_2]) ).

cnf(f_810_4,plain,
    c_Com_Ocom_OLocal(U_2744,U_2745,U_2746) != hAPP(c_Com_Ocom_OBODY,U_2747),
    inference(clausify,[status(thm)],[f_810_3]) ).

fof(f_811_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_811_2,plain,
    ! [U_2752,U_2751,U_2750,U_2749,U_2748] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2748,U_2749,U_2750)),U_2751),U_2752))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2750),U_2751),U_2752))
            | hBOOL(hAPP(U_2748,U_2751)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2749),U_2751),U_2752))
            | ~ hBOOL(hAPP(U_2748,U_2751)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2750),U_2751),U_2752))
          & ~ hBOOL(hAPP(U_2748,U_2751)) )
        | ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2749),U_2751),U_2752))
          & hBOOL(hAPP(U_2748,U_2751)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2748,U_2749,U_2750)),U_2751),U_2752)) ) ),
    inference(variable_rename,[status(thm)],[f_811_1]) ).

fof(f_811_3,plain,
    ( ! [U_2762,U_2760,U_2758,U_2756,U_2754] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2754,U_2756,U_2758)),U_2760),U_2762))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2758),U_2760),U_2762))
            | hBOOL(hAPP(U_2754,U_2760)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2756),U_2760),U_2762))
            | ~ hBOOL(hAPP(U_2754,U_2760)) ) ) )
    & ! [U_2761,U_2759,U_2757,U_2755,U_2753] :
        ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2757),U_2759),U_2761))
          & ~ hBOOL(hAPP(U_2753,U_2759)) )
        | ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2755),U_2759),U_2761))
          & hBOOL(hAPP(U_2753,U_2759)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2753,U_2755,U_2757)),U_2759),U_2761)) ) ),
    inference(miniscope,[status(thm)],[f_811_2]) ).

fof(f_811_4,plain,
    ( ! [U_2756,U_2754,U_2762,U_2758,U_2760] :
        ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2758),U_2760),U_2762))
        | hBOOL(hAPP(U_2754,U_2760))
        | ~ sP230(U_2756,U_2754,U_2762,U_2758,U_2760) )
    & ! [U_2756,U_2754,U_2762,U_2758,U_2760] :
        ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2756),U_2760),U_2762))
        | ~ hBOOL(hAPP(U_2754,U_2760))
        | ~ sP230(U_2756,U_2754,U_2762,U_2758,U_2760) )
    & ! [U_2759,U_2757,U_2753,U_2761] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2757),U_2759),U_2761))
        | ~ sP229(U_2759,U_2757,U_2753,U_2761) )
    & ! [U_2759,U_2757,U_2753,U_2761] :
        ( ~ hBOOL(hAPP(U_2753,U_2759))
        | ~ sP229(U_2759,U_2757,U_2753,U_2761) )
    & ! [U_2759,U_2753,U_2755,U_2761] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2755),U_2759),U_2761))
        | ~ sP228(U_2759,U_2753,U_2755,U_2761) )
    & ! [U_2759,U_2753,U_2755,U_2761] :
        ( hBOOL(hAPP(U_2753,U_2759))
        | ~ sP228(U_2759,U_2753,U_2755,U_2761) )
    & ! [U_2756,U_2754,U_2762,U_2758,U_2760] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2754,U_2756,U_2758)),U_2760),U_2762))
        | sP230(U_2756,U_2754,U_2762,U_2758,U_2760) )
    & ! [U_2759,U_2757,U_2753,U_2755,U_2761] :
        ( sP229(U_2759,U_2757,U_2753,U_2761)
        | sP228(U_2759,U_2753,U_2755,U_2761)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2753,U_2755,U_2757)),U_2759),U_2761)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP228,sP229,sP230])],[f_811_3]) ).

cnf(f_811_5,plain,
    ( sP229(U_2759,U_2757,U_2753,U_2761)
    | sP228(U_2759,U_2753,U_2755,U_2761)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2753,U_2755,U_2757)),U_2759),U_2761)) ),
    inference(clausify,[status(thm)],[f_811_4]) ).

cnf(f_811_6,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2754,U_2756,U_2758)),U_2760),U_2762))
    | sP230(U_2756,U_2754,U_2762,U_2758,U_2760) ),
    inference(clausify,[status(thm)],[f_811_4]) ).

cnf(f_811_7,plain,
    ( hBOOL(hAPP(U_2753,U_2759))
    | ~ sP228(U_2759,U_2753,U_2755,U_2761) ),
    inference(clausify,[status(thm)],[f_811_4]) ).

cnf(f_811_8,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2755),U_2759),U_2761))
    | ~ sP228(U_2759,U_2753,U_2755,U_2761) ),
    inference(clausify,[status(thm)],[f_811_4]) ).

cnf(f_811_9,plain,
    ( ~ hBOOL(hAPP(U_2753,U_2759))
    | ~ sP229(U_2759,U_2757,U_2753,U_2761) ),
    inference(clausify,[status(thm)],[f_811_4]) ).

cnf(f_811_10,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2757),U_2759),U_2761))
    | ~ sP229(U_2759,U_2757,U_2753,U_2761) ),
    inference(clausify,[status(thm)],[f_811_4]) ).

cnf(f_811_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2756),U_2760),U_2762))
    | ~ hBOOL(hAPP(U_2754,U_2760))
    | ~ sP230(U_2756,U_2754,U_2762,U_2758,U_2760) ),
    inference(clausify,[status(thm)],[f_811_4]) ).

cnf(f_811_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2758),U_2760),U_2762))
    | hBOOL(hAPP(U_2754,U_2760))
    | ~ sP230(U_2756,U_2754,U_2762,U_2758,U_2760) ),
    inference(clausify,[status(thm)],[f_811_4]) ).

fof(f_812_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_812_2,plain,
    ! [U_2767,U_2766,U_2765,U_2764,U_2763] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2763,U_2764,U_2765)),U_2766),U_2767))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2765),U_2766),U_2767))
            | hBOOL(hAPP(U_2763,U_2766)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2764),U_2766),U_2767))
            | ~ hBOOL(hAPP(U_2763,U_2766)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2765),U_2766),U_2767))
          & ~ hBOOL(hAPP(U_2763,U_2766)) )
        | ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2764),U_2766),U_2767))
          & hBOOL(hAPP(U_2763,U_2766)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2763,U_2764,U_2765)),U_2766),U_2767)) ) ),
    inference(variable_rename,[status(thm)],[f_812_1]) ).

fof(f_812_3,plain,
    ( ! [U_2777,U_2775,U_2773,U_2771,U_2769] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2769,U_2771,U_2773)),U_2775),U_2777))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2773),U_2775),U_2777))
            | hBOOL(hAPP(U_2769,U_2775)) )
          & ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2771),U_2775),U_2777))
            | ~ hBOOL(hAPP(U_2769,U_2775)) ) ) )
    & ! [U_2776,U_2774,U_2772,U_2770,U_2768] :
        ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2772),U_2774),U_2776))
          & ~ hBOOL(hAPP(U_2768,U_2774)) )
        | ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2770),U_2774),U_2776))
          & hBOOL(hAPP(U_2768,U_2774)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2768,U_2770,U_2772)),U_2774),U_2776)) ) ),
    inference(miniscope,[status(thm)],[f_812_2]) ).

fof(f_812_4,plain,
    ( ! [U_2773,U_2771,U_2769,U_2777,U_2775] :
        ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2773),U_2775),U_2777))
        | hBOOL(hAPP(U_2769,U_2775))
        | ~ sP233(U_2773,U_2771,U_2769,U_2777,U_2775) )
    & ! [U_2773,U_2771,U_2769,U_2777,U_2775] :
        ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2771),U_2775),U_2777))
        | ~ hBOOL(hAPP(U_2769,U_2775))
        | ~ sP233(U_2773,U_2771,U_2769,U_2777,U_2775) )
    & ! [U_2774,U_2768,U_2776,U_2772] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2772),U_2774),U_2776))
        | ~ sP232(U_2774,U_2768,U_2776,U_2772) )
    & ! [U_2774,U_2768,U_2776,U_2772] :
        ( ~ hBOOL(hAPP(U_2768,U_2774))
        | ~ sP232(U_2774,U_2768,U_2776,U_2772) )
    & ! [U_2774,U_2768,U_2776,U_2770] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2770),U_2774),U_2776))
        | ~ sP231(U_2774,U_2768,U_2776,U_2770) )
    & ! [U_2774,U_2768,U_2776,U_2770] :
        ( hBOOL(hAPP(U_2768,U_2774))
        | ~ sP231(U_2774,U_2768,U_2776,U_2770) )
    & ! [U_2773,U_2771,U_2769,U_2777,U_2775] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2769,U_2771,U_2773)),U_2775),U_2777))
        | sP233(U_2773,U_2771,U_2769,U_2777,U_2775) )
    & ! [U_2774,U_2768,U_2776,U_2772,U_2770] :
        ( sP232(U_2774,U_2768,U_2776,U_2772)
        | sP231(U_2774,U_2768,U_2776,U_2770)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2768,U_2770,U_2772)),U_2774),U_2776)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP231,sP232,sP233])],[f_812_3]) ).

cnf(f_812_5,plain,
    ( sP232(U_2774,U_2768,U_2776,U_2772)
    | sP231(U_2774,U_2768,U_2776,U_2770)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2768,U_2770,U_2772)),U_2774),U_2776)) ),
    inference(clausify,[status(thm)],[f_812_4]) ).

cnf(f_812_6,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OCond(U_2769,U_2771,U_2773)),U_2775),U_2777))
    | sP233(U_2773,U_2771,U_2769,U_2777,U_2775) ),
    inference(clausify,[status(thm)],[f_812_4]) ).

cnf(f_812_7,plain,
    ( hBOOL(hAPP(U_2768,U_2774))
    | ~ sP231(U_2774,U_2768,U_2776,U_2770) ),
    inference(clausify,[status(thm)],[f_812_4]) ).

cnf(f_812_8,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2770),U_2774),U_2776))
    | ~ sP231(U_2774,U_2768,U_2776,U_2770) ),
    inference(clausify,[status(thm)],[f_812_4]) ).

cnf(f_812_9,plain,
    ( ~ hBOOL(hAPP(U_2768,U_2774))
    | ~ sP232(U_2774,U_2768,U_2776,U_2772) ),
    inference(clausify,[status(thm)],[f_812_4]) ).

cnf(f_812_10,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2772),U_2774),U_2776))
    | ~ sP232(U_2774,U_2768,U_2776,U_2772) ),
    inference(clausify,[status(thm)],[f_812_4]) ).

cnf(f_812_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2771),U_2775),U_2777))
    | ~ hBOOL(hAPP(U_2769,U_2775))
    | ~ sP233(U_2773,U_2771,U_2769,U_2777,U_2775) ),
    inference(clausify,[status(thm)],[f_812_4]) ).

cnf(f_812_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2773),U_2775),U_2777))
    | hBOOL(hAPP(U_2769,U_2775))
    | ~ sP233(U_2773,U_2771,U_2769,U_2777,U_2775) ),
    inference(clausify,[status(thm)],[f_812_4]) ).

fof(f_813_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_813_2,plain,
    ! [U_2780,U_2779,U_2778] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_2778,U_2779,U_2780)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_2780))
        | ~ hBOOL(hAPP(c_Com_OWT,U_2779)) )
      & ( ( hBOOL(hAPP(c_Com_OWT,U_2780))
          & hBOOL(hAPP(c_Com_OWT,U_2779)) )
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_2778,U_2779,U_2780))) ) ),
    inference(variable_rename,[status(thm)],[f_813_1]) ).

fof(f_813_3,plain,
    ( ! [U_2786,U_2784] :
        ( ! [U_2782] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_2782,U_2784,U_2786)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_2786))
        | ~ hBOOL(hAPP(c_Com_OWT,U_2784)) )
    & ! [U_2785,U_2783] :
        ( ! [U_2781] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_2781,U_2783,U_2785)))
        | ( hBOOL(hAPP(c_Com_OWT,U_2785))
          & hBOOL(hAPP(c_Com_OWT,U_2783)) ) ) ),
    inference(miniscope,[status(thm)],[f_813_2]) ).

fof(f_813_4,plain,
    ( ! [U_2783,U_2785] :
        ( hBOOL(hAPP(c_Com_OWT,U_2785))
        | ~ sP234(U_2783,U_2785) )
    & ! [U_2783,U_2785] :
        ( hBOOL(hAPP(c_Com_OWT,U_2783))
        | ~ sP234(U_2783,U_2785) )
    & ! [U_2784,U_2782,U_2786] :
        ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_2782,U_2784,U_2786)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_2786))
        | ~ hBOOL(hAPP(c_Com_OWT,U_2784)) )
    & ! [U_2781,U_2783,U_2785] :
        ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_2781,U_2783,U_2785)))
        | sP234(U_2783,U_2785) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP234])],[f_813_3]) ).

cnf(f_813_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_2781,U_2783,U_2785)))
    | sP234(U_2783,U_2785) ),
    inference(clausify,[status(thm)],[f_813_4]) ).

cnf(f_813_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_2782,U_2784,U_2786)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_2786))
    | ~ hBOOL(hAPP(c_Com_OWT,U_2784)) ),
    inference(clausify,[status(thm)],[f_813_4]) ).

cnf(f_813_7,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_2783))
    | ~ sP234(U_2783,U_2785) ),
    inference(clausify,[status(thm)],[f_813_4]) ).

cnf(f_813_8,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_2785))
    | ~ sP234(U_2783,U_2785) ),
    inference(clausify,[status(thm)],[f_813_4]) ).

fof(f_814_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_814_2,plain,
    ! [U_2789,U_2788,U_2787] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_2789,U_2787,U_2788)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_2788))
      | ~ hBOOL(hAPP(c_Com_OWT,U_2787)) ),
    inference(variable_rename,[status(thm)],[f_814_1]) ).

fof(f_814_3,plain,
    ! [U_2788,U_2787,U_2789] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_2789,U_2787,U_2788)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_2788))
      | ~ hBOOL(hAPP(c_Com_OWT,U_2787)) ),
    inference(definitional_conversion,[status(esa)],[f_814_2]) ).

cnf(f_814_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(U_2789,U_2787,U_2788)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_2788))
    | ~ hBOOL(hAPP(c_Com_OWT,U_2787)) ),
    inference(clausify,[status(thm)],[f_814_3]) ).

fof(f_815_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_815_2,plain,
    ! [U_2793,U_2792,U_2791,U_2790] : hAPP(c_Com_Ocom_OBODY,U_2790) != c_Com_Ocom_OCond(U_2791,U_2792,U_2793),
    inference(variable_rename,[status(thm)],[f_815_1]) ).

fof(f_815_3,plain,
    ! [U_2791,U_2790,U_2793,U_2792] : hAPP(c_Com_Ocom_OBODY,U_2790) != c_Com_Ocom_OCond(U_2791,U_2792,U_2793),
    inference(definitional_conversion,[status(esa)],[f_815_2]) ).

cnf(f_815_4,plain,
    hAPP(c_Com_Ocom_OBODY,U_2790) != c_Com_Ocom_OCond(U_2791,U_2792,U_2793),
    inference(clausify,[status(thm)],[f_815_3]) ).

fof(f_816_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_816_2,plain,
    ! [U_2797,U_2796,U_2795,U_2794] : c_Com_Ocom_OCond(U_2794,U_2795,U_2796) != hAPP(c_Com_Ocom_OBODY,U_2797),
    inference(variable_rename,[status(thm)],[f_816_1]) ).

fof(f_816_3,plain,
    ! [U_2794,U_2795,U_2796,U_2797] : c_Com_Ocom_OCond(U_2794,U_2795,U_2796) != hAPP(c_Com_Ocom_OBODY,U_2797),
    inference(definitional_conversion,[status(esa)],[f_816_2]) ).

cnf(f_816_4,plain,
    c_Com_Ocom_OCond(U_2794,U_2795,U_2796) != hAPP(c_Com_Ocom_OBODY,U_2797),
    inference(clausify,[status(thm)],[f_816_3]) ).

fof(f_817_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_817_2,plain,
    ! [U_2804,U_2803,U_2802,U_2801,U_2800] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_2800,U_2801),U_2802,U_2803,U_2804)
        | ! [U_2799] :
            ( ~ c_Natural_Oevaln(U_2801,U_2799,U_2803,U_2804)
            | ~ c_Natural_Oevaln(U_2800,U_2802,U_2803,U_2799) ) )
      & ( ? [U_2798] :
            ( c_Natural_Oevaln(U_2801,U_2798,U_2803,U_2804)
            & c_Natural_Oevaln(U_2800,U_2802,U_2803,U_2798) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_2800,U_2801),U_2802,U_2803,U_2804) ) ),
    inference(variable_rename,[status(thm)],[f_817_1]) ).

fof(f_817_3,plain,
    ( ! [U_2814,U_2812,U_2810,U_2808,U_2806] :
        ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_2806,U_2808),U_2810,U_2812,U_2814)
        | ! [U_2799] :
            ( ~ c_Natural_Oevaln(U_2808,U_2799,U_2812,U_2814)
            | ~ c_Natural_Oevaln(U_2806,U_2810,U_2812,U_2799) ) )
    & ! [U_2813,U_2811,U_2809,U_2807,U_2805] :
        ( ? [U_2798] :
            ( c_Natural_Oevaln(U_2807,U_2798,U_2811,U_2813)
            & c_Natural_Oevaln(U_2805,U_2809,U_2811,U_2798) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_2805,U_2807),U_2809,U_2811,U_2813) ) ),
    inference(miniscope,[status(thm)],[f_817_2]) ).

fof(f_817_4,plain,
    ( ! [U_2814,U_2812,U_2810,U_2808,U_2806] :
        ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_2806,U_2808),U_2810,U_2812,U_2814)
        | ! [U_2799] :
            ( ~ c_Natural_Oevaln(U_2808,U_2799,U_2812,U_2814)
            | ~ c_Natural_Oevaln(U_2806,U_2810,U_2812,U_2799) ) )
    & ! [U_2813,U_2811,U_2809,U_2807,U_2805] :
        ( ( c_Natural_Oevaln(U_2807,sK39(U_2813,U_2811,U_2809,U_2807,U_2805),U_2811,U_2813)
          & c_Natural_Oevaln(U_2805,U_2809,U_2811,sK39(U_2813,U_2811,U_2809,U_2807,U_2805)) )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_2805,U_2807),U_2809,U_2811,U_2813) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK39]),skolemize(U_2798,sK39(U_2813,U_2811,U_2809,U_2807,U_2805))],[f_817_3]) ).

fof(f_817_5,plain,
    ( ! [U_2813,U_2809,U_2807,U_2805,U_2811] :
        ( c_Natural_Oevaln(U_2807,sK39(U_2813,U_2811,U_2809,U_2807,U_2805),U_2811,U_2813)
        | ~ sP235(U_2813,U_2809,U_2807,U_2805,U_2811) )
    & ! [U_2813,U_2809,U_2807,U_2805,U_2811] :
        ( c_Natural_Oevaln(U_2805,U_2809,U_2811,sK39(U_2813,U_2811,U_2809,U_2807,U_2805))
        | ~ sP235(U_2813,U_2809,U_2807,U_2805,U_2811) )
    & ! [U_2814,U_2799,U_2810,U_2808,U_2812,U_2806] :
        ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_2806,U_2808),U_2810,U_2812,U_2814)
        | ~ c_Natural_Oevaln(U_2808,U_2799,U_2812,U_2814)
        | ~ c_Natural_Oevaln(U_2806,U_2810,U_2812,U_2799) )
    & ! [U_2813,U_2809,U_2807,U_2805,U_2811] :
        ( sP235(U_2813,U_2809,U_2807,U_2805,U_2811)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_2805,U_2807),U_2809,U_2811,U_2813) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP235])],[f_817_4]) ).

cnf(f_817_6,plain,
    ( sP235(U_2813,U_2809,U_2807,U_2805,U_2811)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OSemi(U_2805,U_2807),U_2809,U_2811,U_2813) ),
    inference(clausify,[status(thm)],[f_817_5]) ).

cnf(f_817_7,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OSemi(U_2806,U_2808),U_2810,U_2812,U_2814)
    | ~ c_Natural_Oevaln(U_2808,U_2799,U_2812,U_2814)
    | ~ c_Natural_Oevaln(U_2806,U_2810,U_2812,U_2799) ),
    inference(clausify,[status(thm)],[f_817_5]) ).

cnf(f_817_8,plain,
    ( c_Natural_Oevaln(U_2805,U_2809,U_2811,sK39(U_2813,U_2811,U_2809,U_2807,U_2805))
    | ~ sP235(U_2813,U_2809,U_2807,U_2805,U_2811) ),
    inference(clausify,[status(thm)],[f_817_5]) ).

cnf(f_817_9,plain,
    ( c_Natural_Oevaln(U_2807,sK39(U_2813,U_2811,U_2809,U_2807,U_2805),U_2811,U_2813)
    | ~ sP235(U_2813,U_2809,U_2807,U_2805,U_2811) ),
    inference(clausify,[status(thm)],[f_817_5]) ).

fof(f_818_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_818_2,plain,
    ! [U_2819,U_2818,U_2817,U_2816,U_2815] : c_Com_Ocom_OAss(U_2815,U_2816) != c_Com_Ocom_OLocal(U_2817,U_2818,U_2819),
    inference(variable_rename,[status(thm)],[f_818_1]) ).

fof(f_818_3,plain,
    ! [U_2818,U_2817,U_2819,U_2815,U_2816] : c_Com_Ocom_OAss(U_2815,U_2816) != c_Com_Ocom_OLocal(U_2817,U_2818,U_2819),
    inference(definitional_conversion,[status(esa)],[f_818_2]) ).

cnf(f_818_4,plain,
    c_Com_Ocom_OAss(U_2815,U_2816) != c_Com_Ocom_OLocal(U_2817,U_2818,U_2819),
    inference(clausify,[status(thm)],[f_818_3]) ).

fof(f_819_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_819_2,plain,
    ! [U_2824,U_2823,U_2822,U_2821,U_2820] : c_Com_Ocom_OLocal(U_2820,U_2821,U_2822) != c_Com_Ocom_OAss(U_2823,U_2824),
    inference(variable_rename,[status(thm)],[f_819_1]) ).

fof(f_819_3,plain,
    ! [U_2824,U_2821,U_2823,U_2822,U_2820] : c_Com_Ocom_OLocal(U_2820,U_2821,U_2822) != c_Com_Ocom_OAss(U_2823,U_2824),
    inference(definitional_conversion,[status(esa)],[f_819_2]) ).

cnf(f_819_4,plain,
    c_Com_Ocom_OLocal(U_2820,U_2821,U_2822) != c_Com_Ocom_OAss(U_2823,U_2824),
    inference(clausify,[status(thm)],[f_819_3]) ).

fof(f_820_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_820_2,plain,
    ! [U_2830,U_2829,U_2828,U_2827,U_2826,U_2825] : c_Com_Ocom_OCall(U_2825,U_2826,U_2827) != c_Com_Ocom_OLocal(U_2828,U_2829,U_2830),
    inference(variable_rename,[status(thm)],[f_820_1]) ).

fof(f_820_3,plain,
    ! [U_2828,U_2829,U_2826,U_2825,U_2827,U_2830] : c_Com_Ocom_OCall(U_2825,U_2826,U_2827) != c_Com_Ocom_OLocal(U_2828,U_2829,U_2830),
    inference(definitional_conversion,[status(esa)],[f_820_2]) ).

cnf(f_820_4,plain,
    c_Com_Ocom_OCall(U_2825,U_2826,U_2827) != c_Com_Ocom_OLocal(U_2828,U_2829,U_2830),
    inference(clausify,[status(thm)],[f_820_3]) ).

fof(f_821_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_821_2,plain,
    ! [U_2836,U_2835,U_2834,U_2833,U_2832,U_2831] : c_Com_Ocom_OLocal(U_2831,U_2832,U_2833) != c_Com_Ocom_OCall(U_2834,U_2835,U_2836),
    inference(variable_rename,[status(thm)],[f_821_1]) ).

fof(f_821_3,plain,
    ! [U_2832,U_2831,U_2833,U_2834,U_2835,U_2836] : c_Com_Ocom_OLocal(U_2831,U_2832,U_2833) != c_Com_Ocom_OCall(U_2834,U_2835,U_2836),
    inference(definitional_conversion,[status(esa)],[f_821_2]) ).

cnf(f_821_4,plain,
    c_Com_Ocom_OLocal(U_2831,U_2832,U_2833) != c_Com_Ocom_OCall(U_2834,U_2835,U_2836),
    inference(clausify,[status(thm)],[f_821_3]) ).

fof(f_822_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_822_2,plain,
    ! [U_2842,U_2841,U_2840,U_2839] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_2839,U_2840)),U_2841),U_2842))
        | ! [U_2838] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2840),U_2838),U_2842))
            | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2839),U_2841),U_2838)) ) )
      & ( ? [U_2837] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2840),U_2837),U_2842))
            & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2839),U_2841),U_2837)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_2839,U_2840)),U_2841),U_2842)) ) ),
    inference(variable_rename,[status(thm)],[f_822_1]) ).

fof(f_822_3,plain,
    ( ! [U_2850,U_2848,U_2846,U_2844] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_2844,U_2846)),U_2848),U_2850))
        | ! [U_2838] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2846),U_2838),U_2850))
            | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2844),U_2848),U_2838)) ) )
    & ! [U_2849,U_2847,U_2845,U_2843] :
        ( ? [U_2837] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2845),U_2837),U_2849))
            & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2843),U_2847),U_2837)) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_2843,U_2845)),U_2847),U_2849)) ) ),
    inference(miniscope,[status(thm)],[f_822_2]) ).

fof(f_822_4,plain,
    ( ! [U_2850,U_2848,U_2846,U_2844] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_2844,U_2846)),U_2848),U_2850))
        | ! [U_2838] :
            ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2846),U_2838),U_2850))
            | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2844),U_2848),U_2838)) ) )
    & ! [U_2849,U_2847,U_2845,U_2843] :
        ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2845),sK40(U_2849,U_2847,U_2845,U_2843)),U_2849))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2843),U_2847),sK40(U_2849,U_2847,U_2845,U_2843))) )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_2843,U_2845)),U_2847),U_2849)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK40]),skolemize(U_2837,sK40(U_2849,U_2847,U_2845,U_2843))],[f_822_3]) ).

fof(f_822_5,plain,
    ( ! [U_2849,U_2845,U_2843,U_2847] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2845),sK40(U_2849,U_2847,U_2845,U_2843)),U_2849))
        | ~ sP236(U_2849,U_2845,U_2843,U_2847) )
    & ! [U_2849,U_2845,U_2843,U_2847] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2843),U_2847),sK40(U_2849,U_2847,U_2845,U_2843)))
        | ~ sP236(U_2849,U_2845,U_2843,U_2847) )
    & ! [U_2838,U_2844,U_2850,U_2846,U_2848] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_2844,U_2846)),U_2848),U_2850))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2846),U_2838),U_2850))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2844),U_2848),U_2838)) )
    & ! [U_2849,U_2845,U_2843,U_2847] :
        ( sP236(U_2849,U_2845,U_2843,U_2847)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_2843,U_2845)),U_2847),U_2849)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP236])],[f_822_4]) ).

cnf(f_822_6,plain,
    ( sP236(U_2849,U_2845,U_2843,U_2847)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_2843,U_2845)),U_2847),U_2849)) ),
    inference(clausify,[status(thm)],[f_822_5]) ).

cnf(f_822_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(U_2844,U_2846)),U_2848),U_2850))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2846),U_2838),U_2850))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2844),U_2848),U_2838)) ),
    inference(clausify,[status(thm)],[f_822_5]) ).

cnf(f_822_8,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2843),U_2847),sK40(U_2849,U_2847,U_2845,U_2843)))
    | ~ sP236(U_2849,U_2845,U_2843,U_2847) ),
    inference(clausify,[status(thm)],[f_822_5]) ).

cnf(f_822_9,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_2845),sK40(U_2849,U_2847,U_2845,U_2843)),U_2849))
    | ~ sP236(U_2849,U_2845,U_2843,U_2847) ),
    inference(clausify,[status(thm)],[f_822_5]) ).

fof(f_823_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_823_2,plain,
    ! [U_2853,U_2852,U_2851] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(U_2851,U_2852,U_2853),
    inference(variable_rename,[status(thm)],[f_823_1]) ).

fof(f_823_3,plain,
    ! [U_2851,U_2853,U_2852] : c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(U_2851,U_2852,U_2853),
    inference(definitional_conversion,[status(esa)],[f_823_2]) ).

cnf(f_823_4,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OLocal(U_2851,U_2852,U_2853),
    inference(clausify,[status(thm)],[f_823_3]) ).

fof(f_824_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_824_2,plain,
    ! [U_2856,U_2855,U_2854] : c_Com_Ocom_OLocal(U_2854,U_2855,U_2856) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_824_1]) ).

fof(f_824_3,plain,
    ! [U_2855,U_2854,U_2856] : c_Com_Ocom_OLocal(U_2854,U_2855,U_2856) != c_Com_Ocom_OSKIP,
    inference(definitional_conversion,[status(esa)],[f_824_2]) ).

cnf(f_824_4,plain,
    c_Com_Ocom_OLocal(U_2854,U_2855,U_2856) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_824_3]) ).

fof(f_825_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_825_2,plain,
    ! [U_2858,U_2857] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_2857,U_2858)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_2858))
        | ~ hBOOL(hAPP(c_Com_OWT,U_2857)) )
      & ( ( hBOOL(hAPP(c_Com_OWT,U_2858))
          & hBOOL(hAPP(c_Com_OWT,U_2857)) )
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_2857,U_2858))) ) ),
    inference(variable_rename,[status(thm)],[f_825_1]) ).

fof(f_825_3,plain,
    ( ! [U_2862,U_2860] :
        ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_2860,U_2862)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_2862))
        | ~ hBOOL(hAPP(c_Com_OWT,U_2860)) )
    & ! [U_2861,U_2859] :
        ( ( hBOOL(hAPP(c_Com_OWT,U_2861))
          & hBOOL(hAPP(c_Com_OWT,U_2859)) )
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_2859,U_2861))) ) ),
    inference(miniscope,[status(thm)],[f_825_2]) ).

fof(f_825_4,plain,
    ( ! [U_2859,U_2861] :
        ( hBOOL(hAPP(c_Com_OWT,U_2861))
        | ~ sP237(U_2859,U_2861) )
    & ! [U_2859,U_2861] :
        ( hBOOL(hAPP(c_Com_OWT,U_2859))
        | ~ sP237(U_2859,U_2861) )
    & ! [U_2862,U_2860] :
        ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_2860,U_2862)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_2862))
        | ~ hBOOL(hAPP(c_Com_OWT,U_2860)) )
    & ! [U_2859,U_2861] :
        ( sP237(U_2859,U_2861)
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_2859,U_2861))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP237])],[f_825_3]) ).

cnf(f_825_5,plain,
    ( sP237(U_2859,U_2861)
    | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_2859,U_2861))) ),
    inference(clausify,[status(thm)],[f_825_4]) ).

cnf(f_825_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_2860,U_2862)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_2862))
    | ~ hBOOL(hAPP(c_Com_OWT,U_2860)) ),
    inference(clausify,[status(thm)],[f_825_4]) ).

cnf(f_825_7,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_2859))
    | ~ sP237(U_2859,U_2861) ),
    inference(clausify,[status(thm)],[f_825_4]) ).

cnf(f_825_8,plain,
    ( hBOOL(hAPP(c_Com_OWT,U_2861))
    | ~ sP237(U_2859,U_2861) ),
    inference(clausify,[status(thm)],[f_825_4]) ).

fof(f_826_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_826_2,plain,
    ! [U_2864,U_2863] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_2863,U_2864)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_2864))
      | ~ hBOOL(hAPP(c_Com_OWT,U_2863)) ),
    inference(variable_rename,[status(thm)],[f_826_1]) ).

fof(f_826_3,plain,
    ! [U_2863,U_2864] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_2863,U_2864)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_2864))
      | ~ hBOOL(hAPP(c_Com_OWT,U_2863)) ),
    inference(definitional_conversion,[status(esa)],[f_826_2]) ).

cnf(f_826_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(U_2863,U_2864)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_2864))
    | ~ hBOOL(hAPP(c_Com_OWT,U_2863)) ),
    inference(clausify,[status(thm)],[f_826_3]) ).

fof(f_827_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_827_2,plain,
    ! [U_2869,U_2868,U_2867,U_2866,U_2865] : c_Com_Ocom_OAss(U_2865,U_2866) != c_Com_Ocom_OCond(U_2867,U_2868,U_2869),
    inference(variable_rename,[status(thm)],[f_827_1]) ).

fof(f_827_3,plain,
    ! [U_2866,U_2865,U_2867,U_2868,U_2869] : c_Com_Ocom_OAss(U_2865,U_2866) != c_Com_Ocom_OCond(U_2867,U_2868,U_2869),
    inference(definitional_conversion,[status(esa)],[f_827_2]) ).

cnf(f_827_4,plain,
    c_Com_Ocom_OAss(U_2865,U_2866) != c_Com_Ocom_OCond(U_2867,U_2868,U_2869),
    inference(clausify,[status(thm)],[f_827_3]) ).

fof(f_828_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_828_2,plain,
    ! [U_2874,U_2873,U_2872,U_2871,U_2870] : c_Com_Ocom_OCond(U_2870,U_2871,U_2872) != c_Com_Ocom_OAss(U_2873,U_2874),
    inference(variable_rename,[status(thm)],[f_828_1]) ).

fof(f_828_3,plain,
    ! [U_2871,U_2870,U_2872,U_2873,U_2874] : c_Com_Ocom_OCond(U_2870,U_2871,U_2872) != c_Com_Ocom_OAss(U_2873,U_2874),
    inference(definitional_conversion,[status(esa)],[f_828_2]) ).

cnf(f_828_4,plain,
    c_Com_Ocom_OCond(U_2870,U_2871,U_2872) != c_Com_Ocom_OAss(U_2873,U_2874),
    inference(clausify,[status(thm)],[f_828_3]) ).

fof(f_829_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_829_2,plain,
    ! [U_2877,U_2876,U_2875] : hAPP(c_Com_Ocom_OBODY,U_2875) != c_Com_Ocom_OSemi(U_2876,U_2877),
    inference(variable_rename,[status(thm)],[f_829_1]) ).

fof(f_829_3,plain,
    ! [U_2875,U_2876,U_2877] : hAPP(c_Com_Ocom_OBODY,U_2875) != c_Com_Ocom_OSemi(U_2876,U_2877),
    inference(definitional_conversion,[status(esa)],[f_829_2]) ).

cnf(f_829_4,plain,
    hAPP(c_Com_Ocom_OBODY,U_2875) != c_Com_Ocom_OSemi(U_2876,U_2877),
    inference(clausify,[status(thm)],[f_829_3]) ).

fof(f_830_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_830_2,plain,
    ! [U_2880,U_2879,U_2878] : c_Com_Ocom_OSemi(U_2878,U_2879) != hAPP(c_Com_Ocom_OBODY,U_2880),
    inference(variable_rename,[status(thm)],[f_830_1]) ).

fof(f_830_3,plain,
    ! [U_2878,U_2879,U_2880] : c_Com_Ocom_OSemi(U_2878,U_2879) != hAPP(c_Com_Ocom_OBODY,U_2880),
    inference(definitional_conversion,[status(esa)],[f_830_2]) ).

cnf(f_830_4,plain,
    c_Com_Ocom_OSemi(U_2878,U_2879) != hAPP(c_Com_Ocom_OBODY,U_2880),
    inference(clausify,[status(thm)],[f_830_3]) ).

fof(f_831_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_831_2,plain,
    ! [U_2886,U_2885,U_2884,U_2883,U_2882,U_2881] : c_Com_Ocom_OCall(U_2881,U_2882,U_2883) != c_Com_Ocom_OCond(U_2884,U_2885,U_2886),
    inference(variable_rename,[status(thm)],[f_831_1]) ).

fof(f_831_3,plain,
    ! [U_2881,U_2882,U_2883,U_2884,U_2885,U_2886] : c_Com_Ocom_OCall(U_2881,U_2882,U_2883) != c_Com_Ocom_OCond(U_2884,U_2885,U_2886),
    inference(definitional_conversion,[status(esa)],[f_831_2]) ).

cnf(f_831_4,plain,
    c_Com_Ocom_OCall(U_2881,U_2882,U_2883) != c_Com_Ocom_OCond(U_2884,U_2885,U_2886),
    inference(clausify,[status(thm)],[f_831_3]) ).

fof(f_832_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_832_2,plain,
    ! [U_2892,U_2891,U_2890,U_2889,U_2888,U_2887] : c_Com_Ocom_OCond(U_2887,U_2888,U_2889) != c_Com_Ocom_OCall(U_2890,U_2891,U_2892),
    inference(variable_rename,[status(thm)],[f_832_1]) ).

fof(f_832_3,plain,
    ! [U_2888,U_2887,U_2889,U_2890,U_2891,U_2892] : c_Com_Ocom_OCond(U_2887,U_2888,U_2889) != c_Com_Ocom_OCall(U_2890,U_2891,U_2892),
    inference(definitional_conversion,[status(esa)],[f_832_2]) ).

cnf(f_832_4,plain,
    c_Com_Ocom_OCond(U_2887,U_2888,U_2889) != c_Com_Ocom_OCall(U_2890,U_2891,U_2892),
    inference(clausify,[status(thm)],[f_832_3]) ).

fof(f_833_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_833_2,plain,
    ! [U_2895,U_2894,U_2893] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(U_2893,U_2894,U_2895),
    inference(variable_rename,[status(thm)],[f_833_1]) ).

fof(f_833_3,plain,
    ! [U_2893,U_2894,U_2895] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(U_2893,U_2894,U_2895),
    inference(definitional_conversion,[status(esa)],[f_833_2]) ).

cnf(f_833_4,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OCond(U_2893,U_2894,U_2895),
    inference(clausify,[status(thm)],[f_833_3]) ).

fof(f_834_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_834_2,plain,
    ! [U_2898,U_2897,U_2896] : c_Com_Ocom_OCond(U_2896,U_2897,U_2898) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_834_1]) ).

fof(f_834_3,plain,
    ! [U_2896,U_2897,U_2898] : c_Com_Ocom_OCond(U_2896,U_2897,U_2898) != c_Com_Ocom_OSKIP,
    inference(definitional_conversion,[status(esa)],[f_834_2]) ).

cnf(f_834_4,plain,
    c_Com_Ocom_OCond(U_2896,U_2897,U_2898) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_834_3]) ).

fof(f_835_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_835_2,plain,
    ! [U_2902,U_2901,U_2900,U_2899] : c_Com_Ocom_OAss(U_2899,U_2900) != c_Com_Ocom_OSemi(U_2901,U_2902),
    inference(variable_rename,[status(thm)],[f_835_1]) ).

fof(f_835_3,plain,
    ! [U_2899,U_2900,U_2901,U_2902] : c_Com_Ocom_OAss(U_2899,U_2900) != c_Com_Ocom_OSemi(U_2901,U_2902),
    inference(definitional_conversion,[status(esa)],[f_835_2]) ).

cnf(f_835_4,plain,
    c_Com_Ocom_OAss(U_2899,U_2900) != c_Com_Ocom_OSemi(U_2901,U_2902),
    inference(clausify,[status(thm)],[f_835_3]) ).

fof(f_836_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_836_2,plain,
    ! [U_2906,U_2905,U_2904,U_2903] : c_Com_Ocom_OSemi(U_2903,U_2904) != c_Com_Ocom_OAss(U_2905,U_2906),
    inference(variable_rename,[status(thm)],[f_836_1]) ).

fof(f_836_3,plain,
    ! [U_2903,U_2904,U_2905,U_2906] : c_Com_Ocom_OSemi(U_2903,U_2904) != c_Com_Ocom_OAss(U_2905,U_2906),
    inference(definitional_conversion,[status(esa)],[f_836_2]) ).

cnf(f_836_4,plain,
    c_Com_Ocom_OSemi(U_2903,U_2904) != c_Com_Ocom_OAss(U_2905,U_2906),
    inference(clausify,[status(thm)],[f_836_3]) ).

fof(f_837_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_837_2,plain,
    ! [U_2911,U_2910,U_2909,U_2908,U_2907] : c_Com_Ocom_OSemi(U_2907,U_2908) != c_Com_Ocom_OCall(U_2909,U_2910,U_2911),
    inference(variable_rename,[status(thm)],[f_837_1]) ).

fof(f_837_3,plain,
    ! [U_2907,U_2908,U_2909,U_2910,U_2911] : c_Com_Ocom_OSemi(U_2907,U_2908) != c_Com_Ocom_OCall(U_2909,U_2910,U_2911),
    inference(definitional_conversion,[status(esa)],[f_837_2]) ).

cnf(f_837_4,plain,
    c_Com_Ocom_OSemi(U_2907,U_2908) != c_Com_Ocom_OCall(U_2909,U_2910,U_2911),
    inference(clausify,[status(thm)],[f_837_3]) ).

fof(f_838_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_838_2,plain,
    ! [U_2916,U_2915,U_2914,U_2913,U_2912] : c_Com_Ocom_OCall(U_2912,U_2913,U_2914) != c_Com_Ocom_OSemi(U_2915,U_2916),
    inference(variable_rename,[status(thm)],[f_838_1]) ).

fof(f_838_3,plain,
    ! [U_2913,U_2912,U_2914,U_2915,U_2916] : c_Com_Ocom_OCall(U_2912,U_2913,U_2914) != c_Com_Ocom_OSemi(U_2915,U_2916),
    inference(definitional_conversion,[status(esa)],[f_838_2]) ).

cnf(f_838_4,plain,
    c_Com_Ocom_OCall(U_2912,U_2913,U_2914) != c_Com_Ocom_OSemi(U_2915,U_2916),
    inference(clausify,[status(thm)],[f_838_3]) ).

fof(f_839_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_839_2,plain,
    ! [U_2918,U_2917] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(U_2917,U_2918),
    inference(variable_rename,[status(thm)],[f_839_1]) ).

fof(f_839_3,plain,
    ! [U_2917,U_2918] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(U_2917,U_2918),
    inference(definitional_conversion,[status(esa)],[f_839_2]) ).

cnf(f_839_4,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(U_2917,U_2918),
    inference(clausify,[status(thm)],[f_839_3]) ).

fof(f_840_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_840_2,plain,
    ! [U_2920,U_2919] : c_Com_Ocom_OSemi(U_2919,U_2920) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_840_1]) ).

fof(f_840_3,plain,
    ! [U_2919,U_2920] : c_Com_Ocom_OSemi(U_2919,U_2920) != c_Com_Ocom_OSKIP,
    inference(definitional_conversion,[status(esa)],[f_840_2]) ).

cnf(f_840_4,plain,
    c_Com_Ocom_OSemi(U_2919,U_2920) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_840_3]) ).

fof(f_841_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_841_2,plain,
    ! [U_2923,U_2922,U_2921] :
      ( c_Divides_Odiv__class_Omod(U_2921,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2921),U_2922),U_2923),U_2923) = c_Groups_Ozero__class_Ozero(U_2921)
      | ~ class_Divides_Osemiring__div(U_2921) ),
    inference(variable_rename,[status(thm)],[f_841_1]) ).

fof(f_841_3,plain,
    ! [U_2921,U_2922,U_2923] :
      ( c_Divides_Odiv__class_Omod(U_2921,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2921),U_2922),U_2923),U_2923) = c_Groups_Ozero__class_Ozero(U_2921)
      | ~ class_Divides_Osemiring__div(U_2921) ),
    inference(definitional_conversion,[status(esa)],[f_841_2]) ).

cnf(f_841_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2921,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2921),U_2922),U_2923),U_2923) = c_Groups_Ozero__class_Ozero(U_2921)
    | ~ class_Divides_Osemiring__div(U_2921) ),
    inference(clausify,[status(thm)],[f_841_3]) ).

fof(f_842_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_842_2,plain,
    ! [U_2926,U_2925,U_2924] :
      ( c_Divides_Odiv__class_Omod(U_2924,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2924),U_2925),U_2926),U_2925) = c_Groups_Ozero__class_Ozero(U_2924)
      | ~ class_Divides_Osemiring__div(U_2924) ),
    inference(variable_rename,[status(thm)],[f_842_1]) ).

fof(f_842_3,plain,
    ! [U_2924,U_2925,U_2926] :
      ( c_Divides_Odiv__class_Omod(U_2924,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2924),U_2925),U_2926),U_2925) = c_Groups_Ozero__class_Ozero(U_2924)
      | ~ class_Divides_Osemiring__div(U_2924) ),
    inference(definitional_conversion,[status(esa)],[f_842_2]) ).

cnf(f_842_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2924,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2924),U_2925),U_2926),U_2925) = c_Groups_Ozero__class_Ozero(U_2924)
    | ~ class_Divides_Osemiring__div(U_2924) ),
    inference(clausify,[status(thm)],[f_842_3]) ).

fof(f_843_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_843_2,plain,
    ! [U_2930,U_2929,U_2928,U_2927] :
      ( c_Divides_Odiv__class_Omod(U_2927,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2927),U_2928),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2927),U_2929),U_2930)),U_2930) = c_Divides_Odiv__class_Omod(U_2927,U_2928,U_2930)
      | ~ class_Divides_Osemiring__div(U_2927) ),
    inference(variable_rename,[status(thm)],[f_843_1]) ).

fof(f_843_3,plain,
    ! [U_2927,U_2928,U_2929,U_2930] :
      ( c_Divides_Odiv__class_Omod(U_2927,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2927),U_2928),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2927),U_2929),U_2930)),U_2930) = c_Divides_Odiv__class_Omod(U_2927,U_2928,U_2930)
      | ~ class_Divides_Osemiring__div(U_2927) ),
    inference(definitional_conversion,[status(esa)],[f_843_2]) ).

cnf(f_843_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2927,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2927),U_2928),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2927),U_2929),U_2930)),U_2930) = c_Divides_Odiv__class_Omod(U_2927,U_2928,U_2930)
    | ~ class_Divides_Osemiring__div(U_2927) ),
    inference(clausify,[status(thm)],[f_843_3]) ).

fof(f_844_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_844_2,plain,
    ! [U_2934,U_2933,U_2932,U_2931] :
      ( c_Divides_Odiv__class_Omod(U_2931,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2931),U_2932),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2931),U_2933),U_2934)),U_2933) = c_Divides_Odiv__class_Omod(U_2931,U_2932,U_2933)
      | ~ class_Divides_Osemiring__div(U_2931) ),
    inference(variable_rename,[status(thm)],[f_844_1]) ).

fof(f_844_3,plain,
    ! [U_2931,U_2932,U_2933,U_2934] :
      ( c_Divides_Odiv__class_Omod(U_2931,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2931),U_2932),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2931),U_2933),U_2934)),U_2933) = c_Divides_Odiv__class_Omod(U_2931,U_2932,U_2933)
      | ~ class_Divides_Osemiring__div(U_2931) ),
    inference(definitional_conversion,[status(esa)],[f_844_2]) ).

cnf(f_844_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2931,hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_2931),U_2932),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_2931),U_2933),U_2934)),U_2933) = c_Divides_Odiv__class_Omod(U_2931,U_2932,U_2933)
    | ~ class_Divides_Osemiring__div(U_2931) ),
    inference(clausify,[status(thm)],[f_844_3]) ).

fof(f_845_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_845_2,plain,
    ! [U_2936,U_2935] :
      ( c_Divides_Odiv__class_Omod(U_2935,U_2936,c_Groups_Oone__class_Oone(U_2935)) = c_Groups_Ozero__class_Ozero(U_2935)
      | ~ class_Divides_Osemiring__div(U_2935) ),
    inference(variable_rename,[status(thm)],[f_845_1]) ).

fof(f_845_3,plain,
    ! [U_2935,U_2936] :
      ( c_Divides_Odiv__class_Omod(U_2935,U_2936,c_Groups_Oone__class_Oone(U_2935)) = c_Groups_Ozero__class_Ozero(U_2935)
      | ~ class_Divides_Osemiring__div(U_2935) ),
    inference(definitional_conversion,[status(esa)],[f_845_2]) ).

cnf(f_845_4,plain,
    ( c_Divides_Odiv__class_Omod(U_2935,U_2936,c_Groups_Oone__class_Oone(U_2935)) = c_Groups_Ozero__class_Ozero(U_2935)
    | ~ class_Divides_Osemiring__div(U_2935) ),
    inference(clausify,[status(thm)],[f_845_3]) ).

fof(f_846_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_846_2,plain,
    ! [U_2938,U_2937] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2937,U_2938)),U_2937))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2937)) ),
    inference(variable_rename,[status(thm)],[f_846_1]) ).

fof(f_846_3,plain,
    ! [U_2937,U_2938] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2937,U_2938)),U_2937))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2937)) ),
    inference(definitional_conversion,[status(esa)],[f_846_2]) ).

cnf(f_846_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2937,U_2938)),U_2937))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2937)) ),
    inference(clausify,[status(thm)],[f_846_3]) ).

fof(f_847_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_847_2,plain,
    ! [U_2940,U_2939] :
      ( 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_2939,U_2940)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2940))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2939)) ),
    inference(variable_rename,[status(thm)],[f_847_1]) ).

fof(f_847_3,plain,
    ! [U_2939,U_2940] :
      ( 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_2939,U_2940)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2940))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2939)) ),
    inference(definitional_conversion,[status(esa)],[f_847_2]) ).

cnf(f_847_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_2939,U_2940)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2940))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2939)) ),
    inference(clausify,[status(thm)],[f_847_3]) ).

fof(f_848_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_848_2,plain,
    ! [U_2942,U_2941] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2941),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2942,U_2941)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2941),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_848_1]) ).

fof(f_848_3,plain,
    ! [U_2941,U_2942] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2941),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2942,U_2941)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2941),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_848_2]) ).

cnf(f_848_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2941),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2942,U_2941)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2941),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_848_3]) ).

fof(f_849_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_849_2,plain,
    ! [U_2944,U_2943] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2944,U_2943)),U_2943))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2943)) ),
    inference(variable_rename,[status(thm)],[f_849_1]) ).

fof(f_849_3,plain,
    ! [U_2943,U_2944] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2944,U_2943)),U_2943))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2943)) ),
    inference(definitional_conversion,[status(esa)],[f_849_2]) ).

cnf(f_849_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2944,U_2943)),U_2943))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2943)) ),
    inference(clausify,[status(thm)],[f_849_3]) ).

fof(f_850_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_850_2,plain,
    ! [U_2948,U_2947] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2947,U_2948) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ! [U_2946] : U_2947 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2948),U_2946) )
      & ( ? [U_2945] : U_2947 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2948),U_2945)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2947,U_2948) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_850_1]) ).

fof(f_850_3,plain,
    ( ! [U_2952,U_2950] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2950,U_2952) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ! [U_2946] : U_2950 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2952),U_2946) )
    & ! [U_2951,U_2949] :
        ( ? [U_2945] : U_2949 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2951),U_2945)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2949,U_2951) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_850_2]) ).

fof(f_850_4,plain,
    ( ! [U_2952,U_2950] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2950,U_2952) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ! [U_2946] : U_2950 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2952),U_2946) )
    & ! [U_2951,U_2949] :
        ( U_2949 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2951),sK41(U_2951,U_2949))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2949,U_2951) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK41]),skolemize(U_2945,sK41(U_2951,U_2949))],[f_850_3]) ).

fof(f_850_5,plain,
    ( ! [U_2946,U_2950,U_2952] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2950,U_2952) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_2950 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2952),U_2946) )
    & ! [U_2949,U_2951] :
        ( U_2949 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2951),sK41(U_2951,U_2949))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2949,U_2951) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa)],[f_850_4]) ).

cnf(f_850_6,plain,
    ( U_2949 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2951),sK41(U_2951,U_2949))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2949,U_2951) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_850_5]) ).

cnf(f_850_7,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2950,U_2952) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_2950 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2952),U_2946) ),
    inference(clausify,[status(thm)],[f_850_5]) ).

fof(f_851_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_851_2,plain,
    ! [U_2954,U_2953] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2953,U_2954) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2953,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2954)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_851_1]) ).

fof(f_851_3,plain,
    ! [U_2954,U_2953] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2953,U_2954) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2953,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2954)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_851_2]) ).

cnf(f_851_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2953,U_2954) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2953,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_2954)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_851_3]) ).

fof(f_852_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_852_2,plain,
    ! [U_2956,U_2955] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2955,U_2956) != 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_2955),U_2956) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_852_1]) ).

fof(f_852_3,plain,
    ! [U_2955,U_2956] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2955,U_2956) != 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_2955),U_2956) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_852_2]) ).

cnf(f_852_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2955,U_2956) != 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_2955),U_2956) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_852_3]) ).

fof(f_853_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_853_2,plain,
    ! [U_2958,U_2957] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2957,U_2958) = U_2957
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2958),U_2957))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2957),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_853_1]) ).

fof(f_853_3,plain,
    ! [U_2957,U_2958] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2957,U_2958) = U_2957
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2958),U_2957))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2957),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_853_2]) ).

cnf(f_853_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2957,U_2958) = U_2957
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2958),U_2957))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2957),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_853_3]) ).

fof(f_854_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_854_2,plain,
    ! [U_2960,U_2959] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2959),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2960,U_2959)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2960,U_2959)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2959),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_854_1]) ).

fof(f_854_3,plain,
    ( ! [U_2959,U_2960] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2959),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2960,U_2959)))
        | ~ sP238(U_2959,U_2960) )
    & ! [U_2959,U_2960] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2960,U_2959)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP238(U_2959,U_2960) )
    & ! [U_2959,U_2960] :
        ( sP238(U_2959,U_2960)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2959),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP238])],[f_854_2]) ).

cnf(f_854_4,plain,
    ( sP238(U_2959,U_2960)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2959),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_854_3]) ).

cnf(f_854_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2960,U_2959)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP238(U_2959,U_2960) ),
    inference(clausify,[status(thm)],[f_854_3]) ).

cnf(f_854_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2959),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2960,U_2959)))
    | ~ sP238(U_2959,U_2960) ),
    inference(clausify,[status(thm)],[f_854_3]) ).

fof(f_855_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_855_2,plain,
    ! [U_2962,U_2961] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2962,U_2961)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2961),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_855_1]) ).

fof(f_855_3,plain,
    ! [U_2961,U_2962] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2962,U_2961)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2961),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_855_2]) ).

cnf(f_855_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2962,U_2961)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2961),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_855_3]) ).

fof(f_856_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_856_2,plain,
    ! [U_2964,U_2963] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2963,U_2964) = U_2963
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2963),U_2964))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2963)) ),
    inference(variable_rename,[status(thm)],[f_856_1]) ).

fof(f_856_3,plain,
    ! [U_2963,U_2964] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2963,U_2964) = U_2963
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2963),U_2964))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2963)) ),
    inference(definitional_conversion,[status(esa)],[f_856_2]) ).

cnf(f_856_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2963,U_2964) = U_2963
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2963),U_2964))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2963)) ),
    inference(clausify,[status(thm)],[f_856_3]) ).

fof(f_857_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_857_2,plain,
    ! [U_2966,U_2965] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2966,U_2965)),U_2965))
        & 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_2966,U_2965))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2965)) ),
    inference(variable_rename,[status(thm)],[f_857_1]) ).

fof(f_857_3,plain,
    ( ! [U_2965,U_2966] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2966,U_2965)),U_2965))
        | ~ sP239(U_2965,U_2966) )
    & ! [U_2965,U_2966] :
        ( 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_2966,U_2965)))
        | ~ sP239(U_2965,U_2966) )
    & ! [U_2965,U_2966] :
        ( sP239(U_2965,U_2966)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2965)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP239])],[f_857_2]) ).

cnf(f_857_4,plain,
    ( sP239(U_2965,U_2966)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2965)) ),
    inference(clausify,[status(thm)],[f_857_3]) ).

cnf(f_857_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_2966,U_2965)))
    | ~ sP239(U_2965,U_2966) ),
    inference(clausify,[status(thm)],[f_857_3]) ).

cnf(f_857_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2966,U_2965)),U_2965))
    | ~ sP239(U_2965,U_2966) ),
    inference(clausify,[status(thm)],[f_857_3]) ).

fof(f_858_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_858_2,plain,
    ! [U_2968,U_2967] :
      ( 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_2968,U_2967)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2967)) ),
    inference(variable_rename,[status(thm)],[f_858_1]) ).

fof(f_858_3,plain,
    ! [U_2967,U_2968] :
      ( 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_2968,U_2967)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2967)) ),
    inference(definitional_conversion,[status(esa)],[f_858_2]) ).

cnf(f_858_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_2968,U_2967)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2967)) ),
    inference(clausify,[status(thm)],[f_858_3]) ).

fof(f_859_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_859_2,plain,
    ! [U_2970,U_2969] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2969,U_2970) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2969),U_2970)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2969),U_2970)),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_2969)) ),
    inference(variable_rename,[status(thm)],[f_859_1]) ).

fof(f_859_3,plain,
    ! [U_2969,U_2970] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2969,U_2970) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2969),U_2970)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2969),U_2970)),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_2969)) ),
    inference(definitional_conversion,[status(esa)],[f_859_2]) ).

cnf(f_859_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2969,U_2970) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2969),U_2970)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_2969),U_2970)),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_2969)) ),
    inference(clausify,[status(thm)],[f_859_3]) ).

fof(f_860_1,plain,
    ! [V_k_2,V_n_2,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2)))
        | ( ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,V_n_2))
          & V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [B_i,B_j] :
                ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,V_n_2))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(V_Pa_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_860_2,plain,
    ! [U_2981,U_2980,U_2979] :
      ( ( hBOOL(hAPP(U_2979,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2980,U_2981)))
        | ( ? [U_2978,U_2977] :
              ( ~ hBOOL(hAPP(U_2979,U_2977))
              & U_2980 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2981),U_2978)),U_2977)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2977),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2981),U_2977)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2981),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_2976,U_2975] :
              ( ~ hBOOL(hAPP(U_2979,U_2975))
              & U_2980 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2981),U_2976)),U_2975)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2975),U_2981))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2975)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2981)) )
        | ( ~ hBOOL(hAPP(U_2979,U_2980))
          & U_2981 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [U_2974,U_2973] :
                ( hBOOL(hAPP(U_2979,U_2973))
                | U_2980 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2981),U_2974)),U_2973)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2973),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2981),U_2973)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2981),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_2972,U_2971] :
                ( hBOOL(hAPP(U_2979,U_2971))
                | U_2980 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2981),U_2972)),U_2971)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2971),U_2981))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2971)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2981)) )
          & ( hBOOL(hAPP(U_2979,U_2980))
            | U_2981 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_2979,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2980,U_2981))) ) ),
    inference(variable_rename,[status(thm)],[f_860_1]) ).

fof(f_860_3,plain,
    ( ! [U_2987,U_2985,U_2983] :
        ( hBOOL(hAPP(U_2983,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2985,U_2987)))
        | ( ? [U_2978,U_2977] :
              ( ~ hBOOL(hAPP(U_2983,U_2977))
              & U_2985 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2987),U_2978)),U_2977)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2977),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2987),U_2977)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2987),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_2976,U_2975] :
              ( ~ hBOOL(hAPP(U_2983,U_2975))
              & U_2985 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2987),U_2976)),U_2975)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2975),U_2987))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2975)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2987)) )
        | ( ~ hBOOL(hAPP(U_2983,U_2985))
          & U_2987 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_2986,U_2984,U_2982] :
        ( ( ( ! [U_2974,U_2973] :
                ( hBOOL(hAPP(U_2982,U_2973))
                | U_2984 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2986),U_2974)),U_2973)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2973),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2986),U_2973)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2986),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_2972,U_2971] :
                ( hBOOL(hAPP(U_2982,U_2971))
                | U_2984 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2986),U_2972)),U_2971)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2971),U_2986))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2971)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2986)) )
          & ( hBOOL(hAPP(U_2982,U_2984))
            | U_2986 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_2982,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2984,U_2986))) ) ),
    inference(miniscope,[status(thm)],[f_860_2]) ).

fof(f_860_4,plain,
    ( ! [U_2987,U_2985,U_2983] :
        ( hBOOL(hAPP(U_2983,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2985,U_2987)))
        | ( ? [U_2978,U_2977] :
              ( ~ hBOOL(hAPP(U_2983,U_2977))
              & U_2985 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2987),U_2978)),U_2977)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2977),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2987),U_2977)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2987),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_2975] :
              ( ~ hBOOL(hAPP(U_2983,U_2975))
              & U_2985 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2987),sK42(U_2987,U_2985,U_2983))),U_2975)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2975),U_2987))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2975)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2987)) )
        | ( ~ hBOOL(hAPP(U_2983,U_2985))
          & U_2987 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_2986,U_2984,U_2982] :
        ( ( ( ! [U_2974,U_2973] :
                ( hBOOL(hAPP(U_2982,U_2973))
                | U_2984 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2986),U_2974)),U_2973)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2973),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2986),U_2973)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2986),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_2972,U_2971] :
                ( hBOOL(hAPP(U_2982,U_2971))
                | U_2984 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2986),U_2972)),U_2971)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2971),U_2986))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2971)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2986)) )
          & ( hBOOL(hAPP(U_2982,U_2984))
            | U_2986 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_2982,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2984,U_2986))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK42]),skolemize(U_2976,sK42(U_2987,U_2985,U_2983))],[f_860_3]) ).

fof(f_860_5,plain,
    ( ! [U_2987,U_2985,U_2983] :
        ( hBOOL(hAPP(U_2983,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2985,U_2987)))
        | ( ? [U_2978,U_2977] :
              ( ~ hBOOL(hAPP(U_2983,U_2977))
              & U_2985 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2987),U_2978)),U_2977)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2977),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2987),U_2977)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2987),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_2983,sK43(U_2987,U_2985,U_2983)))
          & U_2985 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2987),sK42(U_2987,U_2985,U_2983))),sK43(U_2987,U_2985,U_2983))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK43(U_2987,U_2985,U_2983)),U_2987))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK43(U_2987,U_2985,U_2983)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2987)) )
        | ( ~ hBOOL(hAPP(U_2983,U_2985))
          & U_2987 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_2986,U_2984,U_2982] :
        ( ( ( ! [U_2974,U_2973] :
                ( hBOOL(hAPP(U_2982,U_2973))
                | U_2984 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2986),U_2974)),U_2973)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2973),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2986),U_2973)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2986),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_2972,U_2971] :
                ( hBOOL(hAPP(U_2982,U_2971))
                | U_2984 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2986),U_2972)),U_2971)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2971),U_2986))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2971)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2986)) )
          & ( hBOOL(hAPP(U_2982,U_2984))
            | U_2986 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_2982,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2984,U_2986))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK43]),skolemize(U_2975,sK43(U_2987,U_2985,U_2983))],[f_860_4]) ).

fof(f_860_6,plain,
    ( ! [U_2987,U_2985,U_2983] :
        ( hBOOL(hAPP(U_2983,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2985,U_2987)))
        | ( ? [U_2977] :
              ( ~ hBOOL(hAPP(U_2983,U_2977))
              & U_2985 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2987),sK44(U_2987,U_2985,U_2983))),U_2977)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2977),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2987),U_2977)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2987),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_2983,sK43(U_2987,U_2985,U_2983)))
          & U_2985 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2987),sK42(U_2987,U_2985,U_2983))),sK43(U_2987,U_2985,U_2983))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK43(U_2987,U_2985,U_2983)),U_2987))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK43(U_2987,U_2985,U_2983)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2987)) )
        | ( ~ hBOOL(hAPP(U_2983,U_2985))
          & U_2987 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_2986,U_2984,U_2982] :
        ( ( ( ! [U_2974,U_2973] :
                ( hBOOL(hAPP(U_2982,U_2973))
                | U_2984 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2986),U_2974)),U_2973)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2973),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2986),U_2973)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2986),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_2972,U_2971] :
                ( hBOOL(hAPP(U_2982,U_2971))
                | U_2984 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2986),U_2972)),U_2971)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2971),U_2986))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2971)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2986)) )
          & ( hBOOL(hAPP(U_2982,U_2984))
            | U_2986 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_2982,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2984,U_2986))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK44]),skolemize(U_2978,sK44(U_2987,U_2985,U_2983))],[f_860_5]) ).

fof(f_860_7,plain,
    ( ! [U_2987,U_2985,U_2983] :
        ( hBOOL(hAPP(U_2983,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2985,U_2987)))
        | ( ~ hBOOL(hAPP(U_2983,sK45(U_2987,U_2985,U_2983)))
          & U_2985 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2987),sK44(U_2987,U_2985,U_2983))),sK45(U_2987,U_2985,U_2983))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK45(U_2987,U_2985,U_2983)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2987),sK45(U_2987,U_2985,U_2983)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2987),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_2983,sK43(U_2987,U_2985,U_2983)))
          & U_2985 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2987),sK42(U_2987,U_2985,U_2983))),sK43(U_2987,U_2985,U_2983))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK43(U_2987,U_2985,U_2983)),U_2987))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK43(U_2987,U_2985,U_2983)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2987)) )
        | ( ~ hBOOL(hAPP(U_2983,U_2985))
          & U_2987 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_2986,U_2984,U_2982] :
        ( ( ( ! [U_2974,U_2973] :
                ( hBOOL(hAPP(U_2982,U_2973))
                | U_2984 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2986),U_2974)),U_2973)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2973),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2986),U_2973)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2986),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_2972,U_2971] :
                ( hBOOL(hAPP(U_2982,U_2971))
                | U_2984 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2986),U_2972)),U_2971)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2971),U_2986))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2971)) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2986)) )
          & ( hBOOL(hAPP(U_2982,U_2984))
            | U_2986 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_2982,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2984,U_2986))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK45]),skolemize(U_2977,sK45(U_2987,U_2985,U_2983))],[f_860_6]) ).

fof(f_860_8,plain,
    ( ! [U_2987,U_2983,U_2985] :
        ( ~ hBOOL(hAPP(U_2983,sK45(U_2987,U_2985,U_2983)))
        | ~ sP243(U_2987,U_2983,U_2985) )
    & ! [U_2987,U_2983,U_2985] :
        ( U_2985 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2987),sK44(U_2987,U_2985,U_2983))),sK45(U_2987,U_2985,U_2983))
        | ~ sP243(U_2987,U_2983,U_2985) )
    & ! [U_2987,U_2983,U_2985] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK45(U_2987,U_2985,U_2983)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP243(U_2987,U_2983,U_2985) )
    & ! [U_2987,U_2983,U_2985] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2987),sK45(U_2987,U_2985,U_2983)))
        | ~ sP243(U_2987,U_2983,U_2985) )
    & ! [U_2987,U_2983,U_2985] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2987),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP243(U_2987,U_2983,U_2985) )
    & ! [U_2987,U_2983,U_2985] :
        ( ~ hBOOL(hAPP(U_2983,sK43(U_2987,U_2985,U_2983)))
        | ~ sP242(U_2987,U_2983,U_2985) )
    & ! [U_2987,U_2983,U_2985] :
        ( U_2985 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2987),sK42(U_2987,U_2985,U_2983))),sK43(U_2987,U_2985,U_2983))
        | ~ sP242(U_2987,U_2983,U_2985) )
    & ! [U_2987,U_2983,U_2985] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK43(U_2987,U_2985,U_2983)),U_2987))
        | ~ sP242(U_2987,U_2983,U_2985) )
    & ! [U_2987,U_2983,U_2985] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK43(U_2987,U_2985,U_2983)))
        | ~ sP242(U_2987,U_2983,U_2985) )
    & ! [U_2987,U_2983,U_2985] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2987))
        | ~ sP242(U_2987,U_2983,U_2985) )
    & ! [U_2987,U_2983,U_2985] :
        ( ~ hBOOL(hAPP(U_2983,U_2985))
        | ~ sP241(U_2987,U_2983,U_2985) )
    & ! [U_2987,U_2983,U_2985] :
        ( U_2987 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP241(U_2987,U_2983,U_2985) )
    & ! [U_2972,U_2971,U_2973,U_2974,U_2982,U_2986,U_2984] :
        ( hBOOL(hAPP(U_2982,U_2973))
        | U_2984 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2986),U_2974)),U_2973)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2973),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2986),U_2973))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2986),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP240(U_2972,U_2971,U_2973,U_2974,U_2982,U_2986,U_2984) )
    & ! [U_2972,U_2971,U_2973,U_2974,U_2982,U_2986,U_2984] :
        ( hBOOL(hAPP(U_2982,U_2971))
        | U_2984 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2986),U_2972)),U_2971)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2971),U_2986))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2971))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2986))
        | ~ sP240(U_2972,U_2971,U_2973,U_2974,U_2982,U_2986,U_2984) )
    & ! [U_2972,U_2971,U_2973,U_2974,U_2982,U_2986,U_2984] :
        ( hBOOL(hAPP(U_2982,U_2984))
        | U_2986 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP240(U_2972,U_2971,U_2973,U_2974,U_2982,U_2986,U_2984) )
    & ! [U_2987,U_2983,U_2985] :
        ( hBOOL(hAPP(U_2983,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2985,U_2987)))
        | sP243(U_2987,U_2983,U_2985)
        | sP242(U_2987,U_2983,U_2985)
        | sP241(U_2987,U_2983,U_2985) )
    & ! [U_2972,U_2971,U_2973,U_2974,U_2982,U_2986,U_2984] :
        ( sP240(U_2972,U_2971,U_2973,U_2974,U_2982,U_2986,U_2984)
        | ~ hBOOL(hAPP(U_2982,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2984,U_2986))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP240,sP241,sP242,sP243])],[f_860_7]) ).

cnf(f_860_9,plain,
    ( sP240(U_2972,U_2971,U_2973,U_2974,U_2982,U_2986,U_2984)
    | ~ hBOOL(hAPP(U_2982,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2984,U_2986))) ),
    inference(clausify,[status(thm)],[f_860_8]) ).

cnf(f_860_10,plain,
    ( hBOOL(hAPP(U_2983,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2985,U_2987)))
    | sP243(U_2987,U_2983,U_2985)
    | sP242(U_2987,U_2983,U_2985)
    | sP241(U_2987,U_2983,U_2985) ),
    inference(clausify,[status(thm)],[f_860_8]) ).

cnf(f_860_11,plain,
    ( hBOOL(hAPP(U_2982,U_2984))
    | U_2986 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP240(U_2972,U_2971,U_2973,U_2974,U_2982,U_2986,U_2984) ),
    inference(clausify,[status(thm)],[f_860_8]) ).

cnf(f_860_12,plain,
    ( hBOOL(hAPP(U_2982,U_2971))
    | U_2984 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2986),U_2972)),U_2971)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2971),U_2986))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2971))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2986))
    | ~ sP240(U_2972,U_2971,U_2973,U_2974,U_2982,U_2986,U_2984) ),
    inference(clausify,[status(thm)],[f_860_8]) ).

cnf(f_860_13,plain,
    ( hBOOL(hAPP(U_2982,U_2973))
    | U_2984 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2986),U_2974)),U_2973)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2973),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2986),U_2973))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2986),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP240(U_2972,U_2971,U_2973,U_2974,U_2982,U_2986,U_2984) ),
    inference(clausify,[status(thm)],[f_860_8]) ).

cnf(f_860_14,plain,
    ( U_2987 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP241(U_2987,U_2983,U_2985) ),
    inference(clausify,[status(thm)],[f_860_8]) ).

cnf(f_860_15,plain,
    ( ~ hBOOL(hAPP(U_2983,U_2985))
    | ~ sP241(U_2987,U_2983,U_2985) ),
    inference(clausify,[status(thm)],[f_860_8]) ).

cnf(f_860_16,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2987))
    | ~ sP242(U_2987,U_2983,U_2985) ),
    inference(clausify,[status(thm)],[f_860_8]) ).

cnf(f_860_17,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK43(U_2987,U_2985,U_2983)))
    | ~ sP242(U_2987,U_2983,U_2985) ),
    inference(clausify,[status(thm)],[f_860_8]) ).

cnf(f_860_18,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK43(U_2987,U_2985,U_2983)),U_2987))
    | ~ sP242(U_2987,U_2983,U_2985) ),
    inference(clausify,[status(thm)],[f_860_8]) ).

cnf(f_860_19,plain,
    ( U_2985 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2987),sK42(U_2987,U_2985,U_2983))),sK43(U_2987,U_2985,U_2983))
    | ~ sP242(U_2987,U_2983,U_2985) ),
    inference(clausify,[status(thm)],[f_860_8]) ).

cnf(f_860_20,plain,
    ( ~ hBOOL(hAPP(U_2983,sK43(U_2987,U_2985,U_2983)))
    | ~ sP242(U_2987,U_2983,U_2985) ),
    inference(clausify,[status(thm)],[f_860_8]) ).

cnf(f_860_21,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2987),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP243(U_2987,U_2983,U_2985) ),
    inference(clausify,[status(thm)],[f_860_8]) ).

cnf(f_860_22,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2987),sK45(U_2987,U_2985,U_2983)))
    | ~ sP243(U_2987,U_2983,U_2985) ),
    inference(clausify,[status(thm)],[f_860_8]) ).

cnf(f_860_23,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK45(U_2987,U_2985,U_2983)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP243(U_2987,U_2983,U_2985) ),
    inference(clausify,[status(thm)],[f_860_8]) ).

cnf(f_860_24,plain,
    ( U_2985 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2987),sK44(U_2987,U_2985,U_2983))),sK45(U_2987,U_2985,U_2983))
    | ~ sP243(U_2987,U_2983,U_2985) ),
    inference(clausify,[status(thm)],[f_860_8]) ).

cnf(f_860_25,plain,
    ( ~ hBOOL(hAPP(U_2983,sK45(U_2987,U_2985,U_2983)))
    | ~ sP243(U_2987,U_2983,U_2985) ),
    inference(clausify,[status(thm)],[f_860_8]) ).

fof(f_861_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_861_2,plain,
    ! [U_2991,U_2990,U_2989,U_2988] :
      ( 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_2990),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2991,U_2988))),U_2989)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2989),U_2990))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2989))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2988)) ),
    inference(variable_rename,[status(thm)],[f_861_1]) ).

fof(f_861_3,plain,
    ! [U_2990,U_2989,U_2988,U_2991] :
      ( 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_2990),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2991,U_2988))),U_2989)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2989),U_2990))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2989))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2988)) ),
    inference(definitional_conversion,[status(esa)],[f_861_2]) ).

cnf(f_861_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_2990),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2991,U_2988))),U_2989)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2989),U_2990))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2989))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2988)) ),
    inference(clausify,[status(thm)],[f_861_3]) ).

fof(f_862_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_862_2,plain,
    ! [U_2995,U_2994,U_2993,U_2992] :
      ( 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_2994),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2995,U_2992))),U_2993)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2994),U_2992)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2993),U_2994))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2993))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2992)) ),
    inference(variable_rename,[status(thm)],[f_862_1]) ).

fof(f_862_3,plain,
    ! [U_2994,U_2992,U_2993,U_2995] :
      ( 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_2994),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2995,U_2992))),U_2993)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2994),U_2992)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2993),U_2994))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2993))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2992)) ),
    inference(definitional_conversion,[status(esa)],[f_862_2]) ).

cnf(f_862_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_2994),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2995,U_2992))),U_2993)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2994),U_2992)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2993),U_2994))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2993))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2992)) ),
    inference(clausify,[status(thm)],[f_862_3]) ).

fof(f_863_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_863_2,plain,
    ! [U_2999,U_2998,U_2997,U_2996] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2997),U_2996)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2997),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2999,U_2996))),U_2998)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2998),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2997),U_2998))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2996)) ),
    inference(variable_rename,[status(thm)],[f_863_1]) ).

fof(f_863_3,plain,
    ! [U_2998,U_2996,U_2997,U_2999] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2997),U_2996)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2997),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2999,U_2996))),U_2998)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2998),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2997),U_2998))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2996)) ),
    inference(definitional_conversion,[status(esa)],[f_863_2]) ).

cnf(f_863_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2997),U_2996)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_2997),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_2999,U_2996))),U_2998)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_2998),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_2997),U_2998))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_2996)) ),
    inference(clausify,[status(thm)],[f_863_3]) ).

fof(f_864_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_864_2,plain,
    ! [U_3001,U_3000] :
      ( ( c_SMT_Oz3mod(U_3001,U_3000) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3001,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3000))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3000)) )
      & ( c_SMT_Oz3mod(U_3001,U_3000) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3001,U_3000)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3000)) ) ),
    inference(variable_rename,[status(thm)],[f_864_1]) ).

fof(f_864_3,plain,
    ( ! [U_3005,U_3003] :
        ( c_SMT_Oz3mod(U_3005,U_3003) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3005,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3003))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3003)) )
    & ! [U_3004,U_3002] :
        ( c_SMT_Oz3mod(U_3004,U_3002) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3004,U_3002)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3002)) ) ),
    inference(miniscope,[status(thm)],[f_864_2]) ).

fof(f_864_4,plain,
    ( ! [U_3003,U_3005] :
        ( c_SMT_Oz3mod(U_3005,U_3003) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3005,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3003))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3003)) )
    & ! [U_3002,U_3004] :
        ( c_SMT_Oz3mod(U_3004,U_3002) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3004,U_3002)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3002)) ) ),
    inference(definitional_conversion,[status(esa)],[f_864_3]) ).

cnf(f_864_5,plain,
    ( c_SMT_Oz3mod(U_3004,U_3002) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3004,U_3002)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3002)) ),
    inference(clausify,[status(thm)],[f_864_4]) ).

cnf(f_864_6,plain,
    ( c_SMT_Oz3mod(U_3005,U_3003) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3005,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3003))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3003)) ),
    inference(clausify,[status(thm)],[f_864_4]) ).

fof(f_865_1,plain,
    ! [V_n_2,V_Pa_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_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_865_2,plain,
    ! [U_3012,U_3011,U_3010] :
      ( ( ( hBOOL(hAPP(hAPP(U_3011,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3012),U_3010)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3012,U_3010)))
          | ? [U_3009,U_3008] :
              ( ~ hBOOL(hAPP(hAPP(U_3011,U_3009),U_3008))
              & U_3012 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3010),U_3009)),U_3008)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3008),U_3010))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3008)) ) )
        & ( ! [U_3007,U_3006] :
              ( hBOOL(hAPP(hAPP(U_3011,U_3007),U_3006))
              | U_3012 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3010),U_3007)),U_3006)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3006),U_3010))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3006)) )
          | ~ hBOOL(hAPP(hAPP(U_3011,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3012),U_3010)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3012,U_3010))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3010)) ),
    inference(variable_rename,[status(thm)],[f_865_1]) ).

fof(f_865_3,plain,
    ! [U_3012,U_3011,U_3010] :
      ( ( ( hBOOL(hAPP(hAPP(U_3011,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3012),U_3010)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3012,U_3010)))
          | ? [U_3008] :
              ( ~ hBOOL(hAPP(hAPP(U_3011,sK46(U_3012,U_3011,U_3010)),U_3008))
              & U_3012 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3010),sK46(U_3012,U_3011,U_3010))),U_3008)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3008),U_3010))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3008)) ) )
        & ( ! [U_3007,U_3006] :
              ( hBOOL(hAPP(hAPP(U_3011,U_3007),U_3006))
              | U_3012 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3010),U_3007)),U_3006)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3006),U_3010))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3006)) )
          | ~ hBOOL(hAPP(hAPP(U_3011,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3012),U_3010)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3012,U_3010))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3010)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK46]),skolemize(U_3009,sK46(U_3012,U_3011,U_3010))],[f_865_2]) ).

fof(f_865_4,plain,
    ! [U_3012,U_3011,U_3010] :
      ( ( ( hBOOL(hAPP(hAPP(U_3011,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3012),U_3010)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3012,U_3010)))
          | ( ~ hBOOL(hAPP(hAPP(U_3011,sK46(U_3012,U_3011,U_3010)),sK47(U_3012,U_3011,U_3010)))
            & U_3012 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3010),sK46(U_3012,U_3011,U_3010))),sK47(U_3012,U_3011,U_3010))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK47(U_3012,U_3011,U_3010)),U_3010))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK47(U_3012,U_3011,U_3010))) ) )
        & ( ! [U_3007,U_3006] :
              ( hBOOL(hAPP(hAPP(U_3011,U_3007),U_3006))
              | U_3012 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3010),U_3007)),U_3006)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3006),U_3010))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3006)) )
          | ~ hBOOL(hAPP(hAPP(U_3011,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3012),U_3010)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3012,U_3010))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3010)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK47]),skolemize(U_3008,sK47(U_3012,U_3011,U_3010))],[f_865_3]) ).

fof(f_865_5,plain,
    ( ! [U_3010,U_3011,U_3012] :
        ( ~ hBOOL(hAPP(hAPP(U_3011,sK46(U_3012,U_3011,U_3010)),sK47(U_3012,U_3011,U_3010)))
        | ~ sP244(U_3010,U_3011,U_3012) )
    & ! [U_3010,U_3011,U_3012] :
        ( U_3012 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3010),sK46(U_3012,U_3011,U_3010))),sK47(U_3012,U_3011,U_3010))
        | ~ sP244(U_3010,U_3011,U_3012) )
    & ! [U_3010,U_3011,U_3012] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK47(U_3012,U_3011,U_3010)),U_3010))
        | ~ sP244(U_3010,U_3011,U_3012) )
    & ! [U_3010,U_3011,U_3012] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK47(U_3012,U_3011,U_3010)))
        | ~ sP244(U_3010,U_3011,U_3012) )
    & ! [U_3006,U_3010,U_3007,U_3011,U_3012] :
        ( hBOOL(hAPP(hAPP(U_3011,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3012),U_3010)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3012,U_3010)))
        | sP244(U_3010,U_3011,U_3012)
        | ~ sP245(U_3006,U_3010,U_3007,U_3011,U_3012) )
    & ! [U_3006,U_3010,U_3007,U_3011,U_3012] :
        ( hBOOL(hAPP(hAPP(U_3011,U_3007),U_3006))
        | U_3012 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3010),U_3007)),U_3006)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3006),U_3010))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3006))
        | ~ hBOOL(hAPP(hAPP(U_3011,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3012),U_3010)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3012,U_3010)))
        | ~ sP245(U_3006,U_3010,U_3007,U_3011,U_3012) )
    & ! [U_3006,U_3010,U_3007,U_3011,U_3012] :
        ( sP245(U_3006,U_3010,U_3007,U_3011,U_3012)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3010)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP244,sP245])],[f_865_4]) ).

cnf(f_865_6,plain,
    ( sP245(U_3006,U_3010,U_3007,U_3011,U_3012)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3010)) ),
    inference(clausify,[status(thm)],[f_865_5]) ).

cnf(f_865_7,plain,
    ( hBOOL(hAPP(hAPP(U_3011,U_3007),U_3006))
    | U_3012 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3010),U_3007)),U_3006)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3006),U_3010))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3006))
    | ~ hBOOL(hAPP(hAPP(U_3011,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3012),U_3010)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3012,U_3010)))
    | ~ sP245(U_3006,U_3010,U_3007,U_3011,U_3012) ),
    inference(clausify,[status(thm)],[f_865_5]) ).

cnf(f_865_8,plain,
    ( hBOOL(hAPP(hAPP(U_3011,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3012),U_3010)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3012,U_3010)))
    | sP244(U_3010,U_3011,U_3012)
    | ~ sP245(U_3006,U_3010,U_3007,U_3011,U_3012) ),
    inference(clausify,[status(thm)],[f_865_5]) ).

cnf(f_865_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK47(U_3012,U_3011,U_3010)))
    | ~ sP244(U_3010,U_3011,U_3012) ),
    inference(clausify,[status(thm)],[f_865_5]) ).

cnf(f_865_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK47(U_3012,U_3011,U_3010)),U_3010))
    | ~ sP244(U_3010,U_3011,U_3012) ),
    inference(clausify,[status(thm)],[f_865_5]) ).

cnf(f_865_11,plain,
    ( U_3012 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3010),sK46(U_3012,U_3011,U_3010))),sK47(U_3012,U_3011,U_3010))
    | ~ sP244(U_3010,U_3011,U_3012) ),
    inference(clausify,[status(thm)],[f_865_5]) ).

cnf(f_865_12,plain,
    ( ~ hBOOL(hAPP(hAPP(U_3011,sK46(U_3012,U_3011,U_3010)),sK47(U_3012,U_3011,U_3010)))
    | ~ sP244(U_3010,U_3011,U_3012) ),
    inference(clausify,[status(thm)],[f_865_5]) ).

fof(f_866_1,plain,
    ! [V_n_2,V_Pa_2,V_k_2] :
      ( ( ( hBOOL(hAPP(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_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_866_2,plain,
    ! [U_3019,U_3018,U_3017] :
      ( ( ( hBOOL(hAPP(hAPP(U_3018,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3019),U_3017)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3019,U_3017)))
          | ? [U_3016,U_3015] :
              ( ~ hBOOL(hAPP(hAPP(U_3018,U_3016),U_3015))
              & U_3019 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3017),U_3016)),U_3015)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3015),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3017),U_3015)) ) )
        & ( ! [U_3014,U_3013] :
              ( hBOOL(hAPP(hAPP(U_3018,U_3014),U_3013))
              | U_3019 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3017),U_3014)),U_3013)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3013),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3017),U_3013)) )
          | ~ hBOOL(hAPP(hAPP(U_3018,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3019),U_3017)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3019,U_3017))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3017),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_866_1]) ).

fof(f_866_3,plain,
    ! [U_3019,U_3018,U_3017] :
      ( ( ( hBOOL(hAPP(hAPP(U_3018,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3019),U_3017)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3019,U_3017)))
          | ? [U_3015] :
              ( ~ hBOOL(hAPP(hAPP(U_3018,sK48(U_3019,U_3018,U_3017)),U_3015))
              & U_3019 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3017),sK48(U_3019,U_3018,U_3017))),U_3015)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3015),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3017),U_3015)) ) )
        & ( ! [U_3014,U_3013] :
              ( hBOOL(hAPP(hAPP(U_3018,U_3014),U_3013))
              | U_3019 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3017),U_3014)),U_3013)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3013),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3017),U_3013)) )
          | ~ hBOOL(hAPP(hAPP(U_3018,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3019),U_3017)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3019,U_3017))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3017),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK48]),skolemize(U_3016,sK48(U_3019,U_3018,U_3017))],[f_866_2]) ).

fof(f_866_4,plain,
    ! [U_3019,U_3018,U_3017] :
      ( ( ( hBOOL(hAPP(hAPP(U_3018,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3019),U_3017)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3019,U_3017)))
          | ( ~ hBOOL(hAPP(hAPP(U_3018,sK48(U_3019,U_3018,U_3017)),sK49(U_3019,U_3018,U_3017)))
            & U_3019 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3017),sK48(U_3019,U_3018,U_3017))),sK49(U_3019,U_3018,U_3017))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK49(U_3019,U_3018,U_3017)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3017),sK49(U_3019,U_3018,U_3017))) ) )
        & ( ! [U_3014,U_3013] :
              ( hBOOL(hAPP(hAPP(U_3018,U_3014),U_3013))
              | U_3019 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3017),U_3014)),U_3013)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3013),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3017),U_3013)) )
          | ~ hBOOL(hAPP(hAPP(U_3018,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3019),U_3017)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3019,U_3017))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3017),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK49]),skolemize(U_3015,sK49(U_3019,U_3018,U_3017))],[f_866_3]) ).

fof(f_866_5,plain,
    ( ! [U_3017,U_3018,U_3019] :
        ( ~ hBOOL(hAPP(hAPP(U_3018,sK48(U_3019,U_3018,U_3017)),sK49(U_3019,U_3018,U_3017)))
        | ~ sP246(U_3017,U_3018,U_3019) )
    & ! [U_3017,U_3018,U_3019] :
        ( U_3019 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3017),sK48(U_3019,U_3018,U_3017))),sK49(U_3019,U_3018,U_3017))
        | ~ sP246(U_3017,U_3018,U_3019) )
    & ! [U_3017,U_3018,U_3019] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK49(U_3019,U_3018,U_3017)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP246(U_3017,U_3018,U_3019) )
    & ! [U_3017,U_3018,U_3019] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3017),sK49(U_3019,U_3018,U_3017)))
        | ~ sP246(U_3017,U_3018,U_3019) )
    & ! [U_3013,U_3017,U_3018,U_3014,U_3019] :
        ( hBOOL(hAPP(hAPP(U_3018,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3019),U_3017)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3019,U_3017)))
        | sP246(U_3017,U_3018,U_3019)
        | ~ sP247(U_3013,U_3017,U_3018,U_3014,U_3019) )
    & ! [U_3013,U_3017,U_3018,U_3014,U_3019] :
        ( hBOOL(hAPP(hAPP(U_3018,U_3014),U_3013))
        | U_3019 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3017),U_3014)),U_3013)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3013),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3017),U_3013))
        | ~ hBOOL(hAPP(hAPP(U_3018,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3019),U_3017)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3019,U_3017)))
        | ~ sP247(U_3013,U_3017,U_3018,U_3014,U_3019) )
    & ! [U_3013,U_3017,U_3018,U_3014,U_3019] :
        ( sP247(U_3013,U_3017,U_3018,U_3014,U_3019)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3017),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP246,sP247])],[f_866_4]) ).

cnf(f_866_6,plain,
    ( sP247(U_3013,U_3017,U_3018,U_3014,U_3019)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3017),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_866_5]) ).

cnf(f_866_7,plain,
    ( hBOOL(hAPP(hAPP(U_3018,U_3014),U_3013))
    | U_3019 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3017),U_3014)),U_3013)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3013),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3017),U_3013))
    | ~ hBOOL(hAPP(hAPP(U_3018,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3019),U_3017)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3019,U_3017)))
    | ~ sP247(U_3013,U_3017,U_3018,U_3014,U_3019) ),
    inference(clausify,[status(thm)],[f_866_5]) ).

cnf(f_866_8,plain,
    ( hBOOL(hAPP(hAPP(U_3018,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3019),U_3017)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3019,U_3017)))
    | sP246(U_3017,U_3018,U_3019)
    | ~ sP247(U_3013,U_3017,U_3018,U_3014,U_3019) ),
    inference(clausify,[status(thm)],[f_866_5]) ).

cnf(f_866_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3017),sK49(U_3019,U_3018,U_3017)))
    | ~ sP246(U_3017,U_3018,U_3019) ),
    inference(clausify,[status(thm)],[f_866_5]) ).

cnf(f_866_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK49(U_3019,U_3018,U_3017)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP246(U_3017,U_3018,U_3019) ),
    inference(clausify,[status(thm)],[f_866_5]) ).

cnf(f_866_11,plain,
    ( U_3019 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3017),sK48(U_3019,U_3018,U_3017))),sK49(U_3019,U_3018,U_3017))
    | ~ sP246(U_3017,U_3018,U_3019) ),
    inference(clausify,[status(thm)],[f_866_5]) ).

cnf(f_866_12,plain,
    ( ~ hBOOL(hAPP(hAPP(U_3018,sK48(U_3019,U_3018,U_3017)),sK49(U_3019,U_3018,U_3017)))
    | ~ sP246(U_3017,U_3018,U_3019) ),
    inference(clausify,[status(thm)],[f_866_5]) ).

fof(f_867_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_867_2,plain,
    ! [U_3022,U_3021,U_3020] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3021,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3022),U_3020)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3022),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3021),U_3022),U_3020))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3021,U_3022))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3020)) ),
    inference(variable_rename,[status(thm)],[f_867_1]) ).

fof(f_867_3,plain,
    ! [U_3022,U_3020,U_3021] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3021,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3022),U_3020)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3022),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3021),U_3022),U_3020))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3021,U_3022))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3020)) ),
    inference(definitional_conversion,[status(esa)],[f_867_2]) ).

cnf(f_867_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3021,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3022),U_3020)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3022),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3021),U_3022),U_3020))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3021,U_3022))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3020)) ),
    inference(clausify,[status(thm)],[f_867_3]) ).

fof(f_868_1,plain,
    ! [V_k_2,V_n_2,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2)))
        | ( ? [B_i] :
              ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_Pa_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(V_Pa_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_868_2,plain,
    ! [U_3033,U_3032,U_3031] :
      ( ( hBOOL(hAPP(U_3031,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3032),U_3033)))
        | ( ? [U_3030] :
              ( ~ hBOOL(hAPP(U_3031,U_3030))
              & ? [U_3029] :
                  ( U_3032 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3033),U_3030)),U_3029)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3029),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3033),U_3029)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3033),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_3028] :
              ( ~ hBOOL(hAPP(U_3031,U_3028))
              & ? [U_3027] :
                  ( U_3032 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3033),U_3028)),U_3027)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3027),U_3033))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3027)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3033)) )
        | ( ~ hBOOL(hAPP(U_3031,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3033 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( ( ! [U_3026] :
                ( hBOOL(hAPP(U_3031,U_3026))
                | ! [U_3025] :
                    ( U_3032 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3033),U_3026)),U_3025)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3025),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3033),U_3025)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3033),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3024] :
                ( hBOOL(hAPP(U_3031,U_3024))
                | ! [U_3023] :
                    ( U_3032 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3033),U_3024)),U_3023)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3023),U_3033))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3023)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3033)) )
          & ( hBOOL(hAPP(U_3031,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3033 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3031,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3032),U_3033))) ) ),
    inference(variable_rename,[status(thm)],[f_868_1]) ).

fof(f_868_3,plain,
    ( ! [U_3039,U_3037,U_3035] :
        ( hBOOL(hAPP(U_3035,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3037),U_3039)))
        | ( ? [U_3030] :
              ( ~ hBOOL(hAPP(U_3035,U_3030))
              & ? [U_3029] :
                  ( U_3037 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3039),U_3030)),U_3029)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3029),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3039),U_3029)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3039),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ? [U_3028] :
              ( ~ hBOOL(hAPP(U_3035,U_3028))
              & ? [U_3027] :
                  ( U_3037 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3039),U_3028)),U_3027)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3027),U_3039))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3027)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3039)) )
        | ( ~ hBOOL(hAPP(U_3035,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3039 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3038,U_3036,U_3034] :
        ( ( ( ! [U_3026] :
                ( hBOOL(hAPP(U_3034,U_3026))
                | ! [U_3025] :
                    ( U_3036 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3038),U_3026)),U_3025)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3025),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3038),U_3025)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3038),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3024] :
                ( hBOOL(hAPP(U_3034,U_3024))
                | ! [U_3023] :
                    ( U_3036 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3038),U_3024)),U_3023)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3023),U_3038))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3023)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3038)) )
          & ( hBOOL(hAPP(U_3034,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3038 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3034,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3036),U_3038))) ) ),
    inference(miniscope,[status(thm)],[f_868_2]) ).

fof(f_868_4,plain,
    ( ! [U_3039,U_3037,U_3035] :
        ( hBOOL(hAPP(U_3035,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3037),U_3039)))
        | ( ? [U_3030] :
              ( ~ hBOOL(hAPP(U_3035,U_3030))
              & ? [U_3029] :
                  ( U_3037 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3039),U_3030)),U_3029)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3029),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3039),U_3029)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3039),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_3035,sK50(U_3039,U_3037,U_3035)))
          & ? [U_3027] :
              ( U_3037 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3039),sK50(U_3039,U_3037,U_3035))),U_3027)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3027),U_3039))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3027)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3039)) )
        | ( ~ hBOOL(hAPP(U_3035,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3039 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3038,U_3036,U_3034] :
        ( ( ( ! [U_3026] :
                ( hBOOL(hAPP(U_3034,U_3026))
                | ! [U_3025] :
                    ( U_3036 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3038),U_3026)),U_3025)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3025),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3038),U_3025)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3038),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3024] :
                ( hBOOL(hAPP(U_3034,U_3024))
                | ! [U_3023] :
                    ( U_3036 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3038),U_3024)),U_3023)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3023),U_3038))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3023)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3038)) )
          & ( hBOOL(hAPP(U_3034,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3038 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3034,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3036),U_3038))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK50]),skolemize(U_3028,sK50(U_3039,U_3037,U_3035))],[f_868_3]) ).

fof(f_868_5,plain,
    ( ! [U_3039,U_3037,U_3035] :
        ( hBOOL(hAPP(U_3035,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3037),U_3039)))
        | ( ? [U_3030] :
              ( ~ hBOOL(hAPP(U_3035,U_3030))
              & ? [U_3029] :
                  ( U_3037 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3039),U_3030)),U_3029)
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3029),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3039),U_3029)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3039),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_3035,sK50(U_3039,U_3037,U_3035)))
          & U_3037 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3039),sK50(U_3039,U_3037,U_3035))),sK51(U_3039,U_3037,U_3035))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK51(U_3039,U_3037,U_3035)),U_3039))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK51(U_3039,U_3037,U_3035)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3039)) )
        | ( ~ hBOOL(hAPP(U_3035,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3039 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3038,U_3036,U_3034] :
        ( ( ( ! [U_3026] :
                ( hBOOL(hAPP(U_3034,U_3026))
                | ! [U_3025] :
                    ( U_3036 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3038),U_3026)),U_3025)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3025),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3038),U_3025)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3038),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3024] :
                ( hBOOL(hAPP(U_3034,U_3024))
                | ! [U_3023] :
                    ( U_3036 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3038),U_3024)),U_3023)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3023),U_3038))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3023)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3038)) )
          & ( hBOOL(hAPP(U_3034,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3038 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3034,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3036),U_3038))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK51]),skolemize(U_3027,sK51(U_3039,U_3037,U_3035))],[f_868_4]) ).

fof(f_868_6,plain,
    ( ! [U_3039,U_3037,U_3035] :
        ( hBOOL(hAPP(U_3035,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3037),U_3039)))
        | ( ~ hBOOL(hAPP(U_3035,sK52(U_3039,U_3037,U_3035)))
          & ? [U_3029] :
              ( U_3037 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3039),sK52(U_3039,U_3037,U_3035))),U_3029)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3029),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3039),U_3029)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3039),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_3035,sK50(U_3039,U_3037,U_3035)))
          & U_3037 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3039),sK50(U_3039,U_3037,U_3035))),sK51(U_3039,U_3037,U_3035))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK51(U_3039,U_3037,U_3035)),U_3039))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK51(U_3039,U_3037,U_3035)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3039)) )
        | ( ~ hBOOL(hAPP(U_3035,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3039 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3038,U_3036,U_3034] :
        ( ( ( ! [U_3026] :
                ( hBOOL(hAPP(U_3034,U_3026))
                | ! [U_3025] :
                    ( U_3036 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3038),U_3026)),U_3025)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3025),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3038),U_3025)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3038),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3024] :
                ( hBOOL(hAPP(U_3034,U_3024))
                | ! [U_3023] :
                    ( U_3036 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3038),U_3024)),U_3023)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3023),U_3038))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3023)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3038)) )
          & ( hBOOL(hAPP(U_3034,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3038 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3034,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3036),U_3038))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK52]),skolemize(U_3030,sK52(U_3039,U_3037,U_3035))],[f_868_5]) ).

fof(f_868_7,plain,
    ( ! [U_3039,U_3037,U_3035] :
        ( hBOOL(hAPP(U_3035,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3037),U_3039)))
        | ( ~ hBOOL(hAPP(U_3035,sK52(U_3039,U_3037,U_3035)))
          & U_3037 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3039),sK52(U_3039,U_3037,U_3035))),sK53(U_3039,U_3037,U_3035))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK53(U_3039,U_3037,U_3035)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3039),sK53(U_3039,U_3037,U_3035)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3039),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( ~ hBOOL(hAPP(U_3035,sK50(U_3039,U_3037,U_3035)))
          & U_3037 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3039),sK50(U_3039,U_3037,U_3035))),sK51(U_3039,U_3037,U_3035))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK51(U_3039,U_3037,U_3035)),U_3039))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK51(U_3039,U_3037,U_3035)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3039)) )
        | ( ~ hBOOL(hAPP(U_3035,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & U_3039 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3038,U_3036,U_3034] :
        ( ( ( ! [U_3026] :
                ( hBOOL(hAPP(U_3034,U_3026))
                | ! [U_3025] :
                    ( U_3036 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3038),U_3026)),U_3025)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3025),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3038),U_3025)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3038),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ! [U_3024] :
                ( hBOOL(hAPP(U_3034,U_3024))
                | ! [U_3023] :
                    ( U_3036 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3038),U_3024)),U_3023)
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3023),U_3038))
                    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3023)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3038)) )
          & ( hBOOL(hAPP(U_3034,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | U_3038 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | ~ hBOOL(hAPP(U_3034,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3036),U_3038))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK53]),skolemize(U_3029,sK53(U_3039,U_3037,U_3035))],[f_868_6]) ).

fof(f_868_8,plain,
    ( ! [U_3035,U_3037,U_3039] :
        ( ~ hBOOL(hAPP(U_3035,sK52(U_3039,U_3037,U_3035)))
        | ~ sP251(U_3035,U_3037,U_3039) )
    & ! [U_3035,U_3037,U_3039] :
        ( U_3037 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3039),sK52(U_3039,U_3037,U_3035))),sK53(U_3039,U_3037,U_3035))
        | ~ sP251(U_3035,U_3037,U_3039) )
    & ! [U_3035,U_3037,U_3039] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK53(U_3039,U_3037,U_3035)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP251(U_3035,U_3037,U_3039) )
    & ! [U_3035,U_3037,U_3039] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3039),sK53(U_3039,U_3037,U_3035)))
        | ~ sP251(U_3035,U_3037,U_3039) )
    & ! [U_3035,U_3037,U_3039] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3039),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP251(U_3035,U_3037,U_3039) )
    & ! [U_3035,U_3037,U_3039] :
        ( ~ hBOOL(hAPP(U_3035,sK50(U_3039,U_3037,U_3035)))
        | ~ sP250(U_3035,U_3037,U_3039) )
    & ! [U_3035,U_3037,U_3039] :
        ( U_3037 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3039),sK50(U_3039,U_3037,U_3035))),sK51(U_3039,U_3037,U_3035))
        | ~ sP250(U_3035,U_3037,U_3039) )
    & ! [U_3035,U_3037,U_3039] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK51(U_3039,U_3037,U_3035)),U_3039))
        | ~ sP250(U_3035,U_3037,U_3039) )
    & ! [U_3035,U_3037,U_3039] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK51(U_3039,U_3037,U_3035)))
        | ~ sP250(U_3035,U_3037,U_3039) )
    & ! [U_3035,U_3037,U_3039] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3039))
        | ~ sP250(U_3035,U_3037,U_3039) )
    & ! [U_3035,U_3039] :
        ( ~ hBOOL(hAPP(U_3035,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP249(U_3035,U_3039) )
    & ! [U_3035,U_3039] :
        ( U_3039 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP249(U_3035,U_3039) )
    & ! [U_3025,U_3023,U_3024,U_3026,U_3034,U_3036,U_3038] :
        ( hBOOL(hAPP(U_3034,U_3026))
        | U_3036 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3038),U_3026)),U_3025)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3025),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3038),U_3025))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3038),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP248(U_3025,U_3023,U_3024,U_3026,U_3034,U_3036,U_3038) )
    & ! [U_3025,U_3023,U_3024,U_3026,U_3034,U_3036,U_3038] :
        ( hBOOL(hAPP(U_3034,U_3024))
        | U_3036 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3038),U_3024)),U_3023)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3023),U_3038))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3023))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3038))
        | ~ sP248(U_3025,U_3023,U_3024,U_3026,U_3034,U_3036,U_3038) )
    & ! [U_3025,U_3023,U_3024,U_3026,U_3034,U_3036,U_3038] :
        ( hBOOL(hAPP(U_3034,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | U_3038 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP248(U_3025,U_3023,U_3024,U_3026,U_3034,U_3036,U_3038) )
    & ! [U_3035,U_3037,U_3039] :
        ( hBOOL(hAPP(U_3035,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3037),U_3039)))
        | sP251(U_3035,U_3037,U_3039)
        | sP250(U_3035,U_3037,U_3039)
        | sP249(U_3035,U_3039) )
    & ! [U_3025,U_3023,U_3024,U_3026,U_3034,U_3036,U_3038] :
        ( sP248(U_3025,U_3023,U_3024,U_3026,U_3034,U_3036,U_3038)
        | ~ hBOOL(hAPP(U_3034,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3036),U_3038))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP248,sP249,sP250,sP251])],[f_868_7]) ).

cnf(f_868_9,plain,
    ( sP248(U_3025,U_3023,U_3024,U_3026,U_3034,U_3036,U_3038)
    | ~ hBOOL(hAPP(U_3034,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3036),U_3038))) ),
    inference(clausify,[status(thm)],[f_868_8]) ).

cnf(f_868_10,plain,
    ( hBOOL(hAPP(U_3035,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3037),U_3039)))
    | sP251(U_3035,U_3037,U_3039)
    | sP250(U_3035,U_3037,U_3039)
    | sP249(U_3035,U_3039) ),
    inference(clausify,[status(thm)],[f_868_8]) ).

cnf(f_868_11,plain,
    ( hBOOL(hAPP(U_3034,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | U_3038 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP248(U_3025,U_3023,U_3024,U_3026,U_3034,U_3036,U_3038) ),
    inference(clausify,[status(thm)],[f_868_8]) ).

cnf(f_868_12,plain,
    ( hBOOL(hAPP(U_3034,U_3024))
    | U_3036 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3038),U_3024)),U_3023)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3023),U_3038))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3023))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3038))
    | ~ sP248(U_3025,U_3023,U_3024,U_3026,U_3034,U_3036,U_3038) ),
    inference(clausify,[status(thm)],[f_868_8]) ).

cnf(f_868_13,plain,
    ( hBOOL(hAPP(U_3034,U_3026))
    | U_3036 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3038),U_3026)),U_3025)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3025),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3038),U_3025))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3038),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP248(U_3025,U_3023,U_3024,U_3026,U_3034,U_3036,U_3038) ),
    inference(clausify,[status(thm)],[f_868_8]) ).

cnf(f_868_14,plain,
    ( U_3039 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP249(U_3035,U_3039) ),
    inference(clausify,[status(thm)],[f_868_8]) ).

cnf(f_868_15,plain,
    ( ~ hBOOL(hAPP(U_3035,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP249(U_3035,U_3039) ),
    inference(clausify,[status(thm)],[f_868_8]) ).

cnf(f_868_16,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3039))
    | ~ sP250(U_3035,U_3037,U_3039) ),
    inference(clausify,[status(thm)],[f_868_8]) ).

cnf(f_868_17,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK51(U_3039,U_3037,U_3035)))
    | ~ sP250(U_3035,U_3037,U_3039) ),
    inference(clausify,[status(thm)],[f_868_8]) ).

cnf(f_868_18,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK51(U_3039,U_3037,U_3035)),U_3039))
    | ~ sP250(U_3035,U_3037,U_3039) ),
    inference(clausify,[status(thm)],[f_868_8]) ).

cnf(f_868_19,plain,
    ( U_3037 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3039),sK50(U_3039,U_3037,U_3035))),sK51(U_3039,U_3037,U_3035))
    | ~ sP250(U_3035,U_3037,U_3039) ),
    inference(clausify,[status(thm)],[f_868_8]) ).

cnf(f_868_20,plain,
    ( ~ hBOOL(hAPP(U_3035,sK50(U_3039,U_3037,U_3035)))
    | ~ sP250(U_3035,U_3037,U_3039) ),
    inference(clausify,[status(thm)],[f_868_8]) ).

cnf(f_868_21,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3039),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP251(U_3035,U_3037,U_3039) ),
    inference(clausify,[status(thm)],[f_868_8]) ).

cnf(f_868_22,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3039),sK53(U_3039,U_3037,U_3035)))
    | ~ sP251(U_3035,U_3037,U_3039) ),
    inference(clausify,[status(thm)],[f_868_8]) ).

cnf(f_868_23,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK53(U_3039,U_3037,U_3035)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP251(U_3035,U_3037,U_3039) ),
    inference(clausify,[status(thm)],[f_868_8]) ).

cnf(f_868_24,plain,
    ( U_3037 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3039),sK52(U_3039,U_3037,U_3035))),sK53(U_3039,U_3037,U_3035))
    | ~ sP251(U_3035,U_3037,U_3039) ),
    inference(clausify,[status(thm)],[f_868_8]) ).

cnf(f_868_25,plain,
    ( ~ hBOOL(hAPP(U_3035,sK52(U_3039,U_3037,U_3035)))
    | ~ sP251(U_3035,U_3037,U_3039) ),
    inference(clausify,[status(thm)],[f_868_8]) ).

fof(f_869_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_869_2,plain,
    ! [U_3043,U_3042,U_3041,U_3040] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3040),U_3041) = U_3042
      | U_3041 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3043),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3041),U_3043)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3041)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3043),U_3041))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3043)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3041)) )
      | U_3040 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3041),U_3042)),U_3043) ),
    inference(variable_rename,[status(thm)],[f_869_1]) ).

fof(f_869_3,plain,
    ( ! [U_3041,U_3043] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3043),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3041),U_3043))
        | ~ sP253(U_3041,U_3043) )
    & ! [U_3041,U_3043] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3041))
        | ~ sP253(U_3041,U_3043) )
    & ! [U_3041,U_3043] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3043),U_3041))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3043))
        | ~ sP252(U_3041,U_3043) )
    & ! [U_3041,U_3043] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3041))
        | ~ sP252(U_3041,U_3043) )
    & ! [U_3041,U_3043,U_3042,U_3040] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3040),U_3041) = U_3042
        | U_3041 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | sP253(U_3041,U_3043)
        | sP252(U_3041,U_3043)
        | U_3040 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3041),U_3042)),U_3043) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP252,sP253])],[f_869_2]) ).

cnf(f_869_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3040),U_3041) = U_3042
    | U_3041 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | sP253(U_3041,U_3043)
    | sP252(U_3041,U_3043)
    | U_3040 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3041),U_3042)),U_3043) ),
    inference(clausify,[status(thm)],[f_869_3]) ).

cnf(f_869_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3041))
    | ~ sP252(U_3041,U_3043) ),
    inference(clausify,[status(thm)],[f_869_3]) ).

cnf(f_869_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3043),U_3041))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3043))
    | ~ sP252(U_3041,U_3043) ),
    inference(clausify,[status(thm)],[f_869_3]) ).

cnf(f_869_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3041))
    | ~ sP253(U_3041,U_3043) ),
    inference(clausify,[status(thm)],[f_869_3]) ).

cnf(f_869_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3043),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3041),U_3043))
    | ~ sP253(U_3041,U_3043) ),
    inference(clausify,[status(thm)],[f_869_3]) ).

fof(f_870_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_870_2,plain,
    ! [U_3045,U_3044] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(U_3044,U_3045)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_3045)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_870_1]) ).

fof(f_870_3,plain,
    ! [U_3044,U_3045] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(U_3044,U_3045)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_3045)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_870_2]) ).

cnf(f_870_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OWhile(U_3044,U_3045)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),U_3045)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_870_3]) ).

fof(f_871_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_871_2,plain,
    ! [U_3047,U_3046] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(U_3046,U_3047)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_3047)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_871_1]) ).

fof(f_871_3,plain,
    ! [U_3046,U_3047] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(U_3046,U_3047)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_3047)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_871_2]) ).

cnf(f_871_4,plain,
    c_Com_Ocom_Ocom__size(c_Com_Ocom_OWhile(U_3046,U_3047)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Com_Ocom_Ocom__size(U_3047)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_871_3]) ).

fof(f_872_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_872_2,plain,
    ! [U_3051,U_3050,U_3049,U_3048] :
      ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3048,U_3050),U_3049,U_3051,U_3049)
      | hBOOL(hAPP(U_3048,U_3049)) ),
    inference(variable_rename,[status(thm)],[f_872_1]) ).

fof(f_872_3,plain,
    ! [U_3050,U_3048,U_3049,U_3051] :
      ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3048,U_3050),U_3049,U_3051,U_3049)
      | hBOOL(hAPP(U_3048,U_3049)) ),
    inference(definitional_conversion,[status(esa)],[f_872_2]) ).

cnf(f_872_4,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3048,U_3050),U_3049,U_3051,U_3049)
    | hBOOL(hAPP(U_3048,U_3049)) ),
    inference(clausify,[status(thm)],[f_872_3]) ).

fof(f_873_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_873_2,plain,
    ! [U_3057,U_3056,U_3055,U_3054,U_3053,U_3052] :
      ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3052,U_3054),U_3053,U_3055,U_3057)
      | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3052,U_3054),U_3056,U_3055,U_3057)
      | ~ c_Natural_Oevaln(U_3054,U_3053,U_3055,U_3056)
      | ~ hBOOL(hAPP(U_3052,U_3053)) ),
    inference(variable_rename,[status(thm)],[f_873_1]) ).

fof(f_873_3,plain,
    ! [U_3053,U_3056,U_3055,U_3057,U_3054,U_3052] :
      ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3052,U_3054),U_3053,U_3055,U_3057)
      | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3052,U_3054),U_3056,U_3055,U_3057)
      | ~ c_Natural_Oevaln(U_3054,U_3053,U_3055,U_3056)
      | ~ hBOOL(hAPP(U_3052,U_3053)) ),
    inference(definitional_conversion,[status(esa)],[f_873_2]) ).

cnf(f_873_4,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3052,U_3054),U_3053,U_3055,U_3057)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3052,U_3054),U_3056,U_3055,U_3057)
    | ~ c_Natural_Oevaln(U_3054,U_3053,U_3055,U_3056)
    | ~ hBOOL(hAPP(U_3052,U_3053)) ),
    inference(clausify,[status(thm)],[f_873_3]) ).

fof(f_874_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_874_2,plain,
    ! [U_3062,U_3061,U_3060,U_3059,U_3058] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3058,U_3060)),U_3059),U_3062))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3058,U_3060)),U_3061),U_3062))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3060),U_3059),U_3061))
      | ~ hBOOL(hAPP(U_3058,U_3059)) ),
    inference(variable_rename,[status(thm)],[f_874_1]) ).

fof(f_874_3,plain,
    ! [U_3059,U_3058,U_3060,U_3061,U_3062] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3058,U_3060)),U_3059),U_3062))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3058,U_3060)),U_3061),U_3062))
      | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3060),U_3059),U_3061))
      | ~ hBOOL(hAPP(U_3058,U_3059)) ),
    inference(definitional_conversion,[status(esa)],[f_874_2]) ).

cnf(f_874_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3058,U_3060)),U_3059),U_3062))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3058,U_3060)),U_3061),U_3062))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3060),U_3059),U_3061))
    | ~ hBOOL(hAPP(U_3058,U_3059)) ),
    inference(clausify,[status(thm)],[f_874_3]) ).

fof(f_875_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_875_2,plain,
    ! [U_3065,U_3064,U_3063] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3063,U_3065)),U_3064),U_3064))
      | hBOOL(hAPP(U_3063,U_3064)) ),
    inference(variable_rename,[status(thm)],[f_875_1]) ).

fof(f_875_3,plain,
    ! [U_3065,U_3063,U_3064] :
      ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3063,U_3065)),U_3064),U_3064))
      | hBOOL(hAPP(U_3063,U_3064)) ),
    inference(definitional_conversion,[status(esa)],[f_875_2]) ).

cnf(f_875_4,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3063,U_3065)),U_3064),U_3064))
    | hBOOL(hAPP(U_3063,U_3064)) ),
    inference(clausify,[status(thm)],[f_875_3]) ).

fof(f_876_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_876_2,plain,
    ! [U_3067,U_3066] :
      ( hBOOL(hAPP(c_Com_OWT,U_3067))
      | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_3066,U_3067))) ),
    inference(variable_rename,[status(thm)],[f_876_1]) ).

fof(f_876_3,plain,
    ! [U_3067] :
      ( ! [U_3066] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_3066,U_3067)))
      | hBOOL(hAPP(c_Com_OWT,U_3067)) ),
    inference(miniscope,[status(thm)],[f_876_2]) ).

fof(f_876_4,plain,
    ! [U_3066,U_3067] :
      ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_3066,U_3067)))
      | hBOOL(hAPP(c_Com_OWT,U_3067)) ),
    inference(definitional_conversion,[status(esa)],[f_876_3]) ).

cnf(f_876_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_3066,U_3067)))
    | hBOOL(hAPP(c_Com_OWT,U_3067)) ),
    inference(clausify,[status(thm)],[f_876_4]) ).

fof(f_877_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_877_2,plain,
    ! [U_3071,U_3070,U_3069,U_3068] :
      ( ( c_Com_Ocom_OWhile(U_3068,U_3069) = c_Com_Ocom_OWhile(U_3070,U_3071)
        | U_3069 != U_3071
        | U_3068 != U_3070 )
      & ( ( U_3069 = U_3071
          & U_3068 = U_3070 )
        | c_Com_Ocom_OWhile(U_3068,U_3069) != c_Com_Ocom_OWhile(U_3070,U_3071) ) ),
    inference(variable_rename,[status(thm)],[f_877_1]) ).

fof(f_877_3,plain,
    ( ! [U_3079,U_3077,U_3075,U_3073] :
        ( c_Com_Ocom_OWhile(U_3073,U_3075) = c_Com_Ocom_OWhile(U_3077,U_3079)
        | U_3075 != U_3079
        | U_3073 != U_3077 )
    & ! [U_3078,U_3076,U_3074,U_3072] :
        ( ( U_3074 = U_3078
          & U_3072 = U_3076 )
        | c_Com_Ocom_OWhile(U_3072,U_3074) != c_Com_Ocom_OWhile(U_3076,U_3078) ) ),
    inference(miniscope,[status(thm)],[f_877_2]) ).

fof(f_877_4,plain,
    ( ! [U_3074,U_3078,U_3072,U_3076] :
        ( U_3074 = U_3078
        | ~ sP254(U_3074,U_3078,U_3072,U_3076) )
    & ! [U_3074,U_3078,U_3072,U_3076] :
        ( U_3072 = U_3076
        | ~ sP254(U_3074,U_3078,U_3072,U_3076) )
    & ! [U_3077,U_3073,U_3075,U_3079] :
        ( c_Com_Ocom_OWhile(U_3073,U_3075) = c_Com_Ocom_OWhile(U_3077,U_3079)
        | U_3075 != U_3079
        | U_3073 != U_3077 )
    & ! [U_3074,U_3078,U_3072,U_3076] :
        ( sP254(U_3074,U_3078,U_3072,U_3076)
        | c_Com_Ocom_OWhile(U_3072,U_3074) != c_Com_Ocom_OWhile(U_3076,U_3078) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP254])],[f_877_3]) ).

cnf(f_877_5,plain,
    ( sP254(U_3074,U_3078,U_3072,U_3076)
    | c_Com_Ocom_OWhile(U_3072,U_3074) != c_Com_Ocom_OWhile(U_3076,U_3078) ),
    inference(clausify,[status(thm)],[f_877_4]) ).

cnf(f_877_6,plain,
    ( c_Com_Ocom_OWhile(U_3073,U_3075) = c_Com_Ocom_OWhile(U_3077,U_3079)
    | U_3075 != U_3079
    | U_3073 != U_3077 ),
    inference(clausify,[status(thm)],[f_877_4]) ).

cnf(f_877_7,plain,
    ( U_3072 = U_3076
    | ~ sP254(U_3074,U_3078,U_3072,U_3076) ),
    inference(clausify,[status(thm)],[f_877_4]) ).

cnf(f_877_8,plain,
    ( U_3074 = U_3078
    | ~ sP254(U_3074,U_3078,U_3072,U_3076) ),
    inference(clausify,[status(thm)],[f_877_4]) ).

fof(f_878_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_878_2,plain,
    ! [U_3080] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3080) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_878_1]) ).

fof(f_878_3,plain,
    ! [U_3080] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3080) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_878_2]) ).

cnf(f_878_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3080) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_878_3]) ).

fof(f_879_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_879_2,plain,
    ! [U_3082,U_3081] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3081),U_3082) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3081,U_3082)),U_3082),
    inference(variable_rename,[status(thm)],[f_879_1]) ).

fof(f_879_3,plain,
    ! [U_3082,U_3081] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3081),U_3082) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3081,U_3082)),U_3082),
    inference(definitional_conversion,[status(esa)],[f_879_2]) ).

cnf(f_879_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3081),U_3082) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3081,U_3082)),U_3082),
    inference(clausify,[status(thm)],[f_879_3]) ).

fof(f_880_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_880_2,plain,
    ! [U_3084,U_3083] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3083,U_3084) = U_3083
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3083),U_3084)) ),
    inference(variable_rename,[status(thm)],[f_880_1]) ).

fof(f_880_3,plain,
    ! [U_3083,U_3084] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3083,U_3084) = U_3083
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3083),U_3084)) ),
    inference(definitional_conversion,[status(esa)],[f_880_2]) ).

cnf(f_880_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3083,U_3084) = U_3083
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3083),U_3084)) ),
    inference(clausify,[status(thm)],[f_880_3]) ).

fof(f_881_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_881_2,plain,
    ! [U_3086,U_3085] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3085,U_3086)),U_3085)),
    inference(variable_rename,[status(thm)],[f_881_1]) ).

fof(f_881_3,plain,
    ! [U_3085,U_3086] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3085,U_3086)),U_3085)),
    inference(definitional_conversion,[status(esa)],[f_881_2]) ).

cnf(f_881_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3085,U_3086)),U_3085)),
    inference(clausify,[status(thm)],[f_881_3]) ).

fof(f_882_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_882_2,plain,
    ! [U_3089,U_3088,U_3087] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3087),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3088,U_3089)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3087),U_3088),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3087),U_3089)),
    inference(variable_rename,[status(thm)],[f_882_1]) ).

fof(f_882_3,plain,
    ! [U_3087,U_3088,U_3089] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3087),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3088,U_3089)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3087),U_3088),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3087),U_3089)),
    inference(definitional_conversion,[status(esa)],[f_882_2]) ).

cnf(f_882_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3087),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3088,U_3089)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3087),U_3088),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3087),U_3089)),
    inference(clausify,[status(thm)],[f_882_3]) ).

fof(f_883_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_883_2,plain,
    ! [U_3092,U_3091,U_3090] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3090,U_3091)),U_3092) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3090),U_3092),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3091),U_3092)),
    inference(variable_rename,[status(thm)],[f_883_1]) ).

fof(f_883_3,plain,
    ! [U_3090,U_3091,U_3092] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3090,U_3091)),U_3092) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3090),U_3092),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3091),U_3092)),
    inference(definitional_conversion,[status(esa)],[f_883_2]) ).

cnf(f_883_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3090,U_3091)),U_3092) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3090),U_3092),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3091),U_3092)),
    inference(clausify,[status(thm)],[f_883_3]) ).

fof(f_884_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_884_2,plain,
    ! [U_3094,U_3093] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3093)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3094)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3093),U_3094),
    inference(variable_rename,[status(thm)],[f_884_1]) ).

fof(f_884_3,plain,
    ! [U_3093,U_3094] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3093)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3094)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3093),U_3094),
    inference(definitional_conversion,[status(esa)],[f_884_2]) ).

cnf(f_884_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3093)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3094)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3093),U_3094),
    inference(clausify,[status(thm)],[f_884_3]) ).

fof(f_885_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_885_2,plain,
    ! [U_3096,U_3095] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3095),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3096)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3095)),U_3096),
    inference(variable_rename,[status(thm)],[f_885_1]) ).

fof(f_885_3,plain,
    ! [U_3095,U_3096] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3095),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3096)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3095)),U_3096),
    inference(definitional_conversion,[status(esa)],[f_885_2]) ).

cnf(f_885_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3095),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3096)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3095)),U_3096),
    inference(clausify,[status(thm)],[f_885_3]) ).

fof(f_886_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_886_2,plain,
    ! [U_3098,U_3097] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3097),U_3098),c_Groups_Ozero__class_Ozero(U_3097)) = c_Groups_Ozero__class_Ozero(U_3097)
      | ~ class_Divides_Osemiring__div(U_3097) ),
    inference(variable_rename,[status(thm)],[f_886_1]) ).

fof(f_886_3,plain,
    ! [U_3097,U_3098] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3097),U_3098),c_Groups_Ozero__class_Ozero(U_3097)) = c_Groups_Ozero__class_Ozero(U_3097)
      | ~ class_Divides_Osemiring__div(U_3097) ),
    inference(definitional_conversion,[status(esa)],[f_886_2]) ).

cnf(f_886_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3097),U_3098),c_Groups_Ozero__class_Ozero(U_3097)) = c_Groups_Ozero__class_Ozero(U_3097)
    | ~ class_Divides_Osemiring__div(U_3097) ),
    inference(clausify,[status(thm)],[f_886_3]) ).

fof(f_887_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_887_2,plain,
    ! [U_3100,U_3099] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3099),c_Groups_Ozero__class_Ozero(U_3099)),U_3100) = c_Groups_Ozero__class_Ozero(U_3099)
      | ~ class_Divides_Osemiring__div(U_3099) ),
    inference(variable_rename,[status(thm)],[f_887_1]) ).

fof(f_887_3,plain,
    ! [U_3099,U_3100] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3099),c_Groups_Ozero__class_Ozero(U_3099)),U_3100) = c_Groups_Ozero__class_Ozero(U_3099)
      | ~ class_Divides_Osemiring__div(U_3099) ),
    inference(definitional_conversion,[status(esa)],[f_887_2]) ).

cnf(f_887_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3099),c_Groups_Ozero__class_Ozero(U_3099)),U_3100) = c_Groups_Ozero__class_Ozero(U_3099)
    | ~ class_Divides_Osemiring__div(U_3099) ),
    inference(clausify,[status(thm)],[f_887_3]) ).

fof(f_888_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_888_2,plain,
    ! [U_3102,U_3101] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3101),U_3102),c_Groups_Oone__class_Oone(U_3101)) = U_3102
      | ~ class_Divides_Osemiring__div(U_3101) ),
    inference(variable_rename,[status(thm)],[f_888_1]) ).

fof(f_888_3,plain,
    ! [U_3101,U_3102] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3101),U_3102),c_Groups_Oone__class_Oone(U_3101)) = U_3102
      | ~ class_Divides_Osemiring__div(U_3101) ),
    inference(definitional_conversion,[status(esa)],[f_888_2]) ).

cnf(f_888_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3101),U_3102),c_Groups_Oone__class_Oone(U_3101)) = U_3102
    | ~ class_Divides_Osemiring__div(U_3101) ),
    inference(clausify,[status(thm)],[f_888_3]) ).

fof(f_889_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_889_2,plain,
    ! [U_3108,U_3107,U_3106,U_3105] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3105,U_3106),U_3107,U_3108,U_3107)
        | ( ! [U_3104] :
              ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3105,U_3106),U_3104,U_3108,U_3107)
              | ~ c_Natural_Oevaln(U_3106,U_3107,U_3108,U_3104) )
          & hBOOL(hAPP(U_3105,U_3107)) ) )
      & ( ? [U_3103] :
            ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3105,U_3106),U_3103,U_3108,U_3107)
            & c_Natural_Oevaln(U_3106,U_3107,U_3108,U_3103) )
        | ~ hBOOL(hAPP(U_3105,U_3107))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3105,U_3106),U_3107,U_3108,U_3107) ) ),
    inference(variable_rename,[status(thm)],[f_889_1]) ).

fof(f_889_3,plain,
    ( ! [U_3116,U_3114,U_3112,U_3110] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3110,U_3112),U_3114,U_3116,U_3114)
        | ( ! [U_3104] :
              ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3110,U_3112),U_3104,U_3116,U_3114)
              | ~ c_Natural_Oevaln(U_3112,U_3114,U_3116,U_3104) )
          & hBOOL(hAPP(U_3110,U_3114)) ) )
    & ! [U_3115,U_3113,U_3111,U_3109] :
        ( ? [U_3103] :
            ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3109,U_3111),U_3103,U_3115,U_3113)
            & c_Natural_Oevaln(U_3111,U_3113,U_3115,U_3103) )
        | ~ hBOOL(hAPP(U_3109,U_3113))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3109,U_3111),U_3113,U_3115,U_3113) ) ),
    inference(miniscope,[status(thm)],[f_889_2]) ).

fof(f_889_4,plain,
    ( ! [U_3116,U_3114,U_3112,U_3110] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3110,U_3112),U_3114,U_3116,U_3114)
        | ( ! [U_3104] :
              ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3110,U_3112),U_3104,U_3116,U_3114)
              | ~ c_Natural_Oevaln(U_3112,U_3114,U_3116,U_3104) )
          & hBOOL(hAPP(U_3110,U_3114)) ) )
    & ! [U_3115,U_3113,U_3111,U_3109] :
        ( ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3109,U_3111),sK54(U_3115,U_3113,U_3111,U_3109),U_3115,U_3113)
          & c_Natural_Oevaln(U_3111,U_3113,U_3115,sK54(U_3115,U_3113,U_3111,U_3109)) )
        | ~ hBOOL(hAPP(U_3109,U_3113))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3109,U_3111),U_3113,U_3115,U_3113) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK54]),skolemize(U_3103,sK54(U_3115,U_3113,U_3111,U_3109))],[f_889_3]) ).

fof(f_889_5,plain,
    ( ! [U_3104,U_3116,U_3112,U_3114,U_3110] :
        ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3110,U_3112),U_3104,U_3116,U_3114)
        | ~ c_Natural_Oevaln(U_3112,U_3114,U_3116,U_3104)
        | ~ sP256(U_3104,U_3116,U_3112,U_3114,U_3110) )
    & ! [U_3104,U_3116,U_3112,U_3114,U_3110] :
        ( hBOOL(hAPP(U_3110,U_3114))
        | ~ sP256(U_3104,U_3116,U_3112,U_3114,U_3110) )
    & ! [U_3113,U_3111,U_3109,U_3115] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3109,U_3111),sK54(U_3115,U_3113,U_3111,U_3109),U_3115,U_3113)
        | ~ sP255(U_3113,U_3111,U_3109,U_3115) )
    & ! [U_3113,U_3111,U_3109,U_3115] :
        ( c_Natural_Oevaln(U_3111,U_3113,U_3115,sK54(U_3115,U_3113,U_3111,U_3109))
        | ~ sP255(U_3113,U_3111,U_3109,U_3115) )
    & ! [U_3104,U_3116,U_3112,U_3114,U_3110] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3110,U_3112),U_3114,U_3116,U_3114)
        | sP256(U_3104,U_3116,U_3112,U_3114,U_3110) )
    & ! [U_3113,U_3111,U_3109,U_3115] :
        ( sP255(U_3113,U_3111,U_3109,U_3115)
        | ~ hBOOL(hAPP(U_3109,U_3113))
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3109,U_3111),U_3113,U_3115,U_3113) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP255,sP256])],[f_889_4]) ).

cnf(f_889_6,plain,
    ( sP255(U_3113,U_3111,U_3109,U_3115)
    | ~ hBOOL(hAPP(U_3109,U_3113))
    | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3109,U_3111),U_3113,U_3115,U_3113) ),
    inference(clausify,[status(thm)],[f_889_5]) ).

cnf(f_889_7,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3110,U_3112),U_3114,U_3116,U_3114)
    | sP256(U_3104,U_3116,U_3112,U_3114,U_3110) ),
    inference(clausify,[status(thm)],[f_889_5]) ).

cnf(f_889_8,plain,
    ( c_Natural_Oevaln(U_3111,U_3113,U_3115,sK54(U_3115,U_3113,U_3111,U_3109))
    | ~ sP255(U_3113,U_3111,U_3109,U_3115) ),
    inference(clausify,[status(thm)],[f_889_5]) ).

cnf(f_889_9,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3109,U_3111),sK54(U_3115,U_3113,U_3111,U_3109),U_3115,U_3113)
    | ~ sP255(U_3113,U_3111,U_3109,U_3115) ),
    inference(clausify,[status(thm)],[f_889_5]) ).

cnf(f_889_10,plain,
    ( hBOOL(hAPP(U_3110,U_3114))
    | ~ sP256(U_3104,U_3116,U_3112,U_3114,U_3110) ),
    inference(clausify,[status(thm)],[f_889_5]) ).

cnf(f_889_11,plain,
    ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3110,U_3112),U_3104,U_3116,U_3114)
    | ~ c_Natural_Oevaln(U_3112,U_3114,U_3116,U_3104)
    | ~ sP256(U_3104,U_3116,U_3112,U_3114,U_3110) ),
    inference(clausify,[status(thm)],[f_889_5]) ).

fof(f_890_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_890_2,plain,
    ! [U_3123,U_3122,U_3121,U_3120,U_3119] :
      ( ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3119,U_3120),U_3121,U_3122,U_3123)
        | ( ( ! [U_3118] :
                ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3119,U_3120),U_3118,U_3122,U_3123)
                | ~ c_Natural_Oevaln(U_3120,U_3121,U_3122,U_3118) )
            | ~ hBOOL(hAPP(U_3119,U_3121)) )
          & ( hBOOL(hAPP(U_3119,U_3121))
            | U_3123 != U_3121 ) ) )
      & ( ( ? [U_3117] :
              ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3119,U_3120),U_3117,U_3122,U_3123)
              & c_Natural_Oevaln(U_3120,U_3121,U_3122,U_3117) )
          & hBOOL(hAPP(U_3119,U_3121)) )
        | ( ~ hBOOL(hAPP(U_3119,U_3121))
          & U_3123 = U_3121 )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3119,U_3120),U_3121,U_3122,U_3123) ) ),
    inference(variable_rename,[status(thm)],[f_890_1]) ).

fof(f_890_3,plain,
    ( ! [U_3133,U_3131,U_3129,U_3127,U_3125] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3125,U_3127),U_3129,U_3131,U_3133)
        | ( ( ! [U_3118] :
                ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3125,U_3127),U_3118,U_3131,U_3133)
                | ~ c_Natural_Oevaln(U_3127,U_3129,U_3131,U_3118) )
            | ~ hBOOL(hAPP(U_3125,U_3129)) )
          & ( hBOOL(hAPP(U_3125,U_3129))
            | U_3133 != U_3129 ) ) )
    & ! [U_3132,U_3130,U_3128,U_3126,U_3124] :
        ( ( ? [U_3117] :
              ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3124,U_3126),U_3117,U_3130,U_3132)
              & c_Natural_Oevaln(U_3126,U_3128,U_3130,U_3117) )
          & hBOOL(hAPP(U_3124,U_3128)) )
        | ( ~ hBOOL(hAPP(U_3124,U_3128))
          & U_3132 = U_3128 )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3124,U_3126),U_3128,U_3130,U_3132) ) ),
    inference(miniscope,[status(thm)],[f_890_2]) ).

fof(f_890_4,plain,
    ( ! [U_3133,U_3131,U_3129,U_3127,U_3125] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3125,U_3127),U_3129,U_3131,U_3133)
        | ( ( ! [U_3118] :
                ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3125,U_3127),U_3118,U_3131,U_3133)
                | ~ c_Natural_Oevaln(U_3127,U_3129,U_3131,U_3118) )
            | ~ hBOOL(hAPP(U_3125,U_3129)) )
          & ( hBOOL(hAPP(U_3125,U_3129))
            | U_3133 != U_3129 ) ) )
    & ! [U_3132,U_3130,U_3128,U_3126,U_3124] :
        ( ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3124,U_3126),sK55(U_3132,U_3130,U_3128,U_3126,U_3124),U_3130,U_3132)
          & c_Natural_Oevaln(U_3126,U_3128,U_3130,sK55(U_3132,U_3130,U_3128,U_3126,U_3124))
          & hBOOL(hAPP(U_3124,U_3128)) )
        | ( ~ hBOOL(hAPP(U_3124,U_3128))
          & U_3132 = U_3128 )
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3124,U_3126),U_3128,U_3130,U_3132) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK55]),skolemize(U_3117,sK55(U_3132,U_3130,U_3128,U_3126,U_3124))],[f_890_3]) ).

fof(f_890_5,plain,
    ( ! [U_3118,U_3133,U_3131,U_3127,U_3129,U_3125] :
        ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3125,U_3127),U_3118,U_3131,U_3133)
        | ~ c_Natural_Oevaln(U_3127,U_3129,U_3131,U_3118)
        | ~ hBOOL(hAPP(U_3125,U_3129))
        | ~ sP259(U_3118,U_3133,U_3131,U_3127,U_3129,U_3125) )
    & ! [U_3118,U_3133,U_3131,U_3127,U_3129,U_3125] :
        ( hBOOL(hAPP(U_3125,U_3129))
        | U_3133 != U_3129
        | ~ sP259(U_3118,U_3133,U_3131,U_3127,U_3129,U_3125) )
    & ! [U_3132,U_3128,U_3130,U_3126,U_3124] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3124,U_3126),sK55(U_3132,U_3130,U_3128,U_3126,U_3124),U_3130,U_3132)
        | ~ sP258(U_3132,U_3128,U_3130,U_3126,U_3124) )
    & ! [U_3132,U_3128,U_3130,U_3126,U_3124] :
        ( c_Natural_Oevaln(U_3126,U_3128,U_3130,sK55(U_3132,U_3130,U_3128,U_3126,U_3124))
        | ~ sP258(U_3132,U_3128,U_3130,U_3126,U_3124) )
    & ! [U_3132,U_3128,U_3130,U_3126,U_3124] :
        ( hBOOL(hAPP(U_3124,U_3128))
        | ~ sP258(U_3132,U_3128,U_3130,U_3126,U_3124) )
    & ! [U_3132,U_3128,U_3124] :
        ( ~ hBOOL(hAPP(U_3124,U_3128))
        | ~ sP257(U_3132,U_3128,U_3124) )
    & ! [U_3132,U_3128,U_3124] :
        ( U_3132 = U_3128
        | ~ sP257(U_3132,U_3128,U_3124) )
    & ! [U_3118,U_3133,U_3131,U_3127,U_3129,U_3125] :
        ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3125,U_3127),U_3129,U_3131,U_3133)
        | sP259(U_3118,U_3133,U_3131,U_3127,U_3129,U_3125) )
    & ! [U_3132,U_3128,U_3130,U_3126,U_3124] :
        ( sP258(U_3132,U_3128,U_3130,U_3126,U_3124)
        | sP257(U_3132,U_3128,U_3124)
        | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3124,U_3126),U_3128,U_3130,U_3132) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP257,sP258,sP259])],[f_890_4]) ).

cnf(f_890_6,plain,
    ( sP258(U_3132,U_3128,U_3130,U_3126,U_3124)
    | sP257(U_3132,U_3128,U_3124)
    | ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3124,U_3126),U_3128,U_3130,U_3132) ),
    inference(clausify,[status(thm)],[f_890_5]) ).

cnf(f_890_7,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3125,U_3127),U_3129,U_3131,U_3133)
    | sP259(U_3118,U_3133,U_3131,U_3127,U_3129,U_3125) ),
    inference(clausify,[status(thm)],[f_890_5]) ).

cnf(f_890_8,plain,
    ( U_3132 = U_3128
    | ~ sP257(U_3132,U_3128,U_3124) ),
    inference(clausify,[status(thm)],[f_890_5]) ).

cnf(f_890_9,plain,
    ( ~ hBOOL(hAPP(U_3124,U_3128))
    | ~ sP257(U_3132,U_3128,U_3124) ),
    inference(clausify,[status(thm)],[f_890_5]) ).

cnf(f_890_10,plain,
    ( hBOOL(hAPP(U_3124,U_3128))
    | ~ sP258(U_3132,U_3128,U_3130,U_3126,U_3124) ),
    inference(clausify,[status(thm)],[f_890_5]) ).

cnf(f_890_11,plain,
    ( c_Natural_Oevaln(U_3126,U_3128,U_3130,sK55(U_3132,U_3130,U_3128,U_3126,U_3124))
    | ~ sP258(U_3132,U_3128,U_3130,U_3126,U_3124) ),
    inference(clausify,[status(thm)],[f_890_5]) ).

cnf(f_890_12,plain,
    ( c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3124,U_3126),sK55(U_3132,U_3130,U_3128,U_3126,U_3124),U_3130,U_3132)
    | ~ sP258(U_3132,U_3128,U_3130,U_3126,U_3124) ),
    inference(clausify,[status(thm)],[f_890_5]) ).

cnf(f_890_13,plain,
    ( hBOOL(hAPP(U_3125,U_3129))
    | U_3133 != U_3129
    | ~ sP259(U_3118,U_3133,U_3131,U_3127,U_3129,U_3125) ),
    inference(clausify,[status(thm)],[f_890_5]) ).

cnf(f_890_14,plain,
    ( ~ c_Natural_Oevaln(c_Com_Ocom_OWhile(U_3125,U_3127),U_3118,U_3131,U_3133)
    | ~ c_Natural_Oevaln(U_3127,U_3129,U_3131,U_3118)
    | ~ hBOOL(hAPP(U_3125,U_3129))
    | ~ sP259(U_3118,U_3133,U_3131,U_3127,U_3129,U_3125) ),
    inference(clausify,[status(thm)],[f_890_5]) ).

fof(f_891_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_891_2,plain,
    ! [U_3139,U_3138,U_3137,U_3136] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3136,U_3137)),U_3138),U_3139))
        | ( ( ! [U_3135] :
                ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3136,U_3137)),U_3135),U_3139))
                | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3137),U_3138),U_3135)) )
            | ~ hBOOL(hAPP(U_3136,U_3138)) )
          & ( hBOOL(hAPP(U_3136,U_3138))
            | U_3139 != U_3138 ) ) )
      & ( ( ? [U_3134] :
              ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3136,U_3137)),U_3134),U_3139))
              & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3137),U_3138),U_3134)) )
          & hBOOL(hAPP(U_3136,U_3138)) )
        | ( ~ hBOOL(hAPP(U_3136,U_3138))
          & U_3139 = U_3138 )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3136,U_3137)),U_3138),U_3139)) ) ),
    inference(variable_rename,[status(thm)],[f_891_1]) ).

fof(f_891_3,plain,
    ( ! [U_3147,U_3145,U_3143,U_3141] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3141,U_3143)),U_3145),U_3147))
        | ( ( ! [U_3135] :
                ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3141,U_3143)),U_3135),U_3147))
                | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3143),U_3145),U_3135)) )
            | ~ hBOOL(hAPP(U_3141,U_3145)) )
          & ( hBOOL(hAPP(U_3141,U_3145))
            | U_3147 != U_3145 ) ) )
    & ! [U_3146,U_3144,U_3142,U_3140] :
        ( ( ? [U_3134] :
              ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3140,U_3142)),U_3134),U_3146))
              & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3142),U_3144),U_3134)) )
          & hBOOL(hAPP(U_3140,U_3144)) )
        | ( ~ hBOOL(hAPP(U_3140,U_3144))
          & U_3146 = U_3144 )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3140,U_3142)),U_3144),U_3146)) ) ),
    inference(miniscope,[status(thm)],[f_891_2]) ).

fof(f_891_4,plain,
    ( ! [U_3147,U_3145,U_3143,U_3141] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3141,U_3143)),U_3145),U_3147))
        | ( ( ! [U_3135] :
                ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3141,U_3143)),U_3135),U_3147))
                | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3143),U_3145),U_3135)) )
            | ~ hBOOL(hAPP(U_3141,U_3145)) )
          & ( hBOOL(hAPP(U_3141,U_3145))
            | U_3147 != U_3145 ) ) )
    & ! [U_3146,U_3144,U_3142,U_3140] :
        ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3140,U_3142)),sK56(U_3146,U_3144,U_3142,U_3140)),U_3146))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3142),U_3144),sK56(U_3146,U_3144,U_3142,U_3140)))
          & hBOOL(hAPP(U_3140,U_3144)) )
        | ( ~ hBOOL(hAPP(U_3140,U_3144))
          & U_3146 = U_3144 )
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3140,U_3142)),U_3144),U_3146)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK56]),skolemize(U_3134,sK56(U_3146,U_3144,U_3142,U_3140))],[f_891_3]) ).

fof(f_891_5,plain,
    ( ! [U_3141,U_3135,U_3143,U_3145,U_3147] :
        ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3141,U_3143)),U_3135),U_3147))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3143),U_3145),U_3135))
        | ~ hBOOL(hAPP(U_3141,U_3145))
        | ~ sP262(U_3141,U_3135,U_3143,U_3145,U_3147) )
    & ! [U_3141,U_3135,U_3143,U_3145,U_3147] :
        ( hBOOL(hAPP(U_3141,U_3145))
        | U_3147 != U_3145
        | ~ sP262(U_3141,U_3135,U_3143,U_3145,U_3147) )
    & ! [U_3140,U_3144,U_3142,U_3146] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3140,U_3142)),sK56(U_3146,U_3144,U_3142,U_3140)),U_3146))
        | ~ sP261(U_3140,U_3144,U_3142,U_3146) )
    & ! [U_3140,U_3144,U_3142,U_3146] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3142),U_3144),sK56(U_3146,U_3144,U_3142,U_3140)))
        | ~ sP261(U_3140,U_3144,U_3142,U_3146) )
    & ! [U_3140,U_3144,U_3142,U_3146] :
        ( hBOOL(hAPP(U_3140,U_3144))
        | ~ sP261(U_3140,U_3144,U_3142,U_3146) )
    & ! [U_3140,U_3144,U_3146] :
        ( ~ hBOOL(hAPP(U_3140,U_3144))
        | ~ sP260(U_3140,U_3144,U_3146) )
    & ! [U_3140,U_3144,U_3146] :
        ( U_3146 = U_3144
        | ~ sP260(U_3140,U_3144,U_3146) )
    & ! [U_3141,U_3135,U_3143,U_3145,U_3147] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3141,U_3143)),U_3145),U_3147))
        | sP262(U_3141,U_3135,U_3143,U_3145,U_3147) )
    & ! [U_3140,U_3144,U_3142,U_3146] :
        ( sP261(U_3140,U_3144,U_3142,U_3146)
        | sP260(U_3140,U_3144,U_3146)
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3140,U_3142)),U_3144),U_3146)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP260,sP261,sP262])],[f_891_4]) ).

cnf(f_891_6,plain,
    ( sP261(U_3140,U_3144,U_3142,U_3146)
    | sP260(U_3140,U_3144,U_3146)
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3140,U_3142)),U_3144),U_3146)) ),
    inference(clausify,[status(thm)],[f_891_5]) ).

cnf(f_891_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3141,U_3143)),U_3145),U_3147))
    | sP262(U_3141,U_3135,U_3143,U_3145,U_3147) ),
    inference(clausify,[status(thm)],[f_891_5]) ).

cnf(f_891_8,plain,
    ( U_3146 = U_3144
    | ~ sP260(U_3140,U_3144,U_3146) ),
    inference(clausify,[status(thm)],[f_891_5]) ).

cnf(f_891_9,plain,
    ( ~ hBOOL(hAPP(U_3140,U_3144))
    | ~ sP260(U_3140,U_3144,U_3146) ),
    inference(clausify,[status(thm)],[f_891_5]) ).

cnf(f_891_10,plain,
    ( hBOOL(hAPP(U_3140,U_3144))
    | ~ sP261(U_3140,U_3144,U_3142,U_3146) ),
    inference(clausify,[status(thm)],[f_891_5]) ).

cnf(f_891_11,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3142),U_3144),sK56(U_3146,U_3144,U_3142,U_3140)))
    | ~ sP261(U_3140,U_3144,U_3142,U_3146) ),
    inference(clausify,[status(thm)],[f_891_5]) ).

cnf(f_891_12,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3140,U_3142)),sK56(U_3146,U_3144,U_3142,U_3140)),U_3146))
    | ~ sP261(U_3140,U_3144,U_3142,U_3146) ),
    inference(clausify,[status(thm)],[f_891_5]) ).

cnf(f_891_13,plain,
    ( hBOOL(hAPP(U_3141,U_3145))
    | U_3147 != U_3145
    | ~ sP262(U_3141,U_3135,U_3143,U_3145,U_3147) ),
    inference(clausify,[status(thm)],[f_891_5]) ).

cnf(f_891_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3141,U_3143)),U_3135),U_3147))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3143),U_3145),U_3135))
    | ~ hBOOL(hAPP(U_3141,U_3145))
    | ~ sP262(U_3141,U_3135,U_3143,U_3145,U_3147) ),
    inference(clausify,[status(thm)],[f_891_5]) ).

fof(f_892_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_892_2,plain,
    ! [U_3152,U_3151,U_3150] :
      ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3150,U_3151)),U_3152),U_3152))
        | ( ! [U_3149] :
              ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3150,U_3151)),U_3149),U_3152))
              | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3151),U_3152),U_3149)) )
          & hBOOL(hAPP(U_3150,U_3152)) ) )
      & ( ? [U_3148] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3150,U_3151)),U_3148),U_3152))
            & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3151),U_3152),U_3148)) )
        | ~ hBOOL(hAPP(U_3150,U_3152))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3150,U_3151)),U_3152),U_3152)) ) ),
    inference(variable_rename,[status(thm)],[f_892_1]) ).

fof(f_892_3,plain,
    ( ! [U_3158,U_3156,U_3154] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3154,U_3156)),U_3158),U_3158))
        | ( ! [U_3149] :
              ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3154,U_3156)),U_3149),U_3158))
              | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3156),U_3158),U_3149)) )
          & hBOOL(hAPP(U_3154,U_3158)) ) )
    & ! [U_3157,U_3155,U_3153] :
        ( ? [U_3148] :
            ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3153,U_3155)),U_3148),U_3157))
            & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3155),U_3157),U_3148)) )
        | ~ hBOOL(hAPP(U_3153,U_3157))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3153,U_3155)),U_3157),U_3157)) ) ),
    inference(miniscope,[status(thm)],[f_892_2]) ).

fof(f_892_4,plain,
    ( ! [U_3158,U_3156,U_3154] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3154,U_3156)),U_3158),U_3158))
        | ( ! [U_3149] :
              ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3154,U_3156)),U_3149),U_3158))
              | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3156),U_3158),U_3149)) )
          & hBOOL(hAPP(U_3154,U_3158)) ) )
    & ! [U_3157,U_3155,U_3153] :
        ( ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3153,U_3155)),sK57(U_3157,U_3155,U_3153)),U_3157))
          & hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3155),U_3157),sK57(U_3157,U_3155,U_3153))) )
        | ~ hBOOL(hAPP(U_3153,U_3157))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3153,U_3155)),U_3157),U_3157)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK57]),skolemize(U_3148,sK57(U_3157,U_3155,U_3153))],[f_892_3]) ).

fof(f_892_5,plain,
    ( ! [U_3149,U_3158,U_3154,U_3156] :
        ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3154,U_3156)),U_3149),U_3158))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3156),U_3158),U_3149))
        | ~ sP264(U_3149,U_3158,U_3154,U_3156) )
    & ! [U_3149,U_3158,U_3154,U_3156] :
        ( hBOOL(hAPP(U_3154,U_3158))
        | ~ sP264(U_3149,U_3158,U_3154,U_3156) )
    & ! [U_3155,U_3153,U_3157] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3153,U_3155)),sK57(U_3157,U_3155,U_3153)),U_3157))
        | ~ sP263(U_3155,U_3153,U_3157) )
    & ! [U_3155,U_3153,U_3157] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3155),U_3157),sK57(U_3157,U_3155,U_3153)))
        | ~ sP263(U_3155,U_3153,U_3157) )
    & ! [U_3149,U_3158,U_3154,U_3156] :
        ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3154,U_3156)),U_3158),U_3158))
        | sP264(U_3149,U_3158,U_3154,U_3156) )
    & ! [U_3155,U_3153,U_3157] :
        ( sP263(U_3155,U_3153,U_3157)
        | ~ hBOOL(hAPP(U_3153,U_3157))
        | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3153,U_3155)),U_3157),U_3157)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP263,sP264])],[f_892_4]) ).

cnf(f_892_6,plain,
    ( sP263(U_3155,U_3153,U_3157)
    | ~ hBOOL(hAPP(U_3153,U_3157))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3153,U_3155)),U_3157),U_3157)) ),
    inference(clausify,[status(thm)],[f_892_5]) ).

cnf(f_892_7,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3154,U_3156)),U_3158),U_3158))
    | sP264(U_3149,U_3158,U_3154,U_3156) ),
    inference(clausify,[status(thm)],[f_892_5]) ).

cnf(f_892_8,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3155),U_3157),sK57(U_3157,U_3155,U_3153)))
    | ~ sP263(U_3155,U_3153,U_3157) ),
    inference(clausify,[status(thm)],[f_892_5]) ).

cnf(f_892_9,plain,
    ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3153,U_3155)),sK57(U_3157,U_3155,U_3153)),U_3157))
    | ~ sP263(U_3155,U_3153,U_3157) ),
    inference(clausify,[status(thm)],[f_892_5]) ).

cnf(f_892_10,plain,
    ( hBOOL(hAPP(U_3154,U_3158))
    | ~ sP264(U_3149,U_3158,U_3154,U_3156) ),
    inference(clausify,[status(thm)],[f_892_5]) ).

cnf(f_892_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(U_3154,U_3156)),U_3149),U_3158))
    | ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(U_3156),U_3158),U_3149))
    | ~ sP264(U_3149,U_3158,U_3154,U_3156) ),
    inference(clausify,[status(thm)],[f_892_5]) ).

fof(f_893_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_893_2,plain,
    ! [U_3160,U_3159] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_3160,U_3159)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_3159)) ),
    inference(variable_rename,[status(thm)],[f_893_1]) ).

fof(f_893_3,plain,
    ! [U_3159,U_3160] :
      ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_3160,U_3159)))
      | ~ hBOOL(hAPP(c_Com_OWT,U_3159)) ),
    inference(definitional_conversion,[status(esa)],[f_893_2]) ).

cnf(f_893_4,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_3160,U_3159)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_3159)) ),
    inference(clausify,[status(thm)],[f_893_3]) ).

fof(f_894_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_894_2,plain,
    ! [U_3162,U_3161] :
      ( ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_3161,U_3162)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_3162)) )
      & ( hBOOL(hAPP(c_Com_OWT,U_3162))
        | ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_3161,U_3162))) ) ),
    inference(variable_rename,[status(thm)],[f_894_1]) ).

fof(f_894_3,plain,
    ( ! [U_3166] :
        ( ! [U_3164] : hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_3164,U_3166)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_3166)) )
    & ! [U_3165] :
        ( ! [U_3163] : ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_3163,U_3165)))
        | hBOOL(hAPP(c_Com_OWT,U_3165)) ) ),
    inference(miniscope,[status(thm)],[f_894_2]) ).

fof(f_894_4,plain,
    ( ! [U_3166,U_3164] :
        ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_3164,U_3166)))
        | ~ hBOOL(hAPP(c_Com_OWT,U_3166)) )
    & ! [U_3163,U_3165] :
        ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_3163,U_3165)))
        | hBOOL(hAPP(c_Com_OWT,U_3165)) ) ),
    inference(definitional_conversion,[status(esa)],[f_894_3]) ).

cnf(f_894_5,plain,
    ( ~ hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_3163,U_3165)))
    | hBOOL(hAPP(c_Com_OWT,U_3165)) ),
    inference(clausify,[status(thm)],[f_894_4]) ).

cnf(f_894_6,plain,
    ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(U_3164,U_3166)))
    | ~ hBOOL(hAPP(c_Com_OWT,U_3166)) ),
    inference(clausify,[status(thm)],[f_894_4]) ).

fof(f_895_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_895_2,plain,
    ! [U_3169,U_3168,U_3167] : c_Com_Ocom_OWhile(U_3167,U_3168) != hAPP(c_Com_Ocom_OBODY,U_3169),
    inference(variable_rename,[status(thm)],[f_895_1]) ).

fof(f_895_3,plain,
    ! [U_3168,U_3169,U_3167] : c_Com_Ocom_OWhile(U_3167,U_3168) != hAPP(c_Com_Ocom_OBODY,U_3169),
    inference(definitional_conversion,[status(esa)],[f_895_2]) ).

cnf(f_895_4,plain,
    c_Com_Ocom_OWhile(U_3167,U_3168) != hAPP(c_Com_Ocom_OBODY,U_3169),
    inference(clausify,[status(thm)],[f_895_3]) ).

fof(f_896_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_896_2,plain,
    ! [U_3172,U_3171,U_3170] : hAPP(c_Com_Ocom_OBODY,U_3170) != c_Com_Ocom_OWhile(U_3171,U_3172),
    inference(variable_rename,[status(thm)],[f_896_1]) ).

fof(f_896_3,plain,
    ! [U_3170,U_3171,U_3172] : hAPP(c_Com_Ocom_OBODY,U_3170) != c_Com_Ocom_OWhile(U_3171,U_3172),
    inference(definitional_conversion,[status(esa)],[f_896_2]) ).

cnf(f_896_4,plain,
    hAPP(c_Com_Ocom_OBODY,U_3170) != c_Com_Ocom_OWhile(U_3171,U_3172),
    inference(clausify,[status(thm)],[f_896_3]) ).

fof(f_897_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_897_2,plain,
    ! [U_3177,U_3176,U_3175,U_3174,U_3173] : c_Com_Ocom_OCond(U_3173,U_3174,U_3175) != c_Com_Ocom_OWhile(U_3176,U_3177),
    inference(variable_rename,[status(thm)],[f_897_1]) ).

fof(f_897_3,plain,
    ! [U_3174,U_3173,U_3175,U_3176,U_3177] : c_Com_Ocom_OCond(U_3173,U_3174,U_3175) != c_Com_Ocom_OWhile(U_3176,U_3177),
    inference(definitional_conversion,[status(esa)],[f_897_2]) ).

cnf(f_897_4,plain,
    c_Com_Ocom_OCond(U_3173,U_3174,U_3175) != c_Com_Ocom_OWhile(U_3176,U_3177),
    inference(clausify,[status(thm)],[f_897_3]) ).

fof(f_898_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_898_2,plain,
    ! [U_3182,U_3181,U_3180,U_3179,U_3178] : c_Com_Ocom_OWhile(U_3178,U_3179) != c_Com_Ocom_OCond(U_3180,U_3181,U_3182),
    inference(variable_rename,[status(thm)],[f_898_1]) ).

fof(f_898_3,plain,
    ! [U_3178,U_3179,U_3180,U_3181,U_3182] : c_Com_Ocom_OWhile(U_3178,U_3179) != c_Com_Ocom_OCond(U_3180,U_3181,U_3182),
    inference(definitional_conversion,[status(esa)],[f_898_2]) ).

cnf(f_898_4,plain,
    c_Com_Ocom_OWhile(U_3178,U_3179) != c_Com_Ocom_OCond(U_3180,U_3181,U_3182),
    inference(clausify,[status(thm)],[f_898_3]) ).

fof(f_899_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_899_2,plain,
    ! [U_3186,U_3185,U_3184,U_3183] : c_Com_Ocom_OWhile(U_3183,U_3184) != c_Com_Ocom_OAss(U_3185,U_3186),
    inference(variable_rename,[status(thm)],[f_899_1]) ).

fof(f_899_3,plain,
    ! [U_3183,U_3184,U_3185,U_3186] : c_Com_Ocom_OWhile(U_3183,U_3184) != c_Com_Ocom_OAss(U_3185,U_3186),
    inference(definitional_conversion,[status(esa)],[f_899_2]) ).

cnf(f_899_4,plain,
    c_Com_Ocom_OWhile(U_3183,U_3184) != c_Com_Ocom_OAss(U_3185,U_3186),
    inference(clausify,[status(thm)],[f_899_3]) ).

fof(f_900_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_900_2,plain,
    ! [U_3190,U_3189,U_3188,U_3187] : c_Com_Ocom_OAss(U_3187,U_3188) != c_Com_Ocom_OWhile(U_3189,U_3190),
    inference(variable_rename,[status(thm)],[f_900_1]) ).

fof(f_900_3,plain,
    ! [U_3187,U_3188,U_3189,U_3190] : c_Com_Ocom_OAss(U_3187,U_3188) != c_Com_Ocom_OWhile(U_3189,U_3190),
    inference(definitional_conversion,[status(esa)],[f_900_2]) ).

cnf(f_900_4,plain,
    c_Com_Ocom_OAss(U_3187,U_3188) != c_Com_Ocom_OWhile(U_3189,U_3190),
    inference(clausify,[status(thm)],[f_900_3]) ).

fof(f_901_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_901_2,plain,
    ! [U_3195,U_3194,U_3193,U_3192,U_3191] : c_Com_Ocom_OCall(U_3191,U_3192,U_3193) != c_Com_Ocom_OWhile(U_3194,U_3195),
    inference(variable_rename,[status(thm)],[f_901_1]) ).

fof(f_901_3,plain,
    ! [U_3192,U_3191,U_3193,U_3194,U_3195] : c_Com_Ocom_OCall(U_3191,U_3192,U_3193) != c_Com_Ocom_OWhile(U_3194,U_3195),
    inference(definitional_conversion,[status(esa)],[f_901_2]) ).

cnf(f_901_4,plain,
    c_Com_Ocom_OCall(U_3191,U_3192,U_3193) != c_Com_Ocom_OWhile(U_3194,U_3195),
    inference(clausify,[status(thm)],[f_901_3]) ).

fof(f_902_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_902_2,plain,
    ! [U_3200,U_3199,U_3198,U_3197,U_3196] : c_Com_Ocom_OWhile(U_3196,U_3197) != c_Com_Ocom_OCall(U_3198,U_3199,U_3200),
    inference(variable_rename,[status(thm)],[f_902_1]) ).

fof(f_902_3,plain,
    ! [U_3196,U_3197,U_3198,U_3199,U_3200] : c_Com_Ocom_OWhile(U_3196,U_3197) != c_Com_Ocom_OCall(U_3198,U_3199,U_3200),
    inference(definitional_conversion,[status(esa)],[f_902_2]) ).

cnf(f_902_4,plain,
    c_Com_Ocom_OWhile(U_3196,U_3197) != c_Com_Ocom_OCall(U_3198,U_3199,U_3200),
    inference(clausify,[status(thm)],[f_902_3]) ).

fof(f_903_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_903_2,plain,
    ! [U_3205,U_3204,U_3203,U_3202,U_3201] : c_Com_Ocom_OLocal(U_3201,U_3202,U_3203) != c_Com_Ocom_OWhile(U_3204,U_3205),
    inference(variable_rename,[status(thm)],[f_903_1]) ).

fof(f_903_3,plain,
    ! [U_3202,U_3201,U_3203,U_3204,U_3205] : c_Com_Ocom_OLocal(U_3201,U_3202,U_3203) != c_Com_Ocom_OWhile(U_3204,U_3205),
    inference(definitional_conversion,[status(esa)],[f_903_2]) ).

cnf(f_903_4,plain,
    c_Com_Ocom_OLocal(U_3201,U_3202,U_3203) != c_Com_Ocom_OWhile(U_3204,U_3205),
    inference(clausify,[status(thm)],[f_903_3]) ).

fof(f_904_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_904_2,plain,
    ! [U_3210,U_3209,U_3208,U_3207,U_3206] : c_Com_Ocom_OWhile(U_3206,U_3207) != c_Com_Ocom_OLocal(U_3208,U_3209,U_3210),
    inference(variable_rename,[status(thm)],[f_904_1]) ).

fof(f_904_3,plain,
    ! [U_3206,U_3207,U_3208,U_3209,U_3210] : c_Com_Ocom_OWhile(U_3206,U_3207) != c_Com_Ocom_OLocal(U_3208,U_3209,U_3210),
    inference(definitional_conversion,[status(esa)],[f_904_2]) ).

cnf(f_904_4,plain,
    c_Com_Ocom_OWhile(U_3206,U_3207) != c_Com_Ocom_OLocal(U_3208,U_3209,U_3210),
    inference(clausify,[status(thm)],[f_904_3]) ).

fof(f_905_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_905_2,plain,
    ! [U_3214,U_3213,U_3212,U_3211] : c_Com_Ocom_OWhile(U_3211,U_3212) != c_Com_Ocom_OSemi(U_3213,U_3214),
    inference(variable_rename,[status(thm)],[f_905_1]) ).

fof(f_905_3,plain,
    ! [U_3211,U_3212,U_3213,U_3214] : c_Com_Ocom_OWhile(U_3211,U_3212) != c_Com_Ocom_OSemi(U_3213,U_3214),
    inference(definitional_conversion,[status(esa)],[f_905_2]) ).

cnf(f_905_4,plain,
    c_Com_Ocom_OWhile(U_3211,U_3212) != c_Com_Ocom_OSemi(U_3213,U_3214),
    inference(clausify,[status(thm)],[f_905_3]) ).

fof(f_906_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_906_2,plain,
    ! [U_3218,U_3217,U_3216,U_3215] : c_Com_Ocom_OSemi(U_3215,U_3216) != c_Com_Ocom_OWhile(U_3217,U_3218),
    inference(variable_rename,[status(thm)],[f_906_1]) ).

fof(f_906_3,plain,
    ! [U_3215,U_3216,U_3217,U_3218] : c_Com_Ocom_OSemi(U_3215,U_3216) != c_Com_Ocom_OWhile(U_3217,U_3218),
    inference(definitional_conversion,[status(esa)],[f_906_2]) ).

cnf(f_906_4,plain,
    c_Com_Ocom_OSemi(U_3215,U_3216) != c_Com_Ocom_OWhile(U_3217,U_3218),
    inference(clausify,[status(thm)],[f_906_3]) ).

fof(f_907_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_907_2,plain,
    ! [U_3220,U_3219] : c_Com_Ocom_OWhile(U_3219,U_3220) != c_Com_Ocom_OSKIP,
    inference(variable_rename,[status(thm)],[f_907_1]) ).

fof(f_907_3,plain,
    ! [U_3219,U_3220] : c_Com_Ocom_OWhile(U_3219,U_3220) != c_Com_Ocom_OSKIP,
    inference(definitional_conversion,[status(esa)],[f_907_2]) ).

cnf(f_907_4,plain,
    c_Com_Ocom_OWhile(U_3219,U_3220) != c_Com_Ocom_OSKIP,
    inference(clausify,[status(thm)],[f_907_3]) ).

fof(f_908_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_908_2,plain,
    ! [U_3222,U_3221] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(U_3221,U_3222),
    inference(variable_rename,[status(thm)],[f_908_1]) ).

fof(f_908_3,plain,
    ! [U_3221,U_3222] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(U_3221,U_3222),
    inference(definitional_conversion,[status(esa)],[f_908_2]) ).

cnf(f_908_4,plain,
    c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(U_3221,U_3222),
    inference(clausify,[status(thm)],[f_908_3]) ).

fof(f_909_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_909_2,plain,
    ! [U_3223] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3223,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_909_1]) ).

fof(f_909_3,plain,
    ! [U_3223] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3223,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_909_2]) ).

cnf(f_909_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3223,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_909_3]) ).

fof(f_910_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_910_2,plain,
    ! [U_3225,U_3224] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3224),U_3225) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3224,U_3225))
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3224,U_3225)) = U_3225 )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3224),U_3225) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3224,U_3225)) != U_3225 ) ),
    inference(variable_rename,[status(thm)],[f_910_1]) ).

fof(f_910_3,plain,
    ( ! [U_3229,U_3227] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3227),U_3229) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3227,U_3229))
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3227,U_3229)) = U_3229 )
    & ! [U_3228,U_3226] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3226),U_3228) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3226,U_3228)) != U_3228 ) ),
    inference(miniscope,[status(thm)],[f_910_2]) ).

fof(f_910_4,plain,
    ( ! [U_3227,U_3229] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3227),U_3229) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3227,U_3229))
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3227,U_3229)) = U_3229 )
    & ! [U_3226,U_3228] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3226),U_3228) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3226,U_3228)) != U_3228 ) ),
    inference(definitional_conversion,[status(esa)],[f_910_3]) ).

cnf(f_910_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3226),U_3228) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3226,U_3228)) != U_3228 ),
    inference(clausify,[status(thm)],[f_910_4]) ).

cnf(f_910_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3227),U_3229) = hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3227,U_3229))
    | hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3227,U_3229)) = U_3229 ),
    inference(clausify,[status(thm)],[f_910_4]) ).

fof(f_911_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_911_2,plain,
    ! [U_3231,U_3230] :
      ( 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_3230),U_3231)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3231))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3230)) ),
    inference(variable_rename,[status(thm)],[f_911_1]) ).

fof(f_911_3,plain,
    ! [U_3231,U_3230] :
      ( 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_3230),U_3231)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3231))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3230)) ),
    inference(definitional_conversion,[status(esa)],[f_911_2]) ).

cnf(f_911_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_3230),U_3231)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3231))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3230)) ),
    inference(clausify,[status(thm)],[f_911_3]) ).

fof(f_912_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_912_2,plain,
    ! [U_3233,U_3232] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3233,U_3232)),U_3232))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3232)) ),
    inference(variable_rename,[status(thm)],[f_912_1]) ).

fof(f_912_3,plain,
    ! [U_3232,U_3233] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3233,U_3232)),U_3232))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3232)) ),
    inference(definitional_conversion,[status(esa)],[f_912_2]) ).

cnf(f_912_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3233,U_3232)),U_3232))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3232)) ),
    inference(clausify,[status(thm)],[f_912_3]) ).

fof(f_913_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_913_2,plain,
    ! [U_3235,U_3234] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3235),U_3234)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3235),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3235),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_3235),U_3234)),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_3234)) ),
    inference(variable_rename,[status(thm)],[f_913_1]) ).

fof(f_913_3,plain,
    ( ! [U_3234,U_3235] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3235),U_3234)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3235),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP265(U_3234,U_3235) )
    & ! [U_3234,U_3235] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3235),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_3235),U_3234)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP265(U_3234,U_3235) )
    & ! [U_3234,U_3235] :
        ( sP265(U_3234,U_3235)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3234)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP265])],[f_913_2]) ).

cnf(f_913_4,plain,
    ( sP265(U_3234,U_3235)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3234)) ),
    inference(clausify,[status(thm)],[f_913_3]) ).

cnf(f_913_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3235),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_3235),U_3234)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP265(U_3234,U_3235) ),
    inference(clausify,[status(thm)],[f_913_3]) ).

cnf(f_913_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3235),U_3234)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3235),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP265(U_3234,U_3235) ),
    inference(clausify,[status(thm)],[f_913_3]) ).

fof(f_914_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_914_2,plain,
    ! [U_3237,U_3236] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3237),U_3236)),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_3237)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3237))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3237),U_3236)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3236),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_914_1]) ).

fof(f_914_3,plain,
    ( ! [U_3236,U_3237] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3237),U_3236)),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_3237))
        | ~ sP266(U_3236,U_3237) )
    & ! [U_3236,U_3237] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3237))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3237),U_3236)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP266(U_3236,U_3237) )
    & ! [U_3236,U_3237] :
        ( sP266(U_3236,U_3237)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3236),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP266])],[f_914_2]) ).

cnf(f_914_4,plain,
    ( sP266(U_3236,U_3237)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3236),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_914_3]) ).

cnf(f_914_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3237))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3237),U_3236)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP266(U_3236,U_3237) ),
    inference(clausify,[status(thm)],[f_914_3]) ).

cnf(f_914_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3237),U_3236)),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_3237))
    | ~ sP266(U_3236,U_3237) ),
    inference(clausify,[status(thm)],[f_914_3]) ).

fof(f_915_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_915_2,plain,
    ! [U_3239,U_3238] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3238),U_3239)),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_3239))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3238),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_915_1]) ).

fof(f_915_3,plain,
    ! [U_3238,U_3239] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3238),U_3239)),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_3239))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3238),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_915_2]) ).

cnf(f_915_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3238),U_3239)),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_3239))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3238),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_915_3]) ).

fof(f_916_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_916_2,plain,
    ! [U_3240] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3240),U_3240) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | U_3240 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_916_1]) ).

fof(f_916_3,plain,
    ! [U_3240] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3240),U_3240) = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | U_3240 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_916_2]) ).

cnf(f_916_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3240),U_3240) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_3240 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_916_3]) ).

fof(f_917_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_917_2,plain,
    ! [U_3244,U_3243] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3243,U_3244) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ! [U_3242] : U_3243 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3244),U_3242) )
      & ( ? [U_3241] : U_3243 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3244),U_3241)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3243,U_3244) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_917_1]) ).

fof(f_917_3,plain,
    ( ! [U_3248,U_3246] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3246,U_3248) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ! [U_3242] : U_3246 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3248),U_3242) )
    & ! [U_3247,U_3245] :
        ( ? [U_3241] : U_3245 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3247),U_3241)
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3245,U_3247) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_917_2]) ).

fof(f_917_4,plain,
    ( ! [U_3248,U_3246] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3246,U_3248) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ! [U_3242] : U_3246 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3248),U_3242) )
    & ! [U_3247,U_3245] :
        ( U_3245 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3247),sK58(U_3247,U_3245))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3245,U_3247) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK58]),skolemize(U_3241,sK58(U_3247,U_3245))],[f_917_3]) ).

fof(f_917_5,plain,
    ( ! [U_3242,U_3246,U_3248] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3246,U_3248) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3246 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3248),U_3242) )
    & ! [U_3245,U_3247] :
        ( U_3245 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3247),sK58(U_3247,U_3245))
        | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3245,U_3247) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_917_4]) ).

cnf(f_917_6,plain,
    ( U_3245 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3247),sK58(U_3247,U_3245))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3245,U_3247) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_917_5]) ).

cnf(f_917_7,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3246,U_3248) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3246 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3248),U_3242) ),
    inference(clausify,[status(thm)],[f_917_5]) ).

fof(f_918_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_918_2,plain,
    ! [U_3249] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3249,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_3249
      & hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3249),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_918_1]) ).

fof(f_918_3,plain,
    ( ! [U_3251] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3251,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_3251
    & ! [U_3250] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3250),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(miniscope,[status(thm)],[f_918_2]) ).

fof(f_918_4,plain,
    ( ! [U_3251] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3251,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_3251
    & ! [U_3250] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3250),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_918_3]) ).

cnf(f_918_5,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3250),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_918_4]) ).

cnf(f_918_6,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3251,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = U_3251,
    inference(clausify,[status(thm)],[f_918_4]) ).

fof(f_919_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_919_2,plain,
    ! [U_3253,U_3252] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3252,U_3253)),U_3253) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(variable_rename,[status(thm)],[f_919_1]) ).

fof(f_919_3,plain,
    ! [U_3252,U_3253] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3252,U_3253)),U_3253) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_919_2]) ).

cnf(f_919_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3252,U_3253)),U_3253) = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_919_3]) ).

fof(f_920_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_920_2,plain,
    ! [U_3256,U_3255,U_3254] : 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_3254),U_3255)),U_3256),U_3255) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3256,U_3255),
    inference(variable_rename,[status(thm)],[f_920_1]) ).

fof(f_920_3,plain,
    ! [U_3254,U_3255,U_3256] : 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_3254),U_3255)),U_3256),U_3255) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3256,U_3255),
    inference(definitional_conversion,[status(esa)],[f_920_2]) ).

cnf(f_920_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_3254),U_3255)),U_3256),U_3255) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3256,U_3255),
    inference(clausify,[status(thm)],[f_920_3]) ).

fof(f_921_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_921_2,plain,
    ! [U_3259,U_3258,U_3257] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3257),U_3258)),U_3259) = 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_3257),U_3259)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3258),U_3259))),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_3257,U_3259)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3258,U_3259))),U_3259)),
    inference(variable_rename,[status(thm)],[f_921_1]) ).

fof(f_921_3,plain,
    ! [U_3257,U_3258,U_3259] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3257),U_3258)),U_3259) = 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_3257),U_3259)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3258),U_3259))),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_3257,U_3259)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3258,U_3259))),U_3259)),
    inference(definitional_conversion,[status(esa)],[f_921_2]) ).

cnf(f_921_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3257),U_3258)),U_3259) = 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_3257),U_3259)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3258),U_3259))),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_3257,U_3259)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3258,U_3259))),U_3259)),
    inference(clausify,[status(thm)],[f_921_3]) ).

fof(f_922_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_922_2,plain,
    ! [U_3261,U_3260] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3260),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3261)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3260,U_3261)),
    inference(variable_rename,[status(thm)],[f_922_1]) ).

fof(f_922_3,plain,
    ! [U_3260,U_3261] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3260),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3261)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3260,U_3261)),
    inference(definitional_conversion,[status(esa)],[f_922_2]) ).

cnf(f_922_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3260),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3261)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3260,U_3261)),
    inference(clausify,[status(thm)],[f_922_3]) ).

fof(f_923_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_923_2,plain,
    ! [U_3263,U_3262] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3262,U_3263)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3262),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3263)),
    inference(variable_rename,[status(thm)],[f_923_1]) ).

fof(f_923_3,plain,
    ! [U_3262,U_3263] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3262,U_3263)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3262),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3263)),
    inference(definitional_conversion,[status(esa)],[f_923_2]) ).

cnf(f_923_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3262,U_3263)) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3262),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3263)),
    inference(clausify,[status(thm)],[f_923_3]) ).

fof(f_924_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_924_2,plain,
    ! [U_3267,U_3266,U_3265,U_3264] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3264),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3264),U_3265),U_3266)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3264),U_3265),U_3267)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3264),U_3266),U_3267)
      | U_3265 = c_Groups_Ozero__class_Ozero(U_3264)
      | ~ class_Divides_Osemiring__div(U_3264) ),
    inference(variable_rename,[status(thm)],[f_924_1]) ).

fof(f_924_3,plain,
    ! [U_3264,U_3265,U_3266,U_3267] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3264),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3264),U_3265),U_3266)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3264),U_3265),U_3267)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3264),U_3266),U_3267)
      | U_3265 = c_Groups_Ozero__class_Ozero(U_3264)
      | ~ class_Divides_Osemiring__div(U_3264) ),
    inference(definitional_conversion,[status(esa)],[f_924_2]) ).

cnf(f_924_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3264),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3264),U_3265),U_3266)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3264),U_3265),U_3267)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3264),U_3266),U_3267)
    | U_3265 = c_Groups_Ozero__class_Ozero(U_3264)
    | ~ class_Divides_Osemiring__div(U_3264) ),
    inference(clausify,[status(thm)],[f_924_3]) ).

fof(f_925_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_925_2,plain,
    ! [U_3271,U_3270,U_3269,U_3268] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3268),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3268),U_3270),U_3269)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3268),U_3271),U_3269)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3268),U_3270),U_3271)
      | U_3269 = c_Groups_Ozero__class_Ozero(U_3268)
      | ~ class_Divides_Osemiring__div(U_3268) ),
    inference(variable_rename,[status(thm)],[f_925_1]) ).

fof(f_925_3,plain,
    ! [U_3268,U_3269,U_3270,U_3271] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3268),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3268),U_3270),U_3269)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3268),U_3271),U_3269)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3268),U_3270),U_3271)
      | U_3269 = c_Groups_Ozero__class_Ozero(U_3268)
      | ~ class_Divides_Osemiring__div(U_3268) ),
    inference(definitional_conversion,[status(esa)],[f_925_2]) ).

cnf(f_925_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3268),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3268),U_3270),U_3269)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3268),U_3271),U_3269)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3268),U_3270),U_3271)
    | U_3269 = c_Groups_Ozero__class_Ozero(U_3268)
    | ~ class_Divides_Osemiring__div(U_3268) ),
    inference(clausify,[status(thm)],[f_925_3]) ).

fof(f_926_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_926_2,plain,
    ! [U_3274,U_3273,U_3272] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3272),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3272),U_3273),U_3274)),U_3273) = U_3274
      | U_3273 = c_Groups_Ozero__class_Ozero(U_3272)
      | ~ class_Divides_Osemiring__div(U_3272) ),
    inference(variable_rename,[status(thm)],[f_926_1]) ).

fof(f_926_3,plain,
    ! [U_3272,U_3273,U_3274] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3272),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3272),U_3273),U_3274)),U_3273) = U_3274
      | U_3273 = c_Groups_Ozero__class_Ozero(U_3272)
      | ~ class_Divides_Osemiring__div(U_3272) ),
    inference(definitional_conversion,[status(esa)],[f_926_2]) ).

cnf(f_926_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3272),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3272),U_3273),U_3274)),U_3273) = U_3274
    | U_3273 = c_Groups_Ozero__class_Ozero(U_3272)
    | ~ class_Divides_Osemiring__div(U_3272) ),
    inference(clausify,[status(thm)],[f_926_3]) ).

fof(f_927_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_927_2,plain,
    ! [U_3277,U_3276,U_3275] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3275),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3275),U_3277),U_3276)),U_3276) = U_3277
      | U_3276 = c_Groups_Ozero__class_Ozero(U_3275)
      | ~ class_Divides_Osemiring__div(U_3275) ),
    inference(variable_rename,[status(thm)],[f_927_1]) ).

fof(f_927_3,plain,
    ! [U_3275,U_3276,U_3277] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3275),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3275),U_3277),U_3276)),U_3276) = U_3277
      | U_3276 = c_Groups_Ozero__class_Ozero(U_3275)
      | ~ class_Divides_Osemiring__div(U_3275) ),
    inference(definitional_conversion,[status(esa)],[f_927_2]) ).

cnf(f_927_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3275),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3275),U_3277),U_3276)),U_3276) = U_3277
    | U_3276 = c_Groups_Ozero__class_Ozero(U_3275)
    | ~ class_Divides_Osemiring__div(U_3275) ),
    inference(clausify,[status(thm)],[f_927_3]) ).

fof(f_928_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_928_2,plain,
    ! [U_3281,U_3280,U_3279,U_3278] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3278),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3278),U_3279),U_3280)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3278),U_3279),U_3281)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3278),U_3280),U_3281)
          | U_3279 = c_Groups_Ozero__class_Ozero(U_3278) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3278),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3278),U_3279),U_3280)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3278),U_3279),U_3281)) = c_Groups_Ozero__class_Ozero(U_3278)
          | U_3279 != c_Groups_Ozero__class_Ozero(U_3278) ) )
      | ~ class_Divides_Osemiring__div(U_3278) ),
    inference(variable_rename,[status(thm)],[f_928_1]) ).

fof(f_928_3,plain,
    ( ! [U_3278,U_3279,U_3280,U_3281] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3278),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3278),U_3279),U_3280)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3278),U_3279),U_3281)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3278),U_3280),U_3281)
        | U_3279 = c_Groups_Ozero__class_Ozero(U_3278)
        | ~ sP267(U_3278,U_3279,U_3280,U_3281) )
    & ! [U_3278,U_3279,U_3280,U_3281] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3278),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3278),U_3279),U_3280)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3278),U_3279),U_3281)) = c_Groups_Ozero__class_Ozero(U_3278)
        | U_3279 != c_Groups_Ozero__class_Ozero(U_3278)
        | ~ sP267(U_3278,U_3279,U_3280,U_3281) )
    & ! [U_3278,U_3279,U_3280,U_3281] :
        ( sP267(U_3278,U_3279,U_3280,U_3281)
        | ~ class_Divides_Osemiring__div(U_3278) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP267])],[f_928_2]) ).

cnf(f_928_4,plain,
    ( sP267(U_3278,U_3279,U_3280,U_3281)
    | ~ class_Divides_Osemiring__div(U_3278) ),
    inference(clausify,[status(thm)],[f_928_3]) ).

cnf(f_928_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3278),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3278),U_3279),U_3280)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3278),U_3279),U_3281)) = c_Groups_Ozero__class_Ozero(U_3278)
    | U_3279 != c_Groups_Ozero__class_Ozero(U_3278)
    | ~ sP267(U_3278,U_3279,U_3280,U_3281) ),
    inference(clausify,[status(thm)],[f_928_3]) ).

cnf(f_928_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3278),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3278),U_3279),U_3280)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3278),U_3279),U_3281)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3278),U_3280),U_3281)
    | U_3279 = c_Groups_Ozero__class_Ozero(U_3278)
    | ~ sP267(U_3278,U_3279,U_3280,U_3281) ),
    inference(clausify,[status(thm)],[f_928_3]) ).

fof(f_929_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_929_2,plain,
    ! [U_3283,U_3282] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3282),U_3283),U_3283) = c_Groups_Oone__class_Oone(U_3282)
      | U_3283 = c_Groups_Ozero__class_Ozero(U_3282)
      | ~ class_Divides_Osemiring__div(U_3282) ),
    inference(variable_rename,[status(thm)],[f_929_1]) ).

fof(f_929_3,plain,
    ! [U_3282,U_3283] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3282),U_3283),U_3283) = c_Groups_Oone__class_Oone(U_3282)
      | U_3283 = c_Groups_Ozero__class_Ozero(U_3282)
      | ~ class_Divides_Osemiring__div(U_3282) ),
    inference(definitional_conversion,[status(esa)],[f_929_2]) ).

cnf(f_929_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3282),U_3283),U_3283) = c_Groups_Oone__class_Oone(U_3282)
    | U_3283 = c_Groups_Ozero__class_Ozero(U_3282)
    | ~ class_Divides_Osemiring__div(U_3282) ),
    inference(clausify,[status(thm)],[f_929_3]) ).

fof(f_930_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_930_2,plain,
    ! [U_3286,U_3285,U_3284] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3284),c_Divides_Odiv__class_Omod(U_3284,U_3285,U_3286)),U_3286) = c_Groups_Ozero__class_Ozero(U_3284)
      | ~ class_Divides_Osemiring__div(U_3284) ),
    inference(variable_rename,[status(thm)],[f_930_1]) ).

fof(f_930_3,plain,
    ! [U_3284,U_3285,U_3286] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3284),c_Divides_Odiv__class_Omod(U_3284,U_3285,U_3286)),U_3286) = c_Groups_Ozero__class_Ozero(U_3284)
      | ~ class_Divides_Osemiring__div(U_3284) ),
    inference(definitional_conversion,[status(esa)],[f_930_2]) ).

cnf(f_930_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3284),c_Divides_Odiv__class_Omod(U_3284,U_3285,U_3286)),U_3286) = c_Groups_Ozero__class_Ozero(U_3284)
    | ~ class_Divides_Osemiring__div(U_3284) ),
    inference(clausify,[status(thm)],[f_930_3]) ).

fof(f_931_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_931_2,plain,
    ! [U_3288,U_3287] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3287),U_3288) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3288),U_3287))
            | ~ 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_3287),U_3288))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3287)) )
          & U_3288 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3288),U_3287))
          & 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_3287),U_3288))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3287)) )
        | U_3288 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3287),U_3288) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_931_1]) ).

fof(f_931_3,plain,
    ( ! [U_3292,U_3290] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3290),U_3292) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3292),U_3290))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3290),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
          & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3290),U_3292))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3290)) )
          & U_3292 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_3291,U_3289] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3291),U_3289))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3289),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3289),U_3291))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3289)) )
        | U_3291 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3289),U_3291) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_931_2]) ).

fof(f_931_4,plain,
    ( ! [U_3292,U_3290] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3292),U_3290))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3290),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP270(U_3292,U_3290) )
    & ! [U_3292,U_3290] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3290),U_3292))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3290))
        | ~ sP270(U_3292,U_3290) )
    & ! [U_3292,U_3290] :
        ( U_3292 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP270(U_3292,U_3290) )
    & ! [U_3289,U_3291] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3291),U_3289))
        | ~ sP269(U_3289,U_3291) )
    & ! [U_3289,U_3291] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3289),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP269(U_3289,U_3291) )
    & ! [U_3289,U_3291] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3289),U_3291))
        | ~ sP268(U_3289,U_3291) )
    & ! [U_3289,U_3291] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3289))
        | ~ sP268(U_3289,U_3291) )
    & ! [U_3292,U_3290] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3290),U_3292) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | sP270(U_3292,U_3290) )
    & ! [U_3289,U_3291] :
        ( sP269(U_3289,U_3291)
        | sP268(U_3289,U_3291)
        | U_3291 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3289),U_3291) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP268,sP269,sP270])],[f_931_3]) ).

cnf(f_931_5,plain,
    ( sP269(U_3289,U_3291)
    | sP268(U_3289,U_3291)
    | U_3291 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3289),U_3291) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_931_4]) ).

cnf(f_931_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3290),U_3292) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | sP270(U_3292,U_3290) ),
    inference(clausify,[status(thm)],[f_931_4]) ).

cnf(f_931_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3289))
    | ~ sP268(U_3289,U_3291) ),
    inference(clausify,[status(thm)],[f_931_4]) ).

cnf(f_931_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3289),U_3291))
    | ~ sP268(U_3289,U_3291) ),
    inference(clausify,[status(thm)],[f_931_4]) ).

cnf(f_931_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3289),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP269(U_3289,U_3291) ),
    inference(clausify,[status(thm)],[f_931_4]) ).

cnf(f_931_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3291),U_3289))
    | ~ sP269(U_3289,U_3291) ),
    inference(clausify,[status(thm)],[f_931_4]) ).

cnf(f_931_11,plain,
    ( U_3292 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP270(U_3292,U_3290) ),
    inference(clausify,[status(thm)],[f_931_4]) ).

cnf(f_931_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3290),U_3292))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3290))
    | ~ sP270(U_3292,U_3290) ),
    inference(clausify,[status(thm)],[f_931_4]) ).

cnf(f_931_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3292),U_3290))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3290),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP270(U_3292,U_3290) ),
    inference(clausify,[status(thm)],[f_931_4]) ).

fof(f_932_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_932_2,plain,
    ! [U_3294,U_3293] :
      ( ( ( 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_3294),U_3293)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3294)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3294))
          | ~ 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_3294),U_3293))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3293)) ),
    inference(variable_rename,[status(thm)],[f_932_1]) ).

fof(f_932_3,plain,
    ( ! [U_3294,U_3293] :
        ( 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_3294),U_3293)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3294))
        | ~ sP271(U_3294,U_3293) )
    & ! [U_3294,U_3293] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3294))
        | ~ 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_3294),U_3293)))
        | ~ sP271(U_3294,U_3293) )
    & ! [U_3294,U_3293] :
        ( sP271(U_3294,U_3293)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3293)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP271])],[f_932_2]) ).

cnf(f_932_4,plain,
    ( sP271(U_3294,U_3293)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3293)) ),
    inference(clausify,[status(thm)],[f_932_3]) ).

cnf(f_932_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3294))
    | ~ 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_3294),U_3293)))
    | ~ sP271(U_3294,U_3293) ),
    inference(clausify,[status(thm)],[f_932_3]) ).

cnf(f_932_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_3294),U_3293)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3294))
    | ~ sP271(U_3294,U_3293) ),
    inference(clausify,[status(thm)],[f_932_3]) ).

fof(f_933_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_933_2,plain,
    ! [U_3296,U_3295] :
      ( ( ( 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_3296),U_3295)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3295),U_3296)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3295),U_3296))
          | ~ 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_3296),U_3295))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3295)) ),
    inference(variable_rename,[status(thm)],[f_933_1]) ).

fof(f_933_3,plain,
    ( ! [U_3295,U_3296] :
        ( 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_3296),U_3295)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3295),U_3296))
        | ~ sP272(U_3295,U_3296) )
    & ! [U_3295,U_3296] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3295),U_3296))
        | ~ 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_3296),U_3295)))
        | ~ sP272(U_3295,U_3296) )
    & ! [U_3295,U_3296] :
        ( sP272(U_3295,U_3296)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3295)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP272])],[f_933_2]) ).

cnf(f_933_4,plain,
    ( sP272(U_3295,U_3296)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3295)) ),
    inference(clausify,[status(thm)],[f_933_3]) ).

cnf(f_933_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3295),U_3296))
    | ~ 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_3296),U_3295)))
    | ~ sP272(U_3295,U_3296) ),
    inference(clausify,[status(thm)],[f_933_3]) ).

cnf(f_933_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_3296),U_3295)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3295),U_3296))
    | ~ sP272(U_3295,U_3296) ),
    inference(clausify,[status(thm)],[f_933_3]) ).

fof(f_934_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_934_2,plain,
    ! [U_3298,U_3297] :
      ( ( ( 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_3297),U_3298)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3298))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3298),U_3297)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3298))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3298),U_3297)) )
          | ~ 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_3297),U_3298))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3297)) ),
    inference(variable_rename,[status(thm)],[f_934_1]) ).

fof(f_934_3,plain,
    ( ! [U_3298,U_3297] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3298))
        | ~ sP273(U_3298,U_3297) )
    & ! [U_3298,U_3297] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3298),U_3297))
        | ~ sP273(U_3298,U_3297) )
    & ! [U_3298,U_3297] :
        ( 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_3297),U_3298)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3298))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3298),U_3297))
        | ~ sP274(U_3298,U_3297) )
    & ! [U_3298,U_3297] :
        ( sP273(U_3298,U_3297)
        | ~ 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_3297),U_3298)))
        | ~ sP274(U_3298,U_3297) )
    & ! [U_3298,U_3297] :
        ( sP274(U_3298,U_3297)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3297)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP273,sP274])],[f_934_2]) ).

cnf(f_934_4,plain,
    ( sP274(U_3298,U_3297)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3297)) ),
    inference(clausify,[status(thm)],[f_934_3]) ).

cnf(f_934_5,plain,
    ( sP273(U_3298,U_3297)
    | ~ 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_3297),U_3298)))
    | ~ sP274(U_3298,U_3297) ),
    inference(clausify,[status(thm)],[f_934_3]) ).

cnf(f_934_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_3297),U_3298)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3298))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3298),U_3297))
    | ~ sP274(U_3298,U_3297) ),
    inference(clausify,[status(thm)],[f_934_3]) ).

cnf(f_934_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3298),U_3297))
    | ~ sP273(U_3298,U_3297) ),
    inference(clausify,[status(thm)],[f_934_3]) ).

cnf(f_934_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3298))
    | ~ sP273(U_3298,U_3297) ),
    inference(clausify,[status(thm)],[f_934_3]) ).

fof(f_935_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_935_2,plain,
    ! [U_3301,U_3300,U_3299] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3299),U_3301)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3299),U_3300)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3300),U_3301))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3300))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3299)) ),
    inference(variable_rename,[status(thm)],[f_935_1]) ).

fof(f_935_3,plain,
    ! [U_3300,U_3301,U_3299] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3299),U_3301)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3299),U_3300)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3300),U_3301))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3300))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3299)) ),
    inference(definitional_conversion,[status(esa)],[f_935_2]) ).

cnf(f_935_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_3299),U_3301)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3299),U_3300)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3300),U_3301))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3300))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3299)) ),
    inference(clausify,[status(thm)],[f_935_3]) ).

fof(f_936_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_936_2,plain,
    ! [U_3303,U_3302] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3302),U_3303)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3303),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_3302)) ),
    inference(variable_rename,[status(thm)],[f_936_1]) ).

fof(f_936_3,plain,
    ! [U_3302,U_3303] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3302),U_3303)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3303),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_3302)) ),
    inference(definitional_conversion,[status(esa)],[f_936_2]) ).

cnf(f_936_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_3302),U_3303)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3303),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_3302)) ),
    inference(clausify,[status(thm)],[f_936_3]) ).

fof(f_937_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_937_2,plain,
    ! [U_3305,U_3304] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3304),U_3305) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3304),U_3305))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3304)) ),
    inference(variable_rename,[status(thm)],[f_937_1]) ).

fof(f_937_3,plain,
    ! [U_3304,U_3305] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3304),U_3305) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3304),U_3305))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3304)) ),
    inference(definitional_conversion,[status(esa)],[f_937_2]) ).

cnf(f_937_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3304),U_3305) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3304),U_3305))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3304)) ),
    inference(clausify,[status(thm)],[f_937_3]) ).

fof(f_938_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_938_2,plain,
    ! [U_3307,U_3306] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3307),U_3306)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3307),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3307),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3307),U_3306))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3306),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_938_1]) ).

fof(f_938_3,plain,
    ( ! [U_3307,U_3306] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3307),U_3306)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3307),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP275(U_3307,U_3306) )
    & ! [U_3307,U_3306] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3307),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3307),U_3306)))
        | ~ sP275(U_3307,U_3306) )
    & ! [U_3307,U_3306] :
        ( sP275(U_3307,U_3306)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3306),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP275])],[f_938_2]) ).

cnf(f_938_4,plain,
    ( sP275(U_3307,U_3306)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3306),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_938_3]) ).

cnf(f_938_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3307),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3307),U_3306)))
    | ~ sP275(U_3307,U_3306) ),
    inference(clausify,[status(thm)],[f_938_3]) ).

cnf(f_938_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3307),U_3306)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3307),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP275(U_3307,U_3306) ),
    inference(clausify,[status(thm)],[f_938_3]) ).

fof(f_939_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_939_2,plain,
    ! [U_3309,U_3308] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3308),U_3309)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3309))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3308),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_939_1]) ).

fof(f_939_3,plain,
    ! [U_3308,U_3309] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3308),U_3309)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3309))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3308),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_939_2]) ).

cnf(f_939_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_3308),U_3309)),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_3309))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3308),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_939_3]) ).

fof(f_940_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_940_2,plain,
    ! [U_3312,U_3311,U_3310] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3310),U_3311)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3310),U_3312)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3311),U_3312))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3311))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3310),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_940_1]) ).

fof(f_940_3,plain,
    ! [U_3311,U_3310,U_3312] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3310),U_3311)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3310),U_3312)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3311),U_3312))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3311))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3310),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_940_2]) ).

cnf(f_940_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3310),U_3311)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3310),U_3312)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3311),U_3312))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3311))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3310),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_940_3]) ).

fof(f_941_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_941_2,plain,
    ! [U_3314,U_3313] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3313),U_3314) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3314),U_3313))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3313),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_941_1]) ).

fof(f_941_3,plain,
    ! [U_3313,U_3314] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3313),U_3314) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3314),U_3313))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3313),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_941_2]) ).

cnf(f_941_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3313),U_3314) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3314),U_3313))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3313),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_941_3]) ).

fof(f_942_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_942_2,plain,
    ! [U_3317,U_3316,U_3315] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3315),U_3317)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3316),U_3317)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3317))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3315),U_3316)) ),
    inference(variable_rename,[status(thm)],[f_942_1]) ).

fof(f_942_3,plain,
    ! [U_3315,U_3316,U_3317] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3315),U_3317)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3316),U_3317)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3317))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3315),U_3316)) ),
    inference(definitional_conversion,[status(esa)],[f_942_2]) ).

cnf(f_942_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_3315),U_3317)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3316),U_3317)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3317))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3315),U_3316)) ),
    inference(clausify,[status(thm)],[f_942_3]) ).

fof(f_943_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_943_2,plain,
    ! [U_3320,U_3319,U_3318] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3319),U_3320)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3318),U_3320)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3320),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3318),U_3319)) ),
    inference(variable_rename,[status(thm)],[f_943_1]) ).

fof(f_943_3,plain,
    ! [U_3318,U_3319,U_3320] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3319),U_3320)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3318),U_3320)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3320),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3318),U_3319)) ),
    inference(definitional_conversion,[status(esa)],[f_943_2]) ).

cnf(f_943_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_3319),U_3320)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3318),U_3320)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3320),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3318),U_3319)) ),
    inference(clausify,[status(thm)],[f_943_3]) ).

fof(f_944_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_944_2,plain,
    ! [U_3322,U_3321] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3322,U_3321)),U_3321))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3321)) ),
    inference(variable_rename,[status(thm)],[f_944_1]) ).

fof(f_944_3,plain,
    ! [U_3321,U_3322] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3322,U_3321)),U_3321))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3321)) ),
    inference(definitional_conversion,[status(esa)],[f_944_2]) ).

cnf(f_944_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3322,U_3321)),U_3321))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3321)) ),
    inference(clausify,[status(thm)],[f_944_3]) ).

fof(f_945_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_945_2,plain,
    ! [U_3324,U_3323] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3323),U_3324)),U_3323))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_3324))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3323)) ),
    inference(variable_rename,[status(thm)],[f_945_1]) ).

fof(f_945_3,plain,
    ! [U_3323,U_3324] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3323),U_3324)),U_3323))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_3324))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3323)) ),
    inference(definitional_conversion,[status(esa)],[f_945_2]) ).

cnf(f_945_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3323),U_3324)),U_3323))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_3324))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3323)) ),
    inference(clausify,[status(thm)],[f_945_3]) ).

fof(f_946_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_946_2,plain,
    ! [U_3327,U_3326,U_3325] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3327),U_3325)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3326),U_3327)),U_3325)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3325)) ),
    inference(variable_rename,[status(thm)],[f_946_1]) ).

fof(f_946_3,plain,
    ! [U_3325,U_3326,U_3327] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3327),U_3325)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3326),U_3327)),U_3325)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3325)) ),
    inference(definitional_conversion,[status(esa)],[f_946_2]) ).

cnf(f_946_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3326),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3327),U_3325)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3326),U_3327)),U_3325)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3325)) ),
    inference(clausify,[status(thm)],[f_946_3]) ).

fof(f_947_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_947_2,plain,
    ! [U_3330,U_3329,U_3328] : 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_3328),U_3329)),U_3330)),U_3329) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3330),U_3329),
    inference(variable_rename,[status(thm)],[f_947_1]) ).

fof(f_947_3,plain,
    ! [U_3328,U_3329,U_3330] : 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_3328),U_3329)),U_3330)),U_3329) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3330),U_3329),
    inference(definitional_conversion,[status(esa)],[f_947_2]) ).

cnf(f_947_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_3328),U_3329)),U_3330)),U_3329) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3330),U_3329),
    inference(clausify,[status(thm)],[f_947_3]) ).

fof(f_948_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_948_2,plain,
    ! [U_3333,U_3332,U_3331] : 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_3331),U_3332)),U_3332)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3331,U_3332))),U_3333) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3331),U_3333),
    inference(variable_rename,[status(thm)],[f_948_1]) ).

fof(f_948_3,plain,
    ! [U_3331,U_3332,U_3333] : 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_3331),U_3332)),U_3332)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3331,U_3332))),U_3333) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3331),U_3333),
    inference(definitional_conversion,[status(esa)],[f_948_2]) ).

cnf(f_948_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_3331),U_3332)),U_3332)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3331,U_3332))),U_3333) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3331),U_3333),
    inference(clausify,[status(thm)],[f_948_3]) ).

fof(f_949_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_949_2,plain,
    ! [U_3336,U_3335,U_3334] : 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_3334),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3335),U_3334))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3335,U_3334))),U_3336) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3335),U_3336),
    inference(variable_rename,[status(thm)],[f_949_1]) ).

fof(f_949_3,plain,
    ! [U_3336,U_3334,U_3335] : 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_3334),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3335),U_3334))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3335,U_3334))),U_3336) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3335),U_3336),
    inference(definitional_conversion,[status(esa)],[f_949_2]) ).

cnf(f_949_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_3334),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3335),U_3334))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3335,U_3334))),U_3336) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3335),U_3336),
    inference(clausify,[status(thm)],[f_949_3]) ).

fof(f_950_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_950_2,plain,
    ! [U_3339,U_3338,U_3337] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3337),U_3338)),U_3339) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3337),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3338),U_3339))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3337),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3338,U_3339))),U_3339)),
    inference(variable_rename,[status(thm)],[f_950_1]) ).

fof(f_950_3,plain,
    ! [U_3337,U_3338,U_3339] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3337),U_3338)),U_3339) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3337),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3338),U_3339))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3337),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3338,U_3339))),U_3339)),
    inference(definitional_conversion,[status(esa)],[f_950_2]) ).

cnf(f_950_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3337),U_3338)),U_3339) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3337),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3338),U_3339))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3337),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3338,U_3339))),U_3339)),
    inference(clausify,[status(thm)],[f_950_3]) ).

fof(f_951_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_951_2,plain,
    ! [U_3341,U_3340] : U_3340 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3341),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3340),U_3341))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3340,U_3341)),
    inference(variable_rename,[status(thm)],[f_951_1]) ).

fof(f_951_3,plain,
    ! [U_3340,U_3341] : U_3340 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3341),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3340),U_3341))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3340,U_3341)),
    inference(definitional_conversion,[status(esa)],[f_951_2]) ).

cnf(f_951_4,plain,
    U_3340 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3341),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3340),U_3341))),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3340,U_3341)),
    inference(clausify,[status(thm)],[f_951_3]) ).

fof(f_952_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_952_2,plain,
    ! [U_3345,U_3344,U_3343,U_3342] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3342),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3342),U_3344),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3342),U_3345),U_3343))),U_3343) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3342),U_3345),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3342),U_3344),U_3343))
      | U_3343 = c_Groups_Ozero__class_Ozero(U_3342)
      | ~ class_Divides_Osemiring__div(U_3342) ),
    inference(variable_rename,[status(thm)],[f_952_1]) ).

fof(f_952_3,plain,
    ! [U_3342,U_3343,U_3344,U_3345] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3342),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3342),U_3344),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3342),U_3345),U_3343))),U_3343) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3342),U_3345),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3342),U_3344),U_3343))
      | U_3343 = c_Groups_Ozero__class_Ozero(U_3342)
      | ~ class_Divides_Osemiring__div(U_3342) ),
    inference(definitional_conversion,[status(esa)],[f_952_2]) ).

cnf(f_952_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3342),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3342),U_3344),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3342),U_3345),U_3343))),U_3343) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3342),U_3345),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3342),U_3344),U_3343))
    | U_3343 = c_Groups_Ozero__class_Ozero(U_3342)
    | ~ class_Divides_Osemiring__div(U_3342) ),
    inference(clausify,[status(thm)],[f_952_3]) ).

fof(f_953_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_953_2,plain,
    ! [U_3349,U_3348,U_3347,U_3346] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3346),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3346),U_3348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3346),U_3347),U_3349))),U_3347) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3346),U_3349),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3346),U_3348),U_3347))
      | U_3347 = c_Groups_Ozero__class_Ozero(U_3346)
      | ~ class_Divides_Osemiring__div(U_3346) ),
    inference(variable_rename,[status(thm)],[f_953_1]) ).

fof(f_953_3,plain,
    ! [U_3346,U_3347,U_3348,U_3349] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3346),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3346),U_3348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3346),U_3347),U_3349))),U_3347) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3346),U_3349),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3346),U_3348),U_3347))
      | U_3347 = c_Groups_Ozero__class_Ozero(U_3346)
      | ~ class_Divides_Osemiring__div(U_3346) ),
    inference(definitional_conversion,[status(esa)],[f_953_2]) ).

cnf(f_953_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3346),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3346),U_3348),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3346),U_3347),U_3349))),U_3347) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3346),U_3349),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3346),U_3348),U_3347))
    | U_3347 = c_Groups_Ozero__class_Ozero(U_3346)
    | ~ class_Divides_Osemiring__div(U_3346) ),
    inference(clausify,[status(thm)],[f_953_3]) ).

fof(f_954_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_954_2,plain,
    ! [U_3352,U_3351,U_3350] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3350),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3350),U_3351),U_3352)),U_3351) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3350),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3350),U_3352),U_3351)),c_Groups_Oone__class_Oone(U_3350))
      | U_3351 = c_Groups_Ozero__class_Ozero(U_3350)
      | ~ class_Divides_Osemiring__div(U_3350) ),
    inference(variable_rename,[status(thm)],[f_954_1]) ).

fof(f_954_3,plain,
    ! [U_3350,U_3351,U_3352] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3350),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3350),U_3351),U_3352)),U_3351) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3350),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3350),U_3352),U_3351)),c_Groups_Oone__class_Oone(U_3350))
      | U_3351 = c_Groups_Ozero__class_Ozero(U_3350)
      | ~ class_Divides_Osemiring__div(U_3350) ),
    inference(definitional_conversion,[status(esa)],[f_954_2]) ).

cnf(f_954_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3350),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3350),U_3351),U_3352)),U_3351) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3350),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3350),U_3352),U_3351)),c_Groups_Oone__class_Oone(U_3350))
    | U_3351 = c_Groups_Ozero__class_Ozero(U_3350)
    | ~ class_Divides_Osemiring__div(U_3350) ),
    inference(clausify,[status(thm)],[f_954_3]) ).

fof(f_955_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_955_2,plain,
    ! [U_3355,U_3354,U_3353] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3353),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3353),U_3355),U_3354)),U_3354) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3353),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3353),U_3355),U_3354)),c_Groups_Oone__class_Oone(U_3353))
      | U_3354 = c_Groups_Ozero__class_Ozero(U_3353)
      | ~ class_Divides_Osemiring__div(U_3353) ),
    inference(variable_rename,[status(thm)],[f_955_1]) ).

fof(f_955_3,plain,
    ! [U_3353,U_3354,U_3355] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3353),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3353),U_3355),U_3354)),U_3354) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3353),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3353),U_3355),U_3354)),c_Groups_Oone__class_Oone(U_3353))
      | U_3354 = c_Groups_Ozero__class_Ozero(U_3353)
      | ~ class_Divides_Osemiring__div(U_3353) ),
    inference(definitional_conversion,[status(esa)],[f_955_2]) ).

cnf(f_955_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3353),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3353),U_3355),U_3354)),U_3354) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3353),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3353),U_3355),U_3354)),c_Groups_Oone__class_Oone(U_3353))
    | U_3354 = c_Groups_Ozero__class_Ozero(U_3353)
    | ~ class_Divides_Osemiring__div(U_3353) ),
    inference(clausify,[status(thm)],[f_955_3]) ).

fof(f_956_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_956_2,plain,
    ! [U_3358,U_3357,U_3356] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3356),c_Divides_Odiv__class_Omod(U_3356,U_3357,U_3358)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3356),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3356),U_3357),U_3358)),U_3358)) = U_3357
      | ~ class_Divides_Osemiring__div(U_3356) ),
    inference(variable_rename,[status(thm)],[f_956_1]) ).

fof(f_956_3,plain,
    ! [U_3356,U_3357,U_3358] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3356),c_Divides_Odiv__class_Omod(U_3356,U_3357,U_3358)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3356),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3356),U_3357),U_3358)),U_3358)) = U_3357
      | ~ class_Divides_Osemiring__div(U_3356) ),
    inference(definitional_conversion,[status(esa)],[f_956_2]) ).

cnf(f_956_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3356),c_Divides_Odiv__class_Omod(U_3356,U_3357,U_3358)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3356),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3356),U_3357),U_3358)),U_3358)) = U_3357
    | ~ class_Divides_Osemiring__div(U_3356) ),
    inference(clausify,[status(thm)],[f_956_3]) ).

fof(f_957_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_957_2,plain,
    ! [U_3361,U_3360,U_3359] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3359),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3359),U_3360),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3359),U_3361),U_3360))),c_Divides_Odiv__class_Omod(U_3359,U_3361,U_3360)) = U_3361
      | ~ class_Divides_Osemiring__div(U_3359) ),
    inference(variable_rename,[status(thm)],[f_957_1]) ).

fof(f_957_3,plain,
    ! [U_3359,U_3360,U_3361] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3359),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3359),U_3360),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3359),U_3361),U_3360))),c_Divides_Odiv__class_Omod(U_3359,U_3361,U_3360)) = U_3361
      | ~ class_Divides_Osemiring__div(U_3359) ),
    inference(definitional_conversion,[status(esa)],[f_957_2]) ).

cnf(f_957_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3359),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3359),U_3360),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3359),U_3361),U_3360))),c_Divides_Odiv__class_Omod(U_3359,U_3361,U_3360)) = U_3361
    | ~ class_Divides_Osemiring__div(U_3359) ),
    inference(clausify,[status(thm)],[f_957_3]) ).

fof(f_958_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_958_2,plain,
    ! [U_3364,U_3363,U_3362] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3362),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3362),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3362),U_3363),U_3364)),U_3364)),c_Divides_Odiv__class_Omod(U_3362,U_3363,U_3364)) = U_3363
      | ~ class_Divides_Osemiring__div(U_3362) ),
    inference(variable_rename,[status(thm)],[f_958_1]) ).

fof(f_958_3,plain,
    ! [U_3362,U_3363,U_3364] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3362),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3362),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3362),U_3363),U_3364)),U_3364)),c_Divides_Odiv__class_Omod(U_3362,U_3363,U_3364)) = U_3363
      | ~ class_Divides_Osemiring__div(U_3362) ),
    inference(definitional_conversion,[status(esa)],[f_958_2]) ).

cnf(f_958_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3362),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3362),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3362),U_3363),U_3364)),U_3364)),c_Divides_Odiv__class_Omod(U_3362,U_3363,U_3364)) = U_3363
    | ~ class_Divides_Osemiring__div(U_3362) ),
    inference(clausify,[status(thm)],[f_958_3]) ).

fof(f_959_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_959_2,plain,
    ! [U_3368,U_3367,U_3366,U_3365] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3365),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3365),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3365),U_3366),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3365),U_3367),U_3366))),c_Divides_Odiv__class_Omod(U_3365,U_3367,U_3366))),U_3368) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3365),U_3367),U_3368)
      | ~ class_Divides_Osemiring__div(U_3365) ),
    inference(variable_rename,[status(thm)],[f_959_1]) ).

fof(f_959_3,plain,
    ! [U_3365,U_3366,U_3367,U_3368] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3365),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3365),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3365),U_3366),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3365),U_3367),U_3366))),c_Divides_Odiv__class_Omod(U_3365,U_3367,U_3366))),U_3368) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3365),U_3367),U_3368)
      | ~ class_Divides_Osemiring__div(U_3365) ),
    inference(definitional_conversion,[status(esa)],[f_959_2]) ).

cnf(f_959_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3365),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3365),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3365),U_3366),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3365),U_3367),U_3366))),c_Divides_Odiv__class_Omod(U_3365,U_3367,U_3366))),U_3368) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3365),U_3367),U_3368)
    | ~ class_Divides_Osemiring__div(U_3365) ),
    inference(clausify,[status(thm)],[f_959_3]) ).

fof(f_960_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_960_2,plain,
    ! [U_3372,U_3371,U_3370,U_3369] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3369),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3369),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3369),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3369),U_3370),U_3371)),U_3371)),c_Divides_Odiv__class_Omod(U_3369,U_3370,U_3371))),U_3372) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3369),U_3370),U_3372)
      | ~ class_Divides_Osemiring__div(U_3369) ),
    inference(variable_rename,[status(thm)],[f_960_1]) ).

fof(f_960_3,plain,
    ! [U_3369,U_3370,U_3371,U_3372] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3369),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3369),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3369),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3369),U_3370),U_3371)),U_3371)),c_Divides_Odiv__class_Omod(U_3369,U_3370,U_3371))),U_3372) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3369),U_3370),U_3372)
      | ~ class_Divides_Osemiring__div(U_3369) ),
    inference(definitional_conversion,[status(esa)],[f_960_2]) ).

cnf(f_960_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3369),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3369),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3369),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3369),U_3370),U_3371)),U_3371)),c_Divides_Odiv__class_Omod(U_3369,U_3370,U_3371))),U_3372) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3369),U_3370),U_3372)
    | ~ class_Divides_Osemiring__div(U_3369) ),
    inference(clausify,[status(thm)],[f_960_3]) ).

fof(f_961_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_961_2,plain,
    ! [U_3376,U_3375,U_3374,U_3373] :
      ( 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_3375),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3376,U_3373))),U_3374)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3375),U_3373)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3374),U_3375))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3373)) ),
    inference(variable_rename,[status(thm)],[f_961_1]) ).

fof(f_961_3,plain,
    ! [U_3373,U_3374,U_3375,U_3376] :
      ( 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_3375),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3376,U_3373))),U_3374)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3375),U_3373)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3374),U_3375))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3373)) ),
    inference(definitional_conversion,[status(esa)],[f_961_2]) ).

cnf(f_961_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_3375),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3376,U_3373))),U_3374)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3375),U_3373)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3374),U_3375))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3373)) ),
    inference(clausify,[status(thm)],[f_961_3]) ).

fof(f_962_1,plain,
    ! [V_k_2,V_n_2,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2)))
        | ( ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(V_Pa_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_Pa_2,V_n_2))
          & V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [B_i,B_j] :
                ( hBOOL(hAPP(V_Pa_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_Pa_2,V_n_2))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(V_Pa_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_962_2,plain,
    ! [U_3383,U_3382,U_3381] :
      ( ( hBOOL(hAPP(U_3381,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3382,U_3383)))
        | ( ? [U_3380,U_3379] :
              ( ~ hBOOL(hAPP(U_3381,U_3379))
              & U_3382 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3383),U_3380)),U_3379)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3379),U_3383)) )
          & U_3383 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3381,U_3382))
          & U_3383 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [U_3378,U_3377] :
                ( hBOOL(hAPP(U_3381,U_3377))
                | U_3382 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3383),U_3378)),U_3377)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3377),U_3383)) )
            | U_3383 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3381,U_3382))
            | U_3383 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3381,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3382,U_3383))) ) ),
    inference(variable_rename,[status(thm)],[f_962_1]) ).

fof(f_962_3,plain,
    ( ! [U_3389,U_3387,U_3385] :
        ( hBOOL(hAPP(U_3385,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3387,U_3389)))
        | ( ? [U_3380,U_3379] :
              ( ~ hBOOL(hAPP(U_3385,U_3379))
              & U_3387 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3389),U_3380)),U_3379)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3379),U_3389)) )
          & U_3389 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3385,U_3387))
          & U_3389 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3388,U_3386,U_3384] :
        ( ( ( ! [U_3378,U_3377] :
                ( hBOOL(hAPP(U_3384,U_3377))
                | U_3386 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3388),U_3378)),U_3377)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3377),U_3388)) )
            | U_3388 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3384,U_3386))
            | U_3388 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3384,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3386,U_3388))) ) ),
    inference(miniscope,[status(thm)],[f_962_2]) ).

fof(f_962_4,plain,
    ( ! [U_3389,U_3387,U_3385] :
        ( hBOOL(hAPP(U_3385,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3387,U_3389)))
        | ( ? [U_3379] :
              ( ~ hBOOL(hAPP(U_3385,U_3379))
              & U_3387 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3389),sK59(U_3389,U_3387,U_3385))),U_3379)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3379),U_3389)) )
          & U_3389 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3385,U_3387))
          & U_3389 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3388,U_3386,U_3384] :
        ( ( ( ! [U_3378,U_3377] :
                ( hBOOL(hAPP(U_3384,U_3377))
                | U_3386 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3388),U_3378)),U_3377)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3377),U_3388)) )
            | U_3388 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3384,U_3386))
            | U_3388 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3384,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3386,U_3388))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK59]),skolemize(U_3380,sK59(U_3389,U_3387,U_3385))],[f_962_3]) ).

fof(f_962_5,plain,
    ( ! [U_3389,U_3387,U_3385] :
        ( hBOOL(hAPP(U_3385,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3387,U_3389)))
        | ( ~ hBOOL(hAPP(U_3385,sK60(U_3389,U_3387,U_3385)))
          & U_3387 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3389),sK59(U_3389,U_3387,U_3385))),sK60(U_3389,U_3387,U_3385))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK60(U_3389,U_3387,U_3385)),U_3389))
          & U_3389 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3385,U_3387))
          & U_3389 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3388,U_3386,U_3384] :
        ( ( ( ! [U_3378,U_3377] :
                ( hBOOL(hAPP(U_3384,U_3377))
                | U_3386 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3388),U_3378)),U_3377)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3377),U_3388)) )
            | U_3388 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3384,U_3386))
            | U_3388 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3384,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3386,U_3388))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK60]),skolemize(U_3379,sK60(U_3389,U_3387,U_3385))],[f_962_4]) ).

fof(f_962_6,plain,
    ( ! [U_3387,U_3385,U_3389] :
        ( ~ hBOOL(hAPP(U_3385,sK60(U_3389,U_3387,U_3385)))
        | ~ sP278(U_3387,U_3385,U_3389) )
    & ! [U_3387,U_3385,U_3389] :
        ( U_3387 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3389),sK59(U_3389,U_3387,U_3385))),sK60(U_3389,U_3387,U_3385))
        | ~ sP278(U_3387,U_3385,U_3389) )
    & ! [U_3387,U_3385,U_3389] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK60(U_3389,U_3387,U_3385)),U_3389))
        | ~ sP278(U_3387,U_3385,U_3389) )
    & ! [U_3387,U_3385,U_3389] :
        ( U_3389 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP278(U_3387,U_3385,U_3389) )
    & ! [U_3387,U_3385,U_3389] :
        ( ~ hBOOL(hAPP(U_3385,U_3387))
        | ~ sP277(U_3387,U_3385,U_3389) )
    & ! [U_3387,U_3385,U_3389] :
        ( U_3389 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP277(U_3387,U_3385,U_3389) )
    & ! [U_3378,U_3377,U_3384,U_3386,U_3388] :
        ( hBOOL(hAPP(U_3384,U_3377))
        | U_3386 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3388),U_3378)),U_3377)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3377),U_3388))
        | U_3388 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP276(U_3378,U_3377,U_3384,U_3386,U_3388) )
    & ! [U_3378,U_3377,U_3384,U_3386,U_3388] :
        ( hBOOL(hAPP(U_3384,U_3386))
        | U_3388 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP276(U_3378,U_3377,U_3384,U_3386,U_3388) )
    & ! [U_3387,U_3385,U_3389] :
        ( hBOOL(hAPP(U_3385,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3387,U_3389)))
        | sP278(U_3387,U_3385,U_3389)
        | sP277(U_3387,U_3385,U_3389) )
    & ! [U_3378,U_3377,U_3384,U_3386,U_3388] :
        ( sP276(U_3378,U_3377,U_3384,U_3386,U_3388)
        | ~ hBOOL(hAPP(U_3384,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3386,U_3388))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP276,sP277,sP278])],[f_962_5]) ).

cnf(f_962_7,plain,
    ( sP276(U_3378,U_3377,U_3384,U_3386,U_3388)
    | ~ hBOOL(hAPP(U_3384,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3386,U_3388))) ),
    inference(clausify,[status(thm)],[f_962_6]) ).

cnf(f_962_8,plain,
    ( hBOOL(hAPP(U_3385,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3387,U_3389)))
    | sP278(U_3387,U_3385,U_3389)
    | sP277(U_3387,U_3385,U_3389) ),
    inference(clausify,[status(thm)],[f_962_6]) ).

cnf(f_962_9,plain,
    ( hBOOL(hAPP(U_3384,U_3386))
    | U_3388 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP276(U_3378,U_3377,U_3384,U_3386,U_3388) ),
    inference(clausify,[status(thm)],[f_962_6]) ).

cnf(f_962_10,plain,
    ( hBOOL(hAPP(U_3384,U_3377))
    | U_3386 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3388),U_3378)),U_3377)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3377),U_3388))
    | U_3388 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP276(U_3378,U_3377,U_3384,U_3386,U_3388) ),
    inference(clausify,[status(thm)],[f_962_6]) ).

cnf(f_962_11,plain,
    ( U_3389 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP277(U_3387,U_3385,U_3389) ),
    inference(clausify,[status(thm)],[f_962_6]) ).

cnf(f_962_12,plain,
    ( ~ hBOOL(hAPP(U_3385,U_3387))
    | ~ sP277(U_3387,U_3385,U_3389) ),
    inference(clausify,[status(thm)],[f_962_6]) ).

cnf(f_962_13,plain,
    ( U_3389 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP278(U_3387,U_3385,U_3389) ),
    inference(clausify,[status(thm)],[f_962_6]) ).

cnf(f_962_14,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK60(U_3389,U_3387,U_3385)),U_3389))
    | ~ sP278(U_3387,U_3385,U_3389) ),
    inference(clausify,[status(thm)],[f_962_6]) ).

cnf(f_962_15,plain,
    ( U_3387 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3389),sK59(U_3389,U_3387,U_3385))),sK60(U_3389,U_3387,U_3385))
    | ~ sP278(U_3387,U_3385,U_3389) ),
    inference(clausify,[status(thm)],[f_962_6]) ).

cnf(f_962_16,plain,
    ( ~ hBOOL(hAPP(U_3385,sK60(U_3389,U_3387,U_3385)))
    | ~ sP278(U_3387,U_3385,U_3389) ),
    inference(clausify,[status(thm)],[f_962_6]) ).

fof(f_963_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_963_2,plain,
    ! [U_3391,U_3390] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3390),U_3391)),U_3390) = 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_3390)) ),
    inference(variable_rename,[status(thm)],[f_963_1]) ).

fof(f_963_3,plain,
    ! [U_3391,U_3390] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3390),U_3391)),U_3390) = 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_3390)) ),
    inference(definitional_conversion,[status(esa)],[f_963_2]) ).

cnf(f_963_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_3390),U_3391)),U_3390) = 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_3390)) ),
    inference(clausify,[status(thm)],[f_963_3]) ).

fof(f_964_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_964_2,plain,
    ! [U_3393,U_3392] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3392),hAPP(c_Int_Onat,U_3393)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3392,U_3393))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3393))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3392)) ),
    inference(variable_rename,[status(thm)],[f_964_1]) ).

fof(f_964_3,plain,
    ! [U_3392,U_3393] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3392),hAPP(c_Int_Onat,U_3393)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3392,U_3393))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3393))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3392)) ),
    inference(definitional_conversion,[status(esa)],[f_964_2]) ).

cnf(f_964_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3392),hAPP(c_Int_Onat,U_3393)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3392,U_3393))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3393))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3392)) ),
    inference(clausify,[status(thm)],[f_964_3]) ).

fof(f_965_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_965_2,plain,
    ! [U_3395,U_3394] :
      ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3394,U_3395)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3394),hAPP(c_Int_Onat,U_3395))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3395))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3394)) ),
    inference(variable_rename,[status(thm)],[f_965_1]) ).

fof(f_965_3,plain,
    ! [U_3394,U_3395] :
      ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3394,U_3395)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3394),hAPP(c_Int_Onat,U_3395))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3395))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3394)) ),
    inference(definitional_conversion,[status(esa)],[f_965_2]) ).

cnf(f_965_4,plain,
    ( hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3394,U_3395)) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onat,U_3394),hAPP(c_Int_Onat,U_3395))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3395))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3394)) ),
    inference(clausify,[status(thm)],[f_965_3]) ).

fof(f_966_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_966_2,plain,
    ! [U_3397,U_3396] :
      ( ( c_SMT_Oz3div(U_3397,U_3396) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3397),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3396)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3396)) )
      & ( c_SMT_Oz3div(U_3397,U_3396) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3397),U_3396)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3396)) ) ),
    inference(variable_rename,[status(thm)],[f_966_1]) ).

fof(f_966_3,plain,
    ( ! [U_3401,U_3399] :
        ( c_SMT_Oz3div(U_3401,U_3399) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3401),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3399)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3399)) )
    & ! [U_3400,U_3398] :
        ( c_SMT_Oz3div(U_3400,U_3398) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3400),U_3398)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3398)) ) ),
    inference(miniscope,[status(thm)],[f_966_2]) ).

fof(f_966_4,plain,
    ( ! [U_3401,U_3399] :
        ( c_SMT_Oz3div(U_3401,U_3399) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3401),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3399)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3399)) )
    & ! [U_3400,U_3398] :
        ( c_SMT_Oz3div(U_3400,U_3398) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3400),U_3398)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3398)) ) ),
    inference(definitional_conversion,[status(esa)],[f_966_3]) ).

cnf(f_966_5,plain,
    ( c_SMT_Oz3div(U_3400,U_3398) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3400),U_3398)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3398)) ),
    inference(clausify,[status(thm)],[f_966_4]) ).

cnf(f_966_6,plain,
    ( c_SMT_Oz3div(U_3401,U_3399) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3401),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3399)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3399)) ),
    inference(clausify,[status(thm)],[f_966_4]) ).

fof(f_967_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_967_2,plain,
    ! [U_3403,U_3402] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3403)),U_3402) = 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_3403),U_3402))),c_Groups_Oone__class_Oone(tc_Int_Oint))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3403,U_3402) = 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_3403)),U_3402) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3403),U_3402))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3403,U_3402) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | U_3402 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_967_1]) ).

fof(f_967_3,plain,
    ( ! [U_3402,U_3403] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3403)),U_3402) = 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_3403),U_3402))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3403,U_3402) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP279(U_3402,U_3403) )
    & ! [U_3402,U_3403] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3403)),U_3402) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3403),U_3402))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3403,U_3402) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP279(U_3402,U_3403) )
    & ! [U_3402,U_3403] :
        ( sP279(U_3402,U_3403)
        | U_3402 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP279])],[f_967_2]) ).

cnf(f_967_4,plain,
    ( sP279(U_3402,U_3403)
    | U_3402 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_967_3]) ).

cnf(f_967_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3403)),U_3402) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3403),U_3402))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3403,U_3402) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP279(U_3402,U_3403) ),
    inference(clausify,[status(thm)],[f_967_3]) ).

cnf(f_967_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3403)),U_3402) = 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_3403),U_3402))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3403,U_3402) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP279(U_3402,U_3403) ),
    inference(clausify,[status(thm)],[f_967_3]) ).

fof(f_968_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_968_2,plain,
    ! [U_3405,U_3404] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3405),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3404)) = 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_3405),U_3404))),c_Groups_Oone__class_Oone(tc_Int_Oint))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3405,U_3404) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3405),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3404)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3405),U_3404))
          | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3405,U_3404) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | U_3404 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_968_1]) ).

fof(f_968_3,plain,
    ( ! [U_3405,U_3404] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3405),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3404)) = 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_3405),U_3404))),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3405,U_3404) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP280(U_3405,U_3404) )
    & ! [U_3405,U_3404] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3405),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3404)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3405),U_3404))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3405,U_3404) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP280(U_3405,U_3404) )
    & ! [U_3405,U_3404] :
        ( sP280(U_3405,U_3404)
        | U_3404 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP280])],[f_968_2]) ).

cnf(f_968_4,plain,
    ( sP280(U_3405,U_3404)
    | U_3404 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_968_3]) ).

cnf(f_968_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3405),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3404)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3405),U_3404))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3405,U_3404) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP280(U_3405,U_3404) ),
    inference(clausify,[status(thm)],[f_968_3]) ).

cnf(f_968_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3405),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3404)) = 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_3405),U_3404))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3405,U_3404) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP280(U_3405,U_3404) ),
    inference(clausify,[status(thm)],[f_968_3]) ).

fof(f_969_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_969_2,plain,
    ! [U_3408,U_3407,U_3406] :
      ( U_3407 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3406),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3406),U_3407),U_3408)),U_3408)),c_Divides_Odiv__class_Omod(U_3406,U_3407,U_3408))
      | ~ class_Divides_Osemiring__div(U_3406) ),
    inference(variable_rename,[status(thm)],[f_969_1]) ).

fof(f_969_3,plain,
    ! [U_3407,U_3406,U_3408] :
      ( U_3407 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3406),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3406),U_3407),U_3408)),U_3408)),c_Divides_Odiv__class_Omod(U_3406,U_3407,U_3408))
      | ~ class_Divides_Osemiring__div(U_3406) ),
    inference(definitional_conversion,[status(esa)],[f_969_2]) ).

cnf(f_969_4,plain,
    ( U_3407 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3406),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3406),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_3406),U_3407),U_3408)),U_3408)),c_Divides_Odiv__class_Omod(U_3406,U_3407,U_3408))
    | ~ class_Divides_Osemiring__div(U_3406) ),
    inference(clausify,[status(thm)],[f_969_3]) ).

fof(f_970_1,plain,
    ! [V_n_2,V_m_2,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2)))
        | ( ! [B_q] :
              ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(V_Pa_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_970_2,plain,
    ! [U_3413,U_3412,U_3411] :
      ( ( hBOOL(hAPP(U_3411,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3412),U_3413)))
        | ( ! [U_3410] :
              ( ~ hBOOL(hAPP(U_3411,U_3410))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3413),hAPP(c_Nat_OSuc,U_3410))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3413),U_3410)),U_3412)) )
          & ( ~ hBOOL(hAPP(U_3411,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3413 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
      & ( ? [U_3409] :
            ( hBOOL(hAPP(U_3411,U_3409))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3412),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3413),hAPP(c_Nat_OSuc,U_3409))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3413),U_3409)),U_3412)) )
        | ( hBOOL(hAPP(U_3411,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3413 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(U_3411,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3412),U_3413))) ) ),
    inference(variable_rename,[status(thm)],[f_970_1]) ).

fof(f_970_3,plain,
    ( ! [U_3419,U_3417,U_3415] :
        ( hBOOL(hAPP(U_3415,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3417),U_3419)))
        | ( ! [U_3410] :
              ( ~ hBOOL(hAPP(U_3415,U_3410))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3417),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3419),hAPP(c_Nat_OSuc,U_3410))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3419),U_3410)),U_3417)) )
          & ( ~ hBOOL(hAPP(U_3415,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3419 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
    & ! [U_3418,U_3416,U_3414] :
        ( ? [U_3409] :
            ( hBOOL(hAPP(U_3414,U_3409))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3418),hAPP(c_Nat_OSuc,U_3409))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3418),U_3409)),U_3416)) )
        | ( hBOOL(hAPP(U_3414,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3418 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(U_3414,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3416),U_3418))) ) ),
    inference(miniscope,[status(thm)],[f_970_2]) ).

fof(f_970_4,plain,
    ( ! [U_3419,U_3417,U_3415] :
        ( hBOOL(hAPP(U_3415,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3417),U_3419)))
        | ( ! [U_3410] :
              ( ~ hBOOL(hAPP(U_3415,U_3410))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3417),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3419),hAPP(c_Nat_OSuc,U_3410))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3419),U_3410)),U_3417)) )
          & ( ~ hBOOL(hAPP(U_3415,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3419 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) )
    & ! [U_3418,U_3416,U_3414] :
        ( ( hBOOL(hAPP(U_3414,sK61(U_3418,U_3416,U_3414)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3418),hAPP(c_Nat_OSuc,sK61(U_3418,U_3416,U_3414)))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3418),sK61(U_3418,U_3416,U_3414))),U_3416)) )
        | ( hBOOL(hAPP(U_3414,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3418 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ~ hBOOL(hAPP(U_3414,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3416),U_3418))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK61]),skolemize(U_3409,sK61(U_3418,U_3416,U_3414))],[f_970_3]) ).

fof(f_970_5,plain,
    ( ! [U_3410,U_3417,U_3415,U_3419] :
        ( ~ hBOOL(hAPP(U_3415,U_3410))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3417),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3419),hAPP(c_Nat_OSuc,U_3410))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3419),U_3410)),U_3417))
        | ~ sP283(U_3410,U_3417,U_3415,U_3419) )
    & ! [U_3410,U_3417,U_3415,U_3419] :
        ( ~ hBOOL(hAPP(U_3415,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_3419 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP283(U_3410,U_3417,U_3415,U_3419) )
    & ! [U_3418,U_3414,U_3416] :
        ( hBOOL(hAPP(U_3414,sK61(U_3418,U_3416,U_3414)))
        | ~ sP282(U_3418,U_3414,U_3416) )
    & ! [U_3418,U_3414,U_3416] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3418),hAPP(c_Nat_OSuc,sK61(U_3418,U_3416,U_3414)))))
        | ~ sP282(U_3418,U_3414,U_3416) )
    & ! [U_3418,U_3414,U_3416] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3418),sK61(U_3418,U_3416,U_3414))),U_3416))
        | ~ sP282(U_3418,U_3414,U_3416) )
    & ! [U_3418,U_3414] :
        ( hBOOL(hAPP(U_3414,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP281(U_3418,U_3414) )
    & ! [U_3418,U_3414] :
        ( U_3418 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP281(U_3418,U_3414) )
    & ! [U_3410,U_3417,U_3415,U_3419] :
        ( hBOOL(hAPP(U_3415,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3417),U_3419)))
        | sP283(U_3410,U_3417,U_3415,U_3419) )
    & ! [U_3418,U_3414,U_3416] :
        ( sP282(U_3418,U_3414,U_3416)
        | sP281(U_3418,U_3414)
        | ~ hBOOL(hAPP(U_3414,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3416),U_3418))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP281,sP282,sP283])],[f_970_4]) ).

cnf(f_970_6,plain,
    ( sP282(U_3418,U_3414,U_3416)
    | sP281(U_3418,U_3414)
    | ~ hBOOL(hAPP(U_3414,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3416),U_3418))) ),
    inference(clausify,[status(thm)],[f_970_5]) ).

cnf(f_970_7,plain,
    ( hBOOL(hAPP(U_3415,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3417),U_3419)))
    | sP283(U_3410,U_3417,U_3415,U_3419) ),
    inference(clausify,[status(thm)],[f_970_5]) ).

cnf(f_970_8,plain,
    ( U_3418 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP281(U_3418,U_3414) ),
    inference(clausify,[status(thm)],[f_970_5]) ).

cnf(f_970_9,plain,
    ( hBOOL(hAPP(U_3414,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP281(U_3418,U_3414) ),
    inference(clausify,[status(thm)],[f_970_5]) ).

cnf(f_970_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_3418),sK61(U_3418,U_3416,U_3414))),U_3416))
    | ~ sP282(U_3418,U_3414,U_3416) ),
    inference(clausify,[status(thm)],[f_970_5]) ).

cnf(f_970_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3416),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3418),hAPP(c_Nat_OSuc,sK61(U_3418,U_3416,U_3414)))))
    | ~ sP282(U_3418,U_3414,U_3416) ),
    inference(clausify,[status(thm)],[f_970_5]) ).

cnf(f_970_12,plain,
    ( hBOOL(hAPP(U_3414,sK61(U_3418,U_3416,U_3414)))
    | ~ sP282(U_3418,U_3414,U_3416) ),
    inference(clausify,[status(thm)],[f_970_5]) ).

cnf(f_970_13,plain,
    ( ~ hBOOL(hAPP(U_3415,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_3419 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP283(U_3410,U_3417,U_3415,U_3419) ),
    inference(clausify,[status(thm)],[f_970_5]) ).

cnf(f_970_14,plain,
    ( ~ hBOOL(hAPP(U_3415,U_3410))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3417),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3419),hAPP(c_Nat_OSuc,U_3410))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3419),U_3410)),U_3417))
    | ~ sP283(U_3410,U_3417,U_3415,U_3419) ),
    inference(clausify,[status(thm)],[f_970_5]) ).

fof(f_971_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_971_2,plain,
    ! [U_3422,U_3421,U_3420] :
      ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3420),hAPP(c_Nat_OSuc,U_3421))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3420),U_3421)),U_3422)) )
          | U_3421 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3422),U_3420) )
        & ( U_3421 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3422),U_3420)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3420),hAPP(c_Nat_OSuc,U_3421))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3420),U_3421)),U_3422)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3420)) ),
    inference(variable_rename,[status(thm)],[f_971_1]) ).

fof(f_971_3,plain,
    ( ! [U_3421,U_3420,U_3422] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3420),hAPP(c_Nat_OSuc,U_3421))))
        | ~ sP284(U_3421,U_3420,U_3422) )
    & ! [U_3421,U_3420,U_3422] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3420),U_3421)),U_3422))
        | ~ sP284(U_3421,U_3420,U_3422) )
    & ! [U_3421,U_3420,U_3422] :
        ( sP284(U_3421,U_3420,U_3422)
        | U_3421 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3422),U_3420)
        | ~ sP285(U_3421,U_3420,U_3422) )
    & ! [U_3421,U_3420,U_3422] :
        ( U_3421 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3422),U_3420)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3420),hAPP(c_Nat_OSuc,U_3421))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3420),U_3421)),U_3422))
        | ~ sP285(U_3421,U_3420,U_3422) )
    & ! [U_3421,U_3420,U_3422] :
        ( sP285(U_3421,U_3420,U_3422)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3420)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP284,sP285])],[f_971_2]) ).

cnf(f_971_4,plain,
    ( sP285(U_3421,U_3420,U_3422)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3420)) ),
    inference(clausify,[status(thm)],[f_971_3]) ).

cnf(f_971_5,plain,
    ( U_3421 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3422),U_3420)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3420),hAPP(c_Nat_OSuc,U_3421))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3420),U_3421)),U_3422))
    | ~ sP285(U_3421,U_3420,U_3422) ),
    inference(clausify,[status(thm)],[f_971_3]) ).

cnf(f_971_6,plain,
    ( sP284(U_3421,U_3420,U_3422)
    | U_3421 != hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3422),U_3420)
    | ~ sP285(U_3421,U_3420,U_3422) ),
    inference(clausify,[status(thm)],[f_971_3]) ).

cnf(f_971_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_3420),U_3421)),U_3422))
    | ~ sP284(U_3421,U_3420,U_3422) ),
    inference(clausify,[status(thm)],[f_971_3]) ).

cnf(f_971_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3422),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3420),hAPP(c_Nat_OSuc,U_3421))))
    | ~ sP284(U_3421,U_3420,U_3422) ),
    inference(clausify,[status(thm)],[f_971_3]) ).

fof(f_972_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_972_2,plain,
    ! [U_3424,U_3423] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_3423)),hAPP(c_Int_Onat,U_3424)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_3423,U_3424))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3424))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3423)) ),
    inference(variable_rename,[status(thm)],[f_972_1]) ).

fof(f_972_3,plain,
    ! [U_3424,U_3423] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_3423)),hAPP(c_Int_Onat,U_3424)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_3423,U_3424))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3424))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3423)) ),
    inference(definitional_conversion,[status(esa)],[f_972_2]) ).

cnf(f_972_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_3423)),hAPP(c_Int_Onat,U_3424)) = hAPP(c_Int_Onat,c_Nat__Transfer_Otsub(U_3423,U_3424))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3424))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3423)) ),
    inference(clausify,[status(thm)],[f_972_3]) ).

fof(f_973_1,plain,
    ! [V_k_2,V_Pa_2,V_d_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2)))
          & hBOOL(hAPP(V_Pa_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_973_2,plain,
    ! [U_3429,U_3428,U_3427] :
      ( ! [U_3426] :
          ( hBOOL(hAPP(U_3428,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3429),U_3427))))
          | ~ hBOOL(hAPP(U_3428,U_3426)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3429))
      | ? [U_3425] :
          ( ~ hBOOL(hAPP(U_3428,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3425),U_3427)))
          & hBOOL(hAPP(U_3428,U_3425)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3427)) ),
    inference(variable_rename,[status(thm)],[f_973_1]) ).

fof(f_973_3,plain,
    ! [U_3429,U_3428,U_3427] :
      ( ! [U_3426] :
          ( hBOOL(hAPP(U_3428,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3429),U_3427))))
          | ~ hBOOL(hAPP(U_3428,U_3426)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3429))
      | ( ~ hBOOL(hAPP(U_3428,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK62(U_3429,U_3428,U_3427)),U_3427)))
        & hBOOL(hAPP(U_3428,sK62(U_3429,U_3428,U_3427))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3427)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK62]),skolemize(U_3425,sK62(U_3429,U_3428,U_3427))],[f_973_2]) ).

fof(f_973_4,plain,
    ( ! [U_3427,U_3428,U_3429] :
        ( ~ hBOOL(hAPP(U_3428,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK62(U_3429,U_3428,U_3427)),U_3427)))
        | ~ sP286(U_3427,U_3428,U_3429) )
    & ! [U_3427,U_3428,U_3429] :
        ( hBOOL(hAPP(U_3428,sK62(U_3429,U_3428,U_3427)))
        | ~ sP286(U_3427,U_3428,U_3429) )
    & ! [U_3427,U_3426,U_3428,U_3429] :
        ( hBOOL(hAPP(U_3428,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3429),U_3427))))
        | ~ hBOOL(hAPP(U_3428,U_3426))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3429))
        | sP286(U_3427,U_3428,U_3429)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3427)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP286])],[f_973_3]) ).

cnf(f_973_5,plain,
    ( hBOOL(hAPP(U_3428,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3426),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3429),U_3427))))
    | ~ hBOOL(hAPP(U_3428,U_3426))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3429))
    | sP286(U_3427,U_3428,U_3429)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3427)) ),
    inference(clausify,[status(thm)],[f_973_4]) ).

cnf(f_973_6,plain,
    ( hBOOL(hAPP(U_3428,sK62(U_3429,U_3428,U_3427)))
    | ~ sP286(U_3427,U_3428,U_3429) ),
    inference(clausify,[status(thm)],[f_973_4]) ).

cnf(f_973_7,plain,
    ( ~ hBOOL(hAPP(U_3428,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK62(U_3429,U_3428,U_3427)),U_3427)))
    | ~ sP286(U_3427,U_3428,U_3429) ),
    inference(clausify,[status(thm)],[f_973_4]) ).

fof(f_974_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_974_2,plain,
    ! [U_3431,U_3430] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3430,U_3431) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3430),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3430),U_3431)),U_3431)),
    inference(variable_rename,[status(thm)],[f_974_1]) ).

fof(f_974_3,plain,
    ! [U_3431,U_3430] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3430,U_3431) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3430),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3430),U_3431)),U_3431)),
    inference(definitional_conversion,[status(esa)],[f_974_2]) ).

cnf(f_974_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3430,U_3431) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3430),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3430),U_3431)),U_3431)),
    inference(clausify,[status(thm)],[f_974_3]) ).

fof(f_975_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_975_2,plain,
    ! [U_3433,U_3432] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3432),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3433),U_3432)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3433),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3433,U_3432)),
    inference(variable_rename,[status(thm)],[f_975_1]) ).

fof(f_975_3,plain,
    ! [U_3432,U_3433] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3432),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3433),U_3432)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3433),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3433,U_3432)),
    inference(definitional_conversion,[status(esa)],[f_975_2]) ).

cnf(f_975_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3432),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3433),U_3432)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3433),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3433,U_3432)),
    inference(clausify,[status(thm)],[f_975_3]) ).

fof(f_976_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_976_2,plain,
    ! [U_3435,U_3434] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3434),U_3435)),U_3435) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3434),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3434,U_3435)),
    inference(variable_rename,[status(thm)],[f_976_1]) ).

fof(f_976_3,plain,
    ! [U_3434,U_3435] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3434),U_3435)),U_3435) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3434),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3434,U_3435)),
    inference(definitional_conversion,[status(esa)],[f_976_2]) ).

cnf(f_976_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3434),U_3435)),U_3435) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3434),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3434,U_3435)),
    inference(clausify,[status(thm)],[f_976_3]) ).

fof(f_977_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_977_2,plain,
    ! [U_3440,U_3439,U_3438,U_3437,U_3436] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3437,U_3436)),U_3438),U_3439),U_3440) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3436),hAPP(U_3438,U_3440)),hAPP(U_3439,U_3440))
      | ~ class_Groups_Ominus(U_3436) ),
    inference(variable_rename,[status(thm)],[f_977_1]) ).

fof(f_977_3,plain,
    ! [U_3436,U_3437,U_3438,U_3439,U_3440] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3437,U_3436)),U_3438),U_3439),U_3440) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3436),hAPP(U_3438,U_3440)),hAPP(U_3439,U_3440))
      | ~ class_Groups_Ominus(U_3436) ),
    inference(definitional_conversion,[status(esa)],[f_977_2]) ).

cnf(f_977_4,plain,
    ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3437,U_3436)),U_3438),U_3439),U_3440) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3436),hAPP(U_3438,U_3440)),hAPP(U_3439,U_3440))
    | ~ class_Groups_Ominus(U_3436) ),
    inference(clausify,[status(thm)],[f_977_3]) ).

fof(f_978_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_978_2,plain,
    ! [U_3443,U_3442,U_3441] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_3441),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3442),U_3443)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3441),hAPP(c_Int_Oring__1__class_Oof__int(U_3441),U_3442)),hAPP(c_Int_Oring__1__class_Oof__int(U_3441),U_3443))
      | ~ class_Rings_Oring__1(U_3441) ),
    inference(variable_rename,[status(thm)],[f_978_1]) ).

fof(f_978_3,plain,
    ! [U_3441,U_3442,U_3443] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_3441),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3442),U_3443)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3441),hAPP(c_Int_Oring__1__class_Oof__int(U_3441),U_3442)),hAPP(c_Int_Oring__1__class_Oof__int(U_3441),U_3443))
      | ~ class_Rings_Oring__1(U_3441) ),
    inference(definitional_conversion,[status(esa)],[f_978_2]) ).

cnf(f_978_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_3441),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3442),U_3443)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3441),hAPP(c_Int_Oring__1__class_Oof__int(U_3441),U_3442)),hAPP(c_Int_Oring__1__class_Oof__int(U_3441),U_3443))
    | ~ class_Rings_Oring__1(U_3441) ),
    inference(clausify,[status(thm)],[f_978_3]) ).

fof(f_979_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_979_2,plain,
    ! [U_3446,U_3445,U_3444] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3444),U_3445)),U_3446) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3444),U_3446)),U_3445),
    inference(variable_rename,[status(thm)],[f_979_1]) ).

fof(f_979_3,plain,
    ! [U_3444,U_3445,U_3446] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3444),U_3445)),U_3446) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3444),U_3446)),U_3445),
    inference(definitional_conversion,[status(esa)],[f_979_2]) ).

cnf(f_979_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3444),U_3445)),U_3446) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3444),U_3446)),U_3445),
    inference(clausify,[status(thm)],[f_979_3]) ).

fof(f_980_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_980_2,plain,
    ! [U_3451,U_3450,U_3449,U_3448,U_3447] :
      ( ( ( U_3448 = U_3449
          | U_3450 != U_3451 )
        & ( U_3450 = U_3451
          | U_3448 != U_3449 ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3447),U_3448),U_3449) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3447),U_3450),U_3451)
      | ~ class_Groups_Oab__group__add(U_3447) ),
    inference(variable_rename,[status(thm)],[f_980_1]) ).

fof(f_980_3,plain,
    ( ! [U_3448,U_3449,U_3450,U_3451] :
        ( U_3448 = U_3449
        | U_3450 != U_3451
        | ~ sP287(U_3448,U_3449,U_3450,U_3451) )
    & ! [U_3448,U_3449,U_3450,U_3451] :
        ( U_3450 = U_3451
        | U_3448 != U_3449
        | ~ sP287(U_3448,U_3449,U_3450,U_3451) )
    & ! [U_3447,U_3448,U_3449,U_3450,U_3451] :
        ( sP287(U_3448,U_3449,U_3450,U_3451)
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3447),U_3448),U_3449) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3447),U_3450),U_3451)
        | ~ class_Groups_Oab__group__add(U_3447) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP287])],[f_980_2]) ).

cnf(f_980_4,plain,
    ( sP287(U_3448,U_3449,U_3450,U_3451)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3447),U_3448),U_3449) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3447),U_3450),U_3451)
    | ~ class_Groups_Oab__group__add(U_3447) ),
    inference(clausify,[status(thm)],[f_980_3]) ).

cnf(f_980_5,plain,
    ( U_3450 = U_3451
    | U_3448 != U_3449
    | ~ sP287(U_3448,U_3449,U_3450,U_3451) ),
    inference(clausify,[status(thm)],[f_980_3]) ).

cnf(f_980_6,plain,
    ( U_3448 = U_3449
    | U_3450 != U_3451
    | ~ sP287(U_3448,U_3449,U_3450,U_3451) ),
    inference(clausify,[status(thm)],[f_980_3]) ).

fof(f_981_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_981_2,plain,
    ! [U_3454,U_3453,U_3452] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3452),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3454),U_3453)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3452),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3452),U_3454)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3452),U_3453))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3453),U_3454))
      | ~ class_Rings_Oring__1(U_3452) ),
    inference(variable_rename,[status(thm)],[f_981_1]) ).

fof(f_981_3,plain,
    ! [U_3453,U_3454,U_3452] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3452),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3454),U_3453)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3452),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3452),U_3454)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3452),U_3453))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3453),U_3454))
      | ~ class_Rings_Oring__1(U_3452) ),
    inference(definitional_conversion,[status(esa)],[f_981_2]) ).

cnf(f_981_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3452),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3454),U_3453)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3452),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3452),U_3454)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3452),U_3453))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3453),U_3454))
    | ~ class_Rings_Oring__1(U_3452) ),
    inference(clausify,[status(thm)],[f_981_3]) ).

fof(f_982_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_982_2,plain,
    ! [U_3456,U_3455] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3456)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3455)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3456),U_3455))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3455),U_3456)) ),
    inference(variable_rename,[status(thm)],[f_982_1]) ).

fof(f_982_3,plain,
    ! [U_3455,U_3456] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3456)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3455)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3456),U_3455))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3455),U_3456)) ),
    inference(definitional_conversion,[status(esa)],[f_982_2]) ).

cnf(f_982_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3456)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3455)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3456),U_3455))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3455),U_3456)) ),
    inference(clausify,[status(thm)],[f_982_3]) ).

fof(f_983_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_983_2,plain,
    ! [U_3461,U_3460,U_3459,U_3458,U_3457] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3457),U_3458),U_3459))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3457),U_3460),U_3461)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3457),U_3460),U_3461))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3457),U_3458),U_3459)) ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3457),U_3458),U_3459) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3457),U_3460),U_3461)
      | ~ class_Groups_Oordered__ab__group__add(U_3457) ),
    inference(variable_rename,[status(thm)],[f_983_1]) ).

fof(f_983_3,plain,
    ( ! [U_3457,U_3458,U_3459,U_3460,U_3461] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3457),U_3458),U_3459))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3457),U_3460),U_3461))
        | ~ sP288(U_3457,U_3458,U_3459,U_3460,U_3461) )
    & ! [U_3457,U_3458,U_3459,U_3460,U_3461] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3457),U_3460),U_3461))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3457),U_3458),U_3459))
        | ~ sP288(U_3457,U_3458,U_3459,U_3460,U_3461) )
    & ! [U_3457,U_3458,U_3459,U_3460,U_3461] :
        ( sP288(U_3457,U_3458,U_3459,U_3460,U_3461)
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3457),U_3458),U_3459) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3457),U_3460),U_3461)
        | ~ class_Groups_Oordered__ab__group__add(U_3457) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP288])],[f_983_2]) ).

cnf(f_983_4,plain,
    ( sP288(U_3457,U_3458,U_3459,U_3460,U_3461)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3457),U_3458),U_3459) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3457),U_3460),U_3461)
    | ~ class_Groups_Oordered__ab__group__add(U_3457) ),
    inference(clausify,[status(thm)],[f_983_3]) ).

cnf(f_983_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3457),U_3460),U_3461))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3457),U_3458),U_3459))
    | ~ sP288(U_3457,U_3458,U_3459,U_3460,U_3461) ),
    inference(clausify,[status(thm)],[f_983_3]) ).

cnf(f_983_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3457),U_3458),U_3459))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3457),U_3460),U_3461))
    | ~ sP288(U_3457,U_3458,U_3459,U_3460,U_3461) ),
    inference(clausify,[status(thm)],[f_983_3]) ).

fof(f_984_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_984_2,plain,
    ! [U_3464,U_3463,U_3462] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3462),U_3463),U_3464) = c_Groups_Ozero__class_Ozero(U_3462)
          | U_3463 != U_3464 )
        & ( U_3463 = U_3464
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3462),U_3463),U_3464) != c_Groups_Ozero__class_Ozero(U_3462) ) )
      | ~ class_Groups_Ogroup__add(U_3462) ),
    inference(variable_rename,[status(thm)],[f_984_1]) ).

fof(f_984_3,plain,
    ( ! [U_3462,U_3463,U_3464] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3462),U_3463),U_3464) = c_Groups_Ozero__class_Ozero(U_3462)
        | U_3463 != U_3464
        | ~ sP289(U_3462,U_3463,U_3464) )
    & ! [U_3462,U_3463,U_3464] :
        ( U_3463 = U_3464
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3462),U_3463),U_3464) != c_Groups_Ozero__class_Ozero(U_3462)
        | ~ sP289(U_3462,U_3463,U_3464) )
    & ! [U_3462,U_3463,U_3464] :
        ( sP289(U_3462,U_3463,U_3464)
        | ~ class_Groups_Ogroup__add(U_3462) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP289])],[f_984_2]) ).

cnf(f_984_4,plain,
    ( sP289(U_3462,U_3463,U_3464)
    | ~ class_Groups_Ogroup__add(U_3462) ),
    inference(clausify,[status(thm)],[f_984_3]) ).

cnf(f_984_5,plain,
    ( U_3463 = U_3464
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3462),U_3463),U_3464) != c_Groups_Ozero__class_Ozero(U_3462)
    | ~ sP289(U_3462,U_3463,U_3464) ),
    inference(clausify,[status(thm)],[f_984_3]) ).

cnf(f_984_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3462),U_3463),U_3464) = c_Groups_Ozero__class_Ozero(U_3462)
    | U_3463 != U_3464
    | ~ sP289(U_3462,U_3463,U_3464) ),
    inference(clausify,[status(thm)],[f_984_3]) ).

fof(f_985_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_985_2,plain,
    ! [U_3467,U_3466,U_3465] :
      ( ( ( U_3466 = U_3467
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3465),U_3466),U_3467) != c_Groups_Ozero__class_Ozero(U_3465) )
        & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3465),U_3466),U_3467) = c_Groups_Ozero__class_Ozero(U_3465)
          | U_3466 != U_3467 ) )
      | ~ class_Groups_Oab__group__add(U_3465) ),
    inference(variable_rename,[status(thm)],[f_985_1]) ).

fof(f_985_3,plain,
    ( ! [U_3467,U_3466,U_3465] :
        ( U_3466 = U_3467
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3465),U_3466),U_3467) != c_Groups_Ozero__class_Ozero(U_3465)
        | ~ sP290(U_3467,U_3466,U_3465) )
    & ! [U_3467,U_3466,U_3465] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3465),U_3466),U_3467) = c_Groups_Ozero__class_Ozero(U_3465)
        | U_3466 != U_3467
        | ~ sP290(U_3467,U_3466,U_3465) )
    & ! [U_3467,U_3466,U_3465] :
        ( sP290(U_3467,U_3466,U_3465)
        | ~ class_Groups_Oab__group__add(U_3465) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP290])],[f_985_2]) ).

cnf(f_985_4,plain,
    ( sP290(U_3467,U_3466,U_3465)
    | ~ class_Groups_Oab__group__add(U_3465) ),
    inference(clausify,[status(thm)],[f_985_3]) ).

cnf(f_985_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3465),U_3466),U_3467) = c_Groups_Ozero__class_Ozero(U_3465)
    | U_3466 != U_3467
    | ~ sP290(U_3467,U_3466,U_3465) ),
    inference(clausify,[status(thm)],[f_985_3]) ).

cnf(f_985_6,plain,
    ( U_3466 = U_3467
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3465),U_3466),U_3467) != c_Groups_Ozero__class_Ozero(U_3465)
    | ~ sP290(U_3467,U_3466,U_3465) ),
    inference(clausify,[status(thm)],[f_985_3]) ).

fof(f_986_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_986_2,plain,
    ! [U_3469,U_3468] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3468),U_3469),U_3469) = c_Groups_Ozero__class_Ozero(U_3468)
      | ~ class_Groups_Ogroup__add(U_3468) ),
    inference(variable_rename,[status(thm)],[f_986_1]) ).

fof(f_986_3,plain,
    ! [U_3468,U_3469] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3468),U_3469),U_3469) = c_Groups_Ozero__class_Ozero(U_3468)
      | ~ class_Groups_Ogroup__add(U_3468) ),
    inference(definitional_conversion,[status(esa)],[f_986_2]) ).

cnf(f_986_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3468),U_3469),U_3469) = c_Groups_Ozero__class_Ozero(U_3468)
    | ~ class_Groups_Ogroup__add(U_3468) ),
    inference(clausify,[status(thm)],[f_986_3]) ).

fof(f_987_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_987_2,plain,
    ! [U_3471,U_3470] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3470),U_3471),c_Groups_Ozero__class_Ozero(U_3470)) = U_3471
      | ~ class_Groups_Ogroup__add(U_3470) ),
    inference(variable_rename,[status(thm)],[f_987_1]) ).

fof(f_987_3,plain,
    ! [U_3470,U_3471] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3470),U_3471),c_Groups_Ozero__class_Ozero(U_3470)) = U_3471
      | ~ class_Groups_Ogroup__add(U_3470) ),
    inference(definitional_conversion,[status(esa)],[f_987_2]) ).

cnf(f_987_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3470),U_3471),c_Groups_Ozero__class_Ozero(U_3470)) = U_3471
    | ~ class_Groups_Ogroup__add(U_3470) ),
    inference(clausify,[status(thm)],[f_987_3]) ).

fof(f_988_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_988_2,plain,
    ! [U_3476,U_3475,U_3474,U_3473,U_3472] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3472),U_3473),U_3474))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3472),U_3475),U_3476)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3472),U_3475),U_3476))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3472),U_3473),U_3474)) ) )
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3472),U_3473),U_3474) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3472),U_3475),U_3476)
      | ~ class_Groups_Oordered__ab__group__add(U_3472) ),
    inference(variable_rename,[status(thm)],[f_988_1]) ).

fof(f_988_3,plain,
    ( ! [U_3472,U_3473,U_3474,U_3475,U_3476] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3472),U_3473),U_3474))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3472),U_3475),U_3476))
        | ~ sP291(U_3472,U_3473,U_3474,U_3475,U_3476) )
    & ! [U_3472,U_3473,U_3474,U_3475,U_3476] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3472),U_3475),U_3476))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3472),U_3473),U_3474))
        | ~ sP291(U_3472,U_3473,U_3474,U_3475,U_3476) )
    & ! [U_3472,U_3473,U_3474,U_3475,U_3476] :
        ( sP291(U_3472,U_3473,U_3474,U_3475,U_3476)
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3472),U_3473),U_3474) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3472),U_3475),U_3476)
        | ~ class_Groups_Oordered__ab__group__add(U_3472) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP291])],[f_988_2]) ).

cnf(f_988_4,plain,
    ( sP291(U_3472,U_3473,U_3474,U_3475,U_3476)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3472),U_3473),U_3474) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3472),U_3475),U_3476)
    | ~ class_Groups_Oordered__ab__group__add(U_3472) ),
    inference(clausify,[status(thm)],[f_988_3]) ).

cnf(f_988_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3472),U_3475),U_3476))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3472),U_3473),U_3474))
    | ~ sP291(U_3472,U_3473,U_3474,U_3475,U_3476) ),
    inference(clausify,[status(thm)],[f_988_3]) ).

cnf(f_988_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3472),U_3473),U_3474))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3472),U_3475),U_3476))
    | ~ sP291(U_3472,U_3473,U_3474,U_3475,U_3476) ),
    inference(clausify,[status(thm)],[f_988_3]) ).

fof(f_989_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_989_2,plain,
    ! [U_3479,U_3478,U_3477] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3477),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3477),U_3478),U_3479)),U_3479) = U_3478
      | ~ class_Groups_Ogroup__add(U_3477) ),
    inference(variable_rename,[status(thm)],[f_989_1]) ).

fof(f_989_3,plain,
    ! [U_3477,U_3478,U_3479] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3477),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3477),U_3478),U_3479)),U_3479) = U_3478
      | ~ class_Groups_Ogroup__add(U_3477) ),
    inference(definitional_conversion,[status(esa)],[f_989_2]) ).

cnf(f_989_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3477),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3477),U_3478),U_3479)),U_3479) = U_3478
    | ~ class_Groups_Ogroup__add(U_3477) ),
    inference(clausify,[status(thm)],[f_989_3]) ).

fof(f_990_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_990_2,plain,
    ! [U_3482,U_3481,U_3480] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3480),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3480),U_3481),U_3482)),U_3482) = U_3481
      | ~ class_Groups_Ogroup__add(U_3480) ),
    inference(variable_rename,[status(thm)],[f_990_1]) ).

fof(f_990_3,plain,
    ! [U_3481,U_3480,U_3482] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3480),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3480),U_3481),U_3482)),U_3482) = U_3481
      | ~ class_Groups_Ogroup__add(U_3480) ),
    inference(definitional_conversion,[status(esa)],[f_990_2]) ).

cnf(f_990_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3480),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3480),U_3481),U_3482)),U_3482) = U_3481
    | ~ class_Groups_Ogroup__add(U_3480) ),
    inference(clausify,[status(thm)],[f_990_3]) ).

fof(f_991_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_991_2,plain,
    ! [U_3485,U_3484,U_3483] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3483),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3483),U_3484),U_3485)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3483),U_3485),U_3484)
      | ~ class_Groups_Oab__group__add(U_3483) ),
    inference(variable_rename,[status(thm)],[f_991_1]) ).

fof(f_991_3,plain,
    ! [U_3483,U_3484,U_3485] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3483),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3483),U_3484),U_3485)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3483),U_3485),U_3484)
      | ~ class_Groups_Oab__group__add(U_3483) ),
    inference(definitional_conversion,[status(esa)],[f_991_2]) ).

cnf(f_991_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_3483),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3483),U_3484),U_3485)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3483),U_3485),U_3484)
    | ~ class_Groups_Oab__group__add(U_3483) ),
    inference(clausify,[status(thm)],[f_991_3]) ).

fof(f_992_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_992_2,plain,
    ! [U_3488,U_3487,U_3486] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3486),U_3487)),U_3488) = 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_3486),U_3488)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3487),U_3488))),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_3486,U_3488)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3487,U_3488))),U_3488)),
    inference(variable_rename,[status(thm)],[f_992_1]) ).

fof(f_992_3,plain,
    ! [U_3486,U_3487,U_3488] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3486),U_3487)),U_3488) = 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_3486),U_3488)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3487),U_3488))),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_3486,U_3488)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3487,U_3488))),U_3488)),
    inference(definitional_conversion,[status(esa)],[f_992_2]) ).

cnf(f_992_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3486),U_3487)),U_3488) = 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_3486),U_3488)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3487),U_3488))),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_3486,U_3488)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3487,U_3488))),U_3488)),
    inference(clausify,[status(thm)],[f_992_3]) ).

fof(f_993_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_993_2,plain,
    ! [U_3492,U_3491,U_3490,U_3489] :
      ( c_Divides_Odiv__class_Omod(U_3489,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3489),U_3490),U_3491),U_3492) = c_Divides_Odiv__class_Omod(U_3489,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3489),U_3490),c_Divides_Odiv__class_Omod(U_3489,U_3491,U_3492)),U_3492)
      | ~ class_Divides_Oring__div(U_3489) ),
    inference(variable_rename,[status(thm)],[f_993_1]) ).

fof(f_993_3,plain,
    ! [U_3489,U_3490,U_3491,U_3492] :
      ( c_Divides_Odiv__class_Omod(U_3489,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3489),U_3490),U_3491),U_3492) = c_Divides_Odiv__class_Omod(U_3489,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3489),U_3490),c_Divides_Odiv__class_Omod(U_3489,U_3491,U_3492)),U_3492)
      | ~ class_Divides_Oring__div(U_3489) ),
    inference(definitional_conversion,[status(esa)],[f_993_2]) ).

cnf(f_993_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3489,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3489),U_3490),U_3491),U_3492) = c_Divides_Odiv__class_Omod(U_3489,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3489),U_3490),c_Divides_Odiv__class_Omod(U_3489,U_3491,U_3492)),U_3492)
    | ~ class_Divides_Oring__div(U_3489) ),
    inference(clausify,[status(thm)],[f_993_3]) ).

fof(f_994_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_994_2,plain,
    ! [U_3496,U_3495,U_3494,U_3493] :
      ( c_Divides_Odiv__class_Omod(U_3493,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3493),U_3494),U_3495),U_3496) = c_Divides_Odiv__class_Omod(U_3493,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3493),c_Divides_Odiv__class_Omod(U_3493,U_3494,U_3496)),U_3495),U_3496)
      | ~ class_Divides_Oring__div(U_3493) ),
    inference(variable_rename,[status(thm)],[f_994_1]) ).

fof(f_994_3,plain,
    ! [U_3493,U_3494,U_3495,U_3496] :
      ( c_Divides_Odiv__class_Omod(U_3493,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3493),U_3494),U_3495),U_3496) = c_Divides_Odiv__class_Omod(U_3493,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3493),c_Divides_Odiv__class_Omod(U_3493,U_3494,U_3496)),U_3495),U_3496)
      | ~ class_Divides_Oring__div(U_3493) ),
    inference(definitional_conversion,[status(esa)],[f_994_2]) ).

cnf(f_994_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3493,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3493),U_3494),U_3495),U_3496) = c_Divides_Odiv__class_Omod(U_3493,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3493),c_Divides_Odiv__class_Omod(U_3493,U_3494,U_3496)),U_3495),U_3496)
    | ~ class_Divides_Oring__div(U_3493) ),
    inference(clausify,[status(thm)],[f_994_3]) ).

fof(f_995_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_995_2,plain,
    ! [U_3500,U_3499,U_3498,U_3497] :
      ( c_Divides_Odiv__class_Omod(U_3497,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3497),U_3498),U_3499),U_3500) = c_Divides_Odiv__class_Omod(U_3497,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3497),c_Divides_Odiv__class_Omod(U_3497,U_3498,U_3500)),c_Divides_Odiv__class_Omod(U_3497,U_3499,U_3500)),U_3500)
      | ~ class_Divides_Oring__div(U_3497) ),
    inference(variable_rename,[status(thm)],[f_995_1]) ).

fof(f_995_3,plain,
    ! [U_3497,U_3498,U_3499,U_3500] :
      ( c_Divides_Odiv__class_Omod(U_3497,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3497),U_3498),U_3499),U_3500) = c_Divides_Odiv__class_Omod(U_3497,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3497),c_Divides_Odiv__class_Omod(U_3497,U_3498,U_3500)),c_Divides_Odiv__class_Omod(U_3497,U_3499,U_3500)),U_3500)
      | ~ class_Divides_Oring__div(U_3497) ),
    inference(definitional_conversion,[status(esa)],[f_995_2]) ).

cnf(f_995_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3497,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3497),U_3498),U_3499),U_3500) = c_Divides_Odiv__class_Omod(U_3497,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3497),c_Divides_Odiv__class_Omod(U_3497,U_3498,U_3500)),c_Divides_Odiv__class_Omod(U_3497,U_3499,U_3500)),U_3500)
    | ~ class_Divides_Oring__div(U_3497) ),
    inference(clausify,[status(thm)],[f_995_3]) ).

fof(f_996_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_996_2,plain,
    ! [U_3506,U_3505,U_3504,U_3503,U_3502,U_3501] :
      ( c_Divides_Odiv__class_Omod(U_3501,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3501),U_3502),U_3505),U_3503) = c_Divides_Odiv__class_Omod(U_3501,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3501),U_3504),U_3506),U_3503)
      | c_Divides_Odiv__class_Omod(U_3501,U_3505,U_3503) != c_Divides_Odiv__class_Omod(U_3501,U_3506,U_3503)
      | c_Divides_Odiv__class_Omod(U_3501,U_3502,U_3503) != c_Divides_Odiv__class_Omod(U_3501,U_3504,U_3503)
      | ~ class_Divides_Oring__div(U_3501) ),
    inference(variable_rename,[status(thm)],[f_996_1]) ).

fof(f_996_3,plain,
    ! [U_3501,U_3502,U_3503,U_3504,U_3505,U_3506] :
      ( c_Divides_Odiv__class_Omod(U_3501,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3501),U_3502),U_3505),U_3503) = c_Divides_Odiv__class_Omod(U_3501,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3501),U_3504),U_3506),U_3503)
      | c_Divides_Odiv__class_Omod(U_3501,U_3505,U_3503) != c_Divides_Odiv__class_Omod(U_3501,U_3506,U_3503)
      | c_Divides_Odiv__class_Omod(U_3501,U_3502,U_3503) != c_Divides_Odiv__class_Omod(U_3501,U_3504,U_3503)
      | ~ class_Divides_Oring__div(U_3501) ),
    inference(definitional_conversion,[status(esa)],[f_996_2]) ).

cnf(f_996_4,plain,
    ( c_Divides_Odiv__class_Omod(U_3501,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3501),U_3502),U_3505),U_3503) = c_Divides_Odiv__class_Omod(U_3501,hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3501),U_3504),U_3506),U_3503)
    | c_Divides_Odiv__class_Omod(U_3501,U_3505,U_3503) != c_Divides_Odiv__class_Omod(U_3501,U_3506,U_3503)
    | c_Divides_Odiv__class_Omod(U_3501,U_3502,U_3503) != c_Divides_Odiv__class_Omod(U_3501,U_3504,U_3503)
    | ~ class_Divides_Oring__div(U_3501) ),
    inference(clausify,[status(thm)],[f_996_3]) ).

fof(f_997_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_997_2,plain,
    ! [U_3509,U_3508,U_3507] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3507),U_3509)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3508),U_3509)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3507),U_3508)) ),
    inference(variable_rename,[status(thm)],[f_997_1]) ).

fof(f_997_3,plain,
    ! [U_3507,U_3508,U_3509] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3507),U_3509)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3508),U_3509)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3507),U_3508)) ),
    inference(definitional_conversion,[status(esa)],[f_997_2]) ).

cnf(f_997_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_3507),U_3509)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3508),U_3509)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3507),U_3508)) ),
    inference(clausify,[status(thm)],[f_997_3]) ).

fof(f_998_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_998_2,plain,
    ! [U_3511,U_3510] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3510),U_3511)),U_3510)),
    inference(variable_rename,[status(thm)],[f_998_1]) ).

fof(f_998_3,plain,
    ! [U_3510,U_3511] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3510),U_3511)),U_3510)),
    inference(definitional_conversion,[status(esa)],[f_998_2]) ).

cnf(f_998_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_3510),U_3511)),U_3510)),
    inference(clausify,[status(thm)],[f_998_3]) ).

fof(f_999_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_999_2,plain,
    ! [U_3514,U_3513,U_3512] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3512),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3513),U_3514)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3512),U_3513)),U_3514),
    inference(variable_rename,[status(thm)],[f_999_1]) ).

fof(f_999_3,plain,
    ! [U_3512,U_3513,U_3514] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3512),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3513),U_3514)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3512),U_3513)),U_3514),
    inference(definitional_conversion,[status(esa)],[f_999_2]) ).

cnf(f_999_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3512),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3513),U_3514)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3512),U_3513)),U_3514),
    inference(clausify,[status(thm)],[f_999_3]) ).

fof(f_1000_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_1000_2,plain,
    ! [U_3516,U_3515] :
      ( U_3515 = U_3516
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3516),U_3515) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3515),U_3516) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_1000_1]) ).

fof(f_1000_3,plain,
    ! [U_3515,U_3516] :
      ( U_3515 = U_3516
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3516),U_3515) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3515),U_3516) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_1000_2]) ).

cnf(f_1000_4,plain,
    ( U_3515 = U_3516
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3516),U_3515) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3515),U_3516) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1000_3]) ).

fof(f_1001_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_1001_2,plain,
    ! [U_3517] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3517),U_3517) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1001_1]) ).

fof(f_1001_3,plain,
    ! [U_3517] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3517),U_3517) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1001_2]) ).

cnf(f_1001_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3517),U_3517) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1001_3]) ).

fof(f_1002_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_1002_2,plain,
    ! [U_3518] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3518),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3518,
    inference(variable_rename,[status(thm)],[f_1002_1]) ).

fof(f_1002_3,plain,
    ! [U_3518] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3518),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3518,
    inference(definitional_conversion,[status(esa)],[f_1002_2]) ).

cnf(f_1002_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3518),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_3518,
    inference(clausify,[status(thm)],[f_1002_3]) ).

fof(f_1003_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_1003_2,plain,
    ! [U_3519] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3519) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1003_1]) ).

fof(f_1003_3,plain,
    ! [U_3519] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3519) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1003_2]) ).

cnf(f_1003_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3519) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1003_3]) ).

fof(f_1004_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_1004_2,plain,
    ! [U_3521,U_3520] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3520)),hAPP(c_Nat_OSuc,U_3521)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3520),U_3521),
    inference(variable_rename,[status(thm)],[f_1004_1]) ).

fof(f_1004_3,plain,
    ! [U_3520,U_3521] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3520)),hAPP(c_Nat_OSuc,U_3521)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3520),U_3521),
    inference(definitional_conversion,[status(esa)],[f_1004_2]) ).

cnf(f_1004_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3520)),hAPP(c_Nat_OSuc,U_3521)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3520),U_3521),
    inference(clausify,[status(thm)],[f_1004_3]) ).

fof(f_1005_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_1005_2,plain,
    ! [U_3524,U_3523,U_3522] : 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_3522)),U_3523)),hAPP(c_Nat_OSuc,U_3524)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3522),U_3523)),U_3524),
    inference(variable_rename,[status(thm)],[f_1005_1]) ).

fof(f_1005_3,plain,
    ! [U_3522,U_3523,U_3524] : 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_3522)),U_3523)),hAPP(c_Nat_OSuc,U_3524)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3522),U_3523)),U_3524),
    inference(definitional_conversion,[status(esa)],[f_1005_2]) ).

cnf(f_1005_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_3522)),U_3523)),hAPP(c_Nat_OSuc,U_3524)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3522),U_3523)),U_3524),
    inference(clausify,[status(thm)],[f_1005_3]) ).

fof(f_1006_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_1006_2,plain,
    ! [U_3527,U_3526,U_3525] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3525),U_3527)),U_3526))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3525),U_3526)) ),
    inference(variable_rename,[status(thm)],[f_1006_1]) ).

fof(f_1006_3,plain,
    ! [U_3525,U_3526,U_3527] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3525),U_3527)),U_3526))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3525),U_3526)) ),
    inference(definitional_conversion,[status(esa)],[f_1006_2]) ).

cnf(f_1006_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3525),U_3527)),U_3526))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3525),U_3526)) ),
    inference(clausify,[status(thm)],[f_1006_3]) ).

fof(f_1007_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_1007_2,plain,
    ! [U_3530,U_3529,U_3528] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3530),U_3529)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3530),U_3528)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3528),U_3530))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3528),U_3529)) ),
    inference(variable_rename,[status(thm)],[f_1007_1]) ).

fof(f_1007_3,plain,
    ! [U_3528,U_3529,U_3530] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3530),U_3529)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3530),U_3528)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3528),U_3530))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3528),U_3529)) ),
    inference(definitional_conversion,[status(esa)],[f_1007_2]) ).

cnf(f_1007_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3530),U_3529)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3530),U_3528)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3528),U_3530))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3528),U_3529)) ),
    inference(clausify,[status(thm)],[f_1007_3]) ).

fof(f_1008_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_1008_2,plain,
    ! [U_3532,U_3531] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3531,U_3532) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3531),U_3532),U_3532)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3531),U_3532)) ),
    inference(variable_rename,[status(thm)],[f_1008_1]) ).

fof(f_1008_3,plain,
    ! [U_3531,U_3532] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3531,U_3532) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3531),U_3532),U_3532)
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3531),U_3532)) ),
    inference(definitional_conversion,[status(esa)],[f_1008_2]) ).

cnf(f_1008_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3531,U_3532) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3531),U_3532),U_3532)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3531),U_3532)) ),
    inference(clausify,[status(thm)],[f_1008_3]) ).

fof(f_1009_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_1009_2,plain,
    ! [U_3534,U_3533] :
      ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3533,U_3534) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3533),U_3534),U_3534)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3533),U_3534)) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3533,U_3534) = U_3533
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3533),U_3534)) ) ),
    inference(variable_rename,[status(thm)],[f_1009_1]) ).

fof(f_1009_3,plain,
    ( ! [U_3538,U_3536] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3536,U_3538) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3536),U_3538),U_3538)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3536),U_3538)) )
    & ! [U_3537,U_3535] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3535,U_3537) = U_3535
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3535),U_3537)) ) ),
    inference(miniscope,[status(thm)],[f_1009_2]) ).

fof(f_1009_4,plain,
    ( ! [U_3538,U_3536] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3536,U_3538) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3536),U_3538),U_3538)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3536),U_3538)) )
    & ! [U_3535,U_3537] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3535,U_3537) = U_3535
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3535),U_3537)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1009_3]) ).

cnf(f_1009_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3535,U_3537) = U_3535
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3535),U_3537)) ),
    inference(clausify,[status(thm)],[f_1009_4]) ).

cnf(f_1009_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3536,U_3538) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3536),U_3538),U_3538)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3536),U_3538)) ),
    inference(clausify,[status(thm)],[f_1009_4]) ).

fof(f_1010_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_1010_2,plain,
    ! [U_3540,U_3539] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3539),U_3540)),U_3540) = U_3539,
    inference(variable_rename,[status(thm)],[f_1010_1]) ).

fof(f_1010_3,plain,
    ! [U_3539,U_3540] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3539),U_3540)),U_3540) = U_3539,
    inference(definitional_conversion,[status(esa)],[f_1010_2]) ).

cnf(f_1010_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3539),U_3540)),U_3540) = U_3539,
    inference(clausify,[status(thm)],[f_1010_3]) ).

fof(f_1011_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_1011_2,plain,
    ! [U_3542,U_3541] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3541),U_3542)),U_3541) = U_3542,
    inference(variable_rename,[status(thm)],[f_1011_1]) ).

fof(f_1011_3,plain,
    ! [U_3541,U_3542] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3541),U_3542)),U_3541) = U_3542,
    inference(definitional_conversion,[status(esa)],[f_1011_2]) ).

cnf(f_1011_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3541),U_3542)),U_3541) = U_3542,
    inference(clausify,[status(thm)],[f_1011_3]) ).

fof(f_1012_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_1012_2,plain,
    ! [U_3545,U_3544,U_3543] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3543),U_3544)),U_3545) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3543),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3544),U_3545)),
    inference(variable_rename,[status(thm)],[f_1012_1]) ).

fof(f_1012_3,plain,
    ! [U_3543,U_3544,U_3545] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3543),U_3544)),U_3545) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3543),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3544),U_3545)),
    inference(definitional_conversion,[status(esa)],[f_1012_2]) ).

cnf(f_1012_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3543),U_3544)),U_3545) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3543),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3544),U_3545)),
    inference(clausify,[status(thm)],[f_1012_3]) ).

fof(f_1013_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_1013_2,plain,
    ! [U_3548,U_3547,U_3546] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3546),U_3547)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3546),U_3548)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3547),U_3548),
    inference(variable_rename,[status(thm)],[f_1013_1]) ).

fof(f_1013_3,plain,
    ! [U_3546,U_3547,U_3548] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3546),U_3547)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3546),U_3548)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3547),U_3548),
    inference(definitional_conversion,[status(esa)],[f_1013_2]) ).

cnf(f_1013_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3546),U_3547)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3546),U_3548)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3547),U_3548),
    inference(clausify,[status(thm)],[f_1013_3]) ).

fof(f_1014_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_1014_2,plain,
    ! [U_3551,U_3550,U_3549] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3549),U_3550)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3551),U_3550)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3549),U_3551),
    inference(variable_rename,[status(thm)],[f_1014_1]) ).

fof(f_1014_3,plain,
    ! [U_3549,U_3550,U_3551] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3549),U_3550)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3551),U_3550)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3549),U_3551),
    inference(definitional_conversion,[status(esa)],[f_1014_2]) ).

cnf(f_1014_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3549),U_3550)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3551),U_3550)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3549),U_3551),
    inference(clausify,[status(thm)],[f_1014_3]) ).

fof(f_1015_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_1015_2,plain,
    ! [U_3554,U_3553,U_3552] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3553),U_3552)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3554),U_3552)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3553),U_3554)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3553),U_3554))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3553),U_3552)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3554),U_3552))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3552),U_3554))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3552),U_3553)) ),
    inference(variable_rename,[status(thm)],[f_1015_1]) ).

fof(f_1015_3,plain,
    ( ! [U_3552,U_3553,U_3554] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3553),U_3552)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3554),U_3552)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3553),U_3554))
        | ~ sP292(U_3552,U_3553,U_3554) )
    & ! [U_3552,U_3553,U_3554] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3553),U_3554))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3553),U_3552)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3554),U_3552)))
        | ~ sP292(U_3552,U_3553,U_3554) )
    & ! [U_3552,U_3553,U_3554] :
        ( sP292(U_3552,U_3553,U_3554)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3552),U_3554))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3552),U_3553)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP292])],[f_1015_2]) ).

cnf(f_1015_4,plain,
    ( sP292(U_3552,U_3553,U_3554)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3552),U_3554))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3552),U_3553)) ),
    inference(clausify,[status(thm)],[f_1015_3]) ).

cnf(f_1015_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3553),U_3554))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3553),U_3552)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3554),U_3552)))
    | ~ sP292(U_3552,U_3553,U_3554) ),
    inference(clausify,[status(thm)],[f_1015_3]) ).

cnf(f_1015_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_3553),U_3552)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3554),U_3552)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3553),U_3554))
    | ~ sP292(U_3552,U_3553,U_3554) ),
    inference(clausify,[status(thm)],[f_1015_3]) ).

fof(f_1016_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_1016_2,plain,
    ! [U_3557,U_3556,U_3555] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3556),U_3555)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3557),U_3555)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3556),U_3557)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3555),U_3557))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3555),U_3556)) ),
    inference(variable_rename,[status(thm)],[f_1016_1]) ).

fof(f_1016_3,plain,
    ! [U_3557,U_3555,U_3556] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3556),U_3555)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3557),U_3555)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3556),U_3557)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3555),U_3557))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3555),U_3556)) ),
    inference(definitional_conversion,[status(esa)],[f_1016_2]) ).

cnf(f_1016_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3556),U_3555)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3557),U_3555)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3556),U_3557)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3555),U_3557))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3555),U_3556)) ),
    inference(clausify,[status(thm)],[f_1016_3]) ).

fof(f_1017_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_1017_2,plain,
    ! [U_3560,U_3559,U_3558] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3559),U_3558) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3560),U_3558)
          | U_3559 != U_3560 )
        & ( U_3559 = U_3560
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3559),U_3558) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3560),U_3558) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3558),U_3560))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3558),U_3559)) ),
    inference(variable_rename,[status(thm)],[f_1017_1]) ).

fof(f_1017_3,plain,
    ( ! [U_3558,U_3559,U_3560] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3559),U_3558) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3560),U_3558)
        | U_3559 != U_3560
        | ~ sP293(U_3558,U_3559,U_3560) )
    & ! [U_3558,U_3559,U_3560] :
        ( U_3559 = U_3560
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3559),U_3558) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3560),U_3558)
        | ~ sP293(U_3558,U_3559,U_3560) )
    & ! [U_3558,U_3559,U_3560] :
        ( sP293(U_3558,U_3559,U_3560)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3558),U_3560))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3558),U_3559)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP293])],[f_1017_2]) ).

cnf(f_1017_4,plain,
    ( sP293(U_3558,U_3559,U_3560)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3558),U_3560))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3558),U_3559)) ),
    inference(clausify,[status(thm)],[f_1017_3]) ).

cnf(f_1017_5,plain,
    ( U_3559 = U_3560
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3559),U_3558) != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3560),U_3558)
    | ~ sP293(U_3558,U_3559,U_3560) ),
    inference(clausify,[status(thm)],[f_1017_3]) ).

cnf(f_1017_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3559),U_3558) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3560),U_3558)
    | U_3559 != U_3560
    | ~ sP293(U_3558,U_3559,U_3560) ),
    inference(clausify,[status(thm)],[f_1017_3]) ).

fof(f_1018_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_1018_2,plain,
    ! [U_3562,U_3561] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3562),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3562),U_3561)) = U_3561
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3561),U_3562)) ),
    inference(variable_rename,[status(thm)],[f_1018_1]) ).

fof(f_1018_3,plain,
    ! [U_3562,U_3561] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3562),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3562),U_3561)) = U_3561
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3561),U_3562)) ),
    inference(definitional_conversion,[status(esa)],[f_1018_2]) ).

cnf(f_1018_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3562),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3562),U_3561)) = U_3561
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3561),U_3562)) ),
    inference(clausify,[status(thm)],[f_1018_3]) ).

fof(f_1019_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_1019_2,plain,
    ! [U_3565,U_3564,U_3563] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3563),U_3565)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3564),U_3565)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3563),U_3564)) ),
    inference(variable_rename,[status(thm)],[f_1019_1]) ).

fof(f_1019_3,plain,
    ! [U_3563,U_3564,U_3565] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3563),U_3565)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3564),U_3565)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3563),U_3564)) ),
    inference(definitional_conversion,[status(esa)],[f_1019_2]) ).

cnf(f_1019_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_3563),U_3565)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3564),U_3565)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3563),U_3564)) ),
    inference(clausify,[status(thm)],[f_1019_3]) ).

fof(f_1020_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_1020_2,plain,
    ! [U_3568,U_3567,U_3566] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3568),U_3567)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3568),U_3566)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3566),U_3567)) ),
    inference(variable_rename,[status(thm)],[f_1020_1]) ).

fof(f_1020_3,plain,
    ! [U_3566,U_3567,U_3568] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3568),U_3567)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3568),U_3566)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3566),U_3567)) ),
    inference(definitional_conversion,[status(esa)],[f_1020_2]) ).

cnf(f_1020_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_3568),U_3567)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3568),U_3566)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3566),U_3567)) ),
    inference(clausify,[status(thm)],[f_1020_3]) ).

fof(f_1021_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_1021_2,plain,
    ! [U_3570,U_3569] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3569),U_3570)),U_3569)),
    inference(variable_rename,[status(thm)],[f_1021_1]) ).

fof(f_1021_3,plain,
    ! [U_3569,U_3570] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3569),U_3570)),U_3569)),
    inference(definitional_conversion,[status(esa)],[f_1021_2]) ).

cnf(f_1021_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_3569),U_3570)),U_3569)),
    inference(clausify,[status(thm)],[f_1021_3]) ).

fof(f_1022_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_1022_2,plain,
    ! [U_3572,U_3571] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3572,U_3571) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3572),U_3571),U_3571)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3571),U_3572)) ),
    inference(variable_rename,[status(thm)],[f_1022_1]) ).

fof(f_1022_3,plain,
    ! [U_3571,U_3572] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3572,U_3571) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3572),U_3571),U_3571)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3571),U_3572)) ),
    inference(definitional_conversion,[status(esa)],[f_1022_2]) ).

cnf(f_1022_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3572,U_3571) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3572),U_3571),U_3571)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3571),U_3572)) ),
    inference(clausify,[status(thm)],[f_1022_3]) ).

fof(f_1023_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_1023_2,plain,
    ! [U_3575,U_3574,U_3573] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3573),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3574),U_3575)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3573),U_3574)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3573),U_3575)),
    inference(variable_rename,[status(thm)],[f_1023_1]) ).

fof(f_1023_3,plain,
    ! [U_3573,U_3574,U_3575] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3573),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3574),U_3575)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3573),U_3574)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3573),U_3575)),
    inference(definitional_conversion,[status(esa)],[f_1023_2]) ).

cnf(f_1023_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3573),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3574),U_3575)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3573),U_3574)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3573),U_3575)),
    inference(clausify,[status(thm)],[f_1023_3]) ).

fof(f_1024_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_1024_2,plain,
    ! [U_3578,U_3577,U_3576] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3576),U_3577)),U_3578) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3576),U_3578)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3577),U_3578)),
    inference(variable_rename,[status(thm)],[f_1024_1]) ).

fof(f_1024_3,plain,
    ! [U_3576,U_3577,U_3578] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3576),U_3577)),U_3578) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3576),U_3578)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3577),U_3578)),
    inference(definitional_conversion,[status(esa)],[f_1024_2]) ).

cnf(f_1024_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3576),U_3577)),U_3578) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3576),U_3578)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3577),U_3578)),
    inference(clausify,[status(thm)],[f_1024_3]) ).

fof(f_1025_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_1025_2,plain,
    ! [U_3581,U_3580,U_3579] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3579),U_3580)),U_3581) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3579),U_3581)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3580),U_3581)),
    inference(variable_rename,[status(thm)],[f_1025_1]) ).

fof(f_1025_3,plain,
    ! [U_3580,U_3581,U_3579] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3579),U_3580)),U_3581) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3579),U_3581)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3580),U_3581)),
    inference(definitional_conversion,[status(esa)],[f_1025_2]) ).

cnf(f_1025_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3579),U_3580)),U_3581) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3579),U_3581)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3580),U_3581)),
    inference(clausify,[status(thm)],[f_1025_3]) ).

fof(f_1026_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_1026_2,plain,
    ! [U_3584,U_3583,U_3582] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3582),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3583),U_3584)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3582),U_3583)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3582),U_3584)),
    inference(variable_rename,[status(thm)],[f_1026_1]) ).

fof(f_1026_3,plain,
    ! [U_3583,U_3584,U_3582] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3582),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3583),U_3584)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3582),U_3583)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3582),U_3584)),
    inference(definitional_conversion,[status(esa)],[f_1026_2]) ).

cnf(f_1026_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3582),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3583),U_3584)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3582),U_3583)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3582),U_3584)),
    inference(clausify,[status(thm)],[f_1026_3]) ).

fof(f_1027_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_1027_2,plain,
    ! [U_3587,U_3586,U_3585] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3585),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3586,U_3587)),U_3587) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3585),U_3586),U_3587),
    inference(variable_rename,[status(thm)],[f_1027_1]) ).

fof(f_1027_3,plain,
    ! [U_3585,U_3586,U_3587] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3585),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3586,U_3587)),U_3587) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3585),U_3586),U_3587),
    inference(definitional_conversion,[status(esa)],[f_1027_2]) ).

cnf(f_1027_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3585),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3586,U_3587)),U_3587) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3585),U_3586),U_3587),
    inference(clausify,[status(thm)],[f_1027_3]) ).

fof(f_1028_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_1028_2,plain,
    ! [U_3590,U_3589,U_3588] : 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_3588,U_3589)),U_3590),U_3589) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3588),U_3590),U_3589),
    inference(variable_rename,[status(thm)],[f_1028_1]) ).

fof(f_1028_3,plain,
    ! [U_3588,U_3589,U_3590] : 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_3588,U_3589)),U_3590),U_3589) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3588),U_3590),U_3589),
    inference(definitional_conversion,[status(esa)],[f_1028_2]) ).

cnf(f_1028_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_3588,U_3589)),U_3590),U_3589) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3588),U_3590),U_3589),
    inference(clausify,[status(thm)],[f_1028_3]) ).

fof(f_1029_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_1029_2,plain,
    ! [U_3592,U_3591] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3592),U_3591) = 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_3592),U_3591)),U_3591))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3592),U_3591))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3591)) ),
    inference(variable_rename,[status(thm)],[f_1029_1]) ).

fof(f_1029_3,plain,
    ! [U_3591,U_3592] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3592),U_3591) = 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_3592),U_3591)),U_3591))
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3592),U_3591))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3591)) ),
    inference(definitional_conversion,[status(esa)],[f_1029_2]) ).

cnf(f_1029_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3592),U_3591) = 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_3592),U_3591)),U_3591))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3592),U_3591))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3591)) ),
    inference(clausify,[status(thm)],[f_1029_3]) ).

fof(f_1030_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_1030_2,plain,
    ! [U_3594,U_3593] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3594),U_3593) = 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_3594),U_3593)),U_3593))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3594),U_3593)) )
        & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3594),U_3593) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3594),U_3593)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3593)) ),
    inference(variable_rename,[status(thm)],[f_1030_1]) ).

fof(f_1030_3,plain,
    ( ! [U_3593,U_3594] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3594),U_3593) = 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_3594),U_3593)),U_3593))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3594),U_3593))
        | ~ sP294(U_3593,U_3594) )
    & ! [U_3593,U_3594] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3594),U_3593) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3594),U_3593))
        | ~ sP294(U_3593,U_3594) )
    & ! [U_3593,U_3594] :
        ( sP294(U_3593,U_3594)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3593)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP294])],[f_1030_2]) ).

cnf(f_1030_4,plain,
    ( sP294(U_3593,U_3594)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3593)) ),
    inference(clausify,[status(thm)],[f_1030_3]) ).

cnf(f_1030_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3594),U_3593) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3594),U_3593))
    | ~ sP294(U_3593,U_3594) ),
    inference(clausify,[status(thm)],[f_1030_3]) ).

cnf(f_1030_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3594),U_3593) = 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_3594),U_3593)),U_3593))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3594),U_3593))
    | ~ sP294(U_3593,U_3594) ),
    inference(clausify,[status(thm)],[f_1030_3]) ).

fof(f_1031_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_1031_2,plain,
    ! [U_3596,U_3595] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3596),U_3595)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_3596)),hAPP(c_Int_Onat,U_3595))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3595),U_3596))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3595)) ),
    inference(variable_rename,[status(thm)],[f_1031_1]) ).

fof(f_1031_3,plain,
    ! [U_3596,U_3595] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3596),U_3595)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_3596)),hAPP(c_Int_Onat,U_3595))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3595),U_3596))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3595)) ),
    inference(definitional_conversion,[status(esa)],[f_1031_2]) ).

cnf(f_1031_4,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3596),U_3595)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_3596)),hAPP(c_Int_Onat,U_3595))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3595),U_3596))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3595)) ),
    inference(clausify,[status(thm)],[f_1031_3]) ).

fof(f_1032_1,plain,
    ! [V_y_2,V_x_2,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_1032_2,plain,
    ! [U_3599,U_3598,U_3597] :
      ( ( hBOOL(hAPP(U_3597,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3598),U_3599))))
        | ( ~ hBOOL(hAPP(U_3597,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3598),U_3599)) )
        | ( ~ hBOOL(hAPP(U_3597,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3598)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3599))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3599),U_3598)) ) )
      & ( ( ( hBOOL(hAPP(U_3597,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3598),U_3599)) )
          & ( hBOOL(hAPP(U_3597,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3598)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3599))))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3599),U_3598)) ) )
        | ~ hBOOL(hAPP(U_3597,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3598),U_3599)))) ) ),
    inference(variable_rename,[status(thm)],[f_1032_1]) ).

fof(f_1032_3,plain,
    ( ! [U_3605,U_3603,U_3601] :
        ( hBOOL(hAPP(U_3601,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3603),U_3605))))
        | ( ~ hBOOL(hAPP(U_3601,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3603),U_3605)) )
        | ( ~ hBOOL(hAPP(U_3601,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3603)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3605))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3605),U_3603)) ) )
    & ! [U_3604,U_3602,U_3600] :
        ( ( ( hBOOL(hAPP(U_3600,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3602),U_3604)) )
          & ( hBOOL(hAPP(U_3600,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3602)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3604))))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3604),U_3602)) ) )
        | ~ hBOOL(hAPP(U_3600,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3602),U_3604)))) ) ),
    inference(miniscope,[status(thm)],[f_1032_2]) ).

fof(f_1032_4,plain,
    ( ! [U_3601,U_3605,U_3603] :
        ( ~ hBOOL(hAPP(U_3601,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP297(U_3601,U_3605,U_3603) )
    & ! [U_3601,U_3605,U_3603] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3603),U_3605))
        | ~ sP297(U_3601,U_3605,U_3603) )
    & ! [U_3601,U_3605,U_3603] :
        ( ~ hBOOL(hAPP(U_3601,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3603)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3605))))
        | ~ sP296(U_3601,U_3605,U_3603) )
    & ! [U_3601,U_3605,U_3603] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3605),U_3603))
        | ~ sP296(U_3601,U_3605,U_3603) )
    & ! [U_3602,U_3600,U_3604] :
        ( hBOOL(hAPP(U_3600,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3602),U_3604))
        | ~ sP295(U_3602,U_3600,U_3604) )
    & ! [U_3602,U_3600,U_3604] :
        ( hBOOL(hAPP(U_3600,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3602)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3604))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3604),U_3602))
        | ~ sP295(U_3602,U_3600,U_3604) )
    & ! [U_3601,U_3605,U_3603] :
        ( hBOOL(hAPP(U_3601,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3603),U_3605))))
        | sP297(U_3601,U_3605,U_3603)
        | sP296(U_3601,U_3605,U_3603) )
    & ! [U_3602,U_3600,U_3604] :
        ( sP295(U_3602,U_3600,U_3604)
        | ~ hBOOL(hAPP(U_3600,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3602),U_3604)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP295,sP296,sP297])],[f_1032_3]) ).

cnf(f_1032_5,plain,
    ( sP295(U_3602,U_3600,U_3604)
    | ~ hBOOL(hAPP(U_3600,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3602),U_3604)))) ),
    inference(clausify,[status(thm)],[f_1032_4]) ).

cnf(f_1032_6,plain,
    ( hBOOL(hAPP(U_3601,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3603),U_3605))))
    | sP297(U_3601,U_3605,U_3603)
    | sP296(U_3601,U_3605,U_3603) ),
    inference(clausify,[status(thm)],[f_1032_4]) ).

cnf(f_1032_7,plain,
    ( hBOOL(hAPP(U_3600,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3602)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3604))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3604),U_3602))
    | ~ sP295(U_3602,U_3600,U_3604) ),
    inference(clausify,[status(thm)],[f_1032_4]) ).

cnf(f_1032_8,plain,
    ( hBOOL(hAPP(U_3600,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3602),U_3604))
    | ~ sP295(U_3602,U_3600,U_3604) ),
    inference(clausify,[status(thm)],[f_1032_4]) ).

cnf(f_1032_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3605),U_3603))
    | ~ sP296(U_3601,U_3605,U_3603) ),
    inference(clausify,[status(thm)],[f_1032_4]) ).

cnf(f_1032_10,plain,
    ( ~ hBOOL(hAPP(U_3601,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3603)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3605))))
    | ~ sP296(U_3601,U_3605,U_3603) ),
    inference(clausify,[status(thm)],[f_1032_4]) ).

cnf(f_1032_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3603),U_3605))
    | ~ sP297(U_3601,U_3605,U_3603) ),
    inference(clausify,[status(thm)],[f_1032_4]) ).

cnf(f_1032_12,plain,
    ( ~ hBOOL(hAPP(U_3601,c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP297(U_3601,U_3605,U_3603) ),
    inference(clausify,[status(thm)],[f_1032_4]) ).

fof(f_1033_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_1033_2,plain,
    ! [U_3607,U_3606] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3607),U_3606) = 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_3607),U_3606)),U_3606))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3606),U_3607))
      | ~ 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_1033_1]) ).

fof(f_1033_3,plain,
    ! [U_3606,U_3607] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3607),U_3606) = 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_3607),U_3606)),U_3606))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3606),U_3607))
      | ~ 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_1033_2]) ).

cnf(f_1033_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3607),U_3606) = 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_3607),U_3606)),U_3606))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3606),U_3607))
    | ~ 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_1033_3]) ).

fof(f_1034_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_1034_2,plain,
    ! [U_3610,U_3609,U_3608] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3608),U_3609),U_3610))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3608),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3608),U_3609),U_3610)),c_Groups_Ozero__class_Ozero(U_3608))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3608),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3608),U_3609),U_3610)),c_Groups_Ozero__class_Ozero(U_3608)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3608),U_3609),U_3610)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_3608) ),
    inference(variable_rename,[status(thm)],[f_1034_1]) ).

fof(f_1034_3,plain,
    ( ! [U_3608,U_3609,U_3610] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3608),U_3609),U_3610))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3608),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3608),U_3609),U_3610)),c_Groups_Ozero__class_Ozero(U_3608)))
        | ~ sP298(U_3608,U_3609,U_3610) )
    & ! [U_3608,U_3609,U_3610] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3608),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3608),U_3609),U_3610)),c_Groups_Ozero__class_Ozero(U_3608)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3608),U_3609),U_3610))
        | ~ sP298(U_3608,U_3609,U_3610) )
    & ! [U_3608,U_3609,U_3610] :
        ( sP298(U_3608,U_3609,U_3610)
        | ~ class_Groups_Oordered__ab__group__add(U_3608) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP298])],[f_1034_2]) ).

cnf(f_1034_4,plain,
    ( sP298(U_3608,U_3609,U_3610)
    | ~ class_Groups_Oordered__ab__group__add(U_3608) ),
    inference(clausify,[status(thm)],[f_1034_3]) ).

cnf(f_1034_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3608),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3608),U_3609),U_3610)),c_Groups_Ozero__class_Ozero(U_3608)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3608),U_3609),U_3610))
    | ~ sP298(U_3608,U_3609,U_3610) ),
    inference(clausify,[status(thm)],[f_1034_3]) ).

cnf(f_1034_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3608),U_3609),U_3610))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3608),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3608),U_3609),U_3610)),c_Groups_Ozero__class_Ozero(U_3608)))
    | ~ sP298(U_3608,U_3609,U_3610) ),
    inference(clausify,[status(thm)],[f_1034_3]) ).

fof(f_1035_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_1035_2,plain,
    ! [U_3613,U_3612,U_3611] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3611),U_3612),U_3613))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3611),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3611),U_3612),U_3613)),c_Groups_Ozero__class_Ozero(U_3611))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3611),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3611),U_3612),U_3613)),c_Groups_Ozero__class_Ozero(U_3611)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3611),U_3612),U_3613)) ) )
      | ~ class_Groups_Oordered__ab__group__add(U_3611) ),
    inference(variable_rename,[status(thm)],[f_1035_1]) ).

fof(f_1035_3,plain,
    ( ! [U_3612,U_3611,U_3613] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3611),U_3612),U_3613))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3611),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3611),U_3612),U_3613)),c_Groups_Ozero__class_Ozero(U_3611)))
        | ~ sP299(U_3612,U_3611,U_3613) )
    & ! [U_3612,U_3611,U_3613] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3611),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3611),U_3612),U_3613)),c_Groups_Ozero__class_Ozero(U_3611)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3611),U_3612),U_3613))
        | ~ sP299(U_3612,U_3611,U_3613) )
    & ! [U_3612,U_3611,U_3613] :
        ( sP299(U_3612,U_3611,U_3613)
        | ~ class_Groups_Oordered__ab__group__add(U_3611) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP299])],[f_1035_2]) ).

cnf(f_1035_4,plain,
    ( sP299(U_3612,U_3611,U_3613)
    | ~ class_Groups_Oordered__ab__group__add(U_3611) ),
    inference(clausify,[status(thm)],[f_1035_3]) ).

cnf(f_1035_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3611),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3611),U_3612),U_3613)),c_Groups_Ozero__class_Ozero(U_3611)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3611),U_3612),U_3613))
    | ~ sP299(U_3612,U_3611,U_3613) ),
    inference(clausify,[status(thm)],[f_1035_3]) ).

cnf(f_1035_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3611),U_3612),U_3613))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3611),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3611),U_3612),U_3613)),c_Groups_Ozero__class_Ozero(U_3611)))
    | ~ sP299(U_3612,U_3611,U_3613) ),
    inference(clausify,[status(thm)],[f_1035_3]) ).

fof(f_1036_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_1036_2,plain,
    ! [U_3619,U_3618,U_3617,U_3616,U_3615,U_3614] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3614),U_3615),U_3616)),U_3617) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3614),U_3618),U_3616)),U_3619)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3614),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3614),U_3615),U_3618)),U_3616)),U_3617) != U_3619 )
        & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3614),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3614),U_3615),U_3618)),U_3616)),U_3617) = U_3619
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3614),U_3615),U_3616)),U_3617) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3614),U_3618),U_3616)),U_3619) ) )
      | ~ class_Rings_Oring(U_3614) ),
    inference(variable_rename,[status(thm)],[f_1036_1]) ).

fof(f_1036_3,plain,
    ( ! [U_3614,U_3615,U_3616,U_3617,U_3618,U_3619] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3614),U_3615),U_3616)),U_3617) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3614),U_3618),U_3616)),U_3619)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3614),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3614),U_3615),U_3618)),U_3616)),U_3617) != U_3619
        | ~ sP300(U_3614,U_3615,U_3616,U_3617,U_3618,U_3619) )
    & ! [U_3614,U_3615,U_3616,U_3617,U_3618,U_3619] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3614),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3614),U_3615),U_3618)),U_3616)),U_3617) = U_3619
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3614),U_3615),U_3616)),U_3617) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3614),U_3618),U_3616)),U_3619)
        | ~ sP300(U_3614,U_3615,U_3616,U_3617,U_3618,U_3619) )
    & ! [U_3614,U_3615,U_3616,U_3617,U_3618,U_3619] :
        ( sP300(U_3614,U_3615,U_3616,U_3617,U_3618,U_3619)
        | ~ class_Rings_Oring(U_3614) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP300])],[f_1036_2]) ).

cnf(f_1036_4,plain,
    ( sP300(U_3614,U_3615,U_3616,U_3617,U_3618,U_3619)
    | ~ class_Rings_Oring(U_3614) ),
    inference(clausify,[status(thm)],[f_1036_3]) ).

cnf(f_1036_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3614),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3614),U_3615),U_3618)),U_3616)),U_3617) = U_3619
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3614),U_3615),U_3616)),U_3617) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3614),U_3618),U_3616)),U_3619)
    | ~ sP300(U_3614,U_3615,U_3616,U_3617,U_3618,U_3619) ),
    inference(clausify,[status(thm)],[f_1036_3]) ).

cnf(f_1036_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3614),U_3615),U_3616)),U_3617) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3614),U_3618),U_3616)),U_3619)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3614),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3614),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3614),U_3615),U_3618)),U_3616)),U_3617) != U_3619
    | ~ sP300(U_3614,U_3615,U_3616,U_3617,U_3618,U_3619) ),
    inference(clausify,[status(thm)],[f_1036_3]) ).

fof(f_1037_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_1037_2,plain,
    ! [U_3625,U_3624,U_3623,U_3622,U_3621,U_3620] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3621),U_3622)),U_3623) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3624),U_3622)),U_3625)
          | U_3623 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3620),U_3624),U_3621)),U_3622)),U_3625) )
        & ( U_3623 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3620),U_3624),U_3621)),U_3622)),U_3625)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3621),U_3622)),U_3623) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3624),U_3622)),U_3625) ) )
      | ~ class_Rings_Oring(U_3620) ),
    inference(variable_rename,[status(thm)],[f_1037_1]) ).

fof(f_1037_3,plain,
    ( ! [U_3621,U_3620,U_3622,U_3623,U_3624,U_3625] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3621),U_3622)),U_3623) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3624),U_3622)),U_3625)
        | U_3623 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3620),U_3624),U_3621)),U_3622)),U_3625)
        | ~ sP301(U_3621,U_3620,U_3622,U_3623,U_3624,U_3625) )
    & ! [U_3621,U_3620,U_3622,U_3623,U_3624,U_3625] :
        ( U_3623 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3620),U_3624),U_3621)),U_3622)),U_3625)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3621),U_3622)),U_3623) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3624),U_3622)),U_3625)
        | ~ sP301(U_3621,U_3620,U_3622,U_3623,U_3624,U_3625) )
    & ! [U_3621,U_3620,U_3622,U_3623,U_3624,U_3625] :
        ( sP301(U_3621,U_3620,U_3622,U_3623,U_3624,U_3625)
        | ~ class_Rings_Oring(U_3620) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP301])],[f_1037_2]) ).

cnf(f_1037_4,plain,
    ( sP301(U_3621,U_3620,U_3622,U_3623,U_3624,U_3625)
    | ~ class_Rings_Oring(U_3620) ),
    inference(clausify,[status(thm)],[f_1037_3]) ).

cnf(f_1037_5,plain,
    ( U_3623 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3620),U_3624),U_3621)),U_3622)),U_3625)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3621),U_3622)),U_3623) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3624),U_3622)),U_3625)
    | ~ sP301(U_3621,U_3620,U_3622,U_3623,U_3624,U_3625) ),
    inference(clausify,[status(thm)],[f_1037_3]) ).

cnf(f_1037_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3621),U_3622)),U_3623) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),U_3624),U_3622)),U_3625)
    | U_3623 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3620),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3620),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3620),U_3624),U_3621)),U_3622)),U_3625)
    | ~ sP301(U_3621,U_3620,U_3622,U_3623,U_3624,U_3625) ),
    inference(clausify,[status(thm)],[f_1037_3]) ).

fof(f_1038_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_1038_2,plain,
    ! [U_3627,U_3626] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3626),c_Groups_Ozero__class_Ozero(U_3626)),U_3627) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3626),U_3627)
      | ~ class_Groups_Ogroup__add(U_3626) ),
    inference(variable_rename,[status(thm)],[f_1038_1]) ).

fof(f_1038_3,plain,
    ! [U_3626,U_3627] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3626),c_Groups_Ozero__class_Ozero(U_3626)),U_3627) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3626),U_3627)
      | ~ class_Groups_Ogroup__add(U_3626) ),
    inference(definitional_conversion,[status(esa)],[f_1038_2]) ).

cnf(f_1038_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3626),c_Groups_Ozero__class_Ozero(U_3626)),U_3627) = hAPP(c_Groups_Ouminus__class_Ouminus(U_3626),U_3627)
    | ~ class_Groups_Ogroup__add(U_3626) ),
    inference(clausify,[status(thm)],[f_1038_3]) ).

fof(f_1039_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_1039_2,plain,
    ! [U_3630,U_3629,U_3628] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3628),U_3629),hAPP(c_Groups_Ouminus__class_Ouminus(U_3628),U_3630)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3628),U_3629),U_3630)
      | ~ class_Groups_Ogroup__add(U_3628) ),
    inference(variable_rename,[status(thm)],[f_1039_1]) ).

fof(f_1039_3,plain,
    ! [U_3628,U_3629,U_3630] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3628),U_3629),hAPP(c_Groups_Ouminus__class_Ouminus(U_3628),U_3630)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3628),U_3629),U_3630)
      | ~ class_Groups_Ogroup__add(U_3628) ),
    inference(definitional_conversion,[status(esa)],[f_1039_2]) ).

cnf(f_1039_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3628),U_3629),hAPP(c_Groups_Ouminus__class_Ouminus(U_3628),U_3630)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3628),U_3629),U_3630)
    | ~ class_Groups_Ogroup__add(U_3628) ),
    inference(clausify,[status(thm)],[f_1039_3]) ).

fof(f_1040_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_1040_2,plain,
    ! [U_3633,U_3632,U_3631] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3631),U_3632),U_3633) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3631),U_3632),hAPP(c_Groups_Ouminus__class_Ouminus(U_3631),U_3633))
      | ~ class_Groups_Oab__group__add(U_3631) ),
    inference(variable_rename,[status(thm)],[f_1040_1]) ).

fof(f_1040_3,plain,
    ! [U_3631,U_3632,U_3633] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3631),U_3632),U_3633) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3631),U_3632),hAPP(c_Groups_Ouminus__class_Ouminus(U_3631),U_3633))
      | ~ class_Groups_Oab__group__add(U_3631) ),
    inference(definitional_conversion,[status(esa)],[f_1040_2]) ).

cnf(f_1040_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3631),U_3632),U_3633) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3631),U_3632),hAPP(c_Groups_Ouminus__class_Ouminus(U_3631),U_3633))
    | ~ class_Groups_Oab__group__add(U_3631) ),
    inference(clausify,[status(thm)],[f_1040_3]) ).

fof(f_1041_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_1041_2,plain,
    ! [U_3636,U_3635,U_3634] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3634),U_3635),U_3636) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3634),U_3635),hAPP(c_Groups_Ouminus__class_Ouminus(U_3634),U_3636))
      | ~ class_Groups_Ogroup__add(U_3634) ),
    inference(variable_rename,[status(thm)],[f_1041_1]) ).

fof(f_1041_3,plain,
    ! [U_3634,U_3635,U_3636] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3634),U_3635),U_3636) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3634),U_3635),hAPP(c_Groups_Ouminus__class_Ouminus(U_3634),U_3636))
      | ~ class_Groups_Ogroup__add(U_3634) ),
    inference(definitional_conversion,[status(esa)],[f_1041_2]) ).

cnf(f_1041_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3634),U_3635),U_3636) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3634),U_3635),hAPP(c_Groups_Ouminus__class_Ouminus(U_3634),U_3636))
    | ~ class_Groups_Ogroup__add(U_3634) ),
    inference(clausify,[status(thm)],[f_1041_3]) ).

fof(f_1042_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_1042_2,plain,
    ! [U_3639,U_3638,U_3637] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3637),U_3638),U_3639) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3637),U_3638),hAPP(c_Groups_Ouminus__class_Ouminus(U_3637),U_3639))
      | ~ class_Rings_Ocomm__ring__1(U_3637) ),
    inference(variable_rename,[status(thm)],[f_1042_1]) ).

fof(f_1042_3,plain,
    ! [U_3637,U_3638,U_3639] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3637),U_3638),U_3639) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3637),U_3638),hAPP(c_Groups_Ouminus__class_Ouminus(U_3637),U_3639))
      | ~ class_Rings_Ocomm__ring__1(U_3637) ),
    inference(definitional_conversion,[status(esa)],[f_1042_2]) ).

cnf(f_1042_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3637),U_3638),U_3639) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3637),U_3638),hAPP(c_Groups_Ouminus__class_Ouminus(U_3637),U_3639))
    | ~ class_Rings_Ocomm__ring__1(U_3637) ),
    inference(clausify,[status(thm)],[f_1042_3]) ).

fof(f_1043_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_1043_2,plain,
    ! [U_3640] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3640),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_3640,
    inference(variable_rename,[status(thm)],[f_1043_1]) ).

fof(f_1043_3,plain,
    ! [U_3640] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3640),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_3640,
    inference(definitional_conversion,[status(esa)],[f_1043_2]) ).

cnf(f_1043_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3640),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) = U_3640,
    inference(clausify,[status(thm)],[f_1043_3]) ).

fof(f_1044_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_1044_2,plain,
    ! [U_3642,U_3641] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3641),U_3642) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3641),U_3642)) ),
    inference(variable_rename,[status(thm)],[f_1044_1]) ).

fof(f_1044_3,plain,
    ! [U_3641,U_3642] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3641),U_3642) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3641),U_3642)) ),
    inference(definitional_conversion,[status(esa)],[f_1044_2]) ).

cnf(f_1044_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3641),U_3642) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3641),U_3642)) ),
    inference(clausify,[status(thm)],[f_1044_3]) ).

fof(f_1045_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_1045_2,plain,
    ! [U_3645,U_3644,U_3643] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3643),U_3644)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3643),U_3645)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3644),U_3645)
        | U_3643 = 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_3643),U_3644)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3643),U_3645)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3643 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1045_1]) ).

fof(f_1045_3,plain,
    ( ! [U_3651,U_3649,U_3647] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3647),U_3649)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3647),U_3651)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3649),U_3651)
        | U_3647 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3650,U_3648,U_3646] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3646),U_3648)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3646),U_3650)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3646 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1045_2]) ).

fof(f_1045_4,plain,
    ( ! [U_3647,U_3649,U_3651] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3647),U_3649)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3647),U_3651)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3649),U_3651)
        | U_3647 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3648,U_3646,U_3650] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3646),U_3648)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3646),U_3650)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3646 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_1045_3]) ).

cnf(f_1045_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3646),U_3648)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3646),U_3650)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3646 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1045_4]) ).

cnf(f_1045_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3647),U_3649)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3647),U_3651)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3649),U_3651)
    | U_3647 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1045_4]) ).

fof(f_1046_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_1046_2,plain,
    ! [U_3654,U_3653,U_3652] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3652),U_3653)),U_3654) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3652),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3653),U_3654))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3652),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3653,U_3654))),U_3654)),
    inference(variable_rename,[status(thm)],[f_1046_1]) ).

fof(f_1046_3,plain,
    ! [U_3652,U_3653,U_3654] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3652),U_3653)),U_3654) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3652),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3653),U_3654))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3652),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3653,U_3654))),U_3654)),
    inference(definitional_conversion,[status(esa)],[f_1046_2]) ).

cnf(f_1046_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3652),U_3653)),U_3654) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3652),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3653),U_3654))),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3652),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3653,U_3654))),U_3654)),
    inference(clausify,[status(thm)],[f_1046_3]) ).

fof(f_1047_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_1047_2,plain,
    ! [U_3657,U_3656,U_3655] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3655,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3656),U_3657)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3656),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3655),U_3656),U_3657))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3655,U_3656)),
    inference(variable_rename,[status(thm)],[f_1047_1]) ).

fof(f_1047_3,plain,
    ! [U_3655,U_3656,U_3657] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3655,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3656),U_3657)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3656),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3655),U_3656),U_3657))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3655,U_3656)),
    inference(definitional_conversion,[status(esa)],[f_1047_2]) ).

cnf(f_1047_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3655,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3656),U_3657)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3656),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3655),U_3656),U_3657))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3655,U_3656)),
    inference(clausify,[status(thm)],[f_1047_3]) ).

fof(f_1048_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_1048_2,plain,
    ! [U_3659,U_3658] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3658),U_3659))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3658),U_3659)),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_3658),U_3659)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3658),U_3659)) ) ),
    inference(variable_rename,[status(thm)],[f_1048_1]) ).

fof(f_1048_3,plain,
    ( ! [U_3663,U_3661] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3661),U_3663))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3661),U_3663)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_3662,U_3660] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3660),U_3662)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3660),U_3662)) ) ),
    inference(miniscope,[status(thm)],[f_1048_2]) ).

fof(f_1048_4,plain,
    ( ! [U_3661,U_3663] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3661),U_3663))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3661),U_3663)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_3662,U_3660] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3660),U_3662)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3660),U_3662)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1048_3]) ).

cnf(f_1048_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3660),U_3662)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3660),U_3662)) ),
    inference(clausify,[status(thm)],[f_1048_4]) ).

cnf(f_1048_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3661),U_3663))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3661),U_3663)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1048_4]) ).

fof(f_1049_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_1049_2,plain,
    ! [U_3665,U_3664] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3665),U_3664)),U_3665))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),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_1049_1]) ).

fof(f_1049_3,plain,
    ! [U_3664,U_3665] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3665),U_3664)),U_3665))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),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_1049_2]) ).

cnf(f_1049_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3665),U_3664)),U_3665))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),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_1049_3]) ).

fof(f_1050_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_1050_2,plain,
    ! [U_3667,U_3666] :
      ( ( 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_3666),U_3667)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3667),U_3666)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3667),U_3666))
        | ~ 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_3666),U_3667))) ) ),
    inference(variable_rename,[status(thm)],[f_1050_1]) ).

fof(f_1050_3,plain,
    ( ! [U_3671,U_3669] :
        ( 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_3669),U_3671)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3671),U_3669)) )
    & ! [U_3670,U_3668] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3670),U_3668))
        | ~ 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_3668),U_3670))) ) ),
    inference(miniscope,[status(thm)],[f_1050_2]) ).

fof(f_1050_4,plain,
    ( ! [U_3669,U_3671] :
        ( 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_3669),U_3671)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3671),U_3669)) )
    & ! [U_3670,U_3668] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3670),U_3668))
        | ~ 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_3668),U_3670))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1050_3]) ).

cnf(f_1050_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3670),U_3668))
    | ~ 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_3668),U_3670))) ),
    inference(clausify,[status(thm)],[f_1050_4]) ).

cnf(f_1050_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_3669),U_3671)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3671),U_3669)) ),
    inference(clausify,[status(thm)],[f_1050_4]) ).

fof(f_1051_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_1051_2,plain,
    ! [U_3673,U_3672] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3672),U_3673)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3672)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3673)),
    inference(variable_rename,[status(thm)],[f_1051_1]) ).

fof(f_1051_3,plain,
    ! [U_3672,U_3673] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3672),U_3673)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3672)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3673)),
    inference(definitional_conversion,[status(esa)],[f_1051_2]) ).

cnf(f_1051_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3672),U_3673)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3672)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3673)),
    inference(clausify,[status(thm)],[f_1051_3]) ).

fof(f_1052_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_1052_2,plain,
    ! [U_3675,U_3674] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3674)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3675)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3674),U_3675)),
    inference(variable_rename,[status(thm)],[f_1052_1]) ).

fof(f_1052_3,plain,
    ! [U_3674,U_3675] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3674)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3675)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3674),U_3675)),
    inference(definitional_conversion,[status(esa)],[f_1052_2]) ).

cnf(f_1052_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3674)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3675)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3674),U_3675)),
    inference(clausify,[status(thm)],[f_1052_3]) ).

fof(f_1053_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_1053_2,plain,
    ! [U_3677,U_3676] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3676),U_3677)),hAPP(c_Nat_OSuc,U_3676))),
    inference(variable_rename,[status(thm)],[f_1053_1]) ).

fof(f_1053_3,plain,
    ! [U_3676,U_3677] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3676),U_3677)),hAPP(c_Nat_OSuc,U_3676))),
    inference(definitional_conversion,[status(esa)],[f_1053_2]) ).

cnf(f_1053_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3676),U_3677)),hAPP(c_Nat_OSuc,U_3676))),
    inference(clausify,[status(thm)],[f_1053_3]) ).

fof(f_1054_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_1054_2,plain,
    ! [U_3679,U_3678] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3678),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3678),U_3679)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1054_1]) ).

fof(f_1054_3,plain,
    ! [U_3678,U_3679] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3678),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3678),U_3679)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1054_2]) ).

cnf(f_1054_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3678),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3678),U_3679)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1054_3]) ).

fof(f_1055_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_1055_2,plain,
    ! [U_3681,U_3680] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3680),U_3681) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3680),U_3681)) ),
    inference(variable_rename,[status(thm)],[f_1055_1]) ).

fof(f_1055_3,plain,
    ! [U_3680,U_3681] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3680),U_3681) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3680),U_3681)) ),
    inference(definitional_conversion,[status(esa)],[f_1055_2]) ).

cnf(f_1055_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3680),U_3681) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3680),U_3681)) ),
    inference(clausify,[status(thm)],[f_1055_3]) ).

fof(f_1056_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_1056_2,plain,
    ! [U_3683,U_3682] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3682),U_3683) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3682),U_3683)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3682),U_3683))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3682),U_3683) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1056_1]) ).

fof(f_1056_3,plain,
    ( ! [U_3687,U_3685] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3685),U_3687) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3685),U_3687)) )
    & ! [U_3686,U_3684] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3684),U_3686))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3684),U_3686) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1056_2]) ).

fof(f_1056_4,plain,
    ( ! [U_3685,U_3687] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3685),U_3687) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3685),U_3687)) )
    & ! [U_3686,U_3684] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3684),U_3686))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3684),U_3686) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_1056_3]) ).

cnf(f_1056_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3684),U_3686))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3684),U_3686) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1056_4]) ).

cnf(f_1056_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3685),U_3687) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3685),U_3687)) ),
    inference(clausify,[status(thm)],[f_1056_4]) ).

fof(f_1057_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_1057_2,plain,
    ! [U_3690,U_3689,U_3688] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3688),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3689),U_3690)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3688),U_3690)),U_3689)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3688),U_3690)),U_3689))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3688),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3689),U_3690))) ) ),
    inference(variable_rename,[status(thm)],[f_1057_1]) ).

fof(f_1057_3,plain,
    ( ! [U_3696,U_3694,U_3692] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3692),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3694),U_3696)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3692),U_3696)),U_3694)) )
    & ! [U_3695,U_3693,U_3691] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3691),U_3695)),U_3693))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3691),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3693),U_3695))) ) ),
    inference(miniscope,[status(thm)],[f_1057_2]) ).

fof(f_1057_4,plain,
    ( ! [U_3692,U_3694,U_3696] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3692),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3694),U_3696)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3692),U_3696)),U_3694)) )
    & ! [U_3693,U_3691,U_3695] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3691),U_3695)),U_3693))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3691),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3693),U_3695))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1057_3]) ).

cnf(f_1057_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3691),U_3695)),U_3693))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3691),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3693),U_3695))) ),
    inference(clausify,[status(thm)],[f_1057_4]) ).

cnf(f_1057_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3692),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3694),U_3696)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3692),U_3696)),U_3694)) ),
    inference(clausify,[status(thm)],[f_1057_4]) ).

fof(f_1058_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_1058_2,plain,
    ! [U_3698,U_3697] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3698),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3697),U_3698)) = U_3697
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3697),U_3698)) ),
    inference(variable_rename,[status(thm)],[f_1058_1]) ).

fof(f_1058_3,plain,
    ! [U_3698,U_3697] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3698),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3697),U_3698)) = U_3697
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3697),U_3698)) ),
    inference(definitional_conversion,[status(esa)],[f_1058_2]) ).

cnf(f_1058_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3698),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3697),U_3698)) = U_3697
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3697),U_3698)) ),
    inference(clausify,[status(thm)],[f_1058_3]) ).

fof(f_1059_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_1059_2,plain,
    ! [U_3700,U_3699] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3700)),U_3699) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3700),U_3699))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3699),U_3700)) ),
    inference(variable_rename,[status(thm)],[f_1059_1]) ).

fof(f_1059_3,plain,
    ! [U_3699,U_3700] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3700)),U_3699) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3700),U_3699))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3699),U_3700)) ),
    inference(definitional_conversion,[status(esa)],[f_1059_2]) ).

cnf(f_1059_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3700)),U_3699) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3700),U_3699))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3699),U_3700)) ),
    inference(clausify,[status(thm)],[f_1059_3]) ).

fof(f_1060_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_1060_2,plain,
    ! [U_3703,U_3702,U_3701] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3701),U_3703)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3702),U_3703)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3703),U_3701))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3701),U_3702)) ),
    inference(variable_rename,[status(thm)],[f_1060_1]) ).

fof(f_1060_3,plain,
    ! [U_3701,U_3702,U_3703] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3701),U_3703)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3702),U_3703)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3703),U_3701))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3701),U_3702)) ),
    inference(definitional_conversion,[status(esa)],[f_1060_2]) ).

cnf(f_1060_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3701),U_3703)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3702),U_3703)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3703),U_3701))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3701),U_3702)) ),
    inference(clausify,[status(thm)],[f_1060_3]) ).

fof(f_1061_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_1061_2,plain,
    ! [U_3706,U_3705,U_3704] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3705),U_3704)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3706),U_3704)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3705),U_3706)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3705),U_3706))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3705),U_3704)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3706),U_3704))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3704),U_3706))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3704),U_3705)) ),
    inference(variable_rename,[status(thm)],[f_1061_1]) ).

fof(f_1061_3,plain,
    ( ! [U_3704,U_3705,U_3706] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3705),U_3704)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3706),U_3704)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3705),U_3706))
        | ~ sP302(U_3704,U_3705,U_3706) )
    & ! [U_3704,U_3705,U_3706] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3705),U_3706))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3705),U_3704)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3706),U_3704)))
        | ~ sP302(U_3704,U_3705,U_3706) )
    & ! [U_3704,U_3705,U_3706] :
        ( sP302(U_3704,U_3705,U_3706)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3704),U_3706))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3704),U_3705)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP302])],[f_1061_2]) ).

cnf(f_1061_4,plain,
    ( sP302(U_3704,U_3705,U_3706)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3704),U_3706))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3704),U_3705)) ),
    inference(clausify,[status(thm)],[f_1061_3]) ).

cnf(f_1061_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3705),U_3706))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3705),U_3704)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3706),U_3704)))
    | ~ sP302(U_3704,U_3705,U_3706) ),
    inference(clausify,[status(thm)],[f_1061_3]) ).

cnf(f_1061_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3705),U_3704)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3706),U_3704)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3705),U_3706))
    | ~ sP302(U_3704,U_3705,U_3706) ),
    inference(clausify,[status(thm)],[f_1061_3]) ).

fof(f_1062_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_1062_2,plain,
    ! [U_3709,U_3708,U_3707] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3708),U_3709)),U_3707) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3708),U_3707)),U_3709)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3707),U_3708)) ),
    inference(variable_rename,[status(thm)],[f_1062_1]) ).

fof(f_1062_3,plain,
    ! [U_3708,U_3709,U_3707] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3708),U_3709)),U_3707) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3708),U_3707)),U_3709)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3707),U_3708)) ),
    inference(definitional_conversion,[status(esa)],[f_1062_2]) ).

cnf(f_1062_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3708),U_3709)),U_3707) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3708),U_3707)),U_3709)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3707),U_3708)) ),
    inference(clausify,[status(thm)],[f_1062_3]) ).

fof(f_1063_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_1063_2,plain,
    ! [U_3712,U_3711,U_3710] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3711),U_3710)),U_3712) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3711),U_3712)),U_3710)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3710),U_3711)) ),
    inference(variable_rename,[status(thm)],[f_1063_1]) ).

fof(f_1063_3,plain,
    ! [U_3710,U_3711,U_3712] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3711),U_3710)),U_3712) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3711),U_3712)),U_3710)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3710),U_3711)) ),
    inference(definitional_conversion,[status(esa)],[f_1063_2]) ).

cnf(f_1063_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3711),U_3710)),U_3712) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3711),U_3712)),U_3710)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3710),U_3711)) ),
    inference(clausify,[status(thm)],[f_1063_3]) ).

fof(f_1064_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_1064_2,plain,
    ! [U_3715,U_3714,U_3713] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3715),U_3714)),U_3713) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3715),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3714),U_3713))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3713),U_3714)) ),
    inference(variable_rename,[status(thm)],[f_1064_1]) ).

fof(f_1064_3,plain,
    ! [U_3713,U_3714,U_3715] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3715),U_3714)),U_3713) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3715),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3714),U_3713))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3713),U_3714)) ),
    inference(definitional_conversion,[status(esa)],[f_1064_2]) ).

cnf(f_1064_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3715),U_3714)),U_3713) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3715),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3714),U_3713))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3713),U_3714)) ),
    inference(clausify,[status(thm)],[f_1064_3]) ).

fof(f_1065_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_1065_2,plain,
    ! [U_3718,U_3717,U_3716] :
      ( ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3717),U_3716) = U_3718
          | U_3717 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3718),U_3716) )
        & ( U_3717 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3718),U_3716)
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3717),U_3716) != U_3718 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3716),U_3717)) ),
    inference(variable_rename,[status(thm)],[f_1065_1]) ).

fof(f_1065_3,plain,
    ( ! [U_3716,U_3717,U_3718] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3717),U_3716) = U_3718
        | U_3717 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3718),U_3716)
        | ~ sP303(U_3716,U_3717,U_3718) )
    & ! [U_3716,U_3717,U_3718] :
        ( U_3717 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3718),U_3716)
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3717),U_3716) != U_3718
        | ~ sP303(U_3716,U_3717,U_3718) )
    & ! [U_3716,U_3717,U_3718] :
        ( sP303(U_3716,U_3717,U_3718)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3716),U_3717)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP303])],[f_1065_2]) ).

cnf(f_1065_4,plain,
    ( sP303(U_3716,U_3717,U_3718)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3716),U_3717)) ),
    inference(clausify,[status(thm)],[f_1065_3]) ).

cnf(f_1065_5,plain,
    ( U_3717 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3718),U_3716)
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3717),U_3716) != U_3718
    | ~ sP303(U_3716,U_3717,U_3718) ),
    inference(clausify,[status(thm)],[f_1065_3]) ).

cnf(f_1065_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3717),U_3716) = U_3718
    | U_3717 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3718),U_3716)
    | ~ sP303(U_3716,U_3717,U_3718) ),
    inference(clausify,[status(thm)],[f_1065_3]) ).

fof(f_1066_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_1066_2,plain,
    ! [U_3720,U_3719] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3720),U_3719)),U_3719) = U_3720
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3719),U_3720)) ),
    inference(variable_rename,[status(thm)],[f_1066_1]) ).

fof(f_1066_3,plain,
    ! [U_3720,U_3719] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3720),U_3719)),U_3719) = U_3720
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3719),U_3720)) ),
    inference(definitional_conversion,[status(esa)],[f_1066_2]) ).

cnf(f_1066_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3720),U_3719)),U_3719) = U_3720
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3719),U_3720)) ),
    inference(clausify,[status(thm)],[f_1066_3]) ).

fof(f_1067_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_1067_2,plain,
    ! [U_3723,U_3722,U_3721] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3723),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3722),U_3721)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3723),U_3721)),U_3722)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3723),U_3721)),U_3722))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3723),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3722),U_3721))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3721),U_3722)) ),
    inference(variable_rename,[status(thm)],[f_1067_1]) ).

fof(f_1067_3,plain,
    ( ! [U_3721,U_3722,U_3723] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3723),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3722),U_3721)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3723),U_3721)),U_3722))
        | ~ sP304(U_3721,U_3722,U_3723) )
    & ! [U_3721,U_3722,U_3723] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3723),U_3721)),U_3722))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3723),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3722),U_3721)))
        | ~ sP304(U_3721,U_3722,U_3723) )
    & ! [U_3721,U_3722,U_3723] :
        ( sP304(U_3721,U_3722,U_3723)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3721),U_3722)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP304])],[f_1067_2]) ).

cnf(f_1067_4,plain,
    ( sP304(U_3721,U_3722,U_3723)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3721),U_3722)) ),
    inference(clausify,[status(thm)],[f_1067_3]) ).

cnf(f_1067_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_3723),U_3721)),U_3722))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3723),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3722),U_3721)))
    | ~ sP304(U_3721,U_3722,U_3723) ),
    inference(clausify,[status(thm)],[f_1067_3]) ).

cnf(f_1067_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3723),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3722),U_3721)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3723),U_3721)),U_3722))
    | ~ sP304(U_3721,U_3722,U_3723) ),
    inference(clausify,[status(thm)],[f_1067_3]) ).

fof(f_1068_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_1068_2,plain,
    ! [U_3726,U_3725,U_3724] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3726),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3725),U_3724)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3726),U_3725)),U_3724)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3724),U_3725)) ),
    inference(variable_rename,[status(thm)],[f_1068_1]) ).

fof(f_1068_3,plain,
    ! [U_3726,U_3724,U_3725] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3726),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3725),U_3724)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3726),U_3725)),U_3724)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3724),U_3725)) ),
    inference(definitional_conversion,[status(esa)],[f_1068_2]) ).

cnf(f_1068_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3726),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3725),U_3724)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3726),U_3725)),U_3724)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3724),U_3725)) ),
    inference(clausify,[status(thm)],[f_1068_3]) ).

fof(f_1069_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_1069_2,plain,
    ! [U_3728,U_3727] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3727),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3728),U_3727)) = U_3728
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3727),U_3728)) ),
    inference(variable_rename,[status(thm)],[f_1069_1]) ).

fof(f_1069_3,plain,
    ! [U_3727,U_3728] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3727),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3728),U_3727)) = U_3728
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3727),U_3728)) ),
    inference(definitional_conversion,[status(esa)],[f_1069_2]) ).

cnf(f_1069_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3727),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3728),U_3727)) = U_3728
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3727),U_3728)) ),
    inference(clausify,[status(thm)],[f_1069_3]) ).

fof(f_1070_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_1070_2,plain,
    ! [U_3731,U_3730,U_3729] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3731),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3730),U_3731)),U_3729)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3729),U_3730)) ),
    inference(variable_rename,[status(thm)],[f_1070_1]) ).

fof(f_1070_3,plain,
    ! [U_3729,U_3730,U_3731] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3731),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3730),U_3731)),U_3729)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3729),U_3730)) ),
    inference(definitional_conversion,[status(esa)],[f_1070_2]) ).

cnf(f_1070_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3731),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3730),U_3731)),U_3729)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3729),U_3730)) ),
    inference(clausify,[status(thm)],[f_1070_3]) ).

fof(f_1071_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_1071_2,plain,
    ! [U_3734,U_3733,U_3732] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3732),U_3733)),U_3734))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3732),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3734),U_3733))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3732),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3734),U_3733)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3732),U_3733)),U_3734)) ) ),
    inference(variable_rename,[status(thm)],[f_1071_1]) ).

fof(f_1071_3,plain,
    ( ! [U_3740,U_3738,U_3736] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3736),U_3738)),U_3740))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3740),U_3738))) )
    & ! [U_3739,U_3737,U_3735] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3735),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3739),U_3737)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3735),U_3737)),U_3739)) ) ),
    inference(miniscope,[status(thm)],[f_1071_2]) ).

fof(f_1071_4,plain,
    ( ! [U_3736,U_3738,U_3740] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3736),U_3738)),U_3740))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3740),U_3738))) )
    & ! [U_3737,U_3735,U_3739] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3735),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3739),U_3737)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3735),U_3737)),U_3739)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1071_3]) ).

cnf(f_1071_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3735),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3739),U_3737)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3735),U_3737)),U_3739)) ),
    inference(clausify,[status(thm)],[f_1071_4]) ).

cnf(f_1071_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_3736),U_3738)),U_3740))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3736),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3740),U_3738))) ),
    inference(clausify,[status(thm)],[f_1071_4]) ).

fof(f_1072_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_1072_2,plain,
    ! [U_3743,U_3742,U_3741] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3743),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3742),U_3741)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3743),U_3741)),U_3742)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3741),U_3742)) ),
    inference(variable_rename,[status(thm)],[f_1072_1]) ).

fof(f_1072_3,plain,
    ! [U_3741,U_3743,U_3742] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3743),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3742),U_3741)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3743),U_3741)),U_3742)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3741),U_3742)) ),
    inference(definitional_conversion,[status(esa)],[f_1072_2]) ).

cnf(f_1072_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3743),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3742),U_3741)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3743),U_3741)),U_3742)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3741),U_3742)) ),
    inference(clausify,[status(thm)],[f_1072_3]) ).

fof(f_1073_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_1073_2,plain,
    ! [U_3746,U_3745,U_3744] :
      ( hBOOL(hAPP(hAPP(c_member(U_3744),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3744),U_3745),U_3746)),c_Int_Oring__1__class_OInts(U_3744)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3744),U_3746),c_Int_Oring__1__class_OInts(U_3744)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3744),U_3745),c_Int_Oring__1__class_OInts(U_3744)))
      | ~ class_Rings_Oring__1(U_3744) ),
    inference(variable_rename,[status(thm)],[f_1073_1]) ).

fof(f_1073_3,plain,
    ! [U_3744,U_3745,U_3746] :
      ( hBOOL(hAPP(hAPP(c_member(U_3744),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3744),U_3745),U_3746)),c_Int_Oring__1__class_OInts(U_3744)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3744),U_3746),c_Int_Oring__1__class_OInts(U_3744)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3744),U_3745),c_Int_Oring__1__class_OInts(U_3744)))
      | ~ class_Rings_Oring__1(U_3744) ),
    inference(definitional_conversion,[status(esa)],[f_1073_2]) ).

cnf(f_1073_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3744),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3744),U_3745),U_3746)),c_Int_Oring__1__class_OInts(U_3744)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3744),U_3746),c_Int_Oring__1__class_OInts(U_3744)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3744),U_3745),c_Int_Oring__1__class_OInts(U_3744)))
    | ~ class_Rings_Oring__1(U_3744) ),
    inference(clausify,[status(thm)],[f_1073_3]) ).

fof(f_1074_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_1074_2,plain,
    ! [U_3748,U_3747] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3747),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3748)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3747),U_3748),
    inference(variable_rename,[status(thm)],[f_1074_1]) ).

fof(f_1074_3,plain,
    ! [U_3747,U_3748] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3747),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3748)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3747),U_3748),
    inference(definitional_conversion,[status(esa)],[f_1074_2]) ).

cnf(f_1074_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3747),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3748)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3747),U_3748),
    inference(clausify,[status(thm)],[f_1074_3]) ).

fof(f_1075_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_1075_2,plain,
    ! [U_3750,U_3749] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3749),U_3750) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3749),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3750)),
    inference(variable_rename,[status(thm)],[f_1075_1]) ).

fof(f_1075_3,plain,
    ! [U_3749,U_3750] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3749),U_3750) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3749),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3750)),
    inference(definitional_conversion,[status(esa)],[f_1075_2]) ).

cnf(f_1075_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3749),U_3750) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3749),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3750)),
    inference(clausify,[status(thm)],[f_1075_3]) ).

fof(f_1076_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_1076_2,plain,
    ! [U_3752,U_3751] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3751),hAPP(c_Nat_OSuc,U_3752)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3751),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3752),
    inference(variable_rename,[status(thm)],[f_1076_1]) ).

fof(f_1076_3,plain,
    ! [U_3751,U_3752] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3751),hAPP(c_Nat_OSuc,U_3752)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3751),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3752),
    inference(definitional_conversion,[status(esa)],[f_1076_2]) ).

cnf(f_1076_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3751),hAPP(c_Nat_OSuc,U_3752)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3751),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3752),
    inference(clausify,[status(thm)],[f_1076_3]) ).

fof(f_1077_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_1077_2,plain,
    ! [U_3753] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3753)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3753,
    inference(variable_rename,[status(thm)],[f_1077_1]) ).

fof(f_1077_3,plain,
    ! [U_3753] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3753)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3753,
    inference(definitional_conversion,[status(esa)],[f_1077_2]) ).

cnf(f_1077_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3753)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_3753,
    inference(clausify,[status(thm)],[f_1077_3]) ).

fof(f_1078_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_1078_2,plain,
    ! [U_3755,U_3754] :
      ( c_Nat__Transfer_Otsub(U_3755,U_3754) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3755),U_3754)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3754),U_3755)) ),
    inference(variable_rename,[status(thm)],[f_1078_1]) ).

fof(f_1078_3,plain,
    ! [U_3754,U_3755] :
      ( c_Nat__Transfer_Otsub(U_3755,U_3754) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3755),U_3754)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3754),U_3755)) ),
    inference(definitional_conversion,[status(esa)],[f_1078_2]) ).

cnf(f_1078_4,plain,
    ( c_Nat__Transfer_Otsub(U_3755,U_3754) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3755),U_3754)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3754),U_3755)) ),
    inference(clausify,[status(thm)],[f_1078_3]) ).

fof(f_1079_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_1079_2,plain,
    ! [U_3757,U_3756] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3756),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3757)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3756),U_3757)),
    inference(variable_rename,[status(thm)],[f_1079_1]) ).

fof(f_1079_3,plain,
    ! [U_3757,U_3756] : c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3756),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3757)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3756),U_3757)),
    inference(definitional_conversion,[status(esa)],[f_1079_2]) ).

cnf(f_1079_4,plain,
    c_Nat__Transfer_Otsub(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3756),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_3757)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3756),U_3757)),
    inference(clausify,[status(thm)],[f_1079_3]) ).

fof(f_1080_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_1080_2,plain,
    ! [U_3763,U_3762,U_3761,U_3760,U_3759,U_3758] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3758),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),U_3759),U_3760)),U_3761)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),U_3762),U_3760)),U_3763)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3758),U_3761),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3758),U_3762),U_3759)),U_3760)),U_3763))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3758),U_3761),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3758),U_3762),U_3759)),U_3760)),U_3763)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3758),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),U_3759),U_3760)),U_3761)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),U_3762),U_3760)),U_3763))) ) )
      | ~ class_Rings_Oordered__ring(U_3758) ),
    inference(variable_rename,[status(thm)],[f_1080_1]) ).

fof(f_1080_3,plain,
    ( ! [U_3758,U_3759,U_3760,U_3761,U_3762,U_3763] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3758),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),U_3759),U_3760)),U_3761)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),U_3762),U_3760)),U_3763)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3758),U_3761),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3758),U_3762),U_3759)),U_3760)),U_3763)))
        | ~ sP305(U_3758,U_3759,U_3760,U_3761,U_3762,U_3763) )
    & ! [U_3758,U_3759,U_3760,U_3761,U_3762,U_3763] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3758),U_3761),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3758),U_3762),U_3759)),U_3760)),U_3763)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3758),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),U_3759),U_3760)),U_3761)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),U_3762),U_3760)),U_3763)))
        | ~ sP305(U_3758,U_3759,U_3760,U_3761,U_3762,U_3763) )
    & ! [U_3758,U_3759,U_3760,U_3761,U_3762,U_3763] :
        ( sP305(U_3758,U_3759,U_3760,U_3761,U_3762,U_3763)
        | ~ class_Rings_Oordered__ring(U_3758) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP305])],[f_1080_2]) ).

cnf(f_1080_4,plain,
    ( sP305(U_3758,U_3759,U_3760,U_3761,U_3762,U_3763)
    | ~ class_Rings_Oordered__ring(U_3758) ),
    inference(clausify,[status(thm)],[f_1080_3]) ).

cnf(f_1080_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3758),U_3761),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3758),U_3762),U_3759)),U_3760)),U_3763)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3758),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),U_3759),U_3760)),U_3761)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),U_3762),U_3760)),U_3763)))
    | ~ sP305(U_3758,U_3759,U_3760,U_3761,U_3762,U_3763) ),
    inference(clausify,[status(thm)],[f_1080_3]) ).

cnf(f_1080_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3758),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),U_3759),U_3760)),U_3761)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),U_3762),U_3760)),U_3763)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3758),U_3761),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3758),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3758),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3758),U_3762),U_3759)),U_3760)),U_3763)))
    | ~ sP305(U_3758,U_3759,U_3760,U_3761,U_3762,U_3763) ),
    inference(clausify,[status(thm)],[f_1080_3]) ).

fof(f_1081_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_1081_2,plain,
    ! [U_3769,U_3768,U_3767,U_3766,U_3765,U_3764] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3764),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),U_3765),U_3766)),U_3767)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),U_3768),U_3766)),U_3769)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3764),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3764),U_3765),U_3768)),U_3766)),U_3767)),U_3769)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3764),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3764),U_3765),U_3768)),U_3766)),U_3767)),U_3769))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3764),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),U_3765),U_3766)),U_3767)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),U_3768),U_3766)),U_3769))) ) )
      | ~ class_Rings_Oordered__ring(U_3764) ),
    inference(variable_rename,[status(thm)],[f_1081_1]) ).

fof(f_1081_3,plain,
    ( ! [U_3764,U_3765,U_3766,U_3767,U_3768,U_3769] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3764),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),U_3765),U_3766)),U_3767)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),U_3768),U_3766)),U_3769)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3764),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3764),U_3765),U_3768)),U_3766)),U_3767)),U_3769))
        | ~ sP306(U_3764,U_3765,U_3766,U_3767,U_3768,U_3769) )
    & ! [U_3764,U_3765,U_3766,U_3767,U_3768,U_3769] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3764),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3764),U_3765),U_3768)),U_3766)),U_3767)),U_3769))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3764),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),U_3765),U_3766)),U_3767)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),U_3768),U_3766)),U_3769)))
        | ~ sP306(U_3764,U_3765,U_3766,U_3767,U_3768,U_3769) )
    & ! [U_3764,U_3765,U_3766,U_3767,U_3768,U_3769] :
        ( sP306(U_3764,U_3765,U_3766,U_3767,U_3768,U_3769)
        | ~ class_Rings_Oordered__ring(U_3764) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP306])],[f_1081_2]) ).

cnf(f_1081_4,plain,
    ( sP306(U_3764,U_3765,U_3766,U_3767,U_3768,U_3769)
    | ~ class_Rings_Oordered__ring(U_3764) ),
    inference(clausify,[status(thm)],[f_1081_3]) ).

cnf(f_1081_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3764),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3764),U_3765),U_3768)),U_3766)),U_3767)),U_3769))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3764),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),U_3765),U_3766)),U_3767)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),U_3768),U_3766)),U_3769)))
    | ~ sP306(U_3764,U_3765,U_3766,U_3767,U_3768,U_3769) ),
    inference(clausify,[status(thm)],[f_1081_3]) ).

cnf(f_1081_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3764),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),U_3765),U_3766)),U_3767)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),U_3768),U_3766)),U_3769)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3764),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3764),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3764),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3764),U_3765),U_3768)),U_3766)),U_3767)),U_3769))
    | ~ sP306(U_3764,U_3765,U_3766,U_3767,U_3768,U_3769) ),
    inference(clausify,[status(thm)],[f_1081_3]) ).

fof(f_1082_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_1082_2,plain,
    ! [U_3775,U_3774,U_3773,U_3772,U_3771,U_3770] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3770),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3770),U_3771),U_3772)),U_3773)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3770),U_3774),U_3772)),U_3775)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3770),U_3773),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3770),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3770),U_3774),U_3771)),U_3772)),U_3775))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3770),U_3773),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3770),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3770),U_3774),U_3771)),U_3772)),U_3775)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3770),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3770),U_3771),U_3772)),U_3773)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3770),U_3774),U_3772)),U_3775))) ) )
      | ~ class_Rings_Oordered__ring(U_3770) ),
    inference(variable_rename,[status(thm)],[f_1082_1]) ).

fof(f_1082_3,plain,
    ( ! [U_3775,U_3770,U_3771,U_3772,U_3773,U_3774] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3770),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3770),U_3771),U_3772)),U_3773)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3770),U_3774),U_3772)),U_3775)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3770),U_3773),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3770),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3770),U_3774),U_3771)),U_3772)),U_3775)))
        | ~ sP307(U_3775,U_3770,U_3771,U_3772,U_3773,U_3774) )
    & ! [U_3775,U_3770,U_3771,U_3772,U_3773,U_3774] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3770),U_3773),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3770),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3770),U_3774),U_3771)),U_3772)),U_3775)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3770),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3770),U_3771),U_3772)),U_3773)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3770),U_3774),U_3772)),U_3775)))
        | ~ sP307(U_3775,U_3770,U_3771,U_3772,U_3773,U_3774) )
    & ! [U_3775,U_3770,U_3771,U_3772,U_3773,U_3774] :
        ( sP307(U_3775,U_3770,U_3771,U_3772,U_3773,U_3774)
        | ~ class_Rings_Oordered__ring(U_3770) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP307])],[f_1082_2]) ).

cnf(f_1082_4,plain,
    ( sP307(U_3775,U_3770,U_3771,U_3772,U_3773,U_3774)
    | ~ class_Rings_Oordered__ring(U_3770) ),
    inference(clausify,[status(thm)],[f_1082_3]) ).

cnf(f_1082_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3770),U_3773),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3770),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3770),U_3774),U_3771)),U_3772)),U_3775)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3770),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3770),U_3771),U_3772)),U_3773)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3770),U_3774),U_3772)),U_3775)))
    | ~ sP307(U_3775,U_3770,U_3771,U_3772,U_3773,U_3774) ),
    inference(clausify,[status(thm)],[f_1082_3]) ).

cnf(f_1082_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3770),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3770),U_3771),U_3772)),U_3773)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3770),U_3774),U_3772)),U_3775)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3770),U_3773),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3770),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3770),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3770),U_3774),U_3771)),U_3772)),U_3775)))
    | ~ sP307(U_3775,U_3770,U_3771,U_3772,U_3773,U_3774) ),
    inference(clausify,[status(thm)],[f_1082_3]) ).

fof(f_1083_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_1083_2,plain,
    ! [U_3781,U_3780,U_3779,U_3778,U_3777,U_3776] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),U_3777),U_3778)),U_3779)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),U_3780),U_3778)),U_3781)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3776),U_3777),U_3780)),U_3778)),U_3779)),U_3781)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3776),U_3777),U_3780)),U_3778)),U_3779)),U_3781))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),U_3777),U_3778)),U_3779)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),U_3780),U_3778)),U_3781))) ) )
      | ~ class_Rings_Oordered__ring(U_3776) ),
    inference(variable_rename,[status(thm)],[f_1083_1]) ).

fof(f_1083_3,plain,
    ( ! [U_3777,U_3776,U_3778,U_3779,U_3780,U_3781] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),U_3777),U_3778)),U_3779)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),U_3780),U_3778)),U_3781)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3776),U_3777),U_3780)),U_3778)),U_3779)),U_3781))
        | ~ sP308(U_3777,U_3776,U_3778,U_3779,U_3780,U_3781) )
    & ! [U_3777,U_3776,U_3778,U_3779,U_3780,U_3781] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3776),U_3777),U_3780)),U_3778)),U_3779)),U_3781))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),U_3777),U_3778)),U_3779)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),U_3780),U_3778)),U_3781)))
        | ~ sP308(U_3777,U_3776,U_3778,U_3779,U_3780,U_3781) )
    & ! [U_3777,U_3776,U_3778,U_3779,U_3780,U_3781] :
        ( sP308(U_3777,U_3776,U_3778,U_3779,U_3780,U_3781)
        | ~ class_Rings_Oordered__ring(U_3776) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP308])],[f_1083_2]) ).

cnf(f_1083_4,plain,
    ( sP308(U_3777,U_3776,U_3778,U_3779,U_3780,U_3781)
    | ~ class_Rings_Oordered__ring(U_3776) ),
    inference(clausify,[status(thm)],[f_1083_3]) ).

cnf(f_1083_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3776),U_3777),U_3780)),U_3778)),U_3779)),U_3781))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),U_3777),U_3778)),U_3779)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),U_3780),U_3778)),U_3781)))
    | ~ sP308(U_3777,U_3776,U_3778,U_3779,U_3780,U_3781) ),
    inference(clausify,[status(thm)],[f_1083_3]) ).

cnf(f_1083_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),U_3777),U_3778)),U_3779)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),U_3780),U_3778)),U_3781)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_3776),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3776),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3776),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3776),U_3777),U_3780)),U_3778)),U_3779)),U_3781))
    | ~ sP308(U_3777,U_3776,U_3778,U_3779,U_3780,U_3781) ),
    inference(clausify,[status(thm)],[f_1083_3]) ).

fof(f_1084_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_1084_2,plain,
    ! [U_3784,U_3783,U_3782] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3784),U_3783)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3784),U_3782)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3782),U_3783))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3782)) ),
    inference(variable_rename,[status(thm)],[f_1084_1]) ).

fof(f_1084_3,plain,
    ! [U_3784,U_3782,U_3783] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3784),U_3783)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3784),U_3782)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3782),U_3783))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3782)) ),
    inference(definitional_conversion,[status(esa)],[f_1084_2]) ).

cnf(f_1084_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_3784),U_3783)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3784),U_3782)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3782),U_3783))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3782)) ),
    inference(clausify,[status(thm)],[f_1084_3]) ).

fof(f_1085_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_1085_2,plain,
    ! [U_3787,U_3786,U_3785] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3785),U_3786)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3785),U_3787)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3786),U_3787)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3785)) ),
    inference(variable_rename,[status(thm)],[f_1085_1]) ).

fof(f_1085_3,plain,
    ! [U_3785,U_3786,U_3787] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3785),U_3786)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3785),U_3787)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3786),U_3787)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3785)) ),
    inference(definitional_conversion,[status(esa)],[f_1085_2]) ).

cnf(f_1085_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3785),U_3786)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3785),U_3787)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3786),U_3787)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3785)) ),
    inference(clausify,[status(thm)],[f_1085_3]) ).

fof(f_1086_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_1086_2,plain,
    ! [U_3789,U_3788] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3788),U_3789)),U_3788) = U_3789
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3788)) ),
    inference(variable_rename,[status(thm)],[f_1086_1]) ).

fof(f_1086_3,plain,
    ! [U_3789,U_3788] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3788),U_3789)),U_3788) = U_3789
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3788)) ),
    inference(definitional_conversion,[status(esa)],[f_1086_2]) ).

cnf(f_1086_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3788),U_3789)),U_3788) = U_3789
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3788)) ),
    inference(clausify,[status(thm)],[f_1086_3]) ).

fof(f_1087_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_1087_2,plain,
    ! [U_3791,U_3790] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3791),U_3790)),U_3790) = U_3791
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3790)) ),
    inference(variable_rename,[status(thm)],[f_1087_1]) ).

fof(f_1087_3,plain,
    ! [U_3790,U_3791] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3791),U_3790)),U_3790) = U_3791
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3790)) ),
    inference(definitional_conversion,[status(esa)],[f_1087_2]) ).

cnf(f_1087_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3791),U_3790)),U_3790) = U_3791
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3790)) ),
    inference(clausify,[status(thm)],[f_1087_3]) ).

fof(f_1088_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_1088_2,plain,
    ! [U_3793,U_3792] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3793),U_3792)),U_3793))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3793))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3792)) ),
    inference(variable_rename,[status(thm)],[f_1088_1]) ).

fof(f_1088_3,plain,
    ! [U_3792,U_3793] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3793),U_3792)),U_3793))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3793))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3792)) ),
    inference(definitional_conversion,[status(esa)],[f_1088_2]) ).

cnf(f_1088_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3793),U_3792)),U_3793))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3793))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_3792)) ),
    inference(clausify,[status(thm)],[f_1088_3]) ).

fof(f_1089_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_1089_2,plain,
    ! [U_3795,U_3794] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3794),hAPP(c_Nat_OSuc,U_3795))),U_3794))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3794)) ),
    inference(variable_rename,[status(thm)],[f_1089_1]) ).

fof(f_1089_3,plain,
    ! [U_3795,U_3794] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3794),hAPP(c_Nat_OSuc,U_3795))),U_3794))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3794)) ),
    inference(definitional_conversion,[status(esa)],[f_1089_2]) ).

cnf(f_1089_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3794),hAPP(c_Nat_OSuc,U_3795))),U_3794))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3794)) ),
    inference(clausify,[status(thm)],[f_1089_3]) ).

fof(f_1090_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_1090_2,plain,
    ! [U_3796] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3796),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_3796
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3796)) ),
    inference(variable_rename,[status(thm)],[f_1090_1]) ).

fof(f_1090_3,plain,
    ! [U_3796] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3796),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_3796
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3796)) ),
    inference(definitional_conversion,[status(esa)],[f_1090_2]) ).

cnf(f_1090_4,plain,
    ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3796),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) = U_3796
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3796)) ),
    inference(clausify,[status(thm)],[f_1090_3]) ).

fof(f_1091_1,plain,
    ! [V_b_2,V_a_2,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
        | ? [B_d] :
            ( ~ hBOOL(hAPP(V_Pa_2,B_d))
            & V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
        | ( ~ hBOOL(hAPP(V_Pa_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_Pa_2,B_d))
              | V_a_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
          & ( hBOOL(hAPP(V_Pa_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_Pa_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_1091_2,plain,
    ! [U_3801,U_3800,U_3799] :
      ( ( hBOOL(hAPP(U_3799,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3800),U_3801)))
        | ? [U_3798] :
            ( ~ hBOOL(hAPP(U_3799,U_3798))
            & U_3800 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3801),U_3798) )
        | ( ~ hBOOL(hAPP(U_3799,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3800),U_3801)) ) )
      & ( ( ! [U_3797] :
              ( hBOOL(hAPP(U_3799,U_3797))
              | U_3800 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3801),U_3797) )
          & ( hBOOL(hAPP(U_3799,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3800),U_3801)) ) )
        | ~ hBOOL(hAPP(U_3799,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3800),U_3801))) ) ),
    inference(variable_rename,[status(thm)],[f_1091_1]) ).

fof(f_1091_3,plain,
    ( ! [U_3807,U_3805,U_3803] :
        ( hBOOL(hAPP(U_3803,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3805),U_3807)))
        | ? [U_3798] :
            ( ~ hBOOL(hAPP(U_3803,U_3798))
            & U_3805 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3807),U_3798) )
        | ( ~ hBOOL(hAPP(U_3803,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3805),U_3807)) ) )
    & ! [U_3806,U_3804,U_3802] :
        ( ( ! [U_3797] :
              ( hBOOL(hAPP(U_3802,U_3797))
              | U_3804 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3806),U_3797) )
          & ( hBOOL(hAPP(U_3802,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3804),U_3806)) ) )
        | ~ hBOOL(hAPP(U_3802,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3804),U_3806))) ) ),
    inference(miniscope,[status(thm)],[f_1091_2]) ).

fof(f_1091_4,plain,
    ( ! [U_3807,U_3805,U_3803] :
        ( hBOOL(hAPP(U_3803,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3805),U_3807)))
        | ( ~ hBOOL(hAPP(U_3803,sK63(U_3807,U_3805,U_3803)))
          & U_3805 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3807),sK63(U_3807,U_3805,U_3803)) )
        | ( ~ hBOOL(hAPP(U_3803,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3805),U_3807)) ) )
    & ! [U_3806,U_3804,U_3802] :
        ( ( ! [U_3797] :
              ( hBOOL(hAPP(U_3802,U_3797))
              | U_3804 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3806),U_3797) )
          & ( hBOOL(hAPP(U_3802,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3804),U_3806)) ) )
        | ~ hBOOL(hAPP(U_3802,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3804),U_3806))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK63]),skolemize(U_3798,sK63(U_3807,U_3805,U_3803))],[f_1091_3]) ).

fof(f_1091_5,plain,
    ( ! [U_3807,U_3803,U_3805] :
        ( ~ hBOOL(hAPP(U_3803,sK63(U_3807,U_3805,U_3803)))
        | ~ sP311(U_3807,U_3803,U_3805) )
    & ! [U_3807,U_3803,U_3805] :
        ( U_3805 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3807),sK63(U_3807,U_3805,U_3803))
        | ~ sP311(U_3807,U_3803,U_3805) )
    & ! [U_3807,U_3803,U_3805] :
        ( ~ hBOOL(hAPP(U_3803,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP310(U_3807,U_3803,U_3805) )
    & ! [U_3807,U_3803,U_3805] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3805),U_3807))
        | ~ sP310(U_3807,U_3803,U_3805) )
    & ! [U_3797,U_3802,U_3804,U_3806] :
        ( hBOOL(hAPP(U_3802,U_3797))
        | U_3804 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3806),U_3797)
        | ~ sP309(U_3797,U_3802,U_3804,U_3806) )
    & ! [U_3797,U_3802,U_3804,U_3806] :
        ( hBOOL(hAPP(U_3802,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3804),U_3806))
        | ~ sP309(U_3797,U_3802,U_3804,U_3806) )
    & ! [U_3807,U_3803,U_3805] :
        ( hBOOL(hAPP(U_3803,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3805),U_3807)))
        | sP311(U_3807,U_3803,U_3805)
        | sP310(U_3807,U_3803,U_3805) )
    & ! [U_3797,U_3802,U_3804,U_3806] :
        ( sP309(U_3797,U_3802,U_3804,U_3806)
        | ~ hBOOL(hAPP(U_3802,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3804),U_3806))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP309,sP310,sP311])],[f_1091_4]) ).

cnf(f_1091_6,plain,
    ( sP309(U_3797,U_3802,U_3804,U_3806)
    | ~ hBOOL(hAPP(U_3802,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3804),U_3806))) ),
    inference(clausify,[status(thm)],[f_1091_5]) ).

cnf(f_1091_7,plain,
    ( hBOOL(hAPP(U_3803,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3805),U_3807)))
    | sP311(U_3807,U_3803,U_3805)
    | sP310(U_3807,U_3803,U_3805) ),
    inference(clausify,[status(thm)],[f_1091_5]) ).

cnf(f_1091_8,plain,
    ( hBOOL(hAPP(U_3802,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3804),U_3806))
    | ~ sP309(U_3797,U_3802,U_3804,U_3806) ),
    inference(clausify,[status(thm)],[f_1091_5]) ).

cnf(f_1091_9,plain,
    ( hBOOL(hAPP(U_3802,U_3797))
    | U_3804 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3806),U_3797)
    | ~ sP309(U_3797,U_3802,U_3804,U_3806) ),
    inference(clausify,[status(thm)],[f_1091_5]) ).

cnf(f_1091_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3805),U_3807))
    | ~ sP310(U_3807,U_3803,U_3805) ),
    inference(clausify,[status(thm)],[f_1091_5]) ).

cnf(f_1091_11,plain,
    ( ~ hBOOL(hAPP(U_3803,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP310(U_3807,U_3803,U_3805) ),
    inference(clausify,[status(thm)],[f_1091_5]) ).

cnf(f_1091_12,plain,
    ( U_3805 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3807),sK63(U_3807,U_3805,U_3803))
    | ~ sP311(U_3807,U_3803,U_3805) ),
    inference(clausify,[status(thm)],[f_1091_5]) ).

cnf(f_1091_13,plain,
    ( ~ hBOOL(hAPP(U_3803,sK63(U_3807,U_3805,U_3803)))
    | ~ sP311(U_3807,U_3803,U_3805) ),
    inference(clausify,[status(thm)],[f_1091_5]) ).

fof(f_1092_1,plain,
    ! [V_b_2,V_a_2,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2)))
        | ? [B_d] :
            ( ~ hBOOL(hAPP(V_Pa_2,B_d))
            & V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
        | ( ~ hBOOL(hAPP(V_Pa_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_Pa_2,B_d))
              | V_a_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) )
          & ( hBOOL(hAPP(V_Pa_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_Pa_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_1092_2,plain,
    ! [U_3812,U_3811,U_3810] :
      ( ( hBOOL(hAPP(U_3810,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3811),U_3812)))
        | ? [U_3809] :
            ( ~ hBOOL(hAPP(U_3810,U_3809))
            & U_3811 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3812),U_3809) )
        | ( ~ hBOOL(hAPP(U_3810,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3811),U_3812)) ) )
      & ( ( ! [U_3808] :
              ( hBOOL(hAPP(U_3810,U_3808))
              | U_3811 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3812),U_3808) )
          & ( hBOOL(hAPP(U_3810,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3811),U_3812)) ) )
        | ~ hBOOL(hAPP(U_3810,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3811),U_3812))) ) ),
    inference(variable_rename,[status(thm)],[f_1092_1]) ).

fof(f_1092_3,plain,
    ( ! [U_3818,U_3816,U_3814] :
        ( hBOOL(hAPP(U_3814,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3816),U_3818)))
        | ? [U_3809] :
            ( ~ hBOOL(hAPP(U_3814,U_3809))
            & U_3816 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3818),U_3809) )
        | ( ~ hBOOL(hAPP(U_3814,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3816),U_3818)) ) )
    & ! [U_3817,U_3815,U_3813] :
        ( ( ! [U_3808] :
              ( hBOOL(hAPP(U_3813,U_3808))
              | U_3815 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3817),U_3808) )
          & ( hBOOL(hAPP(U_3813,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3815),U_3817)) ) )
        | ~ hBOOL(hAPP(U_3813,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3815),U_3817))) ) ),
    inference(miniscope,[status(thm)],[f_1092_2]) ).

fof(f_1092_4,plain,
    ( ! [U_3818,U_3816,U_3814] :
        ( hBOOL(hAPP(U_3814,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3816),U_3818)))
        | ( ~ hBOOL(hAPP(U_3814,sK64(U_3818,U_3816,U_3814)))
          & U_3816 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3818),sK64(U_3818,U_3816,U_3814)) )
        | ( ~ hBOOL(hAPP(U_3814,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3816),U_3818)) ) )
    & ! [U_3817,U_3815,U_3813] :
        ( ( ! [U_3808] :
              ( hBOOL(hAPP(U_3813,U_3808))
              | U_3815 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3817),U_3808) )
          & ( hBOOL(hAPP(U_3813,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3815),U_3817)) ) )
        | ~ hBOOL(hAPP(U_3813,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3815),U_3817))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK64]),skolemize(U_3809,sK64(U_3818,U_3816,U_3814))],[f_1092_3]) ).

fof(f_1092_5,plain,
    ( ! [U_3816,U_3814,U_3818] :
        ( ~ hBOOL(hAPP(U_3814,sK64(U_3818,U_3816,U_3814)))
        | ~ sP314(U_3816,U_3814,U_3818) )
    & ! [U_3816,U_3814,U_3818] :
        ( U_3816 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3818),sK64(U_3818,U_3816,U_3814))
        | ~ sP314(U_3816,U_3814,U_3818) )
    & ! [U_3816,U_3814,U_3818] :
        ( ~ hBOOL(hAPP(U_3814,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP313(U_3816,U_3814,U_3818) )
    & ! [U_3816,U_3814,U_3818] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3816),U_3818))
        | ~ sP313(U_3816,U_3814,U_3818) )
    & ! [U_3815,U_3808,U_3813,U_3817] :
        ( hBOOL(hAPP(U_3813,U_3808))
        | U_3815 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3817),U_3808)
        | ~ sP312(U_3815,U_3808,U_3813,U_3817) )
    & ! [U_3815,U_3808,U_3813,U_3817] :
        ( hBOOL(hAPP(U_3813,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3815),U_3817))
        | ~ sP312(U_3815,U_3808,U_3813,U_3817) )
    & ! [U_3816,U_3814,U_3818] :
        ( hBOOL(hAPP(U_3814,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3816),U_3818)))
        | sP314(U_3816,U_3814,U_3818)
        | sP313(U_3816,U_3814,U_3818) )
    & ! [U_3815,U_3808,U_3813,U_3817] :
        ( sP312(U_3815,U_3808,U_3813,U_3817)
        | ~ hBOOL(hAPP(U_3813,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3815),U_3817))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP312,sP313,sP314])],[f_1092_4]) ).

cnf(f_1092_6,plain,
    ( sP312(U_3815,U_3808,U_3813,U_3817)
    | ~ hBOOL(hAPP(U_3813,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3815),U_3817))) ),
    inference(clausify,[status(thm)],[f_1092_5]) ).

cnf(f_1092_7,plain,
    ( hBOOL(hAPP(U_3814,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3816),U_3818)))
    | sP314(U_3816,U_3814,U_3818)
    | sP313(U_3816,U_3814,U_3818) ),
    inference(clausify,[status(thm)],[f_1092_5]) ).

cnf(f_1092_8,plain,
    ( hBOOL(hAPP(U_3813,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3815),U_3817))
    | ~ sP312(U_3815,U_3808,U_3813,U_3817) ),
    inference(clausify,[status(thm)],[f_1092_5]) ).

cnf(f_1092_9,plain,
    ( hBOOL(hAPP(U_3813,U_3808))
    | U_3815 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3817),U_3808)
    | ~ sP312(U_3815,U_3808,U_3813,U_3817) ),
    inference(clausify,[status(thm)],[f_1092_5]) ).

cnf(f_1092_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3816),U_3818))
    | ~ sP313(U_3816,U_3814,U_3818) ),
    inference(clausify,[status(thm)],[f_1092_5]) ).

cnf(f_1092_11,plain,
    ( ~ hBOOL(hAPP(U_3814,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP313(U_3816,U_3814,U_3818) ),
    inference(clausify,[status(thm)],[f_1092_5]) ).

cnf(f_1092_12,plain,
    ( U_3816 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3818),sK64(U_3818,U_3816,U_3814))
    | ~ sP314(U_3816,U_3814,U_3818) ),
    inference(clausify,[status(thm)],[f_1092_5]) ).

cnf(f_1092_13,plain,
    ( ~ hBOOL(hAPP(U_3814,sK64(U_3818,U_3816,U_3814)))
    | ~ sP314(U_3816,U_3814,U_3818) ),
    inference(clausify,[status(thm)],[f_1092_5]) ).

fof(f_1093_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_1093_2,plain,
    ! [U_3820,U_3819] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3819),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3820),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3819),U_3820)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3819),U_3820))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3819),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3820),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(variable_rename,[status(thm)],[f_1093_1]) ).

fof(f_1093_3,plain,
    ( ! [U_3824,U_3822] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3822),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3824),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3822),U_3824)) )
    & ! [U_3823,U_3821] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3821),U_3823))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3821),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3823),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(miniscope,[status(thm)],[f_1093_2]) ).

fof(f_1093_4,plain,
    ( ! [U_3822,U_3824] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3822),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3824),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3822),U_3824)) )
    & ! [U_3821,U_3823] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3821),U_3823))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3821),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3823),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1093_3]) ).

cnf(f_1093_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3821),U_3823))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3821),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3823),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ),
    inference(clausify,[status(thm)],[f_1093_4]) ).

cnf(f_1093_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3822),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3824),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3822),U_3824)) ),
    inference(clausify,[status(thm)],[f_1093_4]) ).

fof(f_1094_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_1094_2,plain,
    ! [U_3827,U_3826,U_3825] :
      ( 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_3826),U_3825))),U_3827) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3826)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3825),U_3827))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3825),U_3826)) ),
    inference(variable_rename,[status(thm)],[f_1094_1]) ).

fof(f_1094_3,plain,
    ! [U_3826,U_3825,U_3827] :
      ( 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_3826),U_3825))),U_3827) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3826)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3825),U_3827))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3825),U_3826)) ),
    inference(definitional_conversion,[status(esa)],[f_1094_2]) ).

cnf(f_1094_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_3826),U_3825))),U_3827) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_3826)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3825),U_3827))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3825),U_3826)) ),
    inference(clausify,[status(thm)],[f_1094_3]) ).

fof(f_1095_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_1095_2,plain,
    ! [U_3830,U_3829,U_3828] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3830),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3829),U_3828))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3830),U_3828)),hAPP(c_Nat_OSuc,U_3829))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3828),U_3829)) ),
    inference(variable_rename,[status(thm)],[f_1095_1]) ).

fof(f_1095_3,plain,
    ! [U_3828,U_3829,U_3830] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3830),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3829),U_3828))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3830),U_3828)),hAPP(c_Nat_OSuc,U_3829))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3828),U_3829)) ),
    inference(definitional_conversion,[status(esa)],[f_1095_2]) ).

cnf(f_1095_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3830),hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3829),U_3828))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3830),U_3828)),hAPP(c_Nat_OSuc,U_3829))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3828),U_3829)) ),
    inference(clausify,[status(thm)],[f_1095_3]) ).

fof(f_1096_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_1096_2,plain,
    ! [U_3835,U_3834,U_3833,U_3832,U_3831] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3831),U_3833)),U_3834) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3832),U_3833)),U_3835)
          | U_3834 != 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_3832),U_3831)),U_3833)),U_3835) )
        & ( U_3834 = 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_3832),U_3831)),U_3833)),U_3835)
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3831),U_3833)),U_3834) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3832),U_3833)),U_3835) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3831),U_3832)) ),
    inference(variable_rename,[status(thm)],[f_1096_1]) ).

fof(f_1096_3,plain,
    ( ! [U_3831,U_3832,U_3833,U_3834,U_3835] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3831),U_3833)),U_3834) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3832),U_3833)),U_3835)
        | U_3834 != 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_3832),U_3831)),U_3833)),U_3835)
        | ~ sP315(U_3831,U_3832,U_3833,U_3834,U_3835) )
    & ! [U_3831,U_3832,U_3833,U_3834,U_3835] :
        ( U_3834 = 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_3832),U_3831)),U_3833)),U_3835)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3831),U_3833)),U_3834) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3832),U_3833)),U_3835)
        | ~ sP315(U_3831,U_3832,U_3833,U_3834,U_3835) )
    & ! [U_3831,U_3832,U_3833,U_3834,U_3835] :
        ( sP315(U_3831,U_3832,U_3833,U_3834,U_3835)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3831),U_3832)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP315])],[f_1096_2]) ).

cnf(f_1096_4,plain,
    ( sP315(U_3831,U_3832,U_3833,U_3834,U_3835)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3831),U_3832)) ),
    inference(clausify,[status(thm)],[f_1096_3]) ).

cnf(f_1096_5,plain,
    ( U_3834 = 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_3832),U_3831)),U_3833)),U_3835)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3831),U_3833)),U_3834) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3832),U_3833)),U_3835)
    | ~ sP315(U_3831,U_3832,U_3833,U_3834,U_3835) ),
    inference(clausify,[status(thm)],[f_1096_3]) ).

cnf(f_1096_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3831),U_3833)),U_3834) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3832),U_3833)),U_3835)
    | U_3834 != 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_3832),U_3831)),U_3833)),U_3835)
    | ~ sP315(U_3831,U_3832,U_3833,U_3834,U_3835) ),
    inference(clausify,[status(thm)],[f_1096_3]) ).

fof(f_1097_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_1097_2,plain,
    ! [U_3840,U_3839,U_3838,U_3837,U_3836] :
      ( 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_3836),U_3838)),U_3839)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3837),U_3838)),U_3840)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3839),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_3837),U_3836)),U_3838)),U_3840))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3836),U_3837)) ),
    inference(variable_rename,[status(thm)],[f_1097_1]) ).

fof(f_1097_3,plain,
    ! [U_3837,U_3838,U_3836,U_3839,U_3840] :
      ( 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_3836),U_3838)),U_3839)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3837),U_3838)),U_3840)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3839),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_3837),U_3836)),U_3838)),U_3840))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3836),U_3837)) ),
    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),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3836),U_3838)),U_3839)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3837),U_3838)),U_3840)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3839),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_3837),U_3836)),U_3838)),U_3840))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3836),U_3837)) ),
    inference(clausify,[status(thm)],[f_1097_3]) ).

fof(f_1098_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_1098_2,plain,
    ! [U_3845,U_3844,U_3843,U_3842,U_3841] :
      ( ( ( 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_3841),U_3843)),U_3844)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3842),U_3843)),U_3845)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3844),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_3842),U_3841)),U_3843)),U_3845))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3844),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_3842),U_3841)),U_3843)),U_3845)))
          | ~ 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_3841),U_3843)),U_3844)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3842),U_3843)),U_3845))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3841),U_3842)) ),
    inference(variable_rename,[status(thm)],[f_1098_1]) ).

fof(f_1098_3,plain,
    ( ! [U_3841,U_3842,U_3843,U_3844,U_3845] :
        ( 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_3841),U_3843)),U_3844)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3842),U_3843)),U_3845)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3844),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_3842),U_3841)),U_3843)),U_3845)))
        | ~ sP316(U_3841,U_3842,U_3843,U_3844,U_3845) )
    & ! [U_3841,U_3842,U_3843,U_3844,U_3845] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3844),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_3842),U_3841)),U_3843)),U_3845)))
        | ~ 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_3841),U_3843)),U_3844)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3842),U_3843)),U_3845)))
        | ~ sP316(U_3841,U_3842,U_3843,U_3844,U_3845) )
    & ! [U_3841,U_3842,U_3843,U_3844,U_3845] :
        ( sP316(U_3841,U_3842,U_3843,U_3844,U_3845)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3841),U_3842)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP316])],[f_1098_2]) ).

cnf(f_1098_4,plain,
    ( sP316(U_3841,U_3842,U_3843,U_3844,U_3845)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3841),U_3842)) ),
    inference(clausify,[status(thm)],[f_1098_3]) ).

cnf(f_1098_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3844),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_3842),U_3841)),U_3843)),U_3845)))
    | ~ 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_3841),U_3843)),U_3844)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3842),U_3843)),U_3845)))
    | ~ sP316(U_3841,U_3842,U_3843,U_3844,U_3845) ),
    inference(clausify,[status(thm)],[f_1098_3]) ).

cnf(f_1098_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_3841),U_3843)),U_3844)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3842),U_3843)),U_3845)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3844),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_3842),U_3841)),U_3843)),U_3845)))
    | ~ sP316(U_3841,U_3842,U_3843,U_3844,U_3845) ),
    inference(clausify,[status(thm)],[f_1098_3]) ).

fof(f_1099_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_1099_2,plain,
    ! [U_3850,U_3849,U_3848,U_3847,U_3846] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3847),U_3848)),U_3849) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3846),U_3848)),U_3850)
          | 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_3847),U_3846)),U_3848)),U_3849) != U_3850 )
        & ( 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_3847),U_3846)),U_3848)),U_3849) = U_3850
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3847),U_3848)),U_3849) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3846),U_3848)),U_3850) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3846),U_3847)) ),
    inference(variable_rename,[status(thm)],[f_1099_1]) ).

fof(f_1099_3,plain,
    ( ! [U_3847,U_3848,U_3846,U_3850,U_3849] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3847),U_3848)),U_3849) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3846),U_3848)),U_3850)
        | 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_3847),U_3846)),U_3848)),U_3849) != U_3850
        | ~ sP317(U_3847,U_3848,U_3846,U_3850,U_3849) )
    & ! [U_3847,U_3848,U_3846,U_3850,U_3849] :
        ( 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_3847),U_3846)),U_3848)),U_3849) = U_3850
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3847),U_3848)),U_3849) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3846),U_3848)),U_3850)
        | ~ sP317(U_3847,U_3848,U_3846,U_3850,U_3849) )
    & ! [U_3847,U_3848,U_3846,U_3850,U_3849] :
        ( sP317(U_3847,U_3848,U_3846,U_3850,U_3849)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3846),U_3847)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP317])],[f_1099_2]) ).

cnf(f_1099_4,plain,
    ( sP317(U_3847,U_3848,U_3846,U_3850,U_3849)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3846),U_3847)) ),
    inference(clausify,[status(thm)],[f_1099_3]) ).

cnf(f_1099_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_3847),U_3846)),U_3848)),U_3849) = U_3850
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3847),U_3848)),U_3849) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3846),U_3848)),U_3850)
    | ~ sP317(U_3847,U_3848,U_3846,U_3850,U_3849) ),
    inference(clausify,[status(thm)],[f_1099_3]) ).

cnf(f_1099_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3847),U_3848)),U_3849) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3846),U_3848)),U_3850)
    | 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_3847),U_3846)),U_3848)),U_3849) != U_3850
    | ~ sP317(U_3847,U_3848,U_3846,U_3850,U_3849) ),
    inference(clausify,[status(thm)],[f_1099_3]) ).

fof(f_1100_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_1100_2,plain,
    ! [U_3855,U_3854,U_3853,U_3852,U_3851] :
      ( 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_3852),U_3853)),U_3854)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3851),U_3853)),U_3855)) = 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_3852),U_3851)),U_3853)),U_3854)),U_3855)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3851),U_3852)) ),
    inference(variable_rename,[status(thm)],[f_1100_1]) ).

fof(f_1100_3,plain,
    ! [U_3852,U_3851,U_3853,U_3854,U_3855] :
      ( 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_3852),U_3853)),U_3854)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3851),U_3853)),U_3855)) = 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_3852),U_3851)),U_3853)),U_3854)),U_3855)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3851),U_3852)) ),
    inference(definitional_conversion,[status(esa)],[f_1100_2]) ).

cnf(f_1100_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_3852),U_3853)),U_3854)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3851),U_3853)),U_3855)) = 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_3852),U_3851)),U_3853)),U_3854)),U_3855)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3851),U_3852)) ),
    inference(clausify,[status(thm)],[f_1100_3]) ).

fof(f_1101_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_1101_2,plain,
    ! [U_3860,U_3859,U_3858,U_3857,U_3856] :
      ( ( ( 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_3857),U_3858)),U_3859)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3856),U_3858)),U_3860)))
          | ~ 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_3857),U_3856)),U_3858)),U_3859)),U_3860)) )
        & ( 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_3857),U_3856)),U_3858)),U_3859)),U_3860))
          | ~ 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_3857),U_3858)),U_3859)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3856),U_3858)),U_3860))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3856),U_3857)) ),
    inference(variable_rename,[status(thm)],[f_1101_1]) ).

fof(f_1101_3,plain,
    ( ! [U_3856,U_3857,U_3858,U_3859,U_3860] :
        ( 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_3857),U_3858)),U_3859)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3856),U_3858)),U_3860)))
        | ~ 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_3857),U_3856)),U_3858)),U_3859)),U_3860))
        | ~ sP318(U_3856,U_3857,U_3858,U_3859,U_3860) )
    & ! [U_3856,U_3857,U_3858,U_3859,U_3860] :
        ( 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_3857),U_3856)),U_3858)),U_3859)),U_3860))
        | ~ 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_3857),U_3858)),U_3859)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3856),U_3858)),U_3860)))
        | ~ sP318(U_3856,U_3857,U_3858,U_3859,U_3860) )
    & ! [U_3856,U_3857,U_3858,U_3859,U_3860] :
        ( sP318(U_3856,U_3857,U_3858,U_3859,U_3860)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3856),U_3857)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP318])],[f_1101_2]) ).

cnf(f_1101_4,plain,
    ( sP318(U_3856,U_3857,U_3858,U_3859,U_3860)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3856),U_3857)) ),
    inference(clausify,[status(thm)],[f_1101_3]) ).

cnf(f_1101_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_3857),U_3856)),U_3858)),U_3859)),U_3860))
    | ~ 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_3857),U_3858)),U_3859)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3856),U_3858)),U_3860)))
    | ~ sP318(U_3856,U_3857,U_3858,U_3859,U_3860) ),
    inference(clausify,[status(thm)],[f_1101_3]) ).

cnf(f_1101_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_3857),U_3858)),U_3859)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3856),U_3858)),U_3860)))
    | ~ 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_3857),U_3856)),U_3858)),U_3859)),U_3860))
    | ~ sP318(U_3856,U_3857,U_3858,U_3859,U_3860) ),
    inference(clausify,[status(thm)],[f_1101_3]) ).

fof(f_1102_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_1102_2,plain,
    ! [U_3862,U_3861] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3861,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3862)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3861,U_3862)),U_3862)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3861,U_3862) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3861,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3862)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3861,U_3862) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1102_1]) ).

fof(f_1102_3,plain,
    ( ! [U_3866,U_3864] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3864,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3866)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3864,U_3866)),U_3866)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3864,U_3866) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_3865,U_3863] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3863,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3865)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3863,U_3865) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1102_2]) ).

fof(f_1102_4,plain,
    ( ! [U_3864,U_3866] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3864,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3866)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3864,U_3866)),U_3866)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3864,U_3866) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_3865,U_3863] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3863,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3865)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3863,U_3865) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa)],[f_1102_3]) ).

cnf(f_1102_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3863,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3865)) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3863,U_3865) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1102_4]) ).

cnf(f_1102_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3864,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3866)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3864,U_3866)),U_3866)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3864,U_3866) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1102_4]) ).

fof(f_1103_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_1103_2,plain,
    ! [U_3868,U_3867] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3867),U_3868) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3868),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3867,U_3868))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3867,U_3868) = 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_3867),U_3868) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3867,U_3868) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1103_1]) ).

fof(f_1103_3,plain,
    ( ! [U_3872,U_3870] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3870),U_3872) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3872),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3870,U_3872))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3870,U_3872) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_3871,U_3869] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3869),U_3871) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3869,U_3871) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1103_2]) ).

fof(f_1103_4,plain,
    ( ! [U_3872,U_3870] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3870),U_3872) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3872),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3870,U_3872))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3870,U_3872) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_3869,U_3871] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3869),U_3871) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3869,U_3871) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa)],[f_1103_3]) ).

cnf(f_1103_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3869),U_3871) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3869,U_3871) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1103_4]) ).

cnf(f_1103_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_3870),U_3872) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3872),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3870,U_3872))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3870,U_3872) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1103_4]) ).

fof(f_1104_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_1104_2,plain,
    ! [U_3874,U_3873] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3873,U_3874) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3873),U_3874)),U_3874)),
    inference(variable_rename,[status(thm)],[f_1104_1]) ).

fof(f_1104_3,plain,
    ! [U_3874,U_3873] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3873,U_3874) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3873),U_3874)),U_3874)),
    inference(definitional_conversion,[status(esa)],[f_1104_2]) ).

cnf(f_1104_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3873,U_3874) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3873),U_3874)),U_3874)),
    inference(clausify,[status(thm)],[f_1104_3]) ).

fof(f_1105_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_1105_2,plain,
    ! [U_3876,U_3875] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3875),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3876),U_3875)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3876),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3876,U_3875)),
    inference(variable_rename,[status(thm)],[f_1105_1]) ).

fof(f_1105_3,plain,
    ! [U_3875,U_3876] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3875),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3876),U_3875)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3876),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3876,U_3875)),
    inference(definitional_conversion,[status(esa)],[f_1105_2]) ).

cnf(f_1105_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3875),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3876),U_3875)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3876),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_3876,U_3875)),
    inference(clausify,[status(thm)],[f_1105_3]) ).

fof(f_1106_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_1106_2,plain,
    ! [U_3878,U_3877] :
      ( ( c_Nat__Transfer_Otsub(U_3878,U_3877) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3877),U_3878)) )
      & ( c_Nat__Transfer_Otsub(U_3878,U_3877) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3878),U_3877)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3877),U_3878)) ) ),
    inference(variable_rename,[status(thm)],[f_1106_1]) ).

fof(f_1106_3,plain,
    ( ! [U_3882,U_3880] :
        ( c_Nat__Transfer_Otsub(U_3882,U_3880) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3880),U_3882)) )
    & ! [U_3881,U_3879] :
        ( c_Nat__Transfer_Otsub(U_3881,U_3879) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3881),U_3879)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3879),U_3881)) ) ),
    inference(miniscope,[status(thm)],[f_1106_2]) ).

fof(f_1106_4,plain,
    ( ! [U_3880,U_3882] :
        ( c_Nat__Transfer_Otsub(U_3882,U_3880) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3880),U_3882)) )
    & ! [U_3881,U_3879] :
        ( c_Nat__Transfer_Otsub(U_3881,U_3879) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3881),U_3879)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3879),U_3881)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1106_3]) ).

cnf(f_1106_5,plain,
    ( c_Nat__Transfer_Otsub(U_3881,U_3879) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3881),U_3879)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3879),U_3881)) ),
    inference(clausify,[status(thm)],[f_1106_4]) ).

cnf(f_1106_6,plain,
    ( c_Nat__Transfer_Otsub(U_3882,U_3880) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_3880),U_3882)) ),
    inference(clausify,[status(thm)],[f_1106_4]) ).

fof(f_1107_1,plain,
    ! [V_k_2,V_n_2,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2)))
        | ( ? [B_i,B_j] :
              ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(V_Pa_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_1107_2,plain,
    ! [U_3889,U_3888,U_3887] :
      ( ( hBOOL(hAPP(U_3887,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3888),U_3889)))
        | ( ? [U_3886,U_3885] :
              ( ~ hBOOL(hAPP(U_3887,U_3886))
              & U_3888 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3889),U_3886)),U_3885)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3885),U_3889)) )
          & U_3889 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3887,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3889 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( ( ( ! [U_3884,U_3883] :
                ( hBOOL(hAPP(U_3887,U_3884))
                | U_3888 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3889),U_3884)),U_3883)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3883),U_3889)) )
            | U_3889 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3887,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3889 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3887,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3888),U_3889))) ) ),
    inference(variable_rename,[status(thm)],[f_1107_1]) ).

fof(f_1107_3,plain,
    ( ! [U_3895,U_3893,U_3891] :
        ( hBOOL(hAPP(U_3891,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3893),U_3895)))
        | ( ? [U_3886,U_3885] :
              ( ~ hBOOL(hAPP(U_3891,U_3886))
              & U_3893 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3895),U_3886)),U_3885)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3885),U_3895)) )
          & U_3895 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3891,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3895 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3894,U_3892,U_3890] :
        ( ( ( ! [U_3884,U_3883] :
                ( hBOOL(hAPP(U_3890,U_3884))
                | U_3892 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3894),U_3884)),U_3883)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3883),U_3894)) )
            | U_3894 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3890,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3894 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3890,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3892),U_3894))) ) ),
    inference(miniscope,[status(thm)],[f_1107_2]) ).

fof(f_1107_4,plain,
    ( ! [U_3895,U_3893,U_3891] :
        ( hBOOL(hAPP(U_3891,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3893),U_3895)))
        | ( ? [U_3885] :
              ( ~ hBOOL(hAPP(U_3891,sK65(U_3895,U_3893,U_3891)))
              & U_3893 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3895),sK65(U_3895,U_3893,U_3891))),U_3885)
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3885),U_3895)) )
          & U_3895 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3891,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3895 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3894,U_3892,U_3890] :
        ( ( ( ! [U_3884,U_3883] :
                ( hBOOL(hAPP(U_3890,U_3884))
                | U_3892 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3894),U_3884)),U_3883)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3883),U_3894)) )
            | U_3894 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3890,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3894 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3890,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3892),U_3894))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK65]),skolemize(U_3886,sK65(U_3895,U_3893,U_3891))],[f_1107_3]) ).

fof(f_1107_5,plain,
    ( ! [U_3895,U_3893,U_3891] :
        ( hBOOL(hAPP(U_3891,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3893),U_3895)))
        | ( ~ hBOOL(hAPP(U_3891,sK65(U_3895,U_3893,U_3891)))
          & U_3893 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3895),sK65(U_3895,U_3893,U_3891))),sK66(U_3895,U_3893,U_3891))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK66(U_3895,U_3893,U_3891)),U_3895))
          & U_3895 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( ~ hBOOL(hAPP(U_3891,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          & U_3895 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_3894,U_3892,U_3890] :
        ( ( ( ! [U_3884,U_3883] :
                ( hBOOL(hAPP(U_3890,U_3884))
                | U_3892 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3894),U_3884)),U_3883)
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3883),U_3894)) )
            | U_3894 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hBOOL(hAPP(U_3890,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
            | U_3894 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
        | ~ hBOOL(hAPP(U_3890,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3892),U_3894))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK66]),skolemize(U_3885,sK66(U_3895,U_3893,U_3891))],[f_1107_4]) ).

fof(f_1107_6,plain,
    ( ! [U_3891,U_3893,U_3895] :
        ( ~ hBOOL(hAPP(U_3891,sK65(U_3895,U_3893,U_3891)))
        | ~ sP321(U_3891,U_3893,U_3895) )
    & ! [U_3891,U_3893,U_3895] :
        ( U_3893 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3895),sK65(U_3895,U_3893,U_3891))),sK66(U_3895,U_3893,U_3891))
        | ~ sP321(U_3891,U_3893,U_3895) )
    & ! [U_3891,U_3893,U_3895] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK66(U_3895,U_3893,U_3891)),U_3895))
        | ~ sP321(U_3891,U_3893,U_3895) )
    & ! [U_3891,U_3893,U_3895] :
        ( U_3895 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP321(U_3891,U_3893,U_3895) )
    & ! [U_3891,U_3895] :
        ( ~ hBOOL(hAPP(U_3891,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP320(U_3891,U_3895) )
    & ! [U_3891,U_3895] :
        ( U_3895 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP320(U_3891,U_3895) )
    & ! [U_3884,U_3883,U_3890,U_3892,U_3894] :
        ( hBOOL(hAPP(U_3890,U_3884))
        | U_3892 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3894),U_3884)),U_3883)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3883),U_3894))
        | U_3894 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP319(U_3884,U_3883,U_3890,U_3892,U_3894) )
    & ! [U_3884,U_3883,U_3890,U_3892,U_3894] :
        ( hBOOL(hAPP(U_3890,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_3894 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP319(U_3884,U_3883,U_3890,U_3892,U_3894) )
    & ! [U_3891,U_3893,U_3895] :
        ( hBOOL(hAPP(U_3891,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3893),U_3895)))
        | sP321(U_3891,U_3893,U_3895)
        | sP320(U_3891,U_3895) )
    & ! [U_3884,U_3883,U_3890,U_3892,U_3894] :
        ( sP319(U_3884,U_3883,U_3890,U_3892,U_3894)
        | ~ hBOOL(hAPP(U_3890,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3892),U_3894))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP319,sP320,sP321])],[f_1107_5]) ).

cnf(f_1107_7,plain,
    ( sP319(U_3884,U_3883,U_3890,U_3892,U_3894)
    | ~ hBOOL(hAPP(U_3890,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3892),U_3894))) ),
    inference(clausify,[status(thm)],[f_1107_6]) ).

cnf(f_1107_8,plain,
    ( hBOOL(hAPP(U_3891,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_3893),U_3895)))
    | sP321(U_3891,U_3893,U_3895)
    | sP320(U_3891,U_3895) ),
    inference(clausify,[status(thm)],[f_1107_6]) ).

cnf(f_1107_9,plain,
    ( hBOOL(hAPP(U_3890,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_3894 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP319(U_3884,U_3883,U_3890,U_3892,U_3894) ),
    inference(clausify,[status(thm)],[f_1107_6]) ).

cnf(f_1107_10,plain,
    ( hBOOL(hAPP(U_3890,U_3884))
    | U_3892 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3894),U_3884)),U_3883)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3883),U_3894))
    | U_3894 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP319(U_3884,U_3883,U_3890,U_3892,U_3894) ),
    inference(clausify,[status(thm)],[f_1107_6]) ).

cnf(f_1107_11,plain,
    ( U_3895 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP320(U_3891,U_3895) ),
    inference(clausify,[status(thm)],[f_1107_6]) ).

cnf(f_1107_12,plain,
    ( ~ hBOOL(hAPP(U_3891,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP320(U_3891,U_3895) ),
    inference(clausify,[status(thm)],[f_1107_6]) ).

cnf(f_1107_13,plain,
    ( U_3895 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP321(U_3891,U_3893,U_3895) ),
    inference(clausify,[status(thm)],[f_1107_6]) ).

cnf(f_1107_14,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK66(U_3895,U_3893,U_3891)),U_3895))
    | ~ sP321(U_3891,U_3893,U_3895) ),
    inference(clausify,[status(thm)],[f_1107_6]) ).

cnf(f_1107_15,plain,
    ( U_3893 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3895),sK65(U_3895,U_3893,U_3891))),sK66(U_3895,U_3893,U_3891))
    | ~ sP321(U_3891,U_3893,U_3895) ),
    inference(clausify,[status(thm)],[f_1107_6]) ).

cnf(f_1107_16,plain,
    ( ~ hBOOL(hAPP(U_3891,sK65(U_3895,U_3893,U_3891)))
    | ~ sP321(U_3891,U_3893,U_3895) ),
    inference(clausify,[status(thm)],[f_1107_6]) ).

fof(f_1108_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_1108_2,plain,
    ! [U_3897,U_3896] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3896),U_3897)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3896)),hAPP(c_Int_Onat,U_3897))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3896)) ),
    inference(variable_rename,[status(thm)],[f_1108_1]) ).

fof(f_1108_3,plain,
    ! [U_3896,U_3897] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3896),U_3897)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3896)),hAPP(c_Int_Onat,U_3897))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3896)) ),
    inference(definitional_conversion,[status(esa)],[f_1108_2]) ).

cnf(f_1108_4,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3896),U_3897)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3896)),hAPP(c_Int_Onat,U_3897))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3896)) ),
    inference(clausify,[status(thm)],[f_1108_3]) ).

fof(f_1109_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_1109_2,plain,
    ! [U_3899,U_3898] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3898)),hAPP(c_Int_Onat,U_3899)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3898),U_3899))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3899))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3898)) ),
    inference(variable_rename,[status(thm)],[f_1109_1]) ).

fof(f_1109_3,plain,
    ! [U_3898,U_3899] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3898)),hAPP(c_Int_Onat,U_3899)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3898),U_3899))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3899))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3898)) ),
    inference(definitional_conversion,[status(esa)],[f_1109_2]) ).

cnf(f_1109_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onat,U_3898)),hAPP(c_Int_Onat,U_3899)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_3898),U_3899))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3899))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3898)) ),
    inference(clausify,[status(thm)],[f_1109_3]) ).

fof(f_1110_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_1110_2,plain,
    ! [U_3900] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3900),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_3900
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3900)) ),
    inference(variable_rename,[status(thm)],[f_1110_1]) ).

fof(f_1110_3,plain,
    ! [U_3900] :
      ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3900),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_3900
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3900)) ),
    inference(definitional_conversion,[status(esa)],[f_1110_2]) ).

cnf(f_1110_4,plain,
    ( hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3900),c_Groups_Oone__class_Oone(tc_Nat_Onat))) = U_3900
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3900)) ),
    inference(clausify,[status(thm)],[f_1110_3]) ).

fof(f_1111_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_1111_2,plain,
    ! [U_3901] :
      ( U_3901 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3901),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_3901)) ),
    inference(variable_rename,[status(thm)],[f_1111_1]) ).

fof(f_1111_3,plain,
    ! [U_3901] :
      ( U_3901 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3901),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_3901)) ),
    inference(definitional_conversion,[status(esa)],[f_1111_2]) ).

cnf(f_1111_4,plain,
    ( U_3901 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3901),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_3901)) ),
    inference(clausify,[status(thm)],[f_1111_3]) ).

fof(f_1112_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_1112_2,plain,
    ! [U_3906,U_3905,U_3904,U_3903,U_3902] :
      ( ( ( 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_3902),U_3904)),U_3905)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3903),U_3904)),U_3906)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3905),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_3903),U_3902)),U_3904)),U_3906))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3905),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_3903),U_3902)),U_3904)),U_3906)))
          | ~ 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_3902),U_3904)),U_3905)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3903),U_3904)),U_3906))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3902),U_3903)) ),
    inference(variable_rename,[status(thm)],[f_1112_1]) ).

fof(f_1112_3,plain,
    ( ! [U_3902,U_3903,U_3904,U_3905,U_3906] :
        ( 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_3902),U_3904)),U_3905)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3903),U_3904)),U_3906)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3905),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_3903),U_3902)),U_3904)),U_3906)))
        | ~ sP322(U_3902,U_3903,U_3904,U_3905,U_3906) )
    & ! [U_3902,U_3903,U_3904,U_3905,U_3906] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3905),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_3903),U_3902)),U_3904)),U_3906)))
        | ~ 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_3902),U_3904)),U_3905)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3903),U_3904)),U_3906)))
        | ~ sP322(U_3902,U_3903,U_3904,U_3905,U_3906) )
    & ! [U_3902,U_3903,U_3904,U_3905,U_3906] :
        ( sP322(U_3902,U_3903,U_3904,U_3905,U_3906)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3902),U_3903)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP322])],[f_1112_2]) ).

cnf(f_1112_4,plain,
    ( sP322(U_3902,U_3903,U_3904,U_3905,U_3906)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3902),U_3903)) ),
    inference(clausify,[status(thm)],[f_1112_3]) ).

cnf(f_1112_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3905),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_3903),U_3902)),U_3904)),U_3906)))
    | ~ 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_3902),U_3904)),U_3905)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3903),U_3904)),U_3906)))
    | ~ sP322(U_3902,U_3903,U_3904,U_3905,U_3906) ),
    inference(clausify,[status(thm)],[f_1112_3]) ).

cnf(f_1112_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_3902),U_3904)),U_3905)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3903),U_3904)),U_3906)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3905),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_3903),U_3902)),U_3904)),U_3906)))
    | ~ sP322(U_3902,U_3903,U_3904,U_3905,U_3906) ),
    inference(clausify,[status(thm)],[f_1112_3]) ).

fof(f_1113_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_1113_2,plain,
    ! [U_3911,U_3910,U_3909,U_3908,U_3907] :
      ( ( ( 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_3908),U_3909)),U_3910)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3907),U_3909)),U_3911)))
          | ~ 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_3908),U_3907)),U_3909)),U_3910)),U_3911)) )
        & ( 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_3908),U_3907)),U_3909)),U_3910)),U_3911))
          | ~ 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_3908),U_3909)),U_3910)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3907),U_3909)),U_3911))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3907),U_3908)) ),
    inference(variable_rename,[status(thm)],[f_1113_1]) ).

fof(f_1113_3,plain,
    ( ! [U_3907,U_3908,U_3910,U_3909,U_3911] :
        ( 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_3908),U_3909)),U_3910)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3907),U_3909)),U_3911)))
        | ~ 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_3908),U_3907)),U_3909)),U_3910)),U_3911))
        | ~ sP323(U_3907,U_3908,U_3910,U_3909,U_3911) )
    & ! [U_3907,U_3908,U_3910,U_3909,U_3911] :
        ( 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_3908),U_3907)),U_3909)),U_3910)),U_3911))
        | ~ 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_3908),U_3909)),U_3910)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3907),U_3909)),U_3911)))
        | ~ sP323(U_3907,U_3908,U_3910,U_3909,U_3911) )
    & ! [U_3907,U_3908,U_3910,U_3909,U_3911] :
        ( sP323(U_3907,U_3908,U_3910,U_3909,U_3911)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3907),U_3908)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP323])],[f_1113_2]) ).

cnf(f_1113_4,plain,
    ( sP323(U_3907,U_3908,U_3910,U_3909,U_3911)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3907),U_3908)) ),
    inference(clausify,[status(thm)],[f_1113_3]) ).

cnf(f_1113_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_3908),U_3907)),U_3909)),U_3910)),U_3911))
    | ~ 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_3908),U_3909)),U_3910)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3907),U_3909)),U_3911)))
    | ~ sP323(U_3907,U_3908,U_3910,U_3909,U_3911) ),
    inference(clausify,[status(thm)],[f_1113_3]) ).

cnf(f_1113_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_3908),U_3909)),U_3910)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3907),U_3909)),U_3911)))
    | ~ 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_3908),U_3907)),U_3909)),U_3910)),U_3911))
    | ~ sP323(U_3907,U_3908,U_3910,U_3909,U_3911) ),
    inference(clausify,[status(thm)],[f_1113_3]) ).

fof(f_1114_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_1114_2,plain,
    ! [U_3913,U_3912] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3912),U_3913) = 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_3912),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3913))
        | U_3912 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3912),U_3913) = U_3913
        | U_3912 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1114_1]) ).

fof(f_1114_3,plain,
    ( ! [U_3917,U_3915] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3915),U_3917) = 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_3915),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3917))
        | U_3915 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3916,U_3914] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3914),U_3916) = U_3916
        | U_3914 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1114_2]) ).

fof(f_1114_4,plain,
    ( ! [U_3915,U_3917] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3915),U_3917) = 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_3915),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3917))
        | U_3915 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3916,U_3914] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3914),U_3916) = U_3916
        | U_3914 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_1114_3]) ).

cnf(f_1114_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3914),U_3916) = U_3916
    | U_3914 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1114_4]) ).

cnf(f_1114_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3915),U_3917) = 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_3915),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3917))
    | U_3915 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1114_4]) ).

fof(f_1115_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_1115_2,plain,
    ! [U_3919,U_3918] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3918),U_3919) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3919),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3918),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3919))
        | U_3918 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3918),U_3919) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3918 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1115_1]) ).

fof(f_1115_3,plain,
    ( ! [U_3923,U_3921] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3921),U_3923) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3923),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3921),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3923))
        | U_3921 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3922,U_3920] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3920),U_3922) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3920 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1115_2]) ).

fof(f_1115_4,plain,
    ( ! [U_3921,U_3923] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3921),U_3923) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3923),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3921),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3923))
        | U_3921 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_3922,U_3920] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3920),U_3922) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_3920 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_1115_3]) ).

cnf(f_1115_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3920),U_3922) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_3920 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1115_4]) ).

cnf(f_1115_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3921),U_3923) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3923),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3921),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_3923))
    | U_3921 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1115_4]) ).

fof(f_1116_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_1116_2,plain,
    ! [U_3925,U_3924] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3925),U_3924)),U_3925) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3925),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3924),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_3925))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3924)) ),
    inference(variable_rename,[status(thm)],[f_1116_1]) ).

fof(f_1116_3,plain,
    ! [U_3925,U_3924] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3925),U_3924)),U_3925) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3925),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3924),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_3925))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3924)) ),
    inference(definitional_conversion,[status(esa)],[f_1116_2]) ).

cnf(f_1116_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3925),U_3924)),U_3925) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3925),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3924),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_3925))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3924)) ),
    inference(clausify,[status(thm)],[f_1116_3]) ).

fof(f_1117_1,plain,
    ! [V_k_2,V_Pa_2,V_d_2] :
      ( ! [B_x] :
          ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2)))
          & hBOOL(hAPP(V_Pa_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_1117_2,plain,
    ! [U_3930,U_3929,U_3928] :
      ( ! [U_3927] :
          ( hBOOL(hAPP(U_3929,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3927),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3930),U_3928))))
          | ~ hBOOL(hAPP(U_3929,U_3927)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3930))
      | ? [U_3926] :
          ( ~ hBOOL(hAPP(U_3929,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3926),U_3928)))
          & hBOOL(hAPP(U_3929,U_3926)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3928)) ),
    inference(variable_rename,[status(thm)],[f_1117_1]) ).

fof(f_1117_3,plain,
    ! [U_3930,U_3929,U_3928] :
      ( ! [U_3927] :
          ( hBOOL(hAPP(U_3929,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3927),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3930),U_3928))))
          | ~ hBOOL(hAPP(U_3929,U_3927)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3930))
      | ( ~ hBOOL(hAPP(U_3929,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK67(U_3930,U_3929,U_3928)),U_3928)))
        & hBOOL(hAPP(U_3929,sK67(U_3930,U_3929,U_3928))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3928)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK67]),skolemize(U_3926,sK67(U_3930,U_3929,U_3928))],[f_1117_2]) ).

fof(f_1117_4,plain,
    ( ! [U_3928,U_3929,U_3930] :
        ( ~ hBOOL(hAPP(U_3929,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK67(U_3930,U_3929,U_3928)),U_3928)))
        | ~ sP324(U_3928,U_3929,U_3930) )
    & ! [U_3928,U_3929,U_3930] :
        ( hBOOL(hAPP(U_3929,sK67(U_3930,U_3929,U_3928)))
        | ~ sP324(U_3928,U_3929,U_3930) )
    & ! [U_3927,U_3928,U_3929,U_3930] :
        ( hBOOL(hAPP(U_3929,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3927),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3930),U_3928))))
        | ~ hBOOL(hAPP(U_3929,U_3927))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3930))
        | sP324(U_3928,U_3929,U_3930)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3928)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP324])],[f_1117_3]) ).

cnf(f_1117_5,plain,
    ( hBOOL(hAPP(U_3929,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3927),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_3930),U_3928))))
    | ~ hBOOL(hAPP(U_3929,U_3927))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3930))
    | sP324(U_3928,U_3929,U_3930)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3928)) ),
    inference(clausify,[status(thm)],[f_1117_4]) ).

cnf(f_1117_6,plain,
    ( hBOOL(hAPP(U_3929,sK67(U_3930,U_3929,U_3928)))
    | ~ sP324(U_3928,U_3929,U_3930) ),
    inference(clausify,[status(thm)],[f_1117_4]) ).

cnf(f_1117_7,plain,
    ( ~ hBOOL(hAPP(U_3929,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK67(U_3930,U_3929,U_3928)),U_3928)))
    | ~ sP324(U_3928,U_3929,U_3930) ),
    inference(clausify,[status(thm)],[f_1117_4]) ).

fof(f_1118_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_1118_2,plain,
    ! [U_3933,U_3932,U_3931] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3932),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3933),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_3933),U_3932))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_3931))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3931)) ),
    inference(variable_rename,[status(thm)],[f_1118_1]) ).

fof(f_1118_3,plain,
    ! [U_3932,U_3933,U_3931] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3932),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3933),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_3933),U_3932))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_3931))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3931)) ),
    inference(definitional_conversion,[status(esa)],[f_1118_2]) ).

cnf(f_1118_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_3932),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_3933),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_3933),U_3932))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_3931))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3931)) ),
    inference(clausify,[status(thm)],[f_1118_3]) ).

fof(f_1119_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_1119_2,plain,
    ! [U_3936,U_3935,U_3934] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3935),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_3935),U_3936))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_3934))),U_3936))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3934)) ),
    inference(variable_rename,[status(thm)],[f_1119_1]) ).

fof(f_1119_3,plain,
    ! [U_3935,U_3934,U_3936] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3935),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_3935),U_3936))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_3934))),U_3936))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3934)) ),
    inference(definitional_conversion,[status(esa)],[f_1119_2]) ).

cnf(f_1119_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_3935),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_3935),U_3936))),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_3934))),U_3936))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_3934)) ),
    inference(clausify,[status(thm)],[f_1119_3]) ).

fof(f_1120_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_1120_2,plain,
    ! [U_3940,U_3939,U_3938] :
      ( ? [U_3937] : U_3938 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3940),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3939),U_3937))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3940),U_3938))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3938,U_3939) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3940,U_3939) ),
    inference(variable_rename,[status(thm)],[f_1120_1]) ).

fof(f_1120_3,plain,
    ! [U_3940,U_3939,U_3938] :
      ( U_3938 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3940),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3939),sK68(U_3940,U_3939,U_3938)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3940),U_3938))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3938,U_3939) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3940,U_3939) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK68]),skolemize(U_3937,sK68(U_3940,U_3939,U_3938))],[f_1120_2]) ).

fof(f_1120_4,plain,
    ! [U_3938,U_3939,U_3940] :
      ( U_3938 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3940),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3939),sK68(U_3940,U_3939,U_3938)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3940),U_3938))
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3938,U_3939) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3940,U_3939) ),
    inference(definitional_conversion,[status(esa)],[f_1120_3]) ).

cnf(f_1120_5,plain,
    ( U_3938 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_3940),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_3939),sK68(U_3940,U_3939,U_3938)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3940),U_3938))
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3938,U_3939) != c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_3940,U_3939) ),
    inference(clausify,[status(thm)],[f_1120_4]) ).

fof(f_1121_1,plain,
    ! [V_i_2,V_Pa_2,V_p_2] :
      ( hBOOL(hAPP(V_Pa_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_Pa_2,V_i_2))
      | ? [B_i] :
          ( ~ hBOOL(hAPP(V_Pa_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2)))
          & hBOOL(hAPP(V_Pa_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_1121_2,plain,
    ! [U_3944,U_3943,U_3942] :
      ( hBOOL(hAPP(U_3943,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3944),U_3942))
      | ~ hBOOL(hAPP(U_3943,U_3944))
      | ? [U_3941] :
          ( ~ hBOOL(hAPP(U_3943,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_3941),U_3942)))
          & hBOOL(hAPP(U_3943,U_3941))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3941),U_3942)) ) ),
    inference(variable_rename,[status(thm)],[f_1121_1]) ).

fof(f_1121_3,plain,
    ! [U_3944,U_3943,U_3942] :
      ( hBOOL(hAPP(U_3943,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3944),U_3942))
      | ~ hBOOL(hAPP(U_3943,U_3944))
      | ( ~ hBOOL(hAPP(U_3943,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK69(U_3944,U_3943,U_3942)),U_3942)))
        & hBOOL(hAPP(U_3943,sK69(U_3944,U_3943,U_3942)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK69(U_3944,U_3943,U_3942)),U_3942)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK69]),skolemize(U_3941,sK69(U_3944,U_3943,U_3942))],[f_1121_2]) ).

fof(f_1121_4,plain,
    ( ! [U_3942,U_3943,U_3944] :
        ( ~ hBOOL(hAPP(U_3943,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK69(U_3944,U_3943,U_3942)),U_3942)))
        | ~ sP325(U_3942,U_3943,U_3944) )
    & ! [U_3942,U_3943,U_3944] :
        ( hBOOL(hAPP(U_3943,sK69(U_3944,U_3943,U_3942)))
        | ~ sP325(U_3942,U_3943,U_3944) )
    & ! [U_3942,U_3943,U_3944] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK69(U_3944,U_3943,U_3942)),U_3942))
        | ~ sP325(U_3942,U_3943,U_3944) )
    & ! [U_3942,U_3943,U_3944] :
        ( hBOOL(hAPP(U_3943,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3944),U_3942))
        | ~ hBOOL(hAPP(U_3943,U_3944))
        | sP325(U_3942,U_3943,U_3944) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP325])],[f_1121_3]) ).

cnf(f_1121_5,plain,
    ( hBOOL(hAPP(U_3943,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_3944),U_3942))
    | ~ hBOOL(hAPP(U_3943,U_3944))
    | sP325(U_3942,U_3943,U_3944) ),
    inference(clausify,[status(thm)],[f_1121_4]) ).

cnf(f_1121_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK69(U_3944,U_3943,U_3942)),U_3942))
    | ~ sP325(U_3942,U_3943,U_3944) ),
    inference(clausify,[status(thm)],[f_1121_4]) ).

cnf(f_1121_7,plain,
    ( hBOOL(hAPP(U_3943,sK69(U_3944,U_3943,U_3942)))
    | ~ sP325(U_3942,U_3943,U_3944) ),
    inference(clausify,[status(thm)],[f_1121_4]) ).

cnf(f_1121_8,plain,
    ( ~ hBOOL(hAPP(U_3943,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,sK69(U_3944,U_3943,U_3942)),U_3942)))
    | ~ sP325(U_3942,U_3943,U_3944) ),
    inference(clausify,[status(thm)],[f_1121_4]) ).

fof(f_1122_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_1122_2,plain,
    ! [U_3945] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3945) = 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_3945)),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_3945))) ),
    inference(variable_rename,[status(thm)],[f_1122_1]) ).

fof(f_1122_3,plain,
    ! [U_3945] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3945) = 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_3945)),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_3945))) ),
    inference(definitional_conversion,[status(esa)],[f_1122_2]) ).

cnf(f_1122_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3945) = 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_3945)),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_3945))) ),
    inference(clausify,[status(thm)],[f_1122_3]) ).

fof(f_1123_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_1123_2,plain,
    ! [U_3947,U_3946] :
      ( c_Divides_Odivmod__nat(U_3947,U_3946) = 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_3947),U_3946)),U_3946))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3947),U_3946),U_3946))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3946),U_3947))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3946)) ),
    inference(variable_rename,[status(thm)],[f_1123_1]) ).

fof(f_1123_3,plain,
    ! [U_3947,U_3946] :
      ( c_Divides_Odivmod__nat(U_3947,U_3946) = 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_3947),U_3946)),U_3946))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3947),U_3946),U_3946))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3946),U_3947))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3946)) ),
    inference(definitional_conversion,[status(esa)],[f_1123_2]) ).

cnf(f_1123_4,plain,
    ( c_Divides_Odivmod__nat(U_3947,U_3946) = 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_3947),U_3946)),U_3946))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_3947),U_3946),U_3946))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_3946),U_3947))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_3946)) ),
    inference(clausify,[status(thm)],[f_1123_3]) ).

fof(f_1124_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_1124_2,plain,
    ! [U_3951,U_3950,U_3949,U_3948] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_3948),U_3949),U_3951))
        & hBOOL(hAPP(hAPP(c_member(U_3948),U_3949),U_3950)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_3948),U_3949),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3948,tc_HOL_Obool)),U_3950),U_3951))) ),
    inference(variable_rename,[status(thm)],[f_1124_1]) ).

fof(f_1124_3,plain,
    ( ! [U_3948,U_3949,U_3950,U_3951] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_3948),U_3949),U_3951))
        | ~ sP326(U_3948,U_3949,U_3950,U_3951) )
    & ! [U_3948,U_3949,U_3950,U_3951] :
        ( hBOOL(hAPP(hAPP(c_member(U_3948),U_3949),U_3950))
        | ~ sP326(U_3948,U_3949,U_3950,U_3951) )
    & ! [U_3948,U_3949,U_3950,U_3951] :
        ( sP326(U_3948,U_3949,U_3950,U_3951)
        | ~ hBOOL(hAPP(hAPP(c_member(U_3948),U_3949),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3948,tc_HOL_Obool)),U_3950),U_3951))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP326])],[f_1124_2]) ).

cnf(f_1124_4,plain,
    ( sP326(U_3948,U_3949,U_3950,U_3951)
    | ~ hBOOL(hAPP(hAPP(c_member(U_3948),U_3949),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3948,tc_HOL_Obool)),U_3950),U_3951))) ),
    inference(clausify,[status(thm)],[f_1124_3]) ).

cnf(f_1124_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3948),U_3949),U_3950))
    | ~ sP326(U_3948,U_3949,U_3950,U_3951) ),
    inference(clausify,[status(thm)],[f_1124_3]) ).

cnf(f_1124_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_3948),U_3949),U_3951))
    | ~ sP326(U_3948,U_3949,U_3950,U_3951) ),
    inference(clausify,[status(thm)],[f_1124_3]) ).

fof(f_1125_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_1125_2,plain,
    ! [U_3955,U_3954,U_3953,U_3952] :
      ( hBOOL(hAPP(hAPP(c_member(U_3952),U_3953),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3952,tc_HOL_Obool)),U_3954),U_3955)))
      | hBOOL(hAPP(hAPP(c_member(U_3952),U_3953),U_3955))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3952),U_3953),U_3954)) ),
    inference(variable_rename,[status(thm)],[f_1125_1]) ).

fof(f_1125_3,plain,
    ! [U_3952,U_3953,U_3954,U_3955] :
      ( hBOOL(hAPP(hAPP(c_member(U_3952),U_3953),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3952,tc_HOL_Obool)),U_3954),U_3955)))
      | hBOOL(hAPP(hAPP(c_member(U_3952),U_3953),U_3955))
      | ~ hBOOL(hAPP(hAPP(c_member(U_3952),U_3953),U_3954)) ),
    inference(definitional_conversion,[status(esa)],[f_1125_2]) ).

cnf(f_1125_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_3952),U_3953),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_3952,tc_HOL_Obool)),U_3954),U_3955)))
    | hBOOL(hAPP(hAPP(c_member(U_3952),U_3953),U_3955))
    | ~ hBOOL(hAPP(hAPP(c_member(U_3952),U_3953),U_3954)) ),
    inference(clausify,[status(thm)],[f_1125_3]) ).

fof(f_1126_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_1126_2,plain,
    ! [U_3958,U_3957,U_3956] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_3956),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3957),U_3958)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3956),hAPP(c_Int_Oring__1__class_Oof__int(U_3956),U_3957)),U_3958)
      | ~ class_Rings_Oring__1(U_3956) ),
    inference(variable_rename,[status(thm)],[f_1126_1]) ).

fof(f_1126_3,plain,
    ! [U_3957,U_3956,U_3958] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_3956),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3957),U_3958)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3956),hAPP(c_Int_Oring__1__class_Oof__int(U_3956),U_3957)),U_3958)
      | ~ class_Rings_Oring__1(U_3956) ),
    inference(definitional_conversion,[status(esa)],[f_1126_2]) ).

cnf(f_1126_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_3956),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_3957),U_3958)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_3956),hAPP(c_Int_Oring__1__class_Oof__int(U_3956),U_3957)),U_3958)
    | ~ class_Rings_Oring__1(U_3956) ),
    inference(clausify,[status(thm)],[f_1126_3]) ).

fof(f_1127_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_1127_2,plain,
    ! [U_3960,U_3959] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_3959),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3960)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3959),U_3960)
      | ~ class_Int_Onumber__ring(U_3959) ),
    inference(variable_rename,[status(thm)],[f_1127_1]) ).

fof(f_1127_3,plain,
    ! [U_3959,U_3960] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_3959),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3960)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3959),U_3960)
      | ~ class_Int_Onumber__ring(U_3959) ),
    inference(definitional_conversion,[status(esa)],[f_1127_2]) ).

cnf(f_1127_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_3959),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3960)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3959),U_3960)
    | ~ class_Int_Onumber__ring(U_3959) ),
    inference(clausify,[status(thm)],[f_1127_3]) ).

fof(f_1128_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_1128_2,plain,
    ! [U_3962,U_3961] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3961),hAPP(c_Groups_Oabs__class_Oabs(U_3961),U_3962)) = hAPP(c_Groups_Oabs__class_Oabs(U_3961),U_3962)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3961) ),
    inference(variable_rename,[status(thm)],[f_1128_1]) ).

fof(f_1128_3,plain,
    ! [U_3961,U_3962] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3961),hAPP(c_Groups_Oabs__class_Oabs(U_3961),U_3962)) = hAPP(c_Groups_Oabs__class_Oabs(U_3961),U_3962)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3961) ),
    inference(definitional_conversion,[status(esa)],[f_1128_2]) ).

cnf(f_1128_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_3961),hAPP(c_Groups_Oabs__class_Oabs(U_3961),U_3962)) = hAPP(c_Groups_Oabs__class_Oabs(U_3961),U_3962)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3961) ),
    inference(clausify,[status(thm)],[f_1128_3]) ).

fof(f_1129_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_1129_2,plain,
    ! [U_3965,U_3964,U_3963] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_3963),U_3964) = hAPP(c_Int_Onumber__class_Onumber__of(U_3963),U_3965)
          | U_3964 != U_3965 )
        & ( U_3964 = U_3965
          | hAPP(c_Int_Onumber__class_Onumber__of(U_3963),U_3964) != hAPP(c_Int_Onumber__class_Onumber__of(U_3963),U_3965) ) )
      | ~ class_Int_Oring__char__0(U_3963)
      | ~ class_Int_Onumber__ring(U_3963) ),
    inference(variable_rename,[status(thm)],[f_1129_1]) ).

fof(f_1129_3,plain,
    ( ! [U_3963,U_3964,U_3965] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_3963),U_3964) = hAPP(c_Int_Onumber__class_Onumber__of(U_3963),U_3965)
        | U_3964 != U_3965
        | ~ sP327(U_3963,U_3964,U_3965) )
    & ! [U_3963,U_3964,U_3965] :
        ( U_3964 = U_3965
        | hAPP(c_Int_Onumber__class_Onumber__of(U_3963),U_3964) != hAPP(c_Int_Onumber__class_Onumber__of(U_3963),U_3965)
        | ~ sP327(U_3963,U_3964,U_3965) )
    & ! [U_3963,U_3964,U_3965] :
        ( sP327(U_3963,U_3964,U_3965)
        | ~ class_Int_Oring__char__0(U_3963)
        | ~ class_Int_Onumber__ring(U_3963) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP327])],[f_1129_2]) ).

cnf(f_1129_4,plain,
    ( sP327(U_3963,U_3964,U_3965)
    | ~ class_Int_Oring__char__0(U_3963)
    | ~ class_Int_Onumber__ring(U_3963) ),
    inference(clausify,[status(thm)],[f_1129_3]) ).

cnf(f_1129_5,plain,
    ( U_3964 = U_3965
    | hAPP(c_Int_Onumber__class_Onumber__of(U_3963),U_3964) != hAPP(c_Int_Onumber__class_Onumber__of(U_3963),U_3965)
    | ~ sP327(U_3963,U_3964,U_3965) ),
    inference(clausify,[status(thm)],[f_1129_3]) ).

cnf(f_1129_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_3963),U_3964) = hAPP(c_Int_Onumber__class_Onumber__of(U_3963),U_3965)
    | U_3964 != U_3965
    | ~ sP327(U_3963,U_3964,U_3965) ),
    inference(clausify,[status(thm)],[f_1129_3]) ).

fof(f_1130_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_1130_2,plain,
    ! [U_3968,U_3967,U_3966] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_3966),U_3967) = U_3968
          | U_3968 != hAPP(c_Int_Onumber__class_Onumber__of(U_3966),U_3967) )
        & ( U_3968 = hAPP(c_Int_Onumber__class_Onumber__of(U_3966),U_3967)
          | hAPP(c_Int_Onumber__class_Onumber__of(U_3966),U_3967) != U_3968 ) )
      | ~ class_Int_Onumber(U_3966) ),
    inference(variable_rename,[status(thm)],[f_1130_1]) ).

fof(f_1130_3,plain,
    ( ! [U_3967,U_3968,U_3966] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_3966),U_3967) = U_3968
        | U_3968 != hAPP(c_Int_Onumber__class_Onumber__of(U_3966),U_3967)
        | ~ sP328(U_3967,U_3968,U_3966) )
    & ! [U_3967,U_3968,U_3966] :
        ( U_3968 = hAPP(c_Int_Onumber__class_Onumber__of(U_3966),U_3967)
        | hAPP(c_Int_Onumber__class_Onumber__of(U_3966),U_3967) != U_3968
        | ~ sP328(U_3967,U_3968,U_3966) )
    & ! [U_3967,U_3968,U_3966] :
        ( sP328(U_3967,U_3968,U_3966)
        | ~ class_Int_Onumber(U_3966) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP328])],[f_1130_2]) ).

cnf(f_1130_4,plain,
    ( sP328(U_3967,U_3968,U_3966)
    | ~ class_Int_Onumber(U_3966) ),
    inference(clausify,[status(thm)],[f_1130_3]) ).

cnf(f_1130_5,plain,
    ( U_3968 = hAPP(c_Int_Onumber__class_Onumber__of(U_3966),U_3967)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_3966),U_3967) != U_3968
    | ~ sP328(U_3967,U_3968,U_3966) ),
    inference(clausify,[status(thm)],[f_1130_3]) ).

cnf(f_1130_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_3966),U_3967) = U_3968
    | U_3968 != hAPP(c_Int_Onumber__class_Onumber__of(U_3966),U_3967)
    | ~ sP328(U_3967,U_3968,U_3966) ),
    inference(clausify,[status(thm)],[f_1130_3]) ).

fof(f_1131_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_1131_2,plain,
    ! [U_3969] : c_Divides_Odivmod__nat(U_3969,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_3969),
    inference(variable_rename,[status(thm)],[f_1131_1]) ).

fof(f_1131_3,plain,
    ! [U_3969] : c_Divides_Odivmod__nat(U_3969,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_3969),
    inference(definitional_conversion,[status(esa)],[f_1131_2]) ).

cnf(f_1131_4,plain,
    c_Divides_Odivmod__nat(U_3969,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_3969),
    inference(clausify,[status(thm)],[f_1131_3]) ).

fof(f_1132_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_1132_2,plain,
    ! [U_3971,U_3970] : 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_3970)),U_3971))),
    inference(variable_rename,[status(thm)],[f_1132_1]) ).

fof(f_1132_3,plain,
    ! [U_3970,U_3971] : 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_3970)),U_3971))),
    inference(definitional_conversion,[status(esa)],[f_1132_2]) ).

cnf(f_1132_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_3970)),U_3971))),
    inference(clausify,[status(thm)],[f_1132_3]) ).

fof(f_1133_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_1133_2,plain,
    ! [U_3973,U_3972] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3972),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3973)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3972),U_3973)
          | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3973))) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3972),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3973)) = c_Groups_Ozero__class_Ozero(U_3972)
          | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3973))) ) )
      | ~ class_Int_Onumber__ring(U_3972) ),
    inference(variable_rename,[status(thm)],[f_1133_1]) ).

fof(f_1133_3,plain,
    ( ! [U_3973,U_3972] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3972),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3973)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3972),U_3973)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3973)))
        | ~ sP329(U_3973,U_3972) )
    & ! [U_3973,U_3972] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3972),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3973)) = c_Groups_Ozero__class_Ozero(U_3972)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3973)))
        | ~ sP329(U_3973,U_3972) )
    & ! [U_3973,U_3972] :
        ( sP329(U_3973,U_3972)
        | ~ class_Int_Onumber__ring(U_3972) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP329])],[f_1133_2]) ).

cnf(f_1133_4,plain,
    ( sP329(U_3973,U_3972)
    | ~ class_Int_Onumber__ring(U_3972) ),
    inference(clausify,[status(thm)],[f_1133_3]) ).

cnf(f_1133_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3972),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3973)) = c_Groups_Ozero__class_Ozero(U_3972)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3973)))
    | ~ sP329(U_3973,U_3972) ),
    inference(clausify,[status(thm)],[f_1133_3]) ).

cnf(f_1133_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_3972),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_3973)) = hAPP(c_Int_Onumber__class_Onumber__of(U_3972),U_3973)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_3973)))
    | ~ sP329(U_3973,U_3972) ),
    inference(clausify,[status(thm)],[f_1133_3]) ).

fof(f_1134_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_1134_2,plain,
    ! [U_3976,U_3975,U_3974] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3974),U_3975),U_3976))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3974),hAPP(c_Groups_Oabs__class_Oabs(U_3974),U_3975)),U_3976))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3974) ),
    inference(variable_rename,[status(thm)],[f_1134_1]) ).

fof(f_1134_3,plain,
    ! [U_3975,U_3976,U_3974] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3974),U_3975),U_3976))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3974),hAPP(c_Groups_Oabs__class_Oabs(U_3974),U_3975)),U_3976))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3974) ),
    inference(definitional_conversion,[status(esa)],[f_1134_2]) ).

cnf(f_1134_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3974),U_3975),U_3976))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3974),hAPP(c_Groups_Oabs__class_Oabs(U_3974),U_3975)),U_3976))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3974) ),
    inference(clausify,[status(thm)],[f_1134_3]) ).

fof(f_1135_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_1135_2,plain,
    ! [U_3978,U_3977] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3977),U_3978),hAPP(c_Groups_Oabs__class_Oabs(U_3977),U_3978)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3977) ),
    inference(variable_rename,[status(thm)],[f_1135_1]) ).

fof(f_1135_3,plain,
    ! [U_3977,U_3978] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3977),U_3978),hAPP(c_Groups_Oabs__class_Oabs(U_3977),U_3978)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3977) ),
    inference(definitional_conversion,[status(esa)],[f_1135_2]) ).

cnf(f_1135_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_3977),U_3978),hAPP(c_Groups_Oabs__class_Oabs(U_3977),U_3978)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3977) ),
    inference(clausify,[status(thm)],[f_1135_3]) ).

fof(f_1136_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_1136_2,plain,
    ! [U_3979] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3979),c_Groups_Ozero__class_Ozero(U_3979)) = c_Groups_Ozero__class_Ozero(U_3979)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3979) ),
    inference(variable_rename,[status(thm)],[f_1136_1]) ).

fof(f_1136_3,plain,
    ! [U_3979] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3979),c_Groups_Ozero__class_Ozero(U_3979)) = c_Groups_Ozero__class_Ozero(U_3979)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3979) ),
    inference(definitional_conversion,[status(esa)],[f_1136_2]) ).

cnf(f_1136_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_3979),c_Groups_Ozero__class_Ozero(U_3979)) = c_Groups_Ozero__class_Ozero(U_3979)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3979) ),
    inference(clausify,[status(thm)],[f_1136_3]) ).

fof(f_1137_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_1137_2,plain,
    ! [U_3981,U_3980] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_3980),U_3981) = c_Groups_Ozero__class_Ozero(U_3980)
          | U_3981 != c_Groups_Ozero__class_Ozero(U_3980) )
        & ( U_3981 = c_Groups_Ozero__class_Ozero(U_3980)
          | hAPP(c_Groups_Oabs__class_Oabs(U_3980),U_3981) != c_Groups_Ozero__class_Ozero(U_3980) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3980) ),
    inference(variable_rename,[status(thm)],[f_1137_1]) ).

fof(f_1137_3,plain,
    ( ! [U_3980,U_3981] :
        ( hAPP(c_Groups_Oabs__class_Oabs(U_3980),U_3981) = c_Groups_Ozero__class_Ozero(U_3980)
        | U_3981 != c_Groups_Ozero__class_Ozero(U_3980)
        | ~ sP330(U_3980,U_3981) )
    & ! [U_3980,U_3981] :
        ( U_3981 = c_Groups_Ozero__class_Ozero(U_3980)
        | hAPP(c_Groups_Oabs__class_Oabs(U_3980),U_3981) != c_Groups_Ozero__class_Ozero(U_3980)
        | ~ sP330(U_3980,U_3981) )
    & ! [U_3980,U_3981] :
        ( sP330(U_3980,U_3981)
        | ~ class_Groups_Oordered__ab__group__add__abs(U_3980) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP330])],[f_1137_2]) ).

cnf(f_1137_4,plain,
    ( sP330(U_3980,U_3981)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3980) ),
    inference(clausify,[status(thm)],[f_1137_3]) ).

cnf(f_1137_5,plain,
    ( U_3981 = c_Groups_Ozero__class_Ozero(U_3980)
    | hAPP(c_Groups_Oabs__class_Oabs(U_3980),U_3981) != c_Groups_Ozero__class_Ozero(U_3980)
    | ~ sP330(U_3980,U_3981) ),
    inference(clausify,[status(thm)],[f_1137_3]) ).

cnf(f_1137_6,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_3980),U_3981) = c_Groups_Ozero__class_Ozero(U_3980)
    | U_3981 != c_Groups_Ozero__class_Ozero(U_3980)
    | ~ sP330(U_3980,U_3981) ),
    inference(clausify,[status(thm)],[f_1137_3]) ).

fof(f_1138_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_1138_2,plain,
    ! [U_3984,U_3983,U_3982] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3982),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3982),hAPP(c_Groups_Oabs__class_Oabs(U_3982),U_3983)),hAPP(c_Groups_Oabs__class_Oabs(U_3982),U_3984))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3982),hAPP(c_Groups_Oabs__class_Oabs(U_3982),U_3983)),hAPP(c_Groups_Oabs__class_Oabs(U_3982),U_3984))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3982) ),
    inference(variable_rename,[status(thm)],[f_1138_1]) ).

fof(f_1138_3,plain,
    ! [U_3984,U_3983,U_3982] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3982),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3982),hAPP(c_Groups_Oabs__class_Oabs(U_3982),U_3983)),hAPP(c_Groups_Oabs__class_Oabs(U_3982),U_3984))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3982),hAPP(c_Groups_Oabs__class_Oabs(U_3982),U_3983)),hAPP(c_Groups_Oabs__class_Oabs(U_3982),U_3984))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3982) ),
    inference(definitional_conversion,[status(esa)],[f_1138_2]) ).

cnf(f_1138_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_3982),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3982),hAPP(c_Groups_Oabs__class_Oabs(U_3982),U_3983)),hAPP(c_Groups_Oabs__class_Oabs(U_3982),U_3984))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_3982),hAPP(c_Groups_Oabs__class_Oabs(U_3982),U_3983)),hAPP(c_Groups_Oabs__class_Oabs(U_3982),U_3984))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3982) ),
    inference(clausify,[status(thm)],[f_1138_3]) ).

fof(f_1139_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_1139_2,plain,
    ! [U_3986,U_3985] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),hAPP(c_Groups_Oabs__class_Oabs(U_3985),U_3986)),hAPP(c_Groups_Oabs__class_Oabs(U_3985),U_3986)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),U_3986),U_3986)
      | ~ class_Rings_Olinordered__idom(U_3985) ),
    inference(variable_rename,[status(thm)],[f_1139_1]) ).

fof(f_1139_3,plain,
    ! [U_3985,U_3986] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),hAPP(c_Groups_Oabs__class_Oabs(U_3985),U_3986)),hAPP(c_Groups_Oabs__class_Oabs(U_3985),U_3986)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),U_3986),U_3986)
      | ~ class_Rings_Olinordered__idom(U_3985) ),
    inference(definitional_conversion,[status(esa)],[f_1139_2]) ).

cnf(f_1139_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),hAPP(c_Groups_Oabs__class_Oabs(U_3985),U_3986)),hAPP(c_Groups_Oabs__class_Oabs(U_3985),U_3986)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3985),U_3986),U_3986)
    | ~ class_Rings_Olinordered__idom(U_3985) ),
    inference(clausify,[status(thm)],[f_1139_3]) ).

fof(f_1140_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_1140_2,plain,
    ! [U_3989,U_3988,U_3987] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3987),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3987),U_3988),U_3989)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3987),hAPP(c_Groups_Oabs__class_Oabs(U_3987),U_3988)),hAPP(c_Groups_Oabs__class_Oabs(U_3987),U_3989))
      | ~ class_Rings_Olinordered__idom(U_3987) ),
    inference(variable_rename,[status(thm)],[f_1140_1]) ).

fof(f_1140_3,plain,
    ! [U_3987,U_3988,U_3989] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3987),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3987),U_3988),U_3989)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3987),hAPP(c_Groups_Oabs__class_Oabs(U_3987),U_3988)),hAPP(c_Groups_Oabs__class_Oabs(U_3987),U_3989))
      | ~ class_Rings_Olinordered__idom(U_3987) ),
    inference(definitional_conversion,[status(esa)],[f_1140_2]) ).

cnf(f_1140_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_3987),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3987),U_3988),U_3989)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3987),hAPP(c_Groups_Oabs__class_Oabs(U_3987),U_3988)),hAPP(c_Groups_Oabs__class_Oabs(U_3987),U_3989))
    | ~ class_Rings_Olinordered__idom(U_3987) ),
    inference(clausify,[status(thm)],[f_1140_3]) ).

fof(f_1141_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_1141_2,plain,
    ! [U_3992,U_3991,U_3990] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3990),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3990),U_3991),U_3992)) = hAPP(c_Groups_Oabs__class_Oabs(U_3990),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3990),U_3992),U_3991))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3990) ),
    inference(variable_rename,[status(thm)],[f_1141_1]) ).

fof(f_1141_3,plain,
    ! [U_3990,U_3991,U_3992] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3990),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3990),U_3991),U_3992)) = hAPP(c_Groups_Oabs__class_Oabs(U_3990),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3990),U_3992),U_3991))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3990) ),
    inference(definitional_conversion,[status(esa)],[f_1141_2]) ).

cnf(f_1141_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_3990),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3990),U_3991),U_3992)) = hAPP(c_Groups_Oabs__class_Oabs(U_3990),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_3990),U_3992),U_3991))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3990) ),
    inference(clausify,[status(thm)],[f_1141_3]) ).

fof(f_1142_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_1142_2,plain,
    ! [U_3993] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3993),c_Groups_Oone__class_Oone(U_3993)) = c_Groups_Oone__class_Oone(U_3993)
      | ~ class_Rings_Olinordered__idom(U_3993) ),
    inference(variable_rename,[status(thm)],[f_1142_1]) ).

fof(f_1142_3,plain,
    ! [U_3993] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3993),c_Groups_Oone__class_Oone(U_3993)) = c_Groups_Oone__class_Oone(U_3993)
      | ~ class_Rings_Olinordered__idom(U_3993) ),
    inference(definitional_conversion,[status(esa)],[f_1142_2]) ).

cnf(f_1142_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_3993),c_Groups_Oone__class_Oone(U_3993)) = c_Groups_Oone__class_Oone(U_3993)
    | ~ class_Rings_Olinordered__idom(U_3993) ),
    inference(clausify,[status(thm)],[f_1142_3]) ).

fof(f_1143_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_1143_2,plain,
    ! [U_3995,U_3994] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3994),hAPP(c_Groups_Ouminus__class_Ouminus(U_3994),U_3995)) = hAPP(c_Groups_Oabs__class_Oabs(U_3994),U_3995)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3994) ),
    inference(variable_rename,[status(thm)],[f_1143_1]) ).

fof(f_1143_3,plain,
    ! [U_3994,U_3995] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_3994),hAPP(c_Groups_Ouminus__class_Ouminus(U_3994),U_3995)) = hAPP(c_Groups_Oabs__class_Oabs(U_3994),U_3995)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_3994) ),
    inference(definitional_conversion,[status(esa)],[f_1143_2]) ).

cnf(f_1143_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_3994),hAPP(c_Groups_Ouminus__class_Ouminus(U_3994),U_3995)) = hAPP(c_Groups_Oabs__class_Oabs(U_3994),U_3995)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_3994) ),
    inference(clausify,[status(thm)],[f_1143_3]) ).

fof(f_1144_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_1144_2,plain,
    ! [U_3999,U_3998,U_3997,U_3996] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_3996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3996),U_3997),U_3998)),U_3999) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3996),hAPP(hAPP(c_Power_Opower__class_Opower(U_3996),U_3997),U_3999)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3996),U_3998),U_3999))
      | ~ class_Rings_Ocomm__semiring__1(U_3996) ),
    inference(variable_rename,[status(thm)],[f_1144_1]) ).

fof(f_1144_3,plain,
    ! [U_3996,U_3997,U_3998,U_3999] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_3996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3996),U_3997),U_3998)),U_3999) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3996),hAPP(hAPP(c_Power_Opower__class_Opower(U_3996),U_3997),U_3999)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3996),U_3998),U_3999))
      | ~ class_Rings_Ocomm__semiring__1(U_3996) ),
    inference(definitional_conversion,[status(esa)],[f_1144_2]) ).

cnf(f_1144_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_3996),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3996),U_3997),U_3998)),U_3999) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_3996),hAPP(hAPP(c_Power_Opower__class_Opower(U_3996),U_3997),U_3999)),hAPP(hAPP(c_Power_Opower__class_Opower(U_3996),U_3998),U_3999))
    | ~ class_Rings_Ocomm__semiring__1(U_3996) ),
    inference(clausify,[status(thm)],[f_1144_3]) ).

fof(f_1145_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_1145_2,plain,
    ! [U_4001,U_4000] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4000),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4000),U_4001)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4000),U_4001)
      | ~ class_Rings_Olinordered__idom(U_4000) ),
    inference(variable_rename,[status(thm)],[f_1145_1]) ).

fof(f_1145_3,plain,
    ! [U_4001,U_4000] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4000),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4000),U_4001)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4000),U_4001)
      | ~ class_Rings_Olinordered__idom(U_4000) ),
    inference(definitional_conversion,[status(esa)],[f_1145_2]) ).

cnf(f_1145_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4000),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4000),U_4001)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4000),U_4001)
    | ~ class_Rings_Olinordered__idom(U_4000) ),
    inference(clausify,[status(thm)],[f_1145_3]) ).

fof(f_1146_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_1146_2,plain,
    ! [U_4005,U_4004,U_4003,U_4002] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_4002),U_4003),U_4005))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4002),U_4003),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4002,tc_HOL_Obool)),U_4004),U_4005))) ),
    inference(variable_rename,[status(thm)],[f_1146_1]) ).

fof(f_1146_3,plain,
    ! [U_4002,U_4003,U_4004,U_4005] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_4002),U_4003),U_4005))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4002),U_4003),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4002,tc_HOL_Obool)),U_4004),U_4005))) ),
    inference(definitional_conversion,[status(esa)],[f_1146_2]) ).

cnf(f_1146_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_4002),U_4003),U_4005))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4002),U_4003),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4002,tc_HOL_Obool)),U_4004),U_4005))) ),
    inference(clausify,[status(thm)],[f_1146_3]) ).

fof(f_1147_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_1147_2,plain,
    ! [U_4009,U_4008,U_4007,U_4006] :
      ( hBOOL(hAPP(hAPP(c_member(U_4006),U_4007),U_4008))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4006),U_4007),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4006,tc_HOL_Obool)),U_4008),U_4009))) ),
    inference(variable_rename,[status(thm)],[f_1147_1]) ).

fof(f_1147_3,plain,
    ! [U_4006,U_4007,U_4008,U_4009] :
      ( hBOOL(hAPP(hAPP(c_member(U_4006),U_4007),U_4008))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4006),U_4007),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4006,tc_HOL_Obool)),U_4008),U_4009))) ),
    inference(definitional_conversion,[status(esa)],[f_1147_2]) ).

cnf(f_1147_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4006),U_4007),U_4008))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4006),U_4007),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4006,tc_HOL_Obool)),U_4008),U_4009))) ),
    inference(clausify,[status(thm)],[f_1147_3]) ).

fof(f_1148_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_1148_2,plain,
    ! [U_4013,U_4012,U_4011,U_4010] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_4010),U_4011),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4010,tc_HOL_Obool)),U_4012),U_4013)))
        | hBOOL(hAPP(hAPP(c_member(U_4010),U_4011),U_4013))
        | ~ hBOOL(hAPP(hAPP(c_member(U_4010),U_4011),U_4012)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(U_4010),U_4011),U_4013))
          & hBOOL(hAPP(hAPP(c_member(U_4010),U_4011),U_4012)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_4010),U_4011),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4010,tc_HOL_Obool)),U_4012),U_4013))) ) ),
    inference(variable_rename,[status(thm)],[f_1148_1]) ).

fof(f_1148_3,plain,
    ( ! [U_4021,U_4019,U_4017,U_4015] :
        ( hBOOL(hAPP(hAPP(c_member(U_4015),U_4017),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4015,tc_HOL_Obool)),U_4019),U_4021)))
        | hBOOL(hAPP(hAPP(c_member(U_4015),U_4017),U_4021))
        | ~ hBOOL(hAPP(hAPP(c_member(U_4015),U_4017),U_4019)) )
    & ! [U_4020,U_4018,U_4016,U_4014] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_4014),U_4016),U_4020))
          & hBOOL(hAPP(hAPP(c_member(U_4014),U_4016),U_4018)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_4014),U_4016),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4014,tc_HOL_Obool)),U_4018),U_4020))) ) ),
    inference(miniscope,[status(thm)],[f_1148_2]) ).

fof(f_1148_4,plain,
    ( ! [U_4016,U_4020,U_4014,U_4018] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_4014),U_4016),U_4020))
        | ~ sP331(U_4016,U_4020,U_4014,U_4018) )
    & ! [U_4016,U_4020,U_4014,U_4018] :
        ( hBOOL(hAPP(hAPP(c_member(U_4014),U_4016),U_4018))
        | ~ sP331(U_4016,U_4020,U_4014,U_4018) )
    & ! [U_4017,U_4015,U_4021,U_4019] :
        ( hBOOL(hAPP(hAPP(c_member(U_4015),U_4017),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4015,tc_HOL_Obool)),U_4019),U_4021)))
        | hBOOL(hAPP(hAPP(c_member(U_4015),U_4017),U_4021))
        | ~ hBOOL(hAPP(hAPP(c_member(U_4015),U_4017),U_4019)) )
    & ! [U_4016,U_4020,U_4014,U_4018] :
        ( sP331(U_4016,U_4020,U_4014,U_4018)
        | ~ hBOOL(hAPP(hAPP(c_member(U_4014),U_4016),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4014,tc_HOL_Obool)),U_4018),U_4020))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP331])],[f_1148_3]) ).

cnf(f_1148_5,plain,
    ( sP331(U_4016,U_4020,U_4014,U_4018)
    | ~ hBOOL(hAPP(hAPP(c_member(U_4014),U_4016),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4014,tc_HOL_Obool)),U_4018),U_4020))) ),
    inference(clausify,[status(thm)],[f_1148_4]) ).

cnf(f_1148_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4015),U_4017),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4015,tc_HOL_Obool)),U_4019),U_4021)))
    | hBOOL(hAPP(hAPP(c_member(U_4015),U_4017),U_4021))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4015),U_4017),U_4019)) ),
    inference(clausify,[status(thm)],[f_1148_4]) ).

cnf(f_1148_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4014),U_4016),U_4018))
    | ~ sP331(U_4016,U_4020,U_4014,U_4018) ),
    inference(clausify,[status(thm)],[f_1148_4]) ).

cnf(f_1148_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_4014),U_4016),U_4020))
    | ~ sP331(U_4016,U_4020,U_4014,U_4018) ),
    inference(clausify,[status(thm)],[f_1148_4]) ).

fof(f_1149_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_1149_2,plain,
    ! [U_4022] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4022)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4022),
    inference(variable_rename,[status(thm)],[f_1149_1]) ).

fof(f_1149_3,plain,
    ! [U_4022] : hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4022)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4022),
    inference(definitional_conversion,[status(esa)],[f_1149_2]) ).

cnf(f_1149_4,plain,
    hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4022)) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4022),
    inference(clausify,[status(thm)],[f_1149_3]) ).

fof(f_1150_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_1150_2,plain,
    ! [U_4026,U_4025,U_4024,U_4023] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4023),hAPP(hAPP(c_Power_Opower__class_Opower(U_4023),U_4024),U_4025)),U_4026) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4023),U_4024),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4025),U_4026))
      | ~ class_Rings_Ocomm__semiring__1(U_4023) ),
    inference(variable_rename,[status(thm)],[f_1150_1]) ).

fof(f_1150_3,plain,
    ! [U_4023,U_4024,U_4025,U_4026] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4023),hAPP(hAPP(c_Power_Opower__class_Opower(U_4023),U_4024),U_4025)),U_4026) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4023),U_4024),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4025),U_4026))
      | ~ class_Rings_Ocomm__semiring__1(U_4023) ),
    inference(definitional_conversion,[status(esa)],[f_1150_2]) ).

cnf(f_1150_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4023),hAPP(hAPP(c_Power_Opower__class_Opower(U_4023),U_4024),U_4025)),U_4026) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4023),U_4024),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4025),U_4026))
    | ~ class_Rings_Ocomm__semiring__1(U_4023) ),
    inference(clausify,[status(thm)],[f_1150_3]) ).

fof(f_1151_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_1151_2,plain,
    ! [U_4030,U_4029,U_4028,U_4027] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4027,tc_HOL_Obool)),U_4029),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4027,tc_HOL_Obool)),U_4030),U_4028)) = U_4028
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4027,tc_HOL_Obool)),U_4029),U_4030))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4027,tc_HOL_Obool)),U_4028),U_4029)) ),
    inference(variable_rename,[status(thm)],[f_1151_1]) ).

fof(f_1151_3,plain,
    ! [U_4027,U_4028,U_4029,U_4030] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4027,tc_HOL_Obool)),U_4029),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4027,tc_HOL_Obool)),U_4030),U_4028)) = U_4028
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4027,tc_HOL_Obool)),U_4029),U_4030))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4027,tc_HOL_Obool)),U_4028),U_4029)) ),
    inference(definitional_conversion,[status(esa)],[f_1151_2]) ).

cnf(f_1151_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4027,tc_HOL_Obool)),U_4029),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4027,tc_HOL_Obool)),U_4030),U_4028)) = U_4028
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4027,tc_HOL_Obool)),U_4029),U_4030))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4027,tc_HOL_Obool)),U_4028),U_4029)) ),
    inference(clausify,[status(thm)],[f_1151_3]) ).

fof(f_1152_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_1152_2,plain,
    ! [U_4035,U_4034,U_4033,U_4032,U_4031] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4031,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4031,tc_HOL_Obool)),U_4032),U_4035)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4031,tc_HOL_Obool)),U_4033),U_4034)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4031,tc_HOL_Obool)),U_4034),U_4035))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4031,tc_HOL_Obool)),U_4032),U_4033)) ),
    inference(variable_rename,[status(thm)],[f_1152_1]) ).

fof(f_1152_3,plain,
    ! [U_4032,U_4031,U_4033,U_4034,U_4035] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4031,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4031,tc_HOL_Obool)),U_4032),U_4035)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4031,tc_HOL_Obool)),U_4033),U_4034)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4031,tc_HOL_Obool)),U_4034),U_4035))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4031,tc_HOL_Obool)),U_4032),U_4033)) ),
    inference(definitional_conversion,[status(esa)],[f_1152_2]) ).

cnf(f_1152_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4031,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4031,tc_HOL_Obool)),U_4032),U_4035)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4031,tc_HOL_Obool)),U_4033),U_4034)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4031,tc_HOL_Obool)),U_4034),U_4035))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4031,tc_HOL_Obool)),U_4032),U_4033)) ),
    inference(clausify,[status(thm)],[f_1152_3]) ).

fof(f_1153_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_1153_2,plain,
    ! [U_4038,U_4037,U_4036] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4036,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4036,tc_HOL_Obool)),U_4037),U_4038)),U_4037)),
    inference(variable_rename,[status(thm)],[f_1153_1]) ).

fof(f_1153_3,plain,
    ! [U_4036,U_4037,U_4038] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4036,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4036,tc_HOL_Obool)),U_4037),U_4038)),U_4037)),
    inference(definitional_conversion,[status(esa)],[f_1153_2]) ).

cnf(f_1153_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_4036,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4036,tc_HOL_Obool)),U_4037),U_4038)),U_4037)),
    inference(clausify,[status(thm)],[f_1153_3]) ).

fof(f_1154_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_1154_2,plain,
    ! [U_4041,U_4040,U_4039] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4039),U_4040)),U_4041) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4039),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4040),U_4041)),
    inference(variable_rename,[status(thm)],[f_1154_1]) ).

fof(f_1154_3,plain,
    ! [U_4039,U_4040,U_4041] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4039),U_4040)),U_4041) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4039),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4040),U_4041)),
    inference(definitional_conversion,[status(esa)],[f_1154_2]) ).

cnf(f_1154_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4039),U_4040)),U_4041) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4039),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4040),U_4041)),
    inference(clausify,[status(thm)],[f_1154_3]) ).

fof(f_1155_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_1155_2,plain,
    ! [U_4043,U_4042] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4042),U_4043),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4043
      | ~ class_Rings_Ocomm__semiring__1(U_4042) ),
    inference(variable_rename,[status(thm)],[f_1155_1]) ).

fof(f_1155_3,plain,
    ! [U_4042,U_4043] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4042),U_4043),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4043
      | ~ class_Rings_Ocomm__semiring__1(U_4042) ),
    inference(definitional_conversion,[status(esa)],[f_1155_2]) ).

cnf(f_1155_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4042),U_4043),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4043
    | ~ class_Rings_Ocomm__semiring__1(U_4042) ),
    inference(clausify,[status(thm)],[f_1155_3]) ).

fof(f_1156_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_1156_2,plain,
    ! [U_4046,U_4045,U_4044] : 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_4044,U_4045)),U_4046),U_4045) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4044),U_4046),U_4045),
    inference(variable_rename,[status(thm)],[f_1156_1]) ).

fof(f_1156_3,plain,
    ! [U_4044,U_4045,U_4046] : 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_4044,U_4045)),U_4046),U_4045) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4044),U_4046),U_4045),
    inference(definitional_conversion,[status(esa)],[f_1156_2]) ).

cnf(f_1156_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_4044,U_4045)),U_4046),U_4045) = c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4044),U_4046),U_4045),
    inference(clausify,[status(thm)],[f_1156_3]) ).

fof(f_1157_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_1157_2,plain,
    ! [U_4048,U_4047] :
      ( ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4047),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4048)) = c_Groups_Ozero__class_Ozero(U_4047)
          | 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_4048))) )
        & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4047),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4048)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4047),U_4048)
          | ~ 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_4048))) ) )
      | ~ class_Int_Onumber__ring(U_4047) ),
    inference(variable_rename,[status(thm)],[f_1157_1]) ).

fof(f_1157_3,plain,
    ( ! [U_4047,U_4048] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4047),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4048)) = c_Groups_Ozero__class_Ozero(U_4047)
        | 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_4048)))
        | ~ sP332(U_4047,U_4048) )
    & ! [U_4047,U_4048] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4047),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4048)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4047),U_4048)
        | ~ 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_4048)))
        | ~ sP332(U_4047,U_4048) )
    & ! [U_4047,U_4048] :
        ( sP332(U_4047,U_4048)
        | ~ class_Int_Onumber__ring(U_4047) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP332])],[f_1157_2]) ).

cnf(f_1157_4,plain,
    ( sP332(U_4047,U_4048)
    | ~ class_Int_Onumber__ring(U_4047) ),
    inference(clausify,[status(thm)],[f_1157_3]) ).

cnf(f_1157_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4047),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4048)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4047),U_4048)
    | ~ 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_4048)))
    | ~ sP332(U_4047,U_4048) ),
    inference(clausify,[status(thm)],[f_1157_3]) ).

cnf(f_1157_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4047),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4048)) = c_Groups_Ozero__class_Ozero(U_4047)
    | 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_4048)))
    | ~ sP332(U_4047,U_4048) ),
    inference(clausify,[status(thm)],[f_1157_3]) ).

fof(f_1158_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_1158_2,plain,
    ! [U_4050,U_4049] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4049),U_4050) = hAPP(c_Int_Oring__1__class_Oof__int(U_4049),U_4050)
      | ~ class_Int_Onumber__ring(U_4049) ),
    inference(variable_rename,[status(thm)],[f_1158_1]) ).

fof(f_1158_3,plain,
    ! [U_4049,U_4050] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4049),U_4050) = hAPP(c_Int_Oring__1__class_Oof__int(U_4049),U_4050)
      | ~ class_Int_Onumber__ring(U_4049) ),
    inference(definitional_conversion,[status(esa)],[f_1158_2]) ).

cnf(f_1158_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4049),U_4050) = hAPP(c_Int_Oring__1__class_Oof__int(U_4049),U_4050)
    | ~ class_Int_Onumber__ring(U_4049) ),
    inference(clausify,[status(thm)],[f_1158_3]) ).

fof(f_1159_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_1159_2,plain,
    ! [U_4052,U_4051] :
      ( c_Divides_Odivmod__nat(U_4051,U_4052) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4051)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4051),U_4052)) ),
    inference(variable_rename,[status(thm)],[f_1159_1]) ).

fof(f_1159_3,plain,
    ! [U_4051,U_4052] :
      ( c_Divides_Odivmod__nat(U_4051,U_4052) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4051)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4051),U_4052)) ),
    inference(definitional_conversion,[status(esa)],[f_1159_2]) ).

cnf(f_1159_4,plain,
    ( c_Divides_Odivmod__nat(U_4051,U_4052) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4051)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4051),U_4052)) ),
    inference(clausify,[status(thm)],[f_1159_3]) ).

fof(f_1160_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_1160_2,plain,
    ! [U_4054,U_4053] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_4053),hAPP(c_Int_Onumber__class_Onumber__of(U_4053),U_4054)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4053),U_4054)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4053),hAPP(c_Int_Onumber__class_Onumber__of(U_4053),U_4054)),c_Groups_Ozero__class_Ozero(U_4053))) )
        & ( hAPP(c_Groups_Oabs__class_Oabs(U_4053),hAPP(c_Int_Onumber__class_Onumber__of(U_4053),U_4054)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4053),hAPP(c_Int_Onumber__class_Onumber__of(U_4053),U_4054))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4053),hAPP(c_Int_Onumber__class_Onumber__of(U_4053),U_4054)),c_Groups_Ozero__class_Ozero(U_4053))) ) )
      | ~ class_Rings_Olinordered__idom(U_4053)
      | ~ class_Int_Onumber__ring(U_4053) ),
    inference(variable_rename,[status(thm)],[f_1160_1]) ).

fof(f_1160_3,plain,
    ( ! [U_4053,U_4054] :
        ( hAPP(c_Groups_Oabs__class_Oabs(U_4053),hAPP(c_Int_Onumber__class_Onumber__of(U_4053),U_4054)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4053),U_4054)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4053),hAPP(c_Int_Onumber__class_Onumber__of(U_4053),U_4054)),c_Groups_Ozero__class_Ozero(U_4053)))
        | ~ sP333(U_4053,U_4054) )
    & ! [U_4053,U_4054] :
        ( hAPP(c_Groups_Oabs__class_Oabs(U_4053),hAPP(c_Int_Onumber__class_Onumber__of(U_4053),U_4054)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4053),hAPP(c_Int_Onumber__class_Onumber__of(U_4053),U_4054))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4053),hAPP(c_Int_Onumber__class_Onumber__of(U_4053),U_4054)),c_Groups_Ozero__class_Ozero(U_4053)))
        | ~ sP333(U_4053,U_4054) )
    & ! [U_4053,U_4054] :
        ( sP333(U_4053,U_4054)
        | ~ class_Rings_Olinordered__idom(U_4053)
        | ~ class_Int_Onumber__ring(U_4053) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP333])],[f_1160_2]) ).

cnf(f_1160_4,plain,
    ( sP333(U_4053,U_4054)
    | ~ class_Rings_Olinordered__idom(U_4053)
    | ~ class_Int_Onumber__ring(U_4053) ),
    inference(clausify,[status(thm)],[f_1160_3]) ).

cnf(f_1160_5,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4053),hAPP(c_Int_Onumber__class_Onumber__of(U_4053),U_4054)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4053),hAPP(c_Int_Onumber__class_Onumber__of(U_4053),U_4054))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4053),hAPP(c_Int_Onumber__class_Onumber__of(U_4053),U_4054)),c_Groups_Ozero__class_Ozero(U_4053)))
    | ~ sP333(U_4053,U_4054) ),
    inference(clausify,[status(thm)],[f_1160_3]) ).

cnf(f_1160_6,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4053),hAPP(c_Int_Onumber__class_Onumber__of(U_4053),U_4054)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4053),U_4054)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4053),hAPP(c_Int_Onumber__class_Onumber__of(U_4053),U_4054)),c_Groups_Ozero__class_Ozero(U_4053)))
    | ~ sP333(U_4053,U_4054) ),
    inference(clausify,[status(thm)],[f_1160_3]) ).

fof(f_1161_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_1161_2,plain,
    ! [U_4056,U_4055] :
      ( ( 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_4055)),U_4056)))
        | ( U_4056 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_4055 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      & ( U_4056 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4055 != 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_4055)),U_4056))) ) ),
    inference(variable_rename,[status(thm)],[f_1161_1]) ).

fof(f_1161_3,plain,
    ( ! [U_4060,U_4058] :
        ( 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_4058)),U_4060)))
        | ( U_4060 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_4058 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
    & ! [U_4059,U_4057] :
        ( U_4059 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4057 != 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_4057)),U_4059))) ) ),
    inference(miniscope,[status(thm)],[f_1161_2]) ).

fof(f_1161_4,plain,
    ( ! [U_4060,U_4058] :
        ( U_4060 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP334(U_4060,U_4058) )
    & ! [U_4060,U_4058] :
        ( U_4058 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP334(U_4060,U_4058) )
    & ! [U_4060,U_4058] :
        ( 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_4058)),U_4060)))
        | sP334(U_4060,U_4058) )
    & ! [U_4057,U_4059] :
        ( U_4059 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4057 != 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_4057)),U_4059))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP334])],[f_1161_3]) ).

cnf(f_1161_5,plain,
    ( U_4059 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_4057 != 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_4057)),U_4059))) ),
    inference(clausify,[status(thm)],[f_1161_4]) ).

cnf(f_1161_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_4058)),U_4060)))
    | sP334(U_4060,U_4058) ),
    inference(clausify,[status(thm)],[f_1161_4]) ).

cnf(f_1161_7,plain,
    ( U_4058 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP334(U_4060,U_4058) ),
    inference(clausify,[status(thm)],[f_1161_4]) ).

cnf(f_1161_8,plain,
    ( U_4060 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP334(U_4060,U_4058) ),
    inference(clausify,[status(thm)],[f_1161_4]) ).

fof(f_1162_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_1162_2,plain,
    ! [U_4062,U_4061] : c_Divides_Odivmod__nat(U_4061,U_4062) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4061),U_4062)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4061,U_4062)),
    inference(variable_rename,[status(thm)],[f_1162_1]) ).

fof(f_1162_3,plain,
    ! [U_4062,U_4061] : c_Divides_Odivmod__nat(U_4061,U_4062) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4061),U_4062)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4061,U_4062)),
    inference(definitional_conversion,[status(esa)],[f_1162_2]) ).

cnf(f_1162_4,plain,
    c_Divides_Odivmod__nat(U_4061,U_4062) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4061),U_4062)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4061,U_4062)),
    inference(clausify,[status(thm)],[f_1162_3]) ).

fof(f_1163_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_1163_2,plain,
    ! [U_4064,U_4063] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4063),c_Groups_Ozero__class_Ozero(U_4063)),hAPP(c_Groups_Oabs__class_Oabs(U_4063),U_4064)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4063) ),
    inference(variable_rename,[status(thm)],[f_1163_1]) ).

fof(f_1163_3,plain,
    ! [U_4063,U_4064] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4063),c_Groups_Ozero__class_Ozero(U_4063)),hAPP(c_Groups_Oabs__class_Oabs(U_4063),U_4064)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4063) ),
    inference(definitional_conversion,[status(esa)],[f_1163_2]) ).

cnf(f_1163_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4063),c_Groups_Ozero__class_Ozero(U_4063)),hAPP(c_Groups_Oabs__class_Oabs(U_4063),U_4064)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4063) ),
    inference(clausify,[status(thm)],[f_1163_3]) ).

fof(f_1164_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_1164_2,plain,
    ! [U_4066,U_4065] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4065),hAPP(c_Groups_Oabs__class_Oabs(U_4065),U_4066)),c_Groups_Ozero__class_Ozero(U_4065)))
          | U_4066 != c_Groups_Ozero__class_Ozero(U_4065) )
        & ( U_4066 = c_Groups_Ozero__class_Ozero(U_4065)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4065),hAPP(c_Groups_Oabs__class_Oabs(U_4065),U_4066)),c_Groups_Ozero__class_Ozero(U_4065))) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4065) ),
    inference(variable_rename,[status(thm)],[f_1164_1]) ).

fof(f_1164_3,plain,
    ( ! [U_4065,U_4066] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4065),hAPP(c_Groups_Oabs__class_Oabs(U_4065),U_4066)),c_Groups_Ozero__class_Ozero(U_4065)))
        | U_4066 != c_Groups_Ozero__class_Ozero(U_4065)
        | ~ sP335(U_4065,U_4066) )
    & ! [U_4065,U_4066] :
        ( U_4066 = c_Groups_Ozero__class_Ozero(U_4065)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4065),hAPP(c_Groups_Oabs__class_Oabs(U_4065),U_4066)),c_Groups_Ozero__class_Ozero(U_4065)))
        | ~ sP335(U_4065,U_4066) )
    & ! [U_4065,U_4066] :
        ( sP335(U_4065,U_4066)
        | ~ class_Groups_Oordered__ab__group__add__abs(U_4065) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP335])],[f_1164_2]) ).

cnf(f_1164_4,plain,
    ( sP335(U_4065,U_4066)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4065) ),
    inference(clausify,[status(thm)],[f_1164_3]) ).

cnf(f_1164_5,plain,
    ( U_4066 = c_Groups_Ozero__class_Ozero(U_4065)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4065),hAPP(c_Groups_Oabs__class_Oabs(U_4065),U_4066)),c_Groups_Ozero__class_Ozero(U_4065)))
    | ~ sP335(U_4065,U_4066) ),
    inference(clausify,[status(thm)],[f_1164_3]) ).

cnf(f_1164_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4065),hAPP(c_Groups_Oabs__class_Oabs(U_4065),U_4066)),c_Groups_Ozero__class_Ozero(U_4065)))
    | U_4066 != c_Groups_Ozero__class_Ozero(U_4065)
    | ~ sP335(U_4065,U_4066) ),
    inference(clausify,[status(thm)],[f_1164_3]) ).

fof(f_1165_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_1165_2,plain,
    ! [U_4068,U_4067] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4067),U_4068) = U_4068
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4067),c_Groups_Ozero__class_Ozero(U_4067)),U_4068))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4067) ),
    inference(variable_rename,[status(thm)],[f_1165_1]) ).

fof(f_1165_3,plain,
    ! [U_4068,U_4067] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4067),U_4068) = U_4068
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4067),c_Groups_Ozero__class_Ozero(U_4067)),U_4068))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4067) ),
    inference(definitional_conversion,[status(esa)],[f_1165_2]) ).

cnf(f_1165_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4067),U_4068) = U_4068
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4067),c_Groups_Ozero__class_Ozero(U_4067)),U_4068))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4067) ),
    inference(clausify,[status(thm)],[f_1165_3]) ).

fof(f_1166_1,plain,
    ! [V_a,T_a] :
      ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = 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_1166_2,plain,
    ! [U_4070,U_4069] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4069),U_4070) = U_4070
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4069),c_Groups_Ozero__class_Ozero(U_4069)),U_4070))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4069) ),
    inference(variable_rename,[status(thm)],[f_1166_1]) ).

fof(f_1166_3,plain,
    ! [U_4069,U_4070] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4069),U_4070) = U_4070
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4069),c_Groups_Ozero__class_Ozero(U_4069)),U_4070))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4069) ),
    inference(definitional_conversion,[status(esa)],[f_1166_2]) ).

cnf(f_1166_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4069),U_4070) = U_4070
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4069),c_Groups_Ozero__class_Ozero(U_4069)),U_4070))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4069) ),
    inference(clausify,[status(thm)],[f_1166_3]) ).

fof(f_1167_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_1167_2,plain,
    ! [U_4072,U_4071] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4071),c_Groups_Ozero__class_Ozero(U_4071)),hAPP(c_Groups_Oabs__class_Oabs(U_4071),U_4072)))
          | U_4072 = c_Groups_Ozero__class_Ozero(U_4071) )
        & ( U_4072 != c_Groups_Ozero__class_Ozero(U_4071)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4071),c_Groups_Ozero__class_Ozero(U_4071)),hAPP(c_Groups_Oabs__class_Oabs(U_4071),U_4072))) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4071) ),
    inference(variable_rename,[status(thm)],[f_1167_1]) ).

fof(f_1167_3,plain,
    ( ! [U_4071,U_4072] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4071),c_Groups_Ozero__class_Ozero(U_4071)),hAPP(c_Groups_Oabs__class_Oabs(U_4071),U_4072)))
        | U_4072 = c_Groups_Ozero__class_Ozero(U_4071)
        | ~ sP336(U_4071,U_4072) )
    & ! [U_4071,U_4072] :
        ( U_4072 != c_Groups_Ozero__class_Ozero(U_4071)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4071),c_Groups_Ozero__class_Ozero(U_4071)),hAPP(c_Groups_Oabs__class_Oabs(U_4071),U_4072)))
        | ~ sP336(U_4071,U_4072) )
    & ! [U_4071,U_4072] :
        ( sP336(U_4071,U_4072)
        | ~ class_Groups_Oordered__ab__group__add__abs(U_4071) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP336])],[f_1167_2]) ).

cnf(f_1167_4,plain,
    ( sP336(U_4071,U_4072)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4071) ),
    inference(clausify,[status(thm)],[f_1167_3]) ).

cnf(f_1167_5,plain,
    ( U_4072 != c_Groups_Ozero__class_Ozero(U_4071)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4071),c_Groups_Ozero__class_Ozero(U_4071)),hAPP(c_Groups_Oabs__class_Oabs(U_4071),U_4072)))
    | ~ sP336(U_4071,U_4072) ),
    inference(clausify,[status(thm)],[f_1167_3]) ).

cnf(f_1167_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4071),c_Groups_Ozero__class_Ozero(U_4071)),hAPP(c_Groups_Oabs__class_Oabs(U_4071),U_4072)))
    | U_4072 = c_Groups_Ozero__class_Ozero(U_4071)
    | ~ sP336(U_4071,U_4072) ),
    inference(clausify,[status(thm)],[f_1167_3]) ).

fof(f_1168_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_1168_2,plain,
    ! [U_4074,U_4073] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4073),hAPP(c_Groups_Oabs__class_Oabs(U_4073),U_4074)),c_Groups_Ozero__class_Ozero(U_4073)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4073) ),
    inference(variable_rename,[status(thm)],[f_1168_1]) ).

fof(f_1168_3,plain,
    ! [U_4074,U_4073] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4073),hAPP(c_Groups_Oabs__class_Oabs(U_4073),U_4074)),c_Groups_Ozero__class_Ozero(U_4073)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4073) ),
    inference(definitional_conversion,[status(esa)],[f_1168_2]) ).

cnf(f_1168_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4073),hAPP(c_Groups_Oabs__class_Oabs(U_4073),U_4074)),c_Groups_Ozero__class_Ozero(U_4073)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4073) ),
    inference(clausify,[status(thm)],[f_1168_3]) ).

fof(f_1169_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_1169_2,plain,
    ! [U_4077,U_4076,U_4075] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4075),hAPP(c_Groups_Oabs__class_Oabs(U_4075),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4075),U_4076),U_4077))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4075),hAPP(c_Groups_Oabs__class_Oabs(U_4075),U_4076)),hAPP(c_Groups_Oabs__class_Oabs(U_4075),U_4077))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4075) ),
    inference(variable_rename,[status(thm)],[f_1169_1]) ).

fof(f_1169_3,plain,
    ! [U_4075,U_4076,U_4077] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4075),hAPP(c_Groups_Oabs__class_Oabs(U_4075),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4075),U_4076),U_4077))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4075),hAPP(c_Groups_Oabs__class_Oabs(U_4075),U_4076)),hAPP(c_Groups_Oabs__class_Oabs(U_4075),U_4077))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4075) ),
    inference(definitional_conversion,[status(esa)],[f_1169_2]) ).

cnf(f_1169_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4075),hAPP(c_Groups_Oabs__class_Oabs(U_4075),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4075),U_4076),U_4077))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4075),hAPP(c_Groups_Oabs__class_Oabs(U_4075),U_4076)),hAPP(c_Groups_Oabs__class_Oabs(U_4075),U_4077))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4075) ),
    inference(clausify,[status(thm)],[f_1169_3]) ).

fof(f_1170_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_1170_2,plain,
    ! [U_4082,U_4081,U_4080,U_4079,U_4078] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4078),hAPP(c_Groups_Oabs__class_Oabs(U_4078),U_4079)),hAPP(c_Groups_Oabs__class_Oabs(U_4078),U_4081))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4078),U_4080),U_4082)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4078),hAPP(c_Groups_Oabs__class_Oabs(U_4078),U_4081)),U_4082))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4078),hAPP(c_Groups_Oabs__class_Oabs(U_4078),U_4079)),U_4080))
      | ~ class_Rings_Olinordered__idom(U_4078) ),
    inference(variable_rename,[status(thm)],[f_1170_1]) ).

fof(f_1170_3,plain,
    ! [U_4078,U_4079,U_4080,U_4081,U_4082] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4078),hAPP(c_Groups_Oabs__class_Oabs(U_4078),U_4079)),hAPP(c_Groups_Oabs__class_Oabs(U_4078),U_4081))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4078),U_4080),U_4082)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4078),hAPP(c_Groups_Oabs__class_Oabs(U_4078),U_4081)),U_4082))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4078),hAPP(c_Groups_Oabs__class_Oabs(U_4078),U_4079)),U_4080))
      | ~ class_Rings_Olinordered__idom(U_4078) ),
    inference(definitional_conversion,[status(esa)],[f_1170_2]) ).

cnf(f_1170_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4078),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4078),hAPP(c_Groups_Oabs__class_Oabs(U_4078),U_4079)),hAPP(c_Groups_Oabs__class_Oabs(U_4078),U_4081))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4078),U_4080),U_4082)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4078),hAPP(c_Groups_Oabs__class_Oabs(U_4078),U_4081)),U_4082))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4078),hAPP(c_Groups_Oabs__class_Oabs(U_4078),U_4079)),U_4080))
    | ~ class_Rings_Olinordered__idom(U_4078) ),
    inference(clausify,[status(thm)],[f_1170_3]) ).

fof(f_1171_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_1171_2,plain,
    ! [U_4085,U_4084,U_4083] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4083),hAPP(c_Groups_Oabs__class_Oabs(U_4083),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4083),hAPP(c_Groups_Oabs__class_Oabs(U_4083),U_4084)),hAPP(c_Groups_Oabs__class_Oabs(U_4083),U_4085)))),hAPP(c_Groups_Oabs__class_Oabs(U_4083),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4083),U_4084),U_4085))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4083) ),
    inference(variable_rename,[status(thm)],[f_1171_1]) ).

fof(f_1171_3,plain,
    ! [U_4084,U_4083,U_4085] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4083),hAPP(c_Groups_Oabs__class_Oabs(U_4083),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4083),hAPP(c_Groups_Oabs__class_Oabs(U_4083),U_4084)),hAPP(c_Groups_Oabs__class_Oabs(U_4083),U_4085)))),hAPP(c_Groups_Oabs__class_Oabs(U_4083),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4083),U_4084),U_4085))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4083) ),
    inference(definitional_conversion,[status(esa)],[f_1171_2]) ).

cnf(f_1171_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4083),hAPP(c_Groups_Oabs__class_Oabs(U_4083),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4083),hAPP(c_Groups_Oabs__class_Oabs(U_4083),U_4084)),hAPP(c_Groups_Oabs__class_Oabs(U_4083),U_4085)))),hAPP(c_Groups_Oabs__class_Oabs(U_4083),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4083),U_4084),U_4085))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4083) ),
    inference(clausify,[status(thm)],[f_1171_3]) ).

fof(f_1172_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_1172_2,plain,
    ! [U_4088,U_4087,U_4086] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4086),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4086),hAPP(c_Groups_Oabs__class_Oabs(U_4086),U_4087)),hAPP(c_Groups_Oabs__class_Oabs(U_4086),U_4088))),hAPP(c_Groups_Oabs__class_Oabs(U_4086),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4086),U_4087),U_4088))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4086) ),
    inference(variable_rename,[status(thm)],[f_1172_1]) ).

fof(f_1172_3,plain,
    ! [U_4086,U_4087,U_4088] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4086),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4086),hAPP(c_Groups_Oabs__class_Oabs(U_4086),U_4087)),hAPP(c_Groups_Oabs__class_Oabs(U_4086),U_4088))),hAPP(c_Groups_Oabs__class_Oabs(U_4086),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4086),U_4087),U_4088))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4086) ),
    inference(definitional_conversion,[status(esa)],[f_1172_2]) ).

cnf(f_1172_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4086),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4086),hAPP(c_Groups_Oabs__class_Oabs(U_4086),U_4087)),hAPP(c_Groups_Oabs__class_Oabs(U_4086),U_4088))),hAPP(c_Groups_Oabs__class_Oabs(U_4086),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4086),U_4087),U_4088))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4086) ),
    inference(clausify,[status(thm)],[f_1172_3]) ).

fof(f_1173_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_1173_2,plain,
    ! [U_4091,U_4090,U_4089] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4089),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4089),hAPP(c_Groups_Oabs__class_Oabs(U_4089),U_4090)),hAPP(c_Groups_Oabs__class_Oabs(U_4089),U_4091))),hAPP(c_Groups_Oabs__class_Oabs(U_4089),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4089),U_4091),U_4090))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4089) ),
    inference(variable_rename,[status(thm)],[f_1173_1]) ).

fof(f_1173_3,plain,
    ! [U_4089,U_4090,U_4091] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4089),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4089),hAPP(c_Groups_Oabs__class_Oabs(U_4089),U_4090)),hAPP(c_Groups_Oabs__class_Oabs(U_4089),U_4091))),hAPP(c_Groups_Oabs__class_Oabs(U_4089),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4089),U_4091),U_4090))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4089) ),
    inference(definitional_conversion,[status(esa)],[f_1173_2]) ).

cnf(f_1173_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4089),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4089),hAPP(c_Groups_Oabs__class_Oabs(U_4089),U_4090)),hAPP(c_Groups_Oabs__class_Oabs(U_4089),U_4091))),hAPP(c_Groups_Oabs__class_Oabs(U_4089),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4089),U_4091),U_4090))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4089) ),
    inference(clausify,[status(thm)],[f_1173_3]) ).

fof(f_1174_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_1174_2,plain,
    ! [U_4094,U_4093,U_4092] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4092),hAPP(c_Groups_Ouminus__class_Ouminus(U_4092),U_4093)),U_4094))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4092),hAPP(c_Groups_Oabs__class_Oabs(U_4092),U_4093)),U_4094))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4092) ),
    inference(variable_rename,[status(thm)],[f_1174_1]) ).

fof(f_1174_3,plain,
    ! [U_4093,U_4092,U_4094] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4092),hAPP(c_Groups_Ouminus__class_Ouminus(U_4092),U_4093)),U_4094))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4092),hAPP(c_Groups_Oabs__class_Oabs(U_4092),U_4093)),U_4094))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4092) ),
    inference(definitional_conversion,[status(esa)],[f_1174_2]) ).

cnf(f_1174_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4092),hAPP(c_Groups_Ouminus__class_Ouminus(U_4092),U_4093)),U_4094))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4092),hAPP(c_Groups_Oabs__class_Oabs(U_4092),U_4093)),U_4094))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4092) ),
    inference(clausify,[status(thm)],[f_1174_3]) ).

fof(f_1175_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_1175_2,plain,
    ! [U_4097,U_4096,U_4095] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4095),hAPP(c_Groups_Oabs__class_Oabs(U_4095),U_4096)),U_4097))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4095),hAPP(c_Groups_Ouminus__class_Ouminus(U_4095),U_4096)),U_4097))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4095),U_4096),U_4097))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4095) ),
    inference(variable_rename,[status(thm)],[f_1175_1]) ).

fof(f_1175_3,plain,
    ! [U_4095,U_4096,U_4097] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4095),hAPP(c_Groups_Oabs__class_Oabs(U_4095),U_4096)),U_4097))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4095),hAPP(c_Groups_Ouminus__class_Ouminus(U_4095),U_4096)),U_4097))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4095),U_4096),U_4097))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4095) ),
    inference(definitional_conversion,[status(esa)],[f_1175_2]) ).

cnf(f_1175_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4095),hAPP(c_Groups_Oabs__class_Oabs(U_4095),U_4096)),U_4097))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4095),hAPP(c_Groups_Ouminus__class_Ouminus(U_4095),U_4096)),U_4097))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4095),U_4096),U_4097))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4095) ),
    inference(clausify,[status(thm)],[f_1175_3]) ).

fof(f_1176_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_1176_2,plain,
    ! [U_4100,U_4099,U_4098] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4098),hAPP(c_Groups_Oabs__class_Oabs(U_4098),U_4099)),U_4100))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4098),hAPP(c_Groups_Ouminus__class_Ouminus(U_4098),U_4099)),U_4100))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4098),U_4099),U_4100)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4098),hAPP(c_Groups_Ouminus__class_Ouminus(U_4098),U_4099)),U_4100))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4098),U_4099),U_4100)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4098),hAPP(c_Groups_Oabs__class_Oabs(U_4098),U_4099)),U_4100)) ) )
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4098) ),
    inference(variable_rename,[status(thm)],[f_1176_1]) ).

fof(f_1176_3,plain,
    ( ! [U_4099,U_4098,U_4100] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4098),hAPP(c_Groups_Ouminus__class_Ouminus(U_4098),U_4099)),U_4100))
        | ~ sP337(U_4099,U_4098,U_4100) )
    & ! [U_4099,U_4098,U_4100] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4098),U_4099),U_4100))
        | ~ sP337(U_4099,U_4098,U_4100) )
    & ! [U_4099,U_4098,U_4100] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4098),hAPP(c_Groups_Oabs__class_Oabs(U_4098),U_4099)),U_4100))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4098),hAPP(c_Groups_Ouminus__class_Ouminus(U_4098),U_4099)),U_4100))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4098),U_4099),U_4100))
        | ~ sP338(U_4099,U_4098,U_4100) )
    & ! [U_4099,U_4098,U_4100] :
        ( sP337(U_4099,U_4098,U_4100)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4098),hAPP(c_Groups_Oabs__class_Oabs(U_4098),U_4099)),U_4100))
        | ~ sP338(U_4099,U_4098,U_4100) )
    & ! [U_4099,U_4098,U_4100] :
        ( sP338(U_4099,U_4098,U_4100)
        | ~ class_Groups_Oordered__ab__group__add__abs(U_4098) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP337,sP338])],[f_1176_2]) ).

cnf(f_1176_4,plain,
    ( sP338(U_4099,U_4098,U_4100)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4098) ),
    inference(clausify,[status(thm)],[f_1176_3]) ).

cnf(f_1176_5,plain,
    ( sP337(U_4099,U_4098,U_4100)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4098),hAPP(c_Groups_Oabs__class_Oabs(U_4098),U_4099)),U_4100))
    | ~ sP338(U_4099,U_4098,U_4100) ),
    inference(clausify,[status(thm)],[f_1176_3]) ).

cnf(f_1176_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4098),hAPP(c_Groups_Oabs__class_Oabs(U_4098),U_4099)),U_4100))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4098),hAPP(c_Groups_Ouminus__class_Ouminus(U_4098),U_4099)),U_4100))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4098),U_4099),U_4100))
    | ~ sP338(U_4099,U_4098,U_4100) ),
    inference(clausify,[status(thm)],[f_1176_3]) ).

cnf(f_1176_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4098),U_4099),U_4100))
    | ~ sP337(U_4099,U_4098,U_4100) ),
    inference(clausify,[status(thm)],[f_1176_3]) ).

cnf(f_1176_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4098),hAPP(c_Groups_Ouminus__class_Ouminus(U_4098),U_4099)),U_4100))
    | ~ sP337(U_4099,U_4098,U_4100) ),
    inference(clausify,[status(thm)],[f_1176_3]) ).

fof(f_1177_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_1177_2,plain,
    ! [U_4102,U_4101] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4101),hAPP(c_Groups_Ouminus__class_Ouminus(U_4101),U_4102)),hAPP(c_Groups_Oabs__class_Oabs(U_4101),U_4102)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4101) ),
    inference(variable_rename,[status(thm)],[f_1177_1]) ).

fof(f_1177_3,plain,
    ! [U_4102,U_4101] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4101),hAPP(c_Groups_Ouminus__class_Ouminus(U_4101),U_4102)),hAPP(c_Groups_Oabs__class_Oabs(U_4101),U_4102)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4101) ),
    inference(definitional_conversion,[status(esa)],[f_1177_2]) ).

cnf(f_1177_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4101),hAPP(c_Groups_Ouminus__class_Ouminus(U_4101),U_4102)),hAPP(c_Groups_Oabs__class_Oabs(U_4101),U_4102)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4101) ),
    inference(clausify,[status(thm)],[f_1177_3]) ).

fof(f_1178_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_1178_2,plain,
    ! [U_4105,U_4104,U_4103] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4103),hAPP(c_Groups_Oabs__class_Oabs(U_4103),U_4104)),U_4105))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4103),hAPP(c_Groups_Ouminus__class_Ouminus(U_4103),U_4104)),U_4105))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4103),U_4104),U_4105)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4103),hAPP(c_Groups_Ouminus__class_Ouminus(U_4103),U_4104)),U_4105))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4103),U_4104),U_4105)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4103),hAPP(c_Groups_Oabs__class_Oabs(U_4103),U_4104)),U_4105)) ) )
      | ~ class_Rings_Olinordered__idom(U_4103) ),
    inference(variable_rename,[status(thm)],[f_1178_1]) ).

fof(f_1178_3,plain,
    ( ! [U_4103,U_4104,U_4105] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4103),hAPP(c_Groups_Ouminus__class_Ouminus(U_4103),U_4104)),U_4105))
        | ~ sP339(U_4103,U_4104,U_4105) )
    & ! [U_4103,U_4104,U_4105] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4103),U_4104),U_4105))
        | ~ sP339(U_4103,U_4104,U_4105) )
    & ! [U_4103,U_4104,U_4105] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4103),hAPP(c_Groups_Oabs__class_Oabs(U_4103),U_4104)),U_4105))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4103),hAPP(c_Groups_Ouminus__class_Ouminus(U_4103),U_4104)),U_4105))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4103),U_4104),U_4105))
        | ~ sP340(U_4103,U_4104,U_4105) )
    & ! [U_4103,U_4104,U_4105] :
        ( sP339(U_4103,U_4104,U_4105)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4103),hAPP(c_Groups_Oabs__class_Oabs(U_4103),U_4104)),U_4105))
        | ~ sP340(U_4103,U_4104,U_4105) )
    & ! [U_4103,U_4104,U_4105] :
        ( sP340(U_4103,U_4104,U_4105)
        | ~ class_Rings_Olinordered__idom(U_4103) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP339,sP340])],[f_1178_2]) ).

cnf(f_1178_4,plain,
    ( sP340(U_4103,U_4104,U_4105)
    | ~ class_Rings_Olinordered__idom(U_4103) ),
    inference(clausify,[status(thm)],[f_1178_3]) ).

cnf(f_1178_5,plain,
    ( sP339(U_4103,U_4104,U_4105)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4103),hAPP(c_Groups_Oabs__class_Oabs(U_4103),U_4104)),U_4105))
    | ~ sP340(U_4103,U_4104,U_4105) ),
    inference(clausify,[status(thm)],[f_1178_3]) ).

cnf(f_1178_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4103),hAPP(c_Groups_Oabs__class_Oabs(U_4103),U_4104)),U_4105))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4103),hAPP(c_Groups_Ouminus__class_Ouminus(U_4103),U_4104)),U_4105))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4103),U_4104),U_4105))
    | ~ sP340(U_4103,U_4104,U_4105) ),
    inference(clausify,[status(thm)],[f_1178_3]) ).

cnf(f_1178_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4103),U_4104),U_4105))
    | ~ sP339(U_4103,U_4104,U_4105) ),
    inference(clausify,[status(thm)],[f_1178_3]) ).

cnf(f_1178_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4103),hAPP(c_Groups_Ouminus__class_Ouminus(U_4103),U_4104)),U_4105))
    | ~ sP339(U_4103,U_4104,U_4105) ),
    inference(clausify,[status(thm)],[f_1178_3]) ).

fof(f_1179_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_1179_2,plain,
    ! [U_4108,U_4107,U_4106] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4106),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4107)),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4108)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4108)),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4107))) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4108)),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4107)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4106),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4107)),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4108))) ) )
      | ~ class_Orderings_Olinorder(U_4106)
      | ~ class_Int_Onumber(U_4106) ),
    inference(variable_rename,[status(thm)],[f_1179_1]) ).

fof(f_1179_3,plain,
    ( ! [U_4108,U_4107,U_4106] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4106),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4107)),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4108)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4108)),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4107)))
        | ~ sP341(U_4108,U_4107,U_4106) )
    & ! [U_4108,U_4107,U_4106] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4108)),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4107)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4106),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4107)),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4108)))
        | ~ sP341(U_4108,U_4107,U_4106) )
    & ! [U_4108,U_4107,U_4106] :
        ( sP341(U_4108,U_4107,U_4106)
        | ~ class_Orderings_Olinorder(U_4106)
        | ~ class_Int_Onumber(U_4106) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP341])],[f_1179_2]) ).

cnf(f_1179_4,plain,
    ( sP341(U_4108,U_4107,U_4106)
    | ~ class_Orderings_Olinorder(U_4106)
    | ~ class_Int_Onumber(U_4106) ),
    inference(clausify,[status(thm)],[f_1179_3]) ).

cnf(f_1179_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4108)),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4107)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4106),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4107)),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4108)))
    | ~ sP341(U_4108,U_4107,U_4106) ),
    inference(clausify,[status(thm)],[f_1179_3]) ).

cnf(f_1179_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4106),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4107)),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4108)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4106),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4108)),hAPP(c_Int_Onumber__class_Onumber__of(U_4106),U_4107)))
    | ~ sP341(U_4108,U_4107,U_4106) ),
    inference(clausify,[status(thm)],[f_1179_3]) ).

fof(f_1180_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_1180_2,plain,
    ! [U_4112,U_4111,U_4110,U_4109] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4109),hAPP(c_Int_Onumber__class_Onumber__of(U_4109),U_4110)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4109),U_4111),U_4112)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4109),hAPP(c_Int_Onumber__class_Onumber__of(U_4109),U_4110)),U_4111)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4109),hAPP(c_Int_Onumber__class_Onumber__of(U_4109),U_4110)),U_4112))
      | ~ class_Rings_Osemiring(U_4109)
      | ~ class_Int_Onumber(U_4109) ),
    inference(variable_rename,[status(thm)],[f_1180_1]) ).

fof(f_1180_3,plain,
    ! [U_4110,U_4111,U_4109,U_4112] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4109),hAPP(c_Int_Onumber__class_Onumber__of(U_4109),U_4110)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4109),U_4111),U_4112)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4109),hAPP(c_Int_Onumber__class_Onumber__of(U_4109),U_4110)),U_4111)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4109),hAPP(c_Int_Onumber__class_Onumber__of(U_4109),U_4110)),U_4112))
      | ~ class_Rings_Osemiring(U_4109)
      | ~ class_Int_Onumber(U_4109) ),
    inference(definitional_conversion,[status(esa)],[f_1180_2]) ).

cnf(f_1180_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4109),hAPP(c_Int_Onumber__class_Onumber__of(U_4109),U_4110)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4109),U_4111),U_4112)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4109),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4109),hAPP(c_Int_Onumber__class_Onumber__of(U_4109),U_4110)),U_4111)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4109),hAPP(c_Int_Onumber__class_Onumber__of(U_4109),U_4110)),U_4112))
    | ~ class_Rings_Osemiring(U_4109)
    | ~ class_Int_Onumber(U_4109) ),
    inference(clausify,[status(thm)],[f_1180_3]) ).

fof(f_1181_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_1181_2,plain,
    ! [U_4116,U_4115,U_4114,U_4113] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4113),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4113),U_4114),U_4115)),hAPP(c_Int_Onumber__class_Onumber__of(U_4113),U_4116)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4113),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4113),U_4114),hAPP(c_Int_Onumber__class_Onumber__of(U_4113),U_4116))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4113),U_4115),hAPP(c_Int_Onumber__class_Onumber__of(U_4113),U_4116)))
      | ~ class_Rings_Osemiring(U_4113)
      | ~ class_Int_Onumber(U_4113) ),
    inference(variable_rename,[status(thm)],[f_1181_1]) ).

fof(f_1181_3,plain,
    ! [U_4113,U_4114,U_4115,U_4116] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4113),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4113),U_4114),U_4115)),hAPP(c_Int_Onumber__class_Onumber__of(U_4113),U_4116)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4113),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4113),U_4114),hAPP(c_Int_Onumber__class_Onumber__of(U_4113),U_4116))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4113),U_4115),hAPP(c_Int_Onumber__class_Onumber__of(U_4113),U_4116)))
      | ~ class_Rings_Osemiring(U_4113)
      | ~ class_Int_Onumber(U_4113) ),
    inference(definitional_conversion,[status(esa)],[f_1181_2]) ).

cnf(f_1181_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4113),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4113),U_4114),U_4115)),hAPP(c_Int_Onumber__class_Onumber__of(U_4113),U_4116)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4113),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4113),U_4114),hAPP(c_Int_Onumber__class_Onumber__of(U_4113),U_4116))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4113),U_4115),hAPP(c_Int_Onumber__class_Onumber__of(U_4113),U_4116)))
    | ~ class_Rings_Osemiring(U_4113)
    | ~ class_Int_Onumber(U_4113) ),
    inference(clausify,[status(thm)],[f_1181_3]) ).

fof(f_1182_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_1182_2,plain,
    ! [U_4119,U_4118,U_4117] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4117),U_4118),hAPP(c_Nat_OSuc,U_4119)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4117),U_4118),hAPP(hAPP(c_Power_Opower__class_Opower(U_4117),U_4118),U_4119))
      | ~ class_Rings_Ocomm__semiring__1(U_4117) ),
    inference(variable_rename,[status(thm)],[f_1182_1]) ).

fof(f_1182_3,plain,
    ! [U_4119,U_4118,U_4117] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4117),U_4118),hAPP(c_Nat_OSuc,U_4119)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4117),U_4118),hAPP(hAPP(c_Power_Opower__class_Opower(U_4117),U_4118),U_4119))
      | ~ class_Rings_Ocomm__semiring__1(U_4117) ),
    inference(definitional_conversion,[status(esa)],[f_1182_2]) ).

cnf(f_1182_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4117),U_4118),hAPP(c_Nat_OSuc,U_4119)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4117),U_4118),hAPP(hAPP(c_Power_Opower__class_Opower(U_4117),U_4118),U_4119))
    | ~ class_Rings_Ocomm__semiring__1(U_4117) ),
    inference(clausify,[status(thm)],[f_1182_3]) ).

fof(f_1183_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_1183_2,plain,
    ! [U_4122,U_4121,U_4120] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4120),U_4121),hAPP(hAPP(c_Power_Opower__class_Opower(U_4120),U_4121),U_4122)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4120),U_4121),hAPP(c_Nat_OSuc,U_4122))
      | ~ class_Rings_Ocomm__semiring__1(U_4120) ),
    inference(variable_rename,[status(thm)],[f_1183_1]) ).

fof(f_1183_3,plain,
    ! [U_4120,U_4121,U_4122] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4120),U_4121),hAPP(hAPP(c_Power_Opower__class_Opower(U_4120),U_4121),U_4122)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4120),U_4121),hAPP(c_Nat_OSuc,U_4122))
      | ~ class_Rings_Ocomm__semiring__1(U_4120) ),
    inference(definitional_conversion,[status(esa)],[f_1183_2]) ).

cnf(f_1183_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4120),U_4121),hAPP(hAPP(c_Power_Opower__class_Opower(U_4120),U_4121),U_4122)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4120),U_4121),hAPP(c_Nat_OSuc,U_4122))
    | ~ class_Rings_Ocomm__semiring__1(U_4120) ),
    inference(clausify,[status(thm)],[f_1183_3]) ).

fof(f_1184_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_1184_2,plain,
    ! [U_4125,U_4124,U_4123] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4123),hAPP(hAPP(c_Power_Opower__class_Opower(U_4123),U_4124),U_4125)),U_4124) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4123),U_4124),hAPP(c_Nat_OSuc,U_4125))
      | ~ class_Rings_Ocomm__semiring__1(U_4123) ),
    inference(variable_rename,[status(thm)],[f_1184_1]) ).

fof(f_1184_3,plain,
    ! [U_4123,U_4124,U_4125] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4123),hAPP(hAPP(c_Power_Opower__class_Opower(U_4123),U_4124),U_4125)),U_4124) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4123),U_4124),hAPP(c_Nat_OSuc,U_4125))
      | ~ class_Rings_Ocomm__semiring__1(U_4123) ),
    inference(definitional_conversion,[status(esa)],[f_1184_2]) ).

cnf(f_1184_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4123),hAPP(hAPP(c_Power_Opower__class_Opower(U_4123),U_4124),U_4125)),U_4124) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4123),U_4124),hAPP(c_Nat_OSuc,U_4125))
    | ~ class_Rings_Ocomm__semiring__1(U_4123) ),
    inference(clausify,[status(thm)],[f_1184_3]) ).

fof(f_1185_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_1185_2,plain,
    ! [U_4129,U_4128,U_4127,U_4126] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4126),hAPP(c_Int_Onumber__class_Onumber__of(U_4126),U_4127)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4126),U_4128),U_4129)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4126),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4126),hAPP(c_Int_Onumber__class_Onumber__of(U_4126),U_4127)),U_4128)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4126),hAPP(c_Int_Onumber__class_Onumber__of(U_4126),U_4127)),U_4129))
      | ~ class_Rings_Oring(U_4126)
      | ~ class_Int_Onumber(U_4126) ),
    inference(variable_rename,[status(thm)],[f_1185_1]) ).

fof(f_1185_3,plain,
    ! [U_4126,U_4127,U_4128,U_4129] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4126),hAPP(c_Int_Onumber__class_Onumber__of(U_4126),U_4127)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4126),U_4128),U_4129)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4126),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4126),hAPP(c_Int_Onumber__class_Onumber__of(U_4126),U_4127)),U_4128)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4126),hAPP(c_Int_Onumber__class_Onumber__of(U_4126),U_4127)),U_4129))
      | ~ class_Rings_Oring(U_4126)
      | ~ class_Int_Onumber(U_4126) ),
    inference(definitional_conversion,[status(esa)],[f_1185_2]) ).

cnf(f_1185_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4126),hAPP(c_Int_Onumber__class_Onumber__of(U_4126),U_4127)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4126),U_4128),U_4129)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4126),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4126),hAPP(c_Int_Onumber__class_Onumber__of(U_4126),U_4127)),U_4128)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4126),hAPP(c_Int_Onumber__class_Onumber__of(U_4126),U_4127)),U_4129))
    | ~ class_Rings_Oring(U_4126)
    | ~ class_Int_Onumber(U_4126) ),
    inference(clausify,[status(thm)],[f_1185_3]) ).

fof(f_1186_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_1186_2,plain,
    ! [U_4133,U_4132,U_4131,U_4130] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4130),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4130),U_4131),U_4132)),hAPP(c_Int_Onumber__class_Onumber__of(U_4130),U_4133)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4130),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4130),U_4131),hAPP(c_Int_Onumber__class_Onumber__of(U_4130),U_4133))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4130),U_4132),hAPP(c_Int_Onumber__class_Onumber__of(U_4130),U_4133)))
      | ~ class_Rings_Oring(U_4130)
      | ~ class_Int_Onumber(U_4130) ),
    inference(variable_rename,[status(thm)],[f_1186_1]) ).

fof(f_1186_3,plain,
    ! [U_4130,U_4131,U_4132,U_4133] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4130),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4130),U_4131),U_4132)),hAPP(c_Int_Onumber__class_Onumber__of(U_4130),U_4133)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4130),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4130),U_4131),hAPP(c_Int_Onumber__class_Onumber__of(U_4130),U_4133))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4130),U_4132),hAPP(c_Int_Onumber__class_Onumber__of(U_4130),U_4133)))
      | ~ class_Rings_Oring(U_4130)
      | ~ class_Int_Onumber(U_4130) ),
    inference(definitional_conversion,[status(esa)],[f_1186_2]) ).

cnf(f_1186_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4130),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4130),U_4131),U_4132)),hAPP(c_Int_Onumber__class_Onumber__of(U_4130),U_4133)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4130),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4130),U_4131),hAPP(c_Int_Onumber__class_Onumber__of(U_4130),U_4133))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4130),U_4132),hAPP(c_Int_Onumber__class_Onumber__of(U_4130),U_4133)))
    | ~ class_Rings_Oring(U_4130)
    | ~ class_Int_Onumber(U_4130) ),
    inference(clausify,[status(thm)],[f_1186_3]) ).

fof(f_1187_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_1187_2,plain,
    ! [U_4136,U_4135,U_4134] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4134),hAPP(c_Int_Onumber__class_Onumber__of(U_4134),U_4135)),hAPP(c_Int_Onumber__class_Onumber__of(U_4134),U_4136)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4135),U_4136)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4135),U_4136))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4134),hAPP(c_Int_Onumber__class_Onumber__of(U_4134),U_4135)),hAPP(c_Int_Onumber__class_Onumber__of(U_4134),U_4136))) ) )
      | ~ class_Rings_Olinordered__idom(U_4134)
      | ~ class_Int_Onumber__ring(U_4134) ),
    inference(variable_rename,[status(thm)],[f_1187_1]) ).

fof(f_1187_3,plain,
    ( ! [U_4135,U_4134,U_4136] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4134),hAPP(c_Int_Onumber__class_Onumber__of(U_4134),U_4135)),hAPP(c_Int_Onumber__class_Onumber__of(U_4134),U_4136)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4135),U_4136))
        | ~ sP342(U_4135,U_4134,U_4136) )
    & ! [U_4135,U_4134,U_4136] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4135),U_4136))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4134),hAPP(c_Int_Onumber__class_Onumber__of(U_4134),U_4135)),hAPP(c_Int_Onumber__class_Onumber__of(U_4134),U_4136)))
        | ~ sP342(U_4135,U_4134,U_4136) )
    & ! [U_4135,U_4134,U_4136] :
        ( sP342(U_4135,U_4134,U_4136)
        | ~ class_Rings_Olinordered__idom(U_4134)
        | ~ class_Int_Onumber__ring(U_4134) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP342])],[f_1187_2]) ).

cnf(f_1187_4,plain,
    ( sP342(U_4135,U_4134,U_4136)
    | ~ class_Rings_Olinordered__idom(U_4134)
    | ~ class_Int_Onumber__ring(U_4134) ),
    inference(clausify,[status(thm)],[f_1187_3]) ).

cnf(f_1187_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4135),U_4136))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4134),hAPP(c_Int_Onumber__class_Onumber__of(U_4134),U_4135)),hAPP(c_Int_Onumber__class_Onumber__of(U_4134),U_4136)))
    | ~ sP342(U_4135,U_4134,U_4136) ),
    inference(clausify,[status(thm)],[f_1187_3]) ).

cnf(f_1187_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4134),hAPP(c_Int_Onumber__class_Onumber__of(U_4134),U_4135)),hAPP(c_Int_Onumber__class_Onumber__of(U_4134),U_4136)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4135),U_4136))
    | ~ sP342(U_4135,U_4134,U_4136) ),
    inference(clausify,[status(thm)],[f_1187_3]) ).

fof(f_1188_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_1188_2,plain,
    ! [U_4138,U_4137] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4137),U_4138),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4137)
      | ~ class_Rings_Ocomm__semiring__1(U_4137) ),
    inference(variable_rename,[status(thm)],[f_1188_1]) ).

fof(f_1188_3,plain,
    ! [U_4138,U_4137] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4137),U_4138),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4137)
      | ~ class_Rings_Ocomm__semiring__1(U_4137) ),
    inference(definitional_conversion,[status(esa)],[f_1188_2]) ).

cnf(f_1188_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4137),U_4138),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4137)
    | ~ class_Rings_Ocomm__semiring__1(U_4137) ),
    inference(clausify,[status(thm)],[f_1188_3]) ).

fof(f_1189_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_1189_2,plain,
    ! [U_4142,U_4141,U_4140,U_4139] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4139),hAPP(hAPP(c_Power_Opower__class_Opower(U_4139),U_4140),U_4141)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4139),U_4140),U_4142)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4139),U_4140),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4141),U_4142))
      | ~ class_Rings_Ocomm__semiring__1(U_4139) ),
    inference(variable_rename,[status(thm)],[f_1189_1]) ).

fof(f_1189_3,plain,
    ! [U_4139,U_4140,U_4141,U_4142] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4139),hAPP(hAPP(c_Power_Opower__class_Opower(U_4139),U_4140),U_4141)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4139),U_4140),U_4142)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4139),U_4140),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4141),U_4142))
      | ~ class_Rings_Ocomm__semiring__1(U_4139) ),
    inference(definitional_conversion,[status(esa)],[f_1189_2]) ).

cnf(f_1189_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4139),hAPP(hAPP(c_Power_Opower__class_Opower(U_4139),U_4140),U_4141)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4139),U_4140),U_4142)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4139),U_4140),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4141),U_4142))
    | ~ class_Rings_Ocomm__semiring__1(U_4139) ),
    inference(clausify,[status(thm)],[f_1189_3]) ).

fof(f_1190_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_1190_2,plain,
    ! [U_4145,U_4144,U_4143] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4143),hAPP(c_Int_Onumber__class_Onumber__of(U_4143),U_4144)),hAPP(c_Int_Onumber__class_Onumber__of(U_4143),U_4145)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4144),U_4145)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4144),U_4145))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4143),hAPP(c_Int_Onumber__class_Onumber__of(U_4143),U_4144)),hAPP(c_Int_Onumber__class_Onumber__of(U_4143),U_4145))) ) )
      | ~ class_Rings_Olinordered__idom(U_4143)
      | ~ class_Int_Onumber__ring(U_4143) ),
    inference(variable_rename,[status(thm)],[f_1190_1]) ).

fof(f_1190_3,plain,
    ( ! [U_4144,U_4143,U_4145] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4143),hAPP(c_Int_Onumber__class_Onumber__of(U_4143),U_4144)),hAPP(c_Int_Onumber__class_Onumber__of(U_4143),U_4145)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4144),U_4145))
        | ~ sP343(U_4144,U_4143,U_4145) )
    & ! [U_4144,U_4143,U_4145] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4144),U_4145))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4143),hAPP(c_Int_Onumber__class_Onumber__of(U_4143),U_4144)),hAPP(c_Int_Onumber__class_Onumber__of(U_4143),U_4145)))
        | ~ sP343(U_4144,U_4143,U_4145) )
    & ! [U_4144,U_4143,U_4145] :
        ( sP343(U_4144,U_4143,U_4145)
        | ~ class_Rings_Olinordered__idom(U_4143)
        | ~ class_Int_Onumber__ring(U_4143) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP343])],[f_1190_2]) ).

cnf(f_1190_4,plain,
    ( sP343(U_4144,U_4143,U_4145)
    | ~ class_Rings_Olinordered__idom(U_4143)
    | ~ class_Int_Onumber__ring(U_4143) ),
    inference(clausify,[status(thm)],[f_1190_3]) ).

cnf(f_1190_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4144),U_4145))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4143),hAPP(c_Int_Onumber__class_Onumber__of(U_4143),U_4144)),hAPP(c_Int_Onumber__class_Onumber__of(U_4143),U_4145)))
    | ~ sP343(U_4144,U_4143,U_4145) ),
    inference(clausify,[status(thm)],[f_1190_3]) ).

cnf(f_1190_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4143),hAPP(c_Int_Onumber__class_Onumber__of(U_4143),U_4144)),hAPP(c_Int_Onumber__class_Onumber__of(U_4143),U_4145)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4144),U_4145))
    | ~ sP343(U_4144,U_4143,U_4145) ),
    inference(clausify,[status(thm)],[f_1190_3]) ).

fof(f_1191_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_1191_2,plain,
    ! [U_4149,U_4148,U_4147,U_4146] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4146),hAPP(c_Int_Onumber__class_Onumber__of(U_4146),U_4147)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4146),hAPP(c_Int_Onumber__class_Onumber__of(U_4146),U_4148)),U_4149)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4146),hAPP(c_Int_Onumber__class_Onumber__of(U_4146),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4147),U_4148))),U_4149)
      | ~ class_Int_Onumber__ring(U_4146) ),
    inference(variable_rename,[status(thm)],[f_1191_1]) ).

fof(f_1191_3,plain,
    ! [U_4147,U_4148,U_4146,U_4149] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4146),hAPP(c_Int_Onumber__class_Onumber__of(U_4146),U_4147)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4146),hAPP(c_Int_Onumber__class_Onumber__of(U_4146),U_4148)),U_4149)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4146),hAPP(c_Int_Onumber__class_Onumber__of(U_4146),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4147),U_4148))),U_4149)
      | ~ class_Int_Onumber__ring(U_4146) ),
    inference(definitional_conversion,[status(esa)],[f_1191_2]) ).

cnf(f_1191_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4146),hAPP(c_Int_Onumber__class_Onumber__of(U_4146),U_4147)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4146),hAPP(c_Int_Onumber__class_Onumber__of(U_4146),U_4148)),U_4149)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4146),hAPP(c_Int_Onumber__class_Onumber__of(U_4146),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4147),U_4148))),U_4149)
    | ~ class_Int_Onumber__ring(U_4146) ),
    inference(clausify,[status(thm)],[f_1191_3]) ).

fof(f_1192_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_1192_2,plain,
    ! [U_4152,U_4151,U_4150] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4150),hAPP(c_Int_Onumber__class_Onumber__of(U_4150),U_4151)),hAPP(c_Int_Onumber__class_Onumber__of(U_4150),U_4152)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4150),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4151),U_4152))
      | ~ class_Int_Onumber__ring(U_4150) ),
    inference(variable_rename,[status(thm)],[f_1192_1]) ).

fof(f_1192_3,plain,
    ! [U_4150,U_4151,U_4152] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4150),hAPP(c_Int_Onumber__class_Onumber__of(U_4150),U_4151)),hAPP(c_Int_Onumber__class_Onumber__of(U_4150),U_4152)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4150),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4151),U_4152))
      | ~ class_Int_Onumber__ring(U_4150) ),
    inference(definitional_conversion,[status(esa)],[f_1192_2]) ).

cnf(f_1192_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4150),hAPP(c_Int_Onumber__class_Onumber__of(U_4150),U_4151)),hAPP(c_Int_Onumber__class_Onumber__of(U_4150),U_4152)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4150),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4151),U_4152))
    | ~ class_Int_Onumber__ring(U_4150) ),
    inference(clausify,[status(thm)],[f_1192_3]) ).

fof(f_1193_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_1193_2,plain,
    ! [U_4155,U_4154,U_4153] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4153),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4154),U_4155)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4153),hAPP(c_Int_Onumber__class_Onumber__of(U_4153),U_4154)),hAPP(c_Int_Onumber__class_Onumber__of(U_4153),U_4155))
      | ~ class_Int_Onumber__ring(U_4153) ),
    inference(variable_rename,[status(thm)],[f_1193_1]) ).

fof(f_1193_3,plain,
    ! [U_4153,U_4154,U_4155] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4153),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4154),U_4155)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4153),hAPP(c_Int_Onumber__class_Onumber__of(U_4153),U_4154)),hAPP(c_Int_Onumber__class_Onumber__of(U_4153),U_4155))
      | ~ class_Int_Onumber__ring(U_4153) ),
    inference(definitional_conversion,[status(esa)],[f_1193_2]) ).

cnf(f_1193_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4153),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4154),U_4155)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4153),hAPP(c_Int_Onumber__class_Onumber__of(U_4153),U_4154)),hAPP(c_Int_Onumber__class_Onumber__of(U_4153),U_4155))
    | ~ class_Int_Onumber__ring(U_4153) ),
    inference(clausify,[status(thm)],[f_1193_3]) ).

fof(f_1194_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_1194_2,plain,
    ! [U_4157,U_4156] :
      ( 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_4156),U_4157)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4156)) ),
    inference(variable_rename,[status(thm)],[f_1194_1]) ).

fof(f_1194_3,plain,
    ! [U_4156,U_4157] :
      ( 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_4156),U_4157)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4156)) ),
    inference(definitional_conversion,[status(esa)],[f_1194_2]) ).

cnf(f_1194_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_4156),U_4157)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4156)) ),
    inference(clausify,[status(thm)],[f_1194_3]) ).

fof(f_1195_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_1195_2,plain,
    ! [U_4161,U_4160,U_4159,U_4158] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4158),hAPP(c_Int_Onumber__class_Onumber__of(U_4158),U_4159)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4158),hAPP(c_Int_Onumber__class_Onumber__of(U_4158),U_4160)),U_4161)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4158),hAPP(c_Int_Onumber__class_Onumber__of(U_4158),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4159),U_4160))),U_4161)
      | ~ class_Int_Onumber__ring(U_4158) ),
    inference(variable_rename,[status(thm)],[f_1195_1]) ).

fof(f_1195_3,plain,
    ! [U_4158,U_4159,U_4160,U_4161] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4158),hAPP(c_Int_Onumber__class_Onumber__of(U_4158),U_4159)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4158),hAPP(c_Int_Onumber__class_Onumber__of(U_4158),U_4160)),U_4161)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4158),hAPP(c_Int_Onumber__class_Onumber__of(U_4158),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4159),U_4160))),U_4161)
      | ~ class_Int_Onumber__ring(U_4158) ),
    inference(definitional_conversion,[status(esa)],[f_1195_2]) ).

cnf(f_1195_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4158),hAPP(c_Int_Onumber__class_Onumber__of(U_4158),U_4159)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4158),hAPP(c_Int_Onumber__class_Onumber__of(U_4158),U_4160)),U_4161)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4158),hAPP(c_Int_Onumber__class_Onumber__of(U_4158),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4159),U_4160))),U_4161)
    | ~ class_Int_Onumber__ring(U_4158) ),
    inference(clausify,[status(thm)],[f_1195_3]) ).

fof(f_1196_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_1196_2,plain,
    ! [U_4164,U_4163,U_4162] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4162),hAPP(c_Int_Onumber__class_Onumber__of(U_4162),U_4163)),hAPP(c_Int_Onumber__class_Onumber__of(U_4162),U_4164)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4162),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4163),U_4164))
      | ~ class_Int_Onumber__ring(U_4162) ),
    inference(variable_rename,[status(thm)],[f_1196_1]) ).

fof(f_1196_3,plain,
    ! [U_4162,U_4163,U_4164] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4162),hAPP(c_Int_Onumber__class_Onumber__of(U_4162),U_4163)),hAPP(c_Int_Onumber__class_Onumber__of(U_4162),U_4164)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4162),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4163),U_4164))
      | ~ class_Int_Onumber__ring(U_4162) ),
    inference(definitional_conversion,[status(esa)],[f_1196_2]) ).

cnf(f_1196_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4162),hAPP(c_Int_Onumber__class_Onumber__of(U_4162),U_4163)),hAPP(c_Int_Onumber__class_Onumber__of(U_4162),U_4164)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4162),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4163),U_4164))
    | ~ class_Int_Onumber__ring(U_4162) ),
    inference(clausify,[status(thm)],[f_1196_3]) ).

fof(f_1197_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_1197_2,plain,
    ! [U_4167,U_4166,U_4165] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4165),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4166),U_4167)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4165),hAPP(c_Int_Onumber__class_Onumber__of(U_4165),U_4166)),hAPP(c_Int_Onumber__class_Onumber__of(U_4165),U_4167))
      | ~ class_Int_Onumber__ring(U_4165) ),
    inference(variable_rename,[status(thm)],[f_1197_1]) ).

fof(f_1197_3,plain,
    ! [U_4165,U_4166,U_4167] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4165),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4166),U_4167)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4165),hAPP(c_Int_Onumber__class_Onumber__of(U_4165),U_4166)),hAPP(c_Int_Onumber__class_Onumber__of(U_4165),U_4167))
      | ~ class_Int_Onumber__ring(U_4165) ),
    inference(definitional_conversion,[status(esa)],[f_1197_2]) ).

cnf(f_1197_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4165),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4166),U_4167)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4165),hAPP(c_Int_Onumber__class_Onumber__of(U_4165),U_4166)),hAPP(c_Int_Onumber__class_Onumber__of(U_4165),U_4167))
    | ~ class_Int_Onumber__ring(U_4165) ),
    inference(clausify,[status(thm)],[f_1197_3]) ).

fof(f_1198_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_1198_2,plain,
    ! [U_4169,U_4168] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4168) = 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_4168),U_4169)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1198_1]) ).

fof(f_1198_3,plain,
    ! [U_4168,U_4169] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4168) = 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_4168),U_4169)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_1198_2]) ).

cnf(f_1198_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4168) = 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_4168),U_4169)) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    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_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_1199_2,plain,
    ! [U_4172,U_4171,U_4170] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4170),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4171),U_4172)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4170),hAPP(c_Int_Onumber__class_Onumber__of(U_4170),U_4171)),hAPP(c_Int_Onumber__class_Onumber__of(U_4170),U_4172))
      | ~ class_Int_Onumber__ring(U_4170) ),
    inference(variable_rename,[status(thm)],[f_1199_1]) ).

fof(f_1199_3,plain,
    ! [U_4170,U_4171,U_4172] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4170),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4171),U_4172)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4170),hAPP(c_Int_Onumber__class_Onumber__of(U_4170),U_4171)),hAPP(c_Int_Onumber__class_Onumber__of(U_4170),U_4172))
      | ~ class_Int_Onumber__ring(U_4170) ),
    inference(definitional_conversion,[status(esa)],[f_1199_2]) ).

cnf(f_1199_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4170),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4171),U_4172)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4170),hAPP(c_Int_Onumber__class_Onumber__of(U_4170),U_4171)),hAPP(c_Int_Onumber__class_Onumber__of(U_4170),U_4172))
    | ~ class_Int_Onumber__ring(U_4170) ),
    inference(clausify,[status(thm)],[f_1199_3]) ).

fof(f_1200_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_1200_2,plain,
    ! [U_4175,U_4174,U_4173] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4173),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4174),U_4175)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4173),U_4174)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4173),U_4175)),
    inference(variable_rename,[status(thm)],[f_1200_1]) ).

fof(f_1200_3,plain,
    ! [U_4173,U_4174,U_4175] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4173),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4174),U_4175)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4173),U_4174)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4173),U_4175)),
    inference(definitional_conversion,[status(esa)],[f_1200_2]) ).

cnf(f_1200_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4173),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4174),U_4175)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4173),U_4174)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4173),U_4175)),
    inference(clausify,[status(thm)],[f_1200_3]) ).

fof(f_1201_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_1201_2,plain,
    ! [U_4177,U_4176] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4176),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4177)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4176),hAPP(c_Int_Onumber__class_Onumber__of(U_4176),U_4177))
      | ~ class_Int_Onumber__ring(U_4176) ),
    inference(variable_rename,[status(thm)],[f_1201_1]) ).

fof(f_1201_3,plain,
    ! [U_4176,U_4177] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4176),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4177)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4176),hAPP(c_Int_Onumber__class_Onumber__of(U_4176),U_4177))
      | ~ class_Int_Onumber__ring(U_4176) ),
    inference(definitional_conversion,[status(esa)],[f_1201_2]) ).

cnf(f_1201_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4176),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4177)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4176),hAPP(c_Int_Onumber__class_Onumber__of(U_4176),U_4177))
    | ~ class_Int_Onumber__ring(U_4176) ),
    inference(clausify,[status(thm)],[f_1201_3]) ).

fof(f_1202_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_1202_2,plain,
    ! [U_4179,U_4178] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4178),hAPP(c_Int_Onumber__class_Onumber__of(U_4178),U_4179)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4178),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4179))
      | ~ class_Int_Onumber__ring(U_4178) ),
    inference(variable_rename,[status(thm)],[f_1202_1]) ).

fof(f_1202_3,plain,
    ! [U_4178,U_4179] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4178),hAPP(c_Int_Onumber__class_Onumber__of(U_4178),U_4179)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4178),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4179))
      | ~ class_Int_Onumber__ring(U_4178) ),
    inference(definitional_conversion,[status(esa)],[f_1202_2]) ).

cnf(f_1202_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4178),hAPP(c_Int_Onumber__class_Onumber__of(U_4178),U_4179)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4178),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4179))
    | ~ class_Int_Onumber__ring(U_4178) ),
    inference(clausify,[status(thm)],[f_1202_3]) ).

fof(f_1203_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_1203_2,plain,
    ! [U_4181,U_4180] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4180),c_Groups_Osgn__class_Osgn(U_4180,U_4181)),hAPP(c_Groups_Oabs__class_Oabs(U_4180),U_4181)) = U_4181
      | ~ class_Rings_Olinordered__idom(U_4180) ),
    inference(variable_rename,[status(thm)],[f_1203_1]) ).

fof(f_1203_3,plain,
    ! [U_4180,U_4181] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4180),c_Groups_Osgn__class_Osgn(U_4180,U_4181)),hAPP(c_Groups_Oabs__class_Oabs(U_4180),U_4181)) = U_4181
      | ~ class_Rings_Olinordered__idom(U_4180) ),
    inference(definitional_conversion,[status(esa)],[f_1203_2]) ).

cnf(f_1203_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4180),c_Groups_Osgn__class_Osgn(U_4180,U_4181)),hAPP(c_Groups_Oabs__class_Oabs(U_4180),U_4181)) = U_4181
    | ~ class_Rings_Olinordered__idom(U_4180) ),
    inference(clausify,[status(thm)],[f_1203_3]) ).

fof(f_1204_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_1204_2,plain,
    ! [U_4183,U_4182] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4182),U_4183) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4182),U_4183),c_Groups_Osgn__class_Osgn(U_4182,U_4183))
      | ~ class_Rings_Olinordered__idom(U_4182) ),
    inference(variable_rename,[status(thm)],[f_1204_1]) ).

fof(f_1204_3,plain,
    ! [U_4182,U_4183] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4182),U_4183) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4182),U_4183),c_Groups_Osgn__class_Osgn(U_4182,U_4183))
      | ~ class_Rings_Olinordered__idom(U_4182) ),
    inference(definitional_conversion,[status(esa)],[f_1204_2]) ).

cnf(f_1204_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4182),U_4183) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4182),U_4183),c_Groups_Osgn__class_Osgn(U_4182,U_4183))
    | ~ class_Rings_Olinordered__idom(U_4182) ),
    inference(clausify,[status(thm)],[f_1204_3]) ).

fof(f_1205_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_1205_2,plain,
    ! [U_4186,U_4185,U_4184] :
      ( hBOOL(hAPP(hAPP(c_member(U_4184),hAPP(hAPP(c_Power_Opower__class_Opower(U_4184),U_4185),U_4186)),c_Int_Oring__1__class_OInts(U_4184)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4184),U_4185),c_Int_Oring__1__class_OInts(U_4184)))
      | ~ class_Rings_Oring__1(U_4184) ),
    inference(variable_rename,[status(thm)],[f_1205_1]) ).

fof(f_1205_3,plain,
    ! [U_4184,U_4185,U_4186] :
      ( hBOOL(hAPP(hAPP(c_member(U_4184),hAPP(hAPP(c_Power_Opower__class_Opower(U_4184),U_4185),U_4186)),c_Int_Oring__1__class_OInts(U_4184)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_4184),U_4185),c_Int_Oring__1__class_OInts(U_4184)))
      | ~ class_Rings_Oring__1(U_4184) ),
    inference(definitional_conversion,[status(esa)],[f_1205_2]) ).

cnf(f_1205_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4184),hAPP(hAPP(c_Power_Opower__class_Opower(U_4184),U_4185),U_4186)),c_Int_Oring__1__class_OInts(U_4184)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_4184),U_4185),c_Int_Oring__1__class_OInts(U_4184)))
    | ~ class_Rings_Oring__1(U_4184) ),
    inference(clausify,[status(thm)],[f_1205_3]) ).

fof(f_1206_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_1206_2,plain,
    ! [U_4188,U_4187] :
      ( hBOOL(hAPP(hAPP(c_member(U_4187),hAPP(c_Int_Onumber__class_Onumber__of(U_4187),U_4188)),c_Int_Oring__1__class_OInts(U_4187)))
      | ~ class_Int_Onumber__ring(U_4187) ),
    inference(variable_rename,[status(thm)],[f_1206_1]) ).

fof(f_1206_3,plain,
    ! [U_4187,U_4188] :
      ( hBOOL(hAPP(hAPP(c_member(U_4187),hAPP(c_Int_Onumber__class_Onumber__of(U_4187),U_4188)),c_Int_Oring__1__class_OInts(U_4187)))
      | ~ class_Int_Onumber__ring(U_4187) ),
    inference(definitional_conversion,[status(esa)],[f_1206_2]) ).

cnf(f_1206_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4187),hAPP(c_Int_Onumber__class_Onumber__of(U_4187),U_4188)),c_Int_Oring__1__class_OInts(U_4187)))
    | ~ class_Int_Onumber__ring(U_4187) ),
    inference(clausify,[status(thm)],[f_1206_3]) ).

fof(f_1207_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_1207_2,plain,
    ! [U_4191,U_4190,U_4189] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4189),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4189),U_4190),U_4191)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4189),hAPP(c_Groups_Oabs__class_Oabs(U_4189),U_4190)),hAPP(c_Groups_Oabs__class_Oabs(U_4189),U_4191))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4189),U_4191),c_Groups_Ozero__class_Ozero(U_4189)))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4189),c_Groups_Ozero__class_Ozero(U_4189)),U_4191)) )
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4189),U_4190),c_Groups_Ozero__class_Ozero(U_4189)))
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4189),c_Groups_Ozero__class_Ozero(U_4189)),U_4190)) )
      | ~ class_Rings_Oordered__ring__abs(U_4189) ),
    inference(variable_rename,[status(thm)],[f_1207_1]) ).

fof(f_1207_3,plain,
    ( ! [U_4189,U_4191] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4189),U_4191),c_Groups_Ozero__class_Ozero(U_4189)))
        | ~ sP345(U_4189,U_4191) )
    & ! [U_4189,U_4191] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4189),c_Groups_Ozero__class_Ozero(U_4189)),U_4191))
        | ~ sP345(U_4189,U_4191) )
    & ! [U_4189,U_4190] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4189),U_4190),c_Groups_Ozero__class_Ozero(U_4189)))
        | ~ sP344(U_4189,U_4190) )
    & ! [U_4189,U_4190] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4189),c_Groups_Ozero__class_Ozero(U_4189)),U_4190))
        | ~ sP344(U_4189,U_4190) )
    & ! [U_4189,U_4190,U_4191] :
        ( hAPP(c_Groups_Oabs__class_Oabs(U_4189),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4189),U_4190),U_4191)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4189),hAPP(c_Groups_Oabs__class_Oabs(U_4189),U_4190)),hAPP(c_Groups_Oabs__class_Oabs(U_4189),U_4191))
        | sP345(U_4189,U_4191)
        | sP344(U_4189,U_4190)
        | ~ class_Rings_Oordered__ring__abs(U_4189) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP344,sP345])],[f_1207_2]) ).

cnf(f_1207_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4189),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4189),U_4190),U_4191)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4189),hAPP(c_Groups_Oabs__class_Oabs(U_4189),U_4190)),hAPP(c_Groups_Oabs__class_Oabs(U_4189),U_4191))
    | sP345(U_4189,U_4191)
    | sP344(U_4189,U_4190)
    | ~ class_Rings_Oordered__ring__abs(U_4189) ),
    inference(clausify,[status(thm)],[f_1207_3]) ).

cnf(f_1207_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4189),c_Groups_Ozero__class_Ozero(U_4189)),U_4190))
    | ~ sP344(U_4189,U_4190) ),
    inference(clausify,[status(thm)],[f_1207_3]) ).

cnf(f_1207_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4189),U_4190),c_Groups_Ozero__class_Ozero(U_4189)))
    | ~ sP344(U_4189,U_4190) ),
    inference(clausify,[status(thm)],[f_1207_3]) ).

cnf(f_1207_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4189),c_Groups_Ozero__class_Ozero(U_4189)),U_4191))
    | ~ sP345(U_4189,U_4191) ),
    inference(clausify,[status(thm)],[f_1207_3]) ).

cnf(f_1207_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4189),U_4191),c_Groups_Ozero__class_Ozero(U_4189)))
    | ~ sP345(U_4189,U_4191) ),
    inference(clausify,[status(thm)],[f_1207_3]) ).

fof(f_1208_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_1208_2,plain,
    ! [U_4194,U_4193,U_4192] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4192),hAPP(c_Groups_Oabs__class_Oabs(U_4192),U_4194)),U_4193) = hAPP(c_Groups_Oabs__class_Oabs(U_4192),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4192),U_4194),U_4193))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4192),c_Groups_Ozero__class_Ozero(U_4192)),U_4193))
      | ~ class_Rings_Olinordered__idom(U_4192) ),
    inference(variable_rename,[status(thm)],[f_1208_1]) ).

fof(f_1208_3,plain,
    ! [U_4193,U_4192,U_4194] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4192),hAPP(c_Groups_Oabs__class_Oabs(U_4192),U_4194)),U_4193) = hAPP(c_Groups_Oabs__class_Oabs(U_4192),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4192),U_4194),U_4193))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4192),c_Groups_Ozero__class_Ozero(U_4192)),U_4193))
      | ~ class_Rings_Olinordered__idom(U_4192) ),
    inference(definitional_conversion,[status(esa)],[f_1208_2]) ).

cnf(f_1208_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4192),hAPP(c_Groups_Oabs__class_Oabs(U_4192),U_4194)),U_4193) = hAPP(c_Groups_Oabs__class_Oabs(U_4192),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4192),U_4194),U_4193))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4192),c_Groups_Ozero__class_Ozero(U_4192)),U_4193))
    | ~ class_Rings_Olinordered__idom(U_4192) ),
    inference(clausify,[status(thm)],[f_1208_3]) ).

fof(f_1209_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_1209_2,plain,
    ! [U_4197,U_4196,U_4195] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4195),hAPP(c_Groups_Oabs__class_Oabs(U_4195),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4195),U_4196),U_4197))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4195),hAPP(c_Groups_Oabs__class_Oabs(U_4195),U_4196)),hAPP(c_Groups_Oabs__class_Oabs(U_4195),U_4197))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4195) ),
    inference(variable_rename,[status(thm)],[f_1209_1]) ).

fof(f_1209_3,plain,
    ! [U_4195,U_4196,U_4197] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4195),hAPP(c_Groups_Oabs__class_Oabs(U_4195),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4195),U_4196),U_4197))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4195),hAPP(c_Groups_Oabs__class_Oabs(U_4195),U_4196)),hAPP(c_Groups_Oabs__class_Oabs(U_4195),U_4197))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4195) ),
    inference(definitional_conversion,[status(esa)],[f_1209_2]) ).

cnf(f_1209_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4195),hAPP(c_Groups_Oabs__class_Oabs(U_4195),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4195),U_4196),U_4197))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4195),hAPP(c_Groups_Oabs__class_Oabs(U_4195),U_4196)),hAPP(c_Groups_Oabs__class_Oabs(U_4195),U_4197))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4195) ),
    inference(clausify,[status(thm)],[f_1209_3]) ).

fof(f_1210_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_1210_2,plain,
    ! [U_4202,U_4201,U_4200,U_4199,U_4198] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4198),hAPP(c_Groups_Oabs__class_Oabs(U_4198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4198),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4198),U_4199),U_4200)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4198),U_4201),U_4202)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4198),hAPP(c_Groups_Oabs__class_Oabs(U_4198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4198),U_4199),U_4201))),hAPP(c_Groups_Oabs__class_Oabs(U_4198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4198),U_4200),U_4202)))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4198) ),
    inference(variable_rename,[status(thm)],[f_1210_1]) ).

fof(f_1210_3,plain,
    ! [U_4198,U_4199,U_4200,U_4201,U_4202] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4198),hAPP(c_Groups_Oabs__class_Oabs(U_4198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4198),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4198),U_4199),U_4200)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4198),U_4201),U_4202)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4198),hAPP(c_Groups_Oabs__class_Oabs(U_4198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4198),U_4199),U_4201))),hAPP(c_Groups_Oabs__class_Oabs(U_4198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4198),U_4200),U_4202)))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4198) ),
    inference(definitional_conversion,[status(esa)],[f_1210_2]) ).

cnf(f_1210_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4198),hAPP(c_Groups_Oabs__class_Oabs(U_4198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4198),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4198),U_4199),U_4200)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4198),U_4201),U_4202)))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4198),hAPP(c_Groups_Oabs__class_Oabs(U_4198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4198),U_4199),U_4201))),hAPP(c_Groups_Oabs__class_Oabs(U_4198),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4198),U_4200),U_4202)))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4198) ),
    inference(clausify,[status(thm)],[f_1210_3]) ).

fof(f_1211_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_1211_2,plain,
    ! [U_4204,U_4203] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4203),U_4204) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4203),U_4204)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4203),U_4204),c_Groups_Ozero__class_Ozero(U_4203)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4203) ),
    inference(variable_rename,[status(thm)],[f_1211_1]) ).

fof(f_1211_3,plain,
    ! [U_4203,U_4204] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4203),U_4204) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4203),U_4204)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4203),U_4204),c_Groups_Ozero__class_Ozero(U_4203)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4203) ),
    inference(definitional_conversion,[status(esa)],[f_1211_2]) ).

cnf(f_1211_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4203),U_4204) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4203),U_4204)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4203),U_4204),c_Groups_Ozero__class_Ozero(U_4203)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4203) ),
    inference(clausify,[status(thm)],[f_1211_3]) ).

fof(f_1212_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_1212_2,plain,
    ! [U_4206,U_4205] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4205),hAPP(c_Groups_Ouminus__class_Ouminus(U_4205),hAPP(c_Groups_Oabs__class_Oabs(U_4205),U_4206))),c_Groups_Ozero__class_Ozero(U_4205)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4205) ),
    inference(variable_rename,[status(thm)],[f_1212_1]) ).

fof(f_1212_3,plain,
    ! [U_4205,U_4206] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4205),hAPP(c_Groups_Ouminus__class_Ouminus(U_4205),hAPP(c_Groups_Oabs__class_Oabs(U_4205),U_4206))),c_Groups_Ozero__class_Ozero(U_4205)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4205) ),
    inference(definitional_conversion,[status(esa)],[f_1212_2]) ).

cnf(f_1212_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4205),hAPP(c_Groups_Ouminus__class_Ouminus(U_4205),hAPP(c_Groups_Oabs__class_Oabs(U_4205),U_4206))),c_Groups_Ozero__class_Ozero(U_4205)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4205) ),
    inference(clausify,[status(thm)],[f_1212_3]) ).

fof(f_1213_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_1213_2,plain,
    ! [U_4208,U_4207] :
      ( ( ( hAPP(c_Groups_Oabs__class_Oabs(U_4207),U_4208) = U_4208
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4207),U_4208),c_Groups_Ozero__class_Ozero(U_4207))) )
        & ( hAPP(c_Groups_Oabs__class_Oabs(U_4207),U_4208) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4207),U_4208)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4207),U_4208),c_Groups_Ozero__class_Ozero(U_4207))) ) )
      | ~ class_Groups_Oabs__if(U_4207) ),
    inference(variable_rename,[status(thm)],[f_1213_1]) ).

fof(f_1213_3,plain,
    ( ! [U_4207,U_4208] :
        ( hAPP(c_Groups_Oabs__class_Oabs(U_4207),U_4208) = U_4208
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4207),U_4208),c_Groups_Ozero__class_Ozero(U_4207)))
        | ~ sP346(U_4207,U_4208) )
    & ! [U_4207,U_4208] :
        ( hAPP(c_Groups_Oabs__class_Oabs(U_4207),U_4208) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4207),U_4208)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4207),U_4208),c_Groups_Ozero__class_Ozero(U_4207)))
        | ~ sP346(U_4207,U_4208) )
    & ! [U_4207,U_4208] :
        ( sP346(U_4207,U_4208)
        | ~ class_Groups_Oabs__if(U_4207) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP346])],[f_1213_2]) ).

cnf(f_1213_4,plain,
    ( sP346(U_4207,U_4208)
    | ~ class_Groups_Oabs__if(U_4207) ),
    inference(clausify,[status(thm)],[f_1213_3]) ).

cnf(f_1213_5,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4207),U_4208) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4207),U_4208)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4207),U_4208),c_Groups_Ozero__class_Ozero(U_4207)))
    | ~ sP346(U_4207,U_4208) ),
    inference(clausify,[status(thm)],[f_1213_3]) ).

cnf(f_1213_6,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4207),U_4208) = U_4208
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4207),U_4208),c_Groups_Ozero__class_Ozero(U_4207)))
    | ~ sP346(U_4207,U_4208) ),
    inference(clausify,[status(thm)],[f_1213_3]) ).

fof(f_1214_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_1214_2,plain,
    ! [U_4210,U_4209] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4209),U_4210) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4209),U_4210)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4209),U_4210),c_Groups_Ozero__class_Ozero(U_4209)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4209) ),
    inference(variable_rename,[status(thm)],[f_1214_1]) ).

fof(f_1214_3,plain,
    ! [U_4210,U_4209] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4209),U_4210) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4209),U_4210)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4209),U_4210),c_Groups_Ozero__class_Ozero(U_4209)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_4209) ),
    inference(definitional_conversion,[status(esa)],[f_1214_2]) ).

cnf(f_1214_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4209),U_4210) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4209),U_4210)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4209),U_4210),c_Groups_Ozero__class_Ozero(U_4209)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_4209) ),
    inference(clausify,[status(thm)],[f_1214_3]) ).

fof(f_1215_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_1215_2,plain,
    ! [U_4211] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4211)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | U_4211 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( U_4211 = 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_4211)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1215_1]) ).

fof(f_1215_3,plain,
    ( ! [U_4213] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4213)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | U_4213 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_4212] :
        ( U_4212 = 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_4212)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1215_2]) ).

fof(f_1215_4,plain,
    ( ! [U_4213] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4213)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | U_4213 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_4212] :
        ( U_4212 = 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_4212)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1215_3]) ).

cnf(f_1215_5,plain,
    ( U_4212 = 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_4212)),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1215_4]) ).

cnf(f_1215_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4213)),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | U_4213 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1215_4]) ).

fof(f_1216_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_1216_2,plain,
    ! [U_4217,U_4216,U_4215,U_4214] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4214),hAPP(c_Int_Onumber__class_Onumber__of(U_4214),U_4215)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4214),hAPP(c_Int_Onumber__class_Onumber__of(U_4214),U_4216)),U_4217)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4214),hAPP(c_Int_Onumber__class_Onumber__of(U_4214),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4215),U_4216))),U_4217)
      | ~ class_Int_Onumber__ring(U_4214) ),
    inference(variable_rename,[status(thm)],[f_1216_1]) ).

fof(f_1216_3,plain,
    ! [U_4214,U_4215,U_4216,U_4217] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4214),hAPP(c_Int_Onumber__class_Onumber__of(U_4214),U_4215)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4214),hAPP(c_Int_Onumber__class_Onumber__of(U_4214),U_4216)),U_4217)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4214),hAPP(c_Int_Onumber__class_Onumber__of(U_4214),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4215),U_4216))),U_4217)
      | ~ class_Int_Onumber__ring(U_4214) ),
    inference(definitional_conversion,[status(esa)],[f_1216_2]) ).

cnf(f_1216_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4214),hAPP(c_Int_Onumber__class_Onumber__of(U_4214),U_4215)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4214),hAPP(c_Int_Onumber__class_Onumber__of(U_4214),U_4216)),U_4217)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4214),hAPP(c_Int_Onumber__class_Onumber__of(U_4214),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4215),U_4216))),U_4217)
    | ~ class_Int_Onumber__ring(U_4214) ),
    inference(clausify,[status(thm)],[f_1216_3]) ).

fof(f_1217_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_1217_2,plain,
    ! [U_4218] :
      ( ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4218) = U_4218
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4218),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4218) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4218)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4218),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1217_1]) ).

fof(f_1217_3,plain,
    ( ! [U_4220] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4220) = U_4220
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4220),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_4219] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4219) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4219)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4219),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1217_2]) ).

fof(f_1217_4,plain,
    ( ! [U_4220] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4220) = U_4220
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4220),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_4219] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4219) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4219)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4219),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1217_3]) ).

cnf(f_1217_5,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4219) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4219)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4219),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1217_4]) ).

cnf(f_1217_6,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4220) = U_4220
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4220),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1217_4]) ).

fof(f_1218_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_1218_2,plain,
    ! [U_4223,U_4222,U_4221] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4221),hAPP(c_Groups_Ouminus__class_Ouminus(U_4221),hAPP(c_Int_Onumber__class_Onumber__of(U_4221),U_4222))),U_4223) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4221),hAPP(c_Int_Onumber__class_Onumber__of(U_4221),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4222))),U_4223)
      | ~ class_Int_Onumber__ring(U_4221) ),
    inference(variable_rename,[status(thm)],[f_1218_1]) ).

fof(f_1218_3,plain,
    ! [U_4221,U_4222,U_4223] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4221),hAPP(c_Groups_Ouminus__class_Ouminus(U_4221),hAPP(c_Int_Onumber__class_Onumber__of(U_4221),U_4222))),U_4223) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4221),hAPP(c_Int_Onumber__class_Onumber__of(U_4221),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4222))),U_4223)
      | ~ class_Int_Onumber__ring(U_4221) ),
    inference(definitional_conversion,[status(esa)],[f_1218_2]) ).

cnf(f_1218_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4221),hAPP(c_Groups_Ouminus__class_Ouminus(U_4221),hAPP(c_Int_Onumber__class_Onumber__of(U_4221),U_4222))),U_4223) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4221),hAPP(c_Int_Onumber__class_Onumber__of(U_4221),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4222))),U_4223)
    | ~ class_Int_Onumber__ring(U_4221) ),
    inference(clausify,[status(thm)],[f_1218_3]) ).

fof(f_1219_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_1219_2,plain,
    ! [U_4225,U_4224] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4224),U_4225))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4224))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4225))),
    inference(variable_rename,[status(thm)],[f_1219_1]) ).

fof(f_1219_3,plain,
    ! [U_4224,U_4225] : hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4224),U_4225))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4224))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4225))),
    inference(definitional_conversion,[status(esa)],[f_1219_2]) ).

cnf(f_1219_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_4224),U_4225))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4224))),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4225))),
    inference(clausify,[status(thm)],[f_1219_3]) ).

fof(f_1220_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_1220_2,plain,
    ! [U_4228,U_4227,U_4226] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4226),hAPP(c_Int_Onumber__class_Onumber__of(U_4226),U_4227)),hAPP(c_Int_Onumber__class_Onumber__of(U_4226),U_4228)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4226),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4227),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4228)))
      | ~ class_Int_Onumber__ring(U_4226) ),
    inference(variable_rename,[status(thm)],[f_1220_1]) ).

fof(f_1220_3,plain,
    ! [U_4226,U_4227,U_4228] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4226),hAPP(c_Int_Onumber__class_Onumber__of(U_4226),U_4227)),hAPP(c_Int_Onumber__class_Onumber__of(U_4226),U_4228)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4226),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4227),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4228)))
      | ~ class_Int_Onumber__ring(U_4226) ),
    inference(definitional_conversion,[status(esa)],[f_1220_2]) ).

cnf(f_1220_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4226),hAPP(c_Int_Onumber__class_Onumber__of(U_4226),U_4227)),hAPP(c_Int_Onumber__class_Onumber__of(U_4226),U_4228)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4226),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4227),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4228)))
    | ~ class_Int_Onumber__ring(U_4226) ),
    inference(clausify,[status(thm)],[f_1220_3]) ).

fof(f_1221_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_1221_2,plain,
    ! [U_4232,U_4231,U_4230,U_4229] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4229),hAPP(c_Int_Onumber__class_Onumber__of(U_4229),U_4230)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4229),U_4231),hAPP(c_Int_Onumber__class_Onumber__of(U_4229),U_4232))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4229),hAPP(c_Int_Onumber__class_Onumber__of(U_4229),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4230),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4232)))),U_4231)
      | ~ class_Int_Onumber__ring(U_4229) ),
    inference(variable_rename,[status(thm)],[f_1221_1]) ).

fof(f_1221_3,plain,
    ! [U_4229,U_4230,U_4231,U_4232] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4229),hAPP(c_Int_Onumber__class_Onumber__of(U_4229),U_4230)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4229),U_4231),hAPP(c_Int_Onumber__class_Onumber__of(U_4229),U_4232))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4229),hAPP(c_Int_Onumber__class_Onumber__of(U_4229),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4230),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4232)))),U_4231)
      | ~ class_Int_Onumber__ring(U_4229) ),
    inference(definitional_conversion,[status(esa)],[f_1221_2]) ).

cnf(f_1221_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4229),hAPP(c_Int_Onumber__class_Onumber__of(U_4229),U_4230)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4229),U_4231),hAPP(c_Int_Onumber__class_Onumber__of(U_4229),U_4232))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4229),hAPP(c_Int_Onumber__class_Onumber__of(U_4229),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4230),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4232)))),U_4231)
    | ~ class_Int_Onumber__ring(U_4229) ),
    inference(clausify,[status(thm)],[f_1221_3]) ).

fof(f_1222_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_1222_2,plain,
    ! [U_4236,U_4235,U_4234,U_4233] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4233),hAPP(hAPP(c_Power_Opower__class_Opower(U_4233),U_4234),U_4236)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4233),U_4235),U_4236)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4236))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4233),c_Groups_Ozero__class_Ozero(U_4233)),U_4234))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4233),U_4234),U_4235))
      | ~ class_Rings_Olinordered__semidom(U_4233) ),
    inference(variable_rename,[status(thm)],[f_1222_1]) ).

fof(f_1222_3,plain,
    ! [U_4233,U_4234,U_4235,U_4236] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4233),hAPP(hAPP(c_Power_Opower__class_Opower(U_4233),U_4234),U_4236)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4233),U_4235),U_4236)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4236))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4233),c_Groups_Ozero__class_Ozero(U_4233)),U_4234))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4233),U_4234),U_4235))
      | ~ class_Rings_Olinordered__semidom(U_4233) ),
    inference(definitional_conversion,[status(esa)],[f_1222_2]) ).

cnf(f_1222_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4233),hAPP(hAPP(c_Power_Opower__class_Opower(U_4233),U_4234),U_4236)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4233),U_4235),U_4236)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4236))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4233),c_Groups_Ozero__class_Ozero(U_4233)),U_4234))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4233),U_4234),U_4235))
    | ~ class_Rings_Olinordered__semidom(U_4233) ),
    inference(clausify,[status(thm)],[f_1222_3]) ).

fof(f_1223_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_1223_2,plain,
    ! [U_4239,U_4238,U_4237] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4237),c_Groups_Oone__class_Oone(U_4237)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4237),U_4238),U_4239)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4239))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4237),c_Groups_Oone__class_Oone(U_4237)),U_4238))
      | ~ class_Rings_Olinordered__semidom(U_4237) ),
    inference(variable_rename,[status(thm)],[f_1223_1]) ).

fof(f_1223_3,plain,
    ! [U_4239,U_4238,U_4237] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4237),c_Groups_Oone__class_Oone(U_4237)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4237),U_4238),U_4239)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4239))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4237),c_Groups_Oone__class_Oone(U_4237)),U_4238))
      | ~ class_Rings_Olinordered__semidom(U_4237) ),
    inference(definitional_conversion,[status(esa)],[f_1223_2]) ).

cnf(f_1223_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4237),c_Groups_Oone__class_Oone(U_4237)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4237),U_4238),U_4239)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4239))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4237),c_Groups_Oone__class_Oone(U_4237)),U_4238))
    | ~ class_Rings_Olinordered__semidom(U_4237) ),
    inference(clausify,[status(thm)],[f_1223_3]) ).

fof(f_1224_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_1224_2,plain,
    ! [U_4243,U_4242,U_4241,U_4240] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4242),U_4243))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4240),hAPP(hAPP(c_Power_Opower__class_Opower(U_4240),U_4241),U_4242)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4240),U_4241),U_4243)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4240),c_Groups_Oone__class_Oone(U_4240)),U_4241))
      | ~ class_Rings_Olinordered__semidom(U_4240) ),
    inference(variable_rename,[status(thm)],[f_1224_1]) ).

fof(f_1224_3,plain,
    ! [U_4240,U_4241,U_4242,U_4243] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4242),U_4243))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4240),hAPP(hAPP(c_Power_Opower__class_Opower(U_4240),U_4241),U_4242)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4240),U_4241),U_4243)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4240),c_Groups_Oone__class_Oone(U_4240)),U_4241))
      | ~ class_Rings_Olinordered__semidom(U_4240) ),
    inference(definitional_conversion,[status(esa)],[f_1224_2]) ).

cnf(f_1224_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4242),U_4243))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4240),hAPP(hAPP(c_Power_Opower__class_Opower(U_4240),U_4241),U_4242)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4240),U_4241),U_4243)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4240),c_Groups_Oone__class_Oone(U_4240)),U_4241))
    | ~ class_Rings_Olinordered__semidom(U_4240) ),
    inference(clausify,[status(thm)],[f_1224_3]) ).

fof(f_1225_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_1225_2,plain,
    ! [U_4247,U_4246,U_4245,U_4244] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4244),hAPP(hAPP(c_Power_Opower__class_Opower(U_4244),U_4245),U_4246)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4244),U_4245),U_4247)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4246),U_4247)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4246),U_4247))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4244),hAPP(hAPP(c_Power_Opower__class_Opower(U_4244),U_4245),U_4246)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4244),U_4245),U_4247))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4244),c_Groups_Oone__class_Oone(U_4244)),U_4245))
      | ~ class_Rings_Olinordered__semidom(U_4244) ),
    inference(variable_rename,[status(thm)],[f_1225_1]) ).

fof(f_1225_3,plain,
    ( ! [U_4245,U_4244,U_4246,U_4247] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4244),hAPP(hAPP(c_Power_Opower__class_Opower(U_4244),U_4245),U_4246)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4244),U_4245),U_4247)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4246),U_4247))
        | ~ sP347(U_4245,U_4244,U_4246,U_4247) )
    & ! [U_4245,U_4244,U_4246,U_4247] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4246),U_4247))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4244),hAPP(hAPP(c_Power_Opower__class_Opower(U_4244),U_4245),U_4246)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4244),U_4245),U_4247)))
        | ~ sP347(U_4245,U_4244,U_4246,U_4247) )
    & ! [U_4245,U_4244,U_4246,U_4247] :
        ( sP347(U_4245,U_4244,U_4246,U_4247)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4244),c_Groups_Oone__class_Oone(U_4244)),U_4245))
        | ~ class_Rings_Olinordered__semidom(U_4244) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP347])],[f_1225_2]) ).

cnf(f_1225_4,plain,
    ( sP347(U_4245,U_4244,U_4246,U_4247)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4244),c_Groups_Oone__class_Oone(U_4244)),U_4245))
    | ~ class_Rings_Olinordered__semidom(U_4244) ),
    inference(clausify,[status(thm)],[f_1225_3]) ).

cnf(f_1225_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4246),U_4247))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4244),hAPP(hAPP(c_Power_Opower__class_Opower(U_4244),U_4245),U_4246)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4244),U_4245),U_4247)))
    | ~ sP347(U_4245,U_4244,U_4246,U_4247) ),
    inference(clausify,[status(thm)],[f_1225_3]) ).

cnf(f_1225_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4244),hAPP(hAPP(c_Power_Opower__class_Opower(U_4244),U_4245),U_4246)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4244),U_4245),U_4247)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4246),U_4247))
    | ~ sP347(U_4245,U_4244,U_4246,U_4247) ),
    inference(clausify,[status(thm)],[f_1225_3]) ).

fof(f_1226_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_1226_2,plain,
    ! [U_4251,U_4250,U_4249,U_4248] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4248),hAPP(hAPP(c_Power_Opower__class_Opower(U_4248),U_4251),U_4250)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4248),U_4251),U_4249)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4248),U_4251),c_Groups_Oone__class_Oone(U_4248)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4248),c_Groups_Ozero__class_Ozero(U_4248)),U_4251))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4249),U_4250))
      | ~ class_Rings_Olinordered__semidom(U_4248) ),
    inference(variable_rename,[status(thm)],[f_1226_1]) ).

fof(f_1226_3,plain,
    ! [U_4250,U_4249,U_4251,U_4248] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4248),hAPP(hAPP(c_Power_Opower__class_Opower(U_4248),U_4251),U_4250)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4248),U_4251),U_4249)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4248),U_4251),c_Groups_Oone__class_Oone(U_4248)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4248),c_Groups_Ozero__class_Ozero(U_4248)),U_4251))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4249),U_4250))
      | ~ class_Rings_Olinordered__semidom(U_4248) ),
    inference(definitional_conversion,[status(esa)],[f_1226_2]) ).

cnf(f_1226_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4248),hAPP(hAPP(c_Power_Opower__class_Opower(U_4248),U_4251),U_4250)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4248),U_4251),U_4249)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4248),U_4251),c_Groups_Oone__class_Oone(U_4248)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4248),c_Groups_Ozero__class_Ozero(U_4248)),U_4251))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4249),U_4250))
    | ~ class_Rings_Olinordered__semidom(U_4248) ),
    inference(clausify,[status(thm)],[f_1226_3]) ).

fof(f_1227_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_1227_2,plain,
    ! [U_4255,U_4254,U_4253,U_4252] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4252),hAPP(hAPP(c_Power_Opower__class_Opower(U_4252),U_4255),U_4254)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4252),U_4255),U_4253)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4252),U_4255),c_Groups_Oone__class_Oone(U_4252)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4252),c_Groups_Ozero__class_Ozero(U_4252)),U_4255))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4253),U_4254))
      | ~ class_Rings_Olinordered__semidom(U_4252) ),
    inference(variable_rename,[status(thm)],[f_1227_1]) ).

fof(f_1227_3,plain,
    ! [U_4253,U_4254,U_4252,U_4255] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4252),hAPP(hAPP(c_Power_Opower__class_Opower(U_4252),U_4255),U_4254)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4252),U_4255),U_4253)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4252),U_4255),c_Groups_Oone__class_Oone(U_4252)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4252),c_Groups_Ozero__class_Ozero(U_4252)),U_4255))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4253),U_4254))
      | ~ class_Rings_Olinordered__semidom(U_4252) ),
    inference(definitional_conversion,[status(esa)],[f_1227_2]) ).

cnf(f_1227_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4252),hAPP(hAPP(c_Power_Opower__class_Opower(U_4252),U_4255),U_4254)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4252),U_4255),U_4253)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4252),U_4255),c_Groups_Oone__class_Oone(U_4252)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4252),c_Groups_Ozero__class_Ozero(U_4252)),U_4255))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4253),U_4254))
    | ~ class_Rings_Olinordered__semidom(U_4252) ),
    inference(clausify,[status(thm)],[f_1227_3]) ).

fof(f_1228_1,plain,
    ! [V_n,V_a,T_a] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),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_1228_2,plain,
    ! [U_4258,U_4257,U_4256] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4256),hAPP(hAPP(c_Power_Opower__class_Opower(U_4256),U_4257),hAPP(c_Nat_OSuc,U_4258))),c_Groups_Oone__class_Oone(U_4256)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4256),U_4257),c_Groups_Oone__class_Oone(U_4256)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4256),c_Groups_Ozero__class_Ozero(U_4256)),U_4257))
      | ~ class_Rings_Olinordered__semidom(U_4256) ),
    inference(variable_rename,[status(thm)],[f_1228_1]) ).

fof(f_1228_3,plain,
    ! [U_4258,U_4257,U_4256] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4256),hAPP(hAPP(c_Power_Opower__class_Opower(U_4256),U_4257),hAPP(c_Nat_OSuc,U_4258))),c_Groups_Oone__class_Oone(U_4256)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4256),U_4257),c_Groups_Oone__class_Oone(U_4256)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4256),c_Groups_Ozero__class_Ozero(U_4256)),U_4257))
      | ~ class_Rings_Olinordered__semidom(U_4256) ),
    inference(definitional_conversion,[status(esa)],[f_1228_2]) ).

cnf(f_1228_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4256),hAPP(hAPP(c_Power_Opower__class_Opower(U_4256),U_4257),hAPP(c_Nat_OSuc,U_4258))),c_Groups_Oone__class_Oone(U_4256)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4256),U_4257),c_Groups_Oone__class_Oone(U_4256)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4256),c_Groups_Ozero__class_Ozero(U_4256)),U_4257))
    | ~ class_Rings_Olinordered__semidom(U_4256) ),
    inference(clausify,[status(thm)],[f_1228_3]) ).

fof(f_1229_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_1229_2,plain,
    ! [U_4261,U_4260,U_4259] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4259,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4259,tc_HOL_Obool)),U_4260),U_4261)),U_4261) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4259,tc_HOL_Obool)),U_4260),U_4261),
    inference(variable_rename,[status(thm)],[f_1229_1]) ).

fof(f_1229_3,plain,
    ! [U_4260,U_4259,U_4261] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4259,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4259,tc_HOL_Obool)),U_4260),U_4261)),U_4261) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4259,tc_HOL_Obool)),U_4260),U_4261),
    inference(definitional_conversion,[status(esa)],[f_1229_2]) ).

cnf(f_1229_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4259,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4259,tc_HOL_Obool)),U_4260),U_4261)),U_4261) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_4259,tc_HOL_Obool)),U_4260),U_4261),
    inference(clausify,[status(thm)],[f_1229_3]) ).

fof(f_1230_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_1230_2,plain,
    ! [U_4262] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4262) = U_4262,
    inference(variable_rename,[status(thm)],[f_1230_1]) ).

fof(f_1230_3,plain,
    ! [U_4262] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4262) = U_4262,
    inference(definitional_conversion,[status(esa)],[f_1230_2]) ).

cnf(f_1230_4,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4262) = U_4262,
    inference(clausify,[status(thm)],[f_1230_3]) ).

fof(f_1231_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_1231_2,plain,
    ! [U_4264,U_4263] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4263)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4264)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4263),U_4264)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4263),U_4264))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4263)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4264))) ) ),
    inference(variable_rename,[status(thm)],[f_1231_1]) ).

fof(f_1231_3,plain,
    ( ! [U_4268,U_4266] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4266)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4268)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4266),U_4268)) )
    & ! [U_4267,U_4265] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4265),U_4267))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4265)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4267))) ) ),
    inference(miniscope,[status(thm)],[f_1231_2]) ).

fof(f_1231_4,plain,
    ( ! [U_4266,U_4268] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4266)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4268)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4266),U_4268)) )
    & ! [U_4267,U_4265] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4265),U_4267))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4265)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4267))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1231_3]) ).

cnf(f_1231_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4265),U_4267))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4265)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4267))) ),
    inference(clausify,[status(thm)],[f_1231_4]) ).

cnf(f_1231_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_4266)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4268)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4266),U_4268)) ),
    inference(clausify,[status(thm)],[f_1231_4]) ).

fof(f_1232_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_1232_2,plain,
    ! [U_4270,U_4269] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4269)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4270)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4269),U_4270)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4269),U_4270))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4269)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4270))) ) ),
    inference(variable_rename,[status(thm)],[f_1232_1]) ).

fof(f_1232_3,plain,
    ( ! [U_4274,U_4272] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4272)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4274)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4272),U_4274)) )
    & ! [U_4273,U_4271] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4271),U_4273))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4271)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4273))) ) ),
    inference(miniscope,[status(thm)],[f_1232_2]) ).

fof(f_1232_4,plain,
    ( ! [U_4272,U_4274] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4272)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4274)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4272),U_4274)) )
    & ! [U_4273,U_4271] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4271),U_4273))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4271)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4273))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1232_3]) ).

cnf(f_1232_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4271),U_4273))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4271)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4273))) ),
    inference(clausify,[status(thm)],[f_1232_4]) ).

cnf(f_1232_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4272)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4274)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4272),U_4274)) ),
    inference(clausify,[status(thm)],[f_1232_4]) ).

fof(f_1233_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_1233_2,plain,
    ! [U_4276,U_4275] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4275)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4276)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4275),U_4276)),
    inference(variable_rename,[status(thm)],[f_1233_1]) ).

fof(f_1233_3,plain,
    ! [U_4276,U_4275] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4275)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4276)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4275),U_4276)),
    inference(definitional_conversion,[status(esa)],[f_1233_2]) ).

cnf(f_1233_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4275)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4276)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4275),U_4276)),
    inference(clausify,[status(thm)],[f_1233_3]) ).

fof(f_1234_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_1234_2,plain,
    ! [U_4278,U_4277] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4277)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4278)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4277),U_4278)),
    inference(variable_rename,[status(thm)],[f_1234_1]) ).

fof(f_1234_3,plain,
    ! [U_4277,U_4278] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4277)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4278)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4277),U_4278)),
    inference(definitional_conversion,[status(esa)],[f_1234_2]) ).

cnf(f_1234_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4277)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4278)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4277),U_4278)),
    inference(clausify,[status(thm)],[f_1234_3]) ).

fof(f_1235_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_1235_2,plain,
    ! [U_4279] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4279)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4279)),
    inference(variable_rename,[status(thm)],[f_1235_1]) ).

fof(f_1235_3,plain,
    ! [U_4279] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4279)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4279)),
    inference(definitional_conversion,[status(esa)],[f_1235_2]) ).

cnf(f_1235_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4279)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4279)),
    inference(clausify,[status(thm)],[f_1235_3]) ).

fof(f_1236_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_1236_2,plain,
    ! [U_4281,U_4280] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4280),U_4281) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( U_4280 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_4281 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_4280 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_4281 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4280),U_4281) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_1236_1]) ).

fof(f_1236_3,plain,
    ( ! [U_4285,U_4283] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4283),U_4285) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ( U_4283 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          & U_4285 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_4284,U_4282] :
        ( U_4282 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_4284 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4282),U_4284) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_1236_2]) ).

fof(f_1236_4,plain,
    ( ! [U_4285,U_4283] :
        ( U_4283 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP348(U_4285,U_4283) )
    & ! [U_4285,U_4283] :
        ( U_4285 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP348(U_4285,U_4283) )
    & ! [U_4285,U_4283] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4283),U_4285) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | sP348(U_4285,U_4283) )
    & ! [U_4284,U_4282] :
        ( U_4282 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | U_4284 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4282),U_4284) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP348])],[f_1236_3]) ).

cnf(f_1236_5,plain,
    ( U_4282 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_4284 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4282),U_4284) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_1236_4]) ).

cnf(f_1236_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4283),U_4285) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | sP348(U_4285,U_4283) ),
    inference(clausify,[status(thm)],[f_1236_4]) ).

cnf(f_1236_7,plain,
    ( U_4285 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP348(U_4285,U_4283) ),
    inference(clausify,[status(thm)],[f_1236_4]) ).

cnf(f_1236_8,plain,
    ( U_4283 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP348(U_4285,U_4283) ),
    inference(clausify,[status(thm)],[f_1236_4]) ).

fof(f_1237_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_1237_2,plain,
    ! [U_4286] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4286) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_1237_1]) ).

fof(f_1237_3,plain,
    ! [U_4286] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4286) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_1237_2]) ).

cnf(f_1237_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_4286) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_1237_3]) ).

fof(f_1238_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_1238_2,plain,
    ! [U_4289,U_4288,U_4287] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4288),U_4289))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4287),U_4288)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4287),U_4289)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4287)) ),
    inference(variable_rename,[status(thm)],[f_1238_1]) ).

fof(f_1238_3,plain,
    ! [U_4287,U_4289,U_4288] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4288),U_4289))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4287),U_4288)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4287),U_4289)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4287)) ),
    inference(definitional_conversion,[status(esa)],[f_1238_2]) ).

cnf(f_1238_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4288),U_4289))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4287),U_4288)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4287),U_4289)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4287)) ),
    inference(clausify,[status(thm)],[f_1238_3]) ).

fof(f_1239_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_1239_2,plain,
    ! [U_4291,U_4290] :
      ( ( 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_4290),U_4291)))
        | ( U_4291 != 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_4290)) ) )
      & ( U_4291 = 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_4290))
        | ~ 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_4290),U_4291))) ) ),
    inference(variable_rename,[status(thm)],[f_1239_1]) ).

fof(f_1239_3,plain,
    ( ! [U_4295,U_4293] :
        ( 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_4293),U_4295)))
        | ( U_4295 != 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_4293)) ) )
    & ! [U_4294,U_4292] :
        ( U_4294 = 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_4292))
        | ~ 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_4292),U_4294))) ) ),
    inference(miniscope,[status(thm)],[f_1239_2]) ).

fof(f_1239_4,plain,
    ( ! [U_4295,U_4293] :
        ( U_4295 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP349(U_4295,U_4293) )
    & ! [U_4295,U_4293] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4293))
        | ~ sP349(U_4295,U_4293) )
    & ! [U_4295,U_4293] :
        ( 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_4293),U_4295)))
        | sP349(U_4295,U_4293) )
    & ! [U_4294,U_4292] :
        ( U_4294 = 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_4292))
        | ~ 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_4292),U_4294))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP349])],[f_1239_3]) ).

cnf(f_1239_5,plain,
    ( U_4294 = 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_4292))
    | ~ 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_4292),U_4294))) ),
    inference(clausify,[status(thm)],[f_1239_4]) ).

cnf(f_1239_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_4293),U_4295)))
    | sP349(U_4295,U_4293) ),
    inference(clausify,[status(thm)],[f_1239_4]) ).

cnf(f_1239_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4293))
    | ~ sP349(U_4295,U_4293) ),
    inference(clausify,[status(thm)],[f_1239_4]) ).

cnf(f_1239_8,plain,
    ( U_4295 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP349(U_4295,U_4293) ),
    inference(clausify,[status(thm)],[f_1239_4]) ).

fof(f_1240_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_1240_2,plain,
    ! [U_4296] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4296) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_4296),
    inference(variable_rename,[status(thm)],[f_1240_1]) ).

fof(f_1240_3,plain,
    ! [U_4296] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4296) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_4296),
    inference(definitional_conversion,[status(esa)],[f_1240_2]) ).

cnf(f_1240_4,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4296) = hAPP(c_Int_Oring__1__class_Oof__int(tc_Int_Oint),U_4296),
    inference(clausify,[status(thm)],[f_1240_3]) ).

fof(f_1241_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_1241_2,plain,
    ! [U_4298,U_4297] :
      ( 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_4297),U_4298)))
      | ~ 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_4297)) ),
    inference(variable_rename,[status(thm)],[f_1241_1]) ).

fof(f_1241_3,plain,
    ! [U_4298,U_4297] :
      ( 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_4297),U_4298)))
      | ~ 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_4297)) ),
    inference(definitional_conversion,[status(esa)],[f_1241_2]) ).

cnf(f_1241_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_4297),U_4298)))
    | ~ 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_4297)) ),
    inference(clausify,[status(thm)],[f_1241_3]) ).

fof(f_1242_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_1242_2,plain,
    ! [U_4299] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4299)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4299),
    inference(variable_rename,[status(thm)],[f_1242_1]) ).

fof(f_1242_3,plain,
    ! [U_4299] : hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4299)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4299),
    inference(definitional_conversion,[status(esa)],[f_1242_2]) ).

cnf(f_1242_4,plain,
    hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4299)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4299),
    inference(clausify,[status(thm)],[f_1242_3]) ).

fof(f_1243_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_1243_2,plain,
    ! [U_4300] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4300) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4300)),
    inference(variable_rename,[status(thm)],[f_1243_1]) ).

fof(f_1243_3,plain,
    ! [U_4300] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4300) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4300)),
    inference(definitional_conversion,[status(esa)],[f_1243_2]) ).

cnf(f_1243_4,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4300) = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4300)),
    inference(clausify,[status(thm)],[f_1243_3]) ).

fof(f_1244_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_1244_2,plain,
    ! [U_4302,U_4301] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4301)),U_4302) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4301),U_4302)),
    inference(variable_rename,[status(thm)],[f_1244_1]) ).

fof(f_1244_3,plain,
    ! [U_4301,U_4302] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4301)),U_4302) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4301),U_4302)),
    inference(definitional_conversion,[status(esa)],[f_1244_2]) ).

cnf(f_1244_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4301)),U_4302) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4301),U_4302)),
    inference(clausify,[status(thm)],[f_1244_3]) ).

fof(f_1245_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_1245_2,plain,
    ! [U_4304,U_4303] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4303)),U_4304) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4303),U_4304)),
    inference(variable_rename,[status(thm)],[f_1245_1]) ).

fof(f_1245_3,plain,
    ! [U_4303,U_4304] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4303)),U_4304) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4303),U_4304)),
    inference(definitional_conversion,[status(esa)],[f_1245_2]) ).

cnf(f_1245_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4303)),U_4304) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4303),U_4304)),
    inference(clausify,[status(thm)],[f_1245_3]) ).

fof(f_1246_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_1246_2,plain,
    ! [U_4306,U_4305] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4305),U_4306)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4305)),U_4306),
    inference(variable_rename,[status(thm)],[f_1246_1]) ).

fof(f_1246_3,plain,
    ! [U_4305,U_4306] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4305),U_4306)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4305)),U_4306),
    inference(definitional_conversion,[status(esa)],[f_1246_2]) ).

cnf(f_1246_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4305),U_4306)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4305)),U_4306),
    inference(clausify,[status(thm)],[f_1246_3]) ).

fof(f_1247_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_1247_2,plain,
    ! [U_4308,U_4307] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4307)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4308)) = 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_4307)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4308)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4307))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4307)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4308)) = 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_4308))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4307))) ) ),
    inference(variable_rename,[status(thm)],[f_1247_1]) ).

fof(f_1247_3,plain,
    ( ! [U_4312,U_4310] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4310)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4312)) = 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_4310)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4312)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4310))) )
    & ! [U_4311,U_4309] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4309)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4311)) = 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_4311))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4309))) ) ),
    inference(miniscope,[status(thm)],[f_1247_2]) ).

fof(f_1247_4,plain,
    ( ! [U_4310,U_4312] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4310)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4312)) = 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_4310)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4312)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4310))) )
    & ! [U_4309,U_4311] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4309)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4311)) = 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_4311))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4309))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1247_3]) ).

cnf(f_1247_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4309)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4311)) = 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_4311))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4309))) ),
    inference(clausify,[status(thm)],[f_1247_4]) ).

cnf(f_1247_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4310)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4312)) = 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_4310)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4312)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4310))) ),
    inference(clausify,[status(thm)],[f_1247_4]) ).

fof(f_1248_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_1248_2,plain,
    ! [U_4314,U_4313] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4313)),U_4314) = 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_4313)),U_4314))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4313))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4313)),U_4314) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4314)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4313))) ) ),
    inference(variable_rename,[status(thm)],[f_1248_1]) ).

fof(f_1248_3,plain,
    ( ! [U_4318,U_4316] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4316)),U_4318) = 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_4316)),U_4318))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4316))) )
    & ! [U_4317,U_4315] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4315)),U_4317) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4317)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4315))) ) ),
    inference(miniscope,[status(thm)],[f_1248_2]) ).

fof(f_1248_4,plain,
    ( ! [U_4316,U_4318] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4316)),U_4318) = 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_4316)),U_4318))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4316))) )
    & ! [U_4317,U_4315] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4315)),U_4317) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4317)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4315))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1248_3]) ).

cnf(f_1248_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4315)),U_4317) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4317)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4315))) ),
    inference(clausify,[status(thm)],[f_1248_4]) ).

cnf(f_1248_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4316)),U_4318) = 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_4316)),U_4318))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4316))) ),
    inference(clausify,[status(thm)],[f_1248_4]) ).

fof(f_1249_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_1249_2,plain,
    ! [U_4320,U_4319] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4319)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4320)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4319),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4320))),
    inference(variable_rename,[status(thm)],[f_1249_1]) ).

fof(f_1249_3,plain,
    ! [U_4319,U_4320] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4319)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4320)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4319),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4320))),
    inference(definitional_conversion,[status(esa)],[f_1249_2]) ).

cnf(f_1249_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4319)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4320)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4319),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4320))),
    inference(clausify,[status(thm)],[f_1249_3]) ).

fof(f_1250_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_1250_2,plain,
    ! [U_4321] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4321) = 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_4321))) ),
    inference(variable_rename,[status(thm)],[f_1250_1]) ).

fof(f_1250_3,plain,
    ! [U_4321] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4321) = 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_4321))) ),
    inference(definitional_conversion,[status(esa)],[f_1250_2]) ).

cnf(f_1250_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4321) = 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_4321))) ),
    inference(clausify,[status(thm)],[f_1250_3]) ).

fof(f_1251_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_1251_2,plain,
    ! [U_4323,U_4322] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4323),U_4322) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4323),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4323),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4322),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_4322 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4323),U_4322) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_4322 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1251_1]) ).

fof(f_1251_3,plain,
    ( ! [U_4327,U_4325] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4327),U_4325) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4327),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4327),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4325),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_4325 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4326,U_4324] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4326),U_4324) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_4324 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1251_2]) ).

fof(f_1251_4,plain,
    ( ! [U_4325,U_4327] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4327),U_4325) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4327),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4327),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4325),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | U_4325 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_4326,U_4324] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4326),U_4324) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | U_4324 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_1251_3]) ).

cnf(f_1251_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4326),U_4324) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | U_4324 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1251_4]) ).

cnf(f_1251_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4327),U_4325) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4327),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4327),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4325),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | U_4325 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1251_4]) ).

fof(f_1252_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_1252_2,plain,
    ! [U_4329,U_4328] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4328) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),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_4329)))
        | U_4328 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),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_4329)))
          & U_4328 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4329)) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4328) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4329) ) ),
    inference(variable_rename,[status(thm)],[f_1252_1]) ).

fof(f_1252_3,plain,
    ( ! [U_4333,U_4331] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4331) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4333)
        | ~ 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_4333)))
        | U_4331 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4333)) )
    & ! [U_4332,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_4332)))
          & U_4330 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4332)) )
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4330) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4332) ) ),
    inference(miniscope,[status(thm)],[f_1252_2]) ).

fof(f_1252_4,plain,
    ( ! [U_4330,U_4332] :
        ( 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_4332)))
        | ~ sP350(U_4330,U_4332) )
    & ! [U_4330,U_4332] :
        ( U_4330 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4332))
        | ~ sP350(U_4330,U_4332) )
    & ! [U_4333,U_4331] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4331) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4333)
        | ~ 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_4333)))
        | U_4331 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4333)) )
    & ! [U_4330,U_4332] :
        ( sP350(U_4330,U_4332)
        | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4330) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4332) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP350])],[f_1252_3]) ).

cnf(f_1252_5,plain,
    ( sP350(U_4330,U_4332)
    | hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4330) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4332) ),
    inference(clausify,[status(thm)],[f_1252_4]) ).

cnf(f_1252_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_4331) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4333)
    | ~ 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_4333)))
    | U_4331 != hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4333)) ),
    inference(clausify,[status(thm)],[f_1252_4]) ).

cnf(f_1252_7,plain,
    ( U_4330 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4332))
    | ~ sP350(U_4330,U_4332) ),
    inference(clausify,[status(thm)],[f_1252_4]) ).

cnf(f_1252_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_4332)))
    | ~ sP350(U_4330,U_4332) ),
    inference(clausify,[status(thm)],[f_1252_4]) ).

fof(f_1253_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_1253_2,plain,
    ! [U_4335,U_4334] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4334),U_4335)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_4334)),U_4335)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4334)) ),
    inference(variable_rename,[status(thm)],[f_1253_1]) ).

fof(f_1253_3,plain,
    ! [U_4334,U_4335] :
      ( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4334),U_4335)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_4334)),U_4335)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4334)) ),
    inference(definitional_conversion,[status(esa)],[f_1253_2]) ).

cnf(f_1253_4,plain,
    ( hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4334),U_4335)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_4334)),U_4335)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4334)) ),
    inference(clausify,[status(thm)],[f_1253_3]) ).

fof(f_1254_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_1254_2,plain,
    ! [U_4337,U_4336] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_4336)),U_4337) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4336),U_4337))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4336)) ),
    inference(variable_rename,[status(thm)],[f_1254_1]) ).

fof(f_1254_3,plain,
    ! [U_4336,U_4337] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_4336)),U_4337) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4336),U_4337))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4336)) ),
    inference(definitional_conversion,[status(esa)],[f_1254_2]) ).

cnf(f_1254_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Int_Onat,U_4336)),U_4337) = hAPP(c_Int_Onat,hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_4336),U_4337))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4336)) ),
    inference(clausify,[status(thm)],[f_1254_3]) ).

fof(f_1255_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_1255_2,plain,
    ! [U_4339,U_4338] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4338) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4339)
        | ( ( ( U_4338 != U_4339
              & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4339))) )
            | ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4338) != 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_4339))) ) )
          & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4338))) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4339)),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_4338))) ) )
      & ( ( ( ( ( U_4338 = U_4339
                | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4339))) )
              & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4338) = 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_4339))) ) )
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4338))) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4339)),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_4338))) ) )
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4338) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4339) ) ),
    inference(variable_rename,[status(thm)],[f_1255_1]) ).

fof(f_1255_3,plain,
    ( ! [U_4343,U_4341] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4341) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4343)
        | ( ( ( U_4341 != U_4343
              & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4343))) )
            | ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4341) != 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_4343))) ) )
          & ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4341))) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4343)),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_4341))) ) )
    & ! [U_4342,U_4340] :
        ( ( ( ( ( U_4340 = U_4342
                | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4342))) )
              & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4340) = 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_4342))) ) )
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4340))) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4342)),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_4340))) ) )
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4340) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4342) ) ),
    inference(miniscope,[status(thm)],[f_1255_2]) ).

fof(f_1255_4,plain,
    ( ! [U_4341,U_4343] :
        ( U_4341 != U_4343
        | ~ sP355(U_4341,U_4343) )
    & ! [U_4341,U_4343] :
        ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4343)))
        | ~ sP355(U_4341,U_4343) )
    & ! [U_4341,U_4343] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4341) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP354(U_4341,U_4343) )
    & ! [U_4341,U_4343] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4343)))
        | ~ sP354(U_4341,U_4343) )
    & ! [U_4341,U_4343] :
        ( sP355(U_4341,U_4343)
        | sP354(U_4341,U_4343)
        | ~ sP356(U_4341,U_4343) )
    & ! [U_4341,U_4343] :
        ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4341)))
        | ~ sP356(U_4341,U_4343) )
    & ! [U_4341,U_4343] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4343)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP353(U_4341,U_4343) )
    & ! [U_4341,U_4343] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4341)))
        | ~ sP353(U_4341,U_4343) )
    & ! [U_4340,U_4342] :
        ( U_4340 = U_4342
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4342)))
        | ~ sP351(U_4340,U_4342) )
    & ! [U_4340,U_4342] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4340) = 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_4342)))
        | ~ sP351(U_4340,U_4342) )
    & ! [U_4340,U_4342] :
        ( sP351(U_4340,U_4342)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4340)))
        | ~ sP352(U_4340,U_4342) )
    & ! [U_4340,U_4342] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4342)),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_4340)))
        | ~ sP352(U_4340,U_4342) )
    & ! [U_4341,U_4343] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4341) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4343)
        | sP356(U_4341,U_4343)
        | sP353(U_4341,U_4343) )
    & ! [U_4340,U_4342] :
        ( sP352(U_4340,U_4342)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4340) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4342) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP351,sP352,sP353,sP354,sP355,sP356])],[f_1255_3]) ).

cnf(f_1255_5,plain,
    ( sP352(U_4340,U_4342)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4340) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4342) ),
    inference(clausify,[status(thm)],[f_1255_4]) ).

cnf(f_1255_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4341) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4343)
    | sP356(U_4341,U_4343)
    | sP353(U_4341,U_4343) ),
    inference(clausify,[status(thm)],[f_1255_4]) ).

cnf(f_1255_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_4342)),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_4340)))
    | ~ sP352(U_4340,U_4342) ),
    inference(clausify,[status(thm)],[f_1255_4]) ).

cnf(f_1255_8,plain,
    ( sP351(U_4340,U_4342)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4340)))
    | ~ sP352(U_4340,U_4342) ),
    inference(clausify,[status(thm)],[f_1255_4]) ).

cnf(f_1255_9,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4340) = 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_4342)))
    | ~ sP351(U_4340,U_4342) ),
    inference(clausify,[status(thm)],[f_1255_4]) ).

cnf(f_1255_10,plain,
    ( U_4340 = U_4342
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4342)))
    | ~ sP351(U_4340,U_4342) ),
    inference(clausify,[status(thm)],[f_1255_4]) ).

cnf(f_1255_11,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4341)))
    | ~ sP353(U_4341,U_4343) ),
    inference(clausify,[status(thm)],[f_1255_4]) ).

cnf(f_1255_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_4343)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP353(U_4341,U_4343) ),
    inference(clausify,[status(thm)],[f_1255_4]) ).

cnf(f_1255_13,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4341)))
    | ~ sP356(U_4341,U_4343) ),
    inference(clausify,[status(thm)],[f_1255_4]) ).

cnf(f_1255_14,plain,
    ( sP355(U_4341,U_4343)
    | sP354(U_4341,U_4343)
    | ~ sP356(U_4341,U_4343) ),
    inference(clausify,[status(thm)],[f_1255_4]) ).

cnf(f_1255_15,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4343)))
    | ~ sP354(U_4341,U_4343) ),
    inference(clausify,[status(thm)],[f_1255_4]) ).

cnf(f_1255_16,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4341) != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP354(U_4341,U_4343) ),
    inference(clausify,[status(thm)],[f_1255_4]) ).

cnf(f_1255_17,plain,
    ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4343)))
    | ~ sP355(U_4341,U_4343) ),
    inference(clausify,[status(thm)],[f_1255_4]) ).

cnf(f_1255_18,plain,
    ( U_4341 != U_4343
    | ~ sP355(U_4341,U_4343) ),
    inference(clausify,[status(thm)],[f_1255_4]) ).

fof(f_1256_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_1256_2,plain,
    ! [U_4346,U_4345,U_4344] :
      ( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4344)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4345)),U_4346)) = 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_4344),U_4345))),U_4346)
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4345))) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4344)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4345)),U_4346)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4344)),U_4346)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4345))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4344))) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4344)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4345)),U_4346)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4345)),U_4346)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4344))) ) ),
    inference(variable_rename,[status(thm)],[f_1256_1]) ).

fof(f_1256_3,plain,
    ( ! [U_4352,U_4350,U_4348] :
        ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4348)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4350)),U_4352)) = 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_4348),U_4350))),U_4352)
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4350))) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4348)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4350)),U_4352)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4348)),U_4352)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4350))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4348))) )
    & ! [U_4351,U_4349,U_4347] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4347)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4349)),U_4351)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4349)),U_4351)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4347))) ) ),
    inference(miniscope,[status(thm)],[f_1256_2]) ).

fof(f_1256_4,plain,
    ( ! [U_4350,U_4348,U_4352] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4348)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4350)),U_4352)) = 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_4348),U_4350))),U_4352)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4350)))
        | ~ sP357(U_4350,U_4348,U_4352) )
    & ! [U_4350,U_4348,U_4352] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4348)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4350)),U_4352)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4348)),U_4352)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4350)))
        | ~ sP357(U_4350,U_4348,U_4352) )
    & ! [U_4350,U_4348,U_4352] :
        ( sP357(U_4350,U_4348,U_4352)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4348))) )
    & ! [U_4349,U_4347,U_4351] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4347)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4349)),U_4351)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4349)),U_4351)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4347))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP357])],[f_1256_3]) ).

cnf(f_1256_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4347)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4349)),U_4351)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4349)),U_4351)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4347))) ),
    inference(clausify,[status(thm)],[f_1256_4]) ).

cnf(f_1256_6,plain,
    ( sP357(U_4350,U_4348,U_4352)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4348))) ),
    inference(clausify,[status(thm)],[f_1256_4]) ).

cnf(f_1256_7,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4348)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4350)),U_4352)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4348)),U_4352)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4350)))
    | ~ sP357(U_4350,U_4348,U_4352) ),
    inference(clausify,[status(thm)],[f_1256_4]) ).

cnf(f_1256_8,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4348)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4350)),U_4352)) = 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_4348),U_4350))),U_4352)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4350)))
    | ~ sP357(U_4350,U_4348,U_4352) ),
    inference(clausify,[status(thm)],[f_1256_4]) ).

fof(f_1257_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_1257_2,plain,
    ! [U_4353] :
      ( ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4353)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4353)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4353))) )
      & ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4353)) = 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_4353))) ) ),
    inference(variable_rename,[status(thm)],[f_1257_1]) ).

fof(f_1257_3,plain,
    ( ! [U_4355] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4355)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4355)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4355))) )
    & ! [U_4354] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4354)) = 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_4354))) ) ),
    inference(miniscope,[status(thm)],[f_1257_2]) ).

fof(f_1257_4,plain,
    ( ! [U_4355] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4355)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4355)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4355))) )
    & ! [U_4354] :
        ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4354)) = 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_4354))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1257_3]) ).

cnf(f_1257_5,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4354)) = 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_4354))) ),
    inference(clausify,[status(thm)],[f_1257_4]) ).

cnf(f_1257_6,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4355)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4355)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4355))) ),
    inference(clausify,[status(thm)],[f_1257_4]) ).

fof(f_1258_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_1258_2,plain,
    ! [U_4357,U_4356] :
      ( ( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4356),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4357)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4356),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4357)))
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4357))) )
          & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4356),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4357)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4356)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4357))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4356))) )
      & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4356),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4357)) = 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_4356))) ) ),
    inference(variable_rename,[status(thm)],[f_1258_1]) ).

fof(f_1258_3,plain,
    ( ! [U_4361,U_4359] :
        ( ( ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4359),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4361)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4359),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4361)))
            | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4361))) )
          & ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4359),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4361)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4359)
            | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4361))) ) )
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4359))) )
    & ! [U_4360,U_4358] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4358),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4360)) = 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_4358))) ) ),
    inference(miniscope,[status(thm)],[f_1258_2]) ).

fof(f_1258_4,plain,
    ( ! [U_4361,U_4359] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4359),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4361)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4359),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4361)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4361)))
        | ~ sP358(U_4361,U_4359) )
    & ! [U_4361,U_4359] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4359),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4361)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4359)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4361)))
        | ~ sP358(U_4361,U_4359) )
    & ! [U_4361,U_4359] :
        ( sP358(U_4361,U_4359)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4359))) )
    & ! [U_4358,U_4360] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4358),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4360)) = 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_4358))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP358])],[f_1258_3]) ).

cnf(f_1258_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4358),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4360)) = 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_4358))) ),
    inference(clausify,[status(thm)],[f_1258_4]) ).

cnf(f_1258_6,plain,
    ( sP358(U_4361,U_4359)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4359))) ),
    inference(clausify,[status(thm)],[f_1258_4]) ).

cnf(f_1258_7,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4359),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4361)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4359)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4361)))
    | ~ sP358(U_4361,U_4359) ),
    inference(clausify,[status(thm)],[f_1258_4]) ).

cnf(f_1258_8,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4359),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4361)) = hAPP(c_Int_Onat,c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4359),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4361)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4361)))
    | ~ sP358(U_4361,U_4359) ),
    inference(clausify,[status(thm)],[f_1258_4]) ).

fof(f_1259_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_1259_2,plain,
    ! [U_4363,U_4362] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4362)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4363)) = 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_4362)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4363)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4362))) )
      & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4362)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4363)) = 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_4362))) ) ),
    inference(variable_rename,[status(thm)],[f_1259_1]) ).

fof(f_1259_3,plain,
    ( ! [U_4367,U_4365] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4365)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4367)) = 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_4365)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4367)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4365))) )
    & ! [U_4366,U_4364] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4364)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4366)) = 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_4364))) ) ),
    inference(miniscope,[status(thm)],[f_1259_2]) ).

fof(f_1259_4,plain,
    ( ! [U_4367,U_4365] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4365)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4367)) = 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_4365)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4367)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4365))) )
    & ! [U_4366,U_4364] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4364)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4366)) = 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_4364))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1259_3]) ).

cnf(f_1259_5,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4364)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4366)) = 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_4364))) ),
    inference(clausify,[status(thm)],[f_1259_4]) ).

cnf(f_1259_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4365)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4367)) = 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_4365)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4367)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4365))) ),
    inference(clausify,[status(thm)],[f_1259_4]) ).

fof(f_1260_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_1260_2,plain,
    ! [U_4370,U_4369,U_4368] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4368),U_4369),U_4370) != c_Groups_Ozero__class_Ozero(U_4368)
      | U_4369 = c_Groups_Ozero__class_Ozero(U_4368)
      | ~ class_Rings_Oring__1__no__zero__divisors(U_4368) ),
    inference(variable_rename,[status(thm)],[f_1260_1]) ).

fof(f_1260_3,plain,
    ! [U_4369,U_4368,U_4370] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4368),U_4369),U_4370) != c_Groups_Ozero__class_Ozero(U_4368)
      | U_4369 = c_Groups_Ozero__class_Ozero(U_4368)
      | ~ class_Rings_Oring__1__no__zero__divisors(U_4368) ),
    inference(definitional_conversion,[status(esa)],[f_1260_2]) ).

cnf(f_1260_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4368),U_4369),U_4370) != c_Groups_Ozero__class_Ozero(U_4368)
    | U_4369 = c_Groups_Ozero__class_Ozero(U_4368)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_4368) ),
    inference(clausify,[status(thm)],[f_1260_3]) ).

fof(f_1261_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_1261_2,plain,
    ! [U_4373,U_4372,U_4371] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4371),hAPP(hAPP(c_Power_Opower__class_Opower(U_4371),U_4372),U_4373)),U_4372) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4371),U_4372),hAPP(hAPP(c_Power_Opower__class_Opower(U_4371),U_4372),U_4373))
      | ~ class_Groups_Omonoid__mult(U_4371) ),
    inference(variable_rename,[status(thm)],[f_1261_1]) ).

fof(f_1261_3,plain,
    ! [U_4371,U_4372,U_4373] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4371),hAPP(hAPP(c_Power_Opower__class_Opower(U_4371),U_4372),U_4373)),U_4372) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4371),U_4372),hAPP(hAPP(c_Power_Opower__class_Opower(U_4371),U_4372),U_4373))
      | ~ class_Groups_Omonoid__mult(U_4371) ),
    inference(definitional_conversion,[status(esa)],[f_1261_2]) ).

cnf(f_1261_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4371),hAPP(hAPP(c_Power_Opower__class_Opower(U_4371),U_4372),U_4373)),U_4372) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4371),U_4372),hAPP(hAPP(c_Power_Opower__class_Opower(U_4371),U_4372),U_4373))
    | ~ class_Groups_Omonoid__mult(U_4371) ),
    inference(clausify,[status(thm)],[f_1261_3]) ).

fof(f_1262_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_1262_2,plain,
    ! [U_4377,U_4376,U_4375,U_4374] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4374),U_4375),U_4376)),U_4377) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4374),hAPP(hAPP(c_Power_Opower__class_Opower(U_4374),U_4375),U_4377)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4374),U_4376),U_4377))
      | ~ class_Groups_Ocomm__monoid__mult(U_4374) ),
    inference(variable_rename,[status(thm)],[f_1262_1]) ).

fof(f_1262_3,plain,
    ! [U_4374,U_4375,U_4376,U_4377] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4374),U_4375),U_4376)),U_4377) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4374),hAPP(hAPP(c_Power_Opower__class_Opower(U_4374),U_4375),U_4377)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4374),U_4376),U_4377))
      | ~ class_Groups_Ocomm__monoid__mult(U_4374) ),
    inference(definitional_conversion,[status(esa)],[f_1262_2]) ).

cnf(f_1262_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4374),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4374),U_4375),U_4376)),U_4377) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4374),hAPP(hAPP(c_Power_Opower__class_Opower(U_4374),U_4375),U_4377)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4374),U_4376),U_4377))
    | ~ class_Groups_Ocomm__monoid__mult(U_4374) ),
    inference(clausify,[status(thm)],[f_1262_3]) ).

fof(f_1263_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_1263_2,plain,
    ! [U_4379,U_4378] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4378),c_Groups_Oone__class_Oone(U_4378)),U_4379) = c_Groups_Oone__class_Oone(U_4378)
      | ~ class_Groups_Omonoid__mult(U_4378) ),
    inference(variable_rename,[status(thm)],[f_1263_1]) ).

fof(f_1263_3,plain,
    ! [U_4379,U_4378] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4378),c_Groups_Oone__class_Oone(U_4378)),U_4379) = c_Groups_Oone__class_Oone(U_4378)
      | ~ class_Groups_Omonoid__mult(U_4378) ),
    inference(definitional_conversion,[status(esa)],[f_1263_2]) ).

cnf(f_1263_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4378),c_Groups_Oone__class_Oone(U_4378)),U_4379) = c_Groups_Oone__class_Oone(U_4378)
    | ~ class_Groups_Omonoid__mult(U_4378) ),
    inference(clausify,[status(thm)],[f_1263_3]) ).

fof(f_1264_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_1264_2,plain,
    ! [U_4382,U_4381,U_4380] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4380),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4381),U_4382)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4380),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4380),U_4381)),U_4382)
      | ~ class_Rings_Osemiring__1(U_4380) ),
    inference(variable_rename,[status(thm)],[f_1264_1]) ).

fof(f_1264_3,plain,
    ! [U_4380,U_4381,U_4382] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4380),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4381),U_4382)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4380),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4380),U_4381)),U_4382)
      | ~ class_Rings_Osemiring__1(U_4380) ),
    inference(definitional_conversion,[status(esa)],[f_1264_2]) ).

cnf(f_1264_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4380),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_4381),U_4382)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4380),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_4380),U_4381)),U_4382)
    | ~ class_Rings_Osemiring__1(U_4380) ),
    inference(clausify,[status(thm)],[f_1264_3]) ).

fof(f_1265_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_1265_2,plain,
    ! [U_4386,U_4385,U_4384,U_4383] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4383),U_4384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4385),U_4386)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4383),hAPP(hAPP(c_Power_Opower__class_Opower(U_4383),U_4384),U_4385)),U_4386)
      | ~ class_Groups_Omonoid__mult(U_4383) ),
    inference(variable_rename,[status(thm)],[f_1265_1]) ).

fof(f_1265_3,plain,
    ! [U_4383,U_4384,U_4385,U_4386] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4383),U_4384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4385),U_4386)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4383),hAPP(hAPP(c_Power_Opower__class_Opower(U_4383),U_4384),U_4385)),U_4386)
      | ~ class_Groups_Omonoid__mult(U_4383) ),
    inference(definitional_conversion,[status(esa)],[f_1265_2]) ).

cnf(f_1265_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4383),U_4384),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4385),U_4386)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4383),hAPP(hAPP(c_Power_Opower__class_Opower(U_4383),U_4384),U_4385)),U_4386)
    | ~ class_Groups_Omonoid__mult(U_4383) ),
    inference(clausify,[status(thm)],[f_1265_3]) ).

fof(f_1266_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_1266_2,plain,
    ! [U_4387] : 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_4387)) = 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_4387))),
    inference(variable_rename,[status(thm)],[f_1266_1]) ).

fof(f_1266_3,plain,
    ! [U_4387] : 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_4387)) = 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_4387))),
    inference(definitional_conversion,[status(esa)],[f_1266_2]) ).

cnf(f_1266_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_4387)) = 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_4387))),
    inference(clausify,[status(thm)],[f_1266_3]) ).

fof(f_1267_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_1267_2,plain,
    ! [U_4390,U_4389,U_4388] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4388),hAPP(hAPP(c_Power_Opower__class_Opower(U_4388),U_4389),U_4390)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4388),hAPP(c_Groups_Oabs__class_Oabs(U_4388),U_4389)),U_4390)
      | ~ class_Rings_Olinordered__idom(U_4388) ),
    inference(variable_rename,[status(thm)],[f_1267_1]) ).

fof(f_1267_3,plain,
    ! [U_4388,U_4389,U_4390] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4388),hAPP(hAPP(c_Power_Opower__class_Opower(U_4388),U_4389),U_4390)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4388),hAPP(c_Groups_Oabs__class_Oabs(U_4388),U_4389)),U_4390)
      | ~ class_Rings_Olinordered__idom(U_4388) ),
    inference(definitional_conversion,[status(esa)],[f_1267_2]) ).

cnf(f_1267_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4388),hAPP(hAPP(c_Power_Opower__class_Opower(U_4388),U_4389),U_4390)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4388),hAPP(c_Groups_Oabs__class_Oabs(U_4388),U_4389)),U_4390)
    | ~ class_Rings_Olinordered__idom(U_4388) ),
    inference(clausify,[status(thm)],[f_1267_3]) ).

fof(f_1268_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_1268_2,plain,
    ! [U_4392,U_4391] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4391),U_4392),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4392
      | ~ class_Groups_Omonoid__mult(U_4391) ),
    inference(variable_rename,[status(thm)],[f_1268_1]) ).

fof(f_1268_3,plain,
    ! [U_4391,U_4392] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4391),U_4392),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4392
      | ~ class_Groups_Omonoid__mult(U_4391) ),
    inference(definitional_conversion,[status(esa)],[f_1268_2]) ).

cnf(f_1268_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4391),U_4392),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = U_4392
    | ~ class_Groups_Omonoid__mult(U_4391) ),
    inference(clausify,[status(thm)],[f_1268_3]) ).

fof(f_1269_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_1269_2,plain,
    ! [U_4393] :
      ( ( 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_4393)) = 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_4393)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4393))) )
      & ( 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_4393)) = 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_4393))) ) ),
    inference(variable_rename,[status(thm)],[f_1269_1]) ).

fof(f_1269_3,plain,
    ( ! [U_4395] :
        ( 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_4395)) = 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_4395)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4395))) )
    & ! [U_4394] :
        ( 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_4394)) = 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_4394))) ) ),
    inference(miniscope,[status(thm)],[f_1269_2]) ).

fof(f_1269_4,plain,
    ( ! [U_4395] :
        ( 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_4395)) = 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_4395)))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4395))) )
    & ! [U_4394] :
        ( 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_4394)) = 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_4394))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1269_3]) ).

cnf(f_1269_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_4394)) = 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_4394))) ),
    inference(clausify,[status(thm)],[f_1269_4]) ).

cnf(f_1269_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_4395)) = 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_4395)))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4395))) ),
    inference(clausify,[status(thm)],[f_1269_4]) ).

fof(f_1270_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_1270_2,plain,
    ! [U_4398,U_4397,U_4396] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4396),c_Groups_Ozero__class_Ozero(U_4396)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4396),U_4397),U_4398)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4396),c_Groups_Ozero__class_Ozero(U_4396)),U_4397))
      | ~ class_Rings_Olinordered__semidom(U_4396) ),
    inference(variable_rename,[status(thm)],[f_1270_1]) ).

fof(f_1270_3,plain,
    ! [U_4396,U_4397,U_4398] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4396),c_Groups_Ozero__class_Ozero(U_4396)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4396),U_4397),U_4398)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4396),c_Groups_Ozero__class_Ozero(U_4396)),U_4397))
      | ~ class_Rings_Olinordered__semidom(U_4396) ),
    inference(definitional_conversion,[status(esa)],[f_1270_2]) ).

cnf(f_1270_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4396),c_Groups_Ozero__class_Ozero(U_4396)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4396),U_4397),U_4398)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4396),c_Groups_Ozero__class_Ozero(U_4396)),U_4397))
    | ~ class_Rings_Olinordered__semidom(U_4396) ),
    inference(clausify,[status(thm)],[f_1270_3]) ).

fof(f_1271_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_1271_2,plain,
    ! [U_4402,U_4401,U_4400,U_4399] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4399),hAPP(hAPP(c_Power_Opower__class_Opower(U_4399),U_4400),U_4402)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4399),U_4401),U_4402)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4399),c_Groups_Ozero__class_Ozero(U_4399)),U_4400))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4399),U_4400),U_4401))
      | ~ class_Rings_Olinordered__semidom(U_4399) ),
    inference(variable_rename,[status(thm)],[f_1271_1]) ).

fof(f_1271_3,plain,
    ! [U_4399,U_4400,U_4401,U_4402] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4399),hAPP(hAPP(c_Power_Opower__class_Opower(U_4399),U_4400),U_4402)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4399),U_4401),U_4402)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4399),c_Groups_Ozero__class_Ozero(U_4399)),U_4400))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4399),U_4400),U_4401))
      | ~ class_Rings_Olinordered__semidom(U_4399) ),
    inference(definitional_conversion,[status(esa)],[f_1271_2]) ).

cnf(f_1271_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4399),hAPP(hAPP(c_Power_Opower__class_Opower(U_4399),U_4400),U_4402)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4399),U_4401),U_4402)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4399),c_Groups_Ozero__class_Ozero(U_4399)),U_4400))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4399),U_4400),U_4401))
    | ~ class_Rings_Olinordered__semidom(U_4399) ),
    inference(clausify,[status(thm)],[f_1271_3]) ).

fof(f_1272_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_1272_2,plain,
    ! [U_4405,U_4404,U_4403] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4403),c_Groups_Ozero__class_Ozero(U_4403)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4403),U_4404),U_4405)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4403),c_Groups_Ozero__class_Ozero(U_4403)),U_4404))
      | ~ class_Rings_Olinordered__semidom(U_4403) ),
    inference(variable_rename,[status(thm)],[f_1272_1]) ).

fof(f_1272_3,plain,
    ! [U_4404,U_4403,U_4405] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4403),c_Groups_Ozero__class_Ozero(U_4403)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4403),U_4404),U_4405)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4403),c_Groups_Ozero__class_Ozero(U_4403)),U_4404))
      | ~ class_Rings_Olinordered__semidom(U_4403) ),
    inference(definitional_conversion,[status(esa)],[f_1272_2]) ).

cnf(f_1272_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4403),c_Groups_Ozero__class_Ozero(U_4403)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4403),U_4404),U_4405)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4403),c_Groups_Ozero__class_Ozero(U_4403)),U_4404))
    | ~ class_Rings_Olinordered__semidom(U_4403) ),
    inference(clausify,[status(thm)],[f_1272_3]) ).

fof(f_1273_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_1273_2,plain,
    ! [U_4408,U_4407,U_4406] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4406),U_4407),U_4408) = c_Groups_Ozero__class_Ozero(U_4406)
          | U_4408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | U_4407 != c_Groups_Ozero__class_Ozero(U_4406) )
        & ( ( U_4408 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & U_4407 = c_Groups_Ozero__class_Ozero(U_4406) )
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_4406),U_4407),U_4408) != c_Groups_Ozero__class_Ozero(U_4406) ) )
      | ~ class_Rings_Ozero__neq__one(U_4406)
      | ~ class_Rings_Ono__zero__divisors(U_4406)
      | ~ class_Rings_Omult__zero(U_4406)
      | ~ class_Power_Opower(U_4406) ),
    inference(variable_rename,[status(thm)],[f_1273_1]) ).

fof(f_1273_3,plain,
    ( ! [U_4406,U_4407,U_4408] :
        ( U_4408 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP359(U_4406,U_4407,U_4408) )
    & ! [U_4406,U_4407,U_4408] :
        ( U_4407 = c_Groups_Ozero__class_Ozero(U_4406)
        | ~ sP359(U_4406,U_4407,U_4408) )
    & ! [U_4406,U_4407,U_4408] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4406),U_4407),U_4408) = c_Groups_Ozero__class_Ozero(U_4406)
        | U_4408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4407 != c_Groups_Ozero__class_Ozero(U_4406)
        | ~ sP360(U_4406,U_4407,U_4408) )
    & ! [U_4406,U_4407,U_4408] :
        ( sP359(U_4406,U_4407,U_4408)
        | hAPP(hAPP(c_Power_Opower__class_Opower(U_4406),U_4407),U_4408) != c_Groups_Ozero__class_Ozero(U_4406)
        | ~ sP360(U_4406,U_4407,U_4408) )
    & ! [U_4406,U_4407,U_4408] :
        ( sP360(U_4406,U_4407,U_4408)
        | ~ class_Rings_Ozero__neq__one(U_4406)
        | ~ class_Rings_Ono__zero__divisors(U_4406)
        | ~ class_Rings_Omult__zero(U_4406)
        | ~ class_Power_Opower(U_4406) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP359,sP360])],[f_1273_2]) ).

cnf(f_1273_4,plain,
    ( sP360(U_4406,U_4407,U_4408)
    | ~ class_Rings_Ozero__neq__one(U_4406)
    | ~ class_Rings_Ono__zero__divisors(U_4406)
    | ~ class_Rings_Omult__zero(U_4406)
    | ~ class_Power_Opower(U_4406) ),
    inference(clausify,[status(thm)],[f_1273_3]) ).

cnf(f_1273_5,plain,
    ( sP359(U_4406,U_4407,U_4408)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_4406),U_4407),U_4408) != c_Groups_Ozero__class_Ozero(U_4406)
    | ~ sP360(U_4406,U_4407,U_4408) ),
    inference(clausify,[status(thm)],[f_1273_3]) ).

cnf(f_1273_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4406),U_4407),U_4408) = c_Groups_Ozero__class_Ozero(U_4406)
    | U_4408 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_4407 != c_Groups_Ozero__class_Ozero(U_4406)
    | ~ sP360(U_4406,U_4407,U_4408) ),
    inference(clausify,[status(thm)],[f_1273_3]) ).

cnf(f_1273_7,plain,
    ( U_4407 = c_Groups_Ozero__class_Ozero(U_4406)
    | ~ sP359(U_4406,U_4407,U_4408) ),
    inference(clausify,[status(thm)],[f_1273_3]) ).

cnf(f_1273_8,plain,
    ( U_4408 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP359(U_4406,U_4407,U_4408) ),
    inference(clausify,[status(thm)],[f_1273_3]) ).

fof(f_1274_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_1274_2,plain,
    ! [U_4411,U_4410,U_4409] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4409),c_Groups_Oone__class_Oone(U_4409)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4409),U_4410),U_4411)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4409),c_Groups_Oone__class_Oone(U_4409)),U_4410))
      | ~ class_Rings_Olinordered__semidom(U_4409) ),
    inference(variable_rename,[status(thm)],[f_1274_1]) ).

fof(f_1274_3,plain,
    ! [U_4410,U_4411,U_4409] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4409),c_Groups_Oone__class_Oone(U_4409)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4409),U_4410),U_4411)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4409),c_Groups_Oone__class_Oone(U_4409)),U_4410))
      | ~ class_Rings_Olinordered__semidom(U_4409) ),
    inference(definitional_conversion,[status(esa)],[f_1274_2]) ).

cnf(f_1274_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4409),c_Groups_Oone__class_Oone(U_4409)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4409),U_4410),U_4411)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4409),c_Groups_Oone__class_Oone(U_4409)),U_4410))
    | ~ class_Rings_Olinordered__semidom(U_4409) ),
    inference(clausify,[status(thm)],[f_1274_3]) ).

fof(f_1275_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_1275_2,plain,
    ! [U_4413,U_4412] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4412),c_Groups_Ozero__class_Ozero(U_4412)),hAPP(c_Nat_OSuc,U_4413)) = c_Groups_Ozero__class_Ozero(U_4412)
      | ~ class_Rings_Osemiring__0(U_4412)
      | ~ class_Power_Opower(U_4412) ),
    inference(variable_rename,[status(thm)],[f_1275_1]) ).

fof(f_1275_3,plain,
    ! [U_4413,U_4412] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4412),c_Groups_Ozero__class_Ozero(U_4412)),hAPP(c_Nat_OSuc,U_4413)) = c_Groups_Ozero__class_Ozero(U_4412)
      | ~ class_Rings_Osemiring__0(U_4412)
      | ~ class_Power_Opower(U_4412) ),
    inference(definitional_conversion,[status(esa)],[f_1275_2]) ).

cnf(f_1275_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4412),c_Groups_Ozero__class_Ozero(U_4412)),hAPP(c_Nat_OSuc,U_4413)) = c_Groups_Ozero__class_Ozero(U_4412)
    | ~ class_Rings_Osemiring__0(U_4412)
    | ~ class_Power_Opower(U_4412) ),
    inference(clausify,[status(thm)],[f_1275_3]) ).

fof(f_1276_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_1276_2,plain,
    ! [U_4417,U_4416,U_4415,U_4414] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4414),U_4415),U_4416) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4414),U_4415),U_4417)
          | U_4416 != U_4417 )
        & ( U_4416 = U_4417
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_4414),U_4415),U_4416) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4414),U_4415),U_4417) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),c_Groups_Oone__class_Oone(U_4414)),U_4415))
      | ~ class_Rings_Olinordered__semidom(U_4414) ),
    inference(variable_rename,[status(thm)],[f_1276_1]) ).

fof(f_1276_3,plain,
    ( ! [U_4414,U_4415,U_4416,U_4417] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4414),U_4415),U_4416) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4414),U_4415),U_4417)
        | U_4416 != U_4417
        | ~ sP361(U_4414,U_4415,U_4416,U_4417) )
    & ! [U_4414,U_4415,U_4416,U_4417] :
        ( U_4416 = U_4417
        | hAPP(hAPP(c_Power_Opower__class_Opower(U_4414),U_4415),U_4416) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4414),U_4415),U_4417)
        | ~ sP361(U_4414,U_4415,U_4416,U_4417) )
    & ! [U_4414,U_4415,U_4416,U_4417] :
        ( sP361(U_4414,U_4415,U_4416,U_4417)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),c_Groups_Oone__class_Oone(U_4414)),U_4415))
        | ~ class_Rings_Olinordered__semidom(U_4414) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP361])],[f_1276_2]) ).

cnf(f_1276_4,plain,
    ( sP361(U_4414,U_4415,U_4416,U_4417)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4414),c_Groups_Oone__class_Oone(U_4414)),U_4415))
    | ~ class_Rings_Olinordered__semidom(U_4414) ),
    inference(clausify,[status(thm)],[f_1276_3]) ).

cnf(f_1276_5,plain,
    ( U_4416 = U_4417
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_4414),U_4415),U_4416) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4414),U_4415),U_4417)
    | ~ sP361(U_4414,U_4415,U_4416,U_4417) ),
    inference(clausify,[status(thm)],[f_1276_3]) ).

cnf(f_1276_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4414),U_4415),U_4416) = hAPP(hAPP(c_Power_Opower__class_Opower(U_4414),U_4415),U_4417)
    | U_4416 != U_4417
    | ~ sP361(U_4414,U_4415,U_4416,U_4417) ),
    inference(clausify,[status(thm)],[f_1276_3]) ).

fof(f_1277_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_1277_2,plain,
    ! [U_4420,U_4419,U_4418] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4418),U_4419),hAPP(c_Nat_OSuc,U_4420)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4418),hAPP(hAPP(c_Power_Opower__class_Opower(U_4418),U_4419),U_4420)),U_4419)
      | ~ class_Groups_Omonoid__mult(U_4418) ),
    inference(variable_rename,[status(thm)],[f_1277_1]) ).

fof(f_1277_3,plain,
    ! [U_4419,U_4420,U_4418] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4418),U_4419),hAPP(c_Nat_OSuc,U_4420)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4418),hAPP(hAPP(c_Power_Opower__class_Opower(U_4418),U_4419),U_4420)),U_4419)
      | ~ class_Groups_Omonoid__mult(U_4418) ),
    inference(definitional_conversion,[status(esa)],[f_1277_2]) ).

cnf(f_1277_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4418),U_4419),hAPP(c_Nat_OSuc,U_4420)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4418),hAPP(hAPP(c_Power_Opower__class_Opower(U_4418),U_4419),U_4420)),U_4419)
    | ~ class_Groups_Omonoid__mult(U_4418) ),
    inference(clausify,[status(thm)],[f_1277_3]) ).

fof(f_1278_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_1278_2,plain,
    ! [U_4423,U_4422,U_4421] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4421),U_4422),hAPP(c_Nat_OSuc,U_4423)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4421),U_4422),hAPP(hAPP(c_Power_Opower__class_Opower(U_4421),U_4422),U_4423))
      | ~ class_Power_Opower(U_4421) ),
    inference(variable_rename,[status(thm)],[f_1278_1]) ).

fof(f_1278_3,plain,
    ! [U_4421,U_4422,U_4423] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4421),U_4422),hAPP(c_Nat_OSuc,U_4423)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4421),U_4422),hAPP(hAPP(c_Power_Opower__class_Opower(U_4421),U_4422),U_4423))
      | ~ class_Power_Opower(U_4421) ),
    inference(definitional_conversion,[status(esa)],[f_1278_2]) ).

cnf(f_1278_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4421),U_4422),hAPP(c_Nat_OSuc,U_4423)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4421),U_4422),hAPP(hAPP(c_Power_Opower__class_Opower(U_4421),U_4422),U_4423))
    | ~ class_Power_Opower(U_4421) ),
    inference(clausify,[status(thm)],[f_1278_3]) ).

fof(f_1279_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_1279_2,plain,
    ! [U_4425,U_4424] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4424),U_4425),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4424)
      | ~ class_Power_Opower(U_4424) ),
    inference(variable_rename,[status(thm)],[f_1279_1]) ).

fof(f_1279_3,plain,
    ! [U_4424,U_4425] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4424),U_4425),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4424)
      | ~ class_Power_Opower(U_4424) ),
    inference(definitional_conversion,[status(esa)],[f_1279_2]) ).

cnf(f_1279_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4424),U_4425),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Oone__class_Oone(U_4424)
    | ~ class_Power_Opower(U_4424) ),
    inference(clausify,[status(thm)],[f_1279_3]) ).

fof(f_1280_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_1280_2,plain,
    ! [U_4429,U_4428,U_4427,U_4426] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4426),U_4427),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4428),U_4429)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4426),hAPP(hAPP(c_Power_Opower__class_Opower(U_4426),U_4427),U_4428)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4426),U_4427),U_4429))
      | ~ class_Groups_Omonoid__mult(U_4426) ),
    inference(variable_rename,[status(thm)],[f_1280_1]) ).

fof(f_1280_3,plain,
    ! [U_4426,U_4427,U_4428,U_4429] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4426),U_4427),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4428),U_4429)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4426),hAPP(hAPP(c_Power_Opower__class_Opower(U_4426),U_4427),U_4428)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4426),U_4427),U_4429))
      | ~ class_Groups_Omonoid__mult(U_4426) ),
    inference(definitional_conversion,[status(esa)],[f_1280_2]) ).

cnf(f_1280_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4426),U_4427),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4428),U_4429)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4426),hAPP(hAPP(c_Power_Opower__class_Opower(U_4426),U_4427),U_4428)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4426),U_4427),U_4429))
    | ~ class_Groups_Omonoid__mult(U_4426) ),
    inference(clausify,[status(thm)],[f_1280_3]) ).

fof(f_1281_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_1281_2,plain,
    ! [U_4432,U_4431,U_4430] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4430),hAPP(hAPP(c_Power_Opower__class_Opower(U_4430),hAPP(c_Groups_Ouminus__class_Ouminus(U_4430),U_4431)),U_4432)) = hAPP(c_Groups_Oabs__class_Oabs(U_4430),hAPP(hAPP(c_Power_Opower__class_Opower(U_4430),U_4431),U_4432))
      | ~ class_Rings_Olinordered__idom(U_4430) ),
    inference(variable_rename,[status(thm)],[f_1281_1]) ).

fof(f_1281_3,plain,
    ! [U_4430,U_4431,U_4432] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4430),hAPP(hAPP(c_Power_Opower__class_Opower(U_4430),hAPP(c_Groups_Ouminus__class_Ouminus(U_4430),U_4431)),U_4432)) = hAPP(c_Groups_Oabs__class_Oabs(U_4430),hAPP(hAPP(c_Power_Opower__class_Opower(U_4430),U_4431),U_4432))
      | ~ class_Rings_Olinordered__idom(U_4430) ),
    inference(definitional_conversion,[status(esa)],[f_1281_2]) ).

cnf(f_1281_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4430),hAPP(hAPP(c_Power_Opower__class_Opower(U_4430),hAPP(c_Groups_Ouminus__class_Ouminus(U_4430),U_4431)),U_4432)) = hAPP(c_Groups_Oabs__class_Oabs(U_4430),hAPP(hAPP(c_Power_Opower__class_Opower(U_4430),U_4431),U_4432))
    | ~ class_Rings_Olinordered__idom(U_4430) ),
    inference(clausify,[status(thm)],[f_1281_3]) ).

fof(f_1282_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_1282_2,plain,
    ! [U_4436,U_4435,U_4434,U_4433] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4433),U_4434),U_4436))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4433),c_Groups_Ozero__class_Ozero(U_4433)),U_4436))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4433),hAPP(hAPP(c_Power_Opower__class_Opower(U_4433),U_4434),U_4435)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4433),U_4436),U_4435)))
      | ~ class_Rings_Olinordered__semidom(U_4433) ),
    inference(variable_rename,[status(thm)],[f_1282_1]) ).

fof(f_1282_3,plain,
    ! [U_4433,U_4434,U_4435,U_4436] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4433),U_4434),U_4436))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4433),c_Groups_Ozero__class_Ozero(U_4433)),U_4436))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4433),hAPP(hAPP(c_Power_Opower__class_Opower(U_4433),U_4434),U_4435)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4433),U_4436),U_4435)))
      | ~ class_Rings_Olinordered__semidom(U_4433) ),
    inference(definitional_conversion,[status(esa)],[f_1282_2]) ).

cnf(f_1282_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4433),U_4434),U_4436))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4433),c_Groups_Ozero__class_Ozero(U_4433)),U_4436))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4433),hAPP(hAPP(c_Power_Opower__class_Opower(U_4433),U_4434),U_4435)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4433),U_4436),U_4435)))
    | ~ class_Rings_Olinordered__semidom(U_4433) ),
    inference(clausify,[status(thm)],[f_1282_3]) ).

fof(f_1283_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_1283_2,plain,
    ! [U_4440,U_4439,U_4438,U_4437] :
      ( U_4438 = U_4440
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4437),c_Groups_Ozero__class_Ozero(U_4437)),U_4440))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4437),c_Groups_Ozero__class_Ozero(U_4437)),U_4438))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_4437),U_4438),hAPP(c_Nat_OSuc,U_4439)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4437),U_4440),hAPP(c_Nat_OSuc,U_4439))
      | ~ class_Rings_Olinordered__semidom(U_4437) ),
    inference(variable_rename,[status(thm)],[f_1283_1]) ).

fof(f_1283_3,plain,
    ! [U_4437,U_4438,U_4439,U_4440] :
      ( U_4438 = U_4440
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4437),c_Groups_Ozero__class_Ozero(U_4437)),U_4440))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4437),c_Groups_Ozero__class_Ozero(U_4437)),U_4438))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_4437),U_4438),hAPP(c_Nat_OSuc,U_4439)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4437),U_4440),hAPP(c_Nat_OSuc,U_4439))
      | ~ class_Rings_Olinordered__semidom(U_4437) ),
    inference(definitional_conversion,[status(esa)],[f_1283_2]) ).

cnf(f_1283_4,plain,
    ( U_4438 = U_4440
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4437),c_Groups_Ozero__class_Ozero(U_4437)),U_4440))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4437),c_Groups_Ozero__class_Ozero(U_4437)),U_4438))
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_4437),U_4438),hAPP(c_Nat_OSuc,U_4439)) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4437),U_4440),hAPP(c_Nat_OSuc,U_4439))
    | ~ class_Rings_Olinordered__semidom(U_4437) ),
    inference(clausify,[status(thm)],[f_1283_3]) ).

fof(f_1284_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_1284_2,plain,
    ! [U_4444,U_4443,U_4442,U_4441] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4441),U_4442),U_4444))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4441),c_Groups_Ozero__class_Ozero(U_4441)),U_4444))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4441),hAPP(hAPP(c_Power_Opower__class_Opower(U_4441),U_4442),hAPP(c_Nat_OSuc,U_4443))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4441),U_4444),hAPP(c_Nat_OSuc,U_4443))))
      | ~ class_Rings_Olinordered__semidom(U_4441) ),
    inference(variable_rename,[status(thm)],[f_1284_1]) ).

fof(f_1284_3,plain,
    ! [U_4441,U_4442,U_4443,U_4444] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4441),U_4442),U_4444))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4441),c_Groups_Ozero__class_Ozero(U_4441)),U_4444))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4441),hAPP(hAPP(c_Power_Opower__class_Opower(U_4441),U_4442),hAPP(c_Nat_OSuc,U_4443))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4441),U_4444),hAPP(c_Nat_OSuc,U_4443))))
      | ~ class_Rings_Olinordered__semidom(U_4441) ),
    inference(definitional_conversion,[status(esa)],[f_1284_2]) ).

cnf(f_1284_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4441),U_4442),U_4444))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4441),c_Groups_Ozero__class_Ozero(U_4441)),U_4444))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4441),hAPP(hAPP(c_Power_Opower__class_Opower(U_4441),U_4442),hAPP(c_Nat_OSuc,U_4443))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4441),U_4444),hAPP(c_Nat_OSuc,U_4443))))
    | ~ class_Rings_Olinordered__semidom(U_4441) ),
    inference(clausify,[status(thm)],[f_1284_3]) ).

fof(f_1285_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_1285_2,plain,
    ! [U_4447,U_4446,U_4445] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4445),c_Groups_Oone__class_Oone(U_4445)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4445),U_4446),hAPP(hAPP(c_Power_Opower__class_Opower(U_4445),U_4446),U_4447))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4445),c_Groups_Oone__class_Oone(U_4445)),U_4446))
      | ~ class_Rings_Olinordered__semidom(U_4445) ),
    inference(variable_rename,[status(thm)],[f_1285_1]) ).

fof(f_1285_3,plain,
    ! [U_4445,U_4446,U_4447] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4445),c_Groups_Oone__class_Oone(U_4445)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4445),U_4446),hAPP(hAPP(c_Power_Opower__class_Opower(U_4445),U_4446),U_4447))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4445),c_Groups_Oone__class_Oone(U_4445)),U_4446))
      | ~ class_Rings_Olinordered__semidom(U_4445) ),
    inference(definitional_conversion,[status(esa)],[f_1285_2]) ).

cnf(f_1285_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4445),c_Groups_Oone__class_Oone(U_4445)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4445),U_4446),hAPP(hAPP(c_Power_Opower__class_Opower(U_4445),U_4446),U_4447))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4445),c_Groups_Oone__class_Oone(U_4445)),U_4446))
    | ~ class_Rings_Olinordered__semidom(U_4445) ),
    inference(clausify,[status(thm)],[f_1285_3]) ).

fof(f_1286_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_1286_2,plain,
    ! [U_4450,U_4449,U_4448] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4448),hAPP(hAPP(c_Power_Opower__class_Opower(U_4448),U_4449),U_4450)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4448),U_4449),hAPP(hAPP(c_Power_Opower__class_Opower(U_4448),U_4449),U_4450))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4448),c_Groups_Oone__class_Oone(U_4448)),U_4449))
      | ~ class_Rings_Olinordered__semidom(U_4448) ),
    inference(variable_rename,[status(thm)],[f_1286_1]) ).

fof(f_1286_3,plain,
    ! [U_4448,U_4449,U_4450] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4448),hAPP(hAPP(c_Power_Opower__class_Opower(U_4448),U_4449),U_4450)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4448),U_4449),hAPP(hAPP(c_Power_Opower__class_Opower(U_4448),U_4449),U_4450))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4448),c_Groups_Oone__class_Oone(U_4448)),U_4449))
      | ~ class_Rings_Olinordered__semidom(U_4448) ),
    inference(definitional_conversion,[status(esa)],[f_1286_2]) ).

cnf(f_1286_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4448),hAPP(hAPP(c_Power_Opower__class_Opower(U_4448),U_4449),U_4450)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4448),U_4449),hAPP(hAPP(c_Power_Opower__class_Opower(U_4448),U_4449),U_4450))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4448),c_Groups_Oone__class_Oone(U_4448)),U_4449))
    | ~ class_Rings_Olinordered__semidom(U_4448) ),
    inference(clausify,[status(thm)],[f_1286_3]) ).

fof(f_1287_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_1287_2,plain,
    ! [U_4452,U_4451] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4451),c_Groups_Ozero__class_Ozero(U_4451)),U_4452) = c_Groups_Ozero__class_Ozero(U_4451)
          | U_4452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4451),c_Groups_Ozero__class_Ozero(U_4451)),U_4452) = c_Groups_Oone__class_Oone(U_4451)
          | U_4452 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ class_Rings_Osemiring__0(U_4451)
      | ~ class_Power_Opower(U_4451) ),
    inference(variable_rename,[status(thm)],[f_1287_1]) ).

fof(f_1287_3,plain,
    ( ! [U_4451,U_4452] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4451),c_Groups_Ozero__class_Ozero(U_4451)),U_4452) = c_Groups_Ozero__class_Ozero(U_4451)
        | U_4452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP362(U_4451,U_4452) )
    & ! [U_4451,U_4452] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4451),c_Groups_Ozero__class_Ozero(U_4451)),U_4452) = c_Groups_Oone__class_Oone(U_4451)
        | U_4452 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP362(U_4451,U_4452) )
    & ! [U_4451,U_4452] :
        ( sP362(U_4451,U_4452)
        | ~ class_Rings_Osemiring__0(U_4451)
        | ~ class_Power_Opower(U_4451) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP362])],[f_1287_2]) ).

cnf(f_1287_4,plain,
    ( sP362(U_4451,U_4452)
    | ~ class_Rings_Osemiring__0(U_4451)
    | ~ class_Power_Opower(U_4451) ),
    inference(clausify,[status(thm)],[f_1287_3]) ).

cnf(f_1287_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4451),c_Groups_Ozero__class_Ozero(U_4451)),U_4452) = c_Groups_Oone__class_Oone(U_4451)
    | U_4452 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP362(U_4451,U_4452) ),
    inference(clausify,[status(thm)],[f_1287_3]) ).

cnf(f_1287_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4451),c_Groups_Ozero__class_Ozero(U_4451)),U_4452) = c_Groups_Ozero__class_Ozero(U_4451)
    | U_4452 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP362(U_4451,U_4452) ),
    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(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_1288_2,plain,
    ! [U_4455,U_4454,U_4453] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4453),c_Groups_Oone__class_Oone(U_4453)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4453),U_4454),hAPP(c_Nat_OSuc,U_4455))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4453),c_Groups_Oone__class_Oone(U_4453)),U_4454))
      | ~ class_Rings_Olinordered__semidom(U_4453) ),
    inference(variable_rename,[status(thm)],[f_1288_1]) ).

fof(f_1288_3,plain,
    ! [U_4454,U_4455,U_4453] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4453),c_Groups_Oone__class_Oone(U_4453)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4453),U_4454),hAPP(c_Nat_OSuc,U_4455))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4453),c_Groups_Oone__class_Oone(U_4453)),U_4454))
      | ~ class_Rings_Olinordered__semidom(U_4453) ),
    inference(definitional_conversion,[status(esa)],[f_1288_2]) ).

cnf(f_1288_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4453),c_Groups_Oone__class_Oone(U_4453)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4453),U_4454),hAPP(c_Nat_OSuc,U_4455))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4453),c_Groups_Oone__class_Oone(U_4453)),U_4454))
    | ~ class_Rings_Olinordered__semidom(U_4453) ),
    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(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_1289_2,plain,
    ! [U_4459,U_4458,U_4457,U_4456] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4456),hAPP(hAPP(c_Power_Opower__class_Opower(U_4456),U_4459),U_4457)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4456),U_4459),U_4458)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4456),c_Groups_Oone__class_Oone(U_4456)),U_4459))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4457),U_4458))
      | ~ class_Rings_Olinordered__semidom(U_4456) ),
    inference(variable_rename,[status(thm)],[f_1289_1]) ).

fof(f_1289_3,plain,
    ! [U_4456,U_4457,U_4458,U_4459] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4456),hAPP(hAPP(c_Power_Opower__class_Opower(U_4456),U_4459),U_4457)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4456),U_4459),U_4458)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4456),c_Groups_Oone__class_Oone(U_4456)),U_4459))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4457),U_4458))
      | ~ class_Rings_Olinordered__semidom(U_4456) ),
    inference(definitional_conversion,[status(esa)],[f_1289_2]) ).

cnf(f_1289_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4456),hAPP(hAPP(c_Power_Opower__class_Opower(U_4456),U_4459),U_4457)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4456),U_4459),U_4458)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4456),c_Groups_Oone__class_Oone(U_4456)),U_4459))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4457),U_4458))
    | ~ class_Rings_Olinordered__semidom(U_4456) ),
    inference(clausify,[status(thm)],[f_1289_3]) ).

fof(f_1290_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_1290_2,plain,
    ! [U_4463,U_4462,U_4461,U_4460] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4462),U_4463))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4460),hAPP(hAPP(c_Power_Opower__class_Opower(U_4460),U_4461),U_4462)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4460),U_4461),U_4463)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4460),c_Groups_Oone__class_Oone(U_4460)),U_4461))
      | ~ class_Rings_Olinordered__semidom(U_4460) ),
    inference(variable_rename,[status(thm)],[f_1290_1]) ).

fof(f_1290_3,plain,
    ! [U_4460,U_4461,U_4462,U_4463] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4462),U_4463))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4460),hAPP(hAPP(c_Power_Opower__class_Opower(U_4460),U_4461),U_4462)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4460),U_4461),U_4463)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4460),c_Groups_Oone__class_Oone(U_4460)),U_4461))
      | ~ class_Rings_Olinordered__semidom(U_4460) ),
    inference(definitional_conversion,[status(esa)],[f_1290_2]) ).

cnf(f_1290_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4462),U_4463))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4460),hAPP(hAPP(c_Power_Opower__class_Opower(U_4460),U_4461),U_4462)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4460),U_4461),U_4463)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4460),c_Groups_Oone__class_Oone(U_4460)),U_4461))
    | ~ class_Rings_Olinordered__semidom(U_4460) ),
    inference(clausify,[status(thm)],[f_1290_3]) ).

fof(f_1291_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_1291_2,plain,
    ! [U_4467,U_4466,U_4465,U_4464] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4464),hAPP(hAPP(c_Power_Opower__class_Opower(U_4464),U_4465),U_4466)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4464),U_4465),U_4467)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4466),U_4467)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4466),U_4467))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4464),hAPP(hAPP(c_Power_Opower__class_Opower(U_4464),U_4465),U_4466)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4464),U_4465),U_4467))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4464),c_Groups_Oone__class_Oone(U_4464)),U_4465))
      | ~ class_Rings_Olinordered__semidom(U_4464) ),
    inference(variable_rename,[status(thm)],[f_1291_1]) ).

fof(f_1291_3,plain,
    ( ! [U_4465,U_4464,U_4466,U_4467] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4464),hAPP(hAPP(c_Power_Opower__class_Opower(U_4464),U_4465),U_4466)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4464),U_4465),U_4467)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4466),U_4467))
        | ~ sP363(U_4465,U_4464,U_4466,U_4467) )
    & ! [U_4465,U_4464,U_4466,U_4467] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4466),U_4467))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4464),hAPP(hAPP(c_Power_Opower__class_Opower(U_4464),U_4465),U_4466)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4464),U_4465),U_4467)))
        | ~ sP363(U_4465,U_4464,U_4466,U_4467) )
    & ! [U_4465,U_4464,U_4466,U_4467] :
        ( sP363(U_4465,U_4464,U_4466,U_4467)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4464),c_Groups_Oone__class_Oone(U_4464)),U_4465))
        | ~ class_Rings_Olinordered__semidom(U_4464) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP363])],[f_1291_2]) ).

cnf(f_1291_4,plain,
    ( sP363(U_4465,U_4464,U_4466,U_4467)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4464),c_Groups_Oone__class_Oone(U_4464)),U_4465))
    | ~ class_Rings_Olinordered__semidom(U_4464) ),
    inference(clausify,[status(thm)],[f_1291_3]) ).

cnf(f_1291_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4466),U_4467))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4464),hAPP(hAPP(c_Power_Opower__class_Opower(U_4464),U_4465),U_4466)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4464),U_4465),U_4467)))
    | ~ sP363(U_4465,U_4464,U_4466,U_4467) ),
    inference(clausify,[status(thm)],[f_1291_3]) ).

cnf(f_1291_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4464),hAPP(hAPP(c_Power_Opower__class_Opower(U_4464),U_4465),U_4466)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4464),U_4465),U_4467)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4466),U_4467))
    | ~ sP363(U_4465,U_4464,U_4466,U_4467) ),
    inference(clausify,[status(thm)],[f_1291_3]) ).

fof(f_1292_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_1292_2,plain,
    ! [U_4470,U_4469,U_4468] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4468),c_Groups_Ozero__class_Ozero(U_4468)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4468),hAPP(c_Groups_Oabs__class_Oabs(U_4468),U_4469)),U_4470)))
      | ~ class_Rings_Olinordered__idom(U_4468) ),
    inference(variable_rename,[status(thm)],[f_1292_1]) ).

fof(f_1292_3,plain,
    ! [U_4468,U_4469,U_4470] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4468),c_Groups_Ozero__class_Ozero(U_4468)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4468),hAPP(c_Groups_Oabs__class_Oabs(U_4468),U_4469)),U_4470)))
      | ~ class_Rings_Olinordered__idom(U_4468) ),
    inference(definitional_conversion,[status(esa)],[f_1292_2]) ).

cnf(f_1292_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4468),c_Groups_Ozero__class_Ozero(U_4468)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4468),hAPP(c_Groups_Oabs__class_Oabs(U_4468),U_4469)),U_4470)))
    | ~ class_Rings_Olinordered__idom(U_4468) ),
    inference(clausify,[status(thm)],[f_1292_3]) ).

fof(f_1293_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_1293_2,plain,
    ! [U_4474,U_4473,U_4472,U_4471] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4471),hAPP(hAPP(c_Power_Opower__class_Opower(U_4471),U_4474),U_4472)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4471),U_4474),U_4473)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4471),c_Groups_Oone__class_Oone(U_4471)),U_4474))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4472),U_4473))
      | ~ class_Rings_Olinordered__semidom(U_4471) ),
    inference(variable_rename,[status(thm)],[f_1293_1]) ).

fof(f_1293_3,plain,
    ! [U_4471,U_4472,U_4473,U_4474] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4471),hAPP(hAPP(c_Power_Opower__class_Opower(U_4471),U_4474),U_4472)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4471),U_4474),U_4473)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4471),c_Groups_Oone__class_Oone(U_4471)),U_4474))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4472),U_4473))
      | ~ class_Rings_Olinordered__semidom(U_4471) ),
    inference(definitional_conversion,[status(esa)],[f_1293_2]) ).

cnf(f_1293_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4471),hAPP(hAPP(c_Power_Opower__class_Opower(U_4471),U_4474),U_4472)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4471),U_4474),U_4473)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4471),c_Groups_Oone__class_Oone(U_4471)),U_4474))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4472),U_4473))
    | ~ class_Rings_Olinordered__semidom(U_4471) ),
    inference(clausify,[status(thm)],[f_1293_3]) ).

fof(f_1294_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_1294_2,plain,
    ! [U_4477,U_4476,U_4475] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4475),hAPP(c_Groups_Ouminus__class_Ouminus(U_4475),U_4476)),U_4477) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4475),hAPP(hAPP(c_Power_Opower__class_Opower(U_4475),hAPP(c_Groups_Ouminus__class_Ouminus(U_4475),c_Groups_Oone__class_Oone(U_4475))),U_4477)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4475),U_4476),U_4477))
      | ~ class_Rings_Oring__1(U_4475) ),
    inference(variable_rename,[status(thm)],[f_1294_1]) ).

fof(f_1294_3,plain,
    ! [U_4475,U_4476,U_4477] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4475),hAPP(c_Groups_Ouminus__class_Ouminus(U_4475),U_4476)),U_4477) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4475),hAPP(hAPP(c_Power_Opower__class_Opower(U_4475),hAPP(c_Groups_Ouminus__class_Ouminus(U_4475),c_Groups_Oone__class_Oone(U_4475))),U_4477)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4475),U_4476),U_4477))
      | ~ class_Rings_Oring__1(U_4475) ),
    inference(definitional_conversion,[status(esa)],[f_1294_2]) ).

cnf(f_1294_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_4475),hAPP(c_Groups_Ouminus__class_Ouminus(U_4475),U_4476)),U_4477) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4475),hAPP(hAPP(c_Power_Opower__class_Opower(U_4475),hAPP(c_Groups_Ouminus__class_Ouminus(U_4475),c_Groups_Oone__class_Oone(U_4475))),U_4477)),hAPP(hAPP(c_Power_Opower__class_Opower(U_4475),U_4476),U_4477))
    | ~ class_Rings_Oring__1(U_4475) ),
    inference(clausify,[status(thm)],[f_1294_3]) ).

fof(f_1295_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_1295_2,plain,
    ! [U_4480,U_4479,U_4478] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4478),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4478),U_4479),hAPP(hAPP(c_Power_Opower__class_Opower(U_4478),U_4479),U_4480))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4478),U_4479),U_4480)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4478),U_4479),c_Groups_Oone__class_Oone(U_4478)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4478),c_Groups_Ozero__class_Ozero(U_4478)),U_4479))
      | ~ class_Rings_Olinordered__semidom(U_4478) ),
    inference(variable_rename,[status(thm)],[f_1295_1]) ).

fof(f_1295_3,plain,
    ! [U_4478,U_4479,U_4480] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4478),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4478),U_4479),hAPP(hAPP(c_Power_Opower__class_Opower(U_4478),U_4479),U_4480))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4478),U_4479),U_4480)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4478),U_4479),c_Groups_Oone__class_Oone(U_4478)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4478),c_Groups_Ozero__class_Ozero(U_4478)),U_4479))
      | ~ class_Rings_Olinordered__semidom(U_4478) ),
    inference(definitional_conversion,[status(esa)],[f_1295_2]) ).

cnf(f_1295_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4478),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4478),U_4479),hAPP(hAPP(c_Power_Opower__class_Opower(U_4478),U_4479),U_4480))),hAPP(hAPP(c_Power_Opower__class_Opower(U_4478),U_4479),U_4480)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4478),U_4479),c_Groups_Oone__class_Oone(U_4478)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4478),c_Groups_Ozero__class_Ozero(U_4478)),U_4479))
    | ~ class_Rings_Olinordered__semidom(U_4478) ),
    inference(clausify,[status(thm)],[f_1295_3]) ).

fof(f_1296_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_1296_2,plain,
    ! [U_4484,U_4483,U_4482,U_4481] :
      ( U_4482 = U_4484
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4483))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4481),c_Groups_Ozero__class_Ozero(U_4481)),U_4484))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4481),c_Groups_Ozero__class_Ozero(U_4481)),U_4482))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_4481),U_4482),U_4483) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4481),U_4484),U_4483)
      | ~ class_Rings_Olinordered__semidom(U_4481) ),
    inference(variable_rename,[status(thm)],[f_1296_1]) ).

fof(f_1296_3,plain,
    ! [U_4481,U_4482,U_4483,U_4484] :
      ( U_4482 = U_4484
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4483))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4481),c_Groups_Ozero__class_Ozero(U_4481)),U_4484))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4481),c_Groups_Ozero__class_Ozero(U_4481)),U_4482))
      | hAPP(hAPP(c_Power_Opower__class_Opower(U_4481),U_4482),U_4483) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4481),U_4484),U_4483)
      | ~ class_Rings_Olinordered__semidom(U_4481) ),
    inference(definitional_conversion,[status(esa)],[f_1296_2]) ).

cnf(f_1296_4,plain,
    ( U_4482 = U_4484
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4483))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4481),c_Groups_Ozero__class_Ozero(U_4481)),U_4484))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4481),c_Groups_Ozero__class_Ozero(U_4481)),U_4482))
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_4481),U_4482),U_4483) != hAPP(hAPP(c_Power_Opower__class_Opower(U_4481),U_4484),U_4483)
    | ~ class_Rings_Olinordered__semidom(U_4481) ),
    inference(clausify,[status(thm)],[f_1296_3]) ).

fof(f_1297_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_1297_2,plain,
    ! [U_4489,U_4488,U_4487,U_4486,U_4485] :
      ( ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_4485,U_4486,U_4487),U_4488),U_4489))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4485,U_4486)),hAPP(hAPP(c_Product__Type_OPair(U_4485,U_4486),U_4488),U_4489)),U_4487)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_4485,U_4486)),hAPP(hAPP(c_Product__Type_OPair(U_4485,U_4486),U_4488),U_4489)),U_4487))
        | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_4485,U_4486,U_4487),U_4488),U_4489)) ) ),
    inference(variable_rename,[status(thm)],[f_1297_1]) ).

fof(f_1297_3,plain,
    ( ! [U_4499,U_4497,U_4495,U_4493,U_4491] :
        ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_4491,U_4493,U_4495),U_4497),U_4499))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4491,U_4493)),hAPP(hAPP(c_Product__Type_OPair(U_4491,U_4493),U_4497),U_4499)),U_4495)) )
    & ! [U_4498,U_4496,U_4494,U_4492,U_4490] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_4490,U_4492)),hAPP(hAPP(c_Product__Type_OPair(U_4490,U_4492),U_4496),U_4498)),U_4494))
        | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_4490,U_4492,U_4494),U_4496),U_4498)) ) ),
    inference(miniscope,[status(thm)],[f_1297_2]) ).

fof(f_1297_4,plain,
    ( ! [U_4491,U_4493,U_4495,U_4497,U_4499] :
        ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_4491,U_4493,U_4495),U_4497),U_4499))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4491,U_4493)),hAPP(hAPP(c_Product__Type_OPair(U_4491,U_4493),U_4497),U_4499)),U_4495)) )
    & ! [U_4496,U_4494,U_4492,U_4490,U_4498] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_4490,U_4492)),hAPP(hAPP(c_Product__Type_OPair(U_4490,U_4492),U_4496),U_4498)),U_4494))
        | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_4490,U_4492,U_4494),U_4496),U_4498)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1297_3]) ).

cnf(f_1297_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_4490,U_4492)),hAPP(hAPP(c_Product__Type_OPair(U_4490,U_4492),U_4496),U_4498)),U_4494))
    | ~ hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_4490,U_4492,U_4494),U_4496),U_4498)) ),
    inference(clausify,[status(thm)],[f_1297_4]) ).

cnf(f_1297_6,plain,
    ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(U_4491,U_4493,U_4495),U_4497),U_4499))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4491,U_4493)),hAPP(hAPP(c_Product__Type_OPair(U_4491,U_4493),U_4497),U_4499)),U_4495)) ),
    inference(clausify,[status(thm)],[f_1297_4]) ).

fof(f_1298_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_1298_2,plain,
    ! [U_4504,U_4503,U_4502,U_4501,U_4500] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4504),U_4500),U_4501),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_4504),U_4502)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4504),U_4503)),U_4501))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4504),U_4503),U_4501))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4501))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4500,U_4501),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4502),U_4503))) ),
    inference(variable_rename,[status(thm)],[f_1298_1]) ).

fof(f_1298_3,plain,
    ! [U_4500,U_4501,U_4502,U_4503,U_4504] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4504),U_4500),U_4501),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_4504),U_4502)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4504),U_4503)),U_4501))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4504),U_4503),U_4501))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4501))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4500,U_4501),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4502),U_4503))) ),
    inference(definitional_conversion,[status(esa)],[f_1298_2]) ).

cnf(f_1298_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4504),U_4500),U_4501),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_4504),U_4502)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4504),U_4503)),U_4501))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4504),U_4503),U_4501))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4501))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4500,U_4501),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4502),U_4503))) ),
    inference(clausify,[status(thm)],[f_1298_3]) ).

fof(f_1299_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_1299_2,plain,
    ! [U_4509,U_4508,U_4507,U_4506,U_4505] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4505,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4506),U_4509)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4507),U_4509)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4506),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4507,U_4509))),U_4508))))
      | ~ 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(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4506))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4505,U_4506),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4507),U_4508))) ),
    inference(variable_rename,[status(thm)],[f_1299_1]) ).

fof(f_1299_3,plain,
    ! [U_4506,U_4505,U_4507,U_4508,U_4509] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4505,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4506),U_4509)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4507),U_4509)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4506),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4507,U_4509))),U_4508))))
      | ~ 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(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4506))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4505,U_4506),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4507),U_4508))) ),
    inference(definitional_conversion,[status(esa)],[f_1299_2]) ).

cnf(f_1299_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4505,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4506),U_4509)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4507),U_4509)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_4506),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4507,U_4509))),U_4508))))
    | ~ 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(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4506))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4505,U_4506),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4507),U_4508))) ),
    inference(clausify,[status(thm)],[f_1299_3]) ).

fof(f_1300_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_1300_2,plain,
    ! [U_4511,U_4510] :
      ( ( 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_4510)),U_4511)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4510))),U_4511)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4510))) )
      & ( 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_4510)),U_4511)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4511)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4510))) ) ),
    inference(variable_rename,[status(thm)],[f_1300_1]) ).

fof(f_1300_3,plain,
    ( ! [U_4515,U_4513] :
        ( 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_4513)),U_4515)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4513))),U_4515)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4513))) )
    & ! [U_4514,U_4512] :
        ( 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_4512)),U_4514)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4514)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4512))) ) ),
    inference(miniscope,[status(thm)],[f_1300_2]) ).

fof(f_1300_4,plain,
    ( ! [U_4513,U_4515] :
        ( 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_4513)),U_4515)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4513))),U_4515)
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4513))) )
    & ! [U_4512,U_4514] :
        ( 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_4512)),U_4514)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4514)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4512))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1300_3]) ).

cnf(f_1300_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_4512)),U_4514)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_4514)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4512))) ),
    inference(clausify,[status(thm)],[f_1300_4]) ).

cnf(f_1300_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_4513)),U_4515)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4513))),U_4515)
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4513))) ),
    inference(clausify,[status(thm)],[f_1300_4]) ).

fof(f_1301_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_1301_2,plain,
    ! [U_4522,U_4521,U_4520,U_4519,U_4518,U_4517,U_4516] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4516),U_4520),U_4517),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_4518),U_4521)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4519),U_4522)),U_4517))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4519),U_4522),U_4517))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4517))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4520,U_4517),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4521),U_4522)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4516,U_4517),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4518),U_4519))) ),
    inference(variable_rename,[status(thm)],[f_1301_1]) ).

fof(f_1301_3,plain,
    ! [U_4516,U_4517,U_4518,U_4519,U_4520,U_4521,U_4522] :
      ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4516),U_4520),U_4517),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_4518),U_4521)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4519),U_4522)),U_4517))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4519),U_4522),U_4517))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4517))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4520,U_4517),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4521),U_4522)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4516,U_4517),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4518),U_4519))) ),
    inference(definitional_conversion,[status(esa)],[f_1301_2]) ).

cnf(f_1301_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4516),U_4520),U_4517),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_4518),U_4521)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4519),U_4522)),U_4517))),c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4519),U_4522),U_4517))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4517))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4520,U_4517),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4521),U_4522)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4516,U_4517),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4518),U_4519))) ),
    inference(clausify,[status(thm)],[f_1301_3]) ).

fof(f_1302_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_1302_2,plain,
    ! [U_4523] :
      ( ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4523)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4523))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4523))) )
      & ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4523)) = 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_4523))) ) ),
    inference(variable_rename,[status(thm)],[f_1302_1]) ).

fof(f_1302_3,plain,
    ( ! [U_4525] :
        ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4525)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4525))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4525))) )
    & ! [U_4524] :
        ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4524)) = 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_4524))) ) ),
    inference(miniscope,[status(thm)],[f_1302_2]) ).

fof(f_1302_4,plain,
    ( ! [U_4525] :
        ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4525)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4525))
        | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4525))) )
    & ! [U_4524] :
        ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4524)) = 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_4524))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1302_3]) ).

cnf(f_1302_5,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4524)) = 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_4524))) ),
    inference(clausify,[status(thm)],[f_1302_4]) ).

cnf(f_1302_6,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4525)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4525))
    | hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4525))) ),
    inference(clausify,[status(thm)],[f_1302_4]) ).

fof(f_1303_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_1303_2,plain,
    ! [U_4526] :
      ( c_Power_Opower__class_Opower(U_4526) = c_Power_Opower_Opower(U_4526,c_Groups_Oone__class_Oone(U_4526),c_Groups_Otimes__class_Otimes(U_4526))
      | ~ class_Power_Opower(U_4526) ),
    inference(variable_rename,[status(thm)],[f_1303_1]) ).

fof(f_1303_3,plain,
    ! [U_4526] :
      ( c_Power_Opower__class_Opower(U_4526) = c_Power_Opower_Opower(U_4526,c_Groups_Oone__class_Oone(U_4526),c_Groups_Otimes__class_Otimes(U_4526))
      | ~ class_Power_Opower(U_4526) ),
    inference(definitional_conversion,[status(esa)],[f_1303_2]) ).

cnf(f_1303_4,plain,
    ( c_Power_Opower__class_Opower(U_4526) = c_Power_Opower_Opower(U_4526,c_Groups_Oone__class_Oone(U_4526),c_Groups_Otimes__class_Otimes(U_4526))
    | ~ class_Power_Opower(U_4526) ),
    inference(clausify,[status(thm)],[f_1303_3]) ).

fof(f_1304_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_1304_2,plain,
    ! [U_4530,U_4529,U_4528,U_4527] :
      ( U_4529 = U_4530
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4527,U_4528),U_4530))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4527,U_4528),U_4529)) ),
    inference(variable_rename,[status(thm)],[f_1304_1]) ).

fof(f_1304_3,plain,
    ! [U_4527,U_4528,U_4529,U_4530] :
      ( U_4529 = U_4530
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4527,U_4528),U_4530))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4527,U_4528),U_4529)) ),
    inference(definitional_conversion,[status(esa)],[f_1304_2]) ).

cnf(f_1304_4,plain,
    ( U_4529 = U_4530
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4527,U_4528),U_4530))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4527,U_4528),U_4529)) ),
    inference(clausify,[status(thm)],[f_1304_3]) ).

fof(f_1305_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_1305_2,plain,
    ! [U_4533,U_4532,U_4531] :
      ( c_Divides_Odivmod__nat(U_4531,U_4532) = U_4533
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4531,U_4532),U_4533)) ),
    inference(variable_rename,[status(thm)],[f_1305_1]) ).

fof(f_1305_3,plain,
    ! [U_4531,U_4532,U_4533] :
      ( c_Divides_Odivmod__nat(U_4531,U_4532) = U_4533
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4531,U_4532),U_4533)) ),
    inference(definitional_conversion,[status(esa)],[f_1305_2]) ).

cnf(f_1305_4,plain,
    ( c_Divides_Odivmod__nat(U_4531,U_4532) = U_4533
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4531,U_4532),U_4533)) ),
    inference(clausify,[status(thm)],[f_1305_3]) ).

fof(f_1306_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_1306_2,plain,
    ! [U_4535,U_4534] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4534,U_4535),c_Divides_Odivmod__nat(U_4534,U_4535))),
    inference(variable_rename,[status(thm)],[f_1306_1]) ).

fof(f_1306_3,plain,
    ! [U_4534,U_4535] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4534,U_4535),c_Divides_Odivmod__nat(U_4534,U_4535))),
    inference(definitional_conversion,[status(esa)],[f_1306_2]) ).

cnf(f_1306_4,plain,
    hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4534,U_4535),c_Divides_Odivmod__nat(U_4534,U_4535))),
    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_4539,U_4538,U_4537,U_4536] : hAPP(hAPP(c_Power_Opower_Opower(U_4536,U_4537,U_4538),U_4539),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_4537,
    inference(variable_rename,[status(thm)],[f_1307_1]) ).

fof(f_1307_3,plain,
    ! [U_4536,U_4537,U_4538,U_4539] : hAPP(hAPP(c_Power_Opower_Opower(U_4536,U_4537,U_4538),U_4539),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_4537,
    inference(definitional_conversion,[status(esa)],[f_1307_2]) ).

cnf(f_1307_4,plain,
    hAPP(hAPP(c_Power_Opower_Opower(U_4536,U_4537,U_4538),U_4539),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_4537,
    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_4544,U_4543,U_4542,U_4541,U_4540] : hAPP(hAPP(c_Power_Opower_Opower(U_4540,U_4541,U_4542),U_4543),hAPP(c_Nat_OSuc,U_4544)) = hAPP(hAPP(U_4542,U_4543),hAPP(hAPP(c_Power_Opower_Opower(U_4540,U_4541,U_4542),U_4543),U_4544)),
    inference(variable_rename,[status(thm)],[f_1308_1]) ).

fof(f_1308_3,plain,
    ! [U_4540,U_4541,U_4542,U_4543,U_4544] : hAPP(hAPP(c_Power_Opower_Opower(U_4540,U_4541,U_4542),U_4543),hAPP(c_Nat_OSuc,U_4544)) = hAPP(hAPP(U_4542,U_4543),hAPP(hAPP(c_Power_Opower_Opower(U_4540,U_4541,U_4542),U_4543),U_4544)),
    inference(definitional_conversion,[status(esa)],[f_1308_2]) ).

cnf(f_1308_4,plain,
    hAPP(hAPP(c_Power_Opower_Opower(U_4540,U_4541,U_4542),U_4543),hAPP(c_Nat_OSuc,U_4544)) = hAPP(hAPP(U_4542,U_4543),hAPP(hAPP(c_Power_Opower_Opower(U_4540,U_4541,U_4542),U_4543),U_4544)),
    inference(clausify,[status(thm)],[f_1308_3]) ).

fof(f_1309_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_1309_2,plain,
    ! [U_4548,U_4547,U_4546,U_4545] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4545,U_4546) = U_4548
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4545,U_4546),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4547),U_4548))) ),
    inference(variable_rename,[status(thm)],[f_1309_1]) ).

fof(f_1309_3,plain,
    ! [U_4546,U_4545,U_4547,U_4548] :
      ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4545,U_4546) = U_4548
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4545,U_4546),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4547),U_4548))) ),
    inference(definitional_conversion,[status(esa)],[f_1309_2]) ).

cnf(f_1309_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4545,U_4546) = U_4548
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4545,U_4546),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4547),U_4548))) ),
    inference(clausify,[status(thm)],[f_1309_3]) ).

fof(f_1310_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_1310_2,plain,
    ! [U_4549] : c_Int_Osucc(U_4549) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4549),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[f_1310_1]) ).

fof(f_1310_3,plain,
    ! [U_4549] : c_Int_Osucc(U_4549) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4549),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_1310_2]) ).

cnf(f_1310_4,plain,
    c_Int_Osucc(U_4549) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4549),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1310_3]) ).

fof(f_1311_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_1311_2,plain,
    ! [U_4553,U_4552,U_4551,U_4550] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4550),U_4551) = U_4552
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4550,U_4551),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4552),U_4553))) ),
    inference(variable_rename,[status(thm)],[f_1311_1]) ).

fof(f_1311_3,plain,
    ! [U_4550,U_4551,U_4552,U_4553] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4550),U_4551) = U_4552
      | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4550,U_4551),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4552),U_4553))) ),
    inference(definitional_conversion,[status(esa)],[f_1311_2]) ).

cnf(f_1311_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4550),U_4551) = U_4552
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4550,U_4551),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4552),U_4553))) ),
    inference(clausify,[status(thm)],[f_1311_3]) ).

fof(f_1312_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_1312_2,plain,
    ! [U_4555,U_4554] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4554),c_Int_Osucc(U_4555)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4554),c_Groups_Oone__class_Oone(U_4554)),hAPP(c_Int_Onumber__class_Onumber__of(U_4554),U_4555))
      | ~ class_Int_Onumber__ring(U_4554) ),
    inference(variable_rename,[status(thm)],[f_1312_1]) ).

fof(f_1312_3,plain,
    ! [U_4554,U_4555] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4554),c_Int_Osucc(U_4555)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4554),c_Groups_Oone__class_Oone(U_4554)),hAPP(c_Int_Onumber__class_Onumber__of(U_4554),U_4555))
      | ~ class_Int_Onumber__ring(U_4554) ),
    inference(definitional_conversion,[status(esa)],[f_1312_2]) ).

cnf(f_1312_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4554),c_Int_Osucc(U_4555)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4554),c_Groups_Oone__class_Oone(U_4554)),hAPP(c_Int_Onumber__class_Onumber__of(U_4554),U_4555))
    | ~ class_Int_Onumber__ring(U_4554) ),
    inference(clausify,[status(thm)],[f_1312_3]) ).

fof(f_1313_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_1313_2,plain,
    ! [U_4557,U_4556] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4556,U_4557),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4556),U_4557)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4556,U_4557)))),
    inference(variable_rename,[status(thm)],[f_1313_1]) ).

fof(f_1313_3,plain,
    ! [U_4556,U_4557] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4556,U_4557),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4556),U_4557)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4556,U_4557)))),
    inference(definitional_conversion,[status(esa)],[f_1313_2]) ).

cnf(f_1313_4,plain,
    hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4556,U_4557),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4556),U_4557)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4556,U_4557)))),
    inference(clausify,[status(thm)],[f_1313_3]) ).

fof(f_1314_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_1314_2,plain,
    ! [U_4561,U_4560,U_4559,U_4558] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_4558,U_4558)),hAPP(hAPP(c_Product__Type_OPair(U_4558,U_4558),U_4559),U_4560)),hAPP(c_Wellfounded_Omeasure(U_4558),U_4561)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_4561,U_4559)),hAPP(U_4561,U_4560))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_4561,U_4559)),hAPP(U_4561,U_4560)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4558,U_4558)),hAPP(hAPP(c_Product__Type_OPair(U_4558,U_4558),U_4559),U_4560)),hAPP(c_Wellfounded_Omeasure(U_4558),U_4561))) ) ),
    inference(variable_rename,[status(thm)],[f_1314_1]) ).

fof(f_1314_3,plain,
    ( ! [U_4569,U_4567,U_4565] :
        ( ! [U_4563] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_4563,U_4563)),hAPP(hAPP(c_Product__Type_OPair(U_4563,U_4563),U_4565),U_4567)),hAPP(c_Wellfounded_Omeasure(U_4563),U_4569)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_4569,U_4565)),hAPP(U_4569,U_4567))) )
    & ! [U_4568,U_4566,U_4564] :
        ( ! [U_4562] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4562,U_4562)),hAPP(hAPP(c_Product__Type_OPair(U_4562,U_4562),U_4564),U_4566)),hAPP(c_Wellfounded_Omeasure(U_4562),U_4568)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_4568,U_4564)),hAPP(U_4568,U_4566))) ) ),
    inference(miniscope,[status(thm)],[f_1314_2]) ).

fof(f_1314_4,plain,
    ( ! [U_4563,U_4565,U_4567,U_4569] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_4563,U_4563)),hAPP(hAPP(c_Product__Type_OPair(U_4563,U_4563),U_4565),U_4567)),hAPP(c_Wellfounded_Omeasure(U_4563),U_4569)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_4569,U_4565)),hAPP(U_4569,U_4567))) )
    & ! [U_4562,U_4564,U_4568,U_4566] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4562,U_4562)),hAPP(hAPP(c_Product__Type_OPair(U_4562,U_4562),U_4564),U_4566)),hAPP(c_Wellfounded_Omeasure(U_4562),U_4568)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_4568,U_4564)),hAPP(U_4568,U_4566))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1314_3]) ).

cnf(f_1314_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4562,U_4562)),hAPP(hAPP(c_Product__Type_OPair(U_4562,U_4562),U_4564),U_4566)),hAPP(c_Wellfounded_Omeasure(U_4562),U_4568)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_4568,U_4564)),hAPP(U_4568,U_4566))) ),
    inference(clausify,[status(thm)],[f_1314_4]) ).

cnf(f_1314_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_4563,U_4563)),hAPP(hAPP(c_Product__Type_OPair(U_4563,U_4563),U_4565),U_4567)),hAPP(c_Wellfounded_Omeasure(U_4563),U_4569)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_4569,U_4565)),hAPP(U_4569,U_4567))) ),
    inference(clausify,[status(thm)],[f_1314_4]) ).

fof(f_1315_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_1315_2,plain,
    ! [U_4574,U_4573,U_4572,U_4571,U_4570] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4570,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4571),U_4574)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4572),U_4574)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4571),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4572,U_4574))),U_4573))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4574))
      | U_4571 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4570,U_4571),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4572),U_4573))) ),
    inference(variable_rename,[status(thm)],[f_1315_1]) ).

fof(f_1315_3,plain,
    ! [U_4570,U_4571,U_4572,U_4573,U_4574] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4570,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4571),U_4574)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4572),U_4574)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4571),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4572,U_4574))),U_4573))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4574))
      | U_4571 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4570,U_4571),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4572),U_4573))) ),
    inference(definitional_conversion,[status(esa)],[f_1315_2]) ).

cnf(f_1315_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4570,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4571),U_4574)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4572),U_4574)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4571),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4572,U_4574))),U_4573))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4574))
    | U_4571 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4570,U_4571),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4572),U_4573))) ),
    inference(clausify,[status(thm)],[f_1315_3]) ).

fof(f_1316_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_1316_2,plain,
    ! [U_4579,U_4578,U_4577,U_4576,U_4575] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_4578,U_4578)),hAPP(hAPP(c_Product__Type_OPair(U_4578,U_4578),U_4576),U_4577)),c_Wellfounded_Omlex__prod(U_4578,U_4575,U_4579)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4578,U_4578)),hAPP(hAPP(c_Product__Type_OPair(U_4578,U_4578),U_4576),U_4577)),U_4579))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_4575,U_4576)),hAPP(U_4575,U_4577))) ),
    inference(variable_rename,[status(thm)],[f_1316_1]) ).

fof(f_1316_3,plain,
    ! [U_4576,U_4575,U_4577,U_4578,U_4579] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_4578,U_4578)),hAPP(hAPP(c_Product__Type_OPair(U_4578,U_4578),U_4576),U_4577)),c_Wellfounded_Omlex__prod(U_4578,U_4575,U_4579)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4578,U_4578)),hAPP(hAPP(c_Product__Type_OPair(U_4578,U_4578),U_4576),U_4577)),U_4579))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_4575,U_4576)),hAPP(U_4575,U_4577))) ),
    inference(definitional_conversion,[status(esa)],[f_1316_2]) ).

cnf(f_1316_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_4578,U_4578)),hAPP(hAPP(c_Product__Type_OPair(U_4578,U_4578),U_4576),U_4577)),c_Wellfounded_Omlex__prod(U_4578,U_4575,U_4579)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4578,U_4578)),hAPP(hAPP(c_Product__Type_OPair(U_4578,U_4578),U_4576),U_4577)),U_4579))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_4575,U_4576)),hAPP(U_4575,U_4577))) ),
    inference(clausify,[status(thm)],[f_1316_3]) ).

fof(f_1317_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_1317_2,plain,
    ! [U_4584,U_4583,U_4582,U_4581,U_4580] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_4583,U_4583)),hAPP(hAPP(c_Product__Type_OPair(U_4583,U_4583),U_4581),U_4582)),c_Wellfounded_Omlex__prod(U_4583,U_4580,U_4584)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_4580,U_4581)),hAPP(U_4580,U_4582))) ),
    inference(variable_rename,[status(thm)],[f_1317_1]) ).

fof(f_1317_3,plain,
    ! [U_4581,U_4580,U_4582,U_4583,U_4584] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_4583,U_4583)),hAPP(hAPP(c_Product__Type_OPair(U_4583,U_4583),U_4581),U_4582)),c_Wellfounded_Omlex__prod(U_4583,U_4580,U_4584)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_4580,U_4581)),hAPP(U_4580,U_4582))) ),
    inference(definitional_conversion,[status(esa)],[f_1317_2]) ).

cnf(f_1317_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_4583,U_4583)),hAPP(hAPP(c_Product__Type_OPair(U_4583,U_4583),U_4581),U_4582)),c_Wellfounded_Omlex__prod(U_4583,U_4580,U_4584)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_4580,U_4581)),hAPP(U_4580,U_4582))) ),
    inference(clausify,[status(thm)],[f_1317_3]) ).

fof(f_1318_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_1318_2,plain,
    ! [U_4586,U_4585] : c_Divides_Opdivmod(U_4585,U_4586) = 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_4585)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4586))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4585),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4586))),
    inference(variable_rename,[status(thm)],[f_1318_1]) ).

fof(f_1318_3,plain,
    ! [U_4585,U_4586] : c_Divides_Opdivmod(U_4585,U_4586) = 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_4585)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4586))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4585),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4586))),
    inference(definitional_conversion,[status(esa)],[f_1318_2]) ).

cnf(f_1318_4,plain,
    c_Divides_Opdivmod(U_4585,U_4586) = 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_4585)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4586))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4585),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4586))),
    inference(clausify,[status(thm)],[f_1318_3]) ).

fof(f_1319_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_1319_2,plain,
    ! [U_4591,U_4590,U_4589,U_4588,U_4587] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4591),U_4587),U_4588),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_4591),U_4589)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4591),U_4590)),U_4588))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4591),U_4590),U_4588))))
      | U_4588 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4587,U_4588),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4589),U_4590))) ),
    inference(variable_rename,[status(thm)],[f_1319_1]) ).

fof(f_1319_3,plain,
    ! [U_4587,U_4588,U_4589,U_4590,U_4591] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4591),U_4587),U_4588),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_4591),U_4589)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4591),U_4590)),U_4588))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4591),U_4590),U_4588))))
      | U_4588 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4587,U_4588),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4589),U_4590))) ),
    inference(definitional_conversion,[status(esa)],[f_1319_2]) ).

cnf(f_1319_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4591),U_4587),U_4588),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_4591),U_4589)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4591),U_4590)),U_4588))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4591),U_4590),U_4588))))
    | U_4588 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4587,U_4588),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4589),U_4590))) ),
    inference(clausify,[status(thm)],[f_1319_3]) ).

fof(f_1320_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_1320_2,plain,
    ! [U_4599,U_4598,U_4597,U_4596,U_4595,U_4594,U_4593,U_4592] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_4592,U_4593),tc_prod(U_4592,U_4593))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_4592,U_4593),tc_prod(U_4592,U_4593)),hAPP(hAPP(c_Product__Type_OPair(U_4592,U_4593),U_4594),U_4595)),hAPP(hAPP(c_Product__Type_OPair(U_4592,U_4593),U_4596),U_4597))),c_Wellfounded_Olex__prod(U_4592,U_4593,U_4598,U_4599)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4593,U_4593)),hAPP(hAPP(c_Product__Type_OPair(U_4593,U_4593),U_4595),U_4597)),U_4599))
            | U_4594 != U_4596 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4592,U_4592)),hAPP(hAPP(c_Product__Type_OPair(U_4592,U_4592),U_4594),U_4596)),U_4598)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_4593,U_4593)),hAPP(hAPP(c_Product__Type_OPair(U_4593,U_4593),U_4595),U_4597)),U_4599))
          & U_4594 = U_4596 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_4592,U_4592)),hAPP(hAPP(c_Product__Type_OPair(U_4592,U_4592),U_4594),U_4596)),U_4598))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_4592,U_4593),tc_prod(U_4592,U_4593))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_4592,U_4593),tc_prod(U_4592,U_4593)),hAPP(hAPP(c_Product__Type_OPair(U_4592,U_4593),U_4594),U_4595)),hAPP(hAPP(c_Product__Type_OPair(U_4592,U_4593),U_4596),U_4597))),c_Wellfounded_Olex__prod(U_4592,U_4593,U_4598,U_4599))) ) ),
    inference(variable_rename,[status(thm)],[f_1320_1]) ).

fof(f_1320_3,plain,
    ( ! [U_4615,U_4613,U_4611,U_4609,U_4607,U_4605,U_4603,U_4601] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_4601,U_4603),tc_prod(U_4601,U_4603))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_4601,U_4603),tc_prod(U_4601,U_4603)),hAPP(hAPP(c_Product__Type_OPair(U_4601,U_4603),U_4605),U_4607)),hAPP(hAPP(c_Product__Type_OPair(U_4601,U_4603),U_4609),U_4611))),c_Wellfounded_Olex__prod(U_4601,U_4603,U_4613,U_4615)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4603,U_4603)),hAPP(hAPP(c_Product__Type_OPair(U_4603,U_4603),U_4607),U_4611)),U_4615))
            | U_4605 != U_4609 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4601,U_4601)),hAPP(hAPP(c_Product__Type_OPair(U_4601,U_4601),U_4605),U_4609)),U_4613)) ) )
    & ! [U_4614,U_4612,U_4610,U_4608,U_4606,U_4604,U_4602,U_4600] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_4602,U_4602)),hAPP(hAPP(c_Product__Type_OPair(U_4602,U_4602),U_4606),U_4610)),U_4614))
          & U_4604 = U_4608 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_4600,U_4600)),hAPP(hAPP(c_Product__Type_OPair(U_4600,U_4600),U_4604),U_4608)),U_4612))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_4600,U_4602),tc_prod(U_4600,U_4602))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_4600,U_4602),tc_prod(U_4600,U_4602)),hAPP(hAPP(c_Product__Type_OPair(U_4600,U_4602),U_4604),U_4606)),hAPP(hAPP(c_Product__Type_OPair(U_4600,U_4602),U_4608),U_4610))),c_Wellfounded_Olex__prod(U_4600,U_4602,U_4612,U_4614))) ) ),
    inference(miniscope,[status(thm)],[f_1320_2]) ).

fof(f_1320_4,plain,
    ( ! [U_4601,U_4603,U_4605,U_4607,U_4609,U_4611,U_4613,U_4615] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4603,U_4603)),hAPP(hAPP(c_Product__Type_OPair(U_4603,U_4603),U_4607),U_4611)),U_4615))
        | U_4605 != U_4609
        | ~ sP365(U_4601,U_4603,U_4605,U_4607,U_4609,U_4611,U_4613,U_4615) )
    & ! [U_4601,U_4603,U_4605,U_4607,U_4609,U_4611,U_4613,U_4615] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4601,U_4601)),hAPP(hAPP(c_Product__Type_OPair(U_4601,U_4601),U_4605),U_4609)),U_4613))
        | ~ sP365(U_4601,U_4603,U_4605,U_4607,U_4609,U_4611,U_4613,U_4615) )
    & ! [U_4602,U_4604,U_4606,U_4608,U_4610,U_4614] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_4602,U_4602)),hAPP(hAPP(c_Product__Type_OPair(U_4602,U_4602),U_4606),U_4610)),U_4614))
        | ~ sP364(U_4602,U_4604,U_4606,U_4608,U_4610,U_4614) )
    & ! [U_4602,U_4604,U_4606,U_4608,U_4610,U_4614] :
        ( U_4604 = U_4608
        | ~ sP364(U_4602,U_4604,U_4606,U_4608,U_4610,U_4614) )
    & ! [U_4601,U_4603,U_4605,U_4607,U_4609,U_4611,U_4613,U_4615] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_4601,U_4603),tc_prod(U_4601,U_4603))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_4601,U_4603),tc_prod(U_4601,U_4603)),hAPP(hAPP(c_Product__Type_OPair(U_4601,U_4603),U_4605),U_4607)),hAPP(hAPP(c_Product__Type_OPair(U_4601,U_4603),U_4609),U_4611))),c_Wellfounded_Olex__prod(U_4601,U_4603,U_4613,U_4615)))
        | sP365(U_4601,U_4603,U_4605,U_4607,U_4609,U_4611,U_4613,U_4615) )
    & ! [U_4602,U_4600,U_4604,U_4606,U_4608,U_4610,U_4614,U_4612] :
        ( sP364(U_4602,U_4604,U_4606,U_4608,U_4610,U_4614)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_4600,U_4600)),hAPP(hAPP(c_Product__Type_OPair(U_4600,U_4600),U_4604),U_4608)),U_4612))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_4600,U_4602),tc_prod(U_4600,U_4602))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_4600,U_4602),tc_prod(U_4600,U_4602)),hAPP(hAPP(c_Product__Type_OPair(U_4600,U_4602),U_4604),U_4606)),hAPP(hAPP(c_Product__Type_OPair(U_4600,U_4602),U_4608),U_4610))),c_Wellfounded_Olex__prod(U_4600,U_4602,U_4612,U_4614))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP364,sP365])],[f_1320_3]) ).

cnf(f_1320_5,plain,
    ( sP364(U_4602,U_4604,U_4606,U_4608,U_4610,U_4614)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_4600,U_4600)),hAPP(hAPP(c_Product__Type_OPair(U_4600,U_4600),U_4604),U_4608)),U_4612))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_4600,U_4602),tc_prod(U_4600,U_4602))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_4600,U_4602),tc_prod(U_4600,U_4602)),hAPP(hAPP(c_Product__Type_OPair(U_4600,U_4602),U_4604),U_4606)),hAPP(hAPP(c_Product__Type_OPair(U_4600,U_4602),U_4608),U_4610))),c_Wellfounded_Olex__prod(U_4600,U_4602,U_4612,U_4614))) ),
    inference(clausify,[status(thm)],[f_1320_4]) ).

cnf(f_1320_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_4601,U_4603),tc_prod(U_4601,U_4603))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_4601,U_4603),tc_prod(U_4601,U_4603)),hAPP(hAPP(c_Product__Type_OPair(U_4601,U_4603),U_4605),U_4607)),hAPP(hAPP(c_Product__Type_OPair(U_4601,U_4603),U_4609),U_4611))),c_Wellfounded_Olex__prod(U_4601,U_4603,U_4613,U_4615)))
    | sP365(U_4601,U_4603,U_4605,U_4607,U_4609,U_4611,U_4613,U_4615) ),
    inference(clausify,[status(thm)],[f_1320_4]) ).

cnf(f_1320_7,plain,
    ( U_4604 = U_4608
    | ~ sP364(U_4602,U_4604,U_4606,U_4608,U_4610,U_4614) ),
    inference(clausify,[status(thm)],[f_1320_4]) ).

cnf(f_1320_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_4602,U_4602)),hAPP(hAPP(c_Product__Type_OPair(U_4602,U_4602),U_4606),U_4610)),U_4614))
    | ~ sP364(U_4602,U_4604,U_4606,U_4608,U_4610,U_4614) ),
    inference(clausify,[status(thm)],[f_1320_4]) ).

cnf(f_1320_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4601,U_4601)),hAPP(hAPP(c_Product__Type_OPair(U_4601,U_4601),U_4605),U_4609)),U_4613))
    | ~ sP365(U_4601,U_4603,U_4605,U_4607,U_4609,U_4611,U_4613,U_4615) ),
    inference(clausify,[status(thm)],[f_1320_4]) ).

cnf(f_1320_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4603,U_4603)),hAPP(hAPP(c_Product__Type_OPair(U_4603,U_4603),U_4607),U_4611)),U_4615))
    | U_4605 != U_4609
    | ~ sP365(U_4601,U_4603,U_4605,U_4607,U_4609,U_4611,U_4613,U_4615) ),
    inference(clausify,[status(thm)],[f_1320_4]) ).

fof(f_1321_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_1321_2,plain,
    ! [U_4616] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_4616),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_4616 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1321_1]) ).

fof(f_1321_3,plain,
    ! [U_4616] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_4616),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_4616 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_1321_2]) ).

cnf(f_1321_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_4616),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_4616 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1321_3]) ).

fof(f_1322_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_1322_2,plain,
    ! [U_4619,U_4618,U_4617] :
      ( U_4619 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | U_4617 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4617,U_4617),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4618),U_4619))) ),
    inference(variable_rename,[status(thm)],[f_1322_1]) ).

fof(f_1322_3,plain,
    ! [U_4617,U_4619,U_4618] :
      ( U_4619 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | U_4617 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4617,U_4617),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4618),U_4619))) ),
    inference(definitional_conversion,[status(esa)],[f_1322_2]) ).

cnf(f_1322_4,plain,
    ( U_4619 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_4617 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4617,U_4617),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4618),U_4619))) ),
    inference(clausify,[status(thm)],[f_1322_3]) ).

fof(f_1323_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_1323_2,plain,
    ! [U_4625,U_4624,U_4623,U_4622,U_4621,U_4620] :
      ( U_4622 = U_4624
      | U_4621 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4620,U_4621),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4624),U_4625)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4620,U_4621),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4622),U_4623))) ),
    inference(variable_rename,[status(thm)],[f_1323_1]) ).

fof(f_1323_3,plain,
    ! [U_4620,U_4622,U_4621,U_4623,U_4624,U_4625] :
      ( U_4622 = U_4624
      | U_4621 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4620,U_4621),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4624),U_4625)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4620,U_4621),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4622),U_4623))) ),
    inference(definitional_conversion,[status(esa)],[f_1323_2]) ).

cnf(f_1323_4,plain,
    ( U_4622 = U_4624
    | U_4621 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4620,U_4621),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4624),U_4625)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4620,U_4621),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4622),U_4623))) ),
    inference(clausify,[status(thm)],[f_1323_3]) ).

fof(f_1324_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_1324_2,plain,
    ! [U_4631,U_4630,U_4629,U_4628,U_4627,U_4626] :
      ( U_4629 = U_4631
      | U_4627 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4626,U_4627),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4630),U_4631)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4626,U_4627),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4628),U_4629))) ),
    inference(variable_rename,[status(thm)],[f_1324_1]) ).

fof(f_1324_3,plain,
    ! [U_4628,U_4627,U_4626,U_4629,U_4630,U_4631] :
      ( U_4629 = U_4631
      | U_4627 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4626,U_4627),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4630),U_4631)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4626,U_4627),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4628),U_4629))) ),
    inference(definitional_conversion,[status(esa)],[f_1324_2]) ).

cnf(f_1324_4,plain,
    ( U_4629 = U_4631
    | U_4627 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4626,U_4627),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4630),U_4631)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4626,U_4627),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4628),U_4629))) ),
    inference(clausify,[status(thm)],[f_1324_3]) ).

fof(f_1325_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_1325_2,plain,
    ! [U_4634,U_4633,U_4632] :
      ( U_4633 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | U_4632 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4632,U_4632),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4633),U_4634))) ),
    inference(variable_rename,[status(thm)],[f_1325_1]) ).

fof(f_1325_3,plain,
    ! [U_4633,U_4632,U_4634] :
      ( U_4633 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | U_4632 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4632,U_4632),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4633),U_4634))) ),
    inference(definitional_conversion,[status(esa)],[f_1325_2]) ).

cnf(f_1325_4,plain,
    ( U_4633 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_4632 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4632,U_4632),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4633),U_4634))) ),
    inference(clausify,[status(thm)],[f_1325_3]) ).

fof(f_1326_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_1326_2,plain,
    ! [U_4638,U_4637,U_4636,U_4635] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4635,U_4636) = U_4638
      | U_4636 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4635,U_4636),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4637),U_4638))) ),
    inference(variable_rename,[status(thm)],[f_1326_1]) ).

fof(f_1326_3,plain,
    ! [U_4636,U_4635,U_4637,U_4638] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4635,U_4636) = U_4638
      | U_4636 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4635,U_4636),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4637),U_4638))) ),
    inference(definitional_conversion,[status(esa)],[f_1326_2]) ).

cnf(f_1326_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4635,U_4636) = U_4638
    | U_4636 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4635,U_4636),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4637),U_4638))) ),
    inference(clausify,[status(thm)],[f_1326_3]) ).

fof(f_1327_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_1327_2,plain,
    ! [U_4642,U_4641,U_4640,U_4639] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4639),U_4640) = U_4641
      | U_4640 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4639,U_4640),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4641),U_4642))) ),
    inference(variable_rename,[status(thm)],[f_1327_1]) ).

fof(f_1327_3,plain,
    ! [U_4639,U_4640,U_4641,U_4642] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4639),U_4640) = U_4641
      | U_4640 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4639,U_4640),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4641),U_4642))) ),
    inference(definitional_conversion,[status(esa)],[f_1327_2]) ).

cnf(f_1327_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4639),U_4640) = U_4641
    | U_4640 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4639,U_4640),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4641),U_4642))) ),
    inference(clausify,[status(thm)],[f_1327_3]) ).

fof(f_1328_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_1328_2,plain,
    ! [U_4644,U_4643] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4644,U_4643),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4644),U_4643)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4644,U_4643))))
      | U_4643 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1328_1]) ).

fof(f_1328_3,plain,
    ! [U_4643,U_4644] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4644,U_4643),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4644),U_4643)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4644,U_4643))))
      | U_4643 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_1328_2]) ).

cnf(f_1328_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4644,U_4643),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4644),U_4643)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4644,U_4643))))
    | U_4643 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1328_3]) ).

fof(f_1329_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_1329_2,plain,
    ! [U_4651,U_4650,U_4649,U_4648,U_4647,U_4646,U_4645] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4645),U_4649),U_4646),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_4647),U_4650)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4648),U_4651)),U_4646))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4648),U_4651),U_4646))))
      | U_4646 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4649,U_4646),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4650),U_4651)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4645,U_4646),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4647),U_4648))) ),
    inference(variable_rename,[status(thm)],[f_1329_1]) ).

fof(f_1329_3,plain,
    ! [U_4646,U_4645,U_4647,U_4648,U_4649,U_4650,U_4651] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4645),U_4649),U_4646),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_4647),U_4650)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4648),U_4651)),U_4646))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4648),U_4651),U_4646))))
      | U_4646 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4649,U_4646),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4650),U_4651)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4645,U_4646),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4647),U_4648))) ),
    inference(definitional_conversion,[status(esa)],[f_1329_2]) ).

cnf(f_1329_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4645),U_4649),U_4646),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_4647),U_4650)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4648),U_4651)),U_4646))),c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4648),U_4651),U_4646))))
    | U_4646 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4649,U_4646),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4650),U_4651)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4645,U_4646),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4647),U_4648))) ),
    inference(clausify,[status(thm)],[f_1329_3]) ).

fof(f_1330_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_1330_2,plain,
    ! [U_4655,U_4654,U_4653,U_4652] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4652),U_4653),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_4655),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4654)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4654)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_4655),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_4653),U_4655)))))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4652,U_4653),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4654),U_4655))) ),
    inference(variable_rename,[status(thm)],[f_1330_1]) ).

fof(f_1330_3,plain,
    ! [U_4653,U_4654,U_4652,U_4655] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4652),U_4653),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_4655),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4654)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4654)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_4655),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_4653),U_4655)))))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4652,U_4653),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4654),U_4655))) ),
    inference(definitional_conversion,[status(esa)],[f_1330_2]) ).

cnf(f_1330_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4652),U_4653),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_4655),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4654)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4654)),c_Groups_Oone__class_Oone(tc_Int_Oint)))),hAPP(hAPP(hAPP(c_If(tc_Int_Oint),hAPP(hAPP(c_fequal,U_4655),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_4653),U_4655)))))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4652,U_4653),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4654),U_4655))) ),
    inference(clausify,[status(thm)],[f_1330_3]) ).

fof(f_1331_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_1331_2,plain,
    ! [U_4659,U_4658,U_4657,U_4656] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4656,U_4657),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4658),U_4659)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4659),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4657),U_4659)) )
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4657)) )
      | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4659),U_4657))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4659)) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4657)) )
      | U_4656 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4657),U_4658)),U_4659) ),
    inference(variable_rename,[status(thm)],[f_1331_1]) ).

fof(f_1331_3,plain,
    ( ! [U_4657,U_4659] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4659),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4657),U_4659))
        | ~ sP367(U_4657,U_4659) )
    & ! [U_4657,U_4659] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4657))
        | ~ sP367(U_4657,U_4659) )
    & ! [U_4657,U_4659] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4659),U_4657))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4659))
        | ~ sP366(U_4657,U_4659) )
    & ! [U_4657,U_4659] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4657))
        | ~ sP366(U_4657,U_4659) )
    & ! [U_4657,U_4656,U_4658,U_4659] :
        ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4656,U_4657),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4658),U_4659)))
        | sP367(U_4657,U_4659)
        | sP366(U_4657,U_4659)
        | U_4656 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4657),U_4658)),U_4659) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP366,sP367])],[f_1331_2]) ).

cnf(f_1331_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4656,U_4657),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4658),U_4659)))
    | sP367(U_4657,U_4659)
    | sP366(U_4657,U_4659)
    | U_4656 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4657),U_4658)),U_4659) ),
    inference(clausify,[status(thm)],[f_1331_3]) ).

cnf(f_1331_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4657))
    | ~ sP366(U_4657,U_4659) ),
    inference(clausify,[status(thm)],[f_1331_3]) ).

cnf(f_1331_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4659),U_4657))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4659))
    | ~ sP366(U_4657,U_4659) ),
    inference(clausify,[status(thm)],[f_1331_3]) ).

cnf(f_1331_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4657))
    | ~ sP367(U_4657,U_4659) ),
    inference(clausify,[status(thm)],[f_1331_3]) ).

cnf(f_1331_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4659),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4657),U_4659))
    | ~ sP367(U_4657,U_4659) ),
    inference(clausify,[status(thm)],[f_1331_3]) ).

fof(f_1332_1,plain,
    ! [T_b,V_R_2,V_y_2,V_y_H_2,T_c,V_x_2,V_Pa_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_Pa_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_Pa_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_same__fstI]) ).

fof(f_1332_2,plain,
    ! [U_4666,U_4665,U_4664,U_4663,U_4662,U_4661,U_4660] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_4666,U_4662),tc_prod(U_4666,U_4662))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_4666,U_4662),tc_prod(U_4666,U_4662)),hAPP(hAPP(c_Product__Type_OPair(U_4666,U_4662),U_4661),U_4663)),hAPP(hAPP(c_Product__Type_OPair(U_4666,U_4662),U_4661),U_4664))),c_Recdef_Osame__fst(U_4666,U_4662,U_4660,U_4665)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4662,U_4662)),hAPP(hAPP(c_Product__Type_OPair(U_4662,U_4662),U_4663),U_4664)),hAPP(U_4665,U_4661)))
      | ~ hBOOL(hAPP(U_4660,U_4661)) ),
    inference(variable_rename,[status(thm)],[f_1332_1]) ).

fof(f_1332_3,plain,
    ! [U_4661,U_4662,U_4664,U_4663,U_4660,U_4665,U_4666] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_4666,U_4662),tc_prod(U_4666,U_4662))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_4666,U_4662),tc_prod(U_4666,U_4662)),hAPP(hAPP(c_Product__Type_OPair(U_4666,U_4662),U_4661),U_4663)),hAPP(hAPP(c_Product__Type_OPair(U_4666,U_4662),U_4661),U_4664))),c_Recdef_Osame__fst(U_4666,U_4662,U_4660,U_4665)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4662,U_4662)),hAPP(hAPP(c_Product__Type_OPair(U_4662,U_4662),U_4663),U_4664)),hAPP(U_4665,U_4661)))
      | ~ hBOOL(hAPP(U_4660,U_4661)) ),
    inference(definitional_conversion,[status(esa)],[f_1332_2]) ).

cnf(f_1332_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_prod(U_4666,U_4662),tc_prod(U_4666,U_4662))),hAPP(hAPP(c_Product__Type_OPair(tc_prod(U_4666,U_4662),tc_prod(U_4666,U_4662)),hAPP(hAPP(c_Product__Type_OPair(U_4666,U_4662),U_4661),U_4663)),hAPP(hAPP(c_Product__Type_OPair(U_4666,U_4662),U_4661),U_4664))),c_Recdef_Osame__fst(U_4666,U_4662,U_4660,U_4665)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_4662,U_4662)),hAPP(hAPP(c_Product__Type_OPair(U_4662,U_4662),U_4663),U_4664)),hAPP(U_4665,U_4661)))
    | ~ hBOOL(hAPP(U_4660,U_4661)) ),
    inference(clausify,[status(thm)],[f_1332_3]) ).

fof(f_1333_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_1333_2,plain,
    ! [U_4668,U_4667] :
      ( c_Divides_OnegDivAlg(U_4667,U_4668) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4667),U_4668)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4667,U_4668))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4668))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4667),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1333_1]) ).

fof(f_1333_3,plain,
    ! [U_4667,U_4668] :
      ( c_Divides_OnegDivAlg(U_4667,U_4668) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4667),U_4668)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4667,U_4668))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4668))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4667),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1333_2]) ).

cnf(f_1333_4,plain,
    ( c_Divides_OnegDivAlg(U_4667,U_4668) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4667),U_4668)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4667,U_4668))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4668))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4667),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1333_3]) ).

fof(f_1334_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_1334_2,plain,
    ! [U_4670,U_4669] :
      ( c_Divides_OposDivAlg(U_4669,U_4670) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4669),U_4670)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4669,U_4670))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4670))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4669)) ),
    inference(variable_rename,[status(thm)],[f_1334_1]) ).

fof(f_1334_3,plain,
    ! [U_4669,U_4670] :
      ( c_Divides_OposDivAlg(U_4669,U_4670) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4669),U_4670)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4669,U_4670))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4670))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4669)) ),
    inference(definitional_conversion,[status(esa)],[f_1334_2]) ).

cnf(f_1334_4,plain,
    ( c_Divides_OposDivAlg(U_4669,U_4670) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4669),U_4670)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4669,U_4670))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4670))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4669)) ),
    inference(clausify,[status(thm)],[f_1334_3]) ).

fof(f_1335_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_1335_2,plain,
    ! [U_4672,U_4671] : c_Divides_Odivmod__int(U_4671,U_4672) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4671),U_4672)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4671,U_4672)),
    inference(variable_rename,[status(thm)],[f_1335_1]) ).

fof(f_1335_3,plain,
    ! [U_4671,U_4672] : c_Divides_Odivmod__int(U_4671,U_4672) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4671),U_4672)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4671,U_4672)),
    inference(definitional_conversion,[status(esa)],[f_1335_2]) ).

cnf(f_1335_4,plain,
    c_Divides_Odivmod__int(U_4671,U_4672) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4671),U_4672)),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4671,U_4672)),
    inference(clausify,[status(thm)],[f_1335_3]) ).

fof(f_1336_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_1336_2,plain,
    ! [U_4674,U_4673] :
      ( ( c_Divides_Opdivmod(U_4674,U_4673) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4674),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4673))
        | U_4673 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Opdivmod(U_4674,U_4673) = 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_4674))
        | U_4673 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1336_1]) ).

fof(f_1336_3,plain,
    ( ! [U_4678,U_4676] :
        ( c_Divides_Opdivmod(U_4678,U_4676) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4678),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4676))
        | U_4676 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_4677,U_4675] :
        ( c_Divides_Opdivmod(U_4677,U_4675) = 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_4677))
        | U_4675 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1336_2]) ).

fof(f_1336_4,plain,
    ( ! [U_4676,U_4678] :
        ( c_Divides_Opdivmod(U_4678,U_4676) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4678),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4676))
        | U_4676 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_4677,U_4675] :
        ( c_Divides_Opdivmod(U_4677,U_4675) = 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_4677))
        | U_4675 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa)],[f_1336_3]) ).

cnf(f_1336_5,plain,
    ( c_Divides_Opdivmod(U_4677,U_4675) = 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_4677))
    | U_4675 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1336_4]) ).

cnf(f_1336_6,plain,
    ( c_Divides_Opdivmod(U_4678,U_4676) = c_Divides_OposDivAlg(hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4678),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_4676))
    | U_4676 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1336_4]) ).

fof(f_1337_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_1337_2,plain,
    ! [U_4682,U_4681,U_4680,U_4679] :
      ( 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_4679),U_4681)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4680),U_4682))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4681),U_4682))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4679),U_4680)) ),
    inference(variable_rename,[status(thm)],[f_1337_1]) ).

fof(f_1337_3,plain,
    ! [U_4679,U_4680,U_4681,U_4682] :
      ( 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_4679),U_4681)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4680),U_4682))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4681),U_4682))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4679),U_4680)) ),
    inference(definitional_conversion,[status(esa)],[f_1337_2]) ).

cnf(f_1337_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_4679),U_4681)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4680),U_4682))),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4681),U_4682))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4679),U_4680)) ),
    inference(clausify,[status(thm)],[f_1337_3]) ).

fof(f_1338_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_1338_2,plain,
    ! [U_4683] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_4683) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4683),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_4683)) ),
    inference(variable_rename,[status(thm)],[f_1338_1]) ).

fof(f_1338_3,plain,
    ! [U_4683] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_4683) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4683),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_4683)) ),
    inference(definitional_conversion,[status(esa)],[f_1338_2]) ).

cnf(f_1338_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_4683) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4683),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_4683)) ),
    inference(clausify,[status(thm)],[f_1338_3]) ).

fof(f_1339_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_1339_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_1339_1]) ).

cnf(f_1339_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_1339_2]) ).

fof(f_1340_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_1340_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_1340_1]) ).

cnf(f_1340_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)),
    inference(clausify,[status(thm)],[f_1340_2]) ).

fof(f_1341_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_1341_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_1341_1]) ).

cnf(f_1341_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_1341_2]) ).

fof(f_1342_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_1342_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_1342_1]) ).

cnf(f_1342_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_1342_2]) ).

fof(f_1343_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_1343_2,plain,
    ! [U_4684] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_4684) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4684),
    inference(variable_rename,[status(thm)],[f_1343_1]) ).

fof(f_1343_3,plain,
    ! [U_4684] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_4684) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4684),
    inference(definitional_conversion,[status(esa)],[f_1343_2]) ).

cnf(f_1343_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OMin),U_4684) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4684),
    inference(clausify,[status(thm)],[f_1343_3]) ).

fof(f_1344_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_1344_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_1344_1]) ).

cnf(f_1344_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_1344_2]) ).

fof(f_1345_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_1345_2,plain,
    ! [U_4685] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_4685) = 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_4685),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_1345_1]) ).

fof(f_1345_3,plain,
    ! [U_4685] : c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_4685) = 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_4685),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_1345_2]) ).

cnf(f_1345_4,plain,
    c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin),U_4685) = 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_4685),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1345_3]) ).

fof(f_1346_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_1346_2,plain,
    ! [U_4686] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4686),c_Int_OMin) = c_Int_Osucc(U_4686),
    inference(variable_rename,[status(thm)],[f_1346_1]) ).

fof(f_1346_3,plain,
    ! [U_4686] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4686),c_Int_OMin) = c_Int_Osucc(U_4686),
    inference(definitional_conversion,[status(esa)],[f_1346_2]) ).

cnf(f_1346_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4686),c_Int_OMin) = c_Int_Osucc(U_4686),
    inference(clausify,[status(thm)],[f_1346_3]) ).

fof(f_1347_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_1347_2,plain,
    ! [U_4688,U_4687] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4687),U_4688),hAPP(c_Int_Onumber__class_Onumber__of(U_4687),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4687),U_4688)
      | ~ class_Int_Onumber__ring(U_4687) ),
    inference(variable_rename,[status(thm)],[f_1347_1]) ).

fof(f_1347_3,plain,
    ! [U_4687,U_4688] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4687),U_4688),hAPP(c_Int_Onumber__class_Onumber__of(U_4687),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4687),U_4688)
      | ~ class_Int_Onumber__ring(U_4687) ),
    inference(definitional_conversion,[status(esa)],[f_1347_2]) ).

cnf(f_1347_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4687),U_4688),hAPP(c_Int_Onumber__class_Onumber__of(U_4687),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4687),U_4688)
    | ~ class_Int_Onumber__ring(U_4687) ),
    inference(clausify,[status(thm)],[f_1347_3]) ).

fof(f_1348_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_1348_2,plain,
    ! [U_4690,U_4689] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4689),hAPP(c_Int_Onumber__class_Onumber__of(U_4689),c_Int_OMin)),U_4690) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4689),U_4690)
      | ~ class_Int_Onumber__ring(U_4689) ),
    inference(variable_rename,[status(thm)],[f_1348_1]) ).

fof(f_1348_3,plain,
    ! [U_4689,U_4690] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4689),hAPP(c_Int_Onumber__class_Onumber__of(U_4689),c_Int_OMin)),U_4690) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4689),U_4690)
      | ~ class_Int_Onumber__ring(U_4689) ),
    inference(definitional_conversion,[status(esa)],[f_1348_2]) ).

cnf(f_1348_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_4689),hAPP(c_Int_Onumber__class_Onumber__of(U_4689),c_Int_OMin)),U_4690) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4689),U_4690)
    | ~ class_Int_Onumber__ring(U_4689) ),
    inference(clausify,[status(thm)],[f_1348_3]) ).

fof(f_1349_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_1349_2,plain,
    ! [U_4691] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4691),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4691),c_Groups_Oone__class_Oone(U_4691))
      | ~ class_Int_Onumber__ring(U_4691) ),
    inference(variable_rename,[status(thm)],[f_1349_1]) ).

fof(f_1349_3,plain,
    ! [U_4691] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4691),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4691),c_Groups_Oone__class_Oone(U_4691))
      | ~ class_Int_Onumber__ring(U_4691) ),
    inference(definitional_conversion,[status(esa)],[f_1349_2]) ).

cnf(f_1349_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4691),c_Int_OMin) = hAPP(c_Groups_Ouminus__class_Ouminus(U_4691),c_Groups_Oone__class_Oone(U_4691))
    | ~ class_Int_Onumber__ring(U_4691) ),
    inference(clausify,[status(thm)],[f_1349_3]) ).

fof(f_1350_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_1350_2,plain,
    ! [U_4692] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4692),c_Groups_Oone__class_Oone(U_4692)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4692),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_4692) ),
    inference(variable_rename,[status(thm)],[f_1350_1]) ).

fof(f_1350_3,plain,
    ! [U_4692] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4692),c_Groups_Oone__class_Oone(U_4692)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4692),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_4692) ),
    inference(definitional_conversion,[status(esa)],[f_1350_2]) ).

cnf(f_1350_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_4692),c_Groups_Oone__class_Oone(U_4692)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4692),c_Int_OMin)
    | ~ class_Int_Onumber__ring(U_4692) ),
    inference(clausify,[status(thm)],[f_1350_3]) ).

fof(f_1351_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_1351_2,plain,
    ! [U_4693] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4693),hAPP(c_Int_Onumber__class_Onumber__of(U_4693),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_4693)
      | ~ class_Rings_Olinordered__idom(U_4693)
      | ~ class_Int_Onumber__ring(U_4693) ),
    inference(variable_rename,[status(thm)],[f_1351_1]) ).

fof(f_1351_3,plain,
    ! [U_4693] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4693),hAPP(c_Int_Onumber__class_Onumber__of(U_4693),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_4693)
      | ~ class_Rings_Olinordered__idom(U_4693)
      | ~ class_Int_Onumber__ring(U_4693) ),
    inference(definitional_conversion,[status(esa)],[f_1351_2]) ).

cnf(f_1351_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4693),hAPP(c_Int_Onumber__class_Onumber__of(U_4693),c_Int_OMin)) = c_Groups_Oone__class_Oone(U_4693)
    | ~ class_Rings_Olinordered__idom(U_4693)
    | ~ class_Int_Onumber__ring(U_4693) ),
    inference(clausify,[status(thm)],[f_1351_3]) ).

fof(f_1352_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_1352_2,plain,
    ! [U_4694] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_4694) = 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_1352_1]) ).

fof(f_1352_3,plain,
    ! [U_4694] : c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_4694) = 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_1352_2]) ).

cnf(f_1352_4,plain,
    c_Divides_OposDivAlg(c_Groups_Ozero__class_Ozero(tc_Int_Oint),U_4694) = 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_1352_3]) ).

fof(f_1353_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_1353_2,plain,
    ! [U_4695] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4695,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_1353_1]) ).

fof(f_1353_3,plain,
    ! [U_4695] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4695,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_1353_2]) ).

cnf(f_1353_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4695,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_1353_3]) ).

fof(f_1354_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_1354_2,plain,
    ! [U_4697,U_4696] :
      ( U_4696 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
      | U_4696 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4696),U_4697) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1354_1]) ).

fof(f_1354_3,plain,
    ! [U_4696,U_4697] :
      ( U_4696 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
      | U_4696 = c_Groups_Oone__class_Oone(tc_Int_Oint)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4696),U_4697) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_1354_2]) ).

cnf(f_1354_4,plain,
    ( U_4696 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_4696 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4696),U_4697) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1354_3]) ).

fof(f_1355_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_1355_2,plain,
    ! [U_4699,U_4698] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4698),U_4699) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ( ( U_4699 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
            | U_4698 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
          & ( U_4699 != c_Groups_Oone__class_Oone(tc_Int_Oint)
            | U_4698 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
      & ( ( U_4699 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
          & U_4698 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
        | ( U_4699 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & U_4698 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4698),U_4699) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1355_1]) ).

fof(f_1355_3,plain,
    ( ! [U_4703,U_4701] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4701),U_4703) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ( ( U_4703 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
            | U_4701 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
          & ( U_4703 != c_Groups_Oone__class_Oone(tc_Int_Oint)
            | U_4701 != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) )
    & ! [U_4702,U_4700] :
        ( ( U_4702 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
          & U_4700 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) )
        | ( U_4702 = c_Groups_Oone__class_Oone(tc_Int_Oint)
          & U_4700 = c_Groups_Oone__class_Oone(tc_Int_Oint) )
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4700),U_4702) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1355_2]) ).

fof(f_1355_4,plain,
    ( ! [U_4701,U_4703] :
        ( U_4703 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | U_4701 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | ~ sP370(U_4701,U_4703) )
    & ! [U_4701,U_4703] :
        ( U_4703 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | U_4701 != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP370(U_4701,U_4703) )
    & ! [U_4700,U_4702] :
        ( U_4702 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | ~ sP369(U_4700,U_4702) )
    & ! [U_4700,U_4702] :
        ( U_4700 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
        | ~ sP369(U_4700,U_4702) )
    & ! [U_4700,U_4702] :
        ( U_4702 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP368(U_4700,U_4702) )
    & ! [U_4700,U_4702] :
        ( U_4700 = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP368(U_4700,U_4702) )
    & ! [U_4701,U_4703] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4701),U_4703) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | sP370(U_4701,U_4703) )
    & ! [U_4700,U_4702] :
        ( sP369(U_4700,U_4702)
        | sP368(U_4700,U_4702)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4700),U_4702) != c_Groups_Oone__class_Oone(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP368,sP369,sP370])],[f_1355_3]) ).

cnf(f_1355_5,plain,
    ( sP369(U_4700,U_4702)
    | sP368(U_4700,U_4702)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4700),U_4702) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1355_4]) ).

cnf(f_1355_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4701),U_4703) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | sP370(U_4701,U_4703) ),
    inference(clausify,[status(thm)],[f_1355_4]) ).

cnf(f_1355_7,plain,
    ( U_4700 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP368(U_4700,U_4702) ),
    inference(clausify,[status(thm)],[f_1355_4]) ).

cnf(f_1355_8,plain,
    ( U_4702 = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP368(U_4700,U_4702) ),
    inference(clausify,[status(thm)],[f_1355_4]) ).

cnf(f_1355_9,plain,
    ( U_4700 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | ~ sP369(U_4700,U_4702) ),
    inference(clausify,[status(thm)],[f_1355_4]) ).

cnf(f_1355_10,plain,
    ( U_4702 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | ~ sP369(U_4700,U_4702) ),
    inference(clausify,[status(thm)],[f_1355_4]) ).

cnf(f_1355_11,plain,
    ( U_4703 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | U_4701 != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP370(U_4701,U_4703) ),
    inference(clausify,[status(thm)],[f_1355_4]) ).

cnf(f_1355_12,plain,
    ( U_4703 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | U_4701 != hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)
    | ~ sP370(U_4701,U_4703) ),
    inference(clausify,[status(thm)],[f_1355_4]) ).

fof(f_1356_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_1356_2,plain,
    ! [U_4704] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_4704),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4704),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_4704) ),
    inference(variable_rename,[status(thm)],[f_1356_1]) ).

fof(f_1356_3,plain,
    ! [U_4704] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_4704),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4704),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_4704) ),
    inference(definitional_conversion,[status(esa)],[f_1356_2]) ).

cnf(f_1356_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_4704),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4704),c_Int_OMin)
    | ~ class_Int_Onumber__ring(U_4704) ),
    inference(clausify,[status(thm)],[f_1356_3]) ).

fof(f_1357_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_1357_2,plain,
    ! [U_4705] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4705),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4705),
    inference(variable_rename,[status(thm)],[f_1357_1]) ).

fof(f_1357_3,plain,
    ! [U_4705] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4705),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4705),
    inference(definitional_conversion,[status(esa)],[f_1357_2]) ).

cnf(f_1357_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4705),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4705),
    inference(clausify,[status(thm)],[f_1357_3]) ).

fof(f_1358_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_1358_2,plain,
    ! [U_4707,U_4706] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4706),hAPP(hAPP(c_Power_Opower__class_Opower(U_4706),hAPP(c_Int_Onumber__class_Onumber__of(U_4706),c_Int_OMin)),U_4707)) = c_Groups_Oone__class_Oone(U_4706)
      | ~ class_Rings_Olinordered__idom(U_4706)
      | ~ class_Int_Onumber__ring(U_4706) ),
    inference(variable_rename,[status(thm)],[f_1358_1]) ).

fof(f_1358_3,plain,
    ! [U_4706,U_4707] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_4706),hAPP(hAPP(c_Power_Opower__class_Opower(U_4706),hAPP(c_Int_Onumber__class_Onumber__of(U_4706),c_Int_OMin)),U_4707)) = c_Groups_Oone__class_Oone(U_4706)
      | ~ class_Rings_Olinordered__idom(U_4706)
      | ~ class_Int_Onumber__ring(U_4706) ),
    inference(definitional_conversion,[status(esa)],[f_1358_2]) ).

cnf(f_1358_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_4706),hAPP(hAPP(c_Power_Opower__class_Opower(U_4706),hAPP(c_Int_Onumber__class_Onumber__of(U_4706),c_Int_OMin)),U_4707)) = c_Groups_Oone__class_Oone(U_4706)
    | ~ class_Rings_Olinordered__idom(U_4706)
    | ~ class_Int_Onumber__ring(U_4706) ),
    inference(clausify,[status(thm)],[f_1358_3]) ).

fof(f_1359_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_1359_2,plain,
    ! [U_4708] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),U_4708) = 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_4708)) ),
    inference(variable_rename,[status(thm)],[f_1359_1]) ).

fof(f_1359_3,plain,
    ! [U_4708] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin)),U_4708) = 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_4708)) ),
    inference(definitional_conversion,[status(esa)],[f_1359_2]) ).

cnf(f_1359_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_4708) = 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_4708)) ),
    inference(clausify,[status(thm)],[f_1359_3]) ).

fof(f_1360_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_1360_2,plain,
    ! [U_4712,U_4711,U_4710,U_4709] :
      ( 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_4709),U_4711)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4710),U_4712))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4709),U_4710)) ),
    inference(variable_rename,[status(thm)],[f_1360_1]) ).

fof(f_1360_3,plain,
    ! [U_4709,U_4710,U_4711,U_4712] :
      ( 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_4709),U_4711)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4710),U_4712))),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4709),U_4710)) ),
    inference(definitional_conversion,[status(esa)],[f_1360_2]) ).

cnf(f_1360_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_4709),U_4711)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4710),U_4712))),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4709),U_4710)) ),
    inference(clausify,[status(thm)],[f_1360_3]) ).

fof(f_1361_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_1361_2,plain,
    ! [U_4714,U_4713] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4713,U_4714),c_Divides_OnegDivAlg(U_4713,U_4714)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4714))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4713),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1361_1]) ).

fof(f_1361_3,plain,
    ! [U_4713,U_4714] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4713,U_4714),c_Divides_OnegDivAlg(U_4713,U_4714)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4714))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4713),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1361_2]) ).

cnf(f_1361_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4713,U_4714),c_Divides_OnegDivAlg(U_4713,U_4714)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4714))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4713),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1361_3]) ).

fof(f_1362_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_1362_2,plain,
    ! [U_4716,U_4715] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4716,U_4715),c_Divides_Odivmod__int(U_4716,U_4715)))
      | U_4715 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_1362_1]) ).

fof(f_1362_3,plain,
    ! [U_4716,U_4715] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4716,U_4715),c_Divides_Odivmod__int(U_4716,U_4715)))
      | U_4715 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_1362_2]) ).

cnf(f_1362_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4716,U_4715),c_Divides_Odivmod__int(U_4716,U_4715)))
    | U_4715 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1362_3]) ).

fof(f_1363_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_1363_2,plain,
    ! [U_4718,U_4717] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4717,U_4718),c_Divides_OposDivAlg(U_4717,U_4718)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4718))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4717)) ),
    inference(variable_rename,[status(thm)],[f_1363_1]) ).

fof(f_1363_3,plain,
    ! [U_4717,U_4718] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4717,U_4718),c_Divides_OposDivAlg(U_4717,U_4718)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4718))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4717)) ),
    inference(definitional_conversion,[status(esa)],[f_1363_2]) ).

cnf(f_1363_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4717,U_4718),c_Divides_OposDivAlg(U_4717,U_4718)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4718))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4717)) ),
    inference(clausify,[status(thm)],[f_1363_3]) ).

fof(f_1364_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_1364_2,plain,
    ! [U_4720,U_4719] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4719),U_4720) = 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_4719),U_4720)),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_4719)) ),
    inference(variable_rename,[status(thm)],[f_1364_1]) ).

fof(f_1364_3,plain,
    ! [U_4720,U_4719] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4719),U_4720) = 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_4719),U_4720)),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_4719)) ),
    inference(definitional_conversion,[status(esa)],[f_1364_2]) ).

cnf(f_1364_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4719),U_4720) = 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_4719),U_4720)),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_4719)) ),
    inference(clausify,[status(thm)],[f_1364_3]) ).

fof(f_1365_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_1365_2,plain,
    ! [U_4722,U_4721] :
      ( ( ( ( c_Divides_Odivmod__int(U_4721,U_4722) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4721),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4722)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4722)) )
          & ( c_Divides_Odivmod__int(U_4721,U_4722) = c_Divides_OnegDivAlg(U_4721,U_4722)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4722)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4721)) )
      & ( ( ( ( ( c_Divides_Odivmod__int(U_4721,U_4722) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4721),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4722)))
                | U_4721 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
              & ( c_Divides_Odivmod__int(U_4721,U_4722) = 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_4721 != 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_4722)) )
          & ( c_Divides_Odivmod__int(U_4721,U_4722) = c_Divides_OposDivAlg(U_4721,U_4722)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4722)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4721)) ) ),
    inference(variable_rename,[status(thm)],[f_1365_1]) ).

fof(f_1365_3,plain,
    ( ! [U_4726,U_4724] :
        ( ( ( c_Divides_Odivmod__int(U_4724,U_4726) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4724),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4726)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4726)) )
          & ( c_Divides_Odivmod__int(U_4724,U_4726) = c_Divides_OnegDivAlg(U_4724,U_4726)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4726)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4724)) )
    & ! [U_4725,U_4723] :
        ( ( ( ( ( c_Divides_Odivmod__int(U_4723,U_4725) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4723),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4725)))
                | U_4723 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
              & ( c_Divides_Odivmod__int(U_4723,U_4725) = 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_4723 != 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_4725)) )
          & ( c_Divides_Odivmod__int(U_4723,U_4725) = c_Divides_OposDivAlg(U_4723,U_4725)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4725)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4723)) ) ),
    inference(miniscope,[status(thm)],[f_1365_2]) ).

fof(f_1365_4,plain,
    ( ! [U_4724,U_4726] :
        ( c_Divides_Odivmod__int(U_4724,U_4726) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4724),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4726)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4726))
        | ~ sP373(U_4724,U_4726) )
    & ! [U_4724,U_4726] :
        ( c_Divides_Odivmod__int(U_4724,U_4726) = c_Divides_OnegDivAlg(U_4724,U_4726)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4726))
        | ~ sP373(U_4724,U_4726) )
    & ! [U_4723,U_4725] :
        ( c_Divides_Odivmod__int(U_4723,U_4725) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4723),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4725)))
        | U_4723 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP371(U_4723,U_4725) )
    & ! [U_4723,U_4725] :
        ( c_Divides_Odivmod__int(U_4723,U_4725) = 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_4723 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP371(U_4723,U_4725) )
    & ! [U_4723,U_4725] :
        ( sP371(U_4723,U_4725)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4725))
        | ~ sP372(U_4723,U_4725) )
    & ! [U_4723,U_4725] :
        ( c_Divides_Odivmod__int(U_4723,U_4725) = c_Divides_OposDivAlg(U_4723,U_4725)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4725))
        | ~ sP372(U_4723,U_4725) )
    & ! [U_4724,U_4726] :
        ( sP373(U_4724,U_4726)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4724)) )
    & ! [U_4723,U_4725] :
        ( sP372(U_4723,U_4725)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4723)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP371,sP372,sP373])],[f_1365_3]) ).

cnf(f_1365_5,plain,
    ( sP372(U_4723,U_4725)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4723)) ),
    inference(clausify,[status(thm)],[f_1365_4]) ).

cnf(f_1365_6,plain,
    ( sP373(U_4724,U_4726)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4724)) ),
    inference(clausify,[status(thm)],[f_1365_4]) ).

cnf(f_1365_7,plain,
    ( c_Divides_Odivmod__int(U_4723,U_4725) = c_Divides_OposDivAlg(U_4723,U_4725)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4725))
    | ~ sP372(U_4723,U_4725) ),
    inference(clausify,[status(thm)],[f_1365_4]) ).

cnf(f_1365_8,plain,
    ( sP371(U_4723,U_4725)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4725))
    | ~ sP372(U_4723,U_4725) ),
    inference(clausify,[status(thm)],[f_1365_4]) ).

cnf(f_1365_9,plain,
    ( c_Divides_Odivmod__int(U_4723,U_4725) = 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_4723 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP371(U_4723,U_4725) ),
    inference(clausify,[status(thm)],[f_1365_4]) ).

cnf(f_1365_10,plain,
    ( c_Divides_Odivmod__int(U_4723,U_4725) = hAPP(c_Divides_OnegateSnd,c_Divides_OnegDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4723),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4725)))
    | U_4723 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP371(U_4723,U_4725) ),
    inference(clausify,[status(thm)],[f_1365_4]) ).

cnf(f_1365_11,plain,
    ( c_Divides_Odivmod__int(U_4724,U_4726) = c_Divides_OnegDivAlg(U_4724,U_4726)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4726))
    | ~ sP373(U_4724,U_4726) ),
    inference(clausify,[status(thm)],[f_1365_4]) ).

cnf(f_1365_12,plain,
    ( c_Divides_Odivmod__int(U_4724,U_4726) = hAPP(c_Divides_OnegateSnd,c_Divides_OposDivAlg(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4724),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4726)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4726))
    | ~ sP373(U_4724,U_4726) ),
    inference(clausify,[status(thm)],[f_1365_4]) ).

fof(f_1366_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_1366_2,plain,
    ! [U_4730,U_4729,U_4728,U_4727] :
      ( 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_4727),U_4729)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4728),U_4730))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4729),U_4730))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4727),U_4728)) ),
    inference(variable_rename,[status(thm)],[f_1366_1]) ).

fof(f_1366_3,plain,
    ! [U_4729,U_4730,U_4727,U_4728] :
      ( 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_4727),U_4729)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4728),U_4730))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4729),U_4730))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4727),U_4728)) ),
    inference(definitional_conversion,[status(esa)],[f_1366_2]) ).

cnf(f_1366_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_4727),U_4729)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4728),U_4730))),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4729),U_4730))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4727),U_4728)) ),
    inference(clausify,[status(thm)],[f_1366_3]) ).

fof(f_1367_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_1367_2,plain,
    ! [U_4734,U_4733,U_4732,U_4731] :
      ( 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_4731),U_4733)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4732),U_4734))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4731),U_4732)) ),
    inference(variable_rename,[status(thm)],[f_1367_1]) ).

fof(f_1367_3,plain,
    ! [U_4734,U_4732,U_4731,U_4733] :
      ( 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_4731),U_4733)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4732),U_4734))),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4731),U_4732)) ),
    inference(definitional_conversion,[status(esa)],[f_1367_2]) ).

cnf(f_1367_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_4731),U_4733)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4732),U_4734))),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4731),U_4732)) ),
    inference(clausify,[status(thm)],[f_1367_3]) ).

fof(f_1368_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_1368_2,plain,
    ! [U_4738,U_4737,U_4736,U_4735] :
      ( ( 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_4735),U_4736)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4737),U_4738))),c_Int_Ointrel))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4735),U_4738) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4737),U_4736) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4735),U_4738) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4737),U_4736)
        | ~ 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_4735),U_4736)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4737),U_4738))),c_Int_Ointrel)) ) ),
    inference(variable_rename,[status(thm)],[f_1368_1]) ).

fof(f_1368_3,plain,
    ( ! [U_4746,U_4744,U_4742,U_4740] :
        ( 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_4740),U_4742)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4744),U_4746))),c_Int_Ointrel))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4740),U_4746) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4744),U_4742) )
    & ! [U_4745,U_4743,U_4741,U_4739] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4739),U_4745) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4743),U_4741)
        | ~ 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_4739),U_4741)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4743),U_4745))),c_Int_Ointrel)) ) ),
    inference(miniscope,[status(thm)],[f_1368_2]) ).

fof(f_1368_4,plain,
    ( ! [U_4740,U_4742,U_4744,U_4746] :
        ( 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_4740),U_4742)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4744),U_4746))),c_Int_Ointrel))
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4740),U_4746) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4744),U_4742) )
    & ! [U_4741,U_4745,U_4739,U_4743] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4739),U_4745) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4743),U_4741)
        | ~ 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_4739),U_4741)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4743),U_4745))),c_Int_Ointrel)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1368_3]) ).

cnf(f_1368_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4739),U_4745) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4743),U_4741)
    | ~ 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_4739),U_4741)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4743),U_4745))),c_Int_Ointrel)) ),
    inference(clausify,[status(thm)],[f_1368_4]) ).

cnf(f_1368_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_4740),U_4742)),hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),U_4744),U_4746))),c_Int_Ointrel))
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4740),U_4746) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4744),U_4742) ),
    inference(clausify,[status(thm)],[f_1368_4]) ).

fof(f_1369_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_1369_2,plain,
    ! [U_4747] :
      ( 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_4747)) = 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_4747)))
      | ~ 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_4747))) ),
    inference(variable_rename,[status(thm)],[f_1369_1]) ).

fof(f_1369_3,plain,
    ! [U_4747] :
      ( 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_4747)) = 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_4747)))
      | ~ 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_4747))) ),
    inference(definitional_conversion,[status(esa)],[f_1369_2]) ).

cnf(f_1369_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_4747)) = 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_4747)))
    | ~ 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_4747))) ),
    inference(clausify,[status(thm)],[f_1369_3]) ).

fof(f_1370_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_1370_2,plain,
    ! [U_4748] :
      ( 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_4748)) = 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_4748)))
      | ~ 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_4748))) ),
    inference(variable_rename,[status(thm)],[f_1370_1]) ).

fof(f_1370_3,plain,
    ! [U_4748] :
      ( 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_4748)) = 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_4748)))
      | ~ 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_4748))) ),
    inference(definitional_conversion,[status(esa)],[f_1370_2]) ).

cnf(f_1370_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_4748)) = 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_4748)))
    | ~ 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_4748))) ),
    inference(clausify,[status(thm)],[f_1370_3]) ).

fof(f_1371_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_1371_2,plain,
    ! [U_4750,U_4749] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4749),U_4750) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_4749,U_4750)),
    inference(variable_rename,[status(thm)],[f_1371_1]) ).

fof(f_1371_3,plain,
    ! [U_4750,U_4749] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4749),U_4750) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_4749,U_4750)),
    inference(definitional_conversion,[status(esa)],[f_1371_2]) ).

cnf(f_1371_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4749),U_4750) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_4749,U_4750)),
    inference(clausify,[status(thm)],[f_1371_3]) ).

fof(f_1372_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_1372_2,plain,
    ! [U_4752,U_4751] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4751,U_4752) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_4751,U_4752)),
    inference(variable_rename,[status(thm)],[f_1372_1]) ).

fof(f_1372_3,plain,
    ! [U_4751,U_4752] : c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4751,U_4752) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_4751,U_4752)),
    inference(definitional_conversion,[status(esa)],[f_1372_2]) ).

cnf(f_1372_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4751,U_4752) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_Odivmod__int(U_4751,U_4752)),
    inference(clausify,[status(thm)],[f_1372_3]) ).

fof(f_1373_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_1373_2,plain,
    ! [U_4754,U_4753] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4753),U_4754) = 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_4753),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4754))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4754),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_4753)) ),
    inference(variable_rename,[status(thm)],[f_1373_1]) ).

fof(f_1373_3,plain,
    ! [U_4753,U_4754] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4753),U_4754) = 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_4753),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4754))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4754),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_4753)) ),
    inference(definitional_conversion,[status(esa)],[f_1373_2]) ).

cnf(f_1373_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4753),U_4754) = 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_4753),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4754))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4754),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_4753)) ),
    inference(clausify,[status(thm)],[f_1373_3]) ).

fof(f_1374_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_1374_2,plain,
    ! [U_4756,U_4755] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4755,U_4756) = 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_4755),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4756))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4756),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_4755)) ),
    inference(variable_rename,[status(thm)],[f_1374_1]) ).

fof(f_1374_3,plain,
    ! [U_4755,U_4756] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4755,U_4756) = 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_4755),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4756))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4756),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_4755)) ),
    inference(definitional_conversion,[status(esa)],[f_1374_2]) ).

cnf(f_1374_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4755,U_4756) = 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_4755),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4756))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4756),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_4755)) ),
    inference(clausify,[status(thm)],[f_1374_3]) ).

fof(f_1375_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_1375_2,plain,
    ! [U_4758,U_4757] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4757),U_4758) = 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_4757),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4758))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4758),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4757),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1375_1]) ).

fof(f_1375_3,plain,
    ! [U_4758,U_4757] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4757),U_4758) = 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_4757),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4758))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4758),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4757),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1375_2]) ).

cnf(f_1375_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4757),U_4758) = 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_4757),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4758))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4758),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4757),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1375_3]) ).

fof(f_1376_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_1376_2,plain,
    ! [U_4760,U_4759] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4759),U_4760)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4759),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4760)),
    inference(variable_rename,[status(thm)],[f_1376_1]) ).

fof(f_1376_3,plain,
    ! [U_4760,U_4759] : hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4759),U_4760)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4759),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4760)),
    inference(definitional_conversion,[status(esa)],[f_1376_2]) ).

cnf(f_1376_4,plain,
    hAPP(c_Divides_OnegateSnd,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4759),U_4760)) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_4759),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4760)),
    inference(clausify,[status(thm)],[f_1376_3]) ).

fof(f_1377_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_1377_2,plain,
    ! [U_4762,U_4761] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4761,U_4762) = 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_4761),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4762))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4762),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4761),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1377_1]) ).

fof(f_1377_3,plain,
    ! [U_4761,U_4762] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4761,U_4762) = 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_4761),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4762))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4762),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4761),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1377_2]) ).

cnf(f_1377_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4761,U_4762) = 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_4761),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4762))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4762),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4761),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1377_3]) ).

fof(f_1378_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_1378_2,plain,
    ! [U_4765,U_4764,U_4763] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4763,U_4764),hAPP(c_Divides_OnegateSnd,U_4765)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4763),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4764)),U_4765)) ),
    inference(variable_rename,[status(thm)],[f_1378_1]) ).

fof(f_1378_3,plain,
    ! [U_4763,U_4764,U_4765] :
      ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4763,U_4764),hAPP(c_Divides_OnegateSnd,U_4765)))
      | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4763),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4764)),U_4765)) ),
    inference(definitional_conversion,[status(esa)],[f_1378_2]) ).

cnf(f_1378_4,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__int__rel(U_4763,U_4764),hAPP(c_Divides_OnegateSnd,U_4765)))
    | ~ hBOOL(hAPP(c_Divides_Odivmod__int__rel(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4763),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4764)),U_4765)) ),
    inference(clausify,[status(thm)],[f_1378_3]) ).

fof(f_1379_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_1379_2,plain,
    ! [U_4767,U_4766] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4766),U_4767) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_4766,U_4767))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4767))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4766),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1379_1]) ).

fof(f_1379_3,plain,
    ! [U_4766,U_4767] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4766),U_4767) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_4766,U_4767))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4767))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4766),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1379_2]) ).

cnf(f_1379_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4766),U_4767) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_4766,U_4767))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4767))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4766),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1379_3]) ).

fof(f_1380_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_1380_2,plain,
    ! [U_4768] :
      ( 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_4768)) = 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_4768)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4768)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1380_1]) ).

fof(f_1380_3,plain,
    ! [U_4768] :
      ( 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_4768)) = 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_4768)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4768)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1380_2]) ).

cnf(f_1380_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_4768)) = 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_4768)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4768)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1380_3]) ).

fof(f_1381_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_1381_2,plain,
    ! [U_4770,U_4769] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4769,U_4770) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_4769,U_4770))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4770))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4769),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1381_1]) ).

fof(f_1381_3,plain,
    ! [U_4769,U_4770] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4769,U_4770) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_4769,U_4770))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4770))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4769),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1381_2]) ).

cnf(f_1381_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4769,U_4770) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OnegDivAlg(U_4769,U_4770))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4770))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4769),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1381_3]) ).

fof(f_1382_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_1382_2,plain,
    ! [U_4771] :
      ( 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_4771)) = 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_4771)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4771)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1382_1]) ).

fof(f_1382_3,plain,
    ! [U_4771] :
      ( 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_4771)) = 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_4771)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4771)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1382_2]) ).

cnf(f_1382_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_4771)) = 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_4771)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_4771)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1382_3]) ).

fof(f_1383_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_1383_2,plain,
    ! [U_4773,U_4772] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4772),U_4773) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_4772,U_4773))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4773))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4772)) ),
    inference(variable_rename,[status(thm)],[f_1383_1]) ).

fof(f_1383_3,plain,
    ! [U_4772,U_4773] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4772),U_4773) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_4772,U_4773))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4773))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4772)) ),
    inference(definitional_conversion,[status(esa)],[f_1383_2]) ).

cnf(f_1383_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_4772),U_4773) = hAPP(c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_4772,U_4773))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4773))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4772)) ),
    inference(clausify,[status(thm)],[f_1383_3]) ).

fof(f_1384_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_1384_2,plain,
    ! [U_4775,U_4774] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4774,U_4775) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_4774,U_4775))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4775))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4774)) ),
    inference(variable_rename,[status(thm)],[f_1384_1]) ).

fof(f_1384_3,plain,
    ! [U_4774,U_4775] :
      ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4774,U_4775) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_4774,U_4775))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4775))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4774)) ),
    inference(definitional_conversion,[status(esa)],[f_1384_2]) ).

cnf(f_1384_4,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_4774,U_4775) = hAPP(c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint),c_Divides_OposDivAlg(U_4774,U_4775))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4775))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_4774)) ),
    inference(clausify,[status(thm)],[f_1384_3]) ).

fof(f_1385_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_1385_2,plain,
    ! [U_4780,U_4779,U_4778,U_4777,U_4776] : c_Product__Type_Oprod_Oprod__size(U_4776,U_4777,U_4778,U_4779,U_4780) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_4778,hAPP(c_Product__Type_Ofst(U_4776,U_4777),U_4780))),hAPP(U_4779,hAPP(c_Product__Type_Osnd(U_4776,U_4777),U_4780)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1385_1]) ).

fof(f_1385_3,plain,
    ! [U_4776,U_4777,U_4778,U_4779,U_4780] : c_Product__Type_Oprod_Oprod__size(U_4776,U_4777,U_4778,U_4779,U_4780) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_4778,hAPP(c_Product__Type_Ofst(U_4776,U_4777),U_4780))),hAPP(U_4779,hAPP(c_Product__Type_Osnd(U_4776,U_4777),U_4780)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_1385_2]) ).

cnf(f_1385_4,plain,
    c_Product__Type_Oprod_Oprod__size(U_4776,U_4777,U_4778,U_4779,U_4780) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_4778,hAPP(c_Product__Type_Ofst(U_4776,U_4777),U_4780))),hAPP(U_4779,hAPP(c_Product__Type_Osnd(U_4776,U_4777),U_4780)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1385_3]) ).

fof(f_1386_1,plain,
    ! [T_b,T_c,V_x_2,V_y_2,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(V_Pa_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_Pa_2,V_y_2),V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_exI__realizer]) ).

fof(f_1386_2,plain,
    ! [U_4785,U_4784,U_4783,U_4782,U_4781] :
      ( hBOOL(hAPP(hAPP(U_4781,hAPP(c_Product__Type_Osnd(U_4784,U_4785),hAPP(hAPP(c_Product__Type_OPair(U_4784,U_4785),U_4783),U_4782))),hAPP(c_Product__Type_Ofst(U_4784,U_4785),hAPP(hAPP(c_Product__Type_OPair(U_4784,U_4785),U_4783),U_4782))))
      | ~ hBOOL(hAPP(hAPP(U_4781,U_4782),U_4783)) ),
    inference(variable_rename,[status(thm)],[f_1386_1]) ).

fof(f_1386_3,plain,
    ! [U_4782,U_4783,U_4784,U_4785,U_4781] :
      ( hBOOL(hAPP(hAPP(U_4781,hAPP(c_Product__Type_Osnd(U_4784,U_4785),hAPP(hAPP(c_Product__Type_OPair(U_4784,U_4785),U_4783),U_4782))),hAPP(c_Product__Type_Ofst(U_4784,U_4785),hAPP(hAPP(c_Product__Type_OPair(U_4784,U_4785),U_4783),U_4782))))
      | ~ hBOOL(hAPP(hAPP(U_4781,U_4782),U_4783)) ),
    inference(definitional_conversion,[status(esa)],[f_1386_2]) ).

cnf(f_1386_4,plain,
    ( hBOOL(hAPP(hAPP(U_4781,hAPP(c_Product__Type_Osnd(U_4784,U_4785),hAPP(hAPP(c_Product__Type_OPair(U_4784,U_4785),U_4783),U_4782))),hAPP(c_Product__Type_Ofst(U_4784,U_4785),hAPP(hAPP(c_Product__Type_OPair(U_4784,U_4785),U_4783),U_4782))))
    | ~ hBOOL(hAPP(hAPP(U_4781,U_4782),U_4783)) ),
    inference(clausify,[status(thm)],[f_1386_3]) ).

fof(f_1387_1,plain,
    ! [T_c,T_b,V_q_2,V_Qa_2,V_p_2,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Qa_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_Pa_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_Qa_2,V_q_2))
      | ~ hBOOL(hAPP(V_Pa_2,V_p_2)) ),
    inference(fof_nnf,[status(thm)],[fact_conjI__realizer]) ).

fof(f_1387_2,plain,
    ! [U_4791,U_4790,U_4789,U_4788,U_4787,U_4786] :
      ( ( hBOOL(hAPP(U_4788,hAPP(c_Product__Type_Osnd(U_4790,U_4791),hAPP(hAPP(c_Product__Type_OPair(U_4790,U_4791),U_4787),U_4789))))
        & hBOOL(hAPP(U_4786,hAPP(c_Product__Type_Ofst(U_4790,U_4791),hAPP(hAPP(c_Product__Type_OPair(U_4790,U_4791),U_4787),U_4789)))) )
      | ~ hBOOL(hAPP(U_4788,U_4789))
      | ~ hBOOL(hAPP(U_4786,U_4787)) ),
    inference(variable_rename,[status(thm)],[f_1387_1]) ).

fof(f_1387_3,plain,
    ( ! [U_4787,U_4786,U_4788,U_4789,U_4790,U_4791] :
        ( hBOOL(hAPP(U_4788,hAPP(c_Product__Type_Osnd(U_4790,U_4791),hAPP(hAPP(c_Product__Type_OPair(U_4790,U_4791),U_4787),U_4789))))
        | ~ sP374(U_4787,U_4786,U_4788,U_4789,U_4790,U_4791) )
    & ! [U_4787,U_4786,U_4788,U_4789,U_4790,U_4791] :
        ( hBOOL(hAPP(U_4786,hAPP(c_Product__Type_Ofst(U_4790,U_4791),hAPP(hAPP(c_Product__Type_OPair(U_4790,U_4791),U_4787),U_4789))))
        | ~ sP374(U_4787,U_4786,U_4788,U_4789,U_4790,U_4791) )
    & ! [U_4787,U_4786,U_4788,U_4789,U_4790,U_4791] :
        ( sP374(U_4787,U_4786,U_4788,U_4789,U_4790,U_4791)
        | ~ hBOOL(hAPP(U_4788,U_4789))
        | ~ hBOOL(hAPP(U_4786,U_4787)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP374])],[f_1387_2]) ).

cnf(f_1387_4,plain,
    ( sP374(U_4787,U_4786,U_4788,U_4789,U_4790,U_4791)
    | ~ hBOOL(hAPP(U_4788,U_4789))
    | ~ hBOOL(hAPP(U_4786,U_4787)) ),
    inference(clausify,[status(thm)],[f_1387_3]) ).

cnf(f_1387_5,plain,
    ( hBOOL(hAPP(U_4786,hAPP(c_Product__Type_Ofst(U_4790,U_4791),hAPP(hAPP(c_Product__Type_OPair(U_4790,U_4791),U_4787),U_4789))))
    | ~ sP374(U_4787,U_4786,U_4788,U_4789,U_4790,U_4791) ),
    inference(clausify,[status(thm)],[f_1387_3]) ).

cnf(f_1387_6,plain,
    ( hBOOL(hAPP(U_4788,hAPP(c_Product__Type_Osnd(U_4790,U_4791),hAPP(hAPP(c_Product__Type_OPair(U_4790,U_4791),U_4787),U_4789))))
    | ~ sP374(U_4787,U_4786,U_4788,U_4789,U_4790,U_4791) ),
    inference(clausify,[status(thm)],[f_1387_3]) ).

fof(f_1388_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_1388_2,plain,
    ! [U_4794,U_4793,U_4792] : hAPP(hAPP(c_Product__Type_OPair(U_4792,U_4793),hAPP(c_Product__Type_Ofst(U_4792,U_4793),U_4794)),hAPP(c_Product__Type_Osnd(U_4792,U_4793),U_4794)) = U_4794,
    inference(variable_rename,[status(thm)],[f_1388_1]) ).

fof(f_1388_3,plain,
    ! [U_4792,U_4793,U_4794] : hAPP(hAPP(c_Product__Type_OPair(U_4792,U_4793),hAPP(c_Product__Type_Ofst(U_4792,U_4793),U_4794)),hAPP(c_Product__Type_Osnd(U_4792,U_4793),U_4794)) = U_4794,
    inference(definitional_conversion,[status(esa)],[f_1388_2]) ).

cnf(f_1388_4,plain,
    hAPP(hAPP(c_Product__Type_OPair(U_4792,U_4793),hAPP(c_Product__Type_Ofst(U_4792,U_4793),U_4794)),hAPP(c_Product__Type_Osnd(U_4792,U_4793),U_4794)) = U_4794,
    inference(clausify,[status(thm)],[f_1388_3]) ).

fof(f_1389_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_1389_2,plain,
    ! [U_4797,U_4796,U_4795] : U_4795 = hAPP(hAPP(c_Product__Type_OPair(U_4796,U_4797),hAPP(c_Product__Type_Ofst(U_4796,U_4797),U_4795)),hAPP(c_Product__Type_Osnd(U_4796,U_4797),U_4795)),
    inference(variable_rename,[status(thm)],[f_1389_1]) ).

fof(f_1389_3,plain,
    ! [U_4795,U_4796,U_4797] : U_4795 = hAPP(hAPP(c_Product__Type_OPair(U_4796,U_4797),hAPP(c_Product__Type_Ofst(U_4796,U_4797),U_4795)),hAPP(c_Product__Type_Osnd(U_4796,U_4797),U_4795)),
    inference(definitional_conversion,[status(esa)],[f_1389_2]) ).

cnf(f_1389_4,plain,
    U_4795 = hAPP(hAPP(c_Product__Type_OPair(U_4796,U_4797),hAPP(c_Product__Type_Ofst(U_4796,U_4797),U_4795)),hAPP(c_Product__Type_Osnd(U_4796,U_4797),U_4795)),
    inference(clausify,[status(thm)],[f_1389_3]) ).

fof(f_1390_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_1390_2,plain,
    ! [U_4801,U_4800,U_4799,U_4798] :
      ( U_4800 = U_4801
      | hAPP(c_Product__Type_Osnd(U_4798,U_4799),U_4800) != hAPP(c_Product__Type_Osnd(U_4798,U_4799),U_4801)
      | hAPP(c_Product__Type_Ofst(U_4798,U_4799),U_4800) != hAPP(c_Product__Type_Ofst(U_4798,U_4799),U_4801) ),
    inference(variable_rename,[status(thm)],[f_1390_1]) ).

fof(f_1390_3,plain,
    ! [U_4798,U_4799,U_4800,U_4801] :
      ( U_4800 = U_4801
      | hAPP(c_Product__Type_Osnd(U_4798,U_4799),U_4800) != hAPP(c_Product__Type_Osnd(U_4798,U_4799),U_4801)
      | hAPP(c_Product__Type_Ofst(U_4798,U_4799),U_4800) != hAPP(c_Product__Type_Ofst(U_4798,U_4799),U_4801) ),
    inference(definitional_conversion,[status(esa)],[f_1390_2]) ).

cnf(f_1390_4,plain,
    ( U_4800 = U_4801
    | hAPP(c_Product__Type_Osnd(U_4798,U_4799),U_4800) != hAPP(c_Product__Type_Osnd(U_4798,U_4799),U_4801)
    | hAPP(c_Product__Type_Ofst(U_4798,U_4799),U_4800) != hAPP(c_Product__Type_Ofst(U_4798,U_4799),U_4801) ),
    inference(clausify,[status(thm)],[f_1390_3]) ).

fof(f_1391_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_1391_2,plain,
    ! [U_4803,U_4802] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4802),U_4803) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_4802,U_4803)),
    inference(variable_rename,[status(thm)],[f_1391_1]) ).

fof(f_1391_3,plain,
    ! [U_4803,U_4802] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4802),U_4803) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_4802,U_4803)),
    inference(definitional_conversion,[status(esa)],[f_1391_2]) ).

cnf(f_1391_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_4802),U_4803) = hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_4802,U_4803)),
    inference(clausify,[status(thm)],[f_1391_3]) ).

fof(f_1392_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_1392_2,plain,
    ! [U_4805,U_4804] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4804,U_4805) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_4804,U_4805)),
    inference(variable_rename,[status(thm)],[f_1392_1]) ).

fof(f_1392_3,plain,
    ! [U_4804,U_4805] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4804,U_4805) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_4804,U_4805)),
    inference(definitional_conversion,[status(esa)],[f_1392_2]) ).

cnf(f_1392_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_4804,U_4805) = hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat(U_4804,U_4805)),
    inference(clausify,[status(thm)],[f_1392_3]) ).

fof(f_1393_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_1393_2,plain,
    ! [U_4808,U_4807,U_4806] :
      ( ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4806,U_4807),U_4808))
        | ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4808)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4807),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4808))) )
              & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4807)) )
            | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4808)),U_4807))
                | ~ 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_4808))) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4807)) ) )
          & U_4807 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_4808) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_4807 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | U_4806 != 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_4808)),U_4807)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4808)) )
      & ( ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4808)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4807),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4808))) )
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4807)) )
              & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4808)),U_4807))
                  & 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_4808))) )
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4807)) ) )
            | U_4807 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_4808) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_4807 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & U_4806 = 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_4808)),U_4807)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4808)) )
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4806,U_4807),U_4808)) ) ),
    inference(variable_rename,[status(thm)],[f_1393_1]) ).

fof(f_1393_3,plain,
    ( ! [U_4814,U_4812,U_4810] :
        ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4810,U_4812),U_4814))
        | ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4814)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4812),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4814))) )
              & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4812)) )
            | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4814)),U_4812))
                | ~ 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_4814))) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4812)) ) )
          & U_4812 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_4814) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & U_4812 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        | U_4810 != 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_4814)),U_4812)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4814)) )
    & ! [U_4813,U_4811,U_4809] :
        ( ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4813)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4811),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4813))) )
                | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4811)) )
              & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4813)),U_4811))
                  & 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_4813))) )
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4811)) ) )
            | U_4811 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_4813) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | U_4811 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & U_4809 = 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_4813)),U_4811)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4813)) )
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4809,U_4811),U_4813)) ) ),
    inference(miniscope,[status(thm)],[f_1393_2]) ).

fof(f_1393_4,plain,
    ( ! [U_4814,U_4812] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4814)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4812),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4814)))
        | ~ sP381(U_4814,U_4812) )
    & ! [U_4814,U_4812] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4812))
        | ~ sP381(U_4814,U_4812) )
    & ! [U_4814,U_4812] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4814)),U_4812))
        | ~ 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_4814)))
        | ~ sP380(U_4814,U_4812) )
    & ! [U_4814,U_4812] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4812))
        | ~ sP380(U_4814,U_4812) )
    & ! [U_4814,U_4812] :
        ( sP381(U_4814,U_4812)
        | sP380(U_4814,U_4812)
        | ~ sP382(U_4814,U_4812) )
    & ! [U_4814,U_4812] :
        ( U_4812 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP382(U_4814,U_4812) )
    & ! [U_4814,U_4812] :
        ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_4814) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP379(U_4814,U_4812) )
    & ! [U_4814,U_4812] :
        ( U_4812 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP379(U_4814,U_4812) )
    & ! [U_4811,U_4813] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4813)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | ~ sP376(U_4811,U_4813) )
    & ! [U_4811,U_4813] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4811),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4813)))
        | ~ sP376(U_4811,U_4813) )
    & ! [U_4811,U_4813] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4813)),U_4811))
        | ~ sP375(U_4811,U_4813) )
    & ! [U_4811,U_4813] :
        ( 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_4813)))
        | ~ sP375(U_4811,U_4813) )
    & ! [U_4811,U_4813] :
        ( sP376(U_4811,U_4813)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4811))
        | ~ sP377(U_4811,U_4813) )
    & ! [U_4811,U_4813] :
        ( sP375(U_4811,U_4813)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4811))
        | ~ sP377(U_4811,U_4813) )
    & ! [U_4811,U_4809,U_4813] :
        ( sP377(U_4811,U_4813)
        | U_4811 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP378(U_4811,U_4809,U_4813) )
    & ! [U_4811,U_4809,U_4813] :
        ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_4813) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_4811 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP378(U_4811,U_4809,U_4813) )
    & ! [U_4811,U_4809,U_4813] :
        ( U_4809 = 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_4813)),U_4811)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4813))
        | ~ sP378(U_4811,U_4809,U_4813) )
    & ! [U_4810,U_4814,U_4812] :
        ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4810,U_4812),U_4814))
        | sP382(U_4814,U_4812)
        | sP379(U_4814,U_4812)
        | U_4810 != 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_4814)),U_4812)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4814)) )
    & ! [U_4811,U_4809,U_4813] :
        ( sP378(U_4811,U_4809,U_4813)
        | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4809,U_4811),U_4813)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP375,sP376,sP377,sP378,sP379,sP380,sP381,sP382])],[f_1393_3]) ).

cnf(f_1393_5,plain,
    ( sP378(U_4811,U_4809,U_4813)
    | ~ hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4809,U_4811),U_4813)) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_6,plain,
    ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(U_4810,U_4812),U_4814))
    | sP382(U_4814,U_4812)
    | sP379(U_4814,U_4812)
    | U_4810 != 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_4814)),U_4812)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4814)) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_7,plain,
    ( U_4809 = 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_4813)),U_4811)),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4813))
    | ~ sP378(U_4811,U_4809,U_4813) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_8,plain,
    ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_4813) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_4811 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP378(U_4811,U_4809,U_4813) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_9,plain,
    ( sP377(U_4811,U_4813)
    | U_4811 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP378(U_4811,U_4809,U_4813) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_10,plain,
    ( sP375(U_4811,U_4813)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4811))
    | ~ sP377(U_4811,U_4813) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_11,plain,
    ( sP376(U_4811,U_4813)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4811))
    | ~ sP377(U_4811,U_4813) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_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_4813)))
    | ~ sP375(U_4811,U_4813) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_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_4813)),U_4811))
    | ~ sP375(U_4811,U_4813) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_14,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4811),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4813)))
    | ~ sP376(U_4811,U_4813) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_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_4813)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ sP376(U_4811,U_4813) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_16,plain,
    ( U_4812 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP379(U_4814,U_4812) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_17,plain,
    ( hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),U_4814) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP379(U_4814,U_4812) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_18,plain,
    ( U_4812 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP382(U_4814,U_4812) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_19,plain,
    ( sP381(U_4814,U_4812)
    | sP380(U_4814,U_4812)
    | ~ sP382(U_4814,U_4812) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_20,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4812))
    | ~ sP380(U_4814,U_4812) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_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_4814)),U_4812))
    | ~ 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_4814)))
    | ~ sP380(U_4814,U_4812) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_22,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_4812))
    | ~ sP381(U_4814,U_4812) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

cnf(f_1393_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_4814)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4812),hAPP(c_Product__Type_Osnd(tc_Nat_Onat,tc_Nat_Onat),U_4814)))
    | ~ sP381(U_4814,U_4812) ),
    inference(clausify,[status(thm)],[f_1393_4]) ).

fof(f_1394_1,plain,
    ! [T_c,T_b,V_Pa_2] :
      ( ( ! [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
        | ? [B_a,B_b] : ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b))) )
      & ( ! [B_a,B_b] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_a),B_b)))
        | ? [B_x1] : ~ hBOOL(hAPP(V_Pa_2,B_x1)) ) ),
    inference(fof_nnf,[status(thm)],[fact_split__paired__All]) ).

fof(f_1394_2,plain,
    ! [U_4823,U_4822,U_4821] :
      ( ( ! [U_4820] : hBOOL(hAPP(U_4821,U_4820))
        | ? [U_4819,U_4818] : ~ hBOOL(hAPP(U_4821,hAPP(hAPP(c_Product__Type_OPair(U_4822,U_4823),U_4819),U_4818))) )
      & ( ! [U_4817,U_4816] : hBOOL(hAPP(U_4821,hAPP(hAPP(c_Product__Type_OPair(U_4822,U_4823),U_4817),U_4816)))
        | ? [U_4815] : ~ hBOOL(hAPP(U_4821,U_4815)) ) ),
    inference(variable_rename,[status(thm)],[f_1394_1]) ).

fof(f_1394_3,plain,
    ( ! [U_4829,U_4827,U_4825] :
        ( ! [U_4820] : hBOOL(hAPP(U_4825,U_4820))
        | ? [U_4819,U_4818] : ~ hBOOL(hAPP(U_4825,hAPP(hAPP(c_Product__Type_OPair(U_4827,U_4829),U_4819),U_4818))) )
    & ! [U_4828,U_4826,U_4824] :
        ( ! [U_4817,U_4816] : hBOOL(hAPP(U_4824,hAPP(hAPP(c_Product__Type_OPair(U_4826,U_4828),U_4817),U_4816)))
        | ? [U_4815] : ~ hBOOL(hAPP(U_4824,U_4815)) ) ),
    inference(miniscope,[status(thm)],[f_1394_2]) ).

fof(f_1394_4,plain,
    ( ! [U_4829,U_4827,U_4825] :
        ( ! [U_4820] : hBOOL(hAPP(U_4825,U_4820))
        | ? [U_4819,U_4818] : ~ hBOOL(hAPP(U_4825,hAPP(hAPP(c_Product__Type_OPair(U_4827,U_4829),U_4819),U_4818))) )
    & ! [U_4828,U_4826,U_4824] :
        ( ! [U_4817,U_4816] : hBOOL(hAPP(U_4824,hAPP(hAPP(c_Product__Type_OPair(U_4826,U_4828),U_4817),U_4816)))
        | ~ hBOOL(hAPP(U_4824,sK70(U_4828,U_4826,U_4824))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK70]),skolemize(U_4815,sK70(U_4828,U_4826,U_4824))],[f_1394_3]) ).

fof(f_1394_5,plain,
    ( ! [U_4829,U_4827,U_4825] :
        ( ! [U_4820] : hBOOL(hAPP(U_4825,U_4820))
        | ? [U_4818] : ~ hBOOL(hAPP(U_4825,hAPP(hAPP(c_Product__Type_OPair(U_4827,U_4829),sK71(U_4829,U_4827,U_4825)),U_4818))) )
    & ! [U_4828,U_4826,U_4824] :
        ( ! [U_4817,U_4816] : hBOOL(hAPP(U_4824,hAPP(hAPP(c_Product__Type_OPair(U_4826,U_4828),U_4817),U_4816)))
        | ~ hBOOL(hAPP(U_4824,sK70(U_4828,U_4826,U_4824))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK71]),skolemize(U_4819,sK71(U_4829,U_4827,U_4825))],[f_1394_4]) ).

fof(f_1394_6,plain,
    ( ! [U_4829,U_4827,U_4825] :
        ( ! [U_4820] : hBOOL(hAPP(U_4825,U_4820))
        | ~ hBOOL(hAPP(U_4825,hAPP(hAPP(c_Product__Type_OPair(U_4827,U_4829),sK71(U_4829,U_4827,U_4825)),sK72(U_4829,U_4827,U_4825)))) )
    & ! [U_4828,U_4826,U_4824] :
        ( ! [U_4817,U_4816] : hBOOL(hAPP(U_4824,hAPP(hAPP(c_Product__Type_OPair(U_4826,U_4828),U_4817),U_4816)))
        | ~ hBOOL(hAPP(U_4824,sK70(U_4828,U_4826,U_4824))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK72]),skolemize(U_4818,sK72(U_4829,U_4827,U_4825))],[f_1394_5]) ).

fof(f_1394_7,plain,
    ( ! [U_4829,U_4820,U_4827,U_4825] :
        ( hBOOL(hAPP(U_4825,U_4820))
        | ~ hBOOL(hAPP(U_4825,hAPP(hAPP(c_Product__Type_OPair(U_4827,U_4829),sK71(U_4829,U_4827,U_4825)),sK72(U_4829,U_4827,U_4825)))) )
    & ! [U_4816,U_4824,U_4817,U_4826,U_4828] :
        ( hBOOL(hAPP(U_4824,hAPP(hAPP(c_Product__Type_OPair(U_4826,U_4828),U_4817),U_4816)))
        | ~ hBOOL(hAPP(U_4824,sK70(U_4828,U_4826,U_4824))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1394_6]) ).

cnf(f_1394_8,plain,
    ( hBOOL(hAPP(U_4824,hAPP(hAPP(c_Product__Type_OPair(U_4826,U_4828),U_4817),U_4816)))
    | ~ hBOOL(hAPP(U_4824,sK70(U_4828,U_4826,U_4824))) ),
    inference(clausify,[status(thm)],[f_1394_7]) ).

cnf(f_1394_9,plain,
    ( hBOOL(hAPP(U_4825,U_4820))
    | ~ hBOOL(hAPP(U_4825,hAPP(hAPP(c_Product__Type_OPair(U_4827,U_4829),sK71(U_4829,U_4827,U_4825)),sK72(U_4829,U_4827,U_4825)))) ),
    inference(clausify,[status(thm)],[f_1394_7]) ).

fof(f_1395_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_1395_2,plain,
    ! [U_4835,U_4834,U_4833,U_4832,U_4831,U_4830] :
      ( ( hAPP(hAPP(c_Product__Type_OPair(U_4830,U_4831),U_4832),U_4833) = hAPP(hAPP(c_Product__Type_OPair(U_4830,U_4831),U_4834),U_4835)
        | U_4833 != U_4835
        | U_4832 != U_4834 )
      & ( ( U_4833 = U_4835
          & U_4832 = U_4834 )
        | hAPP(hAPP(c_Product__Type_OPair(U_4830,U_4831),U_4832),U_4833) != hAPP(hAPP(c_Product__Type_OPair(U_4830,U_4831),U_4834),U_4835) ) ),
    inference(variable_rename,[status(thm)],[f_1395_1]) ).

fof(f_1395_3,plain,
    ( ! [U_4847,U_4845,U_4843,U_4841] :
        ( ! [U_4839,U_4837] : hAPP(hAPP(c_Product__Type_OPair(U_4837,U_4839),U_4841),U_4843) = hAPP(hAPP(c_Product__Type_OPair(U_4837,U_4839),U_4845),U_4847)
        | U_4843 != U_4847
        | U_4841 != U_4845 )
    & ! [U_4846,U_4844,U_4842,U_4840] :
        ( ! [U_4838,U_4836] : hAPP(hAPP(c_Product__Type_OPair(U_4836,U_4838),U_4840),U_4842) != hAPP(hAPP(c_Product__Type_OPair(U_4836,U_4838),U_4844),U_4846)
        | ( U_4842 = U_4846
          & U_4840 = U_4844 ) ) ),
    inference(miniscope,[status(thm)],[f_1395_2]) ).

fof(f_1395_4,plain,
    ( ! [U_4840,U_4842,U_4846,U_4844] :
        ( U_4842 = U_4846
        | ~ sP383(U_4840,U_4842,U_4846,U_4844) )
    & ! [U_4840,U_4842,U_4846,U_4844] :
        ( U_4840 = U_4844
        | ~ sP383(U_4840,U_4842,U_4846,U_4844) )
    & ! [U_4845,U_4841,U_4839,U_4843,U_4837,U_4847] :
        ( hAPP(hAPP(c_Product__Type_OPair(U_4837,U_4839),U_4841),U_4843) = hAPP(hAPP(c_Product__Type_OPair(U_4837,U_4839),U_4845),U_4847)
        | U_4843 != U_4847
        | U_4841 != U_4845 )
    & ! [U_4840,U_4842,U_4838,U_4836,U_4846,U_4844] :
        ( hAPP(hAPP(c_Product__Type_OPair(U_4836,U_4838),U_4840),U_4842) != hAPP(hAPP(c_Product__Type_OPair(U_4836,U_4838),U_4844),U_4846)
        | sP383(U_4840,U_4842,U_4846,U_4844) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP383])],[f_1395_3]) ).

cnf(f_1395_5,plain,
    ( hAPP(hAPP(c_Product__Type_OPair(U_4836,U_4838),U_4840),U_4842) != hAPP(hAPP(c_Product__Type_OPair(U_4836,U_4838),U_4844),U_4846)
    | sP383(U_4840,U_4842,U_4846,U_4844) ),
    inference(clausify,[status(thm)],[f_1395_4]) ).

cnf(f_1395_6,plain,
    ( hAPP(hAPP(c_Product__Type_OPair(U_4837,U_4839),U_4841),U_4843) = hAPP(hAPP(c_Product__Type_OPair(U_4837,U_4839),U_4845),U_4847)
    | U_4843 != U_4847
    | U_4841 != U_4845 ),
    inference(clausify,[status(thm)],[f_1395_4]) ).

cnf(f_1395_7,plain,
    ( U_4840 = U_4844
    | ~ sP383(U_4840,U_4842,U_4846,U_4844) ),
    inference(clausify,[status(thm)],[f_1395_4]) ).

cnf(f_1395_8,plain,
    ( U_4842 = U_4846
    | ~ sP383(U_4840,U_4842,U_4846,U_4844) ),
    inference(clausify,[status(thm)],[f_1395_4]) ).

fof(f_1396_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_1396_2,plain,
    ! [U_4853,U_4852,U_4851,U_4850,U_4849,U_4848] :
      ( ( U_4851 = U_4853
        & U_4850 = U_4852 )
      | hAPP(hAPP(c_Product__Type_OPair(U_4848,U_4849),U_4850),U_4851) != hAPP(hAPP(c_Product__Type_OPair(U_4848,U_4849),U_4852),U_4853) ),
    inference(variable_rename,[status(thm)],[f_1396_1]) ).

fof(f_1396_3,plain,
    ! [U_4853,U_4852,U_4851,U_4850] :
      ( ! [U_4849,U_4848] : hAPP(hAPP(c_Product__Type_OPair(U_4848,U_4849),U_4850),U_4851) != hAPP(hAPP(c_Product__Type_OPair(U_4848,U_4849),U_4852),U_4853)
      | ( U_4851 = U_4853
        & U_4850 = U_4852 ) ),
    inference(miniscope,[status(thm)],[f_1396_2]) ).

fof(f_1396_4,plain,
    ( ! [U_4852,U_4853,U_4850,U_4851] :
        ( U_4851 = U_4853
        | ~ sP384(U_4852,U_4853,U_4850,U_4851) )
    & ! [U_4852,U_4853,U_4850,U_4851] :
        ( U_4850 = U_4852
        | ~ sP384(U_4852,U_4853,U_4850,U_4851) )
    & ! [U_4849,U_4852,U_4853,U_4848,U_4850,U_4851] :
        ( hAPP(hAPP(c_Product__Type_OPair(U_4848,U_4849),U_4850),U_4851) != hAPP(hAPP(c_Product__Type_OPair(U_4848,U_4849),U_4852),U_4853)
        | sP384(U_4852,U_4853,U_4850,U_4851) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP384])],[f_1396_3]) ).

cnf(f_1396_5,plain,
    ( hAPP(hAPP(c_Product__Type_OPair(U_4848,U_4849),U_4850),U_4851) != hAPP(hAPP(c_Product__Type_OPair(U_4848,U_4849),U_4852),U_4853)
    | sP384(U_4852,U_4853,U_4850,U_4851) ),
    inference(clausify,[status(thm)],[f_1396_4]) ).

cnf(f_1396_6,plain,
    ( U_4850 = U_4852
    | ~ sP384(U_4852,U_4853,U_4850,U_4851) ),
    inference(clausify,[status(thm)],[f_1396_4]) ).

cnf(f_1396_7,plain,
    ( U_4851 = U_4853
    | ~ sP384(U_4852,U_4853,U_4850,U_4851) ),
    inference(clausify,[status(thm)],[f_1396_4]) ).

fof(f_1397_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_1397_2,plain,
    ! [U_4857,U_4856,U_4855,U_4854] : hAPP(c_Product__Type_Ofst(U_4854,U_4855),hAPP(hAPP(c_Product__Type_OPair(U_4854,U_4855),U_4856),U_4857)) = U_4856,
    inference(variable_rename,[status(thm)],[f_1397_1]) ).

fof(f_1397_3,plain,
    ! [U_4855,U_4854,U_4856,U_4857] : hAPP(c_Product__Type_Ofst(U_4854,U_4855),hAPP(hAPP(c_Product__Type_OPair(U_4854,U_4855),U_4856),U_4857)) = U_4856,
    inference(definitional_conversion,[status(esa)],[f_1397_2]) ).

cnf(f_1397_4,plain,
    hAPP(c_Product__Type_Ofst(U_4854,U_4855),hAPP(hAPP(c_Product__Type_OPair(U_4854,U_4855),U_4856),U_4857)) = U_4856,
    inference(clausify,[status(thm)],[f_1397_3]) ).

fof(f_1398_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_1398_2,plain,
    ! [U_4862,U_4861,U_4860,U_4859,U_4858] :
      ( U_4860 = U_4862
      | hAPP(c_Product__Type_Ofst(U_4858,U_4859),hAPP(hAPP(c_Product__Type_OPair(U_4858,U_4859),U_4860),U_4861)) != U_4862 ),
    inference(variable_rename,[status(thm)],[f_1398_1]) ).

fof(f_1398_3,plain,
    ! [U_4862,U_4861,U_4860] :
      ( ! [U_4859,U_4858] : hAPP(c_Product__Type_Ofst(U_4858,U_4859),hAPP(hAPP(c_Product__Type_OPair(U_4858,U_4859),U_4860),U_4861)) != U_4862
      | U_4860 = U_4862 ),
    inference(miniscope,[status(thm)],[f_1398_2]) ).

fof(f_1398_4,plain,
    ! [U_4858,U_4859,U_4860,U_4861,U_4862] :
      ( hAPP(c_Product__Type_Ofst(U_4858,U_4859),hAPP(hAPP(c_Product__Type_OPair(U_4858,U_4859),U_4860),U_4861)) != U_4862
      | U_4860 = U_4862 ),
    inference(definitional_conversion,[status(esa)],[f_1398_3]) ).

cnf(f_1398_5,plain,
    ( hAPP(c_Product__Type_Ofst(U_4858,U_4859),hAPP(hAPP(c_Product__Type_OPair(U_4858,U_4859),U_4860),U_4861)) != U_4862
    | U_4860 = U_4862 ),
    inference(clausify,[status(thm)],[f_1398_4]) ).

fof(f_1399_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_1399_2,plain,
    ! [U_4866,U_4865,U_4864,U_4863] : hAPP(c_Product__Type_Osnd(U_4863,U_4864),hAPP(hAPP(c_Product__Type_OPair(U_4863,U_4864),U_4865),U_4866)) = U_4866,
    inference(variable_rename,[status(thm)],[f_1399_1]) ).

fof(f_1399_3,plain,
    ! [U_4863,U_4864,U_4865,U_4866] : hAPP(c_Product__Type_Osnd(U_4863,U_4864),hAPP(hAPP(c_Product__Type_OPair(U_4863,U_4864),U_4865),U_4866)) = U_4866,
    inference(definitional_conversion,[status(esa)],[f_1399_2]) ).

cnf(f_1399_4,plain,
    hAPP(c_Product__Type_Osnd(U_4863,U_4864),hAPP(hAPP(c_Product__Type_OPair(U_4863,U_4864),U_4865),U_4866)) = U_4866,
    inference(clausify,[status(thm)],[f_1399_3]) ).

fof(f_1400_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_1400_2,plain,
    ! [U_4871,U_4870,U_4869,U_4868,U_4867] :
      ( U_4870 = U_4871
      | hAPP(c_Product__Type_Osnd(U_4867,U_4868),hAPP(hAPP(c_Product__Type_OPair(U_4867,U_4868),U_4869),U_4870)) != U_4871 ),
    inference(variable_rename,[status(thm)],[f_1400_1]) ).

fof(f_1400_3,plain,
    ! [U_4871,U_4870] :
      ( ! [U_4869,U_4868,U_4867] : hAPP(c_Product__Type_Osnd(U_4867,U_4868),hAPP(hAPP(c_Product__Type_OPair(U_4867,U_4868),U_4869),U_4870)) != U_4871
      | U_4870 = U_4871 ),
    inference(miniscope,[status(thm)],[f_1400_2]) ).

fof(f_1400_4,plain,
    ! [U_4867,U_4868,U_4869,U_4870,U_4871] :
      ( hAPP(c_Product__Type_Osnd(U_4867,U_4868),hAPP(hAPP(c_Product__Type_OPair(U_4867,U_4868),U_4869),U_4870)) != U_4871
      | U_4870 = U_4871 ),
    inference(definitional_conversion,[status(esa)],[f_1400_3]) ).

cnf(f_1400_5,plain,
    ( hAPP(c_Product__Type_Osnd(U_4867,U_4868),hAPP(hAPP(c_Product__Type_OPair(U_4867,U_4868),U_4869),U_4870)) != U_4871
    | U_4870 = U_4871 ),
    inference(clausify,[status(thm)],[f_1400_4]) ).

fof(f_1401_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_1401_2,plain,
    ! [U_4875,U_4874,U_4873,U_4872] :
      ( ( U_4872 = U_4873
        | hAPP(c_Product__Type_Osnd(U_4874,U_4875),U_4872) != hAPP(c_Product__Type_Osnd(U_4874,U_4875),U_4873)
        | hAPP(c_Product__Type_Ofst(U_4874,U_4875),U_4872) != hAPP(c_Product__Type_Ofst(U_4874,U_4875),U_4873) )
      & ( ( hAPP(c_Product__Type_Osnd(U_4874,U_4875),U_4872) = hAPP(c_Product__Type_Osnd(U_4874,U_4875),U_4873)
          & hAPP(c_Product__Type_Ofst(U_4874,U_4875),U_4872) = hAPP(c_Product__Type_Ofst(U_4874,U_4875),U_4873) )
        | U_4872 != U_4873 ) ),
    inference(variable_rename,[status(thm)],[f_1401_1]) ).

fof(f_1401_3,plain,
    ( ! [U_4883,U_4881,U_4879,U_4877] :
        ( U_4877 = U_4879
        | hAPP(c_Product__Type_Osnd(U_4881,U_4883),U_4877) != hAPP(c_Product__Type_Osnd(U_4881,U_4883),U_4879)
        | hAPP(c_Product__Type_Ofst(U_4881,U_4883),U_4877) != hAPP(c_Product__Type_Ofst(U_4881,U_4883),U_4879) )
    & ! [U_4882,U_4880,U_4878,U_4876] :
        ( ( hAPP(c_Product__Type_Osnd(U_4880,U_4882),U_4876) = hAPP(c_Product__Type_Osnd(U_4880,U_4882),U_4878)
          & hAPP(c_Product__Type_Ofst(U_4880,U_4882),U_4876) = hAPP(c_Product__Type_Ofst(U_4880,U_4882),U_4878) )
        | U_4876 != U_4878 ) ),
    inference(miniscope,[status(thm)],[f_1401_2]) ).

fof(f_1401_4,plain,
    ( ! [U_4878,U_4876,U_4882,U_4880] :
        ( hAPP(c_Product__Type_Osnd(U_4880,U_4882),U_4876) = hAPP(c_Product__Type_Osnd(U_4880,U_4882),U_4878)
        | ~ sP385(U_4878,U_4876,U_4882,U_4880) )
    & ! [U_4878,U_4876,U_4882,U_4880] :
        ( hAPP(c_Product__Type_Ofst(U_4880,U_4882),U_4876) = hAPP(c_Product__Type_Ofst(U_4880,U_4882),U_4878)
        | ~ sP385(U_4878,U_4876,U_4882,U_4880) )
    & ! [U_4879,U_4877,U_4881,U_4883] :
        ( U_4877 = U_4879
        | hAPP(c_Product__Type_Osnd(U_4881,U_4883),U_4877) != hAPP(c_Product__Type_Osnd(U_4881,U_4883),U_4879)
        | hAPP(c_Product__Type_Ofst(U_4881,U_4883),U_4877) != hAPP(c_Product__Type_Ofst(U_4881,U_4883),U_4879) )
    & ! [U_4878,U_4876,U_4882,U_4880] :
        ( sP385(U_4878,U_4876,U_4882,U_4880)
        | U_4876 != U_4878 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP385])],[f_1401_3]) ).

cnf(f_1401_5,plain,
    ( sP385(U_4878,U_4876,U_4882,U_4880)
    | U_4876 != U_4878 ),
    inference(clausify,[status(thm)],[f_1401_4]) ).

cnf(f_1401_6,plain,
    ( U_4877 = U_4879
    | hAPP(c_Product__Type_Osnd(U_4881,U_4883),U_4877) != hAPP(c_Product__Type_Osnd(U_4881,U_4883),U_4879)
    | hAPP(c_Product__Type_Ofst(U_4881,U_4883),U_4877) != hAPP(c_Product__Type_Ofst(U_4881,U_4883),U_4879) ),
    inference(clausify,[status(thm)],[f_1401_4]) ).

cnf(f_1401_7,plain,
    ( hAPP(c_Product__Type_Ofst(U_4880,U_4882),U_4876) = hAPP(c_Product__Type_Ofst(U_4880,U_4882),U_4878)
    | ~ sP385(U_4878,U_4876,U_4882,U_4880) ),
    inference(clausify,[status(thm)],[f_1401_4]) ).

cnf(f_1401_8,plain,
    ( hAPP(c_Product__Type_Osnd(U_4880,U_4882),U_4876) = hAPP(c_Product__Type_Osnd(U_4880,U_4882),U_4878)
    | ~ sP385(U_4878,U_4876,U_4882,U_4880) ),
    inference(clausify,[status(thm)],[f_1401_4]) ).

fof(f_1402_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_1402_2,plain,
    ! [U_4889,U_4888,U_4887,U_4886,U_4885,U_4884] : c_Product__Type_Oprod_Oprod__rec(U_4884,U_4885,U_4886,U_4887,hAPP(hAPP(c_Product__Type_OPair(U_4884,U_4885),U_4888),U_4889)) = hAPP(hAPP(U_4887,U_4888),U_4889),
    inference(variable_rename,[status(thm)],[f_1402_1]) ).

fof(f_1402_3,plain,
    ! [U_4885,U_4884,U_4887,U_4886,U_4888,U_4889] : c_Product__Type_Oprod_Oprod__rec(U_4884,U_4885,U_4886,U_4887,hAPP(hAPP(c_Product__Type_OPair(U_4884,U_4885),U_4888),U_4889)) = hAPP(hAPP(U_4887,U_4888),U_4889),
    inference(definitional_conversion,[status(esa)],[f_1402_2]) ).

cnf(f_1402_4,plain,
    c_Product__Type_Oprod_Oprod__rec(U_4884,U_4885,U_4886,U_4887,hAPP(hAPP(c_Product__Type_OPair(U_4884,U_4885),U_4888),U_4889)) = hAPP(hAPP(U_4887,U_4888),U_4889),
    inference(clausify,[status(thm)],[f_1402_3]) ).

fof(f_1403_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_1403_2,plain,
    ! [U_4894,U_4893,U_4892] :
      ( ? [U_4891] :
          ( hAPP(U_4893,U_4891) = U_4894
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4891),U_4892)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4894),hAPP(U_4893,U_4892)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4893,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4894))
      | ? [U_4890] :
          ( ~ 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_4893,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4890),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4893,U_4890)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4890),U_4892)) ) ),
    inference(variable_rename,[status(thm)],[f_1403_1]) ).

fof(f_1403_3,plain,
    ! [U_4894,U_4893,U_4892] :
      ( ? [U_4891] :
          ( hAPP(U_4893,U_4891) = U_4894
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4891),U_4892)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4894),hAPP(U_4893,U_4892)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4893,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4894))
      | ( ~ 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_4893,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK73(U_4894,U_4893,U_4892)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4893,sK73(U_4894,U_4893,U_4892))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK73(U_4894,U_4893,U_4892)),U_4892)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK73]),skolemize(U_4890,sK73(U_4894,U_4893,U_4892))],[f_1403_2]) ).

fof(f_1403_4,plain,
    ! [U_4894,U_4893,U_4892] :
      ( ( hAPP(U_4893,sK74(U_4894,U_4893,U_4892)) = U_4894
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK74(U_4894,U_4893,U_4892)),U_4892)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4894),hAPP(U_4893,U_4892)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4893,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4894))
      | ( ~ 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_4893,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK73(U_4894,U_4893,U_4892)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4893,sK73(U_4894,U_4893,U_4892))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK73(U_4894,U_4893,U_4892)),U_4892)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK74]),skolemize(U_4891,sK74(U_4894,U_4893,U_4892))],[f_1403_3]) ).

fof(f_1403_5,plain,
    ( ! [U_4892,U_4893,U_4894] :
        ( hAPP(U_4893,sK74(U_4894,U_4893,U_4892)) = U_4894
        | ~ sP387(U_4892,U_4893,U_4894) )
    & ! [U_4892,U_4893,U_4894] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK74(U_4894,U_4893,U_4892)),U_4892))
        | ~ sP387(U_4892,U_4893,U_4894) )
    & ! [U_4892,U_4893,U_4894] :
        ( ~ 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_4893,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK73(U_4894,U_4893,U_4892)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4893,sK73(U_4894,U_4893,U_4892))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ sP386(U_4892,U_4893,U_4894) )
    & ! [U_4892,U_4893,U_4894] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK73(U_4894,U_4893,U_4892)),U_4892))
        | ~ sP386(U_4892,U_4893,U_4894) )
    & ! [U_4892,U_4893,U_4894] :
        ( sP387(U_4892,U_4893,U_4894)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4894),hAPP(U_4893,U_4892)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4893,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4894))
        | sP386(U_4892,U_4893,U_4894) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP386,sP387])],[f_1403_4]) ).

cnf(f_1403_6,plain,
    ( sP387(U_4892,U_4893,U_4894)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4894),hAPP(U_4893,U_4892)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4893,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4894))
    | sP386(U_4892,U_4893,U_4894) ),
    inference(clausify,[status(thm)],[f_1403_5]) ).

cnf(f_1403_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK73(U_4894,U_4893,U_4892)),U_4892))
    | ~ sP386(U_4892,U_4893,U_4894) ),
    inference(clausify,[status(thm)],[f_1403_5]) ).

cnf(f_1403_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_4893,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK73(U_4894,U_4893,U_4892)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4893,sK73(U_4894,U_4893,U_4892))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ sP386(U_4892,U_4893,U_4894) ),
    inference(clausify,[status(thm)],[f_1403_5]) ).

cnf(f_1403_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK74(U_4894,U_4893,U_4892)),U_4892))
    | ~ sP387(U_4892,U_4893,U_4894) ),
    inference(clausify,[status(thm)],[f_1403_5]) ).

cnf(f_1403_10,plain,
    ( hAPP(U_4893,sK74(U_4894,U_4893,U_4892)) = U_4894
    | ~ sP387(U_4892,U_4893,U_4894) ),
    inference(clausify,[status(thm)],[f_1403_5]) ).

fof(f_1404_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_1404_2,plain,
    ! [U_4899,U_4898,U_4897] :
      ( ? [U_4896] :
          ( hAPP(U_4898,U_4896) = U_4899
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4896),U_4897)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4899),hAPP(U_4898,U_4897)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4898,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4899))
      | ? [U_4895] :
          ( ~ 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_4898,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_4895),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4898,U_4895)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_4895),U_4897)) ) ),
    inference(variable_rename,[status(thm)],[f_1404_1]) ).

fof(f_1404_3,plain,
    ! [U_4899,U_4898,U_4897] :
      ( ? [U_4896] :
          ( hAPP(U_4898,U_4896) = U_4899
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_4896),U_4897)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4899),hAPP(U_4898,U_4897)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4898,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4899))
      | ( ~ 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_4898,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK75(U_4899,U_4898,U_4897)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4898,sK75(U_4899,U_4898,U_4897))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK75(U_4899,U_4898,U_4897)),U_4897)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK75]),skolemize(U_4895,sK75(U_4899,U_4898,U_4897))],[f_1404_2]) ).

fof(f_1404_4,plain,
    ! [U_4899,U_4898,U_4897] :
      ( ( hAPP(U_4898,sK76(U_4899,U_4898,U_4897)) = U_4899
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK76(U_4899,U_4898,U_4897)),U_4897)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4899),hAPP(U_4898,U_4897)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4898,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4899))
      | ( ~ 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_4898,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK75(U_4899,U_4898,U_4897)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4898,sK75(U_4899,U_4898,U_4897))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK75(U_4899,U_4898,U_4897)),U_4897)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK76]),skolemize(U_4896,sK76(U_4899,U_4898,U_4897))],[f_1404_3]) ).

fof(f_1404_5,plain,
    ( ! [U_4897,U_4898,U_4899] :
        ( hAPP(U_4898,sK76(U_4899,U_4898,U_4897)) = U_4899
        | ~ sP389(U_4897,U_4898,U_4899) )
    & ! [U_4897,U_4898,U_4899] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK76(U_4899,U_4898,U_4897)),U_4897))
        | ~ sP389(U_4897,U_4898,U_4899) )
    & ! [U_4897,U_4898,U_4899] :
        ( ~ 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_4898,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK75(U_4899,U_4898,U_4897)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4898,sK75(U_4899,U_4898,U_4897))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ sP388(U_4897,U_4898,U_4899) )
    & ! [U_4897,U_4898,U_4899] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK75(U_4899,U_4898,U_4897)),U_4897))
        | ~ sP388(U_4897,U_4898,U_4899) )
    & ! [U_4897,U_4898,U_4899] :
        ( sP389(U_4897,U_4898,U_4899)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4899),hAPP(U_4898,U_4897)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4898,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4899))
        | sP388(U_4897,U_4898,U_4899) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP388,sP389])],[f_1404_4]) ).

cnf(f_1404_6,plain,
    ( sP389(U_4897,U_4898,U_4899)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4899),hAPP(U_4898,U_4897)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_4898,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_4899))
    | sP388(U_4897,U_4898,U_4899) ),
    inference(clausify,[status(thm)],[f_1404_5]) ).

cnf(f_1404_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK75(U_4899,U_4898,U_4897)),U_4897))
    | ~ sP388(U_4897,U_4898,U_4899) ),
    inference(clausify,[status(thm)],[f_1404_5]) ).

cnf(f_1404_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_4898,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK75(U_4899,U_4898,U_4897)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_4898,sK75(U_4899,U_4898,U_4897))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ sP388(U_4897,U_4898,U_4899) ),
    inference(clausify,[status(thm)],[f_1404_5]) ).

cnf(f_1404_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK76(U_4899,U_4898,U_4897)),U_4897))
    | ~ sP389(U_4897,U_4898,U_4899) ),
    inference(clausify,[status(thm)],[f_1404_5]) ).

cnf(f_1404_10,plain,
    ( hAPP(U_4898,sK76(U_4899,U_4898,U_4897)) = U_4899
    | ~ sP389(U_4897,U_4898,U_4899) ),
    inference(clausify,[status(thm)],[f_1404_5]) ).

fof(f_1405_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_1405_2,plain,
    ! [U_4900] :
      ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4900)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4900))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4900),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4900)),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_4900),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1405_1]) ).

fof(f_1405_3,plain,
    ( ! [U_4902] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4902)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4902))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4902),c_Int_OPls)) )
    & ! [U_4901] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4901)),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_4901),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1405_2]) ).

fof(f_1405_4,plain,
    ( ! [U_4902] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4902)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4902))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4902),c_Int_OPls)) )
    & ! [U_4901] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4901)),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_4901),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1405_3]) ).

cnf(f_1405_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4901)),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_4901),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1405_4]) ).

cnf(f_1405_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4902)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4902))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4902),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1405_4]) ).

fof(f_1406_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_1406_2,plain,
    ! [U_4903] :
      ( ( 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_4903)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4903))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4903),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_4903)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4903),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1406_1]) ).

fof(f_1406_3,plain,
    ( ! [U_4905] :
        ( 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_4905)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4905))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4905),c_Int_OPls)) )
    & ! [U_4904] :
        ( 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_4904)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4904),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1406_2]) ).

fof(f_1406_4,plain,
    ( ! [U_4905] :
        ( 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_4905)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4905))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4905),c_Int_OPls)) )
    & ! [U_4904] :
        ( 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_4904)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4904),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1406_3]) ).

cnf(f_1406_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_4904)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4904),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1406_4]) ).

cnf(f_1406_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_4905)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Osucc(U_4905))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4905),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1406_4]) ).

fof(f_1407_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_1407_2,plain,
    ! [U_4908,U_4907,U_4906] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_4906),U_4907) = hAPP(c_Int_Onumber__class_Onumber__of(U_4906),U_4908)
          | ~ c_Int_Oiszero(U_4906,hAPP(c_Int_Onumber__class_Onumber__of(U_4906),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4907),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4908)))) )
        & ( c_Int_Oiszero(U_4906,hAPP(c_Int_Onumber__class_Onumber__of(U_4906),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4907),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4908))))
          | hAPP(c_Int_Onumber__class_Onumber__of(U_4906),U_4907) != hAPP(c_Int_Onumber__class_Onumber__of(U_4906),U_4908) ) )
      | ~ class_Int_Onumber__ring(U_4906) ),
    inference(variable_rename,[status(thm)],[f_1407_1]) ).

fof(f_1407_3,plain,
    ( ! [U_4907,U_4906,U_4908] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_4906),U_4907) = hAPP(c_Int_Onumber__class_Onumber__of(U_4906),U_4908)
        | ~ c_Int_Oiszero(U_4906,hAPP(c_Int_Onumber__class_Onumber__of(U_4906),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4907),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4908))))
        | ~ sP390(U_4907,U_4906,U_4908) )
    & ! [U_4907,U_4906,U_4908] :
        ( c_Int_Oiszero(U_4906,hAPP(c_Int_Onumber__class_Onumber__of(U_4906),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4907),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4908))))
        | hAPP(c_Int_Onumber__class_Onumber__of(U_4906),U_4907) != hAPP(c_Int_Onumber__class_Onumber__of(U_4906),U_4908)
        | ~ sP390(U_4907,U_4906,U_4908) )
    & ! [U_4907,U_4906,U_4908] :
        ( sP390(U_4907,U_4906,U_4908)
        | ~ class_Int_Onumber__ring(U_4906) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP390])],[f_1407_2]) ).

cnf(f_1407_4,plain,
    ( sP390(U_4907,U_4906,U_4908)
    | ~ class_Int_Onumber__ring(U_4906) ),
    inference(clausify,[status(thm)],[f_1407_3]) ).

cnf(f_1407_5,plain,
    ( c_Int_Oiszero(U_4906,hAPP(c_Int_Onumber__class_Onumber__of(U_4906),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4907),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4908))))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4906),U_4907) != hAPP(c_Int_Onumber__class_Onumber__of(U_4906),U_4908)
    | ~ sP390(U_4907,U_4906,U_4908) ),
    inference(clausify,[status(thm)],[f_1407_3]) ).

cnf(f_1407_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4906),U_4907) = hAPP(c_Int_Onumber__class_Onumber__of(U_4906),U_4908)
    | ~ c_Int_Oiszero(U_4906,hAPP(c_Int_Onumber__class_Onumber__of(U_4906),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4907),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4908))))
    | ~ sP390(U_4907,U_4906,U_4908) ),
    inference(clausify,[status(thm)],[f_1407_3]) ).

fof(f_1408_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_1408_2,plain,
    ! [U_4909] :
      ( c_Int_Oiszero(U_4909,hAPP(c_Int_Onumber__class_Onumber__of(U_4909),c_Int_OPls))
      | ~ class_Int_Onumber__ring(U_4909) ),
    inference(variable_rename,[status(thm)],[f_1408_1]) ).

fof(f_1408_3,plain,
    ! [U_4909] :
      ( c_Int_Oiszero(U_4909,hAPP(c_Int_Onumber__class_Onumber__of(U_4909),c_Int_OPls))
      | ~ class_Int_Onumber__ring(U_4909) ),
    inference(definitional_conversion,[status(esa)],[f_1408_2]) ).

cnf(f_1408_4,plain,
    ( c_Int_Oiszero(U_4909,hAPP(c_Int_Onumber__class_Onumber__of(U_4909),c_Int_OPls))
    | ~ class_Int_Onumber__ring(U_4909) ),
    inference(clausify,[status(thm)],[f_1408_3]) ).

fof(f_1409_1,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(fof_nnf,[status(thm)],[fact_Pls__def]) ).

fof(f_1409_2,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_1409_1]) ).

cnf(f_1409_3,plain,
    c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_1409_2]) ).

fof(f_1410_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_1410_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_1410_1]) ).

cnf(f_1410_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_1410_2]) ).

fof(f_1411_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_1411_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_1411_1]) ).

cnf(f_1411_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)),
    inference(clausify,[status(thm)],[f_1411_2]) ).

fof(f_1412_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_1412_2,plain,
    ! [U_4910] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4910),c_Int_OPls) = U_4910,
    inference(variable_rename,[status(thm)],[f_1412_1]) ).

fof(f_1412_3,plain,
    ! [U_4910] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4910),c_Int_OPls) = U_4910,
    inference(definitional_conversion,[status(esa)],[f_1412_2]) ).

cnf(f_1412_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4910),c_Int_OPls) = U_4910,
    inference(clausify,[status(thm)],[f_1412_3]) ).

fof(f_1413_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_1413_2,plain,
    ! [U_4911] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_4911) = U_4911,
    inference(variable_rename,[status(thm)],[f_1413_1]) ).

fof(f_1413_3,plain,
    ! [U_4911] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_4911) = U_4911,
    inference(definitional_conversion,[status(esa)],[f_1413_2]) ).

cnf(f_1413_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),U_4911) = U_4911,
    inference(clausify,[status(thm)],[f_1413_3]) ).

fof(f_1414_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_1414_2,plain,
    ! [U_4912] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_4912) = c_Int_OPls,
    inference(variable_rename,[status(thm)],[f_1414_1]) ).

fof(f_1414_3,plain,
    ! [U_4912] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_4912) = c_Int_OPls,
    inference(definitional_conversion,[status(esa)],[f_1414_2]) ).

cnf(f_1414_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),U_4912) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_1414_3]) ).

fof(f_1415_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_1415_2,plain,
    ! [U_4913] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4913),c_Int_OPls) = U_4913,
    inference(variable_rename,[status(thm)],[f_1415_1]) ).

fof(f_1415_3,plain,
    ! [U_4913] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4913),c_Int_OPls) = U_4913,
    inference(definitional_conversion,[status(esa)],[f_1415_2]) ).

cnf(f_1415_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_4913),c_Int_OPls) = U_4913,
    inference(clausify,[status(thm)],[f_1415_3]) ).

fof(f_1416_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_1416_2,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
    inference(definitional_conversion,[status(esa)],[f_1416_1]) ).

cnf(f_1416_3,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_1416_2]) ).

fof(f_1417_1,plain,
    c_Int_OMin != c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I40_J]) ).

fof(f_1417_2,plain,
    c_Int_OMin != c_Int_OPls,
    inference(definitional_conversion,[status(esa)],[f_1417_1]) ).

cnf(f_1417_3,plain,
    c_Int_OMin != c_Int_OPls,
    inference(clausify,[status(thm)],[f_1417_2]) ).

fof(f_1418_1,plain,
    c_Int_OPls != c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I37_J]) ).

fof(f_1418_2,plain,
    c_Int_OPls != c_Int_OMin,
    inference(definitional_conversion,[status(esa)],[f_1418_1]) ).

cnf(f_1418_3,plain,
    c_Int_OPls != c_Int_OMin,
    inference(clausify,[status(thm)],[f_1418_2]) ).

fof(f_1419_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_1419_2,plain,
    ! [U_4915,U_4914] :
      ( ( ( c_Int_Oiszero(U_4914,U_4915)
          | U_4915 != c_Groups_Ozero__class_Ozero(U_4914) )
        & ( U_4915 = c_Groups_Ozero__class_Ozero(U_4914)
          | ~ c_Int_Oiszero(U_4914,U_4915) ) )
      | ~ class_Rings_Osemiring__1(U_4914) ),
    inference(variable_rename,[status(thm)],[f_1419_1]) ).

fof(f_1419_3,plain,
    ( ! [U_4914,U_4915] :
        ( c_Int_Oiszero(U_4914,U_4915)
        | U_4915 != c_Groups_Ozero__class_Ozero(U_4914)
        | ~ sP391(U_4914,U_4915) )
    & ! [U_4914,U_4915] :
        ( U_4915 = c_Groups_Ozero__class_Ozero(U_4914)
        | ~ c_Int_Oiszero(U_4914,U_4915)
        | ~ sP391(U_4914,U_4915) )
    & ! [U_4914,U_4915] :
        ( sP391(U_4914,U_4915)
        | ~ class_Rings_Osemiring__1(U_4914) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP391])],[f_1419_2]) ).

cnf(f_1419_4,plain,
    ( sP391(U_4914,U_4915)
    | ~ class_Rings_Osemiring__1(U_4914) ),
    inference(clausify,[status(thm)],[f_1419_3]) ).

cnf(f_1419_5,plain,
    ( U_4915 = c_Groups_Ozero__class_Ozero(U_4914)
    | ~ c_Int_Oiszero(U_4914,U_4915)
    | ~ sP391(U_4914,U_4915) ),
    inference(clausify,[status(thm)],[f_1419_3]) ).

cnf(f_1419_6,plain,
    ( c_Int_Oiszero(U_4914,U_4915)
    | U_4915 != c_Groups_Ozero__class_Ozero(U_4914)
    | ~ sP391(U_4914,U_4915) ),
    inference(clausify,[status(thm)],[f_1419_3]) ).

fof(f_1420_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_1420_2,plain,
    ! [U_4916] :
      ( c_Int_Oiszero(U_4916,c_Groups_Ozero__class_Ozero(U_4916))
      | ~ class_Rings_Osemiring__1(U_4916) ),
    inference(variable_rename,[status(thm)],[f_1420_1]) ).

fof(f_1420_3,plain,
    ! [U_4916] :
      ( c_Int_Oiszero(U_4916,c_Groups_Ozero__class_Ozero(U_4916))
      | ~ class_Rings_Osemiring__1(U_4916) ),
    inference(definitional_conversion,[status(esa)],[f_1420_2]) ).

cnf(f_1420_4,plain,
    ( c_Int_Oiszero(U_4916,c_Groups_Ozero__class_Ozero(U_4916))
    | ~ class_Rings_Osemiring__1(U_4916) ),
    inference(clausify,[status(thm)],[f_1420_3]) ).

fof(f_1421_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_1421_2,plain,
    ! [U_4917] :
      ( ~ c_Int_Oiszero(U_4917,c_Groups_Oone__class_Oone(U_4917))
      | ~ class_Rings_Osemiring__1(U_4917) ),
    inference(variable_rename,[status(thm)],[f_1421_1]) ).

fof(f_1421_3,plain,
    ! [U_4917] :
      ( ~ c_Int_Oiszero(U_4917,c_Groups_Oone__class_Oone(U_4917))
      | ~ class_Rings_Osemiring__1(U_4917) ),
    inference(definitional_conversion,[status(esa)],[f_1421_2]) ).

cnf(f_1421_4,plain,
    ( ~ c_Int_Oiszero(U_4917,c_Groups_Oone__class_Oone(U_4917))
    | ~ class_Rings_Osemiring__1(U_4917) ),
    inference(clausify,[status(thm)],[f_1421_3]) ).

fof(f_1422_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_1422_2,plain,
    ! [U_4918] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4918),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_4918)
      | ~ class_Int_Onumber__ring(U_4918) ),
    inference(variable_rename,[status(thm)],[f_1422_1]) ).

fof(f_1422_3,plain,
    ! [U_4918] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_4918),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_4918)
      | ~ class_Int_Onumber__ring(U_4918) ),
    inference(definitional_conversion,[status(esa)],[f_1422_2]) ).

cnf(f_1422_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4918),c_Int_OPls) = c_Groups_Ozero__class_Ozero(U_4918)
    | ~ class_Int_Onumber__ring(U_4918) ),
    inference(clausify,[status(thm)],[f_1422_3]) ).

fof(f_1423_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_1423_2,plain,
    ! [U_4919] :
      ( c_Groups_Ozero__class_Ozero(U_4919) = hAPP(c_Int_Onumber__class_Onumber__of(U_4919),c_Int_OPls)
      | ~ class_Int_Onumber__ring(U_4919) ),
    inference(variable_rename,[status(thm)],[f_1423_1]) ).

fof(f_1423_3,plain,
    ! [U_4919] :
      ( c_Groups_Ozero__class_Ozero(U_4919) = hAPP(c_Int_Onumber__class_Onumber__of(U_4919),c_Int_OPls)
      | ~ class_Int_Onumber__ring(U_4919) ),
    inference(definitional_conversion,[status(esa)],[f_1423_2]) ).

cnf(f_1423_4,plain,
    ( c_Groups_Ozero__class_Ozero(U_4919) = hAPP(c_Int_Onumber__class_Onumber__of(U_4919),c_Int_OPls)
    | ~ class_Int_Onumber__ring(U_4919) ),
    inference(clausify,[status(thm)],[f_1423_3]) ).

fof(f_1424_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_1424_2,plain,
    ! [U_4921,U_4920] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4920),U_4921),hAPP(c_Int_Onumber__class_Onumber__of(U_4920),c_Int_OPls)) = U_4921
      | ~ class_Int_Onumber__ring(U_4920) ),
    inference(variable_rename,[status(thm)],[f_1424_1]) ).

fof(f_1424_3,plain,
    ! [U_4920,U_4921] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4920),U_4921),hAPP(c_Int_Onumber__class_Onumber__of(U_4920),c_Int_OPls)) = U_4921
      | ~ class_Int_Onumber__ring(U_4920) ),
    inference(definitional_conversion,[status(esa)],[f_1424_2]) ).

cnf(f_1424_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4920),U_4921),hAPP(c_Int_Onumber__class_Onumber__of(U_4920),c_Int_OPls)) = U_4921
    | ~ class_Int_Onumber__ring(U_4920) ),
    inference(clausify,[status(thm)],[f_1424_3]) ).

fof(f_1425_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_1425_2,plain,
    ! [U_4923,U_4922] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4922),hAPP(c_Int_Onumber__class_Onumber__of(U_4922),c_Int_OPls)),U_4923) = U_4923
      | ~ class_Int_Onumber__ring(U_4922) ),
    inference(variable_rename,[status(thm)],[f_1425_1]) ).

fof(f_1425_3,plain,
    ! [U_4922,U_4923] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4922),hAPP(c_Int_Onumber__class_Onumber__of(U_4922),c_Int_OPls)),U_4923) = U_4923
      | ~ class_Int_Onumber__ring(U_4922) ),
    inference(definitional_conversion,[status(esa)],[f_1425_2]) ).

cnf(f_1425_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_4922),hAPP(c_Int_Onumber__class_Onumber__of(U_4922),c_Int_OPls)),U_4923) = U_4923
    | ~ class_Int_Onumber__ring(U_4922) ),
    inference(clausify,[status(thm)],[f_1425_3]) ).

fof(f_1426_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_1426_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_1426_1]) ).

cnf(f_1426_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_1426_2]) ).

fof(f_1427_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_1427_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_1427_1]) ).

cnf(f_1427_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_1427_2]) ).

fof(f_1428_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_1428_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_1428_1]) ).

cnf(f_1428_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_1428_2]) ).

fof(f_1429_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_1429_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_1429_1]) ).

cnf(f_1429_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_1429_2]) ).

fof(f_1430_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_1430_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_1430_1]) ).

cnf(f_1430_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_1430_2]) ).

fof(f_1431_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_1431_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_1431_1]) ).

cnf(f_1431_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_1431_2]) ).

fof(f_1432_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_1432_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_1432_1]) ).

cnf(f_1432_3,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)),
    inference(clausify,[status(thm)],[f_1432_2]) ).

fof(f_1433_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_1433_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_1433_1]) ).

cnf(f_1433_3,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)),
    inference(clausify,[status(thm)],[f_1433_2]) ).

fof(f_1434_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_1434_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_1434_1]) ).

cnf(f_1434_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_1434_2]) ).

fof(f_1435_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_1435_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_1435_1]) ).

cnf(f_1435_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_1435_2]) ).

fof(f_1436_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_1436_2,plain,
    ! [U_4925,U_4924] :
      ( ( ( c_Groups_Ozero__class_Ozero(U_4924) = hAPP(c_Int_Onumber__class_Onumber__of(U_4924),U_4925)
          | ~ c_Int_Oiszero(U_4924,hAPP(c_Int_Onumber__class_Onumber__of(U_4924),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4925)))) )
        & ( c_Int_Oiszero(U_4924,hAPP(c_Int_Onumber__class_Onumber__of(U_4924),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4925))))
          | c_Groups_Ozero__class_Ozero(U_4924) != hAPP(c_Int_Onumber__class_Onumber__of(U_4924),U_4925) ) )
      | ~ class_Int_Onumber__ring(U_4924) ),
    inference(variable_rename,[status(thm)],[f_1436_1]) ).

fof(f_1436_3,plain,
    ( ! [U_4924,U_4925] :
        ( c_Groups_Ozero__class_Ozero(U_4924) = hAPP(c_Int_Onumber__class_Onumber__of(U_4924),U_4925)
        | ~ c_Int_Oiszero(U_4924,hAPP(c_Int_Onumber__class_Onumber__of(U_4924),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4925))))
        | ~ sP392(U_4924,U_4925) )
    & ! [U_4924,U_4925] :
        ( c_Int_Oiszero(U_4924,hAPP(c_Int_Onumber__class_Onumber__of(U_4924),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4925))))
        | c_Groups_Ozero__class_Ozero(U_4924) != hAPP(c_Int_Onumber__class_Onumber__of(U_4924),U_4925)
        | ~ sP392(U_4924,U_4925) )
    & ! [U_4924,U_4925] :
        ( sP392(U_4924,U_4925)
        | ~ class_Int_Onumber__ring(U_4924) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP392])],[f_1436_2]) ).

cnf(f_1436_4,plain,
    ( sP392(U_4924,U_4925)
    | ~ class_Int_Onumber__ring(U_4924) ),
    inference(clausify,[status(thm)],[f_1436_3]) ).

cnf(f_1436_5,plain,
    ( c_Int_Oiszero(U_4924,hAPP(c_Int_Onumber__class_Onumber__of(U_4924),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4925))))
    | c_Groups_Ozero__class_Ozero(U_4924) != hAPP(c_Int_Onumber__class_Onumber__of(U_4924),U_4925)
    | ~ sP392(U_4924,U_4925) ),
    inference(clausify,[status(thm)],[f_1436_3]) ).

cnf(f_1436_6,plain,
    ( c_Groups_Ozero__class_Ozero(U_4924) = hAPP(c_Int_Onumber__class_Onumber__of(U_4924),U_4925)
    | ~ c_Int_Oiszero(U_4924,hAPP(c_Int_Onumber__class_Onumber__of(U_4924),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4925))))
    | ~ sP392(U_4924,U_4925) ),
    inference(clausify,[status(thm)],[f_1436_3]) ).

fof(f_1437_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_1437_2,plain,
    ! [U_4927,U_4926] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_4926),U_4927) = c_Groups_Ozero__class_Ozero(U_4926)
          | ~ c_Int_Oiszero(U_4926,hAPP(c_Int_Onumber__class_Onumber__of(U_4926),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4927),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls)))) )
        & ( c_Int_Oiszero(U_4926,hAPP(c_Int_Onumber__class_Onumber__of(U_4926),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4927),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
          | hAPP(c_Int_Onumber__class_Onumber__of(U_4926),U_4927) != c_Groups_Ozero__class_Ozero(U_4926) ) )
      | ~ class_Int_Onumber__ring(U_4926) ),
    inference(variable_rename,[status(thm)],[f_1437_1]) ).

fof(f_1437_3,plain,
    ( ! [U_4927,U_4926] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_4926),U_4927) = c_Groups_Ozero__class_Ozero(U_4926)
        | ~ c_Int_Oiszero(U_4926,hAPP(c_Int_Onumber__class_Onumber__of(U_4926),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4927),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
        | ~ sP393(U_4927,U_4926) )
    & ! [U_4927,U_4926] :
        ( c_Int_Oiszero(U_4926,hAPP(c_Int_Onumber__class_Onumber__of(U_4926),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4927),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
        | hAPP(c_Int_Onumber__class_Onumber__of(U_4926),U_4927) != c_Groups_Ozero__class_Ozero(U_4926)
        | ~ sP393(U_4927,U_4926) )
    & ! [U_4927,U_4926] :
        ( sP393(U_4927,U_4926)
        | ~ class_Int_Onumber__ring(U_4926) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP393])],[f_1437_2]) ).

cnf(f_1437_4,plain,
    ( sP393(U_4927,U_4926)
    | ~ class_Int_Onumber__ring(U_4926) ),
    inference(clausify,[status(thm)],[f_1437_3]) ).

cnf(f_1437_5,plain,
    ( c_Int_Oiszero(U_4926,hAPP(c_Int_Onumber__class_Onumber__of(U_4926),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4927),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4926),U_4927) != c_Groups_Ozero__class_Ozero(U_4926)
    | ~ sP393(U_4927,U_4926) ),
    inference(clausify,[status(thm)],[f_1437_3]) ).

cnf(f_1437_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4926),U_4927) = c_Groups_Ozero__class_Ozero(U_4926)
    | ~ c_Int_Oiszero(U_4926,hAPP(c_Int_Onumber__class_Onumber__of(U_4926),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4927),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls))))
    | ~ sP393(U_4927,U_4926) ),
    inference(clausify,[status(thm)],[f_1437_3]) ).

fof(f_1438_1,plain,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_succ__Min]) ).

fof(f_1438_2,plain,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    inference(definitional_conversion,[status(esa)],[f_1438_1]) ).

cnf(f_1438_3,plain,
    c_Int_Osucc(c_Int_OMin) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_1438_2]) ).

fof(f_1439_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_1439_2,plain,
    ! [U_4928] :
      ( ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4928)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4928),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4928),c_Int_OPls))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4928) ) ),
    inference(variable_rename,[status(thm)],[f_1439_1]) ).

fof(f_1439_3,plain,
    ( ! [U_4930] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4930)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4930),c_Int_OPls)) )
    & ! [U_4929] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4929),c_Int_OPls))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4929) ) ),
    inference(miniscope,[status(thm)],[f_1439_2]) ).

fof(f_1439_4,plain,
    ( ! [U_4930] :
        ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4930)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4930),c_Int_OPls)) )
    & ! [U_4929] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4929),c_Int_OPls))
        | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4929) ) ),
    inference(definitional_conversion,[status(esa)],[f_1439_3]) ).

cnf(f_1439_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4929),c_Int_OPls))
    | c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4929) ),
    inference(clausify,[status(thm)],[f_1439_4]) ).

cnf(f_1439_6,plain,
    ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4930)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4930),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1439_4]) ).

fof(f_1440_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_1440_2,plain,
    ! [U_4931] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4931) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4931),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4931),c_Int_OPls))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4931) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1440_1]) ).

fof(f_1440_3,plain,
    ( ! [U_4933] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4933) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4933),c_Int_OPls)) )
    & ! [U_4932] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4932),c_Int_OPls))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4932) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1440_2]) ).

fof(f_1440_4,plain,
    ( ! [U_4933] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4933) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4933),c_Int_OPls)) )
    & ! [U_4932] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4932),c_Int_OPls))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4932) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_1440_3]) ).

cnf(f_1440_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4932),c_Int_OPls))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4932) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1440_4]) ).

cnf(f_1440_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4933) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4933),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1440_4]) ).

fof(f_1441_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_1441_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_1441_1]) ).

cnf(f_1441_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_1441_2]) ).

fof(f_1442_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_1442_2,plain,
    ! [U_4935,U_4934] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4934)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4935)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4934),U_4935))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4935))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4934),U_4935)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4934),U_4935))
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4935))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4934),U_4935)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4934)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4935))) ) ),
    inference(variable_rename,[status(thm)],[f_1442_1]) ).

fof(f_1442_3,plain,
    ( ! [U_4939,U_4937] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4937)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4939)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4937),U_4939))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4939))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4937),U_4939)) ) )
    & ! [U_4938,U_4936] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4936),U_4938))
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4938))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4936),U_4938)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4936)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4938))) ) ),
    inference(miniscope,[status(thm)],[f_1442_2]) ).

fof(f_1442_4,plain,
    ( ! [U_4939,U_4937] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4939))
        | ~ sP395(U_4939,U_4937) )
    & ! [U_4939,U_4937] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4937),U_4939))
        | ~ sP395(U_4939,U_4937) )
    & ! [U_4938,U_4936] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4936),U_4938))
        | ~ sP394(U_4938,U_4936) )
    & ! [U_4938,U_4936] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4938))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4936),U_4938))
        | ~ sP394(U_4938,U_4936) )
    & ! [U_4939,U_4937] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4937)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4939)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4937),U_4939))
        | sP395(U_4939,U_4937) )
    & ! [U_4938,U_4936] :
        ( sP394(U_4938,U_4936)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4936)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4938))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP394,sP395])],[f_1442_3]) ).

cnf(f_1442_5,plain,
    ( sP394(U_4938,U_4936)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4936)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4938))) ),
    inference(clausify,[status(thm)],[f_1442_4]) ).

cnf(f_1442_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4937)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4939)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4937),U_4939))
    | sP395(U_4939,U_4937) ),
    inference(clausify,[status(thm)],[f_1442_4]) ).

cnf(f_1442_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4938))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4936),U_4938))
    | ~ sP394(U_4938,U_4936) ),
    inference(clausify,[status(thm)],[f_1442_4]) ).

cnf(f_1442_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4936),U_4938))
    | ~ sP394(U_4938,U_4936) ),
    inference(clausify,[status(thm)],[f_1442_4]) ).

cnf(f_1442_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4937),U_4939))
    | ~ sP395(U_4939,U_4937) ),
    inference(clausify,[status(thm)],[f_1442_4]) ).

cnf(f_1442_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4939))
    | ~ sP395(U_4939,U_4937) ),
    inference(clausify,[status(thm)],[f_1442_4]) ).

fof(f_1443_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_1443_2,plain,
    ! [U_4941,U_4940] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4940)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4941)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4940),c_Int_OPls))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4940),U_4941)) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4940),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4940),U_4941))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4940)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4941))) ) ),
    inference(variable_rename,[status(thm)],[f_1443_1]) ).

fof(f_1443_3,plain,
    ( ! [U_4945,U_4943] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4943)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4945)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4943),c_Int_OPls))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4943),U_4945)) ) )
    & ! [U_4944,U_4942] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4942),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4942),U_4944))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4942)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4944))) ) ),
    inference(miniscope,[status(thm)],[f_1443_2]) ).

fof(f_1443_4,plain,
    ( ! [U_4943,U_4945] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4943),c_Int_OPls))
        | ~ sP396(U_4943,U_4945) )
    & ! [U_4943,U_4945] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4943),U_4945))
        | ~ sP396(U_4943,U_4945) )
    & ! [U_4943,U_4945] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4943)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4945)))
        | sP396(U_4943,U_4945) )
    & ! [U_4944,U_4942] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4942),c_Int_OPls))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4942),U_4944))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4942)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4944))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP396])],[f_1443_3]) ).

cnf(f_1443_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4942),c_Int_OPls))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4942),U_4944))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4942)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4944))) ),
    inference(clausify,[status(thm)],[f_1443_4]) ).

cnf(f_1443_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_4943)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4945)))
    | sP396(U_4943,U_4945) ),
    inference(clausify,[status(thm)],[f_1443_4]) ).

cnf(f_1443_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4943),U_4945))
    | ~ sP396(U_4943,U_4945) ),
    inference(clausify,[status(thm)],[f_1443_4]) ).

cnf(f_1443_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4943),c_Int_OPls))
    | ~ sP396(U_4943,U_4945) ),
    inference(clausify,[status(thm)],[f_1443_4]) ).

fof(f_1444_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_1444_2,plain,
    ! [U_4946] :
      ( ~ c_Int_Oiszero(U_4946,hAPP(c_Int_Onumber__class_Onumber__of(U_4946),c_Int_OMin))
      | ~ class_Int_Onumber__ring(U_4946) ),
    inference(variable_rename,[status(thm)],[f_1444_1]) ).

fof(f_1444_3,plain,
    ! [U_4946] :
      ( ~ c_Int_Oiszero(U_4946,hAPP(c_Int_Onumber__class_Onumber__of(U_4946),c_Int_OMin))
      | ~ class_Int_Onumber__ring(U_4946) ),
    inference(definitional_conversion,[status(esa)],[f_1444_2]) ).

cnf(f_1444_4,plain,
    ( ~ c_Int_Oiszero(U_4946,hAPP(c_Int_Onumber__class_Onumber__of(U_4946),c_Int_OMin))
    | ~ class_Int_Onumber__ring(U_4946) ),
    inference(clausify,[status(thm)],[f_1444_3]) ).

fof(f_1445_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_1445_2,plain,
    ! [U_4948,U_4947] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4947),c_Groups_Ozero__class_Ozero(U_4947)),hAPP(c_Int_Onumber__class_Onumber__of(U_4947),U_4948)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4948)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4948))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4947),c_Groups_Ozero__class_Ozero(U_4947)),hAPP(c_Int_Onumber__class_Onumber__of(U_4947),U_4948))) ) )
      | ~ class_Rings_Olinordered__idom(U_4947)
      | ~ class_Int_Onumber__ring(U_4947) ),
    inference(variable_rename,[status(thm)],[f_1445_1]) ).

fof(f_1445_3,plain,
    ( ! [U_4948,U_4947] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4947),c_Groups_Ozero__class_Ozero(U_4947)),hAPP(c_Int_Onumber__class_Onumber__of(U_4947),U_4948)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4948))
        | ~ sP397(U_4948,U_4947) )
    & ! [U_4948,U_4947] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4948))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4947),c_Groups_Ozero__class_Ozero(U_4947)),hAPP(c_Int_Onumber__class_Onumber__of(U_4947),U_4948)))
        | ~ sP397(U_4948,U_4947) )
    & ! [U_4948,U_4947] :
        ( sP397(U_4948,U_4947)
        | ~ class_Rings_Olinordered__idom(U_4947)
        | ~ class_Int_Onumber__ring(U_4947) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP397])],[f_1445_2]) ).

cnf(f_1445_4,plain,
    ( sP397(U_4948,U_4947)
    | ~ class_Rings_Olinordered__idom(U_4947)
    | ~ class_Int_Onumber__ring(U_4947) ),
    inference(clausify,[status(thm)],[f_1445_3]) ).

cnf(f_1445_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4948))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4947),c_Groups_Ozero__class_Ozero(U_4947)),hAPP(c_Int_Onumber__class_Onumber__of(U_4947),U_4948)))
    | ~ sP397(U_4948,U_4947) ),
    inference(clausify,[status(thm)],[f_1445_3]) ).

cnf(f_1445_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4947),c_Groups_Ozero__class_Ozero(U_4947)),hAPP(c_Int_Onumber__class_Onumber__of(U_4947),U_4948)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4948))
    | ~ sP397(U_4948,U_4947) ),
    inference(clausify,[status(thm)],[f_1445_3]) ).

fof(f_1446_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_1446_2,plain,
    ! [U_4950,U_4949] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4949),hAPP(c_Int_Onumber__class_Onumber__of(U_4949),U_4950)),c_Groups_Ozero__class_Ozero(U_4949)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4950),c_Int_OPls)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4950),c_Int_OPls))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4949),hAPP(c_Int_Onumber__class_Onumber__of(U_4949),U_4950)),c_Groups_Ozero__class_Ozero(U_4949))) ) )
      | ~ class_Rings_Olinordered__idom(U_4949)
      | ~ class_Int_Onumber__ring(U_4949) ),
    inference(variable_rename,[status(thm)],[f_1446_1]) ).

fof(f_1446_3,plain,
    ( ! [U_4950,U_4949] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4949),hAPP(c_Int_Onumber__class_Onumber__of(U_4949),U_4950)),c_Groups_Ozero__class_Ozero(U_4949)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4950),c_Int_OPls))
        | ~ sP398(U_4950,U_4949) )
    & ! [U_4950,U_4949] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4950),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4949),hAPP(c_Int_Onumber__class_Onumber__of(U_4949),U_4950)),c_Groups_Ozero__class_Ozero(U_4949)))
        | ~ sP398(U_4950,U_4949) )
    & ! [U_4950,U_4949] :
        ( sP398(U_4950,U_4949)
        | ~ class_Rings_Olinordered__idom(U_4949)
        | ~ class_Int_Onumber__ring(U_4949) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP398])],[f_1446_2]) ).

cnf(f_1446_4,plain,
    ( sP398(U_4950,U_4949)
    | ~ class_Rings_Olinordered__idom(U_4949)
    | ~ class_Int_Onumber__ring(U_4949) ),
    inference(clausify,[status(thm)],[f_1446_3]) ).

cnf(f_1446_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4950),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4949),hAPP(c_Int_Onumber__class_Onumber__of(U_4949),U_4950)),c_Groups_Ozero__class_Ozero(U_4949)))
    | ~ sP398(U_4950,U_4949) ),
    inference(clausify,[status(thm)],[f_1446_3]) ).

cnf(f_1446_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_4949),hAPP(c_Int_Onumber__class_Onumber__of(U_4949),U_4950)),c_Groups_Ozero__class_Ozero(U_4949)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4950),c_Int_OPls))
    | ~ sP398(U_4950,U_4949) ),
    inference(clausify,[status(thm)],[f_1446_3]) ).

fof(f_1447_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_1447_2,plain,
    ! [U_4952,U_4951] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4951),hAPP(c_Int_Onumber__class_Onumber__of(U_4951),U_4952)),c_Groups_Ozero__class_Ozero(U_4951)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4952),c_Int_OPls)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4952),c_Int_OPls))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4951),hAPP(c_Int_Onumber__class_Onumber__of(U_4951),U_4952)),c_Groups_Ozero__class_Ozero(U_4951))) ) )
      | ~ class_Rings_Olinordered__idom(U_4951)
      | ~ class_Int_Onumber__ring(U_4951) ),
    inference(variable_rename,[status(thm)],[f_1447_1]) ).

fof(f_1447_3,plain,
    ( ! [U_4952,U_4951] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4951),hAPP(c_Int_Onumber__class_Onumber__of(U_4951),U_4952)),c_Groups_Ozero__class_Ozero(U_4951)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4952),c_Int_OPls))
        | ~ sP399(U_4952,U_4951) )
    & ! [U_4952,U_4951] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4952),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4951),hAPP(c_Int_Onumber__class_Onumber__of(U_4951),U_4952)),c_Groups_Ozero__class_Ozero(U_4951)))
        | ~ sP399(U_4952,U_4951) )
    & ! [U_4952,U_4951] :
        ( sP399(U_4952,U_4951)
        | ~ class_Rings_Olinordered__idom(U_4951)
        | ~ class_Int_Onumber__ring(U_4951) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP399])],[f_1447_2]) ).

cnf(f_1447_4,plain,
    ( sP399(U_4952,U_4951)
    | ~ class_Rings_Olinordered__idom(U_4951)
    | ~ class_Int_Onumber__ring(U_4951) ),
    inference(clausify,[status(thm)],[f_1447_3]) ).

cnf(f_1447_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4952),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4951),hAPP(c_Int_Onumber__class_Onumber__of(U_4951),U_4952)),c_Groups_Ozero__class_Ozero(U_4951)))
    | ~ sP399(U_4952,U_4951) ),
    inference(clausify,[status(thm)],[f_1447_3]) ).

cnf(f_1447_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4951),hAPP(c_Int_Onumber__class_Onumber__of(U_4951),U_4952)),c_Groups_Ozero__class_Ozero(U_4951)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4952),c_Int_OPls))
    | ~ sP399(U_4952,U_4951) ),
    inference(clausify,[status(thm)],[f_1447_3]) ).

fof(f_1448_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_1448_2,plain,
    ! [U_4954,U_4953] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4953),c_Groups_Ozero__class_Ozero(U_4953)),hAPP(c_Int_Onumber__class_Onumber__of(U_4953),U_4954)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4954)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4954))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4953),c_Groups_Ozero__class_Ozero(U_4953)),hAPP(c_Int_Onumber__class_Onumber__of(U_4953),U_4954))) ) )
      | ~ class_Rings_Olinordered__idom(U_4953)
      | ~ class_Int_Onumber__ring(U_4953) ),
    inference(variable_rename,[status(thm)],[f_1448_1]) ).

fof(f_1448_3,plain,
    ( ! [U_4953,U_4954] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4953),c_Groups_Ozero__class_Ozero(U_4953)),hAPP(c_Int_Onumber__class_Onumber__of(U_4953),U_4954)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4954))
        | ~ sP400(U_4953,U_4954) )
    & ! [U_4953,U_4954] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4954))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4953),c_Groups_Ozero__class_Ozero(U_4953)),hAPP(c_Int_Onumber__class_Onumber__of(U_4953),U_4954)))
        | ~ sP400(U_4953,U_4954) )
    & ! [U_4953,U_4954] :
        ( sP400(U_4953,U_4954)
        | ~ class_Rings_Olinordered__idom(U_4953)
        | ~ class_Int_Onumber__ring(U_4953) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP400])],[f_1448_2]) ).

cnf(f_1448_4,plain,
    ( sP400(U_4953,U_4954)
    | ~ class_Rings_Olinordered__idom(U_4953)
    | ~ class_Int_Onumber__ring(U_4953) ),
    inference(clausify,[status(thm)],[f_1448_3]) ).

cnf(f_1448_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4954))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4953),c_Groups_Ozero__class_Ozero(U_4953)),hAPP(c_Int_Onumber__class_Onumber__of(U_4953),U_4954)))
    | ~ sP400(U_4953,U_4954) ),
    inference(clausify,[status(thm)],[f_1448_3]) ).

cnf(f_1448_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_4953),c_Groups_Ozero__class_Ozero(U_4953)),hAPP(c_Int_Onumber__class_Onumber__of(U_4953),U_4954)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4954))
    | ~ sP400(U_4953,U_4954) ),
    inference(clausify,[status(thm)],[f_1448_3]) ).

fof(f_1449_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_1449_2,plain,
    ! [U_4955] :
      ( ( 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_4955)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4955)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4955))
        | ~ 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_4955))) ) ),
    inference(variable_rename,[status(thm)],[f_1449_1]) ).

fof(f_1449_3,plain,
    ( ! [U_4957] :
        ( 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_4957)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4957)) )
    & ! [U_4956] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4956))
        | ~ 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_4956))) ) ),
    inference(miniscope,[status(thm)],[f_1449_2]) ).

fof(f_1449_4,plain,
    ( ! [U_4957] :
        ( 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_4957)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4957)) )
    & ! [U_4956] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4956))
        | ~ 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_4956))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1449_3]) ).

cnf(f_1449_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4956))
    | ~ 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_4956))) ),
    inference(clausify,[status(thm)],[f_1449_4]) ).

cnf(f_1449_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_4957)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4957)) ),
    inference(clausify,[status(thm)],[f_1449_4]) ).

fof(f_1450_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_1450_2,plain,
    ! [U_4959,U_4958] :
      ( ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4958)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4959)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4958),U_4959))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4959),c_Int_OPls)) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4958)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4959)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4958)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4959),c_Int_OPls)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4958),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4958)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4959)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4959)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4958),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1450_1]) ).

fof(f_1450_3,plain,
    ( ! [U_4963,U_4961] :
        ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4961)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4963)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4961),U_4963))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4963),c_Int_OPls)) )
          & ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4961)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4963)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4961)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4963),c_Int_OPls)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4961),c_Int_OPls)) )
    & ! [U_4962,U_4960] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4960)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4962)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4962)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4960),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1450_2]) ).

fof(f_1450_4,plain,
    ( ! [U_4963,U_4961] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4961)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4963)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4961),U_4963))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4963),c_Int_OPls))
        | ~ sP401(U_4963,U_4961) )
    & ! [U_4963,U_4961] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4961)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4963)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4961)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4963),c_Int_OPls))
        | ~ sP401(U_4963,U_4961) )
    & ! [U_4963,U_4961] :
        ( sP401(U_4963,U_4961)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4961),c_Int_OPls)) )
    & ! [U_4960,U_4962] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4960)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4962)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4962)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4960),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP401])],[f_1450_3]) ).

cnf(f_1450_5,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4960)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4962)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4962)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4960),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1450_4]) ).

cnf(f_1450_6,plain,
    ( sP401(U_4963,U_4961)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4961),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1450_4]) ).

cnf(f_1450_7,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4961)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4963)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4961)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4963),c_Int_OPls))
    | ~ sP401(U_4963,U_4961) ),
    inference(clausify,[status(thm)],[f_1450_4]) ).

cnf(f_1450_8,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4961)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4963)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4961),U_4963))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4963),c_Int_OPls))
    | ~ sP401(U_4963,U_4961) ),
    inference(clausify,[status(thm)],[f_1450_4]) ).

fof(f_1451_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_1451_2,plain,
    ! [U_4965,U_4964] :
      ( hBOOL(hAPP(hAPP(c_member(U_4964),hAPP(c_Int_Onumber__class_Onumber__of(U_4964),U_4965)),c_Nat_Osemiring__1__class_ONats(U_4964)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4965))
      | ~ class_Int_Onumber__ring(U_4964) ),
    inference(variable_rename,[status(thm)],[f_1451_1]) ).

fof(f_1451_3,plain,
    ! [U_4965,U_4964] :
      ( hBOOL(hAPP(hAPP(c_member(U_4964),hAPP(c_Int_Onumber__class_Onumber__of(U_4964),U_4965)),c_Nat_Osemiring__1__class_ONats(U_4964)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4965))
      | ~ class_Int_Onumber__ring(U_4964) ),
    inference(definitional_conversion,[status(esa)],[f_1451_2]) ).

cnf(f_1451_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_4964),hAPP(c_Int_Onumber__class_Onumber__of(U_4964),U_4965)),c_Nat_Osemiring__1__class_ONats(U_4964)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_4965))
    | ~ class_Int_Onumber__ring(U_4964) ),
    inference(clausify,[status(thm)],[f_1451_3]) ).

fof(f_1452_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_1452_2,plain,
    ! [U_4967,U_4966] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4966)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4967)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4966),U_4967))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4966),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4966)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4967)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4966),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1452_1]) ).

fof(f_1452_3,plain,
    ( ! [U_4971,U_4969] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4969)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4971)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4969),U_4971))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4969),c_Int_OPls)) )
    & ! [U_4970,U_4968] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4968)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4970)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4968),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1452_2]) ).

fof(f_1452_4,plain,
    ( ! [U_4971,U_4969] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4969)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4971)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4969),U_4971))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4969),c_Int_OPls)) )
    & ! [U_4970,U_4968] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4968)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4970)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4968),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1452_3]) ).

cnf(f_1452_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4968)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4970)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4968),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1452_4]) ).

cnf(f_1452_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4969)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4971)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_4969),U_4971))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4969),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1452_4]) ).

fof(f_1453_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_1453_2,plain,
    ! [U_4974,U_4973,U_4972] :
      ( ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4972)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4973)),U_4974)) = 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_4972),U_4973))),U_4974)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4972),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4972)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4973)),U_4974)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4972),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1453_1]) ).

fof(f_1453_3,plain,
    ( ! [U_4980,U_4978,U_4976] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4976)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4978)),U_4980)) = 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_4976),U_4978))),U_4980)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4976),c_Int_OPls)) )
    & ! [U_4979,U_4977,U_4975] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4975)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4977)),U_4979)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4975),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1453_2]) ).

fof(f_1453_4,plain,
    ( ! [U_4976,U_4978,U_4980] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4976)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4978)),U_4980)) = 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_4976),U_4978))),U_4980)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4976),c_Int_OPls)) )
    & ! [U_4977,U_4975,U_4979] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4975)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4977)),U_4979)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4975),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1453_3]) ).

cnf(f_1453_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4975)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4977)),U_4979)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4975),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1453_4]) ).

cnf(f_1453_6,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4976)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4978)),U_4980)) = 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_4976),U_4978))),U_4980)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_4976),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1453_4]) ).

fof(f_1454_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_1454_2,plain,
    ! [U_4981] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4981)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4981))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4981),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4981)),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_4981),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1454_1]) ).

fof(f_1454_3,plain,
    ( ! [U_4983] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4983)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4983))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4983),c_Int_OPls)) )
    & ! [U_4982] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4982)),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_4982),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1454_2]) ).

fof(f_1454_4,plain,
    ( ! [U_4983] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4983)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4983))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4983),c_Int_OPls)) )
    & ! [U_4982] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4982)),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_4982),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1454_3]) ).

cnf(f_1454_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4982)),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_4982),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1454_4]) ).

cnf(f_1454_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4983)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4983))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_4983),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1454_4]) ).

fof(f_1455_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_1455_2,plain,
    ! [U_4985,U_4984] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4985)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4984)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4985),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4984)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4984)) ),
    inference(variable_rename,[status(thm)],[f_1455_1]) ).

fof(f_1455_3,plain,
    ! [U_4984,U_4985] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4985)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4984)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4985),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4984)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4984)) ),
    inference(definitional_conversion,[status(esa)],[f_1455_2]) ).

cnf(f_1455_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_4985)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_4984)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_4985),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_Opred(U_4984)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_4984)) ),
    inference(clausify,[status(thm)],[f_1455_3]) ).

fof(f_1456_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_1456_2,plain,
    ! [U_4987,U_4986] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_4986),U_4987) = c_Groups_Oone__class_Oone(U_4986)
          | ~ c_Int_Oiszero(U_4986,hAPP(c_Int_Onumber__class_Onumber__of(U_4986),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4987),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))) )
        & ( c_Int_Oiszero(U_4986,hAPP(c_Int_Onumber__class_Onumber__of(U_4986),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4987),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
          | hAPP(c_Int_Onumber__class_Onumber__of(U_4986),U_4987) != c_Groups_Oone__class_Oone(U_4986) ) )
      | ~ class_Int_Onumber__ring(U_4986) ),
    inference(variable_rename,[status(thm)],[f_1456_1]) ).

fof(f_1456_3,plain,
    ( ! [U_4986,U_4987] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_4986),U_4987) = c_Groups_Oone__class_Oone(U_4986)
        | ~ c_Int_Oiszero(U_4986,hAPP(c_Int_Onumber__class_Onumber__of(U_4986),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4987),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
        | ~ sP402(U_4986,U_4987) )
    & ! [U_4986,U_4987] :
        ( c_Int_Oiszero(U_4986,hAPP(c_Int_Onumber__class_Onumber__of(U_4986),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4987),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(U_4986),U_4987) != c_Groups_Oone__class_Oone(U_4986)
        | ~ sP402(U_4986,U_4987) )
    & ! [U_4986,U_4987] :
        ( sP402(U_4986,U_4987)
        | ~ class_Int_Onumber__ring(U_4986) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP402])],[f_1456_2]) ).

cnf(f_1456_4,plain,
    ( sP402(U_4986,U_4987)
    | ~ class_Int_Onumber__ring(U_4986) ),
    inference(clausify,[status(thm)],[f_1456_3]) ).

cnf(f_1456_5,plain,
    ( c_Int_Oiszero(U_4986,hAPP(c_Int_Onumber__class_Onumber__of(U_4986),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4987),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_4986),U_4987) != c_Groups_Oone__class_Oone(U_4986)
    | ~ sP402(U_4986,U_4987) ),
    inference(clausify,[status(thm)],[f_1456_3]) ).

cnf(f_1456_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_4986),U_4987) = c_Groups_Oone__class_Oone(U_4986)
    | ~ c_Int_Oiszero(U_4986,hAPP(c_Int_Onumber__class_Onumber__of(U_4986),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4987),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)))))
    | ~ sP402(U_4986,U_4987) ),
    inference(clausify,[status(thm)],[f_1456_3]) ).

fof(f_1457_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_1457_2,plain,
    ! [U_4989,U_4988] :
      ( ( ( c_Groups_Oone__class_Oone(U_4988) = hAPP(c_Int_Onumber__class_Onumber__of(U_4988),U_4989)
          | ~ c_Int_Oiszero(U_4988,hAPP(c_Int_Onumber__class_Onumber__of(U_4988),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_4989)))) )
        & ( c_Int_Oiszero(U_4988,hAPP(c_Int_Onumber__class_Onumber__of(U_4988),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_4989))))
          | c_Groups_Oone__class_Oone(U_4988) != hAPP(c_Int_Onumber__class_Onumber__of(U_4988),U_4989) ) )
      | ~ class_Int_Onumber__ring(U_4988) ),
    inference(variable_rename,[status(thm)],[f_1457_1]) ).

fof(f_1457_3,plain,
    ( ! [U_4989,U_4988] :
        ( c_Groups_Oone__class_Oone(U_4988) = hAPP(c_Int_Onumber__class_Onumber__of(U_4988),U_4989)
        | ~ c_Int_Oiszero(U_4988,hAPP(c_Int_Onumber__class_Onumber__of(U_4988),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_4989))))
        | ~ sP403(U_4989,U_4988) )
    & ! [U_4989,U_4988] :
        ( c_Int_Oiszero(U_4988,hAPP(c_Int_Onumber__class_Onumber__of(U_4988),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_4989))))
        | c_Groups_Oone__class_Oone(U_4988) != hAPP(c_Int_Onumber__class_Onumber__of(U_4988),U_4989)
        | ~ sP403(U_4989,U_4988) )
    & ! [U_4989,U_4988] :
        ( sP403(U_4989,U_4988)
        | ~ class_Int_Onumber__ring(U_4988) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP403])],[f_1457_2]) ).

cnf(f_1457_4,plain,
    ( sP403(U_4989,U_4988)
    | ~ class_Int_Onumber__ring(U_4988) ),
    inference(clausify,[status(thm)],[f_1457_3]) ).

cnf(f_1457_5,plain,
    ( c_Int_Oiszero(U_4988,hAPP(c_Int_Onumber__class_Onumber__of(U_4988),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_4989))))
    | c_Groups_Oone__class_Oone(U_4988) != hAPP(c_Int_Onumber__class_Onumber__of(U_4988),U_4989)
    | ~ sP403(U_4989,U_4988) ),
    inference(clausify,[status(thm)],[f_1457_3]) ).

cnf(f_1457_6,plain,
    ( c_Groups_Oone__class_Oone(U_4988) = hAPP(c_Int_Onumber__class_Onumber__of(U_4988),U_4989)
    | ~ c_Int_Oiszero(U_4988,hAPP(c_Int_Onumber__class_Onumber__of(U_4988),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_4989))))
    | ~ sP403(U_4989,U_4988) ),
    inference(clausify,[status(thm)],[f_1457_3]) ).

fof(f_1458_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_1458_2,plain,
    ! [U_4991,U_4990] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4990),c_Groups_Oone__class_Oone(U_4990)),hAPP(c_Int_Onumber__class_Onumber__of(U_4990),U_4991)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4990),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_4991)))
      | ~ class_Int_Onumber__ring(U_4990) ),
    inference(variable_rename,[status(thm)],[f_1458_1]) ).

fof(f_1458_3,plain,
    ! [U_4991,U_4990] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4990),c_Groups_Oone__class_Oone(U_4990)),hAPP(c_Int_Onumber__class_Onumber__of(U_4990),U_4991)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4990),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_4991)))
      | ~ class_Int_Onumber__ring(U_4990) ),
    inference(definitional_conversion,[status(esa)],[f_1458_2]) ).

cnf(f_1458_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4990),c_Groups_Oone__class_Oone(U_4990)),hAPP(c_Int_Onumber__class_Onumber__of(U_4990),U_4991)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4990),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_4991)))
    | ~ class_Int_Onumber__ring(U_4990) ),
    inference(clausify,[status(thm)],[f_1458_3]) ).

fof(f_1459_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_1459_2,plain,
    ! [U_4993,U_4992] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4992),hAPP(c_Int_Onumber__class_Onumber__of(U_4992),U_4993)),c_Groups_Oone__class_Oone(U_4992)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4992),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4993),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
      | ~ class_Int_Onumber__ring(U_4992) ),
    inference(variable_rename,[status(thm)],[f_1459_1]) ).

fof(f_1459_3,plain,
    ! [U_4992,U_4993] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4992),hAPP(c_Int_Onumber__class_Onumber__of(U_4992),U_4993)),c_Groups_Oone__class_Oone(U_4992)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4992),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4993),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
      | ~ class_Int_Onumber__ring(U_4992) ),
    inference(definitional_conversion,[status(esa)],[f_1459_2]) ).

cnf(f_1459_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_4992),hAPP(c_Int_Onumber__class_Onumber__of(U_4992),U_4993)),c_Groups_Oone__class_Oone(U_4992)) = hAPP(c_Int_Onumber__class_Onumber__of(U_4992),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_4993),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls))))
    | ~ class_Int_Onumber__ring(U_4992) ),
    inference(clausify,[status(thm)],[f_1459_3]) ).

fof(f_1460_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_1460_2,plain,
    ! [U_4994] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_4994)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4994))),
    inference(variable_rename,[status(thm)],[f_1460_1]) ).

fof(f_1460_3,plain,
    ! [U_4994] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_4994)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4994))),
    inference(definitional_conversion,[status(esa)],[f_1460_2]) ).

cnf(f_1460_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit1(U_4994)) = c_Int_OBit1(c_Int_Opred(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_4994))),
    inference(clausify,[status(thm)],[f_1460_3]) ).

fof(f_1461_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_1461_2,plain,
    ! [U_4996,U_4995] :
      ( ( c_Int_OBit1(U_4995) = c_Int_OBit1(U_4996)
        | U_4995 != U_4996 )
      & ( U_4995 = U_4996
        | c_Int_OBit1(U_4995) != c_Int_OBit1(U_4996) ) ),
    inference(variable_rename,[status(thm)],[f_1461_1]) ).

fof(f_1461_3,plain,
    ( ! [U_5000,U_4998] :
        ( c_Int_OBit1(U_4998) = c_Int_OBit1(U_5000)
        | U_4998 != U_5000 )
    & ! [U_4999,U_4997] :
        ( U_4997 = U_4999
        | c_Int_OBit1(U_4997) != c_Int_OBit1(U_4999) ) ),
    inference(miniscope,[status(thm)],[f_1461_2]) ).

fof(f_1461_4,plain,
    ( ! [U_4998,U_5000] :
        ( c_Int_OBit1(U_4998) = c_Int_OBit1(U_5000)
        | U_4998 != U_5000 )
    & ! [U_4999,U_4997] :
        ( U_4997 = U_4999
        | c_Int_OBit1(U_4997) != c_Int_OBit1(U_4999) ) ),
    inference(definitional_conversion,[status(esa)],[f_1461_3]) ).

cnf(f_1461_5,plain,
    ( U_4997 = U_4999
    | c_Int_OBit1(U_4997) != c_Int_OBit1(U_4999) ),
    inference(clausify,[status(thm)],[f_1461_4]) ).

cnf(f_1461_6,plain,
    ( c_Int_OBit1(U_4998) = c_Int_OBit1(U_5000)
    | U_4998 != U_5000 ),
    inference(clausify,[status(thm)],[f_1461_4]) ).

fof(f_1462_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_1462_2,plain,
    ! [U_5002,U_5001] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5001)),c_Int_OBit1(U_5002)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5001),U_5002)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5001),U_5002))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5001)),c_Int_OBit1(U_5002))) ) ),
    inference(variable_rename,[status(thm)],[f_1462_1]) ).

fof(f_1462_3,plain,
    ( ! [U_5006,U_5004] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5004)),c_Int_OBit1(U_5006)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5004),U_5006)) )
    & ! [U_5005,U_5003] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5003),U_5005))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5003)),c_Int_OBit1(U_5005))) ) ),
    inference(miniscope,[status(thm)],[f_1462_2]) ).

fof(f_1462_4,plain,
    ( ! [U_5004,U_5006] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5004)),c_Int_OBit1(U_5006)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5004),U_5006)) )
    & ! [U_5005,U_5003] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5003),U_5005))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5003)),c_Int_OBit1(U_5005))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1462_3]) ).

cnf(f_1462_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5003),U_5005))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5003)),c_Int_OBit1(U_5005))) ),
    inference(clausify,[status(thm)],[f_1462_4]) ).

cnf(f_1462_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5004)),c_Int_OBit1(U_5006)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5004),U_5006)) ),
    inference(clausify,[status(thm)],[f_1462_4]) ).

fof(f_1463_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_1463_2,plain,
    ! [U_5008,U_5007] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5007)),c_Int_OBit1(U_5008)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5007),U_5008)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5007),U_5008))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5007)),c_Int_OBit1(U_5008))) ) ),
    inference(variable_rename,[status(thm)],[f_1463_1]) ).

fof(f_1463_3,plain,
    ( ! [U_5012,U_5010] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5010)),c_Int_OBit1(U_5012)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5010),U_5012)) )
    & ! [U_5011,U_5009] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5009),U_5011))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5009)),c_Int_OBit1(U_5011))) ) ),
    inference(miniscope,[status(thm)],[f_1463_2]) ).

fof(f_1463_4,plain,
    ( ! [U_5010,U_5012] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5010)),c_Int_OBit1(U_5012)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5010),U_5012)) )
    & ! [U_5011,U_5009] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5009),U_5011))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5009)),c_Int_OBit1(U_5011))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1463_3]) ).

cnf(f_1463_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5009),U_5011))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5009)),c_Int_OBit1(U_5011))) ),
    inference(clausify,[status(thm)],[f_1463_4]) ).

cnf(f_1463_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5010)),c_Int_OBit1(U_5012)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5010),U_5012)) ),
    inference(clausify,[status(thm)],[f_1463_4]) ).

fof(f_1464_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_1464_2,plain,
    ! [U_5014,U_5013] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5013)),c_Int_OBit1(U_5014)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5013),U_5014)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5013),U_5014))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5013)),c_Int_OBit1(U_5014))) ) ),
    inference(variable_rename,[status(thm)],[f_1464_1]) ).

fof(f_1464_3,plain,
    ( ! [U_5018,U_5016] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5016)),c_Int_OBit1(U_5018)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5016),U_5018)) )
    & ! [U_5017,U_5015] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5015),U_5017))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5015)),c_Int_OBit1(U_5017))) ) ),
    inference(miniscope,[status(thm)],[f_1464_2]) ).

fof(f_1464_4,plain,
    ( ! [U_5016,U_5018] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5016)),c_Int_OBit1(U_5018)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5016),U_5018)) )
    & ! [U_5017,U_5015] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5015),U_5017))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5015)),c_Int_OBit1(U_5017))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1464_3]) ).

cnf(f_1464_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5015),U_5017))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5015)),c_Int_OBit1(U_5017))) ),
    inference(clausify,[status(thm)],[f_1464_4]) ).

cnf(f_1464_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5016)),c_Int_OBit1(U_5018)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5016),U_5018)) ),
    inference(clausify,[status(thm)],[f_1464_4]) ).

fof(f_1465_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_1465_2,plain,
    ! [U_5020,U_5019] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5019)),c_Int_OBit1(U_5020)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5019),U_5020)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5019),U_5020))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5019)),c_Int_OBit1(U_5020))) ) ),
    inference(variable_rename,[status(thm)],[f_1465_1]) ).

fof(f_1465_3,plain,
    ( ! [U_5024,U_5022] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5022)),c_Int_OBit1(U_5024)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5022),U_5024)) )
    & ! [U_5023,U_5021] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5021),U_5023))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5021)),c_Int_OBit1(U_5023))) ) ),
    inference(miniscope,[status(thm)],[f_1465_2]) ).

fof(f_1465_4,plain,
    ( ! [U_5022,U_5024] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5022)),c_Int_OBit1(U_5024)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5022),U_5024)) )
    & ! [U_5023,U_5021] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5021),U_5023))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5021)),c_Int_OBit1(U_5023))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1465_3]) ).

cnf(f_1465_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5021),U_5023))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5021)),c_Int_OBit1(U_5023))) ),
    inference(clausify,[status(thm)],[f_1465_4]) ).

cnf(f_1465_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5022)),c_Int_OBit1(U_5024)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5022),U_5024)) ),
    inference(clausify,[status(thm)],[f_1465_4]) ).

fof(f_1466_1,plain,
    ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I46_J]) ).

fof(f_1466_2,plain,
    ! [U_5025] : c_Int_OBit1(U_5025) != c_Int_OPls,
    inference(variable_rename,[status(thm)],[f_1466_1]) ).

fof(f_1466_3,plain,
    ! [U_5025] : c_Int_OBit1(U_5025) != c_Int_OPls,
    inference(definitional_conversion,[status(esa)],[f_1466_2]) ).

cnf(f_1466_4,plain,
    c_Int_OBit1(U_5025) != c_Int_OPls,
    inference(clausify,[status(thm)],[f_1466_3]) ).

fof(f_1467_1,plain,
    ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I39_J]) ).

fof(f_1467_2,plain,
    ! [U_5026] : c_Int_OPls != c_Int_OBit1(U_5026),
    inference(variable_rename,[status(thm)],[f_1467_1]) ).

fof(f_1467_3,plain,
    ! [U_5026] : c_Int_OPls != c_Int_OBit1(U_5026),
    inference(definitional_conversion,[status(esa)],[f_1467_2]) ).

cnf(f_1467_4,plain,
    c_Int_OPls != c_Int_OBit1(U_5026),
    inference(clausify,[status(thm)],[f_1467_3]) ).

fof(f_1468_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_1468_2,plain,
    ! [U_5027] :
      ( ( c_Int_OBit1(U_5027) = c_Int_OMin
        | U_5027 != c_Int_OMin )
      & ( U_5027 = c_Int_OMin
        | c_Int_OBit1(U_5027) != c_Int_OMin ) ),
    inference(variable_rename,[status(thm)],[f_1468_1]) ).

fof(f_1468_3,plain,
    ( ! [U_5029] :
        ( c_Int_OBit1(U_5029) = c_Int_OMin
        | U_5029 != c_Int_OMin )
    & ! [U_5028] :
        ( U_5028 = c_Int_OMin
        | c_Int_OBit1(U_5028) != c_Int_OMin ) ),
    inference(miniscope,[status(thm)],[f_1468_2]) ).

fof(f_1468_4,plain,
    ( ! [U_5029] :
        ( c_Int_OBit1(U_5029) = c_Int_OMin
        | U_5029 != c_Int_OMin )
    & ! [U_5028] :
        ( U_5028 = c_Int_OMin
        | c_Int_OBit1(U_5028) != c_Int_OMin ) ),
    inference(definitional_conversion,[status(esa)],[f_1468_3]) ).

cnf(f_1468_5,plain,
    ( U_5028 = c_Int_OMin
    | c_Int_OBit1(U_5028) != c_Int_OMin ),
    inference(clausify,[status(thm)],[f_1468_4]) ).

cnf(f_1468_6,plain,
    ( c_Int_OBit1(U_5029) = c_Int_OMin
    | U_5029 != c_Int_OMin ),
    inference(clausify,[status(thm)],[f_1468_4]) ).

fof(f_1469_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_1469_2,plain,
    ! [U_5030] :
      ( ( c_Int_OMin = c_Int_OBit1(U_5030)
        | c_Int_OMin != U_5030 )
      & ( c_Int_OMin = U_5030
        | c_Int_OMin != c_Int_OBit1(U_5030) ) ),
    inference(variable_rename,[status(thm)],[f_1469_1]) ).

fof(f_1469_3,plain,
    ( ! [U_5032] :
        ( c_Int_OMin = c_Int_OBit1(U_5032)
        | c_Int_OMin != U_5032 )
    & ! [U_5031] :
        ( c_Int_OMin = U_5031
        | c_Int_OMin != c_Int_OBit1(U_5031) ) ),
    inference(miniscope,[status(thm)],[f_1469_2]) ).

fof(f_1469_4,plain,
    ( ! [U_5032] :
        ( c_Int_OMin = c_Int_OBit1(U_5032)
        | c_Int_OMin != U_5032 )
    & ! [U_5031] :
        ( c_Int_OMin = U_5031
        | c_Int_OMin != c_Int_OBit1(U_5031) ) ),
    inference(definitional_conversion,[status(esa)],[f_1469_3]) ).

cnf(f_1469_5,plain,
    ( c_Int_OMin = U_5031
    | c_Int_OMin != c_Int_OBit1(U_5031) ),
    inference(clausify,[status(thm)],[f_1469_4]) ).

cnf(f_1469_6,plain,
    ( c_Int_OMin = c_Int_OBit1(U_5032)
    | c_Int_OMin != U_5032 ),
    inference(clausify,[status(thm)],[f_1469_4]) ).

fof(f_1470_1,plain,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_Bit1__Min]) ).

fof(f_1470_2,plain,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    inference(definitional_conversion,[status(esa)],[f_1470_1]) ).

cnf(f_1470_3,plain,
    c_Int_OBit1(c_Int_OMin) = c_Int_OMin,
    inference(clausify,[status(thm)],[f_1470_2]) ).

fof(f_1471_1,plain,
    ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x,
    inference(fof_nnf,[status(thm)],[fact_succ__pred]) ).

fof(f_1471_2,plain,
    ! [U_5033] : c_Int_Osucc(c_Int_Opred(U_5033)) = U_5033,
    inference(variable_rename,[status(thm)],[f_1471_1]) ).

fof(f_1471_3,plain,
    ! [U_5033] : c_Int_Osucc(c_Int_Opred(U_5033)) = U_5033,
    inference(definitional_conversion,[status(esa)],[f_1471_2]) ).

cnf(f_1471_4,plain,
    c_Int_Osucc(c_Int_Opred(U_5033)) = U_5033,
    inference(clausify,[status(thm)],[f_1471_3]) ).

fof(f_1472_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_1472_2,plain,
    ! [U_5034] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5034)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5034),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5034),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5034)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1472_1]) ).

fof(f_1472_3,plain,
    ( ! [U_5036] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5036)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5036),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_5035] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5035),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5035)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1472_2]) ).

fof(f_1472_4,plain,
    ( ! [U_5036] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5036)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5036),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_5035] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5035),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5035)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    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_5035),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5035)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    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_OBit1(U_5036)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5036),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1472_4]) ).

fof(f_1473_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_1473_2,plain,
    ! [U_5037] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5037)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5037)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5037))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5037))) ) ),
    inference(variable_rename,[status(thm)],[f_1473_1]) ).

fof(f_1473_3,plain,
    ( ! [U_5039] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5039)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5039)) )
    & ! [U_5038] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5038))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5038))) ) ),
    inference(miniscope,[status(thm)],[f_1473_2]) ).

fof(f_1473_4,plain,
    ( ! [U_5039] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5039)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5039)) )
    & ! [U_5038] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5038))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5038))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1473_3]) ).

cnf(f_1473_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5038))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5038))) ),
    inference(clausify,[status(thm)],[f_1473_4]) ).

cnf(f_1473_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5039)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5039)) ),
    inference(clausify,[status(thm)],[f_1473_4]) ).

fof(f_1474_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_1474_2,plain,
    ! [U_5040] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5040)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5040),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5040),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5040)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1474_1]) ).

fof(f_1474_3,plain,
    ( ! [U_5042] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5042)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5042),c_Int_OPls)) )
    & ! [U_5041] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5041),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5041)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1474_2]) ).

fof(f_1474_4,plain,
    ( ! [U_5042] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5042)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5042),c_Int_OPls)) )
    & ! [U_5041] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5041),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5041)),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1474_3]) ).

cnf(f_1474_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5041),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5041)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1474_4]) ).

cnf(f_1474_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5042)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5042),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1474_4]) ).

fof(f_1475_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_1475_2,plain,
    ! [U_5043] : c_Int_OBit1(U_5043) = 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_5043)),U_5043),
    inference(variable_rename,[status(thm)],[f_1475_1]) ).

fof(f_1475_3,plain,
    ! [U_5043] : c_Int_OBit1(U_5043) = 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_5043)),U_5043),
    inference(definitional_conversion,[status(esa)],[f_1475_2]) ).

cnf(f_1475_4,plain,
    c_Int_OBit1(U_5043) = 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_5043)),U_5043),
    inference(clausify,[status(thm)],[f_1475_3]) ).

fof(f_1476_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_1476_2,plain,
    ! [U_5044] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5044)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5044),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5044),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5044)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_1476_1]) ).

fof(f_1476_3,plain,
    ( ! [U_5046] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5046)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5046),c_Int_OMin)) )
    & ! [U_5045] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5045),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5045)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_1476_2]) ).

fof(f_1476_4,plain,
    ( ! [U_5046] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5046)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5046),c_Int_OMin)) )
    & ! [U_5045] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5045),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5045)),c_Int_OMin)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1476_3]) ).

cnf(f_1476_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5045),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5045)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1476_4]) ).

cnf(f_1476_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5046)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5046),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1476_4]) ).

fof(f_1477_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_1477_2,plain,
    ! [U_5047] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5047)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_5047)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_5047))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5047))) ) ),
    inference(variable_rename,[status(thm)],[f_1477_1]) ).

fof(f_1477_3,plain,
    ( ! [U_5049] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5049)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_5049)) )
    & ! [U_5048] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_5048))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5048))) ) ),
    inference(miniscope,[status(thm)],[f_1477_2]) ).

fof(f_1477_4,plain,
    ( ! [U_5049] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5049)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_5049)) )
    & ! [U_5048] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_5048))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5048))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1477_3]) ).

cnf(f_1477_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_5048))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5048))) ),
    inference(clausify,[status(thm)],[f_1477_4]) ).

cnf(f_1477_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5049)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),U_5049)) ),
    inference(clausify,[status(thm)],[f_1477_4]) ).

fof(f_1478_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_1478_2,plain,
    ! [U_5050] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5050)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5050)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5050))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5050))) ) ),
    inference(variable_rename,[status(thm)],[f_1478_1]) ).

fof(f_1478_3,plain,
    ( ! [U_5052] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5052)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5052)) )
    & ! [U_5051] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5051))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5051))) ) ),
    inference(miniscope,[status(thm)],[f_1478_2]) ).

fof(f_1478_4,plain,
    ( ! [U_5052] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5052)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5052)) )
    & ! [U_5051] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5051))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5051))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1478_3]) ).

cnf(f_1478_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5051))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5051))) ),
    inference(clausify,[status(thm)],[f_1478_4]) ).

cnf(f_1478_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5052)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5052)) ),
    inference(clausify,[status(thm)],[f_1478_4]) ).

fof(f_1479_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_1479_2,plain,
    ! [U_5053] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5053)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5053),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5053),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5053)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_1479_1]) ).

fof(f_1479_3,plain,
    ( ! [U_5055] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5055)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5055),c_Int_OMin)) )
    & ! [U_5054] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5054),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5054)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_1479_2]) ).

fof(f_1479_4,plain,
    ( ! [U_5055] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5055)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5055),c_Int_OMin)) )
    & ! [U_5054] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5054),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5054)),c_Int_OMin)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1479_3]) ).

cnf(f_1479_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5054),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5054)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1479_4]) ).

cnf(f_1479_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5055)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5055),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1479_4]) ).

fof(f_1480_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_1480_2,plain,
    ! [U_5056] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5056))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5056))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5056)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5056)))) ) ),
    inference(variable_rename,[status(thm)],[f_1480_1]) ).

fof(f_1480_3,plain,
    ( ! [U_5058] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5058))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5058))) )
    & ! [U_5057] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5057)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5057)))) ) ),
    inference(miniscope,[status(thm)],[f_1480_2]) ).

fof(f_1480_4,plain,
    ( ! [U_5058] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5058))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5058))) )
    & ! [U_5057] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5057)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5057)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1480_3]) ).

cnf(f_1480_5,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5057)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5057)))) ),
    inference(clausify,[status(thm)],[f_1480_4]) ).

cnf(f_1480_6,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5058))))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5058))) ),
    inference(clausify,[status(thm)],[f_1480_4]) ).

fof(f_1481_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_1481_2,plain,
    ! [U_5060,U_5059] :
      ( ~ c_Int_Oiszero(U_5059,hAPP(c_Int_Onumber__class_Onumber__of(U_5059),c_Int_OBit1(U_5060)))
      | ~ class_Int_Oring__char__0(U_5059)
      | ~ class_Int_Onumber__ring(U_5059) ),
    inference(variable_rename,[status(thm)],[f_1481_1]) ).

fof(f_1481_3,plain,
    ! [U_5059,U_5060] :
      ( ~ c_Int_Oiszero(U_5059,hAPP(c_Int_Onumber__class_Onumber__of(U_5059),c_Int_OBit1(U_5060)))
      | ~ class_Int_Oring__char__0(U_5059)
      | ~ class_Int_Onumber__ring(U_5059) ),
    inference(definitional_conversion,[status(esa)],[f_1481_2]) ).

cnf(f_1481_4,plain,
    ( ~ c_Int_Oiszero(U_5059,hAPP(c_Int_Onumber__class_Onumber__of(U_5059),c_Int_OBit1(U_5060)))
    | ~ class_Int_Oring__char__0(U_5059)
    | ~ class_Int_Onumber__ring(U_5059) ),
    inference(clausify,[status(thm)],[f_1481_3]) ).

fof(f_1482_1,plain,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    inference(fof_nnf,[status(thm)],[fact_succ__Pls]) ).

fof(f_1482_2,plain,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    inference(definitional_conversion,[status(esa)],[f_1482_1]) ).

cnf(f_1482_3,plain,
    c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls),
    inference(clausify,[status(thm)],[f_1482_2]) ).

fof(f_1483_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_1483_2,plain,
    ! [U_5062,U_5061] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5061),U_5062))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_5061)),U_5062)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_5061)),U_5062))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5061),U_5062)) ) ),
    inference(variable_rename,[status(thm)],[f_1483_1]) ).

fof(f_1483_3,plain,
    ( ! [U_5066,U_5064] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5064),U_5066))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_5064)),U_5066)) )
    & ! [U_5065,U_5063] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_5063)),U_5065))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5063),U_5065)) ) ),
    inference(miniscope,[status(thm)],[f_1483_2]) ).

fof(f_1483_4,plain,
    ( ! [U_5064,U_5066] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5064),U_5066))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_5064)),U_5066)) )
    & ! [U_5065,U_5063] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_5063)),U_5065))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5063),U_5065)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1483_3]) ).

cnf(f_1483_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_5063)),U_5065))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5063),U_5065)) ),
    inference(clausify,[status(thm)],[f_1483_4]) ).

cnf(f_1483_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5064),U_5066))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(U_5064)),U_5066)) ),
    inference(clausify,[status(thm)],[f_1483_4]) ).

fof(f_1484_1,plain,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_pred__Pls]) ).

fof(f_1484_2,plain,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    inference(definitional_conversion,[status(esa)],[f_1484_1]) ).

cnf(f_1484_3,plain,
    c_Int_Opred(c_Int_OPls) = c_Int_OMin,
    inference(clausify,[status(thm)],[f_1484_2]) ).

fof(f_1485_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_1485_2,plain,
    ! [U_5067] : c_Int_Opred(U_5067) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5067),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(variable_rename,[status(thm)],[f_1485_1]) ).

fof(f_1485_3,plain,
    ! [U_5067] : c_Int_Opred(U_5067) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5067),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_1485_2]) ).

cnf(f_1485_4,plain,
    c_Int_Opred(U_5067) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5067),c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1485_3]) ).

fof(f_1486_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_1486_2,plain,
    ! [U_5068] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5068),c_Int_OMin) = c_Int_Opred(U_5068),
    inference(variable_rename,[status(thm)],[f_1486_1]) ).

fof(f_1486_3,plain,
    ! [U_5068] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5068),c_Int_OMin) = c_Int_Opred(U_5068),
    inference(definitional_conversion,[status(esa)],[f_1486_2]) ).

cnf(f_1486_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5068),c_Int_OMin) = c_Int_Opred(U_5068),
    inference(clausify,[status(thm)],[f_1486_3]) ).

fof(f_1487_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_1487_2,plain,
    ! [U_5069] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_5069) = c_Int_Opred(U_5069),
    inference(variable_rename,[status(thm)],[f_1487_1]) ).

fof(f_1487_3,plain,
    ! [U_5069] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_5069) = c_Int_Opred(U_5069),
    inference(definitional_conversion,[status(esa)],[f_1487_2]) ).

cnf(f_1487_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),U_5069) = c_Int_Opred(U_5069),
    inference(clausify,[status(thm)],[f_1487_3]) ).

fof(f_1488_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_1488_2,plain,
    ! [U_5071,U_5070] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_5070),c_Int_OBit1(U_5071)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5070),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5070),c_Groups_Oone__class_Oone(U_5070)),hAPP(c_Int_Onumber__class_Onumber__of(U_5070),U_5071))),hAPP(c_Int_Onumber__class_Onumber__of(U_5070),U_5071))
      | ~ class_Int_Onumber__ring(U_5070) ),
    inference(variable_rename,[status(thm)],[f_1488_1]) ).

fof(f_1488_3,plain,
    ! [U_5070,U_5071] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_5070),c_Int_OBit1(U_5071)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5070),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5070),c_Groups_Oone__class_Oone(U_5070)),hAPP(c_Int_Onumber__class_Onumber__of(U_5070),U_5071))),hAPP(c_Int_Onumber__class_Onumber__of(U_5070),U_5071))
      | ~ class_Int_Onumber__ring(U_5070) ),
    inference(definitional_conversion,[status(esa)],[f_1488_2]) ).

cnf(f_1488_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5070),c_Int_OBit1(U_5071)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5070),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5070),c_Groups_Oone__class_Oone(U_5070)),hAPP(c_Int_Onumber__class_Onumber__of(U_5070),U_5071))),hAPP(c_Int_Onumber__class_Onumber__of(U_5070),U_5071))
    | ~ class_Int_Onumber__ring(U_5070) ),
    inference(clausify,[status(thm)],[f_1488_3]) ).

fof(f_1489_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_1489_2,plain,
    ! [U_5073,U_5072] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5072),hAPP(c_Int_Onumber__class_Onumber__of(U_5072),c_Int_OBit1(c_Int_OPls))),U_5073) = U_5073
      | ~ class_Int_Onumber__ring(U_5072) ),
    inference(variable_rename,[status(thm)],[f_1489_1]) ).

fof(f_1489_3,plain,
    ! [U_5072,U_5073] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5072),hAPP(c_Int_Onumber__class_Onumber__of(U_5072),c_Int_OBit1(c_Int_OPls))),U_5073) = U_5073
      | ~ class_Int_Onumber__ring(U_5072) ),
    inference(definitional_conversion,[status(esa)],[f_1489_2]) ).

cnf(f_1489_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5072),hAPP(c_Int_Onumber__class_Onumber__of(U_5072),c_Int_OBit1(c_Int_OPls))),U_5073) = U_5073
    | ~ class_Int_Onumber__ring(U_5072) ),
    inference(clausify,[status(thm)],[f_1489_3]) ).

fof(f_1490_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_1490_2,plain,
    ! [U_5075,U_5074] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5074),U_5075),hAPP(c_Int_Onumber__class_Onumber__of(U_5074),c_Int_OBit1(c_Int_OPls))) = U_5075
      | ~ class_Int_Onumber__ring(U_5074) ),
    inference(variable_rename,[status(thm)],[f_1490_1]) ).

fof(f_1490_3,plain,
    ! [U_5074,U_5075] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5074),U_5075),hAPP(c_Int_Onumber__class_Onumber__of(U_5074),c_Int_OBit1(c_Int_OPls))) = U_5075
      | ~ class_Int_Onumber__ring(U_5074) ),
    inference(definitional_conversion,[status(esa)],[f_1490_2]) ).

cnf(f_1490_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5074),U_5075),hAPP(c_Int_Onumber__class_Onumber__of(U_5074),c_Int_OBit1(c_Int_OPls))) = U_5075
    | ~ class_Int_Onumber__ring(U_5074) ),
    inference(clausify,[status(thm)],[f_1490_3]) ).

fof(f_1491_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_1491_2,plain,
    ! [U_5076] :
      ( c_Groups_Oone__class_Oone(U_5076) = hAPP(c_Int_Onumber__class_Onumber__of(U_5076),c_Int_OBit1(c_Int_OPls))
      | ~ class_Int_Onumber__ring(U_5076) ),
    inference(variable_rename,[status(thm)],[f_1491_1]) ).

fof(f_1491_3,plain,
    ! [U_5076] :
      ( c_Groups_Oone__class_Oone(U_5076) = hAPP(c_Int_Onumber__class_Onumber__of(U_5076),c_Int_OBit1(c_Int_OPls))
      | ~ class_Int_Onumber__ring(U_5076) ),
    inference(definitional_conversion,[status(esa)],[f_1491_2]) ).

cnf(f_1491_4,plain,
    ( c_Groups_Oone__class_Oone(U_5076) = hAPP(c_Int_Onumber__class_Onumber__of(U_5076),c_Int_OBit1(c_Int_OPls))
    | ~ class_Int_Onumber__ring(U_5076) ),
    inference(clausify,[status(thm)],[f_1491_3]) ).

fof(f_1492_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_1492_2,plain,
    ! [U_5077] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_5077),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_5077)
      | ~ class_Int_Onumber__ring(U_5077) ),
    inference(variable_rename,[status(thm)],[f_1492_1]) ).

fof(f_1492_3,plain,
    ! [U_5077] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_5077),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_5077)
      | ~ class_Int_Onumber__ring(U_5077) ),
    inference(definitional_conversion,[status(esa)],[f_1492_2]) ).

cnf(f_1492_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5077),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(U_5077)
    | ~ class_Int_Onumber__ring(U_5077) ),
    inference(clausify,[status(thm)],[f_1492_3]) ).

fof(f_1493_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_1493_2,plain,
    ! [U_5078] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5078)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5078),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5078),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5078)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1493_1]) ).

fof(f_1493_3,plain,
    ( ! [U_5080] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5080)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5080),c_Int_OPls)) )
    & ! [U_5079] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5079),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5079)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1493_2]) ).

fof(f_1493_4,plain,
    ( ! [U_5080] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5080)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5080),c_Int_OPls)) )
    & ! [U_5079] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5079),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5079)),c_Int_OPls)) ) ),
    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_5079),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5079)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1493_4]) ).

cnf(f_1493_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5080)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5080),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1493_4]) ).

fof(f_1494_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_1494_2,plain,
    ! [U_5081] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5081)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5081)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5081))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5081))) ) ),
    inference(variable_rename,[status(thm)],[f_1494_1]) ).

fof(f_1494_3,plain,
    ( ! [U_5083] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5083)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5083)) )
    & ! [U_5082] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5082))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5082))) ) ),
    inference(miniscope,[status(thm)],[f_1494_2]) ).

fof(f_1494_4,plain,
    ( ! [U_5083] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5083)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5083)) )
    & ! [U_5082] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5082))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5082))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1494_3]) ).

cnf(f_1494_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5082))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5082))) ),
    inference(clausify,[status(thm)],[f_1494_4]) ).

cnf(f_1494_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5083)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5083)) ),
    inference(clausify,[status(thm)],[f_1494_4]) ).

fof(f_1495_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_1495_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_1495_1]) ).

cnf(f_1495_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_1495_2]) ).

fof(f_1496_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_1496_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_1496_1]) ).

cnf(f_1496_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_1496_2]) ).

fof(f_1497_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_1497_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_1497_1]) ).

cnf(f_1497_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_1497_2]) ).

fof(f_1498_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_1498_2,plain,
    ! [U_5084] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5084)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5084)),
    inference(variable_rename,[status(thm)],[f_1498_1]) ).

fof(f_1498_3,plain,
    ! [U_5084] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(U_5084)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5084)),
    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_OPls),c_Int_OBit1(U_5084)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5084)),
    inference(clausify,[status(thm)],[f_1498_3]) ).

fof(f_1499_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_1499_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_1499_1]) ).

cnf(f_1499_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_1499_2]) ).

fof(f_1500_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_1500_2,plain,
    ! [U_5085] :
      ( ~ c_Int_Oiszero(U_5085,hAPP(c_Int_Onumber__class_Onumber__of(U_5085),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_5085) ),
    inference(variable_rename,[status(thm)],[f_1500_1]) ).

fof(f_1500_3,plain,
    ! [U_5085] :
      ( ~ c_Int_Oiszero(U_5085,hAPP(c_Int_Onumber__class_Onumber__of(U_5085),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_5085) ),
    inference(definitional_conversion,[status(esa)],[f_1500_2]) ).

cnf(f_1500_4,plain,
    ( ~ c_Int_Oiszero(U_5085,hAPP(c_Int_Onumber__class_Onumber__of(U_5085),c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(U_5085) ),
    inference(clausify,[status(thm)],[f_1500_3]) ).

fof(f_1501_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_1501_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_1501_1]) ).

cnf(f_1501_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_1501_2]) ).

fof(f_1502_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_1502_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_1502_1]) ).

cnf(f_1502_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_1502_2]) ).

fof(f_1503_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_1503_2,plain,
    ! [U_5087,U_5086] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5086),U_5087),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_5086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5086),U_5087),U_5087)),U_5087)
      | ~ class_Groups_Omonoid__mult(U_5086) ),
    inference(variable_rename,[status(thm)],[f_1503_1]) ).

fof(f_1503_3,plain,
    ! [U_5086,U_5087] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5086),U_5087),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_5086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5086),U_5087),U_5087)),U_5087)
      | ~ class_Groups_Omonoid__mult(U_5086) ),
    inference(definitional_conversion,[status(esa)],[f_1503_2]) ).

cnf(f_1503_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5086),U_5087),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_5086),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5086),U_5087),U_5087)),U_5087)
    | ~ class_Groups_Omonoid__mult(U_5086) ),
    inference(clausify,[status(thm)],[f_1503_3]) ).

fof(f_1504_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_1504_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_1504_1]) ).

cnf(f_1504_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_1504_2]) ).

fof(f_1505_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_1505_2,plain,
    ! [U_5088] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5088))) = 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_5088),
    inference(variable_rename,[status(thm)],[f_1505_1]) ).

fof(f_1505_3,plain,
    ! [U_5088] : hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5088))) = 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_5088),
    inference(definitional_conversion,[status(esa)],[f_1505_2]) ).

cnf(f_1505_4,plain,
    hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5088))) = 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_5088),
    inference(clausify,[status(thm)],[f_1505_3]) ).

fof(f_1506_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_1506_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_1506_1]) ).

cnf(f_1506_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_1506_2]) ).

fof(f_1507_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_1507_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_1507_1]) ).

cnf(f_1507_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_1507_2]) ).

fof(f_1508_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_1508_2,plain,
    ! [U_5090,U_5089] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5089),c_Groups_Oone__class_Oone(U_5089)),hAPP(c_Int_Onumber__class_Onumber__of(U_5089),U_5090)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5090)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5090))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5089),c_Groups_Oone__class_Oone(U_5089)),hAPP(c_Int_Onumber__class_Onumber__of(U_5089),U_5090))) ) )
      | ~ class_Rings_Olinordered__idom(U_5089)
      | ~ class_Int_Onumber__ring(U_5089) ),
    inference(variable_rename,[status(thm)],[f_1508_1]) ).

fof(f_1508_3,plain,
    ( ! [U_5089,U_5090] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5089),c_Groups_Oone__class_Oone(U_5089)),hAPP(c_Int_Onumber__class_Onumber__of(U_5089),U_5090)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5090))
        | ~ sP404(U_5089,U_5090) )
    & ! [U_5089,U_5090] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5090))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5089),c_Groups_Oone__class_Oone(U_5089)),hAPP(c_Int_Onumber__class_Onumber__of(U_5089),U_5090)))
        | ~ sP404(U_5089,U_5090) )
    & ! [U_5089,U_5090] :
        ( sP404(U_5089,U_5090)
        | ~ class_Rings_Olinordered__idom(U_5089)
        | ~ class_Int_Onumber__ring(U_5089) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP404])],[f_1508_2]) ).

cnf(f_1508_4,plain,
    ( sP404(U_5089,U_5090)
    | ~ class_Rings_Olinordered__idom(U_5089)
    | ~ class_Int_Onumber__ring(U_5089) ),
    inference(clausify,[status(thm)],[f_1508_3]) ).

cnf(f_1508_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5090))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5089),c_Groups_Oone__class_Oone(U_5089)),hAPP(c_Int_Onumber__class_Onumber__of(U_5089),U_5090)))
    | ~ sP404(U_5089,U_5090) ),
    inference(clausify,[status(thm)],[f_1508_3]) ).

cnf(f_1508_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5089),c_Groups_Oone__class_Oone(U_5089)),hAPP(c_Int_Onumber__class_Onumber__of(U_5089),U_5090)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5090))
    | ~ sP404(U_5089,U_5090) ),
    inference(clausify,[status(thm)],[f_1508_3]) ).

fof(f_1509_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_1509_2,plain,
    ! [U_5092,U_5091] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5091),hAPP(c_Int_Onumber__class_Onumber__of(U_5091),U_5092)),c_Groups_Oone__class_Oone(U_5091)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5092),c_Int_OBit1(c_Int_OPls))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5092),c_Int_OBit1(c_Int_OPls)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5091),hAPP(c_Int_Onumber__class_Onumber__of(U_5091),U_5092)),c_Groups_Oone__class_Oone(U_5091))) ) )
      | ~ class_Rings_Olinordered__idom(U_5091)
      | ~ class_Int_Onumber__ring(U_5091) ),
    inference(variable_rename,[status(thm)],[f_1509_1]) ).

fof(f_1509_3,plain,
    ( ! [U_5092,U_5091] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5091),hAPP(c_Int_Onumber__class_Onumber__of(U_5091),U_5092)),c_Groups_Oone__class_Oone(U_5091)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5092),c_Int_OBit1(c_Int_OPls)))
        | ~ sP405(U_5092,U_5091) )
    & ! [U_5092,U_5091] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5092),c_Int_OBit1(c_Int_OPls)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5091),hAPP(c_Int_Onumber__class_Onumber__of(U_5091),U_5092)),c_Groups_Oone__class_Oone(U_5091)))
        | ~ sP405(U_5092,U_5091) )
    & ! [U_5092,U_5091] :
        ( sP405(U_5092,U_5091)
        | ~ class_Rings_Olinordered__idom(U_5091)
        | ~ class_Int_Onumber__ring(U_5091) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP405])],[f_1509_2]) ).

cnf(f_1509_4,plain,
    ( sP405(U_5092,U_5091)
    | ~ class_Rings_Olinordered__idom(U_5091)
    | ~ class_Int_Onumber__ring(U_5091) ),
    inference(clausify,[status(thm)],[f_1509_3]) ).

cnf(f_1509_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5092),c_Int_OBit1(c_Int_OPls)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5091),hAPP(c_Int_Onumber__class_Onumber__of(U_5091),U_5092)),c_Groups_Oone__class_Oone(U_5091)))
    | ~ sP405(U_5092,U_5091) ),
    inference(clausify,[status(thm)],[f_1509_3]) ).

cnf(f_1509_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5091),hAPP(c_Int_Onumber__class_Onumber__of(U_5091),U_5092)),c_Groups_Oone__class_Oone(U_5091)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5092),c_Int_OBit1(c_Int_OPls)))
    | ~ sP405(U_5092,U_5091) ),
    inference(clausify,[status(thm)],[f_1509_3]) ).

fof(f_1510_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_1510_2,plain,
    ! [U_5094,U_5093] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5093),hAPP(c_Int_Onumber__class_Onumber__of(U_5093),U_5094)),c_Groups_Oone__class_Oone(U_5093)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5094),c_Int_OBit1(c_Int_OPls))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5094),c_Int_OBit1(c_Int_OPls)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5093),hAPP(c_Int_Onumber__class_Onumber__of(U_5093),U_5094)),c_Groups_Oone__class_Oone(U_5093))) ) )
      | ~ class_Rings_Olinordered__idom(U_5093)
      | ~ class_Int_Onumber__ring(U_5093) ),
    inference(variable_rename,[status(thm)],[f_1510_1]) ).

fof(f_1510_3,plain,
    ( ! [U_5093,U_5094] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5093),hAPP(c_Int_Onumber__class_Onumber__of(U_5093),U_5094)),c_Groups_Oone__class_Oone(U_5093)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5094),c_Int_OBit1(c_Int_OPls)))
        | ~ sP406(U_5093,U_5094) )
    & ! [U_5093,U_5094] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5094),c_Int_OBit1(c_Int_OPls)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5093),hAPP(c_Int_Onumber__class_Onumber__of(U_5093),U_5094)),c_Groups_Oone__class_Oone(U_5093)))
        | ~ sP406(U_5093,U_5094) )
    & ! [U_5093,U_5094] :
        ( sP406(U_5093,U_5094)
        | ~ class_Rings_Olinordered__idom(U_5093)
        | ~ class_Int_Onumber__ring(U_5093) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP406])],[f_1510_2]) ).

cnf(f_1510_4,plain,
    ( sP406(U_5093,U_5094)
    | ~ class_Rings_Olinordered__idom(U_5093)
    | ~ class_Int_Onumber__ring(U_5093) ),
    inference(clausify,[status(thm)],[f_1510_3]) ).

cnf(f_1510_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5094),c_Int_OBit1(c_Int_OPls)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5093),hAPP(c_Int_Onumber__class_Onumber__of(U_5093),U_5094)),c_Groups_Oone__class_Oone(U_5093)))
    | ~ sP406(U_5093,U_5094) ),
    inference(clausify,[status(thm)],[f_1510_3]) ).

cnf(f_1510_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5093),hAPP(c_Int_Onumber__class_Onumber__of(U_5093),U_5094)),c_Groups_Oone__class_Oone(U_5093)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5094),c_Int_OBit1(c_Int_OPls)))
    | ~ sP406(U_5093,U_5094) ),
    inference(clausify,[status(thm)],[f_1510_3]) ).

fof(f_1511_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_1511_2,plain,
    ! [U_5096,U_5095] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5095),c_Groups_Oone__class_Oone(U_5095)),hAPP(c_Int_Onumber__class_Onumber__of(U_5095),U_5096)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5096)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5096))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5095),c_Groups_Oone__class_Oone(U_5095)),hAPP(c_Int_Onumber__class_Onumber__of(U_5095),U_5096))) ) )
      | ~ class_Rings_Olinordered__idom(U_5095)
      | ~ class_Int_Onumber__ring(U_5095) ),
    inference(variable_rename,[status(thm)],[f_1511_1]) ).

fof(f_1511_3,plain,
    ( ! [U_5095,U_5096] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5095),c_Groups_Oone__class_Oone(U_5095)),hAPP(c_Int_Onumber__class_Onumber__of(U_5095),U_5096)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5096))
        | ~ sP407(U_5095,U_5096) )
    & ! [U_5095,U_5096] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5096))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5095),c_Groups_Oone__class_Oone(U_5095)),hAPP(c_Int_Onumber__class_Onumber__of(U_5095),U_5096)))
        | ~ sP407(U_5095,U_5096) )
    & ! [U_5095,U_5096] :
        ( sP407(U_5095,U_5096)
        | ~ class_Rings_Olinordered__idom(U_5095)
        | ~ class_Int_Onumber__ring(U_5095) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP407])],[f_1511_2]) ).

cnf(f_1511_4,plain,
    ( sP407(U_5095,U_5096)
    | ~ class_Rings_Olinordered__idom(U_5095)
    | ~ class_Int_Onumber__ring(U_5095) ),
    inference(clausify,[status(thm)],[f_1511_3]) ).

cnf(f_1511_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5096))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5095),c_Groups_Oone__class_Oone(U_5095)),hAPP(c_Int_Onumber__class_Onumber__of(U_5095),U_5096)))
    | ~ sP407(U_5095,U_5096) ),
    inference(clausify,[status(thm)],[f_1511_3]) ).

cnf(f_1511_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5095),c_Groups_Oone__class_Oone(U_5095)),hAPP(c_Int_Onumber__class_Onumber__of(U_5095),U_5096)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5096))
    | ~ sP407(U_5095,U_5096) ),
    inference(clausify,[status(thm)],[f_1511_3]) ).

fof(f_1512_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_1512_2,plain,
    ! [U_5098,U_5097] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5097),hAPP(c_Int_Onumber__class_Onumber__of(U_5097),U_5098)),c_Groups_Oone__class_Oone(U_5097)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5097),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5098),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_5097) ),
    inference(variable_rename,[status(thm)],[f_1512_1]) ).

fof(f_1512_3,plain,
    ! [U_5098,U_5097] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5097),hAPP(c_Int_Onumber__class_Onumber__of(U_5097),U_5098)),c_Groups_Oone__class_Oone(U_5097)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5097),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5098),c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_5097) ),
    inference(definitional_conversion,[status(esa)],[f_1512_2]) ).

cnf(f_1512_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5097),hAPP(c_Int_Onumber__class_Onumber__of(U_5097),U_5098)),c_Groups_Oone__class_Oone(U_5097)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5097),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5098),c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(U_5097) ),
    inference(clausify,[status(thm)],[f_1512_3]) ).

fof(f_1513_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_1513_2,plain,
    ! [U_5100,U_5099] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5099),c_Groups_Oone__class_Oone(U_5099)),hAPP(c_Int_Onumber__class_Onumber__of(U_5099),U_5100)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5099),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5100))
      | ~ class_Int_Onumber__ring(U_5099) ),
    inference(variable_rename,[status(thm)],[f_1513_1]) ).

fof(f_1513_3,plain,
    ! [U_5100,U_5099] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5099),c_Groups_Oone__class_Oone(U_5099)),hAPP(c_Int_Onumber__class_Onumber__of(U_5099),U_5100)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5099),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5100))
      | ~ class_Int_Onumber__ring(U_5099) ),
    inference(definitional_conversion,[status(esa)],[f_1513_2]) ).

cnf(f_1513_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5099),c_Groups_Oone__class_Oone(U_5099)),hAPP(c_Int_Onumber__class_Onumber__of(U_5099),U_5100)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5099),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),U_5100))
    | ~ class_Int_Onumber__ring(U_5099) ),
    inference(clausify,[status(thm)],[f_1513_3]) ).

fof(f_1514_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_1514_2,plain,
    ! [U_5102,U_5101] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5102)),U_5101) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5102),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5101),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_5101)) ),
    inference(variable_rename,[status(thm)],[f_1514_1]) ).

fof(f_1514_3,plain,
    ! [U_5101,U_5102] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5102)),U_5101) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5102),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5101),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_5101)) ),
    inference(definitional_conversion,[status(esa)],[f_1514_2]) ).

cnf(f_1514_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5102)),U_5101) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5102),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5101),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_5101)) ),
    inference(clausify,[status(thm)],[f_1514_3]) ).

fof(f_1515_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_1515_2,plain,
    ! [U_5104,U_5103] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_5103),c_Int_Opred(U_5104)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5103),hAPP(c_Groups_Ouminus__class_Ouminus(U_5103),c_Groups_Oone__class_Oone(U_5103))),hAPP(c_Int_Onumber__class_Onumber__of(U_5103),U_5104))
      | ~ class_Int_Onumber__ring(U_5103) ),
    inference(variable_rename,[status(thm)],[f_1515_1]) ).

fof(f_1515_3,plain,
    ! [U_5103,U_5104] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_5103),c_Int_Opred(U_5104)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5103),hAPP(c_Groups_Ouminus__class_Ouminus(U_5103),c_Groups_Oone__class_Oone(U_5103))),hAPP(c_Int_Onumber__class_Onumber__of(U_5103),U_5104))
      | ~ class_Int_Onumber__ring(U_5103) ),
    inference(definitional_conversion,[status(esa)],[f_1515_2]) ).

cnf(f_1515_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5103),c_Int_Opred(U_5104)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5103),hAPP(c_Groups_Ouminus__class_Ouminus(U_5103),c_Groups_Oone__class_Oone(U_5103))),hAPP(c_Int_Onumber__class_Onumber__of(U_5103),U_5104))
    | ~ class_Int_Onumber__ring(U_5103) ),
    inference(clausify,[status(thm)],[f_1515_3]) ).

fof(f_1516_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_1516_2,plain,
    ! [U_5106,U_5105] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5105))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5106)) = 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_5105),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5106)),
    inference(variable_rename,[status(thm)],[f_1516_1]) ).

fof(f_1516_3,plain,
    ! [U_5105,U_5106] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5105))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5106)) = 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_5105),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5106)),
    inference(definitional_conversion,[status(esa)],[f_1516_2]) ).

cnf(f_1516_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5105))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5106)) = 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_5105),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5106)),
    inference(clausify,[status(thm)],[f_1516_3]) ).

fof(f_1517_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_1517_2,plain,
    ! [U_5108,U_5107] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5107))),U_5108) = 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_5107),U_5108),
    inference(variable_rename,[status(thm)],[f_1517_1]) ).

fof(f_1517_3,plain,
    ! [U_5107,U_5108] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5107))),U_5108) = 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_5107),U_5108),
    inference(definitional_conversion,[status(esa)],[f_1517_2]) ).

cnf(f_1517_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5107))),U_5108) = 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_5107),U_5108),
    inference(clausify,[status(thm)],[f_1517_3]) ).

fof(f_1518_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_1518_2,plain,
    ! [U_5110,U_5109] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5109,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5110)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5109,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_5110)),
    inference(variable_rename,[status(thm)],[f_1518_1]) ).

fof(f_1518_3,plain,
    ! [U_5110,U_5109] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5109,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5110)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5109,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_5110)),
    inference(definitional_conversion,[status(esa)],[f_1518_2]) ).

cnf(f_1518_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5109,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5110)))) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5109,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_5110)),
    inference(clausify,[status(thm)],[f_1518_3]) ).

fof(f_1519_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_1519_2,plain,
    ! [U_5112,U_5111] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5111),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5112)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5111),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_5112)),
    inference(variable_rename,[status(thm)],[f_1519_1]) ).

fof(f_1519_3,plain,
    ! [U_5111,U_5112] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5111),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5112)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5111),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_5112)),
    inference(definitional_conversion,[status(esa)],[f_1519_2]) ).

cnf(f_1519_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5111),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5112)))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),U_5111),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_5112)),
    inference(clausify,[status(thm)],[f_1519_3]) ).

fof(f_1520_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_1520_2,plain,
    ! [U_5114,U_5113] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5113)))),U_5114) = 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_5113)),U_5114),
    inference(variable_rename,[status(thm)],[f_1520_1]) ).

fof(f_1520_3,plain,
    ! [U_5113,U_5114] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5113)))),U_5114) = 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_5113)),U_5114),
    inference(definitional_conversion,[status(esa)],[f_1520_2]) ).

cnf(f_1520_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_5113)))),U_5114) = 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_5113)),U_5114),
    inference(clausify,[status(thm)],[f_1520_3]) ).

fof(f_1521_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_1521_2,plain,
    ! [U_5116,U_5115] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5115)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5116)) = 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_5115)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5116)),
    inference(variable_rename,[status(thm)],[f_1521_1]) ).

fof(f_1521_3,plain,
    ! [U_5115,U_5116] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5115)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5116)) = 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_5115)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5116)),
    inference(definitional_conversion,[status(esa)],[f_1521_2]) ).

cnf(f_1521_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_5115)))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5116)) = 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_5115)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5116)),
    inference(clausify,[status(thm)],[f_1521_3]) ).

fof(f_1522_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_1522_2,plain,
    ! [U_5117] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5117))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5117) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5117) = 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_5117)))) ) ),
    inference(variable_rename,[status(thm)],[f_1522_1]) ).

fof(f_1522_3,plain,
    ( ! [U_5119] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5119))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5119) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_5118] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5118) = 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_5118)))) ) ),
    inference(miniscope,[status(thm)],[f_1522_2]) ).

fof(f_1522_4,plain,
    ( ! [U_5119] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5119))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5119) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_5118] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5118) = 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_5118)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1522_3]) ).

cnf(f_1522_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5118) = 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_5118)))) ),
    inference(clausify,[status(thm)],[f_1522_4]) ).

cnf(f_1522_6,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5119))))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5119) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1522_4]) ).

fof(f_1523_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_1523_2,plain,
    ! [U_5121,U_5120] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5121)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5120))) = 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_5121)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5120)))),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_5120))) )
      & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5121)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5120))) = 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_5121),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5120)))),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_5120))) ) ),
    inference(variable_rename,[status(thm)],[f_1523_1]) ).

fof(f_1523_3,plain,
    ( ! [U_5125,U_5123] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5125)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5123))) = 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_5125)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5123)))),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_5123))) )
    & ! [U_5124,U_5122] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5124)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5122))) = 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_5124),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5122)))),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_5122))) ) ),
    inference(miniscope,[status(thm)],[f_1523_2]) ).

fof(f_1523_4,plain,
    ( ! [U_5123,U_5125] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5125)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5123))) = 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_5125)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5123)))),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_5123))) )
    & ! [U_5124,U_5122] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5124)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5122))) = 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_5124),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5122)))),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_5122))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1523_3]) ).

cnf(f_1523_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5124)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5122))) = 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_5124),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5122)))),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_5122))) ),
    inference(clausify,[status(thm)],[f_1523_4]) ).

cnf(f_1523_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5125)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5123))) = 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_5125)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5123)))),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_5123))) ),
    inference(clausify,[status(thm)],[f_1523_4]) ).

fof(f_1524_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_1524_2,plain,
    ! [U_5127,U_5126] :
      ( 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_5127)),hAPP(hAPP(c_Groups_Otimes__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_5126)) = 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_5127),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5126))),c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5126),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1524_1]) ).

fof(f_1524_3,plain,
    ! [U_5126,U_5127] :
      ( 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_5127)),hAPP(hAPP(c_Groups_Otimes__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_5126)) = 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_5127),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5126))),c_Groups_Oone__class_Oone(tc_Int_Oint))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5126),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1524_2]) ).

cnf(f_1524_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_5127)),hAPP(hAPP(c_Groups_Otimes__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_5126)) = 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_5127),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_5126))),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5126),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1524_3]) ).

fof(f_1525_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_1525_2,plain,
    ! [U_5129,U_5128] :
      ( 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_5129))),hAPP(hAPP(c_Groups_Otimes__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_5128)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5129),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5128)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5128),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(variable_rename,[status(thm)],[f_1525_1]) ).

fof(f_1525_3,plain,
    ! [U_5128,U_5129] :
      ( 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_5129))),hAPP(hAPP(c_Groups_Otimes__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_5128)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5129),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5128)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5128),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(definitional_conversion,[status(esa)],[f_1525_2]) ).

cnf(f_1525_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_5129))),hAPP(hAPP(c_Groups_Otimes__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_5128)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5129),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_5128)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5128),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1525_3]) ).

fof(f_1526_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_1526_2,plain,
    ! [U_5131,U_5130] :
      ( 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_5131))),hAPP(hAPP(c_Groups_Otimes__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_5130)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5131),U_5130)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5130)) ),
    inference(variable_rename,[status(thm)],[f_1526_1]) ).

fof(f_1526_3,plain,
    ! [U_5130,U_5131] :
      ( 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_5131))),hAPP(hAPP(c_Groups_Otimes__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_5130)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5131),U_5130)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5130)) ),
    inference(definitional_conversion,[status(esa)],[f_1526_2]) ).

cnf(f_1526_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_5131))),hAPP(hAPP(c_Groups_Otimes__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_5130)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_5131),U_5130)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5130)) ),
    inference(clausify,[status(thm)],[f_1526_3]) ).

fof(f_1527_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_1527_2,plain,
    ! [U_5133,U_5132] :
      ( 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_5133)),hAPP(hAPP(c_Groups_Otimes__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_5132)) = 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_5133,U_5132)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5132)) ),
    inference(variable_rename,[status(thm)],[f_1527_1]) ).

fof(f_1527_3,plain,
    ! [U_5132,U_5133] :
      ( 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_5133)),hAPP(hAPP(c_Groups_Otimes__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_5132)) = 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_5133,U_5132)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5132)) ),
    inference(definitional_conversion,[status(esa)],[f_1527_2]) ).

cnf(f_1527_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_5133)),hAPP(hAPP(c_Groups_Otimes__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_5132)) = 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_5133,U_5132)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5132)) ),
    inference(clausify,[status(thm)],[f_1527_3]) ).

fof(f_1528_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_1528_2,plain,
    ! [U_5135,U_5134] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5134),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_5135))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5134),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5134),hAPP(c_Int_Onat,U_5135))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5134),hAPP(c_Int_Onat,U_5135)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5135))
      | ~ class_Rings_Osemiring__1(U_5134) ),
    inference(variable_rename,[status(thm)],[f_1528_1]) ).

fof(f_1528_3,plain,
    ! [U_5134,U_5135] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5134),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_5135))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5134),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5134),hAPP(c_Int_Onat,U_5135))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5134),hAPP(c_Int_Onat,U_5135)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5135))
      | ~ class_Rings_Osemiring__1(U_5134) ),
    inference(definitional_conversion,[status(esa)],[f_1528_2]) ).

cnf(f_1528_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5134),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_5135))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5134),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5134),hAPP(c_Int_Onat,U_5135))),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5134),hAPP(c_Int_Onat,U_5135)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5135))
    | ~ class_Rings_Osemiring__1(U_5134) ),
    inference(clausify,[status(thm)],[f_1528_3]) ).

fof(f_1529_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_1529_2,plain,
    ! [U_5137,U_5136] :
      ( ( c_Int_OBit0(U_5136) = c_Int_OBit0(U_5137)
        | U_5136 != U_5137 )
      & ( U_5136 = U_5137
        | c_Int_OBit0(U_5136) != c_Int_OBit0(U_5137) ) ),
    inference(variable_rename,[status(thm)],[f_1529_1]) ).

fof(f_1529_3,plain,
    ( ! [U_5141,U_5139] :
        ( c_Int_OBit0(U_5139) = c_Int_OBit0(U_5141)
        | U_5139 != U_5141 )
    & ! [U_5140,U_5138] :
        ( U_5138 = U_5140
        | c_Int_OBit0(U_5138) != c_Int_OBit0(U_5140) ) ),
    inference(miniscope,[status(thm)],[f_1529_2]) ).

fof(f_1529_4,plain,
    ( ! [U_5139,U_5141] :
        ( c_Int_OBit0(U_5139) = c_Int_OBit0(U_5141)
        | U_5139 != U_5141 )
    & ! [U_5138,U_5140] :
        ( U_5138 = U_5140
        | c_Int_OBit0(U_5138) != c_Int_OBit0(U_5140) ) ),
    inference(definitional_conversion,[status(esa)],[f_1529_3]) ).

cnf(f_1529_5,plain,
    ( U_5138 = U_5140
    | c_Int_OBit0(U_5138) != c_Int_OBit0(U_5140) ),
    inference(clausify,[status(thm)],[f_1529_4]) ).

cnf(f_1529_6,plain,
    ( c_Int_OBit0(U_5139) = c_Int_OBit0(U_5141)
    | U_5139 != U_5141 ),
    inference(clausify,[status(thm)],[f_1529_4]) ).

fof(f_1530_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_1530_2,plain,
    ! [U_5143,U_5142] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5142)),c_Int_OBit0(U_5143)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5142),U_5143)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5142),U_5143))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5142)),c_Int_OBit0(U_5143))) ) ),
    inference(variable_rename,[status(thm)],[f_1530_1]) ).

fof(f_1530_3,plain,
    ( ! [U_5147,U_5145] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5145)),c_Int_OBit0(U_5147)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5145),U_5147)) )
    & ! [U_5146,U_5144] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5144),U_5146))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5144)),c_Int_OBit0(U_5146))) ) ),
    inference(miniscope,[status(thm)],[f_1530_2]) ).

fof(f_1530_4,plain,
    ( ! [U_5145,U_5147] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5145)),c_Int_OBit0(U_5147)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5145),U_5147)) )
    & ! [U_5146,U_5144] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5144),U_5146))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5144)),c_Int_OBit0(U_5146))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1530_3]) ).

cnf(f_1530_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5144),U_5146))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5144)),c_Int_OBit0(U_5146))) ),
    inference(clausify,[status(thm)],[f_1530_4]) ).

cnf(f_1530_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5145)),c_Int_OBit0(U_5147)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5145),U_5147)) ),
    inference(clausify,[status(thm)],[f_1530_4]) ).

fof(f_1531_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_1531_2,plain,
    ! [U_5149,U_5148] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5148)),c_Int_OBit0(U_5149)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5148),U_5149)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5148),U_5149))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5148)),c_Int_OBit0(U_5149))) ) ),
    inference(variable_rename,[status(thm)],[f_1531_1]) ).

fof(f_1531_3,plain,
    ( ! [U_5153,U_5151] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5151)),c_Int_OBit0(U_5153)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5151),U_5153)) )
    & ! [U_5152,U_5150] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5150),U_5152))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5150)),c_Int_OBit0(U_5152))) ) ),
    inference(miniscope,[status(thm)],[f_1531_2]) ).

fof(f_1531_4,plain,
    ( ! [U_5151,U_5153] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5151)),c_Int_OBit0(U_5153)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5151),U_5153)) )
    & ! [U_5152,U_5150] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5150),U_5152))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5150)),c_Int_OBit0(U_5152))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1531_3]) ).

cnf(f_1531_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5150),U_5152))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5150)),c_Int_OBit0(U_5152))) ),
    inference(clausify,[status(thm)],[f_1531_4]) ).

cnf(f_1531_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5151)),c_Int_OBit0(U_5153)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5151),U_5153)) ),
    inference(clausify,[status(thm)],[f_1531_4]) ).

fof(f_1532_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_1532_2,plain,
    ! [U_5155,U_5154] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(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_OBit0(U_5154)),c_Int_OBit0(U_5155))) ) ),
    inference(variable_rename,[status(thm)],[f_1532_1]) ).

fof(f_1532_3,plain,
    ( ! [U_5159,U_5157] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(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_OBit0(U_5156)),c_Int_OBit0(U_5158))) ) ),
    inference(miniscope,[status(thm)],[f_1532_2]) ).

fof(f_1532_4,plain,
    ( ! [U_5157,U_5159] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(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_OBit0(U_5156)),c_Int_OBit0(U_5158))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1532_3]) ).

cnf(f_1532_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_OBit0(U_5156)),c_Int_OBit0(U_5158))) ),
    inference(clausify,[status(thm)],[f_1532_4]) ).

cnf(f_1532_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(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_1532_4]) ).

fof(f_1533_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_1533_2,plain,
    ! [U_5161,U_5160] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5160)),c_Int_OBit0(U_5161)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5160),U_5161)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5160),U_5161))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5160)),c_Int_OBit0(U_5161))) ) ),
    inference(variable_rename,[status(thm)],[f_1533_1]) ).

fof(f_1533_3,plain,
    ( ! [U_5165,U_5163] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5163)),c_Int_OBit0(U_5165)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5163),U_5165)) )
    & ! [U_5164,U_5162] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5162),U_5164))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5162)),c_Int_OBit0(U_5164))) ) ),
    inference(miniscope,[status(thm)],[f_1533_2]) ).

fof(f_1533_4,plain,
    ( ! [U_5163,U_5165] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5163)),c_Int_OBit0(U_5165)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5163),U_5165)) )
    & ! [U_5164,U_5162] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5162),U_5164))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5162)),c_Int_OBit0(U_5164))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1533_3]) ).

cnf(f_1533_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5162),U_5164))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5162)),c_Int_OBit0(U_5164))) ),
    inference(clausify,[status(thm)],[f_1533_4]) ).

cnf(f_1533_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5163)),c_Int_OBit0(U_5165)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5163),U_5165)) ),
    inference(clausify,[status(thm)],[f_1533_4]) ).

fof(f_1534_1,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(fof_nnf,[status(thm)],[fact_Bit0__Pls]) ).

fof(f_1534_2,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(definitional_conversion,[status(esa)],[f_1534_1]) ).

cnf(f_1534_3,plain,
    c_Int_OBit0(c_Int_OPls) = c_Int_OPls,
    inference(clausify,[status(thm)],[f_1534_2]) ).

fof(f_1535_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_1535_2,plain,
    ! [U_5166] :
      ( ( c_Int_OPls = c_Int_OBit0(U_5166)
        | c_Int_OPls != U_5166 )
      & ( c_Int_OPls = U_5166
        | c_Int_OPls != c_Int_OBit0(U_5166) ) ),
    inference(variable_rename,[status(thm)],[f_1535_1]) ).

fof(f_1535_3,plain,
    ( ! [U_5168] :
        ( c_Int_OPls = c_Int_OBit0(U_5168)
        | c_Int_OPls != U_5168 )
    & ! [U_5167] :
        ( c_Int_OPls = U_5167
        | c_Int_OPls != c_Int_OBit0(U_5167) ) ),
    inference(miniscope,[status(thm)],[f_1535_2]) ).

fof(f_1535_4,plain,
    ( ! [U_5168] :
        ( c_Int_OPls = c_Int_OBit0(U_5168)
        | c_Int_OPls != U_5168 )
    & ! [U_5167] :
        ( c_Int_OPls = U_5167
        | c_Int_OPls != c_Int_OBit0(U_5167) ) ),
    inference(definitional_conversion,[status(esa)],[f_1535_3]) ).

cnf(f_1535_5,plain,
    ( c_Int_OPls = U_5167
    | c_Int_OPls != c_Int_OBit0(U_5167) ),
    inference(clausify,[status(thm)],[f_1535_4]) ).

cnf(f_1535_6,plain,
    ( c_Int_OPls = c_Int_OBit0(U_5168)
    | c_Int_OPls != U_5168 ),
    inference(clausify,[status(thm)],[f_1535_4]) ).

fof(f_1536_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_1536_2,plain,
    ! [U_5169] :
      ( ( c_Int_OBit0(U_5169) = c_Int_OPls
        | U_5169 != c_Int_OPls )
      & ( U_5169 = c_Int_OPls
        | c_Int_OBit0(U_5169) != c_Int_OPls ) ),
    inference(variable_rename,[status(thm)],[f_1536_1]) ).

fof(f_1536_3,plain,
    ( ! [U_5171] :
        ( c_Int_OBit0(U_5171) = c_Int_OPls
        | U_5171 != c_Int_OPls )
    & ! [U_5170] :
        ( U_5170 = c_Int_OPls
        | c_Int_OBit0(U_5170) != c_Int_OPls ) ),
    inference(miniscope,[status(thm)],[f_1536_2]) ).

fof(f_1536_4,plain,
    ( ! [U_5171] :
        ( c_Int_OBit0(U_5171) = c_Int_OPls
        | U_5171 != c_Int_OPls )
    & ! [U_5170] :
        ( U_5170 = c_Int_OPls
        | c_Int_OBit0(U_5170) != c_Int_OPls ) ),
    inference(definitional_conversion,[status(esa)],[f_1536_3]) ).

cnf(f_1536_5,plain,
    ( U_5170 = c_Int_OPls
    | c_Int_OBit0(U_5170) != c_Int_OPls ),
    inference(clausify,[status(thm)],[f_1536_4]) ).

cnf(f_1536_6,plain,
    ( c_Int_OBit0(U_5171) = c_Int_OPls
    | U_5171 != c_Int_OPls ),
    inference(clausify,[status(thm)],[f_1536_4]) ).

fof(f_1537_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_1537_2,plain,
    ! [U_5173,U_5172] : c_Int_OBit0(U_5172) != c_Int_OBit1(U_5173),
    inference(variable_rename,[status(thm)],[f_1537_1]) ).

fof(f_1537_3,plain,
    ! [U_5172,U_5173] : c_Int_OBit0(U_5172) != c_Int_OBit1(U_5173),
    inference(definitional_conversion,[status(esa)],[f_1537_2]) ).

cnf(f_1537_4,plain,
    c_Int_OBit0(U_5172) != c_Int_OBit1(U_5173),
    inference(clausify,[status(thm)],[f_1537_3]) ).

fof(f_1538_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_1538_2,plain,
    ! [U_5175,U_5174] : c_Int_OBit1(U_5174) != c_Int_OBit0(U_5175),
    inference(variable_rename,[status(thm)],[f_1538_1]) ).

fof(f_1538_3,plain,
    ! [U_5174,U_5175] : c_Int_OBit1(U_5174) != c_Int_OBit0(U_5175),
    inference(definitional_conversion,[status(esa)],[f_1538_2]) ).

cnf(f_1538_4,plain,
    c_Int_OBit1(U_5174) != c_Int_OBit0(U_5175),
    inference(clausify,[status(thm)],[f_1538_3]) ).

fof(f_1539_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_1539_2,plain,
    ! [U_5177,U_5176] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_5176)),c_Int_OBit0(U_5177)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5176),U_5177)),
    inference(variable_rename,[status(thm)],[f_1539_1]) ).

fof(f_1539_3,plain,
    ! [U_5176,U_5177] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_5176)),c_Int_OBit0(U_5177)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5176),U_5177)),
    inference(definitional_conversion,[status(esa)],[f_1539_2]) ).

cnf(f_1539_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_5176)),c_Int_OBit0(U_5177)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5176),U_5177)),
    inference(clausify,[status(thm)],[f_1539_3]) ).

fof(f_1540_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_1540_2,plain,
    ! [U_5178] : c_Int_OBit0(U_5178) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5178),U_5178),
    inference(variable_rename,[status(thm)],[f_1540_1]) ).

fof(f_1540_3,plain,
    ! [U_5178] : c_Int_OBit0(U_5178) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5178),U_5178),
    inference(definitional_conversion,[status(esa)],[f_1540_2]) ).

cnf(f_1540_4,plain,
    c_Int_OBit0(U_5178) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5178),U_5178),
    inference(clausify,[status(thm)],[f_1540_3]) ).

fof(f_1541_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_1541_2,plain,
    ! [U_5180,U_5179] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_5179)),U_5180) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5179),U_5180)),
    inference(variable_rename,[status(thm)],[f_1541_1]) ).

fof(f_1541_3,plain,
    ! [U_5179,U_5180] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_5179)),U_5180) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5179),U_5180)),
    inference(definitional_conversion,[status(esa)],[f_1541_2]) ).

cnf(f_1541_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit0(U_5179)),U_5180) = c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5179),U_5180)),
    inference(clausify,[status(thm)],[f_1541_3]) ).

fof(f_1542_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_1542_2,plain,
    ! [U_5182,U_5181] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_5181)),c_Int_OBit0(U_5182)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5181),U_5182)),
    inference(variable_rename,[status(thm)],[f_1542_1]) ).

fof(f_1542_3,plain,
    ! [U_5181,U_5182] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_5181)),c_Int_OBit0(U_5182)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5181),U_5182)),
    inference(definitional_conversion,[status(esa)],[f_1542_2]) ).

cnf(f_1542_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_5181)),c_Int_OBit0(U_5182)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5181),U_5182)),
    inference(clausify,[status(thm)],[f_1542_3]) ).

fof(f_1543_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_1543_2,plain,
    ! [U_5183] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_5183)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5183)),
    inference(variable_rename,[status(thm)],[f_1543_1]) ).

fof(f_1543_3,plain,
    ! [U_5183] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_5183)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5183)),
    inference(definitional_conversion,[status(esa)],[f_1543_2]) ).

cnf(f_1543_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OBit0(U_5183)) = c_Int_OBit0(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5183)),
    inference(clausify,[status(thm)],[f_1543_3]) ).

fof(f_1544_1,plain,
    ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l),
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I42_J]) ).

fof(f_1544_2,plain,
    ! [U_5184] : c_Int_OMin != c_Int_OBit0(U_5184),
    inference(variable_rename,[status(thm)],[f_1544_1]) ).

fof(f_1544_3,plain,
    ! [U_5184] : c_Int_OMin != c_Int_OBit0(U_5184),
    inference(definitional_conversion,[status(esa)],[f_1544_2]) ).

cnf(f_1544_4,plain,
    c_Int_OMin != c_Int_OBit0(U_5184),
    inference(clausify,[status(thm)],[f_1544_3]) ).

fof(f_1545_1,plain,
    ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin,
    inference(fof_nnf,[status(thm)],[fact_rel__simps_I45_J]) ).

fof(f_1545_2,plain,
    ! [U_5185] : c_Int_OBit0(U_5185) != c_Int_OMin,
    inference(variable_rename,[status(thm)],[f_1545_1]) ).

fof(f_1545_3,plain,
    ! [U_5185] : c_Int_OBit0(U_5185) != c_Int_OMin,
    inference(definitional_conversion,[status(esa)],[f_1545_2]) ).

cnf(f_1545_4,plain,
    c_Int_OBit0(U_5185) != c_Int_OMin,
    inference(clausify,[status(thm)],[f_1545_3]) ).

fof(f_1546_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_1546_2,plain,
    ! [U_5186] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5186)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5186),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5186),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5186)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1546_1]) ).

fof(f_1546_3,plain,
    ( ! [U_5188] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5188)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5188),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_5187] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5187),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5187)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1546_2]) ).

fof(f_1546_4,plain,
    ( ! [U_5188] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5188)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5188),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_5187] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5187),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5187)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1546_3]) ).

cnf(f_1546_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5187),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5187)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1546_4]) ).

cnf(f_1546_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5188)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5188),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1546_4]) ).

fof(f_1547_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_1547_2,plain,
    ! [U_5189] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5189)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5189)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5189))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5189))) ) ),
    inference(variable_rename,[status(thm)],[f_1547_1]) ).

fof(f_1547_3,plain,
    ( ! [U_5191] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5191)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5191)) )
    & ! [U_5190] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5190))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5190))) ) ),
    inference(miniscope,[status(thm)],[f_1547_2]) ).

fof(f_1547_4,plain,
    ( ! [U_5191] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5191)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5191)) )
    & ! [U_5190] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5190))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5190))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1547_3]) ).

cnf(f_1547_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5190))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5190))) ),
    inference(clausify,[status(thm)],[f_1547_4]) ).

cnf(f_1547_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5191)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),U_5191)) ),
    inference(clausify,[status(thm)],[f_1547_4]) ).

fof(f_1548_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_1548_2,plain,
    ! [U_5192] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5192)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5192),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5192),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5192)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1548_1]) ).

fof(f_1548_3,plain,
    ( ! [U_5194] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5194)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5194),c_Int_OPls)) )
    & ! [U_5193] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5193),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5193)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1548_2]) ).

fof(f_1548_4,plain,
    ( ! [U_5194] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5194)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5194),c_Int_OPls)) )
    & ! [U_5193] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5193),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5193)),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1548_3]) ).

cnf(f_1548_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5193),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5193)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1548_4]) ).

cnf(f_1548_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5194)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5194),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1548_4]) ).

fof(f_1549_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_1549_2,plain,
    ! [U_5196,U_5195] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5195)),c_Int_OBit1(U_5196)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5195),U_5196)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5195),U_5196))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5195)),c_Int_OBit1(U_5196))) ) ),
    inference(variable_rename,[status(thm)],[f_1549_1]) ).

fof(f_1549_3,plain,
    ( ! [U_5200,U_5198] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5198)),c_Int_OBit1(U_5200)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5198),U_5200)) )
    & ! [U_5199,U_5197] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5197),U_5199))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5197)),c_Int_OBit1(U_5199))) ) ),
    inference(miniscope,[status(thm)],[f_1549_2]) ).

fof(f_1549_4,plain,
    ( ! [U_5198,U_5200] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5198)),c_Int_OBit1(U_5200)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5198),U_5200)) )
    & ! [U_5199,U_5197] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5197),U_5199))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5197)),c_Int_OBit1(U_5199))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1549_3]) ).

cnf(f_1549_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5197),U_5199))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5197)),c_Int_OBit1(U_5199))) ),
    inference(clausify,[status(thm)],[f_1549_4]) ).

cnf(f_1549_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5198)),c_Int_OBit1(U_5200)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5198),U_5200)) ),
    inference(clausify,[status(thm)],[f_1549_4]) ).

fof(f_1550_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_1550_2,plain,
    ! [U_5202,U_5201] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5201)),c_Int_OBit1(U_5202)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5201),U_5202)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5201),U_5202))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5201)),c_Int_OBit1(U_5202))) ) ),
    inference(variable_rename,[status(thm)],[f_1550_1]) ).

fof(f_1550_3,plain,
    ( ! [U_5206,U_5204] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5204)),c_Int_OBit1(U_5206)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5204),U_5206)) )
    & ! [U_5205,U_5203] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5203),U_5205))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5203)),c_Int_OBit1(U_5205))) ) ),
    inference(miniscope,[status(thm)],[f_1550_2]) ).

fof(f_1550_4,plain,
    ( ! [U_5204,U_5206] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5204)),c_Int_OBit1(U_5206)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5204),U_5206)) )
    & ! [U_5205,U_5203] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5203),U_5205))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5203)),c_Int_OBit1(U_5205))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1550_3]) ).

cnf(f_1550_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5203),U_5205))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5203)),c_Int_OBit1(U_5205))) ),
    inference(clausify,[status(thm)],[f_1550_4]) ).

cnf(f_1550_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5204)),c_Int_OBit1(U_5206)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5204),U_5206)) ),
    inference(clausify,[status(thm)],[f_1550_4]) ).

fof(f_1551_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_1551_2,plain,
    ! [U_5207] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5207)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5207),c_Int_OPls)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5207),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5207)),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1551_1]) ).

fof(f_1551_3,plain,
    ( ! [U_5209] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5209)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5209),c_Int_OPls)) )
    & ! [U_5208] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5208),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5208)),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1551_2]) ).

fof(f_1551_4,plain,
    ( ! [U_5209] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5209)),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5209),c_Int_OPls)) )
    & ! [U_5208] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5208),c_Int_OPls))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5208)),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1551_3]) ).

cnf(f_1551_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5208),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5208)),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1551_4]) ).

cnf(f_1551_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5209)),c_Int_OPls))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5209),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1551_4]) ).

fof(f_1552_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_1552_2,plain,
    ! [U_5210] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5210)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5210)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5210))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5210))) ) ),
    inference(variable_rename,[status(thm)],[f_1552_1]) ).

fof(f_1552_3,plain,
    ( ! [U_5212] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5212)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5212)) )
    & ! [U_5211] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5211))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5211))) ) ),
    inference(miniscope,[status(thm)],[f_1552_2]) ).

fof(f_1552_4,plain,
    ( ! [U_5212] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5212)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5212)) )
    & ! [U_5211] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5211))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5211))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1552_3]) ).

cnf(f_1552_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5211))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5211))) ),
    inference(clausify,[status(thm)],[f_1552_4]) ).

cnf(f_1552_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5212)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),U_5212)) ),
    inference(clausify,[status(thm)],[f_1552_4]) ).

fof(f_1553_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_1553_2,plain,
    ! [U_5214,U_5213] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5213)),c_Int_OBit0(U_5214)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5213),U_5214)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5213),U_5214))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5213)),c_Int_OBit0(U_5214))) ) ),
    inference(variable_rename,[status(thm)],[f_1553_1]) ).

fof(f_1553_3,plain,
    ( ! [U_5218,U_5216] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5216)),c_Int_OBit0(U_5218)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5216),U_5218)) )
    & ! [U_5217,U_5215] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5215),U_5217))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5215)),c_Int_OBit0(U_5217))) ) ),
    inference(miniscope,[status(thm)],[f_1553_2]) ).

fof(f_1553_4,plain,
    ( ! [U_5216,U_5218] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5216)),c_Int_OBit0(U_5218)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5216),U_5218)) )
    & ! [U_5217,U_5215] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5215),U_5217))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5215)),c_Int_OBit0(U_5217))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1553_3]) ).

cnf(f_1553_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5215),U_5217))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5215)),c_Int_OBit0(U_5217))) ),
    inference(clausify,[status(thm)],[f_1553_4]) ).

cnf(f_1553_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5216)),c_Int_OBit0(U_5218)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5216),U_5218)) ),
    inference(clausify,[status(thm)],[f_1553_4]) ).

fof(f_1554_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_1554_2,plain,
    ! [U_5220,U_5219] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5219)),c_Int_OBit0(U_5220)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5219),U_5220)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5219),U_5220))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5219)),c_Int_OBit0(U_5220))) ) ),
    inference(variable_rename,[status(thm)],[f_1554_1]) ).

fof(f_1554_3,plain,
    ( ! [U_5224,U_5222] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5222)),c_Int_OBit0(U_5224)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5222),U_5224)) )
    & ! [U_5223,U_5221] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5221),U_5223))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5221)),c_Int_OBit0(U_5223))) ) ),
    inference(miniscope,[status(thm)],[f_1554_2]) ).

fof(f_1554_4,plain,
    ( ! [U_5222,U_5224] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5222)),c_Int_OBit0(U_5224)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5222),U_5224)) )
    & ! [U_5223,U_5221] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5221),U_5223))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5221)),c_Int_OBit0(U_5223))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1554_3]) ).

cnf(f_1554_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5221),U_5223))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5221)),c_Int_OBit0(U_5223))) ),
    inference(clausify,[status(thm)],[f_1554_4]) ).

cnf(f_1554_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(U_5222)),c_Int_OBit0(U_5224)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5222),U_5224)) ),
    inference(clausify,[status(thm)],[f_1554_4]) ).

fof(f_1555_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_1555_2,plain,
    ! [U_5226,U_5225] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_5225)),c_Int_OBit1(U_5226)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5225),U_5226)),
    inference(variable_rename,[status(thm)],[f_1555_1]) ).

fof(f_1555_3,plain,
    ! [U_5226,U_5225] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_5225)),c_Int_OBit1(U_5226)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5225),U_5226)),
    inference(definitional_conversion,[status(esa)],[f_1555_2]) ).

cnf(f_1555_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(U_5225)),c_Int_OBit1(U_5226)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5225),U_5226)),
    inference(clausify,[status(thm)],[f_1555_3]) ).

fof(f_1556_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_1556_2,plain,
    ! [U_5228,U_5227] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_5227)),c_Int_OBit0(U_5228)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5227),U_5228)),
    inference(variable_rename,[status(thm)],[f_1556_1]) ).

fof(f_1556_3,plain,
    ! [U_5227,U_5228] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_5227)),c_Int_OBit0(U_5228)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5227),U_5228)),
    inference(definitional_conversion,[status(esa)],[f_1556_2]) ).

cnf(f_1556_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_5227)),c_Int_OBit0(U_5228)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5227),U_5228)),
    inference(clausify,[status(thm)],[f_1556_3]) ).

fof(f_1557_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_1557_2,plain,
    ! [U_5229] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5229)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_5229)),
    inference(variable_rename,[status(thm)],[f_1557_1]) ).

fof(f_1557_3,plain,
    ! [U_5229] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5229)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_5229)),
    inference(definitional_conversion,[status(esa)],[f_1557_2]) ).

cnf(f_1557_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(U_5229)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OPls),U_5229)),
    inference(clausify,[status(thm)],[f_1557_3]) ).

fof(f_1558_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_1558_2,plain,
    ! [U_5231,U_5230] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_5230)),c_Int_OBit1(U_5231)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5230),U_5231)),
    inference(variable_rename,[status(thm)],[f_1558_1]) ).

fof(f_1558_3,plain,
    ! [U_5230,U_5231] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_5230)),c_Int_OBit1(U_5231)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5230),U_5231)),
    inference(definitional_conversion,[status(esa)],[f_1558_2]) ).

cnf(f_1558_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_5230)),c_Int_OBit1(U_5231)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5230),U_5231)),
    inference(clausify,[status(thm)],[f_1558_3]) ).

fof(f_1559_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_1559_2,plain,
    ! [U_5233,U_5232] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_5232)),c_Int_OBit0(U_5233)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5232),U_5233)),
    inference(variable_rename,[status(thm)],[f_1559_1]) ).

fof(f_1559_3,plain,
    ! [U_5232,U_5233] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_5232)),c_Int_OBit0(U_5233)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5232),U_5233)),
    inference(definitional_conversion,[status(esa)],[f_1559_2]) ).

cnf(f_1559_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit1(U_5232)),c_Int_OBit0(U_5233)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5232),U_5233)),
    inference(clausify,[status(thm)],[f_1559_3]) ).

fof(f_1560_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_1560_2,plain,
    ! [U_5234] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5234)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5234),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5234),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5234)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_1560_1]) ).

fof(f_1560_3,plain,
    ( ! [U_5236] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5236)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5236),c_Int_OMin)) )
    & ! [U_5235] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5235),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5235)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_1560_2]) ).

fof(f_1560_4,plain,
    ( ! [U_5236] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5236)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5236),c_Int_OMin)) )
    & ! [U_5235] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5235),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5235)),c_Int_OMin)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1560_3]) ).

cnf(f_1560_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5235),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5235)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1560_4]) ).

cnf(f_1560_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(U_5236)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5236),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1560_4]) ).

fof(f_1561_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_1561_2,plain,
    ! [U_5237] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5237)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5237)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5237))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5237))) ) ),
    inference(variable_rename,[status(thm)],[f_1561_1]) ).

fof(f_1561_3,plain,
    ( ! [U_5239] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5239)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5239)) )
    & ! [U_5238] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5238))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5238))) ) ),
    inference(miniscope,[status(thm)],[f_1561_2]) ).

fof(f_1561_4,plain,
    ( ! [U_5239] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5239)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5239)) )
    & ! [U_5238] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5238))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5238))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1561_3]) ).

cnf(f_1561_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5238))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5238))) ),
    inference(clausify,[status(thm)],[f_1561_4]) ).

cnf(f_1561_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5239)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5239)) ),
    inference(clausify,[status(thm)],[f_1561_4]) ).

fof(f_1562_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_1562_2,plain,
    ! [U_5241,U_5240] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5240))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5241))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5240)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5241)),
    inference(variable_rename,[status(thm)],[f_1562_1]) ).

fof(f_1562_3,plain,
    ! [U_5240,U_5241] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5240))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5241))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5240)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5241)),
    inference(definitional_conversion,[status(esa)],[f_1562_2]) ).

cnf(f_1562_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_5240))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5241))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5240)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5241)),
    inference(clausify,[status(thm)],[f_1562_3]) ).

fof(f_1563_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_1563_2,plain,
    ! [U_5242] :
      ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5242))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5242))) )
      & ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5242)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5242)))) ) ),
    inference(variable_rename,[status(thm)],[f_1563_1]) ).

fof(f_1563_3,plain,
    ( ! [U_5244] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5244))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5244))) )
    & ! [U_5243] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5243)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5243)))) ) ),
    inference(miniscope,[status(thm)],[f_1563_2]) ).

fof(f_1563_4,plain,
    ( ! [U_5244] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5244))))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5244))) )
    & ! [U_5243] :
        ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5243)))
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5243)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1563_3]) ).

cnf(f_1563_5,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5243)))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5243)))) ),
    inference(clausify,[status(thm)],[f_1563_4]) ).

cnf(f_1563_6,plain,
    ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5244))))
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5244))) ),
    inference(clausify,[status(thm)],[f_1563_4]) ).

fof(f_1564_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_1564_2,plain,
    ! [U_5245] : c_Int_Opred(c_Int_OBit1(U_5245)) = c_Int_OBit0(U_5245),
    inference(variable_rename,[status(thm)],[f_1564_1]) ).

fof(f_1564_3,plain,
    ! [U_5245] : c_Int_Opred(c_Int_OBit1(U_5245)) = c_Int_OBit0(U_5245),
    inference(definitional_conversion,[status(esa)],[f_1564_2]) ).

cnf(f_1564_4,plain,
    c_Int_Opred(c_Int_OBit1(U_5245)) = c_Int_OBit0(U_5245),
    inference(clausify,[status(thm)],[f_1564_3]) ).

fof(f_1565_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_1565_2,plain,
    ! [U_5246] : c_Int_Opred(c_Int_OBit0(U_5246)) = c_Int_OBit1(c_Int_Opred(U_5246)),
    inference(variable_rename,[status(thm)],[f_1565_1]) ).

fof(f_1565_3,plain,
    ! [U_5246] : c_Int_Opred(c_Int_OBit0(U_5246)) = c_Int_OBit1(c_Int_Opred(U_5246)),
    inference(definitional_conversion,[status(esa)],[f_1565_2]) ).

cnf(f_1565_4,plain,
    c_Int_Opred(c_Int_OBit0(U_5246)) = c_Int_OBit1(c_Int_Opred(U_5246)),
    inference(clausify,[status(thm)],[f_1565_3]) ).

fof(f_1566_1,plain,
    c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
    inference(fof_nnf,[status(thm)],[fact_pred__Min]) ).

fof(f_1566_2,plain,
    c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
    inference(definitional_conversion,[status(esa)],[f_1566_1]) ).

cnf(f_1566_3,plain,
    c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin),
    inference(clausify,[status(thm)],[f_1566_2]) ).

fof(f_1567_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_1567_2,plain,
    ! [U_5248,U_5247] :
      ( ( ( c_Int_Oiszero(U_5247,hAPP(c_Int_Onumber__class_Onumber__of(U_5247),c_Int_OBit0(U_5248)))
          | ~ c_Int_Oiszero(U_5247,hAPP(c_Int_Onumber__class_Onumber__of(U_5247),U_5248)) )
        & ( c_Int_Oiszero(U_5247,hAPP(c_Int_Onumber__class_Onumber__of(U_5247),U_5248))
          | ~ c_Int_Oiszero(U_5247,hAPP(c_Int_Onumber__class_Onumber__of(U_5247),c_Int_OBit0(U_5248))) ) )
      | ~ class_Int_Oring__char__0(U_5247)
      | ~ class_Int_Onumber__ring(U_5247) ),
    inference(variable_rename,[status(thm)],[f_1567_1]) ).

fof(f_1567_3,plain,
    ( ! [U_5247,U_5248] :
        ( c_Int_Oiszero(U_5247,hAPP(c_Int_Onumber__class_Onumber__of(U_5247),c_Int_OBit0(U_5248)))
        | ~ c_Int_Oiszero(U_5247,hAPP(c_Int_Onumber__class_Onumber__of(U_5247),U_5248))
        | ~ sP408(U_5247,U_5248) )
    & ! [U_5247,U_5248] :
        ( c_Int_Oiszero(U_5247,hAPP(c_Int_Onumber__class_Onumber__of(U_5247),U_5248))
        | ~ c_Int_Oiszero(U_5247,hAPP(c_Int_Onumber__class_Onumber__of(U_5247),c_Int_OBit0(U_5248)))
        | ~ sP408(U_5247,U_5248) )
    & ! [U_5247,U_5248] :
        ( sP408(U_5247,U_5248)
        | ~ class_Int_Oring__char__0(U_5247)
        | ~ class_Int_Onumber__ring(U_5247) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP408])],[f_1567_2]) ).

cnf(f_1567_4,plain,
    ( sP408(U_5247,U_5248)
    | ~ class_Int_Oring__char__0(U_5247)
    | ~ class_Int_Onumber__ring(U_5247) ),
    inference(clausify,[status(thm)],[f_1567_3]) ).

cnf(f_1567_5,plain,
    ( c_Int_Oiszero(U_5247,hAPP(c_Int_Onumber__class_Onumber__of(U_5247),U_5248))
    | ~ c_Int_Oiszero(U_5247,hAPP(c_Int_Onumber__class_Onumber__of(U_5247),c_Int_OBit0(U_5248)))
    | ~ sP408(U_5247,U_5248) ),
    inference(clausify,[status(thm)],[f_1567_3]) ).

cnf(f_1567_6,plain,
    ( c_Int_Oiszero(U_5247,hAPP(c_Int_Onumber__class_Onumber__of(U_5247),c_Int_OBit0(U_5248)))
    | ~ c_Int_Oiszero(U_5247,hAPP(c_Int_Onumber__class_Onumber__of(U_5247),U_5248))
    | ~ sP408(U_5247,U_5248) ),
    inference(clausify,[status(thm)],[f_1567_3]) ).

fof(f_1568_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_1568_2,plain,
    ! [U_5249] : c_Int_Osucc(c_Int_OBit1(U_5249)) = c_Int_OBit0(c_Int_Osucc(U_5249)),
    inference(variable_rename,[status(thm)],[f_1568_1]) ).

fof(f_1568_3,plain,
    ! [U_5249] : c_Int_Osucc(c_Int_OBit1(U_5249)) = c_Int_OBit0(c_Int_Osucc(U_5249)),
    inference(definitional_conversion,[status(esa)],[f_1568_2]) ).

cnf(f_1568_4,plain,
    c_Int_Osucc(c_Int_OBit1(U_5249)) = c_Int_OBit0(c_Int_Osucc(U_5249)),
    inference(clausify,[status(thm)],[f_1568_3]) ).

fof(f_1569_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_1569_2,plain,
    ! [U_5250] : c_Int_Osucc(c_Int_OBit0(U_5250)) = c_Int_OBit1(U_5250),
    inference(variable_rename,[status(thm)],[f_1569_1]) ).

fof(f_1569_3,plain,
    ! [U_5250] : c_Int_Osucc(c_Int_OBit0(U_5250)) = c_Int_OBit1(U_5250),
    inference(definitional_conversion,[status(esa)],[f_1569_2]) ).

cnf(f_1569_4,plain,
    c_Int_Osucc(c_Int_OBit0(U_5250)) = c_Int_OBit1(U_5250),
    inference(clausify,[status(thm)],[f_1569_3]) ).

fof(f_1570_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_1570_2,plain,
    ! [U_5252,U_5251] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_5251),c_Int_OBit0(U_5252)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5251),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5251),c_Groups_Ozero__class_Ozero(U_5251)),hAPP(c_Int_Onumber__class_Onumber__of(U_5251),U_5252))),hAPP(c_Int_Onumber__class_Onumber__of(U_5251),U_5252))
      | ~ class_Int_Onumber__ring(U_5251) ),
    inference(variable_rename,[status(thm)],[f_1570_1]) ).

fof(f_1570_3,plain,
    ! [U_5251,U_5252] :
      ( hAPP(c_Int_Onumber__class_Onumber__of(U_5251),c_Int_OBit0(U_5252)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5251),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5251),c_Groups_Ozero__class_Ozero(U_5251)),hAPP(c_Int_Onumber__class_Onumber__of(U_5251),U_5252))),hAPP(c_Int_Onumber__class_Onumber__of(U_5251),U_5252))
      | ~ class_Int_Onumber__ring(U_5251) ),
    inference(definitional_conversion,[status(esa)],[f_1570_2]) ).

cnf(f_1570_4,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5251),c_Int_OBit0(U_5252)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5251),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5251),c_Groups_Ozero__class_Ozero(U_5251)),hAPP(c_Int_Onumber__class_Onumber__of(U_5251),U_5252))),hAPP(c_Int_Onumber__class_Onumber__of(U_5251),U_5252))
    | ~ class_Int_Onumber__ring(U_5251) ),
    inference(clausify,[status(thm)],[f_1570_3]) ).

fof(f_1571_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_1571_2,plain,
    ! [U_5254,U_5253] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5253)),c_Int_OBit1(U_5254)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5253),U_5254)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5253),U_5254))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5253)),c_Int_OBit1(U_5254))) ) ),
    inference(variable_rename,[status(thm)],[f_1571_1]) ).

fof(f_1571_3,plain,
    ( ! [U_5258,U_5256] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5256)),c_Int_OBit1(U_5258)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5256),U_5258)) )
    & ! [U_5257,U_5255] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5255),U_5257))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5255)),c_Int_OBit1(U_5257))) ) ),
    inference(miniscope,[status(thm)],[f_1571_2]) ).

fof(f_1571_4,plain,
    ( ! [U_5256,U_5258] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5256)),c_Int_OBit1(U_5258)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5256),U_5258)) )
    & ! [U_5257,U_5255] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5255),U_5257))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5255)),c_Int_OBit1(U_5257))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1571_3]) ).

cnf(f_1571_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5255),U_5257))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5255)),c_Int_OBit1(U_5257))) ),
    inference(clausify,[status(thm)],[f_1571_4]) ).

cnf(f_1571_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5256)),c_Int_OBit1(U_5258)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5256),U_5258)) ),
    inference(clausify,[status(thm)],[f_1571_4]) ).

fof(f_1572_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_1572_2,plain,
    ! [U_5260,U_5259] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5259)),c_Int_OBit1(U_5260)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5259),U_5260)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5259),U_5260))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5259)),c_Int_OBit1(U_5260))) ) ),
    inference(variable_rename,[status(thm)],[f_1572_1]) ).

fof(f_1572_3,plain,
    ( ! [U_5264,U_5262] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5262)),c_Int_OBit1(U_5264)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5262),U_5264)) )
    & ! [U_5263,U_5261] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5261),U_5263))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5261)),c_Int_OBit1(U_5263))) ) ),
    inference(miniscope,[status(thm)],[f_1572_2]) ).

fof(f_1572_4,plain,
    ( ! [U_5262,U_5264] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5262)),c_Int_OBit1(U_5264)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5262),U_5264)) )
    & ! [U_5263,U_5261] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5261),U_5263))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5261)),c_Int_OBit1(U_5263))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1572_3]) ).

cnf(f_1572_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5261),U_5263))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5261)),c_Int_OBit1(U_5263))) ),
    inference(clausify,[status(thm)],[f_1572_4]) ).

cnf(f_1572_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5262)),c_Int_OBit1(U_5264)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5262),U_5264)) ),
    inference(clausify,[status(thm)],[f_1572_4]) ).

fof(f_1573_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_1573_2,plain,
    ! [U_5266,U_5265] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5265)),c_Int_OBit0(U_5266)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5265),U_5266)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5265),U_5266))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5265)),c_Int_OBit0(U_5266))) ) ),
    inference(variable_rename,[status(thm)],[f_1573_1]) ).

fof(f_1573_3,plain,
    ( ! [U_5270,U_5268] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5268)),c_Int_OBit0(U_5270)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5268),U_5270)) )
    & ! [U_5269,U_5267] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5267),U_5269))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5267)),c_Int_OBit0(U_5269))) ) ),
    inference(miniscope,[status(thm)],[f_1573_2]) ).

fof(f_1573_4,plain,
    ( ! [U_5268,U_5270] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5268)),c_Int_OBit0(U_5270)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5268),U_5270)) )
    & ! [U_5269,U_5267] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5267),U_5269))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5267)),c_Int_OBit0(U_5269))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1573_3]) ).

cnf(f_1573_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5267),U_5269))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5267)),c_Int_OBit0(U_5269))) ),
    inference(clausify,[status(thm)],[f_1573_4]) ).

cnf(f_1573_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5268)),c_Int_OBit0(U_5270)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5268),U_5270)) ),
    inference(clausify,[status(thm)],[f_1573_4]) ).

fof(f_1574_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_1574_2,plain,
    ! [U_5272,U_5271] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5271)),c_Int_OBit0(U_5272)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5271),U_5272)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5271),U_5272))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5271)),c_Int_OBit0(U_5272))) ) ),
    inference(variable_rename,[status(thm)],[f_1574_1]) ).

fof(f_1574_3,plain,
    ( ! [U_5276,U_5274] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5274)),c_Int_OBit0(U_5276)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5274),U_5276)) )
    & ! [U_5275,U_5273] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5273),U_5275))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5273)),c_Int_OBit0(U_5275))) ) ),
    inference(miniscope,[status(thm)],[f_1574_2]) ).

fof(f_1574_4,plain,
    ( ! [U_5274,U_5276] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5274)),c_Int_OBit0(U_5276)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5274),U_5276)) )
    & ! [U_5275,U_5273] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5273),U_5275))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5273)),c_Int_OBit0(U_5275))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1574_3]) ).

cnf(f_1574_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5273),U_5275))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5273)),c_Int_OBit0(U_5275))) ),
    inference(clausify,[status(thm)],[f_1574_4]) ).

cnf(f_1574_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(U_5274)),c_Int_OBit0(U_5276)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5274),U_5276)) ),
    inference(clausify,[status(thm)],[f_1574_4]) ).

fof(f_1575_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_1575_2,plain,
    ! [U_5278,U_5277] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_5277)),U_5278) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5277),U_5278))),U_5278),
    inference(variable_rename,[status(thm)],[f_1575_1]) ).

fof(f_1575_3,plain,
    ! [U_5277,U_5278] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_5277)),U_5278) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5277),U_5278))),U_5278),
    inference(definitional_conversion,[status(esa)],[f_1575_2]) ).

cnf(f_1575_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OBit1(U_5277)),U_5278) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit0(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_5277),U_5278))),U_5278),
    inference(clausify,[status(thm)],[f_1575_3]) ).

fof(f_1576_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_1576_2,plain,
    ! [U_5279] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5279)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5279)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5279))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5279))) ) ),
    inference(variable_rename,[status(thm)],[f_1576_1]) ).

fof(f_1576_3,plain,
    ( ! [U_5281] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5281)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5281)) )
    & ! [U_5280] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5280))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5280))) ) ),
    inference(miniscope,[status(thm)],[f_1576_2]) ).

fof(f_1576_4,plain,
    ( ! [U_5281] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5281)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5281)) )
    & ! [U_5280] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5280))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5280))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1576_3]) ).

cnf(f_1576_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5280))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5280))) ),
    inference(clausify,[status(thm)],[f_1576_4]) ).

cnf(f_1576_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5281)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),U_5281)) ),
    inference(clausify,[status(thm)],[f_1576_4]) ).

fof(f_1577_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_1577_2,plain,
    ! [U_5282] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5282)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5282),c_Int_OMin)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5282),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5282)),c_Int_OMin)) ) ),
    inference(variable_rename,[status(thm)],[f_1577_1]) ).

fof(f_1577_3,plain,
    ( ! [U_5284] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5284)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5284),c_Int_OMin)) )
    & ! [U_5283] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5283),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5283)),c_Int_OMin)) ) ),
    inference(miniscope,[status(thm)],[f_1577_2]) ).

fof(f_1577_4,plain,
    ( ! [U_5284] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5284)),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5284),c_Int_OMin)) )
    & ! [U_5283] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5283),c_Int_OMin))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5283)),c_Int_OMin)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1577_3]) ).

cnf(f_1577_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5283),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5283)),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1577_4]) ).

cnf(f_1577_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(U_5284)),c_Int_OMin))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5284),c_Int_OMin)) ),
    inference(clausify,[status(thm)],[f_1577_4]) ).

fof(f_1578_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_1578_2,plain,
    ! [U_5285] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5285)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5285)),
    inference(variable_rename,[status(thm)],[f_1578_1]) ).

fof(f_1578_3,plain,
    ! [U_5285] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5285)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5285)),
    inference(definitional_conversion,[status(esa)],[f_1578_2]) ).

cnf(f_1578_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(U_5285)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5285)),
    inference(clausify,[status(thm)],[f_1578_3]) ).

fof(f_1579_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_1579_2,plain,
    ! [U_5286] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5286)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5286)),
    inference(variable_rename,[status(thm)],[f_1579_1]) ).

fof(f_1579_3,plain,
    ! [U_5286] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5286)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5286)),
    inference(definitional_conversion,[status(esa)],[f_1579_2]) ).

cnf(f_1579_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(U_5286)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OMin),U_5286)),
    inference(clausify,[status(thm)],[f_1579_3]) ).

fof(f_1580_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_1580_2,plain,
    ! [U_5288,U_5287] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_5287)),c_Int_OBit1(U_5288)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_5287)),U_5288)),
    inference(variable_rename,[status(thm)],[f_1580_1]) ).

fof(f_1580_3,plain,
    ! [U_5287,U_5288] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_5287)),c_Int_OBit1(U_5288)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_5287)),U_5288)),
    inference(definitional_conversion,[status(esa)],[f_1580_2]) ).

cnf(f_1580_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_OBit0(U_5287)),c_Int_OBit1(U_5288)) = c_Int_OBit1(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),c_Int_Opred(U_5287)),U_5288)),
    inference(clausify,[status(thm)],[f_1580_3]) ).

fof(f_1581_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_1581_2,plain,
    ! [U_5290,U_5289] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_5289)),c_Int_OBit1(U_5290)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5289),c_Int_Osucc(U_5290))),
    inference(variable_rename,[status(thm)],[f_1581_1]) ).

fof(f_1581_3,plain,
    ! [U_5289,U_5290] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_5289)),c_Int_OBit1(U_5290)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5289),c_Int_Osucc(U_5290))),
    inference(definitional_conversion,[status(esa)],[f_1581_2]) ).

cnf(f_1581_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OBit1(U_5289)),c_Int_OBit1(U_5290)) = c_Int_OBit0(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5289),c_Int_Osucc(U_5290))),
    inference(clausify,[status(thm)],[f_1581_3]) ).

fof(f_1582_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_1582_2,plain,
    ! [U_5292,U_5291] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5291),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5291),c_Groups_Oone__class_Oone(U_5291)),c_Groups_Oone__class_Oone(U_5291))),hAPP(c_Int_Onumber__class_Onumber__of(U_5291),U_5292)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5291),c_Int_OBit0(U_5292))
      | ~ class_Int_Onumber__ring(U_5291) ),
    inference(variable_rename,[status(thm)],[f_1582_1]) ).

fof(f_1582_3,plain,
    ! [U_5291,U_5292] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5291),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5291),c_Groups_Oone__class_Oone(U_5291)),c_Groups_Oone__class_Oone(U_5291))),hAPP(c_Int_Onumber__class_Onumber__of(U_5291),U_5292)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5291),c_Int_OBit0(U_5292))
      | ~ class_Int_Onumber__ring(U_5291) ),
    inference(definitional_conversion,[status(esa)],[f_1582_2]) ).

cnf(f_1582_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5291),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5291),c_Groups_Oone__class_Oone(U_5291)),c_Groups_Oone__class_Oone(U_5291))),hAPP(c_Int_Onumber__class_Onumber__of(U_5291),U_5292)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5291),c_Int_OBit0(U_5292))
    | ~ class_Int_Onumber__ring(U_5291) ),
    inference(clausify,[status(thm)],[f_1582_3]) ).

fof(f_1583_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_1583_2,plain,
    ! [U_5293] :
      ( ( 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_5293))))
        & 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_5293)))) )
      | ~ 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_5293))) ),
    inference(variable_rename,[status(thm)],[f_1583_1]) ).

fof(f_1583_3,plain,
    ( ! [U_5293] :
        ( 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_5293))))
        | ~ sP409(U_5293) )
    & ! [U_5293] :
        ( 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_5293))))
        | ~ sP409(U_5293) )
    & ! [U_5293] :
        ( sP409(U_5293)
        | ~ 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_5293))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP409])],[f_1583_2]) ).

cnf(f_1583_4,plain,
    ( sP409(U_5293)
    | ~ 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_5293))) ),
    inference(clausify,[status(thm)],[f_1583_3]) ).

cnf(f_1583_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_5293))))
    | ~ sP409(U_5293) ),
    inference(clausify,[status(thm)],[f_1583_3]) ).

cnf(f_1583_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_5293))))
    | ~ sP409(U_5293) ),
    inference(clausify,[status(thm)],[f_1583_3]) ).

fof(f_1584_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_1584_2,plain,
    ! [U_5295,U_5294] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5294),hAPP(c_Int_Onumber__class_Onumber__of(U_5294),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5295) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5294),U_5295),U_5295)
      | ~ class_Int_Onumber__ring(U_5294) ),
    inference(variable_rename,[status(thm)],[f_1584_1]) ).

fof(f_1584_3,plain,
    ! [U_5294,U_5295] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5294),hAPP(c_Int_Onumber__class_Onumber__of(U_5294),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5295) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5294),U_5295),U_5295)
      | ~ class_Int_Onumber__ring(U_5294) ),
    inference(definitional_conversion,[status(esa)],[f_1584_2]) ).

cnf(f_1584_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5294),hAPP(c_Int_Onumber__class_Onumber__of(U_5294),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5295) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5294),U_5295),U_5295)
    | ~ class_Int_Onumber__ring(U_5294) ),
    inference(clausify,[status(thm)],[f_1584_3]) ).

fof(f_1585_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_1585_2,plain,
    ! [U_5297,U_5296] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5296),U_5297),hAPP(c_Int_Onumber__class_Onumber__of(U_5296),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5296),U_5297),U_5297)
      | ~ class_Int_Onumber__ring(U_5296) ),
    inference(variable_rename,[status(thm)],[f_1585_1]) ).

fof(f_1585_3,plain,
    ! [U_5296,U_5297] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5296),U_5297),hAPP(c_Int_Onumber__class_Onumber__of(U_5296),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5296),U_5297),U_5297)
      | ~ class_Int_Onumber__ring(U_5296) ),
    inference(definitional_conversion,[status(esa)],[f_1585_2]) ).

cnf(f_1585_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5296),U_5297),hAPP(c_Int_Onumber__class_Onumber__of(U_5296),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5296),U_5297),U_5297)
    | ~ class_Int_Onumber__ring(U_5296) ),
    inference(clausify,[status(thm)],[f_1585_3]) ).

fof(f_1586_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_1586_2,plain,
    ! [U_5298] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5298),c_Groups_Oone__class_Oone(U_5298)),c_Groups_Oone__class_Oone(U_5298)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5298),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_5298) ),
    inference(variable_rename,[status(thm)],[f_1586_1]) ).

fof(f_1586_3,plain,
    ! [U_5298] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5298),c_Groups_Oone__class_Oone(U_5298)),c_Groups_Oone__class_Oone(U_5298)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5298),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
      | ~ class_Int_Onumber__ring(U_5298) ),
    inference(definitional_conversion,[status(esa)],[f_1586_2]) ).

cnf(f_1586_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5298),c_Groups_Oone__class_Oone(U_5298)),c_Groups_Oone__class_Oone(U_5298)) = hAPP(c_Int_Onumber__class_Onumber__of(U_5298),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))
    | ~ class_Int_Onumber__ring(U_5298) ),
    inference(clausify,[status(thm)],[f_1586_3]) ).

fof(f_1587_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_1587_2,plain,
    ! [U_5300,U_5299] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5299),U_5300),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_5299)
          | U_5300 != c_Groups_Ozero__class_Ozero(U_5299) )
        & ( U_5300 = c_Groups_Ozero__class_Ozero(U_5299)
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_5299),U_5300),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_5299) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(U_5299) ),
    inference(variable_rename,[status(thm)],[f_1587_1]) ).

fof(f_1587_3,plain,
    ( ! [U_5299,U_5300] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5299),U_5300),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_5299)
        | U_5300 != c_Groups_Ozero__class_Ozero(U_5299)
        | ~ sP410(U_5299,U_5300) )
    & ! [U_5299,U_5300] :
        ( U_5300 = c_Groups_Ozero__class_Ozero(U_5299)
        | hAPP(hAPP(c_Power_Opower__class_Opower(U_5299),U_5300),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_5299)
        | ~ sP410(U_5299,U_5300) )
    & ! [U_5299,U_5300] :
        ( sP410(U_5299,U_5300)
        | ~ class_Rings_Oring__1__no__zero__divisors(U_5299) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP410])],[f_1587_2]) ).

cnf(f_1587_4,plain,
    ( sP410(U_5299,U_5300)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_5299) ),
    inference(clausify,[status(thm)],[f_1587_3]) ).

cnf(f_1587_5,plain,
    ( U_5300 = c_Groups_Ozero__class_Ozero(U_5299)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_5299),U_5300),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_5299)
    | ~ sP410(U_5299,U_5300) ),
    inference(clausify,[status(thm)],[f_1587_3]) ).

cnf(f_1587_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5299),U_5300),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_5299)
    | U_5300 != c_Groups_Ozero__class_Ozero(U_5299)
    | ~ sP410(U_5299,U_5300) ),
    inference(clausify,[status(thm)],[f_1587_3]) ).

fof(f_1588_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_1588_2,plain,
    ! [U_5301] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5301),c_Groups_Ozero__class_Ozero(U_5301)),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_5301)
      | ~ class_Rings_Osemiring__1(U_5301) ),
    inference(variable_rename,[status(thm)],[f_1588_1]) ).

fof(f_1588_3,plain,
    ! [U_5301] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5301),c_Groups_Ozero__class_Ozero(U_5301)),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_5301)
      | ~ class_Rings_Osemiring__1(U_5301) ),
    inference(definitional_conversion,[status(esa)],[f_1588_2]) ).

cnf(f_1588_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5301),c_Groups_Ozero__class_Ozero(U_5301)),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_5301)
    | ~ class_Rings_Osemiring__1(U_5301) ),
    inference(clausify,[status(thm)],[f_1588_3]) ).

fof(f_1589_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_1589_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_1589_1]) ).

cnf(f_1589_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_1589_2]) ).

fof(f_1590_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_1590_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_1590_1]) ).

cnf(f_1590_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_1590_2]) ).

fof(f_1591_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_1591_2,plain,
    ! [U_5303,U_5302] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5302),U_5303),U_5303) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5302),U_5303),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_5302) ),
    inference(variable_rename,[status(thm)],[f_1591_1]) ).

fof(f_1591_3,plain,
    ! [U_5302,U_5303] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5302),U_5303),U_5303) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5302),U_5303),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_5302) ),
    inference(definitional_conversion,[status(esa)],[f_1591_2]) ).

cnf(f_1591_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5302),U_5303),U_5303) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5302),U_5303),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_5302) ),
    inference(clausify,[status(thm)],[f_1591_3]) ).

fof(f_1592_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_1592_2,plain,
    ! [U_5305,U_5304] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5304),U_5305),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_5304),U_5305),U_5305)
      | ~ class_Groups_Omonoid__mult(U_5304) ),
    inference(variable_rename,[status(thm)],[f_1592_1]) ).

fof(f_1592_3,plain,
    ! [U_5304,U_5305] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5304),U_5305),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_5304),U_5305),U_5305)
      | ~ class_Groups_Omonoid__mult(U_5304) ),
    inference(definitional_conversion,[status(esa)],[f_1592_2]) ).

cnf(f_1592_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5304),U_5305),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_5304),U_5305),U_5305)
    | ~ class_Groups_Omonoid__mult(U_5304) ),
    inference(clausify,[status(thm)],[f_1592_3]) ).

fof(f_1593_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_1593_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_1593_1]) ).

cnf(f_1593_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_1593_2]) ).

fof(f_1594_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_1594_2,plain,
    ! [U_5306] : 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_5306) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5306)),
    inference(variable_rename,[status(thm)],[f_1594_1]) ).

fof(f_1594_3,plain,
    ! [U_5306] : 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_5306) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5306)),
    inference(definitional_conversion,[status(esa)],[f_1594_2]) ).

cnf(f_1594_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_5306) = hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5306)),
    inference(clausify,[status(thm)],[f_1594_3]) ).

fof(f_1595_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_1595_2,plain,
    ! [U_5307] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5307),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_5307)),
    inference(variable_rename,[status(thm)],[f_1595_1]) ).

fof(f_1595_3,plain,
    ! [U_5307] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5307),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_5307)),
    inference(definitional_conversion,[status(esa)],[f_1595_2]) ).

cnf(f_1595_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5307),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_5307)),
    inference(clausify,[status(thm)],[f_1595_3]) ).

fof(f_1596_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_1596_2,plain,
    ! [U_5308] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5308),c_Groups_Oone__class_Oone(U_5308)),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_5308)
      | ~ class_Rings_Osemiring__1(U_5308) ),
    inference(variable_rename,[status(thm)],[f_1596_1]) ).

fof(f_1596_3,plain,
    ! [U_5308] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5308),c_Groups_Oone__class_Oone(U_5308)),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_5308)
      | ~ class_Rings_Osemiring__1(U_5308) ),
    inference(definitional_conversion,[status(esa)],[f_1596_2]) ).

cnf(f_1596_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5308),c_Groups_Oone__class_Oone(U_5308)),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_5308)
    | ~ class_Rings_Osemiring__1(U_5308) ),
    inference(clausify,[status(thm)],[f_1596_3]) ).

fof(f_1597_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_1597_2,plain,
    ! [U_5310,U_5309] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5309),hAPP(c_Groups_Ouminus__class_Ouminus(U_5309),U_5310)),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_5309),U_5310),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Oring__1(U_5309) ),
    inference(variable_rename,[status(thm)],[f_1597_1]) ).

fof(f_1597_3,plain,
    ! [U_5309,U_5310] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5309),hAPP(c_Groups_Ouminus__class_Ouminus(U_5309),U_5310)),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_5309),U_5310),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Oring__1(U_5309) ),
    inference(definitional_conversion,[status(esa)],[f_1597_2]) ).

cnf(f_1597_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5309),hAPP(c_Groups_Ouminus__class_Ouminus(U_5309),U_5310)),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_5309),U_5310),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Oring__1(U_5309) ),
    inference(clausify,[status(thm)],[f_1597_3]) ).

fof(f_1598_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_1598_2,plain,
    ! [U_5311] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5311),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_5311),U_5311),
    inference(variable_rename,[status(thm)],[f_1598_1]) ).

fof(f_1598_3,plain,
    ! [U_5311] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5311),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_5311),U_5311),
    inference(definitional_conversion,[status(esa)],[f_1598_2]) ).

cnf(f_1598_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_5311),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_5311),U_5311),
    inference(clausify,[status(thm)],[f_1598_3]) ).

fof(f_1599_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_1599_2,plain,
    ! [U_5312] : 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_Oplus__class_Oplus(tc_Nat_Onat),U_5312),U_5312),
    inference(variable_rename,[status(thm)],[f_1599_1]) ).

fof(f_1599_3,plain,
    ! [U_5312] : 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_Oplus__class_Oplus(tc_Nat_Onat),U_5312),U_5312),
    inference(definitional_conversion,[status(esa)],[f_1599_2]) ).

cnf(f_1599_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_5312) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5312),U_5312),
    inference(clausify,[status(thm)],[f_1599_3]) ).

fof(f_1600_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_1600_2,plain,
    ! [U_5315,U_5314,U_5313] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5313),U_5314),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_5315)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5313),hAPP(hAPP(c_Power_Opower__class_Opower(U_5313),U_5314),U_5315)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Groups_Omonoid__mult(U_5313) ),
    inference(variable_rename,[status(thm)],[f_1600_1]) ).

fof(f_1600_3,plain,
    ! [U_5313,U_5314,U_5315] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5313),U_5314),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_5315)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5313),hAPP(hAPP(c_Power_Opower__class_Opower(U_5313),U_5314),U_5315)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Groups_Omonoid__mult(U_5313) ),
    inference(definitional_conversion,[status(esa)],[f_1600_2]) ).

cnf(f_1600_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5313),U_5314),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_5315)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5313),hAPP(hAPP(c_Power_Opower__class_Opower(U_5313),U_5314),U_5315)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Groups_Omonoid__mult(U_5313) ),
    inference(clausify,[status(thm)],[f_1600_3]) ).

fof(f_1601_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_1601_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_1601_1]) ).

cnf(f_1601_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_1601_2]) ).

fof(f_1602_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_1602_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_1602_1]) ).

cnf(f_1602_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_1602_2]) ).

fof(f_1603_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_1603_2,plain,
    ! [U_5317,U_5316] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5316),hAPP(hAPP(c_Power_Opower__class_Opower(U_5316),U_5317),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_5316),U_5317),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(U_5316) ),
    inference(variable_rename,[status(thm)],[f_1603_1]) ).

fof(f_1603_3,plain,
    ! [U_5316,U_5317] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5316),hAPP(hAPP(c_Power_Opower__class_Opower(U_5316),U_5317),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_5316),U_5317),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(U_5316) ),
    inference(definitional_conversion,[status(esa)],[f_1603_2]) ).

cnf(f_1603_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_5316),hAPP(hAPP(c_Power_Opower__class_Opower(U_5316),U_5317),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_5316),U_5317),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__idom(U_5316) ),
    inference(clausify,[status(thm)],[f_1603_3]) ).

fof(f_1604_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_1604_2,plain,
    ! [U_5319,U_5318] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5318),hAPP(c_Groups_Oabs__class_Oabs(U_5318),U_5319)),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_5318),U_5319),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(U_5318) ),
    inference(variable_rename,[status(thm)],[f_1604_1]) ).

fof(f_1604_3,plain,
    ! [U_5318,U_5319] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5318),hAPP(c_Groups_Oabs__class_Oabs(U_5318),U_5319)),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_5318),U_5319),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
      | ~ class_Rings_Olinordered__idom(U_5318) ),
    inference(definitional_conversion,[status(esa)],[f_1604_2]) ).

cnf(f_1604_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5318),hAPP(c_Groups_Oabs__class_Oabs(U_5318),U_5319)),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_5318),U_5319),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))
    | ~ class_Rings_Olinordered__idom(U_5318) ),
    inference(clausify,[status(thm)],[f_1604_3]) ).

fof(f_1605_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_1605_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_1605_1]) ).

cnf(f_1605_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_1605_2]) ).

fof(f_1606_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_1606_2,plain,
    ! [U_5320] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5320)),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_5320,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_1606_1]) ).

fof(f_1606_3,plain,
    ! [U_5320] : c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5320)),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_5320,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_1606_2]) ).

cnf(f_1606_4,plain,
    c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5320)),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_5320,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),
    inference(clausify,[status(thm)],[f_1606_3]) ).

fof(f_1607_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_1607_2,plain,
    ! [U_5321] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5321))),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_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_1607_1]) ).

fof(f_1607_3,plain,
    ! [U_5321] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5321))),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_5321),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_1607_2]) ).

cnf(f_1607_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_OSuc,U_5321))),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_5321),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))),
    inference(clausify,[status(thm)],[f_1607_3]) ).

fof(f_1608_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_1608_2,plain,
    ! [U_5323,U_5322] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5322)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5323))) = hAPP(hAPP(c_Groups_Otimes__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_5322),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5323))),
    inference(variable_rename,[status(thm)],[f_1608_1]) ).

fof(f_1608_3,plain,
    ! [U_5322,U_5323] : c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5322)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5323))) = hAPP(hAPP(c_Groups_Otimes__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_5322),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5323))),
    inference(definitional_conversion,[status(esa)],[f_1608_2]) ).

cnf(f_1608_4,plain,
    c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5322)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5323))) = hAPP(hAPP(c_Groups_Otimes__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_5322),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5323))),
    inference(clausify,[status(thm)],[f_1608_3]) ).

fof(f_1609_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_1609_2,plain,
    ! [U_5324] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5324),U_5324)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_5324,
    inference(variable_rename,[status(thm)],[f_1609_1]) ).

fof(f_1609_3,plain,
    ! [U_5324] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5324),U_5324)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_5324,
    inference(definitional_conversion,[status(esa)],[f_1609_2]) ).

cnf(f_1609_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_5324),U_5324)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) = U_5324,
    inference(clausify,[status(thm)],[f_1609_3]) ).

fof(f_1610_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_1610_2,plain,
    ! [U_5327,U_5326,U_5325] :
      ( U_5326 = U_5327
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),U_5327))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),U_5326))
      | 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))))
      | ~ class_Rings_Olinordered__semidom(U_5325) ),
    inference(variable_rename,[status(thm)],[f_1610_1]) ).

fof(f_1610_3,plain,
    ! [U_5325,U_5326,U_5327] :
      ( U_5326 = U_5327
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),U_5327))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),U_5326))
      | 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))))
      | ~ class_Rings_Olinordered__semidom(U_5325) ),
    inference(definitional_conversion,[status(esa)],[f_1610_2]) ).

cnf(f_1610_4,plain,
    ( U_5326 = U_5327
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),U_5327))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5325),c_Groups_Ozero__class_Ozero(U_5325)),U_5326))
    | 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))))
    | ~ class_Rings_Olinordered__semidom(U_5325) ),
    inference(clausify,[status(thm)],[f_1610_3]) ).

fof(f_1611_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_1611_2,plain,
    ! [U_5330,U_5329,U_5328] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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_5330))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5328),hAPP(hAPP(c_Power_Opower__class_Opower(U_5328),U_5329),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_5328),U_5330),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(U_5328) ),
    inference(variable_rename,[status(thm)],[f_1611_1]) ).

fof(f_1611_3,plain,
    ! [U_5329,U_5330,U_5328] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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_5330))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5328),hAPP(hAPP(c_Power_Opower__class_Opower(U_5328),U_5329),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_5328),U_5330),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(U_5328) ),
    inference(definitional_conversion,[status(esa)],[f_1611_2]) ).

cnf(f_1611_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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_5330))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5328),hAPP(hAPP(c_Power_Opower__class_Opower(U_5328),U_5329),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_5328),U_5330),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__semidom(U_5328) ),
    inference(clausify,[status(thm)],[f_1611_3]) ).

fof(f_1612_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_1612_2,plain,
    ! [U_5332,U_5331] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5331),c_Groups_Ozero__class_Ozero(U_5331)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5331),U_5332),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__idom(U_5331) ),
    inference(variable_rename,[status(thm)],[f_1612_1]) ).

fof(f_1612_3,plain,
    ! [U_5332,U_5331] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5331),c_Groups_Ozero__class_Ozero(U_5331)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5331),U_5332),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__idom(U_5331) ),
    inference(definitional_conversion,[status(esa)],[f_1612_2]) ).

cnf(f_1612_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5331),c_Groups_Ozero__class_Ozero(U_5331)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5331),U_5332),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__idom(U_5331) ),
    inference(clausify,[status(thm)],[f_1612_3]) ).

fof(f_1613_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_1613_2,plain,
    ! [U_5334,U_5333] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5333),c_Groups_Ozero__class_Ozero(U_5333)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5333),U_5334),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
          | U_5334 = c_Groups_Ozero__class_Ozero(U_5333) )
        & ( U_5334 != c_Groups_Ozero__class_Ozero(U_5333)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5333),c_Groups_Ozero__class_Ozero(U_5333)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5333),U_5334),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
      | ~ class_Rings_Olinordered__idom(U_5333) ),
    inference(variable_rename,[status(thm)],[f_1613_1]) ).

fof(f_1613_3,plain,
    ( ! [U_5333,U_5334] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5333),c_Groups_Ozero__class_Ozero(U_5333)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5333),U_5334),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | U_5334 = c_Groups_Ozero__class_Ozero(U_5333)
        | ~ sP411(U_5333,U_5334) )
    & ! [U_5333,U_5334] :
        ( U_5334 != c_Groups_Ozero__class_Ozero(U_5333)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5333),c_Groups_Ozero__class_Ozero(U_5333)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5333),U_5334),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | ~ sP411(U_5333,U_5334) )
    & ! [U_5333,U_5334] :
        ( sP411(U_5333,U_5334)
        | ~ class_Rings_Olinordered__idom(U_5333) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP411])],[f_1613_2]) ).

cnf(f_1613_4,plain,
    ( sP411(U_5333,U_5334)
    | ~ class_Rings_Olinordered__idom(U_5333) ),
    inference(clausify,[status(thm)],[f_1613_3]) ).

cnf(f_1613_5,plain,
    ( U_5334 != c_Groups_Ozero__class_Ozero(U_5333)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5333),c_Groups_Ozero__class_Ozero(U_5333)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5333),U_5334),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ sP411(U_5333,U_5334) ),
    inference(clausify,[status(thm)],[f_1613_3]) ).

cnf(f_1613_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5333),c_Groups_Ozero__class_Ozero(U_5333)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5333),U_5334),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | U_5334 = c_Groups_Ozero__class_Ozero(U_5333)
    | ~ sP411(U_5333,U_5334) ),
    inference(clausify,[status(thm)],[f_1613_3]) ).

fof(f_1614_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_1614_2,plain,
    ! [U_5336,U_5335] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5335),hAPP(hAPP(c_Power_Opower__class_Opower(U_5335),U_5336),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_5335)))
      | ~ class_Rings_Olinordered__idom(U_5335) ),
    inference(variable_rename,[status(thm)],[f_1614_1]) ).

fof(f_1614_3,plain,
    ! [U_5335,U_5336] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5335),hAPP(hAPP(c_Power_Opower__class_Opower(U_5335),U_5336),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_5335)))
      | ~ class_Rings_Olinordered__idom(U_5335) ),
    inference(definitional_conversion,[status(esa)],[f_1614_2]) ).

cnf(f_1614_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5335),hAPP(hAPP(c_Power_Opower__class_Opower(U_5335),U_5336),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_5335)))
    | ~ class_Rings_Olinordered__idom(U_5335) ),
    inference(clausify,[status(thm)],[f_1614_3]) ).

fof(f_1615_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_1615_2,plain,
    ! [U_5339,U_5338,U_5337] :
      ( ( ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5337),hAPP(hAPP(c_Power_Opower__class_Opower(U_5337),U_5338),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_5337),U_5339),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_5337)
          | U_5339 != c_Groups_Ozero__class_Ozero(U_5337)
          | U_5338 != c_Groups_Ozero__class_Ozero(U_5337) )
        & ( ( U_5339 = c_Groups_Ozero__class_Ozero(U_5337)
            & U_5338 = c_Groups_Ozero__class_Ozero(U_5337) )
          | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5337),hAPP(hAPP(c_Power_Opower__class_Opower(U_5337),U_5338),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_5337),U_5339),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_5337) ) )
      | ~ class_Rings_Olinordered__idom(U_5337) ),
    inference(variable_rename,[status(thm)],[f_1615_1]) ).

fof(f_1615_3,plain,
    ( ! [U_5337,U_5338,U_5339] :
        ( U_5339 = c_Groups_Ozero__class_Ozero(U_5337)
        | ~ sP412(U_5337,U_5338,U_5339) )
    & ! [U_5337,U_5338,U_5339] :
        ( U_5338 = c_Groups_Ozero__class_Ozero(U_5337)
        | ~ sP412(U_5337,U_5338,U_5339) )
    & ! [U_5337,U_5338,U_5339] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5337),hAPP(hAPP(c_Power_Opower__class_Opower(U_5337),U_5338),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_5337),U_5339),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_5337)
        | U_5339 != c_Groups_Ozero__class_Ozero(U_5337)
        | U_5338 != c_Groups_Ozero__class_Ozero(U_5337)
        | ~ sP413(U_5337,U_5338,U_5339) )
    & ! [U_5337,U_5338,U_5339] :
        ( sP412(U_5337,U_5338,U_5339)
        | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5337),hAPP(hAPP(c_Power_Opower__class_Opower(U_5337),U_5338),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_5337),U_5339),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_5337)
        | ~ sP413(U_5337,U_5338,U_5339) )
    & ! [U_5337,U_5338,U_5339] :
        ( sP413(U_5337,U_5338,U_5339)
        | ~ class_Rings_Olinordered__idom(U_5337) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP412,sP413])],[f_1615_2]) ).

cnf(f_1615_4,plain,
    ( sP413(U_5337,U_5338,U_5339)
    | ~ class_Rings_Olinordered__idom(U_5337) ),
    inference(clausify,[status(thm)],[f_1615_3]) ).

cnf(f_1615_5,plain,
    ( sP412(U_5337,U_5338,U_5339)
    | hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5337),hAPP(hAPP(c_Power_Opower__class_Opower(U_5337),U_5338),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_5337),U_5339),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_5337)
    | ~ sP413(U_5337,U_5338,U_5339) ),
    inference(clausify,[status(thm)],[f_1615_3]) ).

cnf(f_1615_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5337),hAPP(hAPP(c_Power_Opower__class_Opower(U_5337),U_5338),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_5337),U_5339),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_5337)
    | U_5339 != c_Groups_Ozero__class_Ozero(U_5337)
    | U_5338 != c_Groups_Ozero__class_Ozero(U_5337)
    | ~ sP413(U_5337,U_5338,U_5339) ),
    inference(clausify,[status(thm)],[f_1615_3]) ).

cnf(f_1615_7,plain,
    ( U_5338 = c_Groups_Ozero__class_Ozero(U_5337)
    | ~ sP412(U_5337,U_5338,U_5339) ),
    inference(clausify,[status(thm)],[f_1615_3]) ).

cnf(f_1615_8,plain,
    ( U_5339 = c_Groups_Ozero__class_Ozero(U_5337)
    | ~ sP412(U_5337,U_5338,U_5339) ),
    inference(clausify,[status(thm)],[f_1615_3]) ).

fof(f_1616_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_1616_2,plain,
    ! [U_5341,U_5340] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5340),hAPP(c_Int_Onumber__class_Onumber__of(U_5340),U_5341)),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_5340),hAPP(c_Int_Onumber__class_Onumber__of(U_5340),U_5341)),hAPP(c_Int_Onumber__class_Onumber__of(U_5340),U_5341))
      | ~ class_Int_Onumber(U_5340)
      | ~ class_Groups_Omonoid__mult(U_5340) ),
    inference(variable_rename,[status(thm)],[f_1616_1]) ).

fof(f_1616_3,plain,
    ! [U_5341,U_5340] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5340),hAPP(c_Int_Onumber__class_Onumber__of(U_5340),U_5341)),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_5340),hAPP(c_Int_Onumber__class_Onumber__of(U_5340),U_5341)),hAPP(c_Int_Onumber__class_Onumber__of(U_5340),U_5341))
      | ~ class_Int_Onumber(U_5340)
      | ~ class_Groups_Omonoid__mult(U_5340) ),
    inference(definitional_conversion,[status(esa)],[f_1616_2]) ).

cnf(f_1616_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5340),hAPP(c_Int_Onumber__class_Onumber__of(U_5340),U_5341)),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_5340),hAPP(c_Int_Onumber__class_Onumber__of(U_5340),U_5341)),hAPP(c_Int_Onumber__class_Onumber__of(U_5340),U_5341))
    | ~ class_Int_Onumber(U_5340)
    | ~ class_Groups_Omonoid__mult(U_5340) ),
    inference(clausify,[status(thm)],[f_1616_3]) ).

fof(f_1617_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_1617_2,plain,
    ! [U_5342] :
      ( U_5342 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_5342 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5342),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_1617_1]) ).

fof(f_1617_3,plain,
    ! [U_5342] :
      ( U_5342 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_5342 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5342),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_1617_2]) ).

cnf(f_1617_4,plain,
    ( U_5342 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_5342 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5342),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))) ),
    inference(clausify,[status(thm)],[f_1617_3]) ).

fof(f_1618_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_1618_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_1618_1]) ).

cnf(f_1618_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_1618_2]) ).

fof(f_1619_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_1619_2,plain,
    ! [U_5344,U_5343] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5343),U_5344),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_5343)
          | ( U_5344 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5343),c_Groups_Oone__class_Oone(U_5343))
            & U_5344 != c_Groups_Oone__class_Oone(U_5343) ) )
        & ( U_5344 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5343),c_Groups_Oone__class_Oone(U_5343))
          | U_5344 = c_Groups_Oone__class_Oone(U_5343)
          | hAPP(hAPP(c_Power_Opower__class_Opower(U_5343),U_5344),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_5343) ) )
      | ~ class_Rings_Oring__1__no__zero__divisors(U_5343) ),
    inference(variable_rename,[status(thm)],[f_1619_1]) ).

fof(f_1619_3,plain,
    ( ! [U_5343,U_5344] :
        ( U_5344 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5343),c_Groups_Oone__class_Oone(U_5343))
        | ~ sP414(U_5343,U_5344) )
    & ! [U_5343,U_5344] :
        ( U_5344 != c_Groups_Oone__class_Oone(U_5343)
        | ~ sP414(U_5343,U_5344) )
    & ! [U_5343,U_5344] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5343),U_5344),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_5343)
        | sP414(U_5343,U_5344)
        | ~ sP415(U_5343,U_5344) )
    & ! [U_5343,U_5344] :
        ( U_5344 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5343),c_Groups_Oone__class_Oone(U_5343))
        | U_5344 = c_Groups_Oone__class_Oone(U_5343)
        | hAPP(hAPP(c_Power_Opower__class_Opower(U_5343),U_5344),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_5343)
        | ~ sP415(U_5343,U_5344) )
    & ! [U_5343,U_5344] :
        ( sP415(U_5343,U_5344)
        | ~ class_Rings_Oring__1__no__zero__divisors(U_5343) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP414,sP415])],[f_1619_2]) ).

cnf(f_1619_4,plain,
    ( sP415(U_5343,U_5344)
    | ~ class_Rings_Oring__1__no__zero__divisors(U_5343) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_5,plain,
    ( U_5344 = hAPP(c_Groups_Ouminus__class_Ouminus(U_5343),c_Groups_Oone__class_Oone(U_5343))
    | U_5344 = c_Groups_Oone__class_Oone(U_5343)
    | hAPP(hAPP(c_Power_Opower__class_Opower(U_5343),U_5344),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_5343)
    | ~ sP415(U_5343,U_5344) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5343),U_5344),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_5343)
    | sP414(U_5343,U_5344)
    | ~ sP415(U_5343,U_5344) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_7,plain,
    ( U_5344 != c_Groups_Oone__class_Oone(U_5343)
    | ~ sP414(U_5343,U_5344) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

cnf(f_1619_8,plain,
    ( U_5344 != hAPP(c_Groups_Ouminus__class_Ouminus(U_5343),c_Groups_Oone__class_Oone(U_5343))
    | ~ sP414(U_5343,U_5344) ),
    inference(clausify,[status(thm)],[f_1619_3]) ).

fof(f_1620_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_1620_2,plain,
    ! [U_5347,U_5346,U_5345] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5345),U_5346),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_5347)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5345),hAPP(hAPP(c_Power_Opower__class_Opower(U_5345),U_5346),U_5347)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5345),U_5346),U_5347))
      | ~ class_Rings_Ocomm__semiring__1(U_5345) ),
    inference(variable_rename,[status(thm)],[f_1620_1]) ).

fof(f_1620_3,plain,
    ! [U_5346,U_5347,U_5345] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5345),U_5346),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_5347)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5345),hAPP(hAPP(c_Power_Opower__class_Opower(U_5345),U_5346),U_5347)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5345),U_5346),U_5347))
      | ~ class_Rings_Ocomm__semiring__1(U_5345) ),
    inference(definitional_conversion,[status(esa)],[f_1620_2]) ).

cnf(f_1620_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5345),U_5346),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_5347)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5345),hAPP(hAPP(c_Power_Opower__class_Opower(U_5345),U_5346),U_5347)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5345),U_5346),U_5347))
    | ~ class_Rings_Ocomm__semiring__1(U_5345) ),
    inference(clausify,[status(thm)],[f_1620_3]) ).

fof(f_1621_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_1621_2,plain,
    ! [U_5350,U_5349,U_5348] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5348),hAPP(c_Groups_Ouminus__class_Ouminus(U_5348),U_5349)),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_5350)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5348),U_5349),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_5350))
      | ~ class_Rings_Oring__1(U_5348) ),
    inference(variable_rename,[status(thm)],[f_1621_1]) ).

fof(f_1621_3,plain,
    ! [U_5349,U_5348,U_5350] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5348),hAPP(c_Groups_Ouminus__class_Ouminus(U_5348),U_5349)),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_5350)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5348),U_5349),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_5350))
      | ~ class_Rings_Oring__1(U_5348) ),
    inference(definitional_conversion,[status(esa)],[f_1621_2]) ).

cnf(f_1621_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5348),hAPP(c_Groups_Ouminus__class_Ouminus(U_5348),U_5349)),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_5350)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5348),U_5349),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_5350))
    | ~ class_Rings_Oring__1(U_5348) ),
    inference(clausify,[status(thm)],[f_1621_3]) ).

fof(f_1622_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_1622_2,plain,
    ! [U_5353,U_5352,U_5351] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5351),U_5352),U_5353))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5351),c_Groups_Ozero__class_Ozero(U_5351)),U_5353))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5351),hAPP(hAPP(c_Power_Opower__class_Opower(U_5351),U_5352),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_5351),U_5353),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(U_5351) ),
    inference(variable_rename,[status(thm)],[f_1622_1]) ).

fof(f_1622_3,plain,
    ! [U_5351,U_5352,U_5353] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5351),U_5352),U_5353))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5351),c_Groups_Ozero__class_Ozero(U_5351)),U_5353))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5351),hAPP(hAPP(c_Power_Opower__class_Opower(U_5351),U_5352),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_5351),U_5353),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ class_Rings_Olinordered__semidom(U_5351) ),
    inference(definitional_conversion,[status(esa)],[f_1622_2]) ).

cnf(f_1622_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5351),U_5352),U_5353))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5351),c_Groups_Ozero__class_Ozero(U_5351)),U_5353))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5351),hAPP(hAPP(c_Power_Opower__class_Opower(U_5351),U_5352),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_5351),U_5353),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ class_Rings_Olinordered__semidom(U_5351) ),
    inference(clausify,[status(thm)],[f_1622_3]) ).

fof(f_1623_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_1623_2,plain,
    ! [U_5356,U_5355,U_5354] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5354),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5354),hAPP(hAPP(c_Power_Opower__class_Opower(U_5354),U_5355),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_5354),U_5356),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_5354)))
          | U_5356 != c_Groups_Ozero__class_Ozero(U_5354)
          | U_5355 != c_Groups_Ozero__class_Ozero(U_5354) )
        & ( ( U_5356 = c_Groups_Ozero__class_Ozero(U_5354)
            & U_5355 = c_Groups_Ozero__class_Ozero(U_5354) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5354),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5354),hAPP(hAPP(c_Power_Opower__class_Opower(U_5354),U_5355),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_5354),U_5356),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_5354))) ) )
      | ~ class_Rings_Olinordered__idom(U_5354) ),
    inference(variable_rename,[status(thm)],[f_1623_1]) ).

fof(f_1623_3,plain,
    ( ! [U_5354,U_5355,U_5356] :
        ( U_5356 = c_Groups_Ozero__class_Ozero(U_5354)
        | ~ sP416(U_5354,U_5355,U_5356) )
    & ! [U_5354,U_5355,U_5356] :
        ( U_5355 = c_Groups_Ozero__class_Ozero(U_5354)
        | ~ sP416(U_5354,U_5355,U_5356) )
    & ! [U_5354,U_5355,U_5356] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5354),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5354),hAPP(hAPP(c_Power_Opower__class_Opower(U_5354),U_5355),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_5354),U_5356),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_5354)))
        | U_5356 != c_Groups_Ozero__class_Ozero(U_5354)
        | U_5355 != c_Groups_Ozero__class_Ozero(U_5354)
        | ~ sP417(U_5354,U_5355,U_5356) )
    & ! [U_5354,U_5355,U_5356] :
        ( sP416(U_5354,U_5355,U_5356)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5354),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5354),hAPP(hAPP(c_Power_Opower__class_Opower(U_5354),U_5355),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_5354),U_5356),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_5354)))
        | ~ sP417(U_5354,U_5355,U_5356) )
    & ! [U_5354,U_5355,U_5356] :
        ( sP417(U_5354,U_5355,U_5356)
        | ~ class_Rings_Olinordered__idom(U_5354) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP416,sP417])],[f_1623_2]) ).

cnf(f_1623_4,plain,
    ( sP417(U_5354,U_5355,U_5356)
    | ~ class_Rings_Olinordered__idom(U_5354) ),
    inference(clausify,[status(thm)],[f_1623_3]) ).

cnf(f_1623_5,plain,
    ( sP416(U_5354,U_5355,U_5356)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5354),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5354),hAPP(hAPP(c_Power_Opower__class_Opower(U_5354),U_5355),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_5354),U_5356),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_5354)))
    | ~ sP417(U_5354,U_5355,U_5356) ),
    inference(clausify,[status(thm)],[f_1623_3]) ).

cnf(f_1623_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5354),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5354),hAPP(hAPP(c_Power_Opower__class_Opower(U_5354),U_5355),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_5354),U_5356),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_5354)))
    | U_5356 != c_Groups_Ozero__class_Ozero(U_5354)
    | U_5355 != c_Groups_Ozero__class_Ozero(U_5354)
    | ~ sP417(U_5354,U_5355,U_5356) ),
    inference(clausify,[status(thm)],[f_1623_3]) ).

cnf(f_1623_7,plain,
    ( U_5355 = c_Groups_Ozero__class_Ozero(U_5354)
    | ~ sP416(U_5354,U_5355,U_5356) ),
    inference(clausify,[status(thm)],[f_1623_3]) ).

cnf(f_1623_8,plain,
    ( U_5356 = c_Groups_Ozero__class_Ozero(U_5354)
    | ~ sP416(U_5354,U_5355,U_5356) ),
    inference(clausify,[status(thm)],[f_1623_3]) ).

fof(f_1624_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_1624_2,plain,
    ! [U_5359,U_5358,U_5357] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5357),c_Groups_Ozero__class_Ozero(U_5357)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5357),hAPP(hAPP(c_Power_Opower__class_Opower(U_5357),U_5358),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_5357),U_5359),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
      | ~ class_Rings_Olinordered__idom(U_5357) ),
    inference(variable_rename,[status(thm)],[f_1624_1]) ).

fof(f_1624_3,plain,
    ! [U_5357,U_5358,U_5359] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5357),c_Groups_Ozero__class_Ozero(U_5357)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5357),hAPP(hAPP(c_Power_Opower__class_Opower(U_5357),U_5358),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_5357),U_5359),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
      | ~ class_Rings_Olinordered__idom(U_5357) ),
    inference(definitional_conversion,[status(esa)],[f_1624_2]) ).

cnf(f_1624_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5357),c_Groups_Ozero__class_Ozero(U_5357)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5357),hAPP(hAPP(c_Power_Opower__class_Opower(U_5357),U_5358),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_5357),U_5359),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | ~ class_Rings_Olinordered__idom(U_5357) ),
    inference(clausify,[status(thm)],[f_1624_3]) ).

fof(f_1625_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_1625_2,plain,
    ! [U_5362,U_5361,U_5360] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5360),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5360),hAPP(hAPP(c_Power_Opower__class_Opower(U_5360),U_5361),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_5360),U_5362),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_5360)))
      | ~ class_Rings_Olinordered__idom(U_5360) ),
    inference(variable_rename,[status(thm)],[f_1625_1]) ).

fof(f_1625_3,plain,
    ! [U_5362,U_5360,U_5361] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5360),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5360),hAPP(hAPP(c_Power_Opower__class_Opower(U_5360),U_5361),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_5360),U_5362),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_5360)))
      | ~ class_Rings_Olinordered__idom(U_5360) ),
    inference(definitional_conversion,[status(esa)],[f_1625_2]) ).

cnf(f_1625_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5360),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5360),hAPP(hAPP(c_Power_Opower__class_Opower(U_5360),U_5361),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_5360),U_5362),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_5360)))
    | ~ class_Rings_Olinordered__idom(U_5360) ),
    inference(clausify,[status(thm)],[f_1625_3]) ).

fof(f_1626_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_1626_2,plain,
    ! [U_5365,U_5364,U_5363] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5363),c_Groups_Ozero__class_Ozero(U_5363)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5363),hAPP(hAPP(c_Power_Opower__class_Opower(U_5363),U_5364),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_5363),U_5365),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
          | ( U_5365 = c_Groups_Ozero__class_Ozero(U_5363)
            & U_5364 = c_Groups_Ozero__class_Ozero(U_5363) ) )
        & ( U_5365 != c_Groups_Ozero__class_Ozero(U_5363)
          | U_5364 != c_Groups_Ozero__class_Ozero(U_5363)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5363),c_Groups_Ozero__class_Ozero(U_5363)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5363),hAPP(hAPP(c_Power_Opower__class_Opower(U_5363),U_5364),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_5363),U_5365),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))) ) )
      | ~ class_Rings_Olinordered__idom(U_5363) ),
    inference(variable_rename,[status(thm)],[f_1626_1]) ).

fof(f_1626_3,plain,
    ( ! [U_5363,U_5364,U_5365] :
        ( U_5365 = c_Groups_Ozero__class_Ozero(U_5363)
        | ~ sP418(U_5363,U_5364,U_5365) )
    & ! [U_5363,U_5364,U_5365] :
        ( U_5364 = c_Groups_Ozero__class_Ozero(U_5363)
        | ~ sP418(U_5363,U_5364,U_5365) )
    & ! [U_5363,U_5364,U_5365] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5363),c_Groups_Ozero__class_Ozero(U_5363)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5363),hAPP(hAPP(c_Power_Opower__class_Opower(U_5363),U_5364),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_5363),U_5365),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
        | sP418(U_5363,U_5364,U_5365)
        | ~ sP419(U_5363,U_5364,U_5365) )
    & ! [U_5363,U_5364,U_5365] :
        ( U_5365 != c_Groups_Ozero__class_Ozero(U_5363)
        | U_5364 != c_Groups_Ozero__class_Ozero(U_5363)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5363),c_Groups_Ozero__class_Ozero(U_5363)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5363),hAPP(hAPP(c_Power_Opower__class_Opower(U_5363),U_5364),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_5363),U_5365),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
        | ~ sP419(U_5363,U_5364,U_5365) )
    & ! [U_5363,U_5364,U_5365] :
        ( sP419(U_5363,U_5364,U_5365)
        | ~ class_Rings_Olinordered__idom(U_5363) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP418,sP419])],[f_1626_2]) ).

cnf(f_1626_4,plain,
    ( sP419(U_5363,U_5364,U_5365)
    | ~ class_Rings_Olinordered__idom(U_5363) ),
    inference(clausify,[status(thm)],[f_1626_3]) ).

cnf(f_1626_5,plain,
    ( U_5365 != c_Groups_Ozero__class_Ozero(U_5363)
    | U_5364 != c_Groups_Ozero__class_Ozero(U_5363)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5363),c_Groups_Ozero__class_Ozero(U_5363)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5363),hAPP(hAPP(c_Power_Opower__class_Opower(U_5363),U_5364),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_5363),U_5365),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | ~ sP419(U_5363,U_5364,U_5365) ),
    inference(clausify,[status(thm)],[f_1626_3]) ).

cnf(f_1626_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5363),c_Groups_Ozero__class_Ozero(U_5363)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5363),hAPP(hAPP(c_Power_Opower__class_Opower(U_5363),U_5364),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_5363),U_5365),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))))
    | sP418(U_5363,U_5364,U_5365)
    | ~ sP419(U_5363,U_5364,U_5365) ),
    inference(clausify,[status(thm)],[f_1626_3]) ).

cnf(f_1626_7,plain,
    ( U_5364 = c_Groups_Ozero__class_Ozero(U_5363)
    | ~ sP418(U_5363,U_5364,U_5365) ),
    inference(clausify,[status(thm)],[f_1626_3]) ).

cnf(f_1626_8,plain,
    ( U_5365 = c_Groups_Ozero__class_Ozero(U_5363)
    | ~ sP418(U_5363,U_5364,U_5365) ),
    inference(clausify,[status(thm)],[f_1626_3]) ).

fof(f_1627_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_1627_2,plain,
    ! [U_5368,U_5367,U_5366] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5366),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5366),U_5367),U_5368)),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_5366),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5366),hAPP(hAPP(c_Power_Opower__class_Opower(U_5366),U_5367),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_5366),U_5368),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_5366),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5366),hAPP(c_Int_Onumber__class_Onumber__of(U_5366),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5367)),U_5368))
      | ~ class_Int_Onumber__ring(U_5366) ),
    inference(variable_rename,[status(thm)],[f_1627_1]) ).

fof(f_1627_3,plain,
    ! [U_5367,U_5368,U_5366] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5366),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5366),U_5367),U_5368)),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_5366),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5366),hAPP(hAPP(c_Power_Opower__class_Opower(U_5366),U_5367),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_5366),U_5368),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_5366),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5366),hAPP(c_Int_Onumber__class_Onumber__of(U_5366),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5367)),U_5368))
      | ~ class_Int_Onumber__ring(U_5366) ),
    inference(definitional_conversion,[status(esa)],[f_1627_2]) ).

cnf(f_1627_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5366),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5366),U_5367),U_5368)),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_5366),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5366),hAPP(hAPP(c_Power_Opower__class_Opower(U_5366),U_5367),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_5366),U_5368),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_5366),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5366),hAPP(c_Int_Onumber__class_Onumber__of(U_5366),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5367)),U_5368))
    | ~ class_Int_Onumber__ring(U_5366) ),
    inference(clausify,[status(thm)],[f_1627_3]) ).

fof(f_1628_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_1628_2,plain,
    ! [U_5371,U_5370,U_5369] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5369),c_Groups_Ozero__class_Ozero(U_5369)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5369),U_5370),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_5371))))
      | ~ class_Rings_Olinordered__idom(U_5369) ),
    inference(variable_rename,[status(thm)],[f_1628_1]) ).

fof(f_1628_3,plain,
    ! [U_5369,U_5370,U_5371] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5369),c_Groups_Ozero__class_Ozero(U_5369)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5369),U_5370),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_5371))))
      | ~ class_Rings_Olinordered__idom(U_5369) ),
    inference(definitional_conversion,[status(esa)],[f_1628_2]) ).

cnf(f_1628_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5369),c_Groups_Ozero__class_Ozero(U_5369)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5369),U_5370),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_5371))))
    | ~ class_Rings_Olinordered__idom(U_5369) ),
    inference(clausify,[status(thm)],[f_1628_3]) ).

fof(f_1629_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_1629_2,plain,
    ! [U_5374,U_5373,U_5372] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5372),U_5373),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_5374))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5372),U_5373),hAPP(hAPP(c_Power_Opower__class_Opower(U_5372),hAPP(hAPP(c_Power_Opower__class_Opower(U_5372),U_5373),U_5374)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      | ~ class_Groups_Omonoid__mult(U_5372) ),
    inference(variable_rename,[status(thm)],[f_1629_1]) ).

fof(f_1629_3,plain,
    ! [U_5372,U_5373,U_5374] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5372),U_5373),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_5374))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5372),U_5373),hAPP(hAPP(c_Power_Opower__class_Opower(U_5372),hAPP(hAPP(c_Power_Opower__class_Opower(U_5372),U_5373),U_5374)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
      | ~ class_Groups_Omonoid__mult(U_5372) ),
    inference(definitional_conversion,[status(esa)],[f_1629_2]) ).

cnf(f_1629_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5372),U_5373),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_5374))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5372),U_5373),hAPP(hAPP(c_Power_Opower__class_Opower(U_5372),hAPP(hAPP(c_Power_Opower__class_Opower(U_5372),U_5373),U_5374)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))
    | ~ class_Groups_Omonoid__mult(U_5372) ),
    inference(clausify,[status(thm)],[f_1629_3]) ).

fof(f_1630_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_1630_2,plain,
    ! [U_5377,U_5376,U_5375] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5375),U_5376),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_5377))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5375),U_5376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5375),hAPP(hAPP(c_Power_Opower__class_Opower(U_5375),U_5376),U_5377)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5375),U_5376),U_5377)))
      | ~ class_Rings_Ocomm__semiring__1(U_5375) ),
    inference(variable_rename,[status(thm)],[f_1630_1]) ).

fof(f_1630_3,plain,
    ! [U_5375,U_5376,U_5377] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5375),U_5376),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_5377))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5375),U_5376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5375),hAPP(hAPP(c_Power_Opower__class_Opower(U_5375),U_5376),U_5377)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5375),U_5376),U_5377)))
      | ~ class_Rings_Ocomm__semiring__1(U_5375) ),
    inference(definitional_conversion,[status(esa)],[f_1630_2]) ).

cnf(f_1630_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5375),U_5376),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_5377))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5375),U_5376),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5375),hAPP(hAPP(c_Power_Opower__class_Opower(U_5375),U_5376),U_5377)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5375),U_5376),U_5377)))
    | ~ class_Rings_Ocomm__semiring__1(U_5375) ),
    inference(clausify,[status(thm)],[f_1630_3]) ).

fof(f_1631_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_1631_2,plain,
    ! [U_5379,U_5378] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5378),hAPP(c_Groups_Ouminus__class_Ouminus(U_5378),c_Groups_Oone__class_Oone(U_5378))),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_5379)) = c_Groups_Oone__class_Oone(U_5378)
      | ~ class_Rings_Oring__1(U_5378) ),
    inference(variable_rename,[status(thm)],[f_1631_1]) ).

fof(f_1631_3,plain,
    ! [U_5378,U_5379] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5378),hAPP(c_Groups_Ouminus__class_Ouminus(U_5378),c_Groups_Oone__class_Oone(U_5378))),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_5379)) = c_Groups_Oone__class_Oone(U_5378)
      | ~ class_Rings_Oring__1(U_5378) ),
    inference(definitional_conversion,[status(esa)],[f_1631_2]) ).

cnf(f_1631_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5378),hAPP(c_Groups_Ouminus__class_Ouminus(U_5378),c_Groups_Oone__class_Oone(U_5378))),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_5379)) = c_Groups_Oone__class_Oone(U_5378)
    | ~ class_Rings_Oring__1(U_5378) ),
    inference(clausify,[status(thm)],[f_1631_3]) ).

fof(f_1632_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_1632_2,plain,
    ! [U_5381,U_5380] :
      ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5381))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5380))) = 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_5381)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5380))
        | 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_5380))) )
      & ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5381))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5380))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5381)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5380))
        | ~ 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_5380))) ) ),
    inference(variable_rename,[status(thm)],[f_1632_1]) ).

fof(f_1632_3,plain,
    ( ! [U_5385,U_5383] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5385))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5383))) = 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_5385)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5383))
        | 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_5383))) )
    & ! [U_5384,U_5382] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5384))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5382))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5382))
        | ~ 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_5382))) ) ),
    inference(miniscope,[status(thm)],[f_1632_2]) ).

fof(f_1632_4,plain,
    ( ! [U_5383,U_5385] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5385))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5383))) = 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_5385)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5383))
        | 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_5383))) )
    & ! [U_5384,U_5382] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(U_5384))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5382))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5382))
        | ~ 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_5382))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1632_3]) ).

cnf(f_1632_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_5384))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5382))) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5384)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5382))
    | ~ 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_5382))) ),
    inference(clausify,[status(thm)],[f_1632_4]) ).

cnf(f_1632_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_5385))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(U_5383))) = 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_5385)),c_Groups_Oone__class_Oone(tc_Int_Oint))),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5383))
    | 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_5383))) ),
    inference(clausify,[status(thm)],[f_1632_4]) ).

fof(f_1633_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_1633_2,plain,
    ! [U_5386] :
      ( ( 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_5386,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_5386,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_5386,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_5386,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_1633_1]) ).

fof(f_1633_3,plain,
    ( ! [U_5388] :
        ( 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_5388,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_5388,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_5387] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5387,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_5387,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) ),
    inference(miniscope,[status(thm)],[f_1633_2]) ).

fof(f_1633_4,plain,
    ( ! [U_5388] :
        ( 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_5388,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_5388,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_5387] :
        ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5387,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_5387,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_1633_3]) ).

cnf(f_1633_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_5387,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_5387,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ),
    inference(clausify,[status(thm)],[f_1633_4]) ).

cnf(f_1633_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_5388,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_5388,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_1633_4]) ).

fof(f_1634_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_1634_2,plain,
    ! [U_5389] :
      ( 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_5389),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_5389)) ),
    inference(variable_rename,[status(thm)],[f_1634_1]) ).

fof(f_1634_3,plain,
    ! [U_5389] :
      ( 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_5389),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_5389)) ),
    inference(definitional_conversion,[status(esa)],[f_1634_2]) ).

cnf(f_1634_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_5389),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_5389)) ),
    inference(clausify,[status(thm)],[f_1634_3]) ).

fof(f_1635_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_1635_2,plain,
    ! [U_5392,U_5391,U_5390] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5390),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5390),U_5391),U_5392)),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_5390),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5390),hAPP(hAPP(c_Power_Opower__class_Opower(U_5390),U_5391),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_5390),U_5392),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_5390),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5390),hAPP(c_Int_Onumber__class_Onumber__of(U_5390),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5391)),U_5392))
      | ~ class_Int_Onumber__ring(U_5390) ),
    inference(variable_rename,[status(thm)],[f_1635_1]) ).

fof(f_1635_3,plain,
    ! [U_5390,U_5391,U_5392] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5390),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5390),U_5391),U_5392)),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_5390),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5390),hAPP(hAPP(c_Power_Opower__class_Opower(U_5390),U_5391),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_5390),U_5392),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_5390),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5390),hAPP(c_Int_Onumber__class_Onumber__of(U_5390),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5391)),U_5392))
      | ~ class_Int_Onumber__ring(U_5390) ),
    inference(definitional_conversion,[status(esa)],[f_1635_2]) ).

cnf(f_1635_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5390),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5390),U_5391),U_5392)),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_5390),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5390),hAPP(hAPP(c_Power_Opower__class_Opower(U_5390),U_5391),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_5390),U_5392),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_5390),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5390),hAPP(c_Int_Onumber__class_Onumber__of(U_5390),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5391)),U_5392))
    | ~ class_Int_Onumber__ring(U_5390) ),
    inference(clausify,[status(thm)],[f_1635_3]) ).

fof(f_1636_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_1636_2,plain,
    ! [U_5395,U_5394,U_5393] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5393),c_Groups_Ozero__class_Ozero(U_5393)),U_5394))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5393),c_Groups_Ozero__class_Ozero(U_5393)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5393),U_5394),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_5395)))))
      | ~ class_Rings_Olinordered__idom(U_5393) ),
    inference(variable_rename,[status(thm)],[f_1636_1]) ).

fof(f_1636_3,plain,
    ! [U_5393,U_5394,U_5395] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5393),c_Groups_Ozero__class_Ozero(U_5393)),U_5394))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5393),c_Groups_Ozero__class_Ozero(U_5393)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5393),U_5394),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_5395)))))
      | ~ class_Rings_Olinordered__idom(U_5393) ),
    inference(definitional_conversion,[status(esa)],[f_1636_2]) ).

cnf(f_1636_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5393),c_Groups_Ozero__class_Ozero(U_5393)),U_5394))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5393),c_Groups_Ozero__class_Ozero(U_5393)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5393),U_5394),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_5395)))))
    | ~ class_Rings_Olinordered__idom(U_5393) ),
    inference(clausify,[status(thm)],[f_1636_3]) ).

fof(f_1637_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_1637_2,plain,
    ! [U_5398,U_5397,U_5396] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5396),hAPP(hAPP(c_Power_Opower__class_Opower(U_5396),U_5397),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_5398)))),c_Groups_Ozero__class_Ozero(U_5396)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5396),U_5397),c_Groups_Ozero__class_Ozero(U_5396)))
      | ~ class_Rings_Olinordered__idom(U_5396) ),
    inference(variable_rename,[status(thm)],[f_1637_1]) ).

fof(f_1637_3,plain,
    ! [U_5396,U_5397,U_5398] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5396),hAPP(hAPP(c_Power_Opower__class_Opower(U_5396),U_5397),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_5398)))),c_Groups_Ozero__class_Ozero(U_5396)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5396),U_5397),c_Groups_Ozero__class_Ozero(U_5396)))
      | ~ class_Rings_Olinordered__idom(U_5396) ),
    inference(definitional_conversion,[status(esa)],[f_1637_2]) ).

cnf(f_1637_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5396),hAPP(hAPP(c_Power_Opower__class_Opower(U_5396),U_5397),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_5398)))),c_Groups_Ozero__class_Ozero(U_5396)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5396),U_5397),c_Groups_Ozero__class_Ozero(U_5396)))
    | ~ class_Rings_Olinordered__idom(U_5396) ),
    inference(clausify,[status(thm)],[f_1637_3]) ).

fof(f_1638_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_1638_2,plain,
    ! [U_5400,U_5399] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5399),hAPP(c_Groups_Ouminus__class_Ouminus(U_5399),c_Groups_Oone__class_Oone(U_5399))),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_5400))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5399),c_Groups_Oone__class_Oone(U_5399))
      | ~ class_Rings_Oring__1(U_5399) ),
    inference(variable_rename,[status(thm)],[f_1638_1]) ).

fof(f_1638_3,plain,
    ! [U_5399,U_5400] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5399),hAPP(c_Groups_Ouminus__class_Ouminus(U_5399),c_Groups_Oone__class_Oone(U_5399))),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_5400))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5399),c_Groups_Oone__class_Oone(U_5399))
      | ~ class_Rings_Oring__1(U_5399) ),
    inference(definitional_conversion,[status(esa)],[f_1638_2]) ).

cnf(f_1638_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5399),hAPP(c_Groups_Ouminus__class_Ouminus(U_5399),c_Groups_Oone__class_Oone(U_5399))),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_5400))) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5399),c_Groups_Oone__class_Oone(U_5399))
    | ~ class_Rings_Oring__1(U_5399) ),
    inference(clausify,[status(thm)],[f_1638_3]) ).

fof(f_1639_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_1639_2,plain,
    ! [U_5402,U_5401] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5401),hAPP(c_Int_Onumber__class_Onumber__of(U_5401),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_5402)) = c_Groups_Oone__class_Oone(U_5401)
      | ~ class_Int_Onumber__ring(U_5401) ),
    inference(variable_rename,[status(thm)],[f_1639_1]) ).

fof(f_1639_3,plain,
    ! [U_5401,U_5402] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5401),hAPP(c_Int_Onumber__class_Onumber__of(U_5401),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_5402)) = c_Groups_Oone__class_Oone(U_5401)
      | ~ class_Int_Onumber__ring(U_5401) ),
    inference(definitional_conversion,[status(esa)],[f_1639_2]) ).

cnf(f_1639_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5401),hAPP(c_Int_Onumber__class_Onumber__of(U_5401),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_5402)) = c_Groups_Oone__class_Oone(U_5401)
    | ~ class_Int_Onumber__ring(U_5401) ),
    inference(clausify,[status(thm)],[f_1639_3]) ).

fof(f_1640_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_1640_2,plain,
    ! [U_5404,U_5403] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5403),hAPP(c_Int_Onumber__class_Onumber__of(U_5403),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_5404))) = hAPP(c_Int_Onumber__class_Onumber__of(U_5403),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_5403) ),
    inference(variable_rename,[status(thm)],[f_1640_1]) ).

fof(f_1640_3,plain,
    ! [U_5403,U_5404] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5403),hAPP(c_Int_Onumber__class_Onumber__of(U_5403),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_5404))) = hAPP(c_Int_Onumber__class_Onumber__of(U_5403),c_Int_OMin)
      | ~ class_Int_Onumber__ring(U_5403) ),
    inference(definitional_conversion,[status(esa)],[f_1640_2]) ).

cnf(f_1640_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5403),hAPP(c_Int_Onumber__class_Onumber__of(U_5403),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_5404))) = hAPP(c_Int_Onumber__class_Onumber__of(U_5403),c_Int_OMin)
    | ~ class_Int_Onumber__ring(U_5403) ),
    inference(clausify,[status(thm)],[f_1640_3]) ).

fof(f_1641_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_1641_2,plain,
    ! [U_5405] :
      ( 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_5405),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_5405)) ),
    inference(variable_rename,[status(thm)],[f_1641_1]) ).

fof(f_1641_3,plain,
    ! [U_5405] :
      ( 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_5405),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_5405)) ),
    inference(definitional_conversion,[status(esa)],[f_1641_2]) ).

cnf(f_1641_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_5405),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_5405)) ),
    inference(clausify,[status(thm)],[f_1641_3]) ).

fof(f_1642_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_1642_2,plain,
    ! [U_5406] :
      ( ( ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5406)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5406)),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_5406))))
          | 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_5406)))) )
        & ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5406)) = 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_5406)))
          | ~ 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_5406)))) ) )
      | ~ 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_5406))) ),
    inference(variable_rename,[status(thm)],[f_1642_1]) ).

fof(f_1642_3,plain,
    ( ! [U_5406] :
        ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5406)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5406)),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_5406))))
        | 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_5406))))
        | ~ sP420(U_5406) )
    & ! [U_5406] :
        ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5406)) = 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_5406)))
        | ~ 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_5406))))
        | ~ sP420(U_5406) )
    & ! [U_5406] :
        ( sP420(U_5406)
        | ~ 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_5406))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP420])],[f_1642_2]) ).

cnf(f_1642_4,plain,
    ( sP420(U_5406)
    | ~ 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_5406))) ),
    inference(clausify,[status(thm)],[f_1642_3]) ).

cnf(f_1642_5,plain,
    ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5406)) = 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_5406)))
    | ~ 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_5406))))
    | ~ sP420(U_5406) ),
    inference(clausify,[status(thm)],[f_1642_3]) ).

cnf(f_1642_6,plain,
    ( c_Divides_OnegDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5406)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5406)),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_5406))))
    | 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_5406))))
    | ~ sP420(U_5406) ),
    inference(clausify,[status(thm)],[f_1642_3]) ).

fof(f_1643_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_1643_2,plain,
    ! [U_5408,U_5407] :
      ( ( ( c_Divides_OnegDivAlg(U_5408,U_5407) = hAPP(c_Divides_Oadjust(U_5407),c_Divides_OnegDivAlg(U_5408,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5407)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5408),U_5407))) )
        & ( c_Divides_OnegDivAlg(U_5408,U_5407) = 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_5408),U_5407))
          | ~ 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_5408),U_5407))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5407)) ),
    inference(variable_rename,[status(thm)],[f_1643_1]) ).

fof(f_1643_3,plain,
    ( ! [U_5407,U_5408] :
        ( c_Divides_OnegDivAlg(U_5408,U_5407) = hAPP(c_Divides_Oadjust(U_5407),c_Divides_OnegDivAlg(U_5408,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5407)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5408),U_5407)))
        | ~ sP421(U_5407,U_5408) )
    & ! [U_5407,U_5408] :
        ( c_Divides_OnegDivAlg(U_5408,U_5407) = 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_5408),U_5407))
        | ~ 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_5408),U_5407)))
        | ~ sP421(U_5407,U_5408) )
    & ! [U_5407,U_5408] :
        ( sP421(U_5407,U_5408)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5407)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP421])],[f_1643_2]) ).

cnf(f_1643_4,plain,
    ( sP421(U_5407,U_5408)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5407)) ),
    inference(clausify,[status(thm)],[f_1643_3]) ).

cnf(f_1643_5,plain,
    ( c_Divides_OnegDivAlg(U_5408,U_5407) = 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_5408),U_5407))
    | ~ 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_5408),U_5407)))
    | ~ sP421(U_5407,U_5408) ),
    inference(clausify,[status(thm)],[f_1643_3]) ).

cnf(f_1643_6,plain,
    ( c_Divides_OnegDivAlg(U_5408,U_5407) = hAPP(c_Divides_Oadjust(U_5407),c_Divides_OnegDivAlg(U_5408,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),U_5407)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_5408),U_5407)))
    | ~ sP421(U_5407,U_5408) ),
    inference(clausify,[status(thm)],[f_1643_3]) ).

fof(f_1644_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_1644_2,plain,
    ! [U_5410,U_5409] :
      ( ( ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5410),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5409)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5409)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5410),hAPP(hAPP(c_Groups_Otimes__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_5409))))
          | 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_5410)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5409)))) )
        & ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5410),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5409)) = 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_5410)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5409)))
          | ~ 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_5410)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5409)))) ) )
      | ~ 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_5409))) ),
    inference(variable_rename,[status(thm)],[f_1644_1]) ).

fof(f_1644_3,plain,
    ( ! [U_5410,U_5409] :
        ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5410),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5409)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5409)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5410),hAPP(hAPP(c_Groups_Otimes__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_5409))))
        | 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_5410)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5409))))
        | ~ sP422(U_5410,U_5409) )
    & ! [U_5410,U_5409] :
        ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5410),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5409)) = 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_5410)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5409)))
        | ~ 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_5410)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5409))))
        | ~ sP422(U_5410,U_5409) )
    & ! [U_5410,U_5409] :
        ( sP422(U_5410,U_5409)
        | ~ 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_5409))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP422])],[f_1644_2]) ).

cnf(f_1644_4,plain,
    ( sP422(U_5410,U_5409)
    | ~ 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_5409))) ),
    inference(clausify,[status(thm)],[f_1644_3]) ).

cnf(f_1644_5,plain,
    ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5410),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5409)) = 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_5410)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5409)))
    | ~ 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_5410)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5409))))
    | ~ sP422(U_5410,U_5409) ),
    inference(clausify,[status(thm)],[f_1644_3]) ).

cnf(f_1644_6,plain,
    ( c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5410),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5409)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5409)),c_Divides_OnegDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5410),hAPP(hAPP(c_Groups_Otimes__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_5409))))
    | 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_5410)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5409))))
    | ~ sP422(U_5410,U_5409) ),
    inference(clausify,[status(thm)],[f_1644_3]) ).

fof(f_1645_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_1645_2,plain,
    ! [U_5412,U_5411] :
      ( ( c_Divides_OnegDivAlg(U_5411,U_5412) = hAPP(c_Divides_Oadjust(U_5412),c_Divides_OnegDivAlg(U_5411,hAPP(hAPP(c_Groups_Otimes__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_5412)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5412),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_5411),U_5412))) )
      & ( c_Divides_OnegDivAlg(U_5411,U_5412) = 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_5411),U_5412))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5412),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_5411),U_5412))) ) ) ),
    inference(variable_rename,[status(thm)],[f_1645_1]) ).

fof(f_1645_3,plain,
    ( ! [U_5416,U_5414] :
        ( c_Divides_OnegDivAlg(U_5414,U_5416) = hAPP(c_Divides_Oadjust(U_5416),c_Divides_OnegDivAlg(U_5414,hAPP(hAPP(c_Groups_Otimes__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_5416)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5416),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_5414),U_5416))) )
    & ! [U_5415,U_5413] :
        ( c_Divides_OnegDivAlg(U_5413,U_5415) = 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_5413),U_5415))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5415),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_5413),U_5415))) ) ) ),
    inference(miniscope,[status(thm)],[f_1645_2]) ).

fof(f_1645_4,plain,
    ( ! [U_5413,U_5415] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5415),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP423(U_5413,U_5415) )
    & ! [U_5413,U_5415] :
        ( ~ 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_5413),U_5415)))
        | ~ sP423(U_5413,U_5415) )
    & ! [U_5414,U_5416] :
        ( c_Divides_OnegDivAlg(U_5414,U_5416) = hAPP(c_Divides_Oadjust(U_5416),c_Divides_OnegDivAlg(U_5414,hAPP(hAPP(c_Groups_Otimes__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_5416)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5416),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_5414),U_5416))) )
    & ! [U_5413,U_5415] :
        ( c_Divides_OnegDivAlg(U_5413,U_5415) = 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_5413),U_5415))
        | sP423(U_5413,U_5415) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP423])],[f_1645_3]) ).

cnf(f_1645_5,plain,
    ( c_Divides_OnegDivAlg(U_5413,U_5415) = 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_5413),U_5415))
    | sP423(U_5413,U_5415) ),
    inference(clausify,[status(thm)],[f_1645_4]) ).

cnf(f_1645_6,plain,
    ( c_Divides_OnegDivAlg(U_5414,U_5416) = hAPP(c_Divides_Oadjust(U_5416),c_Divides_OnegDivAlg(U_5414,hAPP(hAPP(c_Groups_Otimes__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_5416)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5416),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_5414),U_5416))) ),
    inference(clausify,[status(thm)],[f_1645_4]) ).

cnf(f_1645_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_5413),U_5415)))
    | ~ sP423(U_5413,U_5415) ),
    inference(clausify,[status(thm)],[f_1645_4]) ).

cnf(f_1645_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5415),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP423(U_5413,U_5415) ),
    inference(clausify,[status(thm)],[f_1645_4]) ).

fof(f_1646_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_1646_2,plain,
    ! [U_5417] :
      ( ( ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5417)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5417)),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_5417))))
          | 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_5417))) )
        & ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5417)) = 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_5417))) ) )
      | ~ 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_5417))) ),
    inference(variable_rename,[status(thm)],[f_1646_1]) ).

fof(f_1646_3,plain,
    ( ! [U_5417] :
        ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5417)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5417)),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_5417))))
        | 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_5417)))
        | ~ sP424(U_5417) )
    & ! [U_5417] :
        ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5417)) = 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_5417)))
        | ~ sP424(U_5417) )
    & ! [U_5417] :
        ( sP424(U_5417)
        | ~ 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_5417))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP424])],[f_1646_2]) ).

cnf(f_1646_4,plain,
    ( sP424(U_5417)
    | ~ 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_5417))) ),
    inference(clausify,[status(thm)],[f_1646_3]) ).

cnf(f_1646_5,plain,
    ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5417)) = 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_5417)))
    | ~ sP424(U_5417) ),
    inference(clausify,[status(thm)],[f_1646_3]) ).

cnf(f_1646_6,plain,
    ( c_Divides_OposDivAlg(c_Groups_Oone__class_Oone(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5417)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5417)),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_5417))))
    | 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_5417)))
    | ~ sP424(U_5417) ),
    inference(clausify,[status(thm)],[f_1646_3]) ).

fof(f_1647_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_1647_2,plain,
    ! [U_5419,U_5418] :
      ( ( c_Divides_OposDivAlg(U_5418,U_5419) = hAPP(c_Divides_Oadjust(U_5419),c_Divides_OposDivAlg(U_5418,hAPP(hAPP(c_Groups_Otimes__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_5419)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5419),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5418),U_5419)) )
      & ( c_Divides_OposDivAlg(U_5418,U_5419) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5418)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5419),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5418),U_5419)) ) ) ),
    inference(variable_rename,[status(thm)],[f_1647_1]) ).

fof(f_1647_3,plain,
    ( ! [U_5423,U_5421] :
        ( c_Divides_OposDivAlg(U_5421,U_5423) = hAPP(c_Divides_Oadjust(U_5423),c_Divides_OposDivAlg(U_5421,hAPP(hAPP(c_Groups_Otimes__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_5423)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5423),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5421),U_5423)) )
    & ! [U_5422,U_5420] :
        ( c_Divides_OposDivAlg(U_5420,U_5422) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5420)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5422),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5420),U_5422)) ) ) ),
    inference(miniscope,[status(thm)],[f_1647_2]) ).

fof(f_1647_4,plain,
    ( ! [U_5422,U_5420] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5422),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP425(U_5422,U_5420) )
    & ! [U_5422,U_5420] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5420),U_5422))
        | ~ sP425(U_5422,U_5420) )
    & ! [U_5421,U_5423] :
        ( c_Divides_OposDivAlg(U_5421,U_5423) = hAPP(c_Divides_Oadjust(U_5423),c_Divides_OposDivAlg(U_5421,hAPP(hAPP(c_Groups_Otimes__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_5423)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5423),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5421),U_5423)) )
    & ! [U_5422,U_5420] :
        ( c_Divides_OposDivAlg(U_5420,U_5422) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5420)
        | sP425(U_5422,U_5420) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP425])],[f_1647_3]) ).

cnf(f_1647_5,plain,
    ( c_Divides_OposDivAlg(U_5420,U_5422) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5420)
    | sP425(U_5422,U_5420) ),
    inference(clausify,[status(thm)],[f_1647_4]) ).

cnf(f_1647_6,plain,
    ( c_Divides_OposDivAlg(U_5421,U_5423) = hAPP(c_Divides_Oadjust(U_5423),c_Divides_OposDivAlg(U_5421,hAPP(hAPP(c_Groups_Otimes__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_5423)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5423),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5421),U_5423)) ),
    inference(clausify,[status(thm)],[f_1647_4]) ).

cnf(f_1647_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5420),U_5422))
    | ~ sP425(U_5422,U_5420) ),
    inference(clausify,[status(thm)],[f_1647_4]) ).

cnf(f_1647_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5422),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP425(U_5422,U_5420) ),
    inference(clausify,[status(thm)],[f_1647_4]) ).

fof(f_1648_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_1648_2,plain,
    ! [U_5425,U_5424] :
      ( ( ( c_Divides_OposDivAlg(U_5425,U_5424) = hAPP(c_Divides_Oadjust(U_5424),c_Divides_OposDivAlg(U_5425,hAPP(hAPP(c_Groups_Otimes__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_5424)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5425),U_5424)) )
        & ( c_Divides_OposDivAlg(U_5425,U_5424) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5425)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5425),U_5424)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5424)) ),
    inference(variable_rename,[status(thm)],[f_1648_1]) ).

fof(f_1648_3,plain,
    ( ! [U_5425,U_5424] :
        ( c_Divides_OposDivAlg(U_5425,U_5424) = hAPP(c_Divides_Oadjust(U_5424),c_Divides_OposDivAlg(U_5425,hAPP(hAPP(c_Groups_Otimes__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_5424)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5425),U_5424))
        | ~ sP426(U_5425,U_5424) )
    & ! [U_5425,U_5424] :
        ( c_Divides_OposDivAlg(U_5425,U_5424) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5425)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5425),U_5424))
        | ~ sP426(U_5425,U_5424) )
    & ! [U_5425,U_5424] :
        ( sP426(U_5425,U_5424)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5424)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP426])],[f_1648_2]) ).

cnf(f_1648_4,plain,
    ( sP426(U_5425,U_5424)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5424)) ),
    inference(clausify,[status(thm)],[f_1648_3]) ).

cnf(f_1648_5,plain,
    ( c_Divides_OposDivAlg(U_5425,U_5424) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5425)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5425),U_5424))
    | ~ sP426(U_5425,U_5424) ),
    inference(clausify,[status(thm)],[f_1648_3]) ).

cnf(f_1648_6,plain,
    ( c_Divides_OposDivAlg(U_5425,U_5424) = hAPP(c_Divides_Oadjust(U_5424),c_Divides_OposDivAlg(U_5425,hAPP(hAPP(c_Groups_Otimes__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_5424)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5425),U_5424))
    | ~ sP426(U_5425,U_5424) ),
    inference(clausify,[status(thm)],[f_1648_3]) ).

fof(f_1649_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_1649_2,plain,
    ! [U_5427,U_5426] :
      ( ( ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5427),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5426)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5426)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5427),hAPP(hAPP(c_Groups_Otimes__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_5426))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5427)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5426))) )
        & ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5427),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5426)) = 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_5427))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5427)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5426))) ) )
      | ~ 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_5426))) ),
    inference(variable_rename,[status(thm)],[f_1649_1]) ).

fof(f_1649_3,plain,
    ( ! [U_5427,U_5426] :
        ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5427),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5426)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5426)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5427),hAPP(hAPP(c_Groups_Otimes__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_5426))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5427)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5426)))
        | ~ sP427(U_5427,U_5426) )
    & ! [U_5427,U_5426] :
        ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5427),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5426)) = 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_5427))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5427)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5426)))
        | ~ sP427(U_5427,U_5426) )
    & ! [U_5427,U_5426] :
        ( sP427(U_5427,U_5426)
        | ~ 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_5426))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP427])],[f_1649_2]) ).

cnf(f_1649_4,plain,
    ( sP427(U_5427,U_5426)
    | ~ 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_5426))) ),
    inference(clausify,[status(thm)],[f_1649_3]) ).

cnf(f_1649_5,plain,
    ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5427),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5426)) = 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_5427))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5427)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5426)))
    | ~ sP427(U_5427,U_5426) ),
    inference(clausify,[status(thm)],[f_1649_3]) ).

cnf(f_1649_6,plain,
    ( c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5427),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5426)) = hAPP(c_Divides_Oadjust(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5426)),c_Divides_OposDivAlg(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5427),hAPP(hAPP(c_Groups_Otimes__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_5426))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5427)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_5426)))
    | ~ sP427(U_5427,U_5426) ),
    inference(clausify,[status(thm)],[f_1649_3]) ).

fof(f_1650_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_1650_2,plain,
    ! [U_5429,U_5428] :
      ( ( ( c_Divides_OnegDivAlg(U_5428,U_5429) = hAPP(c_Divides_Oadjust(U_5429),c_Divides_OnegDivAlg(U_5428,hAPP(hAPP(c_Groups_Otimes__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_5429)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5429),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_5428),U_5429))) )
        & ( c_Divides_OnegDivAlg(U_5428,U_5429) = 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_5428),U_5429))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5429),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_5428),U_5429))) ) ) )
      | ~ 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_5428),U_5429))) ),
    inference(variable_rename,[status(thm)],[f_1650_1]) ).

fof(f_1650_3,plain,
    ( ! [U_5429,U_5428] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5429),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP428(U_5429,U_5428) )
    & ! [U_5429,U_5428] :
        ( ~ 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_5428),U_5429)))
        | ~ sP428(U_5429,U_5428) )
    & ! [U_5429,U_5428] :
        ( c_Divides_OnegDivAlg(U_5428,U_5429) = hAPP(c_Divides_Oadjust(U_5429),c_Divides_OnegDivAlg(U_5428,hAPP(hAPP(c_Groups_Otimes__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_5429)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5429),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_5428),U_5429)))
        | ~ sP429(U_5429,U_5428) )
    & ! [U_5429,U_5428] :
        ( c_Divides_OnegDivAlg(U_5428,U_5429) = 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_5428),U_5429))
        | sP428(U_5429,U_5428)
        | ~ sP429(U_5429,U_5428) )
    & ! [U_5429,U_5428] :
        ( sP429(U_5429,U_5428)
        | ~ 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_5428),U_5429))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP428,sP429])],[f_1650_2]) ).

cnf(f_1650_4,plain,
    ( sP429(U_5429,U_5428)
    | ~ 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_5428),U_5429))) ),
    inference(clausify,[status(thm)],[f_1650_3]) ).

cnf(f_1650_5,plain,
    ( c_Divides_OnegDivAlg(U_5428,U_5429) = 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_5428),U_5429))
    | sP428(U_5429,U_5428)
    | ~ sP429(U_5429,U_5428) ),
    inference(clausify,[status(thm)],[f_1650_3]) ).

cnf(f_1650_6,plain,
    ( c_Divides_OnegDivAlg(U_5428,U_5429) = hAPP(c_Divides_Oadjust(U_5429),c_Divides_OnegDivAlg(U_5428,hAPP(hAPP(c_Groups_Otimes__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_5429)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5429),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_5428),U_5429)))
    | ~ sP429(U_5429,U_5428) ),
    inference(clausify,[status(thm)],[f_1650_3]) ).

cnf(f_1650_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_5428),U_5429)))
    | ~ sP428(U_5429,U_5428) ),
    inference(clausify,[status(thm)],[f_1650_3]) ).

cnf(f_1650_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5429),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP428(U_5429,U_5428) ),
    inference(clausify,[status(thm)],[f_1650_3]) ).

fof(f_1651_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_1651_2,plain,
    ! [U_5430] :
      ( ( ( ( hAPP(c_Code__Numeral_Oint__of,U_5430) = 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_5430),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_5430,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_5430) = hAPP(hAPP(c_Groups_Otimes__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_5430),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_5430,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_5430 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_Code__Numeral_Oint__of,U_5430) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_5430 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_1651_1]) ).

fof(f_1651_3,plain,
    ( ! [U_5432] :
        ( ( ( hAPP(c_Code__Numeral_Oint__of,U_5432) = 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_5432),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_5432,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_5432) = hAPP(hAPP(c_Groups_Otimes__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_5432),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_5432,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_5432 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_5431] :
        ( hAPP(c_Code__Numeral_Oint__of,U_5431) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_5431 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_1651_2]) ).

fof(f_1651_4,plain,
    ( ! [U_5432] :
        ( hAPP(c_Code__Numeral_Oint__of,U_5432) = 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_5432),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_5432,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)
        | ~ sP430(U_5432) )
    & ! [U_5432] :
        ( hAPP(c_Code__Numeral_Oint__of,U_5432) = hAPP(hAPP(c_Groups_Otimes__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_5432),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_5432,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)
        | ~ sP430(U_5432) )
    & ! [U_5432] :
        ( sP430(U_5432)
        | U_5432 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_5431] :
        ( hAPP(c_Code__Numeral_Oint__of,U_5431) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_5431 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP430])],[f_1651_3]) ).

cnf(f_1651_5,plain,
    ( hAPP(c_Code__Numeral_Oint__of,U_5431) = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_5431 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1651_4]) ).

cnf(f_1651_6,plain,
    ( sP430(U_5432)
    | U_5432 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1651_4]) ).

cnf(f_1651_7,plain,
    ( hAPP(c_Code__Numeral_Oint__of,U_5432) = hAPP(hAPP(c_Groups_Otimes__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_5432),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_5432,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)
    | ~ sP430(U_5432) ),
    inference(clausify,[status(thm)],[f_1651_4]) ).

cnf(f_1651_8,plain,
    ( hAPP(c_Code__Numeral_Oint__of,U_5432) = 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_5432),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_5432,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)
    | ~ sP430(U_5432) ),
    inference(clausify,[status(thm)],[f_1651_4]) ).

fof(f_1652_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_1652_2,plain,
    ! [U_5434,U_5433] :
      ( ( ( c_Divides_OposDivAlg(U_5433,U_5434) = hAPP(c_Divides_Oadjust(U_5434),c_Divides_OposDivAlg(U_5433,hAPP(hAPP(c_Groups_Otimes__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_5434)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5434),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5433),U_5434)) )
        & ( c_Divides_OposDivAlg(U_5433,U_5434) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5433)
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5434),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5433),U_5434)) ) ) )
      | ~ 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_5433),U_5434))) ),
    inference(variable_rename,[status(thm)],[f_1652_1]) ).

fof(f_1652_3,plain,
    ( ! [U_5434,U_5433] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5434),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP431(U_5434,U_5433) )
    & ! [U_5434,U_5433] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5433),U_5434))
        | ~ sP431(U_5434,U_5433) )
    & ! [U_5434,U_5433] :
        ( c_Divides_OposDivAlg(U_5433,U_5434) = hAPP(c_Divides_Oadjust(U_5434),c_Divides_OposDivAlg(U_5433,hAPP(hAPP(c_Groups_Otimes__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_5434)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5434),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5433),U_5434))
        | ~ sP432(U_5434,U_5433) )
    & ! [U_5434,U_5433] :
        ( c_Divides_OposDivAlg(U_5433,U_5434) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5433)
        | sP431(U_5434,U_5433)
        | ~ sP432(U_5434,U_5433) )
    & ! [U_5434,U_5433] :
        ( sP432(U_5434,U_5433)
        | ~ 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_5433),U_5434))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP431,sP432])],[f_1652_2]) ).

cnf(f_1652_4,plain,
    ( sP432(U_5434,U_5433)
    | ~ 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_5433),U_5434))) ),
    inference(clausify,[status(thm)],[f_1652_3]) ).

cnf(f_1652_5,plain,
    ( c_Divides_OposDivAlg(U_5433,U_5434) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_5433)
    | sP431(U_5434,U_5433)
    | ~ sP432(U_5434,U_5433) ),
    inference(clausify,[status(thm)],[f_1652_3]) ).

cnf(f_1652_6,plain,
    ( c_Divides_OposDivAlg(U_5433,U_5434) = hAPP(c_Divides_Oadjust(U_5434),c_Divides_OposDivAlg(U_5433,hAPP(hAPP(c_Groups_Otimes__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_5434)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5434),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5433),U_5434))
    | ~ sP432(U_5434,U_5433) ),
    inference(clausify,[status(thm)],[f_1652_3]) ).

cnf(f_1652_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5433),U_5434))
    | ~ sP431(U_5434,U_5433) ),
    inference(clausify,[status(thm)],[f_1652_3]) ).

cnf(f_1652_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5434),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP431(U_5434,U_5433) ),
    inference(clausify,[status(thm)],[f_1652_3]) ).

fof(f_1653_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_1653_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_1653_1]) ).

cnf(f_1653_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_1653_2]) ).

fof(f_1654_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_1654_2,plain,
    ! [U_5437,U_5436,U_5435] : hAPP(c_Divides_Oadjust(U_5435),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5436),U_5437)) = 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_5437),U_5435)),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_5436)),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_5436)),U_5437))),
    inference(variable_rename,[status(thm)],[f_1654_1]) ).

fof(f_1654_3,plain,
    ! [U_5436,U_5437,U_5435] : hAPP(c_Divides_Oadjust(U_5435),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5436),U_5437)) = 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_5437),U_5435)),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_5436)),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_5436)),U_5437))),
    inference(definitional_conversion,[status(esa)],[f_1654_2]) ).

cnf(f_1654_4,plain,
    hAPP(c_Divides_Oadjust(U_5435),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_5436),U_5437)) = 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_5437),U_5435)),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_5436)),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_5436)),U_5437))),
    inference(clausify,[status(thm)],[f_1654_3]) ).

fof(f_1655_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_1655_2,plain,
    ! [U_5439,U_5438] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),c_Groups_Ozero__class_Ozero(U_5438)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5438),U_5439),hAPP(c_Int_Onumber__class_Onumber__of(U_5438),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
          | ~ 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_5439))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),c_Groups_Ozero__class_Ozero(U_5438)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5438),U_5439),hAPP(c_Int_Onumber__class_Onumber__of(U_5438),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))))) ) )
      | ~ class_Int_Onumber__ring(U_5438)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5438) ),
    inference(variable_rename,[status(thm)],[f_1655_1]) ).

fof(f_1655_3,plain,
    ( ! [U_5438,U_5439] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),c_Groups_Ozero__class_Ozero(U_5438)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5438),U_5439),hAPP(c_Int_Onumber__class_Onumber__of(U_5438),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),c_Groups_Ozero__class_Ozero(U_5438)),U_5439))
        | ~ sP433(U_5438,U_5439) )
    & ! [U_5438,U_5439] :
        ( 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)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5438),U_5439),hAPP(c_Int_Onumber__class_Onumber__of(U_5438),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
        | ~ sP433(U_5438,U_5439) )
    & ! [U_5438,U_5439] :
        ( sP433(U_5438,U_5439)
        | ~ class_Int_Onumber__ring(U_5438)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5438) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP433])],[f_1655_2]) ).

cnf(f_1655_4,plain,
    ( sP433(U_5438,U_5439)
    | ~ class_Int_Onumber__ring(U_5438)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5438) ),
    inference(clausify,[status(thm)],[f_1655_3]) ).

cnf(f_1655_5,plain,
    ( 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)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5438),U_5439),hAPP(c_Int_Onumber__class_Onumber__of(U_5438),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ sP433(U_5438,U_5439) ),
    inference(clausify,[status(thm)],[f_1655_3]) ).

cnf(f_1655_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),c_Groups_Ozero__class_Ozero(U_5438)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5438),U_5439),hAPP(c_Int_Onumber__class_Onumber__of(U_5438),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5438),c_Groups_Ozero__class_Ozero(U_5438)),U_5439))
    | ~ sP433(U_5438,U_5439) ),
    inference(clausify,[status(thm)],[f_1655_3]) ).

fof(f_1656_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_1656_2,plain,
    ! [U_5443,U_5442,U_5441,U_5440] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5441,U_5440)),U_5442),U_5443) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5440),hAPP(U_5442,U_5443))
      | ~ class_Groups_Ouminus(U_5440) ),
    inference(variable_rename,[status(thm)],[f_1656_1]) ).

fof(f_1656_3,plain,
    ! [U_5443,U_5442,U_5441,U_5440] :
      ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5441,U_5440)),U_5442),U_5443) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5440),hAPP(U_5442,U_5443))
      | ~ class_Groups_Ouminus(U_5440) ),
    inference(definitional_conversion,[status(esa)],[f_1656_2]) ).

cnf(f_1656_4,plain,
    ( hAPP(hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_5441,U_5440)),U_5442),U_5443) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5440),hAPP(U_5442,U_5443))
    | ~ class_Groups_Ouminus(U_5440) ),
    inference(clausify,[status(thm)],[f_1656_3]) ).

fof(f_1657_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_1657_2,plain,
    ! [U_5446,U_5445,U_5444] :
      ( ( hAPP(hAPP(c_COMBC(U_5444,tc_fun(U_5444,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5444)),U_5445) = hAPP(hAPP(c_COMBC(U_5444,tc_fun(U_5444,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5444)),U_5446)
        | U_5445 != U_5446 )
      & ( U_5445 = U_5446
        | hAPP(hAPP(c_COMBC(U_5444,tc_fun(U_5444,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5444)),U_5445) != hAPP(hAPP(c_COMBC(U_5444,tc_fun(U_5444,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5444)),U_5446) ) ),
    inference(variable_rename,[status(thm)],[f_1657_1]) ).

fof(f_1657_3,plain,
    ( ! [U_5452,U_5450] :
        ( ! [U_5448] : hAPP(hAPP(c_COMBC(U_5448,tc_fun(U_5448,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5448)),U_5450) = hAPP(hAPP(c_COMBC(U_5448,tc_fun(U_5448,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5448)),U_5452)
        | U_5450 != U_5452 )
    & ! [U_5451,U_5449] :
        ( ! [U_5447] : hAPP(hAPP(c_COMBC(U_5447,tc_fun(U_5447,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5447)),U_5449) != hAPP(hAPP(c_COMBC(U_5447,tc_fun(U_5447,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5447)),U_5451)
        | U_5449 = U_5451 ) ),
    inference(miniscope,[status(thm)],[f_1657_2]) ).

fof(f_1657_4,plain,
    ( ! [U_5448,U_5452,U_5450] :
        ( hAPP(hAPP(c_COMBC(U_5448,tc_fun(U_5448,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5448)),U_5450) = hAPP(hAPP(c_COMBC(U_5448,tc_fun(U_5448,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5448)),U_5452)
        | U_5450 != U_5452 )
    & ! [U_5449,U_5447,U_5451] :
        ( hAPP(hAPP(c_COMBC(U_5447,tc_fun(U_5447,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5447)),U_5449) != hAPP(hAPP(c_COMBC(U_5447,tc_fun(U_5447,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5447)),U_5451)
        | U_5449 = U_5451 ) ),
    inference(definitional_conversion,[status(esa)],[f_1657_3]) ).

cnf(f_1657_5,plain,
    ( hAPP(hAPP(c_COMBC(U_5447,tc_fun(U_5447,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5447)),U_5449) != hAPP(hAPP(c_COMBC(U_5447,tc_fun(U_5447,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5447)),U_5451)
    | U_5449 = U_5451 ),
    inference(clausify,[status(thm)],[f_1657_4]) ).

cnf(f_1657_6,plain,
    ( hAPP(hAPP(c_COMBC(U_5448,tc_fun(U_5448,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5448)),U_5450) = hAPP(hAPP(c_COMBC(U_5448,tc_fun(U_5448,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5448)),U_5452)
    | U_5450 != U_5452 ),
    inference(clausify,[status(thm)],[f_1657_4]) ).

fof(f_1658_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_1658_2,plain,
    ! [U_5456,U_5455,U_5454,U_5453] :
      ( ( hAPP(hAPP(c_COMBC(U_5453,tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_fun(U_5454,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5454,tc_fun(tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_fun(U_5454,tc_HOL_Obool)),U_5453),c_COMBC(U_5454,tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5454,tc_prod(U_5453,U_5454)),tc_fun(U_5454,tc_fun(tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_HOL_Obool)),U_5453),hAPP(c_COMBB(tc_prod(U_5453,U_5454),tc_fun(tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_HOL_Obool),U_5454),c_member(tc_prod(U_5453,U_5454)))),c_Product__Type_OPair(U_5453,U_5454)))),U_5455) = hAPP(hAPP(c_COMBC(U_5453,tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_fun(U_5454,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5454,tc_fun(tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_fun(U_5454,tc_HOL_Obool)),U_5453),c_COMBC(U_5454,tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5454,tc_prod(U_5453,U_5454)),tc_fun(U_5454,tc_fun(tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_HOL_Obool)),U_5453),hAPP(c_COMBB(tc_prod(U_5453,U_5454),tc_fun(tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_HOL_Obool),U_5454),c_member(tc_prod(U_5453,U_5454)))),c_Product__Type_OPair(U_5453,U_5454)))),U_5456)
        | U_5455 != U_5456 )
      & ( U_5455 = U_5456
        | hAPP(hAPP(c_COMBC(U_5453,tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_fun(U_5454,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5454,tc_fun(tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_fun(U_5454,tc_HOL_Obool)),U_5453),c_COMBC(U_5454,tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5454,tc_prod(U_5453,U_5454)),tc_fun(U_5454,tc_fun(tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_HOL_Obool)),U_5453),hAPP(c_COMBB(tc_prod(U_5453,U_5454),tc_fun(tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_HOL_Obool),U_5454),c_member(tc_prod(U_5453,U_5454)))),c_Product__Type_OPair(U_5453,U_5454)))),U_5455) != hAPP(hAPP(c_COMBC(U_5453,tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_fun(U_5454,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5454,tc_fun(tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_fun(U_5454,tc_HOL_Obool)),U_5453),c_COMBC(U_5454,tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5454,tc_prod(U_5453,U_5454)),tc_fun(U_5454,tc_fun(tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_HOL_Obool)),U_5453),hAPP(c_COMBB(tc_prod(U_5453,U_5454),tc_fun(tc_fun(tc_prod(U_5453,U_5454),tc_HOL_Obool),tc_HOL_Obool),U_5454),c_member(tc_prod(U_5453,U_5454)))),c_Product__Type_OPair(U_5453,U_5454)))),U_5456) ) ),
    inference(variable_rename,[status(thm)],[f_1658_1]) ).

fof(f_1658_3,plain,
    ( ! [U_5464,U_5462] :
        ( ! [U_5460,U_5458] : hAPP(hAPP(c_COMBC(U_5458,tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_fun(U_5460,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5460,tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_fun(U_5460,tc_HOL_Obool)),U_5458),c_COMBC(U_5460,tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5460,tc_prod(U_5458,U_5460)),tc_fun(U_5460,tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool)),U_5458),hAPP(c_COMBB(tc_prod(U_5458,U_5460),tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool),U_5460),c_member(tc_prod(U_5458,U_5460)))),c_Product__Type_OPair(U_5458,U_5460)))),U_5462) = hAPP(hAPP(c_COMBC(U_5458,tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_fun(U_5460,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5460,tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_fun(U_5460,tc_HOL_Obool)),U_5458),c_COMBC(U_5460,tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5460,tc_prod(U_5458,U_5460)),tc_fun(U_5460,tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool)),U_5458),hAPP(c_COMBB(tc_prod(U_5458,U_5460),tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool),U_5460),c_member(tc_prod(U_5458,U_5460)))),c_Product__Type_OPair(U_5458,U_5460)))),U_5464)
        | U_5462 != U_5464 )
    & ! [U_5463,U_5461] :
        ( ! [U_5459,U_5457] : hAPP(hAPP(c_COMBC(U_5457,tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_fun(U_5459,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5459,tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_fun(U_5459,tc_HOL_Obool)),U_5457),c_COMBC(U_5459,tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5459,tc_prod(U_5457,U_5459)),tc_fun(U_5459,tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool)),U_5457),hAPP(c_COMBB(tc_prod(U_5457,U_5459),tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool),U_5459),c_member(tc_prod(U_5457,U_5459)))),c_Product__Type_OPair(U_5457,U_5459)))),U_5461) != hAPP(hAPP(c_COMBC(U_5457,tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_fun(U_5459,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5459,tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_fun(U_5459,tc_HOL_Obool)),U_5457),c_COMBC(U_5459,tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5459,tc_prod(U_5457,U_5459)),tc_fun(U_5459,tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool)),U_5457),hAPP(c_COMBB(tc_prod(U_5457,U_5459),tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool),U_5459),c_member(tc_prod(U_5457,U_5459)))),c_Product__Type_OPair(U_5457,U_5459)))),U_5463)
        | U_5461 = U_5463 ) ),
    inference(miniscope,[status(thm)],[f_1658_2]) ).

fof(f_1658_4,plain,
    ( ! [U_5462,U_5464,U_5458,U_5460] :
        ( hAPP(hAPP(c_COMBC(U_5458,tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_fun(U_5460,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5460,tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_fun(U_5460,tc_HOL_Obool)),U_5458),c_COMBC(U_5460,tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5460,tc_prod(U_5458,U_5460)),tc_fun(U_5460,tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool)),U_5458),hAPP(c_COMBB(tc_prod(U_5458,U_5460),tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool),U_5460),c_member(tc_prod(U_5458,U_5460)))),c_Product__Type_OPair(U_5458,U_5460)))),U_5462) = hAPP(hAPP(c_COMBC(U_5458,tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_fun(U_5460,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5460,tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_fun(U_5460,tc_HOL_Obool)),U_5458),c_COMBC(U_5460,tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5460,tc_prod(U_5458,U_5460)),tc_fun(U_5460,tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool)),U_5458),hAPP(c_COMBB(tc_prod(U_5458,U_5460),tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool),U_5460),c_member(tc_prod(U_5458,U_5460)))),c_Product__Type_OPair(U_5458,U_5460)))),U_5464)
        | U_5462 != U_5464 )
    & ! [U_5461,U_5459,U_5457,U_5463] :
        ( hAPP(hAPP(c_COMBC(U_5457,tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_fun(U_5459,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5459,tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_fun(U_5459,tc_HOL_Obool)),U_5457),c_COMBC(U_5459,tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5459,tc_prod(U_5457,U_5459)),tc_fun(U_5459,tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool)),U_5457),hAPP(c_COMBB(tc_prod(U_5457,U_5459),tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool),U_5459),c_member(tc_prod(U_5457,U_5459)))),c_Product__Type_OPair(U_5457,U_5459)))),U_5461) != hAPP(hAPP(c_COMBC(U_5457,tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_fun(U_5459,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5459,tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_fun(U_5459,tc_HOL_Obool)),U_5457),c_COMBC(U_5459,tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5459,tc_prod(U_5457,U_5459)),tc_fun(U_5459,tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool)),U_5457),hAPP(c_COMBB(tc_prod(U_5457,U_5459),tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool),U_5459),c_member(tc_prod(U_5457,U_5459)))),c_Product__Type_OPair(U_5457,U_5459)))),U_5463)
        | U_5461 = U_5463 ) ),
    inference(definitional_conversion,[status(esa)],[f_1658_3]) ).

cnf(f_1658_5,plain,
    ( hAPP(hAPP(c_COMBC(U_5457,tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_fun(U_5459,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5459,tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_fun(U_5459,tc_HOL_Obool)),U_5457),c_COMBC(U_5459,tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5459,tc_prod(U_5457,U_5459)),tc_fun(U_5459,tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool)),U_5457),hAPP(c_COMBB(tc_prod(U_5457,U_5459),tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool),U_5459),c_member(tc_prod(U_5457,U_5459)))),c_Product__Type_OPair(U_5457,U_5459)))),U_5461) != hAPP(hAPP(c_COMBC(U_5457,tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_fun(U_5459,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5459,tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_fun(U_5459,tc_HOL_Obool)),U_5457),c_COMBC(U_5459,tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5459,tc_prod(U_5457,U_5459)),tc_fun(U_5459,tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool)),U_5457),hAPP(c_COMBB(tc_prod(U_5457,U_5459),tc_fun(tc_fun(tc_prod(U_5457,U_5459),tc_HOL_Obool),tc_HOL_Obool),U_5459),c_member(tc_prod(U_5457,U_5459)))),c_Product__Type_OPair(U_5457,U_5459)))),U_5463)
    | U_5461 = U_5463 ),
    inference(clausify,[status(thm)],[f_1658_4]) ).

cnf(f_1658_6,plain,
    ( hAPP(hAPP(c_COMBC(U_5458,tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_fun(U_5460,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5460,tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_fun(U_5460,tc_HOL_Obool)),U_5458),c_COMBC(U_5460,tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5460,tc_prod(U_5458,U_5460)),tc_fun(U_5460,tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool)),U_5458),hAPP(c_COMBB(tc_prod(U_5458,U_5460),tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool),U_5460),c_member(tc_prod(U_5458,U_5460)))),c_Product__Type_OPair(U_5458,U_5460)))),U_5462) = hAPP(hAPP(c_COMBC(U_5458,tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_fun(U_5460,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5460,tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_fun(U_5460,tc_HOL_Obool)),U_5458),c_COMBC(U_5460,tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5460,tc_prod(U_5458,U_5460)),tc_fun(U_5460,tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool)),U_5458),hAPP(c_COMBB(tc_prod(U_5458,U_5460),tc_fun(tc_fun(tc_prod(U_5458,U_5460),tc_HOL_Obool),tc_HOL_Obool),U_5460),c_member(tc_prod(U_5458,U_5460)))),c_Product__Type_OPair(U_5458,U_5460)))),U_5464)
    | U_5462 != U_5464 ),
    inference(clausify,[status(thm)],[f_1658_4]) ).

fof(f_1659_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_1659_2,plain,
    ! [U_5468,U_5467,U_5466,U_5465] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5465,tc_fun(U_5466,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_5465,tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_fun(U_5466,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5466,tc_fun(tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_fun(U_5466,tc_HOL_Obool)),U_5465),c_COMBC(U_5466,tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5466,tc_prod(U_5465,U_5466)),tc_fun(U_5466,tc_fun(tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_HOL_Obool)),U_5465),hAPP(c_COMBB(tc_prod(U_5465,U_5466),tc_fun(tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_HOL_Obool),U_5466),c_member(tc_prod(U_5465,U_5466)))),c_Product__Type_OPair(U_5465,U_5466)))),U_5467)),hAPP(hAPP(c_COMBC(U_5465,tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_fun(U_5466,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5466,tc_fun(tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_fun(U_5466,tc_HOL_Obool)),U_5465),c_COMBC(U_5466,tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5466,tc_prod(U_5465,U_5466)),tc_fun(U_5466,tc_fun(tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_HOL_Obool)),U_5465),hAPP(c_COMBB(tc_prod(U_5465,U_5466),tc_fun(tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_HOL_Obool),U_5466),c_member(tc_prod(U_5465,U_5466)))),c_Product__Type_OPair(U_5465,U_5466)))),U_5468)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool)),U_5467),U_5468)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool)),U_5467),U_5468))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5465,tc_fun(U_5466,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_5465,tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_fun(U_5466,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5466,tc_fun(tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_fun(U_5466,tc_HOL_Obool)),U_5465),c_COMBC(U_5466,tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5466,tc_prod(U_5465,U_5466)),tc_fun(U_5466,tc_fun(tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_HOL_Obool)),U_5465),hAPP(c_COMBB(tc_prod(U_5465,U_5466),tc_fun(tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_HOL_Obool),U_5466),c_member(tc_prod(U_5465,U_5466)))),c_Product__Type_OPair(U_5465,U_5466)))),U_5467)),hAPP(hAPP(c_COMBC(U_5465,tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_fun(U_5466,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5466,tc_fun(tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_fun(U_5466,tc_HOL_Obool)),U_5465),c_COMBC(U_5466,tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5466,tc_prod(U_5465,U_5466)),tc_fun(U_5466,tc_fun(tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_HOL_Obool)),U_5465),hAPP(c_COMBB(tc_prod(U_5465,U_5466),tc_fun(tc_fun(tc_prod(U_5465,U_5466),tc_HOL_Obool),tc_HOL_Obool),U_5466),c_member(tc_prod(U_5465,U_5466)))),c_Product__Type_OPair(U_5465,U_5466)))),U_5468))) ) ),
    inference(variable_rename,[status(thm)],[f_1659_1]) ).

fof(f_1659_3,plain,
    ( ! [U_5476,U_5474,U_5472,U_5470] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5470,tc_fun(U_5472,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_5470,tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_fun(U_5472,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5472,tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_fun(U_5472,tc_HOL_Obool)),U_5470),c_COMBC(U_5472,tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5472,tc_prod(U_5470,U_5472)),tc_fun(U_5472,tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool)),U_5470),hAPP(c_COMBB(tc_prod(U_5470,U_5472),tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool),U_5472),c_member(tc_prod(U_5470,U_5472)))),c_Product__Type_OPair(U_5470,U_5472)))),U_5474)),hAPP(hAPP(c_COMBC(U_5470,tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_fun(U_5472,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5472,tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_fun(U_5472,tc_HOL_Obool)),U_5470),c_COMBC(U_5472,tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5472,tc_prod(U_5470,U_5472)),tc_fun(U_5472,tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool)),U_5470),hAPP(c_COMBB(tc_prod(U_5470,U_5472),tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool),U_5472),c_member(tc_prod(U_5470,U_5472)))),c_Product__Type_OPair(U_5470,U_5472)))),U_5476)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool)),U_5474),U_5476)) )
    & ! [U_5475,U_5473,U_5471,U_5469] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool)),U_5473),U_5475))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5469,tc_fun(U_5471,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_5469,tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_fun(U_5471,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5471,tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_fun(U_5471,tc_HOL_Obool)),U_5469),c_COMBC(U_5471,tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5471,tc_prod(U_5469,U_5471)),tc_fun(U_5471,tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool)),U_5469),hAPP(c_COMBB(tc_prod(U_5469,U_5471),tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool),U_5471),c_member(tc_prod(U_5469,U_5471)))),c_Product__Type_OPair(U_5469,U_5471)))),U_5473)),hAPP(hAPP(c_COMBC(U_5469,tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_fun(U_5471,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5471,tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_fun(U_5471,tc_HOL_Obool)),U_5469),c_COMBC(U_5471,tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5471,tc_prod(U_5469,U_5471)),tc_fun(U_5471,tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool)),U_5469),hAPP(c_COMBB(tc_prod(U_5469,U_5471),tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool),U_5471),c_member(tc_prod(U_5469,U_5471)))),c_Product__Type_OPair(U_5469,U_5471)))),U_5475))) ) ),
    inference(miniscope,[status(thm)],[f_1659_2]) ).

fof(f_1659_4,plain,
    ( ! [U_5470,U_5472,U_5474,U_5476] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5470,tc_fun(U_5472,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_5470,tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_fun(U_5472,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5472,tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_fun(U_5472,tc_HOL_Obool)),U_5470),c_COMBC(U_5472,tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5472,tc_prod(U_5470,U_5472)),tc_fun(U_5472,tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool)),U_5470),hAPP(c_COMBB(tc_prod(U_5470,U_5472),tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool),U_5472),c_member(tc_prod(U_5470,U_5472)))),c_Product__Type_OPair(U_5470,U_5472)))),U_5474)),hAPP(hAPP(c_COMBC(U_5470,tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_fun(U_5472,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5472,tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_fun(U_5472,tc_HOL_Obool)),U_5470),c_COMBC(U_5472,tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5472,tc_prod(U_5470,U_5472)),tc_fun(U_5472,tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool)),U_5470),hAPP(c_COMBB(tc_prod(U_5470,U_5472),tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool),U_5472),c_member(tc_prod(U_5470,U_5472)))),c_Product__Type_OPair(U_5470,U_5472)))),U_5476)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool)),U_5474),U_5476)) )
    & ! [U_5475,U_5471,U_5469,U_5473] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool)),U_5473),U_5475))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5469,tc_fun(U_5471,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_5469,tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_fun(U_5471,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5471,tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_fun(U_5471,tc_HOL_Obool)),U_5469),c_COMBC(U_5471,tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5471,tc_prod(U_5469,U_5471)),tc_fun(U_5471,tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool)),U_5469),hAPP(c_COMBB(tc_prod(U_5469,U_5471),tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool),U_5471),c_member(tc_prod(U_5469,U_5471)))),c_Product__Type_OPair(U_5469,U_5471)))),U_5473)),hAPP(hAPP(c_COMBC(U_5469,tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_fun(U_5471,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5471,tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_fun(U_5471,tc_HOL_Obool)),U_5469),c_COMBC(U_5471,tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5471,tc_prod(U_5469,U_5471)),tc_fun(U_5471,tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool)),U_5469),hAPP(c_COMBB(tc_prod(U_5469,U_5471),tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool),U_5471),c_member(tc_prod(U_5469,U_5471)))),c_Product__Type_OPair(U_5469,U_5471)))),U_5475))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1659_3]) ).

cnf(f_1659_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool)),U_5473),U_5475))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5469,tc_fun(U_5471,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_5469,tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_fun(U_5471,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5471,tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_fun(U_5471,tc_HOL_Obool)),U_5469),c_COMBC(U_5471,tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5471,tc_prod(U_5469,U_5471)),tc_fun(U_5471,tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool)),U_5469),hAPP(c_COMBB(tc_prod(U_5469,U_5471),tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool),U_5471),c_member(tc_prod(U_5469,U_5471)))),c_Product__Type_OPair(U_5469,U_5471)))),U_5473)),hAPP(hAPP(c_COMBC(U_5469,tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_fun(U_5471,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5471,tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_fun(U_5471,tc_HOL_Obool)),U_5469),c_COMBC(U_5471,tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5471,tc_prod(U_5469,U_5471)),tc_fun(U_5471,tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool)),U_5469),hAPP(c_COMBB(tc_prod(U_5469,U_5471),tc_fun(tc_fun(tc_prod(U_5469,U_5471),tc_HOL_Obool),tc_HOL_Obool),U_5471),c_member(tc_prod(U_5469,U_5471)))),c_Product__Type_OPair(U_5469,U_5471)))),U_5475))) ),
    inference(clausify,[status(thm)],[f_1659_4]) ).

cnf(f_1659_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5470,tc_fun(U_5472,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_5470,tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_fun(U_5472,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5472,tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_fun(U_5472,tc_HOL_Obool)),U_5470),c_COMBC(U_5472,tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5472,tc_prod(U_5470,U_5472)),tc_fun(U_5472,tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool)),U_5470),hAPP(c_COMBB(tc_prod(U_5470,U_5472),tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool),U_5472),c_member(tc_prod(U_5470,U_5472)))),c_Product__Type_OPair(U_5470,U_5472)))),U_5474)),hAPP(hAPP(c_COMBC(U_5470,tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_fun(U_5472,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5472,tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_fun(U_5472,tc_HOL_Obool)),U_5470),c_COMBC(U_5472,tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_5472,tc_prod(U_5470,U_5472)),tc_fun(U_5472,tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool)),U_5470),hAPP(c_COMBB(tc_prod(U_5470,U_5472),tc_fun(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool),tc_HOL_Obool),U_5472),c_member(tc_prod(U_5470,U_5472)))),c_Product__Type_OPair(U_5470,U_5472)))),U_5476)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_5470,U_5472),tc_HOL_Obool)),U_5474),U_5476)) ),
    inference(clausify,[status(thm)],[f_1659_4]) ).

fof(f_1660_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_1660_2,plain,
    ! [U_5479,U_5478,U_5477] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5477,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_5477,tc_fun(U_5477,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5477)),U_5478)),hAPP(hAPP(c_COMBC(U_5477,tc_fun(U_5477,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5477)),U_5479)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5477,tc_HOL_Obool)),U_5478),U_5479)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5477,tc_HOL_Obool)),U_5478),U_5479))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5477,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_5477,tc_fun(U_5477,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5477)),U_5478)),hAPP(hAPP(c_COMBC(U_5477,tc_fun(U_5477,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5477)),U_5479))) ) ),
    inference(variable_rename,[status(thm)],[f_1660_1]) ).

fof(f_1660_3,plain,
    ( ! [U_5485,U_5483,U_5481] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5481,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_5481,tc_fun(U_5481,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5481)),U_5483)),hAPP(hAPP(c_COMBC(U_5481,tc_fun(U_5481,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5481)),U_5485)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5481,tc_HOL_Obool)),U_5483),U_5485)) )
    & ! [U_5484,U_5482,U_5480] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5480,tc_HOL_Obool)),U_5482),U_5484))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5480,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_5480,tc_fun(U_5480,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5480)),U_5482)),hAPP(hAPP(c_COMBC(U_5480,tc_fun(U_5480,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5480)),U_5484))) ) ),
    inference(miniscope,[status(thm)],[f_1660_2]) ).

fof(f_1660_4,plain,
    ( ! [U_5481,U_5483,U_5485] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5481,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_5481,tc_fun(U_5481,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5481)),U_5483)),hAPP(hAPP(c_COMBC(U_5481,tc_fun(U_5481,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5481)),U_5485)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5481,tc_HOL_Obool)),U_5483),U_5485)) )
    & ! [U_5482,U_5484,U_5480] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5480,tc_HOL_Obool)),U_5482),U_5484))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5480,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_5480,tc_fun(U_5480,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5480)),U_5482)),hAPP(hAPP(c_COMBC(U_5480,tc_fun(U_5480,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5480)),U_5484))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1660_3]) ).

cnf(f_1660_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5480,tc_HOL_Obool)),U_5482),U_5484))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5480,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_5480,tc_fun(U_5480,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5480)),U_5482)),hAPP(hAPP(c_COMBC(U_5480,tc_fun(U_5480,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5480)),U_5484))) ),
    inference(clausify,[status(thm)],[f_1660_4]) ).

cnf(f_1660_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5481,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_5481,tc_fun(U_5481,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5481)),U_5483)),hAPP(hAPP(c_COMBC(U_5481,tc_fun(U_5481,tc_HOL_Obool),tc_HOL_Obool),c_member(U_5481)),U_5485)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5481,tc_HOL_Obool)),U_5483),U_5485)) ),
    inference(clausify,[status(thm)],[f_1660_4]) ).

fof(f_1661_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_1661_2,plain,
    ! [U_5490,U_5489,U_5488] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5488,U_5489),U_5490))
        | ? [U_5487] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5488,U_5489),U_5487))
            & hBOOL(hAPP(hAPP(U_5489,U_5487),U_5490)) ) )
      & ( ! [U_5486] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5488,U_5489),U_5486))
            | ~ hBOOL(hAPP(hAPP(U_5489,U_5486),U_5490)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5488,U_5489),U_5490)) ) ),
    inference(variable_rename,[status(thm)],[f_1661_1]) ).

fof(f_1661_3,plain,
    ( ! [U_5496,U_5494,U_5492] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5492,U_5494),U_5496))
        | ? [U_5487] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5492,U_5494),U_5487))
            & hBOOL(hAPP(hAPP(U_5494,U_5487),U_5496)) ) )
    & ! [U_5495,U_5493,U_5491] :
        ( ! [U_5486] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5491,U_5493),U_5486))
            | ~ hBOOL(hAPP(hAPP(U_5493,U_5486),U_5495)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5491,U_5493),U_5495)) ) ),
    inference(miniscope,[status(thm)],[f_1661_2]) ).

fof(f_1661_4,plain,
    ( ! [U_5496,U_5494,U_5492] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5492,U_5494),U_5496))
        | ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5492,U_5494),sK77(U_5496,U_5494,U_5492)))
          & hBOOL(hAPP(hAPP(U_5494,sK77(U_5496,U_5494,U_5492)),U_5496)) ) )
    & ! [U_5495,U_5493,U_5491] :
        ( ! [U_5486] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5491,U_5493),U_5486))
            | ~ hBOOL(hAPP(hAPP(U_5493,U_5486),U_5495)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5491,U_5493),U_5495)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK77]),skolemize(U_5487,sK77(U_5496,U_5494,U_5492))],[f_1661_3]) ).

fof(f_1661_5,plain,
    ( ! [U_5492,U_5494,U_5496] :
        ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5492,U_5494),sK77(U_5496,U_5494,U_5492)))
        | ~ sP434(U_5492,U_5494,U_5496) )
    & ! [U_5492,U_5494,U_5496] :
        ( hBOOL(hAPP(hAPP(U_5494,sK77(U_5496,U_5494,U_5492)),U_5496))
        | ~ sP434(U_5492,U_5494,U_5496) )
    & ! [U_5492,U_5494,U_5496] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5492,U_5494),U_5496))
        | sP434(U_5492,U_5494,U_5496) )
    & ! [U_5486,U_5493,U_5491,U_5495] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5491,U_5493),U_5486))
        | ~ hBOOL(hAPP(hAPP(U_5493,U_5486),U_5495))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5491,U_5493),U_5495)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP434])],[f_1661_4]) ).

cnf(f_1661_6,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5491,U_5493),U_5486))
    | ~ hBOOL(hAPP(hAPP(U_5493,U_5486),U_5495))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5491,U_5493),U_5495)) ),
    inference(clausify,[status(thm)],[f_1661_5]) ).

cnf(f_1661_7,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5492,U_5494),U_5496))
    | sP434(U_5492,U_5494,U_5496) ),
    inference(clausify,[status(thm)],[f_1661_5]) ).

cnf(f_1661_8,plain,
    ( hBOOL(hAPP(hAPP(U_5494,sK77(U_5496,U_5494,U_5492)),U_5496))
    | ~ sP434(U_5492,U_5494,U_5496) ),
    inference(clausify,[status(thm)],[f_1661_5]) ).

cnf(f_1661_9,plain,
    ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5492,U_5494),sK77(U_5496,U_5494,U_5492)))
    | ~ sP434(U_5492,U_5494,U_5496) ),
    inference(clausify,[status(thm)],[f_1661_5]) ).

fof(f_1662_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_1662_2,plain,
    ! [U_5501,U_5500,U_5499] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5499,U_5500),U_5501))
        | ? [U_5498] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5499,U_5500),U_5498))
            & hBOOL(hAPP(hAPP(U_5500,U_5498),U_5501)) ) )
      & ( ! [U_5497] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5499,U_5500),U_5497))
            | ~ hBOOL(hAPP(hAPP(U_5500,U_5497),U_5501)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5499,U_5500),U_5501)) ) ),
    inference(variable_rename,[status(thm)],[f_1662_1]) ).

fof(f_1662_3,plain,
    ( ! [U_5507,U_5505,U_5503] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5503,U_5505),U_5507))
        | ? [U_5498] :
            ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5503,U_5505),U_5498))
            & hBOOL(hAPP(hAPP(U_5505,U_5498),U_5507)) ) )
    & ! [U_5506,U_5504,U_5502] :
        ( ! [U_5497] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5502,U_5504),U_5497))
            | ~ hBOOL(hAPP(hAPP(U_5504,U_5497),U_5506)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5502,U_5504),U_5506)) ) ),
    inference(miniscope,[status(thm)],[f_1662_2]) ).

fof(f_1662_4,plain,
    ( ! [U_5507,U_5505,U_5503] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5503,U_5505),U_5507))
        | ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5503,U_5505),sK78(U_5507,U_5505,U_5503)))
          & hBOOL(hAPP(hAPP(U_5505,sK78(U_5507,U_5505,U_5503)),U_5507)) ) )
    & ! [U_5506,U_5504,U_5502] :
        ( ! [U_5497] :
            ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5502,U_5504),U_5497))
            | ~ hBOOL(hAPP(hAPP(U_5504,U_5497),U_5506)) )
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5502,U_5504),U_5506)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK78]),skolemize(U_5498,sK78(U_5507,U_5505,U_5503))],[f_1662_3]) ).

fof(f_1662_5,plain,
    ( ! [U_5505,U_5507,U_5503] :
        ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5503,U_5505),sK78(U_5507,U_5505,U_5503)))
        | ~ sP435(U_5505,U_5507,U_5503) )
    & ! [U_5505,U_5507,U_5503] :
        ( hBOOL(hAPP(hAPP(U_5505,sK78(U_5507,U_5505,U_5503)),U_5507))
        | ~ sP435(U_5505,U_5507,U_5503) )
    & ! [U_5505,U_5507,U_5503] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5503,U_5505),U_5507))
        | sP435(U_5505,U_5507,U_5503) )
    & ! [U_5506,U_5504,U_5497,U_5502] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5502,U_5504),U_5497))
        | ~ hBOOL(hAPP(hAPP(U_5504,U_5497),U_5506))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5502,U_5504),U_5506)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP435])],[f_1662_4]) ).

cnf(f_1662_6,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5502,U_5504),U_5497))
    | ~ hBOOL(hAPP(hAPP(U_5504,U_5497),U_5506))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5502,U_5504),U_5506)) ),
    inference(clausify,[status(thm)],[f_1662_5]) ).

cnf(f_1662_7,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5503,U_5505),U_5507))
    | sP435(U_5505,U_5507,U_5503) ),
    inference(clausify,[status(thm)],[f_1662_5]) ).

cnf(f_1662_8,plain,
    ( hBOOL(hAPP(hAPP(U_5505,sK78(U_5507,U_5505,U_5503)),U_5507))
    | ~ sP435(U_5505,U_5507,U_5503) ),
    inference(clausify,[status(thm)],[f_1662_5]) ).

cnf(f_1662_9,plain,
    ( ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5503,U_5505),sK78(U_5507,U_5505,U_5503)))
    | ~ sP435(U_5505,U_5507,U_5503) ),
    inference(clausify,[status(thm)],[f_1662_5]) ).

fof(f_1663_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_1663_2,plain,
    ! [U_5511,U_5510,U_5509,U_5508] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5508,U_5509),U_5511))
      | ~ hBOOL(hAPP(hAPP(U_5509,U_5511),U_5510))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5508,U_5509),U_5510)) ),
    inference(variable_rename,[status(thm)],[f_1663_1]) ).

fof(f_1663_3,plain,
    ! [U_5508,U_5509,U_5511,U_5510] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5508,U_5509),U_5511))
      | ~ hBOOL(hAPP(hAPP(U_5509,U_5511),U_5510))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5508,U_5509),U_5510)) ),
    inference(definitional_conversion,[status(esa)],[f_1663_2]) ).

cnf(f_1663_4,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_5508,U_5509),U_5511))
    | ~ hBOOL(hAPP(hAPP(U_5509,U_5511),U_5510))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_5508,U_5509),U_5510)) ),
    inference(clausify,[status(thm)],[f_1663_3]) ).

fof(f_1664_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_1664_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_1664_1]) ).

cnf(f_1664_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_1664_2]) ).

fof(f_1665_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_1665_2,plain,
    ! [U_5516,U_5515,U_5514,U_5513,U_5512] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5513,U_5512)),U_5514),U_5515),U_5516) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5512),hAPP(U_5514,U_5516)),hAPP(U_5515,U_5516))
      | ~ class_Groups_Ominus(U_5512) ),
    inference(variable_rename,[status(thm)],[f_1665_1]) ).

fof(f_1665_3,plain,
    ! [U_5512,U_5513,U_5514,U_5515,U_5516] :
      ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5513,U_5512)),U_5514),U_5515),U_5516) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5512),hAPP(U_5514,U_5516)),hAPP(U_5515,U_5516))
      | ~ class_Groups_Ominus(U_5512) ),
    inference(definitional_conversion,[status(esa)],[f_1665_2]) ).

cnf(f_1665_4,plain,
    ( hAPP(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_5513,U_5512)),U_5514),U_5515),U_5516) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5512),hAPP(U_5514,U_5516)),hAPP(U_5515,U_5516))
    | ~ class_Groups_Ominus(U_5512) ),
    inference(clausify,[status(thm)],[f_1665_3]) ).

fof(f_1666_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_1666_2,plain,
    ! [U_5518,U_5517] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5517),U_5518),c_Groups_Ozero__class_Ozero(U_5517)) = c_Groups_Ozero__class_Ozero(U_5517)
      | ~ class_Rings_Odivision__ring__inverse__zero(U_5517) ),
    inference(variable_rename,[status(thm)],[f_1666_1]) ).

fof(f_1666_3,plain,
    ! [U_5518,U_5517] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5517),U_5518),c_Groups_Ozero__class_Ozero(U_5517)) = c_Groups_Ozero__class_Ozero(U_5517)
      | ~ class_Rings_Odivision__ring__inverse__zero(U_5517) ),
    inference(definitional_conversion,[status(esa)],[f_1666_2]) ).

cnf(f_1666_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5517),U_5518),c_Groups_Ozero__class_Ozero(U_5517)) = c_Groups_Ozero__class_Ozero(U_5517)
    | ~ class_Rings_Odivision__ring__inverse__zero(U_5517) ),
    inference(clausify,[status(thm)],[f_1666_3]) ).

fof(f_1667_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_1667_2,plain,
    ! [U_5520,U_5519] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5519),c_Groups_Ozero__class_Ozero(U_5519)),U_5520) = c_Groups_Ozero__class_Ozero(U_5519)
      | ~ class_Rings_Odivision__ring(U_5519) ),
    inference(variable_rename,[status(thm)],[f_1667_1]) ).

fof(f_1667_3,plain,
    ! [U_5519,U_5520] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5519),c_Groups_Ozero__class_Ozero(U_5519)),U_5520) = c_Groups_Ozero__class_Ozero(U_5519)
      | ~ class_Rings_Odivision__ring(U_5519) ),
    inference(definitional_conversion,[status(esa)],[f_1667_2]) ).

cnf(f_1667_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5519),c_Groups_Ozero__class_Ozero(U_5519)),U_5520) = c_Groups_Ozero__class_Ozero(U_5519)
    | ~ class_Rings_Odivision__ring(U_5519) ),
    inference(clausify,[status(thm)],[f_1667_3]) ).

fof(f_1668_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_1668_2,plain,
    ! [U_5524,U_5523,U_5522,U_5521] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5521),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5521),U_5522),U_5523)),U_5524) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5521),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5521),U_5522),U_5524)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5521),U_5523),U_5524))
      | ~ class_Rings_Odivision__ring(U_5521) ),
    inference(variable_rename,[status(thm)],[f_1668_1]) ).

fof(f_1668_3,plain,
    ! [U_5521,U_5522,U_5523,U_5524] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5521),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5521),U_5522),U_5523)),U_5524) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5521),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5521),U_5522),U_5524)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5521),U_5523),U_5524))
      | ~ class_Rings_Odivision__ring(U_5521) ),
    inference(definitional_conversion,[status(esa)],[f_1668_2]) ).

cnf(f_1668_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5521),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5521),U_5522),U_5523)),U_5524) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5521),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5521),U_5522),U_5524)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5521),U_5523),U_5524))
    | ~ class_Rings_Odivision__ring(U_5521) ),
    inference(clausify,[status(thm)],[f_1668_3]) ).

fof(f_1669_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_1669_2,plain,
    ! [U_5528,U_5527,U_5526,U_5525] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5525),U_5526),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5525),U_5527),U_5528)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5525),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5525),U_5526),U_5527)),U_5528)
      | ~ class_Rings_Odivision__ring(U_5525) ),
    inference(variable_rename,[status(thm)],[f_1669_1]) ).

fof(f_1669_3,plain,
    ! [U_5525,U_5526,U_5527,U_5528] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5525),U_5526),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5525),U_5527),U_5528)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5525),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5525),U_5526),U_5527)),U_5528)
      | ~ class_Rings_Odivision__ring(U_5525) ),
    inference(definitional_conversion,[status(esa)],[f_1669_2]) ).

cnf(f_1669_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5525),U_5526),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5525),U_5527),U_5528)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5525),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5525),U_5526),U_5527)),U_5528)
    | ~ class_Rings_Odivision__ring(U_5525) ),
    inference(clausify,[status(thm)],[f_1669_3]) ).

fof(f_1670_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_1670_2,plain,
    ! [U_5532,U_5531,U_5530,U_5529] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5529),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5529),U_5530),U_5531)),U_5532) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5529),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5529),U_5530),U_5532)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5529),U_5531),U_5532))
      | ~ class_Rings_Odivision__ring(U_5529) ),
    inference(variable_rename,[status(thm)],[f_1670_1]) ).

fof(f_1670_3,plain,
    ! [U_5529,U_5530,U_5531,U_5532] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5529),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5529),U_5530),U_5531)),U_5532) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5529),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5529),U_5530),U_5532)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5529),U_5531),U_5532))
      | ~ class_Rings_Odivision__ring(U_5529) ),
    inference(definitional_conversion,[status(esa)],[f_1670_2]) ).

cnf(f_1670_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5529),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5529),U_5530),U_5531)),U_5532) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5529),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5529),U_5530),U_5532)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5529),U_5531),U_5532))
    | ~ class_Rings_Odivision__ring(U_5529) ),
    inference(clausify,[status(thm)],[f_1670_3]) ).

fof(f_1671_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_1671_2,plain,
    ! [U_5534,U_5533] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5533),U_5534),c_Groups_Oone__class_Oone(U_5533)) = U_5534
      | ~ class_Rings_Odivision__ring(U_5533) ),
    inference(variable_rename,[status(thm)],[f_1671_1]) ).

fof(f_1671_3,plain,
    ! [U_5534,U_5533] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5533),U_5534),c_Groups_Oone__class_Oone(U_5533)) = U_5534
      | ~ class_Rings_Odivision__ring(U_5533) ),
    inference(definitional_conversion,[status(esa)],[f_1671_2]) ).

cnf(f_1671_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5533),U_5534),c_Groups_Oone__class_Oone(U_5533)) = U_5534
    | ~ class_Rings_Odivision__ring(U_5533) ),
    inference(clausify,[status(thm)],[f_1671_3]) ).

fof(f_1672_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_1672_2,plain,
    ! [U_5537,U_5536,U_5535] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5535),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5535),U_5536),U_5537)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5535),hAPP(c_Groups_Ouminus__class_Ouminus(U_5535),U_5536)),U_5537)
      | ~ class_Rings_Odivision__ring(U_5535) ),
    inference(variable_rename,[status(thm)],[f_1672_1]) ).

fof(f_1672_3,plain,
    ! [U_5537,U_5535,U_5536] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5535),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5535),U_5536),U_5537)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5535),hAPP(c_Groups_Ouminus__class_Ouminus(U_5535),U_5536)),U_5537)
      | ~ class_Rings_Odivision__ring(U_5535) ),
    inference(definitional_conversion,[status(esa)],[f_1672_2]) ).

cnf(f_1672_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5535),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5535),U_5536),U_5537)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5535),hAPP(c_Groups_Ouminus__class_Ouminus(U_5535),U_5536)),U_5537)
    | ~ class_Rings_Odivision__ring(U_5535) ),
    inference(clausify,[status(thm)],[f_1672_3]) ).

fof(f_1673_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_1673_2,plain,
    ! [U_5541,U_5540,U_5539,U_5538] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5538),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5538),U_5539),U_5540)),U_5541) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5538),hAPP(hAPP(c_Power_Opower__class_Opower(U_5538),U_5539),U_5541)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5538),U_5540),U_5541))
      | ~ class_Fields_Ofield__inverse__zero(U_5538) ),
    inference(variable_rename,[status(thm)],[f_1673_1]) ).

fof(f_1673_3,plain,
    ! [U_5538,U_5539,U_5540,U_5541] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5538),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5538),U_5539),U_5540)),U_5541) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5538),hAPP(hAPP(c_Power_Opower__class_Opower(U_5538),U_5539),U_5541)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5538),U_5540),U_5541))
      | ~ class_Fields_Ofield__inverse__zero(U_5538) ),
    inference(definitional_conversion,[status(esa)],[f_1673_2]) ).

cnf(f_1673_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5538),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5538),U_5539),U_5540)),U_5541) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5538),hAPP(hAPP(c_Power_Opower__class_Opower(U_5538),U_5539),U_5541)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5538),U_5540),U_5541))
    | ~ class_Fields_Ofield__inverse__zero(U_5538) ),
    inference(clausify,[status(thm)],[f_1673_3]) ).

fof(f_1674_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_1674_2,plain,
    ! [U_5542] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5542) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5542)),
    inference(variable_rename,[status(thm)],[f_1674_1]) ).

fof(f_1674_3,plain,
    ! [U_5542] : hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5542) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5542)),
    inference(definitional_conversion,[status(esa)],[f_1674_2]) ).

cnf(f_1674_4,plain,
    hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_5542) = hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5542)),
    inference(clausify,[status(thm)],[f_1674_3]) ).

fof(f_1675_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_1675_2,plain,
    ! [U_5543] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5543)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5543)),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_1675_1]) ).

fof(f_1675_3,plain,
    ! [U_5543] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5543)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5543)),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_1675_2]) ).

cnf(f_1675_4,plain,
    hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5543)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5543)),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_1675_3]) ).

fof(f_1676_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_1676_2,plain,
    ! [U_5546,U_5545,U_5544] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5544,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_5544,U_5546)),c_Wellfounded_Oaccp(U_5544,U_5545)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5544,tc_fun(U_5544,tc_HOL_Obool))),U_5545),U_5546)) ),
    inference(variable_rename,[status(thm)],[f_1676_1]) ).

fof(f_1676_3,plain,
    ! [U_5544,U_5545,U_5546] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5544,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_5544,U_5546)),c_Wellfounded_Oaccp(U_5544,U_5545)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5544,tc_fun(U_5544,tc_HOL_Obool))),U_5545),U_5546)) ),
    inference(definitional_conversion,[status(esa)],[f_1676_2]) ).

cnf(f_1676_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5544,tc_HOL_Obool)),c_Wellfounded_Oaccp(U_5544,U_5546)),c_Wellfounded_Oaccp(U_5544,U_5545)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5544,tc_fun(U_5544,tc_HOL_Obool))),U_5545),U_5546)) ),
    inference(clausify,[status(thm)],[f_1676_3]) ).

fof(f_1677_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_1677_2,plain,
    ! [U_5549,U_5548,U_5547] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5547),U_5548),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5549))) = hAPP(hAPP(c_HOL_OLet(U_5547,U_5547),hAPP(hAPP(c_Power_Opower__class_Opower(U_5547),U_5548),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5549))),hAPP(hAPP(c_COMBS(U_5547,U_5547,U_5547),c_Groups_Otimes__class_Otimes(U_5547)),c_COMBI(U_5547)))
      | ~ class_Int_Onumber__ring(U_5547) ),
    inference(variable_rename,[status(thm)],[f_1677_1]) ).

fof(f_1677_3,plain,
    ! [U_5547,U_5548,U_5549] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5547),U_5548),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5549))) = hAPP(hAPP(c_HOL_OLet(U_5547,U_5547),hAPP(hAPP(c_Power_Opower__class_Opower(U_5547),U_5548),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5549))),hAPP(hAPP(c_COMBS(U_5547,U_5547,U_5547),c_Groups_Otimes__class_Otimes(U_5547)),c_COMBI(U_5547)))
      | ~ class_Int_Onumber__ring(U_5547) ),
    inference(definitional_conversion,[status(esa)],[f_1677_2]) ).

cnf(f_1677_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5547),U_5548),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5549))) = hAPP(hAPP(c_HOL_OLet(U_5547,U_5547),hAPP(hAPP(c_Power_Opower__class_Opower(U_5547),U_5548),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5549))),hAPP(hAPP(c_COMBS(U_5547,U_5547,U_5547),c_Groups_Otimes__class_Otimes(U_5547)),c_COMBI(U_5547)))
    | ~ class_Int_Onumber__ring(U_5547) ),
    inference(clausify,[status(thm)],[f_1677_3]) ).

fof(f_1678_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_1678_2,plain,
    ! [U_5551,U_5550] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5550),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5551))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5550),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5551))),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_1678_1]) ).

fof(f_1678_3,plain,
    ! [U_5550,U_5551] : hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5550),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5551))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5550),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5551))),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_1678_2]) ).

cnf(f_1678_4,plain,
    hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5550),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5551))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5550),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5551))),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_1678_3]) ).

fof(f_1679_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_1679_2,plain,
    ! [U_5555,U_5554,U_5553,U_5552] :
      ( U_5554 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5552),U_5555),U_5553)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5552),U_5554),U_5553) != U_5555
      | U_5553 = c_Groups_Ozero__class_Ozero(U_5552)
      | ~ class_Rings_Odivision__ring(U_5552) ),
    inference(variable_rename,[status(thm)],[f_1679_1]) ).

fof(f_1679_3,plain,
    ! [U_5552,U_5553,U_5554,U_5555] :
      ( U_5554 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5552),U_5555),U_5553)
      | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5552),U_5554),U_5553) != U_5555
      | U_5553 = c_Groups_Ozero__class_Ozero(U_5552)
      | ~ class_Rings_Odivision__ring(U_5552) ),
    inference(definitional_conversion,[status(esa)],[f_1679_2]) ).

cnf(f_1679_4,plain,
    ( U_5554 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5552),U_5555),U_5553)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5552),U_5554),U_5553) != U_5555
    | U_5553 = c_Groups_Ozero__class_Ozero(U_5552)
    | ~ class_Rings_Odivision__ring(U_5552) ),
    inference(clausify,[status(thm)],[f_1679_3]) ).

fof(f_1680_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_1680_2,plain,
    ! [U_5559,U_5558,U_5557,U_5556] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5556),U_5558),U_5557) = U_5559
      | U_5558 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5556),U_5559),U_5557)
      | U_5557 = c_Groups_Ozero__class_Ozero(U_5556)
      | ~ class_Rings_Odivision__ring(U_5556) ),
    inference(variable_rename,[status(thm)],[f_1680_1]) ).

fof(f_1680_3,plain,
    ! [U_5556,U_5557,U_5558,U_5559] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5556),U_5558),U_5557) = U_5559
      | U_5558 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5556),U_5559),U_5557)
      | U_5557 = c_Groups_Ozero__class_Ozero(U_5556)
      | ~ class_Rings_Odivision__ring(U_5556) ),
    inference(definitional_conversion,[status(esa)],[f_1680_2]) ).

cnf(f_1680_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5556),U_5558),U_5557) = U_5559
    | U_5558 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5556),U_5559),U_5557)
    | U_5557 = c_Groups_Ozero__class_Ozero(U_5556)
    | ~ class_Rings_Odivision__ring(U_5556) ),
    inference(clausify,[status(thm)],[f_1680_3]) ).

fof(f_1681_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_1681_2,plain,
    ! [U_5563,U_5562,U_5561,U_5560] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5560),U_5562),U_5561) = U_5563
          | U_5562 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5560),U_5563),U_5561) )
        & ( U_5562 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5560),U_5563),U_5561)
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5560),U_5562),U_5561) != U_5563 ) )
      | U_5561 = c_Groups_Ozero__class_Ozero(U_5560)
      | ~ class_Rings_Odivision__ring(U_5560) ),
    inference(variable_rename,[status(thm)],[f_1681_1]) ).

fof(f_1681_3,plain,
    ( ! [U_5560,U_5561,U_5562,U_5563] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5560),U_5562),U_5561) = U_5563
        | U_5562 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5560),U_5563),U_5561)
        | ~ sP436(U_5560,U_5561,U_5562,U_5563) )
    & ! [U_5560,U_5561,U_5562,U_5563] :
        ( U_5562 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5560),U_5563),U_5561)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5560),U_5562),U_5561) != U_5563
        | ~ sP436(U_5560,U_5561,U_5562,U_5563) )
    & ! [U_5560,U_5561,U_5562,U_5563] :
        ( sP436(U_5560,U_5561,U_5562,U_5563)
        | U_5561 = c_Groups_Ozero__class_Ozero(U_5560)
        | ~ class_Rings_Odivision__ring(U_5560) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP436])],[f_1681_2]) ).

cnf(f_1681_4,plain,
    ( sP436(U_5560,U_5561,U_5562,U_5563)
    | U_5561 = c_Groups_Ozero__class_Ozero(U_5560)
    | ~ class_Rings_Odivision__ring(U_5560) ),
    inference(clausify,[status(thm)],[f_1681_3]) ).

cnf(f_1681_5,plain,
    ( U_5562 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5560),U_5563),U_5561)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5560),U_5562),U_5561) != U_5563
    | ~ sP436(U_5560,U_5561,U_5562,U_5563) ),
    inference(clausify,[status(thm)],[f_1681_3]) ).

cnf(f_1681_6,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5560),U_5562),U_5561) = U_5563
    | U_5562 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5560),U_5563),U_5561)
    | ~ sP436(U_5560,U_5561,U_5562,U_5563) ),
    inference(clausify,[status(thm)],[f_1681_3]) ).

fof(f_1682_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_1682_2,plain,
    ! [U_5567,U_5566,U_5565,U_5564] :
      ( ( ( U_5566 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5564),U_5567),U_5565)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5564),U_5566),U_5565) != U_5567 )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5564),U_5566),U_5565) = U_5567
          | U_5566 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5564),U_5567),U_5565) ) )
      | U_5565 = c_Groups_Ozero__class_Ozero(U_5564)
      | ~ class_Rings_Odivision__ring(U_5564) ),
    inference(variable_rename,[status(thm)],[f_1682_1]) ).

fof(f_1682_3,plain,
    ( ! [U_5565,U_5564,U_5567,U_5566] :
        ( U_5566 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5564),U_5567),U_5565)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5564),U_5566),U_5565) != U_5567
        | ~ sP437(U_5565,U_5564,U_5567,U_5566) )
    & ! [U_5565,U_5564,U_5567,U_5566] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5564),U_5566),U_5565) = U_5567
        | U_5566 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5564),U_5567),U_5565)
        | ~ sP437(U_5565,U_5564,U_5567,U_5566) )
    & ! [U_5565,U_5564,U_5567,U_5566] :
        ( sP437(U_5565,U_5564,U_5567,U_5566)
        | U_5565 = c_Groups_Ozero__class_Ozero(U_5564)
        | ~ class_Rings_Odivision__ring(U_5564) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP437])],[f_1682_2]) ).

cnf(f_1682_4,plain,
    ( sP437(U_5565,U_5564,U_5567,U_5566)
    | U_5565 = c_Groups_Ozero__class_Ozero(U_5564)
    | ~ class_Rings_Odivision__ring(U_5564) ),
    inference(clausify,[status(thm)],[f_1682_3]) ).

cnf(f_1682_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5564),U_5566),U_5565) = U_5567
    | U_5566 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5564),U_5567),U_5565)
    | ~ sP437(U_5565,U_5564,U_5567,U_5566) ),
    inference(clausify,[status(thm)],[f_1682_3]) ).

cnf(f_1682_6,plain,
    ( U_5566 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5564),U_5567),U_5565)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5564),U_5566),U_5565) != U_5567
    | ~ sP437(U_5565,U_5564,U_5567,U_5566) ),
    inference(clausify,[status(thm)],[f_1682_3]) ).

fof(f_1683_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_1683_2,plain,
    ! [U_5569,U_5568] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5568),U_5569),U_5569) = c_Groups_Oone__class_Oone(U_5568)
          | U_5569 = c_Groups_Ozero__class_Ozero(U_5568) )
        & ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5568),U_5569),U_5569) = c_Groups_Ozero__class_Ozero(U_5568)
          | U_5569 != c_Groups_Ozero__class_Ozero(U_5568) ) )
      | ~ class_Rings_Odivision__ring__inverse__zero(U_5568) ),
    inference(variable_rename,[status(thm)],[f_1683_1]) ).

fof(f_1683_3,plain,
    ( ! [U_5568,U_5569] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5568),U_5569),U_5569) = c_Groups_Oone__class_Oone(U_5568)
        | U_5569 = c_Groups_Ozero__class_Ozero(U_5568)
        | ~ sP438(U_5568,U_5569) )
    & ! [U_5568,U_5569] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5568),U_5569),U_5569) = c_Groups_Ozero__class_Ozero(U_5568)
        | U_5569 != c_Groups_Ozero__class_Ozero(U_5568)
        | ~ sP438(U_5568,U_5569) )
    & ! [U_5568,U_5569] :
        ( sP438(U_5568,U_5569)
        | ~ class_Rings_Odivision__ring__inverse__zero(U_5568) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP438])],[f_1683_2]) ).

cnf(f_1683_4,plain,
    ( sP438(U_5568,U_5569)
    | ~ class_Rings_Odivision__ring__inverse__zero(U_5568) ),
    inference(clausify,[status(thm)],[f_1683_3]) ).

cnf(f_1683_5,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5568),U_5569),U_5569) = c_Groups_Ozero__class_Ozero(U_5568)
    | U_5569 != c_Groups_Ozero__class_Ozero(U_5568)
    | ~ sP438(U_5568,U_5569) ),
    inference(clausify,[status(thm)],[f_1683_3]) ).

cnf(f_1683_6,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5568),U_5569),U_5569) = c_Groups_Oone__class_Oone(U_5568)
    | U_5569 = c_Groups_Ozero__class_Ozero(U_5568)
    | ~ sP438(U_5568,U_5569) ),
    inference(clausify,[status(thm)],[f_1683_3]) ).

fof(f_1684_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_1684_2,plain,
    ! [U_5571,U_5570] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5570),U_5571),U_5571) = c_Groups_Oone__class_Oone(U_5570)
      | U_5571 = c_Groups_Ozero__class_Ozero(U_5570)
      | ~ class_Rings_Odivision__ring(U_5570) ),
    inference(variable_rename,[status(thm)],[f_1684_1]) ).

fof(f_1684_3,plain,
    ! [U_5571,U_5570] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5570),U_5571),U_5571) = c_Groups_Oone__class_Oone(U_5570)
      | U_5571 = c_Groups_Ozero__class_Ozero(U_5570)
      | ~ class_Rings_Odivision__ring(U_5570) ),
    inference(definitional_conversion,[status(esa)],[f_1684_2]) ).

cnf(f_1684_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5570),U_5571),U_5571) = c_Groups_Oone__class_Oone(U_5570)
    | U_5571 = c_Groups_Ozero__class_Ozero(U_5570)
    | ~ class_Rings_Odivision__ring(U_5570) ),
    inference(clausify,[status(thm)],[f_1684_3]) ).

fof(f_1685_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_1685_2,plain,
    ! [U_5574,U_5573,U_5572] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5572),U_5574),U_5573) = c_Groups_Oone__class_Oone(U_5572)
          | U_5574 != U_5573 )
        & ( U_5574 = U_5573
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5572),U_5574),U_5573) != c_Groups_Oone__class_Oone(U_5572) ) )
      | U_5573 = c_Groups_Ozero__class_Ozero(U_5572)
      | ~ class_Rings_Odivision__ring(U_5572) ),
    inference(variable_rename,[status(thm)],[f_1685_1]) ).

fof(f_1685_3,plain,
    ( ! [U_5572,U_5573,U_5574] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5572),U_5574),U_5573) = c_Groups_Oone__class_Oone(U_5572)
        | U_5574 != U_5573
        | ~ sP439(U_5572,U_5573,U_5574) )
    & ! [U_5572,U_5573,U_5574] :
        ( U_5574 = U_5573
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5572),U_5574),U_5573) != c_Groups_Oone__class_Oone(U_5572)
        | ~ sP439(U_5572,U_5573,U_5574) )
    & ! [U_5572,U_5573,U_5574] :
        ( sP439(U_5572,U_5573,U_5574)
        | U_5573 = c_Groups_Ozero__class_Ozero(U_5572)
        | ~ class_Rings_Odivision__ring(U_5572) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP439])],[f_1685_2]) ).

cnf(f_1685_4,plain,
    ( sP439(U_5572,U_5573,U_5574)
    | U_5573 = c_Groups_Ozero__class_Ozero(U_5572)
    | ~ class_Rings_Odivision__ring(U_5572) ),
    inference(clausify,[status(thm)],[f_1685_3]) ).

cnf(f_1685_5,plain,
    ( U_5574 = U_5573
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5572),U_5574),U_5573) != c_Groups_Oone__class_Oone(U_5572)
    | ~ sP439(U_5572,U_5573,U_5574) ),
    inference(clausify,[status(thm)],[f_1685_3]) ).

cnf(f_1685_6,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5572),U_5574),U_5573) = c_Groups_Oone__class_Oone(U_5572)
    | U_5574 != U_5573
    | ~ sP439(U_5572,U_5573,U_5574) ),
    inference(clausify,[status(thm)],[f_1685_3]) ).

fof(f_1686_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_1686_2,plain,
    ! [U_5577,U_5576,U_5575] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5575),hAPP(c_Groups_Ouminus__class_Ouminus(U_5575),U_5577)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5575),U_5576)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5575),U_5577),U_5576)
      | U_5576 = c_Groups_Ozero__class_Ozero(U_5575)
      | ~ class_Rings_Odivision__ring(U_5575) ),
    inference(variable_rename,[status(thm)],[f_1686_1]) ).

fof(f_1686_3,plain,
    ! [U_5577,U_5576,U_5575] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5575),hAPP(c_Groups_Ouminus__class_Ouminus(U_5575),U_5577)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5575),U_5576)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5575),U_5577),U_5576)
      | U_5576 = c_Groups_Ozero__class_Ozero(U_5575)
      | ~ class_Rings_Odivision__ring(U_5575) ),
    inference(definitional_conversion,[status(esa)],[f_1686_2]) ).

cnf(f_1686_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5575),hAPP(c_Groups_Ouminus__class_Ouminus(U_5575),U_5577)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5575),U_5576)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5575),U_5577),U_5576)
    | U_5576 = c_Groups_Ozero__class_Ozero(U_5575)
    | ~ class_Rings_Odivision__ring(U_5575) ),
    inference(clausify,[status(thm)],[f_1686_3]) ).

fof(f_1687_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_1687_2,plain,
    ! [U_5580,U_5579,U_5578] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5578),U_5580),U_5579)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5578),U_5580),hAPP(c_Groups_Ouminus__class_Ouminus(U_5578),U_5579))
      | U_5579 = c_Groups_Ozero__class_Ozero(U_5578)
      | ~ class_Rings_Odivision__ring(U_5578) ),
    inference(variable_rename,[status(thm)],[f_1687_1]) ).

fof(f_1687_3,plain,
    ! [U_5578,U_5579,U_5580] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5578),U_5580),U_5579)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5578),U_5580),hAPP(c_Groups_Ouminus__class_Ouminus(U_5578),U_5579))
      | U_5579 = c_Groups_Ozero__class_Ozero(U_5578)
      | ~ class_Rings_Odivision__ring(U_5578) ),
    inference(definitional_conversion,[status(esa)],[f_1687_2]) ).

cnf(f_1687_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5578),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5578),U_5580),U_5579)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5578),U_5580),hAPP(c_Groups_Ouminus__class_Ouminus(U_5578),U_5579))
    | U_5579 = c_Groups_Ozero__class_Ozero(U_5578)
    | ~ class_Rings_Odivision__ring(U_5578) ),
    inference(clausify,[status(thm)],[f_1687_3]) ).

fof(f_1688_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_1688_2,plain,
    ! [U_5584,U_5583,U_5582,U_5581] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5581),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5581),U_5583),U_5582)),U_5584) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5581),hAPP(hAPP(c_Power_Opower__class_Opower(U_5581),U_5583),U_5584)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5581),U_5582),U_5584))
      | U_5582 = c_Groups_Ozero__class_Ozero(U_5581)
      | ~ class_Fields_Ofield(U_5581) ),
    inference(variable_rename,[status(thm)],[f_1688_1]) ).

fof(f_1688_3,plain,
    ! [U_5581,U_5582,U_5583,U_5584] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5581),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5581),U_5583),U_5582)),U_5584) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5581),hAPP(hAPP(c_Power_Opower__class_Opower(U_5581),U_5583),U_5584)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5581),U_5582),U_5584))
      | U_5582 = c_Groups_Ozero__class_Ozero(U_5581)
      | ~ class_Fields_Ofield(U_5581) ),
    inference(definitional_conversion,[status(esa)],[f_1688_2]) ).

cnf(f_1688_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5581),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5581),U_5583),U_5582)),U_5584) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5581),hAPP(hAPP(c_Power_Opower__class_Opower(U_5581),U_5583),U_5584)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5581),U_5582),U_5584))
    | U_5582 = c_Groups_Ozero__class_Ozero(U_5581)
    | ~ class_Fields_Ofield(U_5581) ),
    inference(clausify,[status(thm)],[f_1688_3]) ).

fof(f_1689_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_1689_2,plain,
    ! [U_5587,U_5586,U_5585] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5585),c_Groups_Oone__class_Oone(U_5585)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5585),U_5586),U_5587)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5585),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5585),c_Groups_Oone__class_Oone(U_5585)),U_5586)),U_5587)
      | ~ class_Fields_Ofield__inverse__zero(U_5585) ),
    inference(variable_rename,[status(thm)],[f_1689_1]) ).

fof(f_1689_3,plain,
    ! [U_5585,U_5586,U_5587] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5585),c_Groups_Oone__class_Oone(U_5585)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5585),U_5586),U_5587)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5585),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5585),c_Groups_Oone__class_Oone(U_5585)),U_5586)),U_5587)
      | ~ class_Fields_Ofield__inverse__zero(U_5585) ),
    inference(definitional_conversion,[status(esa)],[f_1689_2]) ).

cnf(f_1689_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5585),c_Groups_Oone__class_Oone(U_5585)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5585),U_5586),U_5587)) = hAPP(hAPP(c_Power_Opower__class_Opower(U_5585),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5585),c_Groups_Oone__class_Oone(U_5585)),U_5586)),U_5587)
    | ~ class_Fields_Ofield__inverse__zero(U_5585) ),
    inference(clausify,[status(thm)],[f_1689_3]) ).

fof(f_1690_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_1690_2,plain,
    ! [U_5590,U_5589,U_5588] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5588),hAPP(c_Int_Onumber__class_Onumber__of(U_5588),U_5589)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5590))) = hAPP(hAPP(c_HOL_OLet(U_5588,U_5588),hAPP(hAPP(c_Power_Opower__class_Opower(U_5588),hAPP(c_Int_Onumber__class_Onumber__of(U_5588),U_5589)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5590))),hAPP(hAPP(c_COMBS(U_5588,U_5588,U_5588),c_Groups_Otimes__class_Otimes(U_5588)),c_COMBI(U_5588)))
      | ~ class_Int_Onumber__ring(U_5588) ),
    inference(variable_rename,[status(thm)],[f_1690_1]) ).

fof(f_1690_3,plain,
    ! [U_5588,U_5589,U_5590] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5588),hAPP(c_Int_Onumber__class_Onumber__of(U_5588),U_5589)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5590))) = hAPP(hAPP(c_HOL_OLet(U_5588,U_5588),hAPP(hAPP(c_Power_Opower__class_Opower(U_5588),hAPP(c_Int_Onumber__class_Onumber__of(U_5588),U_5589)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5590))),hAPP(hAPP(c_COMBS(U_5588,U_5588,U_5588),c_Groups_Otimes__class_Otimes(U_5588)),c_COMBI(U_5588)))
      | ~ class_Int_Onumber__ring(U_5588) ),
    inference(definitional_conversion,[status(esa)],[f_1690_2]) ).

cnf(f_1690_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5588),hAPP(c_Int_Onumber__class_Onumber__of(U_5588),U_5589)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit0(U_5590))) = hAPP(hAPP(c_HOL_OLet(U_5588,U_5588),hAPP(hAPP(c_Power_Opower__class_Opower(U_5588),hAPP(c_Int_Onumber__class_Onumber__of(U_5588),U_5589)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5590))),hAPP(hAPP(c_COMBS(U_5588,U_5588,U_5588),c_Groups_Otimes__class_Otimes(U_5588)),c_COMBI(U_5588)))
    | ~ class_Int_Onumber__ring(U_5588) ),
    inference(clausify,[status(thm)],[f_1690_3]) ).

fof(f_1691_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_1691_2,plain,
    ! [U_5592,U_5591] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5592)),hAPP(c_Int_Onat,U_5591)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5592),U_5591)),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_5591)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5592)),hAPP(c_Int_Onat,U_5591)) = hAPP(c_Int_Onat,U_5592)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5591)) ) ),
    inference(variable_rename,[status(thm)],[f_1691_1]) ).

fof(f_1691_3,plain,
    ( ! [U_5596,U_5594] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5596)),hAPP(c_Int_Onat,U_5594)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5596),U_5594)),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_5594)) )
    & ! [U_5595,U_5593] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5595)),hAPP(c_Int_Onat,U_5593)) = hAPP(c_Int_Onat,U_5595)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5593)) ) ),
    inference(miniscope,[status(thm)],[f_1691_2]) ).

fof(f_1691_4,plain,
    ( ! [U_5594,U_5596] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5596)),hAPP(c_Int_Onat,U_5594)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5596),U_5594)),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_5594)) )
    & ! [U_5595,U_5593] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5595)),hAPP(c_Int_Onat,U_5593)) = hAPP(c_Int_Onat,U_5595)
        | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5593)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1691_3]) ).

cnf(f_1691_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5595)),hAPP(c_Int_Onat,U_5593)) = hAPP(c_Int_Onat,U_5595)
    | ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,U_5593)) ),
    inference(clausify,[status(thm)],[f_1691_4]) ).

cnf(f_1691_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onat,U_5596)),hAPP(c_Int_Onat,U_5594)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_5596),U_5594)),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_5594)) ),
    inference(clausify,[status(thm)],[f_1691_4]) ).

fof(f_1692_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_1692_2,plain,
    ! [U_5598,U_5597] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5597),U_5598) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_5597,hAPP(hAPP(c_COMBC(U_5597,U_5597,U_5597),c_Groups_Oplus__class_Oplus(U_5597)),c_Groups_Oone__class_Oone(U_5597)),U_5598,c_Groups_Ozero__class_Ozero(U_5597))
      | ~ class_Rings_Osemiring__1(U_5597) ),
    inference(variable_rename,[status(thm)],[f_1692_1]) ).

fof(f_1692_3,plain,
    ! [U_5597,U_5598] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5597),U_5598) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_5597,hAPP(hAPP(c_COMBC(U_5597,U_5597,U_5597),c_Groups_Oplus__class_Oplus(U_5597)),c_Groups_Oone__class_Oone(U_5597)),U_5598,c_Groups_Ozero__class_Ozero(U_5597))
      | ~ class_Rings_Osemiring__1(U_5597) ),
    inference(definitional_conversion,[status(esa)],[f_1692_2]) ).

cnf(f_1692_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_5597),U_5598) = c_Nat_Osemiring__1__class_Oof__nat__aux(U_5597,hAPP(hAPP(c_COMBC(U_5597,U_5597,U_5597),c_Groups_Oplus__class_Oplus(U_5597)),c_Groups_Oone__class_Oone(U_5597)),U_5598,c_Groups_Ozero__class_Ozero(U_5597))
    | ~ class_Rings_Osemiring__1(U_5597) ),
    inference(clausify,[status(thm)],[f_1692_3]) ).

fof(f_1693_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_1693_2,plain,
    ! [U_5602,U_5601,U_5600,U_5599] :
      ( ( ( U_5600 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5599),U_5601),hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602))
          | ( U_5600 != c_Groups_Ozero__class_Ozero(U_5599)
            & hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602) = c_Groups_Ozero__class_Ozero(U_5599) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5599),U_5600),hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602)) != U_5601
            & hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602) != c_Groups_Ozero__class_Ozero(U_5599) ) )
        & ( ( ( U_5600 = c_Groups_Ozero__class_Ozero(U_5599)
              | hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602) != c_Groups_Ozero__class_Ozero(U_5599) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5599),U_5600),hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602)) = U_5601
              | hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602) = c_Groups_Ozero__class_Ozero(U_5599) ) )
          | U_5600 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5599),U_5601),hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602)) ) )
      | ~ class_Int_Onumber(U_5599)
      | ~ class_Fields_Ofield__inverse__zero(U_5599) ),
    inference(variable_rename,[status(thm)],[f_1693_1]) ).

fof(f_1693_3,plain,
    ( ! [U_5599,U_5600,U_5602] :
        ( U_5600 != c_Groups_Ozero__class_Ozero(U_5599)
        | ~ sP442(U_5599,U_5600,U_5602) )
    & ! [U_5599,U_5600,U_5602] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602) = c_Groups_Ozero__class_Ozero(U_5599)
        | ~ sP442(U_5599,U_5600,U_5602) )
    & ! [U_5599,U_5600,U_5601,U_5602] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5599),U_5600),hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602)) != U_5601
        | ~ sP441(U_5599,U_5600,U_5601,U_5602) )
    & ! [U_5599,U_5600,U_5601,U_5602] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602) != c_Groups_Ozero__class_Ozero(U_5599)
        | ~ sP441(U_5599,U_5600,U_5601,U_5602) )
    & ! [U_5599,U_5600,U_5601,U_5602] :
        ( U_5600 = c_Groups_Ozero__class_Ozero(U_5599)
        | hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602) != c_Groups_Ozero__class_Ozero(U_5599)
        | ~ sP440(U_5599,U_5600,U_5601,U_5602) )
    & ! [U_5599,U_5600,U_5601,U_5602] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5599),U_5600),hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602)) = U_5601
        | hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602) = c_Groups_Ozero__class_Ozero(U_5599)
        | ~ sP440(U_5599,U_5600,U_5601,U_5602) )
    & ! [U_5599,U_5600,U_5601,U_5602] :
        ( U_5600 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5599),U_5601),hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602))
        | sP442(U_5599,U_5600,U_5602)
        | sP441(U_5599,U_5600,U_5601,U_5602)
        | ~ sP443(U_5599,U_5600,U_5601,U_5602) )
    & ! [U_5599,U_5600,U_5601,U_5602] :
        ( sP440(U_5599,U_5600,U_5601,U_5602)
        | U_5600 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5599),U_5601),hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602))
        | ~ sP443(U_5599,U_5600,U_5601,U_5602) )
    & ! [U_5599,U_5600,U_5601,U_5602] :
        ( sP443(U_5599,U_5600,U_5601,U_5602)
        | ~ class_Int_Onumber(U_5599)
        | ~ class_Fields_Ofield__inverse__zero(U_5599) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP440,sP441,sP442,sP443])],[f_1693_2]) ).

cnf(f_1693_4,plain,
    ( sP443(U_5599,U_5600,U_5601,U_5602)
    | ~ class_Int_Onumber(U_5599)
    | ~ class_Fields_Ofield__inverse__zero(U_5599) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_5,plain,
    ( sP440(U_5599,U_5600,U_5601,U_5602)
    | U_5600 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5599),U_5601),hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602))
    | ~ sP443(U_5599,U_5600,U_5601,U_5602) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_6,plain,
    ( U_5600 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5599),U_5601),hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602))
    | sP442(U_5599,U_5600,U_5602)
    | sP441(U_5599,U_5600,U_5601,U_5602)
    | ~ sP443(U_5599,U_5600,U_5601,U_5602) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_7,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5599),U_5600),hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602)) = U_5601
    | hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602) = c_Groups_Ozero__class_Ozero(U_5599)
    | ~ sP440(U_5599,U_5600,U_5601,U_5602) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_8,plain,
    ( U_5600 = c_Groups_Ozero__class_Ozero(U_5599)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602) != c_Groups_Ozero__class_Ozero(U_5599)
    | ~ sP440(U_5599,U_5600,U_5601,U_5602) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_9,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602) != c_Groups_Ozero__class_Ozero(U_5599)
    | ~ sP441(U_5599,U_5600,U_5601,U_5602) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_10,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5599),U_5600),hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602)) != U_5601
    | ~ sP441(U_5599,U_5600,U_5601,U_5602) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_11,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5599),U_5602) = c_Groups_Ozero__class_Ozero(U_5599)
    | ~ sP442(U_5599,U_5600,U_5602) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

cnf(f_1693_12,plain,
    ( U_5600 != c_Groups_Ozero__class_Ozero(U_5599)
    | ~ sP442(U_5599,U_5600,U_5602) ),
    inference(clausify,[status(thm)],[f_1693_3]) ).

fof(f_1694_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_1694_2,plain,
    ! [U_5606,U_5605,U_5604,U_5603] :
      ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_5603),U_5604) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5603),U_5605),U_5606)
          | ( hAPP(c_Int_Onumber__class_Onumber__of(U_5603),U_5604) != c_Groups_Ozero__class_Ozero(U_5603)
            & U_5606 = c_Groups_Ozero__class_Ozero(U_5603) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5603),hAPP(c_Int_Onumber__class_Onumber__of(U_5603),U_5604)),U_5606) != U_5605
            & U_5606 != c_Groups_Ozero__class_Ozero(U_5603) ) )
        & ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_5603),U_5604) = c_Groups_Ozero__class_Ozero(U_5603)
              | U_5606 != c_Groups_Ozero__class_Ozero(U_5603) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5603),hAPP(c_Int_Onumber__class_Onumber__of(U_5603),U_5604)),U_5606) = U_5605
              | U_5606 = c_Groups_Ozero__class_Ozero(U_5603) ) )
          | hAPP(c_Int_Onumber__class_Onumber__of(U_5603),U_5604) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5603),U_5605),U_5606) ) )
      | ~ class_Int_Onumber(U_5603)
      | ~ class_Fields_Ofield__inverse__zero(U_5603) ),
    inference(variable_rename,[status(thm)],[f_1694_1]) ).

fof(f_1694_3,plain,
    ( ! [U_5604,U_5603,U_5606] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5603),U_5604) != c_Groups_Ozero__class_Ozero(U_5603)
        | ~ sP446(U_5604,U_5603,U_5606) )
    & ! [U_5604,U_5603,U_5606] :
        ( U_5606 = c_Groups_Ozero__class_Ozero(U_5603)
        | ~ sP446(U_5604,U_5603,U_5606) )
    & ! [U_5604,U_5603,U_5605,U_5606] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5603),hAPP(c_Int_Onumber__class_Onumber__of(U_5603),U_5604)),U_5606) != U_5605
        | ~ sP445(U_5604,U_5603,U_5605,U_5606) )
    & ! [U_5604,U_5603,U_5605,U_5606] :
        ( U_5606 != c_Groups_Ozero__class_Ozero(U_5603)
        | ~ sP445(U_5604,U_5603,U_5605,U_5606) )
    & ! [U_5604,U_5603,U_5605,U_5606] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5603),U_5604) = c_Groups_Ozero__class_Ozero(U_5603)
        | U_5606 != c_Groups_Ozero__class_Ozero(U_5603)
        | ~ sP444(U_5604,U_5603,U_5605,U_5606) )
    & ! [U_5604,U_5603,U_5605,U_5606] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5603),hAPP(c_Int_Onumber__class_Onumber__of(U_5603),U_5604)),U_5606) = U_5605
        | U_5606 = c_Groups_Ozero__class_Ozero(U_5603)
        | ~ sP444(U_5604,U_5603,U_5605,U_5606) )
    & ! [U_5604,U_5603,U_5605,U_5606] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5603),U_5604) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5603),U_5605),U_5606)
        | sP446(U_5604,U_5603,U_5606)
        | sP445(U_5604,U_5603,U_5605,U_5606)
        | ~ sP447(U_5604,U_5603,U_5605,U_5606) )
    & ! [U_5604,U_5603,U_5605,U_5606] :
        ( sP444(U_5604,U_5603,U_5605,U_5606)
        | hAPP(c_Int_Onumber__class_Onumber__of(U_5603),U_5604) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5603),U_5605),U_5606)
        | ~ sP447(U_5604,U_5603,U_5605,U_5606) )
    & ! [U_5604,U_5603,U_5605,U_5606] :
        ( sP447(U_5604,U_5603,U_5605,U_5606)
        | ~ class_Int_Onumber(U_5603)
        | ~ class_Fields_Ofield__inverse__zero(U_5603) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP444,sP445,sP446,sP447])],[f_1694_2]) ).

cnf(f_1694_4,plain,
    ( sP447(U_5604,U_5603,U_5605,U_5606)
    | ~ class_Int_Onumber(U_5603)
    | ~ class_Fields_Ofield__inverse__zero(U_5603) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_5,plain,
    ( sP444(U_5604,U_5603,U_5605,U_5606)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_5603),U_5604) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5603),U_5605),U_5606)
    | ~ sP447(U_5604,U_5603,U_5605,U_5606) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5603),U_5604) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5603),U_5605),U_5606)
    | sP446(U_5604,U_5603,U_5606)
    | sP445(U_5604,U_5603,U_5605,U_5606)
    | ~ sP447(U_5604,U_5603,U_5605,U_5606) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_7,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5603),hAPP(c_Int_Onumber__class_Onumber__of(U_5603),U_5604)),U_5606) = U_5605
    | U_5606 = c_Groups_Ozero__class_Ozero(U_5603)
    | ~ sP444(U_5604,U_5603,U_5605,U_5606) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_8,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5603),U_5604) = c_Groups_Ozero__class_Ozero(U_5603)
    | U_5606 != c_Groups_Ozero__class_Ozero(U_5603)
    | ~ sP444(U_5604,U_5603,U_5605,U_5606) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_9,plain,
    ( U_5606 != c_Groups_Ozero__class_Ozero(U_5603)
    | ~ sP445(U_5604,U_5603,U_5605,U_5606) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_10,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5603),hAPP(c_Int_Onumber__class_Onumber__of(U_5603),U_5604)),U_5606) != U_5605
    | ~ sP445(U_5604,U_5603,U_5605,U_5606) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_11,plain,
    ( U_5606 = c_Groups_Ozero__class_Ozero(U_5603)
    | ~ sP446(U_5604,U_5603,U_5606) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

cnf(f_1694_12,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5603),U_5604) != c_Groups_Ozero__class_Ozero(U_5603)
    | ~ sP446(U_5604,U_5603,U_5606) ),
    inference(clausify,[status(thm)],[f_1694_3]) ).

fof(f_1695_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_1695_2,plain,
    ! [U_5610,U_5609,U_5608,U_5607] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5607),U_5608),U_5609) = hAPP(c_Int_Onumber__class_Onumber__of(U_5607),U_5610)
          | ( hAPP(c_Int_Onumber__class_Onumber__of(U_5607),U_5610) != c_Groups_Ozero__class_Ozero(U_5607)
            & U_5609 = c_Groups_Ozero__class_Ozero(U_5607) )
          | ( U_5608 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5607),hAPP(c_Int_Onumber__class_Onumber__of(U_5607),U_5610)),U_5609)
            & U_5609 != c_Groups_Ozero__class_Ozero(U_5607) ) )
        & ( ( ( hAPP(c_Int_Onumber__class_Onumber__of(U_5607),U_5610) = c_Groups_Ozero__class_Ozero(U_5607)
              | U_5609 != c_Groups_Ozero__class_Ozero(U_5607) )
            & ( U_5608 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5607),hAPP(c_Int_Onumber__class_Onumber__of(U_5607),U_5610)),U_5609)
              | U_5609 = c_Groups_Ozero__class_Ozero(U_5607) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5607),U_5608),U_5609) != hAPP(c_Int_Onumber__class_Onumber__of(U_5607),U_5610) ) )
      | ~ class_Int_Onumber(U_5607)
      | ~ class_Fields_Ofield__inverse__zero(U_5607) ),
    inference(variable_rename,[status(thm)],[f_1695_1]) ).

fof(f_1695_3,plain,
    ( ! [U_5609,U_5610,U_5607] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5607),U_5610) != c_Groups_Ozero__class_Ozero(U_5607)
        | ~ sP450(U_5609,U_5610,U_5607) )
    & ! [U_5609,U_5610,U_5607] :
        ( U_5609 = c_Groups_Ozero__class_Ozero(U_5607)
        | ~ sP450(U_5609,U_5610,U_5607) )
    & ! [U_5608,U_5609,U_5610,U_5607] :
        ( U_5608 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5607),hAPP(c_Int_Onumber__class_Onumber__of(U_5607),U_5610)),U_5609)
        | ~ sP449(U_5608,U_5609,U_5610,U_5607) )
    & ! [U_5608,U_5609,U_5610,U_5607] :
        ( U_5609 != c_Groups_Ozero__class_Ozero(U_5607)
        | ~ sP449(U_5608,U_5609,U_5610,U_5607) )
    & ! [U_5608,U_5609,U_5610,U_5607] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5607),U_5610) = c_Groups_Ozero__class_Ozero(U_5607)
        | U_5609 != c_Groups_Ozero__class_Ozero(U_5607)
        | ~ sP448(U_5608,U_5609,U_5610,U_5607) )
    & ! [U_5608,U_5609,U_5610,U_5607] :
        ( U_5608 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5607),hAPP(c_Int_Onumber__class_Onumber__of(U_5607),U_5610)),U_5609)
        | U_5609 = c_Groups_Ozero__class_Ozero(U_5607)
        | ~ sP448(U_5608,U_5609,U_5610,U_5607) )
    & ! [U_5608,U_5609,U_5610,U_5607] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5607),U_5608),U_5609) = hAPP(c_Int_Onumber__class_Onumber__of(U_5607),U_5610)
        | sP450(U_5609,U_5610,U_5607)
        | sP449(U_5608,U_5609,U_5610,U_5607)
        | ~ sP451(U_5608,U_5609,U_5610,U_5607) )
    & ! [U_5608,U_5609,U_5610,U_5607] :
        ( sP448(U_5608,U_5609,U_5610,U_5607)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5607),U_5608),U_5609) != hAPP(c_Int_Onumber__class_Onumber__of(U_5607),U_5610)
        | ~ sP451(U_5608,U_5609,U_5610,U_5607) )
    & ! [U_5608,U_5609,U_5610,U_5607] :
        ( sP451(U_5608,U_5609,U_5610,U_5607)
        | ~ class_Int_Onumber(U_5607)
        | ~ class_Fields_Ofield__inverse__zero(U_5607) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP448,sP449,sP450,sP451])],[f_1695_2]) ).

cnf(f_1695_4,plain,
    ( sP451(U_5608,U_5609,U_5610,U_5607)
    | ~ class_Int_Onumber(U_5607)
    | ~ class_Fields_Ofield__inverse__zero(U_5607) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_5,plain,
    ( sP448(U_5608,U_5609,U_5610,U_5607)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5607),U_5608),U_5609) != hAPP(c_Int_Onumber__class_Onumber__of(U_5607),U_5610)
    | ~ sP451(U_5608,U_5609,U_5610,U_5607) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_6,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5607),U_5608),U_5609) = hAPP(c_Int_Onumber__class_Onumber__of(U_5607),U_5610)
    | sP450(U_5609,U_5610,U_5607)
    | sP449(U_5608,U_5609,U_5610,U_5607)
    | ~ sP451(U_5608,U_5609,U_5610,U_5607) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_7,plain,
    ( U_5608 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5607),hAPP(c_Int_Onumber__class_Onumber__of(U_5607),U_5610)),U_5609)
    | U_5609 = c_Groups_Ozero__class_Ozero(U_5607)
    | ~ sP448(U_5608,U_5609,U_5610,U_5607) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_8,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5607),U_5610) = c_Groups_Ozero__class_Ozero(U_5607)
    | U_5609 != c_Groups_Ozero__class_Ozero(U_5607)
    | ~ sP448(U_5608,U_5609,U_5610,U_5607) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_9,plain,
    ( U_5609 != c_Groups_Ozero__class_Ozero(U_5607)
    | ~ sP449(U_5608,U_5609,U_5610,U_5607) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_10,plain,
    ( U_5608 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5607),hAPP(c_Int_Onumber__class_Onumber__of(U_5607),U_5610)),U_5609)
    | ~ sP449(U_5608,U_5609,U_5610,U_5607) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_11,plain,
    ( U_5609 = c_Groups_Ozero__class_Ozero(U_5607)
    | ~ sP450(U_5609,U_5610,U_5607) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

cnf(f_1695_12,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5607),U_5610) != c_Groups_Ozero__class_Ozero(U_5607)
    | ~ sP450(U_5609,U_5610,U_5607) ),
    inference(clausify,[status(thm)],[f_1695_3]) ).

fof(f_1696_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_1696_2,plain,
    ! [U_5614,U_5613,U_5612,U_5611] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5611),U_5612),hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613)) = U_5614
          | ( U_5614 != c_Groups_Ozero__class_Ozero(U_5611)
            & hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613) = c_Groups_Ozero__class_Ozero(U_5611) )
          | ( U_5612 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5611),U_5614),hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613))
            & hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613) != c_Groups_Ozero__class_Ozero(U_5611) ) )
        & ( ( ( U_5614 = c_Groups_Ozero__class_Ozero(U_5611)
              | hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613) != c_Groups_Ozero__class_Ozero(U_5611) )
            & ( U_5612 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5611),U_5614),hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613))
              | hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613) = c_Groups_Ozero__class_Ozero(U_5611) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5611),U_5612),hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613)) != U_5614 ) )
      | ~ class_Int_Onumber(U_5611)
      | ~ class_Fields_Ofield__inverse__zero(U_5611) ),
    inference(variable_rename,[status(thm)],[f_1696_1]) ).

fof(f_1696_3,plain,
    ( ! [U_5613,U_5611,U_5614] :
        ( U_5614 != c_Groups_Ozero__class_Ozero(U_5611)
        | ~ sP454(U_5613,U_5611,U_5614) )
    & ! [U_5613,U_5611,U_5614] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613) = c_Groups_Ozero__class_Ozero(U_5611)
        | ~ sP454(U_5613,U_5611,U_5614) )
    & ! [U_5613,U_5611,U_5612,U_5614] :
        ( U_5612 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5611),U_5614),hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613))
        | ~ sP453(U_5613,U_5611,U_5612,U_5614) )
    & ! [U_5613,U_5611,U_5612,U_5614] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613) != c_Groups_Ozero__class_Ozero(U_5611)
        | ~ sP453(U_5613,U_5611,U_5612,U_5614) )
    & ! [U_5613,U_5611,U_5612,U_5614] :
        ( U_5614 = c_Groups_Ozero__class_Ozero(U_5611)
        | hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613) != c_Groups_Ozero__class_Ozero(U_5611)
        | ~ sP452(U_5613,U_5611,U_5612,U_5614) )
    & ! [U_5613,U_5611,U_5612,U_5614] :
        ( U_5612 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5611),U_5614),hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613))
        | hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613) = c_Groups_Ozero__class_Ozero(U_5611)
        | ~ sP452(U_5613,U_5611,U_5612,U_5614) )
    & ! [U_5613,U_5611,U_5612,U_5614] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5611),U_5612),hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613)) = U_5614
        | sP454(U_5613,U_5611,U_5614)
        | sP453(U_5613,U_5611,U_5612,U_5614)
        | ~ sP455(U_5613,U_5611,U_5612,U_5614) )
    & ! [U_5613,U_5611,U_5612,U_5614] :
        ( sP452(U_5613,U_5611,U_5612,U_5614)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5611),U_5612),hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613)) != U_5614
        | ~ sP455(U_5613,U_5611,U_5612,U_5614) )
    & ! [U_5613,U_5611,U_5612,U_5614] :
        ( sP455(U_5613,U_5611,U_5612,U_5614)
        | ~ class_Int_Onumber(U_5611)
        | ~ class_Fields_Ofield__inverse__zero(U_5611) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP452,sP453,sP454,sP455])],[f_1696_2]) ).

cnf(f_1696_4,plain,
    ( sP455(U_5613,U_5611,U_5612,U_5614)
    | ~ class_Int_Onumber(U_5611)
    | ~ class_Fields_Ofield__inverse__zero(U_5611) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_5,plain,
    ( sP452(U_5613,U_5611,U_5612,U_5614)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5611),U_5612),hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613)) != U_5614
    | ~ sP455(U_5613,U_5611,U_5612,U_5614) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_6,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5611),U_5612),hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613)) = U_5614
    | sP454(U_5613,U_5611,U_5614)
    | sP453(U_5613,U_5611,U_5612,U_5614)
    | ~ sP455(U_5613,U_5611,U_5612,U_5614) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_7,plain,
    ( U_5612 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5611),U_5614),hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613))
    | hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613) = c_Groups_Ozero__class_Ozero(U_5611)
    | ~ sP452(U_5613,U_5611,U_5612,U_5614) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_8,plain,
    ( U_5614 = c_Groups_Ozero__class_Ozero(U_5611)
    | hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613) != c_Groups_Ozero__class_Ozero(U_5611)
    | ~ sP452(U_5613,U_5611,U_5612,U_5614) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_9,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613) != c_Groups_Ozero__class_Ozero(U_5611)
    | ~ sP453(U_5613,U_5611,U_5612,U_5614) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_10,plain,
    ( U_5612 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5611),U_5614),hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613))
    | ~ sP453(U_5613,U_5611,U_5612,U_5614) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_11,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(U_5611),U_5613) = c_Groups_Ozero__class_Ozero(U_5611)
    | ~ sP454(U_5613,U_5611,U_5614) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

cnf(f_1696_12,plain,
    ( U_5614 != c_Groups_Ozero__class_Ozero(U_5611)
    | ~ sP454(U_5613,U_5611,U_5614) ),
    inference(clausify,[status(thm)],[f_1696_3]) ).

fof(f_1697_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_1697_2,plain,
    ! [U_5616,U_5615] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5615) = hAPP(c_Nat_OSuc,U_5616)
        | ~ 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_5615))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5616))))) )
      & ( 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_5615))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5616)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5615) != hAPP(c_Nat_OSuc,U_5616) ) ),
    inference(variable_rename,[status(thm)],[f_1697_1]) ).

fof(f_1697_3,plain,
    ( ! [U_5620,U_5618] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5618) = hAPP(c_Nat_OSuc,U_5620)
        | ~ 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_5618))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5620))))) )
    & ! [U_5619,U_5617] :
        ( 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_5617))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5619)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5617) != hAPP(c_Nat_OSuc,U_5619) ) ),
    inference(miniscope,[status(thm)],[f_1697_2]) ).

fof(f_1697_4,plain,
    ( ! [U_5620,U_5618] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5618) = hAPP(c_Nat_OSuc,U_5620)
        | ~ 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_5618))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5620))))) )
    & ! [U_5619,U_5617] :
        ( 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_5617))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5619)))))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5617) != hAPP(c_Nat_OSuc,U_5619) ) ),
    inference(definitional_conversion,[status(esa)],[f_1697_3]) ).

cnf(f_1697_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_5617))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5619)))))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5617) != hAPP(c_Nat_OSuc,U_5619) ),
    inference(clausify,[status(thm)],[f_1697_4]) ).

cnf(f_1697_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5618) = hAPP(c_Nat_OSuc,U_5620)
    | ~ 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_5618))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5620))))) ),
    inference(clausify,[status(thm)],[f_1697_4]) ).

fof(f_1698_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_1698_2,plain,
    ! [U_5622,U_5621] :
      ( ( hAPP(c_Nat_OSuc,U_5621) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5622)
        | ~ 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_5622))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5621))))) )
      & ( 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_5622))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5621)))))
        | hAPP(c_Nat_OSuc,U_5621) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5622) ) ),
    inference(variable_rename,[status(thm)],[f_1698_1]) ).

fof(f_1698_3,plain,
    ( ! [U_5626,U_5624] :
        ( hAPP(c_Nat_OSuc,U_5624) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5626)
        | ~ 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_5626))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5624))))) )
    & ! [U_5625,U_5623] :
        ( 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_5625))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5623)))))
        | hAPP(c_Nat_OSuc,U_5623) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5625) ) ),
    inference(miniscope,[status(thm)],[f_1698_2]) ).

fof(f_1698_4,plain,
    ( ! [U_5624,U_5626] :
        ( hAPP(c_Nat_OSuc,U_5624) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5626)
        | ~ 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_5626))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5624))))) )
    & ! [U_5623,U_5625] :
        ( 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_5625))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5623)))))
        | hAPP(c_Nat_OSuc,U_5623) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5625) ) ),
    inference(definitional_conversion,[status(esa)],[f_1698_3]) ).

cnf(f_1698_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_5625))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5623)))))
    | hAPP(c_Nat_OSuc,U_5623) != hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5625) ),
    inference(clausify,[status(thm)],[f_1698_4]) ).

cnf(f_1698_6,plain,
    ( hAPP(c_Nat_OSuc,U_5624) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5626)
    | ~ 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_5626))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5624))))) ),
    inference(clausify,[status(thm)],[f_1698_4]) ).

fof(f_1699_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_1699_2,plain,
    ! [U_5628,U_5627] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5627),U_5628),hAPP(c_Int_Onumber__class_Onumber__of(U_5627),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_5627)
      | ~ class_Int_Onumber__ring(U_5627)
      | ~ class_Fields_Ofield__inverse__zero(U_5627) ),
    inference(variable_rename,[status(thm)],[f_1699_1]) ).

fof(f_1699_3,plain,
    ! [U_5628,U_5627] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5627),U_5628),hAPP(c_Int_Onumber__class_Onumber__of(U_5627),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_5627)
      | ~ class_Int_Onumber__ring(U_5627)
      | ~ class_Fields_Ofield__inverse__zero(U_5627) ),
    inference(definitional_conversion,[status(esa)],[f_1699_2]) ).

cnf(f_1699_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5627),U_5628),hAPP(c_Int_Onumber__class_Onumber__of(U_5627),c_Int_OPls)) = c_Groups_Ozero__class_Ozero(U_5627)
    | ~ class_Int_Onumber__ring(U_5627)
    | ~ class_Fields_Ofield__inverse__zero(U_5627) ),
    inference(clausify,[status(thm)],[f_1699_3]) ).

fof(f_1700_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_1700_2,plain,
    ! [U_5630,U_5629] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5629),U_5630),hAPP(c_Int_Onumber__class_Onumber__of(U_5629),c_Int_OBit1(c_Int_OPls))) = U_5630
      | ~ class_Int_Onumber__ring(U_5629)
      | ~ class_Fields_Ofield(U_5629) ),
    inference(variable_rename,[status(thm)],[f_1700_1]) ).

fof(f_1700_3,plain,
    ! [U_5629,U_5630] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5629),U_5630),hAPP(c_Int_Onumber__class_Onumber__of(U_5629),c_Int_OBit1(c_Int_OPls))) = U_5630
      | ~ class_Int_Onumber__ring(U_5629)
      | ~ class_Fields_Ofield(U_5629) ),
    inference(definitional_conversion,[status(esa)],[f_1700_2]) ).

cnf(f_1700_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5629),U_5630),hAPP(c_Int_Onumber__class_Onumber__of(U_5629),c_Int_OBit1(c_Int_OPls))) = U_5630
    | ~ class_Int_Onumber__ring(U_5629)
    | ~ class_Fields_Ofield(U_5629) ),
    inference(clausify,[status(thm)],[f_1700_3]) ).

fof(f_1701_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_1701_2,plain,
    ! [U_5632,U_5631] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5631),U_5632),hAPP(c_Int_Onumber__class_Onumber__of(U_5631),c_Int_OBit1(c_Int_OPls))) = U_5632
      | ~ class_Int_Onumber__ring(U_5631)
      | ~ class_Fields_Ofield(U_5631) ),
    inference(variable_rename,[status(thm)],[f_1701_1]) ).

fof(f_1701_3,plain,
    ! [U_5631,U_5632] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5631),U_5632),hAPP(c_Int_Onumber__class_Onumber__of(U_5631),c_Int_OBit1(c_Int_OPls))) = U_5632
      | ~ class_Int_Onumber__ring(U_5631)
      | ~ class_Fields_Ofield(U_5631) ),
    inference(definitional_conversion,[status(esa)],[f_1701_2]) ).

cnf(f_1701_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5631),U_5632),hAPP(c_Int_Onumber__class_Onumber__of(U_5631),c_Int_OBit1(c_Int_OPls))) = U_5632
    | ~ class_Int_Onumber__ring(U_5631)
    | ~ class_Fields_Ofield(U_5631) ),
    inference(clausify,[status(thm)],[f_1701_3]) ).

fof(f_1702_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_1702_2,plain,
    ! [U_5634,U_5633] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5633),U_5634),hAPP(c_Int_Onumber__class_Onumber__of(U_5633),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5633),U_5634)
      | ~ class_Int_Onumber__ring(U_5633)
      | ~ class_Fields_Ofield__inverse__zero(U_5633) ),
    inference(variable_rename,[status(thm)],[f_1702_1]) ).

fof(f_1702_3,plain,
    ! [U_5633,U_5634] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5633),U_5634),hAPP(c_Int_Onumber__class_Onumber__of(U_5633),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5633),U_5634)
      | ~ class_Int_Onumber__ring(U_5633)
      | ~ class_Fields_Ofield__inverse__zero(U_5633) ),
    inference(definitional_conversion,[status(esa)],[f_1702_2]) ).

cnf(f_1702_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5633),U_5634),hAPP(c_Int_Onumber__class_Onumber__of(U_5633),c_Int_OMin)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5633),U_5634)
    | ~ class_Int_Onumber__ring(U_5633)
    | ~ class_Fields_Ofield__inverse__zero(U_5633) ),
    inference(clausify,[status(thm)],[f_1702_3]) ).

fof(f_1703_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_1703_2,plain,
    ! [U_5635] :
      ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5635)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5635)),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_5635))) )
      & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5635)) = 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_5635))) ) ),
    inference(variable_rename,[status(thm)],[f_1703_1]) ).

fof(f_1703_3,plain,
    ( ! [U_5637] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5637)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5637)),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_5637))) )
    & ! [U_5636] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5636)) = 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_5636))) ) ),
    inference(miniscope,[status(thm)],[f_1703_2]) ).

fof(f_1703_4,plain,
    ( ! [U_5637] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5637)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5637)),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_5637))) )
    & ! [U_5636] :
        ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5636)) = 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_5636))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1703_3]) ).

cnf(f_1703_5,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5636)) = 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_5636))) ),
    inference(clausify,[status(thm)],[f_1703_4]) ).

cnf(f_1703_6,plain,
    ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5637)) = hAPP(hAPP(c_HOL_OLet(tc_Nat_Onat,tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5637)),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_5637))) ),
    inference(clausify,[status(thm)],[f_1703_4]) ).

fof(f_1704_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_1704_2,plain,
    ! [U_5639,U_5638] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5638)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5639)))
        | ~ 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_5639))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5638)),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_5639))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5638)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5638)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5639))) ) ),
    inference(variable_rename,[status(thm)],[f_1704_1]) ).

fof(f_1704_3,plain,
    ( ! [U_5643,U_5641] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5641)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5643)))
        | ~ 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_5643))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5641)),c_Int_Onat))))) )
    & ! [U_5642,U_5640] :
        ( 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_5642))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5640)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5640)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5642))) ) ),
    inference(miniscope,[status(thm)],[f_1704_2]) ).

fof(f_1704_4,plain,
    ( ! [U_5641,U_5643] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5641)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5643)))
        | ~ 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_5643))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5641)),c_Int_Onat))))) )
    & ! [U_5642,U_5640] :
        ( 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_5642))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5640)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5640)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5642))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1704_3]) ).

cnf(f_1704_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_5642))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5640)),c_Int_Onat)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5640)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5642))) ),
    inference(clausify,[status(thm)],[f_1704_4]) ).

cnf(f_1704_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5641)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5643)))
    | ~ 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_5643))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5641)),c_Int_Onat))))) ),
    inference(clausify,[status(thm)],[f_1704_4]) ).

fof(f_1705_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_1705_2,plain,
    ! [U_5645,U_5644] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5644)),hAPP(c_Nat_OSuc,U_5645)))
        | ~ 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_5644))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5645)))) )
      & ( 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_5644))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5645))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5644)),hAPP(c_Nat_OSuc,U_5645))) ) ),
    inference(variable_rename,[status(thm)],[f_1705_1]) ).

fof(f_1705_3,plain,
    ( ! [U_5649,U_5647] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5647)),hAPP(c_Nat_OSuc,U_5649)))
        | ~ 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_5647))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5649)))) )
    & ! [U_5648,U_5646] :
        ( 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_5646))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5648))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5646)),hAPP(c_Nat_OSuc,U_5648))) ) ),
    inference(miniscope,[status(thm)],[f_1705_2]) ).

fof(f_1705_4,plain,
    ( ! [U_5649,U_5647] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5647)),hAPP(c_Nat_OSuc,U_5649)))
        | ~ 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_5647))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5649)))) )
    & ! [U_5648,U_5646] :
        ( 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_5646))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5648))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5646)),hAPP(c_Nat_OSuc,U_5648))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1705_3]) ).

cnf(f_1705_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_5646))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5648))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5646)),hAPP(c_Nat_OSuc,U_5648))) ),
    inference(clausify,[status(thm)],[f_1705_4]) ).

cnf(f_1705_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5647)),hAPP(c_Nat_OSuc,U_5649)))
    | ~ 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_5647))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5649)))) ),
    inference(clausify,[status(thm)],[f_1705_4]) ).

fof(f_1706_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_1706_2,plain,
    ! [U_5651,U_5650] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5650)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5651)))
        | ~ 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_5651))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5650)),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_5651))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5650)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5650)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5651))) ) ),
    inference(variable_rename,[status(thm)],[f_1706_1]) ).

fof(f_1706_3,plain,
    ( ! [U_5655,U_5653] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5653)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5655)))
        | ~ 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_5655))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5653)),c_Int_Onat))))) )
    & ! [U_5654,U_5652] :
        ( 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_5654))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5652)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5652)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5654))) ) ),
    inference(miniscope,[status(thm)],[f_1706_2]) ).

fof(f_1706_4,plain,
    ( ! [U_5653,U_5655] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5653)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5655)))
        | ~ 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_5655))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5653)),c_Int_Onat))))) )
    & ! [U_5654,U_5652] :
        ( 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_5654))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5652)),c_Int_Onat)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5652)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5654))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1706_3]) ).

cnf(f_1706_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_5654))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5652)),c_Int_Onat)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5652)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5654))) ),
    inference(clausify,[status(thm)],[f_1706_4]) ).

cnf(f_1706_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_5653)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5655)))
    | ~ 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_5655))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5653)),c_Int_Onat))))) ),
    inference(clausify,[status(thm)],[f_1706_4]) ).

fof(f_1707_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_1707_2,plain,
    ! [U_5657,U_5656] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5656)),hAPP(c_Nat_OSuc,U_5657)))
        | ~ 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_5656))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5657)))) )
      & ( 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_5656))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5657))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5656)),hAPP(c_Nat_OSuc,U_5657))) ) ),
    inference(variable_rename,[status(thm)],[f_1707_1]) ).

fof(f_1707_3,plain,
    ( ! [U_5661,U_5659] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5659)),hAPP(c_Nat_OSuc,U_5661)))
        | ~ 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_5659))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5661)))) )
    & ! [U_5660,U_5658] :
        ( 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_5658))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5660))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5658)),hAPP(c_Nat_OSuc,U_5660))) ) ),
    inference(miniscope,[status(thm)],[f_1707_2]) ).

fof(f_1707_4,plain,
    ( ! [U_5659,U_5661] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5659)),hAPP(c_Nat_OSuc,U_5661)))
        | ~ 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_5659))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5661)))) )
    & ! [U_5660,U_5658] :
        ( 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_5658))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5660))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5658)),hAPP(c_Nat_OSuc,U_5660))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1707_3]) ).

cnf(f_1707_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_5658))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5660))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5658)),hAPP(c_Nat_OSuc,U_5660))) ),
    inference(clausify,[status(thm)],[f_1707_4]) ).

cnf(f_1707_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_5659)),hAPP(c_Nat_OSuc,U_5661)))
    | ~ 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_5659))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_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_5661)))) ),
    inference(clausify,[status(thm)],[f_1707_4]) ).

fof(f_1708_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_1708_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_1708_1]) ).

cnf(f_1708_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_1708_2]) ).

fof(f_1709_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_1709_2,plain,
    ! [U_5664,U_5663,U_5662] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5662),U_5664),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5663))) = c_Groups_Oone__class_Oone(U_5662)
          | 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_5663))) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5662),U_5664),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5663))) = hAPP(hAPP(c_HOL_OLet(U_5662,U_5662),hAPP(hAPP(c_Power_Opower__class_Opower(U_5662),U_5664),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5663))),hAPP(hAPP(c_COMBS(U_5662,U_5662,U_5662),hAPP(hAPP(c_COMBB(U_5662,tc_fun(U_5662,U_5662),U_5662),c_Groups_Otimes__class_Otimes(U_5662)),hAPP(c_Groups_Otimes__class_Otimes(U_5662),U_5664))),c_COMBI(U_5662)))
          | ~ 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_5663))) ) )
      | ~ class_Int_Onumber__ring(U_5662) ),
    inference(variable_rename,[status(thm)],[f_1709_1]) ).

fof(f_1709_3,plain,
    ( ! [U_5662,U_5663,U_5664] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5662),U_5664),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5663))) = c_Groups_Oone__class_Oone(U_5662)
        | 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_5663)))
        | ~ sP456(U_5662,U_5663,U_5664) )
    & ! [U_5662,U_5663,U_5664] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5662),U_5664),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5663))) = hAPP(hAPP(c_HOL_OLet(U_5662,U_5662),hAPP(hAPP(c_Power_Opower__class_Opower(U_5662),U_5664),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5663))),hAPP(hAPP(c_COMBS(U_5662,U_5662,U_5662),hAPP(hAPP(c_COMBB(U_5662,tc_fun(U_5662,U_5662),U_5662),c_Groups_Otimes__class_Otimes(U_5662)),hAPP(c_Groups_Otimes__class_Otimes(U_5662),U_5664))),c_COMBI(U_5662)))
        | ~ 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_5663)))
        | ~ sP456(U_5662,U_5663,U_5664) )
    & ! [U_5662,U_5663,U_5664] :
        ( sP456(U_5662,U_5663,U_5664)
        | ~ class_Int_Onumber__ring(U_5662) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP456])],[f_1709_2]) ).

cnf(f_1709_4,plain,
    ( sP456(U_5662,U_5663,U_5664)
    | ~ class_Int_Onumber__ring(U_5662) ),
    inference(clausify,[status(thm)],[f_1709_3]) ).

cnf(f_1709_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5662),U_5664),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5663))) = hAPP(hAPP(c_HOL_OLet(U_5662,U_5662),hAPP(hAPP(c_Power_Opower__class_Opower(U_5662),U_5664),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5663))),hAPP(hAPP(c_COMBS(U_5662,U_5662,U_5662),hAPP(hAPP(c_COMBB(U_5662,tc_fun(U_5662,U_5662),U_5662),c_Groups_Otimes__class_Otimes(U_5662)),hAPP(c_Groups_Otimes__class_Otimes(U_5662),U_5664))),c_COMBI(U_5662)))
    | ~ 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_5663)))
    | ~ sP456(U_5662,U_5663,U_5664) ),
    inference(clausify,[status(thm)],[f_1709_3]) ).

cnf(f_1709_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5662),U_5664),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5663))) = c_Groups_Oone__class_Oone(U_5662)
    | 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_5663)))
    | ~ sP456(U_5662,U_5663,U_5664) ),
    inference(clausify,[status(thm)],[f_1709_3]) ).

fof(f_1710_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_1710_2,plain,
    ! [U_5668,U_5667,U_5666,U_5665] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5665),U_5666),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))),U_5668))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),c_Groups_Ozero__class_Ozero(U_5665)),U_5668))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667)),c_Groups_Ozero__class_Ozero(U_5665))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5665),U_5668),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))),U_5666))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667)),c_Groups_Ozero__class_Ozero(U_5665))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),c_Groups_Ozero__class_Ozero(U_5665)),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),U_5666),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5665),U_5668),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),c_Groups_Ozero__class_Ozero(U_5665)),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),c_Groups_Ozero__class_Ozero(U_5665)),U_5668))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667)),c_Groups_Ozero__class_Ozero(U_5665))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5665),U_5668),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))),U_5666))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667)),c_Groups_Ozero__class_Ozero(U_5665))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),c_Groups_Ozero__class_Ozero(U_5665)),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),U_5666),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5665),U_5668),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),c_Groups_Ozero__class_Ozero(U_5665)),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5665),U_5666),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))),U_5668)) ) )
      | ~ class_Int_Onumber(U_5665)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5665) ),
    inference(variable_rename,[status(thm)],[f_1710_1]) ).

fof(f_1710_3,plain,
    ( ! [U_5665,U_5667,U_5668] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),c_Groups_Ozero__class_Ozero(U_5665)),U_5668))
        | ~ sP461(U_5665,U_5667,U_5668) )
    & ! [U_5665,U_5667,U_5668] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667)),c_Groups_Ozero__class_Ozero(U_5665)))
        | ~ sP461(U_5665,U_5667,U_5668) )
    & ! [U_5665,U_5666,U_5667,U_5668] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5665),U_5668),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))),U_5666))
        | ~ sP460(U_5665,U_5666,U_5667,U_5668) )
    & ! [U_5665,U_5666,U_5667,U_5668] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667)),c_Groups_Ozero__class_Ozero(U_5665)))
        | ~ sP460(U_5665,U_5666,U_5667,U_5668) )
    & ! [U_5665,U_5666,U_5667,U_5668] :
        ( sP461(U_5665,U_5667,U_5668)
        | sP460(U_5665,U_5666,U_5667,U_5668)
        | ~ sP462(U_5665,U_5666,U_5667,U_5668) )
    & ! [U_5665,U_5666,U_5667,U_5668] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),c_Groups_Ozero__class_Ozero(U_5665)),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667)))
        | ~ sP462(U_5665,U_5666,U_5667,U_5668) )
    & ! [U_5665,U_5666,U_5667,U_5668] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),U_5666),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5665),U_5668),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))))
        | ~ sP459(U_5665,U_5666,U_5667,U_5668) )
    & ! [U_5665,U_5666,U_5667,U_5668] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),c_Groups_Ozero__class_Ozero(U_5665)),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667)))
        | ~ sP459(U_5665,U_5666,U_5667,U_5668) )
    & ! [U_5665,U_5666,U_5667,U_5668] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),c_Groups_Ozero__class_Ozero(U_5665)),U_5668))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667)),c_Groups_Ozero__class_Ozero(U_5665)))
        | ~ sP457(U_5665,U_5666,U_5667,U_5668) )
    & ! [U_5665,U_5666,U_5667,U_5668] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5665),U_5668),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))),U_5666))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667)),c_Groups_Ozero__class_Ozero(U_5665)))
        | ~ sP457(U_5665,U_5666,U_5667,U_5668) )
    & ! [U_5665,U_5666,U_5667,U_5668] :
        ( sP457(U_5665,U_5666,U_5667,U_5668)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),c_Groups_Ozero__class_Ozero(U_5665)),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667)))
        | ~ sP458(U_5665,U_5666,U_5667,U_5668) )
    & ! [U_5665,U_5666,U_5667,U_5668] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),U_5666),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5665),U_5668),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),c_Groups_Ozero__class_Ozero(U_5665)),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667)))
        | ~ sP458(U_5665,U_5666,U_5667,U_5668) )
    & ! [U_5665,U_5666,U_5667,U_5668] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5665),U_5666),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))),U_5668))
        | sP462(U_5665,U_5666,U_5667,U_5668)
        | sP459(U_5665,U_5666,U_5667,U_5668)
        | ~ sP463(U_5665,U_5666,U_5667,U_5668) )
    & ! [U_5665,U_5666,U_5667,U_5668] :
        ( sP458(U_5665,U_5666,U_5667,U_5668)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5665),U_5666),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))),U_5668))
        | ~ sP463(U_5665,U_5666,U_5667,U_5668) )
    & ! [U_5665,U_5666,U_5667,U_5668] :
        ( sP463(U_5665,U_5666,U_5667,U_5668)
        | ~ class_Int_Onumber(U_5665)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5665) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP457,sP458,sP459,sP460,sP461,sP462,sP463])],[f_1710_2]) ).

cnf(f_1710_4,plain,
    ( sP463(U_5665,U_5666,U_5667,U_5668)
    | ~ class_Int_Onumber(U_5665)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5665) ),
    inference(clausify,[status(thm)],[f_1710_3]) ).

cnf(f_1710_5,plain,
    ( sP458(U_5665,U_5666,U_5667,U_5668)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5665),U_5666),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))),U_5668))
    | ~ sP463(U_5665,U_5666,U_5667,U_5668) ),
    inference(clausify,[status(thm)],[f_1710_3]) ).

cnf(f_1710_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5665),U_5666),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))),U_5668))
    | sP462(U_5665,U_5666,U_5667,U_5668)
    | sP459(U_5665,U_5666,U_5667,U_5668)
    | ~ sP463(U_5665,U_5666,U_5667,U_5668) ),
    inference(clausify,[status(thm)],[f_1710_3]) ).

cnf(f_1710_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),U_5666),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5665),U_5668),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),c_Groups_Ozero__class_Ozero(U_5665)),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667)))
    | ~ sP458(U_5665,U_5666,U_5667,U_5668) ),
    inference(clausify,[status(thm)],[f_1710_3]) ).

cnf(f_1710_8,plain,
    ( sP457(U_5665,U_5666,U_5667,U_5668)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),c_Groups_Ozero__class_Ozero(U_5665)),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667)))
    | ~ sP458(U_5665,U_5666,U_5667,U_5668) ),
    inference(clausify,[status(thm)],[f_1710_3]) ).

cnf(f_1710_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5665),U_5668),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))),U_5666))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667)),c_Groups_Ozero__class_Ozero(U_5665)))
    | ~ sP457(U_5665,U_5666,U_5667,U_5668) ),
    inference(clausify,[status(thm)],[f_1710_3]) ).

cnf(f_1710_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),c_Groups_Ozero__class_Ozero(U_5665)),U_5668))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667)),c_Groups_Ozero__class_Ozero(U_5665)))
    | ~ sP457(U_5665,U_5666,U_5667,U_5668) ),
    inference(clausify,[status(thm)],[f_1710_3]) ).

cnf(f_1710_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),c_Groups_Ozero__class_Ozero(U_5665)),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667)))
    | ~ sP459(U_5665,U_5666,U_5667,U_5668) ),
    inference(clausify,[status(thm)],[f_1710_3]) ).

cnf(f_1710_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),U_5666),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5665),U_5668),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))))
    | ~ sP459(U_5665,U_5666,U_5667,U_5668) ),
    inference(clausify,[status(thm)],[f_1710_3]) ).

cnf(f_1710_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),c_Groups_Ozero__class_Ozero(U_5665)),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667)))
    | ~ sP462(U_5665,U_5666,U_5667,U_5668) ),
    inference(clausify,[status(thm)],[f_1710_3]) ).

cnf(f_1710_14,plain,
    ( sP461(U_5665,U_5667,U_5668)
    | sP460(U_5665,U_5666,U_5667,U_5668)
    | ~ sP462(U_5665,U_5666,U_5667,U_5668) ),
    inference(clausify,[status(thm)],[f_1710_3]) ).

cnf(f_1710_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667)),c_Groups_Ozero__class_Ozero(U_5665)))
    | ~ sP460(U_5665,U_5666,U_5667,U_5668) ),
    inference(clausify,[status(thm)],[f_1710_3]) ).

cnf(f_1710_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5665),U_5668),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667))),U_5666))
    | ~ sP460(U_5665,U_5666,U_5667,U_5668) ),
    inference(clausify,[status(thm)],[f_1710_3]) ).

cnf(f_1710_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),hAPP(c_Int_Onumber__class_Onumber__of(U_5665),U_5667)),c_Groups_Ozero__class_Ozero(U_5665)))
    | ~ sP461(U_5665,U_5667,U_5668) ),
    inference(clausify,[status(thm)],[f_1710_3]) ).

cnf(f_1710_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5665),c_Groups_Ozero__class_Ozero(U_5665)),U_5668))
    | ~ sP461(U_5665,U_5667,U_5668) ),
    inference(clausify,[status(thm)],[f_1710_3]) ).

fof(f_1711_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_1711_2,plain,
    ! [U_5672,U_5671,U_5670,U_5669] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5669),U_5670),U_5671)),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),c_Groups_Ozero__class_Ozero(U_5669)),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),U_5671),c_Groups_Ozero__class_Ozero(U_5669))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5669),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)),U_5671)),U_5670))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),U_5671),c_Groups_Ozero__class_Ozero(U_5669))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),c_Groups_Ozero__class_Ozero(U_5669)),U_5671)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),U_5670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5669),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)),U_5671)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),c_Groups_Ozero__class_Ozero(U_5669)),U_5671)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),c_Groups_Ozero__class_Ozero(U_5669)),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),U_5671),c_Groups_Ozero__class_Ozero(U_5669))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5669),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)),U_5671)),U_5670))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),U_5671),c_Groups_Ozero__class_Ozero(U_5669))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),c_Groups_Ozero__class_Ozero(U_5669)),U_5671)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),U_5670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5669),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)),U_5671)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),c_Groups_Ozero__class_Ozero(U_5669)),U_5671)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5669),U_5670),U_5671)),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672))) ) )
      | ~ class_Int_Onumber(U_5669)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5669) ),
    inference(variable_rename,[status(thm)],[f_1711_1]) ).

fof(f_1711_3,plain,
    ( ! [U_5671,U_5669,U_5672] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),c_Groups_Ozero__class_Ozero(U_5669)),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)))
        | ~ sP468(U_5671,U_5669,U_5672) )
    & ! [U_5671,U_5669,U_5672] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),U_5671),c_Groups_Ozero__class_Ozero(U_5669)))
        | ~ sP468(U_5671,U_5669,U_5672) )
    & ! [U_5671,U_5669,U_5672,U_5670] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5669),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)),U_5671)),U_5670))
        | ~ sP467(U_5671,U_5669,U_5672,U_5670) )
    & ! [U_5671,U_5669,U_5672,U_5670] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),U_5671),c_Groups_Ozero__class_Ozero(U_5669)))
        | ~ sP467(U_5671,U_5669,U_5672,U_5670) )
    & ! [U_5671,U_5669,U_5672,U_5670] :
        ( sP468(U_5671,U_5669,U_5672)
        | sP467(U_5671,U_5669,U_5672,U_5670)
        | ~ sP469(U_5671,U_5669,U_5672,U_5670) )
    & ! [U_5671,U_5669,U_5672,U_5670] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),c_Groups_Ozero__class_Ozero(U_5669)),U_5671))
        | ~ sP469(U_5671,U_5669,U_5672,U_5670) )
    & ! [U_5671,U_5669,U_5672,U_5670] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),U_5670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5669),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)),U_5671)))
        | ~ sP466(U_5671,U_5669,U_5672,U_5670) )
    & ! [U_5671,U_5669,U_5672,U_5670] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),c_Groups_Ozero__class_Ozero(U_5669)),U_5671))
        | ~ sP466(U_5671,U_5669,U_5672,U_5670) )
    & ! [U_5671,U_5669,U_5672,U_5670] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),c_Groups_Ozero__class_Ozero(U_5669)),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),U_5671),c_Groups_Ozero__class_Ozero(U_5669)))
        | ~ sP464(U_5671,U_5669,U_5672,U_5670) )
    & ! [U_5671,U_5669,U_5672,U_5670] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5669),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)),U_5671)),U_5670))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),U_5671),c_Groups_Ozero__class_Ozero(U_5669)))
        | ~ sP464(U_5671,U_5669,U_5672,U_5670) )
    & ! [U_5671,U_5669,U_5672,U_5670] :
        ( sP464(U_5671,U_5669,U_5672,U_5670)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),c_Groups_Ozero__class_Ozero(U_5669)),U_5671))
        | ~ sP465(U_5671,U_5669,U_5672,U_5670) )
    & ! [U_5671,U_5669,U_5672,U_5670] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),U_5670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5669),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)),U_5671)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),c_Groups_Ozero__class_Ozero(U_5669)),U_5671))
        | ~ sP465(U_5671,U_5669,U_5672,U_5670) )
    & ! [U_5671,U_5669,U_5672,U_5670] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5669),U_5670),U_5671)),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)))
        | sP469(U_5671,U_5669,U_5672,U_5670)
        | sP466(U_5671,U_5669,U_5672,U_5670)
        | ~ sP470(U_5671,U_5669,U_5672,U_5670) )
    & ! [U_5671,U_5669,U_5672,U_5670] :
        ( sP465(U_5671,U_5669,U_5672,U_5670)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5669),U_5670),U_5671)),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)))
        | ~ sP470(U_5671,U_5669,U_5672,U_5670) )
    & ! [U_5671,U_5669,U_5672,U_5670] :
        ( sP470(U_5671,U_5669,U_5672,U_5670)
        | ~ class_Int_Onumber(U_5669)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5669) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP464,sP465,sP466,sP467,sP468,sP469,sP470])],[f_1711_2]) ).

cnf(f_1711_4,plain,
    ( sP470(U_5671,U_5669,U_5672,U_5670)
    | ~ class_Int_Onumber(U_5669)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5669) ),
    inference(clausify,[status(thm)],[f_1711_3]) ).

cnf(f_1711_5,plain,
    ( sP465(U_5671,U_5669,U_5672,U_5670)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5669),U_5670),U_5671)),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)))
    | ~ sP470(U_5671,U_5669,U_5672,U_5670) ),
    inference(clausify,[status(thm)],[f_1711_3]) ).

cnf(f_1711_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5669),U_5670),U_5671)),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)))
    | sP469(U_5671,U_5669,U_5672,U_5670)
    | sP466(U_5671,U_5669,U_5672,U_5670)
    | ~ sP470(U_5671,U_5669,U_5672,U_5670) ),
    inference(clausify,[status(thm)],[f_1711_3]) ).

cnf(f_1711_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),U_5670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5669),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)),U_5671)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),c_Groups_Ozero__class_Ozero(U_5669)),U_5671))
    | ~ sP465(U_5671,U_5669,U_5672,U_5670) ),
    inference(clausify,[status(thm)],[f_1711_3]) ).

cnf(f_1711_8,plain,
    ( sP464(U_5671,U_5669,U_5672,U_5670)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),c_Groups_Ozero__class_Ozero(U_5669)),U_5671))
    | ~ sP465(U_5671,U_5669,U_5672,U_5670) ),
    inference(clausify,[status(thm)],[f_1711_3]) ).

cnf(f_1711_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5669),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)),U_5671)),U_5670))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),U_5671),c_Groups_Ozero__class_Ozero(U_5669)))
    | ~ sP464(U_5671,U_5669,U_5672,U_5670) ),
    inference(clausify,[status(thm)],[f_1711_3]) ).

cnf(f_1711_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),c_Groups_Ozero__class_Ozero(U_5669)),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),U_5671),c_Groups_Ozero__class_Ozero(U_5669)))
    | ~ sP464(U_5671,U_5669,U_5672,U_5670) ),
    inference(clausify,[status(thm)],[f_1711_3]) ).

cnf(f_1711_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),c_Groups_Ozero__class_Ozero(U_5669)),U_5671))
    | ~ sP466(U_5671,U_5669,U_5672,U_5670) ),
    inference(clausify,[status(thm)],[f_1711_3]) ).

cnf(f_1711_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),U_5670),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5669),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)),U_5671)))
    | ~ sP466(U_5671,U_5669,U_5672,U_5670) ),
    inference(clausify,[status(thm)],[f_1711_3]) ).

cnf(f_1711_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),c_Groups_Ozero__class_Ozero(U_5669)),U_5671))
    | ~ sP469(U_5671,U_5669,U_5672,U_5670) ),
    inference(clausify,[status(thm)],[f_1711_3]) ).

cnf(f_1711_14,plain,
    ( sP468(U_5671,U_5669,U_5672)
    | sP467(U_5671,U_5669,U_5672,U_5670)
    | ~ sP469(U_5671,U_5669,U_5672,U_5670) ),
    inference(clausify,[status(thm)],[f_1711_3]) ).

cnf(f_1711_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),U_5671),c_Groups_Ozero__class_Ozero(U_5669)))
    | ~ sP467(U_5671,U_5669,U_5672,U_5670) ),
    inference(clausify,[status(thm)],[f_1711_3]) ).

cnf(f_1711_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5669),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)),U_5671)),U_5670))
    | ~ sP467(U_5671,U_5669,U_5672,U_5670) ),
    inference(clausify,[status(thm)],[f_1711_3]) ).

cnf(f_1711_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),U_5671),c_Groups_Ozero__class_Ozero(U_5669)))
    | ~ sP468(U_5671,U_5669,U_5672) ),
    inference(clausify,[status(thm)],[f_1711_3]) ).

cnf(f_1711_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5669),c_Groups_Ozero__class_Ozero(U_5669)),hAPP(c_Int_Onumber__class_Onumber__of(U_5669),U_5672)))
    | ~ sP468(U_5671,U_5669,U_5672) ),
    inference(clausify,[status(thm)],[f_1711_3]) ).

fof(f_1712_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_1712_2,plain,
    ! [U_5676,U_5675,U_5674,U_5673] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5673),U_5675),U_5676)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),c_Groups_Ozero__class_Ozero(U_5673)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),U_5676),c_Groups_Ozero__class_Ozero(U_5673))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),U_5675),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),U_5676)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),U_5676),c_Groups_Ozero__class_Ozero(U_5673))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),c_Groups_Ozero__class_Ozero(U_5673)),U_5676)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),U_5676)),U_5675))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),c_Groups_Ozero__class_Ozero(U_5673)),U_5676)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),c_Groups_Ozero__class_Ozero(U_5673)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),U_5676),c_Groups_Ozero__class_Ozero(U_5673))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),U_5675),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),U_5676)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),U_5676),c_Groups_Ozero__class_Ozero(U_5673))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),c_Groups_Ozero__class_Ozero(U_5673)),U_5676)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),U_5676)),U_5675))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),c_Groups_Ozero__class_Ozero(U_5673)),U_5676)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5673),U_5675),U_5676))) ) )
      | ~ class_Int_Onumber(U_5673)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5673) ),
    inference(variable_rename,[status(thm)],[f_1712_1]) ).

fof(f_1712_3,plain,
    ( ! [U_5674,U_5676,U_5673] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),c_Groups_Ozero__class_Ozero(U_5673)))
        | ~ sP475(U_5674,U_5676,U_5673) )
    & ! [U_5674,U_5676,U_5673] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),U_5676),c_Groups_Ozero__class_Ozero(U_5673)))
        | ~ sP475(U_5674,U_5676,U_5673) )
    & ! [U_5674,U_5675,U_5676,U_5673] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),U_5675),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),U_5676)))
        | ~ sP474(U_5674,U_5675,U_5676,U_5673) )
    & ! [U_5674,U_5675,U_5676,U_5673] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),U_5676),c_Groups_Ozero__class_Ozero(U_5673)))
        | ~ sP474(U_5674,U_5675,U_5676,U_5673) )
    & ! [U_5674,U_5675,U_5676,U_5673] :
        ( sP475(U_5674,U_5676,U_5673)
        | sP474(U_5674,U_5675,U_5676,U_5673)
        | ~ sP476(U_5674,U_5675,U_5676,U_5673) )
    & ! [U_5674,U_5675,U_5676,U_5673] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),c_Groups_Ozero__class_Ozero(U_5673)),U_5676))
        | ~ sP476(U_5674,U_5675,U_5676,U_5673) )
    & ! [U_5674,U_5675,U_5676,U_5673] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),U_5676)),U_5675))
        | ~ sP473(U_5674,U_5675,U_5676,U_5673) )
    & ! [U_5674,U_5675,U_5676,U_5673] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),c_Groups_Ozero__class_Ozero(U_5673)),U_5676))
        | ~ sP473(U_5674,U_5675,U_5676,U_5673) )
    & ! [U_5674,U_5675,U_5676,U_5673] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),c_Groups_Ozero__class_Ozero(U_5673)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),U_5676),c_Groups_Ozero__class_Ozero(U_5673)))
        | ~ sP471(U_5674,U_5675,U_5676,U_5673) )
    & ! [U_5674,U_5675,U_5676,U_5673] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),U_5675),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),U_5676)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),U_5676),c_Groups_Ozero__class_Ozero(U_5673)))
        | ~ sP471(U_5674,U_5675,U_5676,U_5673) )
    & ! [U_5674,U_5675,U_5676,U_5673] :
        ( sP471(U_5674,U_5675,U_5676,U_5673)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),c_Groups_Ozero__class_Ozero(U_5673)),U_5676))
        | ~ sP472(U_5674,U_5675,U_5676,U_5673) )
    & ! [U_5674,U_5675,U_5676,U_5673] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),U_5676)),U_5675))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),c_Groups_Ozero__class_Ozero(U_5673)),U_5676))
        | ~ sP472(U_5674,U_5675,U_5676,U_5673) )
    & ! [U_5674,U_5675,U_5676,U_5673] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5673),U_5675),U_5676)))
        | sP476(U_5674,U_5675,U_5676,U_5673)
        | sP473(U_5674,U_5675,U_5676,U_5673)
        | ~ sP477(U_5674,U_5675,U_5676,U_5673) )
    & ! [U_5674,U_5675,U_5676,U_5673] :
        ( sP472(U_5674,U_5675,U_5676,U_5673)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5673),U_5675),U_5676)))
        | ~ sP477(U_5674,U_5675,U_5676,U_5673) )
    & ! [U_5674,U_5675,U_5676,U_5673] :
        ( sP477(U_5674,U_5675,U_5676,U_5673)
        | ~ class_Int_Onumber(U_5673)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5673) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP471,sP472,sP473,sP474,sP475,sP476,sP477])],[f_1712_2]) ).

cnf(f_1712_4,plain,
    ( sP477(U_5674,U_5675,U_5676,U_5673)
    | ~ class_Int_Onumber(U_5673)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5673) ),
    inference(clausify,[status(thm)],[f_1712_3]) ).

cnf(f_1712_5,plain,
    ( sP472(U_5674,U_5675,U_5676,U_5673)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5673),U_5675),U_5676)))
    | ~ sP477(U_5674,U_5675,U_5676,U_5673) ),
    inference(clausify,[status(thm)],[f_1712_3]) ).

cnf(f_1712_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5673),U_5675),U_5676)))
    | sP476(U_5674,U_5675,U_5676,U_5673)
    | sP473(U_5674,U_5675,U_5676,U_5673)
    | ~ sP477(U_5674,U_5675,U_5676,U_5673) ),
    inference(clausify,[status(thm)],[f_1712_3]) ).

cnf(f_1712_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),U_5676)),U_5675))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),c_Groups_Ozero__class_Ozero(U_5673)),U_5676))
    | ~ sP472(U_5674,U_5675,U_5676,U_5673) ),
    inference(clausify,[status(thm)],[f_1712_3]) ).

cnf(f_1712_8,plain,
    ( sP471(U_5674,U_5675,U_5676,U_5673)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),c_Groups_Ozero__class_Ozero(U_5673)),U_5676))
    | ~ sP472(U_5674,U_5675,U_5676,U_5673) ),
    inference(clausify,[status(thm)],[f_1712_3]) ).

cnf(f_1712_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),U_5675),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),U_5676)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),U_5676),c_Groups_Ozero__class_Ozero(U_5673)))
    | ~ sP471(U_5674,U_5675,U_5676,U_5673) ),
    inference(clausify,[status(thm)],[f_1712_3]) ).

cnf(f_1712_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),c_Groups_Ozero__class_Ozero(U_5673)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),U_5676),c_Groups_Ozero__class_Ozero(U_5673)))
    | ~ sP471(U_5674,U_5675,U_5676,U_5673) ),
    inference(clausify,[status(thm)],[f_1712_3]) ).

cnf(f_1712_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),c_Groups_Ozero__class_Ozero(U_5673)),U_5676))
    | ~ sP473(U_5674,U_5675,U_5676,U_5673) ),
    inference(clausify,[status(thm)],[f_1712_3]) ).

cnf(f_1712_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),U_5676)),U_5675))
    | ~ sP473(U_5674,U_5675,U_5676,U_5673) ),
    inference(clausify,[status(thm)],[f_1712_3]) ).

cnf(f_1712_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),c_Groups_Ozero__class_Ozero(U_5673)),U_5676))
    | ~ sP476(U_5674,U_5675,U_5676,U_5673) ),
    inference(clausify,[status(thm)],[f_1712_3]) ).

cnf(f_1712_14,plain,
    ( sP475(U_5674,U_5676,U_5673)
    | sP474(U_5674,U_5675,U_5676,U_5673)
    | ~ sP476(U_5674,U_5675,U_5676,U_5673) ),
    inference(clausify,[status(thm)],[f_1712_3]) ).

cnf(f_1712_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),U_5676),c_Groups_Ozero__class_Ozero(U_5673)))
    | ~ sP474(U_5674,U_5675,U_5676,U_5673) ),
    inference(clausify,[status(thm)],[f_1712_3]) ).

cnf(f_1712_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),U_5675),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),U_5676)))
    | ~ sP474(U_5674,U_5675,U_5676,U_5673) ),
    inference(clausify,[status(thm)],[f_1712_3]) ).

cnf(f_1712_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),U_5676),c_Groups_Ozero__class_Ozero(U_5673)))
    | ~ sP475(U_5674,U_5676,U_5673) ),
    inference(clausify,[status(thm)],[f_1712_3]) ).

cnf(f_1712_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5673),hAPP(c_Int_Onumber__class_Onumber__of(U_5673),U_5674)),c_Groups_Ozero__class_Ozero(U_5673)))
    | ~ sP475(U_5674,U_5676,U_5673) ),
    inference(clausify,[status(thm)],[f_1712_3]) ).

fof(f_1713_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_1713_2,plain,
    ! [U_5680,U_5679,U_5678,U_5677] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),U_5678),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5677),U_5679),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680))))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),U_5678),c_Groups_Ozero__class_Ozero(U_5677)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680)),c_Groups_Ozero__class_Ozero(U_5677))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),U_5679),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5677),U_5678),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680)),c_Groups_Ozero__class_Ozero(U_5677))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),c_Groups_Ozero__class_Ozero(U_5677)),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5677),U_5678),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680))),U_5679))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),c_Groups_Ozero__class_Ozero(U_5677)),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),U_5678),c_Groups_Ozero__class_Ozero(U_5677)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680)),c_Groups_Ozero__class_Ozero(U_5677))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),U_5679),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5677),U_5678),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680))))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680)),c_Groups_Ozero__class_Ozero(U_5677))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),c_Groups_Ozero__class_Ozero(U_5677)),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5677),U_5678),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680))),U_5679))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),c_Groups_Ozero__class_Ozero(U_5677)),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),U_5678),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5677),U_5679),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680)))) ) )
      | ~ class_Int_Onumber(U_5677)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5677) ),
    inference(variable_rename,[status(thm)],[f_1713_1]) ).

fof(f_1713_3,plain,
    ( ! [U_5680,U_5678,U_5677] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),U_5678),c_Groups_Ozero__class_Ozero(U_5677)))
        | ~ sP482(U_5680,U_5678,U_5677) )
    & ! [U_5680,U_5678,U_5677] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680)),c_Groups_Ozero__class_Ozero(U_5677)))
        | ~ sP482(U_5680,U_5678,U_5677) )
    & ! [U_5679,U_5680,U_5678,U_5677] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),U_5679),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5677),U_5678),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680))))
        | ~ sP481(U_5679,U_5680,U_5678,U_5677) )
    & ! [U_5679,U_5680,U_5678,U_5677] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680)),c_Groups_Ozero__class_Ozero(U_5677)))
        | ~ sP481(U_5679,U_5680,U_5678,U_5677) )
    & ! [U_5679,U_5680,U_5678,U_5677] :
        ( sP482(U_5680,U_5678,U_5677)
        | sP481(U_5679,U_5680,U_5678,U_5677)
        | ~ sP483(U_5679,U_5680,U_5678,U_5677) )
    & ! [U_5679,U_5680,U_5678,U_5677] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),c_Groups_Ozero__class_Ozero(U_5677)),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680)))
        | ~ sP483(U_5679,U_5680,U_5678,U_5677) )
    & ! [U_5679,U_5680,U_5678,U_5677] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5677),U_5678),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680))),U_5679))
        | ~ sP480(U_5679,U_5680,U_5678,U_5677) )
    & ! [U_5679,U_5680,U_5678,U_5677] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),c_Groups_Ozero__class_Ozero(U_5677)),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680)))
        | ~ sP480(U_5679,U_5680,U_5678,U_5677) )
    & ! [U_5679,U_5680,U_5678,U_5677] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),U_5678),c_Groups_Ozero__class_Ozero(U_5677)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680)),c_Groups_Ozero__class_Ozero(U_5677)))
        | ~ sP478(U_5679,U_5680,U_5678,U_5677) )
    & ! [U_5679,U_5680,U_5678,U_5677] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),U_5679),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5677),U_5678),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680)),c_Groups_Ozero__class_Ozero(U_5677)))
        | ~ sP478(U_5679,U_5680,U_5678,U_5677) )
    & ! [U_5679,U_5680,U_5678,U_5677] :
        ( sP478(U_5679,U_5680,U_5678,U_5677)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),c_Groups_Ozero__class_Ozero(U_5677)),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680)))
        | ~ sP479(U_5679,U_5680,U_5678,U_5677) )
    & ! [U_5679,U_5680,U_5678,U_5677] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5677),U_5678),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680))),U_5679))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),c_Groups_Ozero__class_Ozero(U_5677)),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680)))
        | ~ sP479(U_5679,U_5680,U_5678,U_5677) )
    & ! [U_5679,U_5680,U_5678,U_5677] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),U_5678),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5677),U_5679),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680))))
        | sP483(U_5679,U_5680,U_5678,U_5677)
        | sP480(U_5679,U_5680,U_5678,U_5677)
        | ~ sP484(U_5679,U_5680,U_5678,U_5677) )
    & ! [U_5679,U_5680,U_5678,U_5677] :
        ( sP479(U_5679,U_5680,U_5678,U_5677)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),U_5678),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5677),U_5679),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680))))
        | ~ sP484(U_5679,U_5680,U_5678,U_5677) )
    & ! [U_5679,U_5680,U_5678,U_5677] :
        ( sP484(U_5679,U_5680,U_5678,U_5677)
        | ~ class_Int_Onumber(U_5677)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5677) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP478,sP479,sP480,sP481,sP482,sP483,sP484])],[f_1713_2]) ).

cnf(f_1713_4,plain,
    ( sP484(U_5679,U_5680,U_5678,U_5677)
    | ~ class_Int_Onumber(U_5677)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5677) ),
    inference(clausify,[status(thm)],[f_1713_3]) ).

cnf(f_1713_5,plain,
    ( sP479(U_5679,U_5680,U_5678,U_5677)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),U_5678),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5677),U_5679),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680))))
    | ~ sP484(U_5679,U_5680,U_5678,U_5677) ),
    inference(clausify,[status(thm)],[f_1713_3]) ).

cnf(f_1713_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),U_5678),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5677),U_5679),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680))))
    | sP483(U_5679,U_5680,U_5678,U_5677)
    | sP480(U_5679,U_5680,U_5678,U_5677)
    | ~ sP484(U_5679,U_5680,U_5678,U_5677) ),
    inference(clausify,[status(thm)],[f_1713_3]) ).

cnf(f_1713_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5677),U_5678),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680))),U_5679))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),c_Groups_Ozero__class_Ozero(U_5677)),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680)))
    | ~ sP479(U_5679,U_5680,U_5678,U_5677) ),
    inference(clausify,[status(thm)],[f_1713_3]) ).

cnf(f_1713_8,plain,
    ( sP478(U_5679,U_5680,U_5678,U_5677)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),c_Groups_Ozero__class_Ozero(U_5677)),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680)))
    | ~ sP479(U_5679,U_5680,U_5678,U_5677) ),
    inference(clausify,[status(thm)],[f_1713_3]) ).

cnf(f_1713_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),U_5679),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5677),U_5678),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680)),c_Groups_Ozero__class_Ozero(U_5677)))
    | ~ sP478(U_5679,U_5680,U_5678,U_5677) ),
    inference(clausify,[status(thm)],[f_1713_3]) ).

cnf(f_1713_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),U_5678),c_Groups_Ozero__class_Ozero(U_5677)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680)),c_Groups_Ozero__class_Ozero(U_5677)))
    | ~ sP478(U_5679,U_5680,U_5678,U_5677) ),
    inference(clausify,[status(thm)],[f_1713_3]) ).

cnf(f_1713_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),c_Groups_Ozero__class_Ozero(U_5677)),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680)))
    | ~ sP480(U_5679,U_5680,U_5678,U_5677) ),
    inference(clausify,[status(thm)],[f_1713_3]) ).

cnf(f_1713_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5677),U_5678),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680))),U_5679))
    | ~ sP480(U_5679,U_5680,U_5678,U_5677) ),
    inference(clausify,[status(thm)],[f_1713_3]) ).

cnf(f_1713_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),c_Groups_Ozero__class_Ozero(U_5677)),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680)))
    | ~ sP483(U_5679,U_5680,U_5678,U_5677) ),
    inference(clausify,[status(thm)],[f_1713_3]) ).

cnf(f_1713_14,plain,
    ( sP482(U_5680,U_5678,U_5677)
    | sP481(U_5679,U_5680,U_5678,U_5677)
    | ~ sP483(U_5679,U_5680,U_5678,U_5677) ),
    inference(clausify,[status(thm)],[f_1713_3]) ).

cnf(f_1713_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680)),c_Groups_Ozero__class_Ozero(U_5677)))
    | ~ sP481(U_5679,U_5680,U_5678,U_5677) ),
    inference(clausify,[status(thm)],[f_1713_3]) ).

cnf(f_1713_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),U_5679),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5677),U_5678),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680))))
    | ~ sP481(U_5679,U_5680,U_5678,U_5677) ),
    inference(clausify,[status(thm)],[f_1713_3]) ).

cnf(f_1713_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),hAPP(c_Int_Onumber__class_Onumber__of(U_5677),U_5680)),c_Groups_Ozero__class_Ozero(U_5677)))
    | ~ sP482(U_5680,U_5678,U_5677) ),
    inference(clausify,[status(thm)],[f_1713_3]) ).

cnf(f_1713_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5677),U_5678),c_Groups_Ozero__class_Ozero(U_5677)))
    | ~ sP482(U_5680,U_5678,U_5677) ),
    inference(clausify,[status(thm)],[f_1713_3]) ).

fof(f_1714_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_1714_2,plain,
    ! [U_5682,U_5681] :
      ( ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5682),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5681))) = 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_5681))) )
      & ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5682),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5681))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5682),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5681))),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_5682))),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_5681))) ) ),
    inference(variable_rename,[status(thm)],[f_1714_1]) ).

fof(f_1714_3,plain,
    ( ! [U_5686,U_5684] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5686),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5684))) = 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_5684))) )
    & ! [U_5685,U_5683] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5685),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5683))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5685),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5683))),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_5685))),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_5683))) ) ),
    inference(miniscope,[status(thm)],[f_1714_2]) ).

fof(f_1714_4,plain,
    ( ! [U_5684,U_5686] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5686),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5684))) = 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_5684))) )
    & ! [U_5683,U_5685] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5685),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5683))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5685),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5683))),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_5685))),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_5683))) ) ),
    inference(definitional_conversion,[status(esa)],[f_1714_3]) ).

cnf(f_1714_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5685),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5683))) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5685),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5683))),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_5685))),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_5683))) ),
    inference(clausify,[status(thm)],[f_1714_4]) ).

cnf(f_1714_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_5686),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5684))) = 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_5684))) ),
    inference(clausify,[status(thm)],[f_1714_4]) ).

fof(f_1715_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_1715_2,plain,
    ! [U_5690,U_5689,U_5688,U_5687] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5687),U_5688),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5690),U_5689)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5687),hAPP(hAPP(c_Power_Opower__class_Opower(U_5687),U_5688),U_5690)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5687),U_5688),U_5689))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5689),U_5690))
      | U_5688 = c_Groups_Ozero__class_Ozero(U_5687)
      | ~ class_Fields_Ofield(U_5687) ),
    inference(variable_rename,[status(thm)],[f_1715_1]) ).

fof(f_1715_3,plain,
    ! [U_5687,U_5688,U_5689,U_5690] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5687),U_5688),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5690),U_5689)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5687),hAPP(hAPP(c_Power_Opower__class_Opower(U_5687),U_5688),U_5690)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5687),U_5688),U_5689))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5689),U_5690))
      | U_5688 = c_Groups_Ozero__class_Ozero(U_5687)
      | ~ class_Fields_Ofield(U_5687) ),
    inference(definitional_conversion,[status(esa)],[f_1715_2]) ).

cnf(f_1715_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5687),U_5688),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_5690),U_5689)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5687),hAPP(hAPP(c_Power_Opower__class_Opower(U_5687),U_5688),U_5690)),hAPP(hAPP(c_Power_Opower__class_Opower(U_5687),U_5688),U_5689))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_5689),U_5690))
    | U_5688 = c_Groups_Ozero__class_Ozero(U_5687)
    | ~ class_Fields_Ofield(U_5687) ),
    inference(clausify,[status(thm)],[f_1715_3]) ).

fof(f_1716_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_1716_2,plain,
    ! [U_5692,U_5691] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),c_Int_OMin)),U_5692) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5691),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5691),c_Groups_Oone__class_Oone(U_5691)),U_5692))
      | ~ class_Int_Onumber__ring(U_5691)
      | ~ class_Fields_Ofield__inverse__zero(U_5691) ),
    inference(variable_rename,[status(thm)],[f_1716_1]) ).

fof(f_1716_3,plain,
    ! [U_5691,U_5692] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),c_Int_OMin)),U_5692) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5691),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5691),c_Groups_Oone__class_Oone(U_5691)),U_5692))
      | ~ class_Int_Onumber__ring(U_5691)
      | ~ class_Fields_Ofield__inverse__zero(U_5691) ),
    inference(definitional_conversion,[status(esa)],[f_1716_2]) ).

cnf(f_1716_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5691),hAPP(c_Int_Onumber__class_Onumber__of(U_5691),c_Int_OMin)),U_5692) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5691),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5691),c_Groups_Oone__class_Oone(U_5691)),U_5692))
    | ~ class_Int_Onumber__ring(U_5691)
    | ~ class_Fields_Ofield__inverse__zero(U_5691) ),
    inference(clausify,[status(thm)],[f_1716_3]) ).

fof(f_1717_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_1717_2,plain,
    ! [U_5695,U_5694,U_5693] :
      ( ( ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5693),hAPP(c_Int_Onumber__class_Onumber__of(U_5693),U_5695)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5694))) = c_Groups_Oone__class_Oone(U_5693)
          | 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_5694))) )
        & ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5693),hAPP(c_Int_Onumber__class_Onumber__of(U_5693),U_5695)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5694))) = hAPP(hAPP(c_HOL_OLet(U_5693,U_5693),hAPP(hAPP(c_Power_Opower__class_Opower(U_5693),hAPP(c_Int_Onumber__class_Onumber__of(U_5693),U_5695)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5694))),hAPP(hAPP(c_COMBS(U_5693,U_5693,U_5693),hAPP(hAPP(c_COMBB(U_5693,tc_fun(U_5693,U_5693),U_5693),c_Groups_Otimes__class_Otimes(U_5693)),hAPP(c_Groups_Otimes__class_Otimes(U_5693),hAPP(c_Int_Onumber__class_Onumber__of(U_5693),U_5695)))),c_COMBI(U_5693)))
          | ~ 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_5694))) ) )
      | ~ class_Int_Onumber__ring(U_5693) ),
    inference(variable_rename,[status(thm)],[f_1717_1]) ).

fof(f_1717_3,plain,
    ( ! [U_5693,U_5694,U_5695] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5693),hAPP(c_Int_Onumber__class_Onumber__of(U_5693),U_5695)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5694))) = c_Groups_Oone__class_Oone(U_5693)
        | 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_5694)))
        | ~ sP485(U_5693,U_5694,U_5695) )
    & ! [U_5693,U_5694,U_5695] :
        ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5693),hAPP(c_Int_Onumber__class_Onumber__of(U_5693),U_5695)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5694))) = hAPP(hAPP(c_HOL_OLet(U_5693,U_5693),hAPP(hAPP(c_Power_Opower__class_Opower(U_5693),hAPP(c_Int_Onumber__class_Onumber__of(U_5693),U_5695)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5694))),hAPP(hAPP(c_COMBS(U_5693,U_5693,U_5693),hAPP(hAPP(c_COMBB(U_5693,tc_fun(U_5693,U_5693),U_5693),c_Groups_Otimes__class_Otimes(U_5693)),hAPP(c_Groups_Otimes__class_Otimes(U_5693),hAPP(c_Int_Onumber__class_Onumber__of(U_5693),U_5695)))),c_COMBI(U_5693)))
        | ~ 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_5694)))
        | ~ sP485(U_5693,U_5694,U_5695) )
    & ! [U_5693,U_5694,U_5695] :
        ( sP485(U_5693,U_5694,U_5695)
        | ~ class_Int_Onumber__ring(U_5693) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP485])],[f_1717_2]) ).

cnf(f_1717_4,plain,
    ( sP485(U_5693,U_5694,U_5695)
    | ~ class_Int_Onumber__ring(U_5693) ),
    inference(clausify,[status(thm)],[f_1717_3]) ).

cnf(f_1717_5,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5693),hAPP(c_Int_Onumber__class_Onumber__of(U_5693),U_5695)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5694))) = hAPP(hAPP(c_HOL_OLet(U_5693,U_5693),hAPP(hAPP(c_Power_Opower__class_Opower(U_5693),hAPP(c_Int_Onumber__class_Onumber__of(U_5693),U_5695)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5694))),hAPP(hAPP(c_COMBS(U_5693,U_5693,U_5693),hAPP(hAPP(c_COMBB(U_5693,tc_fun(U_5693,U_5693),U_5693),c_Groups_Otimes__class_Otimes(U_5693)),hAPP(c_Groups_Otimes__class_Otimes(U_5693),hAPP(c_Int_Onumber__class_Onumber__of(U_5693),U_5695)))),c_COMBI(U_5693)))
    | ~ 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_5694)))
    | ~ sP485(U_5693,U_5694,U_5695) ),
    inference(clausify,[status(thm)],[f_1717_3]) ).

cnf(f_1717_6,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_5693),hAPP(c_Int_Onumber__class_Onumber__of(U_5693),U_5695)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(U_5694))) = c_Groups_Oone__class_Oone(U_5693)
    | 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_5694)))
    | ~ sP485(U_5693,U_5694,U_5695) ),
    inference(clausify,[status(thm)],[f_1717_3]) ).

fof(f_1718_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_1718_2,plain,
    ! [U_5699,U_5698,U_5697,U_5696] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),U_5697),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5696),U_5698),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699))))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),U_5697),c_Groups_Ozero__class_Ozero(U_5696)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699)),c_Groups_Ozero__class_Ozero(U_5696))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),U_5698),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5696),U_5697),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699)),c_Groups_Ozero__class_Ozero(U_5696))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),c_Groups_Ozero__class_Ozero(U_5696)),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5696),U_5697),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699))),U_5698))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),c_Groups_Ozero__class_Ozero(U_5696)),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),U_5697),c_Groups_Ozero__class_Ozero(U_5696)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699)),c_Groups_Ozero__class_Ozero(U_5696))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),U_5698),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5696),U_5697),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699))))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699)),c_Groups_Ozero__class_Ozero(U_5696))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),c_Groups_Ozero__class_Ozero(U_5696)),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5696),U_5697),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699))),U_5698))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),c_Groups_Ozero__class_Ozero(U_5696)),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),U_5697),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5696),U_5698),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699)))) ) )
      | ~ class_Int_Onumber(U_5696)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5696) ),
    inference(variable_rename,[status(thm)],[f_1718_1]) ).

fof(f_1718_3,plain,
    ( ! [U_5696,U_5697,U_5699] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),U_5697),c_Groups_Ozero__class_Ozero(U_5696)))
        | ~ sP490(U_5696,U_5697,U_5699) )
    & ! [U_5696,U_5697,U_5699] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699)),c_Groups_Ozero__class_Ozero(U_5696)))
        | ~ sP490(U_5696,U_5697,U_5699) )
    & ! [U_5696,U_5697,U_5698,U_5699] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),U_5698),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5696),U_5697),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699))))
        | ~ sP489(U_5696,U_5697,U_5698,U_5699) )
    & ! [U_5696,U_5697,U_5698,U_5699] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699)),c_Groups_Ozero__class_Ozero(U_5696)))
        | ~ sP489(U_5696,U_5697,U_5698,U_5699) )
    & ! [U_5696,U_5697,U_5698,U_5699] :
        ( sP490(U_5696,U_5697,U_5699)
        | sP489(U_5696,U_5697,U_5698,U_5699)
        | ~ sP491(U_5696,U_5697,U_5698,U_5699) )
    & ! [U_5696,U_5697,U_5698,U_5699] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),c_Groups_Ozero__class_Ozero(U_5696)),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699)))
        | ~ sP491(U_5696,U_5697,U_5698,U_5699) )
    & ! [U_5696,U_5697,U_5698,U_5699] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5696),U_5697),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699))),U_5698))
        | ~ sP488(U_5696,U_5697,U_5698,U_5699) )
    & ! [U_5696,U_5697,U_5698,U_5699] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),c_Groups_Ozero__class_Ozero(U_5696)),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699)))
        | ~ sP488(U_5696,U_5697,U_5698,U_5699) )
    & ! [U_5696,U_5697,U_5698,U_5699] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),U_5697),c_Groups_Ozero__class_Ozero(U_5696)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699)),c_Groups_Ozero__class_Ozero(U_5696)))
        | ~ sP486(U_5696,U_5697,U_5698,U_5699) )
    & ! [U_5696,U_5697,U_5698,U_5699] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),U_5698),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5696),U_5697),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699)),c_Groups_Ozero__class_Ozero(U_5696)))
        | ~ sP486(U_5696,U_5697,U_5698,U_5699) )
    & ! [U_5696,U_5697,U_5698,U_5699] :
        ( sP486(U_5696,U_5697,U_5698,U_5699)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),c_Groups_Ozero__class_Ozero(U_5696)),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699)))
        | ~ sP487(U_5696,U_5697,U_5698,U_5699) )
    & ! [U_5696,U_5697,U_5698,U_5699] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5696),U_5697),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699))),U_5698))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),c_Groups_Ozero__class_Ozero(U_5696)),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699)))
        | ~ sP487(U_5696,U_5697,U_5698,U_5699) )
    & ! [U_5696,U_5697,U_5698,U_5699] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),U_5697),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5696),U_5698),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699))))
        | sP491(U_5696,U_5697,U_5698,U_5699)
        | sP488(U_5696,U_5697,U_5698,U_5699)
        | ~ sP492(U_5696,U_5697,U_5698,U_5699) )
    & ! [U_5696,U_5697,U_5698,U_5699] :
        ( sP487(U_5696,U_5697,U_5698,U_5699)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),U_5697),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5696),U_5698),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699))))
        | ~ sP492(U_5696,U_5697,U_5698,U_5699) )
    & ! [U_5696,U_5697,U_5698,U_5699] :
        ( sP492(U_5696,U_5697,U_5698,U_5699)
        | ~ class_Int_Onumber(U_5696)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5696) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP486,sP487,sP488,sP489,sP490,sP491,sP492])],[f_1718_2]) ).

cnf(f_1718_4,plain,
    ( sP492(U_5696,U_5697,U_5698,U_5699)
    | ~ class_Int_Onumber(U_5696)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5696) ),
    inference(clausify,[status(thm)],[f_1718_3]) ).

cnf(f_1718_5,plain,
    ( sP487(U_5696,U_5697,U_5698,U_5699)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),U_5697),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5696),U_5698),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699))))
    | ~ sP492(U_5696,U_5697,U_5698,U_5699) ),
    inference(clausify,[status(thm)],[f_1718_3]) ).

cnf(f_1718_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),U_5697),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5696),U_5698),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699))))
    | sP491(U_5696,U_5697,U_5698,U_5699)
    | sP488(U_5696,U_5697,U_5698,U_5699)
    | ~ sP492(U_5696,U_5697,U_5698,U_5699) ),
    inference(clausify,[status(thm)],[f_1718_3]) ).

cnf(f_1718_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5696),U_5697),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699))),U_5698))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),c_Groups_Ozero__class_Ozero(U_5696)),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699)))
    | ~ sP487(U_5696,U_5697,U_5698,U_5699) ),
    inference(clausify,[status(thm)],[f_1718_3]) ).

cnf(f_1718_8,plain,
    ( sP486(U_5696,U_5697,U_5698,U_5699)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),c_Groups_Ozero__class_Ozero(U_5696)),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699)))
    | ~ sP487(U_5696,U_5697,U_5698,U_5699) ),
    inference(clausify,[status(thm)],[f_1718_3]) ).

cnf(f_1718_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),U_5698),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5696),U_5697),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699)),c_Groups_Ozero__class_Ozero(U_5696)))
    | ~ sP486(U_5696,U_5697,U_5698,U_5699) ),
    inference(clausify,[status(thm)],[f_1718_3]) ).

cnf(f_1718_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),U_5697),c_Groups_Ozero__class_Ozero(U_5696)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699)),c_Groups_Ozero__class_Ozero(U_5696)))
    | ~ sP486(U_5696,U_5697,U_5698,U_5699) ),
    inference(clausify,[status(thm)],[f_1718_3]) ).

cnf(f_1718_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),c_Groups_Ozero__class_Ozero(U_5696)),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699)))
    | ~ sP488(U_5696,U_5697,U_5698,U_5699) ),
    inference(clausify,[status(thm)],[f_1718_3]) ).

cnf(f_1718_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5696),U_5697),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699))),U_5698))
    | ~ sP488(U_5696,U_5697,U_5698,U_5699) ),
    inference(clausify,[status(thm)],[f_1718_3]) ).

cnf(f_1718_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),c_Groups_Ozero__class_Ozero(U_5696)),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699)))
    | ~ sP491(U_5696,U_5697,U_5698,U_5699) ),
    inference(clausify,[status(thm)],[f_1718_3]) ).

cnf(f_1718_14,plain,
    ( sP490(U_5696,U_5697,U_5699)
    | sP489(U_5696,U_5697,U_5698,U_5699)
    | ~ sP491(U_5696,U_5697,U_5698,U_5699) ),
    inference(clausify,[status(thm)],[f_1718_3]) ).

cnf(f_1718_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699)),c_Groups_Ozero__class_Ozero(U_5696)))
    | ~ sP489(U_5696,U_5697,U_5698,U_5699) ),
    inference(clausify,[status(thm)],[f_1718_3]) ).

cnf(f_1718_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),U_5698),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5696),U_5697),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699))))
    | ~ sP489(U_5696,U_5697,U_5698,U_5699) ),
    inference(clausify,[status(thm)],[f_1718_3]) ).

cnf(f_1718_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5696),hAPP(c_Int_Onumber__class_Onumber__of(U_5696),U_5699)),c_Groups_Ozero__class_Ozero(U_5696)))
    | ~ sP490(U_5696,U_5697,U_5699) ),
    inference(clausify,[status(thm)],[f_1718_3]) ).

cnf(f_1718_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5696),U_5697),c_Groups_Ozero__class_Ozero(U_5696)))
    | ~ sP490(U_5696,U_5697,U_5699) ),
    inference(clausify,[status(thm)],[f_1718_3]) ).

fof(f_1719_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_1719_2,plain,
    ! [U_5703,U_5702,U_5701,U_5700] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5700),U_5702),U_5703)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),c_Groups_Ozero__class_Ozero(U_5700)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),U_5703),c_Groups_Ozero__class_Ozero(U_5700))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),U_5702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),U_5703)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),U_5703),c_Groups_Ozero__class_Ozero(U_5700))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),c_Groups_Ozero__class_Ozero(U_5700)),U_5703)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),U_5703)),U_5702))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),c_Groups_Ozero__class_Ozero(U_5700)),U_5703)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),c_Groups_Ozero__class_Ozero(U_5700)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),U_5703),c_Groups_Ozero__class_Ozero(U_5700))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),U_5702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),U_5703)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),U_5703),c_Groups_Ozero__class_Ozero(U_5700))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),c_Groups_Ozero__class_Ozero(U_5700)),U_5703)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),U_5703)),U_5702))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),c_Groups_Ozero__class_Ozero(U_5700)),U_5703)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5700),U_5702),U_5703))) ) )
      | ~ class_Int_Onumber(U_5700)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5700) ),
    inference(variable_rename,[status(thm)],[f_1719_1]) ).

fof(f_1719_3,plain,
    ( ! [U_5700,U_5703,U_5701] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),c_Groups_Ozero__class_Ozero(U_5700)))
        | ~ sP497(U_5700,U_5703,U_5701) )
    & ! [U_5700,U_5703,U_5701] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),U_5703),c_Groups_Ozero__class_Ozero(U_5700)))
        | ~ sP497(U_5700,U_5703,U_5701) )
    & ! [U_5700,U_5703,U_5702,U_5701] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),U_5702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),U_5703)))
        | ~ sP496(U_5700,U_5703,U_5702,U_5701) )
    & ! [U_5700,U_5703,U_5702,U_5701] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),U_5703),c_Groups_Ozero__class_Ozero(U_5700)))
        | ~ sP496(U_5700,U_5703,U_5702,U_5701) )
    & ! [U_5700,U_5703,U_5702,U_5701] :
        ( sP497(U_5700,U_5703,U_5701)
        | sP496(U_5700,U_5703,U_5702,U_5701)
        | ~ sP498(U_5700,U_5703,U_5702,U_5701) )
    & ! [U_5700,U_5703,U_5702,U_5701] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),c_Groups_Ozero__class_Ozero(U_5700)),U_5703))
        | ~ sP498(U_5700,U_5703,U_5702,U_5701) )
    & ! [U_5700,U_5703,U_5702,U_5701] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),U_5703)),U_5702))
        | ~ sP495(U_5700,U_5703,U_5702,U_5701) )
    & ! [U_5700,U_5703,U_5702,U_5701] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),c_Groups_Ozero__class_Ozero(U_5700)),U_5703))
        | ~ sP495(U_5700,U_5703,U_5702,U_5701) )
    & ! [U_5700,U_5703,U_5702,U_5701] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),c_Groups_Ozero__class_Ozero(U_5700)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),U_5703),c_Groups_Ozero__class_Ozero(U_5700)))
        | ~ sP493(U_5700,U_5703,U_5702,U_5701) )
    & ! [U_5700,U_5703,U_5702,U_5701] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),U_5702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),U_5703)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),U_5703),c_Groups_Ozero__class_Ozero(U_5700)))
        | ~ sP493(U_5700,U_5703,U_5702,U_5701) )
    & ! [U_5700,U_5703,U_5702,U_5701] :
        ( sP493(U_5700,U_5703,U_5702,U_5701)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),c_Groups_Ozero__class_Ozero(U_5700)),U_5703))
        | ~ sP494(U_5700,U_5703,U_5702,U_5701) )
    & ! [U_5700,U_5703,U_5702,U_5701] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),U_5703)),U_5702))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),c_Groups_Ozero__class_Ozero(U_5700)),U_5703))
        | ~ sP494(U_5700,U_5703,U_5702,U_5701) )
    & ! [U_5700,U_5703,U_5702,U_5701] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5700),U_5702),U_5703)))
        | sP498(U_5700,U_5703,U_5702,U_5701)
        | sP495(U_5700,U_5703,U_5702,U_5701)
        | ~ sP499(U_5700,U_5703,U_5702,U_5701) )
    & ! [U_5700,U_5703,U_5702,U_5701] :
        ( sP494(U_5700,U_5703,U_5702,U_5701)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5700),U_5702),U_5703)))
        | ~ sP499(U_5700,U_5703,U_5702,U_5701) )
    & ! [U_5700,U_5703,U_5702,U_5701] :
        ( sP499(U_5700,U_5703,U_5702,U_5701)
        | ~ class_Int_Onumber(U_5700)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5700) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP493,sP494,sP495,sP496,sP497,sP498,sP499])],[f_1719_2]) ).

cnf(f_1719_4,plain,
    ( sP499(U_5700,U_5703,U_5702,U_5701)
    | ~ class_Int_Onumber(U_5700)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5700) ),
    inference(clausify,[status(thm)],[f_1719_3]) ).

cnf(f_1719_5,plain,
    ( sP494(U_5700,U_5703,U_5702,U_5701)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5700),U_5702),U_5703)))
    | ~ sP499(U_5700,U_5703,U_5702,U_5701) ),
    inference(clausify,[status(thm)],[f_1719_3]) ).

cnf(f_1719_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5700),U_5702),U_5703)))
    | sP498(U_5700,U_5703,U_5702,U_5701)
    | sP495(U_5700,U_5703,U_5702,U_5701)
    | ~ sP499(U_5700,U_5703,U_5702,U_5701) ),
    inference(clausify,[status(thm)],[f_1719_3]) ).

cnf(f_1719_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),U_5703)),U_5702))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),c_Groups_Ozero__class_Ozero(U_5700)),U_5703))
    | ~ sP494(U_5700,U_5703,U_5702,U_5701) ),
    inference(clausify,[status(thm)],[f_1719_3]) ).

cnf(f_1719_8,plain,
    ( sP493(U_5700,U_5703,U_5702,U_5701)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),c_Groups_Ozero__class_Ozero(U_5700)),U_5703))
    | ~ sP494(U_5700,U_5703,U_5702,U_5701) ),
    inference(clausify,[status(thm)],[f_1719_3]) ).

cnf(f_1719_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),U_5702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),U_5703)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),U_5703),c_Groups_Ozero__class_Ozero(U_5700)))
    | ~ sP493(U_5700,U_5703,U_5702,U_5701) ),
    inference(clausify,[status(thm)],[f_1719_3]) ).

cnf(f_1719_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),c_Groups_Ozero__class_Ozero(U_5700)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),U_5703),c_Groups_Ozero__class_Ozero(U_5700)))
    | ~ sP493(U_5700,U_5703,U_5702,U_5701) ),
    inference(clausify,[status(thm)],[f_1719_3]) ).

cnf(f_1719_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),c_Groups_Ozero__class_Ozero(U_5700)),U_5703))
    | ~ sP495(U_5700,U_5703,U_5702,U_5701) ),
    inference(clausify,[status(thm)],[f_1719_3]) ).

cnf(f_1719_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),U_5703)),U_5702))
    | ~ sP495(U_5700,U_5703,U_5702,U_5701) ),
    inference(clausify,[status(thm)],[f_1719_3]) ).

cnf(f_1719_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),c_Groups_Ozero__class_Ozero(U_5700)),U_5703))
    | ~ sP498(U_5700,U_5703,U_5702,U_5701) ),
    inference(clausify,[status(thm)],[f_1719_3]) ).

cnf(f_1719_14,plain,
    ( sP497(U_5700,U_5703,U_5701)
    | sP496(U_5700,U_5703,U_5702,U_5701)
    | ~ sP498(U_5700,U_5703,U_5702,U_5701) ),
    inference(clausify,[status(thm)],[f_1719_3]) ).

cnf(f_1719_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),U_5703),c_Groups_Ozero__class_Ozero(U_5700)))
    | ~ sP496(U_5700,U_5703,U_5702,U_5701) ),
    inference(clausify,[status(thm)],[f_1719_3]) ).

cnf(f_1719_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),U_5702),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),U_5703)))
    | ~ sP496(U_5700,U_5703,U_5702,U_5701) ),
    inference(clausify,[status(thm)],[f_1719_3]) ).

cnf(f_1719_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5700),U_5703),c_Groups_Ozero__class_Ozero(U_5700)))
    | ~ sP497(U_5700,U_5703,U_5701) ),
    inference(clausify,[status(thm)],[f_1719_3]) ).

cnf(f_1719_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5700),hAPP(c_Int_Onumber__class_Onumber__of(U_5700),U_5701)),c_Groups_Ozero__class_Ozero(U_5700)))
    | ~ sP497(U_5700,U_5703,U_5701) ),
    inference(clausify,[status(thm)],[f_1719_3]) ).

fof(f_1720_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_1720_2,plain,
    ! [U_5707,U_5706,U_5705,U_5704] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5704),U_5705),U_5706)),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),c_Groups_Ozero__class_Ozero(U_5704)),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),U_5706),c_Groups_Ozero__class_Ozero(U_5704))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5704),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)),U_5706)),U_5705))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),U_5706),c_Groups_Ozero__class_Ozero(U_5704))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),c_Groups_Ozero__class_Ozero(U_5704)),U_5706)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),U_5705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5704),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)),U_5706)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),c_Groups_Ozero__class_Ozero(U_5704)),U_5706)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),c_Groups_Ozero__class_Ozero(U_5704)),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),U_5706),c_Groups_Ozero__class_Ozero(U_5704))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5704),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)),U_5706)),U_5705))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),U_5706),c_Groups_Ozero__class_Ozero(U_5704))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),c_Groups_Ozero__class_Ozero(U_5704)),U_5706)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),U_5705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5704),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)),U_5706)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),c_Groups_Ozero__class_Ozero(U_5704)),U_5706)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5704),U_5705),U_5706)),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707))) ) )
      | ~ class_Int_Onumber(U_5704)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5704) ),
    inference(variable_rename,[status(thm)],[f_1720_1]) ).

fof(f_1720_3,plain,
    ( ! [U_5707,U_5706,U_5704] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),c_Groups_Ozero__class_Ozero(U_5704)),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)))
        | ~ sP504(U_5707,U_5706,U_5704) )
    & ! [U_5707,U_5706,U_5704] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),U_5706),c_Groups_Ozero__class_Ozero(U_5704)))
        | ~ sP504(U_5707,U_5706,U_5704) )
    & ! [U_5707,U_5705,U_5706,U_5704] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5704),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)),U_5706)),U_5705))
        | ~ sP503(U_5707,U_5705,U_5706,U_5704) )
    & ! [U_5707,U_5705,U_5706,U_5704] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),U_5706),c_Groups_Ozero__class_Ozero(U_5704)))
        | ~ sP503(U_5707,U_5705,U_5706,U_5704) )
    & ! [U_5707,U_5705,U_5706,U_5704] :
        ( sP504(U_5707,U_5706,U_5704)
        | sP503(U_5707,U_5705,U_5706,U_5704)
        | ~ sP505(U_5707,U_5705,U_5706,U_5704) )
    & ! [U_5707,U_5705,U_5706,U_5704] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),c_Groups_Ozero__class_Ozero(U_5704)),U_5706))
        | ~ sP505(U_5707,U_5705,U_5706,U_5704) )
    & ! [U_5707,U_5705,U_5706,U_5704] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),U_5705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5704),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)),U_5706)))
        | ~ sP502(U_5707,U_5705,U_5706,U_5704) )
    & ! [U_5707,U_5705,U_5706,U_5704] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),c_Groups_Ozero__class_Ozero(U_5704)),U_5706))
        | ~ sP502(U_5707,U_5705,U_5706,U_5704) )
    & ! [U_5707,U_5705,U_5706,U_5704] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),c_Groups_Ozero__class_Ozero(U_5704)),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),U_5706),c_Groups_Ozero__class_Ozero(U_5704)))
        | ~ sP500(U_5707,U_5705,U_5706,U_5704) )
    & ! [U_5707,U_5705,U_5706,U_5704] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5704),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)),U_5706)),U_5705))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),U_5706),c_Groups_Ozero__class_Ozero(U_5704)))
        | ~ sP500(U_5707,U_5705,U_5706,U_5704) )
    & ! [U_5707,U_5705,U_5706,U_5704] :
        ( sP500(U_5707,U_5705,U_5706,U_5704)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),c_Groups_Ozero__class_Ozero(U_5704)),U_5706))
        | ~ sP501(U_5707,U_5705,U_5706,U_5704) )
    & ! [U_5707,U_5705,U_5706,U_5704] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),U_5705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5704),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)),U_5706)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),c_Groups_Ozero__class_Ozero(U_5704)),U_5706))
        | ~ sP501(U_5707,U_5705,U_5706,U_5704) )
    & ! [U_5707,U_5705,U_5706,U_5704] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5704),U_5705),U_5706)),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)))
        | sP505(U_5707,U_5705,U_5706,U_5704)
        | sP502(U_5707,U_5705,U_5706,U_5704)
        | ~ sP506(U_5707,U_5705,U_5706,U_5704) )
    & ! [U_5707,U_5705,U_5706,U_5704] :
        ( sP501(U_5707,U_5705,U_5706,U_5704)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5704),U_5705),U_5706)),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)))
        | ~ sP506(U_5707,U_5705,U_5706,U_5704) )
    & ! [U_5707,U_5705,U_5706,U_5704] :
        ( sP506(U_5707,U_5705,U_5706,U_5704)
        | ~ class_Int_Onumber(U_5704)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5704) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP500,sP501,sP502,sP503,sP504,sP505,sP506])],[f_1720_2]) ).

cnf(f_1720_4,plain,
    ( sP506(U_5707,U_5705,U_5706,U_5704)
    | ~ class_Int_Onumber(U_5704)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5704) ),
    inference(clausify,[status(thm)],[f_1720_3]) ).

cnf(f_1720_5,plain,
    ( sP501(U_5707,U_5705,U_5706,U_5704)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5704),U_5705),U_5706)),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)))
    | ~ sP506(U_5707,U_5705,U_5706,U_5704) ),
    inference(clausify,[status(thm)],[f_1720_3]) ).

cnf(f_1720_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5704),U_5705),U_5706)),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)))
    | sP505(U_5707,U_5705,U_5706,U_5704)
    | sP502(U_5707,U_5705,U_5706,U_5704)
    | ~ sP506(U_5707,U_5705,U_5706,U_5704) ),
    inference(clausify,[status(thm)],[f_1720_3]) ).

cnf(f_1720_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),U_5705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5704),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)),U_5706)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),c_Groups_Ozero__class_Ozero(U_5704)),U_5706))
    | ~ sP501(U_5707,U_5705,U_5706,U_5704) ),
    inference(clausify,[status(thm)],[f_1720_3]) ).

cnf(f_1720_8,plain,
    ( sP500(U_5707,U_5705,U_5706,U_5704)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),c_Groups_Ozero__class_Ozero(U_5704)),U_5706))
    | ~ sP501(U_5707,U_5705,U_5706,U_5704) ),
    inference(clausify,[status(thm)],[f_1720_3]) ).

cnf(f_1720_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5704),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)),U_5706)),U_5705))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),U_5706),c_Groups_Ozero__class_Ozero(U_5704)))
    | ~ sP500(U_5707,U_5705,U_5706,U_5704) ),
    inference(clausify,[status(thm)],[f_1720_3]) ).

cnf(f_1720_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),c_Groups_Ozero__class_Ozero(U_5704)),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),U_5706),c_Groups_Ozero__class_Ozero(U_5704)))
    | ~ sP500(U_5707,U_5705,U_5706,U_5704) ),
    inference(clausify,[status(thm)],[f_1720_3]) ).

cnf(f_1720_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),c_Groups_Ozero__class_Ozero(U_5704)),U_5706))
    | ~ sP502(U_5707,U_5705,U_5706,U_5704) ),
    inference(clausify,[status(thm)],[f_1720_3]) ).

cnf(f_1720_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),U_5705),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5704),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)),U_5706)))
    | ~ sP502(U_5707,U_5705,U_5706,U_5704) ),
    inference(clausify,[status(thm)],[f_1720_3]) ).

cnf(f_1720_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),c_Groups_Ozero__class_Ozero(U_5704)),U_5706))
    | ~ sP505(U_5707,U_5705,U_5706,U_5704) ),
    inference(clausify,[status(thm)],[f_1720_3]) ).

cnf(f_1720_14,plain,
    ( sP504(U_5707,U_5706,U_5704)
    | sP503(U_5707,U_5705,U_5706,U_5704)
    | ~ sP505(U_5707,U_5705,U_5706,U_5704) ),
    inference(clausify,[status(thm)],[f_1720_3]) ).

cnf(f_1720_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),U_5706),c_Groups_Ozero__class_Ozero(U_5704)))
    | ~ sP503(U_5707,U_5705,U_5706,U_5704) ),
    inference(clausify,[status(thm)],[f_1720_3]) ).

cnf(f_1720_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5704),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)),U_5706)),U_5705))
    | ~ sP503(U_5707,U_5705,U_5706,U_5704) ),
    inference(clausify,[status(thm)],[f_1720_3]) ).

cnf(f_1720_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5704),U_5706),c_Groups_Ozero__class_Ozero(U_5704)))
    | ~ sP504(U_5707,U_5706,U_5704) ),
    inference(clausify,[status(thm)],[f_1720_3]) ).

cnf(f_1720_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5704),c_Groups_Ozero__class_Ozero(U_5704)),hAPP(c_Int_Onumber__class_Onumber__of(U_5704),U_5707)))
    | ~ sP504(U_5707,U_5706,U_5704) ),
    inference(clausify,[status(thm)],[f_1720_3]) ).

fof(f_1721_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_1721_2,plain,
    ! [U_5711,U_5710,U_5709,U_5708] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5708),U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))),U_5711))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),c_Groups_Ozero__class_Ozero(U_5708)),U_5711))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710)),c_Groups_Ozero__class_Ozero(U_5708))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5708),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))),U_5709))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710)),c_Groups_Ozero__class_Ozero(U_5708))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),c_Groups_Ozero__class_Ozero(U_5708)),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),U_5709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5708),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),c_Groups_Ozero__class_Ozero(U_5708)),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),c_Groups_Ozero__class_Ozero(U_5708)),U_5711))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710)),c_Groups_Ozero__class_Ozero(U_5708))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5708),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))),U_5709))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710)),c_Groups_Ozero__class_Ozero(U_5708))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),c_Groups_Ozero__class_Ozero(U_5708)),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),U_5709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5708),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),c_Groups_Ozero__class_Ozero(U_5708)),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5708),U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))),U_5711)) ) )
      | ~ class_Int_Onumber(U_5708)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5708) ),
    inference(variable_rename,[status(thm)],[f_1721_1]) ).

fof(f_1721_3,plain,
    ( ! [U_5711,U_5708,U_5710] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),c_Groups_Ozero__class_Ozero(U_5708)),U_5711))
        | ~ sP511(U_5711,U_5708,U_5710) )
    & ! [U_5711,U_5708,U_5710] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710)),c_Groups_Ozero__class_Ozero(U_5708)))
        | ~ sP511(U_5711,U_5708,U_5710) )
    & ! [U_5711,U_5708,U_5709,U_5710] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5708),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))),U_5709))
        | ~ sP510(U_5711,U_5708,U_5709,U_5710) )
    & ! [U_5711,U_5708,U_5709,U_5710] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710)),c_Groups_Ozero__class_Ozero(U_5708)))
        | ~ sP510(U_5711,U_5708,U_5709,U_5710) )
    & ! [U_5711,U_5708,U_5709,U_5710] :
        ( sP511(U_5711,U_5708,U_5710)
        | sP510(U_5711,U_5708,U_5709,U_5710)
        | ~ sP512(U_5711,U_5708,U_5709,U_5710) )
    & ! [U_5711,U_5708,U_5709,U_5710] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),c_Groups_Ozero__class_Ozero(U_5708)),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710)))
        | ~ sP512(U_5711,U_5708,U_5709,U_5710) )
    & ! [U_5711,U_5708,U_5709,U_5710] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),U_5709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5708),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))))
        | ~ sP509(U_5711,U_5708,U_5709,U_5710) )
    & ! [U_5711,U_5708,U_5709,U_5710] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),c_Groups_Ozero__class_Ozero(U_5708)),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710)))
        | ~ sP509(U_5711,U_5708,U_5709,U_5710) )
    & ! [U_5711,U_5708,U_5709,U_5710] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),c_Groups_Ozero__class_Ozero(U_5708)),U_5711))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710)),c_Groups_Ozero__class_Ozero(U_5708)))
        | ~ sP507(U_5711,U_5708,U_5709,U_5710) )
    & ! [U_5711,U_5708,U_5709,U_5710] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5708),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))),U_5709))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710)),c_Groups_Ozero__class_Ozero(U_5708)))
        | ~ sP507(U_5711,U_5708,U_5709,U_5710) )
    & ! [U_5711,U_5708,U_5709,U_5710] :
        ( sP507(U_5711,U_5708,U_5709,U_5710)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),c_Groups_Ozero__class_Ozero(U_5708)),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710)))
        | ~ sP508(U_5711,U_5708,U_5709,U_5710) )
    & ! [U_5711,U_5708,U_5709,U_5710] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),U_5709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5708),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),c_Groups_Ozero__class_Ozero(U_5708)),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710)))
        | ~ sP508(U_5711,U_5708,U_5709,U_5710) )
    & ! [U_5711,U_5708,U_5709,U_5710] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5708),U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))),U_5711))
        | sP512(U_5711,U_5708,U_5709,U_5710)
        | sP509(U_5711,U_5708,U_5709,U_5710)
        | ~ sP513(U_5711,U_5708,U_5709,U_5710) )
    & ! [U_5711,U_5708,U_5709,U_5710] :
        ( sP508(U_5711,U_5708,U_5709,U_5710)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5708),U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))),U_5711))
        | ~ sP513(U_5711,U_5708,U_5709,U_5710) )
    & ! [U_5711,U_5708,U_5709,U_5710] :
        ( sP513(U_5711,U_5708,U_5709,U_5710)
        | ~ class_Int_Onumber(U_5708)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5708) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP507,sP508,sP509,sP510,sP511,sP512,sP513])],[f_1721_2]) ).

cnf(f_1721_4,plain,
    ( sP513(U_5711,U_5708,U_5709,U_5710)
    | ~ class_Int_Onumber(U_5708)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5708) ),
    inference(clausify,[status(thm)],[f_1721_3]) ).

cnf(f_1721_5,plain,
    ( sP508(U_5711,U_5708,U_5709,U_5710)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5708),U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))),U_5711))
    | ~ sP513(U_5711,U_5708,U_5709,U_5710) ),
    inference(clausify,[status(thm)],[f_1721_3]) ).

cnf(f_1721_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5708),U_5709),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))),U_5711))
    | sP512(U_5711,U_5708,U_5709,U_5710)
    | sP509(U_5711,U_5708,U_5709,U_5710)
    | ~ sP513(U_5711,U_5708,U_5709,U_5710) ),
    inference(clausify,[status(thm)],[f_1721_3]) ).

cnf(f_1721_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),U_5709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5708),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),c_Groups_Ozero__class_Ozero(U_5708)),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710)))
    | ~ sP508(U_5711,U_5708,U_5709,U_5710) ),
    inference(clausify,[status(thm)],[f_1721_3]) ).

cnf(f_1721_8,plain,
    ( sP507(U_5711,U_5708,U_5709,U_5710)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),c_Groups_Ozero__class_Ozero(U_5708)),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710)))
    | ~ sP508(U_5711,U_5708,U_5709,U_5710) ),
    inference(clausify,[status(thm)],[f_1721_3]) ).

cnf(f_1721_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5708),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))),U_5709))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710)),c_Groups_Ozero__class_Ozero(U_5708)))
    | ~ sP507(U_5711,U_5708,U_5709,U_5710) ),
    inference(clausify,[status(thm)],[f_1721_3]) ).

cnf(f_1721_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),c_Groups_Ozero__class_Ozero(U_5708)),U_5711))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710)),c_Groups_Ozero__class_Ozero(U_5708)))
    | ~ sP507(U_5711,U_5708,U_5709,U_5710) ),
    inference(clausify,[status(thm)],[f_1721_3]) ).

cnf(f_1721_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),c_Groups_Ozero__class_Ozero(U_5708)),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710)))
    | ~ sP509(U_5711,U_5708,U_5709,U_5710) ),
    inference(clausify,[status(thm)],[f_1721_3]) ).

cnf(f_1721_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),U_5709),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5708),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))))
    | ~ sP509(U_5711,U_5708,U_5709,U_5710) ),
    inference(clausify,[status(thm)],[f_1721_3]) ).

cnf(f_1721_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),c_Groups_Ozero__class_Ozero(U_5708)),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710)))
    | ~ sP512(U_5711,U_5708,U_5709,U_5710) ),
    inference(clausify,[status(thm)],[f_1721_3]) ).

cnf(f_1721_14,plain,
    ( sP511(U_5711,U_5708,U_5710)
    | sP510(U_5711,U_5708,U_5709,U_5710)
    | ~ sP512(U_5711,U_5708,U_5709,U_5710) ),
    inference(clausify,[status(thm)],[f_1721_3]) ).

cnf(f_1721_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710)),c_Groups_Ozero__class_Ozero(U_5708)))
    | ~ sP510(U_5711,U_5708,U_5709,U_5710) ),
    inference(clausify,[status(thm)],[f_1721_3]) ).

cnf(f_1721_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5708),U_5711),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710))),U_5709))
    | ~ sP510(U_5711,U_5708,U_5709,U_5710) ),
    inference(clausify,[status(thm)],[f_1721_3]) ).

cnf(f_1721_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5708),hAPP(c_Int_Onumber__class_Onumber__of(U_5708),U_5710)),c_Groups_Ozero__class_Ozero(U_5708)))
    | ~ sP511(U_5711,U_5708,U_5710) ),
    inference(clausify,[status(thm)],[f_1721_3]) ).

cnf(f_1721_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5708),c_Groups_Ozero__class_Ozero(U_5708)),U_5711))
    | ~ sP511(U_5711,U_5708,U_5710) ),
    inference(clausify,[status(thm)],[f_1721_3]) ).

fof(f_1722_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_1722_2,plain,
    ! [U_5713,U_5712] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5713)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5712)) = 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_5713),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5712)))),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_5712),c_Int_OPls)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5713)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5712)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5713)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5712),c_Int_OPls)) ) ),
    inference(variable_rename,[status(thm)],[f_1722_1]) ).

fof(f_1722_3,plain,
    ( ! [U_5717,U_5715] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5717)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5715)) = 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_5717),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5715)))),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_5715),c_Int_OPls)) )
    & ! [U_5716,U_5714] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5716)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5714)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5716)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5714),c_Int_OPls)) ) ),
    inference(miniscope,[status(thm)],[f_1722_2]) ).

fof(f_1722_4,plain,
    ( ! [U_5717,U_5715] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5717)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5715)) = 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_5717),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5715)))),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_5715),c_Int_OPls)) )
    & ! [U_5716,U_5714] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5716)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5714)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5716)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5714),c_Int_OPls)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1722_3]) ).

cnf(f_1722_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5716)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5714)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5716)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5714),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1722_4]) ).

cnf(f_1722_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5717)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5715)) = 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_5717),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5715)))),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_5715),c_Int_OPls)) ),
    inference(clausify,[status(thm)],[f_1722_4]) ).

fof(f_1723_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_1723_2,plain,
    ! [U_5719,U_5718] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5718),U_5719),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),U_5719))
      | ~ class_Int_Onumber__ring(U_5718)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5718) ),
    inference(variable_rename,[status(thm)],[f_1723_1]) ).

fof(f_1723_3,plain,
    ! [U_5718,U_5719] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5718),U_5719),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),U_5719))
      | ~ class_Int_Onumber__ring(U_5718)
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5718) ),
    inference(definitional_conversion,[status(esa)],[f_1723_2]) ).

cnf(f_1723_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5718),U_5719),hAPP(c_Int_Onumber__class_Onumber__of(U_5718),c_Int_OBit0(c_Int_OBit1(c_Int_OPls))))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5718),c_Groups_Ozero__class_Ozero(U_5718)),U_5719))
    | ~ class_Int_Onumber__ring(U_5718)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5718) ),
    inference(clausify,[status(thm)],[f_1723_3]) ).

fof(f_1724_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_1724_2,plain,
    ! [U_5721,U_5720] : c_Code__Numeral_Odiv__mod__code__numeral(U_5720,U_5721) = 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_5720),U_5721)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_5720,U_5721)),
    inference(variable_rename,[status(thm)],[f_1724_1]) ).

fof(f_1724_3,plain,
    ! [U_5720,U_5721] : c_Code__Numeral_Odiv__mod__code__numeral(U_5720,U_5721) = 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_5720),U_5721)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_5720,U_5721)),
    inference(definitional_conversion,[status(esa)],[f_1724_2]) ).

cnf(f_1724_4,plain,
    c_Code__Numeral_Odiv__mod__code__numeral(U_5720,U_5721) = 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_5720),U_5721)),c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_5720,U_5721)),
    inference(clausify,[status(thm)],[f_1724_3]) ).

fof(f_1725_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_1725_2,plain,
    ! [U_5725,U_5724,U_5723,U_5722] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),U_5723),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5722),U_5724),U_5725)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),U_5723),c_Groups_Ozero__class_Ozero(U_5722)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),U_5725),c_Groups_Ozero__class_Ozero(U_5722))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),U_5724),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5723),U_5725)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),U_5725),c_Groups_Ozero__class_Ozero(U_5722))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),U_5725)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5723),U_5725)),U_5724))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),U_5725)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),U_5723),c_Groups_Ozero__class_Ozero(U_5722)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),U_5725),c_Groups_Ozero__class_Ozero(U_5722))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),U_5724),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5723),U_5725)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),U_5725),c_Groups_Ozero__class_Ozero(U_5722))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),U_5725)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5723),U_5725)),U_5724))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),U_5725)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),U_5723),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5722),U_5724),U_5725))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5722) ),
    inference(variable_rename,[status(thm)],[f_1725_1]) ).

fof(f_1725_3,plain,
    ( ! [U_5722,U_5723,U_5725] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),U_5723),c_Groups_Ozero__class_Ozero(U_5722)))
        | ~ sP518(U_5722,U_5723,U_5725) )
    & ! [U_5722,U_5723,U_5725] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),U_5725),c_Groups_Ozero__class_Ozero(U_5722)))
        | ~ sP518(U_5722,U_5723,U_5725) )
    & ! [U_5722,U_5723,U_5724,U_5725] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),U_5724),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5723),U_5725)))
        | ~ sP517(U_5722,U_5723,U_5724,U_5725) )
    & ! [U_5722,U_5723,U_5724,U_5725] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),U_5725),c_Groups_Ozero__class_Ozero(U_5722)))
        | ~ sP517(U_5722,U_5723,U_5724,U_5725) )
    & ! [U_5722,U_5723,U_5724,U_5725] :
        ( sP518(U_5722,U_5723,U_5725)
        | sP517(U_5722,U_5723,U_5724,U_5725)
        | ~ sP519(U_5722,U_5723,U_5724,U_5725) )
    & ! [U_5722,U_5723,U_5724,U_5725] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),U_5725))
        | ~ sP519(U_5722,U_5723,U_5724,U_5725) )
    & ! [U_5722,U_5723,U_5724,U_5725] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5723),U_5725)),U_5724))
        | ~ sP516(U_5722,U_5723,U_5724,U_5725) )
    & ! [U_5722,U_5723,U_5724,U_5725] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),U_5725))
        | ~ sP516(U_5722,U_5723,U_5724,U_5725) )
    & ! [U_5722,U_5723,U_5724,U_5725] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),U_5723),c_Groups_Ozero__class_Ozero(U_5722)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),U_5725),c_Groups_Ozero__class_Ozero(U_5722)))
        | ~ sP514(U_5722,U_5723,U_5724,U_5725) )
    & ! [U_5722,U_5723,U_5724,U_5725] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),U_5724),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5723),U_5725)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),U_5725),c_Groups_Ozero__class_Ozero(U_5722)))
        | ~ sP514(U_5722,U_5723,U_5724,U_5725) )
    & ! [U_5722,U_5723,U_5724,U_5725] :
        ( sP514(U_5722,U_5723,U_5724,U_5725)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),U_5725))
        | ~ sP515(U_5722,U_5723,U_5724,U_5725) )
    & ! [U_5722,U_5723,U_5724,U_5725] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5723),U_5725)),U_5724))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),U_5725))
        | ~ sP515(U_5722,U_5723,U_5724,U_5725) )
    & ! [U_5722,U_5723,U_5724,U_5725] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),U_5723),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5722),U_5724),U_5725)))
        | sP519(U_5722,U_5723,U_5724,U_5725)
        | sP516(U_5722,U_5723,U_5724,U_5725)
        | ~ sP520(U_5722,U_5723,U_5724,U_5725) )
    & ! [U_5722,U_5723,U_5724,U_5725] :
        ( sP515(U_5722,U_5723,U_5724,U_5725)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),U_5723),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5722),U_5724),U_5725)))
        | ~ sP520(U_5722,U_5723,U_5724,U_5725) )
    & ! [U_5722,U_5723,U_5724,U_5725] :
        ( sP520(U_5722,U_5723,U_5724,U_5725)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5722) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP514,sP515,sP516,sP517,sP518,sP519,sP520])],[f_1725_2]) ).

cnf(f_1725_4,plain,
    ( sP520(U_5722,U_5723,U_5724,U_5725)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5722) ),
    inference(clausify,[status(thm)],[f_1725_3]) ).

cnf(f_1725_5,plain,
    ( sP515(U_5722,U_5723,U_5724,U_5725)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),U_5723),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5722),U_5724),U_5725)))
    | ~ sP520(U_5722,U_5723,U_5724,U_5725) ),
    inference(clausify,[status(thm)],[f_1725_3]) ).

cnf(f_1725_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),U_5723),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5722),U_5724),U_5725)))
    | sP519(U_5722,U_5723,U_5724,U_5725)
    | sP516(U_5722,U_5723,U_5724,U_5725)
    | ~ sP520(U_5722,U_5723,U_5724,U_5725) ),
    inference(clausify,[status(thm)],[f_1725_3]) ).

cnf(f_1725_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5723),U_5725)),U_5724))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),U_5725))
    | ~ sP515(U_5722,U_5723,U_5724,U_5725) ),
    inference(clausify,[status(thm)],[f_1725_3]) ).

cnf(f_1725_8,plain,
    ( sP514(U_5722,U_5723,U_5724,U_5725)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),U_5725))
    | ~ sP515(U_5722,U_5723,U_5724,U_5725) ),
    inference(clausify,[status(thm)],[f_1725_3]) ).

cnf(f_1725_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),U_5724),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5723),U_5725)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),U_5725),c_Groups_Ozero__class_Ozero(U_5722)))
    | ~ sP514(U_5722,U_5723,U_5724,U_5725) ),
    inference(clausify,[status(thm)],[f_1725_3]) ).

cnf(f_1725_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),U_5723),c_Groups_Ozero__class_Ozero(U_5722)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),U_5725),c_Groups_Ozero__class_Ozero(U_5722)))
    | ~ sP514(U_5722,U_5723,U_5724,U_5725) ),
    inference(clausify,[status(thm)],[f_1725_3]) ).

cnf(f_1725_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),U_5725))
    | ~ sP516(U_5722,U_5723,U_5724,U_5725) ),
    inference(clausify,[status(thm)],[f_1725_3]) ).

cnf(f_1725_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5723),U_5725)),U_5724))
    | ~ sP516(U_5722,U_5723,U_5724,U_5725) ),
    inference(clausify,[status(thm)],[f_1725_3]) ).

cnf(f_1725_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),c_Groups_Ozero__class_Ozero(U_5722)),U_5725))
    | ~ sP519(U_5722,U_5723,U_5724,U_5725) ),
    inference(clausify,[status(thm)],[f_1725_3]) ).

cnf(f_1725_14,plain,
    ( sP518(U_5722,U_5723,U_5725)
    | sP517(U_5722,U_5723,U_5724,U_5725)
    | ~ sP519(U_5722,U_5723,U_5724,U_5725) ),
    inference(clausify,[status(thm)],[f_1725_3]) ).

cnf(f_1725_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),U_5725),c_Groups_Ozero__class_Ozero(U_5722)))
    | ~ sP517(U_5722,U_5723,U_5724,U_5725) ),
    inference(clausify,[status(thm)],[f_1725_3]) ).

cnf(f_1725_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),U_5724),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5722),U_5723),U_5725)))
    | ~ sP517(U_5722,U_5723,U_5724,U_5725) ),
    inference(clausify,[status(thm)],[f_1725_3]) ).

cnf(f_1725_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5722),U_5725),c_Groups_Ozero__class_Ozero(U_5722)))
    | ~ sP518(U_5722,U_5723,U_5725) ),
    inference(clausify,[status(thm)],[f_1725_3]) ).

cnf(f_1725_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5722),U_5723),c_Groups_Ozero__class_Ozero(U_5722)))
    | ~ sP518(U_5722,U_5723,U_5725) ),
    inference(clausify,[status(thm)],[f_1725_3]) ).

fof(f_1726_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_1726_2,plain,
    ! [U_5729,U_5728,U_5727,U_5726] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5726),U_5727),U_5728)),U_5729))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),c_Groups_Ozero__class_Ozero(U_5726)),U_5729))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),U_5728),c_Groups_Ozero__class_Ozero(U_5726))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5726),U_5729),U_5728)),U_5727))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),U_5728),c_Groups_Ozero__class_Ozero(U_5726))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),c_Groups_Ozero__class_Ozero(U_5726)),U_5728)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),U_5727),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5726),U_5729),U_5728)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),c_Groups_Ozero__class_Ozero(U_5726)),U_5728)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),c_Groups_Ozero__class_Ozero(U_5726)),U_5729))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),U_5728),c_Groups_Ozero__class_Ozero(U_5726))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5726),U_5729),U_5728)),U_5727))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),U_5728),c_Groups_Ozero__class_Ozero(U_5726))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),c_Groups_Ozero__class_Ozero(U_5726)),U_5728)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),U_5727),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5726),U_5729),U_5728)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),c_Groups_Ozero__class_Ozero(U_5726)),U_5728)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5726),U_5727),U_5728)),U_5729)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5726) ),
    inference(variable_rename,[status(thm)],[f_1726_1]) ).

fof(f_1726_3,plain,
    ( ! [U_5728,U_5729,U_5726] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),c_Groups_Ozero__class_Ozero(U_5726)),U_5729))
        | ~ sP525(U_5728,U_5729,U_5726) )
    & ! [U_5728,U_5729,U_5726] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),U_5728),c_Groups_Ozero__class_Ozero(U_5726)))
        | ~ sP525(U_5728,U_5729,U_5726) )
    & ! [U_5728,U_5727,U_5729,U_5726] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5726),U_5729),U_5728)),U_5727))
        | ~ sP524(U_5728,U_5727,U_5729,U_5726) )
    & ! [U_5728,U_5727,U_5729,U_5726] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),U_5728),c_Groups_Ozero__class_Ozero(U_5726)))
        | ~ sP524(U_5728,U_5727,U_5729,U_5726) )
    & ! [U_5728,U_5727,U_5729,U_5726] :
        ( sP525(U_5728,U_5729,U_5726)
        | sP524(U_5728,U_5727,U_5729,U_5726)
        | ~ sP526(U_5728,U_5727,U_5729,U_5726) )
    & ! [U_5728,U_5727,U_5729,U_5726] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),c_Groups_Ozero__class_Ozero(U_5726)),U_5728))
        | ~ sP526(U_5728,U_5727,U_5729,U_5726) )
    & ! [U_5728,U_5727,U_5729,U_5726] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),U_5727),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5726),U_5729),U_5728)))
        | ~ sP523(U_5728,U_5727,U_5729,U_5726) )
    & ! [U_5728,U_5727,U_5729,U_5726] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),c_Groups_Ozero__class_Ozero(U_5726)),U_5728))
        | ~ sP523(U_5728,U_5727,U_5729,U_5726) )
    & ! [U_5728,U_5727,U_5729,U_5726] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),c_Groups_Ozero__class_Ozero(U_5726)),U_5729))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),U_5728),c_Groups_Ozero__class_Ozero(U_5726)))
        | ~ sP521(U_5728,U_5727,U_5729,U_5726) )
    & ! [U_5728,U_5727,U_5729,U_5726] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5726),U_5729),U_5728)),U_5727))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),U_5728),c_Groups_Ozero__class_Ozero(U_5726)))
        | ~ sP521(U_5728,U_5727,U_5729,U_5726) )
    & ! [U_5728,U_5727,U_5729,U_5726] :
        ( sP521(U_5728,U_5727,U_5729,U_5726)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),c_Groups_Ozero__class_Ozero(U_5726)),U_5728))
        | ~ sP522(U_5728,U_5727,U_5729,U_5726) )
    & ! [U_5728,U_5727,U_5729,U_5726] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),U_5727),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5726),U_5729),U_5728)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),c_Groups_Ozero__class_Ozero(U_5726)),U_5728))
        | ~ sP522(U_5728,U_5727,U_5729,U_5726) )
    & ! [U_5728,U_5727,U_5729,U_5726] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5726),U_5727),U_5728)),U_5729))
        | sP526(U_5728,U_5727,U_5729,U_5726)
        | sP523(U_5728,U_5727,U_5729,U_5726)
        | ~ sP527(U_5728,U_5727,U_5729,U_5726) )
    & ! [U_5728,U_5727,U_5729,U_5726] :
        ( sP522(U_5728,U_5727,U_5729,U_5726)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5726),U_5727),U_5728)),U_5729))
        | ~ sP527(U_5728,U_5727,U_5729,U_5726) )
    & ! [U_5728,U_5727,U_5729,U_5726] :
        ( sP527(U_5728,U_5727,U_5729,U_5726)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5726) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP521,sP522,sP523,sP524,sP525,sP526,sP527])],[f_1726_2]) ).

cnf(f_1726_4,plain,
    ( sP527(U_5728,U_5727,U_5729,U_5726)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5726) ),
    inference(clausify,[status(thm)],[f_1726_3]) ).

cnf(f_1726_5,plain,
    ( sP522(U_5728,U_5727,U_5729,U_5726)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5726),U_5727),U_5728)),U_5729))
    | ~ sP527(U_5728,U_5727,U_5729,U_5726) ),
    inference(clausify,[status(thm)],[f_1726_3]) ).

cnf(f_1726_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5726),U_5727),U_5728)),U_5729))
    | sP526(U_5728,U_5727,U_5729,U_5726)
    | sP523(U_5728,U_5727,U_5729,U_5726)
    | ~ sP527(U_5728,U_5727,U_5729,U_5726) ),
    inference(clausify,[status(thm)],[f_1726_3]) ).

cnf(f_1726_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),U_5727),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5726),U_5729),U_5728)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),c_Groups_Ozero__class_Ozero(U_5726)),U_5728))
    | ~ sP522(U_5728,U_5727,U_5729,U_5726) ),
    inference(clausify,[status(thm)],[f_1726_3]) ).

cnf(f_1726_8,plain,
    ( sP521(U_5728,U_5727,U_5729,U_5726)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),c_Groups_Ozero__class_Ozero(U_5726)),U_5728))
    | ~ sP522(U_5728,U_5727,U_5729,U_5726) ),
    inference(clausify,[status(thm)],[f_1726_3]) ).

cnf(f_1726_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5726),U_5729),U_5728)),U_5727))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),U_5728),c_Groups_Ozero__class_Ozero(U_5726)))
    | ~ sP521(U_5728,U_5727,U_5729,U_5726) ),
    inference(clausify,[status(thm)],[f_1726_3]) ).

cnf(f_1726_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),c_Groups_Ozero__class_Ozero(U_5726)),U_5729))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),U_5728),c_Groups_Ozero__class_Ozero(U_5726)))
    | ~ sP521(U_5728,U_5727,U_5729,U_5726) ),
    inference(clausify,[status(thm)],[f_1726_3]) ).

cnf(f_1726_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),c_Groups_Ozero__class_Ozero(U_5726)),U_5728))
    | ~ sP523(U_5728,U_5727,U_5729,U_5726) ),
    inference(clausify,[status(thm)],[f_1726_3]) ).

cnf(f_1726_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),U_5727),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5726),U_5729),U_5728)))
    | ~ sP523(U_5728,U_5727,U_5729,U_5726) ),
    inference(clausify,[status(thm)],[f_1726_3]) ).

cnf(f_1726_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),c_Groups_Ozero__class_Ozero(U_5726)),U_5728))
    | ~ sP526(U_5728,U_5727,U_5729,U_5726) ),
    inference(clausify,[status(thm)],[f_1726_3]) ).

cnf(f_1726_14,plain,
    ( sP525(U_5728,U_5729,U_5726)
    | sP524(U_5728,U_5727,U_5729,U_5726)
    | ~ sP526(U_5728,U_5727,U_5729,U_5726) ),
    inference(clausify,[status(thm)],[f_1726_3]) ).

cnf(f_1726_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),U_5728),c_Groups_Ozero__class_Ozero(U_5726)))
    | ~ sP524(U_5728,U_5727,U_5729,U_5726) ),
    inference(clausify,[status(thm)],[f_1726_3]) ).

cnf(f_1726_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5726),U_5729),U_5728)),U_5727))
    | ~ sP524(U_5728,U_5727,U_5729,U_5726) ),
    inference(clausify,[status(thm)],[f_1726_3]) ).

cnf(f_1726_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5726),U_5728),c_Groups_Ozero__class_Ozero(U_5726)))
    | ~ sP525(U_5728,U_5729,U_5726) ),
    inference(clausify,[status(thm)],[f_1726_3]) ).

cnf(f_1726_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5726),c_Groups_Ozero__class_Ozero(U_5726)),U_5729))
    | ~ sP525(U_5728,U_5729,U_5726) ),
    inference(clausify,[status(thm)],[f_1726_3]) ).

fof(f_1727_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_1727_2,plain,
    ! [U_5733,U_5732,U_5731,U_5730] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5730),U_5732),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5730),U_5733),U_5731)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5730),U_5732),U_5731)),U_5733)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5730),U_5732),U_5731)),U_5733))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5730),U_5732),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5730),U_5733),U_5731))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5730),c_Groups_Ozero__class_Ozero(U_5730)),U_5731))
      | ~ class_Fields_Olinordered__field(U_5730) ),
    inference(variable_rename,[status(thm)],[f_1727_1]) ).

fof(f_1727_3,plain,
    ( ! [U_5732,U_5730,U_5733,U_5731] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5730),U_5732),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5730),U_5733),U_5731)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5730),U_5732),U_5731)),U_5733))
        | ~ sP528(U_5732,U_5730,U_5733,U_5731) )
    & ! [U_5732,U_5730,U_5733,U_5731] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5730),U_5732),U_5731)),U_5733))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5730),U_5732),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5730),U_5733),U_5731)))
        | ~ sP528(U_5732,U_5730,U_5733,U_5731) )
    & ! [U_5732,U_5730,U_5733,U_5731] :
        ( sP528(U_5732,U_5730,U_5733,U_5731)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5730),c_Groups_Ozero__class_Ozero(U_5730)),U_5731))
        | ~ class_Fields_Olinordered__field(U_5730) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP528])],[f_1727_2]) ).

cnf(f_1727_4,plain,
    ( sP528(U_5732,U_5730,U_5733,U_5731)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5730),c_Groups_Ozero__class_Ozero(U_5730)),U_5731))
    | ~ class_Fields_Olinordered__field(U_5730) ),
    inference(clausify,[status(thm)],[f_1727_3]) ).

cnf(f_1727_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5730),U_5732),U_5731)),U_5733))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5730),U_5732),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5730),U_5733),U_5731)))
    | ~ sP528(U_5732,U_5730,U_5733,U_5731) ),
    inference(clausify,[status(thm)],[f_1727_3]) ).

cnf(f_1727_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5730),U_5732),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5730),U_5733),U_5731)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5730),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5730),U_5732),U_5731)),U_5733))
    | ~ sP528(U_5732,U_5730,U_5733,U_5731) ),
    inference(clausify,[status(thm)],[f_1727_3]) ).

fof(f_1728_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_1728_2,plain,
    ! [U_5737,U_5736,U_5735,U_5734] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5734),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5734),U_5736),U_5735)),U_5737))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5734),U_5736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5734),U_5737),U_5735))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5734),U_5736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5734),U_5737),U_5735)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5734),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5734),U_5736),U_5735)),U_5737)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5734),c_Groups_Ozero__class_Ozero(U_5734)),U_5735))
      | ~ class_Fields_Olinordered__field(U_5734) ),
    inference(variable_rename,[status(thm)],[f_1728_1]) ).

fof(f_1728_3,plain,
    ( ! [U_5736,U_5734,U_5735,U_5737] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5734),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5734),U_5736),U_5735)),U_5737))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5734),U_5736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5734),U_5737),U_5735)))
        | ~ sP529(U_5736,U_5734,U_5735,U_5737) )
    & ! [U_5736,U_5734,U_5735,U_5737] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5734),U_5736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5734),U_5737),U_5735)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5734),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5734),U_5736),U_5735)),U_5737))
        | ~ sP529(U_5736,U_5734,U_5735,U_5737) )
    & ! [U_5736,U_5734,U_5735,U_5737] :
        ( sP529(U_5736,U_5734,U_5735,U_5737)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5734),c_Groups_Ozero__class_Ozero(U_5734)),U_5735))
        | ~ class_Fields_Olinordered__field(U_5734) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP529])],[f_1728_2]) ).

cnf(f_1728_4,plain,
    ( sP529(U_5736,U_5734,U_5735,U_5737)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5734),c_Groups_Ozero__class_Ozero(U_5734)),U_5735))
    | ~ class_Fields_Olinordered__field(U_5734) ),
    inference(clausify,[status(thm)],[f_1728_3]) ).

cnf(f_1728_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5734),U_5736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5734),U_5737),U_5735)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5734),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5734),U_5736),U_5735)),U_5737))
    | ~ sP529(U_5736,U_5734,U_5735,U_5737) ),
    inference(clausify,[status(thm)],[f_1728_3]) ).

cnf(f_1728_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5734),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5734),U_5736),U_5735)),U_5737))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5734),U_5736),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5734),U_5737),U_5735)))
    | ~ sP529(U_5736,U_5734,U_5735,U_5737) ),
    inference(clausify,[status(thm)],[f_1728_3]) ).

fof(f_1729_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_1729_2,plain,
    ! [U_5741,U_5740,U_5739,U_5738] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5738),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5738),U_5740),U_5739)),U_5741))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5738),U_5740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5738),U_5741),U_5739)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5738),c_Groups_Ozero__class_Ozero(U_5738)),U_5739))
      | ~ class_Fields_Olinordered__field(U_5738) ),
    inference(variable_rename,[status(thm)],[f_1729_1]) ).

fof(f_1729_3,plain,
    ! [U_5740,U_5739,U_5741,U_5738] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5738),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5738),U_5740),U_5739)),U_5741))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5738),U_5740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5738),U_5741),U_5739)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5738),c_Groups_Ozero__class_Ozero(U_5738)),U_5739))
      | ~ class_Fields_Olinordered__field(U_5738) ),
    inference(definitional_conversion,[status(esa)],[f_1729_2]) ).

cnf(f_1729_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5738),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5738),U_5740),U_5739)),U_5741))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5738),U_5740),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5738),U_5741),U_5739)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5738),c_Groups_Ozero__class_Ozero(U_5738)),U_5739))
    | ~ class_Fields_Olinordered__field(U_5738) ),
    inference(clausify,[status(thm)],[f_1729_3]) ).

fof(f_1730_1,plain,
    ! [V_y_2,V_x_2,V_Qa_2,V_Pa_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_Qa_2,V_x_2),V_y_2))
      | ~ hBOOL(hAPP(hAPP(V_Pa_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_Pa_2),V_Qa_2)) ),
    inference(fof_nnf,[status(thm)],[fact_predicate2D]) ).

fof(f_1730_2,plain,
    ! [U_5747,U_5746,U_5745,U_5744,U_5743,U_5742] :
      ( hBOOL(hAPP(hAPP(U_5745,U_5746),U_5747))
      | ~ hBOOL(hAPP(hAPP(U_5744,U_5746),U_5747))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5742,tc_fun(U_5743,tc_HOL_Obool))),U_5744),U_5745)) ),
    inference(variable_rename,[status(thm)],[f_1730_1]) ).

fof(f_1730_3,plain,
    ! [U_5747,U_5746,U_5745,U_5744] :
      ( ! [U_5743,U_5742] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5742,tc_fun(U_5743,tc_HOL_Obool))),U_5744),U_5745))
      | hBOOL(hAPP(hAPP(U_5745,U_5746),U_5747))
      | ~ hBOOL(hAPP(hAPP(U_5744,U_5746),U_5747)) ),
    inference(miniscope,[status(thm)],[f_1730_2]) ).

fof(f_1730_4,plain,
    ! [U_5745,U_5744,U_5742,U_5743,U_5746,U_5747] :
      ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5742,tc_fun(U_5743,tc_HOL_Obool))),U_5744),U_5745))
      | hBOOL(hAPP(hAPP(U_5745,U_5746),U_5747))
      | ~ hBOOL(hAPP(hAPP(U_5744,U_5746),U_5747)) ),
    inference(definitional_conversion,[status(esa)],[f_1730_3]) ).

cnf(f_1730_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5742,tc_fun(U_5743,tc_HOL_Obool))),U_5744),U_5745))
    | hBOOL(hAPP(hAPP(U_5745,U_5746),U_5747))
    | ~ hBOOL(hAPP(hAPP(U_5744,U_5746),U_5747)) ),
    inference(clausify,[status(thm)],[f_1730_4]) ).

fof(f_1731_1,plain,
    ! [V_Qa_2,T_c,T_b,V_y_2,V_x_2,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(V_Qa_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_Pa_2),V_Qa_2))
      | ~ hBOOL(hAPP(hAPP(V_Pa_2,V_x_2),V_y_2)) ),
    inference(fof_nnf,[status(thm)],[fact_rev__predicate2D]) ).

fof(f_1731_2,plain,
    ! [U_5753,U_5752,U_5751,U_5750,U_5749,U_5748] :
      ( hBOOL(hAPP(hAPP(U_5753,U_5749),U_5750))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5751,tc_fun(U_5752,tc_HOL_Obool))),U_5748),U_5753))
      | ~ hBOOL(hAPP(hAPP(U_5748,U_5749),U_5750)) ),
    inference(variable_rename,[status(thm)],[f_1731_1]) ).

fof(f_1731_3,plain,
    ! [U_5749,U_5748,U_5750,U_5751,U_5752,U_5753] :
      ( hBOOL(hAPP(hAPP(U_5753,U_5749),U_5750))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5751,tc_fun(U_5752,tc_HOL_Obool))),U_5748),U_5753))
      | ~ hBOOL(hAPP(hAPP(U_5748,U_5749),U_5750)) ),
    inference(definitional_conversion,[status(esa)],[f_1731_2]) ).

cnf(f_1731_4,plain,
    ( hBOOL(hAPP(hAPP(U_5753,U_5749),U_5750))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_5751,tc_fun(U_5752,tc_HOL_Obool))),U_5748),U_5753))
    | ~ hBOOL(hAPP(hAPP(U_5748,U_5749),U_5750)) ),
    inference(clausify,[status(thm)],[f_1731_3]) ).

fof(f_1732_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_1732_2,plain,
    ! [U_5758,U_5757,U_5756,U_5755,U_5754] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5754),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5754),U_5755),U_5756)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5754),U_5757),U_5758)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5754),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5754),U_5755),U_5757)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5754),U_5756),U_5758))
      | ~ class_Fields_Ofield__inverse__zero(U_5754) ),
    inference(variable_rename,[status(thm)],[f_1732_1]) ).

fof(f_1732_3,plain,
    ! [U_5754,U_5755,U_5756,U_5757,U_5758] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5754),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5754),U_5755),U_5756)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5754),U_5757),U_5758)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5754),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5754),U_5755),U_5757)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5754),U_5756),U_5758))
      | ~ class_Fields_Ofield__inverse__zero(U_5754) ),
    inference(definitional_conversion,[status(esa)],[f_1732_2]) ).

cnf(f_1732_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5754),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5754),U_5755),U_5756)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5754),U_5757),U_5758)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5754),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5754),U_5755),U_5757)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5754),U_5756),U_5758))
    | ~ class_Fields_Ofield__inverse__zero(U_5754) ),
    inference(clausify,[status(thm)],[f_1732_3]) ).

fof(f_1733_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_1733_2,plain,
    ! [U_5761,U_5760,U_5759] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5759),hAPP(c_Groups_Ouminus__class_Ouminus(U_5759),U_5760)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5759),U_5761)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5759),U_5760),U_5761)
      | ~ class_Fields_Ofield__inverse__zero(U_5759) ),
    inference(variable_rename,[status(thm)],[f_1733_1]) ).

fof(f_1733_3,plain,
    ! [U_5759,U_5760,U_5761] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5759),hAPP(c_Groups_Ouminus__class_Ouminus(U_5759),U_5760)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5759),U_5761)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5759),U_5760),U_5761)
      | ~ class_Fields_Ofield__inverse__zero(U_5759) ),
    inference(definitional_conversion,[status(esa)],[f_1733_2]) ).

cnf(f_1733_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5759),hAPP(c_Groups_Ouminus__class_Ouminus(U_5759),U_5760)),hAPP(c_Groups_Ouminus__class_Ouminus(U_5759),U_5761)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5759),U_5760),U_5761)
    | ~ class_Fields_Ofield__inverse__zero(U_5759) ),
    inference(clausify,[status(thm)],[f_1733_3]) ).

fof(f_1734_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_1734_2,plain,
    ! [U_5764,U_5763,U_5762] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5762),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5762),U_5763),U_5764)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5762),U_5763),hAPP(c_Groups_Ouminus__class_Ouminus(U_5762),U_5764))
      | ~ class_Fields_Ofield__inverse__zero(U_5762) ),
    inference(variable_rename,[status(thm)],[f_1734_1]) ).

fof(f_1734_3,plain,
    ! [U_5762,U_5763,U_5764] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5762),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5762),U_5763),U_5764)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5762),U_5763),hAPP(c_Groups_Ouminus__class_Ouminus(U_5762),U_5764))
      | ~ class_Fields_Ofield__inverse__zero(U_5762) ),
    inference(definitional_conversion,[status(esa)],[f_1734_2]) ).

cnf(f_1734_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_5762),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5762),U_5763),U_5764)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5762),U_5763),hAPP(c_Groups_Ouminus__class_Ouminus(U_5762),U_5764))
    | ~ class_Fields_Ofield__inverse__zero(U_5762) ),
    inference(clausify,[status(thm)],[f_1734_3]) ).

fof(f_1735_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_1735_2,plain,
    ! [U_5767,U_5766,U_5765] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5765),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5765),U_5766),U_5767)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5765),hAPP(c_Groups_Oabs__class_Oabs(U_5765),U_5766)),hAPP(c_Groups_Oabs__class_Oabs(U_5765),U_5767))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5765) ),
    inference(variable_rename,[status(thm)],[f_1735_1]) ).

fof(f_1735_3,plain,
    ! [U_5765,U_5766,U_5767] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5765),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5765),U_5766),U_5767)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5765),hAPP(c_Groups_Oabs__class_Oabs(U_5765),U_5766)),hAPP(c_Groups_Oabs__class_Oabs(U_5765),U_5767))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5765) ),
    inference(definitional_conversion,[status(esa)],[f_1735_2]) ).

cnf(f_1735_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_5765),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5765),U_5766),U_5767)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5765),hAPP(c_Groups_Oabs__class_Oabs(U_5765),U_5766)),hAPP(c_Groups_Oabs__class_Oabs(U_5765),U_5767))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5765) ),
    inference(clausify,[status(thm)],[f_1735_3]) ).

fof(f_1736_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_1736_2,plain,
    ! [U_5771,U_5770,U_5769,U_5768] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5768),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5768),U_5770),U_5771)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5768),U_5769),U_5771)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5768),U_5771),c_Groups_Ozero__class_Ozero(U_5768)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5768),U_5769),U_5770))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5768) ),
    inference(variable_rename,[status(thm)],[f_1736_1]) ).

fof(f_1736_3,plain,
    ! [U_5768,U_5769,U_5770,U_5771] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5768),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5768),U_5770),U_5771)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5768),U_5769),U_5771)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5768),U_5771),c_Groups_Ozero__class_Ozero(U_5768)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5768),U_5769),U_5770))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5768) ),
    inference(definitional_conversion,[status(esa)],[f_1736_2]) ).

cnf(f_1736_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5768),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5768),U_5770),U_5771)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5768),U_5769),U_5771)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5768),U_5771),c_Groups_Ozero__class_Ozero(U_5768)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5768),U_5769),U_5770))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5768) ),
    inference(clausify,[status(thm)],[f_1736_3]) ).

fof(f_1737_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_1737_2,plain,
    ! [U_5775,U_5774,U_5773,U_5772] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5772),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5772),U_5773),U_5775)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5772),U_5774),U_5775)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5772),c_Groups_Ozero__class_Ozero(U_5772)),U_5775))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5772),U_5773),U_5774))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5772) ),
    inference(variable_rename,[status(thm)],[f_1737_1]) ).

fof(f_1737_3,plain,
    ! [U_5772,U_5774,U_5773,U_5775] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5772),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5772),U_5773),U_5775)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5772),U_5774),U_5775)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5772),c_Groups_Ozero__class_Ozero(U_5772)),U_5775))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5772),U_5773),U_5774))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5772) ),
    inference(definitional_conversion,[status(esa)],[f_1737_2]) ).

cnf(f_1737_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5772),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5772),U_5773),U_5775)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5772),U_5774),U_5775)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5772),c_Groups_Ozero__class_Ozero(U_5772)),U_5775))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5772),U_5773),U_5774))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5772) ),
    inference(clausify,[status(thm)],[f_1737_3]) ).

fof(f_1738_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_1738_2,plain,
    ! [U_5778,U_5777,U_5776] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5776),U_5777),U_5778)),c_Groups_Ozero__class_Ozero(U_5776)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),c_Groups_Ozero__class_Ozero(U_5776)),U_5778))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),U_5777),c_Groups_Ozero__class_Ozero(U_5776))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),U_5778),c_Groups_Ozero__class_Ozero(U_5776)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),c_Groups_Ozero__class_Ozero(U_5776)),U_5777)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),c_Groups_Ozero__class_Ozero(U_5776)),U_5778))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),U_5777),c_Groups_Ozero__class_Ozero(U_5776))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),U_5778),c_Groups_Ozero__class_Ozero(U_5776)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),c_Groups_Ozero__class_Ozero(U_5776)),U_5777)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5776),U_5777),U_5778)),c_Groups_Ozero__class_Ozero(U_5776))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5776) ),
    inference(variable_rename,[status(thm)],[f_1738_1]) ).

fof(f_1738_3,plain,
    ( ! [U_5776,U_5777,U_5778] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),c_Groups_Ozero__class_Ozero(U_5776)),U_5778))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),U_5777),c_Groups_Ozero__class_Ozero(U_5776)))
        | ~ sP532(U_5776,U_5777,U_5778) )
    & ! [U_5776,U_5777,U_5778] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),U_5778),c_Groups_Ozero__class_Ozero(U_5776)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),c_Groups_Ozero__class_Ozero(U_5776)),U_5777))
        | ~ sP532(U_5776,U_5777,U_5778) )
    & ! [U_5776,U_5777,U_5778] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),c_Groups_Ozero__class_Ozero(U_5776)),U_5778))
        | ~ sP531(U_5776,U_5777,U_5778) )
    & ! [U_5776,U_5777,U_5778] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),U_5777),c_Groups_Ozero__class_Ozero(U_5776)))
        | ~ sP531(U_5776,U_5777,U_5778) )
    & ! [U_5776,U_5777,U_5778] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),U_5778),c_Groups_Ozero__class_Ozero(U_5776)))
        | ~ sP530(U_5776,U_5777,U_5778) )
    & ! [U_5776,U_5777,U_5778] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),c_Groups_Ozero__class_Ozero(U_5776)),U_5777))
        | ~ sP530(U_5776,U_5777,U_5778) )
    & ! [U_5776,U_5777,U_5778] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5776),U_5777),U_5778)),c_Groups_Ozero__class_Ozero(U_5776)))
        | sP532(U_5776,U_5777,U_5778)
        | ~ sP533(U_5776,U_5777,U_5778) )
    & ! [U_5776,U_5777,U_5778] :
        ( sP531(U_5776,U_5777,U_5778)
        | sP530(U_5776,U_5777,U_5778)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5776),U_5777),U_5778)),c_Groups_Ozero__class_Ozero(U_5776)))
        | ~ sP533(U_5776,U_5777,U_5778) )
    & ! [U_5776,U_5777,U_5778] :
        ( sP533(U_5776,U_5777,U_5778)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5776) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP530,sP531,sP532,sP533])],[f_1738_2]) ).

cnf(f_1738_4,plain,
    ( sP533(U_5776,U_5777,U_5778)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5776) ),
    inference(clausify,[status(thm)],[f_1738_3]) ).

cnf(f_1738_5,plain,
    ( sP531(U_5776,U_5777,U_5778)
    | sP530(U_5776,U_5777,U_5778)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5776),U_5777),U_5778)),c_Groups_Ozero__class_Ozero(U_5776)))
    | ~ sP533(U_5776,U_5777,U_5778) ),
    inference(clausify,[status(thm)],[f_1738_3]) ).

cnf(f_1738_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5776),U_5777),U_5778)),c_Groups_Ozero__class_Ozero(U_5776)))
    | sP532(U_5776,U_5777,U_5778)
    | ~ sP533(U_5776,U_5777,U_5778) ),
    inference(clausify,[status(thm)],[f_1738_3]) ).

cnf(f_1738_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),c_Groups_Ozero__class_Ozero(U_5776)),U_5777))
    | ~ sP530(U_5776,U_5777,U_5778) ),
    inference(clausify,[status(thm)],[f_1738_3]) ).

cnf(f_1738_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),U_5778),c_Groups_Ozero__class_Ozero(U_5776)))
    | ~ sP530(U_5776,U_5777,U_5778) ),
    inference(clausify,[status(thm)],[f_1738_3]) ).

cnf(f_1738_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),U_5777),c_Groups_Ozero__class_Ozero(U_5776)))
    | ~ sP531(U_5776,U_5777,U_5778) ),
    inference(clausify,[status(thm)],[f_1738_3]) ).

cnf(f_1738_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),c_Groups_Ozero__class_Ozero(U_5776)),U_5778))
    | ~ sP531(U_5776,U_5777,U_5778) ),
    inference(clausify,[status(thm)],[f_1738_3]) ).

cnf(f_1738_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),U_5778),c_Groups_Ozero__class_Ozero(U_5776)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),c_Groups_Ozero__class_Ozero(U_5776)),U_5777))
    | ~ sP532(U_5776,U_5777,U_5778) ),
    inference(clausify,[status(thm)],[f_1738_3]) ).

cnf(f_1738_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),c_Groups_Ozero__class_Ozero(U_5776)),U_5778))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5776),U_5777),c_Groups_Ozero__class_Ozero(U_5776)))
    | ~ sP532(U_5776,U_5777,U_5778) ),
    inference(clausify,[status(thm)],[f_1738_3]) ).

fof(f_1739_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_1739_2,plain,
    ! [U_5781,U_5780,U_5779] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),c_Groups_Ozero__class_Ozero(U_5779)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5779),U_5780),U_5781)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),U_5781),c_Groups_Ozero__class_Ozero(U_5779)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),U_5780),c_Groups_Ozero__class_Ozero(U_5779))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),c_Groups_Ozero__class_Ozero(U_5779)),U_5781))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),c_Groups_Ozero__class_Ozero(U_5779)),U_5780)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),U_5781),c_Groups_Ozero__class_Ozero(U_5779)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),U_5780),c_Groups_Ozero__class_Ozero(U_5779))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),c_Groups_Ozero__class_Ozero(U_5779)),U_5781))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),c_Groups_Ozero__class_Ozero(U_5779)),U_5780)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),c_Groups_Ozero__class_Ozero(U_5779)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5779),U_5780),U_5781))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5779) ),
    inference(variable_rename,[status(thm)],[f_1739_1]) ).

fof(f_1739_3,plain,
    ( ! [U_5781,U_5780,U_5779] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),U_5781),c_Groups_Ozero__class_Ozero(U_5779)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),U_5780),c_Groups_Ozero__class_Ozero(U_5779)))
        | ~ sP536(U_5781,U_5780,U_5779) )
    & ! [U_5781,U_5780,U_5779] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),c_Groups_Ozero__class_Ozero(U_5779)),U_5781))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),c_Groups_Ozero__class_Ozero(U_5779)),U_5780))
        | ~ sP536(U_5781,U_5780,U_5779) )
    & ! [U_5781,U_5780,U_5779] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),U_5781),c_Groups_Ozero__class_Ozero(U_5779)))
        | ~ sP535(U_5781,U_5780,U_5779) )
    & ! [U_5781,U_5780,U_5779] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),U_5780),c_Groups_Ozero__class_Ozero(U_5779)))
        | ~ sP535(U_5781,U_5780,U_5779) )
    & ! [U_5781,U_5780,U_5779] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),c_Groups_Ozero__class_Ozero(U_5779)),U_5781))
        | ~ sP534(U_5781,U_5780,U_5779) )
    & ! [U_5781,U_5780,U_5779] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),c_Groups_Ozero__class_Ozero(U_5779)),U_5780))
        | ~ sP534(U_5781,U_5780,U_5779) )
    & ! [U_5781,U_5780,U_5779] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),c_Groups_Ozero__class_Ozero(U_5779)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5779),U_5780),U_5781)))
        | sP536(U_5781,U_5780,U_5779)
        | ~ sP537(U_5781,U_5780,U_5779) )
    & ! [U_5781,U_5780,U_5779] :
        ( sP535(U_5781,U_5780,U_5779)
        | sP534(U_5781,U_5780,U_5779)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),c_Groups_Ozero__class_Ozero(U_5779)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5779),U_5780),U_5781)))
        | ~ sP537(U_5781,U_5780,U_5779) )
    & ! [U_5781,U_5780,U_5779] :
        ( sP537(U_5781,U_5780,U_5779)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5779) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP534,sP535,sP536,sP537])],[f_1739_2]) ).

cnf(f_1739_4,plain,
    ( sP537(U_5781,U_5780,U_5779)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5779) ),
    inference(clausify,[status(thm)],[f_1739_3]) ).

cnf(f_1739_5,plain,
    ( sP535(U_5781,U_5780,U_5779)
    | sP534(U_5781,U_5780,U_5779)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),c_Groups_Ozero__class_Ozero(U_5779)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5779),U_5780),U_5781)))
    | ~ sP537(U_5781,U_5780,U_5779) ),
    inference(clausify,[status(thm)],[f_1739_3]) ).

cnf(f_1739_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),c_Groups_Ozero__class_Ozero(U_5779)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5779),U_5780),U_5781)))
    | sP536(U_5781,U_5780,U_5779)
    | ~ sP537(U_5781,U_5780,U_5779) ),
    inference(clausify,[status(thm)],[f_1739_3]) ).

cnf(f_1739_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),c_Groups_Ozero__class_Ozero(U_5779)),U_5780))
    | ~ sP534(U_5781,U_5780,U_5779) ),
    inference(clausify,[status(thm)],[f_1739_3]) ).

cnf(f_1739_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),c_Groups_Ozero__class_Ozero(U_5779)),U_5781))
    | ~ sP534(U_5781,U_5780,U_5779) ),
    inference(clausify,[status(thm)],[f_1739_3]) ).

cnf(f_1739_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),U_5780),c_Groups_Ozero__class_Ozero(U_5779)))
    | ~ sP535(U_5781,U_5780,U_5779) ),
    inference(clausify,[status(thm)],[f_1739_3]) ).

cnf(f_1739_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),U_5781),c_Groups_Ozero__class_Ozero(U_5779)))
    | ~ sP535(U_5781,U_5780,U_5779) ),
    inference(clausify,[status(thm)],[f_1739_3]) ).

cnf(f_1739_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),c_Groups_Ozero__class_Ozero(U_5779)),U_5781))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),c_Groups_Ozero__class_Ozero(U_5779)),U_5780))
    | ~ sP536(U_5781,U_5780,U_5779) ),
    inference(clausify,[status(thm)],[f_1739_3]) ).

cnf(f_1739_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),U_5781),c_Groups_Ozero__class_Ozero(U_5779)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5779),U_5780),c_Groups_Ozero__class_Ozero(U_5779)))
    | ~ sP536(U_5781,U_5780,U_5779) ),
    inference(clausify,[status(thm)],[f_1739_3]) ).

fof(f_1740_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_1740_2,plain,
    ! [U_5784,U_5783,U_5782] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),c_Groups_Ozero__class_Ozero(U_5782)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5782),U_5783),U_5784)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),U_5784),c_Groups_Ozero__class_Ozero(U_5782)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),U_5783),c_Groups_Ozero__class_Ozero(U_5782))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),c_Groups_Ozero__class_Ozero(U_5782)),U_5784))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),c_Groups_Ozero__class_Ozero(U_5782)),U_5783)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),U_5784),c_Groups_Ozero__class_Ozero(U_5782)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),U_5783),c_Groups_Ozero__class_Ozero(U_5782))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),c_Groups_Ozero__class_Ozero(U_5782)),U_5784))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),c_Groups_Ozero__class_Ozero(U_5782)),U_5783)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),c_Groups_Ozero__class_Ozero(U_5782)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5782),U_5783),U_5784))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5782) ),
    inference(variable_rename,[status(thm)],[f_1740_1]) ).

fof(f_1740_3,plain,
    ( ! [U_5783,U_5782,U_5784] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),U_5784),c_Groups_Ozero__class_Ozero(U_5782)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),U_5783),c_Groups_Ozero__class_Ozero(U_5782)))
        | ~ sP540(U_5783,U_5782,U_5784) )
    & ! [U_5783,U_5782,U_5784] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),c_Groups_Ozero__class_Ozero(U_5782)),U_5784))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),c_Groups_Ozero__class_Ozero(U_5782)),U_5783))
        | ~ sP540(U_5783,U_5782,U_5784) )
    & ! [U_5783,U_5782,U_5784] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),U_5784),c_Groups_Ozero__class_Ozero(U_5782)))
        | ~ sP539(U_5783,U_5782,U_5784) )
    & ! [U_5783,U_5782,U_5784] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),U_5783),c_Groups_Ozero__class_Ozero(U_5782)))
        | ~ sP539(U_5783,U_5782,U_5784) )
    & ! [U_5783,U_5782,U_5784] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),c_Groups_Ozero__class_Ozero(U_5782)),U_5784))
        | ~ sP538(U_5783,U_5782,U_5784) )
    & ! [U_5783,U_5782,U_5784] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),c_Groups_Ozero__class_Ozero(U_5782)),U_5783))
        | ~ sP538(U_5783,U_5782,U_5784) )
    & ! [U_5783,U_5782,U_5784] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),c_Groups_Ozero__class_Ozero(U_5782)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5782),U_5783),U_5784)))
        | sP540(U_5783,U_5782,U_5784)
        | ~ sP541(U_5783,U_5782,U_5784) )
    & ! [U_5783,U_5782,U_5784] :
        ( sP539(U_5783,U_5782,U_5784)
        | sP538(U_5783,U_5782,U_5784)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),c_Groups_Ozero__class_Ozero(U_5782)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5782),U_5783),U_5784)))
        | ~ sP541(U_5783,U_5782,U_5784) )
    & ! [U_5783,U_5782,U_5784] :
        ( sP541(U_5783,U_5782,U_5784)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5782) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP538,sP539,sP540,sP541])],[f_1740_2]) ).

cnf(f_1740_4,plain,
    ( sP541(U_5783,U_5782,U_5784)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5782) ),
    inference(clausify,[status(thm)],[f_1740_3]) ).

cnf(f_1740_5,plain,
    ( sP539(U_5783,U_5782,U_5784)
    | sP538(U_5783,U_5782,U_5784)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),c_Groups_Ozero__class_Ozero(U_5782)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5782),U_5783),U_5784)))
    | ~ sP541(U_5783,U_5782,U_5784) ),
    inference(clausify,[status(thm)],[f_1740_3]) ).

cnf(f_1740_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),c_Groups_Ozero__class_Ozero(U_5782)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5782),U_5783),U_5784)))
    | sP540(U_5783,U_5782,U_5784)
    | ~ sP541(U_5783,U_5782,U_5784) ),
    inference(clausify,[status(thm)],[f_1740_3]) ).

cnf(f_1740_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),c_Groups_Ozero__class_Ozero(U_5782)),U_5783))
    | ~ sP538(U_5783,U_5782,U_5784) ),
    inference(clausify,[status(thm)],[f_1740_3]) ).

cnf(f_1740_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),c_Groups_Ozero__class_Ozero(U_5782)),U_5784))
    | ~ sP538(U_5783,U_5782,U_5784) ),
    inference(clausify,[status(thm)],[f_1740_3]) ).

cnf(f_1740_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),U_5783),c_Groups_Ozero__class_Ozero(U_5782)))
    | ~ sP539(U_5783,U_5782,U_5784) ),
    inference(clausify,[status(thm)],[f_1740_3]) ).

cnf(f_1740_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),U_5784),c_Groups_Ozero__class_Ozero(U_5782)))
    | ~ sP539(U_5783,U_5782,U_5784) ),
    inference(clausify,[status(thm)],[f_1740_3]) ).

cnf(f_1740_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),c_Groups_Ozero__class_Ozero(U_5782)),U_5784))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),c_Groups_Ozero__class_Ozero(U_5782)),U_5783))
    | ~ sP540(U_5783,U_5782,U_5784) ),
    inference(clausify,[status(thm)],[f_1740_3]) ).

cnf(f_1740_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),U_5784),c_Groups_Ozero__class_Ozero(U_5782)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5782),U_5783),c_Groups_Ozero__class_Ozero(U_5782)))
    | ~ sP540(U_5783,U_5782,U_5784) ),
    inference(clausify,[status(thm)],[f_1740_3]) ).

fof(f_1741_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_1741_2,plain,
    ! [U_5787,U_5786,U_5785] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5785),U_5786),U_5787)),c_Groups_Ozero__class_Ozero(U_5785)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),c_Groups_Ozero__class_Ozero(U_5785)),U_5787))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),U_5786),c_Groups_Ozero__class_Ozero(U_5785))) )
            & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),U_5787),c_Groups_Ozero__class_Ozero(U_5785)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),c_Groups_Ozero__class_Ozero(U_5785)),U_5786)) ) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),c_Groups_Ozero__class_Ozero(U_5785)),U_5787))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),U_5786),c_Groups_Ozero__class_Ozero(U_5785))) )
          | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),U_5787),c_Groups_Ozero__class_Ozero(U_5785)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),c_Groups_Ozero__class_Ozero(U_5785)),U_5786)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5785),U_5786),U_5787)),c_Groups_Ozero__class_Ozero(U_5785))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5785) ),
    inference(variable_rename,[status(thm)],[f_1741_1]) ).

fof(f_1741_3,plain,
    ( ! [U_5785,U_5787,U_5786] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),c_Groups_Ozero__class_Ozero(U_5785)),U_5787))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),U_5786),c_Groups_Ozero__class_Ozero(U_5785)))
        | ~ sP544(U_5785,U_5787,U_5786) )
    & ! [U_5785,U_5787,U_5786] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),U_5787),c_Groups_Ozero__class_Ozero(U_5785)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),c_Groups_Ozero__class_Ozero(U_5785)),U_5786))
        | ~ sP544(U_5785,U_5787,U_5786) )
    & ! [U_5785,U_5787,U_5786] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),c_Groups_Ozero__class_Ozero(U_5785)),U_5787))
        | ~ sP543(U_5785,U_5787,U_5786) )
    & ! [U_5785,U_5787,U_5786] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),U_5786),c_Groups_Ozero__class_Ozero(U_5785)))
        | ~ sP543(U_5785,U_5787,U_5786) )
    & ! [U_5785,U_5787,U_5786] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),U_5787),c_Groups_Ozero__class_Ozero(U_5785)))
        | ~ sP542(U_5785,U_5787,U_5786) )
    & ! [U_5785,U_5787,U_5786] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),c_Groups_Ozero__class_Ozero(U_5785)),U_5786))
        | ~ sP542(U_5785,U_5787,U_5786) )
    & ! [U_5785,U_5787,U_5786] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5785),U_5786),U_5787)),c_Groups_Ozero__class_Ozero(U_5785)))
        | sP544(U_5785,U_5787,U_5786)
        | ~ sP545(U_5785,U_5787,U_5786) )
    & ! [U_5785,U_5787,U_5786] :
        ( sP543(U_5785,U_5787,U_5786)
        | sP542(U_5785,U_5787,U_5786)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5785),U_5786),U_5787)),c_Groups_Ozero__class_Ozero(U_5785)))
        | ~ sP545(U_5785,U_5787,U_5786) )
    & ! [U_5785,U_5787,U_5786] :
        ( sP545(U_5785,U_5787,U_5786)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5785) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP542,sP543,sP544,sP545])],[f_1741_2]) ).

cnf(f_1741_4,plain,
    ( sP545(U_5785,U_5787,U_5786)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5785) ),
    inference(clausify,[status(thm)],[f_1741_3]) ).

cnf(f_1741_5,plain,
    ( sP543(U_5785,U_5787,U_5786)
    | sP542(U_5785,U_5787,U_5786)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5785),U_5786),U_5787)),c_Groups_Ozero__class_Ozero(U_5785)))
    | ~ sP545(U_5785,U_5787,U_5786) ),
    inference(clausify,[status(thm)],[f_1741_3]) ).

cnf(f_1741_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5785),U_5786),U_5787)),c_Groups_Ozero__class_Ozero(U_5785)))
    | sP544(U_5785,U_5787,U_5786)
    | ~ sP545(U_5785,U_5787,U_5786) ),
    inference(clausify,[status(thm)],[f_1741_3]) ).

cnf(f_1741_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),c_Groups_Ozero__class_Ozero(U_5785)),U_5786))
    | ~ sP542(U_5785,U_5787,U_5786) ),
    inference(clausify,[status(thm)],[f_1741_3]) ).

cnf(f_1741_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),U_5787),c_Groups_Ozero__class_Ozero(U_5785)))
    | ~ sP542(U_5785,U_5787,U_5786) ),
    inference(clausify,[status(thm)],[f_1741_3]) ).

cnf(f_1741_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),U_5786),c_Groups_Ozero__class_Ozero(U_5785)))
    | ~ sP543(U_5785,U_5787,U_5786) ),
    inference(clausify,[status(thm)],[f_1741_3]) ).

cnf(f_1741_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),c_Groups_Ozero__class_Ozero(U_5785)),U_5787))
    | ~ sP543(U_5785,U_5787,U_5786) ),
    inference(clausify,[status(thm)],[f_1741_3]) ).

cnf(f_1741_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),U_5787),c_Groups_Ozero__class_Ozero(U_5785)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),c_Groups_Ozero__class_Ozero(U_5785)),U_5786))
    | ~ sP544(U_5785,U_5787,U_5786) ),
    inference(clausify,[status(thm)],[f_1741_3]) ).

cnf(f_1741_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),c_Groups_Ozero__class_Ozero(U_5785)),U_5787))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5785),U_5786),c_Groups_Ozero__class_Ozero(U_5785)))
    | ~ sP544(U_5785,U_5787,U_5786) ),
    inference(clausify,[status(thm)],[f_1741_3]) ).

fof(f_1742_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_1742_2,plain,
    ! [U_5790,U_5789,U_5788] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5788),c_Groups_Ozero__class_Ozero(U_5788)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5788),U_5789),U_5790)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5788),c_Groups_Ozero__class_Ozero(U_5788)),U_5790))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5788),c_Groups_Ozero__class_Ozero(U_5788)),U_5789))
      | ~ class_Fields_Olinordered__field(U_5788) ),
    inference(variable_rename,[status(thm)],[f_1742_1]) ).

fof(f_1742_3,plain,
    ! [U_5790,U_5789,U_5788] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5788),c_Groups_Ozero__class_Ozero(U_5788)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5788),U_5789),U_5790)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5788),c_Groups_Ozero__class_Ozero(U_5788)),U_5790))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5788),c_Groups_Ozero__class_Ozero(U_5788)),U_5789))
      | ~ class_Fields_Olinordered__field(U_5788) ),
    inference(definitional_conversion,[status(esa)],[f_1742_2]) ).

cnf(f_1742_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5788),c_Groups_Ozero__class_Ozero(U_5788)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5788),U_5789),U_5790)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5788),c_Groups_Ozero__class_Ozero(U_5788)),U_5790))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5788),c_Groups_Ozero__class_Ozero(U_5788)),U_5789))
    | ~ class_Fields_Olinordered__field(U_5788) ),
    inference(clausify,[status(thm)],[f_1742_3]) ).

fof(f_1743_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_1743_2,plain,
    ! [U_5793,U_5792,U_5791] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5791),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5791),U_5792),U_5793)),c_Groups_Ozero__class_Ozero(U_5791)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5791),U_5793),c_Groups_Ozero__class_Ozero(U_5791)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5791),c_Groups_Ozero__class_Ozero(U_5791)),U_5792))
      | ~ class_Fields_Olinordered__field(U_5791) ),
    inference(variable_rename,[status(thm)],[f_1743_1]) ).

fof(f_1743_3,plain,
    ! [U_5792,U_5791,U_5793] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5791),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5791),U_5792),U_5793)),c_Groups_Ozero__class_Ozero(U_5791)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5791),U_5793),c_Groups_Ozero__class_Ozero(U_5791)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5791),c_Groups_Ozero__class_Ozero(U_5791)),U_5792))
      | ~ class_Fields_Olinordered__field(U_5791) ),
    inference(definitional_conversion,[status(esa)],[f_1743_2]) ).

cnf(f_1743_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5791),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5791),U_5792),U_5793)),c_Groups_Ozero__class_Ozero(U_5791)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5791),U_5793),c_Groups_Ozero__class_Ozero(U_5791)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5791),c_Groups_Ozero__class_Ozero(U_5791)),U_5792))
    | ~ class_Fields_Olinordered__field(U_5791) ),
    inference(clausify,[status(thm)],[f_1743_3]) ).

fof(f_1744_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_1744_2,plain,
    ! [U_5796,U_5795,U_5794] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5794),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5794),U_5795),U_5796)),c_Groups_Ozero__class_Ozero(U_5794)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5794),c_Groups_Ozero__class_Ozero(U_5794)),U_5796))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5794),U_5795),c_Groups_Ozero__class_Ozero(U_5794)))
      | ~ class_Fields_Olinordered__field(U_5794) ),
    inference(variable_rename,[status(thm)],[f_1744_1]) ).

fof(f_1744_3,plain,
    ! [U_5796,U_5794,U_5795] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5794),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5794),U_5795),U_5796)),c_Groups_Ozero__class_Ozero(U_5794)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5794),c_Groups_Ozero__class_Ozero(U_5794)),U_5796))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5794),U_5795),c_Groups_Ozero__class_Ozero(U_5794)))
      | ~ class_Fields_Olinordered__field(U_5794) ),
    inference(definitional_conversion,[status(esa)],[f_1744_2]) ).

cnf(f_1744_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5794),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5794),U_5795),U_5796)),c_Groups_Ozero__class_Ozero(U_5794)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5794),c_Groups_Ozero__class_Ozero(U_5794)),U_5796))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5794),U_5795),c_Groups_Ozero__class_Ozero(U_5794)))
    | ~ class_Fields_Olinordered__field(U_5794) ),
    inference(clausify,[status(thm)],[f_1744_3]) ).

fof(f_1745_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_1745_2,plain,
    ! [U_5799,U_5798,U_5797] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5797),c_Groups_Ozero__class_Ozero(U_5797)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5797),U_5798),U_5799)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5797),U_5799),c_Groups_Ozero__class_Ozero(U_5797)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5797),U_5798),c_Groups_Ozero__class_Ozero(U_5797)))
      | ~ class_Fields_Olinordered__field(U_5797) ),
    inference(variable_rename,[status(thm)],[f_1745_1]) ).

fof(f_1745_3,plain,
    ! [U_5797,U_5798,U_5799] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5797),c_Groups_Ozero__class_Ozero(U_5797)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5797),U_5798),U_5799)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5797),U_5799),c_Groups_Ozero__class_Ozero(U_5797)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5797),U_5798),c_Groups_Ozero__class_Ozero(U_5797)))
      | ~ class_Fields_Olinordered__field(U_5797) ),
    inference(definitional_conversion,[status(esa)],[f_1745_2]) ).

cnf(f_1745_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5797),c_Groups_Ozero__class_Ozero(U_5797)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5797),U_5798),U_5799)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5797),U_5799),c_Groups_Ozero__class_Ozero(U_5797)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5797),U_5798),c_Groups_Ozero__class_Ozero(U_5797)))
    | ~ class_Fields_Olinordered__field(U_5797) ),
    inference(clausify,[status(thm)],[f_1745_3]) ).

fof(f_1746_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_1746_2,plain,
    ! [U_5803,U_5802,U_5801,U_5800] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5800),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5800),U_5801),U_5803)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5800),U_5802),U_5803)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5800),c_Groups_Ozero__class_Ozero(U_5800)),U_5803))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5800),U_5801),U_5802))
      | ~ class_Fields_Olinordered__field(U_5800) ),
    inference(variable_rename,[status(thm)],[f_1746_1]) ).

fof(f_1746_3,plain,
    ! [U_5800,U_5801,U_5802,U_5803] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5800),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5800),U_5801),U_5803)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5800),U_5802),U_5803)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5800),c_Groups_Ozero__class_Ozero(U_5800)),U_5803))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5800),U_5801),U_5802))
      | ~ class_Fields_Olinordered__field(U_5800) ),
    inference(definitional_conversion,[status(esa)],[f_1746_2]) ).

cnf(f_1746_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5800),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5800),U_5801),U_5803)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5800),U_5802),U_5803)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5800),c_Groups_Ozero__class_Ozero(U_5800)),U_5803))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5800),U_5801),U_5802))
    | ~ class_Fields_Olinordered__field(U_5800) ),
    inference(clausify,[status(thm)],[f_1746_3]) ).

fof(f_1747_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_1747_2,plain,
    ! [U_5807,U_5806,U_5805,U_5804] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5804),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5804),U_5806),U_5807)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5804),U_5805),U_5807)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5804),U_5807),c_Groups_Ozero__class_Ozero(U_5804)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5804),U_5805),U_5806))
      | ~ class_Fields_Olinordered__field(U_5804) ),
    inference(variable_rename,[status(thm)],[f_1747_1]) ).

fof(f_1747_3,plain,
    ! [U_5804,U_5805,U_5806,U_5807] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5804),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5804),U_5806),U_5807)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5804),U_5805),U_5807)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5804),U_5807),c_Groups_Ozero__class_Ozero(U_5804)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5804),U_5805),U_5806))
      | ~ class_Fields_Olinordered__field(U_5804) ),
    inference(definitional_conversion,[status(esa)],[f_1747_2]) ).

cnf(f_1747_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5804),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5804),U_5806),U_5807)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5804),U_5805),U_5807)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5804),U_5807),c_Groups_Ozero__class_Ozero(U_5804)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5804),U_5805),U_5806))
    | ~ class_Fields_Olinordered__field(U_5804) ),
    inference(clausify,[status(thm)],[f_1747_3]) ).

fof(f_1748_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_1748_2,plain,
    ! [U_5812,U_5811,U_5810,U_5809,U_5808] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5808),U_5811),U_5809) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5808),U_5812),U_5810)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5808),U_5811),U_5810) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5808),U_5812),U_5809) )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5808),U_5811),U_5810) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5808),U_5812),U_5809)
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5808),U_5811),U_5809) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5808),U_5812),U_5810) ) )
      | U_5810 = c_Groups_Ozero__class_Ozero(U_5808)
      | U_5809 = c_Groups_Ozero__class_Ozero(U_5808)
      | ~ class_Fields_Ofield(U_5808) ),
    inference(variable_rename,[status(thm)],[f_1748_1]) ).

fof(f_1748_3,plain,
    ( ! [U_5808,U_5809,U_5810,U_5811,U_5812] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5808),U_5811),U_5809) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5808),U_5812),U_5810)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5808),U_5811),U_5810) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5808),U_5812),U_5809)
        | ~ sP546(U_5808,U_5809,U_5810,U_5811,U_5812) )
    & ! [U_5808,U_5809,U_5810,U_5811,U_5812] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5808),U_5811),U_5810) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5808),U_5812),U_5809)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5808),U_5811),U_5809) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5808),U_5812),U_5810)
        | ~ sP546(U_5808,U_5809,U_5810,U_5811,U_5812) )
    & ! [U_5808,U_5809,U_5810,U_5811,U_5812] :
        ( sP546(U_5808,U_5809,U_5810,U_5811,U_5812)
        | U_5810 = c_Groups_Ozero__class_Ozero(U_5808)
        | U_5809 = c_Groups_Ozero__class_Ozero(U_5808)
        | ~ class_Fields_Ofield(U_5808) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP546])],[f_1748_2]) ).

cnf(f_1748_4,plain,
    ( sP546(U_5808,U_5809,U_5810,U_5811,U_5812)
    | U_5810 = c_Groups_Ozero__class_Ozero(U_5808)
    | U_5809 = c_Groups_Ozero__class_Ozero(U_5808)
    | ~ class_Fields_Ofield(U_5808) ),
    inference(clausify,[status(thm)],[f_1748_3]) ).

cnf(f_1748_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5808),U_5811),U_5810) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5808),U_5812),U_5809)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5808),U_5811),U_5809) != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5808),U_5812),U_5810)
    | ~ sP546(U_5808,U_5809,U_5810,U_5811,U_5812) ),
    inference(clausify,[status(thm)],[f_1748_3]) ).

cnf(f_1748_6,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5808),U_5811),U_5809) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5808),U_5812),U_5810)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5808),U_5811),U_5810) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5808),U_5812),U_5809)
    | ~ sP546(U_5808,U_5809,U_5810,U_5811,U_5812) ),
    inference(clausify,[status(thm)],[f_1748_3]) ).

fof(f_1749_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_1749_2,plain,
    ! [U_5816,U_5815,U_5814,U_5813] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5813),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5813),U_5814),U_5815)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5813),U_5814),U_5816)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5813),U_5815),U_5816)
      | U_5814 = c_Groups_Ozero__class_Ozero(U_5813)
      | ~ class_Fields_Ofield__inverse__zero(U_5813) ),
    inference(variable_rename,[status(thm)],[f_1749_1]) ).

fof(f_1749_3,plain,
    ! [U_5814,U_5816,U_5813,U_5815] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5813),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5813),U_5814),U_5815)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5813),U_5814),U_5816)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5813),U_5815),U_5816)
      | U_5814 = c_Groups_Ozero__class_Ozero(U_5813)
      | ~ class_Fields_Ofield__inverse__zero(U_5813) ),
    inference(definitional_conversion,[status(esa)],[f_1749_2]) ).

cnf(f_1749_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5813),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5813),U_5814),U_5815)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5813),U_5814),U_5816)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5813),U_5815),U_5816)
    | U_5814 = c_Groups_Ozero__class_Ozero(U_5813)
    | ~ class_Fields_Ofield__inverse__zero(U_5813) ),
    inference(clausify,[status(thm)],[f_1749_3]) ).

fof(f_1750_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_1750_2,plain,
    ! [U_5820,U_5819,U_5818,U_5817] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5817),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5817),U_5819),U_5818)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5817),U_5820),U_5818)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5817),U_5819),U_5820)
      | U_5818 = c_Groups_Ozero__class_Ozero(U_5817)
      | ~ class_Fields_Ofield__inverse__zero(U_5817) ),
    inference(variable_rename,[status(thm)],[f_1750_1]) ).

fof(f_1750_3,plain,
    ! [U_5818,U_5817,U_5819,U_5820] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5817),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5817),U_5819),U_5818)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5817),U_5820),U_5818)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5817),U_5819),U_5820)
      | U_5818 = c_Groups_Ozero__class_Ozero(U_5817)
      | ~ class_Fields_Ofield__inverse__zero(U_5817) ),
    inference(definitional_conversion,[status(esa)],[f_1750_2]) ).

cnf(f_1750_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5817),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5817),U_5819),U_5818)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5817),U_5820),U_5818)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5817),U_5819),U_5820)
    | U_5818 = c_Groups_Ozero__class_Ozero(U_5817)
    | ~ class_Fields_Ofield__inverse__zero(U_5817) ),
    inference(clausify,[status(thm)],[f_1750_3]) ).

fof(f_1751_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_1751_2,plain,
    ! [U_5824,U_5823,U_5822,U_5821] :
      ( ( ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5821),U_5822),U_5823) = U_5824
          | ( U_5824 != c_Groups_Ozero__class_Ozero(U_5821)
            & U_5823 = c_Groups_Ozero__class_Ozero(U_5821) )
          | ( U_5822 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5821),U_5824),U_5823)
            & U_5823 != c_Groups_Ozero__class_Ozero(U_5821) ) )
        & ( ( ( U_5824 = c_Groups_Ozero__class_Ozero(U_5821)
              | U_5823 != c_Groups_Ozero__class_Ozero(U_5821) )
            & ( U_5822 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5821),U_5824),U_5823)
              | U_5823 = c_Groups_Ozero__class_Ozero(U_5821) ) )
          | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5821),U_5822),U_5823) != U_5824 ) )
      | ~ class_Fields_Ofield__inverse__zero(U_5821) ),
    inference(variable_rename,[status(thm)],[f_1751_1]) ).

fof(f_1751_3,plain,
    ( ! [U_5821,U_5823,U_5824] :
        ( U_5824 != c_Groups_Ozero__class_Ozero(U_5821)
        | ~ sP549(U_5821,U_5823,U_5824) )
    & ! [U_5821,U_5823,U_5824] :
        ( U_5823 = c_Groups_Ozero__class_Ozero(U_5821)
        | ~ sP549(U_5821,U_5823,U_5824) )
    & ! [U_5822,U_5821,U_5823,U_5824] :
        ( U_5822 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5821),U_5824),U_5823)
        | ~ sP548(U_5822,U_5821,U_5823,U_5824) )
    & ! [U_5822,U_5821,U_5823,U_5824] :
        ( U_5823 != c_Groups_Ozero__class_Ozero(U_5821)
        | ~ sP548(U_5822,U_5821,U_5823,U_5824) )
    & ! [U_5822,U_5821,U_5823,U_5824] :
        ( U_5824 = c_Groups_Ozero__class_Ozero(U_5821)
        | U_5823 != c_Groups_Ozero__class_Ozero(U_5821)
        | ~ sP547(U_5822,U_5821,U_5823,U_5824) )
    & ! [U_5822,U_5821,U_5823,U_5824] :
        ( U_5822 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5821),U_5824),U_5823)
        | U_5823 = c_Groups_Ozero__class_Ozero(U_5821)
        | ~ sP547(U_5822,U_5821,U_5823,U_5824) )
    & ! [U_5822,U_5821,U_5823,U_5824] :
        ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5821),U_5822),U_5823) = U_5824
        | sP549(U_5821,U_5823,U_5824)
        | sP548(U_5822,U_5821,U_5823,U_5824)
        | ~ sP550(U_5822,U_5821,U_5823,U_5824) )
    & ! [U_5822,U_5821,U_5823,U_5824] :
        ( sP547(U_5822,U_5821,U_5823,U_5824)
        | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5821),U_5822),U_5823) != U_5824
        | ~ sP550(U_5822,U_5821,U_5823,U_5824) )
    & ! [U_5822,U_5821,U_5823,U_5824] :
        ( sP550(U_5822,U_5821,U_5823,U_5824)
        | ~ class_Fields_Ofield__inverse__zero(U_5821) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP547,sP548,sP549,sP550])],[f_1751_2]) ).

cnf(f_1751_4,plain,
    ( sP550(U_5822,U_5821,U_5823,U_5824)
    | ~ class_Fields_Ofield__inverse__zero(U_5821) ),
    inference(clausify,[status(thm)],[f_1751_3]) ).

cnf(f_1751_5,plain,
    ( sP547(U_5822,U_5821,U_5823,U_5824)
    | hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5821),U_5822),U_5823) != U_5824
    | ~ sP550(U_5822,U_5821,U_5823,U_5824) ),
    inference(clausify,[status(thm)],[f_1751_3]) ).

cnf(f_1751_6,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5821),U_5822),U_5823) = U_5824
    | sP549(U_5821,U_5823,U_5824)
    | sP548(U_5822,U_5821,U_5823,U_5824)
    | ~ sP550(U_5822,U_5821,U_5823,U_5824) ),
    inference(clausify,[status(thm)],[f_1751_3]) ).

cnf(f_1751_7,plain,
    ( U_5822 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5821),U_5824),U_5823)
    | U_5823 = c_Groups_Ozero__class_Ozero(U_5821)
    | ~ sP547(U_5822,U_5821,U_5823,U_5824) ),
    inference(clausify,[status(thm)],[f_1751_3]) ).

cnf(f_1751_8,plain,
    ( U_5824 = c_Groups_Ozero__class_Ozero(U_5821)
    | U_5823 != c_Groups_Ozero__class_Ozero(U_5821)
    | ~ sP547(U_5822,U_5821,U_5823,U_5824) ),
    inference(clausify,[status(thm)],[f_1751_3]) ).

cnf(f_1751_9,plain,
    ( U_5823 != c_Groups_Ozero__class_Ozero(U_5821)
    | ~ sP548(U_5822,U_5821,U_5823,U_5824) ),
    inference(clausify,[status(thm)],[f_1751_3]) ).

cnf(f_1751_10,plain,
    ( U_5822 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5821),U_5824),U_5823)
    | ~ sP548(U_5822,U_5821,U_5823,U_5824) ),
    inference(clausify,[status(thm)],[f_1751_3]) ).

cnf(f_1751_11,plain,
    ( U_5823 = c_Groups_Ozero__class_Ozero(U_5821)
    | ~ sP549(U_5821,U_5823,U_5824) ),
    inference(clausify,[status(thm)],[f_1751_3]) ).

cnf(f_1751_12,plain,
    ( U_5824 != c_Groups_Ozero__class_Ozero(U_5821)
    | ~ sP549(U_5821,U_5823,U_5824) ),
    inference(clausify,[status(thm)],[f_1751_3]) ).

fof(f_1752_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_1752_2,plain,
    ! [U_5828,U_5827,U_5826,U_5825] :
      ( ( ( U_5826 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5825),U_5827),U_5828)
          | ( U_5826 != c_Groups_Ozero__class_Ozero(U_5825)
            & U_5828 = c_Groups_Ozero__class_Ozero(U_5825) )
          | ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5825),U_5826),U_5828) != U_5827
            & U_5828 != c_Groups_Ozero__class_Ozero(U_5825) ) )
        & ( ( ( U_5826 = c_Groups_Ozero__class_Ozero(U_5825)
              | U_5828 != c_Groups_Ozero__class_Ozero(U_5825) )
            & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5825),U_5826),U_5828) = U_5827
              | U_5828 = c_Groups_Ozero__class_Ozero(U_5825) ) )
          | U_5826 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5825),U_5827),U_5828) ) )
      | ~ class_Fields_Ofield__inverse__zero(U_5825) ),
    inference(variable_rename,[status(thm)],[f_1752_1]) ).

fof(f_1752_3,plain,
    ( ! [U_5825,U_5828,U_5826] :
        ( U_5826 != c_Groups_Ozero__class_Ozero(U_5825)
        | ~ sP553(U_5825,U_5828,U_5826) )
    & ! [U_5825,U_5828,U_5826] :
        ( U_5828 = c_Groups_Ozero__class_Ozero(U_5825)
        | ~ sP553(U_5825,U_5828,U_5826) )
    & ! [U_5825,U_5827,U_5828,U_5826] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5825),U_5826),U_5828) != U_5827
        | ~ sP552(U_5825,U_5827,U_5828,U_5826) )
    & ! [U_5825,U_5827,U_5828,U_5826] :
        ( U_5828 != c_Groups_Ozero__class_Ozero(U_5825)
        | ~ sP552(U_5825,U_5827,U_5828,U_5826) )
    & ! [U_5825,U_5827,U_5828,U_5826] :
        ( U_5826 = c_Groups_Ozero__class_Ozero(U_5825)
        | U_5828 != c_Groups_Ozero__class_Ozero(U_5825)
        | ~ sP551(U_5825,U_5827,U_5828,U_5826) )
    & ! [U_5825,U_5827,U_5828,U_5826] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5825),U_5826),U_5828) = U_5827
        | U_5828 = c_Groups_Ozero__class_Ozero(U_5825)
        | ~ sP551(U_5825,U_5827,U_5828,U_5826) )
    & ! [U_5825,U_5827,U_5828,U_5826] :
        ( U_5826 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5825),U_5827),U_5828)
        | sP553(U_5825,U_5828,U_5826)
        | sP552(U_5825,U_5827,U_5828,U_5826)
        | ~ sP554(U_5825,U_5827,U_5828,U_5826) )
    & ! [U_5825,U_5827,U_5828,U_5826] :
        ( sP551(U_5825,U_5827,U_5828,U_5826)
        | U_5826 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5825),U_5827),U_5828)
        | ~ sP554(U_5825,U_5827,U_5828,U_5826) )
    & ! [U_5825,U_5827,U_5828,U_5826] :
        ( sP554(U_5825,U_5827,U_5828,U_5826)
        | ~ class_Fields_Ofield__inverse__zero(U_5825) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP551,sP552,sP553,sP554])],[f_1752_2]) ).

cnf(f_1752_4,plain,
    ( sP554(U_5825,U_5827,U_5828,U_5826)
    | ~ class_Fields_Ofield__inverse__zero(U_5825) ),
    inference(clausify,[status(thm)],[f_1752_3]) ).

cnf(f_1752_5,plain,
    ( sP551(U_5825,U_5827,U_5828,U_5826)
    | U_5826 != hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5825),U_5827),U_5828)
    | ~ sP554(U_5825,U_5827,U_5828,U_5826) ),
    inference(clausify,[status(thm)],[f_1752_3]) ).

cnf(f_1752_6,plain,
    ( U_5826 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5825),U_5827),U_5828)
    | sP553(U_5825,U_5828,U_5826)
    | sP552(U_5825,U_5827,U_5828,U_5826)
    | ~ sP554(U_5825,U_5827,U_5828,U_5826) ),
    inference(clausify,[status(thm)],[f_1752_3]) ).

cnf(f_1752_7,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5825),U_5826),U_5828) = U_5827
    | U_5828 = c_Groups_Ozero__class_Ozero(U_5825)
    | ~ sP551(U_5825,U_5827,U_5828,U_5826) ),
    inference(clausify,[status(thm)],[f_1752_3]) ).

cnf(f_1752_8,plain,
    ( U_5826 = c_Groups_Ozero__class_Ozero(U_5825)
    | U_5828 != c_Groups_Ozero__class_Ozero(U_5825)
    | ~ sP551(U_5825,U_5827,U_5828,U_5826) ),
    inference(clausify,[status(thm)],[f_1752_3]) ).

cnf(f_1752_9,plain,
    ( U_5828 != c_Groups_Ozero__class_Ozero(U_5825)
    | ~ sP552(U_5825,U_5827,U_5828,U_5826) ),
    inference(clausify,[status(thm)],[f_1752_3]) ).

cnf(f_1752_10,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5825),U_5826),U_5828) != U_5827
    | ~ sP552(U_5825,U_5827,U_5828,U_5826) ),
    inference(clausify,[status(thm)],[f_1752_3]) ).

cnf(f_1752_11,plain,
    ( U_5828 = c_Groups_Ozero__class_Ozero(U_5825)
    | ~ sP553(U_5825,U_5828,U_5826) ),
    inference(clausify,[status(thm)],[f_1752_3]) ).

cnf(f_1752_12,plain,
    ( U_5826 != c_Groups_Ozero__class_Ozero(U_5825)
    | ~ sP553(U_5825,U_5828,U_5826) ),
    inference(clausify,[status(thm)],[f_1752_3]) ).

fof(f_1753_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_1753_2,plain,
    ! [U_5831,U_5830,U_5829] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5829),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5829),U_5831),U_5830)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5829),hAPP(c_Groups_Oabs__class_Oabs(U_5829),U_5831)),hAPP(c_Groups_Oabs__class_Oabs(U_5829),U_5830))
      | U_5830 = c_Groups_Ozero__class_Ozero(U_5829)
      | ~ class_Fields_Olinordered__field(U_5829) ),
    inference(variable_rename,[status(thm)],[f_1753_1]) ).

fof(f_1753_3,plain,
    ! [U_5831,U_5830,U_5829] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_5829),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5829),U_5831),U_5830)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5829),hAPP(c_Groups_Oabs__class_Oabs(U_5829),U_5831)),hAPP(c_Groups_Oabs__class_Oabs(U_5829),U_5830))
      | U_5830 = c_Groups_Ozero__class_Ozero(U_5829)
      | ~ class_Fields_Olinordered__field(U_5829) ),
    inference(definitional_conversion,[status(esa)],[f_1753_2]) ).

cnf(f_1753_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_5829),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5829),U_5831),U_5830)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5829),hAPP(c_Groups_Oabs__class_Oabs(U_5829),U_5831)),hAPP(c_Groups_Oabs__class_Oabs(U_5829),U_5830))
    | U_5830 = c_Groups_Ozero__class_Ozero(U_5829)
    | ~ class_Fields_Olinordered__field(U_5829) ),
    inference(clausify,[status(thm)],[f_1753_3]) ).

fof(f_1754_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_1754_2,plain,
    ! [U_5834,U_5833,U_5832] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5832),c_Groups_Ozero__class_Ozero(U_5832)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5832),U_5833),U_5834)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5832),c_Groups_Ozero__class_Ozero(U_5832)),U_5834))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5832),c_Groups_Ozero__class_Ozero(U_5832)),U_5833))
      | ~ class_Fields_Olinordered__field(U_5832) ),
    inference(variable_rename,[status(thm)],[f_1754_1]) ).

fof(f_1754_3,plain,
    ! [U_5832,U_5833,U_5834] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5832),c_Groups_Ozero__class_Ozero(U_5832)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5832),U_5833),U_5834)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5832),c_Groups_Ozero__class_Ozero(U_5832)),U_5834))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5832),c_Groups_Ozero__class_Ozero(U_5832)),U_5833))
      | ~ class_Fields_Olinordered__field(U_5832) ),
    inference(definitional_conversion,[status(esa)],[f_1754_2]) ).

cnf(f_1754_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5832),c_Groups_Ozero__class_Ozero(U_5832)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5832),U_5833),U_5834)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5832),c_Groups_Ozero__class_Ozero(U_5832)),U_5834))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5832),c_Groups_Ozero__class_Ozero(U_5832)),U_5833))
    | ~ class_Fields_Olinordered__field(U_5832) ),
    inference(clausify,[status(thm)],[f_1754_3]) ).

fof(f_1755_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_1755_2,plain,
    ! [U_5837,U_5836,U_5835] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5835),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5835),U_5836),U_5837)),c_Groups_Ozero__class_Ozero(U_5835)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5835),U_5837),c_Groups_Ozero__class_Ozero(U_5835)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5835),c_Groups_Ozero__class_Ozero(U_5835)),U_5836))
      | ~ class_Fields_Olinordered__field(U_5835) ),
    inference(variable_rename,[status(thm)],[f_1755_1]) ).

fof(f_1755_3,plain,
    ! [U_5835,U_5837,U_5836] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5835),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5835),U_5836),U_5837)),c_Groups_Ozero__class_Ozero(U_5835)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5835),U_5837),c_Groups_Ozero__class_Ozero(U_5835)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5835),c_Groups_Ozero__class_Ozero(U_5835)),U_5836))
      | ~ class_Fields_Olinordered__field(U_5835) ),
    inference(definitional_conversion,[status(esa)],[f_1755_2]) ).

cnf(f_1755_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5835),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5835),U_5836),U_5837)),c_Groups_Ozero__class_Ozero(U_5835)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5835),U_5837),c_Groups_Ozero__class_Ozero(U_5835)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5835),c_Groups_Ozero__class_Ozero(U_5835)),U_5836))
    | ~ class_Fields_Olinordered__field(U_5835) ),
    inference(clausify,[status(thm)],[f_1755_3]) ).

fof(f_1756_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_1756_2,plain,
    ! [U_5842,U_5841,U_5840,U_5839,U_5838] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5838),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5838),U_5839),U_5842)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5838),U_5840),U_5841)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5838),U_5841),U_5842))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5838),c_Groups_Ozero__class_Ozero(U_5838)),U_5841))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5838),U_5839),U_5840))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5838),c_Groups_Ozero__class_Ozero(U_5838)),U_5839))
      | ~ class_Fields_Olinordered__field(U_5838) ),
    inference(variable_rename,[status(thm)],[f_1756_1]) ).

fof(f_1756_3,plain,
    ! [U_5838,U_5839,U_5840,U_5841,U_5842] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5838),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5838),U_5839),U_5842)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5838),U_5840),U_5841)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5838),U_5841),U_5842))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5838),c_Groups_Ozero__class_Ozero(U_5838)),U_5841))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5838),U_5839),U_5840))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5838),c_Groups_Ozero__class_Ozero(U_5838)),U_5839))
      | ~ class_Fields_Olinordered__field(U_5838) ),
    inference(definitional_conversion,[status(esa)],[f_1756_2]) ).

cnf(f_1756_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5838),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5838),U_5839),U_5842)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5838),U_5840),U_5841)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5838),U_5841),U_5842))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5838),c_Groups_Ozero__class_Ozero(U_5838)),U_5841))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5838),U_5839),U_5840))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5838),c_Groups_Ozero__class_Ozero(U_5838)),U_5839))
    | ~ class_Fields_Olinordered__field(U_5838) ),
    inference(clausify,[status(thm)],[f_1756_3]) ).

fof(f_1757_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_1757_2,plain,
    ! [U_5847,U_5846,U_5845,U_5844,U_5843] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5843),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5843),U_5844),U_5847)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5843),U_5845),U_5846)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5843),U_5846),U_5847))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5843),c_Groups_Ozero__class_Ozero(U_5843)),U_5846))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5843),U_5844),U_5845))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5843),c_Groups_Ozero__class_Ozero(U_5843)),U_5844))
      | ~ class_Fields_Olinordered__field(U_5843) ),
    inference(variable_rename,[status(thm)],[f_1757_1]) ).

fof(f_1757_3,plain,
    ! [U_5843,U_5845,U_5844,U_5846,U_5847] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5843),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5843),U_5844),U_5847)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5843),U_5845),U_5846)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5843),U_5846),U_5847))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5843),c_Groups_Ozero__class_Ozero(U_5843)),U_5846))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5843),U_5844),U_5845))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5843),c_Groups_Ozero__class_Ozero(U_5843)),U_5844))
      | ~ class_Fields_Olinordered__field(U_5843) ),
    inference(definitional_conversion,[status(esa)],[f_1757_2]) ).

cnf(f_1757_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5843),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5843),U_5844),U_5847)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5843),U_5845),U_5846)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5843),U_5846),U_5847))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5843),c_Groups_Ozero__class_Ozero(U_5843)),U_5846))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5843),U_5844),U_5845))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5843),c_Groups_Ozero__class_Ozero(U_5843)),U_5844))
    | ~ class_Fields_Olinordered__field(U_5843) ),
    inference(clausify,[status(thm)],[f_1757_3]) ).

fof(f_1758_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_1758_2,plain,
    ! [U_5852,U_5851,U_5850,U_5849,U_5848] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5848),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5848),U_5849),U_5852)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5848),U_5850),U_5851)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5848),U_5851),U_5852))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5848),c_Groups_Ozero__class_Ozero(U_5848)),U_5851))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5848),U_5849),U_5850))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5848),c_Groups_Ozero__class_Ozero(U_5848)),U_5849))
      | ~ class_Fields_Olinordered__field(U_5848) ),
    inference(variable_rename,[status(thm)],[f_1758_1]) ).

fof(f_1758_3,plain,
    ! [U_5849,U_5851,U_5850,U_5848,U_5852] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5848),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5848),U_5849),U_5852)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5848),U_5850),U_5851)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5848),U_5851),U_5852))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5848),c_Groups_Ozero__class_Ozero(U_5848)),U_5851))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5848),U_5849),U_5850))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5848),c_Groups_Ozero__class_Ozero(U_5848)),U_5849))
      | ~ class_Fields_Olinordered__field(U_5848) ),
    inference(definitional_conversion,[status(esa)],[f_1758_2]) ).

cnf(f_1758_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5848),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5848),U_5849),U_5852)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5848),U_5850),U_5851)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5848),U_5851),U_5852))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5848),c_Groups_Ozero__class_Ozero(U_5848)),U_5851))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5848),U_5849),U_5850))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5848),c_Groups_Ozero__class_Ozero(U_5848)),U_5849))
    | ~ class_Fields_Olinordered__field(U_5848) ),
    inference(clausify,[status(thm)],[f_1758_3]) ).

fof(f_1759_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_1759_2,plain,
    ! [U_5855,U_5854,U_5853] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5853),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5853),U_5854),U_5855)),c_Groups_Ozero__class_Ozero(U_5853)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5853),c_Groups_Ozero__class_Ozero(U_5853)),U_5855))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5853),U_5854),c_Groups_Ozero__class_Ozero(U_5853)))
      | ~ class_Fields_Olinordered__field(U_5853) ),
    inference(variable_rename,[status(thm)],[f_1759_1]) ).

fof(f_1759_3,plain,
    ! [U_5855,U_5853,U_5854] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5853),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5853),U_5854),U_5855)),c_Groups_Ozero__class_Ozero(U_5853)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5853),c_Groups_Ozero__class_Ozero(U_5853)),U_5855))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5853),U_5854),c_Groups_Ozero__class_Ozero(U_5853)))
      | ~ class_Fields_Olinordered__field(U_5853) ),
    inference(definitional_conversion,[status(esa)],[f_1759_2]) ).

cnf(f_1759_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5853),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5853),U_5854),U_5855)),c_Groups_Ozero__class_Ozero(U_5853)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5853),c_Groups_Ozero__class_Ozero(U_5853)),U_5855))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5853),U_5854),c_Groups_Ozero__class_Ozero(U_5853)))
    | ~ class_Fields_Olinordered__field(U_5853) ),
    inference(clausify,[status(thm)],[f_1759_3]) ).

fof(f_1760_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_1760_2,plain,
    ! [U_5858,U_5857,U_5856] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5856),c_Groups_Ozero__class_Ozero(U_5856)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5856),U_5857),U_5858)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5856),U_5858),c_Groups_Ozero__class_Ozero(U_5856)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5856),U_5857),c_Groups_Ozero__class_Ozero(U_5856)))
      | ~ class_Fields_Olinordered__field(U_5856) ),
    inference(variable_rename,[status(thm)],[f_1760_1]) ).

fof(f_1760_3,plain,
    ! [U_5856,U_5857,U_5858] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5856),c_Groups_Ozero__class_Ozero(U_5856)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5856),U_5857),U_5858)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5856),U_5858),c_Groups_Ozero__class_Ozero(U_5856)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5856),U_5857),c_Groups_Ozero__class_Ozero(U_5856)))
      | ~ class_Fields_Olinordered__field(U_5856) ),
    inference(definitional_conversion,[status(esa)],[f_1760_2]) ).

cnf(f_1760_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5856),c_Groups_Ozero__class_Ozero(U_5856)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5856),U_5857),U_5858)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5856),U_5858),c_Groups_Ozero__class_Ozero(U_5856)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5856),U_5857),c_Groups_Ozero__class_Ozero(U_5856)))
    | ~ class_Fields_Olinordered__field(U_5856) ),
    inference(clausify,[status(thm)],[f_1760_3]) ).

fof(f_1761_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_1761_2,plain,
    ! [U_5862,U_5861,U_5860,U_5859] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5860),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5859),U_5861),U_5862)))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5860),c_Groups_Ozero__class_Ozero(U_5859)))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5862),c_Groups_Ozero__class_Ozero(U_5859))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5861),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5859),U_5860),U_5862)))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5862),c_Groups_Ozero__class_Ozero(U_5859))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),c_Groups_Ozero__class_Ozero(U_5859)),U_5862)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5859),U_5860),U_5862)),U_5861))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),c_Groups_Ozero__class_Ozero(U_5859)),U_5862)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5860),c_Groups_Ozero__class_Ozero(U_5859)))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5862),c_Groups_Ozero__class_Ozero(U_5859))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5861),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5859),U_5860),U_5862)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5862),c_Groups_Ozero__class_Ozero(U_5859))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),c_Groups_Ozero__class_Ozero(U_5859)),U_5862)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5859),U_5860),U_5862)),U_5861))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),c_Groups_Ozero__class_Ozero(U_5859)),U_5862)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5860),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5859),U_5861),U_5862))) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5859) ),
    inference(variable_rename,[status(thm)],[f_1761_1]) ).

fof(f_1761_3,plain,
    ( ! [U_5859,U_5860,U_5862] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5860),c_Groups_Ozero__class_Ozero(U_5859)))
        | ~ sP559(U_5859,U_5860,U_5862) )
    & ! [U_5859,U_5860,U_5862] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5862),c_Groups_Ozero__class_Ozero(U_5859)))
        | ~ sP559(U_5859,U_5860,U_5862) )
    & ! [U_5859,U_5860,U_5861,U_5862] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5861),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5859),U_5860),U_5862)))
        | ~ sP558(U_5859,U_5860,U_5861,U_5862) )
    & ! [U_5859,U_5860,U_5861,U_5862] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5862),c_Groups_Ozero__class_Ozero(U_5859)))
        | ~ sP558(U_5859,U_5860,U_5861,U_5862) )
    & ! [U_5859,U_5860,U_5861,U_5862] :
        ( sP559(U_5859,U_5860,U_5862)
        | sP558(U_5859,U_5860,U_5861,U_5862)
        | ~ sP560(U_5859,U_5860,U_5861,U_5862) )
    & ! [U_5859,U_5860,U_5861,U_5862] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),c_Groups_Ozero__class_Ozero(U_5859)),U_5862))
        | ~ sP560(U_5859,U_5860,U_5861,U_5862) )
    & ! [U_5859,U_5860,U_5861,U_5862] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5859),U_5860),U_5862)),U_5861))
        | ~ sP557(U_5859,U_5860,U_5861,U_5862) )
    & ! [U_5859,U_5860,U_5861,U_5862] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),c_Groups_Ozero__class_Ozero(U_5859)),U_5862))
        | ~ sP557(U_5859,U_5860,U_5861,U_5862) )
    & ! [U_5859,U_5860,U_5861,U_5862] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5860),c_Groups_Ozero__class_Ozero(U_5859)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5862),c_Groups_Ozero__class_Ozero(U_5859)))
        | ~ sP555(U_5859,U_5860,U_5861,U_5862) )
    & ! [U_5859,U_5860,U_5861,U_5862] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5861),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5859),U_5860),U_5862)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5862),c_Groups_Ozero__class_Ozero(U_5859)))
        | ~ sP555(U_5859,U_5860,U_5861,U_5862) )
    & ! [U_5859,U_5860,U_5861,U_5862] :
        ( sP555(U_5859,U_5860,U_5861,U_5862)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),c_Groups_Ozero__class_Ozero(U_5859)),U_5862))
        | ~ sP556(U_5859,U_5860,U_5861,U_5862) )
    & ! [U_5859,U_5860,U_5861,U_5862] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5859),U_5860),U_5862)),U_5861))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),c_Groups_Ozero__class_Ozero(U_5859)),U_5862))
        | ~ sP556(U_5859,U_5860,U_5861,U_5862) )
    & ! [U_5859,U_5860,U_5861,U_5862] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5860),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5859),U_5861),U_5862)))
        | sP560(U_5859,U_5860,U_5861,U_5862)
        | sP557(U_5859,U_5860,U_5861,U_5862)
        | ~ sP561(U_5859,U_5860,U_5861,U_5862) )
    & ! [U_5859,U_5860,U_5861,U_5862] :
        ( sP556(U_5859,U_5860,U_5861,U_5862)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5860),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5859),U_5861),U_5862)))
        | ~ sP561(U_5859,U_5860,U_5861,U_5862) )
    & ! [U_5859,U_5860,U_5861,U_5862] :
        ( sP561(U_5859,U_5860,U_5861,U_5862)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5859) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP555,sP556,sP557,sP558,sP559,sP560,sP561])],[f_1761_2]) ).

cnf(f_1761_4,plain,
    ( sP561(U_5859,U_5860,U_5861,U_5862)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5859) ),
    inference(clausify,[status(thm)],[f_1761_3]) ).

cnf(f_1761_5,plain,
    ( sP556(U_5859,U_5860,U_5861,U_5862)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5860),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5859),U_5861),U_5862)))
    | ~ sP561(U_5859,U_5860,U_5861,U_5862) ),
    inference(clausify,[status(thm)],[f_1761_3]) ).

cnf(f_1761_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5860),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5859),U_5861),U_5862)))
    | sP560(U_5859,U_5860,U_5861,U_5862)
    | sP557(U_5859,U_5860,U_5861,U_5862)
    | ~ sP561(U_5859,U_5860,U_5861,U_5862) ),
    inference(clausify,[status(thm)],[f_1761_3]) ).

cnf(f_1761_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5859),U_5860),U_5862)),U_5861))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),c_Groups_Ozero__class_Ozero(U_5859)),U_5862))
    | ~ sP556(U_5859,U_5860,U_5861,U_5862) ),
    inference(clausify,[status(thm)],[f_1761_3]) ).

cnf(f_1761_8,plain,
    ( sP555(U_5859,U_5860,U_5861,U_5862)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),c_Groups_Ozero__class_Ozero(U_5859)),U_5862))
    | ~ sP556(U_5859,U_5860,U_5861,U_5862) ),
    inference(clausify,[status(thm)],[f_1761_3]) ).

cnf(f_1761_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5861),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5859),U_5860),U_5862)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5862),c_Groups_Ozero__class_Ozero(U_5859)))
    | ~ sP555(U_5859,U_5860,U_5861,U_5862) ),
    inference(clausify,[status(thm)],[f_1761_3]) ).

cnf(f_1761_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5860),c_Groups_Ozero__class_Ozero(U_5859)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5862),c_Groups_Ozero__class_Ozero(U_5859)))
    | ~ sP555(U_5859,U_5860,U_5861,U_5862) ),
    inference(clausify,[status(thm)],[f_1761_3]) ).

cnf(f_1761_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),c_Groups_Ozero__class_Ozero(U_5859)),U_5862))
    | ~ sP557(U_5859,U_5860,U_5861,U_5862) ),
    inference(clausify,[status(thm)],[f_1761_3]) ).

cnf(f_1761_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5859),U_5860),U_5862)),U_5861))
    | ~ sP557(U_5859,U_5860,U_5861,U_5862) ),
    inference(clausify,[status(thm)],[f_1761_3]) ).

cnf(f_1761_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),c_Groups_Ozero__class_Ozero(U_5859)),U_5862))
    | ~ sP560(U_5859,U_5860,U_5861,U_5862) ),
    inference(clausify,[status(thm)],[f_1761_3]) ).

cnf(f_1761_14,plain,
    ( sP559(U_5859,U_5860,U_5862)
    | sP558(U_5859,U_5860,U_5861,U_5862)
    | ~ sP560(U_5859,U_5860,U_5861,U_5862) ),
    inference(clausify,[status(thm)],[f_1761_3]) ).

cnf(f_1761_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5862),c_Groups_Ozero__class_Ozero(U_5859)))
    | ~ sP558(U_5859,U_5860,U_5861,U_5862) ),
    inference(clausify,[status(thm)],[f_1761_3]) ).

cnf(f_1761_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5861),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5859),U_5860),U_5862)))
    | ~ sP558(U_5859,U_5860,U_5861,U_5862) ),
    inference(clausify,[status(thm)],[f_1761_3]) ).

cnf(f_1761_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5862),c_Groups_Ozero__class_Ozero(U_5859)))
    | ~ sP559(U_5859,U_5860,U_5862) ),
    inference(clausify,[status(thm)],[f_1761_3]) ).

cnf(f_1761_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5859),U_5860),c_Groups_Ozero__class_Ozero(U_5859)))
    | ~ sP559(U_5859,U_5860,U_5862) ),
    inference(clausify,[status(thm)],[f_1761_3]) ).

fof(f_1762_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_1762_2,plain,
    ! [U_5866,U_5865,U_5864,U_5863] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5863),U_5864),U_5865)),U_5866))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),c_Groups_Ozero__class_Ozero(U_5863)),U_5866))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),U_5865),c_Groups_Ozero__class_Ozero(U_5863))) )
              | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5863),U_5866),U_5865)),U_5864))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),U_5865),c_Groups_Ozero__class_Ozero(U_5863))) ) )
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),c_Groups_Ozero__class_Ozero(U_5863)),U_5865)) )
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),U_5864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5863),U_5866),U_5865)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),c_Groups_Ozero__class_Ozero(U_5863)),U_5865)) ) )
        & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),c_Groups_Ozero__class_Ozero(U_5863)),U_5866))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),U_5865),c_Groups_Ozero__class_Ozero(U_5863))) )
                & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5863),U_5866),U_5865)),U_5864))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),U_5865),c_Groups_Ozero__class_Ozero(U_5863))) ) )
              | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),c_Groups_Ozero__class_Ozero(U_5863)),U_5865)) )
            & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),U_5864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5863),U_5866),U_5865)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),c_Groups_Ozero__class_Ozero(U_5863)),U_5865)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5863),U_5864),U_5865)),U_5866)) ) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5863) ),
    inference(variable_rename,[status(thm)],[f_1762_1]) ).

fof(f_1762_3,plain,
    ( ! [U_5865,U_5866,U_5863] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),c_Groups_Ozero__class_Ozero(U_5863)),U_5866))
        | ~ sP566(U_5865,U_5866,U_5863) )
    & ! [U_5865,U_5866,U_5863] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),U_5865),c_Groups_Ozero__class_Ozero(U_5863)))
        | ~ sP566(U_5865,U_5866,U_5863) )
    & ! [U_5865,U_5866,U_5864,U_5863] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5863),U_5866),U_5865)),U_5864))
        | ~ sP565(U_5865,U_5866,U_5864,U_5863) )
    & ! [U_5865,U_5866,U_5864,U_5863] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),U_5865),c_Groups_Ozero__class_Ozero(U_5863)))
        | ~ sP565(U_5865,U_5866,U_5864,U_5863) )
    & ! [U_5865,U_5866,U_5864,U_5863] :
        ( sP566(U_5865,U_5866,U_5863)
        | sP565(U_5865,U_5866,U_5864,U_5863)
        | ~ sP567(U_5865,U_5866,U_5864,U_5863) )
    & ! [U_5865,U_5866,U_5864,U_5863] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),c_Groups_Ozero__class_Ozero(U_5863)),U_5865))
        | ~ sP567(U_5865,U_5866,U_5864,U_5863) )
    & ! [U_5865,U_5866,U_5864,U_5863] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),U_5864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5863),U_5866),U_5865)))
        | ~ sP564(U_5865,U_5866,U_5864,U_5863) )
    & ! [U_5865,U_5866,U_5864,U_5863] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),c_Groups_Ozero__class_Ozero(U_5863)),U_5865))
        | ~ sP564(U_5865,U_5866,U_5864,U_5863) )
    & ! [U_5865,U_5866,U_5864,U_5863] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),c_Groups_Ozero__class_Ozero(U_5863)),U_5866))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),U_5865),c_Groups_Ozero__class_Ozero(U_5863)))
        | ~ sP562(U_5865,U_5866,U_5864,U_5863) )
    & ! [U_5865,U_5866,U_5864,U_5863] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5863),U_5866),U_5865)),U_5864))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),U_5865),c_Groups_Ozero__class_Ozero(U_5863)))
        | ~ sP562(U_5865,U_5866,U_5864,U_5863) )
    & ! [U_5865,U_5866,U_5864,U_5863] :
        ( sP562(U_5865,U_5866,U_5864,U_5863)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),c_Groups_Ozero__class_Ozero(U_5863)),U_5865))
        | ~ sP563(U_5865,U_5866,U_5864,U_5863) )
    & ! [U_5865,U_5866,U_5864,U_5863] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),U_5864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5863),U_5866),U_5865)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),c_Groups_Ozero__class_Ozero(U_5863)),U_5865))
        | ~ sP563(U_5865,U_5866,U_5864,U_5863) )
    & ! [U_5865,U_5866,U_5864,U_5863] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5863),U_5864),U_5865)),U_5866))
        | sP567(U_5865,U_5866,U_5864,U_5863)
        | sP564(U_5865,U_5866,U_5864,U_5863)
        | ~ sP568(U_5865,U_5866,U_5864,U_5863) )
    & ! [U_5865,U_5866,U_5864,U_5863] :
        ( sP563(U_5865,U_5866,U_5864,U_5863)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5863),U_5864),U_5865)),U_5866))
        | ~ sP568(U_5865,U_5866,U_5864,U_5863) )
    & ! [U_5865,U_5866,U_5864,U_5863] :
        ( sP568(U_5865,U_5866,U_5864,U_5863)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_5863) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP562,sP563,sP564,sP565,sP566,sP567,sP568])],[f_1762_2]) ).

cnf(f_1762_4,plain,
    ( sP568(U_5865,U_5866,U_5864,U_5863)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5863) ),
    inference(clausify,[status(thm)],[f_1762_3]) ).

cnf(f_1762_5,plain,
    ( sP563(U_5865,U_5866,U_5864,U_5863)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5863),U_5864),U_5865)),U_5866))
    | ~ sP568(U_5865,U_5866,U_5864,U_5863) ),
    inference(clausify,[status(thm)],[f_1762_3]) ).

cnf(f_1762_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5863),U_5864),U_5865)),U_5866))
    | sP567(U_5865,U_5866,U_5864,U_5863)
    | sP564(U_5865,U_5866,U_5864,U_5863)
    | ~ sP568(U_5865,U_5866,U_5864,U_5863) ),
    inference(clausify,[status(thm)],[f_1762_3]) ).

cnf(f_1762_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),U_5864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5863),U_5866),U_5865)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),c_Groups_Ozero__class_Ozero(U_5863)),U_5865))
    | ~ sP563(U_5865,U_5866,U_5864,U_5863) ),
    inference(clausify,[status(thm)],[f_1762_3]) ).

cnf(f_1762_8,plain,
    ( sP562(U_5865,U_5866,U_5864,U_5863)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),c_Groups_Ozero__class_Ozero(U_5863)),U_5865))
    | ~ sP563(U_5865,U_5866,U_5864,U_5863) ),
    inference(clausify,[status(thm)],[f_1762_3]) ).

cnf(f_1762_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5863),U_5866),U_5865)),U_5864))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),U_5865),c_Groups_Ozero__class_Ozero(U_5863)))
    | ~ sP562(U_5865,U_5866,U_5864,U_5863) ),
    inference(clausify,[status(thm)],[f_1762_3]) ).

cnf(f_1762_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),c_Groups_Ozero__class_Ozero(U_5863)),U_5866))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),U_5865),c_Groups_Ozero__class_Ozero(U_5863)))
    | ~ sP562(U_5865,U_5866,U_5864,U_5863) ),
    inference(clausify,[status(thm)],[f_1762_3]) ).

cnf(f_1762_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),c_Groups_Ozero__class_Ozero(U_5863)),U_5865))
    | ~ sP564(U_5865,U_5866,U_5864,U_5863) ),
    inference(clausify,[status(thm)],[f_1762_3]) ).

cnf(f_1762_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),U_5864),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5863),U_5866),U_5865)))
    | ~ sP564(U_5865,U_5866,U_5864,U_5863) ),
    inference(clausify,[status(thm)],[f_1762_3]) ).

cnf(f_1762_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),c_Groups_Ozero__class_Ozero(U_5863)),U_5865))
    | ~ sP567(U_5865,U_5866,U_5864,U_5863) ),
    inference(clausify,[status(thm)],[f_1762_3]) ).

cnf(f_1762_14,plain,
    ( sP566(U_5865,U_5866,U_5863)
    | sP565(U_5865,U_5866,U_5864,U_5863)
    | ~ sP567(U_5865,U_5866,U_5864,U_5863) ),
    inference(clausify,[status(thm)],[f_1762_3]) ).

cnf(f_1762_15,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),U_5865),c_Groups_Ozero__class_Ozero(U_5863)))
    | ~ sP565(U_5865,U_5866,U_5864,U_5863) ),
    inference(clausify,[status(thm)],[f_1762_3]) ).

cnf(f_1762_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5863),U_5866),U_5865)),U_5864))
    | ~ sP565(U_5865,U_5866,U_5864,U_5863) ),
    inference(clausify,[status(thm)],[f_1762_3]) ).

cnf(f_1762_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),U_5865),c_Groups_Ozero__class_Ozero(U_5863)))
    | ~ sP566(U_5865,U_5866,U_5863) ),
    inference(clausify,[status(thm)],[f_1762_3]) ).

cnf(f_1762_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5863),c_Groups_Ozero__class_Ozero(U_5863)),U_5866))
    | ~ sP566(U_5865,U_5866,U_5863) ),
    inference(clausify,[status(thm)],[f_1762_3]) ).

fof(f_1763_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_1763_2,plain,
    ! [U_5870,U_5869,U_5868,U_5867] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5867),U_5869),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5867),U_5870),U_5868)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5867),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5867),U_5869),U_5868)),U_5870)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5867),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5867),U_5869),U_5868)),U_5870))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5867),U_5869),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5867),U_5870),U_5868))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5867),c_Groups_Ozero__class_Ozero(U_5867)),U_5868))
      | ~ class_Fields_Olinordered__field(U_5867) ),
    inference(variable_rename,[status(thm)],[f_1763_1]) ).

fof(f_1763_3,plain,
    ( ! [U_5870,U_5868,U_5869,U_5867] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5867),U_5869),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5867),U_5870),U_5868)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5867),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5867),U_5869),U_5868)),U_5870))
        | ~ sP569(U_5870,U_5868,U_5869,U_5867) )
    & ! [U_5870,U_5868,U_5869,U_5867] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5867),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5867),U_5869),U_5868)),U_5870))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5867),U_5869),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5867),U_5870),U_5868)))
        | ~ sP569(U_5870,U_5868,U_5869,U_5867) )
    & ! [U_5870,U_5868,U_5869,U_5867] :
        ( sP569(U_5870,U_5868,U_5869,U_5867)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5867),c_Groups_Ozero__class_Ozero(U_5867)),U_5868))
        | ~ class_Fields_Olinordered__field(U_5867) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP569])],[f_1763_2]) ).

cnf(f_1763_4,plain,
    ( sP569(U_5870,U_5868,U_5869,U_5867)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5867),c_Groups_Ozero__class_Ozero(U_5867)),U_5868))
    | ~ class_Fields_Olinordered__field(U_5867) ),
    inference(clausify,[status(thm)],[f_1763_3]) ).

cnf(f_1763_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5867),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5867),U_5869),U_5868)),U_5870))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5867),U_5869),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5867),U_5870),U_5868)))
    | ~ sP569(U_5870,U_5868,U_5869,U_5867) ),
    inference(clausify,[status(thm)],[f_1763_3]) ).

cnf(f_1763_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5867),U_5869),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5867),U_5870),U_5868)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5867),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5867),U_5869),U_5868)),U_5870))
    | ~ sP569(U_5870,U_5868,U_5869,U_5867) ),
    inference(clausify,[status(thm)],[f_1763_3]) ).

fof(f_1764_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_1764_2,plain,
    ! [U_5874,U_5873,U_5872,U_5871] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5871),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5871),U_5873),U_5872)),U_5874))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5871),U_5873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5871),U_5874),U_5872))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5871),U_5873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5871),U_5874),U_5872)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5871),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5871),U_5873),U_5872)),U_5874)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5871),c_Groups_Ozero__class_Ozero(U_5871)),U_5872))
      | ~ class_Fields_Olinordered__field(U_5871) ),
    inference(variable_rename,[status(thm)],[f_1764_1]) ).

fof(f_1764_3,plain,
    ( ! [U_5871,U_5873,U_5872,U_5874] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5871),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5871),U_5873),U_5872)),U_5874))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5871),U_5873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5871),U_5874),U_5872)))
        | ~ sP570(U_5871,U_5873,U_5872,U_5874) )
    & ! [U_5871,U_5873,U_5872,U_5874] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5871),U_5873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5871),U_5874),U_5872)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5871),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5871),U_5873),U_5872)),U_5874))
        | ~ sP570(U_5871,U_5873,U_5872,U_5874) )
    & ! [U_5871,U_5873,U_5872,U_5874] :
        ( sP570(U_5871,U_5873,U_5872,U_5874)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5871),c_Groups_Ozero__class_Ozero(U_5871)),U_5872))
        | ~ class_Fields_Olinordered__field(U_5871) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP570])],[f_1764_2]) ).

cnf(f_1764_4,plain,
    ( sP570(U_5871,U_5873,U_5872,U_5874)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5871),c_Groups_Ozero__class_Ozero(U_5871)),U_5872))
    | ~ class_Fields_Olinordered__field(U_5871) ),
    inference(clausify,[status(thm)],[f_1764_3]) ).

cnf(f_1764_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5871),U_5873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5871),U_5874),U_5872)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5871),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5871),U_5873),U_5872)),U_5874))
    | ~ sP570(U_5871,U_5873,U_5872,U_5874) ),
    inference(clausify,[status(thm)],[f_1764_3]) ).

cnf(f_1764_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5871),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5871),U_5873),U_5872)),U_5874))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5871),U_5873),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5871),U_5874),U_5872)))
    | ~ sP570(U_5871,U_5873,U_5872,U_5874) ),
    inference(clausify,[status(thm)],[f_1764_3]) ).

fof(f_1765_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_1765_2,plain,
    ! [U_5878,U_5877,U_5876,U_5875] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5875),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5875),U_5877),U_5876)),U_5878))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5875),U_5877),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5875),U_5878),U_5876)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5875),c_Groups_Ozero__class_Ozero(U_5875)),U_5876))
      | ~ class_Fields_Olinordered__field(U_5875) ),
    inference(variable_rename,[status(thm)],[f_1765_1]) ).

fof(f_1765_3,plain,
    ! [U_5875,U_5877,U_5876,U_5878] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5875),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5875),U_5877),U_5876)),U_5878))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5875),U_5877),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5875),U_5878),U_5876)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5875),c_Groups_Ozero__class_Ozero(U_5875)),U_5876))
      | ~ class_Fields_Olinordered__field(U_5875) ),
    inference(definitional_conversion,[status(esa)],[f_1765_2]) ).

cnf(f_1765_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5875),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5875),U_5877),U_5876)),U_5878))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5875),U_5877),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5875),U_5878),U_5876)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5875),c_Groups_Ozero__class_Ozero(U_5875)),U_5876))
    | ~ class_Fields_Olinordered__field(U_5875) ),
    inference(clausify,[status(thm)],[f_1765_3]) ).

fof(f_1766_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_1766_2,plain,
    ! [U_5882,U_5881,U_5880,U_5879] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5879),U_5881),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5879),U_5882),U_5880)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5879),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5879),U_5881),U_5880)),U_5882))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5879),c_Groups_Ozero__class_Ozero(U_5879)),U_5880))
      | ~ class_Fields_Olinordered__field(U_5879) ),
    inference(variable_rename,[status(thm)],[f_1766_1]) ).

fof(f_1766_3,plain,
    ! [U_5879,U_5880,U_5881,U_5882] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5879),U_5881),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5879),U_5882),U_5880)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5879),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5879),U_5881),U_5880)),U_5882))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5879),c_Groups_Ozero__class_Ozero(U_5879)),U_5880))
      | ~ class_Fields_Olinordered__field(U_5879) ),
    inference(definitional_conversion,[status(esa)],[f_1766_2]) ).

cnf(f_1766_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5879),U_5881),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5879),U_5882),U_5880)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5879),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5879),U_5881),U_5880)),U_5882))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5879),c_Groups_Ozero__class_Ozero(U_5879)),U_5880))
    | ~ class_Fields_Olinordered__field(U_5879) ),
    inference(clausify,[status(thm)],[f_1766_3]) ).

fof(f_1767_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_1767_2,plain,
    ! [U_5886,U_5885,U_5884,U_5883] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5883),U_5885),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5883),U_5886),U_5884)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5883),U_5886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5883),U_5885),U_5884))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5883),U_5886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5883),U_5885),U_5884)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5883),U_5885),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5883),U_5886),U_5884))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5883),U_5884),c_Groups_Ozero__class_Ozero(U_5883)))
      | ~ class_Fields_Olinordered__field(U_5883) ),
    inference(variable_rename,[status(thm)],[f_1767_1]) ).

fof(f_1767_3,plain,
    ( ! [U_5883,U_5884,U_5885,U_5886] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5883),U_5885),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5883),U_5886),U_5884)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5883),U_5886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5883),U_5885),U_5884)))
        | ~ sP571(U_5883,U_5884,U_5885,U_5886) )
    & ! [U_5883,U_5884,U_5885,U_5886] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5883),U_5886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5883),U_5885),U_5884)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5883),U_5885),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5883),U_5886),U_5884)))
        | ~ sP571(U_5883,U_5884,U_5885,U_5886) )
    & ! [U_5883,U_5884,U_5885,U_5886] :
        ( sP571(U_5883,U_5884,U_5885,U_5886)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5883),U_5884),c_Groups_Ozero__class_Ozero(U_5883)))
        | ~ class_Fields_Olinordered__field(U_5883) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP571])],[f_1767_2]) ).

cnf(f_1767_4,plain,
    ( sP571(U_5883,U_5884,U_5885,U_5886)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5883),U_5884),c_Groups_Ozero__class_Ozero(U_5883)))
    | ~ class_Fields_Olinordered__field(U_5883) ),
    inference(clausify,[status(thm)],[f_1767_3]) ).

cnf(f_1767_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5883),U_5886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5883),U_5885),U_5884)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5883),U_5885),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5883),U_5886),U_5884)))
    | ~ sP571(U_5883,U_5884,U_5885,U_5886) ),
    inference(clausify,[status(thm)],[f_1767_3]) ).

cnf(f_1767_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5883),U_5885),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5883),U_5886),U_5884)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5883),U_5886),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5883),U_5885),U_5884)))
    | ~ sP571(U_5883,U_5884,U_5885,U_5886) ),
    inference(clausify,[status(thm)],[f_1767_3]) ).

fof(f_1768_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_1768_2,plain,
    ! [U_5890,U_5889,U_5888,U_5887] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5887),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5887),U_5889),U_5888)),U_5890))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5887),U_5890),U_5888)),U_5889)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5887),U_5890),U_5888)),U_5889))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5887),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5887),U_5889),U_5888)),U_5890)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5887),U_5888),c_Groups_Ozero__class_Ozero(U_5887)))
      | ~ class_Fields_Olinordered__field(U_5887) ),
    inference(variable_rename,[status(thm)],[f_1768_1]) ).

fof(f_1768_3,plain,
    ( ! [U_5889,U_5888,U_5887,U_5890] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5887),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5887),U_5889),U_5888)),U_5890))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5887),U_5890),U_5888)),U_5889))
        | ~ sP572(U_5889,U_5888,U_5887,U_5890) )
    & ! [U_5889,U_5888,U_5887,U_5890] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5887),U_5890),U_5888)),U_5889))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5887),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5887),U_5889),U_5888)),U_5890))
        | ~ sP572(U_5889,U_5888,U_5887,U_5890) )
    & ! [U_5889,U_5888,U_5887,U_5890] :
        ( sP572(U_5889,U_5888,U_5887,U_5890)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5887),U_5888),c_Groups_Ozero__class_Ozero(U_5887)))
        | ~ class_Fields_Olinordered__field(U_5887) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP572])],[f_1768_2]) ).

cnf(f_1768_4,plain,
    ( sP572(U_5889,U_5888,U_5887,U_5890)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5887),U_5888),c_Groups_Ozero__class_Ozero(U_5887)))
    | ~ class_Fields_Olinordered__field(U_5887) ),
    inference(clausify,[status(thm)],[f_1768_3]) ).

cnf(f_1768_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5887),U_5890),U_5888)),U_5889))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5887),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5887),U_5889),U_5888)),U_5890))
    | ~ sP572(U_5889,U_5888,U_5887,U_5890) ),
    inference(clausify,[status(thm)],[f_1768_3]) ).

cnf(f_1768_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5887),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5887),U_5889),U_5888)),U_5890))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5887),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5887),U_5890),U_5888)),U_5889))
    | ~ sP572(U_5889,U_5888,U_5887,U_5890) ),
    inference(clausify,[status(thm)],[f_1768_3]) ).

fof(f_1769_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_1769_2,plain,
    ! [U_5894,U_5893,U_5892,U_5891] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5891),U_5894),U_5893)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5891),U_5894),U_5892)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),c_Groups_Ozero__class_Ozero(U_5891)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5891),U_5893),U_5892)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),c_Groups_Ozero__class_Ozero(U_5891)),U_5894))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),U_5892),U_5893))
      | ~ class_Fields_Olinordered__field(U_5891) ),
    inference(variable_rename,[status(thm)],[f_1769_1]) ).

fof(f_1769_3,plain,
    ! [U_5891,U_5893,U_5892,U_5894] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5891),U_5894),U_5893)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5891),U_5894),U_5892)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),c_Groups_Ozero__class_Ozero(U_5891)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5891),U_5893),U_5892)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),c_Groups_Ozero__class_Ozero(U_5891)),U_5894))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),U_5892),U_5893))
      | ~ class_Fields_Olinordered__field(U_5891) ),
    inference(definitional_conversion,[status(esa)],[f_1769_2]) ).

cnf(f_1769_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5891),U_5894),U_5893)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5891),U_5894),U_5892)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),c_Groups_Ozero__class_Ozero(U_5891)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5891),U_5893),U_5892)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),c_Groups_Ozero__class_Ozero(U_5891)),U_5894))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5891),U_5892),U_5893))
    | ~ class_Fields_Olinordered__field(U_5891) ),
    inference(clausify,[status(thm)],[f_1769_3]) ).

fof(f_1770_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_1770_2,plain,
    ! [U_5898,U_5897,U_5896,U_5895] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5895),U_5898),U_5896)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5895),U_5898),U_5897)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),c_Groups_Ozero__class_Ozero(U_5895)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5895),U_5896),U_5897)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),U_5898),c_Groups_Ozero__class_Ozero(U_5895)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),U_5896),U_5897))
      | ~ class_Fields_Olinordered__field(U_5895) ),
    inference(variable_rename,[status(thm)],[f_1770_1]) ).

fof(f_1770_3,plain,
    ! [U_5896,U_5897,U_5895,U_5898] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5895),U_5898),U_5896)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5895),U_5898),U_5897)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),c_Groups_Ozero__class_Ozero(U_5895)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5895),U_5896),U_5897)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),U_5898),c_Groups_Ozero__class_Ozero(U_5895)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),U_5896),U_5897))
      | ~ class_Fields_Olinordered__field(U_5895) ),
    inference(definitional_conversion,[status(esa)],[f_1770_2]) ).

cnf(f_1770_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5895),U_5898),U_5896)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5895),U_5898),U_5897)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),c_Groups_Ozero__class_Ozero(U_5895)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5895),U_5896),U_5897)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),U_5898),c_Groups_Ozero__class_Ozero(U_5895)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5895),U_5896),U_5897))
    | ~ class_Fields_Olinordered__field(U_5895) ),
    inference(clausify,[status(thm)],[f_1770_3]) ).

fof(f_1771_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_1771_2,plain,
    ! [U_5903,U_5902,U_5901,U_5900,U_5899] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5899),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5899),U_5902),U_5900)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5899),U_5903),U_5901)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5899),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5899),U_5902),U_5901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5899),U_5903),U_5900))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5899),U_5900),U_5901))
      | U_5901 = c_Groups_Ozero__class_Ozero(U_5899)
      | U_5900 = c_Groups_Ozero__class_Ozero(U_5899)
      | ~ class_Fields_Ofield(U_5899) ),
    inference(variable_rename,[status(thm)],[f_1771_1]) ).

fof(f_1771_3,plain,
    ! [U_5899,U_5900,U_5901,U_5902,U_5903] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5899),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5899),U_5902),U_5900)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5899),U_5903),U_5901)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5899),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5899),U_5902),U_5901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5899),U_5903),U_5900))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5899),U_5900),U_5901))
      | U_5901 = c_Groups_Ozero__class_Ozero(U_5899)
      | U_5900 = c_Groups_Ozero__class_Ozero(U_5899)
      | ~ class_Fields_Ofield(U_5899) ),
    inference(definitional_conversion,[status(esa)],[f_1771_2]) ).

cnf(f_1771_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5899),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5899),U_5902),U_5900)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5899),U_5903),U_5901)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5899),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5899),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5899),U_5902),U_5901)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5899),U_5903),U_5900))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5899),U_5900),U_5901))
    | U_5901 = c_Groups_Ozero__class_Ozero(U_5899)
    | U_5900 = c_Groups_Ozero__class_Ozero(U_5899)
    | ~ class_Fields_Ofield(U_5899) ),
    inference(clausify,[status(thm)],[f_1771_3]) ).

fof(f_1772_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_1772_2,plain,
    ! [U_5907,U_5906,U_5905,U_5904] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5904),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5904),U_5906),U_5905)),U_5907) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5904),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5904),U_5906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5904),U_5905),U_5907))),U_5905)
      | U_5905 = c_Groups_Ozero__class_Ozero(U_5904)
      | ~ class_Fields_Ofield(U_5904) ),
    inference(variable_rename,[status(thm)],[f_1772_1]) ).

fof(f_1772_3,plain,
    ! [U_5905,U_5904,U_5906,U_5907] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5904),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5904),U_5906),U_5905)),U_5907) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5904),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5904),U_5906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5904),U_5905),U_5907))),U_5905)
      | U_5905 = c_Groups_Ozero__class_Ozero(U_5904)
      | ~ class_Fields_Ofield(U_5904) ),
    inference(definitional_conversion,[status(esa)],[f_1772_2]) ).

cnf(f_1772_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5904),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5904),U_5906),U_5905)),U_5907) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5904),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5904),U_5906),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5904),U_5905),U_5907))),U_5905)
    | U_5905 = c_Groups_Ozero__class_Ozero(U_5904)
    | ~ class_Fields_Ofield(U_5904) ),
    inference(clausify,[status(thm)],[f_1772_3]) ).

fof(f_1773_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_1773_2,plain,
    ! [U_5911,U_5910,U_5909,U_5908] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5908),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5908),U_5910),U_5909)),U_5911) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5908),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5908),U_5910),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5908),U_5911),U_5909))),U_5909)
      | U_5909 = c_Groups_Ozero__class_Ozero(U_5908)
      | ~ class_Fields_Ofield__inverse__zero(U_5908) ),
    inference(variable_rename,[status(thm)],[f_1773_1]) ).

fof(f_1773_3,plain,
    ! [U_5908,U_5909,U_5910,U_5911] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5908),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5908),U_5910),U_5909)),U_5911) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5908),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5908),U_5910),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5908),U_5911),U_5909))),U_5909)
      | U_5909 = c_Groups_Ozero__class_Ozero(U_5908)
      | ~ class_Fields_Ofield__inverse__zero(U_5908) ),
    inference(definitional_conversion,[status(esa)],[f_1773_2]) ).

cnf(f_1773_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5908),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5908),U_5910),U_5909)),U_5911) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5908),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5908),U_5910),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5908),U_5911),U_5909))),U_5909)
    | U_5909 = c_Groups_Ozero__class_Ozero(U_5908)
    | ~ class_Fields_Ofield__inverse__zero(U_5908) ),
    inference(clausify,[status(thm)],[f_1773_3]) ).

fof(f_1774_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_1774_2,plain,
    ! [U_5915,U_5914,U_5913,U_5912] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5912),U_5914),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5912),U_5915),U_5913)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5912),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5912),U_5913),U_5914)),U_5915)),U_5913)
      | U_5913 = c_Groups_Ozero__class_Ozero(U_5912)
      | ~ class_Fields_Ofield(U_5912) ),
    inference(variable_rename,[status(thm)],[f_1774_1]) ).

fof(f_1774_3,plain,
    ! [U_5912,U_5913,U_5914,U_5915] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5912),U_5914),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5912),U_5915),U_5913)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5912),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5912),U_5913),U_5914)),U_5915)),U_5913)
      | U_5913 = c_Groups_Ozero__class_Ozero(U_5912)
      | ~ class_Fields_Ofield(U_5912) ),
    inference(definitional_conversion,[status(esa)],[f_1774_2]) ).

cnf(f_1774_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5912),U_5914),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5912),U_5915),U_5913)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5912),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5912),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5912),U_5913),U_5914)),U_5915)),U_5913)
    | U_5913 = c_Groups_Ozero__class_Ozero(U_5912)
    | ~ class_Fields_Ofield(U_5912) ),
    inference(clausify,[status(thm)],[f_1774_3]) ).

fof(f_1775_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_1775_2,plain,
    ! [U_5919,U_5918,U_5917,U_5916] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5916),U_5918),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5916),U_5919),U_5917)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5916),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5916),U_5919),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5916),U_5918),U_5917))),U_5917)
      | U_5917 = c_Groups_Ozero__class_Ozero(U_5916)
      | ~ class_Fields_Ofield__inverse__zero(U_5916) ),
    inference(variable_rename,[status(thm)],[f_1775_1]) ).

fof(f_1775_3,plain,
    ! [U_5916,U_5917,U_5918,U_5919] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5916),U_5918),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5916),U_5919),U_5917)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5916),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5916),U_5919),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5916),U_5918),U_5917))),U_5917)
      | U_5917 = c_Groups_Ozero__class_Ozero(U_5916)
      | ~ class_Fields_Ofield__inverse__zero(U_5916) ),
    inference(definitional_conversion,[status(esa)],[f_1775_2]) ).

cnf(f_1775_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5916),U_5918),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5916),U_5919),U_5917)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5916),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5916),U_5919),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5916),U_5918),U_5917))),U_5917)
    | U_5917 = c_Groups_Ozero__class_Ozero(U_5916)
    | ~ class_Fields_Ofield__inverse__zero(U_5916) ),
    inference(clausify,[status(thm)],[f_1775_3]) ).

fof(f_1776_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_1776_2,plain,
    ! [U_5923,U_5922,U_5921,U_5920] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5920),U_5922),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5920),U_5923),U_5921)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5920),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5920),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5920),U_5921),U_5922)),U_5923)),U_5921)
      | U_5921 = c_Groups_Ozero__class_Ozero(U_5920)
      | ~ class_Fields_Ofield(U_5920) ),
    inference(variable_rename,[status(thm)],[f_1776_1]) ).

fof(f_1776_3,plain,
    ! [U_5920,U_5921,U_5922,U_5923] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5920),U_5922),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5920),U_5923),U_5921)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5920),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5920),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5920),U_5921),U_5922)),U_5923)),U_5921)
      | U_5921 = c_Groups_Ozero__class_Ozero(U_5920)
      | ~ class_Fields_Ofield(U_5920) ),
    inference(definitional_conversion,[status(esa)],[f_1776_2]) ).

cnf(f_1776_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5920),U_5922),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5920),U_5923),U_5921)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5920),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5920),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5920),U_5921),U_5922)),U_5923)),U_5921)
    | U_5921 = c_Groups_Ozero__class_Ozero(U_5920)
    | ~ class_Fields_Ofield(U_5920) ),
    inference(clausify,[status(thm)],[f_1776_3]) ).

fof(f_1777_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_1777_2,plain,
    ! [U_5927,U_5926,U_5925,U_5924] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5924),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5924),U_5926),U_5925)),U_5927) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5924),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5924),U_5926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5924),U_5925),U_5927))),U_5925)
      | U_5925 = c_Groups_Ozero__class_Ozero(U_5924)
      | ~ class_Fields_Ofield(U_5924) ),
    inference(variable_rename,[status(thm)],[f_1777_1]) ).

fof(f_1777_3,plain,
    ! [U_5924,U_5925,U_5926,U_5927] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5924),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5924),U_5926),U_5925)),U_5927) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5924),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5924),U_5926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5924),U_5925),U_5927))),U_5925)
      | U_5925 = c_Groups_Ozero__class_Ozero(U_5924)
      | ~ class_Fields_Ofield(U_5924) ),
    inference(definitional_conversion,[status(esa)],[f_1777_2]) ).

cnf(f_1777_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5924),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5924),U_5926),U_5925)),U_5927) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5924),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5924),U_5926),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5924),U_5925),U_5927))),U_5925)
    | U_5925 = c_Groups_Ozero__class_Ozero(U_5924)
    | ~ class_Fields_Ofield(U_5924) ),
    inference(clausify,[status(thm)],[f_1777_3]) ).

fof(f_1778_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_1778_2,plain,
    ! [U_5932,U_5931,U_5930,U_5929,U_5928] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5928),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5928),U_5931),U_5929)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5928),U_5932),U_5930)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5928),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5928),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5928),U_5931),U_5930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5928),U_5932),U_5929))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5928),U_5929),U_5930))
      | U_5930 = c_Groups_Ozero__class_Ozero(U_5928)
      | U_5929 = c_Groups_Ozero__class_Ozero(U_5928)
      | ~ class_Fields_Ofield(U_5928) ),
    inference(variable_rename,[status(thm)],[f_1778_1]) ).

fof(f_1778_3,plain,
    ! [U_5928,U_5929,U_5930,U_5931,U_5932] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5928),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5928),U_5931),U_5929)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5928),U_5932),U_5930)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5928),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5928),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5928),U_5931),U_5930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5928),U_5932),U_5929))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5928),U_5929),U_5930))
      | U_5930 = c_Groups_Ozero__class_Ozero(U_5928)
      | U_5929 = c_Groups_Ozero__class_Ozero(U_5928)
      | ~ class_Fields_Ofield(U_5928) ),
    inference(definitional_conversion,[status(esa)],[f_1778_2]) ).

cnf(f_1778_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5928),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5928),U_5931),U_5929)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5928),U_5932),U_5930)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5928),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_5928),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5928),U_5931),U_5930)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5928),U_5932),U_5929))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5928),U_5929),U_5930))
    | U_5930 = c_Groups_Ozero__class_Ozero(U_5928)
    | U_5929 = c_Groups_Ozero__class_Ozero(U_5928)
    | ~ class_Fields_Ofield(U_5928) ),
    inference(clausify,[status(thm)],[f_1778_3]) ).

fof(f_1779_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_1779_2,plain,
    ! [U_5935,U_5934,U_5933] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5933),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5933),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5933),U_5934),U_5935)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5933),c_Groups_Oone__class_Oone(U_5933)),c_Groups_Oone__class_Oone(U_5933)))),U_5935))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5933),U_5934),U_5935))
      | ~ class_Fields_Olinordered__field(U_5933) ),
    inference(variable_rename,[status(thm)],[f_1779_1]) ).

fof(f_1779_3,plain,
    ! [U_5934,U_5933,U_5935] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5933),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5933),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5933),U_5934),U_5935)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5933),c_Groups_Oone__class_Oone(U_5933)),c_Groups_Oone__class_Oone(U_5933)))),U_5935))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5933),U_5934),U_5935))
      | ~ class_Fields_Olinordered__field(U_5933) ),
    inference(definitional_conversion,[status(esa)],[f_1779_2]) ).

cnf(f_1779_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5933),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5933),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5933),U_5934),U_5935)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5933),c_Groups_Oone__class_Oone(U_5933)),c_Groups_Oone__class_Oone(U_5933)))),U_5935))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5933),U_5934),U_5935))
    | ~ class_Fields_Olinordered__field(U_5933) ),
    inference(clausify,[status(thm)],[f_1779_3]) ).

fof(f_1780_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_1780_2,plain,
    ! [U_5938,U_5937,U_5936] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5936),U_5937),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5936),U_5937),U_5938)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5936),c_Groups_Oone__class_Oone(U_5936)),c_Groups_Oone__class_Oone(U_5936)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5936),U_5937),U_5938))
      | ~ class_Fields_Olinordered__field(U_5936) ),
    inference(variable_rename,[status(thm)],[f_1780_1]) ).

fof(f_1780_3,plain,
    ! [U_5936,U_5937,U_5938] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5936),U_5937),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5936),U_5937),U_5938)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5936),c_Groups_Oone__class_Oone(U_5936)),c_Groups_Oone__class_Oone(U_5936)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5936),U_5937),U_5938))
      | ~ class_Fields_Olinordered__field(U_5936) ),
    inference(definitional_conversion,[status(esa)],[f_1780_2]) ).

cnf(f_1780_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5936),U_5937),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5936),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5936),U_5937),U_5938)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_5936),c_Groups_Oone__class_Oone(U_5936)),c_Groups_Oone__class_Oone(U_5936)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5936),U_5937),U_5938))
    | ~ class_Fields_Olinordered__field(U_5936) ),
    inference(clausify,[status(thm)],[f_1780_3]) ).

fof(f_1781_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_1781_2,plain,
    ! [U_5941,U_5940,U_5939] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5939),hAPP(c_Groups_Oabs__class_Oabs(U_5939),U_5941)),U_5940) = hAPP(c_Groups_Oabs__class_Oabs(U_5939),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5939),U_5941),U_5940))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5939),c_Groups_Ozero__class_Ozero(U_5939)),U_5940))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5939) ),
    inference(variable_rename,[status(thm)],[f_1781_1]) ).

fof(f_1781_3,plain,
    ! [U_5939,U_5940,U_5941] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5939),hAPP(c_Groups_Oabs__class_Oabs(U_5939),U_5941)),U_5940) = hAPP(c_Groups_Oabs__class_Oabs(U_5939),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5939),U_5941),U_5940))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5939),c_Groups_Ozero__class_Ozero(U_5939)),U_5940))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5939) ),
    inference(definitional_conversion,[status(esa)],[f_1781_2]) ).

cnf(f_1781_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5939),hAPP(c_Groups_Oabs__class_Oabs(U_5939),U_5941)),U_5940) = hAPP(c_Groups_Oabs__class_Oabs(U_5939),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5939),U_5941),U_5940))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5939),c_Groups_Ozero__class_Ozero(U_5939)),U_5940))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5939) ),
    inference(clausify,[status(thm)],[f_1781_3]) ).

fof(f_1782_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_1782_2,plain,
    ! [U_5945,U_5944,U_5943,U_5942] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5942),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5942),U_5945),U_5943)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5942),U_5945),U_5944)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5942),c_Groups_Ozero__class_Ozero(U_5942)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5942),U_5943),U_5944)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5942),U_5945),c_Groups_Ozero__class_Ozero(U_5942)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5942),U_5943),U_5944))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5942) ),
    inference(variable_rename,[status(thm)],[f_1782_1]) ).

fof(f_1782_3,plain,
    ! [U_5942,U_5943,U_5944,U_5945] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5942),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5942),U_5945),U_5943)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5942),U_5945),U_5944)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5942),c_Groups_Ozero__class_Ozero(U_5942)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5942),U_5943),U_5944)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5942),U_5945),c_Groups_Ozero__class_Ozero(U_5942)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5942),U_5943),U_5944))
      | ~ class_Fields_Olinordered__field__inverse__zero(U_5942) ),
    inference(definitional_conversion,[status(esa)],[f_1782_2]) ).

cnf(f_1782_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5942),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5942),U_5945),U_5943)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5942),U_5945),U_5944)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5942),c_Groups_Ozero__class_Ozero(U_5942)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5942),U_5943),U_5944)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5942),U_5945),c_Groups_Ozero__class_Ozero(U_5942)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5942),U_5943),U_5944))
    | ~ class_Fields_Olinordered__field__inverse__zero(U_5942) ),
    inference(clausify,[status(thm)],[f_1782_3]) ).

fof(f_1783_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_1783_2,plain,
    ! [U_5949,U_5948,U_5947,U_5946] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5946),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5946),U_5949),U_5948)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5946),U_5949),U_5947)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5946),c_Groups_Ozero__class_Ozero(U_5946)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5946),U_5948),U_5947)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5946),c_Groups_Ozero__class_Ozero(U_5946)),U_5949))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5946),U_5947),U_5948))
      | ~ class_Fields_Olinordered__field(U_5946) ),
    inference(variable_rename,[status(thm)],[f_1783_1]) ).

fof(f_1783_3,plain,
    ! [U_5947,U_5948,U_5946,U_5949] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5946),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5946),U_5949),U_5948)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5946),U_5949),U_5947)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5946),c_Groups_Ozero__class_Ozero(U_5946)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5946),U_5948),U_5947)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5946),c_Groups_Ozero__class_Ozero(U_5946)),U_5949))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5946),U_5947),U_5948))
      | ~ class_Fields_Olinordered__field(U_5946) ),
    inference(definitional_conversion,[status(esa)],[f_1783_2]) ).

cnf(f_1783_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5946),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5946),U_5949),U_5948)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5946),U_5949),U_5947)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5946),c_Groups_Ozero__class_Ozero(U_5946)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5946),U_5948),U_5947)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5946),c_Groups_Ozero__class_Ozero(U_5946)),U_5949))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5946),U_5947),U_5948))
    | ~ class_Fields_Olinordered__field(U_5946) ),
    inference(clausify,[status(thm)],[f_1783_3]) ).

fof(f_1784_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_1784_2,plain,
    ! [U_5953,U_5952,U_5951,U_5950] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5950),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5950),U_5952),U_5951)),U_5953))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5950),U_5953),U_5951)),U_5952)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5950),U_5953),U_5951)),U_5952))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5950),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5950),U_5952),U_5951)),U_5953)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5950),U_5951),c_Groups_Ozero__class_Ozero(U_5950)))
      | ~ class_Fields_Olinordered__field(U_5950) ),
    inference(variable_rename,[status(thm)],[f_1784_1]) ).

fof(f_1784_3,plain,
    ( ! [U_5951,U_5950,U_5952,U_5953] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5950),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5950),U_5952),U_5951)),U_5953))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5950),U_5953),U_5951)),U_5952))
        | ~ sP573(U_5951,U_5950,U_5952,U_5953) )
    & ! [U_5951,U_5950,U_5952,U_5953] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5950),U_5953),U_5951)),U_5952))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5950),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5950),U_5952),U_5951)),U_5953))
        | ~ sP573(U_5951,U_5950,U_5952,U_5953) )
    & ! [U_5951,U_5950,U_5952,U_5953] :
        ( sP573(U_5951,U_5950,U_5952,U_5953)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5950),U_5951),c_Groups_Ozero__class_Ozero(U_5950)))
        | ~ class_Fields_Olinordered__field(U_5950) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP573])],[f_1784_2]) ).

cnf(f_1784_4,plain,
    ( sP573(U_5951,U_5950,U_5952,U_5953)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5950),U_5951),c_Groups_Ozero__class_Ozero(U_5950)))
    | ~ class_Fields_Olinordered__field(U_5950) ),
    inference(clausify,[status(thm)],[f_1784_3]) ).

cnf(f_1784_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5950),U_5953),U_5951)),U_5952))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5950),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5950),U_5952),U_5951)),U_5953))
    | ~ sP573(U_5951,U_5950,U_5952,U_5953) ),
    inference(clausify,[status(thm)],[f_1784_3]) ).

cnf(f_1784_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5950),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5950),U_5952),U_5951)),U_5953))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5950),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5950),U_5953),U_5951)),U_5952))
    | ~ sP573(U_5951,U_5950,U_5952,U_5953) ),
    inference(clausify,[status(thm)],[f_1784_3]) ).

fof(f_1785_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_1785_2,plain,
    ! [U_5957,U_5956,U_5955,U_5954] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5954),U_5956),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5954),U_5957),U_5955)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5954),U_5957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5954),U_5956),U_5955))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5954),U_5957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5954),U_5956),U_5955)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5954),U_5956),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5954),U_5957),U_5955))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5954),U_5955),c_Groups_Ozero__class_Ozero(U_5954)))
      | ~ class_Fields_Olinordered__field(U_5954) ),
    inference(variable_rename,[status(thm)],[f_1785_1]) ).

fof(f_1785_3,plain,
    ( ! [U_5955,U_5957,U_5956,U_5954] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5954),U_5956),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5954),U_5957),U_5955)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5954),U_5957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5954),U_5956),U_5955)))
        | ~ sP574(U_5955,U_5957,U_5956,U_5954) )
    & ! [U_5955,U_5957,U_5956,U_5954] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5954),U_5957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5954),U_5956),U_5955)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5954),U_5956),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5954),U_5957),U_5955)))
        | ~ sP574(U_5955,U_5957,U_5956,U_5954) )
    & ! [U_5955,U_5957,U_5956,U_5954] :
        ( sP574(U_5955,U_5957,U_5956,U_5954)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5954),U_5955),c_Groups_Ozero__class_Ozero(U_5954)))
        | ~ class_Fields_Olinordered__field(U_5954) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP574])],[f_1785_2]) ).

cnf(f_1785_4,plain,
    ( sP574(U_5955,U_5957,U_5956,U_5954)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5954),U_5955),c_Groups_Ozero__class_Ozero(U_5954)))
    | ~ class_Fields_Olinordered__field(U_5954) ),
    inference(clausify,[status(thm)],[f_1785_3]) ).

cnf(f_1785_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5954),U_5957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5954),U_5956),U_5955)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5954),U_5956),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5954),U_5957),U_5955)))
    | ~ sP574(U_5955,U_5957,U_5956,U_5954) ),
    inference(clausify,[status(thm)],[f_1785_3]) ).

cnf(f_1785_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5954),U_5956),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5954),U_5957),U_5955)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5954),U_5957),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5954),U_5956),U_5955)))
    | ~ sP574(U_5955,U_5957,U_5956,U_5954) ),
    inference(clausify,[status(thm)],[f_1785_3]) ).

fof(f_1786_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_1786_2,plain,
    ! [U_5961,U_5960,U_5959,U_5958] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5958),U_5960),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5958),U_5961),U_5959)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5958),U_5960),U_5959)),U_5961))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5958),c_Groups_Ozero__class_Ozero(U_5958)),U_5959))
      | ~ class_Fields_Olinordered__field(U_5958) ),
    inference(variable_rename,[status(thm)],[f_1786_1]) ).

fof(f_1786_3,plain,
    ! [U_5958,U_5960,U_5959,U_5961] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5958),U_5960),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5958),U_5961),U_5959)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5958),U_5960),U_5959)),U_5961))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5958),c_Groups_Ozero__class_Ozero(U_5958)),U_5959))
      | ~ class_Fields_Olinordered__field(U_5958) ),
    inference(definitional_conversion,[status(esa)],[f_1786_2]) ).

cnf(f_1786_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5958),U_5960),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_5958),U_5961),U_5959)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_5958),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_5958),U_5960),U_5959)),U_5961))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_5958),c_Groups_Ozero__class_Ozero(U_5958)),U_5959))
    | ~ class_Fields_Olinordered__field(U_5958) ),
    inference(clausify,[status(thm)],[f_1786_3]) ).

fof(f_1787_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_1787_2,plain,
    ! [U_5963,U_5962] :
      ( ( ( ( ( hAPP(c_Int_Oring__1__class_Oof__int(U_5962),U_5963) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_5962),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_5962,U_5962)),tc_fun(tc_Int_Oint,U_5962)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5962,U_5962),U_5962),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_5962,U_5962)),tc_fun(tc_Int_Oint,U_5962)),tc_Int_Oint),c_COMBB(tc_fun(U_5962,U_5962),U_5962,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_5962,tc_fun(tc_fun(U_5962,U_5962),U_5962),tc_Int_Oint),c_HOL_OLet(U_5962,U_5962)),c_Int_Oring__1__class_Oof__int(U_5962)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_5962,U_5962),tc_fun(U_5962,U_5962)),hAPP(hAPP(c_COMBB(tc_fun(U_5962,tc_fun(U_5962,U_5962)),tc_fun(tc_fun(U_5962,U_5962),tc_fun(U_5962,U_5962)),tc_Int_Oint),c_COMBS(U_5962,U_5962,U_5962)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_5962,U_5962),tc_fun(U_5962,tc_fun(U_5962,U_5962))),hAPP(hAPP(c_COMBB(tc_fun(U_5962,tc_fun(U_5962,U_5962)),tc_fun(tc_fun(U_5962,U_5962),tc_fun(U_5962,tc_fun(U_5962,U_5962))),tc_Int_Oint),c_COMBB(U_5962,tc_fun(U_5962,U_5962),U_5962)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5962,tc_fun(U_5962,U_5962)),tc_Int_Oint),c_If(U_5962)),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_5962,U_5962,U_5962),c_Groups_Oplus__class_Oplus(U_5962)),c_COMBI(U_5962))))),hAPP(hAPP(c_COMBC(U_5962,U_5962,U_5962),hAPP(hAPP(c_COMBB(U_5962,tc_fun(U_5962,U_5962),U_5962),c_Groups_Oplus__class_Oplus(U_5962)),hAPP(hAPP(c_COMBS(U_5962,U_5962,U_5962),c_Groups_Oplus__class_Oplus(U_5962)),c_COMBI(U_5962)))),c_Groups_Oone__class_Oone(U_5962))))),c_Divides_Odivmod__int(U_5963,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_5963),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
            & ( hAPP(c_Int_Oring__1__class_Oof__int(U_5962),U_5963) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5962),hAPP(c_Int_Oring__1__class_Oof__int(U_5962),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5963)))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5963),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) )
          | U_5963 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
        & ( hAPP(c_Int_Oring__1__class_Oof__int(U_5962),U_5963) = c_Groups_Ozero__class_Ozero(U_5962)
          | U_5963 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
      | ~ class_Rings_Oring__1(U_5962) ),
    inference(variable_rename,[status(thm)],[f_1787_1]) ).

fof(f_1787_3,plain,
    ( ! [U_5962,U_5963] :
        ( hAPP(c_Int_Oring__1__class_Oof__int(U_5962),U_5963) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_5962),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_5962,U_5962)),tc_fun(tc_Int_Oint,U_5962)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5962,U_5962),U_5962),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_5962,U_5962)),tc_fun(tc_Int_Oint,U_5962)),tc_Int_Oint),c_COMBB(tc_fun(U_5962,U_5962),U_5962,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_5962,tc_fun(tc_fun(U_5962,U_5962),U_5962),tc_Int_Oint),c_HOL_OLet(U_5962,U_5962)),c_Int_Oring__1__class_Oof__int(U_5962)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_5962,U_5962),tc_fun(U_5962,U_5962)),hAPP(hAPP(c_COMBB(tc_fun(U_5962,tc_fun(U_5962,U_5962)),tc_fun(tc_fun(U_5962,U_5962),tc_fun(U_5962,U_5962)),tc_Int_Oint),c_COMBS(U_5962,U_5962,U_5962)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_5962,U_5962),tc_fun(U_5962,tc_fun(U_5962,U_5962))),hAPP(hAPP(c_COMBB(tc_fun(U_5962,tc_fun(U_5962,U_5962)),tc_fun(tc_fun(U_5962,U_5962),tc_fun(U_5962,tc_fun(U_5962,U_5962))),tc_Int_Oint),c_COMBB(U_5962,tc_fun(U_5962,U_5962),U_5962)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5962,tc_fun(U_5962,U_5962)),tc_Int_Oint),c_If(U_5962)),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_5962,U_5962,U_5962),c_Groups_Oplus__class_Oplus(U_5962)),c_COMBI(U_5962))))),hAPP(hAPP(c_COMBC(U_5962,U_5962,U_5962),hAPP(hAPP(c_COMBB(U_5962,tc_fun(U_5962,U_5962),U_5962),c_Groups_Oplus__class_Oplus(U_5962)),hAPP(hAPP(c_COMBS(U_5962,U_5962,U_5962),c_Groups_Oplus__class_Oplus(U_5962)),c_COMBI(U_5962)))),c_Groups_Oone__class_Oone(U_5962))))),c_Divides_Odivmod__int(U_5963,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_5963),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP575(U_5962,U_5963) )
    & ! [U_5962,U_5963] :
        ( hAPP(c_Int_Oring__1__class_Oof__int(U_5962),U_5963) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5962),hAPP(c_Int_Oring__1__class_Oof__int(U_5962),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5963)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5963),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP575(U_5962,U_5963) )
    & ! [U_5962,U_5963] :
        ( sP575(U_5962,U_5963)
        | U_5963 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP576(U_5962,U_5963) )
    & ! [U_5962,U_5963] :
        ( hAPP(c_Int_Oring__1__class_Oof__int(U_5962),U_5963) = c_Groups_Ozero__class_Ozero(U_5962)
        | U_5963 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP576(U_5962,U_5963) )
    & ! [U_5962,U_5963] :
        ( sP576(U_5962,U_5963)
        | ~ class_Rings_Oring__1(U_5962) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP575,sP576])],[f_1787_2]) ).

cnf(f_1787_4,plain,
    ( sP576(U_5962,U_5963)
    | ~ class_Rings_Oring__1(U_5962) ),
    inference(clausify,[status(thm)],[f_1787_3]) ).

cnf(f_1787_5,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_5962),U_5963) = c_Groups_Ozero__class_Ozero(U_5962)
    | U_5963 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP576(U_5962,U_5963) ),
    inference(clausify,[status(thm)],[f_1787_3]) ).

cnf(f_1787_6,plain,
    ( sP575(U_5962,U_5963)
    | U_5963 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP576(U_5962,U_5963) ),
    inference(clausify,[status(thm)],[f_1787_3]) ).

cnf(f_1787_7,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_5962),U_5963) = hAPP(c_Groups_Ouminus__class_Ouminus(U_5962),hAPP(c_Int_Oring__1__class_Oof__int(U_5962),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_5963)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5963),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP575(U_5962,U_5963) ),
    inference(clausify,[status(thm)],[f_1787_3]) ).

cnf(f_1787_8,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_5962),U_5963) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,U_5962),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_fun(U_5962,U_5962)),tc_fun(tc_Int_Oint,U_5962)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_5962,U_5962),U_5962),tc_fun(tc_fun(tc_Int_Oint,tc_fun(U_5962,U_5962)),tc_fun(tc_Int_Oint,U_5962)),tc_Int_Oint),c_COMBB(tc_fun(U_5962,U_5962),U_5962,tc_Int_Oint)),hAPP(hAPP(c_COMBB(U_5962,tc_fun(tc_fun(U_5962,U_5962),U_5962),tc_Int_Oint),c_HOL_OLet(U_5962,U_5962)),c_Int_Oring__1__class_Oof__int(U_5962)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_5962,U_5962),tc_fun(U_5962,U_5962)),hAPP(hAPP(c_COMBB(tc_fun(U_5962,tc_fun(U_5962,U_5962)),tc_fun(tc_fun(U_5962,U_5962),tc_fun(U_5962,U_5962)),tc_Int_Oint),c_COMBS(U_5962,U_5962,U_5962)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(U_5962,U_5962),tc_fun(U_5962,tc_fun(U_5962,U_5962))),hAPP(hAPP(c_COMBB(tc_fun(U_5962,tc_fun(U_5962,U_5962)),tc_fun(tc_fun(U_5962,U_5962),tc_fun(U_5962,tc_fun(U_5962,U_5962))),tc_Int_Oint),c_COMBB(U_5962,tc_fun(U_5962,U_5962),U_5962)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5962,tc_fun(U_5962,U_5962)),tc_Int_Oint),c_If(U_5962)),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_5962,U_5962,U_5962),c_Groups_Oplus__class_Oplus(U_5962)),c_COMBI(U_5962))))),hAPP(hAPP(c_COMBC(U_5962,U_5962,U_5962),hAPP(hAPP(c_COMBB(U_5962,tc_fun(U_5962,U_5962),U_5962),c_Groups_Oplus__class_Oplus(U_5962)),hAPP(hAPP(c_COMBS(U_5962,U_5962,U_5962),c_Groups_Oplus__class_Oplus(U_5962)),c_COMBI(U_5962)))),c_Groups_Oone__class_Oone(U_5962))))),c_Divides_Odivmod__int(U_5963,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_5963),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP575(U_5962,U_5963) ),
    inference(clausify,[status(thm)],[f_1787_3]) ).

fof(f_1788_1,plain,
    ! [V_Pa_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))
          & ( hBOOL(hAPP(hAPP(V_Pa_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_1788_2,plain,
    ! [U_5968,U_5967,U_5966] :
      ( hBOOL(hAPP(hAPP(U_5968,U_5966),U_5967))
      | ? [U_5965,U_5964] :
          ( ~ hBOOL(hAPP(hAPP(U_5968,U_5965),U_5964))
          & ( hBOOL(hAPP(hAPP(U_5968,U_5965),hAPP(hAPP(c_Groups_Otimes__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_5964)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5964),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_5965),U_5964))) )
          & 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_5965),U_5964))) )
      | ~ 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_5966),U_5967))) ),
    inference(variable_rename,[status(thm)],[f_1788_1]) ).

fof(f_1788_3,plain,
    ! [U_5968,U_5967,U_5966] :
      ( hBOOL(hAPP(hAPP(U_5968,U_5966),U_5967))
      | ? [U_5964] :
          ( ~ hBOOL(hAPP(hAPP(U_5968,sK79(U_5968,U_5967,U_5966)),U_5964))
          & ( hBOOL(hAPP(hAPP(U_5968,sK79(U_5968,U_5967,U_5966)),hAPP(hAPP(c_Groups_Otimes__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_5964)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5964),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),sK79(U_5968,U_5967,U_5966)),U_5964))) )
          & 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),sK79(U_5968,U_5967,U_5966)),U_5964))) )
      | ~ 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_5966),U_5967))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK79]),skolemize(U_5965,sK79(U_5968,U_5967,U_5966))],[f_1788_2]) ).

fof(f_1788_4,plain,
    ! [U_5968,U_5967,U_5966] :
      ( hBOOL(hAPP(hAPP(U_5968,U_5966),U_5967))
      | ( ~ hBOOL(hAPP(hAPP(U_5968,sK79(U_5968,U_5967,U_5966)),sK80(U_5968,U_5967,U_5966)))
        & ( hBOOL(hAPP(hAPP(U_5968,sK79(U_5968,U_5967,U_5966)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK80(U_5968,U_5967,U_5966))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK80(U_5968,U_5967,U_5966)),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),sK79(U_5968,U_5967,U_5966)),sK80(U_5968,U_5967,U_5966)))) )
        & 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),sK79(U_5968,U_5967,U_5966)),sK80(U_5968,U_5967,U_5966)))) )
      | ~ 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_5966),U_5967))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK80]),skolemize(U_5964,sK80(U_5968,U_5967,U_5966))],[f_1788_3]) ).

fof(f_1788_5,plain,
    ( ! [U_5967,U_5968,U_5966] :
        ( ~ hBOOL(hAPP(hAPP(U_5968,sK79(U_5968,U_5967,U_5966)),sK80(U_5968,U_5967,U_5966)))
        | ~ sP577(U_5967,U_5968,U_5966) )
    & ! [U_5967,U_5968,U_5966] :
        ( hBOOL(hAPP(hAPP(U_5968,sK79(U_5968,U_5967,U_5966)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK80(U_5968,U_5967,U_5966))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK80(U_5968,U_5967,U_5966)),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),sK79(U_5968,U_5967,U_5966)),sK80(U_5968,U_5967,U_5966))))
        | ~ sP577(U_5967,U_5968,U_5966) )
    & ! [U_5967,U_5968,U_5966] :
        ( 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),sK79(U_5968,U_5967,U_5966)),sK80(U_5968,U_5967,U_5966))))
        | ~ sP577(U_5967,U_5968,U_5966) )
    & ! [U_5967,U_5968,U_5966] :
        ( hBOOL(hAPP(hAPP(U_5968,U_5966),U_5967))
        | sP577(U_5967,U_5968,U_5966)
        | ~ 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_5966),U_5967))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP577])],[f_1788_4]) ).

cnf(f_1788_6,plain,
    ( hBOOL(hAPP(hAPP(U_5968,U_5966),U_5967))
    | sP577(U_5967,U_5968,U_5966)
    | ~ 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_5966),U_5967))) ),
    inference(clausify,[status(thm)],[f_1788_5]) ).

cnf(f_1788_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),sK79(U_5968,U_5967,U_5966)),sK80(U_5968,U_5967,U_5966))))
    | ~ sP577(U_5967,U_5968,U_5966) ),
    inference(clausify,[status(thm)],[f_1788_5]) ).

cnf(f_1788_8,plain,
    ( hBOOL(hAPP(hAPP(U_5968,sK79(U_5968,U_5967,U_5966)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK80(U_5968,U_5967,U_5966))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK80(U_5968,U_5967,U_5966)),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),sK79(U_5968,U_5967,U_5966)),sK80(U_5968,U_5967,U_5966))))
    | ~ sP577(U_5967,U_5968,U_5966) ),
    inference(clausify,[status(thm)],[f_1788_5]) ).

cnf(f_1788_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_5968,sK79(U_5968,U_5967,U_5966)),sK80(U_5968,U_5967,U_5966)))
    | ~ sP577(U_5967,U_5968,U_5966) ),
    inference(clausify,[status(thm)],[f_1788_5]) ).

fof(f_1789_1,plain,
    ! [V_Pa_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))
          & ( hBOOL(hAPP(hAPP(V_Pa_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_1789_2,plain,
    ! [U_5973,U_5972,U_5971] :
      ( hBOOL(hAPP(hAPP(U_5973,U_5971),U_5972))
      | ? [U_5970,U_5969] :
          ( ~ hBOOL(hAPP(hAPP(U_5973,U_5970),U_5969))
          & ( hBOOL(hAPP(hAPP(U_5973,U_5970),hAPP(hAPP(c_Groups_Otimes__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_5969)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5969),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_5970),U_5969)) )
          & 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_5970),U_5969))) )
      | ~ 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_5971),U_5972))) ),
    inference(variable_rename,[status(thm)],[f_1789_1]) ).

fof(f_1789_3,plain,
    ! [U_5973,U_5972,U_5971] :
      ( hBOOL(hAPP(hAPP(U_5973,U_5971),U_5972))
      | ? [U_5969] :
          ( ~ hBOOL(hAPP(hAPP(U_5973,sK81(U_5973,U_5972,U_5971)),U_5969))
          & ( hBOOL(hAPP(hAPP(U_5973,sK81(U_5973,U_5972,U_5971)),hAPP(hAPP(c_Groups_Otimes__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_5969)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_5969),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK81(U_5973,U_5972,U_5971)),U_5969)) )
          & 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),sK81(U_5973,U_5972,U_5971)),U_5969))) )
      | ~ 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_5971),U_5972))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK81]),skolemize(U_5970,sK81(U_5973,U_5972,U_5971))],[f_1789_2]) ).

fof(f_1789_4,plain,
    ! [U_5973,U_5972,U_5971] :
      ( hBOOL(hAPP(hAPP(U_5973,U_5971),U_5972))
      | ( ~ hBOOL(hAPP(hAPP(U_5973,sK81(U_5973,U_5972,U_5971)),sK82(U_5973,U_5972,U_5971)))
        & ( hBOOL(hAPP(hAPP(U_5973,sK81(U_5973,U_5972,U_5971)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK82(U_5973,U_5972,U_5971))))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK82(U_5973,U_5972,U_5971)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK81(U_5973,U_5972,U_5971)),sK82(U_5973,U_5972,U_5971))) )
        & 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),sK81(U_5973,U_5972,U_5971)),sK82(U_5973,U_5972,U_5971)))) )
      | ~ 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_5971),U_5972))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK82]),skolemize(U_5969,sK82(U_5973,U_5972,U_5971))],[f_1789_3]) ).

fof(f_1789_5,plain,
    ( ! [U_5971,U_5973,U_5972] :
        ( ~ hBOOL(hAPP(hAPP(U_5973,sK81(U_5973,U_5972,U_5971)),sK82(U_5973,U_5972,U_5971)))
        | ~ sP578(U_5971,U_5973,U_5972) )
    & ! [U_5971,U_5973,U_5972] :
        ( hBOOL(hAPP(hAPP(U_5973,sK81(U_5973,U_5972,U_5971)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK82(U_5973,U_5972,U_5971))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK82(U_5973,U_5972,U_5971)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK81(U_5973,U_5972,U_5971)),sK82(U_5973,U_5972,U_5971)))
        | ~ sP578(U_5971,U_5973,U_5972) )
    & ! [U_5971,U_5973,U_5972] :
        ( 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),sK81(U_5973,U_5972,U_5971)),sK82(U_5973,U_5972,U_5971))))
        | ~ sP578(U_5971,U_5973,U_5972) )
    & ! [U_5971,U_5973,U_5972] :
        ( hBOOL(hAPP(hAPP(U_5973,U_5971),U_5972))
        | sP578(U_5971,U_5973,U_5972)
        | ~ 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_5971),U_5972))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP578])],[f_1789_4]) ).

cnf(f_1789_6,plain,
    ( hBOOL(hAPP(hAPP(U_5973,U_5971),U_5972))
    | sP578(U_5971,U_5973,U_5972)
    | ~ 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_5971),U_5972))) ),
    inference(clausify,[status(thm)],[f_1789_5]) ).

cnf(f_1789_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),sK81(U_5973,U_5972,U_5971)),sK82(U_5973,U_5972,U_5971))))
    | ~ sP578(U_5971,U_5973,U_5972) ),
    inference(clausify,[status(thm)],[f_1789_5]) ).

cnf(f_1789_8,plain,
    ( hBOOL(hAPP(hAPP(U_5973,sK81(U_5973,U_5972,U_5971)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))),sK82(U_5973,U_5972,U_5971))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK82(U_5973,U_5972,U_5971)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK81(U_5973,U_5972,U_5971)),sK82(U_5973,U_5972,U_5971)))
    | ~ sP578(U_5971,U_5973,U_5972) ),
    inference(clausify,[status(thm)],[f_1789_5]) ).

cnf(f_1789_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_5973,sK81(U_5973,U_5972,U_5971)),sK82(U_5973,U_5972,U_5971)))
    | ~ sP578(U_5971,U_5973,U_5972) ),
    inference(clausify,[status(thm)],[f_1789_5]) ).

fof(f_1790_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_1790_2,plain,
    ! [U_5978,U_5977,U_5976,U_5975,U_5974] : c_Nat_Onat_Onat__case(U_5974,U_5975,U_5976,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5977)),U_5978)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5974),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5977))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5974,U_5974),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5974,tc_fun(U_5974,U_5974)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5974,tc_fun(U_5974,U_5974)),tc_Int_Oint),c_If(U_5974)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_5974,U_5975,U_5976,U_5978))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5974,tc_Int_Oint),U_5976),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_5978)))),
    inference(variable_rename,[status(thm)],[f_1790_1]) ).

fof(f_1790_3,plain,
    ! [U_5976,U_5977,U_5978,U_5974,U_5975] : c_Nat_Onat_Onat__case(U_5974,U_5975,U_5976,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5977)),U_5978)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5974),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5977))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5974,U_5974),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5974,tc_fun(U_5974,U_5974)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5974,tc_fun(U_5974,U_5974)),tc_Int_Oint),c_If(U_5974)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_5974,U_5975,U_5976,U_5978))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5974,tc_Int_Oint),U_5976),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_5978)))),
    inference(definitional_conversion,[status(esa)],[f_1790_2]) ).

cnf(f_1790_4,plain,
    c_Nat_Onat_Onat__case(U_5974,U_5975,U_5976,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_5977)),U_5978)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_5974),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_5977))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_5974,U_5974),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_5974,tc_fun(U_5974,U_5974)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_5974,tc_fun(U_5974,U_5974)),tc_Int_Oint),c_If(U_5974)),c_Nat__Numeral_Oneg)),c_Nat_Onat_Onat__case(U_5974,U_5975,U_5976,U_5978))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_5974,tc_Int_Oint),U_5976),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_5978)))),
    inference(clausify,[status(thm)],[f_1790_3]) ).

fof(f_1791_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_1791_2,plain,
    ! [U_5979] : c_Divides_Oadjust(U_5979) = 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_5979))))),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_5979))))),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_1791_1]) ).

fof(f_1791_3,plain,
    ! [U_5979] : c_Divides_Oadjust(U_5979) = 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_5979))))),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_5979))))),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_1791_2]) ).

cnf(f_1791_4,plain,
    c_Divides_Oadjust(U_5979) = 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_5979))))),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_5979))))),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_1791_3]) ).

fof(f_1792_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_1792_2,plain,
    ! [U_5985,U_5984,U_5983,U_5982,U_5981,U_5980] :
      ( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5982,U_5983,U_5984),U_5985),U_5980) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5982,U_5983,U_5984),U_5985),U_5981)
      | U_5980 != U_5981 ),
    inference(variable_rename,[status(thm)],[f_1792_1]) ).

fof(f_1792_3,plain,
    ! [U_5980,U_5981,U_5982,U_5983,U_5984,U_5985] :
      ( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5982,U_5983,U_5984),U_5985),U_5980) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5982,U_5983,U_5984),U_5985),U_5981)
      | U_5980 != U_5981 ),
    inference(definitional_conversion,[status(esa)],[f_1792_2]) ).

cnf(f_1792_4,plain,
    ( hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5982,U_5983,U_5984),U_5985),U_5980) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5982,U_5983,U_5984),U_5985),U_5981)
    | U_5980 != U_5981 ),
    inference(clausify,[status(thm)],[f_1792_3]) ).

fof(f_1793_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_1793_2,plain,
    ! [U_5993,U_5992,U_5991,U_5990,U_5989,U_5988,U_5987,U_5986] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5986,U_5987,U_5988),U_5989),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5990,U_5991,tc_prod(U_5986,U_5987)),U_5992),U_5993)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5990,U_5991,U_5988),hAPP(hAPP(c_COMBB(tc_fun(U_5991,tc_prod(U_5986,U_5987)),tc_fun(U_5991,U_5988),U_5990),hAPP(c_COMBB(tc_prod(U_5986,U_5987),U_5988,U_5991),hAPP(c_Product__Type_Oprod_Oprod__case(U_5986,U_5987,U_5988),U_5989))),U_5992)),U_5993),
    inference(variable_rename,[status(thm)],[f_1793_1]) ).

fof(f_1793_3,plain,
    ! [U_5986,U_5987,U_5988,U_5989,U_5990,U_5991,U_5992,U_5993] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5986,U_5987,U_5988),U_5989),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5990,U_5991,tc_prod(U_5986,U_5987)),U_5992),U_5993)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5990,U_5991,U_5988),hAPP(hAPP(c_COMBB(tc_fun(U_5991,tc_prod(U_5986,U_5987)),tc_fun(U_5991,U_5988),U_5990),hAPP(c_COMBB(tc_prod(U_5986,U_5987),U_5988,U_5991),hAPP(c_Product__Type_Oprod_Oprod__case(U_5986,U_5987,U_5988),U_5989))),U_5992)),U_5993),
    inference(definitional_conversion,[status(esa)],[f_1793_2]) ).

cnf(f_1793_4,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5986,U_5987,U_5988),U_5989),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5990,U_5991,tc_prod(U_5986,U_5987)),U_5992),U_5993)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5990,U_5991,U_5988),hAPP(hAPP(c_COMBB(tc_fun(U_5991,tc_prod(U_5986,U_5987)),tc_fun(U_5991,U_5988),U_5990),hAPP(c_COMBB(tc_prod(U_5986,U_5987),U_5988,U_5991),hAPP(c_Product__Type_Oprod_Oprod__case(U_5986,U_5987,U_5988),U_5989))),U_5992)),U_5993),
    inference(clausify,[status(thm)],[f_1793_3]) ).

fof(f_1794_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_1794_2,plain,
    ! [U_5999,U_5998,U_5997,U_5996,U_5995,U_5994] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5994,U_5995,U_5996),U_5997),hAPP(hAPP(c_Product__Type_OPair(U_5994,U_5995),U_5998),U_5999)) = hAPP(hAPP(U_5997,U_5998),U_5999),
    inference(variable_rename,[status(thm)],[f_1794_1]) ).

fof(f_1794_3,plain,
    ! [U_5994,U_5995,U_5996,U_5997,U_5998,U_5999] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5994,U_5995,U_5996),U_5997),hAPP(hAPP(c_Product__Type_OPair(U_5994,U_5995),U_5998),U_5999)) = hAPP(hAPP(U_5997,U_5998),U_5999),
    inference(definitional_conversion,[status(esa)],[f_1794_2]) ).

cnf(f_1794_4,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_5994,U_5995,U_5996),U_5997),hAPP(hAPP(c_Product__Type_OPair(U_5994,U_5995),U_5998),U_5999)) = hAPP(hAPP(U_5997,U_5998),U_5999),
    inference(clausify,[status(thm)],[f_1794_3]) ).

fof(f_1795_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_1795_2,plain,
    ! [U_6005,U_6004,U_6003,U_6002,U_6001,U_6000] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6000,U_6001,U_6002),U_6003),hAPP(hAPP(c_Product__Type_OPair(U_6000,U_6001),U_6004),U_6005)) = hAPP(hAPP(U_6003,U_6004),U_6005),
    inference(variable_rename,[status(thm)],[f_1795_1]) ).

fof(f_1795_3,plain,
    ! [U_6000,U_6001,U_6002,U_6003,U_6004,U_6005] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6000,U_6001,U_6002),U_6003),hAPP(hAPP(c_Product__Type_OPair(U_6000,U_6001),U_6004),U_6005)) = hAPP(hAPP(U_6003,U_6004),U_6005),
    inference(definitional_conversion,[status(esa)],[f_1795_2]) ).

cnf(f_1795_4,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6000,U_6001,U_6002),U_6003),hAPP(hAPP(c_Product__Type_OPair(U_6000,U_6001),U_6004),U_6005)) = hAPP(hAPP(U_6003,U_6004),U_6005),
    inference(clausify,[status(thm)],[f_1795_3]) ).

fof(f_1796_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_1796_2,plain,
    ! [U_6009,U_6008,U_6007,U_6006] : hAPP(c_Product__Type_Oprod_Oprod__case(U_6006,U_6007,U_6008),hAPP(hAPP(c_COMBB(tc_fun(U_6007,tc_prod(U_6006,U_6007)),tc_fun(U_6007,U_6008),U_6006),hAPP(c_COMBB(tc_prod(U_6006,U_6007),U_6008,U_6007),U_6009)),c_Product__Type_OPair(U_6006,U_6007))) = U_6009,
    inference(variable_rename,[status(thm)],[f_1796_1]) ).

fof(f_1796_3,plain,
    ! [U_6006,U_6007,U_6008,U_6009] : hAPP(c_Product__Type_Oprod_Oprod__case(U_6006,U_6007,U_6008),hAPP(hAPP(c_COMBB(tc_fun(U_6007,tc_prod(U_6006,U_6007)),tc_fun(U_6007,U_6008),U_6006),hAPP(c_COMBB(tc_prod(U_6006,U_6007),U_6008,U_6007),U_6009)),c_Product__Type_OPair(U_6006,U_6007))) = U_6009,
    inference(definitional_conversion,[status(esa)],[f_1796_2]) ).

cnf(f_1796_4,plain,
    hAPP(c_Product__Type_Oprod_Oprod__case(U_6006,U_6007,U_6008),hAPP(hAPP(c_COMBB(tc_fun(U_6007,tc_prod(U_6006,U_6007)),tc_fun(U_6007,U_6008),U_6006),hAPP(c_COMBB(tc_prod(U_6006,U_6007),U_6008,U_6007),U_6009)),c_Product__Type_OPair(U_6006,U_6007))) = U_6009,
    inference(clausify,[status(thm)],[f_1796_3]) ).

fof(f_1797_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_1797_2,plain,
    ! [U_6012,U_6011,U_6010] : hAPP(c_Product__Type_Ofst(U_6010,U_6011),U_6012) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6010,U_6011,U_6010),c_COMBK(U_6010,U_6011)),U_6012),
    inference(variable_rename,[status(thm)],[f_1797_1]) ).

fof(f_1797_3,plain,
    ! [U_6010,U_6011,U_6012] : hAPP(c_Product__Type_Ofst(U_6010,U_6011),U_6012) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6010,U_6011,U_6010),c_COMBK(U_6010,U_6011)),U_6012),
    inference(definitional_conversion,[status(esa)],[f_1797_2]) ).

cnf(f_1797_4,plain,
    hAPP(c_Product__Type_Ofst(U_6010,U_6011),U_6012) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6010,U_6011,U_6010),c_COMBK(U_6010,U_6011)),U_6012),
    inference(clausify,[status(thm)],[f_1797_3]) ).

fof(f_1798_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_1798_2,plain,
    ! [U_6015,U_6014,U_6013] : hAPP(c_Product__Type_Osnd(U_6013,U_6014),U_6015) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6013,U_6014,U_6014),hAPP(c_COMBK(tc_fun(U_6014,U_6014),U_6013),c_COMBI(U_6014))),U_6015),
    inference(variable_rename,[status(thm)],[f_1798_1]) ).

fof(f_1798_3,plain,
    ! [U_6013,U_6014,U_6015] : hAPP(c_Product__Type_Osnd(U_6013,U_6014),U_6015) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6013,U_6014,U_6014),hAPP(c_COMBK(tc_fun(U_6014,U_6014),U_6013),c_COMBI(U_6014))),U_6015),
    inference(definitional_conversion,[status(esa)],[f_1798_2]) ).

cnf(f_1798_4,plain,
    hAPP(c_Product__Type_Osnd(U_6013,U_6014),U_6015) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6013,U_6014,U_6014),hAPP(c_COMBK(tc_fun(U_6014,U_6014),U_6013),c_COMBI(U_6014))),U_6015),
    inference(clausify,[status(thm)],[f_1798_3]) ).

fof(f_1799_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_1799_2,plain,
    ! [U_6018,U_6017,U_6016] : c_Nat_Onat_Onat__case(U_6016,U_6017,U_6018,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6017,
    inference(variable_rename,[status(thm)],[f_1799_1]) ).

fof(f_1799_3,plain,
    ! [U_6016,U_6018,U_6017] : c_Nat_Onat_Onat__case(U_6016,U_6017,U_6018,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6017,
    inference(definitional_conversion,[status(esa)],[f_1799_2]) ).

cnf(f_1799_4,plain,
    c_Nat_Onat_Onat__case(U_6016,U_6017,U_6018,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6017,
    inference(clausify,[status(thm)],[f_1799_3]) ).

fof(f_1800_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_1800_2,plain,
    ! [U_6022,U_6021,U_6020,U_6019] : c_Nat_Onat_Onat__case(U_6019,U_6020,U_6021,hAPP(c_Nat_OSuc,U_6022)) = hAPP(U_6021,U_6022),
    inference(variable_rename,[status(thm)],[f_1800_1]) ).

fof(f_1800_3,plain,
    ! [U_6019,U_6020,U_6021,U_6022] : c_Nat_Onat_Onat__case(U_6019,U_6020,U_6021,hAPP(c_Nat_OSuc,U_6022)) = hAPP(U_6021,U_6022),
    inference(definitional_conversion,[status(esa)],[f_1800_2]) ).

cnf(f_1800_4,plain,
    c_Nat_Onat_Onat__case(U_6019,U_6020,U_6021,hAPP(c_Nat_OSuc,U_6022)) = hAPP(U_6021,U_6022),
    inference(clausify,[status(thm)],[f_1800_3]) ).

fof(f_1801_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_1801_2,plain,
    ! [U_6027,U_6026,U_6025,U_6024,U_6023] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6023,U_6024,U_6025),U_6026),U_6027) = hAPP(hAPP(U_6026,hAPP(c_Product__Type_Ofst(U_6023,U_6024),U_6027)),hAPP(c_Product__Type_Osnd(U_6023,U_6024),U_6027)),
    inference(variable_rename,[status(thm)],[f_1801_1]) ).

fof(f_1801_3,plain,
    ! [U_6023,U_6024,U_6025,U_6026,U_6027] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6023,U_6024,U_6025),U_6026),U_6027) = hAPP(hAPP(U_6026,hAPP(c_Product__Type_Ofst(U_6023,U_6024),U_6027)),hAPP(c_Product__Type_Osnd(U_6023,U_6024),U_6027)),
    inference(definitional_conversion,[status(esa)],[f_1801_2]) ).

cnf(f_1801_4,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6023,U_6024,U_6025),U_6026),U_6027) = hAPP(hAPP(U_6026,hAPP(c_Product__Type_Ofst(U_6023,U_6024),U_6027)),hAPP(c_Product__Type_Osnd(U_6023,U_6024),U_6027)),
    inference(clausify,[status(thm)],[f_1801_3]) ).

fof(f_1802_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_1802_2,plain,
    ! [U_6033,U_6032,U_6031,U_6030,U_6029,U_6028] : hAPP(hAPP(c_COMBS(tc_prod(U_6028,U_6029),U_6029,U_6030),hAPP(hAPP(c_COMBB(U_6031,tc_fun(U_6029,U_6030),tc_prod(U_6028,U_6029)),U_6032),hAPP(hAPP(c_COMBB(U_6028,U_6031,tc_prod(U_6028,U_6029)),U_6033),c_Product__Type_Ofst(U_6028,U_6029)))),c_Product__Type_Osnd(U_6028,U_6029)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_6028,U_6029,U_6030),hAPP(hAPP(c_COMBB(U_6031,tc_fun(U_6029,U_6030),U_6028),U_6032),U_6033)),
    inference(variable_rename,[status(thm)],[f_1802_1]) ).

fof(f_1802_3,plain,
    ! [U_6028,U_6029,U_6030,U_6031,U_6032,U_6033] : hAPP(hAPP(c_COMBS(tc_prod(U_6028,U_6029),U_6029,U_6030),hAPP(hAPP(c_COMBB(U_6031,tc_fun(U_6029,U_6030),tc_prod(U_6028,U_6029)),U_6032),hAPP(hAPP(c_COMBB(U_6028,U_6031,tc_prod(U_6028,U_6029)),U_6033),c_Product__Type_Ofst(U_6028,U_6029)))),c_Product__Type_Osnd(U_6028,U_6029)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_6028,U_6029,U_6030),hAPP(hAPP(c_COMBB(U_6031,tc_fun(U_6029,U_6030),U_6028),U_6032),U_6033)),
    inference(definitional_conversion,[status(esa)],[f_1802_2]) ).

cnf(f_1802_4,plain,
    hAPP(hAPP(c_COMBS(tc_prod(U_6028,U_6029),U_6029,U_6030),hAPP(hAPP(c_COMBB(U_6031,tc_fun(U_6029,U_6030),tc_prod(U_6028,U_6029)),U_6032),hAPP(hAPP(c_COMBB(U_6028,U_6031,tc_prod(U_6028,U_6029)),U_6033),c_Product__Type_Ofst(U_6028,U_6029)))),c_Product__Type_Osnd(U_6028,U_6029)) = hAPP(c_Product__Type_Oprod_Oprod__case(U_6028,U_6029,U_6030),hAPP(hAPP(c_COMBB(U_6031,tc_fun(U_6029,U_6030),U_6028),U_6032),U_6033)),
    inference(clausify,[status(thm)],[f_1802_3]) ).

fof(f_1803_1,plain,
    ! [V_z_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_c,T_d,T_b),V_Pa_2),V_z_2) = hAPP(hAPP(V_Pa_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_1803_2,plain,
    ! [U_6038,U_6037,U_6036,U_6035,U_6034] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6034,U_6035,U_6036),U_6037),U_6038) = hAPP(hAPP(U_6037,hAPP(c_Product__Type_Ofst(U_6034,U_6035),U_6038)),hAPP(c_Product__Type_Osnd(U_6034,U_6035),U_6038)),
    inference(variable_rename,[status(thm)],[f_1803_1]) ).

fof(f_1803_3,plain,
    ! [U_6034,U_6035,U_6036,U_6037,U_6038] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6034,U_6035,U_6036),U_6037),U_6038) = hAPP(hAPP(U_6037,hAPP(c_Product__Type_Ofst(U_6034,U_6035),U_6038)),hAPP(c_Product__Type_Osnd(U_6034,U_6035),U_6038)),
    inference(definitional_conversion,[status(esa)],[f_1803_2]) ).

cnf(f_1803_4,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6034,U_6035,U_6036),U_6037),U_6038) = hAPP(hAPP(U_6037,hAPP(c_Product__Type_Ofst(U_6034,U_6035),U_6038)),hAPP(c_Product__Type_Osnd(U_6034,U_6035),U_6038)),
    inference(clausify,[status(thm)],[f_1803_3]) ).

fof(f_1804_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_1804_2,plain,
    ! [U_6043,U_6042,U_6041,U_6040,U_6039] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6039,U_6040,U_6041),U_6042),U_6043) = hAPP(hAPP(U_6042,hAPP(c_Product__Type_Ofst(U_6039,U_6040),U_6043)),hAPP(c_Product__Type_Osnd(U_6039,U_6040),U_6043)),
    inference(variable_rename,[status(thm)],[f_1804_1]) ).

fof(f_1804_3,plain,
    ! [U_6039,U_6040,U_6041,U_6042,U_6043] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6039,U_6040,U_6041),U_6042),U_6043) = hAPP(hAPP(U_6042,hAPP(c_Product__Type_Ofst(U_6039,U_6040),U_6043)),hAPP(c_Product__Type_Osnd(U_6039,U_6040),U_6043)),
    inference(definitional_conversion,[status(esa)],[f_1804_2]) ).

cnf(f_1804_4,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6039,U_6040,U_6041),U_6042),U_6043) = hAPP(hAPP(U_6042,hAPP(c_Product__Type_Ofst(U_6039,U_6040),U_6043)),hAPP(c_Product__Type_Osnd(U_6039,U_6040),U_6043)),
    inference(clausify,[status(thm)],[f_1804_3]) ).

fof(f_1805_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_1805_2,plain,
    ! [U_6045,U_6044] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6044)),U_6045))
        | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6044),U_6045)) )
      & ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6044),U_6045))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6044)),U_6045)) ) ),
    inference(variable_rename,[status(thm)],[f_1805_1]) ).

fof(f_1805_3,plain,
    ( ! [U_6049,U_6047] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6047)),U_6049))
        | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6047),U_6049)) )
    & ! [U_6048,U_6046] :
        ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6046),U_6048))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6046)),U_6048)) ) ),
    inference(miniscope,[status(thm)],[f_1805_2]) ).

fof(f_1805_4,plain,
    ( ! [U_6049,U_6047] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6047)),U_6049))
        | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6047),U_6049)) )
    & ! [U_6048,U_6046] :
        ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6046),U_6048))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6046)),U_6048)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1805_3]) ).

cnf(f_1805_5,plain,
    ( hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6046),U_6048))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6046)),U_6048)) ),
    inference(clausify,[status(thm)],[f_1805_4]) ).

cnf(f_1805_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6047)),U_6049))
    | ~ hBOOL(c_Nat_Onat_Onat__case(tc_HOL_Obool,c_fFalse,hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6047),U_6049)) ),
    inference(clausify,[status(thm)],[f_1805_4]) ).

fof(f_1806_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_1806_2,plain,
    ! [U_6051,U_6050] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6050),hAPP(c_Nat_OSuc,U_6051)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6050),U_6051)),
    inference(variable_rename,[status(thm)],[f_1806_1]) ).

fof(f_1806_3,plain,
    ! [U_6050,U_6051] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6050),hAPP(c_Nat_OSuc,U_6051)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6050),U_6051)),
    inference(definitional_conversion,[status(esa)],[f_1806_2]) ).

cnf(f_1806_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6050),hAPP(c_Nat_OSuc,U_6051)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),c_COMBI(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6050),U_6051)),
    inference(clausify,[status(thm)],[f_1806_3]) ).

fof(f_1807_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_1807_2,plain,
    ! [U_6053,U_6052] : c_Divides_Odivmod__int__rel(U_6052,U_6053) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,U_6052))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6053)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6053))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),U_6053))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6053)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6053))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),
    inference(variable_rename,[status(thm)],[f_1807_1]) ).

fof(f_1807_3,plain,
    ! [U_6052,U_6053] : c_Divides_Odivmod__int__rel(U_6052,U_6053) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,U_6052))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6053)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6053))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),U_6053))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6053)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6053))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),
    inference(definitional_conversion,[status(esa)],[f_1807_2]) ).

cnf(f_1807_4,plain,
    c_Divides_Odivmod__int__rel(U_6052,U_6053) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_HOL_Obool)),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_fun(tc_Int_Oint,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Int_Oint),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj)),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_HOL_Obool),tc_Int_Oint),hAPP(c_COMBB(tc_Int_Oint,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fequal,U_6052))),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint)),hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6053)))))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6053))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Int_Oint)),U_6053))))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Int_Oint),hAPP(c_fimplies,hAPP(c_fNot,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6053)))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Int_Oint),c_fconj),hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6053))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))))),
    inference(clausify,[status(thm)],[f_1807_3]) ).

fof(f_1808_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_1808_2,plain,
    ! [U_6057,U_6056,U_6055,U_6054] : c_Nat_Onat_Onat__case(U_6054,U_6055,U_6056,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6057)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_6054),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6057))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_6054,U_6054),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_6054,tc_fun(U_6054,U_6054)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6054,tc_fun(U_6054,U_6054)),tc_Int_Oint),c_If(U_6054)),c_Nat__Numeral_Oneg)),U_6055)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6054,tc_Int_Oint),U_6056),c_Int_Onat))),
    inference(variable_rename,[status(thm)],[f_1808_1]) ).

fof(f_1808_3,plain,
    ! [U_6054,U_6055,U_6056,U_6057] : c_Nat_Onat_Onat__case(U_6054,U_6055,U_6056,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6057)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_6054),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6057))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_6054,U_6054),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_6054,tc_fun(U_6054,U_6054)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6054,tc_fun(U_6054,U_6054)),tc_Int_Oint),c_If(U_6054)),c_Nat__Numeral_Oneg)),U_6055)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6054,tc_Int_Oint),U_6056),c_Int_Onat))),
    inference(definitional_conversion,[status(esa)],[f_1808_2]) ).

cnf(f_1808_4,plain,
    c_Nat_Onat_Onat__case(U_6054,U_6055,U_6056,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6057)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_6054),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6057))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_6054,U_6054),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_6054,tc_fun(U_6054,U_6054)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6054,tc_fun(U_6054,U_6054)),tc_Int_Oint),c_If(U_6054)),c_Nat__Numeral_Oneg)),U_6055)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6054,tc_Int_Oint),U_6056),c_Int_Onat))),
    inference(clausify,[status(thm)],[f_1808_3]) ).

fof(f_1809_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_1809_2,plain,
    ! [U_6059,U_6058] :
      ( ( ( ( c_Divides_Odivmod__int(U_6058,U_6059) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6059))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6059)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6058))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6059),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6058),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_6058,U_6059)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6059))))),c_Divides_Opdivmod(U_6058,U_6059))))
            | U_6059 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_6058,U_6059) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6058)
            | U_6059 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_6058 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odivmod__int(U_6058,U_6059) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | U_6058 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1809_1]) ).

fof(f_1809_3,plain,
    ( ! [U_6063,U_6061] :
        ( ( ( c_Divides_Odivmod__int(U_6061,U_6063) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6063))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6063)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6061))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6063),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6061),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_6061,U_6063)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6063))))),c_Divides_Opdivmod(U_6061,U_6063))))
            | U_6063 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_6061,U_6063) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6061)
            | U_6063 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_6061 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_6062,U_6060] :
        ( c_Divides_Odivmod__int(U_6060,U_6062) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | U_6060 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1809_2]) ).

fof(f_1809_4,plain,
    ( ! [U_6061,U_6063] :
        ( c_Divides_Odivmod__int(U_6061,U_6063) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6063))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6063)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6061))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6063),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6061),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_6061,U_6063)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6063))))),c_Divides_Opdivmod(U_6061,U_6063))))
        | U_6063 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP579(U_6061,U_6063) )
    & ! [U_6061,U_6063] :
        ( c_Divides_Odivmod__int(U_6061,U_6063) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6061)
        | U_6063 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP579(U_6061,U_6063) )
    & ! [U_6061,U_6063] :
        ( sP579(U_6061,U_6063)
        | U_6061 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_6062,U_6060] :
        ( c_Divides_Odivmod__int(U_6060,U_6062) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | U_6060 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP579])],[f_1809_3]) ).

cnf(f_1809_5,plain,
    ( c_Divides_Odivmod__int(U_6060,U_6062) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | U_6060 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1809_4]) ).

cnf(f_1809_6,plain,
    ( sP579(U_6061,U_6063)
    | U_6061 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1809_4]) ).

cnf(f_1809_7,plain,
    ( c_Divides_Odivmod__int(U_6061,U_6063) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6061)
    | U_6063 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP579(U_6061,U_6063) ),
    inference(clausify,[status(thm)],[f_1809_4]) ).

cnf(f_1809_8,plain,
    ( c_Divides_Odivmod__int(U_6061,U_6063) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6063))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fdisj,hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6063)),hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6061))),hAPP(hAPP(c_fconj,hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6063),c_Groups_Ozero__class_Ozero(tc_Int_Oint))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6061),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),c_Divides_Opdivmod(U_6061,U_6063)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6063))))),c_Divides_Opdivmod(U_6061,U_6063))))
    | U_6063 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP579(U_6061,U_6063) ),
    inference(clausify,[status(thm)],[f_1809_4]) ).

fof(f_1810_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_1810_2,plain,
    ! [U_6065,U_6064] :
      ( ( ( ( c_Divides_Odivmod__int(U_6064,U_6065) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6065))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6064)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6065))),c_Divides_Opdivmod(U_6064,U_6065)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6065))))),c_Divides_Opdivmod(U_6064,U_6065))))
            | U_6065 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_6064,U_6065) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6064)
            | U_6065 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_6064 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
      & ( c_Divides_Odivmod__int(U_6064,U_6065) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | U_6064 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(variable_rename,[status(thm)],[f_1810_1]) ).

fof(f_1810_3,plain,
    ( ! [U_6069,U_6067] :
        ( ( ( c_Divides_Odivmod__int(U_6067,U_6069) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6069))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6067)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6069))),c_Divides_Opdivmod(U_6067,U_6069)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6069))))),c_Divides_Opdivmod(U_6067,U_6069))))
            | U_6069 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Divides_Odivmod__int(U_6067,U_6069) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6067)
            | U_6069 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) )
        | U_6067 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_6068,U_6066] :
        ( c_Divides_Odivmod__int(U_6066,U_6068) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | U_6066 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(miniscope,[status(thm)],[f_1810_2]) ).

fof(f_1810_4,plain,
    ( ! [U_6067,U_6069] :
        ( c_Divides_Odivmod__int(U_6067,U_6069) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6069))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6067)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6069))),c_Divides_Opdivmod(U_6067,U_6069)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6069))))),c_Divides_Opdivmod(U_6067,U_6069))))
        | U_6069 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP580(U_6067,U_6069) )
    & ! [U_6067,U_6069] :
        ( c_Divides_Odivmod__int(U_6067,U_6069) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6067)
        | U_6069 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP580(U_6067,U_6069) )
    & ! [U_6067,U_6069] :
        ( sP580(U_6067,U_6069)
        | U_6067 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_6066,U_6068] :
        ( c_Divides_Odivmod__int(U_6066,U_6068) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
        | U_6066 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP580])],[f_1810_3]) ).

cnf(f_1810_5,plain,
    ( c_Divides_Odivmod__int(U_6066,U_6068) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Ozero__class_Ozero(tc_Int_Oint))
    | U_6066 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1810_4]) ).

cnf(f_1810_6,plain,
    ( sP580(U_6067,U_6069)
    | U_6067 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_1810_4]) ).

cnf(f_1810_7,plain,
    ( c_Divides_Odivmod__int(U_6067,U_6069) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6067)
    | U_6069 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP580(U_6067,U_6069) ),
    inference(clausify,[status(thm)],[f_1810_4]) ).

cnf(f_1810_8,plain,
    ( c_Divides_Odivmod__int(U_6067,U_6069) = hAPP(c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6069))),hAPP(hAPP(hAPP(c_If(tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_fequal,c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6067)),c_Groups_Osgn__class_Osgn(tc_Int_Oint,U_6069))),c_Divides_Opdivmod(U_6067,U_6069)),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_fun(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBS(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),hAPP(c_COMBC(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_If(tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_HOL_Obool),c_fequal),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),hAPP(hAPP(c_COMBB(tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_fun(tc_fun(tc_Int_Oint,tc_Int_Oint),tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint))),tc_Int_Oint),c_COMBB(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint)),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),tc_Int_Oint),c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_COMBC(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint),c_Groups_Ominus__class_Ominus(tc_Int_Oint)),c_Groups_Ouminus__class_Ouminus(tc_Int_Oint))),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6069))))),c_Divides_Opdivmod(U_6067,U_6069))))
    | U_6069 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP580(U_6067,U_6069) ),
    inference(clausify,[status(thm)],[f_1810_4]) ).

fof(f_1811_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_1811_2,plain,
    ! [U_6071,U_6070] :
      ( ( c_Code__Numeral_Onat__of__aux(U_6070,U_6071) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6070),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_6071))
        | U_6070 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( c_Code__Numeral_Onat__of__aux(U_6070,U_6071) = U_6071
        | U_6070 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_1811_1]) ).

fof(f_1811_3,plain,
    ( ! [U_6075,U_6073] :
        ( c_Code__Numeral_Onat__of__aux(U_6073,U_6075) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6073),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_6075))
        | U_6073 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_6074,U_6072] :
        ( c_Code__Numeral_Onat__of__aux(U_6072,U_6074) = U_6074
        | U_6072 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_1811_2]) ).

fof(f_1811_4,plain,
    ( ! [U_6073,U_6075] :
        ( c_Code__Numeral_Onat__of__aux(U_6073,U_6075) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6073),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_6075))
        | U_6073 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_6072,U_6074] :
        ( c_Code__Numeral_Onat__of__aux(U_6072,U_6074) = U_6074
        | U_6072 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(definitional_conversion,[status(esa)],[f_1811_3]) ).

cnf(f_1811_5,plain,
    ( c_Code__Numeral_Onat__of__aux(U_6072,U_6074) = U_6074
    | U_6072 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1811_4]) ).

cnf(f_1811_6,plain,
    ( c_Code__Numeral_Onat__of__aux(U_6073,U_6075) = c_Code__Numeral_Onat__of__aux(hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6073),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),hAPP(c_Nat_OSuc,U_6075))
    | U_6073 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1811_4]) ).

fof(f_1812_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_1812_2,plain,
    ! [U_6080,U_6079,U_6078,U_6077,U_6076] : hAPP(c_Nat_Onat_Onat__rec(U_6076,U_6077,U_6078),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6079)),U_6080)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_6076),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6079))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_6076,U_6076),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_6076,tc_fun(U_6076,U_6076)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6076,tc_fun(U_6076,U_6076)),tc_Int_Oint),c_If(U_6076)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_6076,U_6077,U_6078),U_6080))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_6076,U_6076),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_6076,U_6076),tc_Int_Oint),U_6078),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_6080))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6076,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_6076,U_6077,U_6078)),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_6080))))),
    inference(variable_rename,[status(thm)],[f_1812_1]) ).

fof(f_1812_3,plain,
    ! [U_6076,U_6078,U_6079,U_6077,U_6080] : hAPP(c_Nat_Onat_Onat__rec(U_6076,U_6077,U_6078),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6079)),U_6080)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_6076),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6079))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_6076,U_6076),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_6076,tc_fun(U_6076,U_6076)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6076,tc_fun(U_6076,U_6076)),tc_Int_Oint),c_If(U_6076)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_6076,U_6077,U_6078),U_6080))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_6076,U_6076),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_6076,U_6076),tc_Int_Oint),U_6078),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_6080))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6076,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_6076,U_6077,U_6078)),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_6080))))),
    inference(definitional_conversion,[status(esa)],[f_1812_2]) ).

cnf(f_1812_4,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_6076,U_6077,U_6078),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6079)),U_6080)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_6076),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6079))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_6076,U_6076),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_6076,tc_fun(U_6076,U_6076)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6076,tc_fun(U_6076,U_6076)),tc_Int_Oint),c_If(U_6076)),c_Nat__Numeral_Oneg)),hAPP(c_Nat_Onat_Onat__rec(U_6076,U_6077,U_6078),U_6080))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_6076,U_6076),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_6076,U_6076),tc_Int_Oint),U_6078),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_6080))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6076,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_6076,U_6077,U_6078)),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_6080))))),
    inference(clausify,[status(thm)],[f_1812_3]) ).

fof(f_1813_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_1813_2,plain,
    ! [U_6081] : c_Hoare__Mirabelle_OMGT(U_6081) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),U_6081),c_Natural_Oevalc(U_6081)),
    inference(variable_rename,[status(thm)],[f_1813_1]) ).

fof(f_1813_3,plain,
    ! [U_6081] : c_Hoare__Mirabelle_OMGT(U_6081) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),U_6081),c_Natural_Oevalc(U_6081)),
    inference(definitional_conversion,[status(esa)],[f_1813_2]) ).

cnf(f_1813_4,plain,
    c_Hoare__Mirabelle_OMGT(U_6081) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),U_6081),c_Natural_Oevalc(U_6081)),
    inference(clausify,[status(thm)],[f_1813_3]) ).

fof(f_1814_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_1814_2,plain,
    ! [U_6088,U_6087,U_6086,U_6085,U_6084,U_6083,U_6082] :
      ( hBOOL(hAPP(hAPP(c_member(U_6082),U_6083),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6087,U_6088,tc_fun(U_6082,tc_HOL_Obool)),U_6084),hAPP(hAPP(c_Product__Type_OPair(U_6087,U_6088),U_6085),U_6086))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_6082),U_6083),hAPP(hAPP(U_6084,U_6085),U_6086))) ),
    inference(variable_rename,[status(thm)],[f_1814_1]) ).

fof(f_1814_3,plain,
    ! [U_6082,U_6083,U_6084,U_6085,U_6086,U_6087,U_6088] :
      ( hBOOL(hAPP(hAPP(c_member(U_6082),U_6083),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6087,U_6088,tc_fun(U_6082,tc_HOL_Obool)),U_6084),hAPP(hAPP(c_Product__Type_OPair(U_6087,U_6088),U_6085),U_6086))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_6082),U_6083),hAPP(hAPP(U_6084,U_6085),U_6086))) ),
    inference(definitional_conversion,[status(esa)],[f_1814_2]) ).

cnf(f_1814_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6082),U_6083),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6087,U_6088,tc_fun(U_6082,tc_HOL_Obool)),U_6084),hAPP(hAPP(c_Product__Type_OPair(U_6087,U_6088),U_6085),U_6086))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6082),U_6083),hAPP(hAPP(U_6084,U_6085),U_6086))) ),
    inference(clausify,[status(thm)],[f_1814_3]) ).

fof(f_1815_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_1815_2,plain,
    ! [U_6093,U_6092,U_6091,U_6090,U_6089] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6092,U_6093,tc_HOL_Obool),U_6089),hAPP(hAPP(c_Product__Type_OPair(U_6092,U_6093),U_6090),U_6091)))
      | ~ hBOOL(hAPP(hAPP(U_6089,U_6090),U_6091)) ),
    inference(variable_rename,[status(thm)],[f_1815_1]) ).

fof(f_1815_3,plain,
    ! [U_6090,U_6091,U_6089,U_6092,U_6093] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6092,U_6093,tc_HOL_Obool),U_6089),hAPP(hAPP(c_Product__Type_OPair(U_6092,U_6093),U_6090),U_6091)))
      | ~ hBOOL(hAPP(hAPP(U_6089,U_6090),U_6091)) ),
    inference(definitional_conversion,[status(esa)],[f_1815_2]) ).

cnf(f_1815_4,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6092,U_6093,tc_HOL_Obool),U_6089),hAPP(hAPP(c_Product__Type_OPair(U_6092,U_6093),U_6090),U_6091)))
    | ~ hBOOL(hAPP(hAPP(U_6089,U_6090),U_6091)) ),
    inference(clausify,[status(thm)],[f_1815_3]) ).

fof(f_1816_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_1816_2,plain,
    ! [U_6098,U_6097,U_6096,U_6095,U_6094] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6097,U_6098,tc_HOL_Obool),U_6094),hAPP(hAPP(c_Product__Type_OPair(U_6097,U_6098),U_6095),U_6096)))
      | ~ hBOOL(hAPP(hAPP(U_6094,U_6095),U_6096)) ),
    inference(variable_rename,[status(thm)],[f_1816_1]) ).

fof(f_1816_3,plain,
    ! [U_6095,U_6094,U_6096,U_6097,U_6098] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6097,U_6098,tc_HOL_Obool),U_6094),hAPP(hAPP(c_Product__Type_OPair(U_6097,U_6098),U_6095),U_6096)))
      | ~ hBOOL(hAPP(hAPP(U_6094,U_6095),U_6096)) ),
    inference(definitional_conversion,[status(esa)],[f_1816_2]) ).

cnf(f_1816_4,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6097,U_6098,tc_HOL_Obool),U_6094),hAPP(hAPP(c_Product__Type_OPair(U_6097,U_6098),U_6095),U_6096)))
    | ~ hBOOL(hAPP(hAPP(U_6094,U_6095),U_6096)) ),
    inference(clausify,[status(thm)],[f_1816_3]) ).

fof(f_1817_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_1817_2,plain,
    ! [U_6103,U_6102,U_6101,U_6100,U_6099] :
      ( hBOOL(hAPP(hAPP(U_6101,U_6102),U_6103))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6099,U_6100,tc_HOL_Obool),U_6101),hAPP(hAPP(c_Product__Type_OPair(U_6099,U_6100),U_6102),U_6103))) ),
    inference(variable_rename,[status(thm)],[f_1817_1]) ).

fof(f_1817_3,plain,
    ! [U_6103,U_6102,U_6101] :
      ( ! [U_6100,U_6099] : ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6099,U_6100,tc_HOL_Obool),U_6101),hAPP(hAPP(c_Product__Type_OPair(U_6099,U_6100),U_6102),U_6103)))
      | hBOOL(hAPP(hAPP(U_6101,U_6102),U_6103)) ),
    inference(miniscope,[status(thm)],[f_1817_2]) ).

fof(f_1817_4,plain,
    ! [U_6099,U_6100,U_6101,U_6102,U_6103] :
      ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6099,U_6100,tc_HOL_Obool),U_6101),hAPP(hAPP(c_Product__Type_OPair(U_6099,U_6100),U_6102),U_6103)))
      | hBOOL(hAPP(hAPP(U_6101,U_6102),U_6103)) ),
    inference(definitional_conversion,[status(esa)],[f_1817_3]) ).

cnf(f_1817_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6099,U_6100,tc_HOL_Obool),U_6101),hAPP(hAPP(c_Product__Type_OPair(U_6099,U_6100),U_6102),U_6103)))
    | hBOOL(hAPP(hAPP(U_6101,U_6102),U_6103)) ),
    inference(clausify,[status(thm)],[f_1817_4]) ).

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_6110,U_6109,U_6108,U_6107,U_6106,U_6105,U_6104] :
      ( hBOOL(hAPP(hAPP(hAPP(U_6107,U_6108),U_6109),U_6110))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6104,U_6105,tc_fun(U_6106,tc_HOL_Obool)),U_6107),hAPP(hAPP(c_Product__Type_OPair(U_6104,U_6105),U_6108),U_6109)),U_6110)) ),
    inference(variable_rename,[status(thm)],[f_1818_1]) ).

fof(f_1818_3,plain,
    ! [U_6110,U_6109,U_6108,U_6107] :
      ( ! [U_6106,U_6105,U_6104] : ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6104,U_6105,tc_fun(U_6106,tc_HOL_Obool)),U_6107),hAPP(hAPP(c_Product__Type_OPair(U_6104,U_6105),U_6108),U_6109)),U_6110))
      | hBOOL(hAPP(hAPP(hAPP(U_6107,U_6108),U_6109),U_6110)) ),
    inference(miniscope,[status(thm)],[f_1818_2]) ).

fof(f_1818_4,plain,
    ! [U_6104,U_6105,U_6106,U_6107,U_6108,U_6109,U_6110] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6104,U_6105,tc_fun(U_6106,tc_HOL_Obool)),U_6107),hAPP(hAPP(c_Product__Type_OPair(U_6104,U_6105),U_6108),U_6109)),U_6110))
      | hBOOL(hAPP(hAPP(hAPP(U_6107,U_6108),U_6109),U_6110)) ),
    inference(definitional_conversion,[status(esa)],[f_1818_3]) ).

cnf(f_1818_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6104,U_6105,tc_fun(U_6106,tc_HOL_Obool)),U_6107),hAPP(hAPP(c_Product__Type_OPair(U_6104,U_6105),U_6108),U_6109)),U_6110))
    | hBOOL(hAPP(hAPP(hAPP(U_6107,U_6108),U_6109),U_6110)) ),
    inference(clausify,[status(thm)],[f_1818_4]) ).

fof(f_1819_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_1819_2,plain,
    ! [U_6116,U_6115,U_6114,U_6113,U_6112,U_6111] : hAPP(c_Product__Type_Oapsnd(U_6111,U_6112,U_6113,U_6114),hAPP(hAPP(c_Product__Type_OPair(U_6113,U_6111),U_6115),U_6116)) = hAPP(hAPP(c_Product__Type_OPair(U_6113,U_6112),U_6115),hAPP(U_6114,U_6116)),
    inference(variable_rename,[status(thm)],[f_1819_1]) ).

fof(f_1819_3,plain,
    ! [U_6111,U_6112,U_6113,U_6114,U_6115,U_6116] : hAPP(c_Product__Type_Oapsnd(U_6111,U_6112,U_6113,U_6114),hAPP(hAPP(c_Product__Type_OPair(U_6113,U_6111),U_6115),U_6116)) = hAPP(hAPP(c_Product__Type_OPair(U_6113,U_6112),U_6115),hAPP(U_6114,U_6116)),
    inference(definitional_conversion,[status(esa)],[f_1819_2]) ).

cnf(f_1819_4,plain,
    hAPP(c_Product__Type_Oapsnd(U_6111,U_6112,U_6113,U_6114),hAPP(hAPP(c_Product__Type_OPair(U_6113,U_6111),U_6115),U_6116)) = hAPP(hAPP(c_Product__Type_OPair(U_6113,U_6112),U_6115),hAPP(U_6114,U_6116)),
    inference(clausify,[status(thm)],[f_1819_3]) ).

fof(f_1820_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_1820_2,plain,
    ! [U_6121,U_6120,U_6119,U_6118,U_6117] : hAPP(c_Product__Type_Ofst(U_6117,U_6118),hAPP(c_Product__Type_Oapsnd(U_6119,U_6118,U_6117,U_6120),U_6121)) = hAPP(c_Product__Type_Ofst(U_6117,U_6119),U_6121),
    inference(variable_rename,[status(thm)],[f_1820_1]) ).

fof(f_1820_3,plain,
    ! [U_6117,U_6118,U_6119,U_6120,U_6121] : hAPP(c_Product__Type_Ofst(U_6117,U_6118),hAPP(c_Product__Type_Oapsnd(U_6119,U_6118,U_6117,U_6120),U_6121)) = hAPP(c_Product__Type_Ofst(U_6117,U_6119),U_6121),
    inference(definitional_conversion,[status(esa)],[f_1820_2]) ).

cnf(f_1820_4,plain,
    hAPP(c_Product__Type_Ofst(U_6117,U_6118),hAPP(c_Product__Type_Oapsnd(U_6119,U_6118,U_6117,U_6120),U_6121)) = hAPP(c_Product__Type_Ofst(U_6117,U_6119),U_6121),
    inference(clausify,[status(thm)],[f_1820_3]) ).

fof(f_1821_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_1821_2,plain,
    ! [U_6126,U_6125,U_6124,U_6123,U_6122] : hAPP(c_Product__Type_Osnd(U_6122,U_6123),hAPP(c_Product__Type_Oapsnd(U_6124,U_6123,U_6122,U_6125),U_6126)) = hAPP(U_6125,hAPP(c_Product__Type_Osnd(U_6122,U_6124),U_6126)),
    inference(variable_rename,[status(thm)],[f_1821_1]) ).

fof(f_1821_3,plain,
    ! [U_6122,U_6123,U_6124,U_6125,U_6126] : hAPP(c_Product__Type_Osnd(U_6122,U_6123),hAPP(c_Product__Type_Oapsnd(U_6124,U_6123,U_6122,U_6125),U_6126)) = hAPP(U_6125,hAPP(c_Product__Type_Osnd(U_6122,U_6124),U_6126)),
    inference(definitional_conversion,[status(esa)],[f_1821_2]) ).

cnf(f_1821_4,plain,
    hAPP(c_Product__Type_Osnd(U_6122,U_6123),hAPP(c_Product__Type_Oapsnd(U_6124,U_6123,U_6122,U_6125),U_6126)) = hAPP(U_6125,hAPP(c_Product__Type_Osnd(U_6122,U_6124),U_6126)),
    inference(clausify,[status(thm)],[f_1821_3]) ).

fof(f_1822_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_1822_2,plain,
    ! [U_6132,U_6131,U_6130,U_6129,U_6128,U_6127] :
      ( ( hAPP(c_Product__Type_Oapsnd(U_6127,U_6128,U_6129,U_6130),U_6131) = hAPP(c_Product__Type_Oapsnd(U_6127,U_6128,U_6129,U_6132),U_6131)
        | hAPP(U_6130,hAPP(c_Product__Type_Osnd(U_6129,U_6127),U_6131)) != hAPP(U_6132,hAPP(c_Product__Type_Osnd(U_6129,U_6127),U_6131)) )
      & ( hAPP(U_6130,hAPP(c_Product__Type_Osnd(U_6129,U_6127),U_6131)) = hAPP(U_6132,hAPP(c_Product__Type_Osnd(U_6129,U_6127),U_6131))
        | hAPP(c_Product__Type_Oapsnd(U_6127,U_6128,U_6129,U_6130),U_6131) != hAPP(c_Product__Type_Oapsnd(U_6127,U_6128,U_6129,U_6132),U_6131) ) ),
    inference(variable_rename,[status(thm)],[f_1822_1]) ).

fof(f_1822_3,plain,
    ( ! [U_6144,U_6142,U_6140,U_6138,U_6136,U_6134] :
        ( hAPP(c_Product__Type_Oapsnd(U_6134,U_6136,U_6138,U_6140),U_6142) = hAPP(c_Product__Type_Oapsnd(U_6134,U_6136,U_6138,U_6144),U_6142)
        | hAPP(U_6140,hAPP(c_Product__Type_Osnd(U_6138,U_6134),U_6142)) != hAPP(U_6144,hAPP(c_Product__Type_Osnd(U_6138,U_6134),U_6142)) )
    & ! [U_6143,U_6141,U_6139,U_6137,U_6135,U_6133] :
        ( hAPP(U_6139,hAPP(c_Product__Type_Osnd(U_6137,U_6133),U_6141)) = hAPP(U_6143,hAPP(c_Product__Type_Osnd(U_6137,U_6133),U_6141))
        | hAPP(c_Product__Type_Oapsnd(U_6133,U_6135,U_6137,U_6139),U_6141) != hAPP(c_Product__Type_Oapsnd(U_6133,U_6135,U_6137,U_6143),U_6141) ) ),
    inference(miniscope,[status(thm)],[f_1822_2]) ).

fof(f_1822_4,plain,
    ( ! [U_6134,U_6136,U_6138,U_6140,U_6142,U_6144] :
        ( hAPP(c_Product__Type_Oapsnd(U_6134,U_6136,U_6138,U_6140),U_6142) = hAPP(c_Product__Type_Oapsnd(U_6134,U_6136,U_6138,U_6144),U_6142)
        | hAPP(U_6140,hAPP(c_Product__Type_Osnd(U_6138,U_6134),U_6142)) != hAPP(U_6144,hAPP(c_Product__Type_Osnd(U_6138,U_6134),U_6142)) )
    & ! [U_6135,U_6133,U_6139,U_6137,U_6143,U_6141] :
        ( hAPP(U_6139,hAPP(c_Product__Type_Osnd(U_6137,U_6133),U_6141)) = hAPP(U_6143,hAPP(c_Product__Type_Osnd(U_6137,U_6133),U_6141))
        | hAPP(c_Product__Type_Oapsnd(U_6133,U_6135,U_6137,U_6139),U_6141) != hAPP(c_Product__Type_Oapsnd(U_6133,U_6135,U_6137,U_6143),U_6141) ) ),
    inference(definitional_conversion,[status(esa)],[f_1822_3]) ).

cnf(f_1822_5,plain,
    ( hAPP(U_6139,hAPP(c_Product__Type_Osnd(U_6137,U_6133),U_6141)) = hAPP(U_6143,hAPP(c_Product__Type_Osnd(U_6137,U_6133),U_6141))
    | hAPP(c_Product__Type_Oapsnd(U_6133,U_6135,U_6137,U_6139),U_6141) != hAPP(c_Product__Type_Oapsnd(U_6133,U_6135,U_6137,U_6143),U_6141) ),
    inference(clausify,[status(thm)],[f_1822_4]) ).

cnf(f_1822_6,plain,
    ( hAPP(c_Product__Type_Oapsnd(U_6134,U_6136,U_6138,U_6140),U_6142) = hAPP(c_Product__Type_Oapsnd(U_6134,U_6136,U_6138,U_6144),U_6142)
    | hAPP(U_6140,hAPP(c_Product__Type_Osnd(U_6138,U_6134),U_6142)) != hAPP(U_6144,hAPP(c_Product__Type_Osnd(U_6138,U_6134),U_6142)) ),
    inference(clausify,[status(thm)],[f_1822_4]) ).

fof(f_1823_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_1823_2,plain,
    ! [U_6147,U_6146,U_6145] : hAPP(c_Nat_Onat_Onat__rec(U_6145,U_6146,U_6147),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6146,
    inference(variable_rename,[status(thm)],[f_1823_1]) ).

fof(f_1823_3,plain,
    ! [U_6147,U_6146,U_6145] : hAPP(c_Nat_Onat_Onat__rec(U_6145,U_6146,U_6147),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6146,
    inference(definitional_conversion,[status(esa)],[f_1823_2]) ).

cnf(f_1823_4,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_6145,U_6146,U_6147),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6146,
    inference(clausify,[status(thm)],[f_1823_3]) ).

fof(f_1824_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_1824_2,plain,
    ! [U_6151,U_6150,U_6149,U_6148] : hAPP(c_Nat_Onat_Onat__rec(U_6148,U_6149,U_6150),hAPP(c_Nat_OSuc,U_6151)) = hAPP(hAPP(U_6150,U_6151),hAPP(c_Nat_Onat_Onat__rec(U_6148,U_6149,U_6150),U_6151)),
    inference(variable_rename,[status(thm)],[f_1824_1]) ).

fof(f_1824_3,plain,
    ! [U_6148,U_6149,U_6150,U_6151] : hAPP(c_Nat_Onat_Onat__rec(U_6148,U_6149,U_6150),hAPP(c_Nat_OSuc,U_6151)) = hAPP(hAPP(U_6150,U_6151),hAPP(c_Nat_Onat_Onat__rec(U_6148,U_6149,U_6150),U_6151)),
    inference(definitional_conversion,[status(esa)],[f_1824_2]) ).

cnf(f_1824_4,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_6148,U_6149,U_6150),hAPP(c_Nat_OSuc,U_6151)) = hAPP(hAPP(U_6150,U_6151),hAPP(c_Nat_Onat_Onat__rec(U_6148,U_6149,U_6150),U_6151)),
    inference(clausify,[status(thm)],[f_1824_3]) ).

fof(f_1825_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_1825_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_1825_1]) ).

cnf(f_1825_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_1825_2]) ).

fof(f_1826_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_1826_2,plain,
    ! [U_6153,U_6152] :
      ( ( c_Divides_Odivmod__nat(U_6153,U_6152) = 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_6153),U_6152),U_6152))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6153),U_6152))
        | U_6152 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Divides_Odivmod__nat(U_6153,U_6152) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6153)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6153),U_6152))
          & U_6152 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(variable_rename,[status(thm)],[f_1826_1]) ).

fof(f_1826_3,plain,
    ( ! [U_6157,U_6155] :
        ( c_Divides_Odivmod__nat(U_6157,U_6155) = 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_6157),U_6155),U_6155))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6157),U_6155))
        | U_6155 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_6156,U_6154] :
        ( c_Divides_Odivmod__nat(U_6156,U_6154) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6156)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6156),U_6154))
          & U_6154 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ),
    inference(miniscope,[status(thm)],[f_1826_2]) ).

fof(f_1826_4,plain,
    ( ! [U_6156,U_6154] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6156),U_6154))
        | ~ sP581(U_6156,U_6154) )
    & ! [U_6156,U_6154] :
        ( U_6154 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP581(U_6156,U_6154) )
    & ! [U_6155,U_6157] :
        ( c_Divides_Odivmod__nat(U_6157,U_6155) = 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_6157),U_6155),U_6155))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6157),U_6155))
        | U_6155 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_6156,U_6154] :
        ( c_Divides_Odivmod__nat(U_6156,U_6154) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6156)
        | sP581(U_6156,U_6154) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP581])],[f_1826_3]) ).

cnf(f_1826_5,plain,
    ( c_Divides_Odivmod__nat(U_6156,U_6154) = hAPP(hAPP(c_Product__Type_OPair(tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6156)
    | sP581(U_6156,U_6154) ),
    inference(clausify,[status(thm)],[f_1826_4]) ).

cnf(f_1826_6,plain,
    ( c_Divides_Odivmod__nat(U_6157,U_6155) = 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_6157),U_6155),U_6155))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6157),U_6155))
    | U_6155 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1826_4]) ).

cnf(f_1826_7,plain,
    ( U_6154 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP581(U_6156,U_6154) ),
    inference(clausify,[status(thm)],[f_1826_4]) ).

cnf(f_1826_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6156),U_6154))
    | ~ sP581(U_6156,U_6154) ),
    inference(clausify,[status(thm)],[f_1826_4]) ).

fof(f_1827_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_1827_2,plain,
    ! [U_6161,U_6160,U_6159,U_6158] : hAPP(c_Nat_Onat_Onat__rec(U_6158,U_6159,U_6160),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6161)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_6158),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6161))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_6158,U_6158),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_6158,tc_fun(U_6158,U_6158)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6158,tc_fun(U_6158,U_6158)),tc_Int_Oint),c_If(U_6158)),c_Nat__Numeral_Oneg)),U_6159)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_6158,U_6158),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_6158,U_6158),tc_Int_Oint),U_6160),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6158,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_6158,U_6159,U_6160)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_1827_1]) ).

fof(f_1827_3,plain,
    ! [U_6158,U_6159,U_6160,U_6161] : hAPP(c_Nat_Onat_Onat__rec(U_6158,U_6159,U_6160),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6161)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_6158),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6161))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_6158,U_6158),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_6158,tc_fun(U_6158,U_6158)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6158,tc_fun(U_6158,U_6158)),tc_Int_Oint),c_If(U_6158)),c_Nat__Numeral_Oneg)),U_6159)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_6158,U_6158),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_6158,U_6158),tc_Int_Oint),U_6160),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6158,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_6158,U_6159,U_6160)),c_Int_Onat)))),
    inference(definitional_conversion,[status(esa)],[f_1827_2]) ).

cnf(f_1827_4,plain,
    hAPP(c_Nat_Onat_Onat__rec(U_6158,U_6159,U_6160),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6161)) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_6158),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(U_6161))),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_6158,U_6158),hAPP(hAPP(c_COMBC(tc_Int_Oint,U_6158,tc_fun(U_6158,U_6158)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_6158,tc_fun(U_6158,U_6158)),tc_Int_Oint),c_If(U_6158)),c_Nat__Numeral_Oneg)),U_6159)),hAPP(hAPP(c_COMBS(tc_Int_Oint,U_6158,U_6158),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_6158,U_6158),tc_Int_Oint),U_6160),c_Int_Onat)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_6158,tc_Int_Oint),c_Nat_Onat_Onat__rec(U_6158,U_6159,U_6160)),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_1827_3]) ).

fof(f_1828_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_1828_2,plain,
    ! [U_6163,U_6162] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6162)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6163)) = 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_6163))),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_6162)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_1828_1]) ).

fof(f_1828_3,plain,
    ! [U_6162,U_6163] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6162)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6163)) = 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_6163))),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_6162)),c_Int_Onat)))),
    inference(definitional_conversion,[status(esa)],[f_1828_2]) ).

cnf(f_1828_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6162)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6163)) = 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_6163))),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_6162)),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_1828_3]) ).

fof(f_1829_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_1829_2,plain,
    ! [U_6165,U_6164] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6164)),hAPP(c_Nat_OSuc,U_6165)) = 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_6164))),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_6165)))),
    inference(variable_rename,[status(thm)],[f_1829_1]) ).

fof(f_1829_3,plain,
    ! [U_6164,U_6165] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6164)),hAPP(c_Nat_OSuc,U_6165)) = 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_6164))),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_6165)))),
    inference(definitional_conversion,[status(esa)],[f_1829_2]) ).

cnf(f_1829_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6164)),hAPP(c_Nat_OSuc,U_6165)) = 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_6164))),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_6165)))),
    inference(clausify,[status(thm)],[f_1829_3]) ).

fof(f_1830_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_1830_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_1830_1]) ).

cnf(f_1830_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_1830_2]) ).

fof(f_1831_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_1831_2,plain,
    ! [U_6167,U_6166] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6166)),hAPP(c_Nat_OSuc,U_6167)) = 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_6166))),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_6167))),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_6167)))),
    inference(variable_rename,[status(thm)],[f_1831_1]) ).

fof(f_1831_3,plain,
    ! [U_6166,U_6167] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6166)),hAPP(c_Nat_OSuc,U_6167)) = 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_6166))),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_6167))),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_6167)))),
    inference(definitional_conversion,[status(esa)],[f_1831_2]) ).

cnf(f_1831_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6166)),hAPP(c_Nat_OSuc,U_6167)) = 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_6166))),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_6167))),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_6167)))),
    inference(clausify,[status(thm)],[f_1831_3]) ).

fof(f_1832_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_1832_2,plain,
    ! [U_6169,U_6168] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6168)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6169)) = 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_6169))),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_6168))),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_6168)),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_1832_1]) ).

fof(f_1832_3,plain,
    ! [U_6168,U_6169] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6168)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6169)) = 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_6169))),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_6168))),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_6168)),c_Int_Onat)))),
    inference(definitional_conversion,[status(esa)],[f_1832_2]) ).

cnf(f_1832_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6168)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_6169)) = 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_6169))),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_6168))),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_6168)),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_1832_3]) ).

fof(f_1833_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_1833_2,plain,
    ! [U_6173,U_6172,U_6171,U_6170] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6170),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6170),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6170),U_6171),U_6172)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6170),U_6171),U_6173))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6170),U_6171),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6170),U_6172),U_6173))))
      | ~ class_Orderings_Olinorder(U_6170) ),
    inference(variable_rename,[status(thm)],[f_1833_1]) ).

fof(f_1833_3,plain,
    ! [U_6170,U_6171,U_6172,U_6173] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6170),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6170),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6170),U_6171),U_6172)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6170),U_6171),U_6173))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6170),U_6171),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6170),U_6172),U_6173))))
      | ~ class_Orderings_Olinorder(U_6170) ),
    inference(definitional_conversion,[status(esa)],[f_1833_2]) ).

cnf(f_1833_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6170),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6170),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6170),U_6171),U_6172)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6170),U_6171),U_6173))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6170),U_6171),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6170),U_6172),U_6173))))
    | ~ class_Orderings_Olinorder(U_6170) ),
    inference(clausify,[status(thm)],[f_1833_3]) ).

fof(f_1834_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_1834_2,plain,
    ! [U_6177,U_6176,U_6175,U_6174] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6174),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6174),U_6175),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6174),U_6176),U_6177))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6174),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6174),U_6175),U_6176)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6174),U_6175),U_6177))))
      | ~ class_Orderings_Olinorder(U_6174) ),
    inference(variable_rename,[status(thm)],[f_1834_1]) ).

fof(f_1834_3,plain,
    ! [U_6174,U_6175,U_6176,U_6177] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6174),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6174),U_6175),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6174),U_6176),U_6177))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6174),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6174),U_6175),U_6176)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6174),U_6175),U_6177))))
      | ~ class_Orderings_Olinorder(U_6174) ),
    inference(definitional_conversion,[status(esa)],[f_1834_2]) ).

cnf(f_1834_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6174),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6174),U_6175),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6174),U_6176),U_6177))),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6174),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6174),U_6175),U_6176)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6174),U_6175),U_6177))))
    | ~ class_Orderings_Olinorder(U_6174) ),
    inference(clausify,[status(thm)],[f_1834_3]) ).

fof(f_1835_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_1835_2,plain,
    ! [U_6180,U_6179,U_6178] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6178),U_6179),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6178),U_6179),U_6180)))
      | ~ class_Orderings_Olinorder(U_6178) ),
    inference(variable_rename,[status(thm)],[f_1835_1]) ).

fof(f_1835_3,plain,
    ! [U_6178,U_6179,U_6180] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6178),U_6179),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6178),U_6179),U_6180)))
      | ~ class_Orderings_Olinorder(U_6178) ),
    inference(definitional_conversion,[status(esa)],[f_1835_2]) ).

cnf(f_1835_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6178),U_6179),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6178),U_6179),U_6180)))
    | ~ class_Orderings_Olinorder(U_6178) ),
    inference(clausify,[status(thm)],[f_1835_3]) ).

fof(f_1836_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_1836_2,plain,
    ! [U_6183,U_6182,U_6181] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6181),U_6182),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6181),U_6183),U_6182)))
      | ~ class_Orderings_Olinorder(U_6181) ),
    inference(variable_rename,[status(thm)],[f_1836_1]) ).

fof(f_1836_3,plain,
    ! [U_6181,U_6182,U_6183] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6181),U_6182),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6181),U_6183),U_6182)))
      | ~ class_Orderings_Olinorder(U_6181) ),
    inference(definitional_conversion,[status(esa)],[f_1836_2]) ).

cnf(f_1836_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6181),U_6182),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6181),U_6183),U_6182)))
    | ~ class_Orderings_Olinorder(U_6181) ),
    inference(clausify,[status(thm)],[f_1836_3]) ).

fof(f_1837_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_1837_2,plain,
    ! [U_6186,U_6185,U_6184] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6184),U_6185),U_6186))
          | hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6184),U_6185),U_6186) != U_6186 )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6184),U_6185),U_6186) = U_6186
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6184),U_6185),U_6186)) ) )
      | ~ class_Orderings_Olinorder(U_6184) ),
    inference(variable_rename,[status(thm)],[f_1837_1]) ).

fof(f_1837_3,plain,
    ( ! [U_6184,U_6185,U_6186] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6184),U_6185),U_6186))
        | hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6184),U_6185),U_6186) != U_6186
        | ~ sP582(U_6184,U_6185,U_6186) )
    & ! [U_6184,U_6185,U_6186] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6184),U_6185),U_6186) = U_6186
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6184),U_6185),U_6186))
        | ~ sP582(U_6184,U_6185,U_6186) )
    & ! [U_6184,U_6185,U_6186] :
        ( sP582(U_6184,U_6185,U_6186)
        | ~ class_Orderings_Olinorder(U_6184) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP582])],[f_1837_2]) ).

cnf(f_1837_4,plain,
    ( sP582(U_6184,U_6185,U_6186)
    | ~ class_Orderings_Olinorder(U_6184) ),
    inference(clausify,[status(thm)],[f_1837_3]) ).

cnf(f_1837_5,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6184),U_6185),U_6186) = U_6186
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6184),U_6185),U_6186))
    | ~ sP582(U_6184,U_6185,U_6186) ),
    inference(clausify,[status(thm)],[f_1837_3]) ).

cnf(f_1837_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6184),U_6185),U_6186))
    | hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6184),U_6185),U_6186) != U_6186
    | ~ sP582(U_6184,U_6185,U_6186) ),
    inference(clausify,[status(thm)],[f_1837_3]) ).

fof(f_1838_1,plain,
    ! [V_z_2,V_y_2,V_x_2,T_b] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),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_1838_2,plain,
    ! [U_6190,U_6189,U_6188,U_6187] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6187),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6187),U_6188),U_6189)),U_6190))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6187),U_6189),U_6190))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6187),U_6188),U_6190)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6187),U_6189),U_6190))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6187),U_6188),U_6190)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6187),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6187),U_6188),U_6189)),U_6190)) ) )
      | ~ class_Orderings_Olinorder(U_6187) ),
    inference(variable_rename,[status(thm)],[f_1838_1]) ).

fof(f_1838_3,plain,
    ( ! [U_6188,U_6187,U_6189,U_6190] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6187),U_6189),U_6190))
        | ~ sP583(U_6188,U_6187,U_6189,U_6190) )
    & ! [U_6188,U_6187,U_6189,U_6190] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6187),U_6188),U_6190))
        | ~ sP583(U_6188,U_6187,U_6189,U_6190) )
    & ! [U_6188,U_6187,U_6189,U_6190] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6187),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6187),U_6188),U_6189)),U_6190))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6187),U_6189),U_6190))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6187),U_6188),U_6190))
        | ~ sP584(U_6188,U_6187,U_6189,U_6190) )
    & ! [U_6188,U_6187,U_6189,U_6190] :
        ( sP583(U_6188,U_6187,U_6189,U_6190)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6187),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6187),U_6188),U_6189)),U_6190))
        | ~ sP584(U_6188,U_6187,U_6189,U_6190) )
    & ! [U_6188,U_6187,U_6189,U_6190] :
        ( sP584(U_6188,U_6187,U_6189,U_6190)
        | ~ class_Orderings_Olinorder(U_6187) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP583,sP584])],[f_1838_2]) ).

cnf(f_1838_4,plain,
    ( sP584(U_6188,U_6187,U_6189,U_6190)
    | ~ class_Orderings_Olinorder(U_6187) ),
    inference(clausify,[status(thm)],[f_1838_3]) ).

cnf(f_1838_5,plain,
    ( sP583(U_6188,U_6187,U_6189,U_6190)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6187),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6187),U_6188),U_6189)),U_6190))
    | ~ sP584(U_6188,U_6187,U_6189,U_6190) ),
    inference(clausify,[status(thm)],[f_1838_3]) ).

cnf(f_1838_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6187),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6187),U_6188),U_6189)),U_6190))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6187),U_6189),U_6190))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6187),U_6188),U_6190))
    | ~ sP584(U_6188,U_6187,U_6189,U_6190) ),
    inference(clausify,[status(thm)],[f_1838_3]) ).

cnf(f_1838_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6187),U_6188),U_6190))
    | ~ sP583(U_6188,U_6187,U_6189,U_6190) ),
    inference(clausify,[status(thm)],[f_1838_3]) ).

cnf(f_1838_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6187),U_6189),U_6190))
    | ~ sP583(U_6188,U_6187,U_6189,U_6190) ),
    inference(clausify,[status(thm)],[f_1838_3]) ).

fof(f_1839_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_1839_2,plain,
    ! [U_6194,U_6193,U_6192,U_6191] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6191),U_6192),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6191),U_6193),U_6194)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6191),U_6192),U_6193))
      | ~ class_Orderings_Olinorder(U_6191) ),
    inference(variable_rename,[status(thm)],[f_1839_1]) ).

fof(f_1839_3,plain,
    ! [U_6191,U_6192,U_6193,U_6194] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6191),U_6192),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6191),U_6193),U_6194)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6191),U_6192),U_6193))
      | ~ class_Orderings_Olinorder(U_6191) ),
    inference(definitional_conversion,[status(esa)],[f_1839_2]) ).

cnf(f_1839_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6191),U_6192),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6191),U_6193),U_6194)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6191),U_6192),U_6193))
    | ~ class_Orderings_Olinorder(U_6191) ),
    inference(clausify,[status(thm)],[f_1839_3]) ).

fof(f_1840_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_1840_2,plain,
    ! [U_6198,U_6197,U_6196,U_6195] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6195),U_6196),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6195),U_6198),U_6197)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6195),U_6196),U_6197))
      | ~ class_Orderings_Olinorder(U_6195) ),
    inference(variable_rename,[status(thm)],[f_1840_1]) ).

fof(f_1840_3,plain,
    ! [U_6195,U_6196,U_6197,U_6198] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6195),U_6196),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6195),U_6198),U_6197)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6195),U_6196),U_6197))
      | ~ class_Orderings_Olinorder(U_6195) ),
    inference(definitional_conversion,[status(esa)],[f_1840_2]) ).

cnf(f_1840_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6195),U_6196),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6195),U_6198),U_6197)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6195),U_6196),U_6197))
    | ~ class_Orderings_Olinorder(U_6195) ),
    inference(clausify,[status(thm)],[f_1840_3]) ).

fof(f_1841_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_1841_2,plain,
    ! [U_6201,U_6200,U_6199] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6199),U_6200),U_6201) = U_6201
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6199),U_6200),U_6201))
      | ~ class_Orderings_Olinorder(U_6199) ),
    inference(variable_rename,[status(thm)],[f_1841_1]) ).

fof(f_1841_3,plain,
    ! [U_6199,U_6200,U_6201] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6199),U_6200),U_6201) = U_6201
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6199),U_6200),U_6201))
      | ~ class_Orderings_Olinorder(U_6199) ),
    inference(definitional_conversion,[status(esa)],[f_1841_2]) ).

cnf(f_1841_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6199),U_6200),U_6201) = U_6201
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6199),U_6200),U_6201))
    | ~ class_Orderings_Olinorder(U_6199) ),
    inference(clausify,[status(thm)],[f_1841_3]) ).

fof(f_1842_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_1842_2,plain,
    ! [U_6204,U_6203,U_6202] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6202),U_6204),U_6203) = U_6204
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6202),U_6203),U_6204))
      | ~ class_Orderings_Olinorder(U_6202) ),
    inference(variable_rename,[status(thm)],[f_1842_1]) ).

fof(f_1842_3,plain,
    ! [U_6202,U_6203,U_6204] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6202),U_6204),U_6203) = U_6204
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6202),U_6203),U_6204))
      | ~ class_Orderings_Olinorder(U_6202) ),
    inference(definitional_conversion,[status(esa)],[f_1842_2]) ).

cnf(f_1842_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6202),U_6204),U_6203) = U_6204
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6202),U_6203),U_6204))
    | ~ class_Orderings_Olinorder(U_6202) ),
    inference(clausify,[status(thm)],[f_1842_3]) ).

fof(f_1843_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_1843_2,plain,
    ! [U_6208,U_6207,U_6206,U_6205] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6205),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6205),U_6206),U_6208)),U_6207))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6205),U_6208),U_6207))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6205),U_6206),U_6207))
      | ~ class_Orderings_Olinorder(U_6205) ),
    inference(variable_rename,[status(thm)],[f_1843_1]) ).

fof(f_1843_3,plain,
    ! [U_6205,U_6206,U_6207,U_6208] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6205),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6205),U_6206),U_6208)),U_6207))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6205),U_6208),U_6207))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6205),U_6206),U_6207))
      | ~ class_Orderings_Olinorder(U_6205) ),
    inference(definitional_conversion,[status(esa)],[f_1843_2]) ).

cnf(f_1843_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6205),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6205),U_6206),U_6208)),U_6207))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6205),U_6208),U_6207))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6205),U_6206),U_6207))
    | ~ class_Orderings_Olinorder(U_6205) ),
    inference(clausify,[status(thm)],[f_1843_3]) ).

fof(f_1844_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_1844_2,plain,
    ! [U_6212,U_6211,U_6210,U_6209] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6209),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6209),U_6210),U_6212)),U_6211))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6209),U_6212),U_6211))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6209),U_6210),U_6211))
      | ~ class_Orderings_Olinorder(U_6209) ),
    inference(variable_rename,[status(thm)],[f_1844_1]) ).

fof(f_1844_3,plain,
    ! [U_6209,U_6210,U_6211,U_6212] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6209),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6209),U_6210),U_6212)),U_6211))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6209),U_6212),U_6211))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6209),U_6210),U_6211))
      | ~ class_Orderings_Olinorder(U_6209) ),
    inference(definitional_conversion,[status(esa)],[f_1844_2]) ).

cnf(f_1844_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6209),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6209),U_6210),U_6212)),U_6211))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6209),U_6212),U_6211))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6209),U_6210),U_6211))
    | ~ class_Orderings_Olinorder(U_6209) ),
    inference(clausify,[status(thm)],[f_1844_3]) ).

fof(f_1845_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_1845_2,plain,
    ! [U_6217,U_6216,U_6215,U_6214,U_6213] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6213),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6213),U_6214),U_6216)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6213),U_6215),U_6217)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6213),U_6216),U_6217))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6213),U_6214),U_6215))
      | ~ class_Orderings_Olinorder(U_6213) ),
    inference(variable_rename,[status(thm)],[f_1845_1]) ).

fof(f_1845_3,plain,
    ! [U_6213,U_6214,U_6215,U_6216,U_6217] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6213),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6213),U_6214),U_6216)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6213),U_6215),U_6217)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6213),U_6216),U_6217))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6213),U_6214),U_6215))
      | ~ class_Orderings_Olinorder(U_6213) ),
    inference(definitional_conversion,[status(esa)],[f_1845_2]) ).

cnf(f_1845_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6213),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6213),U_6214),U_6216)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6213),U_6215),U_6217)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6213),U_6216),U_6217))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6213),U_6214),U_6215))
    | ~ class_Orderings_Olinorder(U_6213) ),
    inference(clausify,[status(thm)],[f_1845_3]) ).

fof(f_1846_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_1846_2,plain,
    ! [U_6221,U_6220,U_6219,U_6218] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6218),U_6220),U_6221))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6218),U_6219),U_6221)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6218),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6218),U_6219),U_6220)),U_6221))
      | ~ class_Orderings_Olinorder(U_6218) ),
    inference(variable_rename,[status(thm)],[f_1846_1]) ).

fof(f_1846_3,plain,
    ( ! [U_6219,U_6218,U_6220,U_6221] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6218),U_6220),U_6221))
        | ~ sP585(U_6219,U_6218,U_6220,U_6221) )
    & ! [U_6219,U_6218,U_6220,U_6221] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6218),U_6219),U_6221))
        | ~ sP585(U_6219,U_6218,U_6220,U_6221) )
    & ! [U_6219,U_6218,U_6220,U_6221] :
        ( sP585(U_6219,U_6218,U_6220,U_6221)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6218),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6218),U_6219),U_6220)),U_6221))
        | ~ class_Orderings_Olinorder(U_6218) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP585])],[f_1846_2]) ).

cnf(f_1846_4,plain,
    ( sP585(U_6219,U_6218,U_6220,U_6221)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6218),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6218),U_6219),U_6220)),U_6221))
    | ~ class_Orderings_Olinorder(U_6218) ),
    inference(clausify,[status(thm)],[f_1846_3]) ).

cnf(f_1846_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6218),U_6219),U_6221))
    | ~ sP585(U_6219,U_6218,U_6220,U_6221) ),
    inference(clausify,[status(thm)],[f_1846_3]) ).

cnf(f_1846_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6218),U_6220),U_6221))
    | ~ sP585(U_6219,U_6218,U_6220,U_6221) ),
    inference(clausify,[status(thm)],[f_1846_3]) ).

fof(f_1847_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_1847_2,plain,
    ! [U_6225,U_6224,U_6223,U_6222] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),U_6223),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6222),U_6224),U_6225)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),U_6223),U_6225))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),U_6223),U_6224)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),U_6223),U_6225))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),U_6223),U_6224))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),U_6223),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6222),U_6224),U_6225))) ) )
      | ~ class_Orderings_Olinorder(U_6222) ),
    inference(variable_rename,[status(thm)],[f_1847_1]) ).

fof(f_1847_3,plain,
    ( ! [U_6223,U_6222,U_6224,U_6225] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),U_6223),U_6225))
        | ~ sP586(U_6223,U_6222,U_6224,U_6225) )
    & ! [U_6223,U_6222,U_6224,U_6225] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),U_6223),U_6224))
        | ~ sP586(U_6223,U_6222,U_6224,U_6225) )
    & ! [U_6223,U_6222,U_6224,U_6225] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),U_6223),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6222),U_6224),U_6225)))
        | sP586(U_6223,U_6222,U_6224,U_6225)
        | ~ sP587(U_6223,U_6222,U_6224,U_6225) )
    & ! [U_6223,U_6222,U_6224,U_6225] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),U_6223),U_6225))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),U_6223),U_6224))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),U_6223),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6222),U_6224),U_6225)))
        | ~ sP587(U_6223,U_6222,U_6224,U_6225) )
    & ! [U_6223,U_6222,U_6224,U_6225] :
        ( sP587(U_6223,U_6222,U_6224,U_6225)
        | ~ class_Orderings_Olinorder(U_6222) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP586,sP587])],[f_1847_2]) ).

cnf(f_1847_4,plain,
    ( sP587(U_6223,U_6222,U_6224,U_6225)
    | ~ class_Orderings_Olinorder(U_6222) ),
    inference(clausify,[status(thm)],[f_1847_3]) ).

cnf(f_1847_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),U_6223),U_6225))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),U_6223),U_6224))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),U_6223),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6222),U_6224),U_6225)))
    | ~ sP587(U_6223,U_6222,U_6224,U_6225) ),
    inference(clausify,[status(thm)],[f_1847_3]) ).

cnf(f_1847_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),U_6223),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6222),U_6224),U_6225)))
    | sP586(U_6223,U_6222,U_6224,U_6225)
    | ~ sP587(U_6223,U_6222,U_6224,U_6225) ),
    inference(clausify,[status(thm)],[f_1847_3]) ).

cnf(f_1847_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),U_6223),U_6224))
    | ~ sP586(U_6223,U_6222,U_6224,U_6225) ),
    inference(clausify,[status(thm)],[f_1847_3]) ).

cnf(f_1847_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6222),U_6223),U_6225))
    | ~ sP586(U_6223,U_6222,U_6224,U_6225) ),
    inference(clausify,[status(thm)],[f_1847_3]) ).

fof(f_1848_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_1848_2,plain,
    ! [U_6228,U_6227,U_6226] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6226),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6226),U_6227),U_6228)),U_6227))
      | ~ class_Orderings_Olinorder(U_6226) ),
    inference(variable_rename,[status(thm)],[f_1848_1]) ).

fof(f_1848_3,plain,
    ! [U_6227,U_6226,U_6228] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6226),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6226),U_6227),U_6228)),U_6227))
      | ~ class_Orderings_Olinorder(U_6226) ),
    inference(definitional_conversion,[status(esa)],[f_1848_2]) ).

cnf(f_1848_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6226),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6226),U_6227),U_6228)),U_6227))
    | ~ class_Orderings_Olinorder(U_6226) ),
    inference(clausify,[status(thm)],[f_1848_3]) ).

fof(f_1849_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_1849_2,plain,
    ! [U_6231,U_6230,U_6229] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6229),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6229),U_6230),U_6231)),U_6231))
      | ~ class_Orderings_Olinorder(U_6229) ),
    inference(variable_rename,[status(thm)],[f_1849_1]) ).

fof(f_1849_3,plain,
    ! [U_6229,U_6230,U_6231] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6229),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6229),U_6230),U_6231)),U_6231))
      | ~ class_Orderings_Olinorder(U_6229) ),
    inference(definitional_conversion,[status(esa)],[f_1849_2]) ).

cnf(f_1849_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6229),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6229),U_6230),U_6231)),U_6231))
    | ~ class_Orderings_Olinorder(U_6229) ),
    inference(clausify,[status(thm)],[f_1849_3]) ).

fof(f_1850_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_1850_2,plain,
    ! [U_6234,U_6233,U_6232] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6232),U_6233),U_6234))
          | hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6232),U_6233),U_6234) != U_6233 )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6232),U_6233),U_6234) = U_6233
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6232),U_6233),U_6234)) ) )
      | ~ class_Orderings_Olinorder(U_6232) ),
    inference(variable_rename,[status(thm)],[f_1850_1]) ).

fof(f_1850_3,plain,
    ( ! [U_6232,U_6233,U_6234] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6232),U_6233),U_6234))
        | hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6232),U_6233),U_6234) != U_6233
        | ~ sP588(U_6232,U_6233,U_6234) )
    & ! [U_6232,U_6233,U_6234] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6232),U_6233),U_6234) = U_6233
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6232),U_6233),U_6234))
        | ~ sP588(U_6232,U_6233,U_6234) )
    & ! [U_6232,U_6233,U_6234] :
        ( sP588(U_6232,U_6233,U_6234)
        | ~ class_Orderings_Olinorder(U_6232) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP588])],[f_1850_2]) ).

cnf(f_1850_4,plain,
    ( sP588(U_6232,U_6233,U_6234)
    | ~ class_Orderings_Olinorder(U_6232) ),
    inference(clausify,[status(thm)],[f_1850_3]) ).

cnf(f_1850_5,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6232),U_6233),U_6234) = U_6233
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6232),U_6233),U_6234))
    | ~ sP588(U_6232,U_6233,U_6234) ),
    inference(clausify,[status(thm)],[f_1850_3]) ).

cnf(f_1850_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6232),U_6233),U_6234))
    | hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6232),U_6233),U_6234) != U_6233
    | ~ sP588(U_6232,U_6233,U_6234) ),
    inference(clausify,[status(thm)],[f_1850_3]) ).

fof(f_1851_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_1851_2,plain,
    ! [U_6238,U_6237,U_6236,U_6235] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6235),U_6236),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6235),U_6237),U_6238)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6235),U_6236),U_6238))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6235),U_6236),U_6237)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6235),U_6236),U_6238))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6235),U_6236),U_6237)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6235),U_6236),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6235),U_6237),U_6238))) ) )
      | ~ class_Orderings_Olinorder(U_6235) ),
    inference(variable_rename,[status(thm)],[f_1851_1]) ).

fof(f_1851_3,plain,
    ( ! [U_6237,U_6235,U_6236,U_6238] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6235),U_6236),U_6238))
        | ~ sP589(U_6237,U_6235,U_6236,U_6238) )
    & ! [U_6237,U_6235,U_6236,U_6238] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6235),U_6236),U_6237))
        | ~ sP589(U_6237,U_6235,U_6236,U_6238) )
    & ! [U_6237,U_6235,U_6236,U_6238] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6235),U_6236),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6235),U_6237),U_6238)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6235),U_6236),U_6238))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6235),U_6236),U_6237))
        | ~ sP590(U_6237,U_6235,U_6236,U_6238) )
    & ! [U_6237,U_6235,U_6236,U_6238] :
        ( sP589(U_6237,U_6235,U_6236,U_6238)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6235),U_6236),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6235),U_6237),U_6238)))
        | ~ sP590(U_6237,U_6235,U_6236,U_6238) )
    & ! [U_6237,U_6235,U_6236,U_6238] :
        ( sP590(U_6237,U_6235,U_6236,U_6238)
        | ~ class_Orderings_Olinorder(U_6235) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP589,sP590])],[f_1851_2]) ).

cnf(f_1851_4,plain,
    ( sP590(U_6237,U_6235,U_6236,U_6238)
    | ~ class_Orderings_Olinorder(U_6235) ),
    inference(clausify,[status(thm)],[f_1851_3]) ).

cnf(f_1851_5,plain,
    ( sP589(U_6237,U_6235,U_6236,U_6238)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6235),U_6236),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6235),U_6237),U_6238)))
    | ~ sP590(U_6237,U_6235,U_6236,U_6238) ),
    inference(clausify,[status(thm)],[f_1851_3]) ).

cnf(f_1851_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6235),U_6236),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6235),U_6237),U_6238)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6235),U_6236),U_6238))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6235),U_6236),U_6237))
    | ~ sP590(U_6237,U_6235,U_6236,U_6238) ),
    inference(clausify,[status(thm)],[f_1851_3]) ).

cnf(f_1851_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6235),U_6236),U_6237))
    | ~ sP589(U_6237,U_6235,U_6236,U_6238) ),
    inference(clausify,[status(thm)],[f_1851_3]) ).

cnf(f_1851_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6235),U_6236),U_6238))
    | ~ sP589(U_6237,U_6235,U_6236,U_6238) ),
    inference(clausify,[status(thm)],[f_1851_3]) ).

fof(f_1852_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_1852_2,plain,
    ! [U_6242,U_6241,U_6240,U_6239] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6239),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6239),U_6240),U_6242)),U_6241))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6239),U_6240),U_6241))
      | ~ class_Orderings_Olinorder(U_6239) ),
    inference(variable_rename,[status(thm)],[f_1852_1]) ).

fof(f_1852_3,plain,
    ! [U_6241,U_6242,U_6239,U_6240] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6239),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6239),U_6240),U_6242)),U_6241))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6239),U_6240),U_6241))
      | ~ class_Orderings_Olinorder(U_6239) ),
    inference(definitional_conversion,[status(esa)],[f_1852_2]) ).

cnf(f_1852_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6239),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6239),U_6240),U_6242)),U_6241))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6239),U_6240),U_6241))
    | ~ class_Orderings_Olinorder(U_6239) ),
    inference(clausify,[status(thm)],[f_1852_3]) ).

fof(f_1853_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_1853_2,plain,
    ! [U_6246,U_6245,U_6244,U_6243] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6243),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6243),U_6246),U_6244)),U_6245))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6243),U_6244),U_6245))
      | ~ class_Orderings_Olinorder(U_6243) ),
    inference(variable_rename,[status(thm)],[f_1853_1]) ).

fof(f_1853_3,plain,
    ! [U_6243,U_6244,U_6245,U_6246] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6243),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6243),U_6246),U_6244)),U_6245))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6243),U_6244),U_6245))
      | ~ class_Orderings_Olinorder(U_6243) ),
    inference(definitional_conversion,[status(esa)],[f_1853_2]) ).

cnf(f_1853_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6243),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6243),U_6246),U_6244)),U_6245))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6243),U_6244),U_6245))
    | ~ class_Orderings_Olinorder(U_6243) ),
    inference(clausify,[status(thm)],[f_1853_3]) ).

fof(f_1854_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_1854_2,plain,
    ! [U_6249,U_6248,U_6247] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6247),U_6248),U_6249) = U_6248
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6247),U_6248),U_6249))
      | ~ class_Orderings_Olinorder(U_6247) ),
    inference(variable_rename,[status(thm)],[f_1854_1]) ).

fof(f_1854_3,plain,
    ! [U_6247,U_6248,U_6249] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6247),U_6248),U_6249) = U_6248
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6247),U_6248),U_6249))
      | ~ class_Orderings_Olinorder(U_6247) ),
    inference(definitional_conversion,[status(esa)],[f_1854_2]) ).

cnf(f_1854_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6247),U_6248),U_6249) = U_6248
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6247),U_6248),U_6249))
    | ~ class_Orderings_Olinorder(U_6247) ),
    inference(clausify,[status(thm)],[f_1854_3]) ).

fof(f_1855_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_1855_2,plain,
    ! [U_6252,U_6251,U_6250] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6250),U_6252),U_6251) = U_6251
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6250),U_6251),U_6252))
      | ~ class_Orderings_Olinorder(U_6250) ),
    inference(variable_rename,[status(thm)],[f_1855_1]) ).

fof(f_1855_3,plain,
    ! [U_6250,U_6251,U_6252] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6250),U_6252),U_6251) = U_6251
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6250),U_6251),U_6252))
      | ~ class_Orderings_Olinorder(U_6250) ),
    inference(definitional_conversion,[status(esa)],[f_1855_2]) ).

cnf(f_1855_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6250),U_6252),U_6251) = U_6251
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6250),U_6251),U_6252))
    | ~ class_Orderings_Olinorder(U_6250) ),
    inference(clausify,[status(thm)],[f_1855_3]) ).

fof(f_1856_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_1856_2,plain,
    ! [U_6256,U_6255,U_6254,U_6253] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6253),U_6254),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6253),U_6255),U_6256)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6253),U_6254),U_6256))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6253),U_6254),U_6255))
      | ~ class_Orderings_Olinorder(U_6253) ),
    inference(variable_rename,[status(thm)],[f_1856_1]) ).

fof(f_1856_3,plain,
    ! [U_6253,U_6254,U_6255,U_6256] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6253),U_6254),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6253),U_6255),U_6256)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6253),U_6254),U_6256))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6253),U_6254),U_6255))
      | ~ class_Orderings_Olinorder(U_6253) ),
    inference(definitional_conversion,[status(esa)],[f_1856_2]) ).

cnf(f_1856_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6253),U_6254),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6253),U_6255),U_6256)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6253),U_6254),U_6256))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6253),U_6254),U_6255))
    | ~ class_Orderings_Olinorder(U_6253) ),
    inference(clausify,[status(thm)],[f_1856_3]) ).

fof(f_1857_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_1857_2,plain,
    ! [U_6260,U_6259,U_6258,U_6257] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),U_6258),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6257),U_6259),U_6260)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),U_6258),U_6260))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),U_6258),U_6259))
      | ~ class_Orderings_Olinorder(U_6257) ),
    inference(variable_rename,[status(thm)],[f_1857_1]) ).

fof(f_1857_3,plain,
    ! [U_6257,U_6258,U_6259,U_6260] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),U_6258),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6257),U_6259),U_6260)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),U_6258),U_6260))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),U_6258),U_6259))
      | ~ class_Orderings_Olinorder(U_6257) ),
    inference(definitional_conversion,[status(esa)],[f_1857_2]) ).

cnf(f_1857_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),U_6258),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6257),U_6259),U_6260)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),U_6258),U_6260))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6257),U_6258),U_6259))
    | ~ class_Orderings_Olinorder(U_6257) ),
    inference(clausify,[status(thm)],[f_1857_3]) ).

fof(f_1858_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_1858_2,plain,
    ! [U_6265,U_6264,U_6263,U_6262,U_6261] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6261),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6261),U_6262),U_6264)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6261),U_6263),U_6265)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6261),U_6264),U_6265))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6261),U_6262),U_6263))
      | ~ class_Orderings_Olinorder(U_6261) ),
    inference(variable_rename,[status(thm)],[f_1858_1]) ).

fof(f_1858_3,plain,
    ! [U_6261,U_6262,U_6263,U_6264,U_6265] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6261),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6261),U_6262),U_6264)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6261),U_6263),U_6265)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6261),U_6264),U_6265))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6261),U_6262),U_6263))
      | ~ class_Orderings_Olinorder(U_6261) ),
    inference(definitional_conversion,[status(esa)],[f_1858_2]) ).

cnf(f_1858_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6261),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6261),U_6262),U_6264)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6261),U_6263),U_6265)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6261),U_6264),U_6265))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6261),U_6262),U_6263))
    | ~ class_Orderings_Olinorder(U_6261) ),
    inference(clausify,[status(thm)],[f_1858_3]) ).

fof(f_1859_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_1859_2,plain,
    ! [U_6269,U_6268,U_6267,U_6266] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6266),U_6267),U_6269))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6266),U_6267),U_6268)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6266),U_6267),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6266),U_6268),U_6269)))
      | ~ class_Orderings_Olinorder(U_6266) ),
    inference(variable_rename,[status(thm)],[f_1859_1]) ).

fof(f_1859_3,plain,
    ( ! [U_6266,U_6267,U_6268,U_6269] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6266),U_6267),U_6269))
        | ~ sP591(U_6266,U_6267,U_6268,U_6269) )
    & ! [U_6266,U_6267,U_6268,U_6269] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6266),U_6267),U_6268))
        | ~ sP591(U_6266,U_6267,U_6268,U_6269) )
    & ! [U_6266,U_6267,U_6268,U_6269] :
        ( sP591(U_6266,U_6267,U_6268,U_6269)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6266),U_6267),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6266),U_6268),U_6269)))
        | ~ class_Orderings_Olinorder(U_6266) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP591])],[f_1859_2]) ).

cnf(f_1859_4,plain,
    ( sP591(U_6266,U_6267,U_6268,U_6269)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6266),U_6267),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6266),U_6268),U_6269)))
    | ~ class_Orderings_Olinorder(U_6266) ),
    inference(clausify,[status(thm)],[f_1859_3]) ).

cnf(f_1859_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6266),U_6267),U_6268))
    | ~ sP591(U_6266,U_6267,U_6268,U_6269) ),
    inference(clausify,[status(thm)],[f_1859_3]) ).

cnf(f_1859_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6266),U_6267),U_6269))
    | ~ sP591(U_6266,U_6267,U_6268,U_6269) ),
    inference(clausify,[status(thm)],[f_1859_3]) ).

fof(f_1860_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_1860_2,plain,
    ! [U_6273,U_6272,U_6271,U_6270] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6270),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6270),U_6271),U_6272)),U_6273))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6270),U_6272),U_6273))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6270),U_6271),U_6273)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6270),U_6272),U_6273))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6270),U_6271),U_6273))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6270),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6270),U_6271),U_6272)),U_6273)) ) )
      | ~ class_Orderings_Olinorder(U_6270) ),
    inference(variable_rename,[status(thm)],[f_1860_1]) ).

fof(f_1860_3,plain,
    ( ! [U_6271,U_6270,U_6272,U_6273] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6270),U_6272),U_6273))
        | ~ sP592(U_6271,U_6270,U_6272,U_6273) )
    & ! [U_6271,U_6270,U_6272,U_6273] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6270),U_6271),U_6273))
        | ~ sP592(U_6271,U_6270,U_6272,U_6273) )
    & ! [U_6271,U_6270,U_6272,U_6273] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6270),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6270),U_6271),U_6272)),U_6273))
        | sP592(U_6271,U_6270,U_6272,U_6273)
        | ~ sP593(U_6271,U_6270,U_6272,U_6273) )
    & ! [U_6271,U_6270,U_6272,U_6273] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6270),U_6272),U_6273))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6270),U_6271),U_6273))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6270),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6270),U_6271),U_6272)),U_6273))
        | ~ sP593(U_6271,U_6270,U_6272,U_6273) )
    & ! [U_6271,U_6270,U_6272,U_6273] :
        ( sP593(U_6271,U_6270,U_6272,U_6273)
        | ~ class_Orderings_Olinorder(U_6270) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP592,sP593])],[f_1860_2]) ).

cnf(f_1860_4,plain,
    ( sP593(U_6271,U_6270,U_6272,U_6273)
    | ~ class_Orderings_Olinorder(U_6270) ),
    inference(clausify,[status(thm)],[f_1860_3]) ).

cnf(f_1860_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6270),U_6272),U_6273))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6270),U_6271),U_6273))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6270),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6270),U_6271),U_6272)),U_6273))
    | ~ sP593(U_6271,U_6270,U_6272,U_6273) ),
    inference(clausify,[status(thm)],[f_1860_3]) ).

cnf(f_1860_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6270),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6270),U_6271),U_6272)),U_6273))
    | sP592(U_6271,U_6270,U_6272,U_6273)
    | ~ sP593(U_6271,U_6270,U_6272,U_6273) ),
    inference(clausify,[status(thm)],[f_1860_3]) ).

cnf(f_1860_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6270),U_6271),U_6273))
    | ~ sP592(U_6271,U_6270,U_6272,U_6273) ),
    inference(clausify,[status(thm)],[f_1860_3]) ).

cnf(f_1860_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6270),U_6272),U_6273))
    | ~ sP592(U_6271,U_6270,U_6272,U_6273) ),
    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(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_1861_2,plain,
    ! [U_6277,U_6276,U_6275,U_6274] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6274),U_6275),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6274),U_6276),U_6277)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6274),U_6275),U_6276))
      | ~ class_Orderings_Olinorder(U_6274) ),
    inference(variable_rename,[status(thm)],[f_1861_1]) ).

fof(f_1861_3,plain,
    ! [U_6274,U_6277,U_6276,U_6275] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6274),U_6275),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6274),U_6276),U_6277)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6274),U_6275),U_6276))
      | ~ class_Orderings_Olinorder(U_6274) ),
    inference(definitional_conversion,[status(esa)],[f_1861_2]) ).

cnf(f_1861_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6274),U_6275),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6274),U_6276),U_6277)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6274),U_6275),U_6276))
    | ~ class_Orderings_Olinorder(U_6274) ),
    inference(clausify,[status(thm)],[f_1861_3]) ).

fof(f_1862_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_1862_2,plain,
    ! [U_6281,U_6280,U_6279,U_6278] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6278),U_6279),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6278),U_6281),U_6280)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6278),U_6279),U_6280))
      | ~ class_Orderings_Olinorder(U_6278) ),
    inference(variable_rename,[status(thm)],[f_1862_1]) ).

fof(f_1862_3,plain,
    ! [U_6278,U_6279,U_6280,U_6281] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6278),U_6279),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6278),U_6281),U_6280)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6278),U_6279),U_6280))
      | ~ class_Orderings_Olinorder(U_6278) ),
    inference(definitional_conversion,[status(esa)],[f_1862_2]) ).

cnf(f_1862_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6278),U_6279),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6278),U_6281),U_6280)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6278),U_6279),U_6280))
    | ~ class_Orderings_Olinorder(U_6278) ),
    inference(clausify,[status(thm)],[f_1862_3]) ).

fof(f_1863_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_1863_2,plain,
    ! [U_6285,U_6284,U_6283,U_6282] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6282),U_6283),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6282),U_6284),U_6285)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6282),U_6283),U_6285))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6282),U_6283),U_6284)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6282),U_6283),U_6285))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6282),U_6283),U_6284))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6282),U_6283),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6282),U_6284),U_6285))) ) )
      | ~ class_Orderings_Olinorder(U_6282) ),
    inference(variable_rename,[status(thm)],[f_1863_1]) ).

fof(f_1863_3,plain,
    ( ! [U_6282,U_6283,U_6284,U_6285] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6282),U_6283),U_6285))
        | ~ sP594(U_6282,U_6283,U_6284,U_6285) )
    & ! [U_6282,U_6283,U_6284,U_6285] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6282),U_6283),U_6284))
        | ~ sP594(U_6282,U_6283,U_6284,U_6285) )
    & ! [U_6282,U_6283,U_6284,U_6285] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6282),U_6283),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6282),U_6284),U_6285)))
        | sP594(U_6282,U_6283,U_6284,U_6285)
        | ~ sP595(U_6282,U_6283,U_6284,U_6285) )
    & ! [U_6282,U_6283,U_6284,U_6285] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6282),U_6283),U_6285))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6282),U_6283),U_6284))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6282),U_6283),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6282),U_6284),U_6285)))
        | ~ sP595(U_6282,U_6283,U_6284,U_6285) )
    & ! [U_6282,U_6283,U_6284,U_6285] :
        ( sP595(U_6282,U_6283,U_6284,U_6285)
        | ~ class_Orderings_Olinorder(U_6282) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP594,sP595])],[f_1863_2]) ).

cnf(f_1863_4,plain,
    ( sP595(U_6282,U_6283,U_6284,U_6285)
    | ~ class_Orderings_Olinorder(U_6282) ),
    inference(clausify,[status(thm)],[f_1863_3]) ).

cnf(f_1863_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6282),U_6283),U_6285))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6282),U_6283),U_6284))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6282),U_6283),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6282),U_6284),U_6285)))
    | ~ sP595(U_6282,U_6283,U_6284,U_6285) ),
    inference(clausify,[status(thm)],[f_1863_3]) ).

cnf(f_1863_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6282),U_6283),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6282),U_6284),U_6285)))
    | sP594(U_6282,U_6283,U_6284,U_6285)
    | ~ sP595(U_6282,U_6283,U_6284,U_6285) ),
    inference(clausify,[status(thm)],[f_1863_3]) ).

cnf(f_1863_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6282),U_6283),U_6284))
    | ~ sP594(U_6282,U_6283,U_6284,U_6285) ),
    inference(clausify,[status(thm)],[f_1863_3]) ).

cnf(f_1863_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6282),U_6283),U_6285))
    | ~ sP594(U_6282,U_6283,U_6284,U_6285) ),
    inference(clausify,[status(thm)],[f_1863_3]) ).

fof(f_1864_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_1864_2,plain,
    ! [U_6289,U_6288,U_6287,U_6286] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6286),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6286),U_6287),U_6288)),U_6289))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6286),U_6288),U_6289))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6286),U_6287),U_6289)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6286),U_6288),U_6289))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6286),U_6287),U_6289)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6286),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6286),U_6287),U_6288)),U_6289)) ) )
      | ~ class_Orderings_Olinorder(U_6286) ),
    inference(variable_rename,[status(thm)],[f_1864_1]) ).

fof(f_1864_3,plain,
    ( ! [U_6288,U_6287,U_6289,U_6286] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6286),U_6288),U_6289))
        | ~ sP596(U_6288,U_6287,U_6289,U_6286) )
    & ! [U_6288,U_6287,U_6289,U_6286] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6286),U_6287),U_6289))
        | ~ sP596(U_6288,U_6287,U_6289,U_6286) )
    & ! [U_6288,U_6287,U_6289,U_6286] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6286),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6286),U_6287),U_6288)),U_6289))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6286),U_6288),U_6289))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6286),U_6287),U_6289))
        | ~ sP597(U_6288,U_6287,U_6289,U_6286) )
    & ! [U_6288,U_6287,U_6289,U_6286] :
        ( sP596(U_6288,U_6287,U_6289,U_6286)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6286),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6286),U_6287),U_6288)),U_6289))
        | ~ sP597(U_6288,U_6287,U_6289,U_6286) )
    & ! [U_6288,U_6287,U_6289,U_6286] :
        ( sP597(U_6288,U_6287,U_6289,U_6286)
        | ~ class_Orderings_Olinorder(U_6286) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP596,sP597])],[f_1864_2]) ).

cnf(f_1864_4,plain,
    ( sP597(U_6288,U_6287,U_6289,U_6286)
    | ~ class_Orderings_Olinorder(U_6286) ),
    inference(clausify,[status(thm)],[f_1864_3]) ).

cnf(f_1864_5,plain,
    ( sP596(U_6288,U_6287,U_6289,U_6286)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6286),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6286),U_6287),U_6288)),U_6289))
    | ~ sP597(U_6288,U_6287,U_6289,U_6286) ),
    inference(clausify,[status(thm)],[f_1864_3]) ).

cnf(f_1864_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6286),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6286),U_6287),U_6288)),U_6289))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6286),U_6288),U_6289))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6286),U_6287),U_6289))
    | ~ sP597(U_6288,U_6287,U_6289,U_6286) ),
    inference(clausify,[status(thm)],[f_1864_3]) ).

cnf(f_1864_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6286),U_6287),U_6289))
    | ~ sP596(U_6288,U_6287,U_6289,U_6286) ),
    inference(clausify,[status(thm)],[f_1864_3]) ).

cnf(f_1864_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6286),U_6288),U_6289))
    | ~ sP596(U_6288,U_6287,U_6289,U_6286) ),
    inference(clausify,[status(thm)],[f_1864_3]) ).

fof(f_1865_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_1865_2,plain,
    ! [U_6293,U_6292,U_6291,U_6290] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6290),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6290),U_6291),U_6293)),U_6292))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6290),U_6291),U_6292))
      | ~ class_Orderings_Olinorder(U_6290) ),
    inference(variable_rename,[status(thm)],[f_1865_1]) ).

fof(f_1865_3,plain,
    ! [U_6290,U_6292,U_6293,U_6291] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6290),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6290),U_6291),U_6293)),U_6292))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6290),U_6291),U_6292))
      | ~ class_Orderings_Olinorder(U_6290) ),
    inference(definitional_conversion,[status(esa)],[f_1865_2]) ).

cnf(f_1865_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6290),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6290),U_6291),U_6293)),U_6292))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6290),U_6291),U_6292))
    | ~ class_Orderings_Olinorder(U_6290) ),
    inference(clausify,[status(thm)],[f_1865_3]) ).

fof(f_1866_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_1866_2,plain,
    ! [U_6297,U_6296,U_6295,U_6294] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6294),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6294),U_6297),U_6295)),U_6296))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6294),U_6295),U_6296))
      | ~ class_Orderings_Olinorder(U_6294) ),
    inference(variable_rename,[status(thm)],[f_1866_1]) ).

fof(f_1866_3,plain,
    ! [U_6294,U_6295,U_6296,U_6297] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6294),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6294),U_6297),U_6295)),U_6296))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6294),U_6295),U_6296))
      | ~ class_Orderings_Olinorder(U_6294) ),
    inference(definitional_conversion,[status(esa)],[f_1866_2]) ).

cnf(f_1866_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6294),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6294),U_6297),U_6295)),U_6296))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6294),U_6295),U_6296))
    | ~ class_Orderings_Olinorder(U_6294) ),
    inference(clausify,[status(thm)],[f_1866_3]) ).

fof(f_1867_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_1867_2,plain,
    ! [U_6301,U_6300,U_6299,U_6298] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6298),U_6299),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6298),U_6300),U_6301)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6298),U_6299),U_6301))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6298),U_6299),U_6300)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6298),U_6299),U_6301))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6298),U_6299),U_6300)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6298),U_6299),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6298),U_6300),U_6301))) ) )
      | ~ class_Orderings_Olinorder(U_6298) ),
    inference(variable_rename,[status(thm)],[f_1867_1]) ).

fof(f_1867_3,plain,
    ( ! [U_6298,U_6299,U_6300,U_6301] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6298),U_6299),U_6301))
        | ~ sP598(U_6298,U_6299,U_6300,U_6301) )
    & ! [U_6298,U_6299,U_6300,U_6301] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6298),U_6299),U_6300))
        | ~ sP598(U_6298,U_6299,U_6300,U_6301) )
    & ! [U_6298,U_6299,U_6300,U_6301] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6298),U_6299),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6298),U_6300),U_6301)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6298),U_6299),U_6301))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6298),U_6299),U_6300))
        | ~ sP599(U_6298,U_6299,U_6300,U_6301) )
    & ! [U_6298,U_6299,U_6300,U_6301] :
        ( sP598(U_6298,U_6299,U_6300,U_6301)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6298),U_6299),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6298),U_6300),U_6301)))
        | ~ sP599(U_6298,U_6299,U_6300,U_6301) )
    & ! [U_6298,U_6299,U_6300,U_6301] :
        ( sP599(U_6298,U_6299,U_6300,U_6301)
        | ~ class_Orderings_Olinorder(U_6298) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP598,sP599])],[f_1867_2]) ).

cnf(f_1867_4,plain,
    ( sP599(U_6298,U_6299,U_6300,U_6301)
    | ~ class_Orderings_Olinorder(U_6298) ),
    inference(clausify,[status(thm)],[f_1867_3]) ).

cnf(f_1867_5,plain,
    ( sP598(U_6298,U_6299,U_6300,U_6301)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6298),U_6299),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6298),U_6300),U_6301)))
    | ~ sP599(U_6298,U_6299,U_6300,U_6301) ),
    inference(clausify,[status(thm)],[f_1867_3]) ).

cnf(f_1867_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6298),U_6299),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6298),U_6300),U_6301)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6298),U_6299),U_6301))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6298),U_6299),U_6300))
    | ~ sP599(U_6298,U_6299,U_6300,U_6301) ),
    inference(clausify,[status(thm)],[f_1867_3]) ).

cnf(f_1867_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6298),U_6299),U_6300))
    | ~ sP598(U_6298,U_6299,U_6300,U_6301) ),
    inference(clausify,[status(thm)],[f_1867_3]) ).

cnf(f_1867_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6298),U_6299),U_6301))
    | ~ sP598(U_6298,U_6299,U_6300,U_6301) ),
    inference(clausify,[status(thm)],[f_1867_3]) ).

fof(f_1868_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_1868_2,plain,
    ! [U_6305,U_6304,U_6303,U_6302] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6302),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6302),U_6303),U_6304)),U_6305))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6302),U_6304),U_6305))
            & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6302),U_6303),U_6305)) ) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6302),U_6304),U_6305))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6302),U_6303),U_6305))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6302),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6302),U_6303),U_6304)),U_6305)) ) )
      | ~ class_Orderings_Olinorder(U_6302) ),
    inference(variable_rename,[status(thm)],[f_1868_1]) ).

fof(f_1868_3,plain,
    ( ! [U_6304,U_6303,U_6302,U_6305] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6302),U_6304),U_6305))
        | ~ sP600(U_6304,U_6303,U_6302,U_6305) )
    & ! [U_6304,U_6303,U_6302,U_6305] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6302),U_6303),U_6305))
        | ~ sP600(U_6304,U_6303,U_6302,U_6305) )
    & ! [U_6304,U_6303,U_6302,U_6305] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6302),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6302),U_6303),U_6304)),U_6305))
        | sP600(U_6304,U_6303,U_6302,U_6305)
        | ~ sP601(U_6304,U_6303,U_6302,U_6305) )
    & ! [U_6304,U_6303,U_6302,U_6305] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6302),U_6304),U_6305))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6302),U_6303),U_6305))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6302),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6302),U_6303),U_6304)),U_6305))
        | ~ sP601(U_6304,U_6303,U_6302,U_6305) )
    & ! [U_6304,U_6303,U_6302,U_6305] :
        ( sP601(U_6304,U_6303,U_6302,U_6305)
        | ~ class_Orderings_Olinorder(U_6302) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP600,sP601])],[f_1868_2]) ).

cnf(f_1868_4,plain,
    ( sP601(U_6304,U_6303,U_6302,U_6305)
    | ~ class_Orderings_Olinorder(U_6302) ),
    inference(clausify,[status(thm)],[f_1868_3]) ).

cnf(f_1868_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6302),U_6304),U_6305))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6302),U_6303),U_6305))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6302),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6302),U_6303),U_6304)),U_6305))
    | ~ sP601(U_6304,U_6303,U_6302,U_6305) ),
    inference(clausify,[status(thm)],[f_1868_3]) ).

cnf(f_1868_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6302),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6302),U_6303),U_6304)),U_6305))
    | sP600(U_6304,U_6303,U_6302,U_6305)
    | ~ sP601(U_6304,U_6303,U_6302,U_6305) ),
    inference(clausify,[status(thm)],[f_1868_3]) ).

cnf(f_1868_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6302),U_6303),U_6305))
    | ~ sP600(U_6304,U_6303,U_6302,U_6305) ),
    inference(clausify,[status(thm)],[f_1868_3]) ).

cnf(f_1868_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6302),U_6304),U_6305))
    | ~ sP600(U_6304,U_6303,U_6302,U_6305) ),
    inference(clausify,[status(thm)],[f_1868_3]) ).

fof(f_1869_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_1869_2,plain,
    ! [U_6309,U_6308,U_6307,U_6306] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6306),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6306),U_6307),U_6308)),U_6309) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6306),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6306),U_6307),U_6309)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6306),U_6308),U_6309))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_6306) ),
    inference(variable_rename,[status(thm)],[f_1869_1]) ).

fof(f_1869_3,plain,
    ! [U_6309,U_6307,U_6306,U_6308] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6306),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6306),U_6307),U_6308)),U_6309) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6306),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6306),U_6307),U_6309)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6306),U_6308),U_6309))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_6306) ),
    inference(definitional_conversion,[status(esa)],[f_1869_2]) ).

cnf(f_1869_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6306),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6306),U_6307),U_6308)),U_6309) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6306),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6306),U_6307),U_6309)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6306),U_6308),U_6309))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_6306) ),
    inference(clausify,[status(thm)],[f_1869_3]) ).

fof(f_1870_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_1870_2,plain,
    ! [U_6313,U_6312,U_6311,U_6310] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6310),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6310),U_6311),U_6312)),U_6313) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6310),U_6311),U_6313)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6310),U_6312),U_6313))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_6310) ),
    inference(variable_rename,[status(thm)],[f_1870_1]) ).

fof(f_1870_3,plain,
    ! [U_6310,U_6311,U_6312,U_6313] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6310),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6310),U_6311),U_6312)),U_6313) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6310),U_6311),U_6313)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6310),U_6312),U_6313))
      | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_6310) ),
    inference(definitional_conversion,[status(esa)],[f_1870_2]) ).

cnf(f_1870_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6310),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6310),U_6311),U_6312)),U_6313) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6310),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6310),U_6311),U_6313)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6310),U_6312),U_6313))
    | ~ class_Groups_Oordered__ab__semigroup__add__imp__le(U_6310) ),
    inference(clausify,[status(thm)],[f_1870_3]) ).

fof(f_1871_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_1871_2,plain,
    ! [U_6315,U_6314] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6314),U_6315),U_6315) = U_6315
      | ~ class_Orderings_Olinorder(U_6314) ),
    inference(variable_rename,[status(thm)],[f_1871_1]) ).

fof(f_1871_3,plain,
    ! [U_6315,U_6314] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6314),U_6315),U_6315) = U_6315
      | ~ class_Orderings_Olinorder(U_6314) ),
    inference(definitional_conversion,[status(esa)],[f_1871_2]) ).

cnf(f_1871_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6314),U_6315),U_6315) = U_6315
    | ~ class_Orderings_Olinorder(U_6314) ),
    inference(clausify,[status(thm)],[f_1871_3]) ).

fof(f_1872_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_1872_2,plain,
    ! [U_6317,U_6316] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6316),U_6317),U_6317) = U_6317
      | ~ class_Orderings_Olinorder(U_6316) ),
    inference(variable_rename,[status(thm)],[f_1872_1]) ).

fof(f_1872_3,plain,
    ! [U_6316,U_6317] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6316),U_6317),U_6317) = U_6317
      | ~ class_Orderings_Olinorder(U_6316) ),
    inference(definitional_conversion,[status(esa)],[f_1872_2]) ).

cnf(f_1872_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6316),U_6317),U_6317) = U_6317
    | ~ class_Orderings_Olinorder(U_6316) ),
    inference(clausify,[status(thm)],[f_1872_3]) ).

fof(f_1873_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_1873_2,plain,
    ! [U_6320,U_6319,U_6318] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6318),U_6319),U_6320) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6318),U_6320),U_6319)
      | ~ class_Orderings_Olinorder(U_6318) ),
    inference(variable_rename,[status(thm)],[f_1873_1]) ).

fof(f_1873_3,plain,
    ! [U_6318,U_6319,U_6320] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6318),U_6319),U_6320) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6318),U_6320),U_6319)
      | ~ class_Orderings_Olinorder(U_6318) ),
    inference(definitional_conversion,[status(esa)],[f_1873_2]) ).

cnf(f_1873_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6318),U_6319),U_6320) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6318),U_6320),U_6319)
    | ~ class_Orderings_Olinorder(U_6318) ),
    inference(clausify,[status(thm)],[f_1873_3]) ).

fof(f_1874_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_1874_2,plain,
    ! [U_6323,U_6322,U_6321] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6321),U_6322),U_6323) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6321),U_6323),U_6322)
      | ~ class_Orderings_Olinorder(U_6321) ),
    inference(variable_rename,[status(thm)],[f_1874_1]) ).

fof(f_1874_3,plain,
    ! [U_6321,U_6322,U_6323] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6321),U_6322),U_6323) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6321),U_6323),U_6322)
      | ~ class_Orderings_Olinorder(U_6321) ),
    inference(definitional_conversion,[status(esa)],[f_1874_2]) ).

cnf(f_1874_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6321),U_6322),U_6323) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6321),U_6323),U_6322)
    | ~ class_Orderings_Olinorder(U_6321) ),
    inference(clausify,[status(thm)],[f_1874_3]) ).

fof(f_1875_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_1875_2,plain,
    ! [U_6326,U_6325,U_6324] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6324),U_6325),U_6326) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6324),U_6326),U_6325)
      | ~ class_Orderings_Olinorder(U_6324) ),
    inference(variable_rename,[status(thm)],[f_1875_1]) ).

fof(f_1875_3,plain,
    ! [U_6324,U_6325,U_6326] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6324),U_6325),U_6326) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6324),U_6326),U_6325)
      | ~ class_Orderings_Olinorder(U_6324) ),
    inference(definitional_conversion,[status(esa)],[f_1875_2]) ).

cnf(f_1875_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6324),U_6325),U_6326) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6324),U_6326),U_6325)
    | ~ class_Orderings_Olinorder(U_6324) ),
    inference(clausify,[status(thm)],[f_1875_3]) ).

fof(f_1876_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_1876_2,plain,
    ! [U_6329,U_6328,U_6327] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6327),U_6328),U_6329) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6327),U_6329),U_6328)
      | ~ class_Orderings_Olinorder(U_6327) ),
    inference(variable_rename,[status(thm)],[f_1876_1]) ).

fof(f_1876_3,plain,
    ! [U_6327,U_6328,U_6329] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6327),U_6328),U_6329) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6327),U_6329),U_6328)
      | ~ class_Orderings_Olinorder(U_6327) ),
    inference(definitional_conversion,[status(esa)],[f_1876_2]) ).

cnf(f_1876_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6327),U_6328),U_6329) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6327),U_6329),U_6328)
    | ~ class_Orderings_Olinorder(U_6327) ),
    inference(clausify,[status(thm)],[f_1876_3]) ).

fof(f_1877_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_1877_2,plain,
    ! [U_6332,U_6331,U_6330] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6330),U_6331),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6330),U_6331),U_6332)) = U_6331
      | ~ class_Orderings_Olinorder(U_6330) ),
    inference(variable_rename,[status(thm)],[f_1877_1]) ).

fof(f_1877_3,plain,
    ! [U_6330,U_6331,U_6332] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6330),U_6331),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6330),U_6331),U_6332)) = U_6331
      | ~ class_Orderings_Olinorder(U_6330) ),
    inference(definitional_conversion,[status(esa)],[f_1877_2]) ).

cnf(f_1877_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6330),U_6331),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6330),U_6331),U_6332)) = U_6331
    | ~ class_Orderings_Olinorder(U_6330) ),
    inference(clausify,[status(thm)],[f_1877_3]) ).

fof(f_1878_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_1878_2,plain,
    ! [U_6335,U_6334,U_6333] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6333),U_6334),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6333),U_6334),U_6335)) = U_6334
      | ~ class_Orderings_Olinorder(U_6333) ),
    inference(variable_rename,[status(thm)],[f_1878_1]) ).

fof(f_1878_3,plain,
    ! [U_6333,U_6334,U_6335] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6333),U_6334),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6333),U_6334),U_6335)) = U_6334
      | ~ class_Orderings_Olinorder(U_6333) ),
    inference(definitional_conversion,[status(esa)],[f_1878_2]) ).

cnf(f_1878_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6333),U_6334),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6333),U_6334),U_6335)) = U_6334
    | ~ class_Orderings_Olinorder(U_6333) ),
    inference(clausify,[status(thm)],[f_1878_3]) ).

fof(f_1879_1,plain,
    ! [V_b,V_a,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),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_1879_2,plain,
    ! [U_6338,U_6337,U_6336] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6336),U_6337),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6336),U_6337),U_6338)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6336),U_6337),U_6338)
      | ~ class_Orderings_Olinorder(U_6336) ),
    inference(variable_rename,[status(thm)],[f_1879_1]) ).

fof(f_1879_3,plain,
    ! [U_6336,U_6337,U_6338] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6336),U_6337),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6336),U_6337),U_6338)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6336),U_6337),U_6338)
      | ~ class_Orderings_Olinorder(U_6336) ),
    inference(definitional_conversion,[status(esa)],[f_1879_2]) ).

cnf(f_1879_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6336),U_6337),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6336),U_6337),U_6338)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6336),U_6337),U_6338)
    | ~ class_Orderings_Olinorder(U_6336) ),
    inference(clausify,[status(thm)],[f_1879_3]) ).

fof(f_1880_1,plain,
    ! [V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),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_1880_2,plain,
    ! [U_6341,U_6340,U_6339] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6339),U_6340),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6339),U_6340),U_6341)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6339),U_6340),U_6341)
      | ~ class_Orderings_Olinorder(U_6339) ),
    inference(variable_rename,[status(thm)],[f_1880_1]) ).

fof(f_1880_3,plain,
    ! [U_6339,U_6340,U_6341] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6339),U_6340),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6339),U_6340),U_6341)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6339),U_6340),U_6341)
      | ~ class_Orderings_Olinorder(U_6339) ),
    inference(definitional_conversion,[status(esa)],[f_1880_2]) ).

cnf(f_1880_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6339),U_6340),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6339),U_6340),U_6341)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6339),U_6340),U_6341)
    | ~ class_Orderings_Olinorder(U_6339) ),
    inference(clausify,[status(thm)],[f_1880_3]) ).

fof(f_1881_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_1881_2,plain,
    ! [U_6344,U_6343,U_6342] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6342),U_6343),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6342),U_6343),U_6344)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6342),U_6343),U_6344)
      | ~ class_Orderings_Olinorder(U_6342) ),
    inference(variable_rename,[status(thm)],[f_1881_1]) ).

fof(f_1881_3,plain,
    ! [U_6342,U_6343,U_6344] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6342),U_6343),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6342),U_6343),U_6344)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6342),U_6343),U_6344)
      | ~ class_Orderings_Olinorder(U_6342) ),
    inference(definitional_conversion,[status(esa)],[f_1881_2]) ).

cnf(f_1881_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6342),U_6343),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6342),U_6343),U_6344)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6342),U_6343),U_6344)
    | ~ class_Orderings_Olinorder(U_6342) ),
    inference(clausify,[status(thm)],[f_1881_3]) ).

fof(f_1882_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_1882_2,plain,
    ! [U_6347,U_6346,U_6345] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6345),U_6346),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6345),U_6346),U_6347)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6345),U_6346),U_6347)
      | ~ class_Orderings_Olinorder(U_6345) ),
    inference(variable_rename,[status(thm)],[f_1882_1]) ).

fof(f_1882_3,plain,
    ! [U_6345,U_6346,U_6347] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6345),U_6346),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6345),U_6346),U_6347)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6345),U_6346),U_6347)
      | ~ class_Orderings_Olinorder(U_6345) ),
    inference(definitional_conversion,[status(esa)],[f_1882_2]) ).

cnf(f_1882_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6345),U_6346),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6345),U_6346),U_6347)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6345),U_6346),U_6347)
    | ~ class_Orderings_Olinorder(U_6345) ),
    inference(clausify,[status(thm)],[f_1882_3]) ).

fof(f_1883_1,plain,
    ! [V_c,V_a,V_b,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_c)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b),V_c))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup_Oleft__commute]) ).

fof(f_1883_2,plain,
    ! [U_6351,U_6350,U_6349,U_6348] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6348),U_6349),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6348),U_6350),U_6351)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6348),U_6350),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6348),U_6349),U_6351))
      | ~ class_Orderings_Olinorder(U_6348) ),
    inference(variable_rename,[status(thm)],[f_1883_1]) ).

fof(f_1883_3,plain,
    ! [U_6348,U_6349,U_6350,U_6351] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6348),U_6349),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6348),U_6350),U_6351)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6348),U_6350),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6348),U_6349),U_6351))
      | ~ class_Orderings_Olinorder(U_6348) ),
    inference(definitional_conversion,[status(esa)],[f_1883_2]) ).

cnf(f_1883_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6348),U_6349),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6348),U_6350),U_6351)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6348),U_6350),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6348),U_6349),U_6351))
    | ~ class_Orderings_Olinorder(U_6348) ),
    inference(clausify,[status(thm)],[f_1883_3]) ).

fof(f_1884_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),V_z)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_y),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_z))
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_min__max_Osup__left__commute]) ).

fof(f_1884_2,plain,
    ! [U_6355,U_6354,U_6353,U_6352] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6352),U_6353),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6352),U_6354),U_6355)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6352),U_6354),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6352),U_6353),U_6355))
      | ~ class_Orderings_Olinorder(U_6352) ),
    inference(variable_rename,[status(thm)],[f_1884_1]) ).

fof(f_1884_3,plain,
    ! [U_6352,U_6353,U_6354,U_6355] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6352),U_6353),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6352),U_6354),U_6355)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6352),U_6354),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6352),U_6353),U_6355))
      | ~ class_Orderings_Olinorder(U_6352) ),
    inference(definitional_conversion,[status(esa)],[f_1884_2]) ).

cnf(f_1884_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6352),U_6353),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6352),U_6354),U_6355)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6352),U_6354),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6352),U_6353),U_6355))
    | ~ class_Orderings_Olinorder(U_6352) ),
    inference(clausify,[status(thm)],[f_1884_3]) ).

fof(f_1885_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_1885_2,plain,
    ! [U_6359,U_6358,U_6357,U_6356] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6356),U_6357),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6356),U_6358),U_6359)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6356),U_6358),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6356),U_6357),U_6359))
      | ~ class_Orderings_Olinorder(U_6356) ),
    inference(variable_rename,[status(thm)],[f_1885_1]) ).

fof(f_1885_3,plain,
    ! [U_6356,U_6357,U_6358,U_6359] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6356),U_6357),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6356),U_6358),U_6359)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6356),U_6358),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6356),U_6357),U_6359))
      | ~ class_Orderings_Olinorder(U_6356) ),
    inference(definitional_conversion,[status(esa)],[f_1885_2]) ).

cnf(f_1885_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6356),U_6357),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6356),U_6358),U_6359)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6356),U_6358),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6356),U_6357),U_6359))
    | ~ class_Orderings_Olinorder(U_6356) ),
    inference(clausify,[status(thm)],[f_1885_3]) ).

fof(f_1886_1,plain,
    ! [V_z,V_y,V_x,T_a] :
      ( hAPP(hAPP(c_Orderings_Oord__class_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_1886_2,plain,
    ! [U_6363,U_6362,U_6361,U_6360] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6360),U_6361),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6360),U_6362),U_6363)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6360),U_6362),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6360),U_6361),U_6363))
      | ~ class_Orderings_Olinorder(U_6360) ),
    inference(variable_rename,[status(thm)],[f_1886_1]) ).

fof(f_1886_3,plain,
    ! [U_6360,U_6361,U_6362,U_6363] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6360),U_6361),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6360),U_6362),U_6363)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6360),U_6362),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6360),U_6361),U_6363))
      | ~ class_Orderings_Olinorder(U_6360) ),
    inference(definitional_conversion,[status(esa)],[f_1886_2]) ).

cnf(f_1886_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6360),U_6361),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6360),U_6362),U_6363)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6360),U_6362),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6360),U_6361),U_6363))
    | ~ class_Orderings_Olinorder(U_6360) ),
    inference(clausify,[status(thm)],[f_1886_3]) ).

fof(f_1887_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_1887_2,plain,
    ! [U_6367,U_6366,U_6365,U_6364] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6364),U_6365),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6364),U_6366),U_6367)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6364),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6364),U_6365),U_6366)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6364),U_6365),U_6367))
      | ~ class_Orderings_Olinorder(U_6364) ),
    inference(variable_rename,[status(thm)],[f_1887_1]) ).

fof(f_1887_3,plain,
    ! [U_6364,U_6365,U_6366,U_6367] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6364),U_6365),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6364),U_6366),U_6367)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6364),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6364),U_6365),U_6366)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6364),U_6365),U_6367))
      | ~ class_Orderings_Olinorder(U_6364) ),
    inference(definitional_conversion,[status(esa)],[f_1887_2]) ).

cnf(f_1887_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6364),U_6365),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6364),U_6366),U_6367)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6364),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6364),U_6365),U_6366)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6364),U_6365),U_6367))
    | ~ class_Orderings_Olinorder(U_6364) ),
    inference(clausify,[status(thm)],[f_1887_3]) ).

fof(f_1888_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_1888_2,plain,
    ! [U_6371,U_6370,U_6369,U_6368] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6368),U_6369),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6368),U_6370),U_6371)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6368),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6368),U_6369),U_6370)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6368),U_6369),U_6371))
      | ~ class_Orderings_Olinorder(U_6368) ),
    inference(variable_rename,[status(thm)],[f_1888_1]) ).

fof(f_1888_3,plain,
    ! [U_6368,U_6369,U_6370,U_6371] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6368),U_6369),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6368),U_6370),U_6371)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6368),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6368),U_6369),U_6370)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6368),U_6369),U_6371))
      | ~ class_Orderings_Olinorder(U_6368) ),
    inference(definitional_conversion,[status(esa)],[f_1888_2]) ).

cnf(f_1888_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6368),U_6369),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6368),U_6370),U_6371)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6368),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6368),U_6369),U_6370)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6368),U_6369),U_6371))
    | ~ class_Orderings_Olinorder(U_6368) ),
    inference(clausify,[status(thm)],[f_1888_3]) ).

fof(f_1889_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_1889_2,plain,
    ! [U_6375,U_6374,U_6373,U_6372] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6372),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6372),U_6373),U_6374)),U_6375) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6372),U_6373),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6372),U_6374),U_6375))
      | ~ class_Orderings_Olinorder(U_6372) ),
    inference(variable_rename,[status(thm)],[f_1889_1]) ).

fof(f_1889_3,plain,
    ! [U_6372,U_6373,U_6374,U_6375] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6372),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6372),U_6373),U_6374)),U_6375) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6372),U_6373),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6372),U_6374),U_6375))
      | ~ class_Orderings_Olinorder(U_6372) ),
    inference(definitional_conversion,[status(esa)],[f_1889_2]) ).

cnf(f_1889_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6372),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6372),U_6373),U_6374)),U_6375) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6372),U_6373),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6372),U_6374),U_6375))
    | ~ class_Orderings_Olinorder(U_6372) ),
    inference(clausify,[status(thm)],[f_1889_3]) ).

fof(f_1890_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_1890_2,plain,
    ! [U_6379,U_6378,U_6377,U_6376] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6376),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6376),U_6377),U_6378)),U_6379) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6376),U_6377),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6376),U_6378),U_6379))
      | ~ class_Orderings_Olinorder(U_6376) ),
    inference(variable_rename,[status(thm)],[f_1890_1]) ).

fof(f_1890_3,plain,
    ! [U_6376,U_6377,U_6378,U_6379] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6376),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6376),U_6377),U_6378)),U_6379) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6376),U_6377),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6376),U_6378),U_6379))
      | ~ class_Orderings_Olinorder(U_6376) ),
    inference(definitional_conversion,[status(esa)],[f_1890_2]) ).

cnf(f_1890_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6376),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6376),U_6377),U_6378)),U_6379) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6376),U_6377),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6376),U_6378),U_6379))
    | ~ class_Orderings_Olinorder(U_6376) ),
    inference(clausify,[status(thm)],[f_1890_3]) ).

fof(f_1891_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_1891_2,plain,
    ! [U_6383,U_6382,U_6381,U_6380] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6380),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6380),U_6381),U_6382)),U_6383) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6380),U_6381),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6380),U_6382),U_6383))
      | ~ class_Orderings_Olinorder(U_6380) ),
    inference(variable_rename,[status(thm)],[f_1891_1]) ).

fof(f_1891_3,plain,
    ! [U_6380,U_6381,U_6382,U_6383] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6380),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6380),U_6381),U_6382)),U_6383) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6380),U_6381),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6380),U_6382),U_6383))
      | ~ class_Orderings_Olinorder(U_6380) ),
    inference(definitional_conversion,[status(esa)],[f_1891_2]) ).

cnf(f_1891_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6380),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6380),U_6381),U_6382)),U_6383) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6380),U_6381),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6380),U_6382),U_6383))
    | ~ class_Orderings_Olinorder(U_6380) ),
    inference(clausify,[status(thm)],[f_1891_3]) ).

fof(f_1892_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_1892_2,plain,
    ! [U_6387,U_6386,U_6385,U_6384] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6384),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6384),U_6385),U_6386)),U_6387) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6384),U_6385),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6384),U_6386),U_6387))
      | ~ class_Orderings_Olinorder(U_6384) ),
    inference(variable_rename,[status(thm)],[f_1892_1]) ).

fof(f_1892_3,plain,
    ! [U_6384,U_6385,U_6386,U_6387] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6384),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6384),U_6385),U_6386)),U_6387) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6384),U_6385),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6384),U_6386),U_6387))
      | ~ class_Orderings_Olinorder(U_6384) ),
    inference(definitional_conversion,[status(esa)],[f_1892_2]) ).

cnf(f_1892_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6384),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6384),U_6385),U_6386)),U_6387) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6384),U_6385),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6384),U_6386),U_6387))
    | ~ class_Orderings_Olinorder(U_6384) ),
    inference(clausify,[status(thm)],[f_1892_3]) ).

fof(f_1893_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_1893_2,plain,
    ! [U_6391,U_6390,U_6389,U_6388] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6388),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6388),U_6389),U_6390)),U_6391) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6388),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6388),U_6389),U_6391)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6388),U_6390),U_6391))
      | ~ class_Orderings_Olinorder(U_6388) ),
    inference(variable_rename,[status(thm)],[f_1893_1]) ).

fof(f_1893_3,plain,
    ! [U_6388,U_6389,U_6390,U_6391] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6388),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6388),U_6389),U_6390)),U_6391) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6388),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6388),U_6389),U_6391)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6388),U_6390),U_6391))
      | ~ class_Orderings_Olinorder(U_6388) ),
    inference(definitional_conversion,[status(esa)],[f_1893_2]) ).

cnf(f_1893_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6388),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6388),U_6389),U_6390)),U_6391) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6388),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6388),U_6389),U_6391)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6388),U_6390),U_6391))
    | ~ class_Orderings_Olinorder(U_6388) ),
    inference(clausify,[status(thm)],[f_1893_3]) ).

fof(f_1894_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_1894_2,plain,
    ! [U_6395,U_6394,U_6393,U_6392] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6392),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6392),U_6393),U_6394)),U_6395) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6392),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6392),U_6393),U_6395)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6392),U_6394),U_6395))
      | ~ class_Orderings_Olinorder(U_6392) ),
    inference(variable_rename,[status(thm)],[f_1894_1]) ).

fof(f_1894_3,plain,
    ! [U_6392,U_6393,U_6394,U_6395] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6392),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6392),U_6393),U_6394)),U_6395) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6392),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6392),U_6393),U_6395)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6392),U_6394),U_6395))
      | ~ class_Orderings_Olinorder(U_6392) ),
    inference(definitional_conversion,[status(esa)],[f_1894_2]) ).

cnf(f_1894_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6392),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6392),U_6393),U_6394)),U_6395) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6392),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6392),U_6393),U_6395)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6392),U_6394),U_6395))
    | ~ class_Orderings_Olinorder(U_6392) ),
    inference(clausify,[status(thm)],[f_1894_3]) ).

fof(f_1895_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_1895_2,plain,
    ! [U_6398,U_6397,U_6396] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6396),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6396),U_6397),U_6398)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6396),hAPP(c_Groups_Ouminus__class_Ouminus(U_6396),U_6397)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6396),U_6398))
      | ~ class_Groups_Olinordered__ab__group__add(U_6396) ),
    inference(variable_rename,[status(thm)],[f_1895_1]) ).

fof(f_1895_3,plain,
    ! [U_6396,U_6397,U_6398] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6396),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6396),U_6397),U_6398)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6396),hAPP(c_Groups_Ouminus__class_Ouminus(U_6396),U_6397)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6396),U_6398))
      | ~ class_Groups_Olinordered__ab__group__add(U_6396) ),
    inference(definitional_conversion,[status(esa)],[f_1895_2]) ).

cnf(f_1895_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6396),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6396),U_6397),U_6398)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6396),hAPP(c_Groups_Ouminus__class_Ouminus(U_6396),U_6397)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6396),U_6398))
    | ~ class_Groups_Olinordered__ab__group__add(U_6396) ),
    inference(clausify,[status(thm)],[f_1895_3]) ).

fof(f_1896_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_1896_2,plain,
    ! [U_6401,U_6400,U_6399] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6399),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6399),U_6400),U_6401)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6399),hAPP(c_Groups_Ouminus__class_Ouminus(U_6399),U_6400)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6399),U_6401))
      | ~ class_Groups_Olinordered__ab__group__add(U_6399) ),
    inference(variable_rename,[status(thm)],[f_1896_1]) ).

fof(f_1896_3,plain,
    ! [U_6399,U_6400,U_6401] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6399),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6399),U_6400),U_6401)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6399),hAPP(c_Groups_Ouminus__class_Ouminus(U_6399),U_6400)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6399),U_6401))
      | ~ class_Groups_Olinordered__ab__group__add(U_6399) ),
    inference(definitional_conversion,[status(esa)],[f_1896_2]) ).

cnf(f_1896_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_6399),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6399),U_6400),U_6401)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6399),hAPP(c_Groups_Ouminus__class_Ouminus(U_6399),U_6400)),hAPP(c_Groups_Ouminus__class_Ouminus(U_6399),U_6401))
    | ~ class_Groups_Olinordered__ab__group__add(U_6399) ),
    inference(clausify,[status(thm)],[f_1896_3]) ).

fof(f_1897_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_1897_2,plain,
    ! [U_6403,U_6402] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6402)),hAPP(c_Nat_OSuc,U_6403)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6402),U_6403)),
    inference(variable_rename,[status(thm)],[f_1897_1]) ).

fof(f_1897_3,plain,
    ! [U_6402,U_6403] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6402)),hAPP(c_Nat_OSuc,U_6403)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6402),U_6403)),
    inference(definitional_conversion,[status(esa)],[f_1897_2]) ).

cnf(f_1897_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6402)),hAPP(c_Nat_OSuc,U_6403)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6402),U_6403)),
    inference(clausify,[status(thm)],[f_1897_3]) ).

fof(f_1898_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_1898_2,plain,
    ! [U_6405,U_6404] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6404)),hAPP(c_Nat_OSuc,U_6405)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6404),U_6405)),
    inference(variable_rename,[status(thm)],[f_1898_1]) ).

fof(f_1898_3,plain,
    ! [U_6404,U_6405] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6404)),hAPP(c_Nat_OSuc,U_6405)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6404),U_6405)),
    inference(definitional_conversion,[status(esa)],[f_1898_2]) ).

cnf(f_1898_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6404)),hAPP(c_Nat_OSuc,U_6405)) = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6404),U_6405)),
    inference(clausify,[status(thm)],[f_1898_3]) ).

fof(f_1899_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_1899_2,plain,
    ! [U_6406] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6406) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1899_1]) ).

fof(f_1899_3,plain,
    ! [U_6406] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6406) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1899_2]) ).

cnf(f_1899_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6406) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1899_3]) ).

fof(f_1900_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_1900_2,plain,
    ! [U_6407] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6407),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_1900_1]) ).

fof(f_1900_3,plain,
    ! [U_6407] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6407),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_1900_2]) ).

cnf(f_1900_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6407),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_1900_3]) ).

fof(f_1901_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_1901_2,plain,
    ! [U_6408] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6408) = U_6408,
    inference(variable_rename,[status(thm)],[f_1901_1]) ).

fof(f_1901_3,plain,
    ! [U_6408] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6408) = U_6408,
    inference(definitional_conversion,[status(esa)],[f_1901_2]) ).

cnf(f_1901_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_6408) = U_6408,
    inference(clausify,[status(thm)],[f_1901_3]) ).

fof(f_1902_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_1902_2,plain,
    ! [U_6409] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6409),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6409,
    inference(variable_rename,[status(thm)],[f_1902_1]) ).

fof(f_1902_3,plain,
    ! [U_6409] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6409),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6409,
    inference(definitional_conversion,[status(esa)],[f_1902_2]) ).

cnf(f_1902_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6409),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_6409,
    inference(clausify,[status(thm)],[f_1902_3]) ).

fof(f_1903_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_1903_2,plain,
    ! [U_6413,U_6412,U_6411,U_6410] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6410),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6410),U_6411),U_6412)),U_6413) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6410),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6410),U_6411),U_6413)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6410),U_6412),U_6413))
      | ~ class_Groups_Oordered__ab__group__add(U_6410) ),
    inference(variable_rename,[status(thm)],[f_1903_1]) ).

fof(f_1903_3,plain,
    ! [U_6410,U_6411,U_6412,U_6413] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6410),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6410),U_6411),U_6412)),U_6413) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6410),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6410),U_6411),U_6413)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6410),U_6412),U_6413))
      | ~ class_Groups_Oordered__ab__group__add(U_6410) ),
    inference(definitional_conversion,[status(esa)],[f_1903_2]) ).

cnf(f_1903_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6410),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6410),U_6411),U_6412)),U_6413) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6410),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6410),U_6411),U_6413)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6410),U_6412),U_6413))
    | ~ class_Groups_Oordered__ab__group__add(U_6410) ),
    inference(clausify,[status(thm)],[f_1903_3]) ).

fof(f_1904_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_1904_2,plain,
    ! [U_6417,U_6416,U_6415,U_6414] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6414),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6414),U_6415),U_6416)),U_6417) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6414),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6414),U_6415),U_6417)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6414),U_6416),U_6417))
      | ~ class_Groups_Oordered__ab__group__add(U_6414) ),
    inference(variable_rename,[status(thm)],[f_1904_1]) ).

fof(f_1904_3,plain,
    ! [U_6414,U_6415,U_6416,U_6417] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6414),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6414),U_6415),U_6416)),U_6417) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6414),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6414),U_6415),U_6417)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6414),U_6416),U_6417))
      | ~ class_Groups_Oordered__ab__group__add(U_6414) ),
    inference(definitional_conversion,[status(esa)],[f_1904_2]) ).

cnf(f_1904_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6414),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6414),U_6415),U_6416)),U_6417) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6414),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6414),U_6415),U_6417)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_6414),U_6416),U_6417))
    | ~ class_Groups_Oordered__ab__group__add(U_6414) ),
    inference(clausify,[status(thm)],[f_1904_3]) ).

fof(f_1905_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_1905_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_1905_1]) ).

fof(f_1905_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_1905_2]) ).

cnf(f_1905_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_1905_3]) ).

fof(f_1906_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_1906_2,plain,
    ! [U_6423,U_6422,U_6421] :
      ( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6421),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6422)),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6423)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6422)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6421),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6422)),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6423))) )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6421),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6422)),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6423)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6423)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6421),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6422)),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6423))) ) )
      | ~ class_Orderings_Oord(U_6421)
      | ~ class_Int_Onumber(U_6421) ),
    inference(variable_rename,[status(thm)],[f_1906_1]) ).

fof(f_1906_3,plain,
    ( ! [U_6421,U_6422,U_6423] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6421),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6422)),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6423)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6422)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6421),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6422)),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6423)))
        | ~ sP602(U_6421,U_6422,U_6423) )
    & ! [U_6421,U_6422,U_6423] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6421),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6422)),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6423)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6423)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6421),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6422)),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6423)))
        | ~ sP602(U_6421,U_6422,U_6423) )
    & ! [U_6421,U_6422,U_6423] :
        ( sP602(U_6421,U_6422,U_6423)
        | ~ class_Orderings_Oord(U_6421)
        | ~ class_Int_Onumber(U_6421) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP602])],[f_1906_2]) ).

cnf(f_1906_4,plain,
    ( sP602(U_6421,U_6422,U_6423)
    | ~ class_Orderings_Oord(U_6421)
    | ~ class_Int_Onumber(U_6421) ),
    inference(clausify,[status(thm)],[f_1906_3]) ).

cnf(f_1906_5,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6421),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6422)),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6423)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6423)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6421),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6422)),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6423)))
    | ~ sP602(U_6421,U_6422,U_6423) ),
    inference(clausify,[status(thm)],[f_1906_3]) ).

cnf(f_1906_6,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6421),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6422)),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6423)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6422)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6421),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6422)),hAPP(c_Int_Onumber__class_Onumber__of(U_6421),U_6423)))
    | ~ sP602(U_6421,U_6422,U_6423) ),
    inference(clausify,[status(thm)],[f_1906_3]) ).

fof(f_1907_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_1907_2,plain,
    ! [U_6426,U_6425,U_6424] :
      ( ( ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6424),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6425)),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6426)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6426)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6424),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6425)),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6426))) )
        & ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6424),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6425)),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6426)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6425)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6424),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6425)),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6426))) ) )
      | ~ class_Orderings_Oord(U_6424)
      | ~ class_Int_Onumber(U_6424) ),
    inference(variable_rename,[status(thm)],[f_1907_1]) ).

fof(f_1907_3,plain,
    ( ! [U_6426,U_6424,U_6425] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6424),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6425)),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6426)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6426)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6424),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6425)),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6426)))
        | ~ sP603(U_6426,U_6424,U_6425) )
    & ! [U_6426,U_6424,U_6425] :
        ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6424),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6425)),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6426)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6425)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6424),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6425)),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6426)))
        | ~ sP603(U_6426,U_6424,U_6425) )
    & ! [U_6426,U_6424,U_6425] :
        ( sP603(U_6426,U_6424,U_6425)
        | ~ class_Orderings_Oord(U_6424)
        | ~ class_Int_Onumber(U_6424) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP603])],[f_1907_2]) ).

cnf(f_1907_4,plain,
    ( sP603(U_6426,U_6424,U_6425)
    | ~ class_Orderings_Oord(U_6424)
    | ~ class_Int_Onumber(U_6424) ),
    inference(clausify,[status(thm)],[f_1907_3]) ).

cnf(f_1907_5,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6424),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6425)),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6426)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6425)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6424),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6425)),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6426)))
    | ~ sP603(U_6426,U_6424,U_6425) ),
    inference(clausify,[status(thm)],[f_1907_3]) ).

cnf(f_1907_6,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6424),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6425)),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6426)) = hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6426)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6424),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6425)),hAPP(c_Int_Onumber__class_Onumber__of(U_6424),U_6426)))
    | ~ sP603(U_6426,U_6424,U_6425) ),
    inference(clausify,[status(thm)],[f_1907_3]) ).

fof(f_1908_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_1908_2,plain,
    ! [U_6428,U_6427] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6427),U_6428)),U_6428) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6427),U_6428),
    inference(variable_rename,[status(thm)],[f_1908_1]) ).

fof(f_1908_3,plain,
    ! [U_6428,U_6427] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6427),U_6428)),U_6428) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6427),U_6428),
    inference(definitional_conversion,[status(esa)],[f_1908_2]) ).

cnf(f_1908_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_6427),U_6428)),U_6428) = hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6427),U_6428),
    inference(clausify,[status(thm)],[f_1908_3]) ).

fof(f_1909_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_1909_2,plain,
    ! [U_6430,U_6429] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6429)),U_6430) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6429),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_6429)),U_6430),
    inference(variable_rename,[status(thm)],[f_1909_1]) ).

fof(f_1909_3,plain,
    ! [U_6429,U_6430] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6429)),U_6430) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6429),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_6429)),U_6430),
    inference(definitional_conversion,[status(esa)],[f_1909_2]) ).

cnf(f_1909_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6429)),U_6430) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6429),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_6429)),U_6430),
    inference(clausify,[status(thm)],[f_1909_3]) ).

fof(f_1910_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_1910_2,plain,
    ! [U_6432,U_6431] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6431),hAPP(c_Nat_OSuc,U_6432)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6432),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_6432)),U_6431),
    inference(variable_rename,[status(thm)],[f_1910_1]) ).

fof(f_1910_3,plain,
    ! [U_6431,U_6432] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6431),hAPP(c_Nat_OSuc,U_6432)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6432),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_6432)),U_6431),
    inference(definitional_conversion,[status(esa)],[f_1910_2]) ).

cnf(f_1910_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),U_6431),hAPP(c_Nat_OSuc,U_6432)) = c_Nat_Onat_Onat__case(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_6432),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_6432)),U_6431),
    inference(clausify,[status(thm)],[f_1910_3]) ).

fof(f_1911_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_1911_2,plain,
    ! [U_6434,U_6433] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6433),hAPP(c_Nat_OSuc,U_6434)) = 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_6434)),U_6433),
    inference(variable_rename,[status(thm)],[f_1911_1]) ).

fof(f_1911_3,plain,
    ! [U_6433,U_6434] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6433),hAPP(c_Nat_OSuc,U_6434)) = 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_6434)),U_6433),
    inference(definitional_conversion,[status(esa)],[f_1911_2]) ).

cnf(f_1911_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_6433),hAPP(c_Nat_OSuc,U_6434)) = 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_6434)),U_6433),
    inference(clausify,[status(thm)],[f_1911_3]) ).

fof(f_1912_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_1912_2,plain,
    ! [U_6436,U_6435] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6435)),U_6436) = 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_6435)),U_6436),
    inference(variable_rename,[status(thm)],[f_1912_1]) ).

fof(f_1912_3,plain,
    ! [U_6435,U_6436] : hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6435)),U_6436) = 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_6435)),U_6436),
    inference(definitional_conversion,[status(esa)],[f_1912_2]) ).

cnf(f_1912_4,plain,
    hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_6435)),U_6436) = 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_6435)),U_6436),
    inference(clausify,[status(thm)],[f_1912_3]) ).

fof(f_1913_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_1913_2,plain,
    ! [U_6437] :
      ( c_Orderings_Oord__class_Omax(U_6437) = c_Orderings_Oord_Omax(U_6437,c_Orderings_Oord__class_Oless__eq(U_6437))
      | ~ class_Orderings_Oord(U_6437) ),
    inference(variable_rename,[status(thm)],[f_1913_1]) ).

fof(f_1913_3,plain,
    ! [U_6437] :
      ( c_Orderings_Oord__class_Omax(U_6437) = c_Orderings_Oord_Omax(U_6437,c_Orderings_Oord__class_Oless__eq(U_6437))
      | ~ class_Orderings_Oord(U_6437) ),
    inference(definitional_conversion,[status(esa)],[f_1913_2]) ).

cnf(f_1913_4,plain,
    ( c_Orderings_Oord__class_Omax(U_6437) = c_Orderings_Oord_Omax(U_6437,c_Orderings_Oord__class_Oless__eq(U_6437))
    | ~ class_Orderings_Oord(U_6437) ),
    inference(clausify,[status(thm)],[f_1913_3]) ).

fof(f_1914_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_1914_2,plain,
    ! [U_6438] :
      ( c_Orderings_Oord__class_Omin(U_6438) = c_Orderings_Oord_Omin(U_6438,c_Orderings_Oord__class_Oless__eq(U_6438))
      | ~ class_Orderings_Oord(U_6438) ),
    inference(variable_rename,[status(thm)],[f_1914_1]) ).

fof(f_1914_3,plain,
    ! [U_6438] :
      ( c_Orderings_Oord__class_Omin(U_6438) = c_Orderings_Oord_Omin(U_6438,c_Orderings_Oord__class_Oless__eq(U_6438))
      | ~ class_Orderings_Oord(U_6438) ),
    inference(definitional_conversion,[status(esa)],[f_1914_2]) ).

cnf(f_1914_4,plain,
    ( c_Orderings_Oord__class_Omin(U_6438) = c_Orderings_Oord_Omin(U_6438,c_Orderings_Oord__class_Oless__eq(U_6438))
    | ~ class_Orderings_Oord(U_6438) ),
    inference(clausify,[status(thm)],[f_1914_3]) ).

fof(f_1915_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_1915_2,plain,
    ! [U_6439] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_6439)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_6439)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1915_1]) ).

fof(f_1915_3,plain,
    ! [U_6439] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_6439)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_6439)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_1915_2]) ).

cnf(f_1915_4,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(c_Code__Numeral_OSuc__code__numeral(U_6439)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Code__Numeral_Ocode__numeral_Ocode__numeral__size(U_6439)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1915_3]) ).

fof(f_1916_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_1916_2,plain,
    ! [U_6446,U_6445,U_6444,U_6443,U_6442,U_6441,U_6440] : hAPP(c_Product__Type_Oapsnd(U_6440,U_6441,U_6442,U_6443),hAPP(c_Product__Type_Oapfst(U_6444,U_6442,U_6440,U_6445),U_6446)) = hAPP(hAPP(c_Product__Type_OPair(U_6442,U_6441),hAPP(U_6445,hAPP(c_Product__Type_Ofst(U_6444,U_6440),U_6446))),hAPP(U_6443,hAPP(c_Product__Type_Osnd(U_6444,U_6440),U_6446))),
    inference(variable_rename,[status(thm)],[f_1916_1]) ).

fof(f_1916_3,plain,
    ! [U_6440,U_6441,U_6442,U_6443,U_6444,U_6445,U_6446] : hAPP(c_Product__Type_Oapsnd(U_6440,U_6441,U_6442,U_6443),hAPP(c_Product__Type_Oapfst(U_6444,U_6442,U_6440,U_6445),U_6446)) = hAPP(hAPP(c_Product__Type_OPair(U_6442,U_6441),hAPP(U_6445,hAPP(c_Product__Type_Ofst(U_6444,U_6440),U_6446))),hAPP(U_6443,hAPP(c_Product__Type_Osnd(U_6444,U_6440),U_6446))),
    inference(definitional_conversion,[status(esa)],[f_1916_2]) ).

cnf(f_1916_4,plain,
    hAPP(c_Product__Type_Oapsnd(U_6440,U_6441,U_6442,U_6443),hAPP(c_Product__Type_Oapfst(U_6444,U_6442,U_6440,U_6445),U_6446)) = hAPP(hAPP(c_Product__Type_OPair(U_6442,U_6441),hAPP(U_6445,hAPP(c_Product__Type_Ofst(U_6444,U_6440),U_6446))),hAPP(U_6443,hAPP(c_Product__Type_Osnd(U_6444,U_6440),U_6446))),
    inference(clausify,[status(thm)],[f_1916_3]) ).

fof(f_1917_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_1917_2,plain,
    ! [U_6453,U_6452,U_6451,U_6450,U_6449,U_6448,U_6447] : hAPP(c_Product__Type_Oapfst(U_6447,U_6448,U_6449,U_6450),hAPP(c_Product__Type_Oapsnd(U_6451,U_6449,U_6447,U_6452),U_6453)) = hAPP(hAPP(c_Product__Type_OPair(U_6448,U_6449),hAPP(U_6450,hAPP(c_Product__Type_Ofst(U_6447,U_6451),U_6453))),hAPP(U_6452,hAPP(c_Product__Type_Osnd(U_6447,U_6451),U_6453))),
    inference(variable_rename,[status(thm)],[f_1917_1]) ).

fof(f_1917_3,plain,
    ! [U_6447,U_6448,U_6449,U_6450,U_6451,U_6452,U_6453] : hAPP(c_Product__Type_Oapfst(U_6447,U_6448,U_6449,U_6450),hAPP(c_Product__Type_Oapsnd(U_6451,U_6449,U_6447,U_6452),U_6453)) = hAPP(hAPP(c_Product__Type_OPair(U_6448,U_6449),hAPP(U_6450,hAPP(c_Product__Type_Ofst(U_6447,U_6451),U_6453))),hAPP(U_6452,hAPP(c_Product__Type_Osnd(U_6447,U_6451),U_6453))),
    inference(definitional_conversion,[status(esa)],[f_1917_2]) ).

cnf(f_1917_4,plain,
    hAPP(c_Product__Type_Oapfst(U_6447,U_6448,U_6449,U_6450),hAPP(c_Product__Type_Oapsnd(U_6451,U_6449,U_6447,U_6452),U_6453)) = hAPP(hAPP(c_Product__Type_OPair(U_6448,U_6449),hAPP(U_6450,hAPP(c_Product__Type_Ofst(U_6447,U_6451),U_6453))),hAPP(U_6452,hAPP(c_Product__Type_Osnd(U_6447,U_6451),U_6453))),
    inference(clausify,[status(thm)],[f_1917_3]) ).

fof(f_1918_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_1918_2,plain,
    ! [U_6455,U_6454] :
      ( ( c_Code__Numeral_OSuc__code__numeral(U_6454) = c_Code__Numeral_OSuc__code__numeral(U_6455)
        | U_6454 != U_6455 )
      & ( U_6454 = U_6455
        | c_Code__Numeral_OSuc__code__numeral(U_6454) != c_Code__Numeral_OSuc__code__numeral(U_6455) ) ),
    inference(variable_rename,[status(thm)],[f_1918_1]) ).

fof(f_1918_3,plain,
    ( ! [U_6459,U_6457] :
        ( c_Code__Numeral_OSuc__code__numeral(U_6457) = c_Code__Numeral_OSuc__code__numeral(U_6459)
        | U_6457 != U_6459 )
    & ! [U_6458,U_6456] :
        ( U_6456 = U_6458
        | c_Code__Numeral_OSuc__code__numeral(U_6456) != c_Code__Numeral_OSuc__code__numeral(U_6458) ) ),
    inference(miniscope,[status(thm)],[f_1918_2]) ).

fof(f_1918_4,plain,
    ( ! [U_6459,U_6457] :
        ( c_Code__Numeral_OSuc__code__numeral(U_6457) = c_Code__Numeral_OSuc__code__numeral(U_6459)
        | U_6457 != U_6459 )
    & ! [U_6458,U_6456] :
        ( U_6456 = U_6458
        | c_Code__Numeral_OSuc__code__numeral(U_6456) != c_Code__Numeral_OSuc__code__numeral(U_6458) ) ),
    inference(definitional_conversion,[status(esa)],[f_1918_3]) ).

cnf(f_1918_5,plain,
    ( U_6456 = U_6458
    | c_Code__Numeral_OSuc__code__numeral(U_6456) != c_Code__Numeral_OSuc__code__numeral(U_6458) ),
    inference(clausify,[status(thm)],[f_1918_4]) ).

cnf(f_1918_6,plain,
    ( c_Code__Numeral_OSuc__code__numeral(U_6457) = c_Code__Numeral_OSuc__code__numeral(U_6459)
    | U_6457 != U_6459 ),
    inference(clausify,[status(thm)],[f_1918_4]) ).

fof(f_1919_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_1919_2,plain,
    ! [U_6465,U_6464,U_6463,U_6462,U_6461,U_6460] : hAPP(c_Product__Type_Oapfst(U_6460,U_6461,U_6462,U_6463),hAPP(hAPP(c_Product__Type_OPair(U_6460,U_6462),U_6464),U_6465)) = hAPP(hAPP(c_Product__Type_OPair(U_6461,U_6462),hAPP(U_6463,U_6464)),U_6465),
    inference(variable_rename,[status(thm)],[f_1919_1]) ).

fof(f_1919_3,plain,
    ! [U_6460,U_6461,U_6462,U_6463,U_6464,U_6465] : hAPP(c_Product__Type_Oapfst(U_6460,U_6461,U_6462,U_6463),hAPP(hAPP(c_Product__Type_OPair(U_6460,U_6462),U_6464),U_6465)) = hAPP(hAPP(c_Product__Type_OPair(U_6461,U_6462),hAPP(U_6463,U_6464)),U_6465),
    inference(definitional_conversion,[status(esa)],[f_1919_2]) ).

cnf(f_1919_4,plain,
    hAPP(c_Product__Type_Oapfst(U_6460,U_6461,U_6462,U_6463),hAPP(hAPP(c_Product__Type_OPair(U_6460,U_6462),U_6464),U_6465)) = hAPP(hAPP(c_Product__Type_OPair(U_6461,U_6462),hAPP(U_6463,U_6464)),U_6465),
    inference(clausify,[status(thm)],[f_1919_3]) ).

fof(f_1920_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_1920_2,plain,
    ! [U_6470,U_6469,U_6468,U_6467,U_6466] : hAPP(c_Product__Type_Ofst(U_6466,U_6467),hAPP(c_Product__Type_Oapfst(U_6468,U_6466,U_6467,U_6469),U_6470)) = hAPP(U_6469,hAPP(c_Product__Type_Ofst(U_6468,U_6467),U_6470)),
    inference(variable_rename,[status(thm)],[f_1920_1]) ).

fof(f_1920_3,plain,
    ! [U_6467,U_6466,U_6468,U_6469,U_6470] : hAPP(c_Product__Type_Ofst(U_6466,U_6467),hAPP(c_Product__Type_Oapfst(U_6468,U_6466,U_6467,U_6469),U_6470)) = hAPP(U_6469,hAPP(c_Product__Type_Ofst(U_6468,U_6467),U_6470)),
    inference(definitional_conversion,[status(esa)],[f_1920_2]) ).

cnf(f_1920_4,plain,
    hAPP(c_Product__Type_Ofst(U_6466,U_6467),hAPP(c_Product__Type_Oapfst(U_6468,U_6466,U_6467,U_6469),U_6470)) = hAPP(U_6469,hAPP(c_Product__Type_Ofst(U_6468,U_6467),U_6470)),
    inference(clausify,[status(thm)],[f_1920_3]) ).

fof(f_1921_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_1921_2,plain,
    ! [U_6476,U_6475,U_6474,U_6473,U_6472,U_6471] :
      ( ( hAPP(c_Product__Type_Oapfst(U_6471,U_6472,U_6473,U_6474),U_6475) = hAPP(c_Product__Type_Oapfst(U_6471,U_6472,U_6473,U_6476),U_6475)
        | hAPP(U_6474,hAPP(c_Product__Type_Ofst(U_6471,U_6473),U_6475)) != hAPP(U_6476,hAPP(c_Product__Type_Ofst(U_6471,U_6473),U_6475)) )
      & ( hAPP(U_6474,hAPP(c_Product__Type_Ofst(U_6471,U_6473),U_6475)) = hAPP(U_6476,hAPP(c_Product__Type_Ofst(U_6471,U_6473),U_6475))
        | hAPP(c_Product__Type_Oapfst(U_6471,U_6472,U_6473,U_6474),U_6475) != hAPP(c_Product__Type_Oapfst(U_6471,U_6472,U_6473,U_6476),U_6475) ) ),
    inference(variable_rename,[status(thm)],[f_1921_1]) ).

fof(f_1921_3,plain,
    ( ! [U_6488,U_6486,U_6484,U_6482,U_6480,U_6478] :
        ( hAPP(c_Product__Type_Oapfst(U_6478,U_6480,U_6482,U_6484),U_6486) = hAPP(c_Product__Type_Oapfst(U_6478,U_6480,U_6482,U_6488),U_6486)
        | hAPP(U_6484,hAPP(c_Product__Type_Ofst(U_6478,U_6482),U_6486)) != hAPP(U_6488,hAPP(c_Product__Type_Ofst(U_6478,U_6482),U_6486)) )
    & ! [U_6487,U_6485,U_6483,U_6481,U_6479,U_6477] :
        ( hAPP(U_6483,hAPP(c_Product__Type_Ofst(U_6477,U_6481),U_6485)) = hAPP(U_6487,hAPP(c_Product__Type_Ofst(U_6477,U_6481),U_6485))
        | hAPP(c_Product__Type_Oapfst(U_6477,U_6479,U_6481,U_6483),U_6485) != hAPP(c_Product__Type_Oapfst(U_6477,U_6479,U_6481,U_6487),U_6485) ) ),
    inference(miniscope,[status(thm)],[f_1921_2]) ).

fof(f_1921_4,plain,
    ( ! [U_6480,U_6478,U_6482,U_6484,U_6486,U_6488] :
        ( hAPP(c_Product__Type_Oapfst(U_6478,U_6480,U_6482,U_6484),U_6486) = hAPP(c_Product__Type_Oapfst(U_6478,U_6480,U_6482,U_6488),U_6486)
        | hAPP(U_6484,hAPP(c_Product__Type_Ofst(U_6478,U_6482),U_6486)) != hAPP(U_6488,hAPP(c_Product__Type_Ofst(U_6478,U_6482),U_6486)) )
    & ! [U_6479,U_6477,U_6483,U_6481,U_6487,U_6485] :
        ( hAPP(U_6483,hAPP(c_Product__Type_Ofst(U_6477,U_6481),U_6485)) = hAPP(U_6487,hAPP(c_Product__Type_Ofst(U_6477,U_6481),U_6485))
        | hAPP(c_Product__Type_Oapfst(U_6477,U_6479,U_6481,U_6483),U_6485) != hAPP(c_Product__Type_Oapfst(U_6477,U_6479,U_6481,U_6487),U_6485) ) ),
    inference(definitional_conversion,[status(esa)],[f_1921_3]) ).

cnf(f_1921_5,plain,
    ( hAPP(U_6483,hAPP(c_Product__Type_Ofst(U_6477,U_6481),U_6485)) = hAPP(U_6487,hAPP(c_Product__Type_Ofst(U_6477,U_6481),U_6485))
    | hAPP(c_Product__Type_Oapfst(U_6477,U_6479,U_6481,U_6483),U_6485) != hAPP(c_Product__Type_Oapfst(U_6477,U_6479,U_6481,U_6487),U_6485) ),
    inference(clausify,[status(thm)],[f_1921_4]) ).

cnf(f_1921_6,plain,
    ( hAPP(c_Product__Type_Oapfst(U_6478,U_6480,U_6482,U_6484),U_6486) = hAPP(c_Product__Type_Oapfst(U_6478,U_6480,U_6482,U_6488),U_6486)
    | hAPP(U_6484,hAPP(c_Product__Type_Ofst(U_6478,U_6482),U_6486)) != hAPP(U_6488,hAPP(c_Product__Type_Ofst(U_6478,U_6482),U_6486)) ),
    inference(clausify,[status(thm)],[f_1921_4]) ).

fof(f_1922_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_1922_2,plain,
    ! [U_6493,U_6492,U_6491,U_6490,U_6489] : hAPP(c_Product__Type_Osnd(U_6489,U_6490),hAPP(c_Product__Type_Oapfst(U_6491,U_6489,U_6490,U_6492),U_6493)) = hAPP(c_Product__Type_Osnd(U_6491,U_6490),U_6493),
    inference(variable_rename,[status(thm)],[f_1922_1]) ).

fof(f_1922_3,plain,
    ! [U_6490,U_6489,U_6492,U_6491,U_6493] : hAPP(c_Product__Type_Osnd(U_6489,U_6490),hAPP(c_Product__Type_Oapfst(U_6491,U_6489,U_6490,U_6492),U_6493)) = hAPP(c_Product__Type_Osnd(U_6491,U_6490),U_6493),
    inference(definitional_conversion,[status(esa)],[f_1922_2]) ).

cnf(f_1922_4,plain,
    hAPP(c_Product__Type_Osnd(U_6489,U_6490),hAPP(c_Product__Type_Oapfst(U_6491,U_6489,U_6490,U_6492),U_6493)) = hAPP(c_Product__Type_Osnd(U_6491,U_6490),U_6493),
    inference(clausify,[status(thm)],[f_1922_3]) ).

fof(f_1923_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_1923_2,plain,
    ! [U_6500,U_6499,U_6498,U_6497,U_6496,U_6495,U_6494] : hAPP(c_Product__Type_Oapsnd(U_6494,U_6495,U_6496,U_6497),hAPP(c_Product__Type_Oapfst(U_6498,U_6496,U_6494,U_6499),U_6500)) = hAPP(c_Product__Type_Oapfst(U_6498,U_6496,U_6495,U_6499),hAPP(c_Product__Type_Oapsnd(U_6494,U_6495,U_6498,U_6497),U_6500)),
    inference(variable_rename,[status(thm)],[f_1923_1]) ).

fof(f_1923_3,plain,
    ! [U_6494,U_6495,U_6496,U_6497,U_6498,U_6499,U_6500] : hAPP(c_Product__Type_Oapsnd(U_6494,U_6495,U_6496,U_6497),hAPP(c_Product__Type_Oapfst(U_6498,U_6496,U_6494,U_6499),U_6500)) = hAPP(c_Product__Type_Oapfst(U_6498,U_6496,U_6495,U_6499),hAPP(c_Product__Type_Oapsnd(U_6494,U_6495,U_6498,U_6497),U_6500)),
    inference(definitional_conversion,[status(esa)],[f_1923_2]) ).

cnf(f_1923_4,plain,
    hAPP(c_Product__Type_Oapsnd(U_6494,U_6495,U_6496,U_6497),hAPP(c_Product__Type_Oapfst(U_6498,U_6496,U_6494,U_6499),U_6500)) = hAPP(c_Product__Type_Oapfst(U_6498,U_6496,U_6495,U_6499),hAPP(c_Product__Type_Oapsnd(U_6494,U_6495,U_6498,U_6497),U_6500)),
    inference(clausify,[status(thm)],[f_1923_3]) ).

fof(f_1924_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_1924_2,plain,
    ! [U_6501] : c_Code__Numeral_OSuc__code__numeral(U_6501) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(variable_rename,[status(thm)],[f_1924_1]) ).

fof(f_1924_3,plain,
    ! [U_6501] : c_Code__Numeral_OSuc__code__numeral(U_6501) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_1924_2]) ).

cnf(f_1924_4,plain,
    c_Code__Numeral_OSuc__code__numeral(U_6501) != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_1924_3]) ).

fof(f_1925_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_1925_2,plain,
    ! [U_6502] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_6502),
    inference(variable_rename,[status(thm)],[f_1925_1]) ).

fof(f_1925_3,plain,
    ! [U_6502] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_6502),
    inference(definitional_conversion,[status(esa)],[f_1925_2]) ).

cnf(f_1925_4,plain,
    c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(U_6502),
    inference(clausify,[status(thm)],[f_1925_3]) ).

fof(f_1926_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_1926_2,plain,
    ! [U_6503] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_6503)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_6503,
    inference(variable_rename,[status(thm)],[f_1926_1]) ).

fof(f_1926_3,plain,
    ! [U_6503] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_6503)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_6503,
    inference(definitional_conversion,[status(esa)],[f_1926_2]) ).

cnf(f_1926_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_6503)),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)) = U_6503,
    inference(clausify,[status(thm)],[f_1926_3]) ).

fof(f_1927_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_1927_2,plain,
    ! [U_6504] :
      ( c_Orderings_Oord_Omin(U_6504,hAPP(c_COMBC(U_6504,U_6504,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_6504))) = c_Orderings_Oord__class_Omax(U_6504)
      | ~ class_Orderings_Olinorder(U_6504) ),
    inference(variable_rename,[status(thm)],[f_1927_1]) ).

fof(f_1927_3,plain,
    ! [U_6504] :
      ( c_Orderings_Oord_Omin(U_6504,hAPP(c_COMBC(U_6504,U_6504,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_6504))) = c_Orderings_Oord__class_Omax(U_6504)
      | ~ class_Orderings_Olinorder(U_6504) ),
    inference(definitional_conversion,[status(esa)],[f_1927_2]) ).

cnf(f_1927_4,plain,
    ( c_Orderings_Oord_Omin(U_6504,hAPP(c_COMBC(U_6504,U_6504,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_6504))) = c_Orderings_Oord__class_Omax(U_6504)
    | ~ class_Orderings_Olinorder(U_6504) ),
    inference(clausify,[status(thm)],[f_1927_3]) ).

fof(f_1928_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_1928_2,plain,
    ! [U_6505] :
      ( c_Orderings_Oord_Omax(U_6505,hAPP(c_COMBC(U_6505,U_6505,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_6505))) = c_Orderings_Oord__class_Omin(U_6505)
      | ~ class_Orderings_Olinorder(U_6505) ),
    inference(variable_rename,[status(thm)],[f_1928_1]) ).

fof(f_1928_3,plain,
    ! [U_6505] :
      ( c_Orderings_Oord_Omax(U_6505,hAPP(c_COMBC(U_6505,U_6505,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_6505))) = c_Orderings_Oord__class_Omin(U_6505)
      | ~ class_Orderings_Olinorder(U_6505) ),
    inference(definitional_conversion,[status(esa)],[f_1928_2]) ).

cnf(f_1928_4,plain,
    ( c_Orderings_Oord_Omax(U_6505,hAPP(c_COMBC(U_6505,U_6505,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_6505))) = c_Orderings_Oord__class_Omin(U_6505)
    | ~ class_Orderings_Olinorder(U_6505) ),
    inference(clausify,[status(thm)],[f_1928_3]) ).

fof(f_1929_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_1929_2,plain,
    ! [U_6506] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_6506)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_6506)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_1929_1]) ).

fof(f_1929_3,plain,
    ! [U_6506] : hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_6506)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_6506)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_1929_2]) ).

cnf(f_1929_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),c_Code__Numeral_OSuc__code__numeral(U_6506)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Code__Numeral_Ocode__numeral),U_6506)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_1929_3]) ).

fof(f_1930_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_1930_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_1930_1]) ).

cnf(f_1930_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_1930_2]) ).

fof(f_1931_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_1931_2,plain,
    ! [U_6510,U_6509,U_6508] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6508),U_6509),U_6510))
      | ? [U_6507] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6508),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6508),U_6507),U_6509)),U_6510))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6508),U_6507),c_Groups_Oone__class_Oone(U_6508)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6508),c_Groups_Ozero__class_Ozero(U_6508)),U_6507)) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_6508) ),
    inference(variable_rename,[status(thm)],[f_1931_1]) ).

fof(f_1931_3,plain,
    ! [U_6510,U_6509,U_6508] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6508),U_6509),U_6510))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6508),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6508),sK83(U_6510,U_6509,U_6508)),U_6509)),U_6510))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6508),sK83(U_6510,U_6509,U_6508)),c_Groups_Oone__class_Oone(U_6508)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6508),c_Groups_Ozero__class_Ozero(U_6508)),sK83(U_6510,U_6509,U_6508))) )
      | ~ class_Fields_Olinordered__field__inverse__zero(U_6508) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK83]),skolemize(U_6507,sK83(U_6510,U_6509,U_6508))],[f_1931_2]) ).

fof(f_1931_4,plain,
    ( ! [U_6508,U_6509,U_6510] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6508),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6508),sK83(U_6510,U_6509,U_6508)),U_6509)),U_6510))
        | ~ sP604(U_6508,U_6509,U_6510) )
    & ! [U_6508,U_6509,U_6510] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6508),sK83(U_6510,U_6509,U_6508)),c_Groups_Oone__class_Oone(U_6508)))
        | ~ sP604(U_6508,U_6509,U_6510) )
    & ! [U_6508,U_6509,U_6510] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6508),c_Groups_Ozero__class_Ozero(U_6508)),sK83(U_6510,U_6509,U_6508)))
        | ~ sP604(U_6508,U_6509,U_6510) )
    & ! [U_6508,U_6509,U_6510] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6508),U_6509),U_6510))
        | sP604(U_6508,U_6509,U_6510)
        | ~ class_Fields_Olinordered__field__inverse__zero(U_6508) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP604])],[f_1931_3]) ).

cnf(f_1931_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6508),U_6509),U_6510))
    | sP604(U_6508,U_6509,U_6510)
    | ~ class_Fields_Olinordered__field__inverse__zero(U_6508) ),
    inference(clausify,[status(thm)],[f_1931_4]) ).

cnf(f_1931_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6508),c_Groups_Ozero__class_Ozero(U_6508)),sK83(U_6510,U_6509,U_6508)))
    | ~ sP604(U_6508,U_6509,U_6510) ),
    inference(clausify,[status(thm)],[f_1931_4]) ).

cnf(f_1931_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6508),sK83(U_6510,U_6509,U_6508)),c_Groups_Oone__class_Oone(U_6508)))
    | ~ sP604(U_6508,U_6509,U_6510) ),
    inference(clausify,[status(thm)],[f_1931_4]) ).

cnf(f_1931_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6508),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_6508),sK83(U_6510,U_6509,U_6508)),U_6509)),U_6510))
    | ~ sP604(U_6508,U_6509,U_6510) ),
    inference(clausify,[status(thm)],[f_1931_4]) ).

fof(f_1932_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_1932_2,plain,
    ! [U_6512,U_6511] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6511),U_6512),U_6512) = U_6512
      | ~ class_Orderings_Olinorder(U_6511) ),
    inference(variable_rename,[status(thm)],[f_1932_1]) ).

fof(f_1932_3,plain,
    ! [U_6512,U_6511] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6511),U_6512),U_6512) = U_6512
      | ~ class_Orderings_Olinorder(U_6511) ),
    inference(definitional_conversion,[status(esa)],[f_1932_2]) ).

cnf(f_1932_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_6511),U_6512),U_6512) = U_6512
    | ~ class_Orderings_Olinorder(U_6511) ),
    inference(clausify,[status(thm)],[f_1932_3]) ).

fof(f_1933_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_1933_2,plain,
    ! [U_6514,U_6513] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6513),U_6514),U_6514) = U_6514
      | ~ class_Orderings_Olinorder(U_6513) ),
    inference(variable_rename,[status(thm)],[f_1933_1]) ).

fof(f_1933_3,plain,
    ! [U_6513,U_6514] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6513),U_6514),U_6514) = U_6514
      | ~ class_Orderings_Olinorder(U_6513) ),
    inference(definitional_conversion,[status(esa)],[f_1933_2]) ).

cnf(f_1933_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_6513),U_6514),U_6514) = U_6514
    | ~ class_Orderings_Olinorder(U_6513) ),
    inference(clausify,[status(thm)],[f_1933_3]) ).

fof(f_1934_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_1934_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_1934_1]) ).

cnf(f_1934_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_1934_2]) ).

fof(f_1935_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_1935_2,plain,
    ! [U_6518,U_6517,U_6516,U_6515] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_6515,U_6516,U_6517,c_Code__Numeral_OSuc__code__numeral(U_6518)) = hAPP(U_6517,U_6518),
    inference(variable_rename,[status(thm)],[f_1935_1]) ).

fof(f_1935_3,plain,
    ! [U_6515,U_6516,U_6517,U_6518] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_6515,U_6516,U_6517,c_Code__Numeral_OSuc__code__numeral(U_6518)) = hAPP(U_6517,U_6518),
    inference(definitional_conversion,[status(esa)],[f_1935_2]) ).

cnf(f_1935_4,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_6515,U_6516,U_6517,c_Code__Numeral_OSuc__code__numeral(U_6518)) = hAPP(U_6517,U_6518),
    inference(clausify,[status(thm)],[f_1935_3]) ).

fof(f_1936_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_1936_2,plain,
    ! [U_6520,U_6519] :
      ( ( ( ( c_Nitpick_Onorm__frac(U_6520,U_6519) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_6520),U_6519)),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_6520))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6519)))
            | U_6519 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
            | U_6520 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Nitpick_Onorm__frac(U_6520,U_6519) = 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_6519 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & U_6520 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6519),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( c_Nitpick_Onorm__frac(U_6520,U_6519) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6520),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6519))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6519),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_1936_1]) ).

fof(f_1936_3,plain,
    ( ! [U_6524,U_6522] :
        ( ( ( c_Nitpick_Onorm__frac(U_6524,U_6522) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_6524),U_6522)),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_6524))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6522)))
            | U_6522 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
            | U_6524 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
          & ( c_Nitpick_Onorm__frac(U_6524,U_6522) = 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_6522 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              & U_6524 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6522),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_6523,U_6521] :
        ( c_Nitpick_Onorm__frac(U_6523,U_6521) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6523),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6521))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6521),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_1936_2]) ).

fof(f_1936_4,plain,
    ( ! [U_6522,U_6524] :
        ( U_6522 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP605(U_6522,U_6524) )
    & ! [U_6522,U_6524] :
        ( U_6524 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP605(U_6522,U_6524) )
    & ! [U_6522,U_6524] :
        ( c_Nitpick_Onorm__frac(U_6524,U_6522) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_6524),U_6522)),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_6524))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6522)))
        | U_6522 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_6524 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP606(U_6522,U_6524) )
    & ! [U_6522,U_6524] :
        ( c_Nitpick_Onorm__frac(U_6524,U_6522) = 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))
        | sP605(U_6522,U_6524)
        | ~ sP606(U_6522,U_6524) )
    & ! [U_6522,U_6524] :
        ( sP606(U_6522,U_6524)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6522),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_6521,U_6523] :
        ( c_Nitpick_Onorm__frac(U_6523,U_6521) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6523),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6521))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6521),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP605,sP606])],[f_1936_3]) ).

cnf(f_1936_5,plain,
    ( c_Nitpick_Onorm__frac(U_6523,U_6521) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6523),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6521))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6521),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1936_4]) ).

cnf(f_1936_6,plain,
    ( sP606(U_6522,U_6524)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6522),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1936_4]) ).

cnf(f_1936_7,plain,
    ( c_Nitpick_Onorm__frac(U_6524,U_6522) = 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))
    | sP605(U_6522,U_6524)
    | ~ sP606(U_6522,U_6524) ),
    inference(clausify,[status(thm)],[f_1936_4]) ).

cnf(f_1936_8,plain,
    ( c_Nitpick_Onorm__frac(U_6524,U_6522) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_6524),U_6522)),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_6524))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6522)))
    | U_6522 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6524 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP606(U_6522,U_6524) ),
    inference(clausify,[status(thm)],[f_1936_4]) ).

cnf(f_1936_9,plain,
    ( U_6524 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP605(U_6522,U_6524) ),
    inference(clausify,[status(thm)],[f_1936_4]) ).

cnf(f_1936_10,plain,
    ( U_6522 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP605(U_6522,U_6524) ),
    inference(clausify,[status(thm)],[f_1936_4]) ).

fof(f_1937_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_1937_2,plain,
    ! [U_6527,U_6526,U_6525] :
      ( ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_6525,hAPP(hAPP(c_COMBC(U_6525,tc_fun(tc_prod(U_6525,U_6525),tc_HOL_Obool),tc_fun(U_6525,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_6525,tc_fun(tc_fun(tc_prod(U_6525,U_6525),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_6525,U_6525),tc_HOL_Obool),tc_fun(U_6525,tc_HOL_Obool)),U_6525),c_COMBC(U_6525,tc_fun(tc_prod(U_6525,U_6525),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_6525,tc_prod(U_6525,U_6525)),tc_fun(U_6525,tc_fun(tc_fun(tc_prod(U_6525,U_6525),tc_HOL_Obool),tc_HOL_Obool)),U_6525),hAPP(c_COMBB(tc_prod(U_6525,U_6525),tc_fun(tc_fun(tc_prod(U_6525,U_6525),tc_HOL_Obool),tc_HOL_Obool),U_6525),c_member(tc_prod(U_6525,U_6525)))),c_Product__Type_OPair(U_6525,U_6525)))),U_6526)),U_6527))
        | ~ hBOOL(hAPP(hAPP(c_member(U_6525),U_6527),c_Wellfounded_Oacc(U_6525,U_6526))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_6525),U_6527),c_Wellfounded_Oacc(U_6525,U_6526)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_6525,hAPP(hAPP(c_COMBC(U_6525,tc_fun(tc_prod(U_6525,U_6525),tc_HOL_Obool),tc_fun(U_6525,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_6525,tc_fun(tc_fun(tc_prod(U_6525,U_6525),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_6525,U_6525),tc_HOL_Obool),tc_fun(U_6525,tc_HOL_Obool)),U_6525),c_COMBC(U_6525,tc_fun(tc_prod(U_6525,U_6525),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_6525,tc_prod(U_6525,U_6525)),tc_fun(U_6525,tc_fun(tc_fun(tc_prod(U_6525,U_6525),tc_HOL_Obool),tc_HOL_Obool)),U_6525),hAPP(c_COMBB(tc_prod(U_6525,U_6525),tc_fun(tc_fun(tc_prod(U_6525,U_6525),tc_HOL_Obool),tc_HOL_Obool),U_6525),c_member(tc_prod(U_6525,U_6525)))),c_Product__Type_OPair(U_6525,U_6525)))),U_6526)),U_6527)) ) ),
    inference(variable_rename,[status(thm)],[f_1937_1]) ).

fof(f_1937_3,plain,
    ( ! [U_6533,U_6531,U_6529] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_6529,hAPP(hAPP(c_COMBC(U_6529,tc_fun(tc_prod(U_6529,U_6529),tc_HOL_Obool),tc_fun(U_6529,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_6529,tc_fun(tc_fun(tc_prod(U_6529,U_6529),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_6529,U_6529),tc_HOL_Obool),tc_fun(U_6529,tc_HOL_Obool)),U_6529),c_COMBC(U_6529,tc_fun(tc_prod(U_6529,U_6529),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_6529,tc_prod(U_6529,U_6529)),tc_fun(U_6529,tc_fun(tc_fun(tc_prod(U_6529,U_6529),tc_HOL_Obool),tc_HOL_Obool)),U_6529),hAPP(c_COMBB(tc_prod(U_6529,U_6529),tc_fun(tc_fun(tc_prod(U_6529,U_6529),tc_HOL_Obool),tc_HOL_Obool),U_6529),c_member(tc_prod(U_6529,U_6529)))),c_Product__Type_OPair(U_6529,U_6529)))),U_6531)),U_6533))
        | ~ hBOOL(hAPP(hAPP(c_member(U_6529),U_6533),c_Wellfounded_Oacc(U_6529,U_6531))) )
    & ! [U_6532,U_6530,U_6528] :
        ( hBOOL(hAPP(hAPP(c_member(U_6528),U_6532),c_Wellfounded_Oacc(U_6528,U_6530)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_6528,hAPP(hAPP(c_COMBC(U_6528,tc_fun(tc_prod(U_6528,U_6528),tc_HOL_Obool),tc_fun(U_6528,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_6528,tc_fun(tc_fun(tc_prod(U_6528,U_6528),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_6528,U_6528),tc_HOL_Obool),tc_fun(U_6528,tc_HOL_Obool)),U_6528),c_COMBC(U_6528,tc_fun(tc_prod(U_6528,U_6528),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_6528,tc_prod(U_6528,U_6528)),tc_fun(U_6528,tc_fun(tc_fun(tc_prod(U_6528,U_6528),tc_HOL_Obool),tc_HOL_Obool)),U_6528),hAPP(c_COMBB(tc_prod(U_6528,U_6528),tc_fun(tc_fun(tc_prod(U_6528,U_6528),tc_HOL_Obool),tc_HOL_Obool),U_6528),c_member(tc_prod(U_6528,U_6528)))),c_Product__Type_OPair(U_6528,U_6528)))),U_6530)),U_6532)) ) ),
    inference(miniscope,[status(thm)],[f_1937_2]) ).

fof(f_1937_4,plain,
    ( ! [U_6529,U_6531,U_6533] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_6529,hAPP(hAPP(c_COMBC(U_6529,tc_fun(tc_prod(U_6529,U_6529),tc_HOL_Obool),tc_fun(U_6529,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_6529,tc_fun(tc_fun(tc_prod(U_6529,U_6529),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_6529,U_6529),tc_HOL_Obool),tc_fun(U_6529,tc_HOL_Obool)),U_6529),c_COMBC(U_6529,tc_fun(tc_prod(U_6529,U_6529),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_6529,tc_prod(U_6529,U_6529)),tc_fun(U_6529,tc_fun(tc_fun(tc_prod(U_6529,U_6529),tc_HOL_Obool),tc_HOL_Obool)),U_6529),hAPP(c_COMBB(tc_prod(U_6529,U_6529),tc_fun(tc_fun(tc_prod(U_6529,U_6529),tc_HOL_Obool),tc_HOL_Obool),U_6529),c_member(tc_prod(U_6529,U_6529)))),c_Product__Type_OPair(U_6529,U_6529)))),U_6531)),U_6533))
        | ~ hBOOL(hAPP(hAPP(c_member(U_6529),U_6533),c_Wellfounded_Oacc(U_6529,U_6531))) )
    & ! [U_6528,U_6530,U_6532] :
        ( hBOOL(hAPP(hAPP(c_member(U_6528),U_6532),c_Wellfounded_Oacc(U_6528,U_6530)))
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_6528,hAPP(hAPP(c_COMBC(U_6528,tc_fun(tc_prod(U_6528,U_6528),tc_HOL_Obool),tc_fun(U_6528,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_6528,tc_fun(tc_fun(tc_prod(U_6528,U_6528),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_6528,U_6528),tc_HOL_Obool),tc_fun(U_6528,tc_HOL_Obool)),U_6528),c_COMBC(U_6528,tc_fun(tc_prod(U_6528,U_6528),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_6528,tc_prod(U_6528,U_6528)),tc_fun(U_6528,tc_fun(tc_fun(tc_prod(U_6528,U_6528),tc_HOL_Obool),tc_HOL_Obool)),U_6528),hAPP(c_COMBB(tc_prod(U_6528,U_6528),tc_fun(tc_fun(tc_prod(U_6528,U_6528),tc_HOL_Obool),tc_HOL_Obool),U_6528),c_member(tc_prod(U_6528,U_6528)))),c_Product__Type_OPair(U_6528,U_6528)))),U_6530)),U_6532)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1937_3]) ).

cnf(f_1937_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6528),U_6532),c_Wellfounded_Oacc(U_6528,U_6530)))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_6528,hAPP(hAPP(c_COMBC(U_6528,tc_fun(tc_prod(U_6528,U_6528),tc_HOL_Obool),tc_fun(U_6528,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_6528,tc_fun(tc_fun(tc_prod(U_6528,U_6528),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_6528,U_6528),tc_HOL_Obool),tc_fun(U_6528,tc_HOL_Obool)),U_6528),c_COMBC(U_6528,tc_fun(tc_prod(U_6528,U_6528),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_6528,tc_prod(U_6528,U_6528)),tc_fun(U_6528,tc_fun(tc_fun(tc_prod(U_6528,U_6528),tc_HOL_Obool),tc_HOL_Obool)),U_6528),hAPP(c_COMBB(tc_prod(U_6528,U_6528),tc_fun(tc_fun(tc_prod(U_6528,U_6528),tc_HOL_Obool),tc_HOL_Obool),U_6528),c_member(tc_prod(U_6528,U_6528)))),c_Product__Type_OPair(U_6528,U_6528)))),U_6530)),U_6532)) ),
    inference(clausify,[status(thm)],[f_1937_4]) ).

cnf(f_1937_6,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_6529,hAPP(hAPP(c_COMBC(U_6529,tc_fun(tc_prod(U_6529,U_6529),tc_HOL_Obool),tc_fun(U_6529,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_6529,tc_fun(tc_fun(tc_prod(U_6529,U_6529),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_6529,U_6529),tc_HOL_Obool),tc_fun(U_6529,tc_HOL_Obool)),U_6529),c_COMBC(U_6529,tc_fun(tc_prod(U_6529,U_6529),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_6529,tc_prod(U_6529,U_6529)),tc_fun(U_6529,tc_fun(tc_fun(tc_prod(U_6529,U_6529),tc_HOL_Obool),tc_HOL_Obool)),U_6529),hAPP(c_COMBB(tc_prod(U_6529,U_6529),tc_fun(tc_fun(tc_prod(U_6529,U_6529),tc_HOL_Obool),tc_HOL_Obool),U_6529),c_member(tc_prod(U_6529,U_6529)))),c_Product__Type_OPair(U_6529,U_6529)))),U_6531)),U_6533))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6529),U_6533),c_Wellfounded_Oacc(U_6529,U_6531))) ),
    inference(clausify,[status(thm)],[f_1937_4]) ).

fof(f_1938_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_1938_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_1938_1]) ).

cnf(f_1938_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_1938_2]) ).

fof(f_1939_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_1939_2,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_1939_1]) ).

cnf(f_1939_3,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1939_2]) ).

fof(f_1940_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_1940_2,plain,
    ! [U_6535,U_6534] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6534),U_6535))
      | ~ c_Nat__Transfer_Ois__nat(U_6535)
      | ~ c_Nat__Transfer_Ois__nat(U_6534) ),
    inference(variable_rename,[status(thm)],[f_1940_1]) ).

fof(f_1940_3,plain,
    ! [U_6534,U_6535] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6534),U_6535))
      | ~ c_Nat__Transfer_Ois__nat(U_6535)
      | ~ c_Nat__Transfer_Ois__nat(U_6534) ),
    inference(definitional_conversion,[status(esa)],[f_1940_2]) ).

cnf(f_1940_4,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_6534),U_6535))
    | ~ c_Nat__Transfer_Ois__nat(U_6535)
    | ~ c_Nat__Transfer_Ois__nat(U_6534) ),
    inference(clausify,[status(thm)],[f_1940_3]) ).

fof(f_1941_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_1941_2,plain,
    ! [U_6536] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6536)),
    inference(variable_rename,[status(thm)],[f_1941_1]) ).

fof(f_1941_3,plain,
    ! [U_6536] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6536)),
    inference(definitional_conversion,[status(esa)],[f_1941_2]) ).

cnf(f_1941_4,plain,
    c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6536)),
    inference(clausify,[status(thm)],[f_1941_3]) ).

fof(f_1942_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_1942_2,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_1942_1]) ).

cnf(f_1942_3,plain,
    c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_1942_2]) ).

fof(f_1943_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_1943_2,plain,
    ! [U_6538,U_6537] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6537),U_6538))
      | ~ c_Nat__Transfer_Ois__nat(U_6538)
      | ~ c_Nat__Transfer_Ois__nat(U_6537) ),
    inference(variable_rename,[status(thm)],[f_1943_1]) ).

fof(f_1943_3,plain,
    ! [U_6537,U_6538] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6537),U_6538))
      | ~ c_Nat__Transfer_Ois__nat(U_6538)
      | ~ c_Nat__Transfer_Ois__nat(U_6537) ),
    inference(definitional_conversion,[status(esa)],[f_1943_2]) ).

cnf(f_1943_4,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_6537),U_6538))
    | ~ c_Nat__Transfer_Ois__nat(U_6538)
    | ~ c_Nat__Transfer_Ois__nat(U_6537) ),
    inference(clausify,[status(thm)],[f_1943_3]) ).

fof(f_1944_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_1944_2,plain,
    ! [U_6540,U_6539] :
      ( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6539,U_6540))
      | ~ c_Nat__Transfer_Ois__nat(U_6540)
      | ~ c_Nat__Transfer_Ois__nat(U_6539) ),
    inference(variable_rename,[status(thm)],[f_1944_1]) ).

fof(f_1944_3,plain,
    ! [U_6540,U_6539] :
      ( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6539,U_6540))
      | ~ c_Nat__Transfer_Ois__nat(U_6540)
      | ~ c_Nat__Transfer_Ois__nat(U_6539) ),
    inference(definitional_conversion,[status(esa)],[f_1944_2]) ).

cnf(f_1944_4,plain,
    ( c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,U_6539,U_6540))
    | ~ c_Nat__Transfer_Ois__nat(U_6540)
    | ~ c_Nat__Transfer_Ois__nat(U_6539) ),
    inference(clausify,[status(thm)],[f_1944_3]) ).

fof(f_1945_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_1945_2,plain,
    ! [U_6542,U_6541] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6541),U_6542))
      | ~ c_Nat__Transfer_Ois__nat(U_6542)
      | ~ c_Nat__Transfer_Ois__nat(U_6541) ),
    inference(variable_rename,[status(thm)],[f_1945_1]) ).

fof(f_1945_3,plain,
    ! [U_6542,U_6541] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6541),U_6542))
      | ~ c_Nat__Transfer_Ois__nat(U_6542)
      | ~ c_Nat__Transfer_Ois__nat(U_6541) ),
    inference(definitional_conversion,[status(esa)],[f_1945_2]) ).

cnf(f_1945_4,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6541),U_6542))
    | ~ c_Nat__Transfer_Ois__nat(U_6542)
    | ~ c_Nat__Transfer_Ois__nat(U_6541) ),
    inference(clausify,[status(thm)],[f_1945_3]) ).

fof(f_1946_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_1946_2,plain,
    ! [U_6544,U_6543] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6543),U_6544))
      | ~ c_Nat__Transfer_Ois__nat(U_6543) ),
    inference(variable_rename,[status(thm)],[f_1946_1]) ).

fof(f_1946_3,plain,
    ! [U_6543,U_6544] :
      ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6543),U_6544))
      | ~ c_Nat__Transfer_Ois__nat(U_6543) ),
    inference(definitional_conversion,[status(esa)],[f_1946_2]) ).

cnf(f_1946_4,plain,
    ( c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),U_6543),U_6544))
    | ~ c_Nat__Transfer_Ois__nat(U_6543) ),
    inference(clausify,[status(thm)],[f_1946_3]) ).

fof(f_1947_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_1947_2,plain,
    ! [U_6546,U_6545] :
      ( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_6545,U_6546))
      | ~ c_Nat__Transfer_Ois__nat(U_6546)
      | ~ c_Nat__Transfer_Ois__nat(U_6545) ),
    inference(variable_rename,[status(thm)],[f_1947_1]) ).

fof(f_1947_3,plain,
    ! [U_6545,U_6546] :
      ( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_6545,U_6546))
      | ~ c_Nat__Transfer_Ois__nat(U_6546)
      | ~ c_Nat__Transfer_Ois__nat(U_6545) ),
    inference(definitional_conversion,[status(esa)],[f_1947_2]) ).

cnf(f_1947_4,plain,
    ( c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(U_6545,U_6546))
    | ~ c_Nat__Transfer_Ois__nat(U_6546)
    | ~ c_Nat__Transfer_Ois__nat(U_6545) ),
    inference(clausify,[status(thm)],[f_1947_3]) ).

fof(f_1948_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_1948_2,plain,
    ! [U_6547] :
      ( ( c_Nat__Transfer_Ois__nat(U_6547)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6547)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6547))
        | ~ c_Nat__Transfer_Ois__nat(U_6547) ) ),
    inference(variable_rename,[status(thm)],[f_1948_1]) ).

fof(f_1948_3,plain,
    ( ! [U_6549] :
        ( c_Nat__Transfer_Ois__nat(U_6549)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6549)) )
    & ! [U_6548] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6548))
        | ~ c_Nat__Transfer_Ois__nat(U_6548) ) ),
    inference(miniscope,[status(thm)],[f_1948_2]) ).

fof(f_1948_4,plain,
    ( ! [U_6549] :
        ( c_Nat__Transfer_Ois__nat(U_6549)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6549)) )
    & ! [U_6548] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6548))
        | ~ c_Nat__Transfer_Ois__nat(U_6548) ) ),
    inference(definitional_conversion,[status(esa)],[f_1948_3]) ).

cnf(f_1948_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6548))
    | ~ c_Nat__Transfer_Ois__nat(U_6548) ),
    inference(clausify,[status(thm)],[f_1948_4]) ).

cnf(f_1948_6,plain,
    ( c_Nat__Transfer_Ois__nat(U_6549)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6549)) ),
    inference(clausify,[status(thm)],[f_1948_4]) ).

fof(f_1949_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_1949_2,plain,
    ! [U_6552,U_6551,U_6550] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6550,tc_HOL_Obool)),c_Wellfounded_Oacc(U_6550,U_6552)),c_Wellfounded_Oacc(U_6550,U_6551)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_6550,U_6550),tc_HOL_Obool)),U_6551),U_6552)) ),
    inference(variable_rename,[status(thm)],[f_1949_1]) ).

fof(f_1949_3,plain,
    ! [U_6550,U_6551,U_6552] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6550,tc_HOL_Obool)),c_Wellfounded_Oacc(U_6550,U_6552)),c_Wellfounded_Oacc(U_6550,U_6551)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_6550,U_6550),tc_HOL_Obool)),U_6551),U_6552)) ),
    inference(definitional_conversion,[status(esa)],[f_1949_2]) ).

cnf(f_1949_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6550,tc_HOL_Obool)),c_Wellfounded_Oacc(U_6550,U_6552)),c_Wellfounded_Oacc(U_6550,U_6551)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_6550,U_6550),tc_HOL_Obool)),U_6551),U_6552)) ),
    inference(clausify,[status(thm)],[f_1949_3]) ).

fof(f_1950_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_1950_2,plain,
    ! [U_6557,U_6556,U_6555] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_6555),U_6556),c_Wellfounded_Oacc(U_6555,U_6557)))
        | ? [U_6554] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_6555),U_6554),c_Wellfounded_Oacc(U_6555,U_6557)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_6555,U_6555)),hAPP(hAPP(c_Product__Type_OPair(U_6555,U_6555),U_6554),U_6556)),U_6557)) ) )
      & ( ! [U_6553] :
            ( hBOOL(hAPP(hAPP(c_member(U_6555),U_6553),c_Wellfounded_Oacc(U_6555,U_6557)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_6555,U_6555)),hAPP(hAPP(c_Product__Type_OPair(U_6555,U_6555),U_6553),U_6556)),U_6557)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_6555),U_6556),c_Wellfounded_Oacc(U_6555,U_6557))) ) ),
    inference(variable_rename,[status(thm)],[f_1950_1]) ).

fof(f_1950_3,plain,
    ( ! [U_6563,U_6561,U_6559] :
        ( hBOOL(hAPP(hAPP(c_member(U_6559),U_6561),c_Wellfounded_Oacc(U_6559,U_6563)))
        | ? [U_6554] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_6559),U_6554),c_Wellfounded_Oacc(U_6559,U_6563)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_6559,U_6559)),hAPP(hAPP(c_Product__Type_OPair(U_6559,U_6559),U_6554),U_6561)),U_6563)) ) )
    & ! [U_6562,U_6560,U_6558] :
        ( ! [U_6553] :
            ( hBOOL(hAPP(hAPP(c_member(U_6558),U_6553),c_Wellfounded_Oacc(U_6558,U_6562)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_6558,U_6558)),hAPP(hAPP(c_Product__Type_OPair(U_6558,U_6558),U_6553),U_6560)),U_6562)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_6558),U_6560),c_Wellfounded_Oacc(U_6558,U_6562))) ) ),
    inference(miniscope,[status(thm)],[f_1950_2]) ).

fof(f_1950_4,plain,
    ( ! [U_6563,U_6561,U_6559] :
        ( hBOOL(hAPP(hAPP(c_member(U_6559),U_6561),c_Wellfounded_Oacc(U_6559,U_6563)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_6559),sK84(U_6563,U_6561,U_6559)),c_Wellfounded_Oacc(U_6559,U_6563)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_6559,U_6559)),hAPP(hAPP(c_Product__Type_OPair(U_6559,U_6559),sK84(U_6563,U_6561,U_6559)),U_6561)),U_6563)) ) )
    & ! [U_6562,U_6560,U_6558] :
        ( ! [U_6553] :
            ( hBOOL(hAPP(hAPP(c_member(U_6558),U_6553),c_Wellfounded_Oacc(U_6558,U_6562)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_6558,U_6558)),hAPP(hAPP(c_Product__Type_OPair(U_6558,U_6558),U_6553),U_6560)),U_6562)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_6558),U_6560),c_Wellfounded_Oacc(U_6558,U_6562))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK84]),skolemize(U_6554,sK84(U_6563,U_6561,U_6559))],[f_1950_3]) ).

fof(f_1950_5,plain,
    ( ! [U_6559,U_6561,U_6563] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_6559),sK84(U_6563,U_6561,U_6559)),c_Wellfounded_Oacc(U_6559,U_6563)))
        | ~ sP607(U_6559,U_6561,U_6563) )
    & ! [U_6559,U_6561,U_6563] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_6559,U_6559)),hAPP(hAPP(c_Product__Type_OPair(U_6559,U_6559),sK84(U_6563,U_6561,U_6559)),U_6561)),U_6563))
        | ~ sP607(U_6559,U_6561,U_6563) )
    & ! [U_6559,U_6561,U_6563] :
        ( hBOOL(hAPP(hAPP(c_member(U_6559),U_6561),c_Wellfounded_Oacc(U_6559,U_6563)))
        | sP607(U_6559,U_6561,U_6563) )
    & ! [U_6560,U_6553,U_6558,U_6562] :
        ( hBOOL(hAPP(hAPP(c_member(U_6558),U_6553),c_Wellfounded_Oacc(U_6558,U_6562)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_6558,U_6558)),hAPP(hAPP(c_Product__Type_OPair(U_6558,U_6558),U_6553),U_6560)),U_6562))
        | ~ hBOOL(hAPP(hAPP(c_member(U_6558),U_6560),c_Wellfounded_Oacc(U_6558,U_6562))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP607])],[f_1950_4]) ).

cnf(f_1950_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6558),U_6553),c_Wellfounded_Oacc(U_6558,U_6562)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_6558,U_6558)),hAPP(hAPP(c_Product__Type_OPair(U_6558,U_6558),U_6553),U_6560)),U_6562))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6558),U_6560),c_Wellfounded_Oacc(U_6558,U_6562))) ),
    inference(clausify,[status(thm)],[f_1950_5]) ).

cnf(f_1950_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6559),U_6561),c_Wellfounded_Oacc(U_6559,U_6563)))
    | sP607(U_6559,U_6561,U_6563) ),
    inference(clausify,[status(thm)],[f_1950_5]) ).

cnf(f_1950_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_6559,U_6559)),hAPP(hAPP(c_Product__Type_OPair(U_6559,U_6559),sK84(U_6563,U_6561,U_6559)),U_6561)),U_6563))
    | ~ sP607(U_6559,U_6561,U_6563) ),
    inference(clausify,[status(thm)],[f_1950_5]) ).

cnf(f_1950_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_6559),sK84(U_6563,U_6561,U_6559)),c_Wellfounded_Oacc(U_6559,U_6563)))
    | ~ sP607(U_6559,U_6561,U_6563) ),
    inference(clausify,[status(thm)],[f_1950_5]) ).

fof(f_1951_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_1951_2,plain,
    ! [U_6567,U_6566,U_6565,U_6564] :
      ( hBOOL(hAPP(hAPP(c_member(U_6564),U_6567),c_Wellfounded_Oacc(U_6564,U_6566)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_6564,U_6564)),hAPP(hAPP(c_Product__Type_OPair(U_6564,U_6564),U_6567),U_6565)),U_6566))
      | ~ hBOOL(hAPP(hAPP(c_member(U_6564),U_6565),c_Wellfounded_Oacc(U_6564,U_6566))) ),
    inference(variable_rename,[status(thm)],[f_1951_1]) ).

fof(f_1951_3,plain,
    ! [U_6565,U_6564,U_6566,U_6567] :
      ( hBOOL(hAPP(hAPP(c_member(U_6564),U_6567),c_Wellfounded_Oacc(U_6564,U_6566)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_6564,U_6564)),hAPP(hAPP(c_Product__Type_OPair(U_6564,U_6564),U_6567),U_6565)),U_6566))
      | ~ hBOOL(hAPP(hAPP(c_member(U_6564),U_6565),c_Wellfounded_Oacc(U_6564,U_6566))) ),
    inference(definitional_conversion,[status(esa)],[f_1951_2]) ).

cnf(f_1951_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6564),U_6567),c_Wellfounded_Oacc(U_6564,U_6566)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_6564,U_6564)),hAPP(hAPP(c_Product__Type_OPair(U_6564,U_6564),U_6567),U_6565)),U_6566))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6564),U_6565),c_Wellfounded_Oacc(U_6564,U_6566))) ),
    inference(clausify,[status(thm)],[f_1951_3]) ).

fof(f_1952_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_1952_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_1952_1]) ).

cnf(f_1952_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_1952_2]) ).

fof(f_1953_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_1953_2,plain,
    ! [U_6570,U_6569,U_6568] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_6568,U_6569,U_6570,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_6569,
    inference(variable_rename,[status(thm)],[f_1953_1]) ).

fof(f_1953_3,plain,
    ! [U_6569,U_6568,U_6570] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_6568,U_6569,U_6570,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_6569,
    inference(definitional_conversion,[status(esa)],[f_1953_2]) ).

cnf(f_1953_4,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__case(U_6568,U_6569,U_6570,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_6569,
    inference(clausify,[status(thm)],[f_1953_3]) ).

fof(f_1954_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_1954_2,plain,
    ! [U_6572,U_6571] :
      ( ( ( ( ( c_Nitpick_Onorm__frac(U_6571,U_6572) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_6571),U_6572)),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_6571))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6572)))
              | U_6572 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
              | U_6571 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
            & ( c_Nitpick_Onorm__frac(U_6571,U_6572) = 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_6572 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
                & U_6571 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) )
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6572),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
        & ( c_Nitpick_Onorm__frac(U_6571,U_6572) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6571),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6572))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6572),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_6571),U_6572))) ),
    inference(variable_rename,[status(thm)],[f_1954_1]) ).

fof(f_1954_3,plain,
    ( ! [U_6571,U_6572] :
        ( U_6572 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP608(U_6571,U_6572) )
    & ! [U_6571,U_6572] :
        ( U_6571 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP608(U_6571,U_6572) )
    & ! [U_6571,U_6572] :
        ( c_Nitpick_Onorm__frac(U_6571,U_6572) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_6571),U_6572)),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_6571))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6572)))
        | U_6572 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | U_6571 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
        | ~ sP609(U_6571,U_6572) )
    & ! [U_6571,U_6572] :
        ( c_Nitpick_Onorm__frac(U_6571,U_6572) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
        | sP608(U_6571,U_6572)
        | ~ sP609(U_6571,U_6572) )
    & ! [U_6571,U_6572] :
        ( sP609(U_6571,U_6572)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6572),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP610(U_6571,U_6572) )
    & ! [U_6571,U_6572] :
        ( c_Nitpick_Onorm__frac(U_6571,U_6572) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6571),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6572))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6572),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP610(U_6571,U_6572) )
    & ! [U_6571,U_6572] :
        ( sP610(U_6571,U_6572)
        | ~ 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_6571),U_6572))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP608,sP609,sP610])],[f_1954_2]) ).

cnf(f_1954_4,plain,
    ( sP610(U_6571,U_6572)
    | ~ 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_6571),U_6572))) ),
    inference(clausify,[status(thm)],[f_1954_3]) ).

cnf(f_1954_5,plain,
    ( c_Nitpick_Onorm__frac(U_6571,U_6572) = c_Nitpick_Onorm__frac(hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6571),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6572))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6572),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP610(U_6571,U_6572) ),
    inference(clausify,[status(thm)],[f_1954_3]) ).

cnf(f_1954_6,plain,
    ( sP609(U_6571,U_6572)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6572),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP610(U_6571,U_6572) ),
    inference(clausify,[status(thm)],[f_1954_3]) ).

cnf(f_1954_7,plain,
    ( c_Nitpick_Onorm__frac(U_6571,U_6572) = hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),c_Groups_Oone__class_Oone(tc_Int_Oint))
    | sP608(U_6571,U_6572)
    | ~ sP609(U_6571,U_6572) ),
    inference(clausify,[status(thm)],[f_1954_3]) ).

cnf(f_1954_8,plain,
    ( c_Nitpick_Onorm__frac(U_6571,U_6572) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,tc_prod(tc_Int_Oint,tc_Int_Oint)),hAPP(hAPP(c_Nitpick_Oint__gcd,U_6571),U_6572)),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_6571))),hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_6572)))
    | U_6572 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | U_6571 = c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP609(U_6571,U_6572) ),
    inference(clausify,[status(thm)],[f_1954_3]) ).

cnf(f_1954_9,plain,
    ( U_6571 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP608(U_6571,U_6572) ),
    inference(clausify,[status(thm)],[f_1954_3]) ).

cnf(f_1954_10,plain,
    ( U_6572 != c_Groups_Ozero__class_Ozero(tc_Int_Oint)
    | ~ sP608(U_6571,U_6572) ),
    inference(clausify,[status(thm)],[f_1954_3]) ).

fof(f_1955_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_1955_2,plain,
    ! [U_6576,U_6575] :
      ( ( c_Nitpick_Orefl_H(U_6575,U_6576)
        | ? [U_6574] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_6575,U_6575)),hAPP(hAPP(c_Product__Type_OPair(U_6575,U_6575),U_6574),U_6574)),U_6576)) )
      & ( ! [U_6573] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_6575,U_6575)),hAPP(hAPP(c_Product__Type_OPair(U_6575,U_6575),U_6573),U_6573)),U_6576))
        | ~ c_Nitpick_Orefl_H(U_6575,U_6576) ) ),
    inference(variable_rename,[status(thm)],[f_1955_1]) ).

fof(f_1955_3,plain,
    ( ! [U_6580,U_6578] :
        ( c_Nitpick_Orefl_H(U_6578,U_6580)
        | ? [U_6574] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_6578,U_6578)),hAPP(hAPP(c_Product__Type_OPair(U_6578,U_6578),U_6574),U_6574)),U_6580)) )
    & ! [U_6579,U_6577] :
        ( ! [U_6573] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_6577,U_6577)),hAPP(hAPP(c_Product__Type_OPair(U_6577,U_6577),U_6573),U_6573)),U_6579))
        | ~ c_Nitpick_Orefl_H(U_6577,U_6579) ) ),
    inference(miniscope,[status(thm)],[f_1955_2]) ).

fof(f_1955_4,plain,
    ( ! [U_6580,U_6578] :
        ( c_Nitpick_Orefl_H(U_6578,U_6580)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_6578,U_6578)),hAPP(hAPP(c_Product__Type_OPair(U_6578,U_6578),sK85(U_6580,U_6578)),sK85(U_6580,U_6578))),U_6580)) )
    & ! [U_6579,U_6577] :
        ( ! [U_6573] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_6577,U_6577)),hAPP(hAPP(c_Product__Type_OPair(U_6577,U_6577),U_6573),U_6573)),U_6579))
        | ~ c_Nitpick_Orefl_H(U_6577,U_6579) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK85]),skolemize(U_6574,sK85(U_6580,U_6578))],[f_1955_3]) ).

fof(f_1955_5,plain,
    ( ! [U_6578,U_6580] :
        ( c_Nitpick_Orefl_H(U_6578,U_6580)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_6578,U_6578)),hAPP(hAPP(c_Product__Type_OPair(U_6578,U_6578),sK85(U_6580,U_6578)),sK85(U_6580,U_6578))),U_6580)) )
    & ! [U_6577,U_6573,U_6579] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_6577,U_6577)),hAPP(hAPP(c_Product__Type_OPair(U_6577,U_6577),U_6573),U_6573)),U_6579))
        | ~ c_Nitpick_Orefl_H(U_6577,U_6579) ) ),
    inference(definitional_conversion,[status(esa)],[f_1955_4]) ).

cnf(f_1955_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_6577,U_6577)),hAPP(hAPP(c_Product__Type_OPair(U_6577,U_6577),U_6573),U_6573)),U_6579))
    | ~ c_Nitpick_Orefl_H(U_6577,U_6579) ),
    inference(clausify,[status(thm)],[f_1955_5]) ).

cnf(f_1955_7,plain,
    ( c_Nitpick_Orefl_H(U_6578,U_6580)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_6578,U_6578)),hAPP(hAPP(c_Product__Type_OPair(U_6578,U_6578),sK85(U_6580,U_6578)),sK85(U_6580,U_6578))),U_6580)) ),
    inference(clausify,[status(thm)],[f_1955_5]) ).

fof(f_1956_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_1956_2,plain,
    ! [U_6582,U_6581] : hAPP(hAPP(c_Nitpick_Oint__gcd,U_6581),U_6582) = 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_6581)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6582)))),
    inference(variable_rename,[status(thm)],[f_1956_1]) ).

fof(f_1956_3,plain,
    ! [U_6581,U_6582] : hAPP(hAPP(c_Nitpick_Oint__gcd,U_6581),U_6582) = 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_6581)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6582)))),
    inference(definitional_conversion,[status(esa)],[f_1956_2]) ).

cnf(f_1956_4,plain,
    hAPP(hAPP(c_Nitpick_Oint__gcd,U_6581),U_6582) = 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_6581)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6582)))),
    inference(clausify,[status(thm)],[f_1956_3]) ).

fof(f_1957_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_1957_2,plain,
    ! [U_6584,U_6583] : c_Nitpick_Oint__lcm(U_6583,U_6584) = 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_6583)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6584)))),
    inference(variable_rename,[status(thm)],[f_1957_1]) ).

fof(f_1957_3,plain,
    ! [U_6583,U_6584] : c_Nitpick_Oint__lcm(U_6583,U_6584) = 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_6583)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6584)))),
    inference(definitional_conversion,[status(esa)],[f_1957_2]) ).

cnf(f_1957_4,plain,
    c_Nitpick_Oint__lcm(U_6583,U_6584) = 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_6583)),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_6584)))),
    inference(clausify,[status(thm)],[f_1957_3]) ).

fof(f_1958_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_1958_2,plain,
    ! [U_6585] : c_Nitpick_Ozero__frac(U_6585) = c_Nitpick_OAbs__Frac(U_6585,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_1958_1]) ).

fof(f_1958_3,plain,
    ! [U_6585] : c_Nitpick_Ozero__frac(U_6585) = c_Nitpick_OAbs__Frac(U_6585,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_1958_2]) ).

cnf(f_1958_4,plain,
    c_Nitpick_Ozero__frac(U_6585) = c_Nitpick_OAbs__Frac(U_6585,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_1958_3]) ).

fof(f_1959_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_1959_2,plain,
    ! [U_6587,U_6586] : c_Nitpick_Onat__lcm(U_6586,U_6587) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6586),U_6587)),c_Nitpick_Onat__gcd(U_6586,U_6587)),
    inference(variable_rename,[status(thm)],[f_1959_1]) ).

fof(f_1959_3,plain,
    ! [U_6586,U_6587] : c_Nitpick_Onat__lcm(U_6586,U_6587) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6586),U_6587)),c_Nitpick_Onat__gcd(U_6586,U_6587)),
    inference(definitional_conversion,[status(esa)],[f_1959_2]) ).

cnf(f_1959_4,plain,
    c_Nitpick_Onat__lcm(U_6586,U_6587) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_6586),U_6587)),c_Nitpick_Onat__gcd(U_6586,U_6587)),
    inference(clausify,[status(thm)],[f_1959_3]) ).

fof(f_1960_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_1960_2,plain,
    ! [U_6589,U_6588] :
      ( ( c_Nitpick_Onat__gcd(U_6589,U_6588) = c_Nitpick_Onat__gcd(U_6588,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6589,U_6588))
        | U_6588 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( c_Nitpick_Onat__gcd(U_6589,U_6588) = U_6589
        | U_6588 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_1960_1]) ).

fof(f_1960_3,plain,
    ( ! [U_6593,U_6591] :
        ( c_Nitpick_Onat__gcd(U_6593,U_6591) = c_Nitpick_Onat__gcd(U_6591,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6593,U_6591))
        | U_6591 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_6592,U_6590] :
        ( c_Nitpick_Onat__gcd(U_6592,U_6590) = U_6592
        | U_6590 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_1960_2]) ).

fof(f_1960_4,plain,
    ( ! [U_6591,U_6593] :
        ( c_Nitpick_Onat__gcd(U_6593,U_6591) = c_Nitpick_Onat__gcd(U_6591,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6593,U_6591))
        | U_6591 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_6592,U_6590] :
        ( c_Nitpick_Onat__gcd(U_6592,U_6590) = U_6592
        | U_6590 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_1960_3]) ).

cnf(f_1960_5,plain,
    ( c_Nitpick_Onat__gcd(U_6592,U_6590) = U_6592
    | U_6590 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1960_4]) ).

cnf(f_1960_6,plain,
    ( c_Nitpick_Onat__gcd(U_6593,U_6591) = c_Nitpick_Onat__gcd(U_6591,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6593,U_6591))
    | U_6591 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_1960_4]) ).

fof(f_1961_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_1961_2,plain,
    ! [U_6594] : c_Nitpick_Oone__frac(U_6594) = c_Nitpick_OAbs__Frac(U_6594,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_1961_1]) ).

fof(f_1961_3,plain,
    ! [U_6594] : c_Nitpick_Oone__frac(U_6594) = c_Nitpick_OAbs__Frac(U_6594,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_1961_2]) ).

cnf(f_1961_4,plain,
    c_Nitpick_Oone__frac(U_6594) = c_Nitpick_OAbs__Frac(U_6594,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_1961_3]) ).

fof(f_1962_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_1962_2,plain,
    ! [U_6596,U_6595] : c_Nitpick_Onumber__of__frac(U_6595,U_6596) = c_Nitpick_OAbs__Frac(U_6595,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6596),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_1962_1]) ).

fof(f_1962_3,plain,
    ! [U_6595,U_6596] : c_Nitpick_Onumber__of__frac(U_6595,U_6596) = c_Nitpick_OAbs__Frac(U_6595,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6596),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_1962_2]) ).

cnf(f_1962_4,plain,
    c_Nitpick_Onumber__of__frac(U_6595,U_6596) = c_Nitpick_OAbs__Frac(U_6595,hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_6596),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1962_3]) ).

fof(f_1963_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_1963_2,plain,
    ! [U_6598,U_6597] :
      ( ( ( c_Nitpick_Onat__gcd(U_6597,U_6598) = c_Nitpick_Onat__gcd(U_6598,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6597,U_6598))
          | U_6598 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
        & ( c_Nitpick_Onat__gcd(U_6597,U_6598) = U_6597
          | U_6598 != 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_6597),U_6598))) ),
    inference(variable_rename,[status(thm)],[f_1963_1]) ).

fof(f_1963_3,plain,
    ( ! [U_6597,U_6598] :
        ( c_Nitpick_Onat__gcd(U_6597,U_6598) = c_Nitpick_Onat__gcd(U_6598,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6597,U_6598))
        | U_6598 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP611(U_6597,U_6598) )
    & ! [U_6597,U_6598] :
        ( c_Nitpick_Onat__gcd(U_6597,U_6598) = U_6597
        | U_6598 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP611(U_6597,U_6598) )
    & ! [U_6597,U_6598] :
        ( sP611(U_6597,U_6598)
        | ~ 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_6597),U_6598))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP611])],[f_1963_2]) ).

cnf(f_1963_4,plain,
    ( sP611(U_6597,U_6598)
    | ~ 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_6597),U_6598))) ),
    inference(clausify,[status(thm)],[f_1963_3]) ).

cnf(f_1963_5,plain,
    ( c_Nitpick_Onat__gcd(U_6597,U_6598) = U_6597
    | U_6598 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP611(U_6597,U_6598) ),
    inference(clausify,[status(thm)],[f_1963_3]) ).

cnf(f_1963_6,plain,
    ( c_Nitpick_Onat__gcd(U_6597,U_6598) = c_Nitpick_Onat__gcd(U_6598,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6597,U_6598))
    | U_6598 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP611(U_6597,U_6598) ),
    inference(clausify,[status(thm)],[f_1963_3]) ).

fof(f_1964_1,plain,
    ! [V_Pa_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2))
      | ? [B_a,B_b] :
          ( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_a),B_b))
          & ( hBOOL(hAPP(hAPP(V_Pa_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_1964_2,plain,
    ! [U_6603,U_6602,U_6601] :
      ( hBOOL(hAPP(hAPP(U_6603,U_6601),U_6602))
      | ? [U_6600,U_6599] :
          ( ~ hBOOL(hAPP(hAPP(U_6603,U_6600),U_6599))
          & ( hBOOL(hAPP(hAPP(U_6603,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6600)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6599)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6599),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_6600),U_6599))) )
      | ~ 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_6601),U_6602))) ),
    inference(variable_rename,[status(thm)],[f_1964_1]) ).

fof(f_1964_3,plain,
    ! [U_6603,U_6602,U_6601] :
      ( hBOOL(hAPP(hAPP(U_6603,U_6601),U_6602))
      | ? [U_6599] :
          ( ~ hBOOL(hAPP(hAPP(U_6603,sK86(U_6603,U_6602,U_6601)),U_6599))
          & ( hBOOL(hAPP(hAPP(U_6603,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK86(U_6603,U_6602,U_6601))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_6599)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_6599),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),sK86(U_6603,U_6602,U_6601)),U_6599))) )
      | ~ 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_6601),U_6602))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK86]),skolemize(U_6600,sK86(U_6603,U_6602,U_6601))],[f_1964_2]) ).

fof(f_1964_4,plain,
    ! [U_6603,U_6602,U_6601] :
      ( hBOOL(hAPP(hAPP(U_6603,U_6601),U_6602))
      | ( ~ hBOOL(hAPP(hAPP(U_6603,sK86(U_6603,U_6602,U_6601)),sK87(U_6603,U_6602,U_6601)))
        & ( hBOOL(hAPP(hAPP(U_6603,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK86(U_6603,U_6602,U_6601))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK87(U_6603,U_6602,U_6601))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK87(U_6603,U_6602,U_6601)),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),sK86(U_6603,U_6602,U_6601)),sK87(U_6603,U_6602,U_6601)))) )
      | ~ 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_6601),U_6602))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK87]),skolemize(U_6599,sK87(U_6603,U_6602,U_6601))],[f_1964_3]) ).

fof(f_1964_5,plain,
    ( ! [U_6601,U_6602,U_6603] :
        ( ~ hBOOL(hAPP(hAPP(U_6603,sK86(U_6603,U_6602,U_6601)),sK87(U_6603,U_6602,U_6601)))
        | ~ sP612(U_6601,U_6602,U_6603) )
    & ! [U_6601,U_6602,U_6603] :
        ( hBOOL(hAPP(hAPP(U_6603,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK86(U_6603,U_6602,U_6601))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK87(U_6603,U_6602,U_6601))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK87(U_6603,U_6602,U_6601)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ sP612(U_6601,U_6602,U_6603) )
    & ! [U_6601,U_6602,U_6603] :
        ( 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),sK86(U_6603,U_6602,U_6601)),sK87(U_6603,U_6602,U_6601))))
        | ~ sP612(U_6601,U_6602,U_6603) )
    & ! [U_6601,U_6602,U_6603] :
        ( hBOOL(hAPP(hAPP(U_6603,U_6601),U_6602))
        | sP612(U_6601,U_6602,U_6603)
        | ~ 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_6601),U_6602))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP612])],[f_1964_4]) ).

cnf(f_1964_6,plain,
    ( hBOOL(hAPP(hAPP(U_6603,U_6601),U_6602))
    | sP612(U_6601,U_6602,U_6603)
    | ~ 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_6601),U_6602))) ),
    inference(clausify,[status(thm)],[f_1964_5]) ).

cnf(f_1964_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),sK86(U_6603,U_6602,U_6601)),sK87(U_6603,U_6602,U_6601))))
    | ~ sP612(U_6601,U_6602,U_6603) ),
    inference(clausify,[status(thm)],[f_1964_5]) ).

cnf(f_1964_8,plain,
    ( hBOOL(hAPP(hAPP(U_6603,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK86(U_6603,U_6602,U_6601))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),sK87(U_6603,U_6602,U_6601))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK87(U_6603,U_6602,U_6601)),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ sP612(U_6601,U_6602,U_6603) ),
    inference(clausify,[status(thm)],[f_1964_5]) ).

cnf(f_1964_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_6603,sK86(U_6603,U_6602,U_6601)),sK87(U_6603,U_6602,U_6601)))
    | ~ sP612(U_6601,U_6602,U_6603) ),
    inference(clausify,[status(thm)],[f_1964_5]) ).

fof(f_1965_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_1965_2,plain,
    ! [U_6606,U_6605,U_6604] : hAPP(hAPP(c_Nitpick_Ofrac(U_6604),U_6605),U_6606) = c_Nitpick_OAbs__Frac(U_6604,c_Nitpick_Onorm__frac(U_6605,U_6606)),
    inference(variable_rename,[status(thm)],[f_1965_1]) ).

fof(f_1965_3,plain,
    ! [U_6606,U_6605,U_6604] : hAPP(hAPP(c_Nitpick_Ofrac(U_6604),U_6605),U_6606) = c_Nitpick_OAbs__Frac(U_6604,c_Nitpick_Onorm__frac(U_6605,U_6606)),
    inference(definitional_conversion,[status(esa)],[f_1965_2]) ).

cnf(f_1965_4,plain,
    hAPP(hAPP(c_Nitpick_Ofrac(U_6604),U_6605),U_6606) = c_Nitpick_OAbs__Frac(U_6604,c_Nitpick_Onorm__frac(U_6605,U_6606)),
    inference(clausify,[status(thm)],[f_1965_3]) ).

fof(f_1966_1,plain,
    ! [V_Pa_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2))
      | ? [B_x,B_y] :
          ( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_x),B_y))
          & ( hBOOL(hAPP(hAPP(V_Pa_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_1966_2,plain,
    ! [U_6611,U_6610,U_6609] :
      ( hBOOL(hAPP(hAPP(U_6611,U_6609),U_6610))
      | ? [U_6608,U_6607] :
          ( ~ hBOOL(hAPP(hAPP(U_6611,U_6608),U_6607))
          & ( hBOOL(hAPP(hAPP(U_6611,U_6607),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_6608,U_6607)))
            | U_6607 = 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_6608),U_6607))) )
      | ~ 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_6609),U_6610))) ),
    inference(variable_rename,[status(thm)],[f_1966_1]) ).

fof(f_1966_3,plain,
    ! [U_6611,U_6610,U_6609] :
      ( hBOOL(hAPP(hAPP(U_6611,U_6609),U_6610))
      | ? [U_6607] :
          ( ~ hBOOL(hAPP(hAPP(U_6611,sK88(U_6611,U_6610,U_6609)),U_6607))
          & ( hBOOL(hAPP(hAPP(U_6611,U_6607),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK88(U_6611,U_6610,U_6609),U_6607)))
            | U_6607 = 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),sK88(U_6611,U_6610,U_6609)),U_6607))) )
      | ~ 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_6609),U_6610))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK88]),skolemize(U_6608,sK88(U_6611,U_6610,U_6609))],[f_1966_2]) ).

fof(f_1966_4,plain,
    ! [U_6611,U_6610,U_6609] :
      ( hBOOL(hAPP(hAPP(U_6611,U_6609),U_6610))
      | ( ~ hBOOL(hAPP(hAPP(U_6611,sK88(U_6611,U_6610,U_6609)),sK89(U_6611,U_6610,U_6609)))
        & ( hBOOL(hAPP(hAPP(U_6611,sK89(U_6611,U_6610,U_6609)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK88(U_6611,U_6610,U_6609),sK89(U_6611,U_6610,U_6609))))
          | sK89(U_6611,U_6610,U_6609) = 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),sK88(U_6611,U_6610,U_6609)),sK89(U_6611,U_6610,U_6609)))) )
      | ~ 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_6609),U_6610))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK89]),skolemize(U_6607,sK89(U_6611,U_6610,U_6609))],[f_1966_3]) ).

fof(f_1966_5,plain,
    ( ! [U_6609,U_6610,U_6611] :
        ( ~ hBOOL(hAPP(hAPP(U_6611,sK88(U_6611,U_6610,U_6609)),sK89(U_6611,U_6610,U_6609)))
        | ~ sP613(U_6609,U_6610,U_6611) )
    & ! [U_6609,U_6610,U_6611] :
        ( hBOOL(hAPP(hAPP(U_6611,sK89(U_6611,U_6610,U_6609)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK88(U_6611,U_6610,U_6609),sK89(U_6611,U_6610,U_6609))))
        | sK89(U_6611,U_6610,U_6609) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP613(U_6609,U_6610,U_6611) )
    & ! [U_6609,U_6610,U_6611] :
        ( 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),sK88(U_6611,U_6610,U_6609)),sK89(U_6611,U_6610,U_6609))))
        | ~ sP613(U_6609,U_6610,U_6611) )
    & ! [U_6609,U_6610,U_6611] :
        ( hBOOL(hAPP(hAPP(U_6611,U_6609),U_6610))
        | sP613(U_6609,U_6610,U_6611)
        | ~ 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_6609),U_6610))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP613])],[f_1966_4]) ).

cnf(f_1966_6,plain,
    ( hBOOL(hAPP(hAPP(U_6611,U_6609),U_6610))
    | sP613(U_6609,U_6610,U_6611)
    | ~ 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_6609),U_6610))) ),
    inference(clausify,[status(thm)],[f_1966_5]) ).

cnf(f_1966_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),sK88(U_6611,U_6610,U_6609)),sK89(U_6611,U_6610,U_6609))))
    | ~ sP613(U_6609,U_6610,U_6611) ),
    inference(clausify,[status(thm)],[f_1966_5]) ).

cnf(f_1966_8,plain,
    ( hBOOL(hAPP(hAPP(U_6611,sK89(U_6611,U_6610,U_6609)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,sK88(U_6611,U_6610,U_6609),sK89(U_6611,U_6610,U_6609))))
    | sK89(U_6611,U_6610,U_6609) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP613(U_6609,U_6610,U_6611) ),
    inference(clausify,[status(thm)],[f_1966_5]) ).

cnf(f_1966_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_6611,sK88(U_6611,U_6610,U_6609)),sK89(U_6611,U_6610,U_6609)))
    | ~ sP613(U_6609,U_6610,U_6611) ),
    inference(clausify,[status(thm)],[f_1966_5]) ).

fof(f_1967_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_1967_2,plain,
    ! [U_6619,U_6618,U_6617,U_6616,U_6615,U_6614] :
      ( ? [U_6613,U_6612] :
          ( hBOOL(hAPP(hAPP(c_member(U_6614),U_6615),hAPP(hAPP(U_6618,U_6613),U_6612)))
          & U_6619 = hAPP(hAPP(c_Product__Type_OPair(U_6616,U_6617),U_6613),U_6612) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_6614),U_6615),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6616,U_6617,tc_fun(U_6614,tc_HOL_Obool)),U_6618),U_6619))) ),
    inference(variable_rename,[status(thm)],[f_1967_1]) ).

fof(f_1967_3,plain,
    ! [U_6619,U_6618,U_6617,U_6616,U_6615,U_6614] :
      ( ? [U_6612] :
          ( hBOOL(hAPP(hAPP(c_member(U_6614),U_6615),hAPP(hAPP(U_6618,sK90(U_6619,U_6618,U_6617,U_6616,U_6615,U_6614)),U_6612)))
          & U_6619 = hAPP(hAPP(c_Product__Type_OPair(U_6616,U_6617),sK90(U_6619,U_6618,U_6617,U_6616,U_6615,U_6614)),U_6612) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_6614),U_6615),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6616,U_6617,tc_fun(U_6614,tc_HOL_Obool)),U_6618),U_6619))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK90]),skolemize(U_6613,sK90(U_6619,U_6618,U_6617,U_6616,U_6615,U_6614))],[f_1967_2]) ).

fof(f_1967_4,plain,
    ! [U_6619,U_6618,U_6617,U_6616,U_6615,U_6614] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_6614),U_6615),hAPP(hAPP(U_6618,sK90(U_6619,U_6618,U_6617,U_6616,U_6615,U_6614)),sK91(U_6619,U_6618,U_6617,U_6616,U_6615,U_6614))))
        & U_6619 = hAPP(hAPP(c_Product__Type_OPair(U_6616,U_6617),sK90(U_6619,U_6618,U_6617,U_6616,U_6615,U_6614)),sK91(U_6619,U_6618,U_6617,U_6616,U_6615,U_6614)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_6614),U_6615),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6616,U_6617,tc_fun(U_6614,tc_HOL_Obool)),U_6618),U_6619))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK91]),skolemize(U_6612,sK91(U_6619,U_6618,U_6617,U_6616,U_6615,U_6614))],[f_1967_3]) ).

fof(f_1967_5,plain,
    ( ! [U_6614,U_6616,U_6615,U_6617,U_6618,U_6619] :
        ( hBOOL(hAPP(hAPP(c_member(U_6614),U_6615),hAPP(hAPP(U_6618,sK90(U_6619,U_6618,U_6617,U_6616,U_6615,U_6614)),sK91(U_6619,U_6618,U_6617,U_6616,U_6615,U_6614))))
        | ~ sP614(U_6614,U_6616,U_6615,U_6617,U_6618,U_6619) )
    & ! [U_6614,U_6616,U_6615,U_6617,U_6618,U_6619] :
        ( U_6619 = hAPP(hAPP(c_Product__Type_OPair(U_6616,U_6617),sK90(U_6619,U_6618,U_6617,U_6616,U_6615,U_6614)),sK91(U_6619,U_6618,U_6617,U_6616,U_6615,U_6614))
        | ~ sP614(U_6614,U_6616,U_6615,U_6617,U_6618,U_6619) )
    & ! [U_6614,U_6616,U_6615,U_6617,U_6618,U_6619] :
        ( sP614(U_6614,U_6616,U_6615,U_6617,U_6618,U_6619)
        | ~ hBOOL(hAPP(hAPP(c_member(U_6614),U_6615),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6616,U_6617,tc_fun(U_6614,tc_HOL_Obool)),U_6618),U_6619))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP614])],[f_1967_4]) ).

cnf(f_1967_6,plain,
    ( sP614(U_6614,U_6616,U_6615,U_6617,U_6618,U_6619)
    | ~ hBOOL(hAPP(hAPP(c_member(U_6614),U_6615),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6616,U_6617,tc_fun(U_6614,tc_HOL_Obool)),U_6618),U_6619))) ),
    inference(clausify,[status(thm)],[f_1967_5]) ).

cnf(f_1967_7,plain,
    ( U_6619 = hAPP(hAPP(c_Product__Type_OPair(U_6616,U_6617),sK90(U_6619,U_6618,U_6617,U_6616,U_6615,U_6614)),sK91(U_6619,U_6618,U_6617,U_6616,U_6615,U_6614))
    | ~ sP614(U_6614,U_6616,U_6615,U_6617,U_6618,U_6619) ),
    inference(clausify,[status(thm)],[f_1967_5]) ).

cnf(f_1967_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6614),U_6615),hAPP(hAPP(U_6618,sK90(U_6619,U_6618,U_6617,U_6616,U_6615,U_6614)),sK91(U_6619,U_6618,U_6617,U_6616,U_6615,U_6614))))
    | ~ sP614(U_6614,U_6616,U_6615,U_6617,U_6618,U_6619) ),
    inference(clausify,[status(thm)],[f_1967_5]) ).

fof(f_1968_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_1968_2,plain,
    ! [U_6627,U_6626,U_6625,U_6624,U_6623,U_6622] :
      ( hBOOL(hAPP(hAPP(c_member(U_6625),U_6626),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6623,U_6624,tc_fun(U_6625,tc_HOL_Obool)),U_6627),U_6622)))
      | ? [U_6621,U_6620] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_6625),U_6626),hAPP(hAPP(U_6627,U_6621),U_6620)))
          & U_6622 = hAPP(hAPP(c_Product__Type_OPair(U_6623,U_6624),U_6621),U_6620) ) ),
    inference(variable_rename,[status(thm)],[f_1968_1]) ).

fof(f_1968_3,plain,
    ! [U_6627,U_6626,U_6625,U_6624,U_6623,U_6622] :
      ( hBOOL(hAPP(hAPP(c_member(U_6625),U_6626),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6623,U_6624,tc_fun(U_6625,tc_HOL_Obool)),U_6627),U_6622)))
      | ? [U_6620] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_6625),U_6626),hAPP(hAPP(U_6627,sK92(U_6627,U_6626,U_6625,U_6624,U_6623,U_6622)),U_6620)))
          & U_6622 = hAPP(hAPP(c_Product__Type_OPair(U_6623,U_6624),sK92(U_6627,U_6626,U_6625,U_6624,U_6623,U_6622)),U_6620) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK92]),skolemize(U_6621,sK92(U_6627,U_6626,U_6625,U_6624,U_6623,U_6622))],[f_1968_2]) ).

fof(f_1968_4,plain,
    ! [U_6627,U_6626,U_6625,U_6624,U_6623,U_6622] :
      ( hBOOL(hAPP(hAPP(c_member(U_6625),U_6626),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6623,U_6624,tc_fun(U_6625,tc_HOL_Obool)),U_6627),U_6622)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_6625),U_6626),hAPP(hAPP(U_6627,sK92(U_6627,U_6626,U_6625,U_6624,U_6623,U_6622)),sK93(U_6627,U_6626,U_6625,U_6624,U_6623,U_6622))))
        & U_6622 = hAPP(hAPP(c_Product__Type_OPair(U_6623,U_6624),sK92(U_6627,U_6626,U_6625,U_6624,U_6623,U_6622)),sK93(U_6627,U_6626,U_6625,U_6624,U_6623,U_6622)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK93]),skolemize(U_6620,sK93(U_6627,U_6626,U_6625,U_6624,U_6623,U_6622))],[f_1968_3]) ).

fof(f_1968_5,plain,
    ( ! [U_6623,U_6622,U_6624,U_6625,U_6626,U_6627] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_6625),U_6626),hAPP(hAPP(U_6627,sK92(U_6627,U_6626,U_6625,U_6624,U_6623,U_6622)),sK93(U_6627,U_6626,U_6625,U_6624,U_6623,U_6622))))
        | ~ sP615(U_6623,U_6622,U_6624,U_6625,U_6626,U_6627) )
    & ! [U_6623,U_6622,U_6624,U_6625,U_6626,U_6627] :
        ( U_6622 = hAPP(hAPP(c_Product__Type_OPair(U_6623,U_6624),sK92(U_6627,U_6626,U_6625,U_6624,U_6623,U_6622)),sK93(U_6627,U_6626,U_6625,U_6624,U_6623,U_6622))
        | ~ sP615(U_6623,U_6622,U_6624,U_6625,U_6626,U_6627) )
    & ! [U_6623,U_6622,U_6624,U_6625,U_6626,U_6627] :
        ( hBOOL(hAPP(hAPP(c_member(U_6625),U_6626),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6623,U_6624,tc_fun(U_6625,tc_HOL_Obool)),U_6627),U_6622)))
        | sP615(U_6623,U_6622,U_6624,U_6625,U_6626,U_6627) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP615])],[f_1968_4]) ).

cnf(f_1968_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6625),U_6626),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6623,U_6624,tc_fun(U_6625,tc_HOL_Obool)),U_6627),U_6622)))
    | sP615(U_6623,U_6622,U_6624,U_6625,U_6626,U_6627) ),
    inference(clausify,[status(thm)],[f_1968_5]) ).

cnf(f_1968_7,plain,
    ( U_6622 = hAPP(hAPP(c_Product__Type_OPair(U_6623,U_6624),sK92(U_6627,U_6626,U_6625,U_6624,U_6623,U_6622)),sK93(U_6627,U_6626,U_6625,U_6624,U_6623,U_6622))
    | ~ sP615(U_6623,U_6622,U_6624,U_6625,U_6626,U_6627) ),
    inference(clausify,[status(thm)],[f_1968_5]) ).

cnf(f_1968_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_6625),U_6626),hAPP(hAPP(U_6627,sK92(U_6627,U_6626,U_6625,U_6624,U_6623,U_6622)),sK93(U_6627,U_6626,U_6625,U_6624,U_6623,U_6622))))
    | ~ sP615(U_6623,U_6622,U_6624,U_6625,U_6626,U_6627) ),
    inference(clausify,[status(thm)],[f_1968_5]) ).

fof(f_1969_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_1969_2,plain,
    ! [U_6631,U_6630,U_6629] :
      ( hBOOL(hAPP(hAPP(c_member(U_6629),U_6630),c_Wellfounded_Oacc(U_6629,U_6631)))
      | ? [U_6628] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_6629),U_6628),c_Wellfounded_Oacc(U_6629,U_6631)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_6629,U_6629)),hAPP(hAPP(c_Product__Type_OPair(U_6629,U_6629),U_6628),U_6630)),U_6631)) ) ),
    inference(variable_rename,[status(thm)],[f_1969_1]) ).

fof(f_1969_3,plain,
    ! [U_6631,U_6630,U_6629] :
      ( hBOOL(hAPP(hAPP(c_member(U_6629),U_6630),c_Wellfounded_Oacc(U_6629,U_6631)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_6629),sK94(U_6631,U_6630,U_6629)),c_Wellfounded_Oacc(U_6629,U_6631)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_6629,U_6629)),hAPP(hAPP(c_Product__Type_OPair(U_6629,U_6629),sK94(U_6631,U_6630,U_6629)),U_6630)),U_6631)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK94]),skolemize(U_6628,sK94(U_6631,U_6630,U_6629))],[f_1969_2]) ).

fof(f_1969_4,plain,
    ( ! [U_6629,U_6630,U_6631] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_6629),sK94(U_6631,U_6630,U_6629)),c_Wellfounded_Oacc(U_6629,U_6631)))
        | ~ sP616(U_6629,U_6630,U_6631) )
    & ! [U_6629,U_6630,U_6631] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_6629,U_6629)),hAPP(hAPP(c_Product__Type_OPair(U_6629,U_6629),sK94(U_6631,U_6630,U_6629)),U_6630)),U_6631))
        | ~ sP616(U_6629,U_6630,U_6631) )
    & ! [U_6629,U_6630,U_6631] :
        ( hBOOL(hAPP(hAPP(c_member(U_6629),U_6630),c_Wellfounded_Oacc(U_6629,U_6631)))
        | sP616(U_6629,U_6630,U_6631) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP616])],[f_1969_3]) ).

cnf(f_1969_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6629),U_6630),c_Wellfounded_Oacc(U_6629,U_6631)))
    | sP616(U_6629,U_6630,U_6631) ),
    inference(clausify,[status(thm)],[f_1969_4]) ).

cnf(f_1969_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_6629,U_6629)),hAPP(hAPP(c_Product__Type_OPair(U_6629,U_6629),sK94(U_6631,U_6630,U_6629)),U_6630)),U_6631))
    | ~ sP616(U_6629,U_6630,U_6631) ),
    inference(clausify,[status(thm)],[f_1969_4]) ).

cnf(f_1969_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_6629),sK94(U_6631,U_6630,U_6629)),c_Wellfounded_Oacc(U_6629,U_6631)))
    | ~ sP616(U_6629,U_6630,U_6631) ),
    inference(clausify,[status(thm)],[f_1969_4]) ).

fof(f_1970_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_1970_2,plain,
    ! [U_6635,U_6634,U_6633] :
      ( ? [U_6632] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_6633),U_6632),c_Wellfounded_Oacc(U_6633,U_6635)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_6633,U_6633)),hAPP(hAPP(c_Product__Type_OPair(U_6633,U_6633),U_6632),U_6634)),U_6635)) )
      | hBOOL(hAPP(hAPP(c_member(U_6633),U_6634),c_Wellfounded_Oacc(U_6633,U_6635))) ),
    inference(variable_rename,[status(thm)],[f_1970_1]) ).

fof(f_1970_3,plain,
    ! [U_6635,U_6634,U_6633] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_6633),sK95(U_6635,U_6634,U_6633)),c_Wellfounded_Oacc(U_6633,U_6635)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_6633,U_6633)),hAPP(hAPP(c_Product__Type_OPair(U_6633,U_6633),sK95(U_6635,U_6634,U_6633)),U_6634)),U_6635)) )
      | hBOOL(hAPP(hAPP(c_member(U_6633),U_6634),c_Wellfounded_Oacc(U_6633,U_6635))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK95]),skolemize(U_6632,sK95(U_6635,U_6634,U_6633))],[f_1970_2]) ).

fof(f_1970_4,plain,
    ( ! [U_6633,U_6634,U_6635] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_6633),sK95(U_6635,U_6634,U_6633)),c_Wellfounded_Oacc(U_6633,U_6635)))
        | ~ sP617(U_6633,U_6634,U_6635) )
    & ! [U_6633,U_6634,U_6635] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_6633,U_6633)),hAPP(hAPP(c_Product__Type_OPair(U_6633,U_6633),sK95(U_6635,U_6634,U_6633)),U_6634)),U_6635))
        | ~ sP617(U_6633,U_6634,U_6635) )
    & ! [U_6633,U_6634,U_6635] :
        ( sP617(U_6633,U_6634,U_6635)
        | hBOOL(hAPP(hAPP(c_member(U_6633),U_6634),c_Wellfounded_Oacc(U_6633,U_6635))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP617])],[f_1970_3]) ).

cnf(f_1970_5,plain,
    ( sP617(U_6633,U_6634,U_6635)
    | hBOOL(hAPP(hAPP(c_member(U_6633),U_6634),c_Wellfounded_Oacc(U_6633,U_6635))) ),
    inference(clausify,[status(thm)],[f_1970_4]) ).

cnf(f_1970_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_6633,U_6633)),hAPP(hAPP(c_Product__Type_OPair(U_6633,U_6633),sK95(U_6635,U_6634,U_6633)),U_6634)),U_6635))
    | ~ sP617(U_6633,U_6634,U_6635) ),
    inference(clausify,[status(thm)],[f_1970_4]) ).

cnf(f_1970_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_6633),sK95(U_6635,U_6634,U_6633)),c_Wellfounded_Oacc(U_6633,U_6635)))
    | ~ sP617(U_6633,U_6634,U_6635) ),
    inference(clausify,[status(thm)],[f_1970_4]) ).

fof(f_1971_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_1971_2,plain,
    ! [U_6642,U_6641,U_6640,U_6639,U_6638,U_6637,U_6636] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_6636,U_6637,U_6638,U_6639),U_6640),U_6641),U_6642) = hAPP(hAPP(U_6641,hAPP(c_Product__Type_Ofst(U_6637,U_6638),hAPP(U_6640,U_6642))),hAPP(c_Product__Type_Osnd(U_6637,U_6638),hAPP(U_6640,U_6642))),
    inference(variable_rename,[status(thm)],[f_1971_1]) ).

fof(f_1971_3,plain,
    ! [U_6637,U_6636,U_6638,U_6639,U_6640,U_6641,U_6642] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_6636,U_6637,U_6638,U_6639),U_6640),U_6641),U_6642) = hAPP(hAPP(U_6641,hAPP(c_Product__Type_Ofst(U_6637,U_6638),hAPP(U_6640,U_6642))),hAPP(c_Product__Type_Osnd(U_6637,U_6638),hAPP(U_6640,U_6642))),
    inference(definitional_conversion,[status(esa)],[f_1971_2]) ).

cnf(f_1971_4,plain,
    hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_6636,U_6637,U_6638,U_6639),U_6640),U_6641),U_6642) = hAPP(hAPP(U_6641,hAPP(c_Product__Type_Ofst(U_6637,U_6638),hAPP(U_6640,U_6642))),hAPP(c_Product__Type_Osnd(U_6637,U_6638),hAPP(U_6640,U_6642))),
    inference(clausify,[status(thm)],[f_1971_3]) ).

fof(f_1972_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_1972_2,plain,
    ! [U_6648,U_6647,U_6646,U_6645] :
      ( ? [U_6644] :
          ( hAPP(U_6647,U_6644) = U_6648
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6644),U_6646))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6645),U_6644)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6648),hAPP(U_6647,U_6646)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_6647,U_6645)),U_6648))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6645),U_6646))
      | ? [U_6643] :
          ( ~ 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_6647,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_6643),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_6647,U_6643)))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6643),U_6646))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6645),U_6643)) ) ),
    inference(variable_rename,[status(thm)],[f_1972_1]) ).

fof(f_1972_3,plain,
    ! [U_6648,U_6647,U_6646,U_6645] :
      ( ? [U_6644] :
          ( hAPP(U_6647,U_6644) = U_6648
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6644),U_6646))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6645),U_6644)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6648),hAPP(U_6647,U_6646)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_6647,U_6645)),U_6648))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6645),U_6646))
      | ( ~ 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_6647,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK96(U_6648,U_6647,U_6646,U_6645)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_6647,sK96(U_6648,U_6647,U_6646,U_6645))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK96(U_6648,U_6647,U_6646,U_6645)),U_6646))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6645),sK96(U_6648,U_6647,U_6646,U_6645))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK96]),skolemize(U_6643,sK96(U_6648,U_6647,U_6646,U_6645))],[f_1972_2]) ).

fof(f_1972_4,plain,
    ! [U_6648,U_6647,U_6646,U_6645] :
      ( ( hAPP(U_6647,sK97(U_6648,U_6647,U_6646,U_6645)) = U_6648
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK97(U_6648,U_6647,U_6646,U_6645)),U_6646))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6645),sK97(U_6648,U_6647,U_6646,U_6645))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6648),hAPP(U_6647,U_6646)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_6647,U_6645)),U_6648))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6645),U_6646))
      | ( ~ 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_6647,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK96(U_6648,U_6647,U_6646,U_6645)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_6647,sK96(U_6648,U_6647,U_6646,U_6645))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK96(U_6648,U_6647,U_6646,U_6645)),U_6646))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6645),sK96(U_6648,U_6647,U_6646,U_6645))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK97]),skolemize(U_6644,sK97(U_6648,U_6647,U_6646,U_6645))],[f_1972_3]) ).

fof(f_1972_5,plain,
    ( ! [U_6645,U_6646,U_6647,U_6648] :
        ( hAPP(U_6647,sK97(U_6648,U_6647,U_6646,U_6645)) = U_6648
        | ~ sP619(U_6645,U_6646,U_6647,U_6648) )
    & ! [U_6645,U_6646,U_6647,U_6648] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK97(U_6648,U_6647,U_6646,U_6645)),U_6646))
        | ~ sP619(U_6645,U_6646,U_6647,U_6648) )
    & ! [U_6645,U_6646,U_6647,U_6648] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6645),sK97(U_6648,U_6647,U_6646,U_6645)))
        | ~ sP619(U_6645,U_6646,U_6647,U_6648) )
    & ! [U_6645,U_6646,U_6647,U_6648] :
        ( ~ 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_6647,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK96(U_6648,U_6647,U_6646,U_6645)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_6647,sK96(U_6648,U_6647,U_6646,U_6645))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | ~ sP618(U_6645,U_6646,U_6647,U_6648) )
    & ! [U_6645,U_6646,U_6647,U_6648] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK96(U_6648,U_6647,U_6646,U_6645)),U_6646))
        | ~ sP618(U_6645,U_6646,U_6647,U_6648) )
    & ! [U_6645,U_6646,U_6647,U_6648] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6645),sK96(U_6648,U_6647,U_6646,U_6645)))
        | ~ sP618(U_6645,U_6646,U_6647,U_6648) )
    & ! [U_6645,U_6646,U_6647,U_6648] :
        ( sP619(U_6645,U_6646,U_6647,U_6648)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6648),hAPP(U_6647,U_6646)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_6647,U_6645)),U_6648))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6645),U_6646))
        | sP618(U_6645,U_6646,U_6647,U_6648) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP618,sP619])],[f_1972_4]) ).

cnf(f_1972_6,plain,
    ( sP619(U_6645,U_6646,U_6647,U_6648)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_6648),hAPP(U_6647,U_6646)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(U_6647,U_6645)),U_6648))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_6645),U_6646))
    | sP618(U_6645,U_6646,U_6647,U_6648) ),
    inference(clausify,[status(thm)],[f_1972_5]) ).

cnf(f_1972_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6645),sK96(U_6648,U_6647,U_6646,U_6645)))
    | ~ sP618(U_6645,U_6646,U_6647,U_6648) ),
    inference(clausify,[status(thm)],[f_1972_5]) ).

cnf(f_1972_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK96(U_6648,U_6647,U_6646,U_6645)),U_6646))
    | ~ sP618(U_6645,U_6646,U_6647,U_6648) ),
    inference(clausify,[status(thm)],[f_1972_5]) ).

cnf(f_1972_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_6647,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),sK96(U_6648,U_6647,U_6646,U_6645)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(U_6647,sK96(U_6648,U_6647,U_6646,U_6645))))),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | ~ sP618(U_6645,U_6646,U_6647,U_6648) ),
    inference(clausify,[status(thm)],[f_1972_5]) ).

cnf(f_1972_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_6645),sK97(U_6648,U_6647,U_6646,U_6645)))
    | ~ sP619(U_6645,U_6646,U_6647,U_6648) ),
    inference(clausify,[status(thm)],[f_1972_5]) ).

cnf(f_1972_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK97(U_6648,U_6647,U_6646,U_6645)),U_6646))
    | ~ sP619(U_6645,U_6646,U_6647,U_6648) ),
    inference(clausify,[status(thm)],[f_1972_5]) ).

cnf(f_1972_12,plain,
    ( hAPP(U_6647,sK97(U_6648,U_6647,U_6646,U_6645)) = U_6648
    | ~ sP619(U_6645,U_6646,U_6647,U_6648) ),
    inference(clausify,[status(thm)],[f_1972_5]) ).

fof(f_1973_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_1973_2,plain,
    ! [U_6650,U_6649] :
      ( ( c_Random_Olog(U_6649,U_6650) = 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_6649,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_6650),U_6649)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6650),U_6649))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6649),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
      & ( c_Random_Olog(U_6649,U_6650) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6650),U_6649))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6649),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
    inference(variable_rename,[status(thm)],[f_1973_1]) ).

fof(f_1973_3,plain,
    ( ! [U_6654,U_6652] :
        ( c_Random_Olog(U_6652,U_6654) = 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_6652,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_6654),U_6652)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6654),U_6652))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6652),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
    & ! [U_6653,U_6651] :
        ( c_Random_Olog(U_6651,U_6653) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6653),U_6651))
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6651),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ) ) ),
    inference(miniscope,[status(thm)],[f_1973_2]) ).

fof(f_1973_4,plain,
    ( ! [U_6653,U_6651] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6653),U_6651))
        | ~ sP620(U_6653,U_6651) )
    & ! [U_6653,U_6651] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6651),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
        | ~ sP620(U_6653,U_6651) )
    & ! [U_6652,U_6654] :
        ( c_Random_Olog(U_6652,U_6654) = 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_6652,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_6654),U_6652)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6654),U_6652))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6652),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) )
    & ! [U_6653,U_6651] :
        ( c_Random_Olog(U_6651,U_6653) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | sP620(U_6653,U_6651) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP620])],[f_1973_3]) ).

cnf(f_1973_5,plain,
    ( c_Random_Olog(U_6651,U_6653) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
    | sP620(U_6653,U_6651) ),
    inference(clausify,[status(thm)],[f_1973_4]) ).

cnf(f_1973_6,plain,
    ( c_Random_Olog(U_6652,U_6654) = 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_6652,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_6654),U_6652)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6654),U_6652))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6652),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))) ),
    inference(clausify,[status(thm)],[f_1973_4]) ).

cnf(f_1973_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6651),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))
    | ~ sP620(U_6653,U_6651) ),
    inference(clausify,[status(thm)],[f_1973_4]) ).

cnf(f_1973_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6653),U_6651))
    | ~ sP620(U_6653,U_6651) ),
    inference(clausify,[status(thm)],[f_1973_4]) ).

fof(f_1974_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_1974_2,plain,
    ! [U_6657,U_6656,U_6655] : c_Nitpick_Oplus__frac(U_6655,U_6656,U_6657) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_6655),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(U_6655),U_6656),hAPP(c_Nitpick_Odenom(U_6655),U_6657))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,U_6655),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,U_6655),tc_Int_Oint),c_Nitpick_Ofrac(U_6655)),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_6655),U_6656))),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_6655),U_6656))))),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_6655),U_6657))),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_6655),U_6657)))))),c_COMBI(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_1974_1]) ).

fof(f_1974_3,plain,
    ! [U_6655,U_6656,U_6657] : c_Nitpick_Oplus__frac(U_6655,U_6656,U_6657) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_6655),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(U_6655),U_6656),hAPP(c_Nitpick_Odenom(U_6655),U_6657))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,U_6655),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,U_6655),tc_Int_Oint),c_Nitpick_Ofrac(U_6655)),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_6655),U_6656))),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_6655),U_6656))))),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_6655),U_6657))),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_6655),U_6657)))))),c_COMBI(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_1974_2]) ).

cnf(f_1974_4,plain,
    c_Nitpick_Oplus__frac(U_6655,U_6656,U_6657) = hAPP(hAPP(c_HOL_OLet(tc_Int_Oint,U_6655),c_Nitpick_Oint__lcm(hAPP(c_Nitpick_Odenom(U_6655),U_6656),hAPP(c_Nitpick_Odenom(U_6655),U_6657))),hAPP(hAPP(c_COMBS(tc_Int_Oint,tc_Int_Oint,U_6655),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_fun(tc_Int_Oint,U_6655),tc_Int_Oint),c_Nitpick_Ofrac(U_6655)),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_6655),U_6656))),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_6655),U_6656))))),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_6655),U_6657))),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_6655),U_6657)))))),c_COMBI(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_1974_3]) ).

fof(f_1975_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_1975_2,plain,
    ! [U_6660,U_6659,U_6658] : c_Product__Type_Ointernal__split(U_6658,U_6659,U_6660) = c_Product__Type_Oprod_Oprod__case(U_6658,U_6659,U_6660),
    inference(variable_rename,[status(thm)],[f_1975_1]) ).

fof(f_1975_3,plain,
    ! [U_6660,U_6658,U_6659] : c_Product__Type_Ointernal__split(U_6658,U_6659,U_6660) = c_Product__Type_Oprod_Oprod__case(U_6658,U_6659,U_6660),
    inference(definitional_conversion,[status(esa)],[f_1975_2]) ).

cnf(f_1975_4,plain,
    c_Product__Type_Ointernal__split(U_6658,U_6659,U_6660) = c_Product__Type_Oprod_Oprod__case(U_6658,U_6659,U_6660),
    inference(clausify,[status(thm)],[f_1975_3]) ).

fof(f_1976_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_1976_2,plain,
    ! [U_6669,U_6668,U_6667,U_6666,U_6665,U_6664,U_6663,U_6662,U_6661] : hAPP(hAPP(c_Product__Type_Oscomp(U_6661,U_6662,U_6663,U_6664),hAPP(hAPP(c_Product__Type_Oscomp(U_6661,U_6665,U_6666,tc_prod(U_6662,U_6663)),U_6667),U_6668)),U_6669) = hAPP(hAPP(c_Product__Type_Oscomp(U_6661,U_6665,U_6666,U_6664),U_6667),hAPP(hAPP(c_COMBC(U_6665,tc_fun(U_6662,tc_fun(U_6663,U_6664)),tc_fun(U_6666,U_6664)),hAPP(hAPP(c_COMBB(tc_fun(U_6666,tc_prod(U_6662,U_6663)),tc_fun(tc_fun(U_6662,tc_fun(U_6663,U_6664)),tc_fun(U_6666,U_6664)),U_6665),c_Product__Type_Oscomp(U_6666,U_6662,U_6663,U_6664)),U_6668)),U_6669)),
    inference(variable_rename,[status(thm)],[f_1976_1]) ).

fof(f_1976_3,plain,
    ! [U_6661,U_6662,U_6663,U_6664,U_6665,U_6666,U_6667,U_6668,U_6669] : hAPP(hAPP(c_Product__Type_Oscomp(U_6661,U_6662,U_6663,U_6664),hAPP(hAPP(c_Product__Type_Oscomp(U_6661,U_6665,U_6666,tc_prod(U_6662,U_6663)),U_6667),U_6668)),U_6669) = hAPP(hAPP(c_Product__Type_Oscomp(U_6661,U_6665,U_6666,U_6664),U_6667),hAPP(hAPP(c_COMBC(U_6665,tc_fun(U_6662,tc_fun(U_6663,U_6664)),tc_fun(U_6666,U_6664)),hAPP(hAPP(c_COMBB(tc_fun(U_6666,tc_prod(U_6662,U_6663)),tc_fun(tc_fun(U_6662,tc_fun(U_6663,U_6664)),tc_fun(U_6666,U_6664)),U_6665),c_Product__Type_Oscomp(U_6666,U_6662,U_6663,U_6664)),U_6668)),U_6669)),
    inference(definitional_conversion,[status(esa)],[f_1976_2]) ).

cnf(f_1976_4,plain,
    hAPP(hAPP(c_Product__Type_Oscomp(U_6661,U_6662,U_6663,U_6664),hAPP(hAPP(c_Product__Type_Oscomp(U_6661,U_6665,U_6666,tc_prod(U_6662,U_6663)),U_6667),U_6668)),U_6669) = hAPP(hAPP(c_Product__Type_Oscomp(U_6661,U_6665,U_6666,U_6664),U_6667),hAPP(hAPP(c_COMBC(U_6665,tc_fun(U_6662,tc_fun(U_6663,U_6664)),tc_fun(U_6666,U_6664)),hAPP(hAPP(c_COMBB(tc_fun(U_6666,tc_prod(U_6662,U_6663)),tc_fun(tc_fun(U_6662,tc_fun(U_6663,U_6664)),tc_fun(U_6666,U_6664)),U_6665),c_Product__Type_Oscomp(U_6666,U_6662,U_6663,U_6664)),U_6668)),U_6669)),
    inference(clausify,[status(thm)],[f_1976_3]) ).

fof(f_1977_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_1977_2,plain,
    ! [U_6673,U_6672,U_6671,U_6670] : hAPP(hAPP(c_Product__Type_Oscomp(U_6670,U_6671,U_6672,tc_prod(U_6671,U_6672)),U_6673),c_Product__Type_OPair(U_6671,U_6672)) = U_6673,
    inference(variable_rename,[status(thm)],[f_1977_1]) ).

fof(f_1977_3,plain,
    ! [U_6670,U_6671,U_6672,U_6673] : hAPP(hAPP(c_Product__Type_Oscomp(U_6670,U_6671,U_6672,tc_prod(U_6671,U_6672)),U_6673),c_Product__Type_OPair(U_6671,U_6672)) = U_6673,
    inference(definitional_conversion,[status(esa)],[f_1977_2]) ).

cnf(f_1977_4,plain,
    hAPP(hAPP(c_Product__Type_Oscomp(U_6670,U_6671,U_6672,tc_prod(U_6671,U_6672)),U_6673),c_Product__Type_OPair(U_6671,U_6672)) = U_6673,
    inference(clausify,[status(thm)],[f_1977_3]) ).

fof(f_1978_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_1978_2,plain,
    ! [U_6678,U_6677,U_6676,U_6675,U_6674] : hAPP(hAPP(c_Product__Type_Oscomp(U_6674,U_6675,U_6674,U_6676),hAPP(c_Product__Type_OPair(U_6675,U_6674),U_6677)),U_6678) = hAPP(U_6678,U_6677),
    inference(variable_rename,[status(thm)],[f_1978_1]) ).

fof(f_1978_3,plain,
    ! [U_6674,U_6675,U_6676,U_6677,U_6678] : hAPP(hAPP(c_Product__Type_Oscomp(U_6674,U_6675,U_6674,U_6676),hAPP(c_Product__Type_OPair(U_6675,U_6674),U_6677)),U_6678) = hAPP(U_6678,U_6677),
    inference(definitional_conversion,[status(esa)],[f_1978_2]) ).

cnf(f_1978_4,plain,
    hAPP(hAPP(c_Product__Type_Oscomp(U_6674,U_6675,U_6674,U_6676),hAPP(c_Product__Type_OPair(U_6675,U_6674),U_6677)),U_6678) = hAPP(U_6678,U_6677),
    inference(clausify,[status(thm)],[f_1978_3]) ).

fof(f_1979_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_1979_2,plain,
    ! [U_6685,U_6684,U_6683,U_6682,U_6681,U_6680,U_6679] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_6679,U_6680,U_6681,U_6682),U_6683),U_6684),U_6685) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6680,U_6681,U_6682),U_6684),hAPP(U_6683,U_6685)),
    inference(variable_rename,[status(thm)],[f_1979_1]) ).

fof(f_1979_3,plain,
    ! [U_6679,U_6680,U_6681,U_6682,U_6683,U_6684,U_6685] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_6679,U_6680,U_6681,U_6682),U_6683),U_6684),U_6685) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6680,U_6681,U_6682),U_6684),hAPP(U_6683,U_6685)),
    inference(definitional_conversion,[status(esa)],[f_1979_2]) ).

cnf(f_1979_4,plain,
    hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_6679,U_6680,U_6681,U_6682),U_6683),U_6684),U_6685) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6680,U_6681,U_6682),U_6684),hAPP(U_6683,U_6685)),
    inference(clausify,[status(thm)],[f_1979_3]) ).

fof(f_1980_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_1980_2,plain,
    ! [U_6692,U_6691,U_6690,U_6689,U_6688,U_6687,U_6686] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_6686,U_6687,U_6688,U_6689),U_6690),U_6691),U_6692) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6687,U_6688,U_6689),U_6691),hAPP(U_6690,U_6692)),
    inference(variable_rename,[status(thm)],[f_1980_1]) ).

fof(f_1980_3,plain,
    ! [U_6686,U_6687,U_6688,U_6689,U_6690,U_6691,U_6692] : hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_6686,U_6687,U_6688,U_6689),U_6690),U_6691),U_6692) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6687,U_6688,U_6689),U_6691),hAPP(U_6690,U_6692)),
    inference(definitional_conversion,[status(esa)],[f_1980_2]) ).

cnf(f_1980_4,plain,
    hAPP(hAPP(hAPP(c_Product__Type_Oscomp(U_6686,U_6687,U_6688,U_6689),U_6690),U_6691),U_6692) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6687,U_6688,U_6689),U_6691),hAPP(U_6690,U_6692)),
    inference(clausify,[status(thm)],[f_1980_3]) ).

fof(f_1981_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_1981_2,plain,
    ! [U_6698,U_6697,U_6696,U_6695,U_6694,U_6693] : hAPP(hAPP(c_Product__Type_Ointernal__split(U_6693,U_6694,U_6695),U_6696),hAPP(hAPP(c_Product__Type_OPair(U_6693,U_6694),U_6697),U_6698)) = hAPP(hAPP(U_6696,U_6697),U_6698),
    inference(variable_rename,[status(thm)],[f_1981_1]) ).

fof(f_1981_3,plain,
    ! [U_6693,U_6694,U_6695,U_6696,U_6697,U_6698] : hAPP(hAPP(c_Product__Type_Ointernal__split(U_6693,U_6694,U_6695),U_6696),hAPP(hAPP(c_Product__Type_OPair(U_6693,U_6694),U_6697),U_6698)) = hAPP(hAPP(U_6696,U_6697),U_6698),
    inference(definitional_conversion,[status(esa)],[f_1981_2]) ).

cnf(f_1981_4,plain,
    hAPP(hAPP(c_Product__Type_Ointernal__split(U_6693,U_6694,U_6695),U_6696),hAPP(hAPP(c_Product__Type_OPair(U_6693,U_6694),U_6697),U_6698)) = hAPP(hAPP(U_6696,U_6697),U_6698),
    inference(clausify,[status(thm)],[f_1981_3]) ).

fof(f_1982_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_1982_2,plain,
    ! [U_6701,U_6700,U_6699] : c_Nitpick_Otimes__frac(U_6699,U_6700,U_6701) = hAPP(hAPP(c_Nitpick_Ofrac(U_6699),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6699),U_6700)),hAPP(c_Nitpick_Onum(U_6699),U_6701))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(U_6699),U_6700)),hAPP(c_Nitpick_Odenom(U_6699),U_6701))),
    inference(variable_rename,[status(thm)],[f_1982_1]) ).

fof(f_1982_3,plain,
    ! [U_6699,U_6700,U_6701] : c_Nitpick_Otimes__frac(U_6699,U_6700,U_6701) = hAPP(hAPP(c_Nitpick_Ofrac(U_6699),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6699),U_6700)),hAPP(c_Nitpick_Onum(U_6699),U_6701))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(U_6699),U_6700)),hAPP(c_Nitpick_Odenom(U_6699),U_6701))),
    inference(definitional_conversion,[status(esa)],[f_1982_2]) ).

cnf(f_1982_4,plain,
    c_Nitpick_Otimes__frac(U_6699,U_6700,U_6701) = hAPP(hAPP(c_Nitpick_Ofrac(U_6699),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6699),U_6700)),hAPP(c_Nitpick_Onum(U_6699),U_6701))),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nitpick_Odenom(U_6699),U_6700)),hAPP(c_Nitpick_Odenom(U_6699),U_6701))),
    inference(clausify,[status(thm)],[f_1982_3]) ).

fof(f_1983_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_1983_2,plain,
    ! [U_6704,U_6703,U_6702] :
      ( c_Nitpick_Oof__frac(U_6703,U_6702,U_6704) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6702),hAPP(c_Int_Oring__1__class_Oof__int(U_6702),hAPP(c_Nitpick_Onum(U_6703),U_6704))),hAPP(c_Int_Oring__1__class_Oof__int(U_6702),hAPP(c_Nitpick_Odenom(U_6703),U_6704)))
      | ~ class_Rings_Oring__1(U_6702)
      | ~ class_Rings_Oinverse(U_6702) ),
    inference(variable_rename,[status(thm)],[f_1983_1]) ).

fof(f_1983_3,plain,
    ! [U_6702,U_6703,U_6704] :
      ( c_Nitpick_Oof__frac(U_6703,U_6702,U_6704) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6702),hAPP(c_Int_Oring__1__class_Oof__int(U_6702),hAPP(c_Nitpick_Onum(U_6703),U_6704))),hAPP(c_Int_Oring__1__class_Oof__int(U_6702),hAPP(c_Nitpick_Odenom(U_6703),U_6704)))
      | ~ class_Rings_Oring__1(U_6702)
      | ~ class_Rings_Oinverse(U_6702) ),
    inference(definitional_conversion,[status(esa)],[f_1983_2]) ).

cnf(f_1983_4,plain,
    ( c_Nitpick_Oof__frac(U_6703,U_6702,U_6704) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_6702),hAPP(c_Int_Oring__1__class_Oof__int(U_6702),hAPP(c_Nitpick_Onum(U_6703),U_6704))),hAPP(c_Int_Oring__1__class_Oof__int(U_6702),hAPP(c_Nitpick_Odenom(U_6703),U_6704)))
    | ~ class_Rings_Oring__1(U_6702)
    | ~ class_Rings_Oinverse(U_6702) ),
    inference(clausify,[status(thm)],[f_1983_3]) ).

fof(f_1984_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_1984_2,plain,
    ! [U_6706,U_6705] : c_Nitpick_Oinverse__frac(U_6705,U_6706) = hAPP(hAPP(c_Nitpick_Ofrac(U_6705),hAPP(c_Nitpick_Odenom(U_6705),U_6706)),hAPP(c_Nitpick_Onum(U_6705),U_6706)),
    inference(variable_rename,[status(thm)],[f_1984_1]) ).

fof(f_1984_3,plain,
    ! [U_6705,U_6706] : c_Nitpick_Oinverse__frac(U_6705,U_6706) = hAPP(hAPP(c_Nitpick_Ofrac(U_6705),hAPP(c_Nitpick_Odenom(U_6705),U_6706)),hAPP(c_Nitpick_Onum(U_6705),U_6706)),
    inference(definitional_conversion,[status(esa)],[f_1984_2]) ).

cnf(f_1984_4,plain,
    c_Nitpick_Oinverse__frac(U_6705,U_6706) = hAPP(hAPP(c_Nitpick_Ofrac(U_6705),hAPP(c_Nitpick_Odenom(U_6705),U_6706)),hAPP(c_Nitpick_Onum(U_6705),U_6706)),
    inference(clausify,[status(thm)],[f_1984_3]) ).

fof(f_1985_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_1985_2,plain,
    ! [U_6709,U_6708,U_6707] :
      ( ( c_Random_Ominus__shift(U_6709,U_6707,U_6708) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6707),U_6708)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6707),U_6708)) )
      & ( c_Random_Ominus__shift(U_6709,U_6707,U_6708) = 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_6709),U_6707)),U_6708)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6707),U_6708)) ) ),
    inference(variable_rename,[status(thm)],[f_1985_1]) ).

fof(f_1985_3,plain,
    ( ! [U_6715,U_6713,U_6711] :
        ( c_Random_Ominus__shift(U_6715,U_6711,U_6713) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6711),U_6713)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6711),U_6713)) )
    & ! [U_6714,U_6712,U_6710] :
        ( c_Random_Ominus__shift(U_6714,U_6710,U_6712) = 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_6714),U_6710)),U_6712)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6710),U_6712)) ) ),
    inference(miniscope,[status(thm)],[f_1985_2]) ).

fof(f_1985_4,plain,
    ( ! [U_6713,U_6711,U_6715] :
        ( c_Random_Ominus__shift(U_6715,U_6711,U_6713) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6711),U_6713)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6711),U_6713)) )
    & ! [U_6714,U_6710,U_6712] :
        ( c_Random_Ominus__shift(U_6714,U_6710,U_6712) = 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_6714),U_6710)),U_6712)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6710),U_6712)) ) ),
    inference(definitional_conversion,[status(esa)],[f_1985_3]) ).

cnf(f_1985_5,plain,
    ( c_Random_Ominus__shift(U_6714,U_6710,U_6712) = 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_6714),U_6710)),U_6712)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6710),U_6712)) ),
    inference(clausify,[status(thm)],[f_1985_4]) ).

cnf(f_1985_6,plain,
    ( c_Random_Ominus__shift(U_6715,U_6711,U_6713) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6711),U_6713)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6711),U_6713)) ),
    inference(clausify,[status(thm)],[f_1985_4]) ).

fof(f_1986_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_1986_2,plain,
    ! [U_6717,U_6716] : c_Nitpick_Ouminus__frac(U_6716,U_6717) = c_Nitpick_OAbs__Frac(U_6716,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_6716),U_6717))),hAPP(c_Nitpick_Odenom(U_6716),U_6717))),
    inference(variable_rename,[status(thm)],[f_1986_1]) ).

fof(f_1986_3,plain,
    ! [U_6716,U_6717] : c_Nitpick_Ouminus__frac(U_6716,U_6717) = c_Nitpick_OAbs__Frac(U_6716,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_6716),U_6717))),hAPP(c_Nitpick_Odenom(U_6716),U_6717))),
    inference(definitional_conversion,[status(esa)],[f_1986_2]) ).

cnf(f_1986_4,plain,
    c_Nitpick_Ouminus__frac(U_6716,U_6717) = c_Nitpick_OAbs__Frac(U_6716,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_6716),U_6717))),hAPP(c_Nitpick_Odenom(U_6716),U_6717))),
    inference(clausify,[status(thm)],[f_1986_3]) ).

fof(f_1987_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_1987_2,plain,
    ! [U_6720,U_6719,U_6718] :
      ( ( c_Nitpick_Oless__frac(U_6718,U_6719,U_6720)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6718),c_Nitpick_Oplus__frac(U_6718,U_6719,c_Nitpick_Ouminus__frac(U_6718,U_6720)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6718),c_Nitpick_Oplus__frac(U_6718,U_6719,c_Nitpick_Ouminus__frac(U_6718,U_6720)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__frac(U_6718,U_6719,U_6720) ) ),
    inference(variable_rename,[status(thm)],[f_1987_1]) ).

fof(f_1987_3,plain,
    ( ! [U_6726,U_6724,U_6722] :
        ( c_Nitpick_Oless__frac(U_6722,U_6724,U_6726)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6722),c_Nitpick_Oplus__frac(U_6722,U_6724,c_Nitpick_Ouminus__frac(U_6722,U_6726)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_6725,U_6723,U_6721] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6721),c_Nitpick_Oplus__frac(U_6721,U_6723,c_Nitpick_Ouminus__frac(U_6721,U_6725)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__frac(U_6721,U_6723,U_6725) ) ),
    inference(miniscope,[status(thm)],[f_1987_2]) ).

fof(f_1987_4,plain,
    ( ! [U_6722,U_6724,U_6726] :
        ( c_Nitpick_Oless__frac(U_6722,U_6724,U_6726)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6722),c_Nitpick_Oplus__frac(U_6722,U_6724,c_Nitpick_Ouminus__frac(U_6722,U_6726)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_6723,U_6725,U_6721] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6721),c_Nitpick_Oplus__frac(U_6721,U_6723,c_Nitpick_Ouminus__frac(U_6721,U_6725)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__frac(U_6721,U_6723,U_6725) ) ),
    inference(definitional_conversion,[status(esa)],[f_1987_3]) ).

cnf(f_1987_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6721),c_Nitpick_Oplus__frac(U_6721,U_6723,c_Nitpick_Ouminus__frac(U_6721,U_6725)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ c_Nitpick_Oless__frac(U_6721,U_6723,U_6725) ),
    inference(clausify,[status(thm)],[f_1987_4]) ).

cnf(f_1987_6,plain,
    ( c_Nitpick_Oless__frac(U_6722,U_6724,U_6726)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6722),c_Nitpick_Oplus__frac(U_6722,U_6724,c_Nitpick_Ouminus__frac(U_6722,U_6726)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1987_4]) ).

fof(f_1988_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_1988_2,plain,
    ! [U_6729,U_6728,U_6727] :
      ( ( c_Nitpick_Oless__eq__frac(U_6727,U_6728,U_6729)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6727),c_Nitpick_Oplus__frac(U_6727,U_6728,c_Nitpick_Ouminus__frac(U_6727,U_6729)))),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_6727),c_Nitpick_Oplus__frac(U_6727,U_6728,c_Nitpick_Ouminus__frac(U_6727,U_6729)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__eq__frac(U_6727,U_6728,U_6729) ) ),
    inference(variable_rename,[status(thm)],[f_1988_1]) ).

fof(f_1988_3,plain,
    ( ! [U_6735,U_6733,U_6731] :
        ( c_Nitpick_Oless__eq__frac(U_6731,U_6733,U_6735)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6731),c_Nitpick_Oplus__frac(U_6731,U_6733,c_Nitpick_Ouminus__frac(U_6731,U_6735)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_6734,U_6732,U_6730] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6730),c_Nitpick_Oplus__frac(U_6730,U_6732,c_Nitpick_Ouminus__frac(U_6730,U_6734)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__eq__frac(U_6730,U_6732,U_6734) ) ),
    inference(miniscope,[status(thm)],[f_1988_2]) ).

fof(f_1988_4,plain,
    ( ! [U_6731,U_6733,U_6735] :
        ( c_Nitpick_Oless__eq__frac(U_6731,U_6733,U_6735)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6731),c_Nitpick_Oplus__frac(U_6731,U_6733,c_Nitpick_Ouminus__frac(U_6731,U_6735)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) )
    & ! [U_6732,U_6730,U_6734] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6730),c_Nitpick_Oplus__frac(U_6730,U_6732,c_Nitpick_Ouminus__frac(U_6730,U_6734)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
        | ~ c_Nitpick_Oless__eq__frac(U_6730,U_6732,U_6734) ) ),
    inference(definitional_conversion,[status(esa)],[f_1988_3]) ).

cnf(f_1988_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6730),c_Nitpick_Oplus__frac(U_6730,U_6732,c_Nitpick_Ouminus__frac(U_6730,U_6734)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint)))
    | ~ c_Nitpick_Oless__eq__frac(U_6730,U_6732,U_6734) ),
    inference(clausify,[status(thm)],[f_1988_4]) ).

cnf(f_1988_6,plain,
    ( c_Nitpick_Oless__eq__frac(U_6731,U_6733,U_6735)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Nitpick_Onum(U_6731),c_Nitpick_Oplus__frac(U_6731,U_6733,c_Nitpick_Ouminus__frac(U_6731,U_6735)))),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_1988_4]) ).

fof(f_1989_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_1989_2,plain,
    ! [U_6740,U_6739,U_6738,U_6737,U_6736] :
      ( ( hAPP(c_Random_Oiterate(U_6737,U_6738,U_6736,U_6739),U_6740) = hAPP(hAPP(c_Product__Type_Oscomp(U_6738,U_6737,U_6738,tc_prod(U_6737,U_6738)),hAPP(U_6739,U_6740)),c_Random_Oiterate(U_6737,U_6738,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6736),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6739))
        | U_6736 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_Random_Oiterate(U_6737,U_6738,U_6736,U_6739),U_6740) = hAPP(c_Product__Type_OPair(U_6737,U_6738),U_6740)
        | U_6736 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_1989_1]) ).

fof(f_1989_3,plain,
    ( ! [U_6750,U_6748,U_6746,U_6744,U_6742] :
        ( hAPP(c_Random_Oiterate(U_6744,U_6746,U_6742,U_6748),U_6750) = hAPP(hAPP(c_Product__Type_Oscomp(U_6746,U_6744,U_6746,tc_prod(U_6744,U_6746)),hAPP(U_6748,U_6750)),c_Random_Oiterate(U_6744,U_6746,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6742),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6748))
        | U_6742 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_6749,U_6747,U_6745,U_6743,U_6741] :
        ( hAPP(c_Random_Oiterate(U_6743,U_6745,U_6741,U_6747),U_6749) = hAPP(c_Product__Type_OPair(U_6743,U_6745),U_6749)
        | U_6741 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_1989_2]) ).

fof(f_1989_4,plain,
    ( ! [U_6742,U_6750,U_6744,U_6746,U_6748] :
        ( hAPP(c_Random_Oiterate(U_6744,U_6746,U_6742,U_6748),U_6750) = hAPP(hAPP(c_Product__Type_Oscomp(U_6746,U_6744,U_6746,tc_prod(U_6744,U_6746)),hAPP(U_6748,U_6750)),c_Random_Oiterate(U_6744,U_6746,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6742),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6748))
        | U_6742 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_6747,U_6741,U_6743,U_6745,U_6749] :
        ( hAPP(c_Random_Oiterate(U_6743,U_6745,U_6741,U_6747),U_6749) = hAPP(c_Product__Type_OPair(U_6743,U_6745),U_6749)
        | U_6741 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(definitional_conversion,[status(esa)],[f_1989_3]) ).

cnf(f_1989_5,plain,
    ( hAPP(c_Random_Oiterate(U_6743,U_6745,U_6741,U_6747),U_6749) = hAPP(c_Product__Type_OPair(U_6743,U_6745),U_6749)
    | U_6741 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1989_4]) ).

cnf(f_1989_6,plain,
    ( hAPP(c_Random_Oiterate(U_6744,U_6746,U_6742,U_6748),U_6750) = hAPP(hAPP(c_Product__Type_Oscomp(U_6746,U_6744,U_6746,tc_prod(U_6744,U_6746)),hAPP(U_6748,U_6750)),c_Random_Oiterate(U_6744,U_6746,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6742),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6748))
    | U_6742 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_1989_4]) ).

fof(f_1990_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_1990_2,plain,
    ! [U_6752,U_6751] :
      ( ( c_Random_Oinc__shift(U_6751,U_6752) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_6752),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
        | U_6751 = U_6752 )
      & ( c_Random_Oinc__shift(U_6751,U_6752) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | U_6751 != U_6752 ) ),
    inference(variable_rename,[status(thm)],[f_1990_1]) ).

fof(f_1990_3,plain,
    ( ! [U_6756,U_6754] :
        ( c_Random_Oinc__shift(U_6754,U_6756) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_6756),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
        | U_6754 = U_6756 )
    & ! [U_6755,U_6753] :
        ( c_Random_Oinc__shift(U_6753,U_6755) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | U_6753 != U_6755 ) ),
    inference(miniscope,[status(thm)],[f_1990_2]) ).

fof(f_1990_4,plain,
    ( ! [U_6754,U_6756] :
        ( c_Random_Oinc__shift(U_6754,U_6756) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_6756),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
        | U_6754 = U_6756 )
    & ! [U_6753,U_6755] :
        ( c_Random_Oinc__shift(U_6753,U_6755) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
        | U_6753 != U_6755 ) ),
    inference(definitional_conversion,[status(esa)],[f_1990_3]) ).

cnf(f_1990_5,plain,
    ( c_Random_Oinc__shift(U_6753,U_6755) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)
    | U_6753 != U_6755 ),
    inference(clausify,[status(thm)],[f_1990_4]) ).

cnf(f_1990_6,plain,
    ( c_Random_Oinc__shift(U_6754,U_6756) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_6756),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))
    | U_6754 = U_6756 ),
    inference(clausify,[status(thm)],[f_1990_4]) ).

fof(f_1991_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_1991_2,plain,
    ! [U_6758,U_6757] :
      ( 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_6757),U_6758))),U_6757))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_6757)) ),
    inference(variable_rename,[status(thm)],[f_1991_1]) ).

fof(f_1991_3,plain,
    ! [U_6757,U_6758] :
      ( 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_6757),U_6758))),U_6757))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_6757)) ),
    inference(definitional_conversion,[status(esa)],[f_1991_2]) ).

cnf(f_1991_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_6757),U_6758))),U_6757))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_6757)) ),
    inference(clausify,[status(thm)],[f_1991_3]) ).

fof(f_1992_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_1992_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_1992_1]) ).

cnf(f_1992_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_1992_2]) ).

fof(f_1993_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_1993_2,plain,
    ! [U_6762,U_6761,U_6760] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6760),U_6761),U_6762))
      | ? [U_6759] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6760),U_6761),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6760),U_6762),U_6759)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6760),c_Groups_Ozero__class_Ozero(U_6760)),U_6759)) )
      | ~ class_Fields_Olinordered__field(U_6760) ),
    inference(variable_rename,[status(thm)],[f_1993_1]) ).

fof(f_1993_3,plain,
    ! [U_6762,U_6761,U_6760] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6760),U_6761),U_6762))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6760),U_6761),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6760),U_6762),sK98(U_6762,U_6761,U_6760))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6760),c_Groups_Ozero__class_Ozero(U_6760)),sK98(U_6762,U_6761,U_6760))) )
      | ~ class_Fields_Olinordered__field(U_6760) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK98]),skolemize(U_6759,sK98(U_6762,U_6761,U_6760))],[f_1993_2]) ).

fof(f_1993_4,plain,
    ( ! [U_6760,U_6761,U_6762] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6760),U_6761),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6760),U_6762),sK98(U_6762,U_6761,U_6760))))
        | ~ sP621(U_6760,U_6761,U_6762) )
    & ! [U_6760,U_6761,U_6762] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6760),c_Groups_Ozero__class_Ozero(U_6760)),sK98(U_6762,U_6761,U_6760)))
        | ~ sP621(U_6760,U_6761,U_6762) )
    & ! [U_6760,U_6761,U_6762] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6760),U_6761),U_6762))
        | sP621(U_6760,U_6761,U_6762)
        | ~ class_Fields_Olinordered__field(U_6760) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP621])],[f_1993_3]) ).

cnf(f_1993_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6760),U_6761),U_6762))
    | sP621(U_6760,U_6761,U_6762)
    | ~ class_Fields_Olinordered__field(U_6760) ),
    inference(clausify,[status(thm)],[f_1993_4]) ).

cnf(f_1993_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_6760),c_Groups_Ozero__class_Ozero(U_6760)),sK98(U_6762,U_6761,U_6760)))
    | ~ sP621(U_6760,U_6761,U_6762) ),
    inference(clausify,[status(thm)],[f_1993_4]) ).

cnf(f_1993_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_6760),U_6761),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_6760),U_6762),sK98(U_6762,U_6761,U_6760))))
    | ~ sP621(U_6760,U_6761,U_6762) ),
    inference(clausify,[status(thm)],[f_1993_4]) ).

fof(f_1994_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_1994_2,plain,
    c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
    inference(definitional_conversion,[status(esa)],[f_1994_1]) ).

cnf(f_1994_3,plain,
    c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_1994_2]) ).

fof(f_1995_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_1995_2,plain,
    ! [U_6764,U_6763] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6763),U_6764) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_6763),U_6764),
    inference(variable_rename,[status(thm)],[f_1995_1]) ).

fof(f_1995_3,plain,
    ! [U_6763,U_6764] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6763),U_6764) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_6763),U_6764),
    inference(definitional_conversion,[status(esa)],[f_1995_2]) ).

cnf(f_1995_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6763),U_6764) = hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,U_6763),U_6764),
    inference(clausify,[status(thm)],[f_1995_3]) ).

fof(f_1996_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_1996_2,plain,
    ! [U_6771,U_6770,U_6769,U_6768,U_6767,U_6766,U_6765] :
      ( hBOOL(hAPP(hAPP(c_member(U_6770),hAPP(hAPP(U_6771,U_6767),U_6768)),hAPP(c_Set_Oimage(tc_prod(U_6765,U_6766),U_6770,hAPP(c_Product__Type_Oprod_Oprod__case(U_6765,U_6766,U_6770),U_6771)),U_6769)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_6765,U_6766)),hAPP(hAPP(c_Product__Type_OPair(U_6765,U_6766),U_6767),U_6768)),U_6769)) ),
    inference(variable_rename,[status(thm)],[f_1996_1]) ).

fof(f_1996_3,plain,
    ! [U_6767,U_6765,U_6766,U_6768,U_6769,U_6770,U_6771] :
      ( hBOOL(hAPP(hAPP(c_member(U_6770),hAPP(hAPP(U_6771,U_6767),U_6768)),hAPP(c_Set_Oimage(tc_prod(U_6765,U_6766),U_6770,hAPP(c_Product__Type_Oprod_Oprod__case(U_6765,U_6766,U_6770),U_6771)),U_6769)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_6765,U_6766)),hAPP(hAPP(c_Product__Type_OPair(U_6765,U_6766),U_6767),U_6768)),U_6769)) ),
    inference(definitional_conversion,[status(esa)],[f_1996_2]) ).

cnf(f_1996_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6770),hAPP(hAPP(U_6771,U_6767),U_6768)),hAPP(c_Set_Oimage(tc_prod(U_6765,U_6766),U_6770,hAPP(c_Product__Type_Oprod_Oprod__case(U_6765,U_6766,U_6770),U_6771)),U_6769)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_6765,U_6766)),hAPP(hAPP(c_Product__Type_OPair(U_6765,U_6766),U_6767),U_6768)),U_6769)) ),
    inference(clausify,[status(thm)],[f_1996_3]) ).

fof(f_1997_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_1997_2,plain,
    ! [U_6777,U_6776,U_6775,U_6774,U_6773,U_6772] :
      ( hBOOL(hAPP(hAPP(c_member(U_6777),U_6772),hAPP(c_Set_Oimage(U_6775,U_6777,U_6773),U_6776)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_6775),U_6774),U_6776))
      | U_6772 != hAPP(U_6773,U_6774) ),
    inference(variable_rename,[status(thm)],[f_1997_1]) ).

fof(f_1997_3,plain,
    ! [U_6774,U_6775,U_6773,U_6772,U_6776,U_6777] :
      ( hBOOL(hAPP(hAPP(c_member(U_6777),U_6772),hAPP(c_Set_Oimage(U_6775,U_6777,U_6773),U_6776)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_6775),U_6774),U_6776))
      | U_6772 != hAPP(U_6773,U_6774) ),
    inference(definitional_conversion,[status(esa)],[f_1997_2]) ).

cnf(f_1997_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6777),U_6772),hAPP(c_Set_Oimage(U_6775,U_6777,U_6773),U_6776)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6775),U_6774),U_6776))
    | U_6772 != hAPP(U_6773,U_6774) ),
    inference(clausify,[status(thm)],[f_1997_3]) ).

fof(f_1998_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_1998_2,plain,
    ! [U_6784,U_6783,U_6782,U_6781,U_6780] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6780,tc_HOL_Obool)),U_6781),hAPP(c_Set_Oimage(U_6782,U_6780,U_6783),U_6784)))
        | ! [U_6779] :
            ( U_6781 != hAPP(c_Set_Oimage(U_6782,U_6780,U_6783),U_6779)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6782,tc_HOL_Obool)),U_6779),U_6784)) ) )
      & ( ? [U_6778] :
            ( U_6781 = hAPP(c_Set_Oimage(U_6782,U_6780,U_6783),U_6778)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6782,tc_HOL_Obool)),U_6778),U_6784)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6780,tc_HOL_Obool)),U_6781),hAPP(c_Set_Oimage(U_6782,U_6780,U_6783),U_6784))) ) ),
    inference(variable_rename,[status(thm)],[f_1998_1]) ).

fof(f_1998_3,plain,
    ( ! [U_6794,U_6792,U_6790,U_6788,U_6786] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6786,tc_HOL_Obool)),U_6788),hAPP(c_Set_Oimage(U_6790,U_6786,U_6792),U_6794)))
        | ! [U_6779] :
            ( U_6788 != hAPP(c_Set_Oimage(U_6790,U_6786,U_6792),U_6779)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6790,tc_HOL_Obool)),U_6779),U_6794)) ) )
    & ! [U_6793,U_6791,U_6789,U_6787,U_6785] :
        ( ? [U_6778] :
            ( U_6787 = hAPP(c_Set_Oimage(U_6789,U_6785,U_6791),U_6778)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6789,tc_HOL_Obool)),U_6778),U_6793)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6785,tc_HOL_Obool)),U_6787),hAPP(c_Set_Oimage(U_6789,U_6785,U_6791),U_6793))) ) ),
    inference(miniscope,[status(thm)],[f_1998_2]) ).

fof(f_1998_4,plain,
    ( ! [U_6794,U_6792,U_6790,U_6788,U_6786] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6786,tc_HOL_Obool)),U_6788),hAPP(c_Set_Oimage(U_6790,U_6786,U_6792),U_6794)))
        | ! [U_6779] :
            ( U_6788 != hAPP(c_Set_Oimage(U_6790,U_6786,U_6792),U_6779)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6790,tc_HOL_Obool)),U_6779),U_6794)) ) )
    & ! [U_6793,U_6791,U_6789,U_6787,U_6785] :
        ( ( U_6787 = hAPP(c_Set_Oimage(U_6789,U_6785,U_6791),sK99(U_6793,U_6791,U_6789,U_6787,U_6785))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6789,tc_HOL_Obool)),sK99(U_6793,U_6791,U_6789,U_6787,U_6785)),U_6793)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6785,tc_HOL_Obool)),U_6787),hAPP(c_Set_Oimage(U_6789,U_6785,U_6791),U_6793))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK99]),skolemize(U_6778,sK99(U_6793,U_6791,U_6789,U_6787,U_6785))],[f_1998_3]) ).

fof(f_1998_5,plain,
    ( ! [U_6787,U_6785,U_6789,U_6793,U_6791] :
        ( U_6787 = hAPP(c_Set_Oimage(U_6789,U_6785,U_6791),sK99(U_6793,U_6791,U_6789,U_6787,U_6785))
        | ~ sP622(U_6787,U_6785,U_6789,U_6793,U_6791) )
    & ! [U_6787,U_6785,U_6789,U_6793,U_6791] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6789,tc_HOL_Obool)),sK99(U_6793,U_6791,U_6789,U_6787,U_6785)),U_6793))
        | ~ sP622(U_6787,U_6785,U_6789,U_6793,U_6791) )
    & ! [U_6779,U_6788,U_6786,U_6794,U_6792,U_6790] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6786,tc_HOL_Obool)),U_6788),hAPP(c_Set_Oimage(U_6790,U_6786,U_6792),U_6794)))
        | U_6788 != hAPP(c_Set_Oimage(U_6790,U_6786,U_6792),U_6779)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6790,tc_HOL_Obool)),U_6779),U_6794)) )
    & ! [U_6787,U_6785,U_6789,U_6793,U_6791] :
        ( sP622(U_6787,U_6785,U_6789,U_6793,U_6791)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6785,tc_HOL_Obool)),U_6787),hAPP(c_Set_Oimage(U_6789,U_6785,U_6791),U_6793))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP622])],[f_1998_4]) ).

cnf(f_1998_6,plain,
    ( sP622(U_6787,U_6785,U_6789,U_6793,U_6791)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6785,tc_HOL_Obool)),U_6787),hAPP(c_Set_Oimage(U_6789,U_6785,U_6791),U_6793))) ),
    inference(clausify,[status(thm)],[f_1998_5]) ).

cnf(f_1998_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6786,tc_HOL_Obool)),U_6788),hAPP(c_Set_Oimage(U_6790,U_6786,U_6792),U_6794)))
    | U_6788 != hAPP(c_Set_Oimage(U_6790,U_6786,U_6792),U_6779)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6790,tc_HOL_Obool)),U_6779),U_6794)) ),
    inference(clausify,[status(thm)],[f_1998_5]) ).

cnf(f_1998_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6789,tc_HOL_Obool)),sK99(U_6793,U_6791,U_6789,U_6787,U_6785)),U_6793))
    | ~ sP622(U_6787,U_6785,U_6789,U_6793,U_6791) ),
    inference(clausify,[status(thm)],[f_1998_5]) ).

cnf(f_1998_9,plain,
    ( U_6787 = hAPP(c_Set_Oimage(U_6789,U_6785,U_6791),sK99(U_6793,U_6791,U_6789,U_6787,U_6785))
    | ~ sP622(U_6787,U_6785,U_6789,U_6793,U_6791) ),
    inference(clausify,[status(thm)],[f_1998_5]) ).

fof(f_1999_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_1999_2,plain,
    ! [U_6799,U_6798,U_6797,U_6796,U_6795] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6798,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_6795,U_6798,U_6799),U_6796)),hAPP(c_Set_Oimage(U_6795,U_6798,U_6799),U_6797)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6795,tc_HOL_Obool)),U_6796),U_6797)) ),
    inference(variable_rename,[status(thm)],[f_1999_1]) ).

fof(f_1999_3,plain,
    ! [U_6797,U_6796,U_6795,U_6798,U_6799] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6798,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_6795,U_6798,U_6799),U_6796)),hAPP(c_Set_Oimage(U_6795,U_6798,U_6799),U_6797)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6795,tc_HOL_Obool)),U_6796),U_6797)) ),
    inference(definitional_conversion,[status(esa)],[f_1999_2]) ).

cnf(f_1999_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6798,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_6795,U_6798,U_6799),U_6796)),hAPP(c_Set_Oimage(U_6795,U_6798,U_6799),U_6797)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6795,tc_HOL_Obool)),U_6796),U_6797)) ),
    inference(clausify,[status(thm)],[f_1999_3]) ).

fof(f_2000_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_2000_2,plain,
    ! [U_6805,U_6804,U_6803,U_6802,U_6801,U_6800] : hAPP(c_Set_Oimage(U_6800,U_6801,U_6802),hAPP(c_Set_Oimage(U_6803,U_6800,U_6804),U_6805)) = hAPP(c_Set_Oimage(U_6803,U_6801,hAPP(hAPP(c_COMBB(U_6800,U_6801,U_6803),U_6802),U_6804)),U_6805),
    inference(variable_rename,[status(thm)],[f_2000_1]) ).

fof(f_2000_3,plain,
    ! [U_6800,U_6801,U_6802,U_6803,U_6804,U_6805] : hAPP(c_Set_Oimage(U_6800,U_6801,U_6802),hAPP(c_Set_Oimage(U_6803,U_6800,U_6804),U_6805)) = hAPP(c_Set_Oimage(U_6803,U_6801,hAPP(hAPP(c_COMBB(U_6800,U_6801,U_6803),U_6802),U_6804)),U_6805),
    inference(definitional_conversion,[status(esa)],[f_2000_2]) ).

cnf(f_2000_4,plain,
    hAPP(c_Set_Oimage(U_6800,U_6801,U_6802),hAPP(c_Set_Oimage(U_6803,U_6800,U_6804),U_6805)) = hAPP(c_Set_Oimage(U_6803,U_6801,hAPP(hAPP(c_COMBB(U_6800,U_6801,U_6803),U_6802),U_6804)),U_6805),
    inference(clausify,[status(thm)],[f_2000_3]) ).

fof(f_2001_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_2001_2,plain,
    ! [U_6811,U_6810,U_6809,U_6808,U_6807,U_6806] :
      ( hBOOL(hAPP(hAPP(c_member(U_6811),U_6809),hAPP(c_Set_Oimage(U_6806,U_6811,U_6810),U_6808)))
      | U_6809 != hAPP(U_6810,U_6807)
      | ~ hBOOL(hAPP(hAPP(c_member(U_6806),U_6807),U_6808)) ),
    inference(variable_rename,[status(thm)],[f_2001_1]) ).

fof(f_2001_3,plain,
    ! [U_6806,U_6807,U_6808,U_6809,U_6810,U_6811] :
      ( hBOOL(hAPP(hAPP(c_member(U_6811),U_6809),hAPP(c_Set_Oimage(U_6806,U_6811,U_6810),U_6808)))
      | U_6809 != hAPP(U_6810,U_6807)
      | ~ hBOOL(hAPP(hAPP(c_member(U_6806),U_6807),U_6808)) ),
    inference(definitional_conversion,[status(esa)],[f_2001_2]) ).

cnf(f_2001_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6811),U_6809),hAPP(c_Set_Oimage(U_6806,U_6811,U_6810),U_6808)))
    | U_6809 != hAPP(U_6810,U_6807)
    | ~ hBOOL(hAPP(hAPP(c_member(U_6806),U_6807),U_6808)) ),
    inference(clausify,[status(thm)],[f_2001_3]) ).

fof(f_2002_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_2002_2,plain,
    ! [U_6816,U_6815,U_6814,U_6813,U_6812] :
      ( hBOOL(hAPP(hAPP(c_member(U_6815),hAPP(U_6816,U_6813)),hAPP(c_Set_Oimage(U_6812,U_6815,U_6816),U_6814)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_6812),U_6813),U_6814)) ),
    inference(variable_rename,[status(thm)],[f_2002_1]) ).

fof(f_2002_3,plain,
    ! [U_6812,U_6813,U_6814,U_6815,U_6816] :
      ( hBOOL(hAPP(hAPP(c_member(U_6815),hAPP(U_6816,U_6813)),hAPP(c_Set_Oimage(U_6812,U_6815,U_6816),U_6814)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_6812),U_6813),U_6814)) ),
    inference(definitional_conversion,[status(esa)],[f_2002_2]) ).

cnf(f_2002_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6815),hAPP(U_6816,U_6813)),hAPP(c_Set_Oimage(U_6812,U_6815,U_6816),U_6814)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_6812),U_6813),U_6814)) ),
    inference(clausify,[status(thm)],[f_2002_3]) ).

fof(f_2003_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_2003_2,plain,
    ! [U_6823,U_6822,U_6821,U_6820,U_6819] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_6819),U_6820),hAPP(c_Set_Oimage(U_6821,U_6819,U_6822),U_6823)))
        | ! [U_6818] :
            ( U_6820 != hAPP(U_6822,U_6818)
            | ~ hBOOL(hAPP(hAPP(c_member(U_6821),U_6818),U_6823)) ) )
      & ( ? [U_6817] :
            ( U_6820 = hAPP(U_6822,U_6817)
            & hBOOL(hAPP(hAPP(c_member(U_6821),U_6817),U_6823)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_6819),U_6820),hAPP(c_Set_Oimage(U_6821,U_6819,U_6822),U_6823))) ) ),
    inference(variable_rename,[status(thm)],[f_2003_1]) ).

fof(f_2003_3,plain,
    ( ! [U_6833,U_6831,U_6829,U_6827] :
        ( ! [U_6825] : hBOOL(hAPP(hAPP(c_member(U_6825),U_6827),hAPP(c_Set_Oimage(U_6829,U_6825,U_6831),U_6833)))
        | ! [U_6818] :
            ( U_6827 != hAPP(U_6831,U_6818)
            | ~ hBOOL(hAPP(hAPP(c_member(U_6829),U_6818),U_6833)) ) )
    & ! [U_6832,U_6830,U_6828,U_6826] :
        ( ! [U_6824] : ~ hBOOL(hAPP(hAPP(c_member(U_6824),U_6826),hAPP(c_Set_Oimage(U_6828,U_6824,U_6830),U_6832)))
        | ? [U_6817] :
            ( U_6826 = hAPP(U_6830,U_6817)
            & hBOOL(hAPP(hAPP(c_member(U_6828),U_6817),U_6832)) ) ) ),
    inference(miniscope,[status(thm)],[f_2003_2]) ).

fof(f_2003_4,plain,
    ( ! [U_6833,U_6831,U_6829,U_6827] :
        ( ! [U_6825] : hBOOL(hAPP(hAPP(c_member(U_6825),U_6827),hAPP(c_Set_Oimage(U_6829,U_6825,U_6831),U_6833)))
        | ! [U_6818] :
            ( U_6827 != hAPP(U_6831,U_6818)
            | ~ hBOOL(hAPP(hAPP(c_member(U_6829),U_6818),U_6833)) ) )
    & ! [U_6832,U_6830,U_6828,U_6826] :
        ( ! [U_6824] : ~ hBOOL(hAPP(hAPP(c_member(U_6824),U_6826),hAPP(c_Set_Oimage(U_6828,U_6824,U_6830),U_6832)))
        | ( U_6826 = hAPP(U_6830,sK100(U_6832,U_6830,U_6828,U_6826))
          & hBOOL(hAPP(hAPP(c_member(U_6828),sK100(U_6832,U_6830,U_6828,U_6826)),U_6832)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK100]),skolemize(U_6817,sK100(U_6832,U_6830,U_6828,U_6826))],[f_2003_3]) ).

fof(f_2003_5,plain,
    ( ! [U_6828,U_6826,U_6832,U_6830] :
        ( U_6826 = hAPP(U_6830,sK100(U_6832,U_6830,U_6828,U_6826))
        | ~ sP623(U_6828,U_6826,U_6832,U_6830) )
    & ! [U_6828,U_6826,U_6832,U_6830] :
        ( hBOOL(hAPP(hAPP(c_member(U_6828),sK100(U_6832,U_6830,U_6828,U_6826)),U_6832))
        | ~ sP623(U_6828,U_6826,U_6832,U_6830) )
    & ! [U_6818,U_6833,U_6827,U_6825,U_6831,U_6829] :
        ( hBOOL(hAPP(hAPP(c_member(U_6825),U_6827),hAPP(c_Set_Oimage(U_6829,U_6825,U_6831),U_6833)))
        | U_6827 != hAPP(U_6831,U_6818)
        | ~ hBOOL(hAPP(hAPP(c_member(U_6829),U_6818),U_6833)) )
    & ! [U_6828,U_6824,U_6826,U_6832,U_6830] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_6824),U_6826),hAPP(c_Set_Oimage(U_6828,U_6824,U_6830),U_6832)))
        | sP623(U_6828,U_6826,U_6832,U_6830) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP623])],[f_2003_4]) ).

cnf(f_2003_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_6824),U_6826),hAPP(c_Set_Oimage(U_6828,U_6824,U_6830),U_6832)))
    | sP623(U_6828,U_6826,U_6832,U_6830) ),
    inference(clausify,[status(thm)],[f_2003_5]) ).

cnf(f_2003_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6825),U_6827),hAPP(c_Set_Oimage(U_6829,U_6825,U_6831),U_6833)))
    | U_6827 != hAPP(U_6831,U_6818)
    | ~ hBOOL(hAPP(hAPP(c_member(U_6829),U_6818),U_6833)) ),
    inference(clausify,[status(thm)],[f_2003_5]) ).

cnf(f_2003_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_6828),sK100(U_6832,U_6830,U_6828,U_6826)),U_6832))
    | ~ sP623(U_6828,U_6826,U_6832,U_6830) ),
    inference(clausify,[status(thm)],[f_2003_5]) ).

cnf(f_2003_9,plain,
    ( U_6826 = hAPP(U_6830,sK100(U_6832,U_6830,U_6828,U_6826))
    | ~ sP623(U_6828,U_6826,U_6832,U_6830) ),
    inference(clausify,[status(thm)],[f_2003_5]) ).

fof(f_2004_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_2004_2,plain,
    ! [U_6838,U_6837,U_6836,U_6835,U_6834] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6834,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6834,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_6835,U_6834,U_6836),U_6837)),hAPP(c_Set_Oimage(U_6835,U_6834,U_6836),U_6838))),hAPP(c_Set_Oimage(U_6835,U_6834,U_6836),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6835,tc_HOL_Obool)),U_6837),U_6838)))),
    inference(variable_rename,[status(thm)],[f_2004_1]) ).

fof(f_2004_3,plain,
    ! [U_6834,U_6835,U_6836,U_6837,U_6838] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6834,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6834,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_6835,U_6834,U_6836),U_6837)),hAPP(c_Set_Oimage(U_6835,U_6834,U_6836),U_6838))),hAPP(c_Set_Oimage(U_6835,U_6834,U_6836),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6835,tc_HOL_Obool)),U_6837),U_6838)))),
    inference(definitional_conversion,[status(esa)],[f_2004_2]) ).

cnf(f_2004_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_6834,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6834,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_6835,U_6834,U_6836),U_6837)),hAPP(c_Set_Oimage(U_6835,U_6834,U_6836),U_6838))),hAPP(c_Set_Oimage(U_6835,U_6834,U_6836),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_6835,tc_HOL_Obool)),U_6837),U_6838)))),
    inference(clausify,[status(thm)],[f_2004_3]) ).

fof(f_2005_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_2005_2,plain,
    ! [U_6840,U_6839] : hAPP(c_Set_Oimage(U_6839,U_6839,c_COMBI(U_6839)),U_6840) = U_6840,
    inference(variable_rename,[status(thm)],[f_2005_1]) ).

fof(f_2005_3,plain,
    ! [U_6839,U_6840] : hAPP(c_Set_Oimage(U_6839,U_6839,c_COMBI(U_6839)),U_6840) = U_6840,
    inference(definitional_conversion,[status(esa)],[f_2005_2]) ).

cnf(f_2005_4,plain,
    hAPP(c_Set_Oimage(U_6839,U_6839,c_COMBI(U_6839)),U_6840) = U_6840,
    inference(clausify,[status(thm)],[f_2005_3]) ).

fof(f_2006_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_2006_2,plain,
    ! [U_6846,U_6845,U_6844,U_6843,U_6842,U_6841] : c_Nitpick_Opair__box_Opair__box__size(U_6841,U_6842,U_6843,U_6844,c_Nitpick_Opair__box_OPairBox(U_6841,U_6842,U_6845,U_6846)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_6843,U_6845)),hAPP(U_6844,U_6846))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_2006_1]) ).

fof(f_2006_3,plain,
    ! [U_6842,U_6841,U_6843,U_6844,U_6845,U_6846] : c_Nitpick_Opair__box_Opair__box__size(U_6841,U_6842,U_6843,U_6844,c_Nitpick_Opair__box_OPairBox(U_6841,U_6842,U_6845,U_6846)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_6843,U_6845)),hAPP(U_6844,U_6846))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_2006_2]) ).

cnf(f_2006_4,plain,
    c_Nitpick_Opair__box_Opair__box__size(U_6841,U_6842,U_6843,U_6844,c_Nitpick_Opair__box_OPairBox(U_6841,U_6842,U_6845,U_6846)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_6843,U_6845)),hAPP(U_6844,U_6846))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_2006_3]) ).

fof(f_2007_1,plain,
    ! [V_Pa_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_Pa_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_Pa_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_2007_2,plain,
    ! [U_6849,U_6848,U_6847] : c_HOL_OThe(tc_prod(U_6847,U_6848),hAPP(c_Product__Type_Oprod_Oprod__case(U_6847,U_6848,tc_HOL_Obool),U_6849)) = c_HOL_OThe(tc_prod(U_6847,U_6848),hAPP(hAPP(c_COMBS(tc_prod(U_6847,U_6848),U_6848,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_6847,tc_fun(U_6848,tc_HOL_Obool),tc_prod(U_6847,U_6848)),U_6849),c_Product__Type_Ofst(U_6847,U_6848))),c_Product__Type_Osnd(U_6847,U_6848))),
    inference(variable_rename,[status(thm)],[f_2007_1]) ).

fof(f_2007_3,plain,
    ! [U_6847,U_6848,U_6849] : c_HOL_OThe(tc_prod(U_6847,U_6848),hAPP(c_Product__Type_Oprod_Oprod__case(U_6847,U_6848,tc_HOL_Obool),U_6849)) = c_HOL_OThe(tc_prod(U_6847,U_6848),hAPP(hAPP(c_COMBS(tc_prod(U_6847,U_6848),U_6848,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_6847,tc_fun(U_6848,tc_HOL_Obool),tc_prod(U_6847,U_6848)),U_6849),c_Product__Type_Ofst(U_6847,U_6848))),c_Product__Type_Osnd(U_6847,U_6848))),
    inference(definitional_conversion,[status(esa)],[f_2007_2]) ).

cnf(f_2007_4,plain,
    c_HOL_OThe(tc_prod(U_6847,U_6848),hAPP(c_Product__Type_Oprod_Oprod__case(U_6847,U_6848,tc_HOL_Obool),U_6849)) = c_HOL_OThe(tc_prod(U_6847,U_6848),hAPP(hAPP(c_COMBS(tc_prod(U_6847,U_6848),U_6848,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_6847,tc_fun(U_6848,tc_HOL_Obool),tc_prod(U_6847,U_6848)),U_6849),c_Product__Type_Ofst(U_6847,U_6848))),c_Product__Type_Osnd(U_6847,U_6848))),
    inference(clausify,[status(thm)],[f_2007_3]) ).

fof(f_2008_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_2008_2,plain,
    ! [U_6853,U_6852,U_6851,U_6850] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_6850,U_6851,U_6852,c_Code__Numeral_OSuc__code__numeral(U_6853)) = hAPP(hAPP(U_6852,U_6853),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_6850,U_6851,U_6852,U_6853)),
    inference(variable_rename,[status(thm)],[f_2008_1]) ).

fof(f_2008_3,plain,
    ! [U_6851,U_6850,U_6852,U_6853] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_6850,U_6851,U_6852,c_Code__Numeral_OSuc__code__numeral(U_6853)) = hAPP(hAPP(U_6852,U_6853),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_6850,U_6851,U_6852,U_6853)),
    inference(definitional_conversion,[status(esa)],[f_2008_2]) ).

cnf(f_2008_4,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_6850,U_6851,U_6852,c_Code__Numeral_OSuc__code__numeral(U_6853)) = hAPP(hAPP(U_6852,U_6853),c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_6850,U_6851,U_6852,U_6853)),
    inference(clausify,[status(thm)],[f_2008_3]) ).

fof(f_2009_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_2009_2,plain,
    ! [U_6857,U_6856,U_6855,U_6854] :
      ( ( c_Random__Sequence_ORandom(U_6855,U_6856,U_6854,U_6857) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_6855,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_6855)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(U_6856,U_6857)),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_6855)))),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_6855)))),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_6855)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(U_6855,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_6855)))),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_6855)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(U_6855,U_6856,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6854),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6857))),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_6855)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6855))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6855)))),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_6855)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(U_6855,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_6855)))),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_6855)))),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_6855))))),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_6855)))),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_6855)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6855)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6855))))),tc_prod(U_6855,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(U_6855)),hAPP(hAPP(c_COMBB(U_6855,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6855)))),tc_prod(U_6855,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(U_6855)),c_Product__Type_Ofst(U_6855,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_6854),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) )
      & ( c_Random__Sequence_ORandom(U_6855,U_6856,U_6854,U_6857) = 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_6855)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_6855))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6854),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ) ),
    inference(variable_rename,[status(thm)],[f_2009_1]) ).

fof(f_2009_3,plain,
    ( ! [U_6865,U_6863,U_6861,U_6859] :
        ( c_Random__Sequence_ORandom(U_6861,U_6863,U_6859,U_6865) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_6861,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_6861)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(U_6863,U_6865)),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_6861)))),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_6861)))),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_6861)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(U_6861,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_6861)))),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_6861)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(U_6861,U_6863,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6859),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6865))),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_6861)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6861))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6861)))),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_6861)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(U_6861,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_6861)))),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_6861)))),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_6861))))),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_6861)))),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_6861)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6861)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6861))))),tc_prod(U_6861,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(U_6861)),hAPP(hAPP(c_COMBB(U_6861,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6861)))),tc_prod(U_6861,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(U_6861)),c_Product__Type_Ofst(U_6861,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_6859),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) )
    & ! [U_6864,U_6862,U_6860,U_6858] :
        ( c_Random__Sequence_ORandom(U_6860,U_6862,U_6858,U_6864) = 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_6860)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_6860))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6858),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ) ),
    inference(miniscope,[status(thm)],[f_2009_2]) ).

fof(f_2009_4,plain,
    ( ! [U_6861,U_6859,U_6863,U_6865] :
        ( c_Random__Sequence_ORandom(U_6861,U_6863,U_6859,U_6865) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_6861,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_6861)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(U_6863,U_6865)),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_6861)))),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_6861)))),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_6861)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(U_6861,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_6861)))),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_6861)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(U_6861,U_6863,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6859),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6865))),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_6861)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6861))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6861)))),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_6861)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(U_6861,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_6861)))),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_6861)))),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_6861))))),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_6861)))),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_6861)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6861)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6861))))),tc_prod(U_6861,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(U_6861)),hAPP(hAPP(c_COMBB(U_6861,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6861)))),tc_prod(U_6861,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(U_6861)),c_Product__Type_Ofst(U_6861,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_6859),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) )
    & ! [U_6862,U_6860,U_6858,U_6864] :
        ( c_Random__Sequence_ORandom(U_6860,U_6862,U_6858,U_6864) = 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_6860)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_6860))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6858),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2009_3]) ).

cnf(f_2009_5,plain,
    ( c_Random__Sequence_ORandom(U_6860,U_6862,U_6858,U_6864) = 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_6860)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_6860))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_6858),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ),
    inference(clausify,[status(thm)],[f_2009_4]) ).

cnf(f_2009_6,plain,
    ( c_Random__Sequence_ORandom(U_6861,U_6863,U_6859,U_6865) = hAPP(hAPP(c_Product__Type_Oscomp(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_6861,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_6861)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(U_6863,U_6865)),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_6861)))),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_6861)))),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_6861)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_prod(U_6861,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_6861)))),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_6861)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random__Sequence_ORandom(U_6861,U_6863,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_6859),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)),U_6865))),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_6861)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6861))))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6861)))),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_6861)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)))),tc_prod(U_6861,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_6861)))),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_6861)))),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_6861))))),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_6861)))),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_6861)))),tc_fun(tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6861)))),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6861))))),tc_prod(U_6861,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Ounion(U_6861)),hAPP(hAPP(c_COMBB(U_6861,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_HOL_Obool,tc_Option_Ooption(tc_Lazy__Sequence_Olazy__sequence(U_6861)))),tc_prod(U_6861,tc_fun(tc_Product__Type_Ounit,tc_Code__Evaluation_Oterm))),c_DSequence_Osingle(U_6861)),c_Product__Type_Ofst(U_6861,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_6859),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))) ),
    inference(clausify,[status(thm)],[f_2009_4]) ).

fof(f_2010_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_2010_2,plain,
    ! [U_6867,U_6866] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6866),U_6867))
        | ~ 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_6866)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6867))) )
      & ( 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_6866)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6867)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6866),U_6867)) ) ),
    inference(variable_rename,[status(thm)],[f_2010_1]) ).

fof(f_2010_3,plain,
    ( ! [U_6871,U_6869] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6869),U_6871))
        | ~ 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_6869)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6871))) )
    & ! [U_6870,U_6868] :
        ( 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_6868)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6870)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6868),U_6870)) ) ),
    inference(miniscope,[status(thm)],[f_2010_2]) ).

fof(f_2010_4,plain,
    ( ! [U_6871,U_6869] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6869),U_6871))
        | ~ 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_6869)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6871))) )
    & ! [U_6868,U_6870] :
        ( 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_6868)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6870)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6868),U_6870)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2010_3]) ).

cnf(f_2010_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_6868)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6870)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6868),U_6870)) ),
    inference(clausify,[status(thm)],[f_2010_4]) ).

cnf(f_2010_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6869),U_6871))
    | ~ 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_6869)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6871))) ),
    inference(clausify,[status(thm)],[f_2010_4]) ).

fof(f_2011_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_2011_2,plain,
    ! [U_6873,U_6872] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6872),U_6873))
        | ~ 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_6872)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6873))) )
      & ( 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_6872)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6873)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6872),U_6873)) ) ),
    inference(variable_rename,[status(thm)],[f_2011_1]) ).

fof(f_2011_3,plain,
    ( ! [U_6877,U_6875] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6875),U_6877))
        | ~ 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_6875)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6877))) )
    & ! [U_6876,U_6874] :
        ( 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_6874)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6876)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6874),U_6876)) ) ),
    inference(miniscope,[status(thm)],[f_2011_2]) ).

fof(f_2011_4,plain,
    ( ! [U_6875,U_6877] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6875),U_6877))
        | ~ 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_6875)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6877))) )
    & ! [U_6874,U_6876] :
        ( 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_6874)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6876)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6874),U_6876)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2011_3]) ).

cnf(f_2011_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_6874)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6876)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6874),U_6876)) ),
    inference(clausify,[status(thm)],[f_2011_4]) ).

cnf(f_2011_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_6875),U_6877))
    | ~ 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_6875)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6877))) ),
    inference(clausify,[status(thm)],[f_2011_4]) ).

fof(f_2012_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_2012_2,plain,
    ! [U_6878] : 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_6878)) = U_6878,
    inference(variable_rename,[status(thm)],[f_2012_1]) ).

fof(f_2012_3,plain,
    ! [U_6878] : 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_6878)) = U_6878,
    inference(definitional_conversion,[status(esa)],[f_2012_2]) ).

cnf(f_2012_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_6878)) = U_6878,
    inference(clausify,[status(thm)],[f_2012_3]) ).

fof(f_2013_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_2013_2,plain,
    ! [U_6880,U_6879] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6879),U_6880))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6879)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6880))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6879)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6880)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6879),U_6880)) ) ),
    inference(variable_rename,[status(thm)],[f_2013_1]) ).

fof(f_2013_3,plain,
    ( ! [U_6884,U_6882] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6882),U_6884))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6882)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6884))) )
    & ! [U_6883,U_6881] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6881)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6883)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6881),U_6883)) ) ),
    inference(miniscope,[status(thm)],[f_2013_2]) ).

fof(f_2013_4,plain,
    ( ! [U_6882,U_6884] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6882),U_6884))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6882)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6884))) )
    & ! [U_6883,U_6881] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6881)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6883)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6881),U_6883)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2013_3]) ).

cnf(f_2013_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6881)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6883)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6881),U_6883)) ),
    inference(clausify,[status(thm)],[f_2013_4]) ).

cnf(f_2013_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_6882),U_6884))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_6882)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6884))) ),
    inference(clausify,[status(thm)],[f_2013_4]) ).

fof(f_2014_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_2014_2,plain,
    ! [U_6886,U_6885] :
      ( ( U_6885 = U_6886
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6885) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6886) )
      & ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6885) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6886)
        | U_6885 != U_6886 ) ),
    inference(variable_rename,[status(thm)],[f_2014_1]) ).

fof(f_2014_3,plain,
    ( ! [U_6890,U_6888] :
        ( U_6888 = U_6890
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6888) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6890) )
    & ! [U_6889,U_6887] :
        ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6887) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6889)
        | U_6887 != U_6889 ) ),
    inference(miniscope,[status(thm)],[f_2014_2]) ).

fof(f_2014_4,plain,
    ( ! [U_6888,U_6890] :
        ( U_6888 = U_6890
        | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6888) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6890) )
    & ! [U_6887,U_6889] :
        ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6887) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6889)
        | U_6887 != U_6889 ) ),
    inference(definitional_conversion,[status(esa)],[f_2014_3]) ).

cnf(f_2014_5,plain,
    ( hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6887) = hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6889)
    | U_6887 != U_6889 ),
    inference(clausify,[status(thm)],[f_2014_4]) ).

cnf(f_2014_6,plain,
    ( U_6888 = U_6890
    | hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6888) != hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_6890) ),
    inference(clausify,[status(thm)],[f_2014_4]) ).

fof(f_2015_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_2015_2,plain,
    ! [U_6896,U_6895,U_6894,U_6893,U_6892,U_6891] :
      ( ( c_Nitpick_Opair__box_OPairBox(U_6891,U_6892,U_6893,U_6894) = c_Nitpick_Opair__box_OPairBox(U_6891,U_6892,U_6895,U_6896)
        | U_6894 != U_6896
        | U_6893 != U_6895 )
      & ( ( U_6894 = U_6896
          & U_6893 = U_6895 )
        | c_Nitpick_Opair__box_OPairBox(U_6891,U_6892,U_6893,U_6894) != c_Nitpick_Opair__box_OPairBox(U_6891,U_6892,U_6895,U_6896) ) ),
    inference(variable_rename,[status(thm)],[f_2015_1]) ).

fof(f_2015_3,plain,
    ( ! [U_6908,U_6906,U_6904,U_6902] :
        ( ! [U_6900,U_6898] : c_Nitpick_Opair__box_OPairBox(U_6898,U_6900,U_6902,U_6904) = c_Nitpick_Opair__box_OPairBox(U_6898,U_6900,U_6906,U_6908)
        | U_6904 != U_6908
        | U_6902 != U_6906 )
    & ! [U_6907,U_6905,U_6903,U_6901] :
        ( ! [U_6899,U_6897] : c_Nitpick_Opair__box_OPairBox(U_6897,U_6899,U_6901,U_6903) != c_Nitpick_Opair__box_OPairBox(U_6897,U_6899,U_6905,U_6907)
        | ( U_6903 = U_6907
          & U_6901 = U_6905 ) ) ),
    inference(miniscope,[status(thm)],[f_2015_2]) ).

fof(f_2015_4,plain,
    ( ! [U_6901,U_6905,U_6907,U_6903] :
        ( U_6903 = U_6907
        | ~ sP624(U_6901,U_6905,U_6907,U_6903) )
    & ! [U_6901,U_6905,U_6907,U_6903] :
        ( U_6901 = U_6905
        | ~ sP624(U_6901,U_6905,U_6907,U_6903) )
    & ! [U_6906,U_6904,U_6902,U_6898,U_6908,U_6900] :
        ( c_Nitpick_Opair__box_OPairBox(U_6898,U_6900,U_6902,U_6904) = c_Nitpick_Opair__box_OPairBox(U_6898,U_6900,U_6906,U_6908)
        | U_6904 != U_6908
        | U_6902 != U_6906 )
    & ! [U_6901,U_6905,U_6907,U_6897,U_6899,U_6903] :
        ( c_Nitpick_Opair__box_OPairBox(U_6897,U_6899,U_6901,U_6903) != c_Nitpick_Opair__box_OPairBox(U_6897,U_6899,U_6905,U_6907)
        | sP624(U_6901,U_6905,U_6907,U_6903) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP624])],[f_2015_3]) ).

cnf(f_2015_5,plain,
    ( c_Nitpick_Opair__box_OPairBox(U_6897,U_6899,U_6901,U_6903) != c_Nitpick_Opair__box_OPairBox(U_6897,U_6899,U_6905,U_6907)
    | sP624(U_6901,U_6905,U_6907,U_6903) ),
    inference(clausify,[status(thm)],[f_2015_4]) ).

cnf(f_2015_6,plain,
    ( c_Nitpick_Opair__box_OPairBox(U_6898,U_6900,U_6902,U_6904) = c_Nitpick_Opair__box_OPairBox(U_6898,U_6900,U_6906,U_6908)
    | U_6904 != U_6908
    | U_6902 != U_6906 ),
    inference(clausify,[status(thm)],[f_2015_4]) ).

cnf(f_2015_7,plain,
    ( U_6901 = U_6905
    | ~ sP624(U_6901,U_6905,U_6907,U_6903) ),
    inference(clausify,[status(thm)],[f_2015_4]) ).

cnf(f_2015_8,plain,
    ( U_6903 = U_6907
    | ~ sP624(U_6901,U_6905,U_6907,U_6903) ),
    inference(clausify,[status(thm)],[f_2015_4]) ).

fof(f_2016_1,plain,
    ! [V_Pa_2,T_c,T_b] : c_HOL_OThe(tc_prod(T_b,T_c),V_Pa_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_Pa_2)),c_Product__Type_OPair(T_b,T_c)))),
    inference(fof_nnf,[status(thm)],[fact_split__paired__The]) ).

fof(f_2016_2,plain,
    ! [U_6911,U_6910,U_6909] : c_HOL_OThe(tc_prod(U_6909,U_6910),U_6911) = c_HOL_OThe(tc_prod(U_6909,U_6910),hAPP(c_Product__Type_Oprod_Oprod__case(U_6909,U_6910,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_6910,tc_prod(U_6909,U_6910)),tc_fun(U_6910,tc_HOL_Obool),U_6909),hAPP(c_COMBB(tc_prod(U_6909,U_6910),tc_HOL_Obool,U_6910),U_6911)),c_Product__Type_OPair(U_6909,U_6910)))),
    inference(variable_rename,[status(thm)],[f_2016_1]) ).

fof(f_2016_3,plain,
    ! [U_6909,U_6910,U_6911] : c_HOL_OThe(tc_prod(U_6909,U_6910),U_6911) = c_HOL_OThe(tc_prod(U_6909,U_6910),hAPP(c_Product__Type_Oprod_Oprod__case(U_6909,U_6910,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_6910,tc_prod(U_6909,U_6910)),tc_fun(U_6910,tc_HOL_Obool),U_6909),hAPP(c_COMBB(tc_prod(U_6909,U_6910),tc_HOL_Obool,U_6910),U_6911)),c_Product__Type_OPair(U_6909,U_6910)))),
    inference(definitional_conversion,[status(esa)],[f_2016_2]) ).

cnf(f_2016_4,plain,
    c_HOL_OThe(tc_prod(U_6909,U_6910),U_6911) = c_HOL_OThe(tc_prod(U_6909,U_6910),hAPP(c_Product__Type_Oprod_Oprod__case(U_6909,U_6910,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_6910,tc_prod(U_6909,U_6910)),tc_fun(U_6910,tc_HOL_Obool),U_6909),hAPP(c_COMBB(tc_prod(U_6909,U_6910),tc_HOL_Obool,U_6910),U_6911)),c_Product__Type_OPair(U_6909,U_6910)))),
    inference(clausify,[status(thm)],[f_2016_3]) ).

fof(f_2017_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_2017_2,plain,
    ! [U_6915,U_6914,U_6913,U_6912] : c_HOL_OThe(tc_prod(U_6912,U_6913),hAPP(c_Product__Type_Oprod_Oprod__case(U_6912,U_6913,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_6912,tc_fun(U_6913,tc_HOL_Obool),tc_fun(U_6913,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_6913,tc_HOL_Obool),tc_fun(U_6913,tc_HOL_Obool)),U_6912),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_6913)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_6912),c_fconj),hAPP(c_fequal,U_6914)))),hAPP(c_fequal,U_6915)))) = hAPP(hAPP(c_Product__Type_OPair(U_6912,U_6913),U_6914),U_6915),
    inference(variable_rename,[status(thm)],[f_2017_1]) ).

fof(f_2017_3,plain,
    ! [U_6913,U_6912,U_6914,U_6915] : c_HOL_OThe(tc_prod(U_6912,U_6913),hAPP(c_Product__Type_Oprod_Oprod__case(U_6912,U_6913,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_6912,tc_fun(U_6913,tc_HOL_Obool),tc_fun(U_6913,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_6913,tc_HOL_Obool),tc_fun(U_6913,tc_HOL_Obool)),U_6912),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_6913)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_6912),c_fconj),hAPP(c_fequal,U_6914)))),hAPP(c_fequal,U_6915)))) = hAPP(hAPP(c_Product__Type_OPair(U_6912,U_6913),U_6914),U_6915),
    inference(definitional_conversion,[status(esa)],[f_2017_2]) ).

cnf(f_2017_4,plain,
    c_HOL_OThe(tc_prod(U_6912,U_6913),hAPP(c_Product__Type_Oprod_Oprod__case(U_6912,U_6913,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_6912,tc_fun(U_6913,tc_HOL_Obool),tc_fun(U_6913,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_6913,tc_HOL_Obool),tc_fun(U_6913,tc_HOL_Obool)),U_6912),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_6913)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_6912),c_fconj),hAPP(c_fequal,U_6914)))),hAPP(c_fequal,U_6915)))) = hAPP(hAPP(c_Product__Type_OPair(U_6912,U_6913),U_6914),U_6915),
    inference(clausify,[status(thm)],[f_2017_3]) ).

fof(f_2018_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_2018_2,plain,
    ! [U_6917,U_6916] : c_Divides_Odivmod__nat(U_6916,U_6917) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_6916,U_6917)),
    inference(variable_rename,[status(thm)],[f_2018_1]) ).

fof(f_2018_3,plain,
    ! [U_6916,U_6917] : c_Divides_Odivmod__nat(U_6916,U_6917) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_6916,U_6917)),
    inference(definitional_conversion,[status(esa)],[f_2018_2]) ).

cnf(f_2018_4,plain,
    c_Divides_Odivmod__nat(U_6916,U_6917) = c_HOL_OThe(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_Divides_Odivmod__nat__rel(U_6916,U_6917)),
    inference(clausify,[status(thm)],[f_2018_3]) ).

fof(f_2019_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_2019_2,plain,
    ! [U_6920,U_6919,U_6918] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_6918,U_6919,U_6920,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_6919,
    inference(variable_rename,[status(thm)],[f_2019_1]) ).

fof(f_2019_3,plain,
    ! [U_6918,U_6919,U_6920] : c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_6918,U_6919,U_6920,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_6919,
    inference(definitional_conversion,[status(esa)],[f_2019_2]) ).

cnf(f_2019_4,plain,
    c_Code__Numeral_Ocode__numeral_Ocode__numeral__rec(U_6918,U_6919,U_6920,c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)) = U_6919,
    inference(clausify,[status(thm)],[f_2019_3]) ).

fof(f_2020_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_2020_2,plain,
    ! [U_6923,U_6922,U_6921] : c_Random__Sequence_Oempty(U_6921,U_6922,U_6923) = 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_6921)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_6921)),
    inference(variable_rename,[status(thm)],[f_2020_1]) ).

fof(f_2020_3,plain,
    ! [U_6921,U_6922,U_6923] : c_Random__Sequence_Oempty(U_6921,U_6922,U_6923) = 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_6921)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_6921)),
    inference(definitional_conversion,[status(esa)],[f_2020_2]) ).

cnf(f_2020_4,plain,
    c_Random__Sequence_Oempty(U_6921,U_6922,U_6923) = 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_6921)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),c_DSequence_Oempty(U_6921)),
    inference(clausify,[status(thm)],[f_2020_3]) ).

fof(f_2021_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_2021_2,plain,
    ! [U_6927,U_6926,U_6925,U_6924] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(U_6924),U_6925),U_6926),U_6927) = 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_6924)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(U_6924),U_6925)),
    inference(variable_rename,[status(thm)],[f_2021_1]) ).

fof(f_2021_3,plain,
    ! [U_6924,U_6925,U_6926,U_6927] : hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(U_6924),U_6925),U_6926),U_6927) = 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_6924)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(U_6924),U_6925)),
    inference(definitional_conversion,[status(esa)],[f_2021_2]) ).

cnf(f_2021_4,plain,
    hAPP(hAPP(hAPP(c_Random__Sequence_Osingle(U_6924),U_6925),U_6926),U_6927) = 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_6924)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_DSequence_Osingle(U_6924),U_6925)),
    inference(clausify,[status(thm)],[f_2021_3]) ).

fof(f_2022_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_2022_2,plain,
    ! [U_6931,U_6930,U_6929,U_6928] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(U_6928,U_6929)),c_Nitpick_Opair__box_OPairBox(U_6928,U_6929,U_6930,U_6931)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_2022_1]) ).

fof(f_2022_3,plain,
    ! [U_6928,U_6929,U_6930,U_6931] : hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(U_6928,U_6929)),c_Nitpick_Opair__box_OPairBox(U_6928,U_6929,U_6930,U_6931)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_2022_2]) ).

cnf(f_2022_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_Nitpick_Opair__box(U_6928,U_6929)),c_Nitpick_Opair__box_OPairBox(U_6928,U_6929,U_6930,U_6931)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2022_3]) ).

fof(f_2023_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_2023_2,plain,
    ! [U_6937,U_6936,U_6935,U_6934,U_6933,U_6932] : c_Nitpick_Opair__box_Opair__box__case(U_6932,U_6933,U_6934,U_6935,c_Nitpick_Opair__box_OPairBox(U_6932,U_6933,U_6936,U_6937)) = hAPP(hAPP(U_6935,U_6936),U_6937),
    inference(variable_rename,[status(thm)],[f_2023_1]) ).

fof(f_2023_3,plain,
    ! [U_6932,U_6933,U_6934,U_6935,U_6936,U_6937] : c_Nitpick_Opair__box_Opair__box__case(U_6932,U_6933,U_6934,U_6935,c_Nitpick_Opair__box_OPairBox(U_6932,U_6933,U_6936,U_6937)) = hAPP(hAPP(U_6935,U_6936),U_6937),
    inference(definitional_conversion,[status(esa)],[f_2023_2]) ).

cnf(f_2023_4,plain,
    c_Nitpick_Opair__box_Opair__box__case(U_6932,U_6933,U_6934,U_6935,c_Nitpick_Opair__box_OPairBox(U_6932,U_6933,U_6936,U_6937)) = hAPP(hAPP(U_6935,U_6936),U_6937),
    inference(clausify,[status(thm)],[f_2023_3]) ).

fof(f_2024_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_2024_2,plain,
    ! [U_6943,U_6942,U_6941,U_6940,U_6939,U_6938] : c_Nitpick_Opair__box_Opair__box__rec(U_6938,U_6939,U_6940,U_6941,c_Nitpick_Opair__box_OPairBox(U_6938,U_6939,U_6942,U_6943)) = hAPP(hAPP(U_6941,U_6942),U_6943),
    inference(variable_rename,[status(thm)],[f_2024_1]) ).

fof(f_2024_3,plain,
    ! [U_6939,U_6938,U_6940,U_6941,U_6942,U_6943] : c_Nitpick_Opair__box_Opair__box__rec(U_6938,U_6939,U_6940,U_6941,c_Nitpick_Opair__box_OPairBox(U_6938,U_6939,U_6942,U_6943)) = hAPP(hAPP(U_6941,U_6942),U_6943),
    inference(definitional_conversion,[status(esa)],[f_2024_2]) ).

cnf(f_2024_4,plain,
    c_Nitpick_Opair__box_Opair__box__rec(U_6938,U_6939,U_6940,U_6941,c_Nitpick_Opair__box_OPairBox(U_6938,U_6939,U_6942,U_6943)) = hAPP(hAPP(U_6941,U_6942),U_6943),
    inference(clausify,[status(thm)],[f_2024_3]) ).

fof(f_2025_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_2025_2,plain,
    ! [U_6945,U_6944] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_6944),U_6945))
          | ~ 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_6944)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6945))) )
        & ( 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_6944)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6945)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_6944),U_6945)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_6945)
      | ~ c_Nat__Transfer_Onat__set(U_6944) ),
    inference(variable_rename,[status(thm)],[f_2025_1]) ).

fof(f_2025_3,plain,
    ( ! [U_6944,U_6945] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_6944),U_6945))
        | ~ 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_6944)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6945)))
        | ~ sP625(U_6944,U_6945) )
    & ! [U_6944,U_6945] :
        ( 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_6944)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6945)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_6944),U_6945))
        | ~ sP625(U_6944,U_6945) )
    & ! [U_6944,U_6945] :
        ( sP625(U_6944,U_6945)
        | ~ c_Nat__Transfer_Onat__set(U_6945)
        | ~ c_Nat__Transfer_Onat__set(U_6944) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP625])],[f_2025_2]) ).

cnf(f_2025_4,plain,
    ( sP625(U_6944,U_6945)
    | ~ c_Nat__Transfer_Onat__set(U_6945)
    | ~ c_Nat__Transfer_Onat__set(U_6944) ),
    inference(clausify,[status(thm)],[f_2025_3]) ).

cnf(f_2025_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_6944)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6945)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_6944),U_6945))
    | ~ sP625(U_6944,U_6945) ),
    inference(clausify,[status(thm)],[f_2025_3]) ).

cnf(f_2025_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_6944),U_6945))
    | ~ 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_6944)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6945)))
    | ~ sP625(U_6944,U_6945) ),
    inference(clausify,[status(thm)],[f_2025_3]) ).

fof(f_2026_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_2026_2,plain,
    ! [U_6947,U_6946] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_6946),U_6947))
          | ~ 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_6946)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6947))) )
        & ( 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_6946)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6947)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_6946),U_6947)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_6947)
      | ~ c_Nat__Transfer_Onat__set(U_6946) ),
    inference(variable_rename,[status(thm)],[f_2026_1]) ).

fof(f_2026_3,plain,
    ( ! [U_6946,U_6947] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_6946),U_6947))
        | ~ 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_6946)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6947)))
        | ~ sP626(U_6946,U_6947) )
    & ! [U_6946,U_6947] :
        ( 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_6946)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6947)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_6946),U_6947))
        | ~ sP626(U_6946,U_6947) )
    & ! [U_6946,U_6947] :
        ( sP626(U_6946,U_6947)
        | ~ c_Nat__Transfer_Onat__set(U_6947)
        | ~ c_Nat__Transfer_Onat__set(U_6946) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP626])],[f_2026_2]) ).

cnf(f_2026_4,plain,
    ( sP626(U_6946,U_6947)
    | ~ c_Nat__Transfer_Onat__set(U_6947)
    | ~ c_Nat__Transfer_Onat__set(U_6946) ),
    inference(clausify,[status(thm)],[f_2026_3]) ).

cnf(f_2026_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_6946)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6947)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_6946),U_6947))
    | ~ sP626(U_6946,U_6947) ),
    inference(clausify,[status(thm)],[f_2026_3]) ).

cnf(f_2026_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_6946),U_6947))
    | ~ 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_6946)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6947)))
    | ~ sP626(U_6946,U_6947) ),
    inference(clausify,[status(thm)],[f_2026_3]) ).

fof(f_2027_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_2027_2,plain,
    ! [U_6949,U_6948] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6948),U_6949))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_6948)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6949))) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_6948)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6949)))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6948),U_6949)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_6949)
      | ~ c_Nat__Transfer_Ois__nat(U_6948) ),
    inference(variable_rename,[status(thm)],[f_2027_1]) ).

fof(f_2027_3,plain,
    ( ! [U_6949,U_6948] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6948),U_6949))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_6948)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6949)))
        | ~ sP627(U_6949,U_6948) )
    & ! [U_6949,U_6948] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_6948)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6949)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6948),U_6949))
        | ~ sP627(U_6949,U_6948) )
    & ! [U_6949,U_6948] :
        ( sP627(U_6949,U_6948)
        | ~ c_Nat__Transfer_Onat__set(U_6949)
        | ~ c_Nat__Transfer_Ois__nat(U_6948) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP627])],[f_2027_2]) ).

cnf(f_2027_4,plain,
    ( sP627(U_6949,U_6948)
    | ~ c_Nat__Transfer_Onat__set(U_6949)
    | ~ c_Nat__Transfer_Ois__nat(U_6948) ),
    inference(clausify,[status(thm)],[f_2027_3]) ).

cnf(f_2027_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_6948)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6949)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6948),U_6949))
    | ~ sP627(U_6949,U_6948) ),
    inference(clausify,[status(thm)],[f_2027_3]) ).

cnf(f_2027_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6948),U_6949))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Int_Onat,U_6948)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6949)))
    | ~ sP627(U_6949,U_6948) ),
    inference(clausify,[status(thm)],[f_2027_3]) ).

fof(f_2028_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_2028_2,plain,
    ! [U_6950] :
      ( 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_6950)) = U_6950
      | ~ c_Nat__Transfer_Onat__set(U_6950) ),
    inference(variable_rename,[status(thm)],[f_2028_1]) ).

fof(f_2028_3,plain,
    ! [U_6950] :
      ( 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_6950)) = U_6950
      | ~ c_Nat__Transfer_Onat__set(U_6950) ),
    inference(definitional_conversion,[status(esa)],[f_2028_2]) ).

cnf(f_2028_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_6950)) = U_6950
    | ~ c_Nat__Transfer_Onat__set(U_6950) ),
    inference(clausify,[status(thm)],[f_2028_3]) ).

fof(f_2029_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_2029_2,plain,
    ! [U_6952,U_6951] : c_HOL_OThe(U_6951,hAPP(hAPP(c_COMBC(U_6951,U_6951,tc_HOL_Obool),c_fequal),U_6952)) = U_6952,
    inference(variable_rename,[status(thm)],[f_2029_1]) ).

fof(f_2029_3,plain,
    ! [U_6951,U_6952] : c_HOL_OThe(U_6951,hAPP(hAPP(c_COMBC(U_6951,U_6951,tc_HOL_Obool),c_fequal),U_6952)) = U_6952,
    inference(definitional_conversion,[status(esa)],[f_2029_2]) ).

cnf(f_2029_4,plain,
    c_HOL_OThe(U_6951,hAPP(hAPP(c_COMBC(U_6951,U_6951,tc_HOL_Obool),c_fequal),U_6952)) = U_6952,
    inference(clausify,[status(thm)],[f_2029_3]) ).

fof(f_2030_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_2030_2,plain,
    ! [U_6955] :
      ( ( c_Nat__Transfer_Onat__set(U_6955)
        | ? [U_6954] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6954))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6954),U_6955)) ) )
      & ( ! [U_6953] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6953))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6953),U_6955)) )
        | ~ c_Nat__Transfer_Onat__set(U_6955) ) ),
    inference(variable_rename,[status(thm)],[f_2030_1]) ).

fof(f_2030_3,plain,
    ( ! [U_6957] :
        ( c_Nat__Transfer_Onat__set(U_6957)
        | ? [U_6954] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6954))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6954),U_6957)) ) )
    & ! [U_6956] :
        ( ! [U_6953] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6953))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6953),U_6956)) )
        | ~ c_Nat__Transfer_Onat__set(U_6956) ) ),
    inference(miniscope,[status(thm)],[f_2030_2]) ).

fof(f_2030_4,plain,
    ( ! [U_6957] :
        ( c_Nat__Transfer_Onat__set(U_6957)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK101(U_6957)))
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK101(U_6957)),U_6957)) ) )
    & ! [U_6956] :
        ( ! [U_6953] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6953))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6953),U_6956)) )
        | ~ c_Nat__Transfer_Onat__set(U_6956) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK101]),skolemize(U_6954,sK101(U_6957))],[f_2030_3]) ).

fof(f_2030_5,plain,
    ( ! [U_6957] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK101(U_6957)))
        | ~ sP628(U_6957) )
    & ! [U_6957] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK101(U_6957)),U_6957))
        | ~ sP628(U_6957) )
    & ! [U_6957] :
        ( c_Nat__Transfer_Onat__set(U_6957)
        | sP628(U_6957) )
    & ! [U_6953,U_6956] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6953))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6953),U_6956))
        | ~ c_Nat__Transfer_Onat__set(U_6956) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP628])],[f_2030_4]) ).

cnf(f_2030_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6953))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6953),U_6956))
    | ~ c_Nat__Transfer_Onat__set(U_6956) ),
    inference(clausify,[status(thm)],[f_2030_5]) ).

cnf(f_2030_7,plain,
    ( c_Nat__Transfer_Onat__set(U_6957)
    | sP628(U_6957) ),
    inference(clausify,[status(thm)],[f_2030_5]) ).

cnf(f_2030_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK101(U_6957)),U_6957))
    | ~ sP628(U_6957) ),
    inference(clausify,[status(thm)],[f_2030_5]) ).

cnf(f_2030_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK101(U_6957)))
    | ~ sP628(U_6957) ),
    inference(clausify,[status(thm)],[f_2030_5]) ).

fof(f_2031_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_2031_2,plain,
    ! [U_6958] : 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_6958)),
    inference(variable_rename,[status(thm)],[f_2031_1]) ).

fof(f_2031_3,plain,
    ! [U_6958] : 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_6958)),
    inference(definitional_conversion,[status(esa)],[f_2031_2]) ).

cnf(f_2031_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_6958)),
    inference(clausify,[status(thm)],[f_2031_3]) ).

fof(f_2032_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_2032_2,plain,
    ! [U_6960,U_6959] :
      ( ( ( U_6959 = U_6960
          | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6959) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6960) )
        & ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6959) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6960)
          | U_6959 != U_6960 ) )
      | ~ c_Nat__Transfer_Onat__set(U_6960)
      | ~ c_Nat__Transfer_Onat__set(U_6959) ),
    inference(variable_rename,[status(thm)],[f_2032_1]) ).

fof(f_2032_3,plain,
    ( ! [U_6959,U_6960] :
        ( U_6959 = U_6960
        | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6959) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6960)
        | ~ sP629(U_6959,U_6960) )
    & ! [U_6959,U_6960] :
        ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6959) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6960)
        | U_6959 != U_6960
        | ~ sP629(U_6959,U_6960) )
    & ! [U_6959,U_6960] :
        ( sP629(U_6959,U_6960)
        | ~ c_Nat__Transfer_Onat__set(U_6960)
        | ~ c_Nat__Transfer_Onat__set(U_6959) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP629])],[f_2032_2]) ).

cnf(f_2032_4,plain,
    ( sP629(U_6959,U_6960)
    | ~ c_Nat__Transfer_Onat__set(U_6960)
    | ~ c_Nat__Transfer_Onat__set(U_6959) ),
    inference(clausify,[status(thm)],[f_2032_3]) ).

cnf(f_2032_5,plain,
    ( hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6959) = hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6960)
    | U_6959 != U_6960
    | ~ sP629(U_6959,U_6960) ),
    inference(clausify,[status(thm)],[f_2032_3]) ).

cnf(f_2032_6,plain,
    ( U_6959 = U_6960
    | hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6959) != hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_6960)
    | ~ sP629(U_6959,U_6960) ),
    inference(clausify,[status(thm)],[f_2032_3]) ).

fof(f_2033_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_2033_2,plain,
    ! [U_6962,U_6961] :
      ( c_Nat__Transfer_Ois__nat(U_6962)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6962),U_6961))
      | ~ c_Nat__Transfer_Onat__set(U_6961) ),
    inference(variable_rename,[status(thm)],[f_2033_1]) ).

fof(f_2033_3,plain,
    ! [U_6961,U_6962] :
      ( c_Nat__Transfer_Ois__nat(U_6962)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6962),U_6961))
      | ~ c_Nat__Transfer_Onat__set(U_6961) ),
    inference(definitional_conversion,[status(esa)],[f_2033_2]) ).

cnf(f_2033_4,plain,
    ( c_Nat__Transfer_Ois__nat(U_6962)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6962),U_6961))
    | ~ c_Nat__Transfer_Onat__set(U_6961) ),
    inference(clausify,[status(thm)],[f_2033_3]) ).

fof(f_2034_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_2034_2,plain,
    ! [U_6964,U_6963] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6964))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6964),U_6963))
      | ~ c_Nat__Transfer_Onat__set(U_6963) ),
    inference(variable_rename,[status(thm)],[f_2034_1]) ).

fof(f_2034_3,plain,
    ! [U_6963,U_6964] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6964))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6964),U_6963))
      | ~ c_Nat__Transfer_Onat__set(U_6963) ),
    inference(definitional_conversion,[status(esa)],[f_2034_2]) ).

cnf(f_2034_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_6964))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_6964),U_6963))
    | ~ c_Nat__Transfer_Onat__set(U_6963) ),
    inference(clausify,[status(thm)],[f_2034_3]) ).

fof(f_2035_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_2035_2,plain,
    ! [U_6966,U_6965] : c_HOL_OThe(U_6965,hAPP(c_fequal,U_6966)) = U_6966,
    inference(variable_rename,[status(thm)],[f_2035_1]) ).

fof(f_2035_3,plain,
    ! [U_6966,U_6965] : c_HOL_OThe(U_6965,hAPP(c_fequal,U_6966)) = U_6966,
    inference(definitional_conversion,[status(esa)],[f_2035_2]) ).

cnf(f_2035_4,plain,
    c_HOL_OThe(U_6965,hAPP(c_fequal,U_6966)) = U_6966,
    inference(clausify,[status(thm)],[f_2035_3]) ).

fof(f_2036_1,plain,
    ! [T_d,V_f_2,V_Qa_2,V_p_2,T_b,T_c,V_Pa_2] :
      ( hBOOL(hAPP(V_Qa_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_Qa_2,hAPP(hAPP(V_f_2,B_x),B_y)))
          & hBOOL(hAPP(hAPP(V_Pa_2,B_y),B_x)) )
      | ~ hBOOL(hAPP(hAPP(V_Pa_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_2036_2,plain,
    ! [U_6975,U_6974,U_6973,U_6972,U_6971,U_6970,U_6969] :
      ( hBOOL(hAPP(U_6973,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6970,U_6971,U_6975),U_6974),U_6972)))
      | ? [U_6968,U_6967] :
          ( ~ hBOOL(hAPP(U_6973,hAPP(hAPP(U_6974,U_6968),U_6967)))
          & hBOOL(hAPP(hAPP(U_6969,U_6967),U_6968)) )
      | ~ hBOOL(hAPP(hAPP(U_6969,hAPP(c_Product__Type_Osnd(U_6970,U_6971),U_6972)),hAPP(c_Product__Type_Ofst(U_6970,U_6971),U_6972))) ),
    inference(variable_rename,[status(thm)],[f_2036_1]) ).

fof(f_2036_3,plain,
    ! [U_6975,U_6974,U_6973,U_6972,U_6971,U_6970,U_6969] :
      ( hBOOL(hAPP(U_6973,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6970,U_6971,U_6975),U_6974),U_6972)))
      | ? [U_6967] :
          ( ~ hBOOL(hAPP(U_6973,hAPP(hAPP(U_6974,sK102(U_6975,U_6974,U_6973,U_6972,U_6971,U_6970,U_6969)),U_6967)))
          & hBOOL(hAPP(hAPP(U_6969,U_6967),sK102(U_6975,U_6974,U_6973,U_6972,U_6971,U_6970,U_6969))) )
      | ~ hBOOL(hAPP(hAPP(U_6969,hAPP(c_Product__Type_Osnd(U_6970,U_6971),U_6972)),hAPP(c_Product__Type_Ofst(U_6970,U_6971),U_6972))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK102]),skolemize(U_6968,sK102(U_6975,U_6974,U_6973,U_6972,U_6971,U_6970,U_6969))],[f_2036_2]) ).

fof(f_2036_4,plain,
    ! [U_6975,U_6974,U_6973,U_6972,U_6971,U_6970,U_6969] :
      ( hBOOL(hAPP(U_6973,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6970,U_6971,U_6975),U_6974),U_6972)))
      | ( ~ hBOOL(hAPP(U_6973,hAPP(hAPP(U_6974,sK102(U_6975,U_6974,U_6973,U_6972,U_6971,U_6970,U_6969)),sK103(U_6975,U_6974,U_6973,U_6972,U_6971,U_6970,U_6969))))
        & hBOOL(hAPP(hAPP(U_6969,sK103(U_6975,U_6974,U_6973,U_6972,U_6971,U_6970,U_6969)),sK102(U_6975,U_6974,U_6973,U_6972,U_6971,U_6970,U_6969))) )
      | ~ hBOOL(hAPP(hAPP(U_6969,hAPP(c_Product__Type_Osnd(U_6970,U_6971),U_6972)),hAPP(c_Product__Type_Ofst(U_6970,U_6971),U_6972))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK103]),skolemize(U_6967,sK103(U_6975,U_6974,U_6973,U_6972,U_6971,U_6970,U_6969))],[f_2036_3]) ).

fof(f_2036_5,plain,
    ( ! [U_6969,U_6970,U_6971,U_6972,U_6973,U_6974,U_6975] :
        ( ~ hBOOL(hAPP(U_6973,hAPP(hAPP(U_6974,sK102(U_6975,U_6974,U_6973,U_6972,U_6971,U_6970,U_6969)),sK103(U_6975,U_6974,U_6973,U_6972,U_6971,U_6970,U_6969))))
        | ~ sP630(U_6969,U_6970,U_6971,U_6972,U_6973,U_6974,U_6975) )
    & ! [U_6969,U_6970,U_6971,U_6972,U_6973,U_6974,U_6975] :
        ( hBOOL(hAPP(hAPP(U_6969,sK103(U_6975,U_6974,U_6973,U_6972,U_6971,U_6970,U_6969)),sK102(U_6975,U_6974,U_6973,U_6972,U_6971,U_6970,U_6969)))
        | ~ sP630(U_6969,U_6970,U_6971,U_6972,U_6973,U_6974,U_6975) )
    & ! [U_6969,U_6970,U_6971,U_6972,U_6973,U_6974,U_6975] :
        ( hBOOL(hAPP(U_6973,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6970,U_6971,U_6975),U_6974),U_6972)))
        | sP630(U_6969,U_6970,U_6971,U_6972,U_6973,U_6974,U_6975)
        | ~ hBOOL(hAPP(hAPP(U_6969,hAPP(c_Product__Type_Osnd(U_6970,U_6971),U_6972)),hAPP(c_Product__Type_Ofst(U_6970,U_6971),U_6972))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP630])],[f_2036_4]) ).

cnf(f_2036_6,plain,
    ( hBOOL(hAPP(U_6973,hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_6970,U_6971,U_6975),U_6974),U_6972)))
    | sP630(U_6969,U_6970,U_6971,U_6972,U_6973,U_6974,U_6975)
    | ~ hBOOL(hAPP(hAPP(U_6969,hAPP(c_Product__Type_Osnd(U_6970,U_6971),U_6972)),hAPP(c_Product__Type_Ofst(U_6970,U_6971),U_6972))) ),
    inference(clausify,[status(thm)],[f_2036_5]) ).

cnf(f_2036_7,plain,
    ( hBOOL(hAPP(hAPP(U_6969,sK103(U_6975,U_6974,U_6973,U_6972,U_6971,U_6970,U_6969)),sK102(U_6975,U_6974,U_6973,U_6972,U_6971,U_6970,U_6969)))
    | ~ sP630(U_6969,U_6970,U_6971,U_6972,U_6973,U_6974,U_6975) ),
    inference(clausify,[status(thm)],[f_2036_5]) ).

cnf(f_2036_8,plain,
    ( ~ hBOOL(hAPP(U_6973,hAPP(hAPP(U_6974,sK102(U_6975,U_6974,U_6973,U_6972,U_6971,U_6970,U_6969)),sK103(U_6975,U_6974,U_6973,U_6972,U_6971,U_6970,U_6969))))
    | ~ sP630(U_6969,U_6970,U_6971,U_6972,U_6973,U_6974,U_6975) ),
    inference(clausify,[status(thm)],[f_2036_5]) ).

fof(f_2037_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_2037_2,plain,
    ! [U_6977,U_6976] : hAPP(c_New__DSequence_Opos__not__seq(U_6976),U_6977) = c_Lazy__Sequence_Ohb__not__seq(hAPP(U_6976,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_6977))),
    inference(variable_rename,[status(thm)],[f_2037_1]) ).

fof(f_2037_3,plain,
    ! [U_6977,U_6976] : hAPP(c_New__DSequence_Opos__not__seq(U_6976),U_6977) = c_Lazy__Sequence_Ohb__not__seq(hAPP(U_6976,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_6977))),
    inference(definitional_conversion,[status(esa)],[f_2037_2]) ).

cnf(f_2037_4,plain,
    hAPP(c_New__DSequence_Opos__not__seq(U_6976),U_6977) = c_Lazy__Sequence_Ohb__not__seq(hAPP(U_6976,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_6977))),
    inference(clausify,[status(thm)],[f_2037_3]) ).

fof(f_2038_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_2038_2,plain,
    ! [U_6978] :
      ( ( U_6978 != 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_6978)) )
      & ( 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_6978))
        | U_6978 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_2038_1]) ).

fof(f_2038_3,plain,
    ( ! [U_6980] :
        ( U_6980 != 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_6980)) )
    & ! [U_6979] :
        ( 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_6979))
        | U_6979 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_2038_2]) ).

fof(f_2038_4,plain,
    ( ! [U_6980] :
        ( U_6980 != 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_6980)) )
    & ! [U_6979] :
        ( 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_6979))
        | U_6979 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2038_3]) ).

cnf(f_2038_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_6979))
    | U_6979 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_2038_4]) ).

cnf(f_2038_6,plain,
    ( U_6980 != 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_6980)) ),
    inference(clausify,[status(thm)],[f_2038_4]) ).

fof(f_2039_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_2039_2,plain,
    ! [U_6982,U_6981] :
      ( ( c_Quickcheck_Obeyond(U_6981,U_6982) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6981),U_6982)) )
      & ( c_Quickcheck_Obeyond(U_6981,U_6982) = U_6982
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6981),U_6982)) ) ),
    inference(variable_rename,[status(thm)],[f_2039_1]) ).

fof(f_2039_3,plain,
    ( ! [U_6986,U_6984] :
        ( c_Quickcheck_Obeyond(U_6984,U_6986) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6984),U_6986)) )
    & ! [U_6985,U_6983] :
        ( c_Quickcheck_Obeyond(U_6983,U_6985) = U_6985
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6983),U_6985)) ) ),
    inference(miniscope,[status(thm)],[f_2039_2]) ).

fof(f_2039_4,plain,
    ( ! [U_6984,U_6986] :
        ( c_Quickcheck_Obeyond(U_6984,U_6986) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6984),U_6986)) )
    & ! [U_6983,U_6985] :
        ( c_Quickcheck_Obeyond(U_6983,U_6985) = U_6985
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6983),U_6985)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2039_3]) ).

cnf(f_2039_5,plain,
    ( c_Quickcheck_Obeyond(U_6983,U_6985) = U_6985
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6983),U_6985)) ),
    inference(clausify,[status(thm)],[f_2039_4]) ).

cnf(f_2039_6,plain,
    ( c_Quickcheck_Obeyond(U_6984,U_6986) = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_6984),U_6986)) ),
    inference(clausify,[status(thm)],[f_2039_4]) ).

fof(f_2040_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_2040_2,plain,
    ! [U_6992,U_6991,U_6990,U_6989,U_6988,U_6987] : hAPP(hAPP(c_Product__Type_Ocurry(U_6987,U_6988,U_6989,U_6990),U_6991),U_6992) = hAPP(U_6990,hAPP(hAPP(c_Product__Type_OPair(U_6987,U_6988),U_6991),U_6992)),
    inference(variable_rename,[status(thm)],[f_2040_1]) ).

fof(f_2040_3,plain,
    ! [U_6987,U_6988,U_6989,U_6990,U_6991,U_6992] : hAPP(hAPP(c_Product__Type_Ocurry(U_6987,U_6988,U_6989,U_6990),U_6991),U_6992) = hAPP(U_6990,hAPP(hAPP(c_Product__Type_OPair(U_6987,U_6988),U_6991),U_6992)),
    inference(definitional_conversion,[status(esa)],[f_2040_2]) ).

cnf(f_2040_4,plain,
    hAPP(hAPP(c_Product__Type_Ocurry(U_6987,U_6988,U_6989,U_6990),U_6991),U_6992) = hAPP(U_6990,hAPP(hAPP(c_Product__Type_OPair(U_6987,U_6988),U_6991),U_6992)),
    inference(clausify,[status(thm)],[f_2040_3]) ).

fof(f_2041_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_2041_2,plain,
    ! [U_6997,U_6996,U_6995,U_6994,U_6993] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_6994,U_6995,tc_HOL_Obool,U_6993),U_6996),U_6997))
      | ~ hBOOL(hAPP(U_6993,hAPP(hAPP(c_Product__Type_OPair(U_6994,U_6995),U_6996),U_6997))) ),
    inference(variable_rename,[status(thm)],[f_2041_1]) ).

fof(f_2041_3,plain,
    ! [U_6994,U_6993,U_6995,U_6996,U_6997] :
      ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_6994,U_6995,tc_HOL_Obool,U_6993),U_6996),U_6997))
      | ~ hBOOL(hAPP(U_6993,hAPP(hAPP(c_Product__Type_OPair(U_6994,U_6995),U_6996),U_6997))) ),
    inference(definitional_conversion,[status(esa)],[f_2041_2]) ).

cnf(f_2041_4,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_6994,U_6995,tc_HOL_Obool,U_6993),U_6996),U_6997))
    | ~ hBOOL(hAPP(U_6993,hAPP(hAPP(c_Product__Type_OPair(U_6994,U_6995),U_6996),U_6997))) ),
    inference(clausify,[status(thm)],[f_2041_3]) ).

fof(f_2042_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_2042_2,plain,
    ! [U_6999,U_6998] :
      ( ( hAPP(c_Code__Numeral_Oof__nat,U_6998) = hAPP(c_Code__Numeral_Oof__nat,U_6999)
        | U_6998 != U_6999 )
      & ( U_6998 = U_6999
        | hAPP(c_Code__Numeral_Oof__nat,U_6998) != hAPP(c_Code__Numeral_Oof__nat,U_6999) ) ),
    inference(variable_rename,[status(thm)],[f_2042_1]) ).

fof(f_2042_3,plain,
    ( ! [U_7003,U_7001] :
        ( hAPP(c_Code__Numeral_Oof__nat,U_7001) = hAPP(c_Code__Numeral_Oof__nat,U_7003)
        | U_7001 != U_7003 )
    & ! [U_7002,U_7000] :
        ( U_7000 = U_7002
        | hAPP(c_Code__Numeral_Oof__nat,U_7000) != hAPP(c_Code__Numeral_Oof__nat,U_7002) ) ),
    inference(miniscope,[status(thm)],[f_2042_2]) ).

fof(f_2042_4,plain,
    ( ! [U_7003,U_7001] :
        ( hAPP(c_Code__Numeral_Oof__nat,U_7001) = hAPP(c_Code__Numeral_Oof__nat,U_7003)
        | U_7001 != U_7003 )
    & ! [U_7002,U_7000] :
        ( U_7000 = U_7002
        | hAPP(c_Code__Numeral_Oof__nat,U_7000) != hAPP(c_Code__Numeral_Oof__nat,U_7002) ) ),
    inference(definitional_conversion,[status(esa)],[f_2042_3]) ).

cnf(f_2042_5,plain,
    ( U_7000 = U_7002
    | hAPP(c_Code__Numeral_Oof__nat,U_7000) != hAPP(c_Code__Numeral_Oof__nat,U_7002) ),
    inference(clausify,[status(thm)],[f_2042_4]) ).

cnf(f_2042_6,plain,
    ( hAPP(c_Code__Numeral_Oof__nat,U_7001) = hAPP(c_Code__Numeral_Oof__nat,U_7003)
    | U_7001 != U_7003 ),
    inference(clausify,[status(thm)],[f_2042_4]) ).

fof(f_2043_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_2043_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_2043_1]) ).

cnf(f_2043_3,plain,
    c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral),
    inference(clausify,[status(thm)],[f_2043_2]) ).

fof(f_2044_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_2044_2,plain,
    ! [U_7005,U_7004] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7004)),hAPP(c_Code__Numeral_Oof__nat,U_7005)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7004),U_7005)),
    inference(variable_rename,[status(thm)],[f_2044_1]) ).

fof(f_2044_3,plain,
    ! [U_7004,U_7005] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7004)),hAPP(c_Code__Numeral_Oof__nat,U_7005)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7004),U_7005)),
    inference(definitional_conversion,[status(esa)],[f_2044_2]) ).

cnf(f_2044_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7004)),hAPP(c_Code__Numeral_Oof__nat,U_7005)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7004),U_7005)),
    inference(clausify,[status(thm)],[f_2044_3]) ).

fof(f_2045_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_2045_2,plain,
    ! [U_7006] : c_Quickcheck_Obeyond(U_7006,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_2045_1]) ).

fof(f_2045_3,plain,
    ! [U_7006] : c_Quickcheck_Obeyond(U_7006,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_2045_2]) ).

cnf(f_2045_4,plain,
    c_Quickcheck_Obeyond(U_7006,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_2045_3]) ).

fof(f_2046_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_2046_2,plain,
    ! [U_7011,U_7010,U_7009,U_7008,U_7007] :
      ( hBOOL(hAPP(U_7009,hAPP(hAPP(c_Product__Type_OPair(U_7007,U_7008),U_7010),U_7011)))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_7007,U_7008,tc_HOL_Obool,U_7009),U_7010),U_7011)) ),
    inference(variable_rename,[status(thm)],[f_2046_1]) ).

fof(f_2046_3,plain,
    ! [U_7007,U_7008,U_7009,U_7010,U_7011] :
      ( hBOOL(hAPP(U_7009,hAPP(hAPP(c_Product__Type_OPair(U_7007,U_7008),U_7010),U_7011)))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_7007,U_7008,tc_HOL_Obool,U_7009),U_7010),U_7011)) ),
    inference(definitional_conversion,[status(esa)],[f_2046_2]) ).

cnf(f_2046_4,plain,
    ( hBOOL(hAPP(U_7009,hAPP(hAPP(c_Product__Type_OPair(U_7007,U_7008),U_7010),U_7011)))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_7007,U_7008,tc_HOL_Obool,U_7009),U_7010),U_7011)) ),
    inference(clausify,[status(thm)],[f_2046_3]) ).

fof(f_2047_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_2047_2,plain,
    ! [U_7016,U_7015,U_7014,U_7013,U_7012] :
      ( hBOOL(hAPP(U_7014,hAPP(hAPP(c_Product__Type_OPair(U_7012,U_7013),U_7015),U_7016)))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_7012,U_7013,tc_HOL_Obool,U_7014),U_7015),U_7016)) ),
    inference(variable_rename,[status(thm)],[f_2047_1]) ).

fof(f_2047_3,plain,
    ! [U_7012,U_7013,U_7014,U_7015,U_7016] :
      ( hBOOL(hAPP(U_7014,hAPP(hAPP(c_Product__Type_OPair(U_7012,U_7013),U_7015),U_7016)))
      | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_7012,U_7013,tc_HOL_Obool,U_7014),U_7015),U_7016)) ),
    inference(definitional_conversion,[status(esa)],[f_2047_2]) ).

cnf(f_2047_4,plain,
    ( hBOOL(hAPP(U_7014,hAPP(hAPP(c_Product__Type_OPair(U_7012,U_7013),U_7015),U_7016)))
    | ~ hBOOL(hAPP(hAPP(c_Product__Type_Ocurry(U_7012,U_7013,tc_HOL_Obool,U_7014),U_7015),U_7016)) ),
    inference(clausify,[status(thm)],[f_2047_3]) ).

fof(f_2048_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_2048_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_2048_1]) ).

cnf(f_2048_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_2048_2]) ).

fof(f_2049_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_2049_2,plain,
    ! [U_7022,U_7021,U_7020,U_7019,U_7018,U_7017] : hAPP(hAPP(c_Product__Type_Ocurry(U_7017,U_7018,U_7019,U_7020),U_7021),U_7022) = hAPP(U_7020,hAPP(hAPP(c_Product__Type_OPair(U_7017,U_7018),U_7021),U_7022)),
    inference(variable_rename,[status(thm)],[f_2049_1]) ).

fof(f_2049_3,plain,
    ! [U_7017,U_7018,U_7019,U_7020,U_7021,U_7022] : hAPP(hAPP(c_Product__Type_Ocurry(U_7017,U_7018,U_7019,U_7020),U_7021),U_7022) = hAPP(U_7020,hAPP(hAPP(c_Product__Type_OPair(U_7017,U_7018),U_7021),U_7022)),
    inference(definitional_conversion,[status(esa)],[f_2049_2]) ).

cnf(f_2049_4,plain,
    hAPP(hAPP(c_Product__Type_Ocurry(U_7017,U_7018,U_7019,U_7020),U_7021),U_7022) = hAPP(U_7020,hAPP(hAPP(c_Product__Type_OPair(U_7017,U_7018),U_7021),U_7022)),
    inference(clausify,[status(thm)],[f_2049_3]) ).

fof(f_2050_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_2050_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_2050_1]) ).

cnf(f_2050_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_2050_2]) ).

fof(f_2051_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_2051_2,plain,
    ! [U_7024,U_7023] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7023)),hAPP(c_Code__Numeral_Oof__nat,U_7024)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7023),U_7024)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7023),U_7024))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7023)),hAPP(c_Code__Numeral_Oof__nat,U_7024))) ) ),
    inference(variable_rename,[status(thm)],[f_2051_1]) ).

fof(f_2051_3,plain,
    ( ! [U_7028,U_7026] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7026)),hAPP(c_Code__Numeral_Oof__nat,U_7028)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7026),U_7028)) )
    & ! [U_7027,U_7025] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7025),U_7027))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7025)),hAPP(c_Code__Numeral_Oof__nat,U_7027))) ) ),
    inference(miniscope,[status(thm)],[f_2051_2]) ).

fof(f_2051_4,plain,
    ( ! [U_7028,U_7026] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7026)),hAPP(c_Code__Numeral_Oof__nat,U_7028)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7026),U_7028)) )
    & ! [U_7025,U_7027] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7025),U_7027))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7025)),hAPP(c_Code__Numeral_Oof__nat,U_7027))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2051_3]) ).

cnf(f_2051_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7025),U_7027))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7025)),hAPP(c_Code__Numeral_Oof__nat,U_7027))) ),
    inference(clausify,[status(thm)],[f_2051_4]) ).

cnf(f_2051_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7026)),hAPP(c_Code__Numeral_Oof__nat,U_7028)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7026),U_7028)) ),
    inference(clausify,[status(thm)],[f_2051_4]) ).

fof(f_2052_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_2052_2,plain,
    ! [U_7032,U_7031,U_7030,U_7029] : c_Product__Type_Ocurry(U_7029,U_7030,U_7031,hAPP(c_Product__Type_Oprod_Oprod__case(U_7029,U_7030,U_7031),U_7032)) = U_7032,
    inference(variable_rename,[status(thm)],[f_2052_1]) ).

fof(f_2052_3,plain,
    ! [U_7031,U_7029,U_7030,U_7032] : c_Product__Type_Ocurry(U_7029,U_7030,U_7031,hAPP(c_Product__Type_Oprod_Oprod__case(U_7029,U_7030,U_7031),U_7032)) = U_7032,
    inference(definitional_conversion,[status(esa)],[f_2052_2]) ).

cnf(f_2052_4,plain,
    c_Product__Type_Ocurry(U_7029,U_7030,U_7031,hAPP(c_Product__Type_Oprod_Oprod__case(U_7029,U_7030,U_7031),U_7032)) = U_7032,
    inference(clausify,[status(thm)],[f_2052_3]) ).

fof(f_2053_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_2053_2,plain,
    ! [U_7036,U_7035,U_7034,U_7033] : hAPP(c_Product__Type_Oprod_Oprod__case(U_7033,U_7034,U_7035),c_Product__Type_Ocurry(U_7033,U_7034,U_7035,U_7036)) = U_7036,
    inference(variable_rename,[status(thm)],[f_2053_1]) ).

fof(f_2053_3,plain,
    ! [U_7033,U_7034,U_7035,U_7036] : hAPP(c_Product__Type_Oprod_Oprod__case(U_7033,U_7034,U_7035),c_Product__Type_Ocurry(U_7033,U_7034,U_7035,U_7036)) = U_7036,
    inference(definitional_conversion,[status(esa)],[f_2053_2]) ).

cnf(f_2053_4,plain,
    hAPP(c_Product__Type_Oprod_Oprod__case(U_7033,U_7034,U_7035),c_Product__Type_Ocurry(U_7033,U_7034,U_7035,U_7036)) = U_7036,
    inference(clausify,[status(thm)],[f_2053_3]) ).

fof(f_2054_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_2054_2,plain,
    ! [U_7038,U_7037] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7037)),hAPP(c_Code__Numeral_Oof__nat,U_7038)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7037),U_7038)),
    inference(variable_rename,[status(thm)],[f_2054_1]) ).

fof(f_2054_3,plain,
    ! [U_7037,U_7038] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7037)),hAPP(c_Code__Numeral_Oof__nat,U_7038)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7037),U_7038)),
    inference(definitional_conversion,[status(esa)],[f_2054_2]) ).

cnf(f_2054_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7037)),hAPP(c_Code__Numeral_Oof__nat,U_7038)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7037),U_7038)),
    inference(clausify,[status(thm)],[f_2054_3]) ).

fof(f_2055_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_2055_2,plain,
    ! [U_7040,U_7039] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7039)),hAPP(c_Code__Numeral_Oof__nat,U_7040)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7039),U_7040)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7039),U_7040))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7039)),hAPP(c_Code__Numeral_Oof__nat,U_7040))) ) ),
    inference(variable_rename,[status(thm)],[f_2055_1]) ).

fof(f_2055_3,plain,
    ( ! [U_7044,U_7042] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7042)),hAPP(c_Code__Numeral_Oof__nat,U_7044)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7042),U_7044)) )
    & ! [U_7043,U_7041] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7041),U_7043))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7041)),hAPP(c_Code__Numeral_Oof__nat,U_7043))) ) ),
    inference(miniscope,[status(thm)],[f_2055_2]) ).

fof(f_2055_4,plain,
    ( ! [U_7042,U_7044] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7042)),hAPP(c_Code__Numeral_Oof__nat,U_7044)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7042),U_7044)) )
    & ! [U_7043,U_7041] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7041),U_7043))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7041)),hAPP(c_Code__Numeral_Oof__nat,U_7043))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2055_3]) ).

cnf(f_2055_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7041),U_7043))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7041)),hAPP(c_Code__Numeral_Oof__nat,U_7043))) ),
    inference(clausify,[status(thm)],[f_2055_4]) ).

cnf(f_2055_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),hAPP(c_Code__Numeral_Oof__nat,U_7042)),hAPP(c_Code__Numeral_Oof__nat,U_7044)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7042),U_7044)) ),
    inference(clausify,[status(thm)],[f_2055_4]) ).

fof(f_2056_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_2056_2,plain,
    ! [U_7046,U_7045] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,U_7045)),hAPP(c_Code__Numeral_Oof__nat,U_7046)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7045),U_7046)),
    inference(variable_rename,[status(thm)],[f_2056_1]) ).

fof(f_2056_3,plain,
    ! [U_7045,U_7046] : hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,U_7045)),hAPP(c_Code__Numeral_Oof__nat,U_7046)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7045),U_7046)),
    inference(definitional_conversion,[status(esa)],[f_2056_2]) ).

cnf(f_2056_4,plain,
    hAPP(hAPP(c_Code__Numeral_Osubtract__code__numeral,hAPP(c_Code__Numeral_Oof__nat,U_7045)),hAPP(c_Code__Numeral_Oof__nat,U_7046)) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7045),U_7046)),
    inference(clausify,[status(thm)],[f_2056_3]) ).

fof(f_2057_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_2057_2,plain,
    ! [U_7047] :
      ( 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_7047)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,U_7047)))
      | U_7047 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(variable_rename,[status(thm)],[f_2057_1]) ).

fof(f_2057_3,plain,
    ! [U_7047] :
      ( 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_7047)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,U_7047)))
      | U_7047 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(definitional_conversion,[status(esa)],[f_2057_2]) ).

cnf(f_2057_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_7047)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_Code__Numeral_Onat__of,U_7047)))
    | U_7047 = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_2057_3]) ).

fof(f_2058_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_2058_2,plain,
    ! [U_7051,U_7050,U_7049,U_7048] : c_New__Random__Sequence_Opos__not__random__dseq(U_7048,U_7049,U_7050,U_7051) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(U_7048,U_7049),U_7050),U_7051)),
    inference(variable_rename,[status(thm)],[f_2058_1]) ).

fof(f_2058_3,plain,
    ! [U_7048,U_7049,U_7050,U_7051] : c_New__Random__Sequence_Opos__not__random__dseq(U_7048,U_7049,U_7050,U_7051) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(U_7048,U_7049),U_7050),U_7051)),
    inference(definitional_conversion,[status(esa)],[f_2058_2]) ).

cnf(f_2058_4,plain,
    c_New__Random__Sequence_Opos__not__random__dseq(U_7048,U_7049,U_7050,U_7051) = c_New__DSequence_Opos__not__seq(hAPP(hAPP(hAPP(U_7048,U_7049),U_7050),U_7051)),
    inference(clausify,[status(thm)],[f_2058_3]) ).

fof(f_2059_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_2059_2,plain,
    ! [U_7053,U_7052] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_7052,U_7053) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,U_7052),hAPP(c_Code__Numeral_Onat__of,U_7053))),
    inference(variable_rename,[status(thm)],[f_2059_1]) ).

fof(f_2059_3,plain,
    ! [U_7052,U_7053] : c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_7052,U_7053) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,U_7052),hAPP(c_Code__Numeral_Onat__of,U_7053))),
    inference(definitional_conversion,[status(esa)],[f_2059_2]) ).

cnf(f_2059_4,plain,
    c_Divides_Odiv__class_Omod(tc_Code__Numeral_Ocode__numeral,U_7052,U_7053) = hAPP(c_Code__Numeral_Oof__nat,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Code__Numeral_Onat__of,U_7052),hAPP(c_Code__Numeral_Onat__of,U_7053))),
    inference(clausify,[status(thm)],[f_2059_3]) ).

fof(f_2060_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_2060_2,plain,
    ! [U_7055,U_7054] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),U_7054),U_7055) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7054)),hAPP(c_Code__Numeral_Onat__of,U_7055))),
    inference(variable_rename,[status(thm)],[f_2060_1]) ).

fof(f_2060_3,plain,
    ! [U_7054,U_7055] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),U_7054),U_7055) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7054)),hAPP(c_Code__Numeral_Onat__of,U_7055))),
    inference(definitional_conversion,[status(esa)],[f_2060_2]) ).

cnf(f_2060_4,plain,
    hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Code__Numeral_Ocode__numeral),U_7054),U_7055) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7054)),hAPP(c_Code__Numeral_Onat__of,U_7055))),
    inference(clausify,[status(thm)],[f_2060_3]) ).

fof(f_2061_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_2061_2,plain,
    ! [U_7060,U_7059,U_7058,U_7057,U_7056] :
      ( ( hAPP(c_New__DSequence_Opos__decr__bind(U_7057,U_7058,U_7059,U_7060),U_7056) = c_Lazy__Sequence_Obind(U_7057,U_7058,hAPP(U_7059,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7056),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_7057,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_7058)),U_7060),U_7056))
        | U_7056 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_New__DSequence_Opos__decr__bind(U_7057,U_7058,U_7059,U_7060),U_7056) = c_Lazy__Sequence_Oempty(U_7058)
        | U_7056 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_2061_1]) ).

fof(f_2061_3,plain,
    ( ! [U_7070,U_7068,U_7066,U_7064,U_7062] :
        ( hAPP(c_New__DSequence_Opos__decr__bind(U_7064,U_7066,U_7068,U_7070),U_7062) = c_Lazy__Sequence_Obind(U_7064,U_7066,hAPP(U_7068,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7062),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_7064,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_7066)),U_7070),U_7062))
        | U_7062 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_7069,U_7067,U_7065,U_7063,U_7061] :
        ( hAPP(c_New__DSequence_Opos__decr__bind(U_7063,U_7065,U_7067,U_7069),U_7061) = c_Lazy__Sequence_Oempty(U_7065)
        | U_7061 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_2061_2]) ).

fof(f_2061_4,plain,
    ( ! [U_7068,U_7062,U_7064,U_7066,U_7070] :
        ( hAPP(c_New__DSequence_Opos__decr__bind(U_7064,U_7066,U_7068,U_7070),U_7062) = c_Lazy__Sequence_Obind(U_7064,U_7066,hAPP(U_7068,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7062),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_7064,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_7066)),U_7070),U_7062))
        | U_7062 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_7061,U_7063,U_7065,U_7067,U_7069] :
        ( hAPP(c_New__DSequence_Opos__decr__bind(U_7063,U_7065,U_7067,U_7069),U_7061) = c_Lazy__Sequence_Oempty(U_7065)
        | U_7061 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(definitional_conversion,[status(esa)],[f_2061_3]) ).

cnf(f_2061_5,plain,
    ( hAPP(c_New__DSequence_Opos__decr__bind(U_7063,U_7065,U_7067,U_7069),U_7061) = c_Lazy__Sequence_Oempty(U_7065)
    | U_7061 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_2061_4]) ).

cnf(f_2061_6,plain,
    ( hAPP(c_New__DSequence_Opos__decr__bind(U_7064,U_7066,U_7068,U_7070),U_7062) = c_Lazy__Sequence_Obind(U_7064,U_7066,hAPP(U_7068,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7062),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_7064,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_7066)),U_7070),U_7062))
    | U_7062 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_2061_4]) ).

fof(f_2062_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_2062_2,plain,
    ! [U_7072,U_7071] :
      ( ( hAPP(c_Code__Numeral_Onat__of,U_7071) = hAPP(c_Code__Numeral_Onat__of,U_7072)
        | U_7071 != U_7072 )
      & ( U_7071 = U_7072
        | hAPP(c_Code__Numeral_Onat__of,U_7071) != hAPP(c_Code__Numeral_Onat__of,U_7072) ) ),
    inference(variable_rename,[status(thm)],[f_2062_1]) ).

fof(f_2062_3,plain,
    ( ! [U_7076,U_7074] :
        ( hAPP(c_Code__Numeral_Onat__of,U_7074) = hAPP(c_Code__Numeral_Onat__of,U_7076)
        | U_7074 != U_7076 )
    & ! [U_7075,U_7073] :
        ( U_7073 = U_7075
        | hAPP(c_Code__Numeral_Onat__of,U_7073) != hAPP(c_Code__Numeral_Onat__of,U_7075) ) ),
    inference(miniscope,[status(thm)],[f_2062_2]) ).

fof(f_2062_4,plain,
    ( ! [U_7074,U_7076] :
        ( hAPP(c_Code__Numeral_Onat__of,U_7074) = hAPP(c_Code__Numeral_Onat__of,U_7076)
        | U_7074 != U_7076 )
    & ! [U_7073,U_7075] :
        ( U_7073 = U_7075
        | hAPP(c_Code__Numeral_Onat__of,U_7073) != hAPP(c_Code__Numeral_Onat__of,U_7075) ) ),
    inference(definitional_conversion,[status(esa)],[f_2062_3]) ).

cnf(f_2062_5,plain,
    ( U_7073 = U_7075
    | hAPP(c_Code__Numeral_Onat__of,U_7073) != hAPP(c_Code__Numeral_Onat__of,U_7075) ),
    inference(clausify,[status(thm)],[f_2062_4]) ).

cnf(f_2062_6,plain,
    ( hAPP(c_Code__Numeral_Onat__of,U_7074) = hAPP(c_Code__Numeral_Onat__of,U_7076)
    | U_7074 != U_7076 ),
    inference(clausify,[status(thm)],[f_2062_4]) ).

fof(f_2063_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_2063_2,plain,
    ! [U_7078,U_7077] :
      ( ( hAPP(c_Code__Numeral_Onat__of,U_7077) = hAPP(c_Code__Numeral_Onat__of,U_7078)
        | U_7077 != U_7078 )
      & ( U_7077 = U_7078
        | hAPP(c_Code__Numeral_Onat__of,U_7077) != hAPP(c_Code__Numeral_Onat__of,U_7078) ) ),
    inference(variable_rename,[status(thm)],[f_2063_1]) ).

fof(f_2063_3,plain,
    ( ! [U_7082,U_7080] :
        ( hAPP(c_Code__Numeral_Onat__of,U_7080) = hAPP(c_Code__Numeral_Onat__of,U_7082)
        | U_7080 != U_7082 )
    & ! [U_7081,U_7079] :
        ( U_7079 = U_7081
        | hAPP(c_Code__Numeral_Onat__of,U_7079) != hAPP(c_Code__Numeral_Onat__of,U_7081) ) ),
    inference(miniscope,[status(thm)],[f_2063_2]) ).

fof(f_2063_4,plain,
    ( ! [U_7080,U_7082] :
        ( hAPP(c_Code__Numeral_Onat__of,U_7080) = hAPP(c_Code__Numeral_Onat__of,U_7082)
        | U_7080 != U_7082 )
    & ! [U_7081,U_7079] :
        ( U_7079 = U_7081
        | hAPP(c_Code__Numeral_Onat__of,U_7079) != hAPP(c_Code__Numeral_Onat__of,U_7081) ) ),
    inference(definitional_conversion,[status(esa)],[f_2063_3]) ).

cnf(f_2063_5,plain,
    ( U_7079 = U_7081
    | hAPP(c_Code__Numeral_Onat__of,U_7079) != hAPP(c_Code__Numeral_Onat__of,U_7081) ),
    inference(clausify,[status(thm)],[f_2063_4]) ).

cnf(f_2063_6,plain,
    ( hAPP(c_Code__Numeral_Onat__of,U_7080) = hAPP(c_Code__Numeral_Onat__of,U_7082)
    | U_7080 != U_7082 ),
    inference(clausify,[status(thm)],[f_2063_4]) ).

fof(f_2064_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_2064_2,plain,
    ! [U_7083] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_7083)) = U_7083,
    inference(variable_rename,[status(thm)],[f_2064_1]) ).

fof(f_2064_3,plain,
    ! [U_7083] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_7083)) = U_7083,
    inference(definitional_conversion,[status(esa)],[f_2064_2]) ).

cnf(f_2064_4,plain,
    hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_7083)) = U_7083,
    inference(clausify,[status(thm)],[f_2064_3]) ).

fof(f_2065_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_2065_2,plain,
    ! [U_7084] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_7084)) = U_7084,
    inference(variable_rename,[status(thm)],[f_2065_1]) ).

fof(f_2065_3,plain,
    ! [U_7084] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_7084)) = U_7084,
    inference(definitional_conversion,[status(esa)],[f_2065_2]) ).

cnf(f_2065_4,plain,
    hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,U_7084)) = U_7084,
    inference(clausify,[status(thm)],[f_2065_3]) ).

fof(f_2066_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_2066_2,plain,
    ! [U_7085] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_7085)) = U_7085,
    inference(variable_rename,[status(thm)],[f_2066_1]) ).

fof(f_2066_3,plain,
    ! [U_7085] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_7085)) = U_7085,
    inference(definitional_conversion,[status(esa)],[f_2066_2]) ).

cnf(f_2066_4,plain,
    hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_7085)) = U_7085,
    inference(clausify,[status(thm)],[f_2066_3]) ).

fof(f_2067_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_2067_2,plain,
    ! [U_7087,U_7086] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7086),U_7087))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7086)),hAPP(c_Code__Numeral_Onat__of,U_7087))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7086)),hAPP(c_Code__Numeral_Onat__of,U_7087)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7086),U_7087)) ) ),
    inference(variable_rename,[status(thm)],[f_2067_1]) ).

fof(f_2067_3,plain,
    ( ! [U_7091,U_7089] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7089),U_7091))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7089)),hAPP(c_Code__Numeral_Onat__of,U_7091))) )
    & ! [U_7090,U_7088] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7088)),hAPP(c_Code__Numeral_Onat__of,U_7090)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7088),U_7090)) ) ),
    inference(miniscope,[status(thm)],[f_2067_2]) ).

fof(f_2067_4,plain,
    ( ! [U_7089,U_7091] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7089),U_7091))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7089)),hAPP(c_Code__Numeral_Onat__of,U_7091))) )
    & ! [U_7090,U_7088] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7088)),hAPP(c_Code__Numeral_Onat__of,U_7090)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7088),U_7090)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2067_3]) ).

cnf(f_2067_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7088)),hAPP(c_Code__Numeral_Onat__of,U_7090)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7088),U_7090)) ),
    inference(clausify,[status(thm)],[f_2067_4]) ).

cnf(f_2067_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_7089),U_7091))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7089)),hAPP(c_Code__Numeral_Onat__of,U_7091))) ),
    inference(clausify,[status(thm)],[f_2067_4]) ).

fof(f_2068_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_2068_2,plain,
    ! [U_7092] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),U_7092)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7092),
    inference(variable_rename,[status(thm)],[f_2068_1]) ).

fof(f_2068_3,plain,
    ! [U_7092] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),U_7092)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7092),
    inference(definitional_conversion,[status(esa)],[f_2068_2]) ).

cnf(f_2068_4,plain,
    hAPP(c_Code__Numeral_Onat__of,hAPP(c_Int_Onumber__class_Onumber__of(tc_Code__Numeral_Ocode__numeral),U_7092)) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_7092),
    inference(clausify,[status(thm)],[f_2068_3]) ).

fof(f_2069_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_2069_2,plain,
    ! [U_7094,U_7093] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_7093),U_7094))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7093)),hAPP(c_Code__Numeral_Onat__of,U_7094))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7093)),hAPP(c_Code__Numeral_Onat__of,U_7094)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_7093),U_7094)) ) ),
    inference(variable_rename,[status(thm)],[f_2069_1]) ).

fof(f_2069_3,plain,
    ( ! [U_7098,U_7096] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_7096),U_7098))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7096)),hAPP(c_Code__Numeral_Onat__of,U_7098))) )
    & ! [U_7097,U_7095] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7095)),hAPP(c_Code__Numeral_Onat__of,U_7097)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_7095),U_7097)) ) ),
    inference(miniscope,[status(thm)],[f_2069_2]) ).

fof(f_2069_4,plain,
    ( ! [U_7096,U_7098] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_7096),U_7098))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7096)),hAPP(c_Code__Numeral_Onat__of,U_7098))) )
    & ! [U_7097,U_7095] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7095)),hAPP(c_Code__Numeral_Onat__of,U_7097)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_7095),U_7097)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2069_3]) ).

cnf(f_2069_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7095)),hAPP(c_Code__Numeral_Onat__of,U_7097)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_7095),U_7097)) ),
    inference(clausify,[status(thm)],[f_2069_4]) ).

cnf(f_2069_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),U_7096),U_7098))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7096)),hAPP(c_Code__Numeral_Onat__of,U_7098))) ),
    inference(clausify,[status(thm)],[f_2069_4]) ).

fof(f_2070_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_2070_2,plain,
    ! [U_7099] : hAPP(c_Code__Numeral_Onat__of,U_7099) = c_Code__Numeral_Onat__of__aux(U_7099,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_2070_1]) ).

fof(f_2070_3,plain,
    ! [U_7099] : hAPP(c_Code__Numeral_Onat__of,U_7099) = c_Code__Numeral_Onat__of__aux(U_7099,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_2070_2]) ).

cnf(f_2070_4,plain,
    hAPP(c_Code__Numeral_Onat__of,U_7099) = c_Code__Numeral_Onat__of__aux(U_7099,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_2070_3]) ).

fof(f_2071_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_2071_2,plain,
    ! [U_7101,U_7100] : c_Code__Numeral_Onat__of__aux(U_7100,U_7101) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7100)),U_7101),
    inference(variable_rename,[status(thm)],[f_2071_1]) ).

fof(f_2071_3,plain,
    ! [U_7100,U_7101] : c_Code__Numeral_Onat__of__aux(U_7100,U_7101) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7100)),U_7101),
    inference(definitional_conversion,[status(esa)],[f_2071_2]) ).

cnf(f_2071_4,plain,
    c_Code__Numeral_Onat__of__aux(U_7100,U_7101) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7100)),U_7101),
    inference(clausify,[status(thm)],[f_2071_3]) ).

fof(f_2072_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_2072_2,plain,
    ! [U_7102] : c_Code__Numeral_OSuc__code__numeral(U_7102) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,U_7102))),
    inference(variable_rename,[status(thm)],[f_2072_1]) ).

fof(f_2072_3,plain,
    ! [U_7102] : c_Code__Numeral_OSuc__code__numeral(U_7102) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,U_7102))),
    inference(definitional_conversion,[status(esa)],[f_2072_2]) ).

cnf(f_2072_4,plain,
    c_Code__Numeral_OSuc__code__numeral(U_7102) = hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Nat_OSuc,hAPP(c_Code__Numeral_Onat__of,U_7102))),
    inference(clausify,[status(thm)],[f_2072_3]) ).

fof(f_2073_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_2073_2,plain,
    ! [U_7104,U_7103] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7103),U_7104) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7103)),hAPP(c_Code__Numeral_Onat__of,U_7104))),
    inference(variable_rename,[status(thm)],[f_2073_1]) ).

fof(f_2073_3,plain,
    ! [U_7103,U_7104] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7103),U_7104) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7103)),hAPP(c_Code__Numeral_Onat__of,U_7104))),
    inference(definitional_conversion,[status(esa)],[f_2073_2]) ).

cnf(f_2073_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7103),U_7104) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7103)),hAPP(c_Code__Numeral_Onat__of,U_7104))),
    inference(clausify,[status(thm)],[f_2073_3]) ).

fof(f_2074_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_2074_2,plain,
    ! [U_7106,U_7105] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_7105),U_7106) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7105)),hAPP(c_Code__Numeral_Onat__of,U_7106))),
    inference(variable_rename,[status(thm)],[f_2074_1]) ).

fof(f_2074_3,plain,
    ! [U_7105,U_7106] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_7105),U_7106) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7105)),hAPP(c_Code__Numeral_Onat__of,U_7106))),
    inference(definitional_conversion,[status(esa)],[f_2074_2]) ).

cnf(f_2074_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Code__Numeral_Ocode__numeral),U_7105),U_7106) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7105)),hAPP(c_Code__Numeral_Onat__of,U_7106))),
    inference(clausify,[status(thm)],[f_2074_3]) ).

fof(f_2075_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_2075_2,plain,
    ! [U_7108,U_7107] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_7107),U_7108) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7107)),hAPP(c_Code__Numeral_Onat__of,U_7108))),
    inference(variable_rename,[status(thm)],[f_2075_1]) ).

fof(f_2075_3,plain,
    ! [U_7107,U_7108] : hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_7107),U_7108) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7107)),hAPP(c_Code__Numeral_Onat__of,U_7108))),
    inference(definitional_conversion,[status(esa)],[f_2075_2]) ).

cnf(f_2075_4,plain,
    hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Code__Numeral_Ocode__numeral),U_7107),U_7108) = hAPP(c_Code__Numeral_Oof__nat,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_7107)),hAPP(c_Code__Numeral_Onat__of,U_7108))),
    inference(clausify,[status(thm)],[f_2075_3]) ).

fof(f_2076_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_2076_2,plain,
    ! [U_7115,U_7114,U_7113,U_7112,U_7111,U_7110,U_7109] : c_New__Random__Sequence_Opos__decr__bind(U_7109,U_7110,U_7111,U_7112,U_7113,U_7114,U_7115) = c_New__DSequence_Opos__decr__bind(U_7109,U_7110,hAPP(hAPP(hAPP(U_7111,U_7113),U_7114),U_7115),hAPP(hAPP(c_COMBC(U_7109,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_7110))),hAPP(hAPP(c_COMBC(U_7109,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_7110)))),hAPP(hAPP(c_COMBC(U_7109,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_7110))))),U_7112),U_7113)),U_7114)),U_7115)),
    inference(variable_rename,[status(thm)],[f_2076_1]) ).

fof(f_2076_3,plain,
    ! [U_7109,U_7110,U_7111,U_7112,U_7113,U_7114,U_7115] : c_New__Random__Sequence_Opos__decr__bind(U_7109,U_7110,U_7111,U_7112,U_7113,U_7114,U_7115) = c_New__DSequence_Opos__decr__bind(U_7109,U_7110,hAPP(hAPP(hAPP(U_7111,U_7113),U_7114),U_7115),hAPP(hAPP(c_COMBC(U_7109,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_7110))),hAPP(hAPP(c_COMBC(U_7109,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_7110)))),hAPP(hAPP(c_COMBC(U_7109,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_7110))))),U_7112),U_7113)),U_7114)),U_7115)),
    inference(definitional_conversion,[status(esa)],[f_2076_2]) ).

cnf(f_2076_4,plain,
    c_New__Random__Sequence_Opos__decr__bind(U_7109,U_7110,U_7111,U_7112,U_7113,U_7114,U_7115) = c_New__DSequence_Opos__decr__bind(U_7109,U_7110,hAPP(hAPP(hAPP(U_7111,U_7113),U_7114),U_7115),hAPP(hAPP(c_COMBC(U_7109,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_7110))),hAPP(hAPP(c_COMBC(U_7109,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_7110)))),hAPP(hAPP(c_COMBC(U_7109,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_7110))))),U_7112),U_7113)),U_7114)),U_7115)),
    inference(clausify,[status(thm)],[f_2076_3]) ).

fof(f_2077_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_2077_2,plain,
    ! [U_7117,U_7116] : hAPP(c_New__DSequence_Opos__empty(U_7116),U_7117) = c_Lazy__Sequence_Oempty(U_7116),
    inference(variable_rename,[status(thm)],[f_2077_1]) ).

fof(f_2077_3,plain,
    ! [U_7116,U_7117] : hAPP(c_New__DSequence_Opos__empty(U_7116),U_7117) = c_Lazy__Sequence_Oempty(U_7116),
    inference(definitional_conversion,[status(esa)],[f_2077_2]) ).

cnf(f_2077_4,plain,
    hAPP(c_New__DSequence_Opos__empty(U_7116),U_7117) = c_Lazy__Sequence_Oempty(U_7116),
    inference(clausify,[status(thm)],[f_2077_3]) ).

fof(f_2078_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_2078_2,plain,
    ! [U_7122,U_7121,U_7120,U_7119,U_7118] : hAPP(c_New__DSequence_Opos__bind(U_7118,U_7119,U_7120,U_7121),U_7122) = c_Lazy__Sequence_Obind(U_7118,U_7119,hAPP(U_7120,U_7122),hAPP(hAPP(c_COMBC(U_7118,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_7119)),U_7121),U_7122)),
    inference(variable_rename,[status(thm)],[f_2078_1]) ).

fof(f_2078_3,plain,
    ! [U_7119,U_7118,U_7120,U_7121,U_7122] : hAPP(c_New__DSequence_Opos__bind(U_7118,U_7119,U_7120,U_7121),U_7122) = c_Lazy__Sequence_Obind(U_7118,U_7119,hAPP(U_7120,U_7122),hAPP(hAPP(c_COMBC(U_7118,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_7119)),U_7121),U_7122)),
    inference(definitional_conversion,[status(esa)],[f_2078_2]) ).

cnf(f_2078_4,plain,
    hAPP(c_New__DSequence_Opos__bind(U_7118,U_7119,U_7120,U_7121),U_7122) = c_Lazy__Sequence_Obind(U_7118,U_7119,hAPP(U_7120,U_7122),hAPP(hAPP(c_COMBC(U_7118,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(U_7119)),U_7121),U_7122)),
    inference(clausify,[status(thm)],[f_2078_3]) ).

fof(f_2079_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_2079_2,plain,
    ! [U_7127,U_7126,U_7125,U_7124,U_7123] :
      ( ( hAPP(c_New__DSequence_Oneg__decr__bind(U_7124,U_7125,U_7126,U_7127),U_7123) = c_Lazy__Sequence_Ohb__bind(U_7124,U_7125,hAPP(U_7126,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7123),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_7124,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7125))),U_7127),U_7123))
        | U_7123 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_New__DSequence_Oneg__decr__bind(U_7124,U_7125,U_7126,U_7127),U_7123) = c_Lazy__Sequence_Ohit__bound(U_7125)
        | U_7123 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_2079_1]) ).

fof(f_2079_3,plain,
    ( ! [U_7137,U_7135,U_7133,U_7131,U_7129] :
        ( hAPP(c_New__DSequence_Oneg__decr__bind(U_7131,U_7133,U_7135,U_7137),U_7129) = c_Lazy__Sequence_Ohb__bind(U_7131,U_7133,hAPP(U_7135,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7129),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_7131,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7133))),U_7137),U_7129))
        | U_7129 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_7136,U_7134,U_7132,U_7130,U_7128] :
        ( hAPP(c_New__DSequence_Oneg__decr__bind(U_7130,U_7132,U_7134,U_7136),U_7128) = c_Lazy__Sequence_Ohit__bound(U_7132)
        | U_7128 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_2079_2]) ).

fof(f_2079_4,plain,
    ( ! [U_7135,U_7129,U_7131,U_7133,U_7137] :
        ( hAPP(c_New__DSequence_Oneg__decr__bind(U_7131,U_7133,U_7135,U_7137),U_7129) = c_Lazy__Sequence_Ohb__bind(U_7131,U_7133,hAPP(U_7135,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7129),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_7131,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7133))),U_7137),U_7129))
        | U_7129 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_7128,U_7130,U_7132,U_7134,U_7136] :
        ( hAPP(c_New__DSequence_Oneg__decr__bind(U_7130,U_7132,U_7134,U_7136),U_7128) = c_Lazy__Sequence_Ohit__bound(U_7132)
        | U_7128 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(definitional_conversion,[status(esa)],[f_2079_3]) ).

cnf(f_2079_5,plain,
    ( hAPP(c_New__DSequence_Oneg__decr__bind(U_7130,U_7132,U_7134,U_7136),U_7128) = c_Lazy__Sequence_Ohit__bound(U_7132)
    | U_7128 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_2079_4]) ).

cnf(f_2079_6,plain,
    ( hAPP(c_New__DSequence_Oneg__decr__bind(U_7131,U_7133,U_7135,U_7137),U_7129) = c_Lazy__Sequence_Ohb__bind(U_7131,U_7133,hAPP(U_7135,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_7129),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(U_7131,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7133))),U_7137),U_7129))
    | U_7129 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_2079_4]) ).

fof(f_2080_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_2080_2,plain,
    ! [U_7139,U_7138] :
      ( ( 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_7138),U_7139)),c_Wellfounded_Oless__than))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7138),U_7139)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7138),U_7139))
        | ~ 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_7138),U_7139)),c_Wellfounded_Oless__than)) ) ),
    inference(variable_rename,[status(thm)],[f_2080_1]) ).

fof(f_2080_3,plain,
    ( ! [U_7143,U_7141] :
        ( 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_7141),U_7143)),c_Wellfounded_Oless__than))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7141),U_7143)) )
    & ! [U_7142,U_7140] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7140),U_7142))
        | ~ 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_7140),U_7142)),c_Wellfounded_Oless__than)) ) ),
    inference(miniscope,[status(thm)],[f_2080_2]) ).

fof(f_2080_4,plain,
    ( ! [U_7141,U_7143] :
        ( 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_7141),U_7143)),c_Wellfounded_Oless__than))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7141),U_7143)) )
    & ! [U_7140,U_7142] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7140),U_7142))
        | ~ 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_7140),U_7142)),c_Wellfounded_Oless__than)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2080_3]) ).

cnf(f_2080_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7140),U_7142))
    | ~ 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_7140),U_7142)),c_Wellfounded_Oless__than)) ),
    inference(clausify,[status(thm)],[f_2080_4]) ).

cnf(f_2080_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_7141),U_7143)),c_Wellfounded_Oless__than))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7141),U_7143)) ),
    inference(clausify,[status(thm)],[f_2080_4]) ).

fof(f_2081_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_2081_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_2081_1]) ).

cnf(f_2081_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_2081_2]) ).

fof(f_2082_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_2082_2,plain,
    ! [U_7147,U_7146,U_7145,U_7144] : c_New__Random__Sequence_Opos__empty(U_7144,U_7145,U_7146,U_7147) = c_New__DSequence_Opos__empty(U_7144),
    inference(variable_rename,[status(thm)],[f_2082_1]) ).

fof(f_2082_3,plain,
    ! [U_7144,U_7145,U_7146,U_7147] : c_New__Random__Sequence_Opos__empty(U_7144,U_7145,U_7146,U_7147) = c_New__DSequence_Opos__empty(U_7144),
    inference(definitional_conversion,[status(esa)],[f_2082_2]) ).

cnf(f_2082_4,plain,
    c_New__Random__Sequence_Opos__empty(U_7144,U_7145,U_7146,U_7147) = c_New__DSequence_Opos__empty(U_7144),
    inference(clausify,[status(thm)],[f_2082_3]) ).

fof(f_2083_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_2083_2,plain,
    ! [U_7154,U_7153,U_7152,U_7151,U_7150,U_7149,U_7148] : c_New__Random__Sequence_Oneg__decr__bind(U_7148,U_7149,U_7150,U_7151,U_7152,U_7153,U_7154) = c_New__DSequence_Oneg__decr__bind(U_7148,U_7149,hAPP(hAPP(hAPP(U_7150,U_7152),U_7153),U_7154),hAPP(hAPP(c_COMBC(U_7148,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_7149)))),hAPP(hAPP(c_COMBC(U_7148,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_7149))))),hAPP(hAPP(c_COMBC(U_7148,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_7149)))))),U_7151),U_7152)),U_7153)),U_7154)),
    inference(variable_rename,[status(thm)],[f_2083_1]) ).

fof(f_2083_3,plain,
    ! [U_7149,U_7148,U_7150,U_7151,U_7152,U_7153,U_7154] : c_New__Random__Sequence_Oneg__decr__bind(U_7148,U_7149,U_7150,U_7151,U_7152,U_7153,U_7154) = c_New__DSequence_Oneg__decr__bind(U_7148,U_7149,hAPP(hAPP(hAPP(U_7150,U_7152),U_7153),U_7154),hAPP(hAPP(c_COMBC(U_7148,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_7149)))),hAPP(hAPP(c_COMBC(U_7148,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_7149))))),hAPP(hAPP(c_COMBC(U_7148,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_7149)))))),U_7151),U_7152)),U_7153)),U_7154)),
    inference(definitional_conversion,[status(esa)],[f_2083_2]) ).

cnf(f_2083_4,plain,
    c_New__Random__Sequence_Oneg__decr__bind(U_7148,U_7149,U_7150,U_7151,U_7152,U_7153,U_7154) = c_New__DSequence_Oneg__decr__bind(U_7148,U_7149,hAPP(hAPP(hAPP(U_7150,U_7152),U_7153),U_7154),hAPP(hAPP(c_COMBC(U_7148,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_7149)))),hAPP(hAPP(c_COMBC(U_7148,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_7149))))),hAPP(hAPP(c_COMBC(U_7148,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_7149)))))),U_7151),U_7152)),U_7153)),U_7154)),
    inference(clausify,[status(thm)],[f_2083_3]) ).

fof(f_2084_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_2084_2,plain,
    ! [U_7161,U_7160,U_7159,U_7158,U_7157,U_7156,U_7155] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(U_7155,U_7156,U_7157,U_7158),U_7159),U_7160),U_7161) = c_New__DSequence_Opos__bind(U_7155,U_7156,hAPP(hAPP(hAPP(U_7157,U_7159),U_7160),U_7161),hAPP(hAPP(c_COMBC(U_7155,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_7156))),hAPP(hAPP(c_COMBC(U_7155,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_7156)))),hAPP(hAPP(c_COMBC(U_7155,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_7156))))),U_7158),U_7159)),U_7160)),U_7161)),
    inference(variable_rename,[status(thm)],[f_2084_1]) ).

fof(f_2084_3,plain,
    ! [U_7155,U_7156,U_7157,U_7158,U_7159,U_7160,U_7161] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(U_7155,U_7156,U_7157,U_7158),U_7159),U_7160),U_7161) = c_New__DSequence_Opos__bind(U_7155,U_7156,hAPP(hAPP(hAPP(U_7157,U_7159),U_7160),U_7161),hAPP(hAPP(c_COMBC(U_7155,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_7156))),hAPP(hAPP(c_COMBC(U_7155,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_7156)))),hAPP(hAPP(c_COMBC(U_7155,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_7156))))),U_7158),U_7159)),U_7160)),U_7161)),
    inference(definitional_conversion,[status(esa)],[f_2084_2]) ).

cnf(f_2084_4,plain,
    hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(U_7155,U_7156,U_7157,U_7158),U_7159),U_7160),U_7161) = c_New__DSequence_Opos__bind(U_7155,U_7156,hAPP(hAPP(hAPP(U_7157,U_7159),U_7160),U_7161),hAPP(hAPP(c_COMBC(U_7155,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_7156))),hAPP(hAPP(c_COMBC(U_7155,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_7156)))),hAPP(hAPP(c_COMBC(U_7155,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_7156))))),U_7158),U_7159)),U_7160)),U_7161)),
    inference(clausify,[status(thm)],[f_2084_3]) ).

fof(f_2085_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_2085_2,plain,
    ! [U_7166,U_7165,U_7164,U_7163,U_7162] : hAPP(c_New__DSequence_Oneg__bind(U_7162,U_7163,U_7164,U_7165),U_7166) = c_Lazy__Sequence_Ohb__bind(U_7162,U_7163,hAPP(U_7164,U_7166),hAPP(hAPP(c_COMBC(U_7162,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7163))),U_7165),U_7166)),
    inference(variable_rename,[status(thm)],[f_2085_1]) ).

fof(f_2085_3,plain,
    ! [U_7163,U_7162,U_7164,U_7165,U_7166] : hAPP(c_New__DSequence_Oneg__bind(U_7162,U_7163,U_7164,U_7165),U_7166) = c_Lazy__Sequence_Ohb__bind(U_7162,U_7163,hAPP(U_7164,U_7166),hAPP(hAPP(c_COMBC(U_7162,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7163))),U_7165),U_7166)),
    inference(definitional_conversion,[status(esa)],[f_2085_2]) ).

cnf(f_2085_4,plain,
    hAPP(c_New__DSequence_Oneg__bind(U_7162,U_7163,U_7164,U_7165),U_7166) = c_Lazy__Sequence_Ohb__bind(U_7162,U_7163,hAPP(U_7164,U_7166),hAPP(hAPP(c_COMBC(U_7162,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(U_7163))),U_7165),U_7166)),
    inference(clausify,[status(thm)],[f_2085_3]) ).

fof(f_2086_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_2086_2,plain,
    ! [U_7169,U_7168,U_7167] : c_Wellfounded_Omlex__prod(U_7167,U_7168,U_7169) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_7167),U_7167),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_7167,c_Wellfounded_Oless__than,U_7169)),hAPP(hAPP(c_COMBS(U_7167,U_7167,tc_prod(tc_Nat_Onat,U_7167)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_7167,tc_prod(tc_Nat_Onat,U_7167)),U_7167),c_Product__Type_OPair(tc_Nat_Onat,U_7167)),U_7168)),c_COMBI(U_7167))),
    inference(variable_rename,[status(thm)],[f_2086_1]) ).

fof(f_2086_3,plain,
    ! [U_7167,U_7168,U_7169] : c_Wellfounded_Omlex__prod(U_7167,U_7168,U_7169) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_7167),U_7167),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_7167,c_Wellfounded_Oless__than,U_7169)),hAPP(hAPP(c_COMBS(U_7167,U_7167,tc_prod(tc_Nat_Onat,U_7167)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_7167,tc_prod(tc_Nat_Onat,U_7167)),U_7167),c_Product__Type_OPair(tc_Nat_Onat,U_7167)),U_7168)),c_COMBI(U_7167))),
    inference(definitional_conversion,[status(esa)],[f_2086_2]) ).

cnf(f_2086_4,plain,
    c_Wellfounded_Omlex__prod(U_7167,U_7168,U_7169) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,U_7167),U_7167),c_Wellfounded_Olex__prod(tc_Nat_Onat,U_7167,c_Wellfounded_Oless__than,U_7169)),hAPP(hAPP(c_COMBS(U_7167,U_7167,tc_prod(tc_Nat_Onat,U_7167)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_7167,tc_prod(tc_Nat_Onat,U_7167)),U_7167),c_Product__Type_OPair(tc_Nat_Onat,U_7167)),U_7168)),c_COMBI(U_7167))),
    inference(clausify,[status(thm)],[f_2086_3]) ).

fof(f_2087_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_2087_2,plain,
    ! [U_7175,U_7174,U_7173,U_7172,U_7171,U_7170] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7170,U_7170)),hAPP(hAPP(c_Product__Type_OPair(U_7170,U_7170),U_7171),U_7172)),hAPP(hAPP(c_Relation_Oinv__image(U_7173,U_7170),U_7174),U_7175)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7173,U_7173)),hAPP(hAPP(c_Product__Type_OPair(U_7173,U_7173),hAPP(U_7175,U_7171)),hAPP(U_7175,U_7172))),U_7174)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7173,U_7173)),hAPP(hAPP(c_Product__Type_OPair(U_7173,U_7173),hAPP(U_7175,U_7171)),hAPP(U_7175,U_7172))),U_7174))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7170,U_7170)),hAPP(hAPP(c_Product__Type_OPair(U_7170,U_7170),U_7171),U_7172)),hAPP(hAPP(c_Relation_Oinv__image(U_7173,U_7170),U_7174),U_7175))) ) ),
    inference(variable_rename,[status(thm)],[f_2087_1]) ).

fof(f_2087_3,plain,
    ( ! [U_7187,U_7185,U_7183,U_7181,U_7179] :
        ( ! [U_7177] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_7177,U_7177)),hAPP(hAPP(c_Product__Type_OPair(U_7177,U_7177),U_7179),U_7181)),hAPP(hAPP(c_Relation_Oinv__image(U_7183,U_7177),U_7185),U_7187)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7183,U_7183)),hAPP(hAPP(c_Product__Type_OPair(U_7183,U_7183),hAPP(U_7187,U_7179)),hAPP(U_7187,U_7181))),U_7185)) )
    & ! [U_7186,U_7184,U_7182,U_7180,U_7178] :
        ( ! [U_7176] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7176,U_7176)),hAPP(hAPP(c_Product__Type_OPair(U_7176,U_7176),U_7178),U_7180)),hAPP(hAPP(c_Relation_Oinv__image(U_7182,U_7176),U_7184),U_7186)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_7182,U_7182)),hAPP(hAPP(c_Product__Type_OPair(U_7182,U_7182),hAPP(U_7186,U_7178)),hAPP(U_7186,U_7180))),U_7184)) ) ),
    inference(miniscope,[status(thm)],[f_2087_2]) ).

fof(f_2087_4,plain,
    ( ! [U_7177,U_7179,U_7181,U_7183,U_7185,U_7187] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7177,U_7177)),hAPP(hAPP(c_Product__Type_OPair(U_7177,U_7177),U_7179),U_7181)),hAPP(hAPP(c_Relation_Oinv__image(U_7183,U_7177),U_7185),U_7187)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7183,U_7183)),hAPP(hAPP(c_Product__Type_OPair(U_7183,U_7183),hAPP(U_7187,U_7179)),hAPP(U_7187,U_7181))),U_7185)) )
    & ! [U_7178,U_7176,U_7182,U_7180,U_7184,U_7186] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7176,U_7176)),hAPP(hAPP(c_Product__Type_OPair(U_7176,U_7176),U_7178),U_7180)),hAPP(hAPP(c_Relation_Oinv__image(U_7182,U_7176),U_7184),U_7186)))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_7182,U_7182)),hAPP(hAPP(c_Product__Type_OPair(U_7182,U_7182),hAPP(U_7186,U_7178)),hAPP(U_7186,U_7180))),U_7184)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2087_3]) ).

cnf(f_2087_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7176,U_7176)),hAPP(hAPP(c_Product__Type_OPair(U_7176,U_7176),U_7178),U_7180)),hAPP(hAPP(c_Relation_Oinv__image(U_7182,U_7176),U_7184),U_7186)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_7182,U_7182)),hAPP(hAPP(c_Product__Type_OPair(U_7182,U_7182),hAPP(U_7186,U_7178)),hAPP(U_7186,U_7180))),U_7184)) ),
    inference(clausify,[status(thm)],[f_2087_4]) ).

cnf(f_2087_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7177,U_7177)),hAPP(hAPP(c_Product__Type_OPair(U_7177,U_7177),U_7179),U_7181)),hAPP(hAPP(c_Relation_Oinv__image(U_7183,U_7177),U_7185),U_7187)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7183,U_7183)),hAPP(hAPP(c_Product__Type_OPair(U_7183,U_7183),hAPP(U_7187,U_7179)),hAPP(U_7187,U_7181))),U_7185)) ),
    inference(clausify,[status(thm)],[f_2087_4]) ).

fof(f_2088_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_2088_2,plain,
    ! [U_7194,U_7193,U_7192,U_7191,U_7190,U_7189,U_7188] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(U_7188,U_7189,U_7190,U_7191),U_7192),U_7193),U_7194) = c_New__DSequence_Oneg__bind(U_7188,U_7189,hAPP(hAPP(hAPP(U_7190,U_7192),U_7193),U_7194),hAPP(hAPP(c_COMBC(U_7188,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_7189)))),hAPP(hAPP(c_COMBC(U_7188,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_7189))))),hAPP(hAPP(c_COMBC(U_7188,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_7189)))))),U_7191),U_7192)),U_7193)),U_7194)),
    inference(variable_rename,[status(thm)],[f_2088_1]) ).

fof(f_2088_3,plain,
    ! [U_7188,U_7189,U_7190,U_7191,U_7192,U_7193,U_7194] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(U_7188,U_7189,U_7190,U_7191),U_7192),U_7193),U_7194) = c_New__DSequence_Oneg__bind(U_7188,U_7189,hAPP(hAPP(hAPP(U_7190,U_7192),U_7193),U_7194),hAPP(hAPP(c_COMBC(U_7188,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_7189)))),hAPP(hAPP(c_COMBC(U_7188,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_7189))))),hAPP(hAPP(c_COMBC(U_7188,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_7189)))))),U_7191),U_7192)),U_7193)),U_7194)),
    inference(definitional_conversion,[status(esa)],[f_2088_2]) ).

cnf(f_2088_4,plain,
    hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(U_7188,U_7189,U_7190,U_7191),U_7192),U_7193),U_7194) = c_New__DSequence_Oneg__bind(U_7188,U_7189,hAPP(hAPP(hAPP(U_7190,U_7192),U_7193),U_7194),hAPP(hAPP(c_COMBC(U_7188,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_7189)))),hAPP(hAPP(c_COMBC(U_7188,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_7189))))),hAPP(hAPP(c_COMBC(U_7188,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_7189)))))),U_7191),U_7192)),U_7193)),U_7194)),
    inference(clausify,[status(thm)],[f_2088_3]) ).

fof(f_2089_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_2089_2,plain,
    ! [U_7196,U_7195] : c_FunDef_Orp__inv__image(U_7195,U_7196) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool),tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool),tc_fun(tc_fun(U_7196,U_7195),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool),tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool),tc_fun(tc_fun(U_7196,U_7195),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)),tc_fun(tc_fun(U_7196,U_7195),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool),tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool),tc_fun(tc_fun(U_7196,U_7195),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool))))),tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)),tc_fun(tc_fun(U_7196,U_7195),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool))),tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)),tc_fun(tc_fun(U_7196,U_7195),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)))),tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool)),c_COMBS(tc_fun(U_7196,U_7195),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)),tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)))),tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool))),tc_fun(U_7196,U_7195)),c_Product__Type_OPair(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)))),c_Relation_Oinv__image(U_7195,U_7196))))),c_Relation_Oinv__image(U_7195,U_7196))),
    inference(variable_rename,[status(thm)],[f_2089_1]) ).

fof(f_2089_3,plain,
    ! [U_7195,U_7196] : c_FunDef_Orp__inv__image(U_7195,U_7196) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool),tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool),tc_fun(tc_fun(U_7196,U_7195),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool),tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool),tc_fun(tc_fun(U_7196,U_7195),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)),tc_fun(tc_fun(U_7196,U_7195),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool),tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool),tc_fun(tc_fun(U_7196,U_7195),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool))))),tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)),tc_fun(tc_fun(U_7196,U_7195),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool))),tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)),tc_fun(tc_fun(U_7196,U_7195),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)))),tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool)),c_COMBS(tc_fun(U_7196,U_7195),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)),tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)))),tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool))),tc_fun(U_7196,U_7195)),c_Product__Type_OPair(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)))),c_Relation_Oinv__image(U_7195,U_7196))))),c_Relation_Oinv__image(U_7195,U_7196))),
    inference(definitional_conversion,[status(esa)],[f_2089_2]) ).

cnf(f_2089_4,plain,
    c_FunDef_Orp__inv__image(U_7195,U_7196) = hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool),tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool),tc_fun(tc_fun(U_7196,U_7195),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool),tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool),tc_fun(tc_fun(U_7196,U_7195),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)),tc_fun(tc_fun(U_7196,U_7195),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool),tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool),tc_fun(tc_fun(U_7196,U_7195),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool))))),tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool)),c_COMBB(tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)),tc_fun(tc_fun(U_7196,U_7195),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool))),tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)))),tc_fun(tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)),tc_fun(tc_fun(U_7196,U_7195),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)))),tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool)),c_COMBS(tc_fun(U_7196,U_7195),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)),tc_fun(tc_fun(U_7196,U_7195),tc_fun(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)))),tc_fun(tc_prod(U_7195,U_7195),tc_HOL_Obool)),hAPP(c_COMBB(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_prod(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool))),tc_fun(U_7196,U_7195)),c_Product__Type_OPair(tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool),tc_fun(tc_prod(U_7196,U_7196),tc_HOL_Obool)))),c_Relation_Oinv__image(U_7195,U_7196))))),c_Relation_Oinv__image(U_7195,U_7196))),
    inference(clausify,[status(thm)],[f_2089_3]) ).

fof(f_2090_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_2090_2,plain,
    ! [U_7197] : c_Wellfounded_Omeasure(U_7197) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_7197),c_Wellfounded_Oless__than),
    inference(variable_rename,[status(thm)],[f_2090_1]) ).

fof(f_2090_3,plain,
    ! [U_7197] : c_Wellfounded_Omeasure(U_7197) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_7197),c_Wellfounded_Oless__than),
    inference(definitional_conversion,[status(esa)],[f_2090_2]) ).

cnf(f_2090_4,plain,
    c_Wellfounded_Omeasure(U_7197) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,U_7197),c_Wellfounded_Oless__than),
    inference(clausify,[status(thm)],[f_2090_3]) ).

fof(f_2091_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_2091_2,plain,
    ! [U_7200,U_7199,U_7198] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7199),U_7200))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_7198))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7198),U_7199)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7198),U_7200))) ),
    inference(variable_rename,[status(thm)],[f_2091_1]) ).

fof(f_2091_3,plain,
    ! [U_7198,U_7199,U_7200] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7199),U_7200))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_7198))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7198),U_7199)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7198),U_7200))) ),
    inference(definitional_conversion,[status(esa)],[f_2091_2]) ).

cnf(f_2091_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7199),U_7200))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_7198))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7198),U_7199)),hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),U_7198),U_7200))) ),
    inference(clausify,[status(thm)],[f_2091_3]) ).

fof(f_2092_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_2092_2,plain,
    ! [U_7201] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7201),U_7201)),
    inference(variable_rename,[status(thm)],[f_2092_1]) ).

fof(f_2092_3,plain,
    ! [U_7201] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7201),U_7201)),
    inference(definitional_conversion,[status(esa)],[f_2092_2]) ).

cnf(f_2092_4,plain,
    hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7201),U_7201)),
    inference(clausify,[status(thm)],[f_2092_3]) ).

fof(f_2093_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_2093_2,plain,
    ! [U_7203,U_7202] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7202),U_7203),c_Groups_Ozero__class_Ozero(U_7202)))
      | ~ class_Rings_Ocomm__semiring__1(U_7202) ),
    inference(variable_rename,[status(thm)],[f_2093_1]) ).

fof(f_2093_3,plain,
    ! [U_7202,U_7203] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7202),U_7203),c_Groups_Ozero__class_Ozero(U_7202)))
      | ~ class_Rings_Ocomm__semiring__1(U_7202) ),
    inference(definitional_conversion,[status(esa)],[f_2093_2]) ).

cnf(f_2093_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7202),U_7203),c_Groups_Ozero__class_Ozero(U_7202)))
    | ~ class_Rings_Ocomm__semiring__1(U_7202) ),
    inference(clausify,[status(thm)],[f_2093_3]) ).

fof(f_2094_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_2094_2,plain,
    ! [U_7204] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_7204)),
    inference(variable_rename,[status(thm)],[f_2094_1]) ).

fof(f_2094_3,plain,
    ! [U_7204] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_7204)),
    inference(definitional_conversion,[status(esa)],[f_2094_2]) ).

cnf(f_2094_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_7204)),
    inference(clausify,[status(thm)],[f_2094_3]) ).

fof(f_2095_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_2095_2,plain,
    ! [U_7208,U_7207,U_7206,U_7205] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7205),U_7206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7205),U_7207),U_7208)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7205),U_7206),U_7208))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7205),U_7206),U_7207))
      | ~ class_Rings_Ocomm__semiring__1(U_7205) ),
    inference(variable_rename,[status(thm)],[f_2095_1]) ).

fof(f_2095_3,plain,
    ! [U_7205,U_7206,U_7207,U_7208] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7205),U_7206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7205),U_7207),U_7208)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7205),U_7206),U_7208))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7205),U_7206),U_7207))
      | ~ class_Rings_Ocomm__semiring__1(U_7205) ),
    inference(definitional_conversion,[status(esa)],[f_2095_2]) ).

cnf(f_2095_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7205),U_7206),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7205),U_7207),U_7208)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7205),U_7206),U_7208))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7205),U_7206),U_7207))
    | ~ class_Rings_Ocomm__semiring__1(U_7205) ),
    inference(clausify,[status(thm)],[f_2095_3]) ).

fof(f_2096_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_2096_2,plain,
    ! [U_7210,U_7209] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7209),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7210),U_7209)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7209),U_7210)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7209),U_7210))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7209),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7210),U_7209))) ) ),
    inference(variable_rename,[status(thm)],[f_2096_1]) ).

fof(f_2096_3,plain,
    ( ! [U_7214,U_7212] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7212),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7214),U_7212)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7212),U_7214)) )
    & ! [U_7213,U_7211] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7211),U_7213))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7211),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7213),U_7211))) ) ),
    inference(miniscope,[status(thm)],[f_2096_2]) ).

fof(f_2096_4,plain,
    ( ! [U_7212,U_7214] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7212),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7214),U_7212)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7212),U_7214)) )
    & ! [U_7213,U_7211] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7211),U_7213))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7211),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7213),U_7211))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2096_3]) ).

cnf(f_2096_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7211),U_7213))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7211),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7213),U_7211))) ),
    inference(clausify,[status(thm)],[f_2096_4]) ).

cnf(f_2096_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7212),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_7214),U_7212)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7212),U_7214)) ),
    inference(clausify,[status(thm)],[f_2096_4]) ).

fof(f_2097_1,plain,
    ! [V_n,V_m,V_k] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_k),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_2097_2,plain,
    ! [U_7217,U_7216,U_7215] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7215),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7216),U_7217)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7215),U_7217))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7215),U_7216)) ),
    inference(variable_rename,[status(thm)],[f_2097_1]) ).

fof(f_2097_3,plain,
    ! [U_7216,U_7215,U_7217] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7215),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7216),U_7217)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7215),U_7217))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7215),U_7216)) ),
    inference(definitional_conversion,[status(esa)],[f_2097_2]) ).

cnf(f_2097_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7215),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7216),U_7217)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7215),U_7217))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7215),U_7216)) ),
    inference(clausify,[status(thm)],[f_2097_3]) ).

fof(f_2098_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_2098_2,plain,
    ! [U_7220,U_7219,U_7218] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7218),U_7219),U_7220))
      | hAPP(c_Groups_Oabs__class_Oabs(U_7218),U_7219) != hAPP(c_Groups_Oabs__class_Oabs(U_7218),U_7220)
      | ~ class_Rings_Olinordered__idom(U_7218) ),
    inference(variable_rename,[status(thm)],[f_2098_1]) ).

fof(f_2098_3,plain,
    ! [U_7218,U_7219,U_7220] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7218),U_7219),U_7220))
      | hAPP(c_Groups_Oabs__class_Oabs(U_7218),U_7219) != hAPP(c_Groups_Oabs__class_Oabs(U_7218),U_7220)
      | ~ class_Rings_Olinordered__idom(U_7218) ),
    inference(definitional_conversion,[status(esa)],[f_2098_2]) ).

cnf(f_2098_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7218),U_7219),U_7220))
    | hAPP(c_Groups_Oabs__class_Oabs(U_7218),U_7219) != hAPP(c_Groups_Oabs__class_Oabs(U_7218),U_7220)
    | ~ class_Rings_Olinordered__idom(U_7218) ),
    inference(clausify,[status(thm)],[f_2098_3]) ).

fof(f_2099_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_2099_2,plain,
    ! [U_7223,U_7222,U_7221] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7221),hAPP(c_Groups_Oabs__class_Oabs(U_7221),U_7222)),U_7223))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7221),U_7222),U_7223)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7221),U_7222),U_7223))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7221),hAPP(c_Groups_Oabs__class_Oabs(U_7221),U_7222)),U_7223)) ) )
      | ~ class_Rings_Olinordered__idom(U_7221) ),
    inference(variable_rename,[status(thm)],[f_2099_1]) ).

fof(f_2099_3,plain,
    ( ! [U_7221,U_7222,U_7223] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7221),hAPP(c_Groups_Oabs__class_Oabs(U_7221),U_7222)),U_7223))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7221),U_7222),U_7223))
        | ~ sP631(U_7221,U_7222,U_7223) )
    & ! [U_7221,U_7222,U_7223] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7221),U_7222),U_7223))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7221),hAPP(c_Groups_Oabs__class_Oabs(U_7221),U_7222)),U_7223))
        | ~ sP631(U_7221,U_7222,U_7223) )
    & ! [U_7221,U_7222,U_7223] :
        ( sP631(U_7221,U_7222,U_7223)
        | ~ class_Rings_Olinordered__idom(U_7221) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP631])],[f_2099_2]) ).

cnf(f_2099_4,plain,
    ( sP631(U_7221,U_7222,U_7223)
    | ~ class_Rings_Olinordered__idom(U_7221) ),
    inference(clausify,[status(thm)],[f_2099_3]) ).

cnf(f_2099_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7221),U_7222),U_7223))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7221),hAPP(c_Groups_Oabs__class_Oabs(U_7221),U_7222)),U_7223))
    | ~ sP631(U_7221,U_7222,U_7223) ),
    inference(clausify,[status(thm)],[f_2099_3]) ).

cnf(f_2099_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7221),hAPP(c_Groups_Oabs__class_Oabs(U_7221),U_7222)),U_7223))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7221),U_7222),U_7223))
    | ~ sP631(U_7221,U_7222,U_7223) ),
    inference(clausify,[status(thm)],[f_2099_3]) ).

fof(f_2100_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_2100_2,plain,
    ! [U_7226,U_7225,U_7224] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7224),U_7225),hAPP(c_Groups_Oabs__class_Oabs(U_7224),U_7226)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7224),U_7225),U_7226)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7224),U_7225),U_7226))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7224),U_7225),hAPP(c_Groups_Oabs__class_Oabs(U_7224),U_7226))) ) )
      | ~ class_Rings_Olinordered__idom(U_7224) ),
    inference(variable_rename,[status(thm)],[f_2100_1]) ).

fof(f_2100_3,plain,
    ( ! [U_7225,U_7224,U_7226] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7224),U_7225),hAPP(c_Groups_Oabs__class_Oabs(U_7224),U_7226)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7224),U_7225),U_7226))
        | ~ sP632(U_7225,U_7224,U_7226) )
    & ! [U_7225,U_7224,U_7226] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7224),U_7225),U_7226))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7224),U_7225),hAPP(c_Groups_Oabs__class_Oabs(U_7224),U_7226)))
        | ~ sP632(U_7225,U_7224,U_7226) )
    & ! [U_7225,U_7224,U_7226] :
        ( sP632(U_7225,U_7224,U_7226)
        | ~ class_Rings_Olinordered__idom(U_7224) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP632])],[f_2100_2]) ).

cnf(f_2100_4,plain,
    ( sP632(U_7225,U_7224,U_7226)
    | ~ class_Rings_Olinordered__idom(U_7224) ),
    inference(clausify,[status(thm)],[f_2100_3]) ).

cnf(f_2100_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7224),U_7225),U_7226))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7224),U_7225),hAPP(c_Groups_Oabs__class_Oabs(U_7224),U_7226)))
    | ~ sP632(U_7225,U_7224,U_7226) ),
    inference(clausify,[status(thm)],[f_2100_3]) ).

cnf(f_2100_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7224),U_7225),hAPP(c_Groups_Oabs__class_Oabs(U_7224),U_7226)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7224),U_7225),U_7226))
    | ~ sP632(U_7225,U_7224,U_7226) ),
    inference(clausify,[status(thm)],[f_2100_3]) ).

fof(f_2101_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_2101_2,plain,
    ! [U_7230,U_7229,U_7228,U_7227] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7227),U_7228),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7227),U_7229),U_7230)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7227),U_7228),U_7230))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7227),U_7228),U_7229))
      | ~ class_Rings_Ocomm__ring__1(U_7227) ),
    inference(variable_rename,[status(thm)],[f_2101_1]) ).

fof(f_2101_3,plain,
    ! [U_7229,U_7228,U_7227,U_7230] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7227),U_7228),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7227),U_7229),U_7230)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7227),U_7228),U_7230))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7227),U_7228),U_7229))
      | ~ class_Rings_Ocomm__ring__1(U_7227) ),
    inference(definitional_conversion,[status(esa)],[f_2101_2]) ).

cnf(f_2101_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7227),U_7228),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7227),U_7229),U_7230)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7227),U_7228),U_7230))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7227),U_7228),U_7229))
    | ~ class_Rings_Ocomm__ring__1(U_7227) ),
    inference(clausify,[status(thm)],[f_2101_3]) ).

fof(f_2102_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_2102_2,plain,
    ! [U_7232,U_7231] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7231),c_Groups_Oone__class_Oone(U_7231)),U_7232))
      | ~ class_Rings_Ocomm__semiring__1(U_7231) ),
    inference(variable_rename,[status(thm)],[f_2102_1]) ).

fof(f_2102_3,plain,
    ! [U_7232,U_7231] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7231),c_Groups_Oone__class_Oone(U_7231)),U_7232))
      | ~ class_Rings_Ocomm__semiring__1(U_7231) ),
    inference(definitional_conversion,[status(esa)],[f_2102_2]) ).

cnf(f_2102_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7231),c_Groups_Oone__class_Oone(U_7231)),U_7232))
    | ~ class_Rings_Ocomm__semiring__1(U_7231) ),
    inference(clausify,[status(thm)],[f_2102_3]) ).

fof(f_2103_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_2103_2,plain,
    ! [U_7235,U_7234,U_7233] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7233),hAPP(c_Groups_Ouminus__class_Ouminus(U_7233),U_7234)),U_7235))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7233),U_7234),U_7235)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7233),U_7234),U_7235))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7233),hAPP(c_Groups_Ouminus__class_Ouminus(U_7233),U_7234)),U_7235)) ) )
      | ~ class_Rings_Ocomm__ring__1(U_7233) ),
    inference(variable_rename,[status(thm)],[f_2103_1]) ).

fof(f_2103_3,plain,
    ( ! [U_7233,U_7234,U_7235] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7233),hAPP(c_Groups_Ouminus__class_Ouminus(U_7233),U_7234)),U_7235))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7233),U_7234),U_7235))
        | ~ sP633(U_7233,U_7234,U_7235) )
    & ! [U_7233,U_7234,U_7235] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7233),U_7234),U_7235))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7233),hAPP(c_Groups_Ouminus__class_Ouminus(U_7233),U_7234)),U_7235))
        | ~ sP633(U_7233,U_7234,U_7235) )
    & ! [U_7233,U_7234,U_7235] :
        ( sP633(U_7233,U_7234,U_7235)
        | ~ class_Rings_Ocomm__ring__1(U_7233) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP633])],[f_2103_2]) ).

cnf(f_2103_4,plain,
    ( sP633(U_7233,U_7234,U_7235)
    | ~ class_Rings_Ocomm__ring__1(U_7233) ),
    inference(clausify,[status(thm)],[f_2103_3]) ).

cnf(f_2103_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7233),U_7234),U_7235))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7233),hAPP(c_Groups_Ouminus__class_Ouminus(U_7233),U_7234)),U_7235))
    | ~ sP633(U_7233,U_7234,U_7235) ),
    inference(clausify,[status(thm)],[f_2103_3]) ).

cnf(f_2103_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7233),hAPP(c_Groups_Ouminus__class_Ouminus(U_7233),U_7234)),U_7235))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7233),U_7234),U_7235))
    | ~ sP633(U_7233,U_7234,U_7235) ),
    inference(clausify,[status(thm)],[f_2103_3]) ).

fof(f_2104_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_2104_2,plain,
    ! [U_7238,U_7237,U_7236] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7236),U_7237),hAPP(c_Groups_Ouminus__class_Ouminus(U_7236),U_7238)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7236),U_7237),U_7238)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7236),U_7237),U_7238))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7236),U_7237),hAPP(c_Groups_Ouminus__class_Ouminus(U_7236),U_7238))) ) )
      | ~ class_Rings_Ocomm__ring__1(U_7236) ),
    inference(variable_rename,[status(thm)],[f_2104_1]) ).

fof(f_2104_3,plain,
    ( ! [U_7237,U_7236,U_7238] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7236),U_7237),hAPP(c_Groups_Ouminus__class_Ouminus(U_7236),U_7238)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7236),U_7237),U_7238))
        | ~ sP634(U_7237,U_7236,U_7238) )
    & ! [U_7237,U_7236,U_7238] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7236),U_7237),U_7238))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7236),U_7237),hAPP(c_Groups_Ouminus__class_Ouminus(U_7236),U_7238)))
        | ~ sP634(U_7237,U_7236,U_7238) )
    & ! [U_7237,U_7236,U_7238] :
        ( sP634(U_7237,U_7236,U_7238)
        | ~ class_Rings_Ocomm__ring__1(U_7236) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP634])],[f_2104_2]) ).

cnf(f_2104_4,plain,
    ( sP634(U_7237,U_7236,U_7238)
    | ~ class_Rings_Ocomm__ring__1(U_7236) ),
    inference(clausify,[status(thm)],[f_2104_3]) ).

cnf(f_2104_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7236),U_7237),U_7238))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7236),U_7237),hAPP(c_Groups_Ouminus__class_Ouminus(U_7236),U_7238)))
    | ~ sP634(U_7237,U_7236,U_7238) ),
    inference(clausify,[status(thm)],[f_2104_3]) ).

cnf(f_2104_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7236),U_7237),hAPP(c_Groups_Ouminus__class_Ouminus(U_7236),U_7238)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7236),U_7237),U_7238))
    | ~ sP634(U_7237,U_7236,U_7238) ),
    inference(clausify,[status(thm)],[f_2104_3]) ).

fof(f_2105_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_2105_2,plain,
    ! [U_7242,U_7241,U_7240,U_7239] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7239),U_7240),U_7241))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7239),U_7240),U_7242))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7239),U_7240),c_Divides_Odiv__class_Omod(U_7239,U_7241,U_7242)))
      | ~ class_Divides_Osemiring__div(U_7239) ),
    inference(variable_rename,[status(thm)],[f_2105_1]) ).

fof(f_2105_3,plain,
    ! [U_7240,U_7242,U_7239,U_7241] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7239),U_7240),U_7241))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7239),U_7240),U_7242))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7239),U_7240),c_Divides_Odiv__class_Omod(U_7239,U_7241,U_7242)))
      | ~ class_Divides_Osemiring__div(U_7239) ),
    inference(definitional_conversion,[status(esa)],[f_2105_2]) ).

cnf(f_2105_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7239),U_7240),U_7241))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7239),U_7240),U_7242))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7239),U_7240),c_Divides_Odiv__class_Omod(U_7239,U_7241,U_7242)))
    | ~ class_Divides_Osemiring__div(U_7239) ),
    inference(clausify,[status(thm)],[f_2105_3]) ).

fof(f_2106_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_2106_2,plain,
    ! [U_7246,U_7245,U_7244,U_7243] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7243),U_7244),c_Divides_Odiv__class_Omod(U_7243,U_7245,U_7246)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7243),U_7244),U_7246))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7243),U_7244),U_7245))
      | ~ class_Divides_Osemiring__div(U_7243) ),
    inference(variable_rename,[status(thm)],[f_2106_1]) ).

fof(f_2106_3,plain,
    ! [U_7243,U_7244,U_7245,U_7246] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7243),U_7244),c_Divides_Odiv__class_Omod(U_7243,U_7245,U_7246)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7243),U_7244),U_7246))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7243),U_7244),U_7245))
      | ~ class_Divides_Osemiring__div(U_7243) ),
    inference(definitional_conversion,[status(esa)],[f_2106_2]) ).

cnf(f_2106_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7243),U_7244),c_Divides_Odiv__class_Omod(U_7243,U_7245,U_7246)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7243),U_7244),U_7246))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7243),U_7244),U_7245))
    | ~ class_Divides_Osemiring__div(U_7243) ),
    inference(clausify,[status(thm)],[f_2106_3]) ).

fof(f_2107_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_2107_2,plain,
    ! [U_7250,U_7249,U_7248,U_7247] :
      ( c_Divides_Odiv__class_Omod(U_7247,c_Divides_Odiv__class_Omod(U_7247,U_7250,U_7249),U_7248) = c_Divides_Odiv__class_Omod(U_7247,U_7250,U_7248)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7247),U_7248),U_7249))
      | ~ class_Divides_Osemiring__div(U_7247) ),
    inference(variable_rename,[status(thm)],[f_2107_1]) ).

fof(f_2107_3,plain,
    ! [U_7249,U_7248,U_7247,U_7250] :
      ( c_Divides_Odiv__class_Omod(U_7247,c_Divides_Odiv__class_Omod(U_7247,U_7250,U_7249),U_7248) = c_Divides_Odiv__class_Omod(U_7247,U_7250,U_7248)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7247),U_7248),U_7249))
      | ~ class_Divides_Osemiring__div(U_7247) ),
    inference(definitional_conversion,[status(esa)],[f_2107_2]) ).

cnf(f_2107_4,plain,
    ( c_Divides_Odiv__class_Omod(U_7247,c_Divides_Odiv__class_Omod(U_7247,U_7250,U_7249),U_7248) = c_Divides_Odiv__class_Omod(U_7247,U_7250,U_7248)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7247),U_7248),U_7249))
    | ~ class_Divides_Osemiring__div(U_7247) ),
    inference(clausify,[status(thm)],[f_2107_3]) ).

fof(f_2108_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_2108_2,plain,
    ! [U_7254,U_7253,U_7252,U_7251] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7251),U_7252),c_Divides_Odiv__class_Omod(U_7251,U_7254,U_7253)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7251),U_7252),U_7254)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7251),U_7252),U_7254))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7251),U_7252),c_Divides_Odiv__class_Omod(U_7251,U_7254,U_7253))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7251),U_7252),U_7253))
      | ~ class_Divides_Osemiring__div(U_7251) ),
    inference(variable_rename,[status(thm)],[f_2108_1]) ).

fof(f_2108_3,plain,
    ( ! [U_7251,U_7252,U_7253,U_7254] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7251),U_7252),c_Divides_Odiv__class_Omod(U_7251,U_7254,U_7253)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7251),U_7252),U_7254))
        | ~ sP635(U_7251,U_7252,U_7253,U_7254) )
    & ! [U_7251,U_7252,U_7253,U_7254] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7251),U_7252),U_7254))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7251),U_7252),c_Divides_Odiv__class_Omod(U_7251,U_7254,U_7253)))
        | ~ sP635(U_7251,U_7252,U_7253,U_7254) )
    & ! [U_7251,U_7252,U_7253,U_7254] :
        ( sP635(U_7251,U_7252,U_7253,U_7254)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7251),U_7252),U_7253))
        | ~ class_Divides_Osemiring__div(U_7251) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP635])],[f_2108_2]) ).

cnf(f_2108_4,plain,
    ( sP635(U_7251,U_7252,U_7253,U_7254)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7251),U_7252),U_7253))
    | ~ class_Divides_Osemiring__div(U_7251) ),
    inference(clausify,[status(thm)],[f_2108_3]) ).

cnf(f_2108_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7251),U_7252),U_7254))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7251),U_7252),c_Divides_Odiv__class_Omod(U_7251,U_7254,U_7253)))
    | ~ sP635(U_7251,U_7252,U_7253,U_7254) ),
    inference(clausify,[status(thm)],[f_2108_3]) ).

cnf(f_2108_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7251),U_7252),c_Divides_Odiv__class_Omod(U_7251,U_7254,U_7253)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7251),U_7252),U_7254))
    | ~ sP635(U_7251,U_7252,U_7253,U_7254) ),
    inference(clausify,[status(thm)],[f_2108_3]) ).

fof(f_2109_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_2109_2,plain,
    ! [U_7256,U_7255] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7255),U_7256),U_7256))
      | ~ class_Rings_Ocomm__semiring__1(U_7255) ),
    inference(variable_rename,[status(thm)],[f_2109_1]) ).

fof(f_2109_3,plain,
    ! [U_7256,U_7255] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7255),U_7256),U_7256))
      | ~ class_Rings_Ocomm__semiring__1(U_7255) ),
    inference(definitional_conversion,[status(esa)],[f_2109_2]) ).

cnf(f_2109_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7255),U_7256),U_7256))
    | ~ class_Rings_Ocomm__semiring__1(U_7255) ),
    inference(clausify,[status(thm)],[f_2109_3]) ).

fof(f_2110_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_2110_2,plain,
    ! [U_7260,U_7259,U_7258,U_7257] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7257),U_7258),U_7260))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7257),U_7259),U_7260))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7257),U_7258),U_7259))
      | ~ class_Rings_Ocomm__semiring__1(U_7257) ),
    inference(variable_rename,[status(thm)],[f_2110_1]) ).

fof(f_2110_3,plain,
    ! [U_7257,U_7258,U_7259,U_7260] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7257),U_7258),U_7260))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7257),U_7259),U_7260))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7257),U_7258),U_7259))
      | ~ class_Rings_Ocomm__semiring__1(U_7257) ),
    inference(definitional_conversion,[status(esa)],[f_2110_2]) ).

cnf(f_2110_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7257),U_7258),U_7260))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7257),U_7259),U_7260))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7257),U_7258),U_7259))
    | ~ class_Rings_Ocomm__semiring__1(U_7257) ),
    inference(clausify,[status(thm)],[f_2110_3]) ).

fof(f_2111_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_2111_2,plain,
    ! [U_7262,U_7261] :
      ( ( U_7261 = U_7262
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7262),U_7261))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7261),U_7262)) )
      & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7262),U_7261))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7261),U_7262)) )
        | U_7261 != U_7262 ) ),
    inference(variable_rename,[status(thm)],[f_2111_1]) ).

fof(f_2111_3,plain,
    ( ! [U_7266,U_7264] :
        ( U_7264 = U_7266
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7266),U_7264))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7264),U_7266)) )
    & ! [U_7265,U_7263] :
        ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7265),U_7263))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7263),U_7265)) )
        | U_7263 != U_7265 ) ),
    inference(miniscope,[status(thm)],[f_2111_2]) ).

fof(f_2111_4,plain,
    ( ! [U_7265,U_7263] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7265),U_7263))
        | ~ sP636(U_7265,U_7263) )
    & ! [U_7265,U_7263] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7263),U_7265))
        | ~ sP636(U_7265,U_7263) )
    & ! [U_7266,U_7264] :
        ( U_7264 = U_7266
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7266),U_7264))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7264),U_7266)) )
    & ! [U_7265,U_7263] :
        ( sP636(U_7265,U_7263)
        | U_7263 != U_7265 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP636])],[f_2111_3]) ).

cnf(f_2111_5,plain,
    ( sP636(U_7265,U_7263)
    | U_7263 != U_7265 ),
    inference(clausify,[status(thm)],[f_2111_4]) ).

cnf(f_2111_6,plain,
    ( U_7264 = U_7266
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7266),U_7264))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7264),U_7266)) ),
    inference(clausify,[status(thm)],[f_2111_4]) ).

cnf(f_2111_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7263),U_7265))
    | ~ sP636(U_7265,U_7263) ),
    inference(clausify,[status(thm)],[f_2111_4]) ).

cnf(f_2111_8,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7265),U_7263))
    | ~ sP636(U_7265,U_7263) ),
    inference(clausify,[status(thm)],[f_2111_4]) ).

fof(f_2112_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_2112_2,plain,
    ! [U_7268,U_7267] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7267),U_7268))
        | ( U_7267 != U_7268
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7268),U_7267))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7267),U_7268)) ) ) )
      & ( U_7267 = U_7268
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7268),U_7267))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7267),U_7268)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7267),U_7268)) ) ),
    inference(variable_rename,[status(thm)],[f_2112_1]) ).

fof(f_2112_3,plain,
    ( ! [U_7272,U_7270] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7270),U_7272))
        | ( U_7270 != U_7272
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7272),U_7270))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7270),U_7272)) ) ) )
    & ! [U_7271,U_7269] :
        ( U_7269 = U_7271
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7271),U_7269))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7269),U_7271)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7269),U_7271)) ) ),
    inference(miniscope,[status(thm)],[f_2112_2]) ).

fof(f_2112_4,plain,
    ( ! [U_7270,U_7272] :
        ( U_7270 != U_7272
        | ~ sP638(U_7270,U_7272) )
    & ! [U_7270,U_7272] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7272),U_7270))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7270),U_7272))
        | ~ sP638(U_7270,U_7272) )
    & ! [U_7269,U_7271] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7271),U_7269))
        | ~ sP637(U_7269,U_7271) )
    & ! [U_7269,U_7271] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7269),U_7271))
        | ~ sP637(U_7269,U_7271) )
    & ! [U_7270,U_7272] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7270),U_7272))
        | sP638(U_7270,U_7272) )
    & ! [U_7269,U_7271] :
        ( U_7269 = U_7271
        | sP637(U_7269,U_7271)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7269),U_7271)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP637,sP638])],[f_2112_3]) ).

cnf(f_2112_5,plain,
    ( U_7269 = U_7271
    | sP637(U_7269,U_7271)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7269),U_7271)) ),
    inference(clausify,[status(thm)],[f_2112_4]) ).

cnf(f_2112_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7270),U_7272))
    | sP638(U_7270,U_7272) ),
    inference(clausify,[status(thm)],[f_2112_4]) ).

cnf(f_2112_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7269),U_7271))
    | ~ sP637(U_7269,U_7271) ),
    inference(clausify,[status(thm)],[f_2112_4]) ).

cnf(f_2112_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7271),U_7269))
    | ~ sP637(U_7269,U_7271) ),
    inference(clausify,[status(thm)],[f_2112_4]) ).

cnf(f_2112_9,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7272),U_7270))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7270),U_7272))
    | ~ sP638(U_7270,U_7272) ),
    inference(clausify,[status(thm)],[f_2112_4]) ).

cnf(f_2112_10,plain,
    ( U_7270 != U_7272
    | ~ sP638(U_7270,U_7272) ),
    inference(clausify,[status(thm)],[f_2112_4]) ).

fof(f_2113_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_2113_2,plain,
    ! [U_7274,U_7273] :
      ( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7274),U_7273))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7273),U_7274)) )
        | U_7273 = U_7274
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7273),U_7274)) )
      & ( ( U_7273 != U_7274
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7273),U_7274)) )
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7274),U_7273))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7273),U_7274)) ) ),
    inference(variable_rename,[status(thm)],[f_2113_1]) ).

fof(f_2113_3,plain,
    ( ! [U_7278,U_7276] :
        ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7278),U_7276))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7276),U_7278)) )
        | U_7276 = U_7278
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7276),U_7278)) )
    & ! [U_7277,U_7275] :
        ( ( U_7275 != U_7277
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7275),U_7277)) )
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7277),U_7275))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7275),U_7277)) ) ),
    inference(miniscope,[status(thm)],[f_2113_2]) ).

fof(f_2113_4,plain,
    ( ! [U_7278,U_7276] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7278),U_7276))
        | ~ sP640(U_7278,U_7276) )
    & ! [U_7278,U_7276] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7276),U_7278))
        | ~ sP640(U_7278,U_7276) )
    & ! [U_7275,U_7277] :
        ( U_7275 != U_7277
        | ~ sP639(U_7275,U_7277) )
    & ! [U_7275,U_7277] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7275),U_7277))
        | ~ sP639(U_7275,U_7277) )
    & ! [U_7278,U_7276] :
        ( sP640(U_7278,U_7276)
        | U_7276 = U_7278
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7276),U_7278)) )
    & ! [U_7275,U_7277] :
        ( sP639(U_7275,U_7277)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7277),U_7275))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7275),U_7277)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP639,sP640])],[f_2113_3]) ).

cnf(f_2113_5,plain,
    ( sP639(U_7275,U_7277)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7277),U_7275))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7275),U_7277)) ),
    inference(clausify,[status(thm)],[f_2113_4]) ).

cnf(f_2113_6,plain,
    ( sP640(U_7278,U_7276)
    | U_7276 = U_7278
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7276),U_7278)) ),
    inference(clausify,[status(thm)],[f_2113_4]) ).

cnf(f_2113_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7275),U_7277))
    | ~ sP639(U_7275,U_7277) ),
    inference(clausify,[status(thm)],[f_2113_4]) ).

cnf(f_2113_8,plain,
    ( U_7275 != U_7277
    | ~ sP639(U_7275,U_7277) ),
    inference(clausify,[status(thm)],[f_2113_4]) ).

cnf(f_2113_9,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7276),U_7278))
    | ~ sP640(U_7278,U_7276) ),
    inference(clausify,[status(thm)],[f_2113_4]) ).

cnf(f_2113_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7278),U_7276))
    | ~ sP640(U_7278,U_7276) ),
    inference(clausify,[status(thm)],[f_2113_4]) ).

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)) )
      | ~ 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_2114_2,plain,
    ! [U_7280,U_7279] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7280),U_7279))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7279),U_7280)) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7279),U_7280))
      | U_7279 = U_7280 ),
    inference(variable_rename,[status(thm)],[f_2114_1]) ).

fof(f_2114_3,plain,
    ( ! [U_7280,U_7279] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7280),U_7279))
        | ~ sP641(U_7280,U_7279) )
    & ! [U_7280,U_7279] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7279),U_7280))
        | ~ sP641(U_7280,U_7279) )
    & ! [U_7280,U_7279] :
        ( sP641(U_7280,U_7279)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7279),U_7280))
        | U_7279 = U_7280 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP641])],[f_2114_2]) ).

cnf(f_2114_4,plain,
    ( sP641(U_7280,U_7279)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7279),U_7280))
    | U_7279 = U_7280 ),
    inference(clausify,[status(thm)],[f_2114_3]) ).

cnf(f_2114_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7279),U_7280))
    | ~ sP641(U_7280,U_7279) ),
    inference(clausify,[status(thm)],[f_2114_3]) ).

cnf(f_2114_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7280),U_7279))
    | ~ sP641(U_7280,U_7279) ),
    inference(clausify,[status(thm)],[f_2114_3]) ).

fof(f_2115_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_2115_2,plain,
    ! [U_7282,U_7281] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7281),U_7282))
      | U_7281 != U_7282 ),
    inference(variable_rename,[status(thm)],[f_2115_1]) ).

fof(f_2115_3,plain,
    ! [U_7282,U_7281] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7281),U_7282))
      | U_7281 != U_7282 ),
    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_7281),U_7282))
    | U_7281 != U_7282 ),
    inference(clausify,[status(thm)],[f_2115_3]) ).

fof(f_2116_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_2116_2,plain,
    ! [U_7284,U_7283] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7284),U_7283))
          | U_7284 != U_7283 )
        & ( U_7284 = U_7283
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7284),U_7283)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7283),U_7284)) ),
    inference(variable_rename,[status(thm)],[f_2116_1]) ).

fof(f_2116_3,plain,
    ( ! [U_7283,U_7284] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7284),U_7283))
        | U_7284 != U_7283
        | ~ sP642(U_7283,U_7284) )
    & ! [U_7283,U_7284] :
        ( U_7284 = U_7283
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7284),U_7283))
        | ~ sP642(U_7283,U_7284) )
    & ! [U_7283,U_7284] :
        ( sP642(U_7283,U_7284)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7283),U_7284)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP642])],[f_2116_2]) ).

cnf(f_2116_4,plain,
    ( sP642(U_7283,U_7284)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7283),U_7284)) ),
    inference(clausify,[status(thm)],[f_2116_3]) ).

cnf(f_2116_5,plain,
    ( U_7284 = U_7283
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7284),U_7283))
    | ~ sP642(U_7283,U_7284) ),
    inference(clausify,[status(thm)],[f_2116_3]) ).

cnf(f_2116_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7284),U_7283))
    | U_7284 != U_7283
    | ~ sP642(U_7283,U_7284) ),
    inference(clausify,[status(thm)],[f_2116_3]) ).

fof(f_2117_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_2117_2,plain,
    ! [U_7286,U_7285] :
      ( U_7285 = U_7286
      | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7286),U_7285))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7285),U_7286)) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7285),U_7286)) ),
    inference(variable_rename,[status(thm)],[f_2117_1]) ).

fof(f_2117_3,plain,
    ( ! [U_7286,U_7285] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7286),U_7285))
        | ~ sP643(U_7286,U_7285) )
    & ! [U_7286,U_7285] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7285),U_7286))
        | ~ sP643(U_7286,U_7285) )
    & ! [U_7286,U_7285] :
        ( U_7285 = U_7286
        | sP643(U_7286,U_7285)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7285),U_7286)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP643])],[f_2117_2]) ).

cnf(f_2117_4,plain,
    ( U_7285 = U_7286
    | sP643(U_7286,U_7285)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7285),U_7286)) ),
    inference(clausify,[status(thm)],[f_2117_3]) ).

cnf(f_2117_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7285),U_7286))
    | ~ sP643(U_7286,U_7285) ),
    inference(clausify,[status(thm)],[f_2117_3]) ).

cnf(f_2117_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7286),U_7285))
    | ~ sP643(U_7286,U_7285) ),
    inference(clausify,[status(thm)],[f_2117_3]) ).

fof(f_2118_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_2118_2,plain,
    ! [U_7288,U_7287] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7288),U_7287))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7287),U_7288)) )
      | U_7287 = U_7288
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7287),U_7288)) ),
    inference(variable_rename,[status(thm)],[f_2118_1]) ).

fof(f_2118_3,plain,
    ( ! [U_7288,U_7287] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7288),U_7287))
        | ~ sP644(U_7288,U_7287) )
    & ! [U_7288,U_7287] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7287),U_7288))
        | ~ sP644(U_7288,U_7287) )
    & ! [U_7288,U_7287] :
        ( sP644(U_7288,U_7287)
        | U_7287 = U_7288
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7287),U_7288)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP644])],[f_2118_2]) ).

cnf(f_2118_4,plain,
    ( sP644(U_7288,U_7287)
    | U_7287 = U_7288
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7287),U_7288)) ),
    inference(clausify,[status(thm)],[f_2118_3]) ).

cnf(f_2118_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7287),U_7288))
    | ~ sP644(U_7288,U_7287) ),
    inference(clausify,[status(thm)],[f_2118_3]) ).

cnf(f_2118_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7288),U_7287))
    | ~ sP644(U_7288,U_7287) ),
    inference(clausify,[status(thm)],[f_2118_3]) ).

fof(f_2119_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_2119_2,plain,
    ! [U_7291,U_7290,U_7289] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7289),U_7291))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7290),U_7291))
      | U_7289 != U_7290 ),
    inference(variable_rename,[status(thm)],[f_2119_1]) ).

fof(f_2119_3,plain,
    ! [U_7289,U_7290,U_7291] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7289),U_7291))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7290),U_7291))
      | U_7289 != U_7290 ),
    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_7289),U_7291))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7290),U_7291))
    | U_7289 != U_7290 ),
    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_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_2120_2,plain,
    ! [U_7294,U_7293,U_7292] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7292),U_7294))
      | U_7293 != U_7294
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7292),U_7293)) ),
    inference(variable_rename,[status(thm)],[f_2120_1]) ).

fof(f_2120_3,plain,
    ! [U_7293,U_7292,U_7294] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7292),U_7294))
      | U_7293 != U_7294
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7292),U_7293)) ),
    inference(definitional_conversion,[status(esa)],[f_2120_2]) ).

cnf(f_2120_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7292),U_7294))
    | U_7293 != U_7294
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7292),U_7293)) ),
    inference(clausify,[status(thm)],[f_2120_3]) ).

fof(f_2121_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_2121_2,plain,
    ! [U_7296,U_7295] :
      ( U_7295 = U_7296
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7296),U_7295))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7295),U_7296)) ),
    inference(variable_rename,[status(thm)],[f_2121_1]) ).

fof(f_2121_3,plain,
    ! [U_7295,U_7296] :
      ( U_7295 = U_7296
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7296),U_7295))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7295),U_7296)) ),
    inference(definitional_conversion,[status(esa)],[f_2121_2]) ).

cnf(f_2121_4,plain,
    ( U_7295 = U_7296
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7296),U_7295))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7295),U_7296)) ),
    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_Oantisym]) ).

fof(f_2122_2,plain,
    ! [U_7298,U_7297] :
      ( U_7297 = U_7298
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7298),U_7297))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7297),U_7298)) ),
    inference(variable_rename,[status(thm)],[f_2122_1]) ).

fof(f_2122_3,plain,
    ! [U_7297,U_7298] :
      ( U_7297 = U_7298
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7298),U_7297))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7297),U_7298)) ),
    inference(definitional_conversion,[status(esa)],[f_2122_2]) ).

cnf(f_2122_4,plain,
    ( U_7297 = U_7298
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7298),U_7297))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7297),U_7298)) ),
    inference(clausify,[status(thm)],[f_2122_3]) ).

fof(f_2123_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_2123_2,plain,
    ! [U_7301,U_7300,U_7299] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7299),U_7301))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7300),U_7301))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7299),U_7300)) ),
    inference(variable_rename,[status(thm)],[f_2123_1]) ).

fof(f_2123_3,plain,
    ! [U_7299,U_7300,U_7301] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7299),U_7301))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7300),U_7301))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7299),U_7300)) ),
    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_7299),U_7301))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7300),U_7301))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7299),U_7300)) ),
    inference(clausify,[status(thm)],[f_2123_3]) ).

fof(f_2124_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_2124_2,plain,
    ! [U_7304,U_7303,U_7302] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7304),U_7302))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7302),U_7304)) )
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7304),U_7303))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7303),U_7304))
      | U_7302 != U_7303 ),
    inference(variable_rename,[status(thm)],[f_2124_1]) ).

fof(f_2124_3,plain,
    ( ! [U_7302,U_7304] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7304),U_7302))
        | ~ sP645(U_7302,U_7304) )
    & ! [U_7302,U_7304] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7302),U_7304))
        | ~ sP645(U_7302,U_7304) )
    & ! [U_7302,U_7303,U_7304] :
        ( sP645(U_7302,U_7304)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7304),U_7303))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7303),U_7304))
        | U_7302 != U_7303 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP645])],[f_2124_2]) ).

cnf(f_2124_4,plain,
    ( sP645(U_7302,U_7304)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7304),U_7303))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7303),U_7304))
    | U_7302 != U_7303 ),
    inference(clausify,[status(thm)],[f_2124_3]) ).

cnf(f_2124_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7302),U_7304))
    | ~ sP645(U_7302,U_7304) ),
    inference(clausify,[status(thm)],[f_2124_3]) ).

cnf(f_2124_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7304),U_7302))
    | ~ sP645(U_7302,U_7304) ),
    inference(clausify,[status(thm)],[f_2124_3]) ).

fof(f_2125_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_2125_2,plain,
    ! [U_7307,U_7306,U_7305] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7307),U_7305))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7305),U_7307)) )
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7307),U_7306))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7306),U_7307))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7305),U_7306)) ),
    inference(variable_rename,[status(thm)],[f_2125_1]) ).

fof(f_2125_3,plain,
    ( ! [U_7305,U_7307] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7307),U_7305))
        | ~ sP646(U_7305,U_7307) )
    & ! [U_7305,U_7307] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7305),U_7307))
        | ~ sP646(U_7305,U_7307) )
    & ! [U_7305,U_7306,U_7307] :
        ( sP646(U_7305,U_7307)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7307),U_7306))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7306),U_7307))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7305),U_7306)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP646])],[f_2125_2]) ).

cnf(f_2125_4,plain,
    ( sP646(U_7305,U_7307)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7307),U_7306))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7306),U_7307))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7305),U_7306)) ),
    inference(clausify,[status(thm)],[f_2125_3]) ).

cnf(f_2125_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7305),U_7307))
    | ~ sP646(U_7305,U_7307) ),
    inference(clausify,[status(thm)],[f_2125_3]) ).

cnf(f_2125_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7307),U_7305))
    | ~ sP646(U_7305,U_7307) ),
    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__neq]) ).

fof(f_2126_2,plain,
    ! [U_7309,U_7308] :
      ( U_7308 != U_7309
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7309),U_7308))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7308),U_7309)) ),
    inference(variable_rename,[status(thm)],[f_2126_1]) ).

fof(f_2126_3,plain,
    ! [U_7309,U_7308] :
      ( U_7308 != U_7309
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7309),U_7308))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7308),U_7309)) ),
    inference(definitional_conversion,[status(esa)],[f_2126_2]) ).

cnf(f_2126_4,plain,
    ( U_7308 != U_7309
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7309),U_7308))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7308),U_7309)) ),
    inference(clausify,[status(thm)],[f_2126_3]) ).

fof(f_2127_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_2127_2,plain,
    ! [U_7311,U_7310] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7310),U_7311))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7311),U_7310))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7311),U_7310))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7310),U_7311)) ),
    inference(variable_rename,[status(thm)],[f_2127_1]) ).

fof(f_2127_3,plain,
    ! [U_7310,U_7311] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7310),U_7311))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7311),U_7310))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7311),U_7310))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7310),U_7311)) ),
    inference(definitional_conversion,[status(esa)],[f_2127_2]) ).

cnf(f_2127_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7310),U_7311))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7311),U_7310))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7311),U_7310))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7310),U_7311)) ),
    inference(clausify,[status(thm)],[f_2127_3]) ).

fof(f_2128_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_2128_2,plain,
    ! [U_7313,U_7312] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7312),U_7313))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7313),U_7312))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7312),U_7313)) ),
    inference(variable_rename,[status(thm)],[f_2128_1]) ).

fof(f_2128_3,plain,
    ! [U_7313,U_7312] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7312),U_7313))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7313),U_7312))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7312),U_7313)) ),
    inference(definitional_conversion,[status(esa)],[f_2128_2]) ).

cnf(f_2128_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7312),U_7313))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7313),U_7312))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7312),U_7313)) ),
    inference(clausify,[status(thm)],[f_2128_3]) ).

fof(f_2129_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_2129_2,plain,
    ! [U_7315,U_7314] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7314),U_7315))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7315),U_7314))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7315),U_7314))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7314),U_7315)) ),
    inference(variable_rename,[status(thm)],[f_2129_1]) ).

fof(f_2129_3,plain,
    ! [U_7314,U_7315] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7314),U_7315))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7315),U_7314))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7315),U_7314))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7314),U_7315)) ),
    inference(definitional_conversion,[status(esa)],[f_2129_2]) ).

cnf(f_2129_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7314),U_7315))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7315),U_7314))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7315),U_7314))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7314),U_7315)) ),
    inference(clausify,[status(thm)],[f_2129_3]) ).

fof(f_2130_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_2130_2,plain,
    ! [U_7317,U_7316] :
      ( U_7316 != U_7317
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7317),U_7316))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7316),U_7317)) ),
    inference(variable_rename,[status(thm)],[f_2130_1]) ).

fof(f_2130_3,plain,
    ! [U_7316,U_7317] :
      ( U_7316 != U_7317
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7317),U_7316))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7316),U_7317)) ),
    inference(definitional_conversion,[status(esa)],[f_2130_2]) ).

cnf(f_2130_4,plain,
    ( U_7316 != U_7317
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7317),U_7316))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7316),U_7317)) ),
    inference(clausify,[status(thm)],[f_2130_3]) ).

fof(f_2131_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_2131_2,plain,
    ! [U_7319,U_7318] :
      ( U_7319 != U_7318
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7319),U_7318))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7318),U_7319)) ),
    inference(variable_rename,[status(thm)],[f_2131_1]) ).

fof(f_2131_3,plain,
    ! [U_7318,U_7319] :
      ( U_7319 != U_7318
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7319),U_7318))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7318),U_7319)) ),
    inference(definitional_conversion,[status(esa)],[f_2131_2]) ).

cnf(f_2131_4,plain,
    ( U_7319 != U_7318
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7319),U_7318))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7318),U_7319)) ),
    inference(clausify,[status(thm)],[f_2131_3]) ).

fof(f_2132_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_2132_2,plain,
    ! [U_7322,U_7321,U_7320] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7322),U_7320))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7320),U_7322)) )
      | U_7321 != U_7322
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7321),U_7320))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7320),U_7321)) ),
    inference(variable_rename,[status(thm)],[f_2132_1]) ).

fof(f_2132_3,plain,
    ( ! [U_7320,U_7322] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7322),U_7320))
        | ~ sP647(U_7320,U_7322) )
    & ! [U_7320,U_7322] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7320),U_7322))
        | ~ sP647(U_7320,U_7322) )
    & ! [U_7320,U_7321,U_7322] :
        ( sP647(U_7320,U_7322)
        | U_7321 != U_7322
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7321),U_7320))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7320),U_7321)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP647])],[f_2132_2]) ).

cnf(f_2132_4,plain,
    ( sP647(U_7320,U_7322)
    | U_7321 != U_7322
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7321),U_7320))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7320),U_7321)) ),
    inference(clausify,[status(thm)],[f_2132_3]) ).

cnf(f_2132_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7320),U_7322))
    | ~ sP647(U_7320,U_7322) ),
    inference(clausify,[status(thm)],[f_2132_3]) ).

cnf(f_2132_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7322),U_7320))
    | ~ sP647(U_7320,U_7322) ),
    inference(clausify,[status(thm)],[f_2132_3]) ).

fof(f_2133_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_2133_2,plain,
    ! [U_7325,U_7324,U_7323] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7325),U_7323))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7323),U_7325)) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7324),U_7325))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7324),U_7323))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7323),U_7324)) ),
    inference(variable_rename,[status(thm)],[f_2133_1]) ).

fof(f_2133_3,plain,
    ( ! [U_7323,U_7325] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7325),U_7323))
        | ~ sP648(U_7323,U_7325) )
    & ! [U_7323,U_7325] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7323),U_7325))
        | ~ sP648(U_7323,U_7325) )
    & ! [U_7323,U_7324,U_7325] :
        ( sP648(U_7323,U_7325)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7324),U_7325))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7324),U_7323))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7323),U_7324)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP648])],[f_2133_2]) ).

cnf(f_2133_4,plain,
    ( sP648(U_7323,U_7325)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7324),U_7325))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7324),U_7323))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7323),U_7324)) ),
    inference(clausify,[status(thm)],[f_2133_3]) ).

cnf(f_2133_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7323),U_7325))
    | ~ sP648(U_7323,U_7325) ),
    inference(clausify,[status(thm)],[f_2133_3]) ).

cnf(f_2133_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7325),U_7323))
    | ~ sP648(U_7323,U_7325) ),
    inference(clausify,[status(thm)],[f_2133_3]) ).

fof(f_2134_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_2134_2,plain,
    ! [U_7327,U_7326] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7326),U_7327))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7327),U_7326))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7327),U_7326))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7326),U_7327)) ),
    inference(variable_rename,[status(thm)],[f_2134_1]) ).

fof(f_2134_3,plain,
    ! [U_7327,U_7326] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7326),U_7327))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7327),U_7326))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7327),U_7326))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7326),U_7327)) ),
    inference(definitional_conversion,[status(esa)],[f_2134_2]) ).

cnf(f_2134_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7326),U_7327))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7327),U_7326))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7327),U_7326))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7326),U_7327)) ),
    inference(clausify,[status(thm)],[f_2134_3]) ).

fof(f_2135_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_2135_2,plain,
    ! [U_7330,U_7329,U_7328] :
      ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7330),U_7328))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7328),U_7330)) )
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7330),U_7329))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7329),U_7330))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7329),U_7328))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7328),U_7329)) ),
    inference(variable_rename,[status(thm)],[f_2135_1]) ).

fof(f_2135_3,plain,
    ( ! [U_7328,U_7330] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7330),U_7328))
        | ~ sP649(U_7328,U_7330) )
    & ! [U_7328,U_7330] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7328),U_7330))
        | ~ sP649(U_7328,U_7330) )
    & ! [U_7328,U_7329,U_7330] :
        ( sP649(U_7328,U_7330)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7330),U_7329))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7329),U_7330))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7329),U_7328))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7328),U_7329)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP649])],[f_2135_2]) ).

cnf(f_2135_4,plain,
    ( sP649(U_7328,U_7330)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7330),U_7329))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7329),U_7330))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7329),U_7328))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7328),U_7329)) ),
    inference(clausify,[status(thm)],[f_2135_3]) ).

cnf(f_2135_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7328),U_7330))
    | ~ sP649(U_7328,U_7330) ),
    inference(clausify,[status(thm)],[f_2135_3]) ).

cnf(f_2135_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7330),U_7328))
    | ~ sP649(U_7328,U_7330) ),
    inference(clausify,[status(thm)],[f_2135_3]) ).

fof(f_2136_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_2136_2,plain,
    ! [U_7332,U_7331] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7331),U_7332))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7332),U_7331))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7332),U_7331))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7331),U_7332)) ),
    inference(variable_rename,[status(thm)],[f_2136_1]) ).

fof(f_2136_3,plain,
    ! [U_7332,U_7331] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7331),U_7332))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7332),U_7331))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7332),U_7331))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7331),U_7332)) ),
    inference(definitional_conversion,[status(esa)],[f_2136_2]) ).

cnf(f_2136_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7331),U_7332))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7332),U_7331))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7332),U_7331))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7331),U_7332)) ),
    inference(clausify,[status(thm)],[f_2136_3]) ).

fof(f_2137_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_2137_2,plain,
    ! [U_7334,U_7333] :
      ( U_7334 = c_Groups_Ozero__class_Ozero(U_7333)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7333),c_Groups_Ozero__class_Ozero(U_7333)),U_7334))
      | ~ class_Rings_Ocomm__semiring__1(U_7333) ),
    inference(variable_rename,[status(thm)],[f_2137_1]) ).

fof(f_2137_3,plain,
    ! [U_7333,U_7334] :
      ( U_7334 = c_Groups_Ozero__class_Ozero(U_7333)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7333),c_Groups_Ozero__class_Ozero(U_7333)),U_7334))
      | ~ class_Rings_Ocomm__semiring__1(U_7333) ),
    inference(definitional_conversion,[status(esa)],[f_2137_2]) ).

cnf(f_2137_4,plain,
    ( U_7334 = c_Groups_Ozero__class_Ozero(U_7333)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7333),c_Groups_Ozero__class_Ozero(U_7333)),U_7334))
    | ~ class_Rings_Ocomm__semiring__1(U_7333) ),
    inference(clausify,[status(thm)],[f_2137_3]) ).

fof(f_2138_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_2138_2,plain,
    ! [U_7338,U_7337,U_7336,U_7335] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7335),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7335),U_7337),U_7336)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7335),U_7338),U_7336)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7335),U_7337),U_7338)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7335),U_7337),U_7338))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7335),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7335),U_7337),U_7336)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7335),U_7338),U_7336))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7335),U_7336),U_7338))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7335),U_7336),U_7337))
      | ~ class_Divides_Osemiring__div(U_7335) ),
    inference(variable_rename,[status(thm)],[f_2138_1]) ).

fof(f_2138_3,plain,
    ( ! [U_7335,U_7336,U_7337,U_7338] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7335),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7335),U_7337),U_7336)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7335),U_7338),U_7336)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7335),U_7337),U_7338))
        | ~ sP650(U_7335,U_7336,U_7337,U_7338) )
    & ! [U_7335,U_7336,U_7337,U_7338] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7335),U_7337),U_7338))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7335),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7335),U_7337),U_7336)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7335),U_7338),U_7336)))
        | ~ sP650(U_7335,U_7336,U_7337,U_7338) )
    & ! [U_7335,U_7336,U_7337,U_7338] :
        ( sP650(U_7335,U_7336,U_7337,U_7338)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7335),U_7336),U_7338))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7335),U_7336),U_7337))
        | ~ class_Divides_Osemiring__div(U_7335) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP650])],[f_2138_2]) ).

cnf(f_2138_4,plain,
    ( sP650(U_7335,U_7336,U_7337,U_7338)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7335),U_7336),U_7338))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7335),U_7336),U_7337))
    | ~ class_Divides_Osemiring__div(U_7335) ),
    inference(clausify,[status(thm)],[f_2138_3]) ).

cnf(f_2138_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7335),U_7337),U_7338))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7335),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7335),U_7337),U_7336)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7335),U_7338),U_7336)))
    | ~ sP650(U_7335,U_7336,U_7337,U_7338) ),
    inference(clausify,[status(thm)],[f_2138_3]) ).

cnf(f_2138_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7335),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7335),U_7337),U_7336)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7335),U_7338),U_7336)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7335),U_7337),U_7338))
    | ~ sP650(U_7335,U_7336,U_7337,U_7338) ),
    inference(clausify,[status(thm)],[f_2138_3]) ).

fof(f_2139_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_2139_2,plain,
    ! [U_7342,U_7341,U_7340,U_7339] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7339),hAPP(hAPP(c_Power_Opower__class_Opower(U_7339),U_7340),U_7342)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7339),U_7341),U_7342)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7339),U_7340),U_7341))
      | ~ class_Rings_Ocomm__semiring__1(U_7339) ),
    inference(variable_rename,[status(thm)],[f_2139_1]) ).

fof(f_2139_3,plain,
    ! [U_7341,U_7342,U_7340,U_7339] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7339),hAPP(hAPP(c_Power_Opower__class_Opower(U_7339),U_7340),U_7342)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7339),U_7341),U_7342)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7339),U_7340),U_7341))
      | ~ class_Rings_Ocomm__semiring__1(U_7339) ),
    inference(definitional_conversion,[status(esa)],[f_2139_2]) ).

cnf(f_2139_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7339),hAPP(hAPP(c_Power_Opower__class_Opower(U_7339),U_7340),U_7342)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7339),U_7341),U_7342)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7339),U_7340),U_7341))
    | ~ class_Rings_Ocomm__semiring__1(U_7339) ),
    inference(clausify,[status(thm)],[f_2139_3]) ).

fof(f_2140_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_2140_2,plain,
    ! [U_7343] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7343),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_7343 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
      & ( U_7343 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7343),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(variable_rename,[status(thm)],[f_2140_1]) ).

fof(f_2140_3,plain,
    ( ! [U_7345] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7345),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_7345 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_7344] :
        ( U_7344 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7344),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(miniscope,[status(thm)],[f_2140_2]) ).

fof(f_2140_4,plain,
    ( ! [U_7345] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7345),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_7345 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
    & ! [U_7344] :
        ( U_7344 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7344),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2140_3]) ).

cnf(f_2140_5,plain,
    ( U_7344 = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7344),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_2140_4]) ).

cnf(f_2140_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7345),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | U_7345 != c_Groups_Oone__class_Oone(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2140_4]) ).

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_7348,U_7347,U_7346] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7346),U_7347),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7346),U_7347),U_7348)))
      | ~ class_Rings_Ocomm__semiring__1(U_7346) ),
    inference(variable_rename,[status(thm)],[f_2141_1]) ).

fof(f_2141_3,plain,
    ! [U_7346,U_7347,U_7348] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7346),U_7347),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7346),U_7347),U_7348)))
      | ~ class_Rings_Ocomm__semiring__1(U_7346) ),
    inference(definitional_conversion,[status(esa)],[f_2141_2]) ).

cnf(f_2141_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7346),U_7347),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7346),U_7347),U_7348)))
    | ~ class_Rings_Ocomm__semiring__1(U_7346) ),
    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_7351,U_7350,U_7349] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7349),U_7350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7349),U_7351),U_7350)))
      | ~ class_Rings_Ocomm__semiring__1(U_7349) ),
    inference(variable_rename,[status(thm)],[f_2142_1]) ).

fof(f_2142_3,plain,
    ! [U_7349,U_7350,U_7351] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7349),U_7350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7349),U_7351),U_7350)))
      | ~ class_Rings_Ocomm__semiring__1(U_7349) ),
    inference(definitional_conversion,[status(esa)],[f_2142_2]) ).

cnf(f_2142_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7349),U_7350),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7349),U_7351),U_7350)))
    | ~ class_Rings_Ocomm__semiring__1(U_7349) ),
    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_7355,U_7354,U_7353,U_7352] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7352),U_7353),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7352),U_7354),U_7355)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7352),U_7353),U_7354))
      | ~ class_Rings_Ocomm__semiring__1(U_7352) ),
    inference(variable_rename,[status(thm)],[f_2143_1]) ).

fof(f_2143_3,plain,
    ! [U_7352,U_7353,U_7354,U_7355] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7352),U_7353),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7352),U_7354),U_7355)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7352),U_7353),U_7354))
      | ~ class_Rings_Ocomm__semiring__1(U_7352) ),
    inference(definitional_conversion,[status(esa)],[f_2143_2]) ).

cnf(f_2143_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7352),U_7353),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7352),U_7354),U_7355)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7352),U_7353),U_7354))
    | ~ class_Rings_Ocomm__semiring__1(U_7352) ),
    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_7359,U_7358,U_7357,U_7356] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7356),U_7357),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7356),U_7359),U_7358)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7356),U_7357),U_7358))
      | ~ class_Rings_Ocomm__semiring__1(U_7356) ),
    inference(variable_rename,[status(thm)],[f_2144_1]) ).

fof(f_2144_3,plain,
    ! [U_7356,U_7357,U_7358,U_7359] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7356),U_7357),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7356),U_7359),U_7358)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7356),U_7357),U_7358))
      | ~ class_Rings_Ocomm__semiring__1(U_7356) ),
    inference(definitional_conversion,[status(esa)],[f_2144_2]) ).

cnf(f_2144_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7356),U_7357),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7356),U_7359),U_7358)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7356),U_7357),U_7358))
    | ~ class_Rings_Ocomm__semiring__1(U_7356) ),
    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_7364,U_7363,U_7362,U_7361,U_7360] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7360),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7360),U_7361),U_7363)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7360),U_7362),U_7364)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7360),U_7363),U_7364))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7360),U_7361),U_7362))
      | ~ class_Rings_Ocomm__semiring__1(U_7360) ),
    inference(variable_rename,[status(thm)],[f_2145_1]) ).

fof(f_2145_3,plain,
    ! [U_7360,U_7361,U_7362,U_7363,U_7364] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7360),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7360),U_7361),U_7363)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7360),U_7362),U_7364)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7360),U_7363),U_7364))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7360),U_7361),U_7362))
      | ~ class_Rings_Ocomm__semiring__1(U_7360) ),
    inference(definitional_conversion,[status(esa)],[f_2145_2]) ).

cnf(f_2145_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7360),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7360),U_7361),U_7363)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7360),U_7362),U_7364)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7360),U_7363),U_7364))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7360),U_7361),U_7362))
    | ~ class_Rings_Ocomm__semiring__1(U_7360) ),
    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_7368,U_7367,U_7366,U_7365] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7365),U_7367),U_7366))
      | U_7366 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7365),U_7367),U_7368)
      | ~ class_Rings_Odvd(U_7365) ),
    inference(variable_rename,[status(thm)],[f_2146_1]) ).

fof(f_2146_3,plain,
    ! [U_7367,U_7366,U_7365,U_7368] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7365),U_7367),U_7366))
      | U_7366 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7365),U_7367),U_7368)
      | ~ class_Rings_Odvd(U_7365) ),
    inference(definitional_conversion,[status(esa)],[f_2146_2]) ).

cnf(f_2146_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7365),U_7367),U_7366))
    | U_7366 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7365),U_7367),U_7368)
    | ~ class_Rings_Odvd(U_7365) ),
    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_7372,U_7371,U_7370,U_7369] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7369),U_7370),U_7372))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7369),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7369),U_7370),U_7371)),U_7372))
      | ~ class_Rings_Ocomm__semiring__1(U_7369) ),
    inference(variable_rename,[status(thm)],[f_2147_1]) ).

fof(f_2147_3,plain,
    ! [U_7369,U_7370,U_7371,U_7372] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7369),U_7370),U_7372))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7369),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7369),U_7370),U_7371)),U_7372))
      | ~ class_Rings_Ocomm__semiring__1(U_7369) ),
    inference(definitional_conversion,[status(esa)],[f_2147_2]) ).

cnf(f_2147_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7369),U_7370),U_7372))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7369),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7369),U_7370),U_7371)),U_7372))
    | ~ class_Rings_Ocomm__semiring__1(U_7369) ),
    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_7376,U_7375,U_7374,U_7373] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7373),U_7375),U_7376))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7373),U_7374),U_7375)),U_7376))
      | ~ class_Rings_Ocomm__semiring__1(U_7373) ),
    inference(variable_rename,[status(thm)],[f_2148_1]) ).

fof(f_2148_3,plain,
    ! [U_7373,U_7374,U_7375,U_7376] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7373),U_7375),U_7376))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7373),U_7374),U_7375)),U_7376))
      | ~ class_Rings_Ocomm__semiring__1(U_7373) ),
    inference(definitional_conversion,[status(esa)],[f_2148_2]) ).

cnf(f_2148_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7373),U_7375),U_7376))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7373),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7373),U_7374),U_7375)),U_7376))
    | ~ class_Rings_Ocomm__semiring__1(U_7373) ),
    inference(clausify,[status(thm)],[f_2148_3]) ).

fof(f_2149_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_2149_2,plain,
    ! [U_7380,U_7379,U_7378,U_7377] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7377),U_7378),U_7379)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7377),U_7378),U_7380)))
          | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7377),U_7379),U_7380))
            & U_7378 != c_Groups_Ozero__class_Ozero(U_7377) ) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7377),U_7379),U_7380))
          | U_7378 = c_Groups_Ozero__class_Ozero(U_7377)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7377),U_7378),U_7379)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7377),U_7378),U_7380))) ) )
      | ~ class_Rings_Oidom(U_7377) ),
    inference(variable_rename,[status(thm)],[f_2149_1]) ).

fof(f_2149_3,plain,
    ( ! [U_7377,U_7378,U_7379,U_7380] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7377),U_7379),U_7380))
        | ~ sP651(U_7377,U_7378,U_7379,U_7380) )
    & ! [U_7377,U_7378,U_7379,U_7380] :
        ( U_7378 != c_Groups_Ozero__class_Ozero(U_7377)
        | ~ sP651(U_7377,U_7378,U_7379,U_7380) )
    & ! [U_7377,U_7378,U_7379,U_7380] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7377),U_7378),U_7379)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7377),U_7378),U_7380)))
        | sP651(U_7377,U_7378,U_7379,U_7380)
        | ~ sP652(U_7377,U_7378,U_7379,U_7380) )
    & ! [U_7377,U_7378,U_7379,U_7380] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7377),U_7379),U_7380))
        | U_7378 = c_Groups_Ozero__class_Ozero(U_7377)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7377),U_7378),U_7379)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7377),U_7378),U_7380)))
        | ~ sP652(U_7377,U_7378,U_7379,U_7380) )
    & ! [U_7377,U_7378,U_7379,U_7380] :
        ( sP652(U_7377,U_7378,U_7379,U_7380)
        | ~ class_Rings_Oidom(U_7377) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP651,sP652])],[f_2149_2]) ).

cnf(f_2149_4,plain,
    ( sP652(U_7377,U_7378,U_7379,U_7380)
    | ~ class_Rings_Oidom(U_7377) ),
    inference(clausify,[status(thm)],[f_2149_3]) ).

cnf(f_2149_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7377),U_7379),U_7380))
    | U_7378 = c_Groups_Ozero__class_Ozero(U_7377)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7377),U_7378),U_7379)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7377),U_7378),U_7380)))
    | ~ sP652(U_7377,U_7378,U_7379,U_7380) ),
    inference(clausify,[status(thm)],[f_2149_3]) ).

cnf(f_2149_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7377),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7377),U_7378),U_7379)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7377),U_7378),U_7380)))
    | sP651(U_7377,U_7378,U_7379,U_7380)
    | ~ sP652(U_7377,U_7378,U_7379,U_7380) ),
    inference(clausify,[status(thm)],[f_2149_3]) ).

cnf(f_2149_7,plain,
    ( U_7378 != c_Groups_Ozero__class_Ozero(U_7377)
    | ~ sP651(U_7377,U_7378,U_7379,U_7380) ),
    inference(clausify,[status(thm)],[f_2149_3]) ).

cnf(f_2149_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7377),U_7379),U_7380))
    | ~ sP651(U_7377,U_7378,U_7379,U_7380) ),
    inference(clausify,[status(thm)],[f_2149_3]) ).

fof(f_2150_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_2150_2,plain,
    ! [U_7384,U_7383,U_7382,U_7381] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7381),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7381),U_7382),U_7383)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7381),U_7384),U_7383)))
          | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7381),U_7382),U_7384))
            & U_7383 != c_Groups_Ozero__class_Ozero(U_7381) ) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7381),U_7382),U_7384))
          | U_7383 = c_Groups_Ozero__class_Ozero(U_7381)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7381),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7381),U_7382),U_7383)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7381),U_7384),U_7383))) ) )
      | ~ class_Rings_Oidom(U_7381) ),
    inference(variable_rename,[status(thm)],[f_2150_1]) ).

fof(f_2150_3,plain,
    ( ! [U_7384,U_7382,U_7381,U_7383] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7381),U_7382),U_7384))
        | ~ sP653(U_7384,U_7382,U_7381,U_7383) )
    & ! [U_7384,U_7382,U_7381,U_7383] :
        ( U_7383 != c_Groups_Ozero__class_Ozero(U_7381)
        | ~ sP653(U_7384,U_7382,U_7381,U_7383) )
    & ! [U_7384,U_7382,U_7381,U_7383] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7381),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7381),U_7382),U_7383)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7381),U_7384),U_7383)))
        | sP653(U_7384,U_7382,U_7381,U_7383)
        | ~ sP654(U_7384,U_7382,U_7381,U_7383) )
    & ! [U_7384,U_7382,U_7381,U_7383] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7381),U_7382),U_7384))
        | U_7383 = c_Groups_Ozero__class_Ozero(U_7381)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7381),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7381),U_7382),U_7383)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7381),U_7384),U_7383)))
        | ~ sP654(U_7384,U_7382,U_7381,U_7383) )
    & ! [U_7384,U_7382,U_7381,U_7383] :
        ( sP654(U_7384,U_7382,U_7381,U_7383)
        | ~ class_Rings_Oidom(U_7381) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP653,sP654])],[f_2150_2]) ).

cnf(f_2150_4,plain,
    ( sP654(U_7384,U_7382,U_7381,U_7383)
    | ~ class_Rings_Oidom(U_7381) ),
    inference(clausify,[status(thm)],[f_2150_3]) ).

cnf(f_2150_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7381),U_7382),U_7384))
    | U_7383 = c_Groups_Ozero__class_Ozero(U_7381)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7381),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7381),U_7382),U_7383)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7381),U_7384),U_7383)))
    | ~ sP654(U_7384,U_7382,U_7381,U_7383) ),
    inference(clausify,[status(thm)],[f_2150_3]) ).

cnf(f_2150_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7381),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7381),U_7382),U_7383)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7381),U_7384),U_7383)))
    | sP653(U_7384,U_7382,U_7381,U_7383)
    | ~ sP654(U_7384,U_7382,U_7381,U_7383) ),
    inference(clausify,[status(thm)],[f_2150_3]) ).

cnf(f_2150_7,plain,
    ( U_7383 != c_Groups_Ozero__class_Ozero(U_7381)
    | ~ sP653(U_7384,U_7382,U_7381,U_7383) ),
    inference(clausify,[status(thm)],[f_2150_3]) ).

cnf(f_2150_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7381),U_7382),U_7384))
    | ~ sP653(U_7384,U_7382,U_7381,U_7383) ),
    inference(clausify,[status(thm)],[f_2150_3]) ).

fof(f_2151_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_2151_2,plain,
    ! [U_7387,U_7386,U_7385] :
      ( c_Divides_Odiv__class_Omod(U_7385,U_7387,U_7386) = c_Groups_Ozero__class_Ozero(U_7385)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7385),U_7386),U_7387))
      | ~ class_Divides_Osemiring__div(U_7385) ),
    inference(variable_rename,[status(thm)],[f_2151_1]) ).

fof(f_2151_3,plain,
    ! [U_7387,U_7385,U_7386] :
      ( c_Divides_Odiv__class_Omod(U_7385,U_7387,U_7386) = c_Groups_Ozero__class_Ozero(U_7385)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7385),U_7386),U_7387))
      | ~ class_Divides_Osemiring__div(U_7385) ),
    inference(definitional_conversion,[status(esa)],[f_2151_2]) ).

cnf(f_2151_4,plain,
    ( c_Divides_Odiv__class_Omod(U_7385,U_7387,U_7386) = c_Groups_Ozero__class_Ozero(U_7385)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7385),U_7386),U_7387))
    | ~ class_Divides_Osemiring__div(U_7385) ),
    inference(clausify,[status(thm)],[f_2151_3]) ).

fof(f_2152_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_2152_2,plain,
    ! [U_7390,U_7389,U_7388] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7388),U_7389),U_7390))
          | c_Divides_Odiv__class_Omod(U_7388,U_7390,U_7389) != c_Groups_Ozero__class_Ozero(U_7388) )
        & ( c_Divides_Odiv__class_Omod(U_7388,U_7390,U_7389) = c_Groups_Ozero__class_Ozero(U_7388)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7388),U_7389),U_7390)) ) )
      | ~ class_Divides_Osemiring__div(U_7388) ),
    inference(variable_rename,[status(thm)],[f_2152_1]) ).

fof(f_2152_3,plain,
    ( ! [U_7389,U_7388,U_7390] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7388),U_7389),U_7390))
        | c_Divides_Odiv__class_Omod(U_7388,U_7390,U_7389) != c_Groups_Ozero__class_Ozero(U_7388)
        | ~ sP655(U_7389,U_7388,U_7390) )
    & ! [U_7389,U_7388,U_7390] :
        ( c_Divides_Odiv__class_Omod(U_7388,U_7390,U_7389) = c_Groups_Ozero__class_Ozero(U_7388)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7388),U_7389),U_7390))
        | ~ sP655(U_7389,U_7388,U_7390) )
    & ! [U_7389,U_7388,U_7390] :
        ( sP655(U_7389,U_7388,U_7390)
        | ~ class_Divides_Osemiring__div(U_7388) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP655])],[f_2152_2]) ).

cnf(f_2152_4,plain,
    ( sP655(U_7389,U_7388,U_7390)
    | ~ class_Divides_Osemiring__div(U_7388) ),
    inference(clausify,[status(thm)],[f_2152_3]) ).

cnf(f_2152_5,plain,
    ( c_Divides_Odiv__class_Omod(U_7388,U_7390,U_7389) = c_Groups_Ozero__class_Ozero(U_7388)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7388),U_7389),U_7390))
    | ~ sP655(U_7389,U_7388,U_7390) ),
    inference(clausify,[status(thm)],[f_2152_3]) ).

cnf(f_2152_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7388),U_7389),U_7390))
    | c_Divides_Odiv__class_Omod(U_7388,U_7390,U_7389) != c_Groups_Ozero__class_Ozero(U_7388)
    | ~ sP655(U_7389,U_7388,U_7390) ),
    inference(clausify,[status(thm)],[f_2152_3]) ).

fof(f_2153_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_2153_2,plain,
    ! [U_7394,U_7393,U_7392,U_7391] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7391),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7391),U_7393),U_7394)),U_7392) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7391),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7391),U_7393),U_7392)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7391),U_7394),U_7392))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7391),U_7392),U_7394))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7391),U_7392),U_7393))
      | ~ class_Divides_Osemiring__div(U_7391) ),
    inference(variable_rename,[status(thm)],[f_2153_1]) ).

fof(f_2153_3,plain,
    ! [U_7391,U_7392,U_7393,U_7394] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7391),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7391),U_7393),U_7394)),U_7392) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7391),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7391),U_7393),U_7392)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7391),U_7394),U_7392))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7391),U_7392),U_7394))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7391),U_7392),U_7393))
      | ~ class_Divides_Osemiring__div(U_7391) ),
    inference(definitional_conversion,[status(esa)],[f_2153_2]) ).

cnf(f_2153_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7391),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7391),U_7393),U_7394)),U_7392) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7391),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7391),U_7393),U_7392)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7391),U_7394),U_7392))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7391),U_7392),U_7394))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7391),U_7392),U_7393))
    | ~ class_Divides_Osemiring__div(U_7391) ),
    inference(clausify,[status(thm)],[f_2153_3]) ).

fof(f_2154_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_2154_2,plain,
    ! [U_7397,U_7396,U_7395] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7395),U_7396),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7395),U_7397),U_7396)) = U_7397
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7395),U_7396),U_7397))
      | ~ class_Divides_Osemiring__div(U_7395) ),
    inference(variable_rename,[status(thm)],[f_2154_1]) ).

fof(f_2154_3,plain,
    ! [U_7396,U_7397,U_7395] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7395),U_7396),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7395),U_7397),U_7396)) = U_7397
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7395),U_7396),U_7397))
      | ~ class_Divides_Osemiring__div(U_7395) ),
    inference(definitional_conversion,[status(esa)],[f_2154_2]) ).

cnf(f_2154_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7395),U_7396),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7395),U_7397),U_7396)) = U_7397
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7395),U_7396),U_7397))
    | ~ class_Divides_Osemiring__div(U_7395) ),
    inference(clausify,[status(thm)],[f_2154_3]) ).

fof(f_2155_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_2155_2,plain,
    ! [U_7401,U_7400,U_7399,U_7398] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7398),U_7401),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7398),U_7400),U_7399)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7398),U_7401),U_7400)),U_7399)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7398),U_7399),U_7400))
      | ~ class_Divides_Osemiring__div(U_7398) ),
    inference(variable_rename,[status(thm)],[f_2155_1]) ).

fof(f_2155_3,plain,
    ! [U_7398,U_7399,U_7400,U_7401] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7398),U_7401),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7398),U_7400),U_7399)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7398),U_7401),U_7400)),U_7399)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7398),U_7399),U_7400))
      | ~ class_Divides_Osemiring__div(U_7398) ),
    inference(definitional_conversion,[status(esa)],[f_2155_2]) ).

cnf(f_2155_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7398),U_7401),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7398),U_7400),U_7399)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7398),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7398),U_7401),U_7400)),U_7399)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7398),U_7399),U_7400))
    | ~ class_Divides_Osemiring__div(U_7398) ),
    inference(clausify,[status(thm)],[f_2155_3]) ).

fof(f_2156_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_2156_2,plain,
    ! [U_7404,U_7403,U_7402] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7402),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7402),U_7404),U_7403)),U_7403) = U_7404
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7402),U_7403),U_7404))
      | ~ class_Divides_Osemiring__div(U_7402) ),
    inference(variable_rename,[status(thm)],[f_2156_1]) ).

fof(f_2156_3,plain,
    ! [U_7403,U_7402,U_7404] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7402),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7402),U_7404),U_7403)),U_7403) = U_7404
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7402),U_7403),U_7404))
      | ~ class_Divides_Osemiring__div(U_7402) ),
    inference(definitional_conversion,[status(esa)],[f_2156_2]) ).

cnf(f_2156_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7402),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7402),U_7404),U_7403)),U_7403) = U_7404
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7402),U_7403),U_7404))
    | ~ class_Divides_Osemiring__div(U_7402) ),
    inference(clausify,[status(thm)],[f_2156_3]) ).

fof(f_2157_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_2157_2,plain,
    ! [U_7408,U_7407,U_7406,U_7405] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7405),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7405),U_7407),U_7406)),U_7408) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7405),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7405),U_7407),U_7408)),U_7406)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7405),U_7406),U_7407))
      | ~ class_Divides_Osemiring__div(U_7405) ),
    inference(variable_rename,[status(thm)],[f_2157_1]) ).

fof(f_2157_3,plain,
    ! [U_7405,U_7406,U_7407,U_7408] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7405),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7405),U_7407),U_7406)),U_7408) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7405),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7405),U_7407),U_7408)),U_7406)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7405),U_7406),U_7407))
      | ~ class_Divides_Osemiring__div(U_7405) ),
    inference(definitional_conversion,[status(esa)],[f_2157_2]) ).

cnf(f_2157_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7405),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7405),U_7407),U_7406)),U_7408) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7405),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7405),U_7407),U_7408)),U_7406)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7405),U_7406),U_7407))
    | ~ class_Divides_Osemiring__div(U_7405) ),
    inference(clausify,[status(thm)],[f_2157_3]) ).

fof(f_2158_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_2158_2,plain,
    ! [U_7413,U_7412,U_7411,U_7410,U_7409] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7409),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7409),U_7411),U_7410)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7409),U_7413),U_7412)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7409),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7409),U_7411),U_7413)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7409),U_7410),U_7412))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7409),U_7412),U_7413))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7409),U_7410),U_7411))
      | ~ class_Divides_Osemiring__div(U_7409) ),
    inference(variable_rename,[status(thm)],[f_2158_1]) ).

fof(f_2158_3,plain,
    ! [U_7409,U_7410,U_7411,U_7412,U_7413] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7409),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7409),U_7411),U_7410)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7409),U_7413),U_7412)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7409),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7409),U_7411),U_7413)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7409),U_7410),U_7412))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7409),U_7412),U_7413))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7409),U_7410),U_7411))
      | ~ class_Divides_Osemiring__div(U_7409) ),
    inference(definitional_conversion,[status(esa)],[f_2158_2]) ).

cnf(f_2158_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7409),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7409),U_7411),U_7410)),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7409),U_7413),U_7412)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7409),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7409),U_7411),U_7413)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7409),U_7410),U_7412))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7409),U_7412),U_7413))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7409),U_7410),U_7411))
    | ~ class_Divides_Osemiring__div(U_7409) ),
    inference(clausify,[status(thm)],[f_2158_3]) ).

fof(f_2159_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_2159_2,plain,
    ! [U_7416,U_7415,U_7414] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7414),U_7416),hAPP(c_Groups_Ouminus__class_Ouminus(U_7414),U_7415)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7414),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7414),U_7416),U_7415))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7414),U_7415),U_7416))
      | ~ class_Divides_Oring__div(U_7414) ),
    inference(variable_rename,[status(thm)],[f_2159_1]) ).

fof(f_2159_3,plain,
    ! [U_7415,U_7414,U_7416] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7414),U_7416),hAPP(c_Groups_Ouminus__class_Ouminus(U_7414),U_7415)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7414),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7414),U_7416),U_7415))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7414),U_7415),U_7416))
      | ~ class_Divides_Oring__div(U_7414) ),
    inference(definitional_conversion,[status(esa)],[f_2159_2]) ).

cnf(f_2159_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7414),U_7416),hAPP(c_Groups_Ouminus__class_Ouminus(U_7414),U_7415)) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7414),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7414),U_7416),U_7415))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7414),U_7415),U_7416))
    | ~ class_Divides_Oring__div(U_7414) ),
    inference(clausify,[status(thm)],[f_2159_3]) ).

fof(f_2160_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_2160_2,plain,
    ! [U_7419,U_7418,U_7417] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7417),hAPP(c_Groups_Ouminus__class_Ouminus(U_7417),U_7419)),U_7418) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7417),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7417),U_7419),U_7418))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7417),U_7418),U_7419))
      | ~ class_Divides_Oring__div(U_7417) ),
    inference(variable_rename,[status(thm)],[f_2160_1]) ).

fof(f_2160_3,plain,
    ! [U_7417,U_7418,U_7419] :
      ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7417),hAPP(c_Groups_Ouminus__class_Ouminus(U_7417),U_7419)),U_7418) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7417),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7417),U_7419),U_7418))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7417),U_7418),U_7419))
      | ~ class_Divides_Oring__div(U_7417) ),
    inference(definitional_conversion,[status(esa)],[f_2160_2]) ).

cnf(f_2160_4,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7417),hAPP(c_Groups_Ouminus__class_Ouminus(U_7417),U_7419)),U_7418) = hAPP(c_Groups_Ouminus__class_Ouminus(U_7417),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7417),U_7419),U_7418))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7417),U_7418),U_7419))
    | ~ class_Divides_Oring__div(U_7417) ),
    inference(clausify,[status(thm)],[f_2160_3]) ).

fof(f_2161_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_2161_2,plain,
    ! [U_7423,U_7422,U_7421,U_7420] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7420),hAPP(hAPP(c_Power_Opower__class_Opower(U_7420),U_7423),U_7421)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7420),U_7423),U_7422)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7421),U_7422))
      | ~ class_Rings_Ocomm__semiring__1(U_7420) ),
    inference(variable_rename,[status(thm)],[f_2161_1]) ).

fof(f_2161_3,plain,
    ! [U_7420,U_7421,U_7422,U_7423] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7420),hAPP(hAPP(c_Power_Opower__class_Opower(U_7420),U_7423),U_7421)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7420),U_7423),U_7422)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7421),U_7422))
      | ~ class_Rings_Ocomm__semiring__1(U_7420) ),
    inference(definitional_conversion,[status(esa)],[f_2161_2]) ).

cnf(f_2161_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7420),hAPP(hAPP(c_Power_Opower__class_Opower(U_7420),U_7423),U_7421)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7420),U_7423),U_7422)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7421),U_7422))
    | ~ class_Rings_Ocomm__semiring__1(U_7420) ),
    inference(clausify,[status(thm)],[f_2161_3]) ).

fof(f_2162_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_2162_2,plain,
    ! [U_7428,U_7427,U_7426,U_7425,U_7424] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7424),hAPP(hAPP(c_Power_Opower__class_Opower(U_7424),U_7425),U_7427)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7424),U_7426),U_7428)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7427),U_7428))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7424),U_7425),U_7426))
      | ~ class_Rings_Ocomm__semiring__1(U_7424) ),
    inference(variable_rename,[status(thm)],[f_2162_1]) ).

fof(f_2162_3,plain,
    ! [U_7424,U_7425,U_7426,U_7427,U_7428] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7424),hAPP(hAPP(c_Power_Opower__class_Opower(U_7424),U_7425),U_7427)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7424),U_7426),U_7428)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7427),U_7428))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7424),U_7425),U_7426))
      | ~ class_Rings_Ocomm__semiring__1(U_7424) ),
    inference(definitional_conversion,[status(esa)],[f_2162_2]) ).

cnf(f_2162_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7424),hAPP(hAPP(c_Power_Opower__class_Opower(U_7424),U_7425),U_7427)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7424),U_7426),U_7428)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7427),U_7428))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7424),U_7425),U_7426))
    | ~ class_Rings_Ocomm__semiring__1(U_7424) ),
    inference(clausify,[status(thm)],[f_2162_3]) ).

fof(f_2163_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_2163_2,plain,
    ! [U_7433,U_7432,U_7431,U_7430,U_7429] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7429),hAPP(hAPP(c_Power_Opower__class_Opower(U_7429),U_7430),U_7433)),U_7432))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7433),U_7431))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7429),hAPP(hAPP(c_Power_Opower__class_Opower(U_7429),U_7430),U_7431)),U_7432))
      | ~ class_Rings_Ocomm__semiring__1(U_7429) ),
    inference(variable_rename,[status(thm)],[f_2163_1]) ).

fof(f_2163_3,plain,
    ! [U_7430,U_7429,U_7431,U_7432,U_7433] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7429),hAPP(hAPP(c_Power_Opower__class_Opower(U_7429),U_7430),U_7433)),U_7432))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7433),U_7431))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7429),hAPP(hAPP(c_Power_Opower__class_Opower(U_7429),U_7430),U_7431)),U_7432))
      | ~ class_Rings_Ocomm__semiring__1(U_7429) ),
    inference(definitional_conversion,[status(esa)],[f_2163_2]) ).

cnf(f_2163_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7429),hAPP(hAPP(c_Power_Opower__class_Opower(U_7429),U_7430),U_7433)),U_7432))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7433),U_7431))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7429),hAPP(hAPP(c_Power_Opower__class_Opower(U_7429),U_7430),U_7431)),U_7432))
    | ~ class_Rings_Ocomm__semiring__1(U_7429) ),
    inference(clausify,[status(thm)],[f_2163_3]) ).

fof(f_2164_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_2164_2,plain,
    ! [U_7437,U_7436,U_7435,U_7434] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7434),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7434),U_7436),U_7435)),U_7437) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7434),hAPP(hAPP(c_Power_Opower__class_Opower(U_7434),U_7436),U_7437)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7434),U_7435),U_7437))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7434),U_7435),U_7436))
      | ~ class_Divides_Osemiring__div(U_7434) ),
    inference(variable_rename,[status(thm)],[f_2164_1]) ).

fof(f_2164_3,plain,
    ! [U_7434,U_7435,U_7436,U_7437] :
      ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7434),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7434),U_7436),U_7435)),U_7437) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7434),hAPP(hAPP(c_Power_Opower__class_Opower(U_7434),U_7436),U_7437)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7434),U_7435),U_7437))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7434),U_7435),U_7436))
      | ~ class_Divides_Osemiring__div(U_7434) ),
    inference(definitional_conversion,[status(esa)],[f_2164_2]) ).

cnf(f_2164_4,plain,
    ( hAPP(hAPP(c_Power_Opower__class_Opower(U_7434),hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7434),U_7436),U_7435)),U_7437) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7434),hAPP(hAPP(c_Power_Opower__class_Opower(U_7434),U_7436),U_7437)),hAPP(hAPP(c_Power_Opower__class_Opower(U_7434),U_7435),U_7437))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7434),U_7435),U_7436))
    | ~ class_Divides_Osemiring__div(U_7434) ),
    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),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_2165_2,plain,
    ! [U_7438] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7438),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_7438 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
      & ( U_7438 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7438),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(variable_rename,[status(thm)],[f_2165_1]) ).

fof(f_2165_3,plain,
    ( ! [U_7440] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7440),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_7440 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_7439] :
        ( U_7439 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7439),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(miniscope,[status(thm)],[f_2165_2]) ).

fof(f_2165_4,plain,
    ( ! [U_7440] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7440),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
        | U_7440 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) )
    & ! [U_7439] :
        ( U_7439 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7439),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2165_3]) ).

cnf(f_2165_5,plain,
    ( U_7439 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7439),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(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_7440),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))))
    | U_7440 != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_2165_4]) ).

fof(f_2166_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_2166_2,plain,
    ! [U_7442,U_7441] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7442),U_7441))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7441),U_7442))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7441)) ),
    inference(variable_rename,[status(thm)],[f_2166_1]) ).

fof(f_2166_3,plain,
    ! [U_7441,U_7442] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7442),U_7441))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7441),U_7442))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7441)) ),
    inference(definitional_conversion,[status(esa)],[f_2166_2]) ).

cnf(f_2166_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7442),U_7441))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_7441),U_7442))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7441)) ),
    inference(clausify,[status(thm)],[f_2166_3]) ).

fof(f_2167_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_2167_2,plain,
    ! [U_7445,U_7444,U_7443] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7443),U_7444)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7443),U_7445)))
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7444),U_7445))
          & U_7443 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7444),U_7445))
        | U_7443 = 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_7443),U_7444)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7443),U_7445))) ) ),
    inference(variable_rename,[status(thm)],[f_2167_1]) ).

fof(f_2167_3,plain,
    ( ! [U_7451,U_7449,U_7447] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7447),U_7449)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7447),U_7451)))
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7449),U_7451))
          & U_7447 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_7450,U_7448,U_7446] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7448),U_7450))
        | U_7446 = 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_7446),U_7448)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7446),U_7450))) ) ),
    inference(miniscope,[status(thm)],[f_2167_2]) ).

fof(f_2167_4,plain,
    ( ! [U_7451,U_7449,U_7447] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7449),U_7451))
        | ~ sP656(U_7451,U_7449,U_7447) )
    & ! [U_7451,U_7449,U_7447] :
        ( U_7447 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP656(U_7451,U_7449,U_7447) )
    & ! [U_7451,U_7449,U_7447] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7447),U_7449)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7447),U_7451)))
        | sP656(U_7451,U_7449,U_7447) )
    & ! [U_7448,U_7446,U_7450] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7448),U_7450))
        | U_7446 = 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_7446),U_7448)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7446),U_7450))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP656])],[f_2167_3]) ).

cnf(f_2167_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7448),U_7450))
    | U_7446 = 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_7446),U_7448)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7446),U_7450))) ),
    inference(clausify,[status(thm)],[f_2167_4]) ).

cnf(f_2167_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7447),U_7449)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7447),U_7451)))
    | sP656(U_7451,U_7449,U_7447) ),
    inference(clausify,[status(thm)],[f_2167_4]) ).

cnf(f_2167_7,plain,
    ( U_7447 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP656(U_7451,U_7449,U_7447) ),
    inference(clausify,[status(thm)],[f_2167_4]) ).

cnf(f_2167_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7449),U_7451))
    | ~ sP656(U_7451,U_7449,U_7447) ),
    inference(clausify,[status(thm)],[f_2167_4]) ).

fof(f_2168_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_2168_2,plain,
    ! [U_7454,U_7453,U_7452] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7452),U_7453))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7454),U_7453))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7452),U_7454))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7452),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7453),U_7454))) ),
    inference(variable_rename,[status(thm)],[f_2168_1]) ).

fof(f_2168_3,plain,
    ! [U_7452,U_7453,U_7454] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7452),U_7453))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7454),U_7453))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7452),U_7454))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7452),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7453),U_7454))) ),
    inference(definitional_conversion,[status(esa)],[f_2168_2]) ).

cnf(f_2168_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7452),U_7453))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7454),U_7453))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7452),U_7454))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7452),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7453),U_7454))) ),
    inference(clausify,[status(thm)],[f_2168_3]) ).

fof(f_2169_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_2169_2,plain,
    ! [U_7457,U_7456,U_7455] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7455),U_7457))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7457),U_7456))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7455),U_7456))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7455),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7456),U_7457))) ),
    inference(variable_rename,[status(thm)],[f_2169_1]) ).

fof(f_2169_3,plain,
    ! [U_7455,U_7456,U_7457] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7455),U_7457))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7457),U_7456))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7455),U_7456))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7455),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7456),U_7457))) ),
    inference(definitional_conversion,[status(esa)],[f_2169_2]) ).

cnf(f_2169_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7455),U_7457))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7457),U_7456))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7455),U_7456))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7455),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_7456),U_7457))) ),
    inference(clausify,[status(thm)],[f_2169_3]) ).

fof(f_2170_1,plain,
    ! [V_l_2,V_Pa_2,T_b] :
      ( ( ( ? [B_x] : hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),V_l_2),B_x)))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_2170_2,plain,
    ! [U_7464,U_7463,U_7462] :
      ( ( ( ? [U_7461] : hBOOL(hAPP(U_7463,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),U_7464),U_7461)))
          | ! [U_7460] :
              ( ~ hBOOL(hAPP(U_7463,U_7460))
              | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7462),U_7464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7462),U_7460),c_Groups_Ozero__class_Ozero(U_7462)))) ) )
        & ( ? [U_7459] :
              ( hBOOL(hAPP(U_7463,U_7459))
              & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7462),U_7464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7462),U_7459),c_Groups_Ozero__class_Ozero(U_7462)))) )
          | ! [U_7458] : ~ hBOOL(hAPP(U_7463,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),U_7464),U_7458))) ) )
      | ~ class_Rings_Osemiring__0(U_7462)
      | ~ class_Rings_Odvd(U_7462) ),
    inference(variable_rename,[status(thm)],[f_2170_1]) ).

fof(f_2170_3,plain,
    ! [U_7464,U_7463,U_7462] :
      ( ( ( ? [U_7461] : hBOOL(hAPP(U_7463,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),U_7464),U_7461)))
          | ! [U_7460] :
              ( ~ hBOOL(hAPP(U_7463,U_7460))
              | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7462),U_7464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7462),U_7460),c_Groups_Ozero__class_Ozero(U_7462)))) ) )
        & ( ( hBOOL(hAPP(U_7463,sK104(U_7464,U_7463,U_7462)))
            & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7462),U_7464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7462),sK104(U_7464,U_7463,U_7462)),c_Groups_Ozero__class_Ozero(U_7462)))) )
          | ! [U_7458] : ~ hBOOL(hAPP(U_7463,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),U_7464),U_7458))) ) )
      | ~ class_Rings_Osemiring__0(U_7462)
      | ~ class_Rings_Odvd(U_7462) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK104]),skolemize(U_7459,sK104(U_7464,U_7463,U_7462))],[f_2170_2]) ).

fof(f_2170_4,plain,
    ! [U_7464,U_7463,U_7462] :
      ( ( ( hBOOL(hAPP(U_7463,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),U_7464),sK105(U_7464,U_7463,U_7462))))
          | ! [U_7460] :
              ( ~ hBOOL(hAPP(U_7463,U_7460))
              | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7462),U_7464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7462),U_7460),c_Groups_Ozero__class_Ozero(U_7462)))) ) )
        & ( ( hBOOL(hAPP(U_7463,sK104(U_7464,U_7463,U_7462)))
            & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7462),U_7464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7462),sK104(U_7464,U_7463,U_7462)),c_Groups_Ozero__class_Ozero(U_7462)))) )
          | ! [U_7458] : ~ hBOOL(hAPP(U_7463,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),U_7464),U_7458))) ) )
      | ~ class_Rings_Osemiring__0(U_7462)
      | ~ class_Rings_Odvd(U_7462) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK105]),skolemize(U_7461,sK105(U_7464,U_7463,U_7462))],[f_2170_3]) ).

fof(f_2170_5,plain,
    ( ! [U_7462,U_7463,U_7464] :
        ( hBOOL(hAPP(U_7463,sK104(U_7464,U_7463,U_7462)))
        | ~ sP657(U_7462,U_7463,U_7464) )
    & ! [U_7462,U_7463,U_7464] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7462),U_7464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7462),sK104(U_7464,U_7463,U_7462)),c_Groups_Ozero__class_Ozero(U_7462))))
        | ~ sP657(U_7462,U_7463,U_7464) )
    & ! [U_7460,U_7458,U_7462,U_7463,U_7464] :
        ( hBOOL(hAPP(U_7463,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),U_7464),sK105(U_7464,U_7463,U_7462))))
        | ~ hBOOL(hAPP(U_7463,U_7460))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7462),U_7464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7462),U_7460),c_Groups_Ozero__class_Ozero(U_7462))))
        | ~ sP658(U_7460,U_7458,U_7462,U_7463,U_7464) )
    & ! [U_7460,U_7458,U_7462,U_7463,U_7464] :
        ( sP657(U_7462,U_7463,U_7464)
        | ~ hBOOL(hAPP(U_7463,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),U_7464),U_7458)))
        | ~ sP658(U_7460,U_7458,U_7462,U_7463,U_7464) )
    & ! [U_7460,U_7458,U_7462,U_7463,U_7464] :
        ( sP658(U_7460,U_7458,U_7462,U_7463,U_7464)
        | ~ class_Rings_Osemiring__0(U_7462)
        | ~ class_Rings_Odvd(U_7462) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP657,sP658])],[f_2170_4]) ).

cnf(f_2170_6,plain,
    ( sP658(U_7460,U_7458,U_7462,U_7463,U_7464)
    | ~ class_Rings_Osemiring__0(U_7462)
    | ~ class_Rings_Odvd(U_7462) ),
    inference(clausify,[status(thm)],[f_2170_5]) ).

cnf(f_2170_7,plain,
    ( sP657(U_7462,U_7463,U_7464)
    | ~ hBOOL(hAPP(U_7463,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),U_7464),U_7458)))
    | ~ sP658(U_7460,U_7458,U_7462,U_7463,U_7464) ),
    inference(clausify,[status(thm)],[f_2170_5]) ).

cnf(f_2170_8,plain,
    ( hBOOL(hAPP(U_7463,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7462),U_7464),sK105(U_7464,U_7463,U_7462))))
    | ~ hBOOL(hAPP(U_7463,U_7460))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7462),U_7464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7462),U_7460),c_Groups_Ozero__class_Ozero(U_7462))))
    | ~ sP658(U_7460,U_7458,U_7462,U_7463,U_7464) ),
    inference(clausify,[status(thm)],[f_2170_5]) ).

cnf(f_2170_9,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7462),U_7464),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7462),sK104(U_7464,U_7463,U_7462)),c_Groups_Ozero__class_Ozero(U_7462))))
    | ~ sP657(U_7462,U_7463,U_7464) ),
    inference(clausify,[status(thm)],[f_2170_5]) ).

cnf(f_2170_10,plain,
    ( hBOOL(hAPP(U_7463,sK104(U_7464,U_7463,U_7462)))
    | ~ sP657(U_7462,U_7463,U_7464) ),
    inference(clausify,[status(thm)],[f_2170_5]) ).

fof(f_2171_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_2171_2,plain,
    ! [U_7470,U_7469,U_7468,U_7467] :
      ( ! [U_7466,U_7465] :
          ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7467),U_7468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7467),U_7466),U_7470)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7467),U_7468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7467),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7467),U_7466),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7467),U_7465),U_7469))),U_7470))) )
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7467),U_7468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7467),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7467),U_7466),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7467),U_7465),U_7469))),U_7470)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7467),U_7468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7467),U_7466),U_7470))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7467),U_7468),U_7469))
      | ~ class_Rings_Odvd(U_7467)
      | ~ class_Rings_Ocomm__ring(U_7467) ),
    inference(variable_rename,[status(thm)],[f_2171_1]) ).

fof(f_2171_3,plain,
    ! [U_7470,U_7469,U_7468,U_7467] :
      ( ( ! [U_7474] :
            ( ! [U_7472] : ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7467),U_7468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7467),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7467),U_7474),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7467),U_7472),U_7469))),U_7470)))
            | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7467),U_7468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7467),U_7474),U_7470))) )
        & ! [U_7473] :
            ( ! [U_7471] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7467),U_7468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7467),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7467),U_7473),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7467),U_7471),U_7469))),U_7470)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7467),U_7468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7467),U_7473),U_7470))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7467),U_7468),U_7469))
      | ~ class_Rings_Odvd(U_7467)
      | ~ class_Rings_Ocomm__ring(U_7467) ),
    inference(miniscope,[status(thm)],[f_2171_2]) ).

fof(f_2171_4,plain,
    ( ! [U_7469,U_7468,U_7470,U_7467,U_7473,U_7471,U_7472,U_7474] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7467),U_7468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7467),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7467),U_7474),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7467),U_7472),U_7469))),U_7470)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7467),U_7468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7467),U_7474),U_7470)))
        | ~ sP659(U_7469,U_7468,U_7470,U_7467,U_7473,U_7471,U_7472,U_7474) )
    & ! [U_7469,U_7468,U_7470,U_7467,U_7473,U_7471,U_7472,U_7474] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7467),U_7468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7467),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7467),U_7473),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7467),U_7471),U_7469))),U_7470)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7467),U_7468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7467),U_7473),U_7470)))
        | ~ sP659(U_7469,U_7468,U_7470,U_7467,U_7473,U_7471,U_7472,U_7474) )
    & ! [U_7469,U_7468,U_7470,U_7467,U_7473,U_7471,U_7472,U_7474] :
        ( sP659(U_7469,U_7468,U_7470,U_7467,U_7473,U_7471,U_7472,U_7474)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7467),U_7468),U_7469))
        | ~ class_Rings_Odvd(U_7467)
        | ~ class_Rings_Ocomm__ring(U_7467) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP659])],[f_2171_3]) ).

cnf(f_2171_5,plain,
    ( sP659(U_7469,U_7468,U_7470,U_7467,U_7473,U_7471,U_7472,U_7474)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7467),U_7468),U_7469))
    | ~ class_Rings_Odvd(U_7467)
    | ~ class_Rings_Ocomm__ring(U_7467) ),
    inference(clausify,[status(thm)],[f_2171_4]) ).

cnf(f_2171_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7467),U_7468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7467),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7467),U_7473),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7467),U_7471),U_7469))),U_7470)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7467),U_7468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7467),U_7473),U_7470)))
    | ~ sP659(U_7469,U_7468,U_7470,U_7467,U_7473,U_7471,U_7472,U_7474) ),
    inference(clausify,[status(thm)],[f_2171_4]) ).

cnf(f_2171_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7467),U_7468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7467),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7467),U_7474),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7467),U_7472),U_7469))),U_7470)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7467),U_7468),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7467),U_7474),U_7470)))
    | ~ sP659(U_7469,U_7468,U_7470,U_7467,U_7473,U_7471,U_7472,U_7474) ),
    inference(clausify,[status(thm)],[f_2171_4]) ).

fof(f_2172_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_2172_2,plain,
    ! [U_7480,U_7479,U_7478,U_7477] :
      ( ! [U_7476,U_7475] :
          ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7477),U_7478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7477),U_7476),U_7480)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7477),U_7478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7477),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7477),U_7476),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7477),U_7475),U_7479))),U_7480))) )
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7477),U_7478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7477),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7477),U_7476),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7477),U_7475),U_7479))),U_7480)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7477),U_7478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7477),U_7476),U_7480))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7477),U_7478),U_7479))
      | ~ class_Rings_Odvd(U_7477)
      | ~ class_Rings_Ocomm__ring(U_7477) ),
    inference(variable_rename,[status(thm)],[f_2172_1]) ).

fof(f_2172_3,plain,
    ! [U_7480,U_7479,U_7478,U_7477] :
      ( ( ! [U_7484] :
            ( ! [U_7482] : ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7477),U_7478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7477),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7477),U_7484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7477),U_7482),U_7479))),U_7480)))
            | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7477),U_7478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7477),U_7484),U_7480))) )
        & ! [U_7483] :
            ( ! [U_7481] : hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7477),U_7478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7477),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7477),U_7483),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7477),U_7481),U_7479))),U_7480)))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7477),U_7478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7477),U_7483),U_7480))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7477),U_7478),U_7479))
      | ~ class_Rings_Odvd(U_7477)
      | ~ class_Rings_Ocomm__ring(U_7477) ),
    inference(miniscope,[status(thm)],[f_2172_2]) ).

fof(f_2172_4,plain,
    ( ! [U_7483,U_7478,U_7479,U_7481,U_7480,U_7477,U_7482,U_7484] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7477),U_7478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7477),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7477),U_7484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7477),U_7482),U_7479))),U_7480)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7477),U_7478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7477),U_7484),U_7480)))
        | ~ sP660(U_7483,U_7478,U_7479,U_7481,U_7480,U_7477,U_7482,U_7484) )
    & ! [U_7483,U_7478,U_7479,U_7481,U_7480,U_7477,U_7482,U_7484] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7477),U_7478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7477),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7477),U_7483),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7477),U_7481),U_7479))),U_7480)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7477),U_7478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7477),U_7483),U_7480)))
        | ~ sP660(U_7483,U_7478,U_7479,U_7481,U_7480,U_7477,U_7482,U_7484) )
    & ! [U_7483,U_7478,U_7479,U_7481,U_7480,U_7477,U_7482,U_7484] :
        ( sP660(U_7483,U_7478,U_7479,U_7481,U_7480,U_7477,U_7482,U_7484)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7477),U_7478),U_7479))
        | ~ class_Rings_Odvd(U_7477)
        | ~ class_Rings_Ocomm__ring(U_7477) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP660])],[f_2172_3]) ).

cnf(f_2172_5,plain,
    ( sP660(U_7483,U_7478,U_7479,U_7481,U_7480,U_7477,U_7482,U_7484)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7477),U_7478),U_7479))
    | ~ class_Rings_Odvd(U_7477)
    | ~ class_Rings_Ocomm__ring(U_7477) ),
    inference(clausify,[status(thm)],[f_2172_4]) ).

cnf(f_2172_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7477),U_7478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7477),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7477),U_7483),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7477),U_7481),U_7479))),U_7480)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7477),U_7478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7477),U_7483),U_7480)))
    | ~ sP660(U_7483,U_7478,U_7479,U_7481,U_7480,U_7477,U_7482,U_7484) ),
    inference(clausify,[status(thm)],[f_2172_4]) ).

cnf(f_2172_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7477),U_7478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7477),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_7477),U_7484),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7477),U_7482),U_7479))),U_7480)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7477),U_7478),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_7477),U_7484),U_7480)))
    | ~ sP660(U_7483,U_7478,U_7479,U_7481,U_7480,U_7477,U_7482,U_7484) ),
    inference(clausify,[status(thm)],[f_2172_4]) ).

fof(f_2173_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_2173_2,plain,
    ! [U_7487,U_7486,U_7485] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7485),hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7486)),hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7487)))
          | c_Divides_Odiv__class_Omod(U_7485,hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7487),hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7486)) != c_Groups_Ozero__class_Ozero(U_7485) )
        & ( c_Divides_Odiv__class_Omod(U_7485,hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7487),hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7486)) = c_Groups_Ozero__class_Ozero(U_7485)
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7485),hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7486)),hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7487))) ) )
      | ~ class_Int_Onumber(U_7485)
      | ~ class_Divides_Osemiring__div(U_7485) ),
    inference(variable_rename,[status(thm)],[f_2173_1]) ).

fof(f_2173_3,plain,
    ( ! [U_7485,U_7486,U_7487] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7485),hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7486)),hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7487)))
        | c_Divides_Odiv__class_Omod(U_7485,hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7487),hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7486)) != c_Groups_Ozero__class_Ozero(U_7485)
        | ~ sP661(U_7485,U_7486,U_7487) )
    & ! [U_7485,U_7486,U_7487] :
        ( c_Divides_Odiv__class_Omod(U_7485,hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7487),hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7486)) = c_Groups_Ozero__class_Ozero(U_7485)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7485),hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7486)),hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7487)))
        | ~ sP661(U_7485,U_7486,U_7487) )
    & ! [U_7485,U_7486,U_7487] :
        ( sP661(U_7485,U_7486,U_7487)
        | ~ class_Int_Onumber(U_7485)
        | ~ class_Divides_Osemiring__div(U_7485) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP661])],[f_2173_2]) ).

cnf(f_2173_4,plain,
    ( sP661(U_7485,U_7486,U_7487)
    | ~ class_Int_Onumber(U_7485)
    | ~ class_Divides_Osemiring__div(U_7485) ),
    inference(clausify,[status(thm)],[f_2173_3]) ).

cnf(f_2173_5,plain,
    ( c_Divides_Odiv__class_Omod(U_7485,hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7487),hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7486)) = c_Groups_Ozero__class_Ozero(U_7485)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7485),hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7486)),hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7487)))
    | ~ sP661(U_7485,U_7486,U_7487) ),
    inference(clausify,[status(thm)],[f_2173_3]) ).

cnf(f_2173_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7485),hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7486)),hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7487)))
    | c_Divides_Odiv__class_Omod(U_7485,hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7487),hAPP(c_Int_Onumber__class_Onumber__of(U_7485),U_7486)) != c_Groups_Ozero__class_Ozero(U_7485)
    | ~ sP661(U_7485,U_7486,U_7487) ),
    inference(clausify,[status(thm)],[f_2173_3]) ).

fof(f_2174_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_2174_2,plain,
    ! [U_7492,U_7491,U_7490,U_7489,U_7488] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7488),U_7491),U_7489) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7488),U_7492),U_7490)
          | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7488),U_7491),U_7490) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7488),U_7489),U_7492) )
        & ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7488),U_7491),U_7490) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7488),U_7489),U_7492)
          | hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7488),U_7491),U_7489) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7488),U_7492),U_7490) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7488),U_7490),U_7492))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7488),U_7489),U_7491))
      | U_7490 = c_Groups_Ozero__class_Ozero(U_7488)
      | U_7489 = c_Groups_Ozero__class_Ozero(U_7488)
      | ~ class_Divides_Osemiring__div(U_7488) ),
    inference(variable_rename,[status(thm)],[f_2174_1]) ).

fof(f_2174_3,plain,
    ( ! [U_7490,U_7488,U_7489,U_7491,U_7492] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7488),U_7491),U_7489) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7488),U_7492),U_7490)
        | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7488),U_7491),U_7490) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7488),U_7489),U_7492)
        | ~ sP662(U_7490,U_7488,U_7489,U_7491,U_7492) )
    & ! [U_7490,U_7488,U_7489,U_7491,U_7492] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7488),U_7491),U_7490) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7488),U_7489),U_7492)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7488),U_7491),U_7489) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7488),U_7492),U_7490)
        | ~ sP662(U_7490,U_7488,U_7489,U_7491,U_7492) )
    & ! [U_7490,U_7488,U_7489,U_7491,U_7492] :
        ( sP662(U_7490,U_7488,U_7489,U_7491,U_7492)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7488),U_7490),U_7492))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7488),U_7489),U_7491))
        | U_7490 = c_Groups_Ozero__class_Ozero(U_7488)
        | U_7489 = c_Groups_Ozero__class_Ozero(U_7488)
        | ~ class_Divides_Osemiring__div(U_7488) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP662])],[f_2174_2]) ).

cnf(f_2174_4,plain,
    ( sP662(U_7490,U_7488,U_7489,U_7491,U_7492)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7488),U_7490),U_7492))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7488),U_7489),U_7491))
    | U_7490 = c_Groups_Ozero__class_Ozero(U_7488)
    | U_7489 = c_Groups_Ozero__class_Ozero(U_7488)
    | ~ class_Divides_Osemiring__div(U_7488) ),
    inference(clausify,[status(thm)],[f_2174_3]) ).

cnf(f_2174_5,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7488),U_7491),U_7490) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7488),U_7489),U_7492)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7488),U_7491),U_7489) != hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7488),U_7492),U_7490)
    | ~ sP662(U_7490,U_7488,U_7489,U_7491,U_7492) ),
    inference(clausify,[status(thm)],[f_2174_3]) ).

cnf(f_2174_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7488),U_7491),U_7489) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7488),U_7492),U_7490)
    | hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7488),U_7491),U_7490) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7488),U_7489),U_7492)
    | ~ sP662(U_7490,U_7488,U_7489,U_7491,U_7492) ),
    inference(clausify,[status(thm)],[f_2174_3]) ).

fof(f_2175_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_2175_2,plain,
    ! [U_7496,U_7495,U_7494,U_7493] :
      ( ( ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7493),U_7495),U_7494) = U_7496
          | U_7495 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7493),U_7496),U_7494) )
        & ( U_7495 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7493),U_7496),U_7494)
          | hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7493),U_7495),U_7494) != U_7496 ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7493),U_7494),U_7495))
      | U_7494 = c_Groups_Ozero__class_Ozero(U_7493)
      | ~ class_Divides_Osemiring__div(U_7493) ),
    inference(variable_rename,[status(thm)],[f_2175_1]) ).

fof(f_2175_3,plain,
    ( ! [U_7495,U_7494,U_7496,U_7493] :
        ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7493),U_7495),U_7494) = U_7496
        | U_7495 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7493),U_7496),U_7494)
        | ~ sP663(U_7495,U_7494,U_7496,U_7493) )
    & ! [U_7495,U_7494,U_7496,U_7493] :
        ( U_7495 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7493),U_7496),U_7494)
        | hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7493),U_7495),U_7494) != U_7496
        | ~ sP663(U_7495,U_7494,U_7496,U_7493) )
    & ! [U_7495,U_7494,U_7496,U_7493] :
        ( sP663(U_7495,U_7494,U_7496,U_7493)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7493),U_7494),U_7495))
        | U_7494 = c_Groups_Ozero__class_Ozero(U_7493)
        | ~ class_Divides_Osemiring__div(U_7493) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP663])],[f_2175_2]) ).

cnf(f_2175_4,plain,
    ( sP663(U_7495,U_7494,U_7496,U_7493)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7493),U_7494),U_7495))
    | U_7494 = c_Groups_Ozero__class_Ozero(U_7493)
    | ~ class_Divides_Osemiring__div(U_7493) ),
    inference(clausify,[status(thm)],[f_2175_3]) ).

cnf(f_2175_5,plain,
    ( U_7495 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7493),U_7496),U_7494)
    | hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7493),U_7495),U_7494) != U_7496
    | ~ sP663(U_7495,U_7494,U_7496,U_7493) ),
    inference(clausify,[status(thm)],[f_2175_3]) ).

cnf(f_2175_6,plain,
    ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(U_7493),U_7495),U_7494) = U_7496
    | U_7495 != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_7493),U_7496),U_7494)
    | ~ sP663(U_7495,U_7494,U_7496,U_7493) ),
    inference(clausify,[status(thm)],[f_2175_3]) ).

fof(f_2176_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_2176_2,plain,
    ! [U_7498,U_7497] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7497),U_7498))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7498))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7497),U_7498)) ),
    inference(variable_rename,[status(thm)],[f_2176_1]) ).

fof(f_2176_3,plain,
    ! [U_7498,U_7497] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7497),U_7498))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7498))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7497),U_7498)) ),
    inference(definitional_conversion,[status(esa)],[f_2176_2]) ).

cnf(f_2176_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_7497),U_7498))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7498))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7497),U_7498)) ),
    inference(clausify,[status(thm)],[f_2176_3]) ).

fof(f_2177_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_2177_2,plain,
    ! [U_7501,U_7500,U_7499] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7499),U_7500)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7499),U_7501)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7500),U_7501)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7500),U_7501))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7499),U_7500)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7499),U_7501))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7499)) ),
    inference(variable_rename,[status(thm)],[f_2177_1]) ).

fof(f_2177_3,plain,
    ( ! [U_7500,U_7501,U_7499] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7499),U_7500)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7499),U_7501)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7500),U_7501))
        | ~ sP664(U_7500,U_7501,U_7499) )
    & ! [U_7500,U_7501,U_7499] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7500),U_7501))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7499),U_7500)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7499),U_7501)))
        | ~ sP664(U_7500,U_7501,U_7499) )
    & ! [U_7500,U_7501,U_7499] :
        ( sP664(U_7500,U_7501,U_7499)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7499)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP664])],[f_2177_2]) ).

cnf(f_2177_4,plain,
    ( sP664(U_7500,U_7501,U_7499)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7499)) ),
    inference(clausify,[status(thm)],[f_2177_3]) ).

cnf(f_2177_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7500),U_7501))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7499),U_7500)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7499),U_7501)))
    | ~ sP664(U_7500,U_7501,U_7499) ),
    inference(clausify,[status(thm)],[f_2177_3]) ).

cnf(f_2177_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7499),U_7500)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7499),U_7501)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7500),U_7501))
    | ~ sP664(U_7500,U_7501,U_7499) ),
    inference(clausify,[status(thm)],[f_2177_3]) ).

fof(f_2178_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_2178_2,plain,
    ! [U_7504,U_7503,U_7502] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7503),U_7504))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7502))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7502),U_7503)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7502),U_7504))) ),
    inference(variable_rename,[status(thm)],[f_2178_1]) ).

fof(f_2178_3,plain,
    ! [U_7502,U_7503,U_7504] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7503),U_7504))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7502))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7502),U_7503)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7502),U_7504))) ),
    inference(definitional_conversion,[status(esa)],[f_2178_2]) ).

cnf(f_2178_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7503),U_7504))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7502))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7502),U_7503)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7502),U_7504))) ),
    inference(clausify,[status(thm)],[f_2178_3]) ).

fof(f_2179_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_2179_2,plain,
    ! [U_7507,U_7506,U_7505] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7505),U_7507),hAPP(hAPP(c_Power_Opower__class_Opower(U_7505),U_7507),U_7506)))
      | ( U_7507 != c_Groups_Oone__class_Oone(U_7505)
        & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7506)) )
      | ~ class_Rings_Ocomm__semiring__1(U_7505) ),
    inference(variable_rename,[status(thm)],[f_2179_1]) ).

fof(f_2179_3,plain,
    ( ! [U_7505,U_7506,U_7507] :
        ( U_7507 != c_Groups_Oone__class_Oone(U_7505)
        | ~ sP665(U_7505,U_7506,U_7507) )
    & ! [U_7505,U_7506,U_7507] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7506))
        | ~ sP665(U_7505,U_7506,U_7507) )
    & ! [U_7505,U_7506,U_7507] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7505),U_7507),hAPP(hAPP(c_Power_Opower__class_Opower(U_7505),U_7507),U_7506)))
        | sP665(U_7505,U_7506,U_7507)
        | ~ class_Rings_Ocomm__semiring__1(U_7505) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP665])],[f_2179_2]) ).

cnf(f_2179_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_7505),U_7507),hAPP(hAPP(c_Power_Opower__class_Opower(U_7505),U_7507),U_7506)))
    | sP665(U_7505,U_7506,U_7507)
    | ~ class_Rings_Ocomm__semiring__1(U_7505) ),
    inference(clausify,[status(thm)],[f_2179_3]) ).

cnf(f_2179_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7506))
    | ~ sP665(U_7505,U_7506,U_7507) ),
    inference(clausify,[status(thm)],[f_2179_3]) ).

cnf(f_2179_6,plain,
    ( U_7507 != c_Groups_Oone__class_Oone(U_7505)
    | ~ sP665(U_7505,U_7506,U_7507) ),
    inference(clausify,[status(thm)],[f_2179_3]) ).

fof(f_2180_1,plain,
    ! [V_n_2,V_m_2] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_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_2180_2,plain,
    ! [U_7509,U_7508] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7509),U_7508)),U_7508))
          | U_7509 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        & ( U_7509 = 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_7509),U_7508)),U_7508)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7508)) ),
    inference(variable_rename,[status(thm)],[f_2180_1]) ).

fof(f_2180_3,plain,
    ( ! [U_7508,U_7509] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7509),U_7508)),U_7508))
        | U_7509 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP666(U_7508,U_7509) )
    & ! [U_7508,U_7509] :
        ( U_7509 = 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_7509),U_7508)),U_7508))
        | ~ sP666(U_7508,U_7509) )
    & ! [U_7508,U_7509] :
        ( sP666(U_7508,U_7509)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7508)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP666])],[f_2180_2]) ).

cnf(f_2180_4,plain,
    ( sP666(U_7508,U_7509)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7508)) ),
    inference(clausify,[status(thm)],[f_2180_3]) ).

cnf(f_2180_5,plain,
    ( U_7509 = 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_7509),U_7508)),U_7508))
    | ~ sP666(U_7508,U_7509) ),
    inference(clausify,[status(thm)],[f_2180_3]) ).

cnf(f_2180_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7509),U_7508)),U_7508))
    | U_7509 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP666(U_7508,U_7509) ),
    inference(clausify,[status(thm)],[f_2180_3]) ).

fof(f_2181_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_2181_2,plain,
    ! [U_7511,U_7510] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7510),U_7511)),U_7510))
          | U_7511 != c_Groups_Oone__class_Oone(tc_Nat_Onat) )
        & ( U_7511 = 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_7510),U_7511)),U_7510)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7510)) ),
    inference(variable_rename,[status(thm)],[f_2181_1]) ).

fof(f_2181_3,plain,
    ( ! [U_7511,U_7510] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7510),U_7511)),U_7510))
        | U_7511 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP667(U_7511,U_7510) )
    & ! [U_7511,U_7510] :
        ( U_7511 = 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_7510),U_7511)),U_7510))
        | ~ sP667(U_7511,U_7510) )
    & ! [U_7511,U_7510] :
        ( sP667(U_7511,U_7510)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7510)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP667])],[f_2181_2]) ).

cnf(f_2181_4,plain,
    ( sP667(U_7511,U_7510)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_7510)) ),
    inference(clausify,[status(thm)],[f_2181_3]) ).

cnf(f_2181_5,plain,
    ( U_7511 = 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_7510),U_7511)),U_7510))
    | ~ sP667(U_7511,U_7510) ),
    inference(clausify,[status(thm)],[f_2181_3]) ).

cnf(f_2181_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_7510),U_7511)),U_7510))
    | U_7511 != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP667(U_7511,U_7510) ),
    inference(clausify,[status(thm)],[f_2181_3]) ).

fof(f_2182_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_2182_2,plain,
    ! [U_7515,U_7514] :
      ( ( c_Relation_Oirrefl(U_7514,U_7515)
        | ? [U_7513] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_7514,U_7514)),hAPP(hAPP(c_Product__Type_OPair(U_7514,U_7514),U_7513),U_7513)),U_7515)) )
      & ( ! [U_7512] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7514,U_7514)),hAPP(hAPP(c_Product__Type_OPair(U_7514,U_7514),U_7512),U_7512)),U_7515))
        | ~ c_Relation_Oirrefl(U_7514,U_7515) ) ),
    inference(variable_rename,[status(thm)],[f_2182_1]) ).

fof(f_2182_3,plain,
    ( ! [U_7519,U_7517] :
        ( c_Relation_Oirrefl(U_7517,U_7519)
        | ? [U_7513] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_7517,U_7517)),hAPP(hAPP(c_Product__Type_OPair(U_7517,U_7517),U_7513),U_7513)),U_7519)) )
    & ! [U_7518,U_7516] :
        ( ! [U_7512] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7516,U_7516)),hAPP(hAPP(c_Product__Type_OPair(U_7516,U_7516),U_7512),U_7512)),U_7518))
        | ~ c_Relation_Oirrefl(U_7516,U_7518) ) ),
    inference(miniscope,[status(thm)],[f_2182_2]) ).

fof(f_2182_4,plain,
    ( ! [U_7519,U_7517] :
        ( c_Relation_Oirrefl(U_7517,U_7519)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_7517,U_7517)),hAPP(hAPP(c_Product__Type_OPair(U_7517,U_7517),sK106(U_7519,U_7517)),sK106(U_7519,U_7517))),U_7519)) )
    & ! [U_7518,U_7516] :
        ( ! [U_7512] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7516,U_7516)),hAPP(hAPP(c_Product__Type_OPair(U_7516,U_7516),U_7512),U_7512)),U_7518))
        | ~ c_Relation_Oirrefl(U_7516,U_7518) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK106]),skolemize(U_7513,sK106(U_7519,U_7517))],[f_2182_3]) ).

fof(f_2182_5,plain,
    ( ! [U_7519,U_7517] :
        ( c_Relation_Oirrefl(U_7517,U_7519)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_7517,U_7517)),hAPP(hAPP(c_Product__Type_OPair(U_7517,U_7517),sK106(U_7519,U_7517)),sK106(U_7519,U_7517))),U_7519)) )
    & ! [U_7512,U_7518,U_7516] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7516,U_7516)),hAPP(hAPP(c_Product__Type_OPair(U_7516,U_7516),U_7512),U_7512)),U_7518))
        | ~ c_Relation_Oirrefl(U_7516,U_7518) ) ),
    inference(definitional_conversion,[status(esa)],[f_2182_4]) ).

cnf(f_2182_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7516,U_7516)),hAPP(hAPP(c_Product__Type_OPair(U_7516,U_7516),U_7512),U_7512)),U_7518))
    | ~ c_Relation_Oirrefl(U_7516,U_7518) ),
    inference(clausify,[status(thm)],[f_2182_5]) ).

cnf(f_2182_7,plain,
    ( c_Relation_Oirrefl(U_7517,U_7519)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_7517,U_7517)),hAPP(hAPP(c_Product__Type_OPair(U_7517,U_7517),sK106(U_7519,U_7517)),sK106(U_7519,U_7517))),U_7519)) ),
    inference(clausify,[status(thm)],[f_2182_5]) ).

fof(f_2183_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_2183_2,plain,
    ! [U_7523,U_7522,U_7521,U_7520] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7520),hAPP(U_7521,U_7522)),hAPP(U_7521,U_7523)))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7523),U_7522))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7522),U_7523))
      | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7520,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_7521)
      | ~ class_Orderings_Oorder(U_7520) ),
    inference(variable_rename,[status(thm)],[f_2183_1]) ).

fof(f_2183_3,plain,
    ! [U_7521,U_7520,U_7522,U_7523] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7520),hAPP(U_7521,U_7522)),hAPP(U_7521,U_7523)))
      | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7523),U_7522))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7522),U_7523))
      | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7520,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_7521)
      | ~ class_Orderings_Oorder(U_7520) ),
    inference(definitional_conversion,[status(esa)],[f_2183_2]) ).

cnf(f_2183_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7520),hAPP(U_7521,U_7522)),hAPP(U_7521,U_7523)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7523),U_7522))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7522),U_7523))
    | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7520,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_7521)
    | ~ class_Orderings_Oorder(U_7520) ),
    inference(clausify,[status(thm)],[f_2183_3]) ).

fof(f_2184_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_2184_2,plain,
    ! [U_7527,U_7526,U_7525,U_7524] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7524),hAPP(U_7525,U_7526)),hAPP(U_7525,U_7527)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7526),U_7527))
      | ~ c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7524,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7525)
      | ~ class_Orderings_Oorder(U_7524) ),
    inference(variable_rename,[status(thm)],[f_2184_1]) ).

fof(f_2184_3,plain,
    ! [U_7525,U_7524,U_7526,U_7527] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7524),hAPP(U_7525,U_7526)),hAPP(U_7525,U_7527)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7526),U_7527))
      | ~ c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7524,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7525)
      | ~ class_Orderings_Oorder(U_7524) ),
    inference(definitional_conversion,[status(esa)],[f_2184_2]) ).

cnf(f_2184_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7524),hAPP(U_7525,U_7526)),hAPP(U_7525,U_7527)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7526),U_7527))
    | ~ c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7524,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7525)
    | ~ class_Orderings_Oorder(U_7524) ),
    inference(clausify,[status(thm)],[f_2184_3]) ).

fof(f_2185_1,plain,
    ! [V_f_2,T_c,V_Pa_2,T_b] :
      ( c_FunDef_Oreduction__pair(T_c,hAPP(hAPP(c_FunDef_Orp__inv__image(T_b,T_c),V_Pa_2),V_f_2))
      | ~ c_FunDef_Oreduction__pair(T_b,V_Pa_2) ),
    inference(fof_nnf,[status(thm)],[fact_rp__inv__image__rp]) ).

fof(f_2185_2,plain,
    ! [U_7531,U_7530,U_7529,U_7528] :
      ( c_FunDef_Oreduction__pair(U_7530,hAPP(hAPP(c_FunDef_Orp__inv__image(U_7528,U_7530),U_7529),U_7531))
      | ~ c_FunDef_Oreduction__pair(U_7528,U_7529) ),
    inference(variable_rename,[status(thm)],[f_2185_1]) ).

fof(f_2185_3,plain,
    ! [U_7528,U_7529,U_7531,U_7530] :
      ( c_FunDef_Oreduction__pair(U_7530,hAPP(hAPP(c_FunDef_Orp__inv__image(U_7528,U_7530),U_7529),U_7531))
      | ~ c_FunDef_Oreduction__pair(U_7528,U_7529) ),
    inference(definitional_conversion,[status(esa)],[f_2185_2]) ).

cnf(f_2185_4,plain,
    ( c_FunDef_Oreduction__pair(U_7530,hAPP(hAPP(c_FunDef_Orp__inv__image(U_7528,U_7530),U_7529),U_7531))
    | ~ c_FunDef_Oreduction__pair(U_7528,U_7529) ),
    inference(clausify,[status(thm)],[f_2185_3]) ).

fof(f_2186_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_2186_2,plain,
    ! [U_7533,U_7532] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7532)),U_7533))
        | ( U_7533 != 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_7532)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7532),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7533)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7532)) ) )
      & ( ( ( U_7533 = 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_7532)) )
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7532),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7533)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7532)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7532)),U_7533)) ) ),
    inference(variable_rename,[status(thm)],[f_2186_1]) ).

fof(f_2186_3,plain,
    ( ! [U_7537,U_7535] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7535)),U_7537))
        | ( U_7537 != 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_7535)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7535),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7537)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7535)) ) )
    & ! [U_7536,U_7534] :
        ( ( ( U_7536 = 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_7534)) )
          & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7534),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7536)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7534)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7534)),U_7536)) ) ),
    inference(miniscope,[status(thm)],[f_2186_2]) ).

fof(f_2186_4,plain,
    ( ! [U_7535,U_7537] :
        ( U_7537 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP670(U_7535,U_7537) )
    & ! [U_7535,U_7537] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7535))
        | ~ sP670(U_7535,U_7537) )
    & ! [U_7535,U_7537] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7535),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7537)))
        | ~ sP669(U_7535,U_7537) )
    & ! [U_7535,U_7537] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7535))
        | ~ sP669(U_7535,U_7537) )
    & ! [U_7534,U_7536] :
        ( U_7536 = 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_7534))
        | ~ sP668(U_7534,U_7536) )
    & ! [U_7534,U_7536] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7534),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7536)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7534))
        | ~ sP668(U_7534,U_7536) )
    & ! [U_7535,U_7537] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7535)),U_7537))
        | sP670(U_7535,U_7537)
        | sP669(U_7535,U_7537) )
    & ! [U_7534,U_7536] :
        ( sP668(U_7534,U_7536)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7534)),U_7536)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP668,sP669,sP670])],[f_2186_3]) ).

cnf(f_2186_5,plain,
    ( sP668(U_7534,U_7536)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7534)),U_7536)) ),
    inference(clausify,[status(thm)],[f_2186_4]) ).

cnf(f_2186_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7535)),U_7537))
    | sP670(U_7535,U_7537)
    | sP669(U_7535,U_7537) ),
    inference(clausify,[status(thm)],[f_2186_4]) ).

cnf(f_2186_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7534),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7536)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7534))
    | ~ sP668(U_7534,U_7536) ),
    inference(clausify,[status(thm)],[f_2186_4]) ).

cnf(f_2186_8,plain,
    ( U_7536 = 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_7534))
    | ~ sP668(U_7534,U_7536) ),
    inference(clausify,[status(thm)],[f_2186_4]) ).

cnf(f_2186_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7535))
    | ~ sP669(U_7535,U_7537) ),
    inference(clausify,[status(thm)],[f_2186_4]) ).

cnf(f_2186_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7535),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7537)))
    | ~ sP669(U_7535,U_7537) ),
    inference(clausify,[status(thm)],[f_2186_4]) ).

cnf(f_2186_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7535))
    | ~ sP670(U_7535,U_7537) ),
    inference(clausify,[status(thm)],[f_2186_4]) ).

cnf(f_2186_12,plain,
    ( U_7537 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP670(U_7535,U_7537) ),
    inference(clausify,[status(thm)],[f_2186_4]) ).

fof(f_2187_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_2187_2,plain,
    ! [U_7540,U_7539,U_7538] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7538),U_7539))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7538),U_7540))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7538),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7539),U_7540))) ),
    inference(variable_rename,[status(thm)],[f_2187_1]) ).

fof(f_2187_3,plain,
    ! [U_7540,U_7538,U_7539] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7538),U_7539))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7538),U_7540))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7538),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7539),U_7540))) ),
    inference(definitional_conversion,[status(esa)],[f_2187_2]) ).

cnf(f_2187_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7538),U_7539))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7538),U_7540))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7538),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7539),U_7540))) ),
    inference(clausify,[status(thm)],[f_2187_3]) ).

fof(f_2188_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_2188_2,plain,
    ! [U_7542,U_7541] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7541),U_7542))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7541)),U_7542)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7541)),U_7542))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7541),U_7542)) ) ),
    inference(variable_rename,[status(thm)],[f_2188_1]) ).

fof(f_2188_3,plain,
    ( ! [U_7546,U_7544] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7544),U_7546))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7544)),U_7546)) )
    & ! [U_7545,U_7543] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7543)),U_7545))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7543),U_7545)) ) ),
    inference(miniscope,[status(thm)],[f_2188_2]) ).

fof(f_2188_4,plain,
    ( ! [U_7546,U_7544] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7544),U_7546))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7544)),U_7546)) )
    & ! [U_7545,U_7543] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7543)),U_7545))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7543),U_7545)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2188_3]) ).

cnf(f_2188_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7543)),U_7545))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7543),U_7545)) ),
    inference(clausify,[status(thm)],[f_2188_4]) ).

cnf(f_2188_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7544),U_7546))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7544)),U_7546)) ),
    inference(clausify,[status(thm)],[f_2188_4]) ).

fof(f_2189_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_2189_2,plain,
    ! [U_7548,U_7547] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7547),U_7548))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7547),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7548))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7547),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7548)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7547),U_7548)) ) ),
    inference(variable_rename,[status(thm)],[f_2189_1]) ).

fof(f_2189_3,plain,
    ( ! [U_7552,U_7550] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7550),U_7552))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7550),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7552))) )
    & ! [U_7551,U_7549] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7549),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7551)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7549),U_7551)) ) ),
    inference(miniscope,[status(thm)],[f_2189_2]) ).

fof(f_2189_4,plain,
    ( ! [U_7550,U_7552] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7550),U_7552))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7550),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7552))) )
    & ! [U_7549,U_7551] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7549),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7551)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7549),U_7551)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2189_3]) ).

cnf(f_2189_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7549),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7551)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7549),U_7551)) ),
    inference(clausify,[status(thm)],[f_2189_4]) ).

cnf(f_2189_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7550),U_7552))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7550),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_7552))) ),
    inference(clausify,[status(thm)],[f_2189_4]) ).

fof(f_2190_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_2190_2,plain,
    ! [U_7555,U_7554,U_7553] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7553),U_7554))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7553),U_7555))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7553),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7554,U_7555))) ),
    inference(variable_rename,[status(thm)],[f_2190_1]) ).

fof(f_2190_3,plain,
    ! [U_7554,U_7553,U_7555] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7553),U_7554))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7553),U_7555))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7553),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7554,U_7555))) ),
    inference(definitional_conversion,[status(esa)],[f_2190_2]) ).

cnf(f_2190_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7553),U_7554))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7553),U_7555))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7553),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7554,U_7555))) ),
    inference(clausify,[status(thm)],[f_2190_3]) ).

fof(f_2191_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_2191_2,plain,
    ! [U_7558,U_7557,U_7556] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7556),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7557,U_7558)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7556),U_7558))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7556),U_7557)) ),
    inference(variable_rename,[status(thm)],[f_2191_1]) ).

fof(f_2191_3,plain,
    ! [U_7556,U_7557,U_7558] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7556),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7557,U_7558)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7556),U_7558))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7556),U_7557)) ),
    inference(definitional_conversion,[status(esa)],[f_2191_2]) ).

cnf(f_2191_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7556),c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7557,U_7558)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7556),U_7558))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7556),U_7557)) ),
    inference(clausify,[status(thm)],[f_2191_3]) ).

fof(f_2192_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_2192_2,plain,
    ! [U_7560,U_7559] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7559) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7560)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7560),U_7559))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7559),U_7560)) ),
    inference(variable_rename,[status(thm)],[f_2192_1]) ).

fof(f_2192_3,plain,
    ! [U_7560,U_7559] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7559) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7560)
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7560),U_7559))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7559),U_7560)) ),
    inference(definitional_conversion,[status(esa)],[f_2192_2]) ).

cnf(f_2192_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7559) = hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7560)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7560),U_7559))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7559),U_7560)) ),
    inference(clausify,[status(thm)],[f_2192_3]) ).

fof(f_2193_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_2193_2,plain,
    ! [U_7562,U_7561] :
      ( U_7561 = U_7562
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7562),U_7561))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7561),U_7562))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7562))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7561)) ),
    inference(variable_rename,[status(thm)],[f_2193_1]) ).

fof(f_2193_3,plain,
    ! [U_7561,U_7562] :
      ( U_7561 = U_7562
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7562),U_7561))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7561),U_7562))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7562))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7561)) ),
    inference(definitional_conversion,[status(esa)],[f_2193_2]) ).

cnf(f_2193_4,plain,
    ( U_7561 = U_7562
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7562),U_7561))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7561),U_7562))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7562))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7561)) ),
    inference(clausify,[status(thm)],[f_2193_3]) ).

fof(f_2194_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_2194_2,plain,
    ! [U_7564,U_7563] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7564),U_7563))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7563),U_7564))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7563)) ),
    inference(variable_rename,[status(thm)],[f_2194_1]) ).

fof(f_2194_3,plain,
    ! [U_7564,U_7563] :
      ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7564),U_7563))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7563),U_7564))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7563)) ),
    inference(definitional_conversion,[status(esa)],[f_2194_2]) ).

cnf(f_2194_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7564),U_7563))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_7563),U_7564))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7563)) ),
    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_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_2195_2,plain,
    ! [U_7567,U_7566,U_7565] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7566),U_7567))
      | U_7565 = 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_7565),U_7566)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7565),U_7567))) ),
    inference(variable_rename,[status(thm)],[f_2195_1]) ).

fof(f_2195_3,plain,
    ! [U_7565,U_7566,U_7567] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7566),U_7567))
      | U_7565 = 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_7565),U_7566)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7565),U_7567))) ),
    inference(definitional_conversion,[status(esa)],[f_2195_2]) ).

cnf(f_2195_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7566),U_7567))
    | U_7565 = 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_7565),U_7566)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7565),U_7567))) ),
    inference(clausify,[status(thm)],[f_2195_3]) ).

fof(f_2196_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_2196_2,plain,
    ! [U_7570,U_7569,U_7568] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7569),U_7570))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7568),U_7569)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7568),U_7570))) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7568),U_7569)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7568),U_7570)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7569),U_7570)) ) )
      | U_7568 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2196_1]) ).

fof(f_2196_3,plain,
    ( ! [U_7569,U_7570,U_7568] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7569),U_7570))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7568),U_7569)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7568),U_7570)))
        | ~ sP671(U_7569,U_7570,U_7568) )
    & ! [U_7569,U_7570,U_7568] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7568),U_7569)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7568),U_7570)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7569),U_7570))
        | ~ sP671(U_7569,U_7570,U_7568) )
    & ! [U_7569,U_7570,U_7568] :
        ( sP671(U_7569,U_7570,U_7568)
        | U_7568 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP671])],[f_2196_2]) ).

cnf(f_2196_4,plain,
    ( sP671(U_7569,U_7570,U_7568)
    | U_7568 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2196_3]) ).

cnf(f_2196_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7568),U_7569)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7568),U_7570)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7569),U_7570))
    | ~ sP671(U_7569,U_7570,U_7568) ),
    inference(clausify,[status(thm)],[f_2196_3]) ).

cnf(f_2196_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7569),U_7570))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7568),U_7569)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7568),U_7570)))
    | ~ sP671(U_7569,U_7570,U_7568) ),
    inference(clausify,[status(thm)],[f_2196_3]) ).

fof(f_2197_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_2197_2,plain,
    ! [U_7573,U_7572,U_7571] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7571),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7572),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7571),U_7573))))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7571),U_7572)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7571),U_7572))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7571),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7572),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7571),U_7573)))) ) ),
    inference(variable_rename,[status(thm)],[f_2197_1]) ).

fof(f_2197_3,plain,
    ( ! [U_7579,U_7577,U_7575] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7575),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7575),U_7579))))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7575),U_7577)) )
    & ! [U_7578,U_7576,U_7574] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7574),U_7576))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7574),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7576),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7574),U_7578)))) ) ),
    inference(miniscope,[status(thm)],[f_2197_2]) ).

fof(f_2197_4,plain,
    ( ! [U_7575,U_7577,U_7579] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7575),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7575),U_7579))))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7575),U_7577)) )
    & ! [U_7574,U_7576,U_7578] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7574),U_7576))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7574),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7576),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7574),U_7578)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2197_3]) ).

cnf(f_2197_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7574),U_7576))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7574),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7576),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7574),U_7578)))) ),
    inference(clausify,[status(thm)],[f_2197_4]) ).

cnf(f_2197_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7575),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7577),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7575),U_7579))))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7575),U_7577)) ),
    inference(clausify,[status(thm)],[f_2197_4]) ).

fof(f_2198_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_2198_2,plain,
    ! [U_7584,U_7583,U_7582,U_7581,U_7580] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7582),U_7583)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7582),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7584),U_7581))),U_7583))) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7582),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7584),U_7581))),U_7583)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7582),U_7583))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7580),U_7581)) ),
    inference(variable_rename,[status(thm)],[f_2198_1]) ).

fof(f_2198_3,plain,
    ( ! [U_7580,U_7581,U_7582,U_7583,U_7584] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7582),U_7583)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7582),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7584),U_7581))),U_7583)))
        | ~ sP672(U_7580,U_7581,U_7582,U_7583,U_7584) )
    & ! [U_7580,U_7581,U_7582,U_7583,U_7584] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7582),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7584),U_7581))),U_7583)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7582),U_7583)))
        | ~ sP672(U_7580,U_7581,U_7582,U_7583,U_7584) )
    & ! [U_7580,U_7581,U_7582,U_7583,U_7584] :
        ( sP672(U_7580,U_7581,U_7582,U_7583,U_7584)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7580),U_7581)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP672])],[f_2198_2]) ).

cnf(f_2198_4,plain,
    ( sP672(U_7580,U_7581,U_7582,U_7583,U_7584)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7580),U_7581)) ),
    inference(clausify,[status(thm)],[f_2198_3]) ).

cnf(f_2198_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7582),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7584),U_7581))),U_7583)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7582),U_7583)))
    | ~ sP672(U_7580,U_7581,U_7582,U_7583,U_7584) ),
    inference(clausify,[status(thm)],[f_2198_3]) ).

cnf(f_2198_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7582),U_7583)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7580),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_7582),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7584),U_7581))),U_7583)))
    | ~ sP672(U_7580,U_7581,U_7582,U_7583,U_7584) ),
    inference(clausify,[status(thm)],[f_2198_3]) ).

fof(f_2199_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_2199_2,plain,
    ! [U_7586,U_7585] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7585)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7586)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7585),U_7586)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7585),U_7586))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7585)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7586))) ) ),
    inference(variable_rename,[status(thm)],[f_2199_1]) ).

fof(f_2199_3,plain,
    ( ! [U_7590,U_7588] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7588)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7590)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7588),U_7590)) )
    & ! [U_7589,U_7587] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7587),U_7589))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7587)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7589))) ) ),
    inference(miniscope,[status(thm)],[f_2199_2]) ).

fof(f_2199_4,plain,
    ( ! [U_7588,U_7590] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7588)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7590)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7588),U_7590)) )
    & ! [U_7587,U_7589] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7587),U_7589))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7587)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7589))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2199_3]) ).

cnf(f_2199_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7587),U_7589))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7587)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7589))) ),
    inference(clausify,[status(thm)],[f_2199_4]) ).

cnf(f_2199_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_7588)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7590)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7588),U_7590)) ),
    inference(clausify,[status(thm)],[f_2199_4]) ).

fof(f_2200_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_2200_2,plain,
    ! [U_7592,U_7591] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7591),U_7592))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7591)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7592))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7591)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7592)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7591),U_7592)) ) ),
    inference(variable_rename,[status(thm)],[f_2200_1]) ).

fof(f_2200_3,plain,
    ( ! [U_7596,U_7594] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7594),U_7596))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7594)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7596))) )
    & ! [U_7595,U_7593] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7593)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7595)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7593),U_7595)) ) ),
    inference(miniscope,[status(thm)],[f_2200_2]) ).

fof(f_2200_4,plain,
    ( ! [U_7594,U_7596] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7594),U_7596))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7594)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7596))) )
    & ! [U_7593,U_7595] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7593)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7595)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7593),U_7595)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2200_3]) ).

cnf(f_2200_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_7593)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7595)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7593),U_7595)) ),
    inference(clausify,[status(thm)],[f_2200_4]) ).

cnf(f_2200_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7594),U_7596))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7594)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7596))) ),
    inference(clausify,[status(thm)],[f_2200_4]) ).

fof(f_2201_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_2201_2,plain,
    ! [U_7598,U_7597] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7597),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7598),U_7597)) = U_7598
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7597),U_7598)) ),
    inference(variable_rename,[status(thm)],[f_2201_1]) ).

fof(f_2201_3,plain,
    ! [U_7598,U_7597] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7597),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7598),U_7597)) = U_7598
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7597),U_7598)) ),
    inference(definitional_conversion,[status(esa)],[f_2201_2]) ).

cnf(f_2201_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7597),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7598),U_7597)) = U_7598
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7597),U_7598)) ),
    inference(clausify,[status(thm)],[f_2201_3]) ).

fof(f_2202_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_2202_2,plain,
    ! [U_7601,U_7600,U_7599] :
      ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7599,U_7600) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7601,U_7600)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7600),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7599),U_7601))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7600),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7599),U_7601)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7599,U_7600) != c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7601,U_7600) ) ),
    inference(variable_rename,[status(thm)],[f_2202_1]) ).

fof(f_2202_3,plain,
    ( ! [U_7607,U_7605,U_7603] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7603,U_7605) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7607,U_7605)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7605),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7603),U_7607))) )
    & ! [U_7606,U_7604,U_7602] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7604),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7602),U_7606)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7602,U_7604) != c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7606,U_7604) ) ),
    inference(miniscope,[status(thm)],[f_2202_2]) ).

fof(f_2202_4,plain,
    ( ! [U_7603,U_7605,U_7607] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7603,U_7605) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7607,U_7605)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7605),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7603),U_7607))) )
    & ! [U_7602,U_7604,U_7606] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7604),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7602),U_7606)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7602,U_7604) != c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7606,U_7604) ) ),
    inference(definitional_conversion,[status(esa)],[f_2202_3]) ).

cnf(f_2202_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7604),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7602),U_7606)))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7602,U_7604) != c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7606,U_7604) ),
    inference(clausify,[status(thm)],[f_2202_4]) ).

cnf(f_2202_6,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7603,U_7605) = c_Divides_Odiv__class_Omod(tc_Int_Oint,U_7607,U_7605)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7605),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_7603),U_7607))) ),
    inference(clausify,[status(thm)],[f_2202_4]) ).

fof(f_2203_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_2203_2,plain,
    ! [U_7608] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7608),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7608) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
      & ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7608) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7608),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(variable_rename,[status(thm)],[f_2203_1]) ).

fof(f_2203_3,plain,
    ( ! [U_7610] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7610),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7610) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
    & ! [U_7609] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7609) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7609),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(miniscope,[status(thm)],[f_2203_2]) ).

fof(f_2203_4,plain,
    ( ! [U_7610] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7610),c_Groups_Oone__class_Oone(tc_Int_Oint)))
        | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7610) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
    & ! [U_7609] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7609) = c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7609),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2203_3]) ).

cnf(f_2203_5,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7609) = c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7609),c_Groups_Oone__class_Oone(tc_Int_Oint))) ),
    inference(clausify,[status(thm)],[f_2203_4]) ).

cnf(f_2203_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7610),c_Groups_Oone__class_Oone(tc_Int_Oint)))
    | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7610) != c_Groups_Oone__class_Oone(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2203_4]) ).

fof(f_2204_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_2204_2,plain,
    ! [U_7612,U_7611] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7612),U_7611)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7612)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7611))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7611),U_7612)) ),
    inference(variable_rename,[status(thm)],[f_2204_1]) ).

fof(f_2204_3,plain,
    ! [U_7612,U_7611] :
      ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7612),U_7611)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7612)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7611))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7611),U_7612)) ),
    inference(definitional_conversion,[status(esa)],[f_2204_2]) ).

cnf(f_2204_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),U_7612),U_7611)) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7612)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7611))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7611),U_7612)) ),
    inference(clausify,[status(thm)],[f_2204_3]) ).

fof(f_2205_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_2205_2,plain,
    ! [U_7614,U_7613] :
      ( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7613,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7614)
      | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7613,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_7614)
      | ~ class_Orderings_Oorder(U_7613) ),
    inference(variable_rename,[status(thm)],[f_2205_1]) ).

fof(f_2205_3,plain,
    ! [U_7614,U_7613] :
      ( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7613,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7614)
      | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7613,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_7614)
      | ~ class_Orderings_Oorder(U_7613) ),
    inference(definitional_conversion,[status(esa)],[f_2205_2]) ).

cnf(f_2205_4,plain,
    ( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7613,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7614)
    | ~ c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7613,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_7614)
    | ~ class_Orderings_Oorder(U_7613) ),
    inference(clausify,[status(thm)],[f_2205_3]) ).

fof(f_2206_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_2206_2,plain,
    ! [U_7616,U_7615] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7615),U_7616))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7616))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7615),U_7616)) ),
    inference(variable_rename,[status(thm)],[f_2206_1]) ).

fof(f_2206_3,plain,
    ! [U_7615,U_7616] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7615),U_7616))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7616))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7615),U_7616)) ),
    inference(definitional_conversion,[status(esa)],[f_2206_2]) ).

cnf(f_2206_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_7615),U_7616))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7616))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7615),U_7616)) ),
    inference(clausify,[status(thm)],[f_2206_3]) ).

fof(f_2207_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_2207_2,plain,
    ! [U_7618,U_7617] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7617)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7618)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7618),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7617)) != 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_7618),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7617)) = 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_7617)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7618))) ) ),
    inference(variable_rename,[status(thm)],[f_2207_1]) ).

fof(f_2207_3,plain,
    ( ! [U_7622,U_7620] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7620)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7622)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7622),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7620)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_7621,U_7619] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7621),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7619)) = 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_7619)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7621))) ) ),
    inference(miniscope,[status(thm)],[f_2207_2]) ).

fof(f_2207_4,plain,
    ( ! [U_7620,U_7622] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7620)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7622)))
        | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7622),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7620)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) )
    & ! [U_7621,U_7619] :
        ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7621),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7619)) = 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_7619)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7621))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2207_3]) ).

cnf(f_2207_5,plain,
    ( c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7621),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7619)) = 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_7619)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7621))) ),
    inference(clausify,[status(thm)],[f_2207_4]) ).

cnf(f_2207_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7620)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7622)))
    | c_Divides_Odiv__class_Omod(tc_Int_Oint,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7622),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_7620)) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2207_4]) ).

fof(f_2208_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_2208_2,plain,
    ! [U_7624,U_7623] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7624)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7623)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7624),U_7623))
      | U_7623 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2208_1]) ).

fof(f_2208_3,plain,
    ! [U_7623,U_7624] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7624)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7623)))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7624),U_7623))
      | U_7623 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(definitional_conversion,[status(esa)],[f_2208_2]) ).

cnf(f_2208_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7624)),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7623)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7624),U_7623))
    | U_7623 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2208_3]) ).

fof(f_2209_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_2209_2,plain,
    ! [U_7626,U_7625] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7625)),hAPP(c_Int_Onat,U_7626)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7625),U_7626)) )
        & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7625),U_7626))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7625)),hAPP(c_Int_Onat,U_7626))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7626))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7625)) ),
    inference(variable_rename,[status(thm)],[f_2209_1]) ).

fof(f_2209_3,plain,
    ( ! [U_7625,U_7626] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7625)),hAPP(c_Int_Onat,U_7626)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7625),U_7626))
        | ~ sP673(U_7625,U_7626) )
    & ! [U_7625,U_7626] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7625),U_7626))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7625)),hAPP(c_Int_Onat,U_7626)))
        | ~ sP673(U_7625,U_7626) )
    & ! [U_7625,U_7626] :
        ( sP673(U_7625,U_7626)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7626))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7625)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP673])],[f_2209_2]) ).

cnf(f_2209_4,plain,
    ( sP673(U_7625,U_7626)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7626))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7625)) ),
    inference(clausify,[status(thm)],[f_2209_3]) ).

cnf(f_2209_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7625),U_7626))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7625)),hAPP(c_Int_Onat,U_7626)))
    | ~ sP673(U_7625,U_7626) ),
    inference(clausify,[status(thm)],[f_2209_3]) ).

cnf(f_2209_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),hAPP(c_Int_Onat,U_7625)),hAPP(c_Int_Onat,U_7626)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7625),U_7626))
    | ~ sP673(U_7625,U_7626) ),
    inference(clausify,[status(thm)],[f_2209_3]) ).

fof(f_2210_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_2210_2,plain,
    ! [U_7628,U_7627] :
      ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7627),U_7628)),U_7627))
          | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7628) != c_Groups_Oone__class_Oone(tc_Int_Oint) )
        & ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7628) = 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_7627),U_7628)),U_7627)) ) )
      | U_7627 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(variable_rename,[status(thm)],[f_2210_1]) ).

fof(f_2210_3,plain,
    ( ! [U_7627,U_7628] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7627),U_7628)),U_7627))
        | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7628) != c_Groups_Oone__class_Oone(tc_Int_Oint)
        | ~ sP674(U_7627,U_7628) )
    & ! [U_7627,U_7628] :
        ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7628) = 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_7627),U_7628)),U_7627))
        | ~ sP674(U_7627,U_7628) )
    & ! [U_7627,U_7628] :
        ( sP674(U_7627,U_7628)
        | U_7627 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP674])],[f_2210_2]) ).

cnf(f_2210_4,plain,
    ( sP674(U_7627,U_7628)
    | U_7627 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ),
    inference(clausify,[status(thm)],[f_2210_3]) ).

cnf(f_2210_5,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7628) = 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_7627),U_7628)),U_7627))
    | ~ sP674(U_7627,U_7628) ),
    inference(clausify,[status(thm)],[f_2210_3]) ).

cnf(f_2210_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_7627),U_7628)),U_7627))
    | hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7628) != c_Groups_Oone__class_Oone(tc_Int_Oint)
    | ~ sP674(U_7627,U_7628) ),
    inference(clausify,[status(thm)],[f_2210_3]) ).

fof(f_2211_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_2211_2,plain,
    ! [U_7630,U_7629] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7629)),U_7630))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7629),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7630)))) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7629),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7630))))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7629)),U_7630)) ) ),
    inference(variable_rename,[status(thm)],[f_2211_1]) ).

fof(f_2211_3,plain,
    ( ! [U_7634,U_7632] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7632)),U_7634))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7632),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7634)))) )
    & ! [U_7633,U_7631] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7631),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7633))))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7631)),U_7633)) ) ),
    inference(miniscope,[status(thm)],[f_2211_2]) ).

fof(f_2211_4,plain,
    ( ! [U_7632,U_7634] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7632)),U_7634))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7632),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7634)))) )
    & ! [U_7631,U_7633] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7631),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7633))))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7631)),U_7633)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2211_3]) ).

cnf(f_2211_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7631),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7633))))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7631)),U_7633)) ),
    inference(clausify,[status(thm)],[f_2211_4]) ).

cnf(f_2211_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_7632)),U_7634))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7632),hAPP(c_Int_Onat,hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),U_7634)))) ),
    inference(clausify,[status(thm)],[f_2211_4]) ).

fof(f_2212_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_2212_2,plain,
    ! [U_7636,U_7635] :
      ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7635),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7636)))
        | ~ 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_7635))),U_7636)) )
      & ( 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_7635))),U_7636))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7635),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7636))) ) ),
    inference(variable_rename,[status(thm)],[f_2212_1]) ).

fof(f_2212_3,plain,
    ( ! [U_7640,U_7638] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7638),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7640)))
        | ~ 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_7638))),U_7640)) )
    & ! [U_7639,U_7637] :
        ( 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_7637))),U_7639))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7637),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7639))) ) ),
    inference(miniscope,[status(thm)],[f_2212_2]) ).

fof(f_2212_4,plain,
    ( ! [U_7638,U_7640] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7638),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7640)))
        | ~ 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_7638))),U_7640)) )
    & ! [U_7639,U_7637] :
        ( 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_7637))),U_7639))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7637),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7639))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2212_3]) ).

cnf(f_2212_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_7637))),U_7639))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7637),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7639))) ),
    inference(clausify,[status(thm)],[f_2212_4]) ).

cnf(f_2212_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_7638),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_7640)))
    | ~ 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_7638))),U_7640)) ),
    inference(clausify,[status(thm)],[f_2212_4]) ).

fof(f_2213_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_2213_2,plain,
    ! [U_7644,U_7643] :
      ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7643,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_7644)
      | ? [U_7642,U_7641] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7643),hAPP(U_7644,U_7642)),hAPP(U_7644,U_7641)))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7641),U_7642))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7642),U_7641)) )
      | ~ class_Orderings_Oorder(U_7643) ),
    inference(variable_rename,[status(thm)],[f_2213_1]) ).

fof(f_2213_3,plain,
    ! [U_7644,U_7643] :
      ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7643,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_7644)
      | ? [U_7641] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7643),hAPP(U_7644,sK107(U_7644,U_7643))),hAPP(U_7644,U_7641)))
          & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7641),sK107(U_7644,U_7643)))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK107(U_7644,U_7643)),U_7641)) )
      | ~ class_Orderings_Oorder(U_7643) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK107]),skolemize(U_7642,sK107(U_7644,U_7643))],[f_2213_2]) ).

fof(f_2213_4,plain,
    ! [U_7644,U_7643] :
      ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7643,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_7644)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7643),hAPP(U_7644,sK107(U_7644,U_7643))),hAPP(U_7644,sK108(U_7644,U_7643))))
        & ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK108(U_7644,U_7643)),sK107(U_7644,U_7643)))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK107(U_7644,U_7643)),sK108(U_7644,U_7643))) )
      | ~ class_Orderings_Oorder(U_7643) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK108]),skolemize(U_7641,sK108(U_7644,U_7643))],[f_2213_3]) ).

fof(f_2213_5,plain,
    ( ! [U_7643,U_7644] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7643),hAPP(U_7644,sK107(U_7644,U_7643))),hAPP(U_7644,sK108(U_7644,U_7643))))
        | ~ sP675(U_7643,U_7644) )
    & ! [U_7643,U_7644] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK108(U_7644,U_7643)),sK107(U_7644,U_7643)))
        | ~ sP675(U_7643,U_7644) )
    & ! [U_7643,U_7644] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK107(U_7644,U_7643)),sK108(U_7644,U_7643)))
        | ~ sP675(U_7643,U_7644) )
    & ! [U_7643,U_7644] :
        ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7643,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_7644)
        | sP675(U_7643,U_7644)
        | ~ class_Orderings_Oorder(U_7643) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP675])],[f_2213_4]) ).

cnf(f_2213_6,plain,
    ( c_Orderings_Oorder_Ostrict__mono(tc_Nat_Onat,U_7643,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_7644)
    | sP675(U_7643,U_7644)
    | ~ class_Orderings_Oorder(U_7643) ),
    inference(clausify,[status(thm)],[f_2213_5]) ).

cnf(f_2213_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK107(U_7644,U_7643)),sK108(U_7644,U_7643)))
    | ~ sP675(U_7643,U_7644) ),
    inference(clausify,[status(thm)],[f_2213_5]) ).

cnf(f_2213_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK108(U_7644,U_7643)),sK107(U_7644,U_7643)))
    | ~ sP675(U_7643,U_7644) ),
    inference(clausify,[status(thm)],[f_2213_5]) ).

cnf(f_2213_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_7643),hAPP(U_7644,sK107(U_7644,U_7643))),hAPP(U_7644,sK108(U_7644,U_7643))))
    | ~ sP675(U_7643,U_7644) ),
    inference(clausify,[status(thm)],[f_2213_5]) ).

fof(f_2214_1,plain,
    ! [V_f_2,T_b] :
      ( c_Orderings_Oorder_Omono(tc_Nat_Onat,T_b,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),V_f_2)
      | ? [B_x,B_y] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_f_2,B_y)))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),B_x),B_y)) )
      | ~ class_Orderings_Oorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_dvd_OmonoI]) ).

fof(f_2214_2,plain,
    ! [U_7648,U_7647] :
      ( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7647,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7648)
      | ? [U_7646,U_7645] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7647),hAPP(U_7648,U_7646)),hAPP(U_7648,U_7645)))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7646),U_7645)) )
      | ~ class_Orderings_Oorder(U_7647) ),
    inference(variable_rename,[status(thm)],[f_2214_1]) ).

fof(f_2214_3,plain,
    ! [U_7648,U_7647] :
      ( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7647,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7648)
      | ? [U_7645] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7647),hAPP(U_7648,sK109(U_7648,U_7647))),hAPP(U_7648,U_7645)))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK109(U_7648,U_7647)),U_7645)) )
      | ~ class_Orderings_Oorder(U_7647) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK109]),skolemize(U_7646,sK109(U_7648,U_7647))],[f_2214_2]) ).

fof(f_2214_4,plain,
    ! [U_7648,U_7647] :
      ( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7647,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7648)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7647),hAPP(U_7648,sK109(U_7648,U_7647))),hAPP(U_7648,sK110(U_7648,U_7647))))
        & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK109(U_7648,U_7647)),sK110(U_7648,U_7647))) )
      | ~ class_Orderings_Oorder(U_7647) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK110]),skolemize(U_7645,sK110(U_7648,U_7647))],[f_2214_3]) ).

fof(f_2214_5,plain,
    ( ! [U_7648,U_7647] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7647),hAPP(U_7648,sK109(U_7648,U_7647))),hAPP(U_7648,sK110(U_7648,U_7647))))
        | ~ sP676(U_7648,U_7647) )
    & ! [U_7648,U_7647] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK109(U_7648,U_7647)),sK110(U_7648,U_7647)))
        | ~ sP676(U_7648,U_7647) )
    & ! [U_7648,U_7647] :
        ( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7647,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7648)
        | sP676(U_7648,U_7647)
        | ~ class_Orderings_Oorder(U_7647) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP676])],[f_2214_4]) ).

cnf(f_2214_6,plain,
    ( c_Orderings_Oorder_Omono(tc_Nat_Onat,U_7647,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7648)
    | sP676(U_7648,U_7647)
    | ~ class_Orderings_Oorder(U_7647) ),
    inference(clausify,[status(thm)],[f_2214_5]) ).

cnf(f_2214_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),sK109(U_7648,U_7647)),sK110(U_7648,U_7647)))
    | ~ sP676(U_7648,U_7647) ),
    inference(clausify,[status(thm)],[f_2214_5]) ).

cnf(f_2214_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_7647),hAPP(U_7648,sK109(U_7648,U_7647))),hAPP(U_7648,sK110(U_7648,U_7647))))
    | ~ sP676(U_7648,U_7647) ),
    inference(clausify,[status(thm)],[f_2214_5]) ).

fof(f_2215_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_2215_2,plain,
    ! [U_7655,U_7654,U_7653] :
      ( ( c_Relation_Ototal__on(U_7653,U_7654,U_7655)
        | ? [U_7652] :
            ( ? [U_7651] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7653,U_7653)),hAPP(hAPP(c_Product__Type_OPair(U_7653,U_7653),U_7651),U_7652)),U_7655))
                & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7653,U_7653)),hAPP(hAPP(c_Product__Type_OPair(U_7653,U_7653),U_7652),U_7651)),U_7655))
                & U_7652 != U_7651
                & hBOOL(hAPP(hAPP(c_member(U_7653),U_7651),U_7654)) )
            & hBOOL(hAPP(hAPP(c_member(U_7653),U_7652),U_7654)) ) )
      & ( ! [U_7650] :
            ( ! [U_7649] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7653,U_7653)),hAPP(hAPP(c_Product__Type_OPair(U_7653,U_7653),U_7649),U_7650)),U_7655))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_7653,U_7653)),hAPP(hAPP(c_Product__Type_OPair(U_7653,U_7653),U_7650),U_7649)),U_7655))
                | U_7650 = U_7649
                | ~ hBOOL(hAPP(hAPP(c_member(U_7653),U_7649),U_7654)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_7653),U_7650),U_7654)) )
        | ~ c_Relation_Ototal__on(U_7653,U_7654,U_7655) ) ),
    inference(variable_rename,[status(thm)],[f_2215_1]) ).

fof(f_2215_3,plain,
    ( ! [U_7661,U_7659,U_7657] :
        ( c_Relation_Ototal__on(U_7657,U_7659,U_7661)
        | ? [U_7652] :
            ( ? [U_7651] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7657,U_7657)),hAPP(hAPP(c_Product__Type_OPair(U_7657,U_7657),U_7651),U_7652)),U_7661))
                & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7657,U_7657)),hAPP(hAPP(c_Product__Type_OPair(U_7657,U_7657),U_7652),U_7651)),U_7661))
                & U_7652 != U_7651
                & hBOOL(hAPP(hAPP(c_member(U_7657),U_7651),U_7659)) )
            & hBOOL(hAPP(hAPP(c_member(U_7657),U_7652),U_7659)) ) )
    & ! [U_7660,U_7658,U_7656] :
        ( ! [U_7650] :
            ( ! [U_7649] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7656,U_7656)),hAPP(hAPP(c_Product__Type_OPair(U_7656,U_7656),U_7649),U_7650)),U_7660))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_7656,U_7656)),hAPP(hAPP(c_Product__Type_OPair(U_7656,U_7656),U_7650),U_7649)),U_7660))
                | U_7650 = U_7649
                | ~ hBOOL(hAPP(hAPP(c_member(U_7656),U_7649),U_7658)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_7656),U_7650),U_7658)) )
        | ~ c_Relation_Ototal__on(U_7656,U_7658,U_7660) ) ),
    inference(miniscope,[status(thm)],[f_2215_2]) ).

fof(f_2215_4,plain,
    ( ! [U_7661,U_7659,U_7657] :
        ( c_Relation_Ototal__on(U_7657,U_7659,U_7661)
        | ( ? [U_7651] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7657,U_7657)),hAPP(hAPP(c_Product__Type_OPair(U_7657,U_7657),U_7651),sK111(U_7661,U_7659,U_7657))),U_7661))
              & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7657,U_7657)),hAPP(hAPP(c_Product__Type_OPair(U_7657,U_7657),sK111(U_7661,U_7659,U_7657)),U_7651)),U_7661))
              & sK111(U_7661,U_7659,U_7657) != U_7651
              & hBOOL(hAPP(hAPP(c_member(U_7657),U_7651),U_7659)) )
          & hBOOL(hAPP(hAPP(c_member(U_7657),sK111(U_7661,U_7659,U_7657)),U_7659)) ) )
    & ! [U_7660,U_7658,U_7656] :
        ( ! [U_7650] :
            ( ! [U_7649] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7656,U_7656)),hAPP(hAPP(c_Product__Type_OPair(U_7656,U_7656),U_7649),U_7650)),U_7660))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_7656,U_7656)),hAPP(hAPP(c_Product__Type_OPair(U_7656,U_7656),U_7650),U_7649)),U_7660))
                | U_7650 = U_7649
                | ~ hBOOL(hAPP(hAPP(c_member(U_7656),U_7649),U_7658)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_7656),U_7650),U_7658)) )
        | ~ c_Relation_Ototal__on(U_7656,U_7658,U_7660) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK111]),skolemize(U_7652,sK111(U_7661,U_7659,U_7657))],[f_2215_3]) ).

fof(f_2215_5,plain,
    ( ! [U_7661,U_7659,U_7657] :
        ( c_Relation_Ototal__on(U_7657,U_7659,U_7661)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7657,U_7657)),hAPP(hAPP(c_Product__Type_OPair(U_7657,U_7657),sK112(U_7661,U_7659,U_7657)),sK111(U_7661,U_7659,U_7657))),U_7661))
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7657,U_7657)),hAPP(hAPP(c_Product__Type_OPair(U_7657,U_7657),sK111(U_7661,U_7659,U_7657)),sK112(U_7661,U_7659,U_7657))),U_7661))
          & sK111(U_7661,U_7659,U_7657) != sK112(U_7661,U_7659,U_7657)
          & hBOOL(hAPP(hAPP(c_member(U_7657),sK112(U_7661,U_7659,U_7657)),U_7659))
          & hBOOL(hAPP(hAPP(c_member(U_7657),sK111(U_7661,U_7659,U_7657)),U_7659)) ) )
    & ! [U_7660,U_7658,U_7656] :
        ( ! [U_7650] :
            ( ! [U_7649] :
                ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7656,U_7656)),hAPP(hAPP(c_Product__Type_OPair(U_7656,U_7656),U_7649),U_7650)),U_7660))
                | hBOOL(hAPP(hAPP(c_member(tc_prod(U_7656,U_7656)),hAPP(hAPP(c_Product__Type_OPair(U_7656,U_7656),U_7650),U_7649)),U_7660))
                | U_7650 = U_7649
                | ~ hBOOL(hAPP(hAPP(c_member(U_7656),U_7649),U_7658)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_7656),U_7650),U_7658)) )
        | ~ c_Relation_Ototal__on(U_7656,U_7658,U_7660) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK112]),skolemize(U_7651,sK112(U_7661,U_7659,U_7657))],[f_2215_4]) ).

fof(f_2215_6,plain,
    ( ! [U_7659,U_7657,U_7661] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7657,U_7657)),hAPP(hAPP(c_Product__Type_OPair(U_7657,U_7657),sK112(U_7661,U_7659,U_7657)),sK111(U_7661,U_7659,U_7657))),U_7661))
        | ~ sP677(U_7659,U_7657,U_7661) )
    & ! [U_7659,U_7657,U_7661] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7657,U_7657)),hAPP(hAPP(c_Product__Type_OPair(U_7657,U_7657),sK111(U_7661,U_7659,U_7657)),sK112(U_7661,U_7659,U_7657))),U_7661))
        | ~ sP677(U_7659,U_7657,U_7661) )
    & ! [U_7659,U_7657,U_7661] :
        ( sK111(U_7661,U_7659,U_7657) != sK112(U_7661,U_7659,U_7657)
        | ~ sP677(U_7659,U_7657,U_7661) )
    & ! [U_7659,U_7657,U_7661] :
        ( hBOOL(hAPP(hAPP(c_member(U_7657),sK112(U_7661,U_7659,U_7657)),U_7659))
        | ~ sP677(U_7659,U_7657,U_7661) )
    & ! [U_7659,U_7657,U_7661] :
        ( hBOOL(hAPP(hAPP(c_member(U_7657),sK111(U_7661,U_7659,U_7657)),U_7659))
        | ~ sP677(U_7659,U_7657,U_7661) )
    & ! [U_7659,U_7657,U_7661] :
        ( c_Relation_Ototal__on(U_7657,U_7659,U_7661)
        | sP677(U_7659,U_7657,U_7661) )
    & ! [U_7649,U_7650,U_7656,U_7660,U_7658] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7656,U_7656)),hAPP(hAPP(c_Product__Type_OPair(U_7656,U_7656),U_7649),U_7650)),U_7660))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_7656,U_7656)),hAPP(hAPP(c_Product__Type_OPair(U_7656,U_7656),U_7650),U_7649)),U_7660))
        | U_7650 = U_7649
        | ~ hBOOL(hAPP(hAPP(c_member(U_7656),U_7649),U_7658))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7656),U_7650),U_7658))
        | ~ c_Relation_Ototal__on(U_7656,U_7658,U_7660) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP677])],[f_2215_5]) ).

cnf(f_2215_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7656,U_7656)),hAPP(hAPP(c_Product__Type_OPair(U_7656,U_7656),U_7649),U_7650)),U_7660))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_7656,U_7656)),hAPP(hAPP(c_Product__Type_OPair(U_7656,U_7656),U_7650),U_7649)),U_7660))
    | U_7650 = U_7649
    | ~ hBOOL(hAPP(hAPP(c_member(U_7656),U_7649),U_7658))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7656),U_7650),U_7658))
    | ~ c_Relation_Ototal__on(U_7656,U_7658,U_7660) ),
    inference(clausify,[status(thm)],[f_2215_6]) ).

cnf(f_2215_8,plain,
    ( c_Relation_Ototal__on(U_7657,U_7659,U_7661)
    | sP677(U_7659,U_7657,U_7661) ),
    inference(clausify,[status(thm)],[f_2215_6]) ).

cnf(f_2215_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7657),sK111(U_7661,U_7659,U_7657)),U_7659))
    | ~ sP677(U_7659,U_7657,U_7661) ),
    inference(clausify,[status(thm)],[f_2215_6]) ).

cnf(f_2215_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7657),sK112(U_7661,U_7659,U_7657)),U_7659))
    | ~ sP677(U_7659,U_7657,U_7661) ),
    inference(clausify,[status(thm)],[f_2215_6]) ).

cnf(f_2215_11,plain,
    ( sK111(U_7661,U_7659,U_7657) != sK112(U_7661,U_7659,U_7657)
    | ~ sP677(U_7659,U_7657,U_7661) ),
    inference(clausify,[status(thm)],[f_2215_6]) ).

cnf(f_2215_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7657,U_7657)),hAPP(hAPP(c_Product__Type_OPair(U_7657,U_7657),sK111(U_7661,U_7659,U_7657)),sK112(U_7661,U_7659,U_7657))),U_7661))
    | ~ sP677(U_7659,U_7657,U_7661) ),
    inference(clausify,[status(thm)],[f_2215_6]) ).

cnf(f_2215_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7657,U_7657)),hAPP(hAPP(c_Product__Type_OPair(U_7657,U_7657),sK112(U_7661,U_7659,U_7657)),sK111(U_7661,U_7659,U_7657))),U_7661))
    | ~ sP677(U_7659,U_7657,U_7661) ),
    inference(clausify,[status(thm)],[f_2215_6]) ).

fof(f_2216_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_2216_2,plain,
    ! [U_7665,U_7664,U_7663,U_7662] : hAPP(hAPP(c_Relation_Oinv__image(U_7662,U_7663),U_7664),U_7665) = hAPP(c_Set_OCollect(tc_prod(U_7663,U_7663)),hAPP(c_Product__Type_Oprod_Oprod__case(U_7663,U_7663,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_7663,tc_fun(tc_prod(U_7662,U_7662),tc_HOL_Obool),tc_fun(U_7663,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7663,tc_fun(tc_fun(tc_prod(U_7662,U_7662),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7662,U_7662),tc_HOL_Obool),tc_fun(U_7663,tc_HOL_Obool)),U_7663),c_COMBC(U_7663,tc_fun(tc_prod(U_7662,U_7662),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7663,tc_prod(U_7662,U_7662)),tc_fun(U_7663,tc_fun(tc_fun(tc_prod(U_7662,U_7662),tc_HOL_Obool),tc_HOL_Obool)),U_7663),hAPP(c_COMBB(tc_prod(U_7662,U_7662),tc_fun(tc_fun(tc_prod(U_7662,U_7662),tc_HOL_Obool),tc_HOL_Obool),U_7663),c_member(tc_prod(U_7662,U_7662)))),hAPP(hAPP(c_COMBC(U_7663,tc_fun(U_7663,U_7662),tc_fun(U_7663,tc_prod(U_7662,U_7662))),hAPP(hAPP(c_COMBB(tc_fun(U_7662,tc_prod(U_7662,U_7662)),tc_fun(tc_fun(U_7663,U_7662),tc_fun(U_7663,tc_prod(U_7662,U_7662))),U_7663),c_COMBB(U_7662,tc_prod(U_7662,U_7662),U_7663)),hAPP(hAPP(c_COMBB(U_7662,tc_fun(U_7662,tc_prod(U_7662,U_7662)),U_7663),c_Product__Type_OPair(U_7662,U_7662)),U_7665))),U_7665)))),U_7664))),
    inference(variable_rename,[status(thm)],[f_2216_1]) ).

fof(f_2216_3,plain,
    ! [U_7662,U_7663,U_7664,U_7665] : hAPP(hAPP(c_Relation_Oinv__image(U_7662,U_7663),U_7664),U_7665) = hAPP(c_Set_OCollect(tc_prod(U_7663,U_7663)),hAPP(c_Product__Type_Oprod_Oprod__case(U_7663,U_7663,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_7663,tc_fun(tc_prod(U_7662,U_7662),tc_HOL_Obool),tc_fun(U_7663,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7663,tc_fun(tc_fun(tc_prod(U_7662,U_7662),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7662,U_7662),tc_HOL_Obool),tc_fun(U_7663,tc_HOL_Obool)),U_7663),c_COMBC(U_7663,tc_fun(tc_prod(U_7662,U_7662),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7663,tc_prod(U_7662,U_7662)),tc_fun(U_7663,tc_fun(tc_fun(tc_prod(U_7662,U_7662),tc_HOL_Obool),tc_HOL_Obool)),U_7663),hAPP(c_COMBB(tc_prod(U_7662,U_7662),tc_fun(tc_fun(tc_prod(U_7662,U_7662),tc_HOL_Obool),tc_HOL_Obool),U_7663),c_member(tc_prod(U_7662,U_7662)))),hAPP(hAPP(c_COMBC(U_7663,tc_fun(U_7663,U_7662),tc_fun(U_7663,tc_prod(U_7662,U_7662))),hAPP(hAPP(c_COMBB(tc_fun(U_7662,tc_prod(U_7662,U_7662)),tc_fun(tc_fun(U_7663,U_7662),tc_fun(U_7663,tc_prod(U_7662,U_7662))),U_7663),c_COMBB(U_7662,tc_prod(U_7662,U_7662),U_7663)),hAPP(hAPP(c_COMBB(U_7662,tc_fun(U_7662,tc_prod(U_7662,U_7662)),U_7663),c_Product__Type_OPair(U_7662,U_7662)),U_7665))),U_7665)))),U_7664))),
    inference(definitional_conversion,[status(esa)],[f_2216_2]) ).

cnf(f_2216_4,plain,
    hAPP(hAPP(c_Relation_Oinv__image(U_7662,U_7663),U_7664),U_7665) = hAPP(c_Set_OCollect(tc_prod(U_7663,U_7663)),hAPP(c_Product__Type_Oprod_Oprod__case(U_7663,U_7663,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_7663,tc_fun(tc_prod(U_7662,U_7662),tc_HOL_Obool),tc_fun(U_7663,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7663,tc_fun(tc_fun(tc_prod(U_7662,U_7662),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7662,U_7662),tc_HOL_Obool),tc_fun(U_7663,tc_HOL_Obool)),U_7663),c_COMBC(U_7663,tc_fun(tc_prod(U_7662,U_7662),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7663,tc_prod(U_7662,U_7662)),tc_fun(U_7663,tc_fun(tc_fun(tc_prod(U_7662,U_7662),tc_HOL_Obool),tc_HOL_Obool)),U_7663),hAPP(c_COMBB(tc_prod(U_7662,U_7662),tc_fun(tc_fun(tc_prod(U_7662,U_7662),tc_HOL_Obool),tc_HOL_Obool),U_7663),c_member(tc_prod(U_7662,U_7662)))),hAPP(hAPP(c_COMBC(U_7663,tc_fun(U_7663,U_7662),tc_fun(U_7663,tc_prod(U_7662,U_7662))),hAPP(hAPP(c_COMBB(tc_fun(U_7662,tc_prod(U_7662,U_7662)),tc_fun(tc_fun(U_7663,U_7662),tc_fun(U_7663,tc_prod(U_7662,U_7662))),U_7663),c_COMBB(U_7662,tc_prod(U_7662,U_7662),U_7663)),hAPP(hAPP(c_COMBB(U_7662,tc_fun(U_7662,tc_prod(U_7662,U_7662)),U_7663),c_Product__Type_OPair(U_7662,U_7662)),U_7665))),U_7665)))),U_7664))),
    inference(clausify,[status(thm)],[f_2216_3]) ).

fof(f_2217_1,plain,
    ! [T_b,V_a_2,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
      | ~ hBOOL(hAPP(V_Pa_2,V_a_2)) ),
    inference(fof_nnf,[status(thm)],[fact_CollectI]) ).

fof(f_2217_2,plain,
    ! [U_7668,U_7667,U_7666] :
      ( hBOOL(hAPP(hAPP(c_member(U_7668),U_7667),hAPP(c_Set_OCollect(U_7668),U_7666)))
      | ~ hBOOL(hAPP(U_7666,U_7667)) ),
    inference(variable_rename,[status(thm)],[f_2217_1]) ).

fof(f_2217_3,plain,
    ! [U_7666,U_7667,U_7668] :
      ( hBOOL(hAPP(hAPP(c_member(U_7668),U_7667),hAPP(c_Set_OCollect(U_7668),U_7666)))
      | ~ hBOOL(hAPP(U_7666,U_7667)) ),
    inference(definitional_conversion,[status(esa)],[f_2217_2]) ).

cnf(f_2217_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7668),U_7667),hAPP(c_Set_OCollect(U_7668),U_7666)))
    | ~ hBOOL(hAPP(U_7666,U_7667)) ),
    inference(clausify,[status(thm)],[f_2217_3]) ).

fof(f_2218_1,plain,
    ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),V_Pa_2) = V_Pa_2,
    inference(fof_nnf,[status(thm)],[fact_Collect__def]) ).

fof(f_2218_2,plain,
    ! [U_7670,U_7669] : hAPP(c_Set_OCollect(U_7669),U_7670) = U_7670,
    inference(variable_rename,[status(thm)],[f_2218_1]) ).

fof(f_2218_3,plain,
    ! [U_7669,U_7670] : hAPP(c_Set_OCollect(U_7669),U_7670) = U_7670,
    inference(definitional_conversion,[status(esa)],[f_2218_2]) ).

cnf(f_2218_4,plain,
    hAPP(c_Set_OCollect(U_7669),U_7670) = U_7670,
    inference(clausify,[status(thm)],[f_2218_3]) ).

fof(f_2219_1,plain,
    ! [V_Pa_2,V_a_2,T_b] :
      ( hBOOL(hAPP(V_Pa_2,V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ),
    inference(fof_nnf,[status(thm)],[fact_CollectE]) ).

fof(f_2219_2,plain,
    ! [U_7673,U_7672,U_7671] :
      ( hBOOL(hAPP(U_7673,U_7672))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7671),U_7672),hAPP(c_Set_OCollect(U_7671),U_7673))) ),
    inference(variable_rename,[status(thm)],[f_2219_1]) ).

fof(f_2219_3,plain,
    ! [U_7673,U_7672] :
      ( ! [U_7671] : ~ hBOOL(hAPP(hAPP(c_member(U_7671),U_7672),hAPP(c_Set_OCollect(U_7671),U_7673)))
      | hBOOL(hAPP(U_7673,U_7672)) ),
    inference(miniscope,[status(thm)],[f_2219_2]) ).

fof(f_2219_4,plain,
    ! [U_7671,U_7672,U_7673] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_7671),U_7672),hAPP(c_Set_OCollect(U_7671),U_7673)))
      | hBOOL(hAPP(U_7673,U_7672)) ),
    inference(definitional_conversion,[status(esa)],[f_2219_3]) ).

cnf(f_2219_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7671),U_7672),hAPP(c_Set_OCollect(U_7671),U_7673)))
    | hBOOL(hAPP(U_7673,U_7672)) ),
    inference(clausify,[status(thm)],[f_2219_4]) ).

fof(f_2220_1,plain,
    ! [V_Pa_2,V_a_2,T_b] :
      ( hBOOL(hAPP(V_Pa_2,V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ),
    inference(fof_nnf,[status(thm)],[fact_CollectD]) ).

fof(f_2220_2,plain,
    ! [U_7676,U_7675,U_7674] :
      ( hBOOL(hAPP(U_7676,U_7675))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7674),U_7675),hAPP(c_Set_OCollect(U_7674),U_7676))) ),
    inference(variable_rename,[status(thm)],[f_2220_1]) ).

fof(f_2220_3,plain,
    ! [U_7676,U_7675] :
      ( ! [U_7674] : ~ hBOOL(hAPP(hAPP(c_member(U_7674),U_7675),hAPP(c_Set_OCollect(U_7674),U_7676)))
      | hBOOL(hAPP(U_7676,U_7675)) ),
    inference(miniscope,[status(thm)],[f_2220_2]) ).

fof(f_2220_4,plain,
    ! [U_7674,U_7675,U_7676] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_7674),U_7675),hAPP(c_Set_OCollect(U_7674),U_7676)))
      | hBOOL(hAPP(U_7676,U_7675)) ),
    inference(definitional_conversion,[status(esa)],[f_2220_3]) ).

cnf(f_2220_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7674),U_7675),hAPP(c_Set_OCollect(U_7674),U_7676)))
    | hBOOL(hAPP(U_7676,U_7675)) ),
    inference(clausify,[status(thm)],[f_2220_4]) ).

fof(f_2221_1,plain,
    ! [V_Pa_2,V_a_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2)))
        | ~ hBOOL(hAPP(V_Pa_2,V_a_2)) )
      & ( hBOOL(hAPP(V_Pa_2,V_a_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_mem__Collect__eq]) ).

fof(f_2221_2,plain,
    ! [U_7679,U_7678,U_7677] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_7677),U_7678),hAPP(c_Set_OCollect(U_7677),U_7679)))
        | ~ hBOOL(hAPP(U_7679,U_7678)) )
      & ( hBOOL(hAPP(U_7679,U_7678))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7677),U_7678),hAPP(c_Set_OCollect(U_7677),U_7679))) ) ),
    inference(variable_rename,[status(thm)],[f_2221_1]) ).

fof(f_2221_3,plain,
    ( ! [U_7685,U_7683] :
        ( ! [U_7681] : hBOOL(hAPP(hAPP(c_member(U_7681),U_7683),hAPP(c_Set_OCollect(U_7681),U_7685)))
        | ~ hBOOL(hAPP(U_7685,U_7683)) )
    & ! [U_7684,U_7682] :
        ( ! [U_7680] : ~ hBOOL(hAPP(hAPP(c_member(U_7680),U_7682),hAPP(c_Set_OCollect(U_7680),U_7684)))
        | hBOOL(hAPP(U_7684,U_7682)) ) ),
    inference(miniscope,[status(thm)],[f_2221_2]) ).

fof(f_2221_4,plain,
    ( ! [U_7685,U_7681,U_7683] :
        ( hBOOL(hAPP(hAPP(c_member(U_7681),U_7683),hAPP(c_Set_OCollect(U_7681),U_7685)))
        | ~ hBOOL(hAPP(U_7685,U_7683)) )
    & ! [U_7680,U_7682,U_7684] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7680),U_7682),hAPP(c_Set_OCollect(U_7680),U_7684)))
        | hBOOL(hAPP(U_7684,U_7682)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2221_3]) ).

cnf(f_2221_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7680),U_7682),hAPP(c_Set_OCollect(U_7680),U_7684)))
    | hBOOL(hAPP(U_7684,U_7682)) ),
    inference(clausify,[status(thm)],[f_2221_4]) ).

cnf(f_2221_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7681),U_7683),hAPP(c_Set_OCollect(U_7681),U_7685)))
    | ~ hBOOL(hAPP(U_7685,U_7683)) ),
    inference(clausify,[status(thm)],[f_2221_4]) ).

fof(f_2222_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_2222_2,plain,
    ! [U_7687,U_7686] : hAPP(c_Set_OCollect(U_7686),hAPP(hAPP(c_COMBC(U_7686,tc_fun(U_7686,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7686)),U_7687)) = U_7687,
    inference(variable_rename,[status(thm)],[f_2222_1]) ).

fof(f_2222_3,plain,
    ! [U_7686,U_7687] : hAPP(c_Set_OCollect(U_7686),hAPP(hAPP(c_COMBC(U_7686,tc_fun(U_7686,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7686)),U_7687)) = U_7687,
    inference(definitional_conversion,[status(esa)],[f_2222_2]) ).

cnf(f_2222_4,plain,
    hAPP(c_Set_OCollect(U_7686),hAPP(hAPP(c_COMBC(U_7686,tc_fun(U_7686,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7686)),U_7687)) = U_7687,
    inference(clausify,[status(thm)],[f_2222_3]) ).

fof(f_2223_1,plain,
    ! [V_Pa_2,T_b] : hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),V_Pa_2)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),
    inference(fof_nnf,[status(thm)],[fact_Collect__neg__eq]) ).

fof(f_2223_2,plain,
    ! [U_7689,U_7688] : hAPP(c_Set_OCollect(U_7688),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_7688),c_fNot),U_7689)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7688,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_7688),U_7689)),
    inference(variable_rename,[status(thm)],[f_2223_1]) ).

fof(f_2223_3,plain,
    ! [U_7688,U_7689] : hAPP(c_Set_OCollect(U_7688),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_7688),c_fNot),U_7689)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7688,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_7688),U_7689)),
    inference(definitional_conversion,[status(esa)],[f_2223_2]) ).

cnf(f_2223_4,plain,
    hAPP(c_Set_OCollect(U_7688),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_7688),c_fNot),U_7689)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7688,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_7688),U_7689)),
    inference(clausify,[status(thm)],[f_2223_3]) ).

fof(f_2224_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_2224_2,plain,
    ! [U_7692,U_7691,U_7690] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7690,tc_HOL_Obool)),U_7691),U_7692) = hAPP(c_Set_OCollect(U_7690),hAPP(hAPP(c_COMBS(U_7690,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_7690),c_fconj),hAPP(hAPP(c_COMBC(U_7690,tc_fun(U_7690,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7690)),U_7691))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_7690),c_fNot),hAPP(hAPP(c_COMBC(U_7690,tc_fun(U_7690,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7690)),U_7692)))),
    inference(variable_rename,[status(thm)],[f_2224_1]) ).

fof(f_2224_3,plain,
    ! [U_7690,U_7691,U_7692] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7690,tc_HOL_Obool)),U_7691),U_7692) = hAPP(c_Set_OCollect(U_7690),hAPP(hAPP(c_COMBS(U_7690,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_7690),c_fconj),hAPP(hAPP(c_COMBC(U_7690,tc_fun(U_7690,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7690)),U_7691))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_7690),c_fNot),hAPP(hAPP(c_COMBC(U_7690,tc_fun(U_7690,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7690)),U_7692)))),
    inference(definitional_conversion,[status(esa)],[f_2224_2]) ).

cnf(f_2224_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7690,tc_HOL_Obool)),U_7691),U_7692) = hAPP(c_Set_OCollect(U_7690),hAPP(hAPP(c_COMBS(U_7690,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_7690),c_fconj),hAPP(hAPP(c_COMBC(U_7690,tc_fun(U_7690,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7690)),U_7691))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_7690),c_fNot),hAPP(hAPP(c_COMBC(U_7690,tc_fun(U_7690,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7690)),U_7692)))),
    inference(clausify,[status(thm)],[f_2224_3]) ).

fof(f_2225_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_2225_2,plain,
    ! [U_7694,U_7693] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7693,tc_HOL_Obool)),U_7694) = hAPP(c_Set_OCollect(U_7693),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_7693),c_fNot),hAPP(hAPP(c_COMBC(U_7693,tc_fun(U_7693,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7693)),U_7694))),
    inference(variable_rename,[status(thm)],[f_2225_1]) ).

fof(f_2225_3,plain,
    ! [U_7693,U_7694] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7693,tc_HOL_Obool)),U_7694) = hAPP(c_Set_OCollect(U_7693),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_7693),c_fNot),hAPP(hAPP(c_COMBC(U_7693,tc_fun(U_7693,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7693)),U_7694))),
    inference(definitional_conversion,[status(esa)],[f_2225_2]) ).

cnf(f_2225_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_7693,tc_HOL_Obool)),U_7694) = hAPP(c_Set_OCollect(U_7693),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_7693),c_fNot),hAPP(hAPP(c_COMBC(U_7693,tc_fun(U_7693,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7693)),U_7694))),
    inference(clausify,[status(thm)],[f_2225_3]) ).

fof(f_2226_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_2226_2,plain,
    ! [U_7698,U_7697,U_7696,U_7695] : c_Nitpick_Oprod(U_7695,U_7696,U_7697,U_7698) = hAPP(c_Set_OCollect(tc_prod(U_7695,U_7696)),hAPP(c_Product__Type_Oprod_Oprod__case(U_7695,U_7696,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_7695,tc_fun(U_7696,tc_HOL_Obool),tc_fun(U_7696,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_7696,tc_HOL_Obool),tc_fun(U_7696,tc_HOL_Obool)),U_7695),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_7696)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_7695),c_fconj),hAPP(hAPP(c_COMBC(U_7695,tc_fun(U_7695,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7695)),U_7697)))),hAPP(hAPP(c_COMBC(U_7696,tc_fun(U_7696,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7696)),U_7698)))),
    inference(variable_rename,[status(thm)],[f_2226_1]) ).

fof(f_2226_3,plain,
    ! [U_7695,U_7696,U_7697,U_7698] : c_Nitpick_Oprod(U_7695,U_7696,U_7697,U_7698) = hAPP(c_Set_OCollect(tc_prod(U_7695,U_7696)),hAPP(c_Product__Type_Oprod_Oprod__case(U_7695,U_7696,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_7695,tc_fun(U_7696,tc_HOL_Obool),tc_fun(U_7696,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_7696,tc_HOL_Obool),tc_fun(U_7696,tc_HOL_Obool)),U_7695),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_7696)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_7695),c_fconj),hAPP(hAPP(c_COMBC(U_7695,tc_fun(U_7695,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7695)),U_7697)))),hAPP(hAPP(c_COMBC(U_7696,tc_fun(U_7696,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7696)),U_7698)))),
    inference(definitional_conversion,[status(esa)],[f_2226_2]) ).

cnf(f_2226_4,plain,
    c_Nitpick_Oprod(U_7695,U_7696,U_7697,U_7698) = hAPP(c_Set_OCollect(tc_prod(U_7695,U_7696)),hAPP(c_Product__Type_Oprod_Oprod__case(U_7695,U_7696,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_7695,tc_fun(U_7696,tc_HOL_Obool),tc_fun(U_7696,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_7696,tc_HOL_Obool),tc_fun(U_7696,tc_HOL_Obool)),U_7695),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_7696)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_7695),c_fconj),hAPP(hAPP(c_COMBC(U_7695,tc_fun(U_7695,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7695)),U_7697)))),hAPP(hAPP(c_COMBC(U_7696,tc_fun(U_7696,tc_HOL_Obool),tc_HOL_Obool),c_member(U_7696)),U_7698)))),
    inference(clausify,[status(thm)],[f_2226_3]) ).

fof(f_2227_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_2227_2,plain,
    ! [U_7699] : c_Int_Oint__ge__less__than2(U_7699) = 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_7699)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_2227_1]) ).

fof(f_2227_3,plain,
    ! [U_7699] : c_Int_Oint__ge__less__than2(U_7699) = 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_7699)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(definitional_conversion,[status(esa)],[f_2227_2]) ).

cnf(f_2227_4,plain,
    c_Int_Oint__ge__less__than2(U_7699) = 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_7699)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_2227_3]) ).

fof(f_2228_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_2228_2,plain,
    ! [U_7700] : c_Int_Oint__ge__less__than(U_7700) = 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_7700)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_2228_1]) ).

fof(f_2228_3,plain,
    ! [U_7700] : c_Int_Oint__ge__less__than(U_7700) = 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_7700)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(definitional_conversion,[status(esa)],[f_2228_2]) ).

cnf(f_2228_4,plain,
    c_Int_Oint__ge__less__than(U_7700) = 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_7700)))),c_Orderings_Oord__class_Oless(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_2228_3]) ).

fof(f_2229_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_2229_2,plain,
    ! [U_7703,U_7702,U_7701] : hAPP(c_Relation_Oconverse(U_7701,U_7702),U_7703) = hAPP(c_Set_OCollect(tc_prod(U_7702,U_7701)),hAPP(c_Product__Type_Oprod_Oprod__case(U_7702,U_7701,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_7702,tc_fun(tc_prod(U_7701,U_7702),tc_HOL_Obool),tc_fun(U_7701,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7701,tc_fun(tc_fun(tc_prod(U_7701,U_7702),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7701,U_7702),tc_HOL_Obool),tc_fun(U_7701,tc_HOL_Obool)),U_7702),c_COMBC(U_7701,tc_fun(tc_prod(U_7701,U_7702),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7701,tc_prod(U_7701,U_7702)),tc_fun(U_7701,tc_fun(tc_fun(tc_prod(U_7701,U_7702),tc_HOL_Obool),tc_HOL_Obool)),U_7702),hAPP(c_COMBB(tc_prod(U_7701,U_7702),tc_fun(tc_fun(tc_prod(U_7701,U_7702),tc_HOL_Obool),tc_HOL_Obool),U_7701),c_member(tc_prod(U_7701,U_7702)))),hAPP(c_COMBC(U_7701,U_7702,tc_prod(U_7701,U_7702)),c_Product__Type_OPair(U_7701,U_7702))))),U_7703))),
    inference(variable_rename,[status(thm)],[f_2229_1]) ).

fof(f_2229_3,plain,
    ! [U_7701,U_7702,U_7703] : hAPP(c_Relation_Oconverse(U_7701,U_7702),U_7703) = hAPP(c_Set_OCollect(tc_prod(U_7702,U_7701)),hAPP(c_Product__Type_Oprod_Oprod__case(U_7702,U_7701,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_7702,tc_fun(tc_prod(U_7701,U_7702),tc_HOL_Obool),tc_fun(U_7701,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7701,tc_fun(tc_fun(tc_prod(U_7701,U_7702),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7701,U_7702),tc_HOL_Obool),tc_fun(U_7701,tc_HOL_Obool)),U_7702),c_COMBC(U_7701,tc_fun(tc_prod(U_7701,U_7702),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7701,tc_prod(U_7701,U_7702)),tc_fun(U_7701,tc_fun(tc_fun(tc_prod(U_7701,U_7702),tc_HOL_Obool),tc_HOL_Obool)),U_7702),hAPP(c_COMBB(tc_prod(U_7701,U_7702),tc_fun(tc_fun(tc_prod(U_7701,U_7702),tc_HOL_Obool),tc_HOL_Obool),U_7701),c_member(tc_prod(U_7701,U_7702)))),hAPP(c_COMBC(U_7701,U_7702,tc_prod(U_7701,U_7702)),c_Product__Type_OPair(U_7701,U_7702))))),U_7703))),
    inference(definitional_conversion,[status(esa)],[f_2229_2]) ).

cnf(f_2229_4,plain,
    hAPP(c_Relation_Oconverse(U_7701,U_7702),U_7703) = hAPP(c_Set_OCollect(tc_prod(U_7702,U_7701)),hAPP(c_Product__Type_Oprod_Oprod__case(U_7702,U_7701,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_7702,tc_fun(tc_prod(U_7701,U_7702),tc_HOL_Obool),tc_fun(U_7701,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7701,tc_fun(tc_fun(tc_prod(U_7701,U_7702),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7701,U_7702),tc_HOL_Obool),tc_fun(U_7701,tc_HOL_Obool)),U_7702),c_COMBC(U_7701,tc_fun(tc_prod(U_7701,U_7702),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7701,tc_prod(U_7701,U_7702)),tc_fun(U_7701,tc_fun(tc_fun(tc_prod(U_7701,U_7702),tc_HOL_Obool),tc_HOL_Obool)),U_7702),hAPP(c_COMBB(tc_prod(U_7701,U_7702),tc_fun(tc_fun(tc_prod(U_7701,U_7702),tc_HOL_Obool),tc_HOL_Obool),U_7701),c_member(tc_prod(U_7701,U_7702)))),hAPP(c_COMBC(U_7701,U_7702,tc_prod(U_7701,U_7702)),c_Product__Type_OPair(U_7701,U_7702))))),U_7703))),
    inference(clausify,[status(thm)],[f_2229_3]) ).

fof(f_2230_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_2230_2,plain,
    ! [U_7706,U_7705,U_7704] : hAPP(c_Relation_Oconverse(U_7704,U_7705),hAPP(c_Relation_Oconverse(U_7705,U_7704),U_7706)) = U_7706,
    inference(variable_rename,[status(thm)],[f_2230_1]) ).

fof(f_2230_3,plain,
    ! [U_7704,U_7705,U_7706] : hAPP(c_Relation_Oconverse(U_7704,U_7705),hAPP(c_Relation_Oconverse(U_7705,U_7704),U_7706)) = U_7706,
    inference(definitional_conversion,[status(esa)],[f_2230_2]) ).

cnf(f_2230_4,plain,
    hAPP(c_Relation_Oconverse(U_7704,U_7705),hAPP(c_Relation_Oconverse(U_7705,U_7704),U_7706)) = U_7706,
    inference(clausify,[status(thm)],[f_2230_3]) ).

fof(f_2231_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_2231_2,plain,
    ! [U_7710,U_7709,U_7708,U_7707] : hAPP(c_Relation_Oconverse(U_7707,U_7707),hAPP(hAPP(c_Relation_Oinv__image(U_7708,U_7707),U_7709),U_7710)) = hAPP(hAPP(c_Relation_Oinv__image(U_7708,U_7707),hAPP(c_Relation_Oconverse(U_7708,U_7708),U_7709)),U_7710),
    inference(variable_rename,[status(thm)],[f_2231_1]) ).

fof(f_2231_3,plain,
    ! [U_7707,U_7708,U_7709,U_7710] : hAPP(c_Relation_Oconverse(U_7707,U_7707),hAPP(hAPP(c_Relation_Oinv__image(U_7708,U_7707),U_7709),U_7710)) = hAPP(hAPP(c_Relation_Oinv__image(U_7708,U_7707),hAPP(c_Relation_Oconverse(U_7708,U_7708),U_7709)),U_7710),
    inference(definitional_conversion,[status(esa)],[f_2231_2]) ).

cnf(f_2231_4,plain,
    hAPP(c_Relation_Oconverse(U_7707,U_7707),hAPP(hAPP(c_Relation_Oinv__image(U_7708,U_7707),U_7709),U_7710)) = hAPP(hAPP(c_Relation_Oinv__image(U_7708,U_7707),hAPP(c_Relation_Oconverse(U_7708,U_7708),U_7709)),U_7710),
    inference(clausify,[status(thm)],[f_2231_3]) ).

fof(f_2232_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_2232_2,plain,
    ! [U_7713,U_7712,U_7711] :
      ( ( c_Relation_Ototal__on(U_7711,U_7712,hAPP(c_Relation_Oconverse(U_7711,U_7711),U_7713))
        | ~ c_Relation_Ototal__on(U_7711,U_7712,U_7713) )
      & ( c_Relation_Ototal__on(U_7711,U_7712,U_7713)
        | ~ c_Relation_Ototal__on(U_7711,U_7712,hAPP(c_Relation_Oconverse(U_7711,U_7711),U_7713)) ) ),
    inference(variable_rename,[status(thm)],[f_2232_1]) ).

fof(f_2232_3,plain,
    ( ! [U_7719,U_7717,U_7715] :
        ( c_Relation_Ototal__on(U_7715,U_7717,hAPP(c_Relation_Oconverse(U_7715,U_7715),U_7719))
        | ~ c_Relation_Ototal__on(U_7715,U_7717,U_7719) )
    & ! [U_7718,U_7716,U_7714] :
        ( c_Relation_Ototal__on(U_7714,U_7716,U_7718)
        | ~ c_Relation_Ototal__on(U_7714,U_7716,hAPP(c_Relation_Oconverse(U_7714,U_7714),U_7718)) ) ),
    inference(miniscope,[status(thm)],[f_2232_2]) ).

fof(f_2232_4,plain,
    ( ! [U_7719,U_7717,U_7715] :
        ( c_Relation_Ototal__on(U_7715,U_7717,hAPP(c_Relation_Oconverse(U_7715,U_7715),U_7719))
        | ~ c_Relation_Ototal__on(U_7715,U_7717,U_7719) )
    & ! [U_7716,U_7714,U_7718] :
        ( c_Relation_Ototal__on(U_7714,U_7716,U_7718)
        | ~ c_Relation_Ototal__on(U_7714,U_7716,hAPP(c_Relation_Oconverse(U_7714,U_7714),U_7718)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2232_3]) ).

cnf(f_2232_5,plain,
    ( c_Relation_Ototal__on(U_7714,U_7716,U_7718)
    | ~ c_Relation_Ototal__on(U_7714,U_7716,hAPP(c_Relation_Oconverse(U_7714,U_7714),U_7718)) ),
    inference(clausify,[status(thm)],[f_2232_4]) ).

cnf(f_2232_6,plain,
    ( c_Relation_Ototal__on(U_7715,U_7717,hAPP(c_Relation_Oconverse(U_7715,U_7715),U_7719))
    | ~ c_Relation_Ototal__on(U_7715,U_7717,U_7719) ),
    inference(clausify,[status(thm)],[f_2232_4]) ).

fof(f_2233_1,plain,
    ! [V_Pa_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_Pa_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_Pa_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_2233_2,plain,
    ! [U_7720] : 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_7720)) = 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_7720),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_2233_1]) ).

fof(f_2233_3,plain,
    ! [U_7720] : 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_7720)) = 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_7720),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    inference(definitional_conversion,[status(esa)],[f_2233_2]) ).

cnf(f_2233_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_7720)) = 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_7720),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_2233_3]) ).

fof(f_2234_1,plain,
    ! [V_Pa_2] : hAPP(c_Set_OCollect(tc_Nat_Onat),V_Pa_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_Pa_2),c_Int_Onat)))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J]) ).

fof(f_2234_2,plain,
    ! [U_7721] : hAPP(c_Set_OCollect(tc_Nat_Onat),U_7721) = 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_7721),c_Int_Onat)))),
    inference(variable_rename,[status(thm)],[f_2234_1]) ).

fof(f_2234_3,plain,
    ! [U_7721] : hAPP(c_Set_OCollect(tc_Nat_Onat),U_7721) = 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_7721),c_Int_Onat)))),
    inference(definitional_conversion,[status(esa)],[f_2234_2]) ).

cnf(f_2234_4,plain,
    hAPP(c_Set_OCollect(tc_Nat_Onat),U_7721) = 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_7721),c_Int_Onat)))),
    inference(clausify,[status(thm)],[f_2234_3]) ).

fof(f_2235_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_2235_2,plain,
    ! [U_7726,U_7725,U_7724,U_7723,U_7722] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7722,U_7723)),hAPP(hAPP(c_Product__Type_OPair(U_7722,U_7723),U_7724),U_7725)),hAPP(c_Relation_Oconverse(U_7723,U_7722),U_7726)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7723,U_7722)),hAPP(hAPP(c_Product__Type_OPair(U_7723,U_7722),U_7725),U_7724)),U_7726)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7723,U_7722)),hAPP(hAPP(c_Product__Type_OPair(U_7723,U_7722),U_7725),U_7724)),U_7726))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7722,U_7723)),hAPP(hAPP(c_Product__Type_OPair(U_7722,U_7723),U_7724),U_7725)),hAPP(c_Relation_Oconverse(U_7723,U_7722),U_7726))) ) ),
    inference(variable_rename,[status(thm)],[f_2235_1]) ).

fof(f_2235_3,plain,
    ( ! [U_7736,U_7734,U_7732,U_7730,U_7728] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7728,U_7730)),hAPP(hAPP(c_Product__Type_OPair(U_7728,U_7730),U_7732),U_7734)),hAPP(c_Relation_Oconverse(U_7730,U_7728),U_7736)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7730,U_7728)),hAPP(hAPP(c_Product__Type_OPair(U_7730,U_7728),U_7734),U_7732)),U_7736)) )
    & ! [U_7735,U_7733,U_7731,U_7729,U_7727] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7729,U_7727)),hAPP(hAPP(c_Product__Type_OPair(U_7729,U_7727),U_7733),U_7731)),U_7735))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7727,U_7729)),hAPP(hAPP(c_Product__Type_OPair(U_7727,U_7729),U_7731),U_7733)),hAPP(c_Relation_Oconverse(U_7729,U_7727),U_7735))) ) ),
    inference(miniscope,[status(thm)],[f_2235_2]) ).

fof(f_2235_4,plain,
    ( ! [U_7728,U_7730,U_7732,U_7734,U_7736] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7728,U_7730)),hAPP(hAPP(c_Product__Type_OPair(U_7728,U_7730),U_7732),U_7734)),hAPP(c_Relation_Oconverse(U_7730,U_7728),U_7736)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7730,U_7728)),hAPP(hAPP(c_Product__Type_OPair(U_7730,U_7728),U_7734),U_7732)),U_7736)) )
    & ! [U_7729,U_7733,U_7727,U_7731,U_7735] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7729,U_7727)),hAPP(hAPP(c_Product__Type_OPair(U_7729,U_7727),U_7733),U_7731)),U_7735))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7727,U_7729)),hAPP(hAPP(c_Product__Type_OPair(U_7727,U_7729),U_7731),U_7733)),hAPP(c_Relation_Oconverse(U_7729,U_7727),U_7735))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2235_3]) ).

cnf(f_2235_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7729,U_7727)),hAPP(hAPP(c_Product__Type_OPair(U_7729,U_7727),U_7733),U_7731)),U_7735))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7727,U_7729)),hAPP(hAPP(c_Product__Type_OPair(U_7727,U_7729),U_7731),U_7733)),hAPP(c_Relation_Oconverse(U_7729,U_7727),U_7735))) ),
    inference(clausify,[status(thm)],[f_2235_4]) ).

cnf(f_2235_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7728,U_7730)),hAPP(hAPP(c_Product__Type_OPair(U_7728,U_7730),U_7732),U_7734)),hAPP(c_Relation_Oconverse(U_7730,U_7728),U_7736)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7730,U_7728)),hAPP(hAPP(c_Product__Type_OPair(U_7730,U_7728),U_7734),U_7732)),U_7736)) ),
    inference(clausify,[status(thm)],[f_2235_4]) ).

fof(f_2236_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_2236_2,plain,
    ! [U_7741,U_7740,U_7739,U_7738,U_7737] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7738,U_7737)),hAPP(hAPP(c_Product__Type_OPair(U_7738,U_7737),U_7740),U_7739)),hAPP(c_Relation_Oconverse(U_7737,U_7738),U_7741)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7737,U_7738)),hAPP(hAPP(c_Product__Type_OPair(U_7737,U_7738),U_7739),U_7740)),U_7741)) ),
    inference(variable_rename,[status(thm)],[f_2236_1]) ).

fof(f_2236_3,plain,
    ! [U_7737,U_7738,U_7739,U_7740,U_7741] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7738,U_7737)),hAPP(hAPP(c_Product__Type_OPair(U_7738,U_7737),U_7740),U_7739)),hAPP(c_Relation_Oconverse(U_7737,U_7738),U_7741)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7737,U_7738)),hAPP(hAPP(c_Product__Type_OPair(U_7737,U_7738),U_7739),U_7740)),U_7741)) ),
    inference(definitional_conversion,[status(esa)],[f_2236_2]) ).

cnf(f_2236_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7738,U_7737)),hAPP(hAPP(c_Product__Type_OPair(U_7738,U_7737),U_7740),U_7739)),hAPP(c_Relation_Oconverse(U_7737,U_7738),U_7741)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7737,U_7738)),hAPP(hAPP(c_Product__Type_OPair(U_7737,U_7738),U_7739),U_7740)),U_7741)) ),
    inference(clausify,[status(thm)],[f_2236_3]) ).

fof(f_2237_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_2237_2,plain,
    ! [U_7746,U_7745,U_7744,U_7743,U_7742] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7743,U_7742)),hAPP(hAPP(c_Product__Type_OPair(U_7743,U_7742),U_7745),U_7744)),U_7746))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7742,U_7743)),hAPP(hAPP(c_Product__Type_OPair(U_7742,U_7743),U_7744),U_7745)),hAPP(c_Relation_Oconverse(U_7743,U_7742),U_7746))) ),
    inference(variable_rename,[status(thm)],[f_2237_1]) ).

fof(f_2237_3,plain,
    ! [U_7742,U_7743,U_7744,U_7745,U_7746] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7743,U_7742)),hAPP(hAPP(c_Product__Type_OPair(U_7743,U_7742),U_7745),U_7744)),U_7746))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7742,U_7743)),hAPP(hAPP(c_Product__Type_OPair(U_7742,U_7743),U_7744),U_7745)),hAPP(c_Relation_Oconverse(U_7743,U_7742),U_7746))) ),
    inference(definitional_conversion,[status(esa)],[f_2237_2]) ).

cnf(f_2237_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7743,U_7742)),hAPP(hAPP(c_Product__Type_OPair(U_7743,U_7742),U_7745),U_7744)),U_7746))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7742,U_7743)),hAPP(hAPP(c_Product__Type_OPair(U_7742,U_7743),U_7744),U_7745)),hAPP(c_Relation_Oconverse(U_7743,U_7742),U_7746))) ),
    inference(clausify,[status(thm)],[f_2237_3]) ).

fof(f_2238_1,plain,
    ! [V_Pa_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_Pa_2))),
    inference(fof_nnf,[status(thm)],[fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J]) ).

fof(f_2238_2,plain,
    ! [U_7747] : 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_7747))),
    inference(variable_rename,[status(thm)],[f_2238_1]) ).

fof(f_2238_3,plain,
    ! [U_7747] : 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_7747))),
    inference(definitional_conversion,[status(esa)],[f_2238_2]) ).

cnf(f_2238_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_7747))),
    inference(clausify,[status(thm)],[f_2238_3]) ).

fof(f_2239_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_2239_2,plain,
    ! [U_7753,U_7752,U_7751,U_7750] :
      ( ? [U_7749,U_7748] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7751,U_7750)),hAPP(hAPP(c_Product__Type_OPair(U_7751,U_7750),U_7749),U_7748)),U_7753))
          & U_7752 = hAPP(hAPP(c_Product__Type_OPair(U_7750,U_7751),U_7748),U_7749) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7750,U_7751)),U_7752),hAPP(c_Relation_Oconverse(U_7751,U_7750),U_7753))) ),
    inference(variable_rename,[status(thm)],[f_2239_1]) ).

fof(f_2239_3,plain,
    ! [U_7753,U_7752,U_7751,U_7750] :
      ( ? [U_7748] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7751,U_7750)),hAPP(hAPP(c_Product__Type_OPair(U_7751,U_7750),sK113(U_7753,U_7752,U_7751,U_7750)),U_7748)),U_7753))
          & U_7752 = hAPP(hAPP(c_Product__Type_OPair(U_7750,U_7751),U_7748),sK113(U_7753,U_7752,U_7751,U_7750)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7750,U_7751)),U_7752),hAPP(c_Relation_Oconverse(U_7751,U_7750),U_7753))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK113]),skolemize(U_7749,sK113(U_7753,U_7752,U_7751,U_7750))],[f_2239_2]) ).

fof(f_2239_4,plain,
    ! [U_7753,U_7752,U_7751,U_7750] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7751,U_7750)),hAPP(hAPP(c_Product__Type_OPair(U_7751,U_7750),sK113(U_7753,U_7752,U_7751,U_7750)),sK114(U_7753,U_7752,U_7751,U_7750))),U_7753))
        & U_7752 = hAPP(hAPP(c_Product__Type_OPair(U_7750,U_7751),sK114(U_7753,U_7752,U_7751,U_7750)),sK113(U_7753,U_7752,U_7751,U_7750)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7750,U_7751)),U_7752),hAPP(c_Relation_Oconverse(U_7751,U_7750),U_7753))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK114]),skolemize(U_7748,sK114(U_7753,U_7752,U_7751,U_7750))],[f_2239_3]) ).

fof(f_2239_5,plain,
    ( ! [U_7750,U_7751,U_7752,U_7753] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7751,U_7750)),hAPP(hAPP(c_Product__Type_OPair(U_7751,U_7750),sK113(U_7753,U_7752,U_7751,U_7750)),sK114(U_7753,U_7752,U_7751,U_7750))),U_7753))
        | ~ sP678(U_7750,U_7751,U_7752,U_7753) )
    & ! [U_7750,U_7751,U_7752,U_7753] :
        ( U_7752 = hAPP(hAPP(c_Product__Type_OPair(U_7750,U_7751),sK114(U_7753,U_7752,U_7751,U_7750)),sK113(U_7753,U_7752,U_7751,U_7750))
        | ~ sP678(U_7750,U_7751,U_7752,U_7753) )
    & ! [U_7750,U_7751,U_7752,U_7753] :
        ( sP678(U_7750,U_7751,U_7752,U_7753)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7750,U_7751)),U_7752),hAPP(c_Relation_Oconverse(U_7751,U_7750),U_7753))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP678])],[f_2239_4]) ).

cnf(f_2239_6,plain,
    ( sP678(U_7750,U_7751,U_7752,U_7753)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7750,U_7751)),U_7752),hAPP(c_Relation_Oconverse(U_7751,U_7750),U_7753))) ),
    inference(clausify,[status(thm)],[f_2239_5]) ).

cnf(f_2239_7,plain,
    ( U_7752 = hAPP(hAPP(c_Product__Type_OPair(U_7750,U_7751),sK114(U_7753,U_7752,U_7751,U_7750)),sK113(U_7753,U_7752,U_7751,U_7750))
    | ~ sP678(U_7750,U_7751,U_7752,U_7753) ),
    inference(clausify,[status(thm)],[f_2239_5]) ).

cnf(f_2239_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7751,U_7750)),hAPP(hAPP(c_Product__Type_OPair(U_7751,U_7750),sK113(U_7753,U_7752,U_7751,U_7750)),sK114(U_7753,U_7752,U_7751,U_7750))),U_7753))
    | ~ sP678(U_7750,U_7751,U_7752,U_7753) ),
    inference(clausify,[status(thm)],[f_2239_5]) ).

fof(f_2240_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_2240_2,plain,
    ! [U_7758,U_7757,U_7756,U_7755,U_7754] :
      ( hBOOL(hAPP(hAPP(c_member(U_7755),U_7757),hAPP(c_Relation_ORange(U_7754,U_7755),U_7758)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7754,U_7755)),hAPP(hAPP(c_Product__Type_OPair(U_7754,U_7755),U_7756),U_7757)),U_7758)) ),
    inference(variable_rename,[status(thm)],[f_2240_1]) ).

fof(f_2240_3,plain,
    ! [U_7754,U_7755,U_7756,U_7757,U_7758] :
      ( hBOOL(hAPP(hAPP(c_member(U_7755),U_7757),hAPP(c_Relation_ORange(U_7754,U_7755),U_7758)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7754,U_7755)),hAPP(hAPP(c_Product__Type_OPair(U_7754,U_7755),U_7756),U_7757)),U_7758)) ),
    inference(definitional_conversion,[status(esa)],[f_2240_2]) ).

cnf(f_2240_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7755),U_7757),hAPP(c_Relation_ORange(U_7754,U_7755),U_7758)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7754,U_7755)),hAPP(hAPP(c_Product__Type_OPair(U_7754,U_7755),U_7756),U_7757)),U_7758)) ),
    inference(clausify,[status(thm)],[f_2240_3]) ).

fof(f_2241_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_2241_2,plain,
    ! [U_7762,U_7761,U_7760,U_7759] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7761,U_7761)),hAPP(hAPP(c_Product__Type_OPair(U_7761,U_7761),U_7759),U_7760)),c_Relation_OId__on(U_7761,U_7762)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7761),U_7759),U_7762))
      | U_7759 != U_7760 ),
    inference(variable_rename,[status(thm)],[f_2241_1]) ).

fof(f_2241_3,plain,
    ! [U_7759,U_7760,U_7761,U_7762] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7761,U_7761)),hAPP(hAPP(c_Product__Type_OPair(U_7761,U_7761),U_7759),U_7760)),c_Relation_OId__on(U_7761,U_7762)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7761),U_7759),U_7762))
      | U_7759 != U_7760 ),
    inference(definitional_conversion,[status(esa)],[f_2241_2]) ).

cnf(f_2241_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7761,U_7761)),hAPP(hAPP(c_Product__Type_OPair(U_7761,U_7761),U_7759),U_7760)),c_Relation_OId__on(U_7761,U_7762)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7761),U_7759),U_7762))
    | U_7759 != U_7760 ),
    inference(clausify,[status(thm)],[f_2241_3]) ).

fof(f_2242_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_2242_2,plain,
    ! [U_7766,U_7765,U_7764,U_7763] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7763,U_7763)),hAPP(hAPP(c_Product__Type_OPair(U_7763,U_7763),U_7764),U_7765)),c_Relation_OId__on(U_7763,U_7766)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7763),U_7764),U_7766))
        | U_7764 != U_7765 )
      & ( ( hBOOL(hAPP(hAPP(c_member(U_7763),U_7764),U_7766))
          & U_7764 = U_7765 )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7763,U_7763)),hAPP(hAPP(c_Product__Type_OPair(U_7763,U_7763),U_7764),U_7765)),c_Relation_OId__on(U_7763,U_7766))) ) ),
    inference(variable_rename,[status(thm)],[f_2242_1]) ).

fof(f_2242_3,plain,
    ( ! [U_7774,U_7772,U_7770,U_7768] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7768,U_7768)),hAPP(hAPP(c_Product__Type_OPair(U_7768,U_7768),U_7770),U_7772)),c_Relation_OId__on(U_7768,U_7774)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7768),U_7770),U_7774))
        | U_7770 != U_7772 )
    & ! [U_7773,U_7771,U_7769,U_7767] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_7767),U_7769),U_7773))
          & U_7769 = U_7771 )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7767,U_7767)),hAPP(hAPP(c_Product__Type_OPair(U_7767,U_7767),U_7769),U_7771)),c_Relation_OId__on(U_7767,U_7773))) ) ),
    inference(miniscope,[status(thm)],[f_2242_2]) ).

fof(f_2242_4,plain,
    ( ! [U_7769,U_7767,U_7771,U_7773] :
        ( hBOOL(hAPP(hAPP(c_member(U_7767),U_7769),U_7773))
        | ~ sP679(U_7769,U_7767,U_7771,U_7773) )
    & ! [U_7769,U_7767,U_7771,U_7773] :
        ( U_7769 = U_7771
        | ~ sP679(U_7769,U_7767,U_7771,U_7773) )
    & ! [U_7772,U_7768,U_7774,U_7770] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7768,U_7768)),hAPP(hAPP(c_Product__Type_OPair(U_7768,U_7768),U_7770),U_7772)),c_Relation_OId__on(U_7768,U_7774)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7768),U_7770),U_7774))
        | U_7770 != U_7772 )
    & ! [U_7769,U_7767,U_7771,U_7773] :
        ( sP679(U_7769,U_7767,U_7771,U_7773)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7767,U_7767)),hAPP(hAPP(c_Product__Type_OPair(U_7767,U_7767),U_7769),U_7771)),c_Relation_OId__on(U_7767,U_7773))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP679])],[f_2242_3]) ).

cnf(f_2242_5,plain,
    ( sP679(U_7769,U_7767,U_7771,U_7773)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7767,U_7767)),hAPP(hAPP(c_Product__Type_OPair(U_7767,U_7767),U_7769),U_7771)),c_Relation_OId__on(U_7767,U_7773))) ),
    inference(clausify,[status(thm)],[f_2242_4]) ).

cnf(f_2242_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7768,U_7768)),hAPP(hAPP(c_Product__Type_OPair(U_7768,U_7768),U_7770),U_7772)),c_Relation_OId__on(U_7768,U_7774)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7768),U_7770),U_7774))
    | U_7770 != U_7772 ),
    inference(clausify,[status(thm)],[f_2242_4]) ).

cnf(f_2242_7,plain,
    ( U_7769 = U_7771
    | ~ sP679(U_7769,U_7767,U_7771,U_7773) ),
    inference(clausify,[status(thm)],[f_2242_4]) ).

cnf(f_2242_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7767),U_7769),U_7773))
    | ~ sP679(U_7769,U_7767,U_7771,U_7773) ),
    inference(clausify,[status(thm)],[f_2242_4]) ).

fof(f_2243_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_2243_2,plain,
    ! [U_7776,U_7775] : hAPP(c_Relation_ORange(U_7775,U_7775),c_Relation_OId__on(U_7775,U_7776)) = U_7776,
    inference(variable_rename,[status(thm)],[f_2243_1]) ).

fof(f_2243_3,plain,
    ! [U_7775,U_7776] : hAPP(c_Relation_ORange(U_7775,U_7775),c_Relation_OId__on(U_7775,U_7776)) = U_7776,
    inference(definitional_conversion,[status(esa)],[f_2243_2]) ).

cnf(f_2243_4,plain,
    hAPP(c_Relation_ORange(U_7775,U_7775),c_Relation_OId__on(U_7775,U_7776)) = U_7776,
    inference(clausify,[status(thm)],[f_2243_3]) ).

fof(f_2244_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_2244_2,plain,
    ! [U_7778,U_7777] : hAPP(c_Relation_Oconverse(U_7777,U_7777),c_Relation_OId__on(U_7777,U_7778)) = c_Relation_OId__on(U_7777,U_7778),
    inference(variable_rename,[status(thm)],[f_2244_1]) ).

fof(f_2244_3,plain,
    ! [U_7777,U_7778] : hAPP(c_Relation_Oconverse(U_7777,U_7777),c_Relation_OId__on(U_7777,U_7778)) = c_Relation_OId__on(U_7777,U_7778),
    inference(definitional_conversion,[status(esa)],[f_2244_2]) ).

cnf(f_2244_4,plain,
    hAPP(c_Relation_Oconverse(U_7777,U_7777),c_Relation_OId__on(U_7777,U_7778)) = c_Relation_OId__on(U_7777,U_7778),
    inference(clausify,[status(thm)],[f_2244_3]) ).

fof(f_2245_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_2245_2,plain,
    ! [U_7780,U_7779] : c_Relation_OId__on(U_7779,U_7780) = hAPP(c_Product__Type_Oprod_Oprod__case(U_7779,U_7779,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_7779,tc_HOL_Obool,tc_fun(U_7779,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7779,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(U_7779,tc_HOL_Obool)),U_7779),c_COMBC(U_7779,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7779,tc_HOL_Obool),tc_fun(U_7779,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_7779),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_7779),c_fconj)),c_fequal))),U_7780)),
    inference(variable_rename,[status(thm)],[f_2245_1]) ).

fof(f_2245_3,plain,
    ! [U_7779,U_7780] : c_Relation_OId__on(U_7779,U_7780) = hAPP(c_Product__Type_Oprod_Oprod__case(U_7779,U_7779,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_7779,tc_HOL_Obool,tc_fun(U_7779,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7779,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(U_7779,tc_HOL_Obool)),U_7779),c_COMBC(U_7779,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7779,tc_HOL_Obool),tc_fun(U_7779,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_7779),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_7779),c_fconj)),c_fequal))),U_7780)),
    inference(definitional_conversion,[status(esa)],[f_2245_2]) ).

cnf(f_2245_4,plain,
    c_Relation_OId__on(U_7779,U_7780) = hAPP(c_Product__Type_Oprod_Oprod__case(U_7779,U_7779,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_7779,tc_HOL_Obool,tc_fun(U_7779,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7779,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_HOL_Obool,tc_fun(U_7779,tc_HOL_Obool)),U_7779),c_COMBC(U_7779,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7779,tc_HOL_Obool),tc_fun(U_7779,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_7779),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_7779),c_fconj)),c_fequal))),U_7780)),
    inference(clausify,[status(thm)],[f_2245_3]) ).

fof(f_2246_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_2246_2,plain,
    ! [U_7784,U_7783,U_7782,U_7781] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7781,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7781,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_7782,U_7781),U_7783)),hAPP(c_Relation_ORange(U_7782,U_7781),U_7784))),hAPP(c_Relation_ORange(U_7782,U_7781),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_7782,U_7781),tc_HOL_Obool)),U_7783),U_7784)))),
    inference(variable_rename,[status(thm)],[f_2246_1]) ).

fof(f_2246_3,plain,
    ! [U_7781,U_7782,U_7783,U_7784] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7781,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7781,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_7782,U_7781),U_7783)),hAPP(c_Relation_ORange(U_7782,U_7781),U_7784))),hAPP(c_Relation_ORange(U_7782,U_7781),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_7782,U_7781),tc_HOL_Obool)),U_7783),U_7784)))),
    inference(definitional_conversion,[status(esa)],[f_2246_2]) ).

cnf(f_2246_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_7781,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_7781,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_7782,U_7781),U_7783)),hAPP(c_Relation_ORange(U_7782,U_7781),U_7784))),hAPP(c_Relation_ORange(U_7782,U_7781),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_7782,U_7781),tc_HOL_Obool)),U_7783),U_7784)))),
    inference(clausify,[status(thm)],[f_2246_3]) ).

fof(f_2247_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_2247_2,plain,
    ! [U_7787,U_7786,U_7785] : hAPP(c_Set_Oimage(tc_prod(U_7785,U_7786),U_7786,c_Product__Type_Osnd(U_7785,U_7786)),U_7787) = hAPP(c_Relation_ORange(U_7785,U_7786),U_7787),
    inference(variable_rename,[status(thm)],[f_2247_1]) ).

fof(f_2247_3,plain,
    ! [U_7785,U_7786,U_7787] : hAPP(c_Set_Oimage(tc_prod(U_7785,U_7786),U_7786,c_Product__Type_Osnd(U_7785,U_7786)),U_7787) = hAPP(c_Relation_ORange(U_7785,U_7786),U_7787),
    inference(definitional_conversion,[status(esa)],[f_2247_2]) ).

cnf(f_2247_4,plain,
    hAPP(c_Set_Oimage(tc_prod(U_7785,U_7786),U_7786,c_Product__Type_Osnd(U_7785,U_7786)),U_7787) = hAPP(c_Relation_ORange(U_7785,U_7786),U_7787),
    inference(clausify,[status(thm)],[f_2247_3]) ).

fof(f_2248_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_2248_2,plain,
    ! [U_7793,U_7792,U_7791,U_7790] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_7790),U_7791),hAPP(c_Relation_ORange(U_7792,U_7790),U_7793)))
        | ! [U_7789] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7792,U_7790)),hAPP(hAPP(c_Product__Type_OPair(U_7792,U_7790),U_7789),U_7791)),U_7793)) )
      & ( ? [U_7788] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_7792,U_7790)),hAPP(hAPP(c_Product__Type_OPair(U_7792,U_7790),U_7788),U_7791)),U_7793))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7790),U_7791),hAPP(c_Relation_ORange(U_7792,U_7790),U_7793))) ) ),
    inference(variable_rename,[status(thm)],[f_2248_1]) ).

fof(f_2248_3,plain,
    ( ! [U_7801,U_7799,U_7797,U_7795] :
        ( hBOOL(hAPP(hAPP(c_member(U_7795),U_7797),hAPP(c_Relation_ORange(U_7799,U_7795),U_7801)))
        | ! [U_7789] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7799,U_7795)),hAPP(hAPP(c_Product__Type_OPair(U_7799,U_7795),U_7789),U_7797)),U_7801)) )
    & ! [U_7800,U_7798,U_7796,U_7794] :
        ( ? [U_7788] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_7798,U_7794)),hAPP(hAPP(c_Product__Type_OPair(U_7798,U_7794),U_7788),U_7796)),U_7800))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7794),U_7796),hAPP(c_Relation_ORange(U_7798,U_7794),U_7800))) ) ),
    inference(miniscope,[status(thm)],[f_2248_2]) ).

fof(f_2248_4,plain,
    ( ! [U_7801,U_7799,U_7797,U_7795] :
        ( hBOOL(hAPP(hAPP(c_member(U_7795),U_7797),hAPP(c_Relation_ORange(U_7799,U_7795),U_7801)))
        | ! [U_7789] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7799,U_7795)),hAPP(hAPP(c_Product__Type_OPair(U_7799,U_7795),U_7789),U_7797)),U_7801)) )
    & ! [U_7800,U_7798,U_7796,U_7794] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7798,U_7794)),hAPP(hAPP(c_Product__Type_OPair(U_7798,U_7794),sK115(U_7800,U_7798,U_7796,U_7794)),U_7796)),U_7800))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7794),U_7796),hAPP(c_Relation_ORange(U_7798,U_7794),U_7800))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK115]),skolemize(U_7788,sK115(U_7800,U_7798,U_7796,U_7794))],[f_2248_3]) ).

fof(f_2248_5,plain,
    ( ! [U_7789,U_7795,U_7797,U_7799,U_7801] :
        ( hBOOL(hAPP(hAPP(c_member(U_7795),U_7797),hAPP(c_Relation_ORange(U_7799,U_7795),U_7801)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7799,U_7795)),hAPP(hAPP(c_Product__Type_OPair(U_7799,U_7795),U_7789),U_7797)),U_7801)) )
    & ! [U_7800,U_7796,U_7794,U_7798] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7798,U_7794)),hAPP(hAPP(c_Product__Type_OPair(U_7798,U_7794),sK115(U_7800,U_7798,U_7796,U_7794)),U_7796)),U_7800))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7794),U_7796),hAPP(c_Relation_ORange(U_7798,U_7794),U_7800))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2248_4]) ).

cnf(f_2248_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7798,U_7794)),hAPP(hAPP(c_Product__Type_OPair(U_7798,U_7794),sK115(U_7800,U_7798,U_7796,U_7794)),U_7796)),U_7800))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7794),U_7796),hAPP(c_Relation_ORange(U_7798,U_7794),U_7800))) ),
    inference(clausify,[status(thm)],[f_2248_5]) ).

cnf(f_2248_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7795),U_7797),hAPP(c_Relation_ORange(U_7799,U_7795),U_7801)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7799,U_7795)),hAPP(hAPP(c_Product__Type_OPair(U_7799,U_7795),U_7789),U_7797)),U_7801)) ),
    inference(clausify,[status(thm)],[f_2248_5]) ).

fof(f_2249_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_2249_2,plain,
    ! [U_7805,U_7804,U_7803,U_7802] :
      ( ( hBOOL(hAPP(c_Predicate_ORangeP(U_7802,U_7803,hAPP(hAPP(c_COMBC(U_7802,tc_fun(tc_prod(U_7802,U_7803),tc_HOL_Obool),tc_fun(U_7803,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7803,tc_fun(tc_fun(tc_prod(U_7802,U_7803),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7802,U_7803),tc_HOL_Obool),tc_fun(U_7803,tc_HOL_Obool)),U_7802),c_COMBC(U_7803,tc_fun(tc_prod(U_7802,U_7803),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7803,tc_prod(U_7802,U_7803)),tc_fun(U_7803,tc_fun(tc_fun(tc_prod(U_7802,U_7803),tc_HOL_Obool),tc_HOL_Obool)),U_7802),hAPP(c_COMBB(tc_prod(U_7802,U_7803),tc_fun(tc_fun(tc_prod(U_7802,U_7803),tc_HOL_Obool),tc_HOL_Obool),U_7803),c_member(tc_prod(U_7802,U_7803)))),c_Product__Type_OPair(U_7802,U_7803)))),U_7804)),U_7805))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7803),U_7805),hAPP(c_Relation_ORange(U_7802,U_7803),U_7804))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_7803),U_7805),hAPP(c_Relation_ORange(U_7802,U_7803),U_7804)))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_7802,U_7803,hAPP(hAPP(c_COMBC(U_7802,tc_fun(tc_prod(U_7802,U_7803),tc_HOL_Obool),tc_fun(U_7803,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7803,tc_fun(tc_fun(tc_prod(U_7802,U_7803),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7802,U_7803),tc_HOL_Obool),tc_fun(U_7803,tc_HOL_Obool)),U_7802),c_COMBC(U_7803,tc_fun(tc_prod(U_7802,U_7803),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7803,tc_prod(U_7802,U_7803)),tc_fun(U_7803,tc_fun(tc_fun(tc_prod(U_7802,U_7803),tc_HOL_Obool),tc_HOL_Obool)),U_7802),hAPP(c_COMBB(tc_prod(U_7802,U_7803),tc_fun(tc_fun(tc_prod(U_7802,U_7803),tc_HOL_Obool),tc_HOL_Obool),U_7803),c_member(tc_prod(U_7802,U_7803)))),c_Product__Type_OPair(U_7802,U_7803)))),U_7804)),U_7805)) ) ),
    inference(variable_rename,[status(thm)],[f_2249_1]) ).

fof(f_2249_3,plain,
    ( ! [U_7813,U_7811,U_7809,U_7807] :
        ( hBOOL(hAPP(c_Predicate_ORangeP(U_7807,U_7809,hAPP(hAPP(c_COMBC(U_7807,tc_fun(tc_prod(U_7807,U_7809),tc_HOL_Obool),tc_fun(U_7809,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7809,tc_fun(tc_fun(tc_prod(U_7807,U_7809),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7807,U_7809),tc_HOL_Obool),tc_fun(U_7809,tc_HOL_Obool)),U_7807),c_COMBC(U_7809,tc_fun(tc_prod(U_7807,U_7809),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7809,tc_prod(U_7807,U_7809)),tc_fun(U_7809,tc_fun(tc_fun(tc_prod(U_7807,U_7809),tc_HOL_Obool),tc_HOL_Obool)),U_7807),hAPP(c_COMBB(tc_prod(U_7807,U_7809),tc_fun(tc_fun(tc_prod(U_7807,U_7809),tc_HOL_Obool),tc_HOL_Obool),U_7809),c_member(tc_prod(U_7807,U_7809)))),c_Product__Type_OPair(U_7807,U_7809)))),U_7811)),U_7813))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7809),U_7813),hAPP(c_Relation_ORange(U_7807,U_7809),U_7811))) )
    & ! [U_7812,U_7810,U_7808,U_7806] :
        ( hBOOL(hAPP(hAPP(c_member(U_7808),U_7812),hAPP(c_Relation_ORange(U_7806,U_7808),U_7810)))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_7806,U_7808,hAPP(hAPP(c_COMBC(U_7806,tc_fun(tc_prod(U_7806,U_7808),tc_HOL_Obool),tc_fun(U_7808,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7808,tc_fun(tc_fun(tc_prod(U_7806,U_7808),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7806,U_7808),tc_HOL_Obool),tc_fun(U_7808,tc_HOL_Obool)),U_7806),c_COMBC(U_7808,tc_fun(tc_prod(U_7806,U_7808),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7808,tc_prod(U_7806,U_7808)),tc_fun(U_7808,tc_fun(tc_fun(tc_prod(U_7806,U_7808),tc_HOL_Obool),tc_HOL_Obool)),U_7806),hAPP(c_COMBB(tc_prod(U_7806,U_7808),tc_fun(tc_fun(tc_prod(U_7806,U_7808),tc_HOL_Obool),tc_HOL_Obool),U_7808),c_member(tc_prod(U_7806,U_7808)))),c_Product__Type_OPair(U_7806,U_7808)))),U_7810)),U_7812)) ) ),
    inference(miniscope,[status(thm)],[f_2249_2]) ).

fof(f_2249_4,plain,
    ( ! [U_7807,U_7809,U_7811,U_7813] :
        ( hBOOL(hAPP(c_Predicate_ORangeP(U_7807,U_7809,hAPP(hAPP(c_COMBC(U_7807,tc_fun(tc_prod(U_7807,U_7809),tc_HOL_Obool),tc_fun(U_7809,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7809,tc_fun(tc_fun(tc_prod(U_7807,U_7809),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7807,U_7809),tc_HOL_Obool),tc_fun(U_7809,tc_HOL_Obool)),U_7807),c_COMBC(U_7809,tc_fun(tc_prod(U_7807,U_7809),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7809,tc_prod(U_7807,U_7809)),tc_fun(U_7809,tc_fun(tc_fun(tc_prod(U_7807,U_7809),tc_HOL_Obool),tc_HOL_Obool)),U_7807),hAPP(c_COMBB(tc_prod(U_7807,U_7809),tc_fun(tc_fun(tc_prod(U_7807,U_7809),tc_HOL_Obool),tc_HOL_Obool),U_7809),c_member(tc_prod(U_7807,U_7809)))),c_Product__Type_OPair(U_7807,U_7809)))),U_7811)),U_7813))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7809),U_7813),hAPP(c_Relation_ORange(U_7807,U_7809),U_7811))) )
    & ! [U_7812,U_7810,U_7808,U_7806] :
        ( hBOOL(hAPP(hAPP(c_member(U_7808),U_7812),hAPP(c_Relation_ORange(U_7806,U_7808),U_7810)))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_7806,U_7808,hAPP(hAPP(c_COMBC(U_7806,tc_fun(tc_prod(U_7806,U_7808),tc_HOL_Obool),tc_fun(U_7808,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7808,tc_fun(tc_fun(tc_prod(U_7806,U_7808),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7806,U_7808),tc_HOL_Obool),tc_fun(U_7808,tc_HOL_Obool)),U_7806),c_COMBC(U_7808,tc_fun(tc_prod(U_7806,U_7808),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7808,tc_prod(U_7806,U_7808)),tc_fun(U_7808,tc_fun(tc_fun(tc_prod(U_7806,U_7808),tc_HOL_Obool),tc_HOL_Obool)),U_7806),hAPP(c_COMBB(tc_prod(U_7806,U_7808),tc_fun(tc_fun(tc_prod(U_7806,U_7808),tc_HOL_Obool),tc_HOL_Obool),U_7808),c_member(tc_prod(U_7806,U_7808)))),c_Product__Type_OPair(U_7806,U_7808)))),U_7810)),U_7812)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2249_3]) ).

cnf(f_2249_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7808),U_7812),hAPP(c_Relation_ORange(U_7806,U_7808),U_7810)))
    | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_7806,U_7808,hAPP(hAPP(c_COMBC(U_7806,tc_fun(tc_prod(U_7806,U_7808),tc_HOL_Obool),tc_fun(U_7808,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7808,tc_fun(tc_fun(tc_prod(U_7806,U_7808),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7806,U_7808),tc_HOL_Obool),tc_fun(U_7808,tc_HOL_Obool)),U_7806),c_COMBC(U_7808,tc_fun(tc_prod(U_7806,U_7808),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7808,tc_prod(U_7806,U_7808)),tc_fun(U_7808,tc_fun(tc_fun(tc_prod(U_7806,U_7808),tc_HOL_Obool),tc_HOL_Obool)),U_7806),hAPP(c_COMBB(tc_prod(U_7806,U_7808),tc_fun(tc_fun(tc_prod(U_7806,U_7808),tc_HOL_Obool),tc_HOL_Obool),U_7808),c_member(tc_prod(U_7806,U_7808)))),c_Product__Type_OPair(U_7806,U_7808)))),U_7810)),U_7812)) ),
    inference(clausify,[status(thm)],[f_2249_4]) ).

cnf(f_2249_6,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(U_7807,U_7809,hAPP(hAPP(c_COMBC(U_7807,tc_fun(tc_prod(U_7807,U_7809),tc_HOL_Obool),tc_fun(U_7809,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7809,tc_fun(tc_fun(tc_prod(U_7807,U_7809),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_7807,U_7809),tc_HOL_Obool),tc_fun(U_7809,tc_HOL_Obool)),U_7807),c_COMBC(U_7809,tc_fun(tc_prod(U_7807,U_7809),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_7809,tc_prod(U_7807,U_7809)),tc_fun(U_7809,tc_fun(tc_fun(tc_prod(U_7807,U_7809),tc_HOL_Obool),tc_HOL_Obool)),U_7807),hAPP(c_COMBB(tc_prod(U_7807,U_7809),tc_fun(tc_fun(tc_prod(U_7807,U_7809),tc_HOL_Obool),tc_HOL_Obool),U_7809),c_member(tc_prod(U_7807,U_7809)))),c_Product__Type_OPair(U_7807,U_7809)))),U_7811)),U_7813))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7809),U_7813),hAPP(c_Relation_ORange(U_7807,U_7809),U_7811))) ),
    inference(clausify,[status(thm)],[f_2249_4]) ).

fof(f_2250_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_2250_2,plain,
    ! [U_7817,U_7816,U_7815] :
      ( ? [U_7814] :
          ( U_7816 = hAPP(hAPP(c_Product__Type_OPair(U_7815,U_7815),U_7814),U_7814)
          & hBOOL(hAPP(hAPP(c_member(U_7815),U_7814),U_7817)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7815,U_7815)),U_7816),c_Relation_OId__on(U_7815,U_7817))) ),
    inference(variable_rename,[status(thm)],[f_2250_1]) ).

fof(f_2250_3,plain,
    ! [U_7817,U_7816,U_7815] :
      ( ( U_7816 = hAPP(hAPP(c_Product__Type_OPair(U_7815,U_7815),sK116(U_7817,U_7816,U_7815)),sK116(U_7817,U_7816,U_7815))
        & hBOOL(hAPP(hAPP(c_member(U_7815),sK116(U_7817,U_7816,U_7815)),U_7817)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7815,U_7815)),U_7816),c_Relation_OId__on(U_7815,U_7817))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK116]),skolemize(U_7814,sK116(U_7817,U_7816,U_7815))],[f_2250_2]) ).

fof(f_2250_4,plain,
    ( ! [U_7815,U_7816,U_7817] :
        ( U_7816 = hAPP(hAPP(c_Product__Type_OPair(U_7815,U_7815),sK116(U_7817,U_7816,U_7815)),sK116(U_7817,U_7816,U_7815))
        | ~ sP680(U_7815,U_7816,U_7817) )
    & ! [U_7815,U_7816,U_7817] :
        ( hBOOL(hAPP(hAPP(c_member(U_7815),sK116(U_7817,U_7816,U_7815)),U_7817))
        | ~ sP680(U_7815,U_7816,U_7817) )
    & ! [U_7815,U_7816,U_7817] :
        ( sP680(U_7815,U_7816,U_7817)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7815,U_7815)),U_7816),c_Relation_OId__on(U_7815,U_7817))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP680])],[f_2250_3]) ).

cnf(f_2250_5,plain,
    ( sP680(U_7815,U_7816,U_7817)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7815,U_7815)),U_7816),c_Relation_OId__on(U_7815,U_7817))) ),
    inference(clausify,[status(thm)],[f_2250_4]) ).

cnf(f_2250_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7815),sK116(U_7817,U_7816,U_7815)),U_7817))
    | ~ sP680(U_7815,U_7816,U_7817) ),
    inference(clausify,[status(thm)],[f_2250_4]) ).

cnf(f_2250_7,plain,
    ( U_7816 = hAPP(hAPP(c_Product__Type_OPair(U_7815,U_7815),sK116(U_7817,U_7816,U_7815)),sK116(U_7817,U_7816,U_7815))
    | ~ sP680(U_7815,U_7816,U_7817) ),
    inference(clausify,[status(thm)],[f_2250_4]) ).

fof(f_2251_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_2251_2,plain,
    ! [U_7822,U_7821,U_7820,U_7819] :
      ( ? [U_7818] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_7821,U_7819)),hAPP(hAPP(c_Product__Type_OPair(U_7821,U_7819),U_7818),U_7820)),U_7822))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7819),U_7820),hAPP(c_Relation_ORange(U_7821,U_7819),U_7822))) ),
    inference(variable_rename,[status(thm)],[f_2251_1]) ).

fof(f_2251_3,plain,
    ! [U_7822,U_7821,U_7820,U_7819] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7821,U_7819)),hAPP(hAPP(c_Product__Type_OPair(U_7821,U_7819),sK117(U_7822,U_7821,U_7820,U_7819)),U_7820)),U_7822))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7819),U_7820),hAPP(c_Relation_ORange(U_7821,U_7819),U_7822))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK117]),skolemize(U_7818,sK117(U_7822,U_7821,U_7820,U_7819))],[f_2251_2]) ).

fof(f_2251_4,plain,
    ! [U_7819,U_7820,U_7821,U_7822] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7821,U_7819)),hAPP(hAPP(c_Product__Type_OPair(U_7821,U_7819),sK117(U_7822,U_7821,U_7820,U_7819)),U_7820)),U_7822))
      | ~ hBOOL(hAPP(hAPP(c_member(U_7819),U_7820),hAPP(c_Relation_ORange(U_7821,U_7819),U_7822))) ),
    inference(definitional_conversion,[status(esa)],[f_2251_3]) ).

cnf(f_2251_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7821,U_7819)),hAPP(hAPP(c_Product__Type_OPair(U_7821,U_7819),sK117(U_7822,U_7821,U_7820,U_7819)),U_7820)),U_7822))
    | ~ hBOOL(hAPP(hAPP(c_member(U_7819),U_7820),hAPP(c_Relation_ORange(U_7821,U_7819),U_7822))) ),
    inference(clausify,[status(thm)],[f_2251_4]) ).

fof(f_2252_1,plain,
    ! [V_P_H_2,V_Pa_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_Pa_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_Pa_2,B_x))
              & hBOOL(hAPP(V_P_H_2,B_x)) )
            | ( ~ hBOOL(hAPP(V_P_H_2,B_x))
              & hBOOL(hAPP(V_Pa_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_2252_2,plain,
    ! [U_7825,U_7824] :
      ( 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_7824)) = 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_7825))
      | ? [U_7823] :
          ( ( ( ~ hBOOL(hAPP(U_7824,U_7823))
              & hBOOL(hAPP(U_7825,U_7823)) )
            | ( ~ hBOOL(hAPP(U_7825,U_7823))
              & hBOOL(hAPP(U_7824,U_7823)) ) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_7823)) ) ),
    inference(variable_rename,[status(thm)],[f_2252_1]) ).

fof(f_2252_3,plain,
    ! [U_7825,U_7824] :
      ( 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_7824)) = 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_7825))
      | ( ( ( ~ hBOOL(hAPP(U_7824,sK118(U_7825,U_7824)))
            & hBOOL(hAPP(U_7825,sK118(U_7825,U_7824))) )
          | ( ~ hBOOL(hAPP(U_7825,sK118(U_7825,U_7824)))
            & hBOOL(hAPP(U_7824,sK118(U_7825,U_7824))) ) )
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK118(U_7825,U_7824))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK118]),skolemize(U_7823,sK118(U_7825,U_7824))],[f_2252_2]) ).

fof(f_2252_4,plain,
    ( ! [U_7824,U_7825] :
        ( ~ hBOOL(hAPP(U_7824,sK118(U_7825,U_7824)))
        | ~ sP682(U_7824,U_7825) )
    & ! [U_7824,U_7825] :
        ( hBOOL(hAPP(U_7825,sK118(U_7825,U_7824)))
        | ~ sP682(U_7824,U_7825) )
    & ! [U_7824,U_7825] :
        ( ~ hBOOL(hAPP(U_7825,sK118(U_7825,U_7824)))
        | ~ sP681(U_7824,U_7825) )
    & ! [U_7824,U_7825] :
        ( hBOOL(hAPP(U_7824,sK118(U_7825,U_7824)))
        | ~ sP681(U_7824,U_7825) )
    & ! [U_7824,U_7825] :
        ( sP682(U_7824,U_7825)
        | sP681(U_7824,U_7825)
        | ~ sP683(U_7824,U_7825) )
    & ! [U_7824,U_7825] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK118(U_7825,U_7824)))
        | ~ sP683(U_7824,U_7825) )
    & ! [U_7824,U_7825] :
        ( 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_7824)) = 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_7825))
        | sP683(U_7824,U_7825) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP681,sP682,sP683])],[f_2252_3]) ).

cnf(f_2252_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_7824)) = 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_7825))
    | sP683(U_7824,U_7825) ),
    inference(clausify,[status(thm)],[f_2252_4]) ).

cnf(f_2252_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK118(U_7825,U_7824)))
    | ~ sP683(U_7824,U_7825) ),
    inference(clausify,[status(thm)],[f_2252_4]) ).

cnf(f_2252_7,plain,
    ( sP682(U_7824,U_7825)
    | sP681(U_7824,U_7825)
    | ~ sP683(U_7824,U_7825) ),
    inference(clausify,[status(thm)],[f_2252_4]) ).

cnf(f_2252_8,plain,
    ( hBOOL(hAPP(U_7824,sK118(U_7825,U_7824)))
    | ~ sP681(U_7824,U_7825) ),
    inference(clausify,[status(thm)],[f_2252_4]) ).

cnf(f_2252_9,plain,
    ( ~ hBOOL(hAPP(U_7825,sK118(U_7825,U_7824)))
    | ~ sP681(U_7824,U_7825) ),
    inference(clausify,[status(thm)],[f_2252_4]) ).

cnf(f_2252_10,plain,
    ( hBOOL(hAPP(U_7825,sK118(U_7825,U_7824)))
    | ~ sP682(U_7824,U_7825) ),
    inference(clausify,[status(thm)],[f_2252_4]) ).

cnf(f_2252_11,plain,
    ( ~ hBOOL(hAPP(U_7824,sK118(U_7825,U_7824)))
    | ~ sP682(U_7824,U_7825) ),
    inference(clausify,[status(thm)],[f_2252_4]) ).

fof(f_2253_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_2253_2,plain,
    ! [U_7830,U_7829,U_7828,U_7827,U_7826] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(U_7829,U_7830,U_7826),U_7828))
      | ~ hBOOL(hAPP(hAPP(U_7826,U_7827),U_7828)) ),
    inference(variable_rename,[status(thm)],[f_2253_1]) ).

fof(f_2253_3,plain,
    ! [U_7830,U_7828,U_7826,U_7829,U_7827] :
      ( hBOOL(hAPP(c_Predicate_ORangeP(U_7829,U_7830,U_7826),U_7828))
      | ~ hBOOL(hAPP(hAPP(U_7826,U_7827),U_7828)) ),
    inference(definitional_conversion,[status(esa)],[f_2253_2]) ).

cnf(f_2253_4,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(U_7829,U_7830,U_7826),U_7828))
    | ~ hBOOL(hAPP(hAPP(U_7826,U_7827),U_7828)) ),
    inference(clausify,[status(thm)],[f_2253_3]) ).

fof(f_2254_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_2254_2,plain,
    ! [U_7836,U_7835,U_7834,U_7833] :
      ( ( hBOOL(hAPP(c_Predicate_ORangeP(U_7833,U_7834,U_7835),U_7836))
        | ! [U_7832] : ~ hBOOL(hAPP(hAPP(U_7835,U_7832),U_7836)) )
      & ( ? [U_7831] : hBOOL(hAPP(hAPP(U_7835,U_7831),U_7836))
        | ~ hBOOL(hAPP(c_Predicate_ORangeP(U_7833,U_7834,U_7835),U_7836)) ) ),
    inference(variable_rename,[status(thm)],[f_2254_1]) ).

fof(f_2254_3,plain,
    ( ! [U_7844,U_7842] :
        ( ! [U_7840,U_7838] : hBOOL(hAPP(c_Predicate_ORangeP(U_7838,U_7840,U_7842),U_7844))
        | ! [U_7832] : ~ hBOOL(hAPP(hAPP(U_7842,U_7832),U_7844)) )
    & ! [U_7843,U_7841] :
        ( ! [U_7839,U_7837] : ~ hBOOL(hAPP(c_Predicate_ORangeP(U_7837,U_7839,U_7841),U_7843))
        | ? [U_7831] : hBOOL(hAPP(hAPP(U_7841,U_7831),U_7843)) ) ),
    inference(miniscope,[status(thm)],[f_2254_2]) ).

fof(f_2254_4,plain,
    ( ! [U_7844,U_7842] :
        ( ! [U_7840,U_7838] : hBOOL(hAPP(c_Predicate_ORangeP(U_7838,U_7840,U_7842),U_7844))
        | ! [U_7832] : ~ hBOOL(hAPP(hAPP(U_7842,U_7832),U_7844)) )
    & ! [U_7843,U_7841] :
        ( ! [U_7839,U_7837] : ~ hBOOL(hAPP(c_Predicate_ORangeP(U_7837,U_7839,U_7841),U_7843))
        | hBOOL(hAPP(hAPP(U_7841,sK119(U_7843,U_7841)),U_7843)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK119]),skolemize(U_7831,sK119(U_7843,U_7841))],[f_2254_3]) ).

fof(f_2254_5,plain,
    ( ! [U_7832,U_7844,U_7838,U_7840,U_7842] :
        ( hBOOL(hAPP(c_Predicate_ORangeP(U_7838,U_7840,U_7842),U_7844))
        | ~ hBOOL(hAPP(hAPP(U_7842,U_7832),U_7844)) )
    & ! [U_7841,U_7837,U_7839,U_7843] :
        ( ~ hBOOL(hAPP(c_Predicate_ORangeP(U_7837,U_7839,U_7841),U_7843))
        | hBOOL(hAPP(hAPP(U_7841,sK119(U_7843,U_7841)),U_7843)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2254_4]) ).

cnf(f_2254_6,plain,
    ( ~ hBOOL(hAPP(c_Predicate_ORangeP(U_7837,U_7839,U_7841),U_7843))
    | hBOOL(hAPP(hAPP(U_7841,sK119(U_7843,U_7841)),U_7843)) ),
    inference(clausify,[status(thm)],[f_2254_5]) ).

cnf(f_2254_7,plain,
    ( hBOOL(hAPP(c_Predicate_ORangeP(U_7838,U_7840,U_7842),U_7844))
    | ~ hBOOL(hAPP(hAPP(U_7842,U_7832),U_7844)) ),
    inference(clausify,[status(thm)],[f_2254_5]) ).

fof(f_2255_1,plain,
    ! [V_Pa_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_Pa_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_Pa_2))),
    inference(fof_nnf,[status(thm)],[fact_Range__Collect__split]) ).

fof(f_2255_2,plain,
    ! [U_7847,U_7846,U_7845] : hAPP(c_Relation_ORange(U_7845,U_7846),hAPP(c_Set_OCollect(tc_prod(U_7845,U_7846)),hAPP(c_Product__Type_Oprod_Oprod__case(U_7845,U_7846,tc_HOL_Obool),U_7847))) = hAPP(c_Set_OCollect(U_7846),hAPP(hAPP(c_COMBB(tc_fun(U_7845,tc_HOL_Obool),tc_HOL_Obool,U_7846),c_HOL_OEx(U_7845)),hAPP(c_COMBC(U_7845,U_7846,tc_HOL_Obool),U_7847))),
    inference(variable_rename,[status(thm)],[f_2255_1]) ).

fof(f_2255_3,plain,
    ! [U_7845,U_7846,U_7847] : hAPP(c_Relation_ORange(U_7845,U_7846),hAPP(c_Set_OCollect(tc_prod(U_7845,U_7846)),hAPP(c_Product__Type_Oprod_Oprod__case(U_7845,U_7846,tc_HOL_Obool),U_7847))) = hAPP(c_Set_OCollect(U_7846),hAPP(hAPP(c_COMBB(tc_fun(U_7845,tc_HOL_Obool),tc_HOL_Obool,U_7846),c_HOL_OEx(U_7845)),hAPP(c_COMBC(U_7845,U_7846,tc_HOL_Obool),U_7847))),
    inference(definitional_conversion,[status(esa)],[f_2255_2]) ).

cnf(f_2255_4,plain,
    hAPP(c_Relation_ORange(U_7845,U_7846),hAPP(c_Set_OCollect(tc_prod(U_7845,U_7846)),hAPP(c_Product__Type_Oprod_Oprod__case(U_7845,U_7846,tc_HOL_Obool),U_7847))) = hAPP(c_Set_OCollect(U_7846),hAPP(hAPP(c_COMBB(tc_fun(U_7845,tc_HOL_Obool),tc_HOL_Obool,U_7846),c_HOL_OEx(U_7845)),hAPP(c_COMBC(U_7845,U_7846,tc_HOL_Obool),U_7847))),
    inference(clausify,[status(thm)],[f_2255_3]) ).

fof(f_2256_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_2256_2,plain,
    ! [U_7849,U_7848] : c_Relation_Oirrefl(U_7848,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_7848,U_7848),tc_HOL_Obool)),U_7849),c_Relation_OId(U_7848))),
    inference(variable_rename,[status(thm)],[f_2256_1]) ).

fof(f_2256_3,plain,
    ! [U_7848,U_7849] : c_Relation_Oirrefl(U_7848,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_7848,U_7848),tc_HOL_Obool)),U_7849),c_Relation_OId(U_7848))),
    inference(definitional_conversion,[status(esa)],[f_2256_2]) ).

cnf(f_2256_4,plain,
    c_Relation_Oirrefl(U_7848,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_7848,U_7848),tc_HOL_Obool)),U_7849),c_Relation_OId(U_7848))),
    inference(clausify,[status(thm)],[f_2256_3]) ).

fof(f_2257_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_2257_2,plain,
    ! [U_7851,U_7850] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7850),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_7851)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7851),U_7850))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7850),U_7851)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7851),U_7850))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7850),U_7851)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7850),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_7851))) ) ),
    inference(variable_rename,[status(thm)],[f_2257_1]) ).

fof(f_2257_3,plain,
    ( ! [U_7855,U_7853] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7853),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_7855)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7855),U_7853))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7853),U_7855)) )
    & ! [U_7854,U_7852] :
        ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7854),U_7852))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7852),U_7854)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7852),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_7854))) ) ),
    inference(miniscope,[status(thm)],[f_2257_2]) ).

fof(f_2257_4,plain,
    ( ! [U_7852,U_7854] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7854),U_7852))
        | ~ sP684(U_7852,U_7854) )
    & ! [U_7852,U_7854] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7852),U_7854))
        | ~ sP684(U_7852,U_7854) )
    & ! [U_7855,U_7853] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7853),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_7855)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7855),U_7853))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7853),U_7855)) )
    & ! [U_7852,U_7854] :
        ( sP684(U_7852,U_7854)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7852),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_7854))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP684])],[f_2257_3]) ).

cnf(f_2257_5,plain,
    ( sP684(U_7852,U_7854)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7852),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_7854))) ),
    inference(clausify,[status(thm)],[f_2257_4]) ).

cnf(f_2257_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7853),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_7855)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7855),U_7853))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7853),U_7855)) ),
    inference(clausify,[status(thm)],[f_2257_4]) ).

cnf(f_2257_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7852),U_7854))
    | ~ sP684(U_7852,U_7854) ),
    inference(clausify,[status(thm)],[f_2257_4]) ).

cnf(f_2257_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7854),U_7852))
    | ~ sP684(U_7852,U_7854) ),
    inference(clausify,[status(thm)],[f_2257_4]) ).

fof(f_2258_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_2258_2,plain,
    ! [U_7857,U_7856] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7856),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_7857)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7856),U_7857))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7857),U_7856)) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7856),U_7857))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7857),U_7856)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7856),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_7857))) ) ),
    inference(variable_rename,[status(thm)],[f_2258_1]) ).

fof(f_2258_3,plain,
    ( ! [U_7861,U_7859] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7859),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_7861)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7859),U_7861))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7861),U_7859)) )
    & ! [U_7860,U_7858] :
        ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7858),U_7860))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7860),U_7858)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7858),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_7860))) ) ),
    inference(miniscope,[status(thm)],[f_2258_2]) ).

fof(f_2258_4,plain,
    ( ! [U_7858,U_7860] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7858),U_7860))
        | ~ sP685(U_7858,U_7860) )
    & ! [U_7858,U_7860] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7860),U_7858))
        | ~ sP685(U_7858,U_7860) )
    & ! [U_7859,U_7861] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7859),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_7861)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7859),U_7861))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7861),U_7859)) )
    & ! [U_7858,U_7860] :
        ( sP685(U_7858,U_7860)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7858),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_7860))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP685])],[f_2258_3]) ).

cnf(f_2258_5,plain,
    ( sP685(U_7858,U_7860)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7858),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_7860))) ),
    inference(clausify,[status(thm)],[f_2258_4]) ).

cnf(f_2258_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7859),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_7861)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7859),U_7861))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7861),U_7859)) ),
    inference(clausify,[status(thm)],[f_2258_4]) ).

cnf(f_2258_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7860),U_7858))
    | ~ sP685(U_7858,U_7860) ),
    inference(clausify,[status(thm)],[f_2258_4]) ).

cnf(f_2258_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7858),U_7860))
    | ~ sP685(U_7858,U_7860) ),
    inference(clausify,[status(thm)],[f_2258_4]) ).

fof(f_2259_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_2259_2,plain,
    ! [U_7863,U_7862] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_7862,U_7862)),hAPP(hAPP(c_Product__Type_OPair(U_7862,U_7862),U_7863),U_7863)),c_Relation_OId(U_7862))),
    inference(variable_rename,[status(thm)],[f_2259_1]) ).

fof(f_2259_3,plain,
    ! [U_7863,U_7862] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_7862,U_7862)),hAPP(hAPP(c_Product__Type_OPair(U_7862,U_7862),U_7863),U_7863)),c_Relation_OId(U_7862))),
    inference(definitional_conversion,[status(esa)],[f_2259_2]) ).

cnf(f_2259_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(U_7862,U_7862)),hAPP(hAPP(c_Product__Type_OPair(U_7862,U_7862),U_7863),U_7863)),c_Relation_OId(U_7862))),
    inference(clausify,[status(thm)],[f_2259_3]) ).

fof(f_2260_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_2260_2,plain,
    ! [U_7864] : c_Relation_OId(U_7864) = hAPP(c_Set_OCollect(tc_prod(U_7864,U_7864)),hAPP(hAPP(c_COMBB(tc_fun(U_7864,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_7864,U_7864)),c_HOL_OEx(U_7864)),hAPP(hAPP(c_COMBC(tc_prod(U_7864,U_7864),tc_fun(U_7864,tc_prod(U_7864,U_7864)),tc_fun(U_7864,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_7864,U_7864),tc_HOL_Obool),tc_fun(tc_fun(U_7864,tc_prod(U_7864,U_7864)),tc_fun(U_7864,tc_HOL_Obool)),tc_prod(U_7864,U_7864)),c_COMBB(tc_prod(U_7864,U_7864),tc_HOL_Obool,U_7864)),c_fequal)),hAPP(hAPP(c_COMBS(U_7864,U_7864,tc_prod(U_7864,U_7864)),c_Product__Type_OPair(U_7864,U_7864)),c_COMBI(U_7864))))),
    inference(variable_rename,[status(thm)],[f_2260_1]) ).

fof(f_2260_3,plain,
    ! [U_7864] : c_Relation_OId(U_7864) = hAPP(c_Set_OCollect(tc_prod(U_7864,U_7864)),hAPP(hAPP(c_COMBB(tc_fun(U_7864,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_7864,U_7864)),c_HOL_OEx(U_7864)),hAPP(hAPP(c_COMBC(tc_prod(U_7864,U_7864),tc_fun(U_7864,tc_prod(U_7864,U_7864)),tc_fun(U_7864,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_7864,U_7864),tc_HOL_Obool),tc_fun(tc_fun(U_7864,tc_prod(U_7864,U_7864)),tc_fun(U_7864,tc_HOL_Obool)),tc_prod(U_7864,U_7864)),c_COMBB(tc_prod(U_7864,U_7864),tc_HOL_Obool,U_7864)),c_fequal)),hAPP(hAPP(c_COMBS(U_7864,U_7864,tc_prod(U_7864,U_7864)),c_Product__Type_OPair(U_7864,U_7864)),c_COMBI(U_7864))))),
    inference(definitional_conversion,[status(esa)],[f_2260_2]) ).

cnf(f_2260_4,plain,
    c_Relation_OId(U_7864) = hAPP(c_Set_OCollect(tc_prod(U_7864,U_7864)),hAPP(hAPP(c_COMBB(tc_fun(U_7864,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_7864,U_7864)),c_HOL_OEx(U_7864)),hAPP(hAPP(c_COMBC(tc_prod(U_7864,U_7864),tc_fun(U_7864,tc_prod(U_7864,U_7864)),tc_fun(U_7864,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_7864,U_7864),tc_HOL_Obool),tc_fun(tc_fun(U_7864,tc_prod(U_7864,U_7864)),tc_fun(U_7864,tc_HOL_Obool)),tc_prod(U_7864,U_7864)),c_COMBB(tc_prod(U_7864,U_7864),tc_HOL_Obool,U_7864)),c_fequal)),hAPP(hAPP(c_COMBS(U_7864,U_7864,tc_prod(U_7864,U_7864)),c_Product__Type_OPair(U_7864,U_7864)),c_COMBI(U_7864))))),
    inference(clausify,[status(thm)],[f_2260_3]) ).

fof(f_2261_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_2261_2,plain,
    ! [U_7865] : hAPP(c_Relation_Oconverse(U_7865,U_7865),c_Relation_OId(U_7865)) = c_Relation_OId(U_7865),
    inference(variable_rename,[status(thm)],[f_2261_1]) ).

fof(f_2261_3,plain,
    ! [U_7865] : hAPP(c_Relation_Oconverse(U_7865,U_7865),c_Relation_OId(U_7865)) = c_Relation_OId(U_7865),
    inference(definitional_conversion,[status(esa)],[f_2261_2]) ).

cnf(f_2261_4,plain,
    hAPP(c_Relation_Oconverse(U_7865,U_7865),c_Relation_OId(U_7865)) = c_Relation_OId(U_7865),
    inference(clausify,[status(thm)],[f_2261_3]) ).

fof(f_2262_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_2262_2,plain,
    ! [U_7869,U_7868,U_7867,U_7866] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_7866),U_7867),c_SetInterval_Oord_OlessThan(U_7866,U_7868,U_7869)))
        | ~ hBOOL(hAPP(hAPP(U_7868,U_7867),U_7869)) )
      & ( hBOOL(hAPP(hAPP(U_7868,U_7867),U_7869))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7866),U_7867),c_SetInterval_Oord_OlessThan(U_7866,U_7868,U_7869))) ) ),
    inference(variable_rename,[status(thm)],[f_2262_1]) ).

fof(f_2262_3,plain,
    ( ! [U_7877,U_7875,U_7873] :
        ( ! [U_7871] : hBOOL(hAPP(hAPP(c_member(U_7871),U_7873),c_SetInterval_Oord_OlessThan(U_7871,U_7875,U_7877)))
        | ~ hBOOL(hAPP(hAPP(U_7875,U_7873),U_7877)) )
    & ! [U_7876,U_7874,U_7872] :
        ( ! [U_7870] : ~ hBOOL(hAPP(hAPP(c_member(U_7870),U_7872),c_SetInterval_Oord_OlessThan(U_7870,U_7874,U_7876)))
        | hBOOL(hAPP(hAPP(U_7874,U_7872),U_7876)) ) ),
    inference(miniscope,[status(thm)],[f_2262_2]) ).

fof(f_2262_4,plain,
    ( ! [U_7871,U_7877,U_7873,U_7875] :
        ( hBOOL(hAPP(hAPP(c_member(U_7871),U_7873),c_SetInterval_Oord_OlessThan(U_7871,U_7875,U_7877)))
        | ~ hBOOL(hAPP(hAPP(U_7875,U_7873),U_7877)) )
    & ! [U_7872,U_7870,U_7876,U_7874] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7870),U_7872),c_SetInterval_Oord_OlessThan(U_7870,U_7874,U_7876)))
        | hBOOL(hAPP(hAPP(U_7874,U_7872),U_7876)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2262_3]) ).

cnf(f_2262_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7870),U_7872),c_SetInterval_Oord_OlessThan(U_7870,U_7874,U_7876)))
    | hBOOL(hAPP(hAPP(U_7874,U_7872),U_7876)) ),
    inference(clausify,[status(thm)],[f_2262_4]) ).

cnf(f_2262_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7871),U_7873),c_SetInterval_Oord_OlessThan(U_7871,U_7875,U_7877)))
    | ~ hBOOL(hAPP(hAPP(U_7875,U_7873),U_7877)) ),
    inference(clausify,[status(thm)],[f_2262_4]) ).

fof(f_2263_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_2263_2,plain,
    ! [U_7881,U_7880,U_7879,U_7878] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_7878),U_7879),c_SetInterval_Oord_OgreaterThan(U_7878,U_7880,U_7881)))
        | ~ hBOOL(hAPP(hAPP(U_7880,U_7881),U_7879)) )
      & ( hBOOL(hAPP(hAPP(U_7880,U_7881),U_7879))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7878),U_7879),c_SetInterval_Oord_OgreaterThan(U_7878,U_7880,U_7881))) ) ),
    inference(variable_rename,[status(thm)],[f_2263_1]) ).

fof(f_2263_3,plain,
    ( ! [U_7889,U_7887,U_7885] :
        ( ! [U_7883] : hBOOL(hAPP(hAPP(c_member(U_7883),U_7885),c_SetInterval_Oord_OgreaterThan(U_7883,U_7887,U_7889)))
        | ~ hBOOL(hAPP(hAPP(U_7887,U_7889),U_7885)) )
    & ! [U_7888,U_7886,U_7884] :
        ( ! [U_7882] : ~ hBOOL(hAPP(hAPP(c_member(U_7882),U_7884),c_SetInterval_Oord_OgreaterThan(U_7882,U_7886,U_7888)))
        | hBOOL(hAPP(hAPP(U_7886,U_7888),U_7884)) ) ),
    inference(miniscope,[status(thm)],[f_2263_2]) ).

fof(f_2263_4,plain,
    ( ! [U_7883,U_7885,U_7887,U_7889] :
        ( hBOOL(hAPP(hAPP(c_member(U_7883),U_7885),c_SetInterval_Oord_OgreaterThan(U_7883,U_7887,U_7889)))
        | ~ hBOOL(hAPP(hAPP(U_7887,U_7889),U_7885)) )
    & ! [U_7882,U_7884,U_7886,U_7888] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7882),U_7884),c_SetInterval_Oord_OgreaterThan(U_7882,U_7886,U_7888)))
        | hBOOL(hAPP(hAPP(U_7886,U_7888),U_7884)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2263_3]) ).

cnf(f_2263_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7882),U_7884),c_SetInterval_Oord_OgreaterThan(U_7882,U_7886,U_7888)))
    | hBOOL(hAPP(hAPP(U_7886,U_7888),U_7884)) ),
    inference(clausify,[status(thm)],[f_2263_4]) ).

cnf(f_2263_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7883),U_7885),c_SetInterval_Oord_OgreaterThan(U_7883,U_7887,U_7889)))
    | ~ hBOOL(hAPP(hAPP(U_7887,U_7889),U_7885)) ),
    inference(clausify,[status(thm)],[f_2263_4]) ).

fof(f_2264_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_2264_2,plain,
    ! [U_7892,U_7891,U_7890] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7890,U_7890)),hAPP(hAPP(c_Product__Type_OPair(U_7890,U_7890),U_7891),U_7892)),c_Relation_OId(U_7890)))
        | U_7891 != U_7892 )
      & ( U_7891 = U_7892
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7890,U_7890)),hAPP(hAPP(c_Product__Type_OPair(U_7890,U_7890),U_7891),U_7892)),c_Relation_OId(U_7890))) ) ),
    inference(variable_rename,[status(thm)],[f_2264_1]) ).

fof(f_2264_3,plain,
    ( ! [U_7898,U_7896] :
        ( ! [U_7894] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_7894,U_7894)),hAPP(hAPP(c_Product__Type_OPair(U_7894,U_7894),U_7896),U_7898)),c_Relation_OId(U_7894)))
        | U_7896 != U_7898 )
    & ! [U_7897,U_7895] :
        ( ! [U_7893] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7893,U_7893)),hAPP(hAPP(c_Product__Type_OPair(U_7893,U_7893),U_7895),U_7897)),c_Relation_OId(U_7893)))
        | U_7895 = U_7897 ) ),
    inference(miniscope,[status(thm)],[f_2264_2]) ).

fof(f_2264_4,plain,
    ( ! [U_7894,U_7896,U_7898] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7894,U_7894)),hAPP(hAPP(c_Product__Type_OPair(U_7894,U_7894),U_7896),U_7898)),c_Relation_OId(U_7894)))
        | U_7896 != U_7898 )
    & ! [U_7897,U_7895,U_7893] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7893,U_7893)),hAPP(hAPP(c_Product__Type_OPair(U_7893,U_7893),U_7895),U_7897)),c_Relation_OId(U_7893)))
        | U_7895 = U_7897 ) ),
    inference(definitional_conversion,[status(esa)],[f_2264_3]) ).

cnf(f_2264_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_7893,U_7893)),hAPP(hAPP(c_Product__Type_OPair(U_7893,U_7893),U_7895),U_7897)),c_Relation_OId(U_7893)))
    | U_7895 = U_7897 ),
    inference(clausify,[status(thm)],[f_2264_4]) ).

cnf(f_2264_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_7894,U_7894)),hAPP(hAPP(c_Product__Type_OPair(U_7894,U_7894),U_7896),U_7898)),c_Relation_OId(U_7894)))
    | U_7896 != U_7898 ),
    inference(clausify,[status(thm)],[f_2264_4]) ).

fof(f_2265_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_2265_2,plain,
    ! [U_7901,U_7900,U_7899] :
      ( ( c_Relation_Ototal__on(U_7899,U_7900,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_7899,U_7899),tc_HOL_Obool)),U_7901),c_Relation_OId(U_7899)))
        | ~ c_Relation_Ototal__on(U_7899,U_7900,U_7901) )
      & ( c_Relation_Ototal__on(U_7899,U_7900,U_7901)
        | ~ c_Relation_Ototal__on(U_7899,U_7900,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_7899,U_7899),tc_HOL_Obool)),U_7901),c_Relation_OId(U_7899))) ) ),
    inference(variable_rename,[status(thm)],[f_2265_1]) ).

fof(f_2265_3,plain,
    ( ! [U_7907,U_7905,U_7903] :
        ( c_Relation_Ototal__on(U_7903,U_7905,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_7903,U_7903),tc_HOL_Obool)),U_7907),c_Relation_OId(U_7903)))
        | ~ c_Relation_Ototal__on(U_7903,U_7905,U_7907) )
    & ! [U_7906,U_7904,U_7902] :
        ( c_Relation_Ototal__on(U_7902,U_7904,U_7906)
        | ~ c_Relation_Ototal__on(U_7902,U_7904,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_7902,U_7902),tc_HOL_Obool)),U_7906),c_Relation_OId(U_7902))) ) ),
    inference(miniscope,[status(thm)],[f_2265_2]) ).

fof(f_2265_4,plain,
    ( ! [U_7905,U_7903,U_7907] :
        ( c_Relation_Ototal__on(U_7903,U_7905,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_7903,U_7903),tc_HOL_Obool)),U_7907),c_Relation_OId(U_7903)))
        | ~ c_Relation_Ototal__on(U_7903,U_7905,U_7907) )
    & ! [U_7906,U_7904,U_7902] :
        ( c_Relation_Ototal__on(U_7902,U_7904,U_7906)
        | ~ c_Relation_Ototal__on(U_7902,U_7904,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_7902,U_7902),tc_HOL_Obool)),U_7906),c_Relation_OId(U_7902))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2265_3]) ).

cnf(f_2265_5,plain,
    ( c_Relation_Ototal__on(U_7902,U_7904,U_7906)
    | ~ c_Relation_Ototal__on(U_7902,U_7904,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_7902,U_7902),tc_HOL_Obool)),U_7906),c_Relation_OId(U_7902))) ),
    inference(clausify,[status(thm)],[f_2265_4]) ).

cnf(f_2265_6,plain,
    ( c_Relation_Ototal__on(U_7903,U_7905,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_7903,U_7903),tc_HOL_Obool)),U_7907),c_Relation_OId(U_7903)))
    | ~ c_Relation_Ototal__on(U_7903,U_7905,U_7907) ),
    inference(clausify,[status(thm)],[f_2265_4]) ).

fof(f_2266_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_2266_2,plain,
    ! [U_7909,U_7908] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7908),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7909)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7909),U_7908)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7909),U_7908))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7908),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7909))) ) ),
    inference(variable_rename,[status(thm)],[f_2266_1]) ).

fof(f_2266_3,plain,
    ( ! [U_7913,U_7911] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7911),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7913)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7913),U_7911)) )
    & ! [U_7912,U_7910] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7912),U_7910))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7910),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7912))) ) ),
    inference(miniscope,[status(thm)],[f_2266_2]) ).

fof(f_2266_4,plain,
    ( ! [U_7911,U_7913] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7911),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7913)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7913),U_7911)) )
    & ! [U_7912,U_7910] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7912),U_7910))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7910),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7912))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2266_3]) ).

cnf(f_2266_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7912),U_7910))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7910),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7912))) ),
    inference(clausify,[status(thm)],[f_2266_4]) ).

cnf(f_2266_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7911),c_SetInterval_Oord_OatLeast(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7913)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7913),U_7911)) ),
    inference(clausify,[status(thm)],[f_2266_4]) ).

fof(f_2267_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_2267_2,plain,
    ! [U_7915,U_7914] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7914),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7915)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7914),U_7915)) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7914),U_7915))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7914),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7915))) ) ),
    inference(variable_rename,[status(thm)],[f_2267_1]) ).

fof(f_2267_3,plain,
    ( ! [U_7919,U_7917] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7917),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7919)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7917),U_7919)) )
    & ! [U_7918,U_7916] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7916),U_7918))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7916),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7918))) ) ),
    inference(miniscope,[status(thm)],[f_2267_2]) ).

fof(f_2267_4,plain,
    ( ! [U_7917,U_7919] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7917),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7919)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7917),U_7919)) )
    & ! [U_7918,U_7916] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7916),U_7918))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7916),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7918))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2267_3]) ).

cnf(f_2267_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7916),U_7918))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7916),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7918))) ),
    inference(clausify,[status(thm)],[f_2267_4]) ).

cnf(f_2267_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_7917),c_SetInterval_Oord_OatMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7919)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_7917),U_7919)) ),
    inference(clausify,[status(thm)],[f_2267_4]) ).

fof(f_2268_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_2268_2,plain,
    ! [U_7923,U_7922,U_7921,U_7920] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_7920),U_7921),c_SetInterval_Oord_OatMost(U_7920,U_7922,U_7923)))
        | ~ hBOOL(hAPP(hAPP(U_7922,U_7921),U_7923)) )
      & ( hBOOL(hAPP(hAPP(U_7922,U_7921),U_7923))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7920),U_7921),c_SetInterval_Oord_OatMost(U_7920,U_7922,U_7923))) ) ),
    inference(variable_rename,[status(thm)],[f_2268_1]) ).

fof(f_2268_3,plain,
    ( ! [U_7931,U_7929,U_7927] :
        ( ! [U_7925] : hBOOL(hAPP(hAPP(c_member(U_7925),U_7927),c_SetInterval_Oord_OatMost(U_7925,U_7929,U_7931)))
        | ~ hBOOL(hAPP(hAPP(U_7929,U_7927),U_7931)) )
    & ! [U_7930,U_7928,U_7926] :
        ( ! [U_7924] : ~ hBOOL(hAPP(hAPP(c_member(U_7924),U_7926),c_SetInterval_Oord_OatMost(U_7924,U_7928,U_7930)))
        | hBOOL(hAPP(hAPP(U_7928,U_7926),U_7930)) ) ),
    inference(miniscope,[status(thm)],[f_2268_2]) ).

fof(f_2268_4,plain,
    ( ! [U_7931,U_7925,U_7927,U_7929] :
        ( hBOOL(hAPP(hAPP(c_member(U_7925),U_7927),c_SetInterval_Oord_OatMost(U_7925,U_7929,U_7931)))
        | ~ hBOOL(hAPP(hAPP(U_7929,U_7927),U_7931)) )
    & ! [U_7926,U_7924,U_7930,U_7928] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7924),U_7926),c_SetInterval_Oord_OatMost(U_7924,U_7928,U_7930)))
        | hBOOL(hAPP(hAPP(U_7928,U_7926),U_7930)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2268_3]) ).

cnf(f_2268_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7924),U_7926),c_SetInterval_Oord_OatMost(U_7924,U_7928,U_7930)))
    | hBOOL(hAPP(hAPP(U_7928,U_7926),U_7930)) ),
    inference(clausify,[status(thm)],[f_2268_4]) ).

cnf(f_2268_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7925),U_7927),c_SetInterval_Oord_OatMost(U_7925,U_7929,U_7931)))
    | ~ hBOOL(hAPP(hAPP(U_7929,U_7927),U_7931)) ),
    inference(clausify,[status(thm)],[f_2268_4]) ).

fof(f_2269_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_2269_2,plain,
    ! [U_7935,U_7934,U_7933,U_7932] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_7932),U_7933),c_SetInterval_Oord_OatLeast(U_7932,U_7934,U_7935)))
        | ~ hBOOL(hAPP(hAPP(U_7934,U_7935),U_7933)) )
      & ( hBOOL(hAPP(hAPP(U_7934,U_7935),U_7933))
        | ~ hBOOL(hAPP(hAPP(c_member(U_7932),U_7933),c_SetInterval_Oord_OatLeast(U_7932,U_7934,U_7935))) ) ),
    inference(variable_rename,[status(thm)],[f_2269_1]) ).

fof(f_2269_3,plain,
    ( ! [U_7943,U_7941,U_7939] :
        ( ! [U_7937] : hBOOL(hAPP(hAPP(c_member(U_7937),U_7939),c_SetInterval_Oord_OatLeast(U_7937,U_7941,U_7943)))
        | ~ hBOOL(hAPP(hAPP(U_7941,U_7943),U_7939)) )
    & ! [U_7942,U_7940,U_7938] :
        ( ! [U_7936] : ~ hBOOL(hAPP(hAPP(c_member(U_7936),U_7938),c_SetInterval_Oord_OatLeast(U_7936,U_7940,U_7942)))
        | hBOOL(hAPP(hAPP(U_7940,U_7942),U_7938)) ) ),
    inference(miniscope,[status(thm)],[f_2269_2]) ).

fof(f_2269_4,plain,
    ( ! [U_7937,U_7939,U_7941,U_7943] :
        ( hBOOL(hAPP(hAPP(c_member(U_7937),U_7939),c_SetInterval_Oord_OatLeast(U_7937,U_7941,U_7943)))
        | ~ hBOOL(hAPP(hAPP(U_7941,U_7943),U_7939)) )
    & ! [U_7940,U_7938,U_7936,U_7942] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7936),U_7938),c_SetInterval_Oord_OatLeast(U_7936,U_7940,U_7942)))
        | hBOOL(hAPP(hAPP(U_7940,U_7942),U_7938)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2269_3]) ).

cnf(f_2269_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7936),U_7938),c_SetInterval_Oord_OatLeast(U_7936,U_7940,U_7942)))
    | hBOOL(hAPP(hAPP(U_7940,U_7942),U_7938)) ),
    inference(clausify,[status(thm)],[f_2269_4]) ).

cnf(f_2269_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7937),U_7939),c_SetInterval_Oord_OatLeast(U_7937,U_7941,U_7943)))
    | ~ hBOOL(hAPP(hAPP(U_7941,U_7943),U_7939)) ),
    inference(clausify,[status(thm)],[f_2269_4]) ).

fof(f_2270_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_2270_2,plain,
    ! [U_7949,U_7948,U_7947,U_7946,U_7945,U_7944] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_7944),U_7945),c_SetInterval_Oord_OgreaterThanAtMost(U_7944,U_7946,U_7947,U_7948,U_7949)))
        | ~ hBOOL(hAPP(hAPP(U_7946,U_7945),U_7949))
        | ~ hBOOL(hAPP(hAPP(U_7947,U_7948),U_7945)) )
      & ( ( hBOOL(hAPP(hAPP(U_7946,U_7945),U_7949))
          & hBOOL(hAPP(hAPP(U_7947,U_7948),U_7945)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_7944),U_7945),c_SetInterval_Oord_OgreaterThanAtMost(U_7944,U_7946,U_7947,U_7948,U_7949))) ) ),
    inference(variable_rename,[status(thm)],[f_2270_1]) ).

fof(f_2270_3,plain,
    ( ! [U_7961,U_7959,U_7957,U_7955,U_7953] :
        ( ! [U_7951] : hBOOL(hAPP(hAPP(c_member(U_7951),U_7953),c_SetInterval_Oord_OgreaterThanAtMost(U_7951,U_7955,U_7957,U_7959,U_7961)))
        | ~ hBOOL(hAPP(hAPP(U_7955,U_7953),U_7961))
        | ~ hBOOL(hAPP(hAPP(U_7957,U_7959),U_7953)) )
    & ! [U_7960,U_7958,U_7956,U_7954,U_7952] :
        ( ! [U_7950] : ~ hBOOL(hAPP(hAPP(c_member(U_7950),U_7952),c_SetInterval_Oord_OgreaterThanAtMost(U_7950,U_7954,U_7956,U_7958,U_7960)))
        | ( hBOOL(hAPP(hAPP(U_7954,U_7952),U_7960))
          & hBOOL(hAPP(hAPP(U_7956,U_7958),U_7952)) ) ) ),
    inference(miniscope,[status(thm)],[f_2270_2]) ).

fof(f_2270_4,plain,
    ( ! [U_7954,U_7952,U_7956,U_7958,U_7960] :
        ( hBOOL(hAPP(hAPP(U_7954,U_7952),U_7960))
        | ~ sP686(U_7954,U_7952,U_7956,U_7958,U_7960) )
    & ! [U_7954,U_7952,U_7956,U_7958,U_7960] :
        ( hBOOL(hAPP(hAPP(U_7956,U_7958),U_7952))
        | ~ sP686(U_7954,U_7952,U_7956,U_7958,U_7960) )
    & ! [U_7955,U_7951,U_7957,U_7953,U_7961,U_7959] :
        ( hBOOL(hAPP(hAPP(c_member(U_7951),U_7953),c_SetInterval_Oord_OgreaterThanAtMost(U_7951,U_7955,U_7957,U_7959,U_7961)))
        | ~ hBOOL(hAPP(hAPP(U_7955,U_7953),U_7961))
        | ~ hBOOL(hAPP(hAPP(U_7957,U_7959),U_7953)) )
    & ! [U_7954,U_7952,U_7950,U_7956,U_7958,U_7960] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7950),U_7952),c_SetInterval_Oord_OgreaterThanAtMost(U_7950,U_7954,U_7956,U_7958,U_7960)))
        | sP686(U_7954,U_7952,U_7956,U_7958,U_7960) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP686])],[f_2270_3]) ).

cnf(f_2270_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7950),U_7952),c_SetInterval_Oord_OgreaterThanAtMost(U_7950,U_7954,U_7956,U_7958,U_7960)))
    | sP686(U_7954,U_7952,U_7956,U_7958,U_7960) ),
    inference(clausify,[status(thm)],[f_2270_4]) ).

cnf(f_2270_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7951),U_7953),c_SetInterval_Oord_OgreaterThanAtMost(U_7951,U_7955,U_7957,U_7959,U_7961)))
    | ~ hBOOL(hAPP(hAPP(U_7955,U_7953),U_7961))
    | ~ hBOOL(hAPP(hAPP(U_7957,U_7959),U_7953)) ),
    inference(clausify,[status(thm)],[f_2270_4]) ).

cnf(f_2270_7,plain,
    ( hBOOL(hAPP(hAPP(U_7956,U_7958),U_7952))
    | ~ sP686(U_7954,U_7952,U_7956,U_7958,U_7960) ),
    inference(clausify,[status(thm)],[f_2270_4]) ).

cnf(f_2270_8,plain,
    ( hBOOL(hAPP(hAPP(U_7954,U_7952),U_7960))
    | ~ sP686(U_7954,U_7952,U_7956,U_7958,U_7960) ),
    inference(clausify,[status(thm)],[f_2270_4]) ).

fof(f_2271_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_2271_2,plain,
    ! [U_7967,U_7966,U_7965,U_7964,U_7963,U_7962] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_7962),U_7963),c_SetInterval_Oord_OatLeastLessThan(U_7962,U_7964,U_7965,U_7966,U_7967)))
        | ~ hBOOL(hAPP(hAPP(U_7965,U_7963),U_7967))
        | ~ hBOOL(hAPP(hAPP(U_7964,U_7966),U_7963)) )
      & ( ( hBOOL(hAPP(hAPP(U_7965,U_7963),U_7967))
          & hBOOL(hAPP(hAPP(U_7964,U_7966),U_7963)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_7962),U_7963),c_SetInterval_Oord_OatLeastLessThan(U_7962,U_7964,U_7965,U_7966,U_7967))) ) ),
    inference(variable_rename,[status(thm)],[f_2271_1]) ).

fof(f_2271_3,plain,
    ( ! [U_7979,U_7977,U_7975,U_7973,U_7971] :
        ( ! [U_7969] : hBOOL(hAPP(hAPP(c_member(U_7969),U_7971),c_SetInterval_Oord_OatLeastLessThan(U_7969,U_7973,U_7975,U_7977,U_7979)))
        | ~ hBOOL(hAPP(hAPP(U_7975,U_7971),U_7979))
        | ~ hBOOL(hAPP(hAPP(U_7973,U_7977),U_7971)) )
    & ! [U_7978,U_7976,U_7974,U_7972,U_7970] :
        ( ! [U_7968] : ~ hBOOL(hAPP(hAPP(c_member(U_7968),U_7970),c_SetInterval_Oord_OatLeastLessThan(U_7968,U_7972,U_7974,U_7976,U_7978)))
        | ( hBOOL(hAPP(hAPP(U_7974,U_7970),U_7978))
          & hBOOL(hAPP(hAPP(U_7972,U_7976),U_7970)) ) ) ),
    inference(miniscope,[status(thm)],[f_2271_2]) ).

fof(f_2271_4,plain,
    ( ! [U_7972,U_7970,U_7974,U_7976,U_7978] :
        ( hBOOL(hAPP(hAPP(U_7974,U_7970),U_7978))
        | ~ sP687(U_7972,U_7970,U_7974,U_7976,U_7978) )
    & ! [U_7972,U_7970,U_7974,U_7976,U_7978] :
        ( hBOOL(hAPP(hAPP(U_7972,U_7976),U_7970))
        | ~ sP687(U_7972,U_7970,U_7974,U_7976,U_7978) )
    & ! [U_7973,U_7971,U_7969,U_7975,U_7979,U_7977] :
        ( hBOOL(hAPP(hAPP(c_member(U_7969),U_7971),c_SetInterval_Oord_OatLeastLessThan(U_7969,U_7973,U_7975,U_7977,U_7979)))
        | ~ hBOOL(hAPP(hAPP(U_7975,U_7971),U_7979))
        | ~ hBOOL(hAPP(hAPP(U_7973,U_7977),U_7971)) )
    & ! [U_7972,U_7970,U_7974,U_7968,U_7976,U_7978] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7968),U_7970),c_SetInterval_Oord_OatLeastLessThan(U_7968,U_7972,U_7974,U_7976,U_7978)))
        | sP687(U_7972,U_7970,U_7974,U_7976,U_7978) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP687])],[f_2271_3]) ).

cnf(f_2271_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7968),U_7970),c_SetInterval_Oord_OatLeastLessThan(U_7968,U_7972,U_7974,U_7976,U_7978)))
    | sP687(U_7972,U_7970,U_7974,U_7976,U_7978) ),
    inference(clausify,[status(thm)],[f_2271_4]) ).

cnf(f_2271_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7969),U_7971),c_SetInterval_Oord_OatLeastLessThan(U_7969,U_7973,U_7975,U_7977,U_7979)))
    | ~ hBOOL(hAPP(hAPP(U_7975,U_7971),U_7979))
    | ~ hBOOL(hAPP(hAPP(U_7973,U_7977),U_7971)) ),
    inference(clausify,[status(thm)],[f_2271_4]) ).

cnf(f_2271_7,plain,
    ( hBOOL(hAPP(hAPP(U_7972,U_7976),U_7970))
    | ~ sP687(U_7972,U_7970,U_7974,U_7976,U_7978) ),
    inference(clausify,[status(thm)],[f_2271_4]) ).

cnf(f_2271_8,plain,
    ( hBOOL(hAPP(hAPP(U_7974,U_7970),U_7978))
    | ~ sP687(U_7972,U_7970,U_7974,U_7976,U_7978) ),
    inference(clausify,[status(thm)],[f_2271_4]) ).

fof(f_2272_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_2272_2,plain,
    ! [U_7984,U_7983,U_7982,U_7981,U_7980] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_7980),U_7981),c_SetInterval_Oord_OgreaterThanLessThan(U_7980,U_7982,U_7983,U_7984)))
        | ~ hBOOL(hAPP(hAPP(U_7982,U_7981),U_7984))
        | ~ hBOOL(hAPP(hAPP(U_7982,U_7983),U_7981)) )
      & ( ( hBOOL(hAPP(hAPP(U_7982,U_7981),U_7984))
          & hBOOL(hAPP(hAPP(U_7982,U_7983),U_7981)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_7980),U_7981),c_SetInterval_Oord_OgreaterThanLessThan(U_7980,U_7982,U_7983,U_7984))) ) ),
    inference(variable_rename,[status(thm)],[f_2272_1]) ).

fof(f_2272_3,plain,
    ( ! [U_7994,U_7992,U_7990,U_7988] :
        ( ! [U_7986] : hBOOL(hAPP(hAPP(c_member(U_7986),U_7988),c_SetInterval_Oord_OgreaterThanLessThan(U_7986,U_7990,U_7992,U_7994)))
        | ~ hBOOL(hAPP(hAPP(U_7990,U_7988),U_7994))
        | ~ hBOOL(hAPP(hAPP(U_7990,U_7992),U_7988)) )
    & ! [U_7993,U_7991,U_7989,U_7987] :
        ( ! [U_7985] : ~ hBOOL(hAPP(hAPP(c_member(U_7985),U_7987),c_SetInterval_Oord_OgreaterThanLessThan(U_7985,U_7989,U_7991,U_7993)))
        | ( hBOOL(hAPP(hAPP(U_7989,U_7987),U_7993))
          & hBOOL(hAPP(hAPP(U_7989,U_7991),U_7987)) ) ) ),
    inference(miniscope,[status(thm)],[f_2272_2]) ).

fof(f_2272_4,plain,
    ( ! [U_7987,U_7989,U_7991,U_7993] :
        ( hBOOL(hAPP(hAPP(U_7989,U_7987),U_7993))
        | ~ sP688(U_7987,U_7989,U_7991,U_7993) )
    & ! [U_7987,U_7989,U_7991,U_7993] :
        ( hBOOL(hAPP(hAPP(U_7989,U_7991),U_7987))
        | ~ sP688(U_7987,U_7989,U_7991,U_7993) )
    & ! [U_7990,U_7992,U_7986,U_7988,U_7994] :
        ( hBOOL(hAPP(hAPP(c_member(U_7986),U_7988),c_SetInterval_Oord_OgreaterThanLessThan(U_7986,U_7990,U_7992,U_7994)))
        | ~ hBOOL(hAPP(hAPP(U_7990,U_7988),U_7994))
        | ~ hBOOL(hAPP(hAPP(U_7990,U_7992),U_7988)) )
    & ! [U_7985,U_7987,U_7989,U_7991,U_7993] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_7985),U_7987),c_SetInterval_Oord_OgreaterThanLessThan(U_7985,U_7989,U_7991,U_7993)))
        | sP688(U_7987,U_7989,U_7991,U_7993) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP688])],[f_2272_3]) ).

cnf(f_2272_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_7985),U_7987),c_SetInterval_Oord_OgreaterThanLessThan(U_7985,U_7989,U_7991,U_7993)))
    | sP688(U_7987,U_7989,U_7991,U_7993) ),
    inference(clausify,[status(thm)],[f_2272_4]) ).

cnf(f_2272_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_7986),U_7988),c_SetInterval_Oord_OgreaterThanLessThan(U_7986,U_7990,U_7992,U_7994)))
    | ~ hBOOL(hAPP(hAPP(U_7990,U_7988),U_7994))
    | ~ hBOOL(hAPP(hAPP(U_7990,U_7992),U_7988)) ),
    inference(clausify,[status(thm)],[f_2272_4]) ).

cnf(f_2272_7,plain,
    ( hBOOL(hAPP(hAPP(U_7989,U_7991),U_7987))
    | ~ sP688(U_7987,U_7989,U_7991,U_7993) ),
    inference(clausify,[status(thm)],[f_2272_4]) ).

cnf(f_2272_8,plain,
    ( hBOOL(hAPP(hAPP(U_7989,U_7987),U_7993))
    | ~ sP688(U_7987,U_7989,U_7991,U_7993) ),
    inference(clausify,[status(thm)],[f_2272_4]) ).

fof(f_2273_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_2273_2,plain,
    ! [U_7999,U_7998,U_7997,U_7996,U_7995] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_7995),U_7996),c_SetInterval_Oord_OatLeastAtMost(U_7995,U_7997,U_7998,U_7999)))
        | ~ hBOOL(hAPP(hAPP(U_7997,U_7996),U_7999))
        | ~ hBOOL(hAPP(hAPP(U_7997,U_7998),U_7996)) )
      & ( ( hBOOL(hAPP(hAPP(U_7997,U_7996),U_7999))
          & hBOOL(hAPP(hAPP(U_7997,U_7998),U_7996)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_7995),U_7996),c_SetInterval_Oord_OatLeastAtMost(U_7995,U_7997,U_7998,U_7999))) ) ),
    inference(variable_rename,[status(thm)],[f_2273_1]) ).

fof(f_2273_3,plain,
    ( ! [U_8009,U_8007,U_8005,U_8003] :
        ( ! [U_8001] : hBOOL(hAPP(hAPP(c_member(U_8001),U_8003),c_SetInterval_Oord_OatLeastAtMost(U_8001,U_8005,U_8007,U_8009)))
        | ~ hBOOL(hAPP(hAPP(U_8005,U_8003),U_8009))
        | ~ hBOOL(hAPP(hAPP(U_8005,U_8007),U_8003)) )
    & ! [U_8008,U_8006,U_8004,U_8002] :
        ( ! [U_8000] : ~ hBOOL(hAPP(hAPP(c_member(U_8000),U_8002),c_SetInterval_Oord_OatLeastAtMost(U_8000,U_8004,U_8006,U_8008)))
        | ( hBOOL(hAPP(hAPP(U_8004,U_8002),U_8008))
          & hBOOL(hAPP(hAPP(U_8004,U_8006),U_8002)) ) ) ),
    inference(miniscope,[status(thm)],[f_2273_2]) ).

fof(f_2273_4,plain,
    ( ! [U_8002,U_8004,U_8006,U_8008] :
        ( hBOOL(hAPP(hAPP(U_8004,U_8002),U_8008))
        | ~ sP689(U_8002,U_8004,U_8006,U_8008) )
    & ! [U_8002,U_8004,U_8006,U_8008] :
        ( hBOOL(hAPP(hAPP(U_8004,U_8006),U_8002))
        | ~ sP689(U_8002,U_8004,U_8006,U_8008) )
    & ! [U_8007,U_8005,U_8001,U_8003,U_8009] :
        ( hBOOL(hAPP(hAPP(c_member(U_8001),U_8003),c_SetInterval_Oord_OatLeastAtMost(U_8001,U_8005,U_8007,U_8009)))
        | ~ hBOOL(hAPP(hAPP(U_8005,U_8003),U_8009))
        | ~ hBOOL(hAPP(hAPP(U_8005,U_8007),U_8003)) )
    & ! [U_8000,U_8002,U_8004,U_8006,U_8008] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8000),U_8002),c_SetInterval_Oord_OatLeastAtMost(U_8000,U_8004,U_8006,U_8008)))
        | sP689(U_8002,U_8004,U_8006,U_8008) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP689])],[f_2273_3]) ).

cnf(f_2273_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8000),U_8002),c_SetInterval_Oord_OatLeastAtMost(U_8000,U_8004,U_8006,U_8008)))
    | sP689(U_8002,U_8004,U_8006,U_8008) ),
    inference(clausify,[status(thm)],[f_2273_4]) ).

cnf(f_2273_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8001),U_8003),c_SetInterval_Oord_OatLeastAtMost(U_8001,U_8005,U_8007,U_8009)))
    | ~ hBOOL(hAPP(hAPP(U_8005,U_8003),U_8009))
    | ~ hBOOL(hAPP(hAPP(U_8005,U_8007),U_8003)) ),
    inference(clausify,[status(thm)],[f_2273_4]) ).

cnf(f_2273_7,plain,
    ( hBOOL(hAPP(hAPP(U_8004,U_8006),U_8002))
    | ~ sP689(U_8002,U_8004,U_8006,U_8008) ),
    inference(clausify,[status(thm)],[f_2273_4]) ).

cnf(f_2273_8,plain,
    ( hBOOL(hAPP(hAPP(U_8004,U_8002),U_8008))
    | ~ sP689(U_8002,U_8004,U_8006,U_8008) ),
    inference(clausify,[status(thm)],[f_2273_4]) ).

fof(f_2274_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_2274_2,plain,
    ! [U_8013,U_8012,U_8011,U_8010] :
      ( ( 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_8010,U_8011)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8012,U_8013)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8011),U_8013))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8012),U_8010)) )
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8010),U_8011)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8011),U_8013))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8012),U_8010)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8010),U_8011))
        | ~ 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_8010,U_8011)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8012,U_8013))) ) ),
    inference(variable_rename,[status(thm)],[f_2274_1]) ).

fof(f_2274_3,plain,
    ( ! [U_8021,U_8019,U_8017,U_8015] :
        ( 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_8015,U_8017)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8019,U_8021)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8017),U_8021))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8019),U_8015)) )
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8015),U_8017)) ) )
    & ! [U_8020,U_8018,U_8016,U_8014] :
        ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8016),U_8020))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8018),U_8014)) )
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8014),U_8016))
        | ~ 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_8014,U_8016)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8018,U_8020))) ) ),
    inference(miniscope,[status(thm)],[f_2274_2]) ).

fof(f_2274_4,plain,
    ( ! [U_8015,U_8017,U_8019,U_8021] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8017),U_8021))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8019),U_8015))
        | ~ sP691(U_8015,U_8017,U_8019,U_8021) )
    & ! [U_8015,U_8017,U_8019,U_8021] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8015),U_8017))
        | ~ sP691(U_8015,U_8017,U_8019,U_8021) )
    & ! [U_8016,U_8014,U_8020,U_8018] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8016),U_8020))
        | ~ sP690(U_8016,U_8014,U_8020,U_8018) )
    & ! [U_8016,U_8014,U_8020,U_8018] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8018),U_8014))
        | ~ sP690(U_8016,U_8014,U_8020,U_8018) )
    & ! [U_8015,U_8017,U_8019,U_8021] :
        ( 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_8015,U_8017)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8019,U_8021)))
        | sP691(U_8015,U_8017,U_8019,U_8021) )
    & ! [U_8016,U_8014,U_8020,U_8018] :
        ( sP690(U_8016,U_8014,U_8020,U_8018)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8014),U_8016))
        | ~ 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_8014,U_8016)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8018,U_8020))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP690,sP691])],[f_2274_3]) ).

cnf(f_2274_5,plain,
    ( sP690(U_8016,U_8014,U_8020,U_8018)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8014),U_8016))
    | ~ 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_8014,U_8016)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8018,U_8020))) ),
    inference(clausify,[status(thm)],[f_2274_4]) ).

cnf(f_2274_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_8015,U_8017)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8019,U_8021)))
    | sP691(U_8015,U_8017,U_8019,U_8021) ),
    inference(clausify,[status(thm)],[f_2274_4]) ).

cnf(f_2274_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8018),U_8014))
    | ~ sP690(U_8016,U_8014,U_8020,U_8018) ),
    inference(clausify,[status(thm)],[f_2274_4]) ).

cnf(f_2274_8,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8016),U_8020))
    | ~ sP690(U_8016,U_8014,U_8020,U_8018) ),
    inference(clausify,[status(thm)],[f_2274_4]) ).

cnf(f_2274_9,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8015),U_8017))
    | ~ sP691(U_8015,U_8017,U_8019,U_8021) ),
    inference(clausify,[status(thm)],[f_2274_4]) ).

cnf(f_2274_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8017),U_8021))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8019),U_8015))
    | ~ sP691(U_8015,U_8017,U_8019,U_8021) ),
    inference(clausify,[status(thm)],[f_2274_4]) ).

fof(f_2275_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_2275_2,plain,
    ! [U_8025,U_8024,U_8023,U_8022] :
      ( ( 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_8022,U_8023)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8024,U_8025)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8024),U_8025))
        | ( ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8025),U_8023))
                | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8023),U_8025)) )
              & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8022),U_8024))
                | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8024),U_8022)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8023),U_8025))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8024),U_8022)) )
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8022),U_8023)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8024),U_8025))
          & ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8025),U_8023))
                  & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8023),U_8025)) )
                | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8022),U_8024))
                  & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8024),U_8022)) ) )
              & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8023),U_8025))
              & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8024),U_8022)) )
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8022),U_8023)) ) )
        | ~ 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_8022,U_8023)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8024,U_8025))) ) ),
    inference(variable_rename,[status(thm)],[f_2275_1]) ).

fof(f_2275_3,plain,
    ( ! [U_8033,U_8031,U_8029,U_8027] :
        ( 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_8027,U_8029)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8031,U_8033)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8031),U_8033))
        | ( ( ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8033),U_8029))
                | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8029),U_8033)) )
              & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8027),U_8031))
                | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8031),U_8027)) ) )
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8029),U_8033))
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8031),U_8027)) )
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8027),U_8029)) ) )
    & ! [U_8032,U_8030,U_8028,U_8026] :
        ( ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8030),U_8032))
          & ( ( ( ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8032),U_8028))
                  & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8028),U_8032)) )
                | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8026),U_8030))
                  & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8030),U_8026)) ) )
              & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8028),U_8032))
              & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8030),U_8026)) )
            | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8026),U_8028)) ) )
        | ~ 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_8026,U_8028)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8030,U_8032))) ) ),
    inference(miniscope,[status(thm)],[f_2275_2]) ).

fof(f_2275_4,plain,
    ( ! [U_8031,U_8029,U_8027,U_8033] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8033),U_8029))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8029),U_8033))
        | ~ sP696(U_8031,U_8029,U_8027,U_8033) )
    & ! [U_8031,U_8029,U_8027,U_8033] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8027),U_8031))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8031),U_8027))
        | ~ sP696(U_8031,U_8029,U_8027,U_8033) )
    & ! [U_8031,U_8029,U_8027,U_8033] :
        ( sP696(U_8031,U_8029,U_8027,U_8033)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8029),U_8033))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8031),U_8027))
        | ~ sP697(U_8031,U_8029,U_8027,U_8033) )
    & ! [U_8031,U_8029,U_8027,U_8033] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8027),U_8029))
        | ~ sP697(U_8031,U_8029,U_8027,U_8033) )
    & ! [U_8028,U_8032] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8032),U_8028))
        | ~ sP693(U_8028,U_8032) )
    & ! [U_8028,U_8032] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8028),U_8032))
        | ~ sP693(U_8028,U_8032) )
    & ! [U_8026,U_8030] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8026),U_8030))
        | ~ sP692(U_8026,U_8030) )
    & ! [U_8026,U_8030] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8030),U_8026))
        | ~ sP692(U_8026,U_8030) )
    & ! [U_8028,U_8032,U_8026,U_8030] :
        ( sP693(U_8028,U_8032)
        | sP692(U_8026,U_8030)
        | ~ sP694(U_8028,U_8032,U_8026,U_8030) )
    & ! [U_8028,U_8032,U_8026,U_8030] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8028),U_8032))
        | ~ sP694(U_8028,U_8032,U_8026,U_8030) )
    & ! [U_8028,U_8032,U_8026,U_8030] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8030),U_8026))
        | ~ sP694(U_8028,U_8032,U_8026,U_8030) )
    & ! [U_8028,U_8032,U_8026,U_8030] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8030),U_8032))
        | ~ sP695(U_8028,U_8032,U_8026,U_8030) )
    & ! [U_8028,U_8032,U_8026,U_8030] :
        ( sP694(U_8028,U_8032,U_8026,U_8030)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8026),U_8028))
        | ~ sP695(U_8028,U_8032,U_8026,U_8030) )
    & ! [U_8031,U_8029,U_8027,U_8033] :
        ( 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_8027,U_8029)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8031,U_8033)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8031),U_8033))
        | sP697(U_8031,U_8029,U_8027,U_8033) )
    & ! [U_8028,U_8032,U_8026,U_8030] :
        ( sP695(U_8028,U_8032,U_8026,U_8030)
        | ~ 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_8026,U_8028)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8030,U_8032))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP692,sP693,sP694,sP695,sP696,sP697])],[f_2275_3]) ).

cnf(f_2275_5,plain,
    ( sP695(U_8028,U_8032,U_8026,U_8030)
    | ~ 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_8026,U_8028)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8030,U_8032))) ),
    inference(clausify,[status(thm)],[f_2275_4]) ).

cnf(f_2275_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_8027,U_8029)),c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8031,U_8033)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8031),U_8033))
    | sP697(U_8031,U_8029,U_8027,U_8033) ),
    inference(clausify,[status(thm)],[f_2275_4]) ).

cnf(f_2275_7,plain,
    ( sP694(U_8028,U_8032,U_8026,U_8030)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8026),U_8028))
    | ~ sP695(U_8028,U_8032,U_8026,U_8030) ),
    inference(clausify,[status(thm)],[f_2275_4]) ).

cnf(f_2275_8,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8030),U_8032))
    | ~ sP695(U_8028,U_8032,U_8026,U_8030) ),
    inference(clausify,[status(thm)],[f_2275_4]) ).

cnf(f_2275_9,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8030),U_8026))
    | ~ sP694(U_8028,U_8032,U_8026,U_8030) ),
    inference(clausify,[status(thm)],[f_2275_4]) ).

cnf(f_2275_10,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8028),U_8032))
    | ~ sP694(U_8028,U_8032,U_8026,U_8030) ),
    inference(clausify,[status(thm)],[f_2275_4]) ).

cnf(f_2275_11,plain,
    ( sP693(U_8028,U_8032)
    | sP692(U_8026,U_8030)
    | ~ sP694(U_8028,U_8032,U_8026,U_8030) ),
    inference(clausify,[status(thm)],[f_2275_4]) ).

cnf(f_2275_12,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8030),U_8026))
    | ~ sP692(U_8026,U_8030) ),
    inference(clausify,[status(thm)],[f_2275_4]) ).

cnf(f_2275_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8026),U_8030))
    | ~ sP692(U_8026,U_8030) ),
    inference(clausify,[status(thm)],[f_2275_4]) ).

cnf(f_2275_14,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8028),U_8032))
    | ~ sP693(U_8028,U_8032) ),
    inference(clausify,[status(thm)],[f_2275_4]) ).

cnf(f_2275_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8032),U_8028))
    | ~ sP693(U_8028,U_8032) ),
    inference(clausify,[status(thm)],[f_2275_4]) ).

cnf(f_2275_16,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8027),U_8029))
    | ~ sP697(U_8031,U_8029,U_8027,U_8033) ),
    inference(clausify,[status(thm)],[f_2275_4]) ).

cnf(f_2275_17,plain,
    ( sP696(U_8031,U_8029,U_8027,U_8033)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8029),U_8033))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8031),U_8027))
    | ~ sP697(U_8031,U_8029,U_8027,U_8033) ),
    inference(clausify,[status(thm)],[f_2275_4]) ).

cnf(f_2275_18,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8027),U_8031))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8031),U_8027))
    | ~ sP696(U_8031,U_8029,U_8027,U_8033) ),
    inference(clausify,[status(thm)],[f_2275_4]) ).

cnf(f_2275_19,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8033),U_8029))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_8029),U_8033))
    | ~ sP696(U_8031,U_8029,U_8027,U_8033) ),
    inference(clausify,[status(thm)],[f_2275_4]) ).

fof(f_2276_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_2276_2,plain,
    ! [U_8038,U_8037,U_8036,U_8035,U_8034] : hAPP(hAPP(c_Relation_Orel__comp(U_8034,U_8035,U_8036),U_8037),U_8038) = hAPP(c_Set_OCollect(tc_prod(U_8034,U_8036)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8034,U_8036,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_8036,tc_fun(U_8035,tc_HOL_Obool)),tc_fun(U_8036,tc_HOL_Obool),U_8034),hAPP(c_COMBB(tc_fun(U_8035,tc_HOL_Obool),tc_HOL_Obool,U_8036),c_HOL_OEx(U_8035))),hAPP(hAPP(c_COMBC(U_8034,tc_fun(U_8036,tc_fun(U_8035,tc_HOL_Obool)),tc_fun(U_8036,tc_fun(U_8035,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8035,tc_HOL_Obool),tc_fun(U_8035,tc_HOL_Obool)),tc_fun(tc_fun(U_8036,tc_fun(U_8035,tc_HOL_Obool)),tc_fun(U_8036,tc_fun(U_8035,tc_HOL_Obool))),U_8034),c_COMBB(tc_fun(U_8035,tc_HOL_Obool),tc_fun(U_8035,tc_HOL_Obool),U_8036)),hAPP(hAPP(c_COMBB(tc_fun(U_8035,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_8035,tc_HOL_Obool),tc_fun(U_8035,tc_HOL_Obool)),U_8034),c_COMBS(U_8035,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8035,tc_HOL_Obool),tc_fun(U_8035,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_8034),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8035),c_fconj)),hAPP(hAPP(c_COMBC(U_8034,tc_fun(tc_prod(U_8034,U_8035),tc_HOL_Obool),tc_fun(U_8035,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8035,tc_fun(tc_fun(tc_prod(U_8034,U_8035),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8034,U_8035),tc_HOL_Obool),tc_fun(U_8035,tc_HOL_Obool)),U_8034),c_COMBC(U_8035,tc_fun(tc_prod(U_8034,U_8035),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8035,tc_prod(U_8034,U_8035)),tc_fun(U_8035,tc_fun(tc_fun(tc_prod(U_8034,U_8035),tc_HOL_Obool),tc_HOL_Obool)),U_8034),hAPP(c_COMBB(tc_prod(U_8034,U_8035),tc_fun(tc_fun(tc_prod(U_8034,U_8035),tc_HOL_Obool),tc_HOL_Obool),U_8035),c_member(tc_prod(U_8034,U_8035)))),c_Product__Type_OPair(U_8034,U_8035)))),U_8037))))),hAPP(hAPP(c_COMBC(U_8036,tc_fun(tc_prod(U_8035,U_8036),tc_HOL_Obool),tc_fun(U_8035,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8035,tc_fun(tc_fun(tc_prod(U_8035,U_8036),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8035,U_8036),tc_HOL_Obool),tc_fun(U_8035,tc_HOL_Obool)),U_8036),c_COMBC(U_8035,tc_fun(tc_prod(U_8035,U_8036),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8035,tc_prod(U_8035,U_8036)),tc_fun(U_8035,tc_fun(tc_fun(tc_prod(U_8035,U_8036),tc_HOL_Obool),tc_HOL_Obool)),U_8036),hAPP(c_COMBB(tc_prod(U_8035,U_8036),tc_fun(tc_fun(tc_prod(U_8035,U_8036),tc_HOL_Obool),tc_HOL_Obool),U_8035),c_member(tc_prod(U_8035,U_8036)))),hAPP(c_COMBC(U_8035,U_8036,tc_prod(U_8035,U_8036)),c_Product__Type_OPair(U_8035,U_8036))))),U_8038))))),
    inference(variable_rename,[status(thm)],[f_2276_1]) ).

fof(f_2276_3,plain,
    ! [U_8034,U_8037,U_8036,U_8038,U_8035] : hAPP(hAPP(c_Relation_Orel__comp(U_8034,U_8035,U_8036),U_8037),U_8038) = hAPP(c_Set_OCollect(tc_prod(U_8034,U_8036)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8034,U_8036,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_8036,tc_fun(U_8035,tc_HOL_Obool)),tc_fun(U_8036,tc_HOL_Obool),U_8034),hAPP(c_COMBB(tc_fun(U_8035,tc_HOL_Obool),tc_HOL_Obool,U_8036),c_HOL_OEx(U_8035))),hAPP(hAPP(c_COMBC(U_8034,tc_fun(U_8036,tc_fun(U_8035,tc_HOL_Obool)),tc_fun(U_8036,tc_fun(U_8035,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8035,tc_HOL_Obool),tc_fun(U_8035,tc_HOL_Obool)),tc_fun(tc_fun(U_8036,tc_fun(U_8035,tc_HOL_Obool)),tc_fun(U_8036,tc_fun(U_8035,tc_HOL_Obool))),U_8034),c_COMBB(tc_fun(U_8035,tc_HOL_Obool),tc_fun(U_8035,tc_HOL_Obool),U_8036)),hAPP(hAPP(c_COMBB(tc_fun(U_8035,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_8035,tc_HOL_Obool),tc_fun(U_8035,tc_HOL_Obool)),U_8034),c_COMBS(U_8035,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8035,tc_HOL_Obool),tc_fun(U_8035,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_8034),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8035),c_fconj)),hAPP(hAPP(c_COMBC(U_8034,tc_fun(tc_prod(U_8034,U_8035),tc_HOL_Obool),tc_fun(U_8035,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8035,tc_fun(tc_fun(tc_prod(U_8034,U_8035),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8034,U_8035),tc_HOL_Obool),tc_fun(U_8035,tc_HOL_Obool)),U_8034),c_COMBC(U_8035,tc_fun(tc_prod(U_8034,U_8035),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8035,tc_prod(U_8034,U_8035)),tc_fun(U_8035,tc_fun(tc_fun(tc_prod(U_8034,U_8035),tc_HOL_Obool),tc_HOL_Obool)),U_8034),hAPP(c_COMBB(tc_prod(U_8034,U_8035),tc_fun(tc_fun(tc_prod(U_8034,U_8035),tc_HOL_Obool),tc_HOL_Obool),U_8035),c_member(tc_prod(U_8034,U_8035)))),c_Product__Type_OPair(U_8034,U_8035)))),U_8037))))),hAPP(hAPP(c_COMBC(U_8036,tc_fun(tc_prod(U_8035,U_8036),tc_HOL_Obool),tc_fun(U_8035,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8035,tc_fun(tc_fun(tc_prod(U_8035,U_8036),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8035,U_8036),tc_HOL_Obool),tc_fun(U_8035,tc_HOL_Obool)),U_8036),c_COMBC(U_8035,tc_fun(tc_prod(U_8035,U_8036),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8035,tc_prod(U_8035,U_8036)),tc_fun(U_8035,tc_fun(tc_fun(tc_prod(U_8035,U_8036),tc_HOL_Obool),tc_HOL_Obool)),U_8036),hAPP(c_COMBB(tc_prod(U_8035,U_8036),tc_fun(tc_fun(tc_prod(U_8035,U_8036),tc_HOL_Obool),tc_HOL_Obool),U_8035),c_member(tc_prod(U_8035,U_8036)))),hAPP(c_COMBC(U_8035,U_8036,tc_prod(U_8035,U_8036)),c_Product__Type_OPair(U_8035,U_8036))))),U_8038))))),
    inference(definitional_conversion,[status(esa)],[f_2276_2]) ).

cnf(f_2276_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_8034,U_8035,U_8036),U_8037),U_8038) = hAPP(c_Set_OCollect(tc_prod(U_8034,U_8036)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8034,U_8036,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_8036,tc_fun(U_8035,tc_HOL_Obool)),tc_fun(U_8036,tc_HOL_Obool),U_8034),hAPP(c_COMBB(tc_fun(U_8035,tc_HOL_Obool),tc_HOL_Obool,U_8036),c_HOL_OEx(U_8035))),hAPP(hAPP(c_COMBC(U_8034,tc_fun(U_8036,tc_fun(U_8035,tc_HOL_Obool)),tc_fun(U_8036,tc_fun(U_8035,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_8035,tc_HOL_Obool),tc_fun(U_8035,tc_HOL_Obool)),tc_fun(tc_fun(U_8036,tc_fun(U_8035,tc_HOL_Obool)),tc_fun(U_8036,tc_fun(U_8035,tc_HOL_Obool))),U_8034),c_COMBB(tc_fun(U_8035,tc_HOL_Obool),tc_fun(U_8035,tc_HOL_Obool),U_8036)),hAPP(hAPP(c_COMBB(tc_fun(U_8035,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_8035,tc_HOL_Obool),tc_fun(U_8035,tc_HOL_Obool)),U_8034),c_COMBS(U_8035,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8035,tc_HOL_Obool),tc_fun(U_8035,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_8034),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8035),c_fconj)),hAPP(hAPP(c_COMBC(U_8034,tc_fun(tc_prod(U_8034,U_8035),tc_HOL_Obool),tc_fun(U_8035,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8035,tc_fun(tc_fun(tc_prod(U_8034,U_8035),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8034,U_8035),tc_HOL_Obool),tc_fun(U_8035,tc_HOL_Obool)),U_8034),c_COMBC(U_8035,tc_fun(tc_prod(U_8034,U_8035),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8035,tc_prod(U_8034,U_8035)),tc_fun(U_8035,tc_fun(tc_fun(tc_prod(U_8034,U_8035),tc_HOL_Obool),tc_HOL_Obool)),U_8034),hAPP(c_COMBB(tc_prod(U_8034,U_8035),tc_fun(tc_fun(tc_prod(U_8034,U_8035),tc_HOL_Obool),tc_HOL_Obool),U_8035),c_member(tc_prod(U_8034,U_8035)))),c_Product__Type_OPair(U_8034,U_8035)))),U_8037))))),hAPP(hAPP(c_COMBC(U_8036,tc_fun(tc_prod(U_8035,U_8036),tc_HOL_Obool),tc_fun(U_8035,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8035,tc_fun(tc_fun(tc_prod(U_8035,U_8036),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8035,U_8036),tc_HOL_Obool),tc_fun(U_8035,tc_HOL_Obool)),U_8036),c_COMBC(U_8035,tc_fun(tc_prod(U_8035,U_8036),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8035,tc_prod(U_8035,U_8036)),tc_fun(U_8035,tc_fun(tc_fun(tc_prod(U_8035,U_8036),tc_HOL_Obool),tc_HOL_Obool)),U_8036),hAPP(c_COMBB(tc_prod(U_8035,U_8036),tc_fun(tc_fun(tc_prod(U_8035,U_8036),tc_HOL_Obool),tc_HOL_Obool),U_8035),c_member(tc_prod(U_8035,U_8036)))),hAPP(c_COMBC(U_8035,U_8036,tc_prod(U_8035,U_8036)),c_Product__Type_OPair(U_8035,U_8036))))),U_8038))))),
    inference(clausify,[status(thm)],[f_2276_3]) ).

fof(f_2277_1,plain,
    ! [V_Pa_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_Pa_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_Pa_2)),
    inference(fof_nnf,[status(thm)],[fact_Domain__Collect__split]) ).

fof(f_2277_2,plain,
    ! [U_8041,U_8040,U_8039] : hAPP(c_Relation_ODomain(U_8039,U_8040),hAPP(c_Set_OCollect(tc_prod(U_8039,U_8040)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8039,U_8040,tc_HOL_Obool),U_8041))) = hAPP(c_Set_OCollect(U_8039),hAPP(hAPP(c_COMBB(tc_fun(U_8040,tc_HOL_Obool),tc_HOL_Obool,U_8039),c_HOL_OEx(U_8040)),U_8041)),
    inference(variable_rename,[status(thm)],[f_2277_1]) ).

fof(f_2277_3,plain,
    ! [U_8040,U_8039,U_8041] : hAPP(c_Relation_ODomain(U_8039,U_8040),hAPP(c_Set_OCollect(tc_prod(U_8039,U_8040)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8039,U_8040,tc_HOL_Obool),U_8041))) = hAPP(c_Set_OCollect(U_8039),hAPP(hAPP(c_COMBB(tc_fun(U_8040,tc_HOL_Obool),tc_HOL_Obool,U_8039),c_HOL_OEx(U_8040)),U_8041)),
    inference(definitional_conversion,[status(esa)],[f_2277_2]) ).

cnf(f_2277_4,plain,
    hAPP(c_Relation_ODomain(U_8039,U_8040),hAPP(c_Set_OCollect(tc_prod(U_8039,U_8040)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8039,U_8040,tc_HOL_Obool),U_8041))) = hAPP(c_Set_OCollect(U_8039),hAPP(hAPP(c_COMBB(tc_fun(U_8040,tc_HOL_Obool),tc_HOL_Obool,U_8039),c_HOL_OEx(U_8040)),U_8041)),
    inference(clausify,[status(thm)],[f_2277_3]) ).

fof(f_2278_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_2278_2,plain,
    ! [U_8043,U_8042] :
      ( 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_8042))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_8043)))) = 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_8042))),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_8043)))))
      | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8042)) ),
    inference(variable_rename,[status(thm)],[f_2278_1]) ).

fof(f_2278_3,plain,
    ! [U_8042,U_8043] :
      ( 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_8042))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_8043)))) = 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_8042))),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_8043)))))
      | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8042)) ),
    inference(definitional_conversion,[status(esa)],[f_2278_2]) ).

cnf(f_2278_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_8042))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_8043)))) = 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_8042))),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_8043)))))
    | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8042)) ),
    inference(clausify,[status(thm)],[f_2278_3]) ).

fof(f_2279_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_2279_2,plain,
    ! [U_8045,U_8044] :
      ( 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_8044))),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_8045))))) != 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_8044)) ),
    inference(variable_rename,[status(thm)],[f_2279_1]) ).

fof(f_2279_3,plain,
    ! [U_8044,U_8045] :
      ( 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_8044))),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_8045))))) != 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_8044)) ),
    inference(definitional_conversion,[status(esa)],[f_2279_2]) ).

cnf(f_2279_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_8044))),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_8045))))) != 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_8044)) ),
    inference(clausify,[status(thm)],[f_2279_3]) ).

fof(f_2280_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_2280_2,plain,
    ! [U_8053,U_8052,U_8051,U_8050,U_8049,U_8048,U_8047,U_8046] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8046,U_8051)),hAPP(hAPP(c_Product__Type_OPair(U_8046,U_8051),U_8048),U_8052)),hAPP(hAPP(c_Relation_Orel__comp(U_8046,U_8047,U_8051),U_8050),U_8053)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8047,U_8051)),hAPP(hAPP(c_Product__Type_OPair(U_8047,U_8051),U_8049),U_8052)),U_8053))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8046,U_8047)),hAPP(hAPP(c_Product__Type_OPair(U_8046,U_8047),U_8048),U_8049)),U_8050)) ),
    inference(variable_rename,[status(thm)],[f_2280_1]) ).

fof(f_2280_3,plain,
    ! [U_8046,U_8047,U_8048,U_8049,U_8050,U_8051,U_8052,U_8053] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8046,U_8051)),hAPP(hAPP(c_Product__Type_OPair(U_8046,U_8051),U_8048),U_8052)),hAPP(hAPP(c_Relation_Orel__comp(U_8046,U_8047,U_8051),U_8050),U_8053)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8047,U_8051)),hAPP(hAPP(c_Product__Type_OPair(U_8047,U_8051),U_8049),U_8052)),U_8053))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8046,U_8047)),hAPP(hAPP(c_Product__Type_OPair(U_8046,U_8047),U_8048),U_8049)),U_8050)) ),
    inference(definitional_conversion,[status(esa)],[f_2280_2]) ).

cnf(f_2280_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8046,U_8051)),hAPP(hAPP(c_Product__Type_OPair(U_8046,U_8051),U_8048),U_8052)),hAPP(hAPP(c_Relation_Orel__comp(U_8046,U_8047,U_8051),U_8050),U_8053)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8047,U_8051)),hAPP(hAPP(c_Product__Type_OPair(U_8047,U_8051),U_8049),U_8052)),U_8053))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8046,U_8047)),hAPP(hAPP(c_Product__Type_OPair(U_8046,U_8047),U_8048),U_8049)),U_8050)) ),
    inference(clausify,[status(thm)],[f_2280_3]) ).

fof(f_2281_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_2281_2,plain,
    ! [U_8058,U_8057,U_8056,U_8055,U_8054] :
      ( hBOOL(hAPP(hAPP(c_member(U_8054),U_8056),hAPP(c_Relation_ODomain(U_8054,U_8055),U_8058)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8054,U_8055)),hAPP(hAPP(c_Product__Type_OPair(U_8054,U_8055),U_8056),U_8057)),U_8058)) ),
    inference(variable_rename,[status(thm)],[f_2281_1]) ).

fof(f_2281_3,plain,
    ! [U_8054,U_8055,U_8056,U_8057,U_8058] :
      ( hBOOL(hAPP(hAPP(c_member(U_8054),U_8056),hAPP(c_Relation_ODomain(U_8054,U_8055),U_8058)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8054,U_8055)),hAPP(hAPP(c_Product__Type_OPair(U_8054,U_8055),U_8056),U_8057)),U_8058)) ),
    inference(definitional_conversion,[status(esa)],[f_2281_2]) ).

cnf(f_2281_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8054),U_8056),hAPP(c_Relation_ODomain(U_8054,U_8055),U_8058)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8054,U_8055)),hAPP(hAPP(c_Product__Type_OPair(U_8054,U_8055),U_8056),U_8057)),U_8058)) ),
    inference(clausify,[status(thm)],[f_2281_3]) ).

fof(f_2282_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_2282_2,plain,
    ! [U_8065,U_8064,U_8063,U_8062,U_8061,U_8060,U_8059] : hAPP(hAPP(c_Relation_Orel__comp(U_8059,U_8060,U_8061),hAPP(hAPP(c_Relation_Orel__comp(U_8059,U_8062,U_8060),U_8063),U_8064)),U_8065) = hAPP(hAPP(c_Relation_Orel__comp(U_8059,U_8062,U_8061),U_8063),hAPP(hAPP(c_Relation_Orel__comp(U_8062,U_8060,U_8061),U_8064),U_8065)),
    inference(variable_rename,[status(thm)],[f_2282_1]) ).

fof(f_2282_3,plain,
    ! [U_8059,U_8060,U_8061,U_8062,U_8063,U_8064,U_8065] : hAPP(hAPP(c_Relation_Orel__comp(U_8059,U_8060,U_8061),hAPP(hAPP(c_Relation_Orel__comp(U_8059,U_8062,U_8060),U_8063),U_8064)),U_8065) = hAPP(hAPP(c_Relation_Orel__comp(U_8059,U_8062,U_8061),U_8063),hAPP(hAPP(c_Relation_Orel__comp(U_8062,U_8060,U_8061),U_8064),U_8065)),
    inference(definitional_conversion,[status(esa)],[f_2282_2]) ).

cnf(f_2282_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_8059,U_8060,U_8061),hAPP(hAPP(c_Relation_Orel__comp(U_8059,U_8062,U_8060),U_8063),U_8064)),U_8065) = hAPP(hAPP(c_Relation_Orel__comp(U_8059,U_8062,U_8061),U_8063),hAPP(hAPP(c_Relation_Orel__comp(U_8062,U_8060,U_8061),U_8064),U_8065)),
    inference(clausify,[status(thm)],[f_2282_3]) ).

fof(f_2283_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_2283_2,plain,
    ! [U_8072,U_8071,U_8070,U_8069,U_8068,U_8067,U_8066] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8066,U_8070),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8066,U_8067,U_8070),U_8068),U_8071)),hAPP(hAPP(c_Relation_Orel__comp(U_8066,U_8067,U_8070),U_8069),U_8072)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8067,U_8070),tc_HOL_Obool)),U_8071),U_8072))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8066,U_8067),tc_HOL_Obool)),U_8068),U_8069)) ),
    inference(variable_rename,[status(thm)],[f_2283_1]) ).

fof(f_2283_3,plain,
    ! [U_8066,U_8067,U_8068,U_8069,U_8070,U_8071,U_8072] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8066,U_8070),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8066,U_8067,U_8070),U_8068),U_8071)),hAPP(hAPP(c_Relation_Orel__comp(U_8066,U_8067,U_8070),U_8069),U_8072)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8067,U_8070),tc_HOL_Obool)),U_8071),U_8072))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8066,U_8067),tc_HOL_Obool)),U_8068),U_8069)) ),
    inference(definitional_conversion,[status(esa)],[f_2283_2]) ).

cnf(f_2283_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8066,U_8070),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8066,U_8067,U_8070),U_8068),U_8071)),hAPP(hAPP(c_Relation_Orel__comp(U_8066,U_8067,U_8070),U_8069),U_8072)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8067,U_8070),tc_HOL_Obool)),U_8071),U_8072))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8066,U_8067),tc_HOL_Obool)),U_8068),U_8069)) ),
    inference(clausify,[status(thm)],[f_2283_3]) ).

fof(f_2284_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_2284_2,plain,
    ! [U_8077,U_8076,U_8075,U_8074,U_8073] : hAPP(c_Relation_Oconverse(U_8073,U_8074),hAPP(hAPP(c_Relation_Orel__comp(U_8073,U_8075,U_8074),U_8076),U_8077)) = hAPP(hAPP(c_Relation_Orel__comp(U_8074,U_8075,U_8073),hAPP(c_Relation_Oconverse(U_8075,U_8074),U_8077)),hAPP(c_Relation_Oconverse(U_8073,U_8075),U_8076)),
    inference(variable_rename,[status(thm)],[f_2284_1]) ).

fof(f_2284_3,plain,
    ! [U_8074,U_8073,U_8075,U_8076,U_8077] : hAPP(c_Relation_Oconverse(U_8073,U_8074),hAPP(hAPP(c_Relation_Orel__comp(U_8073,U_8075,U_8074),U_8076),U_8077)) = hAPP(hAPP(c_Relation_Orel__comp(U_8074,U_8075,U_8073),hAPP(c_Relation_Oconverse(U_8075,U_8074),U_8077)),hAPP(c_Relation_Oconverse(U_8073,U_8075),U_8076)),
    inference(definitional_conversion,[status(esa)],[f_2284_2]) ).

cnf(f_2284_4,plain,
    hAPP(c_Relation_Oconverse(U_8073,U_8074),hAPP(hAPP(c_Relation_Orel__comp(U_8073,U_8075,U_8074),U_8076),U_8077)) = hAPP(hAPP(c_Relation_Orel__comp(U_8074,U_8075,U_8073),hAPP(c_Relation_Oconverse(U_8075,U_8074),U_8077)),hAPP(c_Relation_Oconverse(U_8073,U_8075),U_8076)),
    inference(clausify,[status(thm)],[f_2284_3]) ).

fof(f_2285_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_2285_2,plain,
    ! [U_8080,U_8079,U_8078] : hAPP(hAPP(c_Relation_Orel__comp(U_8078,U_8079,U_8079),U_8080),c_Relation_OId(U_8079)) = U_8080,
    inference(variable_rename,[status(thm)],[f_2285_1]) ).

fof(f_2285_3,plain,
    ! [U_8079,U_8078,U_8080] : hAPP(hAPP(c_Relation_Orel__comp(U_8078,U_8079,U_8079),U_8080),c_Relation_OId(U_8079)) = U_8080,
    inference(definitional_conversion,[status(esa)],[f_2285_2]) ).

cnf(f_2285_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_8078,U_8079,U_8079),U_8080),c_Relation_OId(U_8079)) = U_8080,
    inference(clausify,[status(thm)],[f_2285_3]) ).

fof(f_2286_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_2286_2,plain,
    ! [U_8083,U_8082,U_8081] : hAPP(hAPP(c_Relation_Orel__comp(U_8081,U_8081,U_8082),c_Relation_OId(U_8081)),U_8083) = U_8083,
    inference(variable_rename,[status(thm)],[f_2286_1]) ).

fof(f_2286_3,plain,
    ! [U_8081,U_8082,U_8083] : hAPP(hAPP(c_Relation_Orel__comp(U_8081,U_8081,U_8082),c_Relation_OId(U_8081)),U_8083) = U_8083,
    inference(definitional_conversion,[status(esa)],[f_2286_2]) ).

cnf(f_2286_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_8081,U_8081,U_8082),c_Relation_OId(U_8081)),U_8083) = U_8083,
    inference(clausify,[status(thm)],[f_2286_3]) ).

fof(f_2287_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_2287_2,plain,
    ! [U_8085,U_8084] : hAPP(c_Relation_ODomain(U_8084,U_8084),c_Relation_OId__on(U_8084,U_8085)) = U_8085,
    inference(variable_rename,[status(thm)],[f_2287_1]) ).

fof(f_2287_3,plain,
    ! [U_8084,U_8085] : hAPP(c_Relation_ODomain(U_8084,U_8084),c_Relation_OId__on(U_8084,U_8085)) = U_8085,
    inference(definitional_conversion,[status(esa)],[f_2287_2]) ).

cnf(f_2287_4,plain,
    hAPP(c_Relation_ODomain(U_8084,U_8084),c_Relation_OId__on(U_8084,U_8085)) = U_8085,
    inference(clausify,[status(thm)],[f_2287_3]) ).

fof(f_2288_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_2288_2,plain,
    ! [U_8089,U_8088,U_8087,U_8086] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8086,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_8086,U_8087),U_8088)),hAPP(c_Relation_ODomain(U_8086,U_8087),U_8089)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8086,U_8087),tc_HOL_Obool)),U_8088),U_8089)) ),
    inference(variable_rename,[status(thm)],[f_2288_1]) ).

fof(f_2288_3,plain,
    ! [U_8086,U_8087,U_8088,U_8089] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8086,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_8086,U_8087),U_8088)),hAPP(c_Relation_ODomain(U_8086,U_8087),U_8089)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8086,U_8087),tc_HOL_Obool)),U_8088),U_8089)) ),
    inference(definitional_conversion,[status(esa)],[f_2288_2]) ).

cnf(f_2288_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8086,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_8086,U_8087),U_8088)),hAPP(c_Relation_ODomain(U_8086,U_8087),U_8089)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8086,U_8087),tc_HOL_Obool)),U_8088),U_8089)) ),
    inference(clausify,[status(thm)],[f_2288_3]) ).

fof(f_2289_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_2289_2,plain,
    ! [U_8092,U_8091,U_8090] : hAPP(c_Relation_ORange(U_8090,U_8091),hAPP(c_Relation_Oconverse(U_8091,U_8090),U_8092)) = hAPP(c_Relation_ODomain(U_8091,U_8090),U_8092),
    inference(variable_rename,[status(thm)],[f_2289_1]) ).

fof(f_2289_3,plain,
    ! [U_8090,U_8091,U_8092] : hAPP(c_Relation_ORange(U_8090,U_8091),hAPP(c_Relation_Oconverse(U_8091,U_8090),U_8092)) = hAPP(c_Relation_ODomain(U_8091,U_8090),U_8092),
    inference(definitional_conversion,[status(esa)],[f_2289_2]) ).

cnf(f_2289_4,plain,
    hAPP(c_Relation_ORange(U_8090,U_8091),hAPP(c_Relation_Oconverse(U_8091,U_8090),U_8092)) = hAPP(c_Relation_ODomain(U_8091,U_8090),U_8092),
    inference(clausify,[status(thm)],[f_2289_3]) ).

fof(f_2290_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_2290_2,plain,
    ! [U_8095,U_8094,U_8093] : hAPP(c_Relation_ODomain(U_8093,U_8094),hAPP(c_Relation_Oconverse(U_8094,U_8093),U_8095)) = hAPP(c_Relation_ORange(U_8094,U_8093),U_8095),
    inference(variable_rename,[status(thm)],[f_2290_1]) ).

fof(f_2290_3,plain,
    ! [U_8093,U_8094,U_8095] : hAPP(c_Relation_ODomain(U_8093,U_8094),hAPP(c_Relation_Oconverse(U_8094,U_8093),U_8095)) = hAPP(c_Relation_ORange(U_8094,U_8093),U_8095),
    inference(definitional_conversion,[status(esa)],[f_2290_2]) ).

cnf(f_2290_4,plain,
    hAPP(c_Relation_ODomain(U_8093,U_8094),hAPP(c_Relation_Oconverse(U_8094,U_8093),U_8095)) = hAPP(c_Relation_ORange(U_8094,U_8093),U_8095),
    inference(clausify,[status(thm)],[f_2290_3]) ).

fof(f_2291_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_2291_2,plain,
    ! [U_8098,U_8097,U_8096] : hAPP(c_Relation_ORange(U_8096,U_8097),U_8098) = hAPP(c_Relation_ODomain(U_8097,U_8096),hAPP(c_Relation_Oconverse(U_8096,U_8097),U_8098)),
    inference(variable_rename,[status(thm)],[f_2291_1]) ).

fof(f_2291_3,plain,
    ! [U_8096,U_8097,U_8098] : hAPP(c_Relation_ORange(U_8096,U_8097),U_8098) = hAPP(c_Relation_ODomain(U_8097,U_8096),hAPP(c_Relation_Oconverse(U_8096,U_8097),U_8098)),
    inference(definitional_conversion,[status(esa)],[f_2291_2]) ).

cnf(f_2291_4,plain,
    hAPP(c_Relation_ORange(U_8096,U_8097),U_8098) = hAPP(c_Relation_ODomain(U_8097,U_8096),hAPP(c_Relation_Oconverse(U_8096,U_8097),U_8098)),
    inference(clausify,[status(thm)],[f_2291_3]) ).

fof(f_2292_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_2292_2,plain,
    ! [U_8101,U_8100,U_8099] : hAPP(c_Set_Oimage(tc_prod(U_8099,U_8100),U_8099,c_Product__Type_Ofst(U_8099,U_8100)),U_8101) = hAPP(c_Relation_ODomain(U_8099,U_8100),U_8101),
    inference(variable_rename,[status(thm)],[f_2292_1]) ).

fof(f_2292_3,plain,
    ! [U_8099,U_8100,U_8101] : hAPP(c_Set_Oimage(tc_prod(U_8099,U_8100),U_8099,c_Product__Type_Ofst(U_8099,U_8100)),U_8101) = hAPP(c_Relation_ODomain(U_8099,U_8100),U_8101),
    inference(definitional_conversion,[status(esa)],[f_2292_2]) ).

cnf(f_2292_4,plain,
    hAPP(c_Set_Oimage(tc_prod(U_8099,U_8100),U_8099,c_Product__Type_Ofst(U_8099,U_8100)),U_8101) = hAPP(c_Relation_ODomain(U_8099,U_8100),U_8101),
    inference(clausify,[status(thm)],[f_2292_3]) ).

fof(f_2293_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_2293_2,plain,
    ! [U_8107,U_8106,U_8105,U_8104] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8104),U_8105),hAPP(c_Relation_ODomain(U_8104,U_8106),U_8107)))
        | ! [U_8103] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8104,U_8106)),hAPP(hAPP(c_Product__Type_OPair(U_8104,U_8106),U_8105),U_8103)),U_8107)) )
      & ( ? [U_8102] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_8104,U_8106)),hAPP(hAPP(c_Product__Type_OPair(U_8104,U_8106),U_8105),U_8102)),U_8107))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8104),U_8105),hAPP(c_Relation_ODomain(U_8104,U_8106),U_8107))) ) ),
    inference(variable_rename,[status(thm)],[f_2293_1]) ).

fof(f_2293_3,plain,
    ( ! [U_8115,U_8113,U_8111,U_8109] :
        ( hBOOL(hAPP(hAPP(c_member(U_8109),U_8111),hAPP(c_Relation_ODomain(U_8109,U_8113),U_8115)))
        | ! [U_8103] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8109,U_8113)),hAPP(hAPP(c_Product__Type_OPair(U_8109,U_8113),U_8111),U_8103)),U_8115)) )
    & ! [U_8114,U_8112,U_8110,U_8108] :
        ( ? [U_8102] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_8108,U_8112)),hAPP(hAPP(c_Product__Type_OPair(U_8108,U_8112),U_8110),U_8102)),U_8114))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8108),U_8110),hAPP(c_Relation_ODomain(U_8108,U_8112),U_8114))) ) ),
    inference(miniscope,[status(thm)],[f_2293_2]) ).

fof(f_2293_4,plain,
    ( ! [U_8115,U_8113,U_8111,U_8109] :
        ( hBOOL(hAPP(hAPP(c_member(U_8109),U_8111),hAPP(c_Relation_ODomain(U_8109,U_8113),U_8115)))
        | ! [U_8103] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8109,U_8113)),hAPP(hAPP(c_Product__Type_OPair(U_8109,U_8113),U_8111),U_8103)),U_8115)) )
    & ! [U_8114,U_8112,U_8110,U_8108] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8108,U_8112)),hAPP(hAPP(c_Product__Type_OPair(U_8108,U_8112),U_8110),sK120(U_8114,U_8112,U_8110,U_8108))),U_8114))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8108),U_8110),hAPP(c_Relation_ODomain(U_8108,U_8112),U_8114))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK120]),skolemize(U_8102,sK120(U_8114,U_8112,U_8110,U_8108))],[f_2293_3]) ).

fof(f_2293_5,plain,
    ( ! [U_8103,U_8109,U_8111,U_8113,U_8115] :
        ( hBOOL(hAPP(hAPP(c_member(U_8109),U_8111),hAPP(c_Relation_ODomain(U_8109,U_8113),U_8115)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8109,U_8113)),hAPP(hAPP(c_Product__Type_OPair(U_8109,U_8113),U_8111),U_8103)),U_8115)) )
    & ! [U_8110,U_8114,U_8108,U_8112] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8108,U_8112)),hAPP(hAPP(c_Product__Type_OPair(U_8108,U_8112),U_8110),sK120(U_8114,U_8112,U_8110,U_8108))),U_8114))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8108),U_8110),hAPP(c_Relation_ODomain(U_8108,U_8112),U_8114))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2293_4]) ).

cnf(f_2293_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8108,U_8112)),hAPP(hAPP(c_Product__Type_OPair(U_8108,U_8112),U_8110),sK120(U_8114,U_8112,U_8110,U_8108))),U_8114))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8108),U_8110),hAPP(c_Relation_ODomain(U_8108,U_8112),U_8114))) ),
    inference(clausify,[status(thm)],[f_2293_5]) ).

cnf(f_2293_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8109),U_8111),hAPP(c_Relation_ODomain(U_8109,U_8113),U_8115)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8109,U_8113)),hAPP(hAPP(c_Product__Type_OPair(U_8109,U_8113),U_8111),U_8103)),U_8115)) ),
    inference(clausify,[status(thm)],[f_2293_5]) ).

fof(f_2294_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_2294_2,plain,
    ! [U_8119,U_8118,U_8117,U_8116] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8116,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8116,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_8116,U_8117),U_8118)),hAPP(c_Relation_ODomain(U_8116,U_8117),U_8119))),hAPP(c_Relation_ODomain(U_8116,U_8117),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_8116,U_8117),tc_HOL_Obool)),U_8118),U_8119)))),
    inference(variable_rename,[status(thm)],[f_2294_1]) ).

fof(f_2294_3,plain,
    ! [U_8116,U_8117,U_8118,U_8119] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8116,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8116,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_8116,U_8117),U_8118)),hAPP(c_Relation_ODomain(U_8116,U_8117),U_8119))),hAPP(c_Relation_ODomain(U_8116,U_8117),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_8116,U_8117),tc_HOL_Obool)),U_8118),U_8119)))),
    inference(definitional_conversion,[status(esa)],[f_2294_2]) ).

cnf(f_2294_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8116,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8116,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_8116,U_8117),U_8118)),hAPP(c_Relation_ODomain(U_8116,U_8117),U_8119))),hAPP(c_Relation_ODomain(U_8116,U_8117),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_8116,U_8117),tc_HOL_Obool)),U_8118),U_8119)))),
    inference(clausify,[status(thm)],[f_2294_3]) ).

fof(f_2295_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_2295_2,plain,
    ! [U_8121,U_8120] :
      ( 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_8120))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_8121))))) = 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_8120))),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_8121)))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8120)) ),
    inference(variable_rename,[status(thm)],[f_2295_1]) ).

fof(f_2295_3,plain,
    ! [U_8121,U_8120] :
      ( 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_8120))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_8121))))) = 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_8120))),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_8121)))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8120)) ),
    inference(definitional_conversion,[status(esa)],[f_2295_2]) ).

cnf(f_2295_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_8120))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_8121))))) = 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_8120))),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_8121)))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_8120)) ),
    inference(clausify,[status(thm)],[f_2295_3]) ).

fof(f_2296_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_2296_2,plain,
    ! [U_8125,U_8124,U_8123,U_8122] :
      ( ( hBOOL(hAPP(c_Predicate_ODomainP(U_8122,U_8123,hAPP(hAPP(c_COMBC(U_8122,tc_fun(tc_prod(U_8122,U_8123),tc_HOL_Obool),tc_fun(U_8123,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8123,tc_fun(tc_fun(tc_prod(U_8122,U_8123),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8122,U_8123),tc_HOL_Obool),tc_fun(U_8123,tc_HOL_Obool)),U_8122),c_COMBC(U_8123,tc_fun(tc_prod(U_8122,U_8123),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8123,tc_prod(U_8122,U_8123)),tc_fun(U_8123,tc_fun(tc_fun(tc_prod(U_8122,U_8123),tc_HOL_Obool),tc_HOL_Obool)),U_8122),hAPP(c_COMBB(tc_prod(U_8122,U_8123),tc_fun(tc_fun(tc_prod(U_8122,U_8123),tc_HOL_Obool),tc_HOL_Obool),U_8123),c_member(tc_prod(U_8122,U_8123)))),c_Product__Type_OPair(U_8122,U_8123)))),U_8124)),U_8125))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8122),U_8125),hAPP(c_Relation_ODomain(U_8122,U_8123),U_8124))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_8122),U_8125),hAPP(c_Relation_ODomain(U_8122,U_8123),U_8124)))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_8122,U_8123,hAPP(hAPP(c_COMBC(U_8122,tc_fun(tc_prod(U_8122,U_8123),tc_HOL_Obool),tc_fun(U_8123,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8123,tc_fun(tc_fun(tc_prod(U_8122,U_8123),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8122,U_8123),tc_HOL_Obool),tc_fun(U_8123,tc_HOL_Obool)),U_8122),c_COMBC(U_8123,tc_fun(tc_prod(U_8122,U_8123),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8123,tc_prod(U_8122,U_8123)),tc_fun(U_8123,tc_fun(tc_fun(tc_prod(U_8122,U_8123),tc_HOL_Obool),tc_HOL_Obool)),U_8122),hAPP(c_COMBB(tc_prod(U_8122,U_8123),tc_fun(tc_fun(tc_prod(U_8122,U_8123),tc_HOL_Obool),tc_HOL_Obool),U_8123),c_member(tc_prod(U_8122,U_8123)))),c_Product__Type_OPair(U_8122,U_8123)))),U_8124)),U_8125)) ) ),
    inference(variable_rename,[status(thm)],[f_2296_1]) ).

fof(f_2296_3,plain,
    ( ! [U_8133,U_8131,U_8129,U_8127] :
        ( hBOOL(hAPP(c_Predicate_ODomainP(U_8127,U_8129,hAPP(hAPP(c_COMBC(U_8127,tc_fun(tc_prod(U_8127,U_8129),tc_HOL_Obool),tc_fun(U_8129,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8129,tc_fun(tc_fun(tc_prod(U_8127,U_8129),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8127,U_8129),tc_HOL_Obool),tc_fun(U_8129,tc_HOL_Obool)),U_8127),c_COMBC(U_8129,tc_fun(tc_prod(U_8127,U_8129),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8129,tc_prod(U_8127,U_8129)),tc_fun(U_8129,tc_fun(tc_fun(tc_prod(U_8127,U_8129),tc_HOL_Obool),tc_HOL_Obool)),U_8127),hAPP(c_COMBB(tc_prod(U_8127,U_8129),tc_fun(tc_fun(tc_prod(U_8127,U_8129),tc_HOL_Obool),tc_HOL_Obool),U_8129),c_member(tc_prod(U_8127,U_8129)))),c_Product__Type_OPair(U_8127,U_8129)))),U_8131)),U_8133))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8127),U_8133),hAPP(c_Relation_ODomain(U_8127,U_8129),U_8131))) )
    & ! [U_8132,U_8130,U_8128,U_8126] :
        ( hBOOL(hAPP(hAPP(c_member(U_8126),U_8132),hAPP(c_Relation_ODomain(U_8126,U_8128),U_8130)))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_8126,U_8128,hAPP(hAPP(c_COMBC(U_8126,tc_fun(tc_prod(U_8126,U_8128),tc_HOL_Obool),tc_fun(U_8128,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8128,tc_fun(tc_fun(tc_prod(U_8126,U_8128),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8126,U_8128),tc_HOL_Obool),tc_fun(U_8128,tc_HOL_Obool)),U_8126),c_COMBC(U_8128,tc_fun(tc_prod(U_8126,U_8128),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8128,tc_prod(U_8126,U_8128)),tc_fun(U_8128,tc_fun(tc_fun(tc_prod(U_8126,U_8128),tc_HOL_Obool),tc_HOL_Obool)),U_8126),hAPP(c_COMBB(tc_prod(U_8126,U_8128),tc_fun(tc_fun(tc_prod(U_8126,U_8128),tc_HOL_Obool),tc_HOL_Obool),U_8128),c_member(tc_prod(U_8126,U_8128)))),c_Product__Type_OPair(U_8126,U_8128)))),U_8130)),U_8132)) ) ),
    inference(miniscope,[status(thm)],[f_2296_2]) ).

fof(f_2296_4,plain,
    ( ! [U_8127,U_8129,U_8131,U_8133] :
        ( hBOOL(hAPP(c_Predicate_ODomainP(U_8127,U_8129,hAPP(hAPP(c_COMBC(U_8127,tc_fun(tc_prod(U_8127,U_8129),tc_HOL_Obool),tc_fun(U_8129,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8129,tc_fun(tc_fun(tc_prod(U_8127,U_8129),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8127,U_8129),tc_HOL_Obool),tc_fun(U_8129,tc_HOL_Obool)),U_8127),c_COMBC(U_8129,tc_fun(tc_prod(U_8127,U_8129),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8129,tc_prod(U_8127,U_8129)),tc_fun(U_8129,tc_fun(tc_fun(tc_prod(U_8127,U_8129),tc_HOL_Obool),tc_HOL_Obool)),U_8127),hAPP(c_COMBB(tc_prod(U_8127,U_8129),tc_fun(tc_fun(tc_prod(U_8127,U_8129),tc_HOL_Obool),tc_HOL_Obool),U_8129),c_member(tc_prod(U_8127,U_8129)))),c_Product__Type_OPair(U_8127,U_8129)))),U_8131)),U_8133))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8127),U_8133),hAPP(c_Relation_ODomain(U_8127,U_8129),U_8131))) )
    & ! [U_8128,U_8132,U_8126,U_8130] :
        ( hBOOL(hAPP(hAPP(c_member(U_8126),U_8132),hAPP(c_Relation_ODomain(U_8126,U_8128),U_8130)))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_8126,U_8128,hAPP(hAPP(c_COMBC(U_8126,tc_fun(tc_prod(U_8126,U_8128),tc_HOL_Obool),tc_fun(U_8128,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8128,tc_fun(tc_fun(tc_prod(U_8126,U_8128),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8126,U_8128),tc_HOL_Obool),tc_fun(U_8128,tc_HOL_Obool)),U_8126),c_COMBC(U_8128,tc_fun(tc_prod(U_8126,U_8128),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8128,tc_prod(U_8126,U_8128)),tc_fun(U_8128,tc_fun(tc_fun(tc_prod(U_8126,U_8128),tc_HOL_Obool),tc_HOL_Obool)),U_8126),hAPP(c_COMBB(tc_prod(U_8126,U_8128),tc_fun(tc_fun(tc_prod(U_8126,U_8128),tc_HOL_Obool),tc_HOL_Obool),U_8128),c_member(tc_prod(U_8126,U_8128)))),c_Product__Type_OPair(U_8126,U_8128)))),U_8130)),U_8132)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2296_3]) ).

cnf(f_2296_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8126),U_8132),hAPP(c_Relation_ODomain(U_8126,U_8128),U_8130)))
    | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_8126,U_8128,hAPP(hAPP(c_COMBC(U_8126,tc_fun(tc_prod(U_8126,U_8128),tc_HOL_Obool),tc_fun(U_8128,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8128,tc_fun(tc_fun(tc_prod(U_8126,U_8128),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8126,U_8128),tc_HOL_Obool),tc_fun(U_8128,tc_HOL_Obool)),U_8126),c_COMBC(U_8128,tc_fun(tc_prod(U_8126,U_8128),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8128,tc_prod(U_8126,U_8128)),tc_fun(U_8128,tc_fun(tc_fun(tc_prod(U_8126,U_8128),tc_HOL_Obool),tc_HOL_Obool)),U_8126),hAPP(c_COMBB(tc_prod(U_8126,U_8128),tc_fun(tc_fun(tc_prod(U_8126,U_8128),tc_HOL_Obool),tc_HOL_Obool),U_8128),c_member(tc_prod(U_8126,U_8128)))),c_Product__Type_OPair(U_8126,U_8128)))),U_8130)),U_8132)) ),
    inference(clausify,[status(thm)],[f_2296_4]) ).

cnf(f_2296_6,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(U_8127,U_8129,hAPP(hAPP(c_COMBC(U_8127,tc_fun(tc_prod(U_8127,U_8129),tc_HOL_Obool),tc_fun(U_8129,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8129,tc_fun(tc_fun(tc_prod(U_8127,U_8129),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8127,U_8129),tc_HOL_Obool),tc_fun(U_8129,tc_HOL_Obool)),U_8127),c_COMBC(U_8129,tc_fun(tc_prod(U_8127,U_8129),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8129,tc_prod(U_8127,U_8129)),tc_fun(U_8129,tc_fun(tc_fun(tc_prod(U_8127,U_8129),tc_HOL_Obool),tc_HOL_Obool)),U_8127),hAPP(c_COMBB(tc_prod(U_8127,U_8129),tc_fun(tc_fun(tc_prod(U_8127,U_8129),tc_HOL_Obool),tc_HOL_Obool),U_8129),c_member(tc_prod(U_8127,U_8129)))),c_Product__Type_OPair(U_8127,U_8129)))),U_8131)),U_8133))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8127),U_8133),hAPP(c_Relation_ODomain(U_8127,U_8129),U_8131))) ),
    inference(clausify,[status(thm)],[f_2296_4]) ).

fof(f_2297_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_2297_2,plain,
    ! [U_8138,U_8137,U_8136,U_8135] :
      ( ? [U_8134] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_8135,U_8137)),hAPP(hAPP(c_Product__Type_OPair(U_8135,U_8137),U_8136),U_8134)),U_8138))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8135),U_8136),hAPP(c_Relation_ODomain(U_8135,U_8137),U_8138))) ),
    inference(variable_rename,[status(thm)],[f_2297_1]) ).

fof(f_2297_3,plain,
    ! [U_8138,U_8137,U_8136,U_8135] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8135,U_8137)),hAPP(hAPP(c_Product__Type_OPair(U_8135,U_8137),U_8136),sK121(U_8138,U_8137,U_8136,U_8135))),U_8138))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8135),U_8136),hAPP(c_Relation_ODomain(U_8135,U_8137),U_8138))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK121]),skolemize(U_8134,sK121(U_8138,U_8137,U_8136,U_8135))],[f_2297_2]) ).

fof(f_2297_4,plain,
    ! [U_8135,U_8136,U_8137,U_8138] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8135,U_8137)),hAPP(hAPP(c_Product__Type_OPair(U_8135,U_8137),U_8136),sK121(U_8138,U_8137,U_8136,U_8135))),U_8138))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8135),U_8136),hAPP(c_Relation_ODomain(U_8135,U_8137),U_8138))) ),
    inference(definitional_conversion,[status(esa)],[f_2297_3]) ).

cnf(f_2297_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8135,U_8137)),hAPP(hAPP(c_Product__Type_OPair(U_8135,U_8137),U_8136),sK121(U_8138,U_8137,U_8136,U_8135))),U_8138))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8135),U_8136),hAPP(c_Relation_ODomain(U_8135,U_8137),U_8138))) ),
    inference(clausify,[status(thm)],[f_2297_4]) ).

fof(f_2298_1,plain,
    ! [V_y_2,V_x_2,V_s_2,V_r_2,T_d,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(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)))
        | ~ hBOOL(hAPP(hAPP(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_2298_2,plain,
    ! [U_8145,U_8144,U_8143,U_8142,U_8141,U_8140,U_8139] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_8139,U_8140,U_8141,hAPP(hAPP(c_COMBC(U_8139,tc_fun(tc_prod(U_8139,U_8140),tc_HOL_Obool),tc_fun(U_8140,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8140,tc_fun(tc_fun(tc_prod(U_8139,U_8140),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8139,U_8140),tc_HOL_Obool),tc_fun(U_8140,tc_HOL_Obool)),U_8139),c_COMBC(U_8140,tc_fun(tc_prod(U_8139,U_8140),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8140,tc_prod(U_8139,U_8140)),tc_fun(U_8140,tc_fun(tc_fun(tc_prod(U_8139,U_8140),tc_HOL_Obool),tc_HOL_Obool)),U_8139),hAPP(c_COMBB(tc_prod(U_8139,U_8140),tc_fun(tc_fun(tc_prod(U_8139,U_8140),tc_HOL_Obool),tc_HOL_Obool),U_8140),c_member(tc_prod(U_8139,U_8140)))),c_Product__Type_OPair(U_8139,U_8140)))),U_8142),hAPP(hAPP(c_COMBC(U_8140,tc_fun(tc_prod(U_8140,U_8141),tc_HOL_Obool),tc_fun(U_8141,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8141,tc_fun(tc_fun(tc_prod(U_8140,U_8141),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8140,U_8141),tc_HOL_Obool),tc_fun(U_8141,tc_HOL_Obool)),U_8140),c_COMBC(U_8141,tc_fun(tc_prod(U_8140,U_8141),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8141,tc_prod(U_8140,U_8141)),tc_fun(U_8141,tc_fun(tc_fun(tc_prod(U_8140,U_8141),tc_HOL_Obool),tc_HOL_Obool)),U_8140),hAPP(c_COMBB(tc_prod(U_8140,U_8141),tc_fun(tc_fun(tc_prod(U_8140,U_8141),tc_HOL_Obool),tc_HOL_Obool),U_8141),c_member(tc_prod(U_8140,U_8141)))),c_Product__Type_OPair(U_8140,U_8141)))),U_8143)),U_8144),U_8145))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8139,U_8141)),hAPP(hAPP(c_Product__Type_OPair(U_8139,U_8141),U_8144),U_8145)),hAPP(hAPP(c_Relation_Orel__comp(U_8139,U_8140,U_8141),U_8142),U_8143))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8139,U_8141)),hAPP(hAPP(c_Product__Type_OPair(U_8139,U_8141),U_8144),U_8145)),hAPP(hAPP(c_Relation_Orel__comp(U_8139,U_8140,U_8141),U_8142),U_8143)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_8139,U_8140,U_8141,hAPP(hAPP(c_COMBC(U_8139,tc_fun(tc_prod(U_8139,U_8140),tc_HOL_Obool),tc_fun(U_8140,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8140,tc_fun(tc_fun(tc_prod(U_8139,U_8140),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8139,U_8140),tc_HOL_Obool),tc_fun(U_8140,tc_HOL_Obool)),U_8139),c_COMBC(U_8140,tc_fun(tc_prod(U_8139,U_8140),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8140,tc_prod(U_8139,U_8140)),tc_fun(U_8140,tc_fun(tc_fun(tc_prod(U_8139,U_8140),tc_HOL_Obool),tc_HOL_Obool)),U_8139),hAPP(c_COMBB(tc_prod(U_8139,U_8140),tc_fun(tc_fun(tc_prod(U_8139,U_8140),tc_HOL_Obool),tc_HOL_Obool),U_8140),c_member(tc_prod(U_8139,U_8140)))),c_Product__Type_OPair(U_8139,U_8140)))),U_8142),hAPP(hAPP(c_COMBC(U_8140,tc_fun(tc_prod(U_8140,U_8141),tc_HOL_Obool),tc_fun(U_8141,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8141,tc_fun(tc_fun(tc_prod(U_8140,U_8141),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8140,U_8141),tc_HOL_Obool),tc_fun(U_8141,tc_HOL_Obool)),U_8140),c_COMBC(U_8141,tc_fun(tc_prod(U_8140,U_8141),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8141,tc_prod(U_8140,U_8141)),tc_fun(U_8141,tc_fun(tc_fun(tc_prod(U_8140,U_8141),tc_HOL_Obool),tc_HOL_Obool)),U_8140),hAPP(c_COMBB(tc_prod(U_8140,U_8141),tc_fun(tc_fun(tc_prod(U_8140,U_8141),tc_HOL_Obool),tc_HOL_Obool),U_8141),c_member(tc_prod(U_8140,U_8141)))),c_Product__Type_OPair(U_8140,U_8141)))),U_8143)),U_8144),U_8145)) ) ),
    inference(variable_rename,[status(thm)],[f_2298_1]) ).

fof(f_2298_3,plain,
    ( ! [U_8159,U_8157,U_8155,U_8153,U_8151,U_8149,U_8147] :
        ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_8147,U_8149,U_8151,hAPP(hAPP(c_COMBC(U_8147,tc_fun(tc_prod(U_8147,U_8149),tc_HOL_Obool),tc_fun(U_8149,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8149,tc_fun(tc_fun(tc_prod(U_8147,U_8149),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8147,U_8149),tc_HOL_Obool),tc_fun(U_8149,tc_HOL_Obool)),U_8147),c_COMBC(U_8149,tc_fun(tc_prod(U_8147,U_8149),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8149,tc_prod(U_8147,U_8149)),tc_fun(U_8149,tc_fun(tc_fun(tc_prod(U_8147,U_8149),tc_HOL_Obool),tc_HOL_Obool)),U_8147),hAPP(c_COMBB(tc_prod(U_8147,U_8149),tc_fun(tc_fun(tc_prod(U_8147,U_8149),tc_HOL_Obool),tc_HOL_Obool),U_8149),c_member(tc_prod(U_8147,U_8149)))),c_Product__Type_OPair(U_8147,U_8149)))),U_8153),hAPP(hAPP(c_COMBC(U_8149,tc_fun(tc_prod(U_8149,U_8151),tc_HOL_Obool),tc_fun(U_8151,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8151,tc_fun(tc_fun(tc_prod(U_8149,U_8151),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8149,U_8151),tc_HOL_Obool),tc_fun(U_8151,tc_HOL_Obool)),U_8149),c_COMBC(U_8151,tc_fun(tc_prod(U_8149,U_8151),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8151,tc_prod(U_8149,U_8151)),tc_fun(U_8151,tc_fun(tc_fun(tc_prod(U_8149,U_8151),tc_HOL_Obool),tc_HOL_Obool)),U_8149),hAPP(c_COMBB(tc_prod(U_8149,U_8151),tc_fun(tc_fun(tc_prod(U_8149,U_8151),tc_HOL_Obool),tc_HOL_Obool),U_8151),c_member(tc_prod(U_8149,U_8151)))),c_Product__Type_OPair(U_8149,U_8151)))),U_8155)),U_8157),U_8159))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8147,U_8151)),hAPP(hAPP(c_Product__Type_OPair(U_8147,U_8151),U_8157),U_8159)),hAPP(hAPP(c_Relation_Orel__comp(U_8147,U_8149,U_8151),U_8153),U_8155))) )
    & ! [U_8158,U_8156,U_8154,U_8152,U_8150,U_8148,U_8146] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8146,U_8150)),hAPP(hAPP(c_Product__Type_OPair(U_8146,U_8150),U_8156),U_8158)),hAPP(hAPP(c_Relation_Orel__comp(U_8146,U_8148,U_8150),U_8152),U_8154)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_8146,U_8148,U_8150,hAPP(hAPP(c_COMBC(U_8146,tc_fun(tc_prod(U_8146,U_8148),tc_HOL_Obool),tc_fun(U_8148,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8148,tc_fun(tc_fun(tc_prod(U_8146,U_8148),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8146,U_8148),tc_HOL_Obool),tc_fun(U_8148,tc_HOL_Obool)),U_8146),c_COMBC(U_8148,tc_fun(tc_prod(U_8146,U_8148),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8148,tc_prod(U_8146,U_8148)),tc_fun(U_8148,tc_fun(tc_fun(tc_prod(U_8146,U_8148),tc_HOL_Obool),tc_HOL_Obool)),U_8146),hAPP(c_COMBB(tc_prod(U_8146,U_8148),tc_fun(tc_fun(tc_prod(U_8146,U_8148),tc_HOL_Obool),tc_HOL_Obool),U_8148),c_member(tc_prod(U_8146,U_8148)))),c_Product__Type_OPair(U_8146,U_8148)))),U_8152),hAPP(hAPP(c_COMBC(U_8148,tc_fun(tc_prod(U_8148,U_8150),tc_HOL_Obool),tc_fun(U_8150,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8150,tc_fun(tc_fun(tc_prod(U_8148,U_8150),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8148,U_8150),tc_HOL_Obool),tc_fun(U_8150,tc_HOL_Obool)),U_8148),c_COMBC(U_8150,tc_fun(tc_prod(U_8148,U_8150),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8150,tc_prod(U_8148,U_8150)),tc_fun(U_8150,tc_fun(tc_fun(tc_prod(U_8148,U_8150),tc_HOL_Obool),tc_HOL_Obool)),U_8148),hAPP(c_COMBB(tc_prod(U_8148,U_8150),tc_fun(tc_fun(tc_prod(U_8148,U_8150),tc_HOL_Obool),tc_HOL_Obool),U_8150),c_member(tc_prod(U_8148,U_8150)))),c_Product__Type_OPair(U_8148,U_8150)))),U_8154)),U_8156),U_8158)) ) ),
    inference(miniscope,[status(thm)],[f_2298_2]) ).

fof(f_2298_4,plain,
    ( ! [U_8147,U_8149,U_8151,U_8153,U_8155,U_8157,U_8159] :
        ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_8147,U_8149,U_8151,hAPP(hAPP(c_COMBC(U_8147,tc_fun(tc_prod(U_8147,U_8149),tc_HOL_Obool),tc_fun(U_8149,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8149,tc_fun(tc_fun(tc_prod(U_8147,U_8149),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8147,U_8149),tc_HOL_Obool),tc_fun(U_8149,tc_HOL_Obool)),U_8147),c_COMBC(U_8149,tc_fun(tc_prod(U_8147,U_8149),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8149,tc_prod(U_8147,U_8149)),tc_fun(U_8149,tc_fun(tc_fun(tc_prod(U_8147,U_8149),tc_HOL_Obool),tc_HOL_Obool)),U_8147),hAPP(c_COMBB(tc_prod(U_8147,U_8149),tc_fun(tc_fun(tc_prod(U_8147,U_8149),tc_HOL_Obool),tc_HOL_Obool),U_8149),c_member(tc_prod(U_8147,U_8149)))),c_Product__Type_OPair(U_8147,U_8149)))),U_8153),hAPP(hAPP(c_COMBC(U_8149,tc_fun(tc_prod(U_8149,U_8151),tc_HOL_Obool),tc_fun(U_8151,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8151,tc_fun(tc_fun(tc_prod(U_8149,U_8151),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8149,U_8151),tc_HOL_Obool),tc_fun(U_8151,tc_HOL_Obool)),U_8149),c_COMBC(U_8151,tc_fun(tc_prod(U_8149,U_8151),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8151,tc_prod(U_8149,U_8151)),tc_fun(U_8151,tc_fun(tc_fun(tc_prod(U_8149,U_8151),tc_HOL_Obool),tc_HOL_Obool)),U_8149),hAPP(c_COMBB(tc_prod(U_8149,U_8151),tc_fun(tc_fun(tc_prod(U_8149,U_8151),tc_HOL_Obool),tc_HOL_Obool),U_8151),c_member(tc_prod(U_8149,U_8151)))),c_Product__Type_OPair(U_8149,U_8151)))),U_8155)),U_8157),U_8159))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8147,U_8151)),hAPP(hAPP(c_Product__Type_OPair(U_8147,U_8151),U_8157),U_8159)),hAPP(hAPP(c_Relation_Orel__comp(U_8147,U_8149,U_8151),U_8153),U_8155))) )
    & ! [U_8150,U_8154,U_8148,U_8146,U_8152,U_8156,U_8158] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8146,U_8150)),hAPP(hAPP(c_Product__Type_OPair(U_8146,U_8150),U_8156),U_8158)),hAPP(hAPP(c_Relation_Orel__comp(U_8146,U_8148,U_8150),U_8152),U_8154)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_8146,U_8148,U_8150,hAPP(hAPP(c_COMBC(U_8146,tc_fun(tc_prod(U_8146,U_8148),tc_HOL_Obool),tc_fun(U_8148,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8148,tc_fun(tc_fun(tc_prod(U_8146,U_8148),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8146,U_8148),tc_HOL_Obool),tc_fun(U_8148,tc_HOL_Obool)),U_8146),c_COMBC(U_8148,tc_fun(tc_prod(U_8146,U_8148),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8148,tc_prod(U_8146,U_8148)),tc_fun(U_8148,tc_fun(tc_fun(tc_prod(U_8146,U_8148),tc_HOL_Obool),tc_HOL_Obool)),U_8146),hAPP(c_COMBB(tc_prod(U_8146,U_8148),tc_fun(tc_fun(tc_prod(U_8146,U_8148),tc_HOL_Obool),tc_HOL_Obool),U_8148),c_member(tc_prod(U_8146,U_8148)))),c_Product__Type_OPair(U_8146,U_8148)))),U_8152),hAPP(hAPP(c_COMBC(U_8148,tc_fun(tc_prod(U_8148,U_8150),tc_HOL_Obool),tc_fun(U_8150,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8150,tc_fun(tc_fun(tc_prod(U_8148,U_8150),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8148,U_8150),tc_HOL_Obool),tc_fun(U_8150,tc_HOL_Obool)),U_8148),c_COMBC(U_8150,tc_fun(tc_prod(U_8148,U_8150),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8150,tc_prod(U_8148,U_8150)),tc_fun(U_8150,tc_fun(tc_fun(tc_prod(U_8148,U_8150),tc_HOL_Obool),tc_HOL_Obool)),U_8148),hAPP(c_COMBB(tc_prod(U_8148,U_8150),tc_fun(tc_fun(tc_prod(U_8148,U_8150),tc_HOL_Obool),tc_HOL_Obool),U_8150),c_member(tc_prod(U_8148,U_8150)))),c_Product__Type_OPair(U_8148,U_8150)))),U_8154)),U_8156),U_8158)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2298_3]) ).

cnf(f_2298_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8146,U_8150)),hAPP(hAPP(c_Product__Type_OPair(U_8146,U_8150),U_8156),U_8158)),hAPP(hAPP(c_Relation_Orel__comp(U_8146,U_8148,U_8150),U_8152),U_8154)))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_8146,U_8148,U_8150,hAPP(hAPP(c_COMBC(U_8146,tc_fun(tc_prod(U_8146,U_8148),tc_HOL_Obool),tc_fun(U_8148,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8148,tc_fun(tc_fun(tc_prod(U_8146,U_8148),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8146,U_8148),tc_HOL_Obool),tc_fun(U_8148,tc_HOL_Obool)),U_8146),c_COMBC(U_8148,tc_fun(tc_prod(U_8146,U_8148),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8148,tc_prod(U_8146,U_8148)),tc_fun(U_8148,tc_fun(tc_fun(tc_prod(U_8146,U_8148),tc_HOL_Obool),tc_HOL_Obool)),U_8146),hAPP(c_COMBB(tc_prod(U_8146,U_8148),tc_fun(tc_fun(tc_prod(U_8146,U_8148),tc_HOL_Obool),tc_HOL_Obool),U_8148),c_member(tc_prod(U_8146,U_8148)))),c_Product__Type_OPair(U_8146,U_8148)))),U_8152),hAPP(hAPP(c_COMBC(U_8148,tc_fun(tc_prod(U_8148,U_8150),tc_HOL_Obool),tc_fun(U_8150,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8150,tc_fun(tc_fun(tc_prod(U_8148,U_8150),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8148,U_8150),tc_HOL_Obool),tc_fun(U_8150,tc_HOL_Obool)),U_8148),c_COMBC(U_8150,tc_fun(tc_prod(U_8148,U_8150),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8150,tc_prod(U_8148,U_8150)),tc_fun(U_8150,tc_fun(tc_fun(tc_prod(U_8148,U_8150),tc_HOL_Obool),tc_HOL_Obool)),U_8148),hAPP(c_COMBB(tc_prod(U_8148,U_8150),tc_fun(tc_fun(tc_prod(U_8148,U_8150),tc_HOL_Obool),tc_HOL_Obool),U_8150),c_member(tc_prod(U_8148,U_8150)))),c_Product__Type_OPair(U_8148,U_8150)))),U_8154)),U_8156),U_8158)) ),
    inference(clausify,[status(thm)],[f_2298_4]) ).

cnf(f_2298_6,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_8147,U_8149,U_8151,hAPP(hAPP(c_COMBC(U_8147,tc_fun(tc_prod(U_8147,U_8149),tc_HOL_Obool),tc_fun(U_8149,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8149,tc_fun(tc_fun(tc_prod(U_8147,U_8149),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8147,U_8149),tc_HOL_Obool),tc_fun(U_8149,tc_HOL_Obool)),U_8147),c_COMBC(U_8149,tc_fun(tc_prod(U_8147,U_8149),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8149,tc_prod(U_8147,U_8149)),tc_fun(U_8149,tc_fun(tc_fun(tc_prod(U_8147,U_8149),tc_HOL_Obool),tc_HOL_Obool)),U_8147),hAPP(c_COMBB(tc_prod(U_8147,U_8149),tc_fun(tc_fun(tc_prod(U_8147,U_8149),tc_HOL_Obool),tc_HOL_Obool),U_8149),c_member(tc_prod(U_8147,U_8149)))),c_Product__Type_OPair(U_8147,U_8149)))),U_8153),hAPP(hAPP(c_COMBC(U_8149,tc_fun(tc_prod(U_8149,U_8151),tc_HOL_Obool),tc_fun(U_8151,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8151,tc_fun(tc_fun(tc_prod(U_8149,U_8151),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8149,U_8151),tc_HOL_Obool),tc_fun(U_8151,tc_HOL_Obool)),U_8149),c_COMBC(U_8151,tc_fun(tc_prod(U_8149,U_8151),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8151,tc_prod(U_8149,U_8151)),tc_fun(U_8151,tc_fun(tc_fun(tc_prod(U_8149,U_8151),tc_HOL_Obool),tc_HOL_Obool)),U_8149),hAPP(c_COMBB(tc_prod(U_8149,U_8151),tc_fun(tc_fun(tc_prod(U_8149,U_8151),tc_HOL_Obool),tc_HOL_Obool),U_8151),c_member(tc_prod(U_8149,U_8151)))),c_Product__Type_OPair(U_8149,U_8151)))),U_8155)),U_8157),U_8159))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8147,U_8151)),hAPP(hAPP(c_Product__Type_OPair(U_8147,U_8151),U_8157),U_8159)),hAPP(hAPP(c_Relation_Orel__comp(U_8147,U_8149,U_8151),U_8153),U_8155))) ),
    inference(clausify,[status(thm)],[f_2298_4]) ).

fof(f_2299_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_2299_2,plain,
    ! [U_8162,U_8161,U_8160] :
      ( c_FunDef_Oreduction__pair(U_8160,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_8160,U_8160),tc_HOL_Obool),tc_fun(tc_prod(U_8160,U_8160),tc_HOL_Obool)),U_8161),U_8162))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8160,U_8160),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8160,U_8160,U_8160),U_8161),U_8162)),U_8161))
      | ~ c_Wellfounded_Owf(U_8160,U_8161) ),
    inference(variable_rename,[status(thm)],[f_2299_1]) ).

fof(f_2299_3,plain,
    ! [U_8160,U_8161,U_8162] :
      ( c_FunDef_Oreduction__pair(U_8160,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_8160,U_8160),tc_HOL_Obool),tc_fun(tc_prod(U_8160,U_8160),tc_HOL_Obool)),U_8161),U_8162))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8160,U_8160),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8160,U_8160,U_8160),U_8161),U_8162)),U_8161))
      | ~ c_Wellfounded_Owf(U_8160,U_8161) ),
    inference(definitional_conversion,[status(esa)],[f_2299_2]) ).

cnf(f_2299_4,plain,
    ( c_FunDef_Oreduction__pair(U_8160,hAPP(hAPP(c_Product__Type_OPair(tc_fun(tc_prod(U_8160,U_8160),tc_HOL_Obool),tc_fun(tc_prod(U_8160,U_8160),tc_HOL_Obool)),U_8161),U_8162))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8160,U_8160),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8160,U_8160,U_8160),U_8161),U_8162)),U_8161))
    | ~ c_Wellfounded_Owf(U_8160,U_8161) ),
    inference(clausify,[status(thm)],[f_2299_3]) ).

fof(f_2300_1,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(fof_nnf,[status(thm)],[fact_wf__less__than]) ).

fof(f_2300_2,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(definitional_conversion,[status(esa)],[f_2300_1]) ).

cnf(f_2300_3,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than),
    inference(clausify,[status(thm)],[f_2300_2]) ).

fof(f_2301_1,plain,
    ! [T_d,T_c,T_b,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] :
      ( hBOOL(hAPP(hAPP(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_2301_2,plain,
    ! [U_8170,U_8169,U_8168,U_8167,U_8166,U_8165,U_8164,U_8163] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_8168,U_8169,U_8170,U_8163,U_8166),U_8164),U_8167))
      | ~ hBOOL(hAPP(hAPP(U_8166,U_8165),U_8167))
      | ~ hBOOL(hAPP(hAPP(U_8163,U_8164),U_8165)) ),
    inference(variable_rename,[status(thm)],[f_2301_1]) ).

fof(f_2301_3,plain,
    ! [U_8163,U_8164,U_8165,U_8166,U_8167,U_8168,U_8169,U_8170] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_8168,U_8169,U_8170,U_8163,U_8166),U_8164),U_8167))
      | ~ hBOOL(hAPP(hAPP(U_8166,U_8165),U_8167))
      | ~ hBOOL(hAPP(hAPP(U_8163,U_8164),U_8165)) ),
    inference(definitional_conversion,[status(esa)],[f_2301_2]) ).

cnf(f_2301_4,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_8168,U_8169,U_8170,U_8163,U_8166),U_8164),U_8167))
    | ~ hBOOL(hAPP(hAPP(U_8166,U_8165),U_8167))
    | ~ hBOOL(hAPP(hAPP(U_8163,U_8164),U_8165)) ),
    inference(clausify,[status(thm)],[f_2301_3]) ).

fof(f_2302_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_2302_2,plain,
    ! [U_8175,U_8174,U_8173,U_8172,U_8171] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(U_8174,U_8175,U_8171),U_8172))
      | ~ hBOOL(hAPP(hAPP(U_8171,U_8172),U_8173)) ),
    inference(variable_rename,[status(thm)],[f_2302_1]) ).

fof(f_2302_3,plain,
    ! [U_8172,U_8173,U_8174,U_8171,U_8175] :
      ( hBOOL(hAPP(c_Predicate_ODomainP(U_8174,U_8175,U_8171),U_8172))
      | ~ hBOOL(hAPP(hAPP(U_8171,U_8172),U_8173)) ),
    inference(definitional_conversion,[status(esa)],[f_2302_2]) ).

cnf(f_2302_4,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(U_8174,U_8175,U_8171),U_8172))
    | ~ hBOOL(hAPP(hAPP(U_8171,U_8172),U_8173)) ),
    inference(clausify,[status(thm)],[f_2302_3]) ).

fof(f_2303_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_2303_2,plain,
    ! [U_8179,U_8178,U_8177,U_8176] :
      ( c_Wellfounded_Owf(U_8178,hAPP(hAPP(c_Relation_Oinv__image(U_8176,U_8178),U_8177),U_8179))
      | ~ c_Wellfounded_Owf(U_8176,U_8177) ),
    inference(variable_rename,[status(thm)],[f_2303_1]) ).

fof(f_2303_3,plain,
    ! [U_8176,U_8177,U_8178,U_8179] :
      ( c_Wellfounded_Owf(U_8178,hAPP(hAPP(c_Relation_Oinv__image(U_8176,U_8178),U_8177),U_8179))
      | ~ c_Wellfounded_Owf(U_8176,U_8177) ),
    inference(definitional_conversion,[status(esa)],[f_2303_2]) ).

cnf(f_2303_4,plain,
    ( c_Wellfounded_Owf(U_8178,hAPP(hAPP(c_Relation_Oinv__image(U_8176,U_8178),U_8177),U_8179))
    | ~ c_Wellfounded_Owf(U_8176,U_8177) ),
    inference(clausify,[status(thm)],[f_2303_3]) ).

fof(f_2304_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_2304_2,plain,
    ! [U_8183,U_8182,U_8181,U_8180] :
      ( c_Wellfounded_Owf(tc_prod(U_8180,U_8182),c_Wellfounded_Olex__prod(U_8180,U_8182,U_8181,U_8183))
      | ~ c_Wellfounded_Owf(U_8182,U_8183)
      | ~ c_Wellfounded_Owf(U_8180,U_8181) ),
    inference(variable_rename,[status(thm)],[f_2304_1]) ).

fof(f_2304_3,plain,
    ! [U_8182,U_8181,U_8180,U_8183] :
      ( c_Wellfounded_Owf(tc_prod(U_8180,U_8182),c_Wellfounded_Olex__prod(U_8180,U_8182,U_8181,U_8183))
      | ~ c_Wellfounded_Owf(U_8182,U_8183)
      | ~ c_Wellfounded_Owf(U_8180,U_8181) ),
    inference(definitional_conversion,[status(esa)],[f_2304_2]) ).

cnf(f_2304_4,plain,
    ( c_Wellfounded_Owf(tc_prod(U_8180,U_8182),c_Wellfounded_Olex__prod(U_8180,U_8182,U_8181,U_8183))
    | ~ c_Wellfounded_Owf(U_8182,U_8183)
    | ~ c_Wellfounded_Owf(U_8180,U_8181) ),
    inference(clausify,[status(thm)],[f_2304_3]) ).

fof(f_2305_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_2305_2,plain,
    ! [U_8185,U_8184] : c_Wellfounded_Owf(U_8184,hAPP(c_Wellfounded_Omeasure(U_8184),U_8185)),
    inference(variable_rename,[status(thm)],[f_2305_1]) ).

fof(f_2305_3,plain,
    ! [U_8185,U_8184] : c_Wellfounded_Owf(U_8184,hAPP(c_Wellfounded_Omeasure(U_8184),U_8185)),
    inference(definitional_conversion,[status(esa)],[f_2305_2]) ).

cnf(f_2305_4,plain,
    c_Wellfounded_Owf(U_8184,hAPP(c_Wellfounded_Omeasure(U_8184),U_8185)),
    inference(clausify,[status(thm)],[f_2305_3]) ).

fof(f_2306_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_2306_2,plain,
    ! [U_8187,U_8186] :
      ( ( c_Wellfounded_Owf(U_8186,U_8187)
        | ~ c_Wellfounded_Owf(U_8186,hAPP(hAPP(c_Relation_Orel__comp(U_8186,U_8186,U_8186),U_8187),U_8187)) )
      & ( c_Wellfounded_Owf(U_8186,hAPP(hAPP(c_Relation_Orel__comp(U_8186,U_8186,U_8186),U_8187),U_8187))
        | ~ c_Wellfounded_Owf(U_8186,U_8187) ) ),
    inference(variable_rename,[status(thm)],[f_2306_1]) ).

fof(f_2306_3,plain,
    ( ! [U_8191,U_8189] :
        ( c_Wellfounded_Owf(U_8189,U_8191)
        | ~ c_Wellfounded_Owf(U_8189,hAPP(hAPP(c_Relation_Orel__comp(U_8189,U_8189,U_8189),U_8191),U_8191)) )
    & ! [U_8190,U_8188] :
        ( c_Wellfounded_Owf(U_8188,hAPP(hAPP(c_Relation_Orel__comp(U_8188,U_8188,U_8188),U_8190),U_8190))
        | ~ c_Wellfounded_Owf(U_8188,U_8190) ) ),
    inference(miniscope,[status(thm)],[f_2306_2]) ).

fof(f_2306_4,plain,
    ( ! [U_8189,U_8191] :
        ( c_Wellfounded_Owf(U_8189,U_8191)
        | ~ c_Wellfounded_Owf(U_8189,hAPP(hAPP(c_Relation_Orel__comp(U_8189,U_8189,U_8189),U_8191),U_8191)) )
    & ! [U_8190,U_8188] :
        ( c_Wellfounded_Owf(U_8188,hAPP(hAPP(c_Relation_Orel__comp(U_8188,U_8188,U_8188),U_8190),U_8190))
        | ~ c_Wellfounded_Owf(U_8188,U_8190) ) ),
    inference(definitional_conversion,[status(esa)],[f_2306_3]) ).

cnf(f_2306_5,plain,
    ( c_Wellfounded_Owf(U_8188,hAPP(hAPP(c_Relation_Orel__comp(U_8188,U_8188,U_8188),U_8190),U_8190))
    | ~ c_Wellfounded_Owf(U_8188,U_8190) ),
    inference(clausify,[status(thm)],[f_2306_4]) ).

cnf(f_2306_6,plain,
    ( c_Wellfounded_Owf(U_8189,U_8191)
    | ~ c_Wellfounded_Owf(U_8189,hAPP(hAPP(c_Relation_Orel__comp(U_8189,U_8189,U_8189),U_8191),U_8191)) ),
    inference(clausify,[status(thm)],[f_2306_4]) ).

fof(f_2307_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_2307_2,plain,
    ! [U_8194,U_8193,U_8192] :
      ( c_Wellfounded_Owf(U_8192,U_8194)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8192,U_8192),tc_HOL_Obool)),U_8194),U_8193))
      | ~ c_Wellfounded_Owf(U_8192,U_8193) ),
    inference(variable_rename,[status(thm)],[f_2307_1]) ).

fof(f_2307_3,plain,
    ! [U_8192,U_8193,U_8194] :
      ( c_Wellfounded_Owf(U_8192,U_8194)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8192,U_8192),tc_HOL_Obool)),U_8194),U_8193))
      | ~ c_Wellfounded_Owf(U_8192,U_8193) ),
    inference(definitional_conversion,[status(esa)],[f_2307_2]) ).

cnf(f_2307_4,plain,
    ( c_Wellfounded_Owf(U_8192,U_8194)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8192,U_8192),tc_HOL_Obool)),U_8194),U_8193))
    | ~ c_Wellfounded_Owf(U_8192,U_8193) ),
    inference(clausify,[status(thm)],[f_2307_3]) ).

fof(f_2308_1,plain,
    ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_d,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(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)) )
        | ~ hBOOL(hAPP(hAPP(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_2308_2,plain,
    ! [U_8203,U_8202,U_8201,U_8200,U_8199,U_8198,U_8197] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_8197,U_8198,U_8199,U_8200,U_8201),U_8202),U_8203))
        | ! [U_8196] :
            ( ~ hBOOL(hAPP(hAPP(U_8201,U_8196),U_8203))
            | ~ hBOOL(hAPP(hAPP(U_8200,U_8202),U_8196)) ) )
      & ( ? [U_8195] :
            ( hBOOL(hAPP(hAPP(U_8201,U_8195),U_8203))
            & hBOOL(hAPP(hAPP(U_8200,U_8202),U_8195)) )
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_8197,U_8198,U_8199,U_8200,U_8201),U_8202),U_8203)) ) ),
    inference(variable_rename,[status(thm)],[f_2308_1]) ).

fof(f_2308_3,plain,
    ( ! [U_8217,U_8215,U_8213,U_8211] :
        ( ! [U_8209,U_8207,U_8205] : hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_8205,U_8207,U_8209,U_8211,U_8213),U_8215),U_8217))
        | ! [U_8196] :
            ( ~ hBOOL(hAPP(hAPP(U_8213,U_8196),U_8217))
            | ~ hBOOL(hAPP(hAPP(U_8211,U_8215),U_8196)) ) )
    & ! [U_8216,U_8214,U_8212,U_8210] :
        ( ! [U_8208,U_8206,U_8204] : ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_8204,U_8206,U_8208,U_8210,U_8212),U_8214),U_8216))
        | ? [U_8195] :
            ( hBOOL(hAPP(hAPP(U_8212,U_8195),U_8216))
            & hBOOL(hAPP(hAPP(U_8210,U_8214),U_8195)) ) ) ),
    inference(miniscope,[status(thm)],[f_2308_2]) ).

fof(f_2308_4,plain,
    ( ! [U_8217,U_8215,U_8213,U_8211] :
        ( ! [U_8209,U_8207,U_8205] : hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_8205,U_8207,U_8209,U_8211,U_8213),U_8215),U_8217))
        | ! [U_8196] :
            ( ~ hBOOL(hAPP(hAPP(U_8213,U_8196),U_8217))
            | ~ hBOOL(hAPP(hAPP(U_8211,U_8215),U_8196)) ) )
    & ! [U_8216,U_8214,U_8212,U_8210] :
        ( ! [U_8208,U_8206,U_8204] : ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_8204,U_8206,U_8208,U_8210,U_8212),U_8214),U_8216))
        | ( hBOOL(hAPP(hAPP(U_8212,sK122(U_8216,U_8214,U_8212,U_8210)),U_8216))
          & hBOOL(hAPP(hAPP(U_8210,U_8214),sK122(U_8216,U_8214,U_8212,U_8210))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(U_8195,sK122(U_8216,U_8214,U_8212,U_8210))],[f_2308_3]) ).

fof(f_2308_5,plain,
    ( ! [U_8212,U_8210,U_8214,U_8216] :
        ( hBOOL(hAPP(hAPP(U_8212,sK122(U_8216,U_8214,U_8212,U_8210)),U_8216))
        | ~ sP698(U_8212,U_8210,U_8214,U_8216) )
    & ! [U_8212,U_8210,U_8214,U_8216] :
        ( hBOOL(hAPP(hAPP(U_8210,U_8214),sK122(U_8216,U_8214,U_8212,U_8210)))
        | ~ sP698(U_8212,U_8210,U_8214,U_8216) )
    & ! [U_8209,U_8211,U_8196,U_8207,U_8205,U_8213,U_8215,U_8217] :
        ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_8205,U_8207,U_8209,U_8211,U_8213),U_8215),U_8217))
        | ~ hBOOL(hAPP(hAPP(U_8213,U_8196),U_8217))
        | ~ hBOOL(hAPP(hAPP(U_8211,U_8215),U_8196)) )
    & ! [U_8212,U_8210,U_8208,U_8204,U_8206,U_8214,U_8216] :
        ( ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_8204,U_8206,U_8208,U_8210,U_8212),U_8214),U_8216))
        | sP698(U_8212,U_8210,U_8214,U_8216) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP698])],[f_2308_4]) ).

cnf(f_2308_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_8204,U_8206,U_8208,U_8210,U_8212),U_8214),U_8216))
    | sP698(U_8212,U_8210,U_8214,U_8216) ),
    inference(clausify,[status(thm)],[f_2308_5]) ).

cnf(f_2308_7,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(U_8205,U_8207,U_8209,U_8211,U_8213),U_8215),U_8217))
    | ~ hBOOL(hAPP(hAPP(U_8213,U_8196),U_8217))
    | ~ hBOOL(hAPP(hAPP(U_8211,U_8215),U_8196)) ),
    inference(clausify,[status(thm)],[f_2308_5]) ).

cnf(f_2308_8,plain,
    ( hBOOL(hAPP(hAPP(U_8210,U_8214),sK122(U_8216,U_8214,U_8212,U_8210)))
    | ~ sP698(U_8212,U_8210,U_8214,U_8216) ),
    inference(clausify,[status(thm)],[f_2308_5]) ).

cnf(f_2308_9,plain,
    ( hBOOL(hAPP(hAPP(U_8212,sK122(U_8216,U_8214,U_8212,U_8210)),U_8216))
    | ~ sP698(U_8212,U_8210,U_8214,U_8216) ),
    inference(clausify,[status(thm)],[f_2308_5]) ).

fof(f_2309_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_2309_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_2309_1]) ).

cnf(f_2309_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_2309_2]) ).

fof(f_2310_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_2310_2,plain,
    c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(definitional_conversion,[status(esa)],[f_2310_1]) ).

cnf(f_2310_3,plain,
    c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less),
    inference(clausify,[status(thm)],[f_2310_2]) ).

fof(f_2311_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_2311_2,plain,
    ! [U_8220,U_8219,U_8218] :
      ( c_Wellfounded_Owf(U_8218,c_Wellfounded_Omlex__prod(U_8218,U_8220,U_8219))
      | ~ c_Wellfounded_Owf(U_8218,U_8219) ),
    inference(variable_rename,[status(thm)],[f_2311_1]) ).

fof(f_2311_3,plain,
    ! [U_8218,U_8220,U_8219] :
      ( c_Wellfounded_Owf(U_8218,c_Wellfounded_Omlex__prod(U_8218,U_8220,U_8219))
      | ~ c_Wellfounded_Owf(U_8218,U_8219) ),
    inference(definitional_conversion,[status(esa)],[f_2311_2]) ).

cnf(f_2311_4,plain,
    ( c_Wellfounded_Owf(U_8218,c_Wellfounded_Omlex__prod(U_8218,U_8220,U_8219))
    | ~ c_Wellfounded_Owf(U_8218,U_8219) ),
    inference(clausify,[status(thm)],[f_2311_3]) ).

fof(f_2312_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_2312_2,plain,
    ! [U_8223,U_8222,U_8221] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8221,U_8221)),hAPP(hAPP(c_Product__Type_OPair(U_8221,U_8221),U_8223),U_8223)),U_8222))
      | ~ c_Wellfounded_Owf(U_8221,U_8222) ),
    inference(variable_rename,[status(thm)],[f_2312_1]) ).

fof(f_2312_3,plain,
    ! [U_8221,U_8222,U_8223] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8221,U_8221)),hAPP(hAPP(c_Product__Type_OPair(U_8221,U_8221),U_8223),U_8223)),U_8222))
      | ~ c_Wellfounded_Owf(U_8221,U_8222) ),
    inference(definitional_conversion,[status(esa)],[f_2312_2]) ).

cnf(f_2312_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8221,U_8221)),hAPP(hAPP(c_Product__Type_OPair(U_8221,U_8221),U_8223),U_8223)),U_8222))
    | ~ c_Wellfounded_Owf(U_8221,U_8222) ),
    inference(clausify,[status(thm)],[f_2312_3]) ).

fof(f_2313_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_2313_2,plain,
    ! [U_8227,U_8226,U_8225,U_8224] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8224,U_8224)),hAPP(hAPP(c_Product__Type_OPair(U_8224,U_8224),U_8227),U_8226)),U_8225))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8224,U_8224)),hAPP(hAPP(c_Product__Type_OPair(U_8224,U_8224),U_8226),U_8227)),U_8225))
      | ~ c_Wellfounded_Owf(U_8224,U_8225) ),
    inference(variable_rename,[status(thm)],[f_2313_1]) ).

fof(f_2313_3,plain,
    ! [U_8224,U_8225,U_8226,U_8227] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8224,U_8224)),hAPP(hAPP(c_Product__Type_OPair(U_8224,U_8224),U_8227),U_8226)),U_8225))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8224,U_8224)),hAPP(hAPP(c_Product__Type_OPair(U_8224,U_8224),U_8226),U_8227)),U_8225))
      | ~ c_Wellfounded_Owf(U_8224,U_8225) ),
    inference(definitional_conversion,[status(esa)],[f_2313_2]) ).

cnf(f_2313_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8224,U_8224)),hAPP(hAPP(c_Product__Type_OPair(U_8224,U_8224),U_8227),U_8226)),U_8225))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8224,U_8224)),hAPP(hAPP(c_Product__Type_OPair(U_8224,U_8224),U_8226),U_8227)),U_8225))
    | ~ c_Wellfounded_Owf(U_8224,U_8225) ),
    inference(clausify,[status(thm)],[f_2313_3]) ).

fof(f_2314_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_2314_2,plain,
    ! [U_8231,U_8230,U_8229,U_8228] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8228,U_8228)),hAPP(hAPP(c_Product__Type_OPair(U_8228,U_8228),U_8231),U_8230)),U_8229))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8228,U_8228)),hAPP(hAPP(c_Product__Type_OPair(U_8228,U_8228),U_8230),U_8231)),U_8229))
      | ~ c_Wellfounded_Owf(U_8228,U_8229) ),
    inference(variable_rename,[status(thm)],[f_2314_1]) ).

fof(f_2314_3,plain,
    ! [U_8228,U_8229,U_8230,U_8231] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8228,U_8228)),hAPP(hAPP(c_Product__Type_OPair(U_8228,U_8228),U_8231),U_8230)),U_8229))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8228,U_8228)),hAPP(hAPP(c_Product__Type_OPair(U_8228,U_8228),U_8230),U_8231)),U_8229))
      | ~ c_Wellfounded_Owf(U_8228,U_8229) ),
    inference(definitional_conversion,[status(esa)],[f_2314_2]) ).

cnf(f_2314_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8228,U_8228)),hAPP(hAPP(c_Product__Type_OPair(U_8228,U_8228),U_8231),U_8230)),U_8229))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8228,U_8228)),hAPP(hAPP(c_Product__Type_OPair(U_8228,U_8228),U_8230),U_8231)),U_8229))
    | ~ c_Wellfounded_Owf(U_8228,U_8229) ),
    inference(clausify,[status(thm)],[f_2314_3]) ).

fof(f_2315_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_2315_2,plain,
    ! [U_8234,U_8233,U_8232] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8232,U_8232)),hAPP(hAPP(c_Product__Type_OPair(U_8232,U_8232),U_8234),U_8234)),U_8233))
      | ~ c_Wellfounded_Owf(U_8232,U_8233) ),
    inference(variable_rename,[status(thm)],[f_2315_1]) ).

fof(f_2315_3,plain,
    ! [U_8232,U_8233,U_8234] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8232,U_8232)),hAPP(hAPP(c_Product__Type_OPair(U_8232,U_8232),U_8234),U_8234)),U_8233))
      | ~ c_Wellfounded_Owf(U_8232,U_8233) ),
    inference(definitional_conversion,[status(esa)],[f_2315_2]) ).

cnf(f_2315_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8232,U_8232)),hAPP(hAPP(c_Product__Type_OPair(U_8232,U_8232),U_8234),U_8234)),U_8233))
    | ~ c_Wellfounded_Owf(U_8232,U_8233) ),
    inference(clausify,[status(thm)],[f_2315_3]) ).

fof(f_2316_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_2316_2,plain,
    ! [U_8235] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(U_8235)),
    inference(variable_rename,[status(thm)],[f_2316_1]) ).

fof(f_2316_3,plain,
    ! [U_8235] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(U_8235)),
    inference(definitional_conversion,[status(esa)],[f_2316_2]) ).

cnf(f_2316_4,plain,
    c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(U_8235)),
    inference(clausify,[status(thm)],[f_2316_3]) ).

fof(f_2317_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_2317_2,plain,
    ! [U_8236] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(U_8236)),
    inference(variable_rename,[status(thm)],[f_2317_1]) ).

fof(f_2317_3,plain,
    ! [U_8236] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(U_8236)),
    inference(definitional_conversion,[status(esa)],[f_2317_2]) ).

cnf(f_2317_4,plain,
    c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(U_8236)),
    inference(clausify,[status(thm)],[f_2317_3]) ).

fof(f_2318_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_2318_2,plain,
    ! [U_8240,U_8239] :
      ( ( c_Wellfounded_Owf(U_8239,U_8240)
        | ? [U_8238] : ~ hBOOL(hAPP(hAPP(c_member(U_8239),U_8238),c_Wellfounded_Oacc(U_8239,U_8240))) )
      & ( ! [U_8237] : hBOOL(hAPP(hAPP(c_member(U_8239),U_8237),c_Wellfounded_Oacc(U_8239,U_8240)))
        | ~ c_Wellfounded_Owf(U_8239,U_8240) ) ),
    inference(variable_rename,[status(thm)],[f_2318_1]) ).

fof(f_2318_3,plain,
    ( ! [U_8244,U_8242] :
        ( c_Wellfounded_Owf(U_8242,U_8244)
        | ? [U_8238] : ~ hBOOL(hAPP(hAPP(c_member(U_8242),U_8238),c_Wellfounded_Oacc(U_8242,U_8244))) )
    & ! [U_8243,U_8241] :
        ( ! [U_8237] : hBOOL(hAPP(hAPP(c_member(U_8241),U_8237),c_Wellfounded_Oacc(U_8241,U_8243)))
        | ~ c_Wellfounded_Owf(U_8241,U_8243) ) ),
    inference(miniscope,[status(thm)],[f_2318_2]) ).

fof(f_2318_4,plain,
    ( ! [U_8244,U_8242] :
        ( c_Wellfounded_Owf(U_8242,U_8244)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8242),sK123(U_8244,U_8242)),c_Wellfounded_Oacc(U_8242,U_8244))) )
    & ! [U_8243,U_8241] :
        ( ! [U_8237] : hBOOL(hAPP(hAPP(c_member(U_8241),U_8237),c_Wellfounded_Oacc(U_8241,U_8243)))
        | ~ c_Wellfounded_Owf(U_8241,U_8243) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK123]),skolemize(U_8238,sK123(U_8244,U_8242))],[f_2318_3]) ).

fof(f_2318_5,plain,
    ( ! [U_8242,U_8244] :
        ( c_Wellfounded_Owf(U_8242,U_8244)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8242),sK123(U_8244,U_8242)),c_Wellfounded_Oacc(U_8242,U_8244))) )
    & ! [U_8243,U_8237,U_8241] :
        ( hBOOL(hAPP(hAPP(c_member(U_8241),U_8237),c_Wellfounded_Oacc(U_8241,U_8243)))
        | ~ c_Wellfounded_Owf(U_8241,U_8243) ) ),
    inference(definitional_conversion,[status(esa)],[f_2318_4]) ).

cnf(f_2318_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8241),U_8237),c_Wellfounded_Oacc(U_8241,U_8243)))
    | ~ c_Wellfounded_Owf(U_8241,U_8243) ),
    inference(clausify,[status(thm)],[f_2318_5]) ).

cnf(f_2318_7,plain,
    ( c_Wellfounded_Owf(U_8242,U_8244)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8242),sK123(U_8244,U_8242)),c_Wellfounded_Oacc(U_8242,U_8244))) ),
    inference(clausify,[status(thm)],[f_2318_5]) ).

fof(f_2319_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_2319_2,plain,
    ! [U_8247,U_8246,U_8245] :
      ( hBOOL(hAPP(hAPP(c_member(U_8245),U_8247),c_Wellfounded_Oacc(U_8245,U_8246)))
      | ~ c_Wellfounded_Owf(U_8245,U_8246) ),
    inference(variable_rename,[status(thm)],[f_2319_1]) ).

fof(f_2319_3,plain,
    ! [U_8245,U_8246,U_8247] :
      ( hBOOL(hAPP(hAPP(c_member(U_8245),U_8247),c_Wellfounded_Oacc(U_8245,U_8246)))
      | ~ c_Wellfounded_Owf(U_8245,U_8246) ),
    inference(definitional_conversion,[status(esa)],[f_2319_2]) ).

cnf(f_2319_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8245),U_8247),c_Wellfounded_Oacc(U_8245,U_8246)))
    | ~ c_Wellfounded_Owf(U_8245,U_8246) ),
    inference(clausify,[status(thm)],[f_2319_3]) ).

fof(f_2320_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_2320_2,plain,
    ! [U_8253,U_8252,U_8251,U_8250] :
      ( ( hBOOL(hAPP(c_Predicate_ODomainP(U_8250,U_8251,U_8252),U_8253))
        | ! [U_8249] : ~ hBOOL(hAPP(hAPP(U_8252,U_8253),U_8249)) )
      & ( ? [U_8248] : hBOOL(hAPP(hAPP(U_8252,U_8253),U_8248))
        | ~ hBOOL(hAPP(c_Predicate_ODomainP(U_8250,U_8251,U_8252),U_8253)) ) ),
    inference(variable_rename,[status(thm)],[f_2320_1]) ).

fof(f_2320_3,plain,
    ( ! [U_8261,U_8259] :
        ( ! [U_8257,U_8255] : hBOOL(hAPP(c_Predicate_ODomainP(U_8255,U_8257,U_8259),U_8261))
        | ! [U_8249] : ~ hBOOL(hAPP(hAPP(U_8259,U_8261),U_8249)) )
    & ! [U_8260,U_8258] :
        ( ! [U_8256,U_8254] : ~ hBOOL(hAPP(c_Predicate_ODomainP(U_8254,U_8256,U_8258),U_8260))
        | ? [U_8248] : hBOOL(hAPP(hAPP(U_8258,U_8260),U_8248)) ) ),
    inference(miniscope,[status(thm)],[f_2320_2]) ).

fof(f_2320_4,plain,
    ( ! [U_8261,U_8259] :
        ( ! [U_8257,U_8255] : hBOOL(hAPP(c_Predicate_ODomainP(U_8255,U_8257,U_8259),U_8261))
        | ! [U_8249] : ~ hBOOL(hAPP(hAPP(U_8259,U_8261),U_8249)) )
    & ! [U_8260,U_8258] :
        ( ! [U_8256,U_8254] : ~ hBOOL(hAPP(c_Predicate_ODomainP(U_8254,U_8256,U_8258),U_8260))
        | hBOOL(hAPP(hAPP(U_8258,U_8260),sK124(U_8260,U_8258))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK124]),skolemize(U_8248,sK124(U_8260,U_8258))],[f_2320_3]) ).

fof(f_2320_5,plain,
    ( ! [U_8249,U_8255,U_8257,U_8259,U_8261] :
        ( hBOOL(hAPP(c_Predicate_ODomainP(U_8255,U_8257,U_8259),U_8261))
        | ~ hBOOL(hAPP(hAPP(U_8259,U_8261),U_8249)) )
    & ! [U_8258,U_8254,U_8256,U_8260] :
        ( ~ hBOOL(hAPP(c_Predicate_ODomainP(U_8254,U_8256,U_8258),U_8260))
        | hBOOL(hAPP(hAPP(U_8258,U_8260),sK124(U_8260,U_8258))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2320_4]) ).

cnf(f_2320_6,plain,
    ( ~ hBOOL(hAPP(c_Predicate_ODomainP(U_8254,U_8256,U_8258),U_8260))
    | hBOOL(hAPP(hAPP(U_8258,U_8260),sK124(U_8260,U_8258))) ),
    inference(clausify,[status(thm)],[f_2320_5]) ).

cnf(f_2320_7,plain,
    ( hBOOL(hAPP(c_Predicate_ODomainP(U_8255,U_8257,U_8259),U_8261))
    | ~ hBOOL(hAPP(hAPP(U_8259,U_8261),U_8249)) ),
    inference(clausify,[status(thm)],[f_2320_5]) ).

fof(f_2321_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_2321_2,plain,
    ! [U_8262] :
      ( c_Wellfounded_Owf(U_8262,hAPP(c_Set_OCollect(tc_prod(U_8262,U_8262)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8262,U_8262,tc_HOL_Obool),c_Orderings_Oord__class_Oless(U_8262))))
      | ~ class_Orderings_Owellorder(U_8262) ),
    inference(variable_rename,[status(thm)],[f_2321_1]) ).

fof(f_2321_3,plain,
    ! [U_8262] :
      ( c_Wellfounded_Owf(U_8262,hAPP(c_Set_OCollect(tc_prod(U_8262,U_8262)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8262,U_8262,tc_HOL_Obool),c_Orderings_Oord__class_Oless(U_8262))))
      | ~ class_Orderings_Owellorder(U_8262) ),
    inference(definitional_conversion,[status(esa)],[f_2321_2]) ).

cnf(f_2321_4,plain,
    ( c_Wellfounded_Owf(U_8262,hAPP(c_Set_OCollect(tc_prod(U_8262,U_8262)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8262,U_8262,tc_HOL_Obool),c_Orderings_Oord__class_Oless(U_8262))))
    | ~ class_Orderings_Owellorder(U_8262) ),
    inference(clausify,[status(thm)],[f_2321_3]) ).

fof(f_2322_1,plain,
    ! [V_Pa_2,T_b] :
      ( ( c_FunDef_Oreduction__pair(T_b,V_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_Pa_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_Pa_2)) )
        | ~ c_FunDef_Oreduction__pair(T_b,V_Pa_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_reduction__pair__def]) ).

fof(f_2322_2,plain,
    ! [U_8264,U_8263] :
      ( ( c_FunDef_Oreduction__pair(U_8263,U_8264)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8263,U_8263),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8263,U_8263,U_8263),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8263,U_8263),tc_HOL_Obool),tc_fun(tc_prod(U_8263,U_8263),tc_HOL_Obool)),U_8264)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_8263,U_8263),tc_HOL_Obool),tc_fun(tc_prod(U_8263,U_8263),tc_HOL_Obool)),U_8264))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8263,U_8263),tc_HOL_Obool),tc_fun(tc_prod(U_8263,U_8263),tc_HOL_Obool)),U_8264)))
        | ~ c_Wellfounded_Owf(U_8263,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8263,U_8263),tc_HOL_Obool),tc_fun(tc_prod(U_8263,U_8263),tc_HOL_Obool)),U_8264)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8263,U_8263),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8263,U_8263,U_8263),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8263,U_8263),tc_HOL_Obool),tc_fun(tc_prod(U_8263,U_8263),tc_HOL_Obool)),U_8264)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_8263,U_8263),tc_HOL_Obool),tc_fun(tc_prod(U_8263,U_8263),tc_HOL_Obool)),U_8264))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8263,U_8263),tc_HOL_Obool),tc_fun(tc_prod(U_8263,U_8263),tc_HOL_Obool)),U_8264)))
          & c_Wellfounded_Owf(U_8263,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8263,U_8263),tc_HOL_Obool),tc_fun(tc_prod(U_8263,U_8263),tc_HOL_Obool)),U_8264)) )
        | ~ c_FunDef_Oreduction__pair(U_8263,U_8264) ) ),
    inference(variable_rename,[status(thm)],[f_2322_1]) ).

fof(f_2322_3,plain,
    ( ! [U_8268,U_8266] :
        ( c_FunDef_Oreduction__pair(U_8266,U_8268)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8266,U_8266,U_8266),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool),tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool)),U_8268)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool),tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool)),U_8268))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool),tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool)),U_8268)))
        | ~ c_Wellfounded_Owf(U_8266,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool),tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool)),U_8268)) )
    & ! [U_8267,U_8265] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8265,U_8265,U_8265),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool),tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool)),U_8267)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool),tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool)),U_8267))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool),tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool)),U_8267)))
          & c_Wellfounded_Owf(U_8265,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool),tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool)),U_8267)) )
        | ~ c_FunDef_Oreduction__pair(U_8265,U_8267) ) ),
    inference(miniscope,[status(thm)],[f_2322_2]) ).

fof(f_2322_4,plain,
    ( ! [U_8265,U_8267] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8265,U_8265,U_8265),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool),tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool)),U_8267)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool),tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool)),U_8267))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool),tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool)),U_8267)))
        | ~ sP699(U_8265,U_8267) )
    & ! [U_8265,U_8267] :
        ( c_Wellfounded_Owf(U_8265,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool),tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool)),U_8267))
        | ~ sP699(U_8265,U_8267) )
    & ! [U_8266,U_8268] :
        ( c_FunDef_Oreduction__pair(U_8266,U_8268)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8266,U_8266,U_8266),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool),tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool)),U_8268)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool),tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool)),U_8268))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool),tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool)),U_8268)))
        | ~ c_Wellfounded_Owf(U_8266,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool),tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool)),U_8268)) )
    & ! [U_8265,U_8267] :
        ( sP699(U_8265,U_8267)
        | ~ c_FunDef_Oreduction__pair(U_8265,U_8267) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP699])],[f_2322_3]) ).

cnf(f_2322_5,plain,
    ( sP699(U_8265,U_8267)
    | ~ c_FunDef_Oreduction__pair(U_8265,U_8267) ),
    inference(clausify,[status(thm)],[f_2322_4]) ).

cnf(f_2322_6,plain,
    ( c_FunDef_Oreduction__pair(U_8266,U_8268)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8266,U_8266,U_8266),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool),tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool)),U_8268)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool),tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool)),U_8268))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool),tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool)),U_8268)))
    | ~ c_Wellfounded_Owf(U_8266,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool),tc_fun(tc_prod(U_8266,U_8266),tc_HOL_Obool)),U_8268)) ),
    inference(clausify,[status(thm)],[f_2322_4]) ).

cnf(f_2322_7,plain,
    ( c_Wellfounded_Owf(U_8265,hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool),tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool)),U_8267))
    | ~ sP699(U_8265,U_8267) ),
    inference(clausify,[status(thm)],[f_2322_4]) ).

cnf(f_2322_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8265,U_8265,U_8265),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool),tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool)),U_8267)),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool),tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool)),U_8267))),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool),tc_fun(tc_prod(U_8265,U_8265),tc_HOL_Obool)),U_8267)))
    | ~ sP699(U_8265,U_8267) ),
    inference(clausify,[status(thm)],[f_2322_4]) ).

fof(f_2323_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_2323_2,plain,
    ! [U_8274,U_8273] :
      ( ( c_Wellfounded_Owf(U_8273,U_8274)
        | ? [U_8272] :
          ! [U_8271] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_8273,U_8273)),hAPP(hAPP(c_Product__Type_OPair(U_8273,U_8273),hAPP(U_8272,hAPP(c_Nat_OSuc,U_8271))),hAPP(U_8272,U_8271))),U_8274)) )
      & ( ! [U_8270] :
          ? [U_8269] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8273,U_8273)),hAPP(hAPP(c_Product__Type_OPair(U_8273,U_8273),hAPP(U_8270,hAPP(c_Nat_OSuc,U_8269))),hAPP(U_8270,U_8269))),U_8274))
        | ~ c_Wellfounded_Owf(U_8273,U_8274) ) ),
    inference(variable_rename,[status(thm)],[f_2323_1]) ).

fof(f_2323_3,plain,
    ( ! [U_8278,U_8276] :
        ( c_Wellfounded_Owf(U_8276,U_8278)
        | ? [U_8272] :
          ! [U_8271] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_8276,U_8276)),hAPP(hAPP(c_Product__Type_OPair(U_8276,U_8276),hAPP(U_8272,hAPP(c_Nat_OSuc,U_8271))),hAPP(U_8272,U_8271))),U_8278)) )
    & ! [U_8277,U_8275] :
        ( ! [U_8270] :
          ? [U_8269] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8275,U_8275)),hAPP(hAPP(c_Product__Type_OPair(U_8275,U_8275),hAPP(U_8270,hAPP(c_Nat_OSuc,U_8269))),hAPP(U_8270,U_8269))),U_8277))
        | ~ c_Wellfounded_Owf(U_8275,U_8277) ) ),
    inference(miniscope,[status(thm)],[f_2323_2]) ).

fof(f_2323_4,plain,
    ( ! [U_8278,U_8276] :
        ( c_Wellfounded_Owf(U_8276,U_8278)
        | ? [U_8272] :
          ! [U_8271] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_8276,U_8276)),hAPP(hAPP(c_Product__Type_OPair(U_8276,U_8276),hAPP(U_8272,hAPP(c_Nat_OSuc,U_8271))),hAPP(U_8272,U_8271))),U_8278)) )
    & ! [U_8277,U_8275] :
        ( ! [U_8270] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8275,U_8275)),hAPP(hAPP(c_Product__Type_OPair(U_8275,U_8275),hAPP(U_8270,hAPP(c_Nat_OSuc,sK125(U_8277,U_8275,U_8270)))),hAPP(U_8270,sK125(U_8277,U_8275,U_8270)))),U_8277))
        | ~ c_Wellfounded_Owf(U_8275,U_8277) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK125]),skolemize(U_8269,sK125(U_8277,U_8275,U_8270))],[f_2323_3]) ).

fof(f_2323_5,plain,
    ( ! [U_8278,U_8276] :
        ( c_Wellfounded_Owf(U_8276,U_8278)
        | ! [U_8271] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_8276,U_8276)),hAPP(hAPP(c_Product__Type_OPair(U_8276,U_8276),hAPP(sK126(U_8278,U_8276),hAPP(c_Nat_OSuc,U_8271))),hAPP(sK126(U_8278,U_8276),U_8271))),U_8278)) )
    & ! [U_8277,U_8275] :
        ( ! [U_8270] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8275,U_8275)),hAPP(hAPP(c_Product__Type_OPair(U_8275,U_8275),hAPP(U_8270,hAPP(c_Nat_OSuc,sK125(U_8277,U_8275,U_8270)))),hAPP(U_8270,sK125(U_8277,U_8275,U_8270)))),U_8277))
        | ~ c_Wellfounded_Owf(U_8275,U_8277) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK126]),skolemize(U_8272,sK126(U_8278,U_8276))],[f_2323_4]) ).

fof(f_2323_6,plain,
    ( ! [U_8278,U_8271,U_8276] :
        ( c_Wellfounded_Owf(U_8276,U_8278)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8276,U_8276)),hAPP(hAPP(c_Product__Type_OPair(U_8276,U_8276),hAPP(sK126(U_8278,U_8276),hAPP(c_Nat_OSuc,U_8271))),hAPP(sK126(U_8278,U_8276),U_8271))),U_8278)) )
    & ! [U_8270,U_8277,U_8275] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8275,U_8275)),hAPP(hAPP(c_Product__Type_OPair(U_8275,U_8275),hAPP(U_8270,hAPP(c_Nat_OSuc,sK125(U_8277,U_8275,U_8270)))),hAPP(U_8270,sK125(U_8277,U_8275,U_8270)))),U_8277))
        | ~ c_Wellfounded_Owf(U_8275,U_8277) ) ),
    inference(definitional_conversion,[status(esa)],[f_2323_5]) ).

cnf(f_2323_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8275,U_8275)),hAPP(hAPP(c_Product__Type_OPair(U_8275,U_8275),hAPP(U_8270,hAPP(c_Nat_OSuc,sK125(U_8277,U_8275,U_8270)))),hAPP(U_8270,sK125(U_8277,U_8275,U_8270)))),U_8277))
    | ~ c_Wellfounded_Owf(U_8275,U_8277) ),
    inference(clausify,[status(thm)],[f_2323_6]) ).

cnf(f_2323_8,plain,
    ( c_Wellfounded_Owf(U_8276,U_8278)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8276,U_8276)),hAPP(hAPP(c_Product__Type_OPair(U_8276,U_8276),hAPP(sK126(U_8278,U_8276),hAPP(c_Nat_OSuc,U_8271))),hAPP(sK126(U_8278,U_8276),U_8271))),U_8278)) ),
    inference(clausify,[status(thm)],[f_2323_6]) ).

fof(f_2324_1,plain,
    ! [T_b,V_g_2,V_f_2,V_Pa_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_Pa_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_Pa_2,B_x)) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__if__measure]) ).

fof(f_2324_2,plain,
    ! [U_8283,U_8282,U_8281,U_8280] :
      ( c_Wellfounded_Owf(U_8283,hAPP(c_Set_OCollect(tc_prod(U_8283,U_8283)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8283,U_8283,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_8283,tc_HOL_Obool),tc_fun(U_8283,tc_HOL_Obool),U_8283),hAPP(c_COMBS(U_8283,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8283),c_fconj),U_8280))),hAPP(hAPP(c_COMBC(U_8283,tc_fun(U_8283,U_8283),tc_fun(U_8283,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8283,tc_HOL_Obool),tc_fun(tc_fun(U_8283,U_8283),tc_fun(U_8283,tc_HOL_Obool)),U_8283),c_COMBB(U_8283,tc_HOL_Obool,U_8283)),c_fequal)),U_8282)))))
      | ? [U_8279] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8281,hAPP(U_8282,U_8279))),hAPP(U_8281,U_8279)))
          & hBOOL(hAPP(U_8280,U_8279)) ) ),
    inference(variable_rename,[status(thm)],[f_2324_1]) ).

fof(f_2324_3,plain,
    ! [U_8283,U_8282,U_8281,U_8280] :
      ( c_Wellfounded_Owf(U_8283,hAPP(c_Set_OCollect(tc_prod(U_8283,U_8283)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8283,U_8283,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_8283,tc_HOL_Obool),tc_fun(U_8283,tc_HOL_Obool),U_8283),hAPP(c_COMBS(U_8283,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8283),c_fconj),U_8280))),hAPP(hAPP(c_COMBC(U_8283,tc_fun(U_8283,U_8283),tc_fun(U_8283,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8283,tc_HOL_Obool),tc_fun(tc_fun(U_8283,U_8283),tc_fun(U_8283,tc_HOL_Obool)),U_8283),c_COMBB(U_8283,tc_HOL_Obool,U_8283)),c_fequal)),U_8282)))))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8281,hAPP(U_8282,sK127(U_8283,U_8282,U_8281,U_8280)))),hAPP(U_8281,sK127(U_8283,U_8282,U_8281,U_8280))))
        & hBOOL(hAPP(U_8280,sK127(U_8283,U_8282,U_8281,U_8280))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK127]),skolemize(U_8279,sK127(U_8283,U_8282,U_8281,U_8280))],[f_2324_2]) ).

fof(f_2324_4,plain,
    ( ! [U_8280,U_8281,U_8282,U_8283] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8281,hAPP(U_8282,sK127(U_8283,U_8282,U_8281,U_8280)))),hAPP(U_8281,sK127(U_8283,U_8282,U_8281,U_8280))))
        | ~ sP700(U_8280,U_8281,U_8282,U_8283) )
    & ! [U_8280,U_8281,U_8282,U_8283] :
        ( hBOOL(hAPP(U_8280,sK127(U_8283,U_8282,U_8281,U_8280)))
        | ~ sP700(U_8280,U_8281,U_8282,U_8283) )
    & ! [U_8280,U_8281,U_8282,U_8283] :
        ( c_Wellfounded_Owf(U_8283,hAPP(c_Set_OCollect(tc_prod(U_8283,U_8283)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8283,U_8283,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_8283,tc_HOL_Obool),tc_fun(U_8283,tc_HOL_Obool),U_8283),hAPP(c_COMBS(U_8283,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8283),c_fconj),U_8280))),hAPP(hAPP(c_COMBC(U_8283,tc_fun(U_8283,U_8283),tc_fun(U_8283,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8283,tc_HOL_Obool),tc_fun(tc_fun(U_8283,U_8283),tc_fun(U_8283,tc_HOL_Obool)),U_8283),c_COMBB(U_8283,tc_HOL_Obool,U_8283)),c_fequal)),U_8282)))))
        | sP700(U_8280,U_8281,U_8282,U_8283) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP700])],[f_2324_3]) ).

cnf(f_2324_5,plain,
    ( c_Wellfounded_Owf(U_8283,hAPP(c_Set_OCollect(tc_prod(U_8283,U_8283)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8283,U_8283,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_8283,tc_HOL_Obool),tc_fun(U_8283,tc_HOL_Obool),U_8283),hAPP(c_COMBS(U_8283,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8283),c_fconj),U_8280))),hAPP(hAPP(c_COMBC(U_8283,tc_fun(U_8283,U_8283),tc_fun(U_8283,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8283,tc_HOL_Obool),tc_fun(tc_fun(U_8283,U_8283),tc_fun(U_8283,tc_HOL_Obool)),U_8283),c_COMBB(U_8283,tc_HOL_Obool,U_8283)),c_fequal)),U_8282)))))
    | sP700(U_8280,U_8281,U_8282,U_8283) ),
    inference(clausify,[status(thm)],[f_2324_4]) ).

cnf(f_2324_6,plain,
    ( hBOOL(hAPP(U_8280,sK127(U_8283,U_8282,U_8281,U_8280)))
    | ~ sP700(U_8280,U_8281,U_8282,U_8283) ),
    inference(clausify,[status(thm)],[f_2324_4]) ).

cnf(f_2324_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_8281,hAPP(U_8282,sK127(U_8283,U_8282,U_8281,U_8280)))),hAPP(U_8281,sK127(U_8283,U_8282,U_8281,U_8280))))
    | ~ sP700(U_8280,U_8281,U_8282,U_8283) ),
    inference(clausify,[status(thm)],[f_2324_4]) ).

fof(f_2325_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_2325_2,plain,
    ! [U_8285,U_8284] :
      ( ( c_Wellfounded_OwfP(U_8284,U_8285)
        | ~ c_Wellfounded_Owf(U_8284,hAPP(c_Set_OCollect(tc_prod(U_8284,U_8284)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8284,U_8284,tc_HOL_Obool),U_8285))) )
      & ( c_Wellfounded_Owf(U_8284,hAPP(c_Set_OCollect(tc_prod(U_8284,U_8284)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8284,U_8284,tc_HOL_Obool),U_8285)))
        | ~ c_Wellfounded_OwfP(U_8284,U_8285) ) ),
    inference(variable_rename,[status(thm)],[f_2325_1]) ).

fof(f_2325_3,plain,
    ( ! [U_8289,U_8287] :
        ( c_Wellfounded_OwfP(U_8287,U_8289)
        | ~ c_Wellfounded_Owf(U_8287,hAPP(c_Set_OCollect(tc_prod(U_8287,U_8287)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8287,U_8287,tc_HOL_Obool),U_8289))) )
    & ! [U_8288,U_8286] :
        ( c_Wellfounded_Owf(U_8286,hAPP(c_Set_OCollect(tc_prod(U_8286,U_8286)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8286,U_8286,tc_HOL_Obool),U_8288)))
        | ~ c_Wellfounded_OwfP(U_8286,U_8288) ) ),
    inference(miniscope,[status(thm)],[f_2325_2]) ).

fof(f_2325_4,plain,
    ( ! [U_8287,U_8289] :
        ( c_Wellfounded_OwfP(U_8287,U_8289)
        | ~ c_Wellfounded_Owf(U_8287,hAPP(c_Set_OCollect(tc_prod(U_8287,U_8287)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8287,U_8287,tc_HOL_Obool),U_8289))) )
    & ! [U_8288,U_8286] :
        ( c_Wellfounded_Owf(U_8286,hAPP(c_Set_OCollect(tc_prod(U_8286,U_8286)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8286,U_8286,tc_HOL_Obool),U_8288)))
        | ~ c_Wellfounded_OwfP(U_8286,U_8288) ) ),
    inference(definitional_conversion,[status(esa)],[f_2325_3]) ).

cnf(f_2325_5,plain,
    ( c_Wellfounded_Owf(U_8286,hAPP(c_Set_OCollect(tc_prod(U_8286,U_8286)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8286,U_8286,tc_HOL_Obool),U_8288)))
    | ~ c_Wellfounded_OwfP(U_8286,U_8288) ),
    inference(clausify,[status(thm)],[f_2325_4]) ).

cnf(f_2325_6,plain,
    ( c_Wellfounded_OwfP(U_8287,U_8289)
    | ~ c_Wellfounded_Owf(U_8287,hAPP(c_Set_OCollect(tc_prod(U_8287,U_8287)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8287,U_8287,tc_HOL_Obool),U_8289))) ),
    inference(clausify,[status(thm)],[f_2325_4]) ).

fof(f_2326_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_2326_2,plain,
    ! [U_8291,U_8290] :
      ( ( c_Wellfounded_OwfP(U_8290,hAPP(hAPP(c_COMBC(U_8290,tc_fun(tc_prod(U_8290,U_8290),tc_HOL_Obool),tc_fun(U_8290,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8290,tc_fun(tc_fun(tc_prod(U_8290,U_8290),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8290,U_8290),tc_HOL_Obool),tc_fun(U_8290,tc_HOL_Obool)),U_8290),c_COMBC(U_8290,tc_fun(tc_prod(U_8290,U_8290),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8290,tc_prod(U_8290,U_8290)),tc_fun(U_8290,tc_fun(tc_fun(tc_prod(U_8290,U_8290),tc_HOL_Obool),tc_HOL_Obool)),U_8290),hAPP(c_COMBB(tc_prod(U_8290,U_8290),tc_fun(tc_fun(tc_prod(U_8290,U_8290),tc_HOL_Obool),tc_HOL_Obool),U_8290),c_member(tc_prod(U_8290,U_8290)))),c_Product__Type_OPair(U_8290,U_8290)))),U_8291))
        | ~ c_Wellfounded_Owf(U_8290,U_8291) )
      & ( c_Wellfounded_Owf(U_8290,U_8291)
        | ~ c_Wellfounded_OwfP(U_8290,hAPP(hAPP(c_COMBC(U_8290,tc_fun(tc_prod(U_8290,U_8290),tc_HOL_Obool),tc_fun(U_8290,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8290,tc_fun(tc_fun(tc_prod(U_8290,U_8290),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8290,U_8290),tc_HOL_Obool),tc_fun(U_8290,tc_HOL_Obool)),U_8290),c_COMBC(U_8290,tc_fun(tc_prod(U_8290,U_8290),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8290,tc_prod(U_8290,U_8290)),tc_fun(U_8290,tc_fun(tc_fun(tc_prod(U_8290,U_8290),tc_HOL_Obool),tc_HOL_Obool)),U_8290),hAPP(c_COMBB(tc_prod(U_8290,U_8290),tc_fun(tc_fun(tc_prod(U_8290,U_8290),tc_HOL_Obool),tc_HOL_Obool),U_8290),c_member(tc_prod(U_8290,U_8290)))),c_Product__Type_OPair(U_8290,U_8290)))),U_8291)) ) ),
    inference(variable_rename,[status(thm)],[f_2326_1]) ).

fof(f_2326_3,plain,
    ( ! [U_8295,U_8293] :
        ( c_Wellfounded_OwfP(U_8293,hAPP(hAPP(c_COMBC(U_8293,tc_fun(tc_prod(U_8293,U_8293),tc_HOL_Obool),tc_fun(U_8293,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8293,tc_fun(tc_fun(tc_prod(U_8293,U_8293),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8293,U_8293),tc_HOL_Obool),tc_fun(U_8293,tc_HOL_Obool)),U_8293),c_COMBC(U_8293,tc_fun(tc_prod(U_8293,U_8293),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8293,tc_prod(U_8293,U_8293)),tc_fun(U_8293,tc_fun(tc_fun(tc_prod(U_8293,U_8293),tc_HOL_Obool),tc_HOL_Obool)),U_8293),hAPP(c_COMBB(tc_prod(U_8293,U_8293),tc_fun(tc_fun(tc_prod(U_8293,U_8293),tc_HOL_Obool),tc_HOL_Obool),U_8293),c_member(tc_prod(U_8293,U_8293)))),c_Product__Type_OPair(U_8293,U_8293)))),U_8295))
        | ~ c_Wellfounded_Owf(U_8293,U_8295) )
    & ! [U_8294,U_8292] :
        ( c_Wellfounded_Owf(U_8292,U_8294)
        | ~ c_Wellfounded_OwfP(U_8292,hAPP(hAPP(c_COMBC(U_8292,tc_fun(tc_prod(U_8292,U_8292),tc_HOL_Obool),tc_fun(U_8292,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8292,tc_fun(tc_fun(tc_prod(U_8292,U_8292),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8292,U_8292),tc_HOL_Obool),tc_fun(U_8292,tc_HOL_Obool)),U_8292),c_COMBC(U_8292,tc_fun(tc_prod(U_8292,U_8292),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8292,tc_prod(U_8292,U_8292)),tc_fun(U_8292,tc_fun(tc_fun(tc_prod(U_8292,U_8292),tc_HOL_Obool),tc_HOL_Obool)),U_8292),hAPP(c_COMBB(tc_prod(U_8292,U_8292),tc_fun(tc_fun(tc_prod(U_8292,U_8292),tc_HOL_Obool),tc_HOL_Obool),U_8292),c_member(tc_prod(U_8292,U_8292)))),c_Product__Type_OPair(U_8292,U_8292)))),U_8294)) ) ),
    inference(miniscope,[status(thm)],[f_2326_2]) ).

fof(f_2326_4,plain,
    ( ! [U_8295,U_8293] :
        ( c_Wellfounded_OwfP(U_8293,hAPP(hAPP(c_COMBC(U_8293,tc_fun(tc_prod(U_8293,U_8293),tc_HOL_Obool),tc_fun(U_8293,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8293,tc_fun(tc_fun(tc_prod(U_8293,U_8293),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8293,U_8293),tc_HOL_Obool),tc_fun(U_8293,tc_HOL_Obool)),U_8293),c_COMBC(U_8293,tc_fun(tc_prod(U_8293,U_8293),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8293,tc_prod(U_8293,U_8293)),tc_fun(U_8293,tc_fun(tc_fun(tc_prod(U_8293,U_8293),tc_HOL_Obool),tc_HOL_Obool)),U_8293),hAPP(c_COMBB(tc_prod(U_8293,U_8293),tc_fun(tc_fun(tc_prod(U_8293,U_8293),tc_HOL_Obool),tc_HOL_Obool),U_8293),c_member(tc_prod(U_8293,U_8293)))),c_Product__Type_OPair(U_8293,U_8293)))),U_8295))
        | ~ c_Wellfounded_Owf(U_8293,U_8295) )
    & ! [U_8294,U_8292] :
        ( c_Wellfounded_Owf(U_8292,U_8294)
        | ~ c_Wellfounded_OwfP(U_8292,hAPP(hAPP(c_COMBC(U_8292,tc_fun(tc_prod(U_8292,U_8292),tc_HOL_Obool),tc_fun(U_8292,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8292,tc_fun(tc_fun(tc_prod(U_8292,U_8292),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8292,U_8292),tc_HOL_Obool),tc_fun(U_8292,tc_HOL_Obool)),U_8292),c_COMBC(U_8292,tc_fun(tc_prod(U_8292,U_8292),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8292,tc_prod(U_8292,U_8292)),tc_fun(U_8292,tc_fun(tc_fun(tc_prod(U_8292,U_8292),tc_HOL_Obool),tc_HOL_Obool)),U_8292),hAPP(c_COMBB(tc_prod(U_8292,U_8292),tc_fun(tc_fun(tc_prod(U_8292,U_8292),tc_HOL_Obool),tc_HOL_Obool),U_8292),c_member(tc_prod(U_8292,U_8292)))),c_Product__Type_OPair(U_8292,U_8292)))),U_8294)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2326_3]) ).

cnf(f_2326_5,plain,
    ( c_Wellfounded_Owf(U_8292,U_8294)
    | ~ c_Wellfounded_OwfP(U_8292,hAPP(hAPP(c_COMBC(U_8292,tc_fun(tc_prod(U_8292,U_8292),tc_HOL_Obool),tc_fun(U_8292,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8292,tc_fun(tc_fun(tc_prod(U_8292,U_8292),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8292,U_8292),tc_HOL_Obool),tc_fun(U_8292,tc_HOL_Obool)),U_8292),c_COMBC(U_8292,tc_fun(tc_prod(U_8292,U_8292),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8292,tc_prod(U_8292,U_8292)),tc_fun(U_8292,tc_fun(tc_fun(tc_prod(U_8292,U_8292),tc_HOL_Obool),tc_HOL_Obool)),U_8292),hAPP(c_COMBB(tc_prod(U_8292,U_8292),tc_fun(tc_fun(tc_prod(U_8292,U_8292),tc_HOL_Obool),tc_HOL_Obool),U_8292),c_member(tc_prod(U_8292,U_8292)))),c_Product__Type_OPair(U_8292,U_8292)))),U_8294)) ),
    inference(clausify,[status(thm)],[f_2326_4]) ).

cnf(f_2326_6,plain,
    ( c_Wellfounded_OwfP(U_8293,hAPP(hAPP(c_COMBC(U_8293,tc_fun(tc_prod(U_8293,U_8293),tc_HOL_Obool),tc_fun(U_8293,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8293,tc_fun(tc_fun(tc_prod(U_8293,U_8293),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8293,U_8293),tc_HOL_Obool),tc_fun(U_8293,tc_HOL_Obool)),U_8293),c_COMBC(U_8293,tc_fun(tc_prod(U_8293,U_8293),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8293,tc_prod(U_8293,U_8293)),tc_fun(U_8293,tc_fun(tc_fun(tc_prod(U_8293,U_8293),tc_HOL_Obool),tc_HOL_Obool)),U_8293),hAPP(c_COMBB(tc_prod(U_8293,U_8293),tc_fun(tc_fun(tc_prod(U_8293,U_8293),tc_HOL_Obool),tc_HOL_Obool),U_8293),c_member(tc_prod(U_8293,U_8293)))),c_Product__Type_OPair(U_8293,U_8293)))),U_8295))
    | ~ c_Wellfounded_Owf(U_8293,U_8295) ),
    inference(clausify,[status(thm)],[f_2326_4]) ).

fof(f_2327_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_2327_2,plain,
    ! [U_8296] : c_Wellfounded_OwfP(U_8296,hAPP(c_COMBK(tc_fun(U_8296,tc_HOL_Obool),U_8296),hAPP(c_COMBK(tc_HOL_Obool,U_8296),c_fFalse))),
    inference(variable_rename,[status(thm)],[f_2327_1]) ).

fof(f_2327_3,plain,
    ! [U_8296] : c_Wellfounded_OwfP(U_8296,hAPP(c_COMBK(tc_fun(U_8296,tc_HOL_Obool),U_8296),hAPP(c_COMBK(tc_HOL_Obool,U_8296),c_fFalse))),
    inference(definitional_conversion,[status(esa)],[f_2327_2]) ).

cnf(f_2327_4,plain,
    c_Wellfounded_OwfP(U_8296,hAPP(c_COMBK(tc_fun(U_8296,tc_HOL_Obool),U_8296),hAPP(c_COMBK(tc_HOL_Obool,U_8296),c_fFalse))),
    inference(clausify,[status(thm)],[f_2327_3]) ).

fof(f_2328_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_2328_2,plain,
    ! [U_8299,U_8298,U_8297] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8297,U_8298),U_8299))
      | ~ c_Wellfounded_OwfP(U_8297,U_8298) ),
    inference(variable_rename,[status(thm)],[f_2328_1]) ).

fof(f_2328_3,plain,
    ! [U_8297,U_8298,U_8299] :
      ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8297,U_8298),U_8299))
      | ~ c_Wellfounded_OwfP(U_8297,U_8298) ),
    inference(definitional_conversion,[status(esa)],[f_2328_2]) ).

cnf(f_2328_4,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8297,U_8298),U_8299))
    | ~ c_Wellfounded_OwfP(U_8297,U_8298) ),
    inference(clausify,[status(thm)],[f_2328_3]) ).

fof(f_2329_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_2329_2,plain,
    ! [U_8303,U_8302] :
      ( ( c_Wellfounded_OwfP(U_8302,U_8303)
        | ? [U_8301] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8302,U_8303),U_8301)) )
      & ( ! [U_8300] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_8302,U_8303),U_8300))
        | ~ c_Wellfounded_OwfP(U_8302,U_8303) ) ),
    inference(variable_rename,[status(thm)],[f_2329_1]) ).

fof(f_2329_3,plain,
    ( ! [U_8307,U_8305] :
        ( c_Wellfounded_OwfP(U_8305,U_8307)
        | ? [U_8301] : ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8305,U_8307),U_8301)) )
    & ! [U_8306,U_8304] :
        ( ! [U_8300] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_8304,U_8306),U_8300))
        | ~ c_Wellfounded_OwfP(U_8304,U_8306) ) ),
    inference(miniscope,[status(thm)],[f_2329_2]) ).

fof(f_2329_4,plain,
    ( ! [U_8307,U_8305] :
        ( c_Wellfounded_OwfP(U_8305,U_8307)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8305,U_8307),sK128(U_8307,U_8305))) )
    & ! [U_8306,U_8304] :
        ( ! [U_8300] : hBOOL(hAPP(c_Wellfounded_Oaccp(U_8304,U_8306),U_8300))
        | ~ c_Wellfounded_OwfP(U_8304,U_8306) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK128]),skolemize(U_8301,sK128(U_8307,U_8305))],[f_2329_3]) ).

fof(f_2329_5,plain,
    ( ! [U_8305,U_8307] :
        ( c_Wellfounded_OwfP(U_8305,U_8307)
        | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8305,U_8307),sK128(U_8307,U_8305))) )
    & ! [U_8306,U_8300,U_8304] :
        ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8304,U_8306),U_8300))
        | ~ c_Wellfounded_OwfP(U_8304,U_8306) ) ),
    inference(definitional_conversion,[status(esa)],[f_2329_4]) ).

cnf(f_2329_6,plain,
    ( hBOOL(hAPP(c_Wellfounded_Oaccp(U_8304,U_8306),U_8300))
    | ~ c_Wellfounded_OwfP(U_8304,U_8306) ),
    inference(clausify,[status(thm)],[f_2329_5]) ).

cnf(f_2329_7,plain,
    ( c_Wellfounded_OwfP(U_8305,U_8307)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(U_8305,U_8307),sK128(U_8307,U_8305))) ),
    inference(clausify,[status(thm)],[f_2329_5]) ).

fof(f_2330_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_2330_2,plain,
    ! [U_8310,U_8309,U_8308] :
      ( c_Wellfounded_OwfP(U_8308,U_8310)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8308,tc_fun(U_8308,tc_HOL_Obool))),U_8310),U_8309))
      | ~ c_Wellfounded_OwfP(U_8308,U_8309) ),
    inference(variable_rename,[status(thm)],[f_2330_1]) ).

fof(f_2330_3,plain,
    ! [U_8310,U_8308,U_8309] :
      ( c_Wellfounded_OwfP(U_8308,U_8310)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8308,tc_fun(U_8308,tc_HOL_Obool))),U_8310),U_8309))
      | ~ c_Wellfounded_OwfP(U_8308,U_8309) ),
    inference(definitional_conversion,[status(esa)],[f_2330_2]) ).

cnf(f_2330_4,plain,
    ( c_Wellfounded_OwfP(U_8308,U_8310)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8308,tc_fun(U_8308,tc_HOL_Obool))),U_8310),U_8309))
    | ~ c_Wellfounded_OwfP(U_8308,U_8309) ),
    inference(clausify,[status(thm)],[f_2330_3]) ).

fof(f_2331_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_2331_2,plain,
    ! [U_8312,U_8311] :
      ( c_Wellfounded_OwfP(U_8311,c_FunDef_Oin__rel(U_8311,U_8311,U_8312))
      | ~ c_Wellfounded_Owf(U_8311,U_8312) ),
    inference(variable_rename,[status(thm)],[f_2331_1]) ).

fof(f_2331_3,plain,
    ! [U_8311,U_8312] :
      ( c_Wellfounded_OwfP(U_8311,c_FunDef_Oin__rel(U_8311,U_8311,U_8312))
      | ~ c_Wellfounded_Owf(U_8311,U_8312) ),
    inference(definitional_conversion,[status(esa)],[f_2331_2]) ).

cnf(f_2331_4,plain,
    ( c_Wellfounded_OwfP(U_8311,c_FunDef_Oin__rel(U_8311,U_8311,U_8312))
    | ~ c_Wellfounded_Owf(U_8311,U_8312) ),
    inference(clausify,[status(thm)],[f_2331_3]) ).

fof(f_2332_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_2332_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_2332_1]) ).

cnf(f_2332_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_2332_2]) ).

fof(f_2333_1,plain,
    ! [V_S_2,V_R_2,V_Pa_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_Pa_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_Pa_2)))
      | ~ c_FunDef_Oreduction__pair(T_b,V_Pa_2) ),
    inference(fof_nnf,[status(thm)],[fact_reduction__pair__lemma]) ).

fof(f_2333_2,plain,
    ! [U_8316,U_8315,U_8314,U_8313] :
      ( c_Wellfounded_Owf(U_8313,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8313,U_8313),tc_HOL_Obool)),U_8315),U_8316))
      | ~ c_Wellfounded_Owf(U_8313,U_8316)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8313,U_8313),tc_HOL_Obool)),U_8316),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_8313,U_8313),tc_HOL_Obool),tc_fun(tc_prod(U_8313,U_8313),tc_HOL_Obool)),U_8314)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8313,U_8313),tc_HOL_Obool)),U_8315),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8313,U_8313),tc_HOL_Obool),tc_fun(tc_prod(U_8313,U_8313),tc_HOL_Obool)),U_8314)))
      | ~ c_FunDef_Oreduction__pair(U_8313,U_8314) ),
    inference(variable_rename,[status(thm)],[f_2333_1]) ).

fof(f_2333_3,plain,
    ! [U_8313,U_8314,U_8315,U_8316] :
      ( c_Wellfounded_Owf(U_8313,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8313,U_8313),tc_HOL_Obool)),U_8315),U_8316))
      | ~ c_Wellfounded_Owf(U_8313,U_8316)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8313,U_8313),tc_HOL_Obool)),U_8316),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_8313,U_8313),tc_HOL_Obool),tc_fun(tc_prod(U_8313,U_8313),tc_HOL_Obool)),U_8314)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8313,U_8313),tc_HOL_Obool)),U_8315),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8313,U_8313),tc_HOL_Obool),tc_fun(tc_prod(U_8313,U_8313),tc_HOL_Obool)),U_8314)))
      | ~ c_FunDef_Oreduction__pair(U_8313,U_8314) ),
    inference(definitional_conversion,[status(esa)],[f_2333_2]) ).

cnf(f_2333_4,plain,
    ( c_Wellfounded_Owf(U_8313,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8313,U_8313),tc_HOL_Obool)),U_8315),U_8316))
    | ~ c_Wellfounded_Owf(U_8313,U_8316)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8313,U_8313),tc_HOL_Obool)),U_8316),hAPP(c_Product__Type_Osnd(tc_fun(tc_prod(U_8313,U_8313),tc_HOL_Obool),tc_fun(tc_prod(U_8313,U_8313),tc_HOL_Obool)),U_8314)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8313,U_8313),tc_HOL_Obool)),U_8315),hAPP(c_Product__Type_Ofst(tc_fun(tc_prod(U_8313,U_8313),tc_HOL_Obool),tc_fun(tc_prod(U_8313,U_8313),tc_HOL_Obool)),U_8314)))
    | ~ c_FunDef_Oreduction__pair(U_8313,U_8314) ),
    inference(clausify,[status(thm)],[f_2333_3]) ).

fof(f_2334_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_2334_2,plain,
    ! [U_8318,U_8317] :
      ( c_Wellfounded_Oacyclic(U_8317,hAPP(c_Set_OCollect(tc_prod(U_8317,U_8317)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8317,U_8317,tc_HOL_Obool),U_8318)))
      | ~ c_Wellfounded_OwfP(U_8317,U_8318) ),
    inference(variable_rename,[status(thm)],[f_2334_1]) ).

fof(f_2334_3,plain,
    ! [U_8318,U_8317] :
      ( c_Wellfounded_Oacyclic(U_8317,hAPP(c_Set_OCollect(tc_prod(U_8317,U_8317)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8317,U_8317,tc_HOL_Obool),U_8318)))
      | ~ c_Wellfounded_OwfP(U_8317,U_8318) ),
    inference(definitional_conversion,[status(esa)],[f_2334_2]) ).

cnf(f_2334_4,plain,
    ( c_Wellfounded_Oacyclic(U_8317,hAPP(c_Set_OCollect(tc_prod(U_8317,U_8317)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8317,U_8317,tc_HOL_Obool),U_8318)))
    | ~ c_Wellfounded_OwfP(U_8317,U_8318) ),
    inference(clausify,[status(thm)],[f_2334_3]) ).

fof(f_2335_1,plain,
    ! [T_b,V_R_2,T_c,V_Pa_2] :
      ( c_Wellfounded_Owf(tc_prod(T_b,T_c),c_Recdef_Osame__fst(T_b,T_c,V_Pa_2,V_R_2))
      | ? [B_x] :
          ( ~ c_Wellfounded_Owf(T_c,hAPP(V_R_2,B_x))
          & hBOOL(hAPP(V_Pa_2,B_x)) ) ),
    inference(fof_nnf,[status(thm)],[fact_wf__same__fst]) ).

fof(f_2335_2,plain,
    ! [U_8323,U_8322,U_8321,U_8320] :
      ( c_Wellfounded_Owf(tc_prod(U_8323,U_8321),c_Recdef_Osame__fst(U_8323,U_8321,U_8320,U_8322))
      | ? [U_8319] :
          ( ~ c_Wellfounded_Owf(U_8321,hAPP(U_8322,U_8319))
          & hBOOL(hAPP(U_8320,U_8319)) ) ),
    inference(variable_rename,[status(thm)],[f_2335_1]) ).

fof(f_2335_3,plain,
    ! [U_8323,U_8322,U_8321,U_8320] :
      ( c_Wellfounded_Owf(tc_prod(U_8323,U_8321),c_Recdef_Osame__fst(U_8323,U_8321,U_8320,U_8322))
      | ( ~ c_Wellfounded_Owf(U_8321,hAPP(U_8322,sK129(U_8323,U_8322,U_8321,U_8320)))
        & hBOOL(hAPP(U_8320,sK129(U_8323,U_8322,U_8321,U_8320))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK129]),skolemize(U_8319,sK129(U_8323,U_8322,U_8321,U_8320))],[f_2335_2]) ).

fof(f_2335_4,plain,
    ( ! [U_8320,U_8321,U_8322,U_8323] :
        ( ~ c_Wellfounded_Owf(U_8321,hAPP(U_8322,sK129(U_8323,U_8322,U_8321,U_8320)))
        | ~ sP701(U_8320,U_8321,U_8322,U_8323) )
    & ! [U_8320,U_8321,U_8322,U_8323] :
        ( hBOOL(hAPP(U_8320,sK129(U_8323,U_8322,U_8321,U_8320)))
        | ~ sP701(U_8320,U_8321,U_8322,U_8323) )
    & ! [U_8320,U_8321,U_8322,U_8323] :
        ( c_Wellfounded_Owf(tc_prod(U_8323,U_8321),c_Recdef_Osame__fst(U_8323,U_8321,U_8320,U_8322))
        | sP701(U_8320,U_8321,U_8322,U_8323) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP701])],[f_2335_3]) ).

cnf(f_2335_5,plain,
    ( c_Wellfounded_Owf(tc_prod(U_8323,U_8321),c_Recdef_Osame__fst(U_8323,U_8321,U_8320,U_8322))
    | sP701(U_8320,U_8321,U_8322,U_8323) ),
    inference(clausify,[status(thm)],[f_2335_4]) ).

cnf(f_2335_6,plain,
    ( hBOOL(hAPP(U_8320,sK129(U_8323,U_8322,U_8321,U_8320)))
    | ~ sP701(U_8320,U_8321,U_8322,U_8323) ),
    inference(clausify,[status(thm)],[f_2335_4]) ).

cnf(f_2335_7,plain,
    ( ~ c_Wellfounded_Owf(U_8321,hAPP(U_8322,sK129(U_8323,U_8322,U_8321,U_8320)))
    | ~ sP701(U_8320,U_8321,U_8322,U_8323) ),
    inference(clausify,[status(thm)],[f_2335_4]) ).

fof(f_2336_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_2336_2,plain,
    ! [U_8327,U_8326,U_8325,U_8324] :
      ( hBOOL(hAPP(U_8326,U_8327))
      | hBOOL(hAPP(U_8325,U_8327))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8324,tc_HOL_Obool)),U_8325),U_8326),U_8327)) ),
    inference(variable_rename,[status(thm)],[f_2336_1]) ).

fof(f_2336_3,plain,
    ! [U_8327,U_8326,U_8325] :
      ( ! [U_8324] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8324,tc_HOL_Obool)),U_8325),U_8326),U_8327))
      | hBOOL(hAPP(U_8326,U_8327))
      | hBOOL(hAPP(U_8325,U_8327)) ),
    inference(miniscope,[status(thm)],[f_2336_2]) ).

fof(f_2336_4,plain,
    ! [U_8325,U_8324,U_8326,U_8327] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8324,tc_HOL_Obool)),U_8325),U_8326),U_8327))
      | hBOOL(hAPP(U_8326,U_8327))
      | hBOOL(hAPP(U_8325,U_8327)) ),
    inference(definitional_conversion,[status(esa)],[f_2336_3]) ).

cnf(f_2336_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8324,tc_HOL_Obool)),U_8325),U_8326),U_8327))
    | hBOOL(hAPP(U_8326,U_8327))
    | hBOOL(hAPP(U_8325,U_8327)) ),
    inference(clausify,[status(thm)],[f_2336_4]) ).

fof(f_2337_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_2337_2,plain,
    ! [U_8331,U_8330,U_8329,U_8328] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8331,tc_HOL_Obool)),U_8330),U_8328),U_8329))
      | ( ~ hBOOL(hAPP(U_8330,U_8329))
        & ~ hBOOL(hAPP(U_8328,U_8329)) ) ),
    inference(variable_rename,[status(thm)],[f_2337_1]) ).

fof(f_2337_3,plain,
    ( ! [U_8329,U_8328,U_8330] :
        ( ~ hBOOL(hAPP(U_8330,U_8329))
        | ~ sP702(U_8329,U_8328,U_8330) )
    & ! [U_8329,U_8328,U_8330] :
        ( ~ hBOOL(hAPP(U_8328,U_8329))
        | ~ sP702(U_8329,U_8328,U_8330) )
    & ! [U_8329,U_8328,U_8330,U_8331] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8331,tc_HOL_Obool)),U_8330),U_8328),U_8329))
        | sP702(U_8329,U_8328,U_8330) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP702])],[f_2337_2]) ).

cnf(f_2337_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8331,tc_HOL_Obool)),U_8330),U_8328),U_8329))
    | sP702(U_8329,U_8328,U_8330) ),
    inference(clausify,[status(thm)],[f_2337_3]) ).

cnf(f_2337_5,plain,
    ( ~ hBOOL(hAPP(U_8328,U_8329))
    | ~ sP702(U_8329,U_8328,U_8330) ),
    inference(clausify,[status(thm)],[f_2337_3]) ).

cnf(f_2337_6,plain,
    ( ~ hBOOL(hAPP(U_8330,U_8329))
    | ~ sP702(U_8329,U_8328,U_8330) ),
    inference(clausify,[status(thm)],[f_2337_3]) ).

fof(f_2338_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_2338_2,plain,
    ! [U_8335,U_8334,U_8333,U_8332] :
      ( hBOOL(hAPP(hAPP(c_member(U_8332),U_8333),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8332,tc_HOL_Obool)),U_8335),U_8334)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_8332),U_8333),U_8335))
        & ~ hBOOL(hAPP(hAPP(c_member(U_8332),U_8333),U_8334)) ) ),
    inference(variable_rename,[status(thm)],[f_2338_1]) ).

fof(f_2338_3,plain,
    ( ! [U_8332,U_8333,U_8334,U_8335] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8332),U_8333),U_8335))
        | ~ sP703(U_8332,U_8333,U_8334,U_8335) )
    & ! [U_8332,U_8333,U_8334,U_8335] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8332),U_8333),U_8334))
        | ~ sP703(U_8332,U_8333,U_8334,U_8335) )
    & ! [U_8332,U_8333,U_8334,U_8335] :
        ( hBOOL(hAPP(hAPP(c_member(U_8332),U_8333),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8332,tc_HOL_Obool)),U_8335),U_8334)))
        | sP703(U_8332,U_8333,U_8334,U_8335) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP703])],[f_2338_2]) ).

cnf(f_2338_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8332),U_8333),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8332,tc_HOL_Obool)),U_8335),U_8334)))
    | sP703(U_8332,U_8333,U_8334,U_8335) ),
    inference(clausify,[status(thm)],[f_2338_3]) ).

cnf(f_2338_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8332),U_8333),U_8334))
    | ~ sP703(U_8332,U_8333,U_8334,U_8335) ),
    inference(clausify,[status(thm)],[f_2338_3]) ).

cnf(f_2338_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8332),U_8333),U_8335))
    | ~ sP703(U_8332,U_8333,U_8334,U_8335) ),
    inference(clausify,[status(thm)],[f_2338_3]) ).

fof(f_2339_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_2339_2,plain,
    ! [U_8339,U_8338,U_8337,U_8336] :
      ( hBOOL(hAPP(hAPP(c_member(U_8336),U_8337),U_8339))
      | hBOOL(hAPP(hAPP(c_member(U_8336),U_8337),U_8338))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8336),U_8337),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8336,tc_HOL_Obool)),U_8338),U_8339))) ),
    inference(variable_rename,[status(thm)],[f_2339_1]) ).

fof(f_2339_3,plain,
    ! [U_8336,U_8337,U_8338,U_8339] :
      ( hBOOL(hAPP(hAPP(c_member(U_8336),U_8337),U_8339))
      | hBOOL(hAPP(hAPP(c_member(U_8336),U_8337),U_8338))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8336),U_8337),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8336,tc_HOL_Obool)),U_8338),U_8339))) ),
    inference(definitional_conversion,[status(esa)],[f_2339_2]) ).

cnf(f_2339_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8336),U_8337),U_8339))
    | hBOOL(hAPP(hAPP(c_member(U_8336),U_8337),U_8338))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8336),U_8337),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8336,tc_HOL_Obool)),U_8338),U_8339))) ),
    inference(clausify,[status(thm)],[f_2339_3]) ).

fof(f_2340_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_2340_2,plain,
    ! [U_8345,U_8344,U_8343,U_8342,U_8341,U_8340] : hAPP(hAPP(c_Relation_Orel__comp(U_8340,U_8341,U_8342),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8340,U_8341),tc_HOL_Obool)),U_8343),U_8344)),U_8345) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8340,U_8342),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8340,U_8341,U_8342),U_8343),U_8345)),hAPP(hAPP(c_Relation_Orel__comp(U_8340,U_8341,U_8342),U_8344),U_8345)),
    inference(variable_rename,[status(thm)],[f_2340_1]) ).

fof(f_2340_3,plain,
    ! [U_8340,U_8341,U_8342,U_8343,U_8344,U_8345] : hAPP(hAPP(c_Relation_Orel__comp(U_8340,U_8341,U_8342),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8340,U_8341),tc_HOL_Obool)),U_8343),U_8344)),U_8345) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8340,U_8342),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8340,U_8341,U_8342),U_8343),U_8345)),hAPP(hAPP(c_Relation_Orel__comp(U_8340,U_8341,U_8342),U_8344),U_8345)),
    inference(definitional_conversion,[status(esa)],[f_2340_2]) ).

cnf(f_2340_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_8340,U_8341,U_8342),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8340,U_8341),tc_HOL_Obool)),U_8343),U_8344)),U_8345) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8340,U_8342),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8340,U_8341,U_8342),U_8343),U_8345)),hAPP(hAPP(c_Relation_Orel__comp(U_8340,U_8341,U_8342),U_8344),U_8345)),
    inference(clausify,[status(thm)],[f_2340_3]) ).

fof(f_2341_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_2341_2,plain,
    ! [U_8351,U_8350,U_8349,U_8348,U_8347,U_8346] : hAPP(hAPP(c_Relation_Orel__comp(U_8346,U_8347,U_8348),U_8349),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8347,U_8348),tc_HOL_Obool)),U_8350),U_8351)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8346,U_8348),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8346,U_8347,U_8348),U_8349),U_8350)),hAPP(hAPP(c_Relation_Orel__comp(U_8346,U_8347,U_8348),U_8349),U_8351)),
    inference(variable_rename,[status(thm)],[f_2341_1]) ).

fof(f_2341_3,plain,
    ! [U_8347,U_8346,U_8348,U_8349,U_8350,U_8351] : hAPP(hAPP(c_Relation_Orel__comp(U_8346,U_8347,U_8348),U_8349),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8347,U_8348),tc_HOL_Obool)),U_8350),U_8351)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8346,U_8348),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8346,U_8347,U_8348),U_8349),U_8350)),hAPP(hAPP(c_Relation_Orel__comp(U_8346,U_8347,U_8348),U_8349),U_8351)),
    inference(definitional_conversion,[status(esa)],[f_2341_2]) ).

cnf(f_2341_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_8346,U_8347,U_8348),U_8349),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8347,U_8348),tc_HOL_Obool)),U_8350),U_8351)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8346,U_8348),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8346,U_8347,U_8348),U_8349),U_8350)),hAPP(hAPP(c_Relation_Orel__comp(U_8346,U_8347,U_8348),U_8349),U_8351)),
    inference(clausify,[status(thm)],[f_2341_3]) ).

fof(f_2342_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_2342_2,plain,
    ! [U_8355,U_8354,U_8353,U_8352] : hAPP(c_Relation_ODomain(U_8352,U_8353),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8352,U_8353),tc_HOL_Obool)),U_8354),U_8355)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8352,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_8352,U_8353),U_8354)),hAPP(c_Relation_ODomain(U_8352,U_8353),U_8355)),
    inference(variable_rename,[status(thm)],[f_2342_1]) ).

fof(f_2342_3,plain,
    ! [U_8352,U_8353,U_8354,U_8355] : hAPP(c_Relation_ODomain(U_8352,U_8353),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8352,U_8353),tc_HOL_Obool)),U_8354),U_8355)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8352,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_8352,U_8353),U_8354)),hAPP(c_Relation_ODomain(U_8352,U_8353),U_8355)),
    inference(definitional_conversion,[status(esa)],[f_2342_2]) ).

cnf(f_2342_4,plain,
    hAPP(c_Relation_ODomain(U_8352,U_8353),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8352,U_8353),tc_HOL_Obool)),U_8354),U_8355)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8352,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_8352,U_8353),U_8354)),hAPP(c_Relation_ODomain(U_8352,U_8353),U_8355)),
    inference(clausify,[status(thm)],[f_2342_3]) ).

fof(f_2343_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_2343_2,plain,
    ! [U_8358,U_8357,U_8356] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8356,tc_HOL_Obool)),U_8357),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8356,tc_HOL_Obool)),U_8358),U_8357)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8356,tc_HOL_Obool)),U_8357),U_8358),
    inference(variable_rename,[status(thm)],[f_2343_1]) ).

fof(f_2343_3,plain,
    ! [U_8356,U_8357,U_8358] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8356,tc_HOL_Obool)),U_8357),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8356,tc_HOL_Obool)),U_8358),U_8357)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8356,tc_HOL_Obool)),U_8357),U_8358),
    inference(definitional_conversion,[status(esa)],[f_2343_2]) ).

cnf(f_2343_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8356,tc_HOL_Obool)),U_8357),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8356,tc_HOL_Obool)),U_8358),U_8357)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8356,tc_HOL_Obool)),U_8357),U_8358),
    inference(clausify,[status(thm)],[f_2343_3]) ).

fof(f_2344_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_2344_2,plain,
    ! [U_8361,U_8360,U_8359] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8359,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8359,tc_HOL_Obool)),U_8360),U_8361)),U_8361) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8359,tc_HOL_Obool)),U_8360),U_8361),
    inference(variable_rename,[status(thm)],[f_2344_1]) ).

fof(f_2344_3,plain,
    ! [U_8359,U_8360,U_8361] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8359,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8359,tc_HOL_Obool)),U_8360),U_8361)),U_8361) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8359,tc_HOL_Obool)),U_8360),U_8361),
    inference(definitional_conversion,[status(esa)],[f_2344_2]) ).

cnf(f_2344_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8359,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8359,tc_HOL_Obool)),U_8360),U_8361)),U_8361) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8359,tc_HOL_Obool)),U_8360),U_8361),
    inference(clausify,[status(thm)],[f_2344_3]) ).

fof(f_2345_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_2345_2,plain,
    ! [U_8365,U_8364,U_8363,U_8362] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8362,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8362,tc_HOL_Obool)),U_8363),U_8364)),U_8365) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8362,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8362,tc_HOL_Obool)),U_8363),U_8365)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8362,tc_HOL_Obool)),U_8364),U_8365)),
    inference(variable_rename,[status(thm)],[f_2345_1]) ).

fof(f_2345_3,plain,
    ! [U_8362,U_8363,U_8364,U_8365] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8362,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8362,tc_HOL_Obool)),U_8363),U_8364)),U_8365) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8362,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8362,tc_HOL_Obool)),U_8363),U_8365)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8362,tc_HOL_Obool)),U_8364),U_8365)),
    inference(definitional_conversion,[status(esa)],[f_2345_2]) ).

cnf(f_2345_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8362,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8362,tc_HOL_Obool)),U_8363),U_8364)),U_8365) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8362,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8362,tc_HOL_Obool)),U_8363),U_8365)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8362,tc_HOL_Obool)),U_8364),U_8365)),
    inference(clausify,[status(thm)],[f_2345_3]) ).

fof(f_2346_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_2346_2,plain,
    ! [U_8369,U_8368,U_8367,U_8366] : hAPP(c_Relation_Oconverse(U_8366,U_8367),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8366,U_8367),tc_HOL_Obool)),U_8368),U_8369)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8367,U_8366),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_8366,U_8367),U_8368)),hAPP(c_Relation_Oconverse(U_8366,U_8367),U_8369)),
    inference(variable_rename,[status(thm)],[f_2346_1]) ).

fof(f_2346_3,plain,
    ! [U_8366,U_8367,U_8368,U_8369] : hAPP(c_Relation_Oconverse(U_8366,U_8367),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8366,U_8367),tc_HOL_Obool)),U_8368),U_8369)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8367,U_8366),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_8366,U_8367),U_8368)),hAPP(c_Relation_Oconverse(U_8366,U_8367),U_8369)),
    inference(definitional_conversion,[status(esa)],[f_2346_2]) ).

cnf(f_2346_4,plain,
    hAPP(c_Relation_Oconverse(U_8366,U_8367),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8366,U_8367),tc_HOL_Obool)),U_8368),U_8369)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8367,U_8366),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_8366,U_8367),U_8368)),hAPP(c_Relation_Oconverse(U_8366,U_8367),U_8369)),
    inference(clausify,[status(thm)],[f_2346_3]) ).

fof(f_2347_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_2347_2,plain,
    ! [U_8370] :
      ( c_Lattices_Osemilattice__sup__class_Osup(U_8370) = c_Orderings_Oord__class_Omax(U_8370)
      | ~ class_Orderings_Olinorder(U_8370)
      | ~ class_Lattices_Osemilattice__sup(U_8370) ),
    inference(variable_rename,[status(thm)],[f_2347_1]) ).

fof(f_2347_3,plain,
    ! [U_8370] :
      ( c_Lattices_Osemilattice__sup__class_Osup(U_8370) = c_Orderings_Oord__class_Omax(U_8370)
      | ~ class_Orderings_Olinorder(U_8370)
      | ~ class_Lattices_Osemilattice__sup(U_8370) ),
    inference(definitional_conversion,[status(esa)],[f_2347_2]) ).

cnf(f_2347_4,plain,
    ( c_Lattices_Osemilattice__sup__class_Osup(U_8370) = c_Orderings_Oord__class_Omax(U_8370)
    | ~ class_Orderings_Olinorder(U_8370)
    | ~ class_Lattices_Osemilattice__sup(U_8370) ),
    inference(clausify,[status(thm)],[f_2347_3]) ).

fof(f_2348_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_2348_2,plain,
    ! [U_8375,U_8374,U_8373,U_8372,U_8371] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8372,U_8371)),U_8373),U_8374),U_8375) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8371),hAPP(U_8373,U_8375)),hAPP(U_8374,U_8375))
      | ~ class_Lattices_Olattice(U_8371) ),
    inference(variable_rename,[status(thm)],[f_2348_1]) ).

fof(f_2348_3,plain,
    ! [U_8371,U_8372,U_8373,U_8374,U_8375] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8372,U_8371)),U_8373),U_8374),U_8375) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8371),hAPP(U_8373,U_8375)),hAPP(U_8374,U_8375))
      | ~ class_Lattices_Olattice(U_8371) ),
    inference(definitional_conversion,[status(esa)],[f_2348_2]) ).

cnf(f_2348_4,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8372,U_8371)),U_8373),U_8374),U_8375) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8371),hAPP(U_8373,U_8375)),hAPP(U_8374,U_8375))
    | ~ class_Lattices_Olattice(U_8371) ),
    inference(clausify,[status(thm)],[f_2348_3]) ).

fof(f_2349_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_2349_2,plain,
    ! [U_8377,U_8376] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8376),U_8377),U_8377) = U_8377
      | ~ class_Lattices_Osemilattice__sup(U_8376) ),
    inference(variable_rename,[status(thm)],[f_2349_1]) ).

fof(f_2349_3,plain,
    ! [U_8376,U_8377] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8376),U_8377),U_8377) = U_8377
      | ~ class_Lattices_Osemilattice__sup(U_8376) ),
    inference(definitional_conversion,[status(esa)],[f_2349_2]) ).

cnf(f_2349_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8376),U_8377),U_8377) = U_8377
    | ~ class_Lattices_Osemilattice__sup(U_8376) ),
    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),V_x) = V_x
      | ~ class_Lattices_Osemilattice__sup(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sup__idem]) ).

fof(f_2350_2,plain,
    ! [U_8379,U_8378] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8378),U_8379),U_8379) = U_8379
      | ~ class_Lattices_Osemilattice__sup(U_8378) ),
    inference(variable_rename,[status(thm)],[f_2350_1]) ).

fof(f_2350_3,plain,
    ! [U_8378,U_8379] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8378),U_8379),U_8379) = U_8379
      | ~ class_Lattices_Osemilattice__sup(U_8378) ),
    inference(definitional_conversion,[status(esa)],[f_2350_2]) ).

cnf(f_2350_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8378),U_8379),U_8379) = U_8379
    | ~ class_Lattices_Osemilattice__sup(U_8378) ),
    inference(clausify,[status(thm)],[f_2350_3]) ).

fof(f_2351_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_2351_2,plain,
    ! [U_8382,U_8381,U_8380] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8380),U_8381),U_8382) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8380),U_8382),U_8381)
      | ~ class_Lattices_Osemilattice__sup(U_8380) ),
    inference(variable_rename,[status(thm)],[f_2351_1]) ).

fof(f_2351_3,plain,
    ! [U_8380,U_8381,U_8382] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8380),U_8381),U_8382) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8380),U_8382),U_8381)
      | ~ class_Lattices_Osemilattice__sup(U_8380) ),
    inference(definitional_conversion,[status(esa)],[f_2351_2]) ).

cnf(f_2351_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8380),U_8381),U_8382) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8380),U_8382),U_8381)
    | ~ class_Lattices_Osemilattice__sup(U_8380) ),
    inference(clausify,[status(thm)],[f_2351_3]) ).

fof(f_2352_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_2352_2,plain,
    ! [U_8385,U_8384,U_8383] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8383),U_8384),U_8385) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8383),U_8385),U_8384)
      | ~ class_Lattices_Olattice(U_8383) ),
    inference(variable_rename,[status(thm)],[f_2352_1]) ).

fof(f_2352_3,plain,
    ! [U_8383,U_8384,U_8385] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8383),U_8384),U_8385) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8383),U_8385),U_8384)
      | ~ class_Lattices_Olattice(U_8383) ),
    inference(definitional_conversion,[status(esa)],[f_2352_2]) ).

cnf(f_2352_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8383),U_8384),U_8385) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8383),U_8385),U_8384)
    | ~ class_Lattices_Olattice(U_8383) ),
    inference(clausify,[status(thm)],[f_2352_3]) ).

fof(f_2353_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_2353_2,plain,
    ! [U_8388,U_8387,U_8386] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8386),U_8387),U_8388) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8386),U_8388),U_8387)
      | ~ class_Lattices_Osemilattice__sup(U_8386) ),
    inference(variable_rename,[status(thm)],[f_2353_1]) ).

fof(f_2353_3,plain,
    ! [U_8386,U_8387,U_8388] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8386),U_8387),U_8388) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8386),U_8388),U_8387)
      | ~ class_Lattices_Osemilattice__sup(U_8386) ),
    inference(definitional_conversion,[status(esa)],[f_2353_2]) ).

cnf(f_2353_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8386),U_8387),U_8388) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8386),U_8388),U_8387)
    | ~ class_Lattices_Osemilattice__sup(U_8386) ),
    inference(clausify,[status(thm)],[f_2353_3]) ).

fof(f_2354_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_2354_2,plain,
    ! [U_8391,U_8390,U_8389] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8389),U_8390),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8389),U_8390),U_8391)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8389),U_8390),U_8391)
      | ~ class_Lattices_Osemilattice__sup(U_8389) ),
    inference(variable_rename,[status(thm)],[f_2354_1]) ).

fof(f_2354_3,plain,
    ! [U_8389,U_8390,U_8391] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8389),U_8390),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8389),U_8390),U_8391)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8389),U_8390),U_8391)
      | ~ class_Lattices_Osemilattice__sup(U_8389) ),
    inference(definitional_conversion,[status(esa)],[f_2354_2]) ).

cnf(f_2354_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8389),U_8390),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8389),U_8390),U_8391)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8389),U_8390),U_8391)
    | ~ class_Lattices_Osemilattice__sup(U_8389) ),
    inference(clausify,[status(thm)],[f_2354_3]) ).

fof(f_2355_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_2355_2,plain,
    ! [U_8394,U_8393,U_8392] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8392),U_8393),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8392),U_8393),U_8394)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8392),U_8393),U_8394)
      | ~ class_Lattices_Olattice(U_8392) ),
    inference(variable_rename,[status(thm)],[f_2355_1]) ).

fof(f_2355_3,plain,
    ! [U_8392,U_8393,U_8394] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8392),U_8393),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8392),U_8393),U_8394)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8392),U_8393),U_8394)
      | ~ class_Lattices_Olattice(U_8392) ),
    inference(definitional_conversion,[status(esa)],[f_2355_2]) ).

cnf(f_2355_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8392),U_8393),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8392),U_8393),U_8394)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8392),U_8393),U_8394)
    | ~ class_Lattices_Olattice(U_8392) ),
    inference(clausify,[status(thm)],[f_2355_3]) ).

fof(f_2356_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_2356_2,plain,
    ! [U_8397,U_8396,U_8395] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8395),U_8396),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8395),U_8396),U_8397)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8395),U_8396),U_8397)
      | ~ class_Lattices_Osemilattice__sup(U_8395) ),
    inference(variable_rename,[status(thm)],[f_2356_1]) ).

fof(f_2356_3,plain,
    ! [U_8395,U_8396,U_8397] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8395),U_8396),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8395),U_8396),U_8397)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8395),U_8396),U_8397)
      | ~ class_Lattices_Osemilattice__sup(U_8395) ),
    inference(definitional_conversion,[status(esa)],[f_2356_2]) ).

cnf(f_2356_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8395),U_8396),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8395),U_8396),U_8397)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8395),U_8396),U_8397)
    | ~ class_Lattices_Osemilattice__sup(U_8395) ),
    inference(clausify,[status(thm)],[f_2356_3]) ).

fof(f_2357_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_2357_2,plain,
    ! [U_8401,U_8400,U_8399,U_8398] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8398),U_8399),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8398),U_8400),U_8401)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8398),U_8400),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8398),U_8399),U_8401))
      | ~ class_Lattices_Osemilattice__sup(U_8398) ),
    inference(variable_rename,[status(thm)],[f_2357_1]) ).

fof(f_2357_3,plain,
    ! [U_8398,U_8399,U_8400,U_8401] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8398),U_8399),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8398),U_8400),U_8401)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8398),U_8400),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8398),U_8399),U_8401))
      | ~ class_Lattices_Osemilattice__sup(U_8398) ),
    inference(definitional_conversion,[status(esa)],[f_2357_2]) ).

cnf(f_2357_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8398),U_8399),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8398),U_8400),U_8401)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8398),U_8400),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8398),U_8399),U_8401))
    | ~ class_Lattices_Osemilattice__sup(U_8398) ),
    inference(clausify,[status(thm)],[f_2357_3]) ).

fof(f_2358_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_2358_2,plain,
    ! [U_8405,U_8404,U_8403,U_8402] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8402),U_8403),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8402),U_8404),U_8405)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8402),U_8404),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8402),U_8403),U_8405))
      | ~ class_Lattices_Olattice(U_8402) ),
    inference(variable_rename,[status(thm)],[f_2358_1]) ).

fof(f_2358_3,plain,
    ! [U_8402,U_8403,U_8404,U_8405] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8402),U_8403),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8402),U_8404),U_8405)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8402),U_8404),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8402),U_8403),U_8405))
      | ~ class_Lattices_Olattice(U_8402) ),
    inference(definitional_conversion,[status(esa)],[f_2358_2]) ).

cnf(f_2358_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8402),U_8403),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8402),U_8404),U_8405)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8402),U_8404),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8402),U_8403),U_8405))
    | ~ class_Lattices_Olattice(U_8402) ),
    inference(clausify,[status(thm)],[f_2358_3]) ).

fof(f_2359_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_2359_2,plain,
    ! [U_8409,U_8408,U_8407,U_8406] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8406),U_8407),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8406),U_8408),U_8409)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8406),U_8408),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8406),U_8407),U_8409))
      | ~ class_Lattices_Osemilattice__sup(U_8406) ),
    inference(variable_rename,[status(thm)],[f_2359_1]) ).

fof(f_2359_3,plain,
    ! [U_8406,U_8407,U_8408,U_8409] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8406),U_8407),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8406),U_8408),U_8409)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8406),U_8408),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8406),U_8407),U_8409))
      | ~ class_Lattices_Osemilattice__sup(U_8406) ),
    inference(definitional_conversion,[status(esa)],[f_2359_2]) ).

cnf(f_2359_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8406),U_8407),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8406),U_8408),U_8409)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8406),U_8408),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8406),U_8407),U_8409))
    | ~ class_Lattices_Osemilattice__sup(U_8406) ),
    inference(clausify,[status(thm)],[f_2359_3]) ).

fof(f_2360_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_2360_2,plain,
    ! [U_8413,U_8412,U_8411,U_8410] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8410),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8410),U_8411),U_8412)),U_8413) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8410),U_8411),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8410),U_8412),U_8413))
      | ~ class_Lattices_Osemilattice__sup(U_8410) ),
    inference(variable_rename,[status(thm)],[f_2360_1]) ).

fof(f_2360_3,plain,
    ! [U_8410,U_8411,U_8412,U_8413] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8410),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8410),U_8411),U_8412)),U_8413) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8410),U_8411),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8410),U_8412),U_8413))
      | ~ class_Lattices_Osemilattice__sup(U_8410) ),
    inference(definitional_conversion,[status(esa)],[f_2360_2]) ).

cnf(f_2360_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8410),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8410),U_8411),U_8412)),U_8413) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8410),U_8411),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8410),U_8412),U_8413))
    | ~ class_Lattices_Osemilattice__sup(U_8410) ),
    inference(clausify,[status(thm)],[f_2360_3]) ).

fof(f_2361_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_2361_2,plain,
    ! [U_8417,U_8416,U_8415,U_8414] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8414),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8414),U_8415),U_8416)),U_8417) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8414),U_8415),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8414),U_8416),U_8417))
      | ~ class_Lattices_Olattice(U_8414) ),
    inference(variable_rename,[status(thm)],[f_2361_1]) ).

fof(f_2361_3,plain,
    ! [U_8414,U_8415,U_8416,U_8417] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8414),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8414),U_8415),U_8416)),U_8417) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8414),U_8415),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8414),U_8416),U_8417))
      | ~ class_Lattices_Olattice(U_8414) ),
    inference(definitional_conversion,[status(esa)],[f_2361_2]) ).

cnf(f_2361_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8414),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8414),U_8415),U_8416)),U_8417) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8414),U_8415),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8414),U_8416),U_8417))
    | ~ class_Lattices_Olattice(U_8414) ),
    inference(clausify,[status(thm)],[f_2361_3]) ).

fof(f_2362_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_2362_2,plain,
    ! [U_8421,U_8420,U_8419,U_8418] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8418),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8418),U_8419),U_8420)),U_8421) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8418),U_8419),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8418),U_8420),U_8421))
      | ~ class_Lattices_Osemilattice__sup(U_8418) ),
    inference(variable_rename,[status(thm)],[f_2362_1]) ).

fof(f_2362_3,plain,
    ! [U_8418,U_8419,U_8420,U_8421] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8418),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8418),U_8419),U_8420)),U_8421) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8418),U_8419),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8418),U_8420),U_8421))
      | ~ class_Lattices_Osemilattice__sup(U_8418) ),
    inference(definitional_conversion,[status(esa)],[f_2362_2]) ).

cnf(f_2362_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8418),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8418),U_8419),U_8420)),U_8421) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8418),U_8419),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8418),U_8420),U_8421))
    | ~ class_Lattices_Osemilattice__sup(U_8418) ),
    inference(clausify,[status(thm)],[f_2362_3]) ).

fof(f_2363_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_2363_2,plain,
    ! [U_8426,U_8425,U_8424,U_8423,U_8422] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8423,U_8422)),U_8424),U_8425),U_8426) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8422),hAPP(U_8424,U_8426)),hAPP(U_8425,U_8426))
      | ~ class_Lattices_Olattice(U_8422) ),
    inference(variable_rename,[status(thm)],[f_2363_1]) ).

fof(f_2363_3,plain,
    ! [U_8422,U_8423,U_8424,U_8425,U_8426] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8423,U_8422)),U_8424),U_8425),U_8426) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8422),hAPP(U_8424,U_8426)),hAPP(U_8425,U_8426))
      | ~ class_Lattices_Olattice(U_8422) ),
    inference(definitional_conversion,[status(esa)],[f_2363_2]) ).

cnf(f_2363_4,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8423,U_8422)),U_8424),U_8425),U_8426) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8422),hAPP(U_8424,U_8426)),hAPP(U_8425,U_8426))
    | ~ class_Lattices_Olattice(U_8422) ),
    inference(clausify,[status(thm)],[f_2363_3]) ).

fof(f_2364_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_2364_2,plain,
    ! [U_8428,U_8427] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8427,tc_HOL_Obool)),U_8428),U_8428) = U_8428,
    inference(variable_rename,[status(thm)],[f_2364_1]) ).

fof(f_2364_3,plain,
    ! [U_8428,U_8427] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8427,tc_HOL_Obool)),U_8428),U_8428) = U_8428,
    inference(definitional_conversion,[status(esa)],[f_2364_2]) ).

cnf(f_2364_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8427,tc_HOL_Obool)),U_8428),U_8428) = U_8428,
    inference(clausify,[status(thm)],[f_2364_3]) ).

fof(f_2365_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_2365_2,plain,
    ! [U_8431,U_8430,U_8429] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8429,tc_HOL_Obool)),U_8430),U_8431) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8429,tc_HOL_Obool)),U_8431),U_8430),
    inference(variable_rename,[status(thm)],[f_2365_1]) ).

fof(f_2365_3,plain,
    ! [U_8429,U_8430,U_8431] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8429,tc_HOL_Obool)),U_8430),U_8431) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8429,tc_HOL_Obool)),U_8431),U_8430),
    inference(definitional_conversion,[status(esa)],[f_2365_2]) ).

cnf(f_2365_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8429,tc_HOL_Obool)),U_8430),U_8431) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8429,tc_HOL_Obool)),U_8431),U_8430),
    inference(clausify,[status(thm)],[f_2365_3]) ).

fof(f_2366_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_2366_2,plain,
    ! [U_8434,U_8433,U_8432] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8432,tc_HOL_Obool)),U_8433),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8432,tc_HOL_Obool)),U_8433),U_8434)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8432,tc_HOL_Obool)),U_8433),U_8434),
    inference(variable_rename,[status(thm)],[f_2366_1]) ).

fof(f_2366_3,plain,
    ! [U_8432,U_8433,U_8434] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8432,tc_HOL_Obool)),U_8433),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8432,tc_HOL_Obool)),U_8433),U_8434)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8432,tc_HOL_Obool)),U_8433),U_8434),
    inference(definitional_conversion,[status(esa)],[f_2366_2]) ).

cnf(f_2366_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8432,tc_HOL_Obool)),U_8433),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8432,tc_HOL_Obool)),U_8433),U_8434)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8432,tc_HOL_Obool)),U_8433),U_8434),
    inference(clausify,[status(thm)],[f_2366_3]) ).

fof(f_2367_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_2367_2,plain,
    ! [U_8438,U_8437,U_8436,U_8435] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8435,tc_HOL_Obool)),U_8436),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8435,tc_HOL_Obool)),U_8437),U_8438)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8435,tc_HOL_Obool)),U_8437),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8435,tc_HOL_Obool)),U_8436),U_8438)),
    inference(variable_rename,[status(thm)],[f_2367_1]) ).

fof(f_2367_3,plain,
    ! [U_8435,U_8436,U_8437,U_8438] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8435,tc_HOL_Obool)),U_8436),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8435,tc_HOL_Obool)),U_8437),U_8438)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8435,tc_HOL_Obool)),U_8437),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8435,tc_HOL_Obool)),U_8436),U_8438)),
    inference(definitional_conversion,[status(esa)],[f_2367_2]) ).

cnf(f_2367_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8435,tc_HOL_Obool)),U_8436),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8435,tc_HOL_Obool)),U_8437),U_8438)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8435,tc_HOL_Obool)),U_8437),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8435,tc_HOL_Obool)),U_8436),U_8438)),
    inference(clausify,[status(thm)],[f_2367_3]) ).

fof(f_2368_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_2368_2,plain,
    ! [U_8442,U_8441,U_8440,U_8439] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8439,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8439,tc_HOL_Obool)),U_8440),U_8441)),U_8442) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8439,tc_HOL_Obool)),U_8440),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8439,tc_HOL_Obool)),U_8441),U_8442)),
    inference(variable_rename,[status(thm)],[f_2368_1]) ).

fof(f_2368_3,plain,
    ! [U_8439,U_8440,U_8441,U_8442] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8439,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8439,tc_HOL_Obool)),U_8440),U_8441)),U_8442) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8439,tc_HOL_Obool)),U_8440),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8439,tc_HOL_Obool)),U_8441),U_8442)),
    inference(definitional_conversion,[status(esa)],[f_2368_2]) ).

cnf(f_2368_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8439,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8439,tc_HOL_Obool)),U_8440),U_8441)),U_8442) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8439,tc_HOL_Obool)),U_8440),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8439,tc_HOL_Obool)),U_8441),U_8442)),
    inference(clausify,[status(thm)],[f_2368_3]) ).

fof(f_2369_1,plain,
    ! [V_Pa_2,V_B_2,V_A_2,T_b] :
      ( ( ? [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
          & ! [B_x] :
              ( ~ hBOOL(hAPP(V_Pa_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) )
      & ( ? [B_x] :
            ( hBOOL(hAPP(V_Pa_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
        | ? [B_x] :
            ( hBOOL(hAPP(V_Pa_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_2369_2,plain,
    ! [U_8452,U_8451,U_8450,U_8449] :
      ( ( ? [U_8448] :
            ( hBOOL(hAPP(U_8452,U_8448))
            & hBOOL(hAPP(hAPP(c_member(U_8449),U_8448),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8449,tc_HOL_Obool)),U_8450),U_8451))) )
        | ( ! [U_8447] :
              ( ~ hBOOL(hAPP(U_8452,U_8447))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8449),U_8447),U_8451)) )
          & ! [U_8446] :
              ( ~ hBOOL(hAPP(U_8452,U_8446))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8449),U_8446),U_8450)) ) ) )
      & ( ? [U_8445] :
            ( hBOOL(hAPP(U_8452,U_8445))
            & hBOOL(hAPP(hAPP(c_member(U_8449),U_8445),U_8451)) )
        | ? [U_8444] :
            ( hBOOL(hAPP(U_8452,U_8444))
            & hBOOL(hAPP(hAPP(c_member(U_8449),U_8444),U_8450)) )
        | ! [U_8443] :
            ( ~ hBOOL(hAPP(U_8452,U_8443))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8449),U_8443),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8449,tc_HOL_Obool)),U_8450),U_8451))) ) ) ),
    inference(variable_rename,[status(thm)],[f_2369_1]) ).

fof(f_2369_3,plain,
    ( ! [U_8460,U_8458,U_8456,U_8454] :
        ( ? [U_8448] :
            ( hBOOL(hAPP(U_8460,U_8448))
            & hBOOL(hAPP(hAPP(c_member(U_8454),U_8448),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8454,tc_HOL_Obool)),U_8456),U_8458))) )
        | ( ! [U_8447] :
              ( ~ hBOOL(hAPP(U_8460,U_8447))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8454),U_8447),U_8458)) )
          & ! [U_8446] :
              ( ~ hBOOL(hAPP(U_8460,U_8446))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8454),U_8446),U_8456)) ) ) )
    & ! [U_8459,U_8457,U_8455,U_8453] :
        ( ? [U_8445] :
            ( hBOOL(hAPP(U_8459,U_8445))
            & hBOOL(hAPP(hAPP(c_member(U_8453),U_8445),U_8457)) )
        | ? [U_8444] :
            ( hBOOL(hAPP(U_8459,U_8444))
            & hBOOL(hAPP(hAPP(c_member(U_8453),U_8444),U_8455)) )
        | ! [U_8443] :
            ( ~ hBOOL(hAPP(U_8459,U_8443))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8453),U_8443),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8453,tc_HOL_Obool)),U_8455),U_8457))) ) ) ),
    inference(miniscope,[status(thm)],[f_2369_2]) ).

fof(f_2369_4,plain,
    ( ! [U_8460,U_8458,U_8456,U_8454] :
        ( ? [U_8448] :
            ( hBOOL(hAPP(U_8460,U_8448))
            & hBOOL(hAPP(hAPP(c_member(U_8454),U_8448),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8454,tc_HOL_Obool)),U_8456),U_8458))) )
        | ( ! [U_8447] :
              ( ~ hBOOL(hAPP(U_8460,U_8447))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8454),U_8447),U_8458)) )
          & ! [U_8446] :
              ( ~ hBOOL(hAPP(U_8460,U_8446))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8454),U_8446),U_8456)) ) ) )
    & ! [U_8459,U_8457,U_8455,U_8453] :
        ( ? [U_8445] :
            ( hBOOL(hAPP(U_8459,U_8445))
            & hBOOL(hAPP(hAPP(c_member(U_8453),U_8445),U_8457)) )
        | ( hBOOL(hAPP(U_8459,sK130(U_8459,U_8457,U_8455,U_8453)))
          & hBOOL(hAPP(hAPP(c_member(U_8453),sK130(U_8459,U_8457,U_8455,U_8453)),U_8455)) )
        | ! [U_8443] :
            ( ~ hBOOL(hAPP(U_8459,U_8443))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8453),U_8443),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8453,tc_HOL_Obool)),U_8455),U_8457))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK130]),skolemize(U_8444,sK130(U_8459,U_8457,U_8455,U_8453))],[f_2369_3]) ).

fof(f_2369_5,plain,
    ( ! [U_8460,U_8458,U_8456,U_8454] :
        ( ? [U_8448] :
            ( hBOOL(hAPP(U_8460,U_8448))
            & hBOOL(hAPP(hAPP(c_member(U_8454),U_8448),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8454,tc_HOL_Obool)),U_8456),U_8458))) )
        | ( ! [U_8447] :
              ( ~ hBOOL(hAPP(U_8460,U_8447))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8454),U_8447),U_8458)) )
          & ! [U_8446] :
              ( ~ hBOOL(hAPP(U_8460,U_8446))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8454),U_8446),U_8456)) ) ) )
    & ! [U_8459,U_8457,U_8455,U_8453] :
        ( ( hBOOL(hAPP(U_8459,sK131(U_8459,U_8457,U_8455,U_8453)))
          & hBOOL(hAPP(hAPP(c_member(U_8453),sK131(U_8459,U_8457,U_8455,U_8453)),U_8457)) )
        | ( hBOOL(hAPP(U_8459,sK130(U_8459,U_8457,U_8455,U_8453)))
          & hBOOL(hAPP(hAPP(c_member(U_8453),sK130(U_8459,U_8457,U_8455,U_8453)),U_8455)) )
        | ! [U_8443] :
            ( ~ hBOOL(hAPP(U_8459,U_8443))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8453),U_8443),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8453,tc_HOL_Obool)),U_8455),U_8457))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(U_8445,sK131(U_8459,U_8457,U_8455,U_8453))],[f_2369_4]) ).

fof(f_2369_6,plain,
    ( ! [U_8460,U_8458,U_8456,U_8454] :
        ( ( hBOOL(hAPP(U_8460,sK132(U_8460,U_8458,U_8456,U_8454)))
          & hBOOL(hAPP(hAPP(c_member(U_8454),sK132(U_8460,U_8458,U_8456,U_8454)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8454,tc_HOL_Obool)),U_8456),U_8458))) )
        | ( ! [U_8447] :
              ( ~ hBOOL(hAPP(U_8460,U_8447))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8454),U_8447),U_8458)) )
          & ! [U_8446] :
              ( ~ hBOOL(hAPP(U_8460,U_8446))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8454),U_8446),U_8456)) ) ) )
    & ! [U_8459,U_8457,U_8455,U_8453] :
        ( ( hBOOL(hAPP(U_8459,sK131(U_8459,U_8457,U_8455,U_8453)))
          & hBOOL(hAPP(hAPP(c_member(U_8453),sK131(U_8459,U_8457,U_8455,U_8453)),U_8457)) )
        | ( hBOOL(hAPP(U_8459,sK130(U_8459,U_8457,U_8455,U_8453)))
          & hBOOL(hAPP(hAPP(c_member(U_8453),sK130(U_8459,U_8457,U_8455,U_8453)),U_8455)) )
        | ! [U_8443] :
            ( ~ hBOOL(hAPP(U_8459,U_8443))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8453),U_8443),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8453,tc_HOL_Obool)),U_8455),U_8457))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK132]),skolemize(U_8448,sK132(U_8460,U_8458,U_8456,U_8454))],[f_2369_5]) ).

fof(f_2369_7,plain,
    ( ! [U_8454,U_8460,U_8458,U_8456] :
        ( hBOOL(hAPP(U_8460,sK132(U_8460,U_8458,U_8456,U_8454)))
        | ~ sP707(U_8454,U_8460,U_8458,U_8456) )
    & ! [U_8454,U_8460,U_8458,U_8456] :
        ( hBOOL(hAPP(hAPP(c_member(U_8454),sK132(U_8460,U_8458,U_8456,U_8454)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8454,tc_HOL_Obool)),U_8456),U_8458)))
        | ~ sP707(U_8454,U_8460,U_8458,U_8456) )
    & ! [U_8454,U_8460,U_8458,U_8446,U_8447,U_8456] :
        ( ~ hBOOL(hAPP(U_8460,U_8447))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8454),U_8447),U_8458))
        | ~ sP706(U_8454,U_8460,U_8458,U_8446,U_8447,U_8456) )
    & ! [U_8454,U_8460,U_8458,U_8446,U_8447,U_8456] :
        ( ~ hBOOL(hAPP(U_8460,U_8446))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8454),U_8446),U_8456))
        | ~ sP706(U_8454,U_8460,U_8458,U_8446,U_8447,U_8456) )
    & ! [U_8455,U_8457,U_8453,U_8459] :
        ( hBOOL(hAPP(U_8459,sK131(U_8459,U_8457,U_8455,U_8453)))
        | ~ sP705(U_8455,U_8457,U_8453,U_8459) )
    & ! [U_8455,U_8457,U_8453,U_8459] :
        ( hBOOL(hAPP(hAPP(c_member(U_8453),sK131(U_8459,U_8457,U_8455,U_8453)),U_8457))
        | ~ sP705(U_8455,U_8457,U_8453,U_8459) )
    & ! [U_8455,U_8457,U_8453,U_8459] :
        ( hBOOL(hAPP(U_8459,sK130(U_8459,U_8457,U_8455,U_8453)))
        | ~ sP704(U_8455,U_8457,U_8453,U_8459) )
    & ! [U_8455,U_8457,U_8453,U_8459] :
        ( hBOOL(hAPP(hAPP(c_member(U_8453),sK130(U_8459,U_8457,U_8455,U_8453)),U_8455))
        | ~ sP704(U_8455,U_8457,U_8453,U_8459) )
    & ! [U_8454,U_8460,U_8458,U_8446,U_8447,U_8456] :
        ( sP707(U_8454,U_8460,U_8458,U_8456)
        | sP706(U_8454,U_8460,U_8458,U_8446,U_8447,U_8456) )
    & ! [U_8443,U_8455,U_8457,U_8453,U_8459] :
        ( sP705(U_8455,U_8457,U_8453,U_8459)
        | sP704(U_8455,U_8457,U_8453,U_8459)
        | ~ hBOOL(hAPP(U_8459,U_8443))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8453),U_8443),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8453,tc_HOL_Obool)),U_8455),U_8457))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP704,sP705,sP706,sP707])],[f_2369_6]) ).

cnf(f_2369_8,plain,
    ( sP705(U_8455,U_8457,U_8453,U_8459)
    | sP704(U_8455,U_8457,U_8453,U_8459)
    | ~ hBOOL(hAPP(U_8459,U_8443))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8453),U_8443),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8453,tc_HOL_Obool)),U_8455),U_8457))) ),
    inference(clausify,[status(thm)],[f_2369_7]) ).

cnf(f_2369_9,plain,
    ( sP707(U_8454,U_8460,U_8458,U_8456)
    | sP706(U_8454,U_8460,U_8458,U_8446,U_8447,U_8456) ),
    inference(clausify,[status(thm)],[f_2369_7]) ).

cnf(f_2369_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8453),sK130(U_8459,U_8457,U_8455,U_8453)),U_8455))
    | ~ sP704(U_8455,U_8457,U_8453,U_8459) ),
    inference(clausify,[status(thm)],[f_2369_7]) ).

cnf(f_2369_11,plain,
    ( hBOOL(hAPP(U_8459,sK130(U_8459,U_8457,U_8455,U_8453)))
    | ~ sP704(U_8455,U_8457,U_8453,U_8459) ),
    inference(clausify,[status(thm)],[f_2369_7]) ).

cnf(f_2369_12,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8453),sK131(U_8459,U_8457,U_8455,U_8453)),U_8457))
    | ~ sP705(U_8455,U_8457,U_8453,U_8459) ),
    inference(clausify,[status(thm)],[f_2369_7]) ).

cnf(f_2369_13,plain,
    ( hBOOL(hAPP(U_8459,sK131(U_8459,U_8457,U_8455,U_8453)))
    | ~ sP705(U_8455,U_8457,U_8453,U_8459) ),
    inference(clausify,[status(thm)],[f_2369_7]) ).

cnf(f_2369_14,plain,
    ( ~ hBOOL(hAPP(U_8460,U_8446))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8454),U_8446),U_8456))
    | ~ sP706(U_8454,U_8460,U_8458,U_8446,U_8447,U_8456) ),
    inference(clausify,[status(thm)],[f_2369_7]) ).

cnf(f_2369_15,plain,
    ( ~ hBOOL(hAPP(U_8460,U_8447))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8454),U_8447),U_8458))
    | ~ sP706(U_8454,U_8460,U_8458,U_8446,U_8447,U_8456) ),
    inference(clausify,[status(thm)],[f_2369_7]) ).

cnf(f_2369_16,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8454),sK132(U_8460,U_8458,U_8456,U_8454)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8454,tc_HOL_Obool)),U_8456),U_8458)))
    | ~ sP707(U_8454,U_8460,U_8458,U_8456) ),
    inference(clausify,[status(thm)],[f_2369_7]) ).

cnf(f_2369_17,plain,
    ( hBOOL(hAPP(U_8460,sK132(U_8460,U_8458,U_8456,U_8454)))
    | ~ sP707(U_8454,U_8460,U_8458,U_8456) ),
    inference(clausify,[status(thm)],[f_2369_7]) ).

fof(f_2370_1,plain,
    ! [V_Pa_2,V_B_2,V_A_2,T_b] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_2,B_x))
            & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
      & ( ( ! [B_x] :
              ( hBOOL(hAPP(V_Pa_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_B_2)) )
          & ! [B_x] :
              ( hBOOL(hAPP(V_Pa_2,B_x))
              | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_2370_2,plain,
    ! [U_8470,U_8469,U_8468,U_8467] :
      ( ( ! [U_8466] :
            ( hBOOL(hAPP(U_8470,U_8466))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8467),U_8466),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8467,tc_HOL_Obool)),U_8468),U_8469))) )
        | ? [U_8465] :
            ( ~ hBOOL(hAPP(U_8470,U_8465))
            & hBOOL(hAPP(hAPP(c_member(U_8467),U_8465),U_8469)) )
        | ? [U_8464] :
            ( ~ hBOOL(hAPP(U_8470,U_8464))
            & hBOOL(hAPP(hAPP(c_member(U_8467),U_8464),U_8468)) ) )
      & ( ( ! [U_8463] :
              ( hBOOL(hAPP(U_8470,U_8463))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8467),U_8463),U_8469)) )
          & ! [U_8462] :
              ( hBOOL(hAPP(U_8470,U_8462))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8467),U_8462),U_8468)) ) )
        | ? [U_8461] :
            ( ~ hBOOL(hAPP(U_8470,U_8461))
            & hBOOL(hAPP(hAPP(c_member(U_8467),U_8461),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8467,tc_HOL_Obool)),U_8468),U_8469))) ) ) ),
    inference(variable_rename,[status(thm)],[f_2370_1]) ).

fof(f_2370_3,plain,
    ( ! [U_8478,U_8476,U_8474,U_8472] :
        ( ! [U_8466] :
            ( hBOOL(hAPP(U_8478,U_8466))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8472),U_8466),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8472,tc_HOL_Obool)),U_8474),U_8476))) )
        | ? [U_8465] :
            ( ~ hBOOL(hAPP(U_8478,U_8465))
            & hBOOL(hAPP(hAPP(c_member(U_8472),U_8465),U_8476)) )
        | ? [U_8464] :
            ( ~ hBOOL(hAPP(U_8478,U_8464))
            & hBOOL(hAPP(hAPP(c_member(U_8472),U_8464),U_8474)) ) )
    & ! [U_8477,U_8475,U_8473,U_8471] :
        ( ( ! [U_8463] :
              ( hBOOL(hAPP(U_8477,U_8463))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8471),U_8463),U_8475)) )
          & ! [U_8462] :
              ( hBOOL(hAPP(U_8477,U_8462))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8471),U_8462),U_8473)) ) )
        | ? [U_8461] :
            ( ~ hBOOL(hAPP(U_8477,U_8461))
            & hBOOL(hAPP(hAPP(c_member(U_8471),U_8461),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8471,tc_HOL_Obool)),U_8473),U_8475))) ) ) ),
    inference(miniscope,[status(thm)],[f_2370_2]) ).

fof(f_2370_4,plain,
    ( ! [U_8478,U_8476,U_8474,U_8472] :
        ( ! [U_8466] :
            ( hBOOL(hAPP(U_8478,U_8466))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8472),U_8466),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8472,tc_HOL_Obool)),U_8474),U_8476))) )
        | ? [U_8465] :
            ( ~ hBOOL(hAPP(U_8478,U_8465))
            & hBOOL(hAPP(hAPP(c_member(U_8472),U_8465),U_8476)) )
        | ? [U_8464] :
            ( ~ hBOOL(hAPP(U_8478,U_8464))
            & hBOOL(hAPP(hAPP(c_member(U_8472),U_8464),U_8474)) ) )
    & ! [U_8477,U_8475,U_8473,U_8471] :
        ( ( ! [U_8463] :
              ( hBOOL(hAPP(U_8477,U_8463))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8471),U_8463),U_8475)) )
          & ! [U_8462] :
              ( hBOOL(hAPP(U_8477,U_8462))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8471),U_8462),U_8473)) ) )
        | ( ~ hBOOL(hAPP(U_8477,sK133(U_8477,U_8475,U_8473,U_8471)))
          & hBOOL(hAPP(hAPP(c_member(U_8471),sK133(U_8477,U_8475,U_8473,U_8471)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8471,tc_HOL_Obool)),U_8473),U_8475))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK133]),skolemize(U_8461,sK133(U_8477,U_8475,U_8473,U_8471))],[f_2370_3]) ).

fof(f_2370_5,plain,
    ( ! [U_8478,U_8476,U_8474,U_8472] :
        ( ! [U_8466] :
            ( hBOOL(hAPP(U_8478,U_8466))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8472),U_8466),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8472,tc_HOL_Obool)),U_8474),U_8476))) )
        | ? [U_8465] :
            ( ~ hBOOL(hAPP(U_8478,U_8465))
            & hBOOL(hAPP(hAPP(c_member(U_8472),U_8465),U_8476)) )
        | ( ~ hBOOL(hAPP(U_8478,sK134(U_8478,U_8476,U_8474,U_8472)))
          & hBOOL(hAPP(hAPP(c_member(U_8472),sK134(U_8478,U_8476,U_8474,U_8472)),U_8474)) ) )
    & ! [U_8477,U_8475,U_8473,U_8471] :
        ( ( ! [U_8463] :
              ( hBOOL(hAPP(U_8477,U_8463))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8471),U_8463),U_8475)) )
          & ! [U_8462] :
              ( hBOOL(hAPP(U_8477,U_8462))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8471),U_8462),U_8473)) ) )
        | ( ~ hBOOL(hAPP(U_8477,sK133(U_8477,U_8475,U_8473,U_8471)))
          & hBOOL(hAPP(hAPP(c_member(U_8471),sK133(U_8477,U_8475,U_8473,U_8471)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8471,tc_HOL_Obool)),U_8473),U_8475))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK134]),skolemize(U_8464,sK134(U_8478,U_8476,U_8474,U_8472))],[f_2370_4]) ).

fof(f_2370_6,plain,
    ( ! [U_8478,U_8476,U_8474,U_8472] :
        ( ! [U_8466] :
            ( hBOOL(hAPP(U_8478,U_8466))
            | ~ hBOOL(hAPP(hAPP(c_member(U_8472),U_8466),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8472,tc_HOL_Obool)),U_8474),U_8476))) )
        | ( ~ hBOOL(hAPP(U_8478,sK135(U_8478,U_8476,U_8474,U_8472)))
          & hBOOL(hAPP(hAPP(c_member(U_8472),sK135(U_8478,U_8476,U_8474,U_8472)),U_8476)) )
        | ( ~ hBOOL(hAPP(U_8478,sK134(U_8478,U_8476,U_8474,U_8472)))
          & hBOOL(hAPP(hAPP(c_member(U_8472),sK134(U_8478,U_8476,U_8474,U_8472)),U_8474)) ) )
    & ! [U_8477,U_8475,U_8473,U_8471] :
        ( ( ! [U_8463] :
              ( hBOOL(hAPP(U_8477,U_8463))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8471),U_8463),U_8475)) )
          & ! [U_8462] :
              ( hBOOL(hAPP(U_8477,U_8462))
              | ~ hBOOL(hAPP(hAPP(c_member(U_8471),U_8462),U_8473)) ) )
        | ( ~ hBOOL(hAPP(U_8477,sK133(U_8477,U_8475,U_8473,U_8471)))
          & hBOOL(hAPP(hAPP(c_member(U_8471),sK133(U_8477,U_8475,U_8473,U_8471)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8471,tc_HOL_Obool)),U_8473),U_8475))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK135]),skolemize(U_8465,sK135(U_8478,U_8476,U_8474,U_8472))],[f_2370_5]) ).

fof(f_2370_7,plain,
    ( ! [U_8474,U_8472,U_8478,U_8476] :
        ( ~ hBOOL(hAPP(U_8478,sK135(U_8478,U_8476,U_8474,U_8472)))
        | ~ sP711(U_8474,U_8472,U_8478,U_8476) )
    & ! [U_8474,U_8472,U_8478,U_8476] :
        ( hBOOL(hAPP(hAPP(c_member(U_8472),sK135(U_8478,U_8476,U_8474,U_8472)),U_8476))
        | ~ sP711(U_8474,U_8472,U_8478,U_8476) )
    & ! [U_8474,U_8472,U_8478,U_8476] :
        ( ~ hBOOL(hAPP(U_8478,sK134(U_8478,U_8476,U_8474,U_8472)))
        | ~ sP710(U_8474,U_8472,U_8478,U_8476) )
    & ! [U_8474,U_8472,U_8478,U_8476] :
        ( hBOOL(hAPP(hAPP(c_member(U_8472),sK134(U_8478,U_8476,U_8474,U_8472)),U_8474))
        | ~ sP710(U_8474,U_8472,U_8478,U_8476) )
    & ! [U_8475,U_8471,U_8477,U_8462,U_8463,U_8473] :
        ( hBOOL(hAPP(U_8477,U_8463))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8471),U_8463),U_8475))
        | ~ sP709(U_8475,U_8471,U_8477,U_8462,U_8463,U_8473) )
    & ! [U_8475,U_8471,U_8477,U_8462,U_8463,U_8473] :
        ( hBOOL(hAPP(U_8477,U_8462))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8471),U_8462),U_8473))
        | ~ sP709(U_8475,U_8471,U_8477,U_8462,U_8463,U_8473) )
    & ! [U_8475,U_8471,U_8477,U_8473] :
        ( ~ hBOOL(hAPP(U_8477,sK133(U_8477,U_8475,U_8473,U_8471)))
        | ~ sP708(U_8475,U_8471,U_8477,U_8473) )
    & ! [U_8475,U_8471,U_8477,U_8473] :
        ( hBOOL(hAPP(hAPP(c_member(U_8471),sK133(U_8477,U_8475,U_8473,U_8471)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8471,tc_HOL_Obool)),U_8473),U_8475)))
        | ~ sP708(U_8475,U_8471,U_8477,U_8473) )
    & ! [U_8466,U_8474,U_8472,U_8478,U_8476] :
        ( hBOOL(hAPP(U_8478,U_8466))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8472),U_8466),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8472,tc_HOL_Obool)),U_8474),U_8476)))
        | sP711(U_8474,U_8472,U_8478,U_8476)
        | sP710(U_8474,U_8472,U_8478,U_8476) )
    & ! [U_8475,U_8471,U_8477,U_8462,U_8463,U_8473] :
        ( sP709(U_8475,U_8471,U_8477,U_8462,U_8463,U_8473)
        | sP708(U_8475,U_8471,U_8477,U_8473) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP708,sP709,sP710,sP711])],[f_2370_6]) ).

cnf(f_2370_8,plain,
    ( sP709(U_8475,U_8471,U_8477,U_8462,U_8463,U_8473)
    | sP708(U_8475,U_8471,U_8477,U_8473) ),
    inference(clausify,[status(thm)],[f_2370_7]) ).

cnf(f_2370_9,plain,
    ( hBOOL(hAPP(U_8478,U_8466))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8472),U_8466),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8472,tc_HOL_Obool)),U_8474),U_8476)))
    | sP711(U_8474,U_8472,U_8478,U_8476)
    | sP710(U_8474,U_8472,U_8478,U_8476) ),
    inference(clausify,[status(thm)],[f_2370_7]) ).

cnf(f_2370_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8471),sK133(U_8477,U_8475,U_8473,U_8471)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8471,tc_HOL_Obool)),U_8473),U_8475)))
    | ~ sP708(U_8475,U_8471,U_8477,U_8473) ),
    inference(clausify,[status(thm)],[f_2370_7]) ).

cnf(f_2370_11,plain,
    ( ~ hBOOL(hAPP(U_8477,sK133(U_8477,U_8475,U_8473,U_8471)))
    | ~ sP708(U_8475,U_8471,U_8477,U_8473) ),
    inference(clausify,[status(thm)],[f_2370_7]) ).

cnf(f_2370_12,plain,
    ( hBOOL(hAPP(U_8477,U_8462))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8471),U_8462),U_8473))
    | ~ sP709(U_8475,U_8471,U_8477,U_8462,U_8463,U_8473) ),
    inference(clausify,[status(thm)],[f_2370_7]) ).

cnf(f_2370_13,plain,
    ( hBOOL(hAPP(U_8477,U_8463))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8471),U_8463),U_8475))
    | ~ sP709(U_8475,U_8471,U_8477,U_8462,U_8463,U_8473) ),
    inference(clausify,[status(thm)],[f_2370_7]) ).

cnf(f_2370_14,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8472),sK134(U_8478,U_8476,U_8474,U_8472)),U_8474))
    | ~ sP710(U_8474,U_8472,U_8478,U_8476) ),
    inference(clausify,[status(thm)],[f_2370_7]) ).

cnf(f_2370_15,plain,
    ( ~ hBOOL(hAPP(U_8478,sK134(U_8478,U_8476,U_8474,U_8472)))
    | ~ sP710(U_8474,U_8472,U_8478,U_8476) ),
    inference(clausify,[status(thm)],[f_2370_7]) ).

cnf(f_2370_16,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8472),sK135(U_8478,U_8476,U_8474,U_8472)),U_8476))
    | ~ sP711(U_8474,U_8472,U_8478,U_8476) ),
    inference(clausify,[status(thm)],[f_2370_7]) ).

cnf(f_2370_17,plain,
    ( ~ hBOOL(hAPP(U_8478,sK135(U_8478,U_8476,U_8474,U_8472)))
    | ~ sP711(U_8474,U_8472,U_8478,U_8476) ),
    inference(clausify,[status(thm)],[f_2370_7]) ).

fof(f_2371_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_2371_2,plain,
    ! [U_8482,U_8481,U_8480,U_8479] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8481,tc_HOL_Obool)),U_8479),U_8482),U_8480))
      | ~ hBOOL(hAPP(U_8479,U_8480)) ),
    inference(variable_rename,[status(thm)],[f_2371_1]) ).

fof(f_2371_3,plain,
    ! [U_8480,U_8479,U_8482,U_8481] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8481,tc_HOL_Obool)),U_8479),U_8482),U_8480))
      | ~ hBOOL(hAPP(U_8479,U_8480)) ),
    inference(definitional_conversion,[status(esa)],[f_2371_2]) ).

cnf(f_2371_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8481,tc_HOL_Obool)),U_8479),U_8482),U_8480))
    | ~ hBOOL(hAPP(U_8479,U_8480)) ),
    inference(clausify,[status(thm)],[f_2371_3]) ).

fof(f_2372_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_2372_2,plain,
    ! [U_8486,U_8485,U_8484,U_8483] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8485,tc_HOL_Obool)),U_8486),U_8483),U_8484))
      | ~ hBOOL(hAPP(U_8483,U_8484)) ),
    inference(variable_rename,[status(thm)],[f_2372_1]) ).

fof(f_2372_3,plain,
    ! [U_8483,U_8484,U_8486,U_8485] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8485,tc_HOL_Obool)),U_8486),U_8483),U_8484))
      | ~ hBOOL(hAPP(U_8483,U_8484)) ),
    inference(definitional_conversion,[status(esa)],[f_2372_2]) ).

cnf(f_2372_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8485,tc_HOL_Obool)),U_8486),U_8483),U_8484))
    | ~ hBOOL(hAPP(U_8483,U_8484)) ),
    inference(clausify,[status(thm)],[f_2372_3]) ).

fof(f_2373_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_2373_2,plain,
    ! [U_8488,U_8487] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8487),U_8488),U_8488) = U_8488
      | ~ class_Lattices_Olattice(U_8487) ),
    inference(variable_rename,[status(thm)],[f_2373_1]) ).

fof(f_2373_3,plain,
    ! [U_8488,U_8487] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8487),U_8488),U_8488) = U_8488
      | ~ class_Lattices_Olattice(U_8487) ),
    inference(definitional_conversion,[status(esa)],[f_2373_2]) ).

cnf(f_2373_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8487),U_8488),U_8488) = U_8488
    | ~ class_Lattices_Olattice(U_8487) ),
    inference(clausify,[status(thm)],[f_2373_3]) ).

fof(f_2374_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_2374_2,plain,
    ! [U_8493,U_8492,U_8491,U_8490,U_8489] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8489,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8489,tc_HOL_Obool)),U_8490),U_8492)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8489,tc_HOL_Obool)),U_8491),U_8493)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8489,tc_HOL_Obool)),U_8492),U_8493))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8489,tc_HOL_Obool)),U_8490),U_8491)) ),
    inference(variable_rename,[status(thm)],[f_2374_1]) ).

fof(f_2374_3,plain,
    ! [U_8489,U_8490,U_8491,U_8492,U_8493] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8489,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8489,tc_HOL_Obool)),U_8490),U_8492)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8489,tc_HOL_Obool)),U_8491),U_8493)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8489,tc_HOL_Obool)),U_8492),U_8493))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8489,tc_HOL_Obool)),U_8490),U_8491)) ),
    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_8489,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8489,tc_HOL_Obool)),U_8490),U_8492)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8489,tc_HOL_Obool)),U_8491),U_8493)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8489,tc_HOL_Obool)),U_8492),U_8493))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8489,tc_HOL_Obool)),U_8490),U_8491)) ),
    inference(clausify,[status(thm)],[f_2374_3]) ).

fof(f_2375_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_2375_2,plain,
    ! [U_8497,U_8496,U_8495,U_8494] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8494,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8494,tc_HOL_Obool)),U_8495),U_8497)),U_8496))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8494,tc_HOL_Obool)),U_8497),U_8496))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8494,tc_HOL_Obool)),U_8495),U_8496)) ),
    inference(variable_rename,[status(thm)],[f_2375_1]) ).

fof(f_2375_3,plain,
    ! [U_8494,U_8495,U_8496,U_8497] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8494,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8494,tc_HOL_Obool)),U_8495),U_8497)),U_8496))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8494,tc_HOL_Obool)),U_8497),U_8496))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8494,tc_HOL_Obool)),U_8495),U_8496)) ),
    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_8494,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8494,tc_HOL_Obool)),U_8495),U_8497)),U_8496))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8494,tc_HOL_Obool)),U_8497),U_8496))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8494,tc_HOL_Obool)),U_8495),U_8496)) ),
    inference(clausify,[status(thm)],[f_2375_3]) ).

fof(f_2376_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_2376_2,plain,
    ! [U_8500,U_8499,U_8498] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8498,tc_HOL_Obool)),U_8500),U_8499) = 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_2376_1]) ).

fof(f_2376_3,plain,
    ! [U_8498,U_8499,U_8500] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8498,tc_HOL_Obool)),U_8500),U_8499) = 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_2376_2]) ).

cnf(f_2376_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8498,tc_HOL_Obool)),U_8500),U_8499) = 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_2376_3]) ).

fof(f_2377_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_2377_2,plain,
    ! [U_8503,U_8502,U_8501] :
      ( 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_2377_1]) ).

fof(f_2377_3,plain,
    ! [U_8501,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
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8501,tc_HOL_Obool)),U_8502),U_8503)) ),
    inference(definitional_conversion,[status(esa)],[f_2377_2]) ).

cnf(f_2377_4,plain,
    ( 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(clausify,[status(thm)],[f_2377_3]) ).

fof(f_2378_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_2378_2,plain,
    ! [U_8506,U_8505,U_8504] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8504,tc_HOL_Obool)),U_8505),U_8506))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8504,tc_HOL_Obool)),U_8505),U_8506) != U_8506 )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8504,tc_HOL_Obool)),U_8505),U_8506) = U_8506
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8504,tc_HOL_Obool)),U_8505),U_8506)) ) ),
    inference(variable_rename,[status(thm)],[f_2378_1]) ).

fof(f_2378_3,plain,
    ( ! [U_8512,U_8510,U_8508] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8508,tc_HOL_Obool)),U_8510),U_8512))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8508,tc_HOL_Obool)),U_8510),U_8512) != U_8512 )
    & ! [U_8511,U_8509,U_8507] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8507,tc_HOL_Obool)),U_8509),U_8511) = U_8511
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8507,tc_HOL_Obool)),U_8509),U_8511)) ) ),
    inference(miniscope,[status(thm)],[f_2378_2]) ).

fof(f_2378_4,plain,
    ( ! [U_8510,U_8508,U_8512] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8508,tc_HOL_Obool)),U_8510),U_8512))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8508,tc_HOL_Obool)),U_8510),U_8512) != U_8512 )
    & ! [U_8509,U_8511,U_8507] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8507,tc_HOL_Obool)),U_8509),U_8511) = U_8511
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8507,tc_HOL_Obool)),U_8509),U_8511)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2378_3]) ).

cnf(f_2378_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8507,tc_HOL_Obool)),U_8509),U_8511) = U_8511
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8507,tc_HOL_Obool)),U_8509),U_8511)) ),
    inference(clausify,[status(thm)],[f_2378_4]) ).

cnf(f_2378_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8508,tc_HOL_Obool)),U_8510),U_8512))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8508,tc_HOL_Obool)),U_8510),U_8512) != U_8512 ),
    inference(clausify,[status(thm)],[f_2378_4]) ).

fof(f_2379_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_2379_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_8515),U_8514))),
    inference(variable_rename,[status(thm)],[f_2379_1]) ).

fof(f_2379_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_8515),U_8514))),
    inference(definitional_conversion,[status(esa)],[f_2379_2]) ).

cnf(f_2379_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_8515),U_8514))),
    inference(clausify,[status(thm)],[f_2379_3]) ).

fof(f_2380_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_2380_2,plain,
    ! [U_8518,U_8517,U_8516] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8516,tc_HOL_Obool)),U_8517),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8516,tc_HOL_Obool)),U_8517),U_8518))),
    inference(variable_rename,[status(thm)],[f_2380_1]) ).

fof(f_2380_3,plain,
    ! [U_8516,U_8517,U_8518] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8516,tc_HOL_Obool)),U_8517),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8516,tc_HOL_Obool)),U_8517),U_8518))),
    inference(definitional_conversion,[status(esa)],[f_2380_2]) ).

cnf(f_2380_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8516,tc_HOL_Obool)),U_8517),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8516,tc_HOL_Obool)),U_8517),U_8518))),
    inference(clausify,[status(thm)],[f_2380_3]) ).

fof(f_2381_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_2381_2,plain,
    ! [U_8521,U_8520,U_8519] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8519),U_8520),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8519),U_8520),U_8521)))
      | ~ class_Lattices_Olattice(U_8519) ),
    inference(variable_rename,[status(thm)],[f_2381_1]) ).

fof(f_2381_3,plain,
    ! [U_8519,U_8520,U_8521] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8519),U_8520),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8519),U_8520),U_8521)))
      | ~ class_Lattices_Olattice(U_8519) ),
    inference(definitional_conversion,[status(esa)],[f_2381_2]) ).

cnf(f_2381_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8519),U_8520),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8519),U_8520),U_8521)))
    | ~ class_Lattices_Olattice(U_8519) ),
    inference(clausify,[status(thm)],[f_2381_3]) ).

fof(f_2382_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_2382_2,plain,
    ! [U_8524,U_8523,U_8522] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8522),U_8523),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8522),U_8523),U_8524)))
      | ~ class_Lattices_Osemilattice__sup(U_8522) ),
    inference(variable_rename,[status(thm)],[f_2382_1]) ).

fof(f_2382_3,plain,
    ! [U_8522,U_8523,U_8524] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8522),U_8523),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8522),U_8523),U_8524)))
      | ~ class_Lattices_Osemilattice__sup(U_8522) ),
    inference(definitional_conversion,[status(esa)],[f_2382_2]) ).

cnf(f_2382_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8522),U_8523),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8522),U_8523),U_8524)))
    | ~ class_Lattices_Osemilattice__sup(U_8522) ),
    inference(clausify,[status(thm)],[f_2382_3]) ).

fof(f_2383_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_2383_2,plain,
    ! [U_8527,U_8526,U_8525] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8525),U_8526),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8525),U_8527),U_8526)))
      | ~ class_Lattices_Olattice(U_8525) ),
    inference(variable_rename,[status(thm)],[f_2383_1]) ).

fof(f_2383_3,plain,
    ! [U_8525,U_8526,U_8527] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8525),U_8526),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8525),U_8527),U_8526)))
      | ~ class_Lattices_Olattice(U_8525) ),
    inference(definitional_conversion,[status(esa)],[f_2383_2]) ).

cnf(f_2383_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8525),U_8526),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8525),U_8527),U_8526)))
    | ~ class_Lattices_Olattice(U_8525) ),
    inference(clausify,[status(thm)],[f_2383_3]) ).

fof(f_2384_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_2384_2,plain,
    ! [U_8530,U_8529,U_8528] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8528),U_8529),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8528),U_8530),U_8529)))
      | ~ class_Lattices_Osemilattice__sup(U_8528) ),
    inference(variable_rename,[status(thm)],[f_2384_1]) ).

fof(f_2384_3,plain,
    ! [U_8528,U_8529,U_8530] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8528),U_8529),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8528),U_8530),U_8529)))
      | ~ class_Lattices_Osemilattice__sup(U_8528) ),
    inference(definitional_conversion,[status(esa)],[f_2384_2]) ).

cnf(f_2384_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8528),U_8529),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8528),U_8530),U_8529)))
    | ~ class_Lattices_Osemilattice__sup(U_8528) ),
    inference(clausify,[status(thm)],[f_2384_3]) ).

fof(f_2385_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_2385_2,plain,
    ! [U_8533,U_8532,U_8531] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8531),U_8532),U_8533))
          | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8531),U_8532),U_8533) != U_8533 )
        & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8531),U_8532),U_8533) = U_8533
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8531),U_8532),U_8533)) ) )
      | ~ class_Lattices_Osemilattice__sup(U_8531) ),
    inference(variable_rename,[status(thm)],[f_2385_1]) ).

fof(f_2385_3,plain,
    ( ! [U_8531,U_8532,U_8533] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8531),U_8532),U_8533))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8531),U_8532),U_8533) != U_8533
        | ~ sP712(U_8531,U_8532,U_8533) )
    & ! [U_8531,U_8532,U_8533] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8531),U_8532),U_8533) = U_8533
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8531),U_8532),U_8533))
        | ~ sP712(U_8531,U_8532,U_8533) )
    & ! [U_8531,U_8532,U_8533] :
        ( sP712(U_8531,U_8532,U_8533)
        | ~ class_Lattices_Osemilattice__sup(U_8531) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP712])],[f_2385_2]) ).

cnf(f_2385_4,plain,
    ( sP712(U_8531,U_8532,U_8533)
    | ~ class_Lattices_Osemilattice__sup(U_8531) ),
    inference(clausify,[status(thm)],[f_2385_3]) ).

cnf(f_2385_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8531),U_8532),U_8533) = U_8533
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8531),U_8532),U_8533))
    | ~ sP712(U_8531,U_8532,U_8533) ),
    inference(clausify,[status(thm)],[f_2385_3]) ).

cnf(f_2385_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8531),U_8532),U_8533))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8531),U_8532),U_8533) != U_8533
    | ~ sP712(U_8531,U_8532,U_8533) ),
    inference(clausify,[status(thm)],[f_2385_3]) ).

fof(f_2386_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_2386_2,plain,
    ! [U_8537,U_8536,U_8535,U_8534] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8534),U_8535),U_8536)),U_8537))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),U_8536),U_8537))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),U_8535),U_8537)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),U_8536),U_8537))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),U_8535),U_8537)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8534),U_8535),U_8536)),U_8537)) ) )
      | ~ class_Lattices_Osemilattice__sup(U_8534) ),
    inference(variable_rename,[status(thm)],[f_2386_1]) ).

fof(f_2386_3,plain,
    ( ! [U_8534,U_8535,U_8536,U_8537] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),U_8536),U_8537))
        | ~ sP713(U_8534,U_8535,U_8536,U_8537) )
    & ! [U_8534,U_8535,U_8536,U_8537] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),U_8535),U_8537))
        | ~ sP713(U_8534,U_8535,U_8536,U_8537) )
    & ! [U_8534,U_8535,U_8536,U_8537] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8534),U_8535),U_8536)),U_8537))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),U_8536),U_8537))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),U_8535),U_8537))
        | ~ sP714(U_8534,U_8535,U_8536,U_8537) )
    & ! [U_8534,U_8535,U_8536,U_8537] :
        ( sP713(U_8534,U_8535,U_8536,U_8537)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8534),U_8535),U_8536)),U_8537))
        | ~ sP714(U_8534,U_8535,U_8536,U_8537) )
    & ! [U_8534,U_8535,U_8536,U_8537] :
        ( sP714(U_8534,U_8535,U_8536,U_8537)
        | ~ class_Lattices_Osemilattice__sup(U_8534) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP713,sP714])],[f_2386_2]) ).

cnf(f_2386_4,plain,
    ( sP714(U_8534,U_8535,U_8536,U_8537)
    | ~ class_Lattices_Osemilattice__sup(U_8534) ),
    inference(clausify,[status(thm)],[f_2386_3]) ).

cnf(f_2386_5,plain,
    ( sP713(U_8534,U_8535,U_8536,U_8537)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8534),U_8535),U_8536)),U_8537))
    | ~ sP714(U_8534,U_8535,U_8536,U_8537) ),
    inference(clausify,[status(thm)],[f_2386_3]) ).

cnf(f_2386_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8534),U_8535),U_8536)),U_8537))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),U_8536),U_8537))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),U_8535),U_8537))
    | ~ sP714(U_8534,U_8535,U_8536,U_8537) ),
    inference(clausify,[status(thm)],[f_2386_3]) ).

cnf(f_2386_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),U_8535),U_8537))
    | ~ sP713(U_8534,U_8535,U_8536,U_8537) ),
    inference(clausify,[status(thm)],[f_2386_3]) ).

cnf(f_2386_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8534),U_8536),U_8537))
    | ~ sP713(U_8534,U_8535,U_8536,U_8537) ),
    inference(clausify,[status(thm)],[f_2386_3]) ).

fof(f_2387_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_2387_2,plain,
    ! [U_8541,U_8540,U_8539,U_8538] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8538),U_8539),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8538),U_8540),U_8541)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8538),U_8539),U_8540))
      | ~ class_Lattices_Osemilattice__sup(U_8538) ),
    inference(variable_rename,[status(thm)],[f_2387_1]) ).

fof(f_2387_3,plain,
    ! [U_8540,U_8541,U_8539,U_8538] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8538),U_8539),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8538),U_8540),U_8541)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8538),U_8539),U_8540))
      | ~ class_Lattices_Osemilattice__sup(U_8538) ),
    inference(definitional_conversion,[status(esa)],[f_2387_2]) ).

cnf(f_2387_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8538),U_8539),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8538),U_8540),U_8541)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8538),U_8539),U_8540))
    | ~ class_Lattices_Osemilattice__sup(U_8538) ),
    inference(clausify,[status(thm)],[f_2387_3]) ).

fof(f_2388_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_2388_2,plain,
    ! [U_8545,U_8544,U_8543,U_8542] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8542),U_8543),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8542),U_8545),U_8544)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8542),U_8543),U_8544))
      | ~ class_Lattices_Osemilattice__sup(U_8542) ),
    inference(variable_rename,[status(thm)],[f_2388_1]) ).

fof(f_2388_3,plain,
    ! [U_8543,U_8542,U_8544,U_8545] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8542),U_8543),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8542),U_8545),U_8544)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8542),U_8543),U_8544))
      | ~ class_Lattices_Osemilattice__sup(U_8542) ),
    inference(definitional_conversion,[status(esa)],[f_2388_2]) ).

cnf(f_2388_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8542),U_8543),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8542),U_8545),U_8544)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8542),U_8543),U_8544))
    | ~ class_Lattices_Osemilattice__sup(U_8542) ),
    inference(clausify,[status(thm)],[f_2388_3]) ).

fof(f_2389_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_2389_2,plain,
    ! [U_8548,U_8547,U_8546] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8546),U_8547),U_8548) = U_8548
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8546),U_8547),U_8548))
      | ~ class_Lattices_Osemilattice__sup(U_8546) ),
    inference(variable_rename,[status(thm)],[f_2389_1]) ).

fof(f_2389_3,plain,
    ! [U_8546,U_8547,U_8548] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8546),U_8547),U_8548) = U_8548
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8546),U_8547),U_8548))
      | ~ class_Lattices_Osemilattice__sup(U_8546) ),
    inference(definitional_conversion,[status(esa)],[f_2389_2]) ).

cnf(f_2389_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8546),U_8547),U_8548) = U_8548
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8546),U_8547),U_8548))
    | ~ class_Lattices_Osemilattice__sup(U_8546) ),
    inference(clausify,[status(thm)],[f_2389_3]) ).

fof(f_2390_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_2390_2,plain,
    ! [U_8551,U_8550,U_8549] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8549),U_8551),U_8550) = U_8551
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8549),U_8550),U_8551))
      | ~ class_Lattices_Osemilattice__sup(U_8549) ),
    inference(variable_rename,[status(thm)],[f_2390_1]) ).

fof(f_2390_3,plain,
    ! [U_8549,U_8550,U_8551] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8549),U_8551),U_8550) = U_8551
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8549),U_8550),U_8551))
      | ~ class_Lattices_Osemilattice__sup(U_8549) ),
    inference(definitional_conversion,[status(esa)],[f_2390_2]) ).

cnf(f_2390_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8549),U_8551),U_8550) = U_8551
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8549),U_8550),U_8551))
    | ~ class_Lattices_Osemilattice__sup(U_8549) ),
    inference(clausify,[status(thm)],[f_2390_3]) ).

fof(f_2391_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_2391_2,plain,
    ! [U_8555,U_8554,U_8553,U_8552] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8552),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8552),U_8553),U_8555)),U_8554))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8552),U_8555),U_8554))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8552),U_8553),U_8554))
      | ~ class_Lattices_Osemilattice__sup(U_8552) ),
    inference(variable_rename,[status(thm)],[f_2391_1]) ).

fof(f_2391_3,plain,
    ! [U_8552,U_8553,U_8554,U_8555] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8552),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8552),U_8553),U_8555)),U_8554))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8552),U_8555),U_8554))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8552),U_8553),U_8554))
      | ~ class_Lattices_Osemilattice__sup(U_8552) ),
    inference(definitional_conversion,[status(esa)],[f_2391_2]) ).

cnf(f_2391_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8552),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8552),U_8553),U_8555)),U_8554))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8552),U_8555),U_8554))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8552),U_8553),U_8554))
    | ~ class_Lattices_Osemilattice__sup(U_8552) ),
    inference(clausify,[status(thm)],[f_2391_3]) ).

fof(f_2392_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_2392_2,plain,
    ! [U_8559,U_8558,U_8557,U_8556] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8556),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8556),U_8557),U_8559)),U_8558))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8556),U_8559),U_8558))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8556),U_8557),U_8558))
      | ~ class_Lattices_Osemilattice__sup(U_8556) ),
    inference(variable_rename,[status(thm)],[f_2392_1]) ).

fof(f_2392_3,plain,
    ! [U_8556,U_8557,U_8558,U_8559] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8556),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8556),U_8557),U_8559)),U_8558))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8556),U_8559),U_8558))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8556),U_8557),U_8558))
      | ~ class_Lattices_Osemilattice__sup(U_8556) ),
    inference(definitional_conversion,[status(esa)],[f_2392_2]) ).

cnf(f_2392_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8556),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8556),U_8557),U_8559)),U_8558))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8556),U_8559),U_8558))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8556),U_8557),U_8558))
    | ~ class_Lattices_Osemilattice__sup(U_8556) ),
    inference(clausify,[status(thm)],[f_2392_3]) ).

fof(f_2393_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_2393_2,plain,
    ! [U_8564,U_8563,U_8562,U_8561,U_8560] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8560),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8560),U_8561),U_8563)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8560),U_8562),U_8564)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8560),U_8563),U_8564))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8560),U_8561),U_8562))
      | ~ class_Lattices_Osemilattice__sup(U_8560) ),
    inference(variable_rename,[status(thm)],[f_2393_1]) ).

fof(f_2393_3,plain,
    ! [U_8560,U_8561,U_8562,U_8563,U_8564] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8560),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8560),U_8561),U_8563)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8560),U_8562),U_8564)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8560),U_8563),U_8564))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8560),U_8561),U_8562))
      | ~ class_Lattices_Osemilattice__sup(U_8560) ),
    inference(definitional_conversion,[status(esa)],[f_2393_2]) ).

cnf(f_2393_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8560),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8560),U_8561),U_8563)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8560),U_8562),U_8564)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8560),U_8563),U_8564))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8560),U_8561),U_8562))
    | ~ class_Lattices_Osemilattice__sup(U_8560) ),
    inference(clausify,[status(thm)],[f_2393_3]) ).

fof(f_2394_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_2394_2,plain,
    ! [U_8568,U_8567,U_8566,U_8565] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8565),U_8567),U_8568))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8565),U_8566),U_8568)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8565),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8565),U_8566),U_8567)),U_8568))
      | ~ class_Lattices_Osemilattice__sup(U_8565) ),
    inference(variable_rename,[status(thm)],[f_2394_1]) ).

fof(f_2394_3,plain,
    ( ! [U_8565,U_8566,U_8567,U_8568] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8565),U_8567),U_8568))
        | ~ sP715(U_8565,U_8566,U_8567,U_8568) )
    & ! [U_8565,U_8566,U_8567,U_8568] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8565),U_8566),U_8568))
        | ~ sP715(U_8565,U_8566,U_8567,U_8568) )
    & ! [U_8565,U_8566,U_8567,U_8568] :
        ( sP715(U_8565,U_8566,U_8567,U_8568)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8565),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8565),U_8566),U_8567)),U_8568))
        | ~ class_Lattices_Osemilattice__sup(U_8565) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP715])],[f_2394_2]) ).

cnf(f_2394_4,plain,
    ( sP715(U_8565,U_8566,U_8567,U_8568)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8565),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8565),U_8566),U_8567)),U_8568))
    | ~ class_Lattices_Osemilattice__sup(U_8565) ),
    inference(clausify,[status(thm)],[f_2394_3]) ).

cnf(f_2394_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8565),U_8566),U_8568))
    | ~ sP715(U_8565,U_8566,U_8567,U_8568) ),
    inference(clausify,[status(thm)],[f_2394_3]) ).

cnf(f_2394_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_8565),U_8567),U_8568))
    | ~ sP715(U_8565,U_8566,U_8567,U_8568) ),
    inference(clausify,[status(thm)],[f_2394_3]) ).

fof(f_2395_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_2395_2,plain,
    ! [U_8572,U_8571,U_8570,U_8569] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8569),U_8570),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8569),U_8571),U_8572)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8569),U_8570),U_8571))
      | ~ class_Lattices_Osemilattice__sup(U_8569) ),
    inference(variable_rename,[status(thm)],[f_2395_1]) ).

fof(f_2395_3,plain,
    ! [U_8572,U_8571,U_8569,U_8570] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8569),U_8570),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8569),U_8571),U_8572)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8569),U_8570),U_8571))
      | ~ class_Lattices_Osemilattice__sup(U_8569) ),
    inference(definitional_conversion,[status(esa)],[f_2395_2]) ).

cnf(f_2395_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8569),U_8570),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8569),U_8571),U_8572)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8569),U_8570),U_8571))
    | ~ class_Lattices_Osemilattice__sup(U_8569) ),
    inference(clausify,[status(thm)],[f_2395_3]) ).

fof(f_2396_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_2396_2,plain,
    ! [U_8576,U_8575,U_8574,U_8573] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8573),U_8574),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8573),U_8576),U_8575)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8573),U_8574),U_8575))
      | ~ class_Lattices_Osemilattice__sup(U_8573) ),
    inference(variable_rename,[status(thm)],[f_2396_1]) ).

fof(f_2396_3,plain,
    ! [U_8573,U_8574,U_8575,U_8576] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8573),U_8574),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8573),U_8576),U_8575)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8573),U_8574),U_8575))
      | ~ class_Lattices_Osemilattice__sup(U_8573) ),
    inference(definitional_conversion,[status(esa)],[f_2396_2]) ).

cnf(f_2396_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8573),U_8574),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_8573),U_8576),U_8575)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_8573),U_8574),U_8575))
    | ~ class_Lattices_Osemilattice__sup(U_8573) ),
    inference(clausify,[status(thm)],[f_2396_3]) ).

fof(f_2397_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_2397_2,plain,
    ! [U_8581,U_8580,U_8579,U_8578,U_8577] : hAPP(c_Set_Oimage(U_8577,U_8578,U_8579),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8577,tc_HOL_Obool)),U_8580),U_8581)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8578,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8577,U_8578,U_8579),U_8580)),hAPP(c_Set_Oimage(U_8577,U_8578,U_8579),U_8581)),
    inference(variable_rename,[status(thm)],[f_2397_1]) ).

fof(f_2397_3,plain,
    ! [U_8577,U_8578,U_8579,U_8580,U_8581] : hAPP(c_Set_Oimage(U_8577,U_8578,U_8579),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8577,tc_HOL_Obool)),U_8580),U_8581)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8578,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8577,U_8578,U_8579),U_8580)),hAPP(c_Set_Oimage(U_8577,U_8578,U_8579),U_8581)),
    inference(definitional_conversion,[status(esa)],[f_2397_2]) ).

cnf(f_2397_4,plain,
    hAPP(c_Set_Oimage(U_8577,U_8578,U_8579),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8577,tc_HOL_Obool)),U_8580),U_8581)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8578,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_8577,U_8578,U_8579),U_8580)),hAPP(c_Set_Oimage(U_8577,U_8578,U_8579),U_8581)),
    inference(clausify,[status(thm)],[f_2397_3]) ).

fof(f_2398_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_2398_2,plain,
    ! [U_8585,U_8584,U_8583,U_8582] :
      ( hBOOL(hAPP(hAPP(c_member(U_8582),U_8583),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8582,tc_HOL_Obool)),U_8585),U_8584)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8582),U_8583),U_8584)) ),
    inference(variable_rename,[status(thm)],[f_2398_1]) ).

fof(f_2398_3,plain,
    ! [U_8582,U_8583,U_8584,U_8585] :
      ( hBOOL(hAPP(hAPP(c_member(U_8582),U_8583),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8582,tc_HOL_Obool)),U_8585),U_8584)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8582),U_8583),U_8584)) ),
    inference(definitional_conversion,[status(esa)],[f_2398_2]) ).

cnf(f_2398_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8582),U_8583),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8582,tc_HOL_Obool)),U_8585),U_8584)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8582),U_8583),U_8584)) ),
    inference(clausify,[status(thm)],[f_2398_3]) ).

fof(f_2399_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_2399_2,plain,
    ! [U_8589,U_8588,U_8587,U_8586] :
      ( hBOOL(hAPP(hAPP(c_member(U_8586),U_8587),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8586,tc_HOL_Obool)),U_8588),U_8589)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8586),U_8587),U_8588)) ),
    inference(variable_rename,[status(thm)],[f_2399_1]) ).

fof(f_2399_3,plain,
    ! [U_8586,U_8587,U_8588,U_8589] :
      ( hBOOL(hAPP(hAPP(c_member(U_8586),U_8587),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8586,tc_HOL_Obool)),U_8588),U_8589)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8586),U_8587),U_8588)) ),
    inference(definitional_conversion,[status(esa)],[f_2399_2]) ).

cnf(f_2399_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8586),U_8587),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8586,tc_HOL_Obool)),U_8588),U_8589)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8586),U_8587),U_8588)) ),
    inference(clausify,[status(thm)],[f_2399_3]) ).

fof(f_2400_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_2400_2,plain,
    ! [U_8593,U_8592,U_8591,U_8590] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_8590),U_8591),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8590,tc_HOL_Obool)),U_8592),U_8593)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_8590),U_8591),U_8593))
          & ~ hBOOL(hAPP(hAPP(c_member(U_8590),U_8591),U_8592)) ) )
      & ( hBOOL(hAPP(hAPP(c_member(U_8590),U_8591),U_8593))
        | hBOOL(hAPP(hAPP(c_member(U_8590),U_8591),U_8592))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8590),U_8591),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8590,tc_HOL_Obool)),U_8592),U_8593))) ) ),
    inference(variable_rename,[status(thm)],[f_2400_1]) ).

fof(f_2400_3,plain,
    ( ! [U_8601,U_8599,U_8597,U_8595] :
        ( hBOOL(hAPP(hAPP(c_member(U_8595),U_8597),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8595,tc_HOL_Obool)),U_8599),U_8601)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_8595),U_8597),U_8601))
          & ~ hBOOL(hAPP(hAPP(c_member(U_8595),U_8597),U_8599)) ) )
    & ! [U_8600,U_8598,U_8596,U_8594] :
        ( hBOOL(hAPP(hAPP(c_member(U_8594),U_8596),U_8600))
        | hBOOL(hAPP(hAPP(c_member(U_8594),U_8596),U_8598))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8594),U_8596),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8594,tc_HOL_Obool)),U_8598),U_8600))) ) ),
    inference(miniscope,[status(thm)],[f_2400_2]) ).

fof(f_2400_4,plain,
    ( ! [U_8599,U_8595,U_8597,U_8601] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8595),U_8597),U_8601))
        | ~ sP716(U_8599,U_8595,U_8597,U_8601) )
    & ! [U_8599,U_8595,U_8597,U_8601] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8595),U_8597),U_8599))
        | ~ sP716(U_8599,U_8595,U_8597,U_8601) )
    & ! [U_8599,U_8595,U_8597,U_8601] :
        ( hBOOL(hAPP(hAPP(c_member(U_8595),U_8597),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8595,tc_HOL_Obool)),U_8599),U_8601)))
        | sP716(U_8599,U_8595,U_8597,U_8601) )
    & ! [U_8596,U_8598,U_8600,U_8594] :
        ( hBOOL(hAPP(hAPP(c_member(U_8594),U_8596),U_8600))
        | hBOOL(hAPP(hAPP(c_member(U_8594),U_8596),U_8598))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8594),U_8596),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8594,tc_HOL_Obool)),U_8598),U_8600))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP716])],[f_2400_3]) ).

cnf(f_2400_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8594),U_8596),U_8600))
    | hBOOL(hAPP(hAPP(c_member(U_8594),U_8596),U_8598))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8594),U_8596),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8594,tc_HOL_Obool)),U_8598),U_8600))) ),
    inference(clausify,[status(thm)],[f_2400_4]) ).

cnf(f_2400_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8595),U_8597),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8595,tc_HOL_Obool)),U_8599),U_8601)))
    | sP716(U_8599,U_8595,U_8597,U_8601) ),
    inference(clausify,[status(thm)],[f_2400_4]) ).

cnf(f_2400_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8595),U_8597),U_8599))
    | ~ sP716(U_8599,U_8595,U_8597,U_8601) ),
    inference(clausify,[status(thm)],[f_2400_4]) ).

cnf(f_2400_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8595),U_8597),U_8601))
    | ~ sP716(U_8599,U_8595,U_8597,U_8601) ),
    inference(clausify,[status(thm)],[f_2400_4]) ).

fof(f_2401_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_2401_2,plain,
    ! [U_8605,U_8604,U_8603,U_8602] : hAPP(c_Relation_ORange(U_8602,U_8603),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8602,U_8603),tc_HOL_Obool)),U_8604),U_8605)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8603,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_8602,U_8603),U_8604)),hAPP(c_Relation_ORange(U_8602,U_8603),U_8605)),
    inference(variable_rename,[status(thm)],[f_2401_1]) ).

fof(f_2401_3,plain,
    ! [U_8602,U_8603,U_8604,U_8605] : hAPP(c_Relation_ORange(U_8602,U_8603),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8602,U_8603),tc_HOL_Obool)),U_8604),U_8605)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8603,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_8602,U_8603),U_8604)),hAPP(c_Relation_ORange(U_8602,U_8603),U_8605)),
    inference(definitional_conversion,[status(esa)],[f_2401_2]) ).

cnf(f_2401_4,plain,
    hAPP(c_Relation_ORange(U_8602,U_8603),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8602,U_8603),tc_HOL_Obool)),U_8604),U_8605)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8603,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_8602,U_8603),U_8604)),hAPP(c_Relation_ORange(U_8602,U_8603),U_8605)),
    inference(clausify,[status(thm)],[f_2401_3]) ).

fof(f_2402_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_2402_2,plain,
    ! [U_8609,U_8608,U_8607,U_8606] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8606,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8606,tc_fun(U_8606,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8606)),U_8607)),hAPP(hAPP(c_COMBC(U_8606,tc_fun(U_8606,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8606)),U_8608)),U_8609))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8606),U_8609),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8606,tc_HOL_Obool)),U_8607),U_8608))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_8606),U_8609),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8606,tc_HOL_Obool)),U_8607),U_8608)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8606,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8606,tc_fun(U_8606,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8606)),U_8607)),hAPP(hAPP(c_COMBC(U_8606,tc_fun(U_8606,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8606)),U_8608)),U_8609)) ) ),
    inference(variable_rename,[status(thm)],[f_2402_1]) ).

fof(f_2402_3,plain,
    ( ! [U_8617,U_8615,U_8613,U_8611] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8611,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8611,tc_fun(U_8611,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8611)),U_8613)),hAPP(hAPP(c_COMBC(U_8611,tc_fun(U_8611,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8611)),U_8615)),U_8617))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8611),U_8617),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8611,tc_HOL_Obool)),U_8613),U_8615))) )
    & ! [U_8616,U_8614,U_8612,U_8610] :
        ( hBOOL(hAPP(hAPP(c_member(U_8610),U_8616),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8610,tc_HOL_Obool)),U_8612),U_8614)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8610,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8610,tc_fun(U_8610,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8610)),U_8612)),hAPP(hAPP(c_COMBC(U_8610,tc_fun(U_8610,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8610)),U_8614)),U_8616)) ) ),
    inference(miniscope,[status(thm)],[f_2402_2]) ).

fof(f_2402_4,plain,
    ( ! [U_8611,U_8613,U_8615,U_8617] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8611,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8611,tc_fun(U_8611,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8611)),U_8613)),hAPP(hAPP(c_COMBC(U_8611,tc_fun(U_8611,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8611)),U_8615)),U_8617))
        | ~ hBOOL(hAPP(hAPP(c_member(U_8611),U_8617),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8611,tc_HOL_Obool)),U_8613),U_8615))) )
    & ! [U_8612,U_8614,U_8616,U_8610] :
        ( hBOOL(hAPP(hAPP(c_member(U_8610),U_8616),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8610,tc_HOL_Obool)),U_8612),U_8614)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8610,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8610,tc_fun(U_8610,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8610)),U_8612)),hAPP(hAPP(c_COMBC(U_8610,tc_fun(U_8610,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8610)),U_8614)),U_8616)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2402_3]) ).

cnf(f_2402_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8610),U_8616),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8610,tc_HOL_Obool)),U_8612),U_8614)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8610,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8610,tc_fun(U_8610,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8610)),U_8612)),hAPP(hAPP(c_COMBC(U_8610,tc_fun(U_8610,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8610)),U_8614)),U_8616)) ),
    inference(clausify,[status(thm)],[f_2402_4]) ).

cnf(f_2402_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8611,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_8611,tc_fun(U_8611,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8611)),U_8613)),hAPP(hAPP(c_COMBC(U_8611,tc_fun(U_8611,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8611)),U_8615)),U_8617))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8611),U_8617),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8611,tc_HOL_Obool)),U_8613),U_8615))) ),
    inference(clausify,[status(thm)],[f_2402_4]) ).

fof(f_2403_1,plain,
    ! [V_Qa_2,V_Pa_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_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)),
    inference(fof_nnf,[status(thm)],[fact_Collect__disj__eq]) ).

fof(f_2403_2,plain,
    ! [U_8620,U_8619,U_8618] : hAPP(c_Set_OCollect(U_8618),hAPP(hAPP(c_COMBS(U_8618,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8618),c_fdisj),U_8619)),U_8620)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8618,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8618),U_8619)),hAPP(c_Set_OCollect(U_8618),U_8620)),
    inference(variable_rename,[status(thm)],[f_2403_1]) ).

fof(f_2403_3,plain,
    ! [U_8619,U_8618,U_8620] : hAPP(c_Set_OCollect(U_8618),hAPP(hAPP(c_COMBS(U_8618,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8618),c_fdisj),U_8619)),U_8620)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8618,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8618),U_8619)),hAPP(c_Set_OCollect(U_8618),U_8620)),
    inference(definitional_conversion,[status(esa)],[f_2403_2]) ).

cnf(f_2403_4,plain,
    hAPP(c_Set_OCollect(U_8618),hAPP(hAPP(c_COMBS(U_8618,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8618),c_fdisj),U_8619)),U_8620)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8618,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8618),U_8619)),hAPP(c_Set_OCollect(U_8618),U_8620)),
    inference(clausify,[status(thm)],[f_2403_3]) ).

fof(f_2404_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_2404_2,plain,
    ! [U_8622,U_8621] :
      ( c_Wellfounded_Oacyclic(U_8621,U_8622)
      | ~ c_Wellfounded_Owf(U_8621,U_8622) ),
    inference(variable_rename,[status(thm)],[f_2404_1]) ).

fof(f_2404_3,plain,
    ! [U_8621,U_8622] :
      ( c_Wellfounded_Oacyclic(U_8621,U_8622)
      | ~ c_Wellfounded_Owf(U_8621,U_8622) ),
    inference(definitional_conversion,[status(esa)],[f_2404_2]) ).

cnf(f_2404_4,plain,
    ( c_Wellfounded_Oacyclic(U_8621,U_8622)
    | ~ c_Wellfounded_Owf(U_8621,U_8622) ),
    inference(clausify,[status(thm)],[f_2404_3]) ).

fof(f_2405_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_2405_2,plain,
    ! [U_8625,U_8624,U_8623] :
      ( c_Wellfounded_Oacyclic(U_8623,U_8625)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8623,U_8623),tc_HOL_Obool)),U_8625),U_8624))
      | ~ c_Wellfounded_Oacyclic(U_8623,U_8624) ),
    inference(variable_rename,[status(thm)],[f_2405_1]) ).

fof(f_2405_3,plain,
    ! [U_8623,U_8624,U_8625] :
      ( c_Wellfounded_Oacyclic(U_8623,U_8625)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8623,U_8623),tc_HOL_Obool)),U_8625),U_8624))
      | ~ c_Wellfounded_Oacyclic(U_8623,U_8624) ),
    inference(definitional_conversion,[status(esa)],[f_2405_2]) ).

cnf(f_2405_4,plain,
    ( c_Wellfounded_Oacyclic(U_8623,U_8625)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8623,U_8623),tc_HOL_Obool)),U_8625),U_8624))
    | ~ c_Wellfounded_Oacyclic(U_8623,U_8624) ),
    inference(clausify,[status(thm)],[f_2405_3]) ).

fof(f_2406_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_2406_2,plain,
    ! [U_8627,U_8626] :
      ( ( c_Wellfounded_Oacyclic(U_8626,hAPP(c_Relation_Oconverse(U_8626,U_8626),U_8627))
        | ~ c_Wellfounded_Oacyclic(U_8626,U_8627) )
      & ( c_Wellfounded_Oacyclic(U_8626,U_8627)
        | ~ c_Wellfounded_Oacyclic(U_8626,hAPP(c_Relation_Oconverse(U_8626,U_8626),U_8627)) ) ),
    inference(variable_rename,[status(thm)],[f_2406_1]) ).

fof(f_2406_3,plain,
    ( ! [U_8631,U_8629] :
        ( c_Wellfounded_Oacyclic(U_8629,hAPP(c_Relation_Oconverse(U_8629,U_8629),U_8631))
        | ~ c_Wellfounded_Oacyclic(U_8629,U_8631) )
    & ! [U_8630,U_8628] :
        ( c_Wellfounded_Oacyclic(U_8628,U_8630)
        | ~ c_Wellfounded_Oacyclic(U_8628,hAPP(c_Relation_Oconverse(U_8628,U_8628),U_8630)) ) ),
    inference(miniscope,[status(thm)],[f_2406_2]) ).

fof(f_2406_4,plain,
    ( ! [U_8631,U_8629] :
        ( c_Wellfounded_Oacyclic(U_8629,hAPP(c_Relation_Oconverse(U_8629,U_8629),U_8631))
        | ~ c_Wellfounded_Oacyclic(U_8629,U_8631) )
    & ! [U_8630,U_8628] :
        ( c_Wellfounded_Oacyclic(U_8628,U_8630)
        | ~ c_Wellfounded_Oacyclic(U_8628,hAPP(c_Relation_Oconverse(U_8628,U_8628),U_8630)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2406_3]) ).

cnf(f_2406_5,plain,
    ( c_Wellfounded_Oacyclic(U_8628,U_8630)
    | ~ c_Wellfounded_Oacyclic(U_8628,hAPP(c_Relation_Oconverse(U_8628,U_8628),U_8630)) ),
    inference(clausify,[status(thm)],[f_2406_4]) ).

cnf(f_2406_6,plain,
    ( c_Wellfounded_Oacyclic(U_8629,hAPP(c_Relation_Oconverse(U_8629,U_8629),U_8631))
    | ~ c_Wellfounded_Oacyclic(U_8629,U_8631) ),
    inference(clausify,[status(thm)],[f_2406_4]) ).

fof(f_2407_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_2407_2,plain,
    ! [U_8635,U_8634,U_8633,U_8632] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8632,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8632,tc_HOL_Obool)),U_8633),U_8634)),U_8635))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8632,tc_HOL_Obool)),U_8633),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8632,tc_HOL_Obool)),U_8634),U_8635))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8632,tc_HOL_Obool)),U_8633),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8632,tc_HOL_Obool)),U_8634),U_8635)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8632,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8632,tc_HOL_Obool)),U_8633),U_8634)),U_8635)) ) ),
    inference(variable_rename,[status(thm)],[f_2407_1]) ).

fof(f_2407_3,plain,
    ( ! [U_8643,U_8641,U_8639,U_8637] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8637,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8637,tc_HOL_Obool)),U_8639),U_8641)),U_8643))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8637,tc_HOL_Obool)),U_8639),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8637,tc_HOL_Obool)),U_8641),U_8643))) )
    & ! [U_8642,U_8640,U_8638,U_8636] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8636,tc_HOL_Obool)),U_8638),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8636,tc_HOL_Obool)),U_8640),U_8642)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8636,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8636,tc_HOL_Obool)),U_8638),U_8640)),U_8642)) ) ),
    inference(miniscope,[status(thm)],[f_2407_2]) ).

fof(f_2407_4,plain,
    ( ! [U_8639,U_8637,U_8641,U_8643] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8637,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8637,tc_HOL_Obool)),U_8639),U_8641)),U_8643))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8637,tc_HOL_Obool)),U_8639),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8637,tc_HOL_Obool)),U_8641),U_8643))) )
    & ! [U_8640,U_8638,U_8642,U_8636] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8636,tc_HOL_Obool)),U_8638),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8636,tc_HOL_Obool)),U_8640),U_8642)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8636,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8636,tc_HOL_Obool)),U_8638),U_8640)),U_8642)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2407_3]) ).

cnf(f_2407_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8636,tc_HOL_Obool)),U_8638),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8636,tc_HOL_Obool)),U_8640),U_8642)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8636,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8636,tc_HOL_Obool)),U_8638),U_8640)),U_8642)) ),
    inference(clausify,[status(thm)],[f_2407_4]) ).

cnf(f_2407_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8637,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8637,tc_HOL_Obool)),U_8639),U_8641)),U_8643))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8637,tc_HOL_Obool)),U_8639),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8637,tc_HOL_Obool)),U_8641),U_8643))) ),
    inference(clausify,[status(thm)],[f_2407_4]) ).

fof(f_2408_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_2408_2,plain,
    ! [U_8646,U_8645,U_8644] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8644,tc_HOL_Obool)),U_8645),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8644,tc_HOL_Obool)),U_8646),U_8645)) = U_8646
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8644,tc_HOL_Obool)),U_8645),U_8646)) ),
    inference(variable_rename,[status(thm)],[f_2408_1]) ).

fof(f_2408_3,plain,
    ! [U_8644,U_8645,U_8646] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8644,tc_HOL_Obool)),U_8645),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8644,tc_HOL_Obool)),U_8646),U_8645)) = U_8646
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8644,tc_HOL_Obool)),U_8645),U_8646)) ),
    inference(definitional_conversion,[status(esa)],[f_2408_2]) ).

cnf(f_2408_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8644,tc_HOL_Obool)),U_8645),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8644,tc_HOL_Obool)),U_8646),U_8645)) = U_8646
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8644,tc_HOL_Obool)),U_8645),U_8646)) ),
    inference(clausify,[status(thm)],[f_2408_3]) ).

fof(f_2409_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_2409_2,plain,
    ! [U_8649,U_8648,U_8647] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8647,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8647,tc_HOL_Obool)),U_8648),U_8649)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8647,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8647,tc_HOL_Obool)),U_8648)),U_8649),
    inference(variable_rename,[status(thm)],[f_2409_1]) ).

fof(f_2409_3,plain,
    ! [U_8647,U_8648,U_8649] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8647,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8647,tc_HOL_Obool)),U_8648),U_8649)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8647,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8647,tc_HOL_Obool)),U_8648)),U_8649),
    inference(definitional_conversion,[status(esa)],[f_2409_2]) ).

cnf(f_2409_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8647,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_8647,tc_HOL_Obool)),U_8648),U_8649)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8647,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8647,tc_HOL_Obool)),U_8648)),U_8649),
    inference(clausify,[status(thm)],[f_2409_3]) ).

fof(f_2410_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_2410_2,plain,
    ! [U_8652,U_8651,U_8650] :
      ( ( c_Wellfounded_Owf(U_8650,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8650,U_8650),tc_HOL_Obool)),U_8651),U_8652))
        | ~ c_Wellfounded_Owf(U_8650,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8650,U_8650),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8650,U_8650),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8650,U_8650,U_8650),U_8651),U_8651)),hAPP(hAPP(c_Relation_Orel__comp(U_8650,U_8650,U_8650),U_8652),U_8651))),U_8652)) )
      & ( c_Wellfounded_Owf(U_8650,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8650,U_8650),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8650,U_8650),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8650,U_8650,U_8650),U_8651),U_8651)),hAPP(hAPP(c_Relation_Orel__comp(U_8650,U_8650,U_8650),U_8652),U_8651))),U_8652))
        | ~ c_Wellfounded_Owf(U_8650,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8650,U_8650),tc_HOL_Obool)),U_8651),U_8652)) ) ),
    inference(variable_rename,[status(thm)],[f_2410_1]) ).

fof(f_2410_3,plain,
    ( ! [U_8658,U_8656,U_8654] :
        ( c_Wellfounded_Owf(U_8654,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8654,U_8654),tc_HOL_Obool)),U_8656),U_8658))
        | ~ c_Wellfounded_Owf(U_8654,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8654,U_8654),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8654,U_8654),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8654,U_8654,U_8654),U_8656),U_8656)),hAPP(hAPP(c_Relation_Orel__comp(U_8654,U_8654,U_8654),U_8658),U_8656))),U_8658)) )
    & ! [U_8657,U_8655,U_8653] :
        ( c_Wellfounded_Owf(U_8653,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8653,U_8653),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8653,U_8653),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8653,U_8653,U_8653),U_8655),U_8655)),hAPP(hAPP(c_Relation_Orel__comp(U_8653,U_8653,U_8653),U_8657),U_8655))),U_8657))
        | ~ c_Wellfounded_Owf(U_8653,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8653,U_8653),tc_HOL_Obool)),U_8655),U_8657)) ) ),
    inference(miniscope,[status(thm)],[f_2410_2]) ).

fof(f_2410_4,plain,
    ( ! [U_8654,U_8656,U_8658] :
        ( c_Wellfounded_Owf(U_8654,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8654,U_8654),tc_HOL_Obool)),U_8656),U_8658))
        | ~ c_Wellfounded_Owf(U_8654,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8654,U_8654),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8654,U_8654),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8654,U_8654,U_8654),U_8656),U_8656)),hAPP(hAPP(c_Relation_Orel__comp(U_8654,U_8654,U_8654),U_8658),U_8656))),U_8658)) )
    & ! [U_8655,U_8653,U_8657] :
        ( c_Wellfounded_Owf(U_8653,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8653,U_8653),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8653,U_8653),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8653,U_8653,U_8653),U_8655),U_8655)),hAPP(hAPP(c_Relation_Orel__comp(U_8653,U_8653,U_8653),U_8657),U_8655))),U_8657))
        | ~ c_Wellfounded_Owf(U_8653,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8653,U_8653),tc_HOL_Obool)),U_8655),U_8657)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2410_3]) ).

cnf(f_2410_5,plain,
    ( c_Wellfounded_Owf(U_8653,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8653,U_8653),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8653,U_8653),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8653,U_8653,U_8653),U_8655),U_8655)),hAPP(hAPP(c_Relation_Orel__comp(U_8653,U_8653,U_8653),U_8657),U_8655))),U_8657))
    | ~ c_Wellfounded_Owf(U_8653,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8653,U_8653),tc_HOL_Obool)),U_8655),U_8657)) ),
    inference(clausify,[status(thm)],[f_2410_4]) ).

cnf(f_2410_6,plain,
    ( c_Wellfounded_Owf(U_8654,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8654,U_8654),tc_HOL_Obool)),U_8656),U_8658))
    | ~ c_Wellfounded_Owf(U_8654,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8654,U_8654),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8654,U_8654),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8654,U_8654,U_8654),U_8656),U_8656)),hAPP(hAPP(c_Relation_Orel__comp(U_8654,U_8654,U_8654),U_8658),U_8656))),U_8658)) ),
    inference(clausify,[status(thm)],[f_2410_4]) ).

fof(f_2411_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_2411_2,plain,
    ! [U_8661,U_8660,U_8659] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8659,tc_HOL_Obool)),U_8660),U_8661) = hAPP(c_Set_OCollect(U_8659),hAPP(hAPP(c_COMBS(U_8659,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8659),c_fdisj),hAPP(hAPP(c_COMBC(U_8659,tc_fun(U_8659,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8659)),U_8660))),hAPP(hAPP(c_COMBC(U_8659,tc_fun(U_8659,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8659)),U_8661))),
    inference(variable_rename,[status(thm)],[f_2411_1]) ).

fof(f_2411_3,plain,
    ! [U_8659,U_8660,U_8661] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8659,tc_HOL_Obool)),U_8660),U_8661) = hAPP(c_Set_OCollect(U_8659),hAPP(hAPP(c_COMBS(U_8659,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8659),c_fdisj),hAPP(hAPP(c_COMBC(U_8659,tc_fun(U_8659,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8659)),U_8660))),hAPP(hAPP(c_COMBC(U_8659,tc_fun(U_8659,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8659)),U_8661))),
    inference(definitional_conversion,[status(esa)],[f_2411_2]) ).

cnf(f_2411_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8659,tc_HOL_Obool)),U_8660),U_8661) = hAPP(c_Set_OCollect(U_8659),hAPP(hAPP(c_COMBS(U_8659,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8659),c_fdisj),hAPP(hAPP(c_COMBC(U_8659,tc_fun(U_8659,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8659)),U_8660))),hAPP(hAPP(c_COMBC(U_8659,tc_fun(U_8659,tc_HOL_Obool),tc_HOL_Obool),c_member(U_8659)),U_8661))),
    inference(clausify,[status(thm)],[f_2411_3]) ).

fof(f_2412_1,plain,
    ! [V_Qa_2,V_Pa_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_Pa_2)),V_Qa_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_Pa_2))),hAPP(c_Set_OCollect(T_b),V_Qa_2)),
    inference(fof_nnf,[status(thm)],[fact_Collect__imp__eq]) ).

fof(f_2412_2,plain,
    ! [U_8664,U_8663,U_8662] : hAPP(c_Set_OCollect(U_8662),hAPP(hAPP(c_COMBS(U_8662,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8662),c_fimplies),U_8663)),U_8664)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8662,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8662,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8662),U_8663))),hAPP(c_Set_OCollect(U_8662),U_8664)),
    inference(variable_rename,[status(thm)],[f_2412_1]) ).

fof(f_2412_3,plain,
    ! [U_8662,U_8663,U_8664] : hAPP(c_Set_OCollect(U_8662),hAPP(hAPP(c_COMBS(U_8662,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8662),c_fimplies),U_8663)),U_8664)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8662,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8662,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8662),U_8663))),hAPP(c_Set_OCollect(U_8662),U_8664)),
    inference(definitional_conversion,[status(esa)],[f_2412_2]) ).

cnf(f_2412_4,plain,
    hAPP(c_Set_OCollect(U_8662),hAPP(hAPP(c_COMBS(U_8662,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8662),c_fimplies),U_8663)),U_8664)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8662,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_8662,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_8662),U_8663))),hAPP(c_Set_OCollect(U_8662),U_8664)),
    inference(clausify,[status(thm)],[f_2412_3]) ).

fof(f_2413_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_2413_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_2413_1]) ).

cnf(f_2413_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_2413_2]) ).

fof(f_2414_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_2414_2,plain,
    ! [U_8667,U_8666,U_8665] :
      ( c_Wellfounded_Owf(U_8665,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8665,U_8665),tc_HOL_Obool)),U_8666),U_8667))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8665,U_8665),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8665,U_8665,U_8665),U_8666),U_8667)),U_8666))
      | ~ c_Wellfounded_Owf(U_8665,U_8667)
      | ~ c_Wellfounded_Owf(U_8665,U_8666) ),
    inference(variable_rename,[status(thm)],[f_2414_1]) ).

fof(f_2414_3,plain,
    ! [U_8665,U_8666,U_8667] :
      ( c_Wellfounded_Owf(U_8665,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8665,U_8665),tc_HOL_Obool)),U_8666),U_8667))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8665,U_8665),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8665,U_8665,U_8665),U_8666),U_8667)),U_8666))
      | ~ c_Wellfounded_Owf(U_8665,U_8667)
      | ~ c_Wellfounded_Owf(U_8665,U_8666) ),
    inference(definitional_conversion,[status(esa)],[f_2414_2]) ).

cnf(f_2414_4,plain,
    ( c_Wellfounded_Owf(U_8665,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8665,U_8665),tc_HOL_Obool)),U_8666),U_8667))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8665,U_8665),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_8665,U_8665,U_8665),U_8666),U_8667)),U_8666))
    | ~ c_Wellfounded_Owf(U_8665,U_8667)
    | ~ c_Wellfounded_Owf(U_8665,U_8666) ),
    inference(clausify,[status(thm)],[f_2414_3]) ).

fof(f_2415_1,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(fof_nnf,[status(thm)],[fact_wf__pred__nat]) ).

fof(f_2415_2,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(definitional_conversion,[status(esa)],[f_2415_1]) ).

cnf(f_2415_3,plain,
    c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(clausify,[status(thm)],[f_2415_2]) ).

fof(f_2416_1,plain,
    ! [V_Pa_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_Pa_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_Pa_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_2416_2,plain,
    ! [U_8670,U_8669,U_8668] : c_Hilbert__Choice_OEps(tc_prod(U_8668,U_8669),hAPP(c_Product__Type_Oprod_Oprod__case(U_8668,U_8669,tc_HOL_Obool),U_8670)) = c_Hilbert__Choice_OEps(tc_prod(U_8668,U_8669),hAPP(hAPP(c_COMBS(tc_prod(U_8668,U_8669),U_8669,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_8668,tc_fun(U_8669,tc_HOL_Obool),tc_prod(U_8668,U_8669)),U_8670),c_Product__Type_Ofst(U_8668,U_8669))),c_Product__Type_Osnd(U_8668,U_8669))),
    inference(variable_rename,[status(thm)],[f_2416_1]) ).

fof(f_2416_3,plain,
    ! [U_8668,U_8669,U_8670] : c_Hilbert__Choice_OEps(tc_prod(U_8668,U_8669),hAPP(c_Product__Type_Oprod_Oprod__case(U_8668,U_8669,tc_HOL_Obool),U_8670)) = c_Hilbert__Choice_OEps(tc_prod(U_8668,U_8669),hAPP(hAPP(c_COMBS(tc_prod(U_8668,U_8669),U_8669,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_8668,tc_fun(U_8669,tc_HOL_Obool),tc_prod(U_8668,U_8669)),U_8670),c_Product__Type_Ofst(U_8668,U_8669))),c_Product__Type_Osnd(U_8668,U_8669))),
    inference(definitional_conversion,[status(esa)],[f_2416_2]) ).

cnf(f_2416_4,plain,
    c_Hilbert__Choice_OEps(tc_prod(U_8668,U_8669),hAPP(c_Product__Type_Oprod_Oprod__case(U_8668,U_8669,tc_HOL_Obool),U_8670)) = c_Hilbert__Choice_OEps(tc_prod(U_8668,U_8669),hAPP(hAPP(c_COMBS(tc_prod(U_8668,U_8669),U_8669,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_8668,tc_fun(U_8669,tc_HOL_Obool),tc_prod(U_8668,U_8669)),U_8670),c_Product__Type_Ofst(U_8668,U_8669))),c_Product__Type_Osnd(U_8668,U_8669))),
    inference(clausify,[status(thm)],[f_2416_3]) ).

fof(f_2417_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_2417_2,plain,
    ! [U_8672,U_8671] : hAPP(c_Relation_OField(U_8671),U_8672) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8671,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_8671,U_8671),U_8672)),hAPP(c_Relation_ORange(U_8671,U_8671),U_8672)),
    inference(variable_rename,[status(thm)],[f_2417_1]) ).

fof(f_2417_3,plain,
    ! [U_8671,U_8672] : hAPP(c_Relation_OField(U_8671),U_8672) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8671,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_8671,U_8671),U_8672)),hAPP(c_Relation_ORange(U_8671,U_8671),U_8672)),
    inference(definitional_conversion,[status(esa)],[f_2417_2]) ).

cnf(f_2417_4,plain,
    hAPP(c_Relation_OField(U_8671),U_8672) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8671,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_8671,U_8671),U_8672)),hAPP(c_Relation_ORange(U_8671,U_8671),U_8672)),
    inference(clausify,[status(thm)],[f_2417_3]) ).

fof(f_2418_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_2418_2,plain,
    ! [U_8676,U_8675,U_8674] :
      ( ? [U_8673] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8674,U_8674)),hAPP(hAPP(c_Product__Type_OPair(U_8674,U_8674),hAPP(U_8676,hAPP(c_Nat_OSuc,U_8673))),hAPP(U_8676,U_8673))),U_8675))
      | ~ c_Wellfounded_Owf(U_8674,U_8675) ),
    inference(variable_rename,[status(thm)],[f_2418_1]) ).

fof(f_2418_3,plain,
    ! [U_8676,U_8675,U_8674] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8674,U_8674)),hAPP(hAPP(c_Product__Type_OPair(U_8674,U_8674),hAPP(U_8676,hAPP(c_Nat_OSuc,sK136(U_8676,U_8675,U_8674)))),hAPP(U_8676,sK136(U_8676,U_8675,U_8674)))),U_8675))
      | ~ c_Wellfounded_Owf(U_8674,U_8675) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK136]),skolemize(U_8673,sK136(U_8676,U_8675,U_8674))],[f_2418_2]) ).

fof(f_2418_4,plain,
    ! [U_8674,U_8675,U_8676] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8674,U_8674)),hAPP(hAPP(c_Product__Type_OPair(U_8674,U_8674),hAPP(U_8676,hAPP(c_Nat_OSuc,sK136(U_8676,U_8675,U_8674)))),hAPP(U_8676,sK136(U_8676,U_8675,U_8674)))),U_8675))
      | ~ c_Wellfounded_Owf(U_8674,U_8675) ),
    inference(definitional_conversion,[status(esa)],[f_2418_3]) ).

cnf(f_2418_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8674,U_8674)),hAPP(hAPP(c_Product__Type_OPair(U_8674,U_8674),hAPP(U_8676,hAPP(c_Nat_OSuc,sK136(U_8676,U_8675,U_8674)))),hAPP(U_8676,sK136(U_8676,U_8675,U_8674)))),U_8675))
    | ~ c_Wellfounded_Owf(U_8674,U_8675) ),
    inference(clausify,[status(thm)],[f_2418_4]) ).

fof(f_2419_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_2419_2,plain,
    ! [U_8679,U_8678] :
      ( ? [U_8677] : U_8679 = hAPP(hAPP(c_Product__Type_OPair(U_8678,U_8678),U_8677),U_8677)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8678,U_8678)),U_8679),c_Relation_OId(U_8678))) ),
    inference(variable_rename,[status(thm)],[f_2419_1]) ).

fof(f_2419_3,plain,
    ! [U_8679,U_8678] :
      ( U_8679 = hAPP(hAPP(c_Product__Type_OPair(U_8678,U_8678),sK137(U_8679,U_8678)),sK137(U_8679,U_8678))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8678,U_8678)),U_8679),c_Relation_OId(U_8678))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK137]),skolemize(U_8677,sK137(U_8679,U_8678))],[f_2419_2]) ).

fof(f_2419_4,plain,
    ! [U_8678,U_8679] :
      ( U_8679 = hAPP(hAPP(c_Product__Type_OPair(U_8678,U_8678),sK137(U_8679,U_8678)),sK137(U_8679,U_8678))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8678,U_8678)),U_8679),c_Relation_OId(U_8678))) ),
    inference(definitional_conversion,[status(esa)],[f_2419_3]) ).

cnf(f_2419_5,plain,
    ( U_8679 = hAPP(hAPP(c_Product__Type_OPair(U_8678,U_8678),sK137(U_8679,U_8678)),sK137(U_8679,U_8678))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8678,U_8678)),U_8679),c_Relation_OId(U_8678))) ),
    inference(clausify,[status(thm)],[f_2419_4]) ).

fof(f_2420_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_2420_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_2420_1]) ).

cnf(f_2420_3,plain,
    c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2420_2]) ).

fof(f_2421_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_2421_2,plain,
    ! [U_8681,U_8680] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8680),U_8681))
      | ~ c_Nat__Transfer_Onat__set(U_8681)
      | ~ c_Nat__Transfer_Onat__set(U_8680) ),
    inference(variable_rename,[status(thm)],[f_2421_1]) ).

fof(f_2421_3,plain,
    ! [U_8680,U_8681] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8680),U_8681))
      | ~ c_Nat__Transfer_Onat__set(U_8681)
      | ~ c_Nat__Transfer_Onat__set(U_8680) ),
    inference(definitional_conversion,[status(esa)],[f_2421_2]) ).

cnf(f_2421_4,plain,
    ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8680),U_8681))
    | ~ c_Nat__Transfer_Onat__set(U_8681)
    | ~ c_Nat__Transfer_Onat__set(U_8680) ),
    inference(clausify,[status(thm)],[f_2421_3]) ).

fof(f_2422_1,plain,
    ! [T_b,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2)))
      | ! [B_x1] : ~ hBOOL(hAPP(V_Pa_2,B_x1)) ),
    inference(fof_nnf,[status(thm)],[fact_someI__ex]) ).

fof(f_2422_2,plain,
    ! [U_8684,U_8683] :
      ( hBOOL(hAPP(U_8683,c_Hilbert__Choice_OEps(U_8684,U_8683)))
      | ! [U_8682] : ~ hBOOL(hAPP(U_8683,U_8682)) ),
    inference(variable_rename,[status(thm)],[f_2422_1]) ).

fof(f_2422_3,plain,
    ! [U_8682,U_8683,U_8684] :
      ( hBOOL(hAPP(U_8683,c_Hilbert__Choice_OEps(U_8684,U_8683)))
      | ~ hBOOL(hAPP(U_8683,U_8682)) ),
    inference(definitional_conversion,[status(esa)],[f_2422_2]) ).

cnf(f_2422_4,plain,
    ( hBOOL(hAPP(U_8683,c_Hilbert__Choice_OEps(U_8684,U_8683)))
    | ~ hBOOL(hAPP(U_8683,U_8682)) ),
    inference(clausify,[status(thm)],[f_2422_3]) ).

fof(f_2423_1,plain,
    ! [T_b,V_Pa_2] :
      ( ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2)))
        | ! [B_x1] : ~ hBOOL(hAPP(V_Pa_2,B_x1)) )
      & ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
        | ~ hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_some__eq__ex]) ).

fof(f_2423_2,plain,
    ! [U_8688,U_8687] :
      ( ( hBOOL(hAPP(U_8687,c_Hilbert__Choice_OEps(U_8688,U_8687)))
        | ! [U_8686] : ~ hBOOL(hAPP(U_8687,U_8686)) )
      & ( ? [U_8685] : hBOOL(hAPP(U_8687,U_8685))
        | ~ hBOOL(hAPP(U_8687,c_Hilbert__Choice_OEps(U_8688,U_8687))) ) ),
    inference(variable_rename,[status(thm)],[f_2423_1]) ).

fof(f_2423_3,plain,
    ( ! [U_8692,U_8690] :
        ( hBOOL(hAPP(U_8690,c_Hilbert__Choice_OEps(U_8692,U_8690)))
        | ! [U_8686] : ~ hBOOL(hAPP(U_8690,U_8686)) )
    & ! [U_8691,U_8689] :
        ( ? [U_8685] : hBOOL(hAPP(U_8689,U_8685))
        | ~ hBOOL(hAPP(U_8689,c_Hilbert__Choice_OEps(U_8691,U_8689))) ) ),
    inference(miniscope,[status(thm)],[f_2423_2]) ).

fof(f_2423_4,plain,
    ( ! [U_8692,U_8690] :
        ( hBOOL(hAPP(U_8690,c_Hilbert__Choice_OEps(U_8692,U_8690)))
        | ! [U_8686] : ~ hBOOL(hAPP(U_8690,U_8686)) )
    & ! [U_8691,U_8689] :
        ( hBOOL(hAPP(U_8689,sK138(U_8691,U_8689)))
        | ~ hBOOL(hAPP(U_8689,c_Hilbert__Choice_OEps(U_8691,U_8689))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK138]),skolemize(U_8685,sK138(U_8691,U_8689))],[f_2423_3]) ).

fof(f_2423_5,plain,
    ( ! [U_8686,U_8690,U_8692] :
        ( hBOOL(hAPP(U_8690,c_Hilbert__Choice_OEps(U_8692,U_8690)))
        | ~ hBOOL(hAPP(U_8690,U_8686)) )
    & ! [U_8691,U_8689] :
        ( hBOOL(hAPP(U_8689,sK138(U_8691,U_8689)))
        | ~ hBOOL(hAPP(U_8689,c_Hilbert__Choice_OEps(U_8691,U_8689))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2423_4]) ).

cnf(f_2423_6,plain,
    ( hBOOL(hAPP(U_8689,sK138(U_8691,U_8689)))
    | ~ hBOOL(hAPP(U_8689,c_Hilbert__Choice_OEps(U_8691,U_8689))) ),
    inference(clausify,[status(thm)],[f_2423_5]) ).

cnf(f_2423_7,plain,
    ( hBOOL(hAPP(U_8690,c_Hilbert__Choice_OEps(U_8692,U_8690)))
    | ~ hBOOL(hAPP(U_8690,U_8686)) ),
    inference(clausify,[status(thm)],[f_2423_5]) ).

fof(f_2424_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_2424_2,plain,
    ! [U_8694,U_8693] : c_Hilbert__Choice_OEps(U_8693,hAPP(hAPP(c_COMBC(U_8693,U_8693,tc_HOL_Obool),c_fequal),U_8694)) = U_8694,
    inference(variable_rename,[status(thm)],[f_2424_1]) ).

fof(f_2424_3,plain,
    ! [U_8693,U_8694] : c_Hilbert__Choice_OEps(U_8693,hAPP(hAPP(c_COMBC(U_8693,U_8693,tc_HOL_Obool),c_fequal),U_8694)) = U_8694,
    inference(definitional_conversion,[status(esa)],[f_2424_2]) ).

cnf(f_2424_4,plain,
    c_Hilbert__Choice_OEps(U_8693,hAPP(hAPP(c_COMBC(U_8693,U_8693,tc_HOL_Obool),c_fequal),U_8694)) = U_8694,
    inference(clausify,[status(thm)],[f_2424_3]) ).

fof(f_2425_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_2425_2,plain,
    ! [U_8696,U_8695] : c_Hilbert__Choice_OEps(U_8695,hAPP(c_fequal,U_8696)) = U_8696,
    inference(variable_rename,[status(thm)],[f_2425_1]) ).

fof(f_2425_3,plain,
    ! [U_8695,U_8696] : c_Hilbert__Choice_OEps(U_8695,hAPP(c_fequal,U_8696)) = U_8696,
    inference(definitional_conversion,[status(esa)],[f_2425_2]) ).

cnf(f_2425_4,plain,
    c_Hilbert__Choice_OEps(U_8695,hAPP(c_fequal,U_8696)) = U_8696,
    inference(clausify,[status(thm)],[f_2425_3]) ).

fof(f_2426_1,plain,
    ! [T_b,V_x_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,c_Hilbert__Choice_OEps(T_b,V_Pa_2)))
      | ~ hBOOL(hAPP(V_Pa_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_someI]) ).

fof(f_2426_2,plain,
    ! [U_8699,U_8698,U_8697] :
      ( hBOOL(hAPP(U_8697,c_Hilbert__Choice_OEps(U_8699,U_8697)))
      | ~ hBOOL(hAPP(U_8697,U_8698)) ),
    inference(variable_rename,[status(thm)],[f_2426_1]) ).

fof(f_2426_3,plain,
    ! [U_8697,U_8698,U_8699] :
      ( hBOOL(hAPP(U_8697,c_Hilbert__Choice_OEps(U_8699,U_8697)))
      | ~ hBOOL(hAPP(U_8697,U_8698)) ),
    inference(definitional_conversion,[status(esa)],[f_2426_2]) ).

cnf(f_2426_4,plain,
    ( hBOOL(hAPP(U_8697,c_Hilbert__Choice_OEps(U_8699,U_8697)))
    | ~ hBOOL(hAPP(U_8697,U_8698)) ),
    inference(clausify,[status(thm)],[f_2426_3]) ).

fof(f_2427_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_2427_2,plain,
    ! [U_8702,U_8701] :
      ( hBOOL(hAPP(U_8701,c_Hilbert__Choice_OEps(U_8702,U_8701)))
      | ! [U_8700] : ~ hBOOL(hAPP(U_8701,U_8700)) ),
    inference(variable_rename,[status(thm)],[f_2427_1]) ).

fof(f_2427_3,plain,
    ! [U_8700,U_8701,U_8702] :
      ( hBOOL(hAPP(U_8701,c_Hilbert__Choice_OEps(U_8702,U_8701)))
      | ~ hBOOL(hAPP(U_8701,U_8700)) ),
    inference(definitional_conversion,[status(esa)],[f_2427_2]) ).

cnf(f_2427_4,plain,
    ( hBOOL(hAPP(U_8701,c_Hilbert__Choice_OEps(U_8702,U_8701)))
    | ~ hBOOL(hAPP(U_8701,U_8700)) ),
    inference(clausify,[status(thm)],[f_2427_3]) ).

fof(f_2428_1,plain,
    ! [T_b,V_c_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,V_c_2))
      | V_c_2 != c_Hilbert__Choice_OEps(T_b,V_Pa_2)
      | ! [B_x1] : ~ hBOOL(hAPP(V_Pa_2,B_x1)) ),
    inference(fof_nnf,[status(thm)],[fact_exE__some]) ).

fof(f_2428_2,plain,
    ! [U_8706,U_8705,U_8704] :
      ( hBOOL(hAPP(U_8704,U_8705))
      | U_8705 != c_Hilbert__Choice_OEps(U_8706,U_8704)
      | ! [U_8703] : ~ hBOOL(hAPP(U_8704,U_8703)) ),
    inference(variable_rename,[status(thm)],[f_2428_1]) ).

fof(f_2428_3,plain,
    ! [U_8703,U_8704,U_8705,U_8706] :
      ( hBOOL(hAPP(U_8704,U_8705))
      | U_8705 != c_Hilbert__Choice_OEps(U_8706,U_8704)
      | ~ hBOOL(hAPP(U_8704,U_8703)) ),
    inference(definitional_conversion,[status(esa)],[f_2428_2]) ).

cnf(f_2428_4,plain,
    ( hBOOL(hAPP(U_8704,U_8705))
    | U_8705 != c_Hilbert__Choice_OEps(U_8706,U_8704)
    | ~ hBOOL(hAPP(U_8704,U_8703)) ),
    inference(clausify,[status(thm)],[f_2428_3]) ).

fof(f_2429_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_2429_2,plain,
    ! [U_8708,U_8707] : hAPP(c_Relation_OField(U_8707),hAPP(c_Relation_Oconverse(U_8707,U_8707),U_8708)) = hAPP(c_Relation_OField(U_8707),U_8708),
    inference(variable_rename,[status(thm)],[f_2429_1]) ).

fof(f_2429_3,plain,
    ! [U_8707,U_8708] : hAPP(c_Relation_OField(U_8707),hAPP(c_Relation_Oconverse(U_8707,U_8707),U_8708)) = hAPP(c_Relation_OField(U_8707),U_8708),
    inference(definitional_conversion,[status(esa)],[f_2429_2]) ).

cnf(f_2429_4,plain,
    hAPP(c_Relation_OField(U_8707),hAPP(c_Relation_Oconverse(U_8707,U_8707),U_8708)) = hAPP(c_Relation_OField(U_8707),U_8708),
    inference(clausify,[status(thm)],[f_2429_3]) ).

fof(f_2430_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_2430_2,plain,
    ! [U_8710,U_8709] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8709),U_8710) = 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_8709)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8710))),
    inference(variable_rename,[status(thm)],[f_2430_1]) ).

fof(f_2430_3,plain,
    ! [U_8709,U_8710] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8709),U_8710) = 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_8709)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8710))),
    inference(definitional_conversion,[status(esa)],[f_2430_2]) ).

cnf(f_2430_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_8709),U_8710) = 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_8709)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_8710))),
    inference(clausify,[status(thm)],[f_2430_3]) ).

fof(f_2431_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_2431_2,plain,
    ! [U_8712,U_8711] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8711),U_8712) = 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_8711)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8712)))
      | ~ c_Nat__Transfer_Onat__set(U_8712)
      | ~ c_Nat__Transfer_Onat__set(U_8711) ),
    inference(variable_rename,[status(thm)],[f_2431_1]) ).

fof(f_2431_3,plain,
    ! [U_8711,U_8712] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8711),U_8712) = 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_8711)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8712)))
      | ~ c_Nat__Transfer_Onat__set(U_8712)
      | ~ c_Nat__Transfer_Onat__set(U_8711) ),
    inference(definitional_conversion,[status(esa)],[f_2431_2]) ).

cnf(f_2431_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_8711),U_8712) = 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_8711)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_8712)))
    | ~ c_Nat__Transfer_Onat__set(U_8712)
    | ~ c_Nat__Transfer_Onat__set(U_8711) ),
    inference(clausify,[status(thm)],[f_2431_3]) ).

fof(f_2432_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_2432_2,plain,
    ! [U_8718,U_8717,U_8716,U_8715,U_8714,U_8713] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8713,tc_fun(U_8714,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8713,tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_fun(U_8714,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8714,tc_fun(tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_fun(U_8714,tc_HOL_Obool)),U_8713),c_COMBC(U_8714,tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8714,tc_prod(U_8713,U_8714)),tc_fun(U_8714,tc_fun(tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_HOL_Obool)),U_8713),hAPP(c_COMBB(tc_prod(U_8713,U_8714),tc_fun(tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_HOL_Obool),U_8714),c_member(tc_prod(U_8713,U_8714)))),c_Product__Type_OPair(U_8713,U_8714)))),U_8715)),hAPP(hAPP(c_COMBC(U_8713,tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_fun(U_8714,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8714,tc_fun(tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_fun(U_8714,tc_HOL_Obool)),U_8713),c_COMBC(U_8714,tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8714,tc_prod(U_8713,U_8714)),tc_fun(U_8714,tc_fun(tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_HOL_Obool)),U_8713),hAPP(c_COMBB(tc_prod(U_8713,U_8714),tc_fun(tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_HOL_Obool),U_8714),c_member(tc_prod(U_8713,U_8714)))),c_Product__Type_OPair(U_8713,U_8714)))),U_8716)),U_8717),U_8718))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8713,U_8714)),hAPP(hAPP(c_Product__Type_OPair(U_8713,U_8714),U_8717),U_8718)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool)),U_8715),U_8716))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8713,U_8714)),hAPP(hAPP(c_Product__Type_OPair(U_8713,U_8714),U_8717),U_8718)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool)),U_8715),U_8716)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8713,tc_fun(U_8714,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8713,tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_fun(U_8714,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8714,tc_fun(tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_fun(U_8714,tc_HOL_Obool)),U_8713),c_COMBC(U_8714,tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8714,tc_prod(U_8713,U_8714)),tc_fun(U_8714,tc_fun(tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_HOL_Obool)),U_8713),hAPP(c_COMBB(tc_prod(U_8713,U_8714),tc_fun(tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_HOL_Obool),U_8714),c_member(tc_prod(U_8713,U_8714)))),c_Product__Type_OPair(U_8713,U_8714)))),U_8715)),hAPP(hAPP(c_COMBC(U_8713,tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_fun(U_8714,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8714,tc_fun(tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_fun(U_8714,tc_HOL_Obool)),U_8713),c_COMBC(U_8714,tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8714,tc_prod(U_8713,U_8714)),tc_fun(U_8714,tc_fun(tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_HOL_Obool)),U_8713),hAPP(c_COMBB(tc_prod(U_8713,U_8714),tc_fun(tc_fun(tc_prod(U_8713,U_8714),tc_HOL_Obool),tc_HOL_Obool),U_8714),c_member(tc_prod(U_8713,U_8714)))),c_Product__Type_OPair(U_8713,U_8714)))),U_8716)),U_8717),U_8718)) ) ),
    inference(variable_rename,[status(thm)],[f_2432_1]) ).

fof(f_2432_3,plain,
    ( ! [U_8730,U_8728,U_8726,U_8724,U_8722,U_8720] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8720,tc_fun(U_8722,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8720,tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_fun(U_8722,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8722,tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_fun(U_8722,tc_HOL_Obool)),U_8720),c_COMBC(U_8722,tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8722,tc_prod(U_8720,U_8722)),tc_fun(U_8722,tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool)),U_8720),hAPP(c_COMBB(tc_prod(U_8720,U_8722),tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool),U_8722),c_member(tc_prod(U_8720,U_8722)))),c_Product__Type_OPair(U_8720,U_8722)))),U_8724)),hAPP(hAPP(c_COMBC(U_8720,tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_fun(U_8722,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8722,tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_fun(U_8722,tc_HOL_Obool)),U_8720),c_COMBC(U_8722,tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8722,tc_prod(U_8720,U_8722)),tc_fun(U_8722,tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool)),U_8720),hAPP(c_COMBB(tc_prod(U_8720,U_8722),tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool),U_8722),c_member(tc_prod(U_8720,U_8722)))),c_Product__Type_OPair(U_8720,U_8722)))),U_8726)),U_8728),U_8730))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8720,U_8722)),hAPP(hAPP(c_Product__Type_OPair(U_8720,U_8722),U_8728),U_8730)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool)),U_8724),U_8726))) )
    & ! [U_8729,U_8727,U_8725,U_8723,U_8721,U_8719] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8719,U_8721)),hAPP(hAPP(c_Product__Type_OPair(U_8719,U_8721),U_8727),U_8729)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool)),U_8723),U_8725)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8719,tc_fun(U_8721,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8719,tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_fun(U_8721,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8721,tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_fun(U_8721,tc_HOL_Obool)),U_8719),c_COMBC(U_8721,tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8721,tc_prod(U_8719,U_8721)),tc_fun(U_8721,tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool)),U_8719),hAPP(c_COMBB(tc_prod(U_8719,U_8721),tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool),U_8721),c_member(tc_prod(U_8719,U_8721)))),c_Product__Type_OPair(U_8719,U_8721)))),U_8723)),hAPP(hAPP(c_COMBC(U_8719,tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_fun(U_8721,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8721,tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_fun(U_8721,tc_HOL_Obool)),U_8719),c_COMBC(U_8721,tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8721,tc_prod(U_8719,U_8721)),tc_fun(U_8721,tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool)),U_8719),hAPP(c_COMBB(tc_prod(U_8719,U_8721),tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool),U_8721),c_member(tc_prod(U_8719,U_8721)))),c_Product__Type_OPair(U_8719,U_8721)))),U_8725)),U_8727),U_8729)) ) ),
    inference(miniscope,[status(thm)],[f_2432_2]) ).

fof(f_2432_4,plain,
    ( ! [U_8720,U_8722,U_8724,U_8726,U_8728,U_8730] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8720,tc_fun(U_8722,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8720,tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_fun(U_8722,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8722,tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_fun(U_8722,tc_HOL_Obool)),U_8720),c_COMBC(U_8722,tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8722,tc_prod(U_8720,U_8722)),tc_fun(U_8722,tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool)),U_8720),hAPP(c_COMBB(tc_prod(U_8720,U_8722),tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool),U_8722),c_member(tc_prod(U_8720,U_8722)))),c_Product__Type_OPair(U_8720,U_8722)))),U_8724)),hAPP(hAPP(c_COMBC(U_8720,tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_fun(U_8722,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8722,tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_fun(U_8722,tc_HOL_Obool)),U_8720),c_COMBC(U_8722,tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8722,tc_prod(U_8720,U_8722)),tc_fun(U_8722,tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool)),U_8720),hAPP(c_COMBB(tc_prod(U_8720,U_8722),tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool),U_8722),c_member(tc_prod(U_8720,U_8722)))),c_Product__Type_OPair(U_8720,U_8722)))),U_8726)),U_8728),U_8730))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8720,U_8722)),hAPP(hAPP(c_Product__Type_OPair(U_8720,U_8722),U_8728),U_8730)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool)),U_8724),U_8726))) )
    & ! [U_8721,U_8725,U_8719,U_8723,U_8727,U_8729] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8719,U_8721)),hAPP(hAPP(c_Product__Type_OPair(U_8719,U_8721),U_8727),U_8729)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool)),U_8723),U_8725)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8719,tc_fun(U_8721,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8719,tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_fun(U_8721,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8721,tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_fun(U_8721,tc_HOL_Obool)),U_8719),c_COMBC(U_8721,tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8721,tc_prod(U_8719,U_8721)),tc_fun(U_8721,tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool)),U_8719),hAPP(c_COMBB(tc_prod(U_8719,U_8721),tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool),U_8721),c_member(tc_prod(U_8719,U_8721)))),c_Product__Type_OPair(U_8719,U_8721)))),U_8723)),hAPP(hAPP(c_COMBC(U_8719,tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_fun(U_8721,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8721,tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_fun(U_8721,tc_HOL_Obool)),U_8719),c_COMBC(U_8721,tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8721,tc_prod(U_8719,U_8721)),tc_fun(U_8721,tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool)),U_8719),hAPP(c_COMBB(tc_prod(U_8719,U_8721),tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool),U_8721),c_member(tc_prod(U_8719,U_8721)))),c_Product__Type_OPair(U_8719,U_8721)))),U_8725)),U_8727),U_8729)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2432_3]) ).

cnf(f_2432_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8719,U_8721)),hAPP(hAPP(c_Product__Type_OPair(U_8719,U_8721),U_8727),U_8729)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool)),U_8723),U_8725)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8719,tc_fun(U_8721,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8719,tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_fun(U_8721,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8721,tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_fun(U_8721,tc_HOL_Obool)),U_8719),c_COMBC(U_8721,tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8721,tc_prod(U_8719,U_8721)),tc_fun(U_8721,tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool)),U_8719),hAPP(c_COMBB(tc_prod(U_8719,U_8721),tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool),U_8721),c_member(tc_prod(U_8719,U_8721)))),c_Product__Type_OPair(U_8719,U_8721)))),U_8723)),hAPP(hAPP(c_COMBC(U_8719,tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_fun(U_8721,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8721,tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_fun(U_8721,tc_HOL_Obool)),U_8719),c_COMBC(U_8721,tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8721,tc_prod(U_8719,U_8721)),tc_fun(U_8721,tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool)),U_8719),hAPP(c_COMBB(tc_prod(U_8719,U_8721),tc_fun(tc_fun(tc_prod(U_8719,U_8721),tc_HOL_Obool),tc_HOL_Obool),U_8721),c_member(tc_prod(U_8719,U_8721)))),c_Product__Type_OPair(U_8719,U_8721)))),U_8725)),U_8727),U_8729)) ),
    inference(clausify,[status(thm)],[f_2432_4]) ).

cnf(f_2432_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8720,tc_fun(U_8722,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8720,tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_fun(U_8722,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8722,tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_fun(U_8722,tc_HOL_Obool)),U_8720),c_COMBC(U_8722,tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8722,tc_prod(U_8720,U_8722)),tc_fun(U_8722,tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool)),U_8720),hAPP(c_COMBB(tc_prod(U_8720,U_8722),tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool),U_8722),c_member(tc_prod(U_8720,U_8722)))),c_Product__Type_OPair(U_8720,U_8722)))),U_8724)),hAPP(hAPP(c_COMBC(U_8720,tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_fun(U_8722,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8722,tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_fun(U_8722,tc_HOL_Obool)),U_8720),c_COMBC(U_8722,tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8722,tc_prod(U_8720,U_8722)),tc_fun(U_8722,tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool)),U_8720),hAPP(c_COMBB(tc_prod(U_8720,U_8722),tc_fun(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool),tc_HOL_Obool),U_8722),c_member(tc_prod(U_8720,U_8722)))),c_Product__Type_OPair(U_8720,U_8722)))),U_8726)),U_8728),U_8730))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8720,U_8722)),hAPP(hAPP(c_Product__Type_OPair(U_8720,U_8722),U_8728),U_8730)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8720,U_8722),tc_HOL_Obool)),U_8724),U_8726))) ),
    inference(clausify,[status(thm)],[f_2432_4]) ).

fof(f_2433_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_2433_2,plain,
    ! [U_8733,U_8732,U_8731] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8731,tc_HOL_Obool)),hAPP(c_Relation_OField(U_8731),U_8732)),hAPP(c_Relation_OField(U_8731),U_8733)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8731,U_8731),tc_HOL_Obool)),U_8732),U_8733)) ),
    inference(variable_rename,[status(thm)],[f_2433_1]) ).

fof(f_2433_3,plain,
    ! [U_8731,U_8732,U_8733] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8731,tc_HOL_Obool)),hAPP(c_Relation_OField(U_8731),U_8732)),hAPP(c_Relation_OField(U_8731),U_8733)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8731,U_8731),tc_HOL_Obool)),U_8732),U_8733)) ),
    inference(definitional_conversion,[status(esa)],[f_2433_2]) ).

cnf(f_2433_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8731,tc_HOL_Obool)),hAPP(c_Relation_OField(U_8731),U_8732)),hAPP(c_Relation_OField(U_8731),U_8733)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8731,U_8731),tc_HOL_Obool)),U_8732),U_8733)) ),
    inference(clausify,[status(thm)],[f_2433_3]) ).

fof(f_2434_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_2434_2,plain,
    ! [U_8736,U_8735,U_8734] : hAPP(c_Relation_OField(U_8734),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)),U_8735),U_8736)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8734,tc_HOL_Obool)),hAPP(c_Relation_OField(U_8734),U_8735)),hAPP(c_Relation_OField(U_8734),U_8736)),
    inference(variable_rename,[status(thm)],[f_2434_1]) ).

fof(f_2434_3,plain,
    ! [U_8734,U_8735,U_8736] : hAPP(c_Relation_OField(U_8734),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)),U_8735),U_8736)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8734,tc_HOL_Obool)),hAPP(c_Relation_OField(U_8734),U_8735)),hAPP(c_Relation_OField(U_8734),U_8736)),
    inference(definitional_conversion,[status(esa)],[f_2434_2]) ).

cnf(f_2434_4,plain,
    hAPP(c_Relation_OField(U_8734),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8734,U_8734),tc_HOL_Obool)),U_8735),U_8736)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8734,tc_HOL_Obool)),hAPP(c_Relation_OField(U_8734),U_8735)),hAPP(c_Relation_OField(U_8734),U_8736)),
    inference(clausify,[status(thm)],[f_2434_3]) ).

fof(f_2435_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_2435_2,plain,
    ! [U_8740,U_8739,U_8738,U_8737] : c_Hilbert__Choice_OEps(tc_prod(U_8737,U_8738),hAPP(c_Product__Type_Oprod_Oprod__case(U_8737,U_8738,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_8737,tc_fun(U_8738,tc_HOL_Obool),tc_fun(U_8738,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_8738,tc_HOL_Obool),tc_fun(U_8738,tc_HOL_Obool)),U_8737),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_8738)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8737),c_fconj),hAPP(c_fequal,U_8739)))),hAPP(c_fequal,U_8740)))) = hAPP(hAPP(c_Product__Type_OPair(U_8737,U_8738),U_8739),U_8740),
    inference(variable_rename,[status(thm)],[f_2435_1]) ).

fof(f_2435_3,plain,
    ! [U_8737,U_8738,U_8739,U_8740] : c_Hilbert__Choice_OEps(tc_prod(U_8737,U_8738),hAPP(c_Product__Type_Oprod_Oprod__case(U_8737,U_8738,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_8737,tc_fun(U_8738,tc_HOL_Obool),tc_fun(U_8738,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_8738,tc_HOL_Obool),tc_fun(U_8738,tc_HOL_Obool)),U_8737),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_8738)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8737),c_fconj),hAPP(c_fequal,U_8739)))),hAPP(c_fequal,U_8740)))) = hAPP(hAPP(c_Product__Type_OPair(U_8737,U_8738),U_8739),U_8740),
    inference(definitional_conversion,[status(esa)],[f_2435_2]) ).

cnf(f_2435_4,plain,
    c_Hilbert__Choice_OEps(tc_prod(U_8737,U_8738),hAPP(c_Product__Type_Oprod_Oprod__case(U_8737,U_8738,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_8737,tc_fun(U_8738,tc_HOL_Obool),tc_fun(U_8738,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_8738,tc_HOL_Obool),tc_fun(U_8738,tc_HOL_Obool)),U_8737),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_8738)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_8737),c_fconj),hAPP(c_fequal,U_8739)))),hAPP(c_fequal,U_8740)))) = hAPP(hAPP(c_Product__Type_OPair(U_8737,U_8738),U_8739),U_8740),
    inference(clausify,[status(thm)],[f_2435_3]) ).

fof(f_2436_1,plain,
    ! [V_Pa_2,T_c,T_b] : c_Hilbert__Choice_OEps(tc_prod(T_b,T_c),V_Pa_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_Pa_2)),c_Product__Type_OPair(T_b,T_c)))),
    inference(fof_nnf,[status(thm)],[fact_split__paired__Eps]) ).

fof(f_2436_2,plain,
    ! [U_8743,U_8742,U_8741] : c_Hilbert__Choice_OEps(tc_prod(U_8741,U_8742),U_8743) = c_Hilbert__Choice_OEps(tc_prod(U_8741,U_8742),hAPP(c_Product__Type_Oprod_Oprod__case(U_8741,U_8742,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_8742,tc_prod(U_8741,U_8742)),tc_fun(U_8742,tc_HOL_Obool),U_8741),hAPP(c_COMBB(tc_prod(U_8741,U_8742),tc_HOL_Obool,U_8742),U_8743)),c_Product__Type_OPair(U_8741,U_8742)))),
    inference(variable_rename,[status(thm)],[f_2436_1]) ).

fof(f_2436_3,plain,
    ! [U_8741,U_8742,U_8743] : c_Hilbert__Choice_OEps(tc_prod(U_8741,U_8742),U_8743) = c_Hilbert__Choice_OEps(tc_prod(U_8741,U_8742),hAPP(c_Product__Type_Oprod_Oprod__case(U_8741,U_8742,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_8742,tc_prod(U_8741,U_8742)),tc_fun(U_8742,tc_HOL_Obool),U_8741),hAPP(c_COMBB(tc_prod(U_8741,U_8742),tc_HOL_Obool,U_8742),U_8743)),c_Product__Type_OPair(U_8741,U_8742)))),
    inference(definitional_conversion,[status(esa)],[f_2436_2]) ).

cnf(f_2436_4,plain,
    c_Hilbert__Choice_OEps(tc_prod(U_8741,U_8742),U_8743) = c_Hilbert__Choice_OEps(tc_prod(U_8741,U_8742),hAPP(c_Product__Type_Oprod_Oprod__case(U_8741,U_8742,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_8742,tc_prod(U_8741,U_8742)),tc_fun(U_8742,tc_HOL_Obool),U_8741),hAPP(c_COMBB(tc_prod(U_8741,U_8742),tc_HOL_Obool,U_8742),U_8743)),c_Product__Type_OPair(U_8741,U_8742)))),
    inference(clausify,[status(thm)],[f_2436_3]) ).

fof(f_2437_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_2437_2,plain,
    ! [U_8747,U_8746,U_8745,U_8744] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8744,tc_fun(U_8744,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8744,tc_fun(tc_prod(U_8744,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_8744,U_8744),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8744,U_8744),tc_HOL_Obool),tc_fun(U_8744,tc_HOL_Obool)),U_8744),c_COMBC(U_8744,tc_fun(tc_prod(U_8744,U_8744),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8744,tc_prod(U_8744,U_8744)),tc_fun(U_8744,tc_fun(tc_fun(tc_prod(U_8744,U_8744),tc_HOL_Obool),tc_HOL_Obool)),U_8744),hAPP(c_COMBB(tc_prod(U_8744,U_8744),tc_fun(tc_fun(tc_prod(U_8744,U_8744),tc_HOL_Obool),tc_HOL_Obool),U_8744),c_member(tc_prod(U_8744,U_8744)))),c_Product__Type_OPair(U_8744,U_8744)))),U_8745)),c_fequal),U_8746),U_8747))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8744,U_8744)),hAPP(hAPP(c_Product__Type_OPair(U_8744,U_8744),U_8746),U_8747)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8744,U_8744),tc_HOL_Obool)),U_8745),c_Relation_OId(U_8744)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8744,U_8744)),hAPP(hAPP(c_Product__Type_OPair(U_8744,U_8744),U_8746),U_8747)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8744,U_8744),tc_HOL_Obool)),U_8745),c_Relation_OId(U_8744))))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8744,tc_fun(U_8744,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8744,tc_fun(tc_prod(U_8744,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_8744,U_8744),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8744,U_8744),tc_HOL_Obool),tc_fun(U_8744,tc_HOL_Obool)),U_8744),c_COMBC(U_8744,tc_fun(tc_prod(U_8744,U_8744),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8744,tc_prod(U_8744,U_8744)),tc_fun(U_8744,tc_fun(tc_fun(tc_prod(U_8744,U_8744),tc_HOL_Obool),tc_HOL_Obool)),U_8744),hAPP(c_COMBB(tc_prod(U_8744,U_8744),tc_fun(tc_fun(tc_prod(U_8744,U_8744),tc_HOL_Obool),tc_HOL_Obool),U_8744),c_member(tc_prod(U_8744,U_8744)))),c_Product__Type_OPair(U_8744,U_8744)))),U_8745)),c_fequal),U_8746),U_8747)) ) ),
    inference(variable_rename,[status(thm)],[f_2437_1]) ).

fof(f_2437_3,plain,
    ( ! [U_8755,U_8753,U_8751,U_8749] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8749,tc_fun(U_8749,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8749,tc_fun(tc_prod(U_8749,U_8749),tc_HOL_Obool),tc_fun(U_8749,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8749,tc_fun(tc_fun(tc_prod(U_8749,U_8749),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8749,U_8749),tc_HOL_Obool),tc_fun(U_8749,tc_HOL_Obool)),U_8749),c_COMBC(U_8749,tc_fun(tc_prod(U_8749,U_8749),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8749,tc_prod(U_8749,U_8749)),tc_fun(U_8749,tc_fun(tc_fun(tc_prod(U_8749,U_8749),tc_HOL_Obool),tc_HOL_Obool)),U_8749),hAPP(c_COMBB(tc_prod(U_8749,U_8749),tc_fun(tc_fun(tc_prod(U_8749,U_8749),tc_HOL_Obool),tc_HOL_Obool),U_8749),c_member(tc_prod(U_8749,U_8749)))),c_Product__Type_OPair(U_8749,U_8749)))),U_8751)),c_fequal),U_8753),U_8755))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8749,U_8749)),hAPP(hAPP(c_Product__Type_OPair(U_8749,U_8749),U_8753),U_8755)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8749,U_8749),tc_HOL_Obool)),U_8751),c_Relation_OId(U_8749)))) )
    & ! [U_8754,U_8752,U_8750,U_8748] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8748,U_8748)),hAPP(hAPP(c_Product__Type_OPair(U_8748,U_8748),U_8752),U_8754)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool)),U_8750),c_Relation_OId(U_8748))))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8748,tc_fun(U_8748,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8748,tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool),tc_fun(U_8748,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8748,tc_fun(tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool),tc_fun(U_8748,tc_HOL_Obool)),U_8748),c_COMBC(U_8748,tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8748,tc_prod(U_8748,U_8748)),tc_fun(U_8748,tc_fun(tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool),tc_HOL_Obool)),U_8748),hAPP(c_COMBB(tc_prod(U_8748,U_8748),tc_fun(tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool),tc_HOL_Obool),U_8748),c_member(tc_prod(U_8748,U_8748)))),c_Product__Type_OPair(U_8748,U_8748)))),U_8750)),c_fequal),U_8752),U_8754)) ) ),
    inference(miniscope,[status(thm)],[f_2437_2]) ).

fof(f_2437_4,plain,
    ( ! [U_8749,U_8751,U_8753,U_8755] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8749,tc_fun(U_8749,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8749,tc_fun(tc_prod(U_8749,U_8749),tc_HOL_Obool),tc_fun(U_8749,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8749,tc_fun(tc_fun(tc_prod(U_8749,U_8749),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8749,U_8749),tc_HOL_Obool),tc_fun(U_8749,tc_HOL_Obool)),U_8749),c_COMBC(U_8749,tc_fun(tc_prod(U_8749,U_8749),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8749,tc_prod(U_8749,U_8749)),tc_fun(U_8749,tc_fun(tc_fun(tc_prod(U_8749,U_8749),tc_HOL_Obool),tc_HOL_Obool)),U_8749),hAPP(c_COMBB(tc_prod(U_8749,U_8749),tc_fun(tc_fun(tc_prod(U_8749,U_8749),tc_HOL_Obool),tc_HOL_Obool),U_8749),c_member(tc_prod(U_8749,U_8749)))),c_Product__Type_OPair(U_8749,U_8749)))),U_8751)),c_fequal),U_8753),U_8755))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8749,U_8749)),hAPP(hAPP(c_Product__Type_OPair(U_8749,U_8749),U_8753),U_8755)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8749,U_8749),tc_HOL_Obool)),U_8751),c_Relation_OId(U_8749)))) )
    & ! [U_8750,U_8754,U_8748,U_8752] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8748,U_8748)),hAPP(hAPP(c_Product__Type_OPair(U_8748,U_8748),U_8752),U_8754)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool)),U_8750),c_Relation_OId(U_8748))))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8748,tc_fun(U_8748,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8748,tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool),tc_fun(U_8748,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8748,tc_fun(tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool),tc_fun(U_8748,tc_HOL_Obool)),U_8748),c_COMBC(U_8748,tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8748,tc_prod(U_8748,U_8748)),tc_fun(U_8748,tc_fun(tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool),tc_HOL_Obool)),U_8748),hAPP(c_COMBB(tc_prod(U_8748,U_8748),tc_fun(tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool),tc_HOL_Obool),U_8748),c_member(tc_prod(U_8748,U_8748)))),c_Product__Type_OPair(U_8748,U_8748)))),U_8750)),c_fequal),U_8752),U_8754)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2437_3]) ).

cnf(f_2437_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8748,U_8748)),hAPP(hAPP(c_Product__Type_OPair(U_8748,U_8748),U_8752),U_8754)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool)),U_8750),c_Relation_OId(U_8748))))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8748,tc_fun(U_8748,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8748,tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool),tc_fun(U_8748,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8748,tc_fun(tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool),tc_fun(U_8748,tc_HOL_Obool)),U_8748),c_COMBC(U_8748,tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8748,tc_prod(U_8748,U_8748)),tc_fun(U_8748,tc_fun(tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool),tc_HOL_Obool)),U_8748),hAPP(c_COMBB(tc_prod(U_8748,U_8748),tc_fun(tc_fun(tc_prod(U_8748,U_8748),tc_HOL_Obool),tc_HOL_Obool),U_8748),c_member(tc_prod(U_8748,U_8748)))),c_Product__Type_OPair(U_8748,U_8748)))),U_8750)),c_fequal),U_8752),U_8754)) ),
    inference(clausify,[status(thm)],[f_2437_4]) ).

cnf(f_2437_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8749,tc_fun(U_8749,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_8749,tc_fun(tc_prod(U_8749,U_8749),tc_HOL_Obool),tc_fun(U_8749,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8749,tc_fun(tc_fun(tc_prod(U_8749,U_8749),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_8749,U_8749),tc_HOL_Obool),tc_fun(U_8749,tc_HOL_Obool)),U_8749),c_COMBC(U_8749,tc_fun(tc_prod(U_8749,U_8749),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_8749,tc_prod(U_8749,U_8749)),tc_fun(U_8749,tc_fun(tc_fun(tc_prod(U_8749,U_8749),tc_HOL_Obool),tc_HOL_Obool)),U_8749),hAPP(c_COMBB(tc_prod(U_8749,U_8749),tc_fun(tc_fun(tc_prod(U_8749,U_8749),tc_HOL_Obool),tc_HOL_Obool),U_8749),c_member(tc_prod(U_8749,U_8749)))),c_Product__Type_OPair(U_8749,U_8749)))),U_8751)),c_fequal),U_8753),U_8755))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8749,U_8749)),hAPP(hAPP(c_Product__Type_OPair(U_8749,U_8749),U_8753),U_8755)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8749,U_8749),tc_HOL_Obool)),U_8751),c_Relation_OId(U_8749)))) ),
    inference(clausify,[status(thm)],[f_2437_4]) ).

fof(f_2438_1,plain,
    ! [V_Procsa_2,V_Qa_2,V_Pa_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_Pa_2)),c_Com_Ocom_OBODY)),V_Qa_2)),V_Procsa_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_Pa_2)),c_Com_Ocom_OBODY)),V_Qa_2)),V_Procsa_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_Pa_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_Qa_2)),V_Procsa_2)) ),
    inference(fof_nnf,[status(thm)],[fact_hoare__derivs_OBody]) ).

fof(f_2438_2,plain,
    ! [U_8760,U_8759,U_8758,U_8757,U_8756] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8756,U_8757,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8756),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756))),hAPP(hAPP(c_COMBB(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8756)),U_8758)),c_Com_Ocom_OBODY)),U_8759)),U_8760))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8756,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8756),tc_HOL_Obool)),U_8757),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8756),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756))),hAPP(hAPP(c_COMBB(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8756)),U_8758)),c_Com_Ocom_OBODY)),U_8759)),U_8760)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8756),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756))),hAPP(hAPP(c_COMBB(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8756)),U_8758)),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_8759)),U_8760)) ),
    inference(variable_rename,[status(thm)],[f_2438_1]) ).

fof(f_2438_3,plain,
    ! [U_8756,U_8757,U_8758,U_8759,U_8760] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8756,U_8757,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8756),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756))),hAPP(hAPP(c_COMBB(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8756)),U_8758)),c_Com_Ocom_OBODY)),U_8759)),U_8760))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8756,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8756),tc_HOL_Obool)),U_8757),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8756),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756))),hAPP(hAPP(c_COMBB(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8756)),U_8758)),c_Com_Ocom_OBODY)),U_8759)),U_8760)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8756),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756))),hAPP(hAPP(c_COMBB(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8756)),U_8758)),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_8759)),U_8760)) ),
    inference(definitional_conversion,[status(esa)],[f_2438_2]) ).

cnf(f_2438_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_8756,U_8757,hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8756),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756))),hAPP(hAPP(c_COMBB(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8756)),U_8758)),c_Com_Ocom_OBODY)),U_8759)),U_8760))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8756,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8756),tc_HOL_Obool)),U_8757),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8756),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756))),hAPP(hAPP(c_COMBB(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8756)),U_8758)),c_Com_Ocom_OBODY)),U_8759)),U_8760)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8756),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756))),hAPP(hAPP(c_COMBB(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8756,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8756))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8756)),U_8758)),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_8759)),U_8760)) ),
    inference(clausify,[status(thm)],[f_2438_3]) ).

fof(f_2439_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_2439_2,plain,
    ! [U_8762,U_8761] :
      ( ( 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_8761),U_8762)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8761),U_8762)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8761),U_8762))
        | ~ 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_8761),U_8762)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(variable_rename,[status(thm)],[f_2439_1]) ).

fof(f_2439_3,plain,
    ( ! [U_8766,U_8764] :
        ( 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_8764),U_8766)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8764),U_8766)) )
    & ! [U_8765,U_8763] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8763),U_8765))
        | ~ 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_8763),U_8765)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(miniscope,[status(thm)],[f_2439_2]) ).

fof(f_2439_4,plain,
    ( ! [U_8764,U_8766] :
        ( 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_8764),U_8766)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8764),U_8766)) )
    & ! [U_8765,U_8763] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8763),U_8765))
        | ~ 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_8763),U_8765)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2439_3]) ).

cnf(f_2439_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8763),U_8765))
    | ~ 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_8763),U_8765)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
    inference(clausify,[status(thm)],[f_2439_4]) ).

cnf(f_2439_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_8764),U_8766)),c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_8764),U_8766)) ),
    inference(clausify,[status(thm)],[f_2439_4]) ).

fof(f_2440_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_2440_2,plain,
    ! [U_8776,U_8775] :
      ( ( c_Wellfounded_Owf(U_8775,U_8776)
        | ? [U_8774] :
            ( ! [U_8773] :
                ( ? [U_8772] :
                    ( hBOOL(hAPP(hAPP(c_member(U_8775),U_8772),U_8774))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(U_8775,U_8775)),hAPP(hAPP(c_Product__Type_OPair(U_8775,U_8775),U_8772),U_8773)),U_8776)) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_8775),U_8773),U_8774)) )
            & ? [U_8771] : hBOOL(hAPP(hAPP(c_member(U_8775),U_8771),U_8774)) ) )
      & ( ! [U_8770] :
            ( ? [U_8769] :
                ( ! [U_8768] :
                    ( ~ hBOOL(hAPP(hAPP(c_member(U_8775),U_8768),U_8770))
                    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8775,U_8775)),hAPP(hAPP(c_Product__Type_OPair(U_8775,U_8775),U_8768),U_8769)),U_8776)) )
                & hBOOL(hAPP(hAPP(c_member(U_8775),U_8769),U_8770)) )
            | ! [U_8767] : ~ hBOOL(hAPP(hAPP(c_member(U_8775),U_8767),U_8770)) )
        | ~ c_Wellfounded_Owf(U_8775,U_8776) ) ),
    inference(variable_rename,[status(thm)],[f_2440_1]) ).

fof(f_2440_3,plain,
    ( ! [U_8780,U_8778] :
        ( c_Wellfounded_Owf(U_8778,U_8780)
        | ? [U_8774] :
            ( ! [U_8773] :
                ( ? [U_8772] :
                    ( hBOOL(hAPP(hAPP(c_member(U_8778),U_8772),U_8774))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(U_8778,U_8778)),hAPP(hAPP(c_Product__Type_OPair(U_8778,U_8778),U_8772),U_8773)),U_8780)) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_8778),U_8773),U_8774)) )
            & ? [U_8771] : hBOOL(hAPP(hAPP(c_member(U_8778),U_8771),U_8774)) ) )
    & ! [U_8779,U_8777] :
        ( ! [U_8770] :
            ( ? [U_8769] :
                ( ! [U_8768] :
                    ( ~ hBOOL(hAPP(hAPP(c_member(U_8777),U_8768),U_8770))
                    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8777,U_8777)),hAPP(hAPP(c_Product__Type_OPair(U_8777,U_8777),U_8768),U_8769)),U_8779)) )
                & hBOOL(hAPP(hAPP(c_member(U_8777),U_8769),U_8770)) )
            | ! [U_8767] : ~ hBOOL(hAPP(hAPP(c_member(U_8777),U_8767),U_8770)) )
        | ~ c_Wellfounded_Owf(U_8777,U_8779) ) ),
    inference(miniscope,[status(thm)],[f_2440_2]) ).

fof(f_2440_4,plain,
    ( ! [U_8780,U_8778] :
        ( c_Wellfounded_Owf(U_8778,U_8780)
        | ? [U_8774] :
            ( ! [U_8773] :
                ( ? [U_8772] :
                    ( hBOOL(hAPP(hAPP(c_member(U_8778),U_8772),U_8774))
                    & hBOOL(hAPP(hAPP(c_member(tc_prod(U_8778,U_8778)),hAPP(hAPP(c_Product__Type_OPair(U_8778,U_8778),U_8772),U_8773)),U_8780)) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_8778),U_8773),U_8774)) )
            & ? [U_8771] : hBOOL(hAPP(hAPP(c_member(U_8778),U_8771),U_8774)) ) )
    & ! [U_8779,U_8777] :
        ( ! [U_8770] :
            ( ( ! [U_8768] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_8777),U_8768),U_8770))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8777,U_8777)),hAPP(hAPP(c_Product__Type_OPair(U_8777,U_8777),U_8768),sK139(U_8779,U_8777,U_8770))),U_8779)) )
              & hBOOL(hAPP(hAPP(c_member(U_8777),sK139(U_8779,U_8777,U_8770)),U_8770)) )
            | ! [U_8767] : ~ hBOOL(hAPP(hAPP(c_member(U_8777),U_8767),U_8770)) )
        | ~ c_Wellfounded_Owf(U_8777,U_8779) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK139]),skolemize(U_8769,sK139(U_8779,U_8777,U_8770))],[f_2440_3]) ).

fof(f_2440_5,plain,
    ( ! [U_8780,U_8778] :
        ( c_Wellfounded_Owf(U_8778,U_8780)
        | ( ! [U_8773] :
              ( ? [U_8772] :
                  ( hBOOL(hAPP(hAPP(c_member(U_8778),U_8772),sK140(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_8772),U_8773)),U_8780)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_8778),U_8773),sK140(U_8780,U_8778))) )
          & ? [U_8771] : hBOOL(hAPP(hAPP(c_member(U_8778),U_8771),sK140(U_8780,U_8778))) ) )
    & ! [U_8779,U_8777] :
        ( ! [U_8770] :
            ( ( ! [U_8768] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_8777),U_8768),U_8770))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8777,U_8777)),hAPP(hAPP(c_Product__Type_OPair(U_8777,U_8777),U_8768),sK139(U_8779,U_8777,U_8770))),U_8779)) )
              & hBOOL(hAPP(hAPP(c_member(U_8777),sK139(U_8779,U_8777,U_8770)),U_8770)) )
            | ! [U_8767] : ~ hBOOL(hAPP(hAPP(c_member(U_8777),U_8767),U_8770)) )
        | ~ c_Wellfounded_Owf(U_8777,U_8779) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK140]),skolemize(U_8774,sK140(U_8780,U_8778))],[f_2440_4]) ).

fof(f_2440_6,plain,
    ( ! [U_8780,U_8778] :
        ( c_Wellfounded_Owf(U_8778,U_8780)
        | ( ! [U_8773] :
              ( ? [U_8772] :
                  ( hBOOL(hAPP(hAPP(c_member(U_8778),U_8772),sK140(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_8772),U_8773)),U_8780)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_8778),U_8773),sK140(U_8780,U_8778))) )
          & hBOOL(hAPP(hAPP(c_member(U_8778),sK141(U_8780,U_8778)),sK140(U_8780,U_8778))) ) )
    & ! [U_8779,U_8777] :
        ( ! [U_8770] :
            ( ( ! [U_8768] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_8777),U_8768),U_8770))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8777,U_8777)),hAPP(hAPP(c_Product__Type_OPair(U_8777,U_8777),U_8768),sK139(U_8779,U_8777,U_8770))),U_8779)) )
              & hBOOL(hAPP(hAPP(c_member(U_8777),sK139(U_8779,U_8777,U_8770)),U_8770)) )
            | ! [U_8767] : ~ hBOOL(hAPP(hAPP(c_member(U_8777),U_8767),U_8770)) )
        | ~ c_Wellfounded_Owf(U_8777,U_8779) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK141]),skolemize(U_8771,sK141(U_8780,U_8778))],[f_2440_5]) ).

fof(f_2440_7,plain,
    ( ! [U_8780,U_8778] :
        ( c_Wellfounded_Owf(U_8778,U_8780)
        | ( ! [U_8773] :
              ( ( hBOOL(hAPP(hAPP(c_member(U_8778),sK142(U_8780,U_8778,U_8773)),sK140(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),sK142(U_8780,U_8778,U_8773)),U_8773)),U_8780)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_8778),U_8773),sK140(U_8780,U_8778))) )
          & hBOOL(hAPP(hAPP(c_member(U_8778),sK141(U_8780,U_8778)),sK140(U_8780,U_8778))) ) )
    & ! [U_8779,U_8777] :
        ( ! [U_8770] :
            ( ( ! [U_8768] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(U_8777),U_8768),U_8770))
                  | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8777,U_8777)),hAPP(hAPP(c_Product__Type_OPair(U_8777,U_8777),U_8768),sK139(U_8779,U_8777,U_8770))),U_8779)) )
              & hBOOL(hAPP(hAPP(c_member(U_8777),sK139(U_8779,U_8777,U_8770)),U_8770)) )
            | ! [U_8767] : ~ hBOOL(hAPP(hAPP(c_member(U_8777),U_8767),U_8770)) )
        | ~ c_Wellfounded_Owf(U_8777,U_8779) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK142]),skolemize(U_8772,sK142(U_8780,U_8778,U_8773))],[f_2440_6]) ).

fof(f_2440_8,plain,
    ( ! [U_8778,U_8780,U_8773] :
        ( hBOOL(hAPP(hAPP(c_member(U_8778),sK142(U_8780,U_8778,U_8773)),sK140(U_8780,U_8778)))
        | ~ sP718(U_8778,U_8780,U_8773) )
    & ! [U_8778,U_8780,U_8773] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8778,U_8778)),hAPP(hAPP(c_Product__Type_OPair(U_8778,U_8778),sK142(U_8780,U_8778,U_8773)),U_8773)),U_8780))
        | ~ sP718(U_8778,U_8780,U_8773) )
    & ! [U_8778,U_8780,U_8773] :
        ( sP718(U_8778,U_8780,U_8773)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8778),U_8773),sK140(U_8780,U_8778)))
        | ~ sP719(U_8778,U_8780,U_8773) )
    & ! [U_8778,U_8780,U_8773] :
        ( hBOOL(hAPP(hAPP(c_member(U_8778),sK141(U_8780,U_8778)),sK140(U_8780,U_8778)))
        | ~ sP719(U_8778,U_8780,U_8773) )
    & ! [U_8768,U_8770,U_8777,U_8779] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8777),U_8768),U_8770))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8777,U_8777)),hAPP(hAPP(c_Product__Type_OPair(U_8777,U_8777),U_8768),sK139(U_8779,U_8777,U_8770))),U_8779))
        | ~ sP717(U_8768,U_8770,U_8777,U_8779) )
    & ! [U_8768,U_8770,U_8777,U_8779] :
        ( hBOOL(hAPP(hAPP(c_member(U_8777),sK139(U_8779,U_8777,U_8770)),U_8770))
        | ~ sP717(U_8768,U_8770,U_8777,U_8779) )
    & ! [U_8778,U_8780,U_8773] :
        ( c_Wellfounded_Owf(U_8778,U_8780)
        | sP719(U_8778,U_8780,U_8773) )
    & ! [U_8767,U_8768,U_8770,U_8777,U_8779] :
        ( sP717(U_8768,U_8770,U_8777,U_8779)
        | ~ hBOOL(hAPP(hAPP(c_member(U_8777),U_8767),U_8770))
        | ~ c_Wellfounded_Owf(U_8777,U_8779) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP717,sP718,sP719])],[f_2440_7]) ).

cnf(f_2440_9,plain,
    ( sP717(U_8768,U_8770,U_8777,U_8779)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8777),U_8767),U_8770))
    | ~ c_Wellfounded_Owf(U_8777,U_8779) ),
    inference(clausify,[status(thm)],[f_2440_8]) ).

cnf(f_2440_10,plain,
    ( c_Wellfounded_Owf(U_8778,U_8780)
    | sP719(U_8778,U_8780,U_8773) ),
    inference(clausify,[status(thm)],[f_2440_8]) ).

cnf(f_2440_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8777),sK139(U_8779,U_8777,U_8770)),U_8770))
    | ~ sP717(U_8768,U_8770,U_8777,U_8779) ),
    inference(clausify,[status(thm)],[f_2440_8]) ).

cnf(f_2440_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8777),U_8768),U_8770))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8777,U_8777)),hAPP(hAPP(c_Product__Type_OPair(U_8777,U_8777),U_8768),sK139(U_8779,U_8777,U_8770))),U_8779))
    | ~ sP717(U_8768,U_8770,U_8777,U_8779) ),
    inference(clausify,[status(thm)],[f_2440_8]) ).

cnf(f_2440_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8778),sK141(U_8780,U_8778)),sK140(U_8780,U_8778)))
    | ~ sP719(U_8778,U_8780,U_8773) ),
    inference(clausify,[status(thm)],[f_2440_8]) ).

cnf(f_2440_14,plain,
    ( sP718(U_8778,U_8780,U_8773)
    | ~ hBOOL(hAPP(hAPP(c_member(U_8778),U_8773),sK140(U_8780,U_8778)))
    | ~ sP719(U_8778,U_8780,U_8773) ),
    inference(clausify,[status(thm)],[f_2440_8]) ).

cnf(f_2440_15,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8778,U_8778)),hAPP(hAPP(c_Product__Type_OPair(U_8778,U_8778),sK142(U_8780,U_8778,U_8773)),U_8773)),U_8780))
    | ~ sP718(U_8778,U_8780,U_8773) ),
    inference(clausify,[status(thm)],[f_2440_8]) ).

cnf(f_2440_16,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8778),sK142(U_8780,U_8778,U_8773)),sK140(U_8780,U_8778)))
    | ~ sP718(U_8778,U_8780,U_8773) ),
    inference(clausify,[status(thm)],[f_2440_8]) ).

fof(f_2441_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_2441_2,plain,
    ! [U_8786,U_8785,U_8784,U_8783,U_8782,U_8781] :
      ( hBOOL(hAPP(hAPP(U_8784,U_8785),U_8786))
      | hBOOL(hAPP(hAPP(U_8783,U_8785),U_8786))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8781,tc_fun(U_8782,tc_HOL_Obool))),U_8783),U_8784),U_8785),U_8786)) ),
    inference(variable_rename,[status(thm)],[f_2441_1]) ).

fof(f_2441_3,plain,
    ! [U_8786,U_8785,U_8784,U_8783] :
      ( ! [U_8782,U_8781] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8781,tc_fun(U_8782,tc_HOL_Obool))),U_8783),U_8784),U_8785),U_8786))
      | hBOOL(hAPP(hAPP(U_8784,U_8785),U_8786))
      | hBOOL(hAPP(hAPP(U_8783,U_8785),U_8786)) ),
    inference(miniscope,[status(thm)],[f_2441_2]) ).

fof(f_2441_4,plain,
    ! [U_8784,U_8782,U_8786,U_8781,U_8785,U_8783] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8781,tc_fun(U_8782,tc_HOL_Obool))),U_8783),U_8784),U_8785),U_8786))
      | hBOOL(hAPP(hAPP(U_8784,U_8785),U_8786))
      | hBOOL(hAPP(hAPP(U_8783,U_8785),U_8786)) ),
    inference(definitional_conversion,[status(esa)],[f_2441_3]) ).

cnf(f_2441_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8781,tc_fun(U_8782,tc_HOL_Obool))),U_8783),U_8784),U_8785),U_8786))
    | hBOOL(hAPP(hAPP(U_8784,U_8785),U_8786))
    | hBOOL(hAPP(hAPP(U_8783,U_8785),U_8786)) ),
    inference(clausify,[status(thm)],[f_2441_4]) ).

fof(f_2442_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_2442_2,plain,
    ! [U_8792,U_8791,U_8790,U_8789,U_8788,U_8787] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8791,tc_fun(U_8792,tc_HOL_Obool))),U_8790),U_8787),U_8788),U_8789))
      | ( ~ hBOOL(hAPP(hAPP(U_8790,U_8788),U_8789))
        & ~ hBOOL(hAPP(hAPP(U_8787,U_8788),U_8789)) ) ),
    inference(variable_rename,[status(thm)],[f_2442_1]) ).

fof(f_2442_3,plain,
    ( ! [U_8789,U_8787,U_8788,U_8790] :
        ( ~ hBOOL(hAPP(hAPP(U_8790,U_8788),U_8789))
        | ~ sP720(U_8789,U_8787,U_8788,U_8790) )
    & ! [U_8789,U_8787,U_8788,U_8790] :
        ( ~ hBOOL(hAPP(hAPP(U_8787,U_8788),U_8789))
        | ~ sP720(U_8789,U_8787,U_8788,U_8790) )
    & ! [U_8789,U_8787,U_8788,U_8790,U_8791,U_8792] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8791,tc_fun(U_8792,tc_HOL_Obool))),U_8790),U_8787),U_8788),U_8789))
        | sP720(U_8789,U_8787,U_8788,U_8790) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP720])],[f_2442_2]) ).

cnf(f_2442_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8791,tc_fun(U_8792,tc_HOL_Obool))),U_8790),U_8787),U_8788),U_8789))
    | sP720(U_8789,U_8787,U_8788,U_8790) ),
    inference(clausify,[status(thm)],[f_2442_3]) ).

cnf(f_2442_5,plain,
    ( ~ hBOOL(hAPP(hAPP(U_8787,U_8788),U_8789))
    | ~ sP720(U_8789,U_8787,U_8788,U_8790) ),
    inference(clausify,[status(thm)],[f_2442_3]) ).

cnf(f_2442_6,plain,
    ( ~ hBOOL(hAPP(hAPP(U_8790,U_8788),U_8789))
    | ~ sP720(U_8789,U_8787,U_8788,U_8790) ),
    inference(clausify,[status(thm)],[f_2442_3]) ).

fof(f_2443_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_2443_2,plain,
    ! [U_8796,U_8795,U_8794,U_8793] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8793,U_8793)),hAPP(hAPP(c_Product__Type_OPair(U_8793,U_8793),U_8794),U_8795)),c_Transitive__Closure_Otrancl(U_8793,U_8796)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8793,U_8793)),hAPP(hAPP(c_Product__Type_OPair(U_8793,U_8793),U_8794),U_8795)),U_8796)) ),
    inference(variable_rename,[status(thm)],[f_2443_1]) ).

fof(f_2443_3,plain,
    ! [U_8793,U_8794,U_8795,U_8796] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8793,U_8793)),hAPP(hAPP(c_Product__Type_OPair(U_8793,U_8793),U_8794),U_8795)),c_Transitive__Closure_Otrancl(U_8793,U_8796)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8793,U_8793)),hAPP(hAPP(c_Product__Type_OPair(U_8793,U_8793),U_8794),U_8795)),U_8796)) ),
    inference(definitional_conversion,[status(esa)],[f_2443_2]) ).

cnf(f_2443_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8793,U_8793)),hAPP(hAPP(c_Product__Type_OPair(U_8793,U_8793),U_8794),U_8795)),c_Transitive__Closure_Otrancl(U_8793,U_8796)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8793,U_8793)),hAPP(hAPP(c_Product__Type_OPair(U_8793,U_8793),U_8794),U_8795)),U_8796)) ),
    inference(clausify,[status(thm)],[f_2443_3]) ).

fof(f_2444_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_2444_2,plain,
    ! [U_8802,U_8801,U_8800,U_8799,U_8798,U_8797] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8800,tc_fun(U_8801,tc_HOL_Obool))),U_8797),U_8802),U_8798),U_8799))
      | ~ hBOOL(hAPP(hAPP(U_8797,U_8798),U_8799)) ),
    inference(variable_rename,[status(thm)],[f_2444_1]) ).

fof(f_2444_3,plain,
    ! [U_8797,U_8798,U_8799,U_8800,U_8801,U_8802] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8800,tc_fun(U_8801,tc_HOL_Obool))),U_8797),U_8802),U_8798),U_8799))
      | ~ hBOOL(hAPP(hAPP(U_8797,U_8798),U_8799)) ),
    inference(definitional_conversion,[status(esa)],[f_2444_2]) ).

cnf(f_2444_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8800,tc_fun(U_8801,tc_HOL_Obool))),U_8797),U_8802),U_8798),U_8799))
    | ~ hBOOL(hAPP(hAPP(U_8797,U_8798),U_8799)) ),
    inference(clausify,[status(thm)],[f_2444_3]) ).

fof(f_2445_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_2445_2,plain,
    ! [U_8808,U_8807,U_8806,U_8805,U_8804,U_8803] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8806,tc_fun(U_8807,tc_HOL_Obool))),U_8808),U_8803),U_8804),U_8805))
      | ~ hBOOL(hAPP(hAPP(U_8803,U_8804),U_8805)) ),
    inference(variable_rename,[status(thm)],[f_2445_1]) ).

fof(f_2445_3,plain,
    ! [U_8804,U_8803,U_8805,U_8806,U_8807,U_8808] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8806,tc_fun(U_8807,tc_HOL_Obool))),U_8808),U_8803),U_8804),U_8805))
      | ~ hBOOL(hAPP(hAPP(U_8803,U_8804),U_8805)) ),
    inference(definitional_conversion,[status(esa)],[f_2445_2]) ).

cnf(f_2445_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8806,tc_fun(U_8807,tc_HOL_Obool))),U_8808),U_8803),U_8804),U_8805))
    | ~ hBOOL(hAPP(hAPP(U_8803,U_8804),U_8805)) ),
    inference(clausify,[status(thm)],[f_2445_3]) ).

fof(f_2446_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_2446_2,plain,
    ! [U_8810,U_8809] :
      ( c_Wellfounded_Owf(U_8809,c_Transitive__Closure_Otrancl(U_8809,U_8810))
      | ~ c_Wellfounded_Owf(U_8809,U_8810) ),
    inference(variable_rename,[status(thm)],[f_2446_1]) ).

fof(f_2446_3,plain,
    ! [U_8810,U_8809] :
      ( c_Wellfounded_Owf(U_8809,c_Transitive__Closure_Otrancl(U_8809,U_8810))
      | ~ c_Wellfounded_Owf(U_8809,U_8810) ),
    inference(definitional_conversion,[status(esa)],[f_2446_2]) ).

cnf(f_2446_4,plain,
    ( c_Wellfounded_Owf(U_8809,c_Transitive__Closure_Otrancl(U_8809,U_8810))
    | ~ c_Wellfounded_Owf(U_8809,U_8810) ),
    inference(clausify,[status(thm)],[f_2446_3]) ).

fof(f_2447_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_2447_2,plain,
    ! [U_8814,U_8813,U_8812,U_8811] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8811,U_8811)),U_8812),c_Transitive__Closure_Otrancl(U_8811,U_8814)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8811,U_8811),tc_HOL_Obool)),U_8813),U_8814))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8811,U_8811)),U_8812),c_Transitive__Closure_Otrancl(U_8811,U_8813))) ),
    inference(variable_rename,[status(thm)],[f_2447_1]) ).

fof(f_2447_3,plain,
    ! [U_8811,U_8812,U_8813,U_8814] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8811,U_8811)),U_8812),c_Transitive__Closure_Otrancl(U_8811,U_8814)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8811,U_8811),tc_HOL_Obool)),U_8813),U_8814))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8811,U_8811)),U_8812),c_Transitive__Closure_Otrancl(U_8811,U_8813))) ),
    inference(definitional_conversion,[status(esa)],[f_2447_2]) ).

cnf(f_2447_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8811,U_8811)),U_8812),c_Transitive__Closure_Otrancl(U_8811,U_8814)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_8811,U_8811),tc_HOL_Obool)),U_8813),U_8814))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8811,U_8811)),U_8812),c_Transitive__Closure_Otrancl(U_8811,U_8813))) ),
    inference(clausify,[status(thm)],[f_2447_3]) ).

fof(f_2448_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_2448_2,plain,
    ! [U_8816,U_8815] : hAPP(c_Relation_ODomain(U_8815,U_8815),c_Transitive__Closure_Otrancl(U_8815,U_8816)) = hAPP(c_Relation_ODomain(U_8815,U_8815),U_8816),
    inference(variable_rename,[status(thm)],[f_2448_1]) ).

fof(f_2448_3,plain,
    ! [U_8816,U_8815] : hAPP(c_Relation_ODomain(U_8815,U_8815),c_Transitive__Closure_Otrancl(U_8815,U_8816)) = hAPP(c_Relation_ODomain(U_8815,U_8815),U_8816),
    inference(definitional_conversion,[status(esa)],[f_2448_2]) ).

cnf(f_2448_4,plain,
    hAPP(c_Relation_ODomain(U_8815,U_8815),c_Transitive__Closure_Otrancl(U_8815,U_8816)) = hAPP(c_Relation_ODomain(U_8815,U_8815),U_8816),
    inference(clausify,[status(thm)],[f_2448_3]) ).

fof(f_2449_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_2449_2,plain,
    ! [U_8818,U_8817] : c_Transitive__Closure_Otrancl(U_8817,hAPP(c_Relation_Oconverse(U_8817,U_8817),U_8818)) = hAPP(c_Relation_Oconverse(U_8817,U_8817),c_Transitive__Closure_Otrancl(U_8817,U_8818)),
    inference(variable_rename,[status(thm)],[f_2449_1]) ).

fof(f_2449_3,plain,
    ! [U_8817,U_8818] : c_Transitive__Closure_Otrancl(U_8817,hAPP(c_Relation_Oconverse(U_8817,U_8817),U_8818)) = hAPP(c_Relation_Oconverse(U_8817,U_8817),c_Transitive__Closure_Otrancl(U_8817,U_8818)),
    inference(definitional_conversion,[status(esa)],[f_2449_2]) ).

cnf(f_2449_4,plain,
    c_Transitive__Closure_Otrancl(U_8817,hAPP(c_Relation_Oconverse(U_8817,U_8817),U_8818)) = hAPP(c_Relation_Oconverse(U_8817,U_8817),c_Transitive__Closure_Otrancl(U_8817,U_8818)),
    inference(clausify,[status(thm)],[f_2449_3]) ).

fof(f_2450_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_2450_2,plain,
    ! [U_8823,U_8822,U_8821,U_8820,U_8819] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8819,U_8819)),hAPP(hAPP(c_Product__Type_OPair(U_8819,U_8819),U_8820),U_8823)),c_Transitive__Closure_Otrancl(U_8819,U_8822)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8819,U_8819)),hAPP(hAPP(c_Product__Type_OPair(U_8819,U_8819),U_8821),U_8823)),U_8822))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8819,U_8819)),hAPP(hAPP(c_Product__Type_OPair(U_8819,U_8819),U_8820),U_8821)),U_8822)) ),
    inference(variable_rename,[status(thm)],[f_2450_1]) ).

fof(f_2450_3,plain,
    ! [U_8819,U_8820,U_8821,U_8822,U_8823] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8819,U_8819)),hAPP(hAPP(c_Product__Type_OPair(U_8819,U_8819),U_8820),U_8823)),c_Transitive__Closure_Otrancl(U_8819,U_8822)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8819,U_8819)),hAPP(hAPP(c_Product__Type_OPair(U_8819,U_8819),U_8821),U_8823)),U_8822))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8819,U_8819)),hAPP(hAPP(c_Product__Type_OPair(U_8819,U_8819),U_8820),U_8821)),U_8822)) ),
    inference(definitional_conversion,[status(esa)],[f_2450_2]) ).

cnf(f_2450_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8819,U_8819)),hAPP(hAPP(c_Product__Type_OPair(U_8819,U_8819),U_8820),U_8823)),c_Transitive__Closure_Otrancl(U_8819,U_8822)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8819,U_8819)),hAPP(hAPP(c_Product__Type_OPair(U_8819,U_8819),U_8821),U_8823)),U_8822))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8819,U_8819)),hAPP(hAPP(c_Product__Type_OPair(U_8819,U_8819),U_8820),U_8821)),U_8822)) ),
    inference(clausify,[status(thm)],[f_2450_3]) ).

fof(f_2451_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_2451_2,plain,
    ! [U_8828,U_8827,U_8826,U_8825,U_8824] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8824,U_8824)),hAPP(hAPP(c_Product__Type_OPair(U_8824,U_8824),U_8825),U_8828)),c_Transitive__Closure_Otrancl(U_8824,U_8827)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8824,U_8824)),hAPP(hAPP(c_Product__Type_OPair(U_8824,U_8824),U_8826),U_8828)),c_Transitive__Closure_Otrancl(U_8824,U_8827)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8824,U_8824)),hAPP(hAPP(c_Product__Type_OPair(U_8824,U_8824),U_8825),U_8826)),U_8827)) ),
    inference(variable_rename,[status(thm)],[f_2451_1]) ).

fof(f_2451_3,plain,
    ! [U_8824,U_8825,U_8826,U_8827,U_8828] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8824,U_8824)),hAPP(hAPP(c_Product__Type_OPair(U_8824,U_8824),U_8825),U_8828)),c_Transitive__Closure_Otrancl(U_8824,U_8827)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8824,U_8824)),hAPP(hAPP(c_Product__Type_OPair(U_8824,U_8824),U_8826),U_8828)),c_Transitive__Closure_Otrancl(U_8824,U_8827)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8824,U_8824)),hAPP(hAPP(c_Product__Type_OPair(U_8824,U_8824),U_8825),U_8826)),U_8827)) ),
    inference(definitional_conversion,[status(esa)],[f_2451_2]) ).

cnf(f_2451_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8824,U_8824)),hAPP(hAPP(c_Product__Type_OPair(U_8824,U_8824),U_8825),U_8828)),c_Transitive__Closure_Otrancl(U_8824,U_8827)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8824,U_8824)),hAPP(hAPP(c_Product__Type_OPair(U_8824,U_8824),U_8826),U_8828)),c_Transitive__Closure_Otrancl(U_8824,U_8827)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8824,U_8824)),hAPP(hAPP(c_Product__Type_OPair(U_8824,U_8824),U_8825),U_8826)),U_8827)) ),
    inference(clausify,[status(thm)],[f_2451_3]) ).

fof(f_2452_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_2452_2,plain,
    ! [U_8833,U_8832,U_8831,U_8830,U_8829] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8829,U_8829)),hAPP(hAPP(c_Product__Type_OPair(U_8829,U_8829),U_8830),U_8833)),c_Transitive__Closure_Otrancl(U_8829,U_8832)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8829,U_8829)),hAPP(hAPP(c_Product__Type_OPair(U_8829,U_8829),U_8831),U_8833)),U_8832))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8829,U_8829)),hAPP(hAPP(c_Product__Type_OPair(U_8829,U_8829),U_8830),U_8831)),c_Transitive__Closure_Otrancl(U_8829,U_8832))) ),
    inference(variable_rename,[status(thm)],[f_2452_1]) ).

fof(f_2452_3,plain,
    ! [U_8829,U_8830,U_8831,U_8832,U_8833] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8829,U_8829)),hAPP(hAPP(c_Product__Type_OPair(U_8829,U_8829),U_8830),U_8833)),c_Transitive__Closure_Otrancl(U_8829,U_8832)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8829,U_8829)),hAPP(hAPP(c_Product__Type_OPair(U_8829,U_8829),U_8831),U_8833)),U_8832))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8829,U_8829)),hAPP(hAPP(c_Product__Type_OPair(U_8829,U_8829),U_8830),U_8831)),c_Transitive__Closure_Otrancl(U_8829,U_8832))) ),
    inference(definitional_conversion,[status(esa)],[f_2452_2]) ).

cnf(f_2452_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8829,U_8829)),hAPP(hAPP(c_Product__Type_OPair(U_8829,U_8829),U_8830),U_8833)),c_Transitive__Closure_Otrancl(U_8829,U_8832)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8829,U_8829)),hAPP(hAPP(c_Product__Type_OPair(U_8829,U_8829),U_8831),U_8833)),U_8832))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8829,U_8829)),hAPP(hAPP(c_Product__Type_OPair(U_8829,U_8829),U_8830),U_8831)),c_Transitive__Closure_Otrancl(U_8829,U_8832))) ),
    inference(clausify,[status(thm)],[f_2452_3]) ).

fof(f_2453_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_2453_2,plain,
    ! [U_8838,U_8837,U_8836,U_8835,U_8834] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8834,U_8834)),hAPP(hAPP(c_Product__Type_OPair(U_8834,U_8834),U_8835),U_8838)),c_Transitive__Closure_Otrancl(U_8834,U_8837)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8834,U_8834)),hAPP(hAPP(c_Product__Type_OPair(U_8834,U_8834),U_8836),U_8838)),c_Transitive__Closure_Otrancl(U_8834,U_8837)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8834,U_8834)),hAPP(hAPP(c_Product__Type_OPair(U_8834,U_8834),U_8835),U_8836)),c_Transitive__Closure_Otrancl(U_8834,U_8837))) ),
    inference(variable_rename,[status(thm)],[f_2453_1]) ).

fof(f_2453_3,plain,
    ! [U_8834,U_8835,U_8836,U_8837,U_8838] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8834,U_8834)),hAPP(hAPP(c_Product__Type_OPair(U_8834,U_8834),U_8835),U_8838)),c_Transitive__Closure_Otrancl(U_8834,U_8837)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8834,U_8834)),hAPP(hAPP(c_Product__Type_OPair(U_8834,U_8834),U_8836),U_8838)),c_Transitive__Closure_Otrancl(U_8834,U_8837)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8834,U_8834)),hAPP(hAPP(c_Product__Type_OPair(U_8834,U_8834),U_8835),U_8836)),c_Transitive__Closure_Otrancl(U_8834,U_8837))) ),
    inference(definitional_conversion,[status(esa)],[f_2453_2]) ).

cnf(f_2453_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8834,U_8834)),hAPP(hAPP(c_Product__Type_OPair(U_8834,U_8834),U_8835),U_8838)),c_Transitive__Closure_Otrancl(U_8834,U_8837)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8834,U_8834)),hAPP(hAPP(c_Product__Type_OPair(U_8834,U_8834),U_8836),U_8838)),c_Transitive__Closure_Otrancl(U_8834,U_8837)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8834,U_8834)),hAPP(hAPP(c_Product__Type_OPair(U_8834,U_8834),U_8835),U_8836)),c_Transitive__Closure_Otrancl(U_8834,U_8837))) ),
    inference(clausify,[status(thm)],[f_2453_3]) ).

fof(f_2454_1,plain,
    ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_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_ts_2) ),
    inference(fof_nnf,[status(thm)],[fact_cut]) ).

fof(f_2454_2,plain,
    ! [U_8842,U_8841,U_8840,U_8839] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8839,U_8842,U_8841)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8839,U_8842,U_8840)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8839,U_8840,U_8841) ),
    inference(variable_rename,[status(thm)],[f_2454_1]) ).

fof(f_2454_3,plain,
    ! [U_8839,U_8841,U_8840,U_8842] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8839,U_8842,U_8841)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8839,U_8842,U_8840)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8839,U_8840,U_8841) ),
    inference(definitional_conversion,[status(esa)],[f_2454_2]) ).

cnf(f_2454_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_8839,U_8842,U_8841)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8839,U_8842,U_8840)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8839,U_8840,U_8841) ),
    inference(clausify,[status(thm)],[f_2454_3]) ).

fof(f_2455_1,plain,
    ! [V_Ga_2,V_ts_2,V_G_H_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_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_ts_2) ),
    inference(fof_nnf,[status(thm)],[fact_thin]) ).

fof(f_2455_2,plain,
    ! [U_8846,U_8845,U_8844,U_8843] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8843,U_8846,U_8845)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8843),tc_HOL_Obool)),U_8844),U_8846))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8843,U_8844,U_8845) ),
    inference(variable_rename,[status(thm)],[f_2455_1]) ).

fof(f_2455_3,plain,
    ! [U_8843,U_8844,U_8845,U_8846] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8843,U_8846,U_8845)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8843),tc_HOL_Obool)),U_8844),U_8846))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8843,U_8844,U_8845) ),
    inference(definitional_conversion,[status(esa)],[f_2455_2]) ).

cnf(f_2455_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_8843,U_8846,U_8845)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8843),tc_HOL_Obool)),U_8844),U_8846))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8843,U_8844,U_8845) ),
    inference(clausify,[status(thm)],[f_2455_3]) ).

fof(f_2456_1,plain,
    ! [V_ts_2,V_ts_H_2,V_Ga_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_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_2456_2,plain,
    ! [U_8850,U_8849,U_8848,U_8847] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8847,U_8848,U_8850)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8847),tc_HOL_Obool)),U_8850),U_8849))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8847,U_8848,U_8849) ),
    inference(variable_rename,[status(thm)],[f_2456_1]) ).

fof(f_2456_3,plain,
    ! [U_8847,U_8848,U_8849,U_8850] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8847,U_8848,U_8850)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8847),tc_HOL_Obool)),U_8850),U_8849))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8847,U_8848,U_8849) ),
    inference(definitional_conversion,[status(esa)],[f_2456_2]) ).

cnf(f_2456_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_8847,U_8848,U_8850)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8847),tc_HOL_Obool)),U_8850),U_8849))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8847,U_8848,U_8849) ),
    inference(clausify,[status(thm)],[f_2456_3]) ).

fof(f_2457_1,plain,
    ! [V_Ga_2,V_ts_2,T_b] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool)),V_ts_2),V_Ga_2)) ),
    inference(fof_nnf,[status(thm)],[fact_asm]) ).

fof(f_2457_2,plain,
    ! [U_8853,U_8852,U_8851] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8851,U_8853,U_8852)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8851),tc_HOL_Obool)),U_8852),U_8853)) ),
    inference(variable_rename,[status(thm)],[f_2457_1]) ).

fof(f_2457_3,plain,
    ! [U_8851,U_8852,U_8853] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8851,U_8853,U_8852)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8851),tc_HOL_Obool)),U_8852),U_8853)) ),
    inference(definitional_conversion,[status(esa)],[f_2457_2]) ).

cnf(f_2457_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_8851,U_8853,U_8852)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8851),tc_HOL_Obool)),U_8852),U_8853)) ),
    inference(clausify,[status(thm)],[f_2457_3]) ).

fof(f_2458_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_2458_2,plain,
    ! [U_8856,U_8855,U_8854] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8854,U_8854)),U_8855),c_Transitive__Closure_Otrancl(U_8854,U_8856)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8854,U_8854)),U_8855),U_8856)) ),
    inference(variable_rename,[status(thm)],[f_2458_1]) ).

fof(f_2458_3,plain,
    ! [U_8854,U_8855,U_8856] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8854,U_8854)),U_8855),c_Transitive__Closure_Otrancl(U_8854,U_8856)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8854,U_8854)),U_8855),U_8856)) ),
    inference(definitional_conversion,[status(esa)],[f_2458_2]) ).

cnf(f_2458_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8854,U_8854)),U_8855),c_Transitive__Closure_Otrancl(U_8854,U_8856)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8854,U_8854)),U_8855),U_8856)) ),
    inference(clausify,[status(thm)],[f_2458_3]) ).

fof(f_2459_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_2459_2,plain,
    ! [U_8858,U_8857] : hAPP(c_Relation_ORange(U_8857,U_8857),c_Transitive__Closure_Otrancl(U_8857,U_8858)) = hAPP(c_Relation_ORange(U_8857,U_8857),U_8858),
    inference(variable_rename,[status(thm)],[f_2459_1]) ).

fof(f_2459_3,plain,
    ! [U_8857,U_8858] : hAPP(c_Relation_ORange(U_8857,U_8857),c_Transitive__Closure_Otrancl(U_8857,U_8858)) = hAPP(c_Relation_ORange(U_8857,U_8857),U_8858),
    inference(definitional_conversion,[status(esa)],[f_2459_2]) ).

cnf(f_2459_4,plain,
    hAPP(c_Relation_ORange(U_8857,U_8857),c_Transitive__Closure_Otrancl(U_8857,U_8858)) = hAPP(c_Relation_ORange(U_8857,U_8857),U_8858),
    inference(clausify,[status(thm)],[f_2459_3]) ).

fof(f_2460_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_2460_2,plain,
    ! [U_8860,U_8859] : c_Transitive__Closure_Otrancl(U_8859,U_8860) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8859,U_8859),tc_HOL_Obool)),U_8860),hAPP(hAPP(c_Relation_Orel__comp(U_8859,U_8859,U_8859),c_Transitive__Closure_Otrancl(U_8859,U_8860)),U_8860)),
    inference(variable_rename,[status(thm)],[f_2460_1]) ).

fof(f_2460_3,plain,
    ! [U_8859,U_8860] : c_Transitive__Closure_Otrancl(U_8859,U_8860) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8859,U_8859),tc_HOL_Obool)),U_8860),hAPP(hAPP(c_Relation_Orel__comp(U_8859,U_8859,U_8859),c_Transitive__Closure_Otrancl(U_8859,U_8860)),U_8860)),
    inference(definitional_conversion,[status(esa)],[f_2460_2]) ).

cnf(f_2460_4,plain,
    c_Transitive__Closure_Otrancl(U_8859,U_8860) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_8859,U_8859),tc_HOL_Obool)),U_8860),hAPP(hAPP(c_Relation_Orel__comp(U_8859,U_8859,U_8859),c_Transitive__Closure_Otrancl(U_8859,U_8860)),U_8860)),
    inference(clausify,[status(thm)],[f_2460_3]) ).

fof(f_2461_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_2461_2,plain,
    ! [U_8864,U_8863,U_8862,U_8861] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8861,U_8861)),hAPP(hAPP(c_Product__Type_OPair(U_8861,U_8861),U_8862),U_8863)),c_Transitive__Closure_Otrancl(U_8861,hAPP(c_Relation_Oconverse(U_8861,U_8861),U_8864))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8861,U_8861)),hAPP(hAPP(c_Product__Type_OPair(U_8861,U_8861),U_8862),U_8863)),hAPP(c_Relation_Oconverse(U_8861,U_8861),c_Transitive__Closure_Otrancl(U_8861,U_8864)))) ),
    inference(variable_rename,[status(thm)],[f_2461_1]) ).

fof(f_2461_3,plain,
    ! [U_8861,U_8862,U_8863,U_8864] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8861,U_8861)),hAPP(hAPP(c_Product__Type_OPair(U_8861,U_8861),U_8862),U_8863)),c_Transitive__Closure_Otrancl(U_8861,hAPP(c_Relation_Oconverse(U_8861,U_8861),U_8864))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8861,U_8861)),hAPP(hAPP(c_Product__Type_OPair(U_8861,U_8861),U_8862),U_8863)),hAPP(c_Relation_Oconverse(U_8861,U_8861),c_Transitive__Closure_Otrancl(U_8861,U_8864)))) ),
    inference(definitional_conversion,[status(esa)],[f_2461_2]) ).

cnf(f_2461_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8861,U_8861)),hAPP(hAPP(c_Product__Type_OPair(U_8861,U_8861),U_8862),U_8863)),c_Transitive__Closure_Otrancl(U_8861,hAPP(c_Relation_Oconverse(U_8861,U_8861),U_8864))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8861,U_8861)),hAPP(hAPP(c_Product__Type_OPair(U_8861,U_8861),U_8862),U_8863)),hAPP(c_Relation_Oconverse(U_8861,U_8861),c_Transitive__Closure_Otrancl(U_8861,U_8864)))) ),
    inference(clausify,[status(thm)],[f_2461_3]) ).

fof(f_2462_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_2462_2,plain,
    ! [U_8868,U_8867,U_8866,U_8865] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8865,U_8865)),hAPP(hAPP(c_Product__Type_OPair(U_8865,U_8865),U_8866),U_8867)),hAPP(c_Relation_Oconverse(U_8865,U_8865),c_Transitive__Closure_Otrancl(U_8865,U_8868))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8865,U_8865)),hAPP(hAPP(c_Product__Type_OPair(U_8865,U_8865),U_8866),U_8867)),c_Transitive__Closure_Otrancl(U_8865,hAPP(c_Relation_Oconverse(U_8865,U_8865),U_8868)))) ),
    inference(variable_rename,[status(thm)],[f_2462_1]) ).

fof(f_2462_3,plain,
    ! [U_8865,U_8866,U_8867,U_8868] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8865,U_8865)),hAPP(hAPP(c_Product__Type_OPair(U_8865,U_8865),U_8866),U_8867)),hAPP(c_Relation_Oconverse(U_8865,U_8865),c_Transitive__Closure_Otrancl(U_8865,U_8868))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8865,U_8865)),hAPP(hAPP(c_Product__Type_OPair(U_8865,U_8865),U_8866),U_8867)),c_Transitive__Closure_Otrancl(U_8865,hAPP(c_Relation_Oconverse(U_8865,U_8865),U_8868)))) ),
    inference(definitional_conversion,[status(esa)],[f_2462_2]) ).

cnf(f_2462_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8865,U_8865)),hAPP(hAPP(c_Product__Type_OPair(U_8865,U_8865),U_8866),U_8867)),hAPP(c_Relation_Oconverse(U_8865,U_8865),c_Transitive__Closure_Otrancl(U_8865,U_8868))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8865,U_8865)),hAPP(hAPP(c_Product__Type_OPair(U_8865,U_8865),U_8866),U_8867)),c_Transitive__Closure_Otrancl(U_8865,hAPP(c_Relation_Oconverse(U_8865,U_8865),U_8868)))) ),
    inference(clausify,[status(thm)],[f_2462_3]) ).

fof(f_2463_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_2463_2,plain,
    ! [U_8870,U_8869] :
      ( c_Wellfounded_Owf(U_8869,hAPP(c_Relation_Oconverse(U_8869,U_8869),c_Transitive__Closure_Otrancl(U_8869,U_8870)))
      | ~ c_Wellfounded_Owf(U_8869,hAPP(c_Relation_Oconverse(U_8869,U_8869),U_8870)) ),
    inference(variable_rename,[status(thm)],[f_2463_1]) ).

fof(f_2463_3,plain,
    ! [U_8869,U_8870] :
      ( c_Wellfounded_Owf(U_8869,hAPP(c_Relation_Oconverse(U_8869,U_8869),c_Transitive__Closure_Otrancl(U_8869,U_8870)))
      | ~ c_Wellfounded_Owf(U_8869,hAPP(c_Relation_Oconverse(U_8869,U_8869),U_8870)) ),
    inference(definitional_conversion,[status(esa)],[f_2463_2]) ).

cnf(f_2463_4,plain,
    ( c_Wellfounded_Owf(U_8869,hAPP(c_Relation_Oconverse(U_8869,U_8869),c_Transitive__Closure_Otrancl(U_8869,U_8870)))
    | ~ c_Wellfounded_Owf(U_8869,hAPP(c_Relation_Oconverse(U_8869,U_8869),U_8870)) ),
    inference(clausify,[status(thm)],[f_2463_3]) ).

fof(f_2464_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_2464_2,plain,
    c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(definitional_conversion,[status(esa)],[f_2464_1]) ).

cnf(f_2464_3,plain,
    c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat),
    inference(clausify,[status(thm)],[f_2464_2]) ).

fof(f_2465_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_2465_2,plain,
    ! [U_8874,U_8873] :
      ( ( c_Wellfounded_Oacyclic(U_8873,U_8874)
        | ? [U_8872] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_8873,U_8873)),hAPP(hAPP(c_Product__Type_OPair(U_8873,U_8873),U_8872),U_8872)),c_Transitive__Closure_Otrancl(U_8873,U_8874))) )
      & ( ! [U_8871] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8873,U_8873)),hAPP(hAPP(c_Product__Type_OPair(U_8873,U_8873),U_8871),U_8871)),c_Transitive__Closure_Otrancl(U_8873,U_8874)))
        | ~ c_Wellfounded_Oacyclic(U_8873,U_8874) ) ),
    inference(variable_rename,[status(thm)],[f_2465_1]) ).

fof(f_2465_3,plain,
    ( ! [U_8878,U_8876] :
        ( c_Wellfounded_Oacyclic(U_8876,U_8878)
        | ? [U_8872] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_8876,U_8876)),hAPP(hAPP(c_Product__Type_OPair(U_8876,U_8876),U_8872),U_8872)),c_Transitive__Closure_Otrancl(U_8876,U_8878))) )
    & ! [U_8877,U_8875] :
        ( ! [U_8871] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8875,U_8875)),hAPP(hAPP(c_Product__Type_OPair(U_8875,U_8875),U_8871),U_8871)),c_Transitive__Closure_Otrancl(U_8875,U_8877)))
        | ~ c_Wellfounded_Oacyclic(U_8875,U_8877) ) ),
    inference(miniscope,[status(thm)],[f_2465_2]) ).

fof(f_2465_4,plain,
    ( ! [U_8878,U_8876] :
        ( c_Wellfounded_Oacyclic(U_8876,U_8878)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8876,U_8876)),hAPP(hAPP(c_Product__Type_OPair(U_8876,U_8876),sK143(U_8878,U_8876)),sK143(U_8878,U_8876))),c_Transitive__Closure_Otrancl(U_8876,U_8878))) )
    & ! [U_8877,U_8875] :
        ( ! [U_8871] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8875,U_8875)),hAPP(hAPP(c_Product__Type_OPair(U_8875,U_8875),U_8871),U_8871)),c_Transitive__Closure_Otrancl(U_8875,U_8877)))
        | ~ c_Wellfounded_Oacyclic(U_8875,U_8877) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK143]),skolemize(U_8872,sK143(U_8878,U_8876))],[f_2465_3]) ).

fof(f_2465_5,plain,
    ( ! [U_8876,U_8878] :
        ( c_Wellfounded_Oacyclic(U_8876,U_8878)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8876,U_8876)),hAPP(hAPP(c_Product__Type_OPair(U_8876,U_8876),sK143(U_8878,U_8876)),sK143(U_8878,U_8876))),c_Transitive__Closure_Otrancl(U_8876,U_8878))) )
    & ! [U_8877,U_8871,U_8875] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8875,U_8875)),hAPP(hAPP(c_Product__Type_OPair(U_8875,U_8875),U_8871),U_8871)),c_Transitive__Closure_Otrancl(U_8875,U_8877)))
        | ~ c_Wellfounded_Oacyclic(U_8875,U_8877) ) ),
    inference(definitional_conversion,[status(esa)],[f_2465_4]) ).

cnf(f_2465_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8875,U_8875)),hAPP(hAPP(c_Product__Type_OPair(U_8875,U_8875),U_8871),U_8871)),c_Transitive__Closure_Otrancl(U_8875,U_8877)))
    | ~ c_Wellfounded_Oacyclic(U_8875,U_8877) ),
    inference(clausify,[status(thm)],[f_2465_5]) ).

cnf(f_2465_7,plain,
    ( c_Wellfounded_Oacyclic(U_8876,U_8878)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8876,U_8876)),hAPP(hAPP(c_Product__Type_OPair(U_8876,U_8876),sK143(U_8878,U_8876)),sK143(U_8878,U_8876))),c_Transitive__Closure_Otrancl(U_8876,U_8878))) ),
    inference(clausify,[status(thm)],[f_2465_5]) ).

fof(f_2466_1,plain,
    ! [V_pn_2,V_Procsa_2,V_Qa_2,V_Pa_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_Pa_2,V_pn_2)),hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(V_Qa_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_Procsa_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_Pa_2)),c_Com_Ocom_OBODY)),V_Qa_2)),V_Procsa_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_Pa_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_Qa_2)),V_Procsa_2)) ),
    inference(fof_nnf,[status(thm)],[fact_Body1]) ).

fof(f_2466_2,plain,
    ! [U_8884,U_8883,U_8882,U_8881,U_8880,U_8879] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8879,U_8880,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8879)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8879),hAPP(U_8881,U_8884)),hAPP(c_Com_Ocom_OBODY,U_8884)),hAPP(U_8882,U_8884))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8879),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),U_8884),U_8883))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8879,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8879),tc_HOL_Obool)),U_8880),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8879),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8879)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8879))),hAPP(hAPP(c_COMBB(tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8879))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8879)),U_8881)),c_Com_Ocom_OBODY)),U_8882)),U_8883)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8879),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8879)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8879))),hAPP(hAPP(c_COMBB(tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8879))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8879)),U_8881)),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_8882)),U_8883)) ),
    inference(variable_rename,[status(thm)],[f_2466_1]) ).

fof(f_2466_3,plain,
    ! [U_8879,U_8880,U_8881,U_8882,U_8883,U_8884] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8879,U_8880,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8879)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8879),hAPP(U_8881,U_8884)),hAPP(c_Com_Ocom_OBODY,U_8884)),hAPP(U_8882,U_8884))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8879),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),U_8884),U_8883))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8879,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8879),tc_HOL_Obool)),U_8880),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8879),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8879)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8879))),hAPP(hAPP(c_COMBB(tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8879))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8879)),U_8881)),c_Com_Ocom_OBODY)),U_8882)),U_8883)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8879),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8879)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8879))),hAPP(hAPP(c_COMBB(tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8879))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8879)),U_8881)),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_8882)),U_8883)) ),
    inference(definitional_conversion,[status(esa)],[f_2466_2]) ).

cnf(f_2466_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_8879,U_8880,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8879)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_8879),hAPP(U_8881,U_8884)),hAPP(c_Com_Ocom_OBODY,U_8884)),hAPP(U_8882,U_8884))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8879),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),U_8884),U_8883))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8879,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8879),tc_HOL_Obool)),U_8880),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8879),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8879)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8879))),hAPP(hAPP(c_COMBB(tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8879))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8879)),U_8881)),c_Com_Ocom_OBODY)),U_8882)),U_8883)),hAPP(c_Set_Oimage(tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(U_8879),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8879)),hAPP(hAPP(c_COMBS(tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8879))),hAPP(hAPP(c_COMBB(tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_8879,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_8879))),tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(U_8879)),U_8881)),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_8882)),U_8883)) ),
    inference(clausify,[status(thm)],[f_2466_3]) ).

fof(f_2467_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_2467_2,plain,
    ! [U_8887,U_8886] :
      ( c_Wellfounded_Oacyclic(U_8886,U_8887)
      | ? [U_8885] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_8886,U_8886)),hAPP(hAPP(c_Product__Type_OPair(U_8886,U_8886),U_8885),U_8885)),c_Transitive__Closure_Otrancl(U_8886,U_8887))) ),
    inference(variable_rename,[status(thm)],[f_2467_1]) ).

fof(f_2467_3,plain,
    ! [U_8887,U_8886] :
      ( c_Wellfounded_Oacyclic(U_8886,U_8887)
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8886,U_8886)),hAPP(hAPP(c_Product__Type_OPair(U_8886,U_8886),sK144(U_8887,U_8886)),sK144(U_8887,U_8886))),c_Transitive__Closure_Otrancl(U_8886,U_8887))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK144]),skolemize(U_8885,sK144(U_8887,U_8886))],[f_2467_2]) ).

fof(f_2467_4,plain,
    ! [U_8887,U_8886] :
      ( c_Wellfounded_Oacyclic(U_8886,U_8887)
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8886,U_8886)),hAPP(hAPP(c_Product__Type_OPair(U_8886,U_8886),sK144(U_8887,U_8886)),sK144(U_8887,U_8886))),c_Transitive__Closure_Otrancl(U_8886,U_8887))) ),
    inference(definitional_conversion,[status(esa)],[f_2467_3]) ).

cnf(f_2467_5,plain,
    ( c_Wellfounded_Oacyclic(U_8886,U_8887)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_8886,U_8886)),hAPP(hAPP(c_Product__Type_OPair(U_8886,U_8886),sK144(U_8887,U_8886)),sK144(U_8887,U_8886))),c_Transitive__Closure_Otrancl(U_8886,U_8887))) ),
    inference(clausify,[status(thm)],[f_2467_4]) ).

fof(f_2468_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_2468_2,plain,
    ! [U_8896,U_8895,U_8894,U_8893,U_8892,U_8891] :
      ( ? [U_8890,U_8889,U_8888] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8894,U_8892)),hAPP(hAPP(c_Product__Type_OPair(U_8894,U_8892),U_8889),U_8888)),U_8896))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_8891,U_8894)),hAPP(hAPP(c_Product__Type_OPair(U_8891,U_8894),U_8890),U_8889)),U_8895))
          & U_8893 = hAPP(hAPP(c_Product__Type_OPair(U_8891,U_8892),U_8890),U_8888) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8891,U_8892)),U_8893),hAPP(hAPP(c_Relation_Orel__comp(U_8891,U_8894,U_8892),U_8895),U_8896))) ),
    inference(variable_rename,[status(thm)],[f_2468_1]) ).

fof(f_2468_3,plain,
    ! [U_8896,U_8895,U_8894,U_8893,U_8892,U_8891] :
      ( ? [U_8889,U_8888] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8894,U_8892)),hAPP(hAPP(c_Product__Type_OPair(U_8894,U_8892),U_8889),U_8888)),U_8896))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_8891,U_8894)),hAPP(hAPP(c_Product__Type_OPair(U_8891,U_8894),sK145(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891)),U_8889)),U_8895))
          & U_8893 = hAPP(hAPP(c_Product__Type_OPair(U_8891,U_8892),sK145(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891)),U_8888) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8891,U_8892)),U_8893),hAPP(hAPP(c_Relation_Orel__comp(U_8891,U_8894,U_8892),U_8895),U_8896))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK145]),skolemize(U_8890,sK145(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891))],[f_2468_2]) ).

fof(f_2468_4,plain,
    ! [U_8896,U_8895,U_8894,U_8893,U_8892,U_8891] :
      ( ? [U_8888] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8894,U_8892)),hAPP(hAPP(c_Product__Type_OPair(U_8894,U_8892),sK146(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891)),U_8888)),U_8896))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_8891,U_8894)),hAPP(hAPP(c_Product__Type_OPair(U_8891,U_8894),sK145(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891)),sK146(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891))),U_8895))
          & U_8893 = hAPP(hAPP(c_Product__Type_OPair(U_8891,U_8892),sK145(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891)),U_8888) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8891,U_8892)),U_8893),hAPP(hAPP(c_Relation_Orel__comp(U_8891,U_8894,U_8892),U_8895),U_8896))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK146]),skolemize(U_8889,sK146(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891))],[f_2468_3]) ).

fof(f_2468_5,plain,
    ! [U_8896,U_8895,U_8894,U_8893,U_8892,U_8891] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8894,U_8892)),hAPP(hAPP(c_Product__Type_OPair(U_8894,U_8892),sK146(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891)),sK147(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891))),U_8896))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_8891,U_8894)),hAPP(hAPP(c_Product__Type_OPair(U_8891,U_8894),sK145(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891)),sK146(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891))),U_8895))
        & U_8893 = hAPP(hAPP(c_Product__Type_OPair(U_8891,U_8892),sK145(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891)),sK147(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8891,U_8892)),U_8893),hAPP(hAPP(c_Relation_Orel__comp(U_8891,U_8894,U_8892),U_8895),U_8896))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK147]),skolemize(U_8888,sK147(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891))],[f_2468_4]) ).

fof(f_2468_6,plain,
    ( ! [U_8891,U_8892,U_8893,U_8894,U_8895,U_8896] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8894,U_8892)),hAPP(hAPP(c_Product__Type_OPair(U_8894,U_8892),sK146(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891)),sK147(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891))),U_8896))
        | ~ sP721(U_8891,U_8892,U_8893,U_8894,U_8895,U_8896) )
    & ! [U_8891,U_8892,U_8893,U_8894,U_8895,U_8896] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8891,U_8894)),hAPP(hAPP(c_Product__Type_OPair(U_8891,U_8894),sK145(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891)),sK146(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891))),U_8895))
        | ~ sP721(U_8891,U_8892,U_8893,U_8894,U_8895,U_8896) )
    & ! [U_8891,U_8892,U_8893,U_8894,U_8895,U_8896] :
        ( U_8893 = hAPP(hAPP(c_Product__Type_OPair(U_8891,U_8892),sK145(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891)),sK147(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891))
        | ~ sP721(U_8891,U_8892,U_8893,U_8894,U_8895,U_8896) )
    & ! [U_8891,U_8892,U_8893,U_8894,U_8895,U_8896] :
        ( sP721(U_8891,U_8892,U_8893,U_8894,U_8895,U_8896)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8891,U_8892)),U_8893),hAPP(hAPP(c_Relation_Orel__comp(U_8891,U_8894,U_8892),U_8895),U_8896))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP721])],[f_2468_5]) ).

cnf(f_2468_7,plain,
    ( sP721(U_8891,U_8892,U_8893,U_8894,U_8895,U_8896)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_8891,U_8892)),U_8893),hAPP(hAPP(c_Relation_Orel__comp(U_8891,U_8894,U_8892),U_8895),U_8896))) ),
    inference(clausify,[status(thm)],[f_2468_6]) ).

cnf(f_2468_8,plain,
    ( U_8893 = hAPP(hAPP(c_Product__Type_OPair(U_8891,U_8892),sK145(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891)),sK147(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891))
    | ~ sP721(U_8891,U_8892,U_8893,U_8894,U_8895,U_8896) ),
    inference(clausify,[status(thm)],[f_2468_6]) ).

cnf(f_2468_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8891,U_8894)),hAPP(hAPP(c_Product__Type_OPair(U_8891,U_8894),sK145(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891)),sK146(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891))),U_8895))
    | ~ sP721(U_8891,U_8892,U_8893,U_8894,U_8895,U_8896) ),
    inference(clausify,[status(thm)],[f_2468_6]) ).

cnf(f_2468_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_8894,U_8892)),hAPP(hAPP(c_Product__Type_OPair(U_8894,U_8892),sK146(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891)),sK147(U_8896,U_8895,U_8894,U_8893,U_8892,U_8891))),U_8896))
    | ~ sP721(U_8891,U_8892,U_8893,U_8894,U_8895,U_8896) ),
    inference(clausify,[status(thm)],[f_2468_6]) ).

fof(f_2469_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),c_Predicate_Oconversep(T_b,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))) )
      & ( 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_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),c_Predicate_Oconversep(T_b,T_b,V_r_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_acyclicP__converse]) ).

fof(f_2469_2,plain,
    ! [U_8898,U_8897] :
      ( ( c_Wellfounded_Oacyclic(U_8897,hAPP(c_Set_OCollect(tc_prod(U_8897,U_8897)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8897,U_8897,tc_HOL_Obool),c_Predicate_Oconversep(U_8897,U_8897,U_8898))))
        | ~ c_Wellfounded_Oacyclic(U_8897,hAPP(c_Set_OCollect(tc_prod(U_8897,U_8897)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8897,U_8897,tc_HOL_Obool),U_8898))) )
      & ( c_Wellfounded_Oacyclic(U_8897,hAPP(c_Set_OCollect(tc_prod(U_8897,U_8897)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8897,U_8897,tc_HOL_Obool),U_8898)))
        | ~ c_Wellfounded_Oacyclic(U_8897,hAPP(c_Set_OCollect(tc_prod(U_8897,U_8897)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8897,U_8897,tc_HOL_Obool),c_Predicate_Oconversep(U_8897,U_8897,U_8898)))) ) ),
    inference(variable_rename,[status(thm)],[f_2469_1]) ).

fof(f_2469_3,plain,
    ( ! [U_8902,U_8900] :
        ( c_Wellfounded_Oacyclic(U_8900,hAPP(c_Set_OCollect(tc_prod(U_8900,U_8900)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8900,U_8900,tc_HOL_Obool),c_Predicate_Oconversep(U_8900,U_8900,U_8902))))
        | ~ c_Wellfounded_Oacyclic(U_8900,hAPP(c_Set_OCollect(tc_prod(U_8900,U_8900)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8900,U_8900,tc_HOL_Obool),U_8902))) )
    & ! [U_8901,U_8899] :
        ( c_Wellfounded_Oacyclic(U_8899,hAPP(c_Set_OCollect(tc_prod(U_8899,U_8899)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8899,U_8899,tc_HOL_Obool),U_8901)))
        | ~ c_Wellfounded_Oacyclic(U_8899,hAPP(c_Set_OCollect(tc_prod(U_8899,U_8899)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8899,U_8899,tc_HOL_Obool),c_Predicate_Oconversep(U_8899,U_8899,U_8901)))) ) ),
    inference(miniscope,[status(thm)],[f_2469_2]) ).

fof(f_2469_4,plain,
    ( ! [U_8902,U_8900] :
        ( c_Wellfounded_Oacyclic(U_8900,hAPP(c_Set_OCollect(tc_prod(U_8900,U_8900)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8900,U_8900,tc_HOL_Obool),c_Predicate_Oconversep(U_8900,U_8900,U_8902))))
        | ~ c_Wellfounded_Oacyclic(U_8900,hAPP(c_Set_OCollect(tc_prod(U_8900,U_8900)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8900,U_8900,tc_HOL_Obool),U_8902))) )
    & ! [U_8901,U_8899] :
        ( c_Wellfounded_Oacyclic(U_8899,hAPP(c_Set_OCollect(tc_prod(U_8899,U_8899)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8899,U_8899,tc_HOL_Obool),U_8901)))
        | ~ c_Wellfounded_Oacyclic(U_8899,hAPP(c_Set_OCollect(tc_prod(U_8899,U_8899)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8899,U_8899,tc_HOL_Obool),c_Predicate_Oconversep(U_8899,U_8899,U_8901)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2469_3]) ).

cnf(f_2469_5,plain,
    ( c_Wellfounded_Oacyclic(U_8899,hAPP(c_Set_OCollect(tc_prod(U_8899,U_8899)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8899,U_8899,tc_HOL_Obool),U_8901)))
    | ~ c_Wellfounded_Oacyclic(U_8899,hAPP(c_Set_OCollect(tc_prod(U_8899,U_8899)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8899,U_8899,tc_HOL_Obool),c_Predicate_Oconversep(U_8899,U_8899,U_8901)))) ),
    inference(clausify,[status(thm)],[f_2469_4]) ).

cnf(f_2469_6,plain,
    ( c_Wellfounded_Oacyclic(U_8900,hAPP(c_Set_OCollect(tc_prod(U_8900,U_8900)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8900,U_8900,tc_HOL_Obool),c_Predicate_Oconversep(U_8900,U_8900,U_8902))))
    | ~ c_Wellfounded_Oacyclic(U_8900,hAPP(c_Set_OCollect(tc_prod(U_8900,U_8900)),hAPP(c_Product__Type_Oprod_Oprod__case(U_8900,U_8900,tc_HOL_Obool),U_8902))) ),
    inference(clausify,[status(thm)],[f_2469_4]) ).

fof(f_2470_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_2470_2,plain,
    ! [U_8904,U_8903] : ~ hBOOL(hAPP(hAPP(c_member(U_8903),U_8904),c_Orderings_Obot__class_Obot(tc_fun(U_8903,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2470_1]) ).

fof(f_2470_3,plain,
    ! [U_8904,U_8903] : ~ hBOOL(hAPP(hAPP(c_member(U_8903),U_8904),c_Orderings_Obot__class_Obot(tc_fun(U_8903,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2470_2]) ).

cnf(f_2470_4,plain,
    ~ hBOOL(hAPP(hAPP(c_member(U_8903),U_8904),c_Orderings_Obot__class_Obot(tc_fun(U_8903,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2470_3]) ).

fof(f_2471_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_2471_2,plain,
    ! [U_8908,U_8907,U_8906,U_8905] :
      ( hBOOL(hAPP(hAPP(c_member(U_8905),U_8906),U_8908))
      | U_8906 = U_8907
      | ~ hBOOL(hAPP(hAPP(c_member(U_8905),U_8906),hAPP(hAPP(c_Set_Oinsert(U_8905),U_8907),U_8908))) ),
    inference(variable_rename,[status(thm)],[f_2471_1]) ).

fof(f_2471_3,plain,
    ! [U_8905,U_8906,U_8907,U_8908] :
      ( hBOOL(hAPP(hAPP(c_member(U_8905),U_8906),U_8908))
      | U_8906 = U_8907
      | ~ hBOOL(hAPP(hAPP(c_member(U_8905),U_8906),hAPP(hAPP(c_Set_Oinsert(U_8905),U_8907),U_8908))) ),
    inference(definitional_conversion,[status(esa)],[f_2471_2]) ).

cnf(f_2471_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8905),U_8906),U_8908))
    | U_8906 = U_8907
    | ~ hBOOL(hAPP(hAPP(c_member(U_8905),U_8906),hAPP(hAPP(c_Set_Oinsert(U_8905),U_8907),U_8908))) ),
    inference(clausify,[status(thm)],[f_2471_3]) ).

fof(f_2472_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_2472_2,plain,
    ! [U_8912,U_8911,U_8910,U_8909] :
      ( hBOOL(hAPP(hAPP(c_member(U_8909),U_8910),hAPP(hAPP(c_Set_Oinsert(U_8909),U_8912),U_8911)))
      | ( U_8910 != U_8912
        & ~ hBOOL(hAPP(hAPP(c_member(U_8909),U_8910),U_8911)) ) ),
    inference(variable_rename,[status(thm)],[f_2472_1]) ).

fof(f_2472_3,plain,
    ( ! [U_8909,U_8910,U_8911,U_8912] :
        ( U_8910 != U_8912
        | ~ sP722(U_8909,U_8910,U_8911,U_8912) )
    & ! [U_8909,U_8910,U_8911,U_8912] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_8909),U_8910),U_8911))
        | ~ sP722(U_8909,U_8910,U_8911,U_8912) )
    & ! [U_8909,U_8910,U_8911,U_8912] :
        ( hBOOL(hAPP(hAPP(c_member(U_8909),U_8910),hAPP(hAPP(c_Set_Oinsert(U_8909),U_8912),U_8911)))
        | sP722(U_8909,U_8910,U_8911,U_8912) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP722])],[f_2472_2]) ).

cnf(f_2472_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_8909),U_8910),hAPP(hAPP(c_Set_Oinsert(U_8909),U_8912),U_8911)))
    | sP722(U_8909,U_8910,U_8911,U_8912) ),
    inference(clausify,[status(thm)],[f_2472_3]) ).

cnf(f_2472_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_8909),U_8910),U_8911))
    | ~ sP722(U_8909,U_8910,U_8911,U_8912) ),
    inference(clausify,[status(thm)],[f_2472_3]) ).

cnf(f_2472_6,plain,
    ( U_8910 != U_8912
    | ~ sP722(U_8909,U_8910,U_8911,U_8912) ),
    inference(clausify,[status(thm)],[f_2472_3]) ).

fof(f_2473_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_2473_2,plain,
    ! [U_8914,U_8913] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8913,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_8913,tc_HOL_Obool))),U_8914)),
    inference(variable_rename,[status(thm)],[f_2473_1]) ).

fof(f_2473_3,plain,
    ! [U_8914,U_8913] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8913,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_8913,tc_HOL_Obool))),U_8914)),
    inference(definitional_conversion,[status(esa)],[f_2473_2]) ).

cnf(f_2473_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_8913,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_8913,tc_HOL_Obool))),U_8914)),
    inference(clausify,[status(thm)],[f_2473_3]) ).

fof(f_2474_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_2474_2,plain,
    ! [U_8916,U_8915] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8915,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_8915,tc_HOL_Obool))),U_8916) = U_8916,
    inference(variable_rename,[status(thm)],[f_2474_1]) ).

fof(f_2474_3,plain,
    ! [U_8915,U_8916] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8915,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_8915,tc_HOL_Obool))),U_8916) = U_8916,
    inference(definitional_conversion,[status(esa)],[f_2474_2]) ).

cnf(f_2474_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8915,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_8915,tc_HOL_Obool))),U_8916) = U_8916,
    inference(clausify,[status(thm)],[f_2474_3]) ).

fof(f_2475_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_2475_2,plain,
    ! [U_8918,U_8917] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8917,tc_HOL_Obool)),U_8918),c_Orderings_Obot__class_Obot(tc_fun(U_8917,tc_HOL_Obool))) = U_8918,
    inference(variable_rename,[status(thm)],[f_2475_1]) ).

fof(f_2475_3,plain,
    ! [U_8917,U_8918] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8917,tc_HOL_Obool)),U_8918),c_Orderings_Obot__class_Obot(tc_fun(U_8917,tc_HOL_Obool))) = U_8918,
    inference(definitional_conversion,[status(esa)],[f_2475_2]) ).

cnf(f_2475_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8917,tc_HOL_Obool)),U_8918),c_Orderings_Obot__class_Obot(tc_fun(U_8917,tc_HOL_Obool))) = U_8918,
    inference(clausify,[status(thm)],[f_2475_3]) ).

fof(f_2476_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_2476_2,plain,
    ! [U_8921,U_8920,U_8919] : hAPP(hAPP(c_Set_Oinsert(U_8919),U_8920),U_8921) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8919,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8919),U_8920),c_Orderings_Obot__class_Obot(tc_fun(U_8919,tc_HOL_Obool)))),U_8921),
    inference(variable_rename,[status(thm)],[f_2476_1]) ).

fof(f_2476_3,plain,
    ! [U_8919,U_8920,U_8921] : hAPP(hAPP(c_Set_Oinsert(U_8919),U_8920),U_8921) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8919,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8919),U_8920),c_Orderings_Obot__class_Obot(tc_fun(U_8919,tc_HOL_Obool)))),U_8921),
    inference(definitional_conversion,[status(esa)],[f_2476_2]) ).

cnf(f_2476_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_8919),U_8920),U_8921) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8919,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8919),U_8920),c_Orderings_Obot__class_Obot(tc_fun(U_8919,tc_HOL_Obool)))),U_8921),
    inference(clausify,[status(thm)],[f_2476_3]) ).

fof(f_2477_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_2477_2,plain,
    ! [U_8925,U_8924,U_8923,U_8922] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8922,tc_HOL_Obool)),U_8923),hAPP(hAPP(c_Set_Oinsert(U_8922),U_8924),U_8925)) = hAPP(hAPP(c_Set_Oinsert(U_8922),U_8924),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8922,tc_HOL_Obool)),U_8923),U_8925)),
    inference(variable_rename,[status(thm)],[f_2477_1]) ).

fof(f_2477_3,plain,
    ! [U_8922,U_8923,U_8924,U_8925] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8922,tc_HOL_Obool)),U_8923),hAPP(hAPP(c_Set_Oinsert(U_8922),U_8924),U_8925)) = hAPP(hAPP(c_Set_Oinsert(U_8922),U_8924),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8922,tc_HOL_Obool)),U_8923),U_8925)),
    inference(definitional_conversion,[status(esa)],[f_2477_2]) ).

cnf(f_2477_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8922,tc_HOL_Obool)),U_8923),hAPP(hAPP(c_Set_Oinsert(U_8922),U_8924),U_8925)) = hAPP(hAPP(c_Set_Oinsert(U_8922),U_8924),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8922,tc_HOL_Obool)),U_8923),U_8925)),
    inference(clausify,[status(thm)],[f_2477_3]) ).

fof(f_2478_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_2478_2,plain,
    ! [U_8928,U_8927,U_8926] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8926,tc_HOL_Obool)),U_8927),U_8928) = c_Orderings_Obot__class_Obot(tc_fun(U_8926,tc_HOL_Obool))
        | U_8928 != c_Orderings_Obot__class_Obot(tc_fun(U_8926,tc_HOL_Obool))
        | U_8927 != c_Orderings_Obot__class_Obot(tc_fun(U_8926,tc_HOL_Obool)) )
      & ( ( U_8928 = c_Orderings_Obot__class_Obot(tc_fun(U_8926,tc_HOL_Obool))
          & U_8927 = c_Orderings_Obot__class_Obot(tc_fun(U_8926,tc_HOL_Obool)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8926,tc_HOL_Obool)),U_8927),U_8928) != c_Orderings_Obot__class_Obot(tc_fun(U_8926,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2478_1]) ).

fof(f_2478_3,plain,
    ( ! [U_8934,U_8932,U_8930] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8930,tc_HOL_Obool)),U_8932),U_8934) = c_Orderings_Obot__class_Obot(tc_fun(U_8930,tc_HOL_Obool))
        | U_8934 != c_Orderings_Obot__class_Obot(tc_fun(U_8930,tc_HOL_Obool))
        | U_8932 != c_Orderings_Obot__class_Obot(tc_fun(U_8930,tc_HOL_Obool)) )
    & ! [U_8933,U_8931,U_8929] :
        ( ( U_8933 = c_Orderings_Obot__class_Obot(tc_fun(U_8929,tc_HOL_Obool))
          & U_8931 = c_Orderings_Obot__class_Obot(tc_fun(U_8929,tc_HOL_Obool)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8929,tc_HOL_Obool)),U_8931),U_8933) != c_Orderings_Obot__class_Obot(tc_fun(U_8929,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2478_2]) ).

fof(f_2478_4,plain,
    ( ! [U_8931,U_8929,U_8933] :
        ( U_8933 = c_Orderings_Obot__class_Obot(tc_fun(U_8929,tc_HOL_Obool))
        | ~ sP723(U_8931,U_8929,U_8933) )
    & ! [U_8931,U_8929,U_8933] :
        ( U_8931 = c_Orderings_Obot__class_Obot(tc_fun(U_8929,tc_HOL_Obool))
        | ~ sP723(U_8931,U_8929,U_8933) )
    & ! [U_8934,U_8932,U_8930] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8930,tc_HOL_Obool)),U_8932),U_8934) = c_Orderings_Obot__class_Obot(tc_fun(U_8930,tc_HOL_Obool))
        | U_8934 != c_Orderings_Obot__class_Obot(tc_fun(U_8930,tc_HOL_Obool))
        | U_8932 != c_Orderings_Obot__class_Obot(tc_fun(U_8930,tc_HOL_Obool)) )
    & ! [U_8931,U_8929,U_8933] :
        ( sP723(U_8931,U_8929,U_8933)
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8929,tc_HOL_Obool)),U_8931),U_8933) != c_Orderings_Obot__class_Obot(tc_fun(U_8929,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP723])],[f_2478_3]) ).

cnf(f_2478_5,plain,
    ( sP723(U_8931,U_8929,U_8933)
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8929,tc_HOL_Obool)),U_8931),U_8933) != c_Orderings_Obot__class_Obot(tc_fun(U_8929,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2478_4]) ).

cnf(f_2478_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8930,tc_HOL_Obool)),U_8932),U_8934) = c_Orderings_Obot__class_Obot(tc_fun(U_8930,tc_HOL_Obool))
    | U_8934 != c_Orderings_Obot__class_Obot(tc_fun(U_8930,tc_HOL_Obool))
    | U_8932 != c_Orderings_Obot__class_Obot(tc_fun(U_8930,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2478_4]) ).

cnf(f_2478_7,plain,
    ( U_8931 = c_Orderings_Obot__class_Obot(tc_fun(U_8929,tc_HOL_Obool))
    | ~ sP723(U_8931,U_8929,U_8933) ),
    inference(clausify,[status(thm)],[f_2478_4]) ).

cnf(f_2478_8,plain,
    ( U_8933 = c_Orderings_Obot__class_Obot(tc_fun(U_8929,tc_HOL_Obool))
    | ~ sP723(U_8931,U_8929,U_8933) ),
    inference(clausify,[status(thm)],[f_2478_4]) ).

fof(f_2479_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_2479_2,plain,
    ! [U_8938,U_8937,U_8936,U_8935] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8935,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8935),U_8936),U_8937)),U_8938) = hAPP(hAPP(c_Set_Oinsert(U_8935),U_8936),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8935,tc_HOL_Obool)),U_8937),U_8938)),
    inference(variable_rename,[status(thm)],[f_2479_1]) ).

fof(f_2479_3,plain,
    ! [U_8935,U_8936,U_8937,U_8938] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8935,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8935),U_8936),U_8937)),U_8938) = hAPP(hAPP(c_Set_Oinsert(U_8935),U_8936),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8935,tc_HOL_Obool)),U_8937),U_8938)),
    inference(definitional_conversion,[status(esa)],[f_2479_2]) ).

cnf(f_2479_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8935,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8935),U_8936),U_8937)),U_8938) = hAPP(hAPP(c_Set_Oinsert(U_8935),U_8936),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8935,tc_HOL_Obool)),U_8937),U_8938)),
    inference(clausify,[status(thm)],[f_2479_3]) ).

fof(f_2480_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_2480_2,plain,
    ! [U_8942,U_8941,U_8940,U_8939] : hAPP(c_Relation_OField(U_8939),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_8939,U_8939)),hAPP(hAPP(c_Product__Type_OPair(U_8939,U_8939),U_8940),U_8941)),U_8942)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8939,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8939),U_8940),hAPP(hAPP(c_Set_Oinsert(U_8939),U_8941),c_Orderings_Obot__class_Obot(tc_fun(U_8939,tc_HOL_Obool))))),hAPP(c_Relation_OField(U_8939),U_8942)),
    inference(variable_rename,[status(thm)],[f_2480_1]) ).

fof(f_2480_3,plain,
    ! [U_8939,U_8940,U_8941,U_8942] : hAPP(c_Relation_OField(U_8939),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_8939,U_8939)),hAPP(hAPP(c_Product__Type_OPair(U_8939,U_8939),U_8940),U_8941)),U_8942)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8939,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8939),U_8940),hAPP(hAPP(c_Set_Oinsert(U_8939),U_8941),c_Orderings_Obot__class_Obot(tc_fun(U_8939,tc_HOL_Obool))))),hAPP(c_Relation_OField(U_8939),U_8942)),
    inference(definitional_conversion,[status(esa)],[f_2480_2]) ).

cnf(f_2480_4,plain,
    hAPP(c_Relation_OField(U_8939),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_8939,U_8939)),hAPP(hAPP(c_Product__Type_OPair(U_8939,U_8939),U_8940),U_8941)),U_8942)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_8939,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_8939),U_8940),hAPP(hAPP(c_Set_Oinsert(U_8939),U_8941),c_Orderings_Obot__class_Obot(tc_fun(U_8939,tc_HOL_Obool))))),hAPP(c_Relation_OField(U_8939),U_8942)),
    inference(clausify,[status(thm)],[f_2480_3]) ).

fof(f_2481_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_2481_2,plain,
    ! [U_8946,U_8945,U_8944,U_8943] :
      ( ( hAPP(c_Set_Oimage(U_8943,U_8944,U_8945),U_8946) = c_Orderings_Obot__class_Obot(tc_fun(U_8944,tc_HOL_Obool))
        | U_8946 != c_Orderings_Obot__class_Obot(tc_fun(U_8943,tc_HOL_Obool)) )
      & ( U_8946 = c_Orderings_Obot__class_Obot(tc_fun(U_8943,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(U_8943,U_8944,U_8945),U_8946) != c_Orderings_Obot__class_Obot(tc_fun(U_8944,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2481_1]) ).

fof(f_2481_3,plain,
    ( ! [U_8954,U_8952,U_8950,U_8948] :
        ( hAPP(c_Set_Oimage(U_8948,U_8950,U_8952),U_8954) = c_Orderings_Obot__class_Obot(tc_fun(U_8950,tc_HOL_Obool))
        | U_8954 != c_Orderings_Obot__class_Obot(tc_fun(U_8948,tc_HOL_Obool)) )
    & ! [U_8953,U_8951,U_8949,U_8947] :
        ( U_8953 = c_Orderings_Obot__class_Obot(tc_fun(U_8947,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(U_8947,U_8949,U_8951),U_8953) != c_Orderings_Obot__class_Obot(tc_fun(U_8949,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2481_2]) ).

fof(f_2481_4,plain,
    ( ! [U_8948,U_8954,U_8950,U_8952] :
        ( hAPP(c_Set_Oimage(U_8948,U_8950,U_8952),U_8954) = c_Orderings_Obot__class_Obot(tc_fun(U_8950,tc_HOL_Obool))
        | U_8954 != c_Orderings_Obot__class_Obot(tc_fun(U_8948,tc_HOL_Obool)) )
    & ! [U_8951,U_8953,U_8949,U_8947] :
        ( U_8953 = c_Orderings_Obot__class_Obot(tc_fun(U_8947,tc_HOL_Obool))
        | hAPP(c_Set_Oimage(U_8947,U_8949,U_8951),U_8953) != c_Orderings_Obot__class_Obot(tc_fun(U_8949,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2481_3]) ).

cnf(f_2481_5,plain,
    ( U_8953 = c_Orderings_Obot__class_Obot(tc_fun(U_8947,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_8947,U_8949,U_8951),U_8953) != c_Orderings_Obot__class_Obot(tc_fun(U_8949,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2481_4]) ).

cnf(f_2481_6,plain,
    ( hAPP(c_Set_Oimage(U_8948,U_8950,U_8952),U_8954) = c_Orderings_Obot__class_Obot(tc_fun(U_8950,tc_HOL_Obool))
    | U_8954 != c_Orderings_Obot__class_Obot(tc_fun(U_8948,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2481_4]) ).

fof(f_2482_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_2482_2,plain,
    ! [U_8957,U_8956,U_8955] : hAPP(c_Set_Oimage(U_8955,U_8956,U_8957),c_Orderings_Obot__class_Obot(tc_fun(U_8955,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_8956,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2482_1]) ).

fof(f_2482_3,plain,
    ! [U_8955,U_8956,U_8957] : hAPP(c_Set_Oimage(U_8955,U_8956,U_8957),c_Orderings_Obot__class_Obot(tc_fun(U_8955,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_8956,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2482_2]) ).

cnf(f_2482_4,plain,
    hAPP(c_Set_Oimage(U_8955,U_8956,U_8957),c_Orderings_Obot__class_Obot(tc_fun(U_8955,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_8956,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2482_3]) ).

fof(f_2483_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_2483_2,plain,
    ! [U_8961,U_8960,U_8959,U_8958] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_8958,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_8959,U_8958,U_8960),U_8961)
        | U_8961 != c_Orderings_Obot__class_Obot(tc_fun(U_8959,tc_HOL_Obool)) )
      & ( U_8961 = c_Orderings_Obot__class_Obot(tc_fun(U_8959,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(U_8958,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_8959,U_8958,U_8960),U_8961) ) ),
    inference(variable_rename,[status(thm)],[f_2483_1]) ).

fof(f_2483_3,plain,
    ( ! [U_8969,U_8967,U_8965] :
        ( ! [U_8963] : c_Orderings_Obot__class_Obot(tc_fun(U_8963,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_8965,U_8963,U_8967),U_8969)
        | U_8969 != c_Orderings_Obot__class_Obot(tc_fun(U_8965,tc_HOL_Obool)) )
    & ! [U_8968,U_8966,U_8964] :
        ( ! [U_8962] : c_Orderings_Obot__class_Obot(tc_fun(U_8962,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_8964,U_8962,U_8966),U_8968)
        | U_8968 = c_Orderings_Obot__class_Obot(tc_fun(U_8964,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2483_2]) ).

fof(f_2483_4,plain,
    ( ! [U_8969,U_8967,U_8963,U_8965] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_8963,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_8965,U_8963,U_8967),U_8969)
        | U_8969 != c_Orderings_Obot__class_Obot(tc_fun(U_8965,tc_HOL_Obool)) )
    & ! [U_8966,U_8964,U_8962,U_8968] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_8962,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_8964,U_8962,U_8966),U_8968)
        | U_8968 = c_Orderings_Obot__class_Obot(tc_fun(U_8964,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2483_3]) ).

cnf(f_2483_5,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_8962,tc_HOL_Obool)) != hAPP(c_Set_Oimage(U_8964,U_8962,U_8966),U_8968)
    | U_8968 = c_Orderings_Obot__class_Obot(tc_fun(U_8964,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2483_4]) ).

cnf(f_2483_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_8963,tc_HOL_Obool)) = hAPP(c_Set_Oimage(U_8965,U_8963,U_8967),U_8969)
    | U_8969 != c_Orderings_Obot__class_Obot(tc_fun(U_8965,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2483_4]) ).

fof(f_2484_1,plain,
    ! [V_ts_2,V_t_2,V_Ga_2,T_b] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_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_ts_2)) ),
    inference(fof_nnf,[status(thm)],[fact_derivs__insertD]) ).

fof(f_2484_2,plain,
    ! [U_8973,U_8972,U_8971,U_8970] :
      ( ( c_Hoare__Mirabelle_Ohoare__derivs(U_8970,U_8971,U_8973)
        & c_Hoare__Mirabelle_Ohoare__derivs(U_8970,U_8971,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8970)),U_8972),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8970),tc_HOL_Obool)))) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8970,U_8971,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8970)),U_8972),U_8973)) ),
    inference(variable_rename,[status(thm)],[f_2484_1]) ).

fof(f_2484_3,plain,
    ( ! [U_8970,U_8971,U_8972,U_8973] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(U_8970,U_8971,U_8973)
        | ~ sP724(U_8970,U_8971,U_8972,U_8973) )
    & ! [U_8970,U_8971,U_8972,U_8973] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(U_8970,U_8971,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8970)),U_8972),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8970),tc_HOL_Obool))))
        | ~ sP724(U_8970,U_8971,U_8972,U_8973) )
    & ! [U_8970,U_8971,U_8972,U_8973] :
        ( sP724(U_8970,U_8971,U_8972,U_8973)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8970,U_8971,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8970)),U_8972),U_8973)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP724])],[f_2484_2]) ).

cnf(f_2484_4,plain,
    ( sP724(U_8970,U_8971,U_8972,U_8973)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8970,U_8971,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8970)),U_8972),U_8973)) ),
    inference(clausify,[status(thm)],[f_2484_3]) ).

cnf(f_2484_5,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_8970,U_8971,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8970)),U_8972),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8970),tc_HOL_Obool))))
    | ~ sP724(U_8970,U_8971,U_8972,U_8973) ),
    inference(clausify,[status(thm)],[f_2484_3]) ).

cnf(f_2484_6,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_8970,U_8971,U_8973)
    | ~ sP724(U_8970,U_8971,U_8972,U_8973) ),
    inference(clausify,[status(thm)],[f_2484_3]) ).

fof(f_2485_1,plain,
    ! [V_ts_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_ts_2))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(T_b,V_Ga_2,V_ts_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_2485_2,plain,
    ! [U_8977,U_8976,U_8975,U_8974] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8974,U_8975,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8974)),U_8976),U_8977))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8974,U_8975,U_8977)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8974,U_8975,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8974)),U_8976),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8974),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2485_1]) ).

fof(f_2485_3,plain,
    ! [U_8974,U_8975,U_8976,U_8977] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_8974,U_8975,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8974)),U_8976),U_8977))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8974,U_8975,U_8977)
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8974,U_8975,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8974)),U_8976),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8974),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_2485_2]) ).

cnf(f_2485_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_8974,U_8975,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8974)),U_8976),U_8977))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8974,U_8975,U_8977)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_8974,U_8975,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_8974)),U_8976),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8974),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2485_3]) ).

fof(f_2486_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_2486_2,plain,
    ! [U_8979,U_8978] : c_Hoare__Mirabelle_Ohoare__derivs(U_8978,U_8979,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8978),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2486_1]) ).

fof(f_2486_3,plain,
    ! [U_8979,U_8978] : c_Hoare__Mirabelle_Ohoare__derivs(U_8978,U_8979,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8978),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2486_2]) ).

cnf(f_2486_4,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_8978,U_8979,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8978),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2486_3]) ).

fof(f_2487_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_2487_2,plain,
    ! [U_8981,U_8980] : c_Hoare__Mirabelle_Ohoare__derivs(U_8980,U_8981,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8980),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2487_1]) ).

fof(f_2487_3,plain,
    ! [U_8980,U_8981] : c_Hoare__Mirabelle_Ohoare__derivs(U_8980,U_8981,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8980),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2487_2]) ).

cnf(f_2487_4,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_8980,U_8981,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_8980),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2487_3]) ).

fof(f_2488_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_2488_2,plain,
    ! [U_8986,U_8985,U_8984,U_8983,U_8982] : hAPP(c_Set_Oimage(U_8982,U_8983,U_8984),hAPP(hAPP(c_Set_Oinsert(U_8982),U_8985),U_8986)) = hAPP(hAPP(c_Set_Oinsert(U_8983),hAPP(U_8984,U_8985)),hAPP(c_Set_Oimage(U_8982,U_8983,U_8984),U_8986)),
    inference(variable_rename,[status(thm)],[f_2488_1]) ).

fof(f_2488_3,plain,
    ! [U_8982,U_8983,U_8984,U_8985,U_8986] : hAPP(c_Set_Oimage(U_8982,U_8983,U_8984),hAPP(hAPP(c_Set_Oinsert(U_8982),U_8985),U_8986)) = hAPP(hAPP(c_Set_Oinsert(U_8983),hAPP(U_8984,U_8985)),hAPP(c_Set_Oimage(U_8982,U_8983,U_8984),U_8986)),
    inference(definitional_conversion,[status(esa)],[f_2488_2]) ).

cnf(f_2488_4,plain,
    hAPP(c_Set_Oimage(U_8982,U_8983,U_8984),hAPP(hAPP(c_Set_Oinsert(U_8982),U_8985),U_8986)) = hAPP(hAPP(c_Set_Oinsert(U_8983),hAPP(U_8984,U_8985)),hAPP(c_Set_Oimage(U_8982,U_8983,U_8984),U_8986)),
    inference(clausify,[status(thm)],[f_2488_3]) ).

fof(f_2489_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_2489_2,plain,
    ! [U_8990,U_8989,U_8988,U_8987] :
      ( ( hAPP(c_Set_Oimage(U_8988,U_8989,hAPP(c_COMBK(U_8989,U_8988),U_8990)),U_8987) = hAPP(hAPP(c_Set_Oinsert(U_8989),U_8990),c_Orderings_Obot__class_Obot(tc_fun(U_8989,tc_HOL_Obool)))
        | U_8987 = c_Orderings_Obot__class_Obot(tc_fun(U_8988,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(U_8988,U_8989,hAPP(c_COMBK(U_8989,U_8988),U_8990)),U_8987) = c_Orderings_Obot__class_Obot(tc_fun(U_8989,tc_HOL_Obool))
        | U_8987 != c_Orderings_Obot__class_Obot(tc_fun(U_8988,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2489_1]) ).

fof(f_2489_3,plain,
    ( ! [U_8998,U_8996,U_8994,U_8992] :
        ( hAPP(c_Set_Oimage(U_8994,U_8996,hAPP(c_COMBK(U_8996,U_8994),U_8998)),U_8992) = hAPP(hAPP(c_Set_Oinsert(U_8996),U_8998),c_Orderings_Obot__class_Obot(tc_fun(U_8996,tc_HOL_Obool)))
        | U_8992 = c_Orderings_Obot__class_Obot(tc_fun(U_8994,tc_HOL_Obool)) )
    & ! [U_8997,U_8995,U_8993,U_8991] :
        ( hAPP(c_Set_Oimage(U_8993,U_8995,hAPP(c_COMBK(U_8995,U_8993),U_8997)),U_8991) = c_Orderings_Obot__class_Obot(tc_fun(U_8995,tc_HOL_Obool))
        | U_8991 != c_Orderings_Obot__class_Obot(tc_fun(U_8993,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2489_2]) ).

fof(f_2489_4,plain,
    ( ! [U_8998,U_8992,U_8994,U_8996] :
        ( hAPP(c_Set_Oimage(U_8994,U_8996,hAPP(c_COMBK(U_8996,U_8994),U_8998)),U_8992) = hAPP(hAPP(c_Set_Oinsert(U_8996),U_8998),c_Orderings_Obot__class_Obot(tc_fun(U_8996,tc_HOL_Obool)))
        | U_8992 = c_Orderings_Obot__class_Obot(tc_fun(U_8994,tc_HOL_Obool)) )
    & ! [U_8993,U_8995,U_8997,U_8991] :
        ( hAPP(c_Set_Oimage(U_8993,U_8995,hAPP(c_COMBK(U_8995,U_8993),U_8997)),U_8991) = c_Orderings_Obot__class_Obot(tc_fun(U_8995,tc_HOL_Obool))
        | U_8991 != c_Orderings_Obot__class_Obot(tc_fun(U_8993,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2489_3]) ).

cnf(f_2489_5,plain,
    ( hAPP(c_Set_Oimage(U_8993,U_8995,hAPP(c_COMBK(U_8995,U_8993),U_8997)),U_8991) = c_Orderings_Obot__class_Obot(tc_fun(U_8995,tc_HOL_Obool))
    | U_8991 != c_Orderings_Obot__class_Obot(tc_fun(U_8993,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2489_4]) ).

cnf(f_2489_6,plain,
    ( hAPP(c_Set_Oimage(U_8994,U_8996,hAPP(c_COMBK(U_8996,U_8994),U_8998)),U_8992) = hAPP(hAPP(c_Set_Oinsert(U_8996),U_8998),c_Orderings_Obot__class_Obot(tc_fun(U_8996,tc_HOL_Obool)))
    | U_8992 = c_Orderings_Obot__class_Obot(tc_fun(U_8994,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2489_4]) ).

fof(f_2490_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_2490_2,plain,
    ! [U_9003,U_9002,U_9001,U_9000,U_8999] :
      ( hAPP(c_Set_Oimage(U_8999,U_9002,hAPP(c_COMBK(U_9002,U_8999),U_9003)),U_9001) = hAPP(hAPP(c_Set_Oinsert(U_9002),U_9003),c_Orderings_Obot__class_Obot(tc_fun(U_9002,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8999),U_9000),U_9001)) ),
    inference(variable_rename,[status(thm)],[f_2490_1]) ).

fof(f_2490_3,plain,
    ! [U_9000,U_8999,U_9001,U_9002,U_9003] :
      ( hAPP(c_Set_Oimage(U_8999,U_9002,hAPP(c_COMBK(U_9002,U_8999),U_9003)),U_9001) = hAPP(hAPP(c_Set_Oinsert(U_9002),U_9003),c_Orderings_Obot__class_Obot(tc_fun(U_9002,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_8999),U_9000),U_9001)) ),
    inference(definitional_conversion,[status(esa)],[f_2490_2]) ).

cnf(f_2490_4,plain,
    ( hAPP(c_Set_Oimage(U_8999,U_9002,hAPP(c_COMBK(U_9002,U_8999),U_9003)),U_9001) = hAPP(hAPP(c_Set_Oinsert(U_9002),U_9003),c_Orderings_Obot__class_Obot(tc_fun(U_9002,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_8999),U_9000),U_9001)) ),
    inference(clausify,[status(thm)],[f_2490_3]) ).

fof(f_2491_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_2491_2,plain,
    ! [U_9004] : c_Relation_OId__on(U_9004,c_Orderings_Obot__class_Obot(tc_fun(U_9004,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9004,U_9004),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2491_1]) ).

fof(f_2491_3,plain,
    ! [U_9004] : c_Relation_OId__on(U_9004,c_Orderings_Obot__class_Obot(tc_fun(U_9004,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9004,U_9004),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2491_2]) ).

cnf(f_2491_4,plain,
    c_Relation_OId__on(U_9004,c_Orderings_Obot__class_Obot(tc_fun(U_9004,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9004,U_9004),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2491_3]) ).

fof(f_2492_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_2492_2,plain,
    ! [U_9006,U_9005] : hAPP(c_Relation_ORange(U_9005,U_9006),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9005,U_9006),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9006,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2492_1]) ).

fof(f_2492_3,plain,
    ! [U_9005,U_9006] : hAPP(c_Relation_ORange(U_9005,U_9006),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9005,U_9006),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9006,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2492_2]) ).

cnf(f_2492_4,plain,
    hAPP(c_Relation_ORange(U_9005,U_9006),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9005,U_9006),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9006,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2492_3]) ).

fof(f_2493_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_2493_2,plain,
    ! [U_9009,U_9008,U_9007] :
      ( ( hAPP(c_Relation_ORange(U_9007,U_9008),U_9009) = c_Orderings_Obot__class_Obot(tc_fun(U_9008,tc_HOL_Obool))
        | U_9009 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9007,U_9008),tc_HOL_Obool)) )
      & ( U_9009 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9007,U_9008),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(U_9007,U_9008),U_9009) != c_Orderings_Obot__class_Obot(tc_fun(U_9008,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2493_1]) ).

fof(f_2493_3,plain,
    ( ! [U_9015,U_9013,U_9011] :
        ( hAPP(c_Relation_ORange(U_9011,U_9013),U_9015) = c_Orderings_Obot__class_Obot(tc_fun(U_9013,tc_HOL_Obool))
        | U_9015 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9011,U_9013),tc_HOL_Obool)) )
    & ! [U_9014,U_9012,U_9010] :
        ( U_9014 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9010,U_9012),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(U_9010,U_9012),U_9014) != c_Orderings_Obot__class_Obot(tc_fun(U_9012,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2493_2]) ).

fof(f_2493_4,plain,
    ( ! [U_9015,U_9011,U_9013] :
        ( hAPP(c_Relation_ORange(U_9011,U_9013),U_9015) = c_Orderings_Obot__class_Obot(tc_fun(U_9013,tc_HOL_Obool))
        | U_9015 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9011,U_9013),tc_HOL_Obool)) )
    & ! [U_9012,U_9010,U_9014] :
        ( U_9014 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9010,U_9012),tc_HOL_Obool))
        | hAPP(c_Relation_ORange(U_9010,U_9012),U_9014) != c_Orderings_Obot__class_Obot(tc_fun(U_9012,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2493_3]) ).

cnf(f_2493_5,plain,
    ( U_9014 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9010,U_9012),tc_HOL_Obool))
    | hAPP(c_Relation_ORange(U_9010,U_9012),U_9014) != c_Orderings_Obot__class_Obot(tc_fun(U_9012,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2493_4]) ).

cnf(f_2493_6,plain,
    ( hAPP(c_Relation_ORange(U_9011,U_9013),U_9015) = c_Orderings_Obot__class_Obot(tc_fun(U_9013,tc_HOL_Obool))
    | U_9015 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9011,U_9013),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2493_4]) ).

fof(f_2494_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_2494_2,plain,
    ! [U_9020,U_9019,U_9018,U_9017,U_9016] : hAPP(c_Relation_ORange(U_9016,U_9017),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_9016,U_9017)),hAPP(hAPP(c_Product__Type_OPair(U_9016,U_9017),U_9018),U_9019)),U_9020)) = hAPP(hAPP(c_Set_Oinsert(U_9017),U_9019),hAPP(c_Relation_ORange(U_9016,U_9017),U_9020)),
    inference(variable_rename,[status(thm)],[f_2494_1]) ).

fof(f_2494_3,plain,
    ! [U_9016,U_9017,U_9018,U_9019,U_9020] : hAPP(c_Relation_ORange(U_9016,U_9017),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_9016,U_9017)),hAPP(hAPP(c_Product__Type_OPair(U_9016,U_9017),U_9018),U_9019)),U_9020)) = hAPP(hAPP(c_Set_Oinsert(U_9017),U_9019),hAPP(c_Relation_ORange(U_9016,U_9017),U_9020)),
    inference(definitional_conversion,[status(esa)],[f_2494_2]) ).

cnf(f_2494_4,plain,
    hAPP(c_Relation_ORange(U_9016,U_9017),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_9016,U_9017)),hAPP(hAPP(c_Product__Type_OPair(U_9016,U_9017),U_9018),U_9019)),U_9020)) = hAPP(hAPP(c_Set_Oinsert(U_9017),U_9019),hAPP(c_Relation_ORange(U_9016,U_9017),U_9020)),
    inference(clausify,[status(thm)],[f_2494_3]) ).

fof(f_2495_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_2495_2,plain,
    ! [U_9022,U_9021] : c_Option_Oset(U_9021,hAPP(c_Option_Ooption_OSome(U_9021),U_9022)) = hAPP(hAPP(c_Set_Oinsert(U_9021),U_9022),c_Orderings_Obot__class_Obot(tc_fun(U_9021,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2495_1]) ).

fof(f_2495_3,plain,
    ! [U_9021,U_9022] : c_Option_Oset(U_9021,hAPP(c_Option_Ooption_OSome(U_9021),U_9022)) = hAPP(hAPP(c_Set_Oinsert(U_9021),U_9022),c_Orderings_Obot__class_Obot(tc_fun(U_9021,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2495_2]) ).

cnf(f_2495_4,plain,
    c_Option_Oset(U_9021,hAPP(c_Option_Ooption_OSome(U_9021),U_9022)) = hAPP(hAPP(c_Set_Oinsert(U_9021),U_9022),c_Orderings_Obot__class_Obot(tc_fun(U_9021,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2495_3]) ).

fof(f_2496_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_2496_2,plain,
    ! [U_9026,U_9025] :
      ( ( ! [U_9024] : ~ hBOOL(hAPP(hAPP(c_member(U_9025),U_9024),U_9026))
        | U_9026 != c_Orderings_Obot__class_Obot(tc_fun(U_9025,tc_HOL_Obool)) )
      & ( U_9026 = c_Orderings_Obot__class_Obot(tc_fun(U_9025,tc_HOL_Obool))
        | ? [U_9023] : hBOOL(hAPP(hAPP(c_member(U_9025),U_9023),U_9026)) ) ),
    inference(variable_rename,[status(thm)],[f_2496_1]) ).

fof(f_2496_3,plain,
    ( ! [U_9030,U_9028] :
        ( ! [U_9024] : ~ hBOOL(hAPP(hAPP(c_member(U_9028),U_9024),U_9030))
        | U_9030 != c_Orderings_Obot__class_Obot(tc_fun(U_9028,tc_HOL_Obool)) )
    & ! [U_9029,U_9027] :
        ( U_9029 = c_Orderings_Obot__class_Obot(tc_fun(U_9027,tc_HOL_Obool))
        | ? [U_9023] : hBOOL(hAPP(hAPP(c_member(U_9027),U_9023),U_9029)) ) ),
    inference(miniscope,[status(thm)],[f_2496_2]) ).

fof(f_2496_4,plain,
    ( ! [U_9030,U_9028] :
        ( ! [U_9024] : ~ hBOOL(hAPP(hAPP(c_member(U_9028),U_9024),U_9030))
        | U_9030 != c_Orderings_Obot__class_Obot(tc_fun(U_9028,tc_HOL_Obool)) )
    & ! [U_9029,U_9027] :
        ( U_9029 = c_Orderings_Obot__class_Obot(tc_fun(U_9027,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_9027),sK148(U_9029,U_9027)),U_9029)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK148]),skolemize(U_9023,sK148(U_9029,U_9027))],[f_2496_3]) ).

fof(f_2496_5,plain,
    ( ! [U_9024,U_9028,U_9030] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_9028),U_9024),U_9030))
        | U_9030 != c_Orderings_Obot__class_Obot(tc_fun(U_9028,tc_HOL_Obool)) )
    & ! [U_9029,U_9027] :
        ( U_9029 = c_Orderings_Obot__class_Obot(tc_fun(U_9027,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_9027),sK148(U_9029,U_9027)),U_9029)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2496_4]) ).

cnf(f_2496_6,plain,
    ( U_9029 = c_Orderings_Obot__class_Obot(tc_fun(U_9027,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_9027),sK148(U_9029,U_9027)),U_9029)) ),
    inference(clausify,[status(thm)],[f_2496_5]) ).

cnf(f_2496_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9028),U_9024),U_9030))
    | U_9030 != c_Orderings_Obot__class_Obot(tc_fun(U_9028,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2496_5]) ).

fof(f_2497_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_2497_2,plain,
    ! [U_9034,U_9033] :
      ( ( ? [U_9032] : hBOOL(hAPP(hAPP(c_member(U_9033),U_9032),U_9034))
        | U_9034 = c_Orderings_Obot__class_Obot(tc_fun(U_9033,tc_HOL_Obool)) )
      & ( U_9034 != c_Orderings_Obot__class_Obot(tc_fun(U_9033,tc_HOL_Obool))
        | ! [U_9031] : ~ hBOOL(hAPP(hAPP(c_member(U_9033),U_9031),U_9034)) ) ),
    inference(variable_rename,[status(thm)],[f_2497_1]) ).

fof(f_2497_3,plain,
    ( ! [U_9038,U_9036] :
        ( ? [U_9032] : hBOOL(hAPP(hAPP(c_member(U_9036),U_9032),U_9038))
        | U_9038 = c_Orderings_Obot__class_Obot(tc_fun(U_9036,tc_HOL_Obool)) )
    & ! [U_9037,U_9035] :
        ( U_9037 != c_Orderings_Obot__class_Obot(tc_fun(U_9035,tc_HOL_Obool))
        | ! [U_9031] : ~ hBOOL(hAPP(hAPP(c_member(U_9035),U_9031),U_9037)) ) ),
    inference(miniscope,[status(thm)],[f_2497_2]) ).

fof(f_2497_4,plain,
    ( ! [U_9038,U_9036] :
        ( hBOOL(hAPP(hAPP(c_member(U_9036),sK149(U_9038,U_9036)),U_9038))
        | U_9038 = c_Orderings_Obot__class_Obot(tc_fun(U_9036,tc_HOL_Obool)) )
    & ! [U_9037,U_9035] :
        ( U_9037 != c_Orderings_Obot__class_Obot(tc_fun(U_9035,tc_HOL_Obool))
        | ! [U_9031] : ~ hBOOL(hAPP(hAPP(c_member(U_9035),U_9031),U_9037)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK149]),skolemize(U_9032,sK149(U_9038,U_9036))],[f_2497_3]) ).

fof(f_2497_5,plain,
    ( ! [U_9036,U_9038] :
        ( hBOOL(hAPP(hAPP(c_member(U_9036),sK149(U_9038,U_9036)),U_9038))
        | U_9038 = c_Orderings_Obot__class_Obot(tc_fun(U_9036,tc_HOL_Obool)) )
    & ! [U_9031,U_9037,U_9035] :
        ( U_9037 != c_Orderings_Obot__class_Obot(tc_fun(U_9035,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9035),U_9031),U_9037)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2497_4]) ).

cnf(f_2497_6,plain,
    ( U_9037 != c_Orderings_Obot__class_Obot(tc_fun(U_9035,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9035),U_9031),U_9037)) ),
    inference(clausify,[status(thm)],[f_2497_5]) ).

cnf(f_2497_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9036),sK149(U_9038,U_9036)),U_9038))
    | U_9038 = c_Orderings_Obot__class_Obot(tc_fun(U_9036,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2497_5]) ).

fof(f_2498_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_2498_2,plain,
    ! [U_9040,U_9039] : ~ hBOOL(hAPP(hAPP(c_member(U_9039),U_9040),c_Orderings_Obot__class_Obot(tc_fun(U_9039,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2498_1]) ).

fof(f_2498_3,plain,
    ! [U_9039,U_9040] : ~ hBOOL(hAPP(hAPP(c_member(U_9039),U_9040),c_Orderings_Obot__class_Obot(tc_fun(U_9039,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2498_2]) ).

cnf(f_2498_4,plain,
    ~ hBOOL(hAPP(hAPP(c_member(U_9039),U_9040),c_Orderings_Obot__class_Obot(tc_fun(U_9039,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2498_3]) ).

fof(f_2499_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_2499_2,plain,
    ! [U_9043,U_9042,U_9041] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_9042),U_9043),U_9041))
      | U_9041 != c_Orderings_Obot__class_Obot(tc_fun(U_9042,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2499_1]) ).

fof(f_2499_3,plain,
    ! [U_9041,U_9042,U_9043] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_9042),U_9043),U_9041))
      | U_9041 != c_Orderings_Obot__class_Obot(tc_fun(U_9042,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_2499_2]) ).

cnf(f_2499_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9042),U_9043),U_9041))
    | U_9041 != c_Orderings_Obot__class_Obot(tc_fun(U_9042,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2499_3]) ).

fof(f_2500_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_2500_2,plain,
    ! [U_9046,U_9045,U_9044] : hBOOL(hAPP(hAPP(c_member(U_9044),U_9045),hAPP(hAPP(c_Set_Oinsert(U_9044),U_9045),U_9046))),
    inference(variable_rename,[status(thm)],[f_2500_1]) ).

fof(f_2500_3,plain,
    ! [U_9044,U_9045,U_9046] : hBOOL(hAPP(hAPP(c_member(U_9044),U_9045),hAPP(hAPP(c_Set_Oinsert(U_9044),U_9045),U_9046))),
    inference(definitional_conversion,[status(esa)],[f_2500_2]) ).

cnf(f_2500_4,plain,
    hBOOL(hAPP(hAPP(c_member(U_9044),U_9045),hAPP(hAPP(c_Set_Oinsert(U_9044),U_9045),U_9046))),
    inference(clausify,[status(thm)],[f_2500_3]) ).

fof(f_2501_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_2501_2,plain,
    ! [U_9050,U_9049,U_9048,U_9047] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9047),U_9048),hAPP(hAPP(c_Set_Oinsert(U_9047),U_9049),U_9050)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_9047),U_9048),U_9050))
          & U_9048 != U_9049 ) )
      & ( hBOOL(hAPP(hAPP(c_member(U_9047),U_9048),U_9050))
        | U_9048 = U_9049
        | ~ hBOOL(hAPP(hAPP(c_member(U_9047),U_9048),hAPP(hAPP(c_Set_Oinsert(U_9047),U_9049),U_9050))) ) ),
    inference(variable_rename,[status(thm)],[f_2501_1]) ).

fof(f_2501_3,plain,
    ( ! [U_9058,U_9056,U_9054,U_9052] :
        ( hBOOL(hAPP(hAPP(c_member(U_9052),U_9054),hAPP(hAPP(c_Set_Oinsert(U_9052),U_9056),U_9058)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_9052),U_9054),U_9058))
          & U_9054 != U_9056 ) )
    & ! [U_9057,U_9055,U_9053,U_9051] :
        ( hBOOL(hAPP(hAPP(c_member(U_9051),U_9053),U_9057))
        | U_9053 = U_9055
        | ~ hBOOL(hAPP(hAPP(c_member(U_9051),U_9053),hAPP(hAPP(c_Set_Oinsert(U_9051),U_9055),U_9057))) ) ),
    inference(miniscope,[status(thm)],[f_2501_2]) ).

fof(f_2501_4,plain,
    ( ! [U_9054,U_9056,U_9058,U_9052] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_9052),U_9054),U_9058))
        | ~ sP725(U_9054,U_9056,U_9058,U_9052) )
    & ! [U_9054,U_9056,U_9058,U_9052] :
        ( U_9054 != U_9056
        | ~ sP725(U_9054,U_9056,U_9058,U_9052) )
    & ! [U_9054,U_9056,U_9058,U_9052] :
        ( hBOOL(hAPP(hAPP(c_member(U_9052),U_9054),hAPP(hAPP(c_Set_Oinsert(U_9052),U_9056),U_9058)))
        | sP725(U_9054,U_9056,U_9058,U_9052) )
    & ! [U_9053,U_9055,U_9051,U_9057] :
        ( hBOOL(hAPP(hAPP(c_member(U_9051),U_9053),U_9057))
        | U_9053 = U_9055
        | ~ hBOOL(hAPP(hAPP(c_member(U_9051),U_9053),hAPP(hAPP(c_Set_Oinsert(U_9051),U_9055),U_9057))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP725])],[f_2501_3]) ).

cnf(f_2501_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9051),U_9053),U_9057))
    | U_9053 = U_9055
    | ~ hBOOL(hAPP(hAPP(c_member(U_9051),U_9053),hAPP(hAPP(c_Set_Oinsert(U_9051),U_9055),U_9057))) ),
    inference(clausify,[status(thm)],[f_2501_4]) ).

cnf(f_2501_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9052),U_9054),hAPP(hAPP(c_Set_Oinsert(U_9052),U_9056),U_9058)))
    | sP725(U_9054,U_9056,U_9058,U_9052) ),
    inference(clausify,[status(thm)],[f_2501_4]) ).

cnf(f_2501_7,plain,
    ( U_9054 != U_9056
    | ~ sP725(U_9054,U_9056,U_9058,U_9052) ),
    inference(clausify,[status(thm)],[f_2501_4]) ).

cnf(f_2501_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9052),U_9054),U_9058))
    | ~ sP725(U_9054,U_9056,U_9058,U_9052) ),
    inference(clausify,[status(thm)],[f_2501_4]) ).

fof(f_2502_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_2502_2,plain,
    ! [U_9062,U_9061,U_9060,U_9059] :
      ( ( ( hAPP(hAPP(c_Set_Oinsert(U_9059),U_9060),U_9061) = hAPP(hAPP(c_Set_Oinsert(U_9059),U_9060),U_9062)
          | U_9061 != U_9062 )
        & ( U_9061 = U_9062
          | hAPP(hAPP(c_Set_Oinsert(U_9059),U_9060),U_9061) != hAPP(hAPP(c_Set_Oinsert(U_9059),U_9060),U_9062) ) )
      | hBOOL(hAPP(hAPP(c_member(U_9059),U_9060),U_9062))
      | hBOOL(hAPP(hAPP(c_member(U_9059),U_9060),U_9061)) ),
    inference(variable_rename,[status(thm)],[f_2502_1]) ).

fof(f_2502_3,plain,
    ( ! [U_9060,U_9059,U_9061,U_9062] :
        ( hAPP(hAPP(c_Set_Oinsert(U_9059),U_9060),U_9061) = hAPP(hAPP(c_Set_Oinsert(U_9059),U_9060),U_9062)
        | U_9061 != U_9062
        | ~ sP726(U_9060,U_9059,U_9061,U_9062) )
    & ! [U_9060,U_9059,U_9061,U_9062] :
        ( U_9061 = U_9062
        | hAPP(hAPP(c_Set_Oinsert(U_9059),U_9060),U_9061) != hAPP(hAPP(c_Set_Oinsert(U_9059),U_9060),U_9062)
        | ~ sP726(U_9060,U_9059,U_9061,U_9062) )
    & ! [U_9060,U_9059,U_9061,U_9062] :
        ( sP726(U_9060,U_9059,U_9061,U_9062)
        | hBOOL(hAPP(hAPP(c_member(U_9059),U_9060),U_9062))
        | hBOOL(hAPP(hAPP(c_member(U_9059),U_9060),U_9061)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP726])],[f_2502_2]) ).

cnf(f_2502_4,plain,
    ( sP726(U_9060,U_9059,U_9061,U_9062)
    | hBOOL(hAPP(hAPP(c_member(U_9059),U_9060),U_9062))
    | hBOOL(hAPP(hAPP(c_member(U_9059),U_9060),U_9061)) ),
    inference(clausify,[status(thm)],[f_2502_3]) ).

cnf(f_2502_5,plain,
    ( U_9061 = U_9062
    | hAPP(hAPP(c_Set_Oinsert(U_9059),U_9060),U_9061) != hAPP(hAPP(c_Set_Oinsert(U_9059),U_9060),U_9062)
    | ~ sP726(U_9060,U_9059,U_9061,U_9062) ),
    inference(clausify,[status(thm)],[f_2502_3]) ).

cnf(f_2502_6,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_9059),U_9060),U_9061) = hAPP(hAPP(c_Set_Oinsert(U_9059),U_9060),U_9062)
    | U_9061 != U_9062
    | ~ sP726(U_9060,U_9059,U_9061,U_9062) ),
    inference(clausify,[status(thm)],[f_2502_3]) ).

fof(f_2503_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_2503_2,plain,
    ! [U_9066,U_9065,U_9064,U_9063] :
      ( hBOOL(hAPP(hAPP(c_member(U_9063),U_9064),hAPP(hAPP(c_Set_Oinsert(U_9063),U_9066),U_9065)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9063),U_9064),U_9065)) ),
    inference(variable_rename,[status(thm)],[f_2503_1]) ).

fof(f_2503_3,plain,
    ! [U_9064,U_9065,U_9063,U_9066] :
      ( hBOOL(hAPP(hAPP(c_member(U_9063),U_9064),hAPP(hAPP(c_Set_Oinsert(U_9063),U_9066),U_9065)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9063),U_9064),U_9065)) ),
    inference(definitional_conversion,[status(esa)],[f_2503_2]) ).

cnf(f_2503_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9063),U_9064),hAPP(hAPP(c_Set_Oinsert(U_9063),U_9066),U_9065)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9063),U_9064),U_9065)) ),
    inference(clausify,[status(thm)],[f_2503_3]) ).

fof(f_2504_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_2504_2,plain,
    ! [U_9069,U_9068,U_9067] :
      ( hAPP(hAPP(c_Set_Oinsert(U_9067),U_9068),U_9069) = U_9069
      | ~ hBOOL(hAPP(hAPP(c_member(U_9067),U_9068),U_9069)) ),
    inference(variable_rename,[status(thm)],[f_2504_1]) ).

fof(f_2504_3,plain,
    ! [U_9067,U_9069,U_9068] :
      ( hAPP(hAPP(c_Set_Oinsert(U_9067),U_9068),U_9069) = U_9069
      | ~ hBOOL(hAPP(hAPP(c_member(U_9067),U_9068),U_9069)) ),
    inference(definitional_conversion,[status(esa)],[f_2504_2]) ).

cnf(f_2504_4,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_9067),U_9068),U_9069) = U_9069
    | ~ hBOOL(hAPP(hAPP(c_member(U_9067),U_9068),U_9069)) ),
    inference(clausify,[status(thm)],[f_2504_3]) ).

fof(f_2505_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_2505_2,plain,
    ! [U_9072,U_9071,U_9070] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_9070),U_9071),hAPP(hAPP(c_Set_Oinsert(U_9070),U_9072),c_Orderings_Obot__class_Obot(tc_fun(U_9070,tc_HOL_Obool)))))
        | U_9071 != U_9072 )
      & ( U_9071 = U_9072
        | ~ hBOOL(hAPP(hAPP(c_member(U_9070),U_9071),hAPP(hAPP(c_Set_Oinsert(U_9070),U_9072),c_Orderings_Obot__class_Obot(tc_fun(U_9070,tc_HOL_Obool))))) ) ),
    inference(variable_rename,[status(thm)],[f_2505_1]) ).

fof(f_2505_3,plain,
    ( ! [U_9078,U_9076] :
        ( ! [U_9074] : hBOOL(hAPP(hAPP(c_member(U_9074),U_9076),hAPP(hAPP(c_Set_Oinsert(U_9074),U_9078),c_Orderings_Obot__class_Obot(tc_fun(U_9074,tc_HOL_Obool)))))
        | U_9076 != U_9078 )
    & ! [U_9077,U_9075] :
        ( ! [U_9073] : ~ hBOOL(hAPP(hAPP(c_member(U_9073),U_9075),hAPP(hAPP(c_Set_Oinsert(U_9073),U_9077),c_Orderings_Obot__class_Obot(tc_fun(U_9073,tc_HOL_Obool)))))
        | U_9075 = U_9077 ) ),
    inference(miniscope,[status(thm)],[f_2505_2]) ).

fof(f_2505_4,plain,
    ( ! [U_9078,U_9074,U_9076] :
        ( hBOOL(hAPP(hAPP(c_member(U_9074),U_9076),hAPP(hAPP(c_Set_Oinsert(U_9074),U_9078),c_Orderings_Obot__class_Obot(tc_fun(U_9074,tc_HOL_Obool)))))
        | U_9076 != U_9078 )
    & ! [U_9073,U_9075,U_9077] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_9073),U_9075),hAPP(hAPP(c_Set_Oinsert(U_9073),U_9077),c_Orderings_Obot__class_Obot(tc_fun(U_9073,tc_HOL_Obool)))))
        | U_9075 = U_9077 ) ),
    inference(definitional_conversion,[status(esa)],[f_2505_3]) ).

cnf(f_2505_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9073),U_9075),hAPP(hAPP(c_Set_Oinsert(U_9073),U_9077),c_Orderings_Obot__class_Obot(tc_fun(U_9073,tc_HOL_Obool)))))
    | U_9075 = U_9077 ),
    inference(clausify,[status(thm)],[f_2505_4]) ).

cnf(f_2505_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9074),U_9076),hAPP(hAPP(c_Set_Oinsert(U_9074),U_9078),c_Orderings_Obot__class_Obot(tc_fun(U_9074,tc_HOL_Obool)))))
    | U_9076 != U_9078 ),
    inference(clausify,[status(thm)],[f_2505_4]) ).

fof(f_2506_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_2506_2,plain,
    ! [U_9081,U_9080,U_9079] :
      ( U_9080 = U_9081
      | ~ hBOOL(hAPP(hAPP(c_member(U_9079),U_9080),hAPP(hAPP(c_Set_Oinsert(U_9079),U_9081),c_Orderings_Obot__class_Obot(tc_fun(U_9079,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_2506_1]) ).

fof(f_2506_3,plain,
    ! [U_9081,U_9080] :
      ( ! [U_9079] : ~ hBOOL(hAPP(hAPP(c_member(U_9079),U_9080),hAPP(hAPP(c_Set_Oinsert(U_9079),U_9081),c_Orderings_Obot__class_Obot(tc_fun(U_9079,tc_HOL_Obool)))))
      | U_9080 = U_9081 ),
    inference(miniscope,[status(thm)],[f_2506_2]) ).

fof(f_2506_4,plain,
    ! [U_9079,U_9080,U_9081] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_9079),U_9080),hAPP(hAPP(c_Set_Oinsert(U_9079),U_9081),c_Orderings_Obot__class_Obot(tc_fun(U_9079,tc_HOL_Obool)))))
      | U_9080 = U_9081 ),
    inference(definitional_conversion,[status(esa)],[f_2506_3]) ).

cnf(f_2506_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9079),U_9080),hAPP(hAPP(c_Set_Oinsert(U_9079),U_9081),c_Orderings_Obot__class_Obot(tc_fun(U_9079,tc_HOL_Obool)))))
    | U_9080 = U_9081 ),
    inference(clausify,[status(thm)],[f_2506_4]) ).

fof(f_2507_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_2507_2,plain,
    ! [U_9084,U_9083,U_9082] :
      ( U_9083 = hAPP(hAPP(c_Set_Oinsert(U_9082),U_9084),c_Orderings_Obot__class_Obot(tc_fun(U_9082,tc_HOL_Obool)))
      | U_9083 = c_Orderings_Obot__class_Obot(tc_fun(U_9082,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9082,tc_HOL_Obool)),U_9083),hAPP(hAPP(c_Set_Oinsert(U_9082),U_9084),c_Orderings_Obot__class_Obot(tc_fun(U_9082,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_2507_1]) ).

fof(f_2507_3,plain,
    ! [U_9082,U_9083,U_9084] :
      ( U_9083 = hAPP(hAPP(c_Set_Oinsert(U_9082),U_9084),c_Orderings_Obot__class_Obot(tc_fun(U_9082,tc_HOL_Obool)))
      | U_9083 = c_Orderings_Obot__class_Obot(tc_fun(U_9082,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9082,tc_HOL_Obool)),U_9083),hAPP(hAPP(c_Set_Oinsert(U_9082),U_9084),c_Orderings_Obot__class_Obot(tc_fun(U_9082,tc_HOL_Obool))))) ),
    inference(definitional_conversion,[status(esa)],[f_2507_2]) ).

cnf(f_2507_4,plain,
    ( U_9083 = hAPP(hAPP(c_Set_Oinsert(U_9082),U_9084),c_Orderings_Obot__class_Obot(tc_fun(U_9082,tc_HOL_Obool)))
    | U_9083 = c_Orderings_Obot__class_Obot(tc_fun(U_9082,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9082,tc_HOL_Obool)),U_9083),hAPP(hAPP(c_Set_Oinsert(U_9082),U_9084),c_Orderings_Obot__class_Obot(tc_fun(U_9082,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_2507_3]) ).

fof(f_2508_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_2508_2,plain,
    ! [U_9087,U_9086,U_9085] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9085,tc_HOL_Obool)),U_9086),hAPP(hAPP(c_Set_Oinsert(U_9085),U_9087),U_9086))),
    inference(variable_rename,[status(thm)],[f_2508_1]) ).

fof(f_2508_3,plain,
    ! [U_9085,U_9086,U_9087] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9085,tc_HOL_Obool)),U_9086),hAPP(hAPP(c_Set_Oinsert(U_9085),U_9087),U_9086))),
    inference(definitional_conversion,[status(esa)],[f_2508_2]) ).

cnf(f_2508_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9085,tc_HOL_Obool)),U_9086),hAPP(hAPP(c_Set_Oinsert(U_9085),U_9087),U_9086))),
    inference(clausify,[status(thm)],[f_2508_3]) ).

fof(f_2509_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_2509_2,plain,
    ! [U_9091,U_9090,U_9089,U_9088] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9088,tc_HOL_Obool)),U_9089),hAPP(hAPP(c_Set_Oinsert(U_9088),U_9091),U_9090)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9088,tc_HOL_Obool)),U_9089),U_9090)) ),
    inference(variable_rename,[status(thm)],[f_2509_1]) ).

fof(f_2509_3,plain,
    ! [U_9088,U_9089,U_9090,U_9091] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9088,tc_HOL_Obool)),U_9089),hAPP(hAPP(c_Set_Oinsert(U_9088),U_9091),U_9090)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9088,tc_HOL_Obool)),U_9089),U_9090)) ),
    inference(definitional_conversion,[status(esa)],[f_2509_2]) ).

cnf(f_2509_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9088,tc_HOL_Obool)),U_9089),hAPP(hAPP(c_Set_Oinsert(U_9088),U_9091),U_9090)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9088,tc_HOL_Obool)),U_9089),U_9090)) ),
    inference(clausify,[status(thm)],[f_2509_3]) ).

fof(f_2510_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_2510_2,plain,
    ! [U_9095,U_9094,U_9093,U_9092] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9092,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9092),U_9095),U_9093)),hAPP(hAPP(c_Set_Oinsert(U_9092),U_9095),U_9094)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9092,tc_HOL_Obool)),U_9093),U_9094)) ),
    inference(variable_rename,[status(thm)],[f_2510_1]) ).

fof(f_2510_3,plain,
    ! [U_9092,U_9093,U_9094,U_9095] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9092,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9092),U_9095),U_9093)),hAPP(hAPP(c_Set_Oinsert(U_9092),U_9095),U_9094)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9092,tc_HOL_Obool)),U_9093),U_9094)) ),
    inference(definitional_conversion,[status(esa)],[f_2510_2]) ).

cnf(f_2510_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9092,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9092),U_9095),U_9093)),hAPP(hAPP(c_Set_Oinsert(U_9092),U_9095),U_9094)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9092,tc_HOL_Obool)),U_9093),U_9094)) ),
    inference(clausify,[status(thm)],[f_2510_3]) ).

fof(f_2511_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_2511_2,plain,
    ! [U_9098,U_9097,U_9096] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9097,U_9096)),U_9098) = c_Orderings_Obot__class_Obot(U_9096)
      | ~ class_Orderings_Obot(U_9096) ),
    inference(variable_rename,[status(thm)],[f_2511_1]) ).

fof(f_2511_3,plain,
    ! [U_9096,U_9097,U_9098] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9097,U_9096)),U_9098) = c_Orderings_Obot__class_Obot(U_9096)
      | ~ class_Orderings_Obot(U_9096) ),
    inference(definitional_conversion,[status(esa)],[f_2511_2]) ).

cnf(f_2511_4,plain,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9097,U_9096)),U_9098) = c_Orderings_Obot__class_Obot(U_9096)
    | ~ class_Orderings_Obot(U_9096) ),
    inference(clausify,[status(thm)],[f_2511_3]) ).

fof(f_2512_1,plain,
    ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
      ( hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2))
      | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_conversepD]) ).

fof(f_2512_2,plain,
    ! [U_9103,U_9102,U_9101,U_9100,U_9099] :
      ( hBOOL(hAPP(hAPP(U_9101,U_9103),U_9102))
      | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9099,U_9100,U_9101),U_9102),U_9103)) ),
    inference(variable_rename,[status(thm)],[f_2512_1]) ).

fof(f_2512_3,plain,
    ! [U_9103,U_9102,U_9101] :
      ( ! [U_9100,U_9099] : ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9099,U_9100,U_9101),U_9102),U_9103))
      | hBOOL(hAPP(hAPP(U_9101,U_9103),U_9102)) ),
    inference(miniscope,[status(thm)],[f_2512_2]) ).

fof(f_2512_4,plain,
    ! [U_9099,U_9100,U_9101,U_9102,U_9103] :
      ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9099,U_9100,U_9101),U_9102),U_9103))
      | hBOOL(hAPP(hAPP(U_9101,U_9103),U_9102)) ),
    inference(definitional_conversion,[status(esa)],[f_2512_3]) ).

cnf(f_2512_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9099,U_9100,U_9101),U_9102),U_9103))
    | hBOOL(hAPP(hAPP(U_9101,U_9103),U_9102)) ),
    inference(clausify,[status(thm)],[f_2512_4]) ).

fof(f_2513_1,plain,
    ! [T_c,T_b,V_b_2,V_a_2,V_r_2] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_b_2),V_a_2))
      | ~ hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) ),
    inference(fof_nnf,[status(thm)],[fact_conversep_Ointros]) ).

fof(f_2513_2,plain,
    ! [U_9108,U_9107,U_9106,U_9105,U_9104] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9107,U_9108,U_9104),U_9106),U_9105))
      | ~ hBOOL(hAPP(hAPP(U_9104,U_9105),U_9106)) ),
    inference(variable_rename,[status(thm)],[f_2513_1]) ).

fof(f_2513_3,plain,
    ! [U_9104,U_9105,U_9106,U_9107,U_9108] :
      ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9107,U_9108,U_9104),U_9106),U_9105))
      | ~ hBOOL(hAPP(hAPP(U_9104,U_9105),U_9106)) ),
    inference(definitional_conversion,[status(esa)],[f_2513_2]) ).

cnf(f_2513_4,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9107,U_9108,U_9104),U_9106),U_9105))
    | ~ hBOOL(hAPP(hAPP(U_9104,U_9105),U_9106)) ),
    inference(clausify,[status(thm)],[f_2513_3]) ).

fof(f_2514_1,plain,
    ! [V_a1_2,V_a2_2,V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2))
        | ~ hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) )
      & ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a2_2),V_a1_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_conversep_Oequations]) ).

fof(f_2514_2,plain,
    ! [U_9113,U_9112,U_9111,U_9110,U_9109] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9109,U_9110,U_9111),U_9112),U_9113))
        | ~ hBOOL(hAPP(hAPP(U_9111,U_9113),U_9112)) )
      & ( hBOOL(hAPP(hAPP(U_9111,U_9113),U_9112))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9109,U_9110,U_9111),U_9112),U_9113)) ) ),
    inference(variable_rename,[status(thm)],[f_2514_1]) ).

fof(f_2514_3,plain,
    ( ! [U_9123,U_9121,U_9119] :
        ( ! [U_9117,U_9115] : hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9115,U_9117,U_9119),U_9121),U_9123))
        | ~ hBOOL(hAPP(hAPP(U_9119,U_9123),U_9121)) )
    & ! [U_9122,U_9120,U_9118] :
        ( ! [U_9116,U_9114] : ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9114,U_9116,U_9118),U_9120),U_9122))
        | hBOOL(hAPP(hAPP(U_9118,U_9122),U_9120)) ) ),
    inference(miniscope,[status(thm)],[f_2514_2]) ).

fof(f_2514_4,plain,
    ( ! [U_9115,U_9117,U_9119,U_9121,U_9123] :
        ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9115,U_9117,U_9119),U_9121),U_9123))
        | ~ hBOOL(hAPP(hAPP(U_9119,U_9123),U_9121)) )
    & ! [U_9118,U_9122,U_9114,U_9116,U_9120] :
        ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9114,U_9116,U_9118),U_9120),U_9122))
        | hBOOL(hAPP(hAPP(U_9118,U_9122),U_9120)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2514_3]) ).

cnf(f_2514_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9114,U_9116,U_9118),U_9120),U_9122))
    | hBOOL(hAPP(hAPP(U_9118,U_9122),U_9120)) ),
    inference(clausify,[status(thm)],[f_2514_4]) ).

cnf(f_2514_6,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9115,U_9117,U_9119),U_9121),U_9123))
    | ~ hBOOL(hAPP(hAPP(U_9119,U_9123),U_9121)) ),
    inference(clausify,[status(thm)],[f_2514_4]) ).

fof(f_2515_1,plain,
    ! [V_b_2,V_a_2,V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2))
        | ~ hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) )
      & ( hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_c,V_r_2),V_a_2),V_b_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_conversep__iff]) ).

fof(f_2515_2,plain,
    ! [U_9128,U_9127,U_9126,U_9125,U_9124] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9124,U_9125,U_9126),U_9127),U_9128))
        | ~ hBOOL(hAPP(hAPP(U_9126,U_9128),U_9127)) )
      & ( hBOOL(hAPP(hAPP(U_9126,U_9128),U_9127))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9124,U_9125,U_9126),U_9127),U_9128)) ) ),
    inference(variable_rename,[status(thm)],[f_2515_1]) ).

fof(f_2515_3,plain,
    ( ! [U_9138,U_9136,U_9134] :
        ( ! [U_9132,U_9130] : hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9130,U_9132,U_9134),U_9136),U_9138))
        | ~ hBOOL(hAPP(hAPP(U_9134,U_9138),U_9136)) )
    & ! [U_9137,U_9135,U_9133] :
        ( ! [U_9131,U_9129] : ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9129,U_9131,U_9133),U_9135),U_9137))
        | hBOOL(hAPP(hAPP(U_9133,U_9137),U_9135)) ) ),
    inference(miniscope,[status(thm)],[f_2515_2]) ).

fof(f_2515_4,plain,
    ( ! [U_9130,U_9132,U_9134,U_9136,U_9138] :
        ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9130,U_9132,U_9134),U_9136),U_9138))
        | ~ hBOOL(hAPP(hAPP(U_9134,U_9138),U_9136)) )
    & ! [U_9137,U_9133,U_9131,U_9129,U_9135] :
        ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9129,U_9131,U_9133),U_9135),U_9137))
        | hBOOL(hAPP(hAPP(U_9133,U_9137),U_9135)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2515_3]) ).

cnf(f_2515_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9129,U_9131,U_9133),U_9135),U_9137))
    | hBOOL(hAPP(hAPP(U_9133,U_9137),U_9135)) ),
    inference(clausify,[status(thm)],[f_2515_4]) ).

cnf(f_2515_6,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9130,U_9132,U_9134),U_9136),U_9138))
    | ~ hBOOL(hAPP(hAPP(U_9134,U_9138),U_9136)) ),
    inference(clausify,[status(thm)],[f_2515_4]) ).

fof(f_2516_1,plain,
    ! [V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Oconversep(T_b,T_c,V_r_2)) = V_r_2,
    inference(fof_nnf,[status(thm)],[fact_conversep__conversep]) ).

fof(f_2516_2,plain,
    ! [U_9141,U_9140,U_9139] : c_Predicate_Oconversep(U_9139,U_9140,c_Predicate_Oconversep(U_9140,U_9139,U_9141)) = U_9141,
    inference(variable_rename,[status(thm)],[f_2516_1]) ).

fof(f_2516_3,plain,
    ! [U_9141,U_9140,U_9139] : c_Predicate_Oconversep(U_9139,U_9140,c_Predicate_Oconversep(U_9140,U_9139,U_9141)) = U_9141,
    inference(definitional_conversion,[status(esa)],[f_2516_2]) ).

cnf(f_2516_4,plain,
    c_Predicate_Oconversep(U_9139,U_9140,c_Predicate_Oconversep(U_9140,U_9139,U_9141)) = U_9141,
    inference(clausify,[status(thm)],[f_2516_3]) ).

fof(f_2517_1,plain,
    ! [T_b] : c_Predicate_Oconversep(T_b,T_b,c_fequal) = c_fequal,
    inference(fof_nnf,[status(thm)],[fact_conversep__eq]) ).

fof(f_2517_2,plain,
    ! [U_9142] : c_Predicate_Oconversep(U_9142,U_9142,c_fequal) = c_fequal,
    inference(variable_rename,[status(thm)],[f_2517_1]) ).

fof(f_2517_3,plain,
    ! [U_9142] : c_Predicate_Oconversep(U_9142,U_9142,c_fequal) = c_fequal,
    inference(definitional_conversion,[status(esa)],[f_2517_2]) ).

cnf(f_2517_4,plain,
    c_Predicate_Oconversep(U_9142,U_9142,c_fequal) = c_fequal,
    inference(clausify,[status(thm)],[f_2517_3]) ).

fof(f_2518_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_2518_2,plain,
    ! [U_9145,U_9144,U_9143] :
      ( U_9144 = U_9145
      | hAPP(hAPP(c_Set_Oinsert(U_9143),U_9144),c_Orderings_Obot__class_Obot(tc_fun(U_9143,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_9143),U_9145),c_Orderings_Obot__class_Obot(tc_fun(U_9143,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_2518_1]) ).

fof(f_2518_3,plain,
    ! [U_9145,U_9144] :
      ( ! [U_9143] : hAPP(hAPP(c_Set_Oinsert(U_9143),U_9144),c_Orderings_Obot__class_Obot(tc_fun(U_9143,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_9143),U_9145),c_Orderings_Obot__class_Obot(tc_fun(U_9143,tc_HOL_Obool)))
      | U_9144 = U_9145 ),
    inference(miniscope,[status(thm)],[f_2518_2]) ).

fof(f_2518_4,plain,
    ! [U_9143,U_9144,U_9145] :
      ( hAPP(hAPP(c_Set_Oinsert(U_9143),U_9144),c_Orderings_Obot__class_Obot(tc_fun(U_9143,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_9143),U_9145),c_Orderings_Obot__class_Obot(tc_fun(U_9143,tc_HOL_Obool)))
      | U_9144 = U_9145 ),
    inference(definitional_conversion,[status(esa)],[f_2518_3]) ).

cnf(f_2518_5,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_9143),U_9144),c_Orderings_Obot__class_Obot(tc_fun(U_9143,tc_HOL_Obool))) != hAPP(hAPP(c_Set_Oinsert(U_9143),U_9145),c_Orderings_Obot__class_Obot(tc_fun(U_9143,tc_HOL_Obool)))
    | U_9144 = U_9145 ),
    inference(clausify,[status(thm)],[f_2518_4]) ).

fof(f_2519_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_2519_2,plain,
    ! [U_9149,U_9148,U_9147,U_9146] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_9146),U_9147),U_9148),U_9149))
        | ( ~ hBOOL(hAPP(U_9148,U_9149))
          & U_9147 != U_9149 ) )
      & ( hBOOL(hAPP(U_9148,U_9149))
        | U_9147 = U_9149
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_9146),U_9147),U_9148),U_9149)) ) ),
    inference(variable_rename,[status(thm)],[f_2519_1]) ).

fof(f_2519_3,plain,
    ( ! [U_9157,U_9155,U_9153] :
        ( ! [U_9151] : hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_9151),U_9153),U_9155),U_9157))
        | ( ~ hBOOL(hAPP(U_9155,U_9157))
          & U_9153 != U_9157 ) )
    & ! [U_9156,U_9154,U_9152] :
        ( ! [U_9150] : ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_9150),U_9152),U_9154),U_9156))
        | hBOOL(hAPP(U_9154,U_9156))
        | U_9152 = U_9156 ) ),
    inference(miniscope,[status(thm)],[f_2519_2]) ).

fof(f_2519_4,plain,
    ( ! [U_9155,U_9153,U_9157] :
        ( ~ hBOOL(hAPP(U_9155,U_9157))
        | ~ sP727(U_9155,U_9153,U_9157) )
    & ! [U_9155,U_9153,U_9157] :
        ( U_9153 != U_9157
        | ~ sP727(U_9155,U_9153,U_9157) )
    & ! [U_9155,U_9151,U_9153,U_9157] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_9151),U_9153),U_9155),U_9157))
        | sP727(U_9155,U_9153,U_9157) )
    & ! [U_9154,U_9152,U_9150,U_9156] :
        ( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_9150),U_9152),U_9154),U_9156))
        | hBOOL(hAPP(U_9154,U_9156))
        | U_9152 = U_9156 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP727])],[f_2519_3]) ).

cnf(f_2519_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_9150),U_9152),U_9154),U_9156))
    | hBOOL(hAPP(U_9154,U_9156))
    | U_9152 = U_9156 ),
    inference(clausify,[status(thm)],[f_2519_4]) ).

cnf(f_2519_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(U_9151),U_9153),U_9155),U_9157))
    | sP727(U_9155,U_9153,U_9157) ),
    inference(clausify,[status(thm)],[f_2519_4]) ).

cnf(f_2519_7,plain,
    ( U_9153 != U_9157
    | ~ sP727(U_9155,U_9153,U_9157) ),
    inference(clausify,[status(thm)],[f_2519_4]) ).

cnf(f_2519_8,plain,
    ( ~ hBOOL(hAPP(U_9155,U_9157))
    | ~ sP727(U_9155,U_9153,U_9157) ),
    inference(clausify,[status(thm)],[f_2519_4]) ).

fof(f_2520_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_2520_2,plain,
    ! [U_9162,U_9161,U_9160,U_9159,U_9158] :
      ( ( hAPP(hAPP(c_Set_Oinsert(U_9158),U_9159),hAPP(hAPP(c_Set_Oinsert(U_9158),U_9160),c_Orderings_Obot__class_Obot(tc_fun(U_9158,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_9158),U_9161),hAPP(hAPP(c_Set_Oinsert(U_9158),U_9162),c_Orderings_Obot__class_Obot(tc_fun(U_9158,tc_HOL_Obool))))
        | ( ( U_9160 != U_9161
            | U_9159 != U_9162 )
          & ( U_9160 != U_9162
            | U_9159 != U_9161 ) ) )
      & ( ( U_9160 = U_9161
          & U_9159 = U_9162 )
        | ( U_9160 = U_9162
          & U_9159 = U_9161 )
        | hAPP(hAPP(c_Set_Oinsert(U_9158),U_9159),hAPP(hAPP(c_Set_Oinsert(U_9158),U_9160),c_Orderings_Obot__class_Obot(tc_fun(U_9158,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_9158),U_9161),hAPP(hAPP(c_Set_Oinsert(U_9158),U_9162),c_Orderings_Obot__class_Obot(tc_fun(U_9158,tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_2520_1]) ).

fof(f_2520_3,plain,
    ( ! [U_9172,U_9170,U_9168,U_9166] :
        ( ! [U_9164] : hAPP(hAPP(c_Set_Oinsert(U_9164),U_9166),hAPP(hAPP(c_Set_Oinsert(U_9164),U_9168),c_Orderings_Obot__class_Obot(tc_fun(U_9164,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_9164),U_9170),hAPP(hAPP(c_Set_Oinsert(U_9164),U_9172),c_Orderings_Obot__class_Obot(tc_fun(U_9164,tc_HOL_Obool))))
        | ( ( U_9168 != U_9170
            | U_9166 != U_9172 )
          & ( U_9168 != U_9172
            | U_9166 != U_9170 ) ) )
    & ! [U_9171,U_9169,U_9167,U_9165] :
        ( ! [U_9163] : hAPP(hAPP(c_Set_Oinsert(U_9163),U_9165),hAPP(hAPP(c_Set_Oinsert(U_9163),U_9167),c_Orderings_Obot__class_Obot(tc_fun(U_9163,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_9163),U_9169),hAPP(hAPP(c_Set_Oinsert(U_9163),U_9171),c_Orderings_Obot__class_Obot(tc_fun(U_9163,tc_HOL_Obool))))
        | ( U_9167 = U_9169
          & U_9165 = U_9171 )
        | ( U_9167 = U_9171
          & U_9165 = U_9169 ) ) ),
    inference(miniscope,[status(thm)],[f_2520_2]) ).

fof(f_2520_4,plain,
    ( ! [U_9168,U_9166,U_9170,U_9172] :
        ( U_9168 != U_9170
        | U_9166 != U_9172
        | ~ sP730(U_9168,U_9166,U_9170,U_9172) )
    & ! [U_9168,U_9166,U_9170,U_9172] :
        ( U_9168 != U_9172
        | U_9166 != U_9170
        | ~ sP730(U_9168,U_9166,U_9170,U_9172) )
    & ! [U_9165,U_9171,U_9167,U_9169] :
        ( U_9167 = U_9169
        | ~ sP729(U_9165,U_9171,U_9167,U_9169) )
    & ! [U_9165,U_9171,U_9167,U_9169] :
        ( U_9165 = U_9171
        | ~ sP729(U_9165,U_9171,U_9167,U_9169) )
    & ! [U_9165,U_9171,U_9167,U_9169] :
        ( U_9167 = U_9171
        | ~ sP728(U_9165,U_9171,U_9167,U_9169) )
    & ! [U_9165,U_9171,U_9167,U_9169] :
        ( U_9165 = U_9169
        | ~ sP728(U_9165,U_9171,U_9167,U_9169) )
    & ! [U_9164,U_9168,U_9166,U_9170,U_9172] :
        ( hAPP(hAPP(c_Set_Oinsert(U_9164),U_9166),hAPP(hAPP(c_Set_Oinsert(U_9164),U_9168),c_Orderings_Obot__class_Obot(tc_fun(U_9164,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_9164),U_9170),hAPP(hAPP(c_Set_Oinsert(U_9164),U_9172),c_Orderings_Obot__class_Obot(tc_fun(U_9164,tc_HOL_Obool))))
        | sP730(U_9168,U_9166,U_9170,U_9172) )
    & ! [U_9165,U_9163,U_9171,U_9167,U_9169] :
        ( hAPP(hAPP(c_Set_Oinsert(U_9163),U_9165),hAPP(hAPP(c_Set_Oinsert(U_9163),U_9167),c_Orderings_Obot__class_Obot(tc_fun(U_9163,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_9163),U_9169),hAPP(hAPP(c_Set_Oinsert(U_9163),U_9171),c_Orderings_Obot__class_Obot(tc_fun(U_9163,tc_HOL_Obool))))
        | sP729(U_9165,U_9171,U_9167,U_9169)
        | sP728(U_9165,U_9171,U_9167,U_9169) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP728,sP729,sP730])],[f_2520_3]) ).

cnf(f_2520_5,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_9163),U_9165),hAPP(hAPP(c_Set_Oinsert(U_9163),U_9167),c_Orderings_Obot__class_Obot(tc_fun(U_9163,tc_HOL_Obool)))) != hAPP(hAPP(c_Set_Oinsert(U_9163),U_9169),hAPP(hAPP(c_Set_Oinsert(U_9163),U_9171),c_Orderings_Obot__class_Obot(tc_fun(U_9163,tc_HOL_Obool))))
    | sP729(U_9165,U_9171,U_9167,U_9169)
    | sP728(U_9165,U_9171,U_9167,U_9169) ),
    inference(clausify,[status(thm)],[f_2520_4]) ).

cnf(f_2520_6,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_9164),U_9166),hAPP(hAPP(c_Set_Oinsert(U_9164),U_9168),c_Orderings_Obot__class_Obot(tc_fun(U_9164,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(U_9164),U_9170),hAPP(hAPP(c_Set_Oinsert(U_9164),U_9172),c_Orderings_Obot__class_Obot(tc_fun(U_9164,tc_HOL_Obool))))
    | sP730(U_9168,U_9166,U_9170,U_9172) ),
    inference(clausify,[status(thm)],[f_2520_4]) ).

cnf(f_2520_7,plain,
    ( U_9165 = U_9169
    | ~ sP728(U_9165,U_9171,U_9167,U_9169) ),
    inference(clausify,[status(thm)],[f_2520_4]) ).

cnf(f_2520_8,plain,
    ( U_9167 = U_9171
    | ~ sP728(U_9165,U_9171,U_9167,U_9169) ),
    inference(clausify,[status(thm)],[f_2520_4]) ).

cnf(f_2520_9,plain,
    ( U_9165 = U_9171
    | ~ sP729(U_9165,U_9171,U_9167,U_9169) ),
    inference(clausify,[status(thm)],[f_2520_4]) ).

cnf(f_2520_10,plain,
    ( U_9167 = U_9169
    | ~ sP729(U_9165,U_9171,U_9167,U_9169) ),
    inference(clausify,[status(thm)],[f_2520_4]) ).

cnf(f_2520_11,plain,
    ( U_9168 != U_9172
    | U_9166 != U_9170
    | ~ sP730(U_9168,U_9166,U_9170,U_9172) ),
    inference(clausify,[status(thm)],[f_2520_4]) ).

cnf(f_2520_12,plain,
    ( U_9168 != U_9170
    | U_9166 != U_9172
    | ~ sP730(U_9168,U_9166,U_9170,U_9172) ),
    inference(clausify,[status(thm)],[f_2520_4]) ).

fof(f_2521_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_2521_2,plain,
    ! [U_9176,U_9175,U_9174,U_9173] : hAPP(hAPP(c_Set_Oinsert(U_9173),U_9174),hAPP(hAPP(c_Set_Oinsert(U_9173),U_9175),U_9176)) = hAPP(hAPP(c_Set_Oinsert(U_9173),U_9175),hAPP(hAPP(c_Set_Oinsert(U_9173),U_9174),U_9176)),
    inference(variable_rename,[status(thm)],[f_2521_1]) ).

fof(f_2521_3,plain,
    ! [U_9176,U_9174,U_9175,U_9173] : hAPP(hAPP(c_Set_Oinsert(U_9173),U_9174),hAPP(hAPP(c_Set_Oinsert(U_9173),U_9175),U_9176)) = hAPP(hAPP(c_Set_Oinsert(U_9173),U_9175),hAPP(hAPP(c_Set_Oinsert(U_9173),U_9174),U_9176)),
    inference(definitional_conversion,[status(esa)],[f_2521_2]) ).

cnf(f_2521_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_9173),U_9174),hAPP(hAPP(c_Set_Oinsert(U_9173),U_9175),U_9176)) = hAPP(hAPP(c_Set_Oinsert(U_9173),U_9175),hAPP(hAPP(c_Set_Oinsert(U_9173),U_9174),U_9176)),
    inference(clausify,[status(thm)],[f_2521_3]) ).

fof(f_2522_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_2522_2,plain,
    ! [U_9179,U_9178,U_9177] : hAPP(hAPP(c_Set_Oinsert(U_9177),U_9178),hAPP(hAPP(c_Set_Oinsert(U_9177),U_9178),U_9179)) = hAPP(hAPP(c_Set_Oinsert(U_9177),U_9178),U_9179),
    inference(variable_rename,[status(thm)],[f_2522_1]) ).

fof(f_2522_3,plain,
    ! [U_9177,U_9179,U_9178] : hAPP(hAPP(c_Set_Oinsert(U_9177),U_9178),hAPP(hAPP(c_Set_Oinsert(U_9177),U_9178),U_9179)) = hAPP(hAPP(c_Set_Oinsert(U_9177),U_9178),U_9179),
    inference(definitional_conversion,[status(esa)],[f_2522_2]) ).

cnf(f_2522_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_9177),U_9178),hAPP(hAPP(c_Set_Oinsert(U_9177),U_9178),U_9179)) = hAPP(hAPP(c_Set_Oinsert(U_9177),U_9178),U_9179),
    inference(clausify,[status(thm)],[f_2522_3]) ).

fof(f_2523_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_2523_2,plain,
    ! [U_9182,U_9181,U_9180] : hAPP(hAPP(c_Set_Oinsert(U_9180),U_9181),U_9182) != c_Orderings_Obot__class_Obot(tc_fun(U_9180,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2523_1]) ).

fof(f_2523_3,plain,
    ! [U_9180,U_9181,U_9182] : hAPP(hAPP(c_Set_Oinsert(U_9180),U_9181),U_9182) != c_Orderings_Obot__class_Obot(tc_fun(U_9180,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2523_2]) ).

cnf(f_2523_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_9180),U_9181),U_9182) != c_Orderings_Obot__class_Obot(tc_fun(U_9180,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2523_3]) ).

fof(f_2524_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_2524_2,plain,
    ! [U_9185,U_9184,U_9183] : c_Orderings_Obot__class_Obot(tc_fun(U_9183,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_9183),U_9184),U_9185),
    inference(variable_rename,[status(thm)],[f_2524_1]) ).

fof(f_2524_3,plain,
    ! [U_9183,U_9184,U_9185] : c_Orderings_Obot__class_Obot(tc_fun(U_9183,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_9183),U_9184),U_9185),
    inference(definitional_conversion,[status(esa)],[f_2524_2]) ).

cnf(f_2524_4,plain,
    c_Orderings_Obot__class_Obot(tc_fun(U_9183,tc_HOL_Obool)) != hAPP(hAPP(c_Set_Oinsert(U_9183),U_9184),U_9185),
    inference(clausify,[status(thm)],[f_2524_3]) ).

fof(f_2525_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_2525_2,plain,
    ! [U_9188,U_9187,U_9186] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9187,U_9186)),U_9188) = c_Orderings_Obot__class_Obot(U_9186)
      | ~ class_Orderings_Obot(U_9186) ),
    inference(variable_rename,[status(thm)],[f_2525_1]) ).

fof(f_2525_3,plain,
    ! [U_9186,U_9187,U_9188] :
      ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9187,U_9186)),U_9188) = c_Orderings_Obot__class_Obot(U_9186)
      | ~ class_Orderings_Obot(U_9186) ),
    inference(definitional_conversion,[status(esa)],[f_2525_2]) ).

cnf(f_2525_4,plain,
    ( hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9187,U_9186)),U_9188) = c_Orderings_Obot__class_Obot(U_9186)
    | ~ class_Orderings_Obot(U_9186) ),
    inference(clausify,[status(thm)],[f_2525_3]) ).

fof(f_2526_1,plain,
    ! [V_y_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot)),c_fequal)),V_x_2),V_y_2))
        | V_x_2 = V_y_2 )
      & ( V_x_2 != V_y_2
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_b,T_b,hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_b),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot)),c_fequal)),V_x_2),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_conversep__noteq]) ).

fof(f_2526_2,plain,
    ! [U_9191,U_9190,U_9189] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9189,U_9189,hAPP(hAPP(c_COMBB(tc_fun(U_9189,tc_HOL_Obool),tc_fun(U_9189,tc_HOL_Obool),U_9189),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9189),c_fNot)),c_fequal)),U_9190),U_9191))
        | U_9190 = U_9191 )
      & ( U_9190 != U_9191
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9189,U_9189,hAPP(hAPP(c_COMBB(tc_fun(U_9189,tc_HOL_Obool),tc_fun(U_9189,tc_HOL_Obool),U_9189),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9189),c_fNot)),c_fequal)),U_9190),U_9191)) ) ),
    inference(variable_rename,[status(thm)],[f_2526_1]) ).

fof(f_2526_3,plain,
    ( ! [U_9197,U_9195] :
        ( ! [U_9193] : hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9193,U_9193,hAPP(hAPP(c_COMBB(tc_fun(U_9193,tc_HOL_Obool),tc_fun(U_9193,tc_HOL_Obool),U_9193),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9193),c_fNot)),c_fequal)),U_9195),U_9197))
        | U_9195 = U_9197 )
    & ! [U_9196,U_9194] :
        ( ! [U_9192] : ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9192,U_9192,hAPP(hAPP(c_COMBB(tc_fun(U_9192,tc_HOL_Obool),tc_fun(U_9192,tc_HOL_Obool),U_9192),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9192),c_fNot)),c_fequal)),U_9194),U_9196))
        | U_9194 != U_9196 ) ),
    inference(miniscope,[status(thm)],[f_2526_2]) ).

fof(f_2526_4,plain,
    ( ! [U_9197,U_9193,U_9195] :
        ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9193,U_9193,hAPP(hAPP(c_COMBB(tc_fun(U_9193,tc_HOL_Obool),tc_fun(U_9193,tc_HOL_Obool),U_9193),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9193),c_fNot)),c_fequal)),U_9195),U_9197))
        | U_9195 = U_9197 )
    & ! [U_9196,U_9192,U_9194] :
        ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9192,U_9192,hAPP(hAPP(c_COMBB(tc_fun(U_9192,tc_HOL_Obool),tc_fun(U_9192,tc_HOL_Obool),U_9192),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9192),c_fNot)),c_fequal)),U_9194),U_9196))
        | U_9194 != U_9196 ) ),
    inference(definitional_conversion,[status(esa)],[f_2526_3]) ).

cnf(f_2526_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9192,U_9192,hAPP(hAPP(c_COMBB(tc_fun(U_9192,tc_HOL_Obool),tc_fun(U_9192,tc_HOL_Obool),U_9192),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9192),c_fNot)),c_fequal)),U_9194),U_9196))
    | U_9194 != U_9196 ),
    inference(clausify,[status(thm)],[f_2526_4]) ).

cnf(f_2526_6,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9193,U_9193,hAPP(hAPP(c_COMBB(tc_fun(U_9193,tc_HOL_Obool),tc_fun(U_9193,tc_HOL_Obool),U_9193),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9193),c_fNot)),c_fequal)),U_9195),U_9197))
    | U_9195 = U_9197 ),
    inference(clausify,[status(thm)],[f_2526_4]) ).

fof(f_2527_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_2527_2,plain,
    ! [U_9199,U_9198] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9198,tc_HOL_Obool)),U_9199),c_Orderings_Obot__class_Obot(tc_fun(U_9198,tc_HOL_Obool))))
        | U_9199 != c_Orderings_Obot__class_Obot(tc_fun(U_9198,tc_HOL_Obool)) )
      & ( U_9199 = c_Orderings_Obot__class_Obot(tc_fun(U_9198,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9198,tc_HOL_Obool)),U_9199),c_Orderings_Obot__class_Obot(tc_fun(U_9198,tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_2527_1]) ).

fof(f_2527_3,plain,
    ( ! [U_9203,U_9201] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9201,tc_HOL_Obool)),U_9203),c_Orderings_Obot__class_Obot(tc_fun(U_9201,tc_HOL_Obool))))
        | U_9203 != c_Orderings_Obot__class_Obot(tc_fun(U_9201,tc_HOL_Obool)) )
    & ! [U_9202,U_9200] :
        ( U_9202 = c_Orderings_Obot__class_Obot(tc_fun(U_9200,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9200,tc_HOL_Obool)),U_9202),c_Orderings_Obot__class_Obot(tc_fun(U_9200,tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_2527_2]) ).

fof(f_2527_4,plain,
    ( ! [U_9203,U_9201] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9201,tc_HOL_Obool)),U_9203),c_Orderings_Obot__class_Obot(tc_fun(U_9201,tc_HOL_Obool))))
        | U_9203 != c_Orderings_Obot__class_Obot(tc_fun(U_9201,tc_HOL_Obool)) )
    & ! [U_9200,U_9202] :
        ( U_9202 = c_Orderings_Obot__class_Obot(tc_fun(U_9200,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9200,tc_HOL_Obool)),U_9202),c_Orderings_Obot__class_Obot(tc_fun(U_9200,tc_HOL_Obool)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2527_3]) ).

cnf(f_2527_5,plain,
    ( U_9202 = c_Orderings_Obot__class_Obot(tc_fun(U_9200,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9200,tc_HOL_Obool)),U_9202),c_Orderings_Obot__class_Obot(tc_fun(U_9200,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2527_4]) ).

cnf(f_2527_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9201,tc_HOL_Obool)),U_9203),c_Orderings_Obot__class_Obot(tc_fun(U_9201,tc_HOL_Obool))))
    | U_9203 != c_Orderings_Obot__class_Obot(tc_fun(U_9201,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2527_4]) ).

fof(f_2528_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_2528_2,plain,
    ! [U_9205,U_9204] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9204,tc_HOL_Obool)),U_9205),U_9205) = c_Orderings_Obot__class_Obot(tc_fun(U_9204,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2528_1]) ).

fof(f_2528_3,plain,
    ! [U_9204,U_9205] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9204,tc_HOL_Obool)),U_9205),U_9205) = c_Orderings_Obot__class_Obot(tc_fun(U_9204,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2528_2]) ).

cnf(f_2528_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9204,tc_HOL_Obool)),U_9205),U_9205) = c_Orderings_Obot__class_Obot(tc_fun(U_9204,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2528_3]) ).

fof(f_2529_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_2529_2,plain,
    ! [U_9207,U_9206] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9206,tc_HOL_Obool)),U_9207),c_Orderings_Obot__class_Obot(tc_fun(U_9206,tc_HOL_Obool))) = U_9207,
    inference(variable_rename,[status(thm)],[f_2529_1]) ).

fof(f_2529_3,plain,
    ! [U_9206,U_9207] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9206,tc_HOL_Obool)),U_9207),c_Orderings_Obot__class_Obot(tc_fun(U_9206,tc_HOL_Obool))) = U_9207,
    inference(definitional_conversion,[status(esa)],[f_2529_2]) ).

cnf(f_2529_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9206,tc_HOL_Obool)),U_9207),c_Orderings_Obot__class_Obot(tc_fun(U_9206,tc_HOL_Obool))) = U_9207,
    inference(clausify,[status(thm)],[f_2529_3]) ).

fof(f_2530_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_2530_2,plain,
    ! [U_9209,U_9208] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9208,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9208,tc_HOL_Obool))),U_9209) = c_Orderings_Obot__class_Obot(tc_fun(U_9208,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2530_1]) ).

fof(f_2530_3,plain,
    ! [U_9208,U_9209] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9208,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9208,tc_HOL_Obool))),U_9209) = c_Orderings_Obot__class_Obot(tc_fun(U_9208,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2530_2]) ).

cnf(f_2530_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9208,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9208,tc_HOL_Obool))),U_9209) = c_Orderings_Obot__class_Obot(tc_fun(U_9208,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2530_3]) ).

fof(f_2531_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_2531_2,plain,
    ! [U_9213,U_9212,U_9211,U_9210] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9210,tc_HOL_Obool)),U_9211),hAPP(hAPP(c_Set_Oinsert(U_9210),U_9212),U_9213)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9210,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9210,tc_HOL_Obool)),U_9211),U_9213)),hAPP(hAPP(c_Set_Oinsert(U_9210),U_9212),c_Orderings_Obot__class_Obot(tc_fun(U_9210,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2531_1]) ).

fof(f_2531_3,plain,
    ! [U_9210,U_9211,U_9212,U_9213] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9210,tc_HOL_Obool)),U_9211),hAPP(hAPP(c_Set_Oinsert(U_9210),U_9212),U_9213)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9210,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9210,tc_HOL_Obool)),U_9211),U_9213)),hAPP(hAPP(c_Set_Oinsert(U_9210),U_9212),c_Orderings_Obot__class_Obot(tc_fun(U_9210,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2531_2]) ).

cnf(f_2531_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9210,tc_HOL_Obool)),U_9211),hAPP(hAPP(c_Set_Oinsert(U_9210),U_9212),U_9213)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9210,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9210,tc_HOL_Obool)),U_9211),U_9213)),hAPP(hAPP(c_Set_Oinsert(U_9210),U_9212),c_Orderings_Obot__class_Obot(tc_fun(U_9210,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2531_3]) ).

fof(f_2532_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_2532_2,plain,
    ! [U_9217,U_9216,U_9215,U_9214] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9214,tc_HOL_Obool)),U_9215),hAPP(hAPP(c_Set_Oinsert(U_9214),U_9216),U_9217)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9214,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9214,tc_HOL_Obool)),U_9215),hAPP(hAPP(c_Set_Oinsert(U_9214),U_9216),c_Orderings_Obot__class_Obot(tc_fun(U_9214,tc_HOL_Obool))))),U_9217),
    inference(variable_rename,[status(thm)],[f_2532_1]) ).

fof(f_2532_3,plain,
    ! [U_9214,U_9215,U_9216,U_9217] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9214,tc_HOL_Obool)),U_9215),hAPP(hAPP(c_Set_Oinsert(U_9214),U_9216),U_9217)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9214,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9214,tc_HOL_Obool)),U_9215),hAPP(hAPP(c_Set_Oinsert(U_9214),U_9216),c_Orderings_Obot__class_Obot(tc_fun(U_9214,tc_HOL_Obool))))),U_9217),
    inference(definitional_conversion,[status(esa)],[f_2532_2]) ).

cnf(f_2532_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9214,tc_HOL_Obool)),U_9215),hAPP(hAPP(c_Set_Oinsert(U_9214),U_9216),U_9217)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9214,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9214,tc_HOL_Obool)),U_9215),hAPP(hAPP(c_Set_Oinsert(U_9214),U_9216),c_Orderings_Obot__class_Obot(tc_fun(U_9214,tc_HOL_Obool))))),U_9217),
    inference(clausify,[status(thm)],[f_2532_3]) ).

fof(f_2533_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_2533_2,plain,
    ! [U_9220,U_9219,U_9218] : hAPP(hAPP(c_Set_Oinsert(U_9218),U_9219),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9218,tc_HOL_Obool)),U_9220),hAPP(hAPP(c_Set_Oinsert(U_9218),U_9219),c_Orderings_Obot__class_Obot(tc_fun(U_9218,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_9218),U_9219),U_9220),
    inference(variable_rename,[status(thm)],[f_2533_1]) ).

fof(f_2533_3,plain,
    ! [U_9218,U_9219,U_9220] : hAPP(hAPP(c_Set_Oinsert(U_9218),U_9219),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9218,tc_HOL_Obool)),U_9220),hAPP(hAPP(c_Set_Oinsert(U_9218),U_9219),c_Orderings_Obot__class_Obot(tc_fun(U_9218,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_9218),U_9219),U_9220),
    inference(definitional_conversion,[status(esa)],[f_2533_2]) ).

cnf(f_2533_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_9218),U_9219),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9218,tc_HOL_Obool)),U_9220),hAPP(hAPP(c_Set_Oinsert(U_9218),U_9219),c_Orderings_Obot__class_Obot(tc_fun(U_9218,tc_HOL_Obool))))) = hAPP(hAPP(c_Set_Oinsert(U_9218),U_9219),U_9220),
    inference(clausify,[status(thm)],[f_2533_3]) ).

fof(f_2534_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_2534_2,plain,
    ! [U_9223,U_9222,U_9221] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9221,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9221),U_9222),U_9223)),hAPP(hAPP(c_Set_Oinsert(U_9221),U_9222),c_Orderings_Obot__class_Obot(tc_fun(U_9221,tc_HOL_Obool)))) = U_9223
      | hBOOL(hAPP(hAPP(c_member(U_9221),U_9222),U_9223)) ),
    inference(variable_rename,[status(thm)],[f_2534_1]) ).

fof(f_2534_3,plain,
    ! [U_9221,U_9222,U_9223] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9221,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9221),U_9222),U_9223)),hAPP(hAPP(c_Set_Oinsert(U_9221),U_9222),c_Orderings_Obot__class_Obot(tc_fun(U_9221,tc_HOL_Obool)))) = U_9223
      | hBOOL(hAPP(hAPP(c_member(U_9221),U_9222),U_9223)) ),
    inference(definitional_conversion,[status(esa)],[f_2534_2]) ).

cnf(f_2534_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9221,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9221),U_9222),U_9223)),hAPP(hAPP(c_Set_Oinsert(U_9221),U_9222),c_Orderings_Obot__class_Obot(tc_fun(U_9221,tc_HOL_Obool)))) = U_9223
    | hBOOL(hAPP(hAPP(c_member(U_9221),U_9222),U_9223)) ),
    inference(clausify,[status(thm)],[f_2534_3]) ).

fof(f_2535_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_2535_2,plain,
    ! [U_9226,U_9225,U_9224] :
      ( hAPP(hAPP(c_Set_Oinsert(U_9224),U_9225),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9224,tc_HOL_Obool)),U_9226),hAPP(hAPP(c_Set_Oinsert(U_9224),U_9225),c_Orderings_Obot__class_Obot(tc_fun(U_9224,tc_HOL_Obool))))) = U_9226
      | ~ hBOOL(hAPP(hAPP(c_member(U_9224),U_9225),U_9226)) ),
    inference(variable_rename,[status(thm)],[f_2535_1]) ).

fof(f_2535_3,plain,
    ! [U_9224,U_9225,U_9226] :
      ( hAPP(hAPP(c_Set_Oinsert(U_9224),U_9225),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9224,tc_HOL_Obool)),U_9226),hAPP(hAPP(c_Set_Oinsert(U_9224),U_9225),c_Orderings_Obot__class_Obot(tc_fun(U_9224,tc_HOL_Obool))))) = U_9226
      | ~ hBOOL(hAPP(hAPP(c_member(U_9224),U_9225),U_9226)) ),
    inference(definitional_conversion,[status(esa)],[f_2535_2]) ).

cnf(f_2535_4,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_9224),U_9225),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9224,tc_HOL_Obool)),U_9226),hAPP(hAPP(c_Set_Oinsert(U_9224),U_9225),c_Orderings_Obot__class_Obot(tc_fun(U_9224,tc_HOL_Obool))))) = U_9226
    | ~ hBOOL(hAPP(hAPP(c_member(U_9224),U_9225),U_9226)) ),
    inference(clausify,[status(thm)],[f_2535_3]) ).

fof(f_2536_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_2536_2,plain,
    ! [U_9228,U_9227] : hAPP(c_Relation_ODomain(U_9227,U_9228),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9227,U_9228),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9227,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2536_1]) ).

fof(f_2536_3,plain,
    ! [U_9227,U_9228] : hAPP(c_Relation_ODomain(U_9227,U_9228),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9227,U_9228),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9227,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2536_2]) ).

cnf(f_2536_4,plain,
    hAPP(c_Relation_ODomain(U_9227,U_9228),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9227,U_9228),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9227,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2536_3]) ).

fof(f_2537_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_2537_2,plain,
    ! [U_9231,U_9230,U_9229] :
      ( ( hAPP(c_Relation_ODomain(U_9229,U_9230),U_9231) = c_Orderings_Obot__class_Obot(tc_fun(U_9229,tc_HOL_Obool))
        | U_9231 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9229,U_9230),tc_HOL_Obool)) )
      & ( U_9231 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9229,U_9230),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(U_9229,U_9230),U_9231) != c_Orderings_Obot__class_Obot(tc_fun(U_9229,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2537_1]) ).

fof(f_2537_3,plain,
    ( ! [U_9237,U_9235,U_9233] :
        ( hAPP(c_Relation_ODomain(U_9233,U_9235),U_9237) = c_Orderings_Obot__class_Obot(tc_fun(U_9233,tc_HOL_Obool))
        | U_9237 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9233,U_9235),tc_HOL_Obool)) )
    & ! [U_9236,U_9234,U_9232] :
        ( U_9236 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9232,U_9234),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(U_9232,U_9234),U_9236) != c_Orderings_Obot__class_Obot(tc_fun(U_9232,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2537_2]) ).

fof(f_2537_4,plain,
    ( ! [U_9233,U_9235,U_9237] :
        ( hAPP(c_Relation_ODomain(U_9233,U_9235),U_9237) = c_Orderings_Obot__class_Obot(tc_fun(U_9233,tc_HOL_Obool))
        | U_9237 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9233,U_9235),tc_HOL_Obool)) )
    & ! [U_9236,U_9234,U_9232] :
        ( U_9236 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9232,U_9234),tc_HOL_Obool))
        | hAPP(c_Relation_ODomain(U_9232,U_9234),U_9236) != c_Orderings_Obot__class_Obot(tc_fun(U_9232,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2537_3]) ).

cnf(f_2537_5,plain,
    ( U_9236 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9232,U_9234),tc_HOL_Obool))
    | hAPP(c_Relation_ODomain(U_9232,U_9234),U_9236) != c_Orderings_Obot__class_Obot(tc_fun(U_9232,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2537_4]) ).

cnf(f_2537_6,plain,
    ( hAPP(c_Relation_ODomain(U_9233,U_9235),U_9237) = c_Orderings_Obot__class_Obot(tc_fun(U_9233,tc_HOL_Obool))
    | U_9237 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9233,U_9235),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2537_4]) ).

fof(f_2538_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_2538_2,plain,
    ! [U_9242,U_9241,U_9240,U_9239,U_9238] : hAPP(c_Relation_ODomain(U_9238,U_9239),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_9238,U_9239)),hAPP(hAPP(c_Product__Type_OPair(U_9238,U_9239),U_9240),U_9241)),U_9242)) = hAPP(hAPP(c_Set_Oinsert(U_9238),U_9240),hAPP(c_Relation_ODomain(U_9238,U_9239),U_9242)),
    inference(variable_rename,[status(thm)],[f_2538_1]) ).

fof(f_2538_3,plain,
    ! [U_9238,U_9239,U_9240,U_9241,U_9242] : hAPP(c_Relation_ODomain(U_9238,U_9239),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_9238,U_9239)),hAPP(hAPP(c_Product__Type_OPair(U_9238,U_9239),U_9240),U_9241)),U_9242)) = hAPP(hAPP(c_Set_Oinsert(U_9238),U_9240),hAPP(c_Relation_ODomain(U_9238,U_9239),U_9242)),
    inference(definitional_conversion,[status(esa)],[f_2538_2]) ).

cnf(f_2538_4,plain,
    hAPP(c_Relation_ODomain(U_9238,U_9239),hAPP(hAPP(c_Set_Oinsert(tc_prod(U_9238,U_9239)),hAPP(hAPP(c_Product__Type_OPair(U_9238,U_9239),U_9240),U_9241)),U_9242)) = hAPP(hAPP(c_Set_Oinsert(U_9238),U_9240),hAPP(c_Relation_ODomain(U_9238,U_9239),U_9242)),
    inference(clausify,[status(thm)],[f_2538_3]) ).

fof(f_2539_1,plain,
    ! [V_Pa_2,T_b] :
      ( ( hAPP(c_Set_OCollect(T_b),V_Pa_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | ? [B_x] : hBOOL(hAPP(V_Pa_2,B_x)) )
      & ( ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x))
        | hAPP(c_Set_OCollect(T_b),V_Pa_2) != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Collect__empty__eq]) ).

fof(f_2539_2,plain,
    ! [U_9246,U_9245] :
      ( ( hAPP(c_Set_OCollect(U_9245),U_9246) = c_Orderings_Obot__class_Obot(tc_fun(U_9245,tc_HOL_Obool))
        | ? [U_9244] : hBOOL(hAPP(U_9246,U_9244)) )
      & ( ! [U_9243] : ~ hBOOL(hAPP(U_9246,U_9243))
        | hAPP(c_Set_OCollect(U_9245),U_9246) != c_Orderings_Obot__class_Obot(tc_fun(U_9245,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2539_1]) ).

fof(f_2539_3,plain,
    ( ! [U_9250] :
        ( ! [U_9248] : hAPP(c_Set_OCollect(U_9248),U_9250) = c_Orderings_Obot__class_Obot(tc_fun(U_9248,tc_HOL_Obool))
        | ? [U_9244] : hBOOL(hAPP(U_9250,U_9244)) )
    & ! [U_9249] :
        ( ! [U_9247] : hAPP(c_Set_OCollect(U_9247),U_9249) != c_Orderings_Obot__class_Obot(tc_fun(U_9247,tc_HOL_Obool))
        | ! [U_9243] : ~ hBOOL(hAPP(U_9249,U_9243)) ) ),
    inference(miniscope,[status(thm)],[f_2539_2]) ).

fof(f_2539_4,plain,
    ( ! [U_9250] :
        ( ! [U_9248] : hAPP(c_Set_OCollect(U_9248),U_9250) = c_Orderings_Obot__class_Obot(tc_fun(U_9248,tc_HOL_Obool))
        | hBOOL(hAPP(U_9250,sK150(U_9250))) )
    & ! [U_9249] :
        ( ! [U_9247] : hAPP(c_Set_OCollect(U_9247),U_9249) != c_Orderings_Obot__class_Obot(tc_fun(U_9247,tc_HOL_Obool))
        | ! [U_9243] : ~ hBOOL(hAPP(U_9249,U_9243)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK150]),skolemize(U_9244,sK150(U_9250))],[f_2539_3]) ).

fof(f_2539_5,plain,
    ( ! [U_9248,U_9250] :
        ( hAPP(c_Set_OCollect(U_9248),U_9250) = c_Orderings_Obot__class_Obot(tc_fun(U_9248,tc_HOL_Obool))
        | hBOOL(hAPP(U_9250,sK150(U_9250))) )
    & ! [U_9249,U_9243,U_9247] :
        ( hAPP(c_Set_OCollect(U_9247),U_9249) != c_Orderings_Obot__class_Obot(tc_fun(U_9247,tc_HOL_Obool))
        | ~ hBOOL(hAPP(U_9249,U_9243)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2539_4]) ).

cnf(f_2539_6,plain,
    ( hAPP(c_Set_OCollect(U_9247),U_9249) != c_Orderings_Obot__class_Obot(tc_fun(U_9247,tc_HOL_Obool))
    | ~ hBOOL(hAPP(U_9249,U_9243)) ),
    inference(clausify,[status(thm)],[f_2539_5]) ).

cnf(f_2539_7,plain,
    ( hAPP(c_Set_OCollect(U_9248),U_9250) = c_Orderings_Obot__class_Obot(tc_fun(U_9248,tc_HOL_Obool))
    | hBOOL(hAPP(U_9250,sK150(U_9250))) ),
    inference(clausify,[status(thm)],[f_2539_5]) ).

fof(f_2540_1,plain,
    ! [V_Pa_2,T_b] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_b),V_Pa_2)
        | ? [B_x] : hBOOL(hAPP(V_Pa_2,B_x)) )
      & ( ! [B_x] : ~ hBOOL(hAPP(V_Pa_2,B_x))
        | c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) != hAPP(c_Set_OCollect(T_b),V_Pa_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_empty__Collect__eq]) ).

fof(f_2540_2,plain,
    ! [U_9254,U_9253] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_9253,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9253),U_9254)
        | ? [U_9252] : hBOOL(hAPP(U_9254,U_9252)) )
      & ( ! [U_9251] : ~ hBOOL(hAPP(U_9254,U_9251))
        | c_Orderings_Obot__class_Obot(tc_fun(U_9253,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_9253),U_9254) ) ),
    inference(variable_rename,[status(thm)],[f_2540_1]) ).

fof(f_2540_3,plain,
    ( ! [U_9258] :
        ( ! [U_9256] : c_Orderings_Obot__class_Obot(tc_fun(U_9256,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9256),U_9258)
        | ? [U_9252] : hBOOL(hAPP(U_9258,U_9252)) )
    & ! [U_9257] :
        ( ! [U_9255] : c_Orderings_Obot__class_Obot(tc_fun(U_9255,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_9255),U_9257)
        | ! [U_9251] : ~ hBOOL(hAPP(U_9257,U_9251)) ) ),
    inference(miniscope,[status(thm)],[f_2540_2]) ).

fof(f_2540_4,plain,
    ( ! [U_9258] :
        ( ! [U_9256] : c_Orderings_Obot__class_Obot(tc_fun(U_9256,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9256),U_9258)
        | hBOOL(hAPP(U_9258,sK151(U_9258))) )
    & ! [U_9257] :
        ( ! [U_9255] : c_Orderings_Obot__class_Obot(tc_fun(U_9255,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_9255),U_9257)
        | ! [U_9251] : ~ hBOOL(hAPP(U_9257,U_9251)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK151]),skolemize(U_9252,sK151(U_9258))],[f_2540_3]) ).

fof(f_2540_5,plain,
    ( ! [U_9256,U_9258] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_9256,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9256),U_9258)
        | hBOOL(hAPP(U_9258,sK151(U_9258))) )
    & ! [U_9251,U_9257,U_9255] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_9255,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_9255),U_9257)
        | ~ hBOOL(hAPP(U_9257,U_9251)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2540_4]) ).

cnf(f_2540_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_9255,tc_HOL_Obool)) != hAPP(c_Set_OCollect(U_9255),U_9257)
    | ~ hBOOL(hAPP(U_9257,U_9251)) ),
    inference(clausify,[status(thm)],[f_2540_5]) ).

cnf(f_2540_7,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_9256,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9256),U_9258)
    | hBOOL(hAPP(U_9258,sK151(U_9258))) ),
    inference(clausify,[status(thm)],[f_2540_5]) ).

fof(f_2541_1,plain,
    ! [T_b,V_a_2,V_Pa_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_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,V_a_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Collect__conv__if]) ).

fof(f_2541_2,plain,
    ! [U_9261,U_9260,U_9259] :
      ( ( hAPP(c_Set_OCollect(U_9261),hAPP(hAPP(c_COMBS(U_9261,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9261),c_fconj),hAPP(hAPP(c_COMBC(U_9261,U_9261,tc_HOL_Obool),c_fequal),U_9260))),U_9259)) = c_Orderings_Obot__class_Obot(tc_fun(U_9261,tc_HOL_Obool))
        | hBOOL(hAPP(U_9259,U_9260)) )
      & ( hAPP(c_Set_OCollect(U_9261),hAPP(hAPP(c_COMBS(U_9261,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9261),c_fconj),hAPP(hAPP(c_COMBC(U_9261,U_9261,tc_HOL_Obool),c_fequal),U_9260))),U_9259)) = hAPP(hAPP(c_Set_Oinsert(U_9261),U_9260),c_Orderings_Obot__class_Obot(tc_fun(U_9261,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_9259,U_9260)) ) ),
    inference(variable_rename,[status(thm)],[f_2541_1]) ).

fof(f_2541_3,plain,
    ( ! [U_9267,U_9265,U_9263] :
        ( hAPP(c_Set_OCollect(U_9267),hAPP(hAPP(c_COMBS(U_9267,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9267),c_fconj),hAPP(hAPP(c_COMBC(U_9267,U_9267,tc_HOL_Obool),c_fequal),U_9265))),U_9263)) = c_Orderings_Obot__class_Obot(tc_fun(U_9267,tc_HOL_Obool))
        | hBOOL(hAPP(U_9263,U_9265)) )
    & ! [U_9266,U_9264,U_9262] :
        ( hAPP(c_Set_OCollect(U_9266),hAPP(hAPP(c_COMBS(U_9266,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9266),c_fconj),hAPP(hAPP(c_COMBC(U_9266,U_9266,tc_HOL_Obool),c_fequal),U_9264))),U_9262)) = hAPP(hAPP(c_Set_Oinsert(U_9266),U_9264),c_Orderings_Obot__class_Obot(tc_fun(U_9266,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_9262,U_9264)) ) ),
    inference(miniscope,[status(thm)],[f_2541_2]) ).

fof(f_2541_4,plain,
    ( ! [U_9263,U_9265,U_9267] :
        ( hAPP(c_Set_OCollect(U_9267),hAPP(hAPP(c_COMBS(U_9267,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9267),c_fconj),hAPP(hAPP(c_COMBC(U_9267,U_9267,tc_HOL_Obool),c_fequal),U_9265))),U_9263)) = c_Orderings_Obot__class_Obot(tc_fun(U_9267,tc_HOL_Obool))
        | hBOOL(hAPP(U_9263,U_9265)) )
    & ! [U_9266,U_9264,U_9262] :
        ( hAPP(c_Set_OCollect(U_9266),hAPP(hAPP(c_COMBS(U_9266,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9266),c_fconj),hAPP(hAPP(c_COMBC(U_9266,U_9266,tc_HOL_Obool),c_fequal),U_9264))),U_9262)) = hAPP(hAPP(c_Set_Oinsert(U_9266),U_9264),c_Orderings_Obot__class_Obot(tc_fun(U_9266,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_9262,U_9264)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2541_3]) ).

cnf(f_2541_5,plain,
    ( hAPP(c_Set_OCollect(U_9266),hAPP(hAPP(c_COMBS(U_9266,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9266),c_fconj),hAPP(hAPP(c_COMBC(U_9266,U_9266,tc_HOL_Obool),c_fequal),U_9264))),U_9262)) = hAPP(hAPP(c_Set_Oinsert(U_9266),U_9264),c_Orderings_Obot__class_Obot(tc_fun(U_9266,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(U_9262,U_9264)) ),
    inference(clausify,[status(thm)],[f_2541_4]) ).

cnf(f_2541_6,plain,
    ( hAPP(c_Set_OCollect(U_9267),hAPP(hAPP(c_COMBS(U_9267,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9267),c_fconj),hAPP(hAPP(c_COMBC(U_9267,U_9267,tc_HOL_Obool),c_fequal),U_9265))),U_9263)) = c_Orderings_Obot__class_Obot(tc_fun(U_9267,tc_HOL_Obool))
    | hBOOL(hAPP(U_9263,U_9265)) ),
    inference(clausify,[status(thm)],[f_2541_4]) ).

fof(f_2542_1,plain,
    ! [T_b,V_a_2,V_Pa_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_Pa_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
        | hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,V_a_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_Collect__conv__if2]) ).

fof(f_2542_2,plain,
    ! [U_9270,U_9269,U_9268] :
      ( ( hAPP(c_Set_OCollect(U_9270),hAPP(hAPP(c_COMBS(U_9270,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9270),c_fconj),hAPP(c_fequal,U_9269))),U_9268)) = c_Orderings_Obot__class_Obot(tc_fun(U_9270,tc_HOL_Obool))
        | hBOOL(hAPP(U_9268,U_9269)) )
      & ( hAPP(c_Set_OCollect(U_9270),hAPP(hAPP(c_COMBS(U_9270,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9270),c_fconj),hAPP(c_fequal,U_9269))),U_9268)) = hAPP(hAPP(c_Set_Oinsert(U_9270),U_9269),c_Orderings_Obot__class_Obot(tc_fun(U_9270,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_9268,U_9269)) ) ),
    inference(variable_rename,[status(thm)],[f_2542_1]) ).

fof(f_2542_3,plain,
    ( ! [U_9276,U_9274,U_9272] :
        ( hAPP(c_Set_OCollect(U_9276),hAPP(hAPP(c_COMBS(U_9276,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9276),c_fconj),hAPP(c_fequal,U_9274))),U_9272)) = c_Orderings_Obot__class_Obot(tc_fun(U_9276,tc_HOL_Obool))
        | hBOOL(hAPP(U_9272,U_9274)) )
    & ! [U_9275,U_9273,U_9271] :
        ( hAPP(c_Set_OCollect(U_9275),hAPP(hAPP(c_COMBS(U_9275,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9275),c_fconj),hAPP(c_fequal,U_9273))),U_9271)) = hAPP(hAPP(c_Set_Oinsert(U_9275),U_9273),c_Orderings_Obot__class_Obot(tc_fun(U_9275,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_9271,U_9273)) ) ),
    inference(miniscope,[status(thm)],[f_2542_2]) ).

fof(f_2542_4,plain,
    ( ! [U_9274,U_9272,U_9276] :
        ( hAPP(c_Set_OCollect(U_9276),hAPP(hAPP(c_COMBS(U_9276,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9276),c_fconj),hAPP(c_fequal,U_9274))),U_9272)) = c_Orderings_Obot__class_Obot(tc_fun(U_9276,tc_HOL_Obool))
        | hBOOL(hAPP(U_9272,U_9274)) )
    & ! [U_9275,U_9273,U_9271] :
        ( hAPP(c_Set_OCollect(U_9275),hAPP(hAPP(c_COMBS(U_9275,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9275),c_fconj),hAPP(c_fequal,U_9273))),U_9271)) = hAPP(hAPP(c_Set_Oinsert(U_9275),U_9273),c_Orderings_Obot__class_Obot(tc_fun(U_9275,tc_HOL_Obool)))
        | ~ hBOOL(hAPP(U_9271,U_9273)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2542_3]) ).

cnf(f_2542_5,plain,
    ( hAPP(c_Set_OCollect(U_9275),hAPP(hAPP(c_COMBS(U_9275,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9275),c_fconj),hAPP(c_fequal,U_9273))),U_9271)) = hAPP(hAPP(c_Set_Oinsert(U_9275),U_9273),c_Orderings_Obot__class_Obot(tc_fun(U_9275,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(U_9271,U_9273)) ),
    inference(clausify,[status(thm)],[f_2542_4]) ).

cnf(f_2542_6,plain,
    ( hAPP(c_Set_OCollect(U_9276),hAPP(hAPP(c_COMBS(U_9276,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9276),c_fconj),hAPP(c_fequal,U_9274))),U_9272)) = c_Orderings_Obot__class_Obot(tc_fun(U_9276,tc_HOL_Obool))
    | hBOOL(hAPP(U_9272,U_9274)) ),
    inference(clausify,[status(thm)],[f_2542_4]) ).

fof(f_2543_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_2543_2,plain,
    ! [U_9278,U_9277] : hAPP(c_Set_OCollect(U_9277),hAPP(hAPP(c_COMBC(U_9277,U_9277,tc_HOL_Obool),c_fequal),U_9278)) = hAPP(hAPP(c_Set_Oinsert(U_9277),U_9278),c_Orderings_Obot__class_Obot(tc_fun(U_9277,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2543_1]) ).

fof(f_2543_3,plain,
    ! [U_9277,U_9278] : hAPP(c_Set_OCollect(U_9277),hAPP(hAPP(c_COMBC(U_9277,U_9277,tc_HOL_Obool),c_fequal),U_9278)) = hAPP(hAPP(c_Set_Oinsert(U_9277),U_9278),c_Orderings_Obot__class_Obot(tc_fun(U_9277,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2543_2]) ).

cnf(f_2543_4,plain,
    hAPP(c_Set_OCollect(U_9277),hAPP(hAPP(c_COMBC(U_9277,U_9277,tc_HOL_Obool),c_fequal),U_9278)) = hAPP(hAPP(c_Set_Oinsert(U_9277),U_9278),c_Orderings_Obot__class_Obot(tc_fun(U_9277,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2543_3]) ).

fof(f_2544_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_2544_2,plain,
    ! [U_9280,U_9279] : hAPP(c_Set_OCollect(U_9279),hAPP(c_fequal,U_9280)) = hAPP(hAPP(c_Set_Oinsert(U_9279),U_9280),c_Orderings_Obot__class_Obot(tc_fun(U_9279,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2544_1]) ).

fof(f_2544_3,plain,
    ! [U_9279,U_9280] : hAPP(c_Set_OCollect(U_9279),hAPP(c_fequal,U_9280)) = hAPP(hAPP(c_Set_Oinsert(U_9279),U_9280),c_Orderings_Obot__class_Obot(tc_fun(U_9279,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2544_2]) ).

cnf(f_2544_4,plain,
    hAPP(c_Set_OCollect(U_9279),hAPP(c_fequal,U_9280)) = hAPP(hAPP(c_Set_Oinsert(U_9279),U_9280),c_Orderings_Obot__class_Obot(tc_fun(U_9279,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2544_3]) ).

fof(f_2545_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_2545_2,plain,
    ! [U_9282,U_9281] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9281,tc_HOL_Obool)),U_9282),c_Orderings_Obot__class_Obot(tc_fun(U_9281,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2545_1]) ).

fof(f_2545_3,plain,
    ! [U_9281,U_9282] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9281,tc_HOL_Obool)),U_9282),c_Orderings_Obot__class_Obot(tc_fun(U_9281,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2545_2]) ).

cnf(f_2545_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9281,tc_HOL_Obool)),U_9282),c_Orderings_Obot__class_Obot(tc_fun(U_9281,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2545_3]) ).

fof(f_2546_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_2546_2,plain,
    ! [U_9283] : hAPP(c_Relation_OField(U_9283),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9283,U_9283),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9283,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2546_1]) ).

fof(f_2546_3,plain,
    ! [U_9283] : hAPP(c_Relation_OField(U_9283),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9283,U_9283),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9283,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2546_2]) ).

cnf(f_2546_4,plain,
    hAPP(c_Relation_OField(U_9283),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9283,U_9283),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_9283,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2546_3]) ).

fof(f_2547_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_2547_2,plain,
    ! [U_9287,U_9286,U_9285,U_9284] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9284,tc_HOL_Obool)),U_9285),hAPP(hAPP(c_Set_Oinsert(U_9284),U_9286),U_9287)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9284),U_9286),U_9285))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9284,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9284,tc_HOL_Obool)),U_9285),hAPP(hAPP(c_Set_Oinsert(U_9284),U_9286),c_Orderings_Obot__class_Obot(tc_fun(U_9284,tc_HOL_Obool))))),U_9287)) ),
    inference(variable_rename,[status(thm)],[f_2547_1]) ).

fof(f_2547_3,plain,
    ! [U_9284,U_9285,U_9286,U_9287] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9284,tc_HOL_Obool)),U_9285),hAPP(hAPP(c_Set_Oinsert(U_9284),U_9286),U_9287)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9284),U_9286),U_9285))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9284,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9284,tc_HOL_Obool)),U_9285),hAPP(hAPP(c_Set_Oinsert(U_9284),U_9286),c_Orderings_Obot__class_Obot(tc_fun(U_9284,tc_HOL_Obool))))),U_9287)) ),
    inference(definitional_conversion,[status(esa)],[f_2547_2]) ).

cnf(f_2547_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9284,tc_HOL_Obool)),U_9285),hAPP(hAPP(c_Set_Oinsert(U_9284),U_9286),U_9287)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9284),U_9286),U_9285))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9284,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9284,tc_HOL_Obool)),U_9285),hAPP(hAPP(c_Set_Oinsert(U_9284),U_9286),c_Orderings_Obot__class_Obot(tc_fun(U_9284,tc_HOL_Obool))))),U_9287)) ),
    inference(clausify,[status(thm)],[f_2547_3]) ).

fof(f_2548_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_2548_2,plain,
    ! [U_9291,U_9290,U_9289,U_9288] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9288,tc_HOL_Obool)),U_9289),hAPP(hAPP(c_Set_Oinsert(U_9288),U_9290),U_9291)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9288,tc_HOL_Obool)),U_9289),U_9291))
          & ~ hBOOL(hAPP(hAPP(c_member(U_9288),U_9290),U_9289)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9288,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9288,tc_HOL_Obool)),U_9289),hAPP(hAPP(c_Set_Oinsert(U_9288),U_9290),c_Orderings_Obot__class_Obot(tc_fun(U_9288,tc_HOL_Obool))))),U_9291))
          & hBOOL(hAPP(hAPP(c_member(U_9288),U_9290),U_9289)) ) )
      & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9288,tc_HOL_Obool)),U_9289),U_9291))
            | hBOOL(hAPP(hAPP(c_member(U_9288),U_9290),U_9289)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9288,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9288,tc_HOL_Obool)),U_9289),hAPP(hAPP(c_Set_Oinsert(U_9288),U_9290),c_Orderings_Obot__class_Obot(tc_fun(U_9288,tc_HOL_Obool))))),U_9291))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9288),U_9290),U_9289)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9288,tc_HOL_Obool)),U_9289),hAPP(hAPP(c_Set_Oinsert(U_9288),U_9290),U_9291))) ) ),
    inference(variable_rename,[status(thm)],[f_2548_1]) ).

fof(f_2548_3,plain,
    ( ! [U_9299,U_9297,U_9295,U_9293] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9293,tc_HOL_Obool)),U_9295),hAPP(hAPP(c_Set_Oinsert(U_9293),U_9297),U_9299)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9293,tc_HOL_Obool)),U_9295),U_9299))
          & ~ hBOOL(hAPP(hAPP(c_member(U_9293),U_9297),U_9295)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9293,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9293,tc_HOL_Obool)),U_9295),hAPP(hAPP(c_Set_Oinsert(U_9293),U_9297),c_Orderings_Obot__class_Obot(tc_fun(U_9293,tc_HOL_Obool))))),U_9299))
          & hBOOL(hAPP(hAPP(c_member(U_9293),U_9297),U_9295)) ) )
    & ! [U_9298,U_9296,U_9294,U_9292] :
        ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9292,tc_HOL_Obool)),U_9294),U_9298))
            | hBOOL(hAPP(hAPP(c_member(U_9292),U_9296),U_9294)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9292,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9292,tc_HOL_Obool)),U_9294),hAPP(hAPP(c_Set_Oinsert(U_9292),U_9296),c_Orderings_Obot__class_Obot(tc_fun(U_9292,tc_HOL_Obool))))),U_9298))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9292),U_9296),U_9294)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9292,tc_HOL_Obool)),U_9294),hAPP(hAPP(c_Set_Oinsert(U_9292),U_9296),U_9298))) ) ),
    inference(miniscope,[status(thm)],[f_2548_2]) ).

fof(f_2548_4,plain,
    ( ! [U_9293,U_9295,U_9297,U_9299] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9293,tc_HOL_Obool)),U_9295),U_9299))
        | ~ sP733(U_9293,U_9295,U_9297,U_9299) )
    & ! [U_9293,U_9295,U_9297,U_9299] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_9293),U_9297),U_9295))
        | ~ sP733(U_9293,U_9295,U_9297,U_9299) )
    & ! [U_9293,U_9295,U_9297,U_9299] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9293,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9293,tc_HOL_Obool)),U_9295),hAPP(hAPP(c_Set_Oinsert(U_9293),U_9297),c_Orderings_Obot__class_Obot(tc_fun(U_9293,tc_HOL_Obool))))),U_9299))
        | ~ sP732(U_9293,U_9295,U_9297,U_9299) )
    & ! [U_9293,U_9295,U_9297,U_9299] :
        ( hBOOL(hAPP(hAPP(c_member(U_9293),U_9297),U_9295))
        | ~ sP732(U_9293,U_9295,U_9297,U_9299) )
    & ! [U_9292,U_9294,U_9296,U_9298] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9292,tc_HOL_Obool)),U_9294),U_9298))
        | hBOOL(hAPP(hAPP(c_member(U_9292),U_9296),U_9294))
        | ~ sP731(U_9292,U_9294,U_9296,U_9298) )
    & ! [U_9292,U_9294,U_9296,U_9298] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9292,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9292,tc_HOL_Obool)),U_9294),hAPP(hAPP(c_Set_Oinsert(U_9292),U_9296),c_Orderings_Obot__class_Obot(tc_fun(U_9292,tc_HOL_Obool))))),U_9298))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9292),U_9296),U_9294))
        | ~ sP731(U_9292,U_9294,U_9296,U_9298) )
    & ! [U_9293,U_9295,U_9297,U_9299] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9293,tc_HOL_Obool)),U_9295),hAPP(hAPP(c_Set_Oinsert(U_9293),U_9297),U_9299)))
        | sP733(U_9293,U_9295,U_9297,U_9299)
        | sP732(U_9293,U_9295,U_9297,U_9299) )
    & ! [U_9292,U_9294,U_9296,U_9298] :
        ( sP731(U_9292,U_9294,U_9296,U_9298)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9292,tc_HOL_Obool)),U_9294),hAPP(hAPP(c_Set_Oinsert(U_9292),U_9296),U_9298))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP731,sP732,sP733])],[f_2548_3]) ).

cnf(f_2548_5,plain,
    ( sP731(U_9292,U_9294,U_9296,U_9298)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9292,tc_HOL_Obool)),U_9294),hAPP(hAPP(c_Set_Oinsert(U_9292),U_9296),U_9298))) ),
    inference(clausify,[status(thm)],[f_2548_4]) ).

cnf(f_2548_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9293,tc_HOL_Obool)),U_9295),hAPP(hAPP(c_Set_Oinsert(U_9293),U_9297),U_9299)))
    | sP733(U_9293,U_9295,U_9297,U_9299)
    | sP732(U_9293,U_9295,U_9297,U_9299) ),
    inference(clausify,[status(thm)],[f_2548_4]) ).

cnf(f_2548_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9292,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9292,tc_HOL_Obool)),U_9294),hAPP(hAPP(c_Set_Oinsert(U_9292),U_9296),c_Orderings_Obot__class_Obot(tc_fun(U_9292,tc_HOL_Obool))))),U_9298))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9292),U_9296),U_9294))
    | ~ sP731(U_9292,U_9294,U_9296,U_9298) ),
    inference(clausify,[status(thm)],[f_2548_4]) ).

cnf(f_2548_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9292,tc_HOL_Obool)),U_9294),U_9298))
    | hBOOL(hAPP(hAPP(c_member(U_9292),U_9296),U_9294))
    | ~ sP731(U_9292,U_9294,U_9296,U_9298) ),
    inference(clausify,[status(thm)],[f_2548_4]) ).

cnf(f_2548_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9293),U_9297),U_9295))
    | ~ sP732(U_9293,U_9295,U_9297,U_9299) ),
    inference(clausify,[status(thm)],[f_2548_4]) ).

cnf(f_2548_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9293,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9293,tc_HOL_Obool)),U_9295),hAPP(hAPP(c_Set_Oinsert(U_9293),U_9297),c_Orderings_Obot__class_Obot(tc_fun(U_9293,tc_HOL_Obool))))),U_9299))
    | ~ sP732(U_9293,U_9295,U_9297,U_9299) ),
    inference(clausify,[status(thm)],[f_2548_4]) ).

cnf(f_2548_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9293),U_9297),U_9295))
    | ~ sP733(U_9293,U_9295,U_9297,U_9299) ),
    inference(clausify,[status(thm)],[f_2548_4]) ).

cnf(f_2548_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9293,tc_HOL_Obool)),U_9295),U_9299))
    | ~ sP733(U_9293,U_9295,U_9297,U_9299) ),
    inference(clausify,[status(thm)],[f_2548_4]) ).

fof(f_2549_1,plain,
    ! [V_Pa_2,V_a_2,T_b] : hAPP(hAPP(c_Set_Oinsert(T_b),V_a_2),hAPP(c_Set_OCollect(T_b),V_Pa_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_Pa_2)),
    inference(fof_nnf,[status(thm)],[fact_insert__Collect]) ).

fof(f_2549_2,plain,
    ! [U_9302,U_9301,U_9300] : hAPP(hAPP(c_Set_Oinsert(U_9300),U_9301),hAPP(c_Set_OCollect(U_9300),U_9302)) = hAPP(c_Set_OCollect(U_9300),hAPP(hAPP(c_COMBS(U_9300,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9300),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9300),c_fNot),hAPP(hAPP(c_COMBC(U_9300,U_9300,tc_HOL_Obool),c_fequal),U_9301)))),U_9302)),
    inference(variable_rename,[status(thm)],[f_2549_1]) ).

fof(f_2549_3,plain,
    ! [U_9301,U_9300,U_9302] : hAPP(hAPP(c_Set_Oinsert(U_9300),U_9301),hAPP(c_Set_OCollect(U_9300),U_9302)) = hAPP(c_Set_OCollect(U_9300),hAPP(hAPP(c_COMBS(U_9300,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9300),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9300),c_fNot),hAPP(hAPP(c_COMBC(U_9300,U_9300,tc_HOL_Obool),c_fequal),U_9301)))),U_9302)),
    inference(definitional_conversion,[status(esa)],[f_2549_2]) ).

cnf(f_2549_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_9300),U_9301),hAPP(c_Set_OCollect(U_9300),U_9302)) = hAPP(c_Set_OCollect(U_9300),hAPP(hAPP(c_COMBS(U_9300,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9300),c_fimplies),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9300),c_fNot),hAPP(hAPP(c_COMBC(U_9300,U_9300,tc_HOL_Obool),c_fequal),U_9301)))),U_9302)),
    inference(clausify,[status(thm)],[f_2549_3]) ).

fof(f_2550_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_2550_2,plain,
    ! [U_9304,U_9303] :
      ( ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9303,tc_HOL_Obool)),U_9304))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9303),U_9304),c_Orderings_Obot__class_Obot(tc_fun(U_9303,tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_9303),U_9304),c_Orderings_Obot__class_Obot(tc_fun(U_9303,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9303,tc_HOL_Obool)),U_9304)) ) ),
    inference(variable_rename,[status(thm)],[f_2550_1]) ).

fof(f_2550_3,plain,
    ( ! [U_9308,U_9306] :
        ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9306,tc_HOL_Obool)),U_9308))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9306),U_9308),c_Orderings_Obot__class_Obot(tc_fun(U_9306,tc_HOL_Obool)))) )
    & ! [U_9307,U_9305] :
        ( hBOOL(hAPP(hAPP(c_member(U_9305),U_9307),c_Orderings_Obot__class_Obot(tc_fun(U_9305,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9305,tc_HOL_Obool)),U_9307)) ) ),
    inference(miniscope,[status(thm)],[f_2550_2]) ).

fof(f_2550_4,plain,
    ( ! [U_9308,U_9306] :
        ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9306,tc_HOL_Obool)),U_9308))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9306),U_9308),c_Orderings_Obot__class_Obot(tc_fun(U_9306,tc_HOL_Obool)))) )
    & ! [U_9307,U_9305] :
        ( hBOOL(hAPP(hAPP(c_member(U_9305),U_9307),c_Orderings_Obot__class_Obot(tc_fun(U_9305,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9305,tc_HOL_Obool)),U_9307)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2550_3]) ).

cnf(f_2550_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9305),U_9307),c_Orderings_Obot__class_Obot(tc_fun(U_9305,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9305,tc_HOL_Obool)),U_9307)) ),
    inference(clausify,[status(thm)],[f_2550_4]) ).

cnf(f_2550_6,plain,
    ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9306,tc_HOL_Obool)),U_9308))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9306),U_9308),c_Orderings_Obot__class_Obot(tc_fun(U_9306,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2550_4]) ).

fof(f_2551_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_2551_2,plain,
    ! [U_9309] : c_Orderings_Obot__class_Obot(tc_fun(U_9309,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9309),hAPP(c_COMBK(tc_HOL_Obool,U_9309),c_fFalse)),
    inference(variable_rename,[status(thm)],[f_2551_1]) ).

fof(f_2551_3,plain,
    ! [U_9309] : c_Orderings_Obot__class_Obot(tc_fun(U_9309,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9309),hAPP(c_COMBK(tc_HOL_Obool,U_9309),c_fFalse)),
    inference(definitional_conversion,[status(esa)],[f_2551_2]) ).

cnf(f_2551_4,plain,
    c_Orderings_Obot__class_Obot(tc_fun(U_9309,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_9309),hAPP(c_COMBK(tc_HOL_Obool,U_9309),c_fFalse)),
    inference(clausify,[status(thm)],[f_2551_3]) ).

fof(f_2552_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_2552_2,plain,
    ! [U_9311,U_9310] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9310),c_Orderings_Obot__class_Obot(U_9310)),U_9311))
      | ~ class_Orderings_Obot(U_9310) ),
    inference(variable_rename,[status(thm)],[f_2552_1]) ).

fof(f_2552_3,plain,
    ! [U_9310,U_9311] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9310),c_Orderings_Obot__class_Obot(U_9310)),U_9311))
      | ~ class_Orderings_Obot(U_9310) ),
    inference(definitional_conversion,[status(esa)],[f_2552_2]) ).

cnf(f_2552_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9310),c_Orderings_Obot__class_Obot(U_9310)),U_9311))
    | ~ class_Orderings_Obot(U_9310) ),
    inference(clausify,[status(thm)],[f_2552_3]) ).

fof(f_2553_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_2553_2,plain,
    ! [U_9314,U_9313,U_9312] :
      ( ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9312),U_9313),U_9314) = c_Orderings_Obot__class_Obot(U_9312)
          | U_9314 != c_Orderings_Obot__class_Obot(U_9312)
          | U_9313 != c_Orderings_Obot__class_Obot(U_9312) )
        & ( ( U_9314 = c_Orderings_Obot__class_Obot(U_9312)
            & U_9313 = c_Orderings_Obot__class_Obot(U_9312) )
          | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9312),U_9313),U_9314) != c_Orderings_Obot__class_Obot(U_9312) ) )
      | ~ class_Lattices_Obounded__lattice__bot(U_9312) ),
    inference(variable_rename,[status(thm)],[f_2553_1]) ).

fof(f_2553_3,plain,
    ( ! [U_9312,U_9313,U_9314] :
        ( U_9314 = c_Orderings_Obot__class_Obot(U_9312)
        | ~ sP734(U_9312,U_9313,U_9314) )
    & ! [U_9312,U_9313,U_9314] :
        ( U_9313 = c_Orderings_Obot__class_Obot(U_9312)
        | ~ sP734(U_9312,U_9313,U_9314) )
    & ! [U_9312,U_9313,U_9314] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9312),U_9313),U_9314) = c_Orderings_Obot__class_Obot(U_9312)
        | U_9314 != c_Orderings_Obot__class_Obot(U_9312)
        | U_9313 != c_Orderings_Obot__class_Obot(U_9312)
        | ~ sP735(U_9312,U_9313,U_9314) )
    & ! [U_9312,U_9313,U_9314] :
        ( sP734(U_9312,U_9313,U_9314)
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9312),U_9313),U_9314) != c_Orderings_Obot__class_Obot(U_9312)
        | ~ sP735(U_9312,U_9313,U_9314) )
    & ! [U_9312,U_9313,U_9314] :
        ( sP735(U_9312,U_9313,U_9314)
        | ~ class_Lattices_Obounded__lattice__bot(U_9312) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP734,sP735])],[f_2553_2]) ).

cnf(f_2553_4,plain,
    ( sP735(U_9312,U_9313,U_9314)
    | ~ class_Lattices_Obounded__lattice__bot(U_9312) ),
    inference(clausify,[status(thm)],[f_2553_3]) ).

cnf(f_2553_5,plain,
    ( sP734(U_9312,U_9313,U_9314)
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9312),U_9313),U_9314) != c_Orderings_Obot__class_Obot(U_9312)
    | ~ sP735(U_9312,U_9313,U_9314) ),
    inference(clausify,[status(thm)],[f_2553_3]) ).

cnf(f_2553_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9312),U_9313),U_9314) = c_Orderings_Obot__class_Obot(U_9312)
    | U_9314 != c_Orderings_Obot__class_Obot(U_9312)
    | U_9313 != c_Orderings_Obot__class_Obot(U_9312)
    | ~ sP735(U_9312,U_9313,U_9314) ),
    inference(clausify,[status(thm)],[f_2553_3]) ).

cnf(f_2553_7,plain,
    ( U_9313 = c_Orderings_Obot__class_Obot(U_9312)
    | ~ sP734(U_9312,U_9313,U_9314) ),
    inference(clausify,[status(thm)],[f_2553_3]) ).

cnf(f_2553_8,plain,
    ( U_9314 = c_Orderings_Obot__class_Obot(U_9312)
    | ~ sP734(U_9312,U_9313,U_9314) ),
    inference(clausify,[status(thm)],[f_2553_3]) ).

fof(f_2554_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_2554_2,plain,
    ! [U_9316,U_9315] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9315),U_9316),c_Orderings_Obot__class_Obot(U_9315)) = U_9316
      | ~ class_Lattices_Obounded__lattice__bot(U_9315) ),
    inference(variable_rename,[status(thm)],[f_2554_1]) ).

fof(f_2554_3,plain,
    ! [U_9315,U_9316] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9315),U_9316),c_Orderings_Obot__class_Obot(U_9315)) = U_9316
      | ~ class_Lattices_Obounded__lattice__bot(U_9315) ),
    inference(definitional_conversion,[status(esa)],[f_2554_2]) ).

cnf(f_2554_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9315),U_9316),c_Orderings_Obot__class_Obot(U_9315)) = U_9316
    | ~ class_Lattices_Obounded__lattice__bot(U_9315) ),
    inference(clausify,[status(thm)],[f_2554_3]) ).

fof(f_2555_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_2555_2,plain,
    ! [U_9318,U_9317] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9317),c_Orderings_Obot__class_Obot(U_9317)),U_9318) = U_9318
      | ~ class_Lattices_Obounded__lattice__bot(U_9317) ),
    inference(variable_rename,[status(thm)],[f_2555_1]) ).

fof(f_2555_3,plain,
    ! [U_9318,U_9317] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9317),c_Orderings_Obot__class_Obot(U_9317)),U_9318) = U_9318
      | ~ class_Lattices_Obounded__lattice__bot(U_9317) ),
    inference(definitional_conversion,[status(esa)],[f_2555_2]) ).

cnf(f_2555_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_9317),c_Orderings_Obot__class_Obot(U_9317)),U_9318) = U_9318
    | ~ class_Lattices_Obounded__lattice__bot(U_9317) ),
    inference(clausify,[status(thm)],[f_2555_3]) ).

fof(f_2556_1,plain,
    ! [V_R_2,V_d_2,V_Qa_2,V_c_2,V_Pa_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_Pa_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_Qa_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_Pa_2),V_c_2),V_Qa_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_2556_2,plain,
    ! [U_9325,U_9324,U_9323,U_9322,U_9321,U_9320,U_9319] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_9319,U_9320,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9319)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9319),U_9321),c_Com_Ocom_OSemi(U_9322,U_9324)),U_9325)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9319),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9319,U_9320,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9319)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9319),U_9323),U_9324),U_9325)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9319),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9319,U_9320,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9319)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9319),U_9321),U_9322),U_9323)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9319),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2556_1]) ).

fof(f_2556_3,plain,
    ! [U_9319,U_9320,U_9321,U_9322,U_9323,U_9324,U_9325] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_9319,U_9320,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9319)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9319),U_9321),c_Com_Ocom_OSemi(U_9322,U_9324)),U_9325)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9319),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9319,U_9320,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9319)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9319),U_9323),U_9324),U_9325)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9319),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9319,U_9320,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9319)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9319),U_9321),U_9322),U_9323)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9319),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_2556_2]) ).

cnf(f_2556_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_9319,U_9320,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9319)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9319),U_9321),c_Com_Ocom_OSemi(U_9322,U_9324)),U_9325)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9319),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9319,U_9320,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9319)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9319),U_9323),U_9324),U_9325)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9319),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9319,U_9320,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9319)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9319),U_9321),U_9322),U_9323)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9319),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2556_3]) ).

fof(f_2557_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_2557_2,plain,
    ! [U_9328,U_9327,U_9326] : c_Hoare__Mirabelle_Ohoare__derivs(U_9326,U_9327,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9326)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9326),U_9328),c_Com_Ocom_OSKIP),U_9328)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9326),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2557_1]) ).

fof(f_2557_3,plain,
    ! [U_9327,U_9328,U_9326] : c_Hoare__Mirabelle_Ohoare__derivs(U_9326,U_9327,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9326)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9326),U_9328),c_Com_Ocom_OSKIP),U_9328)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9326),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2557_2]) ).

cnf(f_2557_4,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_9326,U_9327,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9326)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9326),U_9328),c_Com_Ocom_OSKIP),U_9328)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9326),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2557_3]) ).

fof(f_2558_1,plain,
    ! [V_Pa_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_Pa_2),c_Com_Ocom_OSKIP),V_Pa_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_2558_2,plain,
    ! [U_9331,U_9330,U_9329] : c_Hoare__Mirabelle_Ohoare__derivs(U_9329,U_9330,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9329)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9329),U_9331),c_Com_Ocom_OSKIP),U_9331)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9329),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2558_1]) ).

fof(f_2558_3,plain,
    ! [U_9329,U_9330,U_9331] : c_Hoare__Mirabelle_Ohoare__derivs(U_9329,U_9330,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9329)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9329),U_9331),c_Com_Ocom_OSKIP),U_9331)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9329),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2558_2]) ).

cnf(f_2558_4,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_9329,U_9330,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9329)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9329),U_9331),c_Com_Ocom_OSKIP),U_9331)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9329),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2558_3]) ).

fof(f_2559_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_2559_2,plain,
    ! [U_9333,U_9332] : c_Relation_Ototal__on(U_9332,c_Orderings_Obot__class_Obot(tc_fun(U_9332,tc_HOL_Obool)),U_9333),
    inference(variable_rename,[status(thm)],[f_2559_1]) ).

fof(f_2559_3,plain,
    ! [U_9332,U_9333] : c_Relation_Ototal__on(U_9332,c_Orderings_Obot__class_Obot(tc_fun(U_9332,tc_HOL_Obool)),U_9333),
    inference(definitional_conversion,[status(esa)],[f_2559_2]) ).

cnf(f_2559_4,plain,
    c_Relation_Ototal__on(U_9332,c_Orderings_Obot__class_Obot(tc_fun(U_9332,tc_HOL_Obool)),U_9333),
    inference(clausify,[status(thm)],[f_2559_3]) ).

fof(f_2560_1,plain,
    ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__join]) ).

fof(f_2560_2,plain,
    ! [U_9337,U_9336,U_9335,U_9334] : c_Predicate_Oconversep(U_9334,U_9335,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9334,tc_fun(U_9335,tc_HOL_Obool))),U_9336),U_9337)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9335,tc_fun(U_9334,tc_HOL_Obool))),c_Predicate_Oconversep(U_9334,U_9335,U_9336)),c_Predicate_Oconversep(U_9334,U_9335,U_9337)),
    inference(variable_rename,[status(thm)],[f_2560_1]) ).

fof(f_2560_3,plain,
    ! [U_9334,U_9335,U_9336,U_9337] : c_Predicate_Oconversep(U_9334,U_9335,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9334,tc_fun(U_9335,tc_HOL_Obool))),U_9336),U_9337)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9335,tc_fun(U_9334,tc_HOL_Obool))),c_Predicate_Oconversep(U_9334,U_9335,U_9336)),c_Predicate_Oconversep(U_9334,U_9335,U_9337)),
    inference(definitional_conversion,[status(esa)],[f_2560_2]) ).

cnf(f_2560_4,plain,
    c_Predicate_Oconversep(U_9334,U_9335,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9334,tc_fun(U_9335,tc_HOL_Obool))),U_9336),U_9337)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9335,tc_fun(U_9334,tc_HOL_Obool))),c_Predicate_Oconversep(U_9334,U_9335,U_9336)),c_Predicate_Oconversep(U_9334,U_9335,U_9337)),
    inference(clausify,[status(thm)],[f_2560_3]) ).

fof(f_2561_1,plain,
    ! [V_c_2,V_b_2,V_Pa_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_Pa_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_Pa_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_2561_2,plain,
    ! [U_9342,U_9341,U_9340,U_9339,U_9338] : c_Hoare__Mirabelle_Ohoare__derivs(U_9338,U_9339,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9338)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9338),hAPP(hAPP(c_COMBC(U_9338,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_9338),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_9338),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),U_9340))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),U_9341))),c_Com_Ocom_OWhile(U_9341,U_9342)),U_9340)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9338),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2561_1]) ).

fof(f_2561_3,plain,
    ! [U_9338,U_9339,U_9340,U_9341,U_9342] : c_Hoare__Mirabelle_Ohoare__derivs(U_9338,U_9339,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9338)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9338),hAPP(hAPP(c_COMBC(U_9338,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_9338),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_9338),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),U_9340))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),U_9341))),c_Com_Ocom_OWhile(U_9341,U_9342)),U_9340)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9338),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2561_2]) ).

cnf(f_2561_4,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_9338,U_9339,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9338)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9338),hAPP(hAPP(c_COMBC(U_9338,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_9338),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_9338),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),U_9340))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),U_9341))),c_Com_Ocom_OWhile(U_9341,U_9342)),U_9340)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9338),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2561_3]) ).

fof(f_2562_1,plain,
    ! [V_s_2,V_r_2,T_d,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,c_Predicate_Opred__comp(T_c,T_d,T_b,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_b,T_d,T_c,c_Predicate_Oconversep(T_d,T_b,V_s_2),c_Predicate_Oconversep(T_c,T_d,V_r_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__pred__comp]) ).

fof(f_2562_2,plain,
    ! [U_9347,U_9346,U_9345,U_9344,U_9343] : c_Predicate_Oconversep(U_9343,U_9344,c_Predicate_Opred__comp(U_9343,U_9345,U_9344,U_9346,U_9347)) = c_Predicate_Opred__comp(U_9344,U_9345,U_9343,c_Predicate_Oconversep(U_9345,U_9344,U_9347),c_Predicate_Oconversep(U_9343,U_9345,U_9346)),
    inference(variable_rename,[status(thm)],[f_2562_1]) ).

fof(f_2562_3,plain,
    ! [U_9344,U_9343,U_9345,U_9346,U_9347] : c_Predicate_Oconversep(U_9343,U_9344,c_Predicate_Opred__comp(U_9343,U_9345,U_9344,U_9346,U_9347)) = c_Predicate_Opred__comp(U_9344,U_9345,U_9343,c_Predicate_Oconversep(U_9345,U_9344,U_9347),c_Predicate_Oconversep(U_9343,U_9345,U_9346)),
    inference(definitional_conversion,[status(esa)],[f_2562_2]) ).

cnf(f_2562_4,plain,
    c_Predicate_Oconversep(U_9343,U_9344,c_Predicate_Opred__comp(U_9343,U_9345,U_9344,U_9346,U_9347)) = c_Predicate_Opred__comp(U_9344,U_9345,U_9343,c_Predicate_Oconversep(U_9345,U_9344,U_9347),c_Predicate_Oconversep(U_9343,U_9345,U_9346)),
    inference(clausify,[status(thm)],[f_2562_3]) ).

fof(f_2563_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_2563_2,plain,
    ! [U_9351,U_9350,U_9349,U_9348] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9348,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9348),U_9349),U_9350)),U_9351))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9348,tc_HOL_Obool)),U_9350),U_9351))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9348),U_9349),U_9351)) )
      & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9348,tc_HOL_Obool)),U_9350),U_9351))
          & hBOOL(hAPP(hAPP(c_member(U_9348),U_9349),U_9351)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9348,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9348),U_9349),U_9350)),U_9351)) ) ),
    inference(variable_rename,[status(thm)],[f_2563_1]) ).

fof(f_2563_3,plain,
    ( ! [U_9359,U_9357,U_9355,U_9353] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9353,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9353),U_9355),U_9357)),U_9359))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9353,tc_HOL_Obool)),U_9357),U_9359))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9353),U_9355),U_9359)) )
    & ! [U_9358,U_9356,U_9354,U_9352] :
        ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9352,tc_HOL_Obool)),U_9356),U_9358))
          & hBOOL(hAPP(hAPP(c_member(U_9352),U_9354),U_9358)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9352,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9352),U_9354),U_9356)),U_9358)) ) ),
    inference(miniscope,[status(thm)],[f_2563_2]) ).

fof(f_2563_4,plain,
    ( ! [U_9354,U_9352,U_9356,U_9358] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9352,tc_HOL_Obool)),U_9356),U_9358))
        | ~ sP736(U_9354,U_9352,U_9356,U_9358) )
    & ! [U_9354,U_9352,U_9356,U_9358] :
        ( hBOOL(hAPP(hAPP(c_member(U_9352),U_9354),U_9358))
        | ~ sP736(U_9354,U_9352,U_9356,U_9358) )
    & ! [U_9357,U_9355,U_9353,U_9359] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9353,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9353),U_9355),U_9357)),U_9359))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9353,tc_HOL_Obool)),U_9357),U_9359))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9353),U_9355),U_9359)) )
    & ! [U_9354,U_9352,U_9356,U_9358] :
        ( sP736(U_9354,U_9352,U_9356,U_9358)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9352,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9352),U_9354),U_9356)),U_9358)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP736])],[f_2563_3]) ).

cnf(f_2563_5,plain,
    ( sP736(U_9354,U_9352,U_9356,U_9358)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9352,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9352),U_9354),U_9356)),U_9358)) ),
    inference(clausify,[status(thm)],[f_2563_4]) ).

cnf(f_2563_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9353,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9353),U_9355),U_9357)),U_9359))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9353,tc_HOL_Obool)),U_9357),U_9359))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9353),U_9355),U_9359)) ),
    inference(clausify,[status(thm)],[f_2563_4]) ).

cnf(f_2563_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9352),U_9354),U_9358))
    | ~ sP736(U_9354,U_9352,U_9356,U_9358) ),
    inference(clausify,[status(thm)],[f_2563_4]) ).

cnf(f_2563_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9352,tc_HOL_Obool)),U_9356),U_9358))
    | ~ sP736(U_9354,U_9352,U_9356,U_9358) ),
    inference(clausify,[status(thm)],[f_2563_4]) ).

fof(f_2564_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_2564_2,plain,
    ! [U_9363,U_9362,U_9361,U_9360] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9360,tc_HOL_Obool)),U_9362),hAPP(hAPP(c_Set_Oinsert(U_9360),U_9361),U_9363)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9360,tc_HOL_Obool)),U_9362),U_9363)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9360,tc_HOL_Obool)),U_9362),U_9363))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9360,tc_HOL_Obool)),U_9362),hAPP(hAPP(c_Set_Oinsert(U_9360),U_9361),U_9363))) ) )
      | hBOOL(hAPP(hAPP(c_member(U_9360),U_9361),U_9362)) ),
    inference(variable_rename,[status(thm)],[f_2564_1]) ).

fof(f_2564_3,plain,
    ( ! [U_9360,U_9361,U_9363,U_9362] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9360,tc_HOL_Obool)),U_9362),hAPP(hAPP(c_Set_Oinsert(U_9360),U_9361),U_9363)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9360,tc_HOL_Obool)),U_9362),U_9363))
        | ~ sP737(U_9360,U_9361,U_9363,U_9362) )
    & ! [U_9360,U_9361,U_9363,U_9362] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9360,tc_HOL_Obool)),U_9362),U_9363))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9360,tc_HOL_Obool)),U_9362),hAPP(hAPP(c_Set_Oinsert(U_9360),U_9361),U_9363)))
        | ~ sP737(U_9360,U_9361,U_9363,U_9362) )
    & ! [U_9360,U_9361,U_9363,U_9362] :
        ( sP737(U_9360,U_9361,U_9363,U_9362)
        | hBOOL(hAPP(hAPP(c_member(U_9360),U_9361),U_9362)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP737])],[f_2564_2]) ).

cnf(f_2564_4,plain,
    ( sP737(U_9360,U_9361,U_9363,U_9362)
    | hBOOL(hAPP(hAPP(c_member(U_9360),U_9361),U_9362)) ),
    inference(clausify,[status(thm)],[f_2564_3]) ).

cnf(f_2564_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9360,tc_HOL_Obool)),U_9362),U_9363))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9360,tc_HOL_Obool)),U_9362),hAPP(hAPP(c_Set_Oinsert(U_9360),U_9361),U_9363)))
    | ~ sP737(U_9360,U_9361,U_9363,U_9362) ),
    inference(clausify,[status(thm)],[f_2564_3]) ).

cnf(f_2564_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9360,tc_HOL_Obool)),U_9362),hAPP(hAPP(c_Set_Oinsert(U_9360),U_9361),U_9363)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9360,tc_HOL_Obool)),U_9362),U_9363))
    | ~ sP737(U_9360,U_9361,U_9363,U_9362) ),
    inference(clausify,[status(thm)],[f_2564_3]) ).

fof(f_2565_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_2565_2,plain,
    ! [U_9368,U_9367,U_9366,U_9365,U_9364] :
      ( hAPP(hAPP(c_Set_Oinsert(U_9367),hAPP(U_9368,U_9365)),hAPP(c_Set_Oimage(U_9364,U_9367,U_9368),U_9366)) = hAPP(c_Set_Oimage(U_9364,U_9367,U_9368),U_9366)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9364),U_9365),U_9366)) ),
    inference(variable_rename,[status(thm)],[f_2565_1]) ).

fof(f_2565_3,plain,
    ! [U_9365,U_9366,U_9367,U_9368,U_9364] :
      ( hAPP(hAPP(c_Set_Oinsert(U_9367),hAPP(U_9368,U_9365)),hAPP(c_Set_Oimage(U_9364,U_9367,U_9368),U_9366)) = hAPP(c_Set_Oimage(U_9364,U_9367,U_9368),U_9366)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9364),U_9365),U_9366)) ),
    inference(definitional_conversion,[status(esa)],[f_2565_2]) ).

cnf(f_2565_4,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_9367),hAPP(U_9368,U_9365)),hAPP(c_Set_Oimage(U_9364,U_9367,U_9368),U_9366)) = hAPP(c_Set_Oimage(U_9364,U_9367,U_9368),U_9366)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9364),U_9365),U_9366)) ),
    inference(clausify,[status(thm)],[f_2565_3]) ).

fof(f_2566_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_2566_2,plain,
    ! [U_9372,U_9371,U_9370,U_9369] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9369,tc_HOL_Obool)),U_9370),hAPP(hAPP(c_Set_Oinsert(U_9369),U_9371),U_9372)))
        | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9369,tc_HOL_Obool)),U_9370),U_9372))
              & ~ hBOOL(hAPP(hAPP(c_member(U_9369),U_9371),U_9370)) )
            | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9369,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9369,tc_HOL_Obool)),U_9370),hAPP(hAPP(c_Set_Oinsert(U_9369),U_9371),c_Orderings_Obot__class_Obot(tc_fun(U_9369,tc_HOL_Obool))))),U_9372))
              & hBOOL(hAPP(hAPP(c_member(U_9369),U_9371),U_9370)) ) )
          & ~ hBOOL(hAPP(hAPP(c_member(U_9369),U_9371),U_9372)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9369,tc_HOL_Obool)),U_9370),U_9372))
          & hBOOL(hAPP(hAPP(c_member(U_9369),U_9371),U_9372)) ) )
      & ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9369,tc_HOL_Obool)),U_9370),U_9372))
                | hBOOL(hAPP(hAPP(c_member(U_9369),U_9371),U_9370)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9369,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9369,tc_HOL_Obool)),U_9370),hAPP(hAPP(c_Set_Oinsert(U_9369),U_9371),c_Orderings_Obot__class_Obot(tc_fun(U_9369,tc_HOL_Obool))))),U_9372))
                | ~ hBOOL(hAPP(hAPP(c_member(U_9369),U_9371),U_9370)) ) )
            | hBOOL(hAPP(hAPP(c_member(U_9369),U_9371),U_9372)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9369,tc_HOL_Obool)),U_9370),U_9372))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9369),U_9371),U_9372)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9369,tc_HOL_Obool)),U_9370),hAPP(hAPP(c_Set_Oinsert(U_9369),U_9371),U_9372))) ) ),
    inference(variable_rename,[status(thm)],[f_2566_1]) ).

fof(f_2566_3,plain,
    ( ! [U_9380,U_9378,U_9376,U_9374] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9374,tc_HOL_Obool)),U_9376),hAPP(hAPP(c_Set_Oinsert(U_9374),U_9378),U_9380)))
        | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9374,tc_HOL_Obool)),U_9376),U_9380))
              & ~ hBOOL(hAPP(hAPP(c_member(U_9374),U_9378),U_9376)) )
            | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9374,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9374,tc_HOL_Obool)),U_9376),hAPP(hAPP(c_Set_Oinsert(U_9374),U_9378),c_Orderings_Obot__class_Obot(tc_fun(U_9374,tc_HOL_Obool))))),U_9380))
              & hBOOL(hAPP(hAPP(c_member(U_9374),U_9378),U_9376)) ) )
          & ~ hBOOL(hAPP(hAPP(c_member(U_9374),U_9378),U_9380)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9374,tc_HOL_Obool)),U_9376),U_9380))
          & hBOOL(hAPP(hAPP(c_member(U_9374),U_9378),U_9380)) ) )
    & ! [U_9379,U_9377,U_9375,U_9373] :
        ( ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9373,tc_HOL_Obool)),U_9375),U_9379))
                | hBOOL(hAPP(hAPP(c_member(U_9373),U_9377),U_9375)) )
              & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9373,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9373,tc_HOL_Obool)),U_9375),hAPP(hAPP(c_Set_Oinsert(U_9373),U_9377),c_Orderings_Obot__class_Obot(tc_fun(U_9373,tc_HOL_Obool))))),U_9379))
                | ~ hBOOL(hAPP(hAPP(c_member(U_9373),U_9377),U_9375)) ) )
            | hBOOL(hAPP(hAPP(c_member(U_9373),U_9377),U_9379)) )
          & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9373,tc_HOL_Obool)),U_9375),U_9379))
            | ~ hBOOL(hAPP(hAPP(c_member(U_9373),U_9377),U_9379)) ) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9373,tc_HOL_Obool)),U_9375),hAPP(hAPP(c_Set_Oinsert(U_9373),U_9377),U_9379))) ) ),
    inference(miniscope,[status(thm)],[f_2566_2]) ).

fof(f_2566_4,plain,
    ( ! [U_9380,U_9374,U_9376,U_9378] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9374,tc_HOL_Obool)),U_9376),U_9380))
        | ~ sP742(U_9380,U_9374,U_9376,U_9378) )
    & ! [U_9380,U_9374,U_9376,U_9378] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_9374),U_9378),U_9376))
        | ~ sP742(U_9380,U_9374,U_9376,U_9378) )
    & ! [U_9380,U_9374,U_9376,U_9378] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9374,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9374,tc_HOL_Obool)),U_9376),hAPP(hAPP(c_Set_Oinsert(U_9374),U_9378),c_Orderings_Obot__class_Obot(tc_fun(U_9374,tc_HOL_Obool))))),U_9380))
        | ~ sP741(U_9380,U_9374,U_9376,U_9378) )
    & ! [U_9380,U_9374,U_9376,U_9378] :
        ( hBOOL(hAPP(hAPP(c_member(U_9374),U_9378),U_9376))
        | ~ sP741(U_9380,U_9374,U_9376,U_9378) )
    & ! [U_9380,U_9374,U_9376,U_9378] :
        ( sP742(U_9380,U_9374,U_9376,U_9378)
        | sP741(U_9380,U_9374,U_9376,U_9378)
        | ~ sP743(U_9380,U_9374,U_9376,U_9378) )
    & ! [U_9380,U_9374,U_9376,U_9378] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_9374),U_9378),U_9380))
        | ~ sP743(U_9380,U_9374,U_9376,U_9378) )
    & ! [U_9380,U_9374,U_9376,U_9378] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9374,tc_HOL_Obool)),U_9376),U_9380))
        | ~ sP740(U_9380,U_9374,U_9376,U_9378) )
    & ! [U_9380,U_9374,U_9376,U_9378] :
        ( hBOOL(hAPP(hAPP(c_member(U_9374),U_9378),U_9380))
        | ~ sP740(U_9380,U_9374,U_9376,U_9378) )
    & ! [U_9379,U_9373,U_9375,U_9377] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9373,tc_HOL_Obool)),U_9375),U_9379))
        | hBOOL(hAPP(hAPP(c_member(U_9373),U_9377),U_9375))
        | ~ sP738(U_9379,U_9373,U_9375,U_9377) )
    & ! [U_9379,U_9373,U_9375,U_9377] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9373,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9373,tc_HOL_Obool)),U_9375),hAPP(hAPP(c_Set_Oinsert(U_9373),U_9377),c_Orderings_Obot__class_Obot(tc_fun(U_9373,tc_HOL_Obool))))),U_9379))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9373),U_9377),U_9375))
        | ~ sP738(U_9379,U_9373,U_9375,U_9377) )
    & ! [U_9379,U_9373,U_9375,U_9377] :
        ( sP738(U_9379,U_9373,U_9375,U_9377)
        | hBOOL(hAPP(hAPP(c_member(U_9373),U_9377),U_9379))
        | ~ sP739(U_9379,U_9373,U_9375,U_9377) )
    & ! [U_9379,U_9373,U_9375,U_9377] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9373,tc_HOL_Obool)),U_9375),U_9379))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9373),U_9377),U_9379))
        | ~ sP739(U_9379,U_9373,U_9375,U_9377) )
    & ! [U_9380,U_9374,U_9376,U_9378] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9374,tc_HOL_Obool)),U_9376),hAPP(hAPP(c_Set_Oinsert(U_9374),U_9378),U_9380)))
        | sP743(U_9380,U_9374,U_9376,U_9378)
        | sP740(U_9380,U_9374,U_9376,U_9378) )
    & ! [U_9379,U_9373,U_9375,U_9377] :
        ( sP739(U_9379,U_9373,U_9375,U_9377)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9373,tc_HOL_Obool)),U_9375),hAPP(hAPP(c_Set_Oinsert(U_9373),U_9377),U_9379))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP738,sP739,sP740,sP741,sP742,sP743])],[f_2566_3]) ).

cnf(f_2566_5,plain,
    ( sP739(U_9379,U_9373,U_9375,U_9377)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9373,tc_HOL_Obool)),U_9375),hAPP(hAPP(c_Set_Oinsert(U_9373),U_9377),U_9379))) ),
    inference(clausify,[status(thm)],[f_2566_4]) ).

cnf(f_2566_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9374,tc_HOL_Obool)),U_9376),hAPP(hAPP(c_Set_Oinsert(U_9374),U_9378),U_9380)))
    | sP743(U_9380,U_9374,U_9376,U_9378)
    | sP740(U_9380,U_9374,U_9376,U_9378) ),
    inference(clausify,[status(thm)],[f_2566_4]) ).

cnf(f_2566_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9373,tc_HOL_Obool)),U_9375),U_9379))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9373),U_9377),U_9379))
    | ~ sP739(U_9379,U_9373,U_9375,U_9377) ),
    inference(clausify,[status(thm)],[f_2566_4]) ).

cnf(f_2566_8,plain,
    ( sP738(U_9379,U_9373,U_9375,U_9377)
    | hBOOL(hAPP(hAPP(c_member(U_9373),U_9377),U_9379))
    | ~ sP739(U_9379,U_9373,U_9375,U_9377) ),
    inference(clausify,[status(thm)],[f_2566_4]) ).

cnf(f_2566_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9373,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9373,tc_HOL_Obool)),U_9375),hAPP(hAPP(c_Set_Oinsert(U_9373),U_9377),c_Orderings_Obot__class_Obot(tc_fun(U_9373,tc_HOL_Obool))))),U_9379))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9373),U_9377),U_9375))
    | ~ sP738(U_9379,U_9373,U_9375,U_9377) ),
    inference(clausify,[status(thm)],[f_2566_4]) ).

cnf(f_2566_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9373,tc_HOL_Obool)),U_9375),U_9379))
    | hBOOL(hAPP(hAPP(c_member(U_9373),U_9377),U_9375))
    | ~ sP738(U_9379,U_9373,U_9375,U_9377) ),
    inference(clausify,[status(thm)],[f_2566_4]) ).

cnf(f_2566_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9374),U_9378),U_9380))
    | ~ sP740(U_9380,U_9374,U_9376,U_9378) ),
    inference(clausify,[status(thm)],[f_2566_4]) ).

cnf(f_2566_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9374,tc_HOL_Obool)),U_9376),U_9380))
    | ~ sP740(U_9380,U_9374,U_9376,U_9378) ),
    inference(clausify,[status(thm)],[f_2566_4]) ).

cnf(f_2566_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9374),U_9378),U_9380))
    | ~ sP743(U_9380,U_9374,U_9376,U_9378) ),
    inference(clausify,[status(thm)],[f_2566_4]) ).

cnf(f_2566_14,plain,
    ( sP742(U_9380,U_9374,U_9376,U_9378)
    | sP741(U_9380,U_9374,U_9376,U_9378)
    | ~ sP743(U_9380,U_9374,U_9376,U_9378) ),
    inference(clausify,[status(thm)],[f_2566_4]) ).

cnf(f_2566_15,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9374),U_9378),U_9376))
    | ~ sP741(U_9380,U_9374,U_9376,U_9378) ),
    inference(clausify,[status(thm)],[f_2566_4]) ).

cnf(f_2566_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9374,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9374,tc_HOL_Obool)),U_9376),hAPP(hAPP(c_Set_Oinsert(U_9374),U_9378),c_Orderings_Obot__class_Obot(tc_fun(U_9374,tc_HOL_Obool))))),U_9380))
    | ~ sP741(U_9380,U_9374,U_9376,U_9378) ),
    inference(clausify,[status(thm)],[f_2566_4]) ).

cnf(f_2566_17,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_9374),U_9378),U_9376))
    | ~ sP742(U_9380,U_9374,U_9376,U_9378) ),
    inference(clausify,[status(thm)],[f_2566_4]) ).

cnf(f_2566_18,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9374,tc_HOL_Obool)),U_9376),U_9380))
    | ~ sP742(U_9380,U_9374,U_9376,U_9378) ),
    inference(clausify,[status(thm)],[f_2566_4]) ).

fof(f_2567_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_2567_2,plain,
    ! [U_9384,U_9383,U_9382,U_9381] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9381,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9381),U_9382),U_9384)),U_9383) = hAPP(hAPP(c_Set_Oinsert(U_9381),U_9382),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9381,tc_HOL_Obool)),U_9384),U_9383))
        | hBOOL(hAPP(hAPP(c_member(U_9381),U_9382),U_9383)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9381,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9381),U_9382),U_9384)),U_9383) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9381,tc_HOL_Obool)),U_9384),U_9383)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9381),U_9382),U_9383)) ) ),
    inference(variable_rename,[status(thm)],[f_2567_1]) ).

fof(f_2567_3,plain,
    ( ! [U_9392,U_9390,U_9388,U_9386] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9386,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9386),U_9388),U_9392)),U_9390) = hAPP(hAPP(c_Set_Oinsert(U_9386),U_9388),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9386,tc_HOL_Obool)),U_9392),U_9390))
        | hBOOL(hAPP(hAPP(c_member(U_9386),U_9388),U_9390)) )
    & ! [U_9391,U_9389,U_9387,U_9385] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9385,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9385),U_9387),U_9391)),U_9389) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9385,tc_HOL_Obool)),U_9391),U_9389)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9385),U_9387),U_9389)) ) ),
    inference(miniscope,[status(thm)],[f_2567_2]) ).

fof(f_2567_4,plain,
    ( ! [U_9386,U_9390,U_9388,U_9392] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9386,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9386),U_9388),U_9392)),U_9390) = hAPP(hAPP(c_Set_Oinsert(U_9386),U_9388),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9386,tc_HOL_Obool)),U_9392),U_9390))
        | hBOOL(hAPP(hAPP(c_member(U_9386),U_9388),U_9390)) )
    & ! [U_9385,U_9387,U_9389,U_9391] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9385,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9385),U_9387),U_9391)),U_9389) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9385,tc_HOL_Obool)),U_9391),U_9389)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9385),U_9387),U_9389)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2567_3]) ).

cnf(f_2567_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9385,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9385),U_9387),U_9391)),U_9389) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9385,tc_HOL_Obool)),U_9391),U_9389)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9385),U_9387),U_9389)) ),
    inference(clausify,[status(thm)],[f_2567_4]) ).

cnf(f_2567_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9386,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9386),U_9388),U_9392)),U_9390) = hAPP(hAPP(c_Set_Oinsert(U_9386),U_9388),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9386,tc_HOL_Obool)),U_9392),U_9390))
    | hBOOL(hAPP(hAPP(c_member(U_9386),U_9388),U_9390)) ),
    inference(clausify,[status(thm)],[f_2567_4]) ).

fof(f_2568_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_2568_2,plain,
    ! [U_9396,U_9395,U_9394,U_9393] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9393,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9393),U_9394),U_9396)),U_9395) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9393,tc_HOL_Obool)),U_9396),U_9395)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9393),U_9394),U_9395)) ),
    inference(variable_rename,[status(thm)],[f_2568_1]) ).

fof(f_2568_3,plain,
    ! [U_9393,U_9394,U_9395,U_9396] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9393,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9393),U_9394),U_9396)),U_9395) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9393,tc_HOL_Obool)),U_9396),U_9395)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9393),U_9394),U_9395)) ),
    inference(definitional_conversion,[status(esa)],[f_2568_2]) ).

cnf(f_2568_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9393,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_9393),U_9394),U_9396)),U_9395) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9393,tc_HOL_Obool)),U_9396),U_9395)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9393),U_9394),U_9395)) ),
    inference(clausify,[status(thm)],[f_2568_3]) ).

fof(f_2569_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_2569_2,plain,
    ! [U_9398,U_9397] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9397,tc_HOL_Obool)),U_9398),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9397,tc_HOL_Obool)),U_9398)))
        | U_9398 != c_Orderings_Obot__class_Obot(tc_fun(U_9397,tc_HOL_Obool)) )
      & ( U_9398 = c_Orderings_Obot__class_Obot(tc_fun(U_9397,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9397,tc_HOL_Obool)),U_9398),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9397,tc_HOL_Obool)),U_9398))) ) ),
    inference(variable_rename,[status(thm)],[f_2569_1]) ).

fof(f_2569_3,plain,
    ( ! [U_9402,U_9400] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9400,tc_HOL_Obool)),U_9402),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9400,tc_HOL_Obool)),U_9402)))
        | U_9402 != c_Orderings_Obot__class_Obot(tc_fun(U_9400,tc_HOL_Obool)) )
    & ! [U_9401,U_9399] :
        ( U_9401 = c_Orderings_Obot__class_Obot(tc_fun(U_9399,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9399,tc_HOL_Obool)),U_9401),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9399,tc_HOL_Obool)),U_9401))) ) ),
    inference(miniscope,[status(thm)],[f_2569_2]) ).

fof(f_2569_4,plain,
    ( ! [U_9400,U_9402] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9400,tc_HOL_Obool)),U_9402),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9400,tc_HOL_Obool)),U_9402)))
        | U_9402 != c_Orderings_Obot__class_Obot(tc_fun(U_9400,tc_HOL_Obool)) )
    & ! [U_9401,U_9399] :
        ( U_9401 = c_Orderings_Obot__class_Obot(tc_fun(U_9399,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9399,tc_HOL_Obool)),U_9401),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9399,tc_HOL_Obool)),U_9401))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2569_3]) ).

cnf(f_2569_5,plain,
    ( U_9401 = c_Orderings_Obot__class_Obot(tc_fun(U_9399,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9399,tc_HOL_Obool)),U_9401),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9399,tc_HOL_Obool)),U_9401))) ),
    inference(clausify,[status(thm)],[f_2569_4]) ).

cnf(f_2569_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9400,tc_HOL_Obool)),U_9402),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_9400,tc_HOL_Obool)),U_9402)))
    | U_9402 != c_Orderings_Obot__class_Obot(tc_fun(U_9400,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2569_4]) ).

fof(f_2570_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_2570_2,plain,
    ! [U_9405,U_9404,U_9403] : hAPP(hAPP(c_Set_Oinsert(U_9403),U_9404),U_9405) = hAPP(c_Set_OCollect(U_9403),hAPP(hAPP(c_COMBS(U_9403,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9403),c_fdisj),hAPP(hAPP(c_COMBC(U_9403,U_9403,tc_HOL_Obool),c_fequal),U_9404))),hAPP(hAPP(c_COMBC(U_9403,tc_fun(U_9403,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9403)),U_9405))),
    inference(variable_rename,[status(thm)],[f_2570_1]) ).

fof(f_2570_3,plain,
    ! [U_9403,U_9404,U_9405] : hAPP(hAPP(c_Set_Oinsert(U_9403),U_9404),U_9405) = hAPP(c_Set_OCollect(U_9403),hAPP(hAPP(c_COMBS(U_9403,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9403),c_fdisj),hAPP(hAPP(c_COMBC(U_9403,U_9403,tc_HOL_Obool),c_fequal),U_9404))),hAPP(hAPP(c_COMBC(U_9403,tc_fun(U_9403,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9403)),U_9405))),
    inference(definitional_conversion,[status(esa)],[f_2570_2]) ).

cnf(f_2570_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_9403),U_9404),U_9405) = hAPP(c_Set_OCollect(U_9403),hAPP(hAPP(c_COMBS(U_9403,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9403),c_fdisj),hAPP(hAPP(c_COMBC(U_9403,U_9403,tc_HOL_Obool),c_fequal),U_9404))),hAPP(hAPP(c_COMBC(U_9403,tc_fun(U_9403,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9403)),U_9405))),
    inference(clausify,[status(thm)],[f_2570_3]) ).

fof(f_2571_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_2571_2,plain,
    ! [U_9408,U_9407,U_9406] : hAPP(hAPP(c_Set_Oinsert(U_9406),U_9407),U_9408) = hAPP(c_Set_OCollect(U_9406),hAPP(hAPP(c_COMBS(U_9406,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9406),c_fdisj),hAPP(hAPP(c_COMBC(U_9406,U_9406,tc_HOL_Obool),c_fequal),U_9407))),hAPP(hAPP(c_COMBC(U_9406,tc_fun(U_9406,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9406)),U_9408))),
    inference(variable_rename,[status(thm)],[f_2571_1]) ).

fof(f_2571_3,plain,
    ! [U_9406,U_9407,U_9408] : hAPP(hAPP(c_Set_Oinsert(U_9406),U_9407),U_9408) = hAPP(c_Set_OCollect(U_9406),hAPP(hAPP(c_COMBS(U_9406,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9406),c_fdisj),hAPP(hAPP(c_COMBC(U_9406,U_9406,tc_HOL_Obool),c_fequal),U_9407))),hAPP(hAPP(c_COMBC(U_9406,tc_fun(U_9406,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9406)),U_9408))),
    inference(definitional_conversion,[status(esa)],[f_2571_2]) ).

cnf(f_2571_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_9406),U_9407),U_9408) = hAPP(c_Set_OCollect(U_9406),hAPP(hAPP(c_COMBS(U_9406,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9406),c_fdisj),hAPP(hAPP(c_COMBC(U_9406,U_9406,tc_HOL_Obool),c_fequal),U_9407))),hAPP(hAPP(c_COMBC(U_9406,tc_fun(U_9406,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9406)),U_9408))),
    inference(clausify,[status(thm)],[f_2571_3]) ).

fof(f_2572_1,plain,
    ! [V_a_2,V_X_2,V_Pa_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_Pa_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_Pa_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_2572_2,plain,
    ! [U_9413,U_9412,U_9411,U_9410,U_9409] : c_Hoare__Mirabelle_Ohoare__derivs(U_9409,U_9410,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9409)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9409),hAPP(hAPP(c_COMBC(U_9409,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_9409),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_9411)),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_9412)),U_9413))),c_Com_Ocom_OAss(U_9412,U_9413)),U_9411)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9409),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2572_1]) ).

fof(f_2572_3,plain,
    ! [U_9409,U_9410,U_9411,U_9412,U_9413] : c_Hoare__Mirabelle_Ohoare__derivs(U_9409,U_9410,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9409)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9409),hAPP(hAPP(c_COMBC(U_9409,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_9409),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_9411)),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_9412)),U_9413))),c_Com_Ocom_OAss(U_9412,U_9413)),U_9411)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9409),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2572_2]) ).

cnf(f_2572_4,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_9409,U_9410,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9409)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9409),hAPP(hAPP(c_COMBC(U_9409,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_9409),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_9411)),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_9412)),U_9413))),c_Com_Ocom_OAss(U_9412,U_9413)),U_9411)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9409),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2572_3]) ).

fof(f_2573_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_2573_2,plain,
    ! [U_9418,U_9417,U_9416,U_9415,U_9414] : c_Hoare__Mirabelle_Ohoare__derivs(U_9414,U_9415,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9414)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9414),hAPP(hAPP(c_COMBC(U_9414,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_9414),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_9416)),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_9417)),U_9418))),c_Com_Ocom_OAss(U_9417,U_9418)),U_9416)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9414),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2573_1]) ).

fof(f_2573_3,plain,
    ! [U_9414,U_9415,U_9416,U_9417,U_9418] : c_Hoare__Mirabelle_Ohoare__derivs(U_9414,U_9415,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9414)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9414),hAPP(hAPP(c_COMBC(U_9414,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_9414),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_9416)),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_9417)),U_9418))),c_Com_Ocom_OAss(U_9417,U_9418)),U_9416)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9414),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2573_2]) ).

cnf(f_2573_4,plain,
    c_Hoare__Mirabelle_Ohoare__derivs(U_9414,U_9415,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9414)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9414),hAPP(hAPP(c_COMBC(U_9414,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_9414),c_COMBB(tc_Com_Ostate,tc_HOL_Obool,tc_Com_Ostate)),U_9416)),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_9417)),U_9418))),c_Com_Ocom_OAss(U_9417,U_9418)),U_9416)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9414),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2573_3]) ).

fof(f_2574_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_2574_2,plain,
    ! [U_9421,U_9420,U_9419] : hAPP(hAPP(c_Set_Oinsert(U_9419),U_9420),U_9421) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9419,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9419),hAPP(hAPP(c_COMBC(U_9419,U_9419,tc_HOL_Obool),c_fequal),U_9420))),U_9421),
    inference(variable_rename,[status(thm)],[f_2574_1]) ).

fof(f_2574_3,plain,
    ! [U_9419,U_9420,U_9421] : hAPP(hAPP(c_Set_Oinsert(U_9419),U_9420),U_9421) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9419,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9419),hAPP(hAPP(c_COMBC(U_9419,U_9419,tc_HOL_Obool),c_fequal),U_9420))),U_9421),
    inference(definitional_conversion,[status(esa)],[f_2574_2]) ).

cnf(f_2574_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_9419),U_9420),U_9421) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9419,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_9419),hAPP(hAPP(c_COMBC(U_9419,U_9419,tc_HOL_Obool),c_fequal),U_9420))),U_9421),
    inference(clausify,[status(thm)],[f_2574_3]) ).

fof(f_2575_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_2575_2,plain,
    ! [U_9422] : c_Option_Oset(U_9422,c_Option_Ooption_ONone(U_9422)) = c_Orderings_Obot__class_Obot(tc_fun(U_9422,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2575_1]) ).

fof(f_2575_3,plain,
    ! [U_9422] : c_Option_Oset(U_9422,c_Option_Ooption_ONone(U_9422)) = c_Orderings_Obot__class_Obot(tc_fun(U_9422,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2575_2]) ).

cnf(f_2575_4,plain,
    c_Option_Oset(U_9422,c_Option_Ooption_ONone(U_9422)) = c_Orderings_Obot__class_Obot(tc_fun(U_9422,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2575_3]) ).

fof(f_2576_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_2576_2,plain,
    ! [U_9424,U_9423] :
      ( ( c_Option_Oset(U_9423,U_9424) = c_Orderings_Obot__class_Obot(tc_fun(U_9423,tc_HOL_Obool))
        | U_9424 != c_Option_Ooption_ONone(U_9423) )
      & ( U_9424 = c_Option_Ooption_ONone(U_9423)
        | c_Option_Oset(U_9423,U_9424) != c_Orderings_Obot__class_Obot(tc_fun(U_9423,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2576_1]) ).

fof(f_2576_3,plain,
    ( ! [U_9428,U_9426] :
        ( c_Option_Oset(U_9426,U_9428) = c_Orderings_Obot__class_Obot(tc_fun(U_9426,tc_HOL_Obool))
        | U_9428 != c_Option_Ooption_ONone(U_9426) )
    & ! [U_9427,U_9425] :
        ( U_9427 = c_Option_Ooption_ONone(U_9425)
        | c_Option_Oset(U_9425,U_9427) != c_Orderings_Obot__class_Obot(tc_fun(U_9425,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2576_2]) ).

fof(f_2576_4,plain,
    ( ! [U_9428,U_9426] :
        ( c_Option_Oset(U_9426,U_9428) = c_Orderings_Obot__class_Obot(tc_fun(U_9426,tc_HOL_Obool))
        | U_9428 != c_Option_Ooption_ONone(U_9426) )
    & ! [U_9427,U_9425] :
        ( U_9427 = c_Option_Ooption_ONone(U_9425)
        | c_Option_Oset(U_9425,U_9427) != c_Orderings_Obot__class_Obot(tc_fun(U_9425,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2576_3]) ).

cnf(f_2576_5,plain,
    ( U_9427 = c_Option_Ooption_ONone(U_9425)
    | c_Option_Oset(U_9425,U_9427) != c_Orderings_Obot__class_Obot(tc_fun(U_9425,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2576_4]) ).

cnf(f_2576_6,plain,
    ( c_Option_Oset(U_9426,U_9428) = c_Orderings_Obot__class_Obot(tc_fun(U_9426,tc_HOL_Obool))
    | U_9428 != c_Option_Ooption_ONone(U_9426) ),
    inference(clausify,[status(thm)],[f_2576_4]) ).

fof(f_2577_1,plain,
    ! [V_Ga_2,V_Qa_2,V_pn_2,V_Pa_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_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_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_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_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_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_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_2577_2,plain,
    ! [U_9433,U_9432,U_9431,U_9430,U_9429] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_9429,U_9433,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9429)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9429),U_9430),hAPP(c_Com_Ocom_OBODY,U_9431)),U_9432)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9429),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9429,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9429)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9429),U_9430),hAPP(c_Com_Ocom_OBODY,U_9431)),U_9432)),U_9433),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9429)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9429),U_9430),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_9431))),U_9432)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9429),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2577_1]) ).

fof(f_2577_3,plain,
    ! [U_9429,U_9430,U_9431,U_9432,U_9433] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_9429,U_9433,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9429)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9429),U_9430),hAPP(c_Com_Ocom_OBODY,U_9431)),U_9432)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9429),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9429,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9429)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9429),U_9430),hAPP(c_Com_Ocom_OBODY,U_9431)),U_9432)),U_9433),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9429)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9429),U_9430),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_9431))),U_9432)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9429),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_2577_2]) ).

cnf(f_2577_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_9429,U_9433,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9429)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9429),U_9430),hAPP(c_Com_Ocom_OBODY,U_9431)),U_9432)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9429),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9429,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9429)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9429),U_9430),hAPP(c_Com_Ocom_OBODY,U_9431)),U_9432)),U_9433),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9429)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9429),U_9430),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_9431))),U_9432)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9429),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2577_3]) ).

fof(f_2578_1,plain,
    ! [V_Qa_2,V_pn_2,V_Pa_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_Pa_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Qa_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_Pa_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Qa_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_2578_2,plain,
    ! [U_9438,U_9437,U_9436,U_9435,U_9434] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_9434,U_9435,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9434)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9434),U_9436),hAPP(c_Com_Ocom_OBODY,U_9437)),U_9438)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9434),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9434,U_9435,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9434)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9434),U_9436),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_9437))),U_9438)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9434),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_2578_1]) ).

fof(f_2578_3,plain,
    ! [U_9434,U_9435,U_9436,U_9437,U_9438] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_9434,U_9435,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9434)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9434),U_9436),hAPP(c_Com_Ocom_OBODY,U_9437)),U_9438)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9434),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9434,U_9435,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9434)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9434),U_9436),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_9437))),U_9438)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9434),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_2578_2]) ).

cnf(f_2578_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_9434,U_9435,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9434)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9434),U_9436),hAPP(c_Com_Ocom_OBODY,U_9437)),U_9438)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9434),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9434,U_9435,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9434)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9434),U_9436),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_9437))),U_9438)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9434),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2578_3]) ).

fof(f_2579_1,plain,
    ! [V_y_2,V_x_2,V_r_2,T_c,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(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),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_Relation_Oconverse(T_b,T_c),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_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_b,T_c),V_r_2)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(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),V_y_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_conversep__converse__eq]) ).

fof(f_2579_2,plain,
    ! [U_9443,U_9442,U_9441,U_9440,U_9439] :
      ( ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9439,U_9440,hAPP(hAPP(c_COMBC(U_9439,tc_fun(tc_prod(U_9439,U_9440),tc_HOL_Obool),tc_fun(U_9440,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9440,tc_fun(tc_fun(tc_prod(U_9439,U_9440),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9439,U_9440),tc_HOL_Obool),tc_fun(U_9440,tc_HOL_Obool)),U_9439),c_COMBC(U_9440,tc_fun(tc_prod(U_9439,U_9440),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9440,tc_prod(U_9439,U_9440)),tc_fun(U_9440,tc_fun(tc_fun(tc_prod(U_9439,U_9440),tc_HOL_Obool),tc_HOL_Obool)),U_9439),hAPP(c_COMBB(tc_prod(U_9439,U_9440),tc_fun(tc_fun(tc_prod(U_9439,U_9440),tc_HOL_Obool),tc_HOL_Obool),U_9440),c_member(tc_prod(U_9439,U_9440)))),c_Product__Type_OPair(U_9439,U_9440)))),U_9441)),U_9442),U_9443))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9440,U_9439)),hAPP(hAPP(c_Product__Type_OPair(U_9440,U_9439),U_9442),U_9443)),hAPP(c_Relation_Oconverse(U_9439,U_9440),U_9441))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9440,U_9439)),hAPP(hAPP(c_Product__Type_OPair(U_9440,U_9439),U_9442),U_9443)),hAPP(c_Relation_Oconverse(U_9439,U_9440),U_9441)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9439,U_9440,hAPP(hAPP(c_COMBC(U_9439,tc_fun(tc_prod(U_9439,U_9440),tc_HOL_Obool),tc_fun(U_9440,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9440,tc_fun(tc_fun(tc_prod(U_9439,U_9440),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9439,U_9440),tc_HOL_Obool),tc_fun(U_9440,tc_HOL_Obool)),U_9439),c_COMBC(U_9440,tc_fun(tc_prod(U_9439,U_9440),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9440,tc_prod(U_9439,U_9440)),tc_fun(U_9440,tc_fun(tc_fun(tc_prod(U_9439,U_9440),tc_HOL_Obool),tc_HOL_Obool)),U_9439),hAPP(c_COMBB(tc_prod(U_9439,U_9440),tc_fun(tc_fun(tc_prod(U_9439,U_9440),tc_HOL_Obool),tc_HOL_Obool),U_9440),c_member(tc_prod(U_9439,U_9440)))),c_Product__Type_OPair(U_9439,U_9440)))),U_9441)),U_9442),U_9443)) ) ),
    inference(variable_rename,[status(thm)],[f_2579_1]) ).

fof(f_2579_3,plain,
    ( ! [U_9453,U_9451,U_9449,U_9447,U_9445] :
        ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9445,U_9447,hAPP(hAPP(c_COMBC(U_9445,tc_fun(tc_prod(U_9445,U_9447),tc_HOL_Obool),tc_fun(U_9447,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9447,tc_fun(tc_fun(tc_prod(U_9445,U_9447),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9445,U_9447),tc_HOL_Obool),tc_fun(U_9447,tc_HOL_Obool)),U_9445),c_COMBC(U_9447,tc_fun(tc_prod(U_9445,U_9447),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9447,tc_prod(U_9445,U_9447)),tc_fun(U_9447,tc_fun(tc_fun(tc_prod(U_9445,U_9447),tc_HOL_Obool),tc_HOL_Obool)),U_9445),hAPP(c_COMBB(tc_prod(U_9445,U_9447),tc_fun(tc_fun(tc_prod(U_9445,U_9447),tc_HOL_Obool),tc_HOL_Obool),U_9447),c_member(tc_prod(U_9445,U_9447)))),c_Product__Type_OPair(U_9445,U_9447)))),U_9449)),U_9451),U_9453))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9447,U_9445)),hAPP(hAPP(c_Product__Type_OPair(U_9447,U_9445),U_9451),U_9453)),hAPP(c_Relation_Oconverse(U_9445,U_9447),U_9449))) )
    & ! [U_9452,U_9450,U_9448,U_9446,U_9444] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9446,U_9444)),hAPP(hAPP(c_Product__Type_OPair(U_9446,U_9444),U_9450),U_9452)),hAPP(c_Relation_Oconverse(U_9444,U_9446),U_9448)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9444,U_9446,hAPP(hAPP(c_COMBC(U_9444,tc_fun(tc_prod(U_9444,U_9446),tc_HOL_Obool),tc_fun(U_9446,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9446,tc_fun(tc_fun(tc_prod(U_9444,U_9446),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9444,U_9446),tc_HOL_Obool),tc_fun(U_9446,tc_HOL_Obool)),U_9444),c_COMBC(U_9446,tc_fun(tc_prod(U_9444,U_9446),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9446,tc_prod(U_9444,U_9446)),tc_fun(U_9446,tc_fun(tc_fun(tc_prod(U_9444,U_9446),tc_HOL_Obool),tc_HOL_Obool)),U_9444),hAPP(c_COMBB(tc_prod(U_9444,U_9446),tc_fun(tc_fun(tc_prod(U_9444,U_9446),tc_HOL_Obool),tc_HOL_Obool),U_9446),c_member(tc_prod(U_9444,U_9446)))),c_Product__Type_OPair(U_9444,U_9446)))),U_9448)),U_9450),U_9452)) ) ),
    inference(miniscope,[status(thm)],[f_2579_2]) ).

fof(f_2579_4,plain,
    ( ! [U_9445,U_9447,U_9449,U_9451,U_9453] :
        ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9445,U_9447,hAPP(hAPP(c_COMBC(U_9445,tc_fun(tc_prod(U_9445,U_9447),tc_HOL_Obool),tc_fun(U_9447,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9447,tc_fun(tc_fun(tc_prod(U_9445,U_9447),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9445,U_9447),tc_HOL_Obool),tc_fun(U_9447,tc_HOL_Obool)),U_9445),c_COMBC(U_9447,tc_fun(tc_prod(U_9445,U_9447),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9447,tc_prod(U_9445,U_9447)),tc_fun(U_9447,tc_fun(tc_fun(tc_prod(U_9445,U_9447),tc_HOL_Obool),tc_HOL_Obool)),U_9445),hAPP(c_COMBB(tc_prod(U_9445,U_9447),tc_fun(tc_fun(tc_prod(U_9445,U_9447),tc_HOL_Obool),tc_HOL_Obool),U_9447),c_member(tc_prod(U_9445,U_9447)))),c_Product__Type_OPair(U_9445,U_9447)))),U_9449)),U_9451),U_9453))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9447,U_9445)),hAPP(hAPP(c_Product__Type_OPair(U_9447,U_9445),U_9451),U_9453)),hAPP(c_Relation_Oconverse(U_9445,U_9447),U_9449))) )
    & ! [U_9446,U_9448,U_9444,U_9450,U_9452] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9446,U_9444)),hAPP(hAPP(c_Product__Type_OPair(U_9446,U_9444),U_9450),U_9452)),hAPP(c_Relation_Oconverse(U_9444,U_9446),U_9448)))
        | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9444,U_9446,hAPP(hAPP(c_COMBC(U_9444,tc_fun(tc_prod(U_9444,U_9446),tc_HOL_Obool),tc_fun(U_9446,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9446,tc_fun(tc_fun(tc_prod(U_9444,U_9446),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9444,U_9446),tc_HOL_Obool),tc_fun(U_9446,tc_HOL_Obool)),U_9444),c_COMBC(U_9446,tc_fun(tc_prod(U_9444,U_9446),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9446,tc_prod(U_9444,U_9446)),tc_fun(U_9446,tc_fun(tc_fun(tc_prod(U_9444,U_9446),tc_HOL_Obool),tc_HOL_Obool)),U_9444),hAPP(c_COMBB(tc_prod(U_9444,U_9446),tc_fun(tc_fun(tc_prod(U_9444,U_9446),tc_HOL_Obool),tc_HOL_Obool),U_9446),c_member(tc_prod(U_9444,U_9446)))),c_Product__Type_OPair(U_9444,U_9446)))),U_9448)),U_9450),U_9452)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2579_3]) ).

cnf(f_2579_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9446,U_9444)),hAPP(hAPP(c_Product__Type_OPair(U_9446,U_9444),U_9450),U_9452)),hAPP(c_Relation_Oconverse(U_9444,U_9446),U_9448)))
    | ~ hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9444,U_9446,hAPP(hAPP(c_COMBC(U_9444,tc_fun(tc_prod(U_9444,U_9446),tc_HOL_Obool),tc_fun(U_9446,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9446,tc_fun(tc_fun(tc_prod(U_9444,U_9446),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9444,U_9446),tc_HOL_Obool),tc_fun(U_9446,tc_HOL_Obool)),U_9444),c_COMBC(U_9446,tc_fun(tc_prod(U_9444,U_9446),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9446,tc_prod(U_9444,U_9446)),tc_fun(U_9446,tc_fun(tc_fun(tc_prod(U_9444,U_9446),tc_HOL_Obool),tc_HOL_Obool)),U_9444),hAPP(c_COMBB(tc_prod(U_9444,U_9446),tc_fun(tc_fun(tc_prod(U_9444,U_9446),tc_HOL_Obool),tc_HOL_Obool),U_9446),c_member(tc_prod(U_9444,U_9446)))),c_Product__Type_OPair(U_9444,U_9446)))),U_9448)),U_9450),U_9452)) ),
    inference(clausify,[status(thm)],[f_2579_4]) ).

cnf(f_2579_6,plain,
    ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(U_9445,U_9447,hAPP(hAPP(c_COMBC(U_9445,tc_fun(tc_prod(U_9445,U_9447),tc_HOL_Obool),tc_fun(U_9447,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9447,tc_fun(tc_fun(tc_prod(U_9445,U_9447),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9445,U_9447),tc_HOL_Obool),tc_fun(U_9447,tc_HOL_Obool)),U_9445),c_COMBC(U_9447,tc_fun(tc_prod(U_9445,U_9447),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9447,tc_prod(U_9445,U_9447)),tc_fun(U_9447,tc_fun(tc_fun(tc_prod(U_9445,U_9447),tc_HOL_Obool),tc_HOL_Obool)),U_9445),hAPP(c_COMBB(tc_prod(U_9445,U_9447),tc_fun(tc_fun(tc_prod(U_9445,U_9447),tc_HOL_Obool),tc_HOL_Obool),U_9447),c_member(tc_prod(U_9445,U_9447)))),c_Product__Type_OPair(U_9445,U_9447)))),U_9449)),U_9451),U_9453))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9447,U_9445)),hAPP(hAPP(c_Product__Type_OPair(U_9447,U_9445),U_9451),U_9453)),hAPP(c_Relation_Oconverse(U_9445,U_9447),U_9449))) ),
    inference(clausify,[status(thm)],[f_2579_4]) ).

fof(f_2580_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_2580_2,plain,
    ! [U_9455,U_9454] : c_Set_Othe__elem(U_9454,U_9455) = c_HOL_OThe(U_9454,hAPP(hAPP(c_COMBB(tc_fun(U_9454,tc_HOL_Obool),tc_HOL_Obool,U_9454),hAPP(c_fequal,U_9455)),hAPP(hAPP(c_COMBC(U_9454,tc_fun(U_9454,tc_HOL_Obool),tc_fun(U_9454,tc_HOL_Obool)),c_Set_Oinsert(U_9454)),c_Orderings_Obot__class_Obot(tc_fun(U_9454,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_2580_1]) ).

fof(f_2580_3,plain,
    ! [U_9454,U_9455] : c_Set_Othe__elem(U_9454,U_9455) = c_HOL_OThe(U_9454,hAPP(hAPP(c_COMBB(tc_fun(U_9454,tc_HOL_Obool),tc_HOL_Obool,U_9454),hAPP(c_fequal,U_9455)),hAPP(hAPP(c_COMBC(U_9454,tc_fun(U_9454,tc_HOL_Obool),tc_fun(U_9454,tc_HOL_Obool)),c_Set_Oinsert(U_9454)),c_Orderings_Obot__class_Obot(tc_fun(U_9454,tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_2580_2]) ).

cnf(f_2580_4,plain,
    c_Set_Othe__elem(U_9454,U_9455) = c_HOL_OThe(U_9454,hAPP(hAPP(c_COMBB(tc_fun(U_9454,tc_HOL_Obool),tc_HOL_Obool,U_9454),hAPP(c_fequal,U_9455)),hAPP(hAPP(c_COMBC(U_9454,tc_fun(U_9454,tc_HOL_Obool),tc_fun(U_9454,tc_HOL_Obool)),c_Set_Oinsert(U_9454)),c_Orderings_Obot__class_Obot(tc_fun(U_9454,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2580_3]) ).

fof(f_2581_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_2581_2,plain,
    ! [U_9456] : hAPP(c_Finite__Set_Ocard(U_9456),c_Orderings_Obot__class_Obot(tc_fun(U_9456,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_2581_1]) ).

fof(f_2581_3,plain,
    ! [U_9456] : hAPP(c_Finite__Set_Ocard(U_9456),c_Orderings_Obot__class_Obot(tc_fun(U_9456,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_2581_2]) ).

cnf(f_2581_4,plain,
    hAPP(c_Finite__Set_Ocard(U_9456),c_Orderings_Obot__class_Obot(tc_fun(U_9456,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2581_3]) ).

fof(f_2582_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_2582_2,plain,
    ! [U_9458,U_9457] : c_Set_Othe__elem(U_9457,hAPP(hAPP(c_Set_Oinsert(U_9457),U_9458),c_Orderings_Obot__class_Obot(tc_fun(U_9457,tc_HOL_Obool)))) = U_9458,
    inference(variable_rename,[status(thm)],[f_2582_1]) ).

fof(f_2582_3,plain,
    ! [U_9457,U_9458] : c_Set_Othe__elem(U_9457,hAPP(hAPP(c_Set_Oinsert(U_9457),U_9458),c_Orderings_Obot__class_Obot(tc_fun(U_9457,tc_HOL_Obool)))) = U_9458,
    inference(definitional_conversion,[status(esa)],[f_2582_2]) ).

cnf(f_2582_4,plain,
    c_Set_Othe__elem(U_9457,hAPP(hAPP(c_Set_Oinsert(U_9457),U_9458),c_Orderings_Obot__class_Obot(tc_fun(U_9457,tc_HOL_Obool)))) = U_9458,
    inference(clausify,[status(thm)],[f_2582_3]) ).

fof(f_2583_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_2583_2,plain,
    ! [U_9465,U_9464,U_9463,U_9462,U_9461,U_9460,U_9459] :
      ( c_Nitpick_Ofold__graph_H(U_9459,U_9462,U_9463,U_9464,U_9461,hAPP(hAPP(U_9463,U_9460),U_9465))
      | ~ c_Nitpick_Ofold__graph_H(U_9459,U_9462,U_9463,U_9464,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9459,tc_HOL_Obool)),U_9461),hAPP(hAPP(c_Set_Oinsert(U_9459),U_9460),c_Orderings_Obot__class_Obot(tc_fun(U_9459,tc_HOL_Obool)))),U_9465)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9459),U_9460),U_9461)) ),
    inference(variable_rename,[status(thm)],[f_2583_1]) ).

fof(f_2583_3,plain,
    ! [U_9459,U_9460,U_9461,U_9462,U_9463,U_9464,U_9465] :
      ( c_Nitpick_Ofold__graph_H(U_9459,U_9462,U_9463,U_9464,U_9461,hAPP(hAPP(U_9463,U_9460),U_9465))
      | ~ c_Nitpick_Ofold__graph_H(U_9459,U_9462,U_9463,U_9464,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9459,tc_HOL_Obool)),U_9461),hAPP(hAPP(c_Set_Oinsert(U_9459),U_9460),c_Orderings_Obot__class_Obot(tc_fun(U_9459,tc_HOL_Obool)))),U_9465)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9459),U_9460),U_9461)) ),
    inference(definitional_conversion,[status(esa)],[f_2583_2]) ).

cnf(f_2583_4,plain,
    ( c_Nitpick_Ofold__graph_H(U_9459,U_9462,U_9463,U_9464,U_9461,hAPP(hAPP(U_9463,U_9460),U_9465))
    | ~ c_Nitpick_Ofold__graph_H(U_9459,U_9462,U_9463,U_9464,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9459,tc_HOL_Obool)),U_9461),hAPP(hAPP(c_Set_Oinsert(U_9459),U_9460),c_Orderings_Obot__class_Obot(tc_fun(U_9459,tc_HOL_Obool)))),U_9465)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9459),U_9460),U_9461)) ),
    inference(clausify,[status(thm)],[f_2583_3]) ).

fof(f_2584_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_2584_2,plain,
    ! [U_9466] : c_Wellfounded_Owf(U_9466,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9466,U_9466),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2584_1]) ).

fof(f_2584_3,plain,
    ! [U_9466] : c_Wellfounded_Owf(U_9466,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9466,U_9466),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2584_2]) ).

cnf(f_2584_4,plain,
    c_Wellfounded_Owf(U_9466,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9466,U_9466),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2584_3]) ).

fof(f_2585_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_2585_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_2585_1]) ).

cnf(f_2585_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_2585_2]) ).

fof(f_2586_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_2586_2,plain,
    ! [U_9467] : c_Transitive__Closure_Otrancl(U_9467,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9467,U_9467),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9467,U_9467),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2586_1]) ).

fof(f_2586_3,plain,
    ! [U_9467] : c_Transitive__Closure_Otrancl(U_9467,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9467,U_9467),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9467,U_9467),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2586_2]) ).

cnf(f_2586_4,plain,
    c_Transitive__Closure_Otrancl(U_9467,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9467,U_9467),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9467,U_9467),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2586_3]) ).

fof(f_2587_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_2587_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_2587_1]) ).

cnf(f_2587_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_2587_2]) ).

fof(f_2588_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_2588_2,plain,
    ! [U_9471,U_9470,U_9469,U_9468] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9468,tc_fun(U_9469,tc_HOL_Obool))),U_9470),U_9471))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9468,U_9469)),hAPP(hAPP(c_Product__Type_OPair(U_9468,U_9469),U_9470),U_9471)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9468,U_9469),tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9468,U_9469)),hAPP(hAPP(c_Product__Type_OPair(U_9468,U_9469),U_9470),U_9471)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9468,U_9469),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9468,tc_fun(U_9469,tc_HOL_Obool))),U_9470),U_9471)) ) ),
    inference(variable_rename,[status(thm)],[f_2588_1]) ).

fof(f_2588_3,plain,
    ( ! [U_9479,U_9477,U_9475,U_9473] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9473,tc_fun(U_9475,tc_HOL_Obool))),U_9477),U_9479))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9473,U_9475)),hAPP(hAPP(c_Product__Type_OPair(U_9473,U_9475),U_9477),U_9479)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9473,U_9475),tc_HOL_Obool)))) )
    & ! [U_9478,U_9476,U_9474,U_9472] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9472,U_9474)),hAPP(hAPP(c_Product__Type_OPair(U_9472,U_9474),U_9476),U_9478)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9472,U_9474),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9472,tc_fun(U_9474,tc_HOL_Obool))),U_9476),U_9478)) ) ),
    inference(miniscope,[status(thm)],[f_2588_2]) ).

fof(f_2588_4,plain,
    ( ! [U_9473,U_9475,U_9477,U_9479] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9473,tc_fun(U_9475,tc_HOL_Obool))),U_9477),U_9479))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9473,U_9475)),hAPP(hAPP(c_Product__Type_OPair(U_9473,U_9475),U_9477),U_9479)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9473,U_9475),tc_HOL_Obool)))) )
    & ! [U_9476,U_9474,U_9478,U_9472] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9472,U_9474)),hAPP(hAPP(c_Product__Type_OPair(U_9472,U_9474),U_9476),U_9478)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9472,U_9474),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9472,tc_fun(U_9474,tc_HOL_Obool))),U_9476),U_9478)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2588_3]) ).

cnf(f_2588_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_9472,U_9474)),hAPP(hAPP(c_Product__Type_OPair(U_9472,U_9474),U_9476),U_9478)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9472,U_9474),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9472,tc_fun(U_9474,tc_HOL_Obool))),U_9476),U_9478)) ),
    inference(clausify,[status(thm)],[f_2588_4]) ).

cnf(f_2588_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9473,tc_fun(U_9475,tc_HOL_Obool))),U_9477),U_9479))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_9473,U_9475)),hAPP(hAPP(c_Product__Type_OPair(U_9473,U_9475),U_9477),U_9479)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9473,U_9475),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_2588_4]) ).

fof(f_2589_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_2589_2,plain,
    ! [U_9482,U_9481,U_9480] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9481,U_9481),tc_HOL_Obool)),U_9480),U_9482))
      | U_9480 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9481,U_9481),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2589_1]) ).

fof(f_2589_3,plain,
    ! [U_9482,U_9481,U_9480] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9481,U_9481),tc_HOL_Obool)),U_9480),U_9482))
      | U_9480 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9481,U_9481),tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_2589_2]) ).

cnf(f_2589_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9481,U_9481),tc_HOL_Obool)),U_9480),U_9482))
    | U_9480 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9481,U_9481),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2589_3]) ).

fof(f_2590_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_2590_2,plain,
    ! [U_9486,U_9485,U_9484,U_9483] : hAPP(hAPP(c_Relation_Orel__comp(U_9483,U_9484,U_9485),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9483,U_9484),tc_HOL_Obool))),U_9486) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9483,U_9485),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2590_1]) ).

fof(f_2590_3,plain,
    ! [U_9483,U_9484,U_9485,U_9486] : hAPP(hAPP(c_Relation_Orel__comp(U_9483,U_9484,U_9485),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9483,U_9484),tc_HOL_Obool))),U_9486) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9483,U_9485),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2590_2]) ).

cnf(f_2590_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_9483,U_9484,U_9485),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9483,U_9484),tc_HOL_Obool))),U_9486) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9483,U_9485),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2590_3]) ).

fof(f_2591_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_2591_2,plain,
    ! [U_9490,U_9489,U_9488,U_9487] : hAPP(hAPP(c_Relation_Orel__comp(U_9487,U_9488,U_9489),U_9490),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9488,U_9489),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9487,U_9489),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2591_1]) ).

fof(f_2591_3,plain,
    ! [U_9487,U_9488,U_9489,U_9490] : hAPP(hAPP(c_Relation_Orel__comp(U_9487,U_9488,U_9489),U_9490),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9488,U_9489),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9487,U_9489),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2591_2]) ).

cnf(f_2591_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_9487,U_9488,U_9489),U_9490),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9488,U_9489),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9487,U_9489),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2591_3]) ).

fof(f_2592_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_2592_2,plain,
    ! [U_9492,U_9491] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9491,U_9492) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9491),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
      | U_9491 != U_9492 ),
    inference(variable_rename,[status(thm)],[f_2592_1]) ).

fof(f_2592_3,plain,
    ! [U_9491,U_9492] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9491,U_9492) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9491),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
      | U_9491 != U_9492 ),
    inference(definitional_conversion,[status(esa)],[f_2592_2]) ).

cnf(f_2592_4,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9491,U_9492) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9491),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | U_9491 != U_9492 ),
    inference(clausify,[status(thm)],[f_2592_3]) ).

fof(f_2593_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_2593_2,plain,
    ! [U_9493] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9493,U_9493) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9493),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_2593_1]) ).

fof(f_2593_3,plain,
    ! [U_9493] : c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9493,U_9493) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9493),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_2593_2]) ).

cnf(f_2593_4,plain,
    c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9493,U_9493) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9493),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_2593_3]) ).

fof(f_2594_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_2594_2,plain,
    ! [U_9496,U_9495,U_9494] :
      ( ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9494,U_9495) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9496),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
        | U_9495 != U_9496
        | U_9494 != U_9495 )
      & ( ( U_9495 = U_9496
          & U_9494 = U_9495 )
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9494,U_9495) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9496),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[f_2594_1]) ).

fof(f_2594_3,plain,
    ( ! [U_9502,U_9500,U_9498] :
        ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9498,U_9500) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9502),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
        | U_9500 != U_9502
        | U_9498 != U_9500 )
    & ! [U_9501,U_9499,U_9497] :
        ( ( U_9499 = U_9501
          & U_9497 = U_9499 )
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9497,U_9499) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9501),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ),
    inference(miniscope,[status(thm)],[f_2594_2]) ).

fof(f_2594_4,plain,
    ( ! [U_9501,U_9497,U_9499] :
        ( U_9499 = U_9501
        | ~ sP744(U_9501,U_9497,U_9499) )
    & ! [U_9501,U_9497,U_9499] :
        ( U_9497 = U_9499
        | ~ sP744(U_9501,U_9497,U_9499) )
    & ! [U_9502,U_9500,U_9498] :
        ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9498,U_9500) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9502),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
        | U_9500 != U_9502
        | U_9498 != U_9500 )
    & ! [U_9501,U_9497,U_9499] :
        ( sP744(U_9501,U_9497,U_9499)
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9497,U_9499) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9501),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP744])],[f_2594_3]) ).

cnf(f_2594_5,plain,
    ( sP744(U_9501,U_9497,U_9499)
    | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9497,U_9499) != hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9501),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_2594_4]) ).

cnf(f_2594_6,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9498,U_9500) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_9502),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | U_9500 != U_9502
    | U_9498 != U_9500 ),
    inference(clausify,[status(thm)],[f_2594_4]) ).

cnf(f_2594_7,plain,
    ( U_9497 = U_9499
    | ~ sP744(U_9501,U_9497,U_9499) ),
    inference(clausify,[status(thm)],[f_2594_4]) ).

cnf(f_2594_8,plain,
    ( U_9499 = U_9501
    | ~ sP744(U_9501,U_9497,U_9499) ),
    inference(clausify,[status(thm)],[f_2594_4]) ).

fof(f_2595_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_2595_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_2595_1]) ).

cnf(f_2595_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_2595_2]) ).

fof(f_2596_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_2596_2,plain,
    ! [U_9504,U_9503] :
      ( ( 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_9503,U_9504)
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9504),U_9503))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9503),U_9504)) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9504),U_9503))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9503),U_9504))
        | 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_9503,U_9504) ) ),
    inference(variable_rename,[status(thm)],[f_2596_1]) ).

fof(f_2596_3,plain,
    ( ! [U_9508,U_9506] :
        ( 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_9506,U_9508)
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9508),U_9506))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9506),U_9508)) ) )
    & ! [U_9507,U_9505] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9507),U_9505))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9505),U_9507))
        | 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_9505,U_9507) ) ),
    inference(miniscope,[status(thm)],[f_2596_2]) ).

fof(f_2596_4,plain,
    ( ! [U_9506,U_9508] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9508),U_9506))
        | ~ sP745(U_9506,U_9508) )
    & ! [U_9506,U_9508] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9506),U_9508))
        | ~ sP745(U_9506,U_9508) )
    & ! [U_9506,U_9508] :
        ( 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_9506,U_9508)
        | sP745(U_9506,U_9508) )
    & ! [U_9505,U_9507] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9507),U_9505))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9505),U_9507))
        | 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_9505,U_9507) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP745])],[f_2596_3]) ).

cnf(f_2596_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9507),U_9505))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9505),U_9507))
    | 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_9505,U_9507) ),
    inference(clausify,[status(thm)],[f_2596_4]) ).

cnf(f_2596_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_9506,U_9508)
    | sP745(U_9506,U_9508) ),
    inference(clausify,[status(thm)],[f_2596_4]) ).

cnf(f_2596_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9506),U_9508))
    | ~ sP745(U_9506,U_9508) ),
    inference(clausify,[status(thm)],[f_2596_4]) ).

cnf(f_2596_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9508),U_9506))
    | ~ sP745(U_9506,U_9508) ),
    inference(clausify,[status(thm)],[f_2596_4]) ).

fof(f_2597_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_2597_2,plain,
    ! [U_9510,U_9509] :
      ( ( 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_9509,U_9510)
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9510),U_9509))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9509),U_9510)) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9510),U_9509))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9509),U_9510))
        | 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_9509,U_9510) ) ),
    inference(variable_rename,[status(thm)],[f_2597_1]) ).

fof(f_2597_3,plain,
    ( ! [U_9514,U_9512] :
        ( 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_9512,U_9514)
        | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9514),U_9512))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9512),U_9514)) ) )
    & ! [U_9513,U_9511] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9513),U_9511))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9511),U_9513))
        | 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_9511,U_9513) ) ),
    inference(miniscope,[status(thm)],[f_2597_2]) ).

fof(f_2597_4,plain,
    ( ! [U_9512,U_9514] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9514),U_9512))
        | ~ sP746(U_9512,U_9514) )
    & ! [U_9512,U_9514] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9512),U_9514))
        | ~ sP746(U_9512,U_9514) )
    & ! [U_9512,U_9514] :
        ( 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_9512,U_9514)
        | sP746(U_9512,U_9514) )
    & ! [U_9513,U_9511] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9513),U_9511))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9511),U_9513))
        | 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_9511,U_9513) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP746])],[f_2597_3]) ).

cnf(f_2597_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9513),U_9511))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9511),U_9513))
    | 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_9511,U_9513) ),
    inference(clausify,[status(thm)],[f_2597_4]) ).

cnf(f_2597_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_9512,U_9514)
    | sP746(U_9512,U_9514) ),
    inference(clausify,[status(thm)],[f_2597_4]) ).

cnf(f_2597_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9512),U_9514))
    | ~ sP746(U_9512,U_9514) ),
    inference(clausify,[status(thm)],[f_2597_4]) ).

cnf(f_2597_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9514),U_9512))
    | ~ sP746(U_9512,U_9514) ),
    inference(clausify,[status(thm)],[f_2597_4]) ).

fof(f_2598_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_2598_2,plain,
    ! [U_9516,U_9515] :
      ( ( 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_9515,U_9516) = 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_9516),U_9515))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9515),U_9516)) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9516),U_9515))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9515),U_9516))
        | 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_9515,U_9516) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2598_1]) ).

fof(f_2598_3,plain,
    ( ! [U_9520,U_9518] :
        ( 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_9518,U_9520) = 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_9520),U_9518))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9518),U_9520)) ) )
    & ! [U_9519,U_9517] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9519),U_9517))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9517),U_9519))
        | 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_9517,U_9519) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2598_2]) ).

fof(f_2598_4,plain,
    ( ! [U_9520,U_9518] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9520),U_9518))
        | ~ sP747(U_9520,U_9518) )
    & ! [U_9520,U_9518] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9518),U_9520))
        | ~ sP747(U_9520,U_9518) )
    & ! [U_9520,U_9518] :
        ( 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_9518,U_9520) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | sP747(U_9520,U_9518) )
    & ! [U_9519,U_9517] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9519),U_9517))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9517),U_9519))
        | 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_9517,U_9519) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP747])],[f_2598_3]) ).

cnf(f_2598_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9519),U_9517))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9517),U_9519))
    | 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_9517,U_9519) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2598_4]) ).

cnf(f_2598_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_9518,U_9520) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | sP747(U_9520,U_9518) ),
    inference(clausify,[status(thm)],[f_2598_4]) ).

cnf(f_2598_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9518),U_9520))
    | ~ sP747(U_9520,U_9518) ),
    inference(clausify,[status(thm)],[f_2598_4]) ).

cnf(f_2598_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9520),U_9518))
    | ~ sP747(U_9520,U_9518) ),
    inference(clausify,[status(thm)],[f_2598_4]) ).

fof(f_2599_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_2599_2,plain,
    ! [U_9522,U_9521] :
      ( ( 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_9521,U_9522) = 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_9522),U_9521))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9521),U_9522)) ) )
      & ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9522),U_9521))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9521),U_9522))
        | 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_9521,U_9522) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2599_1]) ).

fof(f_2599_3,plain,
    ( ! [U_9526,U_9524] :
        ( 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_9524,U_9526) = 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_9526),U_9524))
          & hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9524),U_9526)) ) )
    & ! [U_9525,U_9523] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9525),U_9523))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9523),U_9525))
        | 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_9523,U_9525) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2599_2]) ).

fof(f_2599_4,plain,
    ( ! [U_9526,U_9524] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9526),U_9524))
        | ~ sP748(U_9526,U_9524) )
    & ! [U_9526,U_9524] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9524),U_9526))
        | ~ sP748(U_9526,U_9524) )
    & ! [U_9526,U_9524] :
        ( 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_9524,U_9526) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
        | sP748(U_9526,U_9524) )
    & ! [U_9523,U_9525] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9525),U_9523))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9523),U_9525))
        | 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_9523,U_9525) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP748])],[f_2599_3]) ).

cnf(f_2599_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9525),U_9523))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9523),U_9525))
    | 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_9523,U_9525) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2599_4]) ).

cnf(f_2599_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_9524,U_9526) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))
    | sP748(U_9526,U_9524) ),
    inference(clausify,[status(thm)],[f_2599_4]) ).

cnf(f_2599_7,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9524),U_9526))
    | ~ sP748(U_9526,U_9524) ),
    inference(clausify,[status(thm)],[f_2599_4]) ).

cnf(f_2599_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9526),U_9524))
    | ~ sP748(U_9526,U_9524) ),
    inference(clausify,[status(thm)],[f_2599_4]) ).

fof(f_2600_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_2600_2,plain,
    ! [U_9528,U_9527] :
      ( 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_9528,U_9527) = 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_9527),U_9528)) ),
    inference(variable_rename,[status(thm)],[f_2600_1]) ).

fof(f_2600_3,plain,
    ! [U_9528,U_9527] :
      ( 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_9528,U_9527) = 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_9527),U_9528)) ),
    inference(definitional_conversion,[status(esa)],[f_2600_2]) ).

cnf(f_2600_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_9528,U_9527) = 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_9527),U_9528)) ),
    inference(clausify,[status(thm)],[f_2600_3]) ).

fof(f_2601_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_2601_2,plain,
    ! [U_9530,U_9529] :
      ( 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_9530,U_9529) = 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_9529),U_9530)) ),
    inference(variable_rename,[status(thm)],[f_2601_1]) ).

fof(f_2601_3,plain,
    ! [U_9530,U_9529] :
      ( 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_9530,U_9529) = 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_9529),U_9530)) ),
    inference(definitional_conversion,[status(esa)],[f_2601_2]) ).

cnf(f_2601_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_9530,U_9529) = 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_9529),U_9530)) ),
    inference(clausify,[status(thm)],[f_2601_3]) ).

fof(f_2602_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_2602_2,plain,
    ! [U_9532,U_9531] :
      ( 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_9532,U_9531) = 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_9531),U_9532)) ),
    inference(variable_rename,[status(thm)],[f_2602_1]) ).

fof(f_2602_3,plain,
    ! [U_9532,U_9531] :
      ( 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_9532,U_9531) = 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_9531),U_9532)) ),
    inference(definitional_conversion,[status(esa)],[f_2602_2]) ).

cnf(f_2602_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_9532,U_9531) = 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_9531),U_9532)) ),
    inference(clausify,[status(thm)],[f_2602_3]) ).

fof(f_2603_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_2603_2,plain,
    c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_2603_1]) ).

cnf(f_2603_3,plain,
    c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_2603_2]) ).

fof(f_2604_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_2604_2,plain,
    ! [U_9534,U_9533] :
      ( c_Wellfounded_Owf(U_9533,U_9534)
      | hAPP(hAPP(c_Relation_Orel__comp(U_9533,U_9533,U_9533),U_9534),U_9534) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9533,U_9533),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2604_1]) ).

fof(f_2604_3,plain,
    ! [U_9533,U_9534] :
      ( c_Wellfounded_Owf(U_9533,U_9534)
      | hAPP(hAPP(c_Relation_Orel__comp(U_9533,U_9533,U_9533),U_9534),U_9534) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9533,U_9533),tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_2604_2]) ).

cnf(f_2604_4,plain,
    ( c_Wellfounded_Owf(U_9533,U_9534)
    | hAPP(hAPP(c_Relation_Orel__comp(U_9533,U_9533,U_9533),U_9534),U_9534) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9533,U_9533),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2604_3]) ).

fof(f_2605_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_2605_2,plain,
    ! [U_9538,U_9537,U_9536,U_9535] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_9535,U_9535,U_9535),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_9535,U_9535),tc_HOL_Obool)),U_9536),U_9538)),U_9537) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9535,U_9535),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_9535,U_9535,U_9535),U_9538),U_9537) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9535,U_9535),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_9535,U_9535,U_9535),U_9536),U_9537) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9535,U_9535),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2605_1]) ).

fof(f_2605_3,plain,
    ! [U_9535,U_9536,U_9537,U_9538] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_9535,U_9535,U_9535),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_9535,U_9535),tc_HOL_Obool)),U_9536),U_9538)),U_9537) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9535,U_9535),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_9535,U_9535,U_9535),U_9538),U_9537) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9535,U_9535),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_9535,U_9535,U_9535),U_9536),U_9537) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9535,U_9535),tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_2605_2]) ).

cnf(f_2605_4,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(U_9535,U_9535,U_9535),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_9535,U_9535),tc_HOL_Obool)),U_9536),U_9538)),U_9537) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9535,U_9535),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_9535,U_9535,U_9535),U_9538),U_9537) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9535,U_9535),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_9535,U_9535,U_9535),U_9536),U_9537) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9535,U_9535),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2605_3]) ).

fof(f_2606_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_2606_2,plain,
    ! [U_9542,U_9541,U_9540,U_9539] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_9539,U_9539,U_9539),U_9540),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_9539,U_9539),tc_HOL_Obool)),U_9541),U_9542)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9539,U_9539),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_9539,U_9539,U_9539),U_9540),U_9542) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9539,U_9539),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_9539,U_9539,U_9539),U_9540),U_9541) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9539,U_9539),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2606_1]) ).

fof(f_2606_3,plain,
    ! [U_9539,U_9540,U_9541,U_9542] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_9539,U_9539,U_9539),U_9540),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_9539,U_9539),tc_HOL_Obool)),U_9541),U_9542)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9539,U_9539),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_9539,U_9539,U_9539),U_9540),U_9542) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9539,U_9539),tc_HOL_Obool))
      | hAPP(hAPP(c_Relation_Orel__comp(U_9539,U_9539,U_9539),U_9540),U_9541) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9539,U_9539),tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_2606_2]) ).

cnf(f_2606_4,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(U_9539,U_9539,U_9539),U_9540),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_9539,U_9539),tc_HOL_Obool)),U_9541),U_9542)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9539,U_9539),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_9539,U_9539,U_9539),U_9540),U_9542) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9539,U_9539),tc_HOL_Obool))
    | hAPP(hAPP(c_Relation_Orel__comp(U_9539,U_9539,U_9539),U_9540),U_9541) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_9539,U_9539),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2606_3]) ).

fof(f_2607_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_2607_2,plain,
    ! [U_9546,U_9545,U_9544,U_9543] : c_Nitpick_Ofold__graph_H(U_9543,U_9544,U_9545,U_9546,c_Orderings_Obot__class_Obot(tc_fun(U_9543,tc_HOL_Obool)),U_9546),
    inference(variable_rename,[status(thm)],[f_2607_1]) ).

fof(f_2607_3,plain,
    ! [U_9546,U_9545,U_9544,U_9543] : c_Nitpick_Ofold__graph_H(U_9543,U_9544,U_9545,U_9546,c_Orderings_Obot__class_Obot(tc_fun(U_9543,tc_HOL_Obool)),U_9546),
    inference(definitional_conversion,[status(esa)],[f_2607_2]) ).

cnf(f_2607_4,plain,
    c_Nitpick_Ofold__graph_H(U_9543,U_9544,U_9545,U_9546,c_Orderings_Obot__class_Obot(tc_fun(U_9543,tc_HOL_Obool)),U_9546),
    inference(clausify,[status(thm)],[f_2607_3]) ).

fof(f_2608_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_2608_2,plain,
    ! [U_9550,U_9549,U_9548,U_9547] : c_Nitpick_Ofold__graph_H(U_9547,U_9548,U_9549,U_9550,c_Orderings_Obot__class_Obot(tc_fun(U_9547,tc_HOL_Obool)),U_9550),
    inference(variable_rename,[status(thm)],[f_2608_1]) ).

fof(f_2608_3,plain,
    ! [U_9547,U_9548,U_9549,U_9550] : c_Nitpick_Ofold__graph_H(U_9547,U_9548,U_9549,U_9550,c_Orderings_Obot__class_Obot(tc_fun(U_9547,tc_HOL_Obool)),U_9550),
    inference(definitional_conversion,[status(esa)],[f_2608_2]) ).

cnf(f_2608_4,plain,
    c_Nitpick_Ofold__graph_H(U_9547,U_9548,U_9549,U_9550,c_Orderings_Obot__class_Obot(tc_fun(U_9547,tc_HOL_Obool)),U_9550),
    inference(clausify,[status(thm)],[f_2608_3]) ).

fof(f_2609_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_2609_2,plain,
    ! [U_9552,U_9551] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9552,U_9551) = 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_9552),U_9551))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9551),U_9552)) ),
    inference(variable_rename,[status(thm)],[f_2609_1]) ).

fof(f_2609_3,plain,
    ! [U_9551,U_9552] :
      ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9552,U_9551) = 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_9552),U_9551))
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9551),U_9552)) ),
    inference(definitional_conversion,[status(esa)],[f_2609_2]) ).

cnf(f_2609_4,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9552,U_9551) = 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_9552),U_9551))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9551),U_9552)) ),
    inference(clausify,[status(thm)],[f_2609_3]) ).

fof(f_2610_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_2610_2,plain,
    ! [U_9554,U_9553] :
      ( ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9553,U_9554) = 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_9553),U_9554)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9553),U_9554))
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9553,U_9554) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2610_1]) ).

fof(f_2610_3,plain,
    ( ! [U_9558,U_9556] :
        ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9556,U_9558) = 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_9556),U_9558)) )
    & ! [U_9557,U_9555] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9555),U_9557))
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9555,U_9557) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2610_2]) ).

fof(f_2610_4,plain,
    ( ! [U_9558,U_9556] :
        ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9556,U_9558) = 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_9556),U_9558)) )
    & ! [U_9555,U_9557] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9555),U_9557))
        | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9555,U_9557) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2610_3]) ).

cnf(f_2610_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9555),U_9557))
    | c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9555,U_9557) != c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2610_4]) ).

cnf(f_2610_6,plain,
    ( c_SetInterval_Oord_OatLeastAtMost(tc_Nat_Onat,c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9556,U_9558) = 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_9556),U_9558)) ),
    inference(clausify,[status(thm)],[f_2610_4]) ).

fof(f_2611_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_2611_2,plain,
    ! [U_9560,U_9559] :
      ( ( 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_9559,U_9560)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9559),U_9560)) )
      & ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9559),U_9560))
        | 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_9559,U_9560) ) ),
    inference(variable_rename,[status(thm)],[f_2611_1]) ).

fof(f_2611_3,plain,
    ( ! [U_9564,U_9562] :
        ( 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_9562,U_9564)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9562),U_9564)) )
    & ! [U_9563,U_9561] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9561),U_9563))
        | 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_9561,U_9563) ) ),
    inference(miniscope,[status(thm)],[f_2611_2]) ).

fof(f_2611_4,plain,
    ( ! [U_9564,U_9562] :
        ( 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_9562,U_9564)
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9562),U_9564)) )
    & ! [U_9561,U_9563] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9561),U_9563))
        | 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_9561,U_9563) ) ),
    inference(definitional_conversion,[status(esa)],[f_2611_3]) ).

cnf(f_2611_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9561),U_9563))
    | 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_9561,U_9563) ),
    inference(clausify,[status(thm)],[f_2611_4]) ).

cnf(f_2611_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_9562,U_9564)
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_9562),U_9564)) ),
    inference(clausify,[status(thm)],[f_2611_4]) ).

fof(f_2612_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_2612_2,plain,
    ! [U_9565] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_9565) = 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_9565)),
    inference(variable_rename,[status(thm)],[f_2612_1]) ).

fof(f_2612_3,plain,
    ! [U_9565] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_9565) = 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_9565)),
    inference(definitional_conversion,[status(esa)],[f_2612_2]) ).

cnf(f_2612_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_9565) = 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_9565)),
    inference(clausify,[status(thm)],[f_2612_3]) ).

fof(f_2613_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_2613_2,plain,
    ! [U_9566] :
      ( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_9566) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9566))
      | ~ c_Nat__Transfer_Onat__set(U_9566) ),
    inference(variable_rename,[status(thm)],[f_2613_1]) ).

fof(f_2613_3,plain,
    ! [U_9566] :
      ( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_9566) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9566))
      | ~ c_Nat__Transfer_Onat__set(U_9566) ),
    inference(definitional_conversion,[status(esa)],[f_2613_2]) ).

cnf(f_2613_4,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_Int_Oint),U_9566) = hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9566))
    | ~ c_Nat__Transfer_Onat__set(U_9566) ),
    inference(clausify,[status(thm)],[f_2613_3]) ).

fof(f_2614_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_2614_2,plain,
    ! [U_9570,U_9569,U_9568,U_9567] :
      ( 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_9568),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9569),U_9570))),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_9568),U_9570)),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_9567),U_9569)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9567),U_9568)) ),
    inference(variable_rename,[status(thm)],[f_2614_1]) ).

fof(f_2614_3,plain,
    ! [U_9567,U_9568,U_9569,U_9570] :
      ( 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_9568),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9569),U_9570))),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_9568),U_9570)),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_9567),U_9569)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9567),U_9568)) ),
    inference(definitional_conversion,[status(esa)],[f_2614_2]) ).

cnf(f_2614_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_9568),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9569),U_9570))),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_9568),U_9570)),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_9567),U_9569)),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9567),U_9568)) ),
    inference(clausify,[status(thm)],[f_2614_3]) ).

fof(f_2615_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_2615_2,plain,
    ! [U_9574,U_9573,U_9572,U_9571] :
      ( 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_9573),U_9574)),U_9572)),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_9574),U_9572)),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_9573),U_9571)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9571),U_9572)) ),
    inference(variable_rename,[status(thm)],[f_2615_1]) ).

fof(f_2615_3,plain,
    ! [U_9573,U_9572,U_9571,U_9574] :
      ( 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_9573),U_9574)),U_9572)),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_9574),U_9572)),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_9573),U_9571)),c_FunDef_Opair__leq))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9571),U_9572)) ),
    inference(definitional_conversion,[status(esa)],[f_2615_2]) ).

cnf(f_2615_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_9573),U_9574)),U_9572)),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_9574),U_9572)),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_9573),U_9571)),c_FunDef_Opair__leq))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9571),U_9572)) ),
    inference(clausify,[status(thm)],[f_2615_3]) ).

fof(f_2616_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_2616_2,plain,
    ! [U_9578,U_9577,U_9576,U_9575] :
      ( 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_9576),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9577),U_9578))),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_9576),U_9578)),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_9575),U_9577)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9575),U_9576)) ),
    inference(variable_rename,[status(thm)],[f_2616_1]) ).

fof(f_2616_3,plain,
    ! [U_9577,U_9576,U_9575,U_9578] :
      ( 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_9576),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9577),U_9578))),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_9576),U_9578)),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_9575),U_9577)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9575),U_9576)) ),
    inference(definitional_conversion,[status(esa)],[f_2616_2]) ).

cnf(f_2616_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_9576),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9577),U_9578))),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_9576),U_9578)),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_9575),U_9577)),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9575),U_9576)) ),
    inference(clausify,[status(thm)],[f_2616_3]) ).

fof(f_2617_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_2617_2,plain,
    ! [U_9582,U_9581,U_9580,U_9579] :
      ( 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_9581),U_9582)),U_9580)),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_9582),U_9580)),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_9581),U_9579)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9579),U_9580)) ),
    inference(variable_rename,[status(thm)],[f_2617_1]) ).

fof(f_2617_3,plain,
    ! [U_9580,U_9581,U_9579,U_9582] :
      ( 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_9581),U_9582)),U_9580)),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_9582),U_9580)),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_9581),U_9579)),c_FunDef_Opair__less))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9579),U_9580)) ),
    inference(definitional_conversion,[status(esa)],[f_2617_2]) ).

cnf(f_2617_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_9581),U_9582)),U_9580)),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_9582),U_9580)),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_9581),U_9579)),c_FunDef_Opair__less))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9579),U_9580)) ),
    inference(clausify,[status(thm)],[f_2617_3]) ).

fof(f_2618_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_2618_2,plain,
    ! [U_9586,U_9585,U_9584,U_9583] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9583,tc_fun(U_9584,tc_HOL_Obool))),U_9585),U_9586)),
    inference(variable_rename,[status(thm)],[f_2618_1]) ).

fof(f_2618_3,plain,
    ! [U_9586,U_9584,U_9585,U_9583] : ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9583,tc_fun(U_9584,tc_HOL_Obool))),U_9585),U_9586)),
    inference(definitional_conversion,[status(esa)],[f_2618_2]) ).

cnf(f_2618_4,plain,
    ~ hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_fun(U_9583,tc_fun(U_9584,tc_HOL_Obool))),U_9585),U_9586)),
    inference(clausify,[status(thm)],[f_2618_3]) ).

fof(f_2619_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_2619_2,plain,
    ! [U_9587] : 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_9587),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_2619_1]) ).

fof(f_2619_3,plain,
    ! [U_9587] : 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_9587),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_2619_2]) ).

cnf(f_2619_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_9587),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_2619_3]) ).

fof(f_2620_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_2620_2,plain,
    ! [U_9588] :
      ( 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_9588),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
      | U_9588 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2620_1]) ).

fof(f_2620_3,plain,
    ! [U_9588] :
      ( 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_9588),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
      | U_9588 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_2620_2]) ).

cnf(f_2620_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_9588),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))),c_FunDef_Omin__strict))
    | U_9588 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2620_3]) ).

fof(f_2621_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_2621_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_2621_1]) ).

cnf(f_2621_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_2621_2]) ).

fof(f_2622_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_2622_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_2622_1]) ).

cnf(f_2622_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_2622_2]) ).

fof(f_2623_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_2623_2,plain,
    ! [U_9591,U_9590,U_9589] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_9589,tc_HOL_Obool),tc_fun(U_9589,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_9589,tc_HOL_Obool),tc_fun(U_9589,tc_HOL_Obool),tc_fun(U_9589,tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_9589,U_9590)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_9589,tc_HOL_Obool),tc_fun(U_9589,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_9589,U_9591)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_9589,tc_HOL_Obool),tc_fun(U_9589,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9589,tc_HOL_Obool),tc_fun(U_9589,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9589,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_9589,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_9589,tc_HOL_Obool),tc_fun(U_9589,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(U_9589,U_9590)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9589,U_9589),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_9589,U_9589,U_9589),U_9590),U_9591)),U_9590)) ),
    inference(variable_rename,[status(thm)],[f_2623_1]) ).

fof(f_2623_3,plain,
    ! [U_9589,U_9590,U_9591] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_9589,tc_HOL_Obool),tc_fun(U_9589,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_9589,tc_HOL_Obool),tc_fun(U_9589,tc_HOL_Obool),tc_fun(U_9589,tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_9589,U_9590)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_9589,tc_HOL_Obool),tc_fun(U_9589,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_9589,U_9591)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_9589,tc_HOL_Obool),tc_fun(U_9589,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9589,tc_HOL_Obool),tc_fun(U_9589,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9589,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_9589,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_9589,tc_HOL_Obool),tc_fun(U_9589,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(U_9589,U_9590)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9589,U_9589),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_9589,U_9589,U_9589),U_9590),U_9591)),U_9590)) ),
    inference(definitional_conversion,[status(esa)],[f_2623_2]) ).

cnf(f_2623_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_9589,tc_HOL_Obool),tc_fun(U_9589,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_9589,tc_HOL_Obool),tc_fun(U_9589,tc_HOL_Obool),tc_fun(U_9589,tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_9589,U_9590)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_9589,tc_HOL_Obool),tc_fun(U_9589,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omin__ext(U_9589,U_9591)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_9589,tc_HOL_Obool),tc_fun(U_9589,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9589,tc_HOL_Obool),tc_fun(U_9589,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9589,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_9589,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_9589,tc_HOL_Obool),tc_fun(U_9589,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omin__ext(U_9589,U_9590)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9589,U_9589),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_9589,U_9589,U_9589),U_9590),U_9591)),U_9590)) ),
    inference(clausify,[status(thm)],[f_2623_3]) ).

fof(f_2624_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_2624_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_2624_1]) ).

cnf(f_2624_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_2624_2]) ).

fof(f_2625_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_2625_2,plain,
    ! [U_9594,U_9593,U_9592] :
      ( ( c_Partial__Function_Oflat__lub(U_9592,U_9594,U_9593) = c_HOL_OThe(U_9592,hAPP(hAPP(c_COMBC(U_9592,tc_fun(U_9592,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9592)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9592,tc_HOL_Obool)),U_9593),hAPP(hAPP(c_Set_Oinsert(U_9592),U_9594),c_Orderings_Obot__class_Obot(tc_fun(U_9592,tc_HOL_Obool))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9592,tc_HOL_Obool)),U_9593),hAPP(hAPP(c_Set_Oinsert(U_9592),U_9594),c_Orderings_Obot__class_Obot(tc_fun(U_9592,tc_HOL_Obool))))) )
      & ( c_Partial__Function_Oflat__lub(U_9592,U_9594,U_9593) = U_9594
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9592,tc_HOL_Obool)),U_9593),hAPP(hAPP(c_Set_Oinsert(U_9592),U_9594),c_Orderings_Obot__class_Obot(tc_fun(U_9592,tc_HOL_Obool))))) ) ),
    inference(variable_rename,[status(thm)],[f_2625_1]) ).

fof(f_2625_3,plain,
    ( ! [U_9600,U_9598,U_9596] :
        ( c_Partial__Function_Oflat__lub(U_9596,U_9600,U_9598) = c_HOL_OThe(U_9596,hAPP(hAPP(c_COMBC(U_9596,tc_fun(U_9596,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9596)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9596,tc_HOL_Obool)),U_9598),hAPP(hAPP(c_Set_Oinsert(U_9596),U_9600),c_Orderings_Obot__class_Obot(tc_fun(U_9596,tc_HOL_Obool))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9596,tc_HOL_Obool)),U_9598),hAPP(hAPP(c_Set_Oinsert(U_9596),U_9600),c_Orderings_Obot__class_Obot(tc_fun(U_9596,tc_HOL_Obool))))) )
    & ! [U_9599,U_9597,U_9595] :
        ( c_Partial__Function_Oflat__lub(U_9595,U_9599,U_9597) = U_9599
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9595,tc_HOL_Obool)),U_9597),hAPP(hAPP(c_Set_Oinsert(U_9595),U_9599),c_Orderings_Obot__class_Obot(tc_fun(U_9595,tc_HOL_Obool))))) ) ),
    inference(miniscope,[status(thm)],[f_2625_2]) ).

fof(f_2625_4,plain,
    ( ! [U_9598,U_9596,U_9600] :
        ( c_Partial__Function_Oflat__lub(U_9596,U_9600,U_9598) = c_HOL_OThe(U_9596,hAPP(hAPP(c_COMBC(U_9596,tc_fun(U_9596,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9596)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9596,tc_HOL_Obool)),U_9598),hAPP(hAPP(c_Set_Oinsert(U_9596),U_9600),c_Orderings_Obot__class_Obot(tc_fun(U_9596,tc_HOL_Obool))))))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9596,tc_HOL_Obool)),U_9598),hAPP(hAPP(c_Set_Oinsert(U_9596),U_9600),c_Orderings_Obot__class_Obot(tc_fun(U_9596,tc_HOL_Obool))))) )
    & ! [U_9597,U_9595,U_9599] :
        ( c_Partial__Function_Oflat__lub(U_9595,U_9599,U_9597) = U_9599
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9595,tc_HOL_Obool)),U_9597),hAPP(hAPP(c_Set_Oinsert(U_9595),U_9599),c_Orderings_Obot__class_Obot(tc_fun(U_9595,tc_HOL_Obool))))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2625_3]) ).

cnf(f_2625_5,plain,
    ( c_Partial__Function_Oflat__lub(U_9595,U_9599,U_9597) = U_9599
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9595,tc_HOL_Obool)),U_9597),hAPP(hAPP(c_Set_Oinsert(U_9595),U_9599),c_Orderings_Obot__class_Obot(tc_fun(U_9595,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_2625_4]) ).

cnf(f_2625_6,plain,
    ( c_Partial__Function_Oflat__lub(U_9596,U_9600,U_9598) = c_HOL_OThe(U_9596,hAPP(hAPP(c_COMBC(U_9596,tc_fun(U_9596,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9596)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9596,tc_HOL_Obool)),U_9598),hAPP(hAPP(c_Set_Oinsert(U_9596),U_9600),c_Orderings_Obot__class_Obot(tc_fun(U_9596,tc_HOL_Obool))))))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9596,tc_HOL_Obool)),U_9598),hAPP(hAPP(c_Set_Oinsert(U_9596),U_9600),c_Orderings_Obot__class_Obot(tc_fun(U_9596,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_2625_4]) ).

fof(f_2626_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_2626_2,plain,
    ! [U_9603,U_9602,U_9601] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_9601,tc_HOL_Obool),tc_fun(U_9601,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_9601,tc_HOL_Obool),tc_fun(U_9601,tc_HOL_Obool),tc_fun(U_9601,tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_9601,U_9602)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_9601,tc_HOL_Obool),tc_fun(U_9601,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_9601,U_9603)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_9601,tc_HOL_Obool),tc_fun(U_9601,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9601,tc_HOL_Obool),tc_fun(U_9601,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9601,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_9601,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_9601,tc_HOL_Obool),tc_fun(U_9601,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(U_9601,U_9602)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9601,U_9601),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_9601,U_9601,U_9601),U_9602),U_9603)),U_9602)) ),
    inference(variable_rename,[status(thm)],[f_2626_1]) ).

fof(f_2626_3,plain,
    ! [U_9601,U_9602,U_9603] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_9601,tc_HOL_Obool),tc_fun(U_9601,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_9601,tc_HOL_Obool),tc_fun(U_9601,tc_HOL_Obool),tc_fun(U_9601,tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_9601,U_9602)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_9601,tc_HOL_Obool),tc_fun(U_9601,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_9601,U_9603)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_9601,tc_HOL_Obool),tc_fun(U_9601,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9601,tc_HOL_Obool),tc_fun(U_9601,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9601,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_9601,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_9601,tc_HOL_Obool),tc_fun(U_9601,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(U_9601,U_9602)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9601,U_9601),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_9601,U_9601,U_9601),U_9602),U_9603)),U_9602)) ),
    inference(definitional_conversion,[status(esa)],[f_2626_2]) ).

cnf(f_2626_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_fun(U_9601,tc_HOL_Obool),tc_fun(U_9601,tc_HOL_Obool)),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(tc_fun(U_9601,tc_HOL_Obool),tc_fun(U_9601,tc_HOL_Obool),tc_fun(U_9601,tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_9601,U_9602)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(tc_fun(U_9601,tc_HOL_Obool),tc_fun(U_9601,tc_HOL_Obool)),tc_HOL_Obool)),c_Wellfounded_Omax__ext(U_9601,U_9603)),hAPP(hAPP(c_Set_Oinsert(tc_prod(tc_fun(U_9601,tc_HOL_Obool),tc_fun(U_9601,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9601,tc_HOL_Obool),tc_fun(U_9601,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_9601,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(U_9601,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_fun(U_9601,tc_HOL_Obool),tc_fun(U_9601,tc_HOL_Obool)),tc_HOL_Obool)))))),c_Wellfounded_Omax__ext(U_9601,U_9602)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_9601,U_9601),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_9601,U_9601,U_9601),U_9602),U_9603)),U_9602)) ),
    inference(clausify,[status(thm)],[f_2626_3]) ).

fof(f_2627_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_2627_2,plain,
    ! [U_9605,U_9604] :
      ( c_Wellfounded_Owf(tc_fun(U_9604,tc_HOL_Obool),c_Wellfounded_Omax__ext(U_9604,U_9605))
      | ~ c_Wellfounded_Owf(U_9604,U_9605) ),
    inference(variable_rename,[status(thm)],[f_2627_1]) ).

fof(f_2627_3,plain,
    ! [U_9605,U_9604] :
      ( c_Wellfounded_Owf(tc_fun(U_9604,tc_HOL_Obool),c_Wellfounded_Omax__ext(U_9604,U_9605))
      | ~ c_Wellfounded_Owf(U_9604,U_9605) ),
    inference(definitional_conversion,[status(esa)],[f_2627_2]) ).

cnf(f_2627_4,plain,
    ( c_Wellfounded_Owf(tc_fun(U_9604,tc_HOL_Obool),c_Wellfounded_Omax__ext(U_9604,U_9605))
    | ~ c_Wellfounded_Owf(U_9604,U_9605) ),
    inference(clausify,[status(thm)],[f_2627_3]) ).

fof(f_2628_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_2628_2,plain,
    ! [U_9607,U_9606] :
      ( c_Wellfounded_Owf(tc_fun(U_9606,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_9606,U_9607))
      | ~ c_Wellfounded_Owf(U_9606,U_9607) ),
    inference(variable_rename,[status(thm)],[f_2628_1]) ).

fof(f_2628_3,plain,
    ! [U_9606,U_9607] :
      ( c_Wellfounded_Owf(tc_fun(U_9606,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_9606,U_9607))
      | ~ c_Wellfounded_Owf(U_9606,U_9607) ),
    inference(definitional_conversion,[status(esa)],[f_2628_2]) ).

cnf(f_2628_4,plain,
    ( c_Wellfounded_Owf(tc_fun(U_9606,tc_HOL_Obool),c_Wellfounded_Omin__ext(U_9606,U_9607))
    | ~ c_Wellfounded_Owf(U_9606,U_9607) ),
    inference(clausify,[status(thm)],[f_2628_3]) ).

fof(f_2629_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_2629_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_2629_1]) ).

cnf(f_2629_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_2629_2]) ).

fof(f_2630_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_2630_2,plain,
    ! [U_9613,U_9612,U_9611,U_9610,U_9609,U_9608] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9608,tc_HOL_Obool),tc_fun(U_9608,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9608,tc_HOL_Obool),tc_fun(U_9608,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9608,tc_HOL_Obool)),U_9609),U_9612)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9608,tc_HOL_Obool)),U_9610),U_9613))),c_Wellfounded_Omax__ext(U_9608,U_9611)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9608,tc_HOL_Obool),tc_fun(U_9608,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9608,tc_HOL_Obool),tc_fun(U_9608,tc_HOL_Obool)),U_9612),U_9613)),c_Wellfounded_Omax__ext(U_9608,U_9611)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9608,tc_HOL_Obool),tc_fun(U_9608,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9608,tc_HOL_Obool),tc_fun(U_9608,tc_HOL_Obool)),U_9609),U_9610)),c_Wellfounded_Omax__ext(U_9608,U_9611))) ),
    inference(variable_rename,[status(thm)],[f_2630_1]) ).

fof(f_2630_3,plain,
    ! [U_9608,U_9609,U_9610,U_9611,U_9612,U_9613] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9608,tc_HOL_Obool),tc_fun(U_9608,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9608,tc_HOL_Obool),tc_fun(U_9608,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9608,tc_HOL_Obool)),U_9609),U_9612)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9608,tc_HOL_Obool)),U_9610),U_9613))),c_Wellfounded_Omax__ext(U_9608,U_9611)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9608,tc_HOL_Obool),tc_fun(U_9608,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9608,tc_HOL_Obool),tc_fun(U_9608,tc_HOL_Obool)),U_9612),U_9613)),c_Wellfounded_Omax__ext(U_9608,U_9611)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9608,tc_HOL_Obool),tc_fun(U_9608,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9608,tc_HOL_Obool),tc_fun(U_9608,tc_HOL_Obool)),U_9609),U_9610)),c_Wellfounded_Omax__ext(U_9608,U_9611))) ),
    inference(definitional_conversion,[status(esa)],[f_2630_2]) ).

cnf(f_2630_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9608,tc_HOL_Obool),tc_fun(U_9608,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9608,tc_HOL_Obool),tc_fun(U_9608,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9608,tc_HOL_Obool)),U_9609),U_9612)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9608,tc_HOL_Obool)),U_9610),U_9613))),c_Wellfounded_Omax__ext(U_9608,U_9611)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9608,tc_HOL_Obool),tc_fun(U_9608,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9608,tc_HOL_Obool),tc_fun(U_9608,tc_HOL_Obool)),U_9612),U_9613)),c_Wellfounded_Omax__ext(U_9608,U_9611)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9608,tc_HOL_Obool),tc_fun(U_9608,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9608,tc_HOL_Obool),tc_fun(U_9608,tc_HOL_Obool)),U_9609),U_9610)),c_Wellfounded_Omax__ext(U_9608,U_9611))) ),
    inference(clausify,[status(thm)],[f_2630_3]) ).

fof(f_2631_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_2631_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_2631_1]) ).

cnf(f_2631_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_2631_2]) ).

fof(f_2632_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_2632_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_2632_1]) ).

cnf(f_2632_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_2632_2]) ).

fof(f_2633_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_2633_2,plain,
    ! [U_9617,U_9616,U_9615,U_9614] :
      ( ( c_Wellfounded_Omax__extp(U_9614,hAPP(hAPP(c_COMBC(U_9614,tc_fun(tc_prod(U_9614,U_9614),tc_HOL_Obool),tc_fun(U_9614,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9614,tc_fun(tc_fun(tc_prod(U_9614,U_9614),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9614,U_9614),tc_HOL_Obool),tc_fun(U_9614,tc_HOL_Obool)),U_9614),c_COMBC(U_9614,tc_fun(tc_prod(U_9614,U_9614),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9614,tc_prod(U_9614,U_9614)),tc_fun(U_9614,tc_fun(tc_fun(tc_prod(U_9614,U_9614),tc_HOL_Obool),tc_HOL_Obool)),U_9614),hAPP(c_COMBB(tc_prod(U_9614,U_9614),tc_fun(tc_fun(tc_prod(U_9614,U_9614),tc_HOL_Obool),tc_HOL_Obool),U_9614),c_member(tc_prod(U_9614,U_9614)))),c_Product__Type_OPair(U_9614,U_9614)))),U_9615),U_9616,U_9617)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9614,tc_HOL_Obool),tc_fun(U_9614,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9614,tc_HOL_Obool),tc_fun(U_9614,tc_HOL_Obool)),U_9616),U_9617)),c_Wellfounded_Omax__ext(U_9614,U_9615))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9614,tc_HOL_Obool),tc_fun(U_9614,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9614,tc_HOL_Obool),tc_fun(U_9614,tc_HOL_Obool)),U_9616),U_9617)),c_Wellfounded_Omax__ext(U_9614,U_9615)))
        | ~ c_Wellfounded_Omax__extp(U_9614,hAPP(hAPP(c_COMBC(U_9614,tc_fun(tc_prod(U_9614,U_9614),tc_HOL_Obool),tc_fun(U_9614,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9614,tc_fun(tc_fun(tc_prod(U_9614,U_9614),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9614,U_9614),tc_HOL_Obool),tc_fun(U_9614,tc_HOL_Obool)),U_9614),c_COMBC(U_9614,tc_fun(tc_prod(U_9614,U_9614),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9614,tc_prod(U_9614,U_9614)),tc_fun(U_9614,tc_fun(tc_fun(tc_prod(U_9614,U_9614),tc_HOL_Obool),tc_HOL_Obool)),U_9614),hAPP(c_COMBB(tc_prod(U_9614,U_9614),tc_fun(tc_fun(tc_prod(U_9614,U_9614),tc_HOL_Obool),tc_HOL_Obool),U_9614),c_member(tc_prod(U_9614,U_9614)))),c_Product__Type_OPair(U_9614,U_9614)))),U_9615),U_9616,U_9617) ) ),
    inference(variable_rename,[status(thm)],[f_2633_1]) ).

fof(f_2633_3,plain,
    ( ! [U_9625,U_9623,U_9621,U_9619] :
        ( c_Wellfounded_Omax__extp(U_9619,hAPP(hAPP(c_COMBC(U_9619,tc_fun(tc_prod(U_9619,U_9619),tc_HOL_Obool),tc_fun(U_9619,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9619,tc_fun(tc_fun(tc_prod(U_9619,U_9619),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9619,U_9619),tc_HOL_Obool),tc_fun(U_9619,tc_HOL_Obool)),U_9619),c_COMBC(U_9619,tc_fun(tc_prod(U_9619,U_9619),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9619,tc_prod(U_9619,U_9619)),tc_fun(U_9619,tc_fun(tc_fun(tc_prod(U_9619,U_9619),tc_HOL_Obool),tc_HOL_Obool)),U_9619),hAPP(c_COMBB(tc_prod(U_9619,U_9619),tc_fun(tc_fun(tc_prod(U_9619,U_9619),tc_HOL_Obool),tc_HOL_Obool),U_9619),c_member(tc_prod(U_9619,U_9619)))),c_Product__Type_OPair(U_9619,U_9619)))),U_9621),U_9623,U_9625)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9619,tc_HOL_Obool),tc_fun(U_9619,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9619,tc_HOL_Obool),tc_fun(U_9619,tc_HOL_Obool)),U_9623),U_9625)),c_Wellfounded_Omax__ext(U_9619,U_9621))) )
    & ! [U_9624,U_9622,U_9620,U_9618] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9618,tc_HOL_Obool),tc_fun(U_9618,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9618,tc_HOL_Obool),tc_fun(U_9618,tc_HOL_Obool)),U_9622),U_9624)),c_Wellfounded_Omax__ext(U_9618,U_9620)))
        | ~ c_Wellfounded_Omax__extp(U_9618,hAPP(hAPP(c_COMBC(U_9618,tc_fun(tc_prod(U_9618,U_9618),tc_HOL_Obool),tc_fun(U_9618,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9618,tc_fun(tc_fun(tc_prod(U_9618,U_9618),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9618,U_9618),tc_HOL_Obool),tc_fun(U_9618,tc_HOL_Obool)),U_9618),c_COMBC(U_9618,tc_fun(tc_prod(U_9618,U_9618),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9618,tc_prod(U_9618,U_9618)),tc_fun(U_9618,tc_fun(tc_fun(tc_prod(U_9618,U_9618),tc_HOL_Obool),tc_HOL_Obool)),U_9618),hAPP(c_COMBB(tc_prod(U_9618,U_9618),tc_fun(tc_fun(tc_prod(U_9618,U_9618),tc_HOL_Obool),tc_HOL_Obool),U_9618),c_member(tc_prod(U_9618,U_9618)))),c_Product__Type_OPair(U_9618,U_9618)))),U_9620),U_9622,U_9624) ) ),
    inference(miniscope,[status(thm)],[f_2633_2]) ).

fof(f_2633_4,plain,
    ( ! [U_9621,U_9619,U_9623,U_9625] :
        ( c_Wellfounded_Omax__extp(U_9619,hAPP(hAPP(c_COMBC(U_9619,tc_fun(tc_prod(U_9619,U_9619),tc_HOL_Obool),tc_fun(U_9619,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9619,tc_fun(tc_fun(tc_prod(U_9619,U_9619),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9619,U_9619),tc_HOL_Obool),tc_fun(U_9619,tc_HOL_Obool)),U_9619),c_COMBC(U_9619,tc_fun(tc_prod(U_9619,U_9619),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9619,tc_prod(U_9619,U_9619)),tc_fun(U_9619,tc_fun(tc_fun(tc_prod(U_9619,U_9619),tc_HOL_Obool),tc_HOL_Obool)),U_9619),hAPP(c_COMBB(tc_prod(U_9619,U_9619),tc_fun(tc_fun(tc_prod(U_9619,U_9619),tc_HOL_Obool),tc_HOL_Obool),U_9619),c_member(tc_prod(U_9619,U_9619)))),c_Product__Type_OPair(U_9619,U_9619)))),U_9621),U_9623,U_9625)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9619,tc_HOL_Obool),tc_fun(U_9619,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9619,tc_HOL_Obool),tc_fun(U_9619,tc_HOL_Obool)),U_9623),U_9625)),c_Wellfounded_Omax__ext(U_9619,U_9621))) )
    & ! [U_9620,U_9618,U_9622,U_9624] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9618,tc_HOL_Obool),tc_fun(U_9618,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9618,tc_HOL_Obool),tc_fun(U_9618,tc_HOL_Obool)),U_9622),U_9624)),c_Wellfounded_Omax__ext(U_9618,U_9620)))
        | ~ c_Wellfounded_Omax__extp(U_9618,hAPP(hAPP(c_COMBC(U_9618,tc_fun(tc_prod(U_9618,U_9618),tc_HOL_Obool),tc_fun(U_9618,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9618,tc_fun(tc_fun(tc_prod(U_9618,U_9618),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9618,U_9618),tc_HOL_Obool),tc_fun(U_9618,tc_HOL_Obool)),U_9618),c_COMBC(U_9618,tc_fun(tc_prod(U_9618,U_9618),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9618,tc_prod(U_9618,U_9618)),tc_fun(U_9618,tc_fun(tc_fun(tc_prod(U_9618,U_9618),tc_HOL_Obool),tc_HOL_Obool)),U_9618),hAPP(c_COMBB(tc_prod(U_9618,U_9618),tc_fun(tc_fun(tc_prod(U_9618,U_9618),tc_HOL_Obool),tc_HOL_Obool),U_9618),c_member(tc_prod(U_9618,U_9618)))),c_Product__Type_OPair(U_9618,U_9618)))),U_9620),U_9622,U_9624) ) ),
    inference(definitional_conversion,[status(esa)],[f_2633_3]) ).

cnf(f_2633_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9618,tc_HOL_Obool),tc_fun(U_9618,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9618,tc_HOL_Obool),tc_fun(U_9618,tc_HOL_Obool)),U_9622),U_9624)),c_Wellfounded_Omax__ext(U_9618,U_9620)))
    | ~ c_Wellfounded_Omax__extp(U_9618,hAPP(hAPP(c_COMBC(U_9618,tc_fun(tc_prod(U_9618,U_9618),tc_HOL_Obool),tc_fun(U_9618,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9618,tc_fun(tc_fun(tc_prod(U_9618,U_9618),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9618,U_9618),tc_HOL_Obool),tc_fun(U_9618,tc_HOL_Obool)),U_9618),c_COMBC(U_9618,tc_fun(tc_prod(U_9618,U_9618),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9618,tc_prod(U_9618,U_9618)),tc_fun(U_9618,tc_fun(tc_fun(tc_prod(U_9618,U_9618),tc_HOL_Obool),tc_HOL_Obool)),U_9618),hAPP(c_COMBB(tc_prod(U_9618,U_9618),tc_fun(tc_fun(tc_prod(U_9618,U_9618),tc_HOL_Obool),tc_HOL_Obool),U_9618),c_member(tc_prod(U_9618,U_9618)))),c_Product__Type_OPair(U_9618,U_9618)))),U_9620),U_9622,U_9624) ),
    inference(clausify,[status(thm)],[f_2633_4]) ).

cnf(f_2633_6,plain,
    ( c_Wellfounded_Omax__extp(U_9619,hAPP(hAPP(c_COMBC(U_9619,tc_fun(tc_prod(U_9619,U_9619),tc_HOL_Obool),tc_fun(U_9619,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9619,tc_fun(tc_fun(tc_prod(U_9619,U_9619),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_9619,U_9619),tc_HOL_Obool),tc_fun(U_9619,tc_HOL_Obool)),U_9619),c_COMBC(U_9619,tc_fun(tc_prod(U_9619,U_9619),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9619,tc_prod(U_9619,U_9619)),tc_fun(U_9619,tc_fun(tc_fun(tc_prod(U_9619,U_9619),tc_HOL_Obool),tc_HOL_Obool)),U_9619),hAPP(c_COMBB(tc_prod(U_9619,U_9619),tc_fun(tc_fun(tc_prod(U_9619,U_9619),tc_HOL_Obool),tc_HOL_Obool),U_9619),c_member(tc_prod(U_9619,U_9619)))),c_Product__Type_OPair(U_9619,U_9619)))),U_9621),U_9623,U_9625)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9619,tc_HOL_Obool),tc_fun(U_9619,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9619,tc_HOL_Obool),tc_fun(U_9619,tc_HOL_Obool)),U_9623),U_9625)),c_Wellfounded_Omax__ext(U_9619,U_9621))) ),
    inference(clausify,[status(thm)],[f_2633_4]) ).

fof(f_2634_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_2634_2,plain,
    ! [U_9628,U_9627,U_9626] :
      ( ( ( hAPP(c_Finite__Set_Ocard(U_9626),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9626,tc_HOL_Obool)),U_9627),hAPP(hAPP(c_Set_Oinsert(U_9626),U_9628),c_Orderings_Obot__class_Obot(tc_fun(U_9626,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_9626),U_9627)
          | hBOOL(hAPP(hAPP(c_member(U_9626),U_9628),U_9627)) )
        & ( hAPP(c_Finite__Set_Ocard(U_9626),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9626,tc_HOL_Obool)),U_9627),hAPP(hAPP(c_Set_Oinsert(U_9626),U_9628),c_Orderings_Obot__class_Obot(tc_fun(U_9626,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9626),U_9627)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
          | ~ hBOOL(hAPP(hAPP(c_member(U_9626),U_9628),U_9627)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9626),U_9627)) ),
    inference(variable_rename,[status(thm)],[f_2634_1]) ).

fof(f_2634_3,plain,
    ( ! [U_9626,U_9627,U_9628] :
        ( hAPP(c_Finite__Set_Ocard(U_9626),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9626,tc_HOL_Obool)),U_9627),hAPP(hAPP(c_Set_Oinsert(U_9626),U_9628),c_Orderings_Obot__class_Obot(tc_fun(U_9626,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_9626),U_9627)
        | hBOOL(hAPP(hAPP(c_member(U_9626),U_9628),U_9627))
        | ~ sP749(U_9626,U_9627,U_9628) )
    & ! [U_9626,U_9627,U_9628] :
        ( hAPP(c_Finite__Set_Ocard(U_9626),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9626,tc_HOL_Obool)),U_9627),hAPP(hAPP(c_Set_Oinsert(U_9626),U_9628),c_Orderings_Obot__class_Obot(tc_fun(U_9626,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9626),U_9627)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(U_9626),U_9628),U_9627))
        | ~ sP749(U_9626,U_9627,U_9628) )
    & ! [U_9626,U_9627,U_9628] :
        ( sP749(U_9626,U_9627,U_9628)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9626),U_9627)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP749])],[f_2634_2]) ).

cnf(f_2634_4,plain,
    ( sP749(U_9626,U_9627,U_9628)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9626),U_9627)) ),
    inference(clausify,[status(thm)],[f_2634_3]) ).

cnf(f_2634_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_9626),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9626,tc_HOL_Obool)),U_9627),hAPP(hAPP(c_Set_Oinsert(U_9626),U_9628),c_Orderings_Obot__class_Obot(tc_fun(U_9626,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9626),U_9627)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9626),U_9628),U_9627))
    | ~ sP749(U_9626,U_9627,U_9628) ),
    inference(clausify,[status(thm)],[f_2634_3]) ).

cnf(f_2634_6,plain,
    ( hAPP(c_Finite__Set_Ocard(U_9626),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9626,tc_HOL_Obool)),U_9627),hAPP(hAPP(c_Set_Oinsert(U_9626),U_9628),c_Orderings_Obot__class_Obot(tc_fun(U_9626,tc_HOL_Obool))))) = hAPP(c_Finite__Set_Ocard(U_9626),U_9627)
    | hBOOL(hAPP(hAPP(c_member(U_9626),U_9628),U_9627))
    | ~ sP749(U_9626,U_9627,U_9628) ),
    inference(clausify,[status(thm)],[f_2634_3]) ).

fof(f_2635_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_2635_2,plain,
    ! [U_9631,U_9630,U_9629] :
      ( hAPP(c_Finite__Set_Ocard(U_9629),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9629,tc_HOL_Obool)),U_9630),hAPP(hAPP(c_Set_Oinsert(U_9629),U_9631),c_Orderings_Obot__class_Obot(tc_fun(U_9629,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9629),U_9630)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9629),U_9631),U_9630))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9629),U_9630)) ),
    inference(variable_rename,[status(thm)],[f_2635_1]) ).

fof(f_2635_3,plain,
    ! [U_9630,U_9629,U_9631] :
      ( hAPP(c_Finite__Set_Ocard(U_9629),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9629,tc_HOL_Obool)),U_9630),hAPP(hAPP(c_Set_Oinsert(U_9629),U_9631),c_Orderings_Obot__class_Obot(tc_fun(U_9629,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9629),U_9630)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9629),U_9631),U_9630))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9629),U_9630)) ),
    inference(definitional_conversion,[status(esa)],[f_2635_2]) ).

cnf(f_2635_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_9629),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9629,tc_HOL_Obool)),U_9630),hAPP(hAPP(c_Set_Oinsert(U_9629),U_9631),c_Orderings_Obot__class_Obot(tc_fun(U_9629,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9629),U_9630)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9629),U_9631),U_9630))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9629),U_9630)) ),
    inference(clausify,[status(thm)],[f_2635_3]) ).

fof(f_2636_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_2636_2,plain,
    ! [U_9634,U_9633,U_9632] :
      ( hAPP(c_Finite__Set_Ocard(U_9632),U_9633) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_9632),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9632,tc_HOL_Obool)),U_9633),hAPP(hAPP(c_Set_Oinsert(U_9632),U_9634),c_Orderings_Obot__class_Obot(tc_fun(U_9632,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9632),U_9634),U_9633))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9632),U_9633)) ),
    inference(variable_rename,[status(thm)],[f_2636_1]) ).

fof(f_2636_3,plain,
    ! [U_9632,U_9633,U_9634] :
      ( hAPP(c_Finite__Set_Ocard(U_9632),U_9633) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_9632),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9632,tc_HOL_Obool)),U_9633),hAPP(hAPP(c_Set_Oinsert(U_9632),U_9634),c_Orderings_Obot__class_Obot(tc_fun(U_9632,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9632),U_9634),U_9633))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9632),U_9633)) ),
    inference(definitional_conversion,[status(esa)],[f_2636_2]) ).

cnf(f_2636_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_9632),U_9633) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_9632),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9632,tc_HOL_Obool)),U_9633),hAPP(hAPP(c_Set_Oinsert(U_9632),U_9634),c_Orderings_Obot__class_Obot(tc_fun(U_9632,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9632),U_9634),U_9633))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9632),U_9633)) ),
    inference(clausify,[status(thm)],[f_2636_3]) ).

fof(f_2637_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_2637_2,plain,
    ! [U_9635] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_9635),c_Orderings_Obot__class_Obot(tc_fun(U_9635,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2637_1]) ).

fof(f_2637_3,plain,
    ! [U_9635] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_9635),c_Orderings_Obot__class_Obot(tc_fun(U_9635,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2637_2]) ).

cnf(f_2637_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_9635),c_Orderings_Obot__class_Obot(tc_fun(U_9635,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2637_3]) ).

fof(f_2638_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_2638_2,plain,
    ! [U_9638,U_9637,U_9636] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9636),hAPP(hAPP(c_Set_Oinsert(U_9636),U_9638),U_9637)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9636),U_9637)) ),
    inference(variable_rename,[status(thm)],[f_2638_1]) ).

fof(f_2638_3,plain,
    ! [U_9636,U_9637,U_9638] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9636),hAPP(hAPP(c_Set_Oinsert(U_9636),U_9638),U_9637)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9636),U_9637)) ),
    inference(definitional_conversion,[status(esa)],[f_2638_2]) ).

cnf(f_2638_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9636),hAPP(hAPP(c_Set_Oinsert(U_9636),U_9638),U_9637)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9636),U_9637)) ),
    inference(clausify,[status(thm)],[f_2638_3]) ).

fof(f_2639_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_2639_2,plain,
    ! [U_9642,U_9641,U_9640,U_9639] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9641),hAPP(c_Set_Oimage(U_9639,U_9641,U_9642),U_9640)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9639),U_9640)) ),
    inference(variable_rename,[status(thm)],[f_2639_1]) ).

fof(f_2639_3,plain,
    ! [U_9639,U_9640,U_9641,U_9642] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9641),hAPP(c_Set_Oimage(U_9639,U_9641,U_9642),U_9640)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9639),U_9640)) ),
    inference(definitional_conversion,[status(esa)],[f_2639_2]) ).

cnf(f_2639_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9641),hAPP(c_Set_Oimage(U_9639,U_9641,U_9642),U_9640)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9639),U_9640)) ),
    inference(clausify,[status(thm)],[f_2639_3]) ).

fof(f_2640_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_2640_2,plain,
    ! [U_9645,U_9644,U_9643] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9643),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9643,tc_HOL_Obool)),U_9644),U_9645)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9643),U_9644)) ),
    inference(variable_rename,[status(thm)],[f_2640_1]) ).

fof(f_2640_3,plain,
    ! [U_9643,U_9644,U_9645] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9643),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9643,tc_HOL_Obool)),U_9644),U_9645)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9643),U_9644)) ),
    inference(definitional_conversion,[status(esa)],[f_2640_2]) ).

cnf(f_2640_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9643),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9643,tc_HOL_Obool)),U_9644),U_9645)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9643),U_9644)) ),
    inference(clausify,[status(thm)],[f_2640_3]) ).

fof(f_2641_1,plain,
    ! [V_Qa_2,V_Pa_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_Pa_2)),V_Qa_2))))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2)))
        & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__conjI]) ).

fof(f_2641_2,plain,
    ! [U_9648,U_9647,U_9646] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9646),hAPP(c_Set_OCollect(U_9646),hAPP(hAPP(c_COMBS(U_9646,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9646),c_fconj),U_9647)),U_9648))))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9646),hAPP(c_Set_OCollect(U_9646),U_9648)))
        & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9646),hAPP(c_Set_OCollect(U_9646),U_9647))) ) ),
    inference(variable_rename,[status(thm)],[f_2641_1]) ).

fof(f_2641_3,plain,
    ( ! [U_9646,U_9647,U_9648] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9646),hAPP(c_Set_OCollect(U_9646),U_9648)))
        | ~ sP750(U_9646,U_9647,U_9648) )
    & ! [U_9646,U_9647,U_9648] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9646),hAPP(c_Set_OCollect(U_9646),U_9647)))
        | ~ sP750(U_9646,U_9647,U_9648) )
    & ! [U_9646,U_9647,U_9648] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9646),hAPP(c_Set_OCollect(U_9646),hAPP(hAPP(c_COMBS(U_9646,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9646),c_fconj),U_9647)),U_9648))))
        | sP750(U_9646,U_9647,U_9648) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP750])],[f_2641_2]) ).

cnf(f_2641_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9646),hAPP(c_Set_OCollect(U_9646),hAPP(hAPP(c_COMBS(U_9646,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9646),c_fconj),U_9647)),U_9648))))
    | sP750(U_9646,U_9647,U_9648) ),
    inference(clausify,[status(thm)],[f_2641_3]) ).

cnf(f_2641_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9646),hAPP(c_Set_OCollect(U_9646),U_9647)))
    | ~ sP750(U_9646,U_9647,U_9648) ),
    inference(clausify,[status(thm)],[f_2641_3]) ).

cnf(f_2641_6,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9646),hAPP(c_Set_OCollect(U_9646),U_9648)))
    | ~ sP750(U_9646,U_9647,U_9648) ),
    inference(clausify,[status(thm)],[f_2641_3]) ).

fof(f_2642_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_2642_2,plain,
    ! [U_9650,U_9649] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_9649,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_9649,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_9649,tc_HOL_Obool),tc_fun(U_9649,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_9649,tc_HOL_Obool))),U_9650))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9649),U_9650)) ),
    inference(variable_rename,[status(thm)],[f_2642_1]) ).

fof(f_2642_3,plain,
    ! [U_9650,U_9649] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_9649,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_9649,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_9649,tc_HOL_Obool),tc_fun(U_9649,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_9649,tc_HOL_Obool))),U_9650))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9649),U_9650)) ),
    inference(definitional_conversion,[status(esa)],[f_2642_2]) ).

cnf(f_2642_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_9649,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_fun(U_9649,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_9649,tc_HOL_Obool),tc_fun(U_9649,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_9649,tc_HOL_Obool))),U_9650))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9649),U_9650)) ),
    inference(clausify,[status(thm)],[f_2642_3]) ).

fof(f_2643_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_2643_2,plain,
    ! [U_9651] : 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_9651)))),
    inference(variable_rename,[status(thm)],[f_2643_1]) ).

fof(f_2643_3,plain,
    ! [U_9651] : 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_9651)))),
    inference(definitional_conversion,[status(esa)],[f_2643_2]) ).

cnf(f_2643_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_9651)))),
    inference(clausify,[status(thm)],[f_2643_3]) ).

fof(f_2644_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_2644_2,plain,
    ! [U_9652] : 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_9652)))),
    inference(variable_rename,[status(thm)],[f_2644_1]) ).

fof(f_2644_3,plain,
    ! [U_9652] : 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_9652)))),
    inference(definitional_conversion,[status(esa)],[f_2644_2]) ).

cnf(f_2644_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_9652)))),
    inference(clausify,[status(thm)],[f_2644_3]) ).

fof(f_2645_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_2645_2,plain,
    ! [U_9653] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_9653),c_Orderings_Obot__class_Obot(tc_fun(U_9653,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_2645_1]) ).

fof(f_2645_3,plain,
    ! [U_9653] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_9653),c_Orderings_Obot__class_Obot(tc_fun(U_9653,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_2645_2]) ).

cnf(f_2645_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_9653),c_Orderings_Obot__class_Obot(tc_fun(U_9653,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_2645_3]) ).

fof(f_2646_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_2646_2,plain,
    ! [U_9656,U_9655,U_9654] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9654),hAPP(hAPP(c_Set_Oinsert(U_9654),U_9655),U_9656)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9654),U_9656)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9654),U_9656))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9654),hAPP(hAPP(c_Set_Oinsert(U_9654),U_9655),U_9656))) ) ),
    inference(variable_rename,[status(thm)],[f_2646_1]) ).

fof(f_2646_3,plain,
    ( ! [U_9662,U_9660,U_9658] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9658),hAPP(hAPP(c_Set_Oinsert(U_9658),U_9660),U_9662)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9658),U_9662)) )
    & ! [U_9661,U_9659,U_9657] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9657),U_9661))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9657),hAPP(hAPP(c_Set_Oinsert(U_9657),U_9659),U_9661))) ) ),
    inference(miniscope,[status(thm)],[f_2646_2]) ).

fof(f_2646_4,plain,
    ( ! [U_9658,U_9660,U_9662] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9658),hAPP(hAPP(c_Set_Oinsert(U_9658),U_9660),U_9662)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9658),U_9662)) )
    & ! [U_9659,U_9661,U_9657] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9657),U_9661))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9657),hAPP(hAPP(c_Set_Oinsert(U_9657),U_9659),U_9661))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2646_3]) ).

cnf(f_2646_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9657),U_9661))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9657),hAPP(hAPP(c_Set_Oinsert(U_9657),U_9659),U_9661))) ),
    inference(clausify,[status(thm)],[f_2646_4]) ).

cnf(f_2646_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9658),hAPP(hAPP(c_Set_Oinsert(U_9658),U_9660),U_9662)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9658),U_9662)) ),
    inference(clausify,[status(thm)],[f_2646_4]) ).

fof(f_2647_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_2647_2,plain,
    ! [U_9667] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9667))
        | ! [U_9666] :
          ? [U_9665] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9665),U_9666))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9665),U_9667)) ) )
      & ( ? [U_9664] :
          ! [U_9663] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9663),U_9664))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9663),U_9667)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9667)) ) ),
    inference(variable_rename,[status(thm)],[f_2647_1]) ).

fof(f_2647_3,plain,
    ( ! [U_9669] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9669))
        | ! [U_9666] :
          ? [U_9665] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9665),U_9666))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9665),U_9669)) ) )
    & ! [U_9668] :
        ( ? [U_9664] :
          ! [U_9663] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9663),U_9664))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9663),U_9668)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9668)) ) ),
    inference(miniscope,[status(thm)],[f_2647_2]) ).

fof(f_2647_4,plain,
    ( ! [U_9669] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9669))
        | ! [U_9666] :
          ? [U_9665] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9665),U_9666))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9665),U_9669)) ) )
    & ! [U_9668] :
        ( ! [U_9663] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9663),sK152(U_9668)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9663),U_9668)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9668)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK152]),skolemize(U_9664,sK152(U_9668))],[f_2647_3]) ).

fof(f_2647_5,plain,
    ( ! [U_9669] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9669))
        | ! [U_9666] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK153(U_9669,U_9666)),U_9666))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK153(U_9669,U_9666)),U_9669)) ) )
    & ! [U_9668] :
        ( ! [U_9663] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9663),sK152(U_9668)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9663),U_9668)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9668)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK153]),skolemize(U_9665,sK153(U_9669,U_9666))],[f_2647_4]) ).

fof(f_2647_6,plain,
    ( ! [U_9666,U_9669] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK153(U_9669,U_9666)),U_9666))
        | ~ sP751(U_9666,U_9669) )
    & ! [U_9666,U_9669] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK153(U_9669,U_9666)),U_9669))
        | ~ sP751(U_9666,U_9669) )
    & ! [U_9666,U_9669] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9669))
        | sP751(U_9666,U_9669) )
    & ! [U_9663,U_9668] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9663),sK152(U_9668)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9663),U_9668))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9668)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP751])],[f_2647_5]) ).

cnf(f_2647_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_9663),sK152(U_9668)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9663),U_9668))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9668)) ),
    inference(clausify,[status(thm)],[f_2647_6]) ).

cnf(f_2647_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9669))
    | sP751(U_9666,U_9669) ),
    inference(clausify,[status(thm)],[f_2647_6]) ).

cnf(f_2647_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK153(U_9669,U_9666)),U_9669))
    | ~ sP751(U_9666,U_9669) ),
    inference(clausify,[status(thm)],[f_2647_6]) ).

cnf(f_2647_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK153(U_9669,U_9666)),U_9666))
    | ~ sP751(U_9666,U_9669) ),
    inference(clausify,[status(thm)],[f_2647_6]) ).

fof(f_2648_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_2648_2,plain,
    ! [U_9672,U_9671,U_9670] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9670),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9670,tc_HOL_Obool)),U_9671),U_9672)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9670),U_9672))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9670),U_9671)) ),
    inference(variable_rename,[status(thm)],[f_2648_1]) ).

fof(f_2648_3,plain,
    ! [U_9671,U_9670,U_9672] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9670),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9670,tc_HOL_Obool)),U_9671),U_9672)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9670),U_9672))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9670),U_9671)) ),
    inference(definitional_conversion,[status(esa)],[f_2648_2]) ).

cnf(f_2648_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9670),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9670,tc_HOL_Obool)),U_9671),U_9672)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9670),U_9672))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9670),U_9671)) ),
    inference(clausify,[status(thm)],[f_2648_3]) ).

fof(f_2649_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_2649_2,plain,
    ! [U_9675,U_9674,U_9673] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9673),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9673,tc_HOL_Obool)),U_9674),U_9675)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9673),U_9675))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9673),U_9674)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9673),U_9675))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_9673),U_9674)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9673),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9673,tc_HOL_Obool)),U_9674),U_9675))) ) ),
    inference(variable_rename,[status(thm)],[f_2649_1]) ).

fof(f_2649_3,plain,
    ( ! [U_9681,U_9679,U_9677] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9677),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9677,tc_HOL_Obool)),U_9679),U_9681)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9677),U_9681))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9677),U_9679)) )
    & ! [U_9680,U_9678,U_9676] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9676),U_9680))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_9676),U_9678)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9676),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9676,tc_HOL_Obool)),U_9678),U_9680))) ) ),
    inference(miniscope,[status(thm)],[f_2649_2]) ).

fof(f_2649_4,plain,
    ( ! [U_9678,U_9676,U_9680] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9676),U_9680))
        | ~ sP752(U_9678,U_9676,U_9680) )
    & ! [U_9678,U_9676,U_9680] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9676),U_9678))
        | ~ sP752(U_9678,U_9676,U_9680) )
    & ! [U_9681,U_9679,U_9677] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9677),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9677,tc_HOL_Obool)),U_9679),U_9681)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9677),U_9681))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9677),U_9679)) )
    & ! [U_9678,U_9676,U_9680] :
        ( sP752(U_9678,U_9676,U_9680)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9676),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9676,tc_HOL_Obool)),U_9678),U_9680))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP752])],[f_2649_3]) ).

cnf(f_2649_5,plain,
    ( sP752(U_9678,U_9676,U_9680)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9676),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9676,tc_HOL_Obool)),U_9678),U_9680))) ),
    inference(clausify,[status(thm)],[f_2649_4]) ).

cnf(f_2649_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9677),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9677,tc_HOL_Obool)),U_9679),U_9681)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9677),U_9681))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9677),U_9679)) ),
    inference(clausify,[status(thm)],[f_2649_4]) ).

cnf(f_2649_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9676),U_9678))
    | ~ sP752(U_9678,U_9676,U_9680) ),
    inference(clausify,[status(thm)],[f_2649_4]) ).

cnf(f_2649_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9676),U_9680))
    | ~ sP752(U_9678,U_9676,U_9680) ),
    inference(clausify,[status(thm)],[f_2649_4]) ).

fof(f_2650_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_2650_2,plain,
    ! [U_9684,U_9683,U_9682] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9682),U_9683))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9682),U_9684))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9682,tc_HOL_Obool)),U_9683),U_9684)) ),
    inference(variable_rename,[status(thm)],[f_2650_1]) ).

fof(f_2650_3,plain,
    ! [U_9682,U_9683,U_9684] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9682),U_9683))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9682),U_9684))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9682,tc_HOL_Obool)),U_9683),U_9684)) ),
    inference(definitional_conversion,[status(esa)],[f_2650_2]) ).

cnf(f_2650_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9682),U_9683))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9682),U_9684))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9682,tc_HOL_Obool)),U_9683),U_9684)) ),
    inference(clausify,[status(thm)],[f_2650_3]) ).

fof(f_2651_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_2651_2,plain,
    ! [U_9687,U_9686,U_9685] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9685),U_9687))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9685,tc_HOL_Obool)),U_9687),U_9686))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9685),U_9686)) ),
    inference(variable_rename,[status(thm)],[f_2651_1]) ).

fof(f_2651_3,plain,
    ! [U_9685,U_9686,U_9687] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9685),U_9687))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9685,tc_HOL_Obool)),U_9687),U_9686))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9685),U_9686)) ),
    inference(definitional_conversion,[status(esa)],[f_2651_2]) ).

cnf(f_2651_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9685),U_9687))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9685,tc_HOL_Obool)),U_9687),U_9686))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9685),U_9686)) ),
    inference(clausify,[status(thm)],[f_2651_3]) ).

fof(f_2652_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_2652_2,plain,
    ! [U_9690,U_9689,U_9688] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9688),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9688,tc_HOL_Obool)),U_9690),U_9689)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9688),U_9690)) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9688),U_9690))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9688),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9688,tc_HOL_Obool)),U_9690),U_9689))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9688),U_9689)) ),
    inference(variable_rename,[status(thm)],[f_2652_1]) ).

fof(f_2652_3,plain,
    ( ! [U_9688,U_9689,U_9690] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9688),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9688,tc_HOL_Obool)),U_9690),U_9689)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9688),U_9690))
        | ~ sP753(U_9688,U_9689,U_9690) )
    & ! [U_9688,U_9689,U_9690] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9688),U_9690))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9688),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9688,tc_HOL_Obool)),U_9690),U_9689)))
        | ~ sP753(U_9688,U_9689,U_9690) )
    & ! [U_9688,U_9689,U_9690] :
        ( sP753(U_9688,U_9689,U_9690)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9688),U_9689)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP753])],[f_2652_2]) ).

cnf(f_2652_4,plain,
    ( sP753(U_9688,U_9689,U_9690)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9688),U_9689)) ),
    inference(clausify,[status(thm)],[f_2652_3]) ).

cnf(f_2652_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9688),U_9690))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9688),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9688,tc_HOL_Obool)),U_9690),U_9689)))
    | ~ sP753(U_9688,U_9689,U_9690) ),
    inference(clausify,[status(thm)],[f_2652_3]) ).

cnf(f_2652_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9688),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9688,tc_HOL_Obool)),U_9690),U_9689)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9688),U_9690))
    | ~ sP753(U_9688,U_9689,U_9690) ),
    inference(clausify,[status(thm)],[f_2652_3]) ).

fof(f_2653_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_2653_2,plain,
    ! [U_9692,U_9691] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9691),U_9692))
      | ~ class_Finite__Set_Ofinite(U_9691) ),
    inference(variable_rename,[status(thm)],[f_2653_1]) ).

fof(f_2653_3,plain,
    ! [U_9692,U_9691] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9691),U_9692))
      | ~ class_Finite__Set_Ofinite(U_9691) ),
    inference(definitional_conversion,[status(esa)],[f_2653_2]) ).

cnf(f_2653_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9691),U_9692))
    | ~ class_Finite__Set_Ofinite(U_9691) ),
    inference(clausify,[status(thm)],[f_2653_3]) ).

fof(f_2654_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_2654_2,plain,
    ! [U_9694,U_9693] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9693),U_9694))
      | ~ class_Finite__Set_Ofinite(U_9693) ),
    inference(variable_rename,[status(thm)],[f_2654_1]) ).

fof(f_2654_3,plain,
    ! [U_9694,U_9693] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9693),U_9694))
      | ~ class_Finite__Set_Ofinite(U_9693) ),
    inference(definitional_conversion,[status(esa)],[f_2654_2]) ).

cnf(f_2654_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9693),U_9694))
    | ~ class_Finite__Set_Ofinite(U_9693) ),
    inference(clausify,[status(thm)],[f_2654_3]) ).

fof(f_2655_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_2655_2,plain,
    ! [U_9695] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9695))
        | ~ 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_9695))) )
      & ( 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_9695)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9695)) ) ),
    inference(variable_rename,[status(thm)],[f_2655_1]) ).

fof(f_2655_3,plain,
    ( ! [U_9697] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9697))
        | ~ 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_9697))) )
    & ! [U_9696] :
        ( 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_9696)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9696)) ) ),
    inference(miniscope,[status(thm)],[f_2655_2]) ).

fof(f_2655_4,plain,
    ( ! [U_9697] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9697))
        | ~ 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_9697))) )
    & ! [U_9696] :
        ( 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_9696)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9696)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2655_3]) ).

cnf(f_2655_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_9696)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9696)) ),
    inference(clausify,[status(thm)],[f_2655_4]) ).

cnf(f_2655_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9697))
    | ~ 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_9697))) ),
    inference(clausify,[status(thm)],[f_2655_4]) ).

fof(f_2656_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_2656_2,plain,
    ! [U_9702] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9702))
        | ! [U_9701] :
          ? [U_9700] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9700),U_9701))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9700),U_9702)) ) )
      & ( ? [U_9699] :
          ! [U_9698] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9698),U_9699))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9698),U_9702)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9702)) ) ),
    inference(variable_rename,[status(thm)],[f_2656_1]) ).

fof(f_2656_3,plain,
    ( ! [U_9704] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9704))
        | ! [U_9701] :
          ? [U_9700] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9700),U_9701))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9700),U_9704)) ) )
    & ! [U_9703] :
        ( ? [U_9699] :
          ! [U_9698] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9698),U_9699))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9698),U_9703)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9703)) ) ),
    inference(miniscope,[status(thm)],[f_2656_2]) ).

fof(f_2656_4,plain,
    ( ! [U_9704] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9704))
        | ! [U_9701] :
          ? [U_9700] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9700),U_9701))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9700),U_9704)) ) )
    & ! [U_9703] :
        ( ! [U_9698] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9698),sK154(U_9703)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9698),U_9703)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9703)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK154]),skolemize(U_9699,sK154(U_9703))],[f_2656_3]) ).

fof(f_2656_5,plain,
    ( ! [U_9704] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9704))
        | ! [U_9701] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK155(U_9704,U_9701)),U_9701))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK155(U_9704,U_9701)),U_9704)) ) )
    & ! [U_9703] :
        ( ! [U_9698] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9698),sK154(U_9703)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9698),U_9703)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9703)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK155]),skolemize(U_9700,sK155(U_9704,U_9701))],[f_2656_4]) ).

fof(f_2656_6,plain,
    ( ! [U_9701,U_9704] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK155(U_9704,U_9701)),U_9701))
        | ~ sP754(U_9701,U_9704) )
    & ! [U_9701,U_9704] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK155(U_9704,U_9701)),U_9704))
        | ~ sP754(U_9701,U_9704) )
    & ! [U_9701,U_9704] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9704))
        | sP754(U_9701,U_9704) )
    & ! [U_9698,U_9703] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9698),sK154(U_9703)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9698),U_9703))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9703)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP754])],[f_2656_5]) ).

cnf(f_2656_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_9698),sK154(U_9703)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_9698),U_9703))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9703)) ),
    inference(clausify,[status(thm)],[f_2656_6]) ).

cnf(f_2656_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),U_9704))
    | sP754(U_9701,U_9704) ),
    inference(clausify,[status(thm)],[f_2656_6]) ).

cnf(f_2656_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK155(U_9704,U_9701)),U_9704))
    | ~ sP754(U_9701,U_9704) ),
    inference(clausify,[status(thm)],[f_2656_6]) ).

cnf(f_2656_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK155(U_9704,U_9701)),U_9701))
    | ~ sP754(U_9701,U_9704) ),
    inference(clausify,[status(thm)],[f_2656_6]) ).

fof(f_2657_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_2657_2,plain,
    ! [U_9707,U_9706,U_9705] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9706),hAPP(c_Relation_ORange(U_9705,U_9706),U_9707)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9705,U_9706)),U_9707)) ),
    inference(variable_rename,[status(thm)],[f_2657_1]) ).

fof(f_2657_3,plain,
    ! [U_9706,U_9705,U_9707] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9706),hAPP(c_Relation_ORange(U_9705,U_9706),U_9707)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9705,U_9706)),U_9707)) ),
    inference(definitional_conversion,[status(esa)],[f_2657_2]) ).

cnf(f_2657_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9706),hAPP(c_Relation_ORange(U_9705,U_9706),U_9707)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9705,U_9706)),U_9707)) ),
    inference(clausify,[status(thm)],[f_2657_3]) ).

fof(f_2658_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_2658_2,plain,
    ! [U_9710,U_9709,U_9708] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9708,U_9709)),hAPP(c_Relation_Oconverse(U_9709,U_9708),U_9710)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9709,U_9708)),U_9710)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9709,U_9708)),U_9710))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9708,U_9709)),hAPP(c_Relation_Oconverse(U_9709,U_9708),U_9710))) ) ),
    inference(variable_rename,[status(thm)],[f_2658_1]) ).

fof(f_2658_3,plain,
    ( ! [U_9716,U_9714,U_9712] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9712,U_9714)),hAPP(c_Relation_Oconverse(U_9714,U_9712),U_9716)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9714,U_9712)),U_9716)) )
    & ! [U_9715,U_9713,U_9711] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9713,U_9711)),U_9715))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9711,U_9713)),hAPP(c_Relation_Oconverse(U_9713,U_9711),U_9715))) ) ),
    inference(miniscope,[status(thm)],[f_2658_2]) ).

fof(f_2658_4,plain,
    ( ! [U_9712,U_9714,U_9716] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9712,U_9714)),hAPP(c_Relation_Oconverse(U_9714,U_9712),U_9716)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9714,U_9712)),U_9716)) )
    & ! [U_9713,U_9711,U_9715] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9713,U_9711)),U_9715))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9711,U_9713)),hAPP(c_Relation_Oconverse(U_9713,U_9711),U_9715))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2658_3]) ).

cnf(f_2658_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9713,U_9711)),U_9715))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9711,U_9713)),hAPP(c_Relation_Oconverse(U_9713,U_9711),U_9715))) ),
    inference(clausify,[status(thm)],[f_2658_4]) ).

cnf(f_2658_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9712,U_9714)),hAPP(c_Relation_Oconverse(U_9714,U_9712),U_9716)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9714,U_9712)),U_9716)) ),
    inference(clausify,[status(thm)],[f_2658_4]) ).

fof(f_2659_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_2659_2,plain,
    ! [U_9719,U_9718,U_9717] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9717),hAPP(c_Relation_ODomain(U_9717,U_9718),U_9719)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9717,U_9718)),U_9719)) ),
    inference(variable_rename,[status(thm)],[f_2659_1]) ).

fof(f_2659_3,plain,
    ! [U_9717,U_9718,U_9719] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9717),hAPP(c_Relation_ODomain(U_9717,U_9718),U_9719)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9717,U_9718)),U_9719)) ),
    inference(definitional_conversion,[status(esa)],[f_2659_2]) ).

cnf(f_2659_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9717),hAPP(c_Relation_ODomain(U_9717,U_9718),U_9719)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9717,U_9718)),U_9719)) ),
    inference(clausify,[status(thm)],[f_2659_3]) ).

fof(f_2660_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_2660_2,plain,
    ! [U_9721,U_9720] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9720),hAPP(c_Relation_OField(U_9720),U_9721)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9720,U_9720)),U_9721)) ),
    inference(variable_rename,[status(thm)],[f_2660_1]) ).

fof(f_2660_3,plain,
    ! [U_9720,U_9721] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9720),hAPP(c_Relation_OField(U_9720),U_9721)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9720,U_9720)),U_9721)) ),
    inference(definitional_conversion,[status(esa)],[f_2660_2]) ).

cnf(f_2660_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9720),hAPP(c_Relation_OField(U_9720),U_9721)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9720,U_9720)),U_9721)) ),
    inference(clausify,[status(thm)],[f_2660_3]) ).

fof(f_2661_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_2661_2,plain,
    ! [U_9723,U_9722] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9722,U_9722)),c_Transitive__Closure_Otrancl(U_9722,U_9723)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9722,U_9722)),U_9723)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9722,U_9722)),U_9723))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9722,U_9722)),c_Transitive__Closure_Otrancl(U_9722,U_9723))) ) ),
    inference(variable_rename,[status(thm)],[f_2661_1]) ).

fof(f_2661_3,plain,
    ( ! [U_9727,U_9725] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9725,U_9725)),c_Transitive__Closure_Otrancl(U_9725,U_9727)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9725,U_9725)),U_9727)) )
    & ! [U_9726,U_9724] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9724,U_9724)),U_9726))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9724,U_9724)),c_Transitive__Closure_Otrancl(U_9724,U_9726))) ) ),
    inference(miniscope,[status(thm)],[f_2661_2]) ).

fof(f_2661_4,plain,
    ( ! [U_9725,U_9727] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9725,U_9725)),c_Transitive__Closure_Otrancl(U_9725,U_9727)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9725,U_9725)),U_9727)) )
    & ! [U_9726,U_9724] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9724,U_9724)),U_9726))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9724,U_9724)),c_Transitive__Closure_Otrancl(U_9724,U_9726))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2661_3]) ).

cnf(f_2661_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9724,U_9724)),U_9726))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9724,U_9724)),c_Transitive__Closure_Otrancl(U_9724,U_9726))) ),
    inference(clausify,[status(thm)],[f_2661_4]) ).

cnf(f_2661_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9725,U_9725)),c_Transitive__Closure_Otrancl(U_9725,U_9727)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9725,U_9725)),U_9727)) ),
    inference(clausify,[status(thm)],[f_2661_4]) ).

fof(f_2662_1,plain,
    ! [V_Qa_2,V_Pa_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_Pa_2)),V_Qa_2))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Qa_2)))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_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_Pa_2)),V_Qa_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__disjI]) ).

fof(f_2662_2,plain,
    ! [U_9730,U_9729,U_9728] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9728),hAPP(c_Set_OCollect(U_9728),hAPP(hAPP(c_COMBS(U_9728,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9728),c_fdisj),U_9729)),U_9730))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9728),hAPP(c_Set_OCollect(U_9728),U_9730)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9728),hAPP(c_Set_OCollect(U_9728),U_9729))) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9728),hAPP(c_Set_OCollect(U_9728),U_9730)))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_9728),hAPP(c_Set_OCollect(U_9728),U_9729))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9728),hAPP(c_Set_OCollect(U_9728),hAPP(hAPP(c_COMBS(U_9728,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9728),c_fdisj),U_9729)),U_9730)))) ) ),
    inference(variable_rename,[status(thm)],[f_2662_1]) ).

fof(f_2662_3,plain,
    ( ! [U_9736,U_9734,U_9732] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9732),hAPP(c_Set_OCollect(U_9732),hAPP(hAPP(c_COMBS(U_9732,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9732),c_fdisj),U_9734)),U_9736))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9732),hAPP(c_Set_OCollect(U_9732),U_9736)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9732),hAPP(c_Set_OCollect(U_9732),U_9734))) )
    & ! [U_9735,U_9733,U_9731] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9731),hAPP(c_Set_OCollect(U_9731),U_9735)))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_9731),hAPP(c_Set_OCollect(U_9731),U_9733))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9731),hAPP(c_Set_OCollect(U_9731),hAPP(hAPP(c_COMBS(U_9731,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9731),c_fdisj),U_9733)),U_9735)))) ) ),
    inference(miniscope,[status(thm)],[f_2662_2]) ).

fof(f_2662_4,plain,
    ( ! [U_9733,U_9735,U_9731] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9731),hAPP(c_Set_OCollect(U_9731),U_9735)))
        | ~ sP755(U_9733,U_9735,U_9731) )
    & ! [U_9733,U_9735,U_9731] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9731),hAPP(c_Set_OCollect(U_9731),U_9733)))
        | ~ sP755(U_9733,U_9735,U_9731) )
    & ! [U_9736,U_9732,U_9734] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9732),hAPP(c_Set_OCollect(U_9732),hAPP(hAPP(c_COMBS(U_9732,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9732),c_fdisj),U_9734)),U_9736))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9732),hAPP(c_Set_OCollect(U_9732),U_9736)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9732),hAPP(c_Set_OCollect(U_9732),U_9734))) )
    & ! [U_9733,U_9735,U_9731] :
        ( sP755(U_9733,U_9735,U_9731)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9731),hAPP(c_Set_OCollect(U_9731),hAPP(hAPP(c_COMBS(U_9731,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9731),c_fdisj),U_9733)),U_9735)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP755])],[f_2662_3]) ).

cnf(f_2662_5,plain,
    ( sP755(U_9733,U_9735,U_9731)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9731),hAPP(c_Set_OCollect(U_9731),hAPP(hAPP(c_COMBS(U_9731,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9731),c_fdisj),U_9733)),U_9735)))) ),
    inference(clausify,[status(thm)],[f_2662_4]) ).

cnf(f_2662_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9732),hAPP(c_Set_OCollect(U_9732),hAPP(hAPP(c_COMBS(U_9732,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9732),c_fdisj),U_9734)),U_9736))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9732),hAPP(c_Set_OCollect(U_9732),U_9736)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9732),hAPP(c_Set_OCollect(U_9732),U_9734))) ),
    inference(clausify,[status(thm)],[f_2662_4]) ).

cnf(f_2662_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9731),hAPP(c_Set_OCollect(U_9731),U_9733)))
    | ~ sP755(U_9733,U_9735,U_9731) ),
    inference(clausify,[status(thm)],[f_2662_4]) ).

cnf(f_2662_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9731),hAPP(c_Set_OCollect(U_9731),U_9735)))
    | ~ sP755(U_9733,U_9735,U_9731) ),
    inference(clausify,[status(thm)],[f_2662_4]) ).

fof(f_2663_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_2663_2,plain,
    ! [U_9737] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_9737))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9737))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9737)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_9737)) ) )
      | ~ c_Nat__Transfer_Onat__set(U_9737) ),
    inference(variable_rename,[status(thm)],[f_2663_1]) ).

fof(f_2663_3,plain,
    ( ! [U_9737] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_9737))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9737)))
        | ~ sP756(U_9737) )
    & ! [U_9737] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9737)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_9737))
        | ~ sP756(U_9737) )
    & ! [U_9737] :
        ( sP756(U_9737)
        | ~ c_Nat__Transfer_Onat__set(U_9737) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP756])],[f_2663_2]) ).

cnf(f_2663_4,plain,
    ( sP756(U_9737)
    | ~ c_Nat__Transfer_Onat__set(U_9737) ),
    inference(clausify,[status(thm)],[f_2663_3]) ).

cnf(f_2663_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_9737)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_9737))
    | ~ sP756(U_9737) ),
    inference(clausify,[status(thm)],[f_2663_3]) ).

cnf(f_2663_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),U_9737))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_9737)))
    | ~ sP756(U_9737) ),
    inference(clausify,[status(thm)],[f_2663_3]) ).

fof(f_2664_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_2664_2,plain,
    ! [U_9742,U_9741,U_9740,U_9739,U_9738] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9740),U_9741))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9740,tc_HOL_Obool)),U_9741),hAPP(c_Set_Oimage(U_9738,U_9740,U_9742),U_9739)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9738),U_9739)) ),
    inference(variable_rename,[status(thm)],[f_2664_1]) ).

fof(f_2664_3,plain,
    ! [U_9738,U_9739,U_9740,U_9741,U_9742] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9740),U_9741))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9740,tc_HOL_Obool)),U_9741),hAPP(c_Set_Oimage(U_9738,U_9740,U_9742),U_9739)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9738),U_9739)) ),
    inference(definitional_conversion,[status(esa)],[f_2664_2]) ).

cnf(f_2664_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9740),U_9741))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9740,tc_HOL_Obool)),U_9741),hAPP(c_Set_Oimage(U_9738,U_9740,U_9742),U_9739)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9738),U_9739)) ),
    inference(clausify,[status(thm)],[f_2664_3]) ).

fof(f_2665_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_2665_2,plain,
    ! [U_9746,U_9745,U_9744,U_9743] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9743),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9743,tc_HOL_Obool)),U_9744),hAPP(hAPP(c_Set_Oinsert(U_9743),U_9745),U_9746))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9743),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9743,tc_HOL_Obool)),U_9744),U_9746))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9743),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9743,tc_HOL_Obool)),U_9744),U_9746)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9743),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9743,tc_HOL_Obool)),U_9744),hAPP(hAPP(c_Set_Oinsert(U_9743),U_9745),U_9746)))) ) ),
    inference(variable_rename,[status(thm)],[f_2665_1]) ).

fof(f_2665_3,plain,
    ( ! [U_9754,U_9752,U_9750,U_9748] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9748),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9748,tc_HOL_Obool)),U_9750),hAPP(hAPP(c_Set_Oinsert(U_9748),U_9752),U_9754))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9748),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9748,tc_HOL_Obool)),U_9750),U_9754))) )
    & ! [U_9753,U_9751,U_9749,U_9747] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9747),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9747,tc_HOL_Obool)),U_9749),U_9753)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9747),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9747,tc_HOL_Obool)),U_9749),hAPP(hAPP(c_Set_Oinsert(U_9747),U_9751),U_9753)))) ) ),
    inference(miniscope,[status(thm)],[f_2665_2]) ).

fof(f_2665_4,plain,
    ( ! [U_9748,U_9750,U_9752,U_9754] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9748),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9748,tc_HOL_Obool)),U_9750),hAPP(hAPP(c_Set_Oinsert(U_9748),U_9752),U_9754))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9748),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9748,tc_HOL_Obool)),U_9750),U_9754))) )
    & ! [U_9749,U_9753,U_9747,U_9751] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9747),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9747,tc_HOL_Obool)),U_9749),U_9753)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9747),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9747,tc_HOL_Obool)),U_9749),hAPP(hAPP(c_Set_Oinsert(U_9747),U_9751),U_9753)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2665_3]) ).

cnf(f_2665_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9747),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9747,tc_HOL_Obool)),U_9749),U_9753)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9747),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9747,tc_HOL_Obool)),U_9749),hAPP(hAPP(c_Set_Oinsert(U_9747),U_9751),U_9753)))) ),
    inference(clausify,[status(thm)],[f_2665_4]) ).

cnf(f_2665_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9748),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9748,tc_HOL_Obool)),U_9750),hAPP(hAPP(c_Set_Oinsert(U_9748),U_9752),U_9754))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9748),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9748,tc_HOL_Obool)),U_9750),U_9754))) ),
    inference(clausify,[status(thm)],[f_2665_4]) ).

fof(f_2666_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_2666_2,plain,
    ! [U_9756,U_9755] :
      ( hAPP(c_Finite__Set_Ocard(U_9755),U_9756) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_9755),U_9756)) ),
    inference(variable_rename,[status(thm)],[f_2666_1]) ).

fof(f_2666_3,plain,
    ! [U_9755,U_9756] :
      ( hAPP(c_Finite__Set_Ocard(U_9755),U_9756) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_9755),U_9756)) ),
    inference(definitional_conversion,[status(esa)],[f_2666_2]) ).

cnf(f_2666_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_9755),U_9756) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_9755),U_9756)) ),
    inference(clausify,[status(thm)],[f_2666_3]) ).

fof(f_2667_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_2667_2,plain,
    ! [U_9758,U_9757] :
      ( c_Wellfounded_Owf(U_9757,U_9758)
      | ~ c_Wellfounded_Oacyclic(U_9757,U_9758)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9757,U_9757)),U_9758)) ),
    inference(variable_rename,[status(thm)],[f_2667_1]) ).

fof(f_2667_3,plain,
    ! [U_9757,U_9758] :
      ( c_Wellfounded_Owf(U_9757,U_9758)
      | ~ c_Wellfounded_Oacyclic(U_9757,U_9758)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9757,U_9757)),U_9758)) ),
    inference(definitional_conversion,[status(esa)],[f_2667_2]) ).

cnf(f_2667_4,plain,
    ( c_Wellfounded_Owf(U_9757,U_9758)
    | ~ c_Wellfounded_Oacyclic(U_9757,U_9758)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9757,U_9757)),U_9758)) ),
    inference(clausify,[status(thm)],[f_2667_3]) ).

fof(f_2668_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_2668_2,plain,
    ! [U_9760,U_9759] :
      ( ( ( c_Wellfounded_Owf(U_9759,U_9760)
          | ~ c_Wellfounded_Oacyclic(U_9759,U_9760) )
        & ( c_Wellfounded_Oacyclic(U_9759,U_9760)
          | ~ c_Wellfounded_Owf(U_9759,U_9760) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9759,U_9759)),U_9760)) ),
    inference(variable_rename,[status(thm)],[f_2668_1]) ).

fof(f_2668_3,plain,
    ( ! [U_9760,U_9759] :
        ( c_Wellfounded_Owf(U_9759,U_9760)
        | ~ c_Wellfounded_Oacyclic(U_9759,U_9760)
        | ~ sP757(U_9760,U_9759) )
    & ! [U_9760,U_9759] :
        ( c_Wellfounded_Oacyclic(U_9759,U_9760)
        | ~ c_Wellfounded_Owf(U_9759,U_9760)
        | ~ sP757(U_9760,U_9759) )
    & ! [U_9760,U_9759] :
        ( sP757(U_9760,U_9759)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9759,U_9759)),U_9760)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP757])],[f_2668_2]) ).

cnf(f_2668_4,plain,
    ( sP757(U_9760,U_9759)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9759,U_9759)),U_9760)) ),
    inference(clausify,[status(thm)],[f_2668_3]) ).

cnf(f_2668_5,plain,
    ( c_Wellfounded_Oacyclic(U_9759,U_9760)
    | ~ c_Wellfounded_Owf(U_9759,U_9760)
    | ~ sP757(U_9760,U_9759) ),
    inference(clausify,[status(thm)],[f_2668_3]) ).

cnf(f_2668_6,plain,
    ( c_Wellfounded_Owf(U_9759,U_9760)
    | ~ c_Wellfounded_Oacyclic(U_9759,U_9760)
    | ~ sP757(U_9760,U_9759) ),
    inference(clausify,[status(thm)],[f_2668_3]) ).

fof(f_2669_1,plain,
    ! [V_Qa_2,T_c,V_Pa_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_Pa_2))),V_Qa_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_Qa_2),B_y))))
              & hBOOL(hAPP(V_Pa_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_Qa_2),B_y))))
              | ~ hBOOL(hAPP(V_Pa_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_Pa_2))),V_Qa_2))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__bounded__ex]) ).

fof(f_2669_2,plain,
    ! [U_9766,U_9765,U_9764,U_9763] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9765),hAPP(c_Set_OCollect(U_9765),hAPP(hAPP(c_COMBB(tc_fun(U_9763,tc_HOL_Obool),tc_HOL_Obool,U_9765),c_HOL_OEx(U_9763)),hAPP(hAPP(c_COMBB(tc_fun(U_9763,tc_HOL_Obool),tc_fun(U_9763,tc_HOL_Obool),U_9765),hAPP(c_COMBS(U_9763,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9763),c_fconj),U_9764))),U_9766)))))
          | ? [U_9762] :
              ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9765),hAPP(c_Set_OCollect(U_9765),hAPP(hAPP(c_COMBC(U_9765,U_9763,tc_HOL_Obool),U_9766),U_9762))))
              & hBOOL(hAPP(U_9764,U_9762)) ) )
        & ( ! [U_9761] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9765),hAPP(c_Set_OCollect(U_9765),hAPP(hAPP(c_COMBC(U_9765,U_9763,tc_HOL_Obool),U_9766),U_9761))))
              | ~ hBOOL(hAPP(U_9764,U_9761)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9765),hAPP(c_Set_OCollect(U_9765),hAPP(hAPP(c_COMBB(tc_fun(U_9763,tc_HOL_Obool),tc_HOL_Obool,U_9765),c_HOL_OEx(U_9763)),hAPP(hAPP(c_COMBB(tc_fun(U_9763,tc_HOL_Obool),tc_fun(U_9763,tc_HOL_Obool),U_9765),hAPP(c_COMBS(U_9763,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9763),c_fconj),U_9764))),U_9766))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9763),hAPP(c_Set_OCollect(U_9763),U_9764))) ),
    inference(variable_rename,[status(thm)],[f_2669_1]) ).

fof(f_2669_3,plain,
    ! [U_9766,U_9765,U_9764,U_9763] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9765),hAPP(c_Set_OCollect(U_9765),hAPP(hAPP(c_COMBB(tc_fun(U_9763,tc_HOL_Obool),tc_HOL_Obool,U_9765),c_HOL_OEx(U_9763)),hAPP(hAPP(c_COMBB(tc_fun(U_9763,tc_HOL_Obool),tc_fun(U_9763,tc_HOL_Obool),U_9765),hAPP(c_COMBS(U_9763,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9763),c_fconj),U_9764))),U_9766)))))
          | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9765),hAPP(c_Set_OCollect(U_9765),hAPP(hAPP(c_COMBC(U_9765,U_9763,tc_HOL_Obool),U_9766),sK156(U_9766,U_9765,U_9764,U_9763)))))
            & hBOOL(hAPP(U_9764,sK156(U_9766,U_9765,U_9764,U_9763))) ) )
        & ( ! [U_9761] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9765),hAPP(c_Set_OCollect(U_9765),hAPP(hAPP(c_COMBC(U_9765,U_9763,tc_HOL_Obool),U_9766),U_9761))))
              | ~ hBOOL(hAPP(U_9764,U_9761)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9765),hAPP(c_Set_OCollect(U_9765),hAPP(hAPP(c_COMBB(tc_fun(U_9763,tc_HOL_Obool),tc_HOL_Obool,U_9765),c_HOL_OEx(U_9763)),hAPP(hAPP(c_COMBB(tc_fun(U_9763,tc_HOL_Obool),tc_fun(U_9763,tc_HOL_Obool),U_9765),hAPP(c_COMBS(U_9763,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9763),c_fconj),U_9764))),U_9766))))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9763),hAPP(c_Set_OCollect(U_9763),U_9764))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK156]),skolemize(U_9762,sK156(U_9766,U_9765,U_9764,U_9763))],[f_2669_2]) ).

fof(f_2669_4,plain,
    ( ! [U_9763,U_9764,U_9765,U_9766] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9765),hAPP(c_Set_OCollect(U_9765),hAPP(hAPP(c_COMBC(U_9765,U_9763,tc_HOL_Obool),U_9766),sK156(U_9766,U_9765,U_9764,U_9763)))))
        | ~ sP758(U_9763,U_9764,U_9765,U_9766) )
    & ! [U_9763,U_9764,U_9765,U_9766] :
        ( hBOOL(hAPP(U_9764,sK156(U_9766,U_9765,U_9764,U_9763)))
        | ~ sP758(U_9763,U_9764,U_9765,U_9766) )
    & ! [U_9763,U_9761,U_9764,U_9765,U_9766] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9765),hAPP(c_Set_OCollect(U_9765),hAPP(hAPP(c_COMBB(tc_fun(U_9763,tc_HOL_Obool),tc_HOL_Obool,U_9765),c_HOL_OEx(U_9763)),hAPP(hAPP(c_COMBB(tc_fun(U_9763,tc_HOL_Obool),tc_fun(U_9763,tc_HOL_Obool),U_9765),hAPP(c_COMBS(U_9763,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9763),c_fconj),U_9764))),U_9766)))))
        | sP758(U_9763,U_9764,U_9765,U_9766)
        | ~ sP759(U_9763,U_9761,U_9764,U_9765,U_9766) )
    & ! [U_9763,U_9761,U_9764,U_9765,U_9766] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9765),hAPP(c_Set_OCollect(U_9765),hAPP(hAPP(c_COMBC(U_9765,U_9763,tc_HOL_Obool),U_9766),U_9761))))
        | ~ hBOOL(hAPP(U_9764,U_9761))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9765),hAPP(c_Set_OCollect(U_9765),hAPP(hAPP(c_COMBB(tc_fun(U_9763,tc_HOL_Obool),tc_HOL_Obool,U_9765),c_HOL_OEx(U_9763)),hAPP(hAPP(c_COMBB(tc_fun(U_9763,tc_HOL_Obool),tc_fun(U_9763,tc_HOL_Obool),U_9765),hAPP(c_COMBS(U_9763,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9763),c_fconj),U_9764))),U_9766)))))
        | ~ sP759(U_9763,U_9761,U_9764,U_9765,U_9766) )
    & ! [U_9763,U_9761,U_9764,U_9765,U_9766] :
        ( sP759(U_9763,U_9761,U_9764,U_9765,U_9766)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9763),hAPP(c_Set_OCollect(U_9763),U_9764))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP758,sP759])],[f_2669_3]) ).

cnf(f_2669_5,plain,
    ( sP759(U_9763,U_9761,U_9764,U_9765,U_9766)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9763),hAPP(c_Set_OCollect(U_9763),U_9764))) ),
    inference(clausify,[status(thm)],[f_2669_4]) ).

cnf(f_2669_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9765),hAPP(c_Set_OCollect(U_9765),hAPP(hAPP(c_COMBC(U_9765,U_9763,tc_HOL_Obool),U_9766),U_9761))))
    | ~ hBOOL(hAPP(U_9764,U_9761))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9765),hAPP(c_Set_OCollect(U_9765),hAPP(hAPP(c_COMBB(tc_fun(U_9763,tc_HOL_Obool),tc_HOL_Obool,U_9765),c_HOL_OEx(U_9763)),hAPP(hAPP(c_COMBB(tc_fun(U_9763,tc_HOL_Obool),tc_fun(U_9763,tc_HOL_Obool),U_9765),hAPP(c_COMBS(U_9763,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9763),c_fconj),U_9764))),U_9766)))))
    | ~ sP759(U_9763,U_9761,U_9764,U_9765,U_9766) ),
    inference(clausify,[status(thm)],[f_2669_4]) ).

cnf(f_2669_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9765),hAPP(c_Set_OCollect(U_9765),hAPP(hAPP(c_COMBB(tc_fun(U_9763,tc_HOL_Obool),tc_HOL_Obool,U_9765),c_HOL_OEx(U_9763)),hAPP(hAPP(c_COMBB(tc_fun(U_9763,tc_HOL_Obool),tc_fun(U_9763,tc_HOL_Obool),U_9765),hAPP(c_COMBS(U_9763,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9763),c_fconj),U_9764))),U_9766)))))
    | sP758(U_9763,U_9764,U_9765,U_9766)
    | ~ sP759(U_9763,U_9761,U_9764,U_9765,U_9766) ),
    inference(clausify,[status(thm)],[f_2669_4]) ).

cnf(f_2669_8,plain,
    ( hBOOL(hAPP(U_9764,sK156(U_9766,U_9765,U_9764,U_9763)))
    | ~ sP758(U_9763,U_9764,U_9765,U_9766) ),
    inference(clausify,[status(thm)],[f_2669_4]) ).

cnf(f_2669_9,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9765),hAPP(c_Set_OCollect(U_9765),hAPP(hAPP(c_COMBC(U_9765,U_9763,tc_HOL_Obool),U_9766),sK156(U_9766,U_9765,U_9764,U_9763)))))
    | ~ sP758(U_9763,U_9764,U_9765,U_9766) ),
    inference(clausify,[status(thm)],[f_2669_4]) ).

fof(f_2670_1,plain,
    ! [V_f_2,T_c,V_Pa_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_Pa_2)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__image__set]) ).

fof(f_2670_2,plain,
    ! [U_9770,U_9769,U_9768,U_9767] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9769),hAPP(c_Set_OCollect(U_9769),hAPP(hAPP(c_COMBB(tc_fun(U_9767,tc_HOL_Obool),tc_HOL_Obool,U_9769),c_HOL_OEx(U_9767)),hAPP(hAPP(c_COMBC(U_9769,tc_fun(U_9767,tc_HOL_Obool),tc_fun(U_9767,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9767,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9767,tc_HOL_Obool),tc_fun(U_9767,tc_HOL_Obool)),U_9769),c_COMBS(U_9767,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9767,tc_HOL_Obool),tc_fun(U_9767,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9769),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9767),c_fconj)),hAPP(hAPP(c_COMBC(U_9769,tc_fun(U_9767,U_9769),tc_fun(U_9767,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9769,tc_HOL_Obool),tc_fun(tc_fun(U_9767,U_9769),tc_fun(U_9767,tc_HOL_Obool)),U_9769),c_COMBB(U_9769,tc_HOL_Obool,U_9767)),c_fequal)),U_9770)))),U_9768)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9767),hAPP(c_Set_OCollect(U_9767),U_9768))) ),
    inference(variable_rename,[status(thm)],[f_2670_1]) ).

fof(f_2670_3,plain,
    ! [U_9769,U_9770,U_9768,U_9767] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9769),hAPP(c_Set_OCollect(U_9769),hAPP(hAPP(c_COMBB(tc_fun(U_9767,tc_HOL_Obool),tc_HOL_Obool,U_9769),c_HOL_OEx(U_9767)),hAPP(hAPP(c_COMBC(U_9769,tc_fun(U_9767,tc_HOL_Obool),tc_fun(U_9767,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9767,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9767,tc_HOL_Obool),tc_fun(U_9767,tc_HOL_Obool)),U_9769),c_COMBS(U_9767,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9767,tc_HOL_Obool),tc_fun(U_9767,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9769),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9767),c_fconj)),hAPP(hAPP(c_COMBC(U_9769,tc_fun(U_9767,U_9769),tc_fun(U_9767,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9769,tc_HOL_Obool),tc_fun(tc_fun(U_9767,U_9769),tc_fun(U_9767,tc_HOL_Obool)),U_9769),c_COMBB(U_9769,tc_HOL_Obool,U_9767)),c_fequal)),U_9770)))),U_9768)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9767),hAPP(c_Set_OCollect(U_9767),U_9768))) ),
    inference(definitional_conversion,[status(esa)],[f_2670_2]) ).

cnf(f_2670_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9769),hAPP(c_Set_OCollect(U_9769),hAPP(hAPP(c_COMBB(tc_fun(U_9767,tc_HOL_Obool),tc_HOL_Obool,U_9769),c_HOL_OEx(U_9767)),hAPP(hAPP(c_COMBC(U_9769,tc_fun(U_9767,tc_HOL_Obool),tc_fun(U_9767,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9767,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9767,tc_HOL_Obool),tc_fun(U_9767,tc_HOL_Obool)),U_9769),c_COMBS(U_9767,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9767,tc_HOL_Obool),tc_fun(U_9767,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9769),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9767),c_fconj)),hAPP(hAPP(c_COMBC(U_9769,tc_fun(U_9767,U_9769),tc_fun(U_9767,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9769,tc_HOL_Obool),tc_fun(tc_fun(U_9767,U_9769),tc_fun(U_9767,tc_HOL_Obool)),U_9769),c_COMBB(U_9769,tc_HOL_Obool,U_9767)),c_fequal)),U_9770)))),U_9768)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9767),hAPP(c_Set_OCollect(U_9767),U_9768))) ),
    inference(clausify,[status(thm)],[f_2670_3]) ).

fof(f_2671_1,plain,
    ! [V_i_2,V_Pa_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_Pa_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_2671_2,plain,
    ! [U_9772,U_9771] : 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_9771)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_9772))))),
    inference(variable_rename,[status(thm)],[f_2671_1]) ).

fof(f_2671_3,plain,
    ! [U_9771,U_9772] : 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_9771)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_9772))))),
    inference(definitional_conversion,[status(esa)],[f_2671_2]) ).

cnf(f_2671_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_9771)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_HOL_Obool),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),U_9772))))),
    inference(clausify,[status(thm)],[f_2671_3]) ).

fof(f_2672_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_2672_2,plain,
    ! [U_9774,U_9773] :
      ( ( hAPP(c_Finite__Set_Ocard(U_9773),U_9774) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9773),U_9774))
          & U_9774 != c_Orderings_Obot__class_Obot(tc_fun(U_9773,tc_HOL_Obool)) ) )
      & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9773),U_9774))
        | U_9774 = c_Orderings_Obot__class_Obot(tc_fun(U_9773,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(U_9773),U_9774) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_2672_1]) ).

fof(f_2672_3,plain,
    ( ! [U_9778,U_9776] :
        ( hAPP(c_Finite__Set_Ocard(U_9776),U_9778) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9776),U_9778))
          & U_9778 != c_Orderings_Obot__class_Obot(tc_fun(U_9776,tc_HOL_Obool)) ) )
    & ! [U_9777,U_9775] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9775),U_9777))
        | U_9777 = c_Orderings_Obot__class_Obot(tc_fun(U_9775,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(U_9775),U_9777) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_2672_2]) ).

fof(f_2672_4,plain,
    ( ! [U_9778,U_9776] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9776),U_9778))
        | ~ sP760(U_9778,U_9776) )
    & ! [U_9778,U_9776] :
        ( U_9778 != c_Orderings_Obot__class_Obot(tc_fun(U_9776,tc_HOL_Obool))
        | ~ sP760(U_9778,U_9776) )
    & ! [U_9778,U_9776] :
        ( hAPP(c_Finite__Set_Ocard(U_9776),U_9778) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP760(U_9778,U_9776) )
    & ! [U_9777,U_9775] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9775),U_9777))
        | U_9777 = c_Orderings_Obot__class_Obot(tc_fun(U_9775,tc_HOL_Obool))
        | hAPP(c_Finite__Set_Ocard(U_9775),U_9777) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP760])],[f_2672_3]) ).

cnf(f_2672_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9775),U_9777))
    | U_9777 = c_Orderings_Obot__class_Obot(tc_fun(U_9775,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(U_9775),U_9777) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_2672_4]) ).

cnf(f_2672_6,plain,
    ( hAPP(c_Finite__Set_Ocard(U_9776),U_9778) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP760(U_9778,U_9776) ),
    inference(clausify,[status(thm)],[f_2672_4]) ).

cnf(f_2672_7,plain,
    ( U_9778 != c_Orderings_Obot__class_Obot(tc_fun(U_9776,tc_HOL_Obool))
    | ~ sP760(U_9778,U_9776) ),
    inference(clausify,[status(thm)],[f_2672_4]) ).

cnf(f_2672_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9776),U_9778))
    | ~ sP760(U_9778,U_9776) ),
    inference(clausify,[status(thm)],[f_2672_4]) ).

fof(f_2673_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_2673_2,plain,
    ! [U_9780,U_9779] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9779),U_9780))
      | ~ 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_9779),U_9780))) ),
    inference(variable_rename,[status(thm)],[f_2673_1]) ).

fof(f_2673_3,plain,
    ! [U_9780,U_9779] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9779),U_9780))
      | ~ 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_9779),U_9780))) ),
    inference(definitional_conversion,[status(esa)],[f_2673_2]) ).

cnf(f_2673_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9779),U_9780))
    | ~ 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_9779),U_9780))) ),
    inference(clausify,[status(thm)],[f_2673_3]) ).

fof(f_2674_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_2674_2,plain,
    ! [U_9783,U_9782,U_9781] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9781),U_9782)),hAPP(c_Finite__Set_Ocard(U_9781),hAPP(hAPP(c_Set_Oinsert(U_9781),U_9783),U_9782))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9781),U_9782)) ),
    inference(variable_rename,[status(thm)],[f_2674_1]) ).

fof(f_2674_3,plain,
    ! [U_9781,U_9782,U_9783] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9781),U_9782)),hAPP(c_Finite__Set_Ocard(U_9781),hAPP(hAPP(c_Set_Oinsert(U_9781),U_9783),U_9782))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9781),U_9782)) ),
    inference(definitional_conversion,[status(esa)],[f_2674_2]) ).

cnf(f_2674_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9781),U_9782)),hAPP(c_Finite__Set_Ocard(U_9781),hAPP(hAPP(c_Set_Oinsert(U_9781),U_9783),U_9782))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9781),U_9782)) ),
    inference(clausify,[status(thm)],[f_2674_3]) ).

fof(f_2675_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_2675_2,plain,
    ! [U_9786,U_9785,U_9784] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9784),U_9786)),hAPP(c_Finite__Set_Ocard(U_9784),U_9785)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9784,tc_HOL_Obool)),U_9786),U_9785))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9784),U_9785)) ),
    inference(variable_rename,[status(thm)],[f_2675_1]) ).

fof(f_2675_3,plain,
    ! [U_9784,U_9785,U_9786] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9784),U_9786)),hAPP(c_Finite__Set_Ocard(U_9784),U_9785)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9784,tc_HOL_Obool)),U_9786),U_9785))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9784),U_9785)) ),
    inference(definitional_conversion,[status(esa)],[f_2675_2]) ).

cnf(f_2675_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9784),U_9786)),hAPP(c_Finite__Set_Ocard(U_9784),U_9785)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9784,tc_HOL_Obool)),U_9786),U_9785))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9784),U_9785)) ),
    inference(clausify,[status(thm)],[f_2675_3]) ).

fof(f_2676_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_2676_2,plain,
    ! [U_9789,U_9788,U_9787] :
      ( U_9789 = U_9788
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9787),U_9788)),hAPP(c_Finite__Set_Ocard(U_9787),U_9789)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9787,tc_HOL_Obool)),U_9789),U_9788))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9787),U_9788)) ),
    inference(variable_rename,[status(thm)],[f_2676_1]) ).

fof(f_2676_3,plain,
    ! [U_9787,U_9788,U_9789] :
      ( U_9789 = U_9788
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9787),U_9788)),hAPP(c_Finite__Set_Ocard(U_9787),U_9789)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9787,tc_HOL_Obool)),U_9789),U_9788))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9787),U_9788)) ),
    inference(definitional_conversion,[status(esa)],[f_2676_2]) ).

cnf(f_2676_4,plain,
    ( U_9789 = U_9788
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9787),U_9788)),hAPP(c_Finite__Set_Ocard(U_9787),U_9789)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9787,tc_HOL_Obool)),U_9789),U_9788))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9787),U_9788)) ),
    inference(clausify,[status(thm)],[f_2676_3]) ).

fof(f_2677_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_2677_2,plain,
    ! [U_9793,U_9792,U_9791,U_9790] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9792),hAPP(c_Set_Oimage(U_9790,U_9792,U_9793),U_9791))),hAPP(c_Finite__Set_Ocard(U_9790),U_9791)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9790),U_9791)) ),
    inference(variable_rename,[status(thm)],[f_2677_1]) ).

fof(f_2677_3,plain,
    ! [U_9791,U_9790,U_9792,U_9793] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9792),hAPP(c_Set_Oimage(U_9790,U_9792,U_9793),U_9791))),hAPP(c_Finite__Set_Ocard(U_9790),U_9791)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9790),U_9791)) ),
    inference(definitional_conversion,[status(esa)],[f_2677_2]) ).

cnf(f_2677_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9792),hAPP(c_Set_Oimage(U_9790,U_9792,U_9793),U_9791))),hAPP(c_Finite__Set_Ocard(U_9790),U_9791)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9790),U_9791)) ),
    inference(clausify,[status(thm)],[f_2677_3]) ).

fof(f_2678_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_2678_2,plain,
    ! [U_9796,U_9795,U_9794] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9794),U_9796)),hAPP(c_Finite__Set_Ocard(U_9794),U_9795)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9794,tc_HOL_Obool)),U_9796),U_9795))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9794),U_9795)) ),
    inference(variable_rename,[status(thm)],[f_2678_1]) ).

fof(f_2678_3,plain,
    ! [U_9794,U_9795,U_9796] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9794),U_9796)),hAPP(c_Finite__Set_Ocard(U_9794),U_9795)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9794,tc_HOL_Obool)),U_9796),U_9795))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9794),U_9795)) ),
    inference(definitional_conversion,[status(esa)],[f_2678_2]) ).

cnf(f_2678_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9794),U_9796)),hAPP(c_Finite__Set_Ocard(U_9794),U_9795)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9794,tc_HOL_Obool)),U_9796),U_9795))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9794),U_9795)) ),
    inference(clausify,[status(thm)],[f_2678_3]) ).

fof(f_2679_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_2679_2,plain,
    ! [U_9798,U_9797] :
      ( c_Wellfounded_Owf(U_9797,hAPP(c_Relation_Oconverse(U_9797,U_9797),U_9798))
      | ~ c_Wellfounded_Oacyclic(U_9797,U_9798)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9797,U_9797)),U_9798)) ),
    inference(variable_rename,[status(thm)],[f_2679_1]) ).

fof(f_2679_3,plain,
    ! [U_9797,U_9798] :
      ( c_Wellfounded_Owf(U_9797,hAPP(c_Relation_Oconverse(U_9797,U_9797),U_9798))
      | ~ c_Wellfounded_Oacyclic(U_9797,U_9798)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9797,U_9797)),U_9798)) ),
    inference(definitional_conversion,[status(esa)],[f_2679_2]) ).

cnf(f_2679_4,plain,
    ( c_Wellfounded_Owf(U_9797,hAPP(c_Relation_Oconverse(U_9797,U_9797),U_9798))
    | ~ c_Wellfounded_Oacyclic(U_9797,U_9798)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9797,U_9797)),U_9798)) ),
    inference(clausify,[status(thm)],[f_2679_3]) ).

fof(f_2680_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_2680_2,plain,
    ! [U_9802,U_9801,U_9800,U_9799] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9800),U_9799))
      | U_9799 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_9800,U_9801),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_9802))) ),
    inference(variable_rename,[status(thm)],[f_2680_1]) ).

fof(f_2680_3,plain,
    ! [U_9799,U_9800,U_9801,U_9802] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9800),U_9799))
      | U_9799 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_9800,U_9801),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_9802))) ),
    inference(definitional_conversion,[status(esa)],[f_2680_2]) ).

cnf(f_2680_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9800),U_9799))
    | U_9799 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_9800,U_9801),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_9802))) ),
    inference(clausify,[status(thm)],[f_2680_3]) ).

fof(f_2681_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_2681_2,plain,
    ! [U_9805,U_9804,U_9803] :
      ( ( ( hAPP(c_Finite__Set_Ocard(U_9803),hAPP(hAPP(c_Set_Oinsert(U_9803),U_9805),U_9804)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_9803),U_9804))
          | hBOOL(hAPP(hAPP(c_member(U_9803),U_9805),U_9804)) )
        & ( hAPP(c_Finite__Set_Ocard(U_9803),hAPP(hAPP(c_Set_Oinsert(U_9803),U_9805),U_9804)) = hAPP(c_Finite__Set_Ocard(U_9803),U_9804)
          | ~ hBOOL(hAPP(hAPP(c_member(U_9803),U_9805),U_9804)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9803),U_9804)) ),
    inference(variable_rename,[status(thm)],[f_2681_1]) ).

fof(f_2681_3,plain,
    ( ! [U_9803,U_9804,U_9805] :
        ( hAPP(c_Finite__Set_Ocard(U_9803),hAPP(hAPP(c_Set_Oinsert(U_9803),U_9805),U_9804)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_9803),U_9804))
        | hBOOL(hAPP(hAPP(c_member(U_9803),U_9805),U_9804))
        | ~ sP761(U_9803,U_9804,U_9805) )
    & ! [U_9803,U_9804,U_9805] :
        ( hAPP(c_Finite__Set_Ocard(U_9803),hAPP(hAPP(c_Set_Oinsert(U_9803),U_9805),U_9804)) = hAPP(c_Finite__Set_Ocard(U_9803),U_9804)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9803),U_9805),U_9804))
        | ~ sP761(U_9803,U_9804,U_9805) )
    & ! [U_9803,U_9804,U_9805] :
        ( sP761(U_9803,U_9804,U_9805)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9803),U_9804)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP761])],[f_2681_2]) ).

cnf(f_2681_4,plain,
    ( sP761(U_9803,U_9804,U_9805)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9803),U_9804)) ),
    inference(clausify,[status(thm)],[f_2681_3]) ).

cnf(f_2681_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_9803),hAPP(hAPP(c_Set_Oinsert(U_9803),U_9805),U_9804)) = hAPP(c_Finite__Set_Ocard(U_9803),U_9804)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9803),U_9805),U_9804))
    | ~ sP761(U_9803,U_9804,U_9805) ),
    inference(clausify,[status(thm)],[f_2681_3]) ).

cnf(f_2681_6,plain,
    ( hAPP(c_Finite__Set_Ocard(U_9803),hAPP(hAPP(c_Set_Oinsert(U_9803),U_9805),U_9804)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_9803),U_9804))
    | hBOOL(hAPP(hAPP(c_member(U_9803),U_9805),U_9804))
    | ~ sP761(U_9803,U_9804,U_9805) ),
    inference(clausify,[status(thm)],[f_2681_3]) ).

fof(f_2682_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_2682_2,plain,
    ! [U_9808,U_9807,U_9806] :
      ( hAPP(c_Finite__Set_Ocard(U_9806),hAPP(hAPP(c_Set_Oinsert(U_9806),U_9808),U_9807)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_9806),U_9807))
      | hBOOL(hAPP(hAPP(c_member(U_9806),U_9808),U_9807))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9806),U_9807)) ),
    inference(variable_rename,[status(thm)],[f_2682_1]) ).

fof(f_2682_3,plain,
    ! [U_9807,U_9806,U_9808] :
      ( hAPP(c_Finite__Set_Ocard(U_9806),hAPP(hAPP(c_Set_Oinsert(U_9806),U_9808),U_9807)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_9806),U_9807))
      | hBOOL(hAPP(hAPP(c_member(U_9806),U_9808),U_9807))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9806),U_9807)) ),
    inference(definitional_conversion,[status(esa)],[f_2682_2]) ).

cnf(f_2682_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_9806),hAPP(hAPP(c_Set_Oinsert(U_9806),U_9808),U_9807)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_9806),U_9807))
    | hBOOL(hAPP(hAPP(c_member(U_9806),U_9808),U_9807))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9806),U_9807)) ),
    inference(clausify,[status(thm)],[f_2682_3]) ).

fof(f_2683_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_2683_2,plain,
    ! [U_9810,U_9809] :
      ( ( 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_9809),U_9810)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9809),U_9810))
        | U_9810 = c_Orderings_Obot__class_Obot(tc_fun(U_9809,tc_HOL_Obool)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9809),U_9810))
          & U_9810 != c_Orderings_Obot__class_Obot(tc_fun(U_9809,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_9809),U_9810))) ) ),
    inference(variable_rename,[status(thm)],[f_2683_1]) ).

fof(f_2683_3,plain,
    ( ! [U_9814,U_9812] :
        ( 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_9812),U_9814)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9812),U_9814))
        | U_9814 = c_Orderings_Obot__class_Obot(tc_fun(U_9812,tc_HOL_Obool)) )
    & ! [U_9813,U_9811] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9811),U_9813))
          & U_9813 != c_Orderings_Obot__class_Obot(tc_fun(U_9811,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_9811),U_9813))) ) ),
    inference(miniscope,[status(thm)],[f_2683_2]) ).

fof(f_2683_4,plain,
    ( ! [U_9813,U_9811] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9811),U_9813))
        | ~ sP762(U_9813,U_9811) )
    & ! [U_9813,U_9811] :
        ( U_9813 != c_Orderings_Obot__class_Obot(tc_fun(U_9811,tc_HOL_Obool))
        | ~ sP762(U_9813,U_9811) )
    & ! [U_9814,U_9812] :
        ( 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_9812),U_9814)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9812),U_9814))
        | U_9814 = c_Orderings_Obot__class_Obot(tc_fun(U_9812,tc_HOL_Obool)) )
    & ! [U_9813,U_9811] :
        ( sP762(U_9813,U_9811)
        | ~ 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_9811),U_9813))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP762])],[f_2683_3]) ).

cnf(f_2683_5,plain,
    ( sP762(U_9813,U_9811)
    | ~ 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_9811),U_9813))) ),
    inference(clausify,[status(thm)],[f_2683_4]) ).

cnf(f_2683_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_9812),U_9814)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9812),U_9814))
    | U_9814 = c_Orderings_Obot__class_Obot(tc_fun(U_9812,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2683_4]) ).

cnf(f_2683_7,plain,
    ( U_9813 != c_Orderings_Obot__class_Obot(tc_fun(U_9811,tc_HOL_Obool))
    | ~ sP762(U_9813,U_9811) ),
    inference(clausify,[status(thm)],[f_2683_4]) ).

cnf(f_2683_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9811),U_9813))
    | ~ sP762(U_9813,U_9811) ),
    inference(clausify,[status(thm)],[f_2683_4]) ).

fof(f_2684_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_2684_2,plain,
    ! [U_9817,U_9816,U_9815] :
      ( hAPP(c_Finite__Set_Ocard(U_9815),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9815,tc_HOL_Obool)),U_9817),U_9816)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9815),U_9817)),hAPP(c_Finite__Set_Ocard(U_9815),U_9816))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9815,tc_HOL_Obool)),U_9816),U_9817))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9815),U_9816)) ),
    inference(variable_rename,[status(thm)],[f_2684_1]) ).

fof(f_2684_3,plain,
    ! [U_9815,U_9816,U_9817] :
      ( hAPP(c_Finite__Set_Ocard(U_9815),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9815,tc_HOL_Obool)),U_9817),U_9816)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9815),U_9817)),hAPP(c_Finite__Set_Ocard(U_9815),U_9816))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9815,tc_HOL_Obool)),U_9816),U_9817))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9815),U_9816)) ),
    inference(definitional_conversion,[status(esa)],[f_2684_2]) ).

cnf(f_2684_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_9815),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9815,tc_HOL_Obool)),U_9817),U_9816)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9815),U_9817)),hAPP(c_Finite__Set_Ocard(U_9815),U_9816))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9815,tc_HOL_Obool)),U_9816),U_9817))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9815),U_9816)) ),
    inference(clausify,[status(thm)],[f_2684_3]) ).

fof(f_2685_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_2685_2,plain,
    ! [U_9820,U_9819,U_9818] :
      ( 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_9818),U_9820)),hAPP(c_Finite__Set_Ocard(U_9818),U_9819))),hAPP(c_Finite__Set_Ocard(U_9818),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9818,tc_HOL_Obool)),U_9820),U_9819))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9818),U_9819)) ),
    inference(variable_rename,[status(thm)],[f_2685_1]) ).

fof(f_2685_3,plain,
    ! [U_9818,U_9819,U_9820] :
      ( 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_9818),U_9820)),hAPP(c_Finite__Set_Ocard(U_9818),U_9819))),hAPP(c_Finite__Set_Ocard(U_9818),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9818,tc_HOL_Obool)),U_9820),U_9819))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9818),U_9819)) ),
    inference(definitional_conversion,[status(esa)],[f_2685_2]) ).

cnf(f_2685_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_9818),U_9820)),hAPP(c_Finite__Set_Ocard(U_9818),U_9819))),hAPP(c_Finite__Set_Ocard(U_9818),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9818,tc_HOL_Obool)),U_9820),U_9819))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9818),U_9819)) ),
    inference(clausify,[status(thm)],[f_2685_3]) ).

fof(f_2686_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_2686_2,plain,
    ! [U_9823,U_9822,U_9821] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9821,tc_HOL_Obool)),U_9823),U_9822))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9821),U_9823)),hAPP(c_Finite__Set_Ocard(U_9821),U_9822)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9821,tc_HOL_Obool)),U_9823),U_9822))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9821),U_9822)) ),
    inference(variable_rename,[status(thm)],[f_2686_1]) ).

fof(f_2686_3,plain,
    ! [U_9821,U_9822,U_9823] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9821,tc_HOL_Obool)),U_9823),U_9822))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9821),U_9823)),hAPP(c_Finite__Set_Ocard(U_9821),U_9822)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9821,tc_HOL_Obool)),U_9823),U_9822))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9821),U_9822)) ),
    inference(definitional_conversion,[status(esa)],[f_2686_2]) ).

cnf(f_2686_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9821,tc_HOL_Obool)),U_9823),U_9822))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9821),U_9823)),hAPP(c_Finite__Set_Ocard(U_9821),U_9822)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9821,tc_HOL_Obool)),U_9823),U_9822))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9821),U_9822)) ),
    inference(clausify,[status(thm)],[f_2686_3]) ).

fof(f_2687_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_2687_2,plain,
    ! [U_9826,U_9825,U_9824] :
      ( hAPP(c_Finite__Set_Ocard(U_9824),hAPP(hAPP(c_Set_Oinsert(U_9824),U_9826),U_9825)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_9824),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9824,tc_HOL_Obool)),U_9825),hAPP(hAPP(c_Set_Oinsert(U_9824),U_9826),c_Orderings_Obot__class_Obot(tc_fun(U_9824,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9824),U_9825)) ),
    inference(variable_rename,[status(thm)],[f_2687_1]) ).

fof(f_2687_3,plain,
    ! [U_9824,U_9825,U_9826] :
      ( hAPP(c_Finite__Set_Ocard(U_9824),hAPP(hAPP(c_Set_Oinsert(U_9824),U_9826),U_9825)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_9824),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9824,tc_HOL_Obool)),U_9825),hAPP(hAPP(c_Set_Oinsert(U_9824),U_9826),c_Orderings_Obot__class_Obot(tc_fun(U_9824,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9824),U_9825)) ),
    inference(definitional_conversion,[status(esa)],[f_2687_2]) ).

cnf(f_2687_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_9824),hAPP(hAPP(c_Set_Oinsert(U_9824),U_9826),U_9825)) = hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_9824),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9824,tc_HOL_Obool)),U_9825),hAPP(hAPP(c_Set_Oinsert(U_9824),U_9826),c_Orderings_Obot__class_Obot(tc_fun(U_9824,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9824),U_9825)) ),
    inference(clausify,[status(thm)],[f_2687_3]) ).

fof(f_2688_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(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_2688_2,plain,
    ! [U_9829,U_9828,U_9827] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9827),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9827,tc_HOL_Obool)),U_9828),hAPP(hAPP(c_Set_Oinsert(U_9827),U_9829),c_Orderings_Obot__class_Obot(tc_fun(U_9827,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_9827),U_9828)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9827),U_9828)) ),
    inference(variable_rename,[status(thm)],[f_2688_1]) ).

fof(f_2688_3,plain,
    ! [U_9828,U_9827,U_9829] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9827),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9827,tc_HOL_Obool)),U_9828),hAPP(hAPP(c_Set_Oinsert(U_9827),U_9829),c_Orderings_Obot__class_Obot(tc_fun(U_9827,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_9827),U_9828)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9827),U_9828)) ),
    inference(definitional_conversion,[status(esa)],[f_2688_2]) ).

cnf(f_2688_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9827),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9827,tc_HOL_Obool)),U_9828),hAPP(hAPP(c_Set_Oinsert(U_9827),U_9829),c_Orderings_Obot__class_Obot(tc_fun(U_9827,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_9827),U_9828)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9827),U_9828)) ),
    inference(clausify,[status(thm)],[f_2688_3]) ).

fof(f_2689_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_2689_2,plain,
    ! [U_9832,U_9831,U_9830] :
      ( hAPP(c_Finite__Set_Ocard(U_9830),hAPP(hAPP(c_Set_Oinsert(U_9830),U_9832),U_9831)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_9830),U_9831))
      | hBOOL(hAPP(hAPP(c_member(U_9830),U_9832),U_9831))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9830),U_9831)) ),
    inference(variable_rename,[status(thm)],[f_2689_1]) ).

fof(f_2689_3,plain,
    ! [U_9830,U_9831,U_9832] :
      ( hAPP(c_Finite__Set_Ocard(U_9830),hAPP(hAPP(c_Set_Oinsert(U_9830),U_9832),U_9831)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_9830),U_9831))
      | hBOOL(hAPP(hAPP(c_member(U_9830),U_9832),U_9831))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9830),U_9831)) ),
    inference(definitional_conversion,[status(esa)],[f_2689_2]) ).

cnf(f_2689_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_9830),hAPP(hAPP(c_Set_Oinsert(U_9830),U_9832),U_9831)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_9830),U_9831))
    | hBOOL(hAPP(hAPP(c_member(U_9830),U_9832),U_9831))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9830),U_9831)) ),
    inference(clausify,[status(thm)],[f_2689_3]) ).

fof(f_2690_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_2690_2,plain,
    ! [U_9833] :
      ( 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_9833)),c_FunDef_Omax__weak))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9833)) ),
    inference(variable_rename,[status(thm)],[f_2690_1]) ).

fof(f_2690_3,plain,
    ! [U_9833] :
      ( 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_9833)),c_FunDef_Omax__weak))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9833)) ),
    inference(definitional_conversion,[status(esa)],[f_2690_2]) ).

cnf(f_2690_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_9833)),c_FunDef_Omax__weak))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),U_9833)) ),
    inference(clausify,[status(thm)],[f_2690_3]) ).

fof(f_2691_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_2691_2,plain,
    ! [U_9834] :
      ( 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_9834)),c_FunDef_Omax__strict))
      | U_9834 = 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_9834)) ),
    inference(variable_rename,[status(thm)],[f_2691_1]) ).

fof(f_2691_3,plain,
    ! [U_9834] :
      ( 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_9834)),c_FunDef_Omax__strict))
      | U_9834 = 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_9834)) ),
    inference(definitional_conversion,[status(esa)],[f_2691_2]) ).

cnf(f_2691_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_9834)),c_FunDef_Omax__strict))
    | U_9834 = 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_9834)) ),
    inference(clausify,[status(thm)],[f_2691_3]) ).

fof(f_2692_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_2692_2,plain,
    ! [U_9837,U_9836,U_9835] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_9835),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9835,tc_HOL_Obool)),U_9836),hAPP(hAPP(c_Set_Oinsert(U_9835),U_9837),c_Orderings_Obot__class_Obot(tc_fun(U_9835,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_9835),U_9836)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9835),U_9837),U_9836))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9835),U_9836)) ),
    inference(variable_rename,[status(thm)],[f_2692_1]) ).

fof(f_2692_3,plain,
    ! [U_9835,U_9836,U_9837] :
      ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_9835),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9835,tc_HOL_Obool)),U_9836),hAPP(hAPP(c_Set_Oinsert(U_9835),U_9837),c_Orderings_Obot__class_Obot(tc_fun(U_9835,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_9835),U_9836)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9835),U_9837),U_9836))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9835),U_9836)) ),
    inference(definitional_conversion,[status(esa)],[f_2692_2]) ).

cnf(f_2692_4,plain,
    ( hAPP(c_Nat_OSuc,hAPP(c_Finite__Set_Ocard(U_9835),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9835,tc_HOL_Obool)),U_9836),hAPP(hAPP(c_Set_Oinsert(U_9835),U_9837),c_Orderings_Obot__class_Obot(tc_fun(U_9835,tc_HOL_Obool)))))) = hAPP(c_Finite__Set_Ocard(U_9835),U_9836)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9835),U_9837),U_9836))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9835),U_9836)) ),
    inference(clausify,[status(thm)],[f_2692_3]) ).

fof(f_2693_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_2693_2,plain,
    ! [U_9841,U_9840,U_9839,U_9838] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9838),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9838,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9838,tc_HOL_Obool)),U_9839),hAPP(hAPP(c_Set_Oinsert(U_9838),U_9840),c_Orderings_Obot__class_Obot(tc_fun(U_9838,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_9838),U_9841),c_Orderings_Obot__class_Obot(tc_fun(U_9838,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_9838),U_9839)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9838),U_9841),U_9839))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9838),U_9840),U_9839))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9838),U_9839)) ),
    inference(variable_rename,[status(thm)],[f_2693_1]) ).

fof(f_2693_3,plain,
    ! [U_9838,U_9839,U_9840,U_9841] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9838),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9838,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9838,tc_HOL_Obool)),U_9839),hAPP(hAPP(c_Set_Oinsert(U_9838),U_9840),c_Orderings_Obot__class_Obot(tc_fun(U_9838,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_9838),U_9841),c_Orderings_Obot__class_Obot(tc_fun(U_9838,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_9838),U_9839)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9838),U_9841),U_9839))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9838),U_9840),U_9839))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9838),U_9839)) ),
    inference(definitional_conversion,[status(esa)],[f_2693_2]) ).

cnf(f_2693_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9838),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9838,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9838,tc_HOL_Obool)),U_9839),hAPP(hAPP(c_Set_Oinsert(U_9838),U_9840),c_Orderings_Obot__class_Obot(tc_fun(U_9838,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_9838),U_9841),c_Orderings_Obot__class_Obot(tc_fun(U_9838,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_9838),U_9839)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9838),U_9841),U_9839))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9838),U_9840),U_9839))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9838),U_9839)) ),
    inference(clausify,[status(thm)],[f_2693_3]) ).

fof(f_2694_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_2694_2,plain,
    ! [U_9844,U_9843,U_9842] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9842),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9842,tc_HOL_Obool)),U_9843),hAPP(hAPP(c_Set_Oinsert(U_9842),U_9844),c_Orderings_Obot__class_Obot(tc_fun(U_9842,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_9842),U_9843)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9842),U_9844),U_9843))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9842),U_9843)) ),
    inference(variable_rename,[status(thm)],[f_2694_1]) ).

fof(f_2694_3,plain,
    ! [U_9842,U_9843,U_9844] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9842),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9842,tc_HOL_Obool)),U_9843),hAPP(hAPP(c_Set_Oinsert(U_9842),U_9844),c_Orderings_Obot__class_Obot(tc_fun(U_9842,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_9842),U_9843)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9842),U_9844),U_9843))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9842),U_9843)) ),
    inference(definitional_conversion,[status(esa)],[f_2694_2]) ).

cnf(f_2694_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9842),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9842,tc_HOL_Obool)),U_9843),hAPP(hAPP(c_Set_Oinsert(U_9842),U_9844),c_Orderings_Obot__class_Obot(tc_fun(U_9842,tc_HOL_Obool)))))),hAPP(c_Finite__Set_Ocard(U_9842),U_9843)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9842),U_9844),U_9843))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9842),U_9843)) ),
    inference(clausify,[status(thm)],[f_2694_3]) ).

fof(f_2695_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_2695_2,plain,
    ! [U_9848,U_9847,U_9846,U_9845] :
      ( hAPP(c_Finite__Set_Ocard(U_9845),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9845,tc_HOL_Obool)),U_9846),hAPP(hAPP(c_Set_Oinsert(U_9845),U_9847),U_9848))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9845),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9845,tc_HOL_Obool)),U_9846),U_9848))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | hBOOL(hAPP(hAPP(c_member(U_9845),U_9847),U_9848))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9845),U_9847),U_9846))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9845),U_9846)) ),
    inference(variable_rename,[status(thm)],[f_2695_1]) ).

fof(f_2695_3,plain,
    ! [U_9845,U_9846,U_9847,U_9848] :
      ( hAPP(c_Finite__Set_Ocard(U_9845),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9845,tc_HOL_Obool)),U_9846),hAPP(hAPP(c_Set_Oinsert(U_9845),U_9847),U_9848))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9845),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9845,tc_HOL_Obool)),U_9846),U_9848))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | hBOOL(hAPP(hAPP(c_member(U_9845),U_9847),U_9848))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9845),U_9847),U_9846))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9845),U_9846)) ),
    inference(definitional_conversion,[status(esa)],[f_2695_2]) ).

cnf(f_2695_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_9845),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9845,tc_HOL_Obool)),U_9846),hAPP(hAPP(c_Set_Oinsert(U_9845),U_9847),U_9848))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_9845),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9845,tc_HOL_Obool)),U_9846),U_9848))),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | hBOOL(hAPP(hAPP(c_member(U_9845),U_9847),U_9848))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9845),U_9847),U_9846))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9845),U_9846)) ),
    inference(clausify,[status(thm)],[f_2695_3]) ).

fof(f_2696_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_2696_2,plain,
    ! [U_9851,U_9850,U_9849] :
      ( hAPP(c_Finite__Set_Ocard(U_9849),hAPP(hAPP(c_Set_Oinsert(U_9849),U_9851),U_9850)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_9849),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9849,tc_HOL_Obool)),U_9850),hAPP(hAPP(c_Set_Oinsert(U_9849),U_9851),c_Orderings_Obot__class_Obot(tc_fun(U_9849,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9849),U_9850)) ),
    inference(variable_rename,[status(thm)],[f_2696_1]) ).

fof(f_2696_3,plain,
    ! [U_9849,U_9850,U_9851] :
      ( hAPP(c_Finite__Set_Ocard(U_9849),hAPP(hAPP(c_Set_Oinsert(U_9849),U_9851),U_9850)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_9849),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9849,tc_HOL_Obool)),U_9850),hAPP(hAPP(c_Set_Oinsert(U_9849),U_9851),c_Orderings_Obot__class_Obot(tc_fun(U_9849,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9849),U_9850)) ),
    inference(definitional_conversion,[status(esa)],[f_2696_2]) ).

cnf(f_2696_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_9849),hAPP(hAPP(c_Set_Oinsert(U_9849),U_9851),U_9850)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(c_Finite__Set_Ocard(U_9849),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9849,tc_HOL_Obool)),U_9850),hAPP(hAPP(c_Set_Oinsert(U_9849),U_9851),c_Orderings_Obot__class_Obot(tc_fun(U_9849,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9849),U_9850)) ),
    inference(clausify,[status(thm)],[f_2696_3]) ).

fof(f_2697_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_2697_2,plain,
    ! [U_9854,U_9853,U_9852] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9852,tc_HOL_Obool),tc_fun(U_9852,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9852,tc_HOL_Obool),tc_fun(U_9852,tc_HOL_Obool)),U_9853),U_9854)),c_Wellfounded_Ofinite__psubset(U_9852)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9852),U_9854))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9852,tc_HOL_Obool)),U_9853),U_9854)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9852),U_9854))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9852,tc_HOL_Obool)),U_9853),U_9854)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9852,tc_HOL_Obool),tc_fun(U_9852,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9852,tc_HOL_Obool),tc_fun(U_9852,tc_HOL_Obool)),U_9853),U_9854)),c_Wellfounded_Ofinite__psubset(U_9852))) ) ),
    inference(variable_rename,[status(thm)],[f_2697_1]) ).

fof(f_2697_3,plain,
    ( ! [U_9860,U_9858,U_9856] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9856,tc_HOL_Obool),tc_fun(U_9856,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9856,tc_HOL_Obool),tc_fun(U_9856,tc_HOL_Obool)),U_9858),U_9860)),c_Wellfounded_Ofinite__psubset(U_9856)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9856),U_9860))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9856,tc_HOL_Obool)),U_9858),U_9860)) )
    & ! [U_9859,U_9857,U_9855] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9855),U_9859))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9855,tc_HOL_Obool)),U_9857),U_9859)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9855,tc_HOL_Obool),tc_fun(U_9855,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9855,tc_HOL_Obool),tc_fun(U_9855,tc_HOL_Obool)),U_9857),U_9859)),c_Wellfounded_Ofinite__psubset(U_9855))) ) ),
    inference(miniscope,[status(thm)],[f_2697_2]) ).

fof(f_2697_4,plain,
    ( ! [U_9857,U_9855,U_9859] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9855),U_9859))
        | ~ sP763(U_9857,U_9855,U_9859) )
    & ! [U_9857,U_9855,U_9859] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9855,tc_HOL_Obool)),U_9857),U_9859))
        | ~ sP763(U_9857,U_9855,U_9859) )
    & ! [U_9860,U_9856,U_9858] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9856,tc_HOL_Obool),tc_fun(U_9856,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9856,tc_HOL_Obool),tc_fun(U_9856,tc_HOL_Obool)),U_9858),U_9860)),c_Wellfounded_Ofinite__psubset(U_9856)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9856),U_9860))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9856,tc_HOL_Obool)),U_9858),U_9860)) )
    & ! [U_9857,U_9855,U_9859] :
        ( sP763(U_9857,U_9855,U_9859)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9855,tc_HOL_Obool),tc_fun(U_9855,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9855,tc_HOL_Obool),tc_fun(U_9855,tc_HOL_Obool)),U_9857),U_9859)),c_Wellfounded_Ofinite__psubset(U_9855))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP763])],[f_2697_3]) ).

cnf(f_2697_5,plain,
    ( sP763(U_9857,U_9855,U_9859)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9855,tc_HOL_Obool),tc_fun(U_9855,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9855,tc_HOL_Obool),tc_fun(U_9855,tc_HOL_Obool)),U_9857),U_9859)),c_Wellfounded_Ofinite__psubset(U_9855))) ),
    inference(clausify,[status(thm)],[f_2697_4]) ).

cnf(f_2697_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_9856,tc_HOL_Obool),tc_fun(U_9856,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_9856,tc_HOL_Obool),tc_fun(U_9856,tc_HOL_Obool)),U_9858),U_9860)),c_Wellfounded_Ofinite__psubset(U_9856)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9856),U_9860))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9856,tc_HOL_Obool)),U_9858),U_9860)) ),
    inference(clausify,[status(thm)],[f_2697_4]) ).

cnf(f_2697_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_9855,tc_HOL_Obool)),U_9857),U_9859))
    | ~ sP763(U_9857,U_9855,U_9859) ),
    inference(clausify,[status(thm)],[f_2697_4]) ).

cnf(f_2697_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_9855),U_9859))
    | ~ sP763(U_9857,U_9855,U_9859) ),
    inference(clausify,[status(thm)],[f_2697_4]) ).

fof(f_2698_1,plain,
    ! [V_Qa_2,V_Pa_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_Pa_2)),V_c0_2)),V_Qa_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_Pa_2,B_p)),hAPP(V_c0_2,B_p)),hAPP(V_Qa_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_2698_2,plain,
    ! [U_9870,U_9869,U_9868,U_9867,U_9866,U_9865,U_9864,U_9863,U_9862] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_9864,U_9865,hAPP(c_Set_Oimage(U_9862,tc_Hoare__Mirabelle_Otriple(U_9864),hAPP(hAPP(c_COMBS(U_9862,tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864)),hAPP(hAPP(c_COMBS(U_9862,tc_Com_Ocom,tc_fun(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864))),hAPP(hAPP(c_COMBB(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864))),U_9862),c_Hoare__Mirabelle_Otriple_Otriple(U_9864)),U_9869)),U_9867)),U_9870)),U_9863))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9864,U_9865,hAPP(c_Set_Oimage(U_9862,tc_Hoare__Mirabelle_Otriple(U_9864),hAPP(hAPP(c_COMBS(U_9862,tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864)),hAPP(hAPP(c_COMBS(U_9862,tc_Com_Ocom,tc_fun(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864))),hAPP(hAPP(c_COMBB(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864))),U_9862),c_Hoare__Mirabelle_Otriple_Otriple(U_9864)),U_9866)),U_9867)),U_9868)),U_9863))
      | ? [U_9861] :
          ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9864,U_9865,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9864)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9864),hAPP(U_9869,U_9861)),hAPP(U_9867,U_9861)),hAPP(U_9870,U_9861))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9864),tc_HOL_Obool))))
          & c_Hoare__Mirabelle_Ohoare__derivs(U_9864,U_9865,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9864)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9864),hAPP(U_9866,U_9861)),hAPP(U_9867,U_9861)),hAPP(U_9868,U_9861))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9864),tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9862),U_9863)) ),
    inference(variable_rename,[status(thm)],[f_2698_1]) ).

fof(f_2698_3,plain,
    ! [U_9870,U_9869,U_9868,U_9867,U_9866,U_9865,U_9864,U_9863,U_9862] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_9864,U_9865,hAPP(c_Set_Oimage(U_9862,tc_Hoare__Mirabelle_Otriple(U_9864),hAPP(hAPP(c_COMBS(U_9862,tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864)),hAPP(hAPP(c_COMBS(U_9862,tc_Com_Ocom,tc_fun(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864))),hAPP(hAPP(c_COMBB(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864))),U_9862),c_Hoare__Mirabelle_Otriple_Otriple(U_9864)),U_9869)),U_9867)),U_9870)),U_9863))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9864,U_9865,hAPP(c_Set_Oimage(U_9862,tc_Hoare__Mirabelle_Otriple(U_9864),hAPP(hAPP(c_COMBS(U_9862,tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864)),hAPP(hAPP(c_COMBS(U_9862,tc_Com_Ocom,tc_fun(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864))),hAPP(hAPP(c_COMBB(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864))),U_9862),c_Hoare__Mirabelle_Otriple_Otriple(U_9864)),U_9866)),U_9867)),U_9868)),U_9863))
      | ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9864,U_9865,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9864)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9864),hAPP(U_9869,sK157(U_9870,U_9869,U_9868,U_9867,U_9866,U_9865,U_9864,U_9863,U_9862))),hAPP(U_9867,sK157(U_9870,U_9869,U_9868,U_9867,U_9866,U_9865,U_9864,U_9863,U_9862))),hAPP(U_9870,sK157(U_9870,U_9869,U_9868,U_9867,U_9866,U_9865,U_9864,U_9863,U_9862)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9864),tc_HOL_Obool))))
        & c_Hoare__Mirabelle_Ohoare__derivs(U_9864,U_9865,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9864)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9864),hAPP(U_9866,sK157(U_9870,U_9869,U_9868,U_9867,U_9866,U_9865,U_9864,U_9863,U_9862))),hAPP(U_9867,sK157(U_9870,U_9869,U_9868,U_9867,U_9866,U_9865,U_9864,U_9863,U_9862))),hAPP(U_9868,sK157(U_9870,U_9869,U_9868,U_9867,U_9866,U_9865,U_9864,U_9863,U_9862)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9864),tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9862),U_9863)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK157]),skolemize(U_9861,sK157(U_9870,U_9869,U_9868,U_9867,U_9866,U_9865,U_9864,U_9863,U_9862))],[f_2698_2]) ).

fof(f_2698_4,plain,
    ( ! [U_9862,U_9863,U_9864,U_9865,U_9866,U_9867,U_9868,U_9869,U_9870] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9864,U_9865,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9864)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9864),hAPP(U_9869,sK157(U_9870,U_9869,U_9868,U_9867,U_9866,U_9865,U_9864,U_9863,U_9862))),hAPP(U_9867,sK157(U_9870,U_9869,U_9868,U_9867,U_9866,U_9865,U_9864,U_9863,U_9862))),hAPP(U_9870,sK157(U_9870,U_9869,U_9868,U_9867,U_9866,U_9865,U_9864,U_9863,U_9862)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9864),tc_HOL_Obool))))
        | ~ sP764(U_9862,U_9863,U_9864,U_9865,U_9866,U_9867,U_9868,U_9869,U_9870) )
    & ! [U_9862,U_9863,U_9864,U_9865,U_9866,U_9867,U_9868,U_9869,U_9870] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(U_9864,U_9865,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9864)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9864),hAPP(U_9866,sK157(U_9870,U_9869,U_9868,U_9867,U_9866,U_9865,U_9864,U_9863,U_9862))),hAPP(U_9867,sK157(U_9870,U_9869,U_9868,U_9867,U_9866,U_9865,U_9864,U_9863,U_9862))),hAPP(U_9868,sK157(U_9870,U_9869,U_9868,U_9867,U_9866,U_9865,U_9864,U_9863,U_9862)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9864),tc_HOL_Obool))))
        | ~ sP764(U_9862,U_9863,U_9864,U_9865,U_9866,U_9867,U_9868,U_9869,U_9870) )
    & ! [U_9862,U_9863,U_9864,U_9865,U_9866,U_9867,U_9868,U_9869,U_9870] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(U_9864,U_9865,hAPP(c_Set_Oimage(U_9862,tc_Hoare__Mirabelle_Otriple(U_9864),hAPP(hAPP(c_COMBS(U_9862,tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864)),hAPP(hAPP(c_COMBS(U_9862,tc_Com_Ocom,tc_fun(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864))),hAPP(hAPP(c_COMBB(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864))),U_9862),c_Hoare__Mirabelle_Otriple_Otriple(U_9864)),U_9869)),U_9867)),U_9870)),U_9863))
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9864,U_9865,hAPP(c_Set_Oimage(U_9862,tc_Hoare__Mirabelle_Otriple(U_9864),hAPP(hAPP(c_COMBS(U_9862,tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864)),hAPP(hAPP(c_COMBS(U_9862,tc_Com_Ocom,tc_fun(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864))),hAPP(hAPP(c_COMBB(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864))),U_9862),c_Hoare__Mirabelle_Otriple_Otriple(U_9864)),U_9866)),U_9867)),U_9868)),U_9863))
        | sP764(U_9862,U_9863,U_9864,U_9865,U_9866,U_9867,U_9868,U_9869,U_9870)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9862),U_9863)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP764])],[f_2698_3]) ).

cnf(f_2698_5,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_9864,U_9865,hAPP(c_Set_Oimage(U_9862,tc_Hoare__Mirabelle_Otriple(U_9864),hAPP(hAPP(c_COMBS(U_9862,tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864)),hAPP(hAPP(c_COMBS(U_9862,tc_Com_Ocom,tc_fun(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864))),hAPP(hAPP(c_COMBB(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864))),U_9862),c_Hoare__Mirabelle_Otriple_Otriple(U_9864)),U_9869)),U_9867)),U_9870)),U_9863))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9864,U_9865,hAPP(c_Set_Oimage(U_9862,tc_Hoare__Mirabelle_Otriple(U_9864),hAPP(hAPP(c_COMBS(U_9862,tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864)),hAPP(hAPP(c_COMBS(U_9862,tc_Com_Ocom,tc_fun(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864))),hAPP(hAPP(c_COMBB(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(U_9864,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Hoare__Mirabelle_Otriple(U_9864))),U_9862),c_Hoare__Mirabelle_Otriple_Otriple(U_9864)),U_9866)),U_9867)),U_9868)),U_9863))
    | sP764(U_9862,U_9863,U_9864,U_9865,U_9866,U_9867,U_9868,U_9869,U_9870)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9862),U_9863)) ),
    inference(clausify,[status(thm)],[f_2698_4]) ).

cnf(f_2698_6,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_9864,U_9865,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9864)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9864),hAPP(U_9866,sK157(U_9870,U_9869,U_9868,U_9867,U_9866,U_9865,U_9864,U_9863,U_9862))),hAPP(U_9867,sK157(U_9870,U_9869,U_9868,U_9867,U_9866,U_9865,U_9864,U_9863,U_9862))),hAPP(U_9868,sK157(U_9870,U_9869,U_9868,U_9867,U_9866,U_9865,U_9864,U_9863,U_9862)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9864),tc_HOL_Obool))))
    | ~ sP764(U_9862,U_9863,U_9864,U_9865,U_9866,U_9867,U_9868,U_9869,U_9870) ),
    inference(clausify,[status(thm)],[f_2698_4]) ).

cnf(f_2698_7,plain,
    ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_9864,U_9865,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_9864)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_9864),hAPP(U_9869,sK157(U_9870,U_9869,U_9868,U_9867,U_9866,U_9865,U_9864,U_9863,U_9862))),hAPP(U_9867,sK157(U_9870,U_9869,U_9868,U_9867,U_9866,U_9865,U_9864,U_9863,U_9862))),hAPP(U_9870,sK157(U_9870,U_9869,U_9868,U_9867,U_9866,U_9865,U_9864,U_9863,U_9862)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_9864),tc_HOL_Obool))))
    | ~ sP764(U_9862,U_9863,U_9864,U_9865,U_9866,U_9867,U_9868,U_9869,U_9870) ),
    inference(clausify,[status(thm)],[f_2698_4]) ).

fof(f_2699_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_2699_2,plain,
    ! [U_9878,U_9877,U_9876,U_9875,U_9874,U_9873,U_9872,U_9871] :
      ( hAPP(U_9876,U_9877) = hAPP(hAPP(U_9873,hAPP(U_9875,U_9878)),hAPP(U_9876,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9872,tc_HOL_Obool)),U_9877),hAPP(hAPP(c_Set_Oinsert(U_9872),U_9878),c_Orderings_Obot__class_Obot(tc_fun(U_9872,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9872),U_9878),U_9877))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9872),U_9877))
      | ~ c_Finite__Set_Ofolding__image__simple(U_9871,U_9872,U_9873,U_9874,U_9875,U_9876) ),
    inference(variable_rename,[status(thm)],[f_2699_1]) ).

fof(f_2699_3,plain,
    ! [U_9878,U_9877,U_9876,U_9875,U_9874,U_9873,U_9872] :
      ( ! [U_9871] : ~ c_Finite__Set_Ofolding__image__simple(U_9871,U_9872,U_9873,U_9874,U_9875,U_9876)
      | hAPP(U_9876,U_9877) = hAPP(hAPP(U_9873,hAPP(U_9875,U_9878)),hAPP(U_9876,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9872,tc_HOL_Obool)),U_9877),hAPP(hAPP(c_Set_Oinsert(U_9872),U_9878),c_Orderings_Obot__class_Obot(tc_fun(U_9872,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9872),U_9878),U_9877))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9872),U_9877)) ),
    inference(miniscope,[status(thm)],[f_2699_2]) ).

fof(f_2699_4,plain,
    ! [U_9875,U_9872,U_9873,U_9871,U_9874,U_9876,U_9877,U_9878] :
      ( ~ c_Finite__Set_Ofolding__image__simple(U_9871,U_9872,U_9873,U_9874,U_9875,U_9876)
      | hAPP(U_9876,U_9877) = hAPP(hAPP(U_9873,hAPP(U_9875,U_9878)),hAPP(U_9876,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9872,tc_HOL_Obool)),U_9877),hAPP(hAPP(c_Set_Oinsert(U_9872),U_9878),c_Orderings_Obot__class_Obot(tc_fun(U_9872,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9872),U_9878),U_9877))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9872),U_9877)) ),
    inference(definitional_conversion,[status(esa)],[f_2699_3]) ).

cnf(f_2699_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_9871,U_9872,U_9873,U_9874,U_9875,U_9876)
    | hAPP(U_9876,U_9877) = hAPP(hAPP(U_9873,hAPP(U_9875,U_9878)),hAPP(U_9876,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9872,tc_HOL_Obool)),U_9877),hAPP(hAPP(c_Set_Oinsert(U_9872),U_9878),c_Orderings_Obot__class_Obot(tc_fun(U_9872,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9872),U_9878),U_9877))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9872),U_9877)) ),
    inference(clausify,[status(thm)],[f_2699_4]) ).

fof(f_2700_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_2700_2,plain,
    ! [U_9883,U_9882,U_9881,U_9880,U_9879] :
      ( ( ( hAPP(U_9881,U_9882) = hAPP(hAPP(U_9880,U_9883),hAPP(U_9881,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9879,tc_HOL_Obool)),U_9882),hAPP(hAPP(c_Set_Oinsert(U_9879),U_9883),c_Orderings_Obot__class_Obot(tc_fun(U_9879,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9879,tc_HOL_Obool)),U_9882),hAPP(hAPP(c_Set_Oinsert(U_9879),U_9883),c_Orderings_Obot__class_Obot(tc_fun(U_9879,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9879,tc_HOL_Obool)) )
        & ( hAPP(U_9881,U_9882) = U_9883
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9879,tc_HOL_Obool)),U_9882),hAPP(hAPP(c_Set_Oinsert(U_9879),U_9883),c_Orderings_Obot__class_Obot(tc_fun(U_9879,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9879,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_9879),U_9883),U_9882))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9879),U_9882))
      | ~ c_Finite__Set_Ofolding__one(U_9879,U_9880,U_9881) ),
    inference(variable_rename,[status(thm)],[f_2700_1]) ).

fof(f_2700_3,plain,
    ( ! [U_9880,U_9879,U_9881,U_9882,U_9883] :
        ( hAPP(U_9881,U_9882) = hAPP(hAPP(U_9880,U_9883),hAPP(U_9881,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9879,tc_HOL_Obool)),U_9882),hAPP(hAPP(c_Set_Oinsert(U_9879),U_9883),c_Orderings_Obot__class_Obot(tc_fun(U_9879,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9879,tc_HOL_Obool)),U_9882),hAPP(hAPP(c_Set_Oinsert(U_9879),U_9883),c_Orderings_Obot__class_Obot(tc_fun(U_9879,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9879,tc_HOL_Obool))
        | ~ sP765(U_9880,U_9879,U_9881,U_9882,U_9883) )
    & ! [U_9880,U_9879,U_9881,U_9882,U_9883] :
        ( hAPP(U_9881,U_9882) = U_9883
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9879,tc_HOL_Obool)),U_9882),hAPP(hAPP(c_Set_Oinsert(U_9879),U_9883),c_Orderings_Obot__class_Obot(tc_fun(U_9879,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9879,tc_HOL_Obool))
        | ~ sP765(U_9880,U_9879,U_9881,U_9882,U_9883) )
    & ! [U_9880,U_9879,U_9881,U_9882,U_9883] :
        ( sP765(U_9880,U_9879,U_9881,U_9882,U_9883)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9879),U_9883),U_9882))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9879),U_9882))
        | ~ c_Finite__Set_Ofolding__one(U_9879,U_9880,U_9881) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP765])],[f_2700_2]) ).

cnf(f_2700_4,plain,
    ( sP765(U_9880,U_9879,U_9881,U_9882,U_9883)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9879),U_9883),U_9882))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9879),U_9882))
    | ~ c_Finite__Set_Ofolding__one(U_9879,U_9880,U_9881) ),
    inference(clausify,[status(thm)],[f_2700_3]) ).

cnf(f_2700_5,plain,
    ( hAPP(U_9881,U_9882) = U_9883
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9879,tc_HOL_Obool)),U_9882),hAPP(hAPP(c_Set_Oinsert(U_9879),U_9883),c_Orderings_Obot__class_Obot(tc_fun(U_9879,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9879,tc_HOL_Obool))
    | ~ sP765(U_9880,U_9879,U_9881,U_9882,U_9883) ),
    inference(clausify,[status(thm)],[f_2700_3]) ).

cnf(f_2700_6,plain,
    ( hAPP(U_9881,U_9882) = hAPP(hAPP(U_9880,U_9883),hAPP(U_9881,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9879,tc_HOL_Obool)),U_9882),hAPP(hAPP(c_Set_Oinsert(U_9879),U_9883),c_Orderings_Obot__class_Obot(tc_fun(U_9879,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9879,tc_HOL_Obool)),U_9882),hAPP(hAPP(c_Set_Oinsert(U_9879),U_9883),c_Orderings_Obot__class_Obot(tc_fun(U_9879,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9879,tc_HOL_Obool))
    | ~ sP765(U_9880,U_9879,U_9881,U_9882,U_9883) ),
    inference(clausify,[status(thm)],[f_2700_3]) ).

fof(f_2701_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_2701_2,plain,
    ! [U_9889,U_9888,U_9887,U_9886,U_9885,U_9884] :
      ( hAPP(U_9889,c_Orderings_Obot__class_Obot(tc_fun(U_9885,tc_HOL_Obool))) = U_9887
      | ~ c_Finite__Set_Ofolding__image__simple(U_9884,U_9885,U_9886,U_9887,U_9888,U_9889) ),
    inference(variable_rename,[status(thm)],[f_2701_1]) ).

fof(f_2701_3,plain,
    ! [U_9889,U_9888,U_9887,U_9886,U_9885] :
      ( ! [U_9884] : ~ c_Finite__Set_Ofolding__image__simple(U_9884,U_9885,U_9886,U_9887,U_9888,U_9889)
      | hAPP(U_9889,c_Orderings_Obot__class_Obot(tc_fun(U_9885,tc_HOL_Obool))) = U_9887 ),
    inference(miniscope,[status(thm)],[f_2701_2]) ).

fof(f_2701_4,plain,
    ! [U_9888,U_9887,U_9889,U_9885,U_9884,U_9886] :
      ( ~ c_Finite__Set_Ofolding__image__simple(U_9884,U_9885,U_9886,U_9887,U_9888,U_9889)
      | hAPP(U_9889,c_Orderings_Obot__class_Obot(tc_fun(U_9885,tc_HOL_Obool))) = U_9887 ),
    inference(definitional_conversion,[status(esa)],[f_2701_3]) ).

cnf(f_2701_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_9884,U_9885,U_9886,U_9887,U_9888,U_9889)
    | hAPP(U_9889,c_Orderings_Obot__class_Obot(tc_fun(U_9885,tc_HOL_Obool))) = U_9887 ),
    inference(clausify,[status(thm)],[f_2701_4]) ).

fof(f_2702_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_2702_2,plain,
    ! [U_9893,U_9892,U_9891,U_9890] :
      ( hAPP(U_9892,hAPP(hAPP(c_Set_Oinsert(U_9890),U_9893),c_Orderings_Obot__class_Obot(tc_fun(U_9890,tc_HOL_Obool)))) = U_9893
      | ~ c_Finite__Set_Ofolding__one(U_9890,U_9891,U_9892) ),
    inference(variable_rename,[status(thm)],[f_2702_1]) ).

fof(f_2702_3,plain,
    ! [U_9893,U_9892,U_9891,U_9890] :
      ( hAPP(U_9892,hAPP(hAPP(c_Set_Oinsert(U_9890),U_9893),c_Orderings_Obot__class_Obot(tc_fun(U_9890,tc_HOL_Obool)))) = U_9893
      | ~ c_Finite__Set_Ofolding__one(U_9890,U_9891,U_9892) ),
    inference(definitional_conversion,[status(esa)],[f_2702_2]) ).

cnf(f_2702_4,plain,
    ( hAPP(U_9892,hAPP(hAPP(c_Set_Oinsert(U_9890),U_9893),c_Orderings_Obot__class_Obot(tc_fun(U_9890,tc_HOL_Obool)))) = U_9893
    | ~ c_Finite__Set_Ofolding__one(U_9890,U_9891,U_9892) ),
    inference(clausify,[status(thm)],[f_2702_3]) ).

fof(f_2703_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_2703_2,plain,
    ! [U_9901,U_9900,U_9899,U_9898,U_9897,U_9896,U_9895,U_9894] :
      ( hAPP(U_9899,hAPP(hAPP(c_Set_Oinsert(U_9895),U_9901),U_9900)) = hAPP(hAPP(U_9896,hAPP(U_9898,U_9901)),hAPP(U_9899,U_9900))
      | hBOOL(hAPP(hAPP(c_member(U_9895),U_9901),U_9900))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9895),U_9900))
      | ~ c_Finite__Set_Ofolding__image__simple(U_9894,U_9895,U_9896,U_9897,U_9898,U_9899) ),
    inference(variable_rename,[status(thm)],[f_2703_1]) ).

fof(f_2703_3,plain,
    ! [U_9901,U_9900,U_9899,U_9898,U_9897,U_9896,U_9895] :
      ( ! [U_9894] : ~ c_Finite__Set_Ofolding__image__simple(U_9894,U_9895,U_9896,U_9897,U_9898,U_9899)
      | hAPP(U_9899,hAPP(hAPP(c_Set_Oinsert(U_9895),U_9901),U_9900)) = hAPP(hAPP(U_9896,hAPP(U_9898,U_9901)),hAPP(U_9899,U_9900))
      | hBOOL(hAPP(hAPP(c_member(U_9895),U_9901),U_9900))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9895),U_9900)) ),
    inference(miniscope,[status(thm)],[f_2703_2]) ).

fof(f_2703_4,plain,
    ! [U_9894,U_9895,U_9896,U_9897,U_9898,U_9899,U_9900,U_9901] :
      ( ~ c_Finite__Set_Ofolding__image__simple(U_9894,U_9895,U_9896,U_9897,U_9898,U_9899)
      | hAPP(U_9899,hAPP(hAPP(c_Set_Oinsert(U_9895),U_9901),U_9900)) = hAPP(hAPP(U_9896,hAPP(U_9898,U_9901)),hAPP(U_9899,U_9900))
      | hBOOL(hAPP(hAPP(c_member(U_9895),U_9901),U_9900))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9895),U_9900)) ),
    inference(definitional_conversion,[status(esa)],[f_2703_3]) ).

cnf(f_2703_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_9894,U_9895,U_9896,U_9897,U_9898,U_9899)
    | hAPP(U_9899,hAPP(hAPP(c_Set_Oinsert(U_9895),U_9901),U_9900)) = hAPP(hAPP(U_9896,hAPP(U_9898,U_9901)),hAPP(U_9899,U_9900))
    | hBOOL(hAPP(hAPP(c_member(U_9895),U_9901),U_9900))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9895),U_9900)) ),
    inference(clausify,[status(thm)],[f_2703_4]) ).

fof(f_2704_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_2704_2,plain,
    ! [U_9902] : c_Wellfounded_Owf(tc_fun(U_9902,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_9902)),
    inference(variable_rename,[status(thm)],[f_2704_1]) ).

fof(f_2704_3,plain,
    ! [U_9902] : c_Wellfounded_Owf(tc_fun(U_9902,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_9902)),
    inference(definitional_conversion,[status(esa)],[f_2704_2]) ).

cnf(f_2704_4,plain,
    c_Wellfounded_Owf(tc_fun(U_9902,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(U_9902)),
    inference(clausify,[status(thm)],[f_2704_3]) ).

fof(f_2705_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_2705_2,plain,
    ! [U_9907,U_9906,U_9905,U_9904,U_9903] :
      ( hAPP(U_9905,hAPP(hAPP(c_Set_Oinsert(U_9903),U_9907),U_9906)) = hAPP(hAPP(U_9904,U_9907),hAPP(U_9905,U_9906))
      | U_9906 = c_Orderings_Obot__class_Obot(tc_fun(U_9903,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9903),U_9907),U_9906))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9903),U_9906))
      | ~ c_Finite__Set_Ofolding__one(U_9903,U_9904,U_9905) ),
    inference(variable_rename,[status(thm)],[f_2705_1]) ).

fof(f_2705_3,plain,
    ! [U_9903,U_9904,U_9905,U_9906,U_9907] :
      ( hAPP(U_9905,hAPP(hAPP(c_Set_Oinsert(U_9903),U_9907),U_9906)) = hAPP(hAPP(U_9904,U_9907),hAPP(U_9905,U_9906))
      | U_9906 = c_Orderings_Obot__class_Obot(tc_fun(U_9903,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9903),U_9907),U_9906))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9903),U_9906))
      | ~ c_Finite__Set_Ofolding__one(U_9903,U_9904,U_9905) ),
    inference(definitional_conversion,[status(esa)],[f_2705_2]) ).

cnf(f_2705_4,plain,
    ( hAPP(U_9905,hAPP(hAPP(c_Set_Oinsert(U_9903),U_9907),U_9906)) = hAPP(hAPP(U_9904,U_9907),hAPP(U_9905,U_9906))
    | U_9906 = c_Orderings_Obot__class_Obot(tc_fun(U_9903,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_9903),U_9907),U_9906))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9903),U_9906))
    | ~ c_Finite__Set_Ofolding__one(U_9903,U_9904,U_9905) ),
    inference(clausify,[status(thm)],[f_2705_3]) ).

fof(f_2706_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_2706_2,plain,
    ! [U_9915,U_9914,U_9913,U_9912,U_9911,U_9910,U_9909,U_9908] :
      ( hAPP(U_9913,hAPP(hAPP(c_Set_Oinsert(U_9909),U_9915),U_9914)) = hAPP(hAPP(U_9910,hAPP(U_9912,U_9915)),hAPP(U_9913,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9909,tc_HOL_Obool)),U_9914),hAPP(hAPP(c_Set_Oinsert(U_9909),U_9915),c_Orderings_Obot__class_Obot(tc_fun(U_9909,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9909),U_9914))
      | ~ c_Finite__Set_Ofolding__image__simple(U_9908,U_9909,U_9910,U_9911,U_9912,U_9913) ),
    inference(variable_rename,[status(thm)],[f_2706_1]) ).

fof(f_2706_3,plain,
    ! [U_9915,U_9914,U_9913,U_9912,U_9911,U_9910,U_9909] :
      ( ! [U_9908] : ~ c_Finite__Set_Ofolding__image__simple(U_9908,U_9909,U_9910,U_9911,U_9912,U_9913)
      | hAPP(U_9913,hAPP(hAPP(c_Set_Oinsert(U_9909),U_9915),U_9914)) = hAPP(hAPP(U_9910,hAPP(U_9912,U_9915)),hAPP(U_9913,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9909,tc_HOL_Obool)),U_9914),hAPP(hAPP(c_Set_Oinsert(U_9909),U_9915),c_Orderings_Obot__class_Obot(tc_fun(U_9909,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9909),U_9914)) ),
    inference(miniscope,[status(thm)],[f_2706_2]) ).

fof(f_2706_4,plain,
    ! [U_9909,U_9908,U_9910,U_9911,U_9912,U_9913,U_9914,U_9915] :
      ( ~ c_Finite__Set_Ofolding__image__simple(U_9908,U_9909,U_9910,U_9911,U_9912,U_9913)
      | hAPP(U_9913,hAPP(hAPP(c_Set_Oinsert(U_9909),U_9915),U_9914)) = hAPP(hAPP(U_9910,hAPP(U_9912,U_9915)),hAPP(U_9913,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9909,tc_HOL_Obool)),U_9914),hAPP(hAPP(c_Set_Oinsert(U_9909),U_9915),c_Orderings_Obot__class_Obot(tc_fun(U_9909,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9909),U_9914)) ),
    inference(definitional_conversion,[status(esa)],[f_2706_3]) ).

cnf(f_2706_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_9908,U_9909,U_9910,U_9911,U_9912,U_9913)
    | hAPP(U_9913,hAPP(hAPP(c_Set_Oinsert(U_9909),U_9915),U_9914)) = hAPP(hAPP(U_9910,hAPP(U_9912,U_9915)),hAPP(U_9913,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9909,tc_HOL_Obool)),U_9914),hAPP(hAPP(c_Set_Oinsert(U_9909),U_9915),c_Orderings_Obot__class_Obot(tc_fun(U_9909,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9909),U_9914)) ),
    inference(clausify,[status(thm)],[f_2706_4]) ).

fof(f_2707_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_2707_2,plain,
    ! [U_9920,U_9919,U_9918,U_9917,U_9916] :
      ( ( ( hAPP(U_9918,hAPP(hAPP(c_Set_Oinsert(U_9916),U_9920),U_9919)) = hAPP(hAPP(U_9917,U_9920),hAPP(U_9918,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9916,tc_HOL_Obool)),U_9919),hAPP(hAPP(c_Set_Oinsert(U_9916),U_9920),c_Orderings_Obot__class_Obot(tc_fun(U_9916,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9916,tc_HOL_Obool)),U_9919),hAPP(hAPP(c_Set_Oinsert(U_9916),U_9920),c_Orderings_Obot__class_Obot(tc_fun(U_9916,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9916,tc_HOL_Obool)) )
        & ( hAPP(U_9918,hAPP(hAPP(c_Set_Oinsert(U_9916),U_9920),U_9919)) = U_9920
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9916,tc_HOL_Obool)),U_9919),hAPP(hAPP(c_Set_Oinsert(U_9916),U_9920),c_Orderings_Obot__class_Obot(tc_fun(U_9916,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9916,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9916),U_9919))
      | ~ c_Finite__Set_Ofolding__one(U_9916,U_9917,U_9918) ),
    inference(variable_rename,[status(thm)],[f_2707_1]) ).

fof(f_2707_3,plain,
    ( ! [U_9916,U_9917,U_9918,U_9919,U_9920] :
        ( hAPP(U_9918,hAPP(hAPP(c_Set_Oinsert(U_9916),U_9920),U_9919)) = hAPP(hAPP(U_9917,U_9920),hAPP(U_9918,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9916,tc_HOL_Obool)),U_9919),hAPP(hAPP(c_Set_Oinsert(U_9916),U_9920),c_Orderings_Obot__class_Obot(tc_fun(U_9916,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9916,tc_HOL_Obool)),U_9919),hAPP(hAPP(c_Set_Oinsert(U_9916),U_9920),c_Orderings_Obot__class_Obot(tc_fun(U_9916,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9916,tc_HOL_Obool))
        | ~ sP766(U_9916,U_9917,U_9918,U_9919,U_9920) )
    & ! [U_9916,U_9917,U_9918,U_9919,U_9920] :
        ( hAPP(U_9918,hAPP(hAPP(c_Set_Oinsert(U_9916),U_9920),U_9919)) = U_9920
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9916,tc_HOL_Obool)),U_9919),hAPP(hAPP(c_Set_Oinsert(U_9916),U_9920),c_Orderings_Obot__class_Obot(tc_fun(U_9916,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9916,tc_HOL_Obool))
        | ~ sP766(U_9916,U_9917,U_9918,U_9919,U_9920) )
    & ! [U_9916,U_9917,U_9918,U_9919,U_9920] :
        ( sP766(U_9916,U_9917,U_9918,U_9919,U_9920)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9916),U_9919))
        | ~ c_Finite__Set_Ofolding__one(U_9916,U_9917,U_9918) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP766])],[f_2707_2]) ).

cnf(f_2707_4,plain,
    ( sP766(U_9916,U_9917,U_9918,U_9919,U_9920)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9916),U_9919))
    | ~ c_Finite__Set_Ofolding__one(U_9916,U_9917,U_9918) ),
    inference(clausify,[status(thm)],[f_2707_3]) ).

cnf(f_2707_5,plain,
    ( hAPP(U_9918,hAPP(hAPP(c_Set_Oinsert(U_9916),U_9920),U_9919)) = U_9920
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9916,tc_HOL_Obool)),U_9919),hAPP(hAPP(c_Set_Oinsert(U_9916),U_9920),c_Orderings_Obot__class_Obot(tc_fun(U_9916,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9916,tc_HOL_Obool))
    | ~ sP766(U_9916,U_9917,U_9918,U_9919,U_9920) ),
    inference(clausify,[status(thm)],[f_2707_3]) ).

cnf(f_2707_6,plain,
    ( hAPP(U_9918,hAPP(hAPP(c_Set_Oinsert(U_9916),U_9920),U_9919)) = hAPP(hAPP(U_9917,U_9920),hAPP(U_9918,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9916,tc_HOL_Obool)),U_9919),hAPP(hAPP(c_Set_Oinsert(U_9916),U_9920),c_Orderings_Obot__class_Obot(tc_fun(U_9916,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9916,tc_HOL_Obool)),U_9919),hAPP(hAPP(c_Set_Oinsert(U_9916),U_9920),c_Orderings_Obot__class_Obot(tc_fun(U_9916,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9916,tc_HOL_Obool))
    | ~ sP766(U_9916,U_9917,U_9918,U_9919,U_9920) ),
    inference(clausify,[status(thm)],[f_2707_3]) ).

fof(f_2708_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_2708_2,plain,
    ! [U_9921] : c_Wellfounded_Ofinite__psubset(U_9921) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_9921,tc_HOL_Obool),tc_fun(U_9921,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_9921,tc_HOL_Obool),tc_fun(U_9921,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_9921,tc_HOL_Obool),tc_fun(tc_fun(U_9921,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9921,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9921,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_9921,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9921,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_9921,tc_HOL_Obool)),c_COMBS(tc_fun(U_9921,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9921,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9921,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_9921,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_9921,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_9921,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_9921)))),
    inference(variable_rename,[status(thm)],[f_2708_1]) ).

fof(f_2708_3,plain,
    ! [U_9921] : c_Wellfounded_Ofinite__psubset(U_9921) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_9921,tc_HOL_Obool),tc_fun(U_9921,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_9921,tc_HOL_Obool),tc_fun(U_9921,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_9921,tc_HOL_Obool),tc_fun(tc_fun(U_9921,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9921,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9921,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_9921,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9921,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_9921,tc_HOL_Obool)),c_COMBS(tc_fun(U_9921,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9921,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9921,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_9921,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_9921,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_9921,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_9921)))),
    inference(definitional_conversion,[status(esa)],[f_2708_2]) ).

cnf(f_2708_4,plain,
    c_Wellfounded_Ofinite__psubset(U_9921) = hAPP(c_Set_OCollect(tc_prod(tc_fun(U_9921,tc_HOL_Obool),tc_fun(U_9921,tc_HOL_Obool))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_fun(U_9921,tc_HOL_Obool),tc_fun(U_9921,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_fun(U_9921,tc_HOL_Obool),tc_fun(tc_fun(U_9921,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9921,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9921,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_9921,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9921,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_9921,tc_HOL_Obool)),c_COMBS(tc_fun(U_9921,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9921,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_9921,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_9921,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_9921,tc_HOL_Obool)),c_fconj)),c_Orderings_Oord__class_Oless(tc_fun(U_9921,tc_HOL_Obool))))),c_Finite__Set_Ofinite(U_9921)))),
    inference(clausify,[status(thm)],[f_2708_3]) ).

fof(f_2709_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_2709_2,plain,
    ! [U_9923,U_9922] :
      ( ( c_Nitpick_Owf_H(U_9922,U_9923)
        | ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
          & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9922,U_9922)),U_9923)) )
        | ~ c_Wellfounded_Oacyclic(U_9922,U_9923) )
      & ( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
            | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9922,U_9922)),U_9923)) )
          & c_Wellfounded_Oacyclic(U_9922,U_9923) )
        | ~ c_Nitpick_Owf_H(U_9922,U_9923) ) ),
    inference(variable_rename,[status(thm)],[f_2709_1]) ).

fof(f_2709_3,plain,
    ( ! [U_9927,U_9925] :
        ( c_Nitpick_Owf_H(U_9925,U_9927)
        | ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
          & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9925,U_9925)),U_9927)) )
        | ~ c_Wellfounded_Oacyclic(U_9925,U_9927) )
    & ! [U_9926,U_9924] :
        ( ( ( c_Nitpick_Ounknown(tc_HOL_Obool)
            | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9924,U_9924)),U_9926)) )
          & c_Wellfounded_Oacyclic(U_9924,U_9926) )
        | ~ c_Nitpick_Owf_H(U_9924,U_9926) ) ),
    inference(miniscope,[status(thm)],[f_2709_2]) ).

fof(f_2709_4,plain,
    ( ! [U_9927,U_9925] :
        ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
        | ~ sP768(U_9927,U_9925) )
    & ! [U_9927,U_9925] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9925,U_9925)),U_9927))
        | ~ sP768(U_9927,U_9925) )
    & ! [U_9924,U_9926] :
        ( c_Nitpick_Ounknown(tc_HOL_Obool)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9924,U_9924)),U_9926))
        | ~ sP767(U_9924,U_9926) )
    & ! [U_9924,U_9926] :
        ( c_Wellfounded_Oacyclic(U_9924,U_9926)
        | ~ sP767(U_9924,U_9926) )
    & ! [U_9927,U_9925] :
        ( c_Nitpick_Owf_H(U_9925,U_9927)
        | sP768(U_9927,U_9925)
        | ~ c_Wellfounded_Oacyclic(U_9925,U_9927) )
    & ! [U_9924,U_9926] :
        ( sP767(U_9924,U_9926)
        | ~ c_Nitpick_Owf_H(U_9924,U_9926) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP767,sP768])],[f_2709_3]) ).

cnf(f_2709_5,plain,
    ( sP767(U_9924,U_9926)
    | ~ c_Nitpick_Owf_H(U_9924,U_9926) ),
    inference(clausify,[status(thm)],[f_2709_4]) ).

cnf(f_2709_6,plain,
    ( c_Nitpick_Owf_H(U_9925,U_9927)
    | sP768(U_9927,U_9925)
    | ~ c_Wellfounded_Oacyclic(U_9925,U_9927) ),
    inference(clausify,[status(thm)],[f_2709_4]) ).

cnf(f_2709_7,plain,
    ( c_Wellfounded_Oacyclic(U_9924,U_9926)
    | ~ sP767(U_9924,U_9926) ),
    inference(clausify,[status(thm)],[f_2709_4]) ).

cnf(f_2709_8,plain,
    ( c_Nitpick_Ounknown(tc_HOL_Obool)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9924,U_9924)),U_9926))
    | ~ sP767(U_9924,U_9926) ),
    inference(clausify,[status(thm)],[f_2709_4]) ).

cnf(f_2709_9,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_9925,U_9925)),U_9927))
    | ~ sP768(U_9927,U_9925) ),
    inference(clausify,[status(thm)],[f_2709_4]) ).

cnf(f_2709_10,plain,
    ( ~ c_Nitpick_Ounknown(tc_HOL_Obool)
    | ~ sP768(U_9927,U_9925) ),
    inference(clausify,[status(thm)],[f_2709_4]) ).

fof(f_2710_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_2710_2,plain,
    ! [U_9930,U_9929,U_9928] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9928),c_Big__Operators_Olattice_OSup__fin(U_9928,c_Orderings_Oord__class_Omax(U_9928),U_9929)),c_Big__Operators_Olattice_OSup__fin(U_9928,c_Orderings_Oord__class_Omax(U_9928),U_9930)) = c_Big__Operators_Olattice_OSup__fin(U_9928,c_Orderings_Oord__class_Omax(U_9928),hAPP(c_Set_OCollect(U_9928),hAPP(hAPP(c_COMBB(tc_fun(U_9928,tc_HOL_Obool),tc_HOL_Obool,U_9928),c_HOL_OEx(U_9928)),hAPP(hAPP(c_COMBB(tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool)),tc_fun(U_9928,tc_HOL_Obool),U_9928),hAPP(c_COMBB(tc_fun(U_9928,tc_HOL_Obool),tc_HOL_Obool,U_9928),c_HOL_OEx(U_9928))),hAPP(hAPP(c_COMBC(U_9928,tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool)),tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9928,tc_fun(tc_fun(U_9928,tc_HOL_Obool),tc_fun(U_9928,tc_HOL_Obool))),tc_fun(tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool)),tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool))),U_9928),c_COMBS(U_9928,tc_fun(U_9928,tc_HOL_Obool),tc_fun(U_9928,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9928,tc_fun(U_9928,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9928,tc_fun(tc_fun(U_9928,tc_HOL_Obool),tc_fun(U_9928,tc_HOL_Obool))),U_9928),hAPP(c_COMBB(tc_fun(U_9928,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9928,tc_HOL_Obool),tc_fun(U_9928,tc_HOL_Obool)),U_9928),c_COMBS(U_9928,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool)),tc_fun(U_9928,tc_fun(U_9928,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9928),hAPP(c_COMBB(tc_fun(U_9928,tc_HOL_Obool),tc_fun(U_9928,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9928),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9928),c_fconj))),hAPP(hAPP(c_COMBC(U_9928,tc_fun(U_9928,tc_fun(U_9928,U_9928)),tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9928,U_9928),tc_fun(U_9928,tc_HOL_Obool)),tc_fun(tc_fun(U_9928,tc_fun(U_9928,U_9928)),tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool))),U_9928),c_COMBB(tc_fun(U_9928,U_9928),tc_fun(U_9928,tc_HOL_Obool),U_9928)),hAPP(hAPP(c_COMBB(tc_fun(U_9928,tc_HOL_Obool),tc_fun(tc_fun(U_9928,U_9928),tc_fun(U_9928,tc_HOL_Obool)),U_9928),c_COMBB(U_9928,tc_HOL_Obool,U_9928)),c_fequal))),c_Orderings_Oord__class_Omin(U_9928)))))),hAPP(hAPP(c_COMBC(U_9928,tc_fun(U_9928,tc_HOL_Obool),tc_fun(U_9928,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9928,tc_HOL_Obool),tc_fun(U_9928,tc_HOL_Obool)),U_9928),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9928)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9928),c_fconj),hAPP(hAPP(c_COMBC(U_9928,tc_fun(U_9928,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9928)),U_9929)))),hAPP(hAPP(c_COMBC(U_9928,tc_fun(U_9928,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9928)),U_9930)))))))
      | U_9930 = c_Orderings_Obot__class_Obot(tc_fun(U_9928,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9928),U_9930))
      | U_9929 = c_Orderings_Obot__class_Obot(tc_fun(U_9928,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9928),U_9929))
      | ~ class_Orderings_Olinorder(U_9928) ),
    inference(variable_rename,[status(thm)],[f_2710_1]) ).

fof(f_2710_3,plain,
    ! [U_9928,U_9929,U_9930] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9928),c_Big__Operators_Olattice_OSup__fin(U_9928,c_Orderings_Oord__class_Omax(U_9928),U_9929)),c_Big__Operators_Olattice_OSup__fin(U_9928,c_Orderings_Oord__class_Omax(U_9928),U_9930)) = c_Big__Operators_Olattice_OSup__fin(U_9928,c_Orderings_Oord__class_Omax(U_9928),hAPP(c_Set_OCollect(U_9928),hAPP(hAPP(c_COMBB(tc_fun(U_9928,tc_HOL_Obool),tc_HOL_Obool,U_9928),c_HOL_OEx(U_9928)),hAPP(hAPP(c_COMBB(tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool)),tc_fun(U_9928,tc_HOL_Obool),U_9928),hAPP(c_COMBB(tc_fun(U_9928,tc_HOL_Obool),tc_HOL_Obool,U_9928),c_HOL_OEx(U_9928))),hAPP(hAPP(c_COMBC(U_9928,tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool)),tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9928,tc_fun(tc_fun(U_9928,tc_HOL_Obool),tc_fun(U_9928,tc_HOL_Obool))),tc_fun(tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool)),tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool))),U_9928),c_COMBS(U_9928,tc_fun(U_9928,tc_HOL_Obool),tc_fun(U_9928,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9928,tc_fun(U_9928,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9928,tc_fun(tc_fun(U_9928,tc_HOL_Obool),tc_fun(U_9928,tc_HOL_Obool))),U_9928),hAPP(c_COMBB(tc_fun(U_9928,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9928,tc_HOL_Obool),tc_fun(U_9928,tc_HOL_Obool)),U_9928),c_COMBS(U_9928,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool)),tc_fun(U_9928,tc_fun(U_9928,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9928),hAPP(c_COMBB(tc_fun(U_9928,tc_HOL_Obool),tc_fun(U_9928,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9928),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9928),c_fconj))),hAPP(hAPP(c_COMBC(U_9928,tc_fun(U_9928,tc_fun(U_9928,U_9928)),tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9928,U_9928),tc_fun(U_9928,tc_HOL_Obool)),tc_fun(tc_fun(U_9928,tc_fun(U_9928,U_9928)),tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool))),U_9928),c_COMBB(tc_fun(U_9928,U_9928),tc_fun(U_9928,tc_HOL_Obool),U_9928)),hAPP(hAPP(c_COMBB(tc_fun(U_9928,tc_HOL_Obool),tc_fun(tc_fun(U_9928,U_9928),tc_fun(U_9928,tc_HOL_Obool)),U_9928),c_COMBB(U_9928,tc_HOL_Obool,U_9928)),c_fequal))),c_Orderings_Oord__class_Omin(U_9928)))))),hAPP(hAPP(c_COMBC(U_9928,tc_fun(U_9928,tc_HOL_Obool),tc_fun(U_9928,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9928,tc_HOL_Obool),tc_fun(U_9928,tc_HOL_Obool)),U_9928),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9928)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9928),c_fconj),hAPP(hAPP(c_COMBC(U_9928,tc_fun(U_9928,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9928)),U_9929)))),hAPP(hAPP(c_COMBC(U_9928,tc_fun(U_9928,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9928)),U_9930)))))))
      | U_9930 = c_Orderings_Obot__class_Obot(tc_fun(U_9928,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9928),U_9930))
      | U_9929 = c_Orderings_Obot__class_Obot(tc_fun(U_9928,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9928),U_9929))
      | ~ class_Orderings_Olinorder(U_9928) ),
    inference(definitional_conversion,[status(esa)],[f_2710_2]) ).

cnf(f_2710_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9928),c_Big__Operators_Olattice_OSup__fin(U_9928,c_Orderings_Oord__class_Omax(U_9928),U_9929)),c_Big__Operators_Olattice_OSup__fin(U_9928,c_Orderings_Oord__class_Omax(U_9928),U_9930)) = c_Big__Operators_Olattice_OSup__fin(U_9928,c_Orderings_Oord__class_Omax(U_9928),hAPP(c_Set_OCollect(U_9928),hAPP(hAPP(c_COMBB(tc_fun(U_9928,tc_HOL_Obool),tc_HOL_Obool,U_9928),c_HOL_OEx(U_9928)),hAPP(hAPP(c_COMBB(tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool)),tc_fun(U_9928,tc_HOL_Obool),U_9928),hAPP(c_COMBB(tc_fun(U_9928,tc_HOL_Obool),tc_HOL_Obool,U_9928),c_HOL_OEx(U_9928))),hAPP(hAPP(c_COMBC(U_9928,tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool)),tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9928,tc_fun(tc_fun(U_9928,tc_HOL_Obool),tc_fun(U_9928,tc_HOL_Obool))),tc_fun(tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool)),tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool))),U_9928),c_COMBS(U_9928,tc_fun(U_9928,tc_HOL_Obool),tc_fun(U_9928,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9928,tc_fun(U_9928,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9928,tc_fun(tc_fun(U_9928,tc_HOL_Obool),tc_fun(U_9928,tc_HOL_Obool))),U_9928),hAPP(c_COMBB(tc_fun(U_9928,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9928,tc_HOL_Obool),tc_fun(U_9928,tc_HOL_Obool)),U_9928),c_COMBS(U_9928,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool)),tc_fun(U_9928,tc_fun(U_9928,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9928),hAPP(c_COMBB(tc_fun(U_9928,tc_HOL_Obool),tc_fun(U_9928,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9928),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9928),c_fconj))),hAPP(hAPP(c_COMBC(U_9928,tc_fun(U_9928,tc_fun(U_9928,U_9928)),tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9928,U_9928),tc_fun(U_9928,tc_HOL_Obool)),tc_fun(tc_fun(U_9928,tc_fun(U_9928,U_9928)),tc_fun(U_9928,tc_fun(U_9928,tc_HOL_Obool))),U_9928),c_COMBB(tc_fun(U_9928,U_9928),tc_fun(U_9928,tc_HOL_Obool),U_9928)),hAPP(hAPP(c_COMBB(tc_fun(U_9928,tc_HOL_Obool),tc_fun(tc_fun(U_9928,U_9928),tc_fun(U_9928,tc_HOL_Obool)),U_9928),c_COMBB(U_9928,tc_HOL_Obool,U_9928)),c_fequal))),c_Orderings_Oord__class_Omin(U_9928)))))),hAPP(hAPP(c_COMBC(U_9928,tc_fun(U_9928,tc_HOL_Obool),tc_fun(U_9928,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9928,tc_HOL_Obool),tc_fun(U_9928,tc_HOL_Obool)),U_9928),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9928)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9928),c_fconj),hAPP(hAPP(c_COMBC(U_9928,tc_fun(U_9928,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9928)),U_9929)))),hAPP(hAPP(c_COMBC(U_9928,tc_fun(U_9928,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9928)),U_9930)))))))
    | U_9930 = c_Orderings_Obot__class_Obot(tc_fun(U_9928,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9928),U_9930))
    | U_9929 = c_Orderings_Obot__class_Obot(tc_fun(U_9928,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9928),U_9929))
    | ~ class_Orderings_Olinorder(U_9928) ),
    inference(clausify,[status(thm)],[f_2710_3]) ).

fof(f_2711_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_2711_2,plain,
    ! [U_9933,U_9932,U_9931] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9931),c_Big__Operators_Olattice_OInf__fin(U_9931,c_Orderings_Oord__class_Omin(U_9931),U_9932)),c_Big__Operators_Olattice_OInf__fin(U_9931,c_Orderings_Oord__class_Omin(U_9931),U_9933)) = c_Big__Operators_Olattice_OInf__fin(U_9931,c_Orderings_Oord__class_Omin(U_9931),hAPP(c_Set_OCollect(U_9931),hAPP(hAPP(c_COMBB(tc_fun(U_9931,tc_HOL_Obool),tc_HOL_Obool,U_9931),c_HOL_OEx(U_9931)),hAPP(hAPP(c_COMBB(tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool)),tc_fun(U_9931,tc_HOL_Obool),U_9931),hAPP(c_COMBB(tc_fun(U_9931,tc_HOL_Obool),tc_HOL_Obool,U_9931),c_HOL_OEx(U_9931))),hAPP(hAPP(c_COMBC(U_9931,tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool)),tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9931,tc_fun(tc_fun(U_9931,tc_HOL_Obool),tc_fun(U_9931,tc_HOL_Obool))),tc_fun(tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool)),tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool))),U_9931),c_COMBS(U_9931,tc_fun(U_9931,tc_HOL_Obool),tc_fun(U_9931,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9931,tc_fun(U_9931,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9931,tc_fun(tc_fun(U_9931,tc_HOL_Obool),tc_fun(U_9931,tc_HOL_Obool))),U_9931),hAPP(c_COMBB(tc_fun(U_9931,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9931,tc_HOL_Obool),tc_fun(U_9931,tc_HOL_Obool)),U_9931),c_COMBS(U_9931,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool)),tc_fun(U_9931,tc_fun(U_9931,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9931),hAPP(c_COMBB(tc_fun(U_9931,tc_HOL_Obool),tc_fun(U_9931,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9931),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9931),c_fconj))),hAPP(hAPP(c_COMBC(U_9931,tc_fun(U_9931,tc_fun(U_9931,U_9931)),tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9931,U_9931),tc_fun(U_9931,tc_HOL_Obool)),tc_fun(tc_fun(U_9931,tc_fun(U_9931,U_9931)),tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool))),U_9931),c_COMBB(tc_fun(U_9931,U_9931),tc_fun(U_9931,tc_HOL_Obool),U_9931)),hAPP(hAPP(c_COMBB(tc_fun(U_9931,tc_HOL_Obool),tc_fun(tc_fun(U_9931,U_9931),tc_fun(U_9931,tc_HOL_Obool)),U_9931),c_COMBB(U_9931,tc_HOL_Obool,U_9931)),c_fequal))),c_Orderings_Oord__class_Omax(U_9931)))))),hAPP(hAPP(c_COMBC(U_9931,tc_fun(U_9931,tc_HOL_Obool),tc_fun(U_9931,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9931,tc_HOL_Obool),tc_fun(U_9931,tc_HOL_Obool)),U_9931),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9931)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9931),c_fconj),hAPP(hAPP(c_COMBC(U_9931,tc_fun(U_9931,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9931)),U_9932)))),hAPP(hAPP(c_COMBC(U_9931,tc_fun(U_9931,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9931)),U_9933)))))))
      | U_9933 = c_Orderings_Obot__class_Obot(tc_fun(U_9931,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9931),U_9933))
      | U_9932 = c_Orderings_Obot__class_Obot(tc_fun(U_9931,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9931),U_9932))
      | ~ class_Orderings_Olinorder(U_9931) ),
    inference(variable_rename,[status(thm)],[f_2711_1]) ).

fof(f_2711_3,plain,
    ! [U_9931,U_9932,U_9933] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9931),c_Big__Operators_Olattice_OInf__fin(U_9931,c_Orderings_Oord__class_Omin(U_9931),U_9932)),c_Big__Operators_Olattice_OInf__fin(U_9931,c_Orderings_Oord__class_Omin(U_9931),U_9933)) = c_Big__Operators_Olattice_OInf__fin(U_9931,c_Orderings_Oord__class_Omin(U_9931),hAPP(c_Set_OCollect(U_9931),hAPP(hAPP(c_COMBB(tc_fun(U_9931,tc_HOL_Obool),tc_HOL_Obool,U_9931),c_HOL_OEx(U_9931)),hAPP(hAPP(c_COMBB(tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool)),tc_fun(U_9931,tc_HOL_Obool),U_9931),hAPP(c_COMBB(tc_fun(U_9931,tc_HOL_Obool),tc_HOL_Obool,U_9931),c_HOL_OEx(U_9931))),hAPP(hAPP(c_COMBC(U_9931,tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool)),tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9931,tc_fun(tc_fun(U_9931,tc_HOL_Obool),tc_fun(U_9931,tc_HOL_Obool))),tc_fun(tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool)),tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool))),U_9931),c_COMBS(U_9931,tc_fun(U_9931,tc_HOL_Obool),tc_fun(U_9931,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9931,tc_fun(U_9931,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9931,tc_fun(tc_fun(U_9931,tc_HOL_Obool),tc_fun(U_9931,tc_HOL_Obool))),U_9931),hAPP(c_COMBB(tc_fun(U_9931,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9931,tc_HOL_Obool),tc_fun(U_9931,tc_HOL_Obool)),U_9931),c_COMBS(U_9931,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool)),tc_fun(U_9931,tc_fun(U_9931,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9931),hAPP(c_COMBB(tc_fun(U_9931,tc_HOL_Obool),tc_fun(U_9931,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9931),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9931),c_fconj))),hAPP(hAPP(c_COMBC(U_9931,tc_fun(U_9931,tc_fun(U_9931,U_9931)),tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9931,U_9931),tc_fun(U_9931,tc_HOL_Obool)),tc_fun(tc_fun(U_9931,tc_fun(U_9931,U_9931)),tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool))),U_9931),c_COMBB(tc_fun(U_9931,U_9931),tc_fun(U_9931,tc_HOL_Obool),U_9931)),hAPP(hAPP(c_COMBB(tc_fun(U_9931,tc_HOL_Obool),tc_fun(tc_fun(U_9931,U_9931),tc_fun(U_9931,tc_HOL_Obool)),U_9931),c_COMBB(U_9931,tc_HOL_Obool,U_9931)),c_fequal))),c_Orderings_Oord__class_Omax(U_9931)))))),hAPP(hAPP(c_COMBC(U_9931,tc_fun(U_9931,tc_HOL_Obool),tc_fun(U_9931,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9931,tc_HOL_Obool),tc_fun(U_9931,tc_HOL_Obool)),U_9931),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9931)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9931),c_fconj),hAPP(hAPP(c_COMBC(U_9931,tc_fun(U_9931,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9931)),U_9932)))),hAPP(hAPP(c_COMBC(U_9931,tc_fun(U_9931,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9931)),U_9933)))))))
      | U_9933 = c_Orderings_Obot__class_Obot(tc_fun(U_9931,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9931),U_9933))
      | U_9932 = c_Orderings_Obot__class_Obot(tc_fun(U_9931,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9931),U_9932))
      | ~ class_Orderings_Olinorder(U_9931) ),
    inference(definitional_conversion,[status(esa)],[f_2711_2]) ).

cnf(f_2711_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9931),c_Big__Operators_Olattice_OInf__fin(U_9931,c_Orderings_Oord__class_Omin(U_9931),U_9932)),c_Big__Operators_Olattice_OInf__fin(U_9931,c_Orderings_Oord__class_Omin(U_9931),U_9933)) = c_Big__Operators_Olattice_OInf__fin(U_9931,c_Orderings_Oord__class_Omin(U_9931),hAPP(c_Set_OCollect(U_9931),hAPP(hAPP(c_COMBB(tc_fun(U_9931,tc_HOL_Obool),tc_HOL_Obool,U_9931),c_HOL_OEx(U_9931)),hAPP(hAPP(c_COMBB(tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool)),tc_fun(U_9931,tc_HOL_Obool),U_9931),hAPP(c_COMBB(tc_fun(U_9931,tc_HOL_Obool),tc_HOL_Obool,U_9931),c_HOL_OEx(U_9931))),hAPP(hAPP(c_COMBC(U_9931,tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool)),tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9931,tc_fun(tc_fun(U_9931,tc_HOL_Obool),tc_fun(U_9931,tc_HOL_Obool))),tc_fun(tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool)),tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool))),U_9931),c_COMBS(U_9931,tc_fun(U_9931,tc_HOL_Obool),tc_fun(U_9931,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9931,tc_fun(U_9931,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_9931,tc_fun(tc_fun(U_9931,tc_HOL_Obool),tc_fun(U_9931,tc_HOL_Obool))),U_9931),hAPP(c_COMBB(tc_fun(U_9931,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9931,tc_HOL_Obool),tc_fun(U_9931,tc_HOL_Obool)),U_9931),c_COMBS(U_9931,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool)),tc_fun(U_9931,tc_fun(U_9931,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_9931),hAPP(c_COMBB(tc_fun(U_9931,tc_HOL_Obool),tc_fun(U_9931,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9931),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9931),c_fconj))),hAPP(hAPP(c_COMBC(U_9931,tc_fun(U_9931,tc_fun(U_9931,U_9931)),tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_9931,U_9931),tc_fun(U_9931,tc_HOL_Obool)),tc_fun(tc_fun(U_9931,tc_fun(U_9931,U_9931)),tc_fun(U_9931,tc_fun(U_9931,tc_HOL_Obool))),U_9931),c_COMBB(tc_fun(U_9931,U_9931),tc_fun(U_9931,tc_HOL_Obool),U_9931)),hAPP(hAPP(c_COMBB(tc_fun(U_9931,tc_HOL_Obool),tc_fun(tc_fun(U_9931,U_9931),tc_fun(U_9931,tc_HOL_Obool)),U_9931),c_COMBB(U_9931,tc_HOL_Obool,U_9931)),c_fequal))),c_Orderings_Oord__class_Omax(U_9931)))))),hAPP(hAPP(c_COMBC(U_9931,tc_fun(U_9931,tc_HOL_Obool),tc_fun(U_9931,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_9931,tc_HOL_Obool),tc_fun(U_9931,tc_HOL_Obool)),U_9931),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_9931)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9931),c_fconj),hAPP(hAPP(c_COMBC(U_9931,tc_fun(U_9931,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9931)),U_9932)))),hAPP(hAPP(c_COMBC(U_9931,tc_fun(U_9931,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9931)),U_9933)))))))
    | U_9933 = c_Orderings_Obot__class_Obot(tc_fun(U_9931,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9931),U_9933))
    | U_9932 = c_Orderings_Obot__class_Obot(tc_fun(U_9931,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9931),U_9932))
    | ~ class_Orderings_Olinorder(U_9931) ),
    inference(clausify,[status(thm)],[f_2711_3]) ).

fof(f_2712_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_2712_2,plain,
    ! [U_9936,U_9935,U_9934] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9934),U_9936),c_Big__Operators_Olattice_OSup__fin(U_9934,c_Orderings_Oord__class_Omax(U_9934),U_9935)) = c_Big__Operators_Olattice_OSup__fin(U_9934,c_Orderings_Oord__class_Omax(U_9934),hAPP(c_Set_OCollect(U_9934),hAPP(hAPP(c_COMBB(tc_fun(U_9934,tc_HOL_Obool),tc_HOL_Obool,U_9934),c_HOL_OEx(U_9934)),hAPP(hAPP(c_COMBC(U_9934,tc_fun(U_9934,tc_HOL_Obool),tc_fun(U_9934,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9934,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9934,tc_HOL_Obool),tc_fun(U_9934,tc_HOL_Obool)),U_9934),c_COMBS(U_9934,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9934,tc_HOL_Obool),tc_fun(U_9934,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9934),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9934),c_fconj)),hAPP(hAPP(c_COMBC(U_9934,tc_fun(U_9934,U_9934),tc_fun(U_9934,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9934,tc_HOL_Obool),tc_fun(tc_fun(U_9934,U_9934),tc_fun(U_9934,tc_HOL_Obool)),U_9934),c_COMBB(U_9934,tc_HOL_Obool,U_9934)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_9934),U_9936))))),hAPP(hAPP(c_COMBC(U_9934,tc_fun(U_9934,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9934)),U_9935)))))
      | U_9935 = c_Orderings_Obot__class_Obot(tc_fun(U_9934,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9934),U_9935))
      | ~ class_Orderings_Olinorder(U_9934) ),
    inference(variable_rename,[status(thm)],[f_2712_1]) ).

fof(f_2712_3,plain,
    ! [U_9934,U_9935,U_9936] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9934),U_9936),c_Big__Operators_Olattice_OSup__fin(U_9934,c_Orderings_Oord__class_Omax(U_9934),U_9935)) = c_Big__Operators_Olattice_OSup__fin(U_9934,c_Orderings_Oord__class_Omax(U_9934),hAPP(c_Set_OCollect(U_9934),hAPP(hAPP(c_COMBB(tc_fun(U_9934,tc_HOL_Obool),tc_HOL_Obool,U_9934),c_HOL_OEx(U_9934)),hAPP(hAPP(c_COMBC(U_9934,tc_fun(U_9934,tc_HOL_Obool),tc_fun(U_9934,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9934,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9934,tc_HOL_Obool),tc_fun(U_9934,tc_HOL_Obool)),U_9934),c_COMBS(U_9934,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9934,tc_HOL_Obool),tc_fun(U_9934,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9934),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9934),c_fconj)),hAPP(hAPP(c_COMBC(U_9934,tc_fun(U_9934,U_9934),tc_fun(U_9934,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9934,tc_HOL_Obool),tc_fun(tc_fun(U_9934,U_9934),tc_fun(U_9934,tc_HOL_Obool)),U_9934),c_COMBB(U_9934,tc_HOL_Obool,U_9934)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_9934),U_9936))))),hAPP(hAPP(c_COMBC(U_9934,tc_fun(U_9934,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9934)),U_9935)))))
      | U_9935 = c_Orderings_Obot__class_Obot(tc_fun(U_9934,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9934),U_9935))
      | ~ class_Orderings_Olinorder(U_9934) ),
    inference(definitional_conversion,[status(esa)],[f_2712_2]) ).

cnf(f_2712_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9934),U_9936),c_Big__Operators_Olattice_OSup__fin(U_9934,c_Orderings_Oord__class_Omax(U_9934),U_9935)) = c_Big__Operators_Olattice_OSup__fin(U_9934,c_Orderings_Oord__class_Omax(U_9934),hAPP(c_Set_OCollect(U_9934),hAPP(hAPP(c_COMBB(tc_fun(U_9934,tc_HOL_Obool),tc_HOL_Obool,U_9934),c_HOL_OEx(U_9934)),hAPP(hAPP(c_COMBC(U_9934,tc_fun(U_9934,tc_HOL_Obool),tc_fun(U_9934,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9934,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9934,tc_HOL_Obool),tc_fun(U_9934,tc_HOL_Obool)),U_9934),c_COMBS(U_9934,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9934,tc_HOL_Obool),tc_fun(U_9934,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9934),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9934),c_fconj)),hAPP(hAPP(c_COMBC(U_9934,tc_fun(U_9934,U_9934),tc_fun(U_9934,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9934,tc_HOL_Obool),tc_fun(tc_fun(U_9934,U_9934),tc_fun(U_9934,tc_HOL_Obool)),U_9934),c_COMBB(U_9934,tc_HOL_Obool,U_9934)),c_fequal)),hAPP(c_Orderings_Oord__class_Omin(U_9934),U_9936))))),hAPP(hAPP(c_COMBC(U_9934,tc_fun(U_9934,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9934)),U_9935)))))
    | U_9935 = c_Orderings_Obot__class_Obot(tc_fun(U_9934,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9934),U_9935))
    | ~ class_Orderings_Olinorder(U_9934) ),
    inference(clausify,[status(thm)],[f_2712_3]) ).

fof(f_2713_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_2713_2,plain,
    ! [U_9938,U_9937] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9937),c_Big__Operators_Olattice_OInf__fin(U_9937,c_Orderings_Oord__class_Omin(U_9937),U_9938)),c_Big__Operators_Olattice_OSup__fin(U_9937,c_Orderings_Oord__class_Omax(U_9937),U_9938)))
      | U_9938 = c_Orderings_Obot__class_Obot(tc_fun(U_9937,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9937),U_9938))
      | ~ class_Orderings_Olinorder(U_9937) ),
    inference(variable_rename,[status(thm)],[f_2713_1]) ).

fof(f_2713_3,plain,
    ! [U_9937,U_9938] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9937),c_Big__Operators_Olattice_OInf__fin(U_9937,c_Orderings_Oord__class_Omin(U_9937),U_9938)),c_Big__Operators_Olattice_OSup__fin(U_9937,c_Orderings_Oord__class_Omax(U_9937),U_9938)))
      | U_9938 = c_Orderings_Obot__class_Obot(tc_fun(U_9937,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9937),U_9938))
      | ~ class_Orderings_Olinorder(U_9937) ),
    inference(definitional_conversion,[status(esa)],[f_2713_2]) ).

cnf(f_2713_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_9937),c_Big__Operators_Olattice_OInf__fin(U_9937,c_Orderings_Oord__class_Omin(U_9937),U_9938)),c_Big__Operators_Olattice_OSup__fin(U_9937,c_Orderings_Oord__class_Omax(U_9937),U_9938)))
    | U_9938 = c_Orderings_Obot__class_Obot(tc_fun(U_9937,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9937),U_9938))
    | ~ class_Orderings_Olinorder(U_9937) ),
    inference(clausify,[status(thm)],[f_2713_3]) ).

fof(f_2714_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_2714_2,plain,
    ! [U_9941,U_9940,U_9939] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9939),U_9941),c_Big__Operators_Olattice_OInf__fin(U_9939,c_Orderings_Oord__class_Omin(U_9939),U_9940)) = c_Big__Operators_Olattice_OInf__fin(U_9939,c_Orderings_Oord__class_Omin(U_9939),U_9940)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9939),U_9941),U_9940))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9939),U_9940))
      | ~ class_Orderings_Olinorder(U_9939) ),
    inference(variable_rename,[status(thm)],[f_2714_1]) ).

fof(f_2714_3,plain,
    ! [U_9939,U_9940,U_9941] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9939),U_9941),c_Big__Operators_Olattice_OInf__fin(U_9939,c_Orderings_Oord__class_Omin(U_9939),U_9940)) = c_Big__Operators_Olattice_OInf__fin(U_9939,c_Orderings_Oord__class_Omin(U_9939),U_9940)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9939),U_9941),U_9940))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9939),U_9940))
      | ~ class_Orderings_Olinorder(U_9939) ),
    inference(definitional_conversion,[status(esa)],[f_2714_2]) ).

cnf(f_2714_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9939),U_9941),c_Big__Operators_Olattice_OInf__fin(U_9939,c_Orderings_Oord__class_Omin(U_9939),U_9940)) = c_Big__Operators_Olattice_OInf__fin(U_9939,c_Orderings_Oord__class_Omin(U_9939),U_9940)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9939),U_9941),U_9940))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9939),U_9940))
    | ~ class_Orderings_Olinorder(U_9939) ),
    inference(clausify,[status(thm)],[f_2714_3]) ).

fof(f_2715_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_2715_2,plain,
    ! [U_9944,U_9943,U_9942] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9942),U_9944),c_Big__Operators_Olattice_OSup__fin(U_9942,c_Orderings_Oord__class_Omax(U_9942),U_9943)) = c_Big__Operators_Olattice_OSup__fin(U_9942,c_Orderings_Oord__class_Omax(U_9942),U_9943)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9942),U_9944),U_9943))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9942),U_9943))
      | ~ class_Orderings_Olinorder(U_9942) ),
    inference(variable_rename,[status(thm)],[f_2715_1]) ).

fof(f_2715_3,plain,
    ! [U_9943,U_9942,U_9944] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9942),U_9944),c_Big__Operators_Olattice_OSup__fin(U_9942,c_Orderings_Oord__class_Omax(U_9942),U_9943)) = c_Big__Operators_Olattice_OSup__fin(U_9942,c_Orderings_Oord__class_Omax(U_9942),U_9943)
      | ~ hBOOL(hAPP(hAPP(c_member(U_9942),U_9944),U_9943))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9942),U_9943))
      | ~ class_Orderings_Olinorder(U_9942) ),
    inference(definitional_conversion,[status(esa)],[f_2715_2]) ).

cnf(f_2715_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9942),U_9944),c_Big__Operators_Olattice_OSup__fin(U_9942,c_Orderings_Oord__class_Omax(U_9942),U_9943)) = c_Big__Operators_Olattice_OSup__fin(U_9942,c_Orderings_Oord__class_Omax(U_9942),U_9943)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9942),U_9944),U_9943))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9942),U_9943))
    | ~ class_Orderings_Olinorder(U_9942) ),
    inference(clausify,[status(thm)],[f_2715_3]) ).

fof(f_2716_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_2716_2,plain,
    ! [U_9946,U_9945] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9945,c_Orderings_Oord__class_Omin(U_9945),hAPP(hAPP(c_Set_Oinsert(U_9945),U_9946),c_Orderings_Obot__class_Obot(tc_fun(U_9945,tc_HOL_Obool)))) = U_9946
      | ~ class_Orderings_Olinorder(U_9945) ),
    inference(variable_rename,[status(thm)],[f_2716_1]) ).

fof(f_2716_3,plain,
    ! [U_9945,U_9946] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9945,c_Orderings_Oord__class_Omin(U_9945),hAPP(hAPP(c_Set_Oinsert(U_9945),U_9946),c_Orderings_Obot__class_Obot(tc_fun(U_9945,tc_HOL_Obool)))) = U_9946
      | ~ class_Orderings_Olinorder(U_9945) ),
    inference(definitional_conversion,[status(esa)],[f_2716_2]) ).

cnf(f_2716_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9945,c_Orderings_Oord__class_Omin(U_9945),hAPP(hAPP(c_Set_Oinsert(U_9945),U_9946),c_Orderings_Obot__class_Obot(tc_fun(U_9945,tc_HOL_Obool)))) = U_9946
    | ~ class_Orderings_Olinorder(U_9945) ),
    inference(clausify,[status(thm)],[f_2716_3]) ).

fof(f_2717_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_2717_2,plain,
    ! [U_9948,U_9947] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9947,c_Orderings_Oord__class_Omax(U_9947),hAPP(hAPP(c_Set_Oinsert(U_9947),U_9948),c_Orderings_Obot__class_Obot(tc_fun(U_9947,tc_HOL_Obool)))) = U_9948
      | ~ class_Orderings_Olinorder(U_9947) ),
    inference(variable_rename,[status(thm)],[f_2717_1]) ).

fof(f_2717_3,plain,
    ! [U_9947,U_9948] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9947,c_Orderings_Oord__class_Omax(U_9947),hAPP(hAPP(c_Set_Oinsert(U_9947),U_9948),c_Orderings_Obot__class_Obot(tc_fun(U_9947,tc_HOL_Obool)))) = U_9948
      | ~ class_Orderings_Olinorder(U_9947) ),
    inference(definitional_conversion,[status(esa)],[f_2717_2]) ).

cnf(f_2717_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9947,c_Orderings_Oord__class_Omax(U_9947),hAPP(hAPP(c_Set_Oinsert(U_9947),U_9948),c_Orderings_Obot__class_Obot(tc_fun(U_9947,tc_HOL_Obool)))) = U_9948
    | ~ class_Orderings_Olinorder(U_9947) ),
    inference(clausify,[status(thm)],[f_2717_3]) ).

fof(f_2718_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),V_x_2),c_Big__Operators_Olattice_OInf__fin(T_b,c_Orderings_Oord__class_Omin(T_b),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(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_2718_2,plain,
    ! [U_9951,U_9950,U_9949] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9949,c_Orderings_Oord__class_Omin(U_9949),hAPP(hAPP(c_Set_Oinsert(U_9949),U_9951),U_9950)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9949),U_9951),c_Big__Operators_Olattice_OInf__fin(U_9949,c_Orderings_Oord__class_Omin(U_9949),U_9950))
      | U_9950 = c_Orderings_Obot__class_Obot(tc_fun(U_9949,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9949),U_9950))
      | ~ class_Orderings_Olinorder(U_9949) ),
    inference(variable_rename,[status(thm)],[f_2718_1]) ).

fof(f_2718_3,plain,
    ! [U_9949,U_9950,U_9951] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9949,c_Orderings_Oord__class_Omin(U_9949),hAPP(hAPP(c_Set_Oinsert(U_9949),U_9951),U_9950)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9949),U_9951),c_Big__Operators_Olattice_OInf__fin(U_9949,c_Orderings_Oord__class_Omin(U_9949),U_9950))
      | U_9950 = c_Orderings_Obot__class_Obot(tc_fun(U_9949,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9949),U_9950))
      | ~ class_Orderings_Olinorder(U_9949) ),
    inference(definitional_conversion,[status(esa)],[f_2718_2]) ).

cnf(f_2718_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9949,c_Orderings_Oord__class_Omin(U_9949),hAPP(hAPP(c_Set_Oinsert(U_9949),U_9951),U_9950)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9949),U_9951),c_Big__Operators_Olattice_OInf__fin(U_9949,c_Orderings_Oord__class_Omin(U_9949),U_9950))
    | U_9950 = c_Orderings_Obot__class_Obot(tc_fun(U_9949,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9949),U_9950))
    | ~ class_Orderings_Olinorder(U_9949) ),
    inference(clausify,[status(thm)],[f_2718_3]) ).

fof(f_2719_1,plain,
    ! [V_x_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Set_Oinsert(T_b),V_x_2),V_A_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),V_x_2),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2))
      | V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))
      | ~ hBOOL(hAPP(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_2719_2,plain,
    ! [U_9954,U_9953,U_9952] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9952,c_Orderings_Oord__class_Omax(U_9952),hAPP(hAPP(c_Set_Oinsert(U_9952),U_9954),U_9953)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9952),U_9954),c_Big__Operators_Olattice_OSup__fin(U_9952,c_Orderings_Oord__class_Omax(U_9952),U_9953))
      | U_9953 = c_Orderings_Obot__class_Obot(tc_fun(U_9952,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9952),U_9953))
      | ~ class_Orderings_Olinorder(U_9952) ),
    inference(variable_rename,[status(thm)],[f_2719_1]) ).

fof(f_2719_3,plain,
    ! [U_9954,U_9953,U_9952] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9952,c_Orderings_Oord__class_Omax(U_9952),hAPP(hAPP(c_Set_Oinsert(U_9952),U_9954),U_9953)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9952),U_9954),c_Big__Operators_Olattice_OSup__fin(U_9952,c_Orderings_Oord__class_Omax(U_9952),U_9953))
      | U_9953 = c_Orderings_Obot__class_Obot(tc_fun(U_9952,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9952),U_9953))
      | ~ class_Orderings_Olinorder(U_9952) ),
    inference(definitional_conversion,[status(esa)],[f_2719_2]) ).

cnf(f_2719_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9952,c_Orderings_Oord__class_Omax(U_9952),hAPP(hAPP(c_Set_Oinsert(U_9952),U_9954),U_9953)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9952),U_9954),c_Big__Operators_Olattice_OSup__fin(U_9952,c_Orderings_Oord__class_Omax(U_9952),U_9953))
    | U_9953 = c_Orderings_Obot__class_Obot(tc_fun(U_9952,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9952),U_9953))
    | ~ class_Orderings_Olinorder(U_9952) ),
    inference(clausify,[status(thm)],[f_2719_3]) ).

fof(f_2720_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_2720_2,plain,
    ! [U_9957,U_9956,U_9955] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9955),c_Big__Operators_Olattice_OInf__fin(U_9955,c_Orderings_Oord__class_Omin(U_9955),U_9957)),c_Big__Operators_Olattice_OInf__fin(U_9955,c_Orderings_Oord__class_Omin(U_9955),U_9956)) = c_Big__Operators_Olattice_OInf__fin(U_9955,c_Orderings_Oord__class_Omin(U_9955),U_9956)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9955,tc_HOL_Obool)),U_9957),U_9956))
      | U_9957 = c_Orderings_Obot__class_Obot(tc_fun(U_9955,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9955),U_9956))
      | ~ class_Orderings_Olinorder(U_9955) ),
    inference(variable_rename,[status(thm)],[f_2720_1]) ).

fof(f_2720_3,plain,
    ! [U_9955,U_9956,U_9957] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9955),c_Big__Operators_Olattice_OInf__fin(U_9955,c_Orderings_Oord__class_Omin(U_9955),U_9957)),c_Big__Operators_Olattice_OInf__fin(U_9955,c_Orderings_Oord__class_Omin(U_9955),U_9956)) = c_Big__Operators_Olattice_OInf__fin(U_9955,c_Orderings_Oord__class_Omin(U_9955),U_9956)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9955,tc_HOL_Obool)),U_9957),U_9956))
      | U_9957 = c_Orderings_Obot__class_Obot(tc_fun(U_9955,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9955),U_9956))
      | ~ class_Orderings_Olinorder(U_9955) ),
    inference(definitional_conversion,[status(esa)],[f_2720_2]) ).

cnf(f_2720_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9955),c_Big__Operators_Olattice_OInf__fin(U_9955,c_Orderings_Oord__class_Omin(U_9955),U_9957)),c_Big__Operators_Olattice_OInf__fin(U_9955,c_Orderings_Oord__class_Omin(U_9955),U_9956)) = c_Big__Operators_Olattice_OInf__fin(U_9955,c_Orderings_Oord__class_Omin(U_9955),U_9956)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9955,tc_HOL_Obool)),U_9957),U_9956))
    | U_9957 = c_Orderings_Obot__class_Obot(tc_fun(U_9955,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9955),U_9956))
    | ~ class_Orderings_Olinorder(U_9955) ),
    inference(clausify,[status(thm)],[f_2720_3]) ).

fof(f_2721_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_2721_2,plain,
    ! [U_9960,U_9959,U_9958] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9958),c_Big__Operators_Olattice_OSup__fin(U_9958,c_Orderings_Oord__class_Omax(U_9958),U_9960)),c_Big__Operators_Olattice_OSup__fin(U_9958,c_Orderings_Oord__class_Omax(U_9958),U_9959)) = c_Big__Operators_Olattice_OSup__fin(U_9958,c_Orderings_Oord__class_Omax(U_9958),U_9959)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9958,tc_HOL_Obool)),U_9960),U_9959))
      | U_9960 = c_Orderings_Obot__class_Obot(tc_fun(U_9958,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9958),U_9959))
      | ~ class_Orderings_Olinorder(U_9958) ),
    inference(variable_rename,[status(thm)],[f_2721_1]) ).

fof(f_2721_3,plain,
    ! [U_9958,U_9960,U_9959] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9958),c_Big__Operators_Olattice_OSup__fin(U_9958,c_Orderings_Oord__class_Omax(U_9958),U_9960)),c_Big__Operators_Olattice_OSup__fin(U_9958,c_Orderings_Oord__class_Omax(U_9958),U_9959)) = c_Big__Operators_Olattice_OSup__fin(U_9958,c_Orderings_Oord__class_Omax(U_9958),U_9959)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9958,tc_HOL_Obool)),U_9960),U_9959))
      | U_9960 = c_Orderings_Obot__class_Obot(tc_fun(U_9958,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9958),U_9959))
      | ~ class_Orderings_Olinorder(U_9958) ),
    inference(definitional_conversion,[status(esa)],[f_2721_2]) ).

cnf(f_2721_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9958),c_Big__Operators_Olattice_OSup__fin(U_9958,c_Orderings_Oord__class_Omax(U_9958),U_9960)),c_Big__Operators_Olattice_OSup__fin(U_9958,c_Orderings_Oord__class_Omax(U_9958),U_9959)) = c_Big__Operators_Olattice_OSup__fin(U_9958,c_Orderings_Oord__class_Omax(U_9958),U_9959)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_9958,tc_HOL_Obool)),U_9960),U_9959))
    | U_9960 = c_Orderings_Obot__class_Obot(tc_fun(U_9958,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9958),U_9959))
    | ~ class_Orderings_Olinorder(U_9958) ),
    inference(clausify,[status(thm)],[f_2721_3]) ).

fof(f_2722_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_2722_2,plain,
    ! [U_9963,U_9962,U_9961] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9961),U_9963),c_Big__Operators_Olattice_OInf__fin(U_9961,c_Orderings_Oord__class_Omin(U_9961),U_9962)) = U_9963
      | ~ hBOOL(hAPP(hAPP(c_member(U_9961),U_9963),U_9962))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9961),U_9962))
      | ~ class_Orderings_Olinorder(U_9961) ),
    inference(variable_rename,[status(thm)],[f_2722_1]) ).

fof(f_2722_3,plain,
    ! [U_9962,U_9963,U_9961] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9961),U_9963),c_Big__Operators_Olattice_OInf__fin(U_9961,c_Orderings_Oord__class_Omin(U_9961),U_9962)) = U_9963
      | ~ hBOOL(hAPP(hAPP(c_member(U_9961),U_9963),U_9962))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9961),U_9962))
      | ~ class_Orderings_Olinorder(U_9961) ),
    inference(definitional_conversion,[status(esa)],[f_2722_2]) ).

cnf(f_2722_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9961),U_9963),c_Big__Operators_Olattice_OInf__fin(U_9961,c_Orderings_Oord__class_Omin(U_9961),U_9962)) = U_9963
    | ~ hBOOL(hAPP(hAPP(c_member(U_9961),U_9963),U_9962))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9961),U_9962))
    | ~ class_Orderings_Olinorder(U_9961) ),
    inference(clausify,[status(thm)],[f_2722_3]) ).

fof(f_2723_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_2723_2,plain,
    ! [U_9966,U_9965,U_9964] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9964),U_9966),c_Big__Operators_Olattice_OSup__fin(U_9964,c_Orderings_Oord__class_Omax(U_9964),U_9965)) = U_9966
      | ~ hBOOL(hAPP(hAPP(c_member(U_9964),U_9966),U_9965))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9964),U_9965))
      | ~ class_Orderings_Olinorder(U_9964) ),
    inference(variable_rename,[status(thm)],[f_2723_1]) ).

fof(f_2723_3,plain,
    ! [U_9964,U_9965,U_9966] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9964),U_9966),c_Big__Operators_Olattice_OSup__fin(U_9964,c_Orderings_Oord__class_Omax(U_9964),U_9965)) = U_9966
      | ~ hBOOL(hAPP(hAPP(c_member(U_9964),U_9966),U_9965))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9964),U_9965))
      | ~ class_Orderings_Olinorder(U_9964) ),
    inference(definitional_conversion,[status(esa)],[f_2723_2]) ).

cnf(f_2723_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9964),U_9966),c_Big__Operators_Olattice_OSup__fin(U_9964,c_Orderings_Oord__class_Omax(U_9964),U_9965)) = U_9966
    | ~ hBOOL(hAPP(hAPP(c_member(U_9964),U_9966),U_9965))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9964),U_9965))
    | ~ class_Orderings_Olinorder(U_9964) ),
    inference(clausify,[status(thm)],[f_2723_3]) ).

fof(f_2724_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_2724_2,plain,
    ! [U_9969,U_9968,U_9967] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9967,c_Orderings_Oord__class_Omin(U_9967),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9967,tc_HOL_Obool)),U_9968),U_9969)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9967),c_Big__Operators_Olattice_OInf__fin(U_9967,c_Orderings_Oord__class_Omin(U_9967),U_9968)),c_Big__Operators_Olattice_OInf__fin(U_9967,c_Orderings_Oord__class_Omin(U_9967),U_9969))
      | U_9969 = c_Orderings_Obot__class_Obot(tc_fun(U_9967,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9967),U_9969))
      | U_9968 = c_Orderings_Obot__class_Obot(tc_fun(U_9967,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9967),U_9968))
      | ~ class_Orderings_Olinorder(U_9967) ),
    inference(variable_rename,[status(thm)],[f_2724_1]) ).

fof(f_2724_3,plain,
    ! [U_9967,U_9968,U_9969] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9967,c_Orderings_Oord__class_Omin(U_9967),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9967,tc_HOL_Obool)),U_9968),U_9969)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9967),c_Big__Operators_Olattice_OInf__fin(U_9967,c_Orderings_Oord__class_Omin(U_9967),U_9968)),c_Big__Operators_Olattice_OInf__fin(U_9967,c_Orderings_Oord__class_Omin(U_9967),U_9969))
      | U_9969 = c_Orderings_Obot__class_Obot(tc_fun(U_9967,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9967),U_9969))
      | U_9968 = c_Orderings_Obot__class_Obot(tc_fun(U_9967,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9967),U_9968))
      | ~ class_Orderings_Olinorder(U_9967) ),
    inference(definitional_conversion,[status(esa)],[f_2724_2]) ).

cnf(f_2724_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9967,c_Orderings_Oord__class_Omin(U_9967),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9967,tc_HOL_Obool)),U_9968),U_9969)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9967),c_Big__Operators_Olattice_OInf__fin(U_9967,c_Orderings_Oord__class_Omin(U_9967),U_9968)),c_Big__Operators_Olattice_OInf__fin(U_9967,c_Orderings_Oord__class_Omin(U_9967),U_9969))
    | U_9969 = c_Orderings_Obot__class_Obot(tc_fun(U_9967,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9967),U_9969))
    | U_9968 = c_Orderings_Obot__class_Obot(tc_fun(U_9967,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9967),U_9968))
    | ~ class_Orderings_Olinorder(U_9967) ),
    inference(clausify,[status(thm)],[f_2724_3]) ).

fof(f_2725_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_A_2)),c_Big__Operators_Olattice_OSup__fin(T_b,c_Orderings_Oord__class_Omax(T_b),V_B_2))
      | 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_2725_2,plain,
    ! [U_9972,U_9971,U_9970] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9970,c_Orderings_Oord__class_Omax(U_9970),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9970,tc_HOL_Obool)),U_9971),U_9972)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9970),c_Big__Operators_Olattice_OSup__fin(U_9970,c_Orderings_Oord__class_Omax(U_9970),U_9971)),c_Big__Operators_Olattice_OSup__fin(U_9970,c_Orderings_Oord__class_Omax(U_9970),U_9972))
      | U_9972 = c_Orderings_Obot__class_Obot(tc_fun(U_9970,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9970),U_9972))
      | U_9971 = c_Orderings_Obot__class_Obot(tc_fun(U_9970,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9970),U_9971))
      | ~ class_Orderings_Olinorder(U_9970) ),
    inference(variable_rename,[status(thm)],[f_2725_1]) ).

fof(f_2725_3,plain,
    ! [U_9970,U_9971,U_9972] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9970,c_Orderings_Oord__class_Omax(U_9970),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9970,tc_HOL_Obool)),U_9971),U_9972)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9970),c_Big__Operators_Olattice_OSup__fin(U_9970,c_Orderings_Oord__class_Omax(U_9970),U_9971)),c_Big__Operators_Olattice_OSup__fin(U_9970,c_Orderings_Oord__class_Omax(U_9970),U_9972))
      | U_9972 = c_Orderings_Obot__class_Obot(tc_fun(U_9970,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9970),U_9972))
      | U_9971 = c_Orderings_Obot__class_Obot(tc_fun(U_9970,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9970),U_9971))
      | ~ class_Orderings_Olinorder(U_9970) ),
    inference(definitional_conversion,[status(esa)],[f_2725_2]) ).

cnf(f_2725_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9970,c_Orderings_Oord__class_Omax(U_9970),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_9970,tc_HOL_Obool)),U_9971),U_9972)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9970),c_Big__Operators_Olattice_OSup__fin(U_9970,c_Orderings_Oord__class_Omax(U_9970),U_9971)),c_Big__Operators_Olattice_OSup__fin(U_9970,c_Orderings_Oord__class_Omax(U_9970),U_9972))
    | U_9972 = c_Orderings_Obot__class_Obot(tc_fun(U_9970,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9970),U_9972))
    | U_9971 = c_Orderings_Obot__class_Obot(tc_fun(U_9970,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9970),U_9971))
    | ~ class_Orderings_Olinorder(U_9970) ),
    inference(clausify,[status(thm)],[f_2725_3]) ).

fof(f_2726_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_2726_2,plain,
    ! [U_9975,U_9974,U_9973] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9973,c_Orderings_Oord__class_Omin(U_9973),hAPP(hAPP(c_Set_Oinsert(U_9973),U_9975),U_9974)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9973),U_9975),c_Big__Operators_Olattice_OInf__fin(U_9973,c_Orderings_Oord__class_Omin(U_9973),U_9974))
      | U_9974 = c_Orderings_Obot__class_Obot(tc_fun(U_9973,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9973),U_9975),U_9974))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9973),U_9974))
      | ~ class_Orderings_Olinorder(U_9973) ),
    inference(variable_rename,[status(thm)],[f_2726_1]) ).

fof(f_2726_3,plain,
    ! [U_9973,U_9974,U_9975] :
      ( c_Big__Operators_Olattice_OInf__fin(U_9973,c_Orderings_Oord__class_Omin(U_9973),hAPP(hAPP(c_Set_Oinsert(U_9973),U_9975),U_9974)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9973),U_9975),c_Big__Operators_Olattice_OInf__fin(U_9973,c_Orderings_Oord__class_Omin(U_9973),U_9974))
      | U_9974 = c_Orderings_Obot__class_Obot(tc_fun(U_9973,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9973),U_9975),U_9974))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9973),U_9974))
      | ~ class_Orderings_Olinorder(U_9973) ),
    inference(definitional_conversion,[status(esa)],[f_2726_2]) ).

cnf(f_2726_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9973,c_Orderings_Oord__class_Omin(U_9973),hAPP(hAPP(c_Set_Oinsert(U_9973),U_9975),U_9974)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9973),U_9975),c_Big__Operators_Olattice_OInf__fin(U_9973,c_Orderings_Oord__class_Omin(U_9973),U_9974))
    | U_9974 = c_Orderings_Obot__class_Obot(tc_fun(U_9973,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_9973),U_9975),U_9974))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9973),U_9974))
    | ~ class_Orderings_Olinorder(U_9973) ),
    inference(clausify,[status(thm)],[f_2726_3]) ).

fof(f_2727_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_2727_2,plain,
    ! [U_9978,U_9977,U_9976] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9976,c_Orderings_Oord__class_Omax(U_9976),hAPP(hAPP(c_Set_Oinsert(U_9976),U_9978),U_9977)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9976),U_9978),c_Big__Operators_Olattice_OSup__fin(U_9976,c_Orderings_Oord__class_Omax(U_9976),U_9977))
      | U_9977 = c_Orderings_Obot__class_Obot(tc_fun(U_9976,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9976),U_9978),U_9977))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9976),U_9977))
      | ~ class_Orderings_Olinorder(U_9976) ),
    inference(variable_rename,[status(thm)],[f_2727_1]) ).

fof(f_2727_3,plain,
    ! [U_9976,U_9977,U_9978] :
      ( c_Big__Operators_Olattice_OSup__fin(U_9976,c_Orderings_Oord__class_Omax(U_9976),hAPP(hAPP(c_Set_Oinsert(U_9976),U_9978),U_9977)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9976),U_9978),c_Big__Operators_Olattice_OSup__fin(U_9976,c_Orderings_Oord__class_Omax(U_9976),U_9977))
      | U_9977 = c_Orderings_Obot__class_Obot(tc_fun(U_9976,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_9976),U_9978),U_9977))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9976),U_9977))
      | ~ class_Orderings_Olinorder(U_9976) ),
    inference(definitional_conversion,[status(esa)],[f_2727_2]) ).

cnf(f_2727_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9976,c_Orderings_Oord__class_Omax(U_9976),hAPP(hAPP(c_Set_Oinsert(U_9976),U_9978),U_9977)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9976),U_9978),c_Big__Operators_Olattice_OSup__fin(U_9976,c_Orderings_Oord__class_Omax(U_9976),U_9977))
    | U_9977 = c_Orderings_Obot__class_Obot(tc_fun(U_9976,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_9976),U_9978),U_9977))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9976),U_9977))
    | ~ class_Orderings_Olinorder(U_9976) ),
    inference(clausify,[status(thm)],[f_2727_3]) ).

fof(f_2728_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_2728_2,plain,
    ! [U_9981,U_9980,U_9979] :
      ( ( ( c_Big__Operators_Olattice_OInf__fin(U_9979,c_Orderings_Oord__class_Omin(U_9979),hAPP(hAPP(c_Set_Oinsert(U_9979),U_9981),U_9980)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9979),U_9981),c_Big__Operators_Olattice_OInf__fin(U_9979,c_Orderings_Oord__class_Omin(U_9979),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9979,tc_HOL_Obool)),U_9980),hAPP(hAPP(c_Set_Oinsert(U_9979),U_9981),c_Orderings_Obot__class_Obot(tc_fun(U_9979,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9979,tc_HOL_Obool)),U_9980),hAPP(hAPP(c_Set_Oinsert(U_9979),U_9981),c_Orderings_Obot__class_Obot(tc_fun(U_9979,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9979,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OInf__fin(U_9979,c_Orderings_Oord__class_Omin(U_9979),hAPP(hAPP(c_Set_Oinsert(U_9979),U_9981),U_9980)) = U_9981
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9979,tc_HOL_Obool)),U_9980),hAPP(hAPP(c_Set_Oinsert(U_9979),U_9981),c_Orderings_Obot__class_Obot(tc_fun(U_9979,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9979,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9979),U_9980))
      | ~ class_Orderings_Olinorder(U_9979) ),
    inference(variable_rename,[status(thm)],[f_2728_1]) ).

fof(f_2728_3,plain,
    ( ! [U_9979,U_9981,U_9980] :
        ( c_Big__Operators_Olattice_OInf__fin(U_9979,c_Orderings_Oord__class_Omin(U_9979),hAPP(hAPP(c_Set_Oinsert(U_9979),U_9981),U_9980)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9979),U_9981),c_Big__Operators_Olattice_OInf__fin(U_9979,c_Orderings_Oord__class_Omin(U_9979),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9979,tc_HOL_Obool)),U_9980),hAPP(hAPP(c_Set_Oinsert(U_9979),U_9981),c_Orderings_Obot__class_Obot(tc_fun(U_9979,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9979,tc_HOL_Obool)),U_9980),hAPP(hAPP(c_Set_Oinsert(U_9979),U_9981),c_Orderings_Obot__class_Obot(tc_fun(U_9979,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9979,tc_HOL_Obool))
        | ~ sP769(U_9979,U_9981,U_9980) )
    & ! [U_9979,U_9981,U_9980] :
        ( c_Big__Operators_Olattice_OInf__fin(U_9979,c_Orderings_Oord__class_Omin(U_9979),hAPP(hAPP(c_Set_Oinsert(U_9979),U_9981),U_9980)) = U_9981
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9979,tc_HOL_Obool)),U_9980),hAPP(hAPP(c_Set_Oinsert(U_9979),U_9981),c_Orderings_Obot__class_Obot(tc_fun(U_9979,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9979,tc_HOL_Obool))
        | ~ sP769(U_9979,U_9981,U_9980) )
    & ! [U_9979,U_9981,U_9980] :
        ( sP769(U_9979,U_9981,U_9980)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9979),U_9980))
        | ~ class_Orderings_Olinorder(U_9979) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP769])],[f_2728_2]) ).

cnf(f_2728_4,plain,
    ( sP769(U_9979,U_9981,U_9980)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9979),U_9980))
    | ~ class_Orderings_Olinorder(U_9979) ),
    inference(clausify,[status(thm)],[f_2728_3]) ).

cnf(f_2728_5,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9979,c_Orderings_Oord__class_Omin(U_9979),hAPP(hAPP(c_Set_Oinsert(U_9979),U_9981),U_9980)) = U_9981
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9979,tc_HOL_Obool)),U_9980),hAPP(hAPP(c_Set_Oinsert(U_9979),U_9981),c_Orderings_Obot__class_Obot(tc_fun(U_9979,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9979,tc_HOL_Obool))
    | ~ sP769(U_9979,U_9981,U_9980) ),
    inference(clausify,[status(thm)],[f_2728_3]) ).

cnf(f_2728_6,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9979,c_Orderings_Oord__class_Omin(U_9979),hAPP(hAPP(c_Set_Oinsert(U_9979),U_9981),U_9980)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9979),U_9981),c_Big__Operators_Olattice_OInf__fin(U_9979,c_Orderings_Oord__class_Omin(U_9979),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9979,tc_HOL_Obool)),U_9980),hAPP(hAPP(c_Set_Oinsert(U_9979),U_9981),c_Orderings_Obot__class_Obot(tc_fun(U_9979,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9979,tc_HOL_Obool)),U_9980),hAPP(hAPP(c_Set_Oinsert(U_9979),U_9981),c_Orderings_Obot__class_Obot(tc_fun(U_9979,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9979,tc_HOL_Obool))
    | ~ sP769(U_9979,U_9981,U_9980) ),
    inference(clausify,[status(thm)],[f_2728_3]) ).

fof(f_2729_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_2729_2,plain,
    ! [U_9984,U_9983,U_9982] :
      ( ( ( c_Big__Operators_Olattice_OSup__fin(U_9982,c_Orderings_Oord__class_Omax(U_9982),hAPP(hAPP(c_Set_Oinsert(U_9982),U_9984),U_9983)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9982),U_9984),c_Big__Operators_Olattice_OSup__fin(U_9982,c_Orderings_Oord__class_Omax(U_9982),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9982,tc_HOL_Obool)),U_9983),hAPP(hAPP(c_Set_Oinsert(U_9982),U_9984),c_Orderings_Obot__class_Obot(tc_fun(U_9982,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9982,tc_HOL_Obool)),U_9983),hAPP(hAPP(c_Set_Oinsert(U_9982),U_9984),c_Orderings_Obot__class_Obot(tc_fun(U_9982,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9982,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OSup__fin(U_9982,c_Orderings_Oord__class_Omax(U_9982),hAPP(hAPP(c_Set_Oinsert(U_9982),U_9984),U_9983)) = U_9984
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9982,tc_HOL_Obool)),U_9983),hAPP(hAPP(c_Set_Oinsert(U_9982),U_9984),c_Orderings_Obot__class_Obot(tc_fun(U_9982,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9982,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9982),U_9983))
      | ~ class_Orderings_Olinorder(U_9982) ),
    inference(variable_rename,[status(thm)],[f_2729_1]) ).

fof(f_2729_3,plain,
    ( ! [U_9983,U_9984,U_9982] :
        ( c_Big__Operators_Olattice_OSup__fin(U_9982,c_Orderings_Oord__class_Omax(U_9982),hAPP(hAPP(c_Set_Oinsert(U_9982),U_9984),U_9983)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9982),U_9984),c_Big__Operators_Olattice_OSup__fin(U_9982,c_Orderings_Oord__class_Omax(U_9982),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9982,tc_HOL_Obool)),U_9983),hAPP(hAPP(c_Set_Oinsert(U_9982),U_9984),c_Orderings_Obot__class_Obot(tc_fun(U_9982,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9982,tc_HOL_Obool)),U_9983),hAPP(hAPP(c_Set_Oinsert(U_9982),U_9984),c_Orderings_Obot__class_Obot(tc_fun(U_9982,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9982,tc_HOL_Obool))
        | ~ sP770(U_9983,U_9984,U_9982) )
    & ! [U_9983,U_9984,U_9982] :
        ( c_Big__Operators_Olattice_OSup__fin(U_9982,c_Orderings_Oord__class_Omax(U_9982),hAPP(hAPP(c_Set_Oinsert(U_9982),U_9984),U_9983)) = U_9984
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9982,tc_HOL_Obool)),U_9983),hAPP(hAPP(c_Set_Oinsert(U_9982),U_9984),c_Orderings_Obot__class_Obot(tc_fun(U_9982,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9982,tc_HOL_Obool))
        | ~ sP770(U_9983,U_9984,U_9982) )
    & ! [U_9983,U_9984,U_9982] :
        ( sP770(U_9983,U_9984,U_9982)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9982),U_9983))
        | ~ class_Orderings_Olinorder(U_9982) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP770])],[f_2729_2]) ).

cnf(f_2729_4,plain,
    ( sP770(U_9983,U_9984,U_9982)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9982),U_9983))
    | ~ class_Orderings_Olinorder(U_9982) ),
    inference(clausify,[status(thm)],[f_2729_3]) ).

cnf(f_2729_5,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9982,c_Orderings_Oord__class_Omax(U_9982),hAPP(hAPP(c_Set_Oinsert(U_9982),U_9984),U_9983)) = U_9984
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9982,tc_HOL_Obool)),U_9983),hAPP(hAPP(c_Set_Oinsert(U_9982),U_9984),c_Orderings_Obot__class_Obot(tc_fun(U_9982,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9982,tc_HOL_Obool))
    | ~ sP770(U_9983,U_9984,U_9982) ),
    inference(clausify,[status(thm)],[f_2729_3]) ).

cnf(f_2729_6,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9982,c_Orderings_Oord__class_Omax(U_9982),hAPP(hAPP(c_Set_Oinsert(U_9982),U_9984),U_9983)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9982),U_9984),c_Big__Operators_Olattice_OSup__fin(U_9982,c_Orderings_Oord__class_Omax(U_9982),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9982,tc_HOL_Obool)),U_9983),hAPP(hAPP(c_Set_Oinsert(U_9982),U_9984),c_Orderings_Obot__class_Obot(tc_fun(U_9982,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9982,tc_HOL_Obool)),U_9983),hAPP(hAPP(c_Set_Oinsert(U_9982),U_9984),c_Orderings_Obot__class_Obot(tc_fun(U_9982,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9982,tc_HOL_Obool))
    | ~ sP770(U_9983,U_9984,U_9982) ),
    inference(clausify,[status(thm)],[f_2729_3]) ).

fof(f_2730_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_2730_2,plain,
    ! [U_9987,U_9986,U_9985] :
      ( ( ( c_Big__Operators_Olattice_OInf__fin(U_9985,c_Orderings_Oord__class_Omin(U_9985),U_9986) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9985),U_9987),c_Big__Operators_Olattice_OInf__fin(U_9985,c_Orderings_Oord__class_Omin(U_9985),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9985,tc_HOL_Obool)),U_9986),hAPP(hAPP(c_Set_Oinsert(U_9985),U_9987),c_Orderings_Obot__class_Obot(tc_fun(U_9985,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9985,tc_HOL_Obool)),U_9986),hAPP(hAPP(c_Set_Oinsert(U_9985),U_9987),c_Orderings_Obot__class_Obot(tc_fun(U_9985,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9985,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OInf__fin(U_9985,c_Orderings_Oord__class_Omin(U_9985),U_9986) = U_9987
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9985,tc_HOL_Obool)),U_9986),hAPP(hAPP(c_Set_Oinsert(U_9985),U_9987),c_Orderings_Obot__class_Obot(tc_fun(U_9985,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9985,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_9985),U_9987),U_9986))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9985),U_9986))
      | ~ class_Orderings_Olinorder(U_9985) ),
    inference(variable_rename,[status(thm)],[f_2730_1]) ).

fof(f_2730_3,plain,
    ( ! [U_9985,U_9987,U_9986] :
        ( c_Big__Operators_Olattice_OInf__fin(U_9985,c_Orderings_Oord__class_Omin(U_9985),U_9986) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9985),U_9987),c_Big__Operators_Olattice_OInf__fin(U_9985,c_Orderings_Oord__class_Omin(U_9985),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9985,tc_HOL_Obool)),U_9986),hAPP(hAPP(c_Set_Oinsert(U_9985),U_9987),c_Orderings_Obot__class_Obot(tc_fun(U_9985,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9985,tc_HOL_Obool)),U_9986),hAPP(hAPP(c_Set_Oinsert(U_9985),U_9987),c_Orderings_Obot__class_Obot(tc_fun(U_9985,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9985,tc_HOL_Obool))
        | ~ sP771(U_9985,U_9987,U_9986) )
    & ! [U_9985,U_9987,U_9986] :
        ( c_Big__Operators_Olattice_OInf__fin(U_9985,c_Orderings_Oord__class_Omin(U_9985),U_9986) = U_9987
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9985,tc_HOL_Obool)),U_9986),hAPP(hAPP(c_Set_Oinsert(U_9985),U_9987),c_Orderings_Obot__class_Obot(tc_fun(U_9985,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9985,tc_HOL_Obool))
        | ~ sP771(U_9985,U_9987,U_9986) )
    & ! [U_9985,U_9987,U_9986] :
        ( sP771(U_9985,U_9987,U_9986)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9985),U_9987),U_9986))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9985),U_9986))
        | ~ class_Orderings_Olinorder(U_9985) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP771])],[f_2730_2]) ).

cnf(f_2730_4,plain,
    ( sP771(U_9985,U_9987,U_9986)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9985),U_9987),U_9986))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9985),U_9986))
    | ~ class_Orderings_Olinorder(U_9985) ),
    inference(clausify,[status(thm)],[f_2730_3]) ).

cnf(f_2730_5,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9985,c_Orderings_Oord__class_Omin(U_9985),U_9986) = U_9987
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9985,tc_HOL_Obool)),U_9986),hAPP(hAPP(c_Set_Oinsert(U_9985),U_9987),c_Orderings_Obot__class_Obot(tc_fun(U_9985,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9985,tc_HOL_Obool))
    | ~ sP771(U_9985,U_9987,U_9986) ),
    inference(clausify,[status(thm)],[f_2730_3]) ).

cnf(f_2730_6,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_9985,c_Orderings_Oord__class_Omin(U_9985),U_9986) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_9985),U_9987),c_Big__Operators_Olattice_OInf__fin(U_9985,c_Orderings_Oord__class_Omin(U_9985),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9985,tc_HOL_Obool)),U_9986),hAPP(hAPP(c_Set_Oinsert(U_9985),U_9987),c_Orderings_Obot__class_Obot(tc_fun(U_9985,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9985,tc_HOL_Obool)),U_9986),hAPP(hAPP(c_Set_Oinsert(U_9985),U_9987),c_Orderings_Obot__class_Obot(tc_fun(U_9985,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9985,tc_HOL_Obool))
    | ~ sP771(U_9985,U_9987,U_9986) ),
    inference(clausify,[status(thm)],[f_2730_3]) ).

fof(f_2731_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_2731_2,plain,
    ! [U_9990,U_9989,U_9988] :
      ( ( ( c_Big__Operators_Olattice_OSup__fin(U_9988,c_Orderings_Oord__class_Omax(U_9988),U_9989) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9988),U_9990),c_Big__Operators_Olattice_OSup__fin(U_9988,c_Orderings_Oord__class_Omax(U_9988),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9988,tc_HOL_Obool)),U_9989),hAPP(hAPP(c_Set_Oinsert(U_9988),U_9990),c_Orderings_Obot__class_Obot(tc_fun(U_9988,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9988,tc_HOL_Obool)),U_9989),hAPP(hAPP(c_Set_Oinsert(U_9988),U_9990),c_Orderings_Obot__class_Obot(tc_fun(U_9988,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9988,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice_OSup__fin(U_9988,c_Orderings_Oord__class_Omax(U_9988),U_9989) = U_9990
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9988,tc_HOL_Obool)),U_9989),hAPP(hAPP(c_Set_Oinsert(U_9988),U_9990),c_Orderings_Obot__class_Obot(tc_fun(U_9988,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9988,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_9988),U_9990),U_9989))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9988),U_9989))
      | ~ class_Orderings_Olinorder(U_9988) ),
    inference(variable_rename,[status(thm)],[f_2731_1]) ).

fof(f_2731_3,plain,
    ( ! [U_9990,U_9989,U_9988] :
        ( c_Big__Operators_Olattice_OSup__fin(U_9988,c_Orderings_Oord__class_Omax(U_9988),U_9989) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9988),U_9990),c_Big__Operators_Olattice_OSup__fin(U_9988,c_Orderings_Oord__class_Omax(U_9988),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9988,tc_HOL_Obool)),U_9989),hAPP(hAPP(c_Set_Oinsert(U_9988),U_9990),c_Orderings_Obot__class_Obot(tc_fun(U_9988,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9988,tc_HOL_Obool)),U_9989),hAPP(hAPP(c_Set_Oinsert(U_9988),U_9990),c_Orderings_Obot__class_Obot(tc_fun(U_9988,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9988,tc_HOL_Obool))
        | ~ sP772(U_9990,U_9989,U_9988) )
    & ! [U_9990,U_9989,U_9988] :
        ( c_Big__Operators_Olattice_OSup__fin(U_9988,c_Orderings_Oord__class_Omax(U_9988),U_9989) = U_9990
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9988,tc_HOL_Obool)),U_9989),hAPP(hAPP(c_Set_Oinsert(U_9988),U_9990),c_Orderings_Obot__class_Obot(tc_fun(U_9988,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9988,tc_HOL_Obool))
        | ~ sP772(U_9990,U_9989,U_9988) )
    & ! [U_9990,U_9989,U_9988] :
        ( sP772(U_9990,U_9989,U_9988)
        | ~ hBOOL(hAPP(hAPP(c_member(U_9988),U_9990),U_9989))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9988),U_9989))
        | ~ class_Orderings_Olinorder(U_9988) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP772])],[f_2731_2]) ).

cnf(f_2731_4,plain,
    ( sP772(U_9990,U_9989,U_9988)
    | ~ hBOOL(hAPP(hAPP(c_member(U_9988),U_9990),U_9989))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9988),U_9989))
    | ~ class_Orderings_Olinorder(U_9988) ),
    inference(clausify,[status(thm)],[f_2731_3]) ).

cnf(f_2731_5,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9988,c_Orderings_Oord__class_Omax(U_9988),U_9989) = U_9990
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9988,tc_HOL_Obool)),U_9989),hAPP(hAPP(c_Set_Oinsert(U_9988),U_9990),c_Orderings_Obot__class_Obot(tc_fun(U_9988,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_9988,tc_HOL_Obool))
    | ~ sP772(U_9990,U_9989,U_9988) ),
    inference(clausify,[status(thm)],[f_2731_3]) ).

cnf(f_2731_6,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_9988,c_Orderings_Oord__class_Omax(U_9988),U_9989) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9988),U_9990),c_Big__Operators_Olattice_OSup__fin(U_9988,c_Orderings_Oord__class_Omax(U_9988),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9988,tc_HOL_Obool)),U_9989),hAPP(hAPP(c_Set_Oinsert(U_9988),U_9990),c_Orderings_Obot__class_Obot(tc_fun(U_9988,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_9988,tc_HOL_Obool)),U_9989),hAPP(hAPP(c_Set_Oinsert(U_9988),U_9990),c_Orderings_Obot__class_Obot(tc_fun(U_9988,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_9988,tc_HOL_Obool))
    | ~ sP772(U_9990,U_9989,U_9988) ),
    inference(clausify,[status(thm)],[f_2731_3]) ).

fof(f_2732_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_2732_2,plain,
    ! [U_9993,U_9992,U_9991] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9991),U_9993),c_Big__Operators_Olattice_OInf__fin(U_9991,c_Orderings_Oord__class_Omin(U_9991),U_9992)) = c_Big__Operators_Olattice_OInf__fin(U_9991,c_Orderings_Oord__class_Omin(U_9991),hAPP(c_Set_OCollect(U_9991),hAPP(hAPP(c_COMBB(tc_fun(U_9991,tc_HOL_Obool),tc_HOL_Obool,U_9991),c_HOL_OEx(U_9991)),hAPP(hAPP(c_COMBC(U_9991,tc_fun(U_9991,tc_HOL_Obool),tc_fun(U_9991,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9991,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9991,tc_HOL_Obool),tc_fun(U_9991,tc_HOL_Obool)),U_9991),c_COMBS(U_9991,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9991,tc_HOL_Obool),tc_fun(U_9991,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9991),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9991),c_fconj)),hAPP(hAPP(c_COMBC(U_9991,tc_fun(U_9991,U_9991),tc_fun(U_9991,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9991,tc_HOL_Obool),tc_fun(tc_fun(U_9991,U_9991),tc_fun(U_9991,tc_HOL_Obool)),U_9991),c_COMBB(U_9991,tc_HOL_Obool,U_9991)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_9991),U_9993))))),hAPP(hAPP(c_COMBC(U_9991,tc_fun(U_9991,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9991)),U_9992)))))
      | U_9992 = c_Orderings_Obot__class_Obot(tc_fun(U_9991,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9991),U_9992))
      | ~ class_Orderings_Olinorder(U_9991) ),
    inference(variable_rename,[status(thm)],[f_2732_1]) ).

fof(f_2732_3,plain,
    ! [U_9991,U_9992,U_9993] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9991),U_9993),c_Big__Operators_Olattice_OInf__fin(U_9991,c_Orderings_Oord__class_Omin(U_9991),U_9992)) = c_Big__Operators_Olattice_OInf__fin(U_9991,c_Orderings_Oord__class_Omin(U_9991),hAPP(c_Set_OCollect(U_9991),hAPP(hAPP(c_COMBB(tc_fun(U_9991,tc_HOL_Obool),tc_HOL_Obool,U_9991),c_HOL_OEx(U_9991)),hAPP(hAPP(c_COMBC(U_9991,tc_fun(U_9991,tc_HOL_Obool),tc_fun(U_9991,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9991,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9991,tc_HOL_Obool),tc_fun(U_9991,tc_HOL_Obool)),U_9991),c_COMBS(U_9991,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9991,tc_HOL_Obool),tc_fun(U_9991,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9991),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9991),c_fconj)),hAPP(hAPP(c_COMBC(U_9991,tc_fun(U_9991,U_9991),tc_fun(U_9991,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9991,tc_HOL_Obool),tc_fun(tc_fun(U_9991,U_9991),tc_fun(U_9991,tc_HOL_Obool)),U_9991),c_COMBB(U_9991,tc_HOL_Obool,U_9991)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_9991),U_9993))))),hAPP(hAPP(c_COMBC(U_9991,tc_fun(U_9991,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9991)),U_9992)))))
      | U_9992 = c_Orderings_Obot__class_Obot(tc_fun(U_9991,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9991),U_9992))
      | ~ class_Orderings_Olinorder(U_9991) ),
    inference(definitional_conversion,[status(esa)],[f_2732_2]) ).

cnf(f_2732_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9991),U_9993),c_Big__Operators_Olattice_OInf__fin(U_9991,c_Orderings_Oord__class_Omin(U_9991),U_9992)) = c_Big__Operators_Olattice_OInf__fin(U_9991,c_Orderings_Oord__class_Omin(U_9991),hAPP(c_Set_OCollect(U_9991),hAPP(hAPP(c_COMBB(tc_fun(U_9991,tc_HOL_Obool),tc_HOL_Obool,U_9991),c_HOL_OEx(U_9991)),hAPP(hAPP(c_COMBC(U_9991,tc_fun(U_9991,tc_HOL_Obool),tc_fun(U_9991,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9991,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_9991,tc_HOL_Obool),tc_fun(U_9991,tc_HOL_Obool)),U_9991),c_COMBS(U_9991,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9991,tc_HOL_Obool),tc_fun(U_9991,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_9991),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_9991),c_fconj)),hAPP(hAPP(c_COMBC(U_9991,tc_fun(U_9991,U_9991),tc_fun(U_9991,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_9991,tc_HOL_Obool),tc_fun(tc_fun(U_9991,U_9991),tc_fun(U_9991,tc_HOL_Obool)),U_9991),c_COMBB(U_9991,tc_HOL_Obool,U_9991)),c_fequal)),hAPP(c_Orderings_Oord__class_Omax(U_9991),U_9993))))),hAPP(hAPP(c_COMBC(U_9991,tc_fun(U_9991,tc_HOL_Obool),tc_HOL_Obool),c_member(U_9991)),U_9992)))))
    | U_9992 = c_Orderings_Obot__class_Obot(tc_fun(U_9991,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9991),U_9992))
    | ~ class_Orderings_Olinorder(U_9991) ),
    inference(clausify,[status(thm)],[f_2732_3]) ).

fof(f_2733_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_2733_2,plain,
    ! [U_9997,U_9996] :
      ( hBOOL(hAPP(hAPP(c_member(U_9996),c_Big__Operators_Olattice_OSup__fin(U_9996,c_Orderings_Oord__class_Omax(U_9996),U_9997)),U_9997))
      | ? [U_9995,U_9994] : ~ hBOOL(hAPP(hAPP(c_member(U_9996),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9996),U_9995),U_9994)),hAPP(hAPP(c_Set_Oinsert(U_9996),U_9995),hAPP(hAPP(c_Set_Oinsert(U_9996),U_9994),c_Orderings_Obot__class_Obot(tc_fun(U_9996,tc_HOL_Obool))))))
      | U_9997 = c_Orderings_Obot__class_Obot(tc_fun(U_9996,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9996),U_9997))
      | ~ class_Orderings_Olinorder(U_9996) ),
    inference(variable_rename,[status(thm)],[f_2733_1]) ).

fof(f_2733_3,plain,
    ! [U_9997,U_9996] :
      ( hBOOL(hAPP(hAPP(c_member(U_9996),c_Big__Operators_Olattice_OSup__fin(U_9996,c_Orderings_Oord__class_Omax(U_9996),U_9997)),U_9997))
      | ? [U_9994] : ~ hBOOL(hAPP(hAPP(c_member(U_9996),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9996),sK158(U_9997,U_9996)),U_9994)),hAPP(hAPP(c_Set_Oinsert(U_9996),sK158(U_9997,U_9996)),hAPP(hAPP(c_Set_Oinsert(U_9996),U_9994),c_Orderings_Obot__class_Obot(tc_fun(U_9996,tc_HOL_Obool))))))
      | U_9997 = c_Orderings_Obot__class_Obot(tc_fun(U_9996,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9996),U_9997))
      | ~ class_Orderings_Olinorder(U_9996) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK158]),skolemize(U_9995,sK158(U_9997,U_9996))],[f_2733_2]) ).

fof(f_2733_4,plain,
    ! [U_9997,U_9996] :
      ( hBOOL(hAPP(hAPP(c_member(U_9996),c_Big__Operators_Olattice_OSup__fin(U_9996,c_Orderings_Oord__class_Omax(U_9996),U_9997)),U_9997))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9996),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9996),sK158(U_9997,U_9996)),sK159(U_9997,U_9996))),hAPP(hAPP(c_Set_Oinsert(U_9996),sK158(U_9997,U_9996)),hAPP(hAPP(c_Set_Oinsert(U_9996),sK159(U_9997,U_9996)),c_Orderings_Obot__class_Obot(tc_fun(U_9996,tc_HOL_Obool))))))
      | U_9997 = c_Orderings_Obot__class_Obot(tc_fun(U_9996,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9996),U_9997))
      | ~ class_Orderings_Olinorder(U_9996) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK159]),skolemize(U_9994,sK159(U_9997,U_9996))],[f_2733_3]) ).

fof(f_2733_5,plain,
    ! [U_9996,U_9997] :
      ( hBOOL(hAPP(hAPP(c_member(U_9996),c_Big__Operators_Olattice_OSup__fin(U_9996,c_Orderings_Oord__class_Omax(U_9996),U_9997)),U_9997))
      | ~ hBOOL(hAPP(hAPP(c_member(U_9996),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9996),sK158(U_9997,U_9996)),sK159(U_9997,U_9996))),hAPP(hAPP(c_Set_Oinsert(U_9996),sK158(U_9997,U_9996)),hAPP(hAPP(c_Set_Oinsert(U_9996),sK159(U_9997,U_9996)),c_Orderings_Obot__class_Obot(tc_fun(U_9996,tc_HOL_Obool))))))
      | U_9997 = c_Orderings_Obot__class_Obot(tc_fun(U_9996,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9996),U_9997))
      | ~ class_Orderings_Olinorder(U_9996) ),
    inference(definitional_conversion,[status(esa)],[f_2733_4]) ).

cnf(f_2733_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_9996),c_Big__Operators_Olattice_OSup__fin(U_9996,c_Orderings_Oord__class_Omax(U_9996),U_9997)),U_9997))
    | ~ hBOOL(hAPP(hAPP(c_member(U_9996),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_9996),sK158(U_9997,U_9996)),sK159(U_9997,U_9996))),hAPP(hAPP(c_Set_Oinsert(U_9996),sK158(U_9997,U_9996)),hAPP(hAPP(c_Set_Oinsert(U_9996),sK159(U_9997,U_9996)),c_Orderings_Obot__class_Obot(tc_fun(U_9996,tc_HOL_Obool))))))
    | U_9997 = c_Orderings_Obot__class_Obot(tc_fun(U_9996,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_9996),U_9997))
    | ~ class_Orderings_Olinorder(U_9996) ),
    inference(clausify,[status(thm)],[f_2733_5]) ).

fof(f_2734_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_2734_2,plain,
    ! [U_10001,U_10000] :
      ( hBOOL(hAPP(hAPP(c_member(U_10000),c_Big__Operators_Olattice_OInf__fin(U_10000,c_Orderings_Oord__class_Omin(U_10000),U_10001)),U_10001))
      | ? [U_9999,U_9998] : ~ hBOOL(hAPP(hAPP(c_member(U_10000),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10000),U_9999),U_9998)),hAPP(hAPP(c_Set_Oinsert(U_10000),U_9999),hAPP(hAPP(c_Set_Oinsert(U_10000),U_9998),c_Orderings_Obot__class_Obot(tc_fun(U_10000,tc_HOL_Obool))))))
      | U_10001 = c_Orderings_Obot__class_Obot(tc_fun(U_10000,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10000),U_10001))
      | ~ class_Orderings_Olinorder(U_10000) ),
    inference(variable_rename,[status(thm)],[f_2734_1]) ).

fof(f_2734_3,plain,
    ! [U_10001,U_10000] :
      ( hBOOL(hAPP(hAPP(c_member(U_10000),c_Big__Operators_Olattice_OInf__fin(U_10000,c_Orderings_Oord__class_Omin(U_10000),U_10001)),U_10001))
      | ? [U_9998] : ~ hBOOL(hAPP(hAPP(c_member(U_10000),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10000),sK160(U_10001,U_10000)),U_9998)),hAPP(hAPP(c_Set_Oinsert(U_10000),sK160(U_10001,U_10000)),hAPP(hAPP(c_Set_Oinsert(U_10000),U_9998),c_Orderings_Obot__class_Obot(tc_fun(U_10000,tc_HOL_Obool))))))
      | U_10001 = c_Orderings_Obot__class_Obot(tc_fun(U_10000,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10000),U_10001))
      | ~ class_Orderings_Olinorder(U_10000) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK160]),skolemize(U_9999,sK160(U_10001,U_10000))],[f_2734_2]) ).

fof(f_2734_4,plain,
    ! [U_10001,U_10000] :
      ( hBOOL(hAPP(hAPP(c_member(U_10000),c_Big__Operators_Olattice_OInf__fin(U_10000,c_Orderings_Oord__class_Omin(U_10000),U_10001)),U_10001))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10000),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10000),sK160(U_10001,U_10000)),sK161(U_10001,U_10000))),hAPP(hAPP(c_Set_Oinsert(U_10000),sK160(U_10001,U_10000)),hAPP(hAPP(c_Set_Oinsert(U_10000),sK161(U_10001,U_10000)),c_Orderings_Obot__class_Obot(tc_fun(U_10000,tc_HOL_Obool))))))
      | U_10001 = c_Orderings_Obot__class_Obot(tc_fun(U_10000,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10000),U_10001))
      | ~ class_Orderings_Olinorder(U_10000) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK161]),skolemize(U_9998,sK161(U_10001,U_10000))],[f_2734_3]) ).

fof(f_2734_5,plain,
    ! [U_10000,U_10001] :
      ( hBOOL(hAPP(hAPP(c_member(U_10000),c_Big__Operators_Olattice_OInf__fin(U_10000,c_Orderings_Oord__class_Omin(U_10000),U_10001)),U_10001))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10000),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10000),sK160(U_10001,U_10000)),sK161(U_10001,U_10000))),hAPP(hAPP(c_Set_Oinsert(U_10000),sK160(U_10001,U_10000)),hAPP(hAPP(c_Set_Oinsert(U_10000),sK161(U_10001,U_10000)),c_Orderings_Obot__class_Obot(tc_fun(U_10000,tc_HOL_Obool))))))
      | U_10001 = c_Orderings_Obot__class_Obot(tc_fun(U_10000,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10000),U_10001))
      | ~ class_Orderings_Olinorder(U_10000) ),
    inference(definitional_conversion,[status(esa)],[f_2734_4]) ).

cnf(f_2734_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10000),c_Big__Operators_Olattice_OInf__fin(U_10000,c_Orderings_Oord__class_Omin(U_10000),U_10001)),U_10001))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10000),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10000),sK160(U_10001,U_10000)),sK161(U_10001,U_10000))),hAPP(hAPP(c_Set_Oinsert(U_10000),sK160(U_10001,U_10000)),hAPP(hAPP(c_Set_Oinsert(U_10000),sK161(U_10001,U_10000)),c_Orderings_Obot__class_Obot(tc_fun(U_10000,tc_HOL_Obool))))))
    | U_10001 = c_Orderings_Obot__class_Obot(tc_fun(U_10000,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10000),U_10001))
    | ~ class_Orderings_Olinorder(U_10000) ),
    inference(clausify,[status(thm)],[f_2734_5]) ).

fof(f_2735_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_2735_2,plain,
    ! [U_10005,U_10004,U_10003,U_10002] : c_Transitive__Closure_Otrancl(U_10002,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10002,U_10002)),hAPP(hAPP(c_Product__Type_OPair(U_10002,U_10002),U_10003),U_10004)),U_10005)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10002,U_10002),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_10002,U_10005)),hAPP(c_Set_OCollect(tc_prod(U_10002,U_10002)),hAPP(c_Product__Type_Oprod_Oprod__case(U_10002,U_10002,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_10002,tc_fun(U_10002,tc_HOL_Obool),tc_fun(U_10002,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_10002,tc_HOL_Obool),tc_fun(U_10002,tc_HOL_Obool)),U_10002),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_10002)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10002),c_fconj),hAPP(hAPP(c_COMBC(U_10002,tc_fun(tc_prod(U_10002,U_10002),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_10002,U_10002),tc_fun(tc_fun(tc_prod(U_10002,U_10002),tc_HOL_Obool),tc_HOL_Obool),U_10002),c_member(tc_prod(U_10002,U_10002))),hAPP(hAPP(c_COMBC(U_10002,U_10002,tc_prod(U_10002,U_10002)),c_Product__Type_OPair(U_10002,U_10002)),U_10003))),c_Transitive__Closure_Ortrancl(U_10002,U_10005))))),hAPP(hAPP(c_COMBC(U_10002,tc_fun(tc_prod(U_10002,U_10002),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_10002,U_10002),tc_fun(tc_fun(tc_prod(U_10002,U_10002),tc_HOL_Obool),tc_HOL_Obool),U_10002),c_member(tc_prod(U_10002,U_10002))),hAPP(c_Product__Type_OPair(U_10002,U_10002),U_10004))),c_Transitive__Closure_Ortrancl(U_10002,U_10005)))))),
    inference(variable_rename,[status(thm)],[f_2735_1]) ).

fof(f_2735_3,plain,
    ! [U_10002,U_10003,U_10004,U_10005] : c_Transitive__Closure_Otrancl(U_10002,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10002,U_10002)),hAPP(hAPP(c_Product__Type_OPair(U_10002,U_10002),U_10003),U_10004)),U_10005)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10002,U_10002),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_10002,U_10005)),hAPP(c_Set_OCollect(tc_prod(U_10002,U_10002)),hAPP(c_Product__Type_Oprod_Oprod__case(U_10002,U_10002,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_10002,tc_fun(U_10002,tc_HOL_Obool),tc_fun(U_10002,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_10002,tc_HOL_Obool),tc_fun(U_10002,tc_HOL_Obool)),U_10002),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_10002)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10002),c_fconj),hAPP(hAPP(c_COMBC(U_10002,tc_fun(tc_prod(U_10002,U_10002),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_10002,U_10002),tc_fun(tc_fun(tc_prod(U_10002,U_10002),tc_HOL_Obool),tc_HOL_Obool),U_10002),c_member(tc_prod(U_10002,U_10002))),hAPP(hAPP(c_COMBC(U_10002,U_10002,tc_prod(U_10002,U_10002)),c_Product__Type_OPair(U_10002,U_10002)),U_10003))),c_Transitive__Closure_Ortrancl(U_10002,U_10005))))),hAPP(hAPP(c_COMBC(U_10002,tc_fun(tc_prod(U_10002,U_10002),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_10002,U_10002),tc_fun(tc_fun(tc_prod(U_10002,U_10002),tc_HOL_Obool),tc_HOL_Obool),U_10002),c_member(tc_prod(U_10002,U_10002))),hAPP(c_Product__Type_OPair(U_10002,U_10002),U_10004))),c_Transitive__Closure_Ortrancl(U_10002,U_10005)))))),
    inference(definitional_conversion,[status(esa)],[f_2735_2]) ).

cnf(f_2735_4,plain,
    c_Transitive__Closure_Otrancl(U_10002,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10002,U_10002)),hAPP(hAPP(c_Product__Type_OPair(U_10002,U_10002),U_10003),U_10004)),U_10005)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10002,U_10002),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_10002,U_10005)),hAPP(c_Set_OCollect(tc_prod(U_10002,U_10002)),hAPP(c_Product__Type_Oprod_Oprod__case(U_10002,U_10002,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_10002,tc_fun(U_10002,tc_HOL_Obool),tc_fun(U_10002,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_10002,tc_HOL_Obool),tc_fun(U_10002,tc_HOL_Obool)),U_10002),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_10002)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10002),c_fconj),hAPP(hAPP(c_COMBC(U_10002,tc_fun(tc_prod(U_10002,U_10002),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_10002,U_10002),tc_fun(tc_fun(tc_prod(U_10002,U_10002),tc_HOL_Obool),tc_HOL_Obool),U_10002),c_member(tc_prod(U_10002,U_10002))),hAPP(hAPP(c_COMBC(U_10002,U_10002,tc_prod(U_10002,U_10002)),c_Product__Type_OPair(U_10002,U_10002)),U_10003))),c_Transitive__Closure_Ortrancl(U_10002,U_10005))))),hAPP(hAPP(c_COMBC(U_10002,tc_fun(tc_prod(U_10002,U_10002),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_10002,U_10002),tc_fun(tc_fun(tc_prod(U_10002,U_10002),tc_HOL_Obool),tc_HOL_Obool),U_10002),c_member(tc_prod(U_10002,U_10002))),hAPP(c_Product__Type_OPair(U_10002,U_10002),U_10004))),c_Transitive__Closure_Ortrancl(U_10002,U_10005)))))),
    inference(clausify,[status(thm)],[f_2735_3]) ).

fof(f_2736_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_2736_2,plain,
    ! [U_10012,U_10011,U_10010] :
      ( ( hAPP(c_Finite__Set_Ocard(U_10010),U_10011) = hAPP(c_Nat_OSuc,U_10012)
        | ! [U_10009,U_10008] :
            ( ( U_10008 != c_Orderings_Obot__class_Obot(tc_fun(U_10010,tc_HOL_Obool))
              & U_10012 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_10010),U_10008) != U_10012
            | hBOOL(hAPP(hAPP(c_member(U_10010),U_10009),U_10008))
            | U_10011 != hAPP(hAPP(c_Set_Oinsert(U_10010),U_10009),U_10008) ) )
      & ( ? [U_10007,U_10006] :
            ( ( U_10006 = c_Orderings_Obot__class_Obot(tc_fun(U_10010,tc_HOL_Obool))
              | U_10012 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & hAPP(c_Finite__Set_Ocard(U_10010),U_10006) = U_10012
            & ~ hBOOL(hAPP(hAPP(c_member(U_10010),U_10007),U_10006))
            & U_10011 = hAPP(hAPP(c_Set_Oinsert(U_10010),U_10007),U_10006) )
        | hAPP(c_Finite__Set_Ocard(U_10010),U_10011) != hAPP(c_Nat_OSuc,U_10012) ) ),
    inference(variable_rename,[status(thm)],[f_2736_1]) ).

fof(f_2736_3,plain,
    ( ! [U_10018,U_10016,U_10014] :
        ( hAPP(c_Finite__Set_Ocard(U_10014),U_10016) = hAPP(c_Nat_OSuc,U_10018)
        | ! [U_10009,U_10008] :
            ( ( U_10008 != c_Orderings_Obot__class_Obot(tc_fun(U_10014,tc_HOL_Obool))
              & U_10018 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_10014),U_10008) != U_10018
            | hBOOL(hAPP(hAPP(c_member(U_10014),U_10009),U_10008))
            | U_10016 != hAPP(hAPP(c_Set_Oinsert(U_10014),U_10009),U_10008) ) )
    & ! [U_10017,U_10015,U_10013] :
        ( ? [U_10007,U_10006] :
            ( ( U_10006 = c_Orderings_Obot__class_Obot(tc_fun(U_10013,tc_HOL_Obool))
              | U_10017 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & hAPP(c_Finite__Set_Ocard(U_10013),U_10006) = U_10017
            & ~ hBOOL(hAPP(hAPP(c_member(U_10013),U_10007),U_10006))
            & U_10015 = hAPP(hAPP(c_Set_Oinsert(U_10013),U_10007),U_10006) )
        | hAPP(c_Finite__Set_Ocard(U_10013),U_10015) != hAPP(c_Nat_OSuc,U_10017) ) ),
    inference(miniscope,[status(thm)],[f_2736_2]) ).

fof(f_2736_4,plain,
    ( ! [U_10018,U_10016,U_10014] :
        ( hAPP(c_Finite__Set_Ocard(U_10014),U_10016) = hAPP(c_Nat_OSuc,U_10018)
        | ! [U_10009,U_10008] :
            ( ( U_10008 != c_Orderings_Obot__class_Obot(tc_fun(U_10014,tc_HOL_Obool))
              & U_10018 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_10014),U_10008) != U_10018
            | hBOOL(hAPP(hAPP(c_member(U_10014),U_10009),U_10008))
            | U_10016 != hAPP(hAPP(c_Set_Oinsert(U_10014),U_10009),U_10008) ) )
    & ! [U_10017,U_10015,U_10013] :
        ( ? [U_10006] :
            ( ( U_10006 = c_Orderings_Obot__class_Obot(tc_fun(U_10013,tc_HOL_Obool))
              | U_10017 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            & hAPP(c_Finite__Set_Ocard(U_10013),U_10006) = U_10017
            & ~ hBOOL(hAPP(hAPP(c_member(U_10013),sK162(U_10017,U_10015,U_10013)),U_10006))
            & U_10015 = hAPP(hAPP(c_Set_Oinsert(U_10013),sK162(U_10017,U_10015,U_10013)),U_10006) )
        | hAPP(c_Finite__Set_Ocard(U_10013),U_10015) != hAPP(c_Nat_OSuc,U_10017) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK162]),skolemize(U_10007,sK162(U_10017,U_10015,U_10013))],[f_2736_3]) ).

fof(f_2736_5,plain,
    ( ! [U_10018,U_10016,U_10014] :
        ( hAPP(c_Finite__Set_Ocard(U_10014),U_10016) = hAPP(c_Nat_OSuc,U_10018)
        | ! [U_10009,U_10008] :
            ( ( U_10008 != c_Orderings_Obot__class_Obot(tc_fun(U_10014,tc_HOL_Obool))
              & U_10018 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
            | hAPP(c_Finite__Set_Ocard(U_10014),U_10008) != U_10018
            | hBOOL(hAPP(hAPP(c_member(U_10014),U_10009),U_10008))
            | U_10016 != hAPP(hAPP(c_Set_Oinsert(U_10014),U_10009),U_10008) ) )
    & ! [U_10017,U_10015,U_10013] :
        ( ( ( sK163(U_10017,U_10015,U_10013) = c_Orderings_Obot__class_Obot(tc_fun(U_10013,tc_HOL_Obool))
            | U_10017 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
          & hAPP(c_Finite__Set_Ocard(U_10013),sK163(U_10017,U_10015,U_10013)) = U_10017
          & ~ hBOOL(hAPP(hAPP(c_member(U_10013),sK162(U_10017,U_10015,U_10013)),sK163(U_10017,U_10015,U_10013)))
          & U_10015 = hAPP(hAPP(c_Set_Oinsert(U_10013),sK162(U_10017,U_10015,U_10013)),sK163(U_10017,U_10015,U_10013)) )
        | hAPP(c_Finite__Set_Ocard(U_10013),U_10015) != hAPP(c_Nat_OSuc,U_10017) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK163]),skolemize(U_10006,sK163(U_10017,U_10015,U_10013))],[f_2736_4]) ).

fof(f_2736_6,plain,
    ( ! [U_10018,U_10008,U_10014] :
        ( U_10008 != c_Orderings_Obot__class_Obot(tc_fun(U_10014,tc_HOL_Obool))
        | ~ sP774(U_10018,U_10008,U_10014) )
    & ! [U_10018,U_10008,U_10014] :
        ( U_10018 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP774(U_10018,U_10008,U_10014) )
    & ! [U_10017,U_10015,U_10013] :
        ( sK163(U_10017,U_10015,U_10013) = c_Orderings_Obot__class_Obot(tc_fun(U_10013,tc_HOL_Obool))
        | U_10017 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP773(U_10017,U_10015,U_10013) )
    & ! [U_10017,U_10015,U_10013] :
        ( hAPP(c_Finite__Set_Ocard(U_10013),sK163(U_10017,U_10015,U_10013)) = U_10017
        | ~ sP773(U_10017,U_10015,U_10013) )
    & ! [U_10017,U_10015,U_10013] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_10013),sK162(U_10017,U_10015,U_10013)),sK163(U_10017,U_10015,U_10013)))
        | ~ sP773(U_10017,U_10015,U_10013) )
    & ! [U_10017,U_10015,U_10013] :
        ( U_10015 = hAPP(hAPP(c_Set_Oinsert(U_10013),sK162(U_10017,U_10015,U_10013)),sK163(U_10017,U_10015,U_10013))
        | ~ sP773(U_10017,U_10015,U_10013) )
    & ! [U_10018,U_10008,U_10009,U_10016,U_10014] :
        ( hAPP(c_Finite__Set_Ocard(U_10014),U_10016) = hAPP(c_Nat_OSuc,U_10018)
        | sP774(U_10018,U_10008,U_10014)
        | hAPP(c_Finite__Set_Ocard(U_10014),U_10008) != U_10018
        | hBOOL(hAPP(hAPP(c_member(U_10014),U_10009),U_10008))
        | U_10016 != hAPP(hAPP(c_Set_Oinsert(U_10014),U_10009),U_10008) )
    & ! [U_10017,U_10015,U_10013] :
        ( sP773(U_10017,U_10015,U_10013)
        | hAPP(c_Finite__Set_Ocard(U_10013),U_10015) != hAPP(c_Nat_OSuc,U_10017) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP773,sP774])],[f_2736_5]) ).

cnf(f_2736_7,plain,
    ( sP773(U_10017,U_10015,U_10013)
    | hAPP(c_Finite__Set_Ocard(U_10013),U_10015) != hAPP(c_Nat_OSuc,U_10017) ),
    inference(clausify,[status(thm)],[f_2736_6]) ).

cnf(f_2736_8,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10014),U_10016) = hAPP(c_Nat_OSuc,U_10018)
    | sP774(U_10018,U_10008,U_10014)
    | hAPP(c_Finite__Set_Ocard(U_10014),U_10008) != U_10018
    | hBOOL(hAPP(hAPP(c_member(U_10014),U_10009),U_10008))
    | U_10016 != hAPP(hAPP(c_Set_Oinsert(U_10014),U_10009),U_10008) ),
    inference(clausify,[status(thm)],[f_2736_6]) ).

cnf(f_2736_9,plain,
    ( U_10015 = hAPP(hAPP(c_Set_Oinsert(U_10013),sK162(U_10017,U_10015,U_10013)),sK163(U_10017,U_10015,U_10013))
    | ~ sP773(U_10017,U_10015,U_10013) ),
    inference(clausify,[status(thm)],[f_2736_6]) ).

cnf(f_2736_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_10013),sK162(U_10017,U_10015,U_10013)),sK163(U_10017,U_10015,U_10013)))
    | ~ sP773(U_10017,U_10015,U_10013) ),
    inference(clausify,[status(thm)],[f_2736_6]) ).

cnf(f_2736_11,plain,
    ( hAPP(c_Finite__Set_Ocard(U_10013),sK163(U_10017,U_10015,U_10013)) = U_10017
    | ~ sP773(U_10017,U_10015,U_10013) ),
    inference(clausify,[status(thm)],[f_2736_6]) ).

cnf(f_2736_12,plain,
    ( sK163(U_10017,U_10015,U_10013) = c_Orderings_Obot__class_Obot(tc_fun(U_10013,tc_HOL_Obool))
    | U_10017 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP773(U_10017,U_10015,U_10013) ),
    inference(clausify,[status(thm)],[f_2736_6]) ).

cnf(f_2736_13,plain,
    ( U_10018 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP774(U_10018,U_10008,U_10014) ),
    inference(clausify,[status(thm)],[f_2736_6]) ).

cnf(f_2736_14,plain,
    ( U_10008 != c_Orderings_Obot__class_Obot(tc_fun(U_10014,tc_HOL_Obool))
    | ~ sP774(U_10018,U_10008,U_10014) ),
    inference(clausify,[status(thm)],[f_2736_6]) ).

fof(f_2737_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_2737_2,plain,
    ! [U_10021,U_10020,U_10019] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10019,U_10019)),U_10020),c_Transitive__Closure_Ortrancl(U_10019,U_10021)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10019,U_10019)),U_10020),U_10021)) ),
    inference(variable_rename,[status(thm)],[f_2737_1]) ).

fof(f_2737_3,plain,
    ! [U_10020,U_10019,U_10021] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10019,U_10019)),U_10020),c_Transitive__Closure_Ortrancl(U_10019,U_10021)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10019,U_10019)),U_10020),U_10021)) ),
    inference(definitional_conversion,[status(esa)],[f_2737_2]) ).

cnf(f_2737_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10019,U_10019)),U_10020),c_Transitive__Closure_Ortrancl(U_10019,U_10021)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10019,U_10019)),U_10020),U_10021)) ),
    inference(clausify,[status(thm)],[f_2737_3]) ).

fof(f_2738_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_2738_2,plain,
    ! [U_10024,U_10023,U_10022] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_10022,U_10022)),hAPP(hAPP(c_Product__Type_OPair(U_10022,U_10022),U_10023),U_10023)),c_Transitive__Closure_Ortrancl(U_10022,U_10024))),
    inference(variable_rename,[status(thm)],[f_2738_1]) ).

fof(f_2738_3,plain,
    ! [U_10024,U_10022,U_10023] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_10022,U_10022)),hAPP(hAPP(c_Product__Type_OPair(U_10022,U_10022),U_10023),U_10023)),c_Transitive__Closure_Ortrancl(U_10022,U_10024))),
    inference(definitional_conversion,[status(esa)],[f_2738_2]) ).

cnf(f_2738_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(U_10022,U_10022)),hAPP(hAPP(c_Product__Type_OPair(U_10022,U_10022),U_10023),U_10023)),c_Transitive__Closure_Ortrancl(U_10022,U_10024))),
    inference(clausify,[status(thm)],[f_2738_3]) ).

fof(f_2739_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_2739_2,plain,
    ! [U_10028,U_10027,U_10026,U_10025] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10025,U_10025)),hAPP(hAPP(c_Product__Type_OPair(U_10025,U_10025),U_10026),U_10027)),c_Transitive__Closure_Ortrancl(U_10025,U_10028)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10025,U_10025)),hAPP(hAPP(c_Product__Type_OPair(U_10025,U_10025),U_10026),U_10027)),c_Transitive__Closure_Otrancl(U_10025,U_10028))) ),
    inference(variable_rename,[status(thm)],[f_2739_1]) ).

fof(f_2739_3,plain,
    ! [U_10025,U_10026,U_10027,U_10028] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10025,U_10025)),hAPP(hAPP(c_Product__Type_OPair(U_10025,U_10025),U_10026),U_10027)),c_Transitive__Closure_Ortrancl(U_10025,U_10028)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10025,U_10025)),hAPP(hAPP(c_Product__Type_OPair(U_10025,U_10025),U_10026),U_10027)),c_Transitive__Closure_Otrancl(U_10025,U_10028))) ),
    inference(definitional_conversion,[status(esa)],[f_2739_2]) ).

cnf(f_2739_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10025,U_10025)),hAPP(hAPP(c_Product__Type_OPair(U_10025,U_10025),U_10026),U_10027)),c_Transitive__Closure_Ortrancl(U_10025,U_10028)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10025,U_10025)),hAPP(hAPP(c_Product__Type_OPair(U_10025,U_10025),U_10026),U_10027)),c_Transitive__Closure_Otrancl(U_10025,U_10028))) ),
    inference(clausify,[status(thm)],[f_2739_3]) ).

fof(f_2740_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_2740_2,plain,
    ! [U_10030,U_10029] : c_Transitive__Closure_Ortrancl(U_10029,c_Transitive__Closure_Otrancl(U_10029,U_10030)) = c_Transitive__Closure_Ortrancl(U_10029,U_10030),
    inference(variable_rename,[status(thm)],[f_2740_1]) ).

fof(f_2740_3,plain,
    ! [U_10029,U_10030] : c_Transitive__Closure_Ortrancl(U_10029,c_Transitive__Closure_Otrancl(U_10029,U_10030)) = c_Transitive__Closure_Ortrancl(U_10029,U_10030),
    inference(definitional_conversion,[status(esa)],[f_2740_2]) ).

cnf(f_2740_4,plain,
    c_Transitive__Closure_Ortrancl(U_10029,c_Transitive__Closure_Otrancl(U_10029,U_10030)) = c_Transitive__Closure_Ortrancl(U_10029,U_10030),
    inference(clausify,[status(thm)],[f_2740_3]) ).

fof(f_2741_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_2741_2,plain,
    ! [U_10032,U_10031] : c_Transitive__Closure_Otrancl(U_10031,c_Transitive__Closure_Ortrancl(U_10031,U_10032)) = c_Transitive__Closure_Ortrancl(U_10031,U_10032),
    inference(variable_rename,[status(thm)],[f_2741_1]) ).

fof(f_2741_3,plain,
    ! [U_10031,U_10032] : c_Transitive__Closure_Otrancl(U_10031,c_Transitive__Closure_Ortrancl(U_10031,U_10032)) = c_Transitive__Closure_Ortrancl(U_10031,U_10032),
    inference(definitional_conversion,[status(esa)],[f_2741_2]) ).

cnf(f_2741_4,plain,
    c_Transitive__Closure_Otrancl(U_10031,c_Transitive__Closure_Ortrancl(U_10031,U_10032)) = c_Transitive__Closure_Ortrancl(U_10031,U_10032),
    inference(clausify,[status(thm)],[f_2741_3]) ).

fof(f_2742_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_2742_2,plain,
    ! [U_10034,U_10033] : c_Transitive__Closure_Ortrancl(U_10033,c_Transitive__Closure_Ortrancl(U_10033,U_10034)) = c_Transitive__Closure_Ortrancl(U_10033,U_10034),
    inference(variable_rename,[status(thm)],[f_2742_1]) ).

fof(f_2742_3,plain,
    ! [U_10033,U_10034] : c_Transitive__Closure_Ortrancl(U_10033,c_Transitive__Closure_Ortrancl(U_10033,U_10034)) = c_Transitive__Closure_Ortrancl(U_10033,U_10034),
    inference(definitional_conversion,[status(esa)],[f_2742_2]) ).

cnf(f_2742_4,plain,
    c_Transitive__Closure_Ortrancl(U_10033,c_Transitive__Closure_Ortrancl(U_10033,U_10034)) = c_Transitive__Closure_Ortrancl(U_10033,U_10034),
    inference(clausify,[status(thm)],[f_2742_3]) ).

fof(f_2743_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_2743_2,plain,
    ! [U_10036,U_10035] : c_Transitive__Closure_Ortrancl(U_10035,hAPP(c_Relation_Oconverse(U_10035,U_10035),U_10036)) = hAPP(c_Relation_Oconverse(U_10035,U_10035),c_Transitive__Closure_Ortrancl(U_10035,U_10036)),
    inference(variable_rename,[status(thm)],[f_2743_1]) ).

fof(f_2743_3,plain,
    ! [U_10035,U_10036] : c_Transitive__Closure_Ortrancl(U_10035,hAPP(c_Relation_Oconverse(U_10035,U_10035),U_10036)) = hAPP(c_Relation_Oconverse(U_10035,U_10035),c_Transitive__Closure_Ortrancl(U_10035,U_10036)),
    inference(definitional_conversion,[status(esa)],[f_2743_2]) ).

cnf(f_2743_4,plain,
    c_Transitive__Closure_Ortrancl(U_10035,hAPP(c_Relation_Oconverse(U_10035,U_10035),U_10036)) = hAPP(c_Relation_Oconverse(U_10035,U_10035),c_Transitive__Closure_Ortrancl(U_10035,U_10036)),
    inference(clausify,[status(thm)],[f_2743_3]) ).

fof(f_2744_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_2744_2,plain,
    ! [U_10039,U_10038,U_10037] : c_Transitive__Closure_Ortrancl(U_10037,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10037,U_10037),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_10037,U_10038)),c_Transitive__Closure_Ortrancl(U_10037,U_10039))) = c_Transitive__Closure_Ortrancl(U_10037,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10037,U_10037),tc_HOL_Obool)),U_10038),U_10039)),
    inference(variable_rename,[status(thm)],[f_2744_1]) ).

fof(f_2744_3,plain,
    ! [U_10037,U_10038,U_10039] : c_Transitive__Closure_Ortrancl(U_10037,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10037,U_10037),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_10037,U_10038)),c_Transitive__Closure_Ortrancl(U_10037,U_10039))) = c_Transitive__Closure_Ortrancl(U_10037,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10037,U_10037),tc_HOL_Obool)),U_10038),U_10039)),
    inference(definitional_conversion,[status(esa)],[f_2744_2]) ).

cnf(f_2744_4,plain,
    c_Transitive__Closure_Ortrancl(U_10037,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10037,U_10037),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_10037,U_10038)),c_Transitive__Closure_Ortrancl(U_10037,U_10039))) = c_Transitive__Closure_Ortrancl(U_10037,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10037,U_10037),tc_HOL_Obool)),U_10038),U_10039)),
    inference(clausify,[status(thm)],[f_2744_3]) ).

fof(f_2745_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_2745_2,plain,
    ! [U_10041,U_10040] : hAPP(hAPP(c_Relation_Orel__comp(U_10040,U_10040,U_10040),U_10041),c_Transitive__Closure_Ortrancl(U_10040,U_10041)) = hAPP(hAPP(c_Relation_Orel__comp(U_10040,U_10040,U_10040),c_Transitive__Closure_Ortrancl(U_10040,U_10041)),U_10041),
    inference(variable_rename,[status(thm)],[f_2745_1]) ).

fof(f_2745_3,plain,
    ! [U_10040,U_10041] : hAPP(hAPP(c_Relation_Orel__comp(U_10040,U_10040,U_10040),U_10041),c_Transitive__Closure_Ortrancl(U_10040,U_10041)) = hAPP(hAPP(c_Relation_Orel__comp(U_10040,U_10040,U_10040),c_Transitive__Closure_Ortrancl(U_10040,U_10041)),U_10041),
    inference(definitional_conversion,[status(esa)],[f_2745_2]) ).

cnf(f_2745_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_10040,U_10040,U_10040),U_10041),c_Transitive__Closure_Ortrancl(U_10040,U_10041)) = hAPP(hAPP(c_Relation_Orel__comp(U_10040,U_10040,U_10040),c_Transitive__Closure_Ortrancl(U_10040,U_10041)),U_10041),
    inference(clausify,[status(thm)],[f_2745_3]) ).

fof(f_2746_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_2746_2,plain,
    ! [U_10043,U_10042] : hAPP(hAPP(c_Relation_Orel__comp(U_10042,U_10042,U_10042),c_Transitive__Closure_Ortrancl(U_10042,U_10043)),c_Transitive__Closure_Ortrancl(U_10042,U_10043)) = c_Transitive__Closure_Ortrancl(U_10042,U_10043),
    inference(variable_rename,[status(thm)],[f_2746_1]) ).

fof(f_2746_3,plain,
    ! [U_10042,U_10043] : hAPP(hAPP(c_Relation_Orel__comp(U_10042,U_10042,U_10042),c_Transitive__Closure_Ortrancl(U_10042,U_10043)),c_Transitive__Closure_Ortrancl(U_10042,U_10043)) = c_Transitive__Closure_Ortrancl(U_10042,U_10043),
    inference(definitional_conversion,[status(esa)],[f_2746_2]) ).

cnf(f_2746_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_10042,U_10042,U_10042),c_Transitive__Closure_Ortrancl(U_10042,U_10043)),c_Transitive__Closure_Ortrancl(U_10042,U_10043)) = c_Transitive__Closure_Ortrancl(U_10042,U_10043),
    inference(clausify,[status(thm)],[f_2746_3]) ).

fof(f_2747_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_2747_2,plain,
    ! [U_10046,U_10045,U_10044] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10044,U_10044),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_10044,U_10045)),c_Transitive__Closure_Ortrancl(U_10044,U_10046)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10044,U_10044),tc_HOL_Obool)),U_10045),U_10046)) ),
    inference(variable_rename,[status(thm)],[f_2747_1]) ).

fof(f_2747_3,plain,
    ! [U_10044,U_10045,U_10046] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10044,U_10044),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_10044,U_10045)),c_Transitive__Closure_Ortrancl(U_10044,U_10046)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10044,U_10044),tc_HOL_Obool)),U_10045),U_10046)) ),
    inference(definitional_conversion,[status(esa)],[f_2747_2]) ).

cnf(f_2747_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10044,U_10044),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_10044,U_10045)),c_Transitive__Closure_Ortrancl(U_10044,U_10046)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10044,U_10044),tc_HOL_Obool)),U_10045),U_10046)) ),
    inference(clausify,[status(thm)],[f_2747_3]) ).

fof(f_2748_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_2748_2,plain,
    ! [U_10049,U_10048,U_10047] :
      ( c_Transitive__Closure_Ortrancl(U_10047,U_10049) = c_Transitive__Closure_Ortrancl(U_10047,U_10048)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10047,U_10047),tc_HOL_Obool)),U_10049),c_Transitive__Closure_Ortrancl(U_10047,U_10048)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10047,U_10047),tc_HOL_Obool)),U_10048),U_10049)) ),
    inference(variable_rename,[status(thm)],[f_2748_1]) ).

fof(f_2748_3,plain,
    ! [U_10047,U_10048,U_10049] :
      ( c_Transitive__Closure_Ortrancl(U_10047,U_10049) = c_Transitive__Closure_Ortrancl(U_10047,U_10048)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10047,U_10047),tc_HOL_Obool)),U_10049),c_Transitive__Closure_Ortrancl(U_10047,U_10048)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10047,U_10047),tc_HOL_Obool)),U_10048),U_10049)) ),
    inference(definitional_conversion,[status(esa)],[f_2748_2]) ).

cnf(f_2748_4,plain,
    ( c_Transitive__Closure_Ortrancl(U_10047,U_10049) = c_Transitive__Closure_Ortrancl(U_10047,U_10048)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10047,U_10047),tc_HOL_Obool)),U_10049),c_Transitive__Closure_Ortrancl(U_10047,U_10048)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10047,U_10047),tc_HOL_Obool)),U_10048),U_10049)) ),
    inference(clausify,[status(thm)],[f_2748_3]) ).

fof(f_2749_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_2749_2,plain,
    ! [U_10052,U_10051,U_10050] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10050,U_10050),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_10050,U_10051)),c_Transitive__Closure_Ortrancl(U_10050,U_10052)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10050,U_10050),tc_HOL_Obool)),U_10051),c_Transitive__Closure_Ortrancl(U_10050,U_10052))) ),
    inference(variable_rename,[status(thm)],[f_2749_1]) ).

fof(f_2749_3,plain,
    ! [U_10050,U_10051,U_10052] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10050,U_10050),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_10050,U_10051)),c_Transitive__Closure_Ortrancl(U_10050,U_10052)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10050,U_10050),tc_HOL_Obool)),U_10051),c_Transitive__Closure_Ortrancl(U_10050,U_10052))) ),
    inference(definitional_conversion,[status(esa)],[f_2749_2]) ).

cnf(f_2749_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10050,U_10050),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_10050,U_10051)),c_Transitive__Closure_Ortrancl(U_10050,U_10052)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10050,U_10050),tc_HOL_Obool)),U_10051),c_Transitive__Closure_Ortrancl(U_10050,U_10052))) ),
    inference(clausify,[status(thm)],[f_2749_3]) ).

fof(f_2750_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_2750_2,plain,
    ! [U_10057,U_10056,U_10055,U_10054,U_10053] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10053,U_10053)),hAPP(hAPP(c_Product__Type_OPair(U_10053,U_10053),U_10054),U_10057)),c_Transitive__Closure_Ortrancl(U_10053,U_10056)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10053,U_10053)),hAPP(hAPP(c_Product__Type_OPair(U_10053,U_10053),U_10055),U_10057)),c_Transitive__Closure_Ortrancl(U_10053,U_10056)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10053,U_10053)),hAPP(hAPP(c_Product__Type_OPair(U_10053,U_10053),U_10054),U_10055)),c_Transitive__Closure_Ortrancl(U_10053,U_10056))) ),
    inference(variable_rename,[status(thm)],[f_2750_1]) ).

fof(f_2750_3,plain,
    ! [U_10053,U_10054,U_10055,U_10056,U_10057] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10053,U_10053)),hAPP(hAPP(c_Product__Type_OPair(U_10053,U_10053),U_10054),U_10057)),c_Transitive__Closure_Ortrancl(U_10053,U_10056)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10053,U_10053)),hAPP(hAPP(c_Product__Type_OPair(U_10053,U_10053),U_10055),U_10057)),c_Transitive__Closure_Ortrancl(U_10053,U_10056)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10053,U_10053)),hAPP(hAPP(c_Product__Type_OPair(U_10053,U_10053),U_10054),U_10055)),c_Transitive__Closure_Ortrancl(U_10053,U_10056))) ),
    inference(definitional_conversion,[status(esa)],[f_2750_2]) ).

cnf(f_2750_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10053,U_10053)),hAPP(hAPP(c_Product__Type_OPair(U_10053,U_10053),U_10054),U_10057)),c_Transitive__Closure_Ortrancl(U_10053,U_10056)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10053,U_10053)),hAPP(hAPP(c_Product__Type_OPair(U_10053,U_10053),U_10055),U_10057)),c_Transitive__Closure_Ortrancl(U_10053,U_10056)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10053,U_10053)),hAPP(hAPP(c_Product__Type_OPair(U_10053,U_10053),U_10054),U_10055)),c_Transitive__Closure_Ortrancl(U_10053,U_10056))) ),
    inference(clausify,[status(thm)],[f_2750_3]) ).

fof(f_2751_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_2751_2,plain,
    ! [U_10062,U_10061,U_10060,U_10059,U_10058] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10058,U_10058)),hAPP(hAPP(c_Product__Type_OPair(U_10058,U_10058),U_10059),U_10062)),c_Transitive__Closure_Ortrancl(U_10058,U_10061)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10058,U_10058)),hAPP(hAPP(c_Product__Type_OPair(U_10058,U_10058),U_10060),U_10062)),U_10061))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10058,U_10058)),hAPP(hAPP(c_Product__Type_OPair(U_10058,U_10058),U_10059),U_10060)),c_Transitive__Closure_Ortrancl(U_10058,U_10061))) ),
    inference(variable_rename,[status(thm)],[f_2751_1]) ).

fof(f_2751_3,plain,
    ! [U_10058,U_10059,U_10060,U_10061,U_10062] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10058,U_10058)),hAPP(hAPP(c_Product__Type_OPair(U_10058,U_10058),U_10059),U_10062)),c_Transitive__Closure_Ortrancl(U_10058,U_10061)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10058,U_10058)),hAPP(hAPP(c_Product__Type_OPair(U_10058,U_10058),U_10060),U_10062)),U_10061))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10058,U_10058)),hAPP(hAPP(c_Product__Type_OPair(U_10058,U_10058),U_10059),U_10060)),c_Transitive__Closure_Ortrancl(U_10058,U_10061))) ),
    inference(definitional_conversion,[status(esa)],[f_2751_2]) ).

cnf(f_2751_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10058,U_10058)),hAPP(hAPP(c_Product__Type_OPair(U_10058,U_10058),U_10059),U_10062)),c_Transitive__Closure_Ortrancl(U_10058,U_10061)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10058,U_10058)),hAPP(hAPP(c_Product__Type_OPair(U_10058,U_10058),U_10060),U_10062)),U_10061))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10058,U_10058)),hAPP(hAPP(c_Product__Type_OPair(U_10058,U_10058),U_10059),U_10060)),c_Transitive__Closure_Ortrancl(U_10058,U_10061))) ),
    inference(clausify,[status(thm)],[f_2751_3]) ).

fof(f_2752_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_2752_2,plain,
    ! [U_10067,U_10066,U_10065,U_10064,U_10063] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10063,U_10063)),hAPP(hAPP(c_Product__Type_OPair(U_10063,U_10063),U_10064),U_10067)),c_Transitive__Closure_Ortrancl(U_10063,U_10066)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10063,U_10063)),hAPP(hAPP(c_Product__Type_OPair(U_10063,U_10063),U_10065),U_10067)),c_Transitive__Closure_Ortrancl(U_10063,U_10066)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10063,U_10063)),hAPP(hAPP(c_Product__Type_OPair(U_10063,U_10063),U_10064),U_10065)),U_10066)) ),
    inference(variable_rename,[status(thm)],[f_2752_1]) ).

fof(f_2752_3,plain,
    ! [U_10063,U_10064,U_10065,U_10066,U_10067] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10063,U_10063)),hAPP(hAPP(c_Product__Type_OPair(U_10063,U_10063),U_10064),U_10067)),c_Transitive__Closure_Ortrancl(U_10063,U_10066)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10063,U_10063)),hAPP(hAPP(c_Product__Type_OPair(U_10063,U_10063),U_10065),U_10067)),c_Transitive__Closure_Ortrancl(U_10063,U_10066)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10063,U_10063)),hAPP(hAPP(c_Product__Type_OPair(U_10063,U_10063),U_10064),U_10065)),U_10066)) ),
    inference(definitional_conversion,[status(esa)],[f_2752_2]) ).

cnf(f_2752_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10063,U_10063)),hAPP(hAPP(c_Product__Type_OPair(U_10063,U_10063),U_10064),U_10067)),c_Transitive__Closure_Ortrancl(U_10063,U_10066)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10063,U_10063)),hAPP(hAPP(c_Product__Type_OPair(U_10063,U_10063),U_10065),U_10067)),c_Transitive__Closure_Ortrancl(U_10063,U_10066)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10063,U_10063)),hAPP(hAPP(c_Product__Type_OPair(U_10063,U_10063),U_10064),U_10065)),U_10066)) ),
    inference(clausify,[status(thm)],[f_2752_3]) ).

fof(f_2753_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_2753_2,plain,
    ! [U_10071,U_10070,U_10069,U_10068] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10068,U_10068)),U_10069),c_Transitive__Closure_Ortrancl(U_10068,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10068,U_10068),tc_HOL_Obool)),U_10070),U_10071))))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10068,U_10068)),U_10069),c_Transitive__Closure_Ortrancl(U_10068,U_10071)))
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10068,U_10068)),U_10069),c_Transitive__Closure_Ortrancl(U_10068,U_10070))) ) ),
    inference(variable_rename,[status(thm)],[f_2753_1]) ).

fof(f_2753_3,plain,
    ( ! [U_10068,U_10069,U_10070,U_10071] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10068,U_10068)),U_10069),c_Transitive__Closure_Ortrancl(U_10068,U_10071)))
        | ~ sP775(U_10068,U_10069,U_10070,U_10071) )
    & ! [U_10068,U_10069,U_10070,U_10071] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10068,U_10068)),U_10069),c_Transitive__Closure_Ortrancl(U_10068,U_10070)))
        | ~ sP775(U_10068,U_10069,U_10070,U_10071) )
    & ! [U_10068,U_10069,U_10070,U_10071] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10068,U_10068)),U_10069),c_Transitive__Closure_Ortrancl(U_10068,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10068,U_10068),tc_HOL_Obool)),U_10070),U_10071))))
        | sP775(U_10068,U_10069,U_10070,U_10071) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP775])],[f_2753_2]) ).

cnf(f_2753_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10068,U_10068)),U_10069),c_Transitive__Closure_Ortrancl(U_10068,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10068,U_10068),tc_HOL_Obool)),U_10070),U_10071))))
    | sP775(U_10068,U_10069,U_10070,U_10071) ),
    inference(clausify,[status(thm)],[f_2753_3]) ).

cnf(f_2753_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10068,U_10068)),U_10069),c_Transitive__Closure_Ortrancl(U_10068,U_10070)))
    | ~ sP775(U_10068,U_10069,U_10070,U_10071) ),
    inference(clausify,[status(thm)],[f_2753_3]) ).

cnf(f_2753_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10068,U_10068)),U_10069),c_Transitive__Closure_Ortrancl(U_10068,U_10071)))
    | ~ sP775(U_10068,U_10069,U_10070,U_10071) ),
    inference(clausify,[status(thm)],[f_2753_3]) ).

fof(f_2754_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_2754_2,plain,
    ! [U_10073,U_10072] : c_Transitive__Closure_Otrancl(U_10072,U_10073) = hAPP(hAPP(c_Relation_Orel__comp(U_10072,U_10072,U_10072),U_10073),c_Transitive__Closure_Ortrancl(U_10072,U_10073)),
    inference(variable_rename,[status(thm)],[f_2754_1]) ).

fof(f_2754_3,plain,
    ! [U_10072,U_10073] : c_Transitive__Closure_Otrancl(U_10072,U_10073) = hAPP(hAPP(c_Relation_Orel__comp(U_10072,U_10072,U_10072),U_10073),c_Transitive__Closure_Ortrancl(U_10072,U_10073)),
    inference(definitional_conversion,[status(esa)],[f_2754_2]) ).

cnf(f_2754_4,plain,
    c_Transitive__Closure_Otrancl(U_10072,U_10073) = hAPP(hAPP(c_Relation_Orel__comp(U_10072,U_10072,U_10072),U_10073),c_Transitive__Closure_Ortrancl(U_10072,U_10073)),
    inference(clausify,[status(thm)],[f_2754_3]) ).

fof(f_2755_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_2755_2,plain,
    ! [U_10075,U_10074] : c_Transitive__Closure_Otrancl(U_10074,U_10075) = hAPP(hAPP(c_Relation_Orel__comp(U_10074,U_10074,U_10074),c_Transitive__Closure_Ortrancl(U_10074,U_10075)),U_10075),
    inference(variable_rename,[status(thm)],[f_2755_1]) ).

fof(f_2755_3,plain,
    ! [U_10074,U_10075] : c_Transitive__Closure_Otrancl(U_10074,U_10075) = hAPP(hAPP(c_Relation_Orel__comp(U_10074,U_10074,U_10074),c_Transitive__Closure_Ortrancl(U_10074,U_10075)),U_10075),
    inference(definitional_conversion,[status(esa)],[f_2755_2]) ).

cnf(f_2755_4,plain,
    c_Transitive__Closure_Otrancl(U_10074,U_10075) = hAPP(hAPP(c_Relation_Orel__comp(U_10074,U_10074,U_10074),c_Transitive__Closure_Ortrancl(U_10074,U_10075)),U_10075),
    inference(clausify,[status(thm)],[f_2755_3]) ).

fof(f_2756_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_2756_2,plain,
    ! [U_10078,U_10077,U_10076] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10076,U_10076),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10076,U_10076),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_10076,U_10077)),c_Transitive__Closure_Ortrancl(U_10076,U_10078))),c_Transitive__Closure_Ortrancl(U_10076,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10076,U_10076),tc_HOL_Obool)),U_10077),U_10078)))),
    inference(variable_rename,[status(thm)],[f_2756_1]) ).

fof(f_2756_3,plain,
    ! [U_10076,U_10077,U_10078] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10076,U_10076),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10076,U_10076),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_10076,U_10077)),c_Transitive__Closure_Ortrancl(U_10076,U_10078))),c_Transitive__Closure_Ortrancl(U_10076,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10076,U_10076),tc_HOL_Obool)),U_10077),U_10078)))),
    inference(definitional_conversion,[status(esa)],[f_2756_2]) ).

cnf(f_2756_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_10076,U_10076),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10076,U_10076),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_10076,U_10077)),c_Transitive__Closure_Ortrancl(U_10076,U_10078))),c_Transitive__Closure_Ortrancl(U_10076,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10076,U_10076),tc_HOL_Obool)),U_10077),U_10078)))),
    inference(clausify,[status(thm)],[f_2756_3]) ).

fof(f_2757_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_2757_2,plain,
    ! [U_10079] : c_Transitive__Closure_Ortrancl(U_10079,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10079,U_10079),tc_HOL_Obool))) = c_Relation_OId(U_10079),
    inference(variable_rename,[status(thm)],[f_2757_1]) ).

fof(f_2757_3,plain,
    ! [U_10079] : c_Transitive__Closure_Ortrancl(U_10079,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10079,U_10079),tc_HOL_Obool))) = c_Relation_OId(U_10079),
    inference(definitional_conversion,[status(esa)],[f_2757_2]) ).

cnf(f_2757_4,plain,
    c_Transitive__Closure_Ortrancl(U_10079,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10079,U_10079),tc_HOL_Obool))) = c_Relation_OId(U_10079),
    inference(clausify,[status(thm)],[f_2757_3]) ).

fof(f_2758_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_2758_2,plain,
    ! [U_10081,U_10080] : c_Transitive__Closure_Ortrancl(U_10080,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10080,U_10080),tc_HOL_Obool)),U_10081),c_Relation_OId(U_10080))) = c_Transitive__Closure_Ortrancl(U_10080,U_10081),
    inference(variable_rename,[status(thm)],[f_2758_1]) ).

fof(f_2758_3,plain,
    ! [U_10080,U_10081] : c_Transitive__Closure_Ortrancl(U_10080,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10080,U_10080),tc_HOL_Obool)),U_10081),c_Relation_OId(U_10080))) = c_Transitive__Closure_Ortrancl(U_10080,U_10081),
    inference(definitional_conversion,[status(esa)],[f_2758_2]) ).

cnf(f_2758_4,plain,
    c_Transitive__Closure_Ortrancl(U_10080,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10080,U_10080),tc_HOL_Obool)),U_10081),c_Relation_OId(U_10080))) = c_Transitive__Closure_Ortrancl(U_10080,U_10081),
    inference(clausify,[status(thm)],[f_2758_3]) ).

fof(f_2759_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_2759_2,plain,
    ! [U_10083,U_10082] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10082,U_10082),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_10082,U_10083)),c_Relation_OId(U_10082)) = c_Transitive__Closure_Ortrancl(U_10082,U_10083),
    inference(variable_rename,[status(thm)],[f_2759_1]) ).

fof(f_2759_3,plain,
    ! [U_10082,U_10083] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10082,U_10082),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_10082,U_10083)),c_Relation_OId(U_10082)) = c_Transitive__Closure_Ortrancl(U_10082,U_10083),
    inference(definitional_conversion,[status(esa)],[f_2759_2]) ).

cnf(f_2759_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10082,U_10082),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_10082,U_10083)),c_Relation_OId(U_10082)) = c_Transitive__Closure_Ortrancl(U_10082,U_10083),
    inference(clausify,[status(thm)],[f_2759_3]) ).

fof(f_2760_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_2760_2,plain,
    ! [U_10085,U_10084] : c_Transitive__Closure_Ortrancl(U_10084,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_10084,U_10084),tc_HOL_Obool)),U_10085),c_Relation_OId(U_10084))) = c_Transitive__Closure_Ortrancl(U_10084,U_10085),
    inference(variable_rename,[status(thm)],[f_2760_1]) ).

fof(f_2760_3,plain,
    ! [U_10084,U_10085] : c_Transitive__Closure_Ortrancl(U_10084,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_10084,U_10084),tc_HOL_Obool)),U_10085),c_Relation_OId(U_10084))) = c_Transitive__Closure_Ortrancl(U_10084,U_10085),
    inference(definitional_conversion,[status(esa)],[f_2760_2]) ).

cnf(f_2760_4,plain,
    c_Transitive__Closure_Ortrancl(U_10084,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_10084,U_10084),tc_HOL_Obool)),U_10085),c_Relation_OId(U_10084))) = c_Transitive__Closure_Ortrancl(U_10084,U_10085),
    inference(clausify,[status(thm)],[f_2760_3]) ).

fof(f_2761_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_2761_2,plain,
    ! [U_10089,U_10088,U_10087,U_10086] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10086,U_10086)),hAPP(hAPP(c_Product__Type_OPair(U_10086,U_10086),U_10087),U_10088)),c_Transitive__Closure_Ortrancl(U_10086,U_10089)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10086,U_10086)),hAPP(hAPP(c_Product__Type_OPair(U_10086,U_10086),U_10087),U_10088)),c_Transitive__Closure_Otrancl(U_10086,U_10089)))
            | U_10087 = U_10088 )
          & U_10087 != U_10088 ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10086,U_10086)),hAPP(hAPP(c_Product__Type_OPair(U_10086,U_10086),U_10087),U_10088)),c_Transitive__Closure_Otrancl(U_10086,U_10089)))
          & U_10087 != U_10088 )
        | U_10087 = U_10088
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10086,U_10086)),hAPP(hAPP(c_Product__Type_OPair(U_10086,U_10086),U_10087),U_10088)),c_Transitive__Closure_Ortrancl(U_10086,U_10089))) ) ),
    inference(variable_rename,[status(thm)],[f_2761_1]) ).

fof(f_2761_3,plain,
    ( ! [U_10097,U_10095,U_10093,U_10091] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10091,U_10091)),hAPP(hAPP(c_Product__Type_OPair(U_10091,U_10091),U_10093),U_10095)),c_Transitive__Closure_Ortrancl(U_10091,U_10097)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10091,U_10091)),hAPP(hAPP(c_Product__Type_OPair(U_10091,U_10091),U_10093),U_10095)),c_Transitive__Closure_Otrancl(U_10091,U_10097)))
            | U_10093 = U_10095 )
          & U_10093 != U_10095 ) )
    & ! [U_10096,U_10094,U_10092,U_10090] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10090,U_10090)),hAPP(hAPP(c_Product__Type_OPair(U_10090,U_10090),U_10092),U_10094)),c_Transitive__Closure_Otrancl(U_10090,U_10096)))
          & U_10092 != U_10094 )
        | U_10092 = U_10094
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10090,U_10090)),hAPP(hAPP(c_Product__Type_OPair(U_10090,U_10090),U_10092),U_10094)),c_Transitive__Closure_Ortrancl(U_10090,U_10096))) ) ),
    inference(miniscope,[status(thm)],[f_2761_2]) ).

fof(f_2761_4,plain,
    ( ! [U_10091,U_10093,U_10095,U_10097] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10091,U_10091)),hAPP(hAPP(c_Product__Type_OPair(U_10091,U_10091),U_10093),U_10095)),c_Transitive__Closure_Otrancl(U_10091,U_10097)))
        | U_10093 = U_10095
        | ~ sP777(U_10091,U_10093,U_10095,U_10097) )
    & ! [U_10091,U_10093,U_10095,U_10097] :
        ( U_10093 != U_10095
        | ~ sP777(U_10091,U_10093,U_10095,U_10097) )
    & ! [U_10094,U_10092,U_10090,U_10096] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10090,U_10090)),hAPP(hAPP(c_Product__Type_OPair(U_10090,U_10090),U_10092),U_10094)),c_Transitive__Closure_Otrancl(U_10090,U_10096)))
        | ~ sP776(U_10094,U_10092,U_10090,U_10096) )
    & ! [U_10094,U_10092,U_10090,U_10096] :
        ( U_10092 != U_10094
        | ~ sP776(U_10094,U_10092,U_10090,U_10096) )
    & ! [U_10091,U_10093,U_10095,U_10097] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10091,U_10091)),hAPP(hAPP(c_Product__Type_OPair(U_10091,U_10091),U_10093),U_10095)),c_Transitive__Closure_Ortrancl(U_10091,U_10097)))
        | sP777(U_10091,U_10093,U_10095,U_10097) )
    & ! [U_10094,U_10092,U_10090,U_10096] :
        ( sP776(U_10094,U_10092,U_10090,U_10096)
        | U_10092 = U_10094
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10090,U_10090)),hAPP(hAPP(c_Product__Type_OPair(U_10090,U_10090),U_10092),U_10094)),c_Transitive__Closure_Ortrancl(U_10090,U_10096))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP776,sP777])],[f_2761_3]) ).

cnf(f_2761_5,plain,
    ( sP776(U_10094,U_10092,U_10090,U_10096)
    | U_10092 = U_10094
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10090,U_10090)),hAPP(hAPP(c_Product__Type_OPair(U_10090,U_10090),U_10092),U_10094)),c_Transitive__Closure_Ortrancl(U_10090,U_10096))) ),
    inference(clausify,[status(thm)],[f_2761_4]) ).

cnf(f_2761_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10091,U_10091)),hAPP(hAPP(c_Product__Type_OPair(U_10091,U_10091),U_10093),U_10095)),c_Transitive__Closure_Ortrancl(U_10091,U_10097)))
    | sP777(U_10091,U_10093,U_10095,U_10097) ),
    inference(clausify,[status(thm)],[f_2761_4]) ).

cnf(f_2761_7,plain,
    ( U_10092 != U_10094
    | ~ sP776(U_10094,U_10092,U_10090,U_10096) ),
    inference(clausify,[status(thm)],[f_2761_4]) ).

cnf(f_2761_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10090,U_10090)),hAPP(hAPP(c_Product__Type_OPair(U_10090,U_10090),U_10092),U_10094)),c_Transitive__Closure_Otrancl(U_10090,U_10096)))
    | ~ sP776(U_10094,U_10092,U_10090,U_10096) ),
    inference(clausify,[status(thm)],[f_2761_4]) ).

cnf(f_2761_9,plain,
    ( U_10093 != U_10095
    | ~ sP777(U_10091,U_10093,U_10095,U_10097) ),
    inference(clausify,[status(thm)],[f_2761_4]) ).

cnf(f_2761_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10091,U_10091)),hAPP(hAPP(c_Product__Type_OPair(U_10091,U_10091),U_10093),U_10095)),c_Transitive__Closure_Otrancl(U_10091,U_10097)))
    | U_10093 = U_10095
    | ~ sP777(U_10091,U_10093,U_10095,U_10097) ),
    inference(clausify,[status(thm)],[f_2761_4]) ).

fof(f_2762_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_2762_2,plain,
    ! [U_10102,U_10101,U_10100,U_10099,U_10098] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10098,U_10098)),hAPP(hAPP(c_Product__Type_OPair(U_10098,U_10098),U_10099),U_10102)),c_Transitive__Closure_Otrancl(U_10098,U_10101)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10098,U_10098)),hAPP(hAPP(c_Product__Type_OPair(U_10098,U_10098),U_10100),U_10102)),c_Transitive__Closure_Ortrancl(U_10098,U_10101)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10098,U_10098)),hAPP(hAPP(c_Product__Type_OPair(U_10098,U_10098),U_10099),U_10100)),U_10101)) ),
    inference(variable_rename,[status(thm)],[f_2762_1]) ).

fof(f_2762_3,plain,
    ! [U_10099,U_10100,U_10098,U_10101,U_10102] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10098,U_10098)),hAPP(hAPP(c_Product__Type_OPair(U_10098,U_10098),U_10099),U_10102)),c_Transitive__Closure_Otrancl(U_10098,U_10101)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10098,U_10098)),hAPP(hAPP(c_Product__Type_OPair(U_10098,U_10098),U_10100),U_10102)),c_Transitive__Closure_Ortrancl(U_10098,U_10101)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10098,U_10098)),hAPP(hAPP(c_Product__Type_OPair(U_10098,U_10098),U_10099),U_10100)),U_10101)) ),
    inference(definitional_conversion,[status(esa)],[f_2762_2]) ).

cnf(f_2762_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10098,U_10098)),hAPP(hAPP(c_Product__Type_OPair(U_10098,U_10098),U_10099),U_10102)),c_Transitive__Closure_Otrancl(U_10098,U_10101)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10098,U_10098)),hAPP(hAPP(c_Product__Type_OPair(U_10098,U_10098),U_10100),U_10102)),c_Transitive__Closure_Ortrancl(U_10098,U_10101)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10098,U_10098)),hAPP(hAPP(c_Product__Type_OPair(U_10098,U_10098),U_10099),U_10100)),U_10101)) ),
    inference(clausify,[status(thm)],[f_2762_3]) ).

fof(f_2763_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_2763_2,plain,
    ! [U_10106,U_10105,U_10104,U_10103] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10103,U_10103)),hAPP(hAPP(c_Product__Type_OPair(U_10103,U_10103),U_10104),U_10105)),c_Transitive__Closure_Otrancl(U_10103,U_10106)))
        & U_10104 != U_10105 )
      | U_10104 = U_10105
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10103,U_10103)),hAPP(hAPP(c_Product__Type_OPair(U_10103,U_10103),U_10104),U_10105)),c_Transitive__Closure_Ortrancl(U_10103,U_10106))) ),
    inference(variable_rename,[status(thm)],[f_2763_1]) ).

fof(f_2763_3,plain,
    ( ! [U_10104,U_10103,U_10105,U_10106] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10103,U_10103)),hAPP(hAPP(c_Product__Type_OPair(U_10103,U_10103),U_10104),U_10105)),c_Transitive__Closure_Otrancl(U_10103,U_10106)))
        | ~ sP778(U_10104,U_10103,U_10105,U_10106) )
    & ! [U_10104,U_10103,U_10105,U_10106] :
        ( U_10104 != U_10105
        | ~ sP778(U_10104,U_10103,U_10105,U_10106) )
    & ! [U_10104,U_10103,U_10105,U_10106] :
        ( sP778(U_10104,U_10103,U_10105,U_10106)
        | U_10104 = U_10105
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10103,U_10103)),hAPP(hAPP(c_Product__Type_OPair(U_10103,U_10103),U_10104),U_10105)),c_Transitive__Closure_Ortrancl(U_10103,U_10106))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP778])],[f_2763_2]) ).

cnf(f_2763_4,plain,
    ( sP778(U_10104,U_10103,U_10105,U_10106)
    | U_10104 = U_10105
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10103,U_10103)),hAPP(hAPP(c_Product__Type_OPair(U_10103,U_10103),U_10104),U_10105)),c_Transitive__Closure_Ortrancl(U_10103,U_10106))) ),
    inference(clausify,[status(thm)],[f_2763_3]) ).

cnf(f_2763_5,plain,
    ( U_10104 != U_10105
    | ~ sP778(U_10104,U_10103,U_10105,U_10106) ),
    inference(clausify,[status(thm)],[f_2763_3]) ).

cnf(f_2763_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10103,U_10103)),hAPP(hAPP(c_Product__Type_OPair(U_10103,U_10103),U_10104),U_10105)),c_Transitive__Closure_Otrancl(U_10103,U_10106)))
    | ~ sP778(U_10104,U_10103,U_10105,U_10106) ),
    inference(clausify,[status(thm)],[f_2763_3]) ).

fof(f_2764_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_2764_2,plain,
    ! [U_10111,U_10110,U_10109,U_10108,U_10107] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10107,U_10107)),hAPP(hAPP(c_Product__Type_OPair(U_10107,U_10107),U_10108),U_10111)),c_Transitive__Closure_Otrancl(U_10107,U_10110)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10107,U_10107)),hAPP(hAPP(c_Product__Type_OPair(U_10107,U_10107),U_10109),U_10111)),U_10110))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10107,U_10107)),hAPP(hAPP(c_Product__Type_OPair(U_10107,U_10107),U_10108),U_10109)),c_Transitive__Closure_Ortrancl(U_10107,U_10110))) ),
    inference(variable_rename,[status(thm)],[f_2764_1]) ).

fof(f_2764_3,plain,
    ! [U_10107,U_10108,U_10109,U_10110,U_10111] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10107,U_10107)),hAPP(hAPP(c_Product__Type_OPair(U_10107,U_10107),U_10108),U_10111)),c_Transitive__Closure_Otrancl(U_10107,U_10110)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10107,U_10107)),hAPP(hAPP(c_Product__Type_OPair(U_10107,U_10107),U_10109),U_10111)),U_10110))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10107,U_10107)),hAPP(hAPP(c_Product__Type_OPair(U_10107,U_10107),U_10108),U_10109)),c_Transitive__Closure_Ortrancl(U_10107,U_10110))) ),
    inference(definitional_conversion,[status(esa)],[f_2764_2]) ).

cnf(f_2764_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10107,U_10107)),hAPP(hAPP(c_Product__Type_OPair(U_10107,U_10107),U_10108),U_10111)),c_Transitive__Closure_Otrancl(U_10107,U_10110)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10107,U_10107)),hAPP(hAPP(c_Product__Type_OPair(U_10107,U_10107),U_10109),U_10111)),U_10110))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10107,U_10107)),hAPP(hAPP(c_Product__Type_OPair(U_10107,U_10107),U_10108),U_10109)),c_Transitive__Closure_Ortrancl(U_10107,U_10110))) ),
    inference(clausify,[status(thm)],[f_2764_3]) ).

fof(f_2765_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_2765_2,plain,
    ! [U_10116,U_10115,U_10114,U_10113,U_10112] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10112,U_10112)),hAPP(hAPP(c_Product__Type_OPair(U_10112,U_10112),U_10113),U_10116)),c_Transitive__Closure_Otrancl(U_10112,U_10115)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10112,U_10112)),hAPP(hAPP(c_Product__Type_OPair(U_10112,U_10112),U_10114),U_10116)),c_Transitive__Closure_Ortrancl(U_10112,U_10115)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10112,U_10112)),hAPP(hAPP(c_Product__Type_OPair(U_10112,U_10112),U_10113),U_10114)),c_Transitive__Closure_Otrancl(U_10112,U_10115))) ),
    inference(variable_rename,[status(thm)],[f_2765_1]) ).

fof(f_2765_3,plain,
    ! [U_10112,U_10113,U_10114,U_10115,U_10116] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10112,U_10112)),hAPP(hAPP(c_Product__Type_OPair(U_10112,U_10112),U_10113),U_10116)),c_Transitive__Closure_Otrancl(U_10112,U_10115)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10112,U_10112)),hAPP(hAPP(c_Product__Type_OPair(U_10112,U_10112),U_10114),U_10116)),c_Transitive__Closure_Ortrancl(U_10112,U_10115)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10112,U_10112)),hAPP(hAPP(c_Product__Type_OPair(U_10112,U_10112),U_10113),U_10114)),c_Transitive__Closure_Otrancl(U_10112,U_10115))) ),
    inference(definitional_conversion,[status(esa)],[f_2765_2]) ).

cnf(f_2765_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10112,U_10112)),hAPP(hAPP(c_Product__Type_OPair(U_10112,U_10112),U_10113),U_10116)),c_Transitive__Closure_Otrancl(U_10112,U_10115)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10112,U_10112)),hAPP(hAPP(c_Product__Type_OPair(U_10112,U_10112),U_10114),U_10116)),c_Transitive__Closure_Ortrancl(U_10112,U_10115)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10112,U_10112)),hAPP(hAPP(c_Product__Type_OPair(U_10112,U_10112),U_10113),U_10114)),c_Transitive__Closure_Otrancl(U_10112,U_10115))) ),
    inference(clausify,[status(thm)],[f_2765_3]) ).

fof(f_2766_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_2766_2,plain,
    ! [U_10121,U_10120,U_10119,U_10118,U_10117] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10117,U_10117)),hAPP(hAPP(c_Product__Type_OPair(U_10117,U_10117),U_10118),U_10121)),c_Transitive__Closure_Otrancl(U_10117,U_10120)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10117,U_10117)),hAPP(hAPP(c_Product__Type_OPair(U_10117,U_10117),U_10119),U_10121)),c_Transitive__Closure_Otrancl(U_10117,U_10120)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10117,U_10117)),hAPP(hAPP(c_Product__Type_OPair(U_10117,U_10117),U_10118),U_10119)),c_Transitive__Closure_Ortrancl(U_10117,U_10120))) ),
    inference(variable_rename,[status(thm)],[f_2766_1]) ).

fof(f_2766_3,plain,
    ! [U_10117,U_10118,U_10119,U_10120,U_10121] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10117,U_10117)),hAPP(hAPP(c_Product__Type_OPair(U_10117,U_10117),U_10118),U_10121)),c_Transitive__Closure_Otrancl(U_10117,U_10120)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10117,U_10117)),hAPP(hAPP(c_Product__Type_OPair(U_10117,U_10117),U_10119),U_10121)),c_Transitive__Closure_Otrancl(U_10117,U_10120)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10117,U_10117)),hAPP(hAPP(c_Product__Type_OPair(U_10117,U_10117),U_10118),U_10119)),c_Transitive__Closure_Ortrancl(U_10117,U_10120))) ),
    inference(definitional_conversion,[status(esa)],[f_2766_2]) ).

cnf(f_2766_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10117,U_10117)),hAPP(hAPP(c_Product__Type_OPair(U_10117,U_10117),U_10118),U_10121)),c_Transitive__Closure_Otrancl(U_10117,U_10120)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10117,U_10117)),hAPP(hAPP(c_Product__Type_OPair(U_10117,U_10117),U_10119),U_10121)),c_Transitive__Closure_Otrancl(U_10117,U_10120)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10117,U_10117)),hAPP(hAPP(c_Product__Type_OPair(U_10117,U_10117),U_10118),U_10119)),c_Transitive__Closure_Ortrancl(U_10117,U_10120))) ),
    inference(clausify,[status(thm)],[f_2766_3]) ).

fof(f_2767_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_2767_2,plain,
    ! [U_10125,U_10124,U_10123,U_10122] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10122,U_10122)),hAPP(hAPP(c_Product__Type_OPair(U_10122,U_10122),U_10124),U_10123)),c_Transitive__Closure_Ortrancl(U_10122,hAPP(c_Relation_Oconverse(U_10122,U_10122),U_10125))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10122,U_10122)),hAPP(hAPP(c_Product__Type_OPair(U_10122,U_10122),U_10123),U_10124)),c_Transitive__Closure_Ortrancl(U_10122,U_10125))) ),
    inference(variable_rename,[status(thm)],[f_2767_1]) ).

fof(f_2767_3,plain,
    ! [U_10122,U_10123,U_10124,U_10125] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10122,U_10122)),hAPP(hAPP(c_Product__Type_OPair(U_10122,U_10122),U_10124),U_10123)),c_Transitive__Closure_Ortrancl(U_10122,hAPP(c_Relation_Oconverse(U_10122,U_10122),U_10125))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10122,U_10122)),hAPP(hAPP(c_Product__Type_OPair(U_10122,U_10122),U_10123),U_10124)),c_Transitive__Closure_Ortrancl(U_10122,U_10125))) ),
    inference(definitional_conversion,[status(esa)],[f_2767_2]) ).

cnf(f_2767_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10122,U_10122)),hAPP(hAPP(c_Product__Type_OPair(U_10122,U_10122),U_10124),U_10123)),c_Transitive__Closure_Ortrancl(U_10122,hAPP(c_Relation_Oconverse(U_10122,U_10122),U_10125))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10122,U_10122)),hAPP(hAPP(c_Product__Type_OPair(U_10122,U_10122),U_10123),U_10124)),c_Transitive__Closure_Ortrancl(U_10122,U_10125))) ),
    inference(clausify,[status(thm)],[f_2767_3]) ).

fof(f_2768_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_2768_2,plain,
    ! [U_10129,U_10128,U_10127,U_10126] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10126,U_10126)),hAPP(hAPP(c_Product__Type_OPair(U_10126,U_10126),U_10128),U_10127)),c_Transitive__Closure_Ortrancl(U_10126,U_10129)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10126,U_10126)),hAPP(hAPP(c_Product__Type_OPair(U_10126,U_10126),U_10127),U_10128)),c_Transitive__Closure_Ortrancl(U_10126,hAPP(c_Relation_Oconverse(U_10126,U_10126),U_10129)))) ),
    inference(variable_rename,[status(thm)],[f_2768_1]) ).

fof(f_2768_3,plain,
    ! [U_10126,U_10127,U_10128,U_10129] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10126,U_10126)),hAPP(hAPP(c_Product__Type_OPair(U_10126,U_10126),U_10128),U_10127)),c_Transitive__Closure_Ortrancl(U_10126,U_10129)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10126,U_10126)),hAPP(hAPP(c_Product__Type_OPair(U_10126,U_10126),U_10127),U_10128)),c_Transitive__Closure_Ortrancl(U_10126,hAPP(c_Relation_Oconverse(U_10126,U_10126),U_10129)))) ),
    inference(definitional_conversion,[status(esa)],[f_2768_2]) ).

cnf(f_2768_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10126,U_10126)),hAPP(hAPP(c_Product__Type_OPair(U_10126,U_10126),U_10128),U_10127)),c_Transitive__Closure_Ortrancl(U_10126,U_10129)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10126,U_10126)),hAPP(hAPP(c_Product__Type_OPair(U_10126,U_10126),U_10127),U_10128)),c_Transitive__Closure_Ortrancl(U_10126,hAPP(c_Relation_Oconverse(U_10126,U_10126),U_10129)))) ),
    inference(clausify,[status(thm)],[f_2768_3]) ).

fof(f_2769_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_2769_2,plain,
    ! [U_10131,U_10130] : c_Transitive__Closure_Otrancl(U_10130,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10130,U_10130),tc_HOL_Obool)),U_10131),c_Relation_OId(U_10130))) = c_Transitive__Closure_Ortrancl(U_10130,U_10131),
    inference(variable_rename,[status(thm)],[f_2769_1]) ).

fof(f_2769_3,plain,
    ! [U_10130,U_10131] : c_Transitive__Closure_Otrancl(U_10130,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10130,U_10130),tc_HOL_Obool)),U_10131),c_Relation_OId(U_10130))) = c_Transitive__Closure_Ortrancl(U_10130,U_10131),
    inference(definitional_conversion,[status(esa)],[f_2769_2]) ).

cnf(f_2769_4,plain,
    c_Transitive__Closure_Otrancl(U_10130,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10130,U_10130),tc_HOL_Obool)),U_10131),c_Relation_OId(U_10130))) = c_Transitive__Closure_Ortrancl(U_10130,U_10131),
    inference(clausify,[status(thm)],[f_2769_3]) ).

fof(f_2770_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_2770_2,plain,
    ! [U_10133,U_10132] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10132,U_10132),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_10132,U_10133)),c_Relation_OId(U_10132)) = c_Transitive__Closure_Ortrancl(U_10132,U_10133),
    inference(variable_rename,[status(thm)],[f_2770_1]) ).

fof(f_2770_3,plain,
    ! [U_10132,U_10133] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10132,U_10132),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_10132,U_10133)),c_Relation_OId(U_10132)) = c_Transitive__Closure_Ortrancl(U_10132,U_10133),
    inference(definitional_conversion,[status(esa)],[f_2770_2]) ).

cnf(f_2770_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10132,U_10132),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_10132,U_10133)),c_Relation_OId(U_10132)) = c_Transitive__Closure_Ortrancl(U_10132,U_10133),
    inference(clausify,[status(thm)],[f_2770_3]) ).

fof(f_2771_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_2771_2,plain,
    ! [U_10135,U_10134] : c_Transitive__Closure_Ortrancl(U_10134,U_10135) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10134,U_10134),tc_HOL_Obool)),c_Relation_OId(U_10134)),hAPP(hAPP(c_Relation_Orel__comp(U_10134,U_10134,U_10134),c_Transitive__Closure_Ortrancl(U_10134,U_10135)),U_10135)),
    inference(variable_rename,[status(thm)],[f_2771_1]) ).

fof(f_2771_3,plain,
    ! [U_10134,U_10135] : c_Transitive__Closure_Ortrancl(U_10134,U_10135) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10134,U_10134),tc_HOL_Obool)),c_Relation_OId(U_10134)),hAPP(hAPP(c_Relation_Orel__comp(U_10134,U_10134,U_10134),c_Transitive__Closure_Ortrancl(U_10134,U_10135)),U_10135)),
    inference(definitional_conversion,[status(esa)],[f_2771_2]) ).

cnf(f_2771_4,plain,
    c_Transitive__Closure_Ortrancl(U_10134,U_10135) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_10134,U_10134),tc_HOL_Obool)),c_Relation_OId(U_10134)),hAPP(hAPP(c_Relation_Orel__comp(U_10134,U_10134,U_10134),c_Transitive__Closure_Ortrancl(U_10134,U_10135)),U_10135)),
    inference(clausify,[status(thm)],[f_2771_3]) ).

fof(f_2772_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_2772_2,plain,
    ! [U_10139,U_10138,U_10137,U_10136] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10136,U_10136)),hAPP(hAPP(c_Product__Type_OPair(U_10136,U_10136),U_10137),U_10139)),c_Transitive__Closure_Ortrancl(U_10136,U_10138)))
          | U_10137 != U_10139 )
        & ( U_10137 = U_10139
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10136,U_10136)),hAPP(hAPP(c_Product__Type_OPair(U_10136,U_10136),U_10137),U_10139)),c_Transitive__Closure_Ortrancl(U_10136,U_10138))) ) )
      | hBOOL(hAPP(hAPP(c_member(U_10136),U_10137),hAPP(c_Relation_ODomain(U_10136,U_10136),U_10138))) ),
    inference(variable_rename,[status(thm)],[f_2772_1]) ).

fof(f_2772_3,plain,
    ( ! [U_10136,U_10137,U_10138,U_10139] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10136,U_10136)),hAPP(hAPP(c_Product__Type_OPair(U_10136,U_10136),U_10137),U_10139)),c_Transitive__Closure_Ortrancl(U_10136,U_10138)))
        | U_10137 != U_10139
        | ~ sP779(U_10136,U_10137,U_10138,U_10139) )
    & ! [U_10136,U_10137,U_10138,U_10139] :
        ( U_10137 = U_10139
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10136,U_10136)),hAPP(hAPP(c_Product__Type_OPair(U_10136,U_10136),U_10137),U_10139)),c_Transitive__Closure_Ortrancl(U_10136,U_10138)))
        | ~ sP779(U_10136,U_10137,U_10138,U_10139) )
    & ! [U_10136,U_10137,U_10138,U_10139] :
        ( sP779(U_10136,U_10137,U_10138,U_10139)
        | hBOOL(hAPP(hAPP(c_member(U_10136),U_10137),hAPP(c_Relation_ODomain(U_10136,U_10136),U_10138))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP779])],[f_2772_2]) ).

cnf(f_2772_4,plain,
    ( sP779(U_10136,U_10137,U_10138,U_10139)
    | hBOOL(hAPP(hAPP(c_member(U_10136),U_10137),hAPP(c_Relation_ODomain(U_10136,U_10136),U_10138))) ),
    inference(clausify,[status(thm)],[f_2772_3]) ).

cnf(f_2772_5,plain,
    ( U_10137 = U_10139
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10136,U_10136)),hAPP(hAPP(c_Product__Type_OPair(U_10136,U_10136),U_10137),U_10139)),c_Transitive__Closure_Ortrancl(U_10136,U_10138)))
    | ~ sP779(U_10136,U_10137,U_10138,U_10139) ),
    inference(clausify,[status(thm)],[f_2772_3]) ).

cnf(f_2772_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_10136,U_10136)),hAPP(hAPP(c_Product__Type_OPair(U_10136,U_10136),U_10137),U_10139)),c_Transitive__Closure_Ortrancl(U_10136,U_10138)))
    | U_10137 != U_10139
    | ~ sP779(U_10136,U_10137,U_10138,U_10139) ),
    inference(clausify,[status(thm)],[f_2772_3]) ).

fof(f_2773_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_2773_2,plain,
    ! [U_10143,U_10142,U_10141,U_10140] :
      ( hBOOL(hAPP(hAPP(c_member(U_10140),U_10141),c_Wellfounded_Oacc(U_10140,U_10143)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10140),U_10142),c_Wellfounded_Oacc(U_10140,U_10143)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10140,U_10140)),hAPP(hAPP(c_Product__Type_OPair(U_10140,U_10140),U_10141),U_10142)),c_Transitive__Closure_Ortrancl(U_10140,U_10143))) ),
    inference(variable_rename,[status(thm)],[f_2773_1]) ).

fof(f_2773_3,plain,
    ! [U_10140,U_10141,U_10142,U_10143] :
      ( hBOOL(hAPP(hAPP(c_member(U_10140),U_10141),c_Wellfounded_Oacc(U_10140,U_10143)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10140),U_10142),c_Wellfounded_Oacc(U_10140,U_10143)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10140,U_10140)),hAPP(hAPP(c_Product__Type_OPair(U_10140,U_10140),U_10141),U_10142)),c_Transitive__Closure_Ortrancl(U_10140,U_10143))) ),
    inference(definitional_conversion,[status(esa)],[f_2773_2]) ).

cnf(f_2773_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10140),U_10141),c_Wellfounded_Oacc(U_10140,U_10143)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10140),U_10142),c_Wellfounded_Oacc(U_10140,U_10143)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10140,U_10140)),hAPP(hAPP(c_Product__Type_OPair(U_10140,U_10140),U_10141),U_10142)),c_Transitive__Closure_Ortrancl(U_10140,U_10143))) ),
    inference(clausify,[status(thm)],[f_2773_3]) ).

fof(f_2774_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_2774_2,plain,
    ! [U_10147,U_10146,U_10145,U_10144] :
      ( hBOOL(hAPP(hAPP(c_member(U_10144),U_10147),c_Wellfounded_Oacc(U_10144,U_10146)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10144,U_10144)),hAPP(hAPP(c_Product__Type_OPair(U_10144,U_10144),U_10147),U_10145)),c_Transitive__Closure_Ortrancl(U_10144,U_10146)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10144),U_10145),c_Wellfounded_Oacc(U_10144,U_10146))) ),
    inference(variable_rename,[status(thm)],[f_2774_1]) ).

fof(f_2774_3,plain,
    ! [U_10144,U_10145,U_10146,U_10147] :
      ( hBOOL(hAPP(hAPP(c_member(U_10144),U_10147),c_Wellfounded_Oacc(U_10144,U_10146)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10144,U_10144)),hAPP(hAPP(c_Product__Type_OPair(U_10144,U_10144),U_10147),U_10145)),c_Transitive__Closure_Ortrancl(U_10144,U_10146)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10144),U_10145),c_Wellfounded_Oacc(U_10144,U_10146))) ),
    inference(definitional_conversion,[status(esa)],[f_2774_2]) ).

cnf(f_2774_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10144),U_10147),c_Wellfounded_Oacc(U_10144,U_10146)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10144,U_10144)),hAPP(hAPP(c_Product__Type_OPair(U_10144,U_10144),U_10147),U_10145)),c_Transitive__Closure_Ortrancl(U_10144,U_10146)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10144),U_10145),c_Wellfounded_Oacc(U_10144,U_10146))) ),
    inference(clausify,[status(thm)],[f_2774_3]) ).

fof(f_2775_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_2775_2,plain,
    ! [U_10151,U_10150,U_10149,U_10148] :
      ( ( c_Wellfounded_Owf(U_10148,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10148,U_10148)),hAPP(hAPP(c_Product__Type_OPair(U_10148,U_10148),U_10149),U_10150)),U_10151))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_10148,U_10148)),hAPP(hAPP(c_Product__Type_OPair(U_10148,U_10148),U_10150),U_10149)),c_Transitive__Closure_Ortrancl(U_10148,U_10151)))
        | ~ c_Wellfounded_Owf(U_10148,U_10151) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10148,U_10148)),hAPP(hAPP(c_Product__Type_OPair(U_10148,U_10148),U_10150),U_10149)),c_Transitive__Closure_Ortrancl(U_10148,U_10151)))
          & c_Wellfounded_Owf(U_10148,U_10151) )
        | ~ c_Wellfounded_Owf(U_10148,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10148,U_10148)),hAPP(hAPP(c_Product__Type_OPair(U_10148,U_10148),U_10149),U_10150)),U_10151)) ) ),
    inference(variable_rename,[status(thm)],[f_2775_1]) ).

fof(f_2775_3,plain,
    ( ! [U_10159,U_10157,U_10155,U_10153] :
        ( c_Wellfounded_Owf(U_10153,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10153,U_10153)),hAPP(hAPP(c_Product__Type_OPair(U_10153,U_10153),U_10155),U_10157)),U_10159))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_10153,U_10153)),hAPP(hAPP(c_Product__Type_OPair(U_10153,U_10153),U_10157),U_10155)),c_Transitive__Closure_Ortrancl(U_10153,U_10159)))
        | ~ c_Wellfounded_Owf(U_10153,U_10159) )
    & ! [U_10158,U_10156,U_10154,U_10152] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10152,U_10152)),hAPP(hAPP(c_Product__Type_OPair(U_10152,U_10152),U_10156),U_10154)),c_Transitive__Closure_Ortrancl(U_10152,U_10158)))
          & c_Wellfounded_Owf(U_10152,U_10158) )
        | ~ c_Wellfounded_Owf(U_10152,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10152,U_10152)),hAPP(hAPP(c_Product__Type_OPair(U_10152,U_10152),U_10154),U_10156)),U_10158)) ) ),
    inference(miniscope,[status(thm)],[f_2775_2]) ).

fof(f_2775_4,plain,
    ( ! [U_10154,U_10156,U_10152,U_10158] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10152,U_10152)),hAPP(hAPP(c_Product__Type_OPair(U_10152,U_10152),U_10156),U_10154)),c_Transitive__Closure_Ortrancl(U_10152,U_10158)))
        | ~ sP780(U_10154,U_10156,U_10152,U_10158) )
    & ! [U_10154,U_10156,U_10152,U_10158] :
        ( c_Wellfounded_Owf(U_10152,U_10158)
        | ~ sP780(U_10154,U_10156,U_10152,U_10158) )
    & ! [U_10155,U_10157,U_10153,U_10159] :
        ( c_Wellfounded_Owf(U_10153,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10153,U_10153)),hAPP(hAPP(c_Product__Type_OPair(U_10153,U_10153),U_10155),U_10157)),U_10159))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_10153,U_10153)),hAPP(hAPP(c_Product__Type_OPair(U_10153,U_10153),U_10157),U_10155)),c_Transitive__Closure_Ortrancl(U_10153,U_10159)))
        | ~ c_Wellfounded_Owf(U_10153,U_10159) )
    & ! [U_10154,U_10156,U_10152,U_10158] :
        ( sP780(U_10154,U_10156,U_10152,U_10158)
        | ~ c_Wellfounded_Owf(U_10152,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10152,U_10152)),hAPP(hAPP(c_Product__Type_OPair(U_10152,U_10152),U_10154),U_10156)),U_10158)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP780])],[f_2775_3]) ).

cnf(f_2775_5,plain,
    ( sP780(U_10154,U_10156,U_10152,U_10158)
    | ~ c_Wellfounded_Owf(U_10152,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10152,U_10152)),hAPP(hAPP(c_Product__Type_OPair(U_10152,U_10152),U_10154),U_10156)),U_10158)) ),
    inference(clausify,[status(thm)],[f_2775_4]) ).

cnf(f_2775_6,plain,
    ( c_Wellfounded_Owf(U_10153,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10153,U_10153)),hAPP(hAPP(c_Product__Type_OPair(U_10153,U_10153),U_10155),U_10157)),U_10159))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_10153,U_10153)),hAPP(hAPP(c_Product__Type_OPair(U_10153,U_10153),U_10157),U_10155)),c_Transitive__Closure_Ortrancl(U_10153,U_10159)))
    | ~ c_Wellfounded_Owf(U_10153,U_10159) ),
    inference(clausify,[status(thm)],[f_2775_4]) ).

cnf(f_2775_7,plain,
    ( c_Wellfounded_Owf(U_10152,U_10158)
    | ~ sP780(U_10154,U_10156,U_10152,U_10158) ),
    inference(clausify,[status(thm)],[f_2775_4]) ).

cnf(f_2775_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10152,U_10152)),hAPP(hAPP(c_Product__Type_OPair(U_10152,U_10152),U_10156),U_10154)),c_Transitive__Closure_Ortrancl(U_10152,U_10158)))
    | ~ sP780(U_10154,U_10156,U_10152,U_10158) ),
    inference(clausify,[status(thm)],[f_2775_4]) ).

fof(f_2776_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_2776_2,plain,
    ! [U_10163,U_10162,U_10161,U_10160] :
      ( ( c_Wellfounded_Oacyclic(U_10160,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10160,U_10160)),hAPP(hAPP(c_Product__Type_OPair(U_10160,U_10160),U_10161),U_10162)),U_10163))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_10160,U_10160)),hAPP(hAPP(c_Product__Type_OPair(U_10160,U_10160),U_10162),U_10161)),c_Transitive__Closure_Ortrancl(U_10160,U_10163)))
        | ~ c_Wellfounded_Oacyclic(U_10160,U_10163) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10160,U_10160)),hAPP(hAPP(c_Product__Type_OPair(U_10160,U_10160),U_10162),U_10161)),c_Transitive__Closure_Ortrancl(U_10160,U_10163)))
          & c_Wellfounded_Oacyclic(U_10160,U_10163) )
        | ~ c_Wellfounded_Oacyclic(U_10160,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10160,U_10160)),hAPP(hAPP(c_Product__Type_OPair(U_10160,U_10160),U_10161),U_10162)),U_10163)) ) ),
    inference(variable_rename,[status(thm)],[f_2776_1]) ).

fof(f_2776_3,plain,
    ( ! [U_10171,U_10169,U_10167,U_10165] :
        ( c_Wellfounded_Oacyclic(U_10165,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10165,U_10165)),hAPP(hAPP(c_Product__Type_OPair(U_10165,U_10165),U_10167),U_10169)),U_10171))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_10165,U_10165)),hAPP(hAPP(c_Product__Type_OPair(U_10165,U_10165),U_10169),U_10167)),c_Transitive__Closure_Ortrancl(U_10165,U_10171)))
        | ~ c_Wellfounded_Oacyclic(U_10165,U_10171) )
    & ! [U_10170,U_10168,U_10166,U_10164] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10164,U_10164)),hAPP(hAPP(c_Product__Type_OPair(U_10164,U_10164),U_10168),U_10166)),c_Transitive__Closure_Ortrancl(U_10164,U_10170)))
          & c_Wellfounded_Oacyclic(U_10164,U_10170) )
        | ~ c_Wellfounded_Oacyclic(U_10164,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10164,U_10164)),hAPP(hAPP(c_Product__Type_OPair(U_10164,U_10164),U_10166),U_10168)),U_10170)) ) ),
    inference(miniscope,[status(thm)],[f_2776_2]) ).

fof(f_2776_4,plain,
    ( ! [U_10164,U_10168,U_10166,U_10170] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10164,U_10164)),hAPP(hAPP(c_Product__Type_OPair(U_10164,U_10164),U_10168),U_10166)),c_Transitive__Closure_Ortrancl(U_10164,U_10170)))
        | ~ sP781(U_10164,U_10168,U_10166,U_10170) )
    & ! [U_10164,U_10168,U_10166,U_10170] :
        ( c_Wellfounded_Oacyclic(U_10164,U_10170)
        | ~ sP781(U_10164,U_10168,U_10166,U_10170) )
    & ! [U_10169,U_10165,U_10171,U_10167] :
        ( c_Wellfounded_Oacyclic(U_10165,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10165,U_10165)),hAPP(hAPP(c_Product__Type_OPair(U_10165,U_10165),U_10167),U_10169)),U_10171))
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_10165,U_10165)),hAPP(hAPP(c_Product__Type_OPair(U_10165,U_10165),U_10169),U_10167)),c_Transitive__Closure_Ortrancl(U_10165,U_10171)))
        | ~ c_Wellfounded_Oacyclic(U_10165,U_10171) )
    & ! [U_10164,U_10168,U_10166,U_10170] :
        ( sP781(U_10164,U_10168,U_10166,U_10170)
        | ~ c_Wellfounded_Oacyclic(U_10164,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10164,U_10164)),hAPP(hAPP(c_Product__Type_OPair(U_10164,U_10164),U_10166),U_10168)),U_10170)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP781])],[f_2776_3]) ).

cnf(f_2776_5,plain,
    ( sP781(U_10164,U_10168,U_10166,U_10170)
    | ~ c_Wellfounded_Oacyclic(U_10164,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10164,U_10164)),hAPP(hAPP(c_Product__Type_OPair(U_10164,U_10164),U_10166),U_10168)),U_10170)) ),
    inference(clausify,[status(thm)],[f_2776_4]) ).

cnf(f_2776_6,plain,
    ( c_Wellfounded_Oacyclic(U_10165,hAPP(hAPP(c_Set_Oinsert(tc_prod(U_10165,U_10165)),hAPP(hAPP(c_Product__Type_OPair(U_10165,U_10165),U_10167),U_10169)),U_10171))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_10165,U_10165)),hAPP(hAPP(c_Product__Type_OPair(U_10165,U_10165),U_10169),U_10167)),c_Transitive__Closure_Ortrancl(U_10165,U_10171)))
    | ~ c_Wellfounded_Oacyclic(U_10165,U_10171) ),
    inference(clausify,[status(thm)],[f_2776_4]) ).

cnf(f_2776_7,plain,
    ( c_Wellfounded_Oacyclic(U_10164,U_10170)
    | ~ sP781(U_10164,U_10168,U_10166,U_10170) ),
    inference(clausify,[status(thm)],[f_2776_4]) ).

cnf(f_2776_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10164,U_10164)),hAPP(hAPP(c_Product__Type_OPair(U_10164,U_10164),U_10168),U_10166)),c_Transitive__Closure_Ortrancl(U_10164,U_10170)))
    | ~ sP781(U_10164,U_10168,U_10166,U_10170) ),
    inference(clausify,[status(thm)],[f_2776_4]) ).

fof(f_2777_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_2777_2,plain,
    ! [U_10173,U_10172] :
      ( ( 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_10172),U_10173)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10172),U_10173)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10172),U_10173))
        | ~ 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_10172),U_10173)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(variable_rename,[status(thm)],[f_2777_1]) ).

fof(f_2777_3,plain,
    ( ! [U_10177,U_10175] :
        ( 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_10175),U_10177)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10175),U_10177)) )
    & ! [U_10176,U_10174] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10174),U_10176))
        | ~ 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_10174),U_10176)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(miniscope,[status(thm)],[f_2777_2]) ).

fof(f_2777_4,plain,
    ( ! [U_10175,U_10177] :
        ( 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_10175),U_10177)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10175),U_10177)) )
    & ! [U_10174,U_10176] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10174),U_10176))
        | ~ 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_10174),U_10176)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ) ),
    inference(definitional_conversion,[status(esa)],[f_2777_3]) ).

cnf(f_2777_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10174),U_10176))
    | ~ 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_10174),U_10176)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat))) ),
    inference(clausify,[status(thm)],[f_2777_4]) ).

cnf(f_2777_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_10175),U_10177)),c_Transitive__Closure_Ortrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_10175),U_10177)) ),
    inference(clausify,[status(thm)],[f_2777_4]) ).

fof(f_2778_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_2778_2,plain,
    ! [U_10179,U_10178] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_10178,U_10179)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10179),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10178),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_2778_1]) ).

fof(f_2778_3,plain,
    ! [U_10178,U_10179] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_10178,U_10179)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10179),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10178),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(definitional_conversion,[status(esa)],[f_2778_2]) ).

cnf(f_2778_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_10178,U_10179)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10179),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_10178),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_2778_3]) ).

fof(f_2779_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_2779_2,plain,
    ! [U_10182,U_10181,U_10180] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10180),c_Big__Operators_Olattice__class_OInf__fin(U_10180,U_10181)),c_Big__Operators_Olattice__class_OInf__fin(U_10180,U_10182)) = c_Big__Operators_Olattice__class_OInf__fin(U_10180,hAPP(c_Set_OCollect(U_10180),hAPP(hAPP(c_COMBB(tc_fun(U_10180,tc_HOL_Obool),tc_HOL_Obool,U_10180),c_HOL_OEx(U_10180)),hAPP(hAPP(c_COMBB(tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool)),tc_fun(U_10180,tc_HOL_Obool),U_10180),hAPP(c_COMBB(tc_fun(U_10180,tc_HOL_Obool),tc_HOL_Obool,U_10180),c_HOL_OEx(U_10180))),hAPP(hAPP(c_COMBC(U_10180,tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool)),tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10180,tc_fun(tc_fun(U_10180,tc_HOL_Obool),tc_fun(U_10180,tc_HOL_Obool))),tc_fun(tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool)),tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool))),U_10180),c_COMBS(U_10180,tc_fun(U_10180,tc_HOL_Obool),tc_fun(U_10180,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10180,tc_fun(U_10180,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_10180,tc_fun(tc_fun(U_10180,tc_HOL_Obool),tc_fun(U_10180,tc_HOL_Obool))),U_10180),hAPP(c_COMBB(tc_fun(U_10180,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_10180,tc_HOL_Obool),tc_fun(U_10180,tc_HOL_Obool)),U_10180),c_COMBS(U_10180,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool)),tc_fun(U_10180,tc_fun(U_10180,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_10180),hAPP(c_COMBB(tc_fun(U_10180,tc_HOL_Obool),tc_fun(U_10180,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_10180),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10180),c_fconj))),hAPP(hAPP(c_COMBC(U_10180,tc_fun(U_10180,tc_fun(U_10180,U_10180)),tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10180,U_10180),tc_fun(U_10180,tc_HOL_Obool)),tc_fun(tc_fun(U_10180,tc_fun(U_10180,U_10180)),tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool))),U_10180),c_COMBB(tc_fun(U_10180,U_10180),tc_fun(U_10180,tc_HOL_Obool),U_10180)),hAPP(hAPP(c_COMBB(tc_fun(U_10180,tc_HOL_Obool),tc_fun(tc_fun(U_10180,U_10180),tc_fun(U_10180,tc_HOL_Obool)),U_10180),c_COMBB(U_10180,tc_HOL_Obool,U_10180)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_10180)))))),hAPP(hAPP(c_COMBC(U_10180,tc_fun(U_10180,tc_HOL_Obool),tc_fun(U_10180,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_10180,tc_HOL_Obool),tc_fun(U_10180,tc_HOL_Obool)),U_10180),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_10180)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10180),c_fconj),hAPP(hAPP(c_COMBC(U_10180,tc_fun(U_10180,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10180)),U_10181)))),hAPP(hAPP(c_COMBC(U_10180,tc_fun(U_10180,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10180)),U_10182)))))))
      | U_10182 = c_Orderings_Obot__class_Obot(tc_fun(U_10180,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10180),U_10182))
      | U_10181 = c_Orderings_Obot__class_Obot(tc_fun(U_10180,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10180),U_10181))
      | ~ class_Lattices_Odistrib__lattice(U_10180) ),
    inference(variable_rename,[status(thm)],[f_2779_1]) ).

fof(f_2779_3,plain,
    ! [U_10180,U_10181,U_10182] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10180),c_Big__Operators_Olattice__class_OInf__fin(U_10180,U_10181)),c_Big__Operators_Olattice__class_OInf__fin(U_10180,U_10182)) = c_Big__Operators_Olattice__class_OInf__fin(U_10180,hAPP(c_Set_OCollect(U_10180),hAPP(hAPP(c_COMBB(tc_fun(U_10180,tc_HOL_Obool),tc_HOL_Obool,U_10180),c_HOL_OEx(U_10180)),hAPP(hAPP(c_COMBB(tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool)),tc_fun(U_10180,tc_HOL_Obool),U_10180),hAPP(c_COMBB(tc_fun(U_10180,tc_HOL_Obool),tc_HOL_Obool,U_10180),c_HOL_OEx(U_10180))),hAPP(hAPP(c_COMBC(U_10180,tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool)),tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10180,tc_fun(tc_fun(U_10180,tc_HOL_Obool),tc_fun(U_10180,tc_HOL_Obool))),tc_fun(tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool)),tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool))),U_10180),c_COMBS(U_10180,tc_fun(U_10180,tc_HOL_Obool),tc_fun(U_10180,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10180,tc_fun(U_10180,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_10180,tc_fun(tc_fun(U_10180,tc_HOL_Obool),tc_fun(U_10180,tc_HOL_Obool))),U_10180),hAPP(c_COMBB(tc_fun(U_10180,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_10180,tc_HOL_Obool),tc_fun(U_10180,tc_HOL_Obool)),U_10180),c_COMBS(U_10180,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool)),tc_fun(U_10180,tc_fun(U_10180,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_10180),hAPP(c_COMBB(tc_fun(U_10180,tc_HOL_Obool),tc_fun(U_10180,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_10180),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10180),c_fconj))),hAPP(hAPP(c_COMBC(U_10180,tc_fun(U_10180,tc_fun(U_10180,U_10180)),tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10180,U_10180),tc_fun(U_10180,tc_HOL_Obool)),tc_fun(tc_fun(U_10180,tc_fun(U_10180,U_10180)),tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool))),U_10180),c_COMBB(tc_fun(U_10180,U_10180),tc_fun(U_10180,tc_HOL_Obool),U_10180)),hAPP(hAPP(c_COMBB(tc_fun(U_10180,tc_HOL_Obool),tc_fun(tc_fun(U_10180,U_10180),tc_fun(U_10180,tc_HOL_Obool)),U_10180),c_COMBB(U_10180,tc_HOL_Obool,U_10180)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_10180)))))),hAPP(hAPP(c_COMBC(U_10180,tc_fun(U_10180,tc_HOL_Obool),tc_fun(U_10180,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_10180,tc_HOL_Obool),tc_fun(U_10180,tc_HOL_Obool)),U_10180),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_10180)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10180),c_fconj),hAPP(hAPP(c_COMBC(U_10180,tc_fun(U_10180,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10180)),U_10181)))),hAPP(hAPP(c_COMBC(U_10180,tc_fun(U_10180,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10180)),U_10182)))))))
      | U_10182 = c_Orderings_Obot__class_Obot(tc_fun(U_10180,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10180),U_10182))
      | U_10181 = c_Orderings_Obot__class_Obot(tc_fun(U_10180,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10180),U_10181))
      | ~ class_Lattices_Odistrib__lattice(U_10180) ),
    inference(definitional_conversion,[status(esa)],[f_2779_2]) ).

cnf(f_2779_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10180),c_Big__Operators_Olattice__class_OInf__fin(U_10180,U_10181)),c_Big__Operators_Olattice__class_OInf__fin(U_10180,U_10182)) = c_Big__Operators_Olattice__class_OInf__fin(U_10180,hAPP(c_Set_OCollect(U_10180),hAPP(hAPP(c_COMBB(tc_fun(U_10180,tc_HOL_Obool),tc_HOL_Obool,U_10180),c_HOL_OEx(U_10180)),hAPP(hAPP(c_COMBB(tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool)),tc_fun(U_10180,tc_HOL_Obool),U_10180),hAPP(c_COMBB(tc_fun(U_10180,tc_HOL_Obool),tc_HOL_Obool,U_10180),c_HOL_OEx(U_10180))),hAPP(hAPP(c_COMBC(U_10180,tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool)),tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10180,tc_fun(tc_fun(U_10180,tc_HOL_Obool),tc_fun(U_10180,tc_HOL_Obool))),tc_fun(tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool)),tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool))),U_10180),c_COMBS(U_10180,tc_fun(U_10180,tc_HOL_Obool),tc_fun(U_10180,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10180,tc_fun(U_10180,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_10180,tc_fun(tc_fun(U_10180,tc_HOL_Obool),tc_fun(U_10180,tc_HOL_Obool))),U_10180),hAPP(c_COMBB(tc_fun(U_10180,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_10180,tc_HOL_Obool),tc_fun(U_10180,tc_HOL_Obool)),U_10180),c_COMBS(U_10180,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool)),tc_fun(U_10180,tc_fun(U_10180,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_10180),hAPP(c_COMBB(tc_fun(U_10180,tc_HOL_Obool),tc_fun(U_10180,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_10180),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10180),c_fconj))),hAPP(hAPP(c_COMBC(U_10180,tc_fun(U_10180,tc_fun(U_10180,U_10180)),tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_10180,U_10180),tc_fun(U_10180,tc_HOL_Obool)),tc_fun(tc_fun(U_10180,tc_fun(U_10180,U_10180)),tc_fun(U_10180,tc_fun(U_10180,tc_HOL_Obool))),U_10180),c_COMBB(tc_fun(U_10180,U_10180),tc_fun(U_10180,tc_HOL_Obool),U_10180)),hAPP(hAPP(c_COMBB(tc_fun(U_10180,tc_HOL_Obool),tc_fun(tc_fun(U_10180,U_10180),tc_fun(U_10180,tc_HOL_Obool)),U_10180),c_COMBB(U_10180,tc_HOL_Obool,U_10180)),c_fequal))),c_Lattices_Osemilattice__sup__class_Osup(U_10180)))))),hAPP(hAPP(c_COMBC(U_10180,tc_fun(U_10180,tc_HOL_Obool),tc_fun(U_10180,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_10180,tc_HOL_Obool),tc_fun(U_10180,tc_HOL_Obool)),U_10180),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_10180)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10180),c_fconj),hAPP(hAPP(c_COMBC(U_10180,tc_fun(U_10180,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10180)),U_10181)))),hAPP(hAPP(c_COMBC(U_10180,tc_fun(U_10180,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10180)),U_10182)))))))
    | U_10182 = c_Orderings_Obot__class_Obot(tc_fun(U_10180,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10180),U_10182))
    | U_10181 = c_Orderings_Obot__class_Obot(tc_fun(U_10180,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10180),U_10181))
    | ~ class_Lattices_Odistrib__lattice(U_10180) ),
    inference(clausify,[status(thm)],[f_2779_3]) ).

fof(f_2780_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_2780_2,plain,
    ! [U_10185,U_10184,U_10183] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10183),U_10185),c_Big__Operators_Olattice__class_OInf__fin(U_10183,U_10184)) = c_Big__Operators_Olattice__class_OInf__fin(U_10183,hAPP(c_Set_OCollect(U_10183),hAPP(hAPP(c_COMBB(tc_fun(U_10183,tc_HOL_Obool),tc_HOL_Obool,U_10183),c_HOL_OEx(U_10183)),hAPP(hAPP(c_COMBC(U_10183,tc_fun(U_10183,tc_HOL_Obool),tc_fun(U_10183,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10183,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_10183,tc_HOL_Obool),tc_fun(U_10183,tc_HOL_Obool)),U_10183),c_COMBS(U_10183,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10183,tc_HOL_Obool),tc_fun(U_10183,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_10183),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10183),c_fconj)),hAPP(hAPP(c_COMBC(U_10183,tc_fun(U_10183,U_10183),tc_fun(U_10183,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10183,tc_HOL_Obool),tc_fun(tc_fun(U_10183,U_10183),tc_fun(U_10183,tc_HOL_Obool)),U_10183),c_COMBB(U_10183,tc_HOL_Obool,U_10183)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10183),U_10185))))),hAPP(hAPP(c_COMBC(U_10183,tc_fun(U_10183,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10183)),U_10184)))))
      | U_10184 = c_Orderings_Obot__class_Obot(tc_fun(U_10183,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10183),U_10184))
      | ~ class_Lattices_Odistrib__lattice(U_10183) ),
    inference(variable_rename,[status(thm)],[f_2780_1]) ).

fof(f_2780_3,plain,
    ! [U_10183,U_10184,U_10185] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10183),U_10185),c_Big__Operators_Olattice__class_OInf__fin(U_10183,U_10184)) = c_Big__Operators_Olattice__class_OInf__fin(U_10183,hAPP(c_Set_OCollect(U_10183),hAPP(hAPP(c_COMBB(tc_fun(U_10183,tc_HOL_Obool),tc_HOL_Obool,U_10183),c_HOL_OEx(U_10183)),hAPP(hAPP(c_COMBC(U_10183,tc_fun(U_10183,tc_HOL_Obool),tc_fun(U_10183,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10183,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_10183,tc_HOL_Obool),tc_fun(U_10183,tc_HOL_Obool)),U_10183),c_COMBS(U_10183,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10183,tc_HOL_Obool),tc_fun(U_10183,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_10183),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10183),c_fconj)),hAPP(hAPP(c_COMBC(U_10183,tc_fun(U_10183,U_10183),tc_fun(U_10183,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10183,tc_HOL_Obool),tc_fun(tc_fun(U_10183,U_10183),tc_fun(U_10183,tc_HOL_Obool)),U_10183),c_COMBB(U_10183,tc_HOL_Obool,U_10183)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10183),U_10185))))),hAPP(hAPP(c_COMBC(U_10183,tc_fun(U_10183,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10183)),U_10184)))))
      | U_10184 = c_Orderings_Obot__class_Obot(tc_fun(U_10183,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10183),U_10184))
      | ~ class_Lattices_Odistrib__lattice(U_10183) ),
    inference(definitional_conversion,[status(esa)],[f_2780_2]) ).

cnf(f_2780_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10183),U_10185),c_Big__Operators_Olattice__class_OInf__fin(U_10183,U_10184)) = c_Big__Operators_Olattice__class_OInf__fin(U_10183,hAPP(c_Set_OCollect(U_10183),hAPP(hAPP(c_COMBB(tc_fun(U_10183,tc_HOL_Obool),tc_HOL_Obool,U_10183),c_HOL_OEx(U_10183)),hAPP(hAPP(c_COMBC(U_10183,tc_fun(U_10183,tc_HOL_Obool),tc_fun(U_10183,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10183,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_10183,tc_HOL_Obool),tc_fun(U_10183,tc_HOL_Obool)),U_10183),c_COMBS(U_10183,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10183,tc_HOL_Obool),tc_fun(U_10183,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_10183),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10183),c_fconj)),hAPP(hAPP(c_COMBC(U_10183,tc_fun(U_10183,U_10183),tc_fun(U_10183,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10183,tc_HOL_Obool),tc_fun(tc_fun(U_10183,U_10183),tc_fun(U_10183,tc_HOL_Obool)),U_10183),c_COMBB(U_10183,tc_HOL_Obool,U_10183)),c_fequal)),hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10183),U_10185))))),hAPP(hAPP(c_COMBC(U_10183,tc_fun(U_10183,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10183)),U_10184)))))
    | U_10184 = c_Orderings_Obot__class_Obot(tc_fun(U_10183,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10183),U_10184))
    | ~ class_Lattices_Odistrib__lattice(U_10183) ),
    inference(clausify,[status(thm)],[f_2780_3]) ).

fof(f_2781_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_2781_2,plain,
    ! [U_10187,U_10186] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_10186,U_10187))),
    inference(variable_rename,[status(thm)],[f_2781_1]) ).

fof(f_2781_3,plain,
    ! [U_10187,U_10186] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_10186,U_10187))),
    inference(definitional_conversion,[status(esa)],[f_2781_2]) ).

cnf(f_2781_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_10186,U_10187))),
    inference(clausify,[status(thm)],[f_2781_3]) ).

fof(f_2782_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_2782_2,plain,
    ! [U_10189,U_10188] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_10188,hAPP(hAPP(c_Set_Oinsert(U_10188),U_10189),c_Orderings_Obot__class_Obot(tc_fun(U_10188,tc_HOL_Obool)))) = U_10189
      | ~ class_Lattices_Olattice(U_10188) ),
    inference(variable_rename,[status(thm)],[f_2782_1]) ).

fof(f_2782_3,plain,
    ! [U_10188,U_10189] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_10188,hAPP(hAPP(c_Set_Oinsert(U_10188),U_10189),c_Orderings_Obot__class_Obot(tc_fun(U_10188,tc_HOL_Obool)))) = U_10189
      | ~ class_Lattices_Olattice(U_10188) ),
    inference(definitional_conversion,[status(esa)],[f_2782_2]) ).

cnf(f_2782_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_10188,hAPP(hAPP(c_Set_Oinsert(U_10188),U_10189),c_Orderings_Obot__class_Obot(tc_fun(U_10188,tc_HOL_Obool)))) = U_10189
    | ~ class_Lattices_Olattice(U_10188) ),
    inference(clausify,[status(thm)],[f_2782_3]) ).

fof(f_2783_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_2783_2,plain,
    ! [U_10192,U_10191,U_10190] :
      ( c_SetInterval_Oord__class_OgreaterThanLessThan(U_10190,U_10192,U_10191) = c_Orderings_Obot__class_Obot(tc_fun(U_10190,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10190),U_10191),U_10192))
      | ~ class_Orderings_Oorder(U_10190) ),
    inference(variable_rename,[status(thm)],[f_2783_1]) ).

fof(f_2783_3,plain,
    ! [U_10190,U_10191,U_10192] :
      ( c_SetInterval_Oord__class_OgreaterThanLessThan(U_10190,U_10192,U_10191) = c_Orderings_Obot__class_Obot(tc_fun(U_10190,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10190),U_10191),U_10192))
      | ~ class_Orderings_Oorder(U_10190) ),
    inference(definitional_conversion,[status(esa)],[f_2783_2]) ).

cnf(f_2783_4,plain,
    ( c_SetInterval_Oord__class_OgreaterThanLessThan(U_10190,U_10192,U_10191) = c_Orderings_Obot__class_Obot(tc_fun(U_10190,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10190),U_10191),U_10192))
    | ~ class_Orderings_Oorder(U_10190) ),
    inference(clausify,[status(thm)],[f_2783_3]) ).

fof(f_2784_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_2784_2,plain,
    ! [U_10195,U_10194,U_10193] :
      ( hAPP(c_Set_Oimage(U_10193,U_10193,c_Groups_Ouminus__class_Ouminus(U_10193)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10193,U_10194,U_10195)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10193,hAPP(c_Groups_Ouminus__class_Ouminus(U_10193),U_10195),hAPP(c_Groups_Ouminus__class_Ouminus(U_10193),U_10194))
      | ~ class_Groups_Oordered__ab__group__add(U_10193) ),
    inference(variable_rename,[status(thm)],[f_2784_1]) ).

fof(f_2784_3,plain,
    ! [U_10193,U_10194,U_10195] :
      ( hAPP(c_Set_Oimage(U_10193,U_10193,c_Groups_Ouminus__class_Ouminus(U_10193)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10193,U_10194,U_10195)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10193,hAPP(c_Groups_Ouminus__class_Ouminus(U_10193),U_10195),hAPP(c_Groups_Ouminus__class_Ouminus(U_10193),U_10194))
      | ~ class_Groups_Oordered__ab__group__add(U_10193) ),
    inference(definitional_conversion,[status(esa)],[f_2784_2]) ).

cnf(f_2784_4,plain,
    ( hAPP(c_Set_Oimage(U_10193,U_10193,c_Groups_Ouminus__class_Ouminus(U_10193)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10193,U_10194,U_10195)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10193,hAPP(c_Groups_Ouminus__class_Ouminus(U_10193),U_10195),hAPP(c_Groups_Ouminus__class_Ouminus(U_10193),U_10194))
    | ~ class_Groups_Oordered__ab__group__add(U_10193) ),
    inference(clausify,[status(thm)],[f_2784_3]) ).

fof(f_2785_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_2785_2,plain,
    ! [U_10198,U_10197,U_10196] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10196),U_10198),c_Big__Operators_Olattice__class_OInf__fin(U_10196,U_10197)) = U_10198
      | ~ hBOOL(hAPP(hAPP(c_member(U_10196),U_10198),U_10197))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10196),U_10197))
      | ~ class_Lattices_Olattice(U_10196) ),
    inference(variable_rename,[status(thm)],[f_2785_1]) ).

fof(f_2785_3,plain,
    ! [U_10196,U_10197,U_10198] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10196),U_10198),c_Big__Operators_Olattice__class_OInf__fin(U_10196,U_10197)) = U_10198
      | ~ hBOOL(hAPP(hAPP(c_member(U_10196),U_10198),U_10197))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10196),U_10197))
      | ~ class_Lattices_Olattice(U_10196) ),
    inference(definitional_conversion,[status(esa)],[f_2785_2]) ).

cnf(f_2785_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10196),U_10198),c_Big__Operators_Olattice__class_OInf__fin(U_10196,U_10197)) = U_10198
    | ~ hBOOL(hAPP(hAPP(c_member(U_10196),U_10198),U_10197))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10196),U_10197))
    | ~ class_Lattices_Olattice(U_10196) ),
    inference(clausify,[status(thm)],[f_2785_3]) ).

fof(f_2786_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_2786_2,plain,
    ! [U_10201,U_10200,U_10199] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10199),U_10201),c_Big__Operators_Olinorder__class_OMax(U_10199,U_10200)) = c_Big__Operators_Olinorder__class_OMax(U_10199,hAPP(c_Set_OCollect(U_10199),hAPP(hAPP(c_COMBB(tc_fun(U_10199,tc_HOL_Obool),tc_HOL_Obool,U_10199),c_HOL_OEx(U_10199)),hAPP(hAPP(c_COMBC(U_10199,tc_fun(U_10199,tc_HOL_Obool),tc_fun(U_10199,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10199,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_10199,tc_HOL_Obool),tc_fun(U_10199,tc_HOL_Obool)),U_10199),c_COMBS(U_10199,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10199,tc_HOL_Obool),tc_fun(U_10199,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_10199),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10199),c_fconj)),hAPP(hAPP(c_COMBC(U_10199,tc_fun(U_10199,U_10199),tc_fun(U_10199,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10199,tc_HOL_Obool),tc_fun(tc_fun(U_10199,U_10199),tc_fun(U_10199,tc_HOL_Obool)),U_10199),c_COMBB(U_10199,tc_HOL_Obool,U_10199)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_10199),U_10201))))),hAPP(hAPP(c_COMBC(U_10199,tc_fun(U_10199,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10199)),U_10200)))))
      | U_10200 = c_Orderings_Obot__class_Obot(tc_fun(U_10199,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10199),U_10200))
      | ~ class_Groups_Olinordered__ab__semigroup__add(U_10199) ),
    inference(variable_rename,[status(thm)],[f_2786_1]) ).

fof(f_2786_3,plain,
    ! [U_10199,U_10200,U_10201] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10199),U_10201),c_Big__Operators_Olinorder__class_OMax(U_10199,U_10200)) = c_Big__Operators_Olinorder__class_OMax(U_10199,hAPP(c_Set_OCollect(U_10199),hAPP(hAPP(c_COMBB(tc_fun(U_10199,tc_HOL_Obool),tc_HOL_Obool,U_10199),c_HOL_OEx(U_10199)),hAPP(hAPP(c_COMBC(U_10199,tc_fun(U_10199,tc_HOL_Obool),tc_fun(U_10199,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10199,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_10199,tc_HOL_Obool),tc_fun(U_10199,tc_HOL_Obool)),U_10199),c_COMBS(U_10199,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10199,tc_HOL_Obool),tc_fun(U_10199,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_10199),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10199),c_fconj)),hAPP(hAPP(c_COMBC(U_10199,tc_fun(U_10199,U_10199),tc_fun(U_10199,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10199,tc_HOL_Obool),tc_fun(tc_fun(U_10199,U_10199),tc_fun(U_10199,tc_HOL_Obool)),U_10199),c_COMBB(U_10199,tc_HOL_Obool,U_10199)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_10199),U_10201))))),hAPP(hAPP(c_COMBC(U_10199,tc_fun(U_10199,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10199)),U_10200)))))
      | U_10200 = c_Orderings_Obot__class_Obot(tc_fun(U_10199,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10199),U_10200))
      | ~ class_Groups_Olinordered__ab__semigroup__add(U_10199) ),
    inference(definitional_conversion,[status(esa)],[f_2786_2]) ).

cnf(f_2786_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10199),U_10201),c_Big__Operators_Olinorder__class_OMax(U_10199,U_10200)) = c_Big__Operators_Olinorder__class_OMax(U_10199,hAPP(c_Set_OCollect(U_10199),hAPP(hAPP(c_COMBB(tc_fun(U_10199,tc_HOL_Obool),tc_HOL_Obool,U_10199),c_HOL_OEx(U_10199)),hAPP(hAPP(c_COMBC(U_10199,tc_fun(U_10199,tc_HOL_Obool),tc_fun(U_10199,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10199,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_10199,tc_HOL_Obool),tc_fun(U_10199,tc_HOL_Obool)),U_10199),c_COMBS(U_10199,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10199,tc_HOL_Obool),tc_fun(U_10199,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_10199),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10199),c_fconj)),hAPP(hAPP(c_COMBC(U_10199,tc_fun(U_10199,U_10199),tc_fun(U_10199,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10199,tc_HOL_Obool),tc_fun(tc_fun(U_10199,U_10199),tc_fun(U_10199,tc_HOL_Obool)),U_10199),c_COMBB(U_10199,tc_HOL_Obool,U_10199)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_10199),U_10201))))),hAPP(hAPP(c_COMBC(U_10199,tc_fun(U_10199,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10199)),U_10200)))))
    | U_10200 = c_Orderings_Obot__class_Obot(tc_fun(U_10199,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10199),U_10200))
    | ~ class_Groups_Olinordered__ab__semigroup__add(U_10199) ),
    inference(clausify,[status(thm)],[f_2786_3]) ).

fof(f_2787_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_2787_2,plain,
    ! [U_10204,U_10203,U_10202] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10202),U_10204),c_Big__Operators_Olinorder__class_OMin(U_10202,U_10203)) = c_Big__Operators_Olinorder__class_OMin(U_10202,hAPP(c_Set_OCollect(U_10202),hAPP(hAPP(c_COMBB(tc_fun(U_10202,tc_HOL_Obool),tc_HOL_Obool,U_10202),c_HOL_OEx(U_10202)),hAPP(hAPP(c_COMBC(U_10202,tc_fun(U_10202,tc_HOL_Obool),tc_fun(U_10202,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10202,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_10202,tc_HOL_Obool),tc_fun(U_10202,tc_HOL_Obool)),U_10202),c_COMBS(U_10202,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10202,tc_HOL_Obool),tc_fun(U_10202,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_10202),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10202),c_fconj)),hAPP(hAPP(c_COMBC(U_10202,tc_fun(U_10202,U_10202),tc_fun(U_10202,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10202,tc_HOL_Obool),tc_fun(tc_fun(U_10202,U_10202),tc_fun(U_10202,tc_HOL_Obool)),U_10202),c_COMBB(U_10202,tc_HOL_Obool,U_10202)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_10202),U_10204))))),hAPP(hAPP(c_COMBC(U_10202,tc_fun(U_10202,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10202)),U_10203)))))
      | U_10203 = c_Orderings_Obot__class_Obot(tc_fun(U_10202,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10202),U_10203))
      | ~ class_Groups_Olinordered__ab__semigroup__add(U_10202) ),
    inference(variable_rename,[status(thm)],[f_2787_1]) ).

fof(f_2787_3,plain,
    ! [U_10202,U_10203,U_10204] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10202),U_10204),c_Big__Operators_Olinorder__class_OMin(U_10202,U_10203)) = c_Big__Operators_Olinorder__class_OMin(U_10202,hAPP(c_Set_OCollect(U_10202),hAPP(hAPP(c_COMBB(tc_fun(U_10202,tc_HOL_Obool),tc_HOL_Obool,U_10202),c_HOL_OEx(U_10202)),hAPP(hAPP(c_COMBC(U_10202,tc_fun(U_10202,tc_HOL_Obool),tc_fun(U_10202,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10202,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_10202,tc_HOL_Obool),tc_fun(U_10202,tc_HOL_Obool)),U_10202),c_COMBS(U_10202,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10202,tc_HOL_Obool),tc_fun(U_10202,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_10202),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10202),c_fconj)),hAPP(hAPP(c_COMBC(U_10202,tc_fun(U_10202,U_10202),tc_fun(U_10202,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10202,tc_HOL_Obool),tc_fun(tc_fun(U_10202,U_10202),tc_fun(U_10202,tc_HOL_Obool)),U_10202),c_COMBB(U_10202,tc_HOL_Obool,U_10202)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_10202),U_10204))))),hAPP(hAPP(c_COMBC(U_10202,tc_fun(U_10202,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10202)),U_10203)))))
      | U_10203 = c_Orderings_Obot__class_Obot(tc_fun(U_10202,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10202),U_10203))
      | ~ class_Groups_Olinordered__ab__semigroup__add(U_10202) ),
    inference(definitional_conversion,[status(esa)],[f_2787_2]) ).

cnf(f_2787_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_10202),U_10204),c_Big__Operators_Olinorder__class_OMin(U_10202,U_10203)) = c_Big__Operators_Olinorder__class_OMin(U_10202,hAPP(c_Set_OCollect(U_10202),hAPP(hAPP(c_COMBB(tc_fun(U_10202,tc_HOL_Obool),tc_HOL_Obool,U_10202),c_HOL_OEx(U_10202)),hAPP(hAPP(c_COMBC(U_10202,tc_fun(U_10202,tc_HOL_Obool),tc_fun(U_10202,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10202,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_10202,tc_HOL_Obool),tc_fun(U_10202,tc_HOL_Obool)),U_10202),c_COMBS(U_10202,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10202,tc_HOL_Obool),tc_fun(U_10202,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_10202),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10202),c_fconj)),hAPP(hAPP(c_COMBC(U_10202,tc_fun(U_10202,U_10202),tc_fun(U_10202,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_10202,tc_HOL_Obool),tc_fun(tc_fun(U_10202,U_10202),tc_fun(U_10202,tc_HOL_Obool)),U_10202),c_COMBB(U_10202,tc_HOL_Obool,U_10202)),c_fequal)),hAPP(c_Groups_Oplus__class_Oplus(U_10202),U_10204))))),hAPP(hAPP(c_COMBC(U_10202,tc_fun(U_10202,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10202)),U_10203)))))
    | U_10203 = c_Orderings_Obot__class_Obot(tc_fun(U_10202,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10202),U_10203))
    | ~ class_Groups_Olinordered__ab__semigroup__add(U_10202) ),
    inference(clausify,[status(thm)],[f_2787_3]) ).

fof(f_2788_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_2788_2,plain,
    ! [U_10207,U_10206,U_10205] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10205,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10205,U_10206,U_10207)),hAPP(hAPP(c_Set_Oinsert(U_10205),U_10207),c_Orderings_Obot__class_Obot(tc_fun(U_10205,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10205,U_10206,U_10207)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10205),U_10206),U_10207))
      | ~ class_Orderings_Olinorder(U_10205) ),
    inference(variable_rename,[status(thm)],[f_2788_1]) ).

fof(f_2788_3,plain,
    ! [U_10206,U_10205,U_10207] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10205,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10205,U_10206,U_10207)),hAPP(hAPP(c_Set_Oinsert(U_10205),U_10207),c_Orderings_Obot__class_Obot(tc_fun(U_10205,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10205,U_10206,U_10207)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10205),U_10206),U_10207))
      | ~ class_Orderings_Olinorder(U_10205) ),
    inference(definitional_conversion,[status(esa)],[f_2788_2]) ).

cnf(f_2788_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10205,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10205,U_10206,U_10207)),hAPP(hAPP(c_Set_Oinsert(U_10205),U_10207),c_Orderings_Obot__class_Obot(tc_fun(U_10205,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10205,U_10206,U_10207)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10205),U_10206),U_10207))
    | ~ class_Orderings_Olinorder(U_10205) ),
    inference(clausify,[status(thm)],[f_2788_3]) ).

fof(f_2789_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_2789_2,plain,
    ! [U_10209,U_10208] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10208,U_10209))),
    inference(variable_rename,[status(thm)],[f_2789_1]) ).

fof(f_2789_3,plain,
    ! [U_10208,U_10209] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10208,U_10209))),
    inference(definitional_conversion,[status(esa)],[f_2789_2]) ).

cnf(f_2789_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10208,U_10209))),
    inference(clausify,[status(thm)],[f_2789_3]) ).

fof(f_2790_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_2790_2,plain,
    ! [U_10211,U_10210] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_10210,U_10211))),
    inference(variable_rename,[status(thm)],[f_2790_1]) ).

fof(f_2790_3,plain,
    ! [U_10210,U_10211] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_10210,U_10211))),
    inference(definitional_conversion,[status(esa)],[f_2790_2]) ).

cnf(f_2790_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_10210,U_10211))),
    inference(clausify,[status(thm)],[f_2790_3]) ).

fof(f_2791_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_2791_2,plain,
    ! [U_10213,U_10212] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_10212,U_10213))),
    inference(variable_rename,[status(thm)],[f_2791_1]) ).

fof(f_2791_3,plain,
    ! [U_10212,U_10213] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_10212,U_10213))),
    inference(definitional_conversion,[status(esa)],[f_2791_2]) ).

cnf(f_2791_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_10212,U_10213))),
    inference(clausify,[status(thm)],[f_2791_3]) ).

fof(f_2792_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_2792_2,plain,
    ! [U_10215,U_10214] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_10214),c_Big__Operators_Olinorder__class_OMax(U_10214,U_10215)) = c_Big__Operators_Olinorder__class_OMin(U_10214,hAPP(c_Set_Oimage(U_10214,U_10214,c_Groups_Ouminus__class_Ouminus(U_10214)),U_10215))
      | U_10215 = c_Orderings_Obot__class_Obot(tc_fun(U_10214,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10214),U_10215))
      | ~ class_Groups_Olinordered__ab__group__add(U_10214) ),
    inference(variable_rename,[status(thm)],[f_2792_1]) ).

fof(f_2792_3,plain,
    ! [U_10214,U_10215] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_10214),c_Big__Operators_Olinorder__class_OMax(U_10214,U_10215)) = c_Big__Operators_Olinorder__class_OMin(U_10214,hAPP(c_Set_Oimage(U_10214,U_10214,c_Groups_Ouminus__class_Ouminus(U_10214)),U_10215))
      | U_10215 = c_Orderings_Obot__class_Obot(tc_fun(U_10214,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10214),U_10215))
      | ~ class_Groups_Olinordered__ab__group__add(U_10214) ),
    inference(definitional_conversion,[status(esa)],[f_2792_2]) ).

cnf(f_2792_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_10214),c_Big__Operators_Olinorder__class_OMax(U_10214,U_10215)) = c_Big__Operators_Olinorder__class_OMin(U_10214,hAPP(c_Set_Oimage(U_10214,U_10214,c_Groups_Ouminus__class_Ouminus(U_10214)),U_10215))
    | U_10215 = c_Orderings_Obot__class_Obot(tc_fun(U_10214,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10214),U_10215))
    | ~ class_Groups_Olinordered__ab__group__add(U_10214) ),
    inference(clausify,[status(thm)],[f_2792_3]) ).

fof(f_2793_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_2793_2,plain,
    ! [U_10217,U_10216] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_10216),c_Big__Operators_Olinorder__class_OMin(U_10216,U_10217)) = c_Big__Operators_Olinorder__class_OMax(U_10216,hAPP(c_Set_Oimage(U_10216,U_10216,c_Groups_Ouminus__class_Ouminus(U_10216)),U_10217))
      | U_10217 = c_Orderings_Obot__class_Obot(tc_fun(U_10216,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10216),U_10217))
      | ~ class_Groups_Olinordered__ab__group__add(U_10216) ),
    inference(variable_rename,[status(thm)],[f_2793_1]) ).

fof(f_2793_3,plain,
    ! [U_10216,U_10217] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_10216),c_Big__Operators_Olinorder__class_OMin(U_10216,U_10217)) = c_Big__Operators_Olinorder__class_OMax(U_10216,hAPP(c_Set_Oimage(U_10216,U_10216,c_Groups_Ouminus__class_Ouminus(U_10216)),U_10217))
      | U_10217 = c_Orderings_Obot__class_Obot(tc_fun(U_10216,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10216),U_10217))
      | ~ class_Groups_Olinordered__ab__group__add(U_10216) ),
    inference(definitional_conversion,[status(esa)],[f_2793_2]) ).

cnf(f_2793_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_10216),c_Big__Operators_Olinorder__class_OMin(U_10216,U_10217)) = c_Big__Operators_Olinorder__class_OMax(U_10216,hAPP(c_Set_Oimage(U_10216,U_10216,c_Groups_Ouminus__class_Ouminus(U_10216)),U_10217))
    | U_10217 = c_Orderings_Obot__class_Obot(tc_fun(U_10216,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10216),U_10217))
    | ~ class_Groups_Olinordered__ab__group__add(U_10216) ),
    inference(clausify,[status(thm)],[f_2793_3]) ).

fof(f_2794_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_2794_2,plain,
    ! [U_10219,U_10218] :
      ( c_Big__Operators_Olinorder__class_OMax(U_10218,hAPP(hAPP(c_Set_Oinsert(U_10218),U_10219),c_Orderings_Obot__class_Obot(tc_fun(U_10218,tc_HOL_Obool)))) = U_10219
      | ~ class_Orderings_Olinorder(U_10218) ),
    inference(variable_rename,[status(thm)],[f_2794_1]) ).

fof(f_2794_3,plain,
    ! [U_10218,U_10219] :
      ( c_Big__Operators_Olinorder__class_OMax(U_10218,hAPP(hAPP(c_Set_Oinsert(U_10218),U_10219),c_Orderings_Obot__class_Obot(tc_fun(U_10218,tc_HOL_Obool)))) = U_10219
      | ~ class_Orderings_Olinorder(U_10218) ),
    inference(definitional_conversion,[status(esa)],[f_2794_2]) ).

cnf(f_2794_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_10218,hAPP(hAPP(c_Set_Oinsert(U_10218),U_10219),c_Orderings_Obot__class_Obot(tc_fun(U_10218,tc_HOL_Obool)))) = U_10219
    | ~ class_Orderings_Olinorder(U_10218) ),
    inference(clausify,[status(thm)],[f_2794_3]) ).

fof(f_2795_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_2795_2,plain,
    ! [U_10221,U_10220] :
      ( c_Big__Operators_Olinorder__class_OMin(U_10220,hAPP(hAPP(c_Set_Oinsert(U_10220),U_10221),c_Orderings_Obot__class_Obot(tc_fun(U_10220,tc_HOL_Obool)))) = U_10221
      | ~ class_Orderings_Olinorder(U_10220) ),
    inference(variable_rename,[status(thm)],[f_2795_1]) ).

fof(f_2795_3,plain,
    ! [U_10220,U_10221] :
      ( c_Big__Operators_Olinorder__class_OMin(U_10220,hAPP(hAPP(c_Set_Oinsert(U_10220),U_10221),c_Orderings_Obot__class_Obot(tc_fun(U_10220,tc_HOL_Obool)))) = U_10221
      | ~ class_Orderings_Olinorder(U_10220) ),
    inference(definitional_conversion,[status(esa)],[f_2795_2]) ).

cnf(f_2795_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_10220,hAPP(hAPP(c_Set_Oinsert(U_10220),U_10221),c_Orderings_Obot__class_Obot(tc_fun(U_10220,tc_HOL_Obool)))) = U_10221
    | ~ class_Orderings_Olinorder(U_10220) ),
    inference(clausify,[status(thm)],[f_2795_3]) ).

fof(f_2796_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_2796_2,plain,
    ! [U_10224,U_10223,U_10222] :
      ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_10222,U_10224,U_10223) = c_Orderings_Obot__class_Obot(tc_fun(U_10222,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10222),U_10223),U_10224))
      | ~ class_Orderings_Oorder(U_10222) ),
    inference(variable_rename,[status(thm)],[f_2796_1]) ).

fof(f_2796_3,plain,
    ! [U_10222,U_10223,U_10224] :
      ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_10222,U_10224,U_10223) = c_Orderings_Obot__class_Obot(tc_fun(U_10222,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10222),U_10223),U_10224))
      | ~ class_Orderings_Oorder(U_10222) ),
    inference(definitional_conversion,[status(esa)],[f_2796_2]) ).

cnf(f_2796_4,plain,
    ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_10222,U_10224,U_10223) = c_Orderings_Obot__class_Obot(tc_fun(U_10222,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10222),U_10223),U_10224))
    | ~ class_Orderings_Oorder(U_10222) ),
    inference(clausify,[status(thm)],[f_2796_3]) ).

fof(f_2797_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_2797_2,plain,
    ! [U_10227,U_10226,U_10225] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_10225,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10225,U_10226,U_10227)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10225),U_10226),U_10227)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10225),U_10226),U_10227))
          | c_Orderings_Obot__class_Obot(tc_fun(U_10225,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_10225,U_10226,U_10227) ) )
      | ~ class_Orderings_Oorder(U_10225) ),
    inference(variable_rename,[status(thm)],[f_2797_1]) ).

fof(f_2797_3,plain,
    ( ! [U_10225,U_10226,U_10227] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_10225,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10225,U_10226,U_10227)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10225),U_10226),U_10227))
        | ~ sP782(U_10225,U_10226,U_10227) )
    & ! [U_10225,U_10226,U_10227] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10225),U_10226),U_10227))
        | c_Orderings_Obot__class_Obot(tc_fun(U_10225,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_10225,U_10226,U_10227)
        | ~ sP782(U_10225,U_10226,U_10227) )
    & ! [U_10225,U_10226,U_10227] :
        ( sP782(U_10225,U_10226,U_10227)
        | ~ class_Orderings_Oorder(U_10225) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP782])],[f_2797_2]) ).

cnf(f_2797_4,plain,
    ( sP782(U_10225,U_10226,U_10227)
    | ~ class_Orderings_Oorder(U_10225) ),
    inference(clausify,[status(thm)],[f_2797_3]) ).

cnf(f_2797_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10225),U_10226),U_10227))
    | c_Orderings_Obot__class_Obot(tc_fun(U_10225,tc_HOL_Obool)) != c_SetInterval_Oord__class_OgreaterThanAtMost(U_10225,U_10226,U_10227)
    | ~ sP782(U_10225,U_10226,U_10227) ),
    inference(clausify,[status(thm)],[f_2797_3]) ).

cnf(f_2797_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_10225,tc_HOL_Obool)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10225,U_10226,U_10227)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10225),U_10226),U_10227))
    | ~ sP782(U_10225,U_10226,U_10227) ),
    inference(clausify,[status(thm)],[f_2797_3]) ).

fof(f_2798_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_2798_2,plain,
    ! [U_10230,U_10229,U_10228] :
      ( ( ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_10228,U_10229,U_10230) = c_Orderings_Obot__class_Obot(tc_fun(U_10228,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10228),U_10229),U_10230)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10228),U_10229),U_10230))
          | c_SetInterval_Oord__class_OgreaterThanAtMost(U_10228,U_10229,U_10230) != c_Orderings_Obot__class_Obot(tc_fun(U_10228,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(U_10228) ),
    inference(variable_rename,[status(thm)],[f_2798_1]) ).

fof(f_2798_3,plain,
    ( ! [U_10230,U_10228,U_10229] :
        ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_10228,U_10229,U_10230) = c_Orderings_Obot__class_Obot(tc_fun(U_10228,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10228),U_10229),U_10230))
        | ~ sP783(U_10230,U_10228,U_10229) )
    & ! [U_10230,U_10228,U_10229] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10228),U_10229),U_10230))
        | c_SetInterval_Oord__class_OgreaterThanAtMost(U_10228,U_10229,U_10230) != c_Orderings_Obot__class_Obot(tc_fun(U_10228,tc_HOL_Obool))
        | ~ sP783(U_10230,U_10228,U_10229) )
    & ! [U_10230,U_10228,U_10229] :
        ( sP783(U_10230,U_10228,U_10229)
        | ~ class_Orderings_Oorder(U_10228) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP783])],[f_2798_2]) ).

cnf(f_2798_4,plain,
    ( sP783(U_10230,U_10228,U_10229)
    | ~ class_Orderings_Oorder(U_10228) ),
    inference(clausify,[status(thm)],[f_2798_3]) ).

cnf(f_2798_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10228),U_10229),U_10230))
    | c_SetInterval_Oord__class_OgreaterThanAtMost(U_10228,U_10229,U_10230) != c_Orderings_Obot__class_Obot(tc_fun(U_10228,tc_HOL_Obool))
    | ~ sP783(U_10230,U_10228,U_10229) ),
    inference(clausify,[status(thm)],[f_2798_3]) ).

cnf(f_2798_6,plain,
    ( c_SetInterval_Oord__class_OgreaterThanAtMost(U_10228,U_10229,U_10230) = c_Orderings_Obot__class_Obot(tc_fun(U_10228,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10228),U_10229),U_10230))
    | ~ sP783(U_10230,U_10228,U_10229) ),
    inference(clausify,[status(thm)],[f_2798_3]) ).

fof(f_2799_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_2799_2,plain,
    ! [U_10234,U_10233,U_10232,U_10231] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10231,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10231,U_10232,U_10233)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10231,U_10233,U_10234)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10231,U_10232,U_10234)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10231),U_10233),U_10234))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10231),U_10232),U_10233))
      | ~ class_Orderings_Olinorder(U_10231) ),
    inference(variable_rename,[status(thm)],[f_2799_1]) ).

fof(f_2799_3,plain,
    ! [U_10231,U_10232,U_10233,U_10234] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10231,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10231,U_10232,U_10233)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10231,U_10233,U_10234)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10231,U_10232,U_10234)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10231),U_10233),U_10234))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10231),U_10232),U_10233))
      | ~ class_Orderings_Olinorder(U_10231) ),
    inference(definitional_conversion,[status(esa)],[f_2799_2]) ).

cnf(f_2799_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10231,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10231,U_10232,U_10233)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10231,U_10233,U_10234)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_10231,U_10232,U_10234)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10231),U_10233),U_10234))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10231),U_10232),U_10233))
    | ~ class_Orderings_Olinorder(U_10231) ),
    inference(clausify,[status(thm)],[f_2799_3]) ).

fof(f_2800_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_2800_2,plain,
    ! [U_10236,U_10235] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10235,U_10236)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10236),U_10235),
    inference(variable_rename,[status(thm)],[f_2800_1]) ).

fof(f_2800_3,plain,
    ! [U_10236,U_10235] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10235,U_10236)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10236),U_10235),
    inference(definitional_conversion,[status(esa)],[f_2800_2]) ).

cnf(f_2800_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_10235,U_10236)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10236),U_10235),
    inference(clausify,[status(thm)],[f_2800_3]) ).

fof(f_2801_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_2801_2,plain,
    ! [U_10239,U_10238,U_10237] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10237),U_10239),c_Big__Operators_Olinorder__class_OMax(U_10237,U_10238)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10237),U_10239),U_10238))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10237),U_10238))
      | ~ class_Orderings_Olinorder(U_10237) ),
    inference(variable_rename,[status(thm)],[f_2801_1]) ).

fof(f_2801_3,plain,
    ! [U_10237,U_10238,U_10239] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10237),U_10239),c_Big__Operators_Olinorder__class_OMax(U_10237,U_10238)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10237),U_10239),U_10238))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10237),U_10238))
      | ~ class_Orderings_Olinorder(U_10237) ),
    inference(definitional_conversion,[status(esa)],[f_2801_2]) ).

cnf(f_2801_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10237),U_10239),c_Big__Operators_Olinorder__class_OMax(U_10237,U_10238)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10237),U_10239),U_10238))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10237),U_10238))
    | ~ class_Orderings_Olinorder(U_10237) ),
    inference(clausify,[status(thm)],[f_2801_3]) ).

fof(f_2802_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_2802_2,plain,
    ! [U_10242,U_10241,U_10240] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10240),c_Big__Operators_Olinorder__class_OMin(U_10240,U_10241)),U_10242))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10240),U_10242),U_10241))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10240),U_10241))
      | ~ class_Orderings_Olinorder(U_10240) ),
    inference(variable_rename,[status(thm)],[f_2802_1]) ).

fof(f_2802_3,plain,
    ! [U_10240,U_10241,U_10242] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10240),c_Big__Operators_Olinorder__class_OMin(U_10240,U_10241)),U_10242))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10240),U_10242),U_10241))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10240),U_10241))
      | ~ class_Orderings_Olinorder(U_10240) ),
    inference(definitional_conversion,[status(esa)],[f_2802_2]) ).

cnf(f_2802_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10240),c_Big__Operators_Olinorder__class_OMin(U_10240,U_10241)),U_10242))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10240),U_10242),U_10241))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10240),U_10241))
    | ~ class_Orderings_Olinorder(U_10240) ),
    inference(clausify,[status(thm)],[f_2802_3]) ).

fof(f_2803_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_2803_2,plain,
    ! [U_10244,U_10243] :
      ( hBOOL(hAPP(hAPP(c_member(U_10243),c_Big__Operators_Olinorder__class_OMax(U_10243,U_10244)),U_10244))
      | U_10244 = c_Orderings_Obot__class_Obot(tc_fun(U_10243,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10243),U_10244))
      | ~ class_Orderings_Olinorder(U_10243) ),
    inference(variable_rename,[status(thm)],[f_2803_1]) ).

fof(f_2803_3,plain,
    ! [U_10244,U_10243] :
      ( hBOOL(hAPP(hAPP(c_member(U_10243),c_Big__Operators_Olinorder__class_OMax(U_10243,U_10244)),U_10244))
      | U_10244 = c_Orderings_Obot__class_Obot(tc_fun(U_10243,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10243),U_10244))
      | ~ class_Orderings_Olinorder(U_10243) ),
    inference(definitional_conversion,[status(esa)],[f_2803_2]) ).

cnf(f_2803_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10243),c_Big__Operators_Olinorder__class_OMax(U_10243,U_10244)),U_10244))
    | U_10244 = c_Orderings_Obot__class_Obot(tc_fun(U_10243,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10243),U_10244))
    | ~ class_Orderings_Olinorder(U_10243) ),
    inference(clausify,[status(thm)],[f_2803_3]) ).

fof(f_2804_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_2804_2,plain,
    ! [U_10246,U_10245] :
      ( hBOOL(hAPP(hAPP(c_member(U_10245),c_Big__Operators_Olinorder__class_OMin(U_10245,U_10246)),U_10246))
      | U_10246 = c_Orderings_Obot__class_Obot(tc_fun(U_10245,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10245),U_10246))
      | ~ class_Orderings_Olinorder(U_10245) ),
    inference(variable_rename,[status(thm)],[f_2804_1]) ).

fof(f_2804_3,plain,
    ! [U_10245,U_10246] :
      ( hBOOL(hAPP(hAPP(c_member(U_10245),c_Big__Operators_Olinorder__class_OMin(U_10245,U_10246)),U_10246))
      | U_10246 = c_Orderings_Obot__class_Obot(tc_fun(U_10245,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10245),U_10246))
      | ~ class_Orderings_Olinorder(U_10245) ),
    inference(definitional_conversion,[status(esa)],[f_2804_2]) ).

cnf(f_2804_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10245),c_Big__Operators_Olinorder__class_OMin(U_10245,U_10246)),U_10246))
    | U_10246 = c_Orderings_Obot__class_Obot(tc_fun(U_10245,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10245),U_10246))
    | ~ class_Orderings_Olinorder(U_10245) ),
    inference(clausify,[status(thm)],[f_2804_3]) ).

fof(f_2805_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_2805_2,plain,
    ! [U_10249,U_10248,U_10247] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10247),U_10249),c_Big__Operators_Olinorder__class_OMin(U_10247,U_10248)) = c_Big__Operators_Olinorder__class_OMin(U_10247,U_10248)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10247),U_10249),U_10248))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10247),U_10248))
      | ~ class_Orderings_Olinorder(U_10247) ),
    inference(variable_rename,[status(thm)],[f_2805_1]) ).

fof(f_2805_3,plain,
    ! [U_10248,U_10247,U_10249] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10247),U_10249),c_Big__Operators_Olinorder__class_OMin(U_10247,U_10248)) = c_Big__Operators_Olinorder__class_OMin(U_10247,U_10248)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10247),U_10249),U_10248))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10247),U_10248))
      | ~ class_Orderings_Olinorder(U_10247) ),
    inference(definitional_conversion,[status(esa)],[f_2805_2]) ).

cnf(f_2805_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10247),U_10249),c_Big__Operators_Olinorder__class_OMin(U_10247,U_10248)) = c_Big__Operators_Olinorder__class_OMin(U_10247,U_10248)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10247),U_10249),U_10248))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10247),U_10248))
    | ~ class_Orderings_Olinorder(U_10247) ),
    inference(clausify,[status(thm)],[f_2805_3]) ).

fof(f_2806_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_2806_2,plain,
    ! [U_10252,U_10251,U_10250] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10250),U_10252),c_Big__Operators_Olinorder__class_OMax(U_10250,U_10251)) = c_Big__Operators_Olinorder__class_OMax(U_10250,U_10251)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10250),U_10252),U_10251))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10250),U_10251))
      | ~ class_Orderings_Olinorder(U_10250) ),
    inference(variable_rename,[status(thm)],[f_2806_1]) ).

fof(f_2806_3,plain,
    ! [U_10251,U_10250,U_10252] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10250),U_10252),c_Big__Operators_Olinorder__class_OMax(U_10250,U_10251)) = c_Big__Operators_Olinorder__class_OMax(U_10250,U_10251)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10250),U_10252),U_10251))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10250),U_10251))
      | ~ class_Orderings_Olinorder(U_10250) ),
    inference(definitional_conversion,[status(esa)],[f_2806_2]) ).

cnf(f_2806_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10250),U_10252),c_Big__Operators_Olinorder__class_OMax(U_10250,U_10251)) = c_Big__Operators_Olinorder__class_OMax(U_10250,U_10251)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10250),U_10252),U_10251))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10250),U_10251))
    | ~ class_Orderings_Olinorder(U_10250) ),
    inference(clausify,[status(thm)],[f_2806_3]) ).

fof(f_2807_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_2807_2,plain,
    ! [U_10254,U_10253] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_10253,U_10254)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10254),hAPP(c_Nat_OSuc,U_10253)),
    inference(variable_rename,[status(thm)],[f_2807_1]) ).

fof(f_2807_3,plain,
    ! [U_10253,U_10254] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_10253,U_10254)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10254),hAPP(c_Nat_OSuc,U_10253)),
    inference(definitional_conversion,[status(esa)],[f_2807_2]) ).

cnf(f_2807_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_10253,U_10254)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_10254),hAPP(c_Nat_OSuc,U_10253)),
    inference(clausify,[status(thm)],[f_2807_3]) ).

fof(f_2808_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_2808_2,plain,
    ! [U_10257,U_10256,U_10255] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10255),c_Big__Operators_Olinorder__class_OMax(U_10255,U_10256)),c_Big__Operators_Olinorder__class_OMax(U_10255,U_10257)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10255),U_10257))
      | U_10256 = c_Orderings_Obot__class_Obot(tc_fun(U_10255,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10255,tc_HOL_Obool)),U_10256),U_10257))
      | ~ class_Orderings_Olinorder(U_10255) ),
    inference(variable_rename,[status(thm)],[f_2808_1]) ).

fof(f_2808_3,plain,
    ! [U_10255,U_10256,U_10257] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10255),c_Big__Operators_Olinorder__class_OMax(U_10255,U_10256)),c_Big__Operators_Olinorder__class_OMax(U_10255,U_10257)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10255),U_10257))
      | U_10256 = c_Orderings_Obot__class_Obot(tc_fun(U_10255,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10255,tc_HOL_Obool)),U_10256),U_10257))
      | ~ class_Orderings_Olinorder(U_10255) ),
    inference(definitional_conversion,[status(esa)],[f_2808_2]) ).

cnf(f_2808_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10255),c_Big__Operators_Olinorder__class_OMax(U_10255,U_10256)),c_Big__Operators_Olinorder__class_OMax(U_10255,U_10257)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10255),U_10257))
    | U_10256 = c_Orderings_Obot__class_Obot(tc_fun(U_10255,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10255,tc_HOL_Obool)),U_10256),U_10257))
    | ~ class_Orderings_Olinorder(U_10255) ),
    inference(clausify,[status(thm)],[f_2808_3]) ).

fof(f_2809_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_2809_2,plain,
    ! [U_10260,U_10259,U_10258] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10258),c_Big__Operators_Olinorder__class_OMin(U_10258,U_10260)),c_Big__Operators_Olinorder__class_OMin(U_10258,U_10259)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10258),U_10260))
      | U_10259 = c_Orderings_Obot__class_Obot(tc_fun(U_10258,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10258,tc_HOL_Obool)),U_10259),U_10260))
      | ~ class_Orderings_Olinorder(U_10258) ),
    inference(variable_rename,[status(thm)],[f_2809_1]) ).

fof(f_2809_3,plain,
    ! [U_10259,U_10258,U_10260] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10258),c_Big__Operators_Olinorder__class_OMin(U_10258,U_10260)),c_Big__Operators_Olinorder__class_OMin(U_10258,U_10259)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10258),U_10260))
      | U_10259 = c_Orderings_Obot__class_Obot(tc_fun(U_10258,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10258,tc_HOL_Obool)),U_10259),U_10260))
      | ~ class_Orderings_Olinorder(U_10258) ),
    inference(definitional_conversion,[status(esa)],[f_2809_2]) ).

cnf(f_2809_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10258),c_Big__Operators_Olinorder__class_OMin(U_10258,U_10260)),c_Big__Operators_Olinorder__class_OMin(U_10258,U_10259)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10258),U_10260))
    | U_10259 = c_Orderings_Obot__class_Obot(tc_fun(U_10258,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10258,tc_HOL_Obool)),U_10259),U_10260))
    | ~ class_Orderings_Olinorder(U_10258) ),
    inference(clausify,[status(thm)],[f_2809_3]) ).

fof(f_2810_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_2810_2,plain,
    ! [U_10263,U_10262,U_10261] :
      ( c_Big__Operators_Olinorder__class_OMin(U_10261,hAPP(hAPP(c_Set_Oinsert(U_10261),U_10263),U_10262)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10261),U_10263),c_Big__Operators_Olinorder__class_OMin(U_10261,U_10262))
      | U_10262 = c_Orderings_Obot__class_Obot(tc_fun(U_10261,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10261),U_10262))
      | ~ class_Orderings_Olinorder(U_10261) ),
    inference(variable_rename,[status(thm)],[f_2810_1]) ).

fof(f_2810_3,plain,
    ! [U_10261,U_10262,U_10263] :
      ( c_Big__Operators_Olinorder__class_OMin(U_10261,hAPP(hAPP(c_Set_Oinsert(U_10261),U_10263),U_10262)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10261),U_10263),c_Big__Operators_Olinorder__class_OMin(U_10261,U_10262))
      | U_10262 = c_Orderings_Obot__class_Obot(tc_fun(U_10261,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10261),U_10262))
      | ~ class_Orderings_Olinorder(U_10261) ),
    inference(definitional_conversion,[status(esa)],[f_2810_2]) ).

cnf(f_2810_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_10261,hAPP(hAPP(c_Set_Oinsert(U_10261),U_10263),U_10262)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10261),U_10263),c_Big__Operators_Olinorder__class_OMin(U_10261,U_10262))
    | U_10262 = c_Orderings_Obot__class_Obot(tc_fun(U_10261,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10261),U_10262))
    | ~ class_Orderings_Olinorder(U_10261) ),
    inference(clausify,[status(thm)],[f_2810_3]) ).

fof(f_2811_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_2811_2,plain,
    ! [U_10266,U_10265,U_10264] :
      ( c_Big__Operators_Olinorder__class_OMax(U_10264,hAPP(hAPP(c_Set_Oinsert(U_10264),U_10266),U_10265)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10264),U_10266),c_Big__Operators_Olinorder__class_OMax(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_2811_1]) ).

fof(f_2811_3,plain,
    ! [U_10264,U_10265,U_10266] :
      ( c_Big__Operators_Olinorder__class_OMax(U_10264,hAPP(hAPP(c_Set_Oinsert(U_10264),U_10266),U_10265)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10264),U_10266),c_Big__Operators_Olinorder__class_OMax(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_2811_2]) ).

cnf(f_2811_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_10264,hAPP(hAPP(c_Set_Oinsert(U_10264),U_10266),U_10265)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10264),U_10266),c_Big__Operators_Olinorder__class_OMax(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_2811_3]) ).

fof(f_2812_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_2812_2,plain,
    ! [U_10268,U_10267] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_10267,U_10268)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10268),U_10267)),
    inference(variable_rename,[status(thm)],[f_2812_1]) ).

fof(f_2812_3,plain,
    ! [U_10267,U_10268] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_10267,U_10268)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10268),U_10267)),
    inference(definitional_conversion,[status(esa)],[f_2812_2]) ).

cnf(f_2812_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_10267,U_10268)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_10268),U_10267)),
    inference(clausify,[status(thm)],[f_2812_3]) ).

fof(f_2813_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_2813_2,plain,
    ! [U_10271,U_10270,U_10269] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10269),c_Big__Operators_Olinorder__class_OMin(U_10269,U_10271)),c_Big__Operators_Olinorder__class_OMin(U_10269,U_10270)) = c_Big__Operators_Olinorder__class_OMin(U_10269,U_10270)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10269,tc_HOL_Obool)),U_10271),U_10270))
      | U_10271 = c_Orderings_Obot__class_Obot(tc_fun(U_10269,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10269),U_10270))
      | ~ class_Orderings_Olinorder(U_10269) ),
    inference(variable_rename,[status(thm)],[f_2813_1]) ).

fof(f_2813_3,plain,
    ! [U_10269,U_10270,U_10271] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10269),c_Big__Operators_Olinorder__class_OMin(U_10269,U_10271)),c_Big__Operators_Olinorder__class_OMin(U_10269,U_10270)) = c_Big__Operators_Olinorder__class_OMin(U_10269,U_10270)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10269,tc_HOL_Obool)),U_10271),U_10270))
      | U_10271 = c_Orderings_Obot__class_Obot(tc_fun(U_10269,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10269),U_10270))
      | ~ class_Orderings_Olinorder(U_10269) ),
    inference(definitional_conversion,[status(esa)],[f_2813_2]) ).

cnf(f_2813_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10269),c_Big__Operators_Olinorder__class_OMin(U_10269,U_10271)),c_Big__Operators_Olinorder__class_OMin(U_10269,U_10270)) = c_Big__Operators_Olinorder__class_OMin(U_10269,U_10270)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10269,tc_HOL_Obool)),U_10271),U_10270))
    | U_10271 = c_Orderings_Obot__class_Obot(tc_fun(U_10269,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10269),U_10270))
    | ~ class_Orderings_Olinorder(U_10269) ),
    inference(clausify,[status(thm)],[f_2813_3]) ).

fof(f_2814_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_2814_2,plain,
    ! [U_10274,U_10273,U_10272] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10272),c_Big__Operators_Olinorder__class_OMax(U_10272,U_10274)),c_Big__Operators_Olinorder__class_OMax(U_10272,U_10273)) = c_Big__Operators_Olinorder__class_OMax(U_10272,U_10273)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10272,tc_HOL_Obool)),U_10274),U_10273))
      | U_10274 = c_Orderings_Obot__class_Obot(tc_fun(U_10272,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10272),U_10273))
      | ~ class_Orderings_Olinorder(U_10272) ),
    inference(variable_rename,[status(thm)],[f_2814_1]) ).

fof(f_2814_3,plain,
    ! [U_10273,U_10274,U_10272] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10272),c_Big__Operators_Olinorder__class_OMax(U_10272,U_10274)),c_Big__Operators_Olinorder__class_OMax(U_10272,U_10273)) = c_Big__Operators_Olinorder__class_OMax(U_10272,U_10273)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10272,tc_HOL_Obool)),U_10274),U_10273))
      | U_10274 = c_Orderings_Obot__class_Obot(tc_fun(U_10272,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10272),U_10273))
      | ~ class_Orderings_Olinorder(U_10272) ),
    inference(definitional_conversion,[status(esa)],[f_2814_2]) ).

cnf(f_2814_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10272),c_Big__Operators_Olinorder__class_OMax(U_10272,U_10274)),c_Big__Operators_Olinorder__class_OMax(U_10272,U_10273)) = c_Big__Operators_Olinorder__class_OMax(U_10272,U_10273)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10272,tc_HOL_Obool)),U_10274),U_10273))
    | U_10274 = c_Orderings_Obot__class_Obot(tc_fun(U_10272,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10272),U_10273))
    | ~ class_Orderings_Olinorder(U_10272) ),
    inference(clausify,[status(thm)],[f_2814_3]) ).

fof(f_2815_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_2815_2,plain,
    ! [U_10277,U_10276,U_10275] :
      ( c_Big__Operators_Olinorder__class_OMin(U_10275,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10275,tc_HOL_Obool)),U_10276),U_10277)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10275),c_Big__Operators_Olinorder__class_OMin(U_10275,U_10276)),c_Big__Operators_Olinorder__class_OMin(U_10275,U_10277))
      | U_10277 = c_Orderings_Obot__class_Obot(tc_fun(U_10275,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10275),U_10277))
      | U_10276 = c_Orderings_Obot__class_Obot(tc_fun(U_10275,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10275),U_10276))
      | ~ class_Orderings_Olinorder(U_10275) ),
    inference(variable_rename,[status(thm)],[f_2815_1]) ).

fof(f_2815_3,plain,
    ! [U_10275,U_10276,U_10277] :
      ( c_Big__Operators_Olinorder__class_OMin(U_10275,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10275,tc_HOL_Obool)),U_10276),U_10277)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10275),c_Big__Operators_Olinorder__class_OMin(U_10275,U_10276)),c_Big__Operators_Olinorder__class_OMin(U_10275,U_10277))
      | U_10277 = c_Orderings_Obot__class_Obot(tc_fun(U_10275,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10275),U_10277))
      | U_10276 = c_Orderings_Obot__class_Obot(tc_fun(U_10275,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10275),U_10276))
      | ~ class_Orderings_Olinorder(U_10275) ),
    inference(definitional_conversion,[status(esa)],[f_2815_2]) ).

cnf(f_2815_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_10275,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10275,tc_HOL_Obool)),U_10276),U_10277)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10275),c_Big__Operators_Olinorder__class_OMin(U_10275,U_10276)),c_Big__Operators_Olinorder__class_OMin(U_10275,U_10277))
    | U_10277 = c_Orderings_Obot__class_Obot(tc_fun(U_10275,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10275),U_10277))
    | U_10276 = c_Orderings_Obot__class_Obot(tc_fun(U_10275,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10275),U_10276))
    | ~ class_Orderings_Olinorder(U_10275) ),
    inference(clausify,[status(thm)],[f_2815_3]) ).

fof(f_2816_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_2816_2,plain,
    ! [U_10280,U_10279,U_10278] :
      ( c_Big__Operators_Olinorder__class_OMax(U_10278,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10278,tc_HOL_Obool)),U_10279),U_10280)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10278),c_Big__Operators_Olinorder__class_OMax(U_10278,U_10279)),c_Big__Operators_Olinorder__class_OMax(U_10278,U_10280))
      | U_10280 = c_Orderings_Obot__class_Obot(tc_fun(U_10278,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10278),U_10280))
      | U_10279 = c_Orderings_Obot__class_Obot(tc_fun(U_10278,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10278),U_10279))
      | ~ class_Orderings_Olinorder(U_10278) ),
    inference(variable_rename,[status(thm)],[f_2816_1]) ).

fof(f_2816_3,plain,
    ! [U_10279,U_10280,U_10278] :
      ( c_Big__Operators_Olinorder__class_OMax(U_10278,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10278,tc_HOL_Obool)),U_10279),U_10280)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10278),c_Big__Operators_Olinorder__class_OMax(U_10278,U_10279)),c_Big__Operators_Olinorder__class_OMax(U_10278,U_10280))
      | U_10280 = c_Orderings_Obot__class_Obot(tc_fun(U_10278,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10278),U_10280))
      | U_10279 = c_Orderings_Obot__class_Obot(tc_fun(U_10278,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10278),U_10279))
      | ~ class_Orderings_Olinorder(U_10278) ),
    inference(definitional_conversion,[status(esa)],[f_2816_2]) ).

cnf(f_2816_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_10278,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10278,tc_HOL_Obool)),U_10279),U_10280)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10278),c_Big__Operators_Olinorder__class_OMax(U_10278,U_10279)),c_Big__Operators_Olinorder__class_OMax(U_10278,U_10280))
    | U_10280 = c_Orderings_Obot__class_Obot(tc_fun(U_10278,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10278),U_10280))
    | U_10279 = c_Orderings_Obot__class_Obot(tc_fun(U_10278,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10278),U_10279))
    | ~ class_Orderings_Olinorder(U_10278) ),
    inference(clausify,[status(thm)],[f_2816_3]) ).

fof(f_2817_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_2817_2,plain,
    ! [U_10284,U_10283,U_10282,U_10281] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10281,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10281,U_10282,U_10283)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10281,U_10283,U_10284)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10281,U_10282,U_10284)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10281),U_10283),U_10284))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10281),U_10282),U_10283))
      | ~ class_Orderings_Olinorder(U_10281) ),
    inference(variable_rename,[status(thm)],[f_2817_1]) ).

fof(f_2817_3,plain,
    ! [U_10282,U_10283,U_10281,U_10284] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10281,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10281,U_10282,U_10283)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10281,U_10283,U_10284)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10281,U_10282,U_10284)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10281),U_10283),U_10284))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10281),U_10282),U_10283))
      | ~ class_Orderings_Olinorder(U_10281) ),
    inference(definitional_conversion,[status(esa)],[f_2817_2]) ).

cnf(f_2817_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10281,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_10281,U_10282,U_10283)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_10281,U_10283,U_10284)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_10281,U_10282,U_10284)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_10281),U_10283),U_10284))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10281),U_10282),U_10283))
    | ~ class_Orderings_Olinorder(U_10281) ),
    inference(clausify,[status(thm)],[f_2817_3]) ).

fof(f_2818_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_2818_2,plain,
    ! [U_10287,U_10286,U_10285] :
      ( c_Big__Operators_Olinorder__class_OMin(U_10285,hAPP(hAPP(c_Set_Oinsert(U_10285),U_10287),U_10286)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10285),U_10287),c_Big__Operators_Olinorder__class_OMin(U_10285,U_10286))
      | U_10286 = c_Orderings_Obot__class_Obot(tc_fun(U_10285,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_10285),U_10287),U_10286))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10285),U_10286))
      | ~ class_Orderings_Olinorder(U_10285) ),
    inference(variable_rename,[status(thm)],[f_2818_1]) ).

fof(f_2818_3,plain,
    ! [U_10285,U_10286,U_10287] :
      ( c_Big__Operators_Olinorder__class_OMin(U_10285,hAPP(hAPP(c_Set_Oinsert(U_10285),U_10287),U_10286)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10285),U_10287),c_Big__Operators_Olinorder__class_OMin(U_10285,U_10286))
      | U_10286 = c_Orderings_Obot__class_Obot(tc_fun(U_10285,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_10285),U_10287),U_10286))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10285),U_10286))
      | ~ class_Orderings_Olinorder(U_10285) ),
    inference(definitional_conversion,[status(esa)],[f_2818_2]) ).

cnf(f_2818_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_10285,hAPP(hAPP(c_Set_Oinsert(U_10285),U_10287),U_10286)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10285),U_10287),c_Big__Operators_Olinorder__class_OMin(U_10285,U_10286))
    | U_10286 = c_Orderings_Obot__class_Obot(tc_fun(U_10285,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_10285),U_10287),U_10286))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10285),U_10286))
    | ~ class_Orderings_Olinorder(U_10285) ),
    inference(clausify,[status(thm)],[f_2818_3]) ).

fof(f_2819_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_2819_2,plain,
    ! [U_10290,U_10289,U_10288] :
      ( c_Big__Operators_Olinorder__class_OMax(U_10288,hAPP(hAPP(c_Set_Oinsert(U_10288),U_10290),U_10289)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10288),U_10290),c_Big__Operators_Olinorder__class_OMax(U_10288,U_10289))
      | U_10289 = c_Orderings_Obot__class_Obot(tc_fun(U_10288,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_10288),U_10290),U_10289))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10288),U_10289))
      | ~ class_Orderings_Olinorder(U_10288) ),
    inference(variable_rename,[status(thm)],[f_2819_1]) ).

fof(f_2819_3,plain,
    ! [U_10288,U_10289,U_10290] :
      ( c_Big__Operators_Olinorder__class_OMax(U_10288,hAPP(hAPP(c_Set_Oinsert(U_10288),U_10290),U_10289)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10288),U_10290),c_Big__Operators_Olinorder__class_OMax(U_10288,U_10289))
      | U_10289 = c_Orderings_Obot__class_Obot(tc_fun(U_10288,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_10288),U_10290),U_10289))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10288),U_10289))
      | ~ class_Orderings_Olinorder(U_10288) ),
    inference(definitional_conversion,[status(esa)],[f_2819_2]) ).

cnf(f_2819_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_10288,hAPP(hAPP(c_Set_Oinsert(U_10288),U_10290),U_10289)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10288),U_10290),c_Big__Operators_Olinorder__class_OMax(U_10288,U_10289))
    | U_10289 = c_Orderings_Obot__class_Obot(tc_fun(U_10288,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_10288),U_10290),U_10289))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10288),U_10289))
    | ~ class_Orderings_Olinorder(U_10288) ),
    inference(clausify,[status(thm)],[f_2819_3]) ).

fof(f_2820_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_2820_2,plain,
    ! [U_10293,U_10292,U_10291] :
      ( ( ( c_Big__Operators_Olinorder__class_OMin(U_10291,hAPP(hAPP(c_Set_Oinsert(U_10291),U_10293),U_10292)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10291),U_10293),c_Big__Operators_Olinorder__class_OMin(U_10291,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10291,tc_HOL_Obool)),U_10292),hAPP(hAPP(c_Set_Oinsert(U_10291),U_10293),c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10291,tc_HOL_Obool)),U_10292),hAPP(hAPP(c_Set_Oinsert(U_10291),U_10293),c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMin(U_10291,hAPP(hAPP(c_Set_Oinsert(U_10291),U_10293),U_10292)) = U_10293
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10291,tc_HOL_Obool)),U_10292),hAPP(hAPP(c_Set_Oinsert(U_10291),U_10293),c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool)))) != 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_2820_1]) ).

fof(f_2820_3,plain,
    ( ! [U_10291,U_10292,U_10293] :
        ( c_Big__Operators_Olinorder__class_OMin(U_10291,hAPP(hAPP(c_Set_Oinsert(U_10291),U_10293),U_10292)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10291),U_10293),c_Big__Operators_Olinorder__class_OMin(U_10291,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10291,tc_HOL_Obool)),U_10292),hAPP(hAPP(c_Set_Oinsert(U_10291),U_10293),c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10291,tc_HOL_Obool)),U_10292),hAPP(hAPP(c_Set_Oinsert(U_10291),U_10293),c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool))
        | ~ sP784(U_10291,U_10292,U_10293) )
    & ! [U_10291,U_10292,U_10293] :
        ( c_Big__Operators_Olinorder__class_OMin(U_10291,hAPP(hAPP(c_Set_Oinsert(U_10291),U_10293),U_10292)) = U_10293
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10291,tc_HOL_Obool)),U_10292),hAPP(hAPP(c_Set_Oinsert(U_10291),U_10293),c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool))
        | ~ sP784(U_10291,U_10292,U_10293) )
    & ! [U_10291,U_10292,U_10293] :
        ( sP784(U_10291,U_10292,U_10293)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10291),U_10292))
        | ~ class_Orderings_Olinorder(U_10291) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP784])],[f_2820_2]) ).

cnf(f_2820_4,plain,
    ( sP784(U_10291,U_10292,U_10293)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10291),U_10292))
    | ~ class_Orderings_Olinorder(U_10291) ),
    inference(clausify,[status(thm)],[f_2820_3]) ).

cnf(f_2820_5,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_10291,hAPP(hAPP(c_Set_Oinsert(U_10291),U_10293),U_10292)) = U_10293
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10291,tc_HOL_Obool)),U_10292),hAPP(hAPP(c_Set_Oinsert(U_10291),U_10293),c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool))
    | ~ sP784(U_10291,U_10292,U_10293) ),
    inference(clausify,[status(thm)],[f_2820_3]) ).

cnf(f_2820_6,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_10291,hAPP(hAPP(c_Set_Oinsert(U_10291),U_10293),U_10292)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10291),U_10293),c_Big__Operators_Olinorder__class_OMin(U_10291,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10291,tc_HOL_Obool)),U_10292),hAPP(hAPP(c_Set_Oinsert(U_10291),U_10293),c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10291,tc_HOL_Obool)),U_10292),hAPP(hAPP(c_Set_Oinsert(U_10291),U_10293),c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10291,tc_HOL_Obool))
    | ~ sP784(U_10291,U_10292,U_10293) ),
    inference(clausify,[status(thm)],[f_2820_3]) ).

fof(f_2821_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_2821_2,plain,
    ! [U_10296,U_10295,U_10294] :
      ( ( ( c_Big__Operators_Olinorder__class_OMax(U_10294,hAPP(hAPP(c_Set_Oinsert(U_10294),U_10296),U_10295)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10294),U_10296),c_Big__Operators_Olinorder__class_OMax(U_10294,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10294,tc_HOL_Obool)),U_10295),hAPP(hAPP(c_Set_Oinsert(U_10294),U_10296),c_Orderings_Obot__class_Obot(tc_fun(U_10294,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10294,tc_HOL_Obool)),U_10295),hAPP(hAPP(c_Set_Oinsert(U_10294),U_10296),c_Orderings_Obot__class_Obot(tc_fun(U_10294,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10294,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMax(U_10294,hAPP(hAPP(c_Set_Oinsert(U_10294),U_10296),U_10295)) = U_10296
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10294,tc_HOL_Obool)),U_10295),hAPP(hAPP(c_Set_Oinsert(U_10294),U_10296),c_Orderings_Obot__class_Obot(tc_fun(U_10294,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10294,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10294),U_10295))
      | ~ class_Orderings_Olinorder(U_10294) ),
    inference(variable_rename,[status(thm)],[f_2821_1]) ).

fof(f_2821_3,plain,
    ( ! [U_10295,U_10296,U_10294] :
        ( c_Big__Operators_Olinorder__class_OMax(U_10294,hAPP(hAPP(c_Set_Oinsert(U_10294),U_10296),U_10295)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10294),U_10296),c_Big__Operators_Olinorder__class_OMax(U_10294,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10294,tc_HOL_Obool)),U_10295),hAPP(hAPP(c_Set_Oinsert(U_10294),U_10296),c_Orderings_Obot__class_Obot(tc_fun(U_10294,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10294,tc_HOL_Obool)),U_10295),hAPP(hAPP(c_Set_Oinsert(U_10294),U_10296),c_Orderings_Obot__class_Obot(tc_fun(U_10294,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10294,tc_HOL_Obool))
        | ~ sP785(U_10295,U_10296,U_10294) )
    & ! [U_10295,U_10296,U_10294] :
        ( c_Big__Operators_Olinorder__class_OMax(U_10294,hAPP(hAPP(c_Set_Oinsert(U_10294),U_10296),U_10295)) = U_10296
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10294,tc_HOL_Obool)),U_10295),hAPP(hAPP(c_Set_Oinsert(U_10294),U_10296),c_Orderings_Obot__class_Obot(tc_fun(U_10294,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10294,tc_HOL_Obool))
        | ~ sP785(U_10295,U_10296,U_10294) )
    & ! [U_10295,U_10296,U_10294] :
        ( sP785(U_10295,U_10296,U_10294)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10294),U_10295))
        | ~ class_Orderings_Olinorder(U_10294) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP785])],[f_2821_2]) ).

cnf(f_2821_4,plain,
    ( sP785(U_10295,U_10296,U_10294)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10294),U_10295))
    | ~ class_Orderings_Olinorder(U_10294) ),
    inference(clausify,[status(thm)],[f_2821_3]) ).

cnf(f_2821_5,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_10294,hAPP(hAPP(c_Set_Oinsert(U_10294),U_10296),U_10295)) = U_10296
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10294,tc_HOL_Obool)),U_10295),hAPP(hAPP(c_Set_Oinsert(U_10294),U_10296),c_Orderings_Obot__class_Obot(tc_fun(U_10294,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10294,tc_HOL_Obool))
    | ~ sP785(U_10295,U_10296,U_10294) ),
    inference(clausify,[status(thm)],[f_2821_3]) ).

cnf(f_2821_6,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_10294,hAPP(hAPP(c_Set_Oinsert(U_10294),U_10296),U_10295)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10294),U_10296),c_Big__Operators_Olinorder__class_OMax(U_10294,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10294,tc_HOL_Obool)),U_10295),hAPP(hAPP(c_Set_Oinsert(U_10294),U_10296),c_Orderings_Obot__class_Obot(tc_fun(U_10294,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10294,tc_HOL_Obool)),U_10295),hAPP(hAPP(c_Set_Oinsert(U_10294),U_10296),c_Orderings_Obot__class_Obot(tc_fun(U_10294,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10294,tc_HOL_Obool))
    | ~ sP785(U_10295,U_10296,U_10294) ),
    inference(clausify,[status(thm)],[f_2821_3]) ).

fof(f_2822_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_2822_2,plain,
    ! [U_10299,U_10298,U_10297] :
      ( ( ( c_Big__Operators_Olinorder__class_OMin(U_10297,U_10298) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10297),U_10299),c_Big__Operators_Olinorder__class_OMin(U_10297,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10297,tc_HOL_Obool)),U_10298),hAPP(hAPP(c_Set_Oinsert(U_10297),U_10299),c_Orderings_Obot__class_Obot(tc_fun(U_10297,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10297,tc_HOL_Obool)),U_10298),hAPP(hAPP(c_Set_Oinsert(U_10297),U_10299),c_Orderings_Obot__class_Obot(tc_fun(U_10297,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10297,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMin(U_10297,U_10298) = U_10299
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10297,tc_HOL_Obool)),U_10298),hAPP(hAPP(c_Set_Oinsert(U_10297),U_10299),c_Orderings_Obot__class_Obot(tc_fun(U_10297,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10297,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_10297),U_10299),U_10298))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10297),U_10298))
      | ~ class_Orderings_Olinorder(U_10297) ),
    inference(variable_rename,[status(thm)],[f_2822_1]) ).

fof(f_2822_3,plain,
    ( ! [U_10299,U_10297,U_10298] :
        ( c_Big__Operators_Olinorder__class_OMin(U_10297,U_10298) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10297),U_10299),c_Big__Operators_Olinorder__class_OMin(U_10297,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10297,tc_HOL_Obool)),U_10298),hAPP(hAPP(c_Set_Oinsert(U_10297),U_10299),c_Orderings_Obot__class_Obot(tc_fun(U_10297,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10297,tc_HOL_Obool)),U_10298),hAPP(hAPP(c_Set_Oinsert(U_10297),U_10299),c_Orderings_Obot__class_Obot(tc_fun(U_10297,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10297,tc_HOL_Obool))
        | ~ sP786(U_10299,U_10297,U_10298) )
    & ! [U_10299,U_10297,U_10298] :
        ( c_Big__Operators_Olinorder__class_OMin(U_10297,U_10298) = U_10299
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10297,tc_HOL_Obool)),U_10298),hAPP(hAPP(c_Set_Oinsert(U_10297),U_10299),c_Orderings_Obot__class_Obot(tc_fun(U_10297,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10297,tc_HOL_Obool))
        | ~ sP786(U_10299,U_10297,U_10298) )
    & ! [U_10299,U_10297,U_10298] :
        ( sP786(U_10299,U_10297,U_10298)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10297),U_10299),U_10298))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10297),U_10298))
        | ~ class_Orderings_Olinorder(U_10297) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP786])],[f_2822_2]) ).

cnf(f_2822_4,plain,
    ( sP786(U_10299,U_10297,U_10298)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10297),U_10299),U_10298))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10297),U_10298))
    | ~ class_Orderings_Olinorder(U_10297) ),
    inference(clausify,[status(thm)],[f_2822_3]) ).

cnf(f_2822_5,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_10297,U_10298) = U_10299
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10297,tc_HOL_Obool)),U_10298),hAPP(hAPP(c_Set_Oinsert(U_10297),U_10299),c_Orderings_Obot__class_Obot(tc_fun(U_10297,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10297,tc_HOL_Obool))
    | ~ sP786(U_10299,U_10297,U_10298) ),
    inference(clausify,[status(thm)],[f_2822_3]) ).

cnf(f_2822_6,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_10297,U_10298) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10297),U_10299),c_Big__Operators_Olinorder__class_OMin(U_10297,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10297,tc_HOL_Obool)),U_10298),hAPP(hAPP(c_Set_Oinsert(U_10297),U_10299),c_Orderings_Obot__class_Obot(tc_fun(U_10297,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10297,tc_HOL_Obool)),U_10298),hAPP(hAPP(c_Set_Oinsert(U_10297),U_10299),c_Orderings_Obot__class_Obot(tc_fun(U_10297,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10297,tc_HOL_Obool))
    | ~ sP786(U_10299,U_10297,U_10298) ),
    inference(clausify,[status(thm)],[f_2822_3]) ).

fof(f_2823_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_2823_2,plain,
    ! [U_10302,U_10301,U_10300] :
      ( ( ( c_Big__Operators_Olinorder__class_OMax(U_10300,U_10301) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10300),U_10302),c_Big__Operators_Olinorder__class_OMax(U_10300,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10300,tc_HOL_Obool)),U_10301),hAPP(hAPP(c_Set_Oinsert(U_10300),U_10302),c_Orderings_Obot__class_Obot(tc_fun(U_10300,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10300,tc_HOL_Obool)),U_10301),hAPP(hAPP(c_Set_Oinsert(U_10300),U_10302),c_Orderings_Obot__class_Obot(tc_fun(U_10300,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10300,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olinorder__class_OMax(U_10300,U_10301) = U_10302
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10300,tc_HOL_Obool)),U_10301),hAPP(hAPP(c_Set_Oinsert(U_10300),U_10302),c_Orderings_Obot__class_Obot(tc_fun(U_10300,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10300,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_10300),U_10302),U_10301))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10300),U_10301))
      | ~ class_Orderings_Olinorder(U_10300) ),
    inference(variable_rename,[status(thm)],[f_2823_1]) ).

fof(f_2823_3,plain,
    ( ! [U_10302,U_10301,U_10300] :
        ( c_Big__Operators_Olinorder__class_OMax(U_10300,U_10301) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10300),U_10302),c_Big__Operators_Olinorder__class_OMax(U_10300,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10300,tc_HOL_Obool)),U_10301),hAPP(hAPP(c_Set_Oinsert(U_10300),U_10302),c_Orderings_Obot__class_Obot(tc_fun(U_10300,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10300,tc_HOL_Obool)),U_10301),hAPP(hAPP(c_Set_Oinsert(U_10300),U_10302),c_Orderings_Obot__class_Obot(tc_fun(U_10300,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10300,tc_HOL_Obool))
        | ~ sP787(U_10302,U_10301,U_10300) )
    & ! [U_10302,U_10301,U_10300] :
        ( c_Big__Operators_Olinorder__class_OMax(U_10300,U_10301) = U_10302
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10300,tc_HOL_Obool)),U_10301),hAPP(hAPP(c_Set_Oinsert(U_10300),U_10302),c_Orderings_Obot__class_Obot(tc_fun(U_10300,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10300,tc_HOL_Obool))
        | ~ sP787(U_10302,U_10301,U_10300) )
    & ! [U_10302,U_10301,U_10300] :
        ( sP787(U_10302,U_10301,U_10300)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10300),U_10302),U_10301))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10300),U_10301))
        | ~ class_Orderings_Olinorder(U_10300) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP787])],[f_2823_2]) ).

cnf(f_2823_4,plain,
    ( sP787(U_10302,U_10301,U_10300)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10300),U_10302),U_10301))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10300),U_10301))
    | ~ class_Orderings_Olinorder(U_10300) ),
    inference(clausify,[status(thm)],[f_2823_3]) ).

cnf(f_2823_5,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_10300,U_10301) = U_10302
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10300,tc_HOL_Obool)),U_10301),hAPP(hAPP(c_Set_Oinsert(U_10300),U_10302),c_Orderings_Obot__class_Obot(tc_fun(U_10300,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10300,tc_HOL_Obool))
    | ~ sP787(U_10302,U_10301,U_10300) ),
    inference(clausify,[status(thm)],[f_2823_3]) ).

cnf(f_2823_6,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_10300,U_10301) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10300),U_10302),c_Big__Operators_Olinorder__class_OMax(U_10300,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10300,tc_HOL_Obool)),U_10301),hAPP(hAPP(c_Set_Oinsert(U_10300),U_10302),c_Orderings_Obot__class_Obot(tc_fun(U_10300,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10300,tc_HOL_Obool)),U_10301),hAPP(hAPP(c_Set_Oinsert(U_10300),U_10302),c_Orderings_Obot__class_Obot(tc_fun(U_10300,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10300,tc_HOL_Obool))
    | ~ sP787(U_10302,U_10301,U_10300) ),
    inference(clausify,[status(thm)],[f_2823_3]) ).

fof(f_2824_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_2824_2,plain,
    ! [U_10306,U_10305] :
      ( hBOOL(hAPP(hAPP(c_member(U_10305),c_Big__Operators_Olinorder__class_OMax(U_10305,U_10306)),U_10306))
      | ? [U_10304,U_10303] : ~ hBOOL(hAPP(hAPP(c_member(U_10305),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10305),U_10304),U_10303)),hAPP(hAPP(c_Set_Oinsert(U_10305),U_10304),hAPP(hAPP(c_Set_Oinsert(U_10305),U_10303),c_Orderings_Obot__class_Obot(tc_fun(U_10305,tc_HOL_Obool))))))
      | U_10306 = c_Orderings_Obot__class_Obot(tc_fun(U_10305,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10305),U_10306))
      | ~ class_Orderings_Olinorder(U_10305) ),
    inference(variable_rename,[status(thm)],[f_2824_1]) ).

fof(f_2824_3,plain,
    ! [U_10306,U_10305] :
      ( hBOOL(hAPP(hAPP(c_member(U_10305),c_Big__Operators_Olinorder__class_OMax(U_10305,U_10306)),U_10306))
      | ? [U_10303] : ~ hBOOL(hAPP(hAPP(c_member(U_10305),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10305),sK164(U_10306,U_10305)),U_10303)),hAPP(hAPP(c_Set_Oinsert(U_10305),sK164(U_10306,U_10305)),hAPP(hAPP(c_Set_Oinsert(U_10305),U_10303),c_Orderings_Obot__class_Obot(tc_fun(U_10305,tc_HOL_Obool))))))
      | U_10306 = c_Orderings_Obot__class_Obot(tc_fun(U_10305,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10305),U_10306))
      | ~ class_Orderings_Olinorder(U_10305) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK164]),skolemize(U_10304,sK164(U_10306,U_10305))],[f_2824_2]) ).

fof(f_2824_4,plain,
    ! [U_10306,U_10305] :
      ( hBOOL(hAPP(hAPP(c_member(U_10305),c_Big__Operators_Olinorder__class_OMax(U_10305,U_10306)),U_10306))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10305),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10305),sK164(U_10306,U_10305)),sK165(U_10306,U_10305))),hAPP(hAPP(c_Set_Oinsert(U_10305),sK164(U_10306,U_10305)),hAPP(hAPP(c_Set_Oinsert(U_10305),sK165(U_10306,U_10305)),c_Orderings_Obot__class_Obot(tc_fun(U_10305,tc_HOL_Obool))))))
      | U_10306 = c_Orderings_Obot__class_Obot(tc_fun(U_10305,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10305),U_10306))
      | ~ class_Orderings_Olinorder(U_10305) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK165]),skolemize(U_10303,sK165(U_10306,U_10305))],[f_2824_3]) ).

fof(f_2824_5,plain,
    ! [U_10306,U_10305] :
      ( hBOOL(hAPP(hAPP(c_member(U_10305),c_Big__Operators_Olinorder__class_OMax(U_10305,U_10306)),U_10306))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10305),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10305),sK164(U_10306,U_10305)),sK165(U_10306,U_10305))),hAPP(hAPP(c_Set_Oinsert(U_10305),sK164(U_10306,U_10305)),hAPP(hAPP(c_Set_Oinsert(U_10305),sK165(U_10306,U_10305)),c_Orderings_Obot__class_Obot(tc_fun(U_10305,tc_HOL_Obool))))))
      | U_10306 = c_Orderings_Obot__class_Obot(tc_fun(U_10305,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10305),U_10306))
      | ~ class_Orderings_Olinorder(U_10305) ),
    inference(definitional_conversion,[status(esa)],[f_2824_4]) ).

cnf(f_2824_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10305),c_Big__Operators_Olinorder__class_OMax(U_10305,U_10306)),U_10306))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10305),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10305),sK164(U_10306,U_10305)),sK165(U_10306,U_10305))),hAPP(hAPP(c_Set_Oinsert(U_10305),sK164(U_10306,U_10305)),hAPP(hAPP(c_Set_Oinsert(U_10305),sK165(U_10306,U_10305)),c_Orderings_Obot__class_Obot(tc_fun(U_10305,tc_HOL_Obool))))))
    | U_10306 = c_Orderings_Obot__class_Obot(tc_fun(U_10305,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10305),U_10306))
    | ~ class_Orderings_Olinorder(U_10305) ),
    inference(clausify,[status(thm)],[f_2824_5]) ).

fof(f_2825_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_2825_2,plain,
    ! [U_10310,U_10309] :
      ( hBOOL(hAPP(hAPP(c_member(U_10309),c_Big__Operators_Olinorder__class_OMin(U_10309,U_10310)),U_10310))
      | ? [U_10308,U_10307] : ~ hBOOL(hAPP(hAPP(c_member(U_10309),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10309),U_10308),U_10307)),hAPP(hAPP(c_Set_Oinsert(U_10309),U_10308),hAPP(hAPP(c_Set_Oinsert(U_10309),U_10307),c_Orderings_Obot__class_Obot(tc_fun(U_10309,tc_HOL_Obool))))))
      | U_10310 = c_Orderings_Obot__class_Obot(tc_fun(U_10309,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10309),U_10310))
      | ~ class_Orderings_Olinorder(U_10309) ),
    inference(variable_rename,[status(thm)],[f_2825_1]) ).

fof(f_2825_3,plain,
    ! [U_10310,U_10309] :
      ( hBOOL(hAPP(hAPP(c_member(U_10309),c_Big__Operators_Olinorder__class_OMin(U_10309,U_10310)),U_10310))
      | ? [U_10307] : ~ hBOOL(hAPP(hAPP(c_member(U_10309),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10309),sK166(U_10310,U_10309)),U_10307)),hAPP(hAPP(c_Set_Oinsert(U_10309),sK166(U_10310,U_10309)),hAPP(hAPP(c_Set_Oinsert(U_10309),U_10307),c_Orderings_Obot__class_Obot(tc_fun(U_10309,tc_HOL_Obool))))))
      | U_10310 = c_Orderings_Obot__class_Obot(tc_fun(U_10309,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10309),U_10310))
      | ~ class_Orderings_Olinorder(U_10309) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK166]),skolemize(U_10308,sK166(U_10310,U_10309))],[f_2825_2]) ).

fof(f_2825_4,plain,
    ! [U_10310,U_10309] :
      ( hBOOL(hAPP(hAPP(c_member(U_10309),c_Big__Operators_Olinorder__class_OMin(U_10309,U_10310)),U_10310))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10309),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10309),sK166(U_10310,U_10309)),sK167(U_10310,U_10309))),hAPP(hAPP(c_Set_Oinsert(U_10309),sK166(U_10310,U_10309)),hAPP(hAPP(c_Set_Oinsert(U_10309),sK167(U_10310,U_10309)),c_Orderings_Obot__class_Obot(tc_fun(U_10309,tc_HOL_Obool))))))
      | U_10310 = c_Orderings_Obot__class_Obot(tc_fun(U_10309,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10309),U_10310))
      | ~ class_Orderings_Olinorder(U_10309) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK167]),skolemize(U_10307,sK167(U_10310,U_10309))],[f_2825_3]) ).

fof(f_2825_5,plain,
    ! [U_10309,U_10310] :
      ( hBOOL(hAPP(hAPP(c_member(U_10309),c_Big__Operators_Olinorder__class_OMin(U_10309,U_10310)),U_10310))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10309),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10309),sK166(U_10310,U_10309)),sK167(U_10310,U_10309))),hAPP(hAPP(c_Set_Oinsert(U_10309),sK166(U_10310,U_10309)),hAPP(hAPP(c_Set_Oinsert(U_10309),sK167(U_10310,U_10309)),c_Orderings_Obot__class_Obot(tc_fun(U_10309,tc_HOL_Obool))))))
      | U_10310 = c_Orderings_Obot__class_Obot(tc_fun(U_10309,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10309),U_10310))
      | ~ class_Orderings_Olinorder(U_10309) ),
    inference(definitional_conversion,[status(esa)],[f_2825_4]) ).

cnf(f_2825_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10309),c_Big__Operators_Olinorder__class_OMin(U_10309,U_10310)),U_10310))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10309),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10309),sK166(U_10310,U_10309)),sK167(U_10310,U_10309))),hAPP(hAPP(c_Set_Oinsert(U_10309),sK166(U_10310,U_10309)),hAPP(hAPP(c_Set_Oinsert(U_10309),sK167(U_10310,U_10309)),c_Orderings_Obot__class_Obot(tc_fun(U_10309,tc_HOL_Obool))))))
    | U_10310 = c_Orderings_Obot__class_Obot(tc_fun(U_10309,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10309),U_10310))
    | ~ class_Orderings_Olinorder(U_10309) ),
    inference(clausify,[status(thm)],[f_2825_5]) ).

fof(f_2826_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_2826_2,plain,
    ! [U_10313,U_10312,U_10311] :
      ( ( ( c_Big__Operators_Olattice__class_OSup__fin(U_10311,U_10312) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10311),U_10313),c_Big__Operators_Olattice__class_OSup__fin(U_10311,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10311,tc_HOL_Obool)),U_10312),hAPP(hAPP(c_Set_Oinsert(U_10311),U_10313),c_Orderings_Obot__class_Obot(tc_fun(U_10311,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10311,tc_HOL_Obool)),U_10312),hAPP(hAPP(c_Set_Oinsert(U_10311),U_10313),c_Orderings_Obot__class_Obot(tc_fun(U_10311,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10311,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OSup__fin(U_10311,U_10312) = U_10313
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10311,tc_HOL_Obool)),U_10312),hAPP(hAPP(c_Set_Oinsert(U_10311),U_10313),c_Orderings_Obot__class_Obot(tc_fun(U_10311,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10311,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_10311),U_10313),U_10312))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10311),U_10312))
      | ~ class_Lattices_Olattice(U_10311) ),
    inference(variable_rename,[status(thm)],[f_2826_1]) ).

fof(f_2826_3,plain,
    ( ! [U_10311,U_10312,U_10313] :
        ( c_Big__Operators_Olattice__class_OSup__fin(U_10311,U_10312) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10311),U_10313),c_Big__Operators_Olattice__class_OSup__fin(U_10311,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10311,tc_HOL_Obool)),U_10312),hAPP(hAPP(c_Set_Oinsert(U_10311),U_10313),c_Orderings_Obot__class_Obot(tc_fun(U_10311,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10311,tc_HOL_Obool)),U_10312),hAPP(hAPP(c_Set_Oinsert(U_10311),U_10313),c_Orderings_Obot__class_Obot(tc_fun(U_10311,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10311,tc_HOL_Obool))
        | ~ sP788(U_10311,U_10312,U_10313) )
    & ! [U_10311,U_10312,U_10313] :
        ( c_Big__Operators_Olattice__class_OSup__fin(U_10311,U_10312) = U_10313
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10311,tc_HOL_Obool)),U_10312),hAPP(hAPP(c_Set_Oinsert(U_10311),U_10313),c_Orderings_Obot__class_Obot(tc_fun(U_10311,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10311,tc_HOL_Obool))
        | ~ sP788(U_10311,U_10312,U_10313) )
    & ! [U_10311,U_10312,U_10313] :
        ( sP788(U_10311,U_10312,U_10313)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10311),U_10313),U_10312))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10311),U_10312))
        | ~ class_Lattices_Olattice(U_10311) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP788])],[f_2826_2]) ).

cnf(f_2826_4,plain,
    ( sP788(U_10311,U_10312,U_10313)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10311),U_10313),U_10312))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10311),U_10312))
    | ~ class_Lattices_Olattice(U_10311) ),
    inference(clausify,[status(thm)],[f_2826_3]) ).

cnf(f_2826_5,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_10311,U_10312) = U_10313
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10311,tc_HOL_Obool)),U_10312),hAPP(hAPP(c_Set_Oinsert(U_10311),U_10313),c_Orderings_Obot__class_Obot(tc_fun(U_10311,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10311,tc_HOL_Obool))
    | ~ sP788(U_10311,U_10312,U_10313) ),
    inference(clausify,[status(thm)],[f_2826_3]) ).

cnf(f_2826_6,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_10311,U_10312) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10311),U_10313),c_Big__Operators_Olattice__class_OSup__fin(U_10311,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10311,tc_HOL_Obool)),U_10312),hAPP(hAPP(c_Set_Oinsert(U_10311),U_10313),c_Orderings_Obot__class_Obot(tc_fun(U_10311,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10311,tc_HOL_Obool)),U_10312),hAPP(hAPP(c_Set_Oinsert(U_10311),U_10313),c_Orderings_Obot__class_Obot(tc_fun(U_10311,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10311,tc_HOL_Obool))
    | ~ sP788(U_10311,U_10312,U_10313) ),
    inference(clausify,[status(thm)],[f_2826_3]) ).

fof(f_2827_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_2827_2,plain,
    ! [U_10315,U_10314] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_10314,hAPP(hAPP(c_Set_Oinsert(U_10314),U_10315),c_Orderings_Obot__class_Obot(tc_fun(U_10314,tc_HOL_Obool)))) = U_10315
      | ~ class_Lattices_Olattice(U_10314) ),
    inference(variable_rename,[status(thm)],[f_2827_1]) ).

fof(f_2827_3,plain,
    ! [U_10315,U_10314] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_10314,hAPP(hAPP(c_Set_Oinsert(U_10314),U_10315),c_Orderings_Obot__class_Obot(tc_fun(U_10314,tc_HOL_Obool)))) = U_10315
      | ~ class_Lattices_Olattice(U_10314) ),
    inference(definitional_conversion,[status(esa)],[f_2827_2]) ).

cnf(f_2827_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_10314,hAPP(hAPP(c_Set_Oinsert(U_10314),U_10315),c_Orderings_Obot__class_Obot(tc_fun(U_10314,tc_HOL_Obool)))) = U_10315
    | ~ class_Lattices_Olattice(U_10314) ),
    inference(clausify,[status(thm)],[f_2827_3]) ).

fof(f_2828_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_2828_2,plain,
    ! [U_10318,U_10317,U_10316] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10316),U_10318),c_Big__Operators_Olattice__class_OSup__fin(U_10316,U_10317)) = c_Big__Operators_Olattice__class_OSup__fin(U_10316,U_10317)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10316),U_10318),U_10317))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10316),U_10317))
      | ~ class_Lattices_Olattice(U_10316) ),
    inference(variable_rename,[status(thm)],[f_2828_1]) ).

fof(f_2828_3,plain,
    ! [U_10316,U_10317,U_10318] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10316),U_10318),c_Big__Operators_Olattice__class_OSup__fin(U_10316,U_10317)) = c_Big__Operators_Olattice__class_OSup__fin(U_10316,U_10317)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10316),U_10318),U_10317))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10316),U_10317))
      | ~ class_Lattices_Olattice(U_10316) ),
    inference(definitional_conversion,[status(esa)],[f_2828_2]) ).

cnf(f_2828_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10316),U_10318),c_Big__Operators_Olattice__class_OSup__fin(U_10316,U_10317)) = c_Big__Operators_Olattice__class_OSup__fin(U_10316,U_10317)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10316),U_10318),U_10317))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10316),U_10317))
    | ~ class_Lattices_Olattice(U_10316) ),
    inference(clausify,[status(thm)],[f_2828_3]) ).

fof(f_2829_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_2829_2,plain,
    ! [U_10321,U_10320,U_10319] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_10319,hAPP(hAPP(c_Set_Oinsert(U_10319),U_10321),U_10320)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10319),U_10321),c_Big__Operators_Olattice__class_OSup__fin(U_10319,U_10320))
      | U_10320 = c_Orderings_Obot__class_Obot(tc_fun(U_10319,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10319),U_10320))
      | ~ class_Lattices_Olattice(U_10319) ),
    inference(variable_rename,[status(thm)],[f_2829_1]) ).

fof(f_2829_3,plain,
    ! [U_10319,U_10320,U_10321] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_10319,hAPP(hAPP(c_Set_Oinsert(U_10319),U_10321),U_10320)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10319),U_10321),c_Big__Operators_Olattice__class_OSup__fin(U_10319,U_10320))
      | U_10320 = c_Orderings_Obot__class_Obot(tc_fun(U_10319,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10319),U_10320))
      | ~ class_Lattices_Olattice(U_10319) ),
    inference(definitional_conversion,[status(esa)],[f_2829_2]) ).

cnf(f_2829_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_10319,hAPP(hAPP(c_Set_Oinsert(U_10319),U_10321),U_10320)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10319),U_10321),c_Big__Operators_Olattice__class_OSup__fin(U_10319,U_10320))
    | U_10320 = c_Orderings_Obot__class_Obot(tc_fun(U_10319,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10319),U_10320))
    | ~ class_Lattices_Olattice(U_10319) ),
    inference(clausify,[status(thm)],[f_2829_3]) ).

fof(f_2830_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_2830_2,plain,
    ! [U_10324,U_10323,U_10322] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10322),c_Big__Operators_Olattice__class_OSup__fin(U_10322,U_10324)),c_Big__Operators_Olattice__class_OSup__fin(U_10322,U_10323)) = c_Big__Operators_Olattice__class_OSup__fin(U_10322,U_10323)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10322,tc_HOL_Obool)),U_10324),U_10323))
      | U_10324 = c_Orderings_Obot__class_Obot(tc_fun(U_10322,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10322),U_10323))
      | ~ class_Lattices_Olattice(U_10322) ),
    inference(variable_rename,[status(thm)],[f_2830_1]) ).

fof(f_2830_3,plain,
    ! [U_10322,U_10323,U_10324] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10322),c_Big__Operators_Olattice__class_OSup__fin(U_10322,U_10324)),c_Big__Operators_Olattice__class_OSup__fin(U_10322,U_10323)) = c_Big__Operators_Olattice__class_OSup__fin(U_10322,U_10323)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10322,tc_HOL_Obool)),U_10324),U_10323))
      | U_10324 = c_Orderings_Obot__class_Obot(tc_fun(U_10322,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10322),U_10323))
      | ~ class_Lattices_Olattice(U_10322) ),
    inference(definitional_conversion,[status(esa)],[f_2830_2]) ).

cnf(f_2830_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10322),c_Big__Operators_Olattice__class_OSup__fin(U_10322,U_10324)),c_Big__Operators_Olattice__class_OSup__fin(U_10322,U_10323)) = c_Big__Operators_Olattice__class_OSup__fin(U_10322,U_10323)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10322,tc_HOL_Obool)),U_10324),U_10323))
    | U_10324 = c_Orderings_Obot__class_Obot(tc_fun(U_10322,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10322),U_10323))
    | ~ class_Lattices_Olattice(U_10322) ),
    inference(clausify,[status(thm)],[f_2830_3]) ).

fof(f_2831_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_2831_2,plain,
    ! [U_10327,U_10326,U_10325] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_10325,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10325,tc_HOL_Obool)),U_10326),U_10327)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10325),c_Big__Operators_Olattice__class_OSup__fin(U_10325,U_10326)),c_Big__Operators_Olattice__class_OSup__fin(U_10325,U_10327))
      | U_10327 = c_Orderings_Obot__class_Obot(tc_fun(U_10325,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10325),U_10327))
      | U_10326 = c_Orderings_Obot__class_Obot(tc_fun(U_10325,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10325),U_10326))
      | ~ class_Lattices_Olattice(U_10325) ),
    inference(variable_rename,[status(thm)],[f_2831_1]) ).

fof(f_2831_3,plain,
    ! [U_10325,U_10326,U_10327] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_10325,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10325,tc_HOL_Obool)),U_10326),U_10327)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10325),c_Big__Operators_Olattice__class_OSup__fin(U_10325,U_10326)),c_Big__Operators_Olattice__class_OSup__fin(U_10325,U_10327))
      | U_10327 = c_Orderings_Obot__class_Obot(tc_fun(U_10325,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10325),U_10327))
      | U_10326 = c_Orderings_Obot__class_Obot(tc_fun(U_10325,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10325),U_10326))
      | ~ class_Lattices_Olattice(U_10325) ),
    inference(definitional_conversion,[status(esa)],[f_2831_2]) ).

cnf(f_2831_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_10325,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_10325,tc_HOL_Obool)),U_10326),U_10327)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10325),c_Big__Operators_Olattice__class_OSup__fin(U_10325,U_10326)),c_Big__Operators_Olattice__class_OSup__fin(U_10325,U_10327))
    | U_10327 = c_Orderings_Obot__class_Obot(tc_fun(U_10325,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10325),U_10327))
    | U_10326 = c_Orderings_Obot__class_Obot(tc_fun(U_10325,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10325),U_10326))
    | ~ class_Lattices_Olattice(U_10325) ),
    inference(clausify,[status(thm)],[f_2831_3]) ).

fof(f_2832_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_2832_2,plain,
    ! [U_10329,U_10328] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10328),c_Big__Operators_Olattice__class_OInf__fin(U_10328,U_10329)),c_Big__Operators_Olattice__class_OSup__fin(U_10328,U_10329)))
      | U_10329 = c_Orderings_Obot__class_Obot(tc_fun(U_10328,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10328),U_10329))
      | ~ class_Lattices_Olattice(U_10328) ),
    inference(variable_rename,[status(thm)],[f_2832_1]) ).

fof(f_2832_3,plain,
    ! [U_10329,U_10328] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10328),c_Big__Operators_Olattice__class_OInf__fin(U_10328,U_10329)),c_Big__Operators_Olattice__class_OSup__fin(U_10328,U_10329)))
      | U_10329 = c_Orderings_Obot__class_Obot(tc_fun(U_10328,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10328),U_10329))
      | ~ class_Lattices_Olattice(U_10328) ),
    inference(definitional_conversion,[status(esa)],[f_2832_2]) ).

cnf(f_2832_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_10328),c_Big__Operators_Olattice__class_OInf__fin(U_10328,U_10329)),c_Big__Operators_Olattice__class_OSup__fin(U_10328,U_10329)))
    | U_10329 = c_Orderings_Obot__class_Obot(tc_fun(U_10328,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10328),U_10329))
    | ~ class_Lattices_Olattice(U_10328) ),
    inference(clausify,[status(thm)],[f_2832_3]) ).

fof(f_2833_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_2833_2,plain,
    ! [U_10332,U_10331,U_10330] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_10330,hAPP(hAPP(c_Set_Oinsert(U_10330),U_10332),U_10331)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10330),U_10332),c_Big__Operators_Olattice__class_OSup__fin(U_10330,U_10331))
      | U_10331 = c_Orderings_Obot__class_Obot(tc_fun(U_10330,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_10330),U_10332),U_10331))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10330),U_10331))
      | ~ class_Lattices_Olattice(U_10330) ),
    inference(variable_rename,[status(thm)],[f_2833_1]) ).

fof(f_2833_3,plain,
    ! [U_10330,U_10331,U_10332] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_10330,hAPP(hAPP(c_Set_Oinsert(U_10330),U_10332),U_10331)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10330),U_10332),c_Big__Operators_Olattice__class_OSup__fin(U_10330,U_10331))
      | U_10331 = c_Orderings_Obot__class_Obot(tc_fun(U_10330,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_10330),U_10332),U_10331))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10330),U_10331))
      | ~ class_Lattices_Olattice(U_10330) ),
    inference(definitional_conversion,[status(esa)],[f_2833_2]) ).

cnf(f_2833_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_10330,hAPP(hAPP(c_Set_Oinsert(U_10330),U_10332),U_10331)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10330),U_10332),c_Big__Operators_Olattice__class_OSup__fin(U_10330,U_10331))
    | U_10331 = c_Orderings_Obot__class_Obot(tc_fun(U_10330,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_10330),U_10332),U_10331))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10330),U_10331))
    | ~ class_Lattices_Olattice(U_10330) ),
    inference(clausify,[status(thm)],[f_2833_3]) ).

fof(f_2834_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_2834_2,plain,
    ! [U_10335,U_10334,U_10333] :
      ( ( ( c_Big__Operators_Olattice__class_OSup__fin(U_10333,hAPP(hAPP(c_Set_Oinsert(U_10333),U_10335),U_10334)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10333),U_10335),c_Big__Operators_Olattice__class_OSup__fin(U_10333,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10333,tc_HOL_Obool)),U_10334),hAPP(hAPP(c_Set_Oinsert(U_10333),U_10335),c_Orderings_Obot__class_Obot(tc_fun(U_10333,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10333,tc_HOL_Obool)),U_10334),hAPP(hAPP(c_Set_Oinsert(U_10333),U_10335),c_Orderings_Obot__class_Obot(tc_fun(U_10333,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10333,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OSup__fin(U_10333,hAPP(hAPP(c_Set_Oinsert(U_10333),U_10335),U_10334)) = U_10335
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10333,tc_HOL_Obool)),U_10334),hAPP(hAPP(c_Set_Oinsert(U_10333),U_10335),c_Orderings_Obot__class_Obot(tc_fun(U_10333,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10333,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10333),U_10334))
      | ~ class_Lattices_Olattice(U_10333) ),
    inference(variable_rename,[status(thm)],[f_2834_1]) ).

fof(f_2834_3,plain,
    ( ! [U_10333,U_10334,U_10335] :
        ( c_Big__Operators_Olattice__class_OSup__fin(U_10333,hAPP(hAPP(c_Set_Oinsert(U_10333),U_10335),U_10334)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10333),U_10335),c_Big__Operators_Olattice__class_OSup__fin(U_10333,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10333,tc_HOL_Obool)),U_10334),hAPP(hAPP(c_Set_Oinsert(U_10333),U_10335),c_Orderings_Obot__class_Obot(tc_fun(U_10333,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10333,tc_HOL_Obool)),U_10334),hAPP(hAPP(c_Set_Oinsert(U_10333),U_10335),c_Orderings_Obot__class_Obot(tc_fun(U_10333,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10333,tc_HOL_Obool))
        | ~ sP789(U_10333,U_10334,U_10335) )
    & ! [U_10333,U_10334,U_10335] :
        ( c_Big__Operators_Olattice__class_OSup__fin(U_10333,hAPP(hAPP(c_Set_Oinsert(U_10333),U_10335),U_10334)) = U_10335
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10333,tc_HOL_Obool)),U_10334),hAPP(hAPP(c_Set_Oinsert(U_10333),U_10335),c_Orderings_Obot__class_Obot(tc_fun(U_10333,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10333,tc_HOL_Obool))
        | ~ sP789(U_10333,U_10334,U_10335) )
    & ! [U_10333,U_10334,U_10335] :
        ( sP789(U_10333,U_10334,U_10335)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10333),U_10334))
        | ~ class_Lattices_Olattice(U_10333) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP789])],[f_2834_2]) ).

cnf(f_2834_4,plain,
    ( sP789(U_10333,U_10334,U_10335)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10333),U_10334))
    | ~ class_Lattices_Olattice(U_10333) ),
    inference(clausify,[status(thm)],[f_2834_3]) ).

cnf(f_2834_5,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_10333,hAPP(hAPP(c_Set_Oinsert(U_10333),U_10335),U_10334)) = U_10335
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10333,tc_HOL_Obool)),U_10334),hAPP(hAPP(c_Set_Oinsert(U_10333),U_10335),c_Orderings_Obot__class_Obot(tc_fun(U_10333,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_10333,tc_HOL_Obool))
    | ~ sP789(U_10333,U_10334,U_10335) ),
    inference(clausify,[status(thm)],[f_2834_3]) ).

cnf(f_2834_6,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_10333,hAPP(hAPP(c_Set_Oinsert(U_10333),U_10335),U_10334)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10333),U_10335),c_Big__Operators_Olattice__class_OSup__fin(U_10333,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10333,tc_HOL_Obool)),U_10334),hAPP(hAPP(c_Set_Oinsert(U_10333),U_10335),c_Orderings_Obot__class_Obot(tc_fun(U_10333,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10333,tc_HOL_Obool)),U_10334),hAPP(hAPP(c_Set_Oinsert(U_10333),U_10335),c_Orderings_Obot__class_Obot(tc_fun(U_10333,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_10333,tc_HOL_Obool))
    | ~ sP789(U_10333,U_10334,U_10335) ),
    inference(clausify,[status(thm)],[f_2834_3]) ).

fof(f_2835_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_2835_2,plain,
    ! [U_10339,U_10338] :
      ( hBOOL(hAPP(hAPP(c_member(U_10338),c_Big__Operators_Olattice__class_OSup__fin(U_10338,U_10339)),U_10339))
      | ? [U_10337,U_10336] : ~ hBOOL(hAPP(hAPP(c_member(U_10338),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10338),U_10337),U_10336)),hAPP(hAPP(c_Set_Oinsert(U_10338),U_10337),hAPP(hAPP(c_Set_Oinsert(U_10338),U_10336),c_Orderings_Obot__class_Obot(tc_fun(U_10338,tc_HOL_Obool))))))
      | U_10339 = c_Orderings_Obot__class_Obot(tc_fun(U_10338,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10338),U_10339))
      | ~ class_Lattices_Olattice(U_10338) ),
    inference(variable_rename,[status(thm)],[f_2835_1]) ).

fof(f_2835_3,plain,
    ! [U_10339,U_10338] :
      ( hBOOL(hAPP(hAPP(c_member(U_10338),c_Big__Operators_Olattice__class_OSup__fin(U_10338,U_10339)),U_10339))
      | ? [U_10336] : ~ hBOOL(hAPP(hAPP(c_member(U_10338),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10338),sK168(U_10339,U_10338)),U_10336)),hAPP(hAPP(c_Set_Oinsert(U_10338),sK168(U_10339,U_10338)),hAPP(hAPP(c_Set_Oinsert(U_10338),U_10336),c_Orderings_Obot__class_Obot(tc_fun(U_10338,tc_HOL_Obool))))))
      | U_10339 = c_Orderings_Obot__class_Obot(tc_fun(U_10338,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10338),U_10339))
      | ~ class_Lattices_Olattice(U_10338) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK168]),skolemize(U_10337,sK168(U_10339,U_10338))],[f_2835_2]) ).

fof(f_2835_4,plain,
    ! [U_10339,U_10338] :
      ( hBOOL(hAPP(hAPP(c_member(U_10338),c_Big__Operators_Olattice__class_OSup__fin(U_10338,U_10339)),U_10339))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10338),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10338),sK168(U_10339,U_10338)),sK169(U_10339,U_10338))),hAPP(hAPP(c_Set_Oinsert(U_10338),sK168(U_10339,U_10338)),hAPP(hAPP(c_Set_Oinsert(U_10338),sK169(U_10339,U_10338)),c_Orderings_Obot__class_Obot(tc_fun(U_10338,tc_HOL_Obool))))))
      | U_10339 = c_Orderings_Obot__class_Obot(tc_fun(U_10338,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10338),U_10339))
      | ~ class_Lattices_Olattice(U_10338) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK169]),skolemize(U_10336,sK169(U_10339,U_10338))],[f_2835_3]) ).

fof(f_2835_5,plain,
    ! [U_10338,U_10339] :
      ( hBOOL(hAPP(hAPP(c_member(U_10338),c_Big__Operators_Olattice__class_OSup__fin(U_10338,U_10339)),U_10339))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10338),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10338),sK168(U_10339,U_10338)),sK169(U_10339,U_10338))),hAPP(hAPP(c_Set_Oinsert(U_10338),sK168(U_10339,U_10338)),hAPP(hAPP(c_Set_Oinsert(U_10338),sK169(U_10339,U_10338)),c_Orderings_Obot__class_Obot(tc_fun(U_10338,tc_HOL_Obool))))))
      | U_10339 = c_Orderings_Obot__class_Obot(tc_fun(U_10338,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10338),U_10339))
      | ~ class_Lattices_Olattice(U_10338) ),
    inference(definitional_conversion,[status(esa)],[f_2835_4]) ).

cnf(f_2835_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10338),c_Big__Operators_Olattice__class_OSup__fin(U_10338,U_10339)),U_10339))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10338),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10338),sK168(U_10339,U_10338)),sK169(U_10339,U_10338))),hAPP(hAPP(c_Set_Oinsert(U_10338),sK168(U_10339,U_10338)),hAPP(hAPP(c_Set_Oinsert(U_10338),sK169(U_10339,U_10338)),c_Orderings_Obot__class_Obot(tc_fun(U_10338,tc_HOL_Obool))))))
    | U_10339 = c_Orderings_Obot__class_Obot(tc_fun(U_10338,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10338),U_10339))
    | ~ class_Lattices_Olattice(U_10338) ),
    inference(clausify,[status(thm)],[f_2835_5]) ).

fof(f_2836_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_2836_2,plain,
    ! [U_10350,U_10349,U_10348,U_10347,U_10346,U_10345,U_10344] :
      ( ( c_Nitpick_Ofold__graph_H(U_10344,U_10345,U_10346,U_10347,U_10348,hAPP(hAPP(U_10346,U_10349),U_10350))
        | ( ! [U_10343,U_10342] :
              ( ~ c_Nitpick_Ofold__graph_H(U_10344,U_10345,U_10346,U_10347,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10344,tc_HOL_Obool)),U_10348),hAPP(hAPP(c_Set_Oinsert(U_10344),U_10343),c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool)))),U_10342)
              | ~ hBOOL(hAPP(hAPP(c_member(U_10344),U_10343),U_10348))
              | hAPP(hAPP(U_10346,U_10349),U_10350) != hAPP(hAPP(U_10346,U_10343),U_10342) )
          & ( hAPP(hAPP(U_10346,U_10349),U_10350) != U_10347
            | U_10348 != c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool)) ) ) )
      & ( ? [U_10341,U_10340] :
            ( c_Nitpick_Ofold__graph_H(U_10344,U_10345,U_10346,U_10347,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10344,tc_HOL_Obool)),U_10348),hAPP(hAPP(c_Set_Oinsert(U_10344),U_10341),c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool)))),U_10340)
            & hBOOL(hAPP(hAPP(c_member(U_10344),U_10341),U_10348))
            & hAPP(hAPP(U_10346,U_10349),U_10350) = hAPP(hAPP(U_10346,U_10341),U_10340) )
        | ( hAPP(hAPP(U_10346,U_10349),U_10350) = U_10347
          & U_10348 = c_Orderings_Obot__class_Obot(tc_fun(U_10344,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_10344,U_10345,U_10346,U_10347,U_10348,hAPP(hAPP(U_10346,U_10349),U_10350)) ) ),
    inference(variable_rename,[status(thm)],[f_2836_1]) ).

fof(f_2836_3,plain,
    ( ! [U_10364,U_10362,U_10360,U_10358,U_10356,U_10354,U_10352] :
        ( c_Nitpick_Ofold__graph_H(U_10352,U_10354,U_10356,U_10358,U_10360,hAPP(hAPP(U_10356,U_10362),U_10364))
        | ( ! [U_10343] :
              ( ! [U_10342] :
                  ( ~ c_Nitpick_Ofold__graph_H(U_10352,U_10354,U_10356,U_10358,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10352,tc_HOL_Obool)),U_10360),hAPP(hAPP(c_Set_Oinsert(U_10352),U_10343),c_Orderings_Obot__class_Obot(tc_fun(U_10352,tc_HOL_Obool)))),U_10342)
                  | hAPP(hAPP(U_10356,U_10362),U_10364) != hAPP(hAPP(U_10356,U_10343),U_10342) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_10352),U_10343),U_10360)) )
          & ( hAPP(hAPP(U_10356,U_10362),U_10364) != U_10358
            | U_10360 != c_Orderings_Obot__class_Obot(tc_fun(U_10352,tc_HOL_Obool)) ) ) )
    & ! [U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351] :
        ( ? [U_10341] :
            ( ? [U_10340] :
                ( c_Nitpick_Ofold__graph_H(U_10351,U_10353,U_10355,U_10357,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10351,tc_HOL_Obool)),U_10359),hAPP(hAPP(c_Set_Oinsert(U_10351),U_10341),c_Orderings_Obot__class_Obot(tc_fun(U_10351,tc_HOL_Obool)))),U_10340)
                & hAPP(hAPP(U_10355,U_10361),U_10363) = hAPP(hAPP(U_10355,U_10341),U_10340) )
            & hBOOL(hAPP(hAPP(c_member(U_10351),U_10341),U_10359)) )
        | ( hAPP(hAPP(U_10355,U_10361),U_10363) = U_10357
          & U_10359 = c_Orderings_Obot__class_Obot(tc_fun(U_10351,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_10351,U_10353,U_10355,U_10357,U_10359,hAPP(hAPP(U_10355,U_10361),U_10363)) ) ),
    inference(miniscope,[status(thm)],[f_2836_2]) ).

fof(f_2836_4,plain,
    ( ! [U_10364,U_10362,U_10360,U_10358,U_10356,U_10354,U_10352] :
        ( c_Nitpick_Ofold__graph_H(U_10352,U_10354,U_10356,U_10358,U_10360,hAPP(hAPP(U_10356,U_10362),U_10364))
        | ( ! [U_10343] :
              ( ! [U_10342] :
                  ( ~ c_Nitpick_Ofold__graph_H(U_10352,U_10354,U_10356,U_10358,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10352,tc_HOL_Obool)),U_10360),hAPP(hAPP(c_Set_Oinsert(U_10352),U_10343),c_Orderings_Obot__class_Obot(tc_fun(U_10352,tc_HOL_Obool)))),U_10342)
                  | hAPP(hAPP(U_10356,U_10362),U_10364) != hAPP(hAPP(U_10356,U_10343),U_10342) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_10352),U_10343),U_10360)) )
          & ( hAPP(hAPP(U_10356,U_10362),U_10364) != U_10358
            | U_10360 != c_Orderings_Obot__class_Obot(tc_fun(U_10352,tc_HOL_Obool)) ) ) )
    & ! [U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351] :
        ( ( ? [U_10340] :
              ( c_Nitpick_Ofold__graph_H(U_10351,U_10353,U_10355,U_10357,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10351,tc_HOL_Obool)),U_10359),hAPP(hAPP(c_Set_Oinsert(U_10351),sK170(U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351)),c_Orderings_Obot__class_Obot(tc_fun(U_10351,tc_HOL_Obool)))),U_10340)
              & hAPP(hAPP(U_10355,U_10361),U_10363) = hAPP(hAPP(U_10355,sK170(U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351)),U_10340) )
          & hBOOL(hAPP(hAPP(c_member(U_10351),sK170(U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351)),U_10359)) )
        | ( hAPP(hAPP(U_10355,U_10361),U_10363) = U_10357
          & U_10359 = c_Orderings_Obot__class_Obot(tc_fun(U_10351,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_10351,U_10353,U_10355,U_10357,U_10359,hAPP(hAPP(U_10355,U_10361),U_10363)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK170]),skolemize(U_10341,sK170(U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351))],[f_2836_3]) ).

fof(f_2836_5,plain,
    ( ! [U_10364,U_10362,U_10360,U_10358,U_10356,U_10354,U_10352] :
        ( c_Nitpick_Ofold__graph_H(U_10352,U_10354,U_10356,U_10358,U_10360,hAPP(hAPP(U_10356,U_10362),U_10364))
        | ( ! [U_10343] :
              ( ! [U_10342] :
                  ( ~ c_Nitpick_Ofold__graph_H(U_10352,U_10354,U_10356,U_10358,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10352,tc_HOL_Obool)),U_10360),hAPP(hAPP(c_Set_Oinsert(U_10352),U_10343),c_Orderings_Obot__class_Obot(tc_fun(U_10352,tc_HOL_Obool)))),U_10342)
                  | hAPP(hAPP(U_10356,U_10362),U_10364) != hAPP(hAPP(U_10356,U_10343),U_10342) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_10352),U_10343),U_10360)) )
          & ( hAPP(hAPP(U_10356,U_10362),U_10364) != U_10358
            | U_10360 != c_Orderings_Obot__class_Obot(tc_fun(U_10352,tc_HOL_Obool)) ) ) )
    & ! [U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351] :
        ( ( c_Nitpick_Ofold__graph_H(U_10351,U_10353,U_10355,U_10357,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10351,tc_HOL_Obool)),U_10359),hAPP(hAPP(c_Set_Oinsert(U_10351),sK170(U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351)),c_Orderings_Obot__class_Obot(tc_fun(U_10351,tc_HOL_Obool)))),sK171(U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351))
          & hAPP(hAPP(U_10355,U_10361),U_10363) = hAPP(hAPP(U_10355,sK170(U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351)),sK171(U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351))
          & hBOOL(hAPP(hAPP(c_member(U_10351),sK170(U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351)),U_10359)) )
        | ( hAPP(hAPP(U_10355,U_10361),U_10363) = U_10357
          & U_10359 = c_Orderings_Obot__class_Obot(tc_fun(U_10351,tc_HOL_Obool)) )
        | ~ c_Nitpick_Ofold__graph_H(U_10351,U_10353,U_10355,U_10357,U_10359,hAPP(hAPP(U_10355,U_10361),U_10363)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK171]),skolemize(U_10340,sK171(U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351))],[f_2836_4]) ).

fof(f_2836_6,plain,
    ( ! [U_10354,U_10358,U_10342,U_10343,U_10364,U_10360,U_10356,U_10352,U_10362] :
        ( ~ c_Nitpick_Ofold__graph_H(U_10352,U_10354,U_10356,U_10358,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10352,tc_HOL_Obool)),U_10360),hAPP(hAPP(c_Set_Oinsert(U_10352),U_10343),c_Orderings_Obot__class_Obot(tc_fun(U_10352,tc_HOL_Obool)))),U_10342)
        | hAPP(hAPP(U_10356,U_10362),U_10364) != hAPP(hAPP(U_10356,U_10343),U_10342)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10352),U_10343),U_10360))
        | ~ sP792(U_10354,U_10358,U_10342,U_10343,U_10364,U_10360,U_10356,U_10352,U_10362) )
    & ! [U_10354,U_10358,U_10342,U_10343,U_10364,U_10360,U_10356,U_10352,U_10362] :
        ( hAPP(hAPP(U_10356,U_10362),U_10364) != U_10358
        | U_10360 != c_Orderings_Obot__class_Obot(tc_fun(U_10352,tc_HOL_Obool))
        | ~ sP792(U_10354,U_10358,U_10342,U_10343,U_10364,U_10360,U_10356,U_10352,U_10362) )
    & ! [U_10355,U_10361,U_10353,U_10359,U_10351,U_10357,U_10363] :
        ( c_Nitpick_Ofold__graph_H(U_10351,U_10353,U_10355,U_10357,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10351,tc_HOL_Obool)),U_10359),hAPP(hAPP(c_Set_Oinsert(U_10351),sK170(U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351)),c_Orderings_Obot__class_Obot(tc_fun(U_10351,tc_HOL_Obool)))),sK171(U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351))
        | ~ sP791(U_10355,U_10361,U_10353,U_10359,U_10351,U_10357,U_10363) )
    & ! [U_10355,U_10361,U_10353,U_10359,U_10351,U_10357,U_10363] :
        ( hAPP(hAPP(U_10355,U_10361),U_10363) = hAPP(hAPP(U_10355,sK170(U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351)),sK171(U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351))
        | ~ sP791(U_10355,U_10361,U_10353,U_10359,U_10351,U_10357,U_10363) )
    & ! [U_10355,U_10361,U_10353,U_10359,U_10351,U_10357,U_10363] :
        ( hBOOL(hAPP(hAPP(c_member(U_10351),sK170(U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351)),U_10359))
        | ~ sP791(U_10355,U_10361,U_10353,U_10359,U_10351,U_10357,U_10363) )
    & ! [U_10355,U_10361,U_10359,U_10351,U_10357,U_10363] :
        ( hAPP(hAPP(U_10355,U_10361),U_10363) = U_10357
        | ~ sP790(U_10355,U_10361,U_10359,U_10351,U_10357,U_10363) )
    & ! [U_10355,U_10361,U_10359,U_10351,U_10357,U_10363] :
        ( U_10359 = c_Orderings_Obot__class_Obot(tc_fun(U_10351,tc_HOL_Obool))
        | ~ sP790(U_10355,U_10361,U_10359,U_10351,U_10357,U_10363) )
    & ! [U_10354,U_10358,U_10342,U_10343,U_10364,U_10360,U_10356,U_10352,U_10362] :
        ( c_Nitpick_Ofold__graph_H(U_10352,U_10354,U_10356,U_10358,U_10360,hAPP(hAPP(U_10356,U_10362),U_10364))
        | sP792(U_10354,U_10358,U_10342,U_10343,U_10364,U_10360,U_10356,U_10352,U_10362) )
    & ! [U_10355,U_10361,U_10353,U_10359,U_10351,U_10357,U_10363] :
        ( sP791(U_10355,U_10361,U_10353,U_10359,U_10351,U_10357,U_10363)
        | sP790(U_10355,U_10361,U_10359,U_10351,U_10357,U_10363)
        | ~ c_Nitpick_Ofold__graph_H(U_10351,U_10353,U_10355,U_10357,U_10359,hAPP(hAPP(U_10355,U_10361),U_10363)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP790,sP791,sP792])],[f_2836_5]) ).

cnf(f_2836_7,plain,
    ( sP791(U_10355,U_10361,U_10353,U_10359,U_10351,U_10357,U_10363)
    | sP790(U_10355,U_10361,U_10359,U_10351,U_10357,U_10363)
    | ~ c_Nitpick_Ofold__graph_H(U_10351,U_10353,U_10355,U_10357,U_10359,hAPP(hAPP(U_10355,U_10361),U_10363)) ),
    inference(clausify,[status(thm)],[f_2836_6]) ).

cnf(f_2836_8,plain,
    ( c_Nitpick_Ofold__graph_H(U_10352,U_10354,U_10356,U_10358,U_10360,hAPP(hAPP(U_10356,U_10362),U_10364))
    | sP792(U_10354,U_10358,U_10342,U_10343,U_10364,U_10360,U_10356,U_10352,U_10362) ),
    inference(clausify,[status(thm)],[f_2836_6]) ).

cnf(f_2836_9,plain,
    ( U_10359 = c_Orderings_Obot__class_Obot(tc_fun(U_10351,tc_HOL_Obool))
    | ~ sP790(U_10355,U_10361,U_10359,U_10351,U_10357,U_10363) ),
    inference(clausify,[status(thm)],[f_2836_6]) ).

cnf(f_2836_10,plain,
    ( hAPP(hAPP(U_10355,U_10361),U_10363) = U_10357
    | ~ sP790(U_10355,U_10361,U_10359,U_10351,U_10357,U_10363) ),
    inference(clausify,[status(thm)],[f_2836_6]) ).

cnf(f_2836_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10351),sK170(U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351)),U_10359))
    | ~ sP791(U_10355,U_10361,U_10353,U_10359,U_10351,U_10357,U_10363) ),
    inference(clausify,[status(thm)],[f_2836_6]) ).

cnf(f_2836_12,plain,
    ( hAPP(hAPP(U_10355,U_10361),U_10363) = hAPP(hAPP(U_10355,sK170(U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351)),sK171(U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351))
    | ~ sP791(U_10355,U_10361,U_10353,U_10359,U_10351,U_10357,U_10363) ),
    inference(clausify,[status(thm)],[f_2836_6]) ).

cnf(f_2836_13,plain,
    ( c_Nitpick_Ofold__graph_H(U_10351,U_10353,U_10355,U_10357,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10351,tc_HOL_Obool)),U_10359),hAPP(hAPP(c_Set_Oinsert(U_10351),sK170(U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351)),c_Orderings_Obot__class_Obot(tc_fun(U_10351,tc_HOL_Obool)))),sK171(U_10363,U_10361,U_10359,U_10357,U_10355,U_10353,U_10351))
    | ~ sP791(U_10355,U_10361,U_10353,U_10359,U_10351,U_10357,U_10363) ),
    inference(clausify,[status(thm)],[f_2836_6]) ).

cnf(f_2836_14,plain,
    ( hAPP(hAPP(U_10356,U_10362),U_10364) != U_10358
    | U_10360 != c_Orderings_Obot__class_Obot(tc_fun(U_10352,tc_HOL_Obool))
    | ~ sP792(U_10354,U_10358,U_10342,U_10343,U_10364,U_10360,U_10356,U_10352,U_10362) ),
    inference(clausify,[status(thm)],[f_2836_6]) ).

cnf(f_2836_15,plain,
    ( ~ c_Nitpick_Ofold__graph_H(U_10352,U_10354,U_10356,U_10358,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10352,tc_HOL_Obool)),U_10360),hAPP(hAPP(c_Set_Oinsert(U_10352),U_10343),c_Orderings_Obot__class_Obot(tc_fun(U_10352,tc_HOL_Obool)))),U_10342)
    | hAPP(hAPP(U_10356,U_10362),U_10364) != hAPP(hAPP(U_10356,U_10343),U_10342)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10352),U_10343),U_10360))
    | ~ sP792(U_10354,U_10358,U_10342,U_10343,U_10364,U_10360,U_10356,U_10352,U_10362) ),
    inference(clausify,[status(thm)],[f_2836_6]) ).

fof(f_2837_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_2837_2,plain,
    ! [U_10368,U_10367,U_10366,U_10365] :
      ( ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10365,U_10367)),c_Sum__Type_OPlus(U_10365,U_10367,U_10366,U_10368)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10367),U_10368))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_10365),U_10366)) ) )
      & ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10365,U_10367)),c_Sum__Type_OPlus(U_10365,U_10367,U_10366,U_10368)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10365),U_10366)),hAPP(c_Finite__Set_Ocard(U_10367),U_10368))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10367),U_10368))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10365),U_10366)) ) ),
    inference(variable_rename,[status(thm)],[f_2837_1]) ).

fof(f_2837_3,plain,
    ( ! [U_10376,U_10374,U_10372,U_10370] :
        ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10370,U_10374)),c_Sum__Type_OPlus(U_10370,U_10374,U_10372,U_10376)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10374),U_10376))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_10370),U_10372)) ) )
    & ! [U_10375,U_10373,U_10371,U_10369] :
        ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10369,U_10373)),c_Sum__Type_OPlus(U_10369,U_10373,U_10371,U_10375)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10369),U_10371)),hAPP(c_Finite__Set_Ocard(U_10373),U_10375))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10373),U_10375))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10369),U_10371)) ) ),
    inference(miniscope,[status(thm)],[f_2837_2]) ).

fof(f_2837_4,plain,
    ( ! [U_10370,U_10372,U_10374,U_10376] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10374),U_10376))
        | ~ sP793(U_10370,U_10372,U_10374,U_10376) )
    & ! [U_10370,U_10372,U_10374,U_10376] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10370),U_10372))
        | ~ sP793(U_10370,U_10372,U_10374,U_10376) )
    & ! [U_10370,U_10372,U_10374,U_10376] :
        ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10370,U_10374)),c_Sum__Type_OPlus(U_10370,U_10374,U_10372,U_10376)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP793(U_10370,U_10372,U_10374,U_10376) )
    & ! [U_10369,U_10371,U_10373,U_10375] :
        ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10369,U_10373)),c_Sum__Type_OPlus(U_10369,U_10373,U_10371,U_10375)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10369),U_10371)),hAPP(c_Finite__Set_Ocard(U_10373),U_10375))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10373),U_10375))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10369),U_10371)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP793])],[f_2837_3]) ).

cnf(f_2837_5,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10369,U_10373)),c_Sum__Type_OPlus(U_10369,U_10373,U_10371,U_10375)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10369),U_10371)),hAPP(c_Finite__Set_Ocard(U_10373),U_10375))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10373),U_10375))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10369),U_10371)) ),
    inference(clausify,[status(thm)],[f_2837_4]) ).

cnf(f_2837_6,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10370,U_10374)),c_Sum__Type_OPlus(U_10370,U_10374,U_10372,U_10376)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP793(U_10370,U_10372,U_10374,U_10376) ),
    inference(clausify,[status(thm)],[f_2837_4]) ).

cnf(f_2837_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10370),U_10372))
    | ~ sP793(U_10370,U_10372,U_10374,U_10376) ),
    inference(clausify,[status(thm)],[f_2837_4]) ).

cnf(f_2837_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10374),U_10376))
    | ~ sP793(U_10370,U_10372,U_10374,U_10376) ),
    inference(clausify,[status(thm)],[f_2837_4]) ).

fof(f_2838_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_2838_2,plain,
    ! [U_10380,U_10379,U_10378,U_10377] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10377,U_10378)),c_Sum__Type_OPlus(U_10377,U_10378,U_10379,U_10380)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10378),U_10380))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10377),U_10379)) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10378),U_10380))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_10377),U_10379)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10377,U_10378)),c_Sum__Type_OPlus(U_10377,U_10378,U_10379,U_10380))) ) ),
    inference(variable_rename,[status(thm)],[f_2838_1]) ).

fof(f_2838_3,plain,
    ( ! [U_10388,U_10386,U_10384,U_10382] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10382,U_10384)),c_Sum__Type_OPlus(U_10382,U_10384,U_10386,U_10388)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10384),U_10388))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10382),U_10386)) )
    & ! [U_10387,U_10385,U_10383,U_10381] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10383),U_10387))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_10381),U_10385)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10381,U_10383)),c_Sum__Type_OPlus(U_10381,U_10383,U_10385,U_10387))) ) ),
    inference(miniscope,[status(thm)],[f_2838_2]) ).

fof(f_2838_4,plain,
    ( ! [U_10381,U_10383,U_10387,U_10385] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10383),U_10387))
        | ~ sP794(U_10381,U_10383,U_10387,U_10385) )
    & ! [U_10381,U_10383,U_10387,U_10385] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10381),U_10385))
        | ~ sP794(U_10381,U_10383,U_10387,U_10385) )
    & ! [U_10384,U_10382,U_10388,U_10386] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10382,U_10384)),c_Sum__Type_OPlus(U_10382,U_10384,U_10386,U_10388)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10384),U_10388))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10382),U_10386)) )
    & ! [U_10381,U_10383,U_10387,U_10385] :
        ( sP794(U_10381,U_10383,U_10387,U_10385)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10381,U_10383)),c_Sum__Type_OPlus(U_10381,U_10383,U_10385,U_10387))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP794])],[f_2838_3]) ).

cnf(f_2838_5,plain,
    ( sP794(U_10381,U_10383,U_10387,U_10385)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10381,U_10383)),c_Sum__Type_OPlus(U_10381,U_10383,U_10385,U_10387))) ),
    inference(clausify,[status(thm)],[f_2838_4]) ).

cnf(f_2838_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10382,U_10384)),c_Sum__Type_OPlus(U_10382,U_10384,U_10386,U_10388)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10384),U_10388))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10382),U_10386)) ),
    inference(clausify,[status(thm)],[f_2838_4]) ).

cnf(f_2838_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10381),U_10385))
    | ~ sP794(U_10381,U_10383,U_10387,U_10385) ),
    inference(clausify,[status(thm)],[f_2838_4]) ).

cnf(f_2838_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10383),U_10387))
    | ~ sP794(U_10381,U_10383,U_10387,U_10385) ),
    inference(clausify,[status(thm)],[f_2838_4]) ).

fof(f_2839_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_2839_2,plain,
    ! [U_10392,U_10391,U_10390,U_10389] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10389,U_10391)),c_Sum__Type_OPlus(U_10389,U_10391,U_10390,U_10392)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10391),U_10392))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10389),U_10390)) ),
    inference(variable_rename,[status(thm)],[f_2839_1]) ).

fof(f_2839_3,plain,
    ! [U_10390,U_10389,U_10392,U_10391] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10389,U_10391)),c_Sum__Type_OPlus(U_10389,U_10391,U_10390,U_10392)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10391),U_10392))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10389),U_10390)) ),
    inference(definitional_conversion,[status(esa)],[f_2839_2]) ).

cnf(f_2839_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10389,U_10391)),c_Sum__Type_OPlus(U_10389,U_10391,U_10390,U_10392)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10391),U_10392))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10389),U_10390)) ),
    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_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_2840_2,plain,
    ! [U_10396,U_10395,U_10394,U_10393] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10393),U_10395))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10393,U_10394)),c_Sum__Type_OPlus(U_10393,U_10394,U_10395,U_10396))) ),
    inference(variable_rename,[status(thm)],[f_2840_1]) ).

fof(f_2840_3,plain,
    ! [U_10394,U_10393,U_10395,U_10396] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10393),U_10395))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10393,U_10394)),c_Sum__Type_OPlus(U_10393,U_10394,U_10395,U_10396))) ),
    inference(definitional_conversion,[status(esa)],[f_2840_2]) ).

cnf(f_2840_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10393),U_10395))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10393,U_10394)),c_Sum__Type_OPlus(U_10393,U_10394,U_10395,U_10396))) ),
    inference(clausify,[status(thm)],[f_2840_3]) ).

fof(f_2841_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_2841_2,plain,
    ! [U_10400,U_10399,U_10398,U_10397] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10398),U_10400))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10397,U_10398)),c_Sum__Type_OPlus(U_10397,U_10398,U_10399,U_10400))) ),
    inference(variable_rename,[status(thm)],[f_2841_1]) ).

fof(f_2841_3,plain,
    ! [U_10400,U_10399,U_10398] :
      ( ! [U_10397] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10397,U_10398)),c_Sum__Type_OPlus(U_10397,U_10398,U_10399,U_10400)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10398),U_10400)) ),
    inference(miniscope,[status(thm)],[f_2841_2]) ).

fof(f_2841_4,plain,
    ! [U_10397,U_10398,U_10399,U_10400] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10397,U_10398)),c_Sum__Type_OPlus(U_10397,U_10398,U_10399,U_10400)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10398),U_10400)) ),
    inference(definitional_conversion,[status(esa)],[f_2841_3]) ).

cnf(f_2841_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_10397,U_10398)),c_Sum__Type_OPlus(U_10397,U_10398,U_10399,U_10400)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10398),U_10400)) ),
    inference(clausify,[status(thm)],[f_2841_4]) ).

fof(f_2842_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_2842_2,plain,
    ! [U_10404,U_10403,U_10402,U_10401] :
      ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10401,U_10403)),c_Sum__Type_OPlus(U_10401,U_10403,U_10402,U_10404)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10401),U_10402)),hAPP(c_Finite__Set_Ocard(U_10403),U_10404))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10403),U_10404))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10401),U_10402)) ),
    inference(variable_rename,[status(thm)],[f_2842_1]) ).

fof(f_2842_3,plain,
    ! [U_10401,U_10402,U_10403,U_10404] :
      ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10401,U_10403)),c_Sum__Type_OPlus(U_10401,U_10403,U_10402,U_10404)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10401),U_10402)),hAPP(c_Finite__Set_Ocard(U_10403),U_10404))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10403),U_10404))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10401),U_10402)) ),
    inference(definitional_conversion,[status(esa)],[f_2842_2]) ).

cnf(f_2842_4,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_sum(U_10401,U_10403)),c_Sum__Type_OPlus(U_10401,U_10403,U_10402,U_10404)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10401),U_10402)),hAPP(c_Finite__Set_Ocard(U_10403),U_10404))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10403),U_10404))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10401),U_10402)) ),
    inference(clausify,[status(thm)],[f_2842_3]) ).

fof(f_2843_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_2843_2,plain,
    ! [U_10408,U_10407,U_10406,U_10405] :
      ( ( c_Sum__Type_OPlus(U_10405,U_10406,U_10407,U_10408) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10405,U_10406),tc_HOL_Obool))
        | U_10408 != c_Orderings_Obot__class_Obot(tc_fun(U_10406,tc_HOL_Obool))
        | U_10407 != c_Orderings_Obot__class_Obot(tc_fun(U_10405,tc_HOL_Obool)) )
      & ( ( U_10408 = c_Orderings_Obot__class_Obot(tc_fun(U_10406,tc_HOL_Obool))
          & U_10407 = c_Orderings_Obot__class_Obot(tc_fun(U_10405,tc_HOL_Obool)) )
        | c_Sum__Type_OPlus(U_10405,U_10406,U_10407,U_10408) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10405,U_10406),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2843_1]) ).

fof(f_2843_3,plain,
    ( ! [U_10416,U_10414,U_10412,U_10410] :
        ( c_Sum__Type_OPlus(U_10410,U_10412,U_10414,U_10416) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10410,U_10412),tc_HOL_Obool))
        | U_10416 != c_Orderings_Obot__class_Obot(tc_fun(U_10412,tc_HOL_Obool))
        | U_10414 != c_Orderings_Obot__class_Obot(tc_fun(U_10410,tc_HOL_Obool)) )
    & ! [U_10415,U_10413,U_10411,U_10409] :
        ( ( U_10415 = c_Orderings_Obot__class_Obot(tc_fun(U_10411,tc_HOL_Obool))
          & U_10413 = c_Orderings_Obot__class_Obot(tc_fun(U_10409,tc_HOL_Obool)) )
        | c_Sum__Type_OPlus(U_10409,U_10411,U_10413,U_10415) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10409,U_10411),tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2843_2]) ).

fof(f_2843_4,plain,
    ( ! [U_10411,U_10413,U_10415,U_10409] :
        ( U_10415 = c_Orderings_Obot__class_Obot(tc_fun(U_10411,tc_HOL_Obool))
        | ~ sP795(U_10411,U_10413,U_10415,U_10409) )
    & ! [U_10411,U_10413,U_10415,U_10409] :
        ( U_10413 = c_Orderings_Obot__class_Obot(tc_fun(U_10409,tc_HOL_Obool))
        | ~ sP795(U_10411,U_10413,U_10415,U_10409) )
    & ! [U_10414,U_10416,U_10410,U_10412] :
        ( c_Sum__Type_OPlus(U_10410,U_10412,U_10414,U_10416) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10410,U_10412),tc_HOL_Obool))
        | U_10416 != c_Orderings_Obot__class_Obot(tc_fun(U_10412,tc_HOL_Obool))
        | U_10414 != c_Orderings_Obot__class_Obot(tc_fun(U_10410,tc_HOL_Obool)) )
    & ! [U_10411,U_10413,U_10415,U_10409] :
        ( sP795(U_10411,U_10413,U_10415,U_10409)
        | c_Sum__Type_OPlus(U_10409,U_10411,U_10413,U_10415) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10409,U_10411),tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP795])],[f_2843_3]) ).

cnf(f_2843_5,plain,
    ( sP795(U_10411,U_10413,U_10415,U_10409)
    | c_Sum__Type_OPlus(U_10409,U_10411,U_10413,U_10415) != c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10409,U_10411),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2843_4]) ).

cnf(f_2843_6,plain,
    ( c_Sum__Type_OPlus(U_10410,U_10412,U_10414,U_10416) = c_Orderings_Obot__class_Obot(tc_fun(tc_sum(U_10410,U_10412),tc_HOL_Obool))
    | U_10416 != c_Orderings_Obot__class_Obot(tc_fun(U_10412,tc_HOL_Obool))
    | U_10414 != c_Orderings_Obot__class_Obot(tc_fun(U_10410,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2843_4]) ).

cnf(f_2843_7,plain,
    ( U_10413 = c_Orderings_Obot__class_Obot(tc_fun(U_10409,tc_HOL_Obool))
    | ~ sP795(U_10411,U_10413,U_10415,U_10409) ),
    inference(clausify,[status(thm)],[f_2843_4]) ).

cnf(f_2843_8,plain,
    ( U_10415 = c_Orderings_Obot__class_Obot(tc_fun(U_10411,tc_HOL_Obool))
    | ~ sP795(U_10411,U_10413,U_10415,U_10409) ),
    inference(clausify,[status(thm)],[f_2843_4]) ).

fof(f_2844_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_2844_2,plain,
    ! [U_10422,U_10421,U_10420,U_10419] :
      ( hBOOL(hAPP(hAPP(c_member(U_10419),hAPP(U_10421,U_10422)),U_10422))
      | ? [U_10418,U_10417] : ~ hBOOL(hAPP(hAPP(c_member(U_10419),hAPP(hAPP(U_10420,U_10418),U_10417)),hAPP(hAPP(c_Set_Oinsert(U_10419),U_10418),hAPP(hAPP(c_Set_Oinsert(U_10419),U_10417),c_Orderings_Obot__class_Obot(tc_fun(U_10419,tc_HOL_Obool))))))
      | U_10422 = c_Orderings_Obot__class_Obot(tc_fun(U_10419,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10419),U_10422))
      | ~ c_Finite__Set_Ofolding__one(U_10419,U_10420,U_10421) ),
    inference(variable_rename,[status(thm)],[f_2844_1]) ).

fof(f_2844_3,plain,
    ! [U_10422,U_10421,U_10420,U_10419] :
      ( hBOOL(hAPP(hAPP(c_member(U_10419),hAPP(U_10421,U_10422)),U_10422))
      | ? [U_10417] : ~ hBOOL(hAPP(hAPP(c_member(U_10419),hAPP(hAPP(U_10420,sK172(U_10422,U_10421,U_10420,U_10419)),U_10417)),hAPP(hAPP(c_Set_Oinsert(U_10419),sK172(U_10422,U_10421,U_10420,U_10419)),hAPP(hAPP(c_Set_Oinsert(U_10419),U_10417),c_Orderings_Obot__class_Obot(tc_fun(U_10419,tc_HOL_Obool))))))
      | U_10422 = c_Orderings_Obot__class_Obot(tc_fun(U_10419,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10419),U_10422))
      | ~ c_Finite__Set_Ofolding__one(U_10419,U_10420,U_10421) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK172]),skolemize(U_10418,sK172(U_10422,U_10421,U_10420,U_10419))],[f_2844_2]) ).

fof(f_2844_4,plain,
    ! [U_10422,U_10421,U_10420,U_10419] :
      ( hBOOL(hAPP(hAPP(c_member(U_10419),hAPP(U_10421,U_10422)),U_10422))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10419),hAPP(hAPP(U_10420,sK172(U_10422,U_10421,U_10420,U_10419)),sK173(U_10422,U_10421,U_10420,U_10419))),hAPP(hAPP(c_Set_Oinsert(U_10419),sK172(U_10422,U_10421,U_10420,U_10419)),hAPP(hAPP(c_Set_Oinsert(U_10419),sK173(U_10422,U_10421,U_10420,U_10419)),c_Orderings_Obot__class_Obot(tc_fun(U_10419,tc_HOL_Obool))))))
      | U_10422 = c_Orderings_Obot__class_Obot(tc_fun(U_10419,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10419),U_10422))
      | ~ c_Finite__Set_Ofolding__one(U_10419,U_10420,U_10421) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK173]),skolemize(U_10417,sK173(U_10422,U_10421,U_10420,U_10419))],[f_2844_3]) ).

fof(f_2844_5,plain,
    ! [U_10419,U_10420,U_10421,U_10422] :
      ( hBOOL(hAPP(hAPP(c_member(U_10419),hAPP(U_10421,U_10422)),U_10422))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10419),hAPP(hAPP(U_10420,sK172(U_10422,U_10421,U_10420,U_10419)),sK173(U_10422,U_10421,U_10420,U_10419))),hAPP(hAPP(c_Set_Oinsert(U_10419),sK172(U_10422,U_10421,U_10420,U_10419)),hAPP(hAPP(c_Set_Oinsert(U_10419),sK173(U_10422,U_10421,U_10420,U_10419)),c_Orderings_Obot__class_Obot(tc_fun(U_10419,tc_HOL_Obool))))))
      | U_10422 = c_Orderings_Obot__class_Obot(tc_fun(U_10419,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10419),U_10422))
      | ~ c_Finite__Set_Ofolding__one(U_10419,U_10420,U_10421) ),
    inference(definitional_conversion,[status(esa)],[f_2844_4]) ).

cnf(f_2844_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10419),hAPP(U_10421,U_10422)),U_10422))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10419),hAPP(hAPP(U_10420,sK172(U_10422,U_10421,U_10420,U_10419)),sK173(U_10422,U_10421,U_10420,U_10419))),hAPP(hAPP(c_Set_Oinsert(U_10419),sK172(U_10422,U_10421,U_10420,U_10419)),hAPP(hAPP(c_Set_Oinsert(U_10419),sK173(U_10422,U_10421,U_10420,U_10419)),c_Orderings_Obot__class_Obot(tc_fun(U_10419,tc_HOL_Obool))))))
    | U_10422 = c_Orderings_Obot__class_Obot(tc_fun(U_10419,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10419),U_10422))
    | ~ c_Finite__Set_Ofolding__one(U_10419,U_10420,U_10421) ),
    inference(clausify,[status(thm)],[f_2844_5]) ).

fof(f_2845_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_2845_2,plain,
    ! [U_10428,U_10427,U_10426,U_10425,U_10424,U_10423] :
      ( ( hAPP(c_Set_Oimage(U_10423,U_10426,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10423,U_10426),U_10427),U_10424),U_10428)),U_10425) = hAPP(c_Set_Oimage(U_10423,U_10426,U_10427),U_10425)
        | hBOOL(hAPP(hAPP(c_member(U_10423),U_10424),U_10425)) )
      & ( hAPP(c_Set_Oimage(U_10423,U_10426,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10423,U_10426),U_10427),U_10424),U_10428)),U_10425) = hAPP(hAPP(c_Set_Oinsert(U_10426),U_10428),hAPP(c_Set_Oimage(U_10423,U_10426,U_10427),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10423,tc_HOL_Obool)),U_10425),hAPP(hAPP(c_Set_Oinsert(U_10423),U_10424),c_Orderings_Obot__class_Obot(tc_fun(U_10423,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10423),U_10424),U_10425)) ) ),
    inference(variable_rename,[status(thm)],[f_2845_1]) ).

fof(f_2845_3,plain,
    ( ! [U_10440,U_10438,U_10436,U_10434,U_10432,U_10430] :
        ( hAPP(c_Set_Oimage(U_10430,U_10436,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10430,U_10436),U_10438),U_10432),U_10440)),U_10434) = hAPP(c_Set_Oimage(U_10430,U_10436,U_10438),U_10434)
        | hBOOL(hAPP(hAPP(c_member(U_10430),U_10432),U_10434)) )
    & ! [U_10439,U_10437,U_10435,U_10433,U_10431,U_10429] :
        ( hAPP(c_Set_Oimage(U_10429,U_10435,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10429,U_10435),U_10437),U_10431),U_10439)),U_10433) = hAPP(hAPP(c_Set_Oinsert(U_10435),U_10439),hAPP(c_Set_Oimage(U_10429,U_10435,U_10437),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10429,tc_HOL_Obool)),U_10433),hAPP(hAPP(c_Set_Oinsert(U_10429),U_10431),c_Orderings_Obot__class_Obot(tc_fun(U_10429,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10429),U_10431),U_10433)) ) ),
    inference(miniscope,[status(thm)],[f_2845_2]) ).

fof(f_2845_4,plain,
    ( ! [U_10430,U_10432,U_10434,U_10436,U_10438,U_10440] :
        ( hAPP(c_Set_Oimage(U_10430,U_10436,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10430,U_10436),U_10438),U_10432),U_10440)),U_10434) = hAPP(c_Set_Oimage(U_10430,U_10436,U_10438),U_10434)
        | hBOOL(hAPP(hAPP(c_member(U_10430),U_10432),U_10434)) )
    & ! [U_10435,U_10431,U_10429,U_10437,U_10433,U_10439] :
        ( hAPP(c_Set_Oimage(U_10429,U_10435,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10429,U_10435),U_10437),U_10431),U_10439)),U_10433) = hAPP(hAPP(c_Set_Oinsert(U_10435),U_10439),hAPP(c_Set_Oimage(U_10429,U_10435,U_10437),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10429,tc_HOL_Obool)),U_10433),hAPP(hAPP(c_Set_Oinsert(U_10429),U_10431),c_Orderings_Obot__class_Obot(tc_fun(U_10429,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10429),U_10431),U_10433)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2845_3]) ).

cnf(f_2845_5,plain,
    ( hAPP(c_Set_Oimage(U_10429,U_10435,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10429,U_10435),U_10437),U_10431),U_10439)),U_10433) = hAPP(hAPP(c_Set_Oinsert(U_10435),U_10439),hAPP(c_Set_Oimage(U_10429,U_10435,U_10437),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10429,tc_HOL_Obool)),U_10433),hAPP(hAPP(c_Set_Oinsert(U_10429),U_10431),c_Orderings_Obot__class_Obot(tc_fun(U_10429,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10429),U_10431),U_10433)) ),
    inference(clausify,[status(thm)],[f_2845_4]) ).

cnf(f_2845_6,plain,
    ( hAPP(c_Set_Oimage(U_10430,U_10436,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10430,U_10436),U_10438),U_10432),U_10440)),U_10434) = hAPP(c_Set_Oimage(U_10430,U_10436,U_10438),U_10434)
    | hBOOL(hAPP(hAPP(c_member(U_10430),U_10432),U_10434)) ),
    inference(clausify,[status(thm)],[f_2845_4]) ).

fof(f_2846_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_2846_2,plain,
    ! [U_10444,U_10443,U_10442,U_10441] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10441,U_10442),U_10443),U_10444),hAPP(U_10443,U_10444)) = U_10443,
    inference(variable_rename,[status(thm)],[f_2846_1]) ).

fof(f_2846_3,plain,
    ! [U_10441,U_10442,U_10443,U_10444] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10441,U_10442),U_10443),U_10444),hAPP(U_10443,U_10444)) = U_10443,
    inference(definitional_conversion,[status(esa)],[f_2846_2]) ).

cnf(f_2846_4,plain,
    hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10441,U_10442),U_10443),U_10444),hAPP(U_10443,U_10444)) = U_10443,
    inference(clausify,[status(thm)],[f_2846_3]) ).

fof(f_2847_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_2847_2,plain,
    ! [U_10450,U_10449,U_10448,U_10447,U_10446,U_10445] :
      ( ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10447,U_10448),U_10449),U_10446),U_10450),U_10445) = hAPP(U_10449,U_10445)
        | U_10445 = U_10446 )
      & ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10447,U_10448),U_10449),U_10446),U_10450),U_10445) = U_10450
        | U_10445 != U_10446 ) ),
    inference(variable_rename,[status(thm)],[f_2847_1]) ).

fof(f_2847_3,plain,
    ( ! [U_10462,U_10460,U_10458,U_10456,U_10454,U_10452] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10456,U_10458),U_10460),U_10454),U_10462),U_10452) = hAPP(U_10460,U_10452)
        | U_10452 = U_10454 )
    & ! [U_10461,U_10459,U_10457,U_10455,U_10453,U_10451] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10455,U_10457),U_10459),U_10453),U_10461),U_10451) = U_10461
        | U_10451 != U_10453 ) ),
    inference(miniscope,[status(thm)],[f_2847_2]) ).

fof(f_2847_4,plain,
    ( ! [U_10452,U_10454,U_10456,U_10458,U_10460,U_10462] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10456,U_10458),U_10460),U_10454),U_10462),U_10452) = hAPP(U_10460,U_10452)
        | U_10452 = U_10454 )
    & ! [U_10457,U_10453,U_10451,U_10455,U_10459,U_10461] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10455,U_10457),U_10459),U_10453),U_10461),U_10451) = U_10461
        | U_10451 != U_10453 ) ),
    inference(definitional_conversion,[status(esa)],[f_2847_3]) ).

cnf(f_2847_5,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10455,U_10457),U_10459),U_10453),U_10461),U_10451) = U_10461
    | U_10451 != U_10453 ),
    inference(clausify,[status(thm)],[f_2847_4]) ).

cnf(f_2847_6,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10456,U_10458),U_10460),U_10454),U_10462),U_10452) = hAPP(U_10460,U_10452)
    | U_10452 = U_10454 ),
    inference(clausify,[status(thm)],[f_2847_4]) ).

fof(f_2848_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_2848_2,plain,
    ! [U_10467,U_10466,U_10465,U_10464,U_10463] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10466,U_10467),U_10463),U_10464),U_10465) = U_10463
      | hAPP(U_10463,U_10464) != U_10465 ),
    inference(variable_rename,[status(thm)],[f_2848_1]) ).

fof(f_2848_3,plain,
    ! [U_10463,U_10464,U_10465,U_10466,U_10467] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10466,U_10467),U_10463),U_10464),U_10465) = U_10463
      | hAPP(U_10463,U_10464) != U_10465 ),
    inference(definitional_conversion,[status(esa)],[f_2848_2]) ).

cnf(f_2848_4,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10466,U_10467),U_10463),U_10464),U_10465) = U_10463
    | hAPP(U_10463,U_10464) != U_10465 ),
    inference(clausify,[status(thm)],[f_2848_3]) ).

fof(f_2849_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_2849_2,plain,
    ! [U_10473,U_10472,U_10471,U_10470,U_10469,U_10468] :
      ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10470,U_10471),U_10472),U_10469),U_10473),U_10468) = hAPP(U_10472,U_10468)
      | U_10468 = U_10469 ),
    inference(variable_rename,[status(thm)],[f_2849_1]) ).

fof(f_2849_3,plain,
    ! [U_10469,U_10468,U_10470,U_10471,U_10472,U_10473] :
      ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10470,U_10471),U_10472),U_10469),U_10473),U_10468) = hAPP(U_10472,U_10468)
      | U_10468 = U_10469 ),
    inference(definitional_conversion,[status(esa)],[f_2849_2]) ).

cnf(f_2849_4,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10470,U_10471),U_10472),U_10469),U_10473),U_10468) = hAPP(U_10472,U_10468)
    | U_10468 = U_10469 ),
    inference(clausify,[status(thm)],[f_2849_3]) ).

fof(f_2850_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_2850_2,plain,
    ! [U_10480,U_10479,U_10478,U_10477,U_10476,U_10475,U_10474] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10476,U_10477),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10476,U_10477),U_10478),U_10474),U_10479)),U_10475),U_10480) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10476,U_10477),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10476,U_10477),U_10478),U_10475),U_10480)),U_10474),U_10479)
      | U_10474 = U_10475 ),
    inference(variable_rename,[status(thm)],[f_2850_1]) ).

fof(f_2850_3,plain,
    ! [U_10474,U_10475,U_10476,U_10477,U_10478,U_10479,U_10480] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10476,U_10477),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10476,U_10477),U_10478),U_10474),U_10479)),U_10475),U_10480) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10476,U_10477),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10476,U_10477),U_10478),U_10475),U_10480)),U_10474),U_10479)
      | U_10474 = U_10475 ),
    inference(definitional_conversion,[status(esa)],[f_2850_2]) ).

cnf(f_2850_4,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10476,U_10477),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10476,U_10477),U_10478),U_10474),U_10479)),U_10475),U_10480) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10476,U_10477),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10476,U_10477),U_10478),U_10475),U_10480)),U_10474),U_10479)
    | U_10474 = U_10475 ),
    inference(clausify,[status(thm)],[f_2850_3]) ).

fof(f_2851_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_2851_2,plain,
    ! [U_10486,U_10485,U_10484,U_10483,U_10482,U_10481] :
      ( ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10483,U_10484),U_10485),U_10482),U_10486),U_10481) = hAPP(U_10485,U_10481)
        | U_10481 = U_10482 )
      & ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10483,U_10484),U_10485),U_10482),U_10486),U_10481) = U_10486
        | U_10481 != U_10482 ) ),
    inference(variable_rename,[status(thm)],[f_2851_1]) ).

fof(f_2851_3,plain,
    ( ! [U_10498,U_10496,U_10494,U_10492,U_10490,U_10488] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10492,U_10494),U_10496),U_10490),U_10498),U_10488) = hAPP(U_10496,U_10488)
        | U_10488 = U_10490 )
    & ! [U_10497,U_10495,U_10493,U_10491,U_10489,U_10487] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10491,U_10493),U_10495),U_10489),U_10497),U_10487) = U_10497
        | U_10487 != U_10489 ) ),
    inference(miniscope,[status(thm)],[f_2851_2]) ).

fof(f_2851_4,plain,
    ( ! [U_10488,U_10490,U_10492,U_10494,U_10496,U_10498] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10492,U_10494),U_10496),U_10490),U_10498),U_10488) = hAPP(U_10496,U_10488)
        | U_10488 = U_10490 )
    & ! [U_10493,U_10491,U_10487,U_10489,U_10495,U_10497] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10491,U_10493),U_10495),U_10489),U_10497),U_10487) = U_10497
        | U_10487 != U_10489 ) ),
    inference(definitional_conversion,[status(esa)],[f_2851_3]) ).

cnf(f_2851_5,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10491,U_10493),U_10495),U_10489),U_10497),U_10487) = U_10497
    | U_10487 != U_10489 ),
    inference(clausify,[status(thm)],[f_2851_4]) ).

cnf(f_2851_6,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10492,U_10494),U_10496),U_10490),U_10498),U_10488) = hAPP(U_10496,U_10488)
    | U_10488 = U_10490 ),
    inference(clausify,[status(thm)],[f_2851_4]) ).

fof(f_2852_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_2852_2,plain,
    ! [U_10503,U_10502,U_10501,U_10500,U_10499] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10499,U_10500),U_10501),U_10502),U_10503),U_10502) = U_10503,
    inference(variable_rename,[status(thm)],[f_2852_1]) ).

fof(f_2852_3,plain,
    ! [U_10499,U_10500,U_10501,U_10502,U_10503] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10499,U_10500),U_10501),U_10502),U_10503),U_10502) = U_10503,
    inference(definitional_conversion,[status(esa)],[f_2852_2]) ).

cnf(f_2852_4,plain,
    hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10499,U_10500),U_10501),U_10502),U_10503),U_10502) = U_10503,
    inference(clausify,[status(thm)],[f_2852_3]) ).

fof(f_2853_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_2853_2,plain,
    ! [U_10509,U_10508,U_10507,U_10506,U_10505,U_10504] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10504,U_10505),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10504,U_10505),U_10506),U_10507),U_10508)),U_10507),U_10509) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10504,U_10505),U_10506),U_10507),U_10509),
    inference(variable_rename,[status(thm)],[f_2853_1]) ).

fof(f_2853_3,plain,
    ! [U_10504,U_10505,U_10506,U_10507,U_10508,U_10509] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10504,U_10505),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10504,U_10505),U_10506),U_10507),U_10508)),U_10507),U_10509) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10504,U_10505),U_10506),U_10507),U_10509),
    inference(definitional_conversion,[status(esa)],[f_2853_2]) ).

cnf(f_2853_4,plain,
    hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10504,U_10505),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10504,U_10505),U_10506),U_10507),U_10508)),U_10507),U_10509) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10504,U_10505),U_10506),U_10507),U_10509),
    inference(clausify,[status(thm)],[f_2853_3]) ).

fof(f_2854_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_2854_2,plain,
    ! [U_10514,U_10513,U_10512,U_10511,U_10510] :
      ( ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10510,U_10511),U_10512),U_10513),U_10514) = U_10512
        | hAPP(U_10512,U_10513) != U_10514 )
      & ( hAPP(U_10512,U_10513) = U_10514
        | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10510,U_10511),U_10512),U_10513),U_10514) != U_10512 ) ),
    inference(variable_rename,[status(thm)],[f_2854_1]) ).

fof(f_2854_3,plain,
    ( ! [U_10524,U_10522,U_10520] :
        ( ! [U_10518,U_10516] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10516,U_10518),U_10520),U_10522),U_10524) = U_10520
        | hAPP(U_10520,U_10522) != U_10524 )
    & ! [U_10523,U_10521,U_10519] :
        ( ! [U_10517,U_10515] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10515,U_10517),U_10519),U_10521),U_10523) != U_10519
        | hAPP(U_10519,U_10521) = U_10523 ) ),
    inference(miniscope,[status(thm)],[f_2854_2]) ).

fof(f_2854_4,plain,
    ( ! [U_10524,U_10516,U_10518,U_10520,U_10522] :
        ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10516,U_10518),U_10520),U_10522),U_10524) = U_10520
        | hAPP(U_10520,U_10522) != U_10524 )
    & ! [U_10519,U_10523,U_10517,U_10515,U_10521] :
        ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10515,U_10517),U_10519),U_10521),U_10523) != U_10519
        | hAPP(U_10519,U_10521) = U_10523 ) ),
    inference(definitional_conversion,[status(esa)],[f_2854_3]) ).

cnf(f_2854_5,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10515,U_10517),U_10519),U_10521),U_10523) != U_10519
    | hAPP(U_10519,U_10521) = U_10523 ),
    inference(clausify,[status(thm)],[f_2854_4]) ).

cnf(f_2854_6,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10516,U_10518),U_10520),U_10522),U_10524) = U_10520
    | hAPP(U_10520,U_10522) != U_10524 ),
    inference(clausify,[status(thm)],[f_2854_4]) ).

fof(f_2855_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_2855_2,plain,
    ! [U_10529,U_10528,U_10527,U_10526,U_10525] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10525,tc_Option_Ooption(U_10526)),U_10527),U_10528),hAPP(c_Option_Ooption_OSome(U_10526),U_10529)) != hAPP(c_COMBK(tc_Option_Ooption(U_10526),U_10525),c_Option_Ooption_ONone(U_10526)),
    inference(variable_rename,[status(thm)],[f_2855_1]) ).

fof(f_2855_3,plain,
    ! [U_10525,U_10526,U_10527,U_10528,U_10529] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10525,tc_Option_Ooption(U_10526)),U_10527),U_10528),hAPP(c_Option_Ooption_OSome(U_10526),U_10529)) != hAPP(c_COMBK(tc_Option_Ooption(U_10526),U_10525),c_Option_Ooption_ONone(U_10526)),
    inference(definitional_conversion,[status(esa)],[f_2855_2]) ).

cnf(f_2855_4,plain,
    hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10525,tc_Option_Ooption(U_10526)),U_10527),U_10528),hAPP(c_Option_Ooption_OSome(U_10526),U_10529)) != hAPP(c_COMBK(tc_Option_Ooption(U_10526),U_10525),c_Option_Ooption_ONone(U_10526)),
    inference(clausify,[status(thm)],[f_2855_3]) ).

fof(f_2856_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_2856_2,plain,
    ! [U_10535,U_10534,U_10533,U_10532,U_10531,U_10530] :
      ( hAPP(c_Set_Oimage(U_10530,tc_Option_Ooption(U_10533),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10530,tc_Option_Ooption(U_10533)),U_10534),U_10531),hAPP(c_Option_Ooption_OSome(U_10533),U_10535))),U_10532) = hAPP(c_Set_Oimage(U_10530,tc_Option_Ooption(U_10533),U_10534),U_10532)
      | hBOOL(hAPP(hAPP(c_member(U_10530),U_10531),U_10532)) ),
    inference(variable_rename,[status(thm)],[f_2856_1]) ).

fof(f_2856_3,plain,
    ! [U_10530,U_10531,U_10532,U_10533,U_10534,U_10535] :
      ( hAPP(c_Set_Oimage(U_10530,tc_Option_Ooption(U_10533),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10530,tc_Option_Ooption(U_10533)),U_10534),U_10531),hAPP(c_Option_Ooption_OSome(U_10533),U_10535))),U_10532) = hAPP(c_Set_Oimage(U_10530,tc_Option_Ooption(U_10533),U_10534),U_10532)
      | hBOOL(hAPP(hAPP(c_member(U_10530),U_10531),U_10532)) ),
    inference(definitional_conversion,[status(esa)],[f_2856_2]) ).

cnf(f_2856_4,plain,
    ( hAPP(c_Set_Oimage(U_10530,tc_Option_Ooption(U_10533),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10530,tc_Option_Ooption(U_10533)),U_10534),U_10531),hAPP(c_Option_Ooption_OSome(U_10533),U_10535))),U_10532) = hAPP(c_Set_Oimage(U_10530,tc_Option_Ooption(U_10533),U_10534),U_10532)
    | hBOOL(hAPP(hAPP(c_member(U_10530),U_10531),U_10532)) ),
    inference(clausify,[status(thm)],[f_2856_3]) ).

fof(f_2857_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_2857_2,plain,
    ! [U_10541,U_10540,U_10539,U_10538,U_10537,U_10536] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10537,U_10536),hAPP(hAPP(c_COMBC(U_10537,U_10536,U_10536),hAPP(hAPP(c_COMBS(U_10537,U_10536,tc_fun(U_10536,U_10536)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10536,tc_fun(U_10536,U_10536)),U_10537),c_If(U_10536)),hAPP(hAPP(c_COMBC(U_10537,U_10537,tc_HOL_Obool),c_fequal),U_10539))),U_10540)),U_10541)),U_10538) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10536),U_10541),hAPP(c_Finite__Set_Ocard(U_10537),U_10538))
          | hBOOL(hAPP(hAPP(c_member(U_10537),U_10539),U_10538)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10537,U_10536),hAPP(hAPP(c_COMBC(U_10537,U_10536,U_10536),hAPP(hAPP(c_COMBS(U_10537,U_10536,tc_fun(U_10536,U_10536)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10536,tc_fun(U_10536,U_10536)),U_10537),c_If(U_10536)),hAPP(hAPP(c_COMBC(U_10537,U_10537,tc_HOL_Obool),c_fequal),U_10539))),U_10540)),U_10541)),U_10538) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10536),hAPP(U_10540,U_10539)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10536),U_10541),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10537),U_10538)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          | ~ hBOOL(hAPP(hAPP(c_member(U_10537),U_10539),U_10538)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10537),U_10538))
      | ~ class_Groups_Ocomm__monoid__mult(U_10536) ),
    inference(variable_rename,[status(thm)],[f_2857_1]) ).

fof(f_2857_3,plain,
    ( ! [U_10536,U_10537,U_10538,U_10539,U_10540,U_10541] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10537,U_10536),hAPP(hAPP(c_COMBC(U_10537,U_10536,U_10536),hAPP(hAPP(c_COMBS(U_10537,U_10536,tc_fun(U_10536,U_10536)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10536,tc_fun(U_10536,U_10536)),U_10537),c_If(U_10536)),hAPP(hAPP(c_COMBC(U_10537,U_10537,tc_HOL_Obool),c_fequal),U_10539))),U_10540)),U_10541)),U_10538) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10536),U_10541),hAPP(c_Finite__Set_Ocard(U_10537),U_10538))
        | hBOOL(hAPP(hAPP(c_member(U_10537),U_10539),U_10538))
        | ~ sP796(U_10536,U_10537,U_10538,U_10539,U_10540,U_10541) )
    & ! [U_10536,U_10537,U_10538,U_10539,U_10540,U_10541] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10537,U_10536),hAPP(hAPP(c_COMBC(U_10537,U_10536,U_10536),hAPP(hAPP(c_COMBS(U_10537,U_10536,tc_fun(U_10536,U_10536)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10536,tc_fun(U_10536,U_10536)),U_10537),c_If(U_10536)),hAPP(hAPP(c_COMBC(U_10537,U_10537,tc_HOL_Obool),c_fequal),U_10539))),U_10540)),U_10541)),U_10538) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10536),hAPP(U_10540,U_10539)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10536),U_10541),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10537),U_10538)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10537),U_10539),U_10538))
        | ~ sP796(U_10536,U_10537,U_10538,U_10539,U_10540,U_10541) )
    & ! [U_10536,U_10537,U_10538,U_10539,U_10540,U_10541] :
        ( sP796(U_10536,U_10537,U_10538,U_10539,U_10540,U_10541)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10537),U_10538))
        | ~ class_Groups_Ocomm__monoid__mult(U_10536) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP796])],[f_2857_2]) ).

cnf(f_2857_4,plain,
    ( sP796(U_10536,U_10537,U_10538,U_10539,U_10540,U_10541)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10537),U_10538))
    | ~ class_Groups_Ocomm__monoid__mult(U_10536) ),
    inference(clausify,[status(thm)],[f_2857_3]) ).

cnf(f_2857_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10537,U_10536),hAPP(hAPP(c_COMBC(U_10537,U_10536,U_10536),hAPP(hAPP(c_COMBS(U_10537,U_10536,tc_fun(U_10536,U_10536)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10536,tc_fun(U_10536,U_10536)),U_10537),c_If(U_10536)),hAPP(hAPP(c_COMBC(U_10537,U_10537,tc_HOL_Obool),c_fequal),U_10539))),U_10540)),U_10541)),U_10538) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10536),hAPP(U_10540,U_10539)),hAPP(hAPP(c_Power_Opower__class_Opower(U_10536),U_10541),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_10537),U_10538)),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10537),U_10539),U_10538))
    | ~ sP796(U_10536,U_10537,U_10538,U_10539,U_10540,U_10541) ),
    inference(clausify,[status(thm)],[f_2857_3]) ).

cnf(f_2857_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10537,U_10536),hAPP(hAPP(c_COMBC(U_10537,U_10536,U_10536),hAPP(hAPP(c_COMBS(U_10537,U_10536,tc_fun(U_10536,U_10536)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10536,tc_fun(U_10536,U_10536)),U_10537),c_If(U_10536)),hAPP(hAPP(c_COMBC(U_10537,U_10537,tc_HOL_Obool),c_fequal),U_10539))),U_10540)),U_10541)),U_10538) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10536),U_10541),hAPP(c_Finite__Set_Ocard(U_10537),U_10538))
    | hBOOL(hAPP(hAPP(c_member(U_10537),U_10539),U_10538))
    | ~ sP796(U_10536,U_10537,U_10538,U_10539,U_10540,U_10541) ),
    inference(clausify,[status(thm)],[f_2857_3]) ).

fof(f_2858_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_2858_2,plain,
    ! [U_10546,U_10545,U_10544,U_10543,U_10542] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10543,U_10542),hAPP(hAPP(c_COMBS(U_10543,U_10542,U_10542),hAPP(hAPP(c_COMBB(U_10542,tc_fun(U_10542,U_10542),U_10543),c_Groups_Otimes__class_Otimes(U_10542)),U_10544)),U_10545)),U_10546) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10542),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10543,U_10542),U_10544),U_10546)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10543,U_10542),U_10545),U_10546))
      | ~ class_Groups_Ocomm__monoid__mult(U_10542) ),
    inference(variable_rename,[status(thm)],[f_2858_1]) ).

fof(f_2858_3,plain,
    ! [U_10543,U_10542,U_10544,U_10545,U_10546] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10543,U_10542),hAPP(hAPP(c_COMBS(U_10543,U_10542,U_10542),hAPP(hAPP(c_COMBB(U_10542,tc_fun(U_10542,U_10542),U_10543),c_Groups_Otimes__class_Otimes(U_10542)),U_10544)),U_10545)),U_10546) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10542),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10543,U_10542),U_10544),U_10546)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10543,U_10542),U_10545),U_10546))
      | ~ class_Groups_Ocomm__monoid__mult(U_10542) ),
    inference(definitional_conversion,[status(esa)],[f_2858_2]) ).

cnf(f_2858_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10543,U_10542),hAPP(hAPP(c_COMBS(U_10543,U_10542,U_10542),hAPP(hAPP(c_COMBB(U_10542,tc_fun(U_10542,U_10542),U_10543),c_Groups_Otimes__class_Otimes(U_10542)),U_10544)),U_10545)),U_10546) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10542),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10543,U_10542),U_10544),U_10546)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10543,U_10542),U_10545),U_10546))
    | ~ class_Groups_Ocomm__monoid__mult(U_10542) ),
    inference(clausify,[status(thm)],[f_2858_3]) ).

fof(f_2859_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_2859_2,plain,
    ! [U_10549,U_10548,U_10547] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10547,tc_Nat_Onat),U_10548),U_10549) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10547,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10547),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10548)),U_10549)),
    inference(variable_rename,[status(thm)],[f_2859_1]) ).

fof(f_2859_3,plain,
    ! [U_10547,U_10548,U_10549] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10547,tc_Nat_Onat),U_10548),U_10549) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10547,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10547),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10548)),U_10549)),
    inference(definitional_conversion,[status(esa)],[f_2859_2]) ).

cnf(f_2859_4,plain,
    hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10547,tc_Nat_Onat),U_10548),U_10549) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10547,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10547),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10548)),U_10549)),
    inference(clausify,[status(thm)],[f_2859_3]) ).

fof(f_2860_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_2860_2,plain,
    ! [U_10553,U_10552,U_10551,U_10550] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10550),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10551,tc_Nat_Onat),U_10552),U_10553)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10551,U_10550),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10550,U_10551),c_Nat_Osemiring__1__class_Oof__nat(U_10550)),U_10552)),U_10553)
      | ~ class_Rings_Osemiring__1(U_10550)
      | ~ class_Groups_Ocomm__monoid__mult(U_10550) ),
    inference(variable_rename,[status(thm)],[f_2860_1]) ).

fof(f_2860_3,plain,
    ! [U_10550,U_10551,U_10552,U_10553] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10550),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10551,tc_Nat_Onat),U_10552),U_10553)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10551,U_10550),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10550,U_10551),c_Nat_Osemiring__1__class_Oof__nat(U_10550)),U_10552)),U_10553)
      | ~ class_Rings_Osemiring__1(U_10550)
      | ~ class_Groups_Ocomm__monoid__mult(U_10550) ),
    inference(definitional_conversion,[status(esa)],[f_2860_2]) ).

cnf(f_2860_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_10550),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10551,tc_Nat_Onat),U_10552),U_10553)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10551,U_10550),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10550,U_10551),c_Nat_Osemiring__1__class_Oof__nat(U_10550)),U_10552)),U_10553)
    | ~ class_Rings_Osemiring__1(U_10550)
    | ~ class_Groups_Ocomm__monoid__mult(U_10550) ),
    inference(clausify,[status(thm)],[f_2860_3]) ).

fof(f_2861_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_2861_2,plain,
    ! [U_10556,U_10555,U_10554] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10554,tc_Nat_Onat),U_10555),U_10556)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10554,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10554),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10555)),U_10556),
    inference(variable_rename,[status(thm)],[f_2861_1]) ).

fof(f_2861_3,plain,
    ! [U_10554,U_10555,U_10556] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10554,tc_Nat_Onat),U_10555),U_10556)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10554,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10554),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10555)),U_10556),
    inference(definitional_conversion,[status(esa)],[f_2861_2]) ).

cnf(f_2861_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10554,tc_Nat_Onat),U_10555),U_10556)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10554,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_10554),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10555)),U_10556),
    inference(clausify,[status(thm)],[f_2861_3]) ).

fof(f_2862_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_2862_2,plain,
    ! [U_10560,U_10559,U_10558,U_10557] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_10557),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10558,tc_Int_Oint),U_10559),U_10560)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10558,U_10557),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10557,U_10558),c_Int_Oring__1__class_Oof__int(U_10557)),U_10559)),U_10560)
      | ~ class_Rings_Oring__1(U_10557)
      | ~ class_Groups_Ocomm__monoid__mult(U_10557) ),
    inference(variable_rename,[status(thm)],[f_2862_1]) ).

fof(f_2862_3,plain,
    ! [U_10557,U_10558,U_10559,U_10560] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_10557),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10558,tc_Int_Oint),U_10559),U_10560)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10558,U_10557),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10557,U_10558),c_Int_Oring__1__class_Oof__int(U_10557)),U_10559)),U_10560)
      | ~ class_Rings_Oring__1(U_10557)
      | ~ class_Groups_Ocomm__monoid__mult(U_10557) ),
    inference(definitional_conversion,[status(esa)],[f_2862_2]) ).

cnf(f_2862_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_10557),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10558,tc_Int_Oint),U_10559),U_10560)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10558,U_10557),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10557,U_10558),c_Int_Oring__1__class_Oof__int(U_10557)),U_10559)),U_10560)
    | ~ class_Rings_Oring__1(U_10557)
    | ~ class_Groups_Ocomm__monoid__mult(U_10557) ),
    inference(clausify,[status(thm)],[f_2862_3]) ).

fof(f_2863_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_2863_2,plain,
    ! [U_10563,U_10562,U_10561] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10562,U_10561),hAPP(c_COMBK(U_10561,U_10562),c_Groups_Oone__class_Oone(U_10561))),U_10563) = c_Groups_Oone__class_Oone(U_10561)
      | ~ class_Groups_Ocomm__monoid__mult(U_10561) ),
    inference(variable_rename,[status(thm)],[f_2863_1]) ).

fof(f_2863_3,plain,
    ! [U_10561,U_10562,U_10563] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10562,U_10561),hAPP(c_COMBK(U_10561,U_10562),c_Groups_Oone__class_Oone(U_10561))),U_10563) = c_Groups_Oone__class_Oone(U_10561)
      | ~ class_Groups_Ocomm__monoid__mult(U_10561) ),
    inference(definitional_conversion,[status(esa)],[f_2863_2]) ).

cnf(f_2863_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10562,U_10561),hAPP(c_COMBK(U_10561,U_10562),c_Groups_Oone__class_Oone(U_10561))),U_10563) = c_Groups_Oone__class_Oone(U_10561)
    | ~ class_Groups_Ocomm__monoid__mult(U_10561) ),
    inference(clausify,[status(thm)],[f_2863_3]) ).

fof(f_2864_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_2864_2,plain,
    ! [U_10567,U_10566,U_10565,U_10564] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_10564),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10565,U_10564),U_10566),U_10567)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10565,U_10564),hAPP(hAPP(c_COMBB(U_10564,U_10564,U_10565),c_Groups_Oabs__class_Oabs(U_10564)),U_10566)),U_10567)
      | ~ class_Fields_Olinordered__field(U_10564) ),
    inference(variable_rename,[status(thm)],[f_2864_1]) ).

fof(f_2864_3,plain,
    ! [U_10564,U_10565,U_10566,U_10567] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_10564),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10565,U_10564),U_10566),U_10567)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10565,U_10564),hAPP(hAPP(c_COMBB(U_10564,U_10564,U_10565),c_Groups_Oabs__class_Oabs(U_10564)),U_10566)),U_10567)
      | ~ class_Fields_Olinordered__field(U_10564) ),
    inference(definitional_conversion,[status(esa)],[f_2864_2]) ).

cnf(f_2864_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_10564),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10565,U_10564),U_10566),U_10567)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10565,U_10564),hAPP(hAPP(c_COMBB(U_10564,U_10564,U_10565),c_Groups_Oabs__class_Oabs(U_10564)),U_10566)),U_10567)
    | ~ class_Fields_Olinordered__field(U_10564) ),
    inference(clausify,[status(thm)],[f_2864_3]) ).

fof(f_2865_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_2865_2,plain,
    ! [U_10570,U_10569,U_10568] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10568),U_10569),U_10570) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10568),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10568,tc_Int_Oint),U_10569),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10570))
      | ~ class_Groups_Ocomm__monoid__mult(U_10568)
      | ~ class_Groups_Ocomm__monoid__add(U_10568) ),
    inference(variable_rename,[status(thm)],[f_2865_1]) ).

fof(f_2865_3,plain,
    ! [U_10568,U_10569,U_10570] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10568),U_10569),U_10570) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10568),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10568,tc_Int_Oint),U_10569),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10570))
      | ~ class_Groups_Ocomm__monoid__mult(U_10568)
      | ~ class_Groups_Ocomm__monoid__add(U_10568) ),
    inference(definitional_conversion,[status(esa)],[f_2865_2]) ).

cnf(f_2865_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10568),U_10569),U_10570) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10568),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_10568,tc_Int_Oint),U_10569),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_10570))
    | ~ class_Groups_Ocomm__monoid__mult(U_10568)
    | ~ class_Groups_Ocomm__monoid__add(U_10568) ),
    inference(clausify,[status(thm)],[f_2865_3]) ).

fof(f_2866_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_2866_2,plain,
    ! [U_10576,U_10575,U_10574,U_10573] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10574,U_10573),U_10576),U_10575) = c_Groups_Ozero__class_Ozero(U_10573)
          | ! [U_10572] :
              ( hAPP(U_10576,U_10572) != c_Groups_Ozero__class_Ozero(U_10573)
              | ~ hBOOL(hAPP(hAPP(c_member(U_10574),U_10572),U_10575)) ) )
        & ( ? [U_10571] :
              ( hAPP(U_10576,U_10571) = c_Groups_Ozero__class_Ozero(U_10573)
              & hBOOL(hAPP(hAPP(c_member(U_10574),U_10571),U_10575)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10574,U_10573),U_10576),U_10575) != c_Groups_Ozero__class_Ozero(U_10573) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10574),U_10575))
      | ~ class_Rings_Ono__zero__divisors(U_10573)
      | ~ class_Rings_Ocomm__semiring__1(U_10573) ),
    inference(variable_rename,[status(thm)],[f_2866_1]) ).

fof(f_2866_3,plain,
    ! [U_10576,U_10575,U_10574,U_10573] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10574,U_10573),U_10576),U_10575) = c_Groups_Ozero__class_Ozero(U_10573)
          | ! [U_10572] :
              ( hAPP(U_10576,U_10572) != c_Groups_Ozero__class_Ozero(U_10573)
              | ~ hBOOL(hAPP(hAPP(c_member(U_10574),U_10572),U_10575)) ) )
        & ( ( hAPP(U_10576,sK174(U_10576,U_10575,U_10574,U_10573)) = c_Groups_Ozero__class_Ozero(U_10573)
            & hBOOL(hAPP(hAPP(c_member(U_10574),sK174(U_10576,U_10575,U_10574,U_10573)),U_10575)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10574,U_10573),U_10576),U_10575) != c_Groups_Ozero__class_Ozero(U_10573) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10574),U_10575))
      | ~ class_Rings_Ono__zero__divisors(U_10573)
      | ~ class_Rings_Ocomm__semiring__1(U_10573) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK174]),skolemize(U_10571,sK174(U_10576,U_10575,U_10574,U_10573))],[f_2866_2]) ).

fof(f_2866_4,plain,
    ( ! [U_10573,U_10574,U_10575,U_10576] :
        ( hAPP(U_10576,sK174(U_10576,U_10575,U_10574,U_10573)) = c_Groups_Ozero__class_Ozero(U_10573)
        | ~ sP797(U_10573,U_10574,U_10575,U_10576) )
    & ! [U_10573,U_10574,U_10575,U_10576] :
        ( hBOOL(hAPP(hAPP(c_member(U_10574),sK174(U_10576,U_10575,U_10574,U_10573)),U_10575))
        | ~ sP797(U_10573,U_10574,U_10575,U_10576) )
    & ! [U_10572,U_10573,U_10574,U_10575,U_10576] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10574,U_10573),U_10576),U_10575) = c_Groups_Ozero__class_Ozero(U_10573)
        | hAPP(U_10576,U_10572) != c_Groups_Ozero__class_Ozero(U_10573)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10574),U_10572),U_10575))
        | ~ sP798(U_10572,U_10573,U_10574,U_10575,U_10576) )
    & ! [U_10572,U_10573,U_10574,U_10575,U_10576] :
        ( sP797(U_10573,U_10574,U_10575,U_10576)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10574,U_10573),U_10576),U_10575) != c_Groups_Ozero__class_Ozero(U_10573)
        | ~ sP798(U_10572,U_10573,U_10574,U_10575,U_10576) )
    & ! [U_10572,U_10573,U_10574,U_10575,U_10576] :
        ( sP798(U_10572,U_10573,U_10574,U_10575,U_10576)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10574),U_10575))
        | ~ class_Rings_Ono__zero__divisors(U_10573)
        | ~ class_Rings_Ocomm__semiring__1(U_10573) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP797,sP798])],[f_2866_3]) ).

cnf(f_2866_5,plain,
    ( sP798(U_10572,U_10573,U_10574,U_10575,U_10576)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10574),U_10575))
    | ~ class_Rings_Ono__zero__divisors(U_10573)
    | ~ class_Rings_Ocomm__semiring__1(U_10573) ),
    inference(clausify,[status(thm)],[f_2866_4]) ).

cnf(f_2866_6,plain,
    ( sP797(U_10573,U_10574,U_10575,U_10576)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10574,U_10573),U_10576),U_10575) != c_Groups_Ozero__class_Ozero(U_10573)
    | ~ sP798(U_10572,U_10573,U_10574,U_10575,U_10576) ),
    inference(clausify,[status(thm)],[f_2866_4]) ).

cnf(f_2866_7,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10574,U_10573),U_10576),U_10575) = c_Groups_Ozero__class_Ozero(U_10573)
    | hAPP(U_10576,U_10572) != c_Groups_Ozero__class_Ozero(U_10573)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10574),U_10572),U_10575))
    | ~ sP798(U_10572,U_10573,U_10574,U_10575,U_10576) ),
    inference(clausify,[status(thm)],[f_2866_4]) ).

cnf(f_2866_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10574),sK174(U_10576,U_10575,U_10574,U_10573)),U_10575))
    | ~ sP797(U_10573,U_10574,U_10575,U_10576) ),
    inference(clausify,[status(thm)],[f_2866_4]) ).

cnf(f_2866_9,plain,
    ( hAPP(U_10576,sK174(U_10576,U_10575,U_10574,U_10573)) = c_Groups_Ozero__class_Ozero(U_10573)
    | ~ sP797(U_10573,U_10574,U_10575,U_10576) ),
    inference(clausify,[status(thm)],[f_2866_4]) ).

fof(f_2867_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_2867_2,plain,
    ! [U_10581,U_10580,U_10579,U_10578] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10579,U_10578),U_10581),U_10580) = c_Groups_Ozero__class_Ozero(U_10578)
      | ! [U_10577] :
          ( hAPP(U_10581,U_10577) != c_Groups_Ozero__class_Ozero(U_10578)
          | ~ hBOOL(hAPP(hAPP(c_member(U_10579),U_10577),U_10580)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10579),U_10580))
      | ~ class_Rings_Ocomm__semiring__1(U_10578) ),
    inference(variable_rename,[status(thm)],[f_2867_1]) ).

fof(f_2867_3,plain,
    ! [U_10581,U_10580,U_10579,U_10577,U_10578] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10579,U_10578),U_10581),U_10580) = c_Groups_Ozero__class_Ozero(U_10578)
      | hAPP(U_10581,U_10577) != c_Groups_Ozero__class_Ozero(U_10578)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10579),U_10577),U_10580))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10579),U_10580))
      | ~ class_Rings_Ocomm__semiring__1(U_10578) ),
    inference(definitional_conversion,[status(esa)],[f_2867_2]) ).

cnf(f_2867_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10579,U_10578),U_10581),U_10580) = c_Groups_Ozero__class_Ozero(U_10578)
    | hAPP(U_10581,U_10577) != c_Groups_Ozero__class_Ozero(U_10578)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10579),U_10577),U_10580))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10579),U_10580))
    | ~ class_Rings_Ocomm__semiring__1(U_10578) ),
    inference(clausify,[status(thm)],[f_2867_3]) ).

fof(f_2868_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_2868_2,plain,
    ! [U_10584,U_10583,U_10582] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10583,U_10582),U_10584),c_Orderings_Obot__class_Obot(tc_fun(U_10583,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_10582)
      | ~ class_Groups_Ocomm__monoid__mult(U_10582) ),
    inference(variable_rename,[status(thm)],[f_2868_1]) ).

fof(f_2868_3,plain,
    ! [U_10583,U_10582,U_10584] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10583,U_10582),U_10584),c_Orderings_Obot__class_Obot(tc_fun(U_10583,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_10582)
      | ~ class_Groups_Ocomm__monoid__mult(U_10582) ),
    inference(definitional_conversion,[status(esa)],[f_2868_2]) ).

cnf(f_2868_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10583,U_10582),U_10584),c_Orderings_Obot__class_Obot(tc_fun(U_10583,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_10582)
    | ~ class_Groups_Ocomm__monoid__mult(U_10582) ),
    inference(clausify,[status(thm)],[f_2868_3]) ).

fof(f_2869_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_2869_2,plain,
    ! [U_10587,U_10586,U_10585] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10586,U_10585),U_10587),c_Orderings_Obot__class_Obot(tc_fun(U_10586,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_10585)
      | ~ class_Groups_Ocomm__monoid__mult(U_10585) ),
    inference(variable_rename,[status(thm)],[f_2869_1]) ).

fof(f_2869_3,plain,
    ! [U_10585,U_10586,U_10587] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10586,U_10585),U_10587),c_Orderings_Obot__class_Obot(tc_fun(U_10586,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_10585)
      | ~ class_Groups_Ocomm__monoid__mult(U_10585) ),
    inference(definitional_conversion,[status(esa)],[f_2869_2]) ).

cnf(f_2869_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10586,U_10585),U_10587),c_Orderings_Obot__class_Obot(tc_fun(U_10586,tc_HOL_Obool))) = c_Groups_Oone__class_Oone(U_10585)
    | ~ class_Groups_Ocomm__monoid__mult(U_10585) ),
    inference(clausify,[status(thm)],[f_2869_3]) ).

fof(f_2870_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_2870_2,plain,
    ! [U_10591,U_10590,U_10589,U_10588] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10589,U_10588),U_10591),U_10590) = c_Groups_Oone__class_Oone(U_10588)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10589),U_10590))
      | ~ class_Groups_Ocomm__monoid__mult(U_10588) ),
    inference(variable_rename,[status(thm)],[f_2870_1]) ).

fof(f_2870_3,plain,
    ! [U_10588,U_10589,U_10590,U_10591] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10589,U_10588),U_10591),U_10590) = c_Groups_Oone__class_Oone(U_10588)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10589),U_10590))
      | ~ class_Groups_Ocomm__monoid__mult(U_10588) ),
    inference(definitional_conversion,[status(esa)],[f_2870_2]) ).

cnf(f_2870_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10589,U_10588),U_10591),U_10590) = c_Groups_Oone__class_Oone(U_10588)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10589),U_10590))
    | ~ class_Groups_Ocomm__monoid__mult(U_10588) ),
    inference(clausify,[status(thm)],[f_2870_3]) ).

fof(f_2871_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_2871_2,plain,
    ! [U_10595,U_10594,U_10593,U_10592] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10593,U_10592),U_10595),U_10594) = c_Groups_Oone__class_Oone(U_10592)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10593),U_10594))
      | ~ class_Groups_Ocomm__monoid__mult(U_10592) ),
    inference(variable_rename,[status(thm)],[f_2871_1]) ).

fof(f_2871_3,plain,
    ! [U_10593,U_10592,U_10594,U_10595] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10593,U_10592),U_10595),U_10594) = c_Groups_Oone__class_Oone(U_10592)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10593),U_10594))
      | ~ class_Groups_Ocomm__monoid__mult(U_10592) ),
    inference(definitional_conversion,[status(esa)],[f_2871_2]) ).

cnf(f_2871_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10593,U_10592),U_10595),U_10594) = c_Groups_Oone__class_Oone(U_10592)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_10593),U_10594))
    | ~ class_Groups_Ocomm__monoid__mult(U_10592) ),
    inference(clausify,[status(thm)],[f_2871_3]) ).

fof(f_2872_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_2872_2,plain,
    ! [U_10600,U_10599,U_10598] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10598,tc_Nat_Onat),U_10600),U_10599) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ? [U_10597] :
              ( hAPP(U_10600,U_10597) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(U_10598),U_10597),U_10599)) ) )
        & ( ! [U_10596] :
              ( hAPP(U_10600,U_10596) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_10598),U_10596),U_10599)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10598,tc_Nat_Onat),U_10600),U_10599) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10598),U_10599)) ),
    inference(variable_rename,[status(thm)],[f_2872_1]) ).

fof(f_2872_3,plain,
    ! [U_10600,U_10599,U_10598] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10598,tc_Nat_Onat),U_10600),U_10599) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ( hAPP(U_10600,sK175(U_10600,U_10599,U_10598)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_10598),sK175(U_10600,U_10599,U_10598)),U_10599)) ) )
        & ( ! [U_10596] :
              ( hAPP(U_10600,U_10596) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_10598),U_10596),U_10599)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10598,tc_Nat_Onat),U_10600),U_10599) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10598),U_10599)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK175]),skolemize(U_10597,sK175(U_10600,U_10599,U_10598))],[f_2872_2]) ).

fof(f_2872_4,plain,
    ( ! [U_10598,U_10599,U_10600] :
        ( hAPP(U_10600,sK175(U_10600,U_10599,U_10598)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP799(U_10598,U_10599,U_10600) )
    & ! [U_10598,U_10599,U_10600] :
        ( hBOOL(hAPP(hAPP(c_member(U_10598),sK175(U_10600,U_10599,U_10598)),U_10599))
        | ~ sP799(U_10598,U_10599,U_10600) )
    & ! [U_10598,U_10596,U_10599,U_10600] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10598,tc_Nat_Onat),U_10600),U_10599) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | sP799(U_10598,U_10599,U_10600)
        | ~ sP800(U_10598,U_10596,U_10599,U_10600) )
    & ! [U_10598,U_10596,U_10599,U_10600] :
        ( hAPP(U_10600,U_10596) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10598),U_10596),U_10599))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10598,tc_Nat_Onat),U_10600),U_10599) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP800(U_10598,U_10596,U_10599,U_10600) )
    & ! [U_10598,U_10596,U_10599,U_10600] :
        ( sP800(U_10598,U_10596,U_10599,U_10600)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10598),U_10599)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP799,sP800])],[f_2872_3]) ).

cnf(f_2872_5,plain,
    ( sP800(U_10598,U_10596,U_10599,U_10600)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10598),U_10599)) ),
    inference(clausify,[status(thm)],[f_2872_4]) ).

cnf(f_2872_6,plain,
    ( hAPP(U_10600,U_10596) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10598),U_10596),U_10599))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10598,tc_Nat_Onat),U_10600),U_10599) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP800(U_10598,U_10596,U_10599,U_10600) ),
    inference(clausify,[status(thm)],[f_2872_4]) ).

cnf(f_2872_7,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10598,tc_Nat_Onat),U_10600),U_10599) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | sP799(U_10598,U_10599,U_10600)
    | ~ sP800(U_10598,U_10596,U_10599,U_10600) ),
    inference(clausify,[status(thm)],[f_2872_4]) ).

cnf(f_2872_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10598),sK175(U_10600,U_10599,U_10598)),U_10599))
    | ~ sP799(U_10598,U_10599,U_10600) ),
    inference(clausify,[status(thm)],[f_2872_4]) ).

cnf(f_2872_9,plain,
    ( hAPP(U_10600,sK175(U_10600,U_10599,U_10598)) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP799(U_10598,U_10599,U_10600) ),
    inference(clausify,[status(thm)],[f_2872_4]) ).

fof(f_2873_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_2873_2,plain,
    ! [U_10603,U_10602,U_10601] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10601),U_10603),U_10602) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10601),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10601,tc_Nat_Onat),U_10603),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10602))
      | ~ c_Nat__Transfer_Onat__set(U_10602)
      | ~ class_Groups_Ocomm__monoid__mult(U_10601)
      | ~ class_Groups_Ocomm__monoid__add(U_10601) ),
    inference(variable_rename,[status(thm)],[f_2873_1]) ).

fof(f_2873_3,plain,
    ! [U_10602,U_10603,U_10601] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10601),U_10603),U_10602) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10601),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10601,tc_Nat_Onat),U_10603),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10602))
      | ~ c_Nat__Transfer_Onat__set(U_10602)
      | ~ class_Groups_Ocomm__monoid__mult(U_10601)
      | ~ class_Groups_Ocomm__monoid__add(U_10601) ),
    inference(definitional_conversion,[status(esa)],[f_2873_2]) ).

cnf(f_2873_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_10601),U_10603),U_10602) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Nat_Onat,U_10601),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_10601,tc_Nat_Onat),U_10603),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_10602))
    | ~ c_Nat__Transfer_Onat__set(U_10602)
    | ~ class_Groups_Ocomm__monoid__mult(U_10601)
    | ~ class_Groups_Ocomm__monoid__add(U_10601) ),
    inference(clausify,[status(thm)],[f_2873_3]) ).

fof(f_2874_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_2874_2,plain,
    ! [U_10608,U_10607,U_10606,U_10605,U_10604] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10605,U_10604),hAPP(hAPP(c_COMBS(U_10605,U_10604,U_10604),hAPP(hAPP(c_COMBB(U_10604,tc_fun(U_10604,U_10604),U_10605),c_Groups_Otimes__class_Otimes(U_10604)),U_10607)),U_10608)),U_10606) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10604),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10605,U_10604),U_10607),U_10606)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10605,U_10604),U_10608),U_10606))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10605),U_10606))
      | ~ class_Groups_Ocomm__monoid__mult(U_10604) ),
    inference(variable_rename,[status(thm)],[f_2874_1]) ).

fof(f_2874_3,plain,
    ! [U_10604,U_10605,U_10606,U_10607,U_10608] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10605,U_10604),hAPP(hAPP(c_COMBS(U_10605,U_10604,U_10604),hAPP(hAPP(c_COMBB(U_10604,tc_fun(U_10604,U_10604),U_10605),c_Groups_Otimes__class_Otimes(U_10604)),U_10607)),U_10608)),U_10606) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10604),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10605,U_10604),U_10607),U_10606)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10605,U_10604),U_10608),U_10606))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10605),U_10606))
      | ~ class_Groups_Ocomm__monoid__mult(U_10604) ),
    inference(definitional_conversion,[status(esa)],[f_2874_2]) ).

cnf(f_2874_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10605,U_10604),hAPP(hAPP(c_COMBS(U_10605,U_10604,U_10604),hAPP(hAPP(c_COMBB(U_10604,tc_fun(U_10604,U_10604),U_10605),c_Groups_Otimes__class_Otimes(U_10604)),U_10607)),U_10608)),U_10606) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10604),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10605,U_10604),U_10607),U_10606)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10605,U_10604),U_10608),U_10606))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10605),U_10606))
    | ~ class_Groups_Ocomm__monoid__mult(U_10604) ),
    inference(clausify,[status(thm)],[f_2874_3]) ).

fof(f_2875_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_2875_2,plain,
    ! [U_10613,U_10612,U_10611,U_10610,U_10609] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10610,U_10609),hAPP(hAPP(c_COMBS(U_10610,U_10609,U_10609),hAPP(hAPP(c_COMBB(U_10609,tc_fun(U_10609,U_10609),U_10610),c_Rings_Oinverse__class_Odivide(U_10609)),U_10612)),U_10613)),U_10611) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10609),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10610,U_10609),U_10612),U_10611)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10610,U_10609),U_10613),U_10611))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10610),U_10611))
      | ~ class_Fields_Ofield__inverse__zero(U_10609) ),
    inference(variable_rename,[status(thm)],[f_2875_1]) ).

fof(f_2875_3,plain,
    ! [U_10609,U_10610,U_10611,U_10612,U_10613] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10610,U_10609),hAPP(hAPP(c_COMBS(U_10610,U_10609,U_10609),hAPP(hAPP(c_COMBB(U_10609,tc_fun(U_10609,U_10609),U_10610),c_Rings_Oinverse__class_Odivide(U_10609)),U_10612)),U_10613)),U_10611) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10609),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10610,U_10609),U_10612),U_10611)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10610,U_10609),U_10613),U_10611))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10610),U_10611))
      | ~ class_Fields_Ofield__inverse__zero(U_10609) ),
    inference(definitional_conversion,[status(esa)],[f_2875_2]) ).

cnf(f_2875_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10610,U_10609),hAPP(hAPP(c_COMBS(U_10610,U_10609,U_10609),hAPP(hAPP(c_COMBB(U_10609,tc_fun(U_10609,U_10609),U_10610),c_Rings_Oinverse__class_Odivide(U_10609)),U_10612)),U_10613)),U_10611) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10609),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10610,U_10609),U_10612),U_10611)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10610,U_10609),U_10613),U_10611))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10610),U_10611))
    | ~ class_Fields_Ofield__inverse__zero(U_10609) ),
    inference(clausify,[status(thm)],[f_2875_3]) ).

fof(f_2876_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_2876_2,plain,
    ! [U_10618,U_10617,U_10616,U_10615,U_10614] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_10614),hAPP(U_10618,U_10617)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10615,U_10614),U_10618),U_10616)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10615),U_10617),U_10616))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10615),U_10616))
      | ~ class_Rings_Ocomm__semiring__1(U_10614) ),
    inference(variable_rename,[status(thm)],[f_2876_1]) ).

fof(f_2876_3,plain,
    ! [U_10614,U_10615,U_10616,U_10617,U_10618] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_10614),hAPP(U_10618,U_10617)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10615,U_10614),U_10618),U_10616)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10615),U_10617),U_10616))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10615),U_10616))
      | ~ class_Rings_Ocomm__semiring__1(U_10614) ),
    inference(definitional_conversion,[status(esa)],[f_2876_2]) ).

cnf(f_2876_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_10614),hAPP(U_10618,U_10617)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10615,U_10614),U_10618),U_10616)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10615),U_10617),U_10616))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10615),U_10616))
    | ~ class_Rings_Ocomm__semiring__1(U_10614) ),
    inference(clausify,[status(thm)],[f_2876_3]) ).

fof(f_2877_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_2877_2,plain,
    ! [U_10623,U_10622,U_10621] :
      ( ( ( 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_10621,tc_Nat_Onat),U_10623),U_10622)))
          | ? [U_10620] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10623,U_10620)))
              & hBOOL(hAPP(hAPP(c_member(U_10621),U_10620),U_10622)) ) )
        & ( ! [U_10619] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10623,U_10619)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10621),U_10619),U_10622)) )
          | ~ 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_10621,tc_Nat_Onat),U_10623),U_10622))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10621),U_10622)) ),
    inference(variable_rename,[status(thm)],[f_2877_1]) ).

fof(f_2877_3,plain,
    ! [U_10623,U_10622,U_10621] :
      ( ( ( 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_10621,tc_Nat_Onat),U_10623),U_10622)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10623,sK176(U_10623,U_10622,U_10621))))
            & hBOOL(hAPP(hAPP(c_member(U_10621),sK176(U_10623,U_10622,U_10621)),U_10622)) ) )
        & ( ! [U_10619] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10623,U_10619)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_10621),U_10619),U_10622)) )
          | ~ 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_10621,tc_Nat_Onat),U_10623),U_10622))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10621),U_10622)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK176]),skolemize(U_10620,sK176(U_10623,U_10622,U_10621))],[f_2877_2]) ).

fof(f_2877_4,plain,
    ( ! [U_10621,U_10622,U_10623] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10623,sK176(U_10623,U_10622,U_10621))))
        | ~ sP801(U_10621,U_10622,U_10623) )
    & ! [U_10621,U_10622,U_10623] :
        ( hBOOL(hAPP(hAPP(c_member(U_10621),sK176(U_10623,U_10622,U_10621)),U_10622))
        | ~ sP801(U_10621,U_10622,U_10623) )
    & ! [U_10619,U_10621,U_10622,U_10623] :
        ( 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_10621,tc_Nat_Onat),U_10623),U_10622)))
        | sP801(U_10621,U_10622,U_10623)
        | ~ sP802(U_10619,U_10621,U_10622,U_10623) )
    & ! [U_10619,U_10621,U_10622,U_10623] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10623,U_10619)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10621),U_10619),U_10622))
        | ~ 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_10621,tc_Nat_Onat),U_10623),U_10622)))
        | ~ sP802(U_10619,U_10621,U_10622,U_10623) )
    & ! [U_10619,U_10621,U_10622,U_10623] :
        ( sP802(U_10619,U_10621,U_10622,U_10623)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10621),U_10622)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP801,sP802])],[f_2877_3]) ).

cnf(f_2877_5,plain,
    ( sP802(U_10619,U_10621,U_10622,U_10623)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10621),U_10622)) ),
    inference(clausify,[status(thm)],[f_2877_4]) ).

cnf(f_2877_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10623,U_10619)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10621),U_10619),U_10622))
    | ~ 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_10621,tc_Nat_Onat),U_10623),U_10622)))
    | ~ sP802(U_10619,U_10621,U_10622,U_10623) ),
    inference(clausify,[status(thm)],[f_2877_4]) ).

cnf(f_2877_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_10621,tc_Nat_Onat),U_10623),U_10622)))
    | sP801(U_10621,U_10622,U_10623)
    | ~ sP802(U_10619,U_10621,U_10622,U_10623) ),
    inference(clausify,[status(thm)],[f_2877_4]) ).

cnf(f_2877_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10621),sK176(U_10623,U_10622,U_10621)),U_10622))
    | ~ sP801(U_10621,U_10622,U_10623) ),
    inference(clausify,[status(thm)],[f_2877_4]) ).

cnf(f_2877_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_10623,sK176(U_10623,U_10622,U_10621))))
    | ~ sP801(U_10621,U_10622,U_10623) ),
    inference(clausify,[status(thm)],[f_2877_4]) ).

fof(f_2878_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_2878_2,plain,
    ! [U_10628,U_10627,U_10626,U_10625,U_10624] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_10624),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10625,U_10624),U_10628),U_10627)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10625,U_10624),U_10628),U_10626)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10625,tc_HOL_Obool)),U_10627),U_10626))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10625),U_10626))
      | ~ class_Rings_Odvd(U_10624)
      | ~ class_Groups_Ocomm__monoid__mult(U_10624) ),
    inference(variable_rename,[status(thm)],[f_2878_1]) ).

fof(f_2878_3,plain,
    ! [U_10626,U_10627,U_10625,U_10624,U_10628] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_10624),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10625,U_10624),U_10628),U_10627)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10625,U_10624),U_10628),U_10626)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10625,tc_HOL_Obool)),U_10627),U_10626))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10625),U_10626))
      | ~ class_Rings_Odvd(U_10624)
      | ~ class_Groups_Ocomm__monoid__mult(U_10624) ),
    inference(definitional_conversion,[status(esa)],[f_2878_2]) ).

cnf(f_2878_4,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_10624),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10625,U_10624),U_10628),U_10627)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10625,U_10624),U_10628),U_10626)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10625,tc_HOL_Obool)),U_10627),U_10626))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10625),U_10626))
    | ~ class_Rings_Odvd(U_10624)
    | ~ class_Groups_Ocomm__monoid__mult(U_10624) ),
    inference(clausify,[status(thm)],[f_2878_3]) ).

fof(f_2879_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_2879_2,plain,
    ! [U_10633,U_10632,U_10631,U_10630,U_10629] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10630,U_10629),hAPP(hAPP(c_COMBC(U_10630,U_10629,U_10629),hAPP(hAPP(c_COMBS(U_10630,U_10629,tc_fun(U_10629,U_10629)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10629,tc_fun(U_10629,U_10629)),U_10630),c_If(U_10629)),hAPP(hAPP(c_COMBC(U_10630,U_10630,tc_HOL_Obool),c_fequal),U_10632))),U_10633)),c_Groups_Oone__class_Oone(U_10629))),U_10631) = c_Groups_Oone__class_Oone(U_10629)
          | hBOOL(hAPP(hAPP(c_member(U_10630),U_10632),U_10631)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10630,U_10629),hAPP(hAPP(c_COMBC(U_10630,U_10629,U_10629),hAPP(hAPP(c_COMBS(U_10630,U_10629,tc_fun(U_10629,U_10629)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10629,tc_fun(U_10629,U_10629)),U_10630),c_If(U_10629)),hAPP(hAPP(c_COMBC(U_10630,U_10630,tc_HOL_Obool),c_fequal),U_10632))),U_10633)),c_Groups_Oone__class_Oone(U_10629))),U_10631) = hAPP(U_10633,U_10632)
          | ~ hBOOL(hAPP(hAPP(c_member(U_10630),U_10632),U_10631)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10630),U_10631))
      | ~ class_Groups_Ocomm__monoid__mult(U_10629) ),
    inference(variable_rename,[status(thm)],[f_2879_1]) ).

fof(f_2879_3,plain,
    ( ! [U_10629,U_10630,U_10631,U_10632,U_10633] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10630,U_10629),hAPP(hAPP(c_COMBC(U_10630,U_10629,U_10629),hAPP(hAPP(c_COMBS(U_10630,U_10629,tc_fun(U_10629,U_10629)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10629,tc_fun(U_10629,U_10629)),U_10630),c_If(U_10629)),hAPP(hAPP(c_COMBC(U_10630,U_10630,tc_HOL_Obool),c_fequal),U_10632))),U_10633)),c_Groups_Oone__class_Oone(U_10629))),U_10631) = c_Groups_Oone__class_Oone(U_10629)
        | hBOOL(hAPP(hAPP(c_member(U_10630),U_10632),U_10631))
        | ~ sP803(U_10629,U_10630,U_10631,U_10632,U_10633) )
    & ! [U_10629,U_10630,U_10631,U_10632,U_10633] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10630,U_10629),hAPP(hAPP(c_COMBC(U_10630,U_10629,U_10629),hAPP(hAPP(c_COMBS(U_10630,U_10629,tc_fun(U_10629,U_10629)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10629,tc_fun(U_10629,U_10629)),U_10630),c_If(U_10629)),hAPP(hAPP(c_COMBC(U_10630,U_10630,tc_HOL_Obool),c_fequal),U_10632))),U_10633)),c_Groups_Oone__class_Oone(U_10629))),U_10631) = hAPP(U_10633,U_10632)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10630),U_10632),U_10631))
        | ~ sP803(U_10629,U_10630,U_10631,U_10632,U_10633) )
    & ! [U_10629,U_10630,U_10631,U_10632,U_10633] :
        ( sP803(U_10629,U_10630,U_10631,U_10632,U_10633)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10630),U_10631))
        | ~ class_Groups_Ocomm__monoid__mult(U_10629) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP803])],[f_2879_2]) ).

cnf(f_2879_4,plain,
    ( sP803(U_10629,U_10630,U_10631,U_10632,U_10633)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10630),U_10631))
    | ~ class_Groups_Ocomm__monoid__mult(U_10629) ),
    inference(clausify,[status(thm)],[f_2879_3]) ).

cnf(f_2879_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10630,U_10629),hAPP(hAPP(c_COMBC(U_10630,U_10629,U_10629),hAPP(hAPP(c_COMBS(U_10630,U_10629,tc_fun(U_10629,U_10629)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10629,tc_fun(U_10629,U_10629)),U_10630),c_If(U_10629)),hAPP(hAPP(c_COMBC(U_10630,U_10630,tc_HOL_Obool),c_fequal),U_10632))),U_10633)),c_Groups_Oone__class_Oone(U_10629))),U_10631) = hAPP(U_10633,U_10632)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10630),U_10632),U_10631))
    | ~ sP803(U_10629,U_10630,U_10631,U_10632,U_10633) ),
    inference(clausify,[status(thm)],[f_2879_3]) ).

cnf(f_2879_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10630,U_10629),hAPP(hAPP(c_COMBC(U_10630,U_10629,U_10629),hAPP(hAPP(c_COMBS(U_10630,U_10629,tc_fun(U_10629,U_10629)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10629,tc_fun(U_10629,U_10629)),U_10630),c_If(U_10629)),hAPP(hAPP(c_COMBC(U_10630,U_10630,tc_HOL_Obool),c_fequal),U_10632))),U_10633)),c_Groups_Oone__class_Oone(U_10629))),U_10631) = c_Groups_Oone__class_Oone(U_10629)
    | hBOOL(hAPP(hAPP(c_member(U_10630),U_10632),U_10631))
    | ~ sP803(U_10629,U_10630,U_10631,U_10632,U_10633) ),
    inference(clausify,[status(thm)],[f_2879_3]) ).

fof(f_2880_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_2880_2,plain,
    ! [U_10638,U_10637,U_10636,U_10635,U_10634] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10635,U_10634),hAPP(hAPP(c_COMBC(U_10635,U_10634,U_10634),hAPP(hAPP(c_COMBS(U_10635,U_10634,tc_fun(U_10634,U_10634)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10634,tc_fun(U_10634,U_10634)),U_10635),c_If(U_10634)),hAPP(c_fequal,U_10637))),U_10638)),c_Groups_Oone__class_Oone(U_10634))),U_10636) = c_Groups_Oone__class_Oone(U_10634)
          | hBOOL(hAPP(hAPP(c_member(U_10635),U_10637),U_10636)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10635,U_10634),hAPP(hAPP(c_COMBC(U_10635,U_10634,U_10634),hAPP(hAPP(c_COMBS(U_10635,U_10634,tc_fun(U_10634,U_10634)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10634,tc_fun(U_10634,U_10634)),U_10635),c_If(U_10634)),hAPP(c_fequal,U_10637))),U_10638)),c_Groups_Oone__class_Oone(U_10634))),U_10636) = hAPP(U_10638,U_10637)
          | ~ hBOOL(hAPP(hAPP(c_member(U_10635),U_10637),U_10636)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10635),U_10636))
      | ~ class_Groups_Ocomm__monoid__mult(U_10634) ),
    inference(variable_rename,[status(thm)],[f_2880_1]) ).

fof(f_2880_3,plain,
    ( ! [U_10637,U_10636,U_10634,U_10635,U_10638] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10635,U_10634),hAPP(hAPP(c_COMBC(U_10635,U_10634,U_10634),hAPP(hAPP(c_COMBS(U_10635,U_10634,tc_fun(U_10634,U_10634)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10634,tc_fun(U_10634,U_10634)),U_10635),c_If(U_10634)),hAPP(c_fequal,U_10637))),U_10638)),c_Groups_Oone__class_Oone(U_10634))),U_10636) = c_Groups_Oone__class_Oone(U_10634)
        | hBOOL(hAPP(hAPP(c_member(U_10635),U_10637),U_10636))
        | ~ sP804(U_10637,U_10636,U_10634,U_10635,U_10638) )
    & ! [U_10637,U_10636,U_10634,U_10635,U_10638] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10635,U_10634),hAPP(hAPP(c_COMBC(U_10635,U_10634,U_10634),hAPP(hAPP(c_COMBS(U_10635,U_10634,tc_fun(U_10634,U_10634)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10634,tc_fun(U_10634,U_10634)),U_10635),c_If(U_10634)),hAPP(c_fequal,U_10637))),U_10638)),c_Groups_Oone__class_Oone(U_10634))),U_10636) = hAPP(U_10638,U_10637)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10635),U_10637),U_10636))
        | ~ sP804(U_10637,U_10636,U_10634,U_10635,U_10638) )
    & ! [U_10637,U_10636,U_10634,U_10635,U_10638] :
        ( sP804(U_10637,U_10636,U_10634,U_10635,U_10638)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10635),U_10636))
        | ~ class_Groups_Ocomm__monoid__mult(U_10634) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP804])],[f_2880_2]) ).

cnf(f_2880_4,plain,
    ( sP804(U_10637,U_10636,U_10634,U_10635,U_10638)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10635),U_10636))
    | ~ class_Groups_Ocomm__monoid__mult(U_10634) ),
    inference(clausify,[status(thm)],[f_2880_3]) ).

cnf(f_2880_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10635,U_10634),hAPP(hAPP(c_COMBC(U_10635,U_10634,U_10634),hAPP(hAPP(c_COMBS(U_10635,U_10634,tc_fun(U_10634,U_10634)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10634,tc_fun(U_10634,U_10634)),U_10635),c_If(U_10634)),hAPP(c_fequal,U_10637))),U_10638)),c_Groups_Oone__class_Oone(U_10634))),U_10636) = hAPP(U_10638,U_10637)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10635),U_10637),U_10636))
    | ~ sP804(U_10637,U_10636,U_10634,U_10635,U_10638) ),
    inference(clausify,[status(thm)],[f_2880_3]) ).

cnf(f_2880_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10635,U_10634),hAPP(hAPP(c_COMBC(U_10635,U_10634,U_10634),hAPP(hAPP(c_COMBS(U_10635,U_10634,tc_fun(U_10634,U_10634)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_10634,tc_fun(U_10634,U_10634)),U_10635),c_If(U_10634)),hAPP(c_fequal,U_10637))),U_10638)),c_Groups_Oone__class_Oone(U_10634))),U_10636) = c_Groups_Oone__class_Oone(U_10634)
    | hBOOL(hAPP(hAPP(c_member(U_10635),U_10637),U_10636))
    | ~ sP804(U_10637,U_10636,U_10634,U_10635,U_10638) ),
    inference(clausify,[status(thm)],[f_2880_3]) ).

fof(f_2881_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_2881_2,plain,
    ! [U_10642,U_10641,U_10640,U_10639] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10640,U_10639),hAPP(c_COMBK(U_10639,U_10640),U_10642)),U_10641) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10639),U_10642),hAPP(c_Finite__Set_Ocard(U_10640),U_10641))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10640),U_10641))
      | ~ class_Groups_Ocomm__monoid__mult(U_10639) ),
    inference(variable_rename,[status(thm)],[f_2881_1]) ).

fof(f_2881_3,plain,
    ! [U_10639,U_10642,U_10641,U_10640] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10640,U_10639),hAPP(c_COMBK(U_10639,U_10640),U_10642)),U_10641) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10639),U_10642),hAPP(c_Finite__Set_Ocard(U_10640),U_10641))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10640),U_10641))
      | ~ class_Groups_Ocomm__monoid__mult(U_10639) ),
    inference(definitional_conversion,[status(esa)],[f_2881_2]) ).

cnf(f_2881_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10640,U_10639),hAPP(c_COMBK(U_10639,U_10640),U_10642)),U_10641) = hAPP(hAPP(c_Power_Opower__class_Opower(U_10639),U_10642),hAPP(c_Finite__Set_Ocard(U_10640),U_10641))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10640),U_10641))
    | ~ class_Groups_Ocomm__monoid__mult(U_10639) ),
    inference(clausify,[status(thm)],[f_2881_3]) ).

fof(f_2882_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_2882_2,plain,
    ! [U_10647,U_10646,U_10645,U_10644,U_10643] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10644,U_10643),U_10647),hAPP(hAPP(c_Set_Oinsert(U_10644),U_10646),U_10645)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10643),hAPP(U_10647,U_10646)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10644,U_10643),U_10647),U_10645))
      | hBOOL(hAPP(hAPP(c_member(U_10644),U_10646),U_10645))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10644),U_10645))
      | ~ class_Groups_Ocomm__monoid__mult(U_10643) ),
    inference(variable_rename,[status(thm)],[f_2882_1]) ).

fof(f_2882_3,plain,
    ! [U_10644,U_10643,U_10645,U_10646,U_10647] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10644,U_10643),U_10647),hAPP(hAPP(c_Set_Oinsert(U_10644),U_10646),U_10645)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10643),hAPP(U_10647,U_10646)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10644,U_10643),U_10647),U_10645))
      | hBOOL(hAPP(hAPP(c_member(U_10644),U_10646),U_10645))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10644),U_10645))
      | ~ class_Groups_Ocomm__monoid__mult(U_10643) ),
    inference(definitional_conversion,[status(esa)],[f_2882_2]) ).

cnf(f_2882_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10644,U_10643),U_10647),hAPP(hAPP(c_Set_Oinsert(U_10644),U_10646),U_10645)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10643),hAPP(U_10647,U_10646)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10644,U_10643),U_10647),U_10645))
    | hBOOL(hAPP(hAPP(c_member(U_10644),U_10646),U_10645))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10644),U_10645))
    | ~ class_Groups_Ocomm__monoid__mult(U_10643) ),
    inference(clausify,[status(thm)],[f_2882_3]) ).

fof(f_2883_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_2883_2,plain,
    ! [U_10652,U_10651,U_10650,U_10649,U_10648] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10649,U_10648),U_10652),hAPP(hAPP(c_Set_Oinsert(U_10649),U_10651),U_10650)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10648),hAPP(U_10652,U_10651)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10649,U_10648),U_10652),U_10650))
      | hBOOL(hAPP(hAPP(c_member(U_10649),U_10651),U_10650))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10649),U_10650))
      | ~ class_Groups_Ocomm__monoid__mult(U_10648) ),
    inference(variable_rename,[status(thm)],[f_2883_1]) ).

fof(f_2883_3,plain,
    ! [U_10648,U_10649,U_10650,U_10651,U_10652] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10649,U_10648),U_10652),hAPP(hAPP(c_Set_Oinsert(U_10649),U_10651),U_10650)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10648),hAPP(U_10652,U_10651)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10649,U_10648),U_10652),U_10650))
      | hBOOL(hAPP(hAPP(c_member(U_10649),U_10651),U_10650))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10649),U_10650))
      | ~ class_Groups_Ocomm__monoid__mult(U_10648) ),
    inference(definitional_conversion,[status(esa)],[f_2883_2]) ).

cnf(f_2883_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10649,U_10648),U_10652),hAPP(hAPP(c_Set_Oinsert(U_10649),U_10651),U_10650)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10648),hAPP(U_10652,U_10651)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10649,U_10648),U_10652),U_10650))
    | hBOOL(hAPP(hAPP(c_member(U_10649),U_10651),U_10650))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10649),U_10650))
    | ~ class_Groups_Ocomm__monoid__mult(U_10648) ),
    inference(clausify,[status(thm)],[f_2883_3]) ).

fof(f_2884_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_2884_2,plain,
    ! [U_10659,U_10658,U_10657,U_10656,U_10655,U_10654,U_10653] :
      ( ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10653,tc_Option_Ooption(U_10654)),U_10655),U_10656),hAPP(c_Option_Ooption_OSome(U_10654),U_10657)),U_10658) = hAPP(c_Option_Ooption_OSome(U_10654),U_10659)
        | ( ( hAPP(U_10655,U_10658) != hAPP(c_Option_Ooption_OSome(U_10654),U_10659)
            | U_10658 = U_10656 )
          & ( U_10657 != U_10659
            | U_10658 != U_10656 ) ) )
      & ( ( hAPP(U_10655,U_10658) = hAPP(c_Option_Ooption_OSome(U_10654),U_10659)
          & U_10658 != U_10656 )
        | ( U_10657 = U_10659
          & U_10658 = U_10656 )
        | hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10653,tc_Option_Ooption(U_10654)),U_10655),U_10656),hAPP(c_Option_Ooption_OSome(U_10654),U_10657)),U_10658) != hAPP(c_Option_Ooption_OSome(U_10654),U_10659) ) ),
    inference(variable_rename,[status(thm)],[f_2884_1]) ).

fof(f_2884_3,plain,
    ( ! [U_10673,U_10671,U_10669,U_10667,U_10665,U_10663] :
        ( ! [U_10661] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10661,tc_Option_Ooption(U_10663)),U_10665),U_10667),hAPP(c_Option_Ooption_OSome(U_10663),U_10669)),U_10671) = hAPP(c_Option_Ooption_OSome(U_10663),U_10673)
        | ( ( hAPP(U_10665,U_10671) != hAPP(c_Option_Ooption_OSome(U_10663),U_10673)
            | U_10671 = U_10667 )
          & ( U_10669 != U_10673
            | U_10671 != U_10667 ) ) )
    & ! [U_10672,U_10670,U_10668,U_10666,U_10664,U_10662] :
        ( ! [U_10660] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10660,tc_Option_Ooption(U_10662)),U_10664),U_10666),hAPP(c_Option_Ooption_OSome(U_10662),U_10668)),U_10670) != hAPP(c_Option_Ooption_OSome(U_10662),U_10672)
        | ( hAPP(U_10664,U_10670) = hAPP(c_Option_Ooption_OSome(U_10662),U_10672)
          & U_10670 != U_10666 )
        | ( U_10668 = U_10672
          & U_10670 = U_10666 ) ) ),
    inference(miniscope,[status(thm)],[f_2884_2]) ).

fof(f_2884_4,plain,
    ( ! [U_10669,U_10665,U_10663,U_10673,U_10667,U_10671] :
        ( hAPP(U_10665,U_10671) != hAPP(c_Option_Ooption_OSome(U_10663),U_10673)
        | U_10671 = U_10667
        | ~ sP807(U_10669,U_10665,U_10663,U_10673,U_10667,U_10671) )
    & ! [U_10669,U_10665,U_10663,U_10673,U_10667,U_10671] :
        ( U_10669 != U_10673
        | U_10671 != U_10667
        | ~ sP807(U_10669,U_10665,U_10663,U_10673,U_10667,U_10671) )
    & ! [U_10664,U_10662,U_10666,U_10672,U_10670] :
        ( hAPP(U_10664,U_10670) = hAPP(c_Option_Ooption_OSome(U_10662),U_10672)
        | ~ sP806(U_10664,U_10662,U_10666,U_10672,U_10670) )
    & ! [U_10664,U_10662,U_10666,U_10672,U_10670] :
        ( U_10670 != U_10666
        | ~ sP806(U_10664,U_10662,U_10666,U_10672,U_10670) )
    & ! [U_10666,U_10668,U_10672,U_10670] :
        ( U_10668 = U_10672
        | ~ sP805(U_10666,U_10668,U_10672,U_10670) )
    & ! [U_10666,U_10668,U_10672,U_10670] :
        ( U_10670 = U_10666
        | ~ sP805(U_10666,U_10668,U_10672,U_10670) )
    & ! [U_10669,U_10661,U_10665,U_10663,U_10673,U_10667,U_10671] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10661,tc_Option_Ooption(U_10663)),U_10665),U_10667),hAPP(c_Option_Ooption_OSome(U_10663),U_10669)),U_10671) = hAPP(c_Option_Ooption_OSome(U_10663),U_10673)
        | sP807(U_10669,U_10665,U_10663,U_10673,U_10667,U_10671) )
    & ! [U_10664,U_10662,U_10666,U_10660,U_10668,U_10672,U_10670] :
        ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10660,tc_Option_Ooption(U_10662)),U_10664),U_10666),hAPP(c_Option_Ooption_OSome(U_10662),U_10668)),U_10670) != hAPP(c_Option_Ooption_OSome(U_10662),U_10672)
        | sP806(U_10664,U_10662,U_10666,U_10672,U_10670)
        | sP805(U_10666,U_10668,U_10672,U_10670) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP805,sP806,sP807])],[f_2884_3]) ).

cnf(f_2884_5,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10660,tc_Option_Ooption(U_10662)),U_10664),U_10666),hAPP(c_Option_Ooption_OSome(U_10662),U_10668)),U_10670) != hAPP(c_Option_Ooption_OSome(U_10662),U_10672)
    | sP806(U_10664,U_10662,U_10666,U_10672,U_10670)
    | sP805(U_10666,U_10668,U_10672,U_10670) ),
    inference(clausify,[status(thm)],[f_2884_4]) ).

cnf(f_2884_6,plain,
    ( hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10661,tc_Option_Ooption(U_10663)),U_10665),U_10667),hAPP(c_Option_Ooption_OSome(U_10663),U_10669)),U_10671) = hAPP(c_Option_Ooption_OSome(U_10663),U_10673)
    | sP807(U_10669,U_10665,U_10663,U_10673,U_10667,U_10671) ),
    inference(clausify,[status(thm)],[f_2884_4]) ).

cnf(f_2884_7,plain,
    ( U_10670 = U_10666
    | ~ sP805(U_10666,U_10668,U_10672,U_10670) ),
    inference(clausify,[status(thm)],[f_2884_4]) ).

cnf(f_2884_8,plain,
    ( U_10668 = U_10672
    | ~ sP805(U_10666,U_10668,U_10672,U_10670) ),
    inference(clausify,[status(thm)],[f_2884_4]) ).

cnf(f_2884_9,plain,
    ( U_10670 != U_10666
    | ~ sP806(U_10664,U_10662,U_10666,U_10672,U_10670) ),
    inference(clausify,[status(thm)],[f_2884_4]) ).

cnf(f_2884_10,plain,
    ( hAPP(U_10664,U_10670) = hAPP(c_Option_Ooption_OSome(U_10662),U_10672)
    | ~ sP806(U_10664,U_10662,U_10666,U_10672,U_10670) ),
    inference(clausify,[status(thm)],[f_2884_4]) ).

cnf(f_2884_11,plain,
    ( U_10669 != U_10673
    | U_10671 != U_10667
    | ~ sP807(U_10669,U_10665,U_10663,U_10673,U_10667,U_10671) ),
    inference(clausify,[status(thm)],[f_2884_4]) ).

cnf(f_2884_12,plain,
    ( hAPP(U_10665,U_10671) != hAPP(c_Option_Ooption_OSome(U_10663),U_10673)
    | U_10671 = U_10667
    | ~ sP807(U_10669,U_10665,U_10663,U_10673,U_10667,U_10671) ),
    inference(clausify,[status(thm)],[f_2884_4]) ).

fof(f_2885_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_2885_2,plain,
    ! [U_10678,U_10677,U_10676,U_10675,U_10674] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10678,tc_Option_Ooption(U_10676)),U_10674),U_10675),hAPP(c_Option_Ooption_OSome(U_10676),U_10677)) = U_10674
      | hAPP(U_10674,U_10675) != hAPP(c_Option_Ooption_OSome(U_10676),U_10677) ),
    inference(variable_rename,[status(thm)],[f_2885_1]) ).

fof(f_2885_3,plain,
    ! [U_10675,U_10677,U_10676,U_10678,U_10674] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10678,tc_Option_Ooption(U_10676)),U_10674),U_10675),hAPP(c_Option_Ooption_OSome(U_10676),U_10677)) = U_10674
      | hAPP(U_10674,U_10675) != hAPP(c_Option_Ooption_OSome(U_10676),U_10677) ),
    inference(definitional_conversion,[status(esa)],[f_2885_2]) ).

cnf(f_2885_4,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10678,tc_Option_Ooption(U_10676)),U_10674),U_10675),hAPP(c_Option_Ooption_OSome(U_10676),U_10677)) = U_10674
    | hAPP(U_10674,U_10675) != hAPP(c_Option_Ooption_OSome(U_10676),U_10677) ),
    inference(clausify,[status(thm)],[f_2885_3]) ).

fof(f_2886_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_2886_2,plain,
    ! [U_10685,U_10684,U_10683,U_10682,U_10681,U_10680,U_10679] :
      ( U_10683 = U_10685
      | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10679,tc_Option_Ooption(U_10680)),U_10681),U_10682),hAPP(c_Option_Ooption_OSome(U_10680),U_10683)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10679,tc_Option_Ooption(U_10680)),U_10684),U_10682),hAPP(c_Option_Ooption_OSome(U_10680),U_10685)) ),
    inference(variable_rename,[status(thm)],[f_2886_1]) ).

fof(f_2886_3,plain,
    ! [U_10685,U_10684,U_10683] :
      ( ! [U_10682,U_10681,U_10680,U_10679] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10679,tc_Option_Ooption(U_10680)),U_10681),U_10682),hAPP(c_Option_Ooption_OSome(U_10680),U_10683)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10679,tc_Option_Ooption(U_10680)),U_10684),U_10682),hAPP(c_Option_Ooption_OSome(U_10680),U_10685))
      | U_10683 = U_10685 ),
    inference(miniscope,[status(thm)],[f_2886_2]) ).

fof(f_2886_4,plain,
    ! [U_10679,U_10680,U_10681,U_10682,U_10683,U_10684,U_10685] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10679,tc_Option_Ooption(U_10680)),U_10681),U_10682),hAPP(c_Option_Ooption_OSome(U_10680),U_10683)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10679,tc_Option_Ooption(U_10680)),U_10684),U_10682),hAPP(c_Option_Ooption_OSome(U_10680),U_10685))
      | U_10683 = U_10685 ),
    inference(definitional_conversion,[status(esa)],[f_2886_3]) ).

cnf(f_2886_5,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10679,tc_Option_Ooption(U_10680)),U_10681),U_10682),hAPP(c_Option_Ooption_OSome(U_10680),U_10683)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10679,tc_Option_Ooption(U_10680)),U_10684),U_10682),hAPP(c_Option_Ooption_OSome(U_10680),U_10685))
    | U_10683 = U_10685 ),
    inference(clausify,[status(thm)],[f_2886_4]) ).

fof(f_2887_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_2887_2,plain,
    ! [U_10690,U_10689,U_10688,U_10687,U_10686] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10687,U_10686),U_10689),hAPP(hAPP(c_Set_Oinsert(U_10687),U_10690),U_10688)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10686),hAPP(U_10689,U_10690)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10687,U_10686),U_10689),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10687,tc_HOL_Obool)),U_10688),hAPP(hAPP(c_Set_Oinsert(U_10687),U_10690),c_Orderings_Obot__class_Obot(tc_fun(U_10687,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10687),U_10688))
      | ~ class_Groups_Ocomm__monoid__mult(U_10686) ),
    inference(variable_rename,[status(thm)],[f_2887_1]) ).

fof(f_2887_3,plain,
    ! [U_10687,U_10686,U_10688,U_10689,U_10690] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10687,U_10686),U_10689),hAPP(hAPP(c_Set_Oinsert(U_10687),U_10690),U_10688)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10686),hAPP(U_10689,U_10690)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10687,U_10686),U_10689),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10687,tc_HOL_Obool)),U_10688),hAPP(hAPP(c_Set_Oinsert(U_10687),U_10690),c_Orderings_Obot__class_Obot(tc_fun(U_10687,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10687),U_10688))
      | ~ class_Groups_Ocomm__monoid__mult(U_10686) ),
    inference(definitional_conversion,[status(esa)],[f_2887_2]) ).

cnf(f_2887_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10687,U_10686),U_10689),hAPP(hAPP(c_Set_Oinsert(U_10687),U_10690),U_10688)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10686),hAPP(U_10689,U_10690)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10687,U_10686),U_10689),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10687,tc_HOL_Obool)),U_10688),hAPP(hAPP(c_Set_Oinsert(U_10687),U_10690),c_Orderings_Obot__class_Obot(tc_fun(U_10687,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10687),U_10688))
    | ~ class_Groups_Ocomm__monoid__mult(U_10686) ),
    inference(clausify,[status(thm)],[f_2887_3]) ).

fof(f_2888_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_2888_2,plain,
    ! [U_10694,U_10693,U_10692,U_10691] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10691,tc_Option_Ooption(U_10692)),hAPP(c_COMBK(tc_Option_Ooption(U_10692),U_10691),c_Option_Ooption_ONone(U_10692))),U_10693),c_Option_Ooption_ONone(U_10692)),U_10694) = c_Option_Ooption_ONone(U_10692),
    inference(variable_rename,[status(thm)],[f_2888_1]) ).

fof(f_2888_3,plain,
    ! [U_10692,U_10691,U_10693,U_10694] : hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10691,tc_Option_Ooption(U_10692)),hAPP(c_COMBK(tc_Option_Ooption(U_10692),U_10691),c_Option_Ooption_ONone(U_10692))),U_10693),c_Option_Ooption_ONone(U_10692)),U_10694) = c_Option_Ooption_ONone(U_10692),
    inference(definitional_conversion,[status(esa)],[f_2888_2]) ).

cnf(f_2888_4,plain,
    hAPP(hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10691,tc_Option_Ooption(U_10692)),hAPP(c_COMBK(tc_Option_Ooption(U_10692),U_10691),c_Option_Ooption_ONone(U_10692))),U_10693),c_Option_Ooption_ONone(U_10692)),U_10694) = c_Option_Ooption_ONone(U_10692),
    inference(clausify,[status(thm)],[f_2888_3]) ).

fof(f_2889_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_2889_2,plain,
    ! [U_10699,U_10698,U_10697,U_10696,U_10695] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10696,U_10695),U_10699),U_10697) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10695),hAPP(U_10699,U_10698)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10696,U_10695),U_10699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10696,tc_HOL_Obool)),U_10697),hAPP(hAPP(c_Set_Oinsert(U_10696),U_10698),c_Orderings_Obot__class_Obot(tc_fun(U_10696,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10696),U_10698),U_10697))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10696),U_10697))
      | ~ class_Groups_Ocomm__monoid__mult(U_10695) ),
    inference(variable_rename,[status(thm)],[f_2889_1]) ).

fof(f_2889_3,plain,
    ! [U_10695,U_10696,U_10697,U_10698,U_10699] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10696,U_10695),U_10699),U_10697) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10695),hAPP(U_10699,U_10698)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10696,U_10695),U_10699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10696,tc_HOL_Obool)),U_10697),hAPP(hAPP(c_Set_Oinsert(U_10696),U_10698),c_Orderings_Obot__class_Obot(tc_fun(U_10696,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10696),U_10698),U_10697))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10696),U_10697))
      | ~ class_Groups_Ocomm__monoid__mult(U_10695) ),
    inference(definitional_conversion,[status(esa)],[f_2889_2]) ).

cnf(f_2889_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10696,U_10695),U_10699),U_10697) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_10695),hAPP(U_10699,U_10698)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10696,U_10695),U_10699),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10696,tc_HOL_Obool)),U_10697),hAPP(hAPP(c_Set_Oinsert(U_10696),U_10698),c_Orderings_Obot__class_Obot(tc_fun(U_10696,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10696),U_10698),U_10697))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10696),U_10697))
    | ~ class_Groups_Ocomm__monoid__mult(U_10695) ),
    inference(clausify,[status(thm)],[f_2889_3]) ).

fof(f_2890_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_2890_2,plain,
    ! [U_10704,U_10703,U_10702,U_10701,U_10700] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10701,U_10700),U_10703),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10701,tc_HOL_Obool)),U_10702),hAPP(hAPP(c_Set_Oinsert(U_10701),U_10704),c_Orderings_Obot__class_Obot(tc_fun(U_10701,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10701,U_10700),U_10703),U_10702)
          | hBOOL(hAPP(hAPP(c_member(U_10701),U_10704),U_10702)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10701,U_10700),U_10703),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10701,tc_HOL_Obool)),U_10702),hAPP(hAPP(c_Set_Oinsert(U_10701),U_10704),c_Orderings_Obot__class_Obot(tc_fun(U_10701,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10700),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10701,U_10700),U_10703),U_10702)),hAPP(U_10703,U_10704))
          | ~ hBOOL(hAPP(hAPP(c_member(U_10701),U_10704),U_10702)) ) )
      | hAPP(U_10703,U_10704) = c_Groups_Ozero__class_Ozero(U_10700)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10701),U_10702))
      | ~ class_Fields_Ofield(U_10700) ),
    inference(variable_rename,[status(thm)],[f_2890_1]) ).

fof(f_2890_3,plain,
    ( ! [U_10700,U_10701,U_10702,U_10703,U_10704] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10701,U_10700),U_10703),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10701,tc_HOL_Obool)),U_10702),hAPP(hAPP(c_Set_Oinsert(U_10701),U_10704),c_Orderings_Obot__class_Obot(tc_fun(U_10701,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10701,U_10700),U_10703),U_10702)
        | hBOOL(hAPP(hAPP(c_member(U_10701),U_10704),U_10702))
        | ~ sP808(U_10700,U_10701,U_10702,U_10703,U_10704) )
    & ! [U_10700,U_10701,U_10702,U_10703,U_10704] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10701,U_10700),U_10703),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10701,tc_HOL_Obool)),U_10702),hAPP(hAPP(c_Set_Oinsert(U_10701),U_10704),c_Orderings_Obot__class_Obot(tc_fun(U_10701,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10700),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10701,U_10700),U_10703),U_10702)),hAPP(U_10703,U_10704))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10701),U_10704),U_10702))
        | ~ sP808(U_10700,U_10701,U_10702,U_10703,U_10704) )
    & ! [U_10700,U_10701,U_10702,U_10703,U_10704] :
        ( sP808(U_10700,U_10701,U_10702,U_10703,U_10704)
        | hAPP(U_10703,U_10704) = c_Groups_Ozero__class_Ozero(U_10700)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10701),U_10702))
        | ~ class_Fields_Ofield(U_10700) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP808])],[f_2890_2]) ).

cnf(f_2890_4,plain,
    ( sP808(U_10700,U_10701,U_10702,U_10703,U_10704)
    | hAPP(U_10703,U_10704) = c_Groups_Ozero__class_Ozero(U_10700)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10701),U_10702))
    | ~ class_Fields_Ofield(U_10700) ),
    inference(clausify,[status(thm)],[f_2890_3]) ).

cnf(f_2890_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10701,U_10700),U_10703),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10701,tc_HOL_Obool)),U_10702),hAPP(hAPP(c_Set_Oinsert(U_10701),U_10704),c_Orderings_Obot__class_Obot(tc_fun(U_10701,tc_HOL_Obool))))) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_10700),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10701,U_10700),U_10703),U_10702)),hAPP(U_10703,U_10704))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10701),U_10704),U_10702))
    | ~ sP808(U_10700,U_10701,U_10702,U_10703,U_10704) ),
    inference(clausify,[status(thm)],[f_2890_3]) ).

cnf(f_2890_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10701,U_10700),U_10703),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10701,tc_HOL_Obool)),U_10702),hAPP(hAPP(c_Set_Oinsert(U_10701),U_10704),c_Orderings_Obot__class_Obot(tc_fun(U_10701,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10701,U_10700),U_10703),U_10702)
    | hBOOL(hAPP(hAPP(c_member(U_10701),U_10704),U_10702))
    | ~ sP808(U_10700,U_10701,U_10702,U_10703,U_10704) ),
    inference(clausify,[status(thm)],[f_2890_3]) ).

fof(f_2891_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_2891_2,plain,
    ! [U_10709,U_10708,U_10707,U_10706,U_10705] :
      ( c_Map_Oran(U_10708,U_10707,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10708,tc_Option_Ooption(U_10707)),U_10705),U_10706),hAPP(c_Option_Ooption_OSome(U_10707),U_10709))) = hAPP(hAPP(c_Set_Oinsert(U_10707),U_10709),c_Map_Oran(U_10708,U_10707,U_10705))
      | hAPP(U_10705,U_10706) != c_Option_Ooption_ONone(U_10707) ),
    inference(variable_rename,[status(thm)],[f_2891_1]) ).

fof(f_2891_3,plain,
    ! [U_10707,U_10708,U_10706,U_10709,U_10705] :
      ( c_Map_Oran(U_10708,U_10707,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10708,tc_Option_Ooption(U_10707)),U_10705),U_10706),hAPP(c_Option_Ooption_OSome(U_10707),U_10709))) = hAPP(hAPP(c_Set_Oinsert(U_10707),U_10709),c_Map_Oran(U_10708,U_10707,U_10705))
      | hAPP(U_10705,U_10706) != c_Option_Ooption_ONone(U_10707) ),
    inference(definitional_conversion,[status(esa)],[f_2891_2]) ).

cnf(f_2891_4,plain,
    ( c_Map_Oran(U_10708,U_10707,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10708,tc_Option_Ooption(U_10707)),U_10705),U_10706),hAPP(c_Option_Ooption_OSome(U_10707),U_10709))) = hAPP(hAPP(c_Set_Oinsert(U_10707),U_10709),c_Map_Oran(U_10708,U_10707,U_10705))
    | hAPP(U_10705,U_10706) != c_Option_Ooption_ONone(U_10707) ),
    inference(clausify,[status(thm)],[f_2891_3]) ).

fof(f_2892_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_2892_2,plain,
    ! [U_10714,U_10713,U_10712,U_10711,U_10710] :
      ( ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10710,tc_Option_Ooption(U_10713)),c_Map_Orestrict__map(U_10710,U_10713,U_10714,U_10712)),U_10711),c_Option_Ooption_ONone(U_10713)) = c_Map_Orestrict__map(U_10710,U_10713,U_10714,U_10712)
        | hBOOL(hAPP(hAPP(c_member(U_10710),U_10711),U_10712)) )
      & ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10710,tc_Option_Ooption(U_10713)),c_Map_Orestrict__map(U_10710,U_10713,U_10714,U_10712)),U_10711),c_Option_Ooption_ONone(U_10713)) = c_Map_Orestrict__map(U_10710,U_10713,U_10714,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10710,tc_HOL_Obool)),U_10712),hAPP(hAPP(c_Set_Oinsert(U_10710),U_10711),c_Orderings_Obot__class_Obot(tc_fun(U_10710,tc_HOL_Obool)))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10710),U_10711),U_10712)) ) ),
    inference(variable_rename,[status(thm)],[f_2892_1]) ).

fof(f_2892_3,plain,
    ( ! [U_10724,U_10722,U_10720,U_10718,U_10716] :
        ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10716,tc_Option_Ooption(U_10722)),c_Map_Orestrict__map(U_10716,U_10722,U_10724,U_10720)),U_10718),c_Option_Ooption_ONone(U_10722)) = c_Map_Orestrict__map(U_10716,U_10722,U_10724,U_10720)
        | hBOOL(hAPP(hAPP(c_member(U_10716),U_10718),U_10720)) )
    & ! [U_10723,U_10721,U_10719,U_10717,U_10715] :
        ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10715,tc_Option_Ooption(U_10721)),c_Map_Orestrict__map(U_10715,U_10721,U_10723,U_10719)),U_10717),c_Option_Ooption_ONone(U_10721)) = c_Map_Orestrict__map(U_10715,U_10721,U_10723,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10715,tc_HOL_Obool)),U_10719),hAPP(hAPP(c_Set_Oinsert(U_10715),U_10717),c_Orderings_Obot__class_Obot(tc_fun(U_10715,tc_HOL_Obool)))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10715),U_10717),U_10719)) ) ),
    inference(miniscope,[status(thm)],[f_2892_2]) ).

fof(f_2892_4,plain,
    ( ! [U_10716,U_10718,U_10720,U_10722,U_10724] :
        ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10716,tc_Option_Ooption(U_10722)),c_Map_Orestrict__map(U_10716,U_10722,U_10724,U_10720)),U_10718),c_Option_Ooption_ONone(U_10722)) = c_Map_Orestrict__map(U_10716,U_10722,U_10724,U_10720)
        | hBOOL(hAPP(hAPP(c_member(U_10716),U_10718),U_10720)) )
    & ! [U_10715,U_10717,U_10719,U_10721,U_10723] :
        ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10715,tc_Option_Ooption(U_10721)),c_Map_Orestrict__map(U_10715,U_10721,U_10723,U_10719)),U_10717),c_Option_Ooption_ONone(U_10721)) = c_Map_Orestrict__map(U_10715,U_10721,U_10723,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10715,tc_HOL_Obool)),U_10719),hAPP(hAPP(c_Set_Oinsert(U_10715),U_10717),c_Orderings_Obot__class_Obot(tc_fun(U_10715,tc_HOL_Obool)))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10715),U_10717),U_10719)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2892_3]) ).

cnf(f_2892_5,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10715,tc_Option_Ooption(U_10721)),c_Map_Orestrict__map(U_10715,U_10721,U_10723,U_10719)),U_10717),c_Option_Ooption_ONone(U_10721)) = c_Map_Orestrict__map(U_10715,U_10721,U_10723,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10715,tc_HOL_Obool)),U_10719),hAPP(hAPP(c_Set_Oinsert(U_10715),U_10717),c_Orderings_Obot__class_Obot(tc_fun(U_10715,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10715),U_10717),U_10719)) ),
    inference(clausify,[status(thm)],[f_2892_4]) ).

cnf(f_2892_6,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10716,tc_Option_Ooption(U_10722)),c_Map_Orestrict__map(U_10716,U_10722,U_10724,U_10720)),U_10718),c_Option_Ooption_ONone(U_10722)) = c_Map_Orestrict__map(U_10716,U_10722,U_10724,U_10720)
    | hBOOL(hAPP(hAPP(c_member(U_10716),U_10718),U_10720)) ),
    inference(clausify,[status(thm)],[f_2892_4]) ).

fof(f_2893_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_2893_2,plain,
    ! [U_10727,U_10726,U_10725] : c_Map_Oran(U_10725,U_10726,U_10727) = hAPP(c_Set_OCollect(U_10726),hAPP(hAPP(c_COMBB(tc_fun(U_10725,tc_HOL_Obool),tc_HOL_Obool,U_10726),c_HOL_OEx(U_10725)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_10726),tc_fun(U_10725,tc_HOL_Obool),U_10726),hAPP(c_COMBC(U_10725,tc_Option_Ooption(U_10726),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_10726),tc_fun(tc_Option_Ooption(U_10726),tc_HOL_Obool),U_10725),c_fequal),U_10727))),c_Option_Ooption_OSome(U_10726)))),
    inference(variable_rename,[status(thm)],[f_2893_1]) ).

fof(f_2893_3,plain,
    ! [U_10725,U_10726,U_10727] : c_Map_Oran(U_10725,U_10726,U_10727) = hAPP(c_Set_OCollect(U_10726),hAPP(hAPP(c_COMBB(tc_fun(U_10725,tc_HOL_Obool),tc_HOL_Obool,U_10726),c_HOL_OEx(U_10725)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_10726),tc_fun(U_10725,tc_HOL_Obool),U_10726),hAPP(c_COMBC(U_10725,tc_Option_Ooption(U_10726),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_10726),tc_fun(tc_Option_Ooption(U_10726),tc_HOL_Obool),U_10725),c_fequal),U_10727))),c_Option_Ooption_OSome(U_10726)))),
    inference(definitional_conversion,[status(esa)],[f_2893_2]) ).

cnf(f_2893_4,plain,
    c_Map_Oran(U_10725,U_10726,U_10727) = hAPP(c_Set_OCollect(U_10726),hAPP(hAPP(c_COMBB(tc_fun(U_10725,tc_HOL_Obool),tc_HOL_Obool,U_10726),c_HOL_OEx(U_10725)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_10726),tc_fun(U_10725,tc_HOL_Obool),U_10726),hAPP(c_COMBC(U_10725,tc_Option_Ooption(U_10726),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_10726),tc_fun(tc_Option_Ooption(U_10726),tc_HOL_Obool),U_10725),c_fequal),U_10727))),c_Option_Ooption_OSome(U_10726)))),
    inference(clausify,[status(thm)],[f_2893_3]) ).

fof(f_2894_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_2894_2,plain,
    ! [U_10732,U_10731,U_10730,U_10729,U_10728] :
      ( hAPP(c_Map_Orestrict__map(U_10728,U_10731,U_10732,U_10730),U_10729) = hAPP(U_10732,U_10729)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10728),U_10729),U_10730)) ),
    inference(variable_rename,[status(thm)],[f_2894_1]) ).

fof(f_2894_3,plain,
    ! [U_10728,U_10729,U_10730,U_10731,U_10732] :
      ( hAPP(c_Map_Orestrict__map(U_10728,U_10731,U_10732,U_10730),U_10729) = hAPP(U_10732,U_10729)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10728),U_10729),U_10730)) ),
    inference(definitional_conversion,[status(esa)],[f_2894_2]) ).

cnf(f_2894_4,plain,
    ( hAPP(c_Map_Orestrict__map(U_10728,U_10731,U_10732,U_10730),U_10729) = hAPP(U_10732,U_10729)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10728),U_10729),U_10730)) ),
    inference(clausify,[status(thm)],[f_2894_3]) ).

fof(f_2895_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_2895_2,plain,
    ! [U_10736,U_10735,U_10734,U_10733] : hAPP(c_Map_Orestrict__map(U_10733,U_10734,hAPP(c_COMBK(tc_Option_Ooption(U_10734),U_10733),c_Option_Ooption_ONone(U_10734)),U_10735),U_10736) = c_Option_Ooption_ONone(U_10734),
    inference(variable_rename,[status(thm)],[f_2895_1]) ).

fof(f_2895_3,plain,
    ! [U_10734,U_10733,U_10735,U_10736] : hAPP(c_Map_Orestrict__map(U_10733,U_10734,hAPP(c_COMBK(tc_Option_Ooption(U_10734),U_10733),c_Option_Ooption_ONone(U_10734)),U_10735),U_10736) = c_Option_Ooption_ONone(U_10734),
    inference(definitional_conversion,[status(esa)],[f_2895_2]) ).

cnf(f_2895_4,plain,
    hAPP(c_Map_Orestrict__map(U_10733,U_10734,hAPP(c_COMBK(tc_Option_Ooption(U_10734),U_10733),c_Option_Ooption_ONone(U_10734)),U_10735),U_10736) = c_Option_Ooption_ONone(U_10734),
    inference(clausify,[status(thm)],[f_2895_3]) ).

fof(f_2896_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_2896_2,plain,
    ! [U_10741,U_10740,U_10739,U_10738,U_10737] :
      ( hAPP(c_Map_Orestrict__map(U_10737,U_10740,U_10741,U_10739),U_10738) = c_Option_Ooption_ONone(U_10740)
      | hBOOL(hAPP(hAPP(c_member(U_10737),U_10738),U_10739)) ),
    inference(variable_rename,[status(thm)],[f_2896_1]) ).

fof(f_2896_3,plain,
    ! [U_10737,U_10738,U_10739,U_10740,U_10741] :
      ( hAPP(c_Map_Orestrict__map(U_10737,U_10740,U_10741,U_10739),U_10738) = c_Option_Ooption_ONone(U_10740)
      | hBOOL(hAPP(hAPP(c_member(U_10737),U_10738),U_10739)) ),
    inference(definitional_conversion,[status(esa)],[f_2896_2]) ).

cnf(f_2896_4,plain,
    ( hAPP(c_Map_Orestrict__map(U_10737,U_10740,U_10741,U_10739),U_10738) = c_Option_Ooption_ONone(U_10740)
    | hBOOL(hAPP(hAPP(c_member(U_10737),U_10738),U_10739)) ),
    inference(clausify,[status(thm)],[f_2896_3]) ).

fof(f_2897_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_2897_2,plain,
    ! [U_10746,U_10745,U_10744,U_10743,U_10742] : c_Map_Orestrict__map(U_10742,U_10743,U_10744,hAPP(hAPP(c_Set_Oinsert(U_10742),U_10745),U_10746)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10742,tc_Option_Ooption(U_10743)),c_Map_Orestrict__map(U_10742,U_10743,U_10744,U_10746)),U_10745),hAPP(U_10744,U_10745)),
    inference(variable_rename,[status(thm)],[f_2897_1]) ).

fof(f_2897_3,plain,
    ! [U_10742,U_10743,U_10744,U_10745,U_10746] : c_Map_Orestrict__map(U_10742,U_10743,U_10744,hAPP(hAPP(c_Set_Oinsert(U_10742),U_10745),U_10746)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10742,tc_Option_Ooption(U_10743)),c_Map_Orestrict__map(U_10742,U_10743,U_10744,U_10746)),U_10745),hAPP(U_10744,U_10745)),
    inference(definitional_conversion,[status(esa)],[f_2897_2]) ).

cnf(f_2897_4,plain,
    c_Map_Orestrict__map(U_10742,U_10743,U_10744,hAPP(hAPP(c_Set_Oinsert(U_10742),U_10745),U_10746)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10742,tc_Option_Ooption(U_10743)),c_Map_Orestrict__map(U_10742,U_10743,U_10744,U_10746)),U_10745),hAPP(U_10744,U_10745)),
    inference(clausify,[status(thm)],[f_2897_3]) ).

fof(f_2898_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_2898_2,plain,
    ! [U_10751,U_10750,U_10749,U_10748,U_10747] :
      ( ( hAPP(c_Map_Orestrict__map(U_10747,U_10750,U_10751,U_10749),U_10748) = c_Option_Ooption_ONone(U_10750)
        | hBOOL(hAPP(hAPP(c_member(U_10747),U_10748),U_10749)) )
      & ( hAPP(c_Map_Orestrict__map(U_10747,U_10750,U_10751,U_10749),U_10748) = hAPP(U_10751,U_10748)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10747),U_10748),U_10749)) ) ),
    inference(variable_rename,[status(thm)],[f_2898_1]) ).

fof(f_2898_3,plain,
    ( ! [U_10761,U_10759,U_10757,U_10755,U_10753] :
        ( hAPP(c_Map_Orestrict__map(U_10753,U_10759,U_10761,U_10757),U_10755) = c_Option_Ooption_ONone(U_10759)
        | hBOOL(hAPP(hAPP(c_member(U_10753),U_10755),U_10757)) )
    & ! [U_10760,U_10758,U_10756,U_10754,U_10752] :
        ( hAPP(c_Map_Orestrict__map(U_10752,U_10758,U_10760,U_10756),U_10754) = hAPP(U_10760,U_10754)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10752),U_10754),U_10756)) ) ),
    inference(miniscope,[status(thm)],[f_2898_2]) ).

fof(f_2898_4,plain,
    ( ! [U_10753,U_10757,U_10759,U_10755,U_10761] :
        ( hAPP(c_Map_Orestrict__map(U_10753,U_10759,U_10761,U_10757),U_10755) = c_Option_Ooption_ONone(U_10759)
        | hBOOL(hAPP(hAPP(c_member(U_10753),U_10755),U_10757)) )
    & ! [U_10752,U_10754,U_10760,U_10756,U_10758] :
        ( hAPP(c_Map_Orestrict__map(U_10752,U_10758,U_10760,U_10756),U_10754) = hAPP(U_10760,U_10754)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10752),U_10754),U_10756)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2898_3]) ).

cnf(f_2898_5,plain,
    ( hAPP(c_Map_Orestrict__map(U_10752,U_10758,U_10760,U_10756),U_10754) = hAPP(U_10760,U_10754)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10752),U_10754),U_10756)) ),
    inference(clausify,[status(thm)],[f_2898_4]) ).

cnf(f_2898_6,plain,
    ( hAPP(c_Map_Orestrict__map(U_10753,U_10759,U_10761,U_10757),U_10755) = c_Option_Ooption_ONone(U_10759)
    | hBOOL(hAPP(hAPP(c_member(U_10753),U_10755),U_10757)) ),
    inference(clausify,[status(thm)],[f_2898_4]) ).

fof(f_2899_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_2899_2,plain,
    ! [U_10765,U_10764,U_10763,U_10762] : hAPP(c_Map_Orestrict__map(U_10762,U_10763,U_10764,c_Orderings_Obot__class_Obot(tc_fun(U_10762,tc_HOL_Obool))),U_10765) = c_Option_Ooption_ONone(U_10763),
    inference(variable_rename,[status(thm)],[f_2899_1]) ).

fof(f_2899_3,plain,
    ! [U_10763,U_10762,U_10764,U_10765] : hAPP(c_Map_Orestrict__map(U_10762,U_10763,U_10764,c_Orderings_Obot__class_Obot(tc_fun(U_10762,tc_HOL_Obool))),U_10765) = c_Option_Ooption_ONone(U_10763),
    inference(definitional_conversion,[status(esa)],[f_2899_2]) ).

cnf(f_2899_4,plain,
    hAPP(c_Map_Orestrict__map(U_10762,U_10763,U_10764,c_Orderings_Obot__class_Obot(tc_fun(U_10762,tc_HOL_Obool))),U_10765) = c_Option_Ooption_ONone(U_10763),
    inference(clausify,[status(thm)],[f_2899_3]) ).

fof(f_2900_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_2900_2,plain,
    ! [U_10770,U_10769,U_10768,U_10767,U_10766] :
      ( hBOOL(hAPP(hAPP(c_member(U_10768),U_10769),c_Map_Oran(U_10770,U_10768,U_10766)))
      | hAPP(U_10766,U_10767) != hAPP(c_Option_Ooption_OSome(U_10768),U_10769) ),
    inference(variable_rename,[status(thm)],[f_2900_1]) ).

fof(f_2900_3,plain,
    ! [U_10766,U_10767,U_10768,U_10769,U_10770] :
      ( hBOOL(hAPP(hAPP(c_member(U_10768),U_10769),c_Map_Oran(U_10770,U_10768,U_10766)))
      | hAPP(U_10766,U_10767) != hAPP(c_Option_Ooption_OSome(U_10768),U_10769) ),
    inference(definitional_conversion,[status(esa)],[f_2900_2]) ).

cnf(f_2900_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10768),U_10769),c_Map_Oran(U_10770,U_10768,U_10766)))
    | hAPP(U_10766,U_10767) != hAPP(c_Option_Ooption_OSome(U_10768),U_10769) ),
    inference(clausify,[status(thm)],[f_2900_3]) ).

fof(f_2901_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_2901_2,plain,
    ! [U_10776,U_10775,U_10774,U_10773,U_10772,U_10771] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10771,tc_Option_Ooption(U_10772)),c_Map_Orestrict__map(U_10771,U_10772,U_10773,U_10774)),U_10775),U_10776) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10771,tc_Option_Ooption(U_10772)),c_Map_Orestrict__map(U_10771,U_10772,U_10773,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10771,tc_HOL_Obool)),U_10774),hAPP(hAPP(c_Set_Oinsert(U_10771),U_10775),c_Orderings_Obot__class_Obot(tc_fun(U_10771,tc_HOL_Obool)))))),U_10775),U_10776),
    inference(variable_rename,[status(thm)],[f_2901_1]) ).

fof(f_2901_3,plain,
    ! [U_10771,U_10772,U_10773,U_10774,U_10775,U_10776] : hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10771,tc_Option_Ooption(U_10772)),c_Map_Orestrict__map(U_10771,U_10772,U_10773,U_10774)),U_10775),U_10776) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10771,tc_Option_Ooption(U_10772)),c_Map_Orestrict__map(U_10771,U_10772,U_10773,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10771,tc_HOL_Obool)),U_10774),hAPP(hAPP(c_Set_Oinsert(U_10771),U_10775),c_Orderings_Obot__class_Obot(tc_fun(U_10771,tc_HOL_Obool)))))),U_10775),U_10776),
    inference(definitional_conversion,[status(esa)],[f_2901_2]) ).

cnf(f_2901_4,plain,
    hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10771,tc_Option_Ooption(U_10772)),c_Map_Orestrict__map(U_10771,U_10772,U_10773,U_10774)),U_10775),U_10776) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10771,tc_Option_Ooption(U_10772)),c_Map_Orestrict__map(U_10771,U_10772,U_10773,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10771,tc_HOL_Obool)),U_10774),hAPP(hAPP(c_Set_Oinsert(U_10771),U_10775),c_Orderings_Obot__class_Obot(tc_fun(U_10771,tc_HOL_Obool)))))),U_10775),U_10776),
    inference(clausify,[status(thm)],[f_2901_3]) ).

fof(f_2902_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_2902_2,plain,
    ! [U_10778,U_10777] : c_Map_Oran(U_10777,U_10778,hAPP(c_COMBK(tc_Option_Ooption(U_10778),U_10777),c_Option_Ooption_ONone(U_10778))) = c_Orderings_Obot__class_Obot(tc_fun(U_10778,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2902_1]) ).

fof(f_2902_3,plain,
    ! [U_10778,U_10777] : c_Map_Oran(U_10777,U_10778,hAPP(c_COMBK(tc_Option_Ooption(U_10778),U_10777),c_Option_Ooption_ONone(U_10778))) = c_Orderings_Obot__class_Obot(tc_fun(U_10778,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2902_2]) ).

cnf(f_2902_4,plain,
    c_Map_Oran(U_10777,U_10778,hAPP(c_COMBK(tc_Option_Ooption(U_10778),U_10777),c_Option_Ooption_ONone(U_10778))) = c_Orderings_Obot__class_Obot(tc_fun(U_10778,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2902_3]) ).

fof(f_2903_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_2903_2,plain,
    ! [U_10784,U_10783,U_10782,U_10781,U_10780,U_10779] :
      ( ( c_Map_Orestrict__map(U_10779,U_10782,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10779,tc_Option_Ooption(U_10782)),U_10783),U_10780),U_10784),U_10781) = c_Map_Orestrict__map(U_10779,U_10782,U_10783,U_10781)
        | hBOOL(hAPP(hAPP(c_member(U_10779),U_10780),U_10781)) )
      & ( c_Map_Orestrict__map(U_10779,U_10782,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10779,tc_Option_Ooption(U_10782)),U_10783),U_10780),U_10784),U_10781) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10779,tc_Option_Ooption(U_10782)),c_Map_Orestrict__map(U_10779,U_10782,U_10783,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10779,tc_HOL_Obool)),U_10781),hAPP(hAPP(c_Set_Oinsert(U_10779),U_10780),c_Orderings_Obot__class_Obot(tc_fun(U_10779,tc_HOL_Obool)))))),U_10780),U_10784)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10779),U_10780),U_10781)) ) ),
    inference(variable_rename,[status(thm)],[f_2903_1]) ).

fof(f_2903_3,plain,
    ( ! [U_10796,U_10794,U_10792,U_10790,U_10788,U_10786] :
        ( c_Map_Orestrict__map(U_10786,U_10792,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10786,tc_Option_Ooption(U_10792)),U_10794),U_10788),U_10796),U_10790) = c_Map_Orestrict__map(U_10786,U_10792,U_10794,U_10790)
        | hBOOL(hAPP(hAPP(c_member(U_10786),U_10788),U_10790)) )
    & ! [U_10795,U_10793,U_10791,U_10789,U_10787,U_10785] :
        ( c_Map_Orestrict__map(U_10785,U_10791,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10785,tc_Option_Ooption(U_10791)),U_10793),U_10787),U_10795),U_10789) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10785,tc_Option_Ooption(U_10791)),c_Map_Orestrict__map(U_10785,U_10791,U_10793,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10785,tc_HOL_Obool)),U_10789),hAPP(hAPP(c_Set_Oinsert(U_10785),U_10787),c_Orderings_Obot__class_Obot(tc_fun(U_10785,tc_HOL_Obool)))))),U_10787),U_10795)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10785),U_10787),U_10789)) ) ),
    inference(miniscope,[status(thm)],[f_2903_2]) ).

fof(f_2903_4,plain,
    ( ! [U_10786,U_10788,U_10796,U_10790,U_10792,U_10794] :
        ( c_Map_Orestrict__map(U_10786,U_10792,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10786,tc_Option_Ooption(U_10792)),U_10794),U_10788),U_10796),U_10790) = c_Map_Orestrict__map(U_10786,U_10792,U_10794,U_10790)
        | hBOOL(hAPP(hAPP(c_member(U_10786),U_10788),U_10790)) )
    & ! [U_10785,U_10787,U_10789,U_10791,U_10793,U_10795] :
        ( c_Map_Orestrict__map(U_10785,U_10791,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10785,tc_Option_Ooption(U_10791)),U_10793),U_10787),U_10795),U_10789) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10785,tc_Option_Ooption(U_10791)),c_Map_Orestrict__map(U_10785,U_10791,U_10793,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10785,tc_HOL_Obool)),U_10789),hAPP(hAPP(c_Set_Oinsert(U_10785),U_10787),c_Orderings_Obot__class_Obot(tc_fun(U_10785,tc_HOL_Obool)))))),U_10787),U_10795)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10785),U_10787),U_10789)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2903_3]) ).

cnf(f_2903_5,plain,
    ( c_Map_Orestrict__map(U_10785,U_10791,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10785,tc_Option_Ooption(U_10791)),U_10793),U_10787),U_10795),U_10789) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10785,tc_Option_Ooption(U_10791)),c_Map_Orestrict__map(U_10785,U_10791,U_10793,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10785,tc_HOL_Obool)),U_10789),hAPP(hAPP(c_Set_Oinsert(U_10785),U_10787),c_Orderings_Obot__class_Obot(tc_fun(U_10785,tc_HOL_Obool)))))),U_10787),U_10795)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10785),U_10787),U_10789)) ),
    inference(clausify,[status(thm)],[f_2903_4]) ).

cnf(f_2903_6,plain,
    ( c_Map_Orestrict__map(U_10786,U_10792,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10786,tc_Option_Ooption(U_10792)),U_10794),U_10788),U_10796),U_10790) = c_Map_Orestrict__map(U_10786,U_10792,U_10794,U_10790)
    | hBOOL(hAPP(hAPP(c_member(U_10786),U_10788),U_10790)) ),
    inference(clausify,[status(thm)],[f_2903_4]) ).

fof(f_2904_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_2904_2,plain,
    ! [U_10802,U_10801,U_10800,U_10799,U_10798,U_10797] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10797,tc_Option_Ooption(U_10800)),c_Map_Orestrict__map(U_10797,U_10800,U_10801,U_10799)),U_10798),U_10802) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10797,tc_Option_Ooption(U_10800)),c_Map_Orestrict__map(U_10797,U_10800,U_10801,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10797,tc_HOL_Obool)),U_10799),hAPP(hAPP(c_Set_Oinsert(U_10797),U_10798),c_Orderings_Obot__class_Obot(tc_fun(U_10797,tc_HOL_Obool)))))),U_10798),U_10802)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10797),U_10798),U_10799)) ),
    inference(variable_rename,[status(thm)],[f_2904_1]) ).

fof(f_2904_3,plain,
    ! [U_10797,U_10798,U_10799,U_10800,U_10801,U_10802] :
      ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10797,tc_Option_Ooption(U_10800)),c_Map_Orestrict__map(U_10797,U_10800,U_10801,U_10799)),U_10798),U_10802) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10797,tc_Option_Ooption(U_10800)),c_Map_Orestrict__map(U_10797,U_10800,U_10801,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10797,tc_HOL_Obool)),U_10799),hAPP(hAPP(c_Set_Oinsert(U_10797),U_10798),c_Orderings_Obot__class_Obot(tc_fun(U_10797,tc_HOL_Obool)))))),U_10798),U_10802)
      | ~ hBOOL(hAPP(hAPP(c_member(U_10797),U_10798),U_10799)) ),
    inference(definitional_conversion,[status(esa)],[f_2904_2]) ).

cnf(f_2904_4,plain,
    ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10797,tc_Option_Ooption(U_10800)),c_Map_Orestrict__map(U_10797,U_10800,U_10801,U_10799)),U_10798),U_10802) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10797,tc_Option_Ooption(U_10800)),c_Map_Orestrict__map(U_10797,U_10800,U_10801,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10797,tc_HOL_Obool)),U_10799),hAPP(hAPP(c_Set_Oinsert(U_10797),U_10798),c_Orderings_Obot__class_Obot(tc_fun(U_10797,tc_HOL_Obool)))))),U_10798),U_10802)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10797),U_10798),U_10799)) ),
    inference(clausify,[status(thm)],[f_2904_3]) ).

fof(f_2905_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_2905_2,plain,
    ! [U_10806,U_10805,U_10804,U_10803] : c_Map_Orestrict__map(U_10803,U_10804,U_10805,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10803,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10803),U_10806),c_Orderings_Obot__class_Obot(tc_fun(U_10803,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10803,tc_Option_Ooption(U_10804)),U_10805),U_10806),c_Option_Ooption_ONone(U_10804)),
    inference(variable_rename,[status(thm)],[f_2905_1]) ).

fof(f_2905_3,plain,
    ! [U_10803,U_10804,U_10805,U_10806] : c_Map_Orestrict__map(U_10803,U_10804,U_10805,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10803,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10803),U_10806),c_Orderings_Obot__class_Obot(tc_fun(U_10803,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10803,tc_Option_Ooption(U_10804)),U_10805),U_10806),c_Option_Ooption_ONone(U_10804)),
    inference(definitional_conversion,[status(esa)],[f_2905_2]) ).

cnf(f_2905_4,plain,
    c_Map_Orestrict__map(U_10803,U_10804,U_10805,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10803,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10803),U_10806),c_Orderings_Obot__class_Obot(tc_fun(U_10803,tc_HOL_Obool))))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10803,tc_Option_Ooption(U_10804)),U_10805),U_10806),c_Option_Ooption_ONone(U_10804)),
    inference(clausify,[status(thm)],[f_2905_3]) ).

fof(f_2906_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_2906_2,plain,
    ! [U_10811,U_10810,U_10809,U_10808,U_10807] : c_Map_Orestrict__map(U_10807,U_10808,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10807,tc_Option_Ooption(U_10808)),U_10809),U_10810),hAPP(c_Option_Ooption_OSome(U_10808),U_10811)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10807,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10807),U_10810),c_Orderings_Obot__class_Obot(tc_fun(U_10807,tc_HOL_Obool))))) = c_Map_Orestrict__map(U_10807,U_10808,U_10809,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10807,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10807),U_10810),c_Orderings_Obot__class_Obot(tc_fun(U_10807,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_2906_1]) ).

fof(f_2906_3,plain,
    ! [U_10808,U_10807,U_10809,U_10810,U_10811] : c_Map_Orestrict__map(U_10807,U_10808,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10807,tc_Option_Ooption(U_10808)),U_10809),U_10810),hAPP(c_Option_Ooption_OSome(U_10808),U_10811)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10807,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10807),U_10810),c_Orderings_Obot__class_Obot(tc_fun(U_10807,tc_HOL_Obool))))) = c_Map_Orestrict__map(U_10807,U_10808,U_10809,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10807,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10807),U_10810),c_Orderings_Obot__class_Obot(tc_fun(U_10807,tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_2906_2]) ).

cnf(f_2906_4,plain,
    c_Map_Orestrict__map(U_10807,U_10808,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_10807,tc_Option_Ooption(U_10808)),U_10809),U_10810),hAPP(c_Option_Ooption_OSome(U_10808),U_10811)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10807,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10807),U_10810),c_Orderings_Obot__class_Obot(tc_fun(U_10807,tc_HOL_Obool))))) = c_Map_Orestrict__map(U_10807,U_10808,U_10809,hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_10807,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_10807),U_10810),c_Orderings_Obot__class_Obot(tc_fun(U_10807,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_2906_3]) ).

fof(f_2907_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_2907_2,plain,
    ! [U_10815,U_10814,U_10813] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10813,tc_Int_Oint),U_10815),U_10814) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10813,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_10813),c_Int_Onat),U_10815)),U_10814))
      | ? [U_10812] :
          ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_10815,U_10812))
          & hBOOL(hAPP(hAPP(c_member(U_10813),U_10812),U_10814)) ) ),
    inference(variable_rename,[status(thm)],[f_2907_1]) ).

fof(f_2907_3,plain,
    ! [U_10815,U_10814,U_10813] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10813,tc_Int_Oint),U_10815),U_10814) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10813,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_10813),c_Int_Onat),U_10815)),U_10814))
      | ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_10815,sK177(U_10815,U_10814,U_10813)))
        & hBOOL(hAPP(hAPP(c_member(U_10813),sK177(U_10815,U_10814,U_10813)),U_10814)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK177]),skolemize(U_10812,sK177(U_10815,U_10814,U_10813))],[f_2907_2]) ).

fof(f_2907_4,plain,
    ( ! [U_10813,U_10814,U_10815] :
        ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_10815,sK177(U_10815,U_10814,U_10813)))
        | ~ sP809(U_10813,U_10814,U_10815) )
    & ! [U_10813,U_10814,U_10815] :
        ( hBOOL(hAPP(hAPP(c_member(U_10813),sK177(U_10815,U_10814,U_10813)),U_10814))
        | ~ sP809(U_10813,U_10814,U_10815) )
    & ! [U_10813,U_10814,U_10815] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10813,tc_Int_Oint),U_10815),U_10814) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10813,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_10813),c_Int_Onat),U_10815)),U_10814))
        | sP809(U_10813,U_10814,U_10815) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP809])],[f_2907_3]) ).

cnf(f_2907_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10813,tc_Int_Oint),U_10815),U_10814) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10813,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_10813),c_Int_Onat),U_10815)),U_10814))
    | sP809(U_10813,U_10814,U_10815) ),
    inference(clausify,[status(thm)],[f_2907_4]) ).

cnf(f_2907_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10813),sK177(U_10815,U_10814,U_10813)),U_10814))
    | ~ sP809(U_10813,U_10814,U_10815) ),
    inference(clausify,[status(thm)],[f_2907_4]) ).

cnf(f_2907_7,plain,
    ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_10815,sK177(U_10815,U_10814,U_10813)))
    | ~ sP809(U_10813,U_10814,U_10815) ),
    inference(clausify,[status(thm)],[f_2907_4]) ).

fof(f_2908_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_2908_2,plain,
    ! [U_10820,U_10819,U_10818] :
      ( hAPP(U_10819,c_Big__Operators_Olattice_OSup__fin(U_10818,c_Orderings_Oord__class_Omax(U_10818),U_10820)) = c_Big__Operators_Olattice_OSup__fin(U_10818,c_Orderings_Oord__class_Omax(U_10818),hAPP(c_Set_Oimage(U_10818,U_10818,U_10819),U_10820))
      | U_10820 = c_Orderings_Obot__class_Obot(tc_fun(U_10818,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10818),U_10820))
      | ? [U_10817,U_10816] : hAPP(U_10819,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10818),U_10817),U_10816)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10818),hAPP(U_10819,U_10817)),hAPP(U_10819,U_10816))
      | ~ class_Orderings_Olinorder(U_10818) ),
    inference(variable_rename,[status(thm)],[f_2908_1]) ).

fof(f_2908_3,plain,
    ! [U_10820,U_10819,U_10818] :
      ( hAPP(U_10819,c_Big__Operators_Olattice_OSup__fin(U_10818,c_Orderings_Oord__class_Omax(U_10818),U_10820)) = c_Big__Operators_Olattice_OSup__fin(U_10818,c_Orderings_Oord__class_Omax(U_10818),hAPP(c_Set_Oimage(U_10818,U_10818,U_10819),U_10820))
      | U_10820 = c_Orderings_Obot__class_Obot(tc_fun(U_10818,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10818),U_10820))
      | ? [U_10816] : hAPP(U_10819,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10818),sK178(U_10820,U_10819,U_10818)),U_10816)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10818),hAPP(U_10819,sK178(U_10820,U_10819,U_10818))),hAPP(U_10819,U_10816))
      | ~ class_Orderings_Olinorder(U_10818) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK178]),skolemize(U_10817,sK178(U_10820,U_10819,U_10818))],[f_2908_2]) ).

fof(f_2908_4,plain,
    ! [U_10820,U_10819,U_10818] :
      ( hAPP(U_10819,c_Big__Operators_Olattice_OSup__fin(U_10818,c_Orderings_Oord__class_Omax(U_10818),U_10820)) = c_Big__Operators_Olattice_OSup__fin(U_10818,c_Orderings_Oord__class_Omax(U_10818),hAPP(c_Set_Oimage(U_10818,U_10818,U_10819),U_10820))
      | U_10820 = c_Orderings_Obot__class_Obot(tc_fun(U_10818,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10818),U_10820))
      | hAPP(U_10819,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10818),sK178(U_10820,U_10819,U_10818)),sK179(U_10820,U_10819,U_10818))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10818),hAPP(U_10819,sK178(U_10820,U_10819,U_10818))),hAPP(U_10819,sK179(U_10820,U_10819,U_10818)))
      | ~ class_Orderings_Olinorder(U_10818) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK179]),skolemize(U_10816,sK179(U_10820,U_10819,U_10818))],[f_2908_3]) ).

fof(f_2908_5,plain,
    ! [U_10818,U_10819,U_10820] :
      ( hAPP(U_10819,c_Big__Operators_Olattice_OSup__fin(U_10818,c_Orderings_Oord__class_Omax(U_10818),U_10820)) = c_Big__Operators_Olattice_OSup__fin(U_10818,c_Orderings_Oord__class_Omax(U_10818),hAPP(c_Set_Oimage(U_10818,U_10818,U_10819),U_10820))
      | U_10820 = c_Orderings_Obot__class_Obot(tc_fun(U_10818,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10818),U_10820))
      | hAPP(U_10819,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10818),sK178(U_10820,U_10819,U_10818)),sK179(U_10820,U_10819,U_10818))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10818),hAPP(U_10819,sK178(U_10820,U_10819,U_10818))),hAPP(U_10819,sK179(U_10820,U_10819,U_10818)))
      | ~ class_Orderings_Olinorder(U_10818) ),
    inference(definitional_conversion,[status(esa)],[f_2908_4]) ).

cnf(f_2908_6,plain,
    ( hAPP(U_10819,c_Big__Operators_Olattice_OSup__fin(U_10818,c_Orderings_Oord__class_Omax(U_10818),U_10820)) = c_Big__Operators_Olattice_OSup__fin(U_10818,c_Orderings_Oord__class_Omax(U_10818),hAPP(c_Set_Oimage(U_10818,U_10818,U_10819),U_10820))
    | U_10820 = c_Orderings_Obot__class_Obot(tc_fun(U_10818,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10818),U_10820))
    | hAPP(U_10819,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10818),sK178(U_10820,U_10819,U_10818)),sK179(U_10820,U_10819,U_10818))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10818),hAPP(U_10819,sK178(U_10820,U_10819,U_10818))),hAPP(U_10819,sK179(U_10820,U_10819,U_10818)))
    | ~ class_Orderings_Olinorder(U_10818) ),
    inference(clausify,[status(thm)],[f_2908_5]) ).

fof(f_2909_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_2909_2,plain,
    ! [U_10825,U_10824,U_10823] :
      ( hAPP(U_10824,c_Big__Operators_Olattice_OInf__fin(U_10823,c_Orderings_Oord__class_Omin(U_10823),U_10825)) = c_Big__Operators_Olattice_OInf__fin(U_10823,c_Orderings_Oord__class_Omin(U_10823),hAPP(c_Set_Oimage(U_10823,U_10823,U_10824),U_10825))
      | U_10825 = c_Orderings_Obot__class_Obot(tc_fun(U_10823,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10823),U_10825))
      | ? [U_10822,U_10821] : hAPP(U_10824,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10823),U_10822),U_10821)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10823),hAPP(U_10824,U_10822)),hAPP(U_10824,U_10821))
      | ~ class_Orderings_Olinorder(U_10823) ),
    inference(variable_rename,[status(thm)],[f_2909_1]) ).

fof(f_2909_3,plain,
    ! [U_10825,U_10824,U_10823] :
      ( hAPP(U_10824,c_Big__Operators_Olattice_OInf__fin(U_10823,c_Orderings_Oord__class_Omin(U_10823),U_10825)) = c_Big__Operators_Olattice_OInf__fin(U_10823,c_Orderings_Oord__class_Omin(U_10823),hAPP(c_Set_Oimage(U_10823,U_10823,U_10824),U_10825))
      | U_10825 = c_Orderings_Obot__class_Obot(tc_fun(U_10823,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10823),U_10825))
      | ? [U_10821] : hAPP(U_10824,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10823),sK180(U_10825,U_10824,U_10823)),U_10821)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10823),hAPP(U_10824,sK180(U_10825,U_10824,U_10823))),hAPP(U_10824,U_10821))
      | ~ class_Orderings_Olinorder(U_10823) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK180]),skolemize(U_10822,sK180(U_10825,U_10824,U_10823))],[f_2909_2]) ).

fof(f_2909_4,plain,
    ! [U_10825,U_10824,U_10823] :
      ( hAPP(U_10824,c_Big__Operators_Olattice_OInf__fin(U_10823,c_Orderings_Oord__class_Omin(U_10823),U_10825)) = c_Big__Operators_Olattice_OInf__fin(U_10823,c_Orderings_Oord__class_Omin(U_10823),hAPP(c_Set_Oimage(U_10823,U_10823,U_10824),U_10825))
      | U_10825 = c_Orderings_Obot__class_Obot(tc_fun(U_10823,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10823),U_10825))
      | hAPP(U_10824,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10823),sK180(U_10825,U_10824,U_10823)),sK181(U_10825,U_10824,U_10823))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10823),hAPP(U_10824,sK180(U_10825,U_10824,U_10823))),hAPP(U_10824,sK181(U_10825,U_10824,U_10823)))
      | ~ class_Orderings_Olinorder(U_10823) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK181]),skolemize(U_10821,sK181(U_10825,U_10824,U_10823))],[f_2909_3]) ).

fof(f_2909_5,plain,
    ! [U_10823,U_10824,U_10825] :
      ( hAPP(U_10824,c_Big__Operators_Olattice_OInf__fin(U_10823,c_Orderings_Oord__class_Omin(U_10823),U_10825)) = c_Big__Operators_Olattice_OInf__fin(U_10823,c_Orderings_Oord__class_Omin(U_10823),hAPP(c_Set_Oimage(U_10823,U_10823,U_10824),U_10825))
      | U_10825 = c_Orderings_Obot__class_Obot(tc_fun(U_10823,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10823),U_10825))
      | hAPP(U_10824,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10823),sK180(U_10825,U_10824,U_10823)),sK181(U_10825,U_10824,U_10823))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10823),hAPP(U_10824,sK180(U_10825,U_10824,U_10823))),hAPP(U_10824,sK181(U_10825,U_10824,U_10823)))
      | ~ class_Orderings_Olinorder(U_10823) ),
    inference(definitional_conversion,[status(esa)],[f_2909_4]) ).

cnf(f_2909_6,plain,
    ( hAPP(U_10824,c_Big__Operators_Olattice_OInf__fin(U_10823,c_Orderings_Oord__class_Omin(U_10823),U_10825)) = c_Big__Operators_Olattice_OInf__fin(U_10823,c_Orderings_Oord__class_Omin(U_10823),hAPP(c_Set_Oimage(U_10823,U_10823,U_10824),U_10825))
    | U_10825 = c_Orderings_Obot__class_Obot(tc_fun(U_10823,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10823),U_10825))
    | hAPP(U_10824,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10823),sK180(U_10825,U_10824,U_10823)),sK181(U_10825,U_10824,U_10823))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10823),hAPP(U_10824,sK180(U_10825,U_10824,U_10823))),hAPP(U_10824,sK181(U_10825,U_10824,U_10823)))
    | ~ class_Orderings_Olinorder(U_10823) ),
    inference(clausify,[status(thm)],[f_2909_5]) ).

fof(f_2910_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_2910_2,plain,
    ! [U_10830,U_10829,U_10828] :
      ( hAPP(U_10829,c_Big__Operators_Olinorder__class_OMax(U_10828,U_10830)) = c_Big__Operators_Olinorder__class_OMax(U_10828,hAPP(c_Set_Oimage(U_10828,U_10828,U_10829),U_10830))
      | U_10830 = c_Orderings_Obot__class_Obot(tc_fun(U_10828,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10828),U_10830))
      | ? [U_10827,U_10826] : hAPP(U_10829,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10828),U_10827),U_10826)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10828),hAPP(U_10829,U_10827)),hAPP(U_10829,U_10826))
      | ~ class_Orderings_Olinorder(U_10828) ),
    inference(variable_rename,[status(thm)],[f_2910_1]) ).

fof(f_2910_3,plain,
    ! [U_10830,U_10829,U_10828] :
      ( hAPP(U_10829,c_Big__Operators_Olinorder__class_OMax(U_10828,U_10830)) = c_Big__Operators_Olinorder__class_OMax(U_10828,hAPP(c_Set_Oimage(U_10828,U_10828,U_10829),U_10830))
      | U_10830 = c_Orderings_Obot__class_Obot(tc_fun(U_10828,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10828),U_10830))
      | ? [U_10826] : hAPP(U_10829,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10828),sK182(U_10830,U_10829,U_10828)),U_10826)) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10828),hAPP(U_10829,sK182(U_10830,U_10829,U_10828))),hAPP(U_10829,U_10826))
      | ~ class_Orderings_Olinorder(U_10828) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK182]),skolemize(U_10827,sK182(U_10830,U_10829,U_10828))],[f_2910_2]) ).

fof(f_2910_4,plain,
    ! [U_10830,U_10829,U_10828] :
      ( hAPP(U_10829,c_Big__Operators_Olinorder__class_OMax(U_10828,U_10830)) = c_Big__Operators_Olinorder__class_OMax(U_10828,hAPP(c_Set_Oimage(U_10828,U_10828,U_10829),U_10830))
      | U_10830 = c_Orderings_Obot__class_Obot(tc_fun(U_10828,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10828),U_10830))
      | hAPP(U_10829,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10828),sK182(U_10830,U_10829,U_10828)),sK183(U_10830,U_10829,U_10828))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10828),hAPP(U_10829,sK182(U_10830,U_10829,U_10828))),hAPP(U_10829,sK183(U_10830,U_10829,U_10828)))
      | ~ class_Orderings_Olinorder(U_10828) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK183]),skolemize(U_10826,sK183(U_10830,U_10829,U_10828))],[f_2910_3]) ).

fof(f_2910_5,plain,
    ! [U_10828,U_10829,U_10830] :
      ( hAPP(U_10829,c_Big__Operators_Olinorder__class_OMax(U_10828,U_10830)) = c_Big__Operators_Olinorder__class_OMax(U_10828,hAPP(c_Set_Oimage(U_10828,U_10828,U_10829),U_10830))
      | U_10830 = c_Orderings_Obot__class_Obot(tc_fun(U_10828,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10828),U_10830))
      | hAPP(U_10829,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10828),sK182(U_10830,U_10829,U_10828)),sK183(U_10830,U_10829,U_10828))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10828),hAPP(U_10829,sK182(U_10830,U_10829,U_10828))),hAPP(U_10829,sK183(U_10830,U_10829,U_10828)))
      | ~ class_Orderings_Olinorder(U_10828) ),
    inference(definitional_conversion,[status(esa)],[f_2910_4]) ).

cnf(f_2910_6,plain,
    ( hAPP(U_10829,c_Big__Operators_Olinorder__class_OMax(U_10828,U_10830)) = c_Big__Operators_Olinorder__class_OMax(U_10828,hAPP(c_Set_Oimage(U_10828,U_10828,U_10829),U_10830))
    | U_10830 = c_Orderings_Obot__class_Obot(tc_fun(U_10828,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10828),U_10830))
    | hAPP(U_10829,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10828),sK182(U_10830,U_10829,U_10828)),sK183(U_10830,U_10829,U_10828))) != hAPP(hAPP(c_Orderings_Oord__class_Omax(U_10828),hAPP(U_10829,sK182(U_10830,U_10829,U_10828))),hAPP(U_10829,sK183(U_10830,U_10829,U_10828)))
    | ~ class_Orderings_Olinorder(U_10828) ),
    inference(clausify,[status(thm)],[f_2910_5]) ).

fof(f_2911_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_2911_2,plain,
    ! [U_10835,U_10834,U_10833] :
      ( hAPP(U_10834,c_Big__Operators_Olinorder__class_OMin(U_10833,U_10835)) = c_Big__Operators_Olinorder__class_OMin(U_10833,hAPP(c_Set_Oimage(U_10833,U_10833,U_10834),U_10835))
      | U_10835 = c_Orderings_Obot__class_Obot(tc_fun(U_10833,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10833),U_10835))
      | ? [U_10832,U_10831] : hAPP(U_10834,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10833),U_10832),U_10831)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10833),hAPP(U_10834,U_10832)),hAPP(U_10834,U_10831))
      | ~ class_Orderings_Olinorder(U_10833) ),
    inference(variable_rename,[status(thm)],[f_2911_1]) ).

fof(f_2911_3,plain,
    ! [U_10835,U_10834,U_10833] :
      ( hAPP(U_10834,c_Big__Operators_Olinorder__class_OMin(U_10833,U_10835)) = c_Big__Operators_Olinorder__class_OMin(U_10833,hAPP(c_Set_Oimage(U_10833,U_10833,U_10834),U_10835))
      | U_10835 = c_Orderings_Obot__class_Obot(tc_fun(U_10833,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10833),U_10835))
      | ? [U_10831] : hAPP(U_10834,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10833),sK184(U_10835,U_10834,U_10833)),U_10831)) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10833),hAPP(U_10834,sK184(U_10835,U_10834,U_10833))),hAPP(U_10834,U_10831))
      | ~ class_Orderings_Olinorder(U_10833) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK184]),skolemize(U_10832,sK184(U_10835,U_10834,U_10833))],[f_2911_2]) ).

fof(f_2911_4,plain,
    ! [U_10835,U_10834,U_10833] :
      ( hAPP(U_10834,c_Big__Operators_Olinorder__class_OMin(U_10833,U_10835)) = c_Big__Operators_Olinorder__class_OMin(U_10833,hAPP(c_Set_Oimage(U_10833,U_10833,U_10834),U_10835))
      | U_10835 = c_Orderings_Obot__class_Obot(tc_fun(U_10833,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10833),U_10835))
      | hAPP(U_10834,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10833),sK184(U_10835,U_10834,U_10833)),sK185(U_10835,U_10834,U_10833))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10833),hAPP(U_10834,sK184(U_10835,U_10834,U_10833))),hAPP(U_10834,sK185(U_10835,U_10834,U_10833)))
      | ~ class_Orderings_Olinorder(U_10833) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK185]),skolemize(U_10831,sK185(U_10835,U_10834,U_10833))],[f_2911_3]) ).

fof(f_2911_5,plain,
    ! [U_10833,U_10834,U_10835] :
      ( hAPP(U_10834,c_Big__Operators_Olinorder__class_OMin(U_10833,U_10835)) = c_Big__Operators_Olinorder__class_OMin(U_10833,hAPP(c_Set_Oimage(U_10833,U_10833,U_10834),U_10835))
      | U_10835 = c_Orderings_Obot__class_Obot(tc_fun(U_10833,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10833),U_10835))
      | hAPP(U_10834,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10833),sK184(U_10835,U_10834,U_10833)),sK185(U_10835,U_10834,U_10833))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10833),hAPP(U_10834,sK184(U_10835,U_10834,U_10833))),hAPP(U_10834,sK185(U_10835,U_10834,U_10833)))
      | ~ class_Orderings_Olinorder(U_10833) ),
    inference(definitional_conversion,[status(esa)],[f_2911_4]) ).

cnf(f_2911_6,plain,
    ( hAPP(U_10834,c_Big__Operators_Olinorder__class_OMin(U_10833,U_10835)) = c_Big__Operators_Olinorder__class_OMin(U_10833,hAPP(c_Set_Oimage(U_10833,U_10833,U_10834),U_10835))
    | U_10835 = c_Orderings_Obot__class_Obot(tc_fun(U_10833,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10833),U_10835))
    | hAPP(U_10834,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10833),sK184(U_10835,U_10834,U_10833)),sK185(U_10835,U_10834,U_10833))) != hAPP(hAPP(c_Orderings_Oord__class_Omin(U_10833),hAPP(U_10834,sK184(U_10835,U_10834,U_10833))),hAPP(U_10834,sK185(U_10835,U_10834,U_10833)))
    | ~ class_Orderings_Olinorder(U_10833) ),
    inference(clausify,[status(thm)],[f_2911_5]) ).

fof(f_2912_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_2912_2,plain,
    ! [U_10840,U_10839,U_10838] :
      ( hAPP(U_10839,c_Big__Operators_Olattice__class_OSup__fin(U_10838,U_10840)) = c_Big__Operators_Olattice__class_OSup__fin(U_10838,hAPP(c_Set_Oimage(U_10838,U_10838,U_10839),U_10840))
      | U_10840 = c_Orderings_Obot__class_Obot(tc_fun(U_10838,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10838),U_10840))
      | ? [U_10837,U_10836] : hAPP(U_10839,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10838),U_10837),U_10836)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10838),hAPP(U_10839,U_10837)),hAPP(U_10839,U_10836))
      | ~ class_Lattices_Olattice(U_10838) ),
    inference(variable_rename,[status(thm)],[f_2912_1]) ).

fof(f_2912_3,plain,
    ! [U_10840,U_10839,U_10838] :
      ( hAPP(U_10839,c_Big__Operators_Olattice__class_OSup__fin(U_10838,U_10840)) = c_Big__Operators_Olattice__class_OSup__fin(U_10838,hAPP(c_Set_Oimage(U_10838,U_10838,U_10839),U_10840))
      | U_10840 = c_Orderings_Obot__class_Obot(tc_fun(U_10838,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10838),U_10840))
      | ? [U_10836] : hAPP(U_10839,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10838),sK186(U_10840,U_10839,U_10838)),U_10836)) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10838),hAPP(U_10839,sK186(U_10840,U_10839,U_10838))),hAPP(U_10839,U_10836))
      | ~ class_Lattices_Olattice(U_10838) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK186]),skolemize(U_10837,sK186(U_10840,U_10839,U_10838))],[f_2912_2]) ).

fof(f_2912_4,plain,
    ! [U_10840,U_10839,U_10838] :
      ( hAPP(U_10839,c_Big__Operators_Olattice__class_OSup__fin(U_10838,U_10840)) = c_Big__Operators_Olattice__class_OSup__fin(U_10838,hAPP(c_Set_Oimage(U_10838,U_10838,U_10839),U_10840))
      | U_10840 = c_Orderings_Obot__class_Obot(tc_fun(U_10838,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10838),U_10840))
      | hAPP(U_10839,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10838),sK186(U_10840,U_10839,U_10838)),sK187(U_10840,U_10839,U_10838))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10838),hAPP(U_10839,sK186(U_10840,U_10839,U_10838))),hAPP(U_10839,sK187(U_10840,U_10839,U_10838)))
      | ~ class_Lattices_Olattice(U_10838) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK187]),skolemize(U_10836,sK187(U_10840,U_10839,U_10838))],[f_2912_3]) ).

fof(f_2912_5,plain,
    ! [U_10838,U_10839,U_10840] :
      ( hAPP(U_10839,c_Big__Operators_Olattice__class_OSup__fin(U_10838,U_10840)) = c_Big__Operators_Olattice__class_OSup__fin(U_10838,hAPP(c_Set_Oimage(U_10838,U_10838,U_10839),U_10840))
      | U_10840 = c_Orderings_Obot__class_Obot(tc_fun(U_10838,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10838),U_10840))
      | hAPP(U_10839,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10838),sK186(U_10840,U_10839,U_10838)),sK187(U_10840,U_10839,U_10838))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10838),hAPP(U_10839,sK186(U_10840,U_10839,U_10838))),hAPP(U_10839,sK187(U_10840,U_10839,U_10838)))
      | ~ class_Lattices_Olattice(U_10838) ),
    inference(definitional_conversion,[status(esa)],[f_2912_4]) ).

cnf(f_2912_6,plain,
    ( hAPP(U_10839,c_Big__Operators_Olattice__class_OSup__fin(U_10838,U_10840)) = c_Big__Operators_Olattice__class_OSup__fin(U_10838,hAPP(c_Set_Oimage(U_10838,U_10838,U_10839),U_10840))
    | U_10840 = c_Orderings_Obot__class_Obot(tc_fun(U_10838,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10838),U_10840))
    | hAPP(U_10839,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10838),sK186(U_10840,U_10839,U_10838)),sK187(U_10840,U_10839,U_10838))) != hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_10838),hAPP(U_10839,sK186(U_10840,U_10839,U_10838))),hAPP(U_10839,sK187(U_10840,U_10839,U_10838)))
    | ~ class_Lattices_Olattice(U_10838) ),
    inference(clausify,[status(thm)],[f_2912_5]) ).

fof(f_2913_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_2913_2,plain,
    ! [U_10846,U_10845,U_10844,U_10843,U_10842] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10843,U_10842),U_10846),U_10845) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10843,U_10842),U_10846),U_10844)
      | ? [U_10841] :
          ( hAPP(U_10846,U_10841) != c_Groups_Oone__class_Oone(U_10842)
          & hBOOL(hAPP(hAPP(c_member(U_10843),U_10841),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10843,tc_HOL_Obool)),U_10844),U_10845))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10843,tc_HOL_Obool)),U_10845),U_10844))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10843),U_10844))
      | ~ class_Groups_Ocomm__monoid__mult(U_10842) ),
    inference(variable_rename,[status(thm)],[f_2913_1]) ).

fof(f_2913_3,plain,
    ! [U_10846,U_10845,U_10844,U_10843,U_10842] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10843,U_10842),U_10846),U_10845) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10843,U_10842),U_10846),U_10844)
      | ( hAPP(U_10846,sK188(U_10846,U_10845,U_10844,U_10843,U_10842)) != c_Groups_Oone__class_Oone(U_10842)
        & hBOOL(hAPP(hAPP(c_member(U_10843),sK188(U_10846,U_10845,U_10844,U_10843,U_10842)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10843,tc_HOL_Obool)),U_10844),U_10845))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10843,tc_HOL_Obool)),U_10845),U_10844))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10843),U_10844))
      | ~ class_Groups_Ocomm__monoid__mult(U_10842) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK188]),skolemize(U_10841,sK188(U_10846,U_10845,U_10844,U_10843,U_10842))],[f_2913_2]) ).

fof(f_2913_4,plain,
    ( ! [U_10843,U_10842,U_10844,U_10845,U_10846] :
        ( hAPP(U_10846,sK188(U_10846,U_10845,U_10844,U_10843,U_10842)) != c_Groups_Oone__class_Oone(U_10842)
        | ~ sP810(U_10843,U_10842,U_10844,U_10845,U_10846) )
    & ! [U_10843,U_10842,U_10844,U_10845,U_10846] :
        ( hBOOL(hAPP(hAPP(c_member(U_10843),sK188(U_10846,U_10845,U_10844,U_10843,U_10842)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10843,tc_HOL_Obool)),U_10844),U_10845)))
        | ~ sP810(U_10843,U_10842,U_10844,U_10845,U_10846) )
    & ! [U_10843,U_10842,U_10844,U_10845,U_10846] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10843,U_10842),U_10846),U_10845) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10843,U_10842),U_10846),U_10844)
        | sP810(U_10843,U_10842,U_10844,U_10845,U_10846)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10843,tc_HOL_Obool)),U_10845),U_10844))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10843),U_10844))
        | ~ class_Groups_Ocomm__monoid__mult(U_10842) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP810])],[f_2913_3]) ).

cnf(f_2913_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10843,U_10842),U_10846),U_10845) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10843,U_10842),U_10846),U_10844)
    | sP810(U_10843,U_10842,U_10844,U_10845,U_10846)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10843,tc_HOL_Obool)),U_10845),U_10844))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10843),U_10844))
    | ~ class_Groups_Ocomm__monoid__mult(U_10842) ),
    inference(clausify,[status(thm)],[f_2913_4]) ).

cnf(f_2913_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10843),sK188(U_10846,U_10845,U_10844,U_10843,U_10842)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10843,tc_HOL_Obool)),U_10844),U_10845)))
    | ~ sP810(U_10843,U_10842,U_10844,U_10845,U_10846) ),
    inference(clausify,[status(thm)],[f_2913_4]) ).

cnf(f_2913_7,plain,
    ( hAPP(U_10846,sK188(U_10846,U_10845,U_10844,U_10843,U_10842)) != c_Groups_Oone__class_Oone(U_10842)
    | ~ sP810(U_10843,U_10842,U_10844,U_10845,U_10846) ),
    inference(clausify,[status(thm)],[f_2913_4]) ).

fof(f_2914_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_2914_2,plain,
    ! [U_10852,U_10851,U_10850,U_10849,U_10848] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10849,U_10848),U_10852),U_10850) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10849,U_10848),U_10852),U_10851)
      | ? [U_10847] :
          ( hAPP(U_10852,U_10847) != c_Groups_Oone__class_Oone(U_10848)
          & hBOOL(hAPP(hAPP(c_member(U_10849),U_10847),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10849,tc_HOL_Obool)),U_10850),U_10851))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10849,tc_HOL_Obool)),U_10851),U_10850))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10849),U_10850))
      | ~ class_Groups_Ocomm__monoid__mult(U_10848) ),
    inference(variable_rename,[status(thm)],[f_2914_1]) ).

fof(f_2914_3,plain,
    ! [U_10852,U_10851,U_10850,U_10849,U_10848] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10849,U_10848),U_10852),U_10850) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10849,U_10848),U_10852),U_10851)
      | ( hAPP(U_10852,sK189(U_10852,U_10851,U_10850,U_10849,U_10848)) != c_Groups_Oone__class_Oone(U_10848)
        & hBOOL(hAPP(hAPP(c_member(U_10849),sK189(U_10852,U_10851,U_10850,U_10849,U_10848)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10849,tc_HOL_Obool)),U_10850),U_10851))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10849,tc_HOL_Obool)),U_10851),U_10850))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10849),U_10850))
      | ~ class_Groups_Ocomm__monoid__mult(U_10848) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK189]),skolemize(U_10847,sK189(U_10852,U_10851,U_10850,U_10849,U_10848))],[f_2914_2]) ).

fof(f_2914_4,plain,
    ( ! [U_10849,U_10850,U_10848,U_10852,U_10851] :
        ( hAPP(U_10852,sK189(U_10852,U_10851,U_10850,U_10849,U_10848)) != c_Groups_Oone__class_Oone(U_10848)
        | ~ sP811(U_10849,U_10850,U_10848,U_10852,U_10851) )
    & ! [U_10849,U_10850,U_10848,U_10852,U_10851] :
        ( hBOOL(hAPP(hAPP(c_member(U_10849),sK189(U_10852,U_10851,U_10850,U_10849,U_10848)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10849,tc_HOL_Obool)),U_10850),U_10851)))
        | ~ sP811(U_10849,U_10850,U_10848,U_10852,U_10851) )
    & ! [U_10849,U_10850,U_10848,U_10852,U_10851] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10849,U_10848),U_10852),U_10850) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10849,U_10848),U_10852),U_10851)
        | sP811(U_10849,U_10850,U_10848,U_10852,U_10851)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10849,tc_HOL_Obool)),U_10851),U_10850))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10849),U_10850))
        | ~ class_Groups_Ocomm__monoid__mult(U_10848) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP811])],[f_2914_3]) ).

cnf(f_2914_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10849,U_10848),U_10852),U_10850) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_10849,U_10848),U_10852),U_10851)
    | sP811(U_10849,U_10850,U_10848,U_10852,U_10851)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_10849,tc_HOL_Obool)),U_10851),U_10850))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10849),U_10850))
    | ~ class_Groups_Ocomm__monoid__mult(U_10848) ),
    inference(clausify,[status(thm)],[f_2914_4]) ).

cnf(f_2914_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10849),sK189(U_10852,U_10851,U_10850,U_10849,U_10848)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10849,tc_HOL_Obool)),U_10850),U_10851)))
    | ~ sP811(U_10849,U_10850,U_10848,U_10852,U_10851) ),
    inference(clausify,[status(thm)],[f_2914_4]) ).

cnf(f_2914_7,plain,
    ( hAPP(U_10852,sK189(U_10852,U_10851,U_10850,U_10849,U_10848)) != c_Groups_Oone__class_Oone(U_10848)
    | ~ sP811(U_10849,U_10850,U_10848,U_10852,U_10851) ),
    inference(clausify,[status(thm)],[f_2914_4]) ).

fof(f_2915_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_2915_2,plain,
    ! [U_10855,U_10854,U_10853] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10853,U_10853)),hAPP(hAPP(c_Product__Type_OPair(U_10853,U_10853),U_10855),U_10855)),c_Transitive__Closure_Otrancl(U_10853,U_10854)))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_10853,U_10853),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_10853,U_10853),U_10854)),c_Transitive__Closure_Ortrancl(U_10853,U_10854)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10853,U_10853),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_2915_1]) ).

fof(f_2915_3,plain,
    ! [U_10853,U_10854,U_10855] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10853,U_10853)),hAPP(hAPP(c_Product__Type_OPair(U_10853,U_10853),U_10855),U_10855)),c_Transitive__Closure_Otrancl(U_10853,U_10854)))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_10853,U_10853),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_10853,U_10853),U_10854)),c_Transitive__Closure_Ortrancl(U_10853,U_10854)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10853,U_10853),tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_2915_2]) ).

cnf(f_2915_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_10853,U_10853)),hAPP(hAPP(c_Product__Type_OPair(U_10853,U_10853),U_10855),U_10855)),c_Transitive__Closure_Otrancl(U_10853,U_10854)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_10853,U_10853),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_10853,U_10853),U_10854)),c_Transitive__Closure_Ortrancl(U_10853,U_10854)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_10853,U_10853),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2915_3]) ).

fof(f_2916_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_2916_2,plain,
    ! [U_10859,U_10858,U_10857,U_10856] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10859,tc_HOL_Obool)),U_10856),U_10858),U_10857))
      | ~ hBOOL(hAPP(U_10858,U_10857))
      | ~ hBOOL(hAPP(U_10856,U_10857)) ),
    inference(variable_rename,[status(thm)],[f_2916_1]) ).

fof(f_2916_3,plain,
    ! [U_10857,U_10858,U_10856,U_10859] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10859,tc_HOL_Obool)),U_10856),U_10858),U_10857))
      | ~ hBOOL(hAPP(U_10858,U_10857))
      | ~ hBOOL(hAPP(U_10856,U_10857)) ),
    inference(definitional_conversion,[status(esa)],[f_2916_2]) ).

cnf(f_2916_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10859,tc_HOL_Obool)),U_10856),U_10858),U_10857))
    | ~ hBOOL(hAPP(U_10858,U_10857))
    | ~ hBOOL(hAPP(U_10856,U_10857)) ),
    inference(clausify,[status(thm)],[f_2916_3]) ).

fof(f_2917_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_2917_2,plain,
    ! [U_10863,U_10862,U_10861,U_10860] :
      ( ( hBOOL(hAPP(U_10862,U_10863))
        & hBOOL(hAPP(U_10861,U_10863)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10860,tc_HOL_Obool)),U_10861),U_10862),U_10863)) ),
    inference(variable_rename,[status(thm)],[f_2917_1]) ).

fof(f_2917_3,plain,
    ! [U_10863,U_10862,U_10861] :
      ( ! [U_10860] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10860,tc_HOL_Obool)),U_10861),U_10862),U_10863))
      | ( hBOOL(hAPP(U_10862,U_10863))
        & hBOOL(hAPP(U_10861,U_10863)) ) ),
    inference(miniscope,[status(thm)],[f_2917_2]) ).

fof(f_2917_4,plain,
    ( ! [U_10861,U_10862,U_10863] :
        ( hBOOL(hAPP(U_10862,U_10863))
        | ~ sP812(U_10861,U_10862,U_10863) )
    & ! [U_10861,U_10862,U_10863] :
        ( hBOOL(hAPP(U_10861,U_10863))
        | ~ sP812(U_10861,U_10862,U_10863) )
    & ! [U_10861,U_10860,U_10862,U_10863] :
        ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10860,tc_HOL_Obool)),U_10861),U_10862),U_10863))
        | sP812(U_10861,U_10862,U_10863) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP812])],[f_2917_3]) ).

cnf(f_2917_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10860,tc_HOL_Obool)),U_10861),U_10862),U_10863))
    | sP812(U_10861,U_10862,U_10863) ),
    inference(clausify,[status(thm)],[f_2917_4]) ).

cnf(f_2917_6,plain,
    ( hBOOL(hAPP(U_10861,U_10863))
    | ~ sP812(U_10861,U_10862,U_10863) ),
    inference(clausify,[status(thm)],[f_2917_4]) ).

cnf(f_2917_7,plain,
    ( hBOOL(hAPP(U_10862,U_10863))
    | ~ sP812(U_10861,U_10862,U_10863) ),
    inference(clausify,[status(thm)],[f_2917_4]) ).

fof(f_2918_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_2918_2,plain,
    ! [U_10867,U_10866,U_10865,U_10864] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_10864),U_10865),U_10867))
        & hBOOL(hAPP(hAPP(c_member(U_10864),U_10865),U_10866)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_10864),U_10865),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10864,tc_HOL_Obool)),U_10866),U_10867))) ),
    inference(variable_rename,[status(thm)],[f_2918_1]) ).

fof(f_2918_3,plain,
    ( ! [U_10864,U_10865,U_10866,U_10867] :
        ( hBOOL(hAPP(hAPP(c_member(U_10864),U_10865),U_10867))
        | ~ sP813(U_10864,U_10865,U_10866,U_10867) )
    & ! [U_10864,U_10865,U_10866,U_10867] :
        ( hBOOL(hAPP(hAPP(c_member(U_10864),U_10865),U_10866))
        | ~ sP813(U_10864,U_10865,U_10866,U_10867) )
    & ! [U_10864,U_10865,U_10866,U_10867] :
        ( sP813(U_10864,U_10865,U_10866,U_10867)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10864),U_10865),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10864,tc_HOL_Obool)),U_10866),U_10867))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP813])],[f_2918_2]) ).

cnf(f_2918_4,plain,
    ( sP813(U_10864,U_10865,U_10866,U_10867)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10864),U_10865),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10864,tc_HOL_Obool)),U_10866),U_10867))) ),
    inference(clausify,[status(thm)],[f_2918_3]) ).

cnf(f_2918_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10864),U_10865),U_10866))
    | ~ sP813(U_10864,U_10865,U_10866,U_10867) ),
    inference(clausify,[status(thm)],[f_2918_3]) ).

cnf(f_2918_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10864),U_10865),U_10867))
    | ~ sP813(U_10864,U_10865,U_10866,U_10867) ),
    inference(clausify,[status(thm)],[f_2918_3]) ).

fof(f_2919_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_2919_2,plain,
    ! [U_10871,U_10870,U_10869,U_10868] :
      ( hBOOL(hAPP(hAPP(c_member(U_10868),U_10869),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10868,tc_HOL_Obool)),U_10870),U_10871)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10868),U_10869),U_10871))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10868),U_10869),U_10870)) ),
    inference(variable_rename,[status(thm)],[f_2919_1]) ).

fof(f_2919_3,plain,
    ! [U_10868,U_10869,U_10870,U_10871] :
      ( hBOOL(hAPP(hAPP(c_member(U_10868),U_10869),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10868,tc_HOL_Obool)),U_10870),U_10871)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10868),U_10869),U_10871))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10868),U_10869),U_10870)) ),
    inference(definitional_conversion,[status(esa)],[f_2919_2]) ).

cnf(f_2919_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10868),U_10869),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10868,tc_HOL_Obool)),U_10870),U_10871)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10868),U_10869),U_10871))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10868),U_10869),U_10870)) ),
    inference(clausify,[status(thm)],[f_2919_3]) ).

fof(f_2920_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_2920_2,plain,
    ! [U_10874,U_10873,U_10872] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10872),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10872,tc_HOL_Obool)),U_10873),U_10874)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10872),U_10874))
        & ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10872),U_10873)) ) ),
    inference(variable_rename,[status(thm)],[f_2920_1]) ).

fof(f_2920_3,plain,
    ( ! [U_10872,U_10873,U_10874] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10872),U_10874))
        | ~ sP814(U_10872,U_10873,U_10874) )
    & ! [U_10872,U_10873,U_10874] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10872),U_10873))
        | ~ sP814(U_10872,U_10873,U_10874) )
    & ! [U_10872,U_10873,U_10874] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10872),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10872,tc_HOL_Obool)),U_10873),U_10874)))
        | sP814(U_10872,U_10873,U_10874) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP814])],[f_2920_2]) ).

cnf(f_2920_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_10872),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10872,tc_HOL_Obool)),U_10873),U_10874)))
    | sP814(U_10872,U_10873,U_10874) ),
    inference(clausify,[status(thm)],[f_2920_3]) ).

cnf(f_2920_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10872),U_10873))
    | ~ sP814(U_10872,U_10873,U_10874) ),
    inference(clausify,[status(thm)],[f_2920_3]) ).

cnf(f_2920_6,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_10872),U_10874))
    | ~ sP814(U_10872,U_10873,U_10874) ),
    inference(clausify,[status(thm)],[f_2920_3]) ).

fof(f_2921_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_2921_2,plain,
    ! [U_10879,U_10878,U_10877,U_10876,U_10875] : c_Map_Orestrict__map(U_10875,U_10876,c_Map_Orestrict__map(U_10875,U_10876,U_10877,U_10878),U_10879) = c_Map_Orestrict__map(U_10875,U_10876,U_10877,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10875,tc_HOL_Obool)),U_10878),U_10879)),
    inference(variable_rename,[status(thm)],[f_2921_1]) ).

fof(f_2921_3,plain,
    ! [U_10875,U_10877,U_10876,U_10878,U_10879] : c_Map_Orestrict__map(U_10875,U_10876,c_Map_Orestrict__map(U_10875,U_10876,U_10877,U_10878),U_10879) = c_Map_Orestrict__map(U_10875,U_10876,U_10877,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10875,tc_HOL_Obool)),U_10878),U_10879)),
    inference(definitional_conversion,[status(esa)],[f_2921_2]) ).

cnf(f_2921_4,plain,
    c_Map_Orestrict__map(U_10875,U_10876,c_Map_Orestrict__map(U_10875,U_10876,U_10877,U_10878),U_10879) = c_Map_Orestrict__map(U_10875,U_10876,U_10877,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10875,tc_HOL_Obool)),U_10878),U_10879)),
    inference(clausify,[status(thm)],[f_2921_3]) ).

fof(f_2922_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_2922_2,plain,
    ! [U_10886,U_10885,U_10884] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10884,tc_HOL_Obool)),U_10885),U_10886) = c_Orderings_Obot__class_Obot(tc_fun(U_10884,tc_HOL_Obool))
        | ? [U_10883] :
            ( ? [U_10882] :
                ( U_10883 = U_10882
                & hBOOL(hAPP(hAPP(c_member(U_10884),U_10882),U_10886)) )
            & hBOOL(hAPP(hAPP(c_member(U_10884),U_10883),U_10885)) ) )
      & ( ! [U_10881] :
            ( ! [U_10880] :
                ( U_10881 != U_10880
                | ~ hBOOL(hAPP(hAPP(c_member(U_10884),U_10880),U_10886)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_10884),U_10881),U_10885)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10884,tc_HOL_Obool)),U_10885),U_10886) != c_Orderings_Obot__class_Obot(tc_fun(U_10884,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_2922_1]) ).

fof(f_2922_3,plain,
    ( ! [U_10892,U_10890,U_10888] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10888,tc_HOL_Obool)),U_10890),U_10892) = c_Orderings_Obot__class_Obot(tc_fun(U_10888,tc_HOL_Obool))
        | ? [U_10883] :
            ( ? [U_10882] :
                ( U_10883 = U_10882
                & hBOOL(hAPP(hAPP(c_member(U_10888),U_10882),U_10892)) )
            & hBOOL(hAPP(hAPP(c_member(U_10888),U_10883),U_10890)) ) )
    & ! [U_10891,U_10889,U_10887] :
        ( ! [U_10881] :
            ( ! [U_10880] :
                ( U_10881 != U_10880
                | ~ hBOOL(hAPP(hAPP(c_member(U_10887),U_10880),U_10891)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_10887),U_10881),U_10889)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10887,tc_HOL_Obool)),U_10889),U_10891) != c_Orderings_Obot__class_Obot(tc_fun(U_10887,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_2922_2]) ).

fof(f_2922_4,plain,
    ( ! [U_10892,U_10890,U_10888] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10888,tc_HOL_Obool)),U_10890),U_10892) = c_Orderings_Obot__class_Obot(tc_fun(U_10888,tc_HOL_Obool))
        | ( ? [U_10882] :
              ( sK190(U_10892,U_10890,U_10888) = U_10882
              & hBOOL(hAPP(hAPP(c_member(U_10888),U_10882),U_10892)) )
          & hBOOL(hAPP(hAPP(c_member(U_10888),sK190(U_10892,U_10890,U_10888)),U_10890)) ) )
    & ! [U_10891,U_10889,U_10887] :
        ( ! [U_10881] :
            ( ! [U_10880] :
                ( U_10881 != U_10880
                | ~ hBOOL(hAPP(hAPP(c_member(U_10887),U_10880),U_10891)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_10887),U_10881),U_10889)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10887,tc_HOL_Obool)),U_10889),U_10891) != c_Orderings_Obot__class_Obot(tc_fun(U_10887,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK190]),skolemize(U_10883,sK190(U_10892,U_10890,U_10888))],[f_2922_3]) ).

fof(f_2922_5,plain,
    ( ! [U_10892,U_10890,U_10888] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10888,tc_HOL_Obool)),U_10890),U_10892) = c_Orderings_Obot__class_Obot(tc_fun(U_10888,tc_HOL_Obool))
        | ( sK190(U_10892,U_10890,U_10888) = sK191(U_10892,U_10890,U_10888)
          & hBOOL(hAPP(hAPP(c_member(U_10888),sK191(U_10892,U_10890,U_10888)),U_10892))
          & hBOOL(hAPP(hAPP(c_member(U_10888),sK190(U_10892,U_10890,U_10888)),U_10890)) ) )
    & ! [U_10891,U_10889,U_10887] :
        ( ! [U_10881] :
            ( ! [U_10880] :
                ( U_10881 != U_10880
                | ~ hBOOL(hAPP(hAPP(c_member(U_10887),U_10880),U_10891)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_10887),U_10881),U_10889)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10887,tc_HOL_Obool)),U_10889),U_10891) != c_Orderings_Obot__class_Obot(tc_fun(U_10887,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK191]),skolemize(U_10882,sK191(U_10892,U_10890,U_10888))],[f_2922_4]) ).

fof(f_2922_6,plain,
    ( ! [U_10888,U_10890,U_10892] :
        ( sK190(U_10892,U_10890,U_10888) = sK191(U_10892,U_10890,U_10888)
        | ~ sP815(U_10888,U_10890,U_10892) )
    & ! [U_10888,U_10890,U_10892] :
        ( hBOOL(hAPP(hAPP(c_member(U_10888),sK191(U_10892,U_10890,U_10888)),U_10892))
        | ~ sP815(U_10888,U_10890,U_10892) )
    & ! [U_10888,U_10890,U_10892] :
        ( hBOOL(hAPP(hAPP(c_member(U_10888),sK190(U_10892,U_10890,U_10888)),U_10890))
        | ~ sP815(U_10888,U_10890,U_10892) )
    & ! [U_10888,U_10890,U_10892] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10888,tc_HOL_Obool)),U_10890),U_10892) = c_Orderings_Obot__class_Obot(tc_fun(U_10888,tc_HOL_Obool))
        | sP815(U_10888,U_10890,U_10892) )
    & ! [U_10891,U_10880,U_10881,U_10887,U_10889] :
        ( U_10881 != U_10880
        | ~ hBOOL(hAPP(hAPP(c_member(U_10887),U_10880),U_10891))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10887),U_10881),U_10889))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10887,tc_HOL_Obool)),U_10889),U_10891) != c_Orderings_Obot__class_Obot(tc_fun(U_10887,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP815])],[f_2922_5]) ).

cnf(f_2922_7,plain,
    ( U_10881 != U_10880
    | ~ hBOOL(hAPP(hAPP(c_member(U_10887),U_10880),U_10891))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10887),U_10881),U_10889))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10887,tc_HOL_Obool)),U_10889),U_10891) != c_Orderings_Obot__class_Obot(tc_fun(U_10887,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_2922_6]) ).

cnf(f_2922_8,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10888,tc_HOL_Obool)),U_10890),U_10892) = c_Orderings_Obot__class_Obot(tc_fun(U_10888,tc_HOL_Obool))
    | sP815(U_10888,U_10890,U_10892) ),
    inference(clausify,[status(thm)],[f_2922_6]) ).

cnf(f_2922_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10888),sK190(U_10892,U_10890,U_10888)),U_10890))
    | ~ sP815(U_10888,U_10890,U_10892) ),
    inference(clausify,[status(thm)],[f_2922_6]) ).

cnf(f_2922_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10888),sK191(U_10892,U_10890,U_10888)),U_10892))
    | ~ sP815(U_10888,U_10890,U_10892) ),
    inference(clausify,[status(thm)],[f_2922_6]) ).

cnf(f_2922_11,plain,
    ( sK190(U_10892,U_10890,U_10888) = sK191(U_10892,U_10890,U_10888)
    | ~ sP815(U_10888,U_10890,U_10892) ),
    inference(clausify,[status(thm)],[f_2922_6]) ).

fof(f_2923_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_2923_2,plain,
    ! [U_10894,U_10893] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10893,tc_HOL_Obool)),U_10894),c_Orderings_Obot__class_Obot(tc_fun(U_10893,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_10893,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2923_1]) ).

fof(f_2923_3,plain,
    ! [U_10894,U_10893] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10893,tc_HOL_Obool)),U_10894),c_Orderings_Obot__class_Obot(tc_fun(U_10893,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_10893,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2923_2]) ).

cnf(f_2923_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10893,tc_HOL_Obool)),U_10894),c_Orderings_Obot__class_Obot(tc_fun(U_10893,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_10893,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2923_3]) ).

fof(f_2924_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_2924_2,plain,
    ! [U_10896,U_10895] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10895,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_10895,tc_HOL_Obool))),U_10896) = c_Orderings_Obot__class_Obot(tc_fun(U_10895,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_2924_1]) ).

fof(f_2924_3,plain,
    ! [U_10895,U_10896] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10895,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_10895,tc_HOL_Obool))),U_10896) = c_Orderings_Obot__class_Obot(tc_fun(U_10895,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_2924_2]) ).

cnf(f_2924_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10895,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_10895,tc_HOL_Obool))),U_10896) = c_Orderings_Obot__class_Obot(tc_fun(U_10895,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_2924_3]) ).

fof(f_2925_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_2925_2,plain,
    ! [U_10898,U_10897] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10897),U_10898),c_Orderings_Obot__class_Obot(U_10897)) = c_Orderings_Obot__class_Obot(U_10897)
      | ~ class_Lattices_Obounded__lattice__bot(U_10897) ),
    inference(variable_rename,[status(thm)],[f_2925_1]) ).

fof(f_2925_3,plain,
    ! [U_10897,U_10898] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10897),U_10898),c_Orderings_Obot__class_Obot(U_10897)) = c_Orderings_Obot__class_Obot(U_10897)
      | ~ class_Lattices_Obounded__lattice__bot(U_10897) ),
    inference(definitional_conversion,[status(esa)],[f_2925_2]) ).

cnf(f_2925_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10897),U_10898),c_Orderings_Obot__class_Obot(U_10897)) = c_Orderings_Obot__class_Obot(U_10897)
    | ~ class_Lattices_Obounded__lattice__bot(U_10897) ),
    inference(clausify,[status(thm)],[f_2925_3]) ).

fof(f_2926_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_2926_2,plain,
    ! [U_10900,U_10899] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10899),c_Orderings_Obot__class_Obot(U_10899)),U_10900) = c_Orderings_Obot__class_Obot(U_10899)
      | ~ class_Lattices_Obounded__lattice__bot(U_10899) ),
    inference(variable_rename,[status(thm)],[f_2926_1]) ).

fof(f_2926_3,plain,
    ! [U_10899,U_10900] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10899),c_Orderings_Obot__class_Obot(U_10899)),U_10900) = c_Orderings_Obot__class_Obot(U_10899)
      | ~ class_Lattices_Obounded__lattice__bot(U_10899) ),
    inference(definitional_conversion,[status(esa)],[f_2926_2]) ).

cnf(f_2926_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10899),c_Orderings_Obot__class_Obot(U_10899)),U_10900) = c_Orderings_Obot__class_Obot(U_10899)
    | ~ class_Lattices_Obounded__lattice__bot(U_10899) ),
    inference(clausify,[status(thm)],[f_2926_3]) ).

fof(f_2927_1,plain,
    ! [V_Qa_2,V_Pa_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_Pa_2)),V_Qa_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_Set_OCollect(T_b),V_Qa_2)),
    inference(fof_nnf,[status(thm)],[fact_Collect__conj__eq]) ).

fof(f_2927_2,plain,
    ! [U_10903,U_10902,U_10901] : hAPP(c_Set_OCollect(U_10901),hAPP(hAPP(c_COMBS(U_10901,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10901),c_fconj),U_10902)),U_10903)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10901,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_10901),U_10902)),hAPP(c_Set_OCollect(U_10901),U_10903)),
    inference(variable_rename,[status(thm)],[f_2927_1]) ).

fof(f_2927_3,plain,
    ! [U_10901,U_10902,U_10903] : hAPP(c_Set_OCollect(U_10901),hAPP(hAPP(c_COMBS(U_10901,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10901),c_fconj),U_10902)),U_10903)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10901,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_10901),U_10902)),hAPP(c_Set_OCollect(U_10901),U_10903)),
    inference(definitional_conversion,[status(esa)],[f_2927_2]) ).

cnf(f_2927_4,plain,
    hAPP(c_Set_OCollect(U_10901),hAPP(hAPP(c_COMBS(U_10901,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_10901),c_fconj),U_10902)),U_10903)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10901,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_10901),U_10902)),hAPP(c_Set_OCollect(U_10901),U_10903)),
    inference(clausify,[status(thm)],[f_2927_3]) ).

fof(f_2928_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_2928_2,plain,
    ! [U_10906,U_10905,U_10904] :
      ( c_Wellfounded_Owf(U_10904,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_10904,U_10904),tc_HOL_Obool)),U_10906),U_10905))
      | ~ c_Wellfounded_Owf(U_10904,U_10905) ),
    inference(variable_rename,[status(thm)],[f_2928_1]) ).

fof(f_2928_3,plain,
    ! [U_10904,U_10905,U_10906] :
      ( c_Wellfounded_Owf(U_10904,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_10904,U_10904),tc_HOL_Obool)),U_10906),U_10905))
      | ~ c_Wellfounded_Owf(U_10904,U_10905) ),
    inference(definitional_conversion,[status(esa)],[f_2928_2]) ).

cnf(f_2928_4,plain,
    ( c_Wellfounded_Owf(U_10904,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_10904,U_10904),tc_HOL_Obool)),U_10906),U_10905))
    | ~ c_Wellfounded_Owf(U_10904,U_10905) ),
    inference(clausify,[status(thm)],[f_2928_3]) ).

fof(f_2929_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_2929_2,plain,
    ! [U_10909,U_10908,U_10907] :
      ( c_Wellfounded_Owf(U_10907,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_10907,U_10907),tc_HOL_Obool)),U_10908),U_10909))
      | ~ c_Wellfounded_Owf(U_10907,U_10908) ),
    inference(variable_rename,[status(thm)],[f_2929_1]) ).

fof(f_2929_3,plain,
    ! [U_10908,U_10909,U_10907] :
      ( c_Wellfounded_Owf(U_10907,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_10907,U_10907),tc_HOL_Obool)),U_10908),U_10909))
      | ~ c_Wellfounded_Owf(U_10907,U_10908) ),
    inference(definitional_conversion,[status(esa)],[f_2929_2]) ).

cnf(f_2929_4,plain,
    ( c_Wellfounded_Owf(U_10907,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_10907,U_10907),tc_HOL_Obool)),U_10908),U_10909))
    | ~ c_Wellfounded_Owf(U_10907,U_10908) ),
    inference(clausify,[status(thm)],[f_2929_3]) ).

fof(f_2930_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_2930_2,plain,
    ! [U_10913,U_10912,U_10911,U_10910] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10910,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10910,tc_fun(U_10910,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10910)),U_10911)),hAPP(hAPP(c_COMBC(U_10910,tc_fun(U_10910,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10910)),U_10912)),U_10913))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10910),U_10913),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10910,tc_HOL_Obool)),U_10911),U_10912))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_10910),U_10913),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10910,tc_HOL_Obool)),U_10911),U_10912)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10910,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10910,tc_fun(U_10910,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10910)),U_10911)),hAPP(hAPP(c_COMBC(U_10910,tc_fun(U_10910,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10910)),U_10912)),U_10913)) ) ),
    inference(variable_rename,[status(thm)],[f_2930_1]) ).

fof(f_2930_3,plain,
    ( ! [U_10921,U_10919,U_10917,U_10915] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10915,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10915,tc_fun(U_10915,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10915)),U_10917)),hAPP(hAPP(c_COMBC(U_10915,tc_fun(U_10915,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10915)),U_10919)),U_10921))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10915),U_10921),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10915,tc_HOL_Obool)),U_10917),U_10919))) )
    & ! [U_10920,U_10918,U_10916,U_10914] :
        ( hBOOL(hAPP(hAPP(c_member(U_10914),U_10920),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10914,tc_HOL_Obool)),U_10916),U_10918)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10914,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10914,tc_fun(U_10914,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10914)),U_10916)),hAPP(hAPP(c_COMBC(U_10914,tc_fun(U_10914,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10914)),U_10918)),U_10920)) ) ),
    inference(miniscope,[status(thm)],[f_2930_2]) ).

fof(f_2930_4,plain,
    ( ! [U_10915,U_10917,U_10919,U_10921] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10915,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10915,tc_fun(U_10915,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10915)),U_10917)),hAPP(hAPP(c_COMBC(U_10915,tc_fun(U_10915,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10915)),U_10919)),U_10921))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10915),U_10921),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10915,tc_HOL_Obool)),U_10917),U_10919))) )
    & ! [U_10914,U_10918,U_10920,U_10916] :
        ( hBOOL(hAPP(hAPP(c_member(U_10914),U_10920),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10914,tc_HOL_Obool)),U_10916),U_10918)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10914,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10914,tc_fun(U_10914,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10914)),U_10916)),hAPP(hAPP(c_COMBC(U_10914,tc_fun(U_10914,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10914)),U_10918)),U_10920)) ) ),
    inference(definitional_conversion,[status(esa)],[f_2930_3]) ).

cnf(f_2930_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10914),U_10920),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10914,tc_HOL_Obool)),U_10916),U_10918)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10914,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10914,tc_fun(U_10914,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10914)),U_10916)),hAPP(hAPP(c_COMBC(U_10914,tc_fun(U_10914,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10914)),U_10918)),U_10920)) ),
    inference(clausify,[status(thm)],[f_2930_4]) ).

cnf(f_2930_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10915,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_10915,tc_fun(U_10915,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10915)),U_10917)),hAPP(hAPP(c_COMBC(U_10915,tc_fun(U_10915,tc_HOL_Obool),tc_HOL_Obool),c_member(U_10915)),U_10919)),U_10921))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10915),U_10921),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10915,tc_HOL_Obool)),U_10917),U_10919))) ),
    inference(clausify,[status(thm)],[f_2930_4]) ).

fof(f_2931_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_2931_2,plain,
    ! [U_10925,U_10924,U_10923,U_10922] :
      ( hBOOL(hAPP(hAPP(c_member(U_10922),U_10923),U_10925))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10922),U_10923),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10922,tc_HOL_Obool)),U_10924),U_10925))) ),
    inference(variable_rename,[status(thm)],[f_2931_1]) ).

fof(f_2931_3,plain,
    ! [U_10923,U_10922,U_10925,U_10924] :
      ( hBOOL(hAPP(hAPP(c_member(U_10922),U_10923),U_10925))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10922),U_10923),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10922,tc_HOL_Obool)),U_10924),U_10925))) ),
    inference(definitional_conversion,[status(esa)],[f_2931_2]) ).

cnf(f_2931_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10922),U_10923),U_10925))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10922),U_10923),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10922,tc_HOL_Obool)),U_10924),U_10925))) ),
    inference(clausify,[status(thm)],[f_2931_3]) ).

fof(f_2932_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_2932_2,plain,
    ! [U_10929,U_10928,U_10927,U_10926] :
      ( hBOOL(hAPP(hAPP(c_member(U_10926),U_10927),U_10928))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10926),U_10927),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10926,tc_HOL_Obool)),U_10928),U_10929))) ),
    inference(variable_rename,[status(thm)],[f_2932_1]) ).

fof(f_2932_3,plain,
    ! [U_10926,U_10927,U_10928,U_10929] :
      ( hBOOL(hAPP(hAPP(c_member(U_10926),U_10927),U_10928))
      | ~ hBOOL(hAPP(hAPP(c_member(U_10926),U_10927),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10926,tc_HOL_Obool)),U_10928),U_10929))) ),
    inference(definitional_conversion,[status(esa)],[f_2932_2]) ).

cnf(f_2932_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10926),U_10927),U_10928))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10926),U_10927),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10926,tc_HOL_Obool)),U_10928),U_10929))) ),
    inference(clausify,[status(thm)],[f_2932_3]) ).

fof(f_2933_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_2933_2,plain,
    ! [U_10933,U_10932,U_10931,U_10930] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_10930),U_10931),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10930,tc_HOL_Obool)),U_10932),U_10933)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10930),U_10931),U_10933))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10930),U_10931),U_10932)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(U_10930),U_10931),U_10933))
          & hBOOL(hAPP(hAPP(c_member(U_10930),U_10931),U_10932)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_10930),U_10931),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10930,tc_HOL_Obool)),U_10932),U_10933))) ) ),
    inference(variable_rename,[status(thm)],[f_2933_1]) ).

fof(f_2933_3,plain,
    ( ! [U_10941,U_10939,U_10937,U_10935] :
        ( hBOOL(hAPP(hAPP(c_member(U_10935),U_10937),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10935,tc_HOL_Obool)),U_10939),U_10941)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10935),U_10937),U_10941))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10935),U_10937),U_10939)) )
    & ! [U_10940,U_10938,U_10936,U_10934] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_10934),U_10936),U_10940))
          & hBOOL(hAPP(hAPP(c_member(U_10934),U_10936),U_10938)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_10934),U_10936),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10934,tc_HOL_Obool)),U_10938),U_10940))) ) ),
    inference(miniscope,[status(thm)],[f_2933_2]) ).

fof(f_2933_4,plain,
    ( ! [U_10936,U_10940,U_10934,U_10938] :
        ( hBOOL(hAPP(hAPP(c_member(U_10934),U_10936),U_10940))
        | ~ sP816(U_10936,U_10940,U_10934,U_10938) )
    & ! [U_10936,U_10940,U_10934,U_10938] :
        ( hBOOL(hAPP(hAPP(c_member(U_10934),U_10936),U_10938))
        | ~ sP816(U_10936,U_10940,U_10934,U_10938) )
    & ! [U_10937,U_10935,U_10941,U_10939] :
        ( hBOOL(hAPP(hAPP(c_member(U_10935),U_10937),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10935,tc_HOL_Obool)),U_10939),U_10941)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10935),U_10937),U_10941))
        | ~ hBOOL(hAPP(hAPP(c_member(U_10935),U_10937),U_10939)) )
    & ! [U_10936,U_10940,U_10934,U_10938] :
        ( sP816(U_10936,U_10940,U_10934,U_10938)
        | ~ hBOOL(hAPP(hAPP(c_member(U_10934),U_10936),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10934,tc_HOL_Obool)),U_10938),U_10940))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP816])],[f_2933_3]) ).

cnf(f_2933_5,plain,
    ( sP816(U_10936,U_10940,U_10934,U_10938)
    | ~ hBOOL(hAPP(hAPP(c_member(U_10934),U_10936),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10934,tc_HOL_Obool)),U_10938),U_10940))) ),
    inference(clausify,[status(thm)],[f_2933_4]) ).

cnf(f_2933_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10935),U_10937),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10935,tc_HOL_Obool)),U_10939),U_10941)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10935),U_10937),U_10941))
    | ~ hBOOL(hAPP(hAPP(c_member(U_10935),U_10937),U_10939)) ),
    inference(clausify,[status(thm)],[f_2933_4]) ).

cnf(f_2933_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10934),U_10936),U_10938))
    | ~ sP816(U_10936,U_10940,U_10934,U_10938) ),
    inference(clausify,[status(thm)],[f_2933_4]) ).

cnf(f_2933_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_10934),U_10936),U_10940))
    | ~ sP816(U_10936,U_10940,U_10934,U_10938) ),
    inference(clausify,[status(thm)],[f_2933_4]) ).

fof(f_2934_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_2934_2,plain,
    ! [U_10945,U_10944,U_10943,U_10942] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10942,tc_HOL_Obool)),U_10943),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10942,tc_HOL_Obool)),U_10944),U_10945)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10942,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10942,tc_HOL_Obool)),U_10943),U_10944)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10942,tc_HOL_Obool)),U_10943),U_10945)),
    inference(variable_rename,[status(thm)],[f_2934_1]) ).

fof(f_2934_3,plain,
    ! [U_10943,U_10942,U_10944,U_10945] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10942,tc_HOL_Obool)),U_10943),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10942,tc_HOL_Obool)),U_10944),U_10945)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10942,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10942,tc_HOL_Obool)),U_10943),U_10944)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10942,tc_HOL_Obool)),U_10943),U_10945)),
    inference(definitional_conversion,[status(esa)],[f_2934_2]) ).

cnf(f_2934_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10942,tc_HOL_Obool)),U_10943),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10942,tc_HOL_Obool)),U_10944),U_10945)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10942,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10942,tc_HOL_Obool)),U_10943),U_10944)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10942,tc_HOL_Obool)),U_10943),U_10945)),
    inference(clausify,[status(thm)],[f_2934_3]) ).

fof(f_2935_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_2935_2,plain,
    ! [U_10949,U_10948,U_10947,U_10946] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10946,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10946,tc_HOL_Obool)),U_10947),U_10948)),U_10949) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10946,tc_HOL_Obool)),U_10947),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10946,tc_HOL_Obool)),U_10948),U_10949)),
    inference(variable_rename,[status(thm)],[f_2935_1]) ).

fof(f_2935_3,plain,
    ! [U_10946,U_10947,U_10948,U_10949] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10946,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10946,tc_HOL_Obool)),U_10947),U_10948)),U_10949) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10946,tc_HOL_Obool)),U_10947),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10946,tc_HOL_Obool)),U_10948),U_10949)),
    inference(definitional_conversion,[status(esa)],[f_2935_2]) ).

cnf(f_2935_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10946,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10946,tc_HOL_Obool)),U_10947),U_10948)),U_10949) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10946,tc_HOL_Obool)),U_10947),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10946,tc_HOL_Obool)),U_10948),U_10949)),
    inference(clausify,[status(thm)],[f_2935_3]) ).

fof(f_2936_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_2936_2,plain,
    ! [U_10953,U_10952,U_10951,U_10950] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10950,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10950,tc_HOL_Obool)),U_10951),U_10952)),U_10953) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10950,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10950,tc_HOL_Obool)),U_10951),U_10953)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10950,tc_HOL_Obool)),U_10952),U_10953)),
    inference(variable_rename,[status(thm)],[f_2936_1]) ).

fof(f_2936_3,plain,
    ! [U_10950,U_10951,U_10952,U_10953] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10950,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10950,tc_HOL_Obool)),U_10951),U_10952)),U_10953) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10950,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10950,tc_HOL_Obool)),U_10951),U_10953)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10950,tc_HOL_Obool)),U_10952),U_10953)),
    inference(definitional_conversion,[status(esa)],[f_2936_2]) ).

cnf(f_2936_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10950,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10950,tc_HOL_Obool)),U_10951),U_10952)),U_10953) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10950,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10950,tc_HOL_Obool)),U_10951),U_10953)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10950,tc_HOL_Obool)),U_10952),U_10953)),
    inference(clausify,[status(thm)],[f_2936_3]) ).

fof(f_2937_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_2937_2,plain,
    ! [U_10957,U_10956,U_10955,U_10954] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10954,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10954,tc_HOL_Obool)),U_10955),U_10956)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10954,tc_HOL_Obool)),U_10957),U_10956)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10954,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10954,tc_HOL_Obool)),U_10955),U_10956)),U_10957),
    inference(variable_rename,[status(thm)],[f_2937_1]) ).

fof(f_2937_3,plain,
    ! [U_10954,U_10955,U_10956,U_10957] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10954,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10954,tc_HOL_Obool)),U_10955),U_10956)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10954,tc_HOL_Obool)),U_10957),U_10956)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10954,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10954,tc_HOL_Obool)),U_10955),U_10956)),U_10957),
    inference(definitional_conversion,[status(esa)],[f_2937_2]) ).

cnf(f_2937_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10954,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10954,tc_HOL_Obool)),U_10955),U_10956)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10954,tc_HOL_Obool)),U_10957),U_10956)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_10954,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10954,tc_HOL_Obool)),U_10955),U_10956)),U_10957),
    inference(clausify,[status(thm)],[f_2937_3]) ).

fof(f_2938_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_2938_2,plain,
    ! [U_10961,U_10960,U_10959,U_10958] : hAPP(c_Relation_Oconverse(U_10958,U_10959),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_10958,U_10959),tc_HOL_Obool)),U_10960),U_10961)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_10959,U_10958),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_10958,U_10959),U_10960)),hAPP(c_Relation_Oconverse(U_10958,U_10959),U_10961)),
    inference(variable_rename,[status(thm)],[f_2938_1]) ).

fof(f_2938_3,plain,
    ! [U_10958,U_10959,U_10960,U_10961] : hAPP(c_Relation_Oconverse(U_10958,U_10959),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_10958,U_10959),tc_HOL_Obool)),U_10960),U_10961)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_10959,U_10958),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_10958,U_10959),U_10960)),hAPP(c_Relation_Oconverse(U_10958,U_10959),U_10961)),
    inference(definitional_conversion,[status(esa)],[f_2938_2]) ).

cnf(f_2938_4,plain,
    hAPP(c_Relation_Oconverse(U_10958,U_10959),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_10958,U_10959),tc_HOL_Obool)),U_10960),U_10961)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_10959,U_10958),tc_HOL_Obool)),hAPP(c_Relation_Oconverse(U_10958,U_10959),U_10960)),hAPP(c_Relation_Oconverse(U_10958,U_10959),U_10961)),
    inference(clausify,[status(thm)],[f_2938_3]) ).

fof(f_2939_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_2939_2,plain,
    ! [U_10962] :
      ( c_Lattices_Osemilattice__inf__class_Oinf(U_10962) = c_Orderings_Oord__class_Omin(U_10962)
      | ~ class_Orderings_Olinorder(U_10962)
      | ~ class_Lattices_Osemilattice__inf(U_10962) ),
    inference(variable_rename,[status(thm)],[f_2939_1]) ).

fof(f_2939_3,plain,
    ! [U_10962] :
      ( c_Lattices_Osemilattice__inf__class_Oinf(U_10962) = c_Orderings_Oord__class_Omin(U_10962)
      | ~ class_Orderings_Olinorder(U_10962)
      | ~ class_Lattices_Osemilattice__inf(U_10962) ),
    inference(definitional_conversion,[status(esa)],[f_2939_2]) ).

cnf(f_2939_4,plain,
    ( c_Lattices_Osemilattice__inf__class_Oinf(U_10962) = c_Orderings_Oord__class_Omin(U_10962)
    | ~ class_Orderings_Olinorder(U_10962)
    | ~ class_Lattices_Osemilattice__inf(U_10962) ),
    inference(clausify,[status(thm)],[f_2939_3]) ).

fof(f_2940_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_2940_2,plain,
    ! [U_10967,U_10966,U_10965,U_10964,U_10963] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10964,U_10963)),U_10965),U_10966),U_10967) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10963),hAPP(U_10965,U_10967)),hAPP(U_10966,U_10967))
      | ~ class_Lattices_Olattice(U_10963) ),
    inference(variable_rename,[status(thm)],[f_2940_1]) ).

fof(f_2940_3,plain,
    ! [U_10963,U_10964,U_10965,U_10966,U_10967] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10964,U_10963)),U_10965),U_10966),U_10967) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10963),hAPP(U_10965,U_10967)),hAPP(U_10966,U_10967))
      | ~ class_Lattices_Olattice(U_10963) ),
    inference(definitional_conversion,[status(esa)],[f_2940_2]) ).

cnf(f_2940_4,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_10964,U_10963)),U_10965),U_10966),U_10967) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10963),hAPP(U_10965,U_10967)),hAPP(U_10966,U_10967))
    | ~ class_Lattices_Olattice(U_10963) ),
    inference(clausify,[status(thm)],[f_2940_3]) ).

fof(f_2941_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_2941_2,plain,
    ! [U_10969,U_10968] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10968),U_10969),U_10969) = U_10969
      | ~ class_Lattices_Osemilattice__inf(U_10968) ),
    inference(variable_rename,[status(thm)],[f_2941_1]) ).

fof(f_2941_3,plain,
    ! [U_10968,U_10969] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10968),U_10969),U_10969) = U_10969
      | ~ class_Lattices_Osemilattice__inf(U_10968) ),
    inference(definitional_conversion,[status(esa)],[f_2941_2]) ).

cnf(f_2941_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10968),U_10969),U_10969) = U_10969
    | ~ class_Lattices_Osemilattice__inf(U_10968) ),
    inference(clausify,[status(thm)],[f_2941_3]) ).

fof(f_2942_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_2942_2,plain,
    ! [U_10971,U_10970] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10970),U_10971),U_10971) = U_10971
      | ~ class_Lattices_Osemilattice__inf(U_10970) ),
    inference(variable_rename,[status(thm)],[f_2942_1]) ).

fof(f_2942_3,plain,
    ! [U_10970,U_10971] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10970),U_10971),U_10971) = U_10971
      | ~ class_Lattices_Osemilattice__inf(U_10970) ),
    inference(definitional_conversion,[status(esa)],[f_2942_2]) ).

cnf(f_2942_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10970),U_10971),U_10971) = U_10971
    | ~ class_Lattices_Osemilattice__inf(U_10970) ),
    inference(clausify,[status(thm)],[f_2942_3]) ).

fof(f_2943_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_2943_2,plain,
    ! [U_10974,U_10973,U_10972] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10972),U_10973),U_10974) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10972),U_10974),U_10973)
      | ~ class_Lattices_Osemilattice__inf(U_10972) ),
    inference(variable_rename,[status(thm)],[f_2943_1]) ).

fof(f_2943_3,plain,
    ! [U_10972,U_10973,U_10974] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10972),U_10973),U_10974) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10972),U_10974),U_10973)
      | ~ class_Lattices_Osemilattice__inf(U_10972) ),
    inference(definitional_conversion,[status(esa)],[f_2943_2]) ).

cnf(f_2943_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10972),U_10973),U_10974) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10972),U_10974),U_10973)
    | ~ class_Lattices_Osemilattice__inf(U_10972) ),
    inference(clausify,[status(thm)],[f_2943_3]) ).

fof(f_2944_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_2944_2,plain,
    ! [U_10977,U_10976,U_10975] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10975),U_10976),U_10977) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10975),U_10977),U_10976)
      | ~ class_Lattices_Olattice(U_10975) ),
    inference(variable_rename,[status(thm)],[f_2944_1]) ).

fof(f_2944_3,plain,
    ! [U_10975,U_10976,U_10977] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10975),U_10976),U_10977) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10975),U_10977),U_10976)
      | ~ class_Lattices_Olattice(U_10975) ),
    inference(definitional_conversion,[status(esa)],[f_2944_2]) ).

cnf(f_2944_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10975),U_10976),U_10977) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10975),U_10977),U_10976)
    | ~ class_Lattices_Olattice(U_10975) ),
    inference(clausify,[status(thm)],[f_2944_3]) ).

fof(f_2945_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_2945_2,plain,
    ! [U_10980,U_10979,U_10978] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10978),U_10979),U_10980) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10978),U_10980),U_10979)
      | ~ class_Lattices_Osemilattice__inf(U_10978) ),
    inference(variable_rename,[status(thm)],[f_2945_1]) ).

fof(f_2945_3,plain,
    ! [U_10978,U_10979,U_10980] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10978),U_10979),U_10980) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10978),U_10980),U_10979)
      | ~ class_Lattices_Osemilattice__inf(U_10978) ),
    inference(definitional_conversion,[status(esa)],[f_2945_2]) ).

cnf(f_2945_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10978),U_10979),U_10980) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10978),U_10980),U_10979)
    | ~ class_Lattices_Osemilattice__inf(U_10978) ),
    inference(clausify,[status(thm)],[f_2945_3]) ).

fof(f_2946_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_2946_2,plain,
    ! [U_10983,U_10982,U_10981] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10981),U_10982),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10981),U_10982),U_10983)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10981),U_10982),U_10983)
      | ~ class_Lattices_Osemilattice__inf(U_10981) ),
    inference(variable_rename,[status(thm)],[f_2946_1]) ).

fof(f_2946_3,plain,
    ! [U_10981,U_10982,U_10983] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10981),U_10982),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10981),U_10982),U_10983)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10981),U_10982),U_10983)
      | ~ class_Lattices_Osemilattice__inf(U_10981) ),
    inference(definitional_conversion,[status(esa)],[f_2946_2]) ).

cnf(f_2946_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10981),U_10982),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10981),U_10982),U_10983)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10981),U_10982),U_10983)
    | ~ class_Lattices_Osemilattice__inf(U_10981) ),
    inference(clausify,[status(thm)],[f_2946_3]) ).

fof(f_2947_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_2947_2,plain,
    ! [U_10986,U_10985,U_10984] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10984),U_10985),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10984),U_10985),U_10986)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10984),U_10985),U_10986)
      | ~ class_Lattices_Olattice(U_10984) ),
    inference(variable_rename,[status(thm)],[f_2947_1]) ).

fof(f_2947_3,plain,
    ! [U_10984,U_10985,U_10986] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10984),U_10985),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10984),U_10985),U_10986)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10984),U_10985),U_10986)
      | ~ class_Lattices_Olattice(U_10984) ),
    inference(definitional_conversion,[status(esa)],[f_2947_2]) ).

cnf(f_2947_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10984),U_10985),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10984),U_10985),U_10986)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10984),U_10985),U_10986)
    | ~ class_Lattices_Olattice(U_10984) ),
    inference(clausify,[status(thm)],[f_2947_3]) ).

fof(f_2948_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_2948_2,plain,
    ! [U_10989,U_10988,U_10987] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10987),U_10988),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10987),U_10988),U_10989)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10987),U_10988),U_10989)
      | ~ class_Lattices_Osemilattice__inf(U_10987) ),
    inference(variable_rename,[status(thm)],[f_2948_1]) ).

fof(f_2948_3,plain,
    ! [U_10987,U_10988,U_10989] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10987),U_10988),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10987),U_10988),U_10989)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10987),U_10988),U_10989)
      | ~ class_Lattices_Osemilattice__inf(U_10987) ),
    inference(definitional_conversion,[status(esa)],[f_2948_2]) ).

cnf(f_2948_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10987),U_10988),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10987),U_10988),U_10989)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10987),U_10988),U_10989)
    | ~ class_Lattices_Osemilattice__inf(U_10987) ),
    inference(clausify,[status(thm)],[f_2948_3]) ).

fof(f_2949_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_2949_2,plain,
    ! [U_10993,U_10992,U_10991,U_10990] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10990),U_10991),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10990),U_10992),U_10993)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10990),U_10992),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10990),U_10991),U_10993))
      | ~ class_Lattices_Osemilattice__inf(U_10990) ),
    inference(variable_rename,[status(thm)],[f_2949_1]) ).

fof(f_2949_3,plain,
    ! [U_10990,U_10991,U_10992,U_10993] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10990),U_10991),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10990),U_10992),U_10993)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10990),U_10992),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10990),U_10991),U_10993))
      | ~ class_Lattices_Osemilattice__inf(U_10990) ),
    inference(definitional_conversion,[status(esa)],[f_2949_2]) ).

cnf(f_2949_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10990),U_10991),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10990),U_10992),U_10993)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10990),U_10992),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10990),U_10991),U_10993))
    | ~ class_Lattices_Osemilattice__inf(U_10990) ),
    inference(clausify,[status(thm)],[f_2949_3]) ).

fof(f_2950_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_2950_2,plain,
    ! [U_10997,U_10996,U_10995,U_10994] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10994),U_10995),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10994),U_10996),U_10997)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10994),U_10996),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10994),U_10995),U_10997))
      | ~ class_Lattices_Olattice(U_10994) ),
    inference(variable_rename,[status(thm)],[f_2950_1]) ).

fof(f_2950_3,plain,
    ! [U_10994,U_10995,U_10996,U_10997] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10994),U_10995),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10994),U_10996),U_10997)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10994),U_10996),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10994),U_10995),U_10997))
      | ~ class_Lattices_Olattice(U_10994) ),
    inference(definitional_conversion,[status(esa)],[f_2950_2]) ).

cnf(f_2950_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10994),U_10995),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10994),U_10996),U_10997)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10994),U_10996),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10994),U_10995),U_10997))
    | ~ class_Lattices_Olattice(U_10994) ),
    inference(clausify,[status(thm)],[f_2950_3]) ).

fof(f_2951_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_2951_2,plain,
    ! [U_11001,U_11000,U_10999,U_10998] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10998),U_10999),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10998),U_11000),U_11001)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10998),U_11000),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10998),U_10999),U_11001))
      | ~ class_Lattices_Osemilattice__inf(U_10998) ),
    inference(variable_rename,[status(thm)],[f_2951_1]) ).

fof(f_2951_3,plain,
    ! [U_10998,U_10999,U_11000,U_11001] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10998),U_10999),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10998),U_11000),U_11001)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10998),U_11000),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10998),U_10999),U_11001))
      | ~ class_Lattices_Osemilattice__inf(U_10998) ),
    inference(definitional_conversion,[status(esa)],[f_2951_2]) ).

cnf(f_2951_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10998),U_10999),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10998),U_11000),U_11001)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10998),U_11000),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_10998),U_10999),U_11001))
    | ~ class_Lattices_Osemilattice__inf(U_10998) ),
    inference(clausify,[status(thm)],[f_2951_3]) ).

fof(f_2952_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_2952_2,plain,
    ! [U_11005,U_11004,U_11003,U_11002] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11002),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11002),U_11003),U_11004)),U_11005) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11002),U_11003),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11002),U_11004),U_11005))
      | ~ class_Lattices_Osemilattice__inf(U_11002) ),
    inference(variable_rename,[status(thm)],[f_2952_1]) ).

fof(f_2952_3,plain,
    ! [U_11002,U_11003,U_11004,U_11005] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11002),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11002),U_11003),U_11004)),U_11005) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11002),U_11003),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11002),U_11004),U_11005))
      | ~ class_Lattices_Osemilattice__inf(U_11002) ),
    inference(definitional_conversion,[status(esa)],[f_2952_2]) ).

cnf(f_2952_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11002),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11002),U_11003),U_11004)),U_11005) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11002),U_11003),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11002),U_11004),U_11005))
    | ~ class_Lattices_Osemilattice__inf(U_11002) ),
    inference(clausify,[status(thm)],[f_2952_3]) ).

fof(f_2953_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_2953_2,plain,
    ! [U_11009,U_11008,U_11007,U_11006] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11006),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11006),U_11007),U_11008)),U_11009) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11006),U_11007),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11006),U_11008),U_11009))
      | ~ class_Lattices_Olattice(U_11006) ),
    inference(variable_rename,[status(thm)],[f_2953_1]) ).

fof(f_2953_3,plain,
    ! [U_11006,U_11007,U_11008,U_11009] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11006),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11006),U_11007),U_11008)),U_11009) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11006),U_11007),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11006),U_11008),U_11009))
      | ~ class_Lattices_Olattice(U_11006) ),
    inference(definitional_conversion,[status(esa)],[f_2953_2]) ).

cnf(f_2953_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11006),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11006),U_11007),U_11008)),U_11009) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11006),U_11007),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11006),U_11008),U_11009))
    | ~ class_Lattices_Olattice(U_11006) ),
    inference(clausify,[status(thm)],[f_2953_3]) ).

fof(f_2954_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_2954_2,plain,
    ! [U_11013,U_11012,U_11011,U_11010] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11010),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11010),U_11011),U_11012)),U_11013) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11010),U_11011),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11010),U_11012),U_11013))
      | ~ class_Lattices_Osemilattice__inf(U_11010) ),
    inference(variable_rename,[status(thm)],[f_2954_1]) ).

fof(f_2954_3,plain,
    ! [U_11010,U_11011,U_11012,U_11013] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11010),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11010),U_11011),U_11012)),U_11013) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11010),U_11011),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11010),U_11012),U_11013))
      | ~ class_Lattices_Osemilattice__inf(U_11010) ),
    inference(definitional_conversion,[status(esa)],[f_2954_2]) ).

cnf(f_2954_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11010),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11010),U_11011),U_11012)),U_11013) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11010),U_11011),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11010),U_11012),U_11013))
    | ~ class_Lattices_Osemilattice__inf(U_11010) ),
    inference(clausify,[status(thm)],[f_2954_3]) ).

fof(f_2955_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_2955_2,plain,
    ! [U_11018,U_11017,U_11016,U_11015,U_11014] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11015,U_11014)),U_11016),U_11017),U_11018) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11014),hAPP(U_11016,U_11018)),hAPP(U_11017,U_11018))
      | ~ class_Lattices_Olattice(U_11014) ),
    inference(variable_rename,[status(thm)],[f_2955_1]) ).

fof(f_2955_3,plain,
    ! [U_11014,U_11015,U_11016,U_11017,U_11018] :
      ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11015,U_11014)),U_11016),U_11017),U_11018) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11014),hAPP(U_11016,U_11018)),hAPP(U_11017,U_11018))
      | ~ class_Lattices_Olattice(U_11014) ),
    inference(definitional_conversion,[status(esa)],[f_2955_2]) ).

cnf(f_2955_4,plain,
    ( hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11015,U_11014)),U_11016),U_11017),U_11018) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11014),hAPP(U_11016,U_11018)),hAPP(U_11017,U_11018))
    | ~ class_Lattices_Olattice(U_11014) ),
    inference(clausify,[status(thm)],[f_2955_3]) ).

fof(f_2956_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_2956_2,plain,
    ! [U_11020,U_11019] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11019,tc_HOL_Obool)),U_11020),U_11020) = U_11020,
    inference(variable_rename,[status(thm)],[f_2956_1]) ).

fof(f_2956_3,plain,
    ! [U_11020,U_11019] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11019,tc_HOL_Obool)),U_11020),U_11020) = U_11020,
    inference(definitional_conversion,[status(esa)],[f_2956_2]) ).

cnf(f_2956_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11019,tc_HOL_Obool)),U_11020),U_11020) = U_11020,
    inference(clausify,[status(thm)],[f_2956_3]) ).

fof(f_2957_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_2957_2,plain,
    ! [U_11023,U_11022,U_11021] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11021,tc_HOL_Obool)),U_11022),U_11023) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11021,tc_HOL_Obool)),U_11023),U_11022),
    inference(variable_rename,[status(thm)],[f_2957_1]) ).

fof(f_2957_3,plain,
    ! [U_11021,U_11022,U_11023] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11021,tc_HOL_Obool)),U_11022),U_11023) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11021,tc_HOL_Obool)),U_11023),U_11022),
    inference(definitional_conversion,[status(esa)],[f_2957_2]) ).

cnf(f_2957_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11021,tc_HOL_Obool)),U_11022),U_11023) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11021,tc_HOL_Obool)),U_11023),U_11022),
    inference(clausify,[status(thm)],[f_2957_3]) ).

fof(f_2958_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_2958_2,plain,
    ! [U_11026,U_11025,U_11024] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11024,tc_HOL_Obool)),U_11025),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11024,tc_HOL_Obool)),U_11025),U_11026)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11024,tc_HOL_Obool)),U_11025),U_11026),
    inference(variable_rename,[status(thm)],[f_2958_1]) ).

fof(f_2958_3,plain,
    ! [U_11024,U_11025,U_11026] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11024,tc_HOL_Obool)),U_11025),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11024,tc_HOL_Obool)),U_11025),U_11026)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11024,tc_HOL_Obool)),U_11025),U_11026),
    inference(definitional_conversion,[status(esa)],[f_2958_2]) ).

cnf(f_2958_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11024,tc_HOL_Obool)),U_11025),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11024,tc_HOL_Obool)),U_11025),U_11026)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11024,tc_HOL_Obool)),U_11025),U_11026),
    inference(clausify,[status(thm)],[f_2958_3]) ).

fof(f_2959_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_2959_2,plain,
    ! [U_11030,U_11029,U_11028,U_11027] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11027,tc_HOL_Obool)),U_11028),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11027,tc_HOL_Obool)),U_11029),U_11030)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11027,tc_HOL_Obool)),U_11029),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11027,tc_HOL_Obool)),U_11028),U_11030)),
    inference(variable_rename,[status(thm)],[f_2959_1]) ).

fof(f_2959_3,plain,
    ! [U_11027,U_11028,U_11029,U_11030] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11027,tc_HOL_Obool)),U_11028),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11027,tc_HOL_Obool)),U_11029),U_11030)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11027,tc_HOL_Obool)),U_11029),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11027,tc_HOL_Obool)),U_11028),U_11030)),
    inference(definitional_conversion,[status(esa)],[f_2959_2]) ).

cnf(f_2959_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11027,tc_HOL_Obool)),U_11028),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11027,tc_HOL_Obool)),U_11029),U_11030)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11027,tc_HOL_Obool)),U_11029),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11027,tc_HOL_Obool)),U_11028),U_11030)),
    inference(clausify,[status(thm)],[f_2959_3]) ).

fof(f_2960_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_2960_2,plain,
    ! [U_11034,U_11033,U_11032,U_11031] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11031,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11031,tc_HOL_Obool)),U_11032),U_11033)),U_11034) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11031,tc_HOL_Obool)),U_11032),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11031,tc_HOL_Obool)),U_11033),U_11034)),
    inference(variable_rename,[status(thm)],[f_2960_1]) ).

fof(f_2960_3,plain,
    ! [U_11031,U_11032,U_11033,U_11034] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11031,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11031,tc_HOL_Obool)),U_11032),U_11033)),U_11034) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11031,tc_HOL_Obool)),U_11032),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11031,tc_HOL_Obool)),U_11033),U_11034)),
    inference(definitional_conversion,[status(esa)],[f_2960_2]) ).

cnf(f_2960_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11031,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11031,tc_HOL_Obool)),U_11032),U_11033)),U_11034) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11031,tc_HOL_Obool)),U_11032),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11031,tc_HOL_Obool)),U_11033),U_11034)),
    inference(clausify,[status(thm)],[f_2960_3]) ).

fof(f_2961_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_2961_2,plain,
    ! [U_11038,U_11037,U_11036,U_11035] :
      ( hBOOL(hAPP(U_11036,U_11038))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11035,tc_HOL_Obool)),U_11036),U_11037),U_11038)) ),
    inference(variable_rename,[status(thm)],[f_2961_1]) ).

fof(f_2961_3,plain,
    ! [U_11038,U_11037,U_11036] :
      ( ! [U_11035] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11035,tc_HOL_Obool)),U_11036),U_11037),U_11038))
      | hBOOL(hAPP(U_11036,U_11038)) ),
    inference(miniscope,[status(thm)],[f_2961_2]) ).

fof(f_2961_4,plain,
    ! [U_11035,U_11036,U_11037,U_11038] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11035,tc_HOL_Obool)),U_11036),U_11037),U_11038))
      | hBOOL(hAPP(U_11036,U_11038)) ),
    inference(definitional_conversion,[status(esa)],[f_2961_3]) ).

cnf(f_2961_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11035,tc_HOL_Obool)),U_11036),U_11037),U_11038))
    | hBOOL(hAPP(U_11036,U_11038)) ),
    inference(clausify,[status(thm)],[f_2961_4]) ).

fof(f_2962_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_2962_2,plain,
    ! [U_11042,U_11041,U_11040,U_11039] :
      ( hBOOL(hAPP(U_11041,U_11042))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11039,tc_HOL_Obool)),U_11040),U_11041),U_11042)) ),
    inference(variable_rename,[status(thm)],[f_2962_1]) ).

fof(f_2962_3,plain,
    ! [U_11042,U_11041] :
      ( ! [U_11040,U_11039] : ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11039,tc_HOL_Obool)),U_11040),U_11041),U_11042))
      | hBOOL(hAPP(U_11041,U_11042)) ),
    inference(miniscope,[status(thm)],[f_2962_2]) ).

fof(f_2962_4,plain,
    ! [U_11039,U_11040,U_11041,U_11042] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11039,tc_HOL_Obool)),U_11040),U_11041),U_11042))
      | hBOOL(hAPP(U_11041,U_11042)) ),
    inference(definitional_conversion,[status(esa)],[f_2962_3]) ).

cnf(f_2962_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11039,tc_HOL_Obool)),U_11040),U_11041),U_11042))
    | hBOOL(hAPP(U_11041,U_11042)) ),
    inference(clausify,[status(thm)],[f_2962_4]) ).

fof(f_2963_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_2963_2,plain,
    ! [U_11044,U_11043] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11043),U_11044),U_11044) = U_11044
      | ~ class_Lattices_Olattice(U_11043) ),
    inference(variable_rename,[status(thm)],[f_2963_1]) ).

fof(f_2963_3,plain,
    ! [U_11043,U_11044] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11043),U_11044),U_11044) = U_11044
      | ~ class_Lattices_Olattice(U_11043) ),
    inference(definitional_conversion,[status(esa)],[f_2963_2]) ).

cnf(f_2963_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11043),U_11044),U_11044) = U_11044
    | ~ class_Lattices_Olattice(U_11043) ),
    inference(clausify,[status(thm)],[f_2963_3]) ).

fof(f_2964_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_2964_2,plain,
    ! [U_11048,U_11047,U_11046,U_11045] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11045),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11045),U_11046),U_11048)),U_11047))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11045),U_11046),U_11047))
      | ~ class_Lattices_Osemilattice__inf(U_11045) ),
    inference(variable_rename,[status(thm)],[f_2964_1]) ).

fof(f_2964_3,plain,
    ! [U_11045,U_11046,U_11047,U_11048] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11045),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11045),U_11046),U_11048)),U_11047))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11045),U_11046),U_11047))
      | ~ class_Lattices_Osemilattice__inf(U_11045) ),
    inference(definitional_conversion,[status(esa)],[f_2964_2]) ).

cnf(f_2964_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11045),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11045),U_11046),U_11048)),U_11047))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11045),U_11046),U_11047))
    | ~ class_Lattices_Osemilattice__inf(U_11045) ),
    inference(clausify,[status(thm)],[f_2964_3]) ).

fof(f_2965_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_2965_2,plain,
    ! [U_11052,U_11051,U_11050,U_11049] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11049),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11049),U_11052),U_11050)),U_11051))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11049),U_11050),U_11051))
      | ~ class_Lattices_Osemilattice__inf(U_11049) ),
    inference(variable_rename,[status(thm)],[f_2965_1]) ).

fof(f_2965_3,plain,
    ! [U_11049,U_11050,U_11051,U_11052] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11049),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11049),U_11052),U_11050)),U_11051))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11049),U_11050),U_11051))
      | ~ class_Lattices_Osemilattice__inf(U_11049) ),
    inference(definitional_conversion,[status(esa)],[f_2965_2]) ).

cnf(f_2965_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11049),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11049),U_11052),U_11050)),U_11051))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11049),U_11050),U_11051))
    | ~ class_Lattices_Osemilattice__inf(U_11049) ),
    inference(clausify,[status(thm)],[f_2965_3]) ).

fof(f_2966_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_2966_2,plain,
    ! [U_11055,U_11054,U_11053] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11053),U_11054),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11053),U_11054),U_11055)) = U_11054
      | ~ class_Lattices_Olattice(U_11053) ),
    inference(variable_rename,[status(thm)],[f_2966_1]) ).

fof(f_2966_3,plain,
    ! [U_11053,U_11054,U_11055] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11053),U_11054),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11053),U_11054),U_11055)) = U_11054
      | ~ class_Lattices_Olattice(U_11053) ),
    inference(definitional_conversion,[status(esa)],[f_2966_2]) ).

cnf(f_2966_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11053),U_11054),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11053),U_11054),U_11055)) = U_11054
    | ~ class_Lattices_Olattice(U_11053) ),
    inference(clausify,[status(thm)],[f_2966_3]) ).

fof(f_2967_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_2967_2,plain,
    ! [U_11058,U_11057,U_11056] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11056),U_11057),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11056),U_11057),U_11058)) = U_11057
      | ~ class_Lattices_Olattice(U_11056) ),
    inference(variable_rename,[status(thm)],[f_2967_1]) ).

fof(f_2967_3,plain,
    ! [U_11056,U_11057,U_11058] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11056),U_11057),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11056),U_11057),U_11058)) = U_11057
      | ~ class_Lattices_Olattice(U_11056) ),
    inference(definitional_conversion,[status(esa)],[f_2967_2]) ).

cnf(f_2967_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11056),U_11057),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11056),U_11057),U_11058)) = U_11057
    | ~ class_Lattices_Olattice(U_11056) ),
    inference(clausify,[status(thm)],[f_2967_3]) ).

fof(f_2968_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_2968_2,plain,
    ! [U_11062,U_11061,U_11060,U_11059] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11059),U_11060),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11059),U_11061),U_11062)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11059),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11059),U_11060),U_11061)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11059),U_11060),U_11062))
      | ~ class_Lattices_Odistrib__lattice(U_11059) ),
    inference(variable_rename,[status(thm)],[f_2968_1]) ).

fof(f_2968_3,plain,
    ! [U_11059,U_11060,U_11061,U_11062] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11059),U_11060),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11059),U_11061),U_11062)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11059),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11059),U_11060),U_11061)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11059),U_11060),U_11062))
      | ~ class_Lattices_Odistrib__lattice(U_11059) ),
    inference(definitional_conversion,[status(esa)],[f_2968_2]) ).

cnf(f_2968_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11059),U_11060),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11059),U_11061),U_11062)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11059),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11059),U_11060),U_11061)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11059),U_11060),U_11062))
    | ~ class_Lattices_Odistrib__lattice(U_11059) ),
    inference(clausify,[status(thm)],[f_2968_3]) ).

fof(f_2969_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_2969_2,plain,
    ! [U_11066,U_11065,U_11064,U_11063] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11063),U_11064),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11063),U_11065),U_11066)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11063),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11063),U_11064),U_11065)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11063),U_11064),U_11066))
      | ~ class_Lattices_Odistrib__lattice(U_11063) ),
    inference(variable_rename,[status(thm)],[f_2969_1]) ).

fof(f_2969_3,plain,
    ! [U_11063,U_11064,U_11065,U_11066] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11063),U_11064),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11063),U_11065),U_11066)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11063),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11063),U_11064),U_11065)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11063),U_11064),U_11066))
      | ~ class_Lattices_Odistrib__lattice(U_11063) ),
    inference(definitional_conversion,[status(esa)],[f_2969_2]) ).

cnf(f_2969_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11063),U_11064),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11063),U_11065),U_11066)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11063),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11063),U_11064),U_11065)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11063),U_11064),U_11066))
    | ~ class_Lattices_Odistrib__lattice(U_11063) ),
    inference(clausify,[status(thm)],[f_2969_3]) ).

fof(f_2970_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_2970_2,plain,
    ! [U_11070,U_11069,U_11068,U_11067] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11067),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11067),U_11068),U_11069)),U_11070) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11067),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11067),U_11068),U_11070)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11067),U_11069),U_11070))
      | ~ class_Lattices_Odistrib__lattice(U_11067) ),
    inference(variable_rename,[status(thm)],[f_2970_1]) ).

fof(f_2970_3,plain,
    ! [U_11067,U_11068,U_11069,U_11070] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11067),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11067),U_11068),U_11069)),U_11070) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11067),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11067),U_11068),U_11070)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11067),U_11069),U_11070))
      | ~ class_Lattices_Odistrib__lattice(U_11067) ),
    inference(definitional_conversion,[status(esa)],[f_2970_2]) ).

cnf(f_2970_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11067),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11067),U_11068),U_11069)),U_11070) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11067),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11067),U_11068),U_11070)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11067),U_11069),U_11070))
    | ~ class_Lattices_Odistrib__lattice(U_11067) ),
    inference(clausify,[status(thm)],[f_2970_3]) ).

fof(f_2971_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_2971_2,plain,
    ! [U_11074,U_11073,U_11072,U_11071] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11071),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11071),U_11072),U_11073)),U_11074) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11071),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11071),U_11072),U_11074)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11071),U_11073),U_11074))
      | ~ class_Lattices_Odistrib__lattice(U_11071) ),
    inference(variable_rename,[status(thm)],[f_2971_1]) ).

fof(f_2971_3,plain,
    ! [U_11071,U_11072,U_11073,U_11074] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11071),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11071),U_11072),U_11073)),U_11074) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11071),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11071),U_11072),U_11074)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11071),U_11073),U_11074))
      | ~ class_Lattices_Odistrib__lattice(U_11071) ),
    inference(definitional_conversion,[status(esa)],[f_2971_2]) ).

cnf(f_2971_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11071),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11071),U_11072),U_11073)),U_11074) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11071),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11071),U_11072),U_11074)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11071),U_11073),U_11074))
    | ~ class_Lattices_Odistrib__lattice(U_11071) ),
    inference(clausify,[status(thm)],[f_2971_3]) ).

fof(f_2972_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_2972_2,plain,
    ! [U_11078,U_11077,U_11076,U_11075] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11075,tc_HOL_Obool)),U_11076),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11075,tc_HOL_Obool)),U_11077),U_11078)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11075,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11075,tc_HOL_Obool)),U_11076),U_11077)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11075,tc_HOL_Obool)),U_11076),U_11078)),
    inference(variable_rename,[status(thm)],[f_2972_1]) ).

fof(f_2972_3,plain,
    ! [U_11075,U_11076,U_11077,U_11078] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11075,tc_HOL_Obool)),U_11076),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11075,tc_HOL_Obool)),U_11077),U_11078)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11075,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11075,tc_HOL_Obool)),U_11076),U_11077)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11075,tc_HOL_Obool)),U_11076),U_11078)),
    inference(definitional_conversion,[status(esa)],[f_2972_2]) ).

cnf(f_2972_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11075,tc_HOL_Obool)),U_11076),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11075,tc_HOL_Obool)),U_11077),U_11078)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11075,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11075,tc_HOL_Obool)),U_11076),U_11077)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11075,tc_HOL_Obool)),U_11076),U_11078)),
    inference(clausify,[status(thm)],[f_2972_3]) ).

fof(f_2973_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_2973_2,plain,
    ! [U_11082,U_11081,U_11080,U_11079] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11079,tc_HOL_Obool)),U_11080),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11079,tc_HOL_Obool)),U_11081),U_11082)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11079,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11079,tc_HOL_Obool)),U_11080),U_11081)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11079,tc_HOL_Obool)),U_11080),U_11082)),
    inference(variable_rename,[status(thm)],[f_2973_1]) ).

fof(f_2973_3,plain,
    ! [U_11079,U_11080,U_11081,U_11082] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11079,tc_HOL_Obool)),U_11080),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11079,tc_HOL_Obool)),U_11081),U_11082)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11079,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11079,tc_HOL_Obool)),U_11080),U_11081)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11079,tc_HOL_Obool)),U_11080),U_11082)),
    inference(definitional_conversion,[status(esa)],[f_2973_2]) ).

cnf(f_2973_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11079,tc_HOL_Obool)),U_11080),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11079,tc_HOL_Obool)),U_11081),U_11082)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11079,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11079,tc_HOL_Obool)),U_11080),U_11081)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11079,tc_HOL_Obool)),U_11080),U_11082)),
    inference(clausify,[status(thm)],[f_2973_3]) ).

fof(f_2974_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_2974_2,plain,
    ! [U_11086,U_11085,U_11084,U_11083] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11083,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11083,tc_HOL_Obool)),U_11084),U_11085)),U_11086) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11083,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11083,tc_HOL_Obool)),U_11084),U_11086)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11083,tc_HOL_Obool)),U_11085),U_11086)),
    inference(variable_rename,[status(thm)],[f_2974_1]) ).

fof(f_2974_3,plain,
    ! [U_11083,U_11084,U_11085,U_11086] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11083,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11083,tc_HOL_Obool)),U_11084),U_11085)),U_11086) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11083,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11083,tc_HOL_Obool)),U_11084),U_11086)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11083,tc_HOL_Obool)),U_11085),U_11086)),
    inference(definitional_conversion,[status(esa)],[f_2974_2]) ).

cnf(f_2974_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11083,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11083,tc_HOL_Obool)),U_11084),U_11085)),U_11086) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11083,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11083,tc_HOL_Obool)),U_11084),U_11086)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11083,tc_HOL_Obool)),U_11085),U_11086)),
    inference(clausify,[status(thm)],[f_2974_3]) ).

fof(f_2975_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_2975_2,plain,
    ! [U_11090,U_11089,U_11088,U_11087] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11087,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11087,tc_HOL_Obool)),U_11088),U_11089)),U_11090) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11087,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11087,tc_HOL_Obool)),U_11088),U_11090)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11087,tc_HOL_Obool)),U_11089),U_11090)),
    inference(variable_rename,[status(thm)],[f_2975_1]) ).

fof(f_2975_3,plain,
    ! [U_11087,U_11088,U_11089,U_11090] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11087,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11087,tc_HOL_Obool)),U_11088),U_11089)),U_11090) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11087,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11087,tc_HOL_Obool)),U_11088),U_11090)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11087,tc_HOL_Obool)),U_11089),U_11090)),
    inference(definitional_conversion,[status(esa)],[f_2975_2]) ).

cnf(f_2975_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11087,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11087,tc_HOL_Obool)),U_11088),U_11089)),U_11090) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11087,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11087,tc_HOL_Obool)),U_11088),U_11090)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11087,tc_HOL_Obool)),U_11089),U_11090)),
    inference(clausify,[status(thm)],[f_2975_3]) ).

fof(f_2976_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_2976_2,plain,
    ! [U_11094,U_11093,U_11092,U_11091] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11091,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11091,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11091,tc_HOL_Obool)),U_11092),U_11093)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11091,tc_HOL_Obool)),U_11093),U_11094))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11091,tc_HOL_Obool)),U_11094),U_11092)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11091,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11091,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11091,tc_HOL_Obool)),U_11092),U_11093)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11091,tc_HOL_Obool)),U_11093),U_11094))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11091,tc_HOL_Obool)),U_11094),U_11092)),
    inference(variable_rename,[status(thm)],[f_2976_1]) ).

fof(f_2976_3,plain,
    ! [U_11091,U_11092,U_11093,U_11094] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11091,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11091,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11091,tc_HOL_Obool)),U_11092),U_11093)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11091,tc_HOL_Obool)),U_11093),U_11094))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11091,tc_HOL_Obool)),U_11094),U_11092)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11091,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11091,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11091,tc_HOL_Obool)),U_11092),U_11093)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11091,tc_HOL_Obool)),U_11093),U_11094))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11091,tc_HOL_Obool)),U_11094),U_11092)),
    inference(definitional_conversion,[status(esa)],[f_2976_2]) ).

cnf(f_2976_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11091,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11091,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11091,tc_HOL_Obool)),U_11092),U_11093)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11091,tc_HOL_Obool)),U_11093),U_11094))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11091,tc_HOL_Obool)),U_11094),U_11092)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11091,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11091,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11091,tc_HOL_Obool)),U_11092),U_11093)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11091,tc_HOL_Obool)),U_11093),U_11094))),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11091,tc_HOL_Obool)),U_11094),U_11092)),
    inference(clausify,[status(thm)],[f_2976_3]) ).

fof(f_2977_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_2977_2,plain,
    ! [U_11098,U_11097,U_11096,U_11095] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11095,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_11095,U_11096),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11095,U_11096),tc_HOL_Obool)),U_11097),U_11098))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11095,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_11095,U_11096),U_11097)),hAPP(c_Relation_ODomain(U_11095,U_11096),U_11098)))),
    inference(variable_rename,[status(thm)],[f_2977_1]) ).

fof(f_2977_3,plain,
    ! [U_11095,U_11096,U_11097,U_11098] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11095,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_11095,U_11096),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11095,U_11096),tc_HOL_Obool)),U_11097),U_11098))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11095,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_11095,U_11096),U_11097)),hAPP(c_Relation_ODomain(U_11095,U_11096),U_11098)))),
    inference(definitional_conversion,[status(esa)],[f_2977_2]) ).

cnf(f_2977_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11095,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_11095,U_11096),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11095,U_11096),tc_HOL_Obool)),U_11097),U_11098))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11095,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_11095,U_11096),U_11097)),hAPP(c_Relation_ODomain(U_11095,U_11096),U_11098)))),
    inference(clausify,[status(thm)],[f_2977_3]) ).

fof(f_2978_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_2978_2,plain,
    ! [U_11103,U_11102,U_11101,U_11100,U_11099] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11099,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11099,tc_HOL_Obool)),U_11100),U_11102)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11099,tc_HOL_Obool)),U_11101),U_11103)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11099,tc_HOL_Obool)),U_11102),U_11103))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11099,tc_HOL_Obool)),U_11100),U_11101)) ),
    inference(variable_rename,[status(thm)],[f_2978_1]) ).

fof(f_2978_3,plain,
    ! [U_11099,U_11100,U_11101,U_11102,U_11103] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11099,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11099,tc_HOL_Obool)),U_11100),U_11102)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11099,tc_HOL_Obool)),U_11101),U_11103)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11099,tc_HOL_Obool)),U_11102),U_11103))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11099,tc_HOL_Obool)),U_11100),U_11101)) ),
    inference(definitional_conversion,[status(esa)],[f_2978_2]) ).

cnf(f_2978_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11099,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11099,tc_HOL_Obool)),U_11100),U_11102)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11099,tc_HOL_Obool)),U_11101),U_11103)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11099,tc_HOL_Obool)),U_11102),U_11103))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11099,tc_HOL_Obool)),U_11100),U_11101)) ),
    inference(clausify,[status(thm)],[f_2978_3]) ).

fof(f_2979_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_2979_2,plain,
    ! [U_11107,U_11106,U_11105,U_11104] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11104,tc_HOL_Obool)),U_11105),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11104,tc_HOL_Obool)),U_11106),U_11107)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11104,tc_HOL_Obool)),U_11105),U_11107))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11104,tc_HOL_Obool)),U_11105),U_11106)) ),
    inference(variable_rename,[status(thm)],[f_2979_1]) ).

fof(f_2979_3,plain,
    ! [U_11104,U_11105,U_11106,U_11107] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11104,tc_HOL_Obool)),U_11105),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11104,tc_HOL_Obool)),U_11106),U_11107)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11104,tc_HOL_Obool)),U_11105),U_11107))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11104,tc_HOL_Obool)),U_11105),U_11106)) ),
    inference(definitional_conversion,[status(esa)],[f_2979_2]) ).

cnf(f_2979_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11104,tc_HOL_Obool)),U_11105),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11104,tc_HOL_Obool)),U_11106),U_11107)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11104,tc_HOL_Obool)),U_11105),U_11107))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11104,tc_HOL_Obool)),U_11105),U_11106)) ),
    inference(clausify,[status(thm)],[f_2979_3]) ).

fof(f_2980_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_2980_2,plain,
    ! [U_11110,U_11109,U_11108] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11108,tc_HOL_Obool)),U_11110),U_11109) = U_11109
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11108,tc_HOL_Obool)),U_11109),U_11110)) ),
    inference(variable_rename,[status(thm)],[f_2980_1]) ).

fof(f_2980_3,plain,
    ! [U_11108,U_11109,U_11110] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11108,tc_HOL_Obool)),U_11110),U_11109) = U_11109
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11108,tc_HOL_Obool)),U_11109),U_11110)) ),
    inference(definitional_conversion,[status(esa)],[f_2980_2]) ).

cnf(f_2980_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11108,tc_HOL_Obool)),U_11110),U_11109) = U_11109
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11108,tc_HOL_Obool)),U_11109),U_11110)) ),
    inference(clausify,[status(thm)],[f_2980_3]) ).

fof(f_2981_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_2981_2,plain,
    ! [U_11113,U_11112,U_11111] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11111,tc_HOL_Obool)),U_11112),U_11113) = U_11112
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11111,tc_HOL_Obool)),U_11112),U_11113)) ),
    inference(variable_rename,[status(thm)],[f_2981_1]) ).

fof(f_2981_3,plain,
    ! [U_11111,U_11112,U_11113] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11111,tc_HOL_Obool)),U_11112),U_11113) = U_11112
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11111,tc_HOL_Obool)),U_11112),U_11113)) ),
    inference(definitional_conversion,[status(esa)],[f_2981_2]) ).

cnf(f_2981_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11111,tc_HOL_Obool)),U_11112),U_11113) = U_11112
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11111,tc_HOL_Obool)),U_11112),U_11113)) ),
    inference(clausify,[status(thm)],[f_2981_3]) ).

fof(f_2982_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_2982_2,plain,
    ! [U_11116,U_11115,U_11114] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11114,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11114,tc_HOL_Obool)),U_11115),U_11116)),U_11116)),
    inference(variable_rename,[status(thm)],[f_2982_1]) ).

fof(f_2982_3,plain,
    ! [U_11114,U_11115,U_11116] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11114,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11114,tc_HOL_Obool)),U_11115),U_11116)),U_11116)),
    inference(definitional_conversion,[status(esa)],[f_2982_2]) ).

cnf(f_2982_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11114,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11114,tc_HOL_Obool)),U_11115),U_11116)),U_11116)),
    inference(clausify,[status(thm)],[f_2982_3]) ).

fof(f_2983_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_2983_2,plain,
    ! [U_11119,U_11118,U_11117] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11117,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11117,tc_HOL_Obool)),U_11118),U_11119)),U_11118)),
    inference(variable_rename,[status(thm)],[f_2983_1]) ).

fof(f_2983_3,plain,
    ! [U_11117,U_11118,U_11119] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11117,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11117,tc_HOL_Obool)),U_11118),U_11119)),U_11118)),
    inference(definitional_conversion,[status(esa)],[f_2983_2]) ).

cnf(f_2983_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11117,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11117,tc_HOL_Obool)),U_11118),U_11119)),U_11118)),
    inference(clausify,[status(thm)],[f_2983_3]) ).

fof(f_2984_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_2984_2,plain,
    ! [U_11122,U_11121,U_11120] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11120),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11120),U_11121),U_11122)),U_11121))
      | ~ class_Lattices_Olattice(U_11120) ),
    inference(variable_rename,[status(thm)],[f_2984_1]) ).

fof(f_2984_3,plain,
    ! [U_11120,U_11121,U_11122] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11120),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11120),U_11121),U_11122)),U_11121))
      | ~ class_Lattices_Olattice(U_11120) ),
    inference(definitional_conversion,[status(esa)],[f_2984_2]) ).

cnf(f_2984_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11120),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11120),U_11121),U_11122)),U_11121))
    | ~ class_Lattices_Olattice(U_11120) ),
    inference(clausify,[status(thm)],[f_2984_3]) ).

fof(f_2985_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_2985_2,plain,
    ! [U_11125,U_11124,U_11123] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11123),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11123),U_11124),U_11125)),U_11124))
      | ~ class_Lattices_Osemilattice__inf(U_11123) ),
    inference(variable_rename,[status(thm)],[f_2985_1]) ).

fof(f_2985_3,plain,
    ! [U_11123,U_11124,U_11125] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11123),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11123),U_11124),U_11125)),U_11124))
      | ~ class_Lattices_Osemilattice__inf(U_11123) ),
    inference(definitional_conversion,[status(esa)],[f_2985_2]) ).

cnf(f_2985_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11123),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11123),U_11124),U_11125)),U_11124))
    | ~ class_Lattices_Osemilattice__inf(U_11123) ),
    inference(clausify,[status(thm)],[f_2985_3]) ).

fof(f_2986_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_2986_2,plain,
    ! [U_11128,U_11127,U_11126] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11126),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11126),U_11127),U_11128)),U_11128))
      | ~ class_Lattices_Olattice(U_11126) ),
    inference(variable_rename,[status(thm)],[f_2986_1]) ).

fof(f_2986_3,plain,
    ! [U_11126,U_11127,U_11128] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11126),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11126),U_11127),U_11128)),U_11128))
      | ~ class_Lattices_Olattice(U_11126) ),
    inference(definitional_conversion,[status(esa)],[f_2986_2]) ).

cnf(f_2986_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11126),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11126),U_11127),U_11128)),U_11128))
    | ~ class_Lattices_Olattice(U_11126) ),
    inference(clausify,[status(thm)],[f_2986_3]) ).

fof(f_2987_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_2987_2,plain,
    ! [U_11131,U_11130,U_11129] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11129),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11129),U_11130),U_11131)),U_11131))
      | ~ class_Lattices_Osemilattice__inf(U_11129) ),
    inference(variable_rename,[status(thm)],[f_2987_1]) ).

fof(f_2987_3,plain,
    ! [U_11129,U_11130,U_11131] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11129),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11129),U_11130),U_11131)),U_11131))
      | ~ class_Lattices_Osemilattice__inf(U_11129) ),
    inference(definitional_conversion,[status(esa)],[f_2987_2]) ).

cnf(f_2987_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11129),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11129),U_11130),U_11131)),U_11131))
    | ~ class_Lattices_Osemilattice__inf(U_11129) ),
    inference(clausify,[status(thm)],[f_2987_3]) ).

fof(f_2988_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_2988_2,plain,
    ! [U_11134,U_11133,U_11132] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11132),U_11133),U_11134))
          | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11132),U_11133),U_11134) != U_11133 )
        & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11132),U_11133),U_11134) = U_11133
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11132),U_11133),U_11134)) ) )
      | ~ class_Lattices_Osemilattice__inf(U_11132) ),
    inference(variable_rename,[status(thm)],[f_2988_1]) ).

fof(f_2988_3,plain,
    ( ! [U_11132,U_11133,U_11134] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11132),U_11133),U_11134))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11132),U_11133),U_11134) != U_11133
        | ~ sP817(U_11132,U_11133,U_11134) )
    & ! [U_11132,U_11133,U_11134] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11132),U_11133),U_11134) = U_11133
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11132),U_11133),U_11134))
        | ~ sP817(U_11132,U_11133,U_11134) )
    & ! [U_11132,U_11133,U_11134] :
        ( sP817(U_11132,U_11133,U_11134)
        | ~ class_Lattices_Osemilattice__inf(U_11132) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP817])],[f_2988_2]) ).

cnf(f_2988_4,plain,
    ( sP817(U_11132,U_11133,U_11134)
    | ~ class_Lattices_Osemilattice__inf(U_11132) ),
    inference(clausify,[status(thm)],[f_2988_3]) ).

cnf(f_2988_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11132),U_11133),U_11134) = U_11133
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11132),U_11133),U_11134))
    | ~ sP817(U_11132,U_11133,U_11134) ),
    inference(clausify,[status(thm)],[f_2988_3]) ).

cnf(f_2988_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11132),U_11133),U_11134))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11132),U_11133),U_11134) != U_11133
    | ~ sP817(U_11132,U_11133,U_11134) ),
    inference(clausify,[status(thm)],[f_2988_3]) ).

fof(f_2989_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_2989_2,plain,
    ! [U_11138,U_11137,U_11136,U_11135] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11135),U_11136),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11135),U_11137),U_11138)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11135),U_11136),U_11138))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11135),U_11136),U_11137)) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11135),U_11136),U_11138))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11135),U_11136),U_11137)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11135),U_11136),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11135),U_11137),U_11138))) ) )
      | ~ class_Lattices_Osemilattice__inf(U_11135) ),
    inference(variable_rename,[status(thm)],[f_2989_1]) ).

fof(f_2989_3,plain,
    ( ! [U_11135,U_11136,U_11137,U_11138] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11135),U_11136),U_11138))
        | ~ sP818(U_11135,U_11136,U_11137,U_11138) )
    & ! [U_11135,U_11136,U_11137,U_11138] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11135),U_11136),U_11137))
        | ~ sP818(U_11135,U_11136,U_11137,U_11138) )
    & ! [U_11135,U_11136,U_11137,U_11138] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11135),U_11136),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11135),U_11137),U_11138)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11135),U_11136),U_11138))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11135),U_11136),U_11137))
        | ~ sP819(U_11135,U_11136,U_11137,U_11138) )
    & ! [U_11135,U_11136,U_11137,U_11138] :
        ( sP818(U_11135,U_11136,U_11137,U_11138)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11135),U_11136),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11135),U_11137),U_11138)))
        | ~ sP819(U_11135,U_11136,U_11137,U_11138) )
    & ! [U_11135,U_11136,U_11137,U_11138] :
        ( sP819(U_11135,U_11136,U_11137,U_11138)
        | ~ class_Lattices_Osemilattice__inf(U_11135) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP818,sP819])],[f_2989_2]) ).

cnf(f_2989_4,plain,
    ( sP819(U_11135,U_11136,U_11137,U_11138)
    | ~ class_Lattices_Osemilattice__inf(U_11135) ),
    inference(clausify,[status(thm)],[f_2989_3]) ).

cnf(f_2989_5,plain,
    ( sP818(U_11135,U_11136,U_11137,U_11138)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11135),U_11136),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11135),U_11137),U_11138)))
    | ~ sP819(U_11135,U_11136,U_11137,U_11138) ),
    inference(clausify,[status(thm)],[f_2989_3]) ).

cnf(f_2989_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11135),U_11136),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11135),U_11137),U_11138)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11135),U_11136),U_11138))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11135),U_11136),U_11137))
    | ~ sP819(U_11135,U_11136,U_11137,U_11138) ),
    inference(clausify,[status(thm)],[f_2989_3]) ).

cnf(f_2989_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11135),U_11136),U_11137))
    | ~ sP818(U_11135,U_11136,U_11137,U_11138) ),
    inference(clausify,[status(thm)],[f_2989_3]) ).

cnf(f_2989_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11135),U_11136),U_11138))
    | ~ sP818(U_11135,U_11136,U_11137,U_11138) ),
    inference(clausify,[status(thm)],[f_2989_3]) ).

fof(f_2990_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_2990_2,plain,
    ! [U_11142,U_11141,U_11140,U_11139] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11139),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11139),U_11140),U_11142)),U_11141))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11139),U_11140),U_11141))
      | ~ class_Lattices_Osemilattice__inf(U_11139) ),
    inference(variable_rename,[status(thm)],[f_2990_1]) ).

fof(f_2990_3,plain,
    ! [U_11142,U_11140,U_11141,U_11139] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11139),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11139),U_11140),U_11142)),U_11141))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11139),U_11140),U_11141))
      | ~ class_Lattices_Osemilattice__inf(U_11139) ),
    inference(definitional_conversion,[status(esa)],[f_2990_2]) ).

cnf(f_2990_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11139),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11139),U_11140),U_11142)),U_11141))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11139),U_11140),U_11141))
    | ~ class_Lattices_Osemilattice__inf(U_11139) ),
    inference(clausify,[status(thm)],[f_2990_3]) ).

fof(f_2991_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_2991_2,plain,
    ! [U_11146,U_11145,U_11144,U_11143] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11143),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11143),U_11146),U_11144)),U_11145))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11143),U_11144),U_11145))
      | ~ class_Lattices_Osemilattice__inf(U_11143) ),
    inference(variable_rename,[status(thm)],[f_2991_1]) ).

fof(f_2991_3,plain,
    ! [U_11143,U_11144,U_11145,U_11146] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11143),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11143),U_11146),U_11144)),U_11145))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11143),U_11144),U_11145))
      | ~ class_Lattices_Osemilattice__inf(U_11143) ),
    inference(definitional_conversion,[status(esa)],[f_2991_2]) ).

cnf(f_2991_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11143),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11143),U_11146),U_11144)),U_11145))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11143),U_11144),U_11145))
    | ~ class_Lattices_Osemilattice__inf(U_11143) ),
    inference(clausify,[status(thm)],[f_2991_3]) ).

fof(f_2992_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_2992_2,plain,
    ! [U_11149,U_11148,U_11147] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11147),U_11148),U_11149) = U_11148
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11147),U_11148),U_11149))
      | ~ class_Lattices_Osemilattice__inf(U_11147) ),
    inference(variable_rename,[status(thm)],[f_2992_1]) ).

fof(f_2992_3,plain,
    ! [U_11147,U_11148,U_11149] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11147),U_11148),U_11149) = U_11148
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11147),U_11148),U_11149))
      | ~ class_Lattices_Osemilattice__inf(U_11147) ),
    inference(definitional_conversion,[status(esa)],[f_2992_2]) ).

cnf(f_2992_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11147),U_11148),U_11149) = U_11148
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11147),U_11148),U_11149))
    | ~ class_Lattices_Osemilattice__inf(U_11147) ),
    inference(clausify,[status(thm)],[f_2992_3]) ).

fof(f_2993_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_2993_2,plain,
    ! [U_11152,U_11151,U_11150] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11150),U_11152),U_11151) = U_11151
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11150),U_11151),U_11152))
      | ~ class_Lattices_Osemilattice__inf(U_11150) ),
    inference(variable_rename,[status(thm)],[f_2993_1]) ).

fof(f_2993_3,plain,
    ! [U_11150,U_11151,U_11152] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11150),U_11152),U_11151) = U_11151
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11150),U_11151),U_11152))
      | ~ class_Lattices_Osemilattice__inf(U_11150) ),
    inference(definitional_conversion,[status(esa)],[f_2993_2]) ).

cnf(f_2993_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11150),U_11152),U_11151) = U_11151
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11150),U_11151),U_11152))
    | ~ class_Lattices_Osemilattice__inf(U_11150) ),
    inference(clausify,[status(thm)],[f_2993_3]) ).

fof(f_2994_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_2994_2,plain,
    ! [U_11156,U_11155,U_11154,U_11153] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11153),U_11154),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11153),U_11155),U_11156)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11153),U_11154),U_11156))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11153),U_11154),U_11155))
      | ~ class_Lattices_Osemilattice__inf(U_11153) ),
    inference(variable_rename,[status(thm)],[f_2994_1]) ).

fof(f_2994_3,plain,
    ! [U_11153,U_11154,U_11155,U_11156] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11153),U_11154),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11153),U_11155),U_11156)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11153),U_11154),U_11156))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11153),U_11154),U_11155))
      | ~ class_Lattices_Osemilattice__inf(U_11153) ),
    inference(definitional_conversion,[status(esa)],[f_2994_2]) ).

cnf(f_2994_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11153),U_11154),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11153),U_11155),U_11156)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11153),U_11154),U_11156))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11153),U_11154),U_11155))
    | ~ class_Lattices_Osemilattice__inf(U_11153) ),
    inference(clausify,[status(thm)],[f_2994_3]) ).

fof(f_2995_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_2995_2,plain,
    ! [U_11160,U_11159,U_11158,U_11157] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11157),U_11158),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11157),U_11159),U_11160)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11157),U_11158),U_11160))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11157),U_11158),U_11159))
      | ~ class_Lattices_Osemilattice__inf(U_11157) ),
    inference(variable_rename,[status(thm)],[f_2995_1]) ).

fof(f_2995_3,plain,
    ! [U_11157,U_11158,U_11159,U_11160] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11157),U_11158),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11157),U_11159),U_11160)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11157),U_11158),U_11160))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11157),U_11158),U_11159))
      | ~ class_Lattices_Osemilattice__inf(U_11157) ),
    inference(definitional_conversion,[status(esa)],[f_2995_2]) ).

cnf(f_2995_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11157),U_11158),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11157),U_11159),U_11160)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11157),U_11158),U_11160))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11157),U_11158),U_11159))
    | ~ class_Lattices_Osemilattice__inf(U_11157) ),
    inference(clausify,[status(thm)],[f_2995_3]) ).

fof(f_2996_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_2996_2,plain,
    ! [U_11165,U_11164,U_11163,U_11162,U_11161] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11161),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11161),U_11162),U_11164)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11161),U_11163),U_11165)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11161),U_11164),U_11165))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11161),U_11162),U_11163))
      | ~ class_Lattices_Osemilattice__inf(U_11161) ),
    inference(variable_rename,[status(thm)],[f_2996_1]) ).

fof(f_2996_3,plain,
    ! [U_11161,U_11162,U_11163,U_11164,U_11165] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11161),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11161),U_11162),U_11164)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11161),U_11163),U_11165)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11161),U_11164),U_11165))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11161),U_11162),U_11163))
      | ~ class_Lattices_Osemilattice__inf(U_11161) ),
    inference(definitional_conversion,[status(esa)],[f_2996_2]) ).

cnf(f_2996_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11161),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11161),U_11162),U_11164)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11161),U_11163),U_11165)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11161),U_11164),U_11165))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11161),U_11162),U_11163))
    | ~ class_Lattices_Osemilattice__inf(U_11161) ),
    inference(clausify,[status(thm)],[f_2996_3]) ).

fof(f_2997_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_2997_2,plain,
    ! [U_11169,U_11168,U_11167,U_11166] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11166),U_11167),U_11169))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11166),U_11167),U_11168)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11166),U_11167),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11166),U_11168),U_11169)))
      | ~ class_Lattices_Osemilattice__inf(U_11166) ),
    inference(variable_rename,[status(thm)],[f_2997_1]) ).

fof(f_2997_3,plain,
    ( ! [U_11166,U_11167,U_11168,U_11169] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11166),U_11167),U_11169))
        | ~ sP820(U_11166,U_11167,U_11168,U_11169) )
    & ! [U_11166,U_11167,U_11168,U_11169] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11166),U_11167),U_11168))
        | ~ sP820(U_11166,U_11167,U_11168,U_11169) )
    & ! [U_11166,U_11167,U_11168,U_11169] :
        ( sP820(U_11166,U_11167,U_11168,U_11169)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11166),U_11167),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11166),U_11168),U_11169)))
        | ~ class_Lattices_Osemilattice__inf(U_11166) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP820])],[f_2997_2]) ).

cnf(f_2997_4,plain,
    ( sP820(U_11166,U_11167,U_11168,U_11169)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11166),U_11167),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11166),U_11168),U_11169)))
    | ~ class_Lattices_Osemilattice__inf(U_11166) ),
    inference(clausify,[status(thm)],[f_2997_3]) ).

cnf(f_2997_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11166),U_11167),U_11168))
    | ~ sP820(U_11166,U_11167,U_11168,U_11169) ),
    inference(clausify,[status(thm)],[f_2997_3]) ).

cnf(f_2997_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11166),U_11167),U_11169))
    | ~ sP820(U_11166,U_11167,U_11168,U_11169) ),
    inference(clausify,[status(thm)],[f_2997_3]) ).

fof(f_2998_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_2998_2,plain,
    ! [U_11173,U_11172,U_11171,U_11170] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11170,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_11171,U_11170),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11171,U_11170),tc_HOL_Obool)),U_11172),U_11173))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11170,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_11171,U_11170),U_11172)),hAPP(c_Relation_ORange(U_11171,U_11170),U_11173)))),
    inference(variable_rename,[status(thm)],[f_2998_1]) ).

fof(f_2998_3,plain,
    ! [U_11171,U_11170,U_11172,U_11173] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11170,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_11171,U_11170),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11171,U_11170),tc_HOL_Obool)),U_11172),U_11173))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11170,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_11171,U_11170),U_11172)),hAPP(c_Relation_ORange(U_11171,U_11170),U_11173)))),
    inference(definitional_conversion,[status(esa)],[f_2998_2]) ).

cnf(f_2998_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11170,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_11171,U_11170),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11171,U_11170),tc_HOL_Obool)),U_11172),U_11173))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11170,tc_HOL_Obool)),hAPP(c_Relation_ORange(U_11171,U_11170),U_11172)),hAPP(c_Relation_ORange(U_11171,U_11170),U_11173)))),
    inference(clausify,[status(thm)],[f_2998_3]) ).

fof(f_2999_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_2999_2,plain,
    ! [U_11177,U_11176,U_11175,U_11174] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11174,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11174),U_11175),U_11176)),hAPP(hAPP(c_Set_Oinsert(U_11174),U_11175),U_11177)) = hAPP(hAPP(c_Set_Oinsert(U_11174),U_11175),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11174,tc_HOL_Obool)),U_11176),U_11177)),
    inference(variable_rename,[status(thm)],[f_2999_1]) ).

fof(f_2999_3,plain,
    ! [U_11174,U_11175,U_11176,U_11177] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11174,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11174),U_11175),U_11176)),hAPP(hAPP(c_Set_Oinsert(U_11174),U_11175),U_11177)) = hAPP(hAPP(c_Set_Oinsert(U_11174),U_11175),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11174,tc_HOL_Obool)),U_11176),U_11177)),
    inference(definitional_conversion,[status(esa)],[f_2999_2]) ).

cnf(f_2999_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11174,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11174),U_11175),U_11176)),hAPP(hAPP(c_Set_Oinsert(U_11174),U_11175),U_11177)) = hAPP(hAPP(c_Set_Oinsert(U_11174),U_11175),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11174,tc_HOL_Obool)),U_11176),U_11177)),
    inference(clausify,[status(thm)],[f_2999_3]) ).

fof(f_3000_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_3000_2,plain,
    ! [U_11180,U_11179,U_11178] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_11178,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11178,tc_HOL_Obool)),U_11179),U_11180)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11178),c_Big__Operators_Olattice__class_OInf__fin(U_11178,U_11179)),c_Big__Operators_Olattice__class_OInf__fin(U_11178,U_11180))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11178,tc_HOL_Obool)),U_11179),U_11180) != c_Orderings_Obot__class_Obot(tc_fun(U_11178,tc_HOL_Obool))
      | U_11180 = c_Orderings_Obot__class_Obot(tc_fun(U_11178,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11178),U_11180))
      | U_11179 = c_Orderings_Obot__class_Obot(tc_fun(U_11178,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11178),U_11179))
      | ~ class_Lattices_Olattice(U_11178) ),
    inference(variable_rename,[status(thm)],[f_3000_1]) ).

fof(f_3000_3,plain,
    ! [U_11178,U_11179,U_11180] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_11178,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11178,tc_HOL_Obool)),U_11179),U_11180)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11178),c_Big__Operators_Olattice__class_OInf__fin(U_11178,U_11179)),c_Big__Operators_Olattice__class_OInf__fin(U_11178,U_11180))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11178,tc_HOL_Obool)),U_11179),U_11180) != c_Orderings_Obot__class_Obot(tc_fun(U_11178,tc_HOL_Obool))
      | U_11180 = c_Orderings_Obot__class_Obot(tc_fun(U_11178,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11178),U_11180))
      | U_11179 = c_Orderings_Obot__class_Obot(tc_fun(U_11178,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11178),U_11179))
      | ~ class_Lattices_Olattice(U_11178) ),
    inference(definitional_conversion,[status(esa)],[f_3000_2]) ).

cnf(f_3000_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_11178,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11178,tc_HOL_Obool)),U_11179),U_11180)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11178),c_Big__Operators_Olattice__class_OInf__fin(U_11178,U_11179)),c_Big__Operators_Olattice__class_OInf__fin(U_11178,U_11180))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11178,tc_HOL_Obool)),U_11179),U_11180) != c_Orderings_Obot__class_Obot(tc_fun(U_11178,tc_HOL_Obool))
    | U_11180 = c_Orderings_Obot__class_Obot(tc_fun(U_11178,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11178),U_11180))
    | U_11179 = c_Orderings_Obot__class_Obot(tc_fun(U_11178,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11178),U_11179))
    | ~ class_Lattices_Olattice(U_11178) ),
    inference(clausify,[status(thm)],[f_3000_3]) ).

fof(f_3001_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_3001_2,plain,
    ! [U_11183,U_11182,U_11181] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11181),c_Big__Operators_Olattice__class_OInf__fin(U_11181,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11181,tc_HOL_Obool)),U_11182),U_11183))),c_Big__Operators_Olattice__class_OInf__fin(U_11181,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11181,tc_HOL_Obool)),U_11182),U_11183))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11181),c_Big__Operators_Olattice__class_OInf__fin(U_11181,U_11182)),c_Big__Operators_Olattice__class_OInf__fin(U_11181,U_11183))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11181,tc_HOL_Obool)),U_11182),U_11183) = c_Orderings_Obot__class_Obot(tc_fun(U_11181,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11181),U_11183))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11181),U_11182))
      | ~ class_Lattices_Olattice(U_11181) ),
    inference(variable_rename,[status(thm)],[f_3001_1]) ).

fof(f_3001_3,plain,
    ! [U_11182,U_11181,U_11183] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11181),c_Big__Operators_Olattice__class_OInf__fin(U_11181,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11181,tc_HOL_Obool)),U_11182),U_11183))),c_Big__Operators_Olattice__class_OInf__fin(U_11181,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11181,tc_HOL_Obool)),U_11182),U_11183))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11181),c_Big__Operators_Olattice__class_OInf__fin(U_11181,U_11182)),c_Big__Operators_Olattice__class_OInf__fin(U_11181,U_11183))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11181,tc_HOL_Obool)),U_11182),U_11183) = c_Orderings_Obot__class_Obot(tc_fun(U_11181,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11181),U_11183))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11181),U_11182))
      | ~ class_Lattices_Olattice(U_11181) ),
    inference(definitional_conversion,[status(esa)],[f_3001_2]) ).

cnf(f_3001_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11181),c_Big__Operators_Olattice__class_OInf__fin(U_11181,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11181,tc_HOL_Obool)),U_11182),U_11183))),c_Big__Operators_Olattice__class_OInf__fin(U_11181,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11181,tc_HOL_Obool)),U_11182),U_11183))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11181),c_Big__Operators_Olattice__class_OInf__fin(U_11181,U_11182)),c_Big__Operators_Olattice__class_OInf__fin(U_11181,U_11183))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11181,tc_HOL_Obool)),U_11182),U_11183) = c_Orderings_Obot__class_Obot(tc_fun(U_11181,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11181),U_11183))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11181),U_11182))
    | ~ class_Lattices_Olattice(U_11181) ),
    inference(clausify,[status(thm)],[f_3001_3]) ).

fof(f_3002_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_3002_2,plain,
    ! [U_11187,U_11186,U_11185,U_11184] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11184),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11184),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11184),U_11185),U_11186)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11184),U_11185),U_11187))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11184),U_11185),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11184),U_11186),U_11187))))
      | ~ class_Lattices_Olattice(U_11184) ),
    inference(variable_rename,[status(thm)],[f_3002_1]) ).

fof(f_3002_3,plain,
    ! [U_11184,U_11185,U_11186,U_11187] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11184),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11184),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11184),U_11185),U_11186)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11184),U_11185),U_11187))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11184),U_11185),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11184),U_11186),U_11187))))
      | ~ class_Lattices_Olattice(U_11184) ),
    inference(definitional_conversion,[status(esa)],[f_3002_2]) ).

cnf(f_3002_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11184),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11184),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11184),U_11185),U_11186)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11184),U_11185),U_11187))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11184),U_11185),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11184),U_11186),U_11187))))
    | ~ class_Lattices_Olattice(U_11184) ),
    inference(clausify,[status(thm)],[f_3002_3]) ).

fof(f_3003_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_3003_2,plain,
    ! [U_11191,U_11190,U_11189,U_11188] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11188),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11188),U_11189),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11188),U_11190),U_11191))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11188),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11188),U_11189),U_11190)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11188),U_11189),U_11191))))
      | ~ class_Lattices_Olattice(U_11188) ),
    inference(variable_rename,[status(thm)],[f_3003_1]) ).

fof(f_3003_3,plain,
    ! [U_11188,U_11189,U_11190,U_11191] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11188),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11188),U_11189),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11188),U_11190),U_11191))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11188),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11188),U_11189),U_11190)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11188),U_11189),U_11191))))
      | ~ class_Lattices_Olattice(U_11188) ),
    inference(definitional_conversion,[status(esa)],[f_3003_2]) ).

cnf(f_3003_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11188),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11188),U_11189),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11188),U_11190),U_11191))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11188),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11188),U_11189),U_11190)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11188),U_11189),U_11191))))
    | ~ class_Lattices_Olattice(U_11188) ),
    inference(clausify,[status(thm)],[f_3003_3]) ).

fof(f_3004_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_3004_2,plain,
    ! [U_11193,U_11192] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11192),U_11193),hAPP(c_Groups_Ouminus__class_Ouminus(U_11192),U_11193)) = c_Orderings_Obot__class_Obot(U_11192)
      | ~ class_Lattices_Oboolean__algebra(U_11192) ),
    inference(variable_rename,[status(thm)],[f_3004_1]) ).

fof(f_3004_3,plain,
    ! [U_11193,U_11192] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11192),U_11193),hAPP(c_Groups_Ouminus__class_Ouminus(U_11192),U_11193)) = c_Orderings_Obot__class_Obot(U_11192)
      | ~ class_Lattices_Oboolean__algebra(U_11192) ),
    inference(definitional_conversion,[status(esa)],[f_3004_2]) ).

cnf(f_3004_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11192),U_11193),hAPP(c_Groups_Ouminus__class_Ouminus(U_11192),U_11193)) = c_Orderings_Obot__class_Obot(U_11192)
    | ~ class_Lattices_Oboolean__algebra(U_11192) ),
    inference(clausify,[status(thm)],[f_3004_3]) ).

fof(f_3005_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_3005_2,plain,
    ! [U_11195,U_11194] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11194),hAPP(c_Groups_Ouminus__class_Ouminus(U_11194),U_11195)),U_11195) = c_Orderings_Obot__class_Obot(U_11194)
      | ~ class_Lattices_Oboolean__algebra(U_11194) ),
    inference(variable_rename,[status(thm)],[f_3005_1]) ).

fof(f_3005_3,plain,
    ! [U_11194,U_11195] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11194),hAPP(c_Groups_Ouminus__class_Ouminus(U_11194),U_11195)),U_11195) = c_Orderings_Obot__class_Obot(U_11194)
      | ~ class_Lattices_Oboolean__algebra(U_11194) ),
    inference(definitional_conversion,[status(esa)],[f_3005_2]) ).

cnf(f_3005_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11194),hAPP(c_Groups_Ouminus__class_Ouminus(U_11194),U_11195)),U_11195) = c_Orderings_Obot__class_Obot(U_11194)
    | ~ class_Lattices_Oboolean__algebra(U_11194) ),
    inference(clausify,[status(thm)],[f_3005_3]) ).

fof(f_3006_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_3006_2,plain,
    ! [U_11198,U_11197,U_11196] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11196),U_11197),U_11198) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11196),U_11197),hAPP(c_Groups_Ouminus__class_Ouminus(U_11196),U_11198))
      | ~ class_Lattices_Oboolean__algebra(U_11196) ),
    inference(variable_rename,[status(thm)],[f_3006_1]) ).

fof(f_3006_3,plain,
    ! [U_11196,U_11197,U_11198] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11196),U_11197),U_11198) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11196),U_11197),hAPP(c_Groups_Ouminus__class_Ouminus(U_11196),U_11198))
      | ~ class_Lattices_Oboolean__algebra(U_11196) ),
    inference(definitional_conversion,[status(esa)],[f_3006_2]) ).

cnf(f_3006_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_11196),U_11197),U_11198) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11196),U_11197),hAPP(c_Groups_Ouminus__class_Ouminus(U_11196),U_11198))
    | ~ class_Lattices_Oboolean__algebra(U_11196) ),
    inference(clausify,[status(thm)],[f_3006_3]) ).

fof(f_3007_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_3007_2,plain,
    ! [U_11201,U_11200,U_11199] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_11199),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11199),U_11200),U_11201)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11199),hAPP(c_Groups_Ouminus__class_Ouminus(U_11199),U_11200)),hAPP(c_Groups_Ouminus__class_Ouminus(U_11199),U_11201))
      | ~ class_Lattices_Oboolean__algebra(U_11199) ),
    inference(variable_rename,[status(thm)],[f_3007_1]) ).

fof(f_3007_3,plain,
    ! [U_11199,U_11200,U_11201] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_11199),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11199),U_11200),U_11201)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11199),hAPP(c_Groups_Ouminus__class_Ouminus(U_11199),U_11200)),hAPP(c_Groups_Ouminus__class_Ouminus(U_11199),U_11201))
      | ~ class_Lattices_Oboolean__algebra(U_11199) ),
    inference(definitional_conversion,[status(esa)],[f_3007_2]) ).

cnf(f_3007_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_11199),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11199),U_11200),U_11201)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11199),hAPP(c_Groups_Ouminus__class_Ouminus(U_11199),U_11200)),hAPP(c_Groups_Ouminus__class_Ouminus(U_11199),U_11201))
    | ~ class_Lattices_Oboolean__algebra(U_11199) ),
    inference(clausify,[status(thm)],[f_3007_3]) ).

fof(f_3008_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_3008_2,plain,
    ! [U_11204,U_11203,U_11202] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_11202),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11202),U_11203),U_11204)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11202),hAPP(c_Groups_Ouminus__class_Ouminus(U_11202),U_11203)),hAPP(c_Groups_Ouminus__class_Ouminus(U_11202),U_11204))
      | ~ class_Lattices_Oboolean__algebra(U_11202) ),
    inference(variable_rename,[status(thm)],[f_3008_1]) ).

fof(f_3008_3,plain,
    ! [U_11202,U_11203,U_11204] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_11202),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11202),U_11203),U_11204)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11202),hAPP(c_Groups_Ouminus__class_Ouminus(U_11202),U_11203)),hAPP(c_Groups_Ouminus__class_Ouminus(U_11202),U_11204))
      | ~ class_Lattices_Oboolean__algebra(U_11202) ),
    inference(definitional_conversion,[status(esa)],[f_3008_2]) ).

cnf(f_3008_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_11202),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11202),U_11203),U_11204)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11202),hAPP(c_Groups_Ouminus__class_Ouminus(U_11202),U_11203)),hAPP(c_Groups_Ouminus__class_Ouminus(U_11202),U_11204))
    | ~ class_Lattices_Oboolean__algebra(U_11202) ),
    inference(clausify,[status(thm)],[f_3008_3]) ).

fof(f_3009_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_3009_2,plain,
    ! [U_11208,U_11207,U_11206,U_11205] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11205,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11205),U_11206),U_11208)),U_11207) = hAPP(hAPP(c_Set_Oinsert(U_11205),U_11206),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11205,tc_HOL_Obool)),U_11208),U_11207))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11205),U_11206),U_11207)) ),
    inference(variable_rename,[status(thm)],[f_3009_1]) ).

fof(f_3009_3,plain,
    ! [U_11205,U_11206,U_11207,U_11208] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11205,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11205),U_11206),U_11208)),U_11207) = hAPP(hAPP(c_Set_Oinsert(U_11205),U_11206),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11205,tc_HOL_Obool)),U_11208),U_11207))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11205),U_11206),U_11207)) ),
    inference(definitional_conversion,[status(esa)],[f_3009_2]) ).

cnf(f_3009_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11205,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11205),U_11206),U_11208)),U_11207) = hAPP(hAPP(c_Set_Oinsert(U_11205),U_11206),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11205,tc_HOL_Obool)),U_11208),U_11207))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11205),U_11206),U_11207)) ),
    inference(clausify,[status(thm)],[f_3009_3]) ).

fof(f_3010_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_3010_2,plain,
    ! [U_11212,U_11211,U_11210,U_11209] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11209,tc_HOL_Obool)),U_11211),hAPP(hAPP(c_Set_Oinsert(U_11209),U_11210),U_11212)) = hAPP(hAPP(c_Set_Oinsert(U_11209),U_11210),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11209,tc_HOL_Obool)),U_11211),U_11212))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11209),U_11210),U_11211)) ),
    inference(variable_rename,[status(thm)],[f_3010_1]) ).

fof(f_3010_3,plain,
    ! [U_11209,U_11210,U_11211,U_11212] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11209,tc_HOL_Obool)),U_11211),hAPP(hAPP(c_Set_Oinsert(U_11209),U_11210),U_11212)) = hAPP(hAPP(c_Set_Oinsert(U_11209),U_11210),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11209,tc_HOL_Obool)),U_11211),U_11212))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11209),U_11210),U_11211)) ),
    inference(definitional_conversion,[status(esa)],[f_3010_2]) ).

cnf(f_3010_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11209,tc_HOL_Obool)),U_11211),hAPP(hAPP(c_Set_Oinsert(U_11209),U_11210),U_11212)) = hAPP(hAPP(c_Set_Oinsert(U_11209),U_11210),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11209,tc_HOL_Obool)),U_11211),U_11212))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11209),U_11210),U_11211)) ),
    inference(clausify,[status(thm)],[f_3010_3]) ).

fof(f_3011_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_3011_2,plain,
    ! [U_11216,U_11215,U_11214,U_11213] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11213,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11213),U_11214),U_11216)),U_11215) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11213,tc_HOL_Obool)),U_11216),U_11215)
      | hBOOL(hAPP(hAPP(c_member(U_11213),U_11214),U_11215)) ),
    inference(variable_rename,[status(thm)],[f_3011_1]) ).

fof(f_3011_3,plain,
    ! [U_11213,U_11214,U_11215,U_11216] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11213,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11213),U_11214),U_11216)),U_11215) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11213,tc_HOL_Obool)),U_11216),U_11215)
      | hBOOL(hAPP(hAPP(c_member(U_11213),U_11214),U_11215)) ),
    inference(definitional_conversion,[status(esa)],[f_3011_2]) ).

cnf(f_3011_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11213,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11213),U_11214),U_11216)),U_11215) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11213,tc_HOL_Obool)),U_11216),U_11215)
    | hBOOL(hAPP(hAPP(c_member(U_11213),U_11214),U_11215)) ),
    inference(clausify,[status(thm)],[f_3011_3]) ).

fof(f_3012_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_3012_2,plain,
    ! [U_11220,U_11219,U_11218,U_11217] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11217,tc_HOL_Obool)),U_11219),hAPP(hAPP(c_Set_Oinsert(U_11217),U_11218),U_11220)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11217,tc_HOL_Obool)),U_11219),U_11220)
      | hBOOL(hAPP(hAPP(c_member(U_11217),U_11218),U_11219)) ),
    inference(variable_rename,[status(thm)],[f_3012_1]) ).

fof(f_3012_3,plain,
    ! [U_11217,U_11218,U_11219,U_11220] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11217,tc_HOL_Obool)),U_11219),hAPP(hAPP(c_Set_Oinsert(U_11217),U_11218),U_11220)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11217,tc_HOL_Obool)),U_11219),U_11220)
      | hBOOL(hAPP(hAPP(c_member(U_11217),U_11218),U_11219)) ),
    inference(definitional_conversion,[status(esa)],[f_3012_2]) ).

cnf(f_3012_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11217,tc_HOL_Obool)),U_11219),hAPP(hAPP(c_Set_Oinsert(U_11217),U_11218),U_11220)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11217,tc_HOL_Obool)),U_11219),U_11220)
    | hBOOL(hAPP(hAPP(c_member(U_11217),U_11218),U_11219)) ),
    inference(clausify,[status(thm)],[f_3012_3]) ).

fof(f_3013_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_3013_2,plain,
    ! [U_11224,U_11223,U_11222,U_11221] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11221,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11221),U_11222),U_11224)),U_11223) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11221,tc_HOL_Obool)),U_11224),U_11223)
        | hBOOL(hAPP(hAPP(c_member(U_11221),U_11222),U_11223)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11221,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11221),U_11222),U_11224)),U_11223) = hAPP(hAPP(c_Set_Oinsert(U_11221),U_11222),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11221,tc_HOL_Obool)),U_11224),U_11223))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11221),U_11222),U_11223)) ) ),
    inference(variable_rename,[status(thm)],[f_3013_1]) ).

fof(f_3013_3,plain,
    ( ! [U_11232,U_11230,U_11228,U_11226] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11226,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11226),U_11228),U_11232)),U_11230) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11226,tc_HOL_Obool)),U_11232),U_11230)
        | hBOOL(hAPP(hAPP(c_member(U_11226),U_11228),U_11230)) )
    & ! [U_11231,U_11229,U_11227,U_11225] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11225,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11225),U_11227),U_11231)),U_11229) = hAPP(hAPP(c_Set_Oinsert(U_11225),U_11227),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11225,tc_HOL_Obool)),U_11231),U_11229))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11225),U_11227),U_11229)) ) ),
    inference(miniscope,[status(thm)],[f_3013_2]) ).

fof(f_3013_4,plain,
    ( ! [U_11226,U_11228,U_11230,U_11232] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11226,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11226),U_11228),U_11232)),U_11230) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11226,tc_HOL_Obool)),U_11232),U_11230)
        | hBOOL(hAPP(hAPP(c_member(U_11226),U_11228),U_11230)) )
    & ! [U_11231,U_11227,U_11225,U_11229] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11225,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11225),U_11227),U_11231)),U_11229) = hAPP(hAPP(c_Set_Oinsert(U_11225),U_11227),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11225,tc_HOL_Obool)),U_11231),U_11229))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11225),U_11227),U_11229)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3013_3]) ).

cnf(f_3013_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11225,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11225),U_11227),U_11231)),U_11229) = hAPP(hAPP(c_Set_Oinsert(U_11225),U_11227),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11225,tc_HOL_Obool)),U_11231),U_11229))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11225),U_11227),U_11229)) ),
    inference(clausify,[status(thm)],[f_3013_4]) ).

cnf(f_3013_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11226,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11226),U_11228),U_11232)),U_11230) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11226,tc_HOL_Obool)),U_11232),U_11230)
    | hBOOL(hAPP(hAPP(c_member(U_11226),U_11228),U_11230)) ),
    inference(clausify,[status(thm)],[f_3013_4]) ).

fof(f_3014_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_3014_2,plain,
    ! [U_11236,U_11235,U_11234,U_11233] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11233,tc_HOL_Obool)),U_11235),hAPP(hAPP(c_Set_Oinsert(U_11233),U_11234),U_11236)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11233,tc_HOL_Obool)),U_11235),U_11236)
        | hBOOL(hAPP(hAPP(c_member(U_11233),U_11234),U_11235)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11233,tc_HOL_Obool)),U_11235),hAPP(hAPP(c_Set_Oinsert(U_11233),U_11234),U_11236)) = hAPP(hAPP(c_Set_Oinsert(U_11233),U_11234),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11233,tc_HOL_Obool)),U_11235),U_11236))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11233),U_11234),U_11235)) ) ),
    inference(variable_rename,[status(thm)],[f_3014_1]) ).

fof(f_3014_3,plain,
    ( ! [U_11244,U_11242,U_11240,U_11238] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11238,tc_HOL_Obool)),U_11242),hAPP(hAPP(c_Set_Oinsert(U_11238),U_11240),U_11244)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11238,tc_HOL_Obool)),U_11242),U_11244)
        | hBOOL(hAPP(hAPP(c_member(U_11238),U_11240),U_11242)) )
    & ! [U_11243,U_11241,U_11239,U_11237] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11237,tc_HOL_Obool)),U_11241),hAPP(hAPP(c_Set_Oinsert(U_11237),U_11239),U_11243)) = hAPP(hAPP(c_Set_Oinsert(U_11237),U_11239),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11237,tc_HOL_Obool)),U_11241),U_11243))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11237),U_11239),U_11241)) ) ),
    inference(miniscope,[status(thm)],[f_3014_2]) ).

fof(f_3014_4,plain,
    ( ! [U_11238,U_11240,U_11242,U_11244] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11238,tc_HOL_Obool)),U_11242),hAPP(hAPP(c_Set_Oinsert(U_11238),U_11240),U_11244)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11238,tc_HOL_Obool)),U_11242),U_11244)
        | hBOOL(hAPP(hAPP(c_member(U_11238),U_11240),U_11242)) )
    & ! [U_11243,U_11239,U_11241,U_11237] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11237,tc_HOL_Obool)),U_11241),hAPP(hAPP(c_Set_Oinsert(U_11237),U_11239),U_11243)) = hAPP(hAPP(c_Set_Oinsert(U_11237),U_11239),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11237,tc_HOL_Obool)),U_11241),U_11243))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11237),U_11239),U_11241)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3014_3]) ).

cnf(f_3014_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11237,tc_HOL_Obool)),U_11241),hAPP(hAPP(c_Set_Oinsert(U_11237),U_11239),U_11243)) = hAPP(hAPP(c_Set_Oinsert(U_11237),U_11239),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11237,tc_HOL_Obool)),U_11241),U_11243))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11237),U_11239),U_11241)) ),
    inference(clausify,[status(thm)],[f_3014_4]) ).

cnf(f_3014_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11238,tc_HOL_Obool)),U_11242),hAPP(hAPP(c_Set_Oinsert(U_11238),U_11240),U_11244)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11238,tc_HOL_Obool)),U_11242),U_11244)
    | hBOOL(hAPP(hAPP(c_member(U_11238),U_11240),U_11242)) ),
    inference(clausify,[status(thm)],[f_3014_4]) ).

fof(f_3015_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_3015_2,plain,
    ! [U_11249,U_11248,U_11247,U_11246,U_11245] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11245,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11246,U_11245,U_11247),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11246,tc_HOL_Obool)),U_11248),U_11249))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11245,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11246,U_11245,U_11247),U_11248)),hAPP(c_Set_Oimage(U_11246,U_11245,U_11247),U_11249)))),
    inference(variable_rename,[status(thm)],[f_3015_1]) ).

fof(f_3015_3,plain,
    ! [U_11245,U_11246,U_11247,U_11248,U_11249] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11245,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11246,U_11245,U_11247),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11246,tc_HOL_Obool)),U_11248),U_11249))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11245,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11246,U_11245,U_11247),U_11248)),hAPP(c_Set_Oimage(U_11246,U_11245,U_11247),U_11249)))),
    inference(definitional_conversion,[status(esa)],[f_3015_2]) ).

cnf(f_3015_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11245,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11246,U_11245,U_11247),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11246,tc_HOL_Obool)),U_11248),U_11249))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11245,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11246,U_11245,U_11247),U_11248)),hAPP(c_Set_Oimage(U_11246,U_11245,U_11247),U_11249)))),
    inference(clausify,[status(thm)],[f_3015_3]) ).

fof(f_3016_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_3016_2,plain,
    ! [U_11252,U_11251,U_11250] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11250,tc_HOL_Obool)),U_11251),U_11252) = U_11251
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11250,tc_HOL_Obool)),U_11251),U_11252) != c_Orderings_Obot__class_Obot(tc_fun(U_11250,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3016_1]) ).

fof(f_3016_3,plain,
    ! [U_11250,U_11251,U_11252] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11250,tc_HOL_Obool)),U_11251),U_11252) = U_11251
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11250,tc_HOL_Obool)),U_11251),U_11252) != c_Orderings_Obot__class_Obot(tc_fun(U_11250,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3016_2]) ).

cnf(f_3016_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11250,tc_HOL_Obool)),U_11251),U_11252) = U_11251
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11250,tc_HOL_Obool)),U_11251),U_11252) != c_Orderings_Obot__class_Obot(tc_fun(U_11250,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3016_3]) ).

fof(f_3017_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_3017_2,plain,
    ! [U_11255,U_11254,U_11253] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11253,tc_HOL_Obool)),U_11254),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11253,tc_HOL_Obool)),U_11255),U_11254)) = c_Orderings_Obot__class_Obot(tc_fun(U_11253,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3017_1]) ).

fof(f_3017_3,plain,
    ! [U_11253,U_11254,U_11255] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11253,tc_HOL_Obool)),U_11254),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11253,tc_HOL_Obool)),U_11255),U_11254)) = c_Orderings_Obot__class_Obot(tc_fun(U_11253,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3017_2]) ).

cnf(f_3017_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11253,tc_HOL_Obool)),U_11254),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11253,tc_HOL_Obool)),U_11255),U_11254)) = c_Orderings_Obot__class_Obot(tc_fun(U_11253,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3017_3]) ).

fof(f_3018_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_3018_2,plain,
    ! [U_11259,U_11258,U_11257,U_11256] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11256,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11256,tc_HOL_Obool)),U_11257),U_11258)),U_11259) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11256,tc_HOL_Obool)),U_11257),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11256,tc_HOL_Obool)),U_11258),U_11259))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11256,tc_HOL_Obool)),U_11259),U_11257)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11256,tc_HOL_Obool)),U_11259),U_11257))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11256,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11256,tc_HOL_Obool)),U_11257),U_11258)),U_11259) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11256,tc_HOL_Obool)),U_11257),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11256,tc_HOL_Obool)),U_11258),U_11259)) ) ),
    inference(variable_rename,[status(thm)],[f_3018_1]) ).

fof(f_3018_3,plain,
    ( ! [U_11267,U_11265,U_11263,U_11261] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11261,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11261,tc_HOL_Obool)),U_11263),U_11265)),U_11267) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11261,tc_HOL_Obool)),U_11263),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11261,tc_HOL_Obool)),U_11265),U_11267))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11261,tc_HOL_Obool)),U_11267),U_11263)) )
    & ! [U_11266,U_11264,U_11262,U_11260] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11260,tc_HOL_Obool)),U_11266),U_11262))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11260,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11260,tc_HOL_Obool)),U_11262),U_11264)),U_11266) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11260,tc_HOL_Obool)),U_11262),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11260,tc_HOL_Obool)),U_11264),U_11266)) ) ),
    inference(miniscope,[status(thm)],[f_3018_2]) ).

fof(f_3018_4,plain,
    ( ! [U_11261,U_11263,U_11265,U_11267] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11261,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11261,tc_HOL_Obool)),U_11263),U_11265)),U_11267) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11261,tc_HOL_Obool)),U_11263),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11261,tc_HOL_Obool)),U_11265),U_11267))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11261,tc_HOL_Obool)),U_11267),U_11263)) )
    & ! [U_11264,U_11266,U_11262,U_11260] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11260,tc_HOL_Obool)),U_11266),U_11262))
        | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11260,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11260,tc_HOL_Obool)),U_11262),U_11264)),U_11266) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11260,tc_HOL_Obool)),U_11262),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11260,tc_HOL_Obool)),U_11264),U_11266)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3018_3]) ).

cnf(f_3018_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11260,tc_HOL_Obool)),U_11266),U_11262))
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11260,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11260,tc_HOL_Obool)),U_11262),U_11264)),U_11266) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11260,tc_HOL_Obool)),U_11262),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11260,tc_HOL_Obool)),U_11264),U_11266)) ),
    inference(clausify,[status(thm)],[f_3018_4]) ).

cnf(f_3018_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11261,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11261,tc_HOL_Obool)),U_11263),U_11265)),U_11267) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11261,tc_HOL_Obool)),U_11263),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11261,tc_HOL_Obool)),U_11265),U_11267))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11261,tc_HOL_Obool)),U_11267),U_11263)) ),
    inference(clausify,[status(thm)],[f_3018_4]) ).

fof(f_3019_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_3019_2,plain,
    ! [U_11270,U_11269,U_11268] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11268,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11268,tc_HOL_Obool)),U_11269),U_11270)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11268,tc_HOL_Obool)),U_11269),U_11270)) = U_11269,
    inference(variable_rename,[status(thm)],[f_3019_1]) ).

fof(f_3019_3,plain,
    ! [U_11269,U_11268,U_11270] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11268,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11268,tc_HOL_Obool)),U_11269),U_11270)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11268,tc_HOL_Obool)),U_11269),U_11270)) = U_11269,
    inference(definitional_conversion,[status(esa)],[f_3019_2]) ).

cnf(f_3019_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11268,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11268,tc_HOL_Obool)),U_11269),U_11270)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11268,tc_HOL_Obool)),U_11269),U_11270)) = U_11269,
    inference(clausify,[status(thm)],[f_3019_3]) ).

fof(f_3020_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_3020_2,plain,
    ! [U_11274,U_11273,U_11272,U_11271] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11271,tc_HOL_Obool)),U_11272),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11271,tc_HOL_Obool)),U_11273),U_11274)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11271,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11271,tc_HOL_Obool)),U_11272),U_11273)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11271,tc_HOL_Obool)),U_11272),U_11274)),
    inference(variable_rename,[status(thm)],[f_3020_1]) ).

fof(f_3020_3,plain,
    ! [U_11271,U_11272,U_11273,U_11274] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11271,tc_HOL_Obool)),U_11272),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11271,tc_HOL_Obool)),U_11273),U_11274)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11271,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11271,tc_HOL_Obool)),U_11272),U_11273)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11271,tc_HOL_Obool)),U_11272),U_11274)),
    inference(definitional_conversion,[status(esa)],[f_3020_2]) ).

cnf(f_3020_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11271,tc_HOL_Obool)),U_11272),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11271,tc_HOL_Obool)),U_11273),U_11274)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11271,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11271,tc_HOL_Obool)),U_11272),U_11273)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11271,tc_HOL_Obool)),U_11272),U_11274)),
    inference(clausify,[status(thm)],[f_3020_3]) ).

fof(f_3021_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_3021_2,plain,
    ! [U_11278,U_11277,U_11276,U_11275] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11275,tc_HOL_Obool)),U_11276),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11275,tc_HOL_Obool)),U_11277),U_11278)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11275,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11275,tc_HOL_Obool)),U_11276),U_11277)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11275,tc_HOL_Obool)),U_11276),U_11278)),
    inference(variable_rename,[status(thm)],[f_3021_1]) ).

fof(f_3021_3,plain,
    ! [U_11275,U_11276,U_11277,U_11278] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11275,tc_HOL_Obool)),U_11276),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11275,tc_HOL_Obool)),U_11277),U_11278)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11275,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11275,tc_HOL_Obool)),U_11276),U_11277)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11275,tc_HOL_Obool)),U_11276),U_11278)),
    inference(definitional_conversion,[status(esa)],[f_3021_2]) ).

cnf(f_3021_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11275,tc_HOL_Obool)),U_11276),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11275,tc_HOL_Obool)),U_11277),U_11278)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11275,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11275,tc_HOL_Obool)),U_11276),U_11277)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11275,tc_HOL_Obool)),U_11276),U_11278)),
    inference(clausify,[status(thm)],[f_3021_3]) ).

fof(f_3022_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_3022_2,plain,
    ! [U_11280,U_11279] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11279,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11279,tc_HOL_Obool)),U_11280)),U_11280) = c_Orderings_Obot__class_Obot(tc_fun(U_11279,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3022_1]) ).

fof(f_3022_3,plain,
    ! [U_11279,U_11280] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11279,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11279,tc_HOL_Obool)),U_11280)),U_11280) = c_Orderings_Obot__class_Obot(tc_fun(U_11279,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3022_2]) ).

cnf(f_3022_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11279,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11279,tc_HOL_Obool)),U_11280)),U_11280) = c_Orderings_Obot__class_Obot(tc_fun(U_11279,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3022_3]) ).

fof(f_3023_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_3023_2,plain,
    ! [U_11282,U_11281] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11281,tc_HOL_Obool)),U_11282),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11281,tc_HOL_Obool)),U_11282)) = c_Orderings_Obot__class_Obot(tc_fun(U_11281,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3023_1]) ).

fof(f_3023_3,plain,
    ! [U_11281,U_11282] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11281,tc_HOL_Obool)),U_11282),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11281,tc_HOL_Obool)),U_11282)) = c_Orderings_Obot__class_Obot(tc_fun(U_11281,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3023_2]) ).

cnf(f_3023_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11281,tc_HOL_Obool)),U_11282),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11281,tc_HOL_Obool)),U_11282)) = c_Orderings_Obot__class_Obot(tc_fun(U_11281,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3023_3]) ).

fof(f_3024_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_3024_2,plain,
    ! [U_11285,U_11284,U_11283] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11283,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11283,tc_HOL_Obool)),U_11284),U_11285)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11283,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11283,tc_HOL_Obool)),U_11284)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11283,tc_HOL_Obool)),U_11285)),
    inference(variable_rename,[status(thm)],[f_3024_1]) ).

fof(f_3024_3,plain,
    ! [U_11283,U_11284,U_11285] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11283,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11283,tc_HOL_Obool)),U_11284),U_11285)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11283,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11283,tc_HOL_Obool)),U_11284)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11283,tc_HOL_Obool)),U_11285)),
    inference(definitional_conversion,[status(esa)],[f_3024_2]) ).

cnf(f_3024_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11283,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11283,tc_HOL_Obool)),U_11284),U_11285)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11283,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11283,tc_HOL_Obool)),U_11284)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11283,tc_HOL_Obool)),U_11285)),
    inference(clausify,[status(thm)],[f_3024_3]) ).

fof(f_3025_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_3025_2,plain,
    ! [U_11288,U_11287,U_11286] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11286,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11286,tc_HOL_Obool)),U_11287),U_11288)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11286,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11286,tc_HOL_Obool)),U_11287)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11286,tc_HOL_Obool)),U_11288)),
    inference(variable_rename,[status(thm)],[f_3025_1]) ).

fof(f_3025_3,plain,
    ! [U_11286,U_11287,U_11288] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11286,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11286,tc_HOL_Obool)),U_11287),U_11288)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11286,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11286,tc_HOL_Obool)),U_11287)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11286,tc_HOL_Obool)),U_11288)),
    inference(definitional_conversion,[status(esa)],[f_3025_2]) ).

cnf(f_3025_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11286,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11286,tc_HOL_Obool)),U_11287),U_11288)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11286,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11286,tc_HOL_Obool)),U_11287)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11286,tc_HOL_Obool)),U_11288)),
    inference(clausify,[status(thm)],[f_3025_3]) ).

fof(f_3026_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_3026_2,plain,
    ! [U_11291,U_11290,U_11289] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11289,tc_HOL_Obool)),U_11290),U_11291) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11289,tc_HOL_Obool)),U_11290),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11289,tc_HOL_Obool)),U_11291)),
    inference(variable_rename,[status(thm)],[f_3026_1]) ).

fof(f_3026_3,plain,
    ! [U_11289,U_11290,U_11291] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11289,tc_HOL_Obool)),U_11290),U_11291) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11289,tc_HOL_Obool)),U_11290),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11289,tc_HOL_Obool)),U_11291)),
    inference(definitional_conversion,[status(esa)],[f_3026_2]) ).

cnf(f_3026_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11289,tc_HOL_Obool)),U_11290),U_11291) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11289,tc_HOL_Obool)),U_11290),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11289,tc_HOL_Obool)),U_11291)),
    inference(clausify,[status(thm)],[f_3026_3]) ).

fof(f_3027_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_3027_2,plain,
    ! [U_11294,U_11293,U_11292] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11292,tc_HOL_Obool)),U_11293),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11292,tc_HOL_Obool)),U_11294)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11292,tc_HOL_Obool)),U_11293),U_11294),
    inference(variable_rename,[status(thm)],[f_3027_1]) ).

fof(f_3027_3,plain,
    ! [U_11292,U_11293,U_11294] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11292,tc_HOL_Obool)),U_11293),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11292,tc_HOL_Obool)),U_11294)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11292,tc_HOL_Obool)),U_11293),U_11294),
    inference(definitional_conversion,[status(esa)],[f_3027_2]) ).

cnf(f_3027_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11292,tc_HOL_Obool)),U_11293),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11292,tc_HOL_Obool)),U_11294)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11292,tc_HOL_Obool)),U_11293),U_11294),
    inference(clausify,[status(thm)],[f_3027_3]) ).

fof(f_3028_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_3028_2,plain,
    ! [U_11298,U_11297,U_11296,U_11295] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11295,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11295,U_11296,U_11297)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11295,U_11297,U_11298)) = c_Orderings_Obot__class_Obot(tc_fun(U_11295,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11295) ),
    inference(variable_rename,[status(thm)],[f_3028_1]) ).

fof(f_3028_3,plain,
    ! [U_11295,U_11296,U_11297,U_11298] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11295,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11295,U_11296,U_11297)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11295,U_11297,U_11298)) = c_Orderings_Obot__class_Obot(tc_fun(U_11295,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11295) ),
    inference(definitional_conversion,[status(esa)],[f_3028_2]) ).

cnf(f_3028_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11295,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11295,U_11296,U_11297)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11295,U_11297,U_11298)) = c_Orderings_Obot__class_Obot(tc_fun(U_11295,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11295) ),
    inference(clausify,[status(thm)],[f_3028_3]) ).

fof(f_3029_1,plain,
    ! [V_Pa_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_Pa_2))))
        | ~ hBOOL(hAPP(V_Pa_2,V_x_2))
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) )
      & ( ( hBOOL(hAPP(V_Pa_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_Pa_2)))) ) ),
    inference(fof_nnf,[status(thm)],[fact_Int__Collect]) ).

fof(f_3029_2,plain,
    ! [U_11302,U_11301,U_11300,U_11299] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_11299),U_11300),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11299,tc_HOL_Obool)),U_11301),hAPP(c_Set_OCollect(U_11299),U_11302))))
        | ~ hBOOL(hAPP(U_11302,U_11300))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11299),U_11300),U_11301)) )
      & ( ( hBOOL(hAPP(U_11302,U_11300))
          & hBOOL(hAPP(hAPP(c_member(U_11299),U_11300),U_11301)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_11299),U_11300),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11299,tc_HOL_Obool)),U_11301),hAPP(c_Set_OCollect(U_11299),U_11302)))) ) ),
    inference(variable_rename,[status(thm)],[f_3029_1]) ).

fof(f_3029_3,plain,
    ( ! [U_11310,U_11308,U_11306,U_11304] :
        ( hBOOL(hAPP(hAPP(c_member(U_11304),U_11306),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11304,tc_HOL_Obool)),U_11308),hAPP(c_Set_OCollect(U_11304),U_11310))))
        | ~ hBOOL(hAPP(U_11310,U_11306))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11304),U_11306),U_11308)) )
    & ! [U_11309,U_11307,U_11305,U_11303] :
        ( ( hBOOL(hAPP(U_11309,U_11305))
          & hBOOL(hAPP(hAPP(c_member(U_11303),U_11305),U_11307)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_11303),U_11305),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11303,tc_HOL_Obool)),U_11307),hAPP(c_Set_OCollect(U_11303),U_11309)))) ) ),
    inference(miniscope,[status(thm)],[f_3029_2]) ).

fof(f_3029_4,plain,
    ( ! [U_11305,U_11303,U_11309,U_11307] :
        ( hBOOL(hAPP(U_11309,U_11305))
        | ~ sP821(U_11305,U_11303,U_11309,U_11307) )
    & ! [U_11305,U_11303,U_11309,U_11307] :
        ( hBOOL(hAPP(hAPP(c_member(U_11303),U_11305),U_11307))
        | ~ sP821(U_11305,U_11303,U_11309,U_11307) )
    & ! [U_11308,U_11306,U_11304,U_11310] :
        ( hBOOL(hAPP(hAPP(c_member(U_11304),U_11306),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11304,tc_HOL_Obool)),U_11308),hAPP(c_Set_OCollect(U_11304),U_11310))))
        | ~ hBOOL(hAPP(U_11310,U_11306))
        | ~ hBOOL(hAPP(hAPP(c_member(U_11304),U_11306),U_11308)) )
    & ! [U_11305,U_11303,U_11309,U_11307] :
        ( sP821(U_11305,U_11303,U_11309,U_11307)
        | ~ hBOOL(hAPP(hAPP(c_member(U_11303),U_11305),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11303,tc_HOL_Obool)),U_11307),hAPP(c_Set_OCollect(U_11303),U_11309)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP821])],[f_3029_3]) ).

cnf(f_3029_5,plain,
    ( sP821(U_11305,U_11303,U_11309,U_11307)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11303),U_11305),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11303,tc_HOL_Obool)),U_11307),hAPP(c_Set_OCollect(U_11303),U_11309)))) ),
    inference(clausify,[status(thm)],[f_3029_4]) ).

cnf(f_3029_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11304),U_11306),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11304,tc_HOL_Obool)),U_11308),hAPP(c_Set_OCollect(U_11304),U_11310))))
    | ~ hBOOL(hAPP(U_11310,U_11306))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11304),U_11306),U_11308)) ),
    inference(clausify,[status(thm)],[f_3029_4]) ).

cnf(f_3029_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11303),U_11305),U_11307))
    | ~ sP821(U_11305,U_11303,U_11309,U_11307) ),
    inference(clausify,[status(thm)],[f_3029_4]) ).

cnf(f_3029_8,plain,
    ( hBOOL(hAPP(U_11309,U_11305))
    | ~ sP821(U_11305,U_11303,U_11309,U_11307) ),
    inference(clausify,[status(thm)],[f_3029_4]) ).

fof(f_3030_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_3030_2,plain,
    ! [U_11313,U_11312,U_11311] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11311,tc_HOL_Obool)),U_11312),U_11313) = hAPP(c_Set_OCollect(U_11311),hAPP(hAPP(c_COMBS(U_11311,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11311),c_fconj),hAPP(hAPP(c_COMBC(U_11311,tc_fun(U_11311,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11311)),U_11312))),hAPP(hAPP(c_COMBC(U_11311,tc_fun(U_11311,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11311)),U_11313))),
    inference(variable_rename,[status(thm)],[f_3030_1]) ).

fof(f_3030_3,plain,
    ! [U_11311,U_11312,U_11313] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11311,tc_HOL_Obool)),U_11312),U_11313) = hAPP(c_Set_OCollect(U_11311),hAPP(hAPP(c_COMBS(U_11311,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11311),c_fconj),hAPP(hAPP(c_COMBC(U_11311,tc_fun(U_11311,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11311)),U_11312))),hAPP(hAPP(c_COMBC(U_11311,tc_fun(U_11311,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11311)),U_11313))),
    inference(definitional_conversion,[status(esa)],[f_3030_2]) ).

cnf(f_3030_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11311,tc_HOL_Obool)),U_11312),U_11313) = hAPP(c_Set_OCollect(U_11311),hAPP(hAPP(c_COMBS(U_11311,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11311),c_fconj),hAPP(hAPP(c_COMBC(U_11311,tc_fun(U_11311,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11311)),U_11312))),hAPP(hAPP(c_COMBC(U_11311,tc_fun(U_11311,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11311)),U_11313))),
    inference(clausify,[status(thm)],[f_3030_3]) ).

fof(f_3031_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_3031_2,plain,
    ! [U_11316,U_11315,U_11314] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11314),U_11316),c_Big__Operators_Olattice__class_OInf__fin(U_11314,U_11315)) = c_Big__Operators_Olattice__class_OInf__fin(U_11314,U_11315)
      | ~ hBOOL(hAPP(hAPP(c_member(U_11314),U_11316),U_11315))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11314),U_11315))
      | ~ class_Lattices_Olattice(U_11314) ),
    inference(variable_rename,[status(thm)],[f_3031_1]) ).

fof(f_3031_3,plain,
    ! [U_11314,U_11315,U_11316] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11314),U_11316),c_Big__Operators_Olattice__class_OInf__fin(U_11314,U_11315)) = c_Big__Operators_Olattice__class_OInf__fin(U_11314,U_11315)
      | ~ hBOOL(hAPP(hAPP(c_member(U_11314),U_11316),U_11315))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11314),U_11315))
      | ~ class_Lattices_Olattice(U_11314) ),
    inference(definitional_conversion,[status(esa)],[f_3031_2]) ).

cnf(f_3031_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11314),U_11316),c_Big__Operators_Olattice__class_OInf__fin(U_11314,U_11315)) = c_Big__Operators_Olattice__class_OInf__fin(U_11314,U_11315)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11314),U_11316),U_11315))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11314),U_11315))
    | ~ class_Lattices_Olattice(U_11314) ),
    inference(clausify,[status(thm)],[f_3031_3]) ).

fof(f_3032_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_3032_2,plain,
    ! [U_11319,U_11318,U_11317] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11317),U_11319),c_Big__Operators_Olattice__class_OSup__fin(U_11317,U_11318)) = U_11319
      | ~ hBOOL(hAPP(hAPP(c_member(U_11317),U_11319),U_11318))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11317),U_11318))
      | ~ class_Lattices_Olattice(U_11317) ),
    inference(variable_rename,[status(thm)],[f_3032_1]) ).

fof(f_3032_3,plain,
    ! [U_11318,U_11317,U_11319] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11317),U_11319),c_Big__Operators_Olattice__class_OSup__fin(U_11317,U_11318)) = U_11319
      | ~ hBOOL(hAPP(hAPP(c_member(U_11317),U_11319),U_11318))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11317),U_11318))
      | ~ class_Lattices_Olattice(U_11317) ),
    inference(definitional_conversion,[status(esa)],[f_3032_2]) ).

cnf(f_3032_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11317),U_11319),c_Big__Operators_Olattice__class_OSup__fin(U_11317,U_11318)) = U_11319
    | ~ hBOOL(hAPP(hAPP(c_member(U_11317),U_11319),U_11318))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11317),U_11318))
    | ~ class_Lattices_Olattice(U_11317) ),
    inference(clausify,[status(thm)],[f_3032_3]) ).

fof(f_3033_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_3033_2,plain,
    ! [U_11322,U_11321,U_11320] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11320,tc_HOL_Obool)),U_11321),U_11322) = c_Orderings_Obot__class_Obot(tc_fun(U_11320,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11320,tc_HOL_Obool)),U_11321),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11320,tc_HOL_Obool)),U_11322))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11320,tc_HOL_Obool)),U_11321),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11320,tc_HOL_Obool)),U_11322)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11320,tc_HOL_Obool)),U_11321),U_11322) != c_Orderings_Obot__class_Obot(tc_fun(U_11320,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3033_1]) ).

fof(f_3033_3,plain,
    ( ! [U_11328,U_11326,U_11324] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11324,tc_HOL_Obool)),U_11326),U_11328) = c_Orderings_Obot__class_Obot(tc_fun(U_11324,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11324,tc_HOL_Obool)),U_11326),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11324,tc_HOL_Obool)),U_11328))) )
    & ! [U_11327,U_11325,U_11323] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11323,tc_HOL_Obool)),U_11325),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11323,tc_HOL_Obool)),U_11327)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11323,tc_HOL_Obool)),U_11325),U_11327) != c_Orderings_Obot__class_Obot(tc_fun(U_11323,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3033_2]) ).

fof(f_3033_4,plain,
    ( ! [U_11324,U_11326,U_11328] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11324,tc_HOL_Obool)),U_11326),U_11328) = c_Orderings_Obot__class_Obot(tc_fun(U_11324,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11324,tc_HOL_Obool)),U_11326),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11324,tc_HOL_Obool)),U_11328))) )
    & ! [U_11323,U_11325,U_11327] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11323,tc_HOL_Obool)),U_11325),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11323,tc_HOL_Obool)),U_11327)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11323,tc_HOL_Obool)),U_11325),U_11327) != c_Orderings_Obot__class_Obot(tc_fun(U_11323,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3033_3]) ).

cnf(f_3033_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11323,tc_HOL_Obool)),U_11325),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11323,tc_HOL_Obool)),U_11327)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11323,tc_HOL_Obool)),U_11325),U_11327) != c_Orderings_Obot__class_Obot(tc_fun(U_11323,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3033_4]) ).

cnf(f_3033_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11324,tc_HOL_Obool)),U_11326),U_11328) = c_Orderings_Obot__class_Obot(tc_fun(U_11324,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11324,tc_HOL_Obool)),U_11326),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11324,tc_HOL_Obool)),U_11328))) ),
    inference(clausify,[status(thm)],[f_3033_4]) ).

fof(f_3034_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_3034_2,plain,
    ! [U_11333,U_11332,U_11331,U_11330,U_11329] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11329,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11329,U_11330,U_11331)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11329,U_11332,U_11333)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_11329,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11329),U_11330),U_11332),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11329),U_11331),U_11333))
      | ~ class_Orderings_Olinorder(U_11329) ),
    inference(variable_rename,[status(thm)],[f_3034_1]) ).

fof(f_3034_3,plain,
    ! [U_11329,U_11330,U_11331,U_11332,U_11333] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11329,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11329,U_11330,U_11331)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11329,U_11332,U_11333)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_11329,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11329),U_11330),U_11332),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11329),U_11331),U_11333))
      | ~ class_Orderings_Olinorder(U_11329) ),
    inference(definitional_conversion,[status(esa)],[f_3034_2]) ).

cnf(f_3034_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11329,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11329,U_11330,U_11331)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11329,U_11332,U_11333)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_11329,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11329),U_11330),U_11332),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11329),U_11331),U_11333))
    | ~ class_Orderings_Olinorder(U_11329) ),
    inference(clausify,[status(thm)],[f_3034_3]) ).

fof(f_3035_1,plain,
    ! [V_d_2,V_c_2,V_b_2,V_a_2,T_b] :
      ( 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_3035_2,plain,
    ! [U_11338,U_11337,U_11336,U_11335,U_11334] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11334,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11334,U_11335,U_11336)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11334,U_11337,U_11338)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_11334,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11334),U_11335),U_11337),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11334),U_11336),U_11338))
      | ~ class_Orderings_Olinorder(U_11334) ),
    inference(variable_rename,[status(thm)],[f_3035_1]) ).

fof(f_3035_3,plain,
    ! [U_11334,U_11335,U_11336,U_11337,U_11338] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11334,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11334,U_11335,U_11336)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11334,U_11337,U_11338)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_11334,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11334),U_11335),U_11337),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11334),U_11336),U_11338))
      | ~ class_Orderings_Olinorder(U_11334) ),
    inference(definitional_conversion,[status(esa)],[f_3035_2]) ).

cnf(f_3035_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11334,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11334,U_11335,U_11336)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11334,U_11337,U_11338)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_11334,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11334),U_11335),U_11337),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11334),U_11336),U_11338))
    | ~ class_Orderings_Olinorder(U_11334) ),
    inference(clausify,[status(thm)],[f_3035_3]) ).

fof(f_3036_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_3036_2,plain,
    ! [U_11341,U_11340,U_11339] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11339,U_11339),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_11339,U_11340)),U_11341))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11339,U_11339),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_11339,U_11339,U_11339),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11339,U_11339),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_11339,U_11340)),U_11341)),U_11340)),U_11341))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11339,U_11339),tc_HOL_Obool)),U_11340),U_11341)) ),
    inference(variable_rename,[status(thm)],[f_3036_1]) ).

fof(f_3036_3,plain,
    ! [U_11339,U_11340,U_11341] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11339,U_11339),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_11339,U_11340)),U_11341))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11339,U_11339),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_11339,U_11339,U_11339),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11339,U_11339),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_11339,U_11340)),U_11341)),U_11340)),U_11341))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11339,U_11339),tc_HOL_Obool)),U_11340),U_11341)) ),
    inference(definitional_conversion,[status(esa)],[f_3036_2]) ).

cnf(f_3036_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11339,U_11339),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_11339,U_11340)),U_11341))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11339,U_11339),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_11339,U_11339,U_11339),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11339,U_11339),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_11339,U_11340)),U_11341)),U_11340)),U_11341))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11339,U_11339),tc_HOL_Obool)),U_11340),U_11341)) ),
    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_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_3037_2,plain,
    ! [U_11345,U_11344,U_11343,U_11342] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11342,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11342,U_11343,U_11344)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11342,U_11344,U_11345)) = c_Orderings_Obot__class_Obot(tc_fun(U_11342,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11342) ),
    inference(variable_rename,[status(thm)],[f_3037_1]) ).

fof(f_3037_3,plain,
    ! [U_11343,U_11342,U_11344,U_11345] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11342,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11342,U_11343,U_11344)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11342,U_11344,U_11345)) = c_Orderings_Obot__class_Obot(tc_fun(U_11342,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11342) ),
    inference(definitional_conversion,[status(esa)],[f_3037_2]) ).

cnf(f_3037_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11342,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11342,U_11343,U_11344)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11342,U_11344,U_11345)) = c_Orderings_Obot__class_Obot(tc_fun(U_11342,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11342) ),
    inference(clausify,[status(thm)],[f_3037_3]) ).

fof(f_3038_1,plain,
    ! [V_S_2,V_g_2,V_f_2,V_Pa_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_Pa_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_Pa_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_Pa_2))))),
    inference(fof_nnf,[status(thm)],[fact_if__image__distrib]) ).

fof(f_3038_2,plain,
    ! [U_11351,U_11350,U_11349,U_11348,U_11347,U_11346] : hAPP(c_Set_Oimage(U_11346,U_11347,hAPP(hAPP(c_COMBS(U_11346,U_11347,U_11347),hAPP(hAPP(c_COMBS(U_11346,U_11347,tc_fun(U_11347,U_11347)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11347,tc_fun(U_11347,U_11347)),U_11346),c_If(U_11347)),U_11348)),U_11349)),U_11350)),U_11351) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11347,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11346,U_11347,U_11349),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11346,tc_HOL_Obool)),U_11351),hAPP(c_Set_OCollect(U_11346),U_11348)))),hAPP(c_Set_Oimage(U_11346,U_11347,U_11350),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11346,tc_HOL_Obool)),U_11351),hAPP(c_Set_OCollect(U_11346),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11346),c_fNot),U_11348))))),
    inference(variable_rename,[status(thm)],[f_3038_1]) ).

fof(f_3038_3,plain,
    ! [U_11346,U_11347,U_11348,U_11349,U_11350,U_11351] : hAPP(c_Set_Oimage(U_11346,U_11347,hAPP(hAPP(c_COMBS(U_11346,U_11347,U_11347),hAPP(hAPP(c_COMBS(U_11346,U_11347,tc_fun(U_11347,U_11347)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11347,tc_fun(U_11347,U_11347)),U_11346),c_If(U_11347)),U_11348)),U_11349)),U_11350)),U_11351) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11347,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11346,U_11347,U_11349),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11346,tc_HOL_Obool)),U_11351),hAPP(c_Set_OCollect(U_11346),U_11348)))),hAPP(c_Set_Oimage(U_11346,U_11347,U_11350),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11346,tc_HOL_Obool)),U_11351),hAPP(c_Set_OCollect(U_11346),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11346),c_fNot),U_11348))))),
    inference(definitional_conversion,[status(esa)],[f_3038_2]) ).

cnf(f_3038_4,plain,
    hAPP(c_Set_Oimage(U_11346,U_11347,hAPP(hAPP(c_COMBS(U_11346,U_11347,U_11347),hAPP(hAPP(c_COMBS(U_11346,U_11347,tc_fun(U_11347,U_11347)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_11347,tc_fun(U_11347,U_11347)),U_11346),c_If(U_11347)),U_11348)),U_11349)),U_11350)),U_11351) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11347,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11346,U_11347,U_11349),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11346,tc_HOL_Obool)),U_11351),hAPP(c_Set_OCollect(U_11346),U_11348)))),hAPP(c_Set_Oimage(U_11346,U_11347,U_11350),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11346,tc_HOL_Obool)),U_11351),hAPP(c_Set_OCollect(U_11346),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11346),c_fNot),U_11348))))),
    inference(clausify,[status(thm)],[f_3038_3]) ).

fof(f_3039_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_3039_2,plain,
    ! [U_11359,U_11358,U_11357,U_11356,U_11355,U_11354,U_11353,U_11352] :
      ( hAPP(hAPP(U_11354,hAPP(U_11357,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11353,tc_HOL_Obool)),U_11358),U_11359))),hAPP(U_11357,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11353,tc_HOL_Obool)),U_11358),U_11359))) = hAPP(hAPP(U_11354,hAPP(U_11357,U_11358)),hAPP(U_11357,U_11359))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11353),U_11359))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11353),U_11358))
      | ~ c_Finite__Set_Ofolding__image__simple(U_11352,U_11353,U_11354,U_11355,U_11356,U_11357) ),
    inference(variable_rename,[status(thm)],[f_3039_1]) ).

fof(f_3039_3,plain,
    ! [U_11359,U_11358,U_11357,U_11356,U_11355,U_11354,U_11353] :
      ( ! [U_11352] : ~ c_Finite__Set_Ofolding__image__simple(U_11352,U_11353,U_11354,U_11355,U_11356,U_11357)
      | hAPP(hAPP(U_11354,hAPP(U_11357,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11353,tc_HOL_Obool)),U_11358),U_11359))),hAPP(U_11357,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11353,tc_HOL_Obool)),U_11358),U_11359))) = hAPP(hAPP(U_11354,hAPP(U_11357,U_11358)),hAPP(U_11357,U_11359))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11353),U_11359))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11353),U_11358)) ),
    inference(miniscope,[status(thm)],[f_3039_2]) ).

fof(f_3039_4,plain,
    ! [U_11352,U_11353,U_11354,U_11355,U_11356,U_11357,U_11358,U_11359] :
      ( ~ c_Finite__Set_Ofolding__image__simple(U_11352,U_11353,U_11354,U_11355,U_11356,U_11357)
      | hAPP(hAPP(U_11354,hAPP(U_11357,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11353,tc_HOL_Obool)),U_11358),U_11359))),hAPP(U_11357,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11353,tc_HOL_Obool)),U_11358),U_11359))) = hAPP(hAPP(U_11354,hAPP(U_11357,U_11358)),hAPP(U_11357,U_11359))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11353),U_11359))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11353),U_11358)) ),
    inference(definitional_conversion,[status(esa)],[f_3039_3]) ).

cnf(f_3039_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_11352,U_11353,U_11354,U_11355,U_11356,U_11357)
    | hAPP(hAPP(U_11354,hAPP(U_11357,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11353,tc_HOL_Obool)),U_11358),U_11359))),hAPP(U_11357,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11353,tc_HOL_Obool)),U_11358),U_11359))) = hAPP(hAPP(U_11354,hAPP(U_11357,U_11358)),hAPP(U_11357,U_11359))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11353),U_11359))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11353),U_11358)) ),
    inference(clausify,[status(thm)],[f_3039_4]) ).

fof(f_3040_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_3040_2,plain,
    ! [U_11362,U_11361,U_11360] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_11360,hAPP(hAPP(c_Set_Oinsert(U_11360),U_11362),U_11361)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11360),U_11362),c_Big__Operators_Olattice__class_OInf__fin(U_11360,U_11361))
      | U_11361 = c_Orderings_Obot__class_Obot(tc_fun(U_11360,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11360),U_11361))
      | ~ class_Lattices_Olattice(U_11360) ),
    inference(variable_rename,[status(thm)],[f_3040_1]) ).

fof(f_3040_3,plain,
    ! [U_11361,U_11360,U_11362] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_11360,hAPP(hAPP(c_Set_Oinsert(U_11360),U_11362),U_11361)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11360),U_11362),c_Big__Operators_Olattice__class_OInf__fin(U_11360,U_11361))
      | U_11361 = c_Orderings_Obot__class_Obot(tc_fun(U_11360,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11360),U_11361))
      | ~ class_Lattices_Olattice(U_11360) ),
    inference(definitional_conversion,[status(esa)],[f_3040_2]) ).

cnf(f_3040_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_11360,hAPP(hAPP(c_Set_Oinsert(U_11360),U_11362),U_11361)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11360),U_11362),c_Big__Operators_Olattice__class_OInf__fin(U_11360,U_11361))
    | U_11361 = c_Orderings_Obot__class_Obot(tc_fun(U_11360,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11360),U_11361))
    | ~ class_Lattices_Olattice(U_11360) ),
    inference(clausify,[status(thm)],[f_3040_3]) ).

fof(f_3041_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_3041_2,plain,
    ! [U_11365,U_11364,U_11363] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11363),c_Big__Operators_Olattice__class_OInf__fin(U_11363,U_11365)),c_Big__Operators_Olattice__class_OInf__fin(U_11363,U_11364)) = c_Big__Operators_Olattice__class_OInf__fin(U_11363,U_11364)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11363,tc_HOL_Obool)),U_11365),U_11364))
      | U_11365 = c_Orderings_Obot__class_Obot(tc_fun(U_11363,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11363),U_11364))
      | ~ class_Lattices_Olattice(U_11363) ),
    inference(variable_rename,[status(thm)],[f_3041_1]) ).

fof(f_3041_3,plain,
    ! [U_11363,U_11364,U_11365] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11363),c_Big__Operators_Olattice__class_OInf__fin(U_11363,U_11365)),c_Big__Operators_Olattice__class_OInf__fin(U_11363,U_11364)) = c_Big__Operators_Olattice__class_OInf__fin(U_11363,U_11364)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11363,tc_HOL_Obool)),U_11365),U_11364))
      | U_11365 = c_Orderings_Obot__class_Obot(tc_fun(U_11363,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11363),U_11364))
      | ~ class_Lattices_Olattice(U_11363) ),
    inference(definitional_conversion,[status(esa)],[f_3041_2]) ).

cnf(f_3041_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11363),c_Big__Operators_Olattice__class_OInf__fin(U_11363,U_11365)),c_Big__Operators_Olattice__class_OInf__fin(U_11363,U_11364)) = c_Big__Operators_Olattice__class_OInf__fin(U_11363,U_11364)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11363,tc_HOL_Obool)),U_11365),U_11364))
    | U_11365 = c_Orderings_Obot__class_Obot(tc_fun(U_11363,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11363),U_11364))
    | ~ class_Lattices_Olattice(U_11363) ),
    inference(clausify,[status(thm)],[f_3041_3]) ).

fof(f_3042_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_3042_2,plain,
    ! [U_11368,U_11367,U_11366] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_11366,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11366,tc_HOL_Obool)),U_11367),U_11368)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11366),c_Big__Operators_Olattice__class_OInf__fin(U_11366,U_11367)),c_Big__Operators_Olattice__class_OInf__fin(U_11366,U_11368))
      | U_11368 = c_Orderings_Obot__class_Obot(tc_fun(U_11366,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11366),U_11368))
      | U_11367 = c_Orderings_Obot__class_Obot(tc_fun(U_11366,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11366),U_11367))
      | ~ class_Lattices_Olattice(U_11366) ),
    inference(variable_rename,[status(thm)],[f_3042_1]) ).

fof(f_3042_3,plain,
    ! [U_11367,U_11368,U_11366] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_11366,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11366,tc_HOL_Obool)),U_11367),U_11368)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11366),c_Big__Operators_Olattice__class_OInf__fin(U_11366,U_11367)),c_Big__Operators_Olattice__class_OInf__fin(U_11366,U_11368))
      | U_11368 = c_Orderings_Obot__class_Obot(tc_fun(U_11366,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11366),U_11368))
      | U_11367 = c_Orderings_Obot__class_Obot(tc_fun(U_11366,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11366),U_11367))
      | ~ class_Lattices_Olattice(U_11366) ),
    inference(definitional_conversion,[status(esa)],[f_3042_2]) ).

cnf(f_3042_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_11366,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11366,tc_HOL_Obool)),U_11367),U_11368)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11366),c_Big__Operators_Olattice__class_OInf__fin(U_11366,U_11367)),c_Big__Operators_Olattice__class_OInf__fin(U_11366,U_11368))
    | U_11368 = c_Orderings_Obot__class_Obot(tc_fun(U_11366,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11366),U_11368))
    | U_11367 = c_Orderings_Obot__class_Obot(tc_fun(U_11366,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11366),U_11367))
    | ~ class_Lattices_Olattice(U_11366) ),
    inference(clausify,[status(thm)],[f_3042_3]) ).

fof(f_3043_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_3043_2,plain,
    ! [U_11373,U_11372,U_11371,U_11370,U_11369] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11369),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11370,U_11369),U_11373),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11370,tc_HOL_Obool)),U_11371),U_11372))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11370,U_11369),U_11373),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11370,tc_HOL_Obool)),U_11371),U_11372))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11369),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11370,U_11369),U_11373),U_11371)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11370,U_11369),U_11373),U_11372))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11370),U_11372))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11370),U_11371))
      | ~ class_Groups_Ocomm__monoid__mult(U_11369) ),
    inference(variable_rename,[status(thm)],[f_3043_1]) ).

fof(f_3043_3,plain,
    ! [U_11370,U_11369,U_11371,U_11372,U_11373] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11369),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11370,U_11369),U_11373),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11370,tc_HOL_Obool)),U_11371),U_11372))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11370,U_11369),U_11373),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11370,tc_HOL_Obool)),U_11371),U_11372))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11369),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11370,U_11369),U_11373),U_11371)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11370,U_11369),U_11373),U_11372))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11370),U_11372))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11370),U_11371))
      | ~ class_Groups_Ocomm__monoid__mult(U_11369) ),
    inference(definitional_conversion,[status(esa)],[f_3043_2]) ).

cnf(f_3043_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11369),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11370,U_11369),U_11373),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11370,tc_HOL_Obool)),U_11371),U_11372))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11370,U_11369),U_11373),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11370,tc_HOL_Obool)),U_11371),U_11372))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11369),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11370,U_11369),U_11373),U_11371)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11370,U_11369),U_11373),U_11372))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11370),U_11372))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11370),U_11371))
    | ~ class_Groups_Ocomm__monoid__mult(U_11369) ),
    inference(clausify,[status(thm)],[f_3043_3]) ).

fof(f_3044_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_3044_2,plain,
    ! [U_11378,U_11377,U_11376,U_11375,U_11374] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11374),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11375,U_11374),U_11378),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11375,tc_HOL_Obool)),U_11376),U_11377))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11375,U_11374),U_11378),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11375,tc_HOL_Obool)),U_11376),U_11377))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11374),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11375,U_11374),U_11378),U_11376)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11375,U_11374),U_11378),U_11377))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11375),U_11377))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11375),U_11376))
      | ~ class_Groups_Ocomm__monoid__mult(U_11374) ),
    inference(variable_rename,[status(thm)],[f_3044_1]) ).

fof(f_3044_3,plain,
    ! [U_11374,U_11375,U_11376,U_11377,U_11378] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11374),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11375,U_11374),U_11378),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11375,tc_HOL_Obool)),U_11376),U_11377))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11375,U_11374),U_11378),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11375,tc_HOL_Obool)),U_11376),U_11377))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11374),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11375,U_11374),U_11378),U_11376)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11375,U_11374),U_11378),U_11377))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11375),U_11377))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11375),U_11376))
      | ~ class_Groups_Ocomm__monoid__mult(U_11374) ),
    inference(definitional_conversion,[status(esa)],[f_3044_2]) ).

cnf(f_3044_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11374),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11375,U_11374),U_11378),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11375,tc_HOL_Obool)),U_11376),U_11377))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11375,U_11374),U_11378),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11375,tc_HOL_Obool)),U_11376),U_11377))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11374),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11375,U_11374),U_11378),U_11376)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11375,U_11374),U_11378),U_11377))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11375),U_11377))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11375),U_11376))
    | ~ class_Groups_Ocomm__monoid__mult(U_11374) ),
    inference(clausify,[status(thm)],[f_3044_3]) ).

fof(f_3045_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_3045_2,plain,
    ! [U_11381,U_11380,U_11379] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11379),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11379,tc_HOL_Obool)),U_11380),U_11381))),hAPP(c_Finite__Set_Ocard(U_11379),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11379,tc_HOL_Obool)),U_11380),U_11381))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11379),U_11380)),hAPP(c_Finite__Set_Ocard(U_11379),U_11381))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11379),U_11381))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11379),U_11380)) ),
    inference(variable_rename,[status(thm)],[f_3045_1]) ).

fof(f_3045_3,plain,
    ! [U_11380,U_11379,U_11381] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11379),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11379,tc_HOL_Obool)),U_11380),U_11381))),hAPP(c_Finite__Set_Ocard(U_11379),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11379,tc_HOL_Obool)),U_11380),U_11381))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11379),U_11380)),hAPP(c_Finite__Set_Ocard(U_11379),U_11381))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11379),U_11381))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11379),U_11380)) ),
    inference(definitional_conversion,[status(esa)],[f_3045_2]) ).

cnf(f_3045_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11379),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11379,tc_HOL_Obool)),U_11380),U_11381))),hAPP(c_Finite__Set_Ocard(U_11379),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11379,tc_HOL_Obool)),U_11380),U_11381))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11379),U_11380)),hAPP(c_Finite__Set_Ocard(U_11379),U_11381))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11379),U_11381))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11379),U_11380)) ),
    inference(clausify,[status(thm)],[f_3045_3]) ).

fof(f_3046_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_3046_2,plain,
    ! [U_11384,U_11383,U_11382] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11382),U_11383)),hAPP(c_Finite__Set_Ocard(U_11382),U_11384)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11382),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11382,tc_HOL_Obool)),U_11383),U_11384))),hAPP(c_Finite__Set_Ocard(U_11382),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11382,tc_HOL_Obool)),U_11383),U_11384)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11382),U_11384))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11382),U_11383)) ),
    inference(variable_rename,[status(thm)],[f_3046_1]) ).

fof(f_3046_3,plain,
    ! [U_11382,U_11383,U_11384] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11382),U_11383)),hAPP(c_Finite__Set_Ocard(U_11382),U_11384)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11382),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11382,tc_HOL_Obool)),U_11383),U_11384))),hAPP(c_Finite__Set_Ocard(U_11382),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11382,tc_HOL_Obool)),U_11383),U_11384)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11382),U_11384))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11382),U_11383)) ),
    inference(definitional_conversion,[status(esa)],[f_3046_2]) ).

cnf(f_3046_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11382),U_11383)),hAPP(c_Finite__Set_Ocard(U_11382),U_11384)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11382),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11382,tc_HOL_Obool)),U_11383),U_11384))),hAPP(c_Finite__Set_Ocard(U_11382),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11382,tc_HOL_Obool)),U_11383),U_11384)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11382),U_11384))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11382),U_11383)) ),
    inference(clausify,[status(thm)],[f_3046_3]) ).

fof(f_3047_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_3047_2,plain,
    ! [U_11387,U_11386,U_11385] :
      ( hAPP(c_Finite__Set_Ocard(U_11385),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11385,tc_HOL_Obool)),U_11386),U_11387)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11385),U_11386)),hAPP(c_Finite__Set_Ocard(U_11385),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11385,tc_HOL_Obool)),U_11386),U_11387)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11385),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11385,tc_HOL_Obool)),U_11386),U_11387))) ),
    inference(variable_rename,[status(thm)],[f_3047_1]) ).

fof(f_3047_3,plain,
    ! [U_11385,U_11386,U_11387] :
      ( hAPP(c_Finite__Set_Ocard(U_11385),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11385,tc_HOL_Obool)),U_11386),U_11387)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11385),U_11386)),hAPP(c_Finite__Set_Ocard(U_11385),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11385,tc_HOL_Obool)),U_11386),U_11387)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11385),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11385,tc_HOL_Obool)),U_11386),U_11387))) ),
    inference(definitional_conversion,[status(esa)],[f_3047_2]) ).

cnf(f_3047_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_11385),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11385,tc_HOL_Obool)),U_11386),U_11387)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11385),U_11386)),hAPP(c_Finite__Set_Ocard(U_11385),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11385,tc_HOL_Obool)),U_11386),U_11387)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11385),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11385,tc_HOL_Obool)),U_11386),U_11387))) ),
    inference(clausify,[status(thm)],[f_3047_3]) ).

fof(f_3048_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_3048_2,plain,
    ! [U_11392,U_11391,U_11390,U_11389,U_11388] :
      ( hAPP(hAPP(U_11389,hAPP(U_11390,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11388,tc_HOL_Obool)),U_11391),U_11392))),hAPP(U_11390,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11388,tc_HOL_Obool)),U_11391),U_11392))) = hAPP(hAPP(U_11389,hAPP(U_11390,U_11391)),hAPP(U_11390,U_11392))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11388,tc_HOL_Obool)),U_11391),U_11392) = c_Orderings_Obot__class_Obot(tc_fun(U_11388,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11388),U_11392))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11388),U_11391))
      | ~ c_Finite__Set_Ofolding__one(U_11388,U_11389,U_11390) ),
    inference(variable_rename,[status(thm)],[f_3048_1]) ).

fof(f_3048_3,plain,
    ! [U_11388,U_11389,U_11390,U_11391,U_11392] :
      ( hAPP(hAPP(U_11389,hAPP(U_11390,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11388,tc_HOL_Obool)),U_11391),U_11392))),hAPP(U_11390,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11388,tc_HOL_Obool)),U_11391),U_11392))) = hAPP(hAPP(U_11389,hAPP(U_11390,U_11391)),hAPP(U_11390,U_11392))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11388,tc_HOL_Obool)),U_11391),U_11392) = c_Orderings_Obot__class_Obot(tc_fun(U_11388,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11388),U_11392))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11388),U_11391))
      | ~ c_Finite__Set_Ofolding__one(U_11388,U_11389,U_11390) ),
    inference(definitional_conversion,[status(esa)],[f_3048_2]) ).

cnf(f_3048_4,plain,
    ( hAPP(hAPP(U_11389,hAPP(U_11390,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11388,tc_HOL_Obool)),U_11391),U_11392))),hAPP(U_11390,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11388,tc_HOL_Obool)),U_11391),U_11392))) = hAPP(hAPP(U_11389,hAPP(U_11390,U_11391)),hAPP(U_11390,U_11392))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11388,tc_HOL_Obool)),U_11391),U_11392) = c_Orderings_Obot__class_Obot(tc_fun(U_11388,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11388),U_11392))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11388),U_11391))
    | ~ c_Finite__Set_Ofolding__one(U_11388,U_11389,U_11390) ),
    inference(clausify,[status(thm)],[f_3048_3]) ).

fof(f_3049_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_3049_2,plain,
    ! [U_11397,U_11396,U_11395,U_11394,U_11393] :
      ( hAPP(U_11395,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11393,tc_HOL_Obool)),U_11396),U_11397)) = hAPP(hAPP(U_11394,hAPP(U_11395,U_11396)),hAPP(U_11395,U_11397))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11393,tc_HOL_Obool)),U_11396),U_11397) != c_Orderings_Obot__class_Obot(tc_fun(U_11393,tc_HOL_Obool))
      | U_11397 = c_Orderings_Obot__class_Obot(tc_fun(U_11393,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11393),U_11397))
      | U_11396 = c_Orderings_Obot__class_Obot(tc_fun(U_11393,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11393),U_11396))
      | ~ c_Finite__Set_Ofolding__one(U_11393,U_11394,U_11395) ),
    inference(variable_rename,[status(thm)],[f_3049_1]) ).

fof(f_3049_3,plain,
    ! [U_11393,U_11396,U_11394,U_11395,U_11397] :
      ( hAPP(U_11395,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11393,tc_HOL_Obool)),U_11396),U_11397)) = hAPP(hAPP(U_11394,hAPP(U_11395,U_11396)),hAPP(U_11395,U_11397))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11393,tc_HOL_Obool)),U_11396),U_11397) != c_Orderings_Obot__class_Obot(tc_fun(U_11393,tc_HOL_Obool))
      | U_11397 = c_Orderings_Obot__class_Obot(tc_fun(U_11393,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11393),U_11397))
      | U_11396 = c_Orderings_Obot__class_Obot(tc_fun(U_11393,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11393),U_11396))
      | ~ c_Finite__Set_Ofolding__one(U_11393,U_11394,U_11395) ),
    inference(definitional_conversion,[status(esa)],[f_3049_2]) ).

cnf(f_3049_4,plain,
    ( hAPP(U_11395,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11393,tc_HOL_Obool)),U_11396),U_11397)) = hAPP(hAPP(U_11394,hAPP(U_11395,U_11396)),hAPP(U_11395,U_11397))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11393,tc_HOL_Obool)),U_11396),U_11397) != c_Orderings_Obot__class_Obot(tc_fun(U_11393,tc_HOL_Obool))
    | U_11397 = c_Orderings_Obot__class_Obot(tc_fun(U_11393,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11393),U_11397))
    | U_11396 = c_Orderings_Obot__class_Obot(tc_fun(U_11393,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11393),U_11396))
    | ~ c_Finite__Set_Ofolding__one(U_11393,U_11394,U_11395) ),
    inference(clausify,[status(thm)],[f_3049_3]) ).

fof(f_3050_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_3050_2,plain,
    ! [U_11405,U_11404,U_11403,U_11402,U_11401,U_11400,U_11399,U_11398] :
      ( hAPP(U_11403,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11399,tc_HOL_Obool)),U_11404),U_11405)) = hAPP(hAPP(U_11400,hAPP(U_11403,U_11404)),hAPP(U_11403,U_11405))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11399,tc_HOL_Obool)),U_11404),U_11405) != c_Orderings_Obot__class_Obot(tc_fun(U_11399,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11399),U_11405))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11399),U_11404))
      | ~ c_Finite__Set_Ofolding__image__simple(U_11398,U_11399,U_11400,U_11401,U_11402,U_11403) ),
    inference(variable_rename,[status(thm)],[f_3050_1]) ).

fof(f_3050_3,plain,
    ! [U_11405,U_11404,U_11403,U_11402,U_11401,U_11400,U_11399] :
      ( ! [U_11398] : ~ c_Finite__Set_Ofolding__image__simple(U_11398,U_11399,U_11400,U_11401,U_11402,U_11403)
      | hAPP(U_11403,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11399,tc_HOL_Obool)),U_11404),U_11405)) = hAPP(hAPP(U_11400,hAPP(U_11403,U_11404)),hAPP(U_11403,U_11405))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11399,tc_HOL_Obool)),U_11404),U_11405) != c_Orderings_Obot__class_Obot(tc_fun(U_11399,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11399),U_11405))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11399),U_11404)) ),
    inference(miniscope,[status(thm)],[f_3050_2]) ).

fof(f_3050_4,plain,
    ! [U_11401,U_11398,U_11399,U_11405,U_11402,U_11403,U_11404,U_11400] :
      ( ~ c_Finite__Set_Ofolding__image__simple(U_11398,U_11399,U_11400,U_11401,U_11402,U_11403)
      | hAPP(U_11403,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11399,tc_HOL_Obool)),U_11404),U_11405)) = hAPP(hAPP(U_11400,hAPP(U_11403,U_11404)),hAPP(U_11403,U_11405))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11399,tc_HOL_Obool)),U_11404),U_11405) != c_Orderings_Obot__class_Obot(tc_fun(U_11399,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11399),U_11405))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11399),U_11404)) ),
    inference(definitional_conversion,[status(esa)],[f_3050_3]) ).

cnf(f_3050_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_11398,U_11399,U_11400,U_11401,U_11402,U_11403)
    | hAPP(U_11403,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11399,tc_HOL_Obool)),U_11404),U_11405)) = hAPP(hAPP(U_11400,hAPP(U_11403,U_11404)),hAPP(U_11403,U_11405))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11399,tc_HOL_Obool)),U_11404),U_11405) != c_Orderings_Obot__class_Obot(tc_fun(U_11399,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11399),U_11405))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11399),U_11404)) ),
    inference(clausify,[status(thm)],[f_3050_4]) ).

fof(f_3051_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_3051_2,plain,
    ! [U_11408,U_11407,U_11406] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11406,U_11406),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_11406,U_11408)),U_11407))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11406,U_11406),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_11406,U_11406,U_11406),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11406,U_11406),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_11406,U_11408)),U_11407)),U_11408)),U_11407))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11406,U_11406),tc_HOL_Obool)),c_Relation_OId(U_11406)),U_11407)) ),
    inference(variable_rename,[status(thm)],[f_3051_1]) ).

fof(f_3051_3,plain,
    ! [U_11407,U_11408,U_11406] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11406,U_11406),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_11406,U_11408)),U_11407))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11406,U_11406),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_11406,U_11406,U_11406),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11406,U_11406),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_11406,U_11408)),U_11407)),U_11408)),U_11407))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11406,U_11406),tc_HOL_Obool)),c_Relation_OId(U_11406)),U_11407)) ),
    inference(definitional_conversion,[status(esa)],[f_3051_2]) ).

cnf(f_3051_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11406,U_11406),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_11406,U_11408)),U_11407))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11406,U_11406),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_11406,U_11406,U_11406),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11406,U_11406),tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_11406,U_11408)),U_11407)),U_11408)),U_11407))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_11406,U_11406),tc_HOL_Obool)),c_Relation_OId(U_11406)),U_11407)) ),
    inference(clausify,[status(thm)],[f_3051_3]) ).

fof(f_3052_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_3052_2,plain,
    ! [U_11411,U_11410,U_11409] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_11409,hAPP(hAPP(c_Set_Oinsert(U_11409),U_11411),U_11410)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11409),U_11411),c_Big__Operators_Olattice__class_OInf__fin(U_11409,U_11410))
      | U_11410 = c_Orderings_Obot__class_Obot(tc_fun(U_11409,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_11409),U_11411),U_11410))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11409),U_11410))
      | ~ class_Lattices_Olattice(U_11409) ),
    inference(variable_rename,[status(thm)],[f_3052_1]) ).

fof(f_3052_3,plain,
    ! [U_11409,U_11410,U_11411] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_11409,hAPP(hAPP(c_Set_Oinsert(U_11409),U_11411),U_11410)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11409),U_11411),c_Big__Operators_Olattice__class_OInf__fin(U_11409,U_11410))
      | U_11410 = c_Orderings_Obot__class_Obot(tc_fun(U_11409,tc_HOL_Obool))
      | hBOOL(hAPP(hAPP(c_member(U_11409),U_11411),U_11410))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11409),U_11410))
      | ~ class_Lattices_Olattice(U_11409) ),
    inference(definitional_conversion,[status(esa)],[f_3052_2]) ).

cnf(f_3052_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_11409,hAPP(hAPP(c_Set_Oinsert(U_11409),U_11411),U_11410)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11409),U_11411),c_Big__Operators_Olattice__class_OInf__fin(U_11409,U_11410))
    | U_11410 = c_Orderings_Obot__class_Obot(tc_fun(U_11409,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_11409),U_11411),U_11410))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11409),U_11410))
    | ~ class_Lattices_Olattice(U_11409) ),
    inference(clausify,[status(thm)],[f_3052_3]) ).

fof(f_3053_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_3053_2,plain,
    ! [U_11414,U_11413,U_11412] :
      ( ( ( c_Big__Operators_Olattice__class_OInf__fin(U_11412,hAPP(hAPP(c_Set_Oinsert(U_11412),U_11414),U_11413)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11412),U_11414),c_Big__Operators_Olattice__class_OInf__fin(U_11412,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11412,tc_HOL_Obool)),U_11413),hAPP(hAPP(c_Set_Oinsert(U_11412),U_11414),c_Orderings_Obot__class_Obot(tc_fun(U_11412,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11412,tc_HOL_Obool)),U_11413),hAPP(hAPP(c_Set_Oinsert(U_11412),U_11414),c_Orderings_Obot__class_Obot(tc_fun(U_11412,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_11412,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OInf__fin(U_11412,hAPP(hAPP(c_Set_Oinsert(U_11412),U_11414),U_11413)) = U_11414
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11412,tc_HOL_Obool)),U_11413),hAPP(hAPP(c_Set_Oinsert(U_11412),U_11414),c_Orderings_Obot__class_Obot(tc_fun(U_11412,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_11412,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11412),U_11413))
      | ~ class_Lattices_Olattice(U_11412) ),
    inference(variable_rename,[status(thm)],[f_3053_1]) ).

fof(f_3053_3,plain,
    ( ! [U_11412,U_11413,U_11414] :
        ( c_Big__Operators_Olattice__class_OInf__fin(U_11412,hAPP(hAPP(c_Set_Oinsert(U_11412),U_11414),U_11413)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11412),U_11414),c_Big__Operators_Olattice__class_OInf__fin(U_11412,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11412,tc_HOL_Obool)),U_11413),hAPP(hAPP(c_Set_Oinsert(U_11412),U_11414),c_Orderings_Obot__class_Obot(tc_fun(U_11412,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11412,tc_HOL_Obool)),U_11413),hAPP(hAPP(c_Set_Oinsert(U_11412),U_11414),c_Orderings_Obot__class_Obot(tc_fun(U_11412,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_11412,tc_HOL_Obool))
        | ~ sP822(U_11412,U_11413,U_11414) )
    & ! [U_11412,U_11413,U_11414] :
        ( c_Big__Operators_Olattice__class_OInf__fin(U_11412,hAPP(hAPP(c_Set_Oinsert(U_11412),U_11414),U_11413)) = U_11414
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11412,tc_HOL_Obool)),U_11413),hAPP(hAPP(c_Set_Oinsert(U_11412),U_11414),c_Orderings_Obot__class_Obot(tc_fun(U_11412,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_11412,tc_HOL_Obool))
        | ~ sP822(U_11412,U_11413,U_11414) )
    & ! [U_11412,U_11413,U_11414] :
        ( sP822(U_11412,U_11413,U_11414)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11412),U_11413))
        | ~ class_Lattices_Olattice(U_11412) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP822])],[f_3053_2]) ).

cnf(f_3053_4,plain,
    ( sP822(U_11412,U_11413,U_11414)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11412),U_11413))
    | ~ class_Lattices_Olattice(U_11412) ),
    inference(clausify,[status(thm)],[f_3053_3]) ).

cnf(f_3053_5,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_11412,hAPP(hAPP(c_Set_Oinsert(U_11412),U_11414),U_11413)) = U_11414
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11412,tc_HOL_Obool)),U_11413),hAPP(hAPP(c_Set_Oinsert(U_11412),U_11414),c_Orderings_Obot__class_Obot(tc_fun(U_11412,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_11412,tc_HOL_Obool))
    | ~ sP822(U_11412,U_11413,U_11414) ),
    inference(clausify,[status(thm)],[f_3053_3]) ).

cnf(f_3053_6,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_11412,hAPP(hAPP(c_Set_Oinsert(U_11412),U_11414),U_11413)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11412),U_11414),c_Big__Operators_Olattice__class_OInf__fin(U_11412,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11412,tc_HOL_Obool)),U_11413),hAPP(hAPP(c_Set_Oinsert(U_11412),U_11414),c_Orderings_Obot__class_Obot(tc_fun(U_11412,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11412,tc_HOL_Obool)),U_11413),hAPP(hAPP(c_Set_Oinsert(U_11412),U_11414),c_Orderings_Obot__class_Obot(tc_fun(U_11412,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_11412,tc_HOL_Obool))
    | ~ sP822(U_11412,U_11413,U_11414) ),
    inference(clausify,[status(thm)],[f_3053_3]) ).

fof(f_3054_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_3054_2,plain,
    ! [U_11419,U_11418,U_11417,U_11416,U_11415] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11416,U_11415),U_11419),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11416,tc_HOL_Obool)),U_11417),U_11418)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11415),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11416,U_11415),U_11419),U_11417)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11416,U_11415),U_11419),U_11418))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11416,tc_HOL_Obool)),U_11417),U_11418) != c_Orderings_Obot__class_Obot(tc_fun(U_11416,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11416),U_11418))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11416),U_11417))
      | ~ class_Groups_Ocomm__monoid__mult(U_11415) ),
    inference(variable_rename,[status(thm)],[f_3054_1]) ).

fof(f_3054_3,plain,
    ! [U_11418,U_11417,U_11415,U_11416,U_11419] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11416,U_11415),U_11419),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11416,tc_HOL_Obool)),U_11417),U_11418)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11415),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11416,U_11415),U_11419),U_11417)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11416,U_11415),U_11419),U_11418))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11416,tc_HOL_Obool)),U_11417),U_11418) != c_Orderings_Obot__class_Obot(tc_fun(U_11416,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11416),U_11418))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11416),U_11417))
      | ~ class_Groups_Ocomm__monoid__mult(U_11415) ),
    inference(definitional_conversion,[status(esa)],[f_3054_2]) ).

cnf(f_3054_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11416,U_11415),U_11419),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11416,tc_HOL_Obool)),U_11417),U_11418)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11415),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11416,U_11415),U_11419),U_11417)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11416,U_11415),U_11419),U_11418))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11416,tc_HOL_Obool)),U_11417),U_11418) != c_Orderings_Obot__class_Obot(tc_fun(U_11416,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11416),U_11418))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11416),U_11417))
    | ~ class_Groups_Ocomm__monoid__mult(U_11415) ),
    inference(clausify,[status(thm)],[f_3054_3]) ).

fof(f_3055_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_3055_2,plain,
    ! [U_11424,U_11423,U_11422,U_11421,U_11420] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11421,U_11420),U_11424),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11421,tc_HOL_Obool)),U_11422),U_11423)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11420),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11421,U_11420),U_11424),U_11422)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11421,U_11420),U_11424),U_11423))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11421,tc_HOL_Obool)),U_11422),U_11423) != c_Orderings_Obot__class_Obot(tc_fun(U_11421,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11421),U_11423))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11421),U_11422))
      | ~ class_Groups_Ocomm__monoid__mult(U_11420) ),
    inference(variable_rename,[status(thm)],[f_3055_1]) ).

fof(f_3055_3,plain,
    ! [U_11421,U_11420,U_11422,U_11423,U_11424] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11421,U_11420),U_11424),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11421,tc_HOL_Obool)),U_11422),U_11423)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11420),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11421,U_11420),U_11424),U_11422)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11421,U_11420),U_11424),U_11423))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11421,tc_HOL_Obool)),U_11422),U_11423) != c_Orderings_Obot__class_Obot(tc_fun(U_11421,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11421),U_11423))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11421),U_11422))
      | ~ class_Groups_Ocomm__monoid__mult(U_11420) ),
    inference(definitional_conversion,[status(esa)],[f_3055_2]) ).

cnf(f_3055_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11421,U_11420),U_11424),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11421,tc_HOL_Obool)),U_11422),U_11423)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11420),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11421,U_11420),U_11424),U_11422)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11421,U_11420),U_11424),U_11423))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11421,tc_HOL_Obool)),U_11422),U_11423) != c_Orderings_Obot__class_Obot(tc_fun(U_11421,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11421),U_11423))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11421),U_11422))
    | ~ class_Groups_Ocomm__monoid__mult(U_11420) ),
    inference(clausify,[status(thm)],[f_3055_3]) ).

fof(f_3056_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_3056_2,plain,
    ! [U_11427,U_11426,U_11425] :
      ( hAPP(c_Finite__Set_Ocard(U_11425),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11425,tc_HOL_Obool)),U_11426),U_11427)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11425),U_11426)),hAPP(c_Finite__Set_Ocard(U_11425),U_11427))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11425,tc_HOL_Obool)),U_11426),U_11427) != c_Orderings_Obot__class_Obot(tc_fun(U_11425,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11425),U_11427))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11425),U_11426)) ),
    inference(variable_rename,[status(thm)],[f_3056_1]) ).

fof(f_3056_3,plain,
    ! [U_11426,U_11425,U_11427] :
      ( hAPP(c_Finite__Set_Ocard(U_11425),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11425,tc_HOL_Obool)),U_11426),U_11427)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11425),U_11426)),hAPP(c_Finite__Set_Ocard(U_11425),U_11427))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11425,tc_HOL_Obool)),U_11426),U_11427) != c_Orderings_Obot__class_Obot(tc_fun(U_11425,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11425),U_11427))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11425),U_11426)) ),
    inference(definitional_conversion,[status(esa)],[f_3056_2]) ).

cnf(f_3056_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_11425),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11425,tc_HOL_Obool)),U_11426),U_11427)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11425),U_11426)),hAPP(c_Finite__Set_Ocard(U_11425),U_11427))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11425,tc_HOL_Obool)),U_11426),U_11427) != c_Orderings_Obot__class_Obot(tc_fun(U_11425,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11425),U_11427))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11425),U_11426)) ),
    inference(clausify,[status(thm)],[f_3056_3]) ).

fof(f_3057_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_3057_2,plain,
    ! [U_11430,U_11429,U_11428] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_11428,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11428,tc_HOL_Obool)),U_11429),U_11430)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11428),c_Big__Operators_Olattice__class_OSup__fin(U_11428,U_11429)),c_Big__Operators_Olattice__class_OSup__fin(U_11428,U_11430))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11428,tc_HOL_Obool)),U_11429),U_11430) != c_Orderings_Obot__class_Obot(tc_fun(U_11428,tc_HOL_Obool))
      | U_11430 = c_Orderings_Obot__class_Obot(tc_fun(U_11428,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11428),U_11430))
      | U_11429 = c_Orderings_Obot__class_Obot(tc_fun(U_11428,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11428),U_11429))
      | ~ class_Lattices_Olattice(U_11428) ),
    inference(variable_rename,[status(thm)],[f_3057_1]) ).

fof(f_3057_3,plain,
    ! [U_11428,U_11429,U_11430] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_11428,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11428,tc_HOL_Obool)),U_11429),U_11430)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11428),c_Big__Operators_Olattice__class_OSup__fin(U_11428,U_11429)),c_Big__Operators_Olattice__class_OSup__fin(U_11428,U_11430))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11428,tc_HOL_Obool)),U_11429),U_11430) != c_Orderings_Obot__class_Obot(tc_fun(U_11428,tc_HOL_Obool))
      | U_11430 = c_Orderings_Obot__class_Obot(tc_fun(U_11428,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11428),U_11430))
      | U_11429 = c_Orderings_Obot__class_Obot(tc_fun(U_11428,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11428),U_11429))
      | ~ class_Lattices_Olattice(U_11428) ),
    inference(definitional_conversion,[status(esa)],[f_3057_2]) ).

cnf(f_3057_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_11428,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11428,tc_HOL_Obool)),U_11429),U_11430)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11428),c_Big__Operators_Olattice__class_OSup__fin(U_11428,U_11429)),c_Big__Operators_Olattice__class_OSup__fin(U_11428,U_11430))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11428,tc_HOL_Obool)),U_11429),U_11430) != c_Orderings_Obot__class_Obot(tc_fun(U_11428,tc_HOL_Obool))
    | U_11430 = c_Orderings_Obot__class_Obot(tc_fun(U_11428,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11428),U_11430))
    | U_11429 = c_Orderings_Obot__class_Obot(tc_fun(U_11428,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11428),U_11429))
    | ~ class_Lattices_Olattice(U_11428) ),
    inference(clausify,[status(thm)],[f_3057_3]) ).

fof(f_3058_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_3058_2,plain,
    ! [U_11433,U_11432,U_11431] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11431),c_Big__Operators_Olattice__class_OSup__fin(U_11431,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11431,tc_HOL_Obool)),U_11432),U_11433))),c_Big__Operators_Olattice__class_OSup__fin(U_11431,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11431,tc_HOL_Obool)),U_11432),U_11433))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11431),c_Big__Operators_Olattice__class_OSup__fin(U_11431,U_11432)),c_Big__Operators_Olattice__class_OSup__fin(U_11431,U_11433))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11431,tc_HOL_Obool)),U_11432),U_11433) = c_Orderings_Obot__class_Obot(tc_fun(U_11431,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11431),U_11433))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11431),U_11432))
      | ~ class_Lattices_Olattice(U_11431) ),
    inference(variable_rename,[status(thm)],[f_3058_1]) ).

fof(f_3058_3,plain,
    ! [U_11432,U_11431,U_11433] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11431),c_Big__Operators_Olattice__class_OSup__fin(U_11431,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11431,tc_HOL_Obool)),U_11432),U_11433))),c_Big__Operators_Olattice__class_OSup__fin(U_11431,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11431,tc_HOL_Obool)),U_11432),U_11433))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11431),c_Big__Operators_Olattice__class_OSup__fin(U_11431,U_11432)),c_Big__Operators_Olattice__class_OSup__fin(U_11431,U_11433))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11431,tc_HOL_Obool)),U_11432),U_11433) = c_Orderings_Obot__class_Obot(tc_fun(U_11431,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11431),U_11433))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11431),U_11432))
      | ~ class_Lattices_Olattice(U_11431) ),
    inference(definitional_conversion,[status(esa)],[f_3058_2]) ).

cnf(f_3058_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11431),c_Big__Operators_Olattice__class_OSup__fin(U_11431,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11431,tc_HOL_Obool)),U_11432),U_11433))),c_Big__Operators_Olattice__class_OSup__fin(U_11431,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11431,tc_HOL_Obool)),U_11432),U_11433))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_11431),c_Big__Operators_Olattice__class_OSup__fin(U_11431,U_11432)),c_Big__Operators_Olattice__class_OSup__fin(U_11431,U_11433))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11431,tc_HOL_Obool)),U_11432),U_11433) = c_Orderings_Obot__class_Obot(tc_fun(U_11431,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11431),U_11433))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11431),U_11432))
    | ~ class_Lattices_Olattice(U_11431) ),
    inference(clausify,[status(thm)],[f_3058_3]) ).

fof(f_3059_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_3059_2,plain,
    ! [U_11436,U_11435,U_11434] :
      ( c_Big__Operators_Olinorder__class_OMin(U_11434,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11434,tc_HOL_Obool)),U_11435),U_11436)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11434),c_Big__Operators_Olinorder__class_OMin(U_11434,U_11435)),c_Big__Operators_Olinorder__class_OMin(U_11434,U_11436))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11434,tc_HOL_Obool)),U_11435),U_11436) != c_Orderings_Obot__class_Obot(tc_fun(U_11434,tc_HOL_Obool))
      | U_11436 = c_Orderings_Obot__class_Obot(tc_fun(U_11434,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11434),U_11436))
      | U_11435 = c_Orderings_Obot__class_Obot(tc_fun(U_11434,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11434),U_11435))
      | ~ class_Orderings_Olinorder(U_11434) ),
    inference(variable_rename,[status(thm)],[f_3059_1]) ).

fof(f_3059_3,plain,
    ! [U_11435,U_11434,U_11436] :
      ( c_Big__Operators_Olinorder__class_OMin(U_11434,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11434,tc_HOL_Obool)),U_11435),U_11436)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11434),c_Big__Operators_Olinorder__class_OMin(U_11434,U_11435)),c_Big__Operators_Olinorder__class_OMin(U_11434,U_11436))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11434,tc_HOL_Obool)),U_11435),U_11436) != c_Orderings_Obot__class_Obot(tc_fun(U_11434,tc_HOL_Obool))
      | U_11436 = c_Orderings_Obot__class_Obot(tc_fun(U_11434,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11434),U_11436))
      | U_11435 = c_Orderings_Obot__class_Obot(tc_fun(U_11434,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11434),U_11435))
      | ~ class_Orderings_Olinorder(U_11434) ),
    inference(definitional_conversion,[status(esa)],[f_3059_2]) ).

cnf(f_3059_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_11434,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11434,tc_HOL_Obool)),U_11435),U_11436)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11434),c_Big__Operators_Olinorder__class_OMin(U_11434,U_11435)),c_Big__Operators_Olinorder__class_OMin(U_11434,U_11436))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11434,tc_HOL_Obool)),U_11435),U_11436) != c_Orderings_Obot__class_Obot(tc_fun(U_11434,tc_HOL_Obool))
    | U_11436 = c_Orderings_Obot__class_Obot(tc_fun(U_11434,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11434),U_11436))
    | U_11435 = c_Orderings_Obot__class_Obot(tc_fun(U_11434,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11434),U_11435))
    | ~ class_Orderings_Olinorder(U_11434) ),
    inference(clausify,[status(thm)],[f_3059_3]) ).

fof(f_3060_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_3060_2,plain,
    ! [U_11439,U_11438,U_11437] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11437),c_Big__Operators_Olinorder__class_OMin(U_11437,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11437,tc_HOL_Obool)),U_11438),U_11439))),c_Big__Operators_Olinorder__class_OMin(U_11437,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11437,tc_HOL_Obool)),U_11438),U_11439))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11437),c_Big__Operators_Olinorder__class_OMin(U_11437,U_11438)),c_Big__Operators_Olinorder__class_OMin(U_11437,U_11439))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11437,tc_HOL_Obool)),U_11438),U_11439) = c_Orderings_Obot__class_Obot(tc_fun(U_11437,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11437),U_11439))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11437),U_11438))
      | ~ class_Orderings_Olinorder(U_11437) ),
    inference(variable_rename,[status(thm)],[f_3060_1]) ).

fof(f_3060_3,plain,
    ! [U_11438,U_11437,U_11439] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11437),c_Big__Operators_Olinorder__class_OMin(U_11437,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11437,tc_HOL_Obool)),U_11438),U_11439))),c_Big__Operators_Olinorder__class_OMin(U_11437,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11437,tc_HOL_Obool)),U_11438),U_11439))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11437),c_Big__Operators_Olinorder__class_OMin(U_11437,U_11438)),c_Big__Operators_Olinorder__class_OMin(U_11437,U_11439))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11437,tc_HOL_Obool)),U_11438),U_11439) = c_Orderings_Obot__class_Obot(tc_fun(U_11437,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11437),U_11439))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11437),U_11438))
      | ~ class_Orderings_Olinorder(U_11437) ),
    inference(definitional_conversion,[status(esa)],[f_3060_2]) ).

cnf(f_3060_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11437),c_Big__Operators_Olinorder__class_OMin(U_11437,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11437,tc_HOL_Obool)),U_11438),U_11439))),c_Big__Operators_Olinorder__class_OMin(U_11437,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11437,tc_HOL_Obool)),U_11438),U_11439))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11437),c_Big__Operators_Olinorder__class_OMin(U_11437,U_11438)),c_Big__Operators_Olinorder__class_OMin(U_11437,U_11439))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11437,tc_HOL_Obool)),U_11438),U_11439) = c_Orderings_Obot__class_Obot(tc_fun(U_11437,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11437),U_11439))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11437),U_11438))
    | ~ class_Orderings_Olinorder(U_11437) ),
    inference(clausify,[status(thm)],[f_3060_3]) ).

fof(f_3061_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_3061_2,plain,
    ! [U_11442,U_11441,U_11440] :
      ( c_Big__Operators_Olinorder__class_OMax(U_11440,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11440,tc_HOL_Obool)),U_11441),U_11442)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11440),c_Big__Operators_Olinorder__class_OMax(U_11440,U_11441)),c_Big__Operators_Olinorder__class_OMax(U_11440,U_11442))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11440,tc_HOL_Obool)),U_11441),U_11442) != c_Orderings_Obot__class_Obot(tc_fun(U_11440,tc_HOL_Obool))
      | U_11442 = c_Orderings_Obot__class_Obot(tc_fun(U_11440,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11440),U_11442))
      | U_11441 = c_Orderings_Obot__class_Obot(tc_fun(U_11440,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11440),U_11441))
      | ~ class_Orderings_Olinorder(U_11440) ),
    inference(variable_rename,[status(thm)],[f_3061_1]) ).

fof(f_3061_3,plain,
    ! [U_11441,U_11440,U_11442] :
      ( c_Big__Operators_Olinorder__class_OMax(U_11440,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11440,tc_HOL_Obool)),U_11441),U_11442)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11440),c_Big__Operators_Olinorder__class_OMax(U_11440,U_11441)),c_Big__Operators_Olinorder__class_OMax(U_11440,U_11442))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11440,tc_HOL_Obool)),U_11441),U_11442) != c_Orderings_Obot__class_Obot(tc_fun(U_11440,tc_HOL_Obool))
      | U_11442 = c_Orderings_Obot__class_Obot(tc_fun(U_11440,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11440),U_11442))
      | U_11441 = c_Orderings_Obot__class_Obot(tc_fun(U_11440,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11440),U_11441))
      | ~ class_Orderings_Olinorder(U_11440) ),
    inference(definitional_conversion,[status(esa)],[f_3061_2]) ).

cnf(f_3061_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_11440,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11440,tc_HOL_Obool)),U_11441),U_11442)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11440),c_Big__Operators_Olinorder__class_OMax(U_11440,U_11441)),c_Big__Operators_Olinorder__class_OMax(U_11440,U_11442))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11440,tc_HOL_Obool)),U_11441),U_11442) != c_Orderings_Obot__class_Obot(tc_fun(U_11440,tc_HOL_Obool))
    | U_11442 = c_Orderings_Obot__class_Obot(tc_fun(U_11440,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11440),U_11442))
    | U_11441 = c_Orderings_Obot__class_Obot(tc_fun(U_11440,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11440),U_11441))
    | ~ class_Orderings_Olinorder(U_11440) ),
    inference(clausify,[status(thm)],[f_3061_3]) ).

fof(f_3062_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_3062_2,plain,
    ! [U_11445,U_11444,U_11443] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11443),c_Big__Operators_Olinorder__class_OMax(U_11443,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11443,tc_HOL_Obool)),U_11444),U_11445))),c_Big__Operators_Olinorder__class_OMax(U_11443,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11443,tc_HOL_Obool)),U_11444),U_11445))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11443),c_Big__Operators_Olinorder__class_OMax(U_11443,U_11444)),c_Big__Operators_Olinorder__class_OMax(U_11443,U_11445))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11443,tc_HOL_Obool)),U_11444),U_11445) = c_Orderings_Obot__class_Obot(tc_fun(U_11443,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11443),U_11445))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11443),U_11444))
      | ~ class_Orderings_Olinorder(U_11443) ),
    inference(variable_rename,[status(thm)],[f_3062_1]) ).

fof(f_3062_3,plain,
    ! [U_11445,U_11443,U_11444] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11443),c_Big__Operators_Olinorder__class_OMax(U_11443,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11443,tc_HOL_Obool)),U_11444),U_11445))),c_Big__Operators_Olinorder__class_OMax(U_11443,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11443,tc_HOL_Obool)),U_11444),U_11445))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11443),c_Big__Operators_Olinorder__class_OMax(U_11443,U_11444)),c_Big__Operators_Olinorder__class_OMax(U_11443,U_11445))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11443,tc_HOL_Obool)),U_11444),U_11445) = c_Orderings_Obot__class_Obot(tc_fun(U_11443,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11443),U_11445))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11443),U_11444))
      | ~ class_Orderings_Olinorder(U_11443) ),
    inference(definitional_conversion,[status(esa)],[f_3062_2]) ).

cnf(f_3062_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11443),c_Big__Operators_Olinorder__class_OMax(U_11443,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11443,tc_HOL_Obool)),U_11444),U_11445))),c_Big__Operators_Olinorder__class_OMax(U_11443,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11443,tc_HOL_Obool)),U_11444),U_11445))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11443),c_Big__Operators_Olinorder__class_OMax(U_11443,U_11444)),c_Big__Operators_Olinorder__class_OMax(U_11443,U_11445))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11443,tc_HOL_Obool)),U_11444),U_11445) = c_Orderings_Obot__class_Obot(tc_fun(U_11443,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11443),U_11445))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11443),U_11444))
    | ~ class_Orderings_Olinorder(U_11443) ),
    inference(clausify,[status(thm)],[f_3062_3]) ).

fof(f_3063_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_3063_2,plain,
    ! [U_11448,U_11447,U_11446] :
      ( c_Big__Operators_Olattice_OInf__fin(U_11446,c_Orderings_Oord__class_Omin(U_11446),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11446,tc_HOL_Obool)),U_11447),U_11448)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11446),c_Big__Operators_Olattice_OInf__fin(U_11446,c_Orderings_Oord__class_Omin(U_11446),U_11447)),c_Big__Operators_Olattice_OInf__fin(U_11446,c_Orderings_Oord__class_Omin(U_11446),U_11448))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11446,tc_HOL_Obool)),U_11447),U_11448) != c_Orderings_Obot__class_Obot(tc_fun(U_11446,tc_HOL_Obool))
      | U_11448 = c_Orderings_Obot__class_Obot(tc_fun(U_11446,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11446),U_11448))
      | U_11447 = c_Orderings_Obot__class_Obot(tc_fun(U_11446,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11446),U_11447))
      | ~ class_Orderings_Olinorder(U_11446) ),
    inference(variable_rename,[status(thm)],[f_3063_1]) ).

fof(f_3063_3,plain,
    ! [U_11447,U_11446,U_11448] :
      ( c_Big__Operators_Olattice_OInf__fin(U_11446,c_Orderings_Oord__class_Omin(U_11446),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11446,tc_HOL_Obool)),U_11447),U_11448)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11446),c_Big__Operators_Olattice_OInf__fin(U_11446,c_Orderings_Oord__class_Omin(U_11446),U_11447)),c_Big__Operators_Olattice_OInf__fin(U_11446,c_Orderings_Oord__class_Omin(U_11446),U_11448))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11446,tc_HOL_Obool)),U_11447),U_11448) != c_Orderings_Obot__class_Obot(tc_fun(U_11446,tc_HOL_Obool))
      | U_11448 = c_Orderings_Obot__class_Obot(tc_fun(U_11446,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11446),U_11448))
      | U_11447 = c_Orderings_Obot__class_Obot(tc_fun(U_11446,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11446),U_11447))
      | ~ class_Orderings_Olinorder(U_11446) ),
    inference(definitional_conversion,[status(esa)],[f_3063_2]) ).

cnf(f_3063_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_11446,c_Orderings_Oord__class_Omin(U_11446),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11446,tc_HOL_Obool)),U_11447),U_11448)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11446),c_Big__Operators_Olattice_OInf__fin(U_11446,c_Orderings_Oord__class_Omin(U_11446),U_11447)),c_Big__Operators_Olattice_OInf__fin(U_11446,c_Orderings_Oord__class_Omin(U_11446),U_11448))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11446,tc_HOL_Obool)),U_11447),U_11448) != c_Orderings_Obot__class_Obot(tc_fun(U_11446,tc_HOL_Obool))
    | U_11448 = c_Orderings_Obot__class_Obot(tc_fun(U_11446,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11446),U_11448))
    | U_11447 = c_Orderings_Obot__class_Obot(tc_fun(U_11446,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11446),U_11447))
    | ~ class_Orderings_Olinorder(U_11446) ),
    inference(clausify,[status(thm)],[f_3063_3]) ).

fof(f_3064_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_3064_2,plain,
    ! [U_11451,U_11450,U_11449] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11449),c_Big__Operators_Olattice_OInf__fin(U_11449,c_Orderings_Oord__class_Omin(U_11449),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11449,tc_HOL_Obool)),U_11450),U_11451))),c_Big__Operators_Olattice_OInf__fin(U_11449,c_Orderings_Oord__class_Omin(U_11449),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11449,tc_HOL_Obool)),U_11450),U_11451))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11449),c_Big__Operators_Olattice_OInf__fin(U_11449,c_Orderings_Oord__class_Omin(U_11449),U_11450)),c_Big__Operators_Olattice_OInf__fin(U_11449,c_Orderings_Oord__class_Omin(U_11449),U_11451))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11449,tc_HOL_Obool)),U_11450),U_11451) = c_Orderings_Obot__class_Obot(tc_fun(U_11449,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11449),U_11451))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11449),U_11450))
      | ~ class_Orderings_Olinorder(U_11449) ),
    inference(variable_rename,[status(thm)],[f_3064_1]) ).

fof(f_3064_3,plain,
    ! [U_11450,U_11449,U_11451] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11449),c_Big__Operators_Olattice_OInf__fin(U_11449,c_Orderings_Oord__class_Omin(U_11449),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11449,tc_HOL_Obool)),U_11450),U_11451))),c_Big__Operators_Olattice_OInf__fin(U_11449,c_Orderings_Oord__class_Omin(U_11449),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11449,tc_HOL_Obool)),U_11450),U_11451))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11449),c_Big__Operators_Olattice_OInf__fin(U_11449,c_Orderings_Oord__class_Omin(U_11449),U_11450)),c_Big__Operators_Olattice_OInf__fin(U_11449,c_Orderings_Oord__class_Omin(U_11449),U_11451))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11449,tc_HOL_Obool)),U_11450),U_11451) = c_Orderings_Obot__class_Obot(tc_fun(U_11449,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11449),U_11451))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11449),U_11450))
      | ~ class_Orderings_Olinorder(U_11449) ),
    inference(definitional_conversion,[status(esa)],[f_3064_2]) ).

cnf(f_3064_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11449),c_Big__Operators_Olattice_OInf__fin(U_11449,c_Orderings_Oord__class_Omin(U_11449),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11449,tc_HOL_Obool)),U_11450),U_11451))),c_Big__Operators_Olattice_OInf__fin(U_11449,c_Orderings_Oord__class_Omin(U_11449),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11449,tc_HOL_Obool)),U_11450),U_11451))) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11449),c_Big__Operators_Olattice_OInf__fin(U_11449,c_Orderings_Oord__class_Omin(U_11449),U_11450)),c_Big__Operators_Olattice_OInf__fin(U_11449,c_Orderings_Oord__class_Omin(U_11449),U_11451))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11449,tc_HOL_Obool)),U_11450),U_11451) = c_Orderings_Obot__class_Obot(tc_fun(U_11449,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11449),U_11451))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11449),U_11450))
    | ~ class_Orderings_Olinorder(U_11449) ),
    inference(clausify,[status(thm)],[f_3064_3]) ).

fof(f_3065_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_3065_2,plain,
    ! [U_11454,U_11453,U_11452] :
      ( c_Big__Operators_Olattice_OSup__fin(U_11452,c_Orderings_Oord__class_Omax(U_11452),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11452,tc_HOL_Obool)),U_11453),U_11454)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11452),c_Big__Operators_Olattice_OSup__fin(U_11452,c_Orderings_Oord__class_Omax(U_11452),U_11453)),c_Big__Operators_Olattice_OSup__fin(U_11452,c_Orderings_Oord__class_Omax(U_11452),U_11454))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11452,tc_HOL_Obool)),U_11453),U_11454) != c_Orderings_Obot__class_Obot(tc_fun(U_11452,tc_HOL_Obool))
      | U_11454 = c_Orderings_Obot__class_Obot(tc_fun(U_11452,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11452),U_11454))
      | U_11453 = c_Orderings_Obot__class_Obot(tc_fun(U_11452,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11452),U_11453))
      | ~ class_Orderings_Olinorder(U_11452) ),
    inference(variable_rename,[status(thm)],[f_3065_1]) ).

fof(f_3065_3,plain,
    ! [U_11453,U_11452,U_11454] :
      ( c_Big__Operators_Olattice_OSup__fin(U_11452,c_Orderings_Oord__class_Omax(U_11452),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11452,tc_HOL_Obool)),U_11453),U_11454)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11452),c_Big__Operators_Olattice_OSup__fin(U_11452,c_Orderings_Oord__class_Omax(U_11452),U_11453)),c_Big__Operators_Olattice_OSup__fin(U_11452,c_Orderings_Oord__class_Omax(U_11452),U_11454))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11452,tc_HOL_Obool)),U_11453),U_11454) != c_Orderings_Obot__class_Obot(tc_fun(U_11452,tc_HOL_Obool))
      | U_11454 = c_Orderings_Obot__class_Obot(tc_fun(U_11452,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11452),U_11454))
      | U_11453 = c_Orderings_Obot__class_Obot(tc_fun(U_11452,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11452),U_11453))
      | ~ class_Orderings_Olinorder(U_11452) ),
    inference(definitional_conversion,[status(esa)],[f_3065_2]) ).

cnf(f_3065_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_11452,c_Orderings_Oord__class_Omax(U_11452),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11452,tc_HOL_Obool)),U_11453),U_11454)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11452),c_Big__Operators_Olattice_OSup__fin(U_11452,c_Orderings_Oord__class_Omax(U_11452),U_11453)),c_Big__Operators_Olattice_OSup__fin(U_11452,c_Orderings_Oord__class_Omax(U_11452),U_11454))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11452,tc_HOL_Obool)),U_11453),U_11454) != c_Orderings_Obot__class_Obot(tc_fun(U_11452,tc_HOL_Obool))
    | U_11454 = c_Orderings_Obot__class_Obot(tc_fun(U_11452,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11452),U_11454))
    | U_11453 = c_Orderings_Obot__class_Obot(tc_fun(U_11452,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11452),U_11453))
    | ~ class_Orderings_Olinorder(U_11452) ),
    inference(clausify,[status(thm)],[f_3065_3]) ).

fof(f_3066_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_3066_2,plain,
    ! [U_11457,U_11456,U_11455] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11455),c_Big__Operators_Olattice_OSup__fin(U_11455,c_Orderings_Oord__class_Omax(U_11455),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11455,tc_HOL_Obool)),U_11456),U_11457))),c_Big__Operators_Olattice_OSup__fin(U_11455,c_Orderings_Oord__class_Omax(U_11455),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11455,tc_HOL_Obool)),U_11456),U_11457))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11455),c_Big__Operators_Olattice_OSup__fin(U_11455,c_Orderings_Oord__class_Omax(U_11455),U_11456)),c_Big__Operators_Olattice_OSup__fin(U_11455,c_Orderings_Oord__class_Omax(U_11455),U_11457))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11455,tc_HOL_Obool)),U_11456),U_11457) = c_Orderings_Obot__class_Obot(tc_fun(U_11455,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11455),U_11457))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11455),U_11456))
      | ~ class_Orderings_Olinorder(U_11455) ),
    inference(variable_rename,[status(thm)],[f_3066_1]) ).

fof(f_3066_3,plain,
    ! [U_11456,U_11455,U_11457] :
      ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11455),c_Big__Operators_Olattice_OSup__fin(U_11455,c_Orderings_Oord__class_Omax(U_11455),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11455,tc_HOL_Obool)),U_11456),U_11457))),c_Big__Operators_Olattice_OSup__fin(U_11455,c_Orderings_Oord__class_Omax(U_11455),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11455,tc_HOL_Obool)),U_11456),U_11457))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11455),c_Big__Operators_Olattice_OSup__fin(U_11455,c_Orderings_Oord__class_Omax(U_11455),U_11456)),c_Big__Operators_Olattice_OSup__fin(U_11455,c_Orderings_Oord__class_Omax(U_11455),U_11457))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11455,tc_HOL_Obool)),U_11456),U_11457) = c_Orderings_Obot__class_Obot(tc_fun(U_11455,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11455),U_11457))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11455),U_11456))
      | ~ class_Orderings_Olinorder(U_11455) ),
    inference(definitional_conversion,[status(esa)],[f_3066_2]) ).

cnf(f_3066_4,plain,
    ( hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11455),c_Big__Operators_Olattice_OSup__fin(U_11455,c_Orderings_Oord__class_Omax(U_11455),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11455,tc_HOL_Obool)),U_11456),U_11457))),c_Big__Operators_Olattice_OSup__fin(U_11455,c_Orderings_Oord__class_Omax(U_11455),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11455,tc_HOL_Obool)),U_11456),U_11457))) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11455),c_Big__Operators_Olattice_OSup__fin(U_11455,c_Orderings_Oord__class_Omax(U_11455),U_11456)),c_Big__Operators_Olattice_OSup__fin(U_11455,c_Orderings_Oord__class_Omax(U_11455),U_11457))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11455,tc_HOL_Obool)),U_11456),U_11457) = c_Orderings_Obot__class_Obot(tc_fun(U_11455,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11455),U_11457))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11455),U_11456))
    | ~ class_Orderings_Olinorder(U_11455) ),
    inference(clausify,[status(thm)],[f_3066_3]) ).

fof(f_3067_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_3067_2,plain,
    ! [U_11460,U_11459,U_11458] :
      ( c_Wellfounded_Owf(U_11458,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11458,U_11458),tc_HOL_Obool)),U_11459),U_11460))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11458,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_11458,U_11458),U_11459)),hAPP(c_Relation_ORange(U_11458,U_11458),U_11460)) != c_Orderings_Obot__class_Obot(tc_fun(U_11458,tc_HOL_Obool))
      | ~ c_Wellfounded_Owf(U_11458,U_11460)
      | ~ c_Wellfounded_Owf(U_11458,U_11459) ),
    inference(variable_rename,[status(thm)],[f_3067_1]) ).

fof(f_3067_3,plain,
    ! [U_11459,U_11460,U_11458] :
      ( c_Wellfounded_Owf(U_11458,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11458,U_11458),tc_HOL_Obool)),U_11459),U_11460))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11458,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_11458,U_11458),U_11459)),hAPP(c_Relation_ORange(U_11458,U_11458),U_11460)) != c_Orderings_Obot__class_Obot(tc_fun(U_11458,tc_HOL_Obool))
      | ~ c_Wellfounded_Owf(U_11458,U_11460)
      | ~ c_Wellfounded_Owf(U_11458,U_11459) ),
    inference(definitional_conversion,[status(esa)],[f_3067_2]) ).

cnf(f_3067_4,plain,
    ( c_Wellfounded_Owf(U_11458,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_11458,U_11458),tc_HOL_Obool)),U_11459),U_11460))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11458,tc_HOL_Obool)),hAPP(c_Relation_ODomain(U_11458,U_11458),U_11459)),hAPP(c_Relation_ORange(U_11458,U_11458),U_11460)) != c_Orderings_Obot__class_Obot(tc_fun(U_11458,tc_HOL_Obool))
    | ~ c_Wellfounded_Owf(U_11458,U_11460)
    | ~ c_Wellfounded_Owf(U_11458,U_11459) ),
    inference(clausify,[status(thm)],[f_3067_3]) ).

fof(f_3068_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_3068_2,plain,
    ! [U_11463,U_11462,U_11461] :
      ( ( ( c_Big__Operators_Olattice__class_OInf__fin(U_11461,U_11462) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11461),U_11463),c_Big__Operators_Olattice__class_OInf__fin(U_11461,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11461,tc_HOL_Obool)),U_11462),hAPP(hAPP(c_Set_Oinsert(U_11461),U_11463),c_Orderings_Obot__class_Obot(tc_fun(U_11461,tc_HOL_Obool))))))
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11461,tc_HOL_Obool)),U_11462),hAPP(hAPP(c_Set_Oinsert(U_11461),U_11463),c_Orderings_Obot__class_Obot(tc_fun(U_11461,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_11461,tc_HOL_Obool)) )
        & ( c_Big__Operators_Olattice__class_OInf__fin(U_11461,U_11462) = U_11463
          | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11461,tc_HOL_Obool)),U_11462),hAPP(hAPP(c_Set_Oinsert(U_11461),U_11463),c_Orderings_Obot__class_Obot(tc_fun(U_11461,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_11461,tc_HOL_Obool)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_11461),U_11463),U_11462))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11461),U_11462))
      | ~ class_Lattices_Olattice(U_11461) ),
    inference(variable_rename,[status(thm)],[f_3068_1]) ).

fof(f_3068_3,plain,
    ( ! [U_11461,U_11462,U_11463] :
        ( c_Big__Operators_Olattice__class_OInf__fin(U_11461,U_11462) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11461),U_11463),c_Big__Operators_Olattice__class_OInf__fin(U_11461,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11461,tc_HOL_Obool)),U_11462),hAPP(hAPP(c_Set_Oinsert(U_11461),U_11463),c_Orderings_Obot__class_Obot(tc_fun(U_11461,tc_HOL_Obool))))))
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11461,tc_HOL_Obool)),U_11462),hAPP(hAPP(c_Set_Oinsert(U_11461),U_11463),c_Orderings_Obot__class_Obot(tc_fun(U_11461,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_11461,tc_HOL_Obool))
        | ~ sP823(U_11461,U_11462,U_11463) )
    & ! [U_11461,U_11462,U_11463] :
        ( c_Big__Operators_Olattice__class_OInf__fin(U_11461,U_11462) = U_11463
        | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11461,tc_HOL_Obool)),U_11462),hAPP(hAPP(c_Set_Oinsert(U_11461),U_11463),c_Orderings_Obot__class_Obot(tc_fun(U_11461,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_11461,tc_HOL_Obool))
        | ~ sP823(U_11461,U_11462,U_11463) )
    & ! [U_11461,U_11462,U_11463] :
        ( sP823(U_11461,U_11462,U_11463)
        | ~ hBOOL(hAPP(hAPP(c_member(U_11461),U_11463),U_11462))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11461),U_11462))
        | ~ class_Lattices_Olattice(U_11461) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP823])],[f_3068_2]) ).

cnf(f_3068_4,plain,
    ( sP823(U_11461,U_11462,U_11463)
    | ~ hBOOL(hAPP(hAPP(c_member(U_11461),U_11463),U_11462))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11461),U_11462))
    | ~ class_Lattices_Olattice(U_11461) ),
    inference(clausify,[status(thm)],[f_3068_3]) ).

cnf(f_3068_5,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_11461,U_11462) = U_11463
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11461,tc_HOL_Obool)),U_11462),hAPP(hAPP(c_Set_Oinsert(U_11461),U_11463),c_Orderings_Obot__class_Obot(tc_fun(U_11461,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(U_11461,tc_HOL_Obool))
    | ~ sP823(U_11461,U_11462,U_11463) ),
    inference(clausify,[status(thm)],[f_3068_3]) ).

cnf(f_3068_6,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_11461,U_11462) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11461),U_11463),c_Big__Operators_Olattice__class_OInf__fin(U_11461,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11461,tc_HOL_Obool)),U_11462),hAPP(hAPP(c_Set_Oinsert(U_11461),U_11463),c_Orderings_Obot__class_Obot(tc_fun(U_11461,tc_HOL_Obool))))))
    | hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11461,tc_HOL_Obool)),U_11462),hAPP(hAPP(c_Set_Oinsert(U_11461),U_11463),c_Orderings_Obot__class_Obot(tc_fun(U_11461,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_11461,tc_HOL_Obool))
    | ~ sP823(U_11461,U_11462,U_11463) ),
    inference(clausify,[status(thm)],[f_3068_3]) ).

fof(f_3069_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_3069_2,plain,
    ! [U_11466,U_11465,U_11464] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11464),c_Big__Operators_Olattice__class_OSup__fin(U_11464,U_11465)),c_Big__Operators_Olattice__class_OSup__fin(U_11464,U_11466)) = c_Big__Operators_Olattice__class_OSup__fin(U_11464,hAPP(c_Set_OCollect(U_11464),hAPP(hAPP(c_COMBB(tc_fun(U_11464,tc_HOL_Obool),tc_HOL_Obool,U_11464),c_HOL_OEx(U_11464)),hAPP(hAPP(c_COMBB(tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool)),tc_fun(U_11464,tc_HOL_Obool),U_11464),hAPP(c_COMBB(tc_fun(U_11464,tc_HOL_Obool),tc_HOL_Obool,U_11464),c_HOL_OEx(U_11464))),hAPP(hAPP(c_COMBC(U_11464,tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool)),tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11464,tc_fun(tc_fun(U_11464,tc_HOL_Obool),tc_fun(U_11464,tc_HOL_Obool))),tc_fun(tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool)),tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool))),U_11464),c_COMBS(U_11464,tc_fun(U_11464,tc_HOL_Obool),tc_fun(U_11464,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11464,tc_fun(U_11464,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_11464,tc_fun(tc_fun(U_11464,tc_HOL_Obool),tc_fun(U_11464,tc_HOL_Obool))),U_11464),hAPP(c_COMBB(tc_fun(U_11464,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11464,tc_HOL_Obool),tc_fun(U_11464,tc_HOL_Obool)),U_11464),c_COMBS(U_11464,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool)),tc_fun(U_11464,tc_fun(U_11464,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_11464),hAPP(c_COMBB(tc_fun(U_11464,tc_HOL_Obool),tc_fun(U_11464,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11464),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11464),c_fconj))),hAPP(hAPP(c_COMBC(U_11464,tc_fun(U_11464,tc_fun(U_11464,U_11464)),tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11464,U_11464),tc_fun(U_11464,tc_HOL_Obool)),tc_fun(tc_fun(U_11464,tc_fun(U_11464,U_11464)),tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool))),U_11464),c_COMBB(tc_fun(U_11464,U_11464),tc_fun(U_11464,tc_HOL_Obool),U_11464)),hAPP(hAPP(c_COMBB(tc_fun(U_11464,tc_HOL_Obool),tc_fun(tc_fun(U_11464,U_11464),tc_fun(U_11464,tc_HOL_Obool)),U_11464),c_COMBB(U_11464,tc_HOL_Obool,U_11464)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_11464)))))),hAPP(hAPP(c_COMBC(U_11464,tc_fun(U_11464,tc_HOL_Obool),tc_fun(U_11464,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11464,tc_HOL_Obool),tc_fun(U_11464,tc_HOL_Obool)),U_11464),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11464)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11464),c_fconj),hAPP(hAPP(c_COMBC(U_11464,tc_fun(U_11464,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11464)),U_11465)))),hAPP(hAPP(c_COMBC(U_11464,tc_fun(U_11464,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11464)),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_11465 = c_Orderings_Obot__class_Obot(tc_fun(U_11464,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11464),U_11465))
      | ~ class_Lattices_Odistrib__lattice(U_11464) ),
    inference(variable_rename,[status(thm)],[f_3069_1]) ).

fof(f_3069_3,plain,
    ! [U_11464,U_11465,U_11466] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11464),c_Big__Operators_Olattice__class_OSup__fin(U_11464,U_11465)),c_Big__Operators_Olattice__class_OSup__fin(U_11464,U_11466)) = c_Big__Operators_Olattice__class_OSup__fin(U_11464,hAPP(c_Set_OCollect(U_11464),hAPP(hAPP(c_COMBB(tc_fun(U_11464,tc_HOL_Obool),tc_HOL_Obool,U_11464),c_HOL_OEx(U_11464)),hAPP(hAPP(c_COMBB(tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool)),tc_fun(U_11464,tc_HOL_Obool),U_11464),hAPP(c_COMBB(tc_fun(U_11464,tc_HOL_Obool),tc_HOL_Obool,U_11464),c_HOL_OEx(U_11464))),hAPP(hAPP(c_COMBC(U_11464,tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool)),tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11464,tc_fun(tc_fun(U_11464,tc_HOL_Obool),tc_fun(U_11464,tc_HOL_Obool))),tc_fun(tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool)),tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool))),U_11464),c_COMBS(U_11464,tc_fun(U_11464,tc_HOL_Obool),tc_fun(U_11464,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11464,tc_fun(U_11464,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_11464,tc_fun(tc_fun(U_11464,tc_HOL_Obool),tc_fun(U_11464,tc_HOL_Obool))),U_11464),hAPP(c_COMBB(tc_fun(U_11464,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11464,tc_HOL_Obool),tc_fun(U_11464,tc_HOL_Obool)),U_11464),c_COMBS(U_11464,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool)),tc_fun(U_11464,tc_fun(U_11464,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_11464),hAPP(c_COMBB(tc_fun(U_11464,tc_HOL_Obool),tc_fun(U_11464,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11464),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11464),c_fconj))),hAPP(hAPP(c_COMBC(U_11464,tc_fun(U_11464,tc_fun(U_11464,U_11464)),tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11464,U_11464),tc_fun(U_11464,tc_HOL_Obool)),tc_fun(tc_fun(U_11464,tc_fun(U_11464,U_11464)),tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool))),U_11464),c_COMBB(tc_fun(U_11464,U_11464),tc_fun(U_11464,tc_HOL_Obool),U_11464)),hAPP(hAPP(c_COMBB(tc_fun(U_11464,tc_HOL_Obool),tc_fun(tc_fun(U_11464,U_11464),tc_fun(U_11464,tc_HOL_Obool)),U_11464),c_COMBB(U_11464,tc_HOL_Obool,U_11464)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_11464)))))),hAPP(hAPP(c_COMBC(U_11464,tc_fun(U_11464,tc_HOL_Obool),tc_fun(U_11464,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11464,tc_HOL_Obool),tc_fun(U_11464,tc_HOL_Obool)),U_11464),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11464)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11464),c_fconj),hAPP(hAPP(c_COMBC(U_11464,tc_fun(U_11464,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11464)),U_11465)))),hAPP(hAPP(c_COMBC(U_11464,tc_fun(U_11464,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11464)),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_11465 = c_Orderings_Obot__class_Obot(tc_fun(U_11464,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11464),U_11465))
      | ~ class_Lattices_Odistrib__lattice(U_11464) ),
    inference(definitional_conversion,[status(esa)],[f_3069_2]) ).

cnf(f_3069_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11464),c_Big__Operators_Olattice__class_OSup__fin(U_11464,U_11465)),c_Big__Operators_Olattice__class_OSup__fin(U_11464,U_11466)) = c_Big__Operators_Olattice__class_OSup__fin(U_11464,hAPP(c_Set_OCollect(U_11464),hAPP(hAPP(c_COMBB(tc_fun(U_11464,tc_HOL_Obool),tc_HOL_Obool,U_11464),c_HOL_OEx(U_11464)),hAPP(hAPP(c_COMBB(tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool)),tc_fun(U_11464,tc_HOL_Obool),U_11464),hAPP(c_COMBB(tc_fun(U_11464,tc_HOL_Obool),tc_HOL_Obool,U_11464),c_HOL_OEx(U_11464))),hAPP(hAPP(c_COMBC(U_11464,tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool)),tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11464,tc_fun(tc_fun(U_11464,tc_HOL_Obool),tc_fun(U_11464,tc_HOL_Obool))),tc_fun(tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool)),tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool))),U_11464),c_COMBS(U_11464,tc_fun(U_11464,tc_HOL_Obool),tc_fun(U_11464,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11464,tc_fun(U_11464,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_11464,tc_fun(tc_fun(U_11464,tc_HOL_Obool),tc_fun(U_11464,tc_HOL_Obool))),U_11464),hAPP(c_COMBB(tc_fun(U_11464,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11464,tc_HOL_Obool),tc_fun(U_11464,tc_HOL_Obool)),U_11464),c_COMBS(U_11464,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool)),tc_fun(U_11464,tc_fun(U_11464,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_11464),hAPP(c_COMBB(tc_fun(U_11464,tc_HOL_Obool),tc_fun(U_11464,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11464),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11464),c_fconj))),hAPP(hAPP(c_COMBC(U_11464,tc_fun(U_11464,tc_fun(U_11464,U_11464)),tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11464,U_11464),tc_fun(U_11464,tc_HOL_Obool)),tc_fun(tc_fun(U_11464,tc_fun(U_11464,U_11464)),tc_fun(U_11464,tc_fun(U_11464,tc_HOL_Obool))),U_11464),c_COMBB(tc_fun(U_11464,U_11464),tc_fun(U_11464,tc_HOL_Obool),U_11464)),hAPP(hAPP(c_COMBB(tc_fun(U_11464,tc_HOL_Obool),tc_fun(tc_fun(U_11464,U_11464),tc_fun(U_11464,tc_HOL_Obool)),U_11464),c_COMBB(U_11464,tc_HOL_Obool,U_11464)),c_fequal))),c_Lattices_Osemilattice__inf__class_Oinf(U_11464)))))),hAPP(hAPP(c_COMBC(U_11464,tc_fun(U_11464,tc_HOL_Obool),tc_fun(U_11464,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_11464,tc_HOL_Obool),tc_fun(U_11464,tc_HOL_Obool)),U_11464),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_11464)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11464),c_fconj),hAPP(hAPP(c_COMBC(U_11464,tc_fun(U_11464,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11464)),U_11465)))),hAPP(hAPP(c_COMBC(U_11464,tc_fun(U_11464,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11464)),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_11465 = c_Orderings_Obot__class_Obot(tc_fun(U_11464,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11464),U_11465))
    | ~ class_Lattices_Odistrib__lattice(U_11464) ),
    inference(clausify,[status(thm)],[f_3069_3]) ).

fof(f_3070_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_3070_2,plain,
    ! [U_11469,U_11468,U_11467] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11467),U_11469),c_Big__Operators_Olattice__class_OSup__fin(U_11467,U_11468)) = c_Big__Operators_Olattice__class_OSup__fin(U_11467,hAPP(c_Set_OCollect(U_11467),hAPP(hAPP(c_COMBB(tc_fun(U_11467,tc_HOL_Obool),tc_HOL_Obool,U_11467),c_HOL_OEx(U_11467)),hAPP(hAPP(c_COMBC(U_11467,tc_fun(U_11467,tc_HOL_Obool),tc_fun(U_11467,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11467,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11467,tc_HOL_Obool),tc_fun(U_11467,tc_HOL_Obool)),U_11467),c_COMBS(U_11467,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11467,tc_HOL_Obool),tc_fun(U_11467,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11467),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11467),c_fconj)),hAPP(hAPP(c_COMBC(U_11467,tc_fun(U_11467,U_11467),tc_fun(U_11467,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11467,tc_HOL_Obool),tc_fun(tc_fun(U_11467,U_11467),tc_fun(U_11467,tc_HOL_Obool)),U_11467),c_COMBB(U_11467,tc_HOL_Obool,U_11467)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11467),U_11469))))),hAPP(hAPP(c_COMBC(U_11467,tc_fun(U_11467,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11467)),U_11468)))))
      | U_11468 = c_Orderings_Obot__class_Obot(tc_fun(U_11467,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11467),U_11468))
      | ~ class_Lattices_Odistrib__lattice(U_11467) ),
    inference(variable_rename,[status(thm)],[f_3070_1]) ).

fof(f_3070_3,plain,
    ! [U_11467,U_11468,U_11469] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11467),U_11469),c_Big__Operators_Olattice__class_OSup__fin(U_11467,U_11468)) = c_Big__Operators_Olattice__class_OSup__fin(U_11467,hAPP(c_Set_OCollect(U_11467),hAPP(hAPP(c_COMBB(tc_fun(U_11467,tc_HOL_Obool),tc_HOL_Obool,U_11467),c_HOL_OEx(U_11467)),hAPP(hAPP(c_COMBC(U_11467,tc_fun(U_11467,tc_HOL_Obool),tc_fun(U_11467,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11467,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11467,tc_HOL_Obool),tc_fun(U_11467,tc_HOL_Obool)),U_11467),c_COMBS(U_11467,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11467,tc_HOL_Obool),tc_fun(U_11467,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11467),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11467),c_fconj)),hAPP(hAPP(c_COMBC(U_11467,tc_fun(U_11467,U_11467),tc_fun(U_11467,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11467,tc_HOL_Obool),tc_fun(tc_fun(U_11467,U_11467),tc_fun(U_11467,tc_HOL_Obool)),U_11467),c_COMBB(U_11467,tc_HOL_Obool,U_11467)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11467),U_11469))))),hAPP(hAPP(c_COMBC(U_11467,tc_fun(U_11467,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11467)),U_11468)))))
      | U_11468 = c_Orderings_Obot__class_Obot(tc_fun(U_11467,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11467),U_11468))
      | ~ class_Lattices_Odistrib__lattice(U_11467) ),
    inference(definitional_conversion,[status(esa)],[f_3070_2]) ).

cnf(f_3070_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11467),U_11469),c_Big__Operators_Olattice__class_OSup__fin(U_11467,U_11468)) = c_Big__Operators_Olattice__class_OSup__fin(U_11467,hAPP(c_Set_OCollect(U_11467),hAPP(hAPP(c_COMBB(tc_fun(U_11467,tc_HOL_Obool),tc_HOL_Obool,U_11467),c_HOL_OEx(U_11467)),hAPP(hAPP(c_COMBC(U_11467,tc_fun(U_11467,tc_HOL_Obool),tc_fun(U_11467,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11467,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_11467,tc_HOL_Obool),tc_fun(U_11467,tc_HOL_Obool)),U_11467),c_COMBS(U_11467,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11467,tc_HOL_Obool),tc_fun(U_11467,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_11467),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_11467),c_fconj)),hAPP(hAPP(c_COMBC(U_11467,tc_fun(U_11467,U_11467),tc_fun(U_11467,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11467,tc_HOL_Obool),tc_fun(tc_fun(U_11467,U_11467),tc_fun(U_11467,tc_HOL_Obool)),U_11467),c_COMBB(U_11467,tc_HOL_Obool,U_11467)),c_fequal)),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11467),U_11469))))),hAPP(hAPP(c_COMBC(U_11467,tc_fun(U_11467,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11467)),U_11468)))))
    | U_11468 = c_Orderings_Obot__class_Obot(tc_fun(U_11467,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11467),U_11468))
    | ~ class_Lattices_Odistrib__lattice(U_11467) ),
    inference(clausify,[status(thm)],[f_3070_3]) ).

fof(f_3071_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_3071_2,plain,
    ! [U_11473,U_11472,U_11471] :
      ( hAPP(c_Finite__Set_Ocard(U_11471),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11471,tc_HOL_Obool)),U_11472),U_11473)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11471),U_11472)),hAPP(c_Finite__Set_Ocard(U_11471),U_11473))
      | ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & ? [U_11470] : hBOOL(hAPP(hAPP(c_member(U_11471),U_11470),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11471,tc_HOL_Obool)),U_11472),U_11473))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11471),U_11473))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11471),U_11472)) ),
    inference(variable_rename,[status(thm)],[f_3071_1]) ).

fof(f_3071_3,plain,
    ! [U_11473,U_11472,U_11471] :
      ( hAPP(c_Finite__Set_Ocard(U_11471),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11471,tc_HOL_Obool)),U_11472),U_11473)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11471),U_11472)),hAPP(c_Finite__Set_Ocard(U_11471),U_11473))
      | ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & hBOOL(hAPP(hAPP(c_member(U_11471),sK192(U_11473,U_11472,U_11471)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11471,tc_HOL_Obool)),U_11472),U_11473))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11471),U_11473))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11471),U_11472)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK192]),skolemize(U_11470,sK192(U_11473,U_11472,U_11471))],[f_3071_2]) ).

fof(f_3071_4,plain,
    ( ! [U_11472,U_11471,U_11473] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP824(U_11472,U_11471,U_11473) )
    & ! [U_11472,U_11471,U_11473] :
        ( hBOOL(hAPP(hAPP(c_member(U_11471),sK192(U_11473,U_11472,U_11471)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11471,tc_HOL_Obool)),U_11472),U_11473)))
        | ~ sP824(U_11472,U_11471,U_11473) )
    & ! [U_11472,U_11471,U_11473] :
        ( hAPP(c_Finite__Set_Ocard(U_11471),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11471,tc_HOL_Obool)),U_11472),U_11473)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11471),U_11472)),hAPP(c_Finite__Set_Ocard(U_11471),U_11473))
        | sP824(U_11472,U_11471,U_11473)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11471),U_11473))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11471),U_11472)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP824])],[f_3071_3]) ).

cnf(f_3071_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_11471),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11471,tc_HOL_Obool)),U_11472),U_11473)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_11471),U_11472)),hAPP(c_Finite__Set_Ocard(U_11471),U_11473))
    | sP824(U_11472,U_11471,U_11473)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11471),U_11473))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11471),U_11472)) ),
    inference(clausify,[status(thm)],[f_3071_4]) ).

cnf(f_3071_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11471),sK192(U_11473,U_11472,U_11471)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11471,tc_HOL_Obool)),U_11472),U_11473)))
    | ~ sP824(U_11472,U_11471,U_11473) ),
    inference(clausify,[status(thm)],[f_3071_4]) ).

cnf(f_3071_7,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP824(U_11472,U_11471,U_11473) ),
    inference(clausify,[status(thm)],[f_3071_4]) ).

fof(f_3072_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_3072_2,plain,
    ! [U_11479,U_11478,U_11477,U_11476,U_11475] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11476,U_11475),U_11479),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11476,tc_HOL_Obool)),U_11477),U_11478)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11475),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11476,U_11475),U_11479),U_11477)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11476,U_11475),U_11479),U_11478))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11476,U_11475),U_11479),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11476,tc_HOL_Obool)),U_11477),U_11478)))
      | ? [U_11474] :
          ( hAPP(U_11479,U_11474) = c_Groups_Ozero__class_Ozero(U_11475)
          & hBOOL(hAPP(hAPP(c_member(U_11476),U_11474),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11476,tc_HOL_Obool)),U_11477),U_11478))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11476),U_11478))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11476),U_11477))
      | ~ class_Fields_Ofield(U_11475) ),
    inference(variable_rename,[status(thm)],[f_3072_1]) ).

fof(f_3072_3,plain,
    ! [U_11479,U_11478,U_11477,U_11476,U_11475] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11476,U_11475),U_11479),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11476,tc_HOL_Obool)),U_11477),U_11478)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11475),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11476,U_11475),U_11479),U_11477)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11476,U_11475),U_11479),U_11478))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11476,U_11475),U_11479),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11476,tc_HOL_Obool)),U_11477),U_11478)))
      | ( hAPP(U_11479,sK193(U_11479,U_11478,U_11477,U_11476,U_11475)) = c_Groups_Ozero__class_Ozero(U_11475)
        & hBOOL(hAPP(hAPP(c_member(U_11476),sK193(U_11479,U_11478,U_11477,U_11476,U_11475)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11476,tc_HOL_Obool)),U_11477),U_11478))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11476),U_11478))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11476),U_11477))
      | ~ class_Fields_Ofield(U_11475) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK193]),skolemize(U_11474,sK193(U_11479,U_11478,U_11477,U_11476,U_11475))],[f_3072_2]) ).

fof(f_3072_4,plain,
    ( ! [U_11476,U_11475,U_11477,U_11478,U_11479] :
        ( hAPP(U_11479,sK193(U_11479,U_11478,U_11477,U_11476,U_11475)) = c_Groups_Ozero__class_Ozero(U_11475)
        | ~ sP825(U_11476,U_11475,U_11477,U_11478,U_11479) )
    & ! [U_11476,U_11475,U_11477,U_11478,U_11479] :
        ( hBOOL(hAPP(hAPP(c_member(U_11476),sK193(U_11479,U_11478,U_11477,U_11476,U_11475)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11476,tc_HOL_Obool)),U_11477),U_11478)))
        | ~ sP825(U_11476,U_11475,U_11477,U_11478,U_11479) )
    & ! [U_11476,U_11475,U_11477,U_11478,U_11479] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11476,U_11475),U_11479),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11476,tc_HOL_Obool)),U_11477),U_11478)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11475),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11476,U_11475),U_11479),U_11477)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11476,U_11475),U_11479),U_11478))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11476,U_11475),U_11479),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11476,tc_HOL_Obool)),U_11477),U_11478)))
        | sP825(U_11476,U_11475,U_11477,U_11478,U_11479)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11476),U_11478))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11476),U_11477))
        | ~ class_Fields_Ofield(U_11475) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP825])],[f_3072_3]) ).

cnf(f_3072_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11476,U_11475),U_11479),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11476,tc_HOL_Obool)),U_11477),U_11478)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_11475),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11475),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11476,U_11475),U_11479),U_11477)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11476,U_11475),U_11479),U_11478))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11476,U_11475),U_11479),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11476,tc_HOL_Obool)),U_11477),U_11478)))
    | sP825(U_11476,U_11475,U_11477,U_11478,U_11479)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11476),U_11478))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11476),U_11477))
    | ~ class_Fields_Ofield(U_11475) ),
    inference(clausify,[status(thm)],[f_3072_4]) ).

cnf(f_3072_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11476),sK193(U_11479,U_11478,U_11477,U_11476,U_11475)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11476,tc_HOL_Obool)),U_11477),U_11478)))
    | ~ sP825(U_11476,U_11475,U_11477,U_11478,U_11479) ),
    inference(clausify,[status(thm)],[f_3072_4]) ).

cnf(f_3072_7,plain,
    ( hAPP(U_11479,sK193(U_11479,U_11478,U_11477,U_11476,U_11475)) = c_Groups_Ozero__class_Ozero(U_11475)
    | ~ sP825(U_11476,U_11475,U_11477,U_11478,U_11479) ),
    inference(clausify,[status(thm)],[f_3072_4]) ).

fof(f_3073_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_3073_2,plain,
    ! [U_11483,U_11482] :
      ( hBOOL(hAPP(hAPP(c_member(U_11482),c_Big__Operators_Olattice__class_OInf__fin(U_11482,U_11483)),U_11483))
      | ? [U_11481,U_11480] : ~ hBOOL(hAPP(hAPP(c_member(U_11482),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11482),U_11481),U_11480)),hAPP(hAPP(c_Set_Oinsert(U_11482),U_11481),hAPP(hAPP(c_Set_Oinsert(U_11482),U_11480),c_Orderings_Obot__class_Obot(tc_fun(U_11482,tc_HOL_Obool))))))
      | U_11483 = c_Orderings_Obot__class_Obot(tc_fun(U_11482,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11482),U_11483))
      | ~ class_Lattices_Olattice(U_11482) ),
    inference(variable_rename,[status(thm)],[f_3073_1]) ).

fof(f_3073_3,plain,
    ! [U_11483,U_11482] :
      ( hBOOL(hAPP(hAPP(c_member(U_11482),c_Big__Operators_Olattice__class_OInf__fin(U_11482,U_11483)),U_11483))
      | ? [U_11480] : ~ hBOOL(hAPP(hAPP(c_member(U_11482),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11482),sK194(U_11483,U_11482)),U_11480)),hAPP(hAPP(c_Set_Oinsert(U_11482),sK194(U_11483,U_11482)),hAPP(hAPP(c_Set_Oinsert(U_11482),U_11480),c_Orderings_Obot__class_Obot(tc_fun(U_11482,tc_HOL_Obool))))))
      | U_11483 = c_Orderings_Obot__class_Obot(tc_fun(U_11482,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11482),U_11483))
      | ~ class_Lattices_Olattice(U_11482) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK194]),skolemize(U_11481,sK194(U_11483,U_11482))],[f_3073_2]) ).

fof(f_3073_4,plain,
    ! [U_11483,U_11482] :
      ( hBOOL(hAPP(hAPP(c_member(U_11482),c_Big__Operators_Olattice__class_OInf__fin(U_11482,U_11483)),U_11483))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11482),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11482),sK194(U_11483,U_11482)),sK195(U_11483,U_11482))),hAPP(hAPP(c_Set_Oinsert(U_11482),sK194(U_11483,U_11482)),hAPP(hAPP(c_Set_Oinsert(U_11482),sK195(U_11483,U_11482)),c_Orderings_Obot__class_Obot(tc_fun(U_11482,tc_HOL_Obool))))))
      | U_11483 = c_Orderings_Obot__class_Obot(tc_fun(U_11482,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11482),U_11483))
      | ~ class_Lattices_Olattice(U_11482) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK195]),skolemize(U_11480,sK195(U_11483,U_11482))],[f_3073_3]) ).

fof(f_3073_5,plain,
    ! [U_11482,U_11483] :
      ( hBOOL(hAPP(hAPP(c_member(U_11482),c_Big__Operators_Olattice__class_OInf__fin(U_11482,U_11483)),U_11483))
      | ~ hBOOL(hAPP(hAPP(c_member(U_11482),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11482),sK194(U_11483,U_11482)),sK195(U_11483,U_11482))),hAPP(hAPP(c_Set_Oinsert(U_11482),sK194(U_11483,U_11482)),hAPP(hAPP(c_Set_Oinsert(U_11482),sK195(U_11483,U_11482)),c_Orderings_Obot__class_Obot(tc_fun(U_11482,tc_HOL_Obool))))))
      | U_11483 = c_Orderings_Obot__class_Obot(tc_fun(U_11482,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11482),U_11483))
      | ~ class_Lattices_Olattice(U_11482) ),
    inference(definitional_conversion,[status(esa)],[f_3073_4]) ).

cnf(f_3073_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11482),c_Big__Operators_Olattice__class_OInf__fin(U_11482,U_11483)),U_11483))
    | ~ hBOOL(hAPP(hAPP(c_member(U_11482),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11482),sK194(U_11483,U_11482)),sK195(U_11483,U_11482))),hAPP(hAPP(c_Set_Oinsert(U_11482),sK194(U_11483,U_11482)),hAPP(hAPP(c_Set_Oinsert(U_11482),sK195(U_11483,U_11482)),c_Orderings_Obot__class_Obot(tc_fun(U_11482,tc_HOL_Obool))))))
    | U_11483 = c_Orderings_Obot__class_Obot(tc_fun(U_11482,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11482),U_11483))
    | ~ class_Lattices_Olattice(U_11482) ),
    inference(clausify,[status(thm)],[f_3073_5]) ).

fof(f_3074_1,plain,
    ! [V_s_2,V_r_2,T_b,T_c] : c_Predicate_Oconversep(T_c,T_b,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_c,tc_fun(T_b,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),c_Predicate_Oconversep(T_c,T_b,V_r_2)),c_Predicate_Oconversep(T_c,T_b,V_s_2)),
    inference(fof_nnf,[status(thm)],[fact_converse__meet]) ).

fof(f_3074_2,plain,
    ! [U_11487,U_11486,U_11485,U_11484] : c_Predicate_Oconversep(U_11484,U_11485,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11484,tc_fun(U_11485,tc_HOL_Obool))),U_11486),U_11487)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11485,tc_fun(U_11484,tc_HOL_Obool))),c_Predicate_Oconversep(U_11484,U_11485,U_11486)),c_Predicate_Oconversep(U_11484,U_11485,U_11487)),
    inference(variable_rename,[status(thm)],[f_3074_1]) ).

fof(f_3074_3,plain,
    ! [U_11484,U_11485,U_11486,U_11487] : c_Predicate_Oconversep(U_11484,U_11485,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11484,tc_fun(U_11485,tc_HOL_Obool))),U_11486),U_11487)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11485,tc_fun(U_11484,tc_HOL_Obool))),c_Predicate_Oconversep(U_11484,U_11485,U_11486)),c_Predicate_Oconversep(U_11484,U_11485,U_11487)),
    inference(definitional_conversion,[status(esa)],[f_3074_2]) ).

cnf(f_3074_4,plain,
    c_Predicate_Oconversep(U_11484,U_11485,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11484,tc_fun(U_11485,tc_HOL_Obool))),U_11486),U_11487)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11485,tc_fun(U_11484,tc_HOL_Obool))),c_Predicate_Oconversep(U_11484,U_11485,U_11486)),c_Predicate_Oconversep(U_11484,U_11485,U_11487)),
    inference(clausify,[status(thm)],[f_3074_3]) ).

fof(f_3075_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_3075_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_3075_1]) ).

cnf(f_3075_3,plain,
    c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_3075_2]) ).

fof(f_3076_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_3076_2,plain,
    ! [U_11489,U_11488] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11488),U_11489))
      | ~ c_Nat__Transfer_Onat__set(U_11489)
      | ~ c_Nat__Transfer_Onat__set(U_11488) ),
    inference(variable_rename,[status(thm)],[f_3076_1]) ).

fof(f_3076_3,plain,
    ! [U_11488,U_11489] :
      ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11488),U_11489))
      | ~ c_Nat__Transfer_Onat__set(U_11489)
      | ~ c_Nat__Transfer_Onat__set(U_11488) ),
    inference(definitional_conversion,[status(esa)],[f_3076_2]) ).

cnf(f_3076_4,plain,
    ( c_Nat__Transfer_Onat__set(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11488),U_11489))
    | ~ c_Nat__Transfer_Onat__set(U_11489)
    | ~ c_Nat__Transfer_Onat__set(U_11488) ),
    inference(clausify,[status(thm)],[f_3076_3]) ).

fof(f_3077_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_3077_2,plain,
    ! [U_11491,U_11490] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_11490),U_11491) = 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_11490)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_11491))),
    inference(variable_rename,[status(thm)],[f_3077_1]) ).

fof(f_3077_3,plain,
    ! [U_11490,U_11491] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_11490),U_11491) = 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_11490)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_11491))),
    inference(definitional_conversion,[status(esa)],[f_3077_2]) ).

cnf(f_3077_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_11490),U_11491) = 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_11490)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_11491))),
    inference(clausify,[status(thm)],[f_3077_3]) ).

fof(f_3078_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_3078_2,plain,
    ! [U_11493,U_11492] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11492),U_11493) = 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_11492)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11493)))
      | ~ c_Nat__Transfer_Onat__set(U_11493)
      | ~ c_Nat__Transfer_Onat__set(U_11492) ),
    inference(variable_rename,[status(thm)],[f_3078_1]) ).

fof(f_3078_3,plain,
    ! [U_11492,U_11493] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11492),U_11493) = 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_11492)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11493)))
      | ~ c_Nat__Transfer_Onat__set(U_11493)
      | ~ c_Nat__Transfer_Onat__set(U_11492) ),
    inference(definitional_conversion,[status(esa)],[f_3078_2]) ).

cnf(f_3078_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_Int_Oint,tc_HOL_Obool)),U_11492),U_11493) = 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_11492)),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_11493)))
    | ~ c_Nat__Transfer_Onat__set(U_11493)
    | ~ c_Nat__Transfer_Onat__set(U_11492) ),
    inference(clausify,[status(thm)],[f_3078_3]) ).

fof(f_3079_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_3079_2,plain,
    ! [U_11499,U_11498,U_11497,U_11496,U_11495,U_11494] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11494,tc_fun(U_11495,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11494,tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_fun(U_11495,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11495,tc_fun(tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_fun(U_11495,tc_HOL_Obool)),U_11494),c_COMBC(U_11495,tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11495,tc_prod(U_11494,U_11495)),tc_fun(U_11495,tc_fun(tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_HOL_Obool)),U_11494),hAPP(c_COMBB(tc_prod(U_11494,U_11495),tc_fun(tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_HOL_Obool),U_11495),c_member(tc_prod(U_11494,U_11495)))),c_Product__Type_OPair(U_11494,U_11495)))),U_11496)),hAPP(hAPP(c_COMBC(U_11494,tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_fun(U_11495,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11495,tc_fun(tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_fun(U_11495,tc_HOL_Obool)),U_11494),c_COMBC(U_11495,tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11495,tc_prod(U_11494,U_11495)),tc_fun(U_11495,tc_fun(tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_HOL_Obool)),U_11494),hAPP(c_COMBB(tc_prod(U_11494,U_11495),tc_fun(tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_HOL_Obool),U_11495),c_member(tc_prod(U_11494,U_11495)))),c_Product__Type_OPair(U_11494,U_11495)))),U_11497)),U_11498),U_11499))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11494,U_11495)),hAPP(hAPP(c_Product__Type_OPair(U_11494,U_11495),U_11498),U_11499)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool)),U_11496),U_11497))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11494,U_11495)),hAPP(hAPP(c_Product__Type_OPair(U_11494,U_11495),U_11498),U_11499)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool)),U_11496),U_11497)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11494,tc_fun(U_11495,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11494,tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_fun(U_11495,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11495,tc_fun(tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_fun(U_11495,tc_HOL_Obool)),U_11494),c_COMBC(U_11495,tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11495,tc_prod(U_11494,U_11495)),tc_fun(U_11495,tc_fun(tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_HOL_Obool)),U_11494),hAPP(c_COMBB(tc_prod(U_11494,U_11495),tc_fun(tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_HOL_Obool),U_11495),c_member(tc_prod(U_11494,U_11495)))),c_Product__Type_OPair(U_11494,U_11495)))),U_11496)),hAPP(hAPP(c_COMBC(U_11494,tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_fun(U_11495,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11495,tc_fun(tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_fun(U_11495,tc_HOL_Obool)),U_11494),c_COMBC(U_11495,tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11495,tc_prod(U_11494,U_11495)),tc_fun(U_11495,tc_fun(tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_HOL_Obool)),U_11494),hAPP(c_COMBB(tc_prod(U_11494,U_11495),tc_fun(tc_fun(tc_prod(U_11494,U_11495),tc_HOL_Obool),tc_HOL_Obool),U_11495),c_member(tc_prod(U_11494,U_11495)))),c_Product__Type_OPair(U_11494,U_11495)))),U_11497)),U_11498),U_11499)) ) ),
    inference(variable_rename,[status(thm)],[f_3079_1]) ).

fof(f_3079_3,plain,
    ( ! [U_11511,U_11509,U_11507,U_11505,U_11503,U_11501] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11501,tc_fun(U_11503,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11501,tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_fun(U_11503,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11503,tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_fun(U_11503,tc_HOL_Obool)),U_11501),c_COMBC(U_11503,tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11503,tc_prod(U_11501,U_11503)),tc_fun(U_11503,tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool)),U_11501),hAPP(c_COMBB(tc_prod(U_11501,U_11503),tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool),U_11503),c_member(tc_prod(U_11501,U_11503)))),c_Product__Type_OPair(U_11501,U_11503)))),U_11505)),hAPP(hAPP(c_COMBC(U_11501,tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_fun(U_11503,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11503,tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_fun(U_11503,tc_HOL_Obool)),U_11501),c_COMBC(U_11503,tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11503,tc_prod(U_11501,U_11503)),tc_fun(U_11503,tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool)),U_11501),hAPP(c_COMBB(tc_prod(U_11501,U_11503),tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool),U_11503),c_member(tc_prod(U_11501,U_11503)))),c_Product__Type_OPair(U_11501,U_11503)))),U_11507)),U_11509),U_11511))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11501,U_11503)),hAPP(hAPP(c_Product__Type_OPair(U_11501,U_11503),U_11509),U_11511)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool)),U_11505),U_11507))) )
    & ! [U_11510,U_11508,U_11506,U_11504,U_11502,U_11500] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11500,U_11502)),hAPP(hAPP(c_Product__Type_OPair(U_11500,U_11502),U_11508),U_11510)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool)),U_11504),U_11506)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11500,tc_fun(U_11502,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11500,tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_fun(U_11502,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11502,tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_fun(U_11502,tc_HOL_Obool)),U_11500),c_COMBC(U_11502,tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11502,tc_prod(U_11500,U_11502)),tc_fun(U_11502,tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool)),U_11500),hAPP(c_COMBB(tc_prod(U_11500,U_11502),tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool),U_11502),c_member(tc_prod(U_11500,U_11502)))),c_Product__Type_OPair(U_11500,U_11502)))),U_11504)),hAPP(hAPP(c_COMBC(U_11500,tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_fun(U_11502,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11502,tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_fun(U_11502,tc_HOL_Obool)),U_11500),c_COMBC(U_11502,tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11502,tc_prod(U_11500,U_11502)),tc_fun(U_11502,tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool)),U_11500),hAPP(c_COMBB(tc_prod(U_11500,U_11502),tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool),U_11502),c_member(tc_prod(U_11500,U_11502)))),c_Product__Type_OPair(U_11500,U_11502)))),U_11506)),U_11508),U_11510)) ) ),
    inference(miniscope,[status(thm)],[f_3079_2]) ).

fof(f_3079_4,plain,
    ( ! [U_11501,U_11503,U_11505,U_11507,U_11509,U_11511] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11501,tc_fun(U_11503,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11501,tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_fun(U_11503,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11503,tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_fun(U_11503,tc_HOL_Obool)),U_11501),c_COMBC(U_11503,tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11503,tc_prod(U_11501,U_11503)),tc_fun(U_11503,tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool)),U_11501),hAPP(c_COMBB(tc_prod(U_11501,U_11503),tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool),U_11503),c_member(tc_prod(U_11501,U_11503)))),c_Product__Type_OPair(U_11501,U_11503)))),U_11505)),hAPP(hAPP(c_COMBC(U_11501,tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_fun(U_11503,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11503,tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_fun(U_11503,tc_HOL_Obool)),U_11501),c_COMBC(U_11503,tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11503,tc_prod(U_11501,U_11503)),tc_fun(U_11503,tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool)),U_11501),hAPP(c_COMBB(tc_prod(U_11501,U_11503),tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool),U_11503),c_member(tc_prod(U_11501,U_11503)))),c_Product__Type_OPair(U_11501,U_11503)))),U_11507)),U_11509),U_11511))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11501,U_11503)),hAPP(hAPP(c_Product__Type_OPair(U_11501,U_11503),U_11509),U_11511)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool)),U_11505),U_11507))) )
    & ! [U_11502,U_11506,U_11500,U_11504,U_11508,U_11510] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11500,U_11502)),hAPP(hAPP(c_Product__Type_OPair(U_11500,U_11502),U_11508),U_11510)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool)),U_11504),U_11506)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11500,tc_fun(U_11502,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11500,tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_fun(U_11502,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11502,tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_fun(U_11502,tc_HOL_Obool)),U_11500),c_COMBC(U_11502,tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11502,tc_prod(U_11500,U_11502)),tc_fun(U_11502,tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool)),U_11500),hAPP(c_COMBB(tc_prod(U_11500,U_11502),tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool),U_11502),c_member(tc_prod(U_11500,U_11502)))),c_Product__Type_OPair(U_11500,U_11502)))),U_11504)),hAPP(hAPP(c_COMBC(U_11500,tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_fun(U_11502,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11502,tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_fun(U_11502,tc_HOL_Obool)),U_11500),c_COMBC(U_11502,tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11502,tc_prod(U_11500,U_11502)),tc_fun(U_11502,tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool)),U_11500),hAPP(c_COMBB(tc_prod(U_11500,U_11502),tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool),U_11502),c_member(tc_prod(U_11500,U_11502)))),c_Product__Type_OPair(U_11500,U_11502)))),U_11506)),U_11508),U_11510)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3079_3]) ).

cnf(f_3079_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11500,U_11502)),hAPP(hAPP(c_Product__Type_OPair(U_11500,U_11502),U_11508),U_11510)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool)),U_11504),U_11506)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11500,tc_fun(U_11502,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11500,tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_fun(U_11502,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11502,tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_fun(U_11502,tc_HOL_Obool)),U_11500),c_COMBC(U_11502,tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11502,tc_prod(U_11500,U_11502)),tc_fun(U_11502,tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool)),U_11500),hAPP(c_COMBB(tc_prod(U_11500,U_11502),tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool),U_11502),c_member(tc_prod(U_11500,U_11502)))),c_Product__Type_OPair(U_11500,U_11502)))),U_11504)),hAPP(hAPP(c_COMBC(U_11500,tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_fun(U_11502,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11502,tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_fun(U_11502,tc_HOL_Obool)),U_11500),c_COMBC(U_11502,tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11502,tc_prod(U_11500,U_11502)),tc_fun(U_11502,tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool)),U_11500),hAPP(c_COMBB(tc_prod(U_11500,U_11502),tc_fun(tc_fun(tc_prod(U_11500,U_11502),tc_HOL_Obool),tc_HOL_Obool),U_11502),c_member(tc_prod(U_11500,U_11502)))),c_Product__Type_OPair(U_11500,U_11502)))),U_11506)),U_11508),U_11510)) ),
    inference(clausify,[status(thm)],[f_3079_4]) ).

cnf(f_3079_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11501,tc_fun(U_11503,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11501,tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_fun(U_11503,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11503,tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_fun(U_11503,tc_HOL_Obool)),U_11501),c_COMBC(U_11503,tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11503,tc_prod(U_11501,U_11503)),tc_fun(U_11503,tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool)),U_11501),hAPP(c_COMBB(tc_prod(U_11501,U_11503),tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool),U_11503),c_member(tc_prod(U_11501,U_11503)))),c_Product__Type_OPair(U_11501,U_11503)))),U_11505)),hAPP(hAPP(c_COMBC(U_11501,tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_fun(U_11503,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11503,tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_fun(U_11503,tc_HOL_Obool)),U_11501),c_COMBC(U_11503,tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_11503,tc_prod(U_11501,U_11503)),tc_fun(U_11503,tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool)),U_11501),hAPP(c_COMBB(tc_prod(U_11501,U_11503),tc_fun(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool),tc_HOL_Obool),U_11503),c_member(tc_prod(U_11501,U_11503)))),c_Product__Type_OPair(U_11501,U_11503)))),U_11507)),U_11509),U_11511))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11501,U_11503)),hAPP(hAPP(c_Product__Type_OPair(U_11501,U_11503),U_11509),U_11511)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_11501,U_11503),tc_HOL_Obool)),U_11505),U_11507))) ),
    inference(clausify,[status(thm)],[f_3079_4]) ).

fof(f_3080_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_3080_2,plain,
    ! [U_11517,U_11516,U_11515,U_11514,U_11513] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11514,U_11513),U_11517),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11514,tc_HOL_Obool)),U_11515),U_11516)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11513),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11514,U_11513),U_11517),U_11515)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11514,U_11513),U_11517),U_11516))
      | ? [U_11512] :
          ( hAPP(U_11517,U_11512) != c_Groups_Oone__class_Oone(U_11513)
          & hBOOL(hAPP(hAPP(c_member(U_11514),U_11512),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11514,tc_HOL_Obool)),U_11515),U_11516))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11514),U_11516))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11514),U_11515))
      | ~ class_Groups_Ocomm__monoid__mult(U_11513) ),
    inference(variable_rename,[status(thm)],[f_3080_1]) ).

fof(f_3080_3,plain,
    ! [U_11517,U_11516,U_11515,U_11514,U_11513] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11514,U_11513),U_11517),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11514,tc_HOL_Obool)),U_11515),U_11516)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11513),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11514,U_11513),U_11517),U_11515)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11514,U_11513),U_11517),U_11516))
      | ( hAPP(U_11517,sK196(U_11517,U_11516,U_11515,U_11514,U_11513)) != c_Groups_Oone__class_Oone(U_11513)
        & hBOOL(hAPP(hAPP(c_member(U_11514),sK196(U_11517,U_11516,U_11515,U_11514,U_11513)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11514,tc_HOL_Obool)),U_11515),U_11516))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11514),U_11516))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11514),U_11515))
      | ~ class_Groups_Ocomm__monoid__mult(U_11513) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK196]),skolemize(U_11512,sK196(U_11517,U_11516,U_11515,U_11514,U_11513))],[f_3080_2]) ).

fof(f_3080_4,plain,
    ( ! [U_11513,U_11514,U_11515,U_11516,U_11517] :
        ( hAPP(U_11517,sK196(U_11517,U_11516,U_11515,U_11514,U_11513)) != c_Groups_Oone__class_Oone(U_11513)
        | ~ sP826(U_11513,U_11514,U_11515,U_11516,U_11517) )
    & ! [U_11513,U_11514,U_11515,U_11516,U_11517] :
        ( hBOOL(hAPP(hAPP(c_member(U_11514),sK196(U_11517,U_11516,U_11515,U_11514,U_11513)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11514,tc_HOL_Obool)),U_11515),U_11516)))
        | ~ sP826(U_11513,U_11514,U_11515,U_11516,U_11517) )
    & ! [U_11513,U_11514,U_11515,U_11516,U_11517] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11514,U_11513),U_11517),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11514,tc_HOL_Obool)),U_11515),U_11516)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11513),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11514,U_11513),U_11517),U_11515)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11514,U_11513),U_11517),U_11516))
        | sP826(U_11513,U_11514,U_11515,U_11516,U_11517)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11514),U_11516))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11514),U_11515))
        | ~ class_Groups_Ocomm__monoid__mult(U_11513) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP826])],[f_3080_3]) ).

cnf(f_3080_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11514,U_11513),U_11517),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11514,tc_HOL_Obool)),U_11515),U_11516)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11513),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11514,U_11513),U_11517),U_11515)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11514,U_11513),U_11517),U_11516))
    | sP826(U_11513,U_11514,U_11515,U_11516,U_11517)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11514),U_11516))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11514),U_11515))
    | ~ class_Groups_Ocomm__monoid__mult(U_11513) ),
    inference(clausify,[status(thm)],[f_3080_4]) ).

cnf(f_3080_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11514),sK196(U_11517,U_11516,U_11515,U_11514,U_11513)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11514,tc_HOL_Obool)),U_11515),U_11516)))
    | ~ sP826(U_11513,U_11514,U_11515,U_11516,U_11517) ),
    inference(clausify,[status(thm)],[f_3080_4]) ).

cnf(f_3080_7,plain,
    ( hAPP(U_11517,sK196(U_11517,U_11516,U_11515,U_11514,U_11513)) != c_Groups_Oone__class_Oone(U_11513)
    | ~ sP826(U_11513,U_11514,U_11515,U_11516,U_11517) ),
    inference(clausify,[status(thm)],[f_3080_4]) ).

fof(f_3081_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_3081_2,plain,
    ! [U_11523,U_11522,U_11521,U_11520,U_11519] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11520,U_11519),U_11523),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11520,tc_HOL_Obool)),U_11521),U_11522)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11519),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11520,U_11519),U_11523),U_11521)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11520,U_11519),U_11523),U_11522))
      | ? [U_11518] :
          ( hAPP(U_11523,U_11518) != c_Groups_Oone__class_Oone(U_11519)
          & hBOOL(hAPP(hAPP(c_member(U_11520),U_11518),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11520,tc_HOL_Obool)),U_11521),U_11522))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11520),U_11522))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11520),U_11521))
      | ~ class_Groups_Ocomm__monoid__mult(U_11519) ),
    inference(variable_rename,[status(thm)],[f_3081_1]) ).

fof(f_3081_3,plain,
    ! [U_11523,U_11522,U_11521,U_11520,U_11519] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11520,U_11519),U_11523),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11520,tc_HOL_Obool)),U_11521),U_11522)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11519),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11520,U_11519),U_11523),U_11521)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11520,U_11519),U_11523),U_11522))
      | ( hAPP(U_11523,sK197(U_11523,U_11522,U_11521,U_11520,U_11519)) != c_Groups_Oone__class_Oone(U_11519)
        & hBOOL(hAPP(hAPP(c_member(U_11520),sK197(U_11523,U_11522,U_11521,U_11520,U_11519)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11520,tc_HOL_Obool)),U_11521),U_11522))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11520),U_11522))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11520),U_11521))
      | ~ class_Groups_Ocomm__monoid__mult(U_11519) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK197]),skolemize(U_11518,sK197(U_11523,U_11522,U_11521,U_11520,U_11519))],[f_3081_2]) ).

fof(f_3081_4,plain,
    ( ! [U_11520,U_11519,U_11521,U_11522,U_11523] :
        ( hAPP(U_11523,sK197(U_11523,U_11522,U_11521,U_11520,U_11519)) != c_Groups_Oone__class_Oone(U_11519)
        | ~ sP827(U_11520,U_11519,U_11521,U_11522,U_11523) )
    & ! [U_11520,U_11519,U_11521,U_11522,U_11523] :
        ( hBOOL(hAPP(hAPP(c_member(U_11520),sK197(U_11523,U_11522,U_11521,U_11520,U_11519)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11520,tc_HOL_Obool)),U_11521),U_11522)))
        | ~ sP827(U_11520,U_11519,U_11521,U_11522,U_11523) )
    & ! [U_11520,U_11519,U_11521,U_11522,U_11523] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11520,U_11519),U_11523),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11520,tc_HOL_Obool)),U_11521),U_11522)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11519),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11520,U_11519),U_11523),U_11521)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11520,U_11519),U_11523),U_11522))
        | sP827(U_11520,U_11519,U_11521,U_11522,U_11523)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11520),U_11522))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11520),U_11521))
        | ~ class_Groups_Ocomm__monoid__mult(U_11519) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP827])],[f_3081_3]) ).

cnf(f_3081_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11520,U_11519),U_11523),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11520,tc_HOL_Obool)),U_11521),U_11522)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11519),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11520,U_11519),U_11523),U_11521)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11520,U_11519),U_11523),U_11522))
    | sP827(U_11520,U_11519,U_11521,U_11522,U_11523)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11520),U_11522))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11520),U_11521))
    | ~ class_Groups_Ocomm__monoid__mult(U_11519) ),
    inference(clausify,[status(thm)],[f_3081_4]) ).

cnf(f_3081_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11520),sK197(U_11523,U_11522,U_11521,U_11520,U_11519)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11520,tc_HOL_Obool)),U_11521),U_11522)))
    | ~ sP827(U_11520,U_11519,U_11521,U_11522,U_11523) ),
    inference(clausify,[status(thm)],[f_3081_4]) ).

cnf(f_3081_7,plain,
    ( hAPP(U_11523,sK197(U_11523,U_11522,U_11521,U_11520,U_11519)) != c_Groups_Oone__class_Oone(U_11519)
    | ~ sP827(U_11520,U_11519,U_11521,U_11522,U_11523) ),
    inference(clausify,[status(thm)],[f_3081_4]) ).

fof(f_3082_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_3082_2,plain,
    ! [U_11528,U_11527,U_11526,U_11525,U_11524] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11524,U_11525,c_Groups_Otimes__class_Otimes(U_11524)),U_11528),c_Groups_Oone__class_Oone(U_11524)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11525,tc_HOL_Obool)),U_11526),U_11527)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11524),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11524,U_11525,c_Groups_Otimes__class_Otimes(U_11524)),U_11528),c_Groups_Oone__class_Oone(U_11524)),U_11526)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11524,U_11525,c_Groups_Otimes__class_Otimes(U_11524)),U_11528),c_Groups_Oone__class_Oone(U_11524)),U_11527))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11525,tc_HOL_Obool)),U_11526),U_11527) != c_Orderings_Obot__class_Obot(tc_fun(U_11525,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11525),U_11527))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11525),U_11526))
      | ~ class_Groups_Ocomm__monoid__mult(U_11524) ),
    inference(variable_rename,[status(thm)],[f_3082_1]) ).

fof(f_3082_3,plain,
    ! [U_11525,U_11526,U_11524,U_11527,U_11528] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11524,U_11525,c_Groups_Otimes__class_Otimes(U_11524)),U_11528),c_Groups_Oone__class_Oone(U_11524)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11525,tc_HOL_Obool)),U_11526),U_11527)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11524),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11524,U_11525,c_Groups_Otimes__class_Otimes(U_11524)),U_11528),c_Groups_Oone__class_Oone(U_11524)),U_11526)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11524,U_11525,c_Groups_Otimes__class_Otimes(U_11524)),U_11528),c_Groups_Oone__class_Oone(U_11524)),U_11527))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11525,tc_HOL_Obool)),U_11526),U_11527) != c_Orderings_Obot__class_Obot(tc_fun(U_11525,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11525),U_11527))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11525),U_11526))
      | ~ class_Groups_Ocomm__monoid__mult(U_11524) ),
    inference(definitional_conversion,[status(esa)],[f_3082_2]) ).

cnf(f_3082_4,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11524,U_11525,c_Groups_Otimes__class_Otimes(U_11524)),U_11528),c_Groups_Oone__class_Oone(U_11524)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11525,tc_HOL_Obool)),U_11526),U_11527)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11524),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11524,U_11525,c_Groups_Otimes__class_Otimes(U_11524)),U_11528),c_Groups_Oone__class_Oone(U_11524)),U_11526)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11524,U_11525,c_Groups_Otimes__class_Otimes(U_11524)),U_11528),c_Groups_Oone__class_Oone(U_11524)),U_11527))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11525,tc_HOL_Obool)),U_11526),U_11527) != c_Orderings_Obot__class_Obot(tc_fun(U_11525,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11525),U_11527))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11525),U_11526))
    | ~ class_Groups_Ocomm__monoid__mult(U_11524) ),
    inference(clausify,[status(thm)],[f_3082_3]) ).

fof(f_3083_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_3083_2,plain,
    ! [U_11534,U_11533,U_11532,U_11531,U_11530,U_11529] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11533,tc_fun(U_11534,tc_HOL_Obool))),U_11529),U_11532),U_11530),U_11531))
      | ~ hBOOL(hAPP(hAPP(U_11532,U_11530),U_11531))
      | ~ hBOOL(hAPP(hAPP(U_11529,U_11530),U_11531)) ),
    inference(variable_rename,[status(thm)],[f_3083_1]) ).

fof(f_3083_3,plain,
    ! [U_11530,U_11532,U_11529,U_11531,U_11533,U_11534] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11533,tc_fun(U_11534,tc_HOL_Obool))),U_11529),U_11532),U_11530),U_11531))
      | ~ hBOOL(hAPP(hAPP(U_11532,U_11530),U_11531))
      | ~ hBOOL(hAPP(hAPP(U_11529,U_11530),U_11531)) ),
    inference(definitional_conversion,[status(esa)],[f_3083_2]) ).

cnf(f_3083_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11533,tc_fun(U_11534,tc_HOL_Obool))),U_11529),U_11532),U_11530),U_11531))
    | ~ hBOOL(hAPP(hAPP(U_11532,U_11530),U_11531))
    | ~ hBOOL(hAPP(hAPP(U_11529,U_11530),U_11531)) ),
    inference(clausify,[status(thm)],[f_3083_3]) ).

fof(f_3084_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_3084_2,plain,
    ! [U_11540,U_11539,U_11538,U_11537,U_11536,U_11535] :
      ( ( hBOOL(hAPP(hAPP(U_11538,U_11539),U_11540))
        & hBOOL(hAPP(hAPP(U_11537,U_11539),U_11540)) )
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11535,tc_fun(U_11536,tc_HOL_Obool))),U_11537),U_11538),U_11539),U_11540)) ),
    inference(variable_rename,[status(thm)],[f_3084_1]) ).

fof(f_3084_3,plain,
    ! [U_11540,U_11539,U_11538,U_11537] :
      ( ! [U_11536,U_11535] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11535,tc_fun(U_11536,tc_HOL_Obool))),U_11537),U_11538),U_11539),U_11540))
      | ( hBOOL(hAPP(hAPP(U_11538,U_11539),U_11540))
        & hBOOL(hAPP(hAPP(U_11537,U_11539),U_11540)) ) ),
    inference(miniscope,[status(thm)],[f_3084_2]) ).

fof(f_3084_4,plain,
    ( ! [U_11537,U_11538,U_11539,U_11540] :
        ( hBOOL(hAPP(hAPP(U_11538,U_11539),U_11540))
        | ~ sP828(U_11537,U_11538,U_11539,U_11540) )
    & ! [U_11537,U_11538,U_11539,U_11540] :
        ( hBOOL(hAPP(hAPP(U_11537,U_11539),U_11540))
        | ~ sP828(U_11537,U_11538,U_11539,U_11540) )
    & ! [U_11536,U_11535,U_11537,U_11538,U_11539,U_11540] :
        ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11535,tc_fun(U_11536,tc_HOL_Obool))),U_11537),U_11538),U_11539),U_11540))
        | sP828(U_11537,U_11538,U_11539,U_11540) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP828])],[f_3084_3]) ).

cnf(f_3084_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11535,tc_fun(U_11536,tc_HOL_Obool))),U_11537),U_11538),U_11539),U_11540))
    | sP828(U_11537,U_11538,U_11539,U_11540) ),
    inference(clausify,[status(thm)],[f_3084_4]) ).

cnf(f_3084_6,plain,
    ( hBOOL(hAPP(hAPP(U_11537,U_11539),U_11540))
    | ~ sP828(U_11537,U_11538,U_11539,U_11540) ),
    inference(clausify,[status(thm)],[f_3084_4]) ).

cnf(f_3084_7,plain,
    ( hBOOL(hAPP(hAPP(U_11538,U_11539),U_11540))
    | ~ sP828(U_11537,U_11538,U_11539,U_11540) ),
    inference(clausify,[status(thm)],[f_3084_4]) ).

fof(f_3085_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_3085_2,plain,
    ! [U_11546,U_11545,U_11544,U_11543,U_11542,U_11541] :
      ( hBOOL(hAPP(hAPP(U_11543,U_11545),U_11546))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11541,tc_fun(U_11542,tc_HOL_Obool))),U_11543),U_11544),U_11545),U_11546)) ),
    inference(variable_rename,[status(thm)],[f_3085_1]) ).

fof(f_3085_3,plain,
    ! [U_11546,U_11545,U_11544,U_11543] :
      ( ! [U_11542,U_11541] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11541,tc_fun(U_11542,tc_HOL_Obool))),U_11543),U_11544),U_11545),U_11546))
      | hBOOL(hAPP(hAPP(U_11543,U_11545),U_11546)) ),
    inference(miniscope,[status(thm)],[f_3085_2]) ).

fof(f_3085_4,plain,
    ! [U_11542,U_11541,U_11543,U_11544,U_11545,U_11546] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11541,tc_fun(U_11542,tc_HOL_Obool))),U_11543),U_11544),U_11545),U_11546))
      | hBOOL(hAPP(hAPP(U_11543,U_11545),U_11546)) ),
    inference(definitional_conversion,[status(esa)],[f_3085_3]) ).

cnf(f_3085_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11541,tc_fun(U_11542,tc_HOL_Obool))),U_11543),U_11544),U_11545),U_11546))
    | hBOOL(hAPP(hAPP(U_11543,U_11545),U_11546)) ),
    inference(clausify,[status(thm)],[f_3085_4]) ).

fof(f_3086_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_3086_2,plain,
    ! [U_11552,U_11551,U_11550,U_11549,U_11548,U_11547] :
      ( hBOOL(hAPP(hAPP(U_11550,U_11551),U_11552))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11547,tc_fun(U_11548,tc_HOL_Obool))),U_11549),U_11550),U_11551),U_11552)) ),
    inference(variable_rename,[status(thm)],[f_3086_1]) ).

fof(f_3086_3,plain,
    ! [U_11552,U_11551,U_11550] :
      ( ! [U_11549,U_11548,U_11547] : ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11547,tc_fun(U_11548,tc_HOL_Obool))),U_11549),U_11550),U_11551),U_11552))
      | hBOOL(hAPP(hAPP(U_11550,U_11551),U_11552)) ),
    inference(miniscope,[status(thm)],[f_3086_2]) ).

fof(f_3086_4,plain,
    ! [U_11547,U_11548,U_11549,U_11550,U_11551,U_11552] :
      ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11547,tc_fun(U_11548,tc_HOL_Obool))),U_11549),U_11550),U_11551),U_11552))
      | hBOOL(hAPP(hAPP(U_11550,U_11551),U_11552)) ),
    inference(definitional_conversion,[status(esa)],[f_3086_3]) ).

cnf(f_3086_5,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11547,tc_fun(U_11548,tc_HOL_Obool))),U_11549),U_11550),U_11551),U_11552))
    | hBOOL(hAPP(hAPP(U_11550,U_11551),U_11552)) ),
    inference(clausify,[status(thm)],[f_3086_4]) ).

fof(f_3087_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_3087_2,plain,
    ! [U_11557,U_11556,U_11555,U_11554,U_11553] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11553,U_11554,U_11555),U_11556),U_11557),c_Orderings_Obot__class_Obot(tc_fun(U_11554,tc_HOL_Obool))) = U_11557,
    inference(variable_rename,[status(thm)],[f_3087_1]) ).

fof(f_3087_3,plain,
    ! [U_11554,U_11553,U_11555,U_11556,U_11557] : hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11553,U_11554,U_11555),U_11556),U_11557),c_Orderings_Obot__class_Obot(tc_fun(U_11554,tc_HOL_Obool))) = U_11557,
    inference(definitional_conversion,[status(esa)],[f_3087_2]) ).

cnf(f_3087_4,plain,
    hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11553,U_11554,U_11555),U_11556),U_11557),c_Orderings_Obot__class_Obot(tc_fun(U_11554,tc_HOL_Obool))) = U_11557,
    inference(clausify,[status(thm)],[f_3087_3]) ).

fof(f_3088_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_3088_2,plain,
    ! [U_11564,U_11563,U_11562,U_11561,U_11560,U_11559,U_11558] :
      ( hAPP(U_11563,U_11564) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11558,U_11559,U_11560),U_11562),U_11561),U_11564)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11559),U_11564))
      | ~ c_Finite__Set_Ofolding__image__simple(U_11558,U_11559,U_11560,U_11561,U_11562,U_11563) ),
    inference(variable_rename,[status(thm)],[f_3088_1]) ).

fof(f_3088_3,plain,
    ! [U_11558,U_11559,U_11560,U_11561,U_11562,U_11563,U_11564] :
      ( hAPP(U_11563,U_11564) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11558,U_11559,U_11560),U_11562),U_11561),U_11564)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11559),U_11564))
      | ~ c_Finite__Set_Ofolding__image__simple(U_11558,U_11559,U_11560,U_11561,U_11562,U_11563) ),
    inference(definitional_conversion,[status(esa)],[f_3088_2]) ).

cnf(f_3088_4,plain,
    ( hAPP(U_11563,U_11564) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11558,U_11559,U_11560),U_11562),U_11561),U_11564)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11559),U_11564))
    | ~ c_Finite__Set_Ofolding__image__simple(U_11558,U_11559,U_11560,U_11561,U_11562,U_11563) ),
    inference(clausify,[status(thm)],[f_3088_3]) ).

fof(f_3089_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_3089_2,plain,
    ! [U_11569,U_11568,U_11567,U_11566,U_11565] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11565,U_11566,c_Groups_Otimes__class_Otimes(U_11565)),hAPP(hAPP(c_COMBS(U_11566,U_11565,U_11565),hAPP(hAPP(c_COMBB(U_11565,tc_fun(U_11565,U_11565),U_11566),c_Groups_Otimes__class_Otimes(U_11565)),U_11568)),U_11569)),c_Groups_Oone__class_Oone(U_11565)),U_11567) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11565),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11565,U_11566,c_Groups_Otimes__class_Otimes(U_11565)),U_11568),c_Groups_Oone__class_Oone(U_11565)),U_11567)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11565,U_11566,c_Groups_Otimes__class_Otimes(U_11565)),U_11569),c_Groups_Oone__class_Oone(U_11565)),U_11567))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11566),U_11567))
      | ~ class_Groups_Ocomm__monoid__mult(U_11565) ),
    inference(variable_rename,[status(thm)],[f_3089_1]) ).

fof(f_3089_3,plain,
    ! [U_11565,U_11566,U_11567,U_11568,U_11569] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11565,U_11566,c_Groups_Otimes__class_Otimes(U_11565)),hAPP(hAPP(c_COMBS(U_11566,U_11565,U_11565),hAPP(hAPP(c_COMBB(U_11565,tc_fun(U_11565,U_11565),U_11566),c_Groups_Otimes__class_Otimes(U_11565)),U_11568)),U_11569)),c_Groups_Oone__class_Oone(U_11565)),U_11567) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11565),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11565,U_11566,c_Groups_Otimes__class_Otimes(U_11565)),U_11568),c_Groups_Oone__class_Oone(U_11565)),U_11567)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11565,U_11566,c_Groups_Otimes__class_Otimes(U_11565)),U_11569),c_Groups_Oone__class_Oone(U_11565)),U_11567))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11566),U_11567))
      | ~ class_Groups_Ocomm__monoid__mult(U_11565) ),
    inference(definitional_conversion,[status(esa)],[f_3089_2]) ).

cnf(f_3089_4,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11565,U_11566,c_Groups_Otimes__class_Otimes(U_11565)),hAPP(hAPP(c_COMBS(U_11566,U_11565,U_11565),hAPP(hAPP(c_COMBB(U_11565,tc_fun(U_11565,U_11565),U_11566),c_Groups_Otimes__class_Otimes(U_11565)),U_11568)),U_11569)),c_Groups_Oone__class_Oone(U_11565)),U_11567) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11565),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11565,U_11566,c_Groups_Otimes__class_Otimes(U_11565)),U_11568),c_Groups_Oone__class_Oone(U_11565)),U_11567)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11565,U_11566,c_Groups_Otimes__class_Otimes(U_11565)),U_11569),c_Groups_Oone__class_Oone(U_11565)),U_11567))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11566),U_11567))
    | ~ class_Groups_Ocomm__monoid__mult(U_11565) ),
    inference(clausify,[status(thm)],[f_3089_3]) ).

fof(f_3090_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_3090_2,plain,
    ! [U_11575,U_11574,U_11573,U_11572,U_11571,U_11570] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11570,U_11571,c_Groups_Otimes__class_Otimes(U_11570)),U_11574),U_11575),hAPP(hAPP(c_Set_Oinsert(U_11571),U_11573),U_11572)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11570),hAPP(U_11574,U_11573)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11570,U_11571,c_Groups_Otimes__class_Otimes(U_11570)),U_11574),U_11575),U_11572))
      | hBOOL(hAPP(hAPP(c_member(U_11571),U_11573),U_11572))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11571),U_11572))
      | ~ class_Groups_Oab__semigroup__mult(U_11570) ),
    inference(variable_rename,[status(thm)],[f_3090_1]) ).

fof(f_3090_3,plain,
    ! [U_11570,U_11571,U_11572,U_11573,U_11574,U_11575] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11570,U_11571,c_Groups_Otimes__class_Otimes(U_11570)),U_11574),U_11575),hAPP(hAPP(c_Set_Oinsert(U_11571),U_11573),U_11572)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11570),hAPP(U_11574,U_11573)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11570,U_11571,c_Groups_Otimes__class_Otimes(U_11570)),U_11574),U_11575),U_11572))
      | hBOOL(hAPP(hAPP(c_member(U_11571),U_11573),U_11572))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11571),U_11572))
      | ~ class_Groups_Oab__semigroup__mult(U_11570) ),
    inference(definitional_conversion,[status(esa)],[f_3090_2]) ).

cnf(f_3090_4,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11570,U_11571,c_Groups_Otimes__class_Otimes(U_11570)),U_11574),U_11575),hAPP(hAPP(c_Set_Oinsert(U_11571),U_11573),U_11572)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11570),hAPP(U_11574,U_11573)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11570,U_11571,c_Groups_Otimes__class_Otimes(U_11570)),U_11574),U_11575),U_11572))
    | hBOOL(hAPP(hAPP(c_member(U_11571),U_11573),U_11572))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11571),U_11572))
    | ~ class_Groups_Oab__semigroup__mult(U_11570) ),
    inference(clausify,[status(thm)],[f_3090_3]) ).

fof(f_3091_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_3091_2,plain,
    ! [U_11579,U_11578,U_11577,U_11576] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11577,U_11576),U_11579),U_11578) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11576,U_11577,c_Groups_Otimes__class_Otimes(U_11576)),U_11579),c_Groups_Oone__class_Oone(U_11576)),U_11578)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11577),U_11578))
      | ~ class_Groups_Ocomm__monoid__mult(U_11576) ),
    inference(variable_rename,[status(thm)],[f_3091_1]) ).

fof(f_3091_3,plain,
    ! [U_11576,U_11577,U_11578,U_11579] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11577,U_11576),U_11579),U_11578) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11576,U_11577,c_Groups_Otimes__class_Otimes(U_11576)),U_11579),c_Groups_Oone__class_Oone(U_11576)),U_11578)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11577),U_11578))
      | ~ class_Groups_Ocomm__monoid__mult(U_11576) ),
    inference(definitional_conversion,[status(esa)],[f_3091_2]) ).

cnf(f_3091_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11577,U_11576),U_11579),U_11578) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11576,U_11577,c_Groups_Otimes__class_Otimes(U_11576)),U_11579),c_Groups_Oone__class_Oone(U_11576)),U_11578)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11577),U_11578))
    | ~ class_Groups_Ocomm__monoid__mult(U_11576) ),
    inference(clausify,[status(thm)],[f_3091_3]) ).

fof(f_3092_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_3092_2,plain,
    ! [U_11583,U_11582,U_11581,U_11580] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11581,U_11580),U_11583),U_11582) = c_Groups_Oone__class_Oone(U_11580)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11581),U_11582)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11581,U_11580),U_11583),U_11582) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11580,U_11581,c_Groups_Otimes__class_Otimes(U_11580)),U_11583),c_Groups_Oone__class_Oone(U_11580)),U_11582)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11581),U_11582)) ) )
      | ~ class_Groups_Ocomm__monoid__mult(U_11580) ),
    inference(variable_rename,[status(thm)],[f_3092_1]) ).

fof(f_3092_3,plain,
    ( ! [U_11580,U_11581,U_11582,U_11583] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11581,U_11580),U_11583),U_11582) = c_Groups_Oone__class_Oone(U_11580)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11581),U_11582))
        | ~ sP829(U_11580,U_11581,U_11582,U_11583) )
    & ! [U_11580,U_11581,U_11582,U_11583] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11581,U_11580),U_11583),U_11582) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11580,U_11581,c_Groups_Otimes__class_Otimes(U_11580)),U_11583),c_Groups_Oone__class_Oone(U_11580)),U_11582)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11581),U_11582))
        | ~ sP829(U_11580,U_11581,U_11582,U_11583) )
    & ! [U_11580,U_11581,U_11582,U_11583] :
        ( sP829(U_11580,U_11581,U_11582,U_11583)
        | ~ class_Groups_Ocomm__monoid__mult(U_11580) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP829])],[f_3092_2]) ).

cnf(f_3092_4,plain,
    ( sP829(U_11580,U_11581,U_11582,U_11583)
    | ~ class_Groups_Ocomm__monoid__mult(U_11580) ),
    inference(clausify,[status(thm)],[f_3092_3]) ).

cnf(f_3092_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11581,U_11580),U_11583),U_11582) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11580,U_11581,c_Groups_Otimes__class_Otimes(U_11580)),U_11583),c_Groups_Oone__class_Oone(U_11580)),U_11582)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11581),U_11582))
    | ~ sP829(U_11580,U_11581,U_11582,U_11583) ),
    inference(clausify,[status(thm)],[f_3092_3]) ).

cnf(f_3092_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_11581,U_11580),U_11583),U_11582) = c_Groups_Oone__class_Oone(U_11580)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11581),U_11582))
    | ~ sP829(U_11580,U_11581,U_11582,U_11583) ),
    inference(clausify,[status(thm)],[f_3092_3]) ).

fof(f_3093_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_3093_2,plain,
    ! [U_11588,U_11587,U_11586,U_11585,U_11584] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11584),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11584,U_11585,c_Groups_Otimes__class_Otimes(U_11584)),U_11588),c_Groups_Oone__class_Oone(U_11584)),U_11586)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11584,U_11585,c_Groups_Otimes__class_Otimes(U_11584)),U_11588),c_Groups_Oone__class_Oone(U_11584)),U_11587)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11584),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11584,U_11585,c_Groups_Otimes__class_Otimes(U_11584)),U_11588),c_Groups_Oone__class_Oone(U_11584)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11585,tc_HOL_Obool)),U_11586),U_11587))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11584,U_11585,c_Groups_Otimes__class_Otimes(U_11584)),U_11588),c_Groups_Oone__class_Oone(U_11584)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11585,tc_HOL_Obool)),U_11586),U_11587)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11585),U_11587))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11585),U_11586))
      | ~ class_Groups_Ocomm__monoid__mult(U_11584) ),
    inference(variable_rename,[status(thm)],[f_3093_1]) ).

fof(f_3093_3,plain,
    ! [U_11585,U_11584,U_11586,U_11587,U_11588] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11584),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11584,U_11585,c_Groups_Otimes__class_Otimes(U_11584)),U_11588),c_Groups_Oone__class_Oone(U_11584)),U_11586)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11584,U_11585,c_Groups_Otimes__class_Otimes(U_11584)),U_11588),c_Groups_Oone__class_Oone(U_11584)),U_11587)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11584),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11584,U_11585,c_Groups_Otimes__class_Otimes(U_11584)),U_11588),c_Groups_Oone__class_Oone(U_11584)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11585,tc_HOL_Obool)),U_11586),U_11587))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11584,U_11585,c_Groups_Otimes__class_Otimes(U_11584)),U_11588),c_Groups_Oone__class_Oone(U_11584)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11585,tc_HOL_Obool)),U_11586),U_11587)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11585),U_11587))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11585),U_11586))
      | ~ class_Groups_Ocomm__monoid__mult(U_11584) ),
    inference(definitional_conversion,[status(esa)],[f_3093_2]) ).

cnf(f_3093_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11584),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11584,U_11585,c_Groups_Otimes__class_Otimes(U_11584)),U_11588),c_Groups_Oone__class_Oone(U_11584)),U_11586)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11584,U_11585,c_Groups_Otimes__class_Otimes(U_11584)),U_11588),c_Groups_Oone__class_Oone(U_11584)),U_11587)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11584),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11584,U_11585,c_Groups_Otimes__class_Otimes(U_11584)),U_11588),c_Groups_Oone__class_Oone(U_11584)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11585,tc_HOL_Obool)),U_11586),U_11587))),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11584,U_11585,c_Groups_Otimes__class_Otimes(U_11584)),U_11588),c_Groups_Oone__class_Oone(U_11584)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11585,tc_HOL_Obool)),U_11586),U_11587)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11585),U_11587))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11585),U_11586))
    | ~ class_Groups_Ocomm__monoid__mult(U_11584) ),
    inference(clausify,[status(thm)],[f_3093_3]) ).

fof(f_3094_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_3094_2,plain,
    ! [U_11592,U_11591,U_11590,U_11589] :
      ( hAPP(c_Set_Oimage(U_11589,U_11591,U_11592),U_11590) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_11591,tc_HOL_Obool),U_11589,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11591,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11589,tc_fun(U_11591,tc_HOL_Obool),tc_fun(U_11591,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_11591,tc_fun(tc_fun(U_11591,tc_HOL_Obool),tc_fun(U_11591,tc_HOL_Obool)),U_11589),c_Set_Oinsert(U_11591)),U_11592)),c_Orderings_Obot__class_Obot(tc_fun(U_11591,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_11591,tc_HOL_Obool))),U_11590)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11589),U_11590)) ),
    inference(variable_rename,[status(thm)],[f_3094_1]) ).

fof(f_3094_3,plain,
    ! [U_11591,U_11589,U_11590,U_11592] :
      ( hAPP(c_Set_Oimage(U_11589,U_11591,U_11592),U_11590) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_11591,tc_HOL_Obool),U_11589,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11591,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11589,tc_fun(U_11591,tc_HOL_Obool),tc_fun(U_11591,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_11591,tc_fun(tc_fun(U_11591,tc_HOL_Obool),tc_fun(U_11591,tc_HOL_Obool)),U_11589),c_Set_Oinsert(U_11591)),U_11592)),c_Orderings_Obot__class_Obot(tc_fun(U_11591,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_11591,tc_HOL_Obool))),U_11590)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11589),U_11590)) ),
    inference(definitional_conversion,[status(esa)],[f_3094_2]) ).

cnf(f_3094_4,plain,
    ( hAPP(c_Set_Oimage(U_11589,U_11591,U_11592),U_11590) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_fun(U_11591,tc_HOL_Obool),U_11589,c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11591,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(U_11589,tc_fun(U_11591,tc_HOL_Obool),tc_fun(U_11591,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_11591,tc_fun(tc_fun(U_11591,tc_HOL_Obool),tc_fun(U_11591,tc_HOL_Obool)),U_11589),c_Set_Oinsert(U_11591)),U_11592)),c_Orderings_Obot__class_Obot(tc_fun(U_11591,tc_HOL_Obool)))),c_Orderings_Obot__class_Obot(tc_fun(U_11591,tc_HOL_Obool))),U_11590)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11589),U_11590)) ),
    inference(clausify,[status(thm)],[f_3094_3]) ).

fof(f_3095_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_3095_2,plain,
    ! [U_11594,U_11593] :
      ( hAPP(c_Finite__Set_Ocard(U_11593),U_11594) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_11593,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_11593),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11594)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11593),U_11594)) ),
    inference(variable_rename,[status(thm)],[f_3095_1]) ).

fof(f_3095_3,plain,
    ! [U_11593,U_11594] :
      ( hAPP(c_Finite__Set_Ocard(U_11593),U_11594) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_11593,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_11593),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11594)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11593),U_11594)) ),
    inference(definitional_conversion,[status(esa)],[f_3095_2]) ).

cnf(f_3095_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_11593),U_11594) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_11593,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_11593),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11594)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11593),U_11594)) ),
    inference(clausify,[status(thm)],[f_3095_3]) ).

fof(f_3096_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_3096_2,plain,
    ! [U_11596,U_11595] :
      ( ( hAPP(c_Finite__Set_Ocard(U_11595),U_11596) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11595),U_11596)) )
      & ( hAPP(c_Finite__Set_Ocard(U_11595),U_11596) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_11595,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_11595),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11596)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11595),U_11596)) ) ),
    inference(variable_rename,[status(thm)],[f_3096_1]) ).

fof(f_3096_3,plain,
    ( ! [U_11600,U_11598] :
        ( hAPP(c_Finite__Set_Ocard(U_11598),U_11600) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11598),U_11600)) )
    & ! [U_11599,U_11597] :
        ( hAPP(c_Finite__Set_Ocard(U_11597),U_11599) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_11597,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_11597),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11599)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11597),U_11599)) ) ),
    inference(miniscope,[status(thm)],[f_3096_2]) ).

fof(f_3096_4,plain,
    ( ! [U_11598,U_11600] :
        ( hAPP(c_Finite__Set_Ocard(U_11598),U_11600) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11598),U_11600)) )
    & ! [U_11599,U_11597] :
        ( hAPP(c_Finite__Set_Ocard(U_11597),U_11599) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_11597,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_11597),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11599)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11597),U_11599)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3096_3]) ).

cnf(f_3096_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_11597),U_11599) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(tc_Nat_Onat,U_11597,c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),hAPP(c_COMBK(tc_Nat_Onat,U_11597),c_Groups_Oone__class_Oone(tc_Nat_Onat))),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11599)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11597),U_11599)) ),
    inference(clausify,[status(thm)],[f_3096_4]) ).

cnf(f_3096_6,plain,
    ( hAPP(c_Finite__Set_Ocard(U_11598),U_11600) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11598),U_11600)) ),
    inference(clausify,[status(thm)],[f_3096_4]) ).

fof(f_3097_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_3097_2,plain,
    ! [U_11607,U_11606,U_11605,U_11604,U_11603,U_11602,U_11601] :
      ( ( ( hAPP(hAPP(U_11605,U_11607),U_11606) = U_11604
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11602),U_11606)) )
        & ( hAPP(hAPP(U_11605,U_11607),U_11606) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11601,U_11602,U_11603),U_11607),U_11604),U_11606)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11602),U_11606)) ) )
      | ~ c_Big__Operators_Ocomm__monoid__big(U_11601,U_11602,U_11603,U_11604,U_11605) ),
    inference(variable_rename,[status(thm)],[f_3097_1]) ).

fof(f_3097_3,plain,
    ( ! [U_11601,U_11602,U_11603,U_11604,U_11605,U_11606,U_11607] :
        ( hAPP(hAPP(U_11605,U_11607),U_11606) = U_11604
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11602),U_11606))
        | ~ sP830(U_11601,U_11602,U_11603,U_11604,U_11605,U_11606,U_11607) )
    & ! [U_11601,U_11602,U_11603,U_11604,U_11605,U_11606,U_11607] :
        ( hAPP(hAPP(U_11605,U_11607),U_11606) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11601,U_11602,U_11603),U_11607),U_11604),U_11606)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11602),U_11606))
        | ~ sP830(U_11601,U_11602,U_11603,U_11604,U_11605,U_11606,U_11607) )
    & ! [U_11601,U_11602,U_11603,U_11604,U_11605,U_11606,U_11607] :
        ( sP830(U_11601,U_11602,U_11603,U_11604,U_11605,U_11606,U_11607)
        | ~ c_Big__Operators_Ocomm__monoid__big(U_11601,U_11602,U_11603,U_11604,U_11605) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP830])],[f_3097_2]) ).

cnf(f_3097_4,plain,
    ( sP830(U_11601,U_11602,U_11603,U_11604,U_11605,U_11606,U_11607)
    | ~ c_Big__Operators_Ocomm__monoid__big(U_11601,U_11602,U_11603,U_11604,U_11605) ),
    inference(clausify,[status(thm)],[f_3097_3]) ).

cnf(f_3097_5,plain,
    ( hAPP(hAPP(U_11605,U_11607),U_11606) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11601,U_11602,U_11603),U_11607),U_11604),U_11606)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11602),U_11606))
    | ~ sP830(U_11601,U_11602,U_11603,U_11604,U_11605,U_11606,U_11607) ),
    inference(clausify,[status(thm)],[f_3097_3]) ).

cnf(f_3097_6,plain,
    ( hAPP(hAPP(U_11605,U_11607),U_11606) = U_11604
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11602),U_11606))
    | ~ sP830(U_11601,U_11602,U_11603,U_11604,U_11605,U_11606,U_11607) ),
    inference(clausify,[status(thm)],[f_3097_3]) ).

fof(f_3098_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_3098_2,plain,
    ! [U_11613,U_11612,U_11611,U_11610,U_11609] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11609,U_11610,c_Groups_Otimes__class_Otimes(U_11609)),U_11613),c_Groups_Oone__class_Oone(U_11609)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11610,tc_HOL_Obool)),U_11611),U_11612)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11609),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11609,U_11610,c_Groups_Otimes__class_Otimes(U_11609)),U_11613),c_Groups_Oone__class_Oone(U_11609)),U_11611)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11609,U_11610,c_Groups_Otimes__class_Otimes(U_11609)),U_11613),c_Groups_Oone__class_Oone(U_11609)),U_11612))
      | ? [U_11608] :
          ( hAPP(U_11613,U_11608) != c_Groups_Oone__class_Oone(U_11609)
          & hBOOL(hAPP(hAPP(c_member(U_11610),U_11608),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11610,tc_HOL_Obool)),U_11611),U_11612))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11610),U_11612))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11610),U_11611))
      | ~ class_Groups_Ocomm__monoid__mult(U_11609) ),
    inference(variable_rename,[status(thm)],[f_3098_1]) ).

fof(f_3098_3,plain,
    ! [U_11613,U_11612,U_11611,U_11610,U_11609] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11609,U_11610,c_Groups_Otimes__class_Otimes(U_11609)),U_11613),c_Groups_Oone__class_Oone(U_11609)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11610,tc_HOL_Obool)),U_11611),U_11612)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11609),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11609,U_11610,c_Groups_Otimes__class_Otimes(U_11609)),U_11613),c_Groups_Oone__class_Oone(U_11609)),U_11611)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11609,U_11610,c_Groups_Otimes__class_Otimes(U_11609)),U_11613),c_Groups_Oone__class_Oone(U_11609)),U_11612))
      | ( hAPP(U_11613,sK198(U_11613,U_11612,U_11611,U_11610,U_11609)) != c_Groups_Oone__class_Oone(U_11609)
        & hBOOL(hAPP(hAPP(c_member(U_11610),sK198(U_11613,U_11612,U_11611,U_11610,U_11609)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11610,tc_HOL_Obool)),U_11611),U_11612))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11610),U_11612))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11610),U_11611))
      | ~ class_Groups_Ocomm__monoid__mult(U_11609) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK198]),skolemize(U_11608,sK198(U_11613,U_11612,U_11611,U_11610,U_11609))],[f_3098_2]) ).

fof(f_3098_4,plain,
    ( ! [U_11609,U_11610,U_11611,U_11612,U_11613] :
        ( hAPP(U_11613,sK198(U_11613,U_11612,U_11611,U_11610,U_11609)) != c_Groups_Oone__class_Oone(U_11609)
        | ~ sP831(U_11609,U_11610,U_11611,U_11612,U_11613) )
    & ! [U_11609,U_11610,U_11611,U_11612,U_11613] :
        ( hBOOL(hAPP(hAPP(c_member(U_11610),sK198(U_11613,U_11612,U_11611,U_11610,U_11609)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11610,tc_HOL_Obool)),U_11611),U_11612)))
        | ~ sP831(U_11609,U_11610,U_11611,U_11612,U_11613) )
    & ! [U_11609,U_11610,U_11611,U_11612,U_11613] :
        ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11609,U_11610,c_Groups_Otimes__class_Otimes(U_11609)),U_11613),c_Groups_Oone__class_Oone(U_11609)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11610,tc_HOL_Obool)),U_11611),U_11612)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11609),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11609,U_11610,c_Groups_Otimes__class_Otimes(U_11609)),U_11613),c_Groups_Oone__class_Oone(U_11609)),U_11611)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11609,U_11610,c_Groups_Otimes__class_Otimes(U_11609)),U_11613),c_Groups_Oone__class_Oone(U_11609)),U_11612))
        | sP831(U_11609,U_11610,U_11611,U_11612,U_11613)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11610),U_11612))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11610),U_11611))
        | ~ class_Groups_Ocomm__monoid__mult(U_11609) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP831])],[f_3098_3]) ).

cnf(f_3098_5,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11609,U_11610,c_Groups_Otimes__class_Otimes(U_11609)),U_11613),c_Groups_Oone__class_Oone(U_11609)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11610,tc_HOL_Obool)),U_11611),U_11612)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_11609),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11609,U_11610,c_Groups_Otimes__class_Otimes(U_11609)),U_11613),c_Groups_Oone__class_Oone(U_11609)),U_11611)),hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_11609,U_11610,c_Groups_Otimes__class_Otimes(U_11609)),U_11613),c_Groups_Oone__class_Oone(U_11609)),U_11612))
    | sP831(U_11609,U_11610,U_11611,U_11612,U_11613)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11610),U_11612))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11610),U_11611))
    | ~ class_Groups_Ocomm__monoid__mult(U_11609) ),
    inference(clausify,[status(thm)],[f_3098_4]) ).

cnf(f_3098_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11610),sK198(U_11613,U_11612,U_11611,U_11610,U_11609)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11610,tc_HOL_Obool)),U_11611),U_11612)))
    | ~ sP831(U_11609,U_11610,U_11611,U_11612,U_11613) ),
    inference(clausify,[status(thm)],[f_3098_4]) ).

cnf(f_3098_7,plain,
    ( hAPP(U_11613,sK198(U_11613,U_11612,U_11611,U_11610,U_11609)) != c_Groups_Oone__class_Oone(U_11609)
    | ~ sP831(U_11609,U_11610,U_11611,U_11612,U_11613) ),
    inference(clausify,[status(thm)],[f_3098_4]) ).

fof(f_3099_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_3099_2,plain,
    ! [U_11618,U_11617,U_11616] :
      ( hAPP(U_11617,c_Big__Operators_Olattice__class_OInf__fin(U_11616,U_11618)) = c_Big__Operators_Olattice__class_OInf__fin(U_11616,hAPP(c_Set_Oimage(U_11616,U_11616,U_11617),U_11618))
      | U_11618 = c_Orderings_Obot__class_Obot(tc_fun(U_11616,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11616),U_11618))
      | ? [U_11615,U_11614] : hAPP(U_11617,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11616),U_11615),U_11614)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11616),hAPP(U_11617,U_11615)),hAPP(U_11617,U_11614))
      | ~ class_Lattices_Olattice(U_11616) ),
    inference(variable_rename,[status(thm)],[f_3099_1]) ).

fof(f_3099_3,plain,
    ! [U_11618,U_11617,U_11616] :
      ( hAPP(U_11617,c_Big__Operators_Olattice__class_OInf__fin(U_11616,U_11618)) = c_Big__Operators_Olattice__class_OInf__fin(U_11616,hAPP(c_Set_Oimage(U_11616,U_11616,U_11617),U_11618))
      | U_11618 = c_Orderings_Obot__class_Obot(tc_fun(U_11616,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11616),U_11618))
      | ? [U_11614] : hAPP(U_11617,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11616),sK199(U_11618,U_11617,U_11616)),U_11614)) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11616),hAPP(U_11617,sK199(U_11618,U_11617,U_11616))),hAPP(U_11617,U_11614))
      | ~ class_Lattices_Olattice(U_11616) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK199]),skolemize(U_11615,sK199(U_11618,U_11617,U_11616))],[f_3099_2]) ).

fof(f_3099_4,plain,
    ! [U_11618,U_11617,U_11616] :
      ( hAPP(U_11617,c_Big__Operators_Olattice__class_OInf__fin(U_11616,U_11618)) = c_Big__Operators_Olattice__class_OInf__fin(U_11616,hAPP(c_Set_Oimage(U_11616,U_11616,U_11617),U_11618))
      | U_11618 = c_Orderings_Obot__class_Obot(tc_fun(U_11616,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11616),U_11618))
      | hAPP(U_11617,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11616),sK199(U_11618,U_11617,U_11616)),sK200(U_11618,U_11617,U_11616))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11616),hAPP(U_11617,sK199(U_11618,U_11617,U_11616))),hAPP(U_11617,sK200(U_11618,U_11617,U_11616)))
      | ~ class_Lattices_Olattice(U_11616) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK200]),skolemize(U_11614,sK200(U_11618,U_11617,U_11616))],[f_3099_3]) ).

fof(f_3099_5,plain,
    ! [U_11616,U_11618,U_11617] :
      ( hAPP(U_11617,c_Big__Operators_Olattice__class_OInf__fin(U_11616,U_11618)) = c_Big__Operators_Olattice__class_OInf__fin(U_11616,hAPP(c_Set_Oimage(U_11616,U_11616,U_11617),U_11618))
      | U_11618 = c_Orderings_Obot__class_Obot(tc_fun(U_11616,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11616),U_11618))
      | hAPP(U_11617,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11616),sK199(U_11618,U_11617,U_11616)),sK200(U_11618,U_11617,U_11616))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11616),hAPP(U_11617,sK199(U_11618,U_11617,U_11616))),hAPP(U_11617,sK200(U_11618,U_11617,U_11616)))
      | ~ class_Lattices_Olattice(U_11616) ),
    inference(definitional_conversion,[status(esa)],[f_3099_4]) ).

cnf(f_3099_6,plain,
    ( hAPP(U_11617,c_Big__Operators_Olattice__class_OInf__fin(U_11616,U_11618)) = c_Big__Operators_Olattice__class_OInf__fin(U_11616,hAPP(c_Set_Oimage(U_11616,U_11616,U_11617),U_11618))
    | U_11618 = c_Orderings_Obot__class_Obot(tc_fun(U_11616,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11616),U_11618))
    | hAPP(U_11617,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11616),sK199(U_11618,U_11617,U_11616)),sK200(U_11618,U_11617,U_11616))) != hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_11616),hAPP(U_11617,sK199(U_11618,U_11617,U_11616))),hAPP(U_11617,sK200(U_11618,U_11617,U_11616)))
    | ~ class_Lattices_Olattice(U_11616) ),
    inference(clausify,[status(thm)],[f_3099_5]) ).

fof(f_3100_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_3100_2,plain,
    ! [U_11625,U_11624,U_11623,U_11622,U_11621,U_11620,U_11619] :
      ( hAPP(hAPP(U_11623,U_11625),U_11624) = U_11622
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11620),U_11624))
      | ~ c_Big__Operators_Ocomm__monoid__big(U_11619,U_11620,U_11621,U_11622,U_11623) ),
    inference(variable_rename,[status(thm)],[f_3100_1]) ).

fof(f_3100_3,plain,
    ! [U_11625,U_11624,U_11623,U_11622,U_11621,U_11620] :
      ( ! [U_11619] : ~ c_Big__Operators_Ocomm__monoid__big(U_11619,U_11620,U_11621,U_11622,U_11623)
      | hAPP(hAPP(U_11623,U_11625),U_11624) = U_11622
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11620),U_11624)) ),
    inference(miniscope,[status(thm)],[f_3100_2]) ).

fof(f_3100_4,plain,
    ! [U_11625,U_11621,U_11622,U_11620,U_11623,U_11619,U_11624] :
      ( ~ c_Big__Operators_Ocomm__monoid__big(U_11619,U_11620,U_11621,U_11622,U_11623)
      | hAPP(hAPP(U_11623,U_11625),U_11624) = U_11622
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11620),U_11624)) ),
    inference(definitional_conversion,[status(esa)],[f_3100_3]) ).

cnf(f_3100_5,plain,
    ( ~ c_Big__Operators_Ocomm__monoid__big(U_11619,U_11620,U_11621,U_11622,U_11623)
    | hAPP(hAPP(U_11623,U_11625),U_11624) = U_11622
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_11620),U_11624)) ),
    inference(clausify,[status(thm)],[f_3100_4]) ).

fof(f_3101_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_3101_2,plain,
    ! [U_11631,U_11630,U_11629,U_11628,U_11627] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11627,U_11627)),hAPP(hAPP(c_Product__Type_OPair(U_11627,U_11627),hAPP(U_11628,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11630),U_11631))),hAPP(U_11628,U_11630))),c_Transitive__Closure_Ortrancl(U_11627,U_11629)))
      | ? [U_11626] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11627,U_11627)),hAPP(hAPP(c_Product__Type_OPair(U_11627,U_11627),hAPP(U_11628,hAPP(c_Nat_OSuc,U_11626))),hAPP(U_11628,U_11626))),c_Transitive__Closure_Ortrancl(U_11627,U_11629))) ),
    inference(variable_rename,[status(thm)],[f_3101_1]) ).

fof(f_3101_3,plain,
    ! [U_11631,U_11630,U_11629,U_11628,U_11627] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11627,U_11627)),hAPP(hAPP(c_Product__Type_OPair(U_11627,U_11627),hAPP(U_11628,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11630),U_11631))),hAPP(U_11628,U_11630))),c_Transitive__Closure_Ortrancl(U_11627,U_11629)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11627,U_11627)),hAPP(hAPP(c_Product__Type_OPair(U_11627,U_11627),hAPP(U_11628,hAPP(c_Nat_OSuc,sK201(U_11631,U_11630,U_11629,U_11628,U_11627)))),hAPP(U_11628,sK201(U_11631,U_11630,U_11629,U_11628,U_11627)))),c_Transitive__Closure_Ortrancl(U_11627,U_11629))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK201]),skolemize(U_11626,sK201(U_11631,U_11630,U_11629,U_11628,U_11627))],[f_3101_2]) ).

fof(f_3101_4,plain,
    ! [U_11627,U_11628,U_11629,U_11630,U_11631] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11627,U_11627)),hAPP(hAPP(c_Product__Type_OPair(U_11627,U_11627),hAPP(U_11628,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11630),U_11631))),hAPP(U_11628,U_11630))),c_Transitive__Closure_Ortrancl(U_11627,U_11629)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11627,U_11627)),hAPP(hAPP(c_Product__Type_OPair(U_11627,U_11627),hAPP(U_11628,hAPP(c_Nat_OSuc,sK201(U_11631,U_11630,U_11629,U_11628,U_11627)))),hAPP(U_11628,sK201(U_11631,U_11630,U_11629,U_11628,U_11627)))),c_Transitive__Closure_Ortrancl(U_11627,U_11629))) ),
    inference(definitional_conversion,[status(esa)],[f_3101_3]) ).

cnf(f_3101_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_11627,U_11627)),hAPP(hAPP(c_Product__Type_OPair(U_11627,U_11627),hAPP(U_11628,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11630),U_11631))),hAPP(U_11628,U_11630))),c_Transitive__Closure_Ortrancl(U_11627,U_11629)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_11627,U_11627)),hAPP(hAPP(c_Product__Type_OPair(U_11627,U_11627),hAPP(U_11628,hAPP(c_Nat_OSuc,sK201(U_11631,U_11630,U_11629,U_11628,U_11627)))),hAPP(U_11628,sK201(U_11631,U_11630,U_11629,U_11628,U_11627)))),c_Transitive__Closure_Ortrancl(U_11627,U_11629))) ),
    inference(clausify,[status(thm)],[f_3101_4]) ).

fof(f_3102_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_3102_2,plain,
    ! [U_11633,U_11632] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(U_11632,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11632),U_11633)) = 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_11632),U_11633))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11632),U_11633)) ),
    inference(variable_rename,[status(thm)],[f_3102_1]) ).

fof(f_3102_3,plain,
    ! [U_11632,U_11633] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(U_11632,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11632),U_11633)) = 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_11632),U_11633))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11632),U_11633)) ),
    inference(definitional_conversion,[status(esa)],[f_3102_2]) ).

cnf(f_3102_4,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_fun(U_11632,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11632),U_11633)) = 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_11632),U_11633))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11632),U_11633)) ),
    inference(clausify,[status(thm)],[f_3102_3]) ).

fof(f_3103_1,plain,
    ! [V_Qa_2,V_c_2,V_Ga_2,T_b,V_Pa_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_Pa_2),V_c_2),V_Qa_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_Qa_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_b),tc_HOL_Obool))))
          & hBOOL(hAPP(hAPP(V_Pa_2,B_Z),B_s)) ) ),
    inference(fof_nnf,[status(thm)],[fact_escape]) ).

fof(f_3103_2,plain,
    ! [U_11640,U_11639,U_11638,U_11637,U_11636] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_11637,U_11638,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_11637)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_11637),U_11636),U_11639),U_11640)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_11637),tc_HOL_Obool))))
      | ? [U_11635,U_11634] :
          ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_11637,U_11638,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_11637)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_11637),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_11637),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),U_11634))),U_11639),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_11637),hAPP(U_11640,U_11635)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_11637),tc_HOL_Obool))))
          & hBOOL(hAPP(hAPP(U_11636,U_11635),U_11634)) ) ),
    inference(variable_rename,[status(thm)],[f_3103_1]) ).

fof(f_3103_3,plain,
    ! [U_11640,U_11639,U_11638,U_11637,U_11636] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_11637,U_11638,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_11637)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_11637),U_11636),U_11639),U_11640)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_11637),tc_HOL_Obool))))
      | ? [U_11634] :
          ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_11637,U_11638,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_11637)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_11637),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_11637),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),U_11634))),U_11639),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_11637),hAPP(U_11640,sK202(U_11640,U_11639,U_11638,U_11637,U_11636))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_11637),tc_HOL_Obool))))
          & hBOOL(hAPP(hAPP(U_11636,sK202(U_11640,U_11639,U_11638,U_11637,U_11636)),U_11634)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK202]),skolemize(U_11635,sK202(U_11640,U_11639,U_11638,U_11637,U_11636))],[f_3103_2]) ).

fof(f_3103_4,plain,
    ! [U_11640,U_11639,U_11638,U_11637,U_11636] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_11637,U_11638,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_11637)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_11637),U_11636),U_11639),U_11640)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_11637),tc_HOL_Obool))))
      | ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_11637,U_11638,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_11637)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_11637),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_11637),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK203(U_11640,U_11639,U_11638,U_11637,U_11636)))),U_11639),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_11637),hAPP(U_11640,sK202(U_11640,U_11639,U_11638,U_11637,U_11636))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_11637),tc_HOL_Obool))))
        & hBOOL(hAPP(hAPP(U_11636,sK202(U_11640,U_11639,U_11638,U_11637,U_11636)),sK203(U_11640,U_11639,U_11638,U_11637,U_11636))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK203]),skolemize(U_11634,sK203(U_11640,U_11639,U_11638,U_11637,U_11636))],[f_3103_3]) ).

fof(f_3103_5,plain,
    ( ! [U_11636,U_11637,U_11638,U_11639,U_11640] :
        ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_11637,U_11638,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_11637)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_11637),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_11637),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK203(U_11640,U_11639,U_11638,U_11637,U_11636)))),U_11639),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_11637),hAPP(U_11640,sK202(U_11640,U_11639,U_11638,U_11637,U_11636))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_11637),tc_HOL_Obool))))
        | ~ sP832(U_11636,U_11637,U_11638,U_11639,U_11640) )
    & ! [U_11636,U_11637,U_11638,U_11639,U_11640] :
        ( hBOOL(hAPP(hAPP(U_11636,sK202(U_11640,U_11639,U_11638,U_11637,U_11636)),sK203(U_11640,U_11639,U_11638,U_11637,U_11636)))
        | ~ sP832(U_11636,U_11637,U_11638,U_11639,U_11640) )
    & ! [U_11636,U_11637,U_11638,U_11639,U_11640] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(U_11637,U_11638,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_11637)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_11637),U_11636),U_11639),U_11640)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_11637),tc_HOL_Obool))))
        | sP832(U_11636,U_11637,U_11638,U_11639,U_11640) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP832])],[f_3103_4]) ).

cnf(f_3103_6,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_11637,U_11638,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_11637)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_11637),U_11636),U_11639),U_11640)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_11637),tc_HOL_Obool))))
    | sP832(U_11636,U_11637,U_11638,U_11639,U_11640) ),
    inference(clausify,[status(thm)],[f_3103_5]) ).

cnf(f_3103_7,plain,
    ( hBOOL(hAPP(hAPP(U_11636,sK202(U_11640,U_11639,U_11638,U_11637,U_11636)),sK203(U_11640,U_11639,U_11638,U_11637,U_11636)))
    | ~ sP832(U_11636,U_11637,U_11638,U_11639,U_11640) ),
    inference(clausify,[status(thm)],[f_3103_5]) ).

cnf(f_3103_8,plain,
    ( ~ c_Hoare__Mirabelle_Ohoare__derivs(U_11637,U_11638,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_11637)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_11637),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_11637),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),sK203(U_11640,U_11639,U_11638,U_11637,U_11636)))),U_11639),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),U_11637),hAPP(U_11640,sK202(U_11640,U_11639,U_11638,U_11637,U_11636))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_11637),tc_HOL_Obool))))
    | ~ sP832(U_11636,U_11637,U_11638,U_11639,U_11640) ),
    inference(clausify,[status(thm)],[f_3103_5]) ).

fof(f_3104_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_3104_2,plain,
    ! [U_11643,U_11642,U_11641] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11641,tc_HOL_Obool)),U_11642),hAPP(c_Set_OPow(U_11641),U_11643)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11641,tc_HOL_Obool)),U_11642),U_11643)) ),
    inference(variable_rename,[status(thm)],[f_3104_1]) ).

fof(f_3104_3,plain,
    ! [U_11642,U_11641,U_11643] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11641,tc_HOL_Obool)),U_11642),hAPP(c_Set_OPow(U_11641),U_11643)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11641,tc_HOL_Obool)),U_11642),U_11643)) ),
    inference(definitional_conversion,[status(esa)],[f_3104_2]) ).

cnf(f_3104_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11641,tc_HOL_Obool)),U_11642),hAPP(c_Set_OPow(U_11641),U_11643)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11641,tc_HOL_Obool)),U_11642),U_11643)) ),
    inference(clausify,[status(thm)],[f_3104_3]) ).

fof(f_3105_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_3105_2,plain,
    ! [U_11644] : hAPP(c_Set_OPow(U_11644),c_Orderings_Obot__class_Obot(tc_fun(U_11644,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_11644,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_11644,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11644,tc_HOL_Obool),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3105_1]) ).

fof(f_3105_3,plain,
    ! [U_11644] : hAPP(c_Set_OPow(U_11644),c_Orderings_Obot__class_Obot(tc_fun(U_11644,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_11644,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_11644,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11644,tc_HOL_Obool),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3105_2]) ).

cnf(f_3105_4,plain,
    hAPP(c_Set_OPow(U_11644),c_Orderings_Obot__class_Obot(tc_fun(U_11644,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_11644,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_11644,tc_HOL_Obool))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11644,tc_HOL_Obool),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3105_3]) ).

fof(f_3106_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_3106_2,plain,
    ! [U_11646,U_11645] : hAPP(c_Set_OPow(U_11645),U_11646) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11645,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3106_1]) ).

fof(f_3106_3,plain,
    ! [U_11645,U_11646] : hAPP(c_Set_OPow(U_11645),U_11646) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11645,tc_HOL_Obool),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3106_2]) ).

cnf(f_3106_4,plain,
    hAPP(c_Set_OPow(U_11645),U_11646) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_11645,tc_HOL_Obool),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3106_3]) ).

fof(f_3107_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_3107_2,plain,
    ! [U_11648,U_11647] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_11647,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_11647,tc_HOL_Obool))),hAPP(c_Set_OPow(U_11647),U_11648))),
    inference(variable_rename,[status(thm)],[f_3107_1]) ).

fof(f_3107_3,plain,
    ! [U_11647,U_11648] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_11647,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_11647,tc_HOL_Obool))),hAPP(c_Set_OPow(U_11647),U_11648))),
    inference(definitional_conversion,[status(esa)],[f_3107_2]) ).

cnf(f_3107_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(U_11647,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_11647,tc_HOL_Obool))),hAPP(c_Set_OPow(U_11647),U_11648))),
    inference(clausify,[status(thm)],[f_3107_3]) ).

fof(f_3108_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_3108_2,plain,
    ! [U_11651,U_11650,U_11649] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11649,tc_HOL_Obool)),U_11650),U_11651))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11649,tc_HOL_Obool)),U_11650),hAPP(c_Set_OPow(U_11649),U_11651))) ),
    inference(variable_rename,[status(thm)],[f_3108_1]) ).

fof(f_3108_3,plain,
    ! [U_11649,U_11650,U_11651] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11649,tc_HOL_Obool)),U_11650),U_11651))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11649,tc_HOL_Obool)),U_11650),hAPP(c_Set_OPow(U_11649),U_11651))) ),
    inference(definitional_conversion,[status(esa)],[f_3108_2]) ).

cnf(f_3108_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11649,tc_HOL_Obool)),U_11650),U_11651))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11649,tc_HOL_Obool)),U_11650),hAPP(c_Set_OPow(U_11649),U_11651))) ),
    inference(clausify,[status(thm)],[f_3108_3]) ).

fof(f_3109_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_3109_2,plain,
    ! [U_11654,U_11653,U_11652] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11652,tc_HOL_Obool)),U_11653),hAPP(c_Set_OPow(U_11652),U_11654)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11652,tc_HOL_Obool)),U_11653),U_11654)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11652,tc_HOL_Obool)),U_11653),U_11654))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11652,tc_HOL_Obool)),U_11653),hAPP(c_Set_OPow(U_11652),U_11654))) ) ),
    inference(variable_rename,[status(thm)],[f_3109_1]) ).

fof(f_3109_3,plain,
    ( ! [U_11660,U_11658,U_11656] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11656,tc_HOL_Obool)),U_11658),hAPP(c_Set_OPow(U_11656),U_11660)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11656,tc_HOL_Obool)),U_11658),U_11660)) )
    & ! [U_11659,U_11657,U_11655] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11655,tc_HOL_Obool)),U_11657),U_11659))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11655,tc_HOL_Obool)),U_11657),hAPP(c_Set_OPow(U_11655),U_11659))) ) ),
    inference(miniscope,[status(thm)],[f_3109_2]) ).

fof(f_3109_4,plain,
    ( ! [U_11656,U_11658,U_11660] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11656,tc_HOL_Obool)),U_11658),hAPP(c_Set_OPow(U_11656),U_11660)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11656,tc_HOL_Obool)),U_11658),U_11660)) )
    & ! [U_11657,U_11655,U_11659] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11655,tc_HOL_Obool)),U_11657),U_11659))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11655,tc_HOL_Obool)),U_11657),hAPP(c_Set_OPow(U_11655),U_11659))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3109_3]) ).

cnf(f_3109_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11655,tc_HOL_Obool)),U_11657),U_11659))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11655,tc_HOL_Obool)),U_11657),hAPP(c_Set_OPow(U_11655),U_11659))) ),
    inference(clausify,[status(thm)],[f_3109_4]) ).

cnf(f_3109_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11656,tc_HOL_Obool)),U_11658),hAPP(c_Set_OPow(U_11656),U_11660)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11656,tc_HOL_Obool)),U_11658),U_11660)) ),
    inference(clausify,[status(thm)],[f_3109_4]) ).

fof(f_3110_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_3110_2,plain,
    ! [U_11662,U_11661] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_11661,tc_HOL_Obool)),U_11662),hAPP(c_Set_OPow(U_11661),U_11662))),
    inference(variable_rename,[status(thm)],[f_3110_1]) ).

fof(f_3110_3,plain,
    ! [U_11661,U_11662] : hBOOL(hAPP(hAPP(c_member(tc_fun(U_11661,tc_HOL_Obool)),U_11662),hAPP(c_Set_OPow(U_11661),U_11662))),
    inference(definitional_conversion,[status(esa)],[f_3110_2]) ).

cnf(f_3110_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(U_11661,tc_HOL_Obool)),U_11662),hAPP(c_Set_OPow(U_11661),U_11662))),
    inference(clausify,[status(thm)],[f_3110_3]) ).

fof(f_3111_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_3111_2,plain,
    ! [U_11665,U_11664,U_11663] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11663,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11663),U_11664)),hAPP(c_Set_OPow(U_11663),U_11665)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11663,tc_HOL_Obool)),U_11664),U_11665)) ),
    inference(variable_rename,[status(thm)],[f_3111_1]) ).

fof(f_3111_3,plain,
    ! [U_11663,U_11664,U_11665] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11663,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11663),U_11664)),hAPP(c_Set_OPow(U_11663),U_11665)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11663,tc_HOL_Obool)),U_11664),U_11665)) ),
    inference(definitional_conversion,[status(esa)],[f_3111_2]) ).

cnf(f_3111_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11663,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11663),U_11664)),hAPP(c_Set_OPow(U_11663),U_11665)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11663,tc_HOL_Obool)),U_11664),U_11665)) ),
    inference(clausify,[status(thm)],[f_3111_3]) ).

fof(f_3112_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_3112_2,plain,
    ! [U_11668,U_11667,U_11666] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11666,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_11666,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11666),U_11667)),hAPP(c_Set_OPow(U_11666),U_11668))),hAPP(c_Set_OPow(U_11666),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11666,tc_HOL_Obool)),U_11667),U_11668)))),
    inference(variable_rename,[status(thm)],[f_3112_1]) ).

fof(f_3112_3,plain,
    ! [U_11666,U_11667,U_11668] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11666,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_11666,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11666),U_11667)),hAPP(c_Set_OPow(U_11666),U_11668))),hAPP(c_Set_OPow(U_11666),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11666,tc_HOL_Obool)),U_11667),U_11668)))),
    inference(definitional_conversion,[status(esa)],[f_3112_2]) ).

cnf(f_3112_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11666,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_11666,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11666),U_11667)),hAPP(c_Set_OPow(U_11666),U_11668))),hAPP(c_Set_OPow(U_11666),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11666,tc_HOL_Obool)),U_11667),U_11668)))),
    inference(clausify,[status(thm)],[f_3112_3]) ).

fof(f_3113_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_3113_2,plain,
    ! [U_11671,U_11670,U_11669] : hAPP(c_Set_Oimage(U_11670,tc_fun(U_11670,tc_HOL_Obool),U_11669),U_11671) != hAPP(c_Set_OPow(U_11670),U_11671),
    inference(variable_rename,[status(thm)],[f_3113_1]) ).

fof(f_3113_3,plain,
    ! [U_11669,U_11670,U_11671] : hAPP(c_Set_Oimage(U_11670,tc_fun(U_11670,tc_HOL_Obool),U_11669),U_11671) != hAPP(c_Set_OPow(U_11670),U_11671),
    inference(definitional_conversion,[status(esa)],[f_3113_2]) ).

cnf(f_3113_4,plain,
    hAPP(c_Set_Oimage(U_11670,tc_fun(U_11670,tc_HOL_Obool),U_11669),U_11671) != hAPP(c_Set_OPow(U_11670),U_11671),
    inference(clausify,[status(thm)],[f_3113_3]) ).

fof(f_3114_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_3114_2,plain,
    ! [U_11676,U_11675,U_11674,U_11673,U_11672] :
      ( hAPP(c_Set_Oimage(tc_fun(U_11672,tc_HOL_Obool),tc_fun(U_11673,tc_HOL_Obool),c_Set_Oimage(U_11672,U_11673,U_11674)),hAPP(c_Set_OPow(U_11672),U_11675)) = hAPP(c_Set_OPow(U_11673),U_11676)
      | hAPP(c_Set_Oimage(U_11672,U_11673,U_11674),U_11675) != U_11676 ),
    inference(variable_rename,[status(thm)],[f_3114_1]) ).

fof(f_3114_3,plain,
    ! [U_11672,U_11673,U_11674,U_11675,U_11676] :
      ( hAPP(c_Set_Oimage(tc_fun(U_11672,tc_HOL_Obool),tc_fun(U_11673,tc_HOL_Obool),c_Set_Oimage(U_11672,U_11673,U_11674)),hAPP(c_Set_OPow(U_11672),U_11675)) = hAPP(c_Set_OPow(U_11673),U_11676)
      | hAPP(c_Set_Oimage(U_11672,U_11673,U_11674),U_11675) != U_11676 ),
    inference(definitional_conversion,[status(esa)],[f_3114_2]) ).

cnf(f_3114_4,plain,
    ( hAPP(c_Set_Oimage(tc_fun(U_11672,tc_HOL_Obool),tc_fun(U_11673,tc_HOL_Obool),c_Set_Oimage(U_11672,U_11673,U_11674)),hAPP(c_Set_OPow(U_11672),U_11675)) = hAPP(c_Set_OPow(U_11673),U_11676)
    | hAPP(c_Set_Oimage(U_11672,U_11673,U_11674),U_11675) != U_11676 ),
    inference(clausify,[status(thm)],[f_3114_3]) ).

fof(f_3115_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_3115_2,plain,
    ! [U_11679,U_11678,U_11677] : hAPP(c_Set_OPow(U_11677),hAPP(hAPP(c_Set_Oinsert(U_11677),U_11678),U_11679)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_11677,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11677),U_11679)),hAPP(c_Set_Oimage(tc_fun(U_11677,tc_HOL_Obool),tc_fun(U_11677,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_11677),U_11678)),hAPP(c_Set_OPow(U_11677),U_11679))),
    inference(variable_rename,[status(thm)],[f_3115_1]) ).

fof(f_3115_3,plain,
    ! [U_11677,U_11678,U_11679] : hAPP(c_Set_OPow(U_11677),hAPP(hAPP(c_Set_Oinsert(U_11677),U_11678),U_11679)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_11677,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11677),U_11679)),hAPP(c_Set_Oimage(tc_fun(U_11677,tc_HOL_Obool),tc_fun(U_11677,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_11677),U_11678)),hAPP(c_Set_OPow(U_11677),U_11679))),
    inference(definitional_conversion,[status(esa)],[f_3115_2]) ).

cnf(f_3115_4,plain,
    hAPP(c_Set_OPow(U_11677),hAPP(hAPP(c_Set_Oinsert(U_11677),U_11678),U_11679)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_11677,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11677),U_11679)),hAPP(c_Set_Oimage(tc_fun(U_11677,tc_HOL_Obool),tc_fun(U_11677,tc_HOL_Obool),hAPP(c_Set_Oinsert(U_11677),U_11678)),hAPP(c_Set_OPow(U_11677),U_11679))),
    inference(clausify,[status(thm)],[f_3115_3]) ).

fof(f_3116_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_3116_2,plain,
    ! [U_11682,U_11681,U_11680] : hAPP(c_Set_OPow(U_11680),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11680,tc_HOL_Obool)),U_11681),U_11682)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_11680,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11680),U_11681)),hAPP(c_Set_OPow(U_11680),U_11682)),
    inference(variable_rename,[status(thm)],[f_3116_1]) ).

fof(f_3116_3,plain,
    ! [U_11680,U_11681,U_11682] : hAPP(c_Set_OPow(U_11680),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11680,tc_HOL_Obool)),U_11681),U_11682)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_11680,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11680),U_11681)),hAPP(c_Set_OPow(U_11680),U_11682)),
    inference(definitional_conversion,[status(esa)],[f_3116_2]) ).

cnf(f_3116_4,plain,
    hAPP(c_Set_OPow(U_11680),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11680,tc_HOL_Obool)),U_11681),U_11682)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_11680,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_OPow(U_11680),U_11681)),hAPP(c_Set_OPow(U_11680),U_11682)),
    inference(clausify,[status(thm)],[f_3116_3]) ).

fof(f_3117_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_3117_2,plain,
    ! [U_11687,U_11686,U_11685,U_11684,U_11683] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11683,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_11684,tc_HOL_Obool),tc_fun(U_11683,tc_HOL_Obool),c_Set_Oimage(U_11684,U_11683,U_11685)),hAPP(c_Set_OPow(U_11684),U_11686))),hAPP(c_Set_OPow(U_11683),U_11687)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11683,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11684,U_11683,U_11685),U_11686)),U_11687)) ),
    inference(variable_rename,[status(thm)],[f_3117_1]) ).

fof(f_3117_3,plain,
    ! [U_11683,U_11684,U_11685,U_11686,U_11687] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11683,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_11684,tc_HOL_Obool),tc_fun(U_11683,tc_HOL_Obool),c_Set_Oimage(U_11684,U_11683,U_11685)),hAPP(c_Set_OPow(U_11684),U_11686))),hAPP(c_Set_OPow(U_11683),U_11687)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11683,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11684,U_11683,U_11685),U_11686)),U_11687)) ),
    inference(definitional_conversion,[status(esa)],[f_3117_2]) ).

cnf(f_3117_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11683,tc_HOL_Obool),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_fun(U_11684,tc_HOL_Obool),tc_fun(U_11683,tc_HOL_Obool),c_Set_Oimage(U_11684,U_11683,U_11685)),hAPP(c_Set_OPow(U_11684),U_11686))),hAPP(c_Set_OPow(U_11683),U_11687)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11683,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_11684,U_11683,U_11685),U_11686)),U_11687)) ),
    inference(clausify,[status(thm)],[f_3117_3]) ).

fof(f_3118_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_3118_2,plain,
    ! [U_11689,U_11688] : hAPP(c_Set_OPow(U_11688),U_11689) = hAPP(c_Set_OCollect(tc_fun(U_11688,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_11688,tc_HOL_Obool),tc_fun(U_11688,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_11688,tc_HOL_Obool))),U_11689)),
    inference(variable_rename,[status(thm)],[f_3118_1]) ).

fof(f_3118_3,plain,
    ! [U_11688,U_11689] : hAPP(c_Set_OPow(U_11688),U_11689) = hAPP(c_Set_OCollect(tc_fun(U_11688,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_11688,tc_HOL_Obool),tc_fun(U_11688,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_11688,tc_HOL_Obool))),U_11689)),
    inference(definitional_conversion,[status(esa)],[f_3118_2]) ).

cnf(f_3118_4,plain,
    hAPP(c_Set_OPow(U_11688),U_11689) = hAPP(c_Set_OCollect(tc_fun(U_11688,tc_HOL_Obool)),hAPP(hAPP(c_COMBC(tc_fun(U_11688,tc_HOL_Obool),tc_fun(U_11688,tc_HOL_Obool),tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(tc_fun(U_11688,tc_HOL_Obool))),U_11689)),
    inference(clausify,[status(thm)],[f_3118_3]) ).

fof(f_3119_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_3119_2,plain,
    ! [U_11691,U_11690] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11690,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11690),U_11691)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11690),U_11691)) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11690),U_11691))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11690,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11690),U_11691))) ) ),
    inference(variable_rename,[status(thm)],[f_3119_1]) ).

fof(f_3119_3,plain,
    ( ! [U_11695,U_11693] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11693,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11693),U_11695)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11693),U_11695)) )
    & ! [U_11694,U_11692] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11692),U_11694))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11692,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11692),U_11694))) ) ),
    inference(miniscope,[status(thm)],[f_3119_2]) ).

fof(f_3119_4,plain,
    ( ! [U_11695,U_11693] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11693,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11693),U_11695)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11693),U_11695)) )
    & ! [U_11692,U_11694] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11692),U_11694))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11692,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11692),U_11694))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3119_3]) ).

cnf(f_3119_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11692),U_11694))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11692,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11692),U_11694))) ),
    inference(clausify,[status(thm)],[f_3119_4]) ).

cnf(f_3119_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_11693,tc_HOL_Obool)),hAPP(c_Set_OPow(U_11693),U_11695)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11693),U_11695)) ),
    inference(clausify,[status(thm)],[f_3119_4]) ).

fof(f_3120_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_3120_2,plain,
    ! [U_11697,U_11696] : hAPP(c_Set_OPow(U_11696),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11696,tc_HOL_Obool)),U_11697)) = hAPP(c_Set_OCollect(tc_fun(U_11696,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_11696,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_11696,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_11696,tc_HOL_Obool),tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_11696,tc_HOL_Obool)),c_COMBS(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_11696,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_11696,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_11696,tc_HOL_Obool),tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_fun(U_11696,tc_HOL_Obool)),tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_fun(U_11696,tc_HOL_Obool)),tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_11696,tc_HOL_Obool)),c_COMBB(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_11696,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_11696,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_11696,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_11696,tc_HOL_Obool)),U_11697)),c_Set_OPow(U_11696))))),
    inference(variable_rename,[status(thm)],[f_3120_1]) ).

fof(f_3120_3,plain,
    ! [U_11696,U_11697] : hAPP(c_Set_OPow(U_11696),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11696,tc_HOL_Obool)),U_11697)) = hAPP(c_Set_OCollect(tc_fun(U_11696,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_11696,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_11696,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_11696,tc_HOL_Obool),tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_11696,tc_HOL_Obool)),c_COMBS(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_11696,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_11696,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_11696,tc_HOL_Obool),tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_fun(U_11696,tc_HOL_Obool)),tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_fun(U_11696,tc_HOL_Obool)),tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_11696,tc_HOL_Obool)),c_COMBB(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_11696,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_11696,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_11696,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_11696,tc_HOL_Obool)),U_11697)),c_Set_OPow(U_11696))))),
    inference(definitional_conversion,[status(esa)],[f_3120_2]) ).

cnf(f_3120_4,plain,
    hAPP(c_Set_OPow(U_11696),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_11696,tc_HOL_Obool)),U_11697)) = hAPP(c_Set_OCollect(tc_fun(U_11696,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_11696,tc_HOL_Obool)),c_HOL_OEx(tc_fun(U_11696,tc_HOL_Obool))),hAPP(hAPP(c_COMBC(tc_fun(U_11696,tc_HOL_Obool),tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_11696,tc_HOL_Obool)),c_COMBS(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(U_11696,tc_HOL_Obool)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(U_11696,tc_HOL_Obool)),c_fconj)),hAPP(hAPP(c_COMBC(tc_fun(U_11696,tc_HOL_Obool),tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_fun(U_11696,tc_HOL_Obool)),tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_fun(U_11696,tc_HOL_Obool)),tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool)),tc_fun(U_11696,tc_HOL_Obool)),c_COMBB(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_11696,tc_HOL_Obool))),c_fequal)),c_Groups_Ouminus__class_Ouminus(tc_fun(U_11696,tc_HOL_Obool)))))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_11696,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,tc_fun(U_11696,tc_HOL_Obool)),hAPP(c_member(tc_fun(U_11696,tc_HOL_Obool)),U_11697)),c_Set_OPow(U_11696))))),
    inference(clausify,[status(thm)],[f_3120_3]) ).

fof(f_3121_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_3121_2,plain,
    ! [U_11700,U_11699,U_11698] :
      ( ( hBOOL(hAPP(c_Predicate_OPowp(U_11698,hAPP(hAPP(c_COMBC(U_11698,tc_fun(U_11698,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11698)),U_11699)),U_11700))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11698,tc_HOL_Obool)),U_11700),hAPP(c_Set_OPow(U_11698),U_11699))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11698,tc_HOL_Obool)),U_11700),hAPP(c_Set_OPow(U_11698),U_11699)))
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_11698,hAPP(hAPP(c_COMBC(U_11698,tc_fun(U_11698,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11698)),U_11699)),U_11700)) ) ),
    inference(variable_rename,[status(thm)],[f_3121_1]) ).

fof(f_3121_3,plain,
    ( ! [U_11706,U_11704,U_11702] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_11702,hAPP(hAPP(c_COMBC(U_11702,tc_fun(U_11702,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11702)),U_11704)),U_11706))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11702,tc_HOL_Obool)),U_11706),hAPP(c_Set_OPow(U_11702),U_11704))) )
    & ! [U_11705,U_11703,U_11701] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11701,tc_HOL_Obool)),U_11705),hAPP(c_Set_OPow(U_11701),U_11703)))
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_11701,hAPP(hAPP(c_COMBC(U_11701,tc_fun(U_11701,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11701)),U_11703)),U_11705)) ) ),
    inference(miniscope,[status(thm)],[f_3121_2]) ).

fof(f_3121_4,plain,
    ( ! [U_11702,U_11704,U_11706] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_11702,hAPP(hAPP(c_COMBC(U_11702,tc_fun(U_11702,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11702)),U_11704)),U_11706))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11702,tc_HOL_Obool)),U_11706),hAPP(c_Set_OPow(U_11702),U_11704))) )
    & ! [U_11703,U_11701,U_11705] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11701,tc_HOL_Obool)),U_11705),hAPP(c_Set_OPow(U_11701),U_11703)))
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_11701,hAPP(hAPP(c_COMBC(U_11701,tc_fun(U_11701,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11701)),U_11703)),U_11705)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3121_3]) ).

cnf(f_3121_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_11701,tc_HOL_Obool)),U_11705),hAPP(c_Set_OPow(U_11701),U_11703)))
    | ~ hBOOL(hAPP(c_Predicate_OPowp(U_11701,hAPP(hAPP(c_COMBC(U_11701,tc_fun(U_11701,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11701)),U_11703)),U_11705)) ),
    inference(clausify,[status(thm)],[f_3121_4]) ).

cnf(f_3121_6,plain,
    ( hBOOL(hAPP(c_Predicate_OPowp(U_11702,hAPP(hAPP(c_COMBC(U_11702,tc_fun(U_11702,tc_HOL_Obool),tc_HOL_Obool),c_member(U_11702)),U_11704)),U_11706))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_11702,tc_HOL_Obool)),U_11706),hAPP(c_Set_OPow(U_11702),U_11704))) ),
    inference(clausify,[status(thm)],[f_3121_4]) ).

fof(f_3122_1,plain,
    ! [V_Pa_2,V_A_2,T_b] :
      ( hBOOL(hAPP(V_Pa_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))
      | ? [B_a,B_A] :
          ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_3122_2,plain,
    ! [U_11711,U_11710,U_11709] :
      ( hBOOL(hAPP(U_11711,c_Orderings_Obot__class_Obot(tc_fun(U_11709,tc_HOL_Obool))))
      | ? [U_11708,U_11707] :
          ( ~ hBOOL(hAPP(U_11711,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11709,tc_HOL_Obool)),U_11707),hAPP(hAPP(c_Set_Oinsert(U_11709),U_11708),c_Orderings_Obot__class_Obot(tc_fun(U_11709,tc_HOL_Obool))))))
          & hBOOL(hAPP(U_11711,U_11707))
          & hBOOL(hAPP(hAPP(c_member(U_11709),U_11708),U_11707))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_11709),U_11707)) )
      | ~ hBOOL(hAPP(U_11711,U_11710))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11709),U_11710)) ),
    inference(variable_rename,[status(thm)],[f_3122_1]) ).

fof(f_3122_3,plain,
    ! [U_11711,U_11710,U_11709] :
      ( hBOOL(hAPP(U_11711,c_Orderings_Obot__class_Obot(tc_fun(U_11709,tc_HOL_Obool))))
      | ? [U_11707] :
          ( ~ hBOOL(hAPP(U_11711,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11709,tc_HOL_Obool)),U_11707),hAPP(hAPP(c_Set_Oinsert(U_11709),sK204(U_11711,U_11710,U_11709)),c_Orderings_Obot__class_Obot(tc_fun(U_11709,tc_HOL_Obool))))))
          & hBOOL(hAPP(U_11711,U_11707))
          & hBOOL(hAPP(hAPP(c_member(U_11709),sK204(U_11711,U_11710,U_11709)),U_11707))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_11709),U_11707)) )
      | ~ hBOOL(hAPP(U_11711,U_11710))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11709),U_11710)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK204]),skolemize(U_11708,sK204(U_11711,U_11710,U_11709))],[f_3122_2]) ).

fof(f_3122_4,plain,
    ! [U_11711,U_11710,U_11709] :
      ( hBOOL(hAPP(U_11711,c_Orderings_Obot__class_Obot(tc_fun(U_11709,tc_HOL_Obool))))
      | ( ~ hBOOL(hAPP(U_11711,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11709,tc_HOL_Obool)),sK205(U_11711,U_11710,U_11709)),hAPP(hAPP(c_Set_Oinsert(U_11709),sK204(U_11711,U_11710,U_11709)),c_Orderings_Obot__class_Obot(tc_fun(U_11709,tc_HOL_Obool))))))
        & hBOOL(hAPP(U_11711,sK205(U_11711,U_11710,U_11709)))
        & hBOOL(hAPP(hAPP(c_member(U_11709),sK204(U_11711,U_11710,U_11709)),sK205(U_11711,U_11710,U_11709)))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(U_11709),sK205(U_11711,U_11710,U_11709))) )
      | ~ hBOOL(hAPP(U_11711,U_11710))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11709),U_11710)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK205]),skolemize(U_11707,sK205(U_11711,U_11710,U_11709))],[f_3122_3]) ).

fof(f_3122_5,plain,
    ( ! [U_11709,U_11710,U_11711] :
        ( ~ hBOOL(hAPP(U_11711,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11709,tc_HOL_Obool)),sK205(U_11711,U_11710,U_11709)),hAPP(hAPP(c_Set_Oinsert(U_11709),sK204(U_11711,U_11710,U_11709)),c_Orderings_Obot__class_Obot(tc_fun(U_11709,tc_HOL_Obool))))))
        | ~ sP833(U_11709,U_11710,U_11711) )
    & ! [U_11709,U_11710,U_11711] :
        ( hBOOL(hAPP(U_11711,sK205(U_11711,U_11710,U_11709)))
        | ~ sP833(U_11709,U_11710,U_11711) )
    & ! [U_11709,U_11710,U_11711] :
        ( hBOOL(hAPP(hAPP(c_member(U_11709),sK204(U_11711,U_11710,U_11709)),sK205(U_11711,U_11710,U_11709)))
        | ~ sP833(U_11709,U_11710,U_11711) )
    & ! [U_11709,U_11710,U_11711] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11709),sK205(U_11711,U_11710,U_11709)))
        | ~ sP833(U_11709,U_11710,U_11711) )
    & ! [U_11709,U_11710,U_11711] :
        ( hBOOL(hAPP(U_11711,c_Orderings_Obot__class_Obot(tc_fun(U_11709,tc_HOL_Obool))))
        | sP833(U_11709,U_11710,U_11711)
        | ~ hBOOL(hAPP(U_11711,U_11710))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11709),U_11710)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP833])],[f_3122_4]) ).

cnf(f_3122_6,plain,
    ( hBOOL(hAPP(U_11711,c_Orderings_Obot__class_Obot(tc_fun(U_11709,tc_HOL_Obool))))
    | sP833(U_11709,U_11710,U_11711)
    | ~ hBOOL(hAPP(U_11711,U_11710))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_11709),U_11710)) ),
    inference(clausify,[status(thm)],[f_3122_5]) ).

cnf(f_3122_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_11709),sK205(U_11711,U_11710,U_11709)))
    | ~ sP833(U_11709,U_11710,U_11711) ),
    inference(clausify,[status(thm)],[f_3122_5]) ).

cnf(f_3122_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_11709),sK204(U_11711,U_11710,U_11709)),sK205(U_11711,U_11710,U_11709)))
    | ~ sP833(U_11709,U_11710,U_11711) ),
    inference(clausify,[status(thm)],[f_3122_5]) ).

cnf(f_3122_9,plain,
    ( hBOOL(hAPP(U_11711,sK205(U_11711,U_11710,U_11709)))
    | ~ sP833(U_11709,U_11710,U_11711) ),
    inference(clausify,[status(thm)],[f_3122_5]) ).

cnf(f_3122_10,plain,
    ( ~ hBOOL(hAPP(U_11711,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11709,tc_HOL_Obool)),sK205(U_11711,U_11710,U_11709)),hAPP(hAPP(c_Set_Oinsert(U_11709),sK204(U_11711,U_11710,U_11709)),c_Orderings_Obot__class_Obot(tc_fun(U_11709,tc_HOL_Obool))))))
    | ~ sP833(U_11709,U_11710,U_11711) ),
    inference(clausify,[status(thm)],[f_3122_5]) ).

fof(f_3123_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_3123_2,plain,
    ! [U_11715,U_11714,U_11713,U_11712] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11712,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11712,U_11713,U_11714)),c_SetInterval_Oord__class_OatLeastAtMost(U_11712,U_11714,U_11715)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_11712,U_11713,U_11715)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11712),U_11714),U_11715))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11712),U_11713),U_11714))
      | ~ class_Orderings_Olinorder(U_11712) ),
    inference(variable_rename,[status(thm)],[f_3123_1]) ).

fof(f_3123_3,plain,
    ! [U_11713,U_11715,U_11714,U_11712] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11712,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11712,U_11713,U_11714)),c_SetInterval_Oord__class_OatLeastAtMost(U_11712,U_11714,U_11715)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_11712,U_11713,U_11715)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11712),U_11714),U_11715))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11712),U_11713),U_11714))
      | ~ class_Orderings_Olinorder(U_11712) ),
    inference(definitional_conversion,[status(esa)],[f_3123_2]) ).

cnf(f_3123_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11712,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11712,U_11713,U_11714)),c_SetInterval_Oord__class_OatLeastAtMost(U_11712,U_11714,U_11715)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_11712,U_11713,U_11715)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11712),U_11714),U_11715))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11712),U_11713),U_11714))
    | ~ class_Orderings_Olinorder(U_11712) ),
    inference(clausify,[status(thm)],[f_3123_3]) ).

fof(f_3124_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_3124_2,plain,
    ! [U_11717,U_11716] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11716,U_11717))),
    inference(variable_rename,[status(thm)],[f_3124_1]) ).

fof(f_3124_3,plain,
    ! [U_11717,U_11716] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11716,U_11717))),
    inference(definitional_conversion,[status(esa)],[f_3124_2]) ).

cnf(f_3124_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11716,U_11717))),
    inference(clausify,[status(thm)],[f_3124_3]) ).

fof(f_3125_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_3125_2,plain,
    ! [U_11719,U_11718] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11718,U_11719))),
    inference(variable_rename,[status(thm)],[f_3125_1]) ).

fof(f_3125_3,plain,
    ! [U_11718,U_11719] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11718,U_11719))),
    inference(definitional_conversion,[status(esa)],[f_3125_2]) ).

cnf(f_3125_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11718,U_11719))),
    inference(clausify,[status(thm)],[f_3125_3]) ).

fof(f_3126_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_3126_2,plain,
    ! [U_11722,U_11721,U_11720] : 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_11720)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11721,U_11722)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11721),U_11720),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11722),U_11720)),
    inference(variable_rename,[status(thm)],[f_3126_1]) ).

fof(f_3126_3,plain,
    ! [U_11720,U_11721,U_11722] : 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_11720)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11721,U_11722)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11721),U_11720),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11722),U_11720)),
    inference(definitional_conversion,[status(esa)],[f_3126_2]) ).

cnf(f_3126_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_11720)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11721,U_11722)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11721),U_11720),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11722),U_11720)),
    inference(clausify,[status(thm)],[f_3126_3]) ).

fof(f_3127_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_3127_2,plain,
    ! [U_11724,U_11723] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11723,U_11724) = 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_11723),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11724))),
    inference(variable_rename,[status(thm)],[f_3127_1]) ).

fof(f_3127_3,plain,
    ! [U_11723,U_11724] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11723,U_11724) = 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_11723),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11724))),
    inference(definitional_conversion,[status(esa)],[f_3127_2]) ).

cnf(f_3127_4,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11723,U_11724) = 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_11723),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_11724))),
    inference(clausify,[status(thm)],[f_3127_3]) ).

fof(f_3128_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_3128_2,plain,
    ! [U_11726,U_11725] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11725,U_11726)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11725),hAPP(c_Nat_OSuc,U_11726)),
    inference(variable_rename,[status(thm)],[f_3128_1]) ).

fof(f_3128_3,plain,
    ! [U_11725,U_11726] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11725,U_11726)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11725),hAPP(c_Nat_OSuc,U_11726)),
    inference(definitional_conversion,[status(esa)],[f_3128_2]) ).

cnf(f_3128_4,plain,
    hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11725,U_11726)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11725),hAPP(c_Nat_OSuc,U_11726)),
    inference(clausify,[status(thm)],[f_3128_3]) ).

fof(f_3129_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_3129_2,plain,
    ! [U_11728,U_11727] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11727,U_11728) = 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_11727),hAPP(c_Int_Onat,U_11728)))
      | ~ c_Nat__Transfer_Ois__nat(U_11728)
      | ~ c_Nat__Transfer_Ois__nat(U_11727) ),
    inference(variable_rename,[status(thm)],[f_3129_1]) ).

fof(f_3129_3,plain,
    ! [U_11727,U_11728] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11727,U_11728) = 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_11727),hAPP(c_Int_Onat,U_11728)))
      | ~ c_Nat__Transfer_Ois__nat(U_11728)
      | ~ c_Nat__Transfer_Ois__nat(U_11727) ),
    inference(definitional_conversion,[status(esa)],[f_3129_2]) ).

cnf(f_3129_4,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11727,U_11728) = 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_11727),hAPP(c_Int_Onat,U_11728)))
    | ~ c_Nat__Transfer_Ois__nat(U_11728)
    | ~ c_Nat__Transfer_Ois__nat(U_11727) ),
    inference(clausify,[status(thm)],[f_3129_3]) ).

fof(f_3130_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_3130_2,plain,
    ! [U_11730,U_11729] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11729,U_11730))
      | ~ c_Nat__Transfer_Ois__nat(U_11729) ),
    inference(variable_rename,[status(thm)],[f_3130_1]) ).

fof(f_3130_3,plain,
    ! [U_11730,U_11729] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11729,U_11730))
      | ~ c_Nat__Transfer_Ois__nat(U_11729) ),
    inference(definitional_conversion,[status(esa)],[f_3130_2]) ).

cnf(f_3130_4,plain,
    ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11729,U_11730))
    | ~ c_Nat__Transfer_Ois__nat(U_11729) ),
    inference(clausify,[status(thm)],[f_3130_3]) ).

fof(f_3131_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_3131_2,plain,
    ! [U_11733,U_11732,U_11731] :
      ( ( ( c_SetInterval_Oord__class_OatLeastAtMost(U_11731,U_11732,U_11733) = c_Orderings_Obot__class_Obot(tc_fun(U_11731,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11731),U_11732),U_11733)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11731),U_11732),U_11733))
          | c_SetInterval_Oord__class_OatLeastAtMost(U_11731,U_11732,U_11733) != c_Orderings_Obot__class_Obot(tc_fun(U_11731,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(U_11731) ),
    inference(variable_rename,[status(thm)],[f_3131_1]) ).

fof(f_3131_3,plain,
    ( ! [U_11731,U_11732,U_11733] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(U_11731,U_11732,U_11733) = c_Orderings_Obot__class_Obot(tc_fun(U_11731,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11731),U_11732),U_11733))
        | ~ sP834(U_11731,U_11732,U_11733) )
    & ! [U_11731,U_11732,U_11733] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11731),U_11732),U_11733))
        | c_SetInterval_Oord__class_OatLeastAtMost(U_11731,U_11732,U_11733) != c_Orderings_Obot__class_Obot(tc_fun(U_11731,tc_HOL_Obool))
        | ~ sP834(U_11731,U_11732,U_11733) )
    & ! [U_11731,U_11732,U_11733] :
        ( sP834(U_11731,U_11732,U_11733)
        | ~ class_Orderings_Oorder(U_11731) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP834])],[f_3131_2]) ).

cnf(f_3131_4,plain,
    ( sP834(U_11731,U_11732,U_11733)
    | ~ class_Orderings_Oorder(U_11731) ),
    inference(clausify,[status(thm)],[f_3131_3]) ).

cnf(f_3131_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11731),U_11732),U_11733))
    | c_SetInterval_Oord__class_OatLeastAtMost(U_11731,U_11732,U_11733) != c_Orderings_Obot__class_Obot(tc_fun(U_11731,tc_HOL_Obool))
    | ~ sP834(U_11731,U_11732,U_11733) ),
    inference(clausify,[status(thm)],[f_3131_3]) ).

cnf(f_3131_6,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_11731,U_11732,U_11733) = c_Orderings_Obot__class_Obot(tc_fun(U_11731,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11731),U_11732),U_11733))
    | ~ sP834(U_11731,U_11732,U_11733) ),
    inference(clausify,[status(thm)],[f_3131_3]) ).

fof(f_3132_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_3132_2,plain,
    ! [U_11736,U_11735,U_11734] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_11734,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11734,U_11735,U_11736)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11734),U_11735),U_11736)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11734),U_11735),U_11736))
          | c_Orderings_Obot__class_Obot(tc_fun(U_11734,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_11734,U_11735,U_11736) ) )
      | ~ class_Orderings_Oorder(U_11734) ),
    inference(variable_rename,[status(thm)],[f_3132_1]) ).

fof(f_3132_3,plain,
    ( ! [U_11735,U_11736,U_11734] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_11734,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11734,U_11735,U_11736)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11734),U_11735),U_11736))
        | ~ sP835(U_11735,U_11736,U_11734) )
    & ! [U_11735,U_11736,U_11734] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11734),U_11735),U_11736))
        | c_Orderings_Obot__class_Obot(tc_fun(U_11734,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_11734,U_11735,U_11736)
        | ~ sP835(U_11735,U_11736,U_11734) )
    & ! [U_11735,U_11736,U_11734] :
        ( sP835(U_11735,U_11736,U_11734)
        | ~ class_Orderings_Oorder(U_11734) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP835])],[f_3132_2]) ).

cnf(f_3132_4,plain,
    ( sP835(U_11735,U_11736,U_11734)
    | ~ class_Orderings_Oorder(U_11734) ),
    inference(clausify,[status(thm)],[f_3132_3]) ).

cnf(f_3132_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11734),U_11735),U_11736))
    | c_Orderings_Obot__class_Obot(tc_fun(U_11734,tc_HOL_Obool)) != c_SetInterval_Oord__class_OatLeastAtMost(U_11734,U_11735,U_11736)
    | ~ sP835(U_11735,U_11736,U_11734) ),
    inference(clausify,[status(thm)],[f_3132_3]) ).

cnf(f_3132_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_11734,tc_HOL_Obool)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11734,U_11735,U_11736)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11734),U_11735),U_11736))
    | ~ sP835(U_11735,U_11736,U_11734) ),
    inference(clausify,[status(thm)],[f_3132_3]) ).

fof(f_3133_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_3133_2,plain,
    ! [U_11739,U_11738,U_11737] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_11737,U_11739,U_11738) = c_Orderings_Obot__class_Obot(tc_fun(U_11737,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11737),U_11738),U_11739))
      | ~ class_Orderings_Oorder(U_11737) ),
    inference(variable_rename,[status(thm)],[f_3133_1]) ).

fof(f_3133_3,plain,
    ! [U_11739,U_11738,U_11737] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_11737,U_11739,U_11738) = c_Orderings_Obot__class_Obot(tc_fun(U_11737,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11737),U_11738),U_11739))
      | ~ class_Orderings_Oorder(U_11737) ),
    inference(definitional_conversion,[status(esa)],[f_3133_2]) ).

cnf(f_3133_4,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_11737,U_11739,U_11738) = c_Orderings_Obot__class_Obot(tc_fun(U_11737,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11737),U_11738),U_11739))
    | ~ class_Orderings_Oorder(U_11737) ),
    inference(clausify,[status(thm)],[f_3133_3]) ).

fof(f_3134_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_3134_2,plain,
    ! [U_11744,U_11743,U_11742,U_11741,U_11740] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11740,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11740,U_11741,U_11742)),c_SetInterval_Oord__class_OatLeastAtMost(U_11740,U_11743,U_11744)))
          | ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11740),U_11742),U_11744))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11740),U_11743),U_11741)) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11740),U_11741),U_11742)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11740),U_11742),U_11744))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11740),U_11743),U_11741)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11740),U_11741),U_11742))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11740,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11740,U_11741,U_11742)),c_SetInterval_Oord__class_OatLeastAtMost(U_11740,U_11743,U_11744))) ) )
      | ~ class_Orderings_Oorder(U_11740) ),
    inference(variable_rename,[status(thm)],[f_3134_1]) ).

fof(f_3134_3,plain,
    ( ! [U_11740,U_11741,U_11742,U_11743,U_11744] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11740),U_11742),U_11744))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11740),U_11743),U_11741))
        | ~ sP837(U_11740,U_11741,U_11742,U_11743,U_11744) )
    & ! [U_11740,U_11741,U_11742,U_11743,U_11744] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11740),U_11741),U_11742))
        | ~ sP837(U_11740,U_11741,U_11742,U_11743,U_11744) )
    & ! [U_11740,U_11741,U_11742,U_11743,U_11744] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11740),U_11742),U_11744))
        | ~ sP836(U_11740,U_11741,U_11742,U_11743,U_11744) )
    & ! [U_11740,U_11741,U_11742,U_11743,U_11744] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11740),U_11743),U_11741))
        | ~ sP836(U_11740,U_11741,U_11742,U_11743,U_11744) )
    & ! [U_11740,U_11741,U_11742,U_11743,U_11744] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11740,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11740,U_11741,U_11742)),c_SetInterval_Oord__class_OatLeastAtMost(U_11740,U_11743,U_11744)))
        | sP837(U_11740,U_11741,U_11742,U_11743,U_11744)
        | ~ sP838(U_11740,U_11741,U_11742,U_11743,U_11744) )
    & ! [U_11740,U_11741,U_11742,U_11743,U_11744] :
        ( sP836(U_11740,U_11741,U_11742,U_11743,U_11744)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11740),U_11741),U_11742))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11740,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11740,U_11741,U_11742)),c_SetInterval_Oord__class_OatLeastAtMost(U_11740,U_11743,U_11744)))
        | ~ sP838(U_11740,U_11741,U_11742,U_11743,U_11744) )
    & ! [U_11740,U_11741,U_11742,U_11743,U_11744] :
        ( sP838(U_11740,U_11741,U_11742,U_11743,U_11744)
        | ~ class_Orderings_Oorder(U_11740) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP836,sP837,sP838])],[f_3134_2]) ).

cnf(f_3134_4,plain,
    ( sP838(U_11740,U_11741,U_11742,U_11743,U_11744)
    | ~ class_Orderings_Oorder(U_11740) ),
    inference(clausify,[status(thm)],[f_3134_3]) ).

cnf(f_3134_5,plain,
    ( sP836(U_11740,U_11741,U_11742,U_11743,U_11744)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11740),U_11741),U_11742))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11740,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11740,U_11741,U_11742)),c_SetInterval_Oord__class_OatLeastAtMost(U_11740,U_11743,U_11744)))
    | ~ sP838(U_11740,U_11741,U_11742,U_11743,U_11744) ),
    inference(clausify,[status(thm)],[f_3134_3]) ).

cnf(f_3134_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11740,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11740,U_11741,U_11742)),c_SetInterval_Oord__class_OatLeastAtMost(U_11740,U_11743,U_11744)))
    | sP837(U_11740,U_11741,U_11742,U_11743,U_11744)
    | ~ sP838(U_11740,U_11741,U_11742,U_11743,U_11744) ),
    inference(clausify,[status(thm)],[f_3134_3]) ).

cnf(f_3134_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11740),U_11743),U_11741))
    | ~ sP836(U_11740,U_11741,U_11742,U_11743,U_11744) ),
    inference(clausify,[status(thm)],[f_3134_3]) ).

cnf(f_3134_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11740),U_11742),U_11744))
    | ~ sP836(U_11740,U_11741,U_11742,U_11743,U_11744) ),
    inference(clausify,[status(thm)],[f_3134_3]) ).

cnf(f_3134_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11740),U_11741),U_11742))
    | ~ sP837(U_11740,U_11741,U_11742,U_11743,U_11744) ),
    inference(clausify,[status(thm)],[f_3134_3]) ).

cnf(f_3134_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11740),U_11742),U_11744))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11740),U_11743),U_11741))
    | ~ sP837(U_11740,U_11741,U_11742,U_11743,U_11744) ),
    inference(clausify,[status(thm)],[f_3134_3]) ).

fof(f_3135_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_3135_2,plain,
    ! [U_11747,U_11746,U_11745] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_11745,U_11746,U_11747) = hAPP(hAPP(c_Set_Oinsert(U_11745),U_11746),c_Orderings_Obot__class_Obot(tc_fun(U_11745,tc_HOL_Obool)))
      | U_11746 != U_11747
      | ~ class_Orderings_Oorder(U_11745) ),
    inference(variable_rename,[status(thm)],[f_3135_1]) ).

fof(f_3135_3,plain,
    ! [U_11747,U_11745,U_11746] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_11745,U_11746,U_11747) = hAPP(hAPP(c_Set_Oinsert(U_11745),U_11746),c_Orderings_Obot__class_Obot(tc_fun(U_11745,tc_HOL_Obool)))
      | U_11746 != U_11747
      | ~ class_Orderings_Oorder(U_11745) ),
    inference(definitional_conversion,[status(esa)],[f_3135_2]) ).

cnf(f_3135_4,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_11745,U_11746,U_11747) = hAPP(hAPP(c_Set_Oinsert(U_11745),U_11746),c_Orderings_Obot__class_Obot(tc_fun(U_11745,tc_HOL_Obool)))
    | U_11746 != U_11747
    | ~ class_Orderings_Oorder(U_11745) ),
    inference(clausify,[status(thm)],[f_3135_3]) ).

fof(f_3136_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_3136_2,plain,
    ! [U_11751,U_11750,U_11749,U_11748] :
      ( ( ( c_SetInterval_Oord__class_OatLeastAtMost(U_11748,U_11749,U_11750) = hAPP(hAPP(c_Set_Oinsert(U_11748),U_11751),c_Orderings_Obot__class_Obot(tc_fun(U_11748,tc_HOL_Obool)))
          | U_11750 != U_11751
          | U_11749 != U_11750 )
        & ( ( U_11750 = U_11751
            & U_11749 = U_11750 )
          | c_SetInterval_Oord__class_OatLeastAtMost(U_11748,U_11749,U_11750) != hAPP(hAPP(c_Set_Oinsert(U_11748),U_11751),c_Orderings_Obot__class_Obot(tc_fun(U_11748,tc_HOL_Obool))) ) )
      | ~ class_Orderings_Oorder(U_11748) ),
    inference(variable_rename,[status(thm)],[f_3136_1]) ).

fof(f_3136_3,plain,
    ( ! [U_11751,U_11749,U_11750] :
        ( U_11750 = U_11751
        | ~ sP839(U_11751,U_11749,U_11750) )
    & ! [U_11751,U_11749,U_11750] :
        ( U_11749 = U_11750
        | ~ sP839(U_11751,U_11749,U_11750) )
    & ! [U_11751,U_11749,U_11750,U_11748] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(U_11748,U_11749,U_11750) = hAPP(hAPP(c_Set_Oinsert(U_11748),U_11751),c_Orderings_Obot__class_Obot(tc_fun(U_11748,tc_HOL_Obool)))
        | U_11750 != U_11751
        | U_11749 != U_11750
        | ~ sP840(U_11751,U_11749,U_11750,U_11748) )
    & ! [U_11751,U_11749,U_11750,U_11748] :
        ( sP839(U_11751,U_11749,U_11750)
        | c_SetInterval_Oord__class_OatLeastAtMost(U_11748,U_11749,U_11750) != hAPP(hAPP(c_Set_Oinsert(U_11748),U_11751),c_Orderings_Obot__class_Obot(tc_fun(U_11748,tc_HOL_Obool)))
        | ~ sP840(U_11751,U_11749,U_11750,U_11748) )
    & ! [U_11751,U_11749,U_11750,U_11748] :
        ( sP840(U_11751,U_11749,U_11750,U_11748)
        | ~ class_Orderings_Oorder(U_11748) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP839,sP840])],[f_3136_2]) ).

cnf(f_3136_4,plain,
    ( sP840(U_11751,U_11749,U_11750,U_11748)
    | ~ class_Orderings_Oorder(U_11748) ),
    inference(clausify,[status(thm)],[f_3136_3]) ).

cnf(f_3136_5,plain,
    ( sP839(U_11751,U_11749,U_11750)
    | c_SetInterval_Oord__class_OatLeastAtMost(U_11748,U_11749,U_11750) != hAPP(hAPP(c_Set_Oinsert(U_11748),U_11751),c_Orderings_Obot__class_Obot(tc_fun(U_11748,tc_HOL_Obool)))
    | ~ sP840(U_11751,U_11749,U_11750,U_11748) ),
    inference(clausify,[status(thm)],[f_3136_3]) ).

cnf(f_3136_6,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_11748,U_11749,U_11750) = hAPP(hAPP(c_Set_Oinsert(U_11748),U_11751),c_Orderings_Obot__class_Obot(tc_fun(U_11748,tc_HOL_Obool)))
    | U_11750 != U_11751
    | U_11749 != U_11750
    | ~ sP840(U_11751,U_11749,U_11750,U_11748) ),
    inference(clausify,[status(thm)],[f_3136_3]) ).

cnf(f_3136_7,plain,
    ( U_11749 = U_11750
    | ~ sP839(U_11751,U_11749,U_11750) ),
    inference(clausify,[status(thm)],[f_3136_3]) ).

cnf(f_3136_8,plain,
    ( U_11750 = U_11751
    | ~ sP839(U_11751,U_11749,U_11750) ),
    inference(clausify,[status(thm)],[f_3136_3]) ).

fof(f_3137_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_3137_2,plain,
    ! [U_11753,U_11752] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_11752,U_11753,U_11753) = hAPP(hAPP(c_Set_Oinsert(U_11752),U_11753),c_Orderings_Obot__class_Obot(tc_fun(U_11752,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_11752) ),
    inference(variable_rename,[status(thm)],[f_3137_1]) ).

fof(f_3137_3,plain,
    ! [U_11752,U_11753] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(U_11752,U_11753,U_11753) = hAPP(hAPP(c_Set_Oinsert(U_11752),U_11753),c_Orderings_Obot__class_Obot(tc_fun(U_11752,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_11752) ),
    inference(definitional_conversion,[status(esa)],[f_3137_2]) ).

cnf(f_3137_4,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(U_11752,U_11753,U_11753) = hAPP(hAPP(c_Set_Oinsert(U_11752),U_11753),c_Orderings_Obot__class_Obot(tc_fun(U_11752,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_11752) ),
    inference(clausify,[status(thm)],[f_3137_3]) ).

fof(f_3138_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_3138_2,plain,
    ! [U_11756,U_11755,U_11754] :
      ( hAPP(c_Set_Oimage(U_11754,U_11754,c_Groups_Ouminus__class_Ouminus(U_11754)),c_SetInterval_Oord__class_OatLeastAtMost(U_11754,U_11755,U_11756)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11754,hAPP(c_Groups_Ouminus__class_Ouminus(U_11754),U_11756),hAPP(c_Groups_Ouminus__class_Ouminus(U_11754),U_11755))
      | ~ class_Groups_Oordered__ab__group__add(U_11754) ),
    inference(variable_rename,[status(thm)],[f_3138_1]) ).

fof(f_3138_3,plain,
    ! [U_11754,U_11755,U_11756] :
      ( hAPP(c_Set_Oimage(U_11754,U_11754,c_Groups_Ouminus__class_Ouminus(U_11754)),c_SetInterval_Oord__class_OatLeastAtMost(U_11754,U_11755,U_11756)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11754,hAPP(c_Groups_Ouminus__class_Ouminus(U_11754),U_11756),hAPP(c_Groups_Ouminus__class_Ouminus(U_11754),U_11755))
      | ~ class_Groups_Oordered__ab__group__add(U_11754) ),
    inference(definitional_conversion,[status(esa)],[f_3138_2]) ).

cnf(f_3138_4,plain,
    ( hAPP(c_Set_Oimage(U_11754,U_11754,c_Groups_Ouminus__class_Ouminus(U_11754)),c_SetInterval_Oord__class_OatLeastAtMost(U_11754,U_11755,U_11756)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11754,hAPP(c_Groups_Ouminus__class_Ouminus(U_11754),U_11756),hAPP(c_Groups_Ouminus__class_Ouminus(U_11754),U_11755))
    | ~ class_Groups_Oordered__ab__group__add(U_11754) ),
    inference(clausify,[status(thm)],[f_3138_3]) ).

fof(f_3139_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_3139_2,plain,
    ! [U_11758,U_11757] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11757),U_11758) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_11757,U_11758),
    inference(variable_rename,[status(thm)],[f_3139_1]) ).

fof(f_3139_3,plain,
    ! [U_11758,U_11757] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11757),U_11758) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_11757,U_11758),
    inference(definitional_conversion,[status(esa)],[f_3139_2]) ).

cnf(f_3139_4,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11757),U_11758) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_11757,U_11758),
    inference(clausify,[status(thm)],[f_3139_3]) ).

fof(f_3140_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_3140_2,plain,
    ! [U_11760,U_11759] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11759,U_11760))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11759)) ),
    inference(variable_rename,[status(thm)],[f_3140_1]) ).

fof(f_3140_3,plain,
    ! [U_11759,U_11760] :
      ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11759,U_11760))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11759)) ),
    inference(definitional_conversion,[status(esa)],[f_3140_2]) ).

cnf(f_3140_4,plain,
    ( c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11759,U_11760))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11759)) ),
    inference(clausify,[status(thm)],[f_3140_3]) ).

fof(f_3141_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_3141_2,plain,
    ! [U_11762,U_11761] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11761,U_11762)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11762)),U_11761),
    inference(variable_rename,[status(thm)],[f_3141_1]) ).

fof(f_3141_3,plain,
    ! [U_11761,U_11762] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11761,U_11762)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11762)),U_11761),
    inference(definitional_conversion,[status(esa)],[f_3141_2]) ).

cnf(f_3141_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11761,U_11762)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11762)),U_11761),
    inference(clausify,[status(thm)],[f_3141_3]) ).

fof(f_3142_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_3142_2,plain,
    ! [U_11764,U_11763] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11763,hAPP(c_Nat_OSuc,U_11764)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11764)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11763,U_11764))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11763),hAPP(c_Nat_OSuc,U_11764))) ),
    inference(variable_rename,[status(thm)],[f_3142_1]) ).

fof(f_3142_3,plain,
    ! [U_11763,U_11764] :
      ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11763,hAPP(c_Nat_OSuc,U_11764)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11764)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11763,U_11764))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11763),hAPP(c_Nat_OSuc,U_11764))) ),
    inference(definitional_conversion,[status(esa)],[f_3142_2]) ).

cnf(f_3142_4,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11763,hAPP(c_Nat_OSuc,U_11764)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_11764)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11763,U_11764))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11763),hAPP(c_Nat_OSuc,U_11764))) ),
    inference(clausify,[status(thm)],[f_3142_3]) ).

fof(f_3143_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_3143_2,plain,
    ! [U_11767,U_11766,U_11765] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11765,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_11765,U_11766)),c_Predicate_OPowp(U_11765,U_11767)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11765,tc_HOL_Obool)),U_11766),U_11767)) ),
    inference(variable_rename,[status(thm)],[f_3143_1]) ).

fof(f_3143_3,plain,
    ! [U_11765,U_11766,U_11767] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11765,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_11765,U_11766)),c_Predicate_OPowp(U_11765,U_11767)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11765,tc_HOL_Obool)),U_11766),U_11767)) ),
    inference(definitional_conversion,[status(esa)],[f_3143_2]) ).

cnf(f_3143_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_11765,tc_HOL_Obool),tc_HOL_Obool)),c_Predicate_OPowp(U_11765,U_11766)),c_Predicate_OPowp(U_11765,U_11767)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11765,tc_HOL_Obool)),U_11766),U_11767)) ),
    inference(clausify,[status(thm)],[f_3143_3]) ).

fof(f_3144_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_3144_2,plain,
    ! [U_11769,U_11768] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11768),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11769) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_11768,U_11769),
    inference(variable_rename,[status(thm)],[f_3144_1]) ).

fof(f_3144_3,plain,
    ! [U_11768,U_11769] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11768),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11769) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_11768,U_11769),
    inference(definitional_conversion,[status(esa)],[f_3144_2]) ).

cnf(f_3144_4,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11768),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11769) = c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_11768,U_11769),
    inference(clausify,[status(thm)],[f_3144_3]) ).

fof(f_3145_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_3145_2,plain,
    ! [U_11774,U_11773,U_11772,U_11771,U_11770] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11770,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11770,U_11771,U_11772)),c_SetInterval_Oord__class_OatLeastAtMost(U_11770,U_11773,U_11774)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11770,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11770),U_11771),U_11773),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11770),U_11772),U_11774))
      | ~ class_Orderings_Olinorder(U_11770) ),
    inference(variable_rename,[status(thm)],[f_3145_1]) ).

fof(f_3145_3,plain,
    ! [U_11770,U_11771,U_11772,U_11773,U_11774] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11770,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11770,U_11771,U_11772)),c_SetInterval_Oord__class_OatLeastAtMost(U_11770,U_11773,U_11774)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11770,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11770),U_11771),U_11773),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11770),U_11772),U_11774))
      | ~ class_Orderings_Olinorder(U_11770) ),
    inference(definitional_conversion,[status(esa)],[f_3145_2]) ).

cnf(f_3145_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11770,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11770,U_11771,U_11772)),c_SetInterval_Oord__class_OatLeastAtMost(U_11770,U_11773,U_11774)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11770,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_11770),U_11771),U_11773),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_11770),U_11772),U_11774))
    | ~ class_Orderings_Olinorder(U_11770) ),
    inference(clausify,[status(thm)],[f_3145_3]) ).

fof(f_3146_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_3146_2,plain,
    ! [U_11779,U_11778,U_11777,U_11776,U_11775] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11775,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11775,U_11776,U_11777)),c_SetInterval_Oord__class_OatLeastAtMost(U_11775,U_11778,U_11779)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11778),U_11779))
          | ( ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11775),U_11777),U_11779))
                & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11775),U_11778),U_11776)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11777),U_11779))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11778),U_11776)) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11776),U_11777)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11778),U_11779))
            & ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11775),U_11777),U_11779))
                  | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11775),U_11778),U_11776)) )
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11777),U_11779))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11778),U_11776)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11776),U_11777)) ) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11775,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11775,U_11776,U_11777)),c_SetInterval_Oord__class_OatLeastAtMost(U_11775,U_11778,U_11779))) ) )
      | ~ class_Orderings_Oorder(U_11775) ),
    inference(variable_rename,[status(thm)],[f_3146_1]) ).

fof(f_3146_3,plain,
    ( ! [U_11775,U_11776,U_11777,U_11778,U_11779] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11775),U_11777),U_11779))
        | ~ sP843(U_11775,U_11776,U_11777,U_11778,U_11779) )
    & ! [U_11775,U_11776,U_11777,U_11778,U_11779] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11775),U_11778),U_11776))
        | ~ sP843(U_11775,U_11776,U_11777,U_11778,U_11779) )
    & ! [U_11775,U_11776,U_11777,U_11778,U_11779] :
        ( sP843(U_11775,U_11776,U_11777,U_11778,U_11779)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11777),U_11779))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11778),U_11776))
        | ~ sP844(U_11775,U_11776,U_11777,U_11778,U_11779) )
    & ! [U_11775,U_11776,U_11777,U_11778,U_11779] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11776),U_11777))
        | ~ sP844(U_11775,U_11776,U_11777,U_11778,U_11779) )
    & ! [U_11775,U_11776,U_11777,U_11778,U_11779] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11775),U_11777),U_11779))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11775),U_11778),U_11776))
        | ~ sP841(U_11775,U_11776,U_11777,U_11778,U_11779) )
    & ! [U_11775,U_11776,U_11777,U_11778,U_11779] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11777),U_11779))
        | ~ sP841(U_11775,U_11776,U_11777,U_11778,U_11779) )
    & ! [U_11775,U_11776,U_11777,U_11778,U_11779] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11778),U_11776))
        | ~ sP841(U_11775,U_11776,U_11777,U_11778,U_11779) )
    & ! [U_11775,U_11776,U_11777,U_11778,U_11779] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11778),U_11779))
        | ~ sP842(U_11775,U_11776,U_11777,U_11778,U_11779) )
    & ! [U_11775,U_11776,U_11777,U_11778,U_11779] :
        ( sP841(U_11775,U_11776,U_11777,U_11778,U_11779)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11776),U_11777))
        | ~ sP842(U_11775,U_11776,U_11777,U_11778,U_11779) )
    & ! [U_11775,U_11776,U_11777,U_11778,U_11779] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11775,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11775,U_11776,U_11777)),c_SetInterval_Oord__class_OatLeastAtMost(U_11775,U_11778,U_11779)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11778),U_11779))
        | sP844(U_11775,U_11776,U_11777,U_11778,U_11779)
        | ~ sP845(U_11775,U_11776,U_11777,U_11778,U_11779) )
    & ! [U_11775,U_11776,U_11777,U_11778,U_11779] :
        ( sP842(U_11775,U_11776,U_11777,U_11778,U_11779)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11775,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11775,U_11776,U_11777)),c_SetInterval_Oord__class_OatLeastAtMost(U_11775,U_11778,U_11779)))
        | ~ sP845(U_11775,U_11776,U_11777,U_11778,U_11779) )
    & ! [U_11775,U_11776,U_11777,U_11778,U_11779] :
        ( sP845(U_11775,U_11776,U_11777,U_11778,U_11779)
        | ~ class_Orderings_Oorder(U_11775) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP841,sP842,sP843,sP844,sP845])],[f_3146_2]) ).

cnf(f_3146_4,plain,
    ( sP845(U_11775,U_11776,U_11777,U_11778,U_11779)
    | ~ class_Orderings_Oorder(U_11775) ),
    inference(clausify,[status(thm)],[f_3146_3]) ).

cnf(f_3146_5,plain,
    ( sP842(U_11775,U_11776,U_11777,U_11778,U_11779)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11775,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11775,U_11776,U_11777)),c_SetInterval_Oord__class_OatLeastAtMost(U_11775,U_11778,U_11779)))
    | ~ sP845(U_11775,U_11776,U_11777,U_11778,U_11779) ),
    inference(clausify,[status(thm)],[f_3146_3]) ).

cnf(f_3146_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_11775,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11775,U_11776,U_11777)),c_SetInterval_Oord__class_OatLeastAtMost(U_11775,U_11778,U_11779)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11778),U_11779))
    | sP844(U_11775,U_11776,U_11777,U_11778,U_11779)
    | ~ sP845(U_11775,U_11776,U_11777,U_11778,U_11779) ),
    inference(clausify,[status(thm)],[f_3146_3]) ).

cnf(f_3146_7,plain,
    ( sP841(U_11775,U_11776,U_11777,U_11778,U_11779)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11776),U_11777))
    | ~ sP842(U_11775,U_11776,U_11777,U_11778,U_11779) ),
    inference(clausify,[status(thm)],[f_3146_3]) ).

cnf(f_3146_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11778),U_11779))
    | ~ sP842(U_11775,U_11776,U_11777,U_11778,U_11779) ),
    inference(clausify,[status(thm)],[f_3146_3]) ).

cnf(f_3146_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11778),U_11776))
    | ~ sP841(U_11775,U_11776,U_11777,U_11778,U_11779) ),
    inference(clausify,[status(thm)],[f_3146_3]) ).

cnf(f_3146_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11777),U_11779))
    | ~ sP841(U_11775,U_11776,U_11777,U_11778,U_11779) ),
    inference(clausify,[status(thm)],[f_3146_3]) ).

cnf(f_3146_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11775),U_11777),U_11779))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11775),U_11778),U_11776))
    | ~ sP841(U_11775,U_11776,U_11777,U_11778,U_11779) ),
    inference(clausify,[status(thm)],[f_3146_3]) ).

cnf(f_3146_12,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11776),U_11777))
    | ~ sP844(U_11775,U_11776,U_11777,U_11778,U_11779) ),
    inference(clausify,[status(thm)],[f_3146_3]) ).

cnf(f_3146_13,plain,
    ( sP843(U_11775,U_11776,U_11777,U_11778,U_11779)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11777),U_11779))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11775),U_11778),U_11776))
    | ~ sP844(U_11775,U_11776,U_11777,U_11778,U_11779) ),
    inference(clausify,[status(thm)],[f_3146_3]) ).

cnf(f_3146_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11775),U_11778),U_11776))
    | ~ sP843(U_11775,U_11776,U_11777,U_11778,U_11779) ),
    inference(clausify,[status(thm)],[f_3146_3]) ).

cnf(f_3146_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11775),U_11777),U_11779))
    | ~ sP843(U_11775,U_11776,U_11777,U_11778,U_11779) ),
    inference(clausify,[status(thm)],[f_3146_3]) ).

fof(f_3147_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_3147_2,plain,
    ! [U_11783,U_11782,U_11781,U_11780] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11780,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11780,U_11781,U_11782)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11780,U_11782,U_11783)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11780,U_11781,U_11783)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11780),U_11782),U_11783))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11780),U_11781),U_11782))
      | ~ class_Orderings_Olinorder(U_11780) ),
    inference(variable_rename,[status(thm)],[f_3147_1]) ).

fof(f_3147_3,plain,
    ! [U_11781,U_11783,U_11780,U_11782] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11780,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11780,U_11781,U_11782)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11780,U_11782,U_11783)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11780,U_11781,U_11783)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11780),U_11782),U_11783))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11780),U_11781),U_11782))
      | ~ class_Orderings_Olinorder(U_11780) ),
    inference(definitional_conversion,[status(esa)],[f_3147_2]) ).

cnf(f_3147_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11780,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11780,U_11781,U_11782)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11780,U_11782,U_11783)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11780,U_11781,U_11783)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11780),U_11782),U_11783))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11780),U_11781),U_11782))
    | ~ class_Orderings_Olinorder(U_11780) ),
    inference(clausify,[status(thm)],[f_3147_3]) ).

fof(f_3148_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_3148_2,plain,
    ! [U_11787,U_11786,U_11785,U_11784] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11784,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11784,U_11785,U_11786)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11784,U_11786,U_11787)) = c_Orderings_Obot__class_Obot(tc_fun(U_11784,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11784) ),
    inference(variable_rename,[status(thm)],[f_3148_1]) ).

fof(f_3148_3,plain,
    ! [U_11785,U_11786,U_11787,U_11784] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11784,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11784,U_11785,U_11786)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11784,U_11786,U_11787)) = c_Orderings_Obot__class_Obot(tc_fun(U_11784,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11784) ),
    inference(definitional_conversion,[status(esa)],[f_3148_2]) ).

cnf(f_3148_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11784,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11784,U_11785,U_11786)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11784,U_11786,U_11787)) = c_Orderings_Obot__class_Obot(tc_fun(U_11784,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11784) ),
    inference(clausify,[status(thm)],[f_3148_3]) ).

fof(f_3149_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_3149_2,plain,
    ! [U_11791,U_11790,U_11789,U_11788] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11788,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11788,U_11789,U_11790)),c_SetInterval_Oord__class_OatLeastAtMost(U_11788,U_11790,U_11791)) = c_Orderings_Obot__class_Obot(tc_fun(U_11788,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11788) ),
    inference(variable_rename,[status(thm)],[f_3149_1]) ).

fof(f_3149_3,plain,
    ! [U_11790,U_11791,U_11788,U_11789] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11788,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11788,U_11789,U_11790)),c_SetInterval_Oord__class_OatLeastAtMost(U_11788,U_11790,U_11791)) = c_Orderings_Obot__class_Obot(tc_fun(U_11788,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11788) ),
    inference(definitional_conversion,[status(esa)],[f_3149_2]) ).

cnf(f_3149_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11788,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11788,U_11789,U_11790)),c_SetInterval_Oord__class_OatLeastAtMost(U_11788,U_11790,U_11791)) = c_Orderings_Obot__class_Obot(tc_fun(U_11788,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11788) ),
    inference(clausify,[status(thm)],[f_3149_3]) ).

fof(f_3150_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_3150_2,plain,
    ! [U_11795,U_11794,U_11793,U_11792] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11792,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11792,U_11793,U_11794)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11792,U_11794,U_11795)) = c_Orderings_Obot__class_Obot(tc_fun(U_11792,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11792) ),
    inference(variable_rename,[status(thm)],[f_3150_1]) ).

fof(f_3150_3,plain,
    ! [U_11792,U_11793,U_11794,U_11795] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11792,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11792,U_11793,U_11794)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11792,U_11794,U_11795)) = c_Orderings_Obot__class_Obot(tc_fun(U_11792,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11792) ),
    inference(definitional_conversion,[status(esa)],[f_3150_2]) ).

cnf(f_3150_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11792,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_11792,U_11793,U_11794)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_11792,U_11794,U_11795)) = c_Orderings_Obot__class_Obot(tc_fun(U_11792,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11792) ),
    inference(clausify,[status(thm)],[f_3150_3]) ).

fof(f_3151_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_3151_2,plain,
    ! [U_11797,U_11796] :
      ( ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11797,U_11796) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_11797),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11797),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11796))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11796),U_11797)) )
      & ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11797,U_11796) = 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_11796),U_11797)) ) ),
    inference(variable_rename,[status(thm)],[f_3151_1]) ).

fof(f_3151_3,plain,
    ( ! [U_11801,U_11799] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11801,U_11799) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_11801),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11801),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11799))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11799),U_11801)) )
    & ! [U_11800,U_11798] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11800,U_11798) = 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_11798),U_11800)) ) ),
    inference(miniscope,[status(thm)],[f_3151_2]) ).

fof(f_3151_4,plain,
    ( ! [U_11801,U_11799] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11801,U_11799) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_11801),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11801),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11799))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11799),U_11801)) )
    & ! [U_11800,U_11798] :
        ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11800,U_11798) = 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_11798),U_11800)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3151_3]) ).

cnf(f_3151_5,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11800,U_11798) = 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_11798),U_11800)) ),
    inference(clausify,[status(thm)],[f_3151_4]) ).

cnf(f_3151_6,plain,
    ( c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11801,U_11799) = hAPP(hAPP(c_Set_Oinsert(tc_Int_Oint),U_11801),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11801),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_11799))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11799),U_11801)) ),
    inference(clausify,[status(thm)],[f_3151_4]) ).

fof(f_3152_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_3152_2,plain,
    ! [U_11803,U_11802] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11802,U_11803)) = 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_11803),U_11802)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(variable_rename,[status(thm)],[f_3152_1]) ).

fof(f_3152_3,plain,
    ! [U_11802,U_11803] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11802,U_11803)) = 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_11803),U_11802)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(definitional_conversion,[status(esa)],[f_3152_2]) ).

cnf(f_3152_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_11802,U_11803)) = 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_11803),U_11802)),c_Groups_Oone__class_Oone(tc_Int_Oint))),
    inference(clausify,[status(thm)],[f_3152_3]) ).

fof(f_3153_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_3153_2,plain,
    ! [U_11806,U_11805,U_11804] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11804,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11804),U_11805),c_Orderings_Obot__class_Obot(tc_fun(U_11804,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11804,U_11805,U_11806)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11804,U_11805,U_11806)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11804),U_11805),U_11806))
      | ~ class_Orderings_Olinorder(U_11804) ),
    inference(variable_rename,[status(thm)],[f_3153_1]) ).

fof(f_3153_3,plain,
    ! [U_11804,U_11805,U_11806] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11804,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11804),U_11805),c_Orderings_Obot__class_Obot(tc_fun(U_11804,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11804,U_11805,U_11806)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11804,U_11805,U_11806)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11804),U_11805),U_11806))
      | ~ class_Orderings_Olinorder(U_11804) ),
    inference(definitional_conversion,[status(esa)],[f_3153_2]) ).

cnf(f_3153_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11804,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_11804),U_11805),c_Orderings_Obot__class_Obot(tc_fun(U_11804,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanAtMost(U_11804,U_11805,U_11806)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11804,U_11805,U_11806)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11804),U_11805),U_11806))
    | ~ class_Orderings_Olinorder(U_11804) ),
    inference(clausify,[status(thm)],[f_3153_3]) ).

fof(f_3154_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_3154_2,plain,
    ! [U_11812,U_11811,U_11810] :
      ( ! [U_11809] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11811),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11809),U_11810)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11811),U_11809))
          | ? [U_11808] :
              ( ? [U_11807] :
                  ( U_11809 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11807),U_11808)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11807),U_11812)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11808),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11810))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11811),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11812))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11810)) ),
    inference(variable_rename,[status(thm)],[f_3154_1]) ).

fof(f_3154_3,plain,
    ! [U_11812,U_11811,U_11810] :
      ( ! [U_11809] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11811),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11809),U_11810)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11811),U_11809))
          | ( ? [U_11807] :
                ( U_11809 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11807),sK206(U_11812,U_11811,U_11810,U_11809))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11807),U_11812)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK206(U_11812,U_11811,U_11810,U_11809)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11810))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11811),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11812))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11810)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK206]),skolemize(U_11808,sK206(U_11812,U_11811,U_11810,U_11809))],[f_3154_2]) ).

fof(f_3154_4,plain,
    ! [U_11812,U_11811,U_11810] :
      ( ! [U_11809] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11811),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11809),U_11810)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11811),U_11809))
          | ( U_11809 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK207(U_11812,U_11811,U_11810,U_11809)),sK206(U_11812,U_11811,U_11810,U_11809))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK207(U_11812,U_11811,U_11810,U_11809)),U_11812))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK206(U_11812,U_11811,U_11810,U_11809)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11810))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11811),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11812))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11810)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK207]),skolemize(U_11807,sK207(U_11812,U_11811,U_11810,U_11809))],[f_3154_3]) ).

fof(f_3154_5,plain,
    ( ! [U_11809,U_11810,U_11811,U_11812] :
        ( U_11809 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK207(U_11812,U_11811,U_11810,U_11809)),sK206(U_11812,U_11811,U_11810,U_11809))
        | ~ sP846(U_11809,U_11810,U_11811,U_11812) )
    & ! [U_11809,U_11810,U_11811,U_11812] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK207(U_11812,U_11811,U_11810,U_11809)),U_11812))
        | ~ sP846(U_11809,U_11810,U_11811,U_11812) )
    & ! [U_11809,U_11810,U_11811,U_11812] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK206(U_11812,U_11811,U_11810,U_11809)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11810)))
        | ~ sP846(U_11809,U_11810,U_11811,U_11812) )
    & ! [U_11809,U_11810,U_11811,U_11812] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11811),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11809),U_11810)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11811),U_11809))
        | sP846(U_11809,U_11810,U_11811,U_11812)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11811),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11812))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11810)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP846])],[f_3154_4]) ).

cnf(f_3154_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11811),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11809),U_11810)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11811),U_11809))
    | sP846(U_11809,U_11810,U_11811,U_11812)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11811),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11812))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11810)) ),
    inference(clausify,[status(thm)],[f_3154_5]) ).

cnf(f_3154_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK206(U_11812,U_11811,U_11810,U_11809)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11810)))
    | ~ sP846(U_11809,U_11810,U_11811,U_11812) ),
    inference(clausify,[status(thm)],[f_3154_5]) ).

cnf(f_3154_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK207(U_11812,U_11811,U_11810,U_11809)),U_11812))
    | ~ sP846(U_11809,U_11810,U_11811,U_11812) ),
    inference(clausify,[status(thm)],[f_3154_5]) ).

cnf(f_3154_9,plain,
    ( U_11809 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK207(U_11812,U_11811,U_11810,U_11809)),sK206(U_11812,U_11811,U_11810,U_11809))
    | ~ sP846(U_11809,U_11810,U_11811,U_11812) ),
    inference(clausify,[status(thm)],[f_3154_5]) ).

fof(f_3155_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_3155_2,plain,
    ! [U_11818,U_11817,U_11816] :
      ( ! [U_11815] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11815),U_11816)),U_11817))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11815),U_11817))
          | ? [U_11814] :
              ( ? [U_11813] :
                  ( U_11815 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11813),U_11814)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11813),U_11818)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11814),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11816))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11817),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11818))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11816)) ),
    inference(variable_rename,[status(thm)],[f_3155_1]) ).

fof(f_3155_3,plain,
    ! [U_11818,U_11817,U_11816] :
      ( ! [U_11815] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11815),U_11816)),U_11817))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11815),U_11817))
          | ( ? [U_11813] :
                ( U_11815 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11813),sK208(U_11818,U_11817,U_11816,U_11815))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11813),U_11818)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK208(U_11818,U_11817,U_11816,U_11815)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11816))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11817),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11818))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11816)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK208]),skolemize(U_11814,sK208(U_11818,U_11817,U_11816,U_11815))],[f_3155_2]) ).

fof(f_3155_4,plain,
    ! [U_11818,U_11817,U_11816] :
      ( ! [U_11815] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11815),U_11816)),U_11817))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11815),U_11817))
          | ( U_11815 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK209(U_11818,U_11817,U_11816,U_11815)),sK208(U_11818,U_11817,U_11816,U_11815))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK209(U_11818,U_11817,U_11816,U_11815)),U_11818))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK208(U_11818,U_11817,U_11816,U_11815)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11816))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11817),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11818))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11816)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK209]),skolemize(U_11813,sK209(U_11818,U_11817,U_11816,U_11815))],[f_3155_3]) ).

fof(f_3155_5,plain,
    ( ! [U_11818,U_11815,U_11816,U_11817] :
        ( U_11815 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK209(U_11818,U_11817,U_11816,U_11815)),sK208(U_11818,U_11817,U_11816,U_11815))
        | ~ sP847(U_11818,U_11815,U_11816,U_11817) )
    & ! [U_11818,U_11815,U_11816,U_11817] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK209(U_11818,U_11817,U_11816,U_11815)),U_11818))
        | ~ sP847(U_11818,U_11815,U_11816,U_11817) )
    & ! [U_11818,U_11815,U_11816,U_11817] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK208(U_11818,U_11817,U_11816,U_11815)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11816)))
        | ~ sP847(U_11818,U_11815,U_11816,U_11817) )
    & ! [U_11818,U_11815,U_11816,U_11817] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11815),U_11816)),U_11817))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11815),U_11817))
        | sP847(U_11818,U_11815,U_11816,U_11817)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11817),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11818))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11816)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP847])],[f_3155_4]) ).

cnf(f_3155_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_11815),U_11816)),U_11817))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11815),U_11817))
    | sP847(U_11818,U_11815,U_11816,U_11817)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11817),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11818))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11816)) ),
    inference(clausify,[status(thm)],[f_3155_5]) ).

cnf(f_3155_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK208(U_11818,U_11817,U_11816,U_11815)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11816)))
    | ~ sP847(U_11818,U_11815,U_11816,U_11817) ),
    inference(clausify,[status(thm)],[f_3155_5]) ).

cnf(f_3155_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK209(U_11818,U_11817,U_11816,U_11815)),U_11818))
    | ~ sP847(U_11818,U_11815,U_11816,U_11817) ),
    inference(clausify,[status(thm)],[f_3155_5]) ).

cnf(f_3155_9,plain,
    ( U_11815 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK209(U_11818,U_11817,U_11816,U_11815)),sK208(U_11818,U_11817,U_11816,U_11815))
    | ~ sP847(U_11818,U_11815,U_11816,U_11817) ),
    inference(clausify,[status(thm)],[f_3155_5]) ).

fof(f_3156_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_3156_2,plain,
    ! [U_11823,U_11822,U_11821] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11822),U_11821) = U_11822
      | ? [U_11820] :
          ( ? [U_11819] :
              ( U_11822 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11819),U_11820)
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11819),U_11823)) )
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11820),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11821))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11822),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11823))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11821)) ),
    inference(variable_rename,[status(thm)],[f_3156_1]) ).

fof(f_3156_3,plain,
    ! [U_11823,U_11822,U_11821] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11822),U_11821) = U_11822
      | ( ? [U_11819] :
            ( U_11822 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11819),sK210(U_11823,U_11822,U_11821))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11819),U_11823)) )
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK210(U_11823,U_11822,U_11821)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11821))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11822),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11823))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11821)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK210]),skolemize(U_11820,sK210(U_11823,U_11822,U_11821))],[f_3156_2]) ).

fof(f_3156_4,plain,
    ! [U_11823,U_11822,U_11821] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11822),U_11821) = U_11822
      | ( U_11822 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK211(U_11823,U_11822,U_11821)),sK210(U_11823,U_11822,U_11821))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK211(U_11823,U_11822,U_11821)),U_11823))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK210(U_11823,U_11822,U_11821)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11821))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11822),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11823))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11821)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK211]),skolemize(U_11819,sK211(U_11823,U_11822,U_11821))],[f_3156_3]) ).

fof(f_3156_5,plain,
    ( ! [U_11822,U_11821,U_11823] :
        ( U_11822 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK211(U_11823,U_11822,U_11821)),sK210(U_11823,U_11822,U_11821))
        | ~ sP848(U_11822,U_11821,U_11823) )
    & ! [U_11822,U_11821,U_11823] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK211(U_11823,U_11822,U_11821)),U_11823))
        | ~ sP848(U_11822,U_11821,U_11823) )
    & ! [U_11822,U_11821,U_11823] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK210(U_11823,U_11822,U_11821)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11821)))
        | ~ sP848(U_11822,U_11821,U_11823) )
    & ! [U_11822,U_11821,U_11823] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11822),U_11821) = U_11822
        | sP848(U_11822,U_11821,U_11823)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11822),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11823))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11821)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP848])],[f_3156_4]) ).

cnf(f_3156_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11822),U_11821) = U_11822
    | sP848(U_11822,U_11821,U_11823)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11822),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11823))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11821)) ),
    inference(clausify,[status(thm)],[f_3156_5]) ).

cnf(f_3156_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK210(U_11823,U_11822,U_11821)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11821)))
    | ~ sP848(U_11822,U_11821,U_11823) ),
    inference(clausify,[status(thm)],[f_3156_5]) ).

cnf(f_3156_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK211(U_11823,U_11822,U_11821)),U_11823))
    | ~ sP848(U_11822,U_11821,U_11823) ),
    inference(clausify,[status(thm)],[f_3156_5]) ).

cnf(f_3156_9,plain,
    ( U_11822 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK211(U_11823,U_11822,U_11821)),sK210(U_11823,U_11822,U_11821))
    | ~ sP848(U_11822,U_11821,U_11823) ),
    inference(clausify,[status(thm)],[f_3156_5]) ).

fof(f_3157_1,plain,
    ! [V_Pa_2,V_n_2] :
      ( ( ? [B_m] :
            ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_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_3157_2,plain,
    ! [U_11829,U_11828] :
      ( ( ? [U_11827] :
            ( hBOOL(hAPP(U_11829,U_11827))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11827),U_11828)) )
        | ! [U_11826] :
            ( ~ hBOOL(hAPP(U_11829,U_11826))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11826),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11828))) ) )
      & ( ? [U_11825] :
            ( hBOOL(hAPP(U_11829,U_11825))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11825),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11828))) )
        | ! [U_11824] :
            ( ~ hBOOL(hAPP(U_11829,U_11824))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11824),U_11828)) ) ) ),
    inference(variable_rename,[status(thm)],[f_3157_1]) ).

fof(f_3157_3,plain,
    ( ! [U_11833,U_11831] :
        ( ? [U_11827] :
            ( hBOOL(hAPP(U_11833,U_11827))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11827),U_11831)) )
        | ! [U_11826] :
            ( ~ hBOOL(hAPP(U_11833,U_11826))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11826),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11831))) ) )
    & ! [U_11832,U_11830] :
        ( ? [U_11825] :
            ( hBOOL(hAPP(U_11832,U_11825))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11825),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11830))) )
        | ! [U_11824] :
            ( ~ hBOOL(hAPP(U_11832,U_11824))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11824),U_11830)) ) ) ),
    inference(miniscope,[status(thm)],[f_3157_2]) ).

fof(f_3157_4,plain,
    ( ! [U_11833,U_11831] :
        ( ? [U_11827] :
            ( hBOOL(hAPP(U_11833,U_11827))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11827),U_11831)) )
        | ! [U_11826] :
            ( ~ hBOOL(hAPP(U_11833,U_11826))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11826),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11831))) ) )
    & ! [U_11832,U_11830] :
        ( ( hBOOL(hAPP(U_11832,sK212(U_11832,U_11830)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK212(U_11832,U_11830)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11830))) )
        | ! [U_11824] :
            ( ~ hBOOL(hAPP(U_11832,U_11824))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11824),U_11830)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK212]),skolemize(U_11825,sK212(U_11832,U_11830))],[f_3157_3]) ).

fof(f_3157_5,plain,
    ( ! [U_11833,U_11831] :
        ( ( hBOOL(hAPP(U_11833,sK213(U_11833,U_11831)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK213(U_11833,U_11831)),U_11831)) )
        | ! [U_11826] :
            ( ~ hBOOL(hAPP(U_11833,U_11826))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11826),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11831))) ) )
    & ! [U_11832,U_11830] :
        ( ( hBOOL(hAPP(U_11832,sK212(U_11832,U_11830)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK212(U_11832,U_11830)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11830))) )
        | ! [U_11824] :
            ( ~ hBOOL(hAPP(U_11832,U_11824))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11824),U_11830)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK213]),skolemize(U_11827,sK213(U_11833,U_11831))],[f_3157_4]) ).

fof(f_3157_6,plain,
    ( ! [U_11833,U_11831] :
        ( hBOOL(hAPP(U_11833,sK213(U_11833,U_11831)))
        | ~ sP850(U_11833,U_11831) )
    & ! [U_11833,U_11831] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK213(U_11833,U_11831)),U_11831))
        | ~ sP850(U_11833,U_11831) )
    & ! [U_11830,U_11832] :
        ( hBOOL(hAPP(U_11832,sK212(U_11832,U_11830)))
        | ~ sP849(U_11830,U_11832) )
    & ! [U_11830,U_11832] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK212(U_11832,U_11830)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11830)))
        | ~ sP849(U_11830,U_11832) )
    & ! [U_11833,U_11826,U_11831] :
        ( sP850(U_11833,U_11831)
        | ~ hBOOL(hAPP(U_11833,U_11826))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11826),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11831))) )
    & ! [U_11824,U_11830,U_11832] :
        ( sP849(U_11830,U_11832)
        | ~ hBOOL(hAPP(U_11832,U_11824))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11824),U_11830)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP849,sP850])],[f_3157_5]) ).

cnf(f_3157_7,plain,
    ( sP849(U_11830,U_11832)
    | ~ hBOOL(hAPP(U_11832,U_11824))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11824),U_11830)) ),
    inference(clausify,[status(thm)],[f_3157_6]) ).

cnf(f_3157_8,plain,
    ( sP850(U_11833,U_11831)
    | ~ hBOOL(hAPP(U_11833,U_11826))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11826),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11831))) ),
    inference(clausify,[status(thm)],[f_3157_6]) ).

cnf(f_3157_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK212(U_11832,U_11830)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11830)))
    | ~ sP849(U_11830,U_11832) ),
    inference(clausify,[status(thm)],[f_3157_6]) ).

cnf(f_3157_10,plain,
    ( hBOOL(hAPP(U_11832,sK212(U_11832,U_11830)))
    | ~ sP849(U_11830,U_11832) ),
    inference(clausify,[status(thm)],[f_3157_6]) ).

cnf(f_3157_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK213(U_11833,U_11831)),U_11831))
    | ~ sP850(U_11833,U_11831) ),
    inference(clausify,[status(thm)],[f_3157_6]) ).

cnf(f_3157_12,plain,
    ( hBOOL(hAPP(U_11833,sK213(U_11833,U_11831)))
    | ~ sP850(U_11833,U_11831) ),
    inference(clausify,[status(thm)],[f_3157_6]) ).

fof(f_3158_1,plain,
    ! [V_Pa_2,V_n_2] :
      ( ( ! [B_m] :
            ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_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_3158_2,plain,
    ! [U_11839,U_11838] :
      ( ( ! [U_11837] :
            ( hBOOL(hAPP(U_11839,U_11837))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11837),U_11838)) )
        | ? [U_11836] :
            ( ~ hBOOL(hAPP(U_11839,U_11836))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11836),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11838))) ) )
      & ( ! [U_11835] :
            ( hBOOL(hAPP(U_11839,U_11835))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11835),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11838))) )
        | ? [U_11834] :
            ( ~ hBOOL(hAPP(U_11839,U_11834))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11834),U_11838)) ) ) ),
    inference(variable_rename,[status(thm)],[f_3158_1]) ).

fof(f_3158_3,plain,
    ( ! [U_11843,U_11841] :
        ( ! [U_11837] :
            ( hBOOL(hAPP(U_11843,U_11837))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11837),U_11841)) )
        | ? [U_11836] :
            ( ~ hBOOL(hAPP(U_11843,U_11836))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11836),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11841))) ) )
    & ! [U_11842,U_11840] :
        ( ! [U_11835] :
            ( hBOOL(hAPP(U_11842,U_11835))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11835),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11840))) )
        | ? [U_11834] :
            ( ~ hBOOL(hAPP(U_11842,U_11834))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11834),U_11840)) ) ) ),
    inference(miniscope,[status(thm)],[f_3158_2]) ).

fof(f_3158_4,plain,
    ( ! [U_11843,U_11841] :
        ( ! [U_11837] :
            ( hBOOL(hAPP(U_11843,U_11837))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11837),U_11841)) )
        | ? [U_11836] :
            ( ~ hBOOL(hAPP(U_11843,U_11836))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11836),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11841))) ) )
    & ! [U_11842,U_11840] :
        ( ! [U_11835] :
            ( hBOOL(hAPP(U_11842,U_11835))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11835),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11840))) )
        | ( ~ hBOOL(hAPP(U_11842,sK214(U_11842,U_11840)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK214(U_11842,U_11840)),U_11840)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK214]),skolemize(U_11834,sK214(U_11842,U_11840))],[f_3158_3]) ).

fof(f_3158_5,plain,
    ( ! [U_11843,U_11841] :
        ( ! [U_11837] :
            ( hBOOL(hAPP(U_11843,U_11837))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11837),U_11841)) )
        | ( ~ hBOOL(hAPP(U_11843,sK215(U_11843,U_11841)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK215(U_11843,U_11841)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11841))) ) )
    & ! [U_11842,U_11840] :
        ( ! [U_11835] :
            ( hBOOL(hAPP(U_11842,U_11835))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11835),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11840))) )
        | ( ~ hBOOL(hAPP(U_11842,sK214(U_11842,U_11840)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK214(U_11842,U_11840)),U_11840)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK215]),skolemize(U_11836,sK215(U_11843,U_11841))],[f_3158_4]) ).

fof(f_3158_6,plain,
    ( ! [U_11843,U_11841] :
        ( ~ hBOOL(hAPP(U_11843,sK215(U_11843,U_11841)))
        | ~ sP852(U_11843,U_11841) )
    & ! [U_11843,U_11841] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK215(U_11843,U_11841)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11841)))
        | ~ sP852(U_11843,U_11841) )
    & ! [U_11840,U_11842] :
        ( ~ hBOOL(hAPP(U_11842,sK214(U_11842,U_11840)))
        | ~ sP851(U_11840,U_11842) )
    & ! [U_11840,U_11842] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK214(U_11842,U_11840)),U_11840))
        | ~ sP851(U_11840,U_11842) )
    & ! [U_11837,U_11843,U_11841] :
        ( hBOOL(hAPP(U_11843,U_11837))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11837),U_11841))
        | sP852(U_11843,U_11841) )
    & ! [U_11835,U_11840,U_11842] :
        ( hBOOL(hAPP(U_11842,U_11835))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11835),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11840)))
        | sP851(U_11840,U_11842) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP851,sP852])],[f_3158_5]) ).

cnf(f_3158_7,plain,
    ( hBOOL(hAPP(U_11842,U_11835))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11835),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11840)))
    | sP851(U_11840,U_11842) ),
    inference(clausify,[status(thm)],[f_3158_6]) ).

cnf(f_3158_8,plain,
    ( hBOOL(hAPP(U_11843,U_11837))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_11837),U_11841))
    | sP852(U_11843,U_11841) ),
    inference(clausify,[status(thm)],[f_3158_6]) ).

cnf(f_3158_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK214(U_11842,U_11840)),U_11840))
    | ~ sP851(U_11840,U_11842) ),
    inference(clausify,[status(thm)],[f_3158_6]) ).

cnf(f_3158_10,plain,
    ( ~ hBOOL(hAPP(U_11842,sK214(U_11842,U_11840)))
    | ~ sP851(U_11840,U_11842) ),
    inference(clausify,[status(thm)],[f_3158_6]) ).

cnf(f_3158_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK215(U_11843,U_11841)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_11841)))
    | ~ sP852(U_11843,U_11841) ),
    inference(clausify,[status(thm)],[f_3158_6]) ).

cnf(f_3158_12,plain,
    ( ~ hBOOL(hAPP(U_11843,sK215(U_11843,U_11841)))
    | ~ sP852(U_11843,U_11841) ),
    inference(clausify,[status(thm)],[f_3158_6]) ).

fof(f_3159_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_3159_2,plain,
    ! [U_11849,U_11848,U_11847] :
      ( ! [U_11846] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11846),U_11847) != U_11848
          | U_11846 = U_11848
          | ? [U_11845] :
              ( ? [U_11844] :
                  ( U_11846 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11844),U_11845)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11844),U_11849)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11845),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11847))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11848),U_11849))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11847)) ),
    inference(variable_rename,[status(thm)],[f_3159_1]) ).

fof(f_3159_3,plain,
    ! [U_11849,U_11848,U_11847] :
      ( ! [U_11846] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11846),U_11847) != U_11848
          | U_11846 = U_11848
          | ( ? [U_11844] :
                ( U_11846 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11844),sK216(U_11849,U_11848,U_11847,U_11846))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11844),U_11849)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK216(U_11849,U_11848,U_11847,U_11846)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11847))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11848),U_11849))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11847)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK216]),skolemize(U_11845,sK216(U_11849,U_11848,U_11847,U_11846))],[f_3159_2]) ).

fof(f_3159_4,plain,
    ! [U_11849,U_11848,U_11847] :
      ( ! [U_11846] :
          ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11846),U_11847) != U_11848
          | U_11846 = U_11848
          | ( U_11846 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK217(U_11849,U_11848,U_11847,U_11846)),sK216(U_11849,U_11848,U_11847,U_11846))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK217(U_11849,U_11848,U_11847,U_11846)),U_11849))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK216(U_11849,U_11848,U_11847,U_11846)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11847))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11848),U_11849))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11847)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK217]),skolemize(U_11844,sK217(U_11849,U_11848,U_11847,U_11846))],[f_3159_3]) ).

fof(f_3159_5,plain,
    ( ! [U_11847,U_11848,U_11846,U_11849] :
        ( U_11846 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK217(U_11849,U_11848,U_11847,U_11846)),sK216(U_11849,U_11848,U_11847,U_11846))
        | ~ sP853(U_11847,U_11848,U_11846,U_11849) )
    & ! [U_11847,U_11848,U_11846,U_11849] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK217(U_11849,U_11848,U_11847,U_11846)),U_11849))
        | ~ sP853(U_11847,U_11848,U_11846,U_11849) )
    & ! [U_11847,U_11848,U_11846,U_11849] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK216(U_11849,U_11848,U_11847,U_11846)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11847)))
        | ~ sP853(U_11847,U_11848,U_11846,U_11849) )
    & ! [U_11847,U_11848,U_11846,U_11849] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11846),U_11847) != U_11848
        | U_11846 = U_11848
        | sP853(U_11847,U_11848,U_11846,U_11849)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11848),U_11849))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11847)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP853])],[f_3159_4]) ).

cnf(f_3159_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11846),U_11847) != U_11848
    | U_11846 = U_11848
    | sP853(U_11847,U_11848,U_11846,U_11849)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11848),U_11849))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11847)) ),
    inference(clausify,[status(thm)],[f_3159_5]) ).

cnf(f_3159_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK216(U_11849,U_11848,U_11847,U_11846)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11847)))
    | ~ sP853(U_11847,U_11848,U_11846,U_11849) ),
    inference(clausify,[status(thm)],[f_3159_5]) ).

cnf(f_3159_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK217(U_11849,U_11848,U_11847,U_11846)),U_11849))
    | ~ sP853(U_11847,U_11848,U_11846,U_11849) ),
    inference(clausify,[status(thm)],[f_3159_5]) ).

cnf(f_3159_9,plain,
    ( U_11846 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK217(U_11849,U_11848,U_11847,U_11846)),sK216(U_11849,U_11848,U_11847,U_11846))
    | ~ sP853(U_11847,U_11848,U_11846,U_11849) ),
    inference(clausify,[status(thm)],[f_3159_5]) ).

fof(f_3160_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_3160_2,plain,
    ! [U_11854,U_11853,U_11852] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11853),U_11852) = U_11853
      | ? [U_11851] :
          ( ? [U_11850] :
              ( U_11853 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11850),U_11851)
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11850),U_11854)) )
          & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11851),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11852))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11853),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11854))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11852)) ),
    inference(variable_rename,[status(thm)],[f_3160_1]) ).

fof(f_3160_3,plain,
    ! [U_11854,U_11853,U_11852] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11853),U_11852) = U_11853
      | ( ? [U_11850] :
            ( U_11853 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11850),sK218(U_11854,U_11853,U_11852))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11850),U_11854)) )
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK218(U_11854,U_11853,U_11852)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11852))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11853),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11854))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11852)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK218]),skolemize(U_11851,sK218(U_11854,U_11853,U_11852))],[f_3160_2]) ).

fof(f_3160_4,plain,
    ! [U_11854,U_11853,U_11852] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11853),U_11852) = U_11853
      | ( U_11853 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK219(U_11854,U_11853,U_11852)),sK218(U_11854,U_11853,U_11852))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK219(U_11854,U_11853,U_11852)),U_11854))
        & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK218(U_11854,U_11853,U_11852)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11852))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11853),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11854))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11852)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK219]),skolemize(U_11850,sK219(U_11854,U_11853,U_11852))],[f_3160_3]) ).

fof(f_3160_5,plain,
    ( ! [U_11853,U_11854,U_11852] :
        ( U_11853 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK219(U_11854,U_11853,U_11852)),sK218(U_11854,U_11853,U_11852))
        | ~ sP854(U_11853,U_11854,U_11852) )
    & ! [U_11853,U_11854,U_11852] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK219(U_11854,U_11853,U_11852)),U_11854))
        | ~ sP854(U_11853,U_11854,U_11852) )
    & ! [U_11853,U_11854,U_11852] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK218(U_11854,U_11853,U_11852)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11852)))
        | ~ sP854(U_11853,U_11854,U_11852) )
    & ! [U_11853,U_11854,U_11852] :
        ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11853),U_11852) = U_11853
        | sP854(U_11853,U_11854,U_11852)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11853),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11854))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11852)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP854])],[f_3160_4]) ).

cnf(f_3160_6,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11853),U_11852) = U_11853
    | sP854(U_11853,U_11854,U_11852)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11853),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_11854))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11852)) ),
    inference(clausify,[status(thm)],[f_3160_5]) ).

cnf(f_3160_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK218(U_11854,U_11853,U_11852)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11852)))
    | ~ sP854(U_11853,U_11854,U_11852) ),
    inference(clausify,[status(thm)],[f_3160_5]) ).

cnf(f_3160_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK219(U_11854,U_11853,U_11852)),U_11854))
    | ~ sP854(U_11853,U_11854,U_11852) ),
    inference(clausify,[status(thm)],[f_3160_5]) ).

cnf(f_3160_9,plain,
    ( U_11853 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK219(U_11854,U_11853,U_11852)),sK218(U_11854,U_11853,U_11852))
    | ~ sP854(U_11853,U_11854,U_11852) ),
    inference(clausify,[status(thm)],[f_3160_5]) ).

fof(f_3161_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_3161_2,plain,
    ! [U_11860,U_11859,U_11858] :
      ( ! [U_11857] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11857),U_11858)),U_11859))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11857),U_11859))
          | ? [U_11856] :
              ( ? [U_11855] :
                  ( U_11857 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11855),U_11856)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11855),U_11860)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11856),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11858))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11859),U_11860))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11858)) ),
    inference(variable_rename,[status(thm)],[f_3161_1]) ).

fof(f_3161_3,plain,
    ! [U_11860,U_11859,U_11858] :
      ( ! [U_11857] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11857),U_11858)),U_11859))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11857),U_11859))
          | ( ? [U_11855] :
                ( U_11857 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11855),sK220(U_11860,U_11859,U_11858,U_11857))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11855),U_11860)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK220(U_11860,U_11859,U_11858,U_11857)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11858))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11859),U_11860))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11858)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK220]),skolemize(U_11856,sK220(U_11860,U_11859,U_11858,U_11857))],[f_3161_2]) ).

fof(f_3161_4,plain,
    ! [U_11860,U_11859,U_11858] :
      ( ! [U_11857] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11857),U_11858)),U_11859))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11857),U_11859))
          | ( U_11857 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK221(U_11860,U_11859,U_11858,U_11857)),sK220(U_11860,U_11859,U_11858,U_11857))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK221(U_11860,U_11859,U_11858,U_11857)),U_11860))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK220(U_11860,U_11859,U_11858,U_11857)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11858))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11859),U_11860))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11858)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK221]),skolemize(U_11855,sK221(U_11860,U_11859,U_11858,U_11857))],[f_3161_3]) ).

fof(f_3161_5,plain,
    ( ! [U_11858,U_11857,U_11859,U_11860] :
        ( U_11857 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK221(U_11860,U_11859,U_11858,U_11857)),sK220(U_11860,U_11859,U_11858,U_11857))
        | ~ sP855(U_11858,U_11857,U_11859,U_11860) )
    & ! [U_11858,U_11857,U_11859,U_11860] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK221(U_11860,U_11859,U_11858,U_11857)),U_11860))
        | ~ sP855(U_11858,U_11857,U_11859,U_11860) )
    & ! [U_11858,U_11857,U_11859,U_11860] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK220(U_11860,U_11859,U_11858,U_11857)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11858)))
        | ~ sP855(U_11858,U_11857,U_11859,U_11860) )
    & ! [U_11858,U_11857,U_11859,U_11860] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11857),U_11858)),U_11859))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11857),U_11859))
        | sP855(U_11858,U_11857,U_11859,U_11860)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11859),U_11860))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11858)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP855])],[f_3161_4]) ).

cnf(f_3161_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11857),U_11858)),U_11859))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11857),U_11859))
    | sP855(U_11858,U_11857,U_11859,U_11860)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11859),U_11860))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11858)) ),
    inference(clausify,[status(thm)],[f_3161_5]) ).

cnf(f_3161_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK220(U_11860,U_11859,U_11858,U_11857)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11858)))
    | ~ sP855(U_11858,U_11857,U_11859,U_11860) ),
    inference(clausify,[status(thm)],[f_3161_5]) ).

cnf(f_3161_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK221(U_11860,U_11859,U_11858,U_11857)),U_11860))
    | ~ sP855(U_11858,U_11857,U_11859,U_11860) ),
    inference(clausify,[status(thm)],[f_3161_5]) ).

cnf(f_3161_9,plain,
    ( U_11857 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK221(U_11860,U_11859,U_11858,U_11857)),sK220(U_11860,U_11859,U_11858,U_11857))
    | ~ sP855(U_11858,U_11857,U_11859,U_11860) ),
    inference(clausify,[status(thm)],[f_3161_5]) ).

fof(f_3162_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_3162_2,plain,
    ! [U_11866,U_11865,U_11864] :
      ( ! [U_11863] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11865),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11863),U_11864)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11865),U_11863))
          | ? [U_11862] :
              ( ? [U_11861] :
                  ( U_11863 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11861),U_11862)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11861),U_11866)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11862),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11864))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11865),U_11866))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11864)) ),
    inference(variable_rename,[status(thm)],[f_3162_1]) ).

fof(f_3162_3,plain,
    ! [U_11866,U_11865,U_11864] :
      ( ! [U_11863] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11865),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11863),U_11864)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11865),U_11863))
          | ( ? [U_11861] :
                ( U_11863 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11861),sK222(U_11866,U_11865,U_11864,U_11863))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11861),U_11866)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK222(U_11866,U_11865,U_11864,U_11863)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11864))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11865),U_11866))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11864)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK222]),skolemize(U_11862,sK222(U_11866,U_11865,U_11864,U_11863))],[f_3162_2]) ).

fof(f_3162_4,plain,
    ! [U_11866,U_11865,U_11864] :
      ( ! [U_11863] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11865),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11863),U_11864)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11865),U_11863))
          | ( U_11863 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK223(U_11866,U_11865,U_11864,U_11863)),sK222(U_11866,U_11865,U_11864,U_11863))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK223(U_11866,U_11865,U_11864,U_11863)),U_11866))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK222(U_11866,U_11865,U_11864,U_11863)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11864))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11865),U_11866))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11864)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK223]),skolemize(U_11861,sK223(U_11866,U_11865,U_11864,U_11863))],[f_3162_3]) ).

fof(f_3162_5,plain,
    ( ! [U_11864,U_11865,U_11866,U_11863] :
        ( U_11863 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK223(U_11866,U_11865,U_11864,U_11863)),sK222(U_11866,U_11865,U_11864,U_11863))
        | ~ sP856(U_11864,U_11865,U_11866,U_11863) )
    & ! [U_11864,U_11865,U_11866,U_11863] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK223(U_11866,U_11865,U_11864,U_11863)),U_11866))
        | ~ sP856(U_11864,U_11865,U_11866,U_11863) )
    & ! [U_11864,U_11865,U_11866,U_11863] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK222(U_11866,U_11865,U_11864,U_11863)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11864)))
        | ~ sP856(U_11864,U_11865,U_11866,U_11863) )
    & ! [U_11864,U_11865,U_11866,U_11863] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11865),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11863),U_11864)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11865),U_11863))
        | sP856(U_11864,U_11865,U_11866,U_11863)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11865),U_11866))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11864)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP856])],[f_3162_4]) ).

cnf(f_3162_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11865),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11863),U_11864)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11865),U_11863))
    | sP856(U_11864,U_11865,U_11866,U_11863)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11865),U_11866))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11864)) ),
    inference(clausify,[status(thm)],[f_3162_5]) ).

cnf(f_3162_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK222(U_11866,U_11865,U_11864,U_11863)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11864)))
    | ~ sP856(U_11864,U_11865,U_11866,U_11863) ),
    inference(clausify,[status(thm)],[f_3162_5]) ).

cnf(f_3162_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK223(U_11866,U_11865,U_11864,U_11863)),U_11866))
    | ~ sP856(U_11864,U_11865,U_11866,U_11863) ),
    inference(clausify,[status(thm)],[f_3162_5]) ).

cnf(f_3162_9,plain,
    ( U_11863 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK223(U_11866,U_11865,U_11864,U_11863)),sK222(U_11866,U_11865,U_11864,U_11863))
    | ~ sP856(U_11864,U_11865,U_11866,U_11863) ),
    inference(clausify,[status(thm)],[f_3162_5]) ).

fof(f_3163_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_3163_2,plain,
    ! [U_11872,U_11871,U_11870] :
      ( ! [U_11869] :
          ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11869),U_11870) != U_11871
          | U_11869 = U_11871
          | ? [U_11868] :
              ( ? [U_11867] :
                  ( U_11869 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11867),U_11868)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11867),U_11872)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11868),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11870))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11871),U_11872))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11870)) ),
    inference(variable_rename,[status(thm)],[f_3163_1]) ).

fof(f_3163_3,plain,
    ! [U_11872,U_11871,U_11870] :
      ( ! [U_11869] :
          ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11869),U_11870) != U_11871
          | U_11869 = U_11871
          | ( ? [U_11867] :
                ( U_11869 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11867),sK224(U_11872,U_11871,U_11870,U_11869))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11867),U_11872)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK224(U_11872,U_11871,U_11870,U_11869)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11870))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11871),U_11872))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11870)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK224]),skolemize(U_11868,sK224(U_11872,U_11871,U_11870,U_11869))],[f_3163_2]) ).

fof(f_3163_4,plain,
    ! [U_11872,U_11871,U_11870] :
      ( ! [U_11869] :
          ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11869),U_11870) != U_11871
          | U_11869 = U_11871
          | ( U_11869 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK225(U_11872,U_11871,U_11870,U_11869)),sK224(U_11872,U_11871,U_11870,U_11869))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK225(U_11872,U_11871,U_11870,U_11869)),U_11872))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK224(U_11872,U_11871,U_11870,U_11869)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11870))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11871),U_11872))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11870)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK225]),skolemize(U_11867,sK225(U_11872,U_11871,U_11870,U_11869))],[f_3163_3]) ).

fof(f_3163_5,plain,
    ( ! [U_11872,U_11869,U_11870,U_11871] :
        ( U_11869 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK225(U_11872,U_11871,U_11870,U_11869)),sK224(U_11872,U_11871,U_11870,U_11869))
        | ~ sP857(U_11872,U_11869,U_11870,U_11871) )
    & ! [U_11872,U_11869,U_11870,U_11871] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK225(U_11872,U_11871,U_11870,U_11869)),U_11872))
        | ~ sP857(U_11872,U_11869,U_11870,U_11871) )
    & ! [U_11872,U_11869,U_11870,U_11871] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK224(U_11872,U_11871,U_11870,U_11869)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11870)))
        | ~ sP857(U_11872,U_11869,U_11870,U_11871) )
    & ! [U_11872,U_11869,U_11870,U_11871] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11869),U_11870) != U_11871
        | U_11869 = U_11871
        | sP857(U_11872,U_11869,U_11870,U_11871)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11871),U_11872))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11870)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP857])],[f_3163_4]) ).

cnf(f_3163_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11869),U_11870) != U_11871
    | U_11869 = U_11871
    | sP857(U_11872,U_11869,U_11870,U_11871)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11871),U_11872))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11870)) ),
    inference(clausify,[status(thm)],[f_3163_5]) ).

cnf(f_3163_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK224(U_11872,U_11871,U_11870,U_11869)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11870)))
    | ~ sP857(U_11872,U_11869,U_11870,U_11871) ),
    inference(clausify,[status(thm)],[f_3163_5]) ).

cnf(f_3163_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK225(U_11872,U_11871,U_11870,U_11869)),U_11872))
    | ~ sP857(U_11872,U_11869,U_11870,U_11871) ),
    inference(clausify,[status(thm)],[f_3163_5]) ).

cnf(f_3163_9,plain,
    ( U_11869 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK225(U_11872,U_11871,U_11870,U_11869)),sK224(U_11872,U_11871,U_11870,U_11869))
    | ~ sP857(U_11872,U_11869,U_11870,U_11871) ),
    inference(clausify,[status(thm)],[f_3163_5]) ).

fof(f_3164_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_3164_2,plain,
    ! [U_11878,U_11877,U_11876] :
      ( ! [U_11875] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11875),U_11876)),U_11878))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11875),U_11878))
          | ? [U_11874] :
              ( ? [U_11873] :
                  ( U_11875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11873),U_11874)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11873),U_11877)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11874),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11876))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11876)) ),
    inference(variable_rename,[status(thm)],[f_3164_1]) ).

fof(f_3164_3,plain,
    ! [U_11878,U_11877,U_11876] :
      ( ! [U_11875] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11875),U_11876)),U_11878))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11875),U_11878))
          | ( ? [U_11873] :
                ( U_11875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11873),sK226(U_11878,U_11877,U_11876,U_11875))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11873),U_11877)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK226(U_11878,U_11877,U_11876,U_11875)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11876))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11876)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK226]),skolemize(U_11874,sK226(U_11878,U_11877,U_11876,U_11875))],[f_3164_2]) ).

fof(f_3164_4,plain,
    ! [U_11878,U_11877,U_11876] :
      ( ! [U_11875] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11875),U_11876)),U_11878))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11875),U_11878))
          | ( U_11875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK227(U_11878,U_11877,U_11876,U_11875)),sK226(U_11878,U_11877,U_11876,U_11875))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK227(U_11878,U_11877,U_11876,U_11875)),U_11877))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK226(U_11878,U_11877,U_11876,U_11875)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11876))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11876)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK227]),skolemize(U_11873,sK227(U_11878,U_11877,U_11876,U_11875))],[f_3164_3]) ).

fof(f_3164_5,plain,
    ( ! [U_11876,U_11878,U_11875,U_11877] :
        ( U_11875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK227(U_11878,U_11877,U_11876,U_11875)),sK226(U_11878,U_11877,U_11876,U_11875))
        | ~ sP858(U_11876,U_11878,U_11875,U_11877) )
    & ! [U_11876,U_11878,U_11875,U_11877] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK227(U_11878,U_11877,U_11876,U_11875)),U_11877))
        | ~ sP858(U_11876,U_11878,U_11875,U_11877) )
    & ! [U_11876,U_11878,U_11875,U_11877] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK226(U_11878,U_11877,U_11876,U_11875)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11876)))
        | ~ sP858(U_11876,U_11878,U_11875,U_11877) )
    & ! [U_11876,U_11878,U_11875,U_11877] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11875),U_11876)),U_11878))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11875),U_11878))
        | sP858(U_11876,U_11878,U_11875,U_11877)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11876)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP858])],[f_3164_4]) ).

cnf(f_3164_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_11875),U_11876)),U_11878))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11875),U_11878))
    | sP858(U_11876,U_11878,U_11875,U_11877)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11876)) ),
    inference(clausify,[status(thm)],[f_3164_5]) ).

cnf(f_3164_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK226(U_11878,U_11877,U_11876,U_11875)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11876)))
    | ~ sP858(U_11876,U_11878,U_11875,U_11877) ),
    inference(clausify,[status(thm)],[f_3164_5]) ).

cnf(f_3164_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK227(U_11878,U_11877,U_11876,U_11875)),U_11877))
    | ~ sP858(U_11876,U_11878,U_11875,U_11877) ),
    inference(clausify,[status(thm)],[f_3164_5]) ).

cnf(f_3164_9,plain,
    ( U_11875 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK227(U_11878,U_11877,U_11876,U_11875)),sK226(U_11878,U_11877,U_11876,U_11875))
    | ~ sP858(U_11876,U_11878,U_11875,U_11877) ),
    inference(clausify,[status(thm)],[f_3164_5]) ).

fof(f_3165_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_3165_2,plain,
    ! [U_11884,U_11883,U_11882] :
      ( ! [U_11881] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11884),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11881),U_11882)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11884),U_11881))
          | ? [U_11880] :
              ( ? [U_11879] :
                  ( U_11881 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11879),U_11880)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11879),U_11883)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11880),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11882))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11882)) ),
    inference(variable_rename,[status(thm)],[f_3165_1]) ).

fof(f_3165_3,plain,
    ! [U_11884,U_11883,U_11882] :
      ( ! [U_11881] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11884),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11881),U_11882)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11884),U_11881))
          | ( ? [U_11879] :
                ( U_11881 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11879),sK228(U_11884,U_11883,U_11882,U_11881))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11879),U_11883)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK228(U_11884,U_11883,U_11882,U_11881)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11882))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11882)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK228]),skolemize(U_11880,sK228(U_11884,U_11883,U_11882,U_11881))],[f_3165_2]) ).

fof(f_3165_4,plain,
    ! [U_11884,U_11883,U_11882] :
      ( ! [U_11881] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11884),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11881),U_11882)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11884),U_11881))
          | ( U_11881 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK229(U_11884,U_11883,U_11882,U_11881)),sK228(U_11884,U_11883,U_11882,U_11881))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK229(U_11884,U_11883,U_11882,U_11881)),U_11883))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK228(U_11884,U_11883,U_11882,U_11881)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11882))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11882)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK229]),skolemize(U_11879,sK229(U_11884,U_11883,U_11882,U_11881))],[f_3165_3]) ).

fof(f_3165_5,plain,
    ( ! [U_11881,U_11882,U_11883,U_11884] :
        ( U_11881 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK229(U_11884,U_11883,U_11882,U_11881)),sK228(U_11884,U_11883,U_11882,U_11881))
        | ~ sP859(U_11881,U_11882,U_11883,U_11884) )
    & ! [U_11881,U_11882,U_11883,U_11884] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK229(U_11884,U_11883,U_11882,U_11881)),U_11883))
        | ~ sP859(U_11881,U_11882,U_11883,U_11884) )
    & ! [U_11881,U_11882,U_11883,U_11884] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK228(U_11884,U_11883,U_11882,U_11881)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11882)))
        | ~ sP859(U_11881,U_11882,U_11883,U_11884) )
    & ! [U_11881,U_11882,U_11883,U_11884] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11884),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11881),U_11882)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11884),U_11881))
        | sP859(U_11881,U_11882,U_11883,U_11884)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11882)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP859])],[f_3165_4]) ).

cnf(f_3165_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11884),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11881),U_11882)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_11884),U_11881))
    | sP859(U_11881,U_11882,U_11883,U_11884)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11882)) ),
    inference(clausify,[status(thm)],[f_3165_5]) ).

cnf(f_3165_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK228(U_11884,U_11883,U_11882,U_11881)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11882)))
    | ~ sP859(U_11881,U_11882,U_11883,U_11884) ),
    inference(clausify,[status(thm)],[f_3165_5]) ).

cnf(f_3165_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK229(U_11884,U_11883,U_11882,U_11881)),U_11883))
    | ~ sP859(U_11881,U_11882,U_11883,U_11884) ),
    inference(clausify,[status(thm)],[f_3165_5]) ).

cnf(f_3165_9,plain,
    ( U_11881 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK229(U_11884,U_11883,U_11882,U_11881)),sK228(U_11884,U_11883,U_11882,U_11881))
    | ~ sP859(U_11881,U_11882,U_11883,U_11884) ),
    inference(clausify,[status(thm)],[f_3165_5]) ).

fof(f_3166_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_3166_2,plain,
    ! [U_11886,U_11885] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_11885),c_List_Olenlex(U_11885,U_11886))
      | ~ c_Wellfounded_Owf(U_11885,U_11886) ),
    inference(variable_rename,[status(thm)],[f_3166_1]) ).

fof(f_3166_3,plain,
    ! [U_11885,U_11886] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_11885),c_List_Olenlex(U_11885,U_11886))
      | ~ c_Wellfounded_Owf(U_11885,U_11886) ),
    inference(definitional_conversion,[status(esa)],[f_3166_2]) ).

cnf(f_3166_4,plain,
    ( c_Wellfounded_Owf(tc_List_Olist(U_11885),c_List_Olenlex(U_11885,U_11886))
    | ~ c_Wellfounded_Owf(U_11885,U_11886) ),
    inference(clausify,[status(thm)],[f_3166_3]) ).

fof(f_3167_1,plain,
    ! [V_Pa_2,V_d_2] :
      ( ( ( ? [B_x1] : hBOOL(hAPP(V_Pa_2,B_x1))
          | ! [B_x] :
              ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2,B_x1)) ) )
      | ? [B_x,B_k] :
          ( ( ~ hBOOL(hAPP(V_Pa_2,B_x))
            & hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_3167_2,plain,
    ! [U_11894,U_11893] :
      ( ( ( ? [U_11892] : hBOOL(hAPP(U_11894,U_11892))
          | ! [U_11891] :
              ( ~ hBOOL(hAPP(U_11894,U_11891))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11891),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11893))) ) )
        & ( ? [U_11890] :
              ( hBOOL(hAPP(U_11894,U_11890))
              & 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_11893))) )
          | ! [U_11889] : ~ hBOOL(hAPP(U_11894,U_11889)) ) )
      | ? [U_11888,U_11887] :
          ( ( ~ hBOOL(hAPP(U_11894,U_11888))
            & hBOOL(hAPP(U_11894,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11888),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11887),U_11893)))) )
          | ( ~ hBOOL(hAPP(U_11894,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11888),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11887),U_11893))))
            & hBOOL(hAPP(U_11894,U_11888)) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11893)) ),
    inference(variable_rename,[status(thm)],[f_3167_1]) ).

fof(f_3167_3,plain,
    ! [U_11894,U_11893] :
      ( ( ( ? [U_11892] : hBOOL(hAPP(U_11894,U_11892))
          | ! [U_11891] :
              ( ~ hBOOL(hAPP(U_11894,U_11891))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11891),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11893))) ) )
        & ( ? [U_11890] :
              ( hBOOL(hAPP(U_11894,U_11890))
              & 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_11893))) )
          | ! [U_11889] : ~ hBOOL(hAPP(U_11894,U_11889)) ) )
      | ? [U_11898] :
          ( ? [U_11896] : hBOOL(hAPP(U_11894,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11898),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11896),U_11893))))
          & ~ hBOOL(hAPP(U_11894,U_11898)) )
      | ? [U_11897] :
          ( ? [U_11895] : ~ hBOOL(hAPP(U_11894,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11897),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11895),U_11893))))
          & hBOOL(hAPP(U_11894,U_11897)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11893)) ),
    inference(miniscope,[status(thm)],[f_3167_2]) ).

fof(f_3167_4,plain,
    ! [U_11894,U_11893] :
      ( ( ( ? [U_11892] : hBOOL(hAPP(U_11894,U_11892))
          | ! [U_11891] :
              ( ~ hBOOL(hAPP(U_11894,U_11891))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11891),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11893))) ) )
        & ( ? [U_11890] :
              ( hBOOL(hAPP(U_11894,U_11890))
              & 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_11893))) )
          | ! [U_11889] : ~ hBOOL(hAPP(U_11894,U_11889)) ) )
      | ? [U_11898] :
          ( ? [U_11896] : hBOOL(hAPP(U_11894,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11898),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11896),U_11893))))
          & ~ hBOOL(hAPP(U_11894,U_11898)) )
      | ( ? [U_11895] : ~ hBOOL(hAPP(U_11894,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK230(U_11894,U_11893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11895),U_11893))))
        & hBOOL(hAPP(U_11894,sK230(U_11894,U_11893))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11893)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK230]),skolemize(U_11897,sK230(U_11894,U_11893))],[f_3167_3]) ).

fof(f_3167_5,plain,
    ! [U_11894,U_11893] :
      ( ( ( ? [U_11892] : hBOOL(hAPP(U_11894,U_11892))
          | ! [U_11891] :
              ( ~ hBOOL(hAPP(U_11894,U_11891))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11891),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11893))) ) )
        & ( ? [U_11890] :
              ( hBOOL(hAPP(U_11894,U_11890))
              & 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_11893))) )
          | ! [U_11889] : ~ hBOOL(hAPP(U_11894,U_11889)) ) )
      | ? [U_11898] :
          ( ? [U_11896] : hBOOL(hAPP(U_11894,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11898),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11896),U_11893))))
          & ~ hBOOL(hAPP(U_11894,U_11898)) )
      | ( ~ hBOOL(hAPP(U_11894,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK230(U_11894,U_11893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK231(U_11894,U_11893)),U_11893))))
        & hBOOL(hAPP(U_11894,sK230(U_11894,U_11893))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11893)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK231]),skolemize(U_11895,sK231(U_11894,U_11893))],[f_3167_4]) ).

fof(f_3167_6,plain,
    ! [U_11894,U_11893] :
      ( ( ( ? [U_11892] : hBOOL(hAPP(U_11894,U_11892))
          | ! [U_11891] :
              ( ~ hBOOL(hAPP(U_11894,U_11891))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11891),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11893))) ) )
        & ( ? [U_11890] :
              ( hBOOL(hAPP(U_11894,U_11890))
              & 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_11893))) )
          | ! [U_11889] : ~ hBOOL(hAPP(U_11894,U_11889)) ) )
      | ( ? [U_11896] : hBOOL(hAPP(U_11894,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK232(U_11894,U_11893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),U_11896),U_11893))))
        & ~ hBOOL(hAPP(U_11894,sK232(U_11894,U_11893))) )
      | ( ~ hBOOL(hAPP(U_11894,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK230(U_11894,U_11893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK231(U_11894,U_11893)),U_11893))))
        & hBOOL(hAPP(U_11894,sK230(U_11894,U_11893))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11893)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK232]),skolemize(U_11898,sK232(U_11894,U_11893))],[f_3167_5]) ).

fof(f_3167_7,plain,
    ! [U_11894,U_11893] :
      ( ( ( ? [U_11892] : hBOOL(hAPP(U_11894,U_11892))
          | ! [U_11891] :
              ( ~ hBOOL(hAPP(U_11894,U_11891))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11891),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11893))) ) )
        & ( ? [U_11890] :
              ( hBOOL(hAPP(U_11894,U_11890))
              & 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_11893))) )
          | ! [U_11889] : ~ hBOOL(hAPP(U_11894,U_11889)) ) )
      | ( hBOOL(hAPP(U_11894,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK232(U_11894,U_11893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK233(U_11894,U_11893)),U_11893))))
        & ~ hBOOL(hAPP(U_11894,sK232(U_11894,U_11893))) )
      | ( ~ hBOOL(hAPP(U_11894,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK230(U_11894,U_11893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK231(U_11894,U_11893)),U_11893))))
        & hBOOL(hAPP(U_11894,sK230(U_11894,U_11893))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11893)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK233]),skolemize(U_11896,sK233(U_11894,U_11893))],[f_3167_6]) ).

fof(f_3167_8,plain,
    ! [U_11894,U_11893] :
      ( ( ( ? [U_11892] : hBOOL(hAPP(U_11894,U_11892))
          | ! [U_11891] :
              ( ~ hBOOL(hAPP(U_11894,U_11891))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11891),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11893))) ) )
        & ( ( hBOOL(hAPP(U_11894,sK234(U_11894,U_11893)))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK234(U_11894,U_11893)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11893))) )
          | ! [U_11889] : ~ hBOOL(hAPP(U_11894,U_11889)) ) )
      | ( hBOOL(hAPP(U_11894,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK232(U_11894,U_11893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK233(U_11894,U_11893)),U_11893))))
        & ~ hBOOL(hAPP(U_11894,sK232(U_11894,U_11893))) )
      | ( ~ hBOOL(hAPP(U_11894,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK230(U_11894,U_11893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK231(U_11894,U_11893)),U_11893))))
        & hBOOL(hAPP(U_11894,sK230(U_11894,U_11893))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11893)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK234]),skolemize(U_11890,sK234(U_11894,U_11893))],[f_3167_7]) ).

fof(f_3167_9,plain,
    ! [U_11894,U_11893] :
      ( ( ( hBOOL(hAPP(U_11894,sK235(U_11894,U_11893)))
          | ! [U_11891] :
              ( ~ hBOOL(hAPP(U_11894,U_11891))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11891),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11893))) ) )
        & ( ( hBOOL(hAPP(U_11894,sK234(U_11894,U_11893)))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK234(U_11894,U_11893)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11893))) )
          | ! [U_11889] : ~ hBOOL(hAPP(U_11894,U_11889)) ) )
      | ( hBOOL(hAPP(U_11894,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK232(U_11894,U_11893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK233(U_11894,U_11893)),U_11893))))
        & ~ hBOOL(hAPP(U_11894,sK232(U_11894,U_11893))) )
      | ( ~ hBOOL(hAPP(U_11894,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK230(U_11894,U_11893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK231(U_11894,U_11893)),U_11893))))
        & hBOOL(hAPP(U_11894,sK230(U_11894,U_11893))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11893)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK235]),skolemize(U_11892,sK235(U_11894,U_11893))],[f_3167_8]) ).

fof(f_3167_10,plain,
    ( ! [U_11893,U_11894] :
        ( hBOOL(hAPP(U_11894,sK234(U_11894,U_11893)))
        | ~ sP862(U_11893,U_11894) )
    & ! [U_11893,U_11894] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK234(U_11894,U_11893)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11893)))
        | ~ sP862(U_11893,U_11894) )
    & ! [U_11889,U_11891,U_11893,U_11894] :
        ( hBOOL(hAPP(U_11894,sK235(U_11894,U_11893)))
        | ~ hBOOL(hAPP(U_11894,U_11891))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11891),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11893)))
        | ~ sP863(U_11889,U_11891,U_11893,U_11894) )
    & ! [U_11889,U_11891,U_11893,U_11894] :
        ( sP862(U_11893,U_11894)
        | ~ hBOOL(hAPP(U_11894,U_11889))
        | ~ sP863(U_11889,U_11891,U_11893,U_11894) )
    & ! [U_11893,U_11894] :
        ( hBOOL(hAPP(U_11894,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK232(U_11894,U_11893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK233(U_11894,U_11893)),U_11893))))
        | ~ sP861(U_11893,U_11894) )
    & ! [U_11893,U_11894] :
        ( ~ hBOOL(hAPP(U_11894,sK232(U_11894,U_11893)))
        | ~ sP861(U_11893,U_11894) )
    & ! [U_11893,U_11894] :
        ( ~ hBOOL(hAPP(U_11894,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK230(U_11894,U_11893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK231(U_11894,U_11893)),U_11893))))
        | ~ sP860(U_11893,U_11894) )
    & ! [U_11893,U_11894] :
        ( hBOOL(hAPP(U_11894,sK230(U_11894,U_11893)))
        | ~ sP860(U_11893,U_11894) )
    & ! [U_11889,U_11891,U_11893,U_11894] :
        ( sP863(U_11889,U_11891,U_11893,U_11894)
        | sP861(U_11893,U_11894)
        | sP860(U_11893,U_11894)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11893)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP860,sP861,sP862,sP863])],[f_3167_9]) ).

cnf(f_3167_11,plain,
    ( sP863(U_11889,U_11891,U_11893,U_11894)
    | sP861(U_11893,U_11894)
    | sP860(U_11893,U_11894)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11893)) ),
    inference(clausify,[status(thm)],[f_3167_10]) ).

cnf(f_3167_12,plain,
    ( hBOOL(hAPP(U_11894,sK230(U_11894,U_11893)))
    | ~ sP860(U_11893,U_11894) ),
    inference(clausify,[status(thm)],[f_3167_10]) ).

cnf(f_3167_13,plain,
    ( ~ hBOOL(hAPP(U_11894,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK230(U_11894,U_11893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK231(U_11894,U_11893)),U_11893))))
    | ~ sP860(U_11893,U_11894) ),
    inference(clausify,[status(thm)],[f_3167_10]) ).

cnf(f_3167_14,plain,
    ( ~ hBOOL(hAPP(U_11894,sK232(U_11894,U_11893)))
    | ~ sP861(U_11893,U_11894) ),
    inference(clausify,[status(thm)],[f_3167_10]) ).

cnf(f_3167_15,plain,
    ( hBOOL(hAPP(U_11894,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK232(U_11894,U_11893)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),sK233(U_11894,U_11893)),U_11893))))
    | ~ sP861(U_11893,U_11894) ),
    inference(clausify,[status(thm)],[f_3167_10]) ).

cnf(f_3167_16,plain,
    ( sP862(U_11893,U_11894)
    | ~ hBOOL(hAPP(U_11894,U_11889))
    | ~ sP863(U_11889,U_11891,U_11893,U_11894) ),
    inference(clausify,[status(thm)],[f_3167_10]) ).

cnf(f_3167_17,plain,
    ( hBOOL(hAPP(U_11894,sK235(U_11894,U_11893)))
    | ~ hBOOL(hAPP(U_11894,U_11891))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11891),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11893)))
    | ~ sP863(U_11889,U_11891,U_11893,U_11894) ),
    inference(clausify,[status(thm)],[f_3167_10]) ).

cnf(f_3167_18,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK234(U_11894,U_11893)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11893)))
    | ~ sP862(U_11893,U_11894) ),
    inference(clausify,[status(thm)],[f_3167_10]) ).

cnf(f_3167_19,plain,
    ( hBOOL(hAPP(U_11894,sK234(U_11894,U_11893)))
    | ~ sP862(U_11893,U_11894) ),
    inference(clausify,[status(thm)],[f_3167_10]) ).

fof(f_3168_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_3168_2,plain,
    ! [U_11904,U_11903,U_11902] :
      ( ! [U_11901] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11901),U_11902)),U_11904))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11901),U_11904))
          | ? [U_11900] :
              ( ? [U_11899] :
                  ( U_11901 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11899),U_11900)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11899),U_11903)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11900),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11902))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11902)) ),
    inference(variable_rename,[status(thm)],[f_3168_1]) ).

fof(f_3168_3,plain,
    ! [U_11904,U_11903,U_11902] :
      ( ! [U_11901] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11901),U_11902)),U_11904))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11901),U_11904))
          | ( ? [U_11899] :
                ( U_11901 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11899),sK236(U_11904,U_11903,U_11902,U_11901))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11899),U_11903)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK236(U_11904,U_11903,U_11902,U_11901)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11902))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11902)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK236]),skolemize(U_11900,sK236(U_11904,U_11903,U_11902,U_11901))],[f_3168_2]) ).

fof(f_3168_4,plain,
    ! [U_11904,U_11903,U_11902] :
      ( ! [U_11901] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11901),U_11902)),U_11904))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11901),U_11904))
          | ( U_11901 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK237(U_11904,U_11903,U_11902,U_11901)),sK236(U_11904,U_11903,U_11902,U_11901))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK237(U_11904,U_11903,U_11902,U_11901)),U_11903))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK236(U_11904,U_11903,U_11902,U_11901)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11902))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11902)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK237]),skolemize(U_11899,sK237(U_11904,U_11903,U_11902,U_11901))],[f_3168_3]) ).

fof(f_3168_5,plain,
    ( ! [U_11904,U_11903,U_11901,U_11902] :
        ( U_11901 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK237(U_11904,U_11903,U_11902,U_11901)),sK236(U_11904,U_11903,U_11902,U_11901))
        | ~ sP864(U_11904,U_11903,U_11901,U_11902) )
    & ! [U_11904,U_11903,U_11901,U_11902] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK237(U_11904,U_11903,U_11902,U_11901)),U_11903))
        | ~ sP864(U_11904,U_11903,U_11901,U_11902) )
    & ! [U_11904,U_11903,U_11901,U_11902] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK236(U_11904,U_11903,U_11902,U_11901)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11902)))
        | ~ sP864(U_11904,U_11903,U_11901,U_11902) )
    & ! [U_11904,U_11903,U_11901,U_11902] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11901),U_11902)),U_11904))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11901),U_11904))
        | sP864(U_11904,U_11903,U_11901,U_11902)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11902)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP864])],[f_3168_4]) ).

cnf(f_3168_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11901),U_11902)),U_11904))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11901),U_11904))
    | sP864(U_11904,U_11903,U_11901,U_11902)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11902)) ),
    inference(clausify,[status(thm)],[f_3168_5]) ).

cnf(f_3168_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK236(U_11904,U_11903,U_11902,U_11901)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11902)))
    | ~ sP864(U_11904,U_11903,U_11901,U_11902) ),
    inference(clausify,[status(thm)],[f_3168_5]) ).

cnf(f_3168_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK237(U_11904,U_11903,U_11902,U_11901)),U_11903))
    | ~ sP864(U_11904,U_11903,U_11901,U_11902) ),
    inference(clausify,[status(thm)],[f_3168_5]) ).

cnf(f_3168_9,plain,
    ( U_11901 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK237(U_11904,U_11903,U_11902,U_11901)),sK236(U_11904,U_11903,U_11902,U_11901))
    | ~ sP864(U_11904,U_11903,U_11901,U_11902) ),
    inference(clausify,[status(thm)],[f_3168_5]) ).

fof(f_3169_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_3169_2,plain,
    ! [U_11906,U_11905] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_11905),c_List_Olex(U_11905,U_11906))
      | ~ c_Wellfounded_Owf(U_11905,U_11906) ),
    inference(variable_rename,[status(thm)],[f_3169_1]) ).

fof(f_3169_3,plain,
    ! [U_11905,U_11906] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_11905),c_List_Olex(U_11905,U_11906))
      | ~ c_Wellfounded_Owf(U_11905,U_11906) ),
    inference(definitional_conversion,[status(esa)],[f_3169_2]) ).

cnf(f_3169_4,plain,
    ( c_Wellfounded_Owf(tc_List_Olist(U_11905),c_List_Olex(U_11905,U_11906))
    | ~ c_Wellfounded_Owf(U_11905,U_11906) ),
    inference(clausify,[status(thm)],[f_3169_3]) ).

fof(f_3170_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_3170_2,plain,
    ! [U_11912,U_11911,U_11910] :
      ( ! [U_11909] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11912),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11909),U_11910)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11912),U_11909))
          | ? [U_11908] :
              ( ? [U_11907] :
                  ( U_11909 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11907),U_11908)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11907),U_11911)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11908),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11910))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11910)) ),
    inference(variable_rename,[status(thm)],[f_3170_1]) ).

fof(f_3170_3,plain,
    ! [U_11912,U_11911,U_11910] :
      ( ! [U_11909] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11912),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11909),U_11910)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11912),U_11909))
          | ( ? [U_11907] :
                ( U_11909 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_11907),sK238(U_11912,U_11911,U_11910,U_11909))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_11907),U_11911)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK238(U_11912,U_11911,U_11910,U_11909)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11910))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11910)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK238]),skolemize(U_11908,sK238(U_11912,U_11911,U_11910,U_11909))],[f_3170_2]) ).

fof(f_3170_4,plain,
    ! [U_11912,U_11911,U_11910] :
      ( ! [U_11909] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11912),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11909),U_11910)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11912),U_11909))
          | ( U_11909 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK239(U_11912,U_11911,U_11910,U_11909)),sK238(U_11912,U_11911,U_11910,U_11909))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK239(U_11912,U_11911,U_11910,U_11909)),U_11911))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK238(U_11912,U_11911,U_11910,U_11909)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11910))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11910)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK239]),skolemize(U_11907,sK239(U_11912,U_11911,U_11910,U_11909))],[f_3170_3]) ).

fof(f_3170_5,plain,
    ( ! [U_11911,U_11912,U_11909,U_11910] :
        ( U_11909 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK239(U_11912,U_11911,U_11910,U_11909)),sK238(U_11912,U_11911,U_11910,U_11909))
        | ~ sP865(U_11911,U_11912,U_11909,U_11910) )
    & ! [U_11911,U_11912,U_11909,U_11910] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK239(U_11912,U_11911,U_11910,U_11909)),U_11911))
        | ~ sP865(U_11911,U_11912,U_11909,U_11910) )
    & ! [U_11911,U_11912,U_11909,U_11910] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK238(U_11912,U_11911,U_11910,U_11909)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11910)))
        | ~ sP865(U_11911,U_11912,U_11909,U_11910) )
    & ! [U_11911,U_11912,U_11909,U_11910] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11912),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11909),U_11910)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11912),U_11909))
        | sP865(U_11911,U_11912,U_11909,U_11910)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11910)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP865])],[f_3170_4]) ).

cnf(f_3170_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11912),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_11909),U_11910)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_11912),U_11909))
    | sP865(U_11911,U_11912,U_11909,U_11910)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_11910)) ),
    inference(clausify,[status(thm)],[f_3170_5]) ).

cnf(f_3170_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK238(U_11912,U_11911,U_11910,U_11909)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_11910)))
    | ~ sP865(U_11911,U_11912,U_11909,U_11910) ),
    inference(clausify,[status(thm)],[f_3170_5]) ).

cnf(f_3170_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK239(U_11912,U_11911,U_11910,U_11909)),U_11911))
    | ~ sP865(U_11911,U_11912,U_11909,U_11910) ),
    inference(clausify,[status(thm)],[f_3170_5]) ).

cnf(f_3170_9,plain,
    ( U_11909 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK239(U_11912,U_11911,U_11910,U_11909)),sK238(U_11912,U_11911,U_11910,U_11909))
    | ~ sP865(U_11911,U_11912,U_11909,U_11910) ),
    inference(clausify,[status(thm)],[f_3170_5]) ).

fof(f_3171_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_3171_2,plain,
    ! [U_11915,U_11914,U_11913] :
      ( ( ( ( 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_11913)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11915),U_11914)) = 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_11915),U_11914)) )
          & ( 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_11913)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11915),U_11914)) = 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_11915),U_11914)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11913),U_11914)) )
      & ( 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_11913)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11915),U_11914)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11915),U_11913)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11914),U_11913))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11913),U_11914)) ) ),
    inference(variable_rename,[status(thm)],[f_3171_1]) ).

fof(f_3171_3,plain,
    ( ! [U_11921,U_11919,U_11917] :
        ( ( ( 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_11917)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11921),U_11919)) = 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_11921),U_11919)) )
          & ( 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_11917)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11921),U_11919)) = 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_11921),U_11919)) ) )
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11917),U_11919)) )
    & ! [U_11920,U_11918,U_11916] :
        ( 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_11916)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11920),U_11918)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11920),U_11916)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11918),U_11916))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11916),U_11918)) ) ),
    inference(miniscope,[status(thm)],[f_3171_2]) ).

fof(f_3171_4,plain,
    ( ! [U_11921,U_11919,U_11917] :
        ( 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_11917)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11921),U_11919)) = 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_11921),U_11919))
        | ~ sP866(U_11921,U_11919,U_11917) )
    & ! [U_11921,U_11919,U_11917] :
        ( 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_11917)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11921),U_11919)) = 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_11921),U_11919))
        | ~ sP866(U_11921,U_11919,U_11917) )
    & ! [U_11921,U_11919,U_11917] :
        ( sP866(U_11921,U_11919,U_11917)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11917),U_11919)) )
    & ! [U_11920,U_11916,U_11918] :
        ( 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_11916)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11920),U_11918)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11920),U_11916)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11918),U_11916))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11916),U_11918)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP866])],[f_3171_3]) ).

cnf(f_3171_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_11916)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11920),U_11918)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11920),U_11916)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11918),U_11916))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11916),U_11918)) ),
    inference(clausify,[status(thm)],[f_3171_4]) ).

cnf(f_3171_6,plain,
    ( sP866(U_11921,U_11919,U_11917)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11917),U_11919)) ),
    inference(clausify,[status(thm)],[f_3171_4]) ).

cnf(f_3171_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_11917)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11921),U_11919)) = 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_11921),U_11919))
    | ~ sP866(U_11921,U_11919,U_11917) ),
    inference(clausify,[status(thm)],[f_3171_4]) ).

cnf(f_3171_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_11917)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11921),U_11919)) = 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_11921),U_11919))
    | ~ sP866(U_11921,U_11919,U_11917) ),
    inference(clausify,[status(thm)],[f_3171_4]) ).

fof(f_3172_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_3172_2,plain,
    ! [U_11923,U_11922] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11922),U_11923))),
    inference(variable_rename,[status(thm)],[f_3172_1]) ).

fof(f_3172_3,plain,
    ! [U_11923,U_11922] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11922),U_11923))),
    inference(definitional_conversion,[status(esa)],[f_3172_2]) ).

cnf(f_3172_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11922),U_11923))),
    inference(clausify,[status(thm)],[f_3172_3]) ).

fof(f_3173_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_3173_2,plain,
    ! [U_11928,U_11927,U_11926,U_11925,U_11924] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11924,U_11925),U_11926) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11924,U_11927),U_11928)
          | U_11926 != U_11928
          | U_11925 != U_11927 )
        & ( ( U_11926 = U_11928
            & U_11925 = U_11927 )
          | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11924,U_11925),U_11926) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11924,U_11927),U_11928) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11924),U_11927),U_11928))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11924),U_11925),U_11926))
      | ~ class_Orderings_Olinorder(U_11924) ),
    inference(variable_rename,[status(thm)],[f_3173_1]) ).

fof(f_3173_3,plain,
    ( ! [U_11925,U_11926,U_11927,U_11928] :
        ( U_11926 = U_11928
        | ~ sP867(U_11925,U_11926,U_11927,U_11928) )
    & ! [U_11925,U_11926,U_11927,U_11928] :
        ( U_11925 = U_11927
        | ~ sP867(U_11925,U_11926,U_11927,U_11928) )
    & ! [U_11925,U_11924,U_11926,U_11927,U_11928] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11924,U_11925),U_11926) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11924,U_11927),U_11928)
        | U_11926 != U_11928
        | U_11925 != U_11927
        | ~ sP868(U_11925,U_11924,U_11926,U_11927,U_11928) )
    & ! [U_11925,U_11924,U_11926,U_11927,U_11928] :
        ( sP867(U_11925,U_11926,U_11927,U_11928)
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11924,U_11925),U_11926) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11924,U_11927),U_11928)
        | ~ sP868(U_11925,U_11924,U_11926,U_11927,U_11928) )
    & ! [U_11925,U_11924,U_11926,U_11927,U_11928] :
        ( sP868(U_11925,U_11924,U_11926,U_11927,U_11928)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11924),U_11927),U_11928))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11924),U_11925),U_11926))
        | ~ class_Orderings_Olinorder(U_11924) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP867,sP868])],[f_3173_2]) ).

cnf(f_3173_4,plain,
    ( sP868(U_11925,U_11924,U_11926,U_11927,U_11928)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11924),U_11927),U_11928))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11924),U_11925),U_11926))
    | ~ class_Orderings_Olinorder(U_11924) ),
    inference(clausify,[status(thm)],[f_3173_3]) ).

cnf(f_3173_5,plain,
    ( sP867(U_11925,U_11926,U_11927,U_11928)
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11924,U_11925),U_11926) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11924,U_11927),U_11928)
    | ~ sP868(U_11925,U_11924,U_11926,U_11927,U_11928) ),
    inference(clausify,[status(thm)],[f_3173_3]) ).

cnf(f_3173_6,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11924,U_11925),U_11926) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11924,U_11927),U_11928)
    | U_11926 != U_11928
    | U_11925 != U_11927
    | ~ sP868(U_11925,U_11924,U_11926,U_11927,U_11928) ),
    inference(clausify,[status(thm)],[f_3173_3]) ).

cnf(f_3173_7,plain,
    ( U_11925 = U_11927
    | ~ sP867(U_11925,U_11926,U_11927,U_11928) ),
    inference(clausify,[status(thm)],[f_3173_3]) ).

cnf(f_3173_8,plain,
    ( U_11926 = U_11928
    | ~ sP867(U_11925,U_11926,U_11927,U_11928) ),
    inference(clausify,[status(thm)],[f_3173_3]) ).

fof(f_3174_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_3174_2,plain,
    ! [U_11933,U_11932,U_11931,U_11930,U_11929] :
      ( U_11930 = U_11932
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11929),U_11932),U_11933))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11929),U_11930),U_11931))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11929,U_11930),U_11931) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11929,U_11932),U_11933)
      | ~ class_Orderings_Olinorder(U_11929) ),
    inference(variable_rename,[status(thm)],[f_3174_1]) ).

fof(f_3174_3,plain,
    ! [U_11930,U_11929,U_11931,U_11933,U_11932] :
      ( U_11930 = U_11932
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11929),U_11932),U_11933))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11929),U_11930),U_11931))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11929,U_11930),U_11931) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11929,U_11932),U_11933)
      | ~ class_Orderings_Olinorder(U_11929) ),
    inference(definitional_conversion,[status(esa)],[f_3174_2]) ).

cnf(f_3174_4,plain,
    ( U_11930 = U_11932
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11929),U_11932),U_11933))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11929),U_11930),U_11931))
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11929,U_11930),U_11931) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11929,U_11932),U_11933)
    | ~ class_Orderings_Olinorder(U_11929) ),
    inference(clausify,[status(thm)],[f_3174_3]) ).

fof(f_3175_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_3175_2,plain,
    ! [U_11938,U_11937,U_11936,U_11935,U_11934] :
      ( U_11936 = U_11938
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11934),U_11937),U_11938))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11934),U_11935),U_11936))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11934,U_11935),U_11936) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11934,U_11937),U_11938)
      | ~ class_Orderings_Olinorder(U_11934) ),
    inference(variable_rename,[status(thm)],[f_3175_1]) ).

fof(f_3175_3,plain,
    ! [U_11934,U_11935,U_11937,U_11938,U_11936] :
      ( U_11936 = U_11938
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11934),U_11937),U_11938))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11934),U_11935),U_11936))
      | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11934,U_11935),U_11936) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11934,U_11937),U_11938)
      | ~ class_Orderings_Olinorder(U_11934) ),
    inference(definitional_conversion,[status(esa)],[f_3175_2]) ).

cnf(f_3175_4,plain,
    ( U_11936 = U_11938
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11934),U_11937),U_11938))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11934),U_11935),U_11936))
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11934,U_11935),U_11936) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11934,U_11937),U_11938)
    | ~ class_Orderings_Olinorder(U_11934) ),
    inference(clausify,[status(thm)],[f_3175_3]) ).

fof(f_3176_1,plain,
    ! [V_Pa_2,V_n_2] :
      ( ( ! [B_m] :
            ( hBOOL(hAPP(V_Pa_2,B_m))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) )
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_3176_2,plain,
    ! [U_11944,U_11943] :
      ( ( ! [U_11942] :
            ( hBOOL(hAPP(U_11944,U_11942))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11942),U_11943)) )
        | ? [U_11941] :
            ( ~ hBOOL(hAPP(U_11944,U_11941))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11941),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11943))) ) )
      & ( ! [U_11940] :
            ( hBOOL(hAPP(U_11944,U_11940))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11940),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11943))) )
        | ? [U_11939] :
            ( ~ hBOOL(hAPP(U_11944,U_11939))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11939),U_11943)) ) ) ),
    inference(variable_rename,[status(thm)],[f_3176_1]) ).

fof(f_3176_3,plain,
    ( ! [U_11948,U_11946] :
        ( ! [U_11942] :
            ( hBOOL(hAPP(U_11948,U_11942))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11942),U_11946)) )
        | ? [U_11941] :
            ( ~ hBOOL(hAPP(U_11948,U_11941))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11941),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11946))) ) )
    & ! [U_11947,U_11945] :
        ( ! [U_11940] :
            ( hBOOL(hAPP(U_11947,U_11940))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11940),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11945))) )
        | ? [U_11939] :
            ( ~ hBOOL(hAPP(U_11947,U_11939))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11939),U_11945)) ) ) ),
    inference(miniscope,[status(thm)],[f_3176_2]) ).

fof(f_3176_4,plain,
    ( ! [U_11948,U_11946] :
        ( ! [U_11942] :
            ( hBOOL(hAPP(U_11948,U_11942))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11942),U_11946)) )
        | ? [U_11941] :
            ( ~ hBOOL(hAPP(U_11948,U_11941))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11941),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11946))) ) )
    & ! [U_11947,U_11945] :
        ( ! [U_11940] :
            ( hBOOL(hAPP(U_11947,U_11940))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11940),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11945))) )
        | ( ~ hBOOL(hAPP(U_11947,sK240(U_11947,U_11945)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK240(U_11947,U_11945)),U_11945)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK240]),skolemize(U_11939,sK240(U_11947,U_11945))],[f_3176_3]) ).

fof(f_3176_5,plain,
    ( ! [U_11948,U_11946] :
        ( ! [U_11942] :
            ( hBOOL(hAPP(U_11948,U_11942))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11942),U_11946)) )
        | ( ~ hBOOL(hAPP(U_11948,sK241(U_11948,U_11946)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK241(U_11948,U_11946)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11946))) ) )
    & ! [U_11947,U_11945] :
        ( ! [U_11940] :
            ( hBOOL(hAPP(U_11947,U_11940))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11940),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11945))) )
        | ( ~ hBOOL(hAPP(U_11947,sK240(U_11947,U_11945)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK240(U_11947,U_11945)),U_11945)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK241]),skolemize(U_11941,sK241(U_11948,U_11946))],[f_3176_4]) ).

fof(f_3176_6,plain,
    ( ! [U_11948,U_11946] :
        ( ~ hBOOL(hAPP(U_11948,sK241(U_11948,U_11946)))
        | ~ sP870(U_11948,U_11946) )
    & ! [U_11948,U_11946] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK241(U_11948,U_11946)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11946)))
        | ~ sP870(U_11948,U_11946) )
    & ! [U_11945,U_11947] :
        ( ~ hBOOL(hAPP(U_11947,sK240(U_11947,U_11945)))
        | ~ sP869(U_11945,U_11947) )
    & ! [U_11945,U_11947] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK240(U_11947,U_11945)),U_11945))
        | ~ sP869(U_11945,U_11947) )
    & ! [U_11948,U_11942,U_11946] :
        ( hBOOL(hAPP(U_11948,U_11942))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11942),U_11946))
        | sP870(U_11948,U_11946) )
    & ! [U_11940,U_11945,U_11947] :
        ( hBOOL(hAPP(U_11947,U_11940))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11940),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11945)))
        | sP869(U_11945,U_11947) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP869,sP870])],[f_3176_5]) ).

cnf(f_3176_7,plain,
    ( hBOOL(hAPP(U_11947,U_11940))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11940),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11945)))
    | sP869(U_11945,U_11947) ),
    inference(clausify,[status(thm)],[f_3176_6]) ).

cnf(f_3176_8,plain,
    ( hBOOL(hAPP(U_11948,U_11942))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11942),U_11946))
    | sP870(U_11948,U_11946) ),
    inference(clausify,[status(thm)],[f_3176_6]) ).

cnf(f_3176_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK240(U_11947,U_11945)),U_11945))
    | ~ sP869(U_11945,U_11947) ),
    inference(clausify,[status(thm)],[f_3176_6]) ).

cnf(f_3176_10,plain,
    ( ~ hBOOL(hAPP(U_11947,sK240(U_11947,U_11945)))
    | ~ sP869(U_11945,U_11947) ),
    inference(clausify,[status(thm)],[f_3176_6]) ).

cnf(f_3176_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK241(U_11948,U_11946)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11946)))
    | ~ sP870(U_11948,U_11946) ),
    inference(clausify,[status(thm)],[f_3176_6]) ).

cnf(f_3176_12,plain,
    ( ~ hBOOL(hAPP(U_11948,sK241(U_11948,U_11946)))
    | ~ sP870(U_11948,U_11946) ),
    inference(clausify,[status(thm)],[f_3176_6]) ).

fof(f_3177_1,plain,
    ! [V_Pa_2,V_n_2] :
      ( ( ? [B_m] :
            ( hBOOL(hAPP(V_Pa_2,B_m))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) )
        | ! [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_3177_2,plain,
    ! [U_11954,U_11953] :
      ( ( ? [U_11952] :
            ( hBOOL(hAPP(U_11954,U_11952))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11952),U_11953)) )
        | ! [U_11951] :
            ( ~ hBOOL(hAPP(U_11954,U_11951))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11951),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11953))) ) )
      & ( ? [U_11950] :
            ( hBOOL(hAPP(U_11954,U_11950))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11950),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11953))) )
        | ! [U_11949] :
            ( ~ hBOOL(hAPP(U_11954,U_11949))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11949),U_11953)) ) ) ),
    inference(variable_rename,[status(thm)],[f_3177_1]) ).

fof(f_3177_3,plain,
    ( ! [U_11958,U_11956] :
        ( ? [U_11952] :
            ( hBOOL(hAPP(U_11958,U_11952))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11952),U_11956)) )
        | ! [U_11951] :
            ( ~ hBOOL(hAPP(U_11958,U_11951))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11951),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11956))) ) )
    & ! [U_11957,U_11955] :
        ( ? [U_11950] :
            ( hBOOL(hAPP(U_11957,U_11950))
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11950),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11955))) )
        | ! [U_11949] :
            ( ~ hBOOL(hAPP(U_11957,U_11949))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11949),U_11955)) ) ) ),
    inference(miniscope,[status(thm)],[f_3177_2]) ).

fof(f_3177_4,plain,
    ( ! [U_11958,U_11956] :
        ( ? [U_11952] :
            ( hBOOL(hAPP(U_11958,U_11952))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11952),U_11956)) )
        | ! [U_11951] :
            ( ~ hBOOL(hAPP(U_11958,U_11951))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11951),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11956))) ) )
    & ! [U_11957,U_11955] :
        ( ( hBOOL(hAPP(U_11957,sK242(U_11957,U_11955)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK242(U_11957,U_11955)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11955))) )
        | ! [U_11949] :
            ( ~ hBOOL(hAPP(U_11957,U_11949))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11949),U_11955)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK242]),skolemize(U_11950,sK242(U_11957,U_11955))],[f_3177_3]) ).

fof(f_3177_5,plain,
    ( ! [U_11958,U_11956] :
        ( ( hBOOL(hAPP(U_11958,sK243(U_11958,U_11956)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK243(U_11958,U_11956)),U_11956)) )
        | ! [U_11951] :
            ( ~ hBOOL(hAPP(U_11958,U_11951))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11951),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11956))) ) )
    & ! [U_11957,U_11955] :
        ( ( hBOOL(hAPP(U_11957,sK242(U_11957,U_11955)))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK242(U_11957,U_11955)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11955))) )
        | ! [U_11949] :
            ( ~ hBOOL(hAPP(U_11957,U_11949))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11949),U_11955)) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK243]),skolemize(U_11952,sK243(U_11958,U_11956))],[f_3177_4]) ).

fof(f_3177_6,plain,
    ( ! [U_11958,U_11956] :
        ( hBOOL(hAPP(U_11958,sK243(U_11958,U_11956)))
        | ~ sP872(U_11958,U_11956) )
    & ! [U_11958,U_11956] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK243(U_11958,U_11956)),U_11956))
        | ~ sP872(U_11958,U_11956) )
    & ! [U_11955,U_11957] :
        ( hBOOL(hAPP(U_11957,sK242(U_11957,U_11955)))
        | ~ sP871(U_11955,U_11957) )
    & ! [U_11955,U_11957] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK242(U_11957,U_11955)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11955)))
        | ~ sP871(U_11955,U_11957) )
    & ! [U_11951,U_11958,U_11956] :
        ( sP872(U_11958,U_11956)
        | ~ hBOOL(hAPP(U_11958,U_11951))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11951),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11956))) )
    & ! [U_11949,U_11955,U_11957] :
        ( sP871(U_11955,U_11957)
        | ~ hBOOL(hAPP(U_11957,U_11949))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11949),U_11955)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP871,sP872])],[f_3177_5]) ).

cnf(f_3177_7,plain,
    ( sP871(U_11955,U_11957)
    | ~ hBOOL(hAPP(U_11957,U_11949))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_11949),U_11955)) ),
    inference(clausify,[status(thm)],[f_3177_6]) ).

cnf(f_3177_8,plain,
    ( sP872(U_11958,U_11956)
    | ~ hBOOL(hAPP(U_11958,U_11951))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_11951),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11956))) ),
    inference(clausify,[status(thm)],[f_3177_6]) ).

cnf(f_3177_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK242(U_11957,U_11955)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_11955)))
    | ~ sP871(U_11955,U_11957) ),
    inference(clausify,[status(thm)],[f_3177_6]) ).

cnf(f_3177_10,plain,
    ( hBOOL(hAPP(U_11957,sK242(U_11957,U_11955)))
    | ~ sP871(U_11955,U_11957) ),
    inference(clausify,[status(thm)],[f_3177_6]) ).

cnf(f_3177_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK243(U_11958,U_11956)),U_11956))
    | ~ sP872(U_11958,U_11956) ),
    inference(clausify,[status(thm)],[f_3177_6]) ).

cnf(f_3177_12,plain,
    ( hBOOL(hAPP(U_11958,sK243(U_11958,U_11956)))
    | ~ sP872(U_11958,U_11956) ),
    inference(clausify,[status(thm)],[f_3177_6]) ).

fof(f_3178_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_3178_2,plain,
    ! [U_11960,U_11959] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11959),hAPP(c_Nat_OSuc,U_11960)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11959,U_11960),
    inference(variable_rename,[status(thm)],[f_3178_1]) ).

fof(f_3178_3,plain,
    ! [U_11959,U_11960] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11959),hAPP(c_Nat_OSuc,U_11960)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11959,U_11960),
    inference(definitional_conversion,[status(esa)],[f_3178_2]) ).

cnf(f_3178_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11959),hAPP(c_Nat_OSuc,U_11960)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_11959,U_11960),
    inference(clausify,[status(thm)],[f_3178_3]) ).

fof(f_3179_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_3179_2,plain,
    ! [U_11961] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11961),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_3179_1]) ).

fof(f_3179_3,plain,
    ! [U_11961] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11961),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_3179_2]) ).

cnf(f_3179_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11961),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_3179_3]) ).

fof(f_3180_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_3180_2,plain,
    ! [U_11963,U_11962] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11962),U_11963)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11963),U_11962),
    inference(variable_rename,[status(thm)],[f_3180_1]) ).

fof(f_3180_3,plain,
    ! [U_11962,U_11963] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11962),U_11963)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11963),U_11962),
    inference(definitional_conversion,[status(esa)],[f_3180_2]) ).

cnf(f_3180_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11962),U_11963)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_11963),U_11962),
    inference(clausify,[status(thm)],[f_3180_3]) ).

fof(f_3181_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_3181_2,plain,
    ! [U_11965,U_11964] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11964),U_11965)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11964)),hAPP(c_Nat_OSuc,U_11965)),
    inference(variable_rename,[status(thm)],[f_3181_1]) ).

fof(f_3181_3,plain,
    ! [U_11964,U_11965] : hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11964),U_11965)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11964)),hAPP(c_Nat_OSuc,U_11965)),
    inference(definitional_conversion,[status(esa)],[f_3181_2]) ).

cnf(f_3181_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_11964),U_11965)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11964)),hAPP(c_Nat_OSuc,U_11965)),
    inference(clausify,[status(thm)],[f_3181_3]) ).

fof(f_3182_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_3182_2,plain,
    ! [U_11968,U_11967,U_11966] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11966,U_11968),U_11967) = c_Orderings_Obot__class_Obot(tc_fun(U_11966,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11966),U_11967),U_11968))
      | ~ class_Orderings_Oorder(U_11966) ),
    inference(variable_rename,[status(thm)],[f_3182_1]) ).

fof(f_3182_3,plain,
    ! [U_11966,U_11967,U_11968] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11966,U_11968),U_11967) = c_Orderings_Obot__class_Obot(tc_fun(U_11966,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11966),U_11967),U_11968))
      | ~ class_Orderings_Oorder(U_11966) ),
    inference(definitional_conversion,[status(esa)],[f_3182_2]) ).

cnf(f_3182_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11966,U_11968),U_11967) = c_Orderings_Obot__class_Obot(tc_fun(U_11966,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11966),U_11967),U_11968))
    | ~ class_Orderings_Oorder(U_11966) ),
    inference(clausify,[status(thm)],[f_3182_3]) ).

fof(f_3183_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_3183_2,plain,
    ! [U_11971,U_11970,U_11969] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11969,U_11970),U_11971) = c_Orderings_Obot__class_Obot(tc_fun(U_11969,tc_HOL_Obool))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11969),U_11970),U_11971)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11969),U_11970),U_11971))
          | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11969,U_11970),U_11971) != c_Orderings_Obot__class_Obot(tc_fun(U_11969,tc_HOL_Obool)) ) )
      | ~ class_Orderings_Oorder(U_11969) ),
    inference(variable_rename,[status(thm)],[f_3183_1]) ).

fof(f_3183_3,plain,
    ( ! [U_11969,U_11970,U_11971] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11969,U_11970),U_11971) = c_Orderings_Obot__class_Obot(tc_fun(U_11969,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11969),U_11970),U_11971))
        | ~ sP873(U_11969,U_11970,U_11971) )
    & ! [U_11969,U_11970,U_11971] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11969),U_11970),U_11971))
        | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11969,U_11970),U_11971) != c_Orderings_Obot__class_Obot(tc_fun(U_11969,tc_HOL_Obool))
        | ~ sP873(U_11969,U_11970,U_11971) )
    & ! [U_11969,U_11970,U_11971] :
        ( sP873(U_11969,U_11970,U_11971)
        | ~ class_Orderings_Oorder(U_11969) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP873])],[f_3183_2]) ).

cnf(f_3183_4,plain,
    ( sP873(U_11969,U_11970,U_11971)
    | ~ class_Orderings_Oorder(U_11969) ),
    inference(clausify,[status(thm)],[f_3183_3]) ).

cnf(f_3183_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11969),U_11970),U_11971))
    | hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11969,U_11970),U_11971) != c_Orderings_Obot__class_Obot(tc_fun(U_11969,tc_HOL_Obool))
    | ~ sP873(U_11969,U_11970,U_11971) ),
    inference(clausify,[status(thm)],[f_3183_3]) ).

cnf(f_3183_6,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11969,U_11970),U_11971) = c_Orderings_Obot__class_Obot(tc_fun(U_11969,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11969),U_11970),U_11971))
    | ~ sP873(U_11969,U_11970,U_11971) ),
    inference(clausify,[status(thm)],[f_3183_3]) ).

fof(f_3184_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_3184_2,plain,
    ! [U_11974,U_11973,U_11972] :
      ( ( ( c_Orderings_Obot__class_Obot(tc_fun(U_11972,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11972,U_11973),U_11974)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11972),U_11973),U_11974)) )
        & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11972),U_11973),U_11974))
          | c_Orderings_Obot__class_Obot(tc_fun(U_11972,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11972,U_11973),U_11974) ) )
      | ~ class_Orderings_Oorder(U_11972) ),
    inference(variable_rename,[status(thm)],[f_3184_1]) ).

fof(f_3184_3,plain,
    ( ! [U_11973,U_11974,U_11972] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_11972,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11972,U_11973),U_11974)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11972),U_11973),U_11974))
        | ~ sP874(U_11973,U_11974,U_11972) )
    & ! [U_11973,U_11974,U_11972] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11972),U_11973),U_11974))
        | c_Orderings_Obot__class_Obot(tc_fun(U_11972,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11972,U_11973),U_11974)
        | ~ sP874(U_11973,U_11974,U_11972) )
    & ! [U_11973,U_11974,U_11972] :
        ( sP874(U_11973,U_11974,U_11972)
        | ~ class_Orderings_Oorder(U_11972) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP874])],[f_3184_2]) ).

cnf(f_3184_4,plain,
    ( sP874(U_11973,U_11974,U_11972)
    | ~ class_Orderings_Oorder(U_11972) ),
    inference(clausify,[status(thm)],[f_3184_3]) ).

cnf(f_3184_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11972),U_11973),U_11974))
    | c_Orderings_Obot__class_Obot(tc_fun(U_11972,tc_HOL_Obool)) != hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11972,U_11973),U_11974)
    | ~ sP874(U_11973,U_11974,U_11972) ),
    inference(clausify,[status(thm)],[f_3184_3]) ).

cnf(f_3184_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_11972,tc_HOL_Obool)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11972,U_11973),U_11974)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_11972),U_11973),U_11974))
    | ~ sP874(U_11973,U_11974,U_11972) ),
    inference(clausify,[status(thm)],[f_3184_3]) ).

fof(f_3185_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_3185_2,plain,
    ! [U_11979,U_11978,U_11977,U_11976,U_11975] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11975),U_11977),U_11979))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11975),U_11978),U_11976)) )
      | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11975),U_11977),U_11976))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11975,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11975,U_11976),U_11977)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11975,U_11978),U_11979)))
      | ~ class_Orderings_Olinorder(U_11975) ),
    inference(variable_rename,[status(thm)],[f_3185_1]) ).

fof(f_3185_3,plain,
    ( ! [U_11976,U_11975,U_11977,U_11978,U_11979] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11975),U_11977),U_11979))
        | ~ sP875(U_11976,U_11975,U_11977,U_11978,U_11979) )
    & ! [U_11976,U_11975,U_11977,U_11978,U_11979] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11975),U_11978),U_11976))
        | ~ sP875(U_11976,U_11975,U_11977,U_11978,U_11979) )
    & ! [U_11976,U_11975,U_11977,U_11978,U_11979] :
        ( sP875(U_11976,U_11975,U_11977,U_11978,U_11979)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11975),U_11977),U_11976))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11975,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11975,U_11976),U_11977)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11975,U_11978),U_11979)))
        | ~ class_Orderings_Olinorder(U_11975) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP875])],[f_3185_2]) ).

cnf(f_3185_4,plain,
    ( sP875(U_11976,U_11975,U_11977,U_11978,U_11979)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11975),U_11977),U_11976))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_11975,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11975,U_11976),U_11977)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11975,U_11978),U_11979)))
    | ~ class_Orderings_Olinorder(U_11975) ),
    inference(clausify,[status(thm)],[f_3185_3]) ).

cnf(f_3185_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11975),U_11978),U_11976))
    | ~ sP875(U_11976,U_11975,U_11977,U_11978,U_11979) ),
    inference(clausify,[status(thm)],[f_3185_3]) ).

cnf(f_3185_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11975),U_11977),U_11979))
    | ~ sP875(U_11976,U_11975,U_11977,U_11978,U_11979) ),
    inference(clausify,[status(thm)],[f_3185_3]) ).

fof(f_3186_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_3186_2,plain,
    ! [U_11983,U_11982,U_11981,U_11980] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11980,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11980,U_11981),U_11982)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11980,U_11982),U_11983)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11980,U_11981),U_11983)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11980),U_11982),U_11983))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11980),U_11981),U_11982))
      | ~ class_Orderings_Olinorder(U_11980) ),
    inference(variable_rename,[status(thm)],[f_3186_1]) ).

fof(f_3186_3,plain,
    ! [U_11980,U_11981,U_11982,U_11983] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11980,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11980,U_11981),U_11982)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11980,U_11982),U_11983)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11980,U_11981),U_11983)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11980),U_11982),U_11983))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11980),U_11981),U_11982))
      | ~ class_Orderings_Olinorder(U_11980) ),
    inference(definitional_conversion,[status(esa)],[f_3186_2]) ).

cnf(f_3186_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11980,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11980,U_11981),U_11982)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11980,U_11982),U_11983)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11980,U_11981),U_11983)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11980),U_11982),U_11983))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11980),U_11981),U_11982))
    | ~ class_Orderings_Olinorder(U_11980) ),
    inference(clausify,[status(thm)],[f_3186_3]) ).

fof(f_3187_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_3187_2,plain,
    ! [U_11987,U_11986,U_11985,U_11984] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11984,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11984,U_11985),U_11987)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11984,U_11985),U_11986)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11984,U_11986),U_11987)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11984),U_11985),U_11986))
      | ~ class_Orderings_Olinorder(U_11984) ),
    inference(variable_rename,[status(thm)],[f_3187_1]) ).

fof(f_3187_3,plain,
    ! [U_11984,U_11985,U_11986,U_11987] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11984,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11984,U_11985),U_11987)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11984,U_11985),U_11986)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11984,U_11986),U_11987)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11984),U_11985),U_11986))
      | ~ class_Orderings_Olinorder(U_11984) ),
    inference(definitional_conversion,[status(esa)],[f_3187_2]) ).

cnf(f_3187_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_11984,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11984,U_11985),U_11987)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11984,U_11985),U_11986)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11984,U_11986),U_11987)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11984),U_11985),U_11986))
    | ~ class_Orderings_Olinorder(U_11984) ),
    inference(clausify,[status(thm)],[f_3187_3]) ).

fof(f_3188_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_3188_2,plain,
    ! [U_11991,U_11990,U_11989,U_11988] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11988,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11988,U_11989),U_11990)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11988,U_11990),U_11991)) = c_Orderings_Obot__class_Obot(tc_fun(U_11988,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11988) ),
    inference(variable_rename,[status(thm)],[f_3188_1]) ).

fof(f_3188_3,plain,
    ! [U_11988,U_11989,U_11990,U_11991] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11988,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11988,U_11989),U_11990)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11988,U_11990),U_11991)) = c_Orderings_Obot__class_Obot(tc_fun(U_11988,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_11988) ),
    inference(definitional_conversion,[status(esa)],[f_3188_2]) ).

cnf(f_3188_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_11988,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11988,U_11989),U_11990)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11988,U_11990),U_11991)) = c_Orderings_Obot__class_Obot(tc_fun(U_11988,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_11988) ),
    inference(clausify,[status(thm)],[f_3188_3]) ).

fof(f_3189_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_3189_2,plain,
    ! [U_11993,U_11992] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11992)),U_11993) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_11992,U_11993),
    inference(variable_rename,[status(thm)],[f_3189_1]) ).

fof(f_3189_3,plain,
    ! [U_11992,U_11993] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11992)),U_11993) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_11992,U_11993),
    inference(definitional_conversion,[status(esa)],[f_3189_2]) ).

cnf(f_3189_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_11992)),U_11993) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_11992,U_11993),
    inference(clausify,[status(thm)],[f_3189_3]) ).

fof(f_3190_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_3190_2,plain,
    ! [U_11996,U_11995,U_11994] : 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_11994)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11995),U_11996)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11995),U_11994)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11996),U_11994)),
    inference(variable_rename,[status(thm)],[f_3190_1]) ).

fof(f_3190_3,plain,
    ! [U_11994,U_11995,U_11996] : 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_11994)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11995),U_11996)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11995),U_11994)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11996),U_11994)),
    inference(definitional_conversion,[status(esa)],[f_3190_2]) ).

cnf(f_3190_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_11994)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11995),U_11996)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11995),U_11994)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_11996),U_11994)),
    inference(clausify,[status(thm)],[f_3190_3]) ).

fof(f_3191_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_3191_2,plain,
    ! [U_11997] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11997),hAPP(c_Nat_OSuc,U_11997)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_11997),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3191_1]) ).

fof(f_3191_3,plain,
    ! [U_11997] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11997),hAPP(c_Nat_OSuc,U_11997)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_11997),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3191_2]) ).

cnf(f_3191_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_11997),hAPP(c_Nat_OSuc,U_11997)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_11997),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3191_3]) ).

fof(f_3192_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_3192_2,plain,
    ! [U_12001,U_12000,U_11999,U_11998] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11998,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11998,U_11999),U_12000)),c_SetInterval_Oord__class_OatLeastAtMost(U_11998,U_12000,U_12001)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11998,U_11999,U_12001)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11998),U_12000),U_12001))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11998),U_11999),U_12000))
      | ~ class_Orderings_Olinorder(U_11998) ),
    inference(variable_rename,[status(thm)],[f_3192_1]) ).

fof(f_3192_3,plain,
    ! [U_11998,U_11999,U_12000,U_12001] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11998,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11998,U_11999),U_12000)),c_SetInterval_Oord__class_OatLeastAtMost(U_11998,U_12000,U_12001)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11998,U_11999,U_12001)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11998),U_12000),U_12001))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11998),U_11999),U_12000))
      | ~ class_Orderings_Olinorder(U_11998) ),
    inference(definitional_conversion,[status(esa)],[f_3192_2]) ).

cnf(f_3192_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_11998,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_11998,U_11999),U_12000)),c_SetInterval_Oord__class_OatLeastAtMost(U_11998,U_12000,U_12001)) = c_SetInterval_Oord__class_OatLeastAtMost(U_11998,U_11999,U_12001)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11998),U_12000),U_12001))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_11998),U_11999),U_12000))
    | ~ class_Orderings_Olinorder(U_11998) ),
    inference(clausify,[status(thm)],[f_3192_3]) ).

fof(f_3193_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_3193_2,plain,
    ! [U_12004,U_12003,U_12002] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12002),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12003),U_12004)) = 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_12002),U_12003)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12003),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12003),U_12004)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12002),U_12003)) ),
    inference(variable_rename,[status(thm)],[f_3193_1]) ).

fof(f_3193_3,plain,
    ! [U_12003,U_12004,U_12002] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12002),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12003),U_12004)) = 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_12002),U_12003)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12003),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12003),U_12004)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12002),U_12003)) ),
    inference(definitional_conversion,[status(esa)],[f_3193_2]) ).

cnf(f_3193_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12002),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12003),U_12004)) = 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_12002),U_12003)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12003),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12003),U_12004)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12002),U_12003)) ),
    inference(clausify,[status(thm)],[f_3193_3]) ).

fof(f_3194_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_3194_2,plain,
    ! [U_12008,U_12007,U_12006,U_12005] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12005,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12005,U_12006),U_12007)),c_SetInterval_Oord__class_OatLeastAtMost(U_12005,U_12007,U_12008)) = c_Orderings_Obot__class_Obot(tc_fun(U_12005,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12005) ),
    inference(variable_rename,[status(thm)],[f_3194_1]) ).

fof(f_3194_3,plain,
    ! [U_12005,U_12006,U_12007,U_12008] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12005,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12005,U_12006),U_12007)),c_SetInterval_Oord__class_OatLeastAtMost(U_12005,U_12007,U_12008)) = c_Orderings_Obot__class_Obot(tc_fun(U_12005,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12005) ),
    inference(definitional_conversion,[status(esa)],[f_3194_2]) ).

cnf(f_3194_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12005,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12005,U_12006),U_12007)),c_SetInterval_Oord__class_OatLeastAtMost(U_12005,U_12007,U_12008)) = c_Orderings_Obot__class_Obot(tc_fun(U_12005,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12005) ),
    inference(clausify,[status(thm)],[f_3194_3]) ).

fof(f_3195_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_3195_2,plain,
    ! [U_12013,U_12012,U_12011,U_12010,U_12009] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12009,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12009,U_12010),U_12011)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12009,U_12012),U_12013)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12009,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12009),U_12010),U_12012)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12009),U_12011),U_12013))
      | ~ class_Orderings_Olinorder(U_12009) ),
    inference(variable_rename,[status(thm)],[f_3195_1]) ).

fof(f_3195_3,plain,
    ! [U_12009,U_12010,U_12011,U_12012,U_12013] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12009,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12009,U_12010),U_12011)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12009,U_12012),U_12013)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12009,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12009),U_12010),U_12012)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12009),U_12011),U_12013))
      | ~ class_Orderings_Olinorder(U_12009) ),
    inference(definitional_conversion,[status(esa)],[f_3195_2]) ).

cnf(f_3195_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12009,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12009,U_12010),U_12011)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12009,U_12012),U_12013)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12009,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12009),U_12010),U_12012)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12009),U_12011),U_12013))
    | ~ class_Orderings_Olinorder(U_12009) ),
    inference(clausify,[status(thm)],[f_3195_3]) ).

fof(f_3196_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_3196_2,plain,
    ! [U_12015,U_12014] :
      ( U_12014 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12015),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12015),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_12014)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_12014),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12015),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12015),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_12014))))) ),
    inference(variable_rename,[status(thm)],[f_3196_1]) ).

fof(f_3196_3,plain,
    ! [U_12014,U_12015] :
      ( U_12014 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12015),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12015),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_12014)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_12014),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12015),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12015),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_12014))))) ),
    inference(definitional_conversion,[status(esa)],[f_3196_2]) ).

cnf(f_3196_4,plain,
    ( U_12014 = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12015),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12015),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_12014)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_12014),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12015),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12015),hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),U_12014))))) ),
    inference(clausify,[status(thm)],[f_3196_3]) ).

fof(f_3197_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_3197_2,plain,
    ! [U_12019,U_12018,U_12017,U_12016] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12016,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12016,U_12017,U_12018)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12016,U_12018),U_12019)) = c_Orderings_Obot__class_Obot(tc_fun(U_12016,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12016) ),
    inference(variable_rename,[status(thm)],[f_3197_1]) ).

fof(f_3197_3,plain,
    ! [U_12016,U_12017,U_12018,U_12019] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12016,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12016,U_12017,U_12018)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12016,U_12018),U_12019)) = c_Orderings_Obot__class_Obot(tc_fun(U_12016,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12016) ),
    inference(definitional_conversion,[status(esa)],[f_3197_2]) ).

cnf(f_3197_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12016,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12016,U_12017,U_12018)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12016,U_12018),U_12019)) = c_Orderings_Obot__class_Obot(tc_fun(U_12016,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12016) ),
    inference(clausify,[status(thm)],[f_3197_3]) ).

fof(f_3198_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_3198_2,plain,
    ! [U_12022,U_12021,U_12020] :
      ( hAPP(c_Set_Oimage(U_12020,U_12020,c_Groups_Ouminus__class_Ouminus(U_12020)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12020,U_12021),U_12022)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_12020,hAPP(c_Groups_Ouminus__class_Ouminus(U_12020),U_12022),hAPP(c_Groups_Ouminus__class_Ouminus(U_12020),U_12021))
      | ~ class_Groups_Oordered__ab__group__add(U_12020) ),
    inference(variable_rename,[status(thm)],[f_3198_1]) ).

fof(f_3198_3,plain,
    ! [U_12020,U_12021,U_12022] :
      ( hAPP(c_Set_Oimage(U_12020,U_12020,c_Groups_Ouminus__class_Ouminus(U_12020)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12020,U_12021),U_12022)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_12020,hAPP(c_Groups_Ouminus__class_Ouminus(U_12020),U_12022),hAPP(c_Groups_Ouminus__class_Ouminus(U_12020),U_12021))
      | ~ class_Groups_Oordered__ab__group__add(U_12020) ),
    inference(definitional_conversion,[status(esa)],[f_3198_2]) ).

cnf(f_3198_4,plain,
    ( hAPP(c_Set_Oimage(U_12020,U_12020,c_Groups_Ouminus__class_Ouminus(U_12020)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12020,U_12021),U_12022)) = c_SetInterval_Oord__class_OgreaterThanAtMost(U_12020,hAPP(c_Groups_Ouminus__class_Ouminus(U_12020),U_12022),hAPP(c_Groups_Ouminus__class_Ouminus(U_12020),U_12021))
    | ~ class_Groups_Oordered__ab__group__add(U_12020) ),
    inference(clausify,[status(thm)],[f_3198_3]) ).

fof(f_3199_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_3199_2,plain,
    ! [U_12025,U_12024,U_12023] :
      ( hAPP(c_Set_Oimage(U_12023,U_12023,c_Groups_Ouminus__class_Ouminus(U_12023)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12023,U_12024,U_12025)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12023,hAPP(c_Groups_Ouminus__class_Ouminus(U_12023),U_12025)),hAPP(c_Groups_Ouminus__class_Ouminus(U_12023),U_12024))
      | ~ class_Groups_Oordered__ab__group__add(U_12023) ),
    inference(variable_rename,[status(thm)],[f_3199_1]) ).

fof(f_3199_3,plain,
    ! [U_12023,U_12024,U_12025] :
      ( hAPP(c_Set_Oimage(U_12023,U_12023,c_Groups_Ouminus__class_Ouminus(U_12023)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12023,U_12024,U_12025)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12023,hAPP(c_Groups_Ouminus__class_Ouminus(U_12023),U_12025)),hAPP(c_Groups_Ouminus__class_Ouminus(U_12023),U_12024))
      | ~ class_Groups_Oordered__ab__group__add(U_12023) ),
    inference(definitional_conversion,[status(esa)],[f_3199_2]) ).

cnf(f_3199_4,plain,
    ( hAPP(c_Set_Oimage(U_12023,U_12023,c_Groups_Ouminus__class_Ouminus(U_12023)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12023,U_12024,U_12025)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12023,hAPP(c_Groups_Ouminus__class_Ouminus(U_12023),U_12025)),hAPP(c_Groups_Ouminus__class_Ouminus(U_12023),U_12024))
    | ~ class_Groups_Oordered__ab__group__add(U_12023) ),
    inference(clausify,[status(thm)],[f_3199_3]) ).

fof(f_3200_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_3200_2,plain,
    ! [U_12027,U_12026] :
      ( ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12026),hAPP(c_Nat_OSuc,U_12027)) = 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_12026),U_12027)) )
      & ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12026),hAPP(c_Nat_OSuc,U_12027)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12027),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12026),U_12027))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12026),U_12027)) ) ),
    inference(variable_rename,[status(thm)],[f_3200_1]) ).

fof(f_3200_3,plain,
    ( ! [U_12031,U_12029] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12029),hAPP(c_Nat_OSuc,U_12031)) = 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_12029),U_12031)) )
    & ! [U_12030,U_12028] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12028),hAPP(c_Nat_OSuc,U_12030)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12030),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12028),U_12030))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12028),U_12030)) ) ),
    inference(miniscope,[status(thm)],[f_3200_2]) ).

fof(f_3200_4,plain,
    ( ! [U_12029,U_12031] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12029),hAPP(c_Nat_OSuc,U_12031)) = 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_12029),U_12031)) )
    & ! [U_12030,U_12028] :
        ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12028),hAPP(c_Nat_OSuc,U_12030)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12030),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12028),U_12030))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12028),U_12030)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3200_3]) ).

cnf(f_3200_5,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12028),hAPP(c_Nat_OSuc,U_12030)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12030),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12028),U_12030))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12028),U_12030)) ),
    inference(clausify,[status(thm)],[f_3200_4]) ).

cnf(f_3200_6,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12029),hAPP(c_Nat_OSuc,U_12031)) = 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_12029),U_12031)) ),
    inference(clausify,[status(thm)],[f_3200_4]) ).

fof(f_3201_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_3201_2,plain,
    ! [U_12035,U_12034,U_12033,U_12032] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12032,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12032,U_12033,U_12034)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12032,U_12034),U_12035)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_12032,U_12033,U_12035)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12032),U_12034),U_12035))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12032),U_12033),U_12034))
      | ~ class_Orderings_Olinorder(U_12032) ),
    inference(variable_rename,[status(thm)],[f_3201_1]) ).

fof(f_3201_3,plain,
    ! [U_12032,U_12033,U_12034,U_12035] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12032,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12032,U_12033,U_12034)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12032,U_12034),U_12035)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_12032,U_12033,U_12035)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12032),U_12034),U_12035))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12032),U_12033),U_12034))
      | ~ class_Orderings_Olinorder(U_12032) ),
    inference(definitional_conversion,[status(esa)],[f_3201_2]) ).

cnf(f_3201_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12032,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12032,U_12033,U_12034)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12032,U_12034),U_12035)) = c_SetInterval_Oord__class_OgreaterThanLessThan(U_12032,U_12033,U_12035)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12032),U_12034),U_12035))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12032),U_12033),U_12034))
    | ~ class_Orderings_Olinorder(U_12032) ),
    inference(clausify,[status(thm)],[f_3201_3]) ).

fof(f_3202_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_3202_2,plain,
    ! [U_12038,U_12037,U_12036] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12036,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12036,U_12037),U_12038)),hAPP(hAPP(c_Set_Oinsert(U_12036),U_12038),c_Orderings_Obot__class_Obot(tc_fun(U_12036,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_12036,U_12037,U_12038)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12036),U_12037),U_12038))
      | ~ class_Orderings_Olinorder(U_12036) ),
    inference(variable_rename,[status(thm)],[f_3202_1]) ).

fof(f_3202_3,plain,
    ! [U_12036,U_12037,U_12038] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12036,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12036,U_12037),U_12038)),hAPP(hAPP(c_Set_Oinsert(U_12036),U_12038),c_Orderings_Obot__class_Obot(tc_fun(U_12036,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_12036,U_12037,U_12038)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12036),U_12037),U_12038))
      | ~ class_Orderings_Olinorder(U_12036) ),
    inference(definitional_conversion,[status(esa)],[f_3202_2]) ).

cnf(f_3202_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12036,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12036,U_12037),U_12038)),hAPP(hAPP(c_Set_Oinsert(U_12036),U_12038),c_Orderings_Obot__class_Obot(tc_fun(U_12036,tc_HOL_Obool)))) = c_SetInterval_Oord__class_OatLeastAtMost(U_12036,U_12037,U_12038)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12036),U_12037),U_12038))
    | ~ class_Orderings_Olinorder(U_12036) ),
    inference(clausify,[status(thm)],[f_3202_3]) ).

fof(f_3203_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_3203_2,plain,
    ! [U_12041,U_12040,U_12039] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12039,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12039),U_12040),c_Orderings_Obot__class_Obot(tc_fun(U_12039,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12039,U_12040,U_12041)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12039,U_12040),U_12041)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12039),U_12040),U_12041))
      | ~ class_Orderings_Olinorder(U_12039) ),
    inference(variable_rename,[status(thm)],[f_3203_1]) ).

fof(f_3203_3,plain,
    ! [U_12039,U_12040,U_12041] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12039,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12039),U_12040),c_Orderings_Obot__class_Obot(tc_fun(U_12039,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12039,U_12040,U_12041)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12039,U_12040),U_12041)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12039),U_12040),U_12041))
      | ~ class_Orderings_Olinorder(U_12039) ),
    inference(definitional_conversion,[status(esa)],[f_3203_2]) ).

cnf(f_3203_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12039,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12039),U_12040),c_Orderings_Obot__class_Obot(tc_fun(U_12039,tc_HOL_Obool)))),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12039,U_12040,U_12041)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12039,U_12040),U_12041)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12039),U_12040),U_12041))
    | ~ class_Orderings_Olinorder(U_12039) ),
    inference(clausify,[status(thm)],[f_3203_3]) ).

fof(f_3204_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_3204_2,plain,
    ! [U_12045,U_12044,U_12043,U_12042] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12042,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12042,U_12043,U_12044)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12042,U_12044,U_12045)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12042,U_12043),U_12045)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12042),U_12044),U_12045))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12042),U_12043),U_12044))
      | ~ class_Orderings_Olinorder(U_12042) ),
    inference(variable_rename,[status(thm)],[f_3204_1]) ).

fof(f_3204_3,plain,
    ! [U_12042,U_12043,U_12044,U_12045] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12042,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12042,U_12043,U_12044)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12042,U_12044,U_12045)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12042,U_12043),U_12045)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12042),U_12044),U_12045))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12042),U_12043),U_12044))
      | ~ class_Orderings_Olinorder(U_12042) ),
    inference(definitional_conversion,[status(esa)],[f_3204_2]) ).

cnf(f_3204_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12042,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12042,U_12043,U_12044)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12042,U_12044,U_12045)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12042,U_12043),U_12045)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12042),U_12044),U_12045))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12042),U_12043),U_12044))
    | ~ class_Orderings_Olinorder(U_12042) ),
    inference(clausify,[status(thm)],[f_3204_3]) ).

fof(f_3205_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_3205_2,plain,
    ! [U_12048,U_12047,U_12046] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_12046),hAPP(c_List_Olexn(U_12046,U_12047),U_12048))
      | ~ c_Wellfounded_Owf(U_12046,U_12047) ),
    inference(variable_rename,[status(thm)],[f_3205_1]) ).

fof(f_3205_3,plain,
    ! [U_12047,U_12048,U_12046] :
      ( c_Wellfounded_Owf(tc_List_Olist(U_12046),hAPP(c_List_Olexn(U_12046,U_12047),U_12048))
      | ~ c_Wellfounded_Owf(U_12046,U_12047) ),
    inference(definitional_conversion,[status(esa)],[f_3205_2]) ).

cnf(f_3205_4,plain,
    ( c_Wellfounded_Owf(tc_List_Olist(U_12046),hAPP(c_List_Olexn(U_12046,U_12047),U_12048))
    | ~ c_Wellfounded_Owf(U_12046,U_12047) ),
    inference(clausify,[status(thm)],[f_3205_3]) ).

fof(f_3206_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_3206_2,plain,
    ! [U_12055,U_12054,U_12053,U_12052] :
      ( ! [U_12051] :
          ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12052),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12051),U_12053)),U_12055)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12052),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12051),U_12055)))
          | ? [U_12050] :
              ( ? [U_12049] :
                  ( U_12051 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12049),U_12050)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_12049),U_12054)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_12050),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12053))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12052),U_12053)) ),
    inference(variable_rename,[status(thm)],[f_3206_1]) ).

fof(f_3206_3,plain,
    ! [U_12055,U_12054,U_12053,U_12052] :
      ( ! [U_12051] :
          ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12052),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12051),U_12053)),U_12055)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12052),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12051),U_12055)))
          | ( ? [U_12049] :
                ( U_12051 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12049),sK244(U_12055,U_12054,U_12053,U_12052,U_12051))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_12049),U_12054)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK244(U_12055,U_12054,U_12053,U_12052,U_12051)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12053))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12052),U_12053)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK244]),skolemize(U_12050,sK244(U_12055,U_12054,U_12053,U_12052,U_12051))],[f_3206_2]) ).

fof(f_3206_4,plain,
    ! [U_12055,U_12054,U_12053,U_12052] :
      ( ! [U_12051] :
          ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12052),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12051),U_12053)),U_12055)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12052),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12051),U_12055)))
          | ( U_12051 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK245(U_12055,U_12054,U_12053,U_12052,U_12051)),sK244(U_12055,U_12054,U_12053,U_12052,U_12051))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK245(U_12055,U_12054,U_12053,U_12052,U_12051)),U_12054))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK244(U_12055,U_12054,U_12053,U_12052,U_12051)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12053))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12052),U_12053)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK245]),skolemize(U_12049,sK245(U_12055,U_12054,U_12053,U_12052,U_12051))],[f_3206_3]) ).

fof(f_3206_5,plain,
    ( ! [U_12051,U_12052,U_12053,U_12054,U_12055] :
        ( U_12051 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK245(U_12055,U_12054,U_12053,U_12052,U_12051)),sK244(U_12055,U_12054,U_12053,U_12052,U_12051))
        | ~ sP876(U_12051,U_12052,U_12053,U_12054,U_12055) )
    & ! [U_12051,U_12052,U_12053,U_12054,U_12055] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK245(U_12055,U_12054,U_12053,U_12052,U_12051)),U_12054))
        | ~ sP876(U_12051,U_12052,U_12053,U_12054,U_12055) )
    & ! [U_12051,U_12052,U_12053,U_12054,U_12055] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK244(U_12055,U_12054,U_12053,U_12052,U_12051)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12053)))
        | ~ sP876(U_12051,U_12052,U_12053,U_12054,U_12055) )
    & ! [U_12051,U_12052,U_12053,U_12054,U_12055] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12052),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12051),U_12053)),U_12055)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12052),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12051),U_12055)))
        | sP876(U_12051,U_12052,U_12053,U_12054,U_12055)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12052),U_12053)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP876])],[f_3206_4]) ).

cnf(f_3206_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12052),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12051),U_12053)),U_12055)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12052),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12051),U_12055)))
    | sP876(U_12051,U_12052,U_12053,U_12054,U_12055)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12052),U_12053)) ),
    inference(clausify,[status(thm)],[f_3206_5]) ).

cnf(f_3206_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK244(U_12055,U_12054,U_12053,U_12052,U_12051)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12053)))
    | ~ sP876(U_12051,U_12052,U_12053,U_12054,U_12055) ),
    inference(clausify,[status(thm)],[f_3206_5]) ).

cnf(f_3206_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK245(U_12055,U_12054,U_12053,U_12052,U_12051)),U_12054))
    | ~ sP876(U_12051,U_12052,U_12053,U_12054,U_12055) ),
    inference(clausify,[status(thm)],[f_3206_5]) ).

cnf(f_3206_9,plain,
    ( U_12051 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK245(U_12055,U_12054,U_12053,U_12052,U_12051)),sK244(U_12055,U_12054,U_12053,U_12052,U_12051))
    | ~ sP876(U_12051,U_12052,U_12053,U_12054,U_12055) ),
    inference(clausify,[status(thm)],[f_3206_5]) ).

fof(f_3207_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_3207_2,plain,
    ! [U_12062,U_12061,U_12060,U_12059] :
      ( ! [U_12058] :
          ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12059),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12058),U_12060)),U_12062)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12059),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12058),U_12062)))
          | ? [U_12057] :
              ( ? [U_12056] :
                  ( U_12058 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12056),U_12057)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_12056),U_12061)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_12057),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12060))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12059),U_12060)) ),
    inference(variable_rename,[status(thm)],[f_3207_1]) ).

fof(f_3207_3,plain,
    ! [U_12062,U_12061,U_12060,U_12059] :
      ( ! [U_12058] :
          ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12059),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12058),U_12060)),U_12062)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12059),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12058),U_12062)))
          | ( ? [U_12056] :
                ( U_12058 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12056),sK246(U_12062,U_12061,U_12060,U_12059,U_12058))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_12056),U_12061)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK246(U_12062,U_12061,U_12060,U_12059,U_12058)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12060))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12059),U_12060)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK246]),skolemize(U_12057,sK246(U_12062,U_12061,U_12060,U_12059,U_12058))],[f_3207_2]) ).

fof(f_3207_4,plain,
    ! [U_12062,U_12061,U_12060,U_12059] :
      ( ! [U_12058] :
          ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12059),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12058),U_12060)),U_12062)))
          | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12059),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12058),U_12062)))
          | ( U_12058 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK247(U_12062,U_12061,U_12060,U_12059,U_12058)),sK246(U_12062,U_12061,U_12060,U_12059,U_12058))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK247(U_12062,U_12061,U_12060,U_12059,U_12058)),U_12061))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK246(U_12062,U_12061,U_12060,U_12059,U_12058)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12060))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12059),U_12060)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK247]),skolemize(U_12056,sK247(U_12062,U_12061,U_12060,U_12059,U_12058))],[f_3207_3]) ).

fof(f_3207_5,plain,
    ( ! [U_12060,U_12061,U_12062,U_12058,U_12059] :
        ( U_12058 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK247(U_12062,U_12061,U_12060,U_12059,U_12058)),sK246(U_12062,U_12061,U_12060,U_12059,U_12058))
        | ~ sP877(U_12060,U_12061,U_12062,U_12058,U_12059) )
    & ! [U_12060,U_12061,U_12062,U_12058,U_12059] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK247(U_12062,U_12061,U_12060,U_12059,U_12058)),U_12061))
        | ~ sP877(U_12060,U_12061,U_12062,U_12058,U_12059) )
    & ! [U_12060,U_12061,U_12062,U_12058,U_12059] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK246(U_12062,U_12061,U_12060,U_12059,U_12058)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12060)))
        | ~ sP877(U_12060,U_12061,U_12062,U_12058,U_12059) )
    & ! [U_12060,U_12061,U_12062,U_12058,U_12059] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12059),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12058),U_12060)),U_12062)))
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12059),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12058),U_12062)))
        | sP877(U_12060,U_12061,U_12062,U_12058,U_12059)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12059),U_12060)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP877])],[f_3207_4]) ).

cnf(f_3207_6,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12059),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12058),U_12060)),U_12062)))
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12059),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12058),U_12062)))
    | sP877(U_12060,U_12061,U_12062,U_12058,U_12059)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12059),U_12060)) ),
    inference(clausify,[status(thm)],[f_3207_5]) ).

cnf(f_3207_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK246(U_12062,U_12061,U_12060,U_12059,U_12058)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12060)))
    | ~ sP877(U_12060,U_12061,U_12062,U_12058,U_12059) ),
    inference(clausify,[status(thm)],[f_3207_5]) ).

cnf(f_3207_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK247(U_12062,U_12061,U_12060,U_12059,U_12058)),U_12061))
    | ~ sP877(U_12060,U_12061,U_12062,U_12058,U_12059) ),
    inference(clausify,[status(thm)],[f_3207_5]) ).

cnf(f_3207_9,plain,
    ( U_12058 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK247(U_12062,U_12061,U_12060,U_12059,U_12058)),sK246(U_12062,U_12061,U_12060,U_12059,U_12058))
    | ~ sP877(U_12060,U_12061,U_12062,U_12058,U_12059) ),
    inference(clausify,[status(thm)],[f_3207_5]) ).

fof(f_3208_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_3208_2,plain,
    ! [U_12064,U_12063] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12063),U_12064))),
    inference(variable_rename,[status(thm)],[f_3208_1]) ).

fof(f_3208_3,plain,
    ! [U_12064,U_12063] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12063),U_12064))),
    inference(definitional_conversion,[status(esa)],[f_3208_2]) ).

cnf(f_3208_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12063),U_12064))),
    inference(clausify,[status(thm)],[f_3208_3]) ).

fof(f_3209_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_3209_2,plain,
    ! [U_12066,U_12065] : hAPP(c_List_Olexn(U_12065,U_12066),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(U_12065),tc_List_Olist(U_12065)),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3209_1]) ).

fof(f_3209_3,plain,
    ! [U_12066,U_12065] : hAPP(c_List_Olexn(U_12065,U_12066),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(U_12065),tc_List_Olist(U_12065)),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3209_2]) ).

cnf(f_3209_4,plain,
    hAPP(c_List_Olexn(U_12065,U_12066),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_List_Olist(U_12065),tc_List_Olist(U_12065)),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3209_3]) ).

fof(f_3210_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_3210_2,plain,
    ! [U_12067] : 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_12067))),
    inference(variable_rename,[status(thm)],[f_3210_1]) ).

fof(f_3210_3,plain,
    ! [U_12067] : 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_12067))),
    inference(definitional_conversion,[status(esa)],[f_3210_2]) ).

cnf(f_3210_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_12067))),
    inference(clausify,[status(thm)],[f_3210_3]) ).

fof(f_3211_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_3211_2,plain,
    ! [U_12069,U_12068] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12068),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12069),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_12068,U_12069),
    inference(variable_rename,[status(thm)],[f_3211_1]) ).

fof(f_3211_3,plain,
    ! [U_12068,U_12069] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12068),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12069),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_12068,U_12069),
    inference(definitional_conversion,[status(esa)],[f_3211_2]) ).

cnf(f_3211_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12068),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12069),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_12068,U_12069),
    inference(clausify,[status(thm)],[f_3211_3]) ).

fof(f_3212_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_3212_2,plain,
    ! [U_12071,U_12070] : 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_12070)),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_12071),U_12070))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12070),U_12071),
    inference(variable_rename,[status(thm)],[f_3212_1]) ).

fof(f_3212_3,plain,
    ! [U_12070,U_12071] : 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_12070)),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_12071),U_12070))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12070),U_12071),
    inference(definitional_conversion,[status(esa)],[f_3212_2]) ).

cnf(f_3212_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_12070)),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_12071),U_12070))) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12070),U_12071),
    inference(clausify,[status(thm)],[f_3212_3]) ).

fof(f_3213_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_3213_2,plain,
    ! [U_12072] : 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_12072)) = hAPP(c_Int_Onat,U_12072),
    inference(variable_rename,[status(thm)],[f_3213_1]) ).

fof(f_3213_3,plain,
    ! [U_12072] : 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_12072)) = hAPP(c_Int_Onat,U_12072),
    inference(definitional_conversion,[status(esa)],[f_3213_2]) ).

cnf(f_3213_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_12072)) = hAPP(c_Int_Onat,U_12072),
    inference(clausify,[status(thm)],[f_3213_3]) ).

fof(f_3214_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_3214_2,plain,
    ! [U_12074,U_12073] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12073),U_12074)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12074),U_12073)),
    inference(variable_rename,[status(thm)],[f_3214_1]) ).

fof(f_3214_3,plain,
    ! [U_12073,U_12074] : hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12073),U_12074)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12074),U_12073)),
    inference(definitional_conversion,[status(esa)],[f_3214_2]) ).

cnf(f_3214_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Int_Oint),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_12073),U_12074)) = hAPP(c_Int_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12074),U_12073)),
    inference(clausify,[status(thm)],[f_3214_3]) ).

fof(f_3215_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_3215_2,plain,
    ! [U_12076,U_12075] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12075),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_12076) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_12075,U_12076),
    inference(variable_rename,[status(thm)],[f_3215_1]) ).

fof(f_3215_3,plain,
    ! [U_12075,U_12076] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12075),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_12076) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_12075,U_12076),
    inference(definitional_conversion,[status(esa)],[f_3215_2]) ).

cnf(f_3215_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12075),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_12076) = c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_12075,U_12076),
    inference(clausify,[status(thm)],[f_3215_3]) ).

fof(f_3216_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_3216_2,plain,
    ! [U_12083,U_12082,U_12081,U_12080] :
      ( ! [U_12079] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12080),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12079),U_12081)),U_12083)))
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12080),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12079),U_12083)))
          | ? [U_12078] :
              ( ? [U_12077] :
                  ( U_12079 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12077),U_12078)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_12077),U_12082)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_12078),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12081))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12080),U_12081)) ),
    inference(variable_rename,[status(thm)],[f_3216_1]) ).

fof(f_3216_3,plain,
    ! [U_12083,U_12082,U_12081,U_12080] :
      ( ! [U_12079] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12080),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12079),U_12081)),U_12083)))
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12080),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12079),U_12083)))
          | ( ? [U_12077] :
                ( U_12079 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12077),sK248(U_12083,U_12082,U_12081,U_12080,U_12079))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_12077),U_12082)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK248(U_12083,U_12082,U_12081,U_12080,U_12079)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12081))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12080),U_12081)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK248]),skolemize(U_12078,sK248(U_12083,U_12082,U_12081,U_12080,U_12079))],[f_3216_2]) ).

fof(f_3216_4,plain,
    ! [U_12083,U_12082,U_12081,U_12080] :
      ( ! [U_12079] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12080),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12079),U_12081)),U_12083)))
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12080),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12079),U_12083)))
          | ( U_12079 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK249(U_12083,U_12082,U_12081,U_12080,U_12079)),sK248(U_12083,U_12082,U_12081,U_12080,U_12079))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK249(U_12083,U_12082,U_12081,U_12080,U_12079)),U_12082))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK248(U_12083,U_12082,U_12081,U_12080,U_12079)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12081))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12080),U_12081)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK249]),skolemize(U_12077,sK249(U_12083,U_12082,U_12081,U_12080,U_12079))],[f_3216_3]) ).

fof(f_3216_5,plain,
    ( ! [U_12079,U_12080,U_12081,U_12082,U_12083] :
        ( U_12079 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK249(U_12083,U_12082,U_12081,U_12080,U_12079)),sK248(U_12083,U_12082,U_12081,U_12080,U_12079))
        | ~ sP878(U_12079,U_12080,U_12081,U_12082,U_12083) )
    & ! [U_12079,U_12080,U_12081,U_12082,U_12083] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK249(U_12083,U_12082,U_12081,U_12080,U_12079)),U_12082))
        | ~ sP878(U_12079,U_12080,U_12081,U_12082,U_12083) )
    & ! [U_12079,U_12080,U_12081,U_12082,U_12083] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK248(U_12083,U_12082,U_12081,U_12080,U_12079)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12081)))
        | ~ sP878(U_12079,U_12080,U_12081,U_12082,U_12083) )
    & ! [U_12079,U_12080,U_12081,U_12082,U_12083] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12080),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12079),U_12081)),U_12083)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12080),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12079),U_12083)))
        | sP878(U_12079,U_12080,U_12081,U_12082,U_12083)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12080),U_12081)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP878])],[f_3216_4]) ).

cnf(f_3216_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12080),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12079),U_12081)),U_12083)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12080),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12079),U_12083)))
    | sP878(U_12079,U_12080,U_12081,U_12082,U_12083)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12080),U_12081)) ),
    inference(clausify,[status(thm)],[f_3216_5]) ).

cnf(f_3216_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK248(U_12083,U_12082,U_12081,U_12080,U_12079)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12081)))
    | ~ sP878(U_12079,U_12080,U_12081,U_12082,U_12083) ),
    inference(clausify,[status(thm)],[f_3216_5]) ).

cnf(f_3216_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK249(U_12083,U_12082,U_12081,U_12080,U_12079)),U_12082))
    | ~ sP878(U_12079,U_12080,U_12081,U_12082,U_12083) ),
    inference(clausify,[status(thm)],[f_3216_5]) ).

cnf(f_3216_9,plain,
    ( U_12079 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),sK249(U_12083,U_12082,U_12081,U_12080,U_12079)),sK248(U_12083,U_12082,U_12081,U_12080,U_12079))
    | ~ sP878(U_12079,U_12080,U_12081,U_12082,U_12083) ),
    inference(clausify,[status(thm)],[f_3216_5]) ).

fof(f_3217_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_3217_2,plain,
    ! [U_12090,U_12089,U_12088,U_12087] :
      ( ! [U_12086] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12087),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12086),U_12088)),U_12090)))
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12087),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12086),U_12090)))
          | ? [U_12085] :
              ( ? [U_12084] :
                  ( U_12086 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12084),U_12085)
                  & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_12084),U_12089)) )
              & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_12085),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12088))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12087),U_12088)) ),
    inference(variable_rename,[status(thm)],[f_3217_1]) ).

fof(f_3217_3,plain,
    ! [U_12090,U_12089,U_12088,U_12087] :
      ( ! [U_12086] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12087),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12086),U_12088)),U_12090)))
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12087),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12086),U_12090)))
          | ( ? [U_12084] :
                ( U_12086 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12084),sK250(U_12090,U_12089,U_12088,U_12087,U_12086))
                & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),U_12084),U_12089)) )
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK250(U_12090,U_12089,U_12088,U_12087,U_12086)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12088))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12087),U_12088)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK250]),skolemize(U_12085,sK250(U_12090,U_12089,U_12088,U_12087,U_12086))],[f_3217_2]) ).

fof(f_3217_4,plain,
    ! [U_12090,U_12089,U_12088,U_12087] :
      ( ! [U_12086] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12087),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12086),U_12088)),U_12090)))
          | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12087),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12086),U_12090)))
          | ( U_12086 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK251(U_12090,U_12089,U_12088,U_12087,U_12086)),sK250(U_12090,U_12089,U_12088,U_12087,U_12086))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK251(U_12090,U_12089,U_12088,U_12087,U_12086)),U_12089))
            & hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK250(U_12090,U_12089,U_12088,U_12087,U_12086)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12088))) ) )
      | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12087),U_12088)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK251]),skolemize(U_12084,sK251(U_12090,U_12089,U_12088,U_12087,U_12086))],[f_3217_3]) ).

fof(f_3217_5,plain,
    ( ! [U_12086,U_12087,U_12088,U_12089,U_12090] :
        ( U_12086 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK251(U_12090,U_12089,U_12088,U_12087,U_12086)),sK250(U_12090,U_12089,U_12088,U_12087,U_12086))
        | ~ sP879(U_12086,U_12087,U_12088,U_12089,U_12090) )
    & ! [U_12086,U_12087,U_12088,U_12089,U_12090] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK251(U_12090,U_12089,U_12088,U_12087,U_12086)),U_12089))
        | ~ sP879(U_12086,U_12087,U_12088,U_12089,U_12090) )
    & ! [U_12086,U_12087,U_12088,U_12089,U_12090] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK250(U_12090,U_12089,U_12088,U_12087,U_12086)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12088)))
        | ~ sP879(U_12086,U_12087,U_12088,U_12089,U_12090) )
    & ! [U_12086,U_12087,U_12088,U_12089,U_12090] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12087),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12086),U_12088)),U_12090)))
        | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12087),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12086),U_12090)))
        | sP879(U_12086,U_12087,U_12088,U_12089,U_12090)
        | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12087),U_12088)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP879])],[f_3217_4]) ).

cnf(f_3217_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12087),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_12086),U_12088)),U_12090)))
    | hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12087),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12086),U_12090)))
    | sP879(U_12086,U_12087,U_12088,U_12089,U_12090)
    | ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Int_Oint),U_12087),U_12088)) ),
    inference(clausify,[status(thm)],[f_3217_5]) ).

cnf(f_3217_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK250(U_12090,U_12089,U_12088,U_12087,U_12086)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),U_12088)))
    | ~ sP879(U_12086,U_12087,U_12088,U_12089,U_12090) ),
    inference(clausify,[status(thm)],[f_3217_5]) ).

cnf(f_3217_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),sK251(U_12090,U_12089,U_12088,U_12087,U_12086)),U_12089))
    | ~ sP879(U_12086,U_12087,U_12088,U_12089,U_12090) ),
    inference(clausify,[status(thm)],[f_3217_5]) ).

cnf(f_3217_9,plain,
    ( U_12086 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK251(U_12090,U_12089,U_12088,U_12087,U_12086)),sK250(U_12090,U_12089,U_12088,U_12087,U_12086))
    | ~ sP879(U_12086,U_12087,U_12088,U_12089,U_12090) ),
    inference(clausify,[status(thm)],[f_3217_5]) ).

fof(f_3218_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_3218_2,plain,
    ! [U_12091] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12091) = 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_12091))),
    inference(variable_rename,[status(thm)],[f_3218_1]) ).

fof(f_3218_3,plain,
    ! [U_12091] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12091) = 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_12091))),
    inference(definitional_conversion,[status(esa)],[f_3218_2]) ).

cnf(f_3218_4,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12091) = 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_12091))),
    inference(clausify,[status(thm)],[f_3218_3]) ).

fof(f_3219_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_3219_2,plain,
    ! [U_12092] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12092))),
    inference(variable_rename,[status(thm)],[f_3219_1]) ).

fof(f_3219_3,plain,
    ! [U_12092] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12092))),
    inference(definitional_conversion,[status(esa)],[f_3219_2]) ).

cnf(f_3219_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12092))),
    inference(clausify,[status(thm)],[f_3219_3]) ).

fof(f_3220_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_3220_2,plain,
    ! [U_12095,U_12094,U_12093] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatMost(U_12093),U_12094) = hAPP(c_SetInterval_Oord__class_OatMost(U_12093),U_12095)
          | U_12094 != U_12095 )
        & ( U_12094 = U_12095
          | hAPP(c_SetInterval_Oord__class_OatMost(U_12093),U_12094) != hAPP(c_SetInterval_Oord__class_OatMost(U_12093),U_12095) ) )
      | ~ class_Orderings_Olinorder(U_12093) ),
    inference(variable_rename,[status(thm)],[f_3220_1]) ).

fof(f_3220_3,plain,
    ( ! [U_12093,U_12094,U_12095] :
        ( hAPP(c_SetInterval_Oord__class_OatMost(U_12093),U_12094) = hAPP(c_SetInterval_Oord__class_OatMost(U_12093),U_12095)
        | U_12094 != U_12095
        | ~ sP880(U_12093,U_12094,U_12095) )
    & ! [U_12093,U_12094,U_12095] :
        ( U_12094 = U_12095
        | hAPP(c_SetInterval_Oord__class_OatMost(U_12093),U_12094) != hAPP(c_SetInterval_Oord__class_OatMost(U_12093),U_12095)
        | ~ sP880(U_12093,U_12094,U_12095) )
    & ! [U_12093,U_12094,U_12095] :
        ( sP880(U_12093,U_12094,U_12095)
        | ~ class_Orderings_Olinorder(U_12093) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP880])],[f_3220_2]) ).

cnf(f_3220_4,plain,
    ( sP880(U_12093,U_12094,U_12095)
    | ~ class_Orderings_Olinorder(U_12093) ),
    inference(clausify,[status(thm)],[f_3220_3]) ).

cnf(f_3220_5,plain,
    ( U_12094 = U_12095
    | hAPP(c_SetInterval_Oord__class_OatMost(U_12093),U_12094) != hAPP(c_SetInterval_Oord__class_OatMost(U_12093),U_12095)
    | ~ sP880(U_12093,U_12094,U_12095) ),
    inference(clausify,[status(thm)],[f_3220_3]) ).

cnf(f_3220_6,plain,
    ( hAPP(c_SetInterval_Oord__class_OatMost(U_12093),U_12094) = hAPP(c_SetInterval_Oord__class_OatMost(U_12093),U_12095)
    | U_12094 != U_12095
    | ~ sP880(U_12093,U_12094,U_12095) ),
    inference(clausify,[status(thm)],[f_3220_3]) ).

fof(f_3221_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_3221_2,plain,
    ! [U_12096] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_12096) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12096),
    inference(variable_rename,[status(thm)],[f_3221_1]) ).

fof(f_3221_3,plain,
    ! [U_12096] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_12096) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12096),
    inference(definitional_conversion,[status(esa)],[f_3221_2]) ).

cnf(f_3221_4,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_12096) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12096),
    inference(clausify,[status(thm)],[f_3221_3]) ).

fof(f_3222_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_3222_2,plain,
    ! [U_12097] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12097)) = hAPP(c_Nat_OSuc,U_12097),
    inference(variable_rename,[status(thm)],[f_3222_1]) ).

fof(f_3222_3,plain,
    ! [U_12097] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12097)) = hAPP(c_Nat_OSuc,U_12097),
    inference(definitional_conversion,[status(esa)],[f_3222_2]) ).

cnf(f_3222_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12097)) = hAPP(c_Nat_OSuc,U_12097),
    inference(clausify,[status(thm)],[f_3222_3]) ).

fof(f_3223_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_3223_2,plain,
    ! [U_12098] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12098)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12098)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12098)),
    inference(variable_rename,[status(thm)],[f_3223_1]) ).

fof(f_3223_3,plain,
    ! [U_12098] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12098)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12098)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12098)),
    inference(definitional_conversion,[status(esa)],[f_3223_2]) ).

cnf(f_3223_4,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12098)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12098)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12098)),
    inference(clausify,[status(thm)],[f_3223_3]) ).

fof(f_3224_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_3224_2,plain,
    ! [U_12101,U_12100,U_12099] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_12099),U_12100),hAPP(c_SetInterval_Oord__class_OatMost(U_12099),U_12101)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12099),U_12100),U_12101)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12099),U_12100),U_12101))
          | ~ hBOOL(hAPP(hAPP(c_member(U_12099),U_12100),hAPP(c_SetInterval_Oord__class_OatMost(U_12099),U_12101))) ) )
      | ~ class_Orderings_Oord(U_12099) ),
    inference(variable_rename,[status(thm)],[f_3224_1]) ).

fof(f_3224_3,plain,
    ( ! [U_12099,U_12100,U_12101] :
        ( hBOOL(hAPP(hAPP(c_member(U_12099),U_12100),hAPP(c_SetInterval_Oord__class_OatMost(U_12099),U_12101)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12099),U_12100),U_12101))
        | ~ sP881(U_12099,U_12100,U_12101) )
    & ! [U_12099,U_12100,U_12101] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12099),U_12100),U_12101))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12099),U_12100),hAPP(c_SetInterval_Oord__class_OatMost(U_12099),U_12101)))
        | ~ sP881(U_12099,U_12100,U_12101) )
    & ! [U_12099,U_12100,U_12101] :
        ( sP881(U_12099,U_12100,U_12101)
        | ~ class_Orderings_Oord(U_12099) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP881])],[f_3224_2]) ).

cnf(f_3224_4,plain,
    ( sP881(U_12099,U_12100,U_12101)
    | ~ class_Orderings_Oord(U_12099) ),
    inference(clausify,[status(thm)],[f_3224_3]) ).

cnf(f_3224_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12099),U_12100),U_12101))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12099),U_12100),hAPP(c_SetInterval_Oord__class_OatMost(U_12099),U_12101)))
    | ~ sP881(U_12099,U_12100,U_12101) ),
    inference(clausify,[status(thm)],[f_3224_3]) ).

cnf(f_3224_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12099),U_12100),hAPP(c_SetInterval_Oord__class_OatMost(U_12099),U_12101)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12099),U_12100),U_12101))
    | ~ sP881(U_12099,U_12100,U_12101) ),
    inference(clausify,[status(thm)],[f_3224_3]) ).

fof(f_3225_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_3225_2,plain,
    ! [U_12104,U_12103,U_12102] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12102,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12102),U_12103)),hAPP(c_SetInterval_Oord__class_OatMost(U_12102),U_12104)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12102),U_12103),U_12104)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12102),U_12103),U_12104))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12102,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12102),U_12103)),hAPP(c_SetInterval_Oord__class_OatMost(U_12102),U_12104))) ) )
      | ~ class_Orderings_Oorder(U_12102) ),
    inference(variable_rename,[status(thm)],[f_3225_1]) ).

fof(f_3225_3,plain,
    ( ! [U_12103,U_12104,U_12102] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12102,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12102),U_12103)),hAPP(c_SetInterval_Oord__class_OatMost(U_12102),U_12104)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12102),U_12103),U_12104))
        | ~ sP882(U_12103,U_12104,U_12102) )
    & ! [U_12103,U_12104,U_12102] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12102),U_12103),U_12104))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12102,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12102),U_12103)),hAPP(c_SetInterval_Oord__class_OatMost(U_12102),U_12104)))
        | ~ sP882(U_12103,U_12104,U_12102) )
    & ! [U_12103,U_12104,U_12102] :
        ( sP882(U_12103,U_12104,U_12102)
        | ~ class_Orderings_Oorder(U_12102) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP882])],[f_3225_2]) ).

cnf(f_3225_4,plain,
    ( sP882(U_12103,U_12104,U_12102)
    | ~ class_Orderings_Oorder(U_12102) ),
    inference(clausify,[status(thm)],[f_3225_3]) ).

cnf(f_3225_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12102),U_12103),U_12104))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12102,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12102),U_12103)),hAPP(c_SetInterval_Oord__class_OatMost(U_12102),U_12104)))
    | ~ sP882(U_12103,U_12104,U_12102) ),
    inference(clausify,[status(thm)],[f_3225_3]) ).

cnf(f_3225_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12102,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12102),U_12103)),hAPP(c_SetInterval_Oord__class_OatMost(U_12102),U_12104)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12102),U_12103),U_12104))
    | ~ sP882(U_12103,U_12104,U_12102) ),
    inference(clausify,[status(thm)],[f_3225_3]) ).

fof(f_3226_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_3226_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_3226_1]) ).

cnf(f_3226_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_3226_2]) ).

fof(f_3227_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_3227_2,plain,
    ! [U_12108,U_12107,U_12106,U_12105] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12105,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12105),U_12106)),c_SetInterval_Oord__class_OatLeastAtMost(U_12105,U_12107,U_12108)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12105,U_12107,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12105),U_12106),U_12108))
      | ~ class_Orderings_Olinorder(U_12105) ),
    inference(variable_rename,[status(thm)],[f_3227_1]) ).

fof(f_3227_3,plain,
    ! [U_12105,U_12106,U_12107,U_12108] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12105,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12105),U_12106)),c_SetInterval_Oord__class_OatLeastAtMost(U_12105,U_12107,U_12108)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12105,U_12107,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12105),U_12106),U_12108))
      | ~ class_Orderings_Olinorder(U_12105) ),
    inference(definitional_conversion,[status(esa)],[f_3227_2]) ).

cnf(f_3227_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12105,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12105),U_12106)),c_SetInterval_Oord__class_OatLeastAtMost(U_12105,U_12107,U_12108)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12105,U_12107,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12105),U_12106),U_12108))
    | ~ class_Orderings_Olinorder(U_12105) ),
    inference(clausify,[status(thm)],[f_3227_3]) ).

fof(f_3228_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_3228_2,plain,
    ! [U_12112,U_12111,U_12110,U_12109] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12109,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12109,U_12110,U_12111)),hAPP(c_SetInterval_Oord__class_OatMost(U_12109),U_12112)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12109,U_12110,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12109),U_12111),U_12112))
      | ~ class_Orderings_Olinorder(U_12109) ),
    inference(variable_rename,[status(thm)],[f_3228_1]) ).

fof(f_3228_3,plain,
    ! [U_12109,U_12110,U_12111,U_12112] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12109,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12109,U_12110,U_12111)),hAPP(c_SetInterval_Oord__class_OatMost(U_12109),U_12112)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12109,U_12110,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12109),U_12111),U_12112))
      | ~ class_Orderings_Olinorder(U_12109) ),
    inference(definitional_conversion,[status(esa)],[f_3228_2]) ).

cnf(f_3228_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12109,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12109,U_12110,U_12111)),hAPP(c_SetInterval_Oord__class_OatMost(U_12109),U_12112)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12109,U_12110,hAPP(hAPP(c_Orderings_Oord__class_Omin(U_12109),U_12111),U_12112))
    | ~ class_Orderings_Olinorder(U_12109) ),
    inference(clausify,[status(thm)],[f_3228_3]) ).

fof(f_3229_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_3229_2,plain,
    ! [U_12115,U_12114,U_12113] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12113,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12113),U_12114)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12113,U_12114,U_12115)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12113),U_12115)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12113),U_12114),U_12115))
      | ~ class_Orderings_Olinorder(U_12113) ),
    inference(variable_rename,[status(thm)],[f_3229_1]) ).

fof(f_3229_3,plain,
    ! [U_12113,U_12114,U_12115] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12113,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12113),U_12114)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12113,U_12114,U_12115)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12113),U_12115)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12113),U_12114),U_12115))
      | ~ class_Orderings_Olinorder(U_12113) ),
    inference(definitional_conversion,[status(esa)],[f_3229_2]) ).

cnf(f_3229_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12113,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12113),U_12114)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12113,U_12114,U_12115)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12113),U_12115)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12113),U_12114),U_12115))
    | ~ class_Orderings_Olinorder(U_12113) ),
    inference(clausify,[status(thm)],[f_3229_3]) ).

fof(f_3230_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_3230_2,plain,
    ! [U_12118,U_12117,U_12116] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12116,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12116),U_12117)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12116,U_12117,U_12118)) = c_Orderings_Obot__class_Obot(tc_fun(U_12116,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12116) ),
    inference(variable_rename,[status(thm)],[f_3230_1]) ).

fof(f_3230_3,plain,
    ! [U_12116,U_12117,U_12118] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12116,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12116),U_12117)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12116,U_12117,U_12118)) = c_Orderings_Obot__class_Obot(tc_fun(U_12116,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12116) ),
    inference(definitional_conversion,[status(esa)],[f_3230_2]) ).

cnf(f_3230_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12116,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12116),U_12117)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12116,U_12117,U_12118)) = c_Orderings_Obot__class_Obot(tc_fun(U_12116,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12116) ),
    inference(clausify,[status(thm)],[f_3230_3]) ).

fof(f_3231_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_3231_2,plain,
    ! [U_12121,U_12120,U_12119] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12119,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12119),U_12120)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12119,U_12120,U_12121)) = c_Orderings_Obot__class_Obot(tc_fun(U_12119,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12119) ),
    inference(variable_rename,[status(thm)],[f_3231_1]) ).

fof(f_3231_3,plain,
    ! [U_12119,U_12120,U_12121] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12119,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12119),U_12120)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12119,U_12120,U_12121)) = c_Orderings_Obot__class_Obot(tc_fun(U_12119,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12119) ),
    inference(definitional_conversion,[status(esa)],[f_3231_2]) ).

cnf(f_3231_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12119,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12119),U_12120)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12119,U_12120,U_12121)) = c_Orderings_Obot__class_Obot(tc_fun(U_12119,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12119) ),
    inference(clausify,[status(thm)],[f_3231_3]) ).

fof(f_3232_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_3232_2,plain,
    ! [U_12122] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12122) = 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_12122)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12122)) ),
    inference(variable_rename,[status(thm)],[f_3232_1]) ).

fof(f_3232_3,plain,
    ! [U_12122] :
      ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12122) = 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_12122)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12122)) ),
    inference(definitional_conversion,[status(esa)],[f_3232_2]) ).

cnf(f_3232_4,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12122) = 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_12122)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12122)) ),
    inference(clausify,[status(thm)],[f_3232_3]) ).

fof(f_3233_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_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_3233_2,plain,
    ! [U_12125,U_12124,U_12123] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12123,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12123),U_12124)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12123,U_12124,U_12125)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12123),U_12125)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12123),U_12124),U_12125))
      | ~ class_Orderings_Olinorder(U_12123) ),
    inference(variable_rename,[status(thm)],[f_3233_1]) ).

fof(f_3233_3,plain,
    ! [U_12123,U_12124,U_12125] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12123,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12123),U_12124)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12123,U_12124,U_12125)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12123),U_12125)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12123),U_12124),U_12125))
      | ~ class_Orderings_Olinorder(U_12123) ),
    inference(definitional_conversion,[status(esa)],[f_3233_2]) ).

cnf(f_3233_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12123,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12123),U_12124)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12123,U_12124,U_12125)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12123),U_12125)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12123),U_12124),U_12125))
    | ~ class_Orderings_Olinorder(U_12123) ),
    inference(clausify,[status(thm)],[f_3233_3]) ).

fof(f_3234_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_3234_2,plain,
    ! [U_12130,U_12129,U_12128,U_12127,U_12126] :
      ( hAPP(U_12128,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12126,tc_HOL_Obool)),U_12129),U_12130)) = hAPP(hAPP(U_12127,hAPP(U_12128,U_12129)),hAPP(U_12128,U_12130))
      | U_12130 = c_Orderings_Obot__class_Obot(tc_fun(U_12126,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12126),U_12130))
      | U_12129 = c_Orderings_Obot__class_Obot(tc_fun(U_12126,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12126),U_12129))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12126,U_12127,U_12128) ),
    inference(variable_rename,[status(thm)],[f_3234_1]) ).

fof(f_3234_3,plain,
    ! [U_12126,U_12127,U_12128,U_12129,U_12130] :
      ( hAPP(U_12128,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12126,tc_HOL_Obool)),U_12129),U_12130)) = hAPP(hAPP(U_12127,hAPP(U_12128,U_12129)),hAPP(U_12128,U_12130))
      | U_12130 = c_Orderings_Obot__class_Obot(tc_fun(U_12126,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12126),U_12130))
      | U_12129 = c_Orderings_Obot__class_Obot(tc_fun(U_12126,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12126),U_12129))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12126,U_12127,U_12128) ),
    inference(definitional_conversion,[status(esa)],[f_3234_2]) ).

cnf(f_3234_4,plain,
    ( hAPP(U_12128,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12126,tc_HOL_Obool)),U_12129),U_12130)) = hAPP(hAPP(U_12127,hAPP(U_12128,U_12129)),hAPP(U_12128,U_12130))
    | U_12130 = c_Orderings_Obot__class_Obot(tc_fun(U_12126,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12126),U_12130))
    | U_12129 = c_Orderings_Obot__class_Obot(tc_fun(U_12126,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12126),U_12129))
    | ~ c_Finite__Set_Ofolding__one__idem(U_12126,U_12127,U_12128) ),
    inference(clausify,[status(thm)],[f_3234_3]) ).

fof(f_3235_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_3235_2,plain,
    ! [U_12131] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12131))),
    inference(variable_rename,[status(thm)],[f_3235_1]) ).

fof(f_3235_3,plain,
    ! [U_12131] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12131))),
    inference(definitional_conversion,[status(esa)],[f_3235_2]) ).

cnf(f_3235_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12131))),
    inference(clausify,[status(thm)],[f_3235_3]) ).

fof(f_3236_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_3236_2,plain,
    ! [U_12134,U_12133,U_12132] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OlessThan(U_12132),U_12133) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12132),U_12134)
          | U_12133 != U_12134 )
        & ( U_12133 = U_12134
          | hAPP(c_SetInterval_Oord__class_OlessThan(U_12132),U_12133) != hAPP(c_SetInterval_Oord__class_OlessThan(U_12132),U_12134) ) )
      | ~ class_Orderings_Olinorder(U_12132) ),
    inference(variable_rename,[status(thm)],[f_3236_1]) ).

fof(f_3236_3,plain,
    ( ! [U_12132,U_12134,U_12133] :
        ( hAPP(c_SetInterval_Oord__class_OlessThan(U_12132),U_12133) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12132),U_12134)
        | U_12133 != U_12134
        | ~ sP883(U_12132,U_12134,U_12133) )
    & ! [U_12132,U_12134,U_12133] :
        ( U_12133 = U_12134
        | hAPP(c_SetInterval_Oord__class_OlessThan(U_12132),U_12133) != hAPP(c_SetInterval_Oord__class_OlessThan(U_12132),U_12134)
        | ~ sP883(U_12132,U_12134,U_12133) )
    & ! [U_12132,U_12134,U_12133] :
        ( sP883(U_12132,U_12134,U_12133)
        | ~ class_Orderings_Olinorder(U_12132) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP883])],[f_3236_2]) ).

cnf(f_3236_4,plain,
    ( sP883(U_12132,U_12134,U_12133)
    | ~ class_Orderings_Olinorder(U_12132) ),
    inference(clausify,[status(thm)],[f_3236_3]) ).

cnf(f_3236_5,plain,
    ( U_12133 = U_12134
    | hAPP(c_SetInterval_Oord__class_OlessThan(U_12132),U_12133) != hAPP(c_SetInterval_Oord__class_OlessThan(U_12132),U_12134)
    | ~ sP883(U_12132,U_12134,U_12133) ),
    inference(clausify,[status(thm)],[f_3236_3]) ).

cnf(f_3236_6,plain,
    ( hAPP(c_SetInterval_Oord__class_OlessThan(U_12132),U_12133) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12132),U_12134)
    | U_12133 != U_12134
    | ~ sP883(U_12132,U_12134,U_12133) ),
    inference(clausify,[status(thm)],[f_3236_3]) ).

fof(f_3237_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_3237_2,plain,
    ! [U_12138,U_12137,U_12136,U_12135] :
      ( hAPP(hAPP(U_12136,U_12138),U_12138) = U_12138
      | ~ c_Finite__Set_Ofolding__one__idem(U_12135,U_12136,U_12137) ),
    inference(variable_rename,[status(thm)],[f_3237_1]) ).

fof(f_3237_3,plain,
    ! [U_12138,U_12137,U_12136] :
      ( ! [U_12135] : ~ c_Finite__Set_Ofolding__one__idem(U_12135,U_12136,U_12137)
      | hAPP(hAPP(U_12136,U_12138),U_12138) = U_12138 ),
    inference(miniscope,[status(thm)],[f_3237_2]) ).

fof(f_3237_4,plain,
    ! [U_12137,U_12138,U_12136,U_12135] :
      ( ~ c_Finite__Set_Ofolding__one__idem(U_12135,U_12136,U_12137)
      | hAPP(hAPP(U_12136,U_12138),U_12138) = U_12138 ),
    inference(definitional_conversion,[status(esa)],[f_3237_3]) ).

cnf(f_3237_5,plain,
    ( ~ c_Finite__Set_Ofolding__one__idem(U_12135,U_12136,U_12137)
    | hAPP(hAPP(U_12136,U_12138),U_12138) = U_12138 ),
    inference(clausify,[status(thm)],[f_3237_4]) ).

fof(f_3238_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_3238_2,plain,
    ! [U_12139] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12139)) = U_12139,
    inference(variable_rename,[status(thm)],[f_3238_1]) ).

fof(f_3238_3,plain,
    ! [U_12139] : hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12139)) = U_12139,
    inference(definitional_conversion,[status(esa)],[f_3238_2]) ).

cnf(f_3238_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12139)) = U_12139,
    inference(clausify,[status(thm)],[f_3238_3]) ).

fof(f_3239_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_3239_2,plain,
    ! [U_12140] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12140) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12140),
    inference(variable_rename,[status(thm)],[f_3239_1]) ).

fof(f_3239_3,plain,
    ! [U_12140] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12140) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12140),
    inference(definitional_conversion,[status(esa)],[f_3239_2]) ).

cnf(f_3239_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12140) = hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12140),
    inference(clausify,[status(thm)],[f_3239_3]) ).

fof(f_3240_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_3240_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_3240_1]) ).

cnf(f_3240_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_3240_2]) ).

fof(f_3241_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_3241_2,plain,
    ! [U_12141] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12141)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12141),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12141)),
    inference(variable_rename,[status(thm)],[f_3241_1]) ).

fof(f_3241_3,plain,
    ! [U_12141] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12141)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12141),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12141)),
    inference(definitional_conversion,[status(esa)],[f_3241_2]) ).

cnf(f_3241_4,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12141)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12141),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12141)),
    inference(clausify,[status(thm)],[f_3241_3]) ).

fof(f_3242_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_3242_2,plain,
    ! [U_12142] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12142)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12142),
    inference(variable_rename,[status(thm)],[f_3242_1]) ).

fof(f_3242_3,plain,
    ! [U_12142] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12142)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12142),
    inference(definitional_conversion,[status(esa)],[f_3242_2]) ).

cnf(f_3242_4,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12142)) = hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12142),
    inference(clausify,[status(thm)],[f_3242_3]) ).

fof(f_3243_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_3243_2,plain,
    ! [U_12145,U_12144,U_12143] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_12143),U_12144),hAPP(c_SetInterval_Oord__class_OlessThan(U_12143),U_12145)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12143),U_12144),U_12145)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12143),U_12144),U_12145))
          | ~ hBOOL(hAPP(hAPP(c_member(U_12143),U_12144),hAPP(c_SetInterval_Oord__class_OlessThan(U_12143),U_12145))) ) )
      | ~ class_Orderings_Oord(U_12143) ),
    inference(variable_rename,[status(thm)],[f_3243_1]) ).

fof(f_3243_3,plain,
    ( ! [U_12143,U_12144,U_12145] :
        ( hBOOL(hAPP(hAPP(c_member(U_12143),U_12144),hAPP(c_SetInterval_Oord__class_OlessThan(U_12143),U_12145)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12143),U_12144),U_12145))
        | ~ sP884(U_12143,U_12144,U_12145) )
    & ! [U_12143,U_12144,U_12145] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12143),U_12144),U_12145))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12143),U_12144),hAPP(c_SetInterval_Oord__class_OlessThan(U_12143),U_12145)))
        | ~ sP884(U_12143,U_12144,U_12145) )
    & ! [U_12143,U_12144,U_12145] :
        ( sP884(U_12143,U_12144,U_12145)
        | ~ class_Orderings_Oord(U_12143) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP884])],[f_3243_2]) ).

cnf(f_3243_4,plain,
    ( sP884(U_12143,U_12144,U_12145)
    | ~ class_Orderings_Oord(U_12143) ),
    inference(clausify,[status(thm)],[f_3243_3]) ).

cnf(f_3243_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12143),U_12144),U_12145))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12143),U_12144),hAPP(c_SetInterval_Oord__class_OlessThan(U_12143),U_12145)))
    | ~ sP884(U_12143,U_12144,U_12145) ),
    inference(clausify,[status(thm)],[f_3243_3]) ).

cnf(f_3243_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12143),U_12144),hAPP(c_SetInterval_Oord__class_OlessThan(U_12143),U_12145)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12143),U_12144),U_12145))
    | ~ sP884(U_12143,U_12144,U_12145) ),
    inference(clausify,[status(thm)],[f_3243_3]) ).

fof(f_3244_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_3244_2,plain,
    ! [U_12148,U_12147,U_12146] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12146,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12146),U_12147)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12146),U_12148)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12146),U_12147),U_12148)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12146),U_12147),U_12148))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12146,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12146),U_12147)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12146),U_12148))) ) )
      | ~ class_Orderings_Olinorder(U_12146) ),
    inference(variable_rename,[status(thm)],[f_3244_1]) ).

fof(f_3244_3,plain,
    ( ! [U_12147,U_12148,U_12146] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12146,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12146),U_12147)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12146),U_12148)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12146),U_12147),U_12148))
        | ~ sP885(U_12147,U_12148,U_12146) )
    & ! [U_12147,U_12148,U_12146] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12146),U_12147),U_12148))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12146,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12146),U_12147)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12146),U_12148)))
        | ~ sP885(U_12147,U_12148,U_12146) )
    & ! [U_12147,U_12148,U_12146] :
        ( sP885(U_12147,U_12148,U_12146)
        | ~ class_Orderings_Olinorder(U_12146) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP885])],[f_3244_2]) ).

cnf(f_3244_4,plain,
    ( sP885(U_12147,U_12148,U_12146)
    | ~ class_Orderings_Olinorder(U_12146) ),
    inference(clausify,[status(thm)],[f_3244_3]) ).

cnf(f_3244_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12146),U_12147),U_12148))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12146,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12146),U_12147)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12146),U_12148)))
    | ~ sP885(U_12147,U_12148,U_12146) ),
    inference(clausify,[status(thm)],[f_3244_3]) ).

cnf(f_3244_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12146,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12146),U_12147)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12146),U_12148)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12146),U_12147),U_12148))
    | ~ sP885(U_12147,U_12148,U_12146) ),
    inference(clausify,[status(thm)],[f_3244_3]) ).

fof(f_3245_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_3245_2,plain,
    ! [U_12151,U_12150,U_12149] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_12149,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12149),U_12150)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12149),U_12151)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12149),U_12150),U_12151)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12149),U_12150),U_12151))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_12149,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12149),U_12150)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12149),U_12151))) ) )
      | ~ class_Orderings_Olinorder(U_12149) ),
    inference(variable_rename,[status(thm)],[f_3245_1]) ).

fof(f_3245_3,plain,
    ( ! [U_12150,U_12151,U_12149] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_12149,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12149),U_12150)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12149),U_12151)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12149),U_12150),U_12151))
        | ~ sP886(U_12150,U_12151,U_12149) )
    & ! [U_12150,U_12151,U_12149] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12149),U_12150),U_12151))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_12149,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12149),U_12150)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12149),U_12151)))
        | ~ sP886(U_12150,U_12151,U_12149) )
    & ! [U_12150,U_12151,U_12149] :
        ( sP886(U_12150,U_12151,U_12149)
        | ~ class_Orderings_Olinorder(U_12149) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP886])],[f_3245_2]) ).

cnf(f_3245_4,plain,
    ( sP886(U_12150,U_12151,U_12149)
    | ~ class_Orderings_Olinorder(U_12149) ),
    inference(clausify,[status(thm)],[f_3245_3]) ).

cnf(f_3245_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12149),U_12150),U_12151))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_12149,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12149),U_12150)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12149),U_12151)))
    | ~ sP886(U_12150,U_12151,U_12149) ),
    inference(clausify,[status(thm)],[f_3245_3]) ).

cnf(f_3245_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_12149,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12149),U_12150)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12149),U_12151)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12149),U_12150),U_12151))
    | ~ sP886(U_12150,U_12151,U_12149) ),
    inference(clausify,[status(thm)],[f_3245_3]) ).

fof(f_3246_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_3246_2,plain,
    ! [U_12156,U_12155,U_12154,U_12153,U_12152] :
      ( hAPP(hAPP(U_12153,U_12156),hAPP(U_12154,U_12155)) = hAPP(U_12154,U_12155)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12152),U_12156),U_12155))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12152),U_12155))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12152,U_12153,U_12154) ),
    inference(variable_rename,[status(thm)],[f_3246_1]) ).

fof(f_3246_3,plain,
    ! [U_12155,U_12152,U_12153,U_12154,U_12156] :
      ( hAPP(hAPP(U_12153,U_12156),hAPP(U_12154,U_12155)) = hAPP(U_12154,U_12155)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12152),U_12156),U_12155))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12152),U_12155))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12152,U_12153,U_12154) ),
    inference(definitional_conversion,[status(esa)],[f_3246_2]) ).

cnf(f_3246_4,plain,
    ( hAPP(hAPP(U_12153,U_12156),hAPP(U_12154,U_12155)) = hAPP(U_12154,U_12155)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12152),U_12156),U_12155))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12152),U_12155))
    | ~ c_Finite__Set_Ofolding__one__idem(U_12152,U_12153,U_12154) ),
    inference(clausify,[status(thm)],[f_3246_3]) ).

fof(f_3247_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_3247_2,plain,
    ! [U_12158,U_12157] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12157,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12157),U_12158),c_Orderings_Obot__class_Obot(tc_fun(U_12157,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_12157),U_12158)) = hAPP(hAPP(c_Set_Oinsert(U_12157),U_12158),c_Orderings_Obot__class_Obot(tc_fun(U_12157,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_12157) ),
    inference(variable_rename,[status(thm)],[f_3247_1]) ).

fof(f_3247_3,plain,
    ! [U_12158,U_12157] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12157,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12157),U_12158),c_Orderings_Obot__class_Obot(tc_fun(U_12157,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_12157),U_12158)) = hAPP(hAPP(c_Set_Oinsert(U_12157),U_12158),c_Orderings_Obot__class_Obot(tc_fun(U_12157,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_12157) ),
    inference(definitional_conversion,[status(esa)],[f_3247_2]) ).

cnf(f_3247_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12157,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12157),U_12158),c_Orderings_Obot__class_Obot(tc_fun(U_12157,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OlessThan(U_12157),U_12158)) = hAPP(hAPP(c_Set_Oinsert(U_12157),U_12158),c_Orderings_Obot__class_Obot(tc_fun(U_12157,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_12157) ),
    inference(clausify,[status(thm)],[f_3247_3]) ).

fof(f_3248_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_3248_2,plain,
    ! [U_12161,U_12160,U_12159] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12159,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12159),U_12160)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12159,U_12160),U_12161)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12159),U_12161)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12159),U_12160),U_12161))
      | ~ class_Orderings_Olinorder(U_12159) ),
    inference(variable_rename,[status(thm)],[f_3248_1]) ).

fof(f_3248_3,plain,
    ! [U_12159,U_12160,U_12161] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12159,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12159),U_12160)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12159,U_12160),U_12161)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12159),U_12161)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12159),U_12160),U_12161))
      | ~ class_Orderings_Olinorder(U_12159) ),
    inference(definitional_conversion,[status(esa)],[f_3248_2]) ).

cnf(f_3248_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12159,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12159),U_12160)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12159,U_12160),U_12161)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12159),U_12161)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12159),U_12160),U_12161))
    | ~ class_Orderings_Olinorder(U_12159) ),
    inference(clausify,[status(thm)],[f_3248_3]) ).

fof(f_3249_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_3249_2,plain,
    ! [U_12164,U_12163,U_12162] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12162,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12162),U_12163)),c_SetInterval_Oord__class_OatLeastAtMost(U_12162,U_12163,U_12164)) = c_Orderings_Obot__class_Obot(tc_fun(U_12162,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12162) ),
    inference(variable_rename,[status(thm)],[f_3249_1]) ).

fof(f_3249_3,plain,
    ! [U_12162,U_12163,U_12164] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12162,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12162),U_12163)),c_SetInterval_Oord__class_OatLeastAtMost(U_12162,U_12163,U_12164)) = c_Orderings_Obot__class_Obot(tc_fun(U_12162,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12162) ),
    inference(definitional_conversion,[status(esa)],[f_3249_2]) ).

cnf(f_3249_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12162,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12162),U_12163)),c_SetInterval_Oord__class_OatLeastAtMost(U_12162,U_12163,U_12164)) = c_Orderings_Obot__class_Obot(tc_fun(U_12162,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12162) ),
    inference(clausify,[status(thm)],[f_3249_3]) ).

fof(f_3250_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),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_3250_2,plain,
    ! [U_12167,U_12166,U_12165] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12165,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12165),U_12166)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12165,U_12166),U_12167)) = c_Orderings_Obot__class_Obot(tc_fun(U_12165,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12165) ),
    inference(variable_rename,[status(thm)],[f_3250_1]) ).

fof(f_3250_3,plain,
    ! [U_12165,U_12166,U_12167] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12165,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12165),U_12166)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12165,U_12166),U_12167)) = c_Orderings_Obot__class_Obot(tc_fun(U_12165,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12165) ),
    inference(definitional_conversion,[status(esa)],[f_3250_2]) ).

cnf(f_3250_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12165,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12165),U_12166)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12165,U_12166),U_12167)) = c_Orderings_Obot__class_Obot(tc_fun(U_12165,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12165) ),
    inference(clausify,[status(thm)],[f_3250_3]) ).

fof(f_3251_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_3251_2,plain,
    ! [U_12168] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12168)) = 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_12168))),
    inference(variable_rename,[status(thm)],[f_3251_1]) ).

fof(f_3251_3,plain,
    ! [U_12168] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12168)) = 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_12168))),
    inference(definitional_conversion,[status(esa)],[f_3251_2]) ).

cnf(f_3251_4,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12168)) = 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_12168))),
    inference(clausify,[status(thm)],[f_3251_3]) ).

fof(f_3252_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_3252_2,plain,
    ! [U_12170,U_12169] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12169,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12169),U_12170)),hAPP(hAPP(c_Set_Oinsert(U_12169),U_12170),c_Orderings_Obot__class_Obot(tc_fun(U_12169,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_12169),U_12170)
      | ~ class_Orderings_Olinorder(U_12169) ),
    inference(variable_rename,[status(thm)],[f_3252_1]) ).

fof(f_3252_3,plain,
    ! [U_12169,U_12170] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12169,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12169),U_12170)),hAPP(hAPP(c_Set_Oinsert(U_12169),U_12170),c_Orderings_Obot__class_Obot(tc_fun(U_12169,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_12169),U_12170)
      | ~ class_Orderings_Olinorder(U_12169) ),
    inference(definitional_conversion,[status(esa)],[f_3252_2]) ).

cnf(f_3252_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12169,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12169),U_12170)),hAPP(hAPP(c_Set_Oinsert(U_12169),U_12170),c_Orderings_Obot__class_Obot(tc_fun(U_12169,tc_HOL_Obool)))) = hAPP(c_SetInterval_Oord__class_OatMost(U_12169),U_12170)
    | ~ class_Orderings_Olinorder(U_12169) ),
    inference(clausify,[status(thm)],[f_3252_3]) ).

fof(f_3253_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_3253_2,plain,
    ! [U_12175,U_12174,U_12173,U_12172,U_12171] :
      ( hAPP(U_12173,hAPP(hAPP(c_Set_Oinsert(U_12171),U_12175),U_12174)) = hAPP(hAPP(U_12172,U_12175),hAPP(U_12173,U_12174))
      | U_12174 = c_Orderings_Obot__class_Obot(tc_fun(U_12171,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12171),U_12174))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12171,U_12172,U_12173) ),
    inference(variable_rename,[status(thm)],[f_3253_1]) ).

fof(f_3253_3,plain,
    ! [U_12171,U_12172,U_12173,U_12174,U_12175] :
      ( hAPP(U_12173,hAPP(hAPP(c_Set_Oinsert(U_12171),U_12175),U_12174)) = hAPP(hAPP(U_12172,U_12175),hAPP(U_12173,U_12174))
      | U_12174 = c_Orderings_Obot__class_Obot(tc_fun(U_12171,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12171),U_12174))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12171,U_12172,U_12173) ),
    inference(definitional_conversion,[status(esa)],[f_3253_2]) ).

cnf(f_3253_4,plain,
    ( hAPP(U_12173,hAPP(hAPP(c_Set_Oinsert(U_12171),U_12175),U_12174)) = hAPP(hAPP(U_12172,U_12175),hAPP(U_12173,U_12174))
    | U_12174 = c_Orderings_Obot__class_Obot(tc_fun(U_12171,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12171),U_12174))
    | ~ c_Finite__Set_Ofolding__one__idem(U_12171,U_12172,U_12173) ),
    inference(clausify,[status(thm)],[f_3253_3]) ).

fof(f_3254_1,plain,
    ! [V_u_2,V_l_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__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_3254_2,plain,
    ! [U_12178,U_12177,U_12176] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12176,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12176),U_12177)),c_SetInterval_Oord__class_OatLeastAtMost(U_12176,U_12177,U_12178)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12176),U_12178)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12176),U_12177),U_12178))
      | ~ class_Orderings_Olinorder(U_12176) ),
    inference(variable_rename,[status(thm)],[f_3254_1]) ).

fof(f_3254_3,plain,
    ! [U_12176,U_12177,U_12178] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12176,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12176),U_12177)),c_SetInterval_Oord__class_OatLeastAtMost(U_12176,U_12177,U_12178)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12176),U_12178)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12176),U_12177),U_12178))
      | ~ class_Orderings_Olinorder(U_12176) ),
    inference(definitional_conversion,[status(esa)],[f_3254_2]) ).

cnf(f_3254_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12176,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12176),U_12177)),c_SetInterval_Oord__class_OatLeastAtMost(U_12176,U_12177,U_12178)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12176),U_12178)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12176),U_12177),U_12178))
    | ~ class_Orderings_Olinorder(U_12176) ),
    inference(clausify,[status(thm)],[f_3254_3]) ).

fof(f_3255_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_3255_2,plain,
    ! [U_12183,U_12182,U_12181,U_12180,U_12179] :
      ( hAPP(hAPP(U_12180,hAPP(U_12181,U_12183)),hAPP(U_12181,U_12182)) = hAPP(U_12181,U_12182)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12179,tc_HOL_Obool)),U_12183),U_12182))
      | U_12183 = c_Orderings_Obot__class_Obot(tc_fun(U_12179,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12179),U_12182))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12179,U_12180,U_12181) ),
    inference(variable_rename,[status(thm)],[f_3255_1]) ).

fof(f_3255_3,plain,
    ! [U_12179,U_12180,U_12181,U_12182,U_12183] :
      ( hAPP(hAPP(U_12180,hAPP(U_12181,U_12183)),hAPP(U_12181,U_12182)) = hAPP(U_12181,U_12182)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12179,tc_HOL_Obool)),U_12183),U_12182))
      | U_12183 = c_Orderings_Obot__class_Obot(tc_fun(U_12179,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12179),U_12182))
      | ~ c_Finite__Set_Ofolding__one__idem(U_12179,U_12180,U_12181) ),
    inference(definitional_conversion,[status(esa)],[f_3255_2]) ).

cnf(f_3255_4,plain,
    ( hAPP(hAPP(U_12180,hAPP(U_12181,U_12183)),hAPP(U_12181,U_12182)) = hAPP(U_12181,U_12182)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12179,tc_HOL_Obool)),U_12183),U_12182))
    | U_12183 = c_Orderings_Obot__class_Obot(tc_fun(U_12179,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12179),U_12182))
    | ~ c_Finite__Set_Ofolding__one__idem(U_12179,U_12180,U_12181) ),
    inference(clausify,[status(thm)],[f_3255_3]) ).

fof(f_3256_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_3256_2,plain,
    ! [U_12186,U_12185,U_12184] : hAPP(hAPP(c_Groups_Otimes__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_12184)),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_12185))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12186))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_12186)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12184),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12184),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_12186),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_12185)))),
    inference(variable_rename,[status(thm)],[f_3256_1]) ).

fof(f_3256_3,plain,
    ! [U_12185,U_12184,U_12186] : hAPP(hAPP(c_Groups_Otimes__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_12184)),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_12185))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12186))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_12186)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12184),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12184),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_12186),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_12185)))),
    inference(definitional_conversion,[status(esa)],[f_3256_2]) ).

cnf(f_3256_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_12184)),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_12185))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12186))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_12186)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12184),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_12184),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_12186),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_12185)))),
    inference(clausify,[status(thm)],[f_3256_3]) ).

fof(f_3257_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_3257_2,plain,
    ! [U_12189,U_12188,U_12187] : 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_12187)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_12188))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12189))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12189),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12187),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12187),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12189),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_12188)))),
    inference(variable_rename,[status(thm)],[f_3257_1]) ).

fof(f_3257_3,plain,
    ! [U_12187,U_12188,U_12189] : 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_12187)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_12188))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12189))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12189),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12187),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12187),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12189),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_12188)))),
    inference(definitional_conversion,[status(esa)],[f_3257_2]) ).

cnf(f_3257_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_12187)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Otimes__class_Otimes(tc_Nat_Onat)),U_12188))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12189))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12189),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12187),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12187),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12189),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_12188)))),
    inference(clausify,[status(thm)],[f_3257_3]) ).

fof(f_3258_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_3258_2,plain,
    ! [U_12193,U_12192,U_12191,U_12190] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12190),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12190),c_Groups_Oone__class_Oone(U_12190)),c_Groups_Oone__class_Oone(U_12190))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12190),hAPP(hAPP(c_COMBB(U_12190,U_12190,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_12190),U_12191)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_12190,U_12190),hAPP(hAPP(c_COMBB(U_12190,tc_fun(U_12190,U_12190),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_12190)),c_Nat_Osemiring__1__class_Oof__nat(U_12190))),U_12192))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12193))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12190),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12190),U_12193)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12190),U_12191),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12190),U_12191),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12190),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12190),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12193),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_12192))))
      | ~ class_Rings_Ocomm__semiring__1(U_12190) ),
    inference(variable_rename,[status(thm)],[f_3258_1]) ).

fof(f_3258_3,plain,
    ! [U_12190,U_12191,U_12192,U_12193] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12190),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12190),c_Groups_Oone__class_Oone(U_12190)),c_Groups_Oone__class_Oone(U_12190))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12190),hAPP(hAPP(c_COMBB(U_12190,U_12190,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_12190),U_12191)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_12190,U_12190),hAPP(hAPP(c_COMBB(U_12190,tc_fun(U_12190,U_12190),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_12190)),c_Nat_Osemiring__1__class_Oof__nat(U_12190))),U_12192))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12193))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12190),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12190),U_12193)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12190),U_12191),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12190),U_12191),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12190),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12190),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12193),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_12192))))
      | ~ class_Rings_Ocomm__semiring__1(U_12190) ),
    inference(definitional_conversion,[status(esa)],[f_3258_2]) ).

cnf(f_3258_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12190),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12190),c_Groups_Oone__class_Oone(U_12190)),c_Groups_Oone__class_Oone(U_12190))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12190),hAPP(hAPP(c_COMBB(U_12190,U_12190,tc_Nat_Onat),hAPP(c_Groups_Oplus__class_Oplus(U_12190),U_12191)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_12190,U_12190),hAPP(hAPP(c_COMBB(U_12190,tc_fun(U_12190,U_12190),tc_Nat_Onat),c_Groups_Otimes__class_Otimes(U_12190)),c_Nat_Osemiring__1__class_Oof__nat(U_12190))),U_12192))),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12193))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12190),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12190),U_12193)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12190),U_12191),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12190),U_12191),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12190),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12190),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_12193),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),U_12192))))
    | ~ class_Rings_Ocomm__semiring__1(U_12190) ),
    inference(clausify,[status(thm)],[f_3258_3]) ).

fof(f_3259_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_3259_2,plain,
    ! [U_12197,U_12196,U_12195,U_12194] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12194),hAPP(c_Groups_Oabs__class_Oabs(U_12194),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12195,U_12194),U_12196),U_12197))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12195,U_12194),hAPP(hAPP(c_COMBB(U_12194,U_12194,U_12195),c_Groups_Oabs__class_Oabs(U_12194)),U_12196)),U_12197)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_12194) ),
    inference(variable_rename,[status(thm)],[f_3259_1]) ).

fof(f_3259_3,plain,
    ! [U_12194,U_12195,U_12196,U_12197] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12194),hAPP(c_Groups_Oabs__class_Oabs(U_12194),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12195,U_12194),U_12196),U_12197))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12195,U_12194),hAPP(hAPP(c_COMBB(U_12194,U_12194,U_12195),c_Groups_Oabs__class_Oabs(U_12194)),U_12196)),U_12197)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_12194) ),
    inference(definitional_conversion,[status(esa)],[f_3259_2]) ).

cnf(f_3259_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12194),hAPP(c_Groups_Oabs__class_Oabs(U_12194),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12195,U_12194),U_12196),U_12197))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12195,U_12194),hAPP(hAPP(c_COMBB(U_12194,U_12194,U_12195),c_Groups_Oabs__class_Oabs(U_12194)),U_12196)),U_12197)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_12194) ),
    inference(clausify,[status(thm)],[f_3259_3]) ).

fof(f_3260_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_3260_2,plain,
    ! [U_12201,U_12200,U_12199,U_12198] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12198),c_Groups_Ozero__class_Ozero(U_12198)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12199,U_12198),hAPP(hAPP(c_COMBB(U_12198,U_12198,U_12199),c_Groups_Oabs__class_Oabs(U_12198)),U_12200)),U_12201)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_12198) ),
    inference(variable_rename,[status(thm)],[f_3260_1]) ).

fof(f_3260_3,plain,
    ! [U_12198,U_12199,U_12200,U_12201] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12198),c_Groups_Ozero__class_Ozero(U_12198)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12199,U_12198),hAPP(hAPP(c_COMBB(U_12198,U_12198,U_12199),c_Groups_Oabs__class_Oabs(U_12198)),U_12200)),U_12201)))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_12198) ),
    inference(definitional_conversion,[status(esa)],[f_3260_2]) ).

cnf(f_3260_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12198),c_Groups_Ozero__class_Ozero(U_12198)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12199,U_12198),hAPP(hAPP(c_COMBB(U_12198,U_12198,U_12199),c_Groups_Oabs__class_Oabs(U_12198)),U_12200)),U_12201)))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_12198) ),
    inference(clausify,[status(thm)],[f_3260_3]) ).

fof(f_3261_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_3261_2,plain,
    ! [U_12206,U_12205,U_12204] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12204,tc_Nat_Onat),U_12206),U_12205) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ? [U_12203] :
              ( hAPP(U_12206,U_12203) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(U_12204),U_12203),U_12205)) ) )
        & ( ! [U_12202] :
              ( hAPP(U_12206,U_12202) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_12204),U_12202),U_12205)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12204,tc_Nat_Onat),U_12206),U_12205) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12204),U_12205)) ),
    inference(variable_rename,[status(thm)],[f_3261_1]) ).

fof(f_3261_3,plain,
    ! [U_12206,U_12205,U_12204] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12204,tc_Nat_Onat),U_12206),U_12205) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | ( hAPP(U_12206,sK252(U_12206,U_12205,U_12204)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_12204),sK252(U_12206,U_12205,U_12204)),U_12205)) ) )
        & ( ! [U_12202] :
              ( hAPP(U_12206,U_12202) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_12204),U_12202),U_12205)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12204,tc_Nat_Onat),U_12206),U_12205) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12204),U_12205)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK252]),skolemize(U_12203,sK252(U_12206,U_12205,U_12204))],[f_3261_2]) ).

fof(f_3261_4,plain,
    ( ! [U_12204,U_12205,U_12206] :
        ( hAPP(U_12206,sK252(U_12206,U_12205,U_12204)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP887(U_12204,U_12205,U_12206) )
    & ! [U_12204,U_12205,U_12206] :
        ( hBOOL(hAPP(hAPP(c_member(U_12204),sK252(U_12206,U_12205,U_12204)),U_12205))
        | ~ sP887(U_12204,U_12205,U_12206) )
    & ! [U_12202,U_12204,U_12205,U_12206] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12204,tc_Nat_Onat),U_12206),U_12205) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP887(U_12204,U_12205,U_12206)
        | ~ sP888(U_12202,U_12204,U_12205,U_12206) )
    & ! [U_12202,U_12204,U_12205,U_12206] :
        ( hAPP(U_12206,U_12202) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12204),U_12202),U_12205))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12204,tc_Nat_Onat),U_12206),U_12205) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP888(U_12202,U_12204,U_12205,U_12206) )
    & ! [U_12202,U_12204,U_12205,U_12206] :
        ( sP888(U_12202,U_12204,U_12205,U_12206)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12204),U_12205)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP887,sP888])],[f_3261_3]) ).

cnf(f_3261_5,plain,
    ( sP888(U_12202,U_12204,U_12205,U_12206)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12204),U_12205)) ),
    inference(clausify,[status(thm)],[f_3261_4]) ).

cnf(f_3261_6,plain,
    ( hAPP(U_12206,U_12202) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12204),U_12202),U_12205))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12204,tc_Nat_Onat),U_12206),U_12205) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP888(U_12202,U_12204,U_12205,U_12206) ),
    inference(clausify,[status(thm)],[f_3261_4]) ).

cnf(f_3261_7,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12204,tc_Nat_Onat),U_12206),U_12205) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP887(U_12204,U_12205,U_12206)
    | ~ sP888(U_12202,U_12204,U_12205,U_12206) ),
    inference(clausify,[status(thm)],[f_3261_4]) ).

cnf(f_3261_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12204),sK252(U_12206,U_12205,U_12204)),U_12205))
    | ~ sP887(U_12204,U_12205,U_12206) ),
    inference(clausify,[status(thm)],[f_3261_4]) ).

cnf(f_3261_9,plain,
    ( hAPP(U_12206,sK252(U_12206,U_12205,U_12204)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP887(U_12204,U_12205,U_12206) ),
    inference(clausify,[status(thm)],[f_3261_4]) ).

fof(f_3262_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_3262_2,plain,
    ! [U_12210,U_12209,U_12208,U_12207] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12208,U_12207),hAPP(hAPP(c_COMBB(U_12207,U_12207,U_12208),c_Groups_Ouminus__class_Ouminus(U_12207)),U_12209)),U_12210) = hAPP(c_Groups_Ouminus__class_Ouminus(U_12207),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12208,U_12207),U_12209),U_12210))
      | ~ class_Groups_Oab__group__add(U_12207) ),
    inference(variable_rename,[status(thm)],[f_3262_1]) ).

fof(f_3262_3,plain,
    ! [U_12208,U_12207,U_12209,U_12210] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12208,U_12207),hAPP(hAPP(c_COMBB(U_12207,U_12207,U_12208),c_Groups_Ouminus__class_Ouminus(U_12207)),U_12209)),U_12210) = hAPP(c_Groups_Ouminus__class_Ouminus(U_12207),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12208,U_12207),U_12209),U_12210))
      | ~ class_Groups_Oab__group__add(U_12207) ),
    inference(definitional_conversion,[status(esa)],[f_3262_2]) ).

cnf(f_3262_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12208,U_12207),hAPP(hAPP(c_COMBB(U_12207,U_12207,U_12208),c_Groups_Ouminus__class_Ouminus(U_12207)),U_12209)),U_12210) = hAPP(c_Groups_Ouminus__class_Ouminus(U_12207),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12208,U_12207),U_12209),U_12210))
    | ~ class_Groups_Oab__group__add(U_12207) ),
    inference(clausify,[status(thm)],[f_3262_3]) ).

fof(f_3263_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_3263_2,plain,
    ! [U_12213,U_12212,U_12211] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12212,U_12211),hAPP(c_COMBK(U_12211,U_12212),c_Groups_Ozero__class_Ozero(U_12211))),U_12213) = c_Groups_Ozero__class_Ozero(U_12211)
      | ~ class_Groups_Ocomm__monoid__add(U_12211) ),
    inference(variable_rename,[status(thm)],[f_3263_1]) ).

fof(f_3263_3,plain,
    ! [U_12211,U_12212,U_12213] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12212,U_12211),hAPP(c_COMBK(U_12211,U_12212),c_Groups_Ozero__class_Ozero(U_12211))),U_12213) = c_Groups_Ozero__class_Ozero(U_12211)
      | ~ class_Groups_Ocomm__monoid__add(U_12211) ),
    inference(definitional_conversion,[status(esa)],[f_3263_2]) ).

cnf(f_3263_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12212,U_12211),hAPP(c_COMBK(U_12211,U_12212),c_Groups_Ozero__class_Ozero(U_12211))),U_12213) = c_Groups_Ozero__class_Ozero(U_12211)
    | ~ class_Groups_Ocomm__monoid__add(U_12211) ),
    inference(clausify,[status(thm)],[f_3263_3]) ).

fof(f_3264_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_3264_2,plain,
    ! [U_12219,U_12218,U_12217,U_12216,U_12215,U_12214] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12215,U_12214),hAPP(hAPP(c_COMBC(U_12215,tc_fun(U_12216,tc_HOL_Obool),U_12214),hAPP(hAPP(c_COMBB(tc_fun(U_12216,U_12214),tc_fun(tc_fun(U_12216,tc_HOL_Obool),U_12214),U_12215),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12216,U_12214)),U_12217)),U_12218)),U_12219) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12216,U_12214),hAPP(hAPP(c_COMBC(U_12216,tc_fun(U_12215,tc_HOL_Obool),U_12214),hAPP(hAPP(c_COMBB(tc_fun(U_12215,U_12214),tc_fun(tc_fun(U_12215,tc_HOL_Obool),U_12214),U_12216),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12215,U_12214)),hAPP(c_COMBC(U_12215,U_12216,U_12214),U_12217))),U_12219)),U_12218)
      | ~ class_Groups_Ocomm__monoid__add(U_12214) ),
    inference(variable_rename,[status(thm)],[f_3264_1]) ).

fof(f_3264_3,plain,
    ! [U_12214,U_12215,U_12216,U_12217,U_12218,U_12219] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12215,U_12214),hAPP(hAPP(c_COMBC(U_12215,tc_fun(U_12216,tc_HOL_Obool),U_12214),hAPP(hAPP(c_COMBB(tc_fun(U_12216,U_12214),tc_fun(tc_fun(U_12216,tc_HOL_Obool),U_12214),U_12215),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12216,U_12214)),U_12217)),U_12218)),U_12219) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12216,U_12214),hAPP(hAPP(c_COMBC(U_12216,tc_fun(U_12215,tc_HOL_Obool),U_12214),hAPP(hAPP(c_COMBB(tc_fun(U_12215,U_12214),tc_fun(tc_fun(U_12215,tc_HOL_Obool),U_12214),U_12216),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12215,U_12214)),hAPP(c_COMBC(U_12215,U_12216,U_12214),U_12217))),U_12219)),U_12218)
      | ~ class_Groups_Ocomm__monoid__add(U_12214) ),
    inference(definitional_conversion,[status(esa)],[f_3264_2]) ).

cnf(f_3264_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12215,U_12214),hAPP(hAPP(c_COMBC(U_12215,tc_fun(U_12216,tc_HOL_Obool),U_12214),hAPP(hAPP(c_COMBB(tc_fun(U_12216,U_12214),tc_fun(tc_fun(U_12216,tc_HOL_Obool),U_12214),U_12215),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12216,U_12214)),U_12217)),U_12218)),U_12219) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12216,U_12214),hAPP(hAPP(c_COMBC(U_12216,tc_fun(U_12215,tc_HOL_Obool),U_12214),hAPP(hAPP(c_COMBB(tc_fun(U_12215,U_12214),tc_fun(tc_fun(U_12215,tc_HOL_Obool),U_12214),U_12216),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12215,U_12214)),hAPP(c_COMBC(U_12215,U_12216,U_12214),U_12217))),U_12219)),U_12218)
    | ~ class_Groups_Ocomm__monoid__add(U_12214) ),
    inference(clausify,[status(thm)],[f_3264_3]) ).

fof(f_3265_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_3265_2,plain,
    ! [U_12223,U_12222,U_12221,U_12220] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_12220),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12221,tc_Int_Oint),U_12222),U_12223)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12221,U_12220),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_12220,U_12221),c_Int_Oring__1__class_Oof__int(U_12220)),U_12222)),U_12223)
      | ~ class_Rings_Oring__1(U_12220) ),
    inference(variable_rename,[status(thm)],[f_3265_1]) ).

fof(f_3265_3,plain,
    ! [U_12220,U_12221,U_12222,U_12223] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_12220),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12221,tc_Int_Oint),U_12222),U_12223)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12221,U_12220),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_12220,U_12221),c_Int_Oring__1__class_Oof__int(U_12220)),U_12222)),U_12223)
      | ~ class_Rings_Oring__1(U_12220) ),
    inference(definitional_conversion,[status(esa)],[f_3265_2]) ).

cnf(f_3265_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_12220),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12221,tc_Int_Oint),U_12222),U_12223)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12221,U_12220),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_12220,U_12221),c_Int_Oring__1__class_Oof__int(U_12220)),U_12222)),U_12223)
    | ~ class_Rings_Oring__1(U_12220) ),
    inference(clausify,[status(thm)],[f_3265_3]) ).

fof(f_3266_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_3266_2,plain,
    ! [U_12226,U_12225,U_12224] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12224,tc_Nat_Onat),U_12225),U_12226) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12224,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_12224),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12225)),U_12226)),
    inference(variable_rename,[status(thm)],[f_3266_1]) ).

fof(f_3266_3,plain,
    ! [U_12224,U_12225,U_12226] : hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12224,tc_Nat_Onat),U_12225),U_12226) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12224,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_12224),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12225)),U_12226)),
    inference(definitional_conversion,[status(esa)],[f_3266_2]) ).

cnf(f_3266_4,plain,
    hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12224,tc_Nat_Onat),U_12225),U_12226) = hAPP(c_Int_Onat,hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12224,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_12224),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12225)),U_12226)),
    inference(clausify,[status(thm)],[f_3266_3]) ).

fof(f_3267_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_3267_2,plain,
    ! [U_12229,U_12228,U_12227] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12227,tc_Nat_Onat),U_12228),U_12229)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12227,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_12227),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12228)),U_12229),
    inference(variable_rename,[status(thm)],[f_3267_1]) ).

fof(f_3267_3,plain,
    ! [U_12227,U_12228,U_12229] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12227,tc_Nat_Onat),U_12228),U_12229)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12227,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_12227),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12228)),U_12229),
    inference(definitional_conversion,[status(esa)],[f_3267_2]) ).

cnf(f_3267_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12227,tc_Nat_Onat),U_12228),U_12229)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12227,tc_Int_Oint),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Int_Oint,U_12227),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12228)),U_12229),
    inference(clausify,[status(thm)],[f_3267_3]) ).

fof(f_3268_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_3268_2,plain,
    ! [U_12233,U_12232,U_12231,U_12230] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12230),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12231,tc_Nat_Onat),U_12232),U_12233)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12231,U_12230),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12230,U_12231),c_Nat_Osemiring__1__class_Oof__nat(U_12230)),U_12232)),U_12233)
      | ~ class_Rings_Osemiring__1(U_12230) ),
    inference(variable_rename,[status(thm)],[f_3268_1]) ).

fof(f_3268_3,plain,
    ! [U_12230,U_12231,U_12232,U_12233] :
      ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12230),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12231,tc_Nat_Onat),U_12232),U_12233)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12231,U_12230),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12230,U_12231),c_Nat_Osemiring__1__class_Oof__nat(U_12230)),U_12232)),U_12233)
      | ~ class_Rings_Osemiring__1(U_12230) ),
    inference(definitional_conversion,[status(esa)],[f_3268_2]) ).

cnf(f_3268_4,plain,
    ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12230),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12231,tc_Nat_Onat),U_12232),U_12233)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12231,U_12230),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12230,U_12231),c_Nat_Osemiring__1__class_Oof__nat(U_12230)),U_12232)),U_12233)
    | ~ class_Rings_Osemiring__1(U_12230) ),
    inference(clausify,[status(thm)],[f_3268_3]) ).

fof(f_3269_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_3269_2,plain,
    ! [U_12240,U_12239,U_12238,U_12237,U_12236,U_12235,U_12234] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12234),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12235,U_12234),U_12236),U_12237)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12238,U_12234),U_12239),U_12240)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12235,U_12234),hAPP(hAPP(c_COMBC(U_12235,tc_fun(U_12238,tc_HOL_Obool),U_12234),hAPP(hAPP(c_COMBB(tc_fun(U_12238,U_12234),tc_fun(tc_fun(U_12238,tc_HOL_Obool),U_12234),U_12235),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12238,U_12234)),hAPP(hAPP(c_COMBC(U_12235,tc_fun(U_12238,U_12234),tc_fun(U_12238,U_12234)),hAPP(hAPP(c_COMBB(tc_fun(U_12234,U_12234),tc_fun(tc_fun(U_12238,U_12234),tc_fun(U_12238,U_12234)),U_12235),c_COMBB(U_12234,U_12234,U_12238)),hAPP(hAPP(c_COMBB(U_12234,tc_fun(U_12234,U_12234),U_12235),c_Groups_Otimes__class_Otimes(U_12234)),U_12236))),U_12239))),U_12240)),U_12237)
      | ~ class_Rings_Osemiring__0(U_12234) ),
    inference(variable_rename,[status(thm)],[f_3269_1]) ).

fof(f_3269_3,plain,
    ! [U_12234,U_12235,U_12236,U_12237,U_12238,U_12239,U_12240] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12234),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12235,U_12234),U_12236),U_12237)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12238,U_12234),U_12239),U_12240)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12235,U_12234),hAPP(hAPP(c_COMBC(U_12235,tc_fun(U_12238,tc_HOL_Obool),U_12234),hAPP(hAPP(c_COMBB(tc_fun(U_12238,U_12234),tc_fun(tc_fun(U_12238,tc_HOL_Obool),U_12234),U_12235),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12238,U_12234)),hAPP(hAPP(c_COMBC(U_12235,tc_fun(U_12238,U_12234),tc_fun(U_12238,U_12234)),hAPP(hAPP(c_COMBB(tc_fun(U_12234,U_12234),tc_fun(tc_fun(U_12238,U_12234),tc_fun(U_12238,U_12234)),U_12235),c_COMBB(U_12234,U_12234,U_12238)),hAPP(hAPP(c_COMBB(U_12234,tc_fun(U_12234,U_12234),U_12235),c_Groups_Otimes__class_Otimes(U_12234)),U_12236))),U_12239))),U_12240)),U_12237)
      | ~ class_Rings_Osemiring__0(U_12234) ),
    inference(definitional_conversion,[status(esa)],[f_3269_2]) ).

cnf(f_3269_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12234),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12235,U_12234),U_12236),U_12237)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12238,U_12234),U_12239),U_12240)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12235,U_12234),hAPP(hAPP(c_COMBC(U_12235,tc_fun(U_12238,tc_HOL_Obool),U_12234),hAPP(hAPP(c_COMBB(tc_fun(U_12238,U_12234),tc_fun(tc_fun(U_12238,tc_HOL_Obool),U_12234),U_12235),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12238,U_12234)),hAPP(hAPP(c_COMBC(U_12235,tc_fun(U_12238,U_12234),tc_fun(U_12238,U_12234)),hAPP(hAPP(c_COMBB(tc_fun(U_12234,U_12234),tc_fun(tc_fun(U_12238,U_12234),tc_fun(U_12238,U_12234)),U_12235),c_COMBB(U_12234,U_12234,U_12238)),hAPP(hAPP(c_COMBB(U_12234,tc_fun(U_12234,U_12234),U_12235),c_Groups_Otimes__class_Otimes(U_12234)),U_12236))),U_12239))),U_12240)),U_12237)
    | ~ class_Rings_Osemiring__0(U_12234) ),
    inference(clausify,[status(thm)],[f_3269_3]) ).

fof(f_3270_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_3270_2,plain,
    ! [U_12245,U_12244,U_12243,U_12242,U_12241] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12241),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12242,U_12241),U_12243),U_12244)),U_12245) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12242,U_12241),hAPP(hAPP(c_COMBC(U_12242,U_12241,U_12241),hAPP(hAPP(c_COMBB(U_12241,tc_fun(U_12241,U_12241),U_12242),c_Groups_Otimes__class_Otimes(U_12241)),U_12243)),U_12245)),U_12244)
      | ~ class_Rings_Osemiring__0(U_12241) ),
    inference(variable_rename,[status(thm)],[f_3270_1]) ).

fof(f_3270_3,plain,
    ! [U_12241,U_12242,U_12243,U_12244,U_12245] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12241),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12242,U_12241),U_12243),U_12244)),U_12245) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12242,U_12241),hAPP(hAPP(c_COMBC(U_12242,U_12241,U_12241),hAPP(hAPP(c_COMBB(U_12241,tc_fun(U_12241,U_12241),U_12242),c_Groups_Otimes__class_Otimes(U_12241)),U_12243)),U_12245)),U_12244)
      | ~ class_Rings_Osemiring__0(U_12241) ),
    inference(definitional_conversion,[status(esa)],[f_3270_2]) ).

cnf(f_3270_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12241),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12242,U_12241),U_12243),U_12244)),U_12245) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12242,U_12241),hAPP(hAPP(c_COMBC(U_12242,U_12241,U_12241),hAPP(hAPP(c_COMBB(U_12241,tc_fun(U_12241,U_12241),U_12242),c_Groups_Otimes__class_Otimes(U_12241)),U_12243)),U_12245)),U_12244)
    | ~ class_Rings_Osemiring__0(U_12241) ),
    inference(clausify,[status(thm)],[f_3270_3]) ).

fof(f_3271_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_3271_2,plain,
    ! [U_12250,U_12249,U_12248,U_12247,U_12246] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12246),U_12247),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12248,U_12246),U_12249),U_12250)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12248,U_12246),hAPP(hAPP(c_COMBB(U_12246,U_12246,U_12248),hAPP(c_Groups_Otimes__class_Otimes(U_12246),U_12247)),U_12249)),U_12250)
      | ~ class_Rings_Osemiring__0(U_12246) ),
    inference(variable_rename,[status(thm)],[f_3271_1]) ).

fof(f_3271_3,plain,
    ! [U_12246,U_12247,U_12248,U_12249,U_12250] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12246),U_12247),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12248,U_12246),U_12249),U_12250)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12248,U_12246),hAPP(hAPP(c_COMBB(U_12246,U_12246,U_12248),hAPP(c_Groups_Otimes__class_Otimes(U_12246),U_12247)),U_12249)),U_12250)
      | ~ class_Rings_Osemiring__0(U_12246) ),
    inference(definitional_conversion,[status(esa)],[f_3271_2]) ).

cnf(f_3271_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12246),U_12247),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12248,U_12246),U_12249),U_12250)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12248,U_12246),hAPP(hAPP(c_COMBB(U_12246,U_12246,U_12248),hAPP(c_Groups_Otimes__class_Otimes(U_12246),U_12247)),U_12249)),U_12250)
    | ~ class_Rings_Osemiring__0(U_12246) ),
    inference(clausify,[status(thm)],[f_3271_3]) ).

fof(f_3272_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_3272_2,plain,
    ! [U_12255,U_12254,U_12253,U_12252,U_12251] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12252,U_12251),hAPP(hAPP(c_COMBS(U_12252,U_12251,U_12251),hAPP(hAPP(c_COMBB(U_12251,tc_fun(U_12251,U_12251),U_12252),c_Groups_Oplus__class_Oplus(U_12251)),U_12253)),U_12254)),U_12255) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12251),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12252,U_12251),U_12253),U_12255)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12252,U_12251),U_12254),U_12255))
      | ~ class_Groups_Ocomm__monoid__add(U_12251) ),
    inference(variable_rename,[status(thm)],[f_3272_1]) ).

fof(f_3272_3,plain,
    ! [U_12251,U_12252,U_12253,U_12254,U_12255] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12252,U_12251),hAPP(hAPP(c_COMBS(U_12252,U_12251,U_12251),hAPP(hAPP(c_COMBB(U_12251,tc_fun(U_12251,U_12251),U_12252),c_Groups_Oplus__class_Oplus(U_12251)),U_12253)),U_12254)),U_12255) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12251),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12252,U_12251),U_12253),U_12255)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12252,U_12251),U_12254),U_12255))
      | ~ class_Groups_Ocomm__monoid__add(U_12251) ),
    inference(definitional_conversion,[status(esa)],[f_3272_2]) ).

cnf(f_3272_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12252,U_12251),hAPP(hAPP(c_COMBS(U_12252,U_12251,U_12251),hAPP(hAPP(c_COMBB(U_12251,tc_fun(U_12251,U_12251),U_12252),c_Groups_Oplus__class_Oplus(U_12251)),U_12253)),U_12254)),U_12255) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12251),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12252,U_12251),U_12253),U_12255)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12252,U_12251),U_12254),U_12255))
    | ~ class_Groups_Ocomm__monoid__add(U_12251) ),
    inference(clausify,[status(thm)],[f_3272_3]) ).

fof(f_3273_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_3273_2,plain,
    ! [U_12260,U_12259,U_12258,U_12257,U_12256] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12257,U_12256),hAPP(hAPP(c_COMBS(U_12257,U_12256,U_12256),hAPP(hAPP(c_COMBB(U_12256,tc_fun(U_12256,U_12256),U_12257),c_Groups_Ominus__class_Ominus(U_12256)),U_12258)),U_12259)),U_12260) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12256),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12257,U_12256),U_12258),U_12260)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12257,U_12256),U_12259),U_12260))
      | ~ class_Groups_Oab__group__add(U_12256) ),
    inference(variable_rename,[status(thm)],[f_3273_1]) ).

fof(f_3273_3,plain,
    ! [U_12256,U_12257,U_12258,U_12259,U_12260] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12257,U_12256),hAPP(hAPP(c_COMBS(U_12257,U_12256,U_12256),hAPP(hAPP(c_COMBB(U_12256,tc_fun(U_12256,U_12256),U_12257),c_Groups_Ominus__class_Ominus(U_12256)),U_12258)),U_12259)),U_12260) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12256),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12257,U_12256),U_12258),U_12260)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12257,U_12256),U_12259),U_12260))
      | ~ class_Groups_Oab__group__add(U_12256) ),
    inference(definitional_conversion,[status(esa)],[f_3273_2]) ).

cnf(f_3273_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12257,U_12256),hAPP(hAPP(c_COMBS(U_12257,U_12256,U_12256),hAPP(hAPP(c_COMBB(U_12256,tc_fun(U_12256,U_12256),U_12257),c_Groups_Ominus__class_Ominus(U_12256)),U_12258)),U_12259)),U_12260) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12256),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12257,U_12256),U_12258),U_12260)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12257,U_12256),U_12259),U_12260))
    | ~ class_Groups_Oab__group__add(U_12256) ),
    inference(clausify,[status(thm)],[f_3273_3]) ).

fof(f_3274_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_3274_2,plain,
    ! [U_12264,U_12263,U_12262,U_12261] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_12261),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12262,U_12261),hAPP(hAPP(c_COMBB(U_12261,U_12261,U_12262),c_Groups_Oabs__class_Oabs(U_12261)),U_12263)),U_12264)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12262,U_12261),hAPP(hAPP(c_COMBB(U_12261,U_12261,U_12262),c_Groups_Oabs__class_Oabs(U_12261)),U_12263)),U_12264)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_12261) ),
    inference(variable_rename,[status(thm)],[f_3274_1]) ).

fof(f_3274_3,plain,
    ! [U_12261,U_12262,U_12263,U_12264] :
      ( hAPP(c_Groups_Oabs__class_Oabs(U_12261),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12262,U_12261),hAPP(hAPP(c_COMBB(U_12261,U_12261,U_12262),c_Groups_Oabs__class_Oabs(U_12261)),U_12263)),U_12264)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12262,U_12261),hAPP(hAPP(c_COMBB(U_12261,U_12261,U_12262),c_Groups_Oabs__class_Oabs(U_12261)),U_12263)),U_12264)
      | ~ class_Groups_Oordered__ab__group__add__abs(U_12261) ),
    inference(definitional_conversion,[status(esa)],[f_3274_2]) ).

cnf(f_3274_4,plain,
    ( hAPP(c_Groups_Oabs__class_Oabs(U_12261),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12262,U_12261),hAPP(hAPP(c_COMBB(U_12261,U_12261,U_12262),c_Groups_Oabs__class_Oabs(U_12261)),U_12263)),U_12264)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12262,U_12261),hAPP(hAPP(c_COMBB(U_12261,U_12261,U_12262),c_Groups_Oabs__class_Oabs(U_12261)),U_12263)),U_12264)
    | ~ class_Groups_Oordered__ab__group__add__abs(U_12261) ),
    inference(clausify,[status(thm)],[f_3274_3]) ).

fof(f_3275_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_3275_2,plain,
    ! [U_12269,U_12268,U_12267,U_12266,U_12265] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_12265),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12266,U_12265),U_12267),U_12268)),U_12269) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12266,U_12265),hAPP(hAPP(c_COMBC(U_12266,U_12265,U_12265),hAPP(hAPP(c_COMBB(U_12265,tc_fun(U_12265,U_12265),U_12266),c_Rings_Oinverse__class_Odivide(U_12265)),U_12267)),U_12269)),U_12268)
      | ~ class_Fields_Ofield(U_12265) ),
    inference(variable_rename,[status(thm)],[f_3275_1]) ).

fof(f_3275_3,plain,
    ! [U_12265,U_12266,U_12267,U_12268,U_12269] :
      ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_12265),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12266,U_12265),U_12267),U_12268)),U_12269) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12266,U_12265),hAPP(hAPP(c_COMBC(U_12266,U_12265,U_12265),hAPP(hAPP(c_COMBB(U_12265,tc_fun(U_12265,U_12265),U_12266),c_Rings_Oinverse__class_Odivide(U_12265)),U_12267)),U_12269)),U_12268)
      | ~ class_Fields_Ofield(U_12265) ),
    inference(definitional_conversion,[status(esa)],[f_3275_2]) ).

cnf(f_3275_4,plain,
    ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_12265),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12266,U_12265),U_12267),U_12268)),U_12269) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12266,U_12265),hAPP(hAPP(c_COMBC(U_12266,U_12265,U_12265),hAPP(hAPP(c_COMBB(U_12265,tc_fun(U_12265,U_12265),U_12266),c_Rings_Oinverse__class_Odivide(U_12265)),U_12267)),U_12269)),U_12268)
    | ~ class_Fields_Ofield(U_12265) ),
    inference(clausify,[status(thm)],[f_3275_3]) ).

fof(f_3276_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_3276_2,plain,
    ! [U_12273,U_12272,U_12271,U_12270] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12271,U_12270),U_12273),U_12272) = c_Groups_Ozero__class_Ozero(U_12270)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12271),U_12272))
      | ~ class_Groups_Ocomm__monoid__add(U_12270) ),
    inference(variable_rename,[status(thm)],[f_3276_1]) ).

fof(f_3276_3,plain,
    ! [U_12270,U_12271,U_12272,U_12273] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12271,U_12270),U_12273),U_12272) = c_Groups_Ozero__class_Ozero(U_12270)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12271),U_12272))
      | ~ class_Groups_Ocomm__monoid__add(U_12270) ),
    inference(definitional_conversion,[status(esa)],[f_3276_2]) ).

cnf(f_3276_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12271,U_12270),U_12273),U_12272) = c_Groups_Ozero__class_Ozero(U_12270)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12271),U_12272))
    | ~ class_Groups_Ocomm__monoid__add(U_12270) ),
    inference(clausify,[status(thm)],[f_3276_3]) ).

fof(f_3277_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_3277_2,plain,
    ! [U_12277,U_12276,U_12275,U_12274] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12275,U_12274),U_12277),U_12276) = c_Groups_Ozero__class_Ozero(U_12274)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12275),U_12276))
      | ~ class_Groups_Ocomm__monoid__add(U_12274) ),
    inference(variable_rename,[status(thm)],[f_3277_1]) ).

fof(f_3277_3,plain,
    ! [U_12275,U_12274,U_12276,U_12277] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12275,U_12274),U_12277),U_12276) = c_Groups_Ozero__class_Ozero(U_12274)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12275),U_12276))
      | ~ class_Groups_Ocomm__monoid__add(U_12274) ),
    inference(definitional_conversion,[status(esa)],[f_3277_2]) ).

cnf(f_3277_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12275,U_12274),U_12277),U_12276) = c_Groups_Ozero__class_Ozero(U_12274)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12275),U_12276))
    | ~ class_Groups_Ocomm__monoid__add(U_12274) ),
    inference(clausify,[status(thm)],[f_3277_3]) ).

fof(f_3278_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_3278_2,plain,
    ! [U_12280,U_12279,U_12278] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12279,U_12278),U_12280),c_Orderings_Obot__class_Obot(tc_fun(U_12279,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_12278)
      | ~ class_Groups_Ocomm__monoid__add(U_12278) ),
    inference(variable_rename,[status(thm)],[f_3278_1]) ).

fof(f_3278_3,plain,
    ! [U_12279,U_12278,U_12280] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12279,U_12278),U_12280),c_Orderings_Obot__class_Obot(tc_fun(U_12279,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_12278)
      | ~ class_Groups_Ocomm__monoid__add(U_12278) ),
    inference(definitional_conversion,[status(esa)],[f_3278_2]) ).

cnf(f_3278_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12279,U_12278),U_12280),c_Orderings_Obot__class_Obot(tc_fun(U_12279,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_12278)
    | ~ class_Groups_Ocomm__monoid__add(U_12278) ),
    inference(clausify,[status(thm)],[f_3278_3]) ).

fof(f_3279_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_3279_2,plain,
    ! [U_12283,U_12282,U_12281] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12282,U_12281),U_12283),c_Orderings_Obot__class_Obot(tc_fun(U_12282,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_12281)
      | ~ class_Groups_Ocomm__monoid__add(U_12281) ),
    inference(variable_rename,[status(thm)],[f_3279_1]) ).

fof(f_3279_3,plain,
    ! [U_12281,U_12282,U_12283] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12282,U_12281),U_12283),c_Orderings_Obot__class_Obot(tc_fun(U_12282,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_12281)
      | ~ class_Groups_Ocomm__monoid__add(U_12281) ),
    inference(definitional_conversion,[status(esa)],[f_3279_2]) ).

cnf(f_3279_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12282,U_12281),U_12283),c_Orderings_Obot__class_Obot(tc_fun(U_12282,tc_HOL_Obool))) = c_Groups_Ozero__class_Ozero(U_12281)
    | ~ class_Groups_Ocomm__monoid__add(U_12281) ),
    inference(clausify,[status(thm)],[f_3279_3]) ).

fof(f_3280_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_3280_2,plain,
    ! [U_12288,U_12287,U_12286,U_12285,U_12284] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12285,U_12284),hAPP(hAPP(c_COMBS(U_12285,U_12284,U_12284),hAPP(hAPP(c_COMBB(U_12284,tc_fun(U_12284,U_12284),U_12285),c_Groups_Oplus__class_Oplus(U_12284)),U_12287)),U_12288)),U_12286) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12284),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12285,U_12284),U_12287),U_12286)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12285,U_12284),U_12288),U_12286))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12285),U_12286))
      | ~ class_Groups_Ocomm__monoid__add(U_12284) ),
    inference(variable_rename,[status(thm)],[f_3280_1]) ).

fof(f_3280_3,plain,
    ! [U_12284,U_12285,U_12286,U_12287,U_12288] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12285,U_12284),hAPP(hAPP(c_COMBS(U_12285,U_12284,U_12284),hAPP(hAPP(c_COMBB(U_12284,tc_fun(U_12284,U_12284),U_12285),c_Groups_Oplus__class_Oplus(U_12284)),U_12287)),U_12288)),U_12286) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12284),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12285,U_12284),U_12287),U_12286)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12285,U_12284),U_12288),U_12286))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12285),U_12286))
      | ~ class_Groups_Ocomm__monoid__add(U_12284) ),
    inference(definitional_conversion,[status(esa)],[f_3280_2]) ).

cnf(f_3280_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12285,U_12284),hAPP(hAPP(c_COMBS(U_12285,U_12284,U_12284),hAPP(hAPP(c_COMBB(U_12284,tc_fun(U_12284,U_12284),U_12285),c_Groups_Oplus__class_Oplus(U_12284)),U_12287)),U_12288)),U_12286) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12284),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12285,U_12284),U_12287),U_12286)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12285,U_12284),U_12288),U_12286))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12285),U_12286))
    | ~ class_Groups_Ocomm__monoid__add(U_12284) ),
    inference(clausify,[status(thm)],[f_3280_3]) ).

fof(f_3281_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_3281_2,plain,
    ! [U_12290,U_12289] : hAPP(c_Finite__Set_Ocard(U_12289),U_12290) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12289,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_12289),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_12290),
    inference(variable_rename,[status(thm)],[f_3281_1]) ).

fof(f_3281_3,plain,
    ! [U_12290,U_12289] : hAPP(c_Finite__Set_Ocard(U_12289),U_12290) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12289,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_12289),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_12290),
    inference(definitional_conversion,[status(esa)],[f_3281_2]) ).

cnf(f_3281_4,plain,
    hAPP(c_Finite__Set_Ocard(U_12289),U_12290) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12289,tc_Nat_Onat),hAPP(c_COMBK(tc_Nat_Onat,U_12289),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_12290),
    inference(clausify,[status(thm)],[f_3281_3]) ).

fof(f_3282_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_3282_2,plain,
    ! [U_12294,U_12293,U_12292,U_12291] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12291),U_12292),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12293)),hAPP(c_Nat_OSuc,U_12294))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12291),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12291,tc_Nat_Onat),U_12292),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12293),U_12294))
      | ~ class_Groups_Ocomm__monoid__add(U_12291) ),
    inference(variable_rename,[status(thm)],[f_3282_1]) ).

fof(f_3282_3,plain,
    ! [U_12291,U_12292,U_12293,U_12294] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12291),U_12292),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12293)),hAPP(c_Nat_OSuc,U_12294))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12291),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12291,tc_Nat_Onat),U_12292),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12293),U_12294))
      | ~ class_Groups_Ocomm__monoid__add(U_12291) ),
    inference(definitional_conversion,[status(esa)],[f_3282_2]) ).

cnf(f_3282_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12291),U_12292),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12293)),hAPP(c_Nat_OSuc,U_12294))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12291),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12291,tc_Nat_Onat),U_12292),c_Nat_OSuc)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12293),U_12294))
    | ~ class_Groups_Ocomm__monoid__add(U_12291) ),
    inference(clausify,[status(thm)],[f_3282_3]) ).

fof(f_3283_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_3283_2,plain,
    ! [U_12299,U_12298,U_12297,U_12296,U_12295] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12295),U_12296),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12297),U_12298)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12299),U_12298))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12295),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12295,tc_Nat_Onat),U_12296),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_12298))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12297),U_12299))
      | ~ class_Groups_Ocomm__monoid__add(U_12295) ),
    inference(variable_rename,[status(thm)],[f_3283_1]) ).

fof(f_3283_3,plain,
    ! [U_12295,U_12296,U_12297,U_12298,U_12299] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12295),U_12296),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12297),U_12298)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12299),U_12298))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12295),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12295,tc_Nat_Onat),U_12296),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_12298))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12297),U_12299))
      | ~ class_Groups_Ocomm__monoid__add(U_12295) ),
    inference(definitional_conversion,[status(esa)],[f_3283_2]) ).

cnf(f_3283_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12295),U_12296),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12297),U_12298)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12299),U_12298))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12295),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12295,tc_Nat_Onat),U_12296),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_12298))),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12297),U_12299))
    | ~ class_Groups_Ocomm__monoid__add(U_12295) ),
    inference(clausify,[status(thm)],[f_3283_3]) ).

fof(f_3284_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_3284_2,plain,
    ! [U_12303,U_12302,U_12301,U_12300] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12300),U_12301),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12302),hAPP(c_Nat_OSuc,U_12303))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12300),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12300,tc_Nat_Onat),U_12301),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12302,U_12303))
      | ~ class_Groups_Ocomm__monoid__add(U_12300) ),
    inference(variable_rename,[status(thm)],[f_3284_1]) ).

fof(f_3284_3,plain,
    ! [U_12300,U_12301,U_12302,U_12303] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12300),U_12301),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12302),hAPP(c_Nat_OSuc,U_12303))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12300),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12300,tc_Nat_Onat),U_12301),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12302,U_12303))
      | ~ class_Groups_Ocomm__monoid__add(U_12300) ),
    inference(definitional_conversion,[status(esa)],[f_3284_2]) ).

cnf(f_3284_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12300),U_12301),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12302),hAPP(c_Nat_OSuc,U_12303))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12300),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12300,tc_Nat_Onat),U_12301),c_Nat_OSuc)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12302,U_12303))
    | ~ class_Groups_Ocomm__monoid__add(U_12300) ),
    inference(clausify,[status(thm)],[f_3284_3]) ).

fof(f_3285_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_3285_2,plain,
    ! [U_12308,U_12307,U_12306,U_12305,U_12304] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12304),U_12305),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12306),U_12307),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12308),U_12307))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12304),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12304,tc_Nat_Onat),U_12305),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_12307))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12306,U_12308))
      | ~ class_Groups_Ocomm__monoid__add(U_12304) ),
    inference(variable_rename,[status(thm)],[f_3285_1]) ).

fof(f_3285_3,plain,
    ! [U_12304,U_12305,U_12306,U_12307,U_12308] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12304),U_12305),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12306),U_12307),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12308),U_12307))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12304),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12304,tc_Nat_Onat),U_12305),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_12307))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12306,U_12308))
      | ~ class_Groups_Ocomm__monoid__add(U_12304) ),
    inference(definitional_conversion,[status(esa)],[f_3285_2]) ).

cnf(f_3285_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12304),U_12305),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12306),U_12307),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12308),U_12307))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12304),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12304,tc_Nat_Onat),U_12305),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_12307))),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12306,U_12308))
    | ~ class_Groups_Ocomm__monoid__add(U_12304) ),
    inference(clausify,[status(thm)],[f_3285_3]) ).

fof(f_3286_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_3286_2,plain,
    ! [U_12315,U_12314,U_12313] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12313,tc_Nat_Onat),U_12315),U_12314) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          | ! [U_12312] :
              ( ? [U_12311] :
                  ( hAPP(U_12315,U_12311) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_12312 != U_12311
                  & hBOOL(hAPP(hAPP(c_member(U_12313),U_12311),U_12314)) )
              | hAPP(U_12315,U_12312) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              | ~ hBOOL(hAPP(hAPP(c_member(U_12313),U_12312),U_12314)) ) )
        & ( ? [U_12310] :
              ( ! [U_12309] :
                  ( hAPP(U_12315,U_12309) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  | U_12310 = U_12309
                  | ~ hBOOL(hAPP(hAPP(c_member(U_12313),U_12309),U_12314)) )
              & hAPP(U_12315,U_12310) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              & hBOOL(hAPP(hAPP(c_member(U_12313),U_12310),U_12314)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12313,tc_Nat_Onat),U_12315),U_12314) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12313),U_12314)) ),
    inference(variable_rename,[status(thm)],[f_3286_1]) ).

fof(f_3286_3,plain,
    ! [U_12315,U_12314,U_12313] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12313,tc_Nat_Onat),U_12315),U_12314) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          | ! [U_12312] :
              ( ? [U_12311] :
                  ( hAPP(U_12315,U_12311) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_12312 != U_12311
                  & hBOOL(hAPP(hAPP(c_member(U_12313),U_12311),U_12314)) )
              | hAPP(U_12315,U_12312) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              | ~ hBOOL(hAPP(hAPP(c_member(U_12313),U_12312),U_12314)) ) )
        & ( ( ! [U_12309] :
                ( hAPP(U_12315,U_12309) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK253(U_12315,U_12314,U_12313) = U_12309
                | ~ hBOOL(hAPP(hAPP(c_member(U_12313),U_12309),U_12314)) )
            & hAPP(U_12315,sK253(U_12315,U_12314,U_12313)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            & hBOOL(hAPP(hAPP(c_member(U_12313),sK253(U_12315,U_12314,U_12313)),U_12314)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12313,tc_Nat_Onat),U_12315),U_12314) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12313),U_12314)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK253]),skolemize(U_12310,sK253(U_12315,U_12314,U_12313))],[f_3286_2]) ).

fof(f_3286_4,plain,
    ! [U_12315,U_12314,U_12313] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12313,tc_Nat_Onat),U_12315),U_12314) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
          | ! [U_12312] :
              ( ( hAPP(U_12315,sK254(U_12315,U_12314,U_12313,U_12312)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                & U_12312 != sK254(U_12315,U_12314,U_12313,U_12312)
                & hBOOL(hAPP(hAPP(c_member(U_12313),sK254(U_12315,U_12314,U_12313,U_12312)),U_12314)) )
              | hAPP(U_12315,U_12312) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
              | ~ hBOOL(hAPP(hAPP(c_member(U_12313),U_12312),U_12314)) ) )
        & ( ( ! [U_12309] :
                ( hAPP(U_12315,U_12309) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK253(U_12315,U_12314,U_12313) = U_12309
                | ~ hBOOL(hAPP(hAPP(c_member(U_12313),U_12309),U_12314)) )
            & hAPP(U_12315,sK253(U_12315,U_12314,U_12313)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
            & hBOOL(hAPP(hAPP(c_member(U_12313),sK253(U_12315,U_12314,U_12313)),U_12314)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12313,tc_Nat_Onat),U_12315),U_12314) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12313),U_12314)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK254]),skolemize(U_12311,sK254(U_12315,U_12314,U_12313,U_12312))],[f_3286_3]) ).

fof(f_3286_5,plain,
    ( ! [U_12312,U_12313,U_12314,U_12315] :
        ( hAPP(U_12315,sK254(U_12315,U_12314,U_12313,U_12312)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP890(U_12312,U_12313,U_12314,U_12315) )
    & ! [U_12312,U_12313,U_12314,U_12315] :
        ( U_12312 != sK254(U_12315,U_12314,U_12313,U_12312)
        | ~ sP890(U_12312,U_12313,U_12314,U_12315) )
    & ! [U_12312,U_12313,U_12314,U_12315] :
        ( hBOOL(hAPP(hAPP(c_member(U_12313),sK254(U_12315,U_12314,U_12313,U_12312)),U_12314))
        | ~ sP890(U_12312,U_12313,U_12314,U_12315) )
    & ! [U_12309,U_12313,U_12314,U_12315] :
        ( hAPP(U_12315,U_12309) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sK253(U_12315,U_12314,U_12313) = U_12309
        | ~ hBOOL(hAPP(hAPP(c_member(U_12313),U_12309),U_12314))
        | ~ sP889(U_12309,U_12313,U_12314,U_12315) )
    & ! [U_12309,U_12313,U_12314,U_12315] :
        ( hAPP(U_12315,sK253(U_12315,U_12314,U_12313)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP889(U_12309,U_12313,U_12314,U_12315) )
    & ! [U_12309,U_12313,U_12314,U_12315] :
        ( hBOOL(hAPP(hAPP(c_member(U_12313),sK253(U_12315,U_12314,U_12313)),U_12314))
        | ~ sP889(U_12309,U_12313,U_12314,U_12315) )
    & ! [U_12309,U_12312,U_12313,U_12314,U_12315] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12313,tc_Nat_Onat),U_12315),U_12314) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | sP890(U_12312,U_12313,U_12314,U_12315)
        | hAPP(U_12315,U_12312) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12313),U_12312),U_12314))
        | ~ sP891(U_12309,U_12312,U_12313,U_12314,U_12315) )
    & ! [U_12309,U_12312,U_12313,U_12314,U_12315] :
        ( sP889(U_12309,U_12313,U_12314,U_12315)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12313,tc_Nat_Onat),U_12315),U_12314) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
        | ~ sP891(U_12309,U_12312,U_12313,U_12314,U_12315) )
    & ! [U_12309,U_12312,U_12313,U_12314,U_12315] :
        ( sP891(U_12309,U_12312,U_12313,U_12314,U_12315)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12313),U_12314)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP889,sP890,sP891])],[f_3286_4]) ).

cnf(f_3286_6,plain,
    ( sP891(U_12309,U_12312,U_12313,U_12314,U_12315)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12313),U_12314)) ),
    inference(clausify,[status(thm)],[f_3286_5]) ).

cnf(f_3286_7,plain,
    ( sP889(U_12309,U_12313,U_12314,U_12315)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12313,tc_Nat_Onat),U_12315),U_12314) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP891(U_12309,U_12312,U_12313,U_12314,U_12315) ),
    inference(clausify,[status(thm)],[f_3286_5]) ).

cnf(f_3286_8,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12313,tc_Nat_Onat),U_12315),U_12314) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | sP890(U_12312,U_12313,U_12314,U_12315)
    | hAPP(U_12315,U_12312) != hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12313),U_12312),U_12314))
    | ~ sP891(U_12309,U_12312,U_12313,U_12314,U_12315) ),
    inference(clausify,[status(thm)],[f_3286_5]) ).

cnf(f_3286_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12313),sK253(U_12315,U_12314,U_12313)),U_12314))
    | ~ sP889(U_12309,U_12313,U_12314,U_12315) ),
    inference(clausify,[status(thm)],[f_3286_5]) ).

cnf(f_3286_10,plain,
    ( hAPP(U_12315,sK253(U_12315,U_12314,U_12313)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ sP889(U_12309,U_12313,U_12314,U_12315) ),
    inference(clausify,[status(thm)],[f_3286_5]) ).

cnf(f_3286_11,plain,
    ( hAPP(U_12315,U_12309) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sK253(U_12315,U_12314,U_12313) = U_12309
    | ~ hBOOL(hAPP(hAPP(c_member(U_12313),U_12309),U_12314))
    | ~ sP889(U_12309,U_12313,U_12314,U_12315) ),
    inference(clausify,[status(thm)],[f_3286_5]) ).

cnf(f_3286_12,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12313),sK254(U_12315,U_12314,U_12313,U_12312)),U_12314))
    | ~ sP890(U_12312,U_12313,U_12314,U_12315) ),
    inference(clausify,[status(thm)],[f_3286_5]) ).

cnf(f_3286_13,plain,
    ( U_12312 != sK254(U_12315,U_12314,U_12313,U_12312)
    | ~ sP890(U_12312,U_12313,U_12314,U_12315) ),
    inference(clausify,[status(thm)],[f_3286_5]) ).

cnf(f_3286_14,plain,
    ( hAPP(U_12315,sK254(U_12315,U_12314,U_12313,U_12312)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP890(U_12312,U_12313,U_12314,U_12315) ),
    inference(clausify,[status(thm)],[f_3286_5]) ).

fof(f_3287_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_3287_2,plain,
    ! [U_12322,U_12321,U_12320] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12320,tc_Nat_Onat),U_12322),U_12321) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ! [U_12319] :
              ( ? [U_12318] :
                  ( hAPP(U_12322,U_12318) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_12319 != U_12318
                  & hBOOL(hAPP(hAPP(c_member(U_12320),U_12318),U_12321)) )
              | hAPP(U_12322,U_12319) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_12320),U_12319),U_12321)) ) )
        & ( ? [U_12317] :
              ( ! [U_12316] :
                  ( hAPP(U_12322,U_12316) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  | U_12317 = U_12316
                  | ~ hBOOL(hAPP(hAPP(c_member(U_12320),U_12316),U_12321)) )
              & hAPP(U_12322,U_12317) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
              & hBOOL(hAPP(hAPP(c_member(U_12320),U_12317),U_12321)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12320,tc_Nat_Onat),U_12322),U_12321) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12320),U_12321)) ),
    inference(variable_rename,[status(thm)],[f_3287_1]) ).

fof(f_3287_3,plain,
    ! [U_12322,U_12321,U_12320] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12320,tc_Nat_Onat),U_12322),U_12321) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ! [U_12319] :
              ( ? [U_12318] :
                  ( hAPP(U_12322,U_12318) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                  & U_12319 != U_12318
                  & hBOOL(hAPP(hAPP(c_member(U_12320),U_12318),U_12321)) )
              | hAPP(U_12322,U_12319) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_12320),U_12319),U_12321)) ) )
        & ( ( ! [U_12316] :
                ( hAPP(U_12322,U_12316) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK255(U_12322,U_12321,U_12320) = U_12316
                | ~ hBOOL(hAPP(hAPP(c_member(U_12320),U_12316),U_12321)) )
            & hAPP(U_12322,sK255(U_12322,U_12321,U_12320)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_12320),sK255(U_12322,U_12321,U_12320)),U_12321)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12320,tc_Nat_Onat),U_12322),U_12321) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12320),U_12321)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK255]),skolemize(U_12317,sK255(U_12322,U_12321,U_12320))],[f_3287_2]) ).

fof(f_3287_4,plain,
    ! [U_12322,U_12321,U_12320] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12320,tc_Nat_Onat),U_12322),U_12321) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
          | ! [U_12319] :
              ( ( hAPP(U_12322,sK256(U_12322,U_12321,U_12320,U_12319)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                & U_12319 != sK256(U_12322,U_12321,U_12320,U_12319)
                & hBOOL(hAPP(hAPP(c_member(U_12320),sK256(U_12322,U_12321,U_12320,U_12319)),U_12321)) )
              | hAPP(U_12322,U_12319) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(U_12320),U_12319),U_12321)) ) )
        & ( ( ! [U_12316] :
                ( hAPP(U_12322,U_12316) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
                | sK255(U_12322,U_12321,U_12320) = U_12316
                | ~ hBOOL(hAPP(hAPP(c_member(U_12320),U_12316),U_12321)) )
            & hAPP(U_12322,sK255(U_12322,U_12321,U_12320)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(U_12320),sK255(U_12322,U_12321,U_12320)),U_12321)) )
          | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12320,tc_Nat_Onat),U_12322),U_12321) != c_Groups_Oone__class_Oone(tc_Nat_Onat) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12320),U_12321)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK256]),skolemize(U_12318,sK256(U_12322,U_12321,U_12320,U_12319))],[f_3287_3]) ).

fof(f_3287_5,plain,
    ( ! [U_12320,U_12321,U_12319,U_12322] :
        ( hAPP(U_12322,sK256(U_12322,U_12321,U_12320,U_12319)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP893(U_12320,U_12321,U_12319,U_12322) )
    & ! [U_12320,U_12321,U_12319,U_12322] :
        ( U_12319 != sK256(U_12322,U_12321,U_12320,U_12319)
        | ~ sP893(U_12320,U_12321,U_12319,U_12322) )
    & ! [U_12320,U_12321,U_12319,U_12322] :
        ( hBOOL(hAPP(hAPP(c_member(U_12320),sK256(U_12322,U_12321,U_12320,U_12319)),U_12321))
        | ~ sP893(U_12320,U_12321,U_12319,U_12322) )
    & ! [U_12320,U_12321,U_12316,U_12322] :
        ( hAPP(U_12322,U_12316) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sK255(U_12322,U_12321,U_12320) = U_12316
        | ~ hBOOL(hAPP(hAPP(c_member(U_12320),U_12316),U_12321))
        | ~ sP892(U_12320,U_12321,U_12316,U_12322) )
    & ! [U_12320,U_12321,U_12316,U_12322] :
        ( hAPP(U_12322,sK255(U_12322,U_12321,U_12320)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP892(U_12320,U_12321,U_12316,U_12322) )
    & ! [U_12320,U_12321,U_12316,U_12322] :
        ( hBOOL(hAPP(hAPP(c_member(U_12320),sK255(U_12322,U_12321,U_12320)),U_12321))
        | ~ sP892(U_12320,U_12321,U_12316,U_12322) )
    & ! [U_12320,U_12321,U_12316,U_12319,U_12322] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12320,tc_Nat_Onat),U_12322),U_12321) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | sP893(U_12320,U_12321,U_12319,U_12322)
        | hAPP(U_12322,U_12319) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12320),U_12319),U_12321))
        | ~ sP894(U_12320,U_12321,U_12316,U_12319,U_12322) )
    & ! [U_12320,U_12321,U_12316,U_12319,U_12322] :
        ( sP892(U_12320,U_12321,U_12316,U_12322)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12320,tc_Nat_Onat),U_12322),U_12321) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
        | ~ sP894(U_12320,U_12321,U_12316,U_12319,U_12322) )
    & ! [U_12320,U_12321,U_12316,U_12319,U_12322] :
        ( sP894(U_12320,U_12321,U_12316,U_12319,U_12322)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12320),U_12321)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP892,sP893,sP894])],[f_3287_4]) ).

cnf(f_3287_6,plain,
    ( sP894(U_12320,U_12321,U_12316,U_12319,U_12322)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12320),U_12321)) ),
    inference(clausify,[status(thm)],[f_3287_5]) ).

cnf(f_3287_7,plain,
    ( sP892(U_12320,U_12321,U_12316,U_12322)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12320,tc_Nat_Onat),U_12322),U_12321) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP894(U_12320,U_12321,U_12316,U_12319,U_12322) ),
    inference(clausify,[status(thm)],[f_3287_5]) ).

cnf(f_3287_8,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12320,tc_Nat_Onat),U_12322),U_12321) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | sP893(U_12320,U_12321,U_12319,U_12322)
    | hAPP(U_12322,U_12319) != c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12320),U_12319),U_12321))
    | ~ sP894(U_12320,U_12321,U_12316,U_12319,U_12322) ),
    inference(clausify,[status(thm)],[f_3287_5]) ).

cnf(f_3287_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12320),sK255(U_12322,U_12321,U_12320)),U_12321))
    | ~ sP892(U_12320,U_12321,U_12316,U_12322) ),
    inference(clausify,[status(thm)],[f_3287_5]) ).

cnf(f_3287_10,plain,
    ( hAPP(U_12322,sK255(U_12322,U_12321,U_12320)) = c_Groups_Oone__class_Oone(tc_Nat_Onat)
    | ~ sP892(U_12320,U_12321,U_12316,U_12322) ),
    inference(clausify,[status(thm)],[f_3287_5]) ).

cnf(f_3287_11,plain,
    ( hAPP(U_12322,U_12316) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sK255(U_12322,U_12321,U_12320) = U_12316
    | ~ hBOOL(hAPP(hAPP(c_member(U_12320),U_12316),U_12321))
    | ~ sP892(U_12320,U_12321,U_12316,U_12322) ),
    inference(clausify,[status(thm)],[f_3287_5]) ).

cnf(f_3287_12,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12320),sK256(U_12322,U_12321,U_12320,U_12319)),U_12321))
    | ~ sP893(U_12320,U_12321,U_12319,U_12322) ),
    inference(clausify,[status(thm)],[f_3287_5]) ).

cnf(f_3287_13,plain,
    ( U_12319 != sK256(U_12322,U_12321,U_12320,U_12319)
    | ~ sP893(U_12320,U_12321,U_12319,U_12322) ),
    inference(clausify,[status(thm)],[f_3287_5]) ).

cnf(f_3287_14,plain,
    ( hAPP(U_12322,sK256(U_12322,U_12321,U_12320,U_12319)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP893(U_12320,U_12321,U_12319,U_12322) ),
    inference(clausify,[status(thm)],[f_3287_5]) ).

fof(f_3288_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_3288_2,plain,
    ! [U_12327,U_12326,U_12325,U_12324,U_12323] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12323),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12323),U_12327),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12324),U_12325))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12323),U_12327),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12325),U_12326))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12323),U_12327),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12324),U_12326))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12325),U_12326))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12324),U_12325))
      | ~ class_Groups_Ocomm__monoid__add(U_12323) ),
    inference(variable_rename,[status(thm)],[f_3288_1]) ).

fof(f_3288_3,plain,
    ! [U_12323,U_12327,U_12324,U_12326,U_12325] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12323),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12323),U_12327),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12324),U_12325))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12323),U_12327),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12325),U_12326))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12323),U_12327),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12324),U_12326))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12325),U_12326))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12324),U_12325))
      | ~ class_Groups_Ocomm__monoid__add(U_12323) ),
    inference(definitional_conversion,[status(esa)],[f_3288_2]) ).

cnf(f_3288_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12323),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12323),U_12327),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12324),U_12325))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12323),U_12327),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12325),U_12326))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12323),U_12327),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12324),U_12326))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12325),U_12326))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12324),U_12325))
    | ~ class_Groups_Ocomm__monoid__add(U_12323) ),
    inference(clausify,[status(thm)],[f_3288_3]) ).

fof(f_3289_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_3289_2,plain,
    ! [U_12332,U_12331,U_12330,U_12329,U_12328] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12328),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12328),U_12332),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12329),U_12331))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12328),U_12332),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12329),U_12330))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12328),U_12332),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12330),U_12331))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12330),U_12331))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12329),U_12330))
      | ~ class_Groups_Oab__group__add(U_12328) ),
    inference(variable_rename,[status(thm)],[f_3289_1]) ).

fof(f_3289_3,plain,
    ! [U_12329,U_12330,U_12331,U_12332,U_12328] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12328),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12328),U_12332),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12329),U_12331))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12328),U_12332),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12329),U_12330))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12328),U_12332),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12330),U_12331))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12330),U_12331))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12329),U_12330))
      | ~ class_Groups_Oab__group__add(U_12328) ),
    inference(definitional_conversion,[status(esa)],[f_3289_2]) ).

cnf(f_3289_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12328),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12328),U_12332),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12329),U_12331))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12328),U_12332),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12329),U_12330))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12328),U_12332),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12330),U_12331))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12330),U_12331))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12329),U_12330))
    | ~ class_Groups_Oab__group__add(U_12328) ),
    inference(clausify,[status(thm)],[f_3289_3]) ).

fof(f_3290_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_3290_2,plain,
    ! [U_12334,U_12333] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12333),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12334)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12333),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_12334))
      | hAPP(U_12333,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_3290_1]) ).

fof(f_3290_3,plain,
    ! [U_12334,U_12333] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12333),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12334)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12333),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_12334))
      | hAPP(U_12333,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_3290_2]) ).

cnf(f_3290_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12333),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12334)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12333),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_12334))
    | hAPP(U_12333,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_3290_3]) ).

fof(f_3291_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_3291_2,plain,
    ! [U_12339,U_12338,U_12337,U_12336,U_12335] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12336,U_12335),hAPP(hAPP(c_COMBC(U_12336,U_12335,U_12335),hAPP(hAPP(c_COMBS(U_12336,U_12335,tc_fun(U_12335,U_12335)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12335,tc_fun(U_12335,U_12335)),U_12336),c_If(U_12335)),hAPP(c_fequal,U_12338))),U_12339)),c_Groups_Ozero__class_Ozero(U_12335))),U_12337) = c_Groups_Ozero__class_Ozero(U_12335)
          | hBOOL(hAPP(hAPP(c_member(U_12336),U_12338),U_12337)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12336,U_12335),hAPP(hAPP(c_COMBC(U_12336,U_12335,U_12335),hAPP(hAPP(c_COMBS(U_12336,U_12335,tc_fun(U_12335,U_12335)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12335,tc_fun(U_12335,U_12335)),U_12336),c_If(U_12335)),hAPP(c_fequal,U_12338))),U_12339)),c_Groups_Ozero__class_Ozero(U_12335))),U_12337) = hAPP(U_12339,U_12338)
          | ~ hBOOL(hAPP(hAPP(c_member(U_12336),U_12338),U_12337)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12336),U_12337))
      | ~ class_Groups_Ocomm__monoid__add(U_12335) ),
    inference(variable_rename,[status(thm)],[f_3291_1]) ).

fof(f_3291_3,plain,
    ( ! [U_12335,U_12336,U_12337,U_12338,U_12339] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12336,U_12335),hAPP(hAPP(c_COMBC(U_12336,U_12335,U_12335),hAPP(hAPP(c_COMBS(U_12336,U_12335,tc_fun(U_12335,U_12335)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12335,tc_fun(U_12335,U_12335)),U_12336),c_If(U_12335)),hAPP(c_fequal,U_12338))),U_12339)),c_Groups_Ozero__class_Ozero(U_12335))),U_12337) = c_Groups_Ozero__class_Ozero(U_12335)
        | hBOOL(hAPP(hAPP(c_member(U_12336),U_12338),U_12337))
        | ~ sP895(U_12335,U_12336,U_12337,U_12338,U_12339) )
    & ! [U_12335,U_12336,U_12337,U_12338,U_12339] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12336,U_12335),hAPP(hAPP(c_COMBC(U_12336,U_12335,U_12335),hAPP(hAPP(c_COMBS(U_12336,U_12335,tc_fun(U_12335,U_12335)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12335,tc_fun(U_12335,U_12335)),U_12336),c_If(U_12335)),hAPP(c_fequal,U_12338))),U_12339)),c_Groups_Ozero__class_Ozero(U_12335))),U_12337) = hAPP(U_12339,U_12338)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12336),U_12338),U_12337))
        | ~ sP895(U_12335,U_12336,U_12337,U_12338,U_12339) )
    & ! [U_12335,U_12336,U_12337,U_12338,U_12339] :
        ( sP895(U_12335,U_12336,U_12337,U_12338,U_12339)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12336),U_12337))
        | ~ class_Groups_Ocomm__monoid__add(U_12335) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP895])],[f_3291_2]) ).

cnf(f_3291_4,plain,
    ( sP895(U_12335,U_12336,U_12337,U_12338,U_12339)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12336),U_12337))
    | ~ class_Groups_Ocomm__monoid__add(U_12335) ),
    inference(clausify,[status(thm)],[f_3291_3]) ).

cnf(f_3291_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12336,U_12335),hAPP(hAPP(c_COMBC(U_12336,U_12335,U_12335),hAPP(hAPP(c_COMBS(U_12336,U_12335,tc_fun(U_12335,U_12335)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12335,tc_fun(U_12335,U_12335)),U_12336),c_If(U_12335)),hAPP(c_fequal,U_12338))),U_12339)),c_Groups_Ozero__class_Ozero(U_12335))),U_12337) = hAPP(U_12339,U_12338)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12336),U_12338),U_12337))
    | ~ sP895(U_12335,U_12336,U_12337,U_12338,U_12339) ),
    inference(clausify,[status(thm)],[f_3291_3]) ).

cnf(f_3291_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12336,U_12335),hAPP(hAPP(c_COMBC(U_12336,U_12335,U_12335),hAPP(hAPP(c_COMBS(U_12336,U_12335,tc_fun(U_12335,U_12335)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12335,tc_fun(U_12335,U_12335)),U_12336),c_If(U_12335)),hAPP(c_fequal,U_12338))),U_12339)),c_Groups_Ozero__class_Ozero(U_12335))),U_12337) = c_Groups_Ozero__class_Ozero(U_12335)
    | hBOOL(hAPP(hAPP(c_member(U_12336),U_12338),U_12337))
    | ~ sP895(U_12335,U_12336,U_12337,U_12338,U_12339) ),
    inference(clausify,[status(thm)],[f_3291_3]) ).

fof(f_3292_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_3292_2,plain,
    ! [U_12344,U_12343,U_12342,U_12341,U_12340] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12341,U_12340),hAPP(hAPP(c_COMBC(U_12341,U_12340,U_12340),hAPP(hAPP(c_COMBS(U_12341,U_12340,tc_fun(U_12340,U_12340)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12340,tc_fun(U_12340,U_12340)),U_12341),c_If(U_12340)),hAPP(hAPP(c_COMBC(U_12341,U_12341,tc_HOL_Obool),c_fequal),U_12343))),U_12344)),c_Groups_Ozero__class_Ozero(U_12340))),U_12342) = c_Groups_Ozero__class_Ozero(U_12340)
          | hBOOL(hAPP(hAPP(c_member(U_12341),U_12343),U_12342)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12341,U_12340),hAPP(hAPP(c_COMBC(U_12341,U_12340,U_12340),hAPP(hAPP(c_COMBS(U_12341,U_12340,tc_fun(U_12340,U_12340)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12340,tc_fun(U_12340,U_12340)),U_12341),c_If(U_12340)),hAPP(hAPP(c_COMBC(U_12341,U_12341,tc_HOL_Obool),c_fequal),U_12343))),U_12344)),c_Groups_Ozero__class_Ozero(U_12340))),U_12342) = hAPP(U_12344,U_12343)
          | ~ hBOOL(hAPP(hAPP(c_member(U_12341),U_12343),U_12342)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12341),U_12342))
      | ~ class_Groups_Ocomm__monoid__add(U_12340) ),
    inference(variable_rename,[status(thm)],[f_3292_1]) ).

fof(f_3292_3,plain,
    ( ! [U_12341,U_12340,U_12342,U_12343,U_12344] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12341,U_12340),hAPP(hAPP(c_COMBC(U_12341,U_12340,U_12340),hAPP(hAPP(c_COMBS(U_12341,U_12340,tc_fun(U_12340,U_12340)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12340,tc_fun(U_12340,U_12340)),U_12341),c_If(U_12340)),hAPP(hAPP(c_COMBC(U_12341,U_12341,tc_HOL_Obool),c_fequal),U_12343))),U_12344)),c_Groups_Ozero__class_Ozero(U_12340))),U_12342) = c_Groups_Ozero__class_Ozero(U_12340)
        | hBOOL(hAPP(hAPP(c_member(U_12341),U_12343),U_12342))
        | ~ sP896(U_12341,U_12340,U_12342,U_12343,U_12344) )
    & ! [U_12341,U_12340,U_12342,U_12343,U_12344] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12341,U_12340),hAPP(hAPP(c_COMBC(U_12341,U_12340,U_12340),hAPP(hAPP(c_COMBS(U_12341,U_12340,tc_fun(U_12340,U_12340)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12340,tc_fun(U_12340,U_12340)),U_12341),c_If(U_12340)),hAPP(hAPP(c_COMBC(U_12341,U_12341,tc_HOL_Obool),c_fequal),U_12343))),U_12344)),c_Groups_Ozero__class_Ozero(U_12340))),U_12342) = hAPP(U_12344,U_12343)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12341),U_12343),U_12342))
        | ~ sP896(U_12341,U_12340,U_12342,U_12343,U_12344) )
    & ! [U_12341,U_12340,U_12342,U_12343,U_12344] :
        ( sP896(U_12341,U_12340,U_12342,U_12343,U_12344)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12341),U_12342))
        | ~ class_Groups_Ocomm__monoid__add(U_12340) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP896])],[f_3292_2]) ).

cnf(f_3292_4,plain,
    ( sP896(U_12341,U_12340,U_12342,U_12343,U_12344)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12341),U_12342))
    | ~ class_Groups_Ocomm__monoid__add(U_12340) ),
    inference(clausify,[status(thm)],[f_3292_3]) ).

cnf(f_3292_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12341,U_12340),hAPP(hAPP(c_COMBC(U_12341,U_12340,U_12340),hAPP(hAPP(c_COMBS(U_12341,U_12340,tc_fun(U_12340,U_12340)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12340,tc_fun(U_12340,U_12340)),U_12341),c_If(U_12340)),hAPP(hAPP(c_COMBC(U_12341,U_12341,tc_HOL_Obool),c_fequal),U_12343))),U_12344)),c_Groups_Ozero__class_Ozero(U_12340))),U_12342) = hAPP(U_12344,U_12343)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12341),U_12343),U_12342))
    | ~ sP896(U_12341,U_12340,U_12342,U_12343,U_12344) ),
    inference(clausify,[status(thm)],[f_3292_3]) ).

cnf(f_3292_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12341,U_12340),hAPP(hAPP(c_COMBC(U_12341,U_12340,U_12340),hAPP(hAPP(c_COMBS(U_12341,U_12340,tc_fun(U_12340,U_12340)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12340,tc_fun(U_12340,U_12340)),U_12341),c_If(U_12340)),hAPP(hAPP(c_COMBC(U_12341,U_12341,tc_HOL_Obool),c_fequal),U_12343))),U_12344)),c_Groups_Ozero__class_Ozero(U_12340))),U_12342) = c_Groups_Ozero__class_Ozero(U_12340)
    | hBOOL(hAPP(hAPP(c_member(U_12341),U_12343),U_12342))
    | ~ sP896(U_12341,U_12340,U_12342,U_12343,U_12344) ),
    inference(clausify,[status(thm)],[f_3292_3]) ).

fof(f_3293_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_3293_2,plain,
    ! [U_12351,U_12350,U_12349,U_12348,U_12347,U_12346,U_12345] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12346,U_12345),hAPP(hAPP(c_COMBS(U_12346,tc_fun(U_12348,tc_HOL_Obool),U_12345),hAPP(hAPP(c_COMBB(tc_fun(U_12348,U_12345),tc_fun(tc_fun(U_12348,tc_HOL_Obool),U_12345),U_12346),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12348,U_12345)),U_12350)),hAPP(hAPP(c_COMBB(tc_fun(U_12348,tc_HOL_Obool),tc_fun(U_12348,tc_HOL_Obool),U_12346),c_Set_OCollect(U_12348)),hAPP(hAPP(c_COMBB(tc_fun(U_12348,tc_HOL_Obool),tc_fun(U_12348,tc_HOL_Obool),U_12346),hAPP(c_COMBS(U_12348,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12348),c_fconj),hAPP(hAPP(c_COMBC(U_12348,tc_fun(U_12348,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12348)),U_12349)))),U_12351)))),U_12347) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12348,U_12345),hAPP(hAPP(c_COMBS(U_12348,tc_fun(U_12346,tc_HOL_Obool),U_12345),hAPP(hAPP(c_COMBB(tc_fun(U_12346,U_12345),tc_fun(tc_fun(U_12346,tc_HOL_Obool),U_12345),U_12348),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12346,U_12345)),hAPP(c_COMBC(U_12346,U_12348,U_12345),U_12350))),hAPP(hAPP(c_COMBB(tc_fun(U_12346,tc_HOL_Obool),tc_fun(U_12346,tc_HOL_Obool),U_12348),c_Set_OCollect(U_12346)),hAPP(hAPP(c_COMBB(tc_fun(U_12346,tc_HOL_Obool),tc_fun(U_12346,tc_HOL_Obool),U_12348),hAPP(c_COMBS(U_12346,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12346),c_fconj),hAPP(hAPP(c_COMBC(U_12346,tc_fun(U_12346,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12346)),U_12347)))),hAPP(c_COMBC(U_12346,U_12348,tc_HOL_Obool),U_12351))))),U_12349)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12348),U_12349))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12346),U_12347))
      | ~ class_Groups_Ocomm__monoid__add(U_12345) ),
    inference(variable_rename,[status(thm)],[f_3293_1]) ).

fof(f_3293_3,plain,
    ! [U_12346,U_12345,U_12347,U_12348,U_12349,U_12350,U_12351] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12346,U_12345),hAPP(hAPP(c_COMBS(U_12346,tc_fun(U_12348,tc_HOL_Obool),U_12345),hAPP(hAPP(c_COMBB(tc_fun(U_12348,U_12345),tc_fun(tc_fun(U_12348,tc_HOL_Obool),U_12345),U_12346),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12348,U_12345)),U_12350)),hAPP(hAPP(c_COMBB(tc_fun(U_12348,tc_HOL_Obool),tc_fun(U_12348,tc_HOL_Obool),U_12346),c_Set_OCollect(U_12348)),hAPP(hAPP(c_COMBB(tc_fun(U_12348,tc_HOL_Obool),tc_fun(U_12348,tc_HOL_Obool),U_12346),hAPP(c_COMBS(U_12348,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12348),c_fconj),hAPP(hAPP(c_COMBC(U_12348,tc_fun(U_12348,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12348)),U_12349)))),U_12351)))),U_12347) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12348,U_12345),hAPP(hAPP(c_COMBS(U_12348,tc_fun(U_12346,tc_HOL_Obool),U_12345),hAPP(hAPP(c_COMBB(tc_fun(U_12346,U_12345),tc_fun(tc_fun(U_12346,tc_HOL_Obool),U_12345),U_12348),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12346,U_12345)),hAPP(c_COMBC(U_12346,U_12348,U_12345),U_12350))),hAPP(hAPP(c_COMBB(tc_fun(U_12346,tc_HOL_Obool),tc_fun(U_12346,tc_HOL_Obool),U_12348),c_Set_OCollect(U_12346)),hAPP(hAPP(c_COMBB(tc_fun(U_12346,tc_HOL_Obool),tc_fun(U_12346,tc_HOL_Obool),U_12348),hAPP(c_COMBS(U_12346,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12346),c_fconj),hAPP(hAPP(c_COMBC(U_12346,tc_fun(U_12346,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12346)),U_12347)))),hAPP(c_COMBC(U_12346,U_12348,tc_HOL_Obool),U_12351))))),U_12349)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12348),U_12349))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12346),U_12347))
      | ~ class_Groups_Ocomm__monoid__add(U_12345) ),
    inference(definitional_conversion,[status(esa)],[f_3293_2]) ).

cnf(f_3293_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12346,U_12345),hAPP(hAPP(c_COMBS(U_12346,tc_fun(U_12348,tc_HOL_Obool),U_12345),hAPP(hAPP(c_COMBB(tc_fun(U_12348,U_12345),tc_fun(tc_fun(U_12348,tc_HOL_Obool),U_12345),U_12346),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12348,U_12345)),U_12350)),hAPP(hAPP(c_COMBB(tc_fun(U_12348,tc_HOL_Obool),tc_fun(U_12348,tc_HOL_Obool),U_12346),c_Set_OCollect(U_12348)),hAPP(hAPP(c_COMBB(tc_fun(U_12348,tc_HOL_Obool),tc_fun(U_12348,tc_HOL_Obool),U_12346),hAPP(c_COMBS(U_12348,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12348),c_fconj),hAPP(hAPP(c_COMBC(U_12348,tc_fun(U_12348,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12348)),U_12349)))),U_12351)))),U_12347) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12348,U_12345),hAPP(hAPP(c_COMBS(U_12348,tc_fun(U_12346,tc_HOL_Obool),U_12345),hAPP(hAPP(c_COMBB(tc_fun(U_12346,U_12345),tc_fun(tc_fun(U_12346,tc_HOL_Obool),U_12345),U_12348),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12346,U_12345)),hAPP(c_COMBC(U_12346,U_12348,U_12345),U_12350))),hAPP(hAPP(c_COMBB(tc_fun(U_12346,tc_HOL_Obool),tc_fun(U_12346,tc_HOL_Obool),U_12348),c_Set_OCollect(U_12346)),hAPP(hAPP(c_COMBB(tc_fun(U_12346,tc_HOL_Obool),tc_fun(U_12346,tc_HOL_Obool),U_12348),hAPP(c_COMBS(U_12346,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12346),c_fconj),hAPP(hAPP(c_COMBC(U_12346,tc_fun(U_12346,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12346)),U_12347)))),hAPP(c_COMBC(U_12346,U_12348,tc_HOL_Obool),U_12351))))),U_12349)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12348),U_12349))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12346),U_12347))
    | ~ class_Groups_Ocomm__monoid__add(U_12345) ),
    inference(clausify,[status(thm)],[f_3293_3]) ).

fof(f_3294_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_3294_2,plain,
    ! [U_12355,U_12354,U_12353,U_12352] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12353,U_12352),hAPP(c_COMBK(U_12352,U_12353),U_12354)),U_12355) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12352),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12352),hAPP(c_Finite__Set_Ocard(U_12353),U_12355))),U_12354)
      | ~ class_Rings_Osemiring__1(U_12352) ),
    inference(variable_rename,[status(thm)],[f_3294_1]) ).

fof(f_3294_3,plain,
    ! [U_12353,U_12352,U_12354,U_12355] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12353,U_12352),hAPP(c_COMBK(U_12352,U_12353),U_12354)),U_12355) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12352),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12352),hAPP(c_Finite__Set_Ocard(U_12353),U_12355))),U_12354)
      | ~ class_Rings_Osemiring__1(U_12352) ),
    inference(definitional_conversion,[status(esa)],[f_3294_2]) ).

cnf(f_3294_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12353,U_12352),hAPP(c_COMBK(U_12352,U_12353),U_12354)),U_12355) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12352),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12352),hAPP(c_Finite__Set_Ocard(U_12353),U_12355))),U_12354)
    | ~ class_Rings_Osemiring__1(U_12352) ),
    inference(clausify,[status(thm)],[f_3294_3]) ).

fof(f_3295_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_3295_2,plain,
    ! [U_12358,U_12357,U_12356] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12356),U_12357),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12358))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12356),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12356),U_12357),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12358))),hAPP(U_12357,U_12358))
      | ~ class_Groups_Ocomm__monoid__add(U_12356) ),
    inference(variable_rename,[status(thm)],[f_3295_1]) ).

fof(f_3295_3,plain,
    ! [U_12356,U_12357,U_12358] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12356),U_12357),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12358))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12356),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12356),U_12357),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12358))),hAPP(U_12357,U_12358))
      | ~ class_Groups_Ocomm__monoid__add(U_12356) ),
    inference(definitional_conversion,[status(esa)],[f_3295_2]) ).

cnf(f_3295_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12356),U_12357),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12358))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12356),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12356),U_12357),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12358))),hAPP(U_12357,U_12358))
    | ~ class_Groups_Ocomm__monoid__add(U_12356) ),
    inference(clausify,[status(thm)],[f_3295_3]) ).

fof(f_3296_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_3296_2,plain,
    ! [U_12361,U_12360,U_12359] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12359),U_12360),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12361))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12359),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12359),U_12360),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12361))),hAPP(U_12360,hAPP(c_Nat_OSuc,U_12361)))
      | ~ class_Groups_Ocomm__monoid__add(U_12359) ),
    inference(variable_rename,[status(thm)],[f_3296_1]) ).

fof(f_3296_3,plain,
    ! [U_12359,U_12360,U_12361] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12359),U_12360),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12361))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12359),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12359),U_12360),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12361))),hAPP(U_12360,hAPP(c_Nat_OSuc,U_12361)))
      | ~ class_Groups_Ocomm__monoid__add(U_12359) ),
    inference(definitional_conversion,[status(esa)],[f_3296_2]) ).

cnf(f_3296_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12359),U_12360),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12361))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12359),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12359),U_12360),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_12361))),hAPP(U_12360,hAPP(c_Nat_OSuc,U_12361)))
    | ~ class_Groups_Ocomm__monoid__add(U_12359) ),
    inference(clausify,[status(thm)],[f_3296_3]) ).

fof(f_3297_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_3297_2,plain,
    ! [U_12366,U_12365,U_12364,U_12363,U_12362] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12363,U_12362),U_12366),hAPP(hAPP(c_Set_Oinsert(U_12363),U_12365),U_12364)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12362),hAPP(U_12366,U_12365)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12363,U_12362),U_12366),U_12364))
      | hBOOL(hAPP(hAPP(c_member(U_12363),U_12365),U_12364))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12363),U_12364))
      | ~ class_Groups_Ocomm__monoid__add(U_12362) ),
    inference(variable_rename,[status(thm)],[f_3297_1]) ).

fof(f_3297_3,plain,
    ! [U_12362,U_12363,U_12364,U_12365,U_12366] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12363,U_12362),U_12366),hAPP(hAPP(c_Set_Oinsert(U_12363),U_12365),U_12364)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12362),hAPP(U_12366,U_12365)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12363,U_12362),U_12366),U_12364))
      | hBOOL(hAPP(hAPP(c_member(U_12363),U_12365),U_12364))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12363),U_12364))
      | ~ class_Groups_Ocomm__monoid__add(U_12362) ),
    inference(definitional_conversion,[status(esa)],[f_3297_2]) ).

cnf(f_3297_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12363,U_12362),U_12366),hAPP(hAPP(c_Set_Oinsert(U_12363),U_12365),U_12364)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12362),hAPP(U_12366,U_12365)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12363,U_12362),U_12366),U_12364))
    | hBOOL(hAPP(hAPP(c_member(U_12363),U_12365),U_12364))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12363),U_12364))
    | ~ class_Groups_Ocomm__monoid__add(U_12362) ),
    inference(clausify,[status(thm)],[f_3297_3]) ).

fof(f_3298_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_3298_2,plain,
    ! [U_12371,U_12370,U_12369,U_12368,U_12367] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12368,U_12367),U_12371),hAPP(hAPP(c_Set_Oinsert(U_12368),U_12370),U_12369)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12367),hAPP(U_12371,U_12370)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12368,U_12367),U_12371),U_12369))
      | hBOOL(hAPP(hAPP(c_member(U_12368),U_12370),U_12369))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12368),U_12369))
      | ~ class_Groups_Ocomm__monoid__add(U_12367) ),
    inference(variable_rename,[status(thm)],[f_3298_1]) ).

fof(f_3298_3,plain,
    ! [U_12367,U_12368,U_12369,U_12370,U_12371] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12368,U_12367),U_12371),hAPP(hAPP(c_Set_Oinsert(U_12368),U_12370),U_12369)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12367),hAPP(U_12371,U_12370)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12368,U_12367),U_12371),U_12369))
      | hBOOL(hAPP(hAPP(c_member(U_12368),U_12370),U_12369))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12368),U_12369))
      | ~ class_Groups_Ocomm__monoid__add(U_12367) ),
    inference(definitional_conversion,[status(esa)],[f_3298_2]) ).

cnf(f_3298_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12368,U_12367),U_12371),hAPP(hAPP(c_Set_Oinsert(U_12368),U_12370),U_12369)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12367),hAPP(U_12371,U_12370)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12368,U_12367),U_12371),U_12369))
    | hBOOL(hAPP(hAPP(c_member(U_12368),U_12370),U_12369))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12368),U_12369))
    | ~ class_Groups_Ocomm__monoid__add(U_12367) ),
    inference(clausify,[status(thm)],[f_3298_3]) ).

fof(f_3299_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_3299_2,plain,
    ! [U_12376,U_12375,U_12374,U_12373,U_12372] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12372),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12373,U_12372),U_12376),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12373,tc_HOL_Obool)),U_12374),U_12375))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12373,U_12372),U_12376),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12373,tc_HOL_Obool)),U_12374),U_12375))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12372),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12373,U_12372),U_12376),U_12374)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12373,U_12372),U_12376),U_12375))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12373),U_12375))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12373),U_12374))
      | ~ class_Groups_Ocomm__monoid__add(U_12372) ),
    inference(variable_rename,[status(thm)],[f_3299_1]) ).

fof(f_3299_3,plain,
    ! [U_12372,U_12373,U_12374,U_12375,U_12376] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12372),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12373,U_12372),U_12376),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12373,tc_HOL_Obool)),U_12374),U_12375))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12373,U_12372),U_12376),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12373,tc_HOL_Obool)),U_12374),U_12375))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12372),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12373,U_12372),U_12376),U_12374)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12373,U_12372),U_12376),U_12375))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12373),U_12375))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12373),U_12374))
      | ~ class_Groups_Ocomm__monoid__add(U_12372) ),
    inference(definitional_conversion,[status(esa)],[f_3299_2]) ).

cnf(f_3299_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12372),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12373,U_12372),U_12376),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12373,tc_HOL_Obool)),U_12374),U_12375))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12373,U_12372),U_12376),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12373,tc_HOL_Obool)),U_12374),U_12375))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12372),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12373,U_12372),U_12376),U_12374)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12373,U_12372),U_12376),U_12375))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12373),U_12375))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12373),U_12374))
    | ~ class_Groups_Ocomm__monoid__add(U_12372) ),
    inference(clausify,[status(thm)],[f_3299_3]) ).

fof(f_3300_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_3300_2,plain,
    ! [U_12381,U_12380,U_12379,U_12378,U_12377] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12378,U_12377),U_12381),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12378,tc_HOL_Obool)),U_12379),U_12380)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12377),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12378,U_12377),U_12381),U_12379)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12378,U_12377),U_12381),U_12380))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12378,tc_HOL_Obool)),U_12380),U_12379))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12378),U_12379))
      | ~ class_Groups_Oab__group__add(U_12377) ),
    inference(variable_rename,[status(thm)],[f_3300_1]) ).

fof(f_3300_3,plain,
    ! [U_12377,U_12378,U_12379,U_12380,U_12381] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12378,U_12377),U_12381),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12378,tc_HOL_Obool)),U_12379),U_12380)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12377),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12378,U_12377),U_12381),U_12379)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12378,U_12377),U_12381),U_12380))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12378,tc_HOL_Obool)),U_12380),U_12379))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12378),U_12379))
      | ~ class_Groups_Oab__group__add(U_12377) ),
    inference(definitional_conversion,[status(esa)],[f_3300_2]) ).

cnf(f_3300_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12378,U_12377),U_12381),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12378,tc_HOL_Obool)),U_12379),U_12380)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12377),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12378,U_12377),U_12381),U_12379)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12378,U_12377),U_12381),U_12380))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12378,tc_HOL_Obool)),U_12380),U_12379))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12378),U_12379))
    | ~ class_Groups_Oab__group__add(U_12377) ),
    inference(clausify,[status(thm)],[f_3300_3]) ).

fof(f_3301_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_3301_2,plain,
    ! [U_12385,U_12384,U_12383,U_12382] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12383,U_12382),U_12385),U_12384) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12382,U_12383,c_Groups_Oplus__class_Oplus(U_12382)),U_12385),c_Groups_Ozero__class_Ozero(U_12382)),U_12384)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12383),U_12384))
      | ~ class_Groups_Ocomm__monoid__add(U_12382) ),
    inference(variable_rename,[status(thm)],[f_3301_1]) ).

fof(f_3301_3,plain,
    ! [U_12382,U_12383,U_12384,U_12385] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12383,U_12382),U_12385),U_12384) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12382,U_12383,c_Groups_Oplus__class_Oplus(U_12382)),U_12385),c_Groups_Ozero__class_Ozero(U_12382)),U_12384)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12383),U_12384))
      | ~ class_Groups_Ocomm__monoid__add(U_12382) ),
    inference(definitional_conversion,[status(esa)],[f_3301_2]) ).

cnf(f_3301_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12383,U_12382),U_12385),U_12384) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12382,U_12383,c_Groups_Oplus__class_Oplus(U_12382)),U_12385),c_Groups_Ozero__class_Ozero(U_12382)),U_12384)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12383),U_12384))
    | ~ class_Groups_Ocomm__monoid__add(U_12382) ),
    inference(clausify,[status(thm)],[f_3301_3]) ).

fof(f_3302_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_3302_2,plain,
    ! [U_12389,U_12388,U_12387,U_12386] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12387,U_12386),U_12389),U_12388) = c_Groups_Ozero__class_Ozero(U_12386)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12387),U_12388)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12387,U_12386),U_12389),U_12388) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12386,U_12387,c_Groups_Oplus__class_Oplus(U_12386)),U_12389),c_Groups_Ozero__class_Ozero(U_12386)),U_12388)
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12387),U_12388)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_12386) ),
    inference(variable_rename,[status(thm)],[f_3302_1]) ).

fof(f_3302_3,plain,
    ( ! [U_12386,U_12387,U_12388,U_12389] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12387,U_12386),U_12389),U_12388) = c_Groups_Ozero__class_Ozero(U_12386)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12387),U_12388))
        | ~ sP897(U_12386,U_12387,U_12388,U_12389) )
    & ! [U_12386,U_12387,U_12388,U_12389] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12387,U_12386),U_12389),U_12388) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12386,U_12387,c_Groups_Oplus__class_Oplus(U_12386)),U_12389),c_Groups_Ozero__class_Ozero(U_12386)),U_12388)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12387),U_12388))
        | ~ sP897(U_12386,U_12387,U_12388,U_12389) )
    & ! [U_12386,U_12387,U_12388,U_12389] :
        ( sP897(U_12386,U_12387,U_12388,U_12389)
        | ~ class_Groups_Ocomm__monoid__add(U_12386) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP897])],[f_3302_2]) ).

cnf(f_3302_4,plain,
    ( sP897(U_12386,U_12387,U_12388,U_12389)
    | ~ class_Groups_Ocomm__monoid__add(U_12386) ),
    inference(clausify,[status(thm)],[f_3302_3]) ).

cnf(f_3302_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12387,U_12386),U_12389),U_12388) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_12386,U_12387,c_Groups_Oplus__class_Oplus(U_12386)),U_12389),c_Groups_Ozero__class_Ozero(U_12386)),U_12388)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12387),U_12388))
    | ~ sP897(U_12386,U_12387,U_12388,U_12389) ),
    inference(clausify,[status(thm)],[f_3302_3]) ).

cnf(f_3302_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12387,U_12386),U_12389),U_12388) = c_Groups_Ozero__class_Ozero(U_12386)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_12387),U_12388))
    | ~ sP897(U_12386,U_12387,U_12388,U_12389) ),
    inference(clausify,[status(thm)],[f_3302_3]) ).

fof(f_3303_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_3303_2,plain,
    ! [U_12393,U_12392,U_12391,U_12390] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12390,tc_Nat_Onat),U_12393),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12390,tc_HOL_Obool)),U_12392),U_12391)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12390,tc_Nat_Onat),U_12393),U_12392)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12390,tc_Nat_Onat),U_12393),U_12391))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12390,tc_HOL_Obool)),U_12391),U_12392))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12390),U_12391)) ),
    inference(variable_rename,[status(thm)],[f_3303_1]) ).

fof(f_3303_3,plain,
    ! [U_12391,U_12390,U_12392,U_12393] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12390,tc_Nat_Onat),U_12393),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12390,tc_HOL_Obool)),U_12392),U_12391)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12390,tc_Nat_Onat),U_12393),U_12392)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12390,tc_Nat_Onat),U_12393),U_12391))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12390,tc_HOL_Obool)),U_12391),U_12392))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12390),U_12391)) ),
    inference(definitional_conversion,[status(esa)],[f_3303_2]) ).

cnf(f_3303_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12390,tc_Nat_Onat),U_12393),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12390,tc_HOL_Obool)),U_12392),U_12391)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12390,tc_Nat_Onat),U_12393),U_12392)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12390,tc_Nat_Onat),U_12393),U_12391))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12390,tc_HOL_Obool)),U_12391),U_12392))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12390),U_12391)) ),
    inference(clausify,[status(thm)],[f_3303_3]) ).

fof(f_3304_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_3304_2,plain,
    ! [U_12396,U_12395,U_12394] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12394),U_12395),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_12396)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12394),U_12395),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12396))
      | hAPP(U_12395,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_12394)
      | ~ class_Groups_Ocomm__monoid__add(U_12394) ),
    inference(variable_rename,[status(thm)],[f_3304_1]) ).

fof(f_3304_3,plain,
    ! [U_12395,U_12394,U_12396] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12394),U_12395),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_12396)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12394),U_12395),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12396))
      | hAPP(U_12395,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_12394)
      | ~ class_Groups_Ocomm__monoid__add(U_12394) ),
    inference(definitional_conversion,[status(esa)],[f_3304_2]) ).

cnf(f_3304_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12394),U_12395),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_12396)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12394),U_12395),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12396))
    | hAPP(U_12395,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) != c_Groups_Ozero__class_Ozero(U_12394)
    | ~ class_Groups_Ocomm__monoid__add(U_12394) ),
    inference(clausify,[status(thm)],[f_3304_3]) ).

fof(f_3305_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_3305_2,plain,
    ! [U_12400,U_12399,U_12398,U_12397] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12397),U_12400),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12398),U_12399)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12397),hAPP(U_12400,U_12398)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12397),U_12400),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12398)),U_12399)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12398),U_12399))
      | ~ class_Groups_Ocomm__monoid__add(U_12397) ),
    inference(variable_rename,[status(thm)],[f_3305_1]) ).

fof(f_3305_3,plain,
    ! [U_12398,U_12397,U_12399,U_12400] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12397),U_12400),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12398),U_12399)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12397),hAPP(U_12400,U_12398)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12397),U_12400),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12398)),U_12399)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12398),U_12399))
      | ~ class_Groups_Ocomm__monoid__add(U_12397) ),
    inference(definitional_conversion,[status(esa)],[f_3305_2]) ).

cnf(f_3305_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12397),U_12400),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12398),U_12399)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12397),hAPP(U_12400,U_12398)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12397),U_12400),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12398)),U_12399)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12398),U_12399))
    | ~ class_Groups_Ocomm__monoid__add(U_12397) ),
    inference(clausify,[status(thm)],[f_3305_3]) ).

fof(f_3306_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_3306_2,plain,
    ! [U_12404,U_12403,U_12402,U_12401] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12401),U_12404),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12402,U_12403)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12401),hAPP(U_12404,U_12402)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12401),U_12404),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12402),U_12403)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12402),U_12403))
      | ~ class_Groups_Ocomm__monoid__add(U_12401) ),
    inference(variable_rename,[status(thm)],[f_3306_1]) ).

fof(f_3306_3,plain,
    ! [U_12402,U_12401,U_12403,U_12404] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12401),U_12404),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12402,U_12403)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12401),hAPP(U_12404,U_12402)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12401),U_12404),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12402),U_12403)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12402),U_12403))
      | ~ class_Groups_Ocomm__monoid__add(U_12401) ),
    inference(definitional_conversion,[status(esa)],[f_3306_2]) ).

cnf(f_3306_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12401),U_12404),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12402,U_12403)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12401),hAPP(U_12404,U_12402)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12401),U_12404),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(c_Nat_OSuc,U_12402),U_12403)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12402),U_12403))
    | ~ class_Groups_Ocomm__monoid__add(U_12401) ),
    inference(clausify,[status(thm)],[f_3306_3]) ).

fof(f_3307_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_3307_2,plain,
    ! [U_12409,U_12408,U_12407,U_12406,U_12405] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12406,U_12405),U_12408),hAPP(c_Set_OCollect(U_12406),hAPP(hAPP(c_COMBS(U_12406,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12406),c_fconj),hAPP(hAPP(c_COMBC(U_12406,tc_fun(U_12406,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12406)),U_12407))),hAPP(hAPP(c_COMBC(U_12406,tc_fun(U_12406,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12406)),U_12409)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12406,U_12405),hAPP(hAPP(c_COMBC(U_12406,U_12405,U_12405),hAPP(hAPP(c_COMBS(U_12406,U_12405,tc_fun(U_12405,U_12405)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12405,tc_fun(U_12405,U_12405)),U_12406),c_If(U_12405)),hAPP(hAPP(c_COMBC(U_12406,tc_fun(U_12406,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12406)),U_12409))),U_12408)),c_Groups_Ozero__class_Ozero(U_12405))),U_12407)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12406),U_12407))
      | ~ class_Groups_Ocomm__monoid__add(U_12405) ),
    inference(variable_rename,[status(thm)],[f_3307_1]) ).

fof(f_3307_3,plain,
    ! [U_12405,U_12406,U_12407,U_12408,U_12409] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12406,U_12405),U_12408),hAPP(c_Set_OCollect(U_12406),hAPP(hAPP(c_COMBS(U_12406,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12406),c_fconj),hAPP(hAPP(c_COMBC(U_12406,tc_fun(U_12406,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12406)),U_12407))),hAPP(hAPP(c_COMBC(U_12406,tc_fun(U_12406,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12406)),U_12409)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12406,U_12405),hAPP(hAPP(c_COMBC(U_12406,U_12405,U_12405),hAPP(hAPP(c_COMBS(U_12406,U_12405,tc_fun(U_12405,U_12405)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12405,tc_fun(U_12405,U_12405)),U_12406),c_If(U_12405)),hAPP(hAPP(c_COMBC(U_12406,tc_fun(U_12406,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12406)),U_12409))),U_12408)),c_Groups_Ozero__class_Ozero(U_12405))),U_12407)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12406),U_12407))
      | ~ class_Groups_Ocomm__monoid__add(U_12405) ),
    inference(definitional_conversion,[status(esa)],[f_3307_2]) ).

cnf(f_3307_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12406,U_12405),U_12408),hAPP(c_Set_OCollect(U_12406),hAPP(hAPP(c_COMBS(U_12406,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12406),c_fconj),hAPP(hAPP(c_COMBC(U_12406,tc_fun(U_12406,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12406)),U_12407))),hAPP(hAPP(c_COMBC(U_12406,tc_fun(U_12406,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12406)),U_12409)))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12406,U_12405),hAPP(hAPP(c_COMBC(U_12406,U_12405,U_12405),hAPP(hAPP(c_COMBS(U_12406,U_12405,tc_fun(U_12405,U_12405)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12405,tc_fun(U_12405,U_12405)),U_12406),c_If(U_12405)),hAPP(hAPP(c_COMBC(U_12406,tc_fun(U_12406,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12406)),U_12409))),U_12408)),c_Groups_Ozero__class_Ozero(U_12405))),U_12407)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12406),U_12407))
    | ~ class_Groups_Ocomm__monoid__add(U_12405) ),
    inference(clausify,[status(thm)],[f_3307_3]) ).

fof(f_3308_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_3308_2,plain,
    ! [U_12414,U_12413,U_12412,U_12411,U_12410] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12411,U_12410),U_12413),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12411,tc_HOL_Obool)),U_12412),U_12414)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12411,U_12410),hAPP(hAPP(c_COMBC(U_12411,U_12410,U_12410),hAPP(hAPP(c_COMBS(U_12411,U_12410,tc_fun(U_12410,U_12410)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12410,tc_fun(U_12410,U_12410)),U_12411),c_If(U_12410)),hAPP(hAPP(c_COMBC(U_12411,tc_fun(U_12411,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12411)),U_12414))),U_12413)),c_Groups_Ozero__class_Ozero(U_12410))),U_12412)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12411),U_12412))
      | ~ class_Groups_Ocomm__monoid__add(U_12410) ),
    inference(variable_rename,[status(thm)],[f_3308_1]) ).

fof(f_3308_3,plain,
    ! [U_12411,U_12410,U_12412,U_12413,U_12414] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12411,U_12410),U_12413),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12411,tc_HOL_Obool)),U_12412),U_12414)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12411,U_12410),hAPP(hAPP(c_COMBC(U_12411,U_12410,U_12410),hAPP(hAPP(c_COMBS(U_12411,U_12410,tc_fun(U_12410,U_12410)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12410,tc_fun(U_12410,U_12410)),U_12411),c_If(U_12410)),hAPP(hAPP(c_COMBC(U_12411,tc_fun(U_12411,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12411)),U_12414))),U_12413)),c_Groups_Ozero__class_Ozero(U_12410))),U_12412)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12411),U_12412))
      | ~ class_Groups_Ocomm__monoid__add(U_12410) ),
    inference(definitional_conversion,[status(esa)],[f_3308_2]) ).

cnf(f_3308_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12411,U_12410),U_12413),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12411,tc_HOL_Obool)),U_12412),U_12414)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12411,U_12410),hAPP(hAPP(c_COMBC(U_12411,U_12410,U_12410),hAPP(hAPP(c_COMBS(U_12411,U_12410,tc_fun(U_12410,U_12410)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12410,tc_fun(U_12410,U_12410)),U_12411),c_If(U_12410)),hAPP(hAPP(c_COMBC(U_12411,tc_fun(U_12411,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12411)),U_12414))),U_12413)),c_Groups_Ozero__class_Ozero(U_12410))),U_12412)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12411),U_12412))
    | ~ class_Groups_Ocomm__monoid__add(U_12410) ),
    inference(clausify,[status(thm)],[f_3308_3]) ).

fof(f_3309_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_3309_2,plain,
    ! [U_12420,U_12419,U_12418,U_12417,U_12416,U_12415] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12416,U_12415),U_12418),U_12417) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12419,U_12415),hAPP(hAPP(c_COMBB(tc_fun(U_12416,tc_HOL_Obool),U_12415,U_12419),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12416,U_12415),U_12418)),hAPP(hAPP(c_COMBB(tc_fun(U_12416,tc_HOL_Obool),tc_fun(U_12416,tc_HOL_Obool),U_12419),c_Set_OCollect(U_12416)),hAPP(hAPP(c_COMBB(tc_fun(U_12416,tc_HOL_Obool),tc_fun(U_12416,tc_HOL_Obool),U_12419),hAPP(c_COMBS(U_12416,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12416),c_fconj),hAPP(hAPP(c_COMBC(U_12416,tc_fun(U_12416,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12416)),U_12417)))),hAPP(c_COMBC(U_12416,U_12419,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12419,tc_fun(U_12419,tc_HOL_Obool),U_12416),c_fequal),U_12420)))))),hAPP(c_Set_Oimage(U_12416,U_12419,U_12420),U_12417))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12416),U_12417))
      | ~ class_Groups_Ocomm__monoid__add(U_12415) ),
    inference(variable_rename,[status(thm)],[f_3309_1]) ).

fof(f_3309_3,plain,
    ! [U_12416,U_12415,U_12417,U_12418,U_12419,U_12420] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12416,U_12415),U_12418),U_12417) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12419,U_12415),hAPP(hAPP(c_COMBB(tc_fun(U_12416,tc_HOL_Obool),U_12415,U_12419),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12416,U_12415),U_12418)),hAPP(hAPP(c_COMBB(tc_fun(U_12416,tc_HOL_Obool),tc_fun(U_12416,tc_HOL_Obool),U_12419),c_Set_OCollect(U_12416)),hAPP(hAPP(c_COMBB(tc_fun(U_12416,tc_HOL_Obool),tc_fun(U_12416,tc_HOL_Obool),U_12419),hAPP(c_COMBS(U_12416,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12416),c_fconj),hAPP(hAPP(c_COMBC(U_12416,tc_fun(U_12416,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12416)),U_12417)))),hAPP(c_COMBC(U_12416,U_12419,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12419,tc_fun(U_12419,tc_HOL_Obool),U_12416),c_fequal),U_12420)))))),hAPP(c_Set_Oimage(U_12416,U_12419,U_12420),U_12417))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12416),U_12417))
      | ~ class_Groups_Ocomm__monoid__add(U_12415) ),
    inference(definitional_conversion,[status(esa)],[f_3309_2]) ).

cnf(f_3309_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12416,U_12415),U_12418),U_12417) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12419,U_12415),hAPP(hAPP(c_COMBB(tc_fun(U_12416,tc_HOL_Obool),U_12415,U_12419),hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12416,U_12415),U_12418)),hAPP(hAPP(c_COMBB(tc_fun(U_12416,tc_HOL_Obool),tc_fun(U_12416,tc_HOL_Obool),U_12419),c_Set_OCollect(U_12416)),hAPP(hAPP(c_COMBB(tc_fun(U_12416,tc_HOL_Obool),tc_fun(U_12416,tc_HOL_Obool),U_12419),hAPP(c_COMBS(U_12416,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12416),c_fconj),hAPP(hAPP(c_COMBC(U_12416,tc_fun(U_12416,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12416)),U_12417)))),hAPP(c_COMBC(U_12416,U_12419,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_12419,tc_fun(U_12419,tc_HOL_Obool),U_12416),c_fequal),U_12420)))))),hAPP(c_Set_Oimage(U_12416,U_12419,U_12420),U_12417))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12416),U_12417))
    | ~ class_Groups_Ocomm__monoid__add(U_12415) ),
    inference(clausify,[status(thm)],[f_3309_3]) ).

fof(f_3310_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_3310_2,plain,
    ! [U_12425,U_12424,U_12423,U_12422,U_12421] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12422,U_12421),U_12424),hAPP(hAPP(c_Set_Oinsert(U_12422),U_12425),U_12423)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12421),hAPP(U_12424,U_12425)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12422,U_12421),U_12424),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12422,tc_HOL_Obool)),U_12423),hAPP(hAPP(c_Set_Oinsert(U_12422),U_12425),c_Orderings_Obot__class_Obot(tc_fun(U_12422,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12422),U_12423))
      | ~ class_Groups_Ocomm__monoid__add(U_12421) ),
    inference(variable_rename,[status(thm)],[f_3310_1]) ).

fof(f_3310_3,plain,
    ! [U_12422,U_12421,U_12423,U_12424,U_12425] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12422,U_12421),U_12424),hAPP(hAPP(c_Set_Oinsert(U_12422),U_12425),U_12423)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12421),hAPP(U_12424,U_12425)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12422,U_12421),U_12424),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12422,tc_HOL_Obool)),U_12423),hAPP(hAPP(c_Set_Oinsert(U_12422),U_12425),c_Orderings_Obot__class_Obot(tc_fun(U_12422,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12422),U_12423))
      | ~ class_Groups_Ocomm__monoid__add(U_12421) ),
    inference(definitional_conversion,[status(esa)],[f_3310_2]) ).

cnf(f_3310_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12422,U_12421),U_12424),hAPP(hAPP(c_Set_Oinsert(U_12422),U_12425),U_12423)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12421),hAPP(U_12424,U_12425)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12422,U_12421),U_12424),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12422,tc_HOL_Obool)),U_12423),hAPP(hAPP(c_Set_Oinsert(U_12422),U_12425),c_Orderings_Obot__class_Obot(tc_fun(U_12422,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12422),U_12423))
    | ~ class_Groups_Ocomm__monoid__add(U_12421) ),
    inference(clausify,[status(thm)],[f_3310_3]) ).

fof(f_3311_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_3311_2,plain,
    ! [U_12430,U_12429,U_12428,U_12427,U_12426] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12427,U_12426),U_12430),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12427,tc_HOL_Obool)),U_12428),U_12429)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12426),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12427,U_12426),U_12430),U_12428)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12427,U_12426),U_12430),U_12429))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12427,tc_HOL_Obool)),U_12428),U_12429) != c_Orderings_Obot__class_Obot(tc_fun(U_12427,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12427),U_12429))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12427),U_12428))
      | ~ class_Groups_Ocomm__monoid__add(U_12426) ),
    inference(variable_rename,[status(thm)],[f_3311_1]) ).

fof(f_3311_3,plain,
    ! [U_12426,U_12427,U_12428,U_12429,U_12430] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12427,U_12426),U_12430),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12427,tc_HOL_Obool)),U_12428),U_12429)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12426),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12427,U_12426),U_12430),U_12428)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12427,U_12426),U_12430),U_12429))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12427,tc_HOL_Obool)),U_12428),U_12429) != c_Orderings_Obot__class_Obot(tc_fun(U_12427,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12427),U_12429))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12427),U_12428))
      | ~ class_Groups_Ocomm__monoid__add(U_12426) ),
    inference(definitional_conversion,[status(esa)],[f_3311_2]) ).

cnf(f_3311_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12427,U_12426),U_12430),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12427,tc_HOL_Obool)),U_12428),U_12429)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12426),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12427,U_12426),U_12430),U_12428)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12427,U_12426),U_12430),U_12429))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12427,tc_HOL_Obool)),U_12428),U_12429) != c_Orderings_Obot__class_Obot(tc_fun(U_12427,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12427),U_12429))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12427),U_12428))
    | ~ class_Groups_Ocomm__monoid__add(U_12426) ),
    inference(clausify,[status(thm)],[f_3311_3]) ).

fof(f_3312_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_3312_2,plain,
    ! [U_12435,U_12434,U_12433,U_12432,U_12431] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12432,U_12431),U_12435),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12432,tc_HOL_Obool)),U_12433),U_12434)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12431),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12431),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12432,U_12431),U_12435),U_12433)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12432,U_12431),U_12435),U_12434))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12432,U_12431),U_12435),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12432,tc_HOL_Obool)),U_12433),U_12434)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12432),U_12434))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12432),U_12433))
      | ~ class_Groups_Oab__group__add(U_12431) ),
    inference(variable_rename,[status(thm)],[f_3312_1]) ).

fof(f_3312_3,plain,
    ! [U_12432,U_12431,U_12433,U_12434,U_12435] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12432,U_12431),U_12435),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12432,tc_HOL_Obool)),U_12433),U_12434)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12431),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12431),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12432,U_12431),U_12435),U_12433)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12432,U_12431),U_12435),U_12434))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12432,U_12431),U_12435),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12432,tc_HOL_Obool)),U_12433),U_12434)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12432),U_12434))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12432),U_12433))
      | ~ class_Groups_Oab__group__add(U_12431) ),
    inference(definitional_conversion,[status(esa)],[f_3312_2]) ).

cnf(f_3312_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12432,U_12431),U_12435),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12432,tc_HOL_Obool)),U_12433),U_12434)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12431),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12431),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12432,U_12431),U_12435),U_12433)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12432,U_12431),U_12435),U_12434))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12432,U_12431),U_12435),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12432,tc_HOL_Obool)),U_12433),U_12434)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12432),U_12434))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12432),U_12433))
    | ~ class_Groups_Oab__group__add(U_12431) ),
    inference(clausify,[status(thm)],[f_3312_3]) ).

fof(f_3313_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_3313_2,plain,
    ! [U_12439,U_12438,U_12437,U_12436] :
      ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12436,tc_Nat_Onat),U_12439),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12436,tc_HOL_Obool)),U_12438),hAPP(hAPP(c_Set_Oinsert(U_12436),U_12437),c_Orderings_Obot__class_Obot(tc_fun(U_12436,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12436,tc_Nat_Onat),U_12439),U_12438)
        | hBOOL(hAPP(hAPP(c_member(U_12436),U_12437),U_12438)) )
      & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12436,tc_Nat_Onat),U_12439),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12436,tc_HOL_Obool)),U_12438),hAPP(hAPP(c_Set_Oinsert(U_12436),U_12437),c_Orderings_Obot__class_Obot(tc_fun(U_12436,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12436,tc_Nat_Onat),U_12439),U_12438)),hAPP(U_12439,U_12437))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12436),U_12437),U_12438)) ) ),
    inference(variable_rename,[status(thm)],[f_3313_1]) ).

fof(f_3313_3,plain,
    ( ! [U_12447,U_12445,U_12443,U_12441] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12441,tc_Nat_Onat),U_12447),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12441,tc_HOL_Obool)),U_12445),hAPP(hAPP(c_Set_Oinsert(U_12441),U_12443),c_Orderings_Obot__class_Obot(tc_fun(U_12441,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12441,tc_Nat_Onat),U_12447),U_12445)
        | hBOOL(hAPP(hAPP(c_member(U_12441),U_12443),U_12445)) )
    & ! [U_12446,U_12444,U_12442,U_12440] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12440,tc_Nat_Onat),U_12446),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12440,tc_HOL_Obool)),U_12444),hAPP(hAPP(c_Set_Oinsert(U_12440),U_12442),c_Orderings_Obot__class_Obot(tc_fun(U_12440,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12440,tc_Nat_Onat),U_12446),U_12444)),hAPP(U_12446,U_12442))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12440),U_12442),U_12444)) ) ),
    inference(miniscope,[status(thm)],[f_3313_2]) ).

fof(f_3313_4,plain,
    ( ! [U_12441,U_12443,U_12445,U_12447] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12441,tc_Nat_Onat),U_12447),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12441,tc_HOL_Obool)),U_12445),hAPP(hAPP(c_Set_Oinsert(U_12441),U_12443),c_Orderings_Obot__class_Obot(tc_fun(U_12441,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12441,tc_Nat_Onat),U_12447),U_12445)
        | hBOOL(hAPP(hAPP(c_member(U_12441),U_12443),U_12445)) )
    & ! [U_12442,U_12444,U_12446,U_12440] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12440,tc_Nat_Onat),U_12446),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12440,tc_HOL_Obool)),U_12444),hAPP(hAPP(c_Set_Oinsert(U_12440),U_12442),c_Orderings_Obot__class_Obot(tc_fun(U_12440,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12440,tc_Nat_Onat),U_12446),U_12444)),hAPP(U_12446,U_12442))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12440),U_12442),U_12444)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3313_3]) ).

cnf(f_3313_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12440,tc_Nat_Onat),U_12446),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12440,tc_HOL_Obool)),U_12444),hAPP(hAPP(c_Set_Oinsert(U_12440),U_12442),c_Orderings_Obot__class_Obot(tc_fun(U_12440,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12440,tc_Nat_Onat),U_12446),U_12444)),hAPP(U_12446,U_12442))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12440),U_12442),U_12444)) ),
    inference(clausify,[status(thm)],[f_3313_4]) ).

cnf(f_3313_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12441,tc_Nat_Onat),U_12447),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12441,tc_HOL_Obool)),U_12445),hAPP(hAPP(c_Set_Oinsert(U_12441),U_12443),c_Orderings_Obot__class_Obot(tc_fun(U_12441,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12441,tc_Nat_Onat),U_12447),U_12445)
    | hBOOL(hAPP(hAPP(c_member(U_12441),U_12443),U_12445)) ),
    inference(clausify,[status(thm)],[f_3313_4]) ).

fof(f_3314_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_3314_2,plain,
    ! [U_12451,U_12450,U_12449,U_12448] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12448,tc_Nat_Onat),U_12451),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12448,tc_HOL_Obool)),U_12449),U_12450)) = 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_12448,tc_Nat_Onat),U_12451),U_12449)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12448,tc_Nat_Onat),U_12451),U_12450))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12448,tc_Nat_Onat),U_12451),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12448,tc_HOL_Obool)),U_12449),U_12450)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12448),U_12450))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12448),U_12449)) ),
    inference(variable_rename,[status(thm)],[f_3314_1]) ).

fof(f_3314_3,plain,
    ! [U_12448,U_12449,U_12450,U_12451] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12448,tc_Nat_Onat),U_12451),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12448,tc_HOL_Obool)),U_12449),U_12450)) = 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_12448,tc_Nat_Onat),U_12451),U_12449)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12448,tc_Nat_Onat),U_12451),U_12450))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12448,tc_Nat_Onat),U_12451),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12448,tc_HOL_Obool)),U_12449),U_12450)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12448),U_12450))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12448),U_12449)) ),
    inference(definitional_conversion,[status(esa)],[f_3314_2]) ).

cnf(f_3314_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12448,tc_Nat_Onat),U_12451),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12448,tc_HOL_Obool)),U_12449),U_12450)) = 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_12448,tc_Nat_Onat),U_12451),U_12449)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12448,tc_Nat_Onat),U_12451),U_12450))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12448,tc_Nat_Onat),U_12451),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12448,tc_HOL_Obool)),U_12449),U_12450)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12448),U_12450))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12448),U_12449)) ),
    inference(clausify,[status(thm)],[f_3314_3]) ).

fof(f_3315_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_3315_2,plain,
    ! [U_12455,U_12454,U_12453,U_12452] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12452),U_12455),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12454),hAPP(c_Nat_OSuc,U_12453))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12452),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12452),U_12455),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12454),U_12453))),hAPP(U_12455,U_12453))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12453),U_12454)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12452),U_12455),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12454),hAPP(c_Nat_OSuc,U_12453))) = c_Groups_Ozero__class_Ozero(U_12452)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12453),U_12454)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_12452) ),
    inference(variable_rename,[status(thm)],[f_3315_1]) ).

fof(f_3315_3,plain,
    ( ! [U_12453,U_12452,U_12454,U_12455] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12452),U_12455),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12454),hAPP(c_Nat_OSuc,U_12453))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12452),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12452),U_12455),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12454),U_12453))),hAPP(U_12455,U_12453))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12453),U_12454))
        | ~ sP898(U_12453,U_12452,U_12454,U_12455) )
    & ! [U_12453,U_12452,U_12454,U_12455] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12452),U_12455),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12454),hAPP(c_Nat_OSuc,U_12453))) = c_Groups_Ozero__class_Ozero(U_12452)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12453),U_12454))
        | ~ sP898(U_12453,U_12452,U_12454,U_12455) )
    & ! [U_12453,U_12452,U_12454,U_12455] :
        ( sP898(U_12453,U_12452,U_12454,U_12455)
        | ~ class_Groups_Ocomm__monoid__add(U_12452) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP898])],[f_3315_2]) ).

cnf(f_3315_4,plain,
    ( sP898(U_12453,U_12452,U_12454,U_12455)
    | ~ class_Groups_Ocomm__monoid__add(U_12452) ),
    inference(clausify,[status(thm)],[f_3315_3]) ).

cnf(f_3315_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12452),U_12455),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12454),hAPP(c_Nat_OSuc,U_12453))) = c_Groups_Ozero__class_Ozero(U_12452)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12453),U_12454))
    | ~ sP898(U_12453,U_12452,U_12454,U_12455) ),
    inference(clausify,[status(thm)],[f_3315_3]) ).

cnf(f_3315_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12452),U_12455),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12454),hAPP(c_Nat_OSuc,U_12453))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12452),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12452),U_12455),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_12454),U_12453))),hAPP(U_12455,U_12453))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_12453),U_12454))
    | ~ sP898(U_12453,U_12452,U_12454,U_12455) ),
    inference(clausify,[status(thm)],[f_3315_3]) ).

fof(f_3316_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_3316_2,plain,
    ! [U_12459,U_12458,U_12457,U_12456] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12456),U_12459),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12458,hAPP(c_Nat_OSuc,U_12457))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12456),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12456),U_12459),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12458,U_12457))),hAPP(U_12459,hAPP(c_Nat_OSuc,U_12457)))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12457)),U_12458)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12456),U_12459),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12458,hAPP(c_Nat_OSuc,U_12457))) = c_Groups_Ozero__class_Ozero(U_12456)
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12457)),U_12458)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_12456) ),
    inference(variable_rename,[status(thm)],[f_3316_1]) ).

fof(f_3316_3,plain,
    ( ! [U_12456,U_12459,U_12458,U_12457] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12456),U_12459),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12458,hAPP(c_Nat_OSuc,U_12457))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12456),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12456),U_12459),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12458,U_12457))),hAPP(U_12459,hAPP(c_Nat_OSuc,U_12457)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12457)),U_12458))
        | ~ sP899(U_12456,U_12459,U_12458,U_12457) )
    & ! [U_12456,U_12459,U_12458,U_12457] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12456),U_12459),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12458,hAPP(c_Nat_OSuc,U_12457))) = c_Groups_Ozero__class_Ozero(U_12456)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12457)),U_12458))
        | ~ sP899(U_12456,U_12459,U_12458,U_12457) )
    & ! [U_12456,U_12459,U_12458,U_12457] :
        ( sP899(U_12456,U_12459,U_12458,U_12457)
        | ~ class_Groups_Ocomm__monoid__add(U_12456) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP899])],[f_3316_2]) ).

cnf(f_3316_4,plain,
    ( sP899(U_12456,U_12459,U_12458,U_12457)
    | ~ class_Groups_Ocomm__monoid__add(U_12456) ),
    inference(clausify,[status(thm)],[f_3316_3]) ).

cnf(f_3316_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12456),U_12459),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12458,hAPP(c_Nat_OSuc,U_12457))) = c_Groups_Ozero__class_Ozero(U_12456)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12457)),U_12458))
    | ~ sP899(U_12456,U_12459,U_12458,U_12457) ),
    inference(clausify,[status(thm)],[f_3316_3]) ).

cnf(f_3316_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12456),U_12459),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12458,hAPP(c_Nat_OSuc,U_12457))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12456),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12456),U_12459),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12458,U_12457))),hAPP(U_12459,hAPP(c_Nat_OSuc,U_12457)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12457)),U_12458))
    | ~ sP899(U_12456,U_12459,U_12458,U_12457) ),
    inference(clausify,[status(thm)],[f_3316_3]) ).

fof(f_3317_1,plain,
    ! [V_Pa_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_Pa_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_Pa_2,V_m_2)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,T_b),V_Pa_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_3317_2,plain,
    ! [U_12463,U_12462,U_12461,U_12460] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12460),U_12463),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12461,U_12462)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12460),hAPP(U_12463,U_12461)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12460),U_12463),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_12461,U_12462)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12461),U_12462))
      | ~ class_Groups_Ocomm__monoid__add(U_12460) ),
    inference(variable_rename,[status(thm)],[f_3317_1]) ).

fof(f_3317_3,plain,
    ! [U_12461,U_12462,U_12460,U_12463] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12460),U_12463),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12461,U_12462)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12460),hAPP(U_12463,U_12461)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12460),U_12463),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_12461,U_12462)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12461),U_12462))
      | ~ class_Groups_Ocomm__monoid__add(U_12460) ),
    inference(definitional_conversion,[status(esa)],[f_3317_2]) ).

cnf(f_3317_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12460),U_12463),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12461,U_12462)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12460),hAPP(U_12463,U_12461)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12460),U_12463),c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_12461,U_12462)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12461),U_12462))
    | ~ class_Groups_Ocomm__monoid__add(U_12460) ),
    inference(clausify,[status(thm)],[f_3317_3]) ).

fof(f_3318_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_3318_2,plain,
    ! [U_12468,U_12467,U_12466,U_12465,U_12464] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12464),U_12467),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12465,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12466),U_12468))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12464),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12464),U_12467),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12465,U_12466))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12464),U_12467),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12466),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12466),U_12468))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12465),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12466),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | ~ class_Groups_Ocomm__monoid__add(U_12464) ),
    inference(variable_rename,[status(thm)],[f_3318_1]) ).

fof(f_3318_3,plain,
    ! [U_12465,U_12464,U_12466,U_12467,U_12468] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12464),U_12467),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12465,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12466),U_12468))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12464),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12464),U_12467),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12465,U_12466))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12464),U_12467),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12466),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12466),U_12468))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12465),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12466),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
      | ~ class_Groups_Ocomm__monoid__add(U_12464) ),
    inference(definitional_conversion,[status(esa)],[f_3318_2]) ).

cnf(f_3318_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12464),U_12467),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12465,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12466),U_12468))) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12464),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12464),U_12467),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_12465,U_12466))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12464),U_12467),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12466),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12466),U_12468))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12465),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12466),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ class_Groups_Ocomm__monoid__add(U_12464) ),
    inference(clausify,[status(thm)],[f_3318_3]) ).

fof(f_3319_1,plain,
    ! [V_g_2,V_f_2,V_Pa_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_Pa_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_Pa_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_Pa_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_3319_2,plain,
    ! [U_12474,U_12473,U_12472,U_12471,U_12470,U_12469] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12470,U_12469),hAPP(hAPP(c_COMBS(U_12470,U_12469,U_12469),hAPP(hAPP(c_COMBS(U_12470,U_12469,tc_fun(U_12469,U_12469)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12469,tc_fun(U_12469,U_12469)),U_12470),c_If(U_12469)),U_12472)),U_12473)),U_12474)),U_12471) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12469),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12470,U_12469),U_12473),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12470,tc_HOL_Obool)),U_12471),hAPP(c_Set_OCollect(U_12470),U_12472)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12470,U_12469),U_12474),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12470,tc_HOL_Obool)),U_12471),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12470,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_12470),U_12472)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12470),U_12471))
      | ~ class_Groups_Ocomm__monoid__add(U_12469) ),
    inference(variable_rename,[status(thm)],[f_3319_1]) ).

fof(f_3319_3,plain,
    ! [U_12469,U_12470,U_12471,U_12472,U_12473,U_12474] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12470,U_12469),hAPP(hAPP(c_COMBS(U_12470,U_12469,U_12469),hAPP(hAPP(c_COMBS(U_12470,U_12469,tc_fun(U_12469,U_12469)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12469,tc_fun(U_12469,U_12469)),U_12470),c_If(U_12469)),U_12472)),U_12473)),U_12474)),U_12471) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12469),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12470,U_12469),U_12473),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12470,tc_HOL_Obool)),U_12471),hAPP(c_Set_OCollect(U_12470),U_12472)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12470,U_12469),U_12474),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12470,tc_HOL_Obool)),U_12471),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12470,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_12470),U_12472)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12470),U_12471))
      | ~ class_Groups_Ocomm__monoid__add(U_12469) ),
    inference(definitional_conversion,[status(esa)],[f_3319_2]) ).

cnf(f_3319_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12470,U_12469),hAPP(hAPP(c_COMBS(U_12470,U_12469,U_12469),hAPP(hAPP(c_COMBS(U_12470,U_12469,tc_fun(U_12469,U_12469)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_12469,tc_fun(U_12469,U_12469)),U_12470),c_If(U_12469)),U_12472)),U_12473)),U_12474)),U_12471) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12469),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12470,U_12469),U_12473),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12470,tc_HOL_Obool)),U_12471),hAPP(c_Set_OCollect(U_12470),U_12472)))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12470,U_12469),U_12474),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12470,tc_HOL_Obool)),U_12471),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12470,tc_HOL_Obool)),hAPP(c_Set_OCollect(U_12470),U_12472)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12470),U_12471))
    | ~ class_Groups_Ocomm__monoid__add(U_12469) ),
    inference(clausify,[status(thm)],[f_3319_3]) ).

fof(f_3320_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_3320_2,plain,
    ! [U_12479,U_12478,U_12477,U_12476,U_12475] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12476,U_12475),U_12479),U_12477) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12475),hAPP(U_12479,U_12478)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12476,U_12475),U_12479),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12476,tc_HOL_Obool)),U_12477),hAPP(hAPP(c_Set_Oinsert(U_12476),U_12478),c_Orderings_Obot__class_Obot(tc_fun(U_12476,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12476),U_12478),U_12477))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12476),U_12477))
      | ~ class_Groups_Ocomm__monoid__add(U_12475) ),
    inference(variable_rename,[status(thm)],[f_3320_1]) ).

fof(f_3320_3,plain,
    ! [U_12476,U_12475,U_12477,U_12478,U_12479] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12476,U_12475),U_12479),U_12477) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12475),hAPP(U_12479,U_12478)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12476,U_12475),U_12479),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12476,tc_HOL_Obool)),U_12477),hAPP(hAPP(c_Set_Oinsert(U_12476),U_12478),c_Orderings_Obot__class_Obot(tc_fun(U_12476,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12476),U_12478),U_12477))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12476),U_12477))
      | ~ class_Groups_Ocomm__monoid__add(U_12475) ),
    inference(definitional_conversion,[status(esa)],[f_3320_2]) ).

cnf(f_3320_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12476,U_12475),U_12479),U_12477) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12475),hAPP(U_12479,U_12478)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12476,U_12475),U_12479),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12476,tc_HOL_Obool)),U_12477),hAPP(hAPP(c_Set_Oinsert(U_12476),U_12478),c_Orderings_Obot__class_Obot(tc_fun(U_12476,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12476),U_12478),U_12477))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12476),U_12477))
    | ~ class_Groups_Ocomm__monoid__add(U_12475) ),
    inference(clausify,[status(thm)],[f_3320_3]) ).

fof(f_3321_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_3321_2,plain,
    ! [U_12484,U_12483,U_12482,U_12481,U_12480] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12481,U_12480),U_12484),U_12482) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12480),hAPP(U_12484,U_12483)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12481,U_12480),U_12484),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12481,tc_HOL_Obool)),U_12482),hAPP(hAPP(c_Set_Oinsert(U_12481),U_12483),c_Orderings_Obot__class_Obot(tc_fun(U_12481,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12481),U_12483),U_12482))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12481),U_12482))
      | ~ class_Groups_Ocomm__monoid__add(U_12480) ),
    inference(variable_rename,[status(thm)],[f_3321_1]) ).

fof(f_3321_3,plain,
    ! [U_12480,U_12481,U_12482,U_12483,U_12484] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12481,U_12480),U_12484),U_12482) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12480),hAPP(U_12484,U_12483)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12481,U_12480),U_12484),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12481,tc_HOL_Obool)),U_12482),hAPP(hAPP(c_Set_Oinsert(U_12481),U_12483),c_Orderings_Obot__class_Obot(tc_fun(U_12481,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12481),U_12483),U_12482))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12481),U_12482))
      | ~ class_Groups_Ocomm__monoid__add(U_12480) ),
    inference(definitional_conversion,[status(esa)],[f_3321_2]) ).

cnf(f_3321_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12481,U_12480),U_12484),U_12482) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12480),hAPP(U_12484,U_12483)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12481,U_12480),U_12484),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12481,tc_HOL_Obool)),U_12482),hAPP(hAPP(c_Set_Oinsert(U_12481),U_12483),c_Orderings_Obot__class_Obot(tc_fun(U_12481,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12481),U_12483),U_12482))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12481),U_12482))
    | ~ class_Groups_Ocomm__monoid__add(U_12480) ),
    inference(clausify,[status(thm)],[f_3321_3]) ).

fof(f_3322_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_3322_2,plain,
    ! [U_12489,U_12488,U_12487,U_12486,U_12485] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12486,U_12485),U_12489),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12486,tc_HOL_Obool)),U_12487),hAPP(hAPP(c_Set_Oinsert(U_12486),U_12488),c_Orderings_Obot__class_Obot(tc_fun(U_12486,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12486,U_12485),U_12489),U_12487)
          | hBOOL(hAPP(hAPP(c_member(U_12486),U_12488),U_12487)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12486,U_12485),U_12489),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12486,tc_HOL_Obool)),U_12487),hAPP(hAPP(c_Set_Oinsert(U_12486),U_12488),c_Orderings_Obot__class_Obot(tc_fun(U_12486,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12485),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12486,U_12485),U_12489),U_12487)),hAPP(U_12489,U_12488))
          | ~ hBOOL(hAPP(hAPP(c_member(U_12486),U_12488),U_12487)) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12486),U_12487))
      | ~ class_Groups_Oab__group__add(U_12485) ),
    inference(variable_rename,[status(thm)],[f_3322_1]) ).

fof(f_3322_3,plain,
    ( ! [U_12485,U_12486,U_12487,U_12488,U_12489] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12486,U_12485),U_12489),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12486,tc_HOL_Obool)),U_12487),hAPP(hAPP(c_Set_Oinsert(U_12486),U_12488),c_Orderings_Obot__class_Obot(tc_fun(U_12486,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12486,U_12485),U_12489),U_12487)
        | hBOOL(hAPP(hAPP(c_member(U_12486),U_12488),U_12487))
        | ~ sP900(U_12485,U_12486,U_12487,U_12488,U_12489) )
    & ! [U_12485,U_12486,U_12487,U_12488,U_12489] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12486,U_12485),U_12489),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12486,tc_HOL_Obool)),U_12487),hAPP(hAPP(c_Set_Oinsert(U_12486),U_12488),c_Orderings_Obot__class_Obot(tc_fun(U_12486,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12485),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12486,U_12485),U_12489),U_12487)),hAPP(U_12489,U_12488))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12486),U_12488),U_12487))
        | ~ sP900(U_12485,U_12486,U_12487,U_12488,U_12489) )
    & ! [U_12485,U_12486,U_12487,U_12488,U_12489] :
        ( sP900(U_12485,U_12486,U_12487,U_12488,U_12489)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12486),U_12487))
        | ~ class_Groups_Oab__group__add(U_12485) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP900])],[f_3322_2]) ).

cnf(f_3322_4,plain,
    ( sP900(U_12485,U_12486,U_12487,U_12488,U_12489)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12486),U_12487))
    | ~ class_Groups_Oab__group__add(U_12485) ),
    inference(clausify,[status(thm)],[f_3322_3]) ).

cnf(f_3322_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12486,U_12485),U_12489),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12486,tc_HOL_Obool)),U_12487),hAPP(hAPP(c_Set_Oinsert(U_12486),U_12488),c_Orderings_Obot__class_Obot(tc_fun(U_12486,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12485),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12486,U_12485),U_12489),U_12487)),hAPP(U_12489,U_12488))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12486),U_12488),U_12487))
    | ~ sP900(U_12485,U_12486,U_12487,U_12488,U_12489) ),
    inference(clausify,[status(thm)],[f_3322_3]) ).

cnf(f_3322_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12486,U_12485),U_12489),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12486,tc_HOL_Obool)),U_12487),hAPP(hAPP(c_Set_Oinsert(U_12486),U_12488),c_Orderings_Obot__class_Obot(tc_fun(U_12486,tc_HOL_Obool))))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12486,U_12485),U_12489),U_12487)
    | hBOOL(hAPP(hAPP(c_member(U_12486),U_12488),U_12487))
    | ~ sP900(U_12485,U_12486,U_12487,U_12488,U_12489) ),
    inference(clausify,[status(thm)],[f_3322_3]) ).

fof(f_3323_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_3323_2,plain,
    ! [U_12494,U_12493,U_12492,U_12491,U_12490] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12491,U_12490),U_12494),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12491,tc_HOL_Obool)),U_12492),hAPP(hAPP(c_Set_Oinsert(U_12491),U_12493),c_Orderings_Obot__class_Obot(tc_fun(U_12491,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12490),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12491,U_12490),U_12494),U_12492)),hAPP(U_12494,U_12493))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12491),U_12493),U_12492))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12491),U_12492))
      | ~ class_Rings_Oring(U_12490) ),
    inference(variable_rename,[status(thm)],[f_3323_1]) ).

fof(f_3323_3,plain,
    ! [U_12491,U_12490,U_12492,U_12493,U_12494] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12491,U_12490),U_12494),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12491,tc_HOL_Obool)),U_12492),hAPP(hAPP(c_Set_Oinsert(U_12491),U_12493),c_Orderings_Obot__class_Obot(tc_fun(U_12491,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12490),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12491,U_12490),U_12494),U_12492)),hAPP(U_12494,U_12493))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12491),U_12493),U_12492))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12491),U_12492))
      | ~ class_Rings_Oring(U_12490) ),
    inference(definitional_conversion,[status(esa)],[f_3323_2]) ).

cnf(f_3323_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12491,U_12490),U_12494),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12491,tc_HOL_Obool)),U_12492),hAPP(hAPP(c_Set_Oinsert(U_12491),U_12493),c_Orderings_Obot__class_Obot(tc_fun(U_12491,tc_HOL_Obool))))) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12490),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12491,U_12490),U_12494),U_12492)),hAPP(U_12494,U_12493))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12491),U_12493),U_12492))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12491),U_12492))
    | ~ class_Rings_Oring(U_12490) ),
    inference(clausify,[status(thm)],[f_3323_3]) ).

fof(f_3324_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_3324_2,plain,
    ! [U_12497,U_12496,U_12495] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12495),hAPP(c_Power_Opower__class_Opower(U_12495),U_12496)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12497)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_12495),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12495),hAPP(hAPP(c_Power_Opower__class_Opower(U_12495),U_12496),U_12497)),c_Groups_Oone__class_Oone(U_12495))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12495),U_12496),c_Groups_Oone__class_Oone(U_12495)))
      | U_12496 = c_Groups_Oone__class_Oone(U_12495)
      | ~ class_Fields_Ofield(U_12495) ),
    inference(variable_rename,[status(thm)],[f_3324_1]) ).

fof(f_3324_3,plain,
    ! [U_12496,U_12495,U_12497] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12495),hAPP(c_Power_Opower__class_Opower(U_12495),U_12496)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12497)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_12495),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12495),hAPP(hAPP(c_Power_Opower__class_Opower(U_12495),U_12496),U_12497)),c_Groups_Oone__class_Oone(U_12495))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12495),U_12496),c_Groups_Oone__class_Oone(U_12495)))
      | U_12496 = c_Groups_Oone__class_Oone(U_12495)
      | ~ class_Fields_Ofield(U_12495) ),
    inference(definitional_conversion,[status(esa)],[f_3324_2]) ).

cnf(f_3324_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12495),hAPP(c_Power_Opower__class_Opower(U_12495),U_12496)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_12497)) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(U_12495),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12495),hAPP(hAPP(c_Power_Opower__class_Opower(U_12495),U_12496),U_12497)),c_Groups_Oone__class_Oone(U_12495))),hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12495),U_12496),c_Groups_Oone__class_Oone(U_12495)))
    | U_12496 = c_Groups_Oone__class_Oone(U_12495)
    | ~ class_Fields_Ofield(U_12495) ),
    inference(clausify,[status(thm)],[f_3324_3]) ).

fof(f_3325_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_3325_2,plain,
    ! [U_12499,U_12498] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12498),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12498),c_Groups_Oone__class_Oone(U_12498)),c_Groups_Oone__class_Oone(U_12498))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12498),c_Nat_Osemiring__1__class_Oof__nat(U_12498)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_12499))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12498),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12498),U_12499)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12498),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12498),U_12499)),c_Groups_Oone__class_Oone(U_12498)))
      | ~ class_Rings_Ocomm__semiring__1(U_12498) ),
    inference(variable_rename,[status(thm)],[f_3325_1]) ).

fof(f_3325_3,plain,
    ! [U_12498,U_12499] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12498),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12498),c_Groups_Oone__class_Oone(U_12498)),c_Groups_Oone__class_Oone(U_12498))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12498),c_Nat_Osemiring__1__class_Oof__nat(U_12498)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_12499))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12498),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12498),U_12499)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12498),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12498),U_12499)),c_Groups_Oone__class_Oone(U_12498)))
      | ~ class_Rings_Ocomm__semiring__1(U_12498) ),
    inference(definitional_conversion,[status(esa)],[f_3325_2]) ).

cnf(f_3325_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12498),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12498),c_Groups_Oone__class_Oone(U_12498)),c_Groups_Oone__class_Oone(U_12498))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12498),c_Nat_Osemiring__1__class_Oof__nat(U_12498)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_12499))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12498),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12498),U_12499)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12498),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12498),U_12499)),c_Groups_Oone__class_Oone(U_12498)))
    | ~ class_Rings_Ocomm__semiring__1(U_12498) ),
    inference(clausify,[status(thm)],[f_3325_3]) ).

fof(f_3326_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_3326_2,plain,
    ! [U_12503,U_12502,U_12501,U_12500] :
      ( ( ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12500),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_12500,U_12500),hAPP(hAPP(c_COMBB(U_12500,tc_fun(U_12500,U_12500),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_12500)),U_12503)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12500,tc_Nat_Onat),U_12503),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_12501,U_12502)) = c_Groups_Ozero__class_Ozero(U_12500)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12501),U_12502)) )
        & ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12500),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_12500,U_12500),hAPP(hAPP(c_COMBB(U_12500,tc_fun(U_12500,U_12500),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_12500)),U_12503)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12500,tc_Nat_Onat),U_12503),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_12501,U_12502)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12500),hAPP(U_12503,U_12501)),hAPP(U_12503,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12502),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12501),U_12502)) ) )
      | ~ class_Groups_Oab__group__add(U_12500) ),
    inference(variable_rename,[status(thm)],[f_3326_1]) ).

fof(f_3326_3,plain,
    ( ! [U_12500,U_12501,U_12502,U_12503] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12500),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_12500,U_12500),hAPP(hAPP(c_COMBB(U_12500,tc_fun(U_12500,U_12500),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_12500)),U_12503)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12500,tc_Nat_Onat),U_12503),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_12501,U_12502)) = c_Groups_Ozero__class_Ozero(U_12500)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12501),U_12502))
        | ~ sP901(U_12500,U_12501,U_12502,U_12503) )
    & ! [U_12500,U_12501,U_12502,U_12503] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12500),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_12500,U_12500),hAPP(hAPP(c_COMBB(U_12500,tc_fun(U_12500,U_12500),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_12500)),U_12503)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12500,tc_Nat_Onat),U_12503),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_12501,U_12502)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12500),hAPP(U_12503,U_12501)),hAPP(U_12503,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12502),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12501),U_12502))
        | ~ sP901(U_12500,U_12501,U_12502,U_12503) )
    & ! [U_12500,U_12501,U_12502,U_12503] :
        ( sP901(U_12500,U_12501,U_12502,U_12503)
        | ~ class_Groups_Oab__group__add(U_12500) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP901])],[f_3326_2]) ).

cnf(f_3326_4,plain,
    ( sP901(U_12500,U_12501,U_12502,U_12503)
    | ~ class_Groups_Oab__group__add(U_12500) ),
    inference(clausify,[status(thm)],[f_3326_3]) ).

cnf(f_3326_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12500),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_12500,U_12500),hAPP(hAPP(c_COMBB(U_12500,tc_fun(U_12500,U_12500),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_12500)),U_12503)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12500,tc_Nat_Onat),U_12503),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_12501,U_12502)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_12500),hAPP(U_12503,U_12501)),hAPP(U_12503,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12502),c_Groups_Oone__class_Oone(tc_Nat_Onat))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12501),U_12502))
    | ~ sP901(U_12500,U_12501,U_12502,U_12503) ),
    inference(clausify,[status(thm)],[f_3326_3]) ).

cnf(f_3326_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12500),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_12500,U_12500),hAPP(hAPP(c_COMBB(U_12500,tc_fun(U_12500,U_12500),tc_Nat_Onat),c_Groups_Ominus__class_Ominus(U_12500)),U_12503)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12500,tc_Nat_Onat),U_12503),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_12501,U_12502)) = c_Groups_Ozero__class_Ozero(U_12500)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_12501),U_12502))
    | ~ sP901(U_12500,U_12501,U_12502,U_12503) ),
    inference(clausify,[status(thm)],[f_3326_3]) ).

fof(f_3327_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_3327_2,plain,
    ! [U_12507,U_12506,U_12505] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12505,tc_Int_Oint),U_12507),U_12506) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12505,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_12505),c_Int_Onat),U_12507)),U_12506))
      | ? [U_12504] :
          ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_12507,U_12504))
          & hBOOL(hAPP(hAPP(c_member(U_12505),U_12504),U_12506)) ) ),
    inference(variable_rename,[status(thm)],[f_3327_1]) ).

fof(f_3327_3,plain,
    ! [U_12507,U_12506,U_12505] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12505,tc_Int_Oint),U_12507),U_12506) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12505,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_12505),c_Int_Onat),U_12507)),U_12506))
      | ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_12507,sK257(U_12507,U_12506,U_12505)))
        & hBOOL(hAPP(hAPP(c_member(U_12505),sK257(U_12507,U_12506,U_12505)),U_12506)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK257]),skolemize(U_12504,sK257(U_12507,U_12506,U_12505))],[f_3327_2]) ).

fof(f_3327_4,plain,
    ( ! [U_12507,U_12505,U_12506] :
        ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_12507,sK257(U_12507,U_12506,U_12505)))
        | ~ sP902(U_12507,U_12505,U_12506) )
    & ! [U_12507,U_12505,U_12506] :
        ( hBOOL(hAPP(hAPP(c_member(U_12505),sK257(U_12507,U_12506,U_12505)),U_12506))
        | ~ sP902(U_12507,U_12505,U_12506) )
    & ! [U_12507,U_12505,U_12506] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12505,tc_Int_Oint),U_12507),U_12506) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12505,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_12505),c_Int_Onat),U_12507)),U_12506))
        | sP902(U_12507,U_12505,U_12506) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP902])],[f_3327_3]) ).

cnf(f_3327_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12505,tc_Int_Oint),U_12507),U_12506) = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12505,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Int_Oint,tc_Nat_Onat,U_12505),c_Int_Onat),U_12507)),U_12506))
    | sP902(U_12507,U_12505,U_12506) ),
    inference(clausify,[status(thm)],[f_3327_4]) ).

cnf(f_3327_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12505),sK257(U_12507,U_12506,U_12505)),U_12506))
    | ~ sP902(U_12507,U_12505,U_12506) ),
    inference(clausify,[status(thm)],[f_3327_4]) ).

cnf(f_3327_7,plain,
    ( ~ c_Nat__Transfer_Ois__nat(hAPP(U_12507,sK257(U_12507,U_12506,U_12505)))
    | ~ sP902(U_12507,U_12505,U_12506) ),
    inference(clausify,[status(thm)],[f_3327_4]) ).

fof(f_3328_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_3328_2,plain,
    ! [U_12513,U_12512,U_12511,U_12510,U_12509] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12509),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12510,U_12509),U_12513),U_12512)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12510,U_12509),U_12513),U_12511)))
      | ? [U_12508] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12509),c_Groups_Ozero__class_Ozero(U_12509)),hAPP(U_12513,U_12508)))
          & hBOOL(hAPP(hAPP(c_member(U_12510),U_12508),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12510,tc_HOL_Obool)),U_12511),U_12512))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12510,tc_HOL_Obool)),U_12512),U_12511))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12510),U_12511))
      | ~ class_Groups_Oordered__comm__monoid__add(U_12509) ),
    inference(variable_rename,[status(thm)],[f_3328_1]) ).

fof(f_3328_3,plain,
    ! [U_12513,U_12512,U_12511,U_12510,U_12509] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12509),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12510,U_12509),U_12513),U_12512)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12510,U_12509),U_12513),U_12511)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12509),c_Groups_Ozero__class_Ozero(U_12509)),hAPP(U_12513,sK258(U_12513,U_12512,U_12511,U_12510,U_12509))))
        & hBOOL(hAPP(hAPP(c_member(U_12510),sK258(U_12513,U_12512,U_12511,U_12510,U_12509)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12510,tc_HOL_Obool)),U_12511),U_12512))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12510,tc_HOL_Obool)),U_12512),U_12511))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12510),U_12511))
      | ~ class_Groups_Oordered__comm__monoid__add(U_12509) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK258]),skolemize(U_12508,sK258(U_12513,U_12512,U_12511,U_12510,U_12509))],[f_3328_2]) ).

fof(f_3328_4,plain,
    ( ! [U_12509,U_12510,U_12511,U_12512,U_12513] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12509),c_Groups_Ozero__class_Ozero(U_12509)),hAPP(U_12513,sK258(U_12513,U_12512,U_12511,U_12510,U_12509))))
        | ~ sP903(U_12509,U_12510,U_12511,U_12512,U_12513) )
    & ! [U_12509,U_12510,U_12511,U_12512,U_12513] :
        ( hBOOL(hAPP(hAPP(c_member(U_12510),sK258(U_12513,U_12512,U_12511,U_12510,U_12509)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12510,tc_HOL_Obool)),U_12511),U_12512)))
        | ~ sP903(U_12509,U_12510,U_12511,U_12512,U_12513) )
    & ! [U_12509,U_12510,U_12511,U_12512,U_12513] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12509),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12510,U_12509),U_12513),U_12512)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12510,U_12509),U_12513),U_12511)))
        | sP903(U_12509,U_12510,U_12511,U_12512,U_12513)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12510,tc_HOL_Obool)),U_12512),U_12511))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12510),U_12511))
        | ~ class_Groups_Oordered__comm__monoid__add(U_12509) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP903])],[f_3328_3]) ).

cnf(f_3328_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12509),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12510,U_12509),U_12513),U_12512)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12510,U_12509),U_12513),U_12511)))
    | sP903(U_12509,U_12510,U_12511,U_12512,U_12513)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12510,tc_HOL_Obool)),U_12512),U_12511))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12510),U_12511))
    | ~ class_Groups_Oordered__comm__monoid__add(U_12509) ),
    inference(clausify,[status(thm)],[f_3328_4]) ).

cnf(f_3328_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12510),sK258(U_12513,U_12512,U_12511,U_12510,U_12509)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12510,tc_HOL_Obool)),U_12511),U_12512)))
    | ~ sP903(U_12509,U_12510,U_12511,U_12512,U_12513) ),
    inference(clausify,[status(thm)],[f_3328_4]) ).

cnf(f_3328_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12509),c_Groups_Ozero__class_Ozero(U_12509)),hAPP(U_12513,sK258(U_12513,U_12512,U_12511,U_12510,U_12509))))
    | ~ sP903(U_12509,U_12510,U_12511,U_12512,U_12513) ),
    inference(clausify,[status(thm)],[f_3328_4]) ).

fof(f_3329_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_3329_2,plain,
    ! [U_12520,U_12519,U_12518,U_12517,U_12516,U_12515] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12515,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12517,tc_HOL_Obool),tc_Nat_Onat,U_12515),c_Finite__Set_Ocard(U_12517)),hAPP(hAPP(c_COMBB(tc_fun(U_12517,tc_HOL_Obool),tc_fun(U_12517,tc_HOL_Obool),U_12515),c_Set_OCollect(U_12517)),hAPP(hAPP(c_COMBB(tc_fun(U_12517,tc_HOL_Obool),tc_fun(U_12517,tc_HOL_Obool),U_12515),hAPP(c_COMBS(U_12517,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12517),c_fconj),hAPP(hAPP(c_COMBC(U_12517,tc_fun(U_12517,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12517)),U_12518)))),U_12519)))),U_12516) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12520),hAPP(c_Finite__Set_Ocard(U_12517),U_12518))
      | ? [U_12514] :
          ( hAPP(c_Finite__Set_Ocard(U_12515),hAPP(c_Set_OCollect(U_12515),hAPP(hAPP(c_COMBS(U_12515,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12515),c_fconj),hAPP(hAPP(c_COMBC(U_12515,tc_fun(U_12515,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12515)),U_12516))),hAPP(hAPP(c_COMBC(U_12515,U_12517,tc_HOL_Obool),U_12519),U_12514)))) != U_12520
          & hBOOL(hAPP(hAPP(c_member(U_12517),U_12514),U_12518)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12517),U_12518))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12515),U_12516)) ),
    inference(variable_rename,[status(thm)],[f_3329_1]) ).

fof(f_3329_3,plain,
    ! [U_12520,U_12519,U_12518,U_12517,U_12516,U_12515] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12515,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12517,tc_HOL_Obool),tc_Nat_Onat,U_12515),c_Finite__Set_Ocard(U_12517)),hAPP(hAPP(c_COMBB(tc_fun(U_12517,tc_HOL_Obool),tc_fun(U_12517,tc_HOL_Obool),U_12515),c_Set_OCollect(U_12517)),hAPP(hAPP(c_COMBB(tc_fun(U_12517,tc_HOL_Obool),tc_fun(U_12517,tc_HOL_Obool),U_12515),hAPP(c_COMBS(U_12517,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12517),c_fconj),hAPP(hAPP(c_COMBC(U_12517,tc_fun(U_12517,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12517)),U_12518)))),U_12519)))),U_12516) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12520),hAPP(c_Finite__Set_Ocard(U_12517),U_12518))
      | ( hAPP(c_Finite__Set_Ocard(U_12515),hAPP(c_Set_OCollect(U_12515),hAPP(hAPP(c_COMBS(U_12515,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12515),c_fconj),hAPP(hAPP(c_COMBC(U_12515,tc_fun(U_12515,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12515)),U_12516))),hAPP(hAPP(c_COMBC(U_12515,U_12517,tc_HOL_Obool),U_12519),sK259(U_12520,U_12519,U_12518,U_12517,U_12516,U_12515))))) != U_12520
        & hBOOL(hAPP(hAPP(c_member(U_12517),sK259(U_12520,U_12519,U_12518,U_12517,U_12516,U_12515)),U_12518)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12517),U_12518))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12515),U_12516)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK259]),skolemize(U_12514,sK259(U_12520,U_12519,U_12518,U_12517,U_12516,U_12515))],[f_3329_2]) ).

fof(f_3329_4,plain,
    ( ! [U_12515,U_12516,U_12517,U_12518,U_12519,U_12520] :
        ( hAPP(c_Finite__Set_Ocard(U_12515),hAPP(c_Set_OCollect(U_12515),hAPP(hAPP(c_COMBS(U_12515,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12515),c_fconj),hAPP(hAPP(c_COMBC(U_12515,tc_fun(U_12515,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12515)),U_12516))),hAPP(hAPP(c_COMBC(U_12515,U_12517,tc_HOL_Obool),U_12519),sK259(U_12520,U_12519,U_12518,U_12517,U_12516,U_12515))))) != U_12520
        | ~ sP904(U_12515,U_12516,U_12517,U_12518,U_12519,U_12520) )
    & ! [U_12515,U_12516,U_12517,U_12518,U_12519,U_12520] :
        ( hBOOL(hAPP(hAPP(c_member(U_12517),sK259(U_12520,U_12519,U_12518,U_12517,U_12516,U_12515)),U_12518))
        | ~ sP904(U_12515,U_12516,U_12517,U_12518,U_12519,U_12520) )
    & ! [U_12515,U_12516,U_12517,U_12518,U_12519,U_12520] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12515,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12517,tc_HOL_Obool),tc_Nat_Onat,U_12515),c_Finite__Set_Ocard(U_12517)),hAPP(hAPP(c_COMBB(tc_fun(U_12517,tc_HOL_Obool),tc_fun(U_12517,tc_HOL_Obool),U_12515),c_Set_OCollect(U_12517)),hAPP(hAPP(c_COMBB(tc_fun(U_12517,tc_HOL_Obool),tc_fun(U_12517,tc_HOL_Obool),U_12515),hAPP(c_COMBS(U_12517,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12517),c_fconj),hAPP(hAPP(c_COMBC(U_12517,tc_fun(U_12517,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12517)),U_12518)))),U_12519)))),U_12516) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12520),hAPP(c_Finite__Set_Ocard(U_12517),U_12518))
        | sP904(U_12515,U_12516,U_12517,U_12518,U_12519,U_12520)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12517),U_12518))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12515),U_12516)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP904])],[f_3329_3]) ).

cnf(f_3329_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12515,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12517,tc_HOL_Obool),tc_Nat_Onat,U_12515),c_Finite__Set_Ocard(U_12517)),hAPP(hAPP(c_COMBB(tc_fun(U_12517,tc_HOL_Obool),tc_fun(U_12517,tc_HOL_Obool),U_12515),c_Set_OCollect(U_12517)),hAPP(hAPP(c_COMBB(tc_fun(U_12517,tc_HOL_Obool),tc_fun(U_12517,tc_HOL_Obool),U_12515),hAPP(c_COMBS(U_12517,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12517),c_fconj),hAPP(hAPP(c_COMBC(U_12517,tc_fun(U_12517,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12517)),U_12518)))),U_12519)))),U_12516) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12520),hAPP(c_Finite__Set_Ocard(U_12517),U_12518))
    | sP904(U_12515,U_12516,U_12517,U_12518,U_12519,U_12520)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12517),U_12518))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12515),U_12516)) ),
    inference(clausify,[status(thm)],[f_3329_4]) ).

cnf(f_3329_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12517),sK259(U_12520,U_12519,U_12518,U_12517,U_12516,U_12515)),U_12518))
    | ~ sP904(U_12515,U_12516,U_12517,U_12518,U_12519,U_12520) ),
    inference(clausify,[status(thm)],[f_3329_4]) ).

cnf(f_3329_7,plain,
    ( hAPP(c_Finite__Set_Ocard(U_12515),hAPP(c_Set_OCollect(U_12515),hAPP(hAPP(c_COMBS(U_12515,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12515),c_fconj),hAPP(hAPP(c_COMBC(U_12515,tc_fun(U_12515,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12515)),U_12516))),hAPP(hAPP(c_COMBC(U_12515,U_12517,tc_HOL_Obool),U_12519),sK259(U_12520,U_12519,U_12518,U_12517,U_12516,U_12515))))) != U_12520
    | ~ sP904(U_12515,U_12516,U_12517,U_12518,U_12519,U_12520) ),
    inference(clausify,[status(thm)],[f_3329_4]) ).

fof(f_3330_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_3330_2,plain,
    ! [U_12523,U_12522,U_12521] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12521),U_12522),U_12523) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12521),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12521,tc_Int_Oint),U_12522),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12523))
      | ~ class_Groups_Ocomm__monoid__mult(U_12521)
      | ~ class_Groups_Ocomm__monoid__add(U_12521) ),
    inference(variable_rename,[status(thm)],[f_3330_1]) ).

fof(f_3330_3,plain,
    ! [U_12522,U_12521,U_12523] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12521),U_12522),U_12523) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12521),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12521,tc_Int_Oint),U_12522),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12523))
      | ~ class_Groups_Ocomm__monoid__mult(U_12521)
      | ~ class_Groups_Ocomm__monoid__add(U_12521) ),
    inference(definitional_conversion,[status(esa)],[f_3330_2]) ).

cnf(f_3330_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12521),U_12522),U_12523) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12521),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_12521,tc_Int_Oint),U_12522),c_Int_Onat)),hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Int_Oint,c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_12523))
    | ~ class_Groups_Ocomm__monoid__mult(U_12521)
    | ~ class_Groups_Ocomm__monoid__add(U_12521) ),
    inference(clausify,[status(thm)],[f_3330_3]) ).

fof(f_3331_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_3331_2,plain,
    ! [U_12526,U_12525,U_12524] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12524),U_12526),U_12525) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12524),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_12524,tc_Nat_Onat),U_12526),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_12525))
      | ~ c_Nat__Transfer_Onat__set(U_12525)
      | ~ class_Groups_Ocomm__monoid__mult(U_12524)
      | ~ class_Groups_Ocomm__monoid__add(U_12524) ),
    inference(variable_rename,[status(thm)],[f_3331_1]) ).

fof(f_3331_3,plain,
    ! [U_12524,U_12526,U_12525] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12524),U_12526),U_12525) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12524),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_12524,tc_Nat_Onat),U_12526),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_12525))
      | ~ c_Nat__Transfer_Onat__set(U_12525)
      | ~ class_Groups_Ocomm__monoid__mult(U_12524)
      | ~ class_Groups_Ocomm__monoid__add(U_12524) ),
    inference(definitional_conversion,[status(esa)],[f_3331_2]) ).

cnf(f_3331_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_12524),U_12526),U_12525) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_12524),hAPP(hAPP(c_COMBB(tc_Int_Oint,U_12524,tc_Nat_Onat),U_12526),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint))),hAPP(c_Set_Oimage(tc_Int_Oint,tc_Nat_Onat,c_Int_Onat),U_12525))
    | ~ c_Nat__Transfer_Onat__set(U_12525)
    | ~ class_Groups_Ocomm__monoid__mult(U_12524)
    | ~ class_Groups_Ocomm__monoid__add(U_12524) ),
    inference(clausify,[status(thm)],[f_3331_3]) ).

fof(f_3332_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_3332_2,plain,
    ! [U_12532,U_12531,U_12530,U_12529,U_12528] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12528),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12529,U_12528),U_12531),U_12530)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12528),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12528),hAPP(c_Finite__Set_Ocard(U_12529),U_12530))),U_12532)))
      | ? [U_12527] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12528),hAPP(U_12531,U_12527)),U_12532))
          & hBOOL(hAPP(hAPP(c_member(U_12529),U_12527),U_12530)) )
      | ~ class_Rings_Osemiring__1(U_12528)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_12528) ),
    inference(variable_rename,[status(thm)],[f_3332_1]) ).

fof(f_3332_3,plain,
    ! [U_12532,U_12531,U_12530,U_12529,U_12528] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12528),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12529,U_12528),U_12531),U_12530)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12528),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12528),hAPP(c_Finite__Set_Ocard(U_12529),U_12530))),U_12532)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12528),hAPP(U_12531,sK260(U_12532,U_12531,U_12530,U_12529,U_12528))),U_12532))
        & hBOOL(hAPP(hAPP(c_member(U_12529),sK260(U_12532,U_12531,U_12530,U_12529,U_12528)),U_12530)) )
      | ~ class_Rings_Osemiring__1(U_12528)
      | ~ class_Groups_Oordered__ab__semigroup__add(U_12528) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK260]),skolemize(U_12527,sK260(U_12532,U_12531,U_12530,U_12529,U_12528))],[f_3332_2]) ).

fof(f_3332_4,plain,
    ( ! [U_12528,U_12529,U_12530,U_12531,U_12532] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12528),hAPP(U_12531,sK260(U_12532,U_12531,U_12530,U_12529,U_12528))),U_12532))
        | ~ sP905(U_12528,U_12529,U_12530,U_12531,U_12532) )
    & ! [U_12528,U_12529,U_12530,U_12531,U_12532] :
        ( hBOOL(hAPP(hAPP(c_member(U_12529),sK260(U_12532,U_12531,U_12530,U_12529,U_12528)),U_12530))
        | ~ sP905(U_12528,U_12529,U_12530,U_12531,U_12532) )
    & ! [U_12528,U_12529,U_12530,U_12531,U_12532] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12528),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12529,U_12528),U_12531),U_12530)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12528),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12528),hAPP(c_Finite__Set_Ocard(U_12529),U_12530))),U_12532)))
        | sP905(U_12528,U_12529,U_12530,U_12531,U_12532)
        | ~ class_Rings_Osemiring__1(U_12528)
        | ~ class_Groups_Oordered__ab__semigroup__add(U_12528) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP905])],[f_3332_3]) ).

cnf(f_3332_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12528),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12529,U_12528),U_12531),U_12530)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_12528),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12528),hAPP(c_Finite__Set_Ocard(U_12529),U_12530))),U_12532)))
    | sP905(U_12528,U_12529,U_12530,U_12531,U_12532)
    | ~ class_Rings_Osemiring__1(U_12528)
    | ~ class_Groups_Oordered__ab__semigroup__add(U_12528) ),
    inference(clausify,[status(thm)],[f_3332_4]) ).

cnf(f_3332_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12529),sK260(U_12532,U_12531,U_12530,U_12529,U_12528)),U_12530))
    | ~ sP905(U_12528,U_12529,U_12530,U_12531,U_12532) ),
    inference(clausify,[status(thm)],[f_3332_4]) ).

cnf(f_3332_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12528),hAPP(U_12531,sK260(U_12532,U_12531,U_12530,U_12529,U_12528))),U_12532))
    | ~ sP905(U_12528,U_12529,U_12530,U_12531,U_12532) ),
    inference(clausify,[status(thm)],[f_3332_4]) ).

fof(f_3333_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_3333_2,plain,
    ! [U_12538,U_12537,U_12536,U_12535,U_12534] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12535,U_12534),U_12538),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12535,tc_HOL_Obool)),U_12536),U_12537)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12534),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12535,U_12534),U_12538),U_12536)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12535,U_12534),U_12538),U_12537))
      | ? [U_12533] :
          ( hAPP(U_12538,U_12533) != c_Groups_Ozero__class_Ozero(U_12534)
          & hBOOL(hAPP(hAPP(c_member(U_12535),U_12533),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12535,tc_HOL_Obool)),U_12536),U_12537))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12535),U_12537))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12535),U_12536))
      | ~ class_Groups_Ocomm__monoid__add(U_12534) ),
    inference(variable_rename,[status(thm)],[f_3333_1]) ).

fof(f_3333_3,plain,
    ! [U_12538,U_12537,U_12536,U_12535,U_12534] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12535,U_12534),U_12538),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12535,tc_HOL_Obool)),U_12536),U_12537)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12534),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12535,U_12534),U_12538),U_12536)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12535,U_12534),U_12538),U_12537))
      | ( hAPP(U_12538,sK261(U_12538,U_12537,U_12536,U_12535,U_12534)) != c_Groups_Ozero__class_Ozero(U_12534)
        & hBOOL(hAPP(hAPP(c_member(U_12535),sK261(U_12538,U_12537,U_12536,U_12535,U_12534)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12535,tc_HOL_Obool)),U_12536),U_12537))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12535),U_12537))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12535),U_12536))
      | ~ class_Groups_Ocomm__monoid__add(U_12534) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK261]),skolemize(U_12533,sK261(U_12538,U_12537,U_12536,U_12535,U_12534))],[f_3333_2]) ).

fof(f_3333_4,plain,
    ( ! [U_12534,U_12535,U_12536,U_12537,U_12538] :
        ( hAPP(U_12538,sK261(U_12538,U_12537,U_12536,U_12535,U_12534)) != c_Groups_Ozero__class_Ozero(U_12534)
        | ~ sP906(U_12534,U_12535,U_12536,U_12537,U_12538) )
    & ! [U_12534,U_12535,U_12536,U_12537,U_12538] :
        ( hBOOL(hAPP(hAPP(c_member(U_12535),sK261(U_12538,U_12537,U_12536,U_12535,U_12534)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12535,tc_HOL_Obool)),U_12536),U_12537)))
        | ~ sP906(U_12534,U_12535,U_12536,U_12537,U_12538) )
    & ! [U_12534,U_12535,U_12536,U_12537,U_12538] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12535,U_12534),U_12538),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12535,tc_HOL_Obool)),U_12536),U_12537)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12534),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12535,U_12534),U_12538),U_12536)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12535,U_12534),U_12538),U_12537))
        | sP906(U_12534,U_12535,U_12536,U_12537,U_12538)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12535),U_12537))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12535),U_12536))
        | ~ class_Groups_Ocomm__monoid__add(U_12534) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP906])],[f_3333_3]) ).

cnf(f_3333_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12535,U_12534),U_12538),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12535,tc_HOL_Obool)),U_12536),U_12537)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12534),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12535,U_12534),U_12538),U_12536)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12535,U_12534),U_12538),U_12537))
    | sP906(U_12534,U_12535,U_12536,U_12537,U_12538)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12535),U_12537))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12535),U_12536))
    | ~ class_Groups_Ocomm__monoid__add(U_12534) ),
    inference(clausify,[status(thm)],[f_3333_4]) ).

cnf(f_3333_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12535),sK261(U_12538,U_12537,U_12536,U_12535,U_12534)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12535,tc_HOL_Obool)),U_12536),U_12537)))
    | ~ sP906(U_12534,U_12535,U_12536,U_12537,U_12538) ),
    inference(clausify,[status(thm)],[f_3333_4]) ).

cnf(f_3333_7,plain,
    ( hAPP(U_12538,sK261(U_12538,U_12537,U_12536,U_12535,U_12534)) != c_Groups_Ozero__class_Ozero(U_12534)
    | ~ sP906(U_12534,U_12535,U_12536,U_12537,U_12538) ),
    inference(clausify,[status(thm)],[f_3333_4]) ).

fof(f_3334_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_3334_2,plain,
    ! [U_12544,U_12543,U_12542,U_12541,U_12540] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12541,U_12540),U_12544),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12541,tc_HOL_Obool)),U_12542),U_12543)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12540),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12541,U_12540),U_12544),U_12542)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12541,U_12540),U_12544),U_12543))
      | ? [U_12539] :
          ( hAPP(U_12544,U_12539) != c_Groups_Ozero__class_Ozero(U_12540)
          & hBOOL(hAPP(hAPP(c_member(U_12541),U_12539),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12541,tc_HOL_Obool)),U_12542),U_12543))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12541),U_12543))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12541),U_12542))
      | ~ class_Groups_Ocomm__monoid__add(U_12540) ),
    inference(variable_rename,[status(thm)],[f_3334_1]) ).

fof(f_3334_3,plain,
    ! [U_12544,U_12543,U_12542,U_12541,U_12540] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12541,U_12540),U_12544),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12541,tc_HOL_Obool)),U_12542),U_12543)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12540),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12541,U_12540),U_12544),U_12542)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12541,U_12540),U_12544),U_12543))
      | ( hAPP(U_12544,sK262(U_12544,U_12543,U_12542,U_12541,U_12540)) != c_Groups_Ozero__class_Ozero(U_12540)
        & hBOOL(hAPP(hAPP(c_member(U_12541),sK262(U_12544,U_12543,U_12542,U_12541,U_12540)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12541,tc_HOL_Obool)),U_12542),U_12543))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12541),U_12543))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12541),U_12542))
      | ~ class_Groups_Ocomm__monoid__add(U_12540) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK262]),skolemize(U_12539,sK262(U_12544,U_12543,U_12542,U_12541,U_12540))],[f_3334_2]) ).

fof(f_3334_4,plain,
    ( ! [U_12542,U_12541,U_12540,U_12543,U_12544] :
        ( hAPP(U_12544,sK262(U_12544,U_12543,U_12542,U_12541,U_12540)) != c_Groups_Ozero__class_Ozero(U_12540)
        | ~ sP907(U_12542,U_12541,U_12540,U_12543,U_12544) )
    & ! [U_12542,U_12541,U_12540,U_12543,U_12544] :
        ( hBOOL(hAPP(hAPP(c_member(U_12541),sK262(U_12544,U_12543,U_12542,U_12541,U_12540)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12541,tc_HOL_Obool)),U_12542),U_12543)))
        | ~ sP907(U_12542,U_12541,U_12540,U_12543,U_12544) )
    & ! [U_12542,U_12541,U_12540,U_12543,U_12544] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12541,U_12540),U_12544),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12541,tc_HOL_Obool)),U_12542),U_12543)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12540),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12541,U_12540),U_12544),U_12542)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12541,U_12540),U_12544),U_12543))
        | sP907(U_12542,U_12541,U_12540,U_12543,U_12544)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12541),U_12543))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12541),U_12542))
        | ~ class_Groups_Ocomm__monoid__add(U_12540) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP907])],[f_3334_3]) ).

cnf(f_3334_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12541,U_12540),U_12544),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12541,tc_HOL_Obool)),U_12542),U_12543)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_12540),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12541,U_12540),U_12544),U_12542)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12541,U_12540),U_12544),U_12543))
    | sP907(U_12542,U_12541,U_12540,U_12543,U_12544)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12541),U_12543))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12541),U_12542))
    | ~ class_Groups_Ocomm__monoid__add(U_12540) ),
    inference(clausify,[status(thm)],[f_3334_4]) ).

cnf(f_3334_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12541),sK262(U_12544,U_12543,U_12542,U_12541,U_12540)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12541,tc_HOL_Obool)),U_12542),U_12543)))
    | ~ sP907(U_12542,U_12541,U_12540,U_12543,U_12544) ),
    inference(clausify,[status(thm)],[f_3334_4]) ).

cnf(f_3334_7,plain,
    ( hAPP(U_12544,sK262(U_12544,U_12543,U_12542,U_12541,U_12540)) != c_Groups_Ozero__class_Ozero(U_12540)
    | ~ sP907(U_12542,U_12541,U_12540,U_12543,U_12544) ),
    inference(clausify,[status(thm)],[f_3334_4]) ).

fof(f_3335_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_3335_2,plain,
    ! [U_12550,U_12549,U_12548,U_12547,U_12546] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12546),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12547,U_12546),U_12550),U_12549)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12547,U_12546),U_12550),U_12548)))
      | ? [U_12545] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12546),c_Groups_Ozero__class_Ozero(U_12546)),hAPP(U_12550,U_12545)))
          & hBOOL(hAPP(hAPP(c_member(U_12547),U_12545),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12547,tc_HOL_Obool)),U_12548),U_12549))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12547,tc_HOL_Obool)),U_12549),U_12548))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12547),U_12548))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_12546)
      | ~ class_Groups_Ocomm__monoid__add(U_12546) ),
    inference(variable_rename,[status(thm)],[f_3335_1]) ).

fof(f_3335_3,plain,
    ! [U_12550,U_12549,U_12548,U_12547,U_12546] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12546),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12547,U_12546),U_12550),U_12549)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12547,U_12546),U_12550),U_12548)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12546),c_Groups_Ozero__class_Ozero(U_12546)),hAPP(U_12550,sK263(U_12550,U_12549,U_12548,U_12547,U_12546))))
        & hBOOL(hAPP(hAPP(c_member(U_12547),sK263(U_12550,U_12549,U_12548,U_12547,U_12546)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12547,tc_HOL_Obool)),U_12548),U_12549))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12547,tc_HOL_Obool)),U_12549),U_12548))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12547),U_12548))
      | ~ class_Groups_Oordered__ab__semigroup__add(U_12546)
      | ~ class_Groups_Ocomm__monoid__add(U_12546) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK263]),skolemize(U_12545,sK263(U_12550,U_12549,U_12548,U_12547,U_12546))],[f_3335_2]) ).

fof(f_3335_4,plain,
    ( ! [U_12547,U_12549,U_12548,U_12546,U_12550] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12546),c_Groups_Ozero__class_Ozero(U_12546)),hAPP(U_12550,sK263(U_12550,U_12549,U_12548,U_12547,U_12546))))
        | ~ sP908(U_12547,U_12549,U_12548,U_12546,U_12550) )
    & ! [U_12547,U_12549,U_12548,U_12546,U_12550] :
        ( hBOOL(hAPP(hAPP(c_member(U_12547),sK263(U_12550,U_12549,U_12548,U_12547,U_12546)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12547,tc_HOL_Obool)),U_12548),U_12549)))
        | ~ sP908(U_12547,U_12549,U_12548,U_12546,U_12550) )
    & ! [U_12547,U_12549,U_12548,U_12546,U_12550] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12546),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12547,U_12546),U_12550),U_12549)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12547,U_12546),U_12550),U_12548)))
        | sP908(U_12547,U_12549,U_12548,U_12546,U_12550)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12547,tc_HOL_Obool)),U_12549),U_12548))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12547),U_12548))
        | ~ class_Groups_Oordered__ab__semigroup__add(U_12546)
        | ~ class_Groups_Ocomm__monoid__add(U_12546) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP908])],[f_3335_3]) ).

cnf(f_3335_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12546),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12547,U_12546),U_12550),U_12549)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12547,U_12546),U_12550),U_12548)))
    | sP908(U_12547,U_12549,U_12548,U_12546,U_12550)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12547,tc_HOL_Obool)),U_12549),U_12548))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12547),U_12548))
    | ~ class_Groups_Oordered__ab__semigroup__add(U_12546)
    | ~ class_Groups_Ocomm__monoid__add(U_12546) ),
    inference(clausify,[status(thm)],[f_3335_4]) ).

cnf(f_3335_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12547),sK263(U_12550,U_12549,U_12548,U_12547,U_12546)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12547,tc_HOL_Obool)),U_12548),U_12549)))
    | ~ sP908(U_12547,U_12549,U_12548,U_12546,U_12550) ),
    inference(clausify,[status(thm)],[f_3335_4]) ).

cnf(f_3335_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12546),c_Groups_Ozero__class_Ozero(U_12546)),hAPP(U_12550,sK263(U_12550,U_12549,U_12548,U_12547,U_12546))))
    | ~ sP908(U_12547,U_12549,U_12548,U_12546,U_12550) ),
    inference(clausify,[status(thm)],[f_3335_4]) ).

fof(f_3336_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_3336_2,plain,
    ! [U_12557,U_12556,U_12555,U_12554,U_12553,U_12552] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12552,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12554,tc_HOL_Obool),tc_Nat_Onat,U_12552),c_Finite__Set_Ocard(U_12554)),hAPP(hAPP(c_COMBB(tc_fun(U_12554,tc_HOL_Obool),tc_fun(U_12554,tc_HOL_Obool),U_12552),c_Set_OCollect(U_12554)),hAPP(hAPP(c_COMBB(tc_fun(U_12554,tc_HOL_Obool),tc_fun(U_12554,tc_HOL_Obool),U_12552),hAPP(c_COMBS(U_12554,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12554),c_fconj),hAPP(hAPP(c_COMBC(U_12554,tc_fun(U_12554,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12554)),U_12555)))),U_12556)))),U_12553) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12554,tc_Nat_Onat),U_12557),U_12555)
      | ? [U_12551] :
          ( hAPP(c_Finite__Set_Ocard(U_12552),hAPP(c_Set_OCollect(U_12552),hAPP(hAPP(c_COMBS(U_12552,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12552),c_fconj),hAPP(hAPP(c_COMBC(U_12552,tc_fun(U_12552,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12552)),U_12553))),hAPP(hAPP(c_COMBC(U_12552,U_12554,tc_HOL_Obool),U_12556),U_12551)))) != hAPP(U_12557,U_12551)
          & hBOOL(hAPP(hAPP(c_member(U_12554),U_12551),U_12555)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12554),U_12555))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12552),U_12553)) ),
    inference(variable_rename,[status(thm)],[f_3336_1]) ).

fof(f_3336_3,plain,
    ! [U_12557,U_12556,U_12555,U_12554,U_12553,U_12552] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12552,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12554,tc_HOL_Obool),tc_Nat_Onat,U_12552),c_Finite__Set_Ocard(U_12554)),hAPP(hAPP(c_COMBB(tc_fun(U_12554,tc_HOL_Obool),tc_fun(U_12554,tc_HOL_Obool),U_12552),c_Set_OCollect(U_12554)),hAPP(hAPP(c_COMBB(tc_fun(U_12554,tc_HOL_Obool),tc_fun(U_12554,tc_HOL_Obool),U_12552),hAPP(c_COMBS(U_12554,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12554),c_fconj),hAPP(hAPP(c_COMBC(U_12554,tc_fun(U_12554,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12554)),U_12555)))),U_12556)))),U_12553) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12554,tc_Nat_Onat),U_12557),U_12555)
      | ( hAPP(c_Finite__Set_Ocard(U_12552),hAPP(c_Set_OCollect(U_12552),hAPP(hAPP(c_COMBS(U_12552,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12552),c_fconj),hAPP(hAPP(c_COMBC(U_12552,tc_fun(U_12552,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12552)),U_12553))),hAPP(hAPP(c_COMBC(U_12552,U_12554,tc_HOL_Obool),U_12556),sK264(U_12557,U_12556,U_12555,U_12554,U_12553,U_12552))))) != hAPP(U_12557,sK264(U_12557,U_12556,U_12555,U_12554,U_12553,U_12552))
        & hBOOL(hAPP(hAPP(c_member(U_12554),sK264(U_12557,U_12556,U_12555,U_12554,U_12553,U_12552)),U_12555)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12554),U_12555))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12552),U_12553)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK264]),skolemize(U_12551,sK264(U_12557,U_12556,U_12555,U_12554,U_12553,U_12552))],[f_3336_2]) ).

fof(f_3336_4,plain,
    ( ! [U_12552,U_12553,U_12554,U_12555,U_12556,U_12557] :
        ( hAPP(c_Finite__Set_Ocard(U_12552),hAPP(c_Set_OCollect(U_12552),hAPP(hAPP(c_COMBS(U_12552,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12552),c_fconj),hAPP(hAPP(c_COMBC(U_12552,tc_fun(U_12552,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12552)),U_12553))),hAPP(hAPP(c_COMBC(U_12552,U_12554,tc_HOL_Obool),U_12556),sK264(U_12557,U_12556,U_12555,U_12554,U_12553,U_12552))))) != hAPP(U_12557,sK264(U_12557,U_12556,U_12555,U_12554,U_12553,U_12552))
        | ~ sP909(U_12552,U_12553,U_12554,U_12555,U_12556,U_12557) )
    & ! [U_12552,U_12553,U_12554,U_12555,U_12556,U_12557] :
        ( hBOOL(hAPP(hAPP(c_member(U_12554),sK264(U_12557,U_12556,U_12555,U_12554,U_12553,U_12552)),U_12555))
        | ~ sP909(U_12552,U_12553,U_12554,U_12555,U_12556,U_12557) )
    & ! [U_12552,U_12553,U_12554,U_12555,U_12556,U_12557] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12552,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12554,tc_HOL_Obool),tc_Nat_Onat,U_12552),c_Finite__Set_Ocard(U_12554)),hAPP(hAPP(c_COMBB(tc_fun(U_12554,tc_HOL_Obool),tc_fun(U_12554,tc_HOL_Obool),U_12552),c_Set_OCollect(U_12554)),hAPP(hAPP(c_COMBB(tc_fun(U_12554,tc_HOL_Obool),tc_fun(U_12554,tc_HOL_Obool),U_12552),hAPP(c_COMBS(U_12554,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12554),c_fconj),hAPP(hAPP(c_COMBC(U_12554,tc_fun(U_12554,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12554)),U_12555)))),U_12556)))),U_12553) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12554,tc_Nat_Onat),U_12557),U_12555)
        | sP909(U_12552,U_12553,U_12554,U_12555,U_12556,U_12557)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12554),U_12555))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12552),U_12553)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP909])],[f_3336_3]) ).

cnf(f_3336_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12552,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_12554,tc_HOL_Obool),tc_Nat_Onat,U_12552),c_Finite__Set_Ocard(U_12554)),hAPP(hAPP(c_COMBB(tc_fun(U_12554,tc_HOL_Obool),tc_fun(U_12554,tc_HOL_Obool),U_12552),c_Set_OCollect(U_12554)),hAPP(hAPP(c_COMBB(tc_fun(U_12554,tc_HOL_Obool),tc_fun(U_12554,tc_HOL_Obool),U_12552),hAPP(c_COMBS(U_12554,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12554),c_fconj),hAPP(hAPP(c_COMBC(U_12554,tc_fun(U_12554,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12554)),U_12555)))),U_12556)))),U_12553) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12554,tc_Nat_Onat),U_12557),U_12555)
    | sP909(U_12552,U_12553,U_12554,U_12555,U_12556,U_12557)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12554),U_12555))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12552),U_12553)) ),
    inference(clausify,[status(thm)],[f_3336_4]) ).

cnf(f_3336_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12554),sK264(U_12557,U_12556,U_12555,U_12554,U_12553,U_12552)),U_12555))
    | ~ sP909(U_12552,U_12553,U_12554,U_12555,U_12556,U_12557) ),
    inference(clausify,[status(thm)],[f_3336_4]) ).

cnf(f_3336_7,plain,
    ( hAPP(c_Finite__Set_Ocard(U_12552),hAPP(c_Set_OCollect(U_12552),hAPP(hAPP(c_COMBS(U_12552,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_12552),c_fconj),hAPP(hAPP(c_COMBC(U_12552,tc_fun(U_12552,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12552)),U_12553))),hAPP(hAPP(c_COMBC(U_12552,U_12554,tc_HOL_Obool),U_12556),sK264(U_12557,U_12556,U_12555,U_12554,U_12553,U_12552))))) != hAPP(U_12557,sK264(U_12557,U_12556,U_12555,U_12554,U_12553,U_12552))
    | ~ sP909(U_12552,U_12553,U_12554,U_12555,U_12556,U_12557) ),
    inference(clausify,[status(thm)],[f_3336_4]) ).

fof(f_3337_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_3337_2,plain,
    ! [U_12564,U_12563,U_12562,U_12561,U_12560,U_12559] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12559),hAPP(U_12562,U_12564)),U_12563))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12560),U_12564),U_12561))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12560,U_12559),U_12562),U_12561) != U_12563
      | ? [U_12558] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12559),c_Groups_Ozero__class_Ozero(U_12559)),hAPP(U_12562,U_12558)))
          & hBOOL(hAPP(hAPP(c_member(U_12560),U_12558),U_12561)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12560),U_12561))
      | ~ class_Groups_Oordered__ab__group__add(U_12559) ),
    inference(variable_rename,[status(thm)],[f_3337_1]) ).

fof(f_3337_3,plain,
    ! [U_12564,U_12563,U_12562,U_12561,U_12560,U_12559] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12559),hAPP(U_12562,U_12564)),U_12563))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12560),U_12564),U_12561))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12560,U_12559),U_12562),U_12561) != U_12563
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12559),c_Groups_Ozero__class_Ozero(U_12559)),hAPP(U_12562,sK265(U_12564,U_12563,U_12562,U_12561,U_12560,U_12559))))
        & hBOOL(hAPP(hAPP(c_member(U_12560),sK265(U_12564,U_12563,U_12562,U_12561,U_12560,U_12559)),U_12561)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12560),U_12561))
      | ~ class_Groups_Oordered__ab__group__add(U_12559) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK265]),skolemize(U_12558,sK265(U_12564,U_12563,U_12562,U_12561,U_12560,U_12559))],[f_3337_2]) ).

fof(f_3337_4,plain,
    ( ! [U_12562,U_12561,U_12563,U_12559,U_12560,U_12564] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12559),c_Groups_Ozero__class_Ozero(U_12559)),hAPP(U_12562,sK265(U_12564,U_12563,U_12562,U_12561,U_12560,U_12559))))
        | ~ sP910(U_12562,U_12561,U_12563,U_12559,U_12560,U_12564) )
    & ! [U_12562,U_12561,U_12563,U_12559,U_12560,U_12564] :
        ( hBOOL(hAPP(hAPP(c_member(U_12560),sK265(U_12564,U_12563,U_12562,U_12561,U_12560,U_12559)),U_12561))
        | ~ sP910(U_12562,U_12561,U_12563,U_12559,U_12560,U_12564) )
    & ! [U_12562,U_12561,U_12563,U_12559,U_12560,U_12564] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12559),hAPP(U_12562,U_12564)),U_12563))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12560),U_12564),U_12561))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12560,U_12559),U_12562),U_12561) != U_12563
        | sP910(U_12562,U_12561,U_12563,U_12559,U_12560,U_12564)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12560),U_12561))
        | ~ class_Groups_Oordered__ab__group__add(U_12559) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP910])],[f_3337_3]) ).

cnf(f_3337_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12559),hAPP(U_12562,U_12564)),U_12563))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12560),U_12564),U_12561))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12560,U_12559),U_12562),U_12561) != U_12563
    | sP910(U_12562,U_12561,U_12563,U_12559,U_12560,U_12564)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12560),U_12561))
    | ~ class_Groups_Oordered__ab__group__add(U_12559) ),
    inference(clausify,[status(thm)],[f_3337_4]) ).

cnf(f_3337_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12560),sK265(U_12564,U_12563,U_12562,U_12561,U_12560,U_12559)),U_12561))
    | ~ sP910(U_12562,U_12561,U_12563,U_12559,U_12560,U_12564) ),
    inference(clausify,[status(thm)],[f_3337_4]) ).

cnf(f_3337_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12559),c_Groups_Ozero__class_Ozero(U_12559)),hAPP(U_12562,sK265(U_12564,U_12563,U_12562,U_12561,U_12560,U_12559))))
    | ~ sP910(U_12562,U_12561,U_12563,U_12559,U_12560,U_12564) ),
    inference(clausify,[status(thm)],[f_3337_4]) ).

fof(f_3338_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_3338_2,plain,
    ! [U_12570,U_12569,U_12568,U_12567,U_12566] :
      ( hAPP(U_12569,U_12570) = c_Groups_Ozero__class_Ozero(U_12566)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12567),U_12570),U_12568))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12567,U_12566),U_12569),U_12568) != c_Groups_Ozero__class_Ozero(U_12566)
      | ? [U_12565] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12566),c_Groups_Ozero__class_Ozero(U_12566)),hAPP(U_12569,U_12565)))
          & hBOOL(hAPP(hAPP(c_member(U_12567),U_12565),U_12568)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12567),U_12568))
      | ~ class_Groups_Oordered__ab__group__add(U_12566) ),
    inference(variable_rename,[status(thm)],[f_3338_1]) ).

fof(f_3338_3,plain,
    ! [U_12570,U_12569,U_12568,U_12567,U_12566] :
      ( hAPP(U_12569,U_12570) = c_Groups_Ozero__class_Ozero(U_12566)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12567),U_12570),U_12568))
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12567,U_12566),U_12569),U_12568) != c_Groups_Ozero__class_Ozero(U_12566)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12566),c_Groups_Ozero__class_Ozero(U_12566)),hAPP(U_12569,sK266(U_12570,U_12569,U_12568,U_12567,U_12566))))
        & hBOOL(hAPP(hAPP(c_member(U_12567),sK266(U_12570,U_12569,U_12568,U_12567,U_12566)),U_12568)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12567),U_12568))
      | ~ class_Groups_Oordered__ab__group__add(U_12566) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK266]),skolemize(U_12565,sK266(U_12570,U_12569,U_12568,U_12567,U_12566))],[f_3338_2]) ).

fof(f_3338_4,plain,
    ( ! [U_12567,U_12570,U_12566,U_12569,U_12568] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12566),c_Groups_Ozero__class_Ozero(U_12566)),hAPP(U_12569,sK266(U_12570,U_12569,U_12568,U_12567,U_12566))))
        | ~ sP911(U_12567,U_12570,U_12566,U_12569,U_12568) )
    & ! [U_12567,U_12570,U_12566,U_12569,U_12568] :
        ( hBOOL(hAPP(hAPP(c_member(U_12567),sK266(U_12570,U_12569,U_12568,U_12567,U_12566)),U_12568))
        | ~ sP911(U_12567,U_12570,U_12566,U_12569,U_12568) )
    & ! [U_12567,U_12570,U_12566,U_12569,U_12568] :
        ( hAPP(U_12569,U_12570) = c_Groups_Ozero__class_Ozero(U_12566)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12567),U_12570),U_12568))
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12567,U_12566),U_12569),U_12568) != c_Groups_Ozero__class_Ozero(U_12566)
        | sP911(U_12567,U_12570,U_12566,U_12569,U_12568)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12567),U_12568))
        | ~ class_Groups_Oordered__ab__group__add(U_12566) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP911])],[f_3338_3]) ).

cnf(f_3338_5,plain,
    ( hAPP(U_12569,U_12570) = c_Groups_Ozero__class_Ozero(U_12566)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12567),U_12570),U_12568))
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12567,U_12566),U_12569),U_12568) != c_Groups_Ozero__class_Ozero(U_12566)
    | sP911(U_12567,U_12570,U_12566,U_12569,U_12568)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12567),U_12568))
    | ~ class_Groups_Oordered__ab__group__add(U_12566) ),
    inference(clausify,[status(thm)],[f_3338_4]) ).

cnf(f_3338_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12567),sK266(U_12570,U_12569,U_12568,U_12567,U_12566)),U_12568))
    | ~ sP911(U_12567,U_12570,U_12566,U_12569,U_12568) ),
    inference(clausify,[status(thm)],[f_3338_4]) ).

cnf(f_3338_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12566),c_Groups_Ozero__class_Ozero(U_12566)),hAPP(U_12569,sK266(U_12570,U_12569,U_12568,U_12567,U_12566))))
    | ~ sP911(U_12567,U_12570,U_12566,U_12569,U_12568) ),
    inference(clausify,[status(thm)],[f_3338_4]) ).

fof(f_3339_1,plain,
    ! [V_n_2,V_Pa_2,V_Qa_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_Pa_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_Qa_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_Pa_2)),V_Qa_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_Qa_2,B_x)),hAPP(V_Pa_2,B_x))) ),
    inference(fof_nnf,[status(thm)],[fact_sum__diff__distrib]) ).

fof(f_3339_2,plain,
    ! [U_12574,U_12573,U_12572] :
      ( 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_12573),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12574))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12572),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12574))) = 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_12573)),U_12572)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12574))
      | ? [U_12571] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_12572,U_12571)),hAPP(U_12573,U_12571))) ),
    inference(variable_rename,[status(thm)],[f_3339_1]) ).

fof(f_3339_3,plain,
    ! [U_12574,U_12573,U_12572] :
      ( 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_12573),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12574))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12572),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12574))) = 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_12573)),U_12572)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12574))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_12572,sK267(U_12574,U_12573,U_12572))),hAPP(U_12573,sK267(U_12574,U_12573,U_12572)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK267]),skolemize(U_12571,sK267(U_12574,U_12573,U_12572))],[f_3339_2]) ).

fof(f_3339_4,plain,
    ! [U_12574,U_12572,U_12573] :
      ( 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_12573),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12574))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12572),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12574))) = 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_12573)),U_12572)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12574))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_12572,sK267(U_12574,U_12573,U_12572))),hAPP(U_12573,sK267(U_12574,U_12573,U_12572)))) ),
    inference(definitional_conversion,[status(esa)],[f_3339_3]) ).

cnf(f_3339_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_12573),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12574))),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,tc_Nat_Onat),U_12572),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12574))) = 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_12573)),U_12572)),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_12574))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(U_12572,sK267(U_12574,U_12573,U_12572))),hAPP(U_12573,sK267(U_12574,U_12573,U_12572)))) ),
    inference(clausify,[status(thm)],[f_3339_4]) ).

fof(f_3340_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_3340_2,plain,
    ! [U_12580,U_12579,U_12578,U_12577,U_12576] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12577,U_12576),U_12580),U_12579) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12577,U_12576),U_12580),U_12578)
      | ? [U_12575] :
          ( hAPP(U_12580,U_12575) != c_Groups_Ozero__class_Ozero(U_12576)
          & hBOOL(hAPP(hAPP(c_member(U_12577),U_12575),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12577,tc_HOL_Obool)),U_12578),U_12579))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12577,tc_HOL_Obool)),U_12579),U_12578))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12577),U_12578))
      | ~ class_Groups_Ocomm__monoid__add(U_12576) ),
    inference(variable_rename,[status(thm)],[f_3340_1]) ).

fof(f_3340_3,plain,
    ! [U_12580,U_12579,U_12578,U_12577,U_12576] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12577,U_12576),U_12580),U_12579) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12577,U_12576),U_12580),U_12578)
      | ( hAPP(U_12580,sK268(U_12580,U_12579,U_12578,U_12577,U_12576)) != c_Groups_Ozero__class_Ozero(U_12576)
        & hBOOL(hAPP(hAPP(c_member(U_12577),sK268(U_12580,U_12579,U_12578,U_12577,U_12576)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12577,tc_HOL_Obool)),U_12578),U_12579))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12577,tc_HOL_Obool)),U_12579),U_12578))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12577),U_12578))
      | ~ class_Groups_Ocomm__monoid__add(U_12576) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK268]),skolemize(U_12575,sK268(U_12580,U_12579,U_12578,U_12577,U_12576))],[f_3340_2]) ).

fof(f_3340_4,plain,
    ( ! [U_12576,U_12577,U_12578,U_12579,U_12580] :
        ( hAPP(U_12580,sK268(U_12580,U_12579,U_12578,U_12577,U_12576)) != c_Groups_Ozero__class_Ozero(U_12576)
        | ~ sP912(U_12576,U_12577,U_12578,U_12579,U_12580) )
    & ! [U_12576,U_12577,U_12578,U_12579,U_12580] :
        ( hBOOL(hAPP(hAPP(c_member(U_12577),sK268(U_12580,U_12579,U_12578,U_12577,U_12576)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12577,tc_HOL_Obool)),U_12578),U_12579)))
        | ~ sP912(U_12576,U_12577,U_12578,U_12579,U_12580) )
    & ! [U_12576,U_12577,U_12578,U_12579,U_12580] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12577,U_12576),U_12580),U_12579) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12577,U_12576),U_12580),U_12578)
        | sP912(U_12576,U_12577,U_12578,U_12579,U_12580)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12577,tc_HOL_Obool)),U_12579),U_12578))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12577),U_12578))
        | ~ class_Groups_Ocomm__monoid__add(U_12576) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP912])],[f_3340_3]) ).

cnf(f_3340_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12577,U_12576),U_12580),U_12579) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12577,U_12576),U_12580),U_12578)
    | sP912(U_12576,U_12577,U_12578,U_12579,U_12580)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12577,tc_HOL_Obool)),U_12579),U_12578))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12577),U_12578))
    | ~ class_Groups_Ocomm__monoid__add(U_12576) ),
    inference(clausify,[status(thm)],[f_3340_4]) ).

cnf(f_3340_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12577),sK268(U_12580,U_12579,U_12578,U_12577,U_12576)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12577,tc_HOL_Obool)),U_12578),U_12579)))
    | ~ sP912(U_12576,U_12577,U_12578,U_12579,U_12580) ),
    inference(clausify,[status(thm)],[f_3340_4]) ).

cnf(f_3340_7,plain,
    ( hAPP(U_12580,sK268(U_12580,U_12579,U_12578,U_12577,U_12576)) != c_Groups_Ozero__class_Ozero(U_12576)
    | ~ sP912(U_12576,U_12577,U_12578,U_12579,U_12580) ),
    inference(clausify,[status(thm)],[f_3340_4]) ).

fof(f_3341_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_3341_2,plain,
    ! [U_12586,U_12585,U_12584,U_12583,U_12582] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12583,U_12582),U_12586),U_12584) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12583,U_12582),U_12586),U_12585)
      | ? [U_12581] :
          ( hAPP(U_12586,U_12581) != c_Groups_Ozero__class_Ozero(U_12582)
          & hBOOL(hAPP(hAPP(c_member(U_12583),U_12581),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12583,tc_HOL_Obool)),U_12584),U_12585))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12583,tc_HOL_Obool)),U_12585),U_12584))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12583),U_12584))
      | ~ class_Groups_Ocomm__monoid__add(U_12582) ),
    inference(variable_rename,[status(thm)],[f_3341_1]) ).

fof(f_3341_3,plain,
    ! [U_12586,U_12585,U_12584,U_12583,U_12582] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12583,U_12582),U_12586),U_12584) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12583,U_12582),U_12586),U_12585)
      | ( hAPP(U_12586,sK269(U_12586,U_12585,U_12584,U_12583,U_12582)) != c_Groups_Ozero__class_Ozero(U_12582)
        & hBOOL(hAPP(hAPP(c_member(U_12583),sK269(U_12586,U_12585,U_12584,U_12583,U_12582)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12583,tc_HOL_Obool)),U_12584),U_12585))) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12583,tc_HOL_Obool)),U_12585),U_12584))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12583),U_12584))
      | ~ class_Groups_Ocomm__monoid__add(U_12582) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK269]),skolemize(U_12581,sK269(U_12586,U_12585,U_12584,U_12583,U_12582))],[f_3341_2]) ).

fof(f_3341_4,plain,
    ( ! [U_12583,U_12584,U_12582,U_12586,U_12585] :
        ( hAPP(U_12586,sK269(U_12586,U_12585,U_12584,U_12583,U_12582)) != c_Groups_Ozero__class_Ozero(U_12582)
        | ~ sP913(U_12583,U_12584,U_12582,U_12586,U_12585) )
    & ! [U_12583,U_12584,U_12582,U_12586,U_12585] :
        ( hBOOL(hAPP(hAPP(c_member(U_12583),sK269(U_12586,U_12585,U_12584,U_12583,U_12582)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12583,tc_HOL_Obool)),U_12584),U_12585)))
        | ~ sP913(U_12583,U_12584,U_12582,U_12586,U_12585) )
    & ! [U_12583,U_12584,U_12582,U_12586,U_12585] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12583,U_12582),U_12586),U_12584) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12583,U_12582),U_12586),U_12585)
        | sP913(U_12583,U_12584,U_12582,U_12586,U_12585)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12583,tc_HOL_Obool)),U_12585),U_12584))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12583),U_12584))
        | ~ class_Groups_Ocomm__monoid__add(U_12582) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP913])],[f_3341_3]) ).

cnf(f_3341_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12583,U_12582),U_12586),U_12584) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12583,U_12582),U_12586),U_12585)
    | sP913(U_12583,U_12584,U_12582,U_12586,U_12585)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12583,tc_HOL_Obool)),U_12585),U_12584))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12583),U_12584))
    | ~ class_Groups_Ocomm__monoid__add(U_12582) ),
    inference(clausify,[status(thm)],[f_3341_4]) ).

cnf(f_3341_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12583),sK269(U_12586,U_12585,U_12584,U_12583,U_12582)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12583,tc_HOL_Obool)),U_12584),U_12585)))
    | ~ sP913(U_12583,U_12584,U_12582,U_12586,U_12585) ),
    inference(clausify,[status(thm)],[f_3341_4]) ).

cnf(f_3341_7,plain,
    ( hAPP(U_12586,sK269(U_12586,U_12585,U_12584,U_12583,U_12582)) != c_Groups_Ozero__class_Ozero(U_12582)
    | ~ sP913(U_12583,U_12584,U_12582,U_12586,U_12585) ),
    inference(clausify,[status(thm)],[f_3341_4]) ).

fof(f_3342_1,plain,
    ! [V_Pa_2,V_A_2,V_F_2,T_b] :
      ( hBOOL(hAPP(V_Pa_2,V_F_2))
      | ? [B_a,B_F] :
          ( ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_Set_Oinsert(T_b),B_a),B_F)))
          & hBOOL(hAPP(V_Pa_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_Pa_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_3342_2,plain,
    ! [U_12592,U_12591,U_12590,U_12589] :
      ( hBOOL(hAPP(U_12592,U_12590))
      | ? [U_12588,U_12587] :
          ( ~ hBOOL(hAPP(U_12592,hAPP(hAPP(c_Set_Oinsert(U_12589),U_12588),U_12587)))
          & hBOOL(hAPP(U_12592,U_12587))
          & ~ hBOOL(hAPP(hAPP(c_member(U_12589),U_12588),U_12587))
          & hBOOL(hAPP(hAPP(c_member(U_12589),U_12588),U_12591))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12589),U_12587)) )
      | ~ hBOOL(hAPP(U_12592,c_Orderings_Obot__class_Obot(tc_fun(U_12589,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12589,tc_HOL_Obool)),U_12590),U_12591))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12589),U_12590)) ),
    inference(variable_rename,[status(thm)],[f_3342_1]) ).

fof(f_3342_3,plain,
    ! [U_12592,U_12591,U_12590,U_12589] :
      ( hBOOL(hAPP(U_12592,U_12590))
      | ? [U_12587] :
          ( ~ hBOOL(hAPP(U_12592,hAPP(hAPP(c_Set_Oinsert(U_12589),sK270(U_12592,U_12591,U_12590,U_12589)),U_12587)))
          & hBOOL(hAPP(U_12592,U_12587))
          & ~ hBOOL(hAPP(hAPP(c_member(U_12589),sK270(U_12592,U_12591,U_12590,U_12589)),U_12587))
          & hBOOL(hAPP(hAPP(c_member(U_12589),sK270(U_12592,U_12591,U_12590,U_12589)),U_12591))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12589),U_12587)) )
      | ~ hBOOL(hAPP(U_12592,c_Orderings_Obot__class_Obot(tc_fun(U_12589,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12589,tc_HOL_Obool)),U_12590),U_12591))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12589),U_12590)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK270]),skolemize(U_12588,sK270(U_12592,U_12591,U_12590,U_12589))],[f_3342_2]) ).

fof(f_3342_4,plain,
    ! [U_12592,U_12591,U_12590,U_12589] :
      ( hBOOL(hAPP(U_12592,U_12590))
      | ( ~ hBOOL(hAPP(U_12592,hAPP(hAPP(c_Set_Oinsert(U_12589),sK270(U_12592,U_12591,U_12590,U_12589)),sK271(U_12592,U_12591,U_12590,U_12589))))
        & hBOOL(hAPP(U_12592,sK271(U_12592,U_12591,U_12590,U_12589)))
        & ~ hBOOL(hAPP(hAPP(c_member(U_12589),sK270(U_12592,U_12591,U_12590,U_12589)),sK271(U_12592,U_12591,U_12590,U_12589)))
        & hBOOL(hAPP(hAPP(c_member(U_12589),sK270(U_12592,U_12591,U_12590,U_12589)),U_12591))
        & hBOOL(hAPP(c_Finite__Set_Ofinite(U_12589),sK271(U_12592,U_12591,U_12590,U_12589))) )
      | ~ hBOOL(hAPP(U_12592,c_Orderings_Obot__class_Obot(tc_fun(U_12589,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12589,tc_HOL_Obool)),U_12590),U_12591))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12589),U_12590)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK271]),skolemize(U_12587,sK271(U_12592,U_12591,U_12590,U_12589))],[f_3342_3]) ).

fof(f_3342_5,plain,
    ( ! [U_12589,U_12590,U_12591,U_12592] :
        ( ~ hBOOL(hAPP(U_12592,hAPP(hAPP(c_Set_Oinsert(U_12589),sK270(U_12592,U_12591,U_12590,U_12589)),sK271(U_12592,U_12591,U_12590,U_12589))))
        | ~ sP914(U_12589,U_12590,U_12591,U_12592) )
    & ! [U_12589,U_12590,U_12591,U_12592] :
        ( hBOOL(hAPP(U_12592,sK271(U_12592,U_12591,U_12590,U_12589)))
        | ~ sP914(U_12589,U_12590,U_12591,U_12592) )
    & ! [U_12589,U_12590,U_12591,U_12592] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_12589),sK270(U_12592,U_12591,U_12590,U_12589)),sK271(U_12592,U_12591,U_12590,U_12589)))
        | ~ sP914(U_12589,U_12590,U_12591,U_12592) )
    & ! [U_12589,U_12590,U_12591,U_12592] :
        ( hBOOL(hAPP(hAPP(c_member(U_12589),sK270(U_12592,U_12591,U_12590,U_12589)),U_12591))
        | ~ sP914(U_12589,U_12590,U_12591,U_12592) )
    & ! [U_12589,U_12590,U_12591,U_12592] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12589),sK271(U_12592,U_12591,U_12590,U_12589)))
        | ~ sP914(U_12589,U_12590,U_12591,U_12592) )
    & ! [U_12589,U_12590,U_12591,U_12592] :
        ( hBOOL(hAPP(U_12592,U_12590))
        | sP914(U_12589,U_12590,U_12591,U_12592)
        | ~ hBOOL(hAPP(U_12592,c_Orderings_Obot__class_Obot(tc_fun(U_12589,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12589,tc_HOL_Obool)),U_12590),U_12591))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12589),U_12590)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP914])],[f_3342_4]) ).

cnf(f_3342_6,plain,
    ( hBOOL(hAPP(U_12592,U_12590))
    | sP914(U_12589,U_12590,U_12591,U_12592)
    | ~ hBOOL(hAPP(U_12592,c_Orderings_Obot__class_Obot(tc_fun(U_12589,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12589,tc_HOL_Obool)),U_12590),U_12591))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12589),U_12590)) ),
    inference(clausify,[status(thm)],[f_3342_5]) ).

cnf(f_3342_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12589),sK271(U_12592,U_12591,U_12590,U_12589)))
    | ~ sP914(U_12589,U_12590,U_12591,U_12592) ),
    inference(clausify,[status(thm)],[f_3342_5]) ).

cnf(f_3342_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12589),sK270(U_12592,U_12591,U_12590,U_12589)),U_12591))
    | ~ sP914(U_12589,U_12590,U_12591,U_12592) ),
    inference(clausify,[status(thm)],[f_3342_5]) ).

cnf(f_3342_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_12589),sK270(U_12592,U_12591,U_12590,U_12589)),sK271(U_12592,U_12591,U_12590,U_12589)))
    | ~ sP914(U_12589,U_12590,U_12591,U_12592) ),
    inference(clausify,[status(thm)],[f_3342_5]) ).

cnf(f_3342_10,plain,
    ( hBOOL(hAPP(U_12592,sK271(U_12592,U_12591,U_12590,U_12589)))
    | ~ sP914(U_12589,U_12590,U_12591,U_12592) ),
    inference(clausify,[status(thm)],[f_3342_5]) ).

cnf(f_3342_11,plain,
    ( ~ hBOOL(hAPP(U_12592,hAPP(hAPP(c_Set_Oinsert(U_12589),sK270(U_12592,U_12591,U_12590,U_12589)),sK271(U_12592,U_12591,U_12590,U_12589))))
    | ~ sP914(U_12589,U_12590,U_12591,U_12592) ),
    inference(clausify,[status(thm)],[f_3342_5]) ).

fof(f_3343_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_3343_2,plain,
    ! [U_12598,U_12597,U_12596,U_12595,U_12594] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12594),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12595,U_12594),U_12597),U_12596)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12595,U_12594),U_12598),U_12596)))
      | ? [U_12593] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12594),hAPP(U_12597,U_12593)),hAPP(U_12598,U_12593)))
          & hBOOL(hAPP(hAPP(c_member(U_12595),U_12593),U_12596)) )
      | U_12596 = c_Orderings_Obot__class_Obot(tc_fun(U_12595,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12595),U_12596))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_12594)
      | ~ class_Groups_Ocomm__monoid__add(U_12594) ),
    inference(variable_rename,[status(thm)],[f_3343_1]) ).

fof(f_3343_3,plain,
    ! [U_12598,U_12597,U_12596,U_12595,U_12594] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12594),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12595,U_12594),U_12597),U_12596)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12595,U_12594),U_12598),U_12596)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12594),hAPP(U_12597,sK272(U_12598,U_12597,U_12596,U_12595,U_12594))),hAPP(U_12598,sK272(U_12598,U_12597,U_12596,U_12595,U_12594))))
        & hBOOL(hAPP(hAPP(c_member(U_12595),sK272(U_12598,U_12597,U_12596,U_12595,U_12594)),U_12596)) )
      | U_12596 = c_Orderings_Obot__class_Obot(tc_fun(U_12595,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12595),U_12596))
      | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_12594)
      | ~ class_Groups_Ocomm__monoid__add(U_12594) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK272]),skolemize(U_12593,sK272(U_12598,U_12597,U_12596,U_12595,U_12594))],[f_3343_2]) ).

fof(f_3343_4,plain,
    ( ! [U_12594,U_12595,U_12596,U_12598,U_12597] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12594),hAPP(U_12597,sK272(U_12598,U_12597,U_12596,U_12595,U_12594))),hAPP(U_12598,sK272(U_12598,U_12597,U_12596,U_12595,U_12594))))
        | ~ sP915(U_12594,U_12595,U_12596,U_12598,U_12597) )
    & ! [U_12594,U_12595,U_12596,U_12598,U_12597] :
        ( hBOOL(hAPP(hAPP(c_member(U_12595),sK272(U_12598,U_12597,U_12596,U_12595,U_12594)),U_12596))
        | ~ sP915(U_12594,U_12595,U_12596,U_12598,U_12597) )
    & ! [U_12594,U_12595,U_12596,U_12598,U_12597] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12594),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12595,U_12594),U_12597),U_12596)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12595,U_12594),U_12598),U_12596)))
        | sP915(U_12594,U_12595,U_12596,U_12598,U_12597)
        | U_12596 = c_Orderings_Obot__class_Obot(tc_fun(U_12595,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12595),U_12596))
        | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_12594)
        | ~ class_Groups_Ocomm__monoid__add(U_12594) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP915])],[f_3343_3]) ).

cnf(f_3343_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12594),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12595,U_12594),U_12597),U_12596)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_12595,U_12594),U_12598),U_12596)))
    | sP915(U_12594,U_12595,U_12596,U_12598,U_12597)
    | U_12596 = c_Orderings_Obot__class_Obot(tc_fun(U_12595,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12595),U_12596))
    | ~ class_Groups_Oordered__cancel__ab__semigroup__add(U_12594)
    | ~ class_Groups_Ocomm__monoid__add(U_12594) ),
    inference(clausify,[status(thm)],[f_3343_4]) ).

cnf(f_3343_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12595),sK272(U_12598,U_12597,U_12596,U_12595,U_12594)),U_12596))
    | ~ sP915(U_12594,U_12595,U_12596,U_12598,U_12597) ),
    inference(clausify,[status(thm)],[f_3343_4]) ).

cnf(f_3343_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12594),hAPP(U_12597,sK272(U_12598,U_12597,U_12596,U_12595,U_12594))),hAPP(U_12598,sK272(U_12598,U_12597,U_12596,U_12595,U_12594))))
    | ~ sP915(U_12594,U_12595,U_12596,U_12598,U_12597) ),
    inference(clausify,[status(thm)],[f_3343_4]) ).

fof(f_3344_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_3344_2,plain,
    ! [U_12600,U_12599] :
      ( ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),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_12599),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_12600),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_12599),U_12600)),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_12599),U_12600)),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_12599),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_12600),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_3344_1]) ).

fof(f_3344_3,plain,
    ( ! [U_12604,U_12602] :
        ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),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_12602),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_12604),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_12602),U_12604)),c_Int_Ointrel)) )
    & ! [U_12603,U_12601] :
        ( 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_12601),U_12603)),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_12601),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_12603),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_3344_2]) ).

fof(f_3344_4,plain,
    ( ! [U_12604,U_12602] :
        ( hAPP(c_Relation_OImage(tc_prod(tc_Nat_Onat,tc_Nat_Onat),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_12602),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_12604),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_12602),U_12604)),c_Int_Ointrel)) )
    & ! [U_12603,U_12601] :
        ( 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_12601),U_12603)),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_12601),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_12603),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3344_3]) ).

cnf(f_3344_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_12601),U_12603)),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_12601),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_12603),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3344_4]) ).

cnf(f_3344_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_12602),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_12604),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_12602),U_12604)),c_Int_Ointrel)) ),
    inference(clausify,[status(thm)],[f_3344_4]) ).

fof(f_3345_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_3345_2,plain,
    ! [U_12606,U_12605] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12605,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12605),U_12606)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12605),U_12606)) = hAPP(hAPP(c_Set_Oinsert(U_12605),U_12606),c_Orderings_Obot__class_Obot(tc_fun(U_12605,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_12605) ),
    inference(variable_rename,[status(thm)],[f_3345_1]) ).

fof(f_3345_3,plain,
    ! [U_12605,U_12606] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12605,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12605),U_12606)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12605),U_12606)) = hAPP(hAPP(c_Set_Oinsert(U_12605),U_12606),c_Orderings_Obot__class_Obot(tc_fun(U_12605,tc_HOL_Obool)))
      | ~ class_Orderings_Oorder(U_12605) ),
    inference(definitional_conversion,[status(esa)],[f_3345_2]) ).

cnf(f_3345_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12605,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12605),U_12606)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12605),U_12606)) = hAPP(hAPP(c_Set_Oinsert(U_12605),U_12606),c_Orderings_Obot__class_Obot(tc_fun(U_12605,tc_HOL_Obool)))
    | ~ class_Orderings_Oorder(U_12605) ),
    inference(clausify,[status(thm)],[f_3345_3]) ).

fof(f_3346_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_3346_2,plain,
    ! [U_12612,U_12611,U_12610,U_12609,U_12608] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12608),U_12611),U_12609) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12608),U_12612),U_12610)
      | ? [U_12607] :
          ( hAPP(U_12611,U_12607) != hAPP(U_12612,U_12607)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_12607)) )
      | ~ c_Nat__Transfer_Onat__set(U_12610)
      | U_12609 != U_12610
      | ~ class_Groups_Ocomm__monoid__mult(U_12608)
      | ~ class_Groups_Ocomm__monoid__add(U_12608) ),
    inference(variable_rename,[status(thm)],[f_3346_1]) ).

fof(f_3346_3,plain,
    ! [U_12612,U_12611,U_12610,U_12609,U_12608] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12608),U_12611),U_12609) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12608),U_12612),U_12610)
      | ( hAPP(U_12611,sK273(U_12612,U_12611,U_12610,U_12609,U_12608)) != hAPP(U_12612,sK273(U_12612,U_12611,U_12610,U_12609,U_12608))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK273(U_12612,U_12611,U_12610,U_12609,U_12608))) )
      | ~ c_Nat__Transfer_Onat__set(U_12610)
      | U_12609 != U_12610
      | ~ class_Groups_Ocomm__monoid__mult(U_12608)
      | ~ class_Groups_Ocomm__monoid__add(U_12608) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK273]),skolemize(U_12607,sK273(U_12612,U_12611,U_12610,U_12609,U_12608))],[f_3346_2]) ).

fof(f_3346_4,plain,
    ( ! [U_12608,U_12609,U_12610,U_12611,U_12612] :
        ( hAPP(U_12611,sK273(U_12612,U_12611,U_12610,U_12609,U_12608)) != hAPP(U_12612,sK273(U_12612,U_12611,U_12610,U_12609,U_12608))
        | ~ sP916(U_12608,U_12609,U_12610,U_12611,U_12612) )
    & ! [U_12608,U_12609,U_12610,U_12611,U_12612] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK273(U_12612,U_12611,U_12610,U_12609,U_12608)))
        | ~ sP916(U_12608,U_12609,U_12610,U_12611,U_12612) )
    & ! [U_12608,U_12609,U_12610,U_12611,U_12612] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12608),U_12611),U_12609) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12608),U_12612),U_12610)
        | sP916(U_12608,U_12609,U_12610,U_12611,U_12612)
        | ~ c_Nat__Transfer_Onat__set(U_12610)
        | U_12609 != U_12610
        | ~ class_Groups_Ocomm__monoid__mult(U_12608)
        | ~ class_Groups_Ocomm__monoid__add(U_12608) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP916])],[f_3346_3]) ).

cnf(f_3346_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12608),U_12611),U_12609) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_Int_Oint,U_12608),U_12612),U_12610)
    | sP916(U_12608,U_12609,U_12610,U_12611,U_12612)
    | ~ c_Nat__Transfer_Onat__set(U_12610)
    | U_12609 != U_12610
    | ~ class_Groups_Ocomm__monoid__mult(U_12608)
    | ~ class_Groups_Ocomm__monoid__add(U_12608) ),
    inference(clausify,[status(thm)],[f_3346_4]) ).

cnf(f_3346_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK273(U_12612,U_12611,U_12610,U_12609,U_12608)))
    | ~ sP916(U_12608,U_12609,U_12610,U_12611,U_12612) ),
    inference(clausify,[status(thm)],[f_3346_4]) ).

cnf(f_3346_7,plain,
    ( hAPP(U_12611,sK273(U_12612,U_12611,U_12610,U_12609,U_12608)) != hAPP(U_12612,sK273(U_12612,U_12611,U_12610,U_12609,U_12608))
    | ~ sP916(U_12608,U_12609,U_12610,U_12611,U_12612) ),
    inference(clausify,[status(thm)],[f_3346_4]) ).

fof(f_3347_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_3347_2,plain,
    ! [U_12615,U_12614,U_12613] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OatLeast(U_12613),U_12614) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12613),U_12615)
          | U_12614 != U_12615 )
        & ( U_12614 = U_12615
          | hAPP(c_SetInterval_Oord__class_OatLeast(U_12613),U_12614) != hAPP(c_SetInterval_Oord__class_OatLeast(U_12613),U_12615) ) )
      | ~ class_Orderings_Olinorder(U_12613) ),
    inference(variable_rename,[status(thm)],[f_3347_1]) ).

fof(f_3347_3,plain,
    ( ! [U_12615,U_12613,U_12614] :
        ( hAPP(c_SetInterval_Oord__class_OatLeast(U_12613),U_12614) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12613),U_12615)
        | U_12614 != U_12615
        | ~ sP917(U_12615,U_12613,U_12614) )
    & ! [U_12615,U_12613,U_12614] :
        ( U_12614 = U_12615
        | hAPP(c_SetInterval_Oord__class_OatLeast(U_12613),U_12614) != hAPP(c_SetInterval_Oord__class_OatLeast(U_12613),U_12615)
        | ~ sP917(U_12615,U_12613,U_12614) )
    & ! [U_12615,U_12613,U_12614] :
        ( sP917(U_12615,U_12613,U_12614)
        | ~ class_Orderings_Olinorder(U_12613) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP917])],[f_3347_2]) ).

cnf(f_3347_4,plain,
    ( sP917(U_12615,U_12613,U_12614)
    | ~ class_Orderings_Olinorder(U_12613) ),
    inference(clausify,[status(thm)],[f_3347_3]) ).

cnf(f_3347_5,plain,
    ( U_12614 = U_12615
    | hAPP(c_SetInterval_Oord__class_OatLeast(U_12613),U_12614) != hAPP(c_SetInterval_Oord__class_OatLeast(U_12613),U_12615)
    | ~ sP917(U_12615,U_12613,U_12614) ),
    inference(clausify,[status(thm)],[f_3347_3]) ).

cnf(f_3347_6,plain,
    ( hAPP(c_SetInterval_Oord__class_OatLeast(U_12613),U_12614) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12613),U_12615)
    | U_12614 != U_12615
    | ~ sP917(U_12615,U_12613,U_12614) ),
    inference(clausify,[status(thm)],[f_3347_3]) ).

fof(f_3348_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_3348_2,plain,
    ! [U_12617,U_12616] : hAPP(c_Relation_OImage(U_12616,U_12616,c_Relation_OId(U_12616)),U_12617) = U_12617,
    inference(variable_rename,[status(thm)],[f_3348_1]) ).

fof(f_3348_3,plain,
    ! [U_12617,U_12616] : hAPP(c_Relation_OImage(U_12616,U_12616,c_Relation_OId(U_12616)),U_12617) = U_12617,
    inference(definitional_conversion,[status(esa)],[f_3348_2]) ).

cnf(f_3348_4,plain,
    hAPP(c_Relation_OImage(U_12616,U_12616,c_Relation_OId(U_12616)),U_12617) = U_12617,
    inference(clausify,[status(thm)],[f_3348_3]) ).

fof(f_3349_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_3349_2,plain,
    ! [U_12622,U_12621,U_12620,U_12619,U_12618] : hAPP(c_Relation_OImage(U_12618,U_12619,U_12620),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12618,tc_HOL_Obool)),U_12621),U_12622)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12619,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12618,U_12619,U_12620),U_12621)),hAPP(c_Relation_OImage(U_12618,U_12619,U_12620),U_12622)),
    inference(variable_rename,[status(thm)],[f_3349_1]) ).

fof(f_3349_3,plain,
    ! [U_12618,U_12619,U_12620,U_12621,U_12622] : hAPP(c_Relation_OImage(U_12618,U_12619,U_12620),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12618,tc_HOL_Obool)),U_12621),U_12622)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12619,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12618,U_12619,U_12620),U_12621)),hAPP(c_Relation_OImage(U_12618,U_12619,U_12620),U_12622)),
    inference(definitional_conversion,[status(esa)],[f_3349_2]) ).

cnf(f_3349_4,plain,
    hAPP(c_Relation_OImage(U_12618,U_12619,U_12620),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12618,tc_HOL_Obool)),U_12621),U_12622)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12619,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12618,U_12619,U_12620),U_12621)),hAPP(c_Relation_OImage(U_12618,U_12619,U_12620),U_12622)),
    inference(clausify,[status(thm)],[f_3349_3]) ).

fof(f_3350_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_3350_2,plain,
    ! [U_12625,U_12624,U_12623] : hAPP(c_Relation_OImage(U_12623,U_12624,U_12625),c_Orderings_Obot__class_Obot(tc_fun(U_12623,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12624,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3350_1]) ).

fof(f_3350_3,plain,
    ! [U_12623,U_12624,U_12625] : hAPP(c_Relation_OImage(U_12623,U_12624,U_12625),c_Orderings_Obot__class_Obot(tc_fun(U_12623,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12624,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3350_2]) ).

cnf(f_3350_4,plain,
    hAPP(c_Relation_OImage(U_12623,U_12624,U_12625),c_Orderings_Obot__class_Obot(tc_fun(U_12623,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_12624,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3350_3]) ).

fof(f_3351_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_3351_2,plain,
    ! [U_12630,U_12629,U_12628,U_12627,U_12626] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12626,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12627,U_12626,U_12628),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12627,tc_HOL_Obool)),U_12629),U_12630))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12626,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12627,U_12626,U_12628),U_12629)),hAPP(c_Relation_OImage(U_12627,U_12626,U_12628),U_12630)))),
    inference(variable_rename,[status(thm)],[f_3351_1]) ).

fof(f_3351_3,plain,
    ! [U_12626,U_12627,U_12628,U_12629,U_12630] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12626,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12627,U_12626,U_12628),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12627,tc_HOL_Obool)),U_12629),U_12630))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12626,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12627,U_12626,U_12628),U_12629)),hAPP(c_Relation_OImage(U_12627,U_12626,U_12628),U_12630)))),
    inference(definitional_conversion,[status(esa)],[f_3351_2]) ).

cnf(f_3351_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12626,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12627,U_12626,U_12628),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12627,tc_HOL_Obool)),U_12629),U_12630))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12626,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12627,U_12626,U_12628),U_12629)),hAPP(c_Relation_OImage(U_12627,U_12626,U_12628),U_12630)))),
    inference(clausify,[status(thm)],[f_3351_3]) ).

fof(f_3352_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_3352_2,plain,
    ! [U_12633,U_12632,U_12631] :
      ( hAPP(c_Relation_OImage(U_12631,U_12631,c_Transitive__Closure_Ortrancl(U_12631,U_12632)),U_12633) = U_12633
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12631,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12631,U_12631,U_12632),U_12633)),U_12633)) ),
    inference(variable_rename,[status(thm)],[f_3352_1]) ).

fof(f_3352_3,plain,
    ! [U_12632,U_12631,U_12633] :
      ( hAPP(c_Relation_OImage(U_12631,U_12631,c_Transitive__Closure_Ortrancl(U_12631,U_12632)),U_12633) = U_12633
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12631,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12631,U_12631,U_12632),U_12633)),U_12633)) ),
    inference(definitional_conversion,[status(esa)],[f_3352_2]) ).

cnf(f_3352_4,plain,
    ( hAPP(c_Relation_OImage(U_12631,U_12631,c_Transitive__Closure_Ortrancl(U_12631,U_12632)),U_12633) = U_12633
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12631,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12631,U_12631,U_12632),U_12633)),U_12633)) ),
    inference(clausify,[status(thm)],[f_3352_3]) ).

fof(f_3353_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_3353_2,plain,
    ! [U_12639,U_12638,U_12637,U_12636,U_12635,U_12634] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12635,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12634,U_12635,U_12636),U_12638)),hAPP(c_Relation_OImage(U_12634,U_12635,U_12637),U_12639)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12634,tc_HOL_Obool)),U_12638),U_12639))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12634,U_12635),tc_HOL_Obool)),U_12636),U_12637)) ),
    inference(variable_rename,[status(thm)],[f_3353_1]) ).

fof(f_3353_3,plain,
    ! [U_12634,U_12635,U_12636,U_12637,U_12638,U_12639] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12635,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12634,U_12635,U_12636),U_12638)),hAPP(c_Relation_OImage(U_12634,U_12635,U_12637),U_12639)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12634,tc_HOL_Obool)),U_12638),U_12639))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12634,U_12635),tc_HOL_Obool)),U_12636),U_12637)) ),
    inference(definitional_conversion,[status(esa)],[f_3353_2]) ).

cnf(f_3353_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12635,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12634,U_12635,U_12636),U_12638)),hAPP(c_Relation_OImage(U_12634,U_12635,U_12637),U_12639)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12634,tc_HOL_Obool)),U_12638),U_12639))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_12634,U_12635),tc_HOL_Obool)),U_12636),U_12637)) ),
    inference(clausify,[status(thm)],[f_3353_3]) ).

fof(f_3354_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_3354_2,plain,
    ! [U_12644,U_12643,U_12642,U_12641,U_12640] : hAPP(c_Relation_OImage(U_12640,U_12641,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12640,U_12641),tc_HOL_Obool)),U_12642),U_12643)),U_12644) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12641,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12640,U_12641,U_12642),U_12644)),hAPP(c_Relation_OImage(U_12640,U_12641,U_12643),U_12644)),
    inference(variable_rename,[status(thm)],[f_3354_1]) ).

fof(f_3354_3,plain,
    ! [U_12640,U_12641,U_12642,U_12643,U_12644] : hAPP(c_Relation_OImage(U_12640,U_12641,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12640,U_12641),tc_HOL_Obool)),U_12642),U_12643)),U_12644) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12641,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12640,U_12641,U_12642),U_12644)),hAPP(c_Relation_OImage(U_12640,U_12641,U_12643),U_12644)),
    inference(definitional_conversion,[status(esa)],[f_3354_2]) ).

cnf(f_3354_4,plain,
    hAPP(c_Relation_OImage(U_12640,U_12641,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_12640,U_12641),tc_HOL_Obool)),U_12642),U_12643)),U_12644) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12641,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12640,U_12641,U_12642),U_12644)),hAPP(c_Relation_OImage(U_12640,U_12641,U_12643),U_12644)),
    inference(clausify,[status(thm)],[f_3354_3]) ).

fof(f_3355_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_3355_2,plain,
    ! [U_12647,U_12646,U_12645] : hAPP(c_Relation_OImage(U_12645,U_12645,c_Relation_OId__on(U_12645,U_12646)),U_12647) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12645,tc_HOL_Obool)),U_12646),U_12647),
    inference(variable_rename,[status(thm)],[f_3355_1]) ).

fof(f_3355_3,plain,
    ! [U_12645,U_12646,U_12647] : hAPP(c_Relation_OImage(U_12645,U_12645,c_Relation_OId__on(U_12645,U_12646)),U_12647) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12645,tc_HOL_Obool)),U_12646),U_12647),
    inference(definitional_conversion,[status(esa)],[f_3355_2]) ).

cnf(f_3355_4,plain,
    hAPP(c_Relation_OImage(U_12645,U_12645,c_Relation_OId__on(U_12645,U_12646)),U_12647) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12645,tc_HOL_Obool)),U_12646),U_12647),
    inference(clausify,[status(thm)],[f_3355_3]) ).

fof(f_3356_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_3356_2,plain,
    ! [U_12650,U_12649,U_12648] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_12648),U_12649),hAPP(c_SetInterval_Oord__class_OatLeast(U_12648),U_12650)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12648),U_12650),U_12649)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12648),U_12650),U_12649))
          | ~ hBOOL(hAPP(hAPP(c_member(U_12648),U_12649),hAPP(c_SetInterval_Oord__class_OatLeast(U_12648),U_12650))) ) )
      | ~ class_Orderings_Oord(U_12648) ),
    inference(variable_rename,[status(thm)],[f_3356_1]) ).

fof(f_3356_3,plain,
    ( ! [U_12648,U_12649,U_12650] :
        ( hBOOL(hAPP(hAPP(c_member(U_12648),U_12649),hAPP(c_SetInterval_Oord__class_OatLeast(U_12648),U_12650)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12648),U_12650),U_12649))
        | ~ sP918(U_12648,U_12649,U_12650) )
    & ! [U_12648,U_12649,U_12650] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12648),U_12650),U_12649))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12648),U_12649),hAPP(c_SetInterval_Oord__class_OatLeast(U_12648),U_12650)))
        | ~ sP918(U_12648,U_12649,U_12650) )
    & ! [U_12648,U_12649,U_12650] :
        ( sP918(U_12648,U_12649,U_12650)
        | ~ class_Orderings_Oord(U_12648) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP918])],[f_3356_2]) ).

cnf(f_3356_4,plain,
    ( sP918(U_12648,U_12649,U_12650)
    | ~ class_Orderings_Oord(U_12648) ),
    inference(clausify,[status(thm)],[f_3356_3]) ).

cnf(f_3356_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12648),U_12650),U_12649))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12648),U_12649),hAPP(c_SetInterval_Oord__class_OatLeast(U_12648),U_12650)))
    | ~ sP918(U_12648,U_12649,U_12650) ),
    inference(clausify,[status(thm)],[f_3356_3]) ).

cnf(f_3356_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12648),U_12649),hAPP(c_SetInterval_Oord__class_OatLeast(U_12648),U_12650)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12648),U_12650),U_12649))
    | ~ sP918(U_12648,U_12649,U_12650) ),
    inference(clausify,[status(thm)],[f_3356_3]) ).

fof(f_3357_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_3357_2,plain,
    ! [U_12653,U_12652,U_12651] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12651,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12651),U_12652)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12651),U_12653)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12651),U_12653),U_12652)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12651),U_12653),U_12652))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12651,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12651),U_12652)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12651),U_12653))) ) )
      | ~ class_Orderings_Oorder(U_12651) ),
    inference(variable_rename,[status(thm)],[f_3357_1]) ).

fof(f_3357_3,plain,
    ( ! [U_12653,U_12652,U_12651] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12651,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12651),U_12652)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12651),U_12653)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12651),U_12653),U_12652))
        | ~ sP919(U_12653,U_12652,U_12651) )
    & ! [U_12653,U_12652,U_12651] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12651),U_12653),U_12652))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12651,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12651),U_12652)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12651),U_12653)))
        | ~ sP919(U_12653,U_12652,U_12651) )
    & ! [U_12653,U_12652,U_12651] :
        ( sP919(U_12653,U_12652,U_12651)
        | ~ class_Orderings_Oorder(U_12651) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP919])],[f_3357_2]) ).

cnf(f_3357_4,plain,
    ( sP919(U_12653,U_12652,U_12651)
    | ~ class_Orderings_Oorder(U_12651) ),
    inference(clausify,[status(thm)],[f_3357_3]) ).

cnf(f_3357_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12651),U_12653),U_12652))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12651,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12651),U_12652)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12651),U_12653)))
    | ~ sP919(U_12653,U_12652,U_12651) ),
    inference(clausify,[status(thm)],[f_3357_3]) ).

cnf(f_3357_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12651,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12651),U_12652)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12651),U_12653)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12651),U_12653),U_12652))
    | ~ sP919(U_12653,U_12652,U_12651) ),
    inference(clausify,[status(thm)],[f_3357_3]) ).

fof(f_3358_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_3358_2,plain,
    ! [U_12659,U_12658,U_12657,U_12656,U_12655,U_12654] :
      ( hBOOL(hAPP(hAPP(c_member(U_12657),U_12658),hAPP(c_Relation_OImage(U_12654,U_12657,U_12659),U_12656)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12654,U_12657)),hAPP(hAPP(c_Product__Type_OPair(U_12654,U_12657),U_12655),U_12658)),U_12659))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12654),U_12655),U_12656)) ),
    inference(variable_rename,[status(thm)],[f_3358_1]) ).

fof(f_3358_3,plain,
    ! [U_12655,U_12654,U_12656,U_12657,U_12658,U_12659] :
      ( hBOOL(hAPP(hAPP(c_member(U_12657),U_12658),hAPP(c_Relation_OImage(U_12654,U_12657,U_12659),U_12656)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12654,U_12657)),hAPP(hAPP(c_Product__Type_OPair(U_12654,U_12657),U_12655),U_12658)),U_12659))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12654),U_12655),U_12656)) ),
    inference(definitional_conversion,[status(esa)],[f_3358_2]) ).

cnf(f_3358_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12657),U_12658),hAPP(c_Relation_OImage(U_12654,U_12657,U_12659),U_12656)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12654,U_12657)),hAPP(hAPP(c_Product__Type_OPair(U_12654,U_12657),U_12655),U_12658)),U_12659))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12654),U_12655),U_12656)) ),
    inference(clausify,[status(thm)],[f_3358_3]) ).

fof(f_3359_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_3359_2,plain,
    ! [U_12666,U_12665,U_12664,U_12663,U_12662] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_12662),U_12663),hAPP(c_Relation_OImage(U_12664,U_12662,U_12665),U_12666)))
        | ! [U_12661] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12664,U_12662)),hAPP(hAPP(c_Product__Type_OPair(U_12664,U_12662),U_12661),U_12663)),U_12665))
            | ~ hBOOL(hAPP(hAPP(c_member(U_12664),U_12661),U_12666)) ) )
      & ( ? [U_12660] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12664,U_12662)),hAPP(hAPP(c_Product__Type_OPair(U_12664,U_12662),U_12660),U_12663)),U_12665))
            & hBOOL(hAPP(hAPP(c_member(U_12664),U_12660),U_12666)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_12662),U_12663),hAPP(c_Relation_OImage(U_12664,U_12662,U_12665),U_12666))) ) ),
    inference(variable_rename,[status(thm)],[f_3359_1]) ).

fof(f_3359_3,plain,
    ( ! [U_12676,U_12674,U_12672,U_12670,U_12668] :
        ( hBOOL(hAPP(hAPP(c_member(U_12668),U_12670),hAPP(c_Relation_OImage(U_12672,U_12668,U_12674),U_12676)))
        | ! [U_12661] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12672,U_12668)),hAPP(hAPP(c_Product__Type_OPair(U_12672,U_12668),U_12661),U_12670)),U_12674))
            | ~ hBOOL(hAPP(hAPP(c_member(U_12672),U_12661),U_12676)) ) )
    & ! [U_12675,U_12673,U_12671,U_12669,U_12667] :
        ( ? [U_12660] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12671,U_12667)),hAPP(hAPP(c_Product__Type_OPair(U_12671,U_12667),U_12660),U_12669)),U_12673))
            & hBOOL(hAPP(hAPP(c_member(U_12671),U_12660),U_12675)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_12667),U_12669),hAPP(c_Relation_OImage(U_12671,U_12667,U_12673),U_12675))) ) ),
    inference(miniscope,[status(thm)],[f_3359_2]) ).

fof(f_3359_4,plain,
    ( ! [U_12676,U_12674,U_12672,U_12670,U_12668] :
        ( hBOOL(hAPP(hAPP(c_member(U_12668),U_12670),hAPP(c_Relation_OImage(U_12672,U_12668,U_12674),U_12676)))
        | ! [U_12661] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12672,U_12668)),hAPP(hAPP(c_Product__Type_OPair(U_12672,U_12668),U_12661),U_12670)),U_12674))
            | ~ hBOOL(hAPP(hAPP(c_member(U_12672),U_12661),U_12676)) ) )
    & ! [U_12675,U_12673,U_12671,U_12669,U_12667] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12671,U_12667)),hAPP(hAPP(c_Product__Type_OPair(U_12671,U_12667),sK274(U_12675,U_12673,U_12671,U_12669,U_12667)),U_12669)),U_12673))
          & hBOOL(hAPP(hAPP(c_member(U_12671),sK274(U_12675,U_12673,U_12671,U_12669,U_12667)),U_12675)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_12667),U_12669),hAPP(c_Relation_OImage(U_12671,U_12667,U_12673),U_12675))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK274]),skolemize(U_12660,sK274(U_12675,U_12673,U_12671,U_12669,U_12667))],[f_3359_3]) ).

fof(f_3359_5,plain,
    ( ! [U_12669,U_12671,U_12667,U_12675,U_12673] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12671,U_12667)),hAPP(hAPP(c_Product__Type_OPair(U_12671,U_12667),sK274(U_12675,U_12673,U_12671,U_12669,U_12667)),U_12669)),U_12673))
        | ~ sP920(U_12669,U_12671,U_12667,U_12675,U_12673) )
    & ! [U_12669,U_12671,U_12667,U_12675,U_12673] :
        ( hBOOL(hAPP(hAPP(c_member(U_12671),sK274(U_12675,U_12673,U_12671,U_12669,U_12667)),U_12675))
        | ~ sP920(U_12669,U_12671,U_12667,U_12675,U_12673) )
    & ! [U_12661,U_12676,U_12668,U_12670,U_12674,U_12672] :
        ( hBOOL(hAPP(hAPP(c_member(U_12668),U_12670),hAPP(c_Relation_OImage(U_12672,U_12668,U_12674),U_12676)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12672,U_12668)),hAPP(hAPP(c_Product__Type_OPair(U_12672,U_12668),U_12661),U_12670)),U_12674))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12672),U_12661),U_12676)) )
    & ! [U_12669,U_12671,U_12667,U_12675,U_12673] :
        ( sP920(U_12669,U_12671,U_12667,U_12675,U_12673)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12667),U_12669),hAPP(c_Relation_OImage(U_12671,U_12667,U_12673),U_12675))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP920])],[f_3359_4]) ).

cnf(f_3359_6,plain,
    ( sP920(U_12669,U_12671,U_12667,U_12675,U_12673)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12667),U_12669),hAPP(c_Relation_OImage(U_12671,U_12667,U_12673),U_12675))) ),
    inference(clausify,[status(thm)],[f_3359_5]) ).

cnf(f_3359_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12668),U_12670),hAPP(c_Relation_OImage(U_12672,U_12668,U_12674),U_12676)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12672,U_12668)),hAPP(hAPP(c_Product__Type_OPair(U_12672,U_12668),U_12661),U_12670)),U_12674))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12672),U_12661),U_12676)) ),
    inference(clausify,[status(thm)],[f_3359_5]) ).

cnf(f_3359_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12671),sK274(U_12675,U_12673,U_12671,U_12669,U_12667)),U_12675))
    | ~ sP920(U_12669,U_12671,U_12667,U_12675,U_12673) ),
    inference(clausify,[status(thm)],[f_3359_5]) ).

cnf(f_3359_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12671,U_12667)),hAPP(hAPP(c_Product__Type_OPair(U_12671,U_12667),sK274(U_12675,U_12673,U_12671,U_12669,U_12667)),U_12669)),U_12673))
    | ~ sP920(U_12669,U_12671,U_12667,U_12675,U_12673) ),
    inference(clausify,[status(thm)],[f_3359_5]) ).

fof(f_3360_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_3360_2,plain,
    ! [U_12679,U_12678,U_12677] :
      ( U_12679 = c_Orderings_Obot__class_Obot(tc_fun(U_12677,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12677,tc_HOL_Obool)),U_12679),hAPP(c_Relation_OImage(U_12677,U_12677,U_12678),U_12679)))
      | ~ c_Wellfounded_Owf(U_12677,U_12678) ),
    inference(variable_rename,[status(thm)],[f_3360_1]) ).

fof(f_3360_3,plain,
    ! [U_12679,U_12678,U_12677] :
      ( U_12679 = c_Orderings_Obot__class_Obot(tc_fun(U_12677,tc_HOL_Obool))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12677,tc_HOL_Obool)),U_12679),hAPP(c_Relation_OImage(U_12677,U_12677,U_12678),U_12679)))
      | ~ c_Wellfounded_Owf(U_12677,U_12678) ),
    inference(definitional_conversion,[status(esa)],[f_3360_2]) ).

cnf(f_3360_4,plain,
    ( U_12679 = c_Orderings_Obot__class_Obot(tc_fun(U_12677,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12677,tc_HOL_Obool)),U_12679),hAPP(c_Relation_OImage(U_12677,U_12677,U_12678),U_12679)))
    | ~ c_Wellfounded_Owf(U_12677,U_12678) ),
    inference(clausify,[status(thm)],[f_3360_3]) ).

fof(f_3361_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_3361_2,plain,
    ! [U_12684,U_12683,U_12682,U_12681,U_12680] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12680,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12681,U_12680,U_12682),U_12683)),U_12684))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12681,tc_HOL_Obool)),U_12683),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12681,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12680,U_12681,hAPP(c_Relation_Oconverse(U_12681,U_12680),U_12682)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12680,tc_HOL_Obool)),U_12684))))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12681,tc_HOL_Obool)),U_12683),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12681,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12680,U_12681,hAPP(c_Relation_Oconverse(U_12681,U_12680),U_12682)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12680,tc_HOL_Obool)),U_12684)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12680,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12681,U_12680,U_12682),U_12683)),U_12684)) ) ),
    inference(variable_rename,[status(thm)],[f_3361_1]) ).

fof(f_3361_3,plain,
    ( ! [U_12694,U_12692,U_12690,U_12688,U_12686] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12686,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12688,U_12686,U_12690),U_12692)),U_12694))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12688,tc_HOL_Obool)),U_12692),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12688,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12686,U_12688,hAPP(c_Relation_Oconverse(U_12688,U_12686),U_12690)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12686,tc_HOL_Obool)),U_12694))))) )
    & ! [U_12693,U_12691,U_12689,U_12687,U_12685] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12687,tc_HOL_Obool)),U_12691),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12687,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12685,U_12687,hAPP(c_Relation_Oconverse(U_12687,U_12685),U_12689)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12685,tc_HOL_Obool)),U_12693)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12685,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12687,U_12685,U_12689),U_12691)),U_12693)) ) ),
    inference(miniscope,[status(thm)],[f_3361_2]) ).

fof(f_3361_4,plain,
    ( ! [U_12686,U_12688,U_12690,U_12692,U_12694] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12686,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12688,U_12686,U_12690),U_12692)),U_12694))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12688,tc_HOL_Obool)),U_12692),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12688,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12686,U_12688,hAPP(c_Relation_Oconverse(U_12688,U_12686),U_12690)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12686,tc_HOL_Obool)),U_12694))))) )
    & ! [U_12687,U_12689,U_12691,U_12685,U_12693] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12687,tc_HOL_Obool)),U_12691),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12687,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12685,U_12687,hAPP(c_Relation_Oconverse(U_12687,U_12685),U_12689)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12685,tc_HOL_Obool)),U_12693)))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12685,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12687,U_12685,U_12689),U_12691)),U_12693)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3361_3]) ).

cnf(f_3361_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12687,tc_HOL_Obool)),U_12691),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12687,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12685,U_12687,hAPP(c_Relation_Oconverse(U_12687,U_12685),U_12689)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12685,tc_HOL_Obool)),U_12693)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12685,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12687,U_12685,U_12689),U_12691)),U_12693)) ),
    inference(clausify,[status(thm)],[f_3361_4]) ).

cnf(f_3361_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12686,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12688,U_12686,U_12690),U_12692)),U_12694))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12688,tc_HOL_Obool)),U_12692),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12688,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12686,U_12688,hAPP(c_Relation_Oconverse(U_12688,U_12686),U_12690)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12686,tc_HOL_Obool)),U_12694))))) ),
    inference(clausify,[status(thm)],[f_3361_4]) ).

fof(f_3362_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_3362_2,plain,
    ! [U_12696,U_12695] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12695,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12695),U_12696)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12695),U_12696)
      | ~ class_Orderings_Olinorder(U_12695) ),
    inference(variable_rename,[status(thm)],[f_3362_1]) ).

fof(f_3362_3,plain,
    ! [U_12695,U_12696] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12695,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12695),U_12696)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12695),U_12696)
      | ~ class_Orderings_Olinorder(U_12695) ),
    inference(definitional_conversion,[status(esa)],[f_3362_2]) ).

cnf(f_3362_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12695,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12695),U_12696)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12695),U_12696)
    | ~ class_Orderings_Olinorder(U_12695) ),
    inference(clausify,[status(thm)],[f_3362_3]) ).

fof(f_3363_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_3363_2,plain,
    ! [U_12698,U_12697] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12697,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12697),U_12698)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12697),U_12698)
      | ~ class_Orderings_Olinorder(U_12697) ),
    inference(variable_rename,[status(thm)],[f_3363_1]) ).

fof(f_3363_3,plain,
    ! [U_12697,U_12698] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12697,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12697),U_12698)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12697),U_12698)
      | ~ class_Orderings_Olinorder(U_12697) ),
    inference(definitional_conversion,[status(esa)],[f_3363_2]) ).

cnf(f_3363_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12697,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12697),U_12698)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12697),U_12698)
    | ~ class_Orderings_Olinorder(U_12697) ),
    inference(clausify,[status(thm)],[f_3363_3]) ).

fof(f_3364_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_3364_2,plain,
    ! [U_12701,U_12700,U_12699] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12699,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12699,U_12700),U_12701)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12699),U_12701)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12699),U_12700)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12699),U_12700),U_12701))
      | ~ class_Orderings_Olinorder(U_12699) ),
    inference(variable_rename,[status(thm)],[f_3364_1]) ).

fof(f_3364_3,plain,
    ! [U_12699,U_12700,U_12701] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12699,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12699,U_12700),U_12701)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12699),U_12701)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12699),U_12700)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12699),U_12700),U_12701))
      | ~ class_Orderings_Olinorder(U_12699) ),
    inference(definitional_conversion,[status(esa)],[f_3364_2]) ).

cnf(f_3364_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12699,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12699,U_12700),U_12701)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12699),U_12701)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12699),U_12700)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12699),U_12700),U_12701))
    | ~ class_Orderings_Olinorder(U_12699) ),
    inference(clausify,[status(thm)],[f_3364_3]) ).

fof(f_3365_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_3365_2,plain,
    ! [U_12704,U_12703,U_12702] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12702,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12702,U_12703),U_12704)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12702),U_12704)) = c_Orderings_Obot__class_Obot(tc_fun(U_12702,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12702) ),
    inference(variable_rename,[status(thm)],[f_3365_1]) ).

fof(f_3365_3,plain,
    ! [U_12702,U_12703,U_12704] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12702,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12702,U_12703),U_12704)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12702),U_12704)) = c_Orderings_Obot__class_Obot(tc_fun(U_12702,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12702) ),
    inference(definitional_conversion,[status(esa)],[f_3365_2]) ).

cnf(f_3365_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12702,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_12702,U_12703),U_12704)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12702),U_12704)) = c_Orderings_Obot__class_Obot(tc_fun(U_12702,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12702) ),
    inference(clausify,[status(thm)],[f_3365_3]) ).

fof(f_3366_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_3366_2,plain,
    ! [U_12708,U_12707,U_12706,U_12705] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12705,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12705),U_12706)),c_SetInterval_Oord__class_OatLeastAtMost(U_12705,U_12707,U_12708)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12705,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12705),U_12706),U_12707),U_12708)
      | ~ class_Orderings_Olinorder(U_12705) ),
    inference(variable_rename,[status(thm)],[f_3366_1]) ).

fof(f_3366_3,plain,
    ! [U_12705,U_12706,U_12707,U_12708] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12705,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12705),U_12706)),c_SetInterval_Oord__class_OatLeastAtMost(U_12705,U_12707,U_12708)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12705,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12705),U_12706),U_12707),U_12708)
      | ~ class_Orderings_Olinorder(U_12705) ),
    inference(definitional_conversion,[status(esa)],[f_3366_2]) ).

cnf(f_3366_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12705,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12705),U_12706)),c_SetInterval_Oord__class_OatLeastAtMost(U_12705,U_12707,U_12708)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12705,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12705),U_12706),U_12707),U_12708)
    | ~ class_Orderings_Olinorder(U_12705) ),
    inference(clausify,[status(thm)],[f_3366_3]) ).

fof(f_3367_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_3367_2,plain,
    ! [U_12712,U_12711,U_12710,U_12709] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12709,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12709,U_12710,U_12711)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12709),U_12712)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12709,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12709),U_12710),U_12712),U_12711)
      | ~ class_Orderings_Olinorder(U_12709) ),
    inference(variable_rename,[status(thm)],[f_3367_1]) ).

fof(f_3367_3,plain,
    ! [U_12709,U_12710,U_12711,U_12712] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12709,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12709,U_12710,U_12711)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12709),U_12712)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12709,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12709),U_12710),U_12712),U_12711)
      | ~ class_Orderings_Olinorder(U_12709) ),
    inference(definitional_conversion,[status(esa)],[f_3367_2]) ).

cnf(f_3367_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12709,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12709,U_12710,U_12711)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12709),U_12712)) = c_SetInterval_Oord__class_OatLeastAtMost(U_12709,hAPP(hAPP(c_Orderings_Oord__class_Omax(U_12709),U_12710),U_12712),U_12711)
    | ~ class_Orderings_Olinorder(U_12709) ),
    inference(clausify,[status(thm)],[f_3367_3]) ).

fof(f_3368_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_3368_2,plain,
    ! [U_12715,U_12714,U_12713] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12713,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12713,U_12714,U_12715)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12713),U_12715)) = c_Orderings_Obot__class_Obot(tc_fun(U_12713,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12713) ),
    inference(variable_rename,[status(thm)],[f_3368_1]) ).

fof(f_3368_3,plain,
    ! [U_12713,U_12714,U_12715] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12713,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12713,U_12714,U_12715)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12713),U_12715)) = c_Orderings_Obot__class_Obot(tc_fun(U_12713,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12713) ),
    inference(definitional_conversion,[status(esa)],[f_3368_2]) ).

cnf(f_3368_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12713,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12713,U_12714,U_12715)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12713),U_12715)) = c_Orderings_Obot__class_Obot(tc_fun(U_12713,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12713) ),
    inference(clausify,[status(thm)],[f_3368_3]) ).

fof(f_3369_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_3369_2,plain,
    ! [U_12717,U_12716] :
      ( hAPP(c_Set_Oimage(U_12716,U_12716,c_Groups_Ouminus__class_Ouminus(U_12716)),hAPP(c_SetInterval_Oord__class_OatMost(U_12716),U_12717)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12716),hAPP(c_Groups_Ouminus__class_Ouminus(U_12716),U_12717))
      | ~ class_Groups_Oordered__ab__group__add(U_12716) ),
    inference(variable_rename,[status(thm)],[f_3369_1]) ).

fof(f_3369_3,plain,
    ! [U_12716,U_12717] :
      ( hAPP(c_Set_Oimage(U_12716,U_12716,c_Groups_Ouminus__class_Ouminus(U_12716)),hAPP(c_SetInterval_Oord__class_OatMost(U_12716),U_12717)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12716),hAPP(c_Groups_Ouminus__class_Ouminus(U_12716),U_12717))
      | ~ class_Groups_Oordered__ab__group__add(U_12716) ),
    inference(definitional_conversion,[status(esa)],[f_3369_2]) ).

cnf(f_3369_4,plain,
    ( hAPP(c_Set_Oimage(U_12716,U_12716,c_Groups_Ouminus__class_Ouminus(U_12716)),hAPP(c_SetInterval_Oord__class_OatMost(U_12716),U_12717)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12716),hAPP(c_Groups_Ouminus__class_Ouminus(U_12716),U_12717))
    | ~ class_Groups_Oordered__ab__group__add(U_12716) ),
    inference(clausify,[status(thm)],[f_3369_3]) ).

fof(f_3370_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_3370_2,plain,
    ! [U_12719,U_12718] :
      ( hAPP(c_Set_Oimage(U_12718,U_12718,c_Groups_Ouminus__class_Ouminus(U_12718)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12718),U_12719)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12718),hAPP(c_Groups_Ouminus__class_Ouminus(U_12718),U_12719))
      | ~ class_Groups_Oordered__ab__group__add(U_12718) ),
    inference(variable_rename,[status(thm)],[f_3370_1]) ).

fof(f_3370_3,plain,
    ! [U_12718,U_12719] :
      ( hAPP(c_Set_Oimage(U_12718,U_12718,c_Groups_Ouminus__class_Ouminus(U_12718)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12718),U_12719)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12718),hAPP(c_Groups_Ouminus__class_Ouminus(U_12718),U_12719))
      | ~ class_Groups_Oordered__ab__group__add(U_12718) ),
    inference(definitional_conversion,[status(esa)],[f_3370_2]) ).

cnf(f_3370_4,plain,
    ( hAPP(c_Set_Oimage(U_12718,U_12718,c_Groups_Ouminus__class_Ouminus(U_12718)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12718),U_12719)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12718),hAPP(c_Groups_Ouminus__class_Ouminus(U_12718),U_12719))
    | ~ class_Groups_Oordered__ab__group__add(U_12718) ),
    inference(clausify,[status(thm)],[f_3370_3]) ).

fof(f_3371_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_3371_2,plain,
    ! [U_12720] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12720)) = 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_12720)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12720),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3371_1]) ).

fof(f_3371_3,plain,
    ! [U_12720] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12720)) = 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_12720)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12720),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3371_2]) ).

cnf(f_3371_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12720)) = 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_12720)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),U_12720),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3371_3]) ).

fof(f_3372_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_3372_2,plain,
    ! [U_12725,U_12724,U_12723,U_12722,U_12721] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_12721),U_12722),hAPP(c_Relation_OImage(U_12723,U_12721,U_12724),hAPP(hAPP(c_Set_Oinsert(U_12723),U_12725),c_Orderings_Obot__class_Obot(tc_fun(U_12723,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12723,U_12721)),hAPP(hAPP(c_Product__Type_OPair(U_12723,U_12721),U_12725),U_12722)),U_12724)) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12723,U_12721)),hAPP(hAPP(c_Product__Type_OPair(U_12723,U_12721),U_12725),U_12722)),U_12724))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12721),U_12722),hAPP(c_Relation_OImage(U_12723,U_12721,U_12724),hAPP(hAPP(c_Set_Oinsert(U_12723),U_12725),c_Orderings_Obot__class_Obot(tc_fun(U_12723,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[f_3372_1]) ).

fof(f_3372_3,plain,
    ( ! [U_12735,U_12733,U_12731,U_12729,U_12727] :
        ( hBOOL(hAPP(hAPP(c_member(U_12727),U_12729),hAPP(c_Relation_OImage(U_12731,U_12727,U_12733),hAPP(hAPP(c_Set_Oinsert(U_12731),U_12735),c_Orderings_Obot__class_Obot(tc_fun(U_12731,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12731,U_12727)),hAPP(hAPP(c_Product__Type_OPair(U_12731,U_12727),U_12735),U_12729)),U_12733)) )
    & ! [U_12734,U_12732,U_12730,U_12728,U_12726] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12730,U_12726)),hAPP(hAPP(c_Product__Type_OPair(U_12730,U_12726),U_12734),U_12728)),U_12732))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12726),U_12728),hAPP(c_Relation_OImage(U_12730,U_12726,U_12732),hAPP(hAPP(c_Set_Oinsert(U_12730),U_12734),c_Orderings_Obot__class_Obot(tc_fun(U_12730,tc_HOL_Obool)))))) ) ),
    inference(miniscope,[status(thm)],[f_3372_2]) ).

fof(f_3372_4,plain,
    ( ! [U_12727,U_12729,U_12731,U_12733,U_12735] :
        ( hBOOL(hAPP(hAPP(c_member(U_12727),U_12729),hAPP(c_Relation_OImage(U_12731,U_12727,U_12733),hAPP(hAPP(c_Set_Oinsert(U_12731),U_12735),c_Orderings_Obot__class_Obot(tc_fun(U_12731,tc_HOL_Obool))))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12731,U_12727)),hAPP(hAPP(c_Product__Type_OPair(U_12731,U_12727),U_12735),U_12729)),U_12733)) )
    & ! [U_12728,U_12732,U_12726,U_12730,U_12734] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12730,U_12726)),hAPP(hAPP(c_Product__Type_OPair(U_12730,U_12726),U_12734),U_12728)),U_12732))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12726),U_12728),hAPP(c_Relation_OImage(U_12730,U_12726,U_12732),hAPP(hAPP(c_Set_Oinsert(U_12730),U_12734),c_Orderings_Obot__class_Obot(tc_fun(U_12730,tc_HOL_Obool)))))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3372_3]) ).

cnf(f_3372_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12730,U_12726)),hAPP(hAPP(c_Product__Type_OPair(U_12730,U_12726),U_12734),U_12728)),U_12732))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12726),U_12728),hAPP(c_Relation_OImage(U_12730,U_12726,U_12732),hAPP(hAPP(c_Set_Oinsert(U_12730),U_12734),c_Orderings_Obot__class_Obot(tc_fun(U_12730,tc_HOL_Obool)))))) ),
    inference(clausify,[status(thm)],[f_3372_4]) ).

cnf(f_3372_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12727),U_12729),hAPP(c_Relation_OImage(U_12731,U_12727,U_12733),hAPP(hAPP(c_Set_Oinsert(U_12731),U_12735),c_Orderings_Obot__class_Obot(tc_fun(U_12731,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12731,U_12727)),hAPP(hAPP(c_Product__Type_OPair(U_12731,U_12727),U_12735),U_12729)),U_12733)) ),
    inference(clausify,[status(thm)],[f_3372_4]) ).

fof(f_3373_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_3373_2,plain,
    ! [U_12739,U_12738,U_12737,U_12736] : hAPP(c_Relation_OImage(U_12736,U_12737,U_12738),hAPP(hAPP(c_Set_Oinsert(U_12736),U_12739),c_Orderings_Obot__class_Obot(tc_fun(U_12736,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_12737),hAPP(hAPP(c_COMBC(U_12737,tc_fun(tc_prod(U_12736,U_12737),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_12736,U_12737),tc_fun(tc_fun(tc_prod(U_12736,U_12737),tc_HOL_Obool),tc_HOL_Obool),U_12737),c_member(tc_prod(U_12736,U_12737))),hAPP(c_Product__Type_OPair(U_12736,U_12737),U_12739))),U_12738)),
    inference(variable_rename,[status(thm)],[f_3373_1]) ).

fof(f_3373_3,plain,
    ! [U_12736,U_12737,U_12738,U_12739] : hAPP(c_Relation_OImage(U_12736,U_12737,U_12738),hAPP(hAPP(c_Set_Oinsert(U_12736),U_12739),c_Orderings_Obot__class_Obot(tc_fun(U_12736,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_12737),hAPP(hAPP(c_COMBC(U_12737,tc_fun(tc_prod(U_12736,U_12737),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_12736,U_12737),tc_fun(tc_fun(tc_prod(U_12736,U_12737),tc_HOL_Obool),tc_HOL_Obool),U_12737),c_member(tc_prod(U_12736,U_12737))),hAPP(c_Product__Type_OPair(U_12736,U_12737),U_12739))),U_12738)),
    inference(definitional_conversion,[status(esa)],[f_3373_2]) ).

cnf(f_3373_4,plain,
    hAPP(c_Relation_OImage(U_12736,U_12737,U_12738),hAPP(hAPP(c_Set_Oinsert(U_12736),U_12739),c_Orderings_Obot__class_Obot(tc_fun(U_12736,tc_HOL_Obool)))) = hAPP(c_Set_OCollect(U_12737),hAPP(hAPP(c_COMBC(U_12737,tc_fun(tc_prod(U_12736,U_12737),tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_prod(U_12736,U_12737),tc_fun(tc_fun(tc_prod(U_12736,U_12737),tc_HOL_Obool),tc_HOL_Obool),U_12737),c_member(tc_prod(U_12736,U_12737))),hAPP(c_Product__Type_OPair(U_12736,U_12737),U_12739))),U_12738)),
    inference(clausify,[status(thm)],[f_3373_3]) ).

fof(f_3374_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_3374_2,plain,
    ! [U_12742,U_12741,U_12740] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_12740),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_12741),U_12742)),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_12740),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12740),U_12741)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12740),U_12742))
      | ~ class_Rings_Oring__1(U_12740) ),
    inference(variable_rename,[status(thm)],[f_3374_1]) ).

fof(f_3374_3,plain,
    ! [U_12740,U_12741,U_12742] :
      ( hAPP(c_Int_Oring__1__class_Oof__int(U_12740),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_12741),U_12742)),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_12740),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12740),U_12741)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12740),U_12742))
      | ~ class_Rings_Oring__1(U_12740) ),
    inference(definitional_conversion,[status(esa)],[f_3374_2]) ).

cnf(f_3374_4,plain,
    ( hAPP(c_Int_Oring__1__class_Oof__int(U_12740),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_12741),U_12742)),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_12740),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12740),U_12741)),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_12740),U_12742))
    | ~ class_Rings_Oring__1(U_12740) ),
    inference(clausify,[status(thm)],[f_3374_3]) ).

fof(f_3375_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_3375_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_3375_1]) ).

cnf(f_3375_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_3375_2]) ).

fof(f_3376_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_3376_2,plain,
    ! [U_12746,U_12745,U_12744,U_12743] : 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_12743),U_12744)),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_12745),U_12746)),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_12743),U_12745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12744),U_12746))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12743),U_12746)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12744),U_12745)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3376_1]) ).

fof(f_3376_3,plain,
    ! [U_12743,U_12744,U_12745,U_12746] : 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_12743),U_12744)),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_12745),U_12746)),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_12743),U_12745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12744),U_12746))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12743),U_12746)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12744),U_12745)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_3376_2]) ).

cnf(f_3376_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_12743),U_12744)),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_12745),U_12746)),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_12743),U_12745)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12744),U_12746))),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12743),U_12746)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_12744),U_12745)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3376_3]) ).

fof(f_3377_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_3377_2,plain,
    ! [U_12748,U_12747] : 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_12747),U_12748)),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_12748),U_12747)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3377_1]) ).

fof(f_3377_3,plain,
    ! [U_12747,U_12748] : 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_12747),U_12748)),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_12748),U_12747)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_3377_2]) ).

cnf(f_3377_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_12747),U_12748)),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_12748),U_12747)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3377_3]) ).

fof(f_3378_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_3378_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_3378_1]) ).

cnf(f_3378_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_3378_2]) ).

fof(f_3379_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_3379_2,plain,
    ! [U_12749] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_12749) = 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_12749),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_3379_1]) ).

fof(f_3379_3,plain,
    ! [U_12749] : hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_12749) = 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_12749),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_3379_2]) ).

cnf(f_3379_4,plain,
    hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),U_12749) = 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_12749),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_3379_3]) ).

fof(f_3380_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_3380_2,plain,
    ! [U_12753,U_12752,U_12751,U_12750] : 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_12750),U_12751)),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_12752),U_12753)),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_12750),U_12752)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12751),U_12753))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3380_1]) ).

fof(f_3380_3,plain,
    ! [U_12750,U_12751,U_12752,U_12753] : 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_12750),U_12751)),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_12752),U_12753)),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_12750),U_12752)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12751),U_12753))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_3380_2]) ).

cnf(f_3380_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_12750),U_12751)),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_12752),U_12753)),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_12750),U_12752)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12751),U_12753))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3380_3]) ).

fof(f_3381_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_3381_2,plain,
    ! [U_12755,U_12754] : 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_12754),U_12755)),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_12754),U_12755),
    inference(variable_rename,[status(thm)],[f_3381_1]) ).

fof(f_3381_3,plain,
    ! [U_12754,U_12755] : 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_12754),U_12755)),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_12754),U_12755),
    inference(definitional_conversion,[status(esa)],[f_3381_2]) ).

cnf(f_3381_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_12754),U_12755)),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_12754),U_12755),
    inference(clausify,[status(thm)],[f_3381_3]) ).

fof(f_3382_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_3382_2,plain,
    ! [U_12759,U_12758,U_12757,U_12756] :
      ( ( 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_12756),U_12757)),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_12758),U_12759)),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_12756),U_12759)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12758),U_12757))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12756),U_12759)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12758),U_12757)))
        | ~ 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_12756),U_12757)),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_12758),U_12759)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(variable_rename,[status(thm)],[f_3382_1]) ).

fof(f_3382_3,plain,
    ( ! [U_12767,U_12765,U_12763,U_12761] :
        ( 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_12761),U_12763)),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_12765),U_12767)),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_12761),U_12767)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12765),U_12763))) )
    & ! [U_12766,U_12764,U_12762,U_12760] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12760),U_12766)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12764),U_12762)))
        | ~ 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_12760),U_12762)),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_12764),U_12766)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(miniscope,[status(thm)],[f_3382_2]) ).

fof(f_3382_4,plain,
    ( ! [U_12761,U_12763,U_12765,U_12767] :
        ( 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_12761),U_12763)),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_12765),U_12767)),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_12761),U_12767)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12765),U_12763))) )
    & ! [U_12766,U_12762,U_12760,U_12764] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12760),U_12766)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12764),U_12762)))
        | ~ 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_12760),U_12762)),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_12764),U_12766)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3382_3]) ).

cnf(f_3382_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12760),U_12766)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12764),U_12762)))
    | ~ 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_12760),U_12762)),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_12764),U_12766)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ),
    inference(clausify,[status(thm)],[f_3382_4]) ).

cnf(f_3382_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_12761),U_12763)),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_12765),U_12767)),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_12761),U_12767)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12765),U_12763))) ),
    inference(clausify,[status(thm)],[f_3382_4]) ).

fof(f_3383_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_3383_2,plain,
    ! [U_12771,U_12770,U_12769,U_12768] :
      ( ( 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_12768),U_12769)),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_12770),U_12771)),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_12768),U_12771)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12770),U_12769))) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12768),U_12771)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12770),U_12769)))
        | ~ 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_12768),U_12769)),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_12770),U_12771)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(variable_rename,[status(thm)],[f_3383_1]) ).

fof(f_3383_3,plain,
    ( ! [U_12779,U_12777,U_12775,U_12773] :
        ( 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_12773),U_12775)),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_12777),U_12779)),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_12773),U_12779)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12777),U_12775))) )
    & ! [U_12778,U_12776,U_12774,U_12772] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12772),U_12778)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12776),U_12774)))
        | ~ 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_12772),U_12774)),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_12776),U_12778)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(miniscope,[status(thm)],[f_3383_2]) ).

fof(f_3383_4,plain,
    ( ! [U_12773,U_12775,U_12777,U_12779] :
        ( 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_12773),U_12775)),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_12777),U_12779)),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_12773),U_12779)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12777),U_12775))) )
    & ! [U_12778,U_12774,U_12772,U_12776] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12772),U_12778)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12776),U_12774)))
        | ~ 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_12772),U_12774)),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_12776),U_12778)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3383_3]) ).

cnf(f_3383_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_12772),U_12778)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12776),U_12774)))
    | ~ 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_12772),U_12774)),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_12776),U_12778)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))))) ),
    inference(clausify,[status(thm)],[f_3383_4]) ).

cnf(f_3383_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_12773),U_12775)),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_12777),U_12779)),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_12773),U_12779)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_12777),U_12775))) ),
    inference(clausify,[status(thm)],[f_3383_4]) ).

fof(f_3384_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_3384_2,plain,
    ! [U_12782] :
    ? [U_12781,U_12780] : U_12782 = 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_12781),U_12780)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3384_1]) ).

fof(f_3384_3,plain,
    ! [U_12782] :
    ? [U_12780] : U_12782 = 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),sK275(U_12782)),U_12780)),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,[sK275]),skolemize(U_12781,sK275(U_12782))],[f_3384_2]) ).

fof(f_3384_4,plain,
    ! [U_12782] : U_12782 = 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),sK275(U_12782)),sK276(U_12782))),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,[sK276]),skolemize(U_12780,sK276(U_12782))],[f_3384_3]) ).

fof(f_3384_5,plain,
    ! [U_12782] : U_12782 = 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),sK275(U_12782)),sK276(U_12782))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_3384_4]) ).

cnf(f_3384_6,plain,
    U_12782 = 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),sK275(U_12782)),sK276(U_12782))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3384_5]) ).

fof(f_3385_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_3385_2,plain,
    ! [U_12783] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12783)) = 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_12783)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12783)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3385_1]) ).

fof(f_3385_3,plain,
    ! [U_12783] : hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12783)) = 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_12783)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12783)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3385_2]) ).

cnf(f_3385_4,plain,
    hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12783)) = 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_12783)),hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12783)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3385_3]) ).

fof(f_3386_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_3386_2,plain,
    ! [U_12786,U_12785,U_12784] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12784,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12784,U_12785,U_12786)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12784),U_12786)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12784),U_12785)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12784),U_12785),U_12786))
      | ~ class_Orderings_Olinorder(U_12784) ),
    inference(variable_rename,[status(thm)],[f_3386_1]) ).

fof(f_3386_3,plain,
    ! [U_12784,U_12785,U_12786] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12784,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12784,U_12785,U_12786)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12784),U_12786)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12784),U_12785)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12784),U_12785),U_12786))
      | ~ class_Orderings_Olinorder(U_12784) ),
    inference(definitional_conversion,[status(esa)],[f_3386_2]) ).

cnf(f_3386_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12784,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(U_12784,U_12785,U_12786)),hAPP(c_SetInterval_Oord__class_OatLeast(U_12784),U_12786)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12784),U_12785)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12784),U_12785),U_12786))
    | ~ class_Orderings_Olinorder(U_12784) ),
    inference(clausify,[status(thm)],[f_3386_3]) ).

fof(f_3387_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_3387_2,plain,
    ! [U_12789,U_12788,U_12787] :
      ( ( ( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12787),U_12788) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12787),U_12789)
          | U_12788 != U_12789 )
        & ( U_12788 = U_12789
          | hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12787),U_12788) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12787),U_12789) ) )
      | ~ class_Orderings_Olinorder(U_12787) ),
    inference(variable_rename,[status(thm)],[f_3387_1]) ).

fof(f_3387_3,plain,
    ( ! [U_12788,U_12787,U_12789] :
        ( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12787),U_12788) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12787),U_12789)
        | U_12788 != U_12789
        | ~ sP921(U_12788,U_12787,U_12789) )
    & ! [U_12788,U_12787,U_12789] :
        ( U_12788 = U_12789
        | hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12787),U_12788) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12787),U_12789)
        | ~ sP921(U_12788,U_12787,U_12789) )
    & ! [U_12788,U_12787,U_12789] :
        ( sP921(U_12788,U_12787,U_12789)
        | ~ class_Orderings_Olinorder(U_12787) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP921])],[f_3387_2]) ).

cnf(f_3387_4,plain,
    ( sP921(U_12788,U_12787,U_12789)
    | ~ class_Orderings_Olinorder(U_12787) ),
    inference(clausify,[status(thm)],[f_3387_3]) ).

cnf(f_3387_5,plain,
    ( U_12788 = U_12789
    | hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12787),U_12788) != hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12787),U_12789)
    | ~ sP921(U_12788,U_12787,U_12789) ),
    inference(clausify,[status(thm)],[f_3387_3]) ).

cnf(f_3387_6,plain,
    ( hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12787),U_12788) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12787),U_12789)
    | U_12788 != U_12789
    | ~ sP921(U_12788,U_12787,U_12789) ),
    inference(clausify,[status(thm)],[f_3387_3]) ).

fof(f_3388_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_3388_2,plain,
    ! [U_12792,U_12791,U_12790] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_12790),U_12791),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12790),U_12792)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12790),U_12792),U_12791)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12790),U_12792),U_12791))
          | ~ hBOOL(hAPP(hAPP(c_member(U_12790),U_12791),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12790),U_12792))) ) )
      | ~ class_Orderings_Oord(U_12790) ),
    inference(variable_rename,[status(thm)],[f_3388_1]) ).

fof(f_3388_3,plain,
    ( ! [U_12792,U_12791,U_12790] :
        ( hBOOL(hAPP(hAPP(c_member(U_12790),U_12791),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12790),U_12792)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12790),U_12792),U_12791))
        | ~ sP922(U_12792,U_12791,U_12790) )
    & ! [U_12792,U_12791,U_12790] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12790),U_12792),U_12791))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12790),U_12791),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12790),U_12792)))
        | ~ sP922(U_12792,U_12791,U_12790) )
    & ! [U_12792,U_12791,U_12790] :
        ( sP922(U_12792,U_12791,U_12790)
        | ~ class_Orderings_Oord(U_12790) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP922])],[f_3388_2]) ).

cnf(f_3388_4,plain,
    ( sP922(U_12792,U_12791,U_12790)
    | ~ class_Orderings_Oord(U_12790) ),
    inference(clausify,[status(thm)],[f_3388_3]) ).

cnf(f_3388_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12790),U_12792),U_12791))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12790),U_12791),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12790),U_12792)))
    | ~ sP922(U_12792,U_12791,U_12790) ),
    inference(clausify,[status(thm)],[f_3388_3]) ).

cnf(f_3388_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12790),U_12791),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12790),U_12792)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_12790),U_12792),U_12791))
    | ~ sP922(U_12792,U_12791,U_12790) ),
    inference(clausify,[status(thm)],[f_3388_3]) ).

fof(f_3389_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_3389_2,plain,
    ! [U_12795,U_12794,U_12793] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12793,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12793),U_12794)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12793),U_12795)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12793),U_12795),U_12794)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12793),U_12795),U_12794))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12793,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12793),U_12794)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12793),U_12795))) ) )
      | ~ class_Orderings_Olinorder(U_12793) ),
    inference(variable_rename,[status(thm)],[f_3389_1]) ).

fof(f_3389_3,plain,
    ( ! [U_12794,U_12795,U_12793] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12793,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12793),U_12794)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12793),U_12795)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12793),U_12795),U_12794))
        | ~ sP923(U_12794,U_12795,U_12793) )
    & ! [U_12794,U_12795,U_12793] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12793),U_12795),U_12794))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12793,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12793),U_12794)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12793),U_12795)))
        | ~ sP923(U_12794,U_12795,U_12793) )
    & ! [U_12794,U_12795,U_12793] :
        ( sP923(U_12794,U_12795,U_12793)
        | ~ class_Orderings_Olinorder(U_12793) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP923])],[f_3389_2]) ).

cnf(f_3389_4,plain,
    ( sP923(U_12794,U_12795,U_12793)
    | ~ class_Orderings_Olinorder(U_12793) ),
    inference(clausify,[status(thm)],[f_3389_3]) ).

cnf(f_3389_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12793),U_12795),U_12794))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12793,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12793),U_12794)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12793),U_12795)))
    | ~ sP923(U_12794,U_12795,U_12793) ),
    inference(clausify,[status(thm)],[f_3389_3]) ).

cnf(f_3389_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12793,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12793),U_12794)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12793),U_12795)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12793),U_12795),U_12794))
    | ~ sP923(U_12794,U_12795,U_12793) ),
    inference(clausify,[status(thm)],[f_3389_3]) ).

fof(f_3390_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_3390_2,plain,
    ! [U_12797,U_12796] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12796,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12796),U_12797)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12796),U_12797)
      | ~ class_Orderings_Olinorder(U_12796) ),
    inference(variable_rename,[status(thm)],[f_3390_1]) ).

fof(f_3390_3,plain,
    ! [U_12797,U_12796] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12796,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12796),U_12797)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12796),U_12797)
      | ~ class_Orderings_Olinorder(U_12796) ),
    inference(definitional_conversion,[status(esa)],[f_3390_2]) ).

cnf(f_3390_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12796,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12796),U_12797)) = hAPP(c_SetInterval_Oord__class_OatMost(U_12796),U_12797)
    | ~ class_Orderings_Olinorder(U_12796) ),
    inference(clausify,[status(thm)],[f_3390_3]) ).

fof(f_3391_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_3391_2,plain,
    ! [U_12799,U_12798] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12798,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12798),U_12799)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12798),U_12799)
      | ~ class_Orderings_Olinorder(U_12798) ),
    inference(variable_rename,[status(thm)],[f_3391_1]) ).

fof(f_3391_3,plain,
    ! [U_12798,U_12799] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12798,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12798),U_12799)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12798),U_12799)
      | ~ class_Orderings_Olinorder(U_12798) ),
    inference(definitional_conversion,[status(esa)],[f_3391_2]) ).

cnf(f_3391_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_12798,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(U_12798),U_12799)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12798),U_12799)
    | ~ class_Orderings_Olinorder(U_12798) ),
    inference(clausify,[status(thm)],[f_3391_3]) ).

fof(f_3392_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_3392_2,plain,
    ! [U_12800] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12800)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_12800),
    inference(variable_rename,[status(thm)],[f_3392_1]) ).

fof(f_3392_3,plain,
    ! [U_12800] : hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12800)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_12800),
    inference(definitional_conversion,[status(esa)],[f_3392_2]) ).

cnf(f_3392_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeast(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_12800)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(tc_Nat_Onat),U_12800),
    inference(clausify,[status(thm)],[f_3392_3]) ).

fof(f_3393_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_3393_2,plain,
    ! [U_12803,U_12802,U_12801] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12801,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12801,U_12802,U_12803)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12801),U_12803)) = c_Orderings_Obot__class_Obot(tc_fun(U_12801,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12801) ),
    inference(variable_rename,[status(thm)],[f_3393_1]) ).

fof(f_3393_3,plain,
    ! [U_12801,U_12802,U_12803] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12801,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12801,U_12802,U_12803)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12801),U_12803)) = c_Orderings_Obot__class_Obot(tc_fun(U_12801,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12801) ),
    inference(definitional_conversion,[status(esa)],[f_3393_2]) ).

cnf(f_3393_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12801,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12801,U_12802,U_12803)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12801),U_12803)) = c_Orderings_Obot__class_Obot(tc_fun(U_12801,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12801) ),
    inference(clausify,[status(thm)],[f_3393_3]) ).

fof(f_3394_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_3394_2,plain,
    ! [U_12806,U_12805,U_12804] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12804,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12804,U_12805,U_12806)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12804),U_12806)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12804),U_12805)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12804),U_12805),U_12806))
      | ~ class_Orderings_Olinorder(U_12804) ),
    inference(variable_rename,[status(thm)],[f_3394_1]) ).

fof(f_3394_3,plain,
    ! [U_12804,U_12805,U_12806] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12804,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12804,U_12805,U_12806)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12804),U_12806)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12804),U_12805)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12804),U_12805),U_12806))
      | ~ class_Orderings_Olinorder(U_12804) ),
    inference(definitional_conversion,[status(esa)],[f_3394_2]) ).

cnf(f_3394_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12804,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12804,U_12805,U_12806)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12804),U_12806)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12804),U_12805)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12804),U_12805),U_12806))
    | ~ class_Orderings_Olinorder(U_12804) ),
    inference(clausify,[status(thm)],[f_3394_3]) ).

fof(f_3395_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_3395_2,plain,
    ! [U_12808,U_12807] :
      ( hAPP(c_Set_Oimage(U_12807,U_12807,c_Groups_Ouminus__class_Ouminus(U_12807)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12807),U_12808)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12807),hAPP(c_Groups_Ouminus__class_Ouminus(U_12807),U_12808))
      | ~ class_Groups_Oordered__ab__group__add(U_12807) ),
    inference(variable_rename,[status(thm)],[f_3395_1]) ).

fof(f_3395_3,plain,
    ! [U_12807,U_12808] :
      ( hAPP(c_Set_Oimage(U_12807,U_12807,c_Groups_Ouminus__class_Ouminus(U_12807)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12807),U_12808)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12807),hAPP(c_Groups_Ouminus__class_Ouminus(U_12807),U_12808))
      | ~ class_Groups_Oordered__ab__group__add(U_12807) ),
    inference(definitional_conversion,[status(esa)],[f_3395_2]) ).

cnf(f_3395_4,plain,
    ( hAPP(c_Set_Oimage(U_12807,U_12807,c_Groups_Ouminus__class_Ouminus(U_12807)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12807),U_12808)) = hAPP(c_SetInterval_Oord__class_OlessThan(U_12807),hAPP(c_Groups_Ouminus__class_Ouminus(U_12807),U_12808))
    | ~ class_Groups_Oordered__ab__group__add(U_12807) ),
    inference(clausify,[status(thm)],[f_3395_3]) ).

fof(f_3396_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_3396_2,plain,
    ! [U_12810,U_12809] :
      ( hAPP(c_Set_Oimage(U_12809,U_12809,c_Groups_Ouminus__class_Ouminus(U_12809)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12809),U_12810)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12809),hAPP(c_Groups_Ouminus__class_Ouminus(U_12809),U_12810))
      | ~ class_Groups_Oordered__ab__group__add(U_12809) ),
    inference(variable_rename,[status(thm)],[f_3396_1]) ).

fof(f_3396_3,plain,
    ! [U_12809,U_12810] :
      ( hAPP(c_Set_Oimage(U_12809,U_12809,c_Groups_Ouminus__class_Ouminus(U_12809)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12809),U_12810)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12809),hAPP(c_Groups_Ouminus__class_Ouminus(U_12809),U_12810))
      | ~ class_Groups_Oordered__ab__group__add(U_12809) ),
    inference(definitional_conversion,[status(esa)],[f_3396_2]) ).

cnf(f_3396_4,plain,
    ( hAPP(c_Set_Oimage(U_12809,U_12809,c_Groups_Ouminus__class_Ouminus(U_12809)),hAPP(c_SetInterval_Oord__class_OlessThan(U_12809),U_12810)) = hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12809),hAPP(c_Groups_Ouminus__class_Ouminus(U_12809),U_12810))
    | ~ class_Groups_Oordered__ab__group__add(U_12809) ),
    inference(clausify,[status(thm)],[f_3396_3]) ).

fof(f_3397_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_3397_2,plain,
    ! [U_12813,U_12812,U_12811] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12811,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12811,U_12812,U_12813)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12811),U_12813)) = c_Orderings_Obot__class_Obot(tc_fun(U_12811,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12811) ),
    inference(variable_rename,[status(thm)],[f_3397_1]) ).

fof(f_3397_3,plain,
    ! [U_12811,U_12812,U_12813] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12811,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12811,U_12812,U_12813)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12811),U_12813)) = c_Orderings_Obot__class_Obot(tc_fun(U_12811,tc_HOL_Obool))
      | ~ class_Orderings_Oorder(U_12811) ),
    inference(definitional_conversion,[status(esa)],[f_3397_2]) ).

cnf(f_3397_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12811,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(U_12811,U_12812,U_12813)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12811),U_12813)) = c_Orderings_Obot__class_Obot(tc_fun(U_12811,tc_HOL_Obool))
    | ~ class_Orderings_Oorder(U_12811) ),
    inference(clausify,[status(thm)],[f_3397_3]) ).

fof(f_3398_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_3398_2,plain,
    ! [U_12815,U_12814] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12814,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12814),U_12815),c_Orderings_Obot__class_Obot(tc_fun(U_12814,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12814),U_12815)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12814),U_12815)
      | ~ class_Orderings_Olinorder(U_12814) ),
    inference(variable_rename,[status(thm)],[f_3398_1]) ).

fof(f_3398_3,plain,
    ! [U_12814,U_12815] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12814,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12814),U_12815),c_Orderings_Obot__class_Obot(tc_fun(U_12814,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12814),U_12815)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12814),U_12815)
      | ~ class_Orderings_Olinorder(U_12814) ),
    inference(definitional_conversion,[status(esa)],[f_3398_2]) ).

cnf(f_3398_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12814,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_12814),U_12815),c_Orderings_Obot__class_Obot(tc_fun(U_12814,tc_HOL_Obool)))),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12814),U_12815)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12814),U_12815)
    | ~ class_Orderings_Olinorder(U_12814) ),
    inference(clausify,[status(thm)],[f_3398_3]) ).

fof(f_3399_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_3399_2,plain,
    ! [U_12818,U_12817,U_12816] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12816,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12816,U_12817,U_12818)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12816),U_12818)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12816),U_12817)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12816),U_12817),U_12818))
      | ~ class_Orderings_Olinorder(U_12816) ),
    inference(variable_rename,[status(thm)],[f_3399_1]) ).

fof(f_3399_3,plain,
    ! [U_12816,U_12817,U_12818] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12816,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12816,U_12817,U_12818)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12816),U_12818)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12816),U_12817)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12816),U_12817),U_12818))
      | ~ class_Orderings_Olinorder(U_12816) ),
    inference(definitional_conversion,[status(esa)],[f_3399_2]) ).

cnf(f_3399_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12816,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(U_12816,U_12817,U_12818)),hAPP(c_SetInterval_Oord__class_OgreaterThan(U_12816),U_12818)) = hAPP(c_SetInterval_Oord__class_OatLeast(U_12816),U_12817)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_12816),U_12817),U_12818))
    | ~ class_Orderings_Olinorder(U_12816) ),
    inference(clausify,[status(thm)],[f_3399_3]) ).

fof(f_3400_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_3400_2,plain,
    ! [U_12824,U_12823,U_12822,U_12821,U_12820] :
      ( ? [U_12819] :
          ( hBOOL(hAPP(hAPP(c_member(U_12822),U_12819),U_12824))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_12822,U_12820)),hAPP(hAPP(c_Product__Type_OPair(U_12822,U_12820),U_12819),U_12821)),U_12823)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_12820),U_12821),hAPP(c_Relation_OImage(U_12822,U_12820,U_12823),U_12824))) ),
    inference(variable_rename,[status(thm)],[f_3400_1]) ).

fof(f_3400_3,plain,
    ! [U_12824,U_12823,U_12822,U_12821,U_12820] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_12822),sK277(U_12824,U_12823,U_12822,U_12821,U_12820)),U_12824))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_12822,U_12820)),hAPP(hAPP(c_Product__Type_OPair(U_12822,U_12820),sK277(U_12824,U_12823,U_12822,U_12821,U_12820)),U_12821)),U_12823)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_12820),U_12821),hAPP(c_Relation_OImage(U_12822,U_12820,U_12823),U_12824))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK277]),skolemize(U_12819,sK277(U_12824,U_12823,U_12822,U_12821,U_12820))],[f_3400_2]) ).

fof(f_3400_4,plain,
    ( ! [U_12820,U_12821,U_12822,U_12823,U_12824] :
        ( hBOOL(hAPP(hAPP(c_member(U_12822),sK277(U_12824,U_12823,U_12822,U_12821,U_12820)),U_12824))
        | ~ sP924(U_12820,U_12821,U_12822,U_12823,U_12824) )
    & ! [U_12820,U_12821,U_12822,U_12823,U_12824] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12822,U_12820)),hAPP(hAPP(c_Product__Type_OPair(U_12822,U_12820),sK277(U_12824,U_12823,U_12822,U_12821,U_12820)),U_12821)),U_12823))
        | ~ sP924(U_12820,U_12821,U_12822,U_12823,U_12824) )
    & ! [U_12820,U_12821,U_12822,U_12823,U_12824] :
        ( sP924(U_12820,U_12821,U_12822,U_12823,U_12824)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12820),U_12821),hAPP(c_Relation_OImage(U_12822,U_12820,U_12823),U_12824))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP924])],[f_3400_3]) ).

cnf(f_3400_5,plain,
    ( sP924(U_12820,U_12821,U_12822,U_12823,U_12824)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12820),U_12821),hAPP(c_Relation_OImage(U_12822,U_12820,U_12823),U_12824))) ),
    inference(clausify,[status(thm)],[f_3400_4]) ).

cnf(f_3400_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12822,U_12820)),hAPP(hAPP(c_Product__Type_OPair(U_12822,U_12820),sK277(U_12824,U_12823,U_12822,U_12821,U_12820)),U_12821)),U_12823))
    | ~ sP924(U_12820,U_12821,U_12822,U_12823,U_12824) ),
    inference(clausify,[status(thm)],[f_3400_4]) ).

cnf(f_3400_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12822),sK277(U_12824,U_12823,U_12822,U_12821,U_12820)),U_12824))
    | ~ sP924(U_12820,U_12821,U_12822,U_12823,U_12824) ),
    inference(clausify,[status(thm)],[f_3400_4]) ).

fof(f_3401_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_3401_2,plain,
    ! [U_12830,U_12829] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12829),U_12830))
        | ! [U_12828,U_12827] : U_12830 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_12829,U_12827),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_12828))) )
      & ( ? [U_12826,U_12825] : U_12830 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_12829,U_12825),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_12826)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12829),U_12830)) ) ),
    inference(variable_rename,[status(thm)],[f_3401_1]) ).

fof(f_3401_3,plain,
    ( ! [U_12834,U_12832] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12832),U_12834))
        | ! [U_12828,U_12827] : U_12834 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_12832,U_12827),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_12828))) )
    & ! [U_12833,U_12831] :
        ( ? [U_12826,U_12825] : U_12833 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_12831,U_12825),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_12826)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12831),U_12833)) ) ),
    inference(miniscope,[status(thm)],[f_3401_2]) ).

fof(f_3401_4,plain,
    ( ! [U_12834,U_12832] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12832),U_12834))
        | ! [U_12828,U_12827] : U_12834 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_12832,U_12827),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_12828))) )
    & ! [U_12833,U_12831] :
        ( ? [U_12825] : U_12833 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_12831,U_12825),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)),sK278(U_12833,U_12831))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12831),U_12833)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK278]),skolemize(U_12826,sK278(U_12833,U_12831))],[f_3401_3]) ).

fof(f_3401_5,plain,
    ( ! [U_12834,U_12832] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12832),U_12834))
        | ! [U_12828,U_12827] : U_12834 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_12832,U_12827),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_12828))) )
    & ! [U_12833,U_12831] :
        ( U_12833 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_12831,sK279(U_12833,U_12831)),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)),sK278(U_12833,U_12831))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12831),U_12833)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK279]),skolemize(U_12825,sK279(U_12833,U_12831))],[f_3401_4]) ).

fof(f_3401_6,plain,
    ( ! [U_12834,U_12827,U_12828,U_12832] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12832),U_12834))
        | U_12834 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_12832,U_12827),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_12828))) )
    & ! [U_12833,U_12831] :
        ( U_12833 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_12831,sK279(U_12833,U_12831)),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)),sK278(U_12833,U_12831))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12831),U_12833)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3401_5]) ).

cnf(f_3401_7,plain,
    ( U_12833 = hAPP(c_Set_Oimage(tc_Nat_Onat,U_12831,sK279(U_12833,U_12831)),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)),sK278(U_12833,U_12831))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_12831),U_12833)) ),
    inference(clausify,[status(thm)],[f_3401_6]) ).

cnf(f_3401_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_12832),U_12834))
    | U_12834 != hAPP(c_Set_Oimage(tc_Nat_Onat,U_12832,U_12827),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_12828))) ),
    inference(clausify,[status(thm)],[f_3401_6]) ).

fof(f_3402_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_3402_2,plain,
    ! [U_12840,U_12839,U_12838,U_12837] :
      ( ( c_Map_Odom(U_12837,U_12838,U_12839) = hAPP(hAPP(c_Set_Oinsert(U_12837),U_12840),c_Orderings_Obot__class_Obot(tc_fun(U_12837,tc_HOL_Obool)))
        | ! [U_12836] : U_12839 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12837,tc_Option_Ooption(U_12838)),hAPP(c_COMBK(tc_Option_Ooption(U_12838),U_12837),c_Option_Ooption_ONone(U_12838))),U_12840),hAPP(c_Option_Ooption_OSome(U_12838),U_12836)) )
      & ( ? [U_12835] : U_12839 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12837,tc_Option_Ooption(U_12838)),hAPP(c_COMBK(tc_Option_Ooption(U_12838),U_12837),c_Option_Ooption_ONone(U_12838))),U_12840),hAPP(c_Option_Ooption_OSome(U_12838),U_12835))
        | c_Map_Odom(U_12837,U_12838,U_12839) != hAPP(hAPP(c_Set_Oinsert(U_12837),U_12840),c_Orderings_Obot__class_Obot(tc_fun(U_12837,tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[f_3402_1]) ).

fof(f_3402_3,plain,
    ( ! [U_12848,U_12846,U_12844,U_12842] :
        ( c_Map_Odom(U_12842,U_12844,U_12846) = hAPP(hAPP(c_Set_Oinsert(U_12842),U_12848),c_Orderings_Obot__class_Obot(tc_fun(U_12842,tc_HOL_Obool)))
        | ! [U_12836] : U_12846 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12842,tc_Option_Ooption(U_12844)),hAPP(c_COMBK(tc_Option_Ooption(U_12844),U_12842),c_Option_Ooption_ONone(U_12844))),U_12848),hAPP(c_Option_Ooption_OSome(U_12844),U_12836)) )
    & ! [U_12847,U_12845,U_12843,U_12841] :
        ( ? [U_12835] : U_12845 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12841,tc_Option_Ooption(U_12843)),hAPP(c_COMBK(tc_Option_Ooption(U_12843),U_12841),c_Option_Ooption_ONone(U_12843))),U_12847),hAPP(c_Option_Ooption_OSome(U_12843),U_12835))
        | c_Map_Odom(U_12841,U_12843,U_12845) != hAPP(hAPP(c_Set_Oinsert(U_12841),U_12847),c_Orderings_Obot__class_Obot(tc_fun(U_12841,tc_HOL_Obool))) ) ),
    inference(miniscope,[status(thm)],[f_3402_2]) ).

fof(f_3402_4,plain,
    ( ! [U_12848,U_12846,U_12844,U_12842] :
        ( c_Map_Odom(U_12842,U_12844,U_12846) = hAPP(hAPP(c_Set_Oinsert(U_12842),U_12848),c_Orderings_Obot__class_Obot(tc_fun(U_12842,tc_HOL_Obool)))
        | ! [U_12836] : U_12846 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12842,tc_Option_Ooption(U_12844)),hAPP(c_COMBK(tc_Option_Ooption(U_12844),U_12842),c_Option_Ooption_ONone(U_12844))),U_12848),hAPP(c_Option_Ooption_OSome(U_12844),U_12836)) )
    & ! [U_12847,U_12845,U_12843,U_12841] :
        ( U_12845 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12841,tc_Option_Ooption(U_12843)),hAPP(c_COMBK(tc_Option_Ooption(U_12843),U_12841),c_Option_Ooption_ONone(U_12843))),U_12847),hAPP(c_Option_Ooption_OSome(U_12843),sK280(U_12847,U_12845,U_12843,U_12841)))
        | c_Map_Odom(U_12841,U_12843,U_12845) != hAPP(hAPP(c_Set_Oinsert(U_12841),U_12847),c_Orderings_Obot__class_Obot(tc_fun(U_12841,tc_HOL_Obool))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK280]),skolemize(U_12835,sK280(U_12847,U_12845,U_12843,U_12841))],[f_3402_3]) ).

fof(f_3402_5,plain,
    ( ! [U_12836,U_12846,U_12842,U_12844,U_12848] :
        ( c_Map_Odom(U_12842,U_12844,U_12846) = hAPP(hAPP(c_Set_Oinsert(U_12842),U_12848),c_Orderings_Obot__class_Obot(tc_fun(U_12842,tc_HOL_Obool)))
        | U_12846 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12842,tc_Option_Ooption(U_12844)),hAPP(c_COMBK(tc_Option_Ooption(U_12844),U_12842),c_Option_Ooption_ONone(U_12844))),U_12848),hAPP(c_Option_Ooption_OSome(U_12844),U_12836)) )
    & ! [U_12843,U_12847,U_12841,U_12845] :
        ( U_12845 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12841,tc_Option_Ooption(U_12843)),hAPP(c_COMBK(tc_Option_Ooption(U_12843),U_12841),c_Option_Ooption_ONone(U_12843))),U_12847),hAPP(c_Option_Ooption_OSome(U_12843),sK280(U_12847,U_12845,U_12843,U_12841)))
        | c_Map_Odom(U_12841,U_12843,U_12845) != hAPP(hAPP(c_Set_Oinsert(U_12841),U_12847),c_Orderings_Obot__class_Obot(tc_fun(U_12841,tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3402_4]) ).

cnf(f_3402_6,plain,
    ( U_12845 = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12841,tc_Option_Ooption(U_12843)),hAPP(c_COMBK(tc_Option_Ooption(U_12843),U_12841),c_Option_Ooption_ONone(U_12843))),U_12847),hAPP(c_Option_Ooption_OSome(U_12843),sK280(U_12847,U_12845,U_12843,U_12841)))
    | c_Map_Odom(U_12841,U_12843,U_12845) != hAPP(hAPP(c_Set_Oinsert(U_12841),U_12847),c_Orderings_Obot__class_Obot(tc_fun(U_12841,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3402_5]) ).

cnf(f_3402_7,plain,
    ( c_Map_Odom(U_12842,U_12844,U_12846) = hAPP(hAPP(c_Set_Oinsert(U_12842),U_12848),c_Orderings_Obot__class_Obot(tc_fun(U_12842,tc_HOL_Obool)))
    | U_12846 != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12842,tc_Option_Ooption(U_12844)),hAPP(c_COMBK(tc_Option_Ooption(U_12844),U_12842),c_Option_Ooption_ONone(U_12844))),U_12848),hAPP(c_Option_Ooption_OSome(U_12844),U_12836)) ),
    inference(clausify,[status(thm)],[f_3402_5]) ).

fof(f_3403_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_3403_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_3403_1]) ).

cnf(f_3403_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_3403_2]) ).

fof(f_3404_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_3404_2,plain,
    ! [U_12852,U_12851,U_12850,U_12849] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_12849),U_12850),c_Map_Odom(U_12849,U_12851,U_12852)))
        | hAPP(U_12852,U_12850) = c_Option_Ooption_ONone(U_12851) )
      & ( hAPP(U_12852,U_12850) != c_Option_Ooption_ONone(U_12851)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12849),U_12850),c_Map_Odom(U_12849,U_12851,U_12852))) ) ),
    inference(variable_rename,[status(thm)],[f_3404_1]) ).

fof(f_3404_3,plain,
    ( ! [U_12860,U_12858,U_12856] :
        ( ! [U_12854] : hBOOL(hAPP(hAPP(c_member(U_12854),U_12856),c_Map_Odom(U_12854,U_12858,U_12860)))
        | hAPP(U_12860,U_12856) = c_Option_Ooption_ONone(U_12858) )
    & ! [U_12859,U_12857,U_12855] :
        ( ! [U_12853] : ~ hBOOL(hAPP(hAPP(c_member(U_12853),U_12855),c_Map_Odom(U_12853,U_12857,U_12859)))
        | hAPP(U_12859,U_12855) != c_Option_Ooption_ONone(U_12857) ) ),
    inference(miniscope,[status(thm)],[f_3404_2]) ).

fof(f_3404_4,plain,
    ( ! [U_12854,U_12858,U_12860,U_12856] :
        ( hBOOL(hAPP(hAPP(c_member(U_12854),U_12856),c_Map_Odom(U_12854,U_12858,U_12860)))
        | hAPP(U_12860,U_12856) = c_Option_Ooption_ONone(U_12858) )
    & ! [U_12857,U_12855,U_12859,U_12853] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_12853),U_12855),c_Map_Odom(U_12853,U_12857,U_12859)))
        | hAPP(U_12859,U_12855) != c_Option_Ooption_ONone(U_12857) ) ),
    inference(definitional_conversion,[status(esa)],[f_3404_3]) ).

cnf(f_3404_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_12853),U_12855),c_Map_Odom(U_12853,U_12857,U_12859)))
    | hAPP(U_12859,U_12855) != c_Option_Ooption_ONone(U_12857) ),
    inference(clausify,[status(thm)],[f_3404_4]) ).

cnf(f_3404_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12854),U_12856),c_Map_Odom(U_12854,U_12858,U_12860)))
    | hAPP(U_12860,U_12856) = c_Option_Ooption_ONone(U_12858) ),
    inference(clausify,[status(thm)],[f_3404_4]) ).

fof(f_3405_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_3405_2,plain,
    ! [U_12865,U_12864,U_12863,U_12862,U_12861] :
      ( hBOOL(hAPP(hAPP(c_member(U_12865),U_12862),c_Map_Odom(U_12865,U_12863,U_12861)))
      | hAPP(U_12861,U_12862) != hAPP(c_Option_Ooption_OSome(U_12863),U_12864) ),
    inference(variable_rename,[status(thm)],[f_3405_1]) ).

fof(f_3405_3,plain,
    ! [U_12861,U_12863,U_12862,U_12864,U_12865] :
      ( hBOOL(hAPP(hAPP(c_member(U_12865),U_12862),c_Map_Odom(U_12865,U_12863,U_12861)))
      | hAPP(U_12861,U_12862) != hAPP(c_Option_Ooption_OSome(U_12863),U_12864) ),
    inference(definitional_conversion,[status(esa)],[f_3405_2]) ).

cnf(f_3405_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12865),U_12862),c_Map_Odom(U_12865,U_12863,U_12861)))
    | hAPP(U_12861,U_12862) != hAPP(c_Option_Ooption_OSome(U_12863),U_12864) ),
    inference(clausify,[status(thm)],[f_3405_3]) ).

fof(f_3406_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_3406_2,plain,
    ! [U_12870,U_12869,U_12868,U_12867,U_12866] :
      ( hAPP(hAPP(c_Set_Oinsert(U_12870),U_12867),c_Map_Odom(U_12870,U_12868,U_12866)) = c_Map_Odom(U_12870,U_12868,U_12866)
      | hAPP(U_12866,U_12867) != hAPP(c_Option_Ooption_OSome(U_12868),U_12869) ),
    inference(variable_rename,[status(thm)],[f_3406_1]) ).

fof(f_3406_3,plain,
    ! [U_12867,U_12866,U_12868,U_12869,U_12870] :
      ( hAPP(hAPP(c_Set_Oinsert(U_12870),U_12867),c_Map_Odom(U_12870,U_12868,U_12866)) = c_Map_Odom(U_12870,U_12868,U_12866)
      | hAPP(U_12866,U_12867) != hAPP(c_Option_Ooption_OSome(U_12868),U_12869) ),
    inference(definitional_conversion,[status(esa)],[f_3406_2]) ).

cnf(f_3406_4,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_12870),U_12867),c_Map_Odom(U_12870,U_12868,U_12866)) = c_Map_Odom(U_12870,U_12868,U_12866)
    | hAPP(U_12866,U_12867) != hAPP(c_Option_Ooption_OSome(U_12868),U_12869) ),
    inference(clausify,[status(thm)],[f_3406_3]) ).

fof(f_3407_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_3407_2,plain,
    ! [U_12874,U_12873,U_12872,U_12871] : c_Map_Odom(U_12871,U_12872,c_Map_Orestrict__map(U_12871,U_12872,U_12873,U_12874)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12871,tc_HOL_Obool)),c_Map_Odom(U_12871,U_12872,U_12873)),U_12874),
    inference(variable_rename,[status(thm)],[f_3407_1]) ).

fof(f_3407_3,plain,
    ! [U_12871,U_12872,U_12873,U_12874] : c_Map_Odom(U_12871,U_12872,c_Map_Orestrict__map(U_12871,U_12872,U_12873,U_12874)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12871,tc_HOL_Obool)),c_Map_Odom(U_12871,U_12872,U_12873)),U_12874),
    inference(definitional_conversion,[status(esa)],[f_3407_2]) ).

cnf(f_3407_4,plain,
    c_Map_Odom(U_12871,U_12872,c_Map_Orestrict__map(U_12871,U_12872,U_12873,U_12874)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12871,tc_HOL_Obool)),c_Map_Odom(U_12871,U_12872,U_12873)),U_12874),
    inference(clausify,[status(thm)],[f_3407_3]) ).

fof(f_3408_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_3408_2,plain,
    ! [U_12877,U_12876,U_12875] :
      ( ( c_Map_Odom(U_12875,U_12876,U_12877) = c_Orderings_Obot__class_Obot(tc_fun(U_12875,tc_HOL_Obool))
        | U_12877 != hAPP(c_COMBK(tc_Option_Ooption(U_12876),U_12875),c_Option_Ooption_ONone(U_12876)) )
      & ( U_12877 = hAPP(c_COMBK(tc_Option_Ooption(U_12876),U_12875),c_Option_Ooption_ONone(U_12876))
        | c_Map_Odom(U_12875,U_12876,U_12877) != c_Orderings_Obot__class_Obot(tc_fun(U_12875,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3408_1]) ).

fof(f_3408_3,plain,
    ( ! [U_12883,U_12881,U_12879] :
        ( c_Map_Odom(U_12879,U_12881,U_12883) = c_Orderings_Obot__class_Obot(tc_fun(U_12879,tc_HOL_Obool))
        | U_12883 != hAPP(c_COMBK(tc_Option_Ooption(U_12881),U_12879),c_Option_Ooption_ONone(U_12881)) )
    & ! [U_12882,U_12880,U_12878] :
        ( U_12882 = hAPP(c_COMBK(tc_Option_Ooption(U_12880),U_12878),c_Option_Ooption_ONone(U_12880))
        | c_Map_Odom(U_12878,U_12880,U_12882) != c_Orderings_Obot__class_Obot(tc_fun(U_12878,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3408_2]) ).

fof(f_3408_4,plain,
    ( ! [U_12883,U_12879,U_12881] :
        ( c_Map_Odom(U_12879,U_12881,U_12883) = c_Orderings_Obot__class_Obot(tc_fun(U_12879,tc_HOL_Obool))
        | U_12883 != hAPP(c_COMBK(tc_Option_Ooption(U_12881),U_12879),c_Option_Ooption_ONone(U_12881)) )
    & ! [U_12880,U_12878,U_12882] :
        ( U_12882 = hAPP(c_COMBK(tc_Option_Ooption(U_12880),U_12878),c_Option_Ooption_ONone(U_12880))
        | c_Map_Odom(U_12878,U_12880,U_12882) != c_Orderings_Obot__class_Obot(tc_fun(U_12878,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3408_3]) ).

cnf(f_3408_5,plain,
    ( U_12882 = hAPP(c_COMBK(tc_Option_Ooption(U_12880),U_12878),c_Option_Ooption_ONone(U_12880))
    | c_Map_Odom(U_12878,U_12880,U_12882) != c_Orderings_Obot__class_Obot(tc_fun(U_12878,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3408_4]) ).

cnf(f_3408_6,plain,
    ( c_Map_Odom(U_12879,U_12881,U_12883) = c_Orderings_Obot__class_Obot(tc_fun(U_12879,tc_HOL_Obool))
    | U_12883 != hAPP(c_COMBK(tc_Option_Ooption(U_12881),U_12879),c_Option_Ooption_ONone(U_12881)) ),
    inference(clausify,[status(thm)],[f_3408_4]) ).

fof(f_3409_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_3409_2,plain,
    ! [U_12885,U_12884] : c_Map_Odom(U_12884,U_12885,hAPP(c_COMBK(tc_Option_Ooption(U_12885),U_12884),c_Option_Ooption_ONone(U_12885))) = c_Orderings_Obot__class_Obot(tc_fun(U_12884,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3409_1]) ).

fof(f_3409_3,plain,
    ! [U_12884,U_12885] : c_Map_Odom(U_12884,U_12885,hAPP(c_COMBK(tc_Option_Ooption(U_12885),U_12884),c_Option_Ooption_ONone(U_12885))) = c_Orderings_Obot__class_Obot(tc_fun(U_12884,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3409_2]) ).

cnf(f_3409_4,plain,
    c_Map_Odom(U_12884,U_12885,hAPP(c_COMBK(tc_Option_Ooption(U_12885),U_12884),c_Option_Ooption_ONone(U_12885))) = c_Orderings_Obot__class_Obot(tc_fun(U_12884,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3409_3]) ).

fof(f_3410_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_3410_2,plain,
    ! [U_12888,U_12887,U_12886] : c_Map_Odom(U_12886,U_12887,U_12888) = hAPP(c_Set_OCollect(U_12886),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12886),c_fNot),hAPP(hAPP(c_COMBC(U_12886,tc_Option_Ooption(U_12887),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_12887),tc_fun(tc_Option_Ooption(U_12887),tc_HOL_Obool),U_12886),c_fequal),U_12888)),c_Option_Ooption_ONone(U_12887)))),
    inference(variable_rename,[status(thm)],[f_3410_1]) ).

fof(f_3410_3,plain,
    ! [U_12886,U_12887,U_12888] : c_Map_Odom(U_12886,U_12887,U_12888) = hAPP(c_Set_OCollect(U_12886),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12886),c_fNot),hAPP(hAPP(c_COMBC(U_12886,tc_Option_Ooption(U_12887),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_12887),tc_fun(tc_Option_Ooption(U_12887),tc_HOL_Obool),U_12886),c_fequal),U_12888)),c_Option_Ooption_ONone(U_12887)))),
    inference(definitional_conversion,[status(esa)],[f_3410_2]) ).

cnf(f_3410_4,plain,
    c_Map_Odom(U_12886,U_12887,U_12888) = hAPP(c_Set_OCollect(U_12886),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12886),c_fNot),hAPP(hAPP(c_COMBC(U_12886,tc_Option_Ooption(U_12887),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_12887),tc_fun(tc_Option_Ooption(U_12887),tc_HOL_Obool),U_12886),c_fequal),U_12888)),c_Option_Ooption_ONone(U_12887)))),
    inference(clausify,[status(thm)],[f_3410_3]) ).

fof(f_3411_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_3411_2,plain,
    ! [U_12893,U_12892,U_12891,U_12890,U_12889] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12892,tc_HOL_Obool)),c_Map_Odom(U_12892,U_12891,U_12889)),hAPP(hAPP(c_Set_Oinsert(U_12892),U_12890),U_12893)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12892,tc_HOL_Obool)),c_Map_Odom(U_12892,U_12891,U_12889)),U_12893)
      | hAPP(U_12889,U_12890) != c_Option_Ooption_ONone(U_12891) ),
    inference(variable_rename,[status(thm)],[f_3411_1]) ).

fof(f_3411_3,plain,
    ! [U_12889,U_12890,U_12891,U_12892,U_12893] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12892,tc_HOL_Obool)),c_Map_Odom(U_12892,U_12891,U_12889)),hAPP(hAPP(c_Set_Oinsert(U_12892),U_12890),U_12893)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12892,tc_HOL_Obool)),c_Map_Odom(U_12892,U_12891,U_12889)),U_12893)
      | hAPP(U_12889,U_12890) != c_Option_Ooption_ONone(U_12891) ),
    inference(definitional_conversion,[status(esa)],[f_3411_2]) ).

cnf(f_3411_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12892,tc_HOL_Obool)),c_Map_Odom(U_12892,U_12891,U_12889)),hAPP(hAPP(c_Set_Oinsert(U_12892),U_12890),U_12893)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12892,tc_HOL_Obool)),c_Map_Odom(U_12892,U_12891,U_12889)),U_12893)
    | hAPP(U_12889,U_12890) != c_Option_Ooption_ONone(U_12891) ),
    inference(clausify,[status(thm)],[f_3411_3]) ).

fof(f_3412_1,plain,
    ! [V_g_2,V_f_2,V_Pa_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_Pa_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_Pa_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_Pa_2)))),
    inference(fof_nnf,[status(thm)],[fact_dom__if]) ).

fof(f_3412_2,plain,
    ! [U_12898,U_12897,U_12896,U_12895,U_12894] : c_Map_Odom(U_12894,U_12895,hAPP(hAPP(c_COMBS(U_12894,tc_Option_Ooption(U_12895),tc_Option_Ooption(U_12895)),hAPP(hAPP(c_COMBS(U_12894,tc_Option_Ooption(U_12895),tc_fun(tc_Option_Ooption(U_12895),tc_Option_Ooption(U_12895))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_12895),tc_fun(tc_Option_Ooption(U_12895),tc_Option_Ooption(U_12895))),U_12894),c_If(tc_Option_Ooption(U_12895))),U_12896)),U_12897)),U_12898)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12894,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12894,tc_HOL_Obool)),c_Map_Odom(U_12894,U_12895,U_12897)),hAPP(c_Set_OCollect(U_12894),U_12896))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12894,tc_HOL_Obool)),c_Map_Odom(U_12894,U_12895,U_12898)),hAPP(c_Set_OCollect(U_12894),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12894),c_fNot),U_12896)))),
    inference(variable_rename,[status(thm)],[f_3412_1]) ).

fof(f_3412_3,plain,
    ! [U_12894,U_12895,U_12896,U_12897,U_12898] : c_Map_Odom(U_12894,U_12895,hAPP(hAPP(c_COMBS(U_12894,tc_Option_Ooption(U_12895),tc_Option_Ooption(U_12895)),hAPP(hAPP(c_COMBS(U_12894,tc_Option_Ooption(U_12895),tc_fun(tc_Option_Ooption(U_12895),tc_Option_Ooption(U_12895))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_12895),tc_fun(tc_Option_Ooption(U_12895),tc_Option_Ooption(U_12895))),U_12894),c_If(tc_Option_Ooption(U_12895))),U_12896)),U_12897)),U_12898)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12894,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12894,tc_HOL_Obool)),c_Map_Odom(U_12894,U_12895,U_12897)),hAPP(c_Set_OCollect(U_12894),U_12896))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12894,tc_HOL_Obool)),c_Map_Odom(U_12894,U_12895,U_12898)),hAPP(c_Set_OCollect(U_12894),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12894),c_fNot),U_12896)))),
    inference(definitional_conversion,[status(esa)],[f_3412_2]) ).

cnf(f_3412_4,plain,
    c_Map_Odom(U_12894,U_12895,hAPP(hAPP(c_COMBS(U_12894,tc_Option_Ooption(U_12895),tc_Option_Ooption(U_12895)),hAPP(hAPP(c_COMBS(U_12894,tc_Option_Ooption(U_12895),tc_fun(tc_Option_Ooption(U_12895),tc_Option_Ooption(U_12895))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_12895),tc_fun(tc_Option_Ooption(U_12895),tc_Option_Ooption(U_12895))),U_12894),c_If(tc_Option_Ooption(U_12895))),U_12896)),U_12897)),U_12898)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12894,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12894,tc_HOL_Obool)),c_Map_Odom(U_12894,U_12895,U_12897)),hAPP(c_Set_OCollect(U_12894),U_12896))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12894,tc_HOL_Obool)),c_Map_Odom(U_12894,U_12895,U_12898)),hAPP(c_Set_OCollect(U_12894),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_12894),c_fNot),U_12896)))),
    inference(clausify,[status(thm)],[f_3412_3]) ).

fof(f_3413_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_3413_2,plain,
    ! [U_12903,U_12902,U_12901,U_12900,U_12899] :
      ( ( c_Map_Odom(U_12901,U_12900,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12901,tc_Option_Ooption(U_12900)),U_12902),U_12903),U_12899)) = hAPP(hAPP(c_Set_Oinsert(U_12901),U_12903),c_Map_Odom(U_12901,U_12900,U_12902))
        | U_12899 = c_Option_Ooption_ONone(U_12900) )
      & ( c_Map_Odom(U_12901,U_12900,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12901,tc_Option_Ooption(U_12900)),U_12902),U_12903),U_12899)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12901,tc_HOL_Obool)),c_Map_Odom(U_12901,U_12900,U_12902)),hAPP(hAPP(c_Set_Oinsert(U_12901),U_12903),c_Orderings_Obot__class_Obot(tc_fun(U_12901,tc_HOL_Obool))))
        | U_12899 != c_Option_Ooption_ONone(U_12900) ) ),
    inference(variable_rename,[status(thm)],[f_3413_1]) ).

fof(f_3413_3,plain,
    ( ! [U_12913,U_12911,U_12909,U_12907,U_12905] :
        ( c_Map_Odom(U_12909,U_12907,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12909,tc_Option_Ooption(U_12907)),U_12911),U_12913),U_12905)) = hAPP(hAPP(c_Set_Oinsert(U_12909),U_12913),c_Map_Odom(U_12909,U_12907,U_12911))
        | U_12905 = c_Option_Ooption_ONone(U_12907) )
    & ! [U_12912,U_12910,U_12908,U_12906,U_12904] :
        ( c_Map_Odom(U_12908,U_12906,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12908,tc_Option_Ooption(U_12906)),U_12910),U_12912),U_12904)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12908,tc_HOL_Obool)),c_Map_Odom(U_12908,U_12906,U_12910)),hAPP(hAPP(c_Set_Oinsert(U_12908),U_12912),c_Orderings_Obot__class_Obot(tc_fun(U_12908,tc_HOL_Obool))))
        | U_12904 != c_Option_Ooption_ONone(U_12906) ) ),
    inference(miniscope,[status(thm)],[f_3413_2]) ).

fof(f_3413_4,plain,
    ( ! [U_12905,U_12907,U_12909,U_12911,U_12913] :
        ( c_Map_Odom(U_12909,U_12907,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12909,tc_Option_Ooption(U_12907)),U_12911),U_12913),U_12905)) = hAPP(hAPP(c_Set_Oinsert(U_12909),U_12913),c_Map_Odom(U_12909,U_12907,U_12911))
        | U_12905 = c_Option_Ooption_ONone(U_12907) )
    & ! [U_12910,U_12904,U_12908,U_12906,U_12912] :
        ( c_Map_Odom(U_12908,U_12906,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12908,tc_Option_Ooption(U_12906)),U_12910),U_12912),U_12904)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12908,tc_HOL_Obool)),c_Map_Odom(U_12908,U_12906,U_12910)),hAPP(hAPP(c_Set_Oinsert(U_12908),U_12912),c_Orderings_Obot__class_Obot(tc_fun(U_12908,tc_HOL_Obool))))
        | U_12904 != c_Option_Ooption_ONone(U_12906) ) ),
    inference(definitional_conversion,[status(esa)],[f_3413_3]) ).

cnf(f_3413_5,plain,
    ( c_Map_Odom(U_12908,U_12906,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12908,tc_Option_Ooption(U_12906)),U_12910),U_12912),U_12904)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12908,tc_HOL_Obool)),c_Map_Odom(U_12908,U_12906,U_12910)),hAPP(hAPP(c_Set_Oinsert(U_12908),U_12912),c_Orderings_Obot__class_Obot(tc_fun(U_12908,tc_HOL_Obool))))
    | U_12904 != c_Option_Ooption_ONone(U_12906) ),
    inference(clausify,[status(thm)],[f_3413_4]) ).

cnf(f_3413_6,plain,
    ( c_Map_Odom(U_12909,U_12907,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_12909,tc_Option_Ooption(U_12907)),U_12911),U_12913),U_12905)) = hAPP(hAPP(c_Set_Oinsert(U_12909),U_12913),c_Map_Odom(U_12909,U_12907,U_12911))
    | U_12905 = c_Option_Ooption_ONone(U_12907) ),
    inference(clausify,[status(thm)],[f_3413_4]) ).

fof(f_3414_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_3414_2,plain,
    ! [U_12918,U_12917,U_12916,U_12915,U_12914] : c_Map_Odom(U_12914,U_12915,c_Fun_Ooverride__on(U_12914,tc_Option_Ooption(U_12915),U_12916,U_12917,U_12918)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12914,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12914,tc_HOL_Obool)),c_Map_Odom(U_12914,U_12915,U_12916)),hAPP(c_Set_OCollect(U_12914),hAPP(hAPP(c_COMBC(U_12914,tc_fun(U_12914,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12914)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12914,tc_HOL_Obool)),U_12918),c_Map_Odom(U_12914,U_12915,U_12917)))))),hAPP(c_Set_OCollect(U_12914),hAPP(hAPP(c_COMBC(U_12914,tc_fun(U_12914,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12914)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12914,tc_HOL_Obool)),U_12918),c_Map_Odom(U_12914,U_12915,U_12917))))),
    inference(variable_rename,[status(thm)],[f_3414_1]) ).

fof(f_3414_3,plain,
    ! [U_12914,U_12918,U_12915,U_12916,U_12917] : c_Map_Odom(U_12914,U_12915,c_Fun_Ooverride__on(U_12914,tc_Option_Ooption(U_12915),U_12916,U_12917,U_12918)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12914,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12914,tc_HOL_Obool)),c_Map_Odom(U_12914,U_12915,U_12916)),hAPP(c_Set_OCollect(U_12914),hAPP(hAPP(c_COMBC(U_12914,tc_fun(U_12914,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12914)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12914,tc_HOL_Obool)),U_12918),c_Map_Odom(U_12914,U_12915,U_12917)))))),hAPP(c_Set_OCollect(U_12914),hAPP(hAPP(c_COMBC(U_12914,tc_fun(U_12914,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12914)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12914,tc_HOL_Obool)),U_12918),c_Map_Odom(U_12914,U_12915,U_12917))))),
    inference(definitional_conversion,[status(esa)],[f_3414_2]) ).

cnf(f_3414_4,plain,
    c_Map_Odom(U_12914,U_12915,c_Fun_Ooverride__on(U_12914,tc_Option_Ooption(U_12915),U_12916,U_12917,U_12918)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_12914,tc_HOL_Obool)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12914,tc_HOL_Obool)),c_Map_Odom(U_12914,U_12915,U_12916)),hAPP(c_Set_OCollect(U_12914),hAPP(hAPP(c_COMBC(U_12914,tc_fun(U_12914,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12914)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_12914,tc_HOL_Obool)),U_12918),c_Map_Odom(U_12914,U_12915,U_12917)))))),hAPP(c_Set_OCollect(U_12914),hAPP(hAPP(c_COMBC(U_12914,tc_fun(U_12914,tc_HOL_Obool),tc_HOL_Obool),c_member(U_12914)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12914,tc_HOL_Obool)),U_12918),c_Map_Odom(U_12914,U_12915,U_12917))))),
    inference(clausify,[status(thm)],[f_3414_3]) ).

fof(f_3415_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_3415_2,plain,
    ! [U_12924,U_12923,U_12922,U_12921,U_12920,U_12919] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12919,U_12919)),hAPP(hAPP(c_Product__Type_OPair(U_12919,U_12919),U_12923),U_12924)),U_12921))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12919),U_12922),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12919,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12919,U_12919,U_12921),hAPP(hAPP(c_Set_Oinsert(U_12919),U_12923),c_Orderings_Obot__class_Obot(tc_fun(U_12919,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12919,U_12919,U_12921),hAPP(hAPP(c_Set_Oinsert(U_12919),U_12924),c_Orderings_Obot__class_Obot(tc_fun(U_12919,tc_HOL_Obool)))))))
      | ~ c_Equiv__Relations_Oequiv(U_12919,U_12920,U_12921) ),
    inference(variable_rename,[status(thm)],[f_3415_1]) ).

fof(f_3415_3,plain,
    ! [U_12919,U_12920,U_12921,U_12922,U_12923,U_12924] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12919,U_12919)),hAPP(hAPP(c_Product__Type_OPair(U_12919,U_12919),U_12923),U_12924)),U_12921))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12919),U_12922),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12919,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12919,U_12919,U_12921),hAPP(hAPP(c_Set_Oinsert(U_12919),U_12923),c_Orderings_Obot__class_Obot(tc_fun(U_12919,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12919,U_12919,U_12921),hAPP(hAPP(c_Set_Oinsert(U_12919),U_12924),c_Orderings_Obot__class_Obot(tc_fun(U_12919,tc_HOL_Obool)))))))
      | ~ c_Equiv__Relations_Oequiv(U_12919,U_12920,U_12921) ),
    inference(definitional_conversion,[status(esa)],[f_3415_2]) ).

cnf(f_3415_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12919,U_12919)),hAPP(hAPP(c_Product__Type_OPair(U_12919,U_12919),U_12923),U_12924)),U_12921))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12919),U_12922),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_12919,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12919,U_12919,U_12921),hAPP(hAPP(c_Set_Oinsert(U_12919),U_12923),c_Orderings_Obot__class_Obot(tc_fun(U_12919,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12919,U_12919,U_12921),hAPP(hAPP(c_Set_Oinsert(U_12919),U_12924),c_Orderings_Obot__class_Obot(tc_fun(U_12919,tc_HOL_Obool)))))))
    | ~ c_Equiv__Relations_Oequiv(U_12919,U_12920,U_12921) ),
    inference(clausify,[status(thm)],[f_3415_3]) ).

fof(f_3416_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_3416_2,plain,
    ! [U_12929,U_12928,U_12927,U_12926,U_12925] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12925,U_12925)),hAPP(hAPP(c_Product__Type_OPair(U_12925,U_12925),U_12929),U_12928)),U_12927))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12925),U_12928),U_12926))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12925,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12925,U_12925,U_12927),hAPP(hAPP(c_Set_Oinsert(U_12925),U_12928),c_Orderings_Obot__class_Obot(tc_fun(U_12925,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12925,U_12925,U_12927),hAPP(hAPP(c_Set_Oinsert(U_12925),U_12929),c_Orderings_Obot__class_Obot(tc_fun(U_12925,tc_HOL_Obool))))))
      | ~ c_Equiv__Relations_Oequiv(U_12925,U_12926,U_12927) ),
    inference(variable_rename,[status(thm)],[f_3416_1]) ).

fof(f_3416_3,plain,
    ! [U_12925,U_12926,U_12927,U_12928,U_12929] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12925,U_12925)),hAPP(hAPP(c_Product__Type_OPair(U_12925,U_12925),U_12929),U_12928)),U_12927))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12925),U_12928),U_12926))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12925,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12925,U_12925,U_12927),hAPP(hAPP(c_Set_Oinsert(U_12925),U_12928),c_Orderings_Obot__class_Obot(tc_fun(U_12925,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12925,U_12925,U_12927),hAPP(hAPP(c_Set_Oinsert(U_12925),U_12929),c_Orderings_Obot__class_Obot(tc_fun(U_12925,tc_HOL_Obool))))))
      | ~ c_Equiv__Relations_Oequiv(U_12925,U_12926,U_12927) ),
    inference(definitional_conversion,[status(esa)],[f_3416_2]) ).

cnf(f_3416_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12925,U_12925)),hAPP(hAPP(c_Product__Type_OPair(U_12925,U_12925),U_12929),U_12928)),U_12927))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12925),U_12928),U_12926))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12925,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12925,U_12925,U_12927),hAPP(hAPP(c_Set_Oinsert(U_12925),U_12928),c_Orderings_Obot__class_Obot(tc_fun(U_12925,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12925,U_12925,U_12927),hAPP(hAPP(c_Set_Oinsert(U_12925),U_12929),c_Orderings_Obot__class_Obot(tc_fun(U_12925,tc_HOL_Obool))))))
    | ~ c_Equiv__Relations_Oequiv(U_12925,U_12926,U_12927) ),
    inference(clausify,[status(thm)],[f_3416_3]) ).

fof(f_3417_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_3417_2,plain,
    ! [U_12932,U_12931,U_12930] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_12930,U_12930,U_12930),hAPP(c_Relation_Oconverse(U_12930,U_12930),U_12932)),U_12932) = U_12932
      | ~ c_Equiv__Relations_Oequiv(U_12930,U_12931,U_12932) ),
    inference(variable_rename,[status(thm)],[f_3417_1]) ).

fof(f_3417_3,plain,
    ! [U_12932,U_12931,U_12930] :
      ( hAPP(hAPP(c_Relation_Orel__comp(U_12930,U_12930,U_12930),hAPP(c_Relation_Oconverse(U_12930,U_12930),U_12932)),U_12932) = U_12932
      | ~ c_Equiv__Relations_Oequiv(U_12930,U_12931,U_12932) ),
    inference(definitional_conversion,[status(esa)],[f_3417_2]) ).

cnf(f_3417_4,plain,
    ( hAPP(hAPP(c_Relation_Orel__comp(U_12930,U_12930,U_12930),hAPP(c_Relation_Oconverse(U_12930,U_12930),U_12932)),U_12932) = U_12932
    | ~ c_Equiv__Relations_Oequiv(U_12930,U_12931,U_12932) ),
    inference(clausify,[status(thm)],[f_3417_3]) ).

fof(f_3418_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_3418_2,plain,
    ! [U_12935,U_12934,U_12933] :
      ( c_Equiv__Relations_Oequiv(U_12933,U_12935,U_12934)
      | hAPP(c_Relation_ODomain(U_12933,U_12933),U_12934) != U_12935
      | hAPP(hAPP(c_Relation_Orel__comp(U_12933,U_12933,U_12933),hAPP(c_Relation_Oconverse(U_12933,U_12933),U_12934)),U_12934) != U_12934 ),
    inference(variable_rename,[status(thm)],[f_3418_1]) ).

fof(f_3418_3,plain,
    ! [U_12933,U_12934,U_12935] :
      ( c_Equiv__Relations_Oequiv(U_12933,U_12935,U_12934)
      | hAPP(c_Relation_ODomain(U_12933,U_12933),U_12934) != U_12935
      | hAPP(hAPP(c_Relation_Orel__comp(U_12933,U_12933,U_12933),hAPP(c_Relation_Oconverse(U_12933,U_12933),U_12934)),U_12934) != U_12934 ),
    inference(definitional_conversion,[status(esa)],[f_3418_2]) ).

cnf(f_3418_4,plain,
    ( c_Equiv__Relations_Oequiv(U_12933,U_12935,U_12934)
    | hAPP(c_Relation_ODomain(U_12933,U_12933),U_12934) != U_12935
    | hAPP(hAPP(c_Relation_Orel__comp(U_12933,U_12933,U_12933),hAPP(c_Relation_Oconverse(U_12933,U_12933),U_12934)),U_12934) != U_12934 ),
    inference(clausify,[status(thm)],[f_3418_3]) ).

fof(f_3419_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_3419_2,plain,
    ! [U_12941,U_12940,U_12939,U_12938,U_12937,U_12936] :
      ( hAPP(c_Fun_Ooverride__on(U_12936,U_12939,U_12940,U_12941,U_12938),U_12937) = hAPP(U_12940,U_12937)
      | hBOOL(hAPP(hAPP(c_member(U_12936),U_12937),U_12938)) ),
    inference(variable_rename,[status(thm)],[f_3419_1]) ).

fof(f_3419_3,plain,
    ! [U_12936,U_12937,U_12938,U_12939,U_12940,U_12941] :
      ( hAPP(c_Fun_Ooverride__on(U_12936,U_12939,U_12940,U_12941,U_12938),U_12937) = hAPP(U_12940,U_12937)
      | hBOOL(hAPP(hAPP(c_member(U_12936),U_12937),U_12938)) ),
    inference(definitional_conversion,[status(esa)],[f_3419_2]) ).

cnf(f_3419_4,plain,
    ( hAPP(c_Fun_Ooverride__on(U_12936,U_12939,U_12940,U_12941,U_12938),U_12937) = hAPP(U_12940,U_12937)
    | hBOOL(hAPP(hAPP(c_member(U_12936),U_12937),U_12938)) ),
    inference(clausify,[status(thm)],[f_3419_3]) ).

fof(f_3420_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_3420_2,plain,
    ! [U_12947,U_12946,U_12945,U_12944,U_12943,U_12942] :
      ( hAPP(c_Fun_Ooverride__on(U_12942,U_12945,U_12946,U_12947,U_12944),U_12943) = hAPP(U_12947,U_12943)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12942),U_12943),U_12944)) ),
    inference(variable_rename,[status(thm)],[f_3420_1]) ).

fof(f_3420_3,plain,
    ! [U_12942,U_12943,U_12944,U_12945,U_12946,U_12947] :
      ( hAPP(c_Fun_Ooverride__on(U_12942,U_12945,U_12946,U_12947,U_12944),U_12943) = hAPP(U_12947,U_12943)
      | ~ hBOOL(hAPP(hAPP(c_member(U_12942),U_12943),U_12944)) ),
    inference(definitional_conversion,[status(esa)],[f_3420_2]) ).

cnf(f_3420_4,plain,
    ( hAPP(c_Fun_Ooverride__on(U_12942,U_12945,U_12946,U_12947,U_12944),U_12943) = hAPP(U_12947,U_12943)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12942),U_12943),U_12944)) ),
    inference(clausify,[status(thm)],[f_3420_3]) ).

fof(f_3421_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_3421_2,plain,
    ! [U_12951,U_12950,U_12949,U_12948] : c_Fun_Ooverride__on(U_12948,U_12949,U_12950,U_12951,c_Orderings_Obot__class_Obot(tc_fun(U_12948,tc_HOL_Obool))) = U_12950,
    inference(variable_rename,[status(thm)],[f_3421_1]) ).

fof(f_3421_3,plain,
    ! [U_12949,U_12948,U_12950,U_12951] : c_Fun_Ooverride__on(U_12948,U_12949,U_12950,U_12951,c_Orderings_Obot__class_Obot(tc_fun(U_12948,tc_HOL_Obool))) = U_12950,
    inference(definitional_conversion,[status(esa)],[f_3421_2]) ).

cnf(f_3421_4,plain,
    c_Fun_Ooverride__on(U_12948,U_12949,U_12950,U_12951,c_Orderings_Obot__class_Obot(tc_fun(U_12948,tc_HOL_Obool))) = U_12950,
    inference(clausify,[status(thm)],[f_3421_3]) ).

fof(f_3422_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_3422_2,plain,
    ! [U_12955,U_12954,U_12953,U_12952] :
      ( hBOOL(hAPP(hAPP(c_member(U_12952),U_12955),hAPP(c_Relation_OImage(U_12952,U_12952,U_12954),hAPP(hAPP(c_Set_Oinsert(U_12952),U_12955),c_Orderings_Obot__class_Obot(tc_fun(U_12952,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12952),U_12955),U_12953))
      | ~ c_Equiv__Relations_Oequiv(U_12952,U_12953,U_12954) ),
    inference(variable_rename,[status(thm)],[f_3422_1]) ).

fof(f_3422_3,plain,
    ! [U_12952,U_12953,U_12954,U_12955] :
      ( hBOOL(hAPP(hAPP(c_member(U_12952),U_12955),hAPP(c_Relation_OImage(U_12952,U_12952,U_12954),hAPP(hAPP(c_Set_Oinsert(U_12952),U_12955),c_Orderings_Obot__class_Obot(tc_fun(U_12952,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12952),U_12955),U_12953))
      | ~ c_Equiv__Relations_Oequiv(U_12952,U_12953,U_12954) ),
    inference(definitional_conversion,[status(esa)],[f_3422_2]) ).

cnf(f_3422_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12952),U_12955),hAPP(c_Relation_OImage(U_12952,U_12952,U_12954),hAPP(hAPP(c_Set_Oinsert(U_12952),U_12955),c_Orderings_Obot__class_Obot(tc_fun(U_12952,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12952),U_12955),U_12953))
    | ~ c_Equiv__Relations_Oequiv(U_12952,U_12953,U_12954) ),
    inference(clausify,[status(thm)],[f_3422_3]) ).

fof(f_3423_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_3423_2,plain,
    ! [U_12961,U_12960,U_12959,U_12958,U_12957,U_12956] :
      ( ( hAPP(c_Fun_Ooverride__on(U_12956,U_12959,U_12960,U_12961,U_12958),U_12957) = hAPP(U_12960,U_12957)
        | hBOOL(hAPP(hAPP(c_member(U_12956),U_12957),U_12958)) )
      & ( hAPP(c_Fun_Ooverride__on(U_12956,U_12959,U_12960,U_12961,U_12958),U_12957) = hAPP(U_12961,U_12957)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12956),U_12957),U_12958)) ) ),
    inference(variable_rename,[status(thm)],[f_3423_1]) ).

fof(f_3423_3,plain,
    ( ! [U_12973,U_12971,U_12969,U_12967,U_12965,U_12963] :
        ( hAPP(c_Fun_Ooverride__on(U_12963,U_12969,U_12971,U_12973,U_12967),U_12965) = hAPP(U_12971,U_12965)
        | hBOOL(hAPP(hAPP(c_member(U_12963),U_12965),U_12967)) )
    & ! [U_12972,U_12970,U_12968,U_12966,U_12964,U_12962] :
        ( hAPP(c_Fun_Ooverride__on(U_12962,U_12968,U_12970,U_12972,U_12966),U_12964) = hAPP(U_12972,U_12964)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12962),U_12964),U_12966)) ) ),
    inference(miniscope,[status(thm)],[f_3423_2]) ).

fof(f_3423_4,plain,
    ( ! [U_12963,U_12965,U_12967,U_12969,U_12971,U_12973] :
        ( hAPP(c_Fun_Ooverride__on(U_12963,U_12969,U_12971,U_12973,U_12967),U_12965) = hAPP(U_12971,U_12965)
        | hBOOL(hAPP(hAPP(c_member(U_12963),U_12965),U_12967)) )
    & ! [U_12966,U_12964,U_12968,U_12962,U_12970,U_12972] :
        ( hAPP(c_Fun_Ooverride__on(U_12962,U_12968,U_12970,U_12972,U_12966),U_12964) = hAPP(U_12972,U_12964)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12962),U_12964),U_12966)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3423_3]) ).

cnf(f_3423_5,plain,
    ( hAPP(c_Fun_Ooverride__on(U_12962,U_12968,U_12970,U_12972,U_12966),U_12964) = hAPP(U_12972,U_12964)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12962),U_12964),U_12966)) ),
    inference(clausify,[status(thm)],[f_3423_4]) ).

cnf(f_3423_6,plain,
    ( hAPP(c_Fun_Ooverride__on(U_12963,U_12969,U_12971,U_12973,U_12967),U_12965) = hAPP(U_12971,U_12965)
    | hBOOL(hAPP(hAPP(c_member(U_12963),U_12965),U_12967)) ),
    inference(clausify,[status(thm)],[f_3423_4]) ).

fof(f_3424_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_3424_2,plain,
    ! [U_12978,U_12977,U_12976,U_12975,U_12974] :
      ( hAPP(c_Relation_OImage(U_12974,U_12974,U_12976),hAPP(hAPP(c_Set_Oinsert(U_12974),U_12977),c_Orderings_Obot__class_Obot(tc_fun(U_12974,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12974,U_12974,U_12976),hAPP(hAPP(c_Set_Oinsert(U_12974),U_12978),c_Orderings_Obot__class_Obot(tc_fun(U_12974,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12974,U_12974)),hAPP(hAPP(c_Product__Type_OPair(U_12974,U_12974),U_12977),U_12978)),U_12976))
      | ~ c_Equiv__Relations_Oequiv(U_12974,U_12975,U_12976) ),
    inference(variable_rename,[status(thm)],[f_3424_1]) ).

fof(f_3424_3,plain,
    ! [U_12974,U_12975,U_12976,U_12977,U_12978] :
      ( hAPP(c_Relation_OImage(U_12974,U_12974,U_12976),hAPP(hAPP(c_Set_Oinsert(U_12974),U_12977),c_Orderings_Obot__class_Obot(tc_fun(U_12974,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12974,U_12974,U_12976),hAPP(hAPP(c_Set_Oinsert(U_12974),U_12978),c_Orderings_Obot__class_Obot(tc_fun(U_12974,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12974,U_12974)),hAPP(hAPP(c_Product__Type_OPair(U_12974,U_12974),U_12977),U_12978)),U_12976))
      | ~ c_Equiv__Relations_Oequiv(U_12974,U_12975,U_12976) ),
    inference(definitional_conversion,[status(esa)],[f_3424_2]) ).

cnf(f_3424_4,plain,
    ( hAPP(c_Relation_OImage(U_12974,U_12974,U_12976),hAPP(hAPP(c_Set_Oinsert(U_12974),U_12977),c_Orderings_Obot__class_Obot(tc_fun(U_12974,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12974,U_12974,U_12976),hAPP(hAPP(c_Set_Oinsert(U_12974),U_12978),c_Orderings_Obot__class_Obot(tc_fun(U_12974,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12974,U_12974)),hAPP(hAPP(c_Product__Type_OPair(U_12974,U_12974),U_12977),U_12978)),U_12976))
    | ~ c_Equiv__Relations_Oequiv(U_12974,U_12975,U_12976) ),
    inference(clausify,[status(thm)],[f_3424_3]) ).

fof(f_3425_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_3425_2,plain,
    ! [U_12983,U_12982,U_12981,U_12980,U_12979] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12979,U_12979)),hAPP(hAPP(c_Product__Type_OPair(U_12979,U_12979),U_12981),U_12982)),U_12980))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12979),U_12982),U_12983))
      | ~ c_Equiv__Relations_Oequiv(U_12979,U_12983,U_12980)
      | hAPP(c_Relation_OImage(U_12979,U_12979,U_12980),hAPP(hAPP(c_Set_Oinsert(U_12979),U_12981),c_Orderings_Obot__class_Obot(tc_fun(U_12979,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12979,U_12979,U_12980),hAPP(hAPP(c_Set_Oinsert(U_12979),U_12982),c_Orderings_Obot__class_Obot(tc_fun(U_12979,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3425_1]) ).

fof(f_3425_3,plain,
    ! [U_12979,U_12980,U_12981,U_12982,U_12983] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12979,U_12979)),hAPP(hAPP(c_Product__Type_OPair(U_12979,U_12979),U_12981),U_12982)),U_12980))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12979),U_12982),U_12983))
      | ~ c_Equiv__Relations_Oequiv(U_12979,U_12983,U_12980)
      | hAPP(c_Relation_OImage(U_12979,U_12979,U_12980),hAPP(hAPP(c_Set_Oinsert(U_12979),U_12981),c_Orderings_Obot__class_Obot(tc_fun(U_12979,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12979,U_12979,U_12980),hAPP(hAPP(c_Set_Oinsert(U_12979),U_12982),c_Orderings_Obot__class_Obot(tc_fun(U_12979,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3425_2]) ).

cnf(f_3425_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12979,U_12979)),hAPP(hAPP(c_Product__Type_OPair(U_12979,U_12979),U_12981),U_12982)),U_12980))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12979),U_12982),U_12983))
    | ~ c_Equiv__Relations_Oequiv(U_12979,U_12983,U_12980)
    | hAPP(c_Relation_OImage(U_12979,U_12979,U_12980),hAPP(hAPP(c_Set_Oinsert(U_12979),U_12981),c_Orderings_Obot__class_Obot(tc_fun(U_12979,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12979,U_12979,U_12980),hAPP(hAPP(c_Set_Oinsert(U_12979),U_12982),c_Orderings_Obot__class_Obot(tc_fun(U_12979,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3425_3]) ).

fof(f_3426_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_3426_2,plain,
    ! [U_12988,U_12987,U_12986,U_12985,U_12984] :
      ( ( ( hAPP(c_Relation_OImage(U_12984,U_12984,U_12986),hAPP(hAPP(c_Set_Oinsert(U_12984),U_12987),c_Orderings_Obot__class_Obot(tc_fun(U_12984,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12984,U_12984,U_12986),hAPP(hAPP(c_Set_Oinsert(U_12984),U_12988),c_Orderings_Obot__class_Obot(tc_fun(U_12984,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12984,U_12984)),hAPP(hAPP(c_Product__Type_OPair(U_12984,U_12984),U_12987),U_12988)),U_12986)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12984,U_12984)),hAPP(hAPP(c_Product__Type_OPair(U_12984,U_12984),U_12987),U_12988)),U_12986))
          | hAPP(c_Relation_OImage(U_12984,U_12984,U_12986),hAPP(hAPP(c_Set_Oinsert(U_12984),U_12987),c_Orderings_Obot__class_Obot(tc_fun(U_12984,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12984,U_12984,U_12986),hAPP(hAPP(c_Set_Oinsert(U_12984),U_12988),c_Orderings_Obot__class_Obot(tc_fun(U_12984,tc_HOL_Obool)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_12984),U_12988),U_12985))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12984),U_12987),U_12985))
      | ~ c_Equiv__Relations_Oequiv(U_12984,U_12985,U_12986) ),
    inference(variable_rename,[status(thm)],[f_3426_1]) ).

fof(f_3426_3,plain,
    ( ! [U_12984,U_12986,U_12987,U_12988] :
        ( hAPP(c_Relation_OImage(U_12984,U_12984,U_12986),hAPP(hAPP(c_Set_Oinsert(U_12984),U_12987),c_Orderings_Obot__class_Obot(tc_fun(U_12984,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12984,U_12984,U_12986),hAPP(hAPP(c_Set_Oinsert(U_12984),U_12988),c_Orderings_Obot__class_Obot(tc_fun(U_12984,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12984,U_12984)),hAPP(hAPP(c_Product__Type_OPair(U_12984,U_12984),U_12987),U_12988)),U_12986))
        | ~ sP925(U_12984,U_12986,U_12987,U_12988) )
    & ! [U_12984,U_12986,U_12987,U_12988] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12984,U_12984)),hAPP(hAPP(c_Product__Type_OPair(U_12984,U_12984),U_12987),U_12988)),U_12986))
        | hAPP(c_Relation_OImage(U_12984,U_12984,U_12986),hAPP(hAPP(c_Set_Oinsert(U_12984),U_12987),c_Orderings_Obot__class_Obot(tc_fun(U_12984,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12984,U_12984,U_12986),hAPP(hAPP(c_Set_Oinsert(U_12984),U_12988),c_Orderings_Obot__class_Obot(tc_fun(U_12984,tc_HOL_Obool))))
        | ~ sP925(U_12984,U_12986,U_12987,U_12988) )
    & ! [U_12984,U_12985,U_12986,U_12987,U_12988] :
        ( sP925(U_12984,U_12986,U_12987,U_12988)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12984),U_12988),U_12985))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12984),U_12987),U_12985))
        | ~ c_Equiv__Relations_Oequiv(U_12984,U_12985,U_12986) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP925])],[f_3426_2]) ).

cnf(f_3426_4,plain,
    ( sP925(U_12984,U_12986,U_12987,U_12988)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12984),U_12988),U_12985))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12984),U_12987),U_12985))
    | ~ c_Equiv__Relations_Oequiv(U_12984,U_12985,U_12986) ),
    inference(clausify,[status(thm)],[f_3426_3]) ).

cnf(f_3426_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12984,U_12984)),hAPP(hAPP(c_Product__Type_OPair(U_12984,U_12984),U_12987),U_12988)),U_12986))
    | hAPP(c_Relation_OImage(U_12984,U_12984,U_12986),hAPP(hAPP(c_Set_Oinsert(U_12984),U_12987),c_Orderings_Obot__class_Obot(tc_fun(U_12984,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12984,U_12984,U_12986),hAPP(hAPP(c_Set_Oinsert(U_12984),U_12988),c_Orderings_Obot__class_Obot(tc_fun(U_12984,tc_HOL_Obool))))
    | ~ sP925(U_12984,U_12986,U_12987,U_12988) ),
    inference(clausify,[status(thm)],[f_3426_3]) ).

cnf(f_3426_6,plain,
    ( hAPP(c_Relation_OImage(U_12984,U_12984,U_12986),hAPP(hAPP(c_Set_Oinsert(U_12984),U_12987),c_Orderings_Obot__class_Obot(tc_fun(U_12984,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12984,U_12984,U_12986),hAPP(hAPP(c_Set_Oinsert(U_12984),U_12988),c_Orderings_Obot__class_Obot(tc_fun(U_12984,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12984,U_12984)),hAPP(hAPP(c_Product__Type_OPair(U_12984,U_12984),U_12987),U_12988)),U_12986))
    | ~ sP925(U_12984,U_12986,U_12987,U_12988) ),
    inference(clausify,[status(thm)],[f_3426_3]) ).

fof(f_3427_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_3427_2,plain,
    ! [U_12993,U_12992,U_12991,U_12990,U_12989] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12989,U_12989)),hAPP(hAPP(c_Product__Type_OPair(U_12989,U_12989),U_12992),U_12993)),U_12991))
          | ~ hBOOL(hAPP(hAPP(c_member(U_12989),U_12993),U_12990))
          | ~ hBOOL(hAPP(hAPP(c_member(U_12989),U_12992),U_12990))
          | hAPP(c_Relation_OImage(U_12989,U_12989,U_12991),hAPP(hAPP(c_Set_Oinsert(U_12989),U_12992),c_Orderings_Obot__class_Obot(tc_fun(U_12989,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12989,U_12989,U_12991),hAPP(hAPP(c_Set_Oinsert(U_12989),U_12993),c_Orderings_Obot__class_Obot(tc_fun(U_12989,tc_HOL_Obool)))) )
        & ( ( hBOOL(hAPP(hAPP(c_member(U_12989),U_12993),U_12990))
            & hBOOL(hAPP(hAPP(c_member(U_12989),U_12992),U_12990))
            & hAPP(c_Relation_OImage(U_12989,U_12989,U_12991),hAPP(hAPP(c_Set_Oinsert(U_12989),U_12992),c_Orderings_Obot__class_Obot(tc_fun(U_12989,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12989,U_12989,U_12991),hAPP(hAPP(c_Set_Oinsert(U_12989),U_12993),c_Orderings_Obot__class_Obot(tc_fun(U_12989,tc_HOL_Obool)))) )
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12989,U_12989)),hAPP(hAPP(c_Product__Type_OPair(U_12989,U_12989),U_12992),U_12993)),U_12991)) ) )
      | ~ c_Equiv__Relations_Oequiv(U_12989,U_12990,U_12991) ),
    inference(variable_rename,[status(thm)],[f_3427_1]) ).

fof(f_3427_3,plain,
    ( ! [U_12992,U_12991,U_12993,U_12990,U_12989] :
        ( hBOOL(hAPP(hAPP(c_member(U_12989),U_12993),U_12990))
        | ~ sP926(U_12992,U_12991,U_12993,U_12990,U_12989) )
    & ! [U_12992,U_12991,U_12993,U_12990,U_12989] :
        ( hBOOL(hAPP(hAPP(c_member(U_12989),U_12992),U_12990))
        | ~ sP926(U_12992,U_12991,U_12993,U_12990,U_12989) )
    & ! [U_12992,U_12991,U_12993,U_12990,U_12989] :
        ( hAPP(c_Relation_OImage(U_12989,U_12989,U_12991),hAPP(hAPP(c_Set_Oinsert(U_12989),U_12992),c_Orderings_Obot__class_Obot(tc_fun(U_12989,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12989,U_12989,U_12991),hAPP(hAPP(c_Set_Oinsert(U_12989),U_12993),c_Orderings_Obot__class_Obot(tc_fun(U_12989,tc_HOL_Obool))))
        | ~ sP926(U_12992,U_12991,U_12993,U_12990,U_12989) )
    & ! [U_12992,U_12991,U_12993,U_12990,U_12989] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12989,U_12989)),hAPP(hAPP(c_Product__Type_OPair(U_12989,U_12989),U_12992),U_12993)),U_12991))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12989),U_12993),U_12990))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12989),U_12992),U_12990))
        | hAPP(c_Relation_OImage(U_12989,U_12989,U_12991),hAPP(hAPP(c_Set_Oinsert(U_12989),U_12992),c_Orderings_Obot__class_Obot(tc_fun(U_12989,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12989,U_12989,U_12991),hAPP(hAPP(c_Set_Oinsert(U_12989),U_12993),c_Orderings_Obot__class_Obot(tc_fun(U_12989,tc_HOL_Obool))))
        | ~ sP927(U_12992,U_12991,U_12993,U_12990,U_12989) )
    & ! [U_12992,U_12991,U_12993,U_12990,U_12989] :
        ( sP926(U_12992,U_12991,U_12993,U_12990,U_12989)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12989,U_12989)),hAPP(hAPP(c_Product__Type_OPair(U_12989,U_12989),U_12992),U_12993)),U_12991))
        | ~ sP927(U_12992,U_12991,U_12993,U_12990,U_12989) )
    & ! [U_12992,U_12991,U_12993,U_12990,U_12989] :
        ( sP927(U_12992,U_12991,U_12993,U_12990,U_12989)
        | ~ c_Equiv__Relations_Oequiv(U_12989,U_12990,U_12991) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP926,sP927])],[f_3427_2]) ).

cnf(f_3427_4,plain,
    ( sP927(U_12992,U_12991,U_12993,U_12990,U_12989)
    | ~ c_Equiv__Relations_Oequiv(U_12989,U_12990,U_12991) ),
    inference(clausify,[status(thm)],[f_3427_3]) ).

cnf(f_3427_5,plain,
    ( sP926(U_12992,U_12991,U_12993,U_12990,U_12989)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12989,U_12989)),hAPP(hAPP(c_Product__Type_OPair(U_12989,U_12989),U_12992),U_12993)),U_12991))
    | ~ sP927(U_12992,U_12991,U_12993,U_12990,U_12989) ),
    inference(clausify,[status(thm)],[f_3427_3]) ).

cnf(f_3427_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12989,U_12989)),hAPP(hAPP(c_Product__Type_OPair(U_12989,U_12989),U_12992),U_12993)),U_12991))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12989),U_12993),U_12990))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12989),U_12992),U_12990))
    | hAPP(c_Relation_OImage(U_12989,U_12989,U_12991),hAPP(hAPP(c_Set_Oinsert(U_12989),U_12992),c_Orderings_Obot__class_Obot(tc_fun(U_12989,tc_HOL_Obool)))) != hAPP(c_Relation_OImage(U_12989,U_12989,U_12991),hAPP(hAPP(c_Set_Oinsert(U_12989),U_12993),c_Orderings_Obot__class_Obot(tc_fun(U_12989,tc_HOL_Obool))))
    | ~ sP927(U_12992,U_12991,U_12993,U_12990,U_12989) ),
    inference(clausify,[status(thm)],[f_3427_3]) ).

cnf(f_3427_7,plain,
    ( hAPP(c_Relation_OImage(U_12989,U_12989,U_12991),hAPP(hAPP(c_Set_Oinsert(U_12989),U_12992),c_Orderings_Obot__class_Obot(tc_fun(U_12989,tc_HOL_Obool)))) = hAPP(c_Relation_OImage(U_12989,U_12989,U_12991),hAPP(hAPP(c_Set_Oinsert(U_12989),U_12993),c_Orderings_Obot__class_Obot(tc_fun(U_12989,tc_HOL_Obool))))
    | ~ sP926(U_12992,U_12991,U_12993,U_12990,U_12989) ),
    inference(clausify,[status(thm)],[f_3427_3]) ).

cnf(f_3427_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12989),U_12992),U_12990))
    | ~ sP926(U_12992,U_12991,U_12993,U_12990,U_12989) ),
    inference(clausify,[status(thm)],[f_3427_3]) ).

cnf(f_3427_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_12989),U_12993),U_12990))
    | ~ sP926(U_12992,U_12991,U_12993,U_12990,U_12989) ),
    inference(clausify,[status(thm)],[f_3427_3]) ).

fof(f_3428_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_3428_2,plain,
    ! [U_12998,U_12997,U_12996,U_12995,U_12994] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12994,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12994,U_12994,U_12996),hAPP(hAPP(c_Set_Oinsert(U_12994),U_12997),c_Orderings_Obot__class_Obot(tc_fun(U_12994,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12994,U_12994,U_12996),hAPP(hAPP(c_Set_Oinsert(U_12994),U_12998),c_Orderings_Obot__class_Obot(tc_fun(U_12994,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12994,U_12994)),hAPP(hAPP(c_Product__Type_OPair(U_12994,U_12994),U_12997),U_12998)),U_12996))
      | ~ c_Equiv__Relations_Oequiv(U_12994,U_12995,U_12996) ),
    inference(variable_rename,[status(thm)],[f_3428_1]) ).

fof(f_3428_3,plain,
    ! [U_12996,U_12998,U_12997,U_12995,U_12994] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12994,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12994,U_12994,U_12996),hAPP(hAPP(c_Set_Oinsert(U_12994),U_12997),c_Orderings_Obot__class_Obot(tc_fun(U_12994,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12994,U_12994,U_12996),hAPP(hAPP(c_Set_Oinsert(U_12994),U_12998),c_Orderings_Obot__class_Obot(tc_fun(U_12994,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12994,U_12994)),hAPP(hAPP(c_Product__Type_OPair(U_12994,U_12994),U_12997),U_12998)),U_12996))
      | ~ c_Equiv__Relations_Oequiv(U_12994,U_12995,U_12996) ),
    inference(definitional_conversion,[status(esa)],[f_3428_2]) ).

cnf(f_3428_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_12994,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_12994,U_12994,U_12996),hAPP(hAPP(c_Set_Oinsert(U_12994),U_12997),c_Orderings_Obot__class_Obot(tc_fun(U_12994,tc_HOL_Obool))))),hAPP(c_Relation_OImage(U_12994,U_12994,U_12996),hAPP(hAPP(c_Set_Oinsert(U_12994),U_12998),c_Orderings_Obot__class_Obot(tc_fun(U_12994,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12994,U_12994)),hAPP(hAPP(c_Product__Type_OPair(U_12994,U_12994),U_12997),U_12998)),U_12996))
    | ~ c_Equiv__Relations_Oequiv(U_12994,U_12995,U_12996) ),
    inference(clausify,[status(thm)],[f_3428_3]) ).

fof(f_3429_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_3429_2,plain,
    ! [U_13003,U_13002,U_13001,U_13000,U_12999] :
      ( ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12999),hAPP(hAPP(c_Set_Oinsert(U_12999),U_13002),c_Orderings_Obot__class_Obot(tc_fun(U_12999,tc_HOL_Obool)))),U_13001) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12999),hAPP(hAPP(c_Set_Oinsert(U_12999),U_13003),c_Orderings_Obot__class_Obot(tc_fun(U_12999,tc_HOL_Obool)))),U_13001)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12999,U_12999)),hAPP(hAPP(c_Product__Type_OPair(U_12999,U_12999),U_13002),U_13003)),U_13001)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12999,U_12999)),hAPP(hAPP(c_Product__Type_OPair(U_12999,U_12999),U_13002),U_13003)),U_13001))
          | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12999),hAPP(hAPP(c_Set_Oinsert(U_12999),U_13002),c_Orderings_Obot__class_Obot(tc_fun(U_12999,tc_HOL_Obool)))),U_13001) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12999),hAPP(hAPP(c_Set_Oinsert(U_12999),U_13003),c_Orderings_Obot__class_Obot(tc_fun(U_12999,tc_HOL_Obool)))),U_13001) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_12999),U_13003),U_13000))
      | ~ hBOOL(hAPP(hAPP(c_member(U_12999),U_13002),U_13000))
      | ~ c_Equiv__Relations_Oequiv(U_12999,U_13000,U_13001) ),
    inference(variable_rename,[status(thm)],[f_3429_1]) ).

fof(f_3429_3,plain,
    ( ! [U_12999,U_13001,U_13002,U_13003] :
        ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12999),hAPP(hAPP(c_Set_Oinsert(U_12999),U_13002),c_Orderings_Obot__class_Obot(tc_fun(U_12999,tc_HOL_Obool)))),U_13001) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12999),hAPP(hAPP(c_Set_Oinsert(U_12999),U_13003),c_Orderings_Obot__class_Obot(tc_fun(U_12999,tc_HOL_Obool)))),U_13001)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12999,U_12999)),hAPP(hAPP(c_Product__Type_OPair(U_12999,U_12999),U_13002),U_13003)),U_13001))
        | ~ sP928(U_12999,U_13001,U_13002,U_13003) )
    & ! [U_12999,U_13001,U_13002,U_13003] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12999,U_12999)),hAPP(hAPP(c_Product__Type_OPair(U_12999,U_12999),U_13002),U_13003)),U_13001))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12999),hAPP(hAPP(c_Set_Oinsert(U_12999),U_13002),c_Orderings_Obot__class_Obot(tc_fun(U_12999,tc_HOL_Obool)))),U_13001) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12999),hAPP(hAPP(c_Set_Oinsert(U_12999),U_13003),c_Orderings_Obot__class_Obot(tc_fun(U_12999,tc_HOL_Obool)))),U_13001)
        | ~ sP928(U_12999,U_13001,U_13002,U_13003) )
    & ! [U_12999,U_13000,U_13001,U_13002,U_13003] :
        ( sP928(U_12999,U_13001,U_13002,U_13003)
        | ~ hBOOL(hAPP(hAPP(c_member(U_12999),U_13003),U_13000))
        | ~ hBOOL(hAPP(hAPP(c_member(U_12999),U_13002),U_13000))
        | ~ c_Equiv__Relations_Oequiv(U_12999,U_13000,U_13001) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP928])],[f_3429_2]) ).

cnf(f_3429_4,plain,
    ( sP928(U_12999,U_13001,U_13002,U_13003)
    | ~ hBOOL(hAPP(hAPP(c_member(U_12999),U_13003),U_13000))
    | ~ hBOOL(hAPP(hAPP(c_member(U_12999),U_13002),U_13000))
    | ~ c_Equiv__Relations_Oequiv(U_12999,U_13000,U_13001) ),
    inference(clausify,[status(thm)],[f_3429_3]) ).

cnf(f_3429_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_12999,U_12999)),hAPP(hAPP(c_Product__Type_OPair(U_12999,U_12999),U_13002),U_13003)),U_13001))
    | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12999),hAPP(hAPP(c_Set_Oinsert(U_12999),U_13002),c_Orderings_Obot__class_Obot(tc_fun(U_12999,tc_HOL_Obool)))),U_13001) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12999),hAPP(hAPP(c_Set_Oinsert(U_12999),U_13003),c_Orderings_Obot__class_Obot(tc_fun(U_12999,tc_HOL_Obool)))),U_13001)
    | ~ sP928(U_12999,U_13001,U_13002,U_13003) ),
    inference(clausify,[status(thm)],[f_3429_3]) ).

cnf(f_3429_6,plain,
    ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12999),hAPP(hAPP(c_Set_Oinsert(U_12999),U_13002),c_Orderings_Obot__class_Obot(tc_fun(U_12999,tc_HOL_Obool)))),U_13001) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_12999),hAPP(hAPP(c_Set_Oinsert(U_12999),U_13003),c_Orderings_Obot__class_Obot(tc_fun(U_12999,tc_HOL_Obool)))),U_13001)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_12999,U_12999)),hAPP(hAPP(c_Product__Type_OPair(U_12999,U_12999),U_13002),U_13003)),U_13001))
    | ~ sP928(U_12999,U_13001,U_13002,U_13003) ),
    inference(clausify,[status(thm)],[f_3429_3]) ).

fof(f_3430_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_3430_2,plain,
    ! [U_13006,U_13005,U_13004] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13004),hAPP(hAPP(c_Set_Oinsert(U_13004),U_13005),c_Orderings_Obot__class_Obot(tc_fun(U_13004,tc_HOL_Obool)))),U_13006) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_13004,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13004,U_13004,U_13006),hAPP(hAPP(c_Set_Oinsert(U_13004),U_13005),c_Orderings_Obot__class_Obot(tc_fun(U_13004,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13004,tc_HOL_Obool),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3430_1]) ).

fof(f_3430_3,plain,
    ! [U_13005,U_13006,U_13004] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13004),hAPP(hAPP(c_Set_Oinsert(U_13004),U_13005),c_Orderings_Obot__class_Obot(tc_fun(U_13004,tc_HOL_Obool)))),U_13006) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_13004,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13004,U_13004,U_13006),hAPP(hAPP(c_Set_Oinsert(U_13004),U_13005),c_Orderings_Obot__class_Obot(tc_fun(U_13004,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13004,tc_HOL_Obool),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3430_2]) ).

cnf(f_3430_4,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13004),hAPP(hAPP(c_Set_Oinsert(U_13004),U_13005),c_Orderings_Obot__class_Obot(tc_fun(U_13004,tc_HOL_Obool)))),U_13006) = hAPP(hAPP(c_Set_Oinsert(tc_fun(U_13004,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13004,U_13004,U_13006),hAPP(hAPP(c_Set_Oinsert(U_13004),U_13005),c_Orderings_Obot__class_Obot(tc_fun(U_13004,tc_HOL_Obool))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13004,tc_HOL_Obool),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3430_3]) ).

fof(f_3431_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_3431_2,plain,
    ! [U_13013,U_13012,U_13011,U_13010,U_13009,U_13008,U_13007] :
      ( U_13010 = U_13011
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13007,U_13007)),hAPP(hAPP(c_Product__Type_OPair(U_13007,U_13007),U_13012),U_13013)),U_13009))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13007),U_13013),U_13011))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13007),U_13012),U_13010))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13007,tc_HOL_Obool)),U_13011),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13007),U_13008),U_13009)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13007,tc_HOL_Obool)),U_13010),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13007),U_13008),U_13009)))
      | ~ c_Equiv__Relations_Oequiv(U_13007,U_13008,U_13009) ),
    inference(variable_rename,[status(thm)],[f_3431_1]) ).

fof(f_3431_3,plain,
    ! [U_13007,U_13008,U_13009,U_13010,U_13011,U_13012,U_13013] :
      ( U_13010 = U_13011
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13007,U_13007)),hAPP(hAPP(c_Product__Type_OPair(U_13007,U_13007),U_13012),U_13013)),U_13009))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13007),U_13013),U_13011))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13007),U_13012),U_13010))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13007,tc_HOL_Obool)),U_13011),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13007),U_13008),U_13009)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13007,tc_HOL_Obool)),U_13010),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13007),U_13008),U_13009)))
      | ~ c_Equiv__Relations_Oequiv(U_13007,U_13008,U_13009) ),
    inference(definitional_conversion,[status(esa)],[f_3431_2]) ).

cnf(f_3431_4,plain,
    ( U_13010 = U_13011
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13007,U_13007)),hAPP(hAPP(c_Product__Type_OPair(U_13007,U_13007),U_13012),U_13013)),U_13009))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13007),U_13013),U_13011))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13007),U_13012),U_13010))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13007,tc_HOL_Obool)),U_13011),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13007),U_13008),U_13009)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13007,tc_HOL_Obool)),U_13010),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13007),U_13008),U_13009)))
    | ~ c_Equiv__Relations_Oequiv(U_13007,U_13008,U_13009) ),
    inference(clausify,[status(thm)],[f_3431_3]) ).

fof(f_3432_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_3432_2,plain,
    ! [U_13015,U_13014] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13014),c_Orderings_Obot__class_Obot(tc_fun(U_13014,tc_HOL_Obool))),U_13015) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13014,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3432_1]) ).

fof(f_3432_3,plain,
    ! [U_13014,U_13015] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13014),c_Orderings_Obot__class_Obot(tc_fun(U_13014,tc_HOL_Obool))),U_13015) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13014,tc_HOL_Obool),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3432_2]) ).

cnf(f_3432_4,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13014),c_Orderings_Obot__class_Obot(tc_fun(U_13014,tc_HOL_Obool))),U_13015) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13014,tc_HOL_Obool),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3432_3]) ).

fof(f_3433_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_3433_2,plain,
    ! [U_13018,U_13017,U_13016] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13016,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13016),U_13017),U_13018)
        | U_13017 != c_Orderings_Obot__class_Obot(tc_fun(U_13016,tc_HOL_Obool)) )
      & ( U_13017 = c_Orderings_Obot__class_Obot(tc_fun(U_13016,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13016,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13016),U_13017),U_13018) ) ),
    inference(variable_rename,[status(thm)],[f_3433_1]) ).

fof(f_3433_3,plain,
    ( ! [U_13024,U_13022,U_13020] :
        ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13020,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13020),U_13022),U_13024)
        | U_13022 != c_Orderings_Obot__class_Obot(tc_fun(U_13020,tc_HOL_Obool)) )
    & ! [U_13023,U_13021,U_13019] :
        ( U_13021 = c_Orderings_Obot__class_Obot(tc_fun(U_13019,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13019,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13019),U_13021),U_13023) ) ),
    inference(miniscope,[status(thm)],[f_3433_2]) ).

fof(f_3433_4,plain,
    ( ! [U_13020,U_13022,U_13024] :
        ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13020,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13020),U_13022),U_13024)
        | U_13022 != c_Orderings_Obot__class_Obot(tc_fun(U_13020,tc_HOL_Obool)) )
    & ! [U_13019,U_13021,U_13023] :
        ( U_13021 = c_Orderings_Obot__class_Obot(tc_fun(U_13019,tc_HOL_Obool))
        | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13019,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13019),U_13021),U_13023) ) ),
    inference(definitional_conversion,[status(esa)],[f_3433_3]) ).

cnf(f_3433_5,plain,
    ( U_13021 = c_Orderings_Obot__class_Obot(tc_fun(U_13019,tc_HOL_Obool))
    | c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13019,tc_HOL_Obool),tc_HOL_Obool)) != hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13019),U_13021),U_13023) ),
    inference(clausify,[status(thm)],[f_3433_4]) ).

cnf(f_3433_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13020,tc_HOL_Obool),tc_HOL_Obool)) = hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13020),U_13022),U_13024)
    | U_13022 != c_Orderings_Obot__class_Obot(tc_fun(U_13020,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3433_4]) ).

fof(f_3434_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_3434_2,plain,
    ! [U_13027,U_13026,U_13025] :
      ( ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13025),U_13026),U_13027) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13025,tc_HOL_Obool),tc_HOL_Obool))
        | U_13026 != c_Orderings_Obot__class_Obot(tc_fun(U_13025,tc_HOL_Obool)) )
      & ( U_13026 = c_Orderings_Obot__class_Obot(tc_fun(U_13025,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13025),U_13026),U_13027) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13025,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3434_1]) ).

fof(f_3434_3,plain,
    ( ! [U_13033,U_13031,U_13029] :
        ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13029),U_13031),U_13033) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13029,tc_HOL_Obool),tc_HOL_Obool))
        | U_13031 != c_Orderings_Obot__class_Obot(tc_fun(U_13029,tc_HOL_Obool)) )
    & ! [U_13032,U_13030,U_13028] :
        ( U_13030 = c_Orderings_Obot__class_Obot(tc_fun(U_13028,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13028),U_13030),U_13032) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13028,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3434_2]) ).

fof(f_3434_4,plain,
    ( ! [U_13029,U_13031,U_13033] :
        ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13029),U_13031),U_13033) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13029,tc_HOL_Obool),tc_HOL_Obool))
        | U_13031 != c_Orderings_Obot__class_Obot(tc_fun(U_13029,tc_HOL_Obool)) )
    & ! [U_13030,U_13032,U_13028] :
        ( U_13030 = c_Orderings_Obot__class_Obot(tc_fun(U_13028,tc_HOL_Obool))
        | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13028),U_13030),U_13032) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13028,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3434_3]) ).

cnf(f_3434_5,plain,
    ( U_13030 = c_Orderings_Obot__class_Obot(tc_fun(U_13028,tc_HOL_Obool))
    | hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13028),U_13030),U_13032) != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13028,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3434_4]) ).

cnf(f_3434_6,plain,
    ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13029),U_13031),U_13033) = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13029,tc_HOL_Obool),tc_HOL_Obool))
    | U_13031 != c_Orderings_Obot__class_Obot(tc_fun(U_13029,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3434_4]) ).

fof(f_3435_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_3435_2,plain,
    ! [U_13038,U_13037,U_13036,U_13035,U_13034] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13034,tc_HOL_Obool)),U_13037),U_13038) = c_Orderings_Obot__class_Obot(tc_fun(U_13034,tc_HOL_Obool))
      | U_13037 = U_13038
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13034,tc_HOL_Obool)),U_13038),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13034),U_13035),U_13036)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13034,tc_HOL_Obool)),U_13037),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13034),U_13035),U_13036)))
      | ~ c_Equiv__Relations_Oequiv(U_13034,U_13035,U_13036) ),
    inference(variable_rename,[status(thm)],[f_3435_1]) ).

fof(f_3435_3,plain,
    ! [U_13034,U_13035,U_13036,U_13037,U_13038] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13034,tc_HOL_Obool)),U_13037),U_13038) = c_Orderings_Obot__class_Obot(tc_fun(U_13034,tc_HOL_Obool))
      | U_13037 = U_13038
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13034,tc_HOL_Obool)),U_13038),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13034),U_13035),U_13036)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13034,tc_HOL_Obool)),U_13037),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13034),U_13035),U_13036)))
      | ~ c_Equiv__Relations_Oequiv(U_13034,U_13035,U_13036) ),
    inference(definitional_conversion,[status(esa)],[f_3435_2]) ).

cnf(f_3435_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13034,tc_HOL_Obool)),U_13037),U_13038) = c_Orderings_Obot__class_Obot(tc_fun(U_13034,tc_HOL_Obool))
    | U_13037 = U_13038
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13034,tc_HOL_Obool)),U_13038),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13034),U_13035),U_13036)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13034,tc_HOL_Obool)),U_13037),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13034),U_13035),U_13036)))
    | ~ c_Equiv__Relations_Oequiv(U_13034,U_13035,U_13036) ),
    inference(clausify,[status(thm)],[f_3435_3]) ).

fof(f_3436_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_3436_2,plain,
    ! [U_13042,U_13041,U_13040,U_13039] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_13039,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13039,U_13039,U_13042),hAPP(hAPP(c_Set_Oinsert(U_13039),U_13040),c_Orderings_Obot__class_Obot(tc_fun(U_13039,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13039),U_13041),U_13042)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13039),U_13040),U_13041)) ),
    inference(variable_rename,[status(thm)],[f_3436_1]) ).

fof(f_3436_3,plain,
    ! [U_13040,U_13039,U_13041,U_13042] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_13039,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13039,U_13039,U_13042),hAPP(hAPP(c_Set_Oinsert(U_13039),U_13040),c_Orderings_Obot__class_Obot(tc_fun(U_13039,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13039),U_13041),U_13042)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13039),U_13040),U_13041)) ),
    inference(definitional_conversion,[status(esa)],[f_3436_2]) ).

cnf(f_3436_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_13039,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13039,U_13039,U_13042),hAPP(hAPP(c_Set_Oinsert(U_13039),U_13040),c_Orderings_Obot__class_Obot(tc_fun(U_13039,tc_HOL_Obool))))),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13039),U_13041),U_13042)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13039),U_13040),U_13041)) ),
    inference(clausify,[status(thm)],[f_3436_3]) ).

fof(f_3437_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_3437_2,plain,
    ! [U_13049,U_13048,U_13047,U_13046,U_13045,U_13044,U_13043] :
      ( ( ( U_13046 = U_13047
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13043,U_13043)),hAPP(hAPP(c_Product__Type_OPair(U_13043,U_13043),U_13048),U_13049)),U_13045)) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13043,U_13043)),hAPP(hAPP(c_Product__Type_OPair(U_13043,U_13043),U_13048),U_13049)),U_13045))
          | U_13046 != U_13047 ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13043),U_13049),U_13047))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13043),U_13048),U_13046))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13043,tc_HOL_Obool)),U_13047),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13043),U_13044),U_13045)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13043,tc_HOL_Obool)),U_13046),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13043),U_13044),U_13045)))
      | ~ c_Equiv__Relations_Oequiv(U_13043,U_13044,U_13045) ),
    inference(variable_rename,[status(thm)],[f_3437_1]) ).

fof(f_3437_3,plain,
    ( ! [U_13043,U_13045,U_13046,U_13047,U_13048,U_13049] :
        ( U_13046 = U_13047
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13043,U_13043)),hAPP(hAPP(c_Product__Type_OPair(U_13043,U_13043),U_13048),U_13049)),U_13045))
        | ~ sP929(U_13043,U_13045,U_13046,U_13047,U_13048,U_13049) )
    & ! [U_13043,U_13045,U_13046,U_13047,U_13048,U_13049] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13043,U_13043)),hAPP(hAPP(c_Product__Type_OPair(U_13043,U_13043),U_13048),U_13049)),U_13045))
        | U_13046 != U_13047
        | ~ sP929(U_13043,U_13045,U_13046,U_13047,U_13048,U_13049) )
    & ! [U_13043,U_13044,U_13045,U_13046,U_13047,U_13048,U_13049] :
        ( sP929(U_13043,U_13045,U_13046,U_13047,U_13048,U_13049)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13043),U_13049),U_13047))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13043),U_13048),U_13046))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13043,tc_HOL_Obool)),U_13047),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13043),U_13044),U_13045)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13043,tc_HOL_Obool)),U_13046),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13043),U_13044),U_13045)))
        | ~ c_Equiv__Relations_Oequiv(U_13043,U_13044,U_13045) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP929])],[f_3437_2]) ).

cnf(f_3437_4,plain,
    ( sP929(U_13043,U_13045,U_13046,U_13047,U_13048,U_13049)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13043),U_13049),U_13047))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13043),U_13048),U_13046))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13043,tc_HOL_Obool)),U_13047),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13043),U_13044),U_13045)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13043,tc_HOL_Obool)),U_13046),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13043),U_13044),U_13045)))
    | ~ c_Equiv__Relations_Oequiv(U_13043,U_13044,U_13045) ),
    inference(clausify,[status(thm)],[f_3437_3]) ).

cnf(f_3437_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_13043,U_13043)),hAPP(hAPP(c_Product__Type_OPair(U_13043,U_13043),U_13048),U_13049)),U_13045))
    | U_13046 != U_13047
    | ~ sP929(U_13043,U_13045,U_13046,U_13047,U_13048,U_13049) ),
    inference(clausify,[status(thm)],[f_3437_3]) ).

cnf(f_3437_6,plain,
    ( U_13046 = U_13047
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13043,U_13043)),hAPP(hAPP(c_Product__Type_OPair(U_13043,U_13043),U_13048),U_13049)),U_13045))
    | ~ sP929(U_13043,U_13045,U_13046,U_13047,U_13048,U_13049) ),
    inference(clausify,[status(thm)],[f_3437_3]) ).

fof(f_3438_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_3438_2,plain,
    ! [U_13054,U_13053,U_13052,U_13051] :
      ( ? [U_13050] :
          ( hBOOL(hAPP(hAPP(c_member(U_13051),U_13050),U_13053))
          & U_13052 = hAPP(c_Relation_OImage(U_13051,U_13051,U_13054),hAPP(hAPP(c_Set_Oinsert(U_13051),U_13050),c_Orderings_Obot__class_Obot(tc_fun(U_13051,tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13051,tc_HOL_Obool)),U_13052),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13051),U_13053),U_13054))) ),
    inference(variable_rename,[status(thm)],[f_3438_1]) ).

fof(f_3438_3,plain,
    ! [U_13054,U_13053,U_13052,U_13051] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_13051),sK281(U_13054,U_13053,U_13052,U_13051)),U_13053))
        & U_13052 = hAPP(c_Relation_OImage(U_13051,U_13051,U_13054),hAPP(hAPP(c_Set_Oinsert(U_13051),sK281(U_13054,U_13053,U_13052,U_13051)),c_Orderings_Obot__class_Obot(tc_fun(U_13051,tc_HOL_Obool)))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13051,tc_HOL_Obool)),U_13052),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13051),U_13053),U_13054))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK281]),skolemize(U_13050,sK281(U_13054,U_13053,U_13052,U_13051))],[f_3438_2]) ).

fof(f_3438_4,plain,
    ( ! [U_13051,U_13052,U_13053,U_13054] :
        ( hBOOL(hAPP(hAPP(c_member(U_13051),sK281(U_13054,U_13053,U_13052,U_13051)),U_13053))
        | ~ sP930(U_13051,U_13052,U_13053,U_13054) )
    & ! [U_13051,U_13052,U_13053,U_13054] :
        ( U_13052 = hAPP(c_Relation_OImage(U_13051,U_13051,U_13054),hAPP(hAPP(c_Set_Oinsert(U_13051),sK281(U_13054,U_13053,U_13052,U_13051)),c_Orderings_Obot__class_Obot(tc_fun(U_13051,tc_HOL_Obool))))
        | ~ sP930(U_13051,U_13052,U_13053,U_13054) )
    & ! [U_13051,U_13052,U_13053,U_13054] :
        ( sP930(U_13051,U_13052,U_13053,U_13054)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13051,tc_HOL_Obool)),U_13052),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13051),U_13053),U_13054))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP930])],[f_3438_3]) ).

cnf(f_3438_5,plain,
    ( sP930(U_13051,U_13052,U_13053,U_13054)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13051,tc_HOL_Obool)),U_13052),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13051),U_13053),U_13054))) ),
    inference(clausify,[status(thm)],[f_3438_4]) ).

cnf(f_3438_6,plain,
    ( U_13052 = hAPP(c_Relation_OImage(U_13051,U_13051,U_13054),hAPP(hAPP(c_Set_Oinsert(U_13051),sK281(U_13054,U_13053,U_13052,U_13051)),c_Orderings_Obot__class_Obot(tc_fun(U_13051,tc_HOL_Obool))))
    | ~ sP930(U_13051,U_13052,U_13053,U_13054) ),
    inference(clausify,[status(thm)],[f_3438_4]) ).

cnf(f_3438_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13051),sK281(U_13054,U_13053,U_13052,U_13051)),U_13053))
    | ~ sP930(U_13051,U_13052,U_13053,U_13054) ),
    inference(clausify,[status(thm)],[f_3438_4]) ).

fof(f_3439_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_3439_2,plain,
    ! [U_13059,U_13058,U_13057,U_13056] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_13059),hAPP(c_Finite__Set_Ocard(U_13056),U_13057)))
      | ? [U_13055] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_13059),hAPP(c_Finite__Set_Ocard(U_13056),U_13055)))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_13056,tc_HOL_Obool)),U_13055),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13056),U_13057),U_13058))) )
      | ~ c_Equiv__Relations_Oequiv(U_13056,U_13057,U_13058)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13056),U_13057)) ),
    inference(variable_rename,[status(thm)],[f_3439_1]) ).

fof(f_3439_3,plain,
    ! [U_13059,U_13058,U_13057,U_13056] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_13059),hAPP(c_Finite__Set_Ocard(U_13056),U_13057)))
      | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_13059),hAPP(c_Finite__Set_Ocard(U_13056),sK282(U_13059,U_13058,U_13057,U_13056))))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_13056,tc_HOL_Obool)),sK282(U_13059,U_13058,U_13057,U_13056)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13056),U_13057),U_13058))) )
      | ~ c_Equiv__Relations_Oequiv(U_13056,U_13057,U_13058)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13056),U_13057)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK282]),skolemize(U_13055,sK282(U_13059,U_13058,U_13057,U_13056))],[f_3439_2]) ).

fof(f_3439_4,plain,
    ( ! [U_13056,U_13057,U_13058,U_13059] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_13059),hAPP(c_Finite__Set_Ocard(U_13056),sK282(U_13059,U_13058,U_13057,U_13056))))
        | ~ sP931(U_13056,U_13057,U_13058,U_13059) )
    & ! [U_13056,U_13057,U_13058,U_13059] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_13056,tc_HOL_Obool)),sK282(U_13059,U_13058,U_13057,U_13056)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13056),U_13057),U_13058)))
        | ~ sP931(U_13056,U_13057,U_13058,U_13059) )
    & ! [U_13056,U_13057,U_13058,U_13059] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_13059),hAPP(c_Finite__Set_Ocard(U_13056),U_13057)))
        | sP931(U_13056,U_13057,U_13058,U_13059)
        | ~ c_Equiv__Relations_Oequiv(U_13056,U_13057,U_13058)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13056),U_13057)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP931])],[f_3439_3]) ).

cnf(f_3439_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_13059),hAPP(c_Finite__Set_Ocard(U_13056),U_13057)))
    | sP931(U_13056,U_13057,U_13058,U_13059)
    | ~ c_Equiv__Relations_Oequiv(U_13056,U_13057,U_13058)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13056),U_13057)) ),
    inference(clausify,[status(thm)],[f_3439_4]) ).

cnf(f_3439_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_13056,tc_HOL_Obool)),sK282(U_13059,U_13058,U_13057,U_13056)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13056),U_13057),U_13058)))
    | ~ sP931(U_13056,U_13057,U_13058,U_13059) ),
    inference(clausify,[status(thm)],[f_3439_4]) ).

cnf(f_3439_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(tc_Nat_Onat),U_13059),hAPP(c_Finite__Set_Ocard(U_13056),sK282(U_13059,U_13058,U_13057,U_13056))))
    | ~ sP931(U_13056,U_13057,U_13058,U_13059) ),
    inference(clausify,[status(thm)],[f_3439_4]) ).

fof(f_3440_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_3440_2,plain,
    ! [U_13062,U_13061,U_13060] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(U_13060,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13060),U_13061),U_13062)) = hAPP(c_Finite__Set_Ocard(U_13060),U_13061)
      | ~ c_Fun_Oinj__on(U_13060,tc_fun(tc_fun(U_13060,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13060,tc_fun(tc_prod(U_13060,U_13060),tc_HOL_Obool),tc_fun(tc_fun(U_13060,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13060,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_13060,U_13060),tc_HOL_Obool),tc_fun(tc_fun(U_13060,tc_HOL_Obool),tc_HOL_Obool)),U_13060),c_Equiv__Relations_Oquotient(U_13060)),hAPP(hAPP(c_COMBC(U_13060,tc_fun(U_13060,tc_HOL_Obool),tc_fun(U_13060,tc_HOL_Obool)),c_Set_Oinsert(U_13060)),c_Orderings_Obot__class_Obot(tc_fun(U_13060,tc_HOL_Obool))))),U_13062),U_13061)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13060),U_13061)) ),
    inference(variable_rename,[status(thm)],[f_3440_1]) ).

fof(f_3440_3,plain,
    ! [U_13060,U_13061,U_13062] :
      ( hAPP(c_Finite__Set_Ocard(tc_fun(U_13060,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13060),U_13061),U_13062)) = hAPP(c_Finite__Set_Ocard(U_13060),U_13061)
      | ~ c_Fun_Oinj__on(U_13060,tc_fun(tc_fun(U_13060,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13060,tc_fun(tc_prod(U_13060,U_13060),tc_HOL_Obool),tc_fun(tc_fun(U_13060,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13060,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_13060,U_13060),tc_HOL_Obool),tc_fun(tc_fun(U_13060,tc_HOL_Obool),tc_HOL_Obool)),U_13060),c_Equiv__Relations_Oquotient(U_13060)),hAPP(hAPP(c_COMBC(U_13060,tc_fun(U_13060,tc_HOL_Obool),tc_fun(U_13060,tc_HOL_Obool)),c_Set_Oinsert(U_13060)),c_Orderings_Obot__class_Obot(tc_fun(U_13060,tc_HOL_Obool))))),U_13062),U_13061)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13060),U_13061)) ),
    inference(definitional_conversion,[status(esa)],[f_3440_2]) ).

cnf(f_3440_4,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_fun(U_13060,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13060),U_13061),U_13062)) = hAPP(c_Finite__Set_Ocard(U_13060),U_13061)
    | ~ c_Fun_Oinj__on(U_13060,tc_fun(tc_fun(U_13060,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13060,tc_fun(tc_prod(U_13060,U_13060),tc_HOL_Obool),tc_fun(tc_fun(U_13060,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13060,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_13060,U_13060),tc_HOL_Obool),tc_fun(tc_fun(U_13060,tc_HOL_Obool),tc_HOL_Obool)),U_13060),c_Equiv__Relations_Oquotient(U_13060)),hAPP(hAPP(c_COMBC(U_13060,tc_fun(U_13060,tc_HOL_Obool),tc_fun(U_13060,tc_HOL_Obool)),c_Set_Oinsert(U_13060)),c_Orderings_Obot__class_Obot(tc_fun(U_13060,tc_HOL_Obool))))),U_13062),U_13061)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13060),U_13061)) ),
    inference(clausify,[status(thm)],[f_3440_3]) ).

fof(f_3441_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_3441_2,plain,
    ! [U_13065,U_13064,U_13063] : c_Fun_Oinj__on(U_13063,U_13064,U_13065,c_Orderings_Obot__class_Obot(tc_fun(U_13063,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3441_1]) ).

fof(f_3441_3,plain,
    ! [U_13065,U_13064,U_13063] : c_Fun_Oinj__on(U_13063,U_13064,U_13065,c_Orderings_Obot__class_Obot(tc_fun(U_13063,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3441_2]) ).

cnf(f_3441_4,plain,
    c_Fun_Oinj__on(U_13063,U_13064,U_13065,c_Orderings_Obot__class_Obot(tc_fun(U_13063,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3441_3]) ).

fof(f_3442_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_3442_2,plain,
    ! [U_13067,U_13066] :
      ( c_Fun_Oinj__on(U_13066,U_13066,c_Groups_Ouminus__class_Ouminus(U_13066),U_13067)
      | ~ class_Groups_Oordered__ab__group__add(U_13066) ),
    inference(variable_rename,[status(thm)],[f_3442_1]) ).

fof(f_3442_3,plain,
    ! [U_13066,U_13067] :
      ( c_Fun_Oinj__on(U_13066,U_13066,c_Groups_Ouminus__class_Ouminus(U_13066),U_13067)
      | ~ class_Groups_Oordered__ab__group__add(U_13066) ),
    inference(definitional_conversion,[status(esa)],[f_3442_2]) ).

cnf(f_3442_4,plain,
    ( c_Fun_Oinj__on(U_13066,U_13066,c_Groups_Ouminus__class_Ouminus(U_13066),U_13067)
    | ~ class_Groups_Oordered__ab__group__add(U_13066) ),
    inference(clausify,[status(thm)],[f_3442_3]) ).

fof(f_3443_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_3443_2,plain,
    ! [U_13072,U_13071,U_13070,U_13069,U_13068] :
      ( c_Fun_Oinj__on(U_13068,U_13069,U_13070,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13068,tc_HOL_Obool)),U_13071),U_13072))
      | ~ c_Fun_Oinj__on(U_13068,U_13069,U_13070,U_13071) ),
    inference(variable_rename,[status(thm)],[f_3443_1]) ).

fof(f_3443_3,plain,
    ! [U_13068,U_13069,U_13070,U_13071,U_13072] :
      ( c_Fun_Oinj__on(U_13068,U_13069,U_13070,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13068,tc_HOL_Obool)),U_13071),U_13072))
      | ~ c_Fun_Oinj__on(U_13068,U_13069,U_13070,U_13071) ),
    inference(definitional_conversion,[status(esa)],[f_3443_2]) ).

cnf(f_3443_4,plain,
    ( c_Fun_Oinj__on(U_13068,U_13069,U_13070,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13068,tc_HOL_Obool)),U_13071),U_13072))
    | ~ c_Fun_Oinj__on(U_13068,U_13069,U_13070,U_13071) ),
    inference(clausify,[status(thm)],[f_3443_3]) ).

fof(f_3444_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_3444_2,plain,
    ! [U_13077,U_13076,U_13075,U_13074,U_13073] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_13074,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13073,U_13074,U_13075),U_13077)),hAPP(c_Set_Oimage(U_13073,U_13074,U_13075),U_13076)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_13073,tc_HOL_Obool)),U_13077),U_13076))
      | ~ c_Fun_Oinj__on(U_13073,U_13074,U_13075,U_13076) ),
    inference(variable_rename,[status(thm)],[f_3444_1]) ).

fof(f_3444_3,plain,
    ! [U_13073,U_13074,U_13075,U_13076,U_13077] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_13074,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13073,U_13074,U_13075),U_13077)),hAPP(c_Set_Oimage(U_13073,U_13074,U_13075),U_13076)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_13073,tc_HOL_Obool)),U_13077),U_13076))
      | ~ c_Fun_Oinj__on(U_13073,U_13074,U_13075,U_13076) ),
    inference(definitional_conversion,[status(esa)],[f_3444_2]) ).

cnf(f_3444_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_13074,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13073,U_13074,U_13075),U_13077)),hAPP(c_Set_Oimage(U_13073,U_13074,U_13075),U_13076)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(U_13073,tc_HOL_Obool)),U_13077),U_13076))
    | ~ c_Fun_Oinj__on(U_13073,U_13074,U_13075,U_13076) ),
    inference(clausify,[status(thm)],[f_3444_3]) ).

fof(f_3445_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_3445_2,plain,
    ! [U_13079,U_13078] : c_Fun_Oinj__on(U_13078,U_13078,c_COMBI(U_13078),U_13079),
    inference(variable_rename,[status(thm)],[f_3445_1]) ).

fof(f_3445_3,plain,
    ! [U_13078,U_13079] : c_Fun_Oinj__on(U_13078,U_13078,c_COMBI(U_13078),U_13079),
    inference(definitional_conversion,[status(esa)],[f_3445_2]) ).

cnf(f_3445_4,plain,
    c_Fun_Oinj__on(U_13078,U_13078,c_COMBI(U_13078),U_13079),
    inference(clausify,[status(thm)],[f_3445_3]) ).

fof(f_3446_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_3446_2,plain,
    ! [U_13087,U_13086,U_13085,U_13084] :
      ( ( c_Fun_Oinj__on(U_13084,U_13085,U_13086,U_13087)
        | ? [U_13083] :
            ( ? [U_13082] :
                ( U_13083 != U_13082
                & hAPP(U_13086,U_13083) = hAPP(U_13086,U_13082)
                & hBOOL(hAPP(hAPP(c_member(U_13084),U_13082),U_13087)) )
            & hBOOL(hAPP(hAPP(c_member(U_13084),U_13083),U_13087)) ) )
      & ( ! [U_13081] :
            ( ! [U_13080] :
                ( U_13081 = U_13080
                | hAPP(U_13086,U_13081) != hAPP(U_13086,U_13080)
                | ~ hBOOL(hAPP(hAPP(c_member(U_13084),U_13080),U_13087)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_13084),U_13081),U_13087)) )
        | ~ c_Fun_Oinj__on(U_13084,U_13085,U_13086,U_13087) ) ),
    inference(variable_rename,[status(thm)],[f_3446_1]) ).

fof(f_3446_3,plain,
    ( ! [U_13095,U_13093,U_13091,U_13089] :
        ( c_Fun_Oinj__on(U_13089,U_13091,U_13093,U_13095)
        | ? [U_13083] :
            ( ? [U_13082] :
                ( U_13083 != U_13082
                & hAPP(U_13093,U_13083) = hAPP(U_13093,U_13082)
                & hBOOL(hAPP(hAPP(c_member(U_13089),U_13082),U_13095)) )
            & hBOOL(hAPP(hAPP(c_member(U_13089),U_13083),U_13095)) ) )
    & ! [U_13094,U_13092,U_13090,U_13088] :
        ( ! [U_13081] :
            ( ! [U_13080] :
                ( U_13081 = U_13080
                | hAPP(U_13092,U_13081) != hAPP(U_13092,U_13080)
                | ~ hBOOL(hAPP(hAPP(c_member(U_13088),U_13080),U_13094)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_13088),U_13081),U_13094)) )
        | ~ c_Fun_Oinj__on(U_13088,U_13090,U_13092,U_13094) ) ),
    inference(miniscope,[status(thm)],[f_3446_2]) ).

fof(f_3446_4,plain,
    ( ! [U_13095,U_13093,U_13091,U_13089] :
        ( c_Fun_Oinj__on(U_13089,U_13091,U_13093,U_13095)
        | ( ? [U_13082] :
              ( sK283(U_13095,U_13093,U_13091,U_13089) != U_13082
              & hAPP(U_13093,sK283(U_13095,U_13093,U_13091,U_13089)) = hAPP(U_13093,U_13082)
              & hBOOL(hAPP(hAPP(c_member(U_13089),U_13082),U_13095)) )
          & hBOOL(hAPP(hAPP(c_member(U_13089),sK283(U_13095,U_13093,U_13091,U_13089)),U_13095)) ) )
    & ! [U_13094,U_13092,U_13090,U_13088] :
        ( ! [U_13081] :
            ( ! [U_13080] :
                ( U_13081 = U_13080
                | hAPP(U_13092,U_13081) != hAPP(U_13092,U_13080)
                | ~ hBOOL(hAPP(hAPP(c_member(U_13088),U_13080),U_13094)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_13088),U_13081),U_13094)) )
        | ~ c_Fun_Oinj__on(U_13088,U_13090,U_13092,U_13094) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK283]),skolemize(U_13083,sK283(U_13095,U_13093,U_13091,U_13089))],[f_3446_3]) ).

fof(f_3446_5,plain,
    ( ! [U_13095,U_13093,U_13091,U_13089] :
        ( c_Fun_Oinj__on(U_13089,U_13091,U_13093,U_13095)
        | ( sK283(U_13095,U_13093,U_13091,U_13089) != sK284(U_13095,U_13093,U_13091,U_13089)
          & hAPP(U_13093,sK283(U_13095,U_13093,U_13091,U_13089)) = hAPP(U_13093,sK284(U_13095,U_13093,U_13091,U_13089))
          & hBOOL(hAPP(hAPP(c_member(U_13089),sK284(U_13095,U_13093,U_13091,U_13089)),U_13095))
          & hBOOL(hAPP(hAPP(c_member(U_13089),sK283(U_13095,U_13093,U_13091,U_13089)),U_13095)) ) )
    & ! [U_13094,U_13092,U_13090,U_13088] :
        ( ! [U_13081] :
            ( ! [U_13080] :
                ( U_13081 = U_13080
                | hAPP(U_13092,U_13081) != hAPP(U_13092,U_13080)
                | ~ hBOOL(hAPP(hAPP(c_member(U_13088),U_13080),U_13094)) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_13088),U_13081),U_13094)) )
        | ~ c_Fun_Oinj__on(U_13088,U_13090,U_13092,U_13094) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK284]),skolemize(U_13082,sK284(U_13095,U_13093,U_13091,U_13089))],[f_3446_4]) ).

fof(f_3446_6,plain,
    ( ! [U_13091,U_13095,U_13093,U_13089] :
        ( sK283(U_13095,U_13093,U_13091,U_13089) != sK284(U_13095,U_13093,U_13091,U_13089)
        | ~ sP932(U_13091,U_13095,U_13093,U_13089) )
    & ! [U_13091,U_13095,U_13093,U_13089] :
        ( hAPP(U_13093,sK283(U_13095,U_13093,U_13091,U_13089)) = hAPP(U_13093,sK284(U_13095,U_13093,U_13091,U_13089))
        | ~ sP932(U_13091,U_13095,U_13093,U_13089) )
    & ! [U_13091,U_13095,U_13093,U_13089] :
        ( hBOOL(hAPP(hAPP(c_member(U_13089),sK284(U_13095,U_13093,U_13091,U_13089)),U_13095))
        | ~ sP932(U_13091,U_13095,U_13093,U_13089) )
    & ! [U_13091,U_13095,U_13093,U_13089] :
        ( hBOOL(hAPP(hAPP(c_member(U_13089),sK283(U_13095,U_13093,U_13091,U_13089)),U_13095))
        | ~ sP932(U_13091,U_13095,U_13093,U_13089) )
    & ! [U_13091,U_13095,U_13093,U_13089] :
        ( c_Fun_Oinj__on(U_13089,U_13091,U_13093,U_13095)
        | sP932(U_13091,U_13095,U_13093,U_13089) )
    & ! [U_13080,U_13092,U_13081,U_13090,U_13088,U_13094] :
        ( U_13081 = U_13080
        | hAPP(U_13092,U_13081) != hAPP(U_13092,U_13080)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13088),U_13080),U_13094))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13088),U_13081),U_13094))
        | ~ c_Fun_Oinj__on(U_13088,U_13090,U_13092,U_13094) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP932])],[f_3446_5]) ).

cnf(f_3446_7,plain,
    ( U_13081 = U_13080
    | hAPP(U_13092,U_13081) != hAPP(U_13092,U_13080)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13088),U_13080),U_13094))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13088),U_13081),U_13094))
    | ~ c_Fun_Oinj__on(U_13088,U_13090,U_13092,U_13094) ),
    inference(clausify,[status(thm)],[f_3446_6]) ).

cnf(f_3446_8,plain,
    ( c_Fun_Oinj__on(U_13089,U_13091,U_13093,U_13095)
    | sP932(U_13091,U_13095,U_13093,U_13089) ),
    inference(clausify,[status(thm)],[f_3446_6]) ).

cnf(f_3446_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13089),sK283(U_13095,U_13093,U_13091,U_13089)),U_13095))
    | ~ sP932(U_13091,U_13095,U_13093,U_13089) ),
    inference(clausify,[status(thm)],[f_3446_6]) ).

cnf(f_3446_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13089),sK284(U_13095,U_13093,U_13091,U_13089)),U_13095))
    | ~ sP932(U_13091,U_13095,U_13093,U_13089) ),
    inference(clausify,[status(thm)],[f_3446_6]) ).

cnf(f_3446_11,plain,
    ( hAPP(U_13093,sK283(U_13095,U_13093,U_13091,U_13089)) = hAPP(U_13093,sK284(U_13095,U_13093,U_13091,U_13089))
    | ~ sP932(U_13091,U_13095,U_13093,U_13089) ),
    inference(clausify,[status(thm)],[f_3446_6]) ).

cnf(f_3446_12,plain,
    ( sK283(U_13095,U_13093,U_13091,U_13089) != sK284(U_13095,U_13093,U_13091,U_13089)
    | ~ sP932(U_13091,U_13095,U_13093,U_13089) ),
    inference(clausify,[status(thm)],[f_3446_6]) ).

fof(f_3447_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_3447_2,plain,
    ! [U_13101,U_13100,U_13099,U_13098,U_13097,U_13096] :
      ( U_13100 = U_13101
      | ~ hBOOL(hAPP(hAPP(c_member(U_13096),U_13101),U_13099))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13096),U_13100),U_13099))
      | hAPP(U_13098,U_13100) != hAPP(U_13098,U_13101)
      | ~ c_Fun_Oinj__on(U_13096,U_13097,U_13098,U_13099) ),
    inference(variable_rename,[status(thm)],[f_3447_1]) ).

fof(f_3447_3,plain,
    ! [U_13099,U_13096,U_13101,U_13100,U_13098,U_13097] :
      ( U_13100 = U_13101
      | ~ hBOOL(hAPP(hAPP(c_member(U_13096),U_13101),U_13099))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13096),U_13100),U_13099))
      | hAPP(U_13098,U_13100) != hAPP(U_13098,U_13101)
      | ~ c_Fun_Oinj__on(U_13096,U_13097,U_13098,U_13099) ),
    inference(definitional_conversion,[status(esa)],[f_3447_2]) ).

cnf(f_3447_4,plain,
    ( U_13100 = U_13101
    | ~ hBOOL(hAPP(hAPP(c_member(U_13096),U_13101),U_13099))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13096),U_13100),U_13099))
    | hAPP(U_13098,U_13100) != hAPP(U_13098,U_13101)
    | ~ c_Fun_Oinj__on(U_13096,U_13097,U_13098,U_13099) ),
    inference(clausify,[status(thm)],[f_3447_3]) ).

fof(f_3448_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_3448_2,plain,
    ! [U_13107,U_13106,U_13105,U_13104,U_13103,U_13102] :
      ( ( ( hAPP(U_13104,U_13106) = hAPP(U_13104,U_13107)
          | U_13106 != U_13107 )
        & ( U_13106 = U_13107
          | hAPP(U_13104,U_13106) != hAPP(U_13104,U_13107) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13102),U_13107),U_13105))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13102),U_13106),U_13105))
      | ~ c_Fun_Oinj__on(U_13102,U_13103,U_13104,U_13105) ),
    inference(variable_rename,[status(thm)],[f_3448_1]) ).

fof(f_3448_3,plain,
    ( ! [U_13104,U_13106,U_13107] :
        ( hAPP(U_13104,U_13106) = hAPP(U_13104,U_13107)
        | U_13106 != U_13107
        | ~ sP933(U_13104,U_13106,U_13107) )
    & ! [U_13104,U_13106,U_13107] :
        ( U_13106 = U_13107
        | hAPP(U_13104,U_13106) != hAPP(U_13104,U_13107)
        | ~ sP933(U_13104,U_13106,U_13107) )
    & ! [U_13102,U_13103,U_13104,U_13105,U_13106,U_13107] :
        ( sP933(U_13104,U_13106,U_13107)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13102),U_13107),U_13105))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13102),U_13106),U_13105))
        | ~ c_Fun_Oinj__on(U_13102,U_13103,U_13104,U_13105) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP933])],[f_3448_2]) ).

cnf(f_3448_4,plain,
    ( sP933(U_13104,U_13106,U_13107)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13102),U_13107),U_13105))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13102),U_13106),U_13105))
    | ~ c_Fun_Oinj__on(U_13102,U_13103,U_13104,U_13105) ),
    inference(clausify,[status(thm)],[f_3448_3]) ).

cnf(f_3448_5,plain,
    ( U_13106 = U_13107
    | hAPP(U_13104,U_13106) != hAPP(U_13104,U_13107)
    | ~ sP933(U_13104,U_13106,U_13107) ),
    inference(clausify,[status(thm)],[f_3448_3]) ).

cnf(f_3448_6,plain,
    ( hAPP(U_13104,U_13106) = hAPP(U_13104,U_13107)
    | U_13106 != U_13107
    | ~ sP933(U_13104,U_13106,U_13107) ),
    inference(clausify,[status(thm)],[f_3448_3]) ).

fof(f_3449_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_3449_2,plain,
    ! [U_13113,U_13112,U_13111,U_13110,U_13109,U_13108] :
      ( hAPP(U_13110,U_13112) != hAPP(U_13110,U_13113)
      | ~ hBOOL(hAPP(hAPP(c_member(U_13108),U_13113),U_13111))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13108),U_13112),U_13111))
      | U_13112 = U_13113
      | ~ c_Fun_Oinj__on(U_13108,U_13109,U_13110,U_13111) ),
    inference(variable_rename,[status(thm)],[f_3449_1]) ).

fof(f_3449_3,plain,
    ! [U_13113,U_13112,U_13111,U_13110,U_13108,U_13109] :
      ( hAPP(U_13110,U_13112) != hAPP(U_13110,U_13113)
      | ~ hBOOL(hAPP(hAPP(c_member(U_13108),U_13113),U_13111))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13108),U_13112),U_13111))
      | U_13112 = U_13113
      | ~ c_Fun_Oinj__on(U_13108,U_13109,U_13110,U_13111) ),
    inference(definitional_conversion,[status(esa)],[f_3449_2]) ).

cnf(f_3449_4,plain,
    ( hAPP(U_13110,U_13112) != hAPP(U_13110,U_13113)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13108),U_13113),U_13111))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13108),U_13112),U_13111))
    | U_13112 = U_13113
    | ~ c_Fun_Oinj__on(U_13108,U_13109,U_13110,U_13111) ),
    inference(clausify,[status(thm)],[f_3449_3]) ).

fof(f_3450_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_3450_2,plain,
    ! [U_13118,U_13117,U_13116,U_13115,U_13114] :
      ( c_Fun_Oinj__on(U_13114,U_13115,U_13116,U_13118)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13114,tc_HOL_Obool)),U_13118),U_13117))
      | ~ c_Fun_Oinj__on(U_13114,U_13115,U_13116,U_13117) ),
    inference(variable_rename,[status(thm)],[f_3450_1]) ).

fof(f_3450_3,plain,
    ! [U_13114,U_13116,U_13117,U_13118,U_13115] :
      ( c_Fun_Oinj__on(U_13114,U_13115,U_13116,U_13118)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13114,tc_HOL_Obool)),U_13118),U_13117))
      | ~ c_Fun_Oinj__on(U_13114,U_13115,U_13116,U_13117) ),
    inference(definitional_conversion,[status(esa)],[f_3450_2]) ).

cnf(f_3450_4,plain,
    ( c_Fun_Oinj__on(U_13114,U_13115,U_13116,U_13118)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13114,tc_HOL_Obool)),U_13118),U_13117))
    | ~ c_Fun_Oinj__on(U_13114,U_13115,U_13116,U_13117) ),
    inference(clausify,[status(thm)],[f_3450_3]) ).

fof(f_3451_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_3451_2,plain,
    ! [U_13123,U_13122,U_13121,U_13120,U_13119] :
      ( c_Fun_Oinj__on(U_13119,U_13120,U_13121,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13119,tc_HOL_Obool)),U_13122),U_13123))
      | ~ c_Fun_Oinj__on(U_13119,U_13120,U_13121,U_13123)
      | ~ c_Fun_Oinj__on(U_13119,U_13120,U_13121,U_13122) ),
    inference(variable_rename,[status(thm)],[f_3451_1]) ).

fof(f_3451_3,plain,
    ! [U_13120,U_13121,U_13119,U_13122,U_13123] :
      ( c_Fun_Oinj__on(U_13119,U_13120,U_13121,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13119,tc_HOL_Obool)),U_13122),U_13123))
      | ~ c_Fun_Oinj__on(U_13119,U_13120,U_13121,U_13123)
      | ~ c_Fun_Oinj__on(U_13119,U_13120,U_13121,U_13122) ),
    inference(definitional_conversion,[status(esa)],[f_3451_2]) ).

cnf(f_3451_4,plain,
    ( c_Fun_Oinj__on(U_13119,U_13120,U_13121,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13119,tc_HOL_Obool)),U_13122),U_13123))
    | ~ c_Fun_Oinj__on(U_13119,U_13120,U_13121,U_13123)
    | ~ c_Fun_Oinj__on(U_13119,U_13120,U_13121,U_13122) ),
    inference(clausify,[status(thm)],[f_3451_3]) ).

fof(f_3452_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_3452_2,plain,
    ! [U_13128,U_13127,U_13126,U_13125,U_13124] :
      ( ( ( hAPP(c_Set_Oimage(U_13124,U_13125,U_13126),U_13127) = hAPP(c_Set_Oimage(U_13124,U_13125,U_13126),U_13128)
          | U_13127 != U_13128 )
        & ( U_13127 = U_13128
          | hAPP(c_Set_Oimage(U_13124,U_13125,U_13126),U_13127) != hAPP(c_Set_Oimage(U_13124,U_13125,U_13126),U_13128) ) )
      | ~ c_Fun_Oinj__on(U_13124,U_13125,U_13126,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13124,tc_HOL_Obool)),U_13127),U_13128)) ),
    inference(variable_rename,[status(thm)],[f_3452_1]) ).

fof(f_3452_3,plain,
    ( ! [U_13124,U_13125,U_13126,U_13127,U_13128] :
        ( hAPP(c_Set_Oimage(U_13124,U_13125,U_13126),U_13127) = hAPP(c_Set_Oimage(U_13124,U_13125,U_13126),U_13128)
        | U_13127 != U_13128
        | ~ sP934(U_13124,U_13125,U_13126,U_13127,U_13128) )
    & ! [U_13124,U_13125,U_13126,U_13127,U_13128] :
        ( U_13127 = U_13128
        | hAPP(c_Set_Oimage(U_13124,U_13125,U_13126),U_13127) != hAPP(c_Set_Oimage(U_13124,U_13125,U_13126),U_13128)
        | ~ sP934(U_13124,U_13125,U_13126,U_13127,U_13128) )
    & ! [U_13124,U_13125,U_13126,U_13127,U_13128] :
        ( sP934(U_13124,U_13125,U_13126,U_13127,U_13128)
        | ~ c_Fun_Oinj__on(U_13124,U_13125,U_13126,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13124,tc_HOL_Obool)),U_13127),U_13128)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP934])],[f_3452_2]) ).

cnf(f_3452_4,plain,
    ( sP934(U_13124,U_13125,U_13126,U_13127,U_13128)
    | ~ c_Fun_Oinj__on(U_13124,U_13125,U_13126,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13124,tc_HOL_Obool)),U_13127),U_13128)) ),
    inference(clausify,[status(thm)],[f_3452_3]) ).

cnf(f_3452_5,plain,
    ( U_13127 = U_13128
    | hAPP(c_Set_Oimage(U_13124,U_13125,U_13126),U_13127) != hAPP(c_Set_Oimage(U_13124,U_13125,U_13126),U_13128)
    | ~ sP934(U_13124,U_13125,U_13126,U_13127,U_13128) ),
    inference(clausify,[status(thm)],[f_3452_3]) ).

cnf(f_3452_6,plain,
    ( hAPP(c_Set_Oimage(U_13124,U_13125,U_13126),U_13127) = hAPP(c_Set_Oimage(U_13124,U_13125,U_13126),U_13128)
    | U_13127 != U_13128
    | ~ sP934(U_13124,U_13125,U_13126,U_13127,U_13128) ),
    inference(clausify,[status(thm)],[f_3452_3]) ).

fof(f_3453_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_3453_2,plain,
    ! [U_13132,U_13131,U_13130,U_13129] :
      ( hAPP(c_Finite__Set_Ocard(U_13130),hAPP(c_Set_Oimage(U_13129,U_13130,U_13131),U_13132)) = hAPP(c_Finite__Set_Ocard(U_13129),U_13132)
      | ~ c_Fun_Oinj__on(U_13129,U_13130,U_13131,U_13132) ),
    inference(variable_rename,[status(thm)],[f_3453_1]) ).

fof(f_3453_3,plain,
    ! [U_13132,U_13131,U_13130,U_13129] :
      ( hAPP(c_Finite__Set_Ocard(U_13130),hAPP(c_Set_Oimage(U_13129,U_13130,U_13131),U_13132)) = hAPP(c_Finite__Set_Ocard(U_13129),U_13132)
      | ~ c_Fun_Oinj__on(U_13129,U_13130,U_13131,U_13132) ),
    inference(definitional_conversion,[status(esa)],[f_3453_2]) ).

cnf(f_3453_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_13130),hAPP(c_Set_Oimage(U_13129,U_13130,U_13131),U_13132)) = hAPP(c_Finite__Set_Ocard(U_13129),U_13132)
    | ~ c_Fun_Oinj__on(U_13129,U_13130,U_13131,U_13132) ),
    inference(clausify,[status(thm)],[f_3453_3]) ).

fof(f_3454_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_3454_2,plain,
    ! [U_13136,U_13135,U_13134,U_13133] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13134),U_13136))
      | ~ c_Fun_Oinj__on(U_13134,U_13133,U_13135,U_13136)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13133),hAPP(c_Set_Oimage(U_13134,U_13133,U_13135),U_13136))) ),
    inference(variable_rename,[status(thm)],[f_3454_1]) ).

fof(f_3454_3,plain,
    ! [U_13134,U_13133,U_13135,U_13136] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13134),U_13136))
      | ~ c_Fun_Oinj__on(U_13134,U_13133,U_13135,U_13136)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13133),hAPP(c_Set_Oimage(U_13134,U_13133,U_13135),U_13136))) ),
    inference(definitional_conversion,[status(esa)],[f_3454_2]) ).

cnf(f_3454_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13134),U_13136))
    | ~ c_Fun_Oinj__on(U_13134,U_13133,U_13135,U_13136)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13133),hAPP(c_Set_Oimage(U_13134,U_13133,U_13135),U_13136))) ),
    inference(clausify,[status(thm)],[f_3454_3]) ).

fof(f_3455_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_3455_2,plain,
    ! [U_13144,U_13143,U_13142,U_13141] :
      ( ( ( ? [U_13140] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13143,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13142,U_13143,U_13140),U_13141)),U_13144))
              & c_Fun_Oinj__on(U_13142,U_13143,U_13140,U_13141) )
          | ! [U_13139] : hAPP(c_Set_Oimage(U_13143,U_13142,U_13139),U_13144) != U_13141 )
        & ( ? [U_13138] : hAPP(c_Set_Oimage(U_13143,U_13142,U_13138),U_13144) = U_13141
          | ! [U_13137] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13143,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13142,U_13143,U_13137),U_13141)),U_13144))
              | ~ c_Fun_Oinj__on(U_13142,U_13143,U_13137,U_13141) ) ) )
      | U_13141 = c_Orderings_Obot__class_Obot(tc_fun(U_13142,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3455_1]) ).

fof(f_3455_3,plain,
    ! [U_13144,U_13143,U_13142,U_13141] :
      ( ( ( ? [U_13140] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13143,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13142,U_13143,U_13140),U_13141)),U_13144))
              & c_Fun_Oinj__on(U_13142,U_13143,U_13140,U_13141) )
          | ! [U_13139] : hAPP(c_Set_Oimage(U_13143,U_13142,U_13139),U_13144) != U_13141 )
        & ( hAPP(c_Set_Oimage(U_13143,U_13142,sK285(U_13144,U_13143,U_13142,U_13141)),U_13144) = U_13141
          | ! [U_13137] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13143,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13142,U_13143,U_13137),U_13141)),U_13144))
              | ~ c_Fun_Oinj__on(U_13142,U_13143,U_13137,U_13141) ) ) )
      | U_13141 = c_Orderings_Obot__class_Obot(tc_fun(U_13142,tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK285]),skolemize(U_13138,sK285(U_13144,U_13143,U_13142,U_13141))],[f_3455_2]) ).

fof(f_3455_4,plain,
    ! [U_13144,U_13143,U_13142,U_13141] :
      ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13143,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13142,U_13143,sK286(U_13144,U_13143,U_13142,U_13141)),U_13141)),U_13144))
            & c_Fun_Oinj__on(U_13142,U_13143,sK286(U_13144,U_13143,U_13142,U_13141),U_13141) )
          | ! [U_13139] : hAPP(c_Set_Oimage(U_13143,U_13142,U_13139),U_13144) != U_13141 )
        & ( hAPP(c_Set_Oimage(U_13143,U_13142,sK285(U_13144,U_13143,U_13142,U_13141)),U_13144) = U_13141
          | ! [U_13137] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13143,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13142,U_13143,U_13137),U_13141)),U_13144))
              | ~ c_Fun_Oinj__on(U_13142,U_13143,U_13137,U_13141) ) ) )
      | U_13141 = c_Orderings_Obot__class_Obot(tc_fun(U_13142,tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK286]),skolemize(U_13140,sK286(U_13144,U_13143,U_13142,U_13141))],[f_3455_3]) ).

fof(f_3455_5,plain,
    ( ! [U_13141,U_13142,U_13143,U_13144] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13143,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13142,U_13143,sK286(U_13144,U_13143,U_13142,U_13141)),U_13141)),U_13144))
        | ~ sP935(U_13141,U_13142,U_13143,U_13144) )
    & ! [U_13141,U_13142,U_13143,U_13144] :
        ( c_Fun_Oinj__on(U_13142,U_13143,sK286(U_13144,U_13143,U_13142,U_13141),U_13141)
        | ~ sP935(U_13141,U_13142,U_13143,U_13144) )
    & ! [U_13137,U_13139,U_13141,U_13142,U_13143,U_13144] :
        ( sP935(U_13141,U_13142,U_13143,U_13144)
        | hAPP(c_Set_Oimage(U_13143,U_13142,U_13139),U_13144) != U_13141
        | ~ sP936(U_13137,U_13139,U_13141,U_13142,U_13143,U_13144) )
    & ! [U_13137,U_13139,U_13141,U_13142,U_13143,U_13144] :
        ( hAPP(c_Set_Oimage(U_13143,U_13142,sK285(U_13144,U_13143,U_13142,U_13141)),U_13144) = U_13141
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13143,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13142,U_13143,U_13137),U_13141)),U_13144))
        | ~ c_Fun_Oinj__on(U_13142,U_13143,U_13137,U_13141)
        | ~ sP936(U_13137,U_13139,U_13141,U_13142,U_13143,U_13144) )
    & ! [U_13137,U_13139,U_13141,U_13142,U_13143,U_13144] :
        ( sP936(U_13137,U_13139,U_13141,U_13142,U_13143,U_13144)
        | U_13141 = c_Orderings_Obot__class_Obot(tc_fun(U_13142,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP935,sP936])],[f_3455_4]) ).

cnf(f_3455_6,plain,
    ( sP936(U_13137,U_13139,U_13141,U_13142,U_13143,U_13144)
    | U_13141 = c_Orderings_Obot__class_Obot(tc_fun(U_13142,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3455_5]) ).

cnf(f_3455_7,plain,
    ( hAPP(c_Set_Oimage(U_13143,U_13142,sK285(U_13144,U_13143,U_13142,U_13141)),U_13144) = U_13141
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13143,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13142,U_13143,U_13137),U_13141)),U_13144))
    | ~ c_Fun_Oinj__on(U_13142,U_13143,U_13137,U_13141)
    | ~ sP936(U_13137,U_13139,U_13141,U_13142,U_13143,U_13144) ),
    inference(clausify,[status(thm)],[f_3455_5]) ).

cnf(f_3455_8,plain,
    ( sP935(U_13141,U_13142,U_13143,U_13144)
    | hAPP(c_Set_Oimage(U_13143,U_13142,U_13139),U_13144) != U_13141
    | ~ sP936(U_13137,U_13139,U_13141,U_13142,U_13143,U_13144) ),
    inference(clausify,[status(thm)],[f_3455_5]) ).

cnf(f_3455_9,plain,
    ( c_Fun_Oinj__on(U_13142,U_13143,sK286(U_13144,U_13143,U_13142,U_13141),U_13141)
    | ~ sP935(U_13141,U_13142,U_13143,U_13144) ),
    inference(clausify,[status(thm)],[f_3455_5]) ).

cnf(f_3455_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13143,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13142,U_13143,sK286(U_13144,U_13143,U_13142,U_13141)),U_13141)),U_13144))
    | ~ sP935(U_13141,U_13142,U_13143,U_13144) ),
    inference(clausify,[status(thm)],[f_3455_5]) ).

fof(f_3456_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_3456_2,plain,
    ! [U_13147,U_13146,U_13145] :
      ( c_Fun_Oinj__on(U_13145,U_13145,U_13147,U_13146)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13145,tc_HOL_Obool)),U_13146),hAPP(c_Set_Oimage(U_13145,U_13145,U_13147),U_13146)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13145),U_13146)) ),
    inference(variable_rename,[status(thm)],[f_3456_1]) ).

fof(f_3456_3,plain,
    ! [U_13147,U_13145,U_13146] :
      ( c_Fun_Oinj__on(U_13145,U_13145,U_13147,U_13146)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13145,tc_HOL_Obool)),U_13146),hAPP(c_Set_Oimage(U_13145,U_13145,U_13147),U_13146)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13145),U_13146)) ),
    inference(definitional_conversion,[status(esa)],[f_3456_2]) ).

cnf(f_3456_4,plain,
    ( c_Fun_Oinj__on(U_13145,U_13145,U_13147,U_13146)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13145,tc_HOL_Obool)),U_13146),hAPP(c_Set_Oimage(U_13145,U_13145,U_13147),U_13146)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13145),U_13146)) ),
    inference(clausify,[status(thm)],[f_3456_3]) ).

fof(f_3457_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_3457_2,plain,
    ! [U_13150,U_13149,U_13148] :
      ( hAPP(c_Set_Oimage(U_13148,U_13148,U_13150),U_13149) = U_13149
      | ~ c_Fun_Oinj__on(U_13148,U_13148,U_13150,U_13149)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13148,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13148,U_13148,U_13150),U_13149)),U_13149))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13148),U_13149)) ),
    inference(variable_rename,[status(thm)],[f_3457_1]) ).

fof(f_3457_3,plain,
    ! [U_13149,U_13148,U_13150] :
      ( hAPP(c_Set_Oimage(U_13148,U_13148,U_13150),U_13149) = U_13149
      | ~ c_Fun_Oinj__on(U_13148,U_13148,U_13150,U_13149)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13148,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13148,U_13148,U_13150),U_13149)),U_13149))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13148),U_13149)) ),
    inference(definitional_conversion,[status(esa)],[f_3457_2]) ).

cnf(f_3457_4,plain,
    ( hAPP(c_Set_Oimage(U_13148,U_13148,U_13150),U_13149) = U_13149
    | ~ c_Fun_Oinj__on(U_13148,U_13148,U_13150,U_13149)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13148,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13148,U_13148,U_13150),U_13149)),U_13149))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13148),U_13149)) ),
    inference(clausify,[status(thm)],[f_3457_3]) ).

fof(f_3458_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_3458_2,plain,
    ! [U_13156,U_13155,U_13154,U_13153,U_13152,U_13151] :
      ( hAPP(c_Set_Oimage(U_13151,U_13152,U_13153),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13151,tc_HOL_Obool)),U_13155),U_13156)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13152,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13151,U_13152,U_13153),U_13155)),hAPP(c_Set_Oimage(U_13151,U_13152,U_13153),U_13156))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13151,tc_HOL_Obool)),U_13156),U_13154))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13151,tc_HOL_Obool)),U_13155),U_13154))
      | ~ c_Fun_Oinj__on(U_13151,U_13152,U_13153,U_13154) ),
    inference(variable_rename,[status(thm)],[f_3458_1]) ).

fof(f_3458_3,plain,
    ! [U_13151,U_13152,U_13153,U_13154,U_13155,U_13156] :
      ( hAPP(c_Set_Oimage(U_13151,U_13152,U_13153),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13151,tc_HOL_Obool)),U_13155),U_13156)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13152,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13151,U_13152,U_13153),U_13155)),hAPP(c_Set_Oimage(U_13151,U_13152,U_13153),U_13156))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13151,tc_HOL_Obool)),U_13156),U_13154))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13151,tc_HOL_Obool)),U_13155),U_13154))
      | ~ c_Fun_Oinj__on(U_13151,U_13152,U_13153,U_13154) ),
    inference(definitional_conversion,[status(esa)],[f_3458_2]) ).

cnf(f_3458_4,plain,
    ( hAPP(c_Set_Oimage(U_13151,U_13152,U_13153),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13151,tc_HOL_Obool)),U_13155),U_13156)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13152,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13151,U_13152,U_13153),U_13155)),hAPP(c_Set_Oimage(U_13151,U_13152,U_13153),U_13156))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13151,tc_HOL_Obool)),U_13156),U_13154))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13151,tc_HOL_Obool)),U_13155),U_13154))
    | ~ c_Fun_Oinj__on(U_13151,U_13152,U_13153,U_13154) ),
    inference(clausify,[status(thm)],[f_3458_3]) ).

fof(f_3459_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_3459_2,plain,
    ! [U_13160,U_13159,U_13158,U_13157] :
      ( c_Fun_Oinj__on(U_13157,U_13159,U_13160,U_13158)
      | hAPP(c_Finite__Set_Ocard(U_13159),hAPP(c_Set_Oimage(U_13157,U_13159,U_13160),U_13158)) != hAPP(c_Finite__Set_Ocard(U_13157),U_13158)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13157),U_13158)) ),
    inference(variable_rename,[status(thm)],[f_3459_1]) ).

fof(f_3459_3,plain,
    ! [U_13158,U_13157,U_13159,U_13160] :
      ( c_Fun_Oinj__on(U_13157,U_13159,U_13160,U_13158)
      | hAPP(c_Finite__Set_Ocard(U_13159),hAPP(c_Set_Oimage(U_13157,U_13159,U_13160),U_13158)) != hAPP(c_Finite__Set_Ocard(U_13157),U_13158)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13157),U_13158)) ),
    inference(definitional_conversion,[status(esa)],[f_3459_2]) ).

cnf(f_3459_4,plain,
    ( c_Fun_Oinj__on(U_13157,U_13159,U_13160,U_13158)
    | hAPP(c_Finite__Set_Ocard(U_13159),hAPP(c_Set_Oimage(U_13157,U_13159,U_13160),U_13158)) != hAPP(c_Finite__Set_Ocard(U_13157),U_13158)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13157),U_13158)) ),
    inference(clausify,[status(thm)],[f_3459_3]) ).

fof(f_3460_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_3460_2,plain,
    ! [U_13164,U_13163,U_13162,U_13161] :
      ( ( ( c_Fun_Oinj__on(U_13161,U_13163,U_13164,U_13162)
          | hAPP(c_Finite__Set_Ocard(U_13163),hAPP(c_Set_Oimage(U_13161,U_13163,U_13164),U_13162)) != hAPP(c_Finite__Set_Ocard(U_13161),U_13162) )
        & ( hAPP(c_Finite__Set_Ocard(U_13163),hAPP(c_Set_Oimage(U_13161,U_13163,U_13164),U_13162)) = hAPP(c_Finite__Set_Ocard(U_13161),U_13162)
          | ~ c_Fun_Oinj__on(U_13161,U_13163,U_13164,U_13162) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13161),U_13162)) ),
    inference(variable_rename,[status(thm)],[f_3460_1]) ).

fof(f_3460_3,plain,
    ( ! [U_13161,U_13162,U_13163,U_13164] :
        ( c_Fun_Oinj__on(U_13161,U_13163,U_13164,U_13162)
        | hAPP(c_Finite__Set_Ocard(U_13163),hAPP(c_Set_Oimage(U_13161,U_13163,U_13164),U_13162)) != hAPP(c_Finite__Set_Ocard(U_13161),U_13162)
        | ~ sP937(U_13161,U_13162,U_13163,U_13164) )
    & ! [U_13161,U_13162,U_13163,U_13164] :
        ( hAPP(c_Finite__Set_Ocard(U_13163),hAPP(c_Set_Oimage(U_13161,U_13163,U_13164),U_13162)) = hAPP(c_Finite__Set_Ocard(U_13161),U_13162)
        | ~ c_Fun_Oinj__on(U_13161,U_13163,U_13164,U_13162)
        | ~ sP937(U_13161,U_13162,U_13163,U_13164) )
    & ! [U_13161,U_13162,U_13163,U_13164] :
        ( sP937(U_13161,U_13162,U_13163,U_13164)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13161),U_13162)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP937])],[f_3460_2]) ).

cnf(f_3460_4,plain,
    ( sP937(U_13161,U_13162,U_13163,U_13164)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13161),U_13162)) ),
    inference(clausify,[status(thm)],[f_3460_3]) ).

cnf(f_3460_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_13163),hAPP(c_Set_Oimage(U_13161,U_13163,U_13164),U_13162)) = hAPP(c_Finite__Set_Ocard(U_13161),U_13162)
    | ~ c_Fun_Oinj__on(U_13161,U_13163,U_13164,U_13162)
    | ~ sP937(U_13161,U_13162,U_13163,U_13164) ),
    inference(clausify,[status(thm)],[f_3460_3]) ).

cnf(f_3460_6,plain,
    ( c_Fun_Oinj__on(U_13161,U_13163,U_13164,U_13162)
    | hAPP(c_Finite__Set_Ocard(U_13163),hAPP(c_Set_Oimage(U_13161,U_13163,U_13164),U_13162)) != hAPP(c_Finite__Set_Ocard(U_13161),U_13162)
    | ~ sP937(U_13161,U_13162,U_13163,U_13164) ),
    inference(clausify,[status(thm)],[f_3460_3]) ).

fof(f_3461_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_3461_2,plain,
    ! [U_13170,U_13169,U_13168,U_13167,U_13166,U_13165] :
      ( hAPP(c_Set_Oimage(U_13165,U_13166,U_13167),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13165,tc_HOL_Obool)),U_13169),U_13170)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13166,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13165,U_13166,U_13167),U_13169)),hAPP(c_Set_Oimage(U_13165,U_13166,U_13167),U_13170))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13165,tc_HOL_Obool)),U_13170),U_13168))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13165,tc_HOL_Obool)),U_13169),U_13168))
      | ~ c_Fun_Oinj__on(U_13165,U_13166,U_13167,U_13168) ),
    inference(variable_rename,[status(thm)],[f_3461_1]) ).

fof(f_3461_3,plain,
    ! [U_13166,U_13165,U_13167,U_13168,U_13169,U_13170] :
      ( hAPP(c_Set_Oimage(U_13165,U_13166,U_13167),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13165,tc_HOL_Obool)),U_13169),U_13170)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13166,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13165,U_13166,U_13167),U_13169)),hAPP(c_Set_Oimage(U_13165,U_13166,U_13167),U_13170))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13165,tc_HOL_Obool)),U_13170),U_13168))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13165,tc_HOL_Obool)),U_13169),U_13168))
      | ~ c_Fun_Oinj__on(U_13165,U_13166,U_13167,U_13168) ),
    inference(definitional_conversion,[status(esa)],[f_3461_2]) ).

cnf(f_3461_4,plain,
    ( hAPP(c_Set_Oimage(U_13165,U_13166,U_13167),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13165,tc_HOL_Obool)),U_13169),U_13170)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13166,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13165,U_13166,U_13167),U_13169)),hAPP(c_Set_Oimage(U_13165,U_13166,U_13167),U_13170))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13165,tc_HOL_Obool)),U_13170),U_13168))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13165,tc_HOL_Obool)),U_13169),U_13168))
    | ~ c_Fun_Oinj__on(U_13165,U_13166,U_13167,U_13168) ),
    inference(clausify,[status(thm)],[f_3461_3]) ).

fof(f_3462_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_3462_2,plain,
    ! [U_13174,U_13173,U_13172,U_13171] :
      ( ~ c_Fun_Oinj__on(U_13172,U_13171,U_13173,U_13174)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_13171),hAPP(c_Set_Oimage(U_13172,U_13171,U_13173),U_13174))),hAPP(c_Finite__Set_Ocard(U_13172),U_13174))) ),
    inference(variable_rename,[status(thm)],[f_3462_1]) ).

fof(f_3462_3,plain,
    ! [U_13171,U_13173,U_13172,U_13174] :
      ( ~ c_Fun_Oinj__on(U_13172,U_13171,U_13173,U_13174)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_13171),hAPP(c_Set_Oimage(U_13172,U_13171,U_13173),U_13174))),hAPP(c_Finite__Set_Ocard(U_13172),U_13174))) ),
    inference(definitional_conversion,[status(esa)],[f_3462_2]) ).

cnf(f_3462_4,plain,
    ( ~ c_Fun_Oinj__on(U_13172,U_13171,U_13173,U_13174)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_13171),hAPP(c_Set_Oimage(U_13172,U_13171,U_13173),U_13174))),hAPP(c_Finite__Set_Ocard(U_13172),U_13174))) ),
    inference(clausify,[status(thm)],[f_3462_3]) ).

fof(f_3463_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_3463_2,plain,
    ! [U_13180,U_13179,U_13178,U_13177,U_13176,U_13175] :
      ( c_Fun_Oinj__on(U_13175,U_13176,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_13175,U_13176),U_13177),U_13180),U_13179),U_13178)
      | hBOOL(hAPP(hAPP(c_member(U_13176),U_13179),hAPP(c_Set_Oimage(U_13175,U_13176,U_13177),U_13178)))
      | ~ c_Fun_Oinj__on(U_13175,U_13176,U_13177,U_13178) ),
    inference(variable_rename,[status(thm)],[f_3463_1]) ).

fof(f_3463_3,plain,
    ! [U_13175,U_13176,U_13177,U_13178,U_13179,U_13180] :
      ( c_Fun_Oinj__on(U_13175,U_13176,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_13175,U_13176),U_13177),U_13180),U_13179),U_13178)
      | hBOOL(hAPP(hAPP(c_member(U_13176),U_13179),hAPP(c_Set_Oimage(U_13175,U_13176,U_13177),U_13178)))
      | ~ c_Fun_Oinj__on(U_13175,U_13176,U_13177,U_13178) ),
    inference(definitional_conversion,[status(esa)],[f_3463_2]) ).

cnf(f_3463_4,plain,
    ( c_Fun_Oinj__on(U_13175,U_13176,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_13175,U_13176),U_13177),U_13180),U_13179),U_13178)
    | hBOOL(hAPP(hAPP(c_member(U_13176),U_13179),hAPP(c_Set_Oimage(U_13175,U_13176,U_13177),U_13178)))
    | ~ c_Fun_Oinj__on(U_13175,U_13176,U_13177,U_13178) ),
    inference(clausify,[status(thm)],[f_3463_3]) ).

fof(f_3464_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_3464_2,plain,
    ! [U_13186,U_13185,U_13184,U_13183,U_13182,U_13181] :
      ( hAPP(c_Finite__Set_Ocard(U_13181),U_13184) = hAPP(c_Finite__Set_Ocard(U_13182),U_13185)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13182),U_13185))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13181),U_13184))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13181,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13182,U_13181,U_13186),U_13185)),U_13184))
      | ~ c_Fun_Oinj__on(U_13182,U_13181,U_13186,U_13185)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13182,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13181,U_13182,U_13183),U_13184)),U_13185))
      | ~ c_Fun_Oinj__on(U_13181,U_13182,U_13183,U_13184) ),
    inference(variable_rename,[status(thm)],[f_3464_1]) ).

fof(f_3464_3,plain,
    ! [U_13181,U_13182,U_13183,U_13184,U_13185,U_13186] :
      ( hAPP(c_Finite__Set_Ocard(U_13181),U_13184) = hAPP(c_Finite__Set_Ocard(U_13182),U_13185)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13182),U_13185))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13181),U_13184))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13181,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13182,U_13181,U_13186),U_13185)),U_13184))
      | ~ c_Fun_Oinj__on(U_13182,U_13181,U_13186,U_13185)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13182,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13181,U_13182,U_13183),U_13184)),U_13185))
      | ~ c_Fun_Oinj__on(U_13181,U_13182,U_13183,U_13184) ),
    inference(definitional_conversion,[status(esa)],[f_3464_2]) ).

cnf(f_3464_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_13181),U_13184) = hAPP(c_Finite__Set_Ocard(U_13182),U_13185)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13182),U_13185))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13181),U_13184))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13181,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13182,U_13181,U_13186),U_13185)),U_13184))
    | ~ c_Fun_Oinj__on(U_13182,U_13181,U_13186,U_13185)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13182,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13181,U_13182,U_13183),U_13184)),U_13185))
    | ~ c_Fun_Oinj__on(U_13181,U_13182,U_13183,U_13184) ),
    inference(clausify,[status(thm)],[f_3464_3]) ).

fof(f_3465_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_3465_2,plain,
    ! [U_13191,U_13190,U_13189,U_13188,U_13187] :
      ( ( c_Fun_Oinj__on(U_13187,U_13188,U_13189,hAPP(hAPP(c_Set_Oinsert(U_13187),U_13190),U_13191))
        | hBOOL(hAPP(hAPP(c_member(U_13188),hAPP(U_13189,U_13190)),hAPP(c_Set_Oimage(U_13187,U_13188,U_13189),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13187,tc_HOL_Obool)),U_13191),hAPP(hAPP(c_Set_Oinsert(U_13187),U_13190),c_Orderings_Obot__class_Obot(tc_fun(U_13187,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(U_13187,U_13188,U_13189,U_13191) )
      & ( ( ~ hBOOL(hAPP(hAPP(c_member(U_13188),hAPP(U_13189,U_13190)),hAPP(c_Set_Oimage(U_13187,U_13188,U_13189),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13187,tc_HOL_Obool)),U_13191),hAPP(hAPP(c_Set_Oinsert(U_13187),U_13190),c_Orderings_Obot__class_Obot(tc_fun(U_13187,tc_HOL_Obool)))))))
          & c_Fun_Oinj__on(U_13187,U_13188,U_13189,U_13191) )
        | ~ c_Fun_Oinj__on(U_13187,U_13188,U_13189,hAPP(hAPP(c_Set_Oinsert(U_13187),U_13190),U_13191)) ) ),
    inference(variable_rename,[status(thm)],[f_3465_1]) ).

fof(f_3465_3,plain,
    ( ! [U_13201,U_13199,U_13197,U_13195,U_13193] :
        ( c_Fun_Oinj__on(U_13193,U_13195,U_13197,hAPP(hAPP(c_Set_Oinsert(U_13193),U_13199),U_13201))
        | hBOOL(hAPP(hAPP(c_member(U_13195),hAPP(U_13197,U_13199)),hAPP(c_Set_Oimage(U_13193,U_13195,U_13197),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13193,tc_HOL_Obool)),U_13201),hAPP(hAPP(c_Set_Oinsert(U_13193),U_13199),c_Orderings_Obot__class_Obot(tc_fun(U_13193,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(U_13193,U_13195,U_13197,U_13201) )
    & ! [U_13200,U_13198,U_13196,U_13194,U_13192] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_13194),hAPP(U_13196,U_13198)),hAPP(c_Set_Oimage(U_13192,U_13194,U_13196),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13192,tc_HOL_Obool)),U_13200),hAPP(hAPP(c_Set_Oinsert(U_13192),U_13198),c_Orderings_Obot__class_Obot(tc_fun(U_13192,tc_HOL_Obool)))))))
          & c_Fun_Oinj__on(U_13192,U_13194,U_13196,U_13200) )
        | ~ c_Fun_Oinj__on(U_13192,U_13194,U_13196,hAPP(hAPP(c_Set_Oinsert(U_13192),U_13198),U_13200)) ) ),
    inference(miniscope,[status(thm)],[f_3465_2]) ).

fof(f_3465_4,plain,
    ( ! [U_13194,U_13192,U_13196,U_13198,U_13200] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_13194),hAPP(U_13196,U_13198)),hAPP(c_Set_Oimage(U_13192,U_13194,U_13196),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13192,tc_HOL_Obool)),U_13200),hAPP(hAPP(c_Set_Oinsert(U_13192),U_13198),c_Orderings_Obot__class_Obot(tc_fun(U_13192,tc_HOL_Obool)))))))
        | ~ sP938(U_13194,U_13192,U_13196,U_13198,U_13200) )
    & ! [U_13194,U_13192,U_13196,U_13198,U_13200] :
        ( c_Fun_Oinj__on(U_13192,U_13194,U_13196,U_13200)
        | ~ sP938(U_13194,U_13192,U_13196,U_13198,U_13200) )
    & ! [U_13195,U_13193,U_13199,U_13197,U_13201] :
        ( c_Fun_Oinj__on(U_13193,U_13195,U_13197,hAPP(hAPP(c_Set_Oinsert(U_13193),U_13199),U_13201))
        | hBOOL(hAPP(hAPP(c_member(U_13195),hAPP(U_13197,U_13199)),hAPP(c_Set_Oimage(U_13193,U_13195,U_13197),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13193,tc_HOL_Obool)),U_13201),hAPP(hAPP(c_Set_Oinsert(U_13193),U_13199),c_Orderings_Obot__class_Obot(tc_fun(U_13193,tc_HOL_Obool)))))))
        | ~ c_Fun_Oinj__on(U_13193,U_13195,U_13197,U_13201) )
    & ! [U_13194,U_13192,U_13196,U_13198,U_13200] :
        ( sP938(U_13194,U_13192,U_13196,U_13198,U_13200)
        | ~ c_Fun_Oinj__on(U_13192,U_13194,U_13196,hAPP(hAPP(c_Set_Oinsert(U_13192),U_13198),U_13200)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP938])],[f_3465_3]) ).

cnf(f_3465_5,plain,
    ( sP938(U_13194,U_13192,U_13196,U_13198,U_13200)
    | ~ c_Fun_Oinj__on(U_13192,U_13194,U_13196,hAPP(hAPP(c_Set_Oinsert(U_13192),U_13198),U_13200)) ),
    inference(clausify,[status(thm)],[f_3465_4]) ).

cnf(f_3465_6,plain,
    ( c_Fun_Oinj__on(U_13193,U_13195,U_13197,hAPP(hAPP(c_Set_Oinsert(U_13193),U_13199),U_13201))
    | hBOOL(hAPP(hAPP(c_member(U_13195),hAPP(U_13197,U_13199)),hAPP(c_Set_Oimage(U_13193,U_13195,U_13197),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13193,tc_HOL_Obool)),U_13201),hAPP(hAPP(c_Set_Oinsert(U_13193),U_13199),c_Orderings_Obot__class_Obot(tc_fun(U_13193,tc_HOL_Obool)))))))
    | ~ c_Fun_Oinj__on(U_13193,U_13195,U_13197,U_13201) ),
    inference(clausify,[status(thm)],[f_3465_4]) ).

cnf(f_3465_7,plain,
    ( c_Fun_Oinj__on(U_13192,U_13194,U_13196,U_13200)
    | ~ sP938(U_13194,U_13192,U_13196,U_13198,U_13200) ),
    inference(clausify,[status(thm)],[f_3465_4]) ).

cnf(f_3465_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_13194),hAPP(U_13196,U_13198)),hAPP(c_Set_Oimage(U_13192,U_13194,U_13196),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13192,tc_HOL_Obool)),U_13200),hAPP(hAPP(c_Set_Oinsert(U_13192),U_13198),c_Orderings_Obot__class_Obot(tc_fun(U_13192,tc_HOL_Obool)))))))
    | ~ sP938(U_13194,U_13192,U_13196,U_13198,U_13200) ),
    inference(clausify,[status(thm)],[f_3465_4]) ).

fof(f_3466_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_3466_2,plain,
    ! [U_13206,U_13205,U_13204,U_13203,U_13202] :
      ( ( c_Fun_Oinj__on(U_13202,U_13203,U_13204,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13202,tc_HOL_Obool)),U_13205),U_13206))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13203,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13202,U_13203,U_13204),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13202,tc_HOL_Obool)),U_13205),U_13206))),hAPP(c_Set_Oimage(U_13202,U_13203,U_13204),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13202,tc_HOL_Obool)),U_13206),U_13205))) != c_Orderings_Obot__class_Obot(tc_fun(U_13203,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(U_13202,U_13203,U_13204,U_13206)
        | ~ c_Fun_Oinj__on(U_13202,U_13203,U_13204,U_13205) )
      & ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13203,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13202,U_13203,U_13204),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13202,tc_HOL_Obool)),U_13205),U_13206))),hAPP(c_Set_Oimage(U_13202,U_13203,U_13204),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13202,tc_HOL_Obool)),U_13206),U_13205))) = c_Orderings_Obot__class_Obot(tc_fun(U_13203,tc_HOL_Obool))
          & c_Fun_Oinj__on(U_13202,U_13203,U_13204,U_13206)
          & c_Fun_Oinj__on(U_13202,U_13203,U_13204,U_13205) )
        | ~ c_Fun_Oinj__on(U_13202,U_13203,U_13204,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13202,tc_HOL_Obool)),U_13205),U_13206)) ) ),
    inference(variable_rename,[status(thm)],[f_3466_1]) ).

fof(f_3466_3,plain,
    ( ! [U_13216,U_13214,U_13212,U_13210,U_13208] :
        ( c_Fun_Oinj__on(U_13208,U_13210,U_13212,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13208,tc_HOL_Obool)),U_13214),U_13216))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13210,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13208,U_13210,U_13212),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13208,tc_HOL_Obool)),U_13214),U_13216))),hAPP(c_Set_Oimage(U_13208,U_13210,U_13212),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13208,tc_HOL_Obool)),U_13216),U_13214))) != c_Orderings_Obot__class_Obot(tc_fun(U_13210,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(U_13208,U_13210,U_13212,U_13216)
        | ~ c_Fun_Oinj__on(U_13208,U_13210,U_13212,U_13214) )
    & ! [U_13215,U_13213,U_13211,U_13209,U_13207] :
        ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13209,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13207,U_13209,U_13211),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13207,tc_HOL_Obool)),U_13213),U_13215))),hAPP(c_Set_Oimage(U_13207,U_13209,U_13211),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13207,tc_HOL_Obool)),U_13215),U_13213))) = c_Orderings_Obot__class_Obot(tc_fun(U_13209,tc_HOL_Obool))
          & c_Fun_Oinj__on(U_13207,U_13209,U_13211,U_13215)
          & c_Fun_Oinj__on(U_13207,U_13209,U_13211,U_13213) )
        | ~ c_Fun_Oinj__on(U_13207,U_13209,U_13211,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13207,tc_HOL_Obool)),U_13213),U_13215)) ) ),
    inference(miniscope,[status(thm)],[f_3466_2]) ).

fof(f_3466_4,plain,
    ( ! [U_13211,U_13209,U_13207,U_13213,U_13215] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13209,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13207,U_13209,U_13211),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13207,tc_HOL_Obool)),U_13213),U_13215))),hAPP(c_Set_Oimage(U_13207,U_13209,U_13211),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13207,tc_HOL_Obool)),U_13215),U_13213))) = c_Orderings_Obot__class_Obot(tc_fun(U_13209,tc_HOL_Obool))
        | ~ sP939(U_13211,U_13209,U_13207,U_13213,U_13215) )
    & ! [U_13211,U_13209,U_13207,U_13213,U_13215] :
        ( c_Fun_Oinj__on(U_13207,U_13209,U_13211,U_13215)
        | ~ sP939(U_13211,U_13209,U_13207,U_13213,U_13215) )
    & ! [U_13211,U_13209,U_13207,U_13213,U_13215] :
        ( c_Fun_Oinj__on(U_13207,U_13209,U_13211,U_13213)
        | ~ sP939(U_13211,U_13209,U_13207,U_13213,U_13215) )
    & ! [U_13210,U_13208,U_13212,U_13214,U_13216] :
        ( c_Fun_Oinj__on(U_13208,U_13210,U_13212,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13208,tc_HOL_Obool)),U_13214),U_13216))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13210,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13208,U_13210,U_13212),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13208,tc_HOL_Obool)),U_13214),U_13216))),hAPP(c_Set_Oimage(U_13208,U_13210,U_13212),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13208,tc_HOL_Obool)),U_13216),U_13214))) != c_Orderings_Obot__class_Obot(tc_fun(U_13210,tc_HOL_Obool))
        | ~ c_Fun_Oinj__on(U_13208,U_13210,U_13212,U_13216)
        | ~ c_Fun_Oinj__on(U_13208,U_13210,U_13212,U_13214) )
    & ! [U_13211,U_13209,U_13207,U_13213,U_13215] :
        ( sP939(U_13211,U_13209,U_13207,U_13213,U_13215)
        | ~ c_Fun_Oinj__on(U_13207,U_13209,U_13211,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13207,tc_HOL_Obool)),U_13213),U_13215)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP939])],[f_3466_3]) ).

cnf(f_3466_5,plain,
    ( sP939(U_13211,U_13209,U_13207,U_13213,U_13215)
    | ~ c_Fun_Oinj__on(U_13207,U_13209,U_13211,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13207,tc_HOL_Obool)),U_13213),U_13215)) ),
    inference(clausify,[status(thm)],[f_3466_4]) ).

cnf(f_3466_6,plain,
    ( c_Fun_Oinj__on(U_13208,U_13210,U_13212,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13208,tc_HOL_Obool)),U_13214),U_13216))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13210,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13208,U_13210,U_13212),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13208,tc_HOL_Obool)),U_13214),U_13216))),hAPP(c_Set_Oimage(U_13208,U_13210,U_13212),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13208,tc_HOL_Obool)),U_13216),U_13214))) != c_Orderings_Obot__class_Obot(tc_fun(U_13210,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(U_13208,U_13210,U_13212,U_13216)
    | ~ c_Fun_Oinj__on(U_13208,U_13210,U_13212,U_13214) ),
    inference(clausify,[status(thm)],[f_3466_4]) ).

cnf(f_3466_7,plain,
    ( c_Fun_Oinj__on(U_13207,U_13209,U_13211,U_13213)
    | ~ sP939(U_13211,U_13209,U_13207,U_13213,U_13215) ),
    inference(clausify,[status(thm)],[f_3466_4]) ).

cnf(f_3466_8,plain,
    ( c_Fun_Oinj__on(U_13207,U_13209,U_13211,U_13215)
    | ~ sP939(U_13211,U_13209,U_13207,U_13213,U_13215) ),
    inference(clausify,[status(thm)],[f_3466_4]) ).

cnf(f_3466_9,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13209,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13207,U_13209,U_13211),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13207,tc_HOL_Obool)),U_13213),U_13215))),hAPP(c_Set_Oimage(U_13207,U_13209,U_13211),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13207,tc_HOL_Obool)),U_13215),U_13213))) = c_Orderings_Obot__class_Obot(tc_fun(U_13209,tc_HOL_Obool))
    | ~ sP939(U_13211,U_13209,U_13207,U_13213,U_13215) ),
    inference(clausify,[status(thm)],[f_3466_4]) ).

fof(f_3467_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_3467_2,plain,
    ! [U_13222,U_13221,U_13220,U_13219] :
      ( ( ( ? [U_13218] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13221,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13219,U_13221,U_13218),U_13220)),U_13222))
              & c_Fun_Oinj__on(U_13219,U_13221,U_13218,U_13220) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_13219),U_13220)),hAPP(c_Finite__Set_Ocard(U_13221),U_13222))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_13219),U_13220)),hAPP(c_Finite__Set_Ocard(U_13221),U_13222)))
          | ! [U_13217] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13221,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13219,U_13221,U_13217),U_13220)),U_13222))
              | ~ c_Fun_Oinj__on(U_13219,U_13221,U_13217,U_13220) ) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13221),U_13222))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13219),U_13220)) ),
    inference(variable_rename,[status(thm)],[f_3467_1]) ).

fof(f_3467_3,plain,
    ! [U_13222,U_13221,U_13220,U_13219] :
      ( ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13221,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13219,U_13221,sK287(U_13222,U_13221,U_13220,U_13219)),U_13220)),U_13222))
            & c_Fun_Oinj__on(U_13219,U_13221,sK287(U_13222,U_13221,U_13220,U_13219),U_13220) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_13219),U_13220)),hAPP(c_Finite__Set_Ocard(U_13221),U_13222))) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_13219),U_13220)),hAPP(c_Finite__Set_Ocard(U_13221),U_13222)))
          | ! [U_13217] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13221,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13219,U_13221,U_13217),U_13220)),U_13222))
              | ~ c_Fun_Oinj__on(U_13219,U_13221,U_13217,U_13220) ) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13221),U_13222))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13219),U_13220)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK287]),skolemize(U_13218,sK287(U_13222,U_13221,U_13220,U_13219))],[f_3467_2]) ).

fof(f_3467_4,plain,
    ( ! [U_13219,U_13220,U_13221,U_13222] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13221,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13219,U_13221,sK287(U_13222,U_13221,U_13220,U_13219)),U_13220)),U_13222))
        | ~ sP940(U_13219,U_13220,U_13221,U_13222) )
    & ! [U_13219,U_13220,U_13221,U_13222] :
        ( c_Fun_Oinj__on(U_13219,U_13221,sK287(U_13222,U_13221,U_13220,U_13219),U_13220)
        | ~ sP940(U_13219,U_13220,U_13221,U_13222) )
    & ! [U_13219,U_13217,U_13220,U_13221,U_13222] :
        ( sP940(U_13219,U_13220,U_13221,U_13222)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_13219),U_13220)),hAPP(c_Finite__Set_Ocard(U_13221),U_13222)))
        | ~ sP941(U_13219,U_13217,U_13220,U_13221,U_13222) )
    & ! [U_13219,U_13217,U_13220,U_13221,U_13222] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_13219),U_13220)),hAPP(c_Finite__Set_Ocard(U_13221),U_13222)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13221,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13219,U_13221,U_13217),U_13220)),U_13222))
        | ~ c_Fun_Oinj__on(U_13219,U_13221,U_13217,U_13220)
        | ~ sP941(U_13219,U_13217,U_13220,U_13221,U_13222) )
    & ! [U_13219,U_13217,U_13220,U_13221,U_13222] :
        ( sP941(U_13219,U_13217,U_13220,U_13221,U_13222)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13221),U_13222))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13219),U_13220)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP940,sP941])],[f_3467_3]) ).

cnf(f_3467_5,plain,
    ( sP941(U_13219,U_13217,U_13220,U_13221,U_13222)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13221),U_13222))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13219),U_13220)) ),
    inference(clausify,[status(thm)],[f_3467_4]) ).

cnf(f_3467_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_13219),U_13220)),hAPP(c_Finite__Set_Ocard(U_13221),U_13222)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13221,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13219,U_13221,U_13217),U_13220)),U_13222))
    | ~ c_Fun_Oinj__on(U_13219,U_13221,U_13217,U_13220)
    | ~ sP941(U_13219,U_13217,U_13220,U_13221,U_13222) ),
    inference(clausify,[status(thm)],[f_3467_4]) ).

cnf(f_3467_7,plain,
    ( sP940(U_13219,U_13220,U_13221,U_13222)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_13219),U_13220)),hAPP(c_Finite__Set_Ocard(U_13221),U_13222)))
    | ~ sP941(U_13219,U_13217,U_13220,U_13221,U_13222) ),
    inference(clausify,[status(thm)],[f_3467_4]) ).

cnf(f_3467_8,plain,
    ( c_Fun_Oinj__on(U_13219,U_13221,sK287(U_13222,U_13221,U_13220,U_13219),U_13220)
    | ~ sP940(U_13219,U_13220,U_13221,U_13222) ),
    inference(clausify,[status(thm)],[f_3467_4]) ).

cnf(f_3467_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13221,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13219,U_13221,sK287(U_13222,U_13221,U_13220,U_13219)),U_13220)),U_13222))
    | ~ sP940(U_13219,U_13220,U_13221,U_13222) ),
    inference(clausify,[status(thm)],[f_3467_4]) ).

fof(f_3468_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_3468_2,plain,
    ! [U_13227,U_13226,U_13225,U_13224,U_13223] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_13223),U_13226)),hAPP(c_Finite__Set_Ocard(U_13224),U_13227)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13224),U_13227))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13224,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13223,U_13224,U_13225),U_13226)),U_13227))
      | ~ c_Fun_Oinj__on(U_13223,U_13224,U_13225,U_13226) ),
    inference(variable_rename,[status(thm)],[f_3468_1]) ).

fof(f_3468_3,plain,
    ! [U_13224,U_13226,U_13227,U_13223,U_13225] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_13223),U_13226)),hAPP(c_Finite__Set_Ocard(U_13224),U_13227)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13224),U_13227))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13224,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13223,U_13224,U_13225),U_13226)),U_13227))
      | ~ c_Fun_Oinj__on(U_13223,U_13224,U_13225,U_13226) ),
    inference(definitional_conversion,[status(esa)],[f_3468_2]) ).

cnf(f_3468_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_13223),U_13226)),hAPP(c_Finite__Set_Ocard(U_13224),U_13227)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13224),U_13227))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13224,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13223,U_13224,U_13225),U_13226)),U_13227))
    | ~ c_Fun_Oinj__on(U_13223,U_13224,U_13225,U_13226) ),
    inference(clausify,[status(thm)],[f_3468_3]) ).

fof(f_3469_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_3469_2,plain,
    ! [U_13231,U_13230,U_13229,U_13228] :
      ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13228),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13228,tc_HOL_Obool)),U_13230),hAPP(hAPP(c_Set_Oinsert(U_13228),U_13231),c_Orderings_Obot__class_Obot(tc_fun(U_13228,tc_HOL_Obool))))),U_13229) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_13228,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13228),U_13230),U_13229)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13228),hAPP(hAPP(c_Set_Oinsert(U_13228),U_13231),c_Orderings_Obot__class_Obot(tc_fun(U_13228,tc_HOL_Obool)))),U_13229))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13228),U_13231),U_13230))
      | ~ c_Fun_Oinj__on(U_13228,tc_fun(tc_fun(U_13228,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13228,tc_fun(tc_prod(U_13228,U_13228),tc_HOL_Obool),tc_fun(tc_fun(U_13228,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13228,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_13228,U_13228),tc_HOL_Obool),tc_fun(tc_fun(U_13228,tc_HOL_Obool),tc_HOL_Obool)),U_13228),c_Equiv__Relations_Oquotient(U_13228)),hAPP(hAPP(c_COMBC(U_13228,tc_fun(U_13228,tc_HOL_Obool),tc_fun(U_13228,tc_HOL_Obool)),c_Set_Oinsert(U_13228)),c_Orderings_Obot__class_Obot(tc_fun(U_13228,tc_HOL_Obool))))),U_13229),U_13230) ),
    inference(variable_rename,[status(thm)],[f_3469_1]) ).

fof(f_3469_3,plain,
    ! [U_13228,U_13229,U_13230,U_13231] :
      ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13228),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13228,tc_HOL_Obool)),U_13230),hAPP(hAPP(c_Set_Oinsert(U_13228),U_13231),c_Orderings_Obot__class_Obot(tc_fun(U_13228,tc_HOL_Obool))))),U_13229) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_13228,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13228),U_13230),U_13229)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13228),hAPP(hAPP(c_Set_Oinsert(U_13228),U_13231),c_Orderings_Obot__class_Obot(tc_fun(U_13228,tc_HOL_Obool)))),U_13229))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13228),U_13231),U_13230))
      | ~ c_Fun_Oinj__on(U_13228,tc_fun(tc_fun(U_13228,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13228,tc_fun(tc_prod(U_13228,U_13228),tc_HOL_Obool),tc_fun(tc_fun(U_13228,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13228,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_13228,U_13228),tc_HOL_Obool),tc_fun(tc_fun(U_13228,tc_HOL_Obool),tc_HOL_Obool)),U_13228),c_Equiv__Relations_Oquotient(U_13228)),hAPP(hAPP(c_COMBC(U_13228,tc_fun(U_13228,tc_HOL_Obool),tc_fun(U_13228,tc_HOL_Obool)),c_Set_Oinsert(U_13228)),c_Orderings_Obot__class_Obot(tc_fun(U_13228,tc_HOL_Obool))))),U_13229),U_13230) ),
    inference(definitional_conversion,[status(esa)],[f_3469_2]) ).

cnf(f_3469_4,plain,
    ( hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13228),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13228,tc_HOL_Obool)),U_13230),hAPP(hAPP(c_Set_Oinsert(U_13228),U_13231),c_Orderings_Obot__class_Obot(tc_fun(U_13228,tc_HOL_Obool))))),U_13229) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_fun(U_13228,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13228),U_13230),U_13229)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13228),hAPP(hAPP(c_Set_Oinsert(U_13228),U_13231),c_Orderings_Obot__class_Obot(tc_fun(U_13228,tc_HOL_Obool)))),U_13229))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13228),U_13231),U_13230))
    | ~ c_Fun_Oinj__on(U_13228,tc_fun(tc_fun(U_13228,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_13228,tc_fun(tc_prod(U_13228,U_13228),tc_HOL_Obool),tc_fun(tc_fun(U_13228,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13228,tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_13228,U_13228),tc_HOL_Obool),tc_fun(tc_fun(U_13228,tc_HOL_Obool),tc_HOL_Obool)),U_13228),c_Equiv__Relations_Oquotient(U_13228)),hAPP(hAPP(c_COMBC(U_13228,tc_fun(U_13228,tc_HOL_Obool),tc_fun(U_13228,tc_HOL_Obool)),c_Set_Oinsert(U_13228)),c_Orderings_Obot__class_Obot(tc_fun(U_13228,tc_HOL_Obool))))),U_13229),U_13230) ),
    inference(clausify,[status(thm)],[f_3469_3]) ).

fof(f_3470_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_3470_2,plain,
    ! [U_13237,U_13236,U_13235,U_13234,U_13233,U_13232] :
      ( hBOOL(hAPP(hAPP(c_member(U_13232),hAPP(c_Fun_Othe__inv__into(U_13232,U_13233,U_13235,U_13234),U_13236)),U_13237))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13232,tc_HOL_Obool)),U_13235),U_13237))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13233),U_13236),hAPP(c_Set_Oimage(U_13232,U_13233,U_13234),U_13235)))
      | ~ c_Fun_Oinj__on(U_13232,U_13233,U_13234,U_13235) ),
    inference(variable_rename,[status(thm)],[f_3470_1]) ).

fof(f_3470_3,plain,
    ! [U_13234,U_13232,U_13233,U_13235,U_13236,U_13237] :
      ( hBOOL(hAPP(hAPP(c_member(U_13232),hAPP(c_Fun_Othe__inv__into(U_13232,U_13233,U_13235,U_13234),U_13236)),U_13237))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13232,tc_HOL_Obool)),U_13235),U_13237))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13233),U_13236),hAPP(c_Set_Oimage(U_13232,U_13233,U_13234),U_13235)))
      | ~ c_Fun_Oinj__on(U_13232,U_13233,U_13234,U_13235) ),
    inference(definitional_conversion,[status(esa)],[f_3470_2]) ).

cnf(f_3470_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13232),hAPP(c_Fun_Othe__inv__into(U_13232,U_13233,U_13235,U_13234),U_13236)),U_13237))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13232,tc_HOL_Obool)),U_13235),U_13237))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13233),U_13236),hAPP(c_Set_Oimage(U_13232,U_13233,U_13234),U_13235)))
    | ~ c_Fun_Oinj__on(U_13232,U_13233,U_13234,U_13235) ),
    inference(clausify,[status(thm)],[f_3470_3]) ).

fof(f_3471_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_3471_2,plain,
    ! [U_13240,U_13239,U_13238] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13238),U_13239),U_13240) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13238,tc_fun(tc_fun(U_13238,tc_HOL_Obool),tc_HOL_Obool)),U_13239),hAPP(hAPP(c_COMBC(U_13238,tc_fun(tc_fun(U_13238,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13238,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13238,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_13238,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13238,tc_HOL_Obool),tc_HOL_Obool)),U_13238),c_Set_Oinsert(tc_fun(U_13238,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13238,tc_HOL_Obool),tc_fun(U_13238,tc_HOL_Obool),U_13238),c_Relation_OImage(U_13238,U_13238,U_13240)),hAPP(hAPP(c_COMBC(U_13238,tc_fun(U_13238,tc_HOL_Obool),tc_fun(U_13238,tc_HOL_Obool)),c_Set_Oinsert(U_13238)),c_Orderings_Obot__class_Obot(tc_fun(U_13238,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13238,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3471_1]) ).

fof(f_3471_3,plain,
    ! [U_13238,U_13239,U_13240] : hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13238),U_13239),U_13240) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13238,tc_fun(tc_fun(U_13238,tc_HOL_Obool),tc_HOL_Obool)),U_13239),hAPP(hAPP(c_COMBC(U_13238,tc_fun(tc_fun(U_13238,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13238,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13238,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_13238,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13238,tc_HOL_Obool),tc_HOL_Obool)),U_13238),c_Set_Oinsert(tc_fun(U_13238,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13238,tc_HOL_Obool),tc_fun(U_13238,tc_HOL_Obool),U_13238),c_Relation_OImage(U_13238,U_13238,U_13240)),hAPP(hAPP(c_COMBC(U_13238,tc_fun(U_13238,tc_HOL_Obool),tc_fun(U_13238,tc_HOL_Obool)),c_Set_Oinsert(U_13238)),c_Orderings_Obot__class_Obot(tc_fun(U_13238,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13238,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3471_2]) ).

cnf(f_3471_4,plain,
    hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13238),U_13239),U_13240) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13238,tc_fun(tc_fun(U_13238,tc_HOL_Obool),tc_HOL_Obool)),U_13239),hAPP(hAPP(c_COMBC(U_13238,tc_fun(tc_fun(U_13238,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13238,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13238,tc_HOL_Obool),tc_fun(tc_fun(tc_fun(U_13238,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_13238,tc_HOL_Obool),tc_HOL_Obool)),U_13238),c_Set_Oinsert(tc_fun(U_13238,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13238,tc_HOL_Obool),tc_fun(U_13238,tc_HOL_Obool),U_13238),c_Relation_OImage(U_13238,U_13238,U_13240)),hAPP(hAPP(c_COMBC(U_13238,tc_fun(U_13238,tc_HOL_Obool),tc_fun(U_13238,tc_HOL_Obool)),c_Set_Oinsert(U_13238)),c_Orderings_Obot__class_Obot(tc_fun(U_13238,tc_HOL_Obool)))))),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_13238,tc_HOL_Obool),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3471_3]) ).

fof(f_3472_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_3472_2,plain,
    ! [U_13245,U_13244,U_13243,U_13242,U_13241] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13241,U_13241,c_Groups_Otimes__class_Otimes(U_13241),U_13245,hAPP(hAPP(c_Set_Oinsert(U_13241),U_13242),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13241,tc_HOL_Obool)),U_13243),hAPP(hAPP(c_Set_Oinsert(U_13241),U_13245),c_Orderings_Obot__class_Obot(tc_fun(U_13241,tc_HOL_Obool)))))),U_13244))
      | hBOOL(hAPP(hAPP(c_member(U_13241),U_13242),U_13243))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13241),U_13245),U_13243))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13241,U_13241,c_Groups_Otimes__class_Otimes(U_13241),U_13242,U_13243),U_13244))
      | ~ class_Groups_Oab__semigroup__mult(U_13241) ),
    inference(variable_rename,[status(thm)],[f_3472_1]) ).

fof(f_3472_3,plain,
    ! [U_13241,U_13242,U_13243,U_13244,U_13245] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13241,U_13241,c_Groups_Otimes__class_Otimes(U_13241),U_13245,hAPP(hAPP(c_Set_Oinsert(U_13241),U_13242),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13241,tc_HOL_Obool)),U_13243),hAPP(hAPP(c_Set_Oinsert(U_13241),U_13245),c_Orderings_Obot__class_Obot(tc_fun(U_13241,tc_HOL_Obool)))))),U_13244))
      | hBOOL(hAPP(hAPP(c_member(U_13241),U_13242),U_13243))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13241),U_13245),U_13243))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13241,U_13241,c_Groups_Otimes__class_Otimes(U_13241),U_13242,U_13243),U_13244))
      | ~ class_Groups_Oab__semigroup__mult(U_13241) ),
    inference(definitional_conversion,[status(esa)],[f_3472_2]) ).

cnf(f_3472_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13241,U_13241,c_Groups_Otimes__class_Otimes(U_13241),U_13245,hAPP(hAPP(c_Set_Oinsert(U_13241),U_13242),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13241,tc_HOL_Obool)),U_13243),hAPP(hAPP(c_Set_Oinsert(U_13241),U_13245),c_Orderings_Obot__class_Obot(tc_fun(U_13241,tc_HOL_Obool)))))),U_13244))
    | hBOOL(hAPP(hAPP(c_member(U_13241),U_13242),U_13243))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13241),U_13245),U_13243))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13241,U_13241,c_Groups_Otimes__class_Otimes(U_13241),U_13242,U_13243),U_13244))
    | ~ class_Groups_Oab__semigroup__mult(U_13241) ),
    inference(clausify,[status(thm)],[f_3472_3]) ).

fof(f_3473_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_3473_2,plain,
    ! [U_13251,U_13250,U_13249,U_13248,U_13247,U_13246] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13246,tc_fun(U_13251,tc_HOL_Obool)),U_13248),U_13249),U_13250))
      | ~ hBOOL(hAPP(hAPP(U_13249,U_13247),U_13250))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13246),U_13247),U_13248)) ),
    inference(variable_rename,[status(thm)],[f_3473_1]) ).

fof(f_3473_3,plain,
    ! [U_13247,U_13248,U_13249,U_13246,U_13250,U_13251] :
      ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13246,tc_fun(U_13251,tc_HOL_Obool)),U_13248),U_13249),U_13250))
      | ~ hBOOL(hAPP(hAPP(U_13249,U_13247),U_13250))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13246),U_13247),U_13248)) ),
    inference(definitional_conversion,[status(esa)],[f_3473_2]) ).

cnf(f_3473_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13246,tc_fun(U_13251,tc_HOL_Obool)),U_13248),U_13249),U_13250))
    | ~ hBOOL(hAPP(hAPP(U_13249,U_13247),U_13250))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13246),U_13247),U_13248)) ),
    inference(clausify,[status(thm)],[f_3473_3]) ).

fof(f_3474_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_3474_2,plain,
    ! [U_13253,U_13252] : 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_13252),U_13253),
    inference(variable_rename,[status(thm)],[f_3474_1]) ).

fof(f_3474_3,plain,
    ! [U_13253,U_13252] : 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_13252),U_13253),
    inference(definitional_conversion,[status(esa)],[f_3474_2]) ).

cnf(f_3474_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_13252),U_13253),
    inference(clausify,[status(thm)],[f_3474_3]) ).

fof(f_3475_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_3475_2,plain,
    ! [U_13255,U_13254] : c_Fun_Oinj__on(U_13254,tc_Option_Ooption(U_13254),c_Option_Ooption_OSome(U_13254),U_13255),
    inference(variable_rename,[status(thm)],[f_3475_1]) ).

fof(f_3475_3,plain,
    ! [U_13254,U_13255] : c_Fun_Oinj__on(U_13254,tc_Option_Ooption(U_13254),c_Option_Ooption_OSome(U_13254),U_13255),
    inference(definitional_conversion,[status(esa)],[f_3475_2]) ).

cnf(f_3475_4,plain,
    c_Fun_Oinj__on(U_13254,tc_Option_Ooption(U_13254),c_Option_Ooption_OSome(U_13254),U_13255),
    inference(clausify,[status(thm)],[f_3475_3]) ).

fof(f_3476_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_3476_2,plain,
    ! [U_13256] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_13256),
    inference(variable_rename,[status(thm)],[f_3476_1]) ).

fof(f_3476_3,plain,
    ! [U_13256] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_13256),
    inference(definitional_conversion,[status(esa)],[f_3476_2]) ).

cnf(f_3476_4,plain,
    c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,U_13256),
    inference(clausify,[status(thm)],[f_3476_3]) ).

fof(f_3477_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_3477_2,plain,
    ! [U_13262,U_13261,U_13260,U_13259] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13261),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13259,tc_fun(U_13261,tc_HOL_Obool)),U_13260),U_13262)))
          | ? [U_13258] :
              ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13261),hAPP(U_13262,U_13258)))
              & hBOOL(hAPP(hAPP(c_member(U_13259),U_13258),U_13260)) ) )
        & ( ! [U_13257] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13261),hAPP(U_13262,U_13257)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13259),U_13257),U_13260)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13261),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13259,tc_fun(U_13261,tc_HOL_Obool)),U_13260),U_13262))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13259),U_13260)) ),
    inference(variable_rename,[status(thm)],[f_3477_1]) ).

fof(f_3477_3,plain,
    ! [U_13262,U_13261,U_13260,U_13259] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13261),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13259,tc_fun(U_13261,tc_HOL_Obool)),U_13260),U_13262)))
          | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13261),hAPP(U_13262,sK288(U_13262,U_13261,U_13260,U_13259))))
            & hBOOL(hAPP(hAPP(c_member(U_13259),sK288(U_13262,U_13261,U_13260,U_13259)),U_13260)) ) )
        & ( ! [U_13257] :
              ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13261),hAPP(U_13262,U_13257)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13259),U_13257),U_13260)) )
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13261),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13259,tc_fun(U_13261,tc_HOL_Obool)),U_13260),U_13262))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13259),U_13260)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK288]),skolemize(U_13258,sK288(U_13262,U_13261,U_13260,U_13259))],[f_3477_2]) ).

fof(f_3477_4,plain,
    ( ! [U_13259,U_13260,U_13261,U_13262] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13261),hAPP(U_13262,sK288(U_13262,U_13261,U_13260,U_13259))))
        | ~ sP942(U_13259,U_13260,U_13261,U_13262) )
    & ! [U_13259,U_13260,U_13261,U_13262] :
        ( hBOOL(hAPP(hAPP(c_member(U_13259),sK288(U_13262,U_13261,U_13260,U_13259)),U_13260))
        | ~ sP942(U_13259,U_13260,U_13261,U_13262) )
    & ! [U_13257,U_13259,U_13260,U_13261,U_13262] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13261),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13259,tc_fun(U_13261,tc_HOL_Obool)),U_13260),U_13262)))
        | sP942(U_13259,U_13260,U_13261,U_13262)
        | ~ sP943(U_13257,U_13259,U_13260,U_13261,U_13262) )
    & ! [U_13257,U_13259,U_13260,U_13261,U_13262] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13261),hAPP(U_13262,U_13257)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13259),U_13257),U_13260))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13261),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13259,tc_fun(U_13261,tc_HOL_Obool)),U_13260),U_13262)))
        | ~ sP943(U_13257,U_13259,U_13260,U_13261,U_13262) )
    & ! [U_13257,U_13259,U_13260,U_13261,U_13262] :
        ( sP943(U_13257,U_13259,U_13260,U_13261,U_13262)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13259),U_13260)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP942,sP943])],[f_3477_3]) ).

cnf(f_3477_5,plain,
    ( sP943(U_13257,U_13259,U_13260,U_13261,U_13262)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13259),U_13260)) ),
    inference(clausify,[status(thm)],[f_3477_4]) ).

cnf(f_3477_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13261),hAPP(U_13262,U_13257)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13259),U_13257),U_13260))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13261),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13259,tc_fun(U_13261,tc_HOL_Obool)),U_13260),U_13262)))
    | ~ sP943(U_13257,U_13259,U_13260,U_13261,U_13262) ),
    inference(clausify,[status(thm)],[f_3477_4]) ).

cnf(f_3477_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13261),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13259,tc_fun(U_13261,tc_HOL_Obool)),U_13260),U_13262)))
    | sP942(U_13259,U_13260,U_13261,U_13262)
    | ~ sP943(U_13257,U_13259,U_13260,U_13261,U_13262) ),
    inference(clausify,[status(thm)],[f_3477_4]) ).

cnf(f_3477_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13259),sK288(U_13262,U_13261,U_13260,U_13259)),U_13260))
    | ~ sP942(U_13259,U_13260,U_13261,U_13262) ),
    inference(clausify,[status(thm)],[f_3477_4]) ).

cnf(f_3477_9,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13261),hAPP(U_13262,sK288(U_13262,U_13261,U_13260,U_13259))))
    | ~ sP942(U_13259,U_13260,U_13261,U_13262) ),
    inference(clausify,[status(thm)],[f_3477_4]) ).

fof(f_3478_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_3478_2,plain,
    ! [U_13268,U_13267,U_13266,U_13265,U_13264,U_13263] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13263),U_13267))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13263,U_13264,U_13265,U_13266,U_13267),U_13268)) ),
    inference(variable_rename,[status(thm)],[f_3478_1]) ).

fof(f_3478_3,plain,
    ! [U_13266,U_13268,U_13265,U_13264,U_13267,U_13263] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13263),U_13267))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13263,U_13264,U_13265,U_13266,U_13267),U_13268)) ),
    inference(definitional_conversion,[status(esa)],[f_3478_2]) ).

cnf(f_3478_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13263),U_13267))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13263,U_13264,U_13265,U_13266,U_13267),U_13268)) ),
    inference(clausify,[status(thm)],[f_3478_3]) ).

fof(f_3479_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_3479_2,plain,
    ! [U_13272,U_13271,U_13270,U_13269] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13269,U_13270,U_13271,U_13272,c_Orderings_Obot__class_Obot(tc_fun(U_13269,tc_HOL_Obool))),U_13272)),
    inference(variable_rename,[status(thm)],[f_3479_1]) ).

fof(f_3479_3,plain,
    ! [U_13270,U_13269,U_13271,U_13272] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13269,U_13270,U_13271,U_13272,c_Orderings_Obot__class_Obot(tc_fun(U_13269,tc_HOL_Obool))),U_13272)),
    inference(definitional_conversion,[status(esa)],[f_3479_2]) ).

cnf(f_3479_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13269,U_13270,U_13271,U_13272,c_Orderings_Obot__class_Obot(tc_fun(U_13269,tc_HOL_Obool))),U_13272)),
    inference(clausify,[status(thm)],[f_3479_3]) ).

fof(f_3480_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_3480_2,plain,
    ! [U_13276,U_13275,U_13274,U_13273] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13273,U_13274,U_13275,U_13276,c_Orderings_Obot__class_Obot(tc_fun(U_13273,tc_HOL_Obool))),U_13276)),
    inference(variable_rename,[status(thm)],[f_3480_1]) ).

fof(f_3480_3,plain,
    ! [U_13273,U_13274,U_13275,U_13276] : hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13273,U_13274,U_13275,U_13276,c_Orderings_Obot__class_Obot(tc_fun(U_13273,tc_HOL_Obool))),U_13276)),
    inference(definitional_conversion,[status(esa)],[f_3480_2]) ).

cnf(f_3480_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13273,U_13274,U_13275,U_13276,c_Orderings_Obot__class_Obot(tc_fun(U_13273,tc_HOL_Obool))),U_13276)),
    inference(clausify,[status(thm)],[f_3480_3]) ).

fof(f_3481_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_3481_2,plain,
    ! [U_13281,U_13280,U_13279,U_13278,U_13277] :
      ( U_13281 = U_13280
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13277,U_13278,U_13279,U_13280,c_Orderings_Obot__class_Obot(tc_fun(U_13277,tc_HOL_Obool))),U_13281)) ),
    inference(variable_rename,[status(thm)],[f_3481_1]) ).

fof(f_3481_3,plain,
    ! [U_13281,U_13280] :
      ( ! [U_13279,U_13278,U_13277] : ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13277,U_13278,U_13279,U_13280,c_Orderings_Obot__class_Obot(tc_fun(U_13277,tc_HOL_Obool))),U_13281))
      | U_13281 = U_13280 ),
    inference(miniscope,[status(thm)],[f_3481_2]) ).

fof(f_3481_4,plain,
    ! [U_13277,U_13278,U_13279,U_13280,U_13281] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13277,U_13278,U_13279,U_13280,c_Orderings_Obot__class_Obot(tc_fun(U_13277,tc_HOL_Obool))),U_13281))
      | U_13281 = U_13280 ),
    inference(definitional_conversion,[status(esa)],[f_3481_3]) ).

cnf(f_3481_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13277,U_13278,U_13279,U_13280,c_Orderings_Obot__class_Obot(tc_fun(U_13277,tc_HOL_Obool))),U_13281))
    | U_13281 = U_13280 ),
    inference(clausify,[status(thm)],[f_3481_4]) ).

fof(f_3482_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_3482_2,plain,
    ! [U_13288,U_13287,U_13286,U_13285,U_13284] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13284,tc_fun(U_13285,tc_HOL_Obool)),U_13286),U_13287),U_13288))
        | ! [U_13283] :
            ( ~ hBOOL(hAPP(hAPP(U_13287,U_13283),U_13288))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13284),U_13283),U_13286)) ) )
      & ( ? [U_13282] :
            ( hBOOL(hAPP(hAPP(U_13287,U_13282),U_13288))
            & hBOOL(hAPP(hAPP(c_member(U_13284),U_13282),U_13286)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13284,tc_fun(U_13285,tc_HOL_Obool)),U_13286),U_13287),U_13288)) ) ),
    inference(variable_rename,[status(thm)],[f_3482_1]) ).

fof(f_3482_3,plain,
    ( ! [U_13298,U_13296,U_13294,U_13292,U_13290] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13290,tc_fun(U_13292,tc_HOL_Obool)),U_13294),U_13296),U_13298))
        | ! [U_13283] :
            ( ~ hBOOL(hAPP(hAPP(U_13296,U_13283),U_13298))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13290),U_13283),U_13294)) ) )
    & ! [U_13297,U_13295,U_13293,U_13291,U_13289] :
        ( ? [U_13282] :
            ( hBOOL(hAPP(hAPP(U_13295,U_13282),U_13297))
            & hBOOL(hAPP(hAPP(c_member(U_13289),U_13282),U_13293)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13289,tc_fun(U_13291,tc_HOL_Obool)),U_13293),U_13295),U_13297)) ) ),
    inference(miniscope,[status(thm)],[f_3482_2]) ).

fof(f_3482_4,plain,
    ( ! [U_13298,U_13296,U_13294,U_13292,U_13290] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13290,tc_fun(U_13292,tc_HOL_Obool)),U_13294),U_13296),U_13298))
        | ! [U_13283] :
            ( ~ hBOOL(hAPP(hAPP(U_13296,U_13283),U_13298))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13290),U_13283),U_13294)) ) )
    & ! [U_13297,U_13295,U_13293,U_13291,U_13289] :
        ( ( hBOOL(hAPP(hAPP(U_13295,sK289(U_13297,U_13295,U_13293,U_13291,U_13289)),U_13297))
          & hBOOL(hAPP(hAPP(c_member(U_13289),sK289(U_13297,U_13295,U_13293,U_13291,U_13289)),U_13293)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13289,tc_fun(U_13291,tc_HOL_Obool)),U_13293),U_13295),U_13297)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK289]),skolemize(U_13282,sK289(U_13297,U_13295,U_13293,U_13291,U_13289))],[f_3482_3]) ).

fof(f_3482_5,plain,
    ( ! [U_13295,U_13291,U_13289,U_13293,U_13297] :
        ( hBOOL(hAPP(hAPP(U_13295,sK289(U_13297,U_13295,U_13293,U_13291,U_13289)),U_13297))
        | ~ sP944(U_13295,U_13291,U_13289,U_13293,U_13297) )
    & ! [U_13295,U_13291,U_13289,U_13293,U_13297] :
        ( hBOOL(hAPP(hAPP(c_member(U_13289),sK289(U_13297,U_13295,U_13293,U_13291,U_13289)),U_13293))
        | ~ sP944(U_13295,U_13291,U_13289,U_13293,U_13297) )
    & ! [U_13294,U_13283,U_13290,U_13292,U_13296,U_13298] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13290,tc_fun(U_13292,tc_HOL_Obool)),U_13294),U_13296),U_13298))
        | ~ hBOOL(hAPP(hAPP(U_13296,U_13283),U_13298))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13290),U_13283),U_13294)) )
    & ! [U_13295,U_13291,U_13289,U_13293,U_13297] :
        ( sP944(U_13295,U_13291,U_13289,U_13293,U_13297)
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13289,tc_fun(U_13291,tc_HOL_Obool)),U_13293),U_13295),U_13297)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP944])],[f_3482_4]) ).

cnf(f_3482_6,plain,
    ( sP944(U_13295,U_13291,U_13289,U_13293,U_13297)
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13289,tc_fun(U_13291,tc_HOL_Obool)),U_13293),U_13295),U_13297)) ),
    inference(clausify,[status(thm)],[f_3482_5]) ).

cnf(f_3482_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13290,tc_fun(U_13292,tc_HOL_Obool)),U_13294),U_13296),U_13298))
    | ~ hBOOL(hAPP(hAPP(U_13296,U_13283),U_13298))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13290),U_13283),U_13294)) ),
    inference(clausify,[status(thm)],[f_3482_5]) ).

cnf(f_3482_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13289),sK289(U_13297,U_13295,U_13293,U_13291,U_13289)),U_13293))
    | ~ sP944(U_13295,U_13291,U_13289,U_13293,U_13297) ),
    inference(clausify,[status(thm)],[f_3482_5]) ).

cnf(f_3482_9,plain,
    ( hBOOL(hAPP(hAPP(U_13295,sK289(U_13297,U_13295,U_13293,U_13291,U_13289)),U_13297))
    | ~ sP944(U_13295,U_13291,U_13289,U_13293,U_13297) ),
    inference(clausify,[status(thm)],[f_3482_5]) ).

fof(f_3483_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_3483_2,plain,
    ! [U_13304,U_13303,U_13302,U_13301,U_13300,U_13299] : hAPP(c_Relation_OImage(U_13299,U_13300,U_13301),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13302,tc_fun(U_13299,tc_HOL_Obool)),U_13303),U_13304)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13302,tc_fun(U_13300,tc_HOL_Obool)),U_13303),hAPP(hAPP(c_COMBB(tc_fun(U_13299,tc_HOL_Obool),tc_fun(U_13300,tc_HOL_Obool),U_13302),c_Relation_OImage(U_13299,U_13300,U_13301)),U_13304)),
    inference(variable_rename,[status(thm)],[f_3483_1]) ).

fof(f_3483_3,plain,
    ! [U_13301,U_13300,U_13299,U_13302,U_13303,U_13304] : hAPP(c_Relation_OImage(U_13299,U_13300,U_13301),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13302,tc_fun(U_13299,tc_HOL_Obool)),U_13303),U_13304)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13302,tc_fun(U_13300,tc_HOL_Obool)),U_13303),hAPP(hAPP(c_COMBB(tc_fun(U_13299,tc_HOL_Obool),tc_fun(U_13300,tc_HOL_Obool),U_13302),c_Relation_OImage(U_13299,U_13300,U_13301)),U_13304)),
    inference(definitional_conversion,[status(esa)],[f_3483_2]) ).

cnf(f_3483_4,plain,
    hAPP(c_Relation_OImage(U_13299,U_13300,U_13301),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13302,tc_fun(U_13299,tc_HOL_Obool)),U_13303),U_13304)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13302,tc_fun(U_13300,tc_HOL_Obool)),U_13303),hAPP(hAPP(c_COMBB(tc_fun(U_13299,tc_HOL_Obool),tc_fun(U_13300,tc_HOL_Obool),U_13302),c_Relation_OImage(U_13299,U_13300,U_13301)),U_13304)),
    inference(clausify,[status(thm)],[f_3483_3]) ).

fof(f_3484_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_3484_2,plain,
    ! [U_13307,U_13306,U_13305] : c_Fun_Oinj__on(tc_prod(U_13305,U_13306),tc_prod(U_13306,U_13305),hAPP(c_Product__Type_Oprod_Oprod__case(U_13305,U_13306,tc_prod(U_13306,U_13305)),hAPP(c_COMBC(U_13306,U_13305,tc_prod(U_13306,U_13305)),c_Product__Type_OPair(U_13306,U_13305))),U_13307),
    inference(variable_rename,[status(thm)],[f_3484_1]) ).

fof(f_3484_3,plain,
    ! [U_13305,U_13306,U_13307] : c_Fun_Oinj__on(tc_prod(U_13305,U_13306),tc_prod(U_13306,U_13305),hAPP(c_Product__Type_Oprod_Oprod__case(U_13305,U_13306,tc_prod(U_13306,U_13305)),hAPP(c_COMBC(U_13306,U_13305,tc_prod(U_13306,U_13305)),c_Product__Type_OPair(U_13306,U_13305))),U_13307),
    inference(definitional_conversion,[status(esa)],[f_3484_2]) ).

cnf(f_3484_4,plain,
    c_Fun_Oinj__on(tc_prod(U_13305,U_13306),tc_prod(U_13306,U_13305),hAPP(c_Product__Type_Oprod_Oprod__case(U_13305,U_13306,tc_prod(U_13306,U_13305)),hAPP(c_COMBC(U_13306,U_13305,tc_prod(U_13306,U_13305)),c_Product__Type_OPair(U_13306,U_13305))),U_13307),
    inference(clausify,[status(thm)],[f_3484_3]) ).

fof(f_3485_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_3485_2,plain,
    ! [U_13314,U_13313,U_13312,U_13311,U_13310,U_13309,U_13308] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13308,U_13311,U_13312,U_13313,hAPP(hAPP(c_Set_Oinsert(U_13308),U_13309),U_13310)),hAPP(hAPP(U_13312,U_13309),U_13314)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13308,U_13311,U_13312,U_13313,U_13310),U_13314))
      | hBOOL(hAPP(hAPP(c_member(U_13308),U_13309),U_13310)) ),
    inference(variable_rename,[status(thm)],[f_3485_1]) ).

fof(f_3485_3,plain,
    ! [U_13308,U_13309,U_13310,U_13311,U_13312,U_13313,U_13314] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13308,U_13311,U_13312,U_13313,hAPP(hAPP(c_Set_Oinsert(U_13308),U_13309),U_13310)),hAPP(hAPP(U_13312,U_13309),U_13314)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13308,U_13311,U_13312,U_13313,U_13310),U_13314))
      | hBOOL(hAPP(hAPP(c_member(U_13308),U_13309),U_13310)) ),
    inference(definitional_conversion,[status(esa)],[f_3485_2]) ).

cnf(f_3485_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13308,U_13311,U_13312,U_13313,hAPP(hAPP(c_Set_Oinsert(U_13308),U_13309),U_13310)),hAPP(hAPP(U_13312,U_13309),U_13314)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13308,U_13311,U_13312,U_13313,U_13310),U_13314))
    | hBOOL(hAPP(hAPP(c_member(U_13308),U_13309),U_13310)) ),
    inference(clausify,[status(thm)],[f_3485_3]) ).

fof(f_3486_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_3486_2,plain,
    ! [U_13318,U_13317,U_13316,U_13315] : hAPP(c_Relation_OImage(U_13315,U_13316,U_13317),U_13318) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13315,tc_fun(U_13316,tc_HOL_Obool)),U_13318),hAPP(hAPP(c_COMBB(tc_fun(U_13315,tc_HOL_Obool),tc_fun(U_13316,tc_HOL_Obool),U_13315),c_Relation_OImage(U_13315,U_13316,U_13317)),hAPP(hAPP(c_COMBC(U_13315,tc_fun(U_13315,tc_HOL_Obool),tc_fun(U_13315,tc_HOL_Obool)),c_Set_Oinsert(U_13315)),c_Orderings_Obot__class_Obot(tc_fun(U_13315,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3486_1]) ).

fof(f_3486_3,plain,
    ! [U_13315,U_13316,U_13317,U_13318] : hAPP(c_Relation_OImage(U_13315,U_13316,U_13317),U_13318) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13315,tc_fun(U_13316,tc_HOL_Obool)),U_13318),hAPP(hAPP(c_COMBB(tc_fun(U_13315,tc_HOL_Obool),tc_fun(U_13316,tc_HOL_Obool),U_13315),c_Relation_OImage(U_13315,U_13316,U_13317)),hAPP(hAPP(c_COMBC(U_13315,tc_fun(U_13315,tc_HOL_Obool),tc_fun(U_13315,tc_HOL_Obool)),c_Set_Oinsert(U_13315)),c_Orderings_Obot__class_Obot(tc_fun(U_13315,tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_3486_2]) ).

cnf(f_3486_4,plain,
    hAPP(c_Relation_OImage(U_13315,U_13316,U_13317),U_13318) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13315,tc_fun(U_13316,tc_HOL_Obool)),U_13318),hAPP(hAPP(c_COMBB(tc_fun(U_13315,tc_HOL_Obool),tc_fun(U_13316,tc_HOL_Obool),U_13315),c_Relation_OImage(U_13315,U_13316,U_13317)),hAPP(hAPP(c_COMBC(U_13315,tc_fun(U_13315,tc_HOL_Obool),tc_fun(U_13315,tc_HOL_Obool)),c_Set_Oinsert(U_13315)),c_Orderings_Obot__class_Obot(tc_fun(U_13315,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3486_3]) ).

fof(f_3487_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_3487_2,plain,
    ! [U_13324,U_13323,U_13322,U_13321,U_13320,U_13319] :
      ( hAPP(c_Fun_Othe__inv__into(U_13319,U_13320,U_13322,U_13321),U_13324) = U_13323
      | ~ hBOOL(hAPP(hAPP(c_member(U_13319),U_13323),U_13322))
      | hAPP(U_13321,U_13323) != U_13324
      | ~ c_Fun_Oinj__on(U_13319,U_13320,U_13321,U_13322) ),
    inference(variable_rename,[status(thm)],[f_3487_1]) ).

fof(f_3487_3,plain,
    ! [U_13320,U_13319,U_13321,U_13322,U_13323,U_13324] :
      ( hAPP(c_Fun_Othe__inv__into(U_13319,U_13320,U_13322,U_13321),U_13324) = U_13323
      | ~ hBOOL(hAPP(hAPP(c_member(U_13319),U_13323),U_13322))
      | hAPP(U_13321,U_13323) != U_13324
      | ~ c_Fun_Oinj__on(U_13319,U_13320,U_13321,U_13322) ),
    inference(definitional_conversion,[status(esa)],[f_3487_2]) ).

cnf(f_3487_4,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_13319,U_13320,U_13322,U_13321),U_13324) = U_13323
    | ~ hBOOL(hAPP(hAPP(c_member(U_13319),U_13323),U_13322))
    | hAPP(U_13321,U_13323) != U_13324
    | ~ c_Fun_Oinj__on(U_13319,U_13320,U_13321,U_13322) ),
    inference(clausify,[status(thm)],[f_3487_3]) ).

fof(f_3488_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_3488_2,plain,
    ! [U_13329,U_13328,U_13327,U_13326,U_13325] :
      ( hAPP(c_Fun_Othe__inv__into(U_13325,U_13326,U_13328,U_13327),hAPP(U_13327,U_13329)) = U_13329
      | ~ hBOOL(hAPP(hAPP(c_member(U_13325),U_13329),U_13328))
      | ~ c_Fun_Oinj__on(U_13325,U_13326,U_13327,U_13328) ),
    inference(variable_rename,[status(thm)],[f_3488_1]) ).

fof(f_3488_3,plain,
    ! [U_13325,U_13326,U_13327,U_13328,U_13329] :
      ( hAPP(c_Fun_Othe__inv__into(U_13325,U_13326,U_13328,U_13327),hAPP(U_13327,U_13329)) = U_13329
      | ~ hBOOL(hAPP(hAPP(c_member(U_13325),U_13329),U_13328))
      | ~ c_Fun_Oinj__on(U_13325,U_13326,U_13327,U_13328) ),
    inference(definitional_conversion,[status(esa)],[f_3488_2]) ).

cnf(f_3488_4,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_13325,U_13326,U_13328,U_13327),hAPP(U_13327,U_13329)) = U_13329
    | ~ hBOOL(hAPP(hAPP(c_member(U_13325),U_13329),U_13328))
    | ~ c_Fun_Oinj__on(U_13325,U_13326,U_13327,U_13328) ),
    inference(clausify,[status(thm)],[f_3488_3]) ).

fof(f_3489_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_3489_2,plain,
    ! [U_13333,U_13332,U_13331,U_13330] :
      ( c_Fun_Oinj__on(U_13331,U_13330,c_Fun_Othe__inv__into(U_13330,U_13331,U_13333,U_13332),hAPP(c_Set_Oimage(U_13330,U_13331,U_13332),U_13333))
      | ~ c_Fun_Oinj__on(U_13330,U_13331,U_13332,U_13333) ),
    inference(variable_rename,[status(thm)],[f_3489_1]) ).

fof(f_3489_3,plain,
    ! [U_13331,U_13330,U_13332,U_13333] :
      ( c_Fun_Oinj__on(U_13331,U_13330,c_Fun_Othe__inv__into(U_13330,U_13331,U_13333,U_13332),hAPP(c_Set_Oimage(U_13330,U_13331,U_13332),U_13333))
      | ~ c_Fun_Oinj__on(U_13330,U_13331,U_13332,U_13333) ),
    inference(definitional_conversion,[status(esa)],[f_3489_2]) ).

cnf(f_3489_4,plain,
    ( c_Fun_Oinj__on(U_13331,U_13330,c_Fun_Othe__inv__into(U_13330,U_13331,U_13333,U_13332),hAPP(c_Set_Oimage(U_13330,U_13331,U_13332),U_13333))
    | ~ c_Fun_Oinj__on(U_13330,U_13331,U_13332,U_13333) ),
    inference(clausify,[status(thm)],[f_3489_3]) ).

fof(f_3490_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_3490_2,plain,
    ! [U_13337,U_13336,U_13335,U_13334] :
      ( hAPP(c_Set_Oimage(U_13335,U_13334,c_Fun_Othe__inv__into(U_13334,U_13335,U_13337,U_13336)),hAPP(c_Set_Oimage(U_13334,U_13335,U_13336),U_13337)) = U_13337
      | ~ c_Fun_Oinj__on(U_13334,U_13335,U_13336,U_13337) ),
    inference(variable_rename,[status(thm)],[f_3490_1]) ).

fof(f_3490_3,plain,
    ! [U_13334,U_13335,U_13336,U_13337] :
      ( hAPP(c_Set_Oimage(U_13335,U_13334,c_Fun_Othe__inv__into(U_13334,U_13335,U_13337,U_13336)),hAPP(c_Set_Oimage(U_13334,U_13335,U_13336),U_13337)) = U_13337
      | ~ c_Fun_Oinj__on(U_13334,U_13335,U_13336,U_13337) ),
    inference(definitional_conversion,[status(esa)],[f_3490_2]) ).

cnf(f_3490_4,plain,
    ( hAPP(c_Set_Oimage(U_13335,U_13334,c_Fun_Othe__inv__into(U_13334,U_13335,U_13337,U_13336)),hAPP(c_Set_Oimage(U_13334,U_13335,U_13336),U_13337)) = U_13337
    | ~ c_Fun_Oinj__on(U_13334,U_13335,U_13336,U_13337) ),
    inference(clausify,[status(thm)],[f_3490_3]) ).

fof(f_3491_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_3491_2,plain,
    ! [U_13342,U_13341,U_13340,U_13339,U_13338] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13338,U_13338,c_Groups_Otimes__class_Otimes(U_13338),U_13342,hAPP(hAPP(c_Set_Oinsert(U_13338),U_13339),U_13340)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13338),U_13342),U_13341)))
      | hBOOL(hAPP(hAPP(c_member(U_13338),U_13339),U_13340))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13338,U_13338,c_Groups_Otimes__class_Otimes(U_13338),U_13339,U_13340),U_13341))
      | ~ class_Groups_Oab__semigroup__mult(U_13338) ),
    inference(variable_rename,[status(thm)],[f_3491_1]) ).

fof(f_3491_3,plain,
    ! [U_13338,U_13339,U_13340,U_13341,U_13342] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13338,U_13338,c_Groups_Otimes__class_Otimes(U_13338),U_13342,hAPP(hAPP(c_Set_Oinsert(U_13338),U_13339),U_13340)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13338),U_13342),U_13341)))
      | hBOOL(hAPP(hAPP(c_member(U_13338),U_13339),U_13340))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13338,U_13338,c_Groups_Otimes__class_Otimes(U_13338),U_13339,U_13340),U_13341))
      | ~ class_Groups_Oab__semigroup__mult(U_13338) ),
    inference(definitional_conversion,[status(esa)],[f_3491_2]) ).

cnf(f_3491_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13338,U_13338,c_Groups_Otimes__class_Otimes(U_13338),U_13342,hAPP(hAPP(c_Set_Oinsert(U_13338),U_13339),U_13340)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_13338),U_13342),U_13341)))
    | hBOOL(hAPP(hAPP(c_member(U_13338),U_13339),U_13340))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13338,U_13338,c_Groups_Otimes__class_Otimes(U_13338),U_13339,U_13340),U_13341))
    | ~ class_Groups_Oab__semigroup__mult(U_13338) ),
    inference(clausify,[status(thm)],[f_3491_3]) ).

fof(f_3492_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_3492_2,plain,
    ! [U_13347,U_13346,U_13345,U_13344,U_13343] : hAPP(c_Fun_Othe__inv__into(U_13343,U_13344,U_13345,U_13346),U_13347) = c_HOL_OThe(U_13343,hAPP(hAPP(c_COMBS(U_13343,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13343),c_fconj),hAPP(hAPP(c_COMBC(U_13343,tc_fun(U_13343,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13343)),U_13345))),hAPP(hAPP(c_COMBC(U_13343,U_13344,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13344,tc_fun(U_13344,tc_HOL_Obool),U_13343),c_fequal),U_13346)),U_13347))),
    inference(variable_rename,[status(thm)],[f_3492_1]) ).

fof(f_3492_3,plain,
    ! [U_13343,U_13344,U_13345,U_13346,U_13347] : hAPP(c_Fun_Othe__inv__into(U_13343,U_13344,U_13345,U_13346),U_13347) = c_HOL_OThe(U_13343,hAPP(hAPP(c_COMBS(U_13343,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13343),c_fconj),hAPP(hAPP(c_COMBC(U_13343,tc_fun(U_13343,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13343)),U_13345))),hAPP(hAPP(c_COMBC(U_13343,U_13344,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13344,tc_fun(U_13344,tc_HOL_Obool),U_13343),c_fequal),U_13346)),U_13347))),
    inference(definitional_conversion,[status(esa)],[f_3492_2]) ).

cnf(f_3492_4,plain,
    hAPP(c_Fun_Othe__inv__into(U_13343,U_13344,U_13345,U_13346),U_13347) = c_HOL_OThe(U_13343,hAPP(hAPP(c_COMBS(U_13343,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_13343),c_fconj),hAPP(hAPP(c_COMBC(U_13343,tc_fun(U_13343,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13343)),U_13345))),hAPP(hAPP(c_COMBC(U_13343,U_13344,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_13344,tc_fun(U_13344,tc_HOL_Obool),U_13343),c_fequal),U_13346)),U_13347))),
    inference(clausify,[status(thm)],[f_3492_3]) ).

fof(f_3493_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_3493_2,plain,
    ! [U_13354,U_13353,U_13352,U_13351,U_13350,U_13349,U_13348] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13348,U_13349,U_13350,U_13351,U_13352),hAPP(hAPP(U_13350,U_13353),U_13354)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13348),U_13353),U_13352))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13348,U_13349,U_13350,U_13351,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13348,tc_HOL_Obool)),U_13352),hAPP(hAPP(c_Set_Oinsert(U_13348),U_13353),c_Orderings_Obot__class_Obot(tc_fun(U_13348,tc_HOL_Obool))))),U_13354)) ),
    inference(variable_rename,[status(thm)],[f_3493_1]) ).

fof(f_3493_3,plain,
    ! [U_13348,U_13349,U_13350,U_13351,U_13352,U_13353,U_13354] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13348,U_13349,U_13350,U_13351,U_13352),hAPP(hAPP(U_13350,U_13353),U_13354)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13348),U_13353),U_13352))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13348,U_13349,U_13350,U_13351,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13348,tc_HOL_Obool)),U_13352),hAPP(hAPP(c_Set_Oinsert(U_13348),U_13353),c_Orderings_Obot__class_Obot(tc_fun(U_13348,tc_HOL_Obool))))),U_13354)) ),
    inference(definitional_conversion,[status(esa)],[f_3493_2]) ).

cnf(f_3493_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13348,U_13349,U_13350,U_13351,U_13352),hAPP(hAPP(U_13350,U_13353),U_13354)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13348),U_13353),U_13352))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13348,U_13349,U_13350,U_13351,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13348,tc_HOL_Obool)),U_13352),hAPP(hAPP(c_Set_Oinsert(U_13348),U_13353),c_Orderings_Obot__class_Obot(tc_fun(U_13348,tc_HOL_Obool))))),U_13354)) ),
    inference(clausify,[status(thm)],[f_3493_3]) ).

fof(f_3494_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_3494_2,plain,
    ! [U_13359,U_13358,U_13357,U_13356,U_13355] :
      ( hAPP(U_13357,hAPP(c_Fun_Othe__inv__into(U_13355,U_13356,U_13358,U_13357),U_13359)) = U_13359
      | ~ hBOOL(hAPP(hAPP(c_member(U_13356),U_13359),hAPP(c_Set_Oimage(U_13355,U_13356,U_13357),U_13358)))
      | ~ c_Fun_Oinj__on(U_13355,U_13356,U_13357,U_13358) ),
    inference(variable_rename,[status(thm)],[f_3494_1]) ).

fof(f_3494_3,plain,
    ! [U_13356,U_13355,U_13357,U_13358,U_13359] :
      ( hAPP(U_13357,hAPP(c_Fun_Othe__inv__into(U_13355,U_13356,U_13358,U_13357),U_13359)) = U_13359
      | ~ hBOOL(hAPP(hAPP(c_member(U_13356),U_13359),hAPP(c_Set_Oimage(U_13355,U_13356,U_13357),U_13358)))
      | ~ c_Fun_Oinj__on(U_13355,U_13356,U_13357,U_13358) ),
    inference(definitional_conversion,[status(esa)],[f_3494_2]) ).

cnf(f_3494_4,plain,
    ( hAPP(U_13357,hAPP(c_Fun_Othe__inv__into(U_13355,U_13356,U_13358,U_13357),U_13359)) = U_13359
    | ~ hBOOL(hAPP(hAPP(c_member(U_13356),U_13359),hAPP(c_Set_Oimage(U_13355,U_13356,U_13357),U_13358)))
    | ~ c_Fun_Oinj__on(U_13355,U_13356,U_13357,U_13358) ),
    inference(clausify,[status(thm)],[f_3494_3]) ).

fof(f_3495_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_3495_2,plain,
    ! [U_13365,U_13364,U_13363,U_13362,U_13361,U_13360] :
      ( hBOOL(hAPP(hAPP(c_member(U_13363),U_13364),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13360,tc_fun(U_13363,tc_HOL_Obool)),U_13362),U_13365)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13363),U_13364),hAPP(U_13365,U_13361)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13360),U_13361),U_13362)) ),
    inference(variable_rename,[status(thm)],[f_3495_1]) ).

fof(f_3495_3,plain,
    ! [U_13362,U_13360,U_13361,U_13363,U_13364,U_13365] :
      ( hBOOL(hAPP(hAPP(c_member(U_13363),U_13364),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13360,tc_fun(U_13363,tc_HOL_Obool)),U_13362),U_13365)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13363),U_13364),hAPP(U_13365,U_13361)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13360),U_13361),U_13362)) ),
    inference(definitional_conversion,[status(esa)],[f_3495_2]) ).

cnf(f_3495_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13363),U_13364),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13360,tc_fun(U_13363,tc_HOL_Obool)),U_13362),U_13365)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13363),U_13364),hAPP(U_13365,U_13361)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13360),U_13361),U_13362)) ),
    inference(clausify,[status(thm)],[f_3495_3]) ).

fof(f_3496_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_3496_2,plain,
    ! [U_13369,U_13368,U_13367,U_13366] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_13366,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13367,tc_fun(tc_fun(U_13366,tc_HOL_Obool),tc_HOL_Obool)),U_13368),hAPP(hAPP(c_COMBB(tc_fun(U_13366,tc_HOL_Obool),tc_fun(tc_fun(U_13366,tc_HOL_Obool),tc_HOL_Obool),U_13367),c_Set_OPow(U_13366)),U_13369))),hAPP(c_Set_OPow(U_13366),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13367,tc_fun(U_13366,tc_HOL_Obool)),U_13368),U_13369)))),
    inference(variable_rename,[status(thm)],[f_3496_1]) ).

fof(f_3496_3,plain,
    ! [U_13366,U_13367,U_13368,U_13369] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_13366,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13367,tc_fun(tc_fun(U_13366,tc_HOL_Obool),tc_HOL_Obool)),U_13368),hAPP(hAPP(c_COMBB(tc_fun(U_13366,tc_HOL_Obool),tc_fun(tc_fun(U_13366,tc_HOL_Obool),tc_HOL_Obool),U_13367),c_Set_OPow(U_13366)),U_13369))),hAPP(c_Set_OPow(U_13366),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13367,tc_fun(U_13366,tc_HOL_Obool)),U_13368),U_13369)))),
    inference(definitional_conversion,[status(esa)],[f_3496_2]) ).

cnf(f_3496_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_13366,tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13367,tc_fun(tc_fun(U_13366,tc_HOL_Obool),tc_HOL_Obool)),U_13368),hAPP(hAPP(c_COMBB(tc_fun(U_13366,tc_HOL_Obool),tc_fun(tc_fun(U_13366,tc_HOL_Obool),tc_HOL_Obool),U_13367),c_Set_OPow(U_13366)),U_13369))),hAPP(c_Set_OPow(U_13366),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13367,tc_fun(U_13366,tc_HOL_Obool)),U_13368),U_13369)))),
    inference(clausify,[status(thm)],[f_3496_3]) ).

fof(f_3497_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_3497_2,plain,
    ! [U_13373,U_13372,U_13371,U_13370] : hAPP(c_Set_Oimage(U_13370,U_13371,U_13372),U_13373) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13370,tc_fun(U_13371,tc_HOL_Obool)),U_13373),hAPP(hAPP(c_COMBC(U_13370,tc_fun(U_13371,tc_HOL_Obool),tc_fun(U_13371,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_13371,tc_fun(tc_fun(U_13371,tc_HOL_Obool),tc_fun(U_13371,tc_HOL_Obool)),U_13370),c_Set_Oinsert(U_13371)),U_13372)),c_Orderings_Obot__class_Obot(tc_fun(U_13371,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3497_1]) ).

fof(f_3497_3,plain,
    ! [U_13370,U_13371,U_13372,U_13373] : hAPP(c_Set_Oimage(U_13370,U_13371,U_13372),U_13373) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13370,tc_fun(U_13371,tc_HOL_Obool)),U_13373),hAPP(hAPP(c_COMBC(U_13370,tc_fun(U_13371,tc_HOL_Obool),tc_fun(U_13371,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_13371,tc_fun(tc_fun(U_13371,tc_HOL_Obool),tc_fun(U_13371,tc_HOL_Obool)),U_13370),c_Set_Oinsert(U_13371)),U_13372)),c_Orderings_Obot__class_Obot(tc_fun(U_13371,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3497_2]) ).

cnf(f_3497_4,plain,
    hAPP(c_Set_Oimage(U_13370,U_13371,U_13372),U_13373) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13370,tc_fun(U_13371,tc_HOL_Obool)),U_13373),hAPP(hAPP(c_COMBC(U_13370,tc_fun(U_13371,tc_HOL_Obool),tc_fun(U_13371,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(U_13371,tc_fun(tc_fun(U_13371,tc_HOL_Obool),tc_fun(U_13371,tc_HOL_Obool)),U_13370),c_Set_Oinsert(U_13371)),U_13372)),c_Orderings_Obot__class_Obot(tc_fun(U_13371,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3497_3]) ).

fof(f_3498_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_3498_2,plain,
    ! [U_13378,U_13377,U_13376,U_13375,U_13374] : hAPP(c_Relation_Oconverse(U_13374,U_13375),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13376,tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool)),U_13377),U_13378)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13376,tc_fun(tc_prod(U_13375,U_13374),tc_HOL_Obool)),U_13377),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),tc_fun(tc_prod(U_13375,U_13374),tc_HOL_Obool),U_13376),c_Relation_Oconverse(U_13374,U_13375)),U_13378)),
    inference(variable_rename,[status(thm)],[f_3498_1]) ).

fof(f_3498_3,plain,
    ! [U_13374,U_13375,U_13376,U_13377,U_13378] : hAPP(c_Relation_Oconverse(U_13374,U_13375),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13376,tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool)),U_13377),U_13378)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13376,tc_fun(tc_prod(U_13375,U_13374),tc_HOL_Obool)),U_13377),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),tc_fun(tc_prod(U_13375,U_13374),tc_HOL_Obool),U_13376),c_Relation_Oconverse(U_13374,U_13375)),U_13378)),
    inference(definitional_conversion,[status(esa)],[f_3498_2]) ).

cnf(f_3498_4,plain,
    hAPP(c_Relation_Oconverse(U_13374,U_13375),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13376,tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool)),U_13377),U_13378)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13376,tc_fun(tc_prod(U_13375,U_13374),tc_HOL_Obool)),U_13377),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13374,U_13375),tc_HOL_Obool),tc_fun(tc_prod(U_13375,U_13374),tc_HOL_Obool),U_13376),c_Relation_Oconverse(U_13374,U_13375)),U_13378)),
    inference(clausify,[status(thm)],[f_3498_3]) ).

fof(f_3499_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_3499_2,plain,
    ! [U_13385,U_13384,U_13383,U_13382,U_13381,U_13380,U_13379] : hAPP(hAPP(c_Relation_Orel__comp(U_13379,U_13380,U_13381),U_13382),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13383,tc_fun(tc_prod(U_13380,U_13381),tc_HOL_Obool)),U_13384),U_13385)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13383,tc_fun(tc_prod(U_13379,U_13381),tc_HOL_Obool)),U_13384),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13380,U_13381),tc_HOL_Obool),tc_fun(tc_prod(U_13379,U_13381),tc_HOL_Obool),U_13383),hAPP(c_Relation_Orel__comp(U_13379,U_13380,U_13381),U_13382)),U_13385)),
    inference(variable_rename,[status(thm)],[f_3499_1]) ).

fof(f_3499_3,plain,
    ! [U_13379,U_13380,U_13381,U_13382,U_13383,U_13384,U_13385] : hAPP(hAPP(c_Relation_Orel__comp(U_13379,U_13380,U_13381),U_13382),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13383,tc_fun(tc_prod(U_13380,U_13381),tc_HOL_Obool)),U_13384),U_13385)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13383,tc_fun(tc_prod(U_13379,U_13381),tc_HOL_Obool)),U_13384),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13380,U_13381),tc_HOL_Obool),tc_fun(tc_prod(U_13379,U_13381),tc_HOL_Obool),U_13383),hAPP(c_Relation_Orel__comp(U_13379,U_13380,U_13381),U_13382)),U_13385)),
    inference(definitional_conversion,[status(esa)],[f_3499_2]) ).

cnf(f_3499_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_13379,U_13380,U_13381),U_13382),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13383,tc_fun(tc_prod(U_13380,U_13381),tc_HOL_Obool)),U_13384),U_13385)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13383,tc_fun(tc_prod(U_13379,U_13381),tc_HOL_Obool)),U_13384),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13380,U_13381),tc_HOL_Obool),tc_fun(tc_prod(U_13379,U_13381),tc_HOL_Obool),U_13383),hAPP(c_Relation_Orel__comp(U_13379,U_13380,U_13381),U_13382)),U_13385)),
    inference(clausify,[status(thm)],[f_3499_3]) ).

fof(f_3500_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_3500_2,plain,
    ! [U_13392,U_13391,U_13390,U_13389,U_13388,U_13387,U_13386] : hAPP(hAPP(c_Relation_Orel__comp(U_13386,U_13387,U_13388),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13389,tc_fun(tc_prod(U_13386,U_13387),tc_HOL_Obool)),U_13390),U_13391)),U_13392) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13389,tc_fun(tc_prod(U_13386,U_13388),tc_HOL_Obool)),U_13390),hAPP(hAPP(c_COMBC(U_13389,tc_fun(tc_prod(U_13387,U_13388),tc_HOL_Obool),tc_fun(tc_prod(U_13386,U_13388),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13386,U_13387),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_13387,U_13388),tc_HOL_Obool),tc_fun(tc_prod(U_13386,U_13388),tc_HOL_Obool)),U_13389),c_Relation_Orel__comp(U_13386,U_13387,U_13388)),U_13391)),U_13392)),
    inference(variable_rename,[status(thm)],[f_3500_1]) ).

fof(f_3500_3,plain,
    ! [U_13386,U_13387,U_13388,U_13389,U_13390,U_13391,U_13392] : hAPP(hAPP(c_Relation_Orel__comp(U_13386,U_13387,U_13388),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13389,tc_fun(tc_prod(U_13386,U_13387),tc_HOL_Obool)),U_13390),U_13391)),U_13392) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13389,tc_fun(tc_prod(U_13386,U_13388),tc_HOL_Obool)),U_13390),hAPP(hAPP(c_COMBC(U_13389,tc_fun(tc_prod(U_13387,U_13388),tc_HOL_Obool),tc_fun(tc_prod(U_13386,U_13388),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13386,U_13387),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_13387,U_13388),tc_HOL_Obool),tc_fun(tc_prod(U_13386,U_13388),tc_HOL_Obool)),U_13389),c_Relation_Orel__comp(U_13386,U_13387,U_13388)),U_13391)),U_13392)),
    inference(definitional_conversion,[status(esa)],[f_3500_2]) ).

cnf(f_3500_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_13386,U_13387,U_13388),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13389,tc_fun(tc_prod(U_13386,U_13387),tc_HOL_Obool)),U_13390),U_13391)),U_13392) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13389,tc_fun(tc_prod(U_13386,U_13388),tc_HOL_Obool)),U_13390),hAPP(hAPP(c_COMBC(U_13389,tc_fun(tc_prod(U_13387,U_13388),tc_HOL_Obool),tc_fun(tc_prod(U_13386,U_13388),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_13386,U_13387),tc_HOL_Obool),tc_fun(tc_fun(tc_prod(U_13387,U_13388),tc_HOL_Obool),tc_fun(tc_prod(U_13386,U_13388),tc_HOL_Obool)),U_13389),c_Relation_Orel__comp(U_13386,U_13387,U_13388)),U_13391)),U_13392)),
    inference(clausify,[status(thm)],[f_3500_3]) ).

fof(f_3501_1,plain,
    ! [V_Pa_2,V_B_2,V_A_2,T_c,T_b] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_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_3501_2,plain,
    ! [U_13403,U_13402,U_13401,U_13400,U_13399] :
      ( ( ! [U_13398] :
            ( hBOOL(hAPP(U_13403,U_13398))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13399),U_13398),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13400,tc_fun(U_13399,tc_HOL_Obool)),U_13401),U_13402))) )
        | ? [U_13397] :
            ( ? [U_13396] :
                ( ~ hBOOL(hAPP(U_13403,U_13396))
                & hBOOL(hAPP(hAPP(c_member(U_13399),U_13396),hAPP(U_13402,U_13397))) )
            & hBOOL(hAPP(hAPP(c_member(U_13400),U_13397),U_13401)) ) )
      & ( ! [U_13395] :
            ( ! [U_13394] :
                ( hBOOL(hAPP(U_13403,U_13394))
                | ~ hBOOL(hAPP(hAPP(c_member(U_13399),U_13394),hAPP(U_13402,U_13395))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_13400),U_13395),U_13401)) )
        | ? [U_13393] :
            ( ~ hBOOL(hAPP(U_13403,U_13393))
            & hBOOL(hAPP(hAPP(c_member(U_13399),U_13393),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13400,tc_fun(U_13399,tc_HOL_Obool)),U_13401),U_13402))) ) ) ),
    inference(variable_rename,[status(thm)],[f_3501_1]) ).

fof(f_3501_3,plain,
    ( ! [U_13413,U_13411,U_13409,U_13407,U_13405] :
        ( ! [U_13398] :
            ( hBOOL(hAPP(U_13413,U_13398))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13405),U_13398),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13407,tc_fun(U_13405,tc_HOL_Obool)),U_13409),U_13411))) )
        | ? [U_13397] :
            ( ? [U_13396] :
                ( ~ hBOOL(hAPP(U_13413,U_13396))
                & hBOOL(hAPP(hAPP(c_member(U_13405),U_13396),hAPP(U_13411,U_13397))) )
            & hBOOL(hAPP(hAPP(c_member(U_13407),U_13397),U_13409)) ) )
    & ! [U_13412,U_13410,U_13408,U_13406,U_13404] :
        ( ! [U_13395] :
            ( ! [U_13394] :
                ( hBOOL(hAPP(U_13412,U_13394))
                | ~ hBOOL(hAPP(hAPP(c_member(U_13404),U_13394),hAPP(U_13410,U_13395))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_13406),U_13395),U_13408)) )
        | ? [U_13393] :
            ( ~ hBOOL(hAPP(U_13412,U_13393))
            & hBOOL(hAPP(hAPP(c_member(U_13404),U_13393),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13406,tc_fun(U_13404,tc_HOL_Obool)),U_13408),U_13410))) ) ) ),
    inference(miniscope,[status(thm)],[f_3501_2]) ).

fof(f_3501_4,plain,
    ( ! [U_13413,U_13411,U_13409,U_13407,U_13405] :
        ( ! [U_13398] :
            ( hBOOL(hAPP(U_13413,U_13398))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13405),U_13398),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13407,tc_fun(U_13405,tc_HOL_Obool)),U_13409),U_13411))) )
        | ? [U_13397] :
            ( ? [U_13396] :
                ( ~ hBOOL(hAPP(U_13413,U_13396))
                & hBOOL(hAPP(hAPP(c_member(U_13405),U_13396),hAPP(U_13411,U_13397))) )
            & hBOOL(hAPP(hAPP(c_member(U_13407),U_13397),U_13409)) ) )
    & ! [U_13412,U_13410,U_13408,U_13406,U_13404] :
        ( ! [U_13395] :
            ( ! [U_13394] :
                ( hBOOL(hAPP(U_13412,U_13394))
                | ~ hBOOL(hAPP(hAPP(c_member(U_13404),U_13394),hAPP(U_13410,U_13395))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_13406),U_13395),U_13408)) )
        | ( ~ hBOOL(hAPP(U_13412,sK290(U_13412,U_13410,U_13408,U_13406,U_13404)))
          & hBOOL(hAPP(hAPP(c_member(U_13404),sK290(U_13412,U_13410,U_13408,U_13406,U_13404)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13406,tc_fun(U_13404,tc_HOL_Obool)),U_13408),U_13410))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK290]),skolemize(U_13393,sK290(U_13412,U_13410,U_13408,U_13406,U_13404))],[f_3501_3]) ).

fof(f_3501_5,plain,
    ( ! [U_13413,U_13411,U_13409,U_13407,U_13405] :
        ( ! [U_13398] :
            ( hBOOL(hAPP(U_13413,U_13398))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13405),U_13398),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13407,tc_fun(U_13405,tc_HOL_Obool)),U_13409),U_13411))) )
        | ( ? [U_13396] :
              ( ~ hBOOL(hAPP(U_13413,U_13396))
              & hBOOL(hAPP(hAPP(c_member(U_13405),U_13396),hAPP(U_13411,sK291(U_13413,U_13411,U_13409,U_13407,U_13405)))) )
          & hBOOL(hAPP(hAPP(c_member(U_13407),sK291(U_13413,U_13411,U_13409,U_13407,U_13405)),U_13409)) ) )
    & ! [U_13412,U_13410,U_13408,U_13406,U_13404] :
        ( ! [U_13395] :
            ( ! [U_13394] :
                ( hBOOL(hAPP(U_13412,U_13394))
                | ~ hBOOL(hAPP(hAPP(c_member(U_13404),U_13394),hAPP(U_13410,U_13395))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_13406),U_13395),U_13408)) )
        | ( ~ hBOOL(hAPP(U_13412,sK290(U_13412,U_13410,U_13408,U_13406,U_13404)))
          & hBOOL(hAPP(hAPP(c_member(U_13404),sK290(U_13412,U_13410,U_13408,U_13406,U_13404)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13406,tc_fun(U_13404,tc_HOL_Obool)),U_13408),U_13410))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK291]),skolemize(U_13397,sK291(U_13413,U_13411,U_13409,U_13407,U_13405))],[f_3501_4]) ).

fof(f_3501_6,plain,
    ( ! [U_13413,U_13411,U_13409,U_13407,U_13405] :
        ( ! [U_13398] :
            ( hBOOL(hAPP(U_13413,U_13398))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13405),U_13398),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13407,tc_fun(U_13405,tc_HOL_Obool)),U_13409),U_13411))) )
        | ( ~ hBOOL(hAPP(U_13413,sK292(U_13413,U_13411,U_13409,U_13407,U_13405)))
          & hBOOL(hAPP(hAPP(c_member(U_13405),sK292(U_13413,U_13411,U_13409,U_13407,U_13405)),hAPP(U_13411,sK291(U_13413,U_13411,U_13409,U_13407,U_13405))))
          & hBOOL(hAPP(hAPP(c_member(U_13407),sK291(U_13413,U_13411,U_13409,U_13407,U_13405)),U_13409)) ) )
    & ! [U_13412,U_13410,U_13408,U_13406,U_13404] :
        ( ! [U_13395] :
            ( ! [U_13394] :
                ( hBOOL(hAPP(U_13412,U_13394))
                | ~ hBOOL(hAPP(hAPP(c_member(U_13404),U_13394),hAPP(U_13410,U_13395))) )
            | ~ hBOOL(hAPP(hAPP(c_member(U_13406),U_13395),U_13408)) )
        | ( ~ hBOOL(hAPP(U_13412,sK290(U_13412,U_13410,U_13408,U_13406,U_13404)))
          & hBOOL(hAPP(hAPP(c_member(U_13404),sK290(U_13412,U_13410,U_13408,U_13406,U_13404)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13406,tc_fun(U_13404,tc_HOL_Obool)),U_13408),U_13410))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK292]),skolemize(U_13396,sK292(U_13413,U_13411,U_13409,U_13407,U_13405))],[f_3501_5]) ).

fof(f_3501_7,plain,
    ( ! [U_13409,U_13405,U_13411,U_13407,U_13413] :
        ( ~ hBOOL(hAPP(U_13413,sK292(U_13413,U_13411,U_13409,U_13407,U_13405)))
        | ~ sP946(U_13409,U_13405,U_13411,U_13407,U_13413) )
    & ! [U_13409,U_13405,U_13411,U_13407,U_13413] :
        ( hBOOL(hAPP(hAPP(c_member(U_13405),sK292(U_13413,U_13411,U_13409,U_13407,U_13405)),hAPP(U_13411,sK291(U_13413,U_13411,U_13409,U_13407,U_13405))))
        | ~ sP946(U_13409,U_13405,U_13411,U_13407,U_13413) )
    & ! [U_13409,U_13405,U_13411,U_13407,U_13413] :
        ( hBOOL(hAPP(hAPP(c_member(U_13407),sK291(U_13413,U_13411,U_13409,U_13407,U_13405)),U_13409))
        | ~ sP946(U_13409,U_13405,U_13411,U_13407,U_13413) )
    & ! [U_13408,U_13406,U_13410,U_13404,U_13412] :
        ( ~ hBOOL(hAPP(U_13412,sK290(U_13412,U_13410,U_13408,U_13406,U_13404)))
        | ~ sP945(U_13408,U_13406,U_13410,U_13404,U_13412) )
    & ! [U_13408,U_13406,U_13410,U_13404,U_13412] :
        ( hBOOL(hAPP(hAPP(c_member(U_13404),sK290(U_13412,U_13410,U_13408,U_13406,U_13404)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13406,tc_fun(U_13404,tc_HOL_Obool)),U_13408),U_13410)))
        | ~ sP945(U_13408,U_13406,U_13410,U_13404,U_13412) )
    & ! [U_13409,U_13405,U_13398,U_13411,U_13407,U_13413] :
        ( hBOOL(hAPP(U_13413,U_13398))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13405),U_13398),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13407,tc_fun(U_13405,tc_HOL_Obool)),U_13409),U_13411)))
        | sP946(U_13409,U_13405,U_13411,U_13407,U_13413) )
    & ! [U_13408,U_13406,U_13410,U_13394,U_13395,U_13404,U_13412] :
        ( hBOOL(hAPP(U_13412,U_13394))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13404),U_13394),hAPP(U_13410,U_13395)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13406),U_13395),U_13408))
        | sP945(U_13408,U_13406,U_13410,U_13404,U_13412) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP945,sP946])],[f_3501_6]) ).

cnf(f_3501_8,plain,
    ( hBOOL(hAPP(U_13412,U_13394))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13404),U_13394),hAPP(U_13410,U_13395)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13406),U_13395),U_13408))
    | sP945(U_13408,U_13406,U_13410,U_13404,U_13412) ),
    inference(clausify,[status(thm)],[f_3501_7]) ).

cnf(f_3501_9,plain,
    ( hBOOL(hAPP(U_13413,U_13398))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13405),U_13398),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13407,tc_fun(U_13405,tc_HOL_Obool)),U_13409),U_13411)))
    | sP946(U_13409,U_13405,U_13411,U_13407,U_13413) ),
    inference(clausify,[status(thm)],[f_3501_7]) ).

cnf(f_3501_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13404),sK290(U_13412,U_13410,U_13408,U_13406,U_13404)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13406,tc_fun(U_13404,tc_HOL_Obool)),U_13408),U_13410)))
    | ~ sP945(U_13408,U_13406,U_13410,U_13404,U_13412) ),
    inference(clausify,[status(thm)],[f_3501_7]) ).

cnf(f_3501_11,plain,
    ( ~ hBOOL(hAPP(U_13412,sK290(U_13412,U_13410,U_13408,U_13406,U_13404)))
    | ~ sP945(U_13408,U_13406,U_13410,U_13404,U_13412) ),
    inference(clausify,[status(thm)],[f_3501_7]) ).

cnf(f_3501_12,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13407),sK291(U_13413,U_13411,U_13409,U_13407,U_13405)),U_13409))
    | ~ sP946(U_13409,U_13405,U_13411,U_13407,U_13413) ),
    inference(clausify,[status(thm)],[f_3501_7]) ).

cnf(f_3501_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13405),sK292(U_13413,U_13411,U_13409,U_13407,U_13405)),hAPP(U_13411,sK291(U_13413,U_13411,U_13409,U_13407,U_13405))))
    | ~ sP946(U_13409,U_13405,U_13411,U_13407,U_13413) ),
    inference(clausify,[status(thm)],[f_3501_7]) ).

cnf(f_3501_14,plain,
    ( ~ hBOOL(hAPP(U_13413,sK292(U_13413,U_13411,U_13409,U_13407,U_13405)))
    | ~ sP946(U_13409,U_13405,U_13411,U_13407,U_13413) ),
    inference(clausify,[status(thm)],[f_3501_7]) ).

fof(f_3502_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_3502_2,plain,
    ! [U_13417,U_13416,U_13415,U_13414] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13414,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_13415)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_13414,tc_HOL_Obool),tc_Nat_Onat),U_13416),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_13417))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13414,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_13417,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13415),U_13417))),U_13416),
    inference(variable_rename,[status(thm)],[f_3502_1]) ).

fof(f_3502_3,plain,
    ! [U_13415,U_13416,U_13417,U_13414] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13414,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_13415)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_13414,tc_HOL_Obool),tc_Nat_Onat),U_13416),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_13417))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13414,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_13417,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13415),U_13417))),U_13416),
    inference(definitional_conversion,[status(esa)],[f_3502_2]) ).

cnf(f_3502_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13414,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_13415)),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(U_13414,tc_HOL_Obool),tc_Nat_Onat),U_13416),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),U_13417))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13414,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_13417,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_13415),U_13417))),U_13416),
    inference(clausify,[status(thm)],[f_3502_3]) ).

fof(f_3503_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_3503_2,plain,
    ! [U_13419,U_13418] : c_Relation_OId__on(U_13418,U_13419) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13418,tc_fun(tc_prod(U_13418,U_13418),tc_HOL_Obool)),U_13419),hAPP(hAPP(c_COMBC(U_13418,tc_fun(tc_prod(U_13418,U_13418),tc_HOL_Obool),tc_fun(tc_prod(U_13418,U_13418),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(U_13418,U_13418),tc_fun(tc_fun(tc_prod(U_13418,U_13418),tc_HOL_Obool),tc_fun(tc_prod(U_13418,U_13418),tc_HOL_Obool)),U_13418),c_Set_Oinsert(tc_prod(U_13418,U_13418))),hAPP(hAPP(c_COMBS(U_13418,U_13418,tc_prod(U_13418,U_13418)),c_Product__Type_OPair(U_13418,U_13418)),c_COMBI(U_13418)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13418,U_13418),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3503_1]) ).

fof(f_3503_3,plain,
    ! [U_13419,U_13418] : c_Relation_OId__on(U_13418,U_13419) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13418,tc_fun(tc_prod(U_13418,U_13418),tc_HOL_Obool)),U_13419),hAPP(hAPP(c_COMBC(U_13418,tc_fun(tc_prod(U_13418,U_13418),tc_HOL_Obool),tc_fun(tc_prod(U_13418,U_13418),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(U_13418,U_13418),tc_fun(tc_fun(tc_prod(U_13418,U_13418),tc_HOL_Obool),tc_fun(tc_prod(U_13418,U_13418),tc_HOL_Obool)),U_13418),c_Set_Oinsert(tc_prod(U_13418,U_13418))),hAPP(hAPP(c_COMBS(U_13418,U_13418,tc_prod(U_13418,U_13418)),c_Product__Type_OPair(U_13418,U_13418)),c_COMBI(U_13418)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13418,U_13418),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3503_2]) ).

cnf(f_3503_4,plain,
    c_Relation_OId__on(U_13418,U_13419) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13418,tc_fun(tc_prod(U_13418,U_13418),tc_HOL_Obool)),U_13419),hAPP(hAPP(c_COMBC(U_13418,tc_fun(tc_prod(U_13418,U_13418),tc_HOL_Obool),tc_fun(tc_prod(U_13418,U_13418),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_prod(U_13418,U_13418),tc_fun(tc_fun(tc_prod(U_13418,U_13418),tc_HOL_Obool),tc_fun(tc_prod(U_13418,U_13418),tc_HOL_Obool)),U_13418),c_Set_Oinsert(tc_prod(U_13418,U_13418))),hAPP(hAPP(c_COMBS(U_13418,U_13418,tc_prod(U_13418,U_13418)),c_Product__Type_OPair(U_13418,U_13418)),c_COMBI(U_13418)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_13418,U_13418),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3503_3]) ).

fof(f_3504_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_3504_2,plain,
    ! [U_13425,U_13424,U_13423,U_13422,U_13421,U_13420] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13421,U_13420),U_13422),hAPP(hAPP(c_COMBB(tc_fun(U_13423,U_13420),U_13420,U_13421),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13423,U_13420),U_13424)),U_13425)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13423,U_13420),U_13424),hAPP(hAPP(c_COMBB(tc_fun(U_13421,U_13420),U_13420,U_13423),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13421,U_13420),U_13422)),hAPP(c_COMBC(U_13421,U_13423,U_13420),U_13425)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_13420) ),
    inference(variable_rename,[status(thm)],[f_3504_1]) ).

fof(f_3504_3,plain,
    ! [U_13420,U_13421,U_13422,U_13423,U_13424,U_13425] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13421,U_13420),U_13422),hAPP(hAPP(c_COMBB(tc_fun(U_13423,U_13420),U_13420,U_13421),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13423,U_13420),U_13424)),U_13425)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13423,U_13420),U_13424),hAPP(hAPP(c_COMBB(tc_fun(U_13421,U_13420),U_13420,U_13423),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13421,U_13420),U_13422)),hAPP(c_COMBC(U_13421,U_13423,U_13420),U_13425)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_13420) ),
    inference(definitional_conversion,[status(esa)],[f_3504_2]) ).

cnf(f_3504_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13421,U_13420),U_13422),hAPP(hAPP(c_COMBB(tc_fun(U_13423,U_13420),U_13420,U_13421),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13423,U_13420),U_13424)),U_13425)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13423,U_13420),U_13424),hAPP(hAPP(c_COMBB(tc_fun(U_13421,U_13420),U_13420,U_13423),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13421,U_13420),U_13422)),hAPP(c_COMBC(U_13421,U_13423,U_13420),U_13425)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_13420) ),
    inference(clausify,[status(thm)],[f_3504_3]) ).

fof(f_3505_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_3505_2,plain,
    ! [U_13431,U_13430,U_13429,U_13428,U_13427,U_13426] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13426,tc_fun(U_13427,tc_HOL_Obool)),U_13428),hAPP(hAPP(c_COMBC(U_13426,tc_fun(U_13429,tc_fun(U_13427,tc_HOL_Obool)),tc_fun(U_13427,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13429,tc_HOL_Obool),tc_fun(tc_fun(U_13429,tc_fun(U_13427,tc_HOL_Obool)),tc_fun(U_13427,tc_HOL_Obool)),U_13426),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13429,tc_fun(U_13427,tc_HOL_Obool))),U_13430)),U_13431)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13429,tc_fun(U_13427,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13426,tc_fun(U_13429,tc_HOL_Obool)),U_13428),U_13430)),U_13431),
    inference(variable_rename,[status(thm)],[f_3505_1]) ).

fof(f_3505_3,plain,
    ! [U_13426,U_13427,U_13428,U_13429,U_13430,U_13431] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13426,tc_fun(U_13427,tc_HOL_Obool)),U_13428),hAPP(hAPP(c_COMBC(U_13426,tc_fun(U_13429,tc_fun(U_13427,tc_HOL_Obool)),tc_fun(U_13427,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13429,tc_HOL_Obool),tc_fun(tc_fun(U_13429,tc_fun(U_13427,tc_HOL_Obool)),tc_fun(U_13427,tc_HOL_Obool)),U_13426),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13429,tc_fun(U_13427,tc_HOL_Obool))),U_13430)),U_13431)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13429,tc_fun(U_13427,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13426,tc_fun(U_13429,tc_HOL_Obool)),U_13428),U_13430)),U_13431),
    inference(definitional_conversion,[status(esa)],[f_3505_2]) ).

cnf(f_3505_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13426,tc_fun(U_13427,tc_HOL_Obool)),U_13428),hAPP(hAPP(c_COMBC(U_13426,tc_fun(U_13429,tc_fun(U_13427,tc_HOL_Obool)),tc_fun(U_13427,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13429,tc_HOL_Obool),tc_fun(tc_fun(U_13429,tc_fun(U_13427,tc_HOL_Obool)),tc_fun(U_13427,tc_HOL_Obool)),U_13426),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13429,tc_fun(U_13427,tc_HOL_Obool))),U_13430)),U_13431)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13429,tc_fun(U_13427,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13426,tc_fun(U_13429,tc_HOL_Obool)),U_13428),U_13430)),U_13431),
    inference(clausify,[status(thm)],[f_3505_3]) ).

fof(f_3506_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_3506_2,plain,
    ! [U_13437,U_13436,U_13435,U_13434,U_13433,U_13432] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13432,tc_fun(U_13433,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13434,tc_fun(U_13432,tc_HOL_Obool)),U_13435),U_13436)),U_13437) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13434,tc_fun(U_13433,tc_HOL_Obool)),U_13435),hAPP(hAPP(c_COMBC(U_13434,tc_fun(U_13432,tc_fun(U_13433,tc_HOL_Obool)),tc_fun(U_13433,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13432,tc_HOL_Obool),tc_fun(tc_fun(U_13432,tc_fun(U_13433,tc_HOL_Obool)),tc_fun(U_13433,tc_HOL_Obool)),U_13434),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13432,tc_fun(U_13433,tc_HOL_Obool))),U_13436)),U_13437)),
    inference(variable_rename,[status(thm)],[f_3506_1]) ).

fof(f_3506_3,plain,
    ! [U_13432,U_13433,U_13434,U_13435,U_13436,U_13437] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13432,tc_fun(U_13433,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13434,tc_fun(U_13432,tc_HOL_Obool)),U_13435),U_13436)),U_13437) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13434,tc_fun(U_13433,tc_HOL_Obool)),U_13435),hAPP(hAPP(c_COMBC(U_13434,tc_fun(U_13432,tc_fun(U_13433,tc_HOL_Obool)),tc_fun(U_13433,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13432,tc_HOL_Obool),tc_fun(tc_fun(U_13432,tc_fun(U_13433,tc_HOL_Obool)),tc_fun(U_13433,tc_HOL_Obool)),U_13434),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13432,tc_fun(U_13433,tc_HOL_Obool))),U_13436)),U_13437)),
    inference(definitional_conversion,[status(esa)],[f_3506_2]) ).

cnf(f_3506_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13432,tc_fun(U_13433,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13434,tc_fun(U_13432,tc_HOL_Obool)),U_13435),U_13436)),U_13437) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13434,tc_fun(U_13433,tc_HOL_Obool)),U_13435),hAPP(hAPP(c_COMBC(U_13434,tc_fun(U_13432,tc_fun(U_13433,tc_HOL_Obool)),tc_fun(U_13433,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13432,tc_HOL_Obool),tc_fun(tc_fun(U_13432,tc_fun(U_13433,tc_HOL_Obool)),tc_fun(U_13433,tc_HOL_Obool)),U_13434),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13432,tc_fun(U_13433,tc_HOL_Obool))),U_13436)),U_13437)),
    inference(clausify,[status(thm)],[f_3506_3]) ).

fof(f_3507_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_3507_2,plain,
    ! [U_13443,U_13442,U_13441,U_13440,U_13439,U_13438] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13438,tc_fun(U_13439,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13440,tc_fun(U_13438,tc_HOL_Obool)),U_13441),U_13442)),U_13443) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13440,tc_fun(U_13439,tc_HOL_Obool)),U_13441),hAPP(hAPP(c_COMBC(U_13440,tc_fun(U_13438,tc_fun(U_13439,tc_HOL_Obool)),tc_fun(U_13439,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13438,tc_HOL_Obool),tc_fun(tc_fun(U_13438,tc_fun(U_13439,tc_HOL_Obool)),tc_fun(U_13439,tc_HOL_Obool)),U_13440),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13438,tc_fun(U_13439,tc_HOL_Obool))),U_13442)),U_13443)),
    inference(variable_rename,[status(thm)],[f_3507_1]) ).

fof(f_3507_3,plain,
    ! [U_13438,U_13439,U_13440,U_13441,U_13442,U_13443] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13438,tc_fun(U_13439,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13440,tc_fun(U_13438,tc_HOL_Obool)),U_13441),U_13442)),U_13443) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13440,tc_fun(U_13439,tc_HOL_Obool)),U_13441),hAPP(hAPP(c_COMBC(U_13440,tc_fun(U_13438,tc_fun(U_13439,tc_HOL_Obool)),tc_fun(U_13439,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13438,tc_HOL_Obool),tc_fun(tc_fun(U_13438,tc_fun(U_13439,tc_HOL_Obool)),tc_fun(U_13439,tc_HOL_Obool)),U_13440),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13438,tc_fun(U_13439,tc_HOL_Obool))),U_13442)),U_13443)),
    inference(definitional_conversion,[status(esa)],[f_3507_2]) ).

cnf(f_3507_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13438,tc_fun(U_13439,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13440,tc_fun(U_13438,tc_HOL_Obool)),U_13441),U_13442)),U_13443) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13440,tc_fun(U_13439,tc_HOL_Obool)),U_13441),hAPP(hAPP(c_COMBC(U_13440,tc_fun(U_13438,tc_fun(U_13439,tc_HOL_Obool)),tc_fun(U_13439,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13438,tc_HOL_Obool),tc_fun(tc_fun(U_13438,tc_fun(U_13439,tc_HOL_Obool)),tc_fun(U_13439,tc_HOL_Obool)),U_13440),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13438,tc_fun(U_13439,tc_HOL_Obool))),U_13442)),U_13443)),
    inference(clausify,[status(thm)],[f_3507_3]) ).

fof(f_3508_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_3508_2,plain,
    ! [U_13446,U_13445,U_13444] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13444,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_13445)),U_13446) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13444,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13444,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_13445)),U_13446)),hAPP(U_13446,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_3508_1]) ).

fof(f_3508_3,plain,
    ! [U_13444,U_13445,U_13446] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13444,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_13445)),U_13446) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13444,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13444,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_13445)),U_13446)),hAPP(U_13446,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_3508_2]) ).

cnf(f_3508_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13444,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_13445)),U_13446) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13444,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_13444,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),U_13445)),U_13446)),hAPP(U_13446,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_3508_3]) ).

fof(f_3509_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_3509_2,plain,
    ! [U_13453,U_13452,U_13451,U_13450,U_13449] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13449),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13450,U_13449),U_13451),U_13452)),U_13453))
          | ? [U_13448] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13449),hAPP(U_13452,U_13448)),U_13453))
              & hBOOL(hAPP(hAPP(c_member(U_13450),U_13448),U_13451)) ) )
        & ( ! [U_13447] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13449),hAPP(U_13452,U_13447)),U_13453))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13450),U_13447),U_13451)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13449),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13450,U_13449),U_13451),U_13452)),U_13453)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_13449) ),
    inference(variable_rename,[status(thm)],[f_3509_1]) ).

fof(f_3509_3,plain,
    ! [U_13453,U_13452,U_13451,U_13450,U_13449] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13449),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13450,U_13449),U_13451),U_13452)),U_13453))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13449),hAPP(U_13452,sK293(U_13453,U_13452,U_13451,U_13450,U_13449))),U_13453))
            & hBOOL(hAPP(hAPP(c_member(U_13450),sK293(U_13453,U_13452,U_13451,U_13450,U_13449)),U_13451)) ) )
        & ( ! [U_13447] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13449),hAPP(U_13452,U_13447)),U_13453))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13450),U_13447),U_13451)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13449),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13450,U_13449),U_13451),U_13452)),U_13453)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_13449) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK293]),skolemize(U_13448,sK293(U_13453,U_13452,U_13451,U_13450,U_13449))],[f_3509_2]) ).

fof(f_3509_4,plain,
    ( ! [U_13449,U_13450,U_13451,U_13452,U_13453] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13449),hAPP(U_13452,sK293(U_13453,U_13452,U_13451,U_13450,U_13449))),U_13453))
        | ~ sP947(U_13449,U_13450,U_13451,U_13452,U_13453) )
    & ! [U_13449,U_13450,U_13451,U_13452,U_13453] :
        ( hBOOL(hAPP(hAPP(c_member(U_13450),sK293(U_13453,U_13452,U_13451,U_13450,U_13449)),U_13451))
        | ~ sP947(U_13449,U_13450,U_13451,U_13452,U_13453) )
    & ! [U_13447,U_13449,U_13450,U_13451,U_13452,U_13453] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13449),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13450,U_13449),U_13451),U_13452)),U_13453))
        | sP947(U_13449,U_13450,U_13451,U_13452,U_13453)
        | ~ sP948(U_13447,U_13449,U_13450,U_13451,U_13452,U_13453) )
    & ! [U_13447,U_13449,U_13450,U_13451,U_13452,U_13453] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13449),hAPP(U_13452,U_13447)),U_13453))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13450),U_13447),U_13451))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13449),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13450,U_13449),U_13451),U_13452)),U_13453))
        | ~ sP948(U_13447,U_13449,U_13450,U_13451,U_13452,U_13453) )
    & ! [U_13447,U_13449,U_13450,U_13451,U_13452,U_13453] :
        ( sP948(U_13447,U_13449,U_13450,U_13451,U_13452,U_13453)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_13449) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP947,sP948])],[f_3509_3]) ).

cnf(f_3509_5,plain,
    ( sP948(U_13447,U_13449,U_13450,U_13451,U_13452,U_13453)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_13449) ),
    inference(clausify,[status(thm)],[f_3509_4]) ).

cnf(f_3509_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13449),hAPP(U_13452,U_13447)),U_13453))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13450),U_13447),U_13451))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13449),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13450,U_13449),U_13451),U_13452)),U_13453))
    | ~ sP948(U_13447,U_13449,U_13450,U_13451,U_13452,U_13453) ),
    inference(clausify,[status(thm)],[f_3509_4]) ).

cnf(f_3509_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13449),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13450,U_13449),U_13451),U_13452)),U_13453))
    | sP947(U_13449,U_13450,U_13451,U_13452,U_13453)
    | ~ sP948(U_13447,U_13449,U_13450,U_13451,U_13452,U_13453) ),
    inference(clausify,[status(thm)],[f_3509_4]) ).

cnf(f_3509_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13450),sK293(U_13453,U_13452,U_13451,U_13450,U_13449)),U_13451))
    | ~ sP947(U_13449,U_13450,U_13451,U_13452,U_13453) ),
    inference(clausify,[status(thm)],[f_3509_4]) ).

cnf(f_3509_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13449),hAPP(U_13452,sK293(U_13453,U_13452,U_13451,U_13450,U_13449))),U_13453))
    | ~ sP947(U_13449,U_13450,U_13451,U_13452,U_13453) ),
    inference(clausify,[status(thm)],[f_3509_4]) ).

fof(f_3510_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_3510_2,plain,
    ! [U_13460,U_13459,U_13458,U_13457,U_13456] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13456),U_13457),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13458,U_13456),U_13459),U_13460)))
          | ! [U_13455] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13456),U_13457),hAPP(U_13460,U_13455)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13458),U_13455),U_13459)) ) )
        & ( ? [U_13454] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13456),U_13457),hAPP(U_13460,U_13454)))
              & hBOOL(hAPP(hAPP(c_member(U_13458),U_13454),U_13459)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13456),U_13457),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13458,U_13456),U_13459),U_13460))) ) )
      | ~ class_Orderings_Olinorder(U_13456)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_13456) ),
    inference(variable_rename,[status(thm)],[f_3510_1]) ).

fof(f_3510_3,plain,
    ! [U_13460,U_13459,U_13458,U_13457,U_13456] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13456),U_13457),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13458,U_13456),U_13459),U_13460)))
          | ! [U_13455] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13456),U_13457),hAPP(U_13460,U_13455)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_13458),U_13455),U_13459)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13456),U_13457),hAPP(U_13460,sK294(U_13460,U_13459,U_13458,U_13457,U_13456))))
            & hBOOL(hAPP(hAPP(c_member(U_13458),sK294(U_13460,U_13459,U_13458,U_13457,U_13456)),U_13459)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13456),U_13457),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13458,U_13456),U_13459),U_13460))) ) )
      | ~ class_Orderings_Olinorder(U_13456)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_13456) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK294]),skolemize(U_13454,sK294(U_13460,U_13459,U_13458,U_13457,U_13456))],[f_3510_2]) ).

fof(f_3510_4,plain,
    ( ! [U_13457,U_13458,U_13456,U_13459,U_13460] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13456),U_13457),hAPP(U_13460,sK294(U_13460,U_13459,U_13458,U_13457,U_13456))))
        | ~ sP949(U_13457,U_13458,U_13456,U_13459,U_13460) )
    & ! [U_13457,U_13458,U_13456,U_13459,U_13460] :
        ( hBOOL(hAPP(hAPP(c_member(U_13458),sK294(U_13460,U_13459,U_13458,U_13457,U_13456)),U_13459))
        | ~ sP949(U_13457,U_13458,U_13456,U_13459,U_13460) )
    & ! [U_13457,U_13458,U_13455,U_13456,U_13459,U_13460] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13456),U_13457),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13458,U_13456),U_13459),U_13460)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13456),U_13457),hAPP(U_13460,U_13455)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13458),U_13455),U_13459))
        | ~ sP950(U_13457,U_13458,U_13455,U_13456,U_13459,U_13460) )
    & ! [U_13457,U_13458,U_13455,U_13456,U_13459,U_13460] :
        ( sP949(U_13457,U_13458,U_13456,U_13459,U_13460)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13456),U_13457),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13458,U_13456),U_13459),U_13460)))
        | ~ sP950(U_13457,U_13458,U_13455,U_13456,U_13459,U_13460) )
    & ! [U_13457,U_13458,U_13455,U_13456,U_13459,U_13460] :
        ( sP950(U_13457,U_13458,U_13455,U_13456,U_13459,U_13460)
        | ~ class_Orderings_Olinorder(U_13456)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_13456) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP949,sP950])],[f_3510_3]) ).

cnf(f_3510_5,plain,
    ( sP950(U_13457,U_13458,U_13455,U_13456,U_13459,U_13460)
    | ~ class_Orderings_Olinorder(U_13456)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_13456) ),
    inference(clausify,[status(thm)],[f_3510_4]) ).

cnf(f_3510_6,plain,
    ( sP949(U_13457,U_13458,U_13456,U_13459,U_13460)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13456),U_13457),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13458,U_13456),U_13459),U_13460)))
    | ~ sP950(U_13457,U_13458,U_13455,U_13456,U_13459,U_13460) ),
    inference(clausify,[status(thm)],[f_3510_4]) ).

cnf(f_3510_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13456),U_13457),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13458,U_13456),U_13459),U_13460)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13456),U_13457),hAPP(U_13460,U_13455)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13458),U_13455),U_13459))
    | ~ sP950(U_13457,U_13458,U_13455,U_13456,U_13459,U_13460) ),
    inference(clausify,[status(thm)],[f_3510_4]) ).

cnf(f_3510_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13458),sK294(U_13460,U_13459,U_13458,U_13457,U_13456)),U_13459))
    | ~ sP949(U_13457,U_13458,U_13456,U_13459,U_13460) ),
    inference(clausify,[status(thm)],[f_3510_4]) ).

cnf(f_3510_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_13456),U_13457),hAPP(U_13460,sK294(U_13460,U_13459,U_13458,U_13457,U_13456))))
    | ~ sP949(U_13457,U_13458,U_13456,U_13459,U_13460) ),
    inference(clausify,[status(thm)],[f_3510_4]) ).

fof(f_3511_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_3511_2,plain,
    ! [U_13467,U_13466,U_13465,U_13464,U_13463] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_13463),U_13464),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13465,tc_fun(U_13463,tc_HOL_Obool)),U_13466),U_13467)))
        | ! [U_13462] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_13463),U_13464),hAPP(U_13467,U_13462)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13465),U_13462),U_13466)) ) )
      & ( ? [U_13461] :
            ( hBOOL(hAPP(hAPP(c_member(U_13463),U_13464),hAPP(U_13467,U_13461)))
            & hBOOL(hAPP(hAPP(c_member(U_13465),U_13461),U_13466)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_13463),U_13464),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13465,tc_fun(U_13463,tc_HOL_Obool)),U_13466),U_13467))) ) ),
    inference(variable_rename,[status(thm)],[f_3511_1]) ).

fof(f_3511_3,plain,
    ( ! [U_13477,U_13475,U_13473,U_13471,U_13469] :
        ( hBOOL(hAPP(hAPP(c_member(U_13469),U_13471),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13473,tc_fun(U_13469,tc_HOL_Obool)),U_13475),U_13477)))
        | ! [U_13462] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_13469),U_13471),hAPP(U_13477,U_13462)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13473),U_13462),U_13475)) ) )
    & ! [U_13476,U_13474,U_13472,U_13470,U_13468] :
        ( ? [U_13461] :
            ( hBOOL(hAPP(hAPP(c_member(U_13468),U_13470),hAPP(U_13476,U_13461)))
            & hBOOL(hAPP(hAPP(c_member(U_13472),U_13461),U_13474)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_13468),U_13470),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13472,tc_fun(U_13468,tc_HOL_Obool)),U_13474),U_13476))) ) ),
    inference(miniscope,[status(thm)],[f_3511_2]) ).

fof(f_3511_4,plain,
    ( ! [U_13477,U_13475,U_13473,U_13471,U_13469] :
        ( hBOOL(hAPP(hAPP(c_member(U_13469),U_13471),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13473,tc_fun(U_13469,tc_HOL_Obool)),U_13475),U_13477)))
        | ! [U_13462] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_13469),U_13471),hAPP(U_13477,U_13462)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13473),U_13462),U_13475)) ) )
    & ! [U_13476,U_13474,U_13472,U_13470,U_13468] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_13468),U_13470),hAPP(U_13476,sK295(U_13476,U_13474,U_13472,U_13470,U_13468))))
          & hBOOL(hAPP(hAPP(c_member(U_13472),sK295(U_13476,U_13474,U_13472,U_13470,U_13468)),U_13474)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_13468),U_13470),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13472,tc_fun(U_13468,tc_HOL_Obool)),U_13474),U_13476))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK295]),skolemize(U_13461,sK295(U_13476,U_13474,U_13472,U_13470,U_13468))],[f_3511_3]) ).

fof(f_3511_5,plain,
    ( ! [U_13470,U_13472,U_13468,U_13476,U_13474] :
        ( hBOOL(hAPP(hAPP(c_member(U_13468),U_13470),hAPP(U_13476,sK295(U_13476,U_13474,U_13472,U_13470,U_13468))))
        | ~ sP951(U_13470,U_13472,U_13468,U_13476,U_13474) )
    & ! [U_13470,U_13472,U_13468,U_13476,U_13474] :
        ( hBOOL(hAPP(hAPP(c_member(U_13472),sK295(U_13476,U_13474,U_13472,U_13470,U_13468)),U_13474))
        | ~ sP951(U_13470,U_13472,U_13468,U_13476,U_13474) )
    & ! [U_13462,U_13471,U_13469,U_13475,U_13473,U_13477] :
        ( hBOOL(hAPP(hAPP(c_member(U_13469),U_13471),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13473,tc_fun(U_13469,tc_HOL_Obool)),U_13475),U_13477)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13469),U_13471),hAPP(U_13477,U_13462)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13473),U_13462),U_13475)) )
    & ! [U_13470,U_13472,U_13468,U_13476,U_13474] :
        ( sP951(U_13470,U_13472,U_13468,U_13476,U_13474)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13468),U_13470),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13472,tc_fun(U_13468,tc_HOL_Obool)),U_13474),U_13476))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP951])],[f_3511_4]) ).

cnf(f_3511_6,plain,
    ( sP951(U_13470,U_13472,U_13468,U_13476,U_13474)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13468),U_13470),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13472,tc_fun(U_13468,tc_HOL_Obool)),U_13474),U_13476))) ),
    inference(clausify,[status(thm)],[f_3511_5]) ).

cnf(f_3511_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13469),U_13471),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13473,tc_fun(U_13469,tc_HOL_Obool)),U_13475),U_13477)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13469),U_13471),hAPP(U_13477,U_13462)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13473),U_13462),U_13475)) ),
    inference(clausify,[status(thm)],[f_3511_5]) ).

cnf(f_3511_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13472),sK295(U_13476,U_13474,U_13472,U_13470,U_13468)),U_13474))
    | ~ sP951(U_13470,U_13472,U_13468,U_13476,U_13474) ),
    inference(clausify,[status(thm)],[f_3511_5]) ).

cnf(f_3511_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13468),U_13470),hAPP(U_13476,sK295(U_13476,U_13474,U_13472,U_13470,U_13468))))
    | ~ sP951(U_13470,U_13472,U_13468,U_13476,U_13474) ),
    inference(clausify,[status(thm)],[f_3511_5]) ).

fof(f_3512_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_3512_2,plain,
    ! [U_13481,U_13480,U_13479,U_13478] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13480,U_13478),U_13479),hAPP(c_COMBK(U_13478,U_13480),U_13481)) = U_13481
      | U_13479 = c_Orderings_Obot__class_Obot(tc_fun(U_13480,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_13478) ),
    inference(variable_rename,[status(thm)],[f_3512_1]) ).

fof(f_3512_3,plain,
    ! [U_13479,U_13481,U_13478,U_13480] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13480,U_13478),U_13479),hAPP(c_COMBK(U_13478,U_13480),U_13481)) = U_13481
      | U_13479 = c_Orderings_Obot__class_Obot(tc_fun(U_13480,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_13478) ),
    inference(definitional_conversion,[status(esa)],[f_3512_2]) ).

cnf(f_3512_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13480,U_13478),U_13479),hAPP(c_COMBK(U_13478,U_13480),U_13481)) = U_13481
    | U_13479 = c_Orderings_Obot__class_Obot(tc_fun(U_13480,tc_HOL_Obool))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_13478) ),
    inference(clausify,[status(thm)],[f_3512_3]) ).

fof(f_3513_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_3513_2,plain,
    ! [U_13487,U_13486,U_13485,U_13484] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13484,tc_fun(U_13485,tc_HOL_Obool)),U_13486),U_13487) = c_Orderings_Obot__class_Obot(tc_fun(U_13485,tc_HOL_Obool))
        | ? [U_13483] :
            ( hAPP(U_13487,U_13483) != c_Orderings_Obot__class_Obot(tc_fun(U_13485,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_13484),U_13483),U_13486)) ) )
      & ( ! [U_13482] :
            ( hAPP(U_13487,U_13482) = c_Orderings_Obot__class_Obot(tc_fun(U_13485,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13484),U_13482),U_13486)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13484,tc_fun(U_13485,tc_HOL_Obool)),U_13486),U_13487) != c_Orderings_Obot__class_Obot(tc_fun(U_13485,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3513_1]) ).

fof(f_3513_3,plain,
    ( ! [U_13495,U_13493,U_13491,U_13489] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13489,tc_fun(U_13491,tc_HOL_Obool)),U_13493),U_13495) = c_Orderings_Obot__class_Obot(tc_fun(U_13491,tc_HOL_Obool))
        | ? [U_13483] :
            ( hAPP(U_13495,U_13483) != c_Orderings_Obot__class_Obot(tc_fun(U_13491,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_13489),U_13483),U_13493)) ) )
    & ! [U_13494,U_13492,U_13490,U_13488] :
        ( ! [U_13482] :
            ( hAPP(U_13494,U_13482) = c_Orderings_Obot__class_Obot(tc_fun(U_13490,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13488),U_13482),U_13492)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13488,tc_fun(U_13490,tc_HOL_Obool)),U_13492),U_13494) != c_Orderings_Obot__class_Obot(tc_fun(U_13490,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3513_2]) ).

fof(f_3513_4,plain,
    ( ! [U_13495,U_13493,U_13491,U_13489] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13489,tc_fun(U_13491,tc_HOL_Obool)),U_13493),U_13495) = c_Orderings_Obot__class_Obot(tc_fun(U_13491,tc_HOL_Obool))
        | ( hAPP(U_13495,sK296(U_13495,U_13493,U_13491,U_13489)) != c_Orderings_Obot__class_Obot(tc_fun(U_13491,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_13489),sK296(U_13495,U_13493,U_13491,U_13489)),U_13493)) ) )
    & ! [U_13494,U_13492,U_13490,U_13488] :
        ( ! [U_13482] :
            ( hAPP(U_13494,U_13482) = c_Orderings_Obot__class_Obot(tc_fun(U_13490,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13488),U_13482),U_13492)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13488,tc_fun(U_13490,tc_HOL_Obool)),U_13492),U_13494) != c_Orderings_Obot__class_Obot(tc_fun(U_13490,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK296]),skolemize(U_13483,sK296(U_13495,U_13493,U_13491,U_13489))],[f_3513_3]) ).

fof(f_3513_5,plain,
    ( ! [U_13493,U_13489,U_13491,U_13495] :
        ( hAPP(U_13495,sK296(U_13495,U_13493,U_13491,U_13489)) != c_Orderings_Obot__class_Obot(tc_fun(U_13491,tc_HOL_Obool))
        | ~ sP952(U_13493,U_13489,U_13491,U_13495) )
    & ! [U_13493,U_13489,U_13491,U_13495] :
        ( hBOOL(hAPP(hAPP(c_member(U_13489),sK296(U_13495,U_13493,U_13491,U_13489)),U_13493))
        | ~ sP952(U_13493,U_13489,U_13491,U_13495) )
    & ! [U_13493,U_13489,U_13491,U_13495] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13489,tc_fun(U_13491,tc_HOL_Obool)),U_13493),U_13495) = c_Orderings_Obot__class_Obot(tc_fun(U_13491,tc_HOL_Obool))
        | sP952(U_13493,U_13489,U_13491,U_13495) )
    & ! [U_13490,U_13482,U_13488,U_13494,U_13492] :
        ( hAPP(U_13494,U_13482) = c_Orderings_Obot__class_Obot(tc_fun(U_13490,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13488),U_13482),U_13492))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13488,tc_fun(U_13490,tc_HOL_Obool)),U_13492),U_13494) != c_Orderings_Obot__class_Obot(tc_fun(U_13490,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP952])],[f_3513_4]) ).

cnf(f_3513_6,plain,
    ( hAPP(U_13494,U_13482) = c_Orderings_Obot__class_Obot(tc_fun(U_13490,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13488),U_13482),U_13492))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13488,tc_fun(U_13490,tc_HOL_Obool)),U_13492),U_13494) != c_Orderings_Obot__class_Obot(tc_fun(U_13490,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3513_5]) ).

cnf(f_3513_7,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13489,tc_fun(U_13491,tc_HOL_Obool)),U_13493),U_13495) = c_Orderings_Obot__class_Obot(tc_fun(U_13491,tc_HOL_Obool))
    | sP952(U_13493,U_13489,U_13491,U_13495) ),
    inference(clausify,[status(thm)],[f_3513_5]) ).

cnf(f_3513_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13489),sK296(U_13495,U_13493,U_13491,U_13489)),U_13493))
    | ~ sP952(U_13493,U_13489,U_13491,U_13495) ),
    inference(clausify,[status(thm)],[f_3513_5]) ).

cnf(f_3513_9,plain,
    ( hAPP(U_13495,sK296(U_13495,U_13493,U_13491,U_13489)) != c_Orderings_Obot__class_Obot(tc_fun(U_13491,tc_HOL_Obool))
    | ~ sP952(U_13493,U_13489,U_13491,U_13495) ),
    inference(clausify,[status(thm)],[f_3513_5]) ).

fof(f_3514_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_3514_2,plain,
    ! [U_13499,U_13498,U_13497,U_13496] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13497,tc_fun(U_13498,tc_HOL_Obool)),U_13496),hAPP(c_COMBK(tc_fun(U_13498,tc_HOL_Obool),U_13497),U_13499)) = U_13499
        | U_13496 = c_Orderings_Obot__class_Obot(tc_fun(U_13497,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13497,tc_fun(U_13498,tc_HOL_Obool)),U_13496),hAPP(c_COMBK(tc_fun(U_13498,tc_HOL_Obool),U_13497),U_13499)) = c_Orderings_Obot__class_Obot(tc_fun(U_13498,tc_HOL_Obool))
        | U_13496 != c_Orderings_Obot__class_Obot(tc_fun(U_13497,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3514_1]) ).

fof(f_3514_3,plain,
    ( ! [U_13507,U_13505,U_13503,U_13501] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13503,tc_fun(U_13505,tc_HOL_Obool)),U_13501),hAPP(c_COMBK(tc_fun(U_13505,tc_HOL_Obool),U_13503),U_13507)) = U_13507
        | U_13501 = c_Orderings_Obot__class_Obot(tc_fun(U_13503,tc_HOL_Obool)) )
    & ! [U_13506,U_13504,U_13502,U_13500] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13502,tc_fun(U_13504,tc_HOL_Obool)),U_13500),hAPP(c_COMBK(tc_fun(U_13504,tc_HOL_Obool),U_13502),U_13506)) = c_Orderings_Obot__class_Obot(tc_fun(U_13504,tc_HOL_Obool))
        | U_13500 != c_Orderings_Obot__class_Obot(tc_fun(U_13502,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3514_2]) ).

fof(f_3514_4,plain,
    ( ! [U_13501,U_13503,U_13505,U_13507] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13503,tc_fun(U_13505,tc_HOL_Obool)),U_13501),hAPP(c_COMBK(tc_fun(U_13505,tc_HOL_Obool),U_13503),U_13507)) = U_13507
        | U_13501 = c_Orderings_Obot__class_Obot(tc_fun(U_13503,tc_HOL_Obool)) )
    & ! [U_13500,U_13504,U_13506,U_13502] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13502,tc_fun(U_13504,tc_HOL_Obool)),U_13500),hAPP(c_COMBK(tc_fun(U_13504,tc_HOL_Obool),U_13502),U_13506)) = c_Orderings_Obot__class_Obot(tc_fun(U_13504,tc_HOL_Obool))
        | U_13500 != c_Orderings_Obot__class_Obot(tc_fun(U_13502,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3514_3]) ).

cnf(f_3514_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13502,tc_fun(U_13504,tc_HOL_Obool)),U_13500),hAPP(c_COMBK(tc_fun(U_13504,tc_HOL_Obool),U_13502),U_13506)) = c_Orderings_Obot__class_Obot(tc_fun(U_13504,tc_HOL_Obool))
    | U_13500 != c_Orderings_Obot__class_Obot(tc_fun(U_13502,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3514_4]) ).

cnf(f_3514_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13503,tc_fun(U_13505,tc_HOL_Obool)),U_13501),hAPP(c_COMBK(tc_fun(U_13505,tc_HOL_Obool),U_13503),U_13507)) = U_13507
    | U_13501 = c_Orderings_Obot__class_Obot(tc_fun(U_13503,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3514_4]) ).

fof(f_3515_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_3515_2,plain,
    ! [U_13510,U_13509,U_13508] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13508,tc_fun(U_13509,tc_HOL_Obool)),U_13510),hAPP(c_COMBK(tc_fun(U_13509,tc_HOL_Obool),U_13508),c_Orderings_Obot__class_Obot(tc_fun(U_13509,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_13509,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3515_1]) ).

fof(f_3515_3,plain,
    ! [U_13508,U_13509,U_13510] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13508,tc_fun(U_13509,tc_HOL_Obool)),U_13510),hAPP(c_COMBK(tc_fun(U_13509,tc_HOL_Obool),U_13508),c_Orderings_Obot__class_Obot(tc_fun(U_13509,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_13509,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3515_2]) ).

cnf(f_3515_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13508,tc_fun(U_13509,tc_HOL_Obool)),U_13510),hAPP(c_COMBK(tc_fun(U_13509,tc_HOL_Obool),U_13508),c_Orderings_Obot__class_Obot(tc_fun(U_13509,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(U_13509,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3515_3]) ).

fof(f_3516_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_3516_2,plain,
    ! [U_13516,U_13515,U_13514,U_13513] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_13513,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13514,tc_fun(U_13513,tc_HOL_Obool)),U_13515),U_13516)
        | ? [U_13512] :
            ( hAPP(U_13516,U_13512) != c_Orderings_Obot__class_Obot(tc_fun(U_13513,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_13514),U_13512),U_13515)) ) )
      & ( ! [U_13511] :
            ( hAPP(U_13516,U_13511) = c_Orderings_Obot__class_Obot(tc_fun(U_13513,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13514),U_13511),U_13515)) )
        | c_Orderings_Obot__class_Obot(tc_fun(U_13513,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13514,tc_fun(U_13513,tc_HOL_Obool)),U_13515),U_13516) ) ),
    inference(variable_rename,[status(thm)],[f_3516_1]) ).

fof(f_3516_3,plain,
    ( ! [U_13524,U_13522,U_13520,U_13518] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_13518,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13520,tc_fun(U_13518,tc_HOL_Obool)),U_13522),U_13524)
        | ? [U_13512] :
            ( hAPP(U_13524,U_13512) != c_Orderings_Obot__class_Obot(tc_fun(U_13518,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_13520),U_13512),U_13522)) ) )
    & ! [U_13523,U_13521,U_13519,U_13517] :
        ( ! [U_13511] :
            ( hAPP(U_13523,U_13511) = c_Orderings_Obot__class_Obot(tc_fun(U_13517,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13519),U_13511),U_13521)) )
        | c_Orderings_Obot__class_Obot(tc_fun(U_13517,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13519,tc_fun(U_13517,tc_HOL_Obool)),U_13521),U_13523) ) ),
    inference(miniscope,[status(thm)],[f_3516_2]) ).

fof(f_3516_4,plain,
    ( ! [U_13524,U_13522,U_13520,U_13518] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_13518,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13520,tc_fun(U_13518,tc_HOL_Obool)),U_13522),U_13524)
        | ( hAPP(U_13524,sK297(U_13524,U_13522,U_13520,U_13518)) != c_Orderings_Obot__class_Obot(tc_fun(U_13518,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_13520),sK297(U_13524,U_13522,U_13520,U_13518)),U_13522)) ) )
    & ! [U_13523,U_13521,U_13519,U_13517] :
        ( ! [U_13511] :
            ( hAPP(U_13523,U_13511) = c_Orderings_Obot__class_Obot(tc_fun(U_13517,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13519),U_13511),U_13521)) )
        | c_Orderings_Obot__class_Obot(tc_fun(U_13517,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13519,tc_fun(U_13517,tc_HOL_Obool)),U_13521),U_13523) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK297]),skolemize(U_13512,sK297(U_13524,U_13522,U_13520,U_13518))],[f_3516_3]) ).

fof(f_3516_5,plain,
    ( ! [U_13518,U_13522,U_13524,U_13520] :
        ( hAPP(U_13524,sK297(U_13524,U_13522,U_13520,U_13518)) != c_Orderings_Obot__class_Obot(tc_fun(U_13518,tc_HOL_Obool))
        | ~ sP953(U_13518,U_13522,U_13524,U_13520) )
    & ! [U_13518,U_13522,U_13524,U_13520] :
        ( hBOOL(hAPP(hAPP(c_member(U_13520),sK297(U_13524,U_13522,U_13520,U_13518)),U_13522))
        | ~ sP953(U_13518,U_13522,U_13524,U_13520) )
    & ! [U_13518,U_13522,U_13524,U_13520] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_13518,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13520,tc_fun(U_13518,tc_HOL_Obool)),U_13522),U_13524)
        | sP953(U_13518,U_13522,U_13524,U_13520) )
    & ! [U_13519,U_13523,U_13511,U_13517,U_13521] :
        ( hAPP(U_13523,U_13511) = c_Orderings_Obot__class_Obot(tc_fun(U_13517,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13519),U_13511),U_13521))
        | c_Orderings_Obot__class_Obot(tc_fun(U_13517,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13519,tc_fun(U_13517,tc_HOL_Obool)),U_13521),U_13523) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP953])],[f_3516_4]) ).

cnf(f_3516_6,plain,
    ( hAPP(U_13523,U_13511) = c_Orderings_Obot__class_Obot(tc_fun(U_13517,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13519),U_13511),U_13521))
    | c_Orderings_Obot__class_Obot(tc_fun(U_13517,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13519,tc_fun(U_13517,tc_HOL_Obool)),U_13521),U_13523) ),
    inference(clausify,[status(thm)],[f_3516_5]) ).

cnf(f_3516_7,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_13518,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13520,tc_fun(U_13518,tc_HOL_Obool)),U_13522),U_13524)
    | sP953(U_13518,U_13522,U_13524,U_13520) ),
    inference(clausify,[status(thm)],[f_3516_5]) ).

cnf(f_3516_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13520),sK297(U_13524,U_13522,U_13520,U_13518)),U_13522))
    | ~ sP953(U_13518,U_13522,U_13524,U_13520) ),
    inference(clausify,[status(thm)],[f_3516_5]) ).

cnf(f_3516_9,plain,
    ( hAPP(U_13524,sK297(U_13524,U_13522,U_13520,U_13518)) != c_Orderings_Obot__class_Obot(tc_fun(U_13518,tc_HOL_Obool))
    | ~ sP953(U_13518,U_13522,U_13524,U_13520) ),
    inference(clausify,[status(thm)],[f_3516_5]) ).

fof(f_3517_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_3517_2,plain,
    ! [U_13531,U_13530,U_13529,U_13528,U_13527] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13527,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13528,tc_fun(U_13527,tc_HOL_Obool)),U_13529),U_13530)),U_13531))
        | ? [U_13526] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13527,tc_HOL_Obool)),hAPP(U_13530,U_13526)),U_13531))
            & hBOOL(hAPP(hAPP(c_member(U_13528),U_13526),U_13529)) ) )
      & ( ! [U_13525] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13527,tc_HOL_Obool)),hAPP(U_13530,U_13525)),U_13531))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13528),U_13525),U_13529)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13527,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13528,tc_fun(U_13527,tc_HOL_Obool)),U_13529),U_13530)),U_13531)) ) ),
    inference(variable_rename,[status(thm)],[f_3517_1]) ).

fof(f_3517_3,plain,
    ( ! [U_13541,U_13539,U_13537,U_13535,U_13533] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13533,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13535,tc_fun(U_13533,tc_HOL_Obool)),U_13537),U_13539)),U_13541))
        | ? [U_13526] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13533,tc_HOL_Obool)),hAPP(U_13539,U_13526)),U_13541))
            & hBOOL(hAPP(hAPP(c_member(U_13535),U_13526),U_13537)) ) )
    & ! [U_13540,U_13538,U_13536,U_13534,U_13532] :
        ( ! [U_13525] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13532,tc_HOL_Obool)),hAPP(U_13538,U_13525)),U_13540))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13534),U_13525),U_13536)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13532,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13534,tc_fun(U_13532,tc_HOL_Obool)),U_13536),U_13538)),U_13540)) ) ),
    inference(miniscope,[status(thm)],[f_3517_2]) ).

fof(f_3517_4,plain,
    ( ! [U_13541,U_13539,U_13537,U_13535,U_13533] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13533,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13535,tc_fun(U_13533,tc_HOL_Obool)),U_13537),U_13539)),U_13541))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13533,tc_HOL_Obool)),hAPP(U_13539,sK298(U_13541,U_13539,U_13537,U_13535,U_13533))),U_13541))
          & hBOOL(hAPP(hAPP(c_member(U_13535),sK298(U_13541,U_13539,U_13537,U_13535,U_13533)),U_13537)) ) )
    & ! [U_13540,U_13538,U_13536,U_13534,U_13532] :
        ( ! [U_13525] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13532,tc_HOL_Obool)),hAPP(U_13538,U_13525)),U_13540))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13534),U_13525),U_13536)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13532,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13534,tc_fun(U_13532,tc_HOL_Obool)),U_13536),U_13538)),U_13540)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK298]),skolemize(U_13526,sK298(U_13541,U_13539,U_13537,U_13535,U_13533))],[f_3517_3]) ).

fof(f_3517_5,plain,
    ( ! [U_13537,U_13533,U_13535,U_13539,U_13541] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13533,tc_HOL_Obool)),hAPP(U_13539,sK298(U_13541,U_13539,U_13537,U_13535,U_13533))),U_13541))
        | ~ sP954(U_13537,U_13533,U_13535,U_13539,U_13541) )
    & ! [U_13537,U_13533,U_13535,U_13539,U_13541] :
        ( hBOOL(hAPP(hAPP(c_member(U_13535),sK298(U_13541,U_13539,U_13537,U_13535,U_13533)),U_13537))
        | ~ sP954(U_13537,U_13533,U_13535,U_13539,U_13541) )
    & ! [U_13537,U_13533,U_13535,U_13539,U_13541] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13533,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13535,tc_fun(U_13533,tc_HOL_Obool)),U_13537),U_13539)),U_13541))
        | sP954(U_13537,U_13533,U_13535,U_13539,U_13541) )
    & ! [U_13534,U_13525,U_13532,U_13538,U_13540,U_13536] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13532,tc_HOL_Obool)),hAPP(U_13538,U_13525)),U_13540))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13534),U_13525),U_13536))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13532,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13534,tc_fun(U_13532,tc_HOL_Obool)),U_13536),U_13538)),U_13540)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP954])],[f_3517_4]) ).

cnf(f_3517_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13532,tc_HOL_Obool)),hAPP(U_13538,U_13525)),U_13540))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13534),U_13525),U_13536))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13532,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13534,tc_fun(U_13532,tc_HOL_Obool)),U_13536),U_13538)),U_13540)) ),
    inference(clausify,[status(thm)],[f_3517_5]) ).

cnf(f_3517_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13533,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13535,tc_fun(U_13533,tc_HOL_Obool)),U_13537),U_13539)),U_13541))
    | sP954(U_13537,U_13533,U_13535,U_13539,U_13541) ),
    inference(clausify,[status(thm)],[f_3517_5]) ).

cnf(f_3517_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13535),sK298(U_13541,U_13539,U_13537,U_13535,U_13533)),U_13537))
    | ~ sP954(U_13537,U_13533,U_13535,U_13539,U_13541) ),
    inference(clausify,[status(thm)],[f_3517_5]) ).

cnf(f_3517_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13533,tc_HOL_Obool)),hAPP(U_13539,sK298(U_13541,U_13539,U_13537,U_13535,U_13533))),U_13541))
    | ~ sP954(U_13537,U_13533,U_13535,U_13539,U_13541) ),
    inference(clausify,[status(thm)],[f_3517_5]) ).

fof(f_3518_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_3518_2,plain,
    ! [U_13547,U_13546,U_13545,U_13544,U_13543,U_13542] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13542,tc_fun(U_13543,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13544,U_13542,U_13545),U_13546)),U_13547) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13544,tc_fun(U_13543,tc_HOL_Obool)),U_13546),hAPP(hAPP(c_COMBB(U_13542,tc_fun(U_13543,tc_HOL_Obool),U_13544),U_13547),U_13545)),
    inference(variable_rename,[status(thm)],[f_3518_1]) ).

fof(f_3518_3,plain,
    ! [U_13543,U_13542,U_13544,U_13545,U_13546,U_13547] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13542,tc_fun(U_13543,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13544,U_13542,U_13545),U_13546)),U_13547) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13544,tc_fun(U_13543,tc_HOL_Obool)),U_13546),hAPP(hAPP(c_COMBB(U_13542,tc_fun(U_13543,tc_HOL_Obool),U_13544),U_13547),U_13545)),
    inference(definitional_conversion,[status(esa)],[f_3518_2]) ).

cnf(f_3518_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13542,tc_fun(U_13543,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13544,U_13542,U_13545),U_13546)),U_13547) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13544,tc_fun(U_13543,tc_HOL_Obool)),U_13546),hAPP(hAPP(c_COMBB(U_13542,tc_fun(U_13543,tc_HOL_Obool),U_13544),U_13547),U_13545)),
    inference(clausify,[status(thm)],[f_3518_3]) ).

fof(f_3519_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_3519_2,plain,
    ! [U_13553,U_13552,U_13551,U_13550,U_13549,U_13548] : hAPP(c_Set_Oimage(U_13548,U_13549,U_13550),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13551,tc_fun(U_13548,tc_HOL_Obool)),U_13552),U_13553)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13551,tc_fun(U_13549,tc_HOL_Obool)),U_13552),hAPP(hAPP(c_COMBB(tc_fun(U_13548,tc_HOL_Obool),tc_fun(U_13549,tc_HOL_Obool),U_13551),c_Set_Oimage(U_13548,U_13549,U_13550)),U_13553)),
    inference(variable_rename,[status(thm)],[f_3519_1]) ).

fof(f_3519_3,plain,
    ! [U_13548,U_13549,U_13550,U_13551,U_13552,U_13553] : hAPP(c_Set_Oimage(U_13548,U_13549,U_13550),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13551,tc_fun(U_13548,tc_HOL_Obool)),U_13552),U_13553)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13551,tc_fun(U_13549,tc_HOL_Obool)),U_13552),hAPP(hAPP(c_COMBB(tc_fun(U_13548,tc_HOL_Obool),tc_fun(U_13549,tc_HOL_Obool),U_13551),c_Set_Oimage(U_13548,U_13549,U_13550)),U_13553)),
    inference(definitional_conversion,[status(esa)],[f_3519_2]) ).

cnf(f_3519_4,plain,
    hAPP(c_Set_Oimage(U_13548,U_13549,U_13550),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13551,tc_fun(U_13548,tc_HOL_Obool)),U_13552),U_13553)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13551,tc_fun(U_13549,tc_HOL_Obool)),U_13552),hAPP(hAPP(c_COMBB(tc_fun(U_13548,tc_HOL_Obool),tc_fun(U_13549,tc_HOL_Obool),U_13551),c_Set_Oimage(U_13548,U_13549,U_13550)),U_13553)),
    inference(clausify,[status(thm)],[f_3519_3]) ).

fof(f_3520_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_3520_2,plain,
    ! [U_13559,U_13558,U_13557,U_13556,U_13555,U_13554] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13554,tc_fun(U_13555,tc_HOL_Obool)),U_13556),hAPP(hAPP(c_COMBB(U_13557,tc_fun(U_13555,tc_HOL_Obool),U_13554),U_13558),U_13559)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13557,tc_fun(U_13555,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13554,U_13557,U_13559),U_13556)),U_13558),
    inference(variable_rename,[status(thm)],[f_3520_1]) ).

fof(f_3520_3,plain,
    ! [U_13554,U_13555,U_13556,U_13557,U_13558,U_13559] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13554,tc_fun(U_13555,tc_HOL_Obool)),U_13556),hAPP(hAPP(c_COMBB(U_13557,tc_fun(U_13555,tc_HOL_Obool),U_13554),U_13558),U_13559)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13557,tc_fun(U_13555,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13554,U_13557,U_13559),U_13556)),U_13558),
    inference(definitional_conversion,[status(esa)],[f_3520_2]) ).

cnf(f_3520_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13554,tc_fun(U_13555,tc_HOL_Obool)),U_13556),hAPP(hAPP(c_COMBB(U_13557,tc_fun(U_13555,tc_HOL_Obool),U_13554),U_13558),U_13559)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13557,tc_fun(U_13555,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_13554,U_13557,U_13559),U_13556)),U_13558),
    inference(clausify,[status(thm)],[f_3520_3]) ).

fof(f_3521_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_3521_2,plain,
    ! [U_13564,U_13563,U_13562,U_13561,U_13560] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13560,tc_fun(U_13561,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13560,tc_HOL_Obool)),U_13562),U_13563)),U_13564) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13561,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13560,tc_fun(U_13561,tc_HOL_Obool)),U_13562),U_13564)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13560,tc_fun(U_13561,tc_HOL_Obool)),U_13563),U_13564)),
    inference(variable_rename,[status(thm)],[f_3521_1]) ).

fof(f_3521_3,plain,
    ! [U_13560,U_13561,U_13562,U_13563,U_13564] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13560,tc_fun(U_13561,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13560,tc_HOL_Obool)),U_13562),U_13563)),U_13564) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13561,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13560,tc_fun(U_13561,tc_HOL_Obool)),U_13562),U_13564)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13560,tc_fun(U_13561,tc_HOL_Obool)),U_13563),U_13564)),
    inference(definitional_conversion,[status(esa)],[f_3521_2]) ).

cnf(f_3521_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13560,tc_fun(U_13561,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13560,tc_HOL_Obool)),U_13562),U_13563)),U_13564) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13561,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13560,tc_fun(U_13561,tc_HOL_Obool)),U_13562),U_13564)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13560,tc_fun(U_13561,tc_HOL_Obool)),U_13563),U_13564)),
    inference(clausify,[status(thm)],[f_3521_3]) ).

fof(f_3522_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_3522_2,plain,
    ! [U_13569,U_13568,U_13567,U_13566,U_13565] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13565,tc_fun(U_13566,tc_HOL_Obool)),U_13567),hAPP(hAPP(c_COMBS(U_13565,tc_fun(U_13566,tc_HOL_Obool),tc_fun(U_13566,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13566,tc_HOL_Obool),tc_fun(tc_fun(U_13566,tc_HOL_Obool),tc_fun(U_13566,tc_HOL_Obool)),U_13565),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13566,tc_HOL_Obool))),U_13568)),U_13569)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13566,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13565,tc_fun(U_13566,tc_HOL_Obool)),U_13567),U_13568)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13565,tc_fun(U_13566,tc_HOL_Obool)),U_13567),U_13569)),
    inference(variable_rename,[status(thm)],[f_3522_1]) ).

fof(f_3522_3,plain,
    ! [U_13565,U_13566,U_13567,U_13568,U_13569] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13565,tc_fun(U_13566,tc_HOL_Obool)),U_13567),hAPP(hAPP(c_COMBS(U_13565,tc_fun(U_13566,tc_HOL_Obool),tc_fun(U_13566,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13566,tc_HOL_Obool),tc_fun(tc_fun(U_13566,tc_HOL_Obool),tc_fun(U_13566,tc_HOL_Obool)),U_13565),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13566,tc_HOL_Obool))),U_13568)),U_13569)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13566,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13565,tc_fun(U_13566,tc_HOL_Obool)),U_13567),U_13568)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13565,tc_fun(U_13566,tc_HOL_Obool)),U_13567),U_13569)),
    inference(definitional_conversion,[status(esa)],[f_3522_2]) ).

cnf(f_3522_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13565,tc_fun(U_13566,tc_HOL_Obool)),U_13567),hAPP(hAPP(c_COMBS(U_13565,tc_fun(U_13566,tc_HOL_Obool),tc_fun(U_13566,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13566,tc_HOL_Obool),tc_fun(tc_fun(U_13566,tc_HOL_Obool),tc_fun(U_13566,tc_HOL_Obool)),U_13565),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13566,tc_HOL_Obool))),U_13568)),U_13569)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13566,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13565,tc_fun(U_13566,tc_HOL_Obool)),U_13567),U_13568)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13565,tc_fun(U_13566,tc_HOL_Obool)),U_13567),U_13569)),
    inference(clausify,[status(thm)],[f_3522_3]) ).

fof(f_3523_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_3523_2,plain,
    ! [U_13574,U_13573,U_13572,U_13571,U_13570] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13570,tc_fun(U_13571,tc_HOL_Obool)),U_13572),hAPP(hAPP(c_COMBB(tc_fun(U_13571,tc_HOL_Obool),tc_fun(U_13571,tc_HOL_Obool),U_13570),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13571,tc_HOL_Obool)),U_13573)),U_13574)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13571,tc_HOL_Obool)),U_13573),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13570,tc_fun(U_13571,tc_HOL_Obool)),U_13572),U_13574)),
    inference(variable_rename,[status(thm)],[f_3523_1]) ).

fof(f_3523_3,plain,
    ! [U_13570,U_13571,U_13572,U_13573,U_13574] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13570,tc_fun(U_13571,tc_HOL_Obool)),U_13572),hAPP(hAPP(c_COMBB(tc_fun(U_13571,tc_HOL_Obool),tc_fun(U_13571,tc_HOL_Obool),U_13570),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13571,tc_HOL_Obool)),U_13573)),U_13574)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13571,tc_HOL_Obool)),U_13573),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13570,tc_fun(U_13571,tc_HOL_Obool)),U_13572),U_13574)),
    inference(definitional_conversion,[status(esa)],[f_3523_2]) ).

cnf(f_3523_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13570,tc_fun(U_13571,tc_HOL_Obool)),U_13572),hAPP(hAPP(c_COMBB(tc_fun(U_13571,tc_HOL_Obool),tc_fun(U_13571,tc_HOL_Obool),U_13570),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13571,tc_HOL_Obool)),U_13573)),U_13574)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13571,tc_HOL_Obool)),U_13573),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13570,tc_fun(U_13571,tc_HOL_Obool)),U_13572),U_13574)),
    inference(clausify,[status(thm)],[f_3523_3]) ).

fof(f_3524_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_3524_2,plain,
    ! [U_13579,U_13578,U_13577,U_13576,U_13575] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13575,tc_fun(U_13576,tc_HOL_Obool)),U_13577),hAPP(hAPP(c_COMBC(U_13575,tc_fun(U_13576,tc_HOL_Obool),tc_fun(U_13576,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13576,tc_HOL_Obool),tc_fun(tc_fun(U_13576,tc_HOL_Obool),tc_fun(U_13576,tc_HOL_Obool)),U_13575),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13576,tc_HOL_Obool))),U_13578)),U_13579)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13576,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13575,tc_fun(U_13576,tc_HOL_Obool)),U_13577),U_13578)),U_13579),
    inference(variable_rename,[status(thm)],[f_3524_1]) ).

fof(f_3524_3,plain,
    ! [U_13575,U_13576,U_13577,U_13578,U_13579] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13575,tc_fun(U_13576,tc_HOL_Obool)),U_13577),hAPP(hAPP(c_COMBC(U_13575,tc_fun(U_13576,tc_HOL_Obool),tc_fun(U_13576,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13576,tc_HOL_Obool),tc_fun(tc_fun(U_13576,tc_HOL_Obool),tc_fun(U_13576,tc_HOL_Obool)),U_13575),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13576,tc_HOL_Obool))),U_13578)),U_13579)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13576,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13575,tc_fun(U_13576,tc_HOL_Obool)),U_13577),U_13578)),U_13579),
    inference(definitional_conversion,[status(esa)],[f_3524_2]) ).

cnf(f_3524_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13575,tc_fun(U_13576,tc_HOL_Obool)),U_13577),hAPP(hAPP(c_COMBC(U_13575,tc_fun(U_13576,tc_HOL_Obool),tc_fun(U_13576,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13576,tc_HOL_Obool),tc_fun(tc_fun(U_13576,tc_HOL_Obool),tc_fun(U_13576,tc_HOL_Obool)),U_13575),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13576,tc_HOL_Obool))),U_13578)),U_13579)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13576,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13575,tc_fun(U_13576,tc_HOL_Obool)),U_13577),U_13578)),U_13579),
    inference(clausify,[status(thm)],[f_3524_3]) ).

fof(f_3525_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_3525_2,plain,
    ! [U_13584,U_13583,U_13582,U_13581,U_13580] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13580,tc_HOL_Obool)),U_13581),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13582,tc_fun(U_13580,tc_HOL_Obool)),U_13583),U_13584)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13582,tc_fun(U_13580,tc_HOL_Obool)),U_13583),hAPP(hAPP(c_COMBB(tc_fun(U_13580,tc_HOL_Obool),tc_fun(U_13580,tc_HOL_Obool),U_13582),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13580,tc_HOL_Obool)),U_13581)),U_13584)),
    inference(variable_rename,[status(thm)],[f_3525_1]) ).

fof(f_3525_3,plain,
    ! [U_13580,U_13581,U_13582,U_13583,U_13584] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13580,tc_HOL_Obool)),U_13581),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13582,tc_fun(U_13580,tc_HOL_Obool)),U_13583),U_13584)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13582,tc_fun(U_13580,tc_HOL_Obool)),U_13583),hAPP(hAPP(c_COMBB(tc_fun(U_13580,tc_HOL_Obool),tc_fun(U_13580,tc_HOL_Obool),U_13582),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13580,tc_HOL_Obool)),U_13581)),U_13584)),
    inference(definitional_conversion,[status(esa)],[f_3525_2]) ).

cnf(f_3525_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13580,tc_HOL_Obool)),U_13581),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13582,tc_fun(U_13580,tc_HOL_Obool)),U_13583),U_13584)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13582,tc_fun(U_13580,tc_HOL_Obool)),U_13583),hAPP(hAPP(c_COMBB(tc_fun(U_13580,tc_HOL_Obool),tc_fun(U_13580,tc_HOL_Obool),U_13582),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13580,tc_HOL_Obool)),U_13581)),U_13584)),
    inference(clausify,[status(thm)],[f_3525_3]) ).

fof(f_3526_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_3526_2,plain,
    ! [U_13589,U_13588,U_13587,U_13586,U_13585] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13585,tc_HOL_Obool)),U_13586),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13587,tc_fun(U_13585,tc_HOL_Obool)),U_13588),U_13589)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13587,tc_fun(U_13585,tc_HOL_Obool)),U_13588),hAPP(hAPP(c_COMBB(tc_fun(U_13585,tc_HOL_Obool),tc_fun(U_13585,tc_HOL_Obool),U_13587),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13585,tc_HOL_Obool)),U_13586)),U_13589)),
    inference(variable_rename,[status(thm)],[f_3526_1]) ).

fof(f_3526_3,plain,
    ! [U_13585,U_13586,U_13587,U_13588,U_13589] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13585,tc_HOL_Obool)),U_13586),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13587,tc_fun(U_13585,tc_HOL_Obool)),U_13588),U_13589)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13587,tc_fun(U_13585,tc_HOL_Obool)),U_13588),hAPP(hAPP(c_COMBB(tc_fun(U_13585,tc_HOL_Obool),tc_fun(U_13585,tc_HOL_Obool),U_13587),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13585,tc_HOL_Obool)),U_13586)),U_13589)),
    inference(definitional_conversion,[status(esa)],[f_3526_2]) ).

cnf(f_3526_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13585,tc_HOL_Obool)),U_13586),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13587,tc_fun(U_13585,tc_HOL_Obool)),U_13588),U_13589)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13587,tc_fun(U_13585,tc_HOL_Obool)),U_13588),hAPP(hAPP(c_COMBB(tc_fun(U_13585,tc_HOL_Obool),tc_fun(U_13585,tc_HOL_Obool),U_13587),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13585,tc_HOL_Obool)),U_13586)),U_13589)),
    inference(clausify,[status(thm)],[f_3526_3]) ).

fof(f_3527_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_3527_2,plain,
    ! [U_13594,U_13593,U_13592,U_13591,U_13590] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13590,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13591,tc_fun(U_13590,tc_HOL_Obool)),U_13592),U_13593)),U_13594) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13591,tc_fun(U_13590,tc_HOL_Obool)),U_13592),hAPP(hAPP(c_COMBC(U_13591,tc_fun(U_13590,tc_HOL_Obool),tc_fun(U_13590,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13590,tc_HOL_Obool),tc_fun(tc_fun(U_13590,tc_HOL_Obool),tc_fun(U_13590,tc_HOL_Obool)),U_13591),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13590,tc_HOL_Obool))),U_13593)),U_13594)),
    inference(variable_rename,[status(thm)],[f_3527_1]) ).

fof(f_3527_3,plain,
    ! [U_13590,U_13591,U_13592,U_13593,U_13594] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13590,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13591,tc_fun(U_13590,tc_HOL_Obool)),U_13592),U_13593)),U_13594) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13591,tc_fun(U_13590,tc_HOL_Obool)),U_13592),hAPP(hAPP(c_COMBC(U_13591,tc_fun(U_13590,tc_HOL_Obool),tc_fun(U_13590,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13590,tc_HOL_Obool),tc_fun(tc_fun(U_13590,tc_HOL_Obool),tc_fun(U_13590,tc_HOL_Obool)),U_13591),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13590,tc_HOL_Obool))),U_13593)),U_13594)),
    inference(definitional_conversion,[status(esa)],[f_3527_2]) ).

cnf(f_3527_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13590,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13591,tc_fun(U_13590,tc_HOL_Obool)),U_13592),U_13593)),U_13594) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13591,tc_fun(U_13590,tc_HOL_Obool)),U_13592),hAPP(hAPP(c_COMBC(U_13591,tc_fun(U_13590,tc_HOL_Obool),tc_fun(U_13590,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13590,tc_HOL_Obool),tc_fun(tc_fun(U_13590,tc_HOL_Obool),tc_fun(U_13590,tc_HOL_Obool)),U_13591),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13590,tc_HOL_Obool))),U_13593)),U_13594)),
    inference(clausify,[status(thm)],[f_3527_3]) ).

fof(f_3528_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_3528_2,plain,
    ! [U_13601,U_13600,U_13599,U_13598,U_13597,U_13596,U_13595] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13595,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13596,tc_fun(U_13595,tc_HOL_Obool)),U_13597),U_13598)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13599,tc_fun(U_13595,tc_HOL_Obool)),U_13600),U_13601)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13596,tc_fun(U_13595,tc_HOL_Obool)),U_13597),hAPP(hAPP(c_COMBB(tc_fun(U_13599,tc_fun(U_13595,tc_HOL_Obool)),tc_fun(U_13595,tc_HOL_Obool),U_13596),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13599,tc_fun(U_13595,tc_HOL_Obool)),U_13600)),hAPP(hAPP(c_COMBC(U_13596,tc_fun(U_13599,tc_fun(U_13595,tc_HOL_Obool)),tc_fun(U_13599,tc_fun(U_13595,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13595,tc_HOL_Obool),tc_fun(U_13595,tc_HOL_Obool)),tc_fun(tc_fun(U_13599,tc_fun(U_13595,tc_HOL_Obool)),tc_fun(U_13599,tc_fun(U_13595,tc_HOL_Obool))),U_13596),c_COMBB(tc_fun(U_13595,tc_HOL_Obool),tc_fun(U_13595,tc_HOL_Obool),U_13599)),hAPP(hAPP(c_COMBB(tc_fun(U_13595,tc_HOL_Obool),tc_fun(tc_fun(U_13595,tc_HOL_Obool),tc_fun(U_13595,tc_HOL_Obool)),U_13596),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13595,tc_HOL_Obool))),U_13598))),U_13601))),
    inference(variable_rename,[status(thm)],[f_3528_1]) ).

fof(f_3528_3,plain,
    ! [U_13595,U_13596,U_13597,U_13598,U_13599,U_13600,U_13601] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13595,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13596,tc_fun(U_13595,tc_HOL_Obool)),U_13597),U_13598)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13599,tc_fun(U_13595,tc_HOL_Obool)),U_13600),U_13601)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13596,tc_fun(U_13595,tc_HOL_Obool)),U_13597),hAPP(hAPP(c_COMBB(tc_fun(U_13599,tc_fun(U_13595,tc_HOL_Obool)),tc_fun(U_13595,tc_HOL_Obool),U_13596),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13599,tc_fun(U_13595,tc_HOL_Obool)),U_13600)),hAPP(hAPP(c_COMBC(U_13596,tc_fun(U_13599,tc_fun(U_13595,tc_HOL_Obool)),tc_fun(U_13599,tc_fun(U_13595,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13595,tc_HOL_Obool),tc_fun(U_13595,tc_HOL_Obool)),tc_fun(tc_fun(U_13599,tc_fun(U_13595,tc_HOL_Obool)),tc_fun(U_13599,tc_fun(U_13595,tc_HOL_Obool))),U_13596),c_COMBB(tc_fun(U_13595,tc_HOL_Obool),tc_fun(U_13595,tc_HOL_Obool),U_13599)),hAPP(hAPP(c_COMBB(tc_fun(U_13595,tc_HOL_Obool),tc_fun(tc_fun(U_13595,tc_HOL_Obool),tc_fun(U_13595,tc_HOL_Obool)),U_13596),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13595,tc_HOL_Obool))),U_13598))),U_13601))),
    inference(definitional_conversion,[status(esa)],[f_3528_2]) ).

cnf(f_3528_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13595,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13596,tc_fun(U_13595,tc_HOL_Obool)),U_13597),U_13598)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13599,tc_fun(U_13595,tc_HOL_Obool)),U_13600),U_13601)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13596,tc_fun(U_13595,tc_HOL_Obool)),U_13597),hAPP(hAPP(c_COMBB(tc_fun(U_13599,tc_fun(U_13595,tc_HOL_Obool)),tc_fun(U_13595,tc_HOL_Obool),U_13596),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13599,tc_fun(U_13595,tc_HOL_Obool)),U_13600)),hAPP(hAPP(c_COMBC(U_13596,tc_fun(U_13599,tc_fun(U_13595,tc_HOL_Obool)),tc_fun(U_13599,tc_fun(U_13595,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_13595,tc_HOL_Obool),tc_fun(U_13595,tc_HOL_Obool)),tc_fun(tc_fun(U_13599,tc_fun(U_13595,tc_HOL_Obool)),tc_fun(U_13599,tc_fun(U_13595,tc_HOL_Obool))),U_13596),c_COMBB(tc_fun(U_13595,tc_HOL_Obool),tc_fun(U_13595,tc_HOL_Obool),U_13599)),hAPP(hAPP(c_COMBB(tc_fun(U_13595,tc_HOL_Obool),tc_fun(tc_fun(U_13595,tc_HOL_Obool),tc_fun(U_13595,tc_HOL_Obool)),U_13596),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13595,tc_HOL_Obool))),U_13598))),U_13601))),
    inference(clausify,[status(thm)],[f_3528_3]) ).

fof(f_3529_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_3529_2,plain,
    ! [U_13607,U_13606,U_13605,U_13604,U_13603,U_13602] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13603,tc_fun(U_13604,U_13602)),U_13605),U_13606),U_13607) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13603,U_13602),U_13605),hAPP(hAPP(c_COMBC(U_13603,U_13604,U_13602),U_13606),U_13607))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_13602) ),
    inference(variable_rename,[status(thm)],[f_3529_1]) ).

fof(f_3529_3,plain,
    ! [U_13602,U_13603,U_13604,U_13605,U_13606,U_13607] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13603,tc_fun(U_13604,U_13602)),U_13605),U_13606),U_13607) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13603,U_13602),U_13605),hAPP(hAPP(c_COMBC(U_13603,U_13604,U_13602),U_13606),U_13607))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_13602) ),
    inference(definitional_conversion,[status(esa)],[f_3529_2]) ).

cnf(f_3529_4,plain,
    ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13603,tc_fun(U_13604,U_13602)),U_13605),U_13606),U_13607) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13603,U_13602),U_13605),hAPP(hAPP(c_COMBC(U_13603,U_13604,U_13602),U_13606),U_13607))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_13602) ),
    inference(clausify,[status(thm)],[f_3529_3]) ).

fof(f_3530_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_3530_2,plain,
    ! [U_13612,U_13611,U_13610,U_13609,U_13608] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13608,tc_fun(U_13609,tc_HOL_Obool)),U_13610),hAPP(hAPP(c_COMBC(U_13608,tc_fun(U_13609,tc_HOL_Obool),tc_fun(U_13609,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13609,tc_HOL_Obool),tc_fun(tc_fun(U_13609,tc_HOL_Obool),tc_fun(U_13609,tc_HOL_Obool)),U_13608),c_Groups_Ominus__class_Ominus(tc_fun(U_13609,tc_HOL_Obool))),U_13611)),U_13612)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13609,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13608,tc_fun(U_13609,tc_HOL_Obool)),U_13610),U_13611)),U_13612),
    inference(variable_rename,[status(thm)],[f_3530_1]) ).

fof(f_3530_3,plain,
    ! [U_13608,U_13609,U_13610,U_13611,U_13612] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13608,tc_fun(U_13609,tc_HOL_Obool)),U_13610),hAPP(hAPP(c_COMBC(U_13608,tc_fun(U_13609,tc_HOL_Obool),tc_fun(U_13609,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13609,tc_HOL_Obool),tc_fun(tc_fun(U_13609,tc_HOL_Obool),tc_fun(U_13609,tc_HOL_Obool)),U_13608),c_Groups_Ominus__class_Ominus(tc_fun(U_13609,tc_HOL_Obool))),U_13611)),U_13612)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13609,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13608,tc_fun(U_13609,tc_HOL_Obool)),U_13610),U_13611)),U_13612),
    inference(definitional_conversion,[status(esa)],[f_3530_2]) ).

cnf(f_3530_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13608,tc_fun(U_13609,tc_HOL_Obool)),U_13610),hAPP(hAPP(c_COMBC(U_13608,tc_fun(U_13609,tc_HOL_Obool),tc_fun(U_13609,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13609,tc_HOL_Obool),tc_fun(tc_fun(U_13609,tc_HOL_Obool),tc_fun(U_13609,tc_HOL_Obool)),U_13608),c_Groups_Ominus__class_Ominus(tc_fun(U_13609,tc_HOL_Obool))),U_13611)),U_13612)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13609,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13608,tc_fun(U_13609,tc_HOL_Obool)),U_13610),U_13611)),U_13612),
    inference(clausify,[status(thm)],[f_3530_3]) ).

fof(f_3531_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_3531_2,plain,
    ! [U_13617,U_13616,U_13615,U_13614,U_13613] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13613,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13614,tc_fun(U_13613,tc_HOL_Obool)),U_13615),U_13616)),U_13617) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13614,tc_fun(U_13613,tc_HOL_Obool)),U_13615),hAPP(hAPP(c_COMBC(U_13614,tc_fun(U_13613,tc_HOL_Obool),tc_fun(U_13613,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13613,tc_HOL_Obool),tc_fun(tc_fun(U_13613,tc_HOL_Obool),tc_fun(U_13613,tc_HOL_Obool)),U_13614),c_Groups_Ominus__class_Ominus(tc_fun(U_13613,tc_HOL_Obool))),U_13616)),U_13617)),
    inference(variable_rename,[status(thm)],[f_3531_1]) ).

fof(f_3531_3,plain,
    ! [U_13613,U_13614,U_13615,U_13616,U_13617] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13613,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13614,tc_fun(U_13613,tc_HOL_Obool)),U_13615),U_13616)),U_13617) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13614,tc_fun(U_13613,tc_HOL_Obool)),U_13615),hAPP(hAPP(c_COMBC(U_13614,tc_fun(U_13613,tc_HOL_Obool),tc_fun(U_13613,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13613,tc_HOL_Obool),tc_fun(tc_fun(U_13613,tc_HOL_Obool),tc_fun(U_13613,tc_HOL_Obool)),U_13614),c_Groups_Ominus__class_Ominus(tc_fun(U_13613,tc_HOL_Obool))),U_13616)),U_13617)),
    inference(definitional_conversion,[status(esa)],[f_3531_2]) ).

cnf(f_3531_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13613,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13614,tc_fun(U_13613,tc_HOL_Obool)),U_13615),U_13616)),U_13617) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13614,tc_fun(U_13613,tc_HOL_Obool)),U_13615),hAPP(hAPP(c_COMBC(U_13614,tc_fun(U_13613,tc_HOL_Obool),tc_fun(U_13613,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13613,tc_HOL_Obool),tc_fun(tc_fun(U_13613,tc_HOL_Obool),tc_fun(U_13613,tc_HOL_Obool)),U_13614),c_Groups_Ominus__class_Ominus(tc_fun(U_13613,tc_HOL_Obool))),U_13616)),U_13617)),
    inference(clausify,[status(thm)],[f_3531_3]) ).

fof(f_3532_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_3532_2,plain,
    ! [U_13622,U_13621,U_13620,U_13619,U_13618] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13618),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13619,U_13618),U_13620),U_13622)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13619,U_13618),U_13621),U_13622)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13619,tc_HOL_Obool)),U_13620),U_13621))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_13618) ),
    inference(variable_rename,[status(thm)],[f_3532_1]) ).

fof(f_3532_3,plain,
    ! [U_13618,U_13619,U_13620,U_13621,U_13622] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13618),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13619,U_13618),U_13620),U_13622)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13619,U_13618),U_13621),U_13622)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13619,tc_HOL_Obool)),U_13620),U_13621))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_13618) ),
    inference(definitional_conversion,[status(esa)],[f_3532_2]) ).

cnf(f_3532_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13618),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13619,U_13618),U_13620),U_13622)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13619,U_13618),U_13621),U_13622)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13619,tc_HOL_Obool)),U_13620),U_13621))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_13618) ),
    inference(clausify,[status(thm)],[f_3532_3]) ).

fof(f_3533_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_3533_2,plain,
    ! [U_13627,U_13626,U_13625,U_13624,U_13623] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13623),hAPP(U_13627,U_13625)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13624,U_13623),U_13626),U_13627)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13624),U_13625),U_13626))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_13623) ),
    inference(variable_rename,[status(thm)],[f_3533_1]) ).

fof(f_3533_3,plain,
    ! [U_13624,U_13623,U_13625,U_13626,U_13627] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13623),hAPP(U_13627,U_13625)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13624,U_13623),U_13626),U_13627)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13624),U_13625),U_13626))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_13623) ),
    inference(definitional_conversion,[status(esa)],[f_3533_2]) ).

cnf(f_3533_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13623),hAPP(U_13627,U_13625)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13624,U_13623),U_13626),U_13627)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13624),U_13625),U_13626))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_13623) ),
    inference(clausify,[status(thm)],[f_3533_3]) ).

fof(f_3534_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_3534_2,plain,
    ! [U_13633,U_13632,U_13631,U_13630,U_13629,U_13628] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13628,tc_fun(U_13631,tc_HOL_Obool)),U_13630),hAPP(hAPP(c_COMBB(tc_fun(U_13631,tc_HOL_Obool),tc_fun(U_13631,tc_HOL_Obool),U_13628),hAPP(c_Set_Oinsert(U_13631),U_13632)),U_13633)) = hAPP(hAPP(c_Set_Oinsert(U_13631),U_13632),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13628,tc_fun(U_13631,tc_HOL_Obool)),U_13630),U_13633))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13628),U_13629),U_13630)) ),
    inference(variable_rename,[status(thm)],[f_3534_1]) ).

fof(f_3534_3,plain,
    ! [U_13628,U_13629,U_13630,U_13631,U_13632,U_13633] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13628,tc_fun(U_13631,tc_HOL_Obool)),U_13630),hAPP(hAPP(c_COMBB(tc_fun(U_13631,tc_HOL_Obool),tc_fun(U_13631,tc_HOL_Obool),U_13628),hAPP(c_Set_Oinsert(U_13631),U_13632)),U_13633)) = hAPP(hAPP(c_Set_Oinsert(U_13631),U_13632),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13628,tc_fun(U_13631,tc_HOL_Obool)),U_13630),U_13633))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13628),U_13629),U_13630)) ),
    inference(definitional_conversion,[status(esa)],[f_3534_2]) ).

cnf(f_3534_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13628,tc_fun(U_13631,tc_HOL_Obool)),U_13630),hAPP(hAPP(c_COMBB(tc_fun(U_13631,tc_HOL_Obool),tc_fun(U_13631,tc_HOL_Obool),U_13628),hAPP(c_Set_Oinsert(U_13631),U_13632)),U_13633)) = hAPP(hAPP(c_Set_Oinsert(U_13631),U_13632),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13628,tc_fun(U_13631,tc_HOL_Obool)),U_13630),U_13633))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13628),U_13629),U_13630)) ),
    inference(clausify,[status(thm)],[f_3534_3]) ).

fof(f_3535_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_3535_2,plain,
    ! [U_13638,U_13637,U_13636,U_13635,U_13634] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13637,tc_HOL_Obool)),hAPP(U_13638,U_13635)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13634,tc_fun(U_13637,tc_HOL_Obool)),U_13636),U_13638)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13634),U_13635),U_13636)) ),
    inference(variable_rename,[status(thm)],[f_3535_1]) ).

fof(f_3535_3,plain,
    ! [U_13635,U_13634,U_13636,U_13637,U_13638] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13637,tc_HOL_Obool)),hAPP(U_13638,U_13635)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13634,tc_fun(U_13637,tc_HOL_Obool)),U_13636),U_13638)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13634),U_13635),U_13636)) ),
    inference(definitional_conversion,[status(esa)],[f_3535_2]) ).

cnf(f_3535_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13637,tc_HOL_Obool)),hAPP(U_13638,U_13635)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13634,tc_fun(U_13637,tc_HOL_Obool)),U_13636),U_13638)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13634),U_13635),U_13636)) ),
    inference(clausify,[status(thm)],[f_3535_3]) ).

fof(f_3536_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_3536_2,plain,
    ! [U_13643,U_13642,U_13641,U_13640,U_13639] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13642,tc_HOL_Obool)),hAPP(U_13643,U_13640)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13639,tc_fun(U_13642,tc_HOL_Obool)),U_13641),U_13643)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13639,tc_fun(U_13642,tc_HOL_Obool)),U_13641),U_13643)
      | ~ hBOOL(hAPP(hAPP(c_member(U_13639),U_13640),U_13641)) ),
    inference(variable_rename,[status(thm)],[f_3536_1]) ).

fof(f_3536_3,plain,
    ! [U_13639,U_13640,U_13641,U_13642,U_13643] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13642,tc_HOL_Obool)),hAPP(U_13643,U_13640)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13639,tc_fun(U_13642,tc_HOL_Obool)),U_13641),U_13643)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13639,tc_fun(U_13642,tc_HOL_Obool)),U_13641),U_13643)
      | ~ hBOOL(hAPP(hAPP(c_member(U_13639),U_13640),U_13641)) ),
    inference(definitional_conversion,[status(esa)],[f_3536_2]) ).

cnf(f_3536_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13642,tc_HOL_Obool)),hAPP(U_13643,U_13640)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13639,tc_fun(U_13642,tc_HOL_Obool)),U_13641),U_13643)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13639,tc_fun(U_13642,tc_HOL_Obool)),U_13641),U_13643)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13639),U_13640),U_13641)) ),
    inference(clausify,[status(thm)],[f_3536_3]) ).

fof(f_3537_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_3537_2,plain,
    ! [U_13648,U_13647,U_13646,U_13645,U_13644] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13645,tc_fun(U_13646,tc_HOL_Obool)),U_13644),hAPP(hAPP(c_COMBB(tc_fun(U_13646,tc_HOL_Obool),tc_fun(U_13646,tc_HOL_Obool),U_13645),hAPP(c_Set_Oinsert(U_13646),U_13647)),U_13648)) = hAPP(hAPP(c_Set_Oinsert(U_13646),U_13647),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13645,tc_fun(U_13646,tc_HOL_Obool)),U_13644),U_13648))
        | U_13644 = c_Orderings_Obot__class_Obot(tc_fun(U_13645,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13645,tc_fun(U_13646,tc_HOL_Obool)),U_13644),hAPP(hAPP(c_COMBB(tc_fun(U_13646,tc_HOL_Obool),tc_fun(U_13646,tc_HOL_Obool),U_13645),hAPP(c_Set_Oinsert(U_13646),U_13647)),U_13648)) = c_Orderings_Obot__class_Obot(tc_fun(U_13646,tc_HOL_Obool))
        | U_13644 != c_Orderings_Obot__class_Obot(tc_fun(U_13645,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3537_1]) ).

fof(f_3537_3,plain,
    ( ! [U_13658,U_13656,U_13654,U_13652,U_13650] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13652,tc_fun(U_13654,tc_HOL_Obool)),U_13650),hAPP(hAPP(c_COMBB(tc_fun(U_13654,tc_HOL_Obool),tc_fun(U_13654,tc_HOL_Obool),U_13652),hAPP(c_Set_Oinsert(U_13654),U_13656)),U_13658)) = hAPP(hAPP(c_Set_Oinsert(U_13654),U_13656),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13652,tc_fun(U_13654,tc_HOL_Obool)),U_13650),U_13658))
        | U_13650 = c_Orderings_Obot__class_Obot(tc_fun(U_13652,tc_HOL_Obool)) )
    & ! [U_13657,U_13655,U_13653,U_13651,U_13649] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13651,tc_fun(U_13653,tc_HOL_Obool)),U_13649),hAPP(hAPP(c_COMBB(tc_fun(U_13653,tc_HOL_Obool),tc_fun(U_13653,tc_HOL_Obool),U_13651),hAPP(c_Set_Oinsert(U_13653),U_13655)),U_13657)) = c_Orderings_Obot__class_Obot(tc_fun(U_13653,tc_HOL_Obool))
        | U_13649 != c_Orderings_Obot__class_Obot(tc_fun(U_13651,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3537_2]) ).

fof(f_3537_4,plain,
    ( ! [U_13650,U_13652,U_13654,U_13656,U_13658] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13652,tc_fun(U_13654,tc_HOL_Obool)),U_13650),hAPP(hAPP(c_COMBB(tc_fun(U_13654,tc_HOL_Obool),tc_fun(U_13654,tc_HOL_Obool),U_13652),hAPP(c_Set_Oinsert(U_13654),U_13656)),U_13658)) = hAPP(hAPP(c_Set_Oinsert(U_13654),U_13656),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13652,tc_fun(U_13654,tc_HOL_Obool)),U_13650),U_13658))
        | U_13650 = c_Orderings_Obot__class_Obot(tc_fun(U_13652,tc_HOL_Obool)) )
    & ! [U_13651,U_13655,U_13649,U_13653,U_13657] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13651,tc_fun(U_13653,tc_HOL_Obool)),U_13649),hAPP(hAPP(c_COMBB(tc_fun(U_13653,tc_HOL_Obool),tc_fun(U_13653,tc_HOL_Obool),U_13651),hAPP(c_Set_Oinsert(U_13653),U_13655)),U_13657)) = c_Orderings_Obot__class_Obot(tc_fun(U_13653,tc_HOL_Obool))
        | U_13649 != c_Orderings_Obot__class_Obot(tc_fun(U_13651,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3537_3]) ).

cnf(f_3537_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13651,tc_fun(U_13653,tc_HOL_Obool)),U_13649),hAPP(hAPP(c_COMBB(tc_fun(U_13653,tc_HOL_Obool),tc_fun(U_13653,tc_HOL_Obool),U_13651),hAPP(c_Set_Oinsert(U_13653),U_13655)),U_13657)) = c_Orderings_Obot__class_Obot(tc_fun(U_13653,tc_HOL_Obool))
    | U_13649 != c_Orderings_Obot__class_Obot(tc_fun(U_13651,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3537_4]) ).

cnf(f_3537_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13652,tc_fun(U_13654,tc_HOL_Obool)),U_13650),hAPP(hAPP(c_COMBB(tc_fun(U_13654,tc_HOL_Obool),tc_fun(U_13654,tc_HOL_Obool),U_13652),hAPP(c_Set_Oinsert(U_13654),U_13656)),U_13658)) = hAPP(hAPP(c_Set_Oinsert(U_13654),U_13656),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13652,tc_fun(U_13654,tc_HOL_Obool)),U_13650),U_13658))
    | U_13650 = c_Orderings_Obot__class_Obot(tc_fun(U_13652,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3537_4]) ).

fof(f_3538_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_3538_2,plain,
    ! [U_13660,U_13659] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13659,tc_fun(U_13659,tc_HOL_Obool)),U_13660),hAPP(hAPP(c_COMBC(U_13659,tc_fun(U_13659,tc_HOL_Obool),tc_fun(U_13659,tc_HOL_Obool)),c_Set_Oinsert(U_13659)),c_Orderings_Obot__class_Obot(tc_fun(U_13659,tc_HOL_Obool)))) = U_13660,
    inference(variable_rename,[status(thm)],[f_3538_1]) ).

fof(f_3538_3,plain,
    ! [U_13659,U_13660] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13659,tc_fun(U_13659,tc_HOL_Obool)),U_13660),hAPP(hAPP(c_COMBC(U_13659,tc_fun(U_13659,tc_HOL_Obool),tc_fun(U_13659,tc_HOL_Obool)),c_Set_Oinsert(U_13659)),c_Orderings_Obot__class_Obot(tc_fun(U_13659,tc_HOL_Obool)))) = U_13660,
    inference(definitional_conversion,[status(esa)],[f_3538_2]) ).

cnf(f_3538_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13659,tc_fun(U_13659,tc_HOL_Obool)),U_13660),hAPP(hAPP(c_COMBC(U_13659,tc_fun(U_13659,tc_HOL_Obool),tc_fun(U_13659,tc_HOL_Obool)),c_Set_Oinsert(U_13659)),c_Orderings_Obot__class_Obot(tc_fun(U_13659,tc_HOL_Obool)))) = U_13660,
    inference(clausify,[status(thm)],[f_3538_3]) ).

fof(f_3539_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_3539_2,plain,
    ! [U_13665,U_13664,U_13663,U_13662,U_13661] :
      ( ( hAPP(hAPP(c_Set_Oinsert(U_13663),U_13664),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13662,tc_fun(U_13663,tc_HOL_Obool)),U_13661),U_13665)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13662,tc_fun(U_13663,tc_HOL_Obool)),U_13661),hAPP(hAPP(c_COMBB(tc_fun(U_13663,tc_HOL_Obool),tc_fun(U_13663,tc_HOL_Obool),U_13662),hAPP(c_Set_Oinsert(U_13663),U_13664)),U_13665))
        | U_13661 = c_Orderings_Obot__class_Obot(tc_fun(U_13662,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Set_Oinsert(U_13663),U_13664),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13662,tc_fun(U_13663,tc_HOL_Obool)),U_13661),U_13665)) = hAPP(hAPP(c_Set_Oinsert(U_13663),U_13664),c_Orderings_Obot__class_Obot(tc_fun(U_13663,tc_HOL_Obool)))
        | U_13661 != c_Orderings_Obot__class_Obot(tc_fun(U_13662,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3539_1]) ).

fof(f_3539_3,plain,
    ( ! [U_13675,U_13673,U_13671,U_13669,U_13667] :
        ( hAPP(hAPP(c_Set_Oinsert(U_13671),U_13673),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13669,tc_fun(U_13671,tc_HOL_Obool)),U_13667),U_13675)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13669,tc_fun(U_13671,tc_HOL_Obool)),U_13667),hAPP(hAPP(c_COMBB(tc_fun(U_13671,tc_HOL_Obool),tc_fun(U_13671,tc_HOL_Obool),U_13669),hAPP(c_Set_Oinsert(U_13671),U_13673)),U_13675))
        | U_13667 = c_Orderings_Obot__class_Obot(tc_fun(U_13669,tc_HOL_Obool)) )
    & ! [U_13674,U_13672,U_13670,U_13668,U_13666] :
        ( hAPP(hAPP(c_Set_Oinsert(U_13670),U_13672),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13668,tc_fun(U_13670,tc_HOL_Obool)),U_13666),U_13674)) = hAPP(hAPP(c_Set_Oinsert(U_13670),U_13672),c_Orderings_Obot__class_Obot(tc_fun(U_13670,tc_HOL_Obool)))
        | U_13666 != c_Orderings_Obot__class_Obot(tc_fun(U_13668,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3539_2]) ).

fof(f_3539_4,plain,
    ( ! [U_13667,U_13669,U_13671,U_13673,U_13675] :
        ( hAPP(hAPP(c_Set_Oinsert(U_13671),U_13673),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13669,tc_fun(U_13671,tc_HOL_Obool)),U_13667),U_13675)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13669,tc_fun(U_13671,tc_HOL_Obool)),U_13667),hAPP(hAPP(c_COMBB(tc_fun(U_13671,tc_HOL_Obool),tc_fun(U_13671,tc_HOL_Obool),U_13669),hAPP(c_Set_Oinsert(U_13671),U_13673)),U_13675))
        | U_13667 = c_Orderings_Obot__class_Obot(tc_fun(U_13669,tc_HOL_Obool)) )
    & ! [U_13672,U_13668,U_13666,U_13670,U_13674] :
        ( hAPP(hAPP(c_Set_Oinsert(U_13670),U_13672),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13668,tc_fun(U_13670,tc_HOL_Obool)),U_13666),U_13674)) = hAPP(hAPP(c_Set_Oinsert(U_13670),U_13672),c_Orderings_Obot__class_Obot(tc_fun(U_13670,tc_HOL_Obool)))
        | U_13666 != c_Orderings_Obot__class_Obot(tc_fun(U_13668,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3539_3]) ).

cnf(f_3539_5,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_13670),U_13672),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13668,tc_fun(U_13670,tc_HOL_Obool)),U_13666),U_13674)) = hAPP(hAPP(c_Set_Oinsert(U_13670),U_13672),c_Orderings_Obot__class_Obot(tc_fun(U_13670,tc_HOL_Obool)))
    | U_13666 != c_Orderings_Obot__class_Obot(tc_fun(U_13668,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3539_4]) ).

cnf(f_3539_6,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_13671),U_13673),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13669,tc_fun(U_13671,tc_HOL_Obool)),U_13667),U_13675)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13669,tc_fun(U_13671,tc_HOL_Obool)),U_13667),hAPP(hAPP(c_COMBB(tc_fun(U_13671,tc_HOL_Obool),tc_fun(U_13671,tc_HOL_Obool),U_13669),hAPP(c_Set_Oinsert(U_13671),U_13673)),U_13675))
    | U_13667 = c_Orderings_Obot__class_Obot(tc_fun(U_13669,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3539_4]) ).

fof(f_3540_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_3540_2,plain,
    ! [U_13680,U_13679,U_13678,U_13677,U_13676] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13678,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13677,tc_fun(U_13678,tc_HOL_Obool)),U_13676),U_13679)),U_13680) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13677,tc_fun(U_13678,tc_HOL_Obool)),U_13676),hAPP(hAPP(c_COMBC(U_13677,tc_fun(U_13678,tc_HOL_Obool),tc_fun(U_13678,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13678,tc_HOL_Obool),tc_fun(tc_fun(U_13678,tc_HOL_Obool),tc_fun(U_13678,tc_HOL_Obool)),U_13677),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13678,tc_HOL_Obool))),U_13679)),U_13680))
        | U_13676 = c_Orderings_Obot__class_Obot(tc_fun(U_13677,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13678,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13677,tc_fun(U_13678,tc_HOL_Obool)),U_13676),U_13679)),U_13680) = U_13680
        | U_13676 != c_Orderings_Obot__class_Obot(tc_fun(U_13677,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3540_1]) ).

fof(f_3540_3,plain,
    ( ! [U_13690,U_13688,U_13686,U_13684,U_13682] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13686,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13684,tc_fun(U_13686,tc_HOL_Obool)),U_13682),U_13688)),U_13690) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13684,tc_fun(U_13686,tc_HOL_Obool)),U_13682),hAPP(hAPP(c_COMBC(U_13684,tc_fun(U_13686,tc_HOL_Obool),tc_fun(U_13686,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13686,tc_HOL_Obool),tc_fun(tc_fun(U_13686,tc_HOL_Obool),tc_fun(U_13686,tc_HOL_Obool)),U_13684),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13686,tc_HOL_Obool))),U_13688)),U_13690))
        | U_13682 = c_Orderings_Obot__class_Obot(tc_fun(U_13684,tc_HOL_Obool)) )
    & ! [U_13689,U_13687,U_13685,U_13683,U_13681] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13685,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13683,tc_fun(U_13685,tc_HOL_Obool)),U_13681),U_13687)),U_13689) = U_13689
        | U_13681 != c_Orderings_Obot__class_Obot(tc_fun(U_13683,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3540_2]) ).

fof(f_3540_4,plain,
    ( ! [U_13690,U_13682,U_13684,U_13686,U_13688] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13686,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13684,tc_fun(U_13686,tc_HOL_Obool)),U_13682),U_13688)),U_13690) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13684,tc_fun(U_13686,tc_HOL_Obool)),U_13682),hAPP(hAPP(c_COMBC(U_13684,tc_fun(U_13686,tc_HOL_Obool),tc_fun(U_13686,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13686,tc_HOL_Obool),tc_fun(tc_fun(U_13686,tc_HOL_Obool),tc_fun(U_13686,tc_HOL_Obool)),U_13684),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13686,tc_HOL_Obool))),U_13688)),U_13690))
        | U_13682 = c_Orderings_Obot__class_Obot(tc_fun(U_13684,tc_HOL_Obool)) )
    & ! [U_13687,U_13683,U_13681,U_13689,U_13685] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13685,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13683,tc_fun(U_13685,tc_HOL_Obool)),U_13681),U_13687)),U_13689) = U_13689
        | U_13681 != c_Orderings_Obot__class_Obot(tc_fun(U_13683,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3540_3]) ).

cnf(f_3540_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13685,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13683,tc_fun(U_13685,tc_HOL_Obool)),U_13681),U_13687)),U_13689) = U_13689
    | U_13681 != c_Orderings_Obot__class_Obot(tc_fun(U_13683,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3540_4]) ).

cnf(f_3540_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13686,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13684,tc_fun(U_13686,tc_HOL_Obool)),U_13682),U_13688)),U_13690) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13684,tc_fun(U_13686,tc_HOL_Obool)),U_13682),hAPP(hAPP(c_COMBC(U_13684,tc_fun(U_13686,tc_HOL_Obool),tc_fun(U_13686,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13686,tc_HOL_Obool),tc_fun(tc_fun(U_13686,tc_HOL_Obool),tc_fun(U_13686,tc_HOL_Obool)),U_13684),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13686,tc_HOL_Obool))),U_13688)),U_13690))
    | U_13682 = c_Orderings_Obot__class_Obot(tc_fun(U_13684,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3540_4]) ).

fof(f_3541_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_3541_2,plain,
    ! [U_13695,U_13694,U_13693,U_13692,U_13691] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13693,tc_HOL_Obool)),U_13694),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13692,tc_fun(U_13693,tc_HOL_Obool)),U_13691),U_13695)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13692,tc_fun(U_13693,tc_HOL_Obool)),U_13691),hAPP(hAPP(c_COMBB(tc_fun(U_13693,tc_HOL_Obool),tc_fun(U_13693,tc_HOL_Obool),U_13692),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13693,tc_HOL_Obool)),U_13694)),U_13695))
        | U_13691 = c_Orderings_Obot__class_Obot(tc_fun(U_13692,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13693,tc_HOL_Obool)),U_13694),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13692,tc_fun(U_13693,tc_HOL_Obool)),U_13691),U_13695)) = U_13694
        | U_13691 != c_Orderings_Obot__class_Obot(tc_fun(U_13692,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3541_1]) ).

fof(f_3541_3,plain,
    ( ! [U_13705,U_13703,U_13701,U_13699,U_13697] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13701,tc_HOL_Obool)),U_13703),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13699,tc_fun(U_13701,tc_HOL_Obool)),U_13697),U_13705)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13699,tc_fun(U_13701,tc_HOL_Obool)),U_13697),hAPP(hAPP(c_COMBB(tc_fun(U_13701,tc_HOL_Obool),tc_fun(U_13701,tc_HOL_Obool),U_13699),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13701,tc_HOL_Obool)),U_13703)),U_13705))
        | U_13697 = c_Orderings_Obot__class_Obot(tc_fun(U_13699,tc_HOL_Obool)) )
    & ! [U_13704,U_13702,U_13700,U_13698,U_13696] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13700,tc_HOL_Obool)),U_13702),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13698,tc_fun(U_13700,tc_HOL_Obool)),U_13696),U_13704)) = U_13702
        | U_13696 != c_Orderings_Obot__class_Obot(tc_fun(U_13698,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3541_2]) ).

fof(f_3541_4,plain,
    ( ! [U_13697,U_13699,U_13701,U_13703,U_13705] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13701,tc_HOL_Obool)),U_13703),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13699,tc_fun(U_13701,tc_HOL_Obool)),U_13697),U_13705)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13699,tc_fun(U_13701,tc_HOL_Obool)),U_13697),hAPP(hAPP(c_COMBB(tc_fun(U_13701,tc_HOL_Obool),tc_fun(U_13701,tc_HOL_Obool),U_13699),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13701,tc_HOL_Obool)),U_13703)),U_13705))
        | U_13697 = c_Orderings_Obot__class_Obot(tc_fun(U_13699,tc_HOL_Obool)) )
    & ! [U_13698,U_13702,U_13700,U_13696,U_13704] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13700,tc_HOL_Obool)),U_13702),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13698,tc_fun(U_13700,tc_HOL_Obool)),U_13696),U_13704)) = U_13702
        | U_13696 != c_Orderings_Obot__class_Obot(tc_fun(U_13698,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3541_3]) ).

cnf(f_3541_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13700,tc_HOL_Obool)),U_13702),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13698,tc_fun(U_13700,tc_HOL_Obool)),U_13696),U_13704)) = U_13702
    | U_13696 != c_Orderings_Obot__class_Obot(tc_fun(U_13698,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3541_4]) ).

cnf(f_3541_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13701,tc_HOL_Obool)),U_13703),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13699,tc_fun(U_13701,tc_HOL_Obool)),U_13697),U_13705)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13699,tc_fun(U_13701,tc_HOL_Obool)),U_13697),hAPP(hAPP(c_COMBB(tc_fun(U_13701,tc_HOL_Obool),tc_fun(U_13701,tc_HOL_Obool),U_13699),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13701,tc_HOL_Obool)),U_13703)),U_13705))
    | U_13697 = c_Orderings_Obot__class_Obot(tc_fun(U_13699,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3541_4]) ).

fof(f_3542_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_3542_2,plain,
    ! [U_13710,U_13709,U_13708,U_13707,U_13706] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13707,tc_fun(U_13708,tc_HOL_Obool)),U_13706),hAPP(hAPP(c_COMBC(U_13707,tc_fun(U_13708,tc_HOL_Obool),tc_fun(U_13708,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13708,tc_HOL_Obool),tc_fun(tc_fun(U_13708,tc_HOL_Obool),tc_fun(U_13708,tc_HOL_Obool)),U_13707),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13708,tc_HOL_Obool))),U_13709)),U_13710)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13708,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13707,tc_fun(U_13708,tc_HOL_Obool)),U_13706),U_13709)),U_13710)
        | U_13706 = c_Orderings_Obot__class_Obot(tc_fun(U_13707,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13707,tc_fun(U_13708,tc_HOL_Obool)),U_13706),hAPP(hAPP(c_COMBC(U_13707,tc_fun(U_13708,tc_HOL_Obool),tc_fun(U_13708,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13708,tc_HOL_Obool),tc_fun(tc_fun(U_13708,tc_HOL_Obool),tc_fun(U_13708,tc_HOL_Obool)),U_13707),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13708,tc_HOL_Obool))),U_13709)),U_13710)) = c_Orderings_Obot__class_Obot(tc_fun(U_13708,tc_HOL_Obool))
        | U_13706 != c_Orderings_Obot__class_Obot(tc_fun(U_13707,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3542_1]) ).

fof(f_3542_3,plain,
    ( ! [U_13720,U_13718,U_13716,U_13714,U_13712] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13714,tc_fun(U_13716,tc_HOL_Obool)),U_13712),hAPP(hAPP(c_COMBC(U_13714,tc_fun(U_13716,tc_HOL_Obool),tc_fun(U_13716,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13716,tc_HOL_Obool),tc_fun(tc_fun(U_13716,tc_HOL_Obool),tc_fun(U_13716,tc_HOL_Obool)),U_13714),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13716,tc_HOL_Obool))),U_13718)),U_13720)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13716,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13714,tc_fun(U_13716,tc_HOL_Obool)),U_13712),U_13718)),U_13720)
        | U_13712 = c_Orderings_Obot__class_Obot(tc_fun(U_13714,tc_HOL_Obool)) )
    & ! [U_13719,U_13717,U_13715,U_13713,U_13711] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13713,tc_fun(U_13715,tc_HOL_Obool)),U_13711),hAPP(hAPP(c_COMBC(U_13713,tc_fun(U_13715,tc_HOL_Obool),tc_fun(U_13715,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13715,tc_HOL_Obool),tc_fun(tc_fun(U_13715,tc_HOL_Obool),tc_fun(U_13715,tc_HOL_Obool)),U_13713),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13715,tc_HOL_Obool))),U_13717)),U_13719)) = c_Orderings_Obot__class_Obot(tc_fun(U_13715,tc_HOL_Obool))
        | U_13711 != c_Orderings_Obot__class_Obot(tc_fun(U_13713,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3542_2]) ).

fof(f_3542_4,plain,
    ( ! [U_13712,U_13714,U_13716,U_13718,U_13720] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13714,tc_fun(U_13716,tc_HOL_Obool)),U_13712),hAPP(hAPP(c_COMBC(U_13714,tc_fun(U_13716,tc_HOL_Obool),tc_fun(U_13716,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13716,tc_HOL_Obool),tc_fun(tc_fun(U_13716,tc_HOL_Obool),tc_fun(U_13716,tc_HOL_Obool)),U_13714),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13716,tc_HOL_Obool))),U_13718)),U_13720)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13716,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13714,tc_fun(U_13716,tc_HOL_Obool)),U_13712),U_13718)),U_13720)
        | U_13712 = c_Orderings_Obot__class_Obot(tc_fun(U_13714,tc_HOL_Obool)) )
    & ! [U_13717,U_13713,U_13711,U_13715,U_13719] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13713,tc_fun(U_13715,tc_HOL_Obool)),U_13711),hAPP(hAPP(c_COMBC(U_13713,tc_fun(U_13715,tc_HOL_Obool),tc_fun(U_13715,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13715,tc_HOL_Obool),tc_fun(tc_fun(U_13715,tc_HOL_Obool),tc_fun(U_13715,tc_HOL_Obool)),U_13713),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13715,tc_HOL_Obool))),U_13717)),U_13719)) = c_Orderings_Obot__class_Obot(tc_fun(U_13715,tc_HOL_Obool))
        | U_13711 != c_Orderings_Obot__class_Obot(tc_fun(U_13713,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3542_3]) ).

cnf(f_3542_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13713,tc_fun(U_13715,tc_HOL_Obool)),U_13711),hAPP(hAPP(c_COMBC(U_13713,tc_fun(U_13715,tc_HOL_Obool),tc_fun(U_13715,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13715,tc_HOL_Obool),tc_fun(tc_fun(U_13715,tc_HOL_Obool),tc_fun(U_13715,tc_HOL_Obool)),U_13713),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13715,tc_HOL_Obool))),U_13717)),U_13719)) = c_Orderings_Obot__class_Obot(tc_fun(U_13715,tc_HOL_Obool))
    | U_13711 != c_Orderings_Obot__class_Obot(tc_fun(U_13713,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3542_4]) ).

cnf(f_3542_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13714,tc_fun(U_13716,tc_HOL_Obool)),U_13712),hAPP(hAPP(c_COMBC(U_13714,tc_fun(U_13716,tc_HOL_Obool),tc_fun(U_13716,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_13716,tc_HOL_Obool),tc_fun(tc_fun(U_13716,tc_HOL_Obool),tc_fun(U_13716,tc_HOL_Obool)),U_13714),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13716,tc_HOL_Obool))),U_13718)),U_13720)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13716,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13714,tc_fun(U_13716,tc_HOL_Obool)),U_13712),U_13718)),U_13720)
    | U_13712 = c_Orderings_Obot__class_Obot(tc_fun(U_13714,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3542_4]) ).

fof(f_3543_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_3543_2,plain,
    ! [U_13725,U_13724,U_13723,U_13722,U_13721] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13722,tc_fun(U_13723,tc_HOL_Obool)),U_13721),hAPP(hAPP(c_COMBB(tc_fun(U_13723,tc_HOL_Obool),tc_fun(U_13723,tc_HOL_Obool),U_13722),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13723,tc_HOL_Obool)),U_13724)),U_13725)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13723,tc_HOL_Obool)),U_13724),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13722,tc_fun(U_13723,tc_HOL_Obool)),U_13721),U_13725))
        | U_13721 = c_Orderings_Obot__class_Obot(tc_fun(U_13722,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13722,tc_fun(U_13723,tc_HOL_Obool)),U_13721),hAPP(hAPP(c_COMBB(tc_fun(U_13723,tc_HOL_Obool),tc_fun(U_13723,tc_HOL_Obool),U_13722),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13723,tc_HOL_Obool)),U_13724)),U_13725)) = c_Orderings_Obot__class_Obot(tc_fun(U_13723,tc_HOL_Obool))
        | U_13721 != c_Orderings_Obot__class_Obot(tc_fun(U_13722,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3543_1]) ).

fof(f_3543_3,plain,
    ( ! [U_13735,U_13733,U_13731,U_13729,U_13727] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13729,tc_fun(U_13731,tc_HOL_Obool)),U_13727),hAPP(hAPP(c_COMBB(tc_fun(U_13731,tc_HOL_Obool),tc_fun(U_13731,tc_HOL_Obool),U_13729),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13731,tc_HOL_Obool)),U_13733)),U_13735)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13731,tc_HOL_Obool)),U_13733),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13729,tc_fun(U_13731,tc_HOL_Obool)),U_13727),U_13735))
        | U_13727 = c_Orderings_Obot__class_Obot(tc_fun(U_13729,tc_HOL_Obool)) )
    & ! [U_13734,U_13732,U_13730,U_13728,U_13726] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13728,tc_fun(U_13730,tc_HOL_Obool)),U_13726),hAPP(hAPP(c_COMBB(tc_fun(U_13730,tc_HOL_Obool),tc_fun(U_13730,tc_HOL_Obool),U_13728),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13730,tc_HOL_Obool)),U_13732)),U_13734)) = c_Orderings_Obot__class_Obot(tc_fun(U_13730,tc_HOL_Obool))
        | U_13726 != c_Orderings_Obot__class_Obot(tc_fun(U_13728,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3543_2]) ).

fof(f_3543_4,plain,
    ( ! [U_13727,U_13729,U_13731,U_13733,U_13735] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13729,tc_fun(U_13731,tc_HOL_Obool)),U_13727),hAPP(hAPP(c_COMBB(tc_fun(U_13731,tc_HOL_Obool),tc_fun(U_13731,tc_HOL_Obool),U_13729),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13731,tc_HOL_Obool)),U_13733)),U_13735)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13731,tc_HOL_Obool)),U_13733),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13729,tc_fun(U_13731,tc_HOL_Obool)),U_13727),U_13735))
        | U_13727 = c_Orderings_Obot__class_Obot(tc_fun(U_13729,tc_HOL_Obool)) )
    & ! [U_13728,U_13732,U_13726,U_13730,U_13734] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13728,tc_fun(U_13730,tc_HOL_Obool)),U_13726),hAPP(hAPP(c_COMBB(tc_fun(U_13730,tc_HOL_Obool),tc_fun(U_13730,tc_HOL_Obool),U_13728),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13730,tc_HOL_Obool)),U_13732)),U_13734)) = c_Orderings_Obot__class_Obot(tc_fun(U_13730,tc_HOL_Obool))
        | U_13726 != c_Orderings_Obot__class_Obot(tc_fun(U_13728,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3543_3]) ).

cnf(f_3543_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13728,tc_fun(U_13730,tc_HOL_Obool)),U_13726),hAPP(hAPP(c_COMBB(tc_fun(U_13730,tc_HOL_Obool),tc_fun(U_13730,tc_HOL_Obool),U_13728),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13730,tc_HOL_Obool)),U_13732)),U_13734)) = c_Orderings_Obot__class_Obot(tc_fun(U_13730,tc_HOL_Obool))
    | U_13726 != c_Orderings_Obot__class_Obot(tc_fun(U_13728,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3543_4]) ).

cnf(f_3543_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13729,tc_fun(U_13731,tc_HOL_Obool)),U_13727),hAPP(hAPP(c_COMBB(tc_fun(U_13731,tc_HOL_Obool),tc_fun(U_13731,tc_HOL_Obool),U_13729),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13731,tc_HOL_Obool)),U_13733)),U_13735)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13731,tc_HOL_Obool)),U_13733),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13729,tc_fun(U_13731,tc_HOL_Obool)),U_13727),U_13735))
    | U_13727 = c_Orderings_Obot__class_Obot(tc_fun(U_13729,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3543_4]) ).

fof(f_3544_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_3544_2,plain,
    ! [U_13740,U_13739,U_13738,U_13737,U_13736] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13736,tc_fun(U_13737,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_13736),U_13738),U_13739)),U_13740) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13737,tc_HOL_Obool)),hAPP(U_13740,U_13738)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13736,tc_fun(U_13737,tc_HOL_Obool)),U_13739),U_13740)),
    inference(variable_rename,[status(thm)],[f_3544_1]) ).

fof(f_3544_3,plain,
    ! [U_13736,U_13737,U_13739,U_13738,U_13740] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13736,tc_fun(U_13737,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_13736),U_13738),U_13739)),U_13740) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13737,tc_HOL_Obool)),hAPP(U_13740,U_13738)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13736,tc_fun(U_13737,tc_HOL_Obool)),U_13739),U_13740)),
    inference(definitional_conversion,[status(esa)],[f_3544_2]) ).

cnf(f_3544_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13736,tc_fun(U_13737,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_13736),U_13738),U_13739)),U_13740) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13737,tc_HOL_Obool)),hAPP(U_13740,U_13738)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13736,tc_fun(U_13737,tc_HOL_Obool)),U_13739),U_13740)),
    inference(clausify,[status(thm)],[f_3544_3]) ).

fof(f_3545_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_3545_2,plain,
    ! [U_13741] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_13741) = 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_13741)),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_3545_1]) ).

fof(f_3545_3,plain,
    ! [U_13741] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_13741) = 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_13741)),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_3545_2]) ).

cnf(f_3545_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),U_13741) = 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_13741)),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_3545_3]) ).

fof(f_3546_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_3546_2,plain,
    ! [U_13751,U_13750,U_13749,U_13748,U_13747,U_13746,U_13745,U_13744,U_13743,U_13742] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13742,tc_fun(U_13748,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13742,U_13742,U_13744),hAPP(hAPP(c_Set_Oinsert(U_13742),U_13750),c_Orderings_Obot__class_Obot(tc_fun(U_13742,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_13745,tc_fun(U_13748,tc_HOL_Obool)),tc_fun(U_13748,tc_HOL_Obool),U_13742),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13745,tc_fun(U_13748,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13745,U_13745,U_13747),hAPP(hAPP(c_Set_Oinsert(U_13745),U_13751),c_Orderings_Obot__class_Obot(tc_fun(U_13745,tc_HOL_Obool)))))),U_13749)) = hAPP(hAPP(U_13749,U_13750),U_13751)
      | ~ hBOOL(hAPP(hAPP(c_member(U_13745),U_13751),U_13746))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13742),U_13750),U_13743))
      | ~ c_Equiv__Relations_Ocongruent2(U_13742,U_13745,tc_fun(U_13748,tc_HOL_Obool),U_13744,U_13747,U_13749)
      | ~ c_Equiv__Relations_Oequiv(U_13745,U_13746,U_13747)
      | ~ c_Equiv__Relations_Oequiv(U_13742,U_13743,U_13744) ),
    inference(variable_rename,[status(thm)],[f_3546_1]) ).

fof(f_3546_3,plain,
    ! [U_13742,U_13743,U_13744,U_13745,U_13746,U_13747,U_13748,U_13749,U_13750,U_13751] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13742,tc_fun(U_13748,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13742,U_13742,U_13744),hAPP(hAPP(c_Set_Oinsert(U_13742),U_13750),c_Orderings_Obot__class_Obot(tc_fun(U_13742,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_13745,tc_fun(U_13748,tc_HOL_Obool)),tc_fun(U_13748,tc_HOL_Obool),U_13742),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13745,tc_fun(U_13748,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13745,U_13745,U_13747),hAPP(hAPP(c_Set_Oinsert(U_13745),U_13751),c_Orderings_Obot__class_Obot(tc_fun(U_13745,tc_HOL_Obool)))))),U_13749)) = hAPP(hAPP(U_13749,U_13750),U_13751)
      | ~ hBOOL(hAPP(hAPP(c_member(U_13745),U_13751),U_13746))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13742),U_13750),U_13743))
      | ~ c_Equiv__Relations_Ocongruent2(U_13742,U_13745,tc_fun(U_13748,tc_HOL_Obool),U_13744,U_13747,U_13749)
      | ~ c_Equiv__Relations_Oequiv(U_13745,U_13746,U_13747)
      | ~ c_Equiv__Relations_Oequiv(U_13742,U_13743,U_13744) ),
    inference(definitional_conversion,[status(esa)],[f_3546_2]) ).

cnf(f_3546_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13742,tc_fun(U_13748,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13742,U_13742,U_13744),hAPP(hAPP(c_Set_Oinsert(U_13742),U_13750),c_Orderings_Obot__class_Obot(tc_fun(U_13742,tc_HOL_Obool))))),hAPP(hAPP(c_COMBB(tc_fun(U_13745,tc_fun(U_13748,tc_HOL_Obool)),tc_fun(U_13748,tc_HOL_Obool),U_13742),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13745,tc_fun(U_13748,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13745,U_13745,U_13747),hAPP(hAPP(c_Set_Oinsert(U_13745),U_13751),c_Orderings_Obot__class_Obot(tc_fun(U_13745,tc_HOL_Obool)))))),U_13749)) = hAPP(hAPP(U_13749,U_13750),U_13751)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13745),U_13751),U_13746))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13742),U_13750),U_13743))
    | ~ c_Equiv__Relations_Ocongruent2(U_13742,U_13745,tc_fun(U_13748,tc_HOL_Obool),U_13744,U_13747,U_13749)
    | ~ c_Equiv__Relations_Oequiv(U_13745,U_13746,U_13747)
    | ~ c_Equiv__Relations_Oequiv(U_13742,U_13743,U_13744) ),
    inference(clausify,[status(thm)],[f_3546_3]) ).

fof(f_3547_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_3547_2,plain,
    ! [U_13757,U_13756,U_13755,U_13754,U_13753,U_13752] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13752,tc_fun(U_13755,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13752,U_13752,U_13754),hAPP(hAPP(c_Set_Oinsert(U_13752),U_13757),c_Orderings_Obot__class_Obot(tc_fun(U_13752,tc_HOL_Obool))))),U_13756) = hAPP(U_13756,U_13757)
      | ~ hBOOL(hAPP(hAPP(c_member(U_13752),U_13757),U_13753))
      | ~ c_Equiv__Relations_Ocongruent(U_13752,tc_fun(U_13755,tc_HOL_Obool),U_13754,U_13756)
      | ~ c_Equiv__Relations_Oequiv(U_13752,U_13753,U_13754) ),
    inference(variable_rename,[status(thm)],[f_3547_1]) ).

fof(f_3547_3,plain,
    ! [U_13755,U_13756,U_13752,U_13753,U_13754,U_13757] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13752,tc_fun(U_13755,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13752,U_13752,U_13754),hAPP(hAPP(c_Set_Oinsert(U_13752),U_13757),c_Orderings_Obot__class_Obot(tc_fun(U_13752,tc_HOL_Obool))))),U_13756) = hAPP(U_13756,U_13757)
      | ~ hBOOL(hAPP(hAPP(c_member(U_13752),U_13757),U_13753))
      | ~ c_Equiv__Relations_Ocongruent(U_13752,tc_fun(U_13755,tc_HOL_Obool),U_13754,U_13756)
      | ~ c_Equiv__Relations_Oequiv(U_13752,U_13753,U_13754) ),
    inference(definitional_conversion,[status(esa)],[f_3547_2]) ).

cnf(f_3547_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13752,tc_fun(U_13755,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13752,U_13752,U_13754),hAPP(hAPP(c_Set_Oinsert(U_13752),U_13757),c_Orderings_Obot__class_Obot(tc_fun(U_13752,tc_HOL_Obool))))),U_13756) = hAPP(U_13756,U_13757)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13752),U_13757),U_13753))
    | ~ c_Equiv__Relations_Ocongruent(U_13752,tc_fun(U_13755,tc_HOL_Obool),U_13754,U_13756)
    | ~ c_Equiv__Relations_Oequiv(U_13752,U_13753,U_13754) ),
    inference(clausify,[status(thm)],[f_3547_3]) ).

fof(f_3548_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_3548_2,plain,
    ! [U_13765,U_13764,U_13763,U_13762,U_13761,U_13760,U_13759,U_13758] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13758,tc_fun(U_13764,tc_fun(U_13765,tc_HOL_Obool))),U_13760),U_13761),U_13762),U_13763))
      | ~ hBOOL(hAPP(hAPP(hAPP(U_13761,U_13759),U_13762),U_13763))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13758),U_13759),U_13760)) ),
    inference(variable_rename,[status(thm)],[f_3548_1]) ).

fof(f_3548_3,plain,
    ! [U_13760,U_13758,U_13759,U_13761,U_13762,U_13763,U_13764,U_13765] :
      ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13758,tc_fun(U_13764,tc_fun(U_13765,tc_HOL_Obool))),U_13760),U_13761),U_13762),U_13763))
      | ~ hBOOL(hAPP(hAPP(hAPP(U_13761,U_13759),U_13762),U_13763))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13758),U_13759),U_13760)) ),
    inference(definitional_conversion,[status(esa)],[f_3548_2]) ).

cnf(f_3548_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13758,tc_fun(U_13764,tc_fun(U_13765,tc_HOL_Obool))),U_13760),U_13761),U_13762),U_13763))
    | ~ hBOOL(hAPP(hAPP(hAPP(U_13761,U_13759),U_13762),U_13763))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13758),U_13759),U_13760)) ),
    inference(clausify,[status(thm)],[f_3548_3]) ).

fof(f_3549_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_3549_2,plain,
    ! [U_13767,U_13766] :
      ( ( hAPP(c_Int_ORep__Integ,U_13766) = hAPP(c_Int_ORep__Integ,U_13767)
        | U_13766 != U_13767 )
      & ( U_13766 = U_13767
        | hAPP(c_Int_ORep__Integ,U_13766) != hAPP(c_Int_ORep__Integ,U_13767) ) ),
    inference(variable_rename,[status(thm)],[f_3549_1]) ).

fof(f_3549_3,plain,
    ( ! [U_13771,U_13769] :
        ( hAPP(c_Int_ORep__Integ,U_13769) = hAPP(c_Int_ORep__Integ,U_13771)
        | U_13769 != U_13771 )
    & ! [U_13770,U_13768] :
        ( U_13768 = U_13770
        | hAPP(c_Int_ORep__Integ,U_13768) != hAPP(c_Int_ORep__Integ,U_13770) ) ),
    inference(miniscope,[status(thm)],[f_3549_2]) ).

fof(f_3549_4,plain,
    ( ! [U_13769,U_13771] :
        ( hAPP(c_Int_ORep__Integ,U_13769) = hAPP(c_Int_ORep__Integ,U_13771)
        | U_13769 != U_13771 )
    & ! [U_13770,U_13768] :
        ( U_13768 = U_13770
        | hAPP(c_Int_ORep__Integ,U_13768) != hAPP(c_Int_ORep__Integ,U_13770) ) ),
    inference(definitional_conversion,[status(esa)],[f_3549_3]) ).

cnf(f_3549_5,plain,
    ( U_13768 = U_13770
    | hAPP(c_Int_ORep__Integ,U_13768) != hAPP(c_Int_ORep__Integ,U_13770) ),
    inference(clausify,[status(thm)],[f_3549_4]) ).

cnf(f_3549_6,plain,
    ( hAPP(c_Int_ORep__Integ,U_13769) = hAPP(c_Int_ORep__Integ,U_13771)
    | U_13769 != U_13771 ),
    inference(clausify,[status(thm)],[f_3549_4]) ).

fof(f_3550_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_3550_2,plain,
    ! [U_13772] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_13772)) = U_13772,
    inference(variable_rename,[status(thm)],[f_3550_1]) ).

fof(f_3550_3,plain,
    ! [U_13772] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_13772)) = U_13772,
    inference(definitional_conversion,[status(esa)],[f_3550_2]) ).

cnf(f_3550_4,plain,
    hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,U_13772)) = U_13772,
    inference(clausify,[status(thm)],[f_3550_3]) ).

fof(f_3551_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_3551_2,plain,
    ! [U_13780,U_13779,U_13778,U_13777,U_13776,U_13775,U_13774,U_13773] :
      ( c_Equiv__Relations_Ocongruent(U_13776,U_13777,U_13778,hAPP(U_13779,U_13780))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13773),U_13780),U_13774))
      | ~ c_Equiv__Relations_Ocongruent2(U_13773,U_13776,U_13777,U_13775,U_13778,U_13779)
      | ~ c_Equiv__Relations_Oequiv(U_13773,U_13774,U_13775) ),
    inference(variable_rename,[status(thm)],[f_3551_1]) ).

fof(f_3551_3,plain,
    ! [U_13773,U_13774,U_13775,U_13776,U_13777,U_13778,U_13779,U_13780] :
      ( c_Equiv__Relations_Ocongruent(U_13776,U_13777,U_13778,hAPP(U_13779,U_13780))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13773),U_13780),U_13774))
      | ~ c_Equiv__Relations_Ocongruent2(U_13773,U_13776,U_13777,U_13775,U_13778,U_13779)
      | ~ c_Equiv__Relations_Oequiv(U_13773,U_13774,U_13775) ),
    inference(definitional_conversion,[status(esa)],[f_3551_2]) ).

cnf(f_3551_4,plain,
    ( c_Equiv__Relations_Ocongruent(U_13776,U_13777,U_13778,hAPP(U_13779,U_13780))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13773),U_13780),U_13774))
    | ~ c_Equiv__Relations_Ocongruent2(U_13773,U_13776,U_13777,U_13775,U_13778,U_13779)
    | ~ c_Equiv__Relations_Oequiv(U_13773,U_13774,U_13775) ),
    inference(clausify,[status(thm)],[f_3551_3]) ).

fof(f_3552_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_3552_2,plain,
    ! [U_13790,U_13789,U_13788,U_13787,U_13786,U_13785,U_13784,U_13783,U_13782,U_13781] :
      ( hAPP(hAPP(U_13786,U_13787),U_13789) = hAPP(hAPP(U_13786,U_13788),U_13790)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13782,U_13782)),hAPP(hAPP(c_Product__Type_OPair(U_13782,U_13782),U_13789),U_13790)),U_13785))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13781,U_13781)),hAPP(hAPP(c_Product__Type_OPair(U_13781,U_13781),U_13787),U_13788)),U_13784))
      | ~ c_Equiv__Relations_Ocongruent2(U_13781,U_13782,U_13783,U_13784,U_13785,U_13786) ),
    inference(variable_rename,[status(thm)],[f_3552_1]) ).

fof(f_3552_3,plain,
    ! [U_13786,U_13781,U_13782,U_13783,U_13784,U_13785,U_13787,U_13788,U_13789,U_13790] :
      ( hAPP(hAPP(U_13786,U_13787),U_13789) = hAPP(hAPP(U_13786,U_13788),U_13790)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13782,U_13782)),hAPP(hAPP(c_Product__Type_OPair(U_13782,U_13782),U_13789),U_13790)),U_13785))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13781,U_13781)),hAPP(hAPP(c_Product__Type_OPair(U_13781,U_13781),U_13787),U_13788)),U_13784))
      | ~ c_Equiv__Relations_Ocongruent2(U_13781,U_13782,U_13783,U_13784,U_13785,U_13786) ),
    inference(definitional_conversion,[status(esa)],[f_3552_2]) ).

cnf(f_3552_4,plain,
    ( hAPP(hAPP(U_13786,U_13787),U_13789) = hAPP(hAPP(U_13786,U_13788),U_13790)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13782,U_13782)),hAPP(hAPP(c_Product__Type_OPair(U_13782,U_13782),U_13789),U_13790)),U_13785))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13781,U_13781)),hAPP(hAPP(c_Product__Type_OPair(U_13781,U_13781),U_13787),U_13788)),U_13784))
    | ~ c_Equiv__Relations_Ocongruent2(U_13781,U_13782,U_13783,U_13784,U_13785,U_13786) ),
    inference(clausify,[status(thm)],[f_3552_3]) ).

fof(f_3553_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_3553_2,plain,
    ! [U_13796,U_13795,U_13794,U_13793,U_13792,U_13791] :
      ( hAPP(U_13794,U_13795) = hAPP(U_13794,U_13796)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13791,U_13791)),hAPP(hAPP(c_Product__Type_OPair(U_13791,U_13791),U_13795),U_13796)),U_13793))
      | ~ c_Equiv__Relations_Ocongruent(U_13791,U_13792,U_13793,U_13794) ),
    inference(variable_rename,[status(thm)],[f_3553_1]) ).

fof(f_3553_3,plain,
    ! [U_13792,U_13793,U_13795,U_13791,U_13794,U_13796] :
      ( hAPP(U_13794,U_13795) = hAPP(U_13794,U_13796)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13791,U_13791)),hAPP(hAPP(c_Product__Type_OPair(U_13791,U_13791),U_13795),U_13796)),U_13793))
      | ~ c_Equiv__Relations_Ocongruent(U_13791,U_13792,U_13793,U_13794) ),
    inference(definitional_conversion,[status(esa)],[f_3553_2]) ).

cnf(f_3553_4,plain,
    ( hAPP(U_13794,U_13795) = hAPP(U_13794,U_13796)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13791,U_13791)),hAPP(hAPP(c_Product__Type_OPair(U_13791,U_13791),U_13795),U_13796)),U_13793))
    | ~ c_Equiv__Relations_Ocongruent(U_13791,U_13792,U_13793,U_13794) ),
    inference(clausify,[status(thm)],[f_3553_3]) ).

fof(f_3554_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_3554_2,plain,
    ! [U_13805,U_13804,U_13803,U_13802,U_13801,U_13800,U_13799,U_13798,U_13797] :
      ( c_Equiv__Relations_Ocongruent(U_13797,tc_fun(U_13803,tc_HOL_Obool),U_13799,hAPP(hAPP(c_COMBB(tc_fun(U_13800,tc_fun(U_13803,tc_HOL_Obool)),tc_fun(U_13803,tc_HOL_Obool),U_13797),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13800,tc_fun(U_13803,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13800,U_13800,U_13802),hAPP(hAPP(c_Set_Oinsert(U_13800),U_13805),c_Orderings_Obot__class_Obot(tc_fun(U_13800,tc_HOL_Obool)))))),U_13804))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13800),U_13805),U_13801))
      | ~ c_Equiv__Relations_Ocongruent2(U_13797,U_13800,tc_fun(U_13803,tc_HOL_Obool),U_13799,U_13802,U_13804)
      | ~ c_Equiv__Relations_Oequiv(U_13800,U_13801,U_13802)
      | ~ c_Equiv__Relations_Oequiv(U_13797,U_13798,U_13799) ),
    inference(variable_rename,[status(thm)],[f_3554_1]) ).

fof(f_3554_3,plain,
    ! [U_13797,U_13800,U_13799,U_13798,U_13801,U_13802,U_13803,U_13804,U_13805] :
      ( c_Equiv__Relations_Ocongruent(U_13797,tc_fun(U_13803,tc_HOL_Obool),U_13799,hAPP(hAPP(c_COMBB(tc_fun(U_13800,tc_fun(U_13803,tc_HOL_Obool)),tc_fun(U_13803,tc_HOL_Obool),U_13797),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13800,tc_fun(U_13803,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13800,U_13800,U_13802),hAPP(hAPP(c_Set_Oinsert(U_13800),U_13805),c_Orderings_Obot__class_Obot(tc_fun(U_13800,tc_HOL_Obool)))))),U_13804))
      | ~ hBOOL(hAPP(hAPP(c_member(U_13800),U_13805),U_13801))
      | ~ c_Equiv__Relations_Ocongruent2(U_13797,U_13800,tc_fun(U_13803,tc_HOL_Obool),U_13799,U_13802,U_13804)
      | ~ c_Equiv__Relations_Oequiv(U_13800,U_13801,U_13802)
      | ~ c_Equiv__Relations_Oequiv(U_13797,U_13798,U_13799) ),
    inference(definitional_conversion,[status(esa)],[f_3554_2]) ).

cnf(f_3554_4,plain,
    ( c_Equiv__Relations_Ocongruent(U_13797,tc_fun(U_13803,tc_HOL_Obool),U_13799,hAPP(hAPP(c_COMBB(tc_fun(U_13800,tc_fun(U_13803,tc_HOL_Obool)),tc_fun(U_13803,tc_HOL_Obool),U_13797),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13800,tc_fun(U_13803,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_13800,U_13800,U_13802),hAPP(hAPP(c_Set_Oinsert(U_13800),U_13805),c_Orderings_Obot__class_Obot(tc_fun(U_13800,tc_HOL_Obool)))))),U_13804))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13800),U_13805),U_13801))
    | ~ c_Equiv__Relations_Ocongruent2(U_13797,U_13800,tc_fun(U_13803,tc_HOL_Obool),U_13799,U_13802,U_13804)
    | ~ c_Equiv__Relations_Oequiv(U_13800,U_13801,U_13802)
    | ~ c_Equiv__Relations_Oequiv(U_13797,U_13798,U_13799) ),
    inference(clausify,[status(thm)],[f_3554_3]) ).

fof(f_3555_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_3555_2,plain,
    ! [U_13806] : hAPP(c_Int_Onat,U_13806) = 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_13806)),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_3555_1]) ).

fof(f_3555_3,plain,
    ! [U_13806] : hAPP(c_Int_Onat,U_13806) = 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_13806)),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_3555_2]) ).

cnf(f_3555_4,plain,
    hAPP(c_Int_Onat,U_13806) = 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_13806)),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_3555_3]) ).

fof(f_3556_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_3556_2,plain,
    ! [U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809] :
      ( U_13814 = U_13815
      | ? [U_13808] :
          ( ? [U_13807] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13809,U_13809)),hAPP(hAPP(c_Product__Type_OPair(U_13809,U_13809),U_13808),U_13807)),U_13811))
              & hAPP(U_13813,U_13808) = hAPP(U_13813,U_13807)
              & hBOOL(hAPP(hAPP(c_member(U_13809),U_13807),U_13810)) )
          & hBOOL(hAPP(hAPP(c_member(U_13809),U_13808),U_13810)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13809,tc_HOL_Obool)),U_13815),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13809),U_13810),U_13811)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13809,tc_HOL_Obool)),U_13814),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13809),U_13810),U_13811)))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13809,tc_fun(U_13812,tc_HOL_Obool)),U_13814),U_13813) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13809,tc_fun(U_13812,tc_HOL_Obool)),U_13815),U_13813)
      | ~ c_Equiv__Relations_Ocongruent(U_13809,tc_fun(U_13812,tc_HOL_Obool),U_13811,U_13813)
      | ~ c_Equiv__Relations_Oequiv(U_13809,U_13810,U_13811) ),
    inference(variable_rename,[status(thm)],[f_3556_1]) ).

fof(f_3556_3,plain,
    ! [U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809] :
      ( U_13814 = U_13815
      | ( ? [U_13807] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13809,U_13809)),hAPP(hAPP(c_Product__Type_OPair(U_13809,U_13809),sK299(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809)),U_13807)),U_13811))
            & hAPP(U_13813,sK299(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809)) = hAPP(U_13813,U_13807)
            & hBOOL(hAPP(hAPP(c_member(U_13809),U_13807),U_13810)) )
        & hBOOL(hAPP(hAPP(c_member(U_13809),sK299(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809)),U_13810)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13809,tc_HOL_Obool)),U_13815),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13809),U_13810),U_13811)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13809,tc_HOL_Obool)),U_13814),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13809),U_13810),U_13811)))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13809,tc_fun(U_13812,tc_HOL_Obool)),U_13814),U_13813) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13809,tc_fun(U_13812,tc_HOL_Obool)),U_13815),U_13813)
      | ~ c_Equiv__Relations_Ocongruent(U_13809,tc_fun(U_13812,tc_HOL_Obool),U_13811,U_13813)
      | ~ c_Equiv__Relations_Oequiv(U_13809,U_13810,U_13811) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK299]),skolemize(U_13808,sK299(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809))],[f_3556_2]) ).

fof(f_3556_4,plain,
    ! [U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809] :
      ( U_13814 = U_13815
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13809,U_13809)),hAPP(hAPP(c_Product__Type_OPair(U_13809,U_13809),sK299(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809)),sK300(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809))),U_13811))
        & hAPP(U_13813,sK299(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809)) = hAPP(U_13813,sK300(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809))
        & hBOOL(hAPP(hAPP(c_member(U_13809),sK300(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809)),U_13810))
        & hBOOL(hAPP(hAPP(c_member(U_13809),sK299(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809)),U_13810)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13809,tc_HOL_Obool)),U_13815),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13809),U_13810),U_13811)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13809,tc_HOL_Obool)),U_13814),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13809),U_13810),U_13811)))
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13809,tc_fun(U_13812,tc_HOL_Obool)),U_13814),U_13813) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13809,tc_fun(U_13812,tc_HOL_Obool)),U_13815),U_13813)
      | ~ c_Equiv__Relations_Ocongruent(U_13809,tc_fun(U_13812,tc_HOL_Obool),U_13811,U_13813)
      | ~ c_Equiv__Relations_Oequiv(U_13809,U_13810,U_13811) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK300]),skolemize(U_13807,sK300(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809))],[f_3556_3]) ).

fof(f_3556_5,plain,
    ( ! [U_13809,U_13810,U_13811,U_13812,U_13813,U_13814,U_13815] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13809,U_13809)),hAPP(hAPP(c_Product__Type_OPair(U_13809,U_13809),sK299(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809)),sK300(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809))),U_13811))
        | ~ sP955(U_13809,U_13810,U_13811,U_13812,U_13813,U_13814,U_13815) )
    & ! [U_13809,U_13810,U_13811,U_13812,U_13813,U_13814,U_13815] :
        ( hAPP(U_13813,sK299(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809)) = hAPP(U_13813,sK300(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809))
        | ~ sP955(U_13809,U_13810,U_13811,U_13812,U_13813,U_13814,U_13815) )
    & ! [U_13809,U_13810,U_13811,U_13812,U_13813,U_13814,U_13815] :
        ( hBOOL(hAPP(hAPP(c_member(U_13809),sK300(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809)),U_13810))
        | ~ sP955(U_13809,U_13810,U_13811,U_13812,U_13813,U_13814,U_13815) )
    & ! [U_13809,U_13810,U_13811,U_13812,U_13813,U_13814,U_13815] :
        ( hBOOL(hAPP(hAPP(c_member(U_13809),sK299(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809)),U_13810))
        | ~ sP955(U_13809,U_13810,U_13811,U_13812,U_13813,U_13814,U_13815) )
    & ! [U_13809,U_13810,U_13811,U_13812,U_13813,U_13814,U_13815] :
        ( U_13814 = U_13815
        | sP955(U_13809,U_13810,U_13811,U_13812,U_13813,U_13814,U_13815)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13809,tc_HOL_Obool)),U_13815),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13809),U_13810),U_13811)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13809,tc_HOL_Obool)),U_13814),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13809),U_13810),U_13811)))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13809,tc_fun(U_13812,tc_HOL_Obool)),U_13814),U_13813) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13809,tc_fun(U_13812,tc_HOL_Obool)),U_13815),U_13813)
        | ~ c_Equiv__Relations_Ocongruent(U_13809,tc_fun(U_13812,tc_HOL_Obool),U_13811,U_13813)
        | ~ c_Equiv__Relations_Oequiv(U_13809,U_13810,U_13811) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP955])],[f_3556_4]) ).

cnf(f_3556_6,plain,
    ( U_13814 = U_13815
    | sP955(U_13809,U_13810,U_13811,U_13812,U_13813,U_13814,U_13815)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13809,tc_HOL_Obool)),U_13815),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13809),U_13810),U_13811)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13809,tc_HOL_Obool)),U_13814),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13809),U_13810),U_13811)))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13809,tc_fun(U_13812,tc_HOL_Obool)),U_13814),U_13813) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13809,tc_fun(U_13812,tc_HOL_Obool)),U_13815),U_13813)
    | ~ c_Equiv__Relations_Ocongruent(U_13809,tc_fun(U_13812,tc_HOL_Obool),U_13811,U_13813)
    | ~ c_Equiv__Relations_Oequiv(U_13809,U_13810,U_13811) ),
    inference(clausify,[status(thm)],[f_3556_5]) ).

cnf(f_3556_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13809),sK299(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809)),U_13810))
    | ~ sP955(U_13809,U_13810,U_13811,U_13812,U_13813,U_13814,U_13815) ),
    inference(clausify,[status(thm)],[f_3556_5]) ).

cnf(f_3556_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13809),sK300(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809)),U_13810))
    | ~ sP955(U_13809,U_13810,U_13811,U_13812,U_13813,U_13814,U_13815) ),
    inference(clausify,[status(thm)],[f_3556_5]) ).

cnf(f_3556_9,plain,
    ( hAPP(U_13813,sK299(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809)) = hAPP(U_13813,sK300(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809))
    | ~ sP955(U_13809,U_13810,U_13811,U_13812,U_13813,U_13814,U_13815) ),
    inference(clausify,[status(thm)],[f_3556_5]) ).

cnf(f_3556_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_13809,U_13809)),hAPP(hAPP(c_Product__Type_OPair(U_13809,U_13809),sK299(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809)),sK300(U_13815,U_13814,U_13813,U_13812,U_13811,U_13810,U_13809))),U_13811))
    | ~ sP955(U_13809,U_13810,U_13811,U_13812,U_13813,U_13814,U_13815) ),
    inference(clausify,[status(thm)],[f_3556_5]) ).

fof(f_3557_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_3557_2,plain,
    ! [U_13828,U_13827,U_13826,U_13825,U_13824,U_13823,U_13822,U_13821,U_13820,U_13819,U_13818] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_13824,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13818,tc_fun(U_13824,tc_HOL_Obool)),U_13826),hAPP(hAPP(c_COMBB(tc_fun(U_13821,tc_fun(U_13824,tc_HOL_Obool)),tc_fun(U_13824,tc_HOL_Obool),U_13818),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13821,tc_fun(U_13824,tc_HOL_Obool)),U_13827)),U_13825))),U_13828))
      | ? [U_13817] :
          ( ? [U_13816] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13824,tc_HOL_Obool)),hAPP(hAPP(U_13825,U_13817),U_13816)),U_13828))
              & hBOOL(hAPP(hAPP(c_member(U_13821),U_13816),U_13822)) )
          & hBOOL(hAPP(hAPP(c_member(U_13818),U_13817),U_13819)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13821,tc_HOL_Obool)),U_13827),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13821),U_13822),U_13823)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13818,tc_HOL_Obool)),U_13826),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13818),U_13819),U_13820)))
      | ~ c_Equiv__Relations_Ocongruent2(U_13818,U_13821,tc_fun(U_13824,tc_HOL_Obool),U_13820,U_13823,U_13825)
      | ~ c_Equiv__Relations_Oequiv(U_13821,U_13822,U_13823)
      | ~ c_Equiv__Relations_Oequiv(U_13818,U_13819,U_13820) ),
    inference(variable_rename,[status(thm)],[f_3557_1]) ).

fof(f_3557_3,plain,
    ! [U_13828,U_13827,U_13826,U_13825,U_13824,U_13823,U_13822,U_13821,U_13820,U_13819,U_13818] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_13824,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13818,tc_fun(U_13824,tc_HOL_Obool)),U_13826),hAPP(hAPP(c_COMBB(tc_fun(U_13821,tc_fun(U_13824,tc_HOL_Obool)),tc_fun(U_13824,tc_HOL_Obool),U_13818),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13821,tc_fun(U_13824,tc_HOL_Obool)),U_13827)),U_13825))),U_13828))
      | ( ? [U_13816] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13824,tc_HOL_Obool)),hAPP(hAPP(U_13825,sK301(U_13828,U_13827,U_13826,U_13825,U_13824,U_13823,U_13822,U_13821,U_13820,U_13819,U_13818)),U_13816)),U_13828))
            & hBOOL(hAPP(hAPP(c_member(U_13821),U_13816),U_13822)) )
        & hBOOL(hAPP(hAPP(c_member(U_13818),sK301(U_13828,U_13827,U_13826,U_13825,U_13824,U_13823,U_13822,U_13821,U_13820,U_13819,U_13818)),U_13819)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13821,tc_HOL_Obool)),U_13827),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13821),U_13822),U_13823)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13818,tc_HOL_Obool)),U_13826),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13818),U_13819),U_13820)))
      | ~ c_Equiv__Relations_Ocongruent2(U_13818,U_13821,tc_fun(U_13824,tc_HOL_Obool),U_13820,U_13823,U_13825)
      | ~ c_Equiv__Relations_Oequiv(U_13821,U_13822,U_13823)
      | ~ c_Equiv__Relations_Oequiv(U_13818,U_13819,U_13820) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK301]),skolemize(U_13817,sK301(U_13828,U_13827,U_13826,U_13825,U_13824,U_13823,U_13822,U_13821,U_13820,U_13819,U_13818))],[f_3557_2]) ).

fof(f_3557_4,plain,
    ! [U_13828,U_13827,U_13826,U_13825,U_13824,U_13823,U_13822,U_13821,U_13820,U_13819,U_13818] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_13824,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13818,tc_fun(U_13824,tc_HOL_Obool)),U_13826),hAPP(hAPP(c_COMBB(tc_fun(U_13821,tc_fun(U_13824,tc_HOL_Obool)),tc_fun(U_13824,tc_HOL_Obool),U_13818),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13821,tc_fun(U_13824,tc_HOL_Obool)),U_13827)),U_13825))),U_13828))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13824,tc_HOL_Obool)),hAPP(hAPP(U_13825,sK301(U_13828,U_13827,U_13826,U_13825,U_13824,U_13823,U_13822,U_13821,U_13820,U_13819,U_13818)),sK302(U_13828,U_13827,U_13826,U_13825,U_13824,U_13823,U_13822,U_13821,U_13820,U_13819,U_13818))),U_13828))
        & hBOOL(hAPP(hAPP(c_member(U_13821),sK302(U_13828,U_13827,U_13826,U_13825,U_13824,U_13823,U_13822,U_13821,U_13820,U_13819,U_13818)),U_13822))
        & hBOOL(hAPP(hAPP(c_member(U_13818),sK301(U_13828,U_13827,U_13826,U_13825,U_13824,U_13823,U_13822,U_13821,U_13820,U_13819,U_13818)),U_13819)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13821,tc_HOL_Obool)),U_13827),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13821),U_13822),U_13823)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13818,tc_HOL_Obool)),U_13826),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13818),U_13819),U_13820)))
      | ~ c_Equiv__Relations_Ocongruent2(U_13818,U_13821,tc_fun(U_13824,tc_HOL_Obool),U_13820,U_13823,U_13825)
      | ~ c_Equiv__Relations_Oequiv(U_13821,U_13822,U_13823)
      | ~ c_Equiv__Relations_Oequiv(U_13818,U_13819,U_13820) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK302]),skolemize(U_13816,sK302(U_13828,U_13827,U_13826,U_13825,U_13824,U_13823,U_13822,U_13821,U_13820,U_13819,U_13818))],[f_3557_3]) ).

fof(f_3557_5,plain,
    ( ! [U_13818,U_13820,U_13819,U_13822,U_13823,U_13821,U_13825,U_13826,U_13824,U_13827,U_13828] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13824,tc_HOL_Obool)),hAPP(hAPP(U_13825,sK301(U_13828,U_13827,U_13826,U_13825,U_13824,U_13823,U_13822,U_13821,U_13820,U_13819,U_13818)),sK302(U_13828,U_13827,U_13826,U_13825,U_13824,U_13823,U_13822,U_13821,U_13820,U_13819,U_13818))),U_13828))
        | ~ sP956(U_13818,U_13820,U_13819,U_13822,U_13823,U_13821,U_13825,U_13826,U_13824,U_13827,U_13828) )
    & ! [U_13818,U_13820,U_13819,U_13822,U_13823,U_13821,U_13825,U_13826,U_13824,U_13827,U_13828] :
        ( hBOOL(hAPP(hAPP(c_member(U_13821),sK302(U_13828,U_13827,U_13826,U_13825,U_13824,U_13823,U_13822,U_13821,U_13820,U_13819,U_13818)),U_13822))
        | ~ sP956(U_13818,U_13820,U_13819,U_13822,U_13823,U_13821,U_13825,U_13826,U_13824,U_13827,U_13828) )
    & ! [U_13818,U_13820,U_13819,U_13822,U_13823,U_13821,U_13825,U_13826,U_13824,U_13827,U_13828] :
        ( hBOOL(hAPP(hAPP(c_member(U_13818),sK301(U_13828,U_13827,U_13826,U_13825,U_13824,U_13823,U_13822,U_13821,U_13820,U_13819,U_13818)),U_13819))
        | ~ sP956(U_13818,U_13820,U_13819,U_13822,U_13823,U_13821,U_13825,U_13826,U_13824,U_13827,U_13828) )
    & ! [U_13818,U_13820,U_13819,U_13822,U_13823,U_13821,U_13825,U_13826,U_13824,U_13827,U_13828] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_13824,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13818,tc_fun(U_13824,tc_HOL_Obool)),U_13826),hAPP(hAPP(c_COMBB(tc_fun(U_13821,tc_fun(U_13824,tc_HOL_Obool)),tc_fun(U_13824,tc_HOL_Obool),U_13818),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13821,tc_fun(U_13824,tc_HOL_Obool)),U_13827)),U_13825))),U_13828))
        | sP956(U_13818,U_13820,U_13819,U_13822,U_13823,U_13821,U_13825,U_13826,U_13824,U_13827,U_13828)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13821,tc_HOL_Obool)),U_13827),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13821),U_13822),U_13823)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13818,tc_HOL_Obool)),U_13826),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13818),U_13819),U_13820)))
        | ~ c_Equiv__Relations_Ocongruent2(U_13818,U_13821,tc_fun(U_13824,tc_HOL_Obool),U_13820,U_13823,U_13825)
        | ~ c_Equiv__Relations_Oequiv(U_13821,U_13822,U_13823)
        | ~ c_Equiv__Relations_Oequiv(U_13818,U_13819,U_13820) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP956])],[f_3557_4]) ).

cnf(f_3557_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_13824,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13818,tc_fun(U_13824,tc_HOL_Obool)),U_13826),hAPP(hAPP(c_COMBB(tc_fun(U_13821,tc_fun(U_13824,tc_HOL_Obool)),tc_fun(U_13824,tc_HOL_Obool),U_13818),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13821,tc_fun(U_13824,tc_HOL_Obool)),U_13827)),U_13825))),U_13828))
    | sP956(U_13818,U_13820,U_13819,U_13822,U_13823,U_13821,U_13825,U_13826,U_13824,U_13827,U_13828)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13821,tc_HOL_Obool)),U_13827),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13821),U_13822),U_13823)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13818,tc_HOL_Obool)),U_13826),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13818),U_13819),U_13820)))
    | ~ c_Equiv__Relations_Ocongruent2(U_13818,U_13821,tc_fun(U_13824,tc_HOL_Obool),U_13820,U_13823,U_13825)
    | ~ c_Equiv__Relations_Oequiv(U_13821,U_13822,U_13823)
    | ~ c_Equiv__Relations_Oequiv(U_13818,U_13819,U_13820) ),
    inference(clausify,[status(thm)],[f_3557_5]) ).

cnf(f_3557_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13818),sK301(U_13828,U_13827,U_13826,U_13825,U_13824,U_13823,U_13822,U_13821,U_13820,U_13819,U_13818)),U_13819))
    | ~ sP956(U_13818,U_13820,U_13819,U_13822,U_13823,U_13821,U_13825,U_13826,U_13824,U_13827,U_13828) ),
    inference(clausify,[status(thm)],[f_3557_5]) ).

cnf(f_3557_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13821),sK302(U_13828,U_13827,U_13826,U_13825,U_13824,U_13823,U_13822,U_13821,U_13820,U_13819,U_13818)),U_13822))
    | ~ sP956(U_13818,U_13820,U_13819,U_13822,U_13823,U_13821,U_13825,U_13826,U_13824,U_13827,U_13828) ),
    inference(clausify,[status(thm)],[f_3557_5]) ).

cnf(f_3557_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13824,tc_HOL_Obool)),hAPP(hAPP(U_13825,sK301(U_13828,U_13827,U_13826,U_13825,U_13824,U_13823,U_13822,U_13821,U_13820,U_13819,U_13818)),sK302(U_13828,U_13827,U_13826,U_13825,U_13824,U_13823,U_13822,U_13821,U_13820,U_13819,U_13818))),U_13828))
    | ~ sP956(U_13818,U_13820,U_13819,U_13822,U_13823,U_13821,U_13825,U_13826,U_13824,U_13827,U_13828) ),
    inference(clausify,[status(thm)],[f_3557_5]) ).

fof(f_3558_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_3558_2,plain,
    ! [U_13836,U_13835,U_13834,U_13833,U_13832,U_13831,U_13830] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_13833,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13830,tc_fun(U_13833,tc_HOL_Obool)),U_13835),U_13834)),U_13836))
      | ? [U_13829] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13833,tc_HOL_Obool)),hAPP(U_13834,U_13829)),U_13836))
          & hBOOL(hAPP(hAPP(c_member(U_13830),U_13829),U_13831)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13830,tc_HOL_Obool)),U_13835),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13830),U_13831),U_13832)))
      | ~ c_Equiv__Relations_Ocongruent(U_13830,tc_fun(U_13833,tc_HOL_Obool),U_13832,U_13834)
      | ~ c_Equiv__Relations_Oequiv(U_13830,U_13831,U_13832) ),
    inference(variable_rename,[status(thm)],[f_3558_1]) ).

fof(f_3558_3,plain,
    ! [U_13836,U_13835,U_13834,U_13833,U_13832,U_13831,U_13830] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_13833,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13830,tc_fun(U_13833,tc_HOL_Obool)),U_13835),U_13834)),U_13836))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13833,tc_HOL_Obool)),hAPP(U_13834,sK303(U_13836,U_13835,U_13834,U_13833,U_13832,U_13831,U_13830))),U_13836))
        & hBOOL(hAPP(hAPP(c_member(U_13830),sK303(U_13836,U_13835,U_13834,U_13833,U_13832,U_13831,U_13830)),U_13831)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13830,tc_HOL_Obool)),U_13835),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13830),U_13831),U_13832)))
      | ~ c_Equiv__Relations_Ocongruent(U_13830,tc_fun(U_13833,tc_HOL_Obool),U_13832,U_13834)
      | ~ c_Equiv__Relations_Oequiv(U_13830,U_13831,U_13832) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK303]),skolemize(U_13829,sK303(U_13836,U_13835,U_13834,U_13833,U_13832,U_13831,U_13830))],[f_3558_2]) ).

fof(f_3558_4,plain,
    ( ! [U_13832,U_13834,U_13835,U_13831,U_13836,U_13833,U_13830] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13833,tc_HOL_Obool)),hAPP(U_13834,sK303(U_13836,U_13835,U_13834,U_13833,U_13832,U_13831,U_13830))),U_13836))
        | ~ sP957(U_13832,U_13834,U_13835,U_13831,U_13836,U_13833,U_13830) )
    & ! [U_13832,U_13834,U_13835,U_13831,U_13836,U_13833,U_13830] :
        ( hBOOL(hAPP(hAPP(c_member(U_13830),sK303(U_13836,U_13835,U_13834,U_13833,U_13832,U_13831,U_13830)),U_13831))
        | ~ sP957(U_13832,U_13834,U_13835,U_13831,U_13836,U_13833,U_13830) )
    & ! [U_13832,U_13834,U_13835,U_13831,U_13836,U_13833,U_13830] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_13833,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13830,tc_fun(U_13833,tc_HOL_Obool)),U_13835),U_13834)),U_13836))
        | sP957(U_13832,U_13834,U_13835,U_13831,U_13836,U_13833,U_13830)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13830,tc_HOL_Obool)),U_13835),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13830),U_13831),U_13832)))
        | ~ c_Equiv__Relations_Ocongruent(U_13830,tc_fun(U_13833,tc_HOL_Obool),U_13832,U_13834)
        | ~ c_Equiv__Relations_Oequiv(U_13830,U_13831,U_13832) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP957])],[f_3558_3]) ).

cnf(f_3558_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_13833,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13830,tc_fun(U_13833,tc_HOL_Obool)),U_13835),U_13834)),U_13836))
    | sP957(U_13832,U_13834,U_13835,U_13831,U_13836,U_13833,U_13830)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13830,tc_HOL_Obool)),U_13835),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_13830),U_13831),U_13832)))
    | ~ c_Equiv__Relations_Ocongruent(U_13830,tc_fun(U_13833,tc_HOL_Obool),U_13832,U_13834)
    | ~ c_Equiv__Relations_Oequiv(U_13830,U_13831,U_13832) ),
    inference(clausify,[status(thm)],[f_3558_4]) ).

cnf(f_3558_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13830),sK303(U_13836,U_13835,U_13834,U_13833,U_13832,U_13831,U_13830)),U_13831))
    | ~ sP957(U_13832,U_13834,U_13835,U_13831,U_13836,U_13833,U_13830) ),
    inference(clausify,[status(thm)],[f_3558_4]) ).

cnf(f_3558_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_13833,tc_HOL_Obool)),hAPP(U_13834,sK303(U_13836,U_13835,U_13834,U_13833,U_13832,U_13831,U_13830))),U_13836))
    | ~ sP957(U_13832,U_13834,U_13835,U_13831,U_13836,U_13833,U_13830) ),
    inference(clausify,[status(thm)],[f_3558_4]) ).

fof(f_3559_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_3559_2,plain,
    ! [U_13845,U_13844,U_13843,U_13842,U_13841,U_13840,U_13839] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13839,tc_fun(U_13840,tc_fun(U_13841,tc_HOL_Obool))),U_13842),U_13843),U_13844),U_13845))
        | ! [U_13838] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_13843,U_13838),U_13844),U_13845))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13839),U_13838),U_13842)) ) )
      & ( ? [U_13837] :
            ( hBOOL(hAPP(hAPP(hAPP(U_13843,U_13837),U_13844),U_13845))
            & hBOOL(hAPP(hAPP(c_member(U_13839),U_13837),U_13842)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13839,tc_fun(U_13840,tc_fun(U_13841,tc_HOL_Obool))),U_13842),U_13843),U_13844),U_13845)) ) ),
    inference(variable_rename,[status(thm)],[f_3559_1]) ).

fof(f_3559_3,plain,
    ( ! [U_13859,U_13857,U_13855,U_13853,U_13851,U_13849,U_13847] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13847,tc_fun(U_13849,tc_fun(U_13851,tc_HOL_Obool))),U_13853),U_13855),U_13857),U_13859))
        | ! [U_13838] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_13855,U_13838),U_13857),U_13859))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13847),U_13838),U_13853)) ) )
    & ! [U_13858,U_13856,U_13854,U_13852,U_13850,U_13848,U_13846] :
        ( ? [U_13837] :
            ( hBOOL(hAPP(hAPP(hAPP(U_13854,U_13837),U_13856),U_13858))
            & hBOOL(hAPP(hAPP(c_member(U_13846),U_13837),U_13852)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13846,tc_fun(U_13848,tc_fun(U_13850,tc_HOL_Obool))),U_13852),U_13854),U_13856),U_13858)) ) ),
    inference(miniscope,[status(thm)],[f_3559_2]) ).

fof(f_3559_4,plain,
    ( ! [U_13859,U_13857,U_13855,U_13853,U_13851,U_13849,U_13847] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13847,tc_fun(U_13849,tc_fun(U_13851,tc_HOL_Obool))),U_13853),U_13855),U_13857),U_13859))
        | ! [U_13838] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_13855,U_13838),U_13857),U_13859))
            | ~ hBOOL(hAPP(hAPP(c_member(U_13847),U_13838),U_13853)) ) )
    & ! [U_13858,U_13856,U_13854,U_13852,U_13850,U_13848,U_13846] :
        ( ( hBOOL(hAPP(hAPP(hAPP(U_13854,sK304(U_13858,U_13856,U_13854,U_13852,U_13850,U_13848,U_13846)),U_13856),U_13858))
          & hBOOL(hAPP(hAPP(c_member(U_13846),sK304(U_13858,U_13856,U_13854,U_13852,U_13850,U_13848,U_13846)),U_13852)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13846,tc_fun(U_13848,tc_fun(U_13850,tc_HOL_Obool))),U_13852),U_13854),U_13856),U_13858)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK304]),skolemize(U_13837,sK304(U_13858,U_13856,U_13854,U_13852,U_13850,U_13848,U_13846))],[f_3559_3]) ).

fof(f_3559_5,plain,
    ( ! [U_13850,U_13848,U_13846,U_13854,U_13858,U_13852,U_13856] :
        ( hBOOL(hAPP(hAPP(hAPP(U_13854,sK304(U_13858,U_13856,U_13854,U_13852,U_13850,U_13848,U_13846)),U_13856),U_13858))
        | ~ sP958(U_13850,U_13848,U_13846,U_13854,U_13858,U_13852,U_13856) )
    & ! [U_13850,U_13848,U_13846,U_13854,U_13858,U_13852,U_13856] :
        ( hBOOL(hAPP(hAPP(c_member(U_13846),sK304(U_13858,U_13856,U_13854,U_13852,U_13850,U_13848,U_13846)),U_13852))
        | ~ sP958(U_13850,U_13848,U_13846,U_13854,U_13858,U_13852,U_13856) )
    & ! [U_13838,U_13853,U_13847,U_13849,U_13851,U_13857,U_13855,U_13859] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13847,tc_fun(U_13849,tc_fun(U_13851,tc_HOL_Obool))),U_13853),U_13855),U_13857),U_13859))
        | ~ hBOOL(hAPP(hAPP(hAPP(U_13855,U_13838),U_13857),U_13859))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13847),U_13838),U_13853)) )
    & ! [U_13850,U_13848,U_13846,U_13854,U_13858,U_13852,U_13856] :
        ( sP958(U_13850,U_13848,U_13846,U_13854,U_13858,U_13852,U_13856)
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13846,tc_fun(U_13848,tc_fun(U_13850,tc_HOL_Obool))),U_13852),U_13854),U_13856),U_13858)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP958])],[f_3559_4]) ).

cnf(f_3559_6,plain,
    ( sP958(U_13850,U_13848,U_13846,U_13854,U_13858,U_13852,U_13856)
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13846,tc_fun(U_13848,tc_fun(U_13850,tc_HOL_Obool))),U_13852),U_13854),U_13856),U_13858)) ),
    inference(clausify,[status(thm)],[f_3559_5]) ).

cnf(f_3559_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13847,tc_fun(U_13849,tc_fun(U_13851,tc_HOL_Obool))),U_13853),U_13855),U_13857),U_13859))
    | ~ hBOOL(hAPP(hAPP(hAPP(U_13855,U_13838),U_13857),U_13859))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13847),U_13838),U_13853)) ),
    inference(clausify,[status(thm)],[f_3559_5]) ).

cnf(f_3559_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13846),sK304(U_13858,U_13856,U_13854,U_13852,U_13850,U_13848,U_13846)),U_13852))
    | ~ sP958(U_13850,U_13848,U_13846,U_13854,U_13858,U_13852,U_13856) ),
    inference(clausify,[status(thm)],[f_3559_5]) ).

cnf(f_3559_9,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_13854,sK304(U_13858,U_13856,U_13854,U_13852,U_13850,U_13848,U_13846)),U_13856),U_13858))
    | ~ sP958(U_13850,U_13848,U_13846,U_13854,U_13858,U_13852,U_13856) ),
    inference(clausify,[status(thm)],[f_3559_5]) ).

fof(f_3560_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_3560_2,plain,
    ! [U_13864,U_13863,U_13862,U_13861,U_13860] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13860,U_13861,hAPP(hAPP(c_Set_Oinsert(U_13860),U_13862),U_13863)),U_13864))
      | hBOOL(hAPP(hAPP(c_member(U_13860),U_13862),U_13863))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13860,U_13860,U_13861,U_13862,U_13863),U_13864)) ),
    inference(variable_rename,[status(thm)],[f_3560_1]) ).

fof(f_3560_3,plain,
    ! [U_13863,U_13862,U_13861,U_13860,U_13864] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13860,U_13861,hAPP(hAPP(c_Set_Oinsert(U_13860),U_13862),U_13863)),U_13864))
      | hBOOL(hAPP(hAPP(c_member(U_13860),U_13862),U_13863))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13860,U_13860,U_13861,U_13862,U_13863),U_13864)) ),
    inference(definitional_conversion,[status(esa)],[f_3560_2]) ).

cnf(f_3560_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13860,U_13861,hAPP(hAPP(c_Set_Oinsert(U_13860),U_13862),U_13863)),U_13864))
    | hBOOL(hAPP(hAPP(c_member(U_13860),U_13862),U_13863))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_13860,U_13860,U_13861,U_13862,U_13863),U_13864)) ),
    inference(clausify,[status(thm)],[f_3560_3]) ).

fof(f_3561_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_3561_2,plain,
    ! [U_13870,U_13869,U_13868,U_13867,U_13866] :
      ( ? [U_13865] :
          ( hAPP(U_13869,U_13865) = hAPP(c_Option_Ooption_OSome(U_13866),U_13867)
          & hBOOL(hAPP(hAPP(c_member(U_13868),U_13865),U_13870)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13866),U_13867),c_Map_Oran(U_13868,U_13866,c_Map_Orestrict__map(U_13868,U_13866,U_13869,U_13870)))) ),
    inference(variable_rename,[status(thm)],[f_3561_1]) ).

fof(f_3561_3,plain,
    ! [U_13870,U_13869,U_13868,U_13867,U_13866] :
      ( ( hAPP(U_13869,sK305(U_13870,U_13869,U_13868,U_13867,U_13866)) = hAPP(c_Option_Ooption_OSome(U_13866),U_13867)
        & hBOOL(hAPP(hAPP(c_member(U_13868),sK305(U_13870,U_13869,U_13868,U_13867,U_13866)),U_13870)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_13866),U_13867),c_Map_Oran(U_13868,U_13866,c_Map_Orestrict__map(U_13868,U_13866,U_13869,U_13870)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK305]),skolemize(U_13865,sK305(U_13870,U_13869,U_13868,U_13867,U_13866))],[f_3561_2]) ).

fof(f_3561_4,plain,
    ( ! [U_13866,U_13867,U_13868,U_13869,U_13870] :
        ( hAPP(U_13869,sK305(U_13870,U_13869,U_13868,U_13867,U_13866)) = hAPP(c_Option_Ooption_OSome(U_13866),U_13867)
        | ~ sP959(U_13866,U_13867,U_13868,U_13869,U_13870) )
    & ! [U_13866,U_13867,U_13868,U_13869,U_13870] :
        ( hBOOL(hAPP(hAPP(c_member(U_13868),sK305(U_13870,U_13869,U_13868,U_13867,U_13866)),U_13870))
        | ~ sP959(U_13866,U_13867,U_13868,U_13869,U_13870) )
    & ! [U_13866,U_13867,U_13868,U_13869,U_13870] :
        ( sP959(U_13866,U_13867,U_13868,U_13869,U_13870)
        | ~ hBOOL(hAPP(hAPP(c_member(U_13866),U_13867),c_Map_Oran(U_13868,U_13866,c_Map_Orestrict__map(U_13868,U_13866,U_13869,U_13870)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP959])],[f_3561_3]) ).

cnf(f_3561_5,plain,
    ( sP959(U_13866,U_13867,U_13868,U_13869,U_13870)
    | ~ hBOOL(hAPP(hAPP(c_member(U_13866),U_13867),c_Map_Oran(U_13868,U_13866,c_Map_Orestrict__map(U_13868,U_13866,U_13869,U_13870)))) ),
    inference(clausify,[status(thm)],[f_3561_4]) ).

cnf(f_3561_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13868),sK305(U_13870,U_13869,U_13868,U_13867,U_13866)),U_13870))
    | ~ sP959(U_13866,U_13867,U_13868,U_13869,U_13870) ),
    inference(clausify,[status(thm)],[f_3561_4]) ).

cnf(f_3561_7,plain,
    ( hAPP(U_13869,sK305(U_13870,U_13869,U_13868,U_13867,U_13866)) = hAPP(c_Option_Ooption_OSome(U_13866),U_13867)
    | ~ sP959(U_13866,U_13867,U_13868,U_13869,U_13870) ),
    inference(clausify,[status(thm)],[f_3561_4]) ).

fof(f_3562_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_3562_2,plain,
    ! [U_13873,U_13872,U_13871] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_13871),U_13872) = U_13873
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13871),U_13872),U_13873) != c_Orderings_Otop__class_Otop(U_13871)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13871),U_13872),U_13873) != c_Orderings_Obot__class_Obot(U_13871)
      | ~ class_Lattices_Oboolean__algebra(U_13871) ),
    inference(variable_rename,[status(thm)],[f_3562_1]) ).

fof(f_3562_3,plain,
    ! [U_13871,U_13872,U_13873] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_13871),U_13872) = U_13873
      | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13871),U_13872),U_13873) != c_Orderings_Otop__class_Otop(U_13871)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13871),U_13872),U_13873) != c_Orderings_Obot__class_Obot(U_13871)
      | ~ class_Lattices_Oboolean__algebra(U_13871) ),
    inference(definitional_conversion,[status(esa)],[f_3562_2]) ).

cnf(f_3562_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_13871),U_13872) = U_13873
    | hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13871),U_13872),U_13873) != c_Orderings_Otop__class_Otop(U_13871)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13871),U_13872),U_13873) != c_Orderings_Obot__class_Obot(U_13871)
    | ~ class_Lattices_Oboolean__algebra(U_13871) ),
    inference(clausify,[status(thm)],[f_3562_3]) ).

fof(f_3563_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_3563_2,plain,
    ! [U_13875,U_13874] : hBOOL(hAPP(hAPP(c_member(U_13874),U_13875),c_Orderings_Otop__class_Otop(tc_fun(U_13874,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3563_1]) ).

fof(f_3563_3,plain,
    ! [U_13875,U_13874] : hBOOL(hAPP(hAPP(c_member(U_13874),U_13875),c_Orderings_Otop__class_Otop(tc_fun(U_13874,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3563_2]) ).

cnf(f_3563_4,plain,
    hBOOL(hAPP(hAPP(c_member(U_13874),U_13875),c_Orderings_Otop__class_Otop(tc_fun(U_13874,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3563_3]) ).

fof(f_3564_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_3564_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_3564_1]) ).

cnf(f_3564_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_3564_2]) ).

fof(f_3565_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_3565_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_3565_1]) ).

cnf(f_3565_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_3565_2]) ).

fof(f_3566_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_3566_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_3566_1]) ).

cnf(f_3566_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_3566_2]) ).

fof(f_3567_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_3567_2,plain,
    ! [U_13880,U_13879,U_13878,U_13877,U_13876] :
      ( U_13879 = U_13880
      | hAPP(U_13878,U_13879) != hAPP(U_13878,U_13880)
      | ~ c_Fun_Oinj__on(U_13876,U_13877,U_13878,c_Orderings_Otop__class_Otop(tc_fun(U_13876,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3567_1]) ).

fof(f_3567_3,plain,
    ! [U_13880,U_13879,U_13878] :
      ( ! [U_13877,U_13876] : ~ c_Fun_Oinj__on(U_13876,U_13877,U_13878,c_Orderings_Otop__class_Otop(tc_fun(U_13876,tc_HOL_Obool)))
      | U_13879 = U_13880
      | hAPP(U_13878,U_13879) != hAPP(U_13878,U_13880) ),
    inference(miniscope,[status(thm)],[f_3567_2]) ).

fof(f_3567_4,plain,
    ! [U_13876,U_13877,U_13878,U_13879,U_13880] :
      ( ~ c_Fun_Oinj__on(U_13876,U_13877,U_13878,c_Orderings_Otop__class_Otop(tc_fun(U_13876,tc_HOL_Obool)))
      | U_13879 = U_13880
      | hAPP(U_13878,U_13879) != hAPP(U_13878,U_13880) ),
    inference(definitional_conversion,[status(esa)],[f_3567_3]) ).

cnf(f_3567_5,plain,
    ( ~ c_Fun_Oinj__on(U_13876,U_13877,U_13878,c_Orderings_Otop__class_Otop(tc_fun(U_13876,tc_HOL_Obool)))
    | U_13879 = U_13880
    | hAPP(U_13878,U_13879) != hAPP(U_13878,U_13880) ),
    inference(clausify,[status(thm)],[f_3567_4]) ).

fof(f_3568_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_3568_2,plain,
    ! [U_13885,U_13884,U_13883,U_13882,U_13881] :
      ( ( ( hAPP(U_13883,U_13884) = hAPP(U_13883,U_13885)
          | U_13884 != U_13885 )
        & ( U_13884 = U_13885
          | hAPP(U_13883,U_13884) != hAPP(U_13883,U_13885) ) )
      | ~ c_Fun_Oinj__on(U_13881,U_13882,U_13883,c_Orderings_Otop__class_Otop(tc_fun(U_13881,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3568_1]) ).

fof(f_3568_3,plain,
    ! [U_13885,U_13884,U_13883] :
      ( ! [U_13882,U_13881] : ~ c_Fun_Oinj__on(U_13881,U_13882,U_13883,c_Orderings_Otop__class_Otop(tc_fun(U_13881,tc_HOL_Obool)))
      | ( ( hAPP(U_13883,U_13884) = hAPP(U_13883,U_13885)
          | U_13884 != U_13885 )
        & ( U_13884 = U_13885
          | hAPP(U_13883,U_13884) != hAPP(U_13883,U_13885) ) ) ),
    inference(miniscope,[status(thm)],[f_3568_2]) ).

fof(f_3568_4,plain,
    ( ! [U_13883,U_13884,U_13885] :
        ( hAPP(U_13883,U_13884) = hAPP(U_13883,U_13885)
        | U_13884 != U_13885
        | ~ sP960(U_13883,U_13884,U_13885) )
    & ! [U_13883,U_13884,U_13885] :
        ( U_13884 = U_13885
        | hAPP(U_13883,U_13884) != hAPP(U_13883,U_13885)
        | ~ sP960(U_13883,U_13884,U_13885) )
    & ! [U_13882,U_13883,U_13881,U_13884,U_13885] :
        ( ~ c_Fun_Oinj__on(U_13881,U_13882,U_13883,c_Orderings_Otop__class_Otop(tc_fun(U_13881,tc_HOL_Obool)))
        | sP960(U_13883,U_13884,U_13885) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP960])],[f_3568_3]) ).

cnf(f_3568_5,plain,
    ( ~ c_Fun_Oinj__on(U_13881,U_13882,U_13883,c_Orderings_Otop__class_Otop(tc_fun(U_13881,tc_HOL_Obool)))
    | sP960(U_13883,U_13884,U_13885) ),
    inference(clausify,[status(thm)],[f_3568_4]) ).

cnf(f_3568_6,plain,
    ( U_13884 = U_13885
    | hAPP(U_13883,U_13884) != hAPP(U_13883,U_13885)
    | ~ sP960(U_13883,U_13884,U_13885) ),
    inference(clausify,[status(thm)],[f_3568_4]) ).

cnf(f_3568_7,plain,
    ( hAPP(U_13883,U_13884) = hAPP(U_13883,U_13885)
    | U_13884 != U_13885
    | ~ sP960(U_13883,U_13884,U_13885) ),
    inference(clausify,[status(thm)],[f_3568_4]) ).

fof(f_3569_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_3569_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_3569_1]) ).

cnf(f_3569_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_3569_2]) ).

fof(f_3570_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_3570_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_3570_1]) ).

cnf(f_3570_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_3570_2]) ).

fof(f_3571_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_3571_2,plain,
    ! [U_13886] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13886),c_Orderings_Otop__class_Otop(tc_fun(U_13886,tc_HOL_Obool))))
      | ~ class_Finite__Set_Ofinite(U_13886) ),
    inference(variable_rename,[status(thm)],[f_3571_1]) ).

fof(f_3571_3,plain,
    ! [U_13886] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13886),c_Orderings_Otop__class_Otop(tc_fun(U_13886,tc_HOL_Obool))))
      | ~ class_Finite__Set_Ofinite(U_13886) ),
    inference(definitional_conversion,[status(esa)],[f_3571_2]) ).

cnf(f_3571_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13886),c_Orderings_Otop__class_Otop(tc_fun(U_13886,tc_HOL_Obool))))
    | ~ class_Finite__Set_Ofinite(U_13886) ),
    inference(clausify,[status(thm)],[f_3571_3]) ).

fof(f_3572_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_3572_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_3572_1]) ).

cnf(f_3572_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_3572_2]) ).

fof(f_3573_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_3573_2,plain,
    ! [U_13887] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13887)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13887),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13887),c_Orderings_Otop__class_Otop(tc_fun(U_13887,tc_HOL_Obool)))) )
      & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13887),c_Orderings_Otop__class_Otop(tc_fun(U_13887,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13887)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13887),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_3573_1]) ).

fof(f_3573_3,plain,
    ( ! [U_13889] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13889)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13889),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13889),c_Orderings_Otop__class_Otop(tc_fun(U_13889,tc_HOL_Obool)))) )
    & ! [U_13888] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13888),c_Orderings_Otop__class_Otop(tc_fun(U_13888,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13888)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13888),tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_3573_2]) ).

fof(f_3573_4,plain,
    ( ! [U_13889] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13889)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13889),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13889),c_Orderings_Otop__class_Otop(tc_fun(U_13889,tc_HOL_Obool)))) )
    & ! [U_13888] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13888),c_Orderings_Otop__class_Otop(tc_fun(U_13888,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13888)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13888),tc_HOL_Obool)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3573_3]) ).

cnf(f_3573_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13888),c_Orderings_Otop__class_Otop(tc_fun(U_13888,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13888)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13888),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3573_4]) ).

cnf(f_3573_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_13889)),c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13889),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13889),c_Orderings_Otop__class_Otop(tc_fun(U_13889,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3573_4]) ).

fof(f_3574_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_3574_2,plain,
    ! [U_13891,U_13890] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_13890,U_13891)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13890,U_13891),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13891),c_Orderings_Otop__class_Otop(tc_fun(U_13891,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13890),c_Orderings_Otop__class_Otop(tc_fun(U_13890,tc_HOL_Obool)))) )
      & ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13891),c_Orderings_Otop__class_Otop(tc_fun(U_13891,tc_HOL_Obool))))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13890),c_Orderings_Otop__class_Otop(tc_fun(U_13890,tc_HOL_Obool)))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_13890,U_13891)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13890,U_13891),tc_HOL_Obool)))) ) ),
    inference(variable_rename,[status(thm)],[f_3574_1]) ).

fof(f_3574_3,plain,
    ( ! [U_13895,U_13893] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_13893,U_13895)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13893,U_13895),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13895),c_Orderings_Otop__class_Otop(tc_fun(U_13895,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13893),c_Orderings_Otop__class_Otop(tc_fun(U_13893,tc_HOL_Obool)))) )
    & ! [U_13894,U_13892] :
        ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13894),c_Orderings_Otop__class_Otop(tc_fun(U_13894,tc_HOL_Obool))))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_13892),c_Orderings_Otop__class_Otop(tc_fun(U_13892,tc_HOL_Obool)))) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_13892,U_13894)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13892,U_13894),tc_HOL_Obool)))) ) ),
    inference(miniscope,[status(thm)],[f_3574_2]) ).

fof(f_3574_4,plain,
    ( ! [U_13894,U_13892] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13894),c_Orderings_Otop__class_Otop(tc_fun(U_13894,tc_HOL_Obool))))
        | ~ sP961(U_13894,U_13892) )
    & ! [U_13894,U_13892] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13892),c_Orderings_Otop__class_Otop(tc_fun(U_13892,tc_HOL_Obool))))
        | ~ sP961(U_13894,U_13892) )
    & ! [U_13893,U_13895] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_13893,U_13895)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13893,U_13895),tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13895),c_Orderings_Otop__class_Otop(tc_fun(U_13895,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13893),c_Orderings_Otop__class_Otop(tc_fun(U_13893,tc_HOL_Obool)))) )
    & ! [U_13894,U_13892] :
        ( sP961(U_13894,U_13892)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_13892,U_13894)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13892,U_13894),tc_HOL_Obool)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP961])],[f_3574_3]) ).

cnf(f_3574_5,plain,
    ( sP961(U_13894,U_13892)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_13892,U_13894)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13892,U_13894),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3574_4]) ).

cnf(f_3574_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_sum(U_13893,U_13895)),c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13893,U_13895),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13895),c_Orderings_Otop__class_Otop(tc_fun(U_13895,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13893),c_Orderings_Otop__class_Otop(tc_fun(U_13893,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3574_4]) ).

cnf(f_3574_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13892),c_Orderings_Otop__class_Otop(tc_fun(U_13892,tc_HOL_Obool))))
    | ~ sP961(U_13894,U_13892) ),
    inference(clausify,[status(thm)],[f_3574_4]) ).

cnf(f_3574_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13894),c_Orderings_Otop__class_Otop(tc_fun(U_13894,tc_HOL_Obool))))
    | ~ sP961(U_13894,U_13892) ),
    inference(clausify,[status(thm)],[f_3574_4]) ).

fof(f_3575_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_3575_2,plain,
    ! [U_13897,U_13896] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13897),c_Orderings_Otop__class_Otop(tc_fun(U_13897,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13896,U_13897)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13896,U_13897),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3575_1]) ).

fof(f_3575_3,plain,
    ! [U_13897] :
      ( ! [U_13896] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13896,U_13897)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13896,U_13897),tc_HOL_Obool))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_13897),c_Orderings_Otop__class_Otop(tc_fun(U_13897,tc_HOL_Obool)))) ),
    inference(miniscope,[status(thm)],[f_3575_2]) ).

fof(f_3575_4,plain,
    ! [U_13896,U_13897] :
      ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13896,U_13897)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13896,U_13897),tc_HOL_Obool))))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_13897),c_Orderings_Otop__class_Otop(tc_fun(U_13897,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3575_3]) ).

cnf(f_3575_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_13896,U_13897)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13896,U_13897),tc_HOL_Obool))))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_13897),c_Orderings_Otop__class_Otop(tc_fun(U_13897,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3575_4]) ).

fof(f_3576_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_3576_2,plain,
    ! [U_13899,U_13898] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13898,U_13899)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_13898,U_13899),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13899),c_Orderings_Otop__class_Otop(tc_fun(U_13899,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13898),c_Orderings_Otop__class_Otop(tc_fun(U_13898,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3576_1]) ).

fof(f_3576_3,plain,
    ! [U_13898,U_13899] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13898,U_13899)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_13898,U_13899),tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13899),c_Orderings_Otop__class_Otop(tc_fun(U_13899,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13898),c_Orderings_Otop__class_Otop(tc_fun(U_13898,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3576_2]) ).

cnf(f_3576_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_13898,U_13899)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_13898,U_13899),tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13899),c_Orderings_Otop__class_Otop(tc_fun(U_13899,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13898),c_Orderings_Otop__class_Otop(tc_fun(U_13898,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3576_3]) ).

fof(f_3577_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_3577_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_3577_1]) ).

cnf(f_3577_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_3577_2]) ).

fof(f_3578_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_3578_2,plain,
    ! [U_13904,U_13903,U_13902,U_13901,U_13900] : hAPP(c_Set_Oimage(U_13900,U_13901,hAPP(hAPP(c_COMBB(U_13902,U_13901,U_13900),U_13903),U_13904)),c_Orderings_Otop__class_Otop(tc_fun(U_13900,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_13902,U_13901,U_13903),hAPP(c_Set_Oimage(U_13900,U_13902,U_13904),c_Orderings_Otop__class_Otop(tc_fun(U_13900,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3578_1]) ).

fof(f_3578_3,plain,
    ! [U_13900,U_13901,U_13902,U_13903,U_13904] : hAPP(c_Set_Oimage(U_13900,U_13901,hAPP(hAPP(c_COMBB(U_13902,U_13901,U_13900),U_13903),U_13904)),c_Orderings_Otop__class_Otop(tc_fun(U_13900,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_13902,U_13901,U_13903),hAPP(c_Set_Oimage(U_13900,U_13902,U_13904),c_Orderings_Otop__class_Otop(tc_fun(U_13900,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3578_2]) ).

cnf(f_3578_4,plain,
    hAPP(c_Set_Oimage(U_13900,U_13901,hAPP(hAPP(c_COMBB(U_13902,U_13901,U_13900),U_13903),U_13904)),c_Orderings_Otop__class_Otop(tc_fun(U_13900,tc_HOL_Obool))) = hAPP(c_Set_Oimage(U_13902,U_13901,U_13903),hAPP(c_Set_Oimage(U_13900,U_13902,U_13904),c_Orderings_Otop__class_Otop(tc_fun(U_13900,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3578_3]) ).

fof(f_3579_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_3579_2,plain,
    ! [U_13905] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13905),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(U_13905)),c_Option_Ooption_ONone(U_13905)),hAPP(c_Set_Oimage(U_13905,tc_Option_Ooption(U_13905),c_Option_Ooption_OSome(U_13905)),c_Orderings_Otop__class_Otop(tc_fun(U_13905,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3579_1]) ).

fof(f_3579_3,plain,
    ! [U_13905] : c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13905),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(U_13905)),c_Option_Ooption_ONone(U_13905)),hAPP(c_Set_Oimage(U_13905,tc_Option_Ooption(U_13905),c_Option_Ooption_OSome(U_13905)),c_Orderings_Otop__class_Otop(tc_fun(U_13905,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3579_2]) ).

cnf(f_3579_4,plain,
    c_Orderings_Otop__class_Otop(tc_fun(tc_Option_Ooption(U_13905),tc_HOL_Obool)) = hAPP(hAPP(c_Set_Oinsert(tc_Option_Ooption(U_13905)),c_Option_Ooption_ONone(U_13905)),hAPP(c_Set_Oimage(U_13905,tc_Option_Ooption(U_13905),c_Option_Ooption_OSome(U_13905)),c_Orderings_Otop__class_Otop(tc_fun(U_13905,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3579_3]) ).

fof(f_3580_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_3580_2,plain,
    ! [U_13906] : c_Orderings_Otop__class_Otop(tc_fun(U_13906,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_13906,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3580_1]) ).

fof(f_3580_3,plain,
    ! [U_13906] : c_Orderings_Otop__class_Otop(tc_fun(U_13906,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_13906,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3580_2]) ).

cnf(f_3580_4,plain,
    c_Orderings_Otop__class_Otop(tc_fun(U_13906,tc_HOL_Obool)) != c_Orderings_Obot__class_Obot(tc_fun(U_13906,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3580_3]) ).

fof(f_3581_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_3581_2,plain,
    ! [U_13908,U_13907] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13907),c_Orderings_Otop__class_Otop(U_13907)),U_13908) = U_13908
      | ~ class_Lattices_Obounded__lattice__top(U_13907) ),
    inference(variable_rename,[status(thm)],[f_3581_1]) ).

fof(f_3581_3,plain,
    ! [U_13907,U_13908] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13907),c_Orderings_Otop__class_Otop(U_13907)),U_13908) = U_13908
      | ~ class_Lattices_Obounded__lattice__top(U_13907) ),
    inference(definitional_conversion,[status(esa)],[f_3581_2]) ).

cnf(f_3581_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13907),c_Orderings_Otop__class_Otop(U_13907)),U_13908) = U_13908
    | ~ class_Lattices_Obounded__lattice__top(U_13907) ),
    inference(clausify,[status(thm)],[f_3581_3]) ).

fof(f_3582_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_3582_2,plain,
    ! [U_13910,U_13909] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13909),U_13910),c_Orderings_Otop__class_Otop(U_13909)) = U_13910
      | ~ class_Lattices_Obounded__lattice__top(U_13909) ),
    inference(variable_rename,[status(thm)],[f_3582_1]) ).

fof(f_3582_3,plain,
    ! [U_13909,U_13910] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13909),U_13910),c_Orderings_Otop__class_Otop(U_13909)) = U_13910
      | ~ class_Lattices_Obounded__lattice__top(U_13909) ),
    inference(definitional_conversion,[status(esa)],[f_3582_2]) ).

cnf(f_3582_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13909),U_13910),c_Orderings_Otop__class_Otop(U_13909)) = U_13910
    | ~ class_Lattices_Obounded__lattice__top(U_13909) ),
    inference(clausify,[status(thm)],[f_3582_3]) ).

fof(f_3583_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_3583_2,plain,
    ! [U_13913,U_13912,U_13911] :
      ( ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13911),U_13912),U_13913) = c_Orderings_Otop__class_Otop(U_13911)
          | U_13913 != c_Orderings_Otop__class_Otop(U_13911)
          | U_13912 != c_Orderings_Otop__class_Otop(U_13911) )
        & ( ( U_13913 = c_Orderings_Otop__class_Otop(U_13911)
            & U_13912 = c_Orderings_Otop__class_Otop(U_13911) )
          | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13911),U_13912),U_13913) != c_Orderings_Otop__class_Otop(U_13911) ) )
      | ~ class_Lattices_Obounded__lattice__top(U_13911) ),
    inference(variable_rename,[status(thm)],[f_3583_1]) ).

fof(f_3583_3,plain,
    ( ! [U_13911,U_13912,U_13913] :
        ( U_13913 = c_Orderings_Otop__class_Otop(U_13911)
        | ~ sP962(U_13911,U_13912,U_13913) )
    & ! [U_13911,U_13912,U_13913] :
        ( U_13912 = c_Orderings_Otop__class_Otop(U_13911)
        | ~ sP962(U_13911,U_13912,U_13913) )
    & ! [U_13911,U_13912,U_13913] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13911),U_13912),U_13913) = c_Orderings_Otop__class_Otop(U_13911)
        | U_13913 != c_Orderings_Otop__class_Otop(U_13911)
        | U_13912 != c_Orderings_Otop__class_Otop(U_13911)
        | ~ sP963(U_13911,U_13912,U_13913) )
    & ! [U_13911,U_13912,U_13913] :
        ( sP962(U_13911,U_13912,U_13913)
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13911),U_13912),U_13913) != c_Orderings_Otop__class_Otop(U_13911)
        | ~ sP963(U_13911,U_13912,U_13913) )
    & ! [U_13911,U_13912,U_13913] :
        ( sP963(U_13911,U_13912,U_13913)
        | ~ class_Lattices_Obounded__lattice__top(U_13911) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP962,sP963])],[f_3583_2]) ).

cnf(f_3583_4,plain,
    ( sP963(U_13911,U_13912,U_13913)
    | ~ class_Lattices_Obounded__lattice__top(U_13911) ),
    inference(clausify,[status(thm)],[f_3583_3]) ).

cnf(f_3583_5,plain,
    ( sP962(U_13911,U_13912,U_13913)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13911),U_13912),U_13913) != c_Orderings_Otop__class_Otop(U_13911)
    | ~ sP963(U_13911,U_13912,U_13913) ),
    inference(clausify,[status(thm)],[f_3583_3]) ).

cnf(f_3583_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_13911),U_13912),U_13913) = c_Orderings_Otop__class_Otop(U_13911)
    | U_13913 != c_Orderings_Otop__class_Otop(U_13911)
    | U_13912 != c_Orderings_Otop__class_Otop(U_13911)
    | ~ sP963(U_13911,U_13912,U_13913) ),
    inference(clausify,[status(thm)],[f_3583_3]) ).

cnf(f_3583_7,plain,
    ( U_13912 = c_Orderings_Otop__class_Otop(U_13911)
    | ~ sP962(U_13911,U_13912,U_13913) ),
    inference(clausify,[status(thm)],[f_3583_3]) ).

cnf(f_3583_8,plain,
    ( U_13913 = c_Orderings_Otop__class_Otop(U_13911)
    | ~ sP962(U_13911,U_13912,U_13913) ),
    inference(clausify,[status(thm)],[f_3583_3]) ).

fof(f_3584_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_3584_2,plain,
    ! [U_13915,U_13914] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13914,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13914,tc_HOL_Obool))),U_13915) = U_13915,
    inference(variable_rename,[status(thm)],[f_3584_1]) ).

fof(f_3584_3,plain,
    ! [U_13914,U_13915] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13914,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13914,tc_HOL_Obool))),U_13915) = U_13915,
    inference(definitional_conversion,[status(esa)],[f_3584_2]) ).

cnf(f_3584_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13914,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13914,tc_HOL_Obool))),U_13915) = U_13915,
    inference(clausify,[status(thm)],[f_3584_3]) ).

fof(f_3585_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_3585_2,plain,
    ! [U_13917,U_13916] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13916,tc_HOL_Obool)),U_13917),c_Orderings_Otop__class_Otop(tc_fun(U_13916,tc_HOL_Obool))) = U_13917,
    inference(variable_rename,[status(thm)],[f_3585_1]) ).

fof(f_3585_3,plain,
    ! [U_13917,U_13916] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13916,tc_HOL_Obool)),U_13917),c_Orderings_Otop__class_Otop(tc_fun(U_13916,tc_HOL_Obool))) = U_13917,
    inference(definitional_conversion,[status(esa)],[f_3585_2]) ).

cnf(f_3585_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_13916,tc_HOL_Obool)),U_13917),c_Orderings_Otop__class_Otop(tc_fun(U_13916,tc_HOL_Obool))) = U_13917,
    inference(clausify,[status(thm)],[f_3585_3]) ).

fof(f_3586_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_3586_2,plain,
    ! [U_13919,U_13918] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13918),c_Orderings_Otop__class_Otop(U_13918)),U_13919) = c_Orderings_Otop__class_Otop(U_13918)
      | ~ class_Lattices_Obounded__lattice__top(U_13918) ),
    inference(variable_rename,[status(thm)],[f_3586_1]) ).

fof(f_3586_3,plain,
    ! [U_13918,U_13919] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13918),c_Orderings_Otop__class_Otop(U_13918)),U_13919) = c_Orderings_Otop__class_Otop(U_13918)
      | ~ class_Lattices_Obounded__lattice__top(U_13918) ),
    inference(definitional_conversion,[status(esa)],[f_3586_2]) ).

cnf(f_3586_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13918),c_Orderings_Otop__class_Otop(U_13918)),U_13919) = c_Orderings_Otop__class_Otop(U_13918)
    | ~ class_Lattices_Obounded__lattice__top(U_13918) ),
    inference(clausify,[status(thm)],[f_3586_3]) ).

fof(f_3587_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_3587_2,plain,
    ! [U_13921,U_13920] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13920),U_13921),c_Orderings_Otop__class_Otop(U_13920)) = c_Orderings_Otop__class_Otop(U_13920)
      | ~ class_Lattices_Obounded__lattice__top(U_13920) ),
    inference(variable_rename,[status(thm)],[f_3587_1]) ).

fof(f_3587_3,plain,
    ! [U_13920,U_13921] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13920),U_13921),c_Orderings_Otop__class_Otop(U_13920)) = c_Orderings_Otop__class_Otop(U_13920)
      | ~ class_Lattices_Obounded__lattice__top(U_13920) ),
    inference(definitional_conversion,[status(esa)],[f_3587_2]) ).

cnf(f_3587_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_13920),U_13921),c_Orderings_Otop__class_Otop(U_13920)) = c_Orderings_Otop__class_Otop(U_13920)
    | ~ class_Lattices_Obounded__lattice__top(U_13920) ),
    inference(clausify,[status(thm)],[f_3587_3]) ).

fof(f_3588_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_3588_2,plain,
    ! [U_13923,U_13922] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13922,tc_HOL_Obool)),U_13923),c_Orderings_Otop__class_Otop(tc_fun(U_13922,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3588_1]) ).

fof(f_3588_3,plain,
    ! [U_13922,U_13923] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13922,tc_HOL_Obool)),U_13923),c_Orderings_Otop__class_Otop(tc_fun(U_13922,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3588_2]) ).

cnf(f_3588_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_13922,tc_HOL_Obool)),U_13923),c_Orderings_Otop__class_Otop(tc_fun(U_13922,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3588_3]) ).

fof(f_3589_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_3589_2,plain,
    ! [U_13925,U_13924] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13924,tc_HOL_Obool)),U_13925),c_Orderings_Otop__class_Otop(tc_fun(U_13924,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13924,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3589_1]) ).

fof(f_3589_3,plain,
    ! [U_13924,U_13925] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13924,tc_HOL_Obool)),U_13925),c_Orderings_Otop__class_Otop(tc_fun(U_13924,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13924,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3589_2]) ).

cnf(f_3589_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13924,tc_HOL_Obool)),U_13925),c_Orderings_Otop__class_Otop(tc_fun(U_13924,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13924,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3589_3]) ).

fof(f_3590_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_3590_2,plain,
    ! [U_13927,U_13926] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13926,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13926,tc_HOL_Obool))),U_13927) = c_Orderings_Otop__class_Otop(tc_fun(U_13926,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3590_1]) ).

fof(f_3590_3,plain,
    ! [U_13926,U_13927] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13926,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13926,tc_HOL_Obool))),U_13927) = c_Orderings_Otop__class_Otop(tc_fun(U_13926,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3590_2]) ).

cnf(f_3590_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13926,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13926,tc_HOL_Obool))),U_13927) = c_Orderings_Otop__class_Otop(tc_fun(U_13926,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3590_3]) ).

fof(f_3591_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_3591_2,plain,
    ! [U_13929,U_13928] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13928),U_13929),c_Orderings_Otop__class_Otop(U_13928)))
      | ~ class_Orderings_Otop(U_13928) ),
    inference(variable_rename,[status(thm)],[f_3591_1]) ).

fof(f_3591_3,plain,
    ! [U_13928,U_13929] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13928),U_13929),c_Orderings_Otop__class_Otop(U_13928)))
      | ~ class_Orderings_Otop(U_13928) ),
    inference(definitional_conversion,[status(esa)],[f_3591_2]) ).

cnf(f_3591_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_13928),U_13929),c_Orderings_Otop__class_Otop(U_13928)))
    | ~ class_Orderings_Otop(U_13928) ),
    inference(clausify,[status(thm)],[f_3591_3]) ).

fof(f_3592_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_3592_2,plain,
    ! [U_13931,U_13930] : c_Sum__Type_OPlus(U_13930,U_13931,c_Orderings_Otop__class_Otop(tc_fun(U_13930,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13931,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13930,U_13931),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3592_1]) ).

fof(f_3592_3,plain,
    ! [U_13930,U_13931] : c_Sum__Type_OPlus(U_13930,U_13931,c_Orderings_Otop__class_Otop(tc_fun(U_13930,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13931,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13930,U_13931),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3592_2]) ).

cnf(f_3592_4,plain,
    c_Sum__Type_OPlus(U_13930,U_13931,c_Orderings_Otop__class_Otop(tc_fun(U_13930,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13931,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_sum(U_13930,U_13931),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3592_3]) ).

fof(f_3593_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_3593_2,plain,
    ! [U_13932] : c_Orderings_Otop__class_Otop(tc_fun(U_13932,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13932),hAPP(c_COMBK(tc_HOL_Obool,U_13932),c_fTrue)),
    inference(variable_rename,[status(thm)],[f_3593_1]) ).

fof(f_3593_3,plain,
    ! [U_13932] : c_Orderings_Otop__class_Otop(tc_fun(U_13932,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13932),hAPP(c_COMBK(tc_HOL_Obool,U_13932),c_fTrue)),
    inference(definitional_conversion,[status(esa)],[f_3593_2]) ).

cnf(f_3593_4,plain,
    c_Orderings_Otop__class_Otop(tc_fun(U_13932,tc_HOL_Obool)) = hAPP(c_Set_OCollect(U_13932),hAPP(c_COMBK(tc_HOL_Obool,U_13932),c_fTrue)),
    inference(clausify,[status(thm)],[f_3593_3]) ).

fof(f_3594_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_3594_2,plain,
    ! [U_13935,U_13934,U_13933] :
      ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_13934,U_13933)),U_13935) = c_Orderings_Otop__class_Otop(U_13933)
      | ~ class_Orderings_Otop(U_13933) ),
    inference(variable_rename,[status(thm)],[f_3594_1]) ).

fof(f_3594_3,plain,
    ! [U_13933,U_13934,U_13935] :
      ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_13934,U_13933)),U_13935) = c_Orderings_Otop__class_Otop(U_13933)
      | ~ class_Orderings_Otop(U_13933) ),
    inference(definitional_conversion,[status(esa)],[f_3594_2]) ).

cnf(f_3594_4,plain,
    ( hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_13934,U_13933)),U_13935) = c_Orderings_Otop__class_Otop(U_13933)
    | ~ class_Orderings_Otop(U_13933) ),
    inference(clausify,[status(thm)],[f_3594_3]) ).

fof(f_3595_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_3595_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_3595_1]) ).

cnf(f_3595_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_3595_2]) ).

fof(f_3596_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_3596_2,plain,
    ! [U_13936] : hAPP(c_Set_OPow(U_13936),c_Orderings_Otop__class_Otop(tc_fun(U_13936,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13936,tc_HOL_Obool),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3596_1]) ).

fof(f_3596_3,plain,
    ! [U_13936] : hAPP(c_Set_OPow(U_13936),c_Orderings_Otop__class_Otop(tc_fun(U_13936,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13936,tc_HOL_Obool),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3596_2]) ).

cnf(f_3596_4,plain,
    hAPP(c_Set_OPow(U_13936),c_Orderings_Otop__class_Otop(tc_fun(U_13936,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_13936,tc_HOL_Obool),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3596_3]) ).

fof(f_3597_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_3597_2,plain,
    ! [U_13940,U_13939,U_13938,U_13937] :
      ( U_13939 != c_Orderings_Obot__class_Obot(tc_fun(U_13937,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13937,U_13938,U_13939),U_13940)) ),
    inference(variable_rename,[status(thm)],[f_3597_1]) ).

fof(f_3597_3,plain,
    ! [U_13937,U_13938,U_13939,U_13940] :
      ( U_13939 != c_Orderings_Obot__class_Obot(tc_fun(U_13937,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13937,U_13938,U_13939),U_13940)) ),
    inference(definitional_conversion,[status(esa)],[f_3597_2]) ).

cnf(f_3597_4,plain,
    ( U_13939 != c_Orderings_Obot__class_Obot(tc_fun(U_13937,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13937,U_13938,U_13939),U_13940)) ),
    inference(clausify,[status(thm)],[f_3597_3]) ).

fof(f_3598_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_3598_2,plain,
    ! [U_13943,U_13942,U_13941] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13941,U_13942,c_Orderings_Obot__class_Obot(tc_fun(U_13941,tc_HOL_Obool))),U_13943)),
    inference(variable_rename,[status(thm)],[f_3598_1]) ).

fof(f_3598_3,plain,
    ! [U_13941,U_13942,U_13943] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13941,U_13942,c_Orderings_Obot__class_Obot(tc_fun(U_13941,tc_HOL_Obool))),U_13943)),
    inference(definitional_conversion,[status(esa)],[f_3598_2]) ).

cnf(f_3598_4,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_13941,U_13942,c_Orderings_Obot__class_Obot(tc_fun(U_13941,tc_HOL_Obool))),U_13943)),
    inference(clausify,[status(thm)],[f_3598_3]) ).

fof(f_3599_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_3599_2,plain,
    ! [U_13947,U_13946,U_13945,U_13944] : hBOOL(hAPP(hAPP(c_member(U_13944),hAPP(U_13945,U_13946)),hAPP(c_Set_Oimage(U_13947,U_13944,U_13945),c_Orderings_Otop__class_Otop(tc_fun(U_13947,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3599_1]) ).

fof(f_3599_3,plain,
    ! [U_13944,U_13945,U_13946,U_13947] : hBOOL(hAPP(hAPP(c_member(U_13944),hAPP(U_13945,U_13946)),hAPP(c_Set_Oimage(U_13947,U_13944,U_13945),c_Orderings_Otop__class_Otop(tc_fun(U_13947,tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_3599_2]) ).

cnf(f_3599_4,plain,
    hBOOL(hAPP(hAPP(c_member(U_13944),hAPP(U_13945,U_13946)),hAPP(c_Set_Oimage(U_13947,U_13944,U_13945),c_Orderings_Otop__class_Otop(tc_fun(U_13947,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3599_3]) ).

fof(f_3600_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_3600_2,plain,
    ! [U_13952,U_13951,U_13950,U_13949,U_13948] :
      ( hBOOL(hAPP(hAPP(c_member(U_13951),U_13948),hAPP(c_Set_Oimage(U_13952,U_13951,U_13949),c_Orderings_Otop__class_Otop(tc_fun(U_13952,tc_HOL_Obool)))))
      | U_13948 != hAPP(U_13949,U_13950) ),
    inference(variable_rename,[status(thm)],[f_3600_1]) ).

fof(f_3600_3,plain,
    ! [U_13948,U_13949,U_13950,U_13951,U_13952] :
      ( hBOOL(hAPP(hAPP(c_member(U_13951),U_13948),hAPP(c_Set_Oimage(U_13952,U_13951,U_13949),c_Orderings_Otop__class_Otop(tc_fun(U_13952,tc_HOL_Obool)))))
      | U_13948 != hAPP(U_13949,U_13950) ),
    inference(definitional_conversion,[status(esa)],[f_3600_2]) ).

cnf(f_3600_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13951),U_13948),hAPP(c_Set_Oimage(U_13952,U_13951,U_13949),c_Orderings_Otop__class_Otop(tc_fun(U_13952,tc_HOL_Obool)))))
    | U_13948 != hAPP(U_13949,U_13950) ),
    inference(clausify,[status(thm)],[f_3600_3]) ).

fof(f_3601_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_3601_2,plain,
    ! [U_13954,U_13953] :
      ( U_13954 = c_Orderings_Otop__class_Otop(tc_fun(U_13953,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ocard(U_13953),U_13954) != hAPP(c_Finite__Set_Ocard(U_13953),c_Orderings_Otop__class_Otop(tc_fun(U_13953,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13953),c_Orderings_Otop__class_Otop(tc_fun(U_13953,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3601_1]) ).

fof(f_3601_3,plain,
    ! [U_13953,U_13954] :
      ( U_13954 = c_Orderings_Otop__class_Otop(tc_fun(U_13953,tc_HOL_Obool))
      | hAPP(c_Finite__Set_Ocard(U_13953),U_13954) != hAPP(c_Finite__Set_Ocard(U_13953),c_Orderings_Otop__class_Otop(tc_fun(U_13953,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13953),c_Orderings_Otop__class_Otop(tc_fun(U_13953,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3601_2]) ).

cnf(f_3601_4,plain,
    ( U_13954 = c_Orderings_Otop__class_Otop(tc_fun(U_13953,tc_HOL_Obool))
    | hAPP(c_Finite__Set_Ocard(U_13953),U_13954) != hAPP(c_Finite__Set_Ocard(U_13953),c_Orderings_Otop__class_Otop(tc_fun(U_13953,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13953),c_Orderings_Otop__class_Otop(tc_fun(U_13953,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3601_3]) ).

fof(f_3602_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_3602_2,plain,
    ! [U_13956,U_13955] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13955,tc_HOL_Obool)),U_13956),c_Orderings_Otop__class_Otop(tc_fun(U_13955,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13955,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3602_1]) ).

fof(f_3602_3,plain,
    ! [U_13955,U_13956] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13955,tc_HOL_Obool)),U_13956),c_Orderings_Otop__class_Otop(tc_fun(U_13955,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13955,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3602_2]) ).

cnf(f_3602_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13955,tc_HOL_Obool)),U_13956),c_Orderings_Otop__class_Otop(tc_fun(U_13955,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13955,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3602_3]) ).

fof(f_3603_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_3603_2,plain,
    ! [U_13961,U_13960,U_13959,U_13958,U_13957] :
      ( ( ( hAPP(c_Set_Oimage(U_13957,U_13958,U_13959),U_13960) = hAPP(c_Set_Oimage(U_13957,U_13958,U_13959),U_13961)
          | U_13960 != U_13961 )
        & ( U_13960 = U_13961
          | hAPP(c_Set_Oimage(U_13957,U_13958,U_13959),U_13960) != hAPP(c_Set_Oimage(U_13957,U_13958,U_13959),U_13961) ) )
      | ~ c_Fun_Oinj__on(U_13957,U_13958,U_13959,c_Orderings_Otop__class_Otop(tc_fun(U_13957,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3603_1]) ).

fof(f_3603_3,plain,
    ( ! [U_13957,U_13958,U_13959,U_13960,U_13961] :
        ( hAPP(c_Set_Oimage(U_13957,U_13958,U_13959),U_13960) = hAPP(c_Set_Oimage(U_13957,U_13958,U_13959),U_13961)
        | U_13960 != U_13961
        | ~ sP964(U_13957,U_13958,U_13959,U_13960,U_13961) )
    & ! [U_13957,U_13958,U_13959,U_13960,U_13961] :
        ( U_13960 = U_13961
        | hAPP(c_Set_Oimage(U_13957,U_13958,U_13959),U_13960) != hAPP(c_Set_Oimage(U_13957,U_13958,U_13959),U_13961)
        | ~ sP964(U_13957,U_13958,U_13959,U_13960,U_13961) )
    & ! [U_13957,U_13958,U_13959,U_13960,U_13961] :
        ( sP964(U_13957,U_13958,U_13959,U_13960,U_13961)
        | ~ c_Fun_Oinj__on(U_13957,U_13958,U_13959,c_Orderings_Otop__class_Otop(tc_fun(U_13957,tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP964])],[f_3603_2]) ).

cnf(f_3603_4,plain,
    ( sP964(U_13957,U_13958,U_13959,U_13960,U_13961)
    | ~ c_Fun_Oinj__on(U_13957,U_13958,U_13959,c_Orderings_Otop__class_Otop(tc_fun(U_13957,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3603_3]) ).

cnf(f_3603_5,plain,
    ( U_13960 = U_13961
    | hAPP(c_Set_Oimage(U_13957,U_13958,U_13959),U_13960) != hAPP(c_Set_Oimage(U_13957,U_13958,U_13959),U_13961)
    | ~ sP964(U_13957,U_13958,U_13959,U_13960,U_13961) ),
    inference(clausify,[status(thm)],[f_3603_3]) ).

cnf(f_3603_6,plain,
    ( hAPP(c_Set_Oimage(U_13957,U_13958,U_13959),U_13960) = hAPP(c_Set_Oimage(U_13957,U_13958,U_13959),U_13961)
    | U_13960 != U_13961
    | ~ sP964(U_13957,U_13958,U_13959,U_13960,U_13961) ),
    inference(clausify,[status(thm)],[f_3603_3]) ).

fof(f_3604_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_3604_2,plain,
    ! [U_13962] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13962,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13962,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13962,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3604_1]) ).

fof(f_3604_3,plain,
    ! [U_13962] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13962,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13962,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13962,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3604_2]) ).

cnf(f_3604_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13962,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13962,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_13962,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3604_3]) ).

fof(f_3605_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_3605_2,plain,
    ! [U_13963] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13963,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13963,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13963,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3605_1]) ).

fof(f_3605_3,plain,
    ! [U_13963] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13963,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13963,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13963,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3605_2]) ).

cnf(f_3605_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13963,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_13963,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_13963,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3605_3]) ).

fof(f_3606_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_3606_2,plain,
    ! [U_13965,U_13964] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13964),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13964,tc_HOL_Obool)),U_13965)))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13964),c_Orderings_Otop__class_Otop(tc_fun(U_13964,tc_HOL_Obool)))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13964),c_Orderings_Otop__class_Otop(tc_fun(U_13964,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13964),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13964,tc_HOL_Obool)),U_13965))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13964),U_13965)) ),
    inference(variable_rename,[status(thm)],[f_3606_1]) ).

fof(f_3606_3,plain,
    ( ! [U_13964,U_13965] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13964),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13964,tc_HOL_Obool)),U_13965)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13964),c_Orderings_Otop__class_Otop(tc_fun(U_13964,tc_HOL_Obool))))
        | ~ sP965(U_13964,U_13965) )
    & ! [U_13964,U_13965] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13964),c_Orderings_Otop__class_Otop(tc_fun(U_13964,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13964),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13964,tc_HOL_Obool)),U_13965)))
        | ~ sP965(U_13964,U_13965) )
    & ! [U_13964,U_13965] :
        ( sP965(U_13964,U_13965)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13964),U_13965)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP965])],[f_3606_2]) ).

cnf(f_3606_4,plain,
    ( sP965(U_13964,U_13965)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13964),U_13965)) ),
    inference(clausify,[status(thm)],[f_3606_3]) ).

cnf(f_3606_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13964),c_Orderings_Otop__class_Otop(tc_fun(U_13964,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13964),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13964,tc_HOL_Obool)),U_13965)))
    | ~ sP965(U_13964,U_13965) ),
    inference(clausify,[status(thm)],[f_3606_3]) ).

cnf(f_3606_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13964),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13964,tc_HOL_Obool)),U_13965)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13964),c_Orderings_Otop__class_Otop(tc_fun(U_13964,tc_HOL_Obool))))
    | ~ sP965(U_13964,U_13965) ),
    inference(clausify,[status(thm)],[f_3606_3]) ).

fof(f_3607_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_3607_2,plain,
    ! [U_13967,U_13966] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13966,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13966,tc_HOL_Obool)),U_13967)),U_13967) = c_Orderings_Otop__class_Otop(tc_fun(U_13966,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3607_1]) ).

fof(f_3607_3,plain,
    ! [U_13967,U_13966] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13966,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13966,tc_HOL_Obool)),U_13967)),U_13967) = c_Orderings_Otop__class_Otop(tc_fun(U_13966,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3607_2]) ).

cnf(f_3607_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13966,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13966,tc_HOL_Obool)),U_13967)),U_13967) = c_Orderings_Otop__class_Otop(tc_fun(U_13966,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3607_3]) ).

fof(f_3608_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_3608_2,plain,
    ! [U_13969,U_13968] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13968,tc_HOL_Obool)),U_13969),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13968,tc_HOL_Obool)),U_13969)) = c_Orderings_Otop__class_Otop(tc_fun(U_13968,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3608_1]) ).

fof(f_3608_3,plain,
    ! [U_13968,U_13969] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13968,tc_HOL_Obool)),U_13969),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13968,tc_HOL_Obool)),U_13969)) = c_Orderings_Otop__class_Otop(tc_fun(U_13968,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3608_2]) ).

cnf(f_3608_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_13968,tc_HOL_Obool)),U_13969),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13968,tc_HOL_Obool)),U_13969)) = c_Orderings_Otop__class_Otop(tc_fun(U_13968,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3608_3]) ).

fof(f_3609_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_3609_2,plain,
    ! [U_13971,U_13970] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13970,tc_HOL_Obool)),U_13971) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13970,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13970,tc_HOL_Obool))),U_13971),
    inference(variable_rename,[status(thm)],[f_3609_1]) ).

fof(f_3609_3,plain,
    ! [U_13970,U_13971] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13970,tc_HOL_Obool)),U_13971) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13970,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13970,tc_HOL_Obool))),U_13971),
    inference(definitional_conversion,[status(esa)],[f_3609_2]) ).

cnf(f_3609_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_13970,tc_HOL_Obool)),U_13971) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_13970,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13970,tc_HOL_Obool))),U_13971),
    inference(clausify,[status(thm)],[f_3609_3]) ).

fof(f_3610_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_3610_2,plain,
    ! [U_13973,U_13972] : hAPP(c_Relation_ODomain(U_13972,U_13972),c_Transitive__Closure_Ortrancl(U_13972,U_13973)) = c_Orderings_Otop__class_Otop(tc_fun(U_13972,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3610_1]) ).

fof(f_3610_3,plain,
    ! [U_13972,U_13973] : hAPP(c_Relation_ODomain(U_13972,U_13972),c_Transitive__Closure_Ortrancl(U_13972,U_13973)) = c_Orderings_Otop__class_Otop(tc_fun(U_13972,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3610_2]) ).

cnf(f_3610_4,plain,
    hAPP(c_Relation_ODomain(U_13972,U_13972),c_Transitive__Closure_Ortrancl(U_13972,U_13973)) = c_Orderings_Otop__class_Otop(tc_fun(U_13972,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3610_3]) ).

fof(f_3611_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_3611_2,plain,
    ! [U_13975,U_13974] : hAPP(c_Relation_ORange(U_13974,U_13974),c_Transitive__Closure_Ortrancl(U_13974,U_13975)) = c_Orderings_Otop__class_Otop(tc_fun(U_13974,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3611_1]) ).

fof(f_3611_3,plain,
    ! [U_13974,U_13975] : hAPP(c_Relation_ORange(U_13974,U_13974),c_Transitive__Closure_Ortrancl(U_13974,U_13975)) = c_Orderings_Otop__class_Otop(tc_fun(U_13974,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3611_2]) ).

cnf(f_3611_4,plain,
    hAPP(c_Relation_ORange(U_13974,U_13974),c_Transitive__Closure_Ortrancl(U_13974,U_13975)) = c_Orderings_Otop__class_Otop(tc_fun(U_13974,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3611_3]) ).

fof(f_3612_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_3612_2,plain,
    ! [U_13976] : hAPP(c_Relation_ODomain(U_13976,U_13976),c_Relation_OId(U_13976)) = c_Orderings_Otop__class_Otop(tc_fun(U_13976,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3612_1]) ).

fof(f_3612_3,plain,
    ! [U_13976] : hAPP(c_Relation_ODomain(U_13976,U_13976),c_Relation_OId(U_13976)) = c_Orderings_Otop__class_Otop(tc_fun(U_13976,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3612_2]) ).

cnf(f_3612_4,plain,
    hAPP(c_Relation_ODomain(U_13976,U_13976),c_Relation_OId(U_13976)) = c_Orderings_Otop__class_Otop(tc_fun(U_13976,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3612_3]) ).

fof(f_3613_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_3613_2,plain,
    ! [U_13978,U_13977] :
      ( ( ( hAPP(c_Code__Numeral_Oof__nat,U_13977) = hAPP(c_Code__Numeral_Oof__nat,U_13978)
          | U_13977 != U_13978 )
        & ( U_13977 = U_13978
          | hAPP(c_Code__Numeral_Oof__nat,U_13977) != hAPP(c_Code__Numeral_Oof__nat,U_13978) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_13978),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_13977),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3613_1]) ).

fof(f_3613_3,plain,
    ( ! [U_13977,U_13978] :
        ( hAPP(c_Code__Numeral_Oof__nat,U_13977) = hAPP(c_Code__Numeral_Oof__nat,U_13978)
        | U_13977 != U_13978
        | ~ sP966(U_13977,U_13978) )
    & ! [U_13977,U_13978] :
        ( U_13977 = U_13978
        | hAPP(c_Code__Numeral_Oof__nat,U_13977) != hAPP(c_Code__Numeral_Oof__nat,U_13978)
        | ~ sP966(U_13977,U_13978) )
    & ! [U_13977,U_13978] :
        ( sP966(U_13977,U_13978)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_13978),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_13977),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP966])],[f_3613_2]) ).

cnf(f_3613_4,plain,
    ( sP966(U_13977,U_13978)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_13978),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_13977),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3613_3]) ).

cnf(f_3613_5,plain,
    ( U_13977 = U_13978
    | hAPP(c_Code__Numeral_Oof__nat,U_13977) != hAPP(c_Code__Numeral_Oof__nat,U_13978)
    | ~ sP966(U_13977,U_13978) ),
    inference(clausify,[status(thm)],[f_3613_3]) ).

cnf(f_3613_6,plain,
    ( hAPP(c_Code__Numeral_Oof__nat,U_13977) = hAPP(c_Code__Numeral_Oof__nat,U_13978)
    | U_13977 != U_13978
    | ~ sP966(U_13977,U_13978) ),
    inference(clausify,[status(thm)],[f_3613_3]) ).

fof(f_3614_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_3614_2,plain,
    ! [U_13979] : hAPP(c_Relation_ORange(U_13979,U_13979),c_Relation_OId(U_13979)) = c_Orderings_Otop__class_Otop(tc_fun(U_13979,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3614_1]) ).

fof(f_3614_3,plain,
    ! [U_13979] : hAPP(c_Relation_ORange(U_13979,U_13979),c_Relation_OId(U_13979)) = c_Orderings_Otop__class_Otop(tc_fun(U_13979,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3614_2]) ).

cnf(f_3614_4,plain,
    hAPP(c_Relation_ORange(U_13979,U_13979),c_Relation_OId(U_13979)) = c_Orderings_Otop__class_Otop(tc_fun(U_13979,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3614_3]) ).

fof(f_3615_1,plain,
    ! [V_Pa_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_Pa_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_Pa_2)))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_OCollect(T_b),V_Pa_2))) ),
    inference(fof_nnf,[status(thm)],[fact_finite__Collect__not]) ).

fof(f_3615_2,plain,
    ! [U_13981,U_13980] :
      ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13980),hAPP(c_Set_OCollect(U_13980),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13980),c_fNot),U_13981))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13980),c_Orderings_Otop__class_Otop(tc_fun(U_13980,tc_HOL_Obool)))) )
        & ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13980),c_Orderings_Otop__class_Otop(tc_fun(U_13980,tc_HOL_Obool))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13980),hAPP(c_Set_OCollect(U_13980),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13980),c_fNot),U_13981)))) ) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13980),hAPP(c_Set_OCollect(U_13980),U_13981))) ),
    inference(variable_rename,[status(thm)],[f_3615_1]) ).

fof(f_3615_3,plain,
    ( ! [U_13981,U_13980] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13980),hAPP(c_Set_OCollect(U_13980),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13980),c_fNot),U_13981))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13980),c_Orderings_Otop__class_Otop(tc_fun(U_13980,tc_HOL_Obool))))
        | ~ sP967(U_13981,U_13980) )
    & ! [U_13981,U_13980] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13980),c_Orderings_Otop__class_Otop(tc_fun(U_13980,tc_HOL_Obool))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13980),hAPP(c_Set_OCollect(U_13980),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13980),c_fNot),U_13981))))
        | ~ sP967(U_13981,U_13980) )
    & ! [U_13981,U_13980] :
        ( sP967(U_13981,U_13980)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13980),hAPP(c_Set_OCollect(U_13980),U_13981))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP967])],[f_3615_2]) ).

cnf(f_3615_4,plain,
    ( sP967(U_13981,U_13980)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13980),hAPP(c_Set_OCollect(U_13980),U_13981))) ),
    inference(clausify,[status(thm)],[f_3615_3]) ).

cnf(f_3615_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13980),c_Orderings_Otop__class_Otop(tc_fun(U_13980,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13980),hAPP(c_Set_OCollect(U_13980),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13980),c_fNot),U_13981))))
    | ~ sP967(U_13981,U_13980) ),
    inference(clausify,[status(thm)],[f_3615_3]) ).

cnf(f_3615_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13980),hAPP(c_Set_OCollect(U_13980),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_13980),c_fNot),U_13981))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13980),c_Orderings_Otop__class_Otop(tc_fun(U_13980,tc_HOL_Obool))))
    | ~ sP967(U_13981,U_13980) ),
    inference(clausify,[status(thm)],[f_3615_3]) ).

fof(f_3616_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_3616_2,plain,
    ! [U_13985,U_13984,U_13983,U_13982] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13982,tc_fun(U_13983,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13982,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13983,tc_HOL_Obool),tc_fun(U_13983,tc_HOL_Obool),U_13982),hAPP(c_COMBC(U_13983,tc_fun(U_13983,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13983))),U_13984)),U_13985))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13983),U_13985),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13982,tc_fun(U_13983,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13982,tc_HOL_Obool))),U_13984))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_13983),U_13985),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13982,tc_fun(U_13983,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13982,tc_HOL_Obool))),U_13984)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13982,tc_fun(U_13983,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13982,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13983,tc_HOL_Obool),tc_fun(U_13983,tc_HOL_Obool),U_13982),hAPP(c_COMBC(U_13983,tc_fun(U_13983,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13983))),U_13984)),U_13985)) ) ),
    inference(variable_rename,[status(thm)],[f_3616_1]) ).

fof(f_3616_3,plain,
    ( ! [U_13993,U_13991,U_13989,U_13987] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13987,tc_fun(U_13989,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13987,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13989,tc_HOL_Obool),tc_fun(U_13989,tc_HOL_Obool),U_13987),hAPP(c_COMBC(U_13989,tc_fun(U_13989,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13989))),U_13991)),U_13993))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13989),U_13993),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13987,tc_fun(U_13989,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13987,tc_HOL_Obool))),U_13991))) )
    & ! [U_13992,U_13990,U_13988,U_13986] :
        ( hBOOL(hAPP(hAPP(c_member(U_13988),U_13992),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13986,tc_fun(U_13988,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13986,tc_HOL_Obool))),U_13990)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13986,tc_fun(U_13988,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13986,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13988,tc_HOL_Obool),tc_fun(U_13988,tc_HOL_Obool),U_13986),hAPP(c_COMBC(U_13988,tc_fun(U_13988,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13988))),U_13990)),U_13992)) ) ),
    inference(miniscope,[status(thm)],[f_3616_2]) ).

fof(f_3616_4,plain,
    ( ! [U_13987,U_13989,U_13991,U_13993] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13987,tc_fun(U_13989,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13987,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13989,tc_HOL_Obool),tc_fun(U_13989,tc_HOL_Obool),U_13987),hAPP(c_COMBC(U_13989,tc_fun(U_13989,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13989))),U_13991)),U_13993))
        | ~ hBOOL(hAPP(hAPP(c_member(U_13989),U_13993),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13987,tc_fun(U_13989,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13987,tc_HOL_Obool))),U_13991))) )
    & ! [U_13988,U_13992,U_13986,U_13990] :
        ( hBOOL(hAPP(hAPP(c_member(U_13988),U_13992),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13986,tc_fun(U_13988,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13986,tc_HOL_Obool))),U_13990)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13986,tc_fun(U_13988,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13986,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13988,tc_HOL_Obool),tc_fun(U_13988,tc_HOL_Obool),U_13986),hAPP(c_COMBC(U_13988,tc_fun(U_13988,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13988))),U_13990)),U_13992)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3616_3]) ).

cnf(f_3616_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_13988),U_13992),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13986,tc_fun(U_13988,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13986,tc_HOL_Obool))),U_13990)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13986,tc_fun(U_13988,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13986,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13988,tc_HOL_Obool),tc_fun(U_13988,tc_HOL_Obool),U_13986),hAPP(c_COMBC(U_13988,tc_fun(U_13988,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13988))),U_13990)),U_13992)) ),
    inference(clausify,[status(thm)],[f_3616_4]) ).

cnf(f_3616_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13987,tc_fun(U_13989,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13987,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_13989,tc_HOL_Obool),tc_fun(U_13989,tc_HOL_Obool),U_13987),hAPP(c_COMBC(U_13989,tc_fun(U_13989,tc_HOL_Obool),tc_HOL_Obool),c_member(U_13989))),U_13991)),U_13993))
    | ~ hBOOL(hAPP(hAPP(c_member(U_13989),U_13993),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_13987,tc_fun(U_13989,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_13987,tc_HOL_Obool))),U_13991))) ),
    inference(clausify,[status(thm)],[f_3616_4]) ).

fof(f_3617_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_3617_2,plain,
    ! [U_13998,U_13997,U_13996,U_13995,U_13994] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13997),hAPP(c_Set_Oimage(U_13995,U_13997,hAPP(hAPP(c_COMBB(U_13994,U_13997,U_13995),U_13998),U_13996)),c_Orderings_Otop__class_Otop(tc_fun(U_13995,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13994),hAPP(c_Set_Oimage(U_13995,U_13994,U_13996),c_Orderings_Otop__class_Otop(tc_fun(U_13995,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_3617_1]) ).

fof(f_3617_3,plain,
    ! [U_13994,U_13995,U_13996,U_13997,U_13998] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13997),hAPP(c_Set_Oimage(U_13995,U_13997,hAPP(hAPP(c_COMBB(U_13994,U_13997,U_13995),U_13998),U_13996)),c_Orderings_Otop__class_Otop(tc_fun(U_13995,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13994),hAPP(c_Set_Oimage(U_13995,U_13994,U_13996),c_Orderings_Otop__class_Otop(tc_fun(U_13995,tc_HOL_Obool))))) ),
    inference(definitional_conversion,[status(esa)],[f_3617_2]) ).

cnf(f_3617_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_13997),hAPP(c_Set_Oimage(U_13995,U_13997,hAPP(hAPP(c_COMBB(U_13994,U_13997,U_13995),U_13998),U_13996)),c_Orderings_Otop__class_Otop(tc_fun(U_13995,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_13994),hAPP(c_Set_Oimage(U_13995,U_13994,U_13996),c_Orderings_Otop__class_Otop(tc_fun(U_13995,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_3617_3]) ).

fof(f_3618_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_3618_2,plain,
    ! [U_13999] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_13999)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3618_1]) ).

fof(f_3618_3,plain,
    ! [U_13999] : hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_13999)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3618_2]) ).

cnf(f_3618_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),hAPP(c_Code__Numeral_Onat__of,U_13999)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3618_3]) ).

fof(f_3619_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_3619_2,plain,
    ! [U_14003,U_14002,U_14001,U_14000] :
      ( hAPP(c_Fun_Othe__inv__into(U_14000,U_14001,c_Orderings_Otop__class_Otop(tc_fun(U_14000,tc_HOL_Obool)),U_14002),hAPP(U_14002,U_14003)) = U_14003
      | ~ c_Fun_Oinj__on(U_14000,U_14001,U_14002,c_Orderings_Otop__class_Otop(tc_fun(U_14000,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3619_1]) ).

fof(f_3619_3,plain,
    ! [U_14000,U_14001,U_14002,U_14003] :
      ( hAPP(c_Fun_Othe__inv__into(U_14000,U_14001,c_Orderings_Otop__class_Otop(tc_fun(U_14000,tc_HOL_Obool)),U_14002),hAPP(U_14002,U_14003)) = U_14003
      | ~ c_Fun_Oinj__on(U_14000,U_14001,U_14002,c_Orderings_Otop__class_Otop(tc_fun(U_14000,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3619_2]) ).

cnf(f_3619_4,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_14000,U_14001,c_Orderings_Otop__class_Otop(tc_fun(U_14000,tc_HOL_Obool)),U_14002),hAPP(U_14002,U_14003)) = U_14003
    | ~ c_Fun_Oinj__on(U_14000,U_14001,U_14002,c_Orderings_Otop__class_Otop(tc_fun(U_14000,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3619_3]) ).

fof(f_3620_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_3620_2,plain,
    ! [U_14005,U_14004] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14004),c_Orderings_Otop__class_Otop(tc_fun(U_14004,tc_HOL_Obool))))
      | hAPP(c_Finite__Set_Ocard(U_14005),c_Orderings_Otop__class_Otop(tc_fun(U_14005,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_14004,U_14005)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_14004,U_14005),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3620_1]) ).

fof(f_3620_3,plain,
    ! [U_14004,U_14005] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14004),c_Orderings_Otop__class_Otop(tc_fun(U_14004,tc_HOL_Obool))))
      | hAPP(c_Finite__Set_Ocard(U_14005),c_Orderings_Otop__class_Otop(tc_fun(U_14005,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_14004,U_14005)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_14004,U_14005),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3620_2]) ).

cnf(f_3620_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14004),c_Orderings_Otop__class_Otop(tc_fun(U_14004,tc_HOL_Obool))))
    | hAPP(c_Finite__Set_Ocard(U_14005),c_Orderings_Otop__class_Otop(tc_fun(U_14005,tc_HOL_Obool))) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_14004,U_14005)),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_14004,U_14005),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3620_3]) ).

fof(f_3621_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_3621_2,plain,
    ! [U_14006] :
      ( c_Fun_Oinj__on(tc_Nat_Onat,U_14006,c_Nat_Osemiring__1__class_Oof__nat(U_14006),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
      | ~ class_Nat_Osemiring__char__0(U_14006) ),
    inference(variable_rename,[status(thm)],[f_3621_1]) ).

fof(f_3621_3,plain,
    ! [U_14006] :
      ( c_Fun_Oinj__on(tc_Nat_Onat,U_14006,c_Nat_Osemiring__1__class_Oof__nat(U_14006),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
      | ~ class_Nat_Osemiring__char__0(U_14006) ),
    inference(definitional_conversion,[status(esa)],[f_3621_2]) ).

cnf(f_3621_4,plain,
    ( c_Fun_Oinj__on(tc_Nat_Onat,U_14006,c_Nat_Osemiring__1__class_Oof__nat(U_14006),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))
    | ~ class_Nat_Osemiring__char__0(U_14006) ),
    inference(clausify,[status(thm)],[f_3621_3]) ).

fof(f_3622_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_3622_2,plain,
    ! [U_14009,U_14008,U_14007] : c_Map_Odom(U_14007,U_14008,hAPP(hAPP(c_COMBB(U_14008,tc_Option_Ooption(U_14008),U_14007),c_Option_Ooption_OSome(U_14008)),U_14009)) = c_Orderings_Otop__class_Otop(tc_fun(U_14007,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3622_1]) ).

fof(f_3622_3,plain,
    ! [U_14007,U_14008,U_14009] : c_Map_Odom(U_14007,U_14008,hAPP(hAPP(c_COMBB(U_14008,tc_Option_Ooption(U_14008),U_14007),c_Option_Ooption_OSome(U_14008)),U_14009)) = c_Orderings_Otop__class_Otop(tc_fun(U_14007,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3622_2]) ).

cnf(f_3622_4,plain,
    c_Map_Odom(U_14007,U_14008,hAPP(hAPP(c_COMBB(U_14008,tc_Option_Ooption(U_14008),U_14007),c_Option_Ooption_OSome(U_14008)),U_14009)) = c_Orderings_Otop__class_Otop(tc_fun(U_14007,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3622_3]) ).

fof(f_3623_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_3623_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_3623_1]) ).

cnf(f_3623_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_3623_2]) ).

fof(f_3624_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_3624_2,plain,
    ! [U_14013,U_14012,U_14011,U_14010] :
      ( c_Fun_Oinj__on(U_14010,tc_fun(U_14013,U_14011),hAPP(hAPP(c_COMBB(U_14011,tc_fun(U_14013,U_14011),U_14010),c_COMBK(U_14011,U_14013)),U_14012),c_Orderings_Otop__class_Otop(tc_fun(U_14010,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_14010,U_14011,U_14012,c_Orderings_Otop__class_Otop(tc_fun(U_14010,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3624_1]) ).

fof(f_3624_3,plain,
    ! [U_14010,U_14011,U_14012,U_14013] :
      ( c_Fun_Oinj__on(U_14010,tc_fun(U_14013,U_14011),hAPP(hAPP(c_COMBB(U_14011,tc_fun(U_14013,U_14011),U_14010),c_COMBK(U_14011,U_14013)),U_14012),c_Orderings_Otop__class_Otop(tc_fun(U_14010,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_14010,U_14011,U_14012,c_Orderings_Otop__class_Otop(tc_fun(U_14010,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3624_2]) ).

cnf(f_3624_4,plain,
    ( c_Fun_Oinj__on(U_14010,tc_fun(U_14013,U_14011),hAPP(hAPP(c_COMBB(U_14011,tc_fun(U_14013,U_14011),U_14010),c_COMBK(U_14011,U_14013)),U_14012),c_Orderings_Otop__class_Otop(tc_fun(U_14010,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_14010,U_14011,U_14012,c_Orderings_Otop__class_Otop(tc_fun(U_14010,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3624_3]) ).

fof(f_3625_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_3625_2,plain,
    ! [U_14014] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_14014),c_Orderings_Obot__class_Obot(U_14014)) = c_Orderings_Otop__class_Otop(U_14014)
      | ~ class_Lattices_Oboolean__algebra(U_14014) ),
    inference(variable_rename,[status(thm)],[f_3625_1]) ).

fof(f_3625_3,plain,
    ! [U_14014] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_14014),c_Orderings_Obot__class_Obot(U_14014)) = c_Orderings_Otop__class_Otop(U_14014)
      | ~ class_Lattices_Oboolean__algebra(U_14014) ),
    inference(definitional_conversion,[status(esa)],[f_3625_2]) ).

cnf(f_3625_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_14014),c_Orderings_Obot__class_Obot(U_14014)) = c_Orderings_Otop__class_Otop(U_14014)
    | ~ class_Lattices_Oboolean__algebra(U_14014) ),
    inference(clausify,[status(thm)],[f_3625_3]) ).

fof(f_3626_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_3626_2,plain,
    ! [U_14015] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_14015),c_Orderings_Otop__class_Otop(U_14015)) = c_Orderings_Obot__class_Obot(U_14015)
      | ~ class_Lattices_Oboolean__algebra(U_14015) ),
    inference(variable_rename,[status(thm)],[f_3626_1]) ).

fof(f_3626_3,plain,
    ! [U_14015] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_14015),c_Orderings_Otop__class_Otop(U_14015)) = c_Orderings_Obot__class_Obot(U_14015)
      | ~ class_Lattices_Oboolean__algebra(U_14015) ),
    inference(definitional_conversion,[status(esa)],[f_3626_2]) ).

cnf(f_3626_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_14015),c_Orderings_Otop__class_Otop(U_14015)) = c_Orderings_Obot__class_Obot(U_14015)
    | ~ class_Lattices_Oboolean__algebra(U_14015) ),
    inference(clausify,[status(thm)],[f_3626_3]) ).

fof(f_3627_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_3627_2,plain,
    ! [U_14017,U_14016] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14016),U_14017),hAPP(c_Groups_Ouminus__class_Ouminus(U_14016),U_14017)) = c_Orderings_Otop__class_Otop(U_14016)
      | ~ class_Lattices_Oboolean__algebra(U_14016) ),
    inference(variable_rename,[status(thm)],[f_3627_1]) ).

fof(f_3627_3,plain,
    ! [U_14016,U_14017] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14016),U_14017),hAPP(c_Groups_Ouminus__class_Ouminus(U_14016),U_14017)) = c_Orderings_Otop__class_Otop(U_14016)
      | ~ class_Lattices_Oboolean__algebra(U_14016) ),
    inference(definitional_conversion,[status(esa)],[f_3627_2]) ).

cnf(f_3627_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14016),U_14017),hAPP(c_Groups_Ouminus__class_Ouminus(U_14016),U_14017)) = c_Orderings_Otop__class_Otop(U_14016)
    | ~ class_Lattices_Oboolean__algebra(U_14016) ),
    inference(clausify,[status(thm)],[f_3627_3]) ).

fof(f_3628_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_3628_2,plain,
    ! [U_14019,U_14018] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14018),hAPP(c_Groups_Ouminus__class_Ouminus(U_14018),U_14019)),U_14019) = c_Orderings_Otop__class_Otop(U_14018)
      | ~ class_Lattices_Oboolean__algebra(U_14018) ),
    inference(variable_rename,[status(thm)],[f_3628_1]) ).

fof(f_3628_3,plain,
    ! [U_14018,U_14019] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14018),hAPP(c_Groups_Ouminus__class_Ouminus(U_14018),U_14019)),U_14019) = c_Orderings_Otop__class_Otop(U_14018)
      | ~ class_Lattices_Oboolean__algebra(U_14018) ),
    inference(definitional_conversion,[status(esa)],[f_3628_2]) ).

cnf(f_3628_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_14018),hAPP(c_Groups_Ouminus__class_Ouminus(U_14018),U_14019)),U_14019) = c_Orderings_Otop__class_Otop(U_14018)
    | ~ class_Lattices_Oboolean__algebra(U_14018) ),
    inference(clausify,[status(thm)],[f_3628_3]) ).

fof(f_3629_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_3629_2,plain,
    ! [U_14021,U_14020] : c_Fun_Oinj__on(tc_fun(U_14020,U_14021),tc_fun(tc_prod(U_14020,U_14021),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14020,U_14021),tc_HOL_Obool),tc_fun(tc_prod(U_14020,U_14021),tc_HOL_Obool),tc_fun(U_14020,U_14021)),c_Set_OCollect(tc_prod(U_14020,U_14021))),hAPP(hAPP(c_COMBB(tc_fun(U_14020,tc_fun(U_14021,tc_HOL_Obool)),tc_fun(tc_prod(U_14020,U_14021),tc_HOL_Obool),tc_fun(U_14020,U_14021)),c_Product__Type_Oprod_Oprod__case(U_14020,U_14021,tc_HOL_Obool)),hAPP(c_COMBB(U_14021,tc_fun(U_14021,tc_HOL_Obool),U_14020),hAPP(c_COMBC(U_14021,U_14021,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_14020,U_14021),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3629_1]) ).

fof(f_3629_3,plain,
    ! [U_14020,U_14021] : c_Fun_Oinj__on(tc_fun(U_14020,U_14021),tc_fun(tc_prod(U_14020,U_14021),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14020,U_14021),tc_HOL_Obool),tc_fun(tc_prod(U_14020,U_14021),tc_HOL_Obool),tc_fun(U_14020,U_14021)),c_Set_OCollect(tc_prod(U_14020,U_14021))),hAPP(hAPP(c_COMBB(tc_fun(U_14020,tc_fun(U_14021,tc_HOL_Obool)),tc_fun(tc_prod(U_14020,U_14021),tc_HOL_Obool),tc_fun(U_14020,U_14021)),c_Product__Type_Oprod_Oprod__case(U_14020,U_14021,tc_HOL_Obool)),hAPP(c_COMBB(U_14021,tc_fun(U_14021,tc_HOL_Obool),U_14020),hAPP(c_COMBC(U_14021,U_14021,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_14020,U_14021),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3629_2]) ).

cnf(f_3629_4,plain,
    c_Fun_Oinj__on(tc_fun(U_14020,U_14021),tc_fun(tc_prod(U_14020,U_14021),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14020,U_14021),tc_HOL_Obool),tc_fun(tc_prod(U_14020,U_14021),tc_HOL_Obool),tc_fun(U_14020,U_14021)),c_Set_OCollect(tc_prod(U_14020,U_14021))),hAPP(hAPP(c_COMBB(tc_fun(U_14020,tc_fun(U_14021,tc_HOL_Obool)),tc_fun(tc_prod(U_14020,U_14021),tc_HOL_Obool),tc_fun(U_14020,U_14021)),c_Product__Type_Oprod_Oprod__case(U_14020,U_14021,tc_HOL_Obool)),hAPP(c_COMBB(U_14021,tc_fun(U_14021,tc_HOL_Obool),U_14020),hAPP(c_COMBC(U_14021,U_14021,tc_HOL_Obool),c_fequal)))),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_14020,U_14021),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3629_3]) ).

fof(f_3630_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_3630_2,plain,
    ! [U_14026,U_14025,U_14024,U_14023,U_14022] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_14023),hAPP(U_14024,U_14025)),hAPP(c_Set_Oimage(U_14022,U_14023,U_14024),U_14026)))
          | ~ hBOOL(hAPP(hAPP(c_member(U_14022),U_14025),U_14026)) )
        & ( hBOOL(hAPP(hAPP(c_member(U_14022),U_14025),U_14026))
          | ~ hBOOL(hAPP(hAPP(c_member(U_14023),hAPP(U_14024,U_14025)),hAPP(c_Set_Oimage(U_14022,U_14023,U_14024),U_14026))) ) )
      | ~ c_Fun_Oinj__on(U_14022,U_14023,U_14024,c_Orderings_Otop__class_Otop(tc_fun(U_14022,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3630_1]) ).

fof(f_3630_3,plain,
    ( ! [U_14022,U_14023,U_14024,U_14025,U_14026] :
        ( hBOOL(hAPP(hAPP(c_member(U_14023),hAPP(U_14024,U_14025)),hAPP(c_Set_Oimage(U_14022,U_14023,U_14024),U_14026)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14022),U_14025),U_14026))
        | ~ sP968(U_14022,U_14023,U_14024,U_14025,U_14026) )
    & ! [U_14022,U_14023,U_14024,U_14025,U_14026] :
        ( hBOOL(hAPP(hAPP(c_member(U_14022),U_14025),U_14026))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14023),hAPP(U_14024,U_14025)),hAPP(c_Set_Oimage(U_14022,U_14023,U_14024),U_14026)))
        | ~ sP968(U_14022,U_14023,U_14024,U_14025,U_14026) )
    & ! [U_14022,U_14023,U_14024,U_14025,U_14026] :
        ( sP968(U_14022,U_14023,U_14024,U_14025,U_14026)
        | ~ c_Fun_Oinj__on(U_14022,U_14023,U_14024,c_Orderings_Otop__class_Otop(tc_fun(U_14022,tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP968])],[f_3630_2]) ).

cnf(f_3630_4,plain,
    ( sP968(U_14022,U_14023,U_14024,U_14025,U_14026)
    | ~ c_Fun_Oinj__on(U_14022,U_14023,U_14024,c_Orderings_Otop__class_Otop(tc_fun(U_14022,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3630_3]) ).

cnf(f_3630_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14022),U_14025),U_14026))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14023),hAPP(U_14024,U_14025)),hAPP(c_Set_Oimage(U_14022,U_14023,U_14024),U_14026)))
    | ~ sP968(U_14022,U_14023,U_14024,U_14025,U_14026) ),
    inference(clausify,[status(thm)],[f_3630_3]) ).

cnf(f_3630_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14023),hAPP(U_14024,U_14025)),hAPP(c_Set_Oimage(U_14022,U_14023,U_14024),U_14026)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14022),U_14025),U_14026))
    | ~ sP968(U_14022,U_14023,U_14024,U_14025,U_14026) ),
    inference(clausify,[status(thm)],[f_3630_3]) ).

fof(f_3631_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_3631_2,plain,
    ! [U_14034,U_14033,U_14032,U_14031] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_14032),U_14034),hAPP(c_Set_Oimage(U_14031,U_14032,U_14033),c_Orderings_Otop__class_Otop(tc_fun(U_14031,tc_HOL_Obool)))))
          | ! [U_14030] :
              ( ? [U_14029] :
                  ( U_14029 != U_14030
                  & U_14034 = hAPP(U_14033,U_14029) )
              | U_14034 != hAPP(U_14033,U_14030) ) )
        & ( ? [U_14028] :
              ( ! [U_14027] :
                  ( U_14027 = U_14028
                  | U_14034 != hAPP(U_14033,U_14027) )
              & U_14034 = hAPP(U_14033,U_14028) )
          | ~ hBOOL(hAPP(hAPP(c_member(U_14032),U_14034),hAPP(c_Set_Oimage(U_14031,U_14032,U_14033),c_Orderings_Otop__class_Otop(tc_fun(U_14031,tc_HOL_Obool))))) ) )
      | ~ c_Fun_Oinj__on(U_14031,U_14032,U_14033,c_Orderings_Otop__class_Otop(tc_fun(U_14031,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3631_1]) ).

fof(f_3631_3,plain,
    ! [U_14034,U_14033,U_14032,U_14031] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_14032),U_14034),hAPP(c_Set_Oimage(U_14031,U_14032,U_14033),c_Orderings_Otop__class_Otop(tc_fun(U_14031,tc_HOL_Obool)))))
          | ! [U_14030] :
              ( ? [U_14029] :
                  ( U_14029 != U_14030
                  & U_14034 = hAPP(U_14033,U_14029) )
              | U_14034 != hAPP(U_14033,U_14030) ) )
        & ( ( ! [U_14027] :
                ( U_14027 = sK306(U_14034,U_14033,U_14032,U_14031)
                | U_14034 != hAPP(U_14033,U_14027) )
            & U_14034 = hAPP(U_14033,sK306(U_14034,U_14033,U_14032,U_14031)) )
          | ~ hBOOL(hAPP(hAPP(c_member(U_14032),U_14034),hAPP(c_Set_Oimage(U_14031,U_14032,U_14033),c_Orderings_Otop__class_Otop(tc_fun(U_14031,tc_HOL_Obool))))) ) )
      | ~ c_Fun_Oinj__on(U_14031,U_14032,U_14033,c_Orderings_Otop__class_Otop(tc_fun(U_14031,tc_HOL_Obool))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK306]),skolemize(U_14028,sK306(U_14034,U_14033,U_14032,U_14031))],[f_3631_2]) ).

fof(f_3631_4,plain,
    ! [U_14034,U_14033,U_14032,U_14031] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_14032),U_14034),hAPP(c_Set_Oimage(U_14031,U_14032,U_14033),c_Orderings_Otop__class_Otop(tc_fun(U_14031,tc_HOL_Obool)))))
          | ! [U_14030] :
              ( ( sK307(U_14034,U_14033,U_14032,U_14031,U_14030) != U_14030
                & U_14034 = hAPP(U_14033,sK307(U_14034,U_14033,U_14032,U_14031,U_14030)) )
              | U_14034 != hAPP(U_14033,U_14030) ) )
        & ( ( ! [U_14027] :
                ( U_14027 = sK306(U_14034,U_14033,U_14032,U_14031)
                | U_14034 != hAPP(U_14033,U_14027) )
            & U_14034 = hAPP(U_14033,sK306(U_14034,U_14033,U_14032,U_14031)) )
          | ~ hBOOL(hAPP(hAPP(c_member(U_14032),U_14034),hAPP(c_Set_Oimage(U_14031,U_14032,U_14033),c_Orderings_Otop__class_Otop(tc_fun(U_14031,tc_HOL_Obool))))) ) )
      | ~ c_Fun_Oinj__on(U_14031,U_14032,U_14033,c_Orderings_Otop__class_Otop(tc_fun(U_14031,tc_HOL_Obool))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK307]),skolemize(U_14029,sK307(U_14034,U_14033,U_14032,U_14031,U_14030))],[f_3631_3]) ).

fof(f_3631_5,plain,
    ( ! [U_14032,U_14030,U_14031,U_14033,U_14034] :
        ( sK307(U_14034,U_14033,U_14032,U_14031,U_14030) != U_14030
        | ~ sP970(U_14032,U_14030,U_14031,U_14033,U_14034) )
    & ! [U_14032,U_14030,U_14031,U_14033,U_14034] :
        ( U_14034 = hAPP(U_14033,sK307(U_14034,U_14033,U_14032,U_14031,U_14030))
        | ~ sP970(U_14032,U_14030,U_14031,U_14033,U_14034) )
    & ! [U_14032,U_14031,U_14027,U_14033,U_14034] :
        ( U_14027 = sK306(U_14034,U_14033,U_14032,U_14031)
        | U_14034 != hAPP(U_14033,U_14027)
        | ~ sP969(U_14032,U_14031,U_14027,U_14033,U_14034) )
    & ! [U_14032,U_14031,U_14027,U_14033,U_14034] :
        ( U_14034 = hAPP(U_14033,sK306(U_14034,U_14033,U_14032,U_14031))
        | ~ sP969(U_14032,U_14031,U_14027,U_14033,U_14034) )
    & ! [U_14032,U_14030,U_14031,U_14027,U_14033,U_14034] :
        ( hBOOL(hAPP(hAPP(c_member(U_14032),U_14034),hAPP(c_Set_Oimage(U_14031,U_14032,U_14033),c_Orderings_Otop__class_Otop(tc_fun(U_14031,tc_HOL_Obool)))))
        | sP970(U_14032,U_14030,U_14031,U_14033,U_14034)
        | U_14034 != hAPP(U_14033,U_14030)
        | ~ sP971(U_14032,U_14030,U_14031,U_14027,U_14033,U_14034) )
    & ! [U_14032,U_14030,U_14031,U_14027,U_14033,U_14034] :
        ( sP969(U_14032,U_14031,U_14027,U_14033,U_14034)
        | ~ hBOOL(hAPP(hAPP(c_member(U_14032),U_14034),hAPP(c_Set_Oimage(U_14031,U_14032,U_14033),c_Orderings_Otop__class_Otop(tc_fun(U_14031,tc_HOL_Obool)))))
        | ~ sP971(U_14032,U_14030,U_14031,U_14027,U_14033,U_14034) )
    & ! [U_14032,U_14030,U_14031,U_14027,U_14033,U_14034] :
        ( sP971(U_14032,U_14030,U_14031,U_14027,U_14033,U_14034)
        | ~ c_Fun_Oinj__on(U_14031,U_14032,U_14033,c_Orderings_Otop__class_Otop(tc_fun(U_14031,tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP969,sP970,sP971])],[f_3631_4]) ).

cnf(f_3631_6,plain,
    ( sP971(U_14032,U_14030,U_14031,U_14027,U_14033,U_14034)
    | ~ c_Fun_Oinj__on(U_14031,U_14032,U_14033,c_Orderings_Otop__class_Otop(tc_fun(U_14031,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3631_5]) ).

cnf(f_3631_7,plain,
    ( sP969(U_14032,U_14031,U_14027,U_14033,U_14034)
    | ~ hBOOL(hAPP(hAPP(c_member(U_14032),U_14034),hAPP(c_Set_Oimage(U_14031,U_14032,U_14033),c_Orderings_Otop__class_Otop(tc_fun(U_14031,tc_HOL_Obool)))))
    | ~ sP971(U_14032,U_14030,U_14031,U_14027,U_14033,U_14034) ),
    inference(clausify,[status(thm)],[f_3631_5]) ).

cnf(f_3631_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14032),U_14034),hAPP(c_Set_Oimage(U_14031,U_14032,U_14033),c_Orderings_Otop__class_Otop(tc_fun(U_14031,tc_HOL_Obool)))))
    | sP970(U_14032,U_14030,U_14031,U_14033,U_14034)
    | U_14034 != hAPP(U_14033,U_14030)
    | ~ sP971(U_14032,U_14030,U_14031,U_14027,U_14033,U_14034) ),
    inference(clausify,[status(thm)],[f_3631_5]) ).

cnf(f_3631_9,plain,
    ( U_14034 = hAPP(U_14033,sK306(U_14034,U_14033,U_14032,U_14031))
    | ~ sP969(U_14032,U_14031,U_14027,U_14033,U_14034) ),
    inference(clausify,[status(thm)],[f_3631_5]) ).

cnf(f_3631_10,plain,
    ( U_14027 = sK306(U_14034,U_14033,U_14032,U_14031)
    | U_14034 != hAPP(U_14033,U_14027)
    | ~ sP969(U_14032,U_14031,U_14027,U_14033,U_14034) ),
    inference(clausify,[status(thm)],[f_3631_5]) ).

cnf(f_3631_11,plain,
    ( U_14034 = hAPP(U_14033,sK307(U_14034,U_14033,U_14032,U_14031,U_14030))
    | ~ sP970(U_14032,U_14030,U_14031,U_14033,U_14034) ),
    inference(clausify,[status(thm)],[f_3631_5]) ).

cnf(f_3631_12,plain,
    ( sK307(U_14034,U_14033,U_14032,U_14031,U_14030) != U_14030
    | ~ sP970(U_14032,U_14030,U_14031,U_14033,U_14034) ),
    inference(clausify,[status(thm)],[f_3631_5]) ).

fof(f_3632_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_3632_2,plain,
    ! [U_14036,U_14035] :
      ( hAPP(c_Set_Oimage(U_14035,U_14035,U_14036),c_Orderings_Otop__class_Otop(tc_fun(U_14035,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_14035,tc_HOL_Obool))
      | ~ c_Fun_Oinj__on(U_14035,U_14035,U_14036,c_Orderings_Otop__class_Otop(tc_fun(U_14035,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14035),c_Orderings_Otop__class_Otop(tc_fun(U_14035,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3632_1]) ).

fof(f_3632_3,plain,
    ! [U_14035,U_14036] :
      ( hAPP(c_Set_Oimage(U_14035,U_14035,U_14036),c_Orderings_Otop__class_Otop(tc_fun(U_14035,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_14035,tc_HOL_Obool))
      | ~ c_Fun_Oinj__on(U_14035,U_14035,U_14036,c_Orderings_Otop__class_Otop(tc_fun(U_14035,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14035),c_Orderings_Otop__class_Otop(tc_fun(U_14035,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3632_2]) ).

cnf(f_3632_4,plain,
    ( hAPP(c_Set_Oimage(U_14035,U_14035,U_14036),c_Orderings_Otop__class_Otop(tc_fun(U_14035,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_14035,tc_HOL_Obool))
    | ~ c_Fun_Oinj__on(U_14035,U_14035,U_14036,c_Orderings_Otop__class_Otop(tc_fun(U_14035,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14035),c_Orderings_Otop__class_Otop(tc_fun(U_14035,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3632_3]) ).

fof(f_3633_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_3633_2,plain,
    ! [U_14038,U_14037] :
      ( c_Fun_Oinj__on(U_14037,U_14037,U_14038,c_Orderings_Otop__class_Otop(tc_fun(U_14037,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(U_14037,U_14037,U_14038),c_Orderings_Otop__class_Otop(tc_fun(U_14037,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14037,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14037),c_Orderings_Otop__class_Otop(tc_fun(U_14037,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3633_1]) ).

fof(f_3633_3,plain,
    ! [U_14037,U_14038] :
      ( c_Fun_Oinj__on(U_14037,U_14037,U_14038,c_Orderings_Otop__class_Otop(tc_fun(U_14037,tc_HOL_Obool)))
      | hAPP(c_Set_Oimage(U_14037,U_14037,U_14038),c_Orderings_Otop__class_Otop(tc_fun(U_14037,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14037,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14037),c_Orderings_Otop__class_Otop(tc_fun(U_14037,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3633_2]) ).

cnf(f_3633_4,plain,
    ( c_Fun_Oinj__on(U_14037,U_14037,U_14038,c_Orderings_Otop__class_Otop(tc_fun(U_14037,tc_HOL_Obool)))
    | hAPP(c_Set_Oimage(U_14037,U_14037,U_14038),c_Orderings_Otop__class_Otop(tc_fun(U_14037,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14037,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14037),c_Orderings_Otop__class_Otop(tc_fun(U_14037,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3633_3]) ).

fof(f_3634_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_3634_2,plain,
    ! [U_14043,U_14042,U_14041,U_14040,U_14039] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14040,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14039,U_14040,U_14041),U_14042)),hAPP(c_Set_Oimage(U_14039,U_14040,U_14041),U_14043)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14039,tc_HOL_Obool)),U_14042),U_14043)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14039,tc_HOL_Obool)),U_14042),U_14043))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14040,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14039,U_14040,U_14041),U_14042)),hAPP(c_Set_Oimage(U_14039,U_14040,U_14041),U_14043))) ) )
      | ~ c_Fun_Oinj__on(U_14039,U_14040,U_14041,c_Orderings_Otop__class_Otop(tc_fun(U_14039,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3634_1]) ).

fof(f_3634_3,plain,
    ( ! [U_14041,U_14040,U_14043,U_14039,U_14042] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14040,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14039,U_14040,U_14041),U_14042)),hAPP(c_Set_Oimage(U_14039,U_14040,U_14041),U_14043)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14039,tc_HOL_Obool)),U_14042),U_14043))
        | ~ sP972(U_14041,U_14040,U_14043,U_14039,U_14042) )
    & ! [U_14041,U_14040,U_14043,U_14039,U_14042] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14039,tc_HOL_Obool)),U_14042),U_14043))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14040,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14039,U_14040,U_14041),U_14042)),hAPP(c_Set_Oimage(U_14039,U_14040,U_14041),U_14043)))
        | ~ sP972(U_14041,U_14040,U_14043,U_14039,U_14042) )
    & ! [U_14041,U_14040,U_14043,U_14039,U_14042] :
        ( sP972(U_14041,U_14040,U_14043,U_14039,U_14042)
        | ~ c_Fun_Oinj__on(U_14039,U_14040,U_14041,c_Orderings_Otop__class_Otop(tc_fun(U_14039,tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP972])],[f_3634_2]) ).

cnf(f_3634_4,plain,
    ( sP972(U_14041,U_14040,U_14043,U_14039,U_14042)
    | ~ c_Fun_Oinj__on(U_14039,U_14040,U_14041,c_Orderings_Otop__class_Otop(tc_fun(U_14039,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3634_3]) ).

cnf(f_3634_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14039,tc_HOL_Obool)),U_14042),U_14043))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14040,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14039,U_14040,U_14041),U_14042)),hAPP(c_Set_Oimage(U_14039,U_14040,U_14041),U_14043)))
    | ~ sP972(U_14041,U_14040,U_14043,U_14039,U_14042) ),
    inference(clausify,[status(thm)],[f_3634_3]) ).

cnf(f_3634_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14040,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14039,U_14040,U_14041),U_14042)),hAPP(c_Set_Oimage(U_14039,U_14040,U_14041),U_14043)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14039,tc_HOL_Obool)),U_14042),U_14043))
    | ~ sP972(U_14041,U_14040,U_14043,U_14039,U_14042) ),
    inference(clausify,[status(thm)],[f_3634_3]) ).

fof(f_3635_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_3635_2,plain,
    ! [U_14048,U_14047,U_14046,U_14045,U_14044] :
      ( hAPP(c_Set_Oimage(U_14044,U_14045,U_14046),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14044,tc_HOL_Obool)),U_14047),U_14048)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14045,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14044,U_14045,U_14046),U_14047)),hAPP(c_Set_Oimage(U_14044,U_14045,U_14046),U_14048))
      | ~ c_Fun_Oinj__on(U_14044,U_14045,U_14046,c_Orderings_Otop__class_Otop(tc_fun(U_14044,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3635_1]) ).

fof(f_3635_3,plain,
    ! [U_14044,U_14045,U_14046,U_14047,U_14048] :
      ( hAPP(c_Set_Oimage(U_14044,U_14045,U_14046),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14044,tc_HOL_Obool)),U_14047),U_14048)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14045,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14044,U_14045,U_14046),U_14047)),hAPP(c_Set_Oimage(U_14044,U_14045,U_14046),U_14048))
      | ~ c_Fun_Oinj__on(U_14044,U_14045,U_14046,c_Orderings_Otop__class_Otop(tc_fun(U_14044,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3635_2]) ).

cnf(f_3635_4,plain,
    ( hAPP(c_Set_Oimage(U_14044,U_14045,U_14046),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14044,tc_HOL_Obool)),U_14047),U_14048)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14045,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14044,U_14045,U_14046),U_14047)),hAPP(c_Set_Oimage(U_14044,U_14045,U_14046),U_14048))
    | ~ c_Fun_Oinj__on(U_14044,U_14045,U_14046,c_Orderings_Otop__class_Otop(tc_fun(U_14044,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3635_3]) ).

fof(f_3636_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_3636_2,plain,
    ! [U_14053,U_14052,U_14051,U_14050,U_14049] :
      ( hAPP(c_Set_Oimage(U_14049,U_14050,U_14051),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14049,tc_HOL_Obool)),U_14052),U_14053)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14050,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14049,U_14050,U_14051),U_14052)),hAPP(c_Set_Oimage(U_14049,U_14050,U_14051),U_14053))
      | ~ c_Fun_Oinj__on(U_14049,U_14050,U_14051,c_Orderings_Otop__class_Otop(tc_fun(U_14049,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3636_1]) ).

fof(f_3636_3,plain,
    ! [U_14049,U_14050,U_14051,U_14052,U_14053] :
      ( hAPP(c_Set_Oimage(U_14049,U_14050,U_14051),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14049,tc_HOL_Obool)),U_14052),U_14053)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14050,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14049,U_14050,U_14051),U_14052)),hAPP(c_Set_Oimage(U_14049,U_14050,U_14051),U_14053))
      | ~ c_Fun_Oinj__on(U_14049,U_14050,U_14051,c_Orderings_Otop__class_Otop(tc_fun(U_14049,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3636_2]) ).

cnf(f_3636_4,plain,
    ( hAPP(c_Set_Oimage(U_14049,U_14050,U_14051),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14049,tc_HOL_Obool)),U_14052),U_14053)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14050,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14049,U_14050,U_14051),U_14052)),hAPP(c_Set_Oimage(U_14049,U_14050,U_14051),U_14053))
    | ~ c_Fun_Oinj__on(U_14049,U_14050,U_14051,c_Orderings_Otop__class_Otop(tc_fun(U_14049,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3636_3]) ).

fof(f_3637_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_3637_2,plain,
    ! [U_14057,U_14056,U_14055,U_14054] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14055,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14055,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14054,U_14055,U_14056),U_14057))),hAPP(c_Set_Oimage(U_14054,U_14055,U_14056),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14054,tc_HOL_Obool)),U_14057))))
      | hAPP(c_Set_Oimage(U_14054,U_14055,U_14056),c_Orderings_Otop__class_Otop(tc_fun(U_14054,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14055,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3637_1]) ).

fof(f_3637_3,plain,
    ! [U_14054,U_14055,U_14056,U_14057] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14055,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14055,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14054,U_14055,U_14056),U_14057))),hAPP(c_Set_Oimage(U_14054,U_14055,U_14056),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14054,tc_HOL_Obool)),U_14057))))
      | hAPP(c_Set_Oimage(U_14054,U_14055,U_14056),c_Orderings_Otop__class_Otop(tc_fun(U_14054,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14055,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3637_2]) ).

cnf(f_3637_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14055,tc_HOL_Obool)),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14055,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14054,U_14055,U_14056),U_14057))),hAPP(c_Set_Oimage(U_14054,U_14055,U_14056),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14054,tc_HOL_Obool)),U_14057))))
    | hAPP(c_Set_Oimage(U_14054,U_14055,U_14056),c_Orderings_Otop__class_Otop(tc_fun(U_14054,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14055,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3637_3]) ).

fof(f_3638_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_3638_2,plain,
    ! [U_14059,U_14058] : c_List_Olex(U_14058,U_14059) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(U_14058),tc_List_Olist(U_14058)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(U_14058,U_14059)),
    inference(variable_rename,[status(thm)],[f_3638_1]) ).

fof(f_3638_3,plain,
    ! [U_14059,U_14058] : c_List_Olex(U_14058,U_14059) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(U_14058),tc_List_Olist(U_14058)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(U_14058,U_14059)),
    inference(definitional_conversion,[status(esa)],[f_3638_2]) ).

cnf(f_3638_4,plain,
    c_List_Olex(U_14058,U_14059) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(tc_List_Olist(U_14058),tc_List_Olist(U_14058)),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),c_List_Olexn(U_14058,U_14059)),
    inference(clausify,[status(thm)],[f_3638_3]) ).

fof(f_3639_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_3639_2,plain,
    ! [U_14060] :
      ( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_14060)) = U_14060
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_14060),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3639_1]) ).

fof(f_3639_3,plain,
    ! [U_14060] :
      ( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_14060)) = U_14060
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_14060),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3639_2]) ).

cnf(f_3639_4,plain,
    ( hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,U_14060)) = U_14060
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_14060),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3639_3]) ).

fof(f_3640_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_3640_2,plain,
    ! [U_14064,U_14063,U_14062,U_14061] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14061,U_14062,hAPP(hAPP(c_Set_Oinsert(U_14061),U_14063),c_Orderings_Obot__class_Obot(tc_fun(U_14061,tc_HOL_Obool)))),U_14064))
        | U_14063 != U_14064 )
      & ( U_14063 = U_14064
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14061,U_14062,hAPP(hAPP(c_Set_Oinsert(U_14061),U_14063),c_Orderings_Obot__class_Obot(tc_fun(U_14061,tc_HOL_Obool)))),U_14064)) ) ),
    inference(variable_rename,[status(thm)],[f_3640_1]) ).

fof(f_3640_3,plain,
    ( ! [U_14072,U_14070] :
        ( ! [U_14068,U_14066] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14066,U_14068,hAPP(hAPP(c_Set_Oinsert(U_14066),U_14070),c_Orderings_Obot__class_Obot(tc_fun(U_14066,tc_HOL_Obool)))),U_14072))
        | U_14070 != U_14072 )
    & ! [U_14071,U_14069] :
        ( ! [U_14067,U_14065] : ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14065,U_14067,hAPP(hAPP(c_Set_Oinsert(U_14065),U_14069),c_Orderings_Obot__class_Obot(tc_fun(U_14065,tc_HOL_Obool)))),U_14071))
        | U_14069 = U_14071 ) ),
    inference(miniscope,[status(thm)],[f_3640_2]) ).

fof(f_3640_4,plain,
    ( ! [U_14066,U_14072,U_14068,U_14070] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14066,U_14068,hAPP(hAPP(c_Set_Oinsert(U_14066),U_14070),c_Orderings_Obot__class_Obot(tc_fun(U_14066,tc_HOL_Obool)))),U_14072))
        | U_14070 != U_14072 )
    & ! [U_14067,U_14069,U_14065,U_14071] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14065,U_14067,hAPP(hAPP(c_Set_Oinsert(U_14065),U_14069),c_Orderings_Obot__class_Obot(tc_fun(U_14065,tc_HOL_Obool)))),U_14071))
        | U_14069 = U_14071 ) ),
    inference(definitional_conversion,[status(esa)],[f_3640_3]) ).

cnf(f_3640_5,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14065,U_14067,hAPP(hAPP(c_Set_Oinsert(U_14065),U_14069),c_Orderings_Obot__class_Obot(tc_fun(U_14065,tc_HOL_Obool)))),U_14071))
    | U_14069 = U_14071 ),
    inference(clausify,[status(thm)],[f_3640_4]) ).

cnf(f_3640_6,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14066,U_14068,hAPP(hAPP(c_Set_Oinsert(U_14066),U_14070),c_Orderings_Obot__class_Obot(tc_fun(U_14066,tc_HOL_Obool)))),U_14072))
    | U_14070 != U_14072 ),
    inference(clausify,[status(thm)],[f_3640_4]) ).

fof(f_3641_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_3641_2,plain,
    ! [U_14077,U_14076,U_14075,U_14074,U_14073] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_14073)),hAPP(c_Set_Oimage(U_14074,tc_Option_Ooption(U_14073),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_14074,tc_Option_Ooption(U_14073)),U_14075),U_14076),hAPP(c_Option_Ooption_OSome(U_14073),U_14077))),c_Orderings_Otop__class_Otop(tc_fun(U_14074,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_14073)),hAPP(c_Set_Oimage(U_14074,tc_Option_Ooption(U_14073),U_14075),c_Orderings_Otop__class_Otop(tc_fun(U_14074,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_3641_1]) ).

fof(f_3641_3,plain,
    ! [U_14073,U_14074,U_14075,U_14076,U_14077] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_14073)),hAPP(c_Set_Oimage(U_14074,tc_Option_Ooption(U_14073),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_14074,tc_Option_Ooption(U_14073)),U_14075),U_14076),hAPP(c_Option_Ooption_OSome(U_14073),U_14077))),c_Orderings_Otop__class_Otop(tc_fun(U_14074,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_14073)),hAPP(c_Set_Oimage(U_14074,tc_Option_Ooption(U_14073),U_14075),c_Orderings_Otop__class_Otop(tc_fun(U_14074,tc_HOL_Obool))))) ),
    inference(definitional_conversion,[status(esa)],[f_3641_2]) ).

cnf(f_3641_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_14073)),hAPP(c_Set_Oimage(U_14074,tc_Option_Ooption(U_14073),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_14074,tc_Option_Ooption(U_14073)),U_14075),U_14076),hAPP(c_Option_Ooption_OSome(U_14073),U_14077))),c_Orderings_Otop__class_Otop(tc_fun(U_14074,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_14073)),hAPP(c_Set_Oimage(U_14074,tc_Option_Ooption(U_14073),U_14075),c_Orderings_Otop__class_Otop(tc_fun(U_14074,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_3641_3]) ).

fof(f_3642_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_3642_2,plain,
    ! [U_14079,U_14078] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14078,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_14078,tc_HOL_Obool)),tc_fun(U_14078,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_14078,tc_HOL_Obool)),tc_fun(U_14078,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14078,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_14079)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14078,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14079),
    inference(variable_rename,[status(thm)],[f_3642_1]) ).

fof(f_3642_3,plain,
    ! [U_14079,U_14078] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14078,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_14078,tc_HOL_Obool)),tc_fun(U_14078,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_14078,tc_HOL_Obool)),tc_fun(U_14078,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14078,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_14079)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14078,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14079),
    inference(definitional_conversion,[status(esa)],[f_3642_2]) ).

cnf(f_3642_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14078,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_14078,tc_HOL_Obool)),tc_fun(U_14078,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_14078,tc_HOL_Obool)),tc_fun(U_14078,tc_HOL_Obool)),tc_Nat_Onat),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14078,tc_HOL_Obool))),c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),U_14079)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14078,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14079),
    inference(clausify,[status(thm)],[f_3642_3]) ).

fof(f_3643_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_3643_2,plain,
    ! [U_14080] : c_Fun_Oinj__on(U_14080,tc_fun(U_14080,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14080,tc_fun(U_14080,tc_HOL_Obool),tc_fun(U_14080,tc_HOL_Obool)),c_Set_Oinsert(U_14080)),c_Orderings_Obot__class_Obot(tc_fun(U_14080,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14080,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3643_1]) ).

fof(f_3643_3,plain,
    ! [U_14080] : c_Fun_Oinj__on(U_14080,tc_fun(U_14080,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14080,tc_fun(U_14080,tc_HOL_Obool),tc_fun(U_14080,tc_HOL_Obool)),c_Set_Oinsert(U_14080)),c_Orderings_Obot__class_Obot(tc_fun(U_14080,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14080,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3643_2]) ).

cnf(f_3643_4,plain,
    c_Fun_Oinj__on(U_14080,tc_fun(U_14080,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14080,tc_fun(U_14080,tc_HOL_Obool),tc_fun(U_14080,tc_HOL_Obool)),c_Set_Oinsert(U_14080)),c_Orderings_Obot__class_Obot(tc_fun(U_14080,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14080,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3643_3]) ).

fof(f_3644_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_3644_2,plain,
    ! [U_14081] :
      ( 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_14081),c_Orderings_Otop__class_Otop(tc_fun(U_14081,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14081),c_Orderings_Otop__class_Otop(tc_fun(U_14081,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3644_1]) ).

fof(f_3644_3,plain,
    ! [U_14081] :
      ( 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_14081),c_Orderings_Otop__class_Otop(tc_fun(U_14081,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14081),c_Orderings_Otop__class_Otop(tc_fun(U_14081,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3644_2]) ).

cnf(f_3644_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_14081),c_Orderings_Otop__class_Otop(tc_fun(U_14081,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14081),c_Orderings_Otop__class_Otop(tc_fun(U_14081,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3644_3]) ).

fof(f_3645_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_3645_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_3645_1]) ).

cnf(f_3645_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_3645_2]) ).

fof(f_3646_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_3646_2,plain,
    ! [U_14085,U_14084,U_14083,U_14082] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14083,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14082,U_14083,U_14084),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14082,tc_HOL_Obool)),U_14085))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14083,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14082,U_14083,U_14084),U_14085))))
      | ~ c_Fun_Oinj__on(U_14082,U_14083,U_14084,c_Orderings_Otop__class_Otop(tc_fun(U_14082,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3646_1]) ).

fof(f_3646_3,plain,
    ! [U_14082,U_14083,U_14084,U_14085] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14083,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14082,U_14083,U_14084),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14082,tc_HOL_Obool)),U_14085))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14083,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14082,U_14083,U_14084),U_14085))))
      | ~ c_Fun_Oinj__on(U_14082,U_14083,U_14084,c_Orderings_Otop__class_Otop(tc_fun(U_14082,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3646_2]) ).

cnf(f_3646_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14083,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14082,U_14083,U_14084),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14082,tc_HOL_Obool)),U_14085))),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14083,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14082,U_14083,U_14084),U_14085))))
    | ~ c_Fun_Oinj__on(U_14082,U_14083,U_14084,c_Orderings_Otop__class_Otop(tc_fun(U_14082,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3646_3]) ).

fof(f_3647_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_3647_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_3647_1]) ).

cnf(f_3647_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_3647_2]) ).

fof(f_3648_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_3648_2,plain,
    ! [U_14091,U_14090,U_14089,U_14088,U_14087,U_14086] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14086,tc_fun(U_14087,tc_fun(U_14088,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14086,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14087,U_14088),tc_HOL_Obool),tc_fun(U_14087,tc_fun(U_14088,tc_HOL_Obool)),U_14086),hAPP(c_COMBC(U_14087,tc_fun(tc_prod(U_14087,U_14088),tc_HOL_Obool),tc_fun(U_14088,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14088,tc_fun(tc_fun(tc_prod(U_14087,U_14088),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14087,U_14088),tc_HOL_Obool),tc_fun(U_14088,tc_HOL_Obool)),U_14087),c_COMBC(U_14088,tc_fun(tc_prod(U_14087,U_14088),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14088,tc_prod(U_14087,U_14088)),tc_fun(U_14088,tc_fun(tc_fun(tc_prod(U_14087,U_14088),tc_HOL_Obool),tc_HOL_Obool)),U_14087),hAPP(c_COMBB(tc_prod(U_14087,U_14088),tc_fun(tc_fun(tc_prod(U_14087,U_14088),tc_HOL_Obool),tc_HOL_Obool),U_14088),c_member(tc_prod(U_14087,U_14088)))),c_Product__Type_OPair(U_14087,U_14088))))),U_14089)),U_14090),U_14091))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14087,U_14088)),hAPP(hAPP(c_Product__Type_OPair(U_14087,U_14088),U_14090),U_14091)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14086,tc_fun(tc_prod(U_14087,U_14088),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_14086,tc_HOL_Obool))),U_14089))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14087,U_14088)),hAPP(hAPP(c_Product__Type_OPair(U_14087,U_14088),U_14090),U_14091)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14086,tc_fun(tc_prod(U_14087,U_14088),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_14086,tc_HOL_Obool))),U_14089)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14086,tc_fun(U_14087,tc_fun(U_14088,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14086,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14087,U_14088),tc_HOL_Obool),tc_fun(U_14087,tc_fun(U_14088,tc_HOL_Obool)),U_14086),hAPP(c_COMBC(U_14087,tc_fun(tc_prod(U_14087,U_14088),tc_HOL_Obool),tc_fun(U_14088,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14088,tc_fun(tc_fun(tc_prod(U_14087,U_14088),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14087,U_14088),tc_HOL_Obool),tc_fun(U_14088,tc_HOL_Obool)),U_14087),c_COMBC(U_14088,tc_fun(tc_prod(U_14087,U_14088),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14088,tc_prod(U_14087,U_14088)),tc_fun(U_14088,tc_fun(tc_fun(tc_prod(U_14087,U_14088),tc_HOL_Obool),tc_HOL_Obool)),U_14087),hAPP(c_COMBB(tc_prod(U_14087,U_14088),tc_fun(tc_fun(tc_prod(U_14087,U_14088),tc_HOL_Obool),tc_HOL_Obool),U_14088),c_member(tc_prod(U_14087,U_14088)))),c_Product__Type_OPair(U_14087,U_14088))))),U_14089)),U_14090),U_14091)) ) ),
    inference(variable_rename,[status(thm)],[f_3648_1]) ).

fof(f_3648_3,plain,
    ( ! [U_14103,U_14101,U_14099,U_14097,U_14095,U_14093] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14093,tc_fun(U_14095,tc_fun(U_14097,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14093,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool),tc_fun(U_14095,tc_fun(U_14097,tc_HOL_Obool)),U_14093),hAPP(c_COMBC(U_14095,tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool),tc_fun(U_14097,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14097,tc_fun(tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool),tc_fun(U_14097,tc_HOL_Obool)),U_14095),c_COMBC(U_14097,tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14097,tc_prod(U_14095,U_14097)),tc_fun(U_14097,tc_fun(tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool),tc_HOL_Obool)),U_14095),hAPP(c_COMBB(tc_prod(U_14095,U_14097),tc_fun(tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool),tc_HOL_Obool),U_14097),c_member(tc_prod(U_14095,U_14097)))),c_Product__Type_OPair(U_14095,U_14097))))),U_14099)),U_14101),U_14103))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14095,U_14097)),hAPP(hAPP(c_Product__Type_OPair(U_14095,U_14097),U_14101),U_14103)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14093,tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_14093,tc_HOL_Obool))),U_14099))) )
    & ! [U_14102,U_14100,U_14098,U_14096,U_14094,U_14092] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14094,U_14096)),hAPP(hAPP(c_Product__Type_OPair(U_14094,U_14096),U_14100),U_14102)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14092,tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_14092,tc_HOL_Obool))),U_14098)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14092,tc_fun(U_14094,tc_fun(U_14096,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14092,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool),tc_fun(U_14094,tc_fun(U_14096,tc_HOL_Obool)),U_14092),hAPP(c_COMBC(U_14094,tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool),tc_fun(U_14096,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14096,tc_fun(tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool),tc_fun(U_14096,tc_HOL_Obool)),U_14094),c_COMBC(U_14096,tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14096,tc_prod(U_14094,U_14096)),tc_fun(U_14096,tc_fun(tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool),tc_HOL_Obool)),U_14094),hAPP(c_COMBB(tc_prod(U_14094,U_14096),tc_fun(tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool),tc_HOL_Obool),U_14096),c_member(tc_prod(U_14094,U_14096)))),c_Product__Type_OPair(U_14094,U_14096))))),U_14098)),U_14100),U_14102)) ) ),
    inference(miniscope,[status(thm)],[f_3648_2]) ).

fof(f_3648_4,plain,
    ( ! [U_14093,U_14095,U_14097,U_14099,U_14101,U_14103] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14093,tc_fun(U_14095,tc_fun(U_14097,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14093,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool),tc_fun(U_14095,tc_fun(U_14097,tc_HOL_Obool)),U_14093),hAPP(c_COMBC(U_14095,tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool),tc_fun(U_14097,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14097,tc_fun(tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool),tc_fun(U_14097,tc_HOL_Obool)),U_14095),c_COMBC(U_14097,tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14097,tc_prod(U_14095,U_14097)),tc_fun(U_14097,tc_fun(tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool),tc_HOL_Obool)),U_14095),hAPP(c_COMBB(tc_prod(U_14095,U_14097),tc_fun(tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool),tc_HOL_Obool),U_14097),c_member(tc_prod(U_14095,U_14097)))),c_Product__Type_OPair(U_14095,U_14097))))),U_14099)),U_14101),U_14103))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14095,U_14097)),hAPP(hAPP(c_Product__Type_OPair(U_14095,U_14097),U_14101),U_14103)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14093,tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_14093,tc_HOL_Obool))),U_14099))) )
    & ! [U_14094,U_14092,U_14098,U_14100,U_14096,U_14102] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14094,U_14096)),hAPP(hAPP(c_Product__Type_OPair(U_14094,U_14096),U_14100),U_14102)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14092,tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_14092,tc_HOL_Obool))),U_14098)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14092,tc_fun(U_14094,tc_fun(U_14096,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14092,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool),tc_fun(U_14094,tc_fun(U_14096,tc_HOL_Obool)),U_14092),hAPP(c_COMBC(U_14094,tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool),tc_fun(U_14096,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14096,tc_fun(tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool),tc_fun(U_14096,tc_HOL_Obool)),U_14094),c_COMBC(U_14096,tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14096,tc_prod(U_14094,U_14096)),tc_fun(U_14096,tc_fun(tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool),tc_HOL_Obool)),U_14094),hAPP(c_COMBB(tc_prod(U_14094,U_14096),tc_fun(tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool),tc_HOL_Obool),U_14096),c_member(tc_prod(U_14094,U_14096)))),c_Product__Type_OPair(U_14094,U_14096))))),U_14098)),U_14100),U_14102)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3648_3]) ).

cnf(f_3648_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14094,U_14096)),hAPP(hAPP(c_Product__Type_OPair(U_14094,U_14096),U_14100),U_14102)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14092,tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_14092,tc_HOL_Obool))),U_14098)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14092,tc_fun(U_14094,tc_fun(U_14096,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14092,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool),tc_fun(U_14094,tc_fun(U_14096,tc_HOL_Obool)),U_14092),hAPP(c_COMBC(U_14094,tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool),tc_fun(U_14096,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14096,tc_fun(tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool),tc_fun(U_14096,tc_HOL_Obool)),U_14094),c_COMBC(U_14096,tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14096,tc_prod(U_14094,U_14096)),tc_fun(U_14096,tc_fun(tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool),tc_HOL_Obool)),U_14094),hAPP(c_COMBB(tc_prod(U_14094,U_14096),tc_fun(tc_fun(tc_prod(U_14094,U_14096),tc_HOL_Obool),tc_HOL_Obool),U_14096),c_member(tc_prod(U_14094,U_14096)))),c_Product__Type_OPair(U_14094,U_14096))))),U_14098)),U_14100),U_14102)) ),
    inference(clausify,[status(thm)],[f_3648_4]) ).

cnf(f_3648_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14093,tc_fun(U_14095,tc_fun(U_14097,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_14093,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool),tc_fun(U_14095,tc_fun(U_14097,tc_HOL_Obool)),U_14093),hAPP(c_COMBC(U_14095,tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool),tc_fun(U_14097,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14097,tc_fun(tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool),tc_fun(U_14097,tc_HOL_Obool)),U_14095),c_COMBC(U_14097,tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14097,tc_prod(U_14095,U_14097)),tc_fun(U_14097,tc_fun(tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool),tc_HOL_Obool)),U_14095),hAPP(c_COMBB(tc_prod(U_14095,U_14097),tc_fun(tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool),tc_HOL_Obool),U_14097),c_member(tc_prod(U_14095,U_14097)))),c_Product__Type_OPair(U_14095,U_14097))))),U_14099)),U_14101),U_14103))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14095,U_14097)),hAPP(hAPP(c_Product__Type_OPair(U_14095,U_14097),U_14101),U_14103)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14093,tc_fun(tc_prod(U_14095,U_14097),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_14093,tc_HOL_Obool))),U_14099))) ),
    inference(clausify,[status(thm)],[f_3648_4]) ).

fof(f_3649_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_3649_2,plain,
    ! [U_14108,U_14107,U_14106,U_14105] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14105,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14105,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14106)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14105,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14108)))
      | ? [U_14104] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14105,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14105,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14104)),U_14106)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14105,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_14104),U_14107))),U_14108))) ),
    inference(variable_rename,[status(thm)],[f_3649_1]) ).

fof(f_3649_3,plain,
    ! [U_14108,U_14107,U_14106,U_14105] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14105,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14105,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14106)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14105,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14108)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14105,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14105,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK308(U_14108,U_14107,U_14106,U_14105))),U_14106)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14105,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),sK308(U_14108,U_14107,U_14106,U_14105)),U_14107))),U_14108))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK308]),skolemize(U_14104,sK308(U_14108,U_14107,U_14106,U_14105))],[f_3649_2]) ).

fof(f_3649_4,plain,
    ! [U_14105,U_14107,U_14106,U_14108] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14105,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14105,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14106)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14105,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14108)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14105,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14105,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK308(U_14108,U_14107,U_14106,U_14105))),U_14106)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14105,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),sK308(U_14108,U_14107,U_14106,U_14105)),U_14107))),U_14108))) ),
    inference(definitional_conversion,[status(esa)],[f_3649_3]) ).

cnf(f_3649_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14105,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14105,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14106)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14105,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14108)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14105,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14105,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK308(U_14108,U_14107,U_14106,U_14105))),U_14106)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14105,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),sK308(U_14108,U_14107,U_14106,U_14105)),U_14107))),U_14108))) ),
    inference(clausify,[status(thm)],[f_3649_4]) ).

fof(f_3650_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_3650_2,plain,
    ! [U_14113,U_14112,U_14111,U_14110] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14110,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14111) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14110,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14113)
      | ? [U_14109] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14110,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14109)),U_14111) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14110,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_14109),U_14112))),U_14113) ),
    inference(variable_rename,[status(thm)],[f_3650_1]) ).

fof(f_3650_3,plain,
    ! [U_14113,U_14112,U_14111,U_14110] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14110,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14111) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14110,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14113)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14110,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK309(U_14113,U_14112,U_14111,U_14110))),U_14111) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14110,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),sK309(U_14113,U_14112,U_14111,U_14110)),U_14112))),U_14113) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK309]),skolemize(U_14109,sK309(U_14113,U_14112,U_14111,U_14110))],[f_3650_2]) ).

fof(f_3650_4,plain,
    ! [U_14110,U_14111,U_14112,U_14113] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14110,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14111) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14110,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14113)
      | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14110,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK309(U_14113,U_14112,U_14111,U_14110))),U_14111) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14110,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),sK309(U_14113,U_14112,U_14111,U_14110)),U_14112))),U_14113) ),
    inference(definitional_conversion,[status(esa)],[f_3650_3]) ).

cnf(f_3650_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14110,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14111) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14110,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14113)
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14110,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK309(U_14113,U_14112,U_14111,U_14110))),U_14111) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14110,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),sK309(U_14113,U_14112,U_14111,U_14110)),U_14112))),U_14113) ),
    inference(clausify,[status(thm)],[f_3650_4]) ).

fof(f_3651_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_3651_2,plain,
    ! [U_14117,U_14116,U_14115] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14115,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14115,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14116)),U_14117))
      | ? [U_14114] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14115,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14115,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14114)),U_14116)),U_14117)) ),
    inference(variable_rename,[status(thm)],[f_3651_1]) ).

fof(f_3651_3,plain,
    ! [U_14117,U_14116,U_14115] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14115,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14115,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14116)),U_14117))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14115,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14115,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK310(U_14117,U_14116,U_14115))),U_14116)),U_14117)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK310]),skolemize(U_14114,sK310(U_14117,U_14116,U_14115))],[f_3651_2]) ).

fof(f_3651_4,plain,
    ! [U_14115,U_14116,U_14117] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14115,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14115,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14116)),U_14117))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14115,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14115,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK310(U_14117,U_14116,U_14115))),U_14116)),U_14117)) ),
    inference(definitional_conversion,[status(esa)],[f_3651_3]) ).

cnf(f_3651_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14115,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14115,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool))),U_14116)),U_14117))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14115,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(U_14115,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK310(U_14117,U_14116,U_14115))),U_14116)),U_14117)) ),
    inference(clausify,[status(thm)],[f_3651_4]) ).

fof(f_3652_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_3652_2,plain,
    ! [U_14119,U_14118] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_14118,tc_HOL_Obool)),U_14119)),
    inference(variable_rename,[status(thm)],[f_3652_1]) ).

fof(f_3652_3,plain,
    ! [U_14119,U_14118] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_14118,tc_HOL_Obool)),U_14119)),
    inference(definitional_conversion,[status(esa)],[f_3652_2]) ).

cnf(f_3652_4,plain,
    hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(U_14118,tc_HOL_Obool)),U_14119)),
    inference(clausify,[status(thm)],[f_3652_3]) ).

fof(f_3653_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_3653_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_3653_1]) ).

cnf(f_3653_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_3653_2]) ).

fof(f_3654_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_3654_2,plain,
    ! [U_14121,U_14120] : hBOOL(hAPP(hAPP(c_member(U_14120),U_14121),c_Orderings_Otop__class_Otop(tc_fun(U_14120,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3654_1]) ).

fof(f_3654_3,plain,
    ! [U_14120,U_14121] : hBOOL(hAPP(hAPP(c_member(U_14120),U_14121),c_Orderings_Otop__class_Otop(tc_fun(U_14120,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3654_2]) ).

cnf(f_3654_4,plain,
    hBOOL(hAPP(hAPP(c_member(U_14120),U_14121),c_Orderings_Otop__class_Otop(tc_fun(U_14120,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3654_3]) ).

fof(f_3655_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_3655_2,plain,
    ! [U_14122] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_14122)),c_Int_OInteg)),
    inference(variable_rename,[status(thm)],[f_3655_1]) ).

fof(f_3655_3,plain,
    ! [U_14122] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),hAPP(c_Int_ORep__Integ,U_14122)),c_Int_OInteg)),
    inference(definitional_conversion,[status(esa)],[f_3655_2]) ).

cnf(f_3655_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_14122)),c_Int_OInteg)),
    inference(clausify,[status(thm)],[f_3655_3]) ).

fof(f_3656_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_3656_2,plain,
    ! [U_14124,U_14123] :
      ( ( c_Equiv__Relations_Oequiv(U_14123,c_Orderings_Otop__class_Otop(tc_fun(U_14123,tc_HOL_Obool)),U_14124)
        | ~ c_Equiv__Relations_Oequivp(U_14123,hAPP(hAPP(c_COMBC(U_14123,tc_fun(tc_prod(U_14123,U_14123),tc_HOL_Obool),tc_fun(U_14123,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14123,tc_fun(tc_fun(tc_prod(U_14123,U_14123),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14123,U_14123),tc_HOL_Obool),tc_fun(U_14123,tc_HOL_Obool)),U_14123),c_COMBC(U_14123,tc_fun(tc_prod(U_14123,U_14123),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14123,tc_prod(U_14123,U_14123)),tc_fun(U_14123,tc_fun(tc_fun(tc_prod(U_14123,U_14123),tc_HOL_Obool),tc_HOL_Obool)),U_14123),hAPP(c_COMBB(tc_prod(U_14123,U_14123),tc_fun(tc_fun(tc_prod(U_14123,U_14123),tc_HOL_Obool),tc_HOL_Obool),U_14123),c_member(tc_prod(U_14123,U_14123)))),c_Product__Type_OPair(U_14123,U_14123)))),U_14124)) )
      & ( c_Equiv__Relations_Oequivp(U_14123,hAPP(hAPP(c_COMBC(U_14123,tc_fun(tc_prod(U_14123,U_14123),tc_HOL_Obool),tc_fun(U_14123,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14123,tc_fun(tc_fun(tc_prod(U_14123,U_14123),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14123,U_14123),tc_HOL_Obool),tc_fun(U_14123,tc_HOL_Obool)),U_14123),c_COMBC(U_14123,tc_fun(tc_prod(U_14123,U_14123),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14123,tc_prod(U_14123,U_14123)),tc_fun(U_14123,tc_fun(tc_fun(tc_prod(U_14123,U_14123),tc_HOL_Obool),tc_HOL_Obool)),U_14123),hAPP(c_COMBB(tc_prod(U_14123,U_14123),tc_fun(tc_fun(tc_prod(U_14123,U_14123),tc_HOL_Obool),tc_HOL_Obool),U_14123),c_member(tc_prod(U_14123,U_14123)))),c_Product__Type_OPair(U_14123,U_14123)))),U_14124))
        | ~ c_Equiv__Relations_Oequiv(U_14123,c_Orderings_Otop__class_Otop(tc_fun(U_14123,tc_HOL_Obool)),U_14124) ) ),
    inference(variable_rename,[status(thm)],[f_3656_1]) ).

fof(f_3656_3,plain,
    ( ! [U_14128,U_14126] :
        ( c_Equiv__Relations_Oequiv(U_14126,c_Orderings_Otop__class_Otop(tc_fun(U_14126,tc_HOL_Obool)),U_14128)
        | ~ c_Equiv__Relations_Oequivp(U_14126,hAPP(hAPP(c_COMBC(U_14126,tc_fun(tc_prod(U_14126,U_14126),tc_HOL_Obool),tc_fun(U_14126,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14126,tc_fun(tc_fun(tc_prod(U_14126,U_14126),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14126,U_14126),tc_HOL_Obool),tc_fun(U_14126,tc_HOL_Obool)),U_14126),c_COMBC(U_14126,tc_fun(tc_prod(U_14126,U_14126),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14126,tc_prod(U_14126,U_14126)),tc_fun(U_14126,tc_fun(tc_fun(tc_prod(U_14126,U_14126),tc_HOL_Obool),tc_HOL_Obool)),U_14126),hAPP(c_COMBB(tc_prod(U_14126,U_14126),tc_fun(tc_fun(tc_prod(U_14126,U_14126),tc_HOL_Obool),tc_HOL_Obool),U_14126),c_member(tc_prod(U_14126,U_14126)))),c_Product__Type_OPair(U_14126,U_14126)))),U_14128)) )
    & ! [U_14127,U_14125] :
        ( c_Equiv__Relations_Oequivp(U_14125,hAPP(hAPP(c_COMBC(U_14125,tc_fun(tc_prod(U_14125,U_14125),tc_HOL_Obool),tc_fun(U_14125,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14125,tc_fun(tc_fun(tc_prod(U_14125,U_14125),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14125,U_14125),tc_HOL_Obool),tc_fun(U_14125,tc_HOL_Obool)),U_14125),c_COMBC(U_14125,tc_fun(tc_prod(U_14125,U_14125),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14125,tc_prod(U_14125,U_14125)),tc_fun(U_14125,tc_fun(tc_fun(tc_prod(U_14125,U_14125),tc_HOL_Obool),tc_HOL_Obool)),U_14125),hAPP(c_COMBB(tc_prod(U_14125,U_14125),tc_fun(tc_fun(tc_prod(U_14125,U_14125),tc_HOL_Obool),tc_HOL_Obool),U_14125),c_member(tc_prod(U_14125,U_14125)))),c_Product__Type_OPair(U_14125,U_14125)))),U_14127))
        | ~ c_Equiv__Relations_Oequiv(U_14125,c_Orderings_Otop__class_Otop(tc_fun(U_14125,tc_HOL_Obool)),U_14127) ) ),
    inference(miniscope,[status(thm)],[f_3656_2]) ).

fof(f_3656_4,plain,
    ( ! [U_14128,U_14126] :
        ( c_Equiv__Relations_Oequiv(U_14126,c_Orderings_Otop__class_Otop(tc_fun(U_14126,tc_HOL_Obool)),U_14128)
        | ~ c_Equiv__Relations_Oequivp(U_14126,hAPP(hAPP(c_COMBC(U_14126,tc_fun(tc_prod(U_14126,U_14126),tc_HOL_Obool),tc_fun(U_14126,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14126,tc_fun(tc_fun(tc_prod(U_14126,U_14126),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14126,U_14126),tc_HOL_Obool),tc_fun(U_14126,tc_HOL_Obool)),U_14126),c_COMBC(U_14126,tc_fun(tc_prod(U_14126,U_14126),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14126,tc_prod(U_14126,U_14126)),tc_fun(U_14126,tc_fun(tc_fun(tc_prod(U_14126,U_14126),tc_HOL_Obool),tc_HOL_Obool)),U_14126),hAPP(c_COMBB(tc_prod(U_14126,U_14126),tc_fun(tc_fun(tc_prod(U_14126,U_14126),tc_HOL_Obool),tc_HOL_Obool),U_14126),c_member(tc_prod(U_14126,U_14126)))),c_Product__Type_OPair(U_14126,U_14126)))),U_14128)) )
    & ! [U_14127,U_14125] :
        ( c_Equiv__Relations_Oequivp(U_14125,hAPP(hAPP(c_COMBC(U_14125,tc_fun(tc_prod(U_14125,U_14125),tc_HOL_Obool),tc_fun(U_14125,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14125,tc_fun(tc_fun(tc_prod(U_14125,U_14125),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14125,U_14125),tc_HOL_Obool),tc_fun(U_14125,tc_HOL_Obool)),U_14125),c_COMBC(U_14125,tc_fun(tc_prod(U_14125,U_14125),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14125,tc_prod(U_14125,U_14125)),tc_fun(U_14125,tc_fun(tc_fun(tc_prod(U_14125,U_14125),tc_HOL_Obool),tc_HOL_Obool)),U_14125),hAPP(c_COMBB(tc_prod(U_14125,U_14125),tc_fun(tc_fun(tc_prod(U_14125,U_14125),tc_HOL_Obool),tc_HOL_Obool),U_14125),c_member(tc_prod(U_14125,U_14125)))),c_Product__Type_OPair(U_14125,U_14125)))),U_14127))
        | ~ c_Equiv__Relations_Oequiv(U_14125,c_Orderings_Otop__class_Otop(tc_fun(U_14125,tc_HOL_Obool)),U_14127) ) ),
    inference(definitional_conversion,[status(esa)],[f_3656_3]) ).

cnf(f_3656_5,plain,
    ( c_Equiv__Relations_Oequivp(U_14125,hAPP(hAPP(c_COMBC(U_14125,tc_fun(tc_prod(U_14125,U_14125),tc_HOL_Obool),tc_fun(U_14125,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14125,tc_fun(tc_fun(tc_prod(U_14125,U_14125),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14125,U_14125),tc_HOL_Obool),tc_fun(U_14125,tc_HOL_Obool)),U_14125),c_COMBC(U_14125,tc_fun(tc_prod(U_14125,U_14125),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14125,tc_prod(U_14125,U_14125)),tc_fun(U_14125,tc_fun(tc_fun(tc_prod(U_14125,U_14125),tc_HOL_Obool),tc_HOL_Obool)),U_14125),hAPP(c_COMBB(tc_prod(U_14125,U_14125),tc_fun(tc_fun(tc_prod(U_14125,U_14125),tc_HOL_Obool),tc_HOL_Obool),U_14125),c_member(tc_prod(U_14125,U_14125)))),c_Product__Type_OPair(U_14125,U_14125)))),U_14127))
    | ~ c_Equiv__Relations_Oequiv(U_14125,c_Orderings_Otop__class_Otop(tc_fun(U_14125,tc_HOL_Obool)),U_14127) ),
    inference(clausify,[status(thm)],[f_3656_4]) ).

cnf(f_3656_6,plain,
    ( c_Equiv__Relations_Oequiv(U_14126,c_Orderings_Otop__class_Otop(tc_fun(U_14126,tc_HOL_Obool)),U_14128)
    | ~ c_Equiv__Relations_Oequivp(U_14126,hAPP(hAPP(c_COMBC(U_14126,tc_fun(tc_prod(U_14126,U_14126),tc_HOL_Obool),tc_fun(U_14126,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14126,tc_fun(tc_fun(tc_prod(U_14126,U_14126),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_14126,U_14126),tc_HOL_Obool),tc_fun(U_14126,tc_HOL_Obool)),U_14126),c_COMBC(U_14126,tc_fun(tc_prod(U_14126,U_14126),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14126,tc_prod(U_14126,U_14126)),tc_fun(U_14126,tc_fun(tc_fun(tc_prod(U_14126,U_14126),tc_HOL_Obool),tc_HOL_Obool)),U_14126),hAPP(c_COMBB(tc_prod(U_14126,U_14126),tc_fun(tc_fun(tc_prod(U_14126,U_14126),tc_HOL_Obool),tc_HOL_Obool),U_14126),c_member(tc_prod(U_14126,U_14126)))),c_Product__Type_OPair(U_14126,U_14126)))),U_14128)) ),
    inference(clausify,[status(thm)],[f_3656_4]) ).

fof(f_3657_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_3657_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_3657_1]) ).

cnf(f_3657_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_3657_2]) ).

fof(f_3658_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_3658_2,plain,
    ! [U_14133,U_14132,U_14131,U_14130,U_14129] :
      ( hBOOL(hAPP(hAPP(U_14130,U_14131),U_14133))
      | ~ hBOOL(hAPP(hAPP(U_14130,U_14132),U_14133))
      | ~ hBOOL(hAPP(hAPP(U_14130,U_14131),U_14132))
      | ~ c_Equiv__Relations_Oequivp(U_14129,U_14130) ),
    inference(variable_rename,[status(thm)],[f_3658_1]) ).

fof(f_3658_3,plain,
    ! [U_14133,U_14132,U_14131,U_14130] :
      ( ! [U_14129] : ~ c_Equiv__Relations_Oequivp(U_14129,U_14130)
      | hBOOL(hAPP(hAPP(U_14130,U_14131),U_14133))
      | ~ hBOOL(hAPP(hAPP(U_14130,U_14132),U_14133))
      | ~ hBOOL(hAPP(hAPP(U_14130,U_14131),U_14132)) ),
    inference(miniscope,[status(thm)],[f_3658_2]) ).

fof(f_3658_4,plain,
    ! [U_14130,U_14129,U_14131,U_14132,U_14133] :
      ( ~ c_Equiv__Relations_Oequivp(U_14129,U_14130)
      | hBOOL(hAPP(hAPP(U_14130,U_14131),U_14133))
      | ~ hBOOL(hAPP(hAPP(U_14130,U_14132),U_14133))
      | ~ hBOOL(hAPP(hAPP(U_14130,U_14131),U_14132)) ),
    inference(definitional_conversion,[status(esa)],[f_3658_3]) ).

cnf(f_3658_5,plain,
    ( ~ c_Equiv__Relations_Oequivp(U_14129,U_14130)
    | hBOOL(hAPP(hAPP(U_14130,U_14131),U_14133))
    | ~ hBOOL(hAPP(hAPP(U_14130,U_14132),U_14133))
    | ~ hBOOL(hAPP(hAPP(U_14130,U_14131),U_14132)) ),
    inference(clausify,[status(thm)],[f_3658_4]) ).

fof(f_3659_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_3659_2,plain,
    ! [U_14137,U_14136,U_14135,U_14134] :
      ( hBOOL(hAPP(hAPP(U_14135,U_14137),U_14136))
      | ~ hBOOL(hAPP(hAPP(U_14135,U_14136),U_14137))
      | ~ c_Equiv__Relations_Oequivp(U_14134,U_14135) ),
    inference(variable_rename,[status(thm)],[f_3659_1]) ).

fof(f_3659_3,plain,
    ! [U_14137,U_14136,U_14135] :
      ( ! [U_14134] : ~ c_Equiv__Relations_Oequivp(U_14134,U_14135)
      | hBOOL(hAPP(hAPP(U_14135,U_14137),U_14136))
      | ~ hBOOL(hAPP(hAPP(U_14135,U_14136),U_14137)) ),
    inference(miniscope,[status(thm)],[f_3659_2]) ).

fof(f_3659_4,plain,
    ! [U_14137,U_14134,U_14135,U_14136] :
      ( ~ c_Equiv__Relations_Oequivp(U_14134,U_14135)
      | hBOOL(hAPP(hAPP(U_14135,U_14137),U_14136))
      | ~ hBOOL(hAPP(hAPP(U_14135,U_14136),U_14137)) ),
    inference(definitional_conversion,[status(esa)],[f_3659_3]) ).

cnf(f_3659_5,plain,
    ( ~ c_Equiv__Relations_Oequivp(U_14134,U_14135)
    | hBOOL(hAPP(hAPP(U_14135,U_14137),U_14136))
    | ~ hBOOL(hAPP(hAPP(U_14135,U_14136),U_14137)) ),
    inference(clausify,[status(thm)],[f_3659_4]) ).

fof(f_3660_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_3660_2,plain,
    ! [U_14140,U_14139,U_14138] :
      ( hBOOL(hAPP(hAPP(U_14139,U_14140),U_14140))
      | ~ c_Equiv__Relations_Oequivp(U_14138,U_14139) ),
    inference(variable_rename,[status(thm)],[f_3660_1]) ).

fof(f_3660_3,plain,
    ! [U_14140,U_14139] :
      ( ! [U_14138] : ~ c_Equiv__Relations_Oequivp(U_14138,U_14139)
      | hBOOL(hAPP(hAPP(U_14139,U_14140),U_14140)) ),
    inference(miniscope,[status(thm)],[f_3660_2]) ).

fof(f_3660_4,plain,
    ! [U_14140,U_14139,U_14138] :
      ( ~ c_Equiv__Relations_Oequivp(U_14138,U_14139)
      | hBOOL(hAPP(hAPP(U_14139,U_14140),U_14140)) ),
    inference(definitional_conversion,[status(esa)],[f_3660_3]) ).

cnf(f_3660_5,plain,
    ( ~ c_Equiv__Relations_Oequivp(U_14138,U_14139)
    | hBOOL(hAPP(hAPP(U_14139,U_14140),U_14140)) ),
    inference(clausify,[status(thm)],[f_3660_4]) ).

fof(f_3661_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_3661_2,plain,
    ! [U_14146,U_14145] :
      ( ( c_Equiv__Relations_Oequivp(U_14145,U_14146)
        | ? [U_14144,U_14143] :
            ( ( ~ hBOOL(hAPP(hAPP(U_14146,U_14144),U_14143))
              & hAPP(U_14146,U_14144) = hAPP(U_14146,U_14143) )
            | ( hAPP(U_14146,U_14144) != hAPP(U_14146,U_14143)
              & hBOOL(hAPP(hAPP(U_14146,U_14144),U_14143)) ) ) )
      & ( ! [U_14142,U_14141] :
            ( ( hBOOL(hAPP(hAPP(U_14146,U_14142),U_14141))
              | hAPP(U_14146,U_14142) != hAPP(U_14146,U_14141) )
            & ( hAPP(U_14146,U_14142) = hAPP(U_14146,U_14141)
              | ~ hBOOL(hAPP(hAPP(U_14146,U_14142),U_14141)) ) )
        | ~ c_Equiv__Relations_Oequivp(U_14145,U_14146) ) ),
    inference(variable_rename,[status(thm)],[f_3661_1]) ).

fof(f_3661_3,plain,
    ( ! [U_14158] :
        ( ! [U_14156] : c_Equiv__Relations_Oequivp(U_14156,U_14158)
        | ? [U_14154,U_14152] :
            ( ~ hBOOL(hAPP(hAPP(U_14158,U_14154),U_14152))
            & hAPP(U_14158,U_14154) = hAPP(U_14158,U_14152) )
        | ? [U_14153,U_14151] :
            ( hAPP(U_14158,U_14153) != hAPP(U_14158,U_14151)
            & hBOOL(hAPP(hAPP(U_14158,U_14153),U_14151)) ) )
    & ! [U_14157] :
        ( ! [U_14155] : ~ c_Equiv__Relations_Oequivp(U_14155,U_14157)
        | ( ! [U_14150,U_14148] :
              ( hBOOL(hAPP(hAPP(U_14157,U_14150),U_14148))
              | hAPP(U_14157,U_14150) != hAPP(U_14157,U_14148) )
          & ! [U_14149,U_14147] :
              ( hAPP(U_14157,U_14149) = hAPP(U_14157,U_14147)
              | ~ hBOOL(hAPP(hAPP(U_14157,U_14149),U_14147)) ) ) ) ),
    inference(miniscope,[status(thm)],[f_3661_2]) ).

fof(f_3661_4,plain,
    ( ! [U_14158] :
        ( ! [U_14156] : c_Equiv__Relations_Oequivp(U_14156,U_14158)
        | ? [U_14154,U_14152] :
            ( ~ hBOOL(hAPP(hAPP(U_14158,U_14154),U_14152))
            & hAPP(U_14158,U_14154) = hAPP(U_14158,U_14152) )
        | ? [U_14151] :
            ( hAPP(U_14158,sK311(U_14158)) != hAPP(U_14158,U_14151)
            & hBOOL(hAPP(hAPP(U_14158,sK311(U_14158)),U_14151)) ) )
    & ! [U_14157] :
        ( ! [U_14155] : ~ c_Equiv__Relations_Oequivp(U_14155,U_14157)
        | ( ! [U_14150,U_14148] :
              ( hBOOL(hAPP(hAPP(U_14157,U_14150),U_14148))
              | hAPP(U_14157,U_14150) != hAPP(U_14157,U_14148) )
          & ! [U_14149,U_14147] :
              ( hAPP(U_14157,U_14149) = hAPP(U_14157,U_14147)
              | ~ hBOOL(hAPP(hAPP(U_14157,U_14149),U_14147)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK311]),skolemize(U_14153,sK311(U_14158))],[f_3661_3]) ).

fof(f_3661_5,plain,
    ( ! [U_14158] :
        ( ! [U_14156] : c_Equiv__Relations_Oequivp(U_14156,U_14158)
        | ? [U_14154,U_14152] :
            ( ~ hBOOL(hAPP(hAPP(U_14158,U_14154),U_14152))
            & hAPP(U_14158,U_14154) = hAPP(U_14158,U_14152) )
        | ( hAPP(U_14158,sK311(U_14158)) != hAPP(U_14158,sK312(U_14158))
          & hBOOL(hAPP(hAPP(U_14158,sK311(U_14158)),sK312(U_14158))) ) )
    & ! [U_14157] :
        ( ! [U_14155] : ~ c_Equiv__Relations_Oequivp(U_14155,U_14157)
        | ( ! [U_14150,U_14148] :
              ( hBOOL(hAPP(hAPP(U_14157,U_14150),U_14148))
              | hAPP(U_14157,U_14150) != hAPP(U_14157,U_14148) )
          & ! [U_14149,U_14147] :
              ( hAPP(U_14157,U_14149) = hAPP(U_14157,U_14147)
              | ~ hBOOL(hAPP(hAPP(U_14157,U_14149),U_14147)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK312]),skolemize(U_14151,sK312(U_14158))],[f_3661_4]) ).

fof(f_3661_6,plain,
    ( ! [U_14158] :
        ( ! [U_14156] : c_Equiv__Relations_Oequivp(U_14156,U_14158)
        | ? [U_14152] :
            ( ~ hBOOL(hAPP(hAPP(U_14158,sK313(U_14158)),U_14152))
            & hAPP(U_14158,sK313(U_14158)) = hAPP(U_14158,U_14152) )
        | ( hAPP(U_14158,sK311(U_14158)) != hAPP(U_14158,sK312(U_14158))
          & hBOOL(hAPP(hAPP(U_14158,sK311(U_14158)),sK312(U_14158))) ) )
    & ! [U_14157] :
        ( ! [U_14155] : ~ c_Equiv__Relations_Oequivp(U_14155,U_14157)
        | ( ! [U_14150,U_14148] :
              ( hBOOL(hAPP(hAPP(U_14157,U_14150),U_14148))
              | hAPP(U_14157,U_14150) != hAPP(U_14157,U_14148) )
          & ! [U_14149,U_14147] :
              ( hAPP(U_14157,U_14149) = hAPP(U_14157,U_14147)
              | ~ hBOOL(hAPP(hAPP(U_14157,U_14149),U_14147)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK313]),skolemize(U_14154,sK313(U_14158))],[f_3661_5]) ).

fof(f_3661_7,plain,
    ( ! [U_14158] :
        ( ! [U_14156] : c_Equiv__Relations_Oequivp(U_14156,U_14158)
        | ( ~ hBOOL(hAPP(hAPP(U_14158,sK313(U_14158)),sK314(U_14158)))
          & hAPP(U_14158,sK313(U_14158)) = hAPP(U_14158,sK314(U_14158)) )
        | ( hAPP(U_14158,sK311(U_14158)) != hAPP(U_14158,sK312(U_14158))
          & hBOOL(hAPP(hAPP(U_14158,sK311(U_14158)),sK312(U_14158))) ) )
    & ! [U_14157] :
        ( ! [U_14155] : ~ c_Equiv__Relations_Oequivp(U_14155,U_14157)
        | ( ! [U_14150,U_14148] :
              ( hBOOL(hAPP(hAPP(U_14157,U_14150),U_14148))
              | hAPP(U_14157,U_14150) != hAPP(U_14157,U_14148) )
          & ! [U_14149,U_14147] :
              ( hAPP(U_14157,U_14149) = hAPP(U_14157,U_14147)
              | ~ hBOOL(hAPP(hAPP(U_14157,U_14149),U_14147)) ) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK314]),skolemize(U_14152,sK314(U_14158))],[f_3661_6]) ).

fof(f_3661_8,plain,
    ( ! [U_14158] :
        ( ~ hBOOL(hAPP(hAPP(U_14158,sK313(U_14158)),sK314(U_14158)))
        | ~ sP975(U_14158) )
    & ! [U_14158] :
        ( hAPP(U_14158,sK313(U_14158)) = hAPP(U_14158,sK314(U_14158))
        | ~ sP975(U_14158) )
    & ! [U_14158] :
        ( hAPP(U_14158,sK311(U_14158)) != hAPP(U_14158,sK312(U_14158))
        | ~ sP974(U_14158) )
    & ! [U_14158] :
        ( hBOOL(hAPP(hAPP(U_14158,sK311(U_14158)),sK312(U_14158)))
        | ~ sP974(U_14158) )
    & ! [U_14149,U_14147,U_14148,U_14150,U_14157] :
        ( hBOOL(hAPP(hAPP(U_14157,U_14150),U_14148))
        | hAPP(U_14157,U_14150) != hAPP(U_14157,U_14148)
        | ~ sP973(U_14149,U_14147,U_14148,U_14150,U_14157) )
    & ! [U_14149,U_14147,U_14148,U_14150,U_14157] :
        ( hAPP(U_14157,U_14149) = hAPP(U_14157,U_14147)
        | ~ hBOOL(hAPP(hAPP(U_14157,U_14149),U_14147))
        | ~ sP973(U_14149,U_14147,U_14148,U_14150,U_14157) )
    & ! [U_14156,U_14158] :
        ( c_Equiv__Relations_Oequivp(U_14156,U_14158)
        | sP975(U_14158)
        | sP974(U_14158) )
    & ! [U_14149,U_14147,U_14148,U_14150,U_14155,U_14157] :
        ( ~ c_Equiv__Relations_Oequivp(U_14155,U_14157)
        | sP973(U_14149,U_14147,U_14148,U_14150,U_14157) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP973,sP974,sP975])],[f_3661_7]) ).

cnf(f_3661_9,plain,
    ( ~ c_Equiv__Relations_Oequivp(U_14155,U_14157)
    | sP973(U_14149,U_14147,U_14148,U_14150,U_14157) ),
    inference(clausify,[status(thm)],[f_3661_8]) ).

cnf(f_3661_10,plain,
    ( c_Equiv__Relations_Oequivp(U_14156,U_14158)
    | sP975(U_14158)
    | sP974(U_14158) ),
    inference(clausify,[status(thm)],[f_3661_8]) ).

cnf(f_3661_11,plain,
    ( hAPP(U_14157,U_14149) = hAPP(U_14157,U_14147)
    | ~ hBOOL(hAPP(hAPP(U_14157,U_14149),U_14147))
    | ~ sP973(U_14149,U_14147,U_14148,U_14150,U_14157) ),
    inference(clausify,[status(thm)],[f_3661_8]) ).

cnf(f_3661_12,plain,
    ( hBOOL(hAPP(hAPP(U_14157,U_14150),U_14148))
    | hAPP(U_14157,U_14150) != hAPP(U_14157,U_14148)
    | ~ sP973(U_14149,U_14147,U_14148,U_14150,U_14157) ),
    inference(clausify,[status(thm)],[f_3661_8]) ).

cnf(f_3661_13,plain,
    ( hBOOL(hAPP(hAPP(U_14158,sK311(U_14158)),sK312(U_14158)))
    | ~ sP974(U_14158) ),
    inference(clausify,[status(thm)],[f_3661_8]) ).

cnf(f_3661_14,plain,
    ( hAPP(U_14158,sK311(U_14158)) != hAPP(U_14158,sK312(U_14158))
    | ~ sP974(U_14158) ),
    inference(clausify,[status(thm)],[f_3661_8]) ).

cnf(f_3661_15,plain,
    ( hAPP(U_14158,sK313(U_14158)) = hAPP(U_14158,sK314(U_14158))
    | ~ sP975(U_14158) ),
    inference(clausify,[status(thm)],[f_3661_8]) ).

cnf(f_3661_16,plain,
    ( ~ hBOOL(hAPP(hAPP(U_14158,sK313(U_14158)),sK314(U_14158)))
    | ~ sP975(U_14158) ),
    inference(clausify,[status(thm)],[f_3661_8]) ).

fof(f_3662_1,plain,
    ! [T_b] : c_Equiv__Relations_Oequivp(T_b,c_fequal),
    inference(fof_nnf,[status(thm)],[fact_identity__equivp]) ).

fof(f_3662_2,plain,
    ! [U_14159] : c_Equiv__Relations_Oequivp(U_14159,c_fequal),
    inference(variable_rename,[status(thm)],[f_3662_1]) ).

fof(f_3662_3,plain,
    ! [U_14159] : c_Equiv__Relations_Oequivp(U_14159,c_fequal),
    inference(definitional_conversion,[status(esa)],[f_3662_2]) ).

cnf(f_3662_4,plain,
    c_Equiv__Relations_Oequivp(U_14159,c_fequal),
    inference(clausify,[status(thm)],[f_3662_3]) ).

fof(f_3663_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_3663_2,plain,
    ! [U_14164,U_14163,U_14162,U_14161,U_14160] :
      ( hAPP(c_Set_Oimage(U_14161,U_14160,U_14163),U_14164) = c_Orderings_Otop__class_Otop(tc_fun(U_14160,tc_HOL_Obool))
      | ~ c_Typedef_Otype__definition(U_14160,U_14161,U_14162,U_14163,U_14164) ),
    inference(variable_rename,[status(thm)],[f_3663_1]) ).

fof(f_3663_3,plain,
    ! [U_14161,U_14162,U_14163,U_14164,U_14160] :
      ( hAPP(c_Set_Oimage(U_14161,U_14160,U_14163),U_14164) = c_Orderings_Otop__class_Otop(tc_fun(U_14160,tc_HOL_Obool))
      | ~ c_Typedef_Otype__definition(U_14160,U_14161,U_14162,U_14163,U_14164) ),
    inference(definitional_conversion,[status(esa)],[f_3663_2]) ).

cnf(f_3663_4,plain,
    ( hAPP(c_Set_Oimage(U_14161,U_14160,U_14163),U_14164) = c_Orderings_Otop__class_Otop(tc_fun(U_14160,tc_HOL_Obool))
    | ~ c_Typedef_Otype__definition(U_14160,U_14161,U_14162,U_14163,U_14164) ),
    inference(clausify,[status(thm)],[f_3663_3]) ).

fof(f_3664_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_3664_2,plain,
    ! [U_14169,U_14168,U_14167,U_14166,U_14165] :
      ( hAPP(c_Set_Oimage(U_14165,U_14166,U_14167),c_Orderings_Otop__class_Otop(tc_fun(U_14165,tc_HOL_Obool))) = U_14169
      | ~ c_Typedef_Otype__definition(U_14165,U_14166,U_14167,U_14168,U_14169) ),
    inference(variable_rename,[status(thm)],[f_3664_1]) ).

fof(f_3664_3,plain,
    ! [U_14168,U_14169,U_14167,U_14166,U_14165] :
      ( hAPP(c_Set_Oimage(U_14165,U_14166,U_14167),c_Orderings_Otop__class_Otop(tc_fun(U_14165,tc_HOL_Obool))) = U_14169
      | ~ c_Typedef_Otype__definition(U_14165,U_14166,U_14167,U_14168,U_14169) ),
    inference(definitional_conversion,[status(esa)],[f_3664_2]) ).

cnf(f_3664_4,plain,
    ( hAPP(c_Set_Oimage(U_14165,U_14166,U_14167),c_Orderings_Otop__class_Otop(tc_fun(U_14165,tc_HOL_Obool))) = U_14169
    | ~ c_Typedef_Otype__definition(U_14165,U_14166,U_14167,U_14168,U_14169) ),
    inference(clausify,[status(thm)],[f_3664_3]) ).

fof(f_3665_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_3665_2,plain,
    ! [U_14176,U_14175,U_14174,U_14173,U_14172,U_14171,U_14170] :
      ( ( ( hAPP(U_14172,U_14175) = hAPP(U_14172,U_14176)
          | U_14175 != U_14176 )
        & ( U_14175 = U_14176
          | hAPP(U_14172,U_14175) != hAPP(U_14172,U_14176) ) )
      | ~ c_Typedef_Otype__definition(U_14170,U_14171,U_14172,U_14173,U_14174) ),
    inference(variable_rename,[status(thm)],[f_3665_1]) ).

fof(f_3665_3,plain,
    ! [U_14176,U_14175,U_14174,U_14173,U_14172] :
      ( ! [U_14171,U_14170] : ~ c_Typedef_Otype__definition(U_14170,U_14171,U_14172,U_14173,U_14174)
      | ( ( hAPP(U_14172,U_14175) = hAPP(U_14172,U_14176)
          | U_14175 != U_14176 )
        & ( U_14175 = U_14176
          | hAPP(U_14172,U_14175) != hAPP(U_14172,U_14176) ) ) ),
    inference(miniscope,[status(thm)],[f_3665_2]) ).

fof(f_3665_4,plain,
    ( ! [U_14172,U_14175,U_14176] :
        ( hAPP(U_14172,U_14175) = hAPP(U_14172,U_14176)
        | U_14175 != U_14176
        | ~ sP976(U_14172,U_14175,U_14176) )
    & ! [U_14172,U_14175,U_14176] :
        ( U_14175 = U_14176
        | hAPP(U_14172,U_14175) != hAPP(U_14172,U_14176)
        | ~ sP976(U_14172,U_14175,U_14176) )
    & ! [U_14172,U_14170,U_14173,U_14171,U_14174,U_14175,U_14176] :
        ( ~ c_Typedef_Otype__definition(U_14170,U_14171,U_14172,U_14173,U_14174)
        | sP976(U_14172,U_14175,U_14176) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP976])],[f_3665_3]) ).

cnf(f_3665_5,plain,
    ( ~ c_Typedef_Otype__definition(U_14170,U_14171,U_14172,U_14173,U_14174)
    | sP976(U_14172,U_14175,U_14176) ),
    inference(clausify,[status(thm)],[f_3665_4]) ).

cnf(f_3665_6,plain,
    ( U_14175 = U_14176
    | hAPP(U_14172,U_14175) != hAPP(U_14172,U_14176)
    | ~ sP976(U_14172,U_14175,U_14176) ),
    inference(clausify,[status(thm)],[f_3665_4]) ).

cnf(f_3665_7,plain,
    ( hAPP(U_14172,U_14175) = hAPP(U_14172,U_14176)
    | U_14175 != U_14176
    | ~ sP976(U_14172,U_14175,U_14176) ),
    inference(clausify,[status(thm)],[f_3665_4]) ).

fof(f_3666_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_3666_2,plain,
    ! [U_14182,U_14181,U_14180,U_14179,U_14178,U_14177] :
      ( hAPP(U_14180,hAPP(U_14179,U_14182)) = U_14182
      | ~ c_Typedef_Otype__definition(U_14177,U_14178,U_14179,U_14180,U_14181) ),
    inference(variable_rename,[status(thm)],[f_3666_1]) ).

fof(f_3666_3,plain,
    ! [U_14182,U_14181,U_14180,U_14179] :
      ( ! [U_14178,U_14177] : ~ c_Typedef_Otype__definition(U_14177,U_14178,U_14179,U_14180,U_14181)
      | hAPP(U_14180,hAPP(U_14179,U_14182)) = U_14182 ),
    inference(miniscope,[status(thm)],[f_3666_2]) ).

fof(f_3666_4,plain,
    ! [U_14179,U_14180,U_14177,U_14178,U_14181,U_14182] :
      ( ~ c_Typedef_Otype__definition(U_14177,U_14178,U_14179,U_14180,U_14181)
      | hAPP(U_14180,hAPP(U_14179,U_14182)) = U_14182 ),
    inference(definitional_conversion,[status(esa)],[f_3666_3]) ).

cnf(f_3666_5,plain,
    ( ~ c_Typedef_Otype__definition(U_14177,U_14178,U_14179,U_14180,U_14181)
    | hAPP(U_14180,hAPP(U_14179,U_14182)) = U_14182 ),
    inference(clausify,[status(thm)],[f_3666_4]) ).

fof(f_3667_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_3667_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_3667_1]) ).

cnf(f_3667_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_3667_2]) ).

fof(f_3668_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_3668_2,plain,
    ! [U_14188,U_14187,U_14186,U_14185,U_14184,U_14183] :
      ( hBOOL(hAPP(hAPP(c_member(U_14184),hAPP(U_14185,U_14188)),U_14187))
      | ~ c_Typedef_Otype__definition(U_14183,U_14184,U_14185,U_14186,U_14187) ),
    inference(variable_rename,[status(thm)],[f_3668_1]) ).

fof(f_3668_3,plain,
    ! [U_14188,U_14187,U_14186,U_14185,U_14184] :
      ( ! [U_14183] : ~ c_Typedef_Otype__definition(U_14183,U_14184,U_14185,U_14186,U_14187)
      | hBOOL(hAPP(hAPP(c_member(U_14184),hAPP(U_14185,U_14188)),U_14187)) ),
    inference(miniscope,[status(thm)],[f_3668_2]) ).

fof(f_3668_4,plain,
    ! [U_14183,U_14184,U_14185,U_14186,U_14187,U_14188] :
      ( ~ c_Typedef_Otype__definition(U_14183,U_14184,U_14185,U_14186,U_14187)
      | hBOOL(hAPP(hAPP(c_member(U_14184),hAPP(U_14185,U_14188)),U_14187)) ),
    inference(definitional_conversion,[status(esa)],[f_3668_3]) ).

cnf(f_3668_5,plain,
    ( ~ c_Typedef_Otype__definition(U_14183,U_14184,U_14185,U_14186,U_14187)
    | hBOOL(hAPP(hAPP(c_member(U_14184),hAPP(U_14185,U_14188)),U_14187)) ),
    inference(clausify,[status(thm)],[f_3668_4]) ).

fof(f_3669_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_3669_2,plain,
    ! [U_14194,U_14193,U_14192,U_14191,U_14190,U_14189] :
      ( hAPP(U_14191,hAPP(U_14192,U_14194)) = U_14194
      | ~ hBOOL(hAPP(hAPP(c_member(U_14190),U_14194),U_14193))
      | ~ c_Typedef_Otype__definition(U_14189,U_14190,U_14191,U_14192,U_14193) ),
    inference(variable_rename,[status(thm)],[f_3669_1]) ).

fof(f_3669_3,plain,
    ! [U_14194,U_14193,U_14192,U_14191,U_14190] :
      ( ! [U_14189] : ~ c_Typedef_Otype__definition(U_14189,U_14190,U_14191,U_14192,U_14193)
      | hAPP(U_14191,hAPP(U_14192,U_14194)) = U_14194
      | ~ hBOOL(hAPP(hAPP(c_member(U_14190),U_14194),U_14193)) ),
    inference(miniscope,[status(thm)],[f_3669_2]) ).

fof(f_3669_4,plain,
    ! [U_14190,U_14189,U_14191,U_14192,U_14193,U_14194] :
      ( ~ c_Typedef_Otype__definition(U_14189,U_14190,U_14191,U_14192,U_14193)
      | hAPP(U_14191,hAPP(U_14192,U_14194)) = U_14194
      | ~ hBOOL(hAPP(hAPP(c_member(U_14190),U_14194),U_14193)) ),
    inference(definitional_conversion,[status(esa)],[f_3669_3]) ).

cnf(f_3669_5,plain,
    ( ~ c_Typedef_Otype__definition(U_14189,U_14190,U_14191,U_14192,U_14193)
    | hAPP(U_14191,hAPP(U_14192,U_14194)) = U_14194
    | ~ hBOOL(hAPP(hAPP(c_member(U_14190),U_14194),U_14193)) ),
    inference(clausify,[status(thm)],[f_3669_4]) ).

fof(f_3670_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_3670_2,plain,
    ! [U_14201,U_14200,U_14199,U_14198,U_14197,U_14196,U_14195] :
      ( ( ( hAPP(U_14198,U_14200) = hAPP(U_14198,U_14201)
          | U_14200 != U_14201 )
        & ( U_14200 = U_14201
          | hAPP(U_14198,U_14200) != hAPP(U_14198,U_14201) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_14196),U_14201),U_14199))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14196),U_14200),U_14199))
      | ~ c_Typedef_Otype__definition(U_14195,U_14196,U_14197,U_14198,U_14199) ),
    inference(variable_rename,[status(thm)],[f_3670_1]) ).

fof(f_3670_3,plain,
    ! [U_14201,U_14200,U_14199,U_14198,U_14197,U_14196] :
      ( ! [U_14195] : ~ c_Typedef_Otype__definition(U_14195,U_14196,U_14197,U_14198,U_14199)
      | ( ( hAPP(U_14198,U_14200) = hAPP(U_14198,U_14201)
          | U_14200 != U_14201 )
        & ( U_14200 = U_14201
          | hAPP(U_14198,U_14200) != hAPP(U_14198,U_14201) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_14196),U_14201),U_14199))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14196),U_14200),U_14199)) ),
    inference(miniscope,[status(thm)],[f_3670_2]) ).

fof(f_3670_4,plain,
    ( ! [U_14198,U_14200,U_14201] :
        ( hAPP(U_14198,U_14200) = hAPP(U_14198,U_14201)
        | U_14200 != U_14201
        | ~ sP977(U_14198,U_14200,U_14201) )
    & ! [U_14198,U_14200,U_14201] :
        ( U_14200 = U_14201
        | hAPP(U_14198,U_14200) != hAPP(U_14198,U_14201)
        | ~ sP977(U_14198,U_14200,U_14201) )
    & ! [U_14195,U_14196,U_14197,U_14198,U_14199,U_14200,U_14201] :
        ( ~ c_Typedef_Otype__definition(U_14195,U_14196,U_14197,U_14198,U_14199)
        | sP977(U_14198,U_14200,U_14201)
        | ~ hBOOL(hAPP(hAPP(c_member(U_14196),U_14201),U_14199))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14196),U_14200),U_14199)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP977])],[f_3670_3]) ).

cnf(f_3670_5,plain,
    ( ~ c_Typedef_Otype__definition(U_14195,U_14196,U_14197,U_14198,U_14199)
    | sP977(U_14198,U_14200,U_14201)
    | ~ hBOOL(hAPP(hAPP(c_member(U_14196),U_14201),U_14199))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14196),U_14200),U_14199)) ),
    inference(clausify,[status(thm)],[f_3670_4]) ).

cnf(f_3670_6,plain,
    ( U_14200 = U_14201
    | hAPP(U_14198,U_14200) != hAPP(U_14198,U_14201)
    | ~ sP977(U_14198,U_14200,U_14201) ),
    inference(clausify,[status(thm)],[f_3670_4]) ).

cnf(f_3670_7,plain,
    ( hAPP(U_14198,U_14200) = hAPP(U_14198,U_14201)
    | U_14200 != U_14201
    | ~ sP977(U_14198,U_14200,U_14201) ),
    inference(clausify,[status(thm)],[f_3670_4]) ).

fof(f_3671_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_3671_2,plain,
    ! [U_14205,U_14204,U_14203,U_14202] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14202,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14202,U_14203,U_14204),hAPP(hAPP(c_Set_Oinsert(U_14203),U_14205),c_Orderings_Obot__class_Obot(tc_fun(U_14203,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_14202),c_HOL_OThe(U_14202,hAPP(hAPP(c_COMBC(U_14202,U_14203,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14203,tc_fun(U_14203,tc_HOL_Obool),U_14202),c_fequal),U_14204)),U_14205))),c_Orderings_Obot__class_Obot(tc_fun(U_14202,tc_HOL_Obool)))))
      | ~ c_Fun_Oinj__on(U_14202,U_14203,U_14204,c_Orderings_Otop__class_Otop(tc_fun(U_14202,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3671_1]) ).

fof(f_3671_3,plain,
    ! [U_14204,U_14202,U_14205,U_14203] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14202,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14202,U_14203,U_14204),hAPP(hAPP(c_Set_Oinsert(U_14203),U_14205),c_Orderings_Obot__class_Obot(tc_fun(U_14203,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_14202),c_HOL_OThe(U_14202,hAPP(hAPP(c_COMBC(U_14202,U_14203,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14203,tc_fun(U_14203,tc_HOL_Obool),U_14202),c_fequal),U_14204)),U_14205))),c_Orderings_Obot__class_Obot(tc_fun(U_14202,tc_HOL_Obool)))))
      | ~ c_Fun_Oinj__on(U_14202,U_14203,U_14204,c_Orderings_Otop__class_Otop(tc_fun(U_14202,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3671_2]) ).

cnf(f_3671_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14202,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14202,U_14203,U_14204),hAPP(hAPP(c_Set_Oinsert(U_14203),U_14205),c_Orderings_Obot__class_Obot(tc_fun(U_14203,tc_HOL_Obool))))),hAPP(hAPP(c_Set_Oinsert(U_14202),c_HOL_OThe(U_14202,hAPP(hAPP(c_COMBC(U_14202,U_14203,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14203,tc_fun(U_14203,tc_HOL_Obool),U_14202),c_fequal),U_14204)),U_14205))),c_Orderings_Obot__class_Obot(tc_fun(U_14202,tc_HOL_Obool)))))
    | ~ c_Fun_Oinj__on(U_14202,U_14203,U_14204,c_Orderings_Otop__class_Otop(tc_fun(U_14202,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3671_3]) ).

fof(f_3672_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_3672_2,plain,
    ! [U_14208,U_14207,U_14206] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14206,U_14206)),U_14207),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_14206,U_14206),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_14206,U_14206),tc_HOL_Obool),tc_fun(tc_prod(U_14206,U_14206),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_14206,U_14206),tc_HOL_Obool)),U_14208))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14206,U_14206)),U_14207),c_Transitive__Closure_Ortrancl(U_14206,U_14208))) ),
    inference(variable_rename,[status(thm)],[f_3672_1]) ).

fof(f_3672_3,plain,
    ! [U_14206,U_14207,U_14208] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14206,U_14206)),U_14207),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_14206,U_14206),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_14206,U_14206),tc_HOL_Obool),tc_fun(tc_prod(U_14206,U_14206),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_14206,U_14206),tc_HOL_Obool)),U_14208))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14206,U_14206)),U_14207),c_Transitive__Closure_Ortrancl(U_14206,U_14208))) ),
    inference(definitional_conversion,[status(esa)],[f_3672_2]) ).

cnf(f_3672_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14206,U_14206)),U_14207),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_14206,U_14206),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_14206,U_14206),tc_HOL_Obool),tc_fun(tc_prod(U_14206,U_14206),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_14206,U_14206),tc_HOL_Obool)),U_14208))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14206,U_14206)),U_14207),c_Transitive__Closure_Ortrancl(U_14206,U_14208))) ),
    inference(clausify,[status(thm)],[f_3672_3]) ).

fof(f_3673_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_3673_2,plain,
    ! [U_14214,U_14213,U_14212,U_14211,U_14210,U_14209] :
      ( hBOOL(hAPP(hAPP(c_member(U_14214),U_14210),hAPP(c_Set_Ovimage(U_14214,U_14212,U_14209),U_14213)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14212),U_14211),U_14213))
      | hAPP(U_14209,U_14210) != U_14211 ),
    inference(variable_rename,[status(thm)],[f_3673_1]) ).

fof(f_3673_3,plain,
    ! [U_14209,U_14210,U_14211,U_14212,U_14213,U_14214] :
      ( hBOOL(hAPP(hAPP(c_member(U_14214),U_14210),hAPP(c_Set_Ovimage(U_14214,U_14212,U_14209),U_14213)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14212),U_14211),U_14213))
      | hAPP(U_14209,U_14210) != U_14211 ),
    inference(definitional_conversion,[status(esa)],[f_3673_2]) ).

cnf(f_3673_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14214),U_14210),hAPP(c_Set_Ovimage(U_14214,U_14212,U_14209),U_14213)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14212),U_14211),U_14213))
    | hAPP(U_14209,U_14210) != U_14211 ),
    inference(clausify,[status(thm)],[f_3673_3]) ).

fof(f_3674_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_3674_2,plain,
    ! [U_14219,U_14218,U_14217,U_14216,U_14215] : hAPP(c_Set_Ovimage(U_14215,U_14216,U_14217),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14216,tc_HOL_Obool)),U_14218),U_14219)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14215,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14215,U_14216,U_14217),U_14218)),hAPP(c_Set_Ovimage(U_14215,U_14216,U_14217),U_14219)),
    inference(variable_rename,[status(thm)],[f_3674_1]) ).

fof(f_3674_3,plain,
    ! [U_14216,U_14215,U_14217,U_14218,U_14219] : hAPP(c_Set_Ovimage(U_14215,U_14216,U_14217),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14216,tc_HOL_Obool)),U_14218),U_14219)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14215,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14215,U_14216,U_14217),U_14218)),hAPP(c_Set_Ovimage(U_14215,U_14216,U_14217),U_14219)),
    inference(definitional_conversion,[status(esa)],[f_3674_2]) ).

cnf(f_3674_4,plain,
    hAPP(c_Set_Ovimage(U_14215,U_14216,U_14217),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14216,tc_HOL_Obool)),U_14218),U_14219)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14215,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14215,U_14216,U_14217),U_14218)),hAPP(c_Set_Ovimage(U_14215,U_14216,U_14217),U_14219)),
    inference(clausify,[status(thm)],[f_3674_3]) ).

fof(f_3675_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_3675_2,plain,
    ! [U_14223,U_14222,U_14221,U_14220] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14220,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14221,U_14220,U_14222),hAPP(c_Set_Ovimage(U_14221,U_14220,U_14222),U_14223))),U_14223)),
    inference(variable_rename,[status(thm)],[f_3675_1]) ).

fof(f_3675_3,plain,
    ! [U_14220,U_14221,U_14222,U_14223] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14220,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14221,U_14220,U_14222),hAPP(c_Set_Ovimage(U_14221,U_14220,U_14222),U_14223))),U_14223)),
    inference(definitional_conversion,[status(esa)],[f_3675_2]) ).

cnf(f_3675_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14220,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14221,U_14220,U_14222),hAPP(c_Set_Ovimage(U_14221,U_14220,U_14222),U_14223))),U_14223)),
    inference(clausify,[status(thm)],[f_3675_3]) ).

fof(f_3676_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_3676_2,plain,
    ! [U_14226,U_14225,U_14224] :
      ( c_Wellfounded_Owf(U_14224,U_14226)
      | ~ c_Wellfounded_Owf(U_14224,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14224,U_14224),tc_HOL_Obool),U_14225),U_14226)) ),
    inference(variable_rename,[status(thm)],[f_3676_1]) ).

fof(f_3676_3,plain,
    ! [U_14224,U_14225,U_14226] :
      ( c_Wellfounded_Owf(U_14224,U_14226)
      | ~ c_Wellfounded_Owf(U_14224,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14224,U_14224),tc_HOL_Obool),U_14225),U_14226)) ),
    inference(definitional_conversion,[status(esa)],[f_3676_2]) ).

cnf(f_3676_4,plain,
    ( c_Wellfounded_Owf(U_14224,U_14226)
    | ~ c_Wellfounded_Owf(U_14224,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14224,U_14224),tc_HOL_Obool),U_14225),U_14226)) ),
    inference(clausify,[status(thm)],[f_3676_3]) ).

fof(f_3677_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_3677_2,plain,
    ! [U_14230,U_14229,U_14228,U_14227] : hAPP(hAPP(c_Nat_Ocompow(U_14227,U_14227),U_14228),hAPP(hAPP(c_Nat_Ocompow(U_14227,U_14227),U_14229),U_14230)) = hAPP(hAPP(c_Nat_Ocompow(U_14227,U_14227),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_14229),U_14228)),U_14230),
    inference(variable_rename,[status(thm)],[f_3677_1]) ).

fof(f_3677_3,plain,
    ! [U_14227,U_14228,U_14229,U_14230] : hAPP(hAPP(c_Nat_Ocompow(U_14227,U_14227),U_14228),hAPP(hAPP(c_Nat_Ocompow(U_14227,U_14227),U_14229),U_14230)) = hAPP(hAPP(c_Nat_Ocompow(U_14227,U_14227),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_14229),U_14228)),U_14230),
    inference(definitional_conversion,[status(esa)],[f_3677_2]) ).

cnf(f_3677_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_14227,U_14227),U_14228),hAPP(hAPP(c_Nat_Ocompow(U_14227,U_14227),U_14229),U_14230)) = hAPP(hAPP(c_Nat_Ocompow(U_14227,U_14227),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_14229),U_14228)),U_14230),
    inference(clausify,[status(thm)],[f_3677_3]) ).

fof(f_3678_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_3678_2,plain,
    ! [U_14233,U_14232,U_14231] : hAPP(hAPP(c_Relation_Orel__comp(U_14231,U_14231,U_14231),U_14232),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14231,U_14231),tc_HOL_Obool),U_14233),U_14232)) = hAPP(hAPP(c_Relation_Orel__comp(U_14231,U_14231,U_14231),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14231,U_14231),tc_HOL_Obool),U_14233),U_14232)),U_14232),
    inference(variable_rename,[status(thm)],[f_3678_1]) ).

fof(f_3678_3,plain,
    ! [U_14231,U_14232,U_14233] : hAPP(hAPP(c_Relation_Orel__comp(U_14231,U_14231,U_14231),U_14232),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14231,U_14231),tc_HOL_Obool),U_14233),U_14232)) = hAPP(hAPP(c_Relation_Orel__comp(U_14231,U_14231,U_14231),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14231,U_14231),tc_HOL_Obool),U_14233),U_14232)),U_14232),
    inference(definitional_conversion,[status(esa)],[f_3678_2]) ).

cnf(f_3678_4,plain,
    hAPP(hAPP(c_Relation_Orel__comp(U_14231,U_14231,U_14231),U_14232),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14231,U_14231),tc_HOL_Obool),U_14233),U_14232)) = hAPP(hAPP(c_Relation_Orel__comp(U_14231,U_14231,U_14231),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14231,U_14231),tc_HOL_Obool),U_14233),U_14232)),U_14232),
    inference(clausify,[status(thm)],[f_3678_3]) ).

fof(f_3679_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_3679_2,plain,
    ! [U_14235,U_14234] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14234,U_14234),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_14235) = U_14235,
    inference(variable_rename,[status(thm)],[f_3679_1]) ).

fof(f_3679_3,plain,
    ! [U_14234,U_14235] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14234,U_14234),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_14235) = U_14235,
    inference(definitional_conversion,[status(esa)],[f_3679_2]) ).

cnf(f_3679_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14234,U_14234),tc_HOL_Obool),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_14235) = U_14235,
    inference(clausify,[status(thm)],[f_3679_3]) ).

fof(f_3680_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_3680_2,plain,
    ! [U_14239,U_14238,U_14237,U_14236] : hAPP(U_14236,hAPP(hAPP(hAPP(c_Nat_Ocompow(U_14237,U_14237),U_14238),U_14236),U_14239)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(U_14237,U_14237),U_14238),U_14236),hAPP(U_14236,U_14239)),
    inference(variable_rename,[status(thm)],[f_3680_1]) ).

fof(f_3680_3,plain,
    ! [U_14236,U_14237,U_14238,U_14239] : hAPP(U_14236,hAPP(hAPP(hAPP(c_Nat_Ocompow(U_14237,U_14237),U_14238),U_14236),U_14239)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(U_14237,U_14237),U_14238),U_14236),hAPP(U_14236,U_14239)),
    inference(definitional_conversion,[status(esa)],[f_3680_2]) ).

cnf(f_3680_4,plain,
    hAPP(U_14236,hAPP(hAPP(hAPP(c_Nat_Ocompow(U_14237,U_14237),U_14238),U_14236),U_14239)) = hAPP(hAPP(hAPP(c_Nat_Ocompow(U_14237,U_14237),U_14238),U_14236),hAPP(U_14236,U_14239)),
    inference(clausify,[status(thm)],[f_3680_3]) ).

fof(f_3681_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_3681_2,plain,
    ! [U_14244,U_14243,U_14242,U_14241,U_14240] :
      ( ( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_14240,U_14241,U_14242),U_14243),U_14244))
        | ~ hBOOL(hAPP(U_14243,hAPP(U_14242,U_14244))) )
      & ( hBOOL(hAPP(U_14243,hAPP(U_14242,U_14244)))
        | ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_14240,U_14241,U_14242),U_14243),U_14244)) ) ),
    inference(variable_rename,[status(thm)],[f_3681_1]) ).

fof(f_3681_3,plain,
    ( ! [U_14254,U_14252,U_14250] :
        ( ! [U_14248,U_14246] : hBOOL(hAPP(hAPP(c_Set_Ovimage(U_14246,U_14248,U_14250),U_14252),U_14254))
        | ~ hBOOL(hAPP(U_14252,hAPP(U_14250,U_14254))) )
    & ! [U_14253,U_14251,U_14249] :
        ( ! [U_14247,U_14245] : ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_14245,U_14247,U_14249),U_14251),U_14253))
        | hBOOL(hAPP(U_14251,hAPP(U_14249,U_14253))) ) ),
    inference(miniscope,[status(thm)],[f_3681_2]) ).

fof(f_3681_4,plain,
    ( ! [U_14252,U_14246,U_14248,U_14250,U_14254] :
        ( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_14246,U_14248,U_14250),U_14252),U_14254))
        | ~ hBOOL(hAPP(U_14252,hAPP(U_14250,U_14254))) )
    & ! [U_14253,U_14249,U_14245,U_14247,U_14251] :
        ( ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_14245,U_14247,U_14249),U_14251),U_14253))
        | hBOOL(hAPP(U_14251,hAPP(U_14249,U_14253))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3681_3]) ).

cnf(f_3681_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Set_Ovimage(U_14245,U_14247,U_14249),U_14251),U_14253))
    | hBOOL(hAPP(U_14251,hAPP(U_14249,U_14253))) ),
    inference(clausify,[status(thm)],[f_3681_4]) ).

cnf(f_3681_6,plain,
    ( hBOOL(hAPP(hAPP(c_Set_Ovimage(U_14246,U_14248,U_14250),U_14252),U_14254))
    | ~ hBOOL(hAPP(U_14252,hAPP(U_14250,U_14254))) ),
    inference(clausify,[status(thm)],[f_3681_4]) ).

fof(f_3682_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_3682_2,plain,
    ! [U_14256,U_14255] : hAPP(c_Set_Ovimage(U_14255,U_14255,c_COMBI(U_14255)),U_14256) = U_14256,
    inference(variable_rename,[status(thm)],[f_3682_1]) ).

fof(f_3682_3,plain,
    ! [U_14256,U_14255] : hAPP(c_Set_Ovimage(U_14255,U_14255,c_COMBI(U_14255)),U_14256) = U_14256,
    inference(definitional_conversion,[status(esa)],[f_3682_2]) ).

cnf(f_3682_4,plain,
    hAPP(c_Set_Ovimage(U_14255,U_14255,c_COMBI(U_14255)),U_14256) = U_14256,
    inference(clausify,[status(thm)],[f_3682_3]) ).

fof(f_3683_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_3683_2,plain,
    ! [U_14260,U_14259,U_14258,U_14257] : hAPP(c_Set_Ovimage(U_14257,U_14258,U_14259),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14258,tc_HOL_Obool)),U_14260)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14257,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14257,U_14258,U_14259),U_14260)),
    inference(variable_rename,[status(thm)],[f_3683_1]) ).

fof(f_3683_3,plain,
    ! [U_14257,U_14258,U_14259,U_14260] : hAPP(c_Set_Ovimage(U_14257,U_14258,U_14259),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14258,tc_HOL_Obool)),U_14260)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14257,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14257,U_14258,U_14259),U_14260)),
    inference(definitional_conversion,[status(esa)],[f_3683_2]) ).

cnf(f_3683_4,plain,
    hAPP(c_Set_Ovimage(U_14257,U_14258,U_14259),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14258,tc_HOL_Obool)),U_14260)) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14257,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14257,U_14258,U_14259),U_14260)),
    inference(clausify,[status(thm)],[f_3683_3]) ).

fof(f_3684_1,plain,
    ! [V_Pa_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_Pa_2)) = hAPP(c_Set_OCollect(T_b),hAPP(hAPP(c_COMBB(T_c,tc_HOL_Obool,T_b),V_Pa_2),V_f_2)),
    inference(fof_nnf,[status(thm)],[fact_vimage__Collect__eq]) ).

fof(f_3684_2,plain,
    ! [U_14264,U_14263,U_14262,U_14261] : hAPP(c_Set_Ovimage(U_14261,U_14262,U_14263),hAPP(c_Set_OCollect(U_14262),U_14264)) = hAPP(c_Set_OCollect(U_14261),hAPP(hAPP(c_COMBB(U_14262,tc_HOL_Obool,U_14261),U_14264),U_14263)),
    inference(variable_rename,[status(thm)],[f_3684_1]) ).

fof(f_3684_3,plain,
    ! [U_14261,U_14262,U_14263,U_14264] : hAPP(c_Set_Ovimage(U_14261,U_14262,U_14263),hAPP(c_Set_OCollect(U_14262),U_14264)) = hAPP(c_Set_OCollect(U_14261),hAPP(hAPP(c_COMBB(U_14262,tc_HOL_Obool,U_14261),U_14264),U_14263)),
    inference(definitional_conversion,[status(esa)],[f_3684_2]) ).

cnf(f_3684_4,plain,
    hAPP(c_Set_Ovimage(U_14261,U_14262,U_14263),hAPP(c_Set_OCollect(U_14262),U_14264)) = hAPP(c_Set_OCollect(U_14261),hAPP(hAPP(c_COMBB(U_14262,tc_HOL_Obool,U_14261),U_14264),U_14263)),
    inference(clausify,[status(thm)],[f_3684_3]) ).

fof(f_3685_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_3685_2,plain,
    ! [U_14269,U_14268,U_14267,U_14266,U_14265] : hAPP(c_Set_Ovimage(U_14265,U_14266,U_14267),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14266,tc_HOL_Obool)),U_14268),U_14269)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14265,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14265,U_14266,U_14267),U_14268)),hAPP(c_Set_Ovimage(U_14265,U_14266,U_14267),U_14269)),
    inference(variable_rename,[status(thm)],[f_3685_1]) ).

fof(f_3685_3,plain,
    ! [U_14265,U_14266,U_14267,U_14268,U_14269] : hAPP(c_Set_Ovimage(U_14265,U_14266,U_14267),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14266,tc_HOL_Obool)),U_14268),U_14269)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14265,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14265,U_14266,U_14267),U_14268)),hAPP(c_Set_Ovimage(U_14265,U_14266,U_14267),U_14269)),
    inference(definitional_conversion,[status(esa)],[f_3685_2]) ).

cnf(f_3685_4,plain,
    hAPP(c_Set_Ovimage(U_14265,U_14266,U_14267),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14266,tc_HOL_Obool)),U_14268),U_14269)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14265,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14265,U_14266,U_14267),U_14268)),hAPP(c_Set_Ovimage(U_14265,U_14266,U_14267),U_14269)),
    inference(clausify,[status(thm)],[f_3685_3]) ).

fof(f_3686_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_3686_2,plain,
    ! [U_14274,U_14273,U_14272,U_14271,U_14270] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14273,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14273,U_14270,U_14274),U_14271)),hAPP(c_Set_Ovimage(U_14273,U_14270,U_14274),U_14272)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14270,tc_HOL_Obool)),U_14271),U_14272)) ),
    inference(variable_rename,[status(thm)],[f_3686_1]) ).

fof(f_3686_3,plain,
    ! [U_14270,U_14271,U_14272,U_14273,U_14274] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14273,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14273,U_14270,U_14274),U_14271)),hAPP(c_Set_Ovimage(U_14273,U_14270,U_14274),U_14272)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14270,tc_HOL_Obool)),U_14271),U_14272)) ),
    inference(definitional_conversion,[status(esa)],[f_3686_2]) ).

cnf(f_3686_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14273,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14273,U_14270,U_14274),U_14271)),hAPP(c_Set_Ovimage(U_14273,U_14270,U_14274),U_14272)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14270,tc_HOL_Obool)),U_14271),U_14272)) ),
    inference(clausify,[status(thm)],[f_3686_3]) ).

fof(f_3687_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_3687_2,plain,
    ! [U_14279,U_14278,U_14277,U_14276,U_14275] : hAPP(c_Set_Ovimage(U_14275,U_14276,U_14277),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14276,tc_HOL_Obool)),U_14278),U_14279)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14275,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14275,U_14276,U_14277),U_14278)),hAPP(c_Set_Ovimage(U_14275,U_14276,U_14277),U_14279)),
    inference(variable_rename,[status(thm)],[f_3687_1]) ).

fof(f_3687_3,plain,
    ! [U_14275,U_14276,U_14277,U_14278,U_14279] : hAPP(c_Set_Ovimage(U_14275,U_14276,U_14277),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14276,tc_HOL_Obool)),U_14278),U_14279)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14275,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14275,U_14276,U_14277),U_14278)),hAPP(c_Set_Ovimage(U_14275,U_14276,U_14277),U_14279)),
    inference(definitional_conversion,[status(esa)],[f_3687_2]) ).

cnf(f_3687_4,plain,
    hAPP(c_Set_Ovimage(U_14275,U_14276,U_14277),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14276,tc_HOL_Obool)),U_14278),U_14279)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14275,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14275,U_14276,U_14277),U_14278)),hAPP(c_Set_Ovimage(U_14275,U_14276,U_14277),U_14279)),
    inference(clausify,[status(thm)],[f_3687_3]) ).

fof(f_3688_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_3688_2,plain,
    ! [U_14282,U_14281,U_14280] : hAPP(c_Set_Ovimage(U_14280,U_14281,U_14282),c_Orderings_Obot__class_Obot(tc_fun(U_14281,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_14280,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3688_1]) ).

fof(f_3688_3,plain,
    ! [U_14280,U_14281,U_14282] : hAPP(c_Set_Ovimage(U_14280,U_14281,U_14282),c_Orderings_Obot__class_Obot(tc_fun(U_14281,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_14280,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3688_2]) ).

cnf(f_3688_4,plain,
    hAPP(c_Set_Ovimage(U_14280,U_14281,U_14282),c_Orderings_Obot__class_Obot(tc_fun(U_14281,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_14280,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3688_3]) ).

fof(f_3689_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_3689_2,plain,
    ! [U_14288,U_14287,U_14286,U_14285,U_14284,U_14283] : hAPP(c_Set_Ovimage(U_14283,U_14284,U_14285),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14286,tc_fun(U_14284,tc_HOL_Obool)),U_14287),U_14288)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14286,tc_fun(U_14283,tc_HOL_Obool)),U_14287),hAPP(hAPP(c_COMBB(tc_fun(U_14284,tc_HOL_Obool),tc_fun(U_14283,tc_HOL_Obool),U_14286),c_Set_Ovimage(U_14283,U_14284,U_14285)),U_14288)),
    inference(variable_rename,[status(thm)],[f_3689_1]) ).

fof(f_3689_3,plain,
    ! [U_14283,U_14284,U_14285,U_14286,U_14287,U_14288] : hAPP(c_Set_Ovimage(U_14283,U_14284,U_14285),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14286,tc_fun(U_14284,tc_HOL_Obool)),U_14287),U_14288)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14286,tc_fun(U_14283,tc_HOL_Obool)),U_14287),hAPP(hAPP(c_COMBB(tc_fun(U_14284,tc_HOL_Obool),tc_fun(U_14283,tc_HOL_Obool),U_14286),c_Set_Ovimage(U_14283,U_14284,U_14285)),U_14288)),
    inference(definitional_conversion,[status(esa)],[f_3689_2]) ).

cnf(f_3689_4,plain,
    hAPP(c_Set_Ovimage(U_14283,U_14284,U_14285),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14286,tc_fun(U_14284,tc_HOL_Obool)),U_14287),U_14288)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14286,tc_fun(U_14283,tc_HOL_Obool)),U_14287),hAPP(hAPP(c_COMBB(tc_fun(U_14284,tc_HOL_Obool),tc_fun(U_14283,tc_HOL_Obool),U_14286),c_Set_Ovimage(U_14283,U_14284,U_14285)),U_14288)),
    inference(clausify,[status(thm)],[f_3689_3]) ).

fof(f_3690_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_3690_2,plain,
    ! [U_14291,U_14290,U_14289] : hAPP(c_Set_Ovimage(U_14289,U_14290,U_14291),c_Orderings_Otop__class_Otop(tc_fun(U_14290,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_14289,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3690_1]) ).

fof(f_3690_3,plain,
    ! [U_14289,U_14291,U_14290] : hAPP(c_Set_Ovimage(U_14289,U_14290,U_14291),c_Orderings_Otop__class_Otop(tc_fun(U_14290,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_14289,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3690_2]) ).

cnf(f_3690_4,plain,
    hAPP(c_Set_Ovimage(U_14289,U_14290,U_14291),c_Orderings_Otop__class_Otop(tc_fun(U_14290,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_14289,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3690_3]) ).

fof(f_3691_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_3691_2,plain,
    ! [U_14295,U_14294,U_14293,U_14292] :
      ( hAPP(c_Set_Oimage(U_14292,U_14293,U_14294),hAPP(c_Set_Ovimage(U_14292,U_14293,U_14294),U_14295)) = U_14295
      | hAPP(c_Set_Oimage(U_14292,U_14293,U_14294),c_Orderings_Otop__class_Otop(tc_fun(U_14292,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14293,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3691_1]) ).

fof(f_3691_3,plain,
    ! [U_14292,U_14293,U_14294,U_14295] :
      ( hAPP(c_Set_Oimage(U_14292,U_14293,U_14294),hAPP(c_Set_Ovimage(U_14292,U_14293,U_14294),U_14295)) = U_14295
      | hAPP(c_Set_Oimage(U_14292,U_14293,U_14294),c_Orderings_Otop__class_Otop(tc_fun(U_14292,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14293,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3691_2]) ).

cnf(f_3691_4,plain,
    ( hAPP(c_Set_Oimage(U_14292,U_14293,U_14294),hAPP(c_Set_Ovimage(U_14292,U_14293,U_14294),U_14295)) = U_14295
    | hAPP(c_Set_Oimage(U_14292,U_14293,U_14294),c_Orderings_Otop__class_Otop(tc_fun(U_14292,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14293,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3691_3]) ).

fof(f_3692_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_3692_2,plain,
    ! [U_14300,U_14299,U_14298,U_14297,U_14296] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_14296),U_14297),hAPP(c_Set_Ovimage(U_14296,U_14298,U_14299),U_14300)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14298),hAPP(U_14299,U_14297)),U_14300)) )
      & ( hBOOL(hAPP(hAPP(c_member(U_14298),hAPP(U_14299,U_14297)),U_14300))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14296),U_14297),hAPP(c_Set_Ovimage(U_14296,U_14298,U_14299),U_14300))) ) ),
    inference(variable_rename,[status(thm)],[f_3692_1]) ).

fof(f_3692_3,plain,
    ( ! [U_14310,U_14308,U_14306,U_14304] :
        ( ! [U_14302] : hBOOL(hAPP(hAPP(c_member(U_14302),U_14304),hAPP(c_Set_Ovimage(U_14302,U_14306,U_14308),U_14310)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14306),hAPP(U_14308,U_14304)),U_14310)) )
    & ! [U_14309,U_14307,U_14305,U_14303] :
        ( ! [U_14301] : ~ hBOOL(hAPP(hAPP(c_member(U_14301),U_14303),hAPP(c_Set_Ovimage(U_14301,U_14305,U_14307),U_14309)))
        | hBOOL(hAPP(hAPP(c_member(U_14305),hAPP(U_14307,U_14303)),U_14309)) ) ),
    inference(miniscope,[status(thm)],[f_3692_2]) ).

fof(f_3692_4,plain,
    ( ! [U_14302,U_14304,U_14306,U_14308,U_14310] :
        ( hBOOL(hAPP(hAPP(c_member(U_14302),U_14304),hAPP(c_Set_Ovimage(U_14302,U_14306,U_14308),U_14310)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14306),hAPP(U_14308,U_14304)),U_14310)) )
    & ! [U_14305,U_14303,U_14301,U_14307,U_14309] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_14301),U_14303),hAPP(c_Set_Ovimage(U_14301,U_14305,U_14307),U_14309)))
        | hBOOL(hAPP(hAPP(c_member(U_14305),hAPP(U_14307,U_14303)),U_14309)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3692_3]) ).

cnf(f_3692_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_14301),U_14303),hAPP(c_Set_Ovimage(U_14301,U_14305,U_14307),U_14309)))
    | hBOOL(hAPP(hAPP(c_member(U_14305),hAPP(U_14307,U_14303)),U_14309)) ),
    inference(clausify,[status(thm)],[f_3692_4]) ).

cnf(f_3692_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14302),U_14304),hAPP(c_Set_Ovimage(U_14302,U_14306,U_14308),U_14310)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14306),hAPP(U_14308,U_14304)),U_14310)) ),
    inference(clausify,[status(thm)],[f_3692_4]) ).

fof(f_3693_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_3693_2,plain,
    ! [U_14315,U_14314,U_14313,U_14312,U_14311] :
      ( hBOOL(hAPP(hAPP(c_member(U_14313),hAPP(U_14314,U_14312)),U_14315))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14311),U_14312),hAPP(c_Set_Ovimage(U_14311,U_14313,U_14314),U_14315))) ),
    inference(variable_rename,[status(thm)],[f_3693_1]) ).

fof(f_3693_3,plain,
    ! [U_14315,U_14314,U_14313,U_14312] :
      ( ! [U_14311] : ~ hBOOL(hAPP(hAPP(c_member(U_14311),U_14312),hAPP(c_Set_Ovimage(U_14311,U_14313,U_14314),U_14315)))
      | hBOOL(hAPP(hAPP(c_member(U_14313),hAPP(U_14314,U_14312)),U_14315)) ),
    inference(miniscope,[status(thm)],[f_3693_2]) ).

fof(f_3693_4,plain,
    ! [U_14311,U_14312,U_14313,U_14314,U_14315] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_14311),U_14312),hAPP(c_Set_Ovimage(U_14311,U_14313,U_14314),U_14315)))
      | hBOOL(hAPP(hAPP(c_member(U_14313),hAPP(U_14314,U_14312)),U_14315)) ),
    inference(definitional_conversion,[status(esa)],[f_3693_3]) ).

cnf(f_3693_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_14311),U_14312),hAPP(c_Set_Ovimage(U_14311,U_14313,U_14314),U_14315)))
    | hBOOL(hAPP(hAPP(c_member(U_14313),hAPP(U_14314,U_14312)),U_14315)) ),
    inference(clausify,[status(thm)],[f_3693_4]) ).

fof(f_3694_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_3694_2,plain,
    ! [U_14320,U_14319,U_14318,U_14317,U_14316] :
      ( hBOOL(hAPP(hAPP(c_member(U_14320),U_14318),hAPP(c_Set_Ovimage(U_14320,U_14316,U_14317),U_14319)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14316),hAPP(U_14317,U_14318)),U_14319)) ),
    inference(variable_rename,[status(thm)],[f_3694_1]) ).

fof(f_3694_3,plain,
    ! [U_14317,U_14316,U_14318,U_14319,U_14320] :
      ( hBOOL(hAPP(hAPP(c_member(U_14320),U_14318),hAPP(c_Set_Ovimage(U_14320,U_14316,U_14317),U_14319)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14316),hAPP(U_14317,U_14318)),U_14319)) ),
    inference(definitional_conversion,[status(esa)],[f_3694_2]) ).

cnf(f_3694_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14320),U_14318),hAPP(c_Set_Ovimage(U_14320,U_14316,U_14317),U_14319)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14316),hAPP(U_14317,U_14318)),U_14319)) ),
    inference(clausify,[status(thm)],[f_3694_3]) ).

fof(f_3695_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_3695_2,plain,
    ! [U_14324,U_14323,U_14322,U_14321] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14321,U_14321)),U_14322),c_Transitive__Closure_Ortrancl(U_14321,U_14324)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14321,U_14321)),U_14322),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14321,U_14321),tc_HOL_Obool),U_14323),U_14324))) ),
    inference(variable_rename,[status(thm)],[f_3695_1]) ).

fof(f_3695_3,plain,
    ! [U_14321,U_14322,U_14323,U_14324] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14321,U_14321)),U_14322),c_Transitive__Closure_Ortrancl(U_14321,U_14324)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14321,U_14321)),U_14322),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14321,U_14321),tc_HOL_Obool),U_14323),U_14324))) ),
    inference(definitional_conversion,[status(esa)],[f_3695_2]) ).

cnf(f_3695_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14321,U_14321)),U_14322),c_Transitive__Closure_Ortrancl(U_14321,U_14324)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14321,U_14321)),U_14322),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14321,U_14321),tc_HOL_Obool),U_14323),U_14324))) ),
    inference(clausify,[status(thm)],[f_3695_3]) ).

fof(f_3696_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_3696_2,plain,
    ! [U_14329,U_14328,U_14327] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14327,U_14327)),U_14328),c_Transitive__Closure_Ortrancl(U_14327,U_14329)))
        | ! [U_14326] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14327,U_14327)),U_14328),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14327,U_14327),tc_HOL_Obool),U_14326),U_14329))) )
      & ( ? [U_14325] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14327,U_14327)),U_14328),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14327,U_14327),tc_HOL_Obool),U_14325),U_14329)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14327,U_14327)),U_14328),c_Transitive__Closure_Ortrancl(U_14327,U_14329))) ) ),
    inference(variable_rename,[status(thm)],[f_3696_1]) ).

fof(f_3696_3,plain,
    ( ! [U_14335,U_14333,U_14331] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14331,U_14331)),U_14333),c_Transitive__Closure_Ortrancl(U_14331,U_14335)))
        | ! [U_14326] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14331,U_14331)),U_14333),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14331,U_14331),tc_HOL_Obool),U_14326),U_14335))) )
    & ! [U_14334,U_14332,U_14330] :
        ( ? [U_14325] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14330,U_14330)),U_14332),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14330,U_14330),tc_HOL_Obool),U_14325),U_14334)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14330,U_14330)),U_14332),c_Transitive__Closure_Ortrancl(U_14330,U_14334))) ) ),
    inference(miniscope,[status(thm)],[f_3696_2]) ).

fof(f_3696_4,plain,
    ( ! [U_14335,U_14333,U_14331] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14331,U_14331)),U_14333),c_Transitive__Closure_Ortrancl(U_14331,U_14335)))
        | ! [U_14326] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14331,U_14331)),U_14333),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14331,U_14331),tc_HOL_Obool),U_14326),U_14335))) )
    & ! [U_14334,U_14332,U_14330] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14330,U_14330)),U_14332),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14330,U_14330),tc_HOL_Obool),sK315(U_14334,U_14332,U_14330)),U_14334)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14330,U_14330)),U_14332),c_Transitive__Closure_Ortrancl(U_14330,U_14334))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK315]),skolemize(U_14325,sK315(U_14334,U_14332,U_14330))],[f_3696_3]) ).

fof(f_3696_5,plain,
    ( ! [U_14326,U_14331,U_14333,U_14335] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14331,U_14331)),U_14333),c_Transitive__Closure_Ortrancl(U_14331,U_14335)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14331,U_14331)),U_14333),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14331,U_14331),tc_HOL_Obool),U_14326),U_14335))) )
    & ! [U_14332,U_14330,U_14334] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14330,U_14330)),U_14332),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14330,U_14330),tc_HOL_Obool),sK315(U_14334,U_14332,U_14330)),U_14334)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14330,U_14330)),U_14332),c_Transitive__Closure_Ortrancl(U_14330,U_14334))) ) ),
    inference(definitional_conversion,[status(esa)],[f_3696_4]) ).

cnf(f_3696_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14330,U_14330)),U_14332),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14330,U_14330),tc_HOL_Obool),sK315(U_14334,U_14332,U_14330)),U_14334)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14330,U_14330)),U_14332),c_Transitive__Closure_Ortrancl(U_14330,U_14334))) ),
    inference(clausify,[status(thm)],[f_3696_5]) ).

cnf(f_3696_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14331,U_14331)),U_14333),c_Transitive__Closure_Ortrancl(U_14331,U_14335)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14331,U_14331)),U_14333),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14331,U_14331),tc_HOL_Obool),U_14326),U_14335))) ),
    inference(clausify,[status(thm)],[f_3696_5]) ).

fof(f_3697_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_3697_2,plain,
    ! [U_14339,U_14338,U_14337,U_14336] : hAPP(c_Set_Ovimage(U_14336,U_14337,U_14338),U_14339) = hAPP(c_Set_OCollect(U_14336),hAPP(hAPP(c_COMBC(U_14336,tc_fun(U_14337,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14337,tc_fun(tc_fun(U_14337,tc_HOL_Obool),tc_HOL_Obool),U_14336),c_member(U_14337)),U_14338)),U_14339)),
    inference(variable_rename,[status(thm)],[f_3697_1]) ).

fof(f_3697_3,plain,
    ! [U_14336,U_14337,U_14338,U_14339] : hAPP(c_Set_Ovimage(U_14336,U_14337,U_14338),U_14339) = hAPP(c_Set_OCollect(U_14336),hAPP(hAPP(c_COMBC(U_14336,tc_fun(U_14337,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14337,tc_fun(tc_fun(U_14337,tc_HOL_Obool),tc_HOL_Obool),U_14336),c_member(U_14337)),U_14338)),U_14339)),
    inference(definitional_conversion,[status(esa)],[f_3697_2]) ).

cnf(f_3697_4,plain,
    hAPP(c_Set_Ovimage(U_14336,U_14337,U_14338),U_14339) = hAPP(c_Set_OCollect(U_14336),hAPP(hAPP(c_COMBC(U_14336,tc_fun(U_14337,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_14337,tc_fun(tc_fun(U_14337,tc_HOL_Obool),tc_HOL_Obool),U_14336),c_member(U_14337)),U_14338)),U_14339)),
    inference(clausify,[status(thm)],[f_3697_3]) ).

fof(f_3698_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_3698_2,plain,
    ! [U_14342,U_14341,U_14340] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14340,U_14340),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14341)),U_14342) = hAPP(hAPP(c_Relation_Orel__comp(U_14340,U_14340,U_14340),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14340,U_14340),tc_HOL_Obool),U_14341),U_14342)),U_14342),
    inference(variable_rename,[status(thm)],[f_3698_1]) ).

fof(f_3698_3,plain,
    ! [U_14340,U_14341,U_14342] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14340,U_14340),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14341)),U_14342) = hAPP(hAPP(c_Relation_Orel__comp(U_14340,U_14340,U_14340),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14340,U_14340),tc_HOL_Obool),U_14341),U_14342)),U_14342),
    inference(definitional_conversion,[status(esa)],[f_3698_2]) ).

cnf(f_3698_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14340,U_14340),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14341)),U_14342) = hAPP(hAPP(c_Relation_Orel__comp(U_14340,U_14340,U_14340),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14340,U_14340),tc_HOL_Obool),U_14341),U_14342)),U_14342),
    inference(clausify,[status(thm)],[f_3698_3]) ).

fof(f_3699_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_3699_2,plain,
    ! [U_14346,U_14345,U_14344,U_14343] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14343,U_14343),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_14344),U_14345)),U_14346) = hAPP(hAPP(c_Relation_Orel__comp(U_14343,U_14343,U_14343),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14343,U_14343),tc_HOL_Obool),U_14344),U_14346)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14343,U_14343),tc_HOL_Obool),U_14345),U_14346)),
    inference(variable_rename,[status(thm)],[f_3699_1]) ).

fof(f_3699_3,plain,
    ! [U_14343,U_14344,U_14345,U_14346] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14343,U_14343),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_14344),U_14345)),U_14346) = hAPP(hAPP(c_Relation_Orel__comp(U_14343,U_14343,U_14343),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14343,U_14343),tc_HOL_Obool),U_14344),U_14346)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14343,U_14343),tc_HOL_Obool),U_14345),U_14346)),
    inference(definitional_conversion,[status(esa)],[f_3699_2]) ).

cnf(f_3699_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14343,U_14343),tc_HOL_Obool),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_14344),U_14345)),U_14346) = hAPP(hAPP(c_Relation_Orel__comp(U_14343,U_14343,U_14343),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14343,U_14343),tc_HOL_Obool),U_14344),U_14346)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14343,U_14343),tc_HOL_Obool),U_14345),U_14346)),
    inference(clausify,[status(thm)],[f_3699_3]) ).

fof(f_3700_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_3700_2,plain,
    ! [U_14348,U_14347] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14347,U_14347),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14348) = c_Relation_OId(U_14347),
    inference(variable_rename,[status(thm)],[f_3700_1]) ).

fof(f_3700_3,plain,
    ! [U_14347,U_14348] : hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14347,U_14347),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14348) = c_Relation_OId(U_14347),
    inference(definitional_conversion,[status(esa)],[f_3700_2]) ).

cnf(f_3700_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14347,U_14347),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14348) = c_Relation_OId(U_14347),
    inference(clausify,[status(thm)],[f_3700_3]) ).

fof(f_3701_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_3701_2,plain,
    ! [U_14353,U_14352,U_14351,U_14350,U_14349] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_14349),U_14350),hAPP(c_Set_Ovimage(U_14349,U_14351,U_14352),hAPP(hAPP(c_Set_Oinsert(U_14351),U_14353),c_Orderings_Obot__class_Obot(tc_fun(U_14351,tc_HOL_Obool))))))
        | hAPP(U_14352,U_14350) != U_14353 )
      & ( hAPP(U_14352,U_14350) = U_14353
        | ~ hBOOL(hAPP(hAPP(c_member(U_14349),U_14350),hAPP(c_Set_Ovimage(U_14349,U_14351,U_14352),hAPP(hAPP(c_Set_Oinsert(U_14351),U_14353),c_Orderings_Obot__class_Obot(tc_fun(U_14351,tc_HOL_Obool)))))) ) ),
    inference(variable_rename,[status(thm)],[f_3701_1]) ).

fof(f_3701_3,plain,
    ( ! [U_14363,U_14361,U_14359,U_14357] :
        ( ! [U_14355] : hBOOL(hAPP(hAPP(c_member(U_14355),U_14357),hAPP(c_Set_Ovimage(U_14355,U_14359,U_14361),hAPP(hAPP(c_Set_Oinsert(U_14359),U_14363),c_Orderings_Obot__class_Obot(tc_fun(U_14359,tc_HOL_Obool))))))
        | hAPP(U_14361,U_14357) != U_14363 )
    & ! [U_14362,U_14360,U_14358,U_14356] :
        ( ! [U_14354] : ~ hBOOL(hAPP(hAPP(c_member(U_14354),U_14356),hAPP(c_Set_Ovimage(U_14354,U_14358,U_14360),hAPP(hAPP(c_Set_Oinsert(U_14358),U_14362),c_Orderings_Obot__class_Obot(tc_fun(U_14358,tc_HOL_Obool))))))
        | hAPP(U_14360,U_14356) = U_14362 ) ),
    inference(miniscope,[status(thm)],[f_3701_2]) ).

fof(f_3701_4,plain,
    ( ! [U_14355,U_14357,U_14359,U_14361,U_14363] :
        ( hBOOL(hAPP(hAPP(c_member(U_14355),U_14357),hAPP(c_Set_Ovimage(U_14355,U_14359,U_14361),hAPP(hAPP(c_Set_Oinsert(U_14359),U_14363),c_Orderings_Obot__class_Obot(tc_fun(U_14359,tc_HOL_Obool))))))
        | hAPP(U_14361,U_14357) != U_14363 )
    & ! [U_14358,U_14356,U_14354,U_14360,U_14362] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_14354),U_14356),hAPP(c_Set_Ovimage(U_14354,U_14358,U_14360),hAPP(hAPP(c_Set_Oinsert(U_14358),U_14362),c_Orderings_Obot__class_Obot(tc_fun(U_14358,tc_HOL_Obool))))))
        | hAPP(U_14360,U_14356) = U_14362 ) ),
    inference(definitional_conversion,[status(esa)],[f_3701_3]) ).

cnf(f_3701_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_14354),U_14356),hAPP(c_Set_Ovimage(U_14354,U_14358,U_14360),hAPP(hAPP(c_Set_Oinsert(U_14358),U_14362),c_Orderings_Obot__class_Obot(tc_fun(U_14358,tc_HOL_Obool))))))
    | hAPP(U_14360,U_14356) = U_14362 ),
    inference(clausify,[status(thm)],[f_3701_4]) ).

cnf(f_3701_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14355),U_14357),hAPP(c_Set_Ovimage(U_14355,U_14359,U_14361),hAPP(hAPP(c_Set_Oinsert(U_14359),U_14363),c_Orderings_Obot__class_Obot(tc_fun(U_14359,tc_HOL_Obool))))))
    | hAPP(U_14361,U_14357) != U_14363 ),
    inference(clausify,[status(thm)],[f_3701_4]) ).

fof(f_3702_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_3702_2,plain,
    ! [U_14368,U_14367,U_14366,U_14365,U_14364] : hAPP(c_Set_Ovimage(U_14364,U_14365,U_14366),hAPP(hAPP(c_Set_Oinsert(U_14365),U_14367),U_14368)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14364,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14364,U_14365,U_14366),hAPP(hAPP(c_Set_Oinsert(U_14365),U_14367),c_Orderings_Obot__class_Obot(tc_fun(U_14365,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_14364,U_14365,U_14366),U_14368)),
    inference(variable_rename,[status(thm)],[f_3702_1]) ).

fof(f_3702_3,plain,
    ! [U_14364,U_14365,U_14366,U_14367,U_14368] : hAPP(c_Set_Ovimage(U_14364,U_14365,U_14366),hAPP(hAPP(c_Set_Oinsert(U_14365),U_14367),U_14368)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14364,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14364,U_14365,U_14366),hAPP(hAPP(c_Set_Oinsert(U_14365),U_14367),c_Orderings_Obot__class_Obot(tc_fun(U_14365,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_14364,U_14365,U_14366),U_14368)),
    inference(definitional_conversion,[status(esa)],[f_3702_2]) ).

cnf(f_3702_4,plain,
    hAPP(c_Set_Ovimage(U_14364,U_14365,U_14366),hAPP(hAPP(c_Set_Oinsert(U_14365),U_14367),U_14368)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14364,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14364,U_14365,U_14366),hAPP(hAPP(c_Set_Oinsert(U_14365),U_14367),c_Orderings_Obot__class_Obot(tc_fun(U_14365,tc_HOL_Obool))))),hAPP(c_Set_Ovimage(U_14364,U_14365,U_14366),U_14368)),
    inference(clausify,[status(thm)],[f_3702_3]) ).

fof(f_3703_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_3703_2,plain,
    ! [U_14372,U_14371,U_14370,U_14369] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14370),U_14372))
      | hAPP(c_Set_Oimage(U_14369,U_14370,U_14371),c_Orderings_Otop__class_Otop(tc_fun(U_14369,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14370,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14369),hAPP(c_Set_Ovimage(U_14369,U_14370,U_14371),U_14372))) ),
    inference(variable_rename,[status(thm)],[f_3703_1]) ).

fof(f_3703_3,plain,
    ! [U_14369,U_14370,U_14371,U_14372] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14370),U_14372))
      | hAPP(c_Set_Oimage(U_14369,U_14370,U_14371),c_Orderings_Otop__class_Otop(tc_fun(U_14369,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14370,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14369),hAPP(c_Set_Ovimage(U_14369,U_14370,U_14371),U_14372))) ),
    inference(definitional_conversion,[status(esa)],[f_3703_2]) ).

cnf(f_3703_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14370),U_14372))
    | hAPP(c_Set_Oimage(U_14369,U_14370,U_14371),c_Orderings_Otop__class_Otop(tc_fun(U_14369,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14370,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14369),hAPP(c_Set_Ovimage(U_14369,U_14370,U_14371),U_14372))) ),
    inference(clausify,[status(thm)],[f_3703_3]) ).

fof(f_3704_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_3704_2,plain,
    ! [U_14377,U_14376,U_14375,U_14374,U_14373] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14374,tc_HOL_Obool)),U_14376),hAPP(c_Set_Oimage(U_14373,U_14374,U_14375),U_14377)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14373,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14373,U_14374,U_14375),U_14376)),U_14377))
      | hAPP(c_Set_Oimage(U_14373,U_14374,U_14375),c_Orderings_Otop__class_Otop(tc_fun(U_14373,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14374,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3704_1]) ).

fof(f_3704_3,plain,
    ! [U_14373,U_14374,U_14375,U_14376,U_14377] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14374,tc_HOL_Obool)),U_14376),hAPP(c_Set_Oimage(U_14373,U_14374,U_14375),U_14377)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14373,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14373,U_14374,U_14375),U_14376)),U_14377))
      | hAPP(c_Set_Oimage(U_14373,U_14374,U_14375),c_Orderings_Otop__class_Otop(tc_fun(U_14373,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14374,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3704_2]) ).

cnf(f_3704_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14374,tc_HOL_Obool)),U_14376),hAPP(c_Set_Oimage(U_14373,U_14374,U_14375),U_14377)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14373,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14373,U_14374,U_14375),U_14376)),U_14377))
    | hAPP(c_Set_Oimage(U_14373,U_14374,U_14375),c_Orderings_Otop__class_Otop(tc_fun(U_14373,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14374,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3704_3]) ).

fof(f_3705_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_3705_2,plain,
    ! [U_14381,U_14380,U_14379,U_14378] : hAPP(c_Set_Oimage(U_14378,U_14379,U_14380),hAPP(c_Set_Ovimage(U_14378,U_14379,U_14380),U_14381)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14379,tc_HOL_Obool)),U_14381),hAPP(c_Set_Oimage(U_14378,U_14379,U_14380),c_Orderings_Otop__class_Otop(tc_fun(U_14378,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3705_1]) ).

fof(f_3705_3,plain,
    ! [U_14379,U_14378,U_14380,U_14381] : hAPP(c_Set_Oimage(U_14378,U_14379,U_14380),hAPP(c_Set_Ovimage(U_14378,U_14379,U_14380),U_14381)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14379,tc_HOL_Obool)),U_14381),hAPP(c_Set_Oimage(U_14378,U_14379,U_14380),c_Orderings_Otop__class_Otop(tc_fun(U_14378,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3705_2]) ).

cnf(f_3705_4,plain,
    hAPP(c_Set_Oimage(U_14378,U_14379,U_14380),hAPP(c_Set_Ovimage(U_14378,U_14379,U_14380),U_14381)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14379,tc_HOL_Obool)),U_14381),hAPP(c_Set_Oimage(U_14378,U_14379,U_14380),c_Orderings_Otop__class_Otop(tc_fun(U_14378,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3705_3]) ).

fof(f_3706_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_3706_2,plain,
    ! [U_14385,U_14384,U_14383,U_14382] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14384),hAPP(c_Set_Ovimage(U_14384,U_14382,U_14385),U_14383)))
      | ~ c_Fun_Oinj__on(U_14384,U_14382,U_14385,c_Orderings_Otop__class_Otop(tc_fun(U_14384,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14382),U_14383)) ),
    inference(variable_rename,[status(thm)],[f_3706_1]) ).

fof(f_3706_3,plain,
    ! [U_14382,U_14383,U_14384,U_14385] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14384),hAPP(c_Set_Ovimage(U_14384,U_14382,U_14385),U_14383)))
      | ~ c_Fun_Oinj__on(U_14384,U_14382,U_14385,c_Orderings_Otop__class_Otop(tc_fun(U_14384,tc_HOL_Obool)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14382),U_14383)) ),
    inference(definitional_conversion,[status(esa)],[f_3706_2]) ).

cnf(f_3706_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14384),hAPP(c_Set_Ovimage(U_14384,U_14382,U_14385),U_14383)))
    | ~ c_Fun_Oinj__on(U_14384,U_14382,U_14385,c_Orderings_Otop__class_Otop(tc_fun(U_14384,tc_HOL_Obool)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14382),U_14383)) ),
    inference(clausify,[status(thm)],[f_3706_3]) ).

fof(f_3707_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_3707_2,plain,
    ! [U_14389,U_14388,U_14387,U_14386] :
      ( hAPP(c_Set_Ovimage(U_14386,U_14387,U_14388),hAPP(c_Set_Oimage(U_14386,U_14387,U_14388),U_14389)) = U_14389
      | ~ c_Fun_Oinj__on(U_14386,U_14387,U_14388,c_Orderings_Otop__class_Otop(tc_fun(U_14386,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3707_1]) ).

fof(f_3707_3,plain,
    ! [U_14386,U_14387,U_14388,U_14389] :
      ( hAPP(c_Set_Ovimage(U_14386,U_14387,U_14388),hAPP(c_Set_Oimage(U_14386,U_14387,U_14388),U_14389)) = U_14389
      | ~ c_Fun_Oinj__on(U_14386,U_14387,U_14388,c_Orderings_Otop__class_Otop(tc_fun(U_14386,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3707_2]) ).

cnf(f_3707_4,plain,
    ( hAPP(c_Set_Ovimage(U_14386,U_14387,U_14388),hAPP(c_Set_Oimage(U_14386,U_14387,U_14388),U_14389)) = U_14389
    | ~ c_Fun_Oinj__on(U_14386,U_14387,U_14388,c_Orderings_Otop__class_Otop(tc_fun(U_14386,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3707_3]) ).

fof(f_3708_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_3708_2,plain,
    ! [U_14393,U_14392,U_14391,U_14390] :
      ( U_14391 = U_14392
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14390,U_14390)),hAPP(hAPP(c_Product__Type_OPair(U_14390,U_14390),U_14391),U_14392)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14390,U_14390),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14393))) ),
    inference(variable_rename,[status(thm)],[f_3708_1]) ).

fof(f_3708_3,plain,
    ! [U_14393,U_14392,U_14391] :
      ( ! [U_14390] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14390,U_14390)),hAPP(hAPP(c_Product__Type_OPair(U_14390,U_14390),U_14391),U_14392)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14390,U_14390),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14393)))
      | U_14391 = U_14392 ),
    inference(miniscope,[status(thm)],[f_3708_2]) ).

fof(f_3708_4,plain,
    ! [U_14390,U_14391,U_14392,U_14393] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14390,U_14390)),hAPP(hAPP(c_Product__Type_OPair(U_14390,U_14390),U_14391),U_14392)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14390,U_14390),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14393)))
      | U_14391 = U_14392 ),
    inference(definitional_conversion,[status(esa)],[f_3708_3]) ).

cnf(f_3708_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14390,U_14390)),hAPP(hAPP(c_Product__Type_OPair(U_14390,U_14390),U_14391),U_14392)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14390,U_14390),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14393)))
    | U_14391 = U_14392 ),
    inference(clausify,[status(thm)],[f_3708_4]) ).

fof(f_3709_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_3709_2,plain,
    ! [U_14396,U_14395,U_14394] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14394,U_14394)),hAPP(hAPP(c_Product__Type_OPair(U_14394,U_14394),U_14395),U_14395)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14394,U_14394),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14396))),
    inference(variable_rename,[status(thm)],[f_3709_1]) ).

fof(f_3709_3,plain,
    ! [U_14394,U_14395,U_14396] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_14394,U_14394)),hAPP(hAPP(c_Product__Type_OPair(U_14394,U_14394),U_14395),U_14395)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14394,U_14394),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14396))),
    inference(definitional_conversion,[status(esa)],[f_3709_2]) ).

cnf(f_3709_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(U_14394,U_14394)),hAPP(hAPP(c_Product__Type_OPair(U_14394,U_14394),U_14395),U_14395)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14394,U_14394),tc_HOL_Obool),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14396))),
    inference(clausify,[status(thm)],[f_3709_3]) ).

fof(f_3710_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_3710_2,plain,
    ! [U_14400,U_14399,U_14398,U_14397] :
      ( ( hAPP(c_Set_Ovimage(U_14400,U_14397,hAPP(c_COMBK(U_14397,U_14400),U_14398)),U_14399) = c_Orderings_Obot__class_Obot(tc_fun(U_14400,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_14397),U_14398),U_14399)) )
      & ( hAPP(c_Set_Ovimage(U_14400,U_14397,hAPP(c_COMBK(U_14397,U_14400),U_14398)),U_14399) = c_Orderings_Otop__class_Otop(tc_fun(U_14400,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14397),U_14398),U_14399)) ) ),
    inference(variable_rename,[status(thm)],[f_3710_1]) ).

fof(f_3710_3,plain,
    ( ! [U_14408,U_14406,U_14404,U_14402] :
        ( hAPP(c_Set_Ovimage(U_14408,U_14402,hAPP(c_COMBK(U_14402,U_14408),U_14404)),U_14406) = c_Orderings_Obot__class_Obot(tc_fun(U_14408,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_14402),U_14404),U_14406)) )
    & ! [U_14407,U_14405,U_14403,U_14401] :
        ( hAPP(c_Set_Ovimage(U_14407,U_14401,hAPP(c_COMBK(U_14401,U_14407),U_14403)),U_14405) = c_Orderings_Otop__class_Otop(tc_fun(U_14407,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14401),U_14403),U_14405)) ) ),
    inference(miniscope,[status(thm)],[f_3710_2]) ).

fof(f_3710_4,plain,
    ( ! [U_14402,U_14404,U_14406,U_14408] :
        ( hAPP(c_Set_Ovimage(U_14408,U_14402,hAPP(c_COMBK(U_14402,U_14408),U_14404)),U_14406) = c_Orderings_Obot__class_Obot(tc_fun(U_14408,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_14402),U_14404),U_14406)) )
    & ! [U_14407,U_14405,U_14403,U_14401] :
        ( hAPP(c_Set_Ovimage(U_14407,U_14401,hAPP(c_COMBK(U_14401,U_14407),U_14403)),U_14405) = c_Orderings_Otop__class_Otop(tc_fun(U_14407,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14401),U_14403),U_14405)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3710_3]) ).

cnf(f_3710_5,plain,
    ( hAPP(c_Set_Ovimage(U_14407,U_14401,hAPP(c_COMBK(U_14401,U_14407),U_14403)),U_14405) = c_Orderings_Otop__class_Otop(tc_fun(U_14407,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14401),U_14403),U_14405)) ),
    inference(clausify,[status(thm)],[f_3710_4]) ).

cnf(f_3710_6,plain,
    ( hAPP(c_Set_Ovimage(U_14408,U_14402,hAPP(c_COMBK(U_14402,U_14408),U_14404)),U_14406) = c_Orderings_Obot__class_Obot(tc_fun(U_14408,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_14402),U_14404),U_14406)) ),
    inference(clausify,[status(thm)],[f_3710_4]) ).

fof(f_3711_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_3711_2,plain,
    ! [U_14414,U_14413,U_14412,U_14411,U_14410,U_14409] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14409,U_14409)),hAPP(hAPP(c_Product__Type_OPair(U_14409,U_14409),U_14410),U_14414)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14409,U_14409),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14412)),U_14413)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14409,U_14409)),hAPP(hAPP(c_Product__Type_OPair(U_14409,U_14409),U_14411),U_14414)),U_14413))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14409,U_14409)),hAPP(hAPP(c_Product__Type_OPair(U_14409,U_14409),U_14410),U_14411)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14409,U_14409),tc_HOL_Obool),U_14412),U_14413))) ),
    inference(variable_rename,[status(thm)],[f_3711_1]) ).

fof(f_3711_3,plain,
    ! [U_14409,U_14410,U_14411,U_14412,U_14413,U_14414] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14409,U_14409)),hAPP(hAPP(c_Product__Type_OPair(U_14409,U_14409),U_14410),U_14414)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14409,U_14409),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14412)),U_14413)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14409,U_14409)),hAPP(hAPP(c_Product__Type_OPair(U_14409,U_14409),U_14411),U_14414)),U_14413))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14409,U_14409)),hAPP(hAPP(c_Product__Type_OPair(U_14409,U_14409),U_14410),U_14411)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14409,U_14409),tc_HOL_Obool),U_14412),U_14413))) ),
    inference(definitional_conversion,[status(esa)],[f_3711_2]) ).

cnf(f_3711_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14409,U_14409)),hAPP(hAPP(c_Product__Type_OPair(U_14409,U_14409),U_14410),U_14414)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14409,U_14409),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14412)),U_14413)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14409,U_14409)),hAPP(hAPP(c_Product__Type_OPair(U_14409,U_14409),U_14411),U_14414)),U_14413))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14409,U_14409)),hAPP(hAPP(c_Product__Type_OPair(U_14409,U_14409),U_14410),U_14411)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14409,U_14409),tc_HOL_Obool),U_14412),U_14413))) ),
    inference(clausify,[status(thm)],[f_3711_3]) ).

fof(f_3712_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_3712_2,plain,
    ! [U_14420,U_14419,U_14418,U_14417,U_14416,U_14415] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14415,U_14415)),hAPP(hAPP(c_Product__Type_OPair(U_14415,U_14415),U_14416),U_14419)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14415,U_14415),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14420)),U_14418)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14415,U_14415)),hAPP(hAPP(c_Product__Type_OPair(U_14415,U_14415),U_14417),U_14419)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14415,U_14415),tc_HOL_Obool),U_14420),U_14418)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14415,U_14415)),hAPP(hAPP(c_Product__Type_OPair(U_14415,U_14415),U_14416),U_14417)),U_14418)) ),
    inference(variable_rename,[status(thm)],[f_3712_1]) ).

fof(f_3712_3,plain,
    ! [U_14415,U_14416,U_14417,U_14418,U_14419,U_14420] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14415,U_14415)),hAPP(hAPP(c_Product__Type_OPair(U_14415,U_14415),U_14416),U_14419)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14415,U_14415),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14420)),U_14418)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14415,U_14415)),hAPP(hAPP(c_Product__Type_OPair(U_14415,U_14415),U_14417),U_14419)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14415,U_14415),tc_HOL_Obool),U_14420),U_14418)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14415,U_14415)),hAPP(hAPP(c_Product__Type_OPair(U_14415,U_14415),U_14416),U_14417)),U_14418)) ),
    inference(definitional_conversion,[status(esa)],[f_3712_2]) ).

cnf(f_3712_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14415,U_14415)),hAPP(hAPP(c_Product__Type_OPair(U_14415,U_14415),U_14416),U_14419)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14415,U_14415),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_14420)),U_14418)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14415,U_14415)),hAPP(hAPP(c_Product__Type_OPair(U_14415,U_14415),U_14417),U_14419)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14415,U_14415),tc_HOL_Obool),U_14420),U_14418)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14415,U_14415)),hAPP(hAPP(c_Product__Type_OPair(U_14415,U_14415),U_14416),U_14417)),U_14418)) ),
    inference(clausify,[status(thm)],[f_3712_3]) ).

fof(f_3713_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_3713_2,plain,
    ! [U_14424,U_14423,U_14422,U_14421] : hAPP(c_Set_Ovimage(U_14421,U_14422,U_14423),U_14424) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14422,tc_fun(U_14421,tc_HOL_Obool)),U_14424),hAPP(hAPP(c_COMBB(tc_fun(U_14422,tc_HOL_Obool),tc_fun(U_14421,tc_HOL_Obool),U_14422),c_Set_Ovimage(U_14421,U_14422,U_14423)),hAPP(hAPP(c_COMBC(U_14422,tc_fun(U_14422,tc_HOL_Obool),tc_fun(U_14422,tc_HOL_Obool)),c_Set_Oinsert(U_14422)),c_Orderings_Obot__class_Obot(tc_fun(U_14422,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3713_1]) ).

fof(f_3713_3,plain,
    ! [U_14422,U_14421,U_14423,U_14424] : hAPP(c_Set_Ovimage(U_14421,U_14422,U_14423),U_14424) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14422,tc_fun(U_14421,tc_HOL_Obool)),U_14424),hAPP(hAPP(c_COMBB(tc_fun(U_14422,tc_HOL_Obool),tc_fun(U_14421,tc_HOL_Obool),U_14422),c_Set_Ovimage(U_14421,U_14422,U_14423)),hAPP(hAPP(c_COMBC(U_14422,tc_fun(U_14422,tc_HOL_Obool),tc_fun(U_14422,tc_HOL_Obool)),c_Set_Oinsert(U_14422)),c_Orderings_Obot__class_Obot(tc_fun(U_14422,tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_3713_2]) ).

cnf(f_3713_4,plain,
    hAPP(c_Set_Ovimage(U_14421,U_14422,U_14423),U_14424) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14422,tc_fun(U_14421,tc_HOL_Obool)),U_14424),hAPP(hAPP(c_COMBB(tc_fun(U_14422,tc_HOL_Obool),tc_fun(U_14421,tc_HOL_Obool),U_14422),c_Set_Ovimage(U_14421,U_14422,U_14423)),hAPP(hAPP(c_COMBC(U_14422,tc_fun(U_14422,tc_HOL_Obool),tc_fun(U_14422,tc_HOL_Obool)),c_Set_Oinsert(U_14422)),c_Orderings_Obot__class_Obot(tc_fun(U_14422,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3713_3]) ).

fof(f_3714_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_3714_2,plain,
    ! [U_14429,U_14428,U_14427,U_14426,U_14425] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14425,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14425,U_14426,U_14427),U_14428)),U_14429))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14426,tc_HOL_Obool)),U_14428),hAPP(c_Set_Oimage(U_14425,U_14426,U_14427),U_14429)))
      | ~ c_Fun_Oinj__on(U_14425,U_14426,U_14427,c_Orderings_Otop__class_Otop(tc_fun(U_14425,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3714_1]) ).

fof(f_3714_3,plain,
    ! [U_14425,U_14426,U_14427,U_14428,U_14429] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14425,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14425,U_14426,U_14427),U_14428)),U_14429))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14426,tc_HOL_Obool)),U_14428),hAPP(c_Set_Oimage(U_14425,U_14426,U_14427),U_14429)))
      | ~ c_Fun_Oinj__on(U_14425,U_14426,U_14427,c_Orderings_Otop__class_Otop(tc_fun(U_14425,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3714_2]) ).

cnf(f_3714_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14425,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_14425,U_14426,U_14427),U_14428)),U_14429))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14426,tc_HOL_Obool)),U_14428),hAPP(c_Set_Oimage(U_14425,U_14426,U_14427),U_14429)))
    | ~ c_Fun_Oinj__on(U_14425,U_14426,U_14427,c_Orderings_Otop__class_Otop(tc_fun(U_14425,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3714_3]) ).

fof(f_3715_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_3715_2,plain,
    ! [U_14435,U_14434,U_14433,U_14432,U_14431,U_14430] :
      ( ( ( ( hAPP(c_Set_Ovimage(U_14434,U_14430,hAPP(hAPP(c_COMBC(U_14434,U_14430,U_14430),hAPP(hAPP(c_COMBC(U_14434,U_14430,tc_fun(U_14430,U_14430)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14430,tc_fun(U_14430,U_14430)),U_14434),c_If(U_14430)),hAPP(hAPP(c_COMBC(U_14434,tc_fun(U_14434,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14434)),U_14435))),U_14431)),U_14433)),U_14432) = c_Orderings_Obot__class_Obot(tc_fun(U_14434,tc_HOL_Obool))
            | hBOOL(hAPP(hAPP(c_member(U_14430),U_14433),U_14432)) )
          & ( hAPP(c_Set_Ovimage(U_14434,U_14430,hAPP(hAPP(c_COMBC(U_14434,U_14430,U_14430),hAPP(hAPP(c_COMBC(U_14434,U_14430,tc_fun(U_14430,U_14430)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14430,tc_fun(U_14430,U_14430)),U_14434),c_If(U_14430)),hAPP(hAPP(c_COMBC(U_14434,tc_fun(U_14434,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14434)),U_14435))),U_14431)),U_14433)),U_14432) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14434,tc_HOL_Obool)),U_14435)
            | ~ hBOOL(hAPP(hAPP(c_member(U_14430),U_14433),U_14432)) ) )
        | hBOOL(hAPP(hAPP(c_member(U_14430),U_14431),U_14432)) )
      & ( ( ( hAPP(c_Set_Ovimage(U_14434,U_14430,hAPP(hAPP(c_COMBC(U_14434,U_14430,U_14430),hAPP(hAPP(c_COMBC(U_14434,U_14430,tc_fun(U_14430,U_14430)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14430,tc_fun(U_14430,U_14430)),U_14434),c_If(U_14430)),hAPP(hAPP(c_COMBC(U_14434,tc_fun(U_14434,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14434)),U_14435))),U_14431)),U_14433)),U_14432) = U_14435
            | hBOOL(hAPP(hAPP(c_member(U_14430),U_14433),U_14432)) )
          & ( hAPP(c_Set_Ovimage(U_14434,U_14430,hAPP(hAPP(c_COMBC(U_14434,U_14430,U_14430),hAPP(hAPP(c_COMBC(U_14434,U_14430,tc_fun(U_14430,U_14430)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14430,tc_fun(U_14430,U_14430)),U_14434),c_If(U_14430)),hAPP(hAPP(c_COMBC(U_14434,tc_fun(U_14434,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14434)),U_14435))),U_14431)),U_14433)),U_14432) = c_Orderings_Otop__class_Otop(tc_fun(U_14434,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_14430),U_14433),U_14432)) ) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_14430),U_14431),U_14432)) ) ),
    inference(variable_rename,[status(thm)],[f_3715_1]) ).

fof(f_3715_3,plain,
    ( ! [U_14447,U_14445,U_14443,U_14441,U_14439,U_14437] :
        ( ( ( hAPP(c_Set_Ovimage(U_14445,U_14437,hAPP(hAPP(c_COMBC(U_14445,U_14437,U_14437),hAPP(hAPP(c_COMBC(U_14445,U_14437,tc_fun(U_14437,U_14437)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14437,tc_fun(U_14437,U_14437)),U_14445),c_If(U_14437)),hAPP(hAPP(c_COMBC(U_14445,tc_fun(U_14445,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14445)),U_14447))),U_14439)),U_14443)),U_14441) = c_Orderings_Obot__class_Obot(tc_fun(U_14445,tc_HOL_Obool))
            | hBOOL(hAPP(hAPP(c_member(U_14437),U_14443),U_14441)) )
          & ( hAPP(c_Set_Ovimage(U_14445,U_14437,hAPP(hAPP(c_COMBC(U_14445,U_14437,U_14437),hAPP(hAPP(c_COMBC(U_14445,U_14437,tc_fun(U_14437,U_14437)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14437,tc_fun(U_14437,U_14437)),U_14445),c_If(U_14437)),hAPP(hAPP(c_COMBC(U_14445,tc_fun(U_14445,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14445)),U_14447))),U_14439)),U_14443)),U_14441) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14445,tc_HOL_Obool)),U_14447)
            | ~ hBOOL(hAPP(hAPP(c_member(U_14437),U_14443),U_14441)) ) )
        | hBOOL(hAPP(hAPP(c_member(U_14437),U_14439),U_14441)) )
    & ! [U_14446,U_14444,U_14442,U_14440,U_14438,U_14436] :
        ( ( ( hAPP(c_Set_Ovimage(U_14444,U_14436,hAPP(hAPP(c_COMBC(U_14444,U_14436,U_14436),hAPP(hAPP(c_COMBC(U_14444,U_14436,tc_fun(U_14436,U_14436)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14436,tc_fun(U_14436,U_14436)),U_14444),c_If(U_14436)),hAPP(hAPP(c_COMBC(U_14444,tc_fun(U_14444,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14444)),U_14446))),U_14438)),U_14442)),U_14440) = U_14446
            | hBOOL(hAPP(hAPP(c_member(U_14436),U_14442),U_14440)) )
          & ( hAPP(c_Set_Ovimage(U_14444,U_14436,hAPP(hAPP(c_COMBC(U_14444,U_14436,U_14436),hAPP(hAPP(c_COMBC(U_14444,U_14436,tc_fun(U_14436,U_14436)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14436,tc_fun(U_14436,U_14436)),U_14444),c_If(U_14436)),hAPP(hAPP(c_COMBC(U_14444,tc_fun(U_14444,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14444)),U_14446))),U_14438)),U_14442)),U_14440) = c_Orderings_Otop__class_Otop(tc_fun(U_14444,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_14436),U_14442),U_14440)) ) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_14436),U_14438),U_14440)) ) ),
    inference(miniscope,[status(thm)],[f_3715_2]) ).

fof(f_3715_4,plain,
    ( ! [U_14447,U_14439,U_14437,U_14443,U_14441,U_14445] :
        ( hAPP(c_Set_Ovimage(U_14445,U_14437,hAPP(hAPP(c_COMBC(U_14445,U_14437,U_14437),hAPP(hAPP(c_COMBC(U_14445,U_14437,tc_fun(U_14437,U_14437)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14437,tc_fun(U_14437,U_14437)),U_14445),c_If(U_14437)),hAPP(hAPP(c_COMBC(U_14445,tc_fun(U_14445,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14445)),U_14447))),U_14439)),U_14443)),U_14441) = c_Orderings_Obot__class_Obot(tc_fun(U_14445,tc_HOL_Obool))
        | hBOOL(hAPP(hAPP(c_member(U_14437),U_14443),U_14441))
        | ~ sP979(U_14447,U_14439,U_14437,U_14443,U_14441,U_14445) )
    & ! [U_14447,U_14439,U_14437,U_14443,U_14441,U_14445] :
        ( hAPP(c_Set_Ovimage(U_14445,U_14437,hAPP(hAPP(c_COMBC(U_14445,U_14437,U_14437),hAPP(hAPP(c_COMBC(U_14445,U_14437,tc_fun(U_14437,U_14437)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14437,tc_fun(U_14437,U_14437)),U_14445),c_If(U_14437)),hAPP(hAPP(c_COMBC(U_14445,tc_fun(U_14445,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14445)),U_14447))),U_14439)),U_14443)),U_14441) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14445,tc_HOL_Obool)),U_14447)
        | ~ hBOOL(hAPP(hAPP(c_member(U_14437),U_14443),U_14441))
        | ~ sP979(U_14447,U_14439,U_14437,U_14443,U_14441,U_14445) )
    & ! [U_14436,U_14438,U_14440,U_14442,U_14446,U_14444] :
        ( hAPP(c_Set_Ovimage(U_14444,U_14436,hAPP(hAPP(c_COMBC(U_14444,U_14436,U_14436),hAPP(hAPP(c_COMBC(U_14444,U_14436,tc_fun(U_14436,U_14436)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14436,tc_fun(U_14436,U_14436)),U_14444),c_If(U_14436)),hAPP(hAPP(c_COMBC(U_14444,tc_fun(U_14444,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14444)),U_14446))),U_14438)),U_14442)),U_14440) = U_14446
        | hBOOL(hAPP(hAPP(c_member(U_14436),U_14442),U_14440))
        | ~ sP978(U_14436,U_14438,U_14440,U_14442,U_14446,U_14444) )
    & ! [U_14436,U_14438,U_14440,U_14442,U_14446,U_14444] :
        ( hAPP(c_Set_Ovimage(U_14444,U_14436,hAPP(hAPP(c_COMBC(U_14444,U_14436,U_14436),hAPP(hAPP(c_COMBC(U_14444,U_14436,tc_fun(U_14436,U_14436)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14436,tc_fun(U_14436,U_14436)),U_14444),c_If(U_14436)),hAPP(hAPP(c_COMBC(U_14444,tc_fun(U_14444,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14444)),U_14446))),U_14438)),U_14442)),U_14440) = c_Orderings_Otop__class_Otop(tc_fun(U_14444,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14436),U_14442),U_14440))
        | ~ sP978(U_14436,U_14438,U_14440,U_14442,U_14446,U_14444) )
    & ! [U_14447,U_14439,U_14437,U_14443,U_14441,U_14445] :
        ( sP979(U_14447,U_14439,U_14437,U_14443,U_14441,U_14445)
        | hBOOL(hAPP(hAPP(c_member(U_14437),U_14439),U_14441)) )
    & ! [U_14436,U_14438,U_14440,U_14442,U_14446,U_14444] :
        ( sP978(U_14436,U_14438,U_14440,U_14442,U_14446,U_14444)
        | ~ hBOOL(hAPP(hAPP(c_member(U_14436),U_14438),U_14440)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP978,sP979])],[f_3715_3]) ).

cnf(f_3715_5,plain,
    ( sP978(U_14436,U_14438,U_14440,U_14442,U_14446,U_14444)
    | ~ hBOOL(hAPP(hAPP(c_member(U_14436),U_14438),U_14440)) ),
    inference(clausify,[status(thm)],[f_3715_4]) ).

cnf(f_3715_6,plain,
    ( sP979(U_14447,U_14439,U_14437,U_14443,U_14441,U_14445)
    | hBOOL(hAPP(hAPP(c_member(U_14437),U_14439),U_14441)) ),
    inference(clausify,[status(thm)],[f_3715_4]) ).

cnf(f_3715_7,plain,
    ( hAPP(c_Set_Ovimage(U_14444,U_14436,hAPP(hAPP(c_COMBC(U_14444,U_14436,U_14436),hAPP(hAPP(c_COMBC(U_14444,U_14436,tc_fun(U_14436,U_14436)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14436,tc_fun(U_14436,U_14436)),U_14444),c_If(U_14436)),hAPP(hAPP(c_COMBC(U_14444,tc_fun(U_14444,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14444)),U_14446))),U_14438)),U_14442)),U_14440) = c_Orderings_Otop__class_Otop(tc_fun(U_14444,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14436),U_14442),U_14440))
    | ~ sP978(U_14436,U_14438,U_14440,U_14442,U_14446,U_14444) ),
    inference(clausify,[status(thm)],[f_3715_4]) ).

cnf(f_3715_8,plain,
    ( hAPP(c_Set_Ovimage(U_14444,U_14436,hAPP(hAPP(c_COMBC(U_14444,U_14436,U_14436),hAPP(hAPP(c_COMBC(U_14444,U_14436,tc_fun(U_14436,U_14436)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14436,tc_fun(U_14436,U_14436)),U_14444),c_If(U_14436)),hAPP(hAPP(c_COMBC(U_14444,tc_fun(U_14444,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14444)),U_14446))),U_14438)),U_14442)),U_14440) = U_14446
    | hBOOL(hAPP(hAPP(c_member(U_14436),U_14442),U_14440))
    | ~ sP978(U_14436,U_14438,U_14440,U_14442,U_14446,U_14444) ),
    inference(clausify,[status(thm)],[f_3715_4]) ).

cnf(f_3715_9,plain,
    ( hAPP(c_Set_Ovimage(U_14445,U_14437,hAPP(hAPP(c_COMBC(U_14445,U_14437,U_14437),hAPP(hAPP(c_COMBC(U_14445,U_14437,tc_fun(U_14437,U_14437)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14437,tc_fun(U_14437,U_14437)),U_14445),c_If(U_14437)),hAPP(hAPP(c_COMBC(U_14445,tc_fun(U_14445,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14445)),U_14447))),U_14439)),U_14443)),U_14441) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14445,tc_HOL_Obool)),U_14447)
    | ~ hBOOL(hAPP(hAPP(c_member(U_14437),U_14443),U_14441))
    | ~ sP979(U_14447,U_14439,U_14437,U_14443,U_14441,U_14445) ),
    inference(clausify,[status(thm)],[f_3715_4]) ).

cnf(f_3715_10,plain,
    ( hAPP(c_Set_Ovimage(U_14445,U_14437,hAPP(hAPP(c_COMBC(U_14445,U_14437,U_14437),hAPP(hAPP(c_COMBC(U_14445,U_14437,tc_fun(U_14437,U_14437)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_14437,tc_fun(U_14437,U_14437)),U_14445),c_If(U_14437)),hAPP(hAPP(c_COMBC(U_14445,tc_fun(U_14445,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14445)),U_14447))),U_14439)),U_14443)),U_14441) = c_Orderings_Obot__class_Obot(tc_fun(U_14445,tc_HOL_Obool))
    | hBOOL(hAPP(hAPP(c_member(U_14437),U_14443),U_14441))
    | ~ sP979(U_14447,U_14439,U_14437,U_14443,U_14441,U_14445) ),
    inference(clausify,[status(thm)],[f_3715_4]) ).

fof(f_3716_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_3716_2,plain,
    ! [U_14452,U_14451,U_14450] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14450,U_14450)),U_14451),c_Transitive__Closure_Otrancl(U_14450,U_14452)))
        | ! [U_14449] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14450,U_14450)),U_14451),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14450,U_14450),tc_HOL_Obool),U_14449),U_14452)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14449)) ) )
      & ( ? [U_14448] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14450,U_14450)),U_14451),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14450,U_14450),tc_HOL_Obool),U_14448),U_14452)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14448)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14450,U_14450)),U_14451),c_Transitive__Closure_Otrancl(U_14450,U_14452))) ) ),
    inference(variable_rename,[status(thm)],[f_3716_1]) ).

fof(f_3716_3,plain,
    ( ! [U_14458,U_14456,U_14454] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14454,U_14454)),U_14456),c_Transitive__Closure_Otrancl(U_14454,U_14458)))
        | ! [U_14449] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14454,U_14454)),U_14456),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14454,U_14454),tc_HOL_Obool),U_14449),U_14458)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14449)) ) )
    & ! [U_14457,U_14455,U_14453] :
        ( ? [U_14448] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14453,U_14453)),U_14455),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14453,U_14453),tc_HOL_Obool),U_14448),U_14457)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14448)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14453,U_14453)),U_14455),c_Transitive__Closure_Otrancl(U_14453,U_14457))) ) ),
    inference(miniscope,[status(thm)],[f_3716_2]) ).

fof(f_3716_4,plain,
    ( ! [U_14458,U_14456,U_14454] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14454,U_14454)),U_14456),c_Transitive__Closure_Otrancl(U_14454,U_14458)))
        | ! [U_14449] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14454,U_14454)),U_14456),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14454,U_14454),tc_HOL_Obool),U_14449),U_14458)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14449)) ) )
    & ! [U_14457,U_14455,U_14453] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14453,U_14453)),U_14455),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14453,U_14453),tc_HOL_Obool),sK316(U_14457,U_14455,U_14453)),U_14457)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK316(U_14457,U_14455,U_14453))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14453,U_14453)),U_14455),c_Transitive__Closure_Otrancl(U_14453,U_14457))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK316]),skolemize(U_14448,sK316(U_14457,U_14455,U_14453))],[f_3716_3]) ).

fof(f_3716_5,plain,
    ( ! [U_14453,U_14455,U_14457] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14453,U_14453)),U_14455),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14453,U_14453),tc_HOL_Obool),sK316(U_14457,U_14455,U_14453)),U_14457)))
        | ~ sP980(U_14453,U_14455,U_14457) )
    & ! [U_14453,U_14455,U_14457] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK316(U_14457,U_14455,U_14453)))
        | ~ sP980(U_14453,U_14455,U_14457) )
    & ! [U_14458,U_14449,U_14456,U_14454] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14454,U_14454)),U_14456),c_Transitive__Closure_Otrancl(U_14454,U_14458)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14454,U_14454)),U_14456),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14454,U_14454),tc_HOL_Obool),U_14449),U_14458)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14449)) )
    & ! [U_14453,U_14455,U_14457] :
        ( sP980(U_14453,U_14455,U_14457)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14453,U_14453)),U_14455),c_Transitive__Closure_Otrancl(U_14453,U_14457))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP980])],[f_3716_4]) ).

cnf(f_3716_6,plain,
    ( sP980(U_14453,U_14455,U_14457)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14453,U_14453)),U_14455),c_Transitive__Closure_Otrancl(U_14453,U_14457))) ),
    inference(clausify,[status(thm)],[f_3716_5]) ).

cnf(f_3716_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14454,U_14454)),U_14456),c_Transitive__Closure_Otrancl(U_14454,U_14458)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14454,U_14454)),U_14456),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14454,U_14454),tc_HOL_Obool),U_14449),U_14458)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14449)) ),
    inference(clausify,[status(thm)],[f_3716_5]) ).

cnf(f_3716_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),sK316(U_14457,U_14455,U_14453)))
    | ~ sP980(U_14453,U_14455,U_14457) ),
    inference(clausify,[status(thm)],[f_3716_5]) ).

cnf(f_3716_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14453,U_14453)),U_14455),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14453,U_14453),tc_HOL_Obool),sK316(U_14457,U_14455,U_14453)),U_14457)))
    | ~ sP980(U_14453,U_14455,U_14457) ),
    inference(clausify,[status(thm)],[f_3716_5]) ).

fof(f_3717_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_3717_2,plain,
    ! [U_14460,U_14459] : c_Transitive__Closure_Ortrancl(U_14459,U_14460) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_14459,U_14459),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_14459,U_14459),tc_HOL_Obool),tc_fun(tc_prod(U_14459,U_14459),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_14459,U_14459),tc_HOL_Obool)),U_14460)),
    inference(variable_rename,[status(thm)],[f_3717_1]) ).

fof(f_3717_3,plain,
    ! [U_14459,U_14460] : c_Transitive__Closure_Ortrancl(U_14459,U_14460) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_14459,U_14459),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_14459,U_14459),tc_HOL_Obool),tc_fun(tc_prod(U_14459,U_14459),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_14459,U_14459),tc_HOL_Obool)),U_14460)),
    inference(definitional_conversion,[status(esa)],[f_3717_2]) ).

cnf(f_3717_4,plain,
    c_Transitive__Closure_Ortrancl(U_14459,U_14460) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_Nat_Onat,tc_fun(tc_prod(U_14459,U_14459),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_14459,U_14459),tc_HOL_Obool),tc_fun(tc_prod(U_14459,U_14459),tc_HOL_Obool)),c_Nat_Ocompow(tc_prod(U_14459,U_14459),tc_HOL_Obool)),U_14460)),
    inference(clausify,[status(thm)],[f_3717_3]) ).

fof(f_3718_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_3718_2,plain,
    ! [U_14461] : c_Nat_Ofunpow(U_14461) = c_Nat_Ocompow(U_14461,U_14461),
    inference(variable_rename,[status(thm)],[f_3718_1]) ).

fof(f_3718_3,plain,
    ! [U_14461] : c_Nat_Ofunpow(U_14461) = c_Nat_Ocompow(U_14461,U_14461),
    inference(definitional_conversion,[status(esa)],[f_3718_2]) ).

cnf(f_3718_4,plain,
    c_Nat_Ofunpow(U_14461) = c_Nat_Ocompow(U_14461,U_14461),
    inference(clausify,[status(thm)],[f_3718_3]) ).

fof(f_3719_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_3719_2,plain,
    ! [U_14468,U_14467,U_14466,U_14465,U_14464] :
      ( ? [U_14463,U_14462] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14464,U_14464)),hAPP(hAPP(c_Product__Type_OPair(U_14464,U_14464),U_14463),U_14466)),U_14468))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14464,U_14464)),hAPP(hAPP(c_Product__Type_OPair(U_14464,U_14464),U_14465),U_14463)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14464,U_14464),tc_HOL_Obool),U_14462),U_14468)))
          & U_14467 = hAPP(c_Nat_OSuc,U_14462) )
      | ( U_14465 = U_14466
        & U_14467 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14464,U_14464)),hAPP(hAPP(c_Product__Type_OPair(U_14464,U_14464),U_14465),U_14466)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14464,U_14464),tc_HOL_Obool),U_14467),U_14468))) ),
    inference(variable_rename,[status(thm)],[f_3719_1]) ).

fof(f_3719_3,plain,
    ! [U_14468,U_14467,U_14466,U_14465,U_14464] :
      ( ? [U_14462] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14464,U_14464)),hAPP(hAPP(c_Product__Type_OPair(U_14464,U_14464),sK317(U_14468,U_14467,U_14466,U_14465,U_14464)),U_14466)),U_14468))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14464,U_14464)),hAPP(hAPP(c_Product__Type_OPair(U_14464,U_14464),U_14465),sK317(U_14468,U_14467,U_14466,U_14465,U_14464))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14464,U_14464),tc_HOL_Obool),U_14462),U_14468)))
          & U_14467 = hAPP(c_Nat_OSuc,U_14462) )
      | ( U_14465 = U_14466
        & U_14467 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14464,U_14464)),hAPP(hAPP(c_Product__Type_OPair(U_14464,U_14464),U_14465),U_14466)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14464,U_14464),tc_HOL_Obool),U_14467),U_14468))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK317]),skolemize(U_14463,sK317(U_14468,U_14467,U_14466,U_14465,U_14464))],[f_3719_2]) ).

fof(f_3719_4,plain,
    ! [U_14468,U_14467,U_14466,U_14465,U_14464] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14464,U_14464)),hAPP(hAPP(c_Product__Type_OPair(U_14464,U_14464),sK317(U_14468,U_14467,U_14466,U_14465,U_14464)),U_14466)),U_14468))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14464,U_14464)),hAPP(hAPP(c_Product__Type_OPair(U_14464,U_14464),U_14465),sK317(U_14468,U_14467,U_14466,U_14465,U_14464))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14464,U_14464),tc_HOL_Obool),sK318(U_14468,U_14467,U_14466,U_14465,U_14464)),U_14468)))
        & U_14467 = hAPP(c_Nat_OSuc,sK318(U_14468,U_14467,U_14466,U_14465,U_14464)) )
      | ( U_14465 = U_14466
        & U_14467 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14464,U_14464)),hAPP(hAPP(c_Product__Type_OPair(U_14464,U_14464),U_14465),U_14466)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14464,U_14464),tc_HOL_Obool),U_14467),U_14468))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK318]),skolemize(U_14462,sK318(U_14468,U_14467,U_14466,U_14465,U_14464))],[f_3719_3]) ).

fof(f_3719_5,plain,
    ( ! [U_14464,U_14465,U_14466,U_14467,U_14468] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14464,U_14464)),hAPP(hAPP(c_Product__Type_OPair(U_14464,U_14464),sK317(U_14468,U_14467,U_14466,U_14465,U_14464)),U_14466)),U_14468))
        | ~ sP982(U_14464,U_14465,U_14466,U_14467,U_14468) )
    & ! [U_14464,U_14465,U_14466,U_14467,U_14468] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14464,U_14464)),hAPP(hAPP(c_Product__Type_OPair(U_14464,U_14464),U_14465),sK317(U_14468,U_14467,U_14466,U_14465,U_14464))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14464,U_14464),tc_HOL_Obool),sK318(U_14468,U_14467,U_14466,U_14465,U_14464)),U_14468)))
        | ~ sP982(U_14464,U_14465,U_14466,U_14467,U_14468) )
    & ! [U_14464,U_14465,U_14466,U_14467,U_14468] :
        ( U_14467 = hAPP(c_Nat_OSuc,sK318(U_14468,U_14467,U_14466,U_14465,U_14464))
        | ~ sP982(U_14464,U_14465,U_14466,U_14467,U_14468) )
    & ! [U_14465,U_14466,U_14467] :
        ( U_14465 = U_14466
        | ~ sP981(U_14465,U_14466,U_14467) )
    & ! [U_14465,U_14466,U_14467] :
        ( U_14467 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP981(U_14465,U_14466,U_14467) )
    & ! [U_14464,U_14465,U_14466,U_14467,U_14468] :
        ( sP982(U_14464,U_14465,U_14466,U_14467,U_14468)
        | sP981(U_14465,U_14466,U_14467)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14464,U_14464)),hAPP(hAPP(c_Product__Type_OPair(U_14464,U_14464),U_14465),U_14466)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14464,U_14464),tc_HOL_Obool),U_14467),U_14468))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP981,sP982])],[f_3719_4]) ).

cnf(f_3719_6,plain,
    ( sP982(U_14464,U_14465,U_14466,U_14467,U_14468)
    | sP981(U_14465,U_14466,U_14467)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14464,U_14464)),hAPP(hAPP(c_Product__Type_OPair(U_14464,U_14464),U_14465),U_14466)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14464,U_14464),tc_HOL_Obool),U_14467),U_14468))) ),
    inference(clausify,[status(thm)],[f_3719_5]) ).

cnf(f_3719_7,plain,
    ( U_14467 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP981(U_14465,U_14466,U_14467) ),
    inference(clausify,[status(thm)],[f_3719_5]) ).

cnf(f_3719_8,plain,
    ( U_14465 = U_14466
    | ~ sP981(U_14465,U_14466,U_14467) ),
    inference(clausify,[status(thm)],[f_3719_5]) ).

cnf(f_3719_9,plain,
    ( U_14467 = hAPP(c_Nat_OSuc,sK318(U_14468,U_14467,U_14466,U_14465,U_14464))
    | ~ sP982(U_14464,U_14465,U_14466,U_14467,U_14468) ),
    inference(clausify,[status(thm)],[f_3719_5]) ).

cnf(f_3719_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14464,U_14464)),hAPP(hAPP(c_Product__Type_OPair(U_14464,U_14464),U_14465),sK317(U_14468,U_14467,U_14466,U_14465,U_14464))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14464,U_14464),tc_HOL_Obool),sK318(U_14468,U_14467,U_14466,U_14465,U_14464)),U_14468)))
    | ~ sP982(U_14464,U_14465,U_14466,U_14467,U_14468) ),
    inference(clausify,[status(thm)],[f_3719_5]) ).

cnf(f_3719_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14464,U_14464)),hAPP(hAPP(c_Product__Type_OPair(U_14464,U_14464),sK317(U_14468,U_14467,U_14466,U_14465,U_14464)),U_14466)),U_14468))
    | ~ sP982(U_14464,U_14465,U_14466,U_14467,U_14468) ),
    inference(clausify,[status(thm)],[f_3719_5]) ).

fof(f_3720_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_3720_2,plain,
    ! [U_14475,U_14474,U_14473,U_14472,U_14471] :
      ( ? [U_14470,U_14469] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14471,U_14471)),hAPP(hAPP(c_Product__Type_OPair(U_14471,U_14471),U_14470),U_14473)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14471,U_14471),tc_HOL_Obool),U_14469),U_14475)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14471,U_14471)),hAPP(hAPP(c_Product__Type_OPair(U_14471,U_14471),U_14472),U_14470)),U_14475))
          & U_14474 = hAPP(c_Nat_OSuc,U_14469) )
      | ( U_14472 = U_14473
        & U_14474 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14471,U_14471)),hAPP(hAPP(c_Product__Type_OPair(U_14471,U_14471),U_14472),U_14473)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14471,U_14471),tc_HOL_Obool),U_14474),U_14475))) ),
    inference(variable_rename,[status(thm)],[f_3720_1]) ).

fof(f_3720_3,plain,
    ! [U_14475,U_14474,U_14473,U_14472,U_14471] :
      ( ? [U_14469] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14471,U_14471)),hAPP(hAPP(c_Product__Type_OPair(U_14471,U_14471),sK319(U_14475,U_14474,U_14473,U_14472,U_14471)),U_14473)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14471,U_14471),tc_HOL_Obool),U_14469),U_14475)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14471,U_14471)),hAPP(hAPP(c_Product__Type_OPair(U_14471,U_14471),U_14472),sK319(U_14475,U_14474,U_14473,U_14472,U_14471))),U_14475))
          & U_14474 = hAPP(c_Nat_OSuc,U_14469) )
      | ( U_14472 = U_14473
        & U_14474 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14471,U_14471)),hAPP(hAPP(c_Product__Type_OPair(U_14471,U_14471),U_14472),U_14473)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14471,U_14471),tc_HOL_Obool),U_14474),U_14475))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK319]),skolemize(U_14470,sK319(U_14475,U_14474,U_14473,U_14472,U_14471))],[f_3720_2]) ).

fof(f_3720_4,plain,
    ! [U_14475,U_14474,U_14473,U_14472,U_14471] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14471,U_14471)),hAPP(hAPP(c_Product__Type_OPair(U_14471,U_14471),sK319(U_14475,U_14474,U_14473,U_14472,U_14471)),U_14473)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14471,U_14471),tc_HOL_Obool),sK320(U_14475,U_14474,U_14473,U_14472,U_14471)),U_14475)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_14471,U_14471)),hAPP(hAPP(c_Product__Type_OPair(U_14471,U_14471),U_14472),sK319(U_14475,U_14474,U_14473,U_14472,U_14471))),U_14475))
        & U_14474 = hAPP(c_Nat_OSuc,sK320(U_14475,U_14474,U_14473,U_14472,U_14471)) )
      | ( U_14472 = U_14473
        & U_14474 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14471,U_14471)),hAPP(hAPP(c_Product__Type_OPair(U_14471,U_14471),U_14472),U_14473)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14471,U_14471),tc_HOL_Obool),U_14474),U_14475))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK320]),skolemize(U_14469,sK320(U_14475,U_14474,U_14473,U_14472,U_14471))],[f_3720_3]) ).

fof(f_3720_5,plain,
    ( ! [U_14471,U_14473,U_14472,U_14474,U_14475] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14471,U_14471)),hAPP(hAPP(c_Product__Type_OPair(U_14471,U_14471),sK319(U_14475,U_14474,U_14473,U_14472,U_14471)),U_14473)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14471,U_14471),tc_HOL_Obool),sK320(U_14475,U_14474,U_14473,U_14472,U_14471)),U_14475)))
        | ~ sP984(U_14471,U_14473,U_14472,U_14474,U_14475) )
    & ! [U_14471,U_14473,U_14472,U_14474,U_14475] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14471,U_14471)),hAPP(hAPP(c_Product__Type_OPair(U_14471,U_14471),U_14472),sK319(U_14475,U_14474,U_14473,U_14472,U_14471))),U_14475))
        | ~ sP984(U_14471,U_14473,U_14472,U_14474,U_14475) )
    & ! [U_14471,U_14473,U_14472,U_14474,U_14475] :
        ( U_14474 = hAPP(c_Nat_OSuc,sK320(U_14475,U_14474,U_14473,U_14472,U_14471))
        | ~ sP984(U_14471,U_14473,U_14472,U_14474,U_14475) )
    & ! [U_14473,U_14472,U_14474] :
        ( U_14472 = U_14473
        | ~ sP983(U_14473,U_14472,U_14474) )
    & ! [U_14473,U_14472,U_14474] :
        ( U_14474 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP983(U_14473,U_14472,U_14474) )
    & ! [U_14471,U_14473,U_14472,U_14474,U_14475] :
        ( sP984(U_14471,U_14473,U_14472,U_14474,U_14475)
        | sP983(U_14473,U_14472,U_14474)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14471,U_14471)),hAPP(hAPP(c_Product__Type_OPair(U_14471,U_14471),U_14472),U_14473)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14471,U_14471),tc_HOL_Obool),U_14474),U_14475))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP983,sP984])],[f_3720_4]) ).

cnf(f_3720_6,plain,
    ( sP984(U_14471,U_14473,U_14472,U_14474,U_14475)
    | sP983(U_14473,U_14472,U_14474)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14471,U_14471)),hAPP(hAPP(c_Product__Type_OPair(U_14471,U_14471),U_14472),U_14473)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14471,U_14471),tc_HOL_Obool),U_14474),U_14475))) ),
    inference(clausify,[status(thm)],[f_3720_5]) ).

cnf(f_3720_7,plain,
    ( U_14474 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP983(U_14473,U_14472,U_14474) ),
    inference(clausify,[status(thm)],[f_3720_5]) ).

cnf(f_3720_8,plain,
    ( U_14472 = U_14473
    | ~ sP983(U_14473,U_14472,U_14474) ),
    inference(clausify,[status(thm)],[f_3720_5]) ).

cnf(f_3720_9,plain,
    ( U_14474 = hAPP(c_Nat_OSuc,sK320(U_14475,U_14474,U_14473,U_14472,U_14471))
    | ~ sP984(U_14471,U_14473,U_14472,U_14474,U_14475) ),
    inference(clausify,[status(thm)],[f_3720_5]) ).

cnf(f_3720_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14471,U_14471)),hAPP(hAPP(c_Product__Type_OPair(U_14471,U_14471),U_14472),sK319(U_14475,U_14474,U_14473,U_14472,U_14471))),U_14475))
    | ~ sP984(U_14471,U_14473,U_14472,U_14474,U_14475) ),
    inference(clausify,[status(thm)],[f_3720_5]) ).

cnf(f_3720_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14471,U_14471)),hAPP(hAPP(c_Product__Type_OPair(U_14471,U_14471),sK319(U_14475,U_14474,U_14473,U_14472,U_14471)),U_14473)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_14471,U_14471),tc_HOL_Obool),sK320(U_14475,U_14474,U_14473,U_14472,U_14471)),U_14475)))
    | ~ sP984(U_14471,U_14473,U_14472,U_14474,U_14475) ),
    inference(clausify,[status(thm)],[f_3720_5]) ).

fof(f_3721_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_3721_2,plain,
    ! [U_14481,U_14480,U_14479,U_14478,U_14477] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_14477),U_14480),U_14478) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_14477),U_14481),U_14479)
      | ? [U_14476] :
          ( hAPP(U_14480,U_14476) != hAPP(U_14481,U_14476)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),U_14476)) )
      | ~ c_Nat__Transfer_Onat__set(U_14479)
      | U_14478 != U_14479
      | ~ class_Groups_Ocomm__monoid__mult(U_14477)
      | ~ class_Groups_Ocomm__monoid__add(U_14477) ),
    inference(variable_rename,[status(thm)],[f_3721_1]) ).

fof(f_3721_3,plain,
    ! [U_14481,U_14480,U_14479,U_14478,U_14477] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_14477),U_14480),U_14478) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_14477),U_14481),U_14479)
      | ( hAPP(U_14480,sK321(U_14481,U_14480,U_14479,U_14478,U_14477)) != hAPP(U_14481,sK321(U_14481,U_14480,U_14479,U_14478,U_14477))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK321(U_14481,U_14480,U_14479,U_14478,U_14477))) )
      | ~ c_Nat__Transfer_Onat__set(U_14479)
      | U_14478 != U_14479
      | ~ class_Groups_Ocomm__monoid__mult(U_14477)
      | ~ class_Groups_Ocomm__monoid__add(U_14477) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK321]),skolemize(U_14476,sK321(U_14481,U_14480,U_14479,U_14478,U_14477))],[f_3721_2]) ).

fof(f_3721_4,plain,
    ( ! [U_14477,U_14478,U_14479,U_14480,U_14481] :
        ( hAPP(U_14480,sK321(U_14481,U_14480,U_14479,U_14478,U_14477)) != hAPP(U_14481,sK321(U_14481,U_14480,U_14479,U_14478,U_14477))
        | ~ sP985(U_14477,U_14478,U_14479,U_14480,U_14481) )
    & ! [U_14477,U_14478,U_14479,U_14480,U_14481] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK321(U_14481,U_14480,U_14479,U_14478,U_14477)))
        | ~ sP985(U_14477,U_14478,U_14479,U_14480,U_14481) )
    & ! [U_14477,U_14478,U_14479,U_14480,U_14481] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_14477),U_14480),U_14478) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_14477),U_14481),U_14479)
        | sP985(U_14477,U_14478,U_14479,U_14480,U_14481)
        | ~ c_Nat__Transfer_Onat__set(U_14479)
        | U_14478 != U_14479
        | ~ class_Groups_Ocomm__monoid__mult(U_14477)
        | ~ class_Groups_Ocomm__monoid__add(U_14477) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP985])],[f_3721_3]) ).

cnf(f_3721_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_14477),U_14480),U_14478) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_14477),U_14481),U_14479)
    | sP985(U_14477,U_14478,U_14479,U_14480,U_14481)
    | ~ c_Nat__Transfer_Onat__set(U_14479)
    | U_14478 != U_14479
    | ~ class_Groups_Ocomm__monoid__mult(U_14477)
    | ~ class_Groups_Ocomm__monoid__add(U_14477) ),
    inference(clausify,[status(thm)],[f_3721_4]) ).

cnf(f_3721_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),sK321(U_14481,U_14480,U_14479,U_14478,U_14477)))
    | ~ sP985(U_14477,U_14478,U_14479,U_14480,U_14481) ),
    inference(clausify,[status(thm)],[f_3721_4]) ).

cnf(f_3721_7,plain,
    ( hAPP(U_14480,sK321(U_14481,U_14480,U_14479,U_14478,U_14477)) != hAPP(U_14481,sK321(U_14481,U_14480,U_14479,U_14478,U_14477))
    | ~ sP985(U_14477,U_14478,U_14479,U_14480,U_14481) ),
    inference(clausify,[status(thm)],[f_3721_4]) ).

fof(f_3722_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_3722_2,plain,
    ! [U_14489,U_14488,U_14487,U_14486] :
      ( ( c_Wellfounded_Omax__extp(U_14486,U_14487,U_14488,U_14489)
        | ? [U_14485] :
            ( ! [U_14484] :
                ( ~ hBOOL(hAPP(hAPP(U_14487,U_14485),U_14484))
                | ~ hBOOL(hAPP(hAPP(c_member(U_14486),U_14484),U_14489)) )
            & hBOOL(hAPP(hAPP(c_member(U_14486),U_14485),U_14488)) )
        | U_14489 = c_Orderings_Obot__class_Obot(tc_fun(U_14486,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14486),U_14489))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14486),U_14488)) )
      & ( ( ! [U_14483] :
              ( ? [U_14482] :
                  ( hBOOL(hAPP(hAPP(U_14487,U_14483),U_14482))
                  & hBOOL(hAPP(hAPP(c_member(U_14486),U_14482),U_14489)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_14486),U_14483),U_14488)) )
          & U_14489 != c_Orderings_Obot__class_Obot(tc_fun(U_14486,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14486),U_14489))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14486),U_14488)) )
        | ~ c_Wellfounded_Omax__extp(U_14486,U_14487,U_14488,U_14489) ) ),
    inference(variable_rename,[status(thm)],[f_3722_1]) ).

fof(f_3722_3,plain,
    ( ! [U_14497,U_14495,U_14493,U_14491] :
        ( c_Wellfounded_Omax__extp(U_14491,U_14493,U_14495,U_14497)
        | ? [U_14485] :
            ( ! [U_14484] :
                ( ~ hBOOL(hAPP(hAPP(U_14493,U_14485),U_14484))
                | ~ hBOOL(hAPP(hAPP(c_member(U_14491),U_14484),U_14497)) )
            & hBOOL(hAPP(hAPP(c_member(U_14491),U_14485),U_14495)) )
        | U_14497 = c_Orderings_Obot__class_Obot(tc_fun(U_14491,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14491),U_14497))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14491),U_14495)) )
    & ! [U_14496,U_14494,U_14492,U_14490] :
        ( ( ! [U_14483] :
              ( ? [U_14482] :
                  ( hBOOL(hAPP(hAPP(U_14492,U_14483),U_14482))
                  & hBOOL(hAPP(hAPP(c_member(U_14490),U_14482),U_14496)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_14490),U_14483),U_14494)) )
          & U_14496 != c_Orderings_Obot__class_Obot(tc_fun(U_14490,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14490),U_14496))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14490),U_14494)) )
        | ~ c_Wellfounded_Omax__extp(U_14490,U_14492,U_14494,U_14496) ) ),
    inference(miniscope,[status(thm)],[f_3722_2]) ).

fof(f_3722_4,plain,
    ( ! [U_14497,U_14495,U_14493,U_14491] :
        ( c_Wellfounded_Omax__extp(U_14491,U_14493,U_14495,U_14497)
        | ? [U_14485] :
            ( ! [U_14484] :
                ( ~ hBOOL(hAPP(hAPP(U_14493,U_14485),U_14484))
                | ~ hBOOL(hAPP(hAPP(c_member(U_14491),U_14484),U_14497)) )
            & hBOOL(hAPP(hAPP(c_member(U_14491),U_14485),U_14495)) )
        | U_14497 = c_Orderings_Obot__class_Obot(tc_fun(U_14491,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14491),U_14497))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14491),U_14495)) )
    & ! [U_14496,U_14494,U_14492,U_14490] :
        ( ( ! [U_14483] :
              ( ( hBOOL(hAPP(hAPP(U_14492,U_14483),sK322(U_14496,U_14494,U_14492,U_14490,U_14483)))
                & hBOOL(hAPP(hAPP(c_member(U_14490),sK322(U_14496,U_14494,U_14492,U_14490,U_14483)),U_14496)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_14490),U_14483),U_14494)) )
          & U_14496 != c_Orderings_Obot__class_Obot(tc_fun(U_14490,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14490),U_14496))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14490),U_14494)) )
        | ~ c_Wellfounded_Omax__extp(U_14490,U_14492,U_14494,U_14496) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK322]),skolemize(U_14482,sK322(U_14496,U_14494,U_14492,U_14490,U_14483))],[f_3722_3]) ).

fof(f_3722_5,plain,
    ( ! [U_14497,U_14495,U_14493,U_14491] :
        ( c_Wellfounded_Omax__extp(U_14491,U_14493,U_14495,U_14497)
        | ( ! [U_14484] :
              ( ~ hBOOL(hAPP(hAPP(U_14493,sK323(U_14497,U_14495,U_14493,U_14491)),U_14484))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14491),U_14484),U_14497)) )
          & hBOOL(hAPP(hAPP(c_member(U_14491),sK323(U_14497,U_14495,U_14493,U_14491)),U_14495)) )
        | U_14497 = c_Orderings_Obot__class_Obot(tc_fun(U_14491,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14491),U_14497))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14491),U_14495)) )
    & ! [U_14496,U_14494,U_14492,U_14490] :
        ( ( ! [U_14483] :
              ( ( hBOOL(hAPP(hAPP(U_14492,U_14483),sK322(U_14496,U_14494,U_14492,U_14490,U_14483)))
                & hBOOL(hAPP(hAPP(c_member(U_14490),sK322(U_14496,U_14494,U_14492,U_14490,U_14483)),U_14496)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_14490),U_14483),U_14494)) )
          & U_14496 != c_Orderings_Obot__class_Obot(tc_fun(U_14490,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14490),U_14496))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_14490),U_14494)) )
        | ~ c_Wellfounded_Omax__extp(U_14490,U_14492,U_14494,U_14496) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK323]),skolemize(U_14485,sK323(U_14497,U_14495,U_14493,U_14491))],[f_3722_4]) ).

fof(f_3722_6,plain,
    ( ! [U_14484,U_14495,U_14493,U_14497,U_14491] :
        ( ~ hBOOL(hAPP(hAPP(U_14493,sK323(U_14497,U_14495,U_14493,U_14491)),U_14484))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14491),U_14484),U_14497))
        | ~ sP988(U_14484,U_14495,U_14493,U_14497,U_14491) )
    & ! [U_14484,U_14495,U_14493,U_14497,U_14491] :
        ( hBOOL(hAPP(hAPP(c_member(U_14491),sK323(U_14497,U_14495,U_14493,U_14491)),U_14495))
        | ~ sP988(U_14484,U_14495,U_14493,U_14497,U_14491) )
    & ! [U_14483,U_14494,U_14492,U_14490,U_14496] :
        ( hBOOL(hAPP(hAPP(U_14492,U_14483),sK322(U_14496,U_14494,U_14492,U_14490,U_14483)))
        | ~ sP986(U_14483,U_14494,U_14492,U_14490,U_14496) )
    & ! [U_14483,U_14494,U_14492,U_14490,U_14496] :
        ( hBOOL(hAPP(hAPP(c_member(U_14490),sK322(U_14496,U_14494,U_14492,U_14490,U_14483)),U_14496))
        | ~ sP986(U_14483,U_14494,U_14492,U_14490,U_14496) )
    & ! [U_14483,U_14494,U_14492,U_14490,U_14496] :
        ( sP986(U_14483,U_14494,U_14492,U_14490,U_14496)
        | ~ hBOOL(hAPP(hAPP(c_member(U_14490),U_14483),U_14494))
        | ~ sP987(U_14483,U_14494,U_14492,U_14490,U_14496) )
    & ! [U_14483,U_14494,U_14492,U_14490,U_14496] :
        ( U_14496 != c_Orderings_Obot__class_Obot(tc_fun(U_14490,tc_HOL_Obool))
        | ~ sP987(U_14483,U_14494,U_14492,U_14490,U_14496) )
    & ! [U_14483,U_14494,U_14492,U_14490,U_14496] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14490),U_14496))
        | ~ sP987(U_14483,U_14494,U_14492,U_14490,U_14496) )
    & ! [U_14483,U_14494,U_14492,U_14490,U_14496] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14490),U_14494))
        | ~ sP987(U_14483,U_14494,U_14492,U_14490,U_14496) )
    & ! [U_14484,U_14495,U_14493,U_14497,U_14491] :
        ( c_Wellfounded_Omax__extp(U_14491,U_14493,U_14495,U_14497)
        | sP988(U_14484,U_14495,U_14493,U_14497,U_14491)
        | U_14497 = c_Orderings_Obot__class_Obot(tc_fun(U_14491,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14491),U_14497))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14491),U_14495)) )
    & ! [U_14483,U_14494,U_14492,U_14490,U_14496] :
        ( sP987(U_14483,U_14494,U_14492,U_14490,U_14496)
        | ~ c_Wellfounded_Omax__extp(U_14490,U_14492,U_14494,U_14496) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP986,sP987,sP988])],[f_3722_5]) ).

cnf(f_3722_7,plain,
    ( sP987(U_14483,U_14494,U_14492,U_14490,U_14496)
    | ~ c_Wellfounded_Omax__extp(U_14490,U_14492,U_14494,U_14496) ),
    inference(clausify,[status(thm)],[f_3722_6]) ).

cnf(f_3722_8,plain,
    ( c_Wellfounded_Omax__extp(U_14491,U_14493,U_14495,U_14497)
    | sP988(U_14484,U_14495,U_14493,U_14497,U_14491)
    | U_14497 = c_Orderings_Obot__class_Obot(tc_fun(U_14491,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14491),U_14497))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14491),U_14495)) ),
    inference(clausify,[status(thm)],[f_3722_6]) ).

cnf(f_3722_9,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14490),U_14494))
    | ~ sP987(U_14483,U_14494,U_14492,U_14490,U_14496) ),
    inference(clausify,[status(thm)],[f_3722_6]) ).

cnf(f_3722_10,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14490),U_14496))
    | ~ sP987(U_14483,U_14494,U_14492,U_14490,U_14496) ),
    inference(clausify,[status(thm)],[f_3722_6]) ).

cnf(f_3722_11,plain,
    ( U_14496 != c_Orderings_Obot__class_Obot(tc_fun(U_14490,tc_HOL_Obool))
    | ~ sP987(U_14483,U_14494,U_14492,U_14490,U_14496) ),
    inference(clausify,[status(thm)],[f_3722_6]) ).

cnf(f_3722_12,plain,
    ( sP986(U_14483,U_14494,U_14492,U_14490,U_14496)
    | ~ hBOOL(hAPP(hAPP(c_member(U_14490),U_14483),U_14494))
    | ~ sP987(U_14483,U_14494,U_14492,U_14490,U_14496) ),
    inference(clausify,[status(thm)],[f_3722_6]) ).

cnf(f_3722_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14490),sK322(U_14496,U_14494,U_14492,U_14490,U_14483)),U_14496))
    | ~ sP986(U_14483,U_14494,U_14492,U_14490,U_14496) ),
    inference(clausify,[status(thm)],[f_3722_6]) ).

cnf(f_3722_14,plain,
    ( hBOOL(hAPP(hAPP(U_14492,U_14483),sK322(U_14496,U_14494,U_14492,U_14490,U_14483)))
    | ~ sP986(U_14483,U_14494,U_14492,U_14490,U_14496) ),
    inference(clausify,[status(thm)],[f_3722_6]) ).

cnf(f_3722_15,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14491),sK323(U_14497,U_14495,U_14493,U_14491)),U_14495))
    | ~ sP988(U_14484,U_14495,U_14493,U_14497,U_14491) ),
    inference(clausify,[status(thm)],[f_3722_6]) ).

cnf(f_3722_16,plain,
    ( ~ hBOOL(hAPP(hAPP(U_14493,sK323(U_14497,U_14495,U_14493,U_14491)),U_14484))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14491),U_14484),U_14497))
    | ~ sP988(U_14484,U_14495,U_14493,U_14497,U_14491) ),
    inference(clausify,[status(thm)],[f_3722_6]) ).

fof(f_3723_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_3723_2,plain,
    ! [U_14503,U_14502,U_14501,U_14500] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14500,tc_HOL_Obool),tc_fun(U_14500,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14500,tc_HOL_Obool),tc_fun(U_14500,tc_HOL_Obool)),U_14501),U_14502)),c_Wellfounded_Omax__ext(U_14500,U_14503)))
      | ? [U_14499] :
          ( ! [U_14498] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14500,U_14500)),hAPP(hAPP(c_Product__Type_OPair(U_14500,U_14500),U_14499),U_14498)),U_14503))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14500),U_14498),U_14502)) )
          & hBOOL(hAPP(hAPP(c_member(U_14500),U_14499),U_14501)) )
      | U_14502 = c_Orderings_Obot__class_Obot(tc_fun(U_14500,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14500),U_14502))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14500),U_14501)) ),
    inference(variable_rename,[status(thm)],[f_3723_1]) ).

fof(f_3723_3,plain,
    ! [U_14503,U_14502,U_14501,U_14500] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14500,tc_HOL_Obool),tc_fun(U_14500,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14500,tc_HOL_Obool),tc_fun(U_14500,tc_HOL_Obool)),U_14501),U_14502)),c_Wellfounded_Omax__ext(U_14500,U_14503)))
      | ( ! [U_14498] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14500,U_14500)),hAPP(hAPP(c_Product__Type_OPair(U_14500,U_14500),sK324(U_14503,U_14502,U_14501,U_14500)),U_14498)),U_14503))
            | ~ hBOOL(hAPP(hAPP(c_member(U_14500),U_14498),U_14502)) )
        & hBOOL(hAPP(hAPP(c_member(U_14500),sK324(U_14503,U_14502,U_14501,U_14500)),U_14501)) )
      | U_14502 = c_Orderings_Obot__class_Obot(tc_fun(U_14500,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14500),U_14502))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14500),U_14501)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK324]),skolemize(U_14499,sK324(U_14503,U_14502,U_14501,U_14500))],[f_3723_2]) ).

fof(f_3723_4,plain,
    ( ! [U_14502,U_14501,U_14500,U_14498,U_14503] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14500,U_14500)),hAPP(hAPP(c_Product__Type_OPair(U_14500,U_14500),sK324(U_14503,U_14502,U_14501,U_14500)),U_14498)),U_14503))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14500),U_14498),U_14502))
        | ~ sP989(U_14502,U_14501,U_14500,U_14498,U_14503) )
    & ! [U_14502,U_14501,U_14500,U_14498,U_14503] :
        ( hBOOL(hAPP(hAPP(c_member(U_14500),sK324(U_14503,U_14502,U_14501,U_14500)),U_14501))
        | ~ sP989(U_14502,U_14501,U_14500,U_14498,U_14503) )
    & ! [U_14502,U_14501,U_14500,U_14498,U_14503] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14500,tc_HOL_Obool),tc_fun(U_14500,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14500,tc_HOL_Obool),tc_fun(U_14500,tc_HOL_Obool)),U_14501),U_14502)),c_Wellfounded_Omax__ext(U_14500,U_14503)))
        | sP989(U_14502,U_14501,U_14500,U_14498,U_14503)
        | U_14502 = c_Orderings_Obot__class_Obot(tc_fun(U_14500,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14500),U_14502))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14500),U_14501)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP989])],[f_3723_3]) ).

cnf(f_3723_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_14500,tc_HOL_Obool),tc_fun(U_14500,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_14500,tc_HOL_Obool),tc_fun(U_14500,tc_HOL_Obool)),U_14501),U_14502)),c_Wellfounded_Omax__ext(U_14500,U_14503)))
    | sP989(U_14502,U_14501,U_14500,U_14498,U_14503)
    | U_14502 = c_Orderings_Obot__class_Obot(tc_fun(U_14500,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14500),U_14502))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14500),U_14501)) ),
    inference(clausify,[status(thm)],[f_3723_4]) ).

cnf(f_3723_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14500),sK324(U_14503,U_14502,U_14501,U_14500)),U_14501))
    | ~ sP989(U_14502,U_14501,U_14500,U_14498,U_14503) ),
    inference(clausify,[status(thm)],[f_3723_4]) ).

cnf(f_3723_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14500,U_14500)),hAPP(hAPP(c_Product__Type_OPair(U_14500,U_14500),sK324(U_14503,U_14502,U_14501,U_14500)),U_14498)),U_14503))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14500),U_14498),U_14502))
    | ~ sP989(U_14502,U_14501,U_14500,U_14498,U_14503) ),
    inference(clausify,[status(thm)],[f_3723_4]) ).

fof(f_3724_1,plain,
    ! [V_Qa_2,V_Q_H_2,V_c_2,V_Pa_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_Pa_2),V_c_2),V_Qa_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_Qa_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_Pa_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_3724_2,plain,
    ! [U_14511,U_14510,U_14509,U_14508,U_14507,U_14506] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_14506,U_14507,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14506)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14506),U_14508),U_14509),U_14511)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14506),tc_HOL_Obool))))
      | ? [U_14505,U_14504] :
          ( ~ hBOOL(hAPP(hAPP(U_14511,U_14505),U_14504))
          & hBOOL(hAPP(hAPP(U_14510,U_14505),U_14504)) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_14506,U_14507,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14506)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14506),U_14508),U_14509),U_14510)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14506),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3724_1]) ).

fof(f_3724_3,plain,
    ! [U_14511,U_14510,U_14509,U_14508,U_14507,U_14506] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_14506,U_14507,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14506)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14506),U_14508),U_14509),U_14511)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14506),tc_HOL_Obool))))
      | ? [U_14504] :
          ( ~ hBOOL(hAPP(hAPP(U_14511,sK325(U_14511,U_14510,U_14509,U_14508,U_14507,U_14506)),U_14504))
          & hBOOL(hAPP(hAPP(U_14510,sK325(U_14511,U_14510,U_14509,U_14508,U_14507,U_14506)),U_14504)) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_14506,U_14507,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14506)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14506),U_14508),U_14509),U_14510)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14506),tc_HOL_Obool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK325]),skolemize(U_14505,sK325(U_14511,U_14510,U_14509,U_14508,U_14507,U_14506))],[f_3724_2]) ).

fof(f_3724_4,plain,
    ! [U_14511,U_14510,U_14509,U_14508,U_14507,U_14506] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_14506,U_14507,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14506)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14506),U_14508),U_14509),U_14511)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14506),tc_HOL_Obool))))
      | ( ~ hBOOL(hAPP(hAPP(U_14511,sK325(U_14511,U_14510,U_14509,U_14508,U_14507,U_14506)),sK326(U_14511,U_14510,U_14509,U_14508,U_14507,U_14506)))
        & hBOOL(hAPP(hAPP(U_14510,sK325(U_14511,U_14510,U_14509,U_14508,U_14507,U_14506)),sK326(U_14511,U_14510,U_14509,U_14508,U_14507,U_14506))) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_14506,U_14507,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14506)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14506),U_14508),U_14509),U_14510)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14506),tc_HOL_Obool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK326]),skolemize(U_14504,sK326(U_14511,U_14510,U_14509,U_14508,U_14507,U_14506))],[f_3724_3]) ).

fof(f_3724_5,plain,
    ( ! [U_14507,U_14509,U_14511,U_14506,U_14508,U_14510] :
        ( ~ hBOOL(hAPP(hAPP(U_14511,sK325(U_14511,U_14510,U_14509,U_14508,U_14507,U_14506)),sK326(U_14511,U_14510,U_14509,U_14508,U_14507,U_14506)))
        | ~ sP990(U_14507,U_14509,U_14511,U_14506,U_14508,U_14510) )
    & ! [U_14507,U_14509,U_14511,U_14506,U_14508,U_14510] :
        ( hBOOL(hAPP(hAPP(U_14510,sK325(U_14511,U_14510,U_14509,U_14508,U_14507,U_14506)),sK326(U_14511,U_14510,U_14509,U_14508,U_14507,U_14506)))
        | ~ sP990(U_14507,U_14509,U_14511,U_14506,U_14508,U_14510) )
    & ! [U_14507,U_14509,U_14511,U_14506,U_14508,U_14510] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(U_14506,U_14507,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14506)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14506),U_14508),U_14509),U_14511)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14506),tc_HOL_Obool))))
        | sP990(U_14507,U_14509,U_14511,U_14506,U_14508,U_14510)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_14506,U_14507,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14506)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14506),U_14508),U_14509),U_14510)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14506),tc_HOL_Obool)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP990])],[f_3724_4]) ).

cnf(f_3724_6,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_14506,U_14507,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14506)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14506),U_14508),U_14509),U_14511)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14506),tc_HOL_Obool))))
    | sP990(U_14507,U_14509,U_14511,U_14506,U_14508,U_14510)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_14506,U_14507,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14506)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14506),U_14508),U_14509),U_14510)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14506),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3724_5]) ).

cnf(f_3724_7,plain,
    ( hBOOL(hAPP(hAPP(U_14510,sK325(U_14511,U_14510,U_14509,U_14508,U_14507,U_14506)),sK326(U_14511,U_14510,U_14509,U_14508,U_14507,U_14506)))
    | ~ sP990(U_14507,U_14509,U_14511,U_14506,U_14508,U_14510) ),
    inference(clausify,[status(thm)],[f_3724_5]) ).

cnf(f_3724_8,plain,
    ( ~ hBOOL(hAPP(hAPP(U_14511,sK325(U_14511,U_14510,U_14509,U_14508,U_14507,U_14506)),sK326(U_14511,U_14510,U_14509,U_14508,U_14507,U_14506)))
    | ~ sP990(U_14507,U_14509,U_14511,U_14506,U_14508,U_14510) ),
    inference(clausify,[status(thm)],[f_3724_5]) ).

fof(f_3725_1,plain,
    ! [V_Pa_2,V_Qa_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_Pa_2),V_c_2),V_Qa_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_Pa_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_Qa_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_3725_2,plain,
    ! [U_14519,U_14518,U_14517,U_14516,U_14515,U_14514] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_14514,U_14515,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14514)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14514),U_14519),U_14517),U_14518)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14514),tc_HOL_Obool))))
      | ? [U_14513,U_14512] :
          ( ~ hBOOL(hAPP(hAPP(U_14516,U_14513),U_14512))
          & hBOOL(hAPP(hAPP(U_14519,U_14513),U_14512)) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_14514,U_14515,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14514)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14514),U_14516),U_14517),U_14518)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14514),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3725_1]) ).

fof(f_3725_3,plain,
    ! [U_14519,U_14518,U_14517,U_14516,U_14515,U_14514] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_14514,U_14515,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14514)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14514),U_14519),U_14517),U_14518)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14514),tc_HOL_Obool))))
      | ? [U_14512] :
          ( ~ hBOOL(hAPP(hAPP(U_14516,sK327(U_14519,U_14518,U_14517,U_14516,U_14515,U_14514)),U_14512))
          & hBOOL(hAPP(hAPP(U_14519,sK327(U_14519,U_14518,U_14517,U_14516,U_14515,U_14514)),U_14512)) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_14514,U_14515,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14514)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14514),U_14516),U_14517),U_14518)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14514),tc_HOL_Obool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK327]),skolemize(U_14513,sK327(U_14519,U_14518,U_14517,U_14516,U_14515,U_14514))],[f_3725_2]) ).

fof(f_3725_4,plain,
    ! [U_14519,U_14518,U_14517,U_14516,U_14515,U_14514] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_14514,U_14515,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14514)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14514),U_14519),U_14517),U_14518)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14514),tc_HOL_Obool))))
      | ( ~ hBOOL(hAPP(hAPP(U_14516,sK327(U_14519,U_14518,U_14517,U_14516,U_14515,U_14514)),sK328(U_14519,U_14518,U_14517,U_14516,U_14515,U_14514)))
        & hBOOL(hAPP(hAPP(U_14519,sK327(U_14519,U_14518,U_14517,U_14516,U_14515,U_14514)),sK328(U_14519,U_14518,U_14517,U_14516,U_14515,U_14514))) )
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_14514,U_14515,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14514)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14514),U_14516),U_14517),U_14518)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14514),tc_HOL_Obool)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK328]),skolemize(U_14512,sK328(U_14519,U_14518,U_14517,U_14516,U_14515,U_14514))],[f_3725_3]) ).

fof(f_3725_5,plain,
    ( ! [U_14515,U_14516,U_14514,U_14517,U_14518,U_14519] :
        ( ~ hBOOL(hAPP(hAPP(U_14516,sK327(U_14519,U_14518,U_14517,U_14516,U_14515,U_14514)),sK328(U_14519,U_14518,U_14517,U_14516,U_14515,U_14514)))
        | ~ sP991(U_14515,U_14516,U_14514,U_14517,U_14518,U_14519) )
    & ! [U_14515,U_14516,U_14514,U_14517,U_14518,U_14519] :
        ( hBOOL(hAPP(hAPP(U_14519,sK327(U_14519,U_14518,U_14517,U_14516,U_14515,U_14514)),sK328(U_14519,U_14518,U_14517,U_14516,U_14515,U_14514)))
        | ~ sP991(U_14515,U_14516,U_14514,U_14517,U_14518,U_14519) )
    & ! [U_14515,U_14516,U_14514,U_14517,U_14518,U_14519] :
        ( c_Hoare__Mirabelle_Ohoare__derivs(U_14514,U_14515,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14514)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14514),U_14519),U_14517),U_14518)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14514),tc_HOL_Obool))))
        | sP991(U_14515,U_14516,U_14514,U_14517,U_14518,U_14519)
        | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_14514,U_14515,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14514)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14514),U_14516),U_14517),U_14518)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14514),tc_HOL_Obool)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP991])],[f_3725_4]) ).

cnf(f_3725_6,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_14514,U_14515,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14514)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14514),U_14519),U_14517),U_14518)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14514),tc_HOL_Obool))))
    | sP991(U_14515,U_14516,U_14514,U_14517,U_14518,U_14519)
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_14514,U_14515,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_14514)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_14514),U_14516),U_14517),U_14518)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_14514),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3725_5]) ).

cnf(f_3725_7,plain,
    ( hBOOL(hAPP(hAPP(U_14519,sK327(U_14519,U_14518,U_14517,U_14516,U_14515,U_14514)),sK328(U_14519,U_14518,U_14517,U_14516,U_14515,U_14514)))
    | ~ sP991(U_14515,U_14516,U_14514,U_14517,U_14518,U_14519) ),
    inference(clausify,[status(thm)],[f_3725_5]) ).

cnf(f_3725_8,plain,
    ( ~ hBOOL(hAPP(hAPP(U_14516,sK327(U_14519,U_14518,U_14517,U_14516,U_14515,U_14514)),sK328(U_14519,U_14518,U_14517,U_14516,U_14515,U_14514)))
    | ~ sP991(U_14515,U_14516,U_14514,U_14517,U_14518,U_14519) ),
    inference(clausify,[status(thm)],[f_3725_5]) ).

fof(f_3726_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_3726_2,plain,
    ! [U_14526,U_14525,U_14524,U_14523,U_14522] :
      ( ? [U_14521,U_14520] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_14522),U_14521),U_14520))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14522,U_14522,U_14523,U_14521,U_14520),U_14526))
          & hAPP(hAPP(c_Set_Oinsert(U_14522),U_14524),U_14525) = hAPP(hAPP(c_Set_Oinsert(U_14522),U_14521),U_14520) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14522,U_14523,hAPP(hAPP(c_Set_Oinsert(U_14522),U_14524),U_14525)),U_14526)) ),
    inference(variable_rename,[status(thm)],[f_3726_1]) ).

fof(f_3726_3,plain,
    ! [U_14526,U_14525,U_14524,U_14523,U_14522] :
      ( ? [U_14520] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_14522),sK329(U_14526,U_14525,U_14524,U_14523,U_14522)),U_14520))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14522,U_14522,U_14523,sK329(U_14526,U_14525,U_14524,U_14523,U_14522),U_14520),U_14526))
          & hAPP(hAPP(c_Set_Oinsert(U_14522),U_14524),U_14525) = hAPP(hAPP(c_Set_Oinsert(U_14522),sK329(U_14526,U_14525,U_14524,U_14523,U_14522)),U_14520) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14522,U_14523,hAPP(hAPP(c_Set_Oinsert(U_14522),U_14524),U_14525)),U_14526)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK329]),skolemize(U_14521,sK329(U_14526,U_14525,U_14524,U_14523,U_14522))],[f_3726_2]) ).

fof(f_3726_4,plain,
    ! [U_14526,U_14525,U_14524,U_14523,U_14522] :
      ( ( ~ hBOOL(hAPP(hAPP(c_member(U_14522),sK329(U_14526,U_14525,U_14524,U_14523,U_14522)),sK330(U_14526,U_14525,U_14524,U_14523,U_14522)))
        & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14522,U_14522,U_14523,sK329(U_14526,U_14525,U_14524,U_14523,U_14522),sK330(U_14526,U_14525,U_14524,U_14523,U_14522)),U_14526))
        & hAPP(hAPP(c_Set_Oinsert(U_14522),U_14524),U_14525) = hAPP(hAPP(c_Set_Oinsert(U_14522),sK329(U_14526,U_14525,U_14524,U_14523,U_14522)),sK330(U_14526,U_14525,U_14524,U_14523,U_14522)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14522,U_14523,hAPP(hAPP(c_Set_Oinsert(U_14522),U_14524),U_14525)),U_14526)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK330]),skolemize(U_14520,sK330(U_14526,U_14525,U_14524,U_14523,U_14522))],[f_3726_3]) ).

fof(f_3726_5,plain,
    ( ! [U_14522,U_14523,U_14524,U_14525,U_14526] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_14522),sK329(U_14526,U_14525,U_14524,U_14523,U_14522)),sK330(U_14526,U_14525,U_14524,U_14523,U_14522)))
        | ~ sP992(U_14522,U_14523,U_14524,U_14525,U_14526) )
    & ! [U_14522,U_14523,U_14524,U_14525,U_14526] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14522,U_14522,U_14523,sK329(U_14526,U_14525,U_14524,U_14523,U_14522),sK330(U_14526,U_14525,U_14524,U_14523,U_14522)),U_14526))
        | ~ sP992(U_14522,U_14523,U_14524,U_14525,U_14526) )
    & ! [U_14522,U_14523,U_14524,U_14525,U_14526] :
        ( hAPP(hAPP(c_Set_Oinsert(U_14522),U_14524),U_14525) = hAPP(hAPP(c_Set_Oinsert(U_14522),sK329(U_14526,U_14525,U_14524,U_14523,U_14522)),sK330(U_14526,U_14525,U_14524,U_14523,U_14522))
        | ~ sP992(U_14522,U_14523,U_14524,U_14525,U_14526) )
    & ! [U_14522,U_14523,U_14524,U_14525,U_14526] :
        ( sP992(U_14522,U_14523,U_14524,U_14525,U_14526)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14522,U_14523,hAPP(hAPP(c_Set_Oinsert(U_14522),U_14524),U_14525)),U_14526)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP992])],[f_3726_4]) ).

cnf(f_3726_6,plain,
    ( sP992(U_14522,U_14523,U_14524,U_14525,U_14526)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14522,U_14523,hAPP(hAPP(c_Set_Oinsert(U_14522),U_14524),U_14525)),U_14526)) ),
    inference(clausify,[status(thm)],[f_3726_5]) ).

cnf(f_3726_7,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_14522),U_14524),U_14525) = hAPP(hAPP(c_Set_Oinsert(U_14522),sK329(U_14526,U_14525,U_14524,U_14523,U_14522)),sK330(U_14526,U_14525,U_14524,U_14523,U_14522))
    | ~ sP992(U_14522,U_14523,U_14524,U_14525,U_14526) ),
    inference(clausify,[status(thm)],[f_3726_5]) ).

cnf(f_3726_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14522,U_14522,U_14523,sK329(U_14526,U_14525,U_14524,U_14523,U_14522),sK330(U_14526,U_14525,U_14524,U_14523,U_14522)),U_14526))
    | ~ sP992(U_14522,U_14523,U_14524,U_14525,U_14526) ),
    inference(clausify,[status(thm)],[f_3726_5]) ).

cnf(f_3726_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_14522),sK329(U_14526,U_14525,U_14524,U_14523,U_14522)),sK330(U_14526,U_14525,U_14524,U_14523,U_14522)))
    | ~ sP992(U_14522,U_14523,U_14524,U_14525,U_14526) ),
    inference(clausify,[status(thm)],[f_3726_5]) ).

fof(f_3727_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_3727_2,plain,
    ! [U_14535,U_14534,U_14533,U_14532,U_14531] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14531,U_14532,hAPP(hAPP(c_Set_Oinsert(U_14531),U_14533),U_14534)),U_14535))
        | ! [U_14530,U_14529] :
            ( hBOOL(hAPP(hAPP(c_member(U_14531),U_14530),U_14529))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14531,U_14531,U_14532,U_14530,U_14529),U_14535))
            | hAPP(hAPP(c_Set_Oinsert(U_14531),U_14533),U_14534) != hAPP(hAPP(c_Set_Oinsert(U_14531),U_14530),U_14529) ) )
      & ( ? [U_14528,U_14527] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_14531),U_14528),U_14527))
            & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14531,U_14531,U_14532,U_14528,U_14527),U_14535))
            & hAPP(hAPP(c_Set_Oinsert(U_14531),U_14533),U_14534) = hAPP(hAPP(c_Set_Oinsert(U_14531),U_14528),U_14527) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14531,U_14532,hAPP(hAPP(c_Set_Oinsert(U_14531),U_14533),U_14534)),U_14535)) ) ),
    inference(variable_rename,[status(thm)],[f_3727_1]) ).

fof(f_3727_3,plain,
    ( ! [U_14545,U_14543,U_14541,U_14539,U_14537] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14537,U_14539,hAPP(hAPP(c_Set_Oinsert(U_14537),U_14541),U_14543)),U_14545))
        | ! [U_14530,U_14529] :
            ( hBOOL(hAPP(hAPP(c_member(U_14537),U_14530),U_14529))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14537,U_14537,U_14539,U_14530,U_14529),U_14545))
            | hAPP(hAPP(c_Set_Oinsert(U_14537),U_14541),U_14543) != hAPP(hAPP(c_Set_Oinsert(U_14537),U_14530),U_14529) ) )
    & ! [U_14544,U_14542,U_14540,U_14538,U_14536] :
        ( ? [U_14528,U_14527] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_14536),U_14528),U_14527))
            & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14536,U_14536,U_14538,U_14528,U_14527),U_14544))
            & hAPP(hAPP(c_Set_Oinsert(U_14536),U_14540),U_14542) = hAPP(hAPP(c_Set_Oinsert(U_14536),U_14528),U_14527) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14536,U_14538,hAPP(hAPP(c_Set_Oinsert(U_14536),U_14540),U_14542)),U_14544)) ) ),
    inference(miniscope,[status(thm)],[f_3727_2]) ).

fof(f_3727_4,plain,
    ( ! [U_14545,U_14543,U_14541,U_14539,U_14537] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14537,U_14539,hAPP(hAPP(c_Set_Oinsert(U_14537),U_14541),U_14543)),U_14545))
        | ! [U_14530,U_14529] :
            ( hBOOL(hAPP(hAPP(c_member(U_14537),U_14530),U_14529))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14537,U_14537,U_14539,U_14530,U_14529),U_14545))
            | hAPP(hAPP(c_Set_Oinsert(U_14537),U_14541),U_14543) != hAPP(hAPP(c_Set_Oinsert(U_14537),U_14530),U_14529) ) )
    & ! [U_14544,U_14542,U_14540,U_14538,U_14536] :
        ( ? [U_14527] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_14536),sK331(U_14544,U_14542,U_14540,U_14538,U_14536)),U_14527))
            & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14536,U_14536,U_14538,sK331(U_14544,U_14542,U_14540,U_14538,U_14536),U_14527),U_14544))
            & hAPP(hAPP(c_Set_Oinsert(U_14536),U_14540),U_14542) = hAPP(hAPP(c_Set_Oinsert(U_14536),sK331(U_14544,U_14542,U_14540,U_14538,U_14536)),U_14527) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14536,U_14538,hAPP(hAPP(c_Set_Oinsert(U_14536),U_14540),U_14542)),U_14544)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK331]),skolemize(U_14528,sK331(U_14544,U_14542,U_14540,U_14538,U_14536))],[f_3727_3]) ).

fof(f_3727_5,plain,
    ( ! [U_14545,U_14543,U_14541,U_14539,U_14537] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14537,U_14539,hAPP(hAPP(c_Set_Oinsert(U_14537),U_14541),U_14543)),U_14545))
        | ! [U_14530,U_14529] :
            ( hBOOL(hAPP(hAPP(c_member(U_14537),U_14530),U_14529))
            | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14537,U_14537,U_14539,U_14530,U_14529),U_14545))
            | hAPP(hAPP(c_Set_Oinsert(U_14537),U_14541),U_14543) != hAPP(hAPP(c_Set_Oinsert(U_14537),U_14530),U_14529) ) )
    & ! [U_14544,U_14542,U_14540,U_14538,U_14536] :
        ( ( ~ hBOOL(hAPP(hAPP(c_member(U_14536),sK331(U_14544,U_14542,U_14540,U_14538,U_14536)),sK332(U_14544,U_14542,U_14540,U_14538,U_14536)))
          & hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14536,U_14536,U_14538,sK331(U_14544,U_14542,U_14540,U_14538,U_14536),sK332(U_14544,U_14542,U_14540,U_14538,U_14536)),U_14544))
          & hAPP(hAPP(c_Set_Oinsert(U_14536),U_14540),U_14542) = hAPP(hAPP(c_Set_Oinsert(U_14536),sK331(U_14544,U_14542,U_14540,U_14538,U_14536)),sK332(U_14544,U_14542,U_14540,U_14538,U_14536)) )
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14536,U_14538,hAPP(hAPP(c_Set_Oinsert(U_14536),U_14540),U_14542)),U_14544)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK332]),skolemize(U_14527,sK332(U_14544,U_14542,U_14540,U_14538,U_14536))],[f_3727_4]) ).

fof(f_3727_6,plain,
    ( ! [U_14538,U_14542,U_14536,U_14540,U_14544] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_14536),sK331(U_14544,U_14542,U_14540,U_14538,U_14536)),sK332(U_14544,U_14542,U_14540,U_14538,U_14536)))
        | ~ sP993(U_14538,U_14542,U_14536,U_14540,U_14544) )
    & ! [U_14538,U_14542,U_14536,U_14540,U_14544] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14536,U_14536,U_14538,sK331(U_14544,U_14542,U_14540,U_14538,U_14536),sK332(U_14544,U_14542,U_14540,U_14538,U_14536)),U_14544))
        | ~ sP993(U_14538,U_14542,U_14536,U_14540,U_14544) )
    & ! [U_14538,U_14542,U_14536,U_14540,U_14544] :
        ( hAPP(hAPP(c_Set_Oinsert(U_14536),U_14540),U_14542) = hAPP(hAPP(c_Set_Oinsert(U_14536),sK331(U_14544,U_14542,U_14540,U_14538,U_14536)),sK332(U_14544,U_14542,U_14540,U_14538,U_14536))
        | ~ sP993(U_14538,U_14542,U_14536,U_14540,U_14544) )
    & ! [U_14529,U_14530,U_14543,U_14537,U_14539,U_14541,U_14545] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14537,U_14539,hAPP(hAPP(c_Set_Oinsert(U_14537),U_14541),U_14543)),U_14545))
        | hBOOL(hAPP(hAPP(c_member(U_14537),U_14530),U_14529))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14537,U_14537,U_14539,U_14530,U_14529),U_14545))
        | hAPP(hAPP(c_Set_Oinsert(U_14537),U_14541),U_14543) != hAPP(hAPP(c_Set_Oinsert(U_14537),U_14530),U_14529) )
    & ! [U_14538,U_14542,U_14536,U_14540,U_14544] :
        ( sP993(U_14538,U_14542,U_14536,U_14540,U_14544)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14536,U_14538,hAPP(hAPP(c_Set_Oinsert(U_14536),U_14540),U_14542)),U_14544)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP993])],[f_3727_5]) ).

cnf(f_3727_7,plain,
    ( sP993(U_14538,U_14542,U_14536,U_14540,U_14544)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14536,U_14538,hAPP(hAPP(c_Set_Oinsert(U_14536),U_14540),U_14542)),U_14544)) ),
    inference(clausify,[status(thm)],[f_3727_6]) ).

cnf(f_3727_8,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(U_14537,U_14539,hAPP(hAPP(c_Set_Oinsert(U_14537),U_14541),U_14543)),U_14545))
    | hBOOL(hAPP(hAPP(c_member(U_14537),U_14530),U_14529))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14537,U_14537,U_14539,U_14530,U_14529),U_14545))
    | hAPP(hAPP(c_Set_Oinsert(U_14537),U_14541),U_14543) != hAPP(hAPP(c_Set_Oinsert(U_14537),U_14530),U_14529) ),
    inference(clausify,[status(thm)],[f_3727_6]) ).

cnf(f_3727_9,plain,
    ( hAPP(hAPP(c_Set_Oinsert(U_14536),U_14540),U_14542) = hAPP(hAPP(c_Set_Oinsert(U_14536),sK331(U_14544,U_14542,U_14540,U_14538,U_14536)),sK332(U_14544,U_14542,U_14540,U_14538,U_14536))
    | ~ sP993(U_14538,U_14542,U_14536,U_14540,U_14544) ),
    inference(clausify,[status(thm)],[f_3727_6]) ).

cnf(f_3727_10,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_14536,U_14536,U_14538,sK331(U_14544,U_14542,U_14540,U_14538,U_14536),sK332(U_14544,U_14542,U_14540,U_14538,U_14536)),U_14544))
    | ~ sP993(U_14538,U_14542,U_14536,U_14540,U_14544) ),
    inference(clausify,[status(thm)],[f_3727_6]) ).

cnf(f_3727_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_14536),sK331(U_14544,U_14542,U_14540,U_14538,U_14536)),sK332(U_14544,U_14542,U_14540,U_14538,U_14536)))
    | ~ sP993(U_14538,U_14542,U_14536,U_14540,U_14544) ),
    inference(clausify,[status(thm)],[f_3727_6]) ).

fof(f_3728_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_3728_2,plain,
    ! [U_14551,U_14550,U_14549,U_14548,U_14547,U_14546] : hAPP(c_Set_Oimage(U_14546,tc_prod(U_14547,U_14548),hAPP(hAPP(c_COMBS(U_14546,U_14548,tc_prod(U_14547,U_14548)),hAPP(hAPP(c_COMBB(U_14547,tc_fun(U_14548,tc_prod(U_14547,U_14548)),U_14546),c_Product__Type_OPair(U_14547,U_14548)),U_14549)),U_14550)),U_14551) = hAPP(hAPP(c_Product__Type_OSigma(U_14547,U_14548),hAPP(c_Set_Oimage(U_14546,U_14547,U_14549),U_14551)),hAPP(hAPP(c_COMBB(tc_fun(U_14546,tc_HOL_Obool),tc_fun(U_14548,tc_HOL_Obool),U_14547),c_Set_Oimage(U_14546,U_14548,U_14550)),hAPP(hAPP(c_COMBC(U_14547,tc_fun(U_14546,tc_HOL_Obool),tc_fun(U_14546,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14546,tc_HOL_Obool),tc_fun(tc_fun(U_14546,tc_HOL_Obool),tc_fun(U_14546,tc_HOL_Obool)),U_14547),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14546,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14547,tc_HOL_Obool),tc_fun(U_14546,tc_HOL_Obool),U_14547),c_Set_Ovimage(U_14546,U_14547,U_14549)),hAPP(hAPP(c_COMBC(U_14547,tc_fun(U_14547,tc_HOL_Obool),tc_fun(U_14547,tc_HOL_Obool)),c_Set_Oinsert(U_14547)),c_Orderings_Obot__class_Obot(tc_fun(U_14547,tc_HOL_Obool)))))),U_14551))),
    inference(variable_rename,[status(thm)],[f_3728_1]) ).

fof(f_3728_3,plain,
    ! [U_14547,U_14546,U_14548,U_14549,U_14550,U_14551] : hAPP(c_Set_Oimage(U_14546,tc_prod(U_14547,U_14548),hAPP(hAPP(c_COMBS(U_14546,U_14548,tc_prod(U_14547,U_14548)),hAPP(hAPP(c_COMBB(U_14547,tc_fun(U_14548,tc_prod(U_14547,U_14548)),U_14546),c_Product__Type_OPair(U_14547,U_14548)),U_14549)),U_14550)),U_14551) = hAPP(hAPP(c_Product__Type_OSigma(U_14547,U_14548),hAPP(c_Set_Oimage(U_14546,U_14547,U_14549),U_14551)),hAPP(hAPP(c_COMBB(tc_fun(U_14546,tc_HOL_Obool),tc_fun(U_14548,tc_HOL_Obool),U_14547),c_Set_Oimage(U_14546,U_14548,U_14550)),hAPP(hAPP(c_COMBC(U_14547,tc_fun(U_14546,tc_HOL_Obool),tc_fun(U_14546,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14546,tc_HOL_Obool),tc_fun(tc_fun(U_14546,tc_HOL_Obool),tc_fun(U_14546,tc_HOL_Obool)),U_14547),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14546,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14547,tc_HOL_Obool),tc_fun(U_14546,tc_HOL_Obool),U_14547),c_Set_Ovimage(U_14546,U_14547,U_14549)),hAPP(hAPP(c_COMBC(U_14547,tc_fun(U_14547,tc_HOL_Obool),tc_fun(U_14547,tc_HOL_Obool)),c_Set_Oinsert(U_14547)),c_Orderings_Obot__class_Obot(tc_fun(U_14547,tc_HOL_Obool)))))),U_14551))),
    inference(definitional_conversion,[status(esa)],[f_3728_2]) ).

cnf(f_3728_4,plain,
    hAPP(c_Set_Oimage(U_14546,tc_prod(U_14547,U_14548),hAPP(hAPP(c_COMBS(U_14546,U_14548,tc_prod(U_14547,U_14548)),hAPP(hAPP(c_COMBB(U_14547,tc_fun(U_14548,tc_prod(U_14547,U_14548)),U_14546),c_Product__Type_OPair(U_14547,U_14548)),U_14549)),U_14550)),U_14551) = hAPP(hAPP(c_Product__Type_OSigma(U_14547,U_14548),hAPP(c_Set_Oimage(U_14546,U_14547,U_14549),U_14551)),hAPP(hAPP(c_COMBB(tc_fun(U_14546,tc_HOL_Obool),tc_fun(U_14548,tc_HOL_Obool),U_14547),c_Set_Oimage(U_14546,U_14548,U_14550)),hAPP(hAPP(c_COMBC(U_14547,tc_fun(U_14546,tc_HOL_Obool),tc_fun(U_14546,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14546,tc_HOL_Obool),tc_fun(tc_fun(U_14546,tc_HOL_Obool),tc_fun(U_14546,tc_HOL_Obool)),U_14547),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14546,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14547,tc_HOL_Obool),tc_fun(U_14546,tc_HOL_Obool),U_14547),c_Set_Ovimage(U_14546,U_14547,U_14549)),hAPP(hAPP(c_COMBC(U_14547,tc_fun(U_14547,tc_HOL_Obool),tc_fun(U_14547,tc_HOL_Obool)),c_Set_Oinsert(U_14547)),c_Orderings_Obot__class_Obot(tc_fun(U_14547,tc_HOL_Obool)))))),U_14551))),
    inference(clausify,[status(thm)],[f_3728_3]) ).

fof(f_3729_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_3729_2,plain,
    ! [U_14554,U_14553,U_14552] :
      ( hAPP(c_Finite__Set_Ofold1(U_14552,c_Groups_Otimes__class_Otimes(U_14552)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14552,tc_HOL_Obool)),U_14553),U_14554)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14552),hAPP(c_Finite__Set_Ofold1(U_14552,c_Groups_Otimes__class_Otimes(U_14552)),U_14553)),hAPP(c_Finite__Set_Ofold1(U_14552,c_Groups_Otimes__class_Otimes(U_14552)),U_14554))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14552,tc_HOL_Obool)),U_14553),U_14554) != c_Orderings_Obot__class_Obot(tc_fun(U_14552,tc_HOL_Obool))
      | U_14554 = c_Orderings_Obot__class_Obot(tc_fun(U_14552,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14552),U_14554))
      | U_14553 = c_Orderings_Obot__class_Obot(tc_fun(U_14552,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14552),U_14553))
      | ~ class_Groups_Oab__semigroup__mult(U_14552) ),
    inference(variable_rename,[status(thm)],[f_3729_1]) ).

fof(f_3729_3,plain,
    ! [U_14552,U_14553,U_14554] :
      ( hAPP(c_Finite__Set_Ofold1(U_14552,c_Groups_Otimes__class_Otimes(U_14552)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14552,tc_HOL_Obool)),U_14553),U_14554)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14552),hAPP(c_Finite__Set_Ofold1(U_14552,c_Groups_Otimes__class_Otimes(U_14552)),U_14553)),hAPP(c_Finite__Set_Ofold1(U_14552,c_Groups_Otimes__class_Otimes(U_14552)),U_14554))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14552,tc_HOL_Obool)),U_14553),U_14554) != c_Orderings_Obot__class_Obot(tc_fun(U_14552,tc_HOL_Obool))
      | U_14554 = c_Orderings_Obot__class_Obot(tc_fun(U_14552,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14552),U_14554))
      | U_14553 = c_Orderings_Obot__class_Obot(tc_fun(U_14552,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14552),U_14553))
      | ~ class_Groups_Oab__semigroup__mult(U_14552) ),
    inference(definitional_conversion,[status(esa)],[f_3729_2]) ).

cnf(f_3729_4,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_14552,c_Groups_Otimes__class_Otimes(U_14552)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14552,tc_HOL_Obool)),U_14553),U_14554)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14552),hAPP(c_Finite__Set_Ofold1(U_14552,c_Groups_Otimes__class_Otimes(U_14552)),U_14553)),hAPP(c_Finite__Set_Ofold1(U_14552,c_Groups_Otimes__class_Otimes(U_14552)),U_14554))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14552,tc_HOL_Obool)),U_14553),U_14554) != c_Orderings_Obot__class_Obot(tc_fun(U_14552,tc_HOL_Obool))
    | U_14554 = c_Orderings_Obot__class_Obot(tc_fun(U_14552,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14552),U_14554))
    | U_14553 = c_Orderings_Obot__class_Obot(tc_fun(U_14552,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14552),U_14553))
    | ~ class_Groups_Oab__semigroup__mult(U_14552) ),
    inference(clausify,[status(thm)],[f_3729_3]) ).

fof(f_3730_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_3730_2,plain,
    ! [U_14560,U_14559,U_14558,U_14557,U_14556,U_14555] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14555,U_14558)),hAPP(hAPP(c_Product__Type_OPair(U_14555,U_14558),U_14556),U_14559)),hAPP(hAPP(c_Product__Type_OSigma(U_14555,U_14558),U_14557),U_14560)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14558),U_14559),hAPP(U_14560,U_14556)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14555),U_14556),U_14557)) ),
    inference(variable_rename,[status(thm)],[f_3730_1]) ).

fof(f_3730_3,plain,
    ! [U_14556,U_14555,U_14557,U_14558,U_14559,U_14560] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14555,U_14558)),hAPP(hAPP(c_Product__Type_OPair(U_14555,U_14558),U_14556),U_14559)),hAPP(hAPP(c_Product__Type_OSigma(U_14555,U_14558),U_14557),U_14560)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14558),U_14559),hAPP(U_14560,U_14556)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14555),U_14556),U_14557)) ),
    inference(definitional_conversion,[status(esa)],[f_3730_2]) ).

cnf(f_3730_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14555,U_14558)),hAPP(hAPP(c_Product__Type_OPair(U_14555,U_14558),U_14556),U_14559)),hAPP(hAPP(c_Product__Type_OSigma(U_14555,U_14558),U_14557),U_14560)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14558),U_14559),hAPP(U_14560,U_14556)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14555),U_14556),U_14557)) ),
    inference(clausify,[status(thm)],[f_3730_3]) ).

fof(f_3731_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_3731_2,plain,
    ! [U_14568,U_14567,U_14566,U_14565,U_14564,U_14563,U_14562,U_14561] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14561,U_14566),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14561,U_14562,U_14566),U_14563),U_14567)),hAPP(hAPP(c_Product__Type_OSigma(U_14561,U_14566),U_14564),hAPP(c_COMBK(tc_fun(U_14566,tc_HOL_Obool),U_14561),U_14568))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14562,U_14566),tc_HOL_Obool)),U_14567),hAPP(hAPP(c_Product__Type_OSigma(U_14562,U_14566),U_14565),hAPP(c_COMBK(tc_fun(U_14566,tc_HOL_Obool),U_14562),U_14568))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14561,U_14562),tc_HOL_Obool)),U_14563),hAPP(hAPP(c_Product__Type_OSigma(U_14561,U_14562),U_14564),hAPP(c_COMBK(tc_fun(U_14562,tc_HOL_Obool),U_14561),U_14565)))) ),
    inference(variable_rename,[status(thm)],[f_3731_1]) ).

fof(f_3731_3,plain,
    ! [U_14561,U_14562,U_14563,U_14564,U_14565,U_14566,U_14567,U_14568] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14561,U_14566),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14561,U_14562,U_14566),U_14563),U_14567)),hAPP(hAPP(c_Product__Type_OSigma(U_14561,U_14566),U_14564),hAPP(c_COMBK(tc_fun(U_14566,tc_HOL_Obool),U_14561),U_14568))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14562,U_14566),tc_HOL_Obool)),U_14567),hAPP(hAPP(c_Product__Type_OSigma(U_14562,U_14566),U_14565),hAPP(c_COMBK(tc_fun(U_14566,tc_HOL_Obool),U_14562),U_14568))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14561,U_14562),tc_HOL_Obool)),U_14563),hAPP(hAPP(c_Product__Type_OSigma(U_14561,U_14562),U_14564),hAPP(c_COMBK(tc_fun(U_14562,tc_HOL_Obool),U_14561),U_14565)))) ),
    inference(definitional_conversion,[status(esa)],[f_3731_2]) ).

cnf(f_3731_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14561,U_14566),tc_HOL_Obool)),hAPP(hAPP(c_Relation_Orel__comp(U_14561,U_14562,U_14566),U_14563),U_14567)),hAPP(hAPP(c_Product__Type_OSigma(U_14561,U_14566),U_14564),hAPP(c_COMBK(tc_fun(U_14566,tc_HOL_Obool),U_14561),U_14568))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14562,U_14566),tc_HOL_Obool)),U_14567),hAPP(hAPP(c_Product__Type_OSigma(U_14562,U_14566),U_14565),hAPP(c_COMBK(tc_fun(U_14566,tc_HOL_Obool),U_14562),U_14568))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14561,U_14562),tc_HOL_Obool)),U_14563),hAPP(hAPP(c_Product__Type_OSigma(U_14561,U_14562),U_14564),hAPP(c_COMBK(tc_fun(U_14562,tc_HOL_Obool),U_14561),U_14565)))) ),
    inference(clausify,[status(thm)],[f_3731_3]) ).

fof(f_3732_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_3732_2,plain,
    ! [U_14572,U_14571,U_14570,U_14569] : hAPP(c_Set_Oimage(tc_prod(U_14569,U_14570),tc_prod(U_14570,U_14569),hAPP(c_Product__Type_Oprod_Oprod__case(U_14569,U_14570,tc_prod(U_14570,U_14569)),hAPP(c_COMBC(U_14570,U_14569,tc_prod(U_14570,U_14569)),c_Product__Type_OPair(U_14570,U_14569)))),hAPP(hAPP(c_Product__Type_OSigma(U_14569,U_14570),U_14571),hAPP(c_COMBK(tc_fun(U_14570,tc_HOL_Obool),U_14569),U_14572))) = hAPP(hAPP(c_Product__Type_OSigma(U_14570,U_14569),U_14572),hAPP(c_COMBK(tc_fun(U_14569,tc_HOL_Obool),U_14570),U_14571)),
    inference(variable_rename,[status(thm)],[f_3732_1]) ).

fof(f_3732_3,plain,
    ! [U_14569,U_14570,U_14571,U_14572] : hAPP(c_Set_Oimage(tc_prod(U_14569,U_14570),tc_prod(U_14570,U_14569),hAPP(c_Product__Type_Oprod_Oprod__case(U_14569,U_14570,tc_prod(U_14570,U_14569)),hAPP(c_COMBC(U_14570,U_14569,tc_prod(U_14570,U_14569)),c_Product__Type_OPair(U_14570,U_14569)))),hAPP(hAPP(c_Product__Type_OSigma(U_14569,U_14570),U_14571),hAPP(c_COMBK(tc_fun(U_14570,tc_HOL_Obool),U_14569),U_14572))) = hAPP(hAPP(c_Product__Type_OSigma(U_14570,U_14569),U_14572),hAPP(c_COMBK(tc_fun(U_14569,tc_HOL_Obool),U_14570),U_14571)),
    inference(definitional_conversion,[status(esa)],[f_3732_2]) ).

cnf(f_3732_4,plain,
    hAPP(c_Set_Oimage(tc_prod(U_14569,U_14570),tc_prod(U_14570,U_14569),hAPP(c_Product__Type_Oprod_Oprod__case(U_14569,U_14570,tc_prod(U_14570,U_14569)),hAPP(c_COMBC(U_14570,U_14569,tc_prod(U_14570,U_14569)),c_Product__Type_OPair(U_14570,U_14569)))),hAPP(hAPP(c_Product__Type_OSigma(U_14569,U_14570),U_14571),hAPP(c_COMBK(tc_fun(U_14570,tc_HOL_Obool),U_14569),U_14572))) = hAPP(hAPP(c_Product__Type_OSigma(U_14570,U_14569),U_14572),hAPP(c_COMBK(tc_fun(U_14569,tc_HOL_Obool),U_14570),U_14571)),
    inference(clausify,[status(thm)],[f_3732_3]) ).

fof(f_3733_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_3733_2,plain,
    ! [U_14575,U_14574,U_14573] : hAPP(c_Finite__Set_Ofold1(U_14573,U_14574),hAPP(hAPP(c_Set_Oinsert(U_14573),U_14575),c_Orderings_Obot__class_Obot(tc_fun(U_14573,tc_HOL_Obool)))) = U_14575,
    inference(variable_rename,[status(thm)],[f_3733_1]) ).

fof(f_3733_3,plain,
    ! [U_14573,U_14574,U_14575] : hAPP(c_Finite__Set_Ofold1(U_14573,U_14574),hAPP(hAPP(c_Set_Oinsert(U_14573),U_14575),c_Orderings_Obot__class_Obot(tc_fun(U_14573,tc_HOL_Obool)))) = U_14575,
    inference(definitional_conversion,[status(esa)],[f_3733_2]) ).

cnf(f_3733_4,plain,
    hAPP(c_Finite__Set_Ofold1(U_14573,U_14574),hAPP(hAPP(c_Set_Oinsert(U_14573),U_14575),c_Orderings_Obot__class_Obot(tc_fun(U_14573,tc_HOL_Obool)))) = U_14575,
    inference(clausify,[status(thm)],[f_3733_3]) ).

fof(f_3734_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_3734_2,plain,
    ! [U_14579,U_14578,U_14577,U_14576] :
      ( hAPP(U_14576,hAPP(hAPP(c_Set_Oinsert(U_14577),U_14579),c_Orderings_Obot__class_Obot(tc_fun(U_14577,tc_HOL_Obool)))) = U_14579
      | U_14576 != c_Finite__Set_Ofold1(U_14577,U_14578) ),
    inference(variable_rename,[status(thm)],[f_3734_1]) ).

fof(f_3734_3,plain,
    ! [U_14576,U_14577,U_14578,U_14579] :
      ( hAPP(U_14576,hAPP(hAPP(c_Set_Oinsert(U_14577),U_14579),c_Orderings_Obot__class_Obot(tc_fun(U_14577,tc_HOL_Obool)))) = U_14579
      | U_14576 != c_Finite__Set_Ofold1(U_14577,U_14578) ),
    inference(definitional_conversion,[status(esa)],[f_3734_2]) ).

cnf(f_3734_4,plain,
    ( hAPP(U_14576,hAPP(hAPP(c_Set_Oinsert(U_14577),U_14579),c_Orderings_Obot__class_Obot(tc_fun(U_14577,tc_HOL_Obool)))) = U_14579
    | U_14576 != c_Finite__Set_Ofold1(U_14577,U_14578) ),
    inference(clausify,[status(thm)],[f_3734_3]) ).

fof(f_3735_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_3735_2,plain,
    ! [U_14583,U_14582,U_14581,U_14580] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14580,U_14582)),hAPP(hAPP(c_Product__Type_OSigma(U_14580,U_14582),U_14581),hAPP(c_COMBK(tc_fun(U_14582,tc_HOL_Obool),U_14580),U_14583))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14582),U_14583))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14580),U_14581)) ),
    inference(variable_rename,[status(thm)],[f_3735_1]) ).

fof(f_3735_3,plain,
    ! [U_14580,U_14581,U_14582,U_14583] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14580,U_14582)),hAPP(hAPP(c_Product__Type_OSigma(U_14580,U_14582),U_14581),hAPP(c_COMBK(tc_fun(U_14582,tc_HOL_Obool),U_14580),U_14583))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14582),U_14583))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14580),U_14581)) ),
    inference(definitional_conversion,[status(esa)],[f_3735_2]) ).

cnf(f_3735_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14580,U_14582)),hAPP(hAPP(c_Product__Type_OSigma(U_14580,U_14582),U_14581),hAPP(c_COMBK(tc_fun(U_14582,tc_HOL_Obool),U_14580),U_14583))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14582),U_14583))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14580),U_14581)) ),
    inference(clausify,[status(thm)],[f_3735_3]) ).

fof(f_3736_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_3736_2,plain,
    ! [U_14586,U_14585,U_14584] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14584,U_14584),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14584,U_14585)),hAPP(hAPP(c_Product__Type_OSigma(U_14584,U_14584),U_14586),hAPP(c_COMBK(tc_fun(U_14584,tc_HOL_Obool),U_14584),U_14586))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14584,U_14584),tc_HOL_Obool)),U_14585),hAPP(hAPP(c_Product__Type_OSigma(U_14584,U_14584),U_14586),hAPP(c_COMBK(tc_fun(U_14584,tc_HOL_Obool),U_14584),U_14586)))) ),
    inference(variable_rename,[status(thm)],[f_3736_1]) ).

fof(f_3736_3,plain,
    ! [U_14584,U_14585,U_14586] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14584,U_14584),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14584,U_14585)),hAPP(hAPP(c_Product__Type_OSigma(U_14584,U_14584),U_14586),hAPP(c_COMBK(tc_fun(U_14584,tc_HOL_Obool),U_14584),U_14586))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14584,U_14584),tc_HOL_Obool)),U_14585),hAPP(hAPP(c_Product__Type_OSigma(U_14584,U_14584),U_14586),hAPP(c_COMBK(tc_fun(U_14584,tc_HOL_Obool),U_14584),U_14586)))) ),
    inference(definitional_conversion,[status(esa)],[f_3736_2]) ).

cnf(f_3736_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14584,U_14584),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14584,U_14585)),hAPP(hAPP(c_Product__Type_OSigma(U_14584,U_14584),U_14586),hAPP(c_COMBK(tc_fun(U_14584,tc_HOL_Obool),U_14584),U_14586))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14584,U_14584),tc_HOL_Obool)),U_14585),hAPP(hAPP(c_Product__Type_OSigma(U_14584,U_14584),U_14586),hAPP(c_COMBK(tc_fun(U_14584,tc_HOL_Obool),U_14584),U_14586)))) ),
    inference(clausify,[status(thm)],[f_3736_3]) ).

fof(f_3737_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_3737_2,plain,
    ! [U_14589,U_14588,U_14587] : hAPP(hAPP(c_Product__Type_OSigma(U_14587,U_14588),c_Orderings_Obot__class_Obot(tc_fun(U_14587,tc_HOL_Obool))),U_14589) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14587,U_14588),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3737_1]) ).

fof(f_3737_3,plain,
    ! [U_14587,U_14588,U_14589] : hAPP(hAPP(c_Product__Type_OSigma(U_14587,U_14588),c_Orderings_Obot__class_Obot(tc_fun(U_14587,tc_HOL_Obool))),U_14589) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14587,U_14588),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3737_2]) ).

cnf(f_3737_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14587,U_14588),c_Orderings_Obot__class_Obot(tc_fun(U_14587,tc_HOL_Obool))),U_14589) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14587,U_14588),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3737_3]) ).

fof(f_3738_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_3738_2,plain,
    ! [U_14593,U_14592,U_14591,U_14590] :
      ( ( hAPP(hAPP(c_Product__Type_OSigma(U_14590,U_14591),U_14592),hAPP(c_COMBK(tc_fun(U_14591,tc_HOL_Obool),U_14590),U_14593)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14590,U_14591),tc_HOL_Obool))
        | ( U_14593 != c_Orderings_Obot__class_Obot(tc_fun(U_14591,tc_HOL_Obool))
          & U_14592 != c_Orderings_Obot__class_Obot(tc_fun(U_14590,tc_HOL_Obool)) ) )
      & ( U_14593 = c_Orderings_Obot__class_Obot(tc_fun(U_14591,tc_HOL_Obool))
        | U_14592 = c_Orderings_Obot__class_Obot(tc_fun(U_14590,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(U_14590,U_14591),U_14592),hAPP(c_COMBK(tc_fun(U_14591,tc_HOL_Obool),U_14590),U_14593)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14590,U_14591),tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3738_1]) ).

fof(f_3738_3,plain,
    ( ! [U_14601,U_14599,U_14597,U_14595] :
        ( hAPP(hAPP(c_Product__Type_OSigma(U_14595,U_14597),U_14599),hAPP(c_COMBK(tc_fun(U_14597,tc_HOL_Obool),U_14595),U_14601)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14595,U_14597),tc_HOL_Obool))
        | ( U_14601 != c_Orderings_Obot__class_Obot(tc_fun(U_14597,tc_HOL_Obool))
          & U_14599 != c_Orderings_Obot__class_Obot(tc_fun(U_14595,tc_HOL_Obool)) ) )
    & ! [U_14600,U_14598,U_14596,U_14594] :
        ( U_14600 = c_Orderings_Obot__class_Obot(tc_fun(U_14596,tc_HOL_Obool))
        | U_14598 = c_Orderings_Obot__class_Obot(tc_fun(U_14594,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(U_14594,U_14596),U_14598),hAPP(c_COMBK(tc_fun(U_14596,tc_HOL_Obool),U_14594),U_14600)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14594,U_14596),tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3738_2]) ).

fof(f_3738_4,plain,
    ( ! [U_14595,U_14601,U_14599,U_14597] :
        ( U_14601 != c_Orderings_Obot__class_Obot(tc_fun(U_14597,tc_HOL_Obool))
        | ~ sP994(U_14595,U_14601,U_14599,U_14597) )
    & ! [U_14595,U_14601,U_14599,U_14597] :
        ( U_14599 != c_Orderings_Obot__class_Obot(tc_fun(U_14595,tc_HOL_Obool))
        | ~ sP994(U_14595,U_14601,U_14599,U_14597) )
    & ! [U_14595,U_14601,U_14599,U_14597] :
        ( hAPP(hAPP(c_Product__Type_OSigma(U_14595,U_14597),U_14599),hAPP(c_COMBK(tc_fun(U_14597,tc_HOL_Obool),U_14595),U_14601)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14595,U_14597),tc_HOL_Obool))
        | sP994(U_14595,U_14601,U_14599,U_14597) )
    & ! [U_14596,U_14598,U_14594,U_14600] :
        ( U_14600 = c_Orderings_Obot__class_Obot(tc_fun(U_14596,tc_HOL_Obool))
        | U_14598 = c_Orderings_Obot__class_Obot(tc_fun(U_14594,tc_HOL_Obool))
        | hAPP(hAPP(c_Product__Type_OSigma(U_14594,U_14596),U_14598),hAPP(c_COMBK(tc_fun(U_14596,tc_HOL_Obool),U_14594),U_14600)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14594,U_14596),tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP994])],[f_3738_3]) ).

cnf(f_3738_5,plain,
    ( U_14600 = c_Orderings_Obot__class_Obot(tc_fun(U_14596,tc_HOL_Obool))
    | U_14598 = c_Orderings_Obot__class_Obot(tc_fun(U_14594,tc_HOL_Obool))
    | hAPP(hAPP(c_Product__Type_OSigma(U_14594,U_14596),U_14598),hAPP(c_COMBK(tc_fun(U_14596,tc_HOL_Obool),U_14594),U_14600)) != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14594,U_14596),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3738_4]) ).

cnf(f_3738_6,plain,
    ( hAPP(hAPP(c_Product__Type_OSigma(U_14595,U_14597),U_14599),hAPP(c_COMBK(tc_fun(U_14597,tc_HOL_Obool),U_14595),U_14601)) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14595,U_14597),tc_HOL_Obool))
    | sP994(U_14595,U_14601,U_14599,U_14597) ),
    inference(clausify,[status(thm)],[f_3738_4]) ).

cnf(f_3738_7,plain,
    ( U_14599 != c_Orderings_Obot__class_Obot(tc_fun(U_14595,tc_HOL_Obool))
    | ~ sP994(U_14595,U_14601,U_14599,U_14597) ),
    inference(clausify,[status(thm)],[f_3738_4]) ).

cnf(f_3738_8,plain,
    ( U_14601 != c_Orderings_Obot__class_Obot(tc_fun(U_14597,tc_HOL_Obool))
    | ~ sP994(U_14595,U_14601,U_14599,U_14597) ),
    inference(clausify,[status(thm)],[f_3738_4]) ).

fof(f_3739_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_3739_2,plain,
    ! [U_14604,U_14603,U_14602] : hAPP(hAPP(c_Product__Type_OSigma(U_14602,U_14603),U_14604),hAPP(c_COMBK(tc_fun(U_14603,tc_HOL_Obool),U_14602),c_Orderings_Obot__class_Obot(tc_fun(U_14603,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14602,U_14603),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3739_1]) ).

fof(f_3739_3,plain,
    ! [U_14602,U_14603,U_14604] : hAPP(hAPP(c_Product__Type_OSigma(U_14602,U_14603),U_14604),hAPP(c_COMBK(tc_fun(U_14603,tc_HOL_Obool),U_14602),c_Orderings_Obot__class_Obot(tc_fun(U_14603,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14602,U_14603),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3739_2]) ).

cnf(f_3739_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14602,U_14603),U_14604),hAPP(c_COMBK(tc_fun(U_14603,tc_HOL_Obool),U_14602),c_Orderings_Obot__class_Obot(tc_fun(U_14603,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14602,U_14603),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3739_3]) ).

fof(f_3740_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_3740_2,plain,
    ! [U_14610,U_14609,U_14608,U_14607,U_14606,U_14605] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14606,U_14605),hAPP(hAPP(c_COMBC(U_14606,tc_fun(U_14607,tc_HOL_Obool),U_14605),hAPP(hAPP(c_COMBB(tc_fun(U_14607,U_14605),tc_fun(tc_fun(U_14607,tc_HOL_Obool),U_14605),U_14606),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14607,U_14605)),U_14608)),U_14609)),U_14610) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_14606,U_14607),U_14605),hAPP(c_Product__Type_Oprod_Oprod__case(U_14606,U_14607,U_14605),U_14608)),hAPP(hAPP(c_Product__Type_OSigma(U_14606,U_14607),U_14610),hAPP(c_COMBK(tc_fun(U_14607,tc_HOL_Obool),U_14606),U_14609)))
      | ~ class_Groups_Ocomm__monoid__add(U_14605) ),
    inference(variable_rename,[status(thm)],[f_3740_1]) ).

fof(f_3740_3,plain,
    ! [U_14605,U_14606,U_14607,U_14608,U_14609,U_14610] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14606,U_14605),hAPP(hAPP(c_COMBC(U_14606,tc_fun(U_14607,tc_HOL_Obool),U_14605),hAPP(hAPP(c_COMBB(tc_fun(U_14607,U_14605),tc_fun(tc_fun(U_14607,tc_HOL_Obool),U_14605),U_14606),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14607,U_14605)),U_14608)),U_14609)),U_14610) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_14606,U_14607),U_14605),hAPP(c_Product__Type_Oprod_Oprod__case(U_14606,U_14607,U_14605),U_14608)),hAPP(hAPP(c_Product__Type_OSigma(U_14606,U_14607),U_14610),hAPP(c_COMBK(tc_fun(U_14607,tc_HOL_Obool),U_14606),U_14609)))
      | ~ class_Groups_Ocomm__monoid__add(U_14605) ),
    inference(definitional_conversion,[status(esa)],[f_3740_2]) ).

cnf(f_3740_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14606,U_14605),hAPP(hAPP(c_COMBC(U_14606,tc_fun(U_14607,tc_HOL_Obool),U_14605),hAPP(hAPP(c_COMBB(tc_fun(U_14607,U_14605),tc_fun(tc_fun(U_14607,tc_HOL_Obool),U_14605),U_14606),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14607,U_14605)),U_14608)),U_14609)),U_14610) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_14606,U_14607),U_14605),hAPP(c_Product__Type_Oprod_Oprod__case(U_14606,U_14607,U_14605),U_14608)),hAPP(hAPP(c_Product__Type_OSigma(U_14606,U_14607),U_14610),hAPP(c_COMBK(tc_fun(U_14607,tc_HOL_Obool),U_14606),U_14609)))
    | ~ class_Groups_Ocomm__monoid__add(U_14605) ),
    inference(clausify,[status(thm)],[f_3740_3]) ).

fof(f_3741_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_3741_2,plain,
    ! [U_14615,U_14614,U_14613,U_14612,U_14611] : hAPP(hAPP(c_Product__Type_OSigma(U_14611,U_14612),U_14613),hAPP(hAPP(c_COMBS(U_14611,tc_fun(U_14612,tc_HOL_Obool),tc_fun(U_14612,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14612,tc_HOL_Obool),tc_fun(tc_fun(U_14612,tc_HOL_Obool),tc_fun(U_14612,tc_HOL_Obool)),U_14611),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14612,tc_HOL_Obool))),U_14614)),U_14615)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14611,U_14612),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14611,U_14612),U_14613),U_14614)),hAPP(hAPP(c_Product__Type_OSigma(U_14611,U_14612),U_14613),U_14615)),
    inference(variable_rename,[status(thm)],[f_3741_1]) ).

fof(f_3741_3,plain,
    ! [U_14611,U_14612,U_14613,U_14614,U_14615] : hAPP(hAPP(c_Product__Type_OSigma(U_14611,U_14612),U_14613),hAPP(hAPP(c_COMBS(U_14611,tc_fun(U_14612,tc_HOL_Obool),tc_fun(U_14612,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14612,tc_HOL_Obool),tc_fun(tc_fun(U_14612,tc_HOL_Obool),tc_fun(U_14612,tc_HOL_Obool)),U_14611),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14612,tc_HOL_Obool))),U_14614)),U_14615)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14611,U_14612),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14611,U_14612),U_14613),U_14614)),hAPP(hAPP(c_Product__Type_OSigma(U_14611,U_14612),U_14613),U_14615)),
    inference(definitional_conversion,[status(esa)],[f_3741_2]) ).

cnf(f_3741_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14611,U_14612),U_14613),hAPP(hAPP(c_COMBS(U_14611,tc_fun(U_14612,tc_HOL_Obool),tc_fun(U_14612,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14612,tc_HOL_Obool),tc_fun(tc_fun(U_14612,tc_HOL_Obool),tc_fun(U_14612,tc_HOL_Obool)),U_14611),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14612,tc_HOL_Obool))),U_14614)),U_14615)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14611,U_14612),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14611,U_14612),U_14613),U_14614)),hAPP(hAPP(c_Product__Type_OSigma(U_14611,U_14612),U_14613),U_14615)),
    inference(clausify,[status(thm)],[f_3741_3]) ).

fof(f_3742_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_3742_2,plain,
    ! [U_14620,U_14619,U_14618,U_14617,U_14616] : hAPP(hAPP(c_Product__Type_OSigma(U_14616,U_14617),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14616,tc_HOL_Obool)),U_14618),U_14619)),hAPP(c_COMBK(tc_fun(U_14617,tc_HOL_Obool),U_14616),U_14620)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14616,U_14617),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14616,U_14617),U_14618),hAPP(c_COMBK(tc_fun(U_14617,tc_HOL_Obool),U_14616),U_14620))),hAPP(hAPP(c_Product__Type_OSigma(U_14616,U_14617),U_14619),hAPP(c_COMBK(tc_fun(U_14617,tc_HOL_Obool),U_14616),U_14620))),
    inference(variable_rename,[status(thm)],[f_3742_1]) ).

fof(f_3742_3,plain,
    ! [U_14616,U_14617,U_14618,U_14619,U_14620] : hAPP(hAPP(c_Product__Type_OSigma(U_14616,U_14617),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14616,tc_HOL_Obool)),U_14618),U_14619)),hAPP(c_COMBK(tc_fun(U_14617,tc_HOL_Obool),U_14616),U_14620)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14616,U_14617),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14616,U_14617),U_14618),hAPP(c_COMBK(tc_fun(U_14617,tc_HOL_Obool),U_14616),U_14620))),hAPP(hAPP(c_Product__Type_OSigma(U_14616,U_14617),U_14619),hAPP(c_COMBK(tc_fun(U_14617,tc_HOL_Obool),U_14616),U_14620))),
    inference(definitional_conversion,[status(esa)],[f_3742_2]) ).

cnf(f_3742_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14616,U_14617),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14616,tc_HOL_Obool)),U_14618),U_14619)),hAPP(c_COMBK(tc_fun(U_14617,tc_HOL_Obool),U_14616),U_14620)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14616,U_14617),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14616,U_14617),U_14618),hAPP(c_COMBK(tc_fun(U_14617,tc_HOL_Obool),U_14616),U_14620))),hAPP(hAPP(c_Product__Type_OSigma(U_14616,U_14617),U_14619),hAPP(c_COMBK(tc_fun(U_14617,tc_HOL_Obool),U_14616),U_14620))),
    inference(clausify,[status(thm)],[f_3742_3]) ).

fof(f_3743_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_3743_2,plain,
    ! [U_14625,U_14624,U_14623,U_14622,U_14621] : hAPP(hAPP(c_Product__Type_OSigma(U_14621,U_14622),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14621,tc_HOL_Obool)),U_14623),U_14624)),U_14625) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14621,U_14622),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14621,U_14622),U_14623),U_14625)),hAPP(hAPP(c_Product__Type_OSigma(U_14621,U_14622),U_14624),U_14625)),
    inference(variable_rename,[status(thm)],[f_3743_1]) ).

fof(f_3743_3,plain,
    ! [U_14621,U_14622,U_14623,U_14624,U_14625] : hAPP(hAPP(c_Product__Type_OSigma(U_14621,U_14622),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14621,tc_HOL_Obool)),U_14623),U_14624)),U_14625) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14621,U_14622),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14621,U_14622),U_14623),U_14625)),hAPP(hAPP(c_Product__Type_OSigma(U_14621,U_14622),U_14624),U_14625)),
    inference(definitional_conversion,[status(esa)],[f_3743_2]) ).

cnf(f_3743_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14621,U_14622),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14621,tc_HOL_Obool)),U_14623),U_14624)),U_14625) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14621,U_14622),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14621,U_14622),U_14623),U_14625)),hAPP(hAPP(c_Product__Type_OSigma(U_14621,U_14622),U_14624),U_14625)),
    inference(clausify,[status(thm)],[f_3743_3]) ).

fof(f_3744_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_3744_2,plain,
    ! [U_14631,U_14630,U_14629,U_14628,U_14627,U_14626] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14627,U_14626),hAPP(hAPP(c_COMBC(U_14627,tc_fun(U_14628,tc_HOL_Obool),U_14626),hAPP(hAPP(c_COMBB(tc_fun(U_14628,U_14626),tc_fun(tc_fun(U_14628,tc_HOL_Obool),U_14626),U_14627),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14628,U_14626)),U_14629)),U_14630)),U_14631) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_14627,U_14628),U_14626),hAPP(c_Product__Type_Oprod_Oprod__case(U_14627,U_14628,U_14626),U_14629)),hAPP(hAPP(c_Product__Type_OSigma(U_14627,U_14628),U_14631),hAPP(c_COMBK(tc_fun(U_14628,tc_HOL_Obool),U_14627),U_14630)))
      | ~ class_Groups_Ocomm__monoid__mult(U_14626) ),
    inference(variable_rename,[status(thm)],[f_3744_1]) ).

fof(f_3744_3,plain,
    ! [U_14626,U_14627,U_14628,U_14629,U_14630,U_14631] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14627,U_14626),hAPP(hAPP(c_COMBC(U_14627,tc_fun(U_14628,tc_HOL_Obool),U_14626),hAPP(hAPP(c_COMBB(tc_fun(U_14628,U_14626),tc_fun(tc_fun(U_14628,tc_HOL_Obool),U_14626),U_14627),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14628,U_14626)),U_14629)),U_14630)),U_14631) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_14627,U_14628),U_14626),hAPP(c_Product__Type_Oprod_Oprod__case(U_14627,U_14628,U_14626),U_14629)),hAPP(hAPP(c_Product__Type_OSigma(U_14627,U_14628),U_14631),hAPP(c_COMBK(tc_fun(U_14628,tc_HOL_Obool),U_14627),U_14630)))
      | ~ class_Groups_Ocomm__monoid__mult(U_14626) ),
    inference(definitional_conversion,[status(esa)],[f_3744_2]) ).

cnf(f_3744_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14627,U_14626),hAPP(hAPP(c_COMBC(U_14627,tc_fun(U_14628,tc_HOL_Obool),U_14626),hAPP(hAPP(c_COMBB(tc_fun(U_14628,U_14626),tc_fun(tc_fun(U_14628,tc_HOL_Obool),U_14626),U_14627),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14628,U_14626)),U_14629)),U_14630)),U_14631) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_14627,U_14628),U_14626),hAPP(c_Product__Type_Oprod_Oprod__case(U_14627,U_14628,U_14626),U_14629)),hAPP(hAPP(c_Product__Type_OSigma(U_14627,U_14628),U_14631),hAPP(c_COMBK(tc_fun(U_14628,tc_HOL_Obool),U_14627),U_14630)))
    | ~ class_Groups_Ocomm__monoid__mult(U_14626) ),
    inference(clausify,[status(thm)],[f_3744_3]) ).

fof(f_3745_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_3745_2,plain,
    ! [U_14635,U_14634,U_14633,U_14632] : hAPP(c_Finite__Set_Ocard(tc_prod(U_14632,U_14633)),hAPP(hAPP(c_Product__Type_OSigma(U_14632,U_14633),U_14634),hAPP(c_COMBK(tc_fun(U_14633,tc_HOL_Obool),U_14632),U_14635))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_14632),U_14634)),hAPP(c_Finite__Set_Ocard(U_14633),U_14635)),
    inference(variable_rename,[status(thm)],[f_3745_1]) ).

fof(f_3745_3,plain,
    ! [U_14632,U_14633,U_14634,U_14635] : hAPP(c_Finite__Set_Ocard(tc_prod(U_14632,U_14633)),hAPP(hAPP(c_Product__Type_OSigma(U_14632,U_14633),U_14634),hAPP(c_COMBK(tc_fun(U_14633,tc_HOL_Obool),U_14632),U_14635))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_14632),U_14634)),hAPP(c_Finite__Set_Ocard(U_14633),U_14635)),
    inference(definitional_conversion,[status(esa)],[f_3745_2]) ).

cnf(f_3745_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_prod(U_14632,U_14633)),hAPP(hAPP(c_Product__Type_OSigma(U_14632,U_14633),U_14634),hAPP(c_COMBK(tc_fun(U_14633,tc_HOL_Obool),U_14632),U_14635))) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_14632),U_14634)),hAPP(c_Finite__Set_Ocard(U_14633),U_14635)),
    inference(clausify,[status(thm)],[f_3745_3]) ).

fof(f_3746_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_3746_2,plain,
    ! [U_14638,U_14637,U_14636] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_14636,U_14637),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14636,U_14637),U_14638),hAPP(c_COMBK(tc_fun(U_14637,tc_HOL_Obool),U_14636),c_Orderings_Otop__class_Otop(tc_fun(U_14637,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(U_14636,U_14637),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14636,tc_HOL_Obool)),U_14638)),hAPP(c_COMBK(tc_fun(U_14637,tc_HOL_Obool),U_14636),c_Orderings_Otop__class_Otop(tc_fun(U_14637,tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_3746_1]) ).

fof(f_3746_3,plain,
    ! [U_14636,U_14637,U_14638] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_14636,U_14637),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14636,U_14637),U_14638),hAPP(c_COMBK(tc_fun(U_14637,tc_HOL_Obool),U_14636),c_Orderings_Otop__class_Otop(tc_fun(U_14637,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(U_14636,U_14637),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14636,tc_HOL_Obool)),U_14638)),hAPP(c_COMBK(tc_fun(U_14637,tc_HOL_Obool),U_14636),c_Orderings_Otop__class_Otop(tc_fun(U_14637,tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_3746_2]) ).

cnf(f_3746_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_14636,U_14637),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14636,U_14637),U_14638),hAPP(c_COMBK(tc_fun(U_14637,tc_HOL_Obool),U_14636),c_Orderings_Otop__class_Otop(tc_fun(U_14637,tc_HOL_Obool))))) = hAPP(hAPP(c_Product__Type_OSigma(U_14636,U_14637),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14636,tc_HOL_Obool)),U_14638)),hAPP(c_COMBK(tc_fun(U_14637,tc_HOL_Obool),U_14636),c_Orderings_Otop__class_Otop(tc_fun(U_14637,tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_3746_3]) ).

fof(f_3747_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_3747_2,plain,
    ! [U_14641,U_14640,U_14639] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_14639,U_14640),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14639,U_14640),c_Orderings_Otop__class_Otop(tc_fun(U_14639,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_14640,tc_HOL_Obool),U_14639),U_14641))) = hAPP(hAPP(c_Product__Type_OSigma(U_14639,U_14640),c_Orderings_Otop__class_Otop(tc_fun(U_14639,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_14640,tc_HOL_Obool),U_14639),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14640,tc_HOL_Obool)),U_14641))),
    inference(variable_rename,[status(thm)],[f_3747_1]) ).

fof(f_3747_3,plain,
    ! [U_14639,U_14640,U_14641] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_14639,U_14640),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14639,U_14640),c_Orderings_Otop__class_Otop(tc_fun(U_14639,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_14640,tc_HOL_Obool),U_14639),U_14641))) = hAPP(hAPP(c_Product__Type_OSigma(U_14639,U_14640),c_Orderings_Otop__class_Otop(tc_fun(U_14639,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_14640,tc_HOL_Obool),U_14639),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14640,tc_HOL_Obool)),U_14641))),
    inference(definitional_conversion,[status(esa)],[f_3747_2]) ).

cnf(f_3747_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(tc_prod(U_14639,U_14640),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14639,U_14640),c_Orderings_Otop__class_Otop(tc_fun(U_14639,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_14640,tc_HOL_Obool),U_14639),U_14641))) = hAPP(hAPP(c_Product__Type_OSigma(U_14639,U_14640),c_Orderings_Otop__class_Otop(tc_fun(U_14639,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_14640,tc_HOL_Obool),U_14639),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_14640,tc_HOL_Obool)),U_14641))),
    inference(clausify,[status(thm)],[f_3747_3]) ).

fof(f_3748_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_3748_2,plain,
    ! [U_14647,U_14646,U_14645,U_14644,U_14643,U_14642] :
      ( ( ( hAPP(hAPP(c_Product__Type_OSigma(U_14645,U_14642),U_14646),hAPP(c_COMBK(tc_fun(U_14642,tc_HOL_Obool),U_14645),U_14644)) = hAPP(hAPP(c_Product__Type_OSigma(U_14645,U_14642),U_14647),hAPP(c_COMBK(tc_fun(U_14642,tc_HOL_Obool),U_14645),U_14644))
          | U_14646 != U_14647 )
        & ( U_14646 = U_14647
          | hAPP(hAPP(c_Product__Type_OSigma(U_14645,U_14642),U_14646),hAPP(c_COMBK(tc_fun(U_14642,tc_HOL_Obool),U_14645),U_14644)) != hAPP(hAPP(c_Product__Type_OSigma(U_14645,U_14642),U_14647),hAPP(c_COMBK(tc_fun(U_14642,tc_HOL_Obool),U_14645),U_14644)) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_14642),U_14643),U_14644)) ),
    inference(variable_rename,[status(thm)],[f_3748_1]) ).

fof(f_3748_3,plain,
    ( ! [U_14642,U_14644,U_14645,U_14646,U_14647] :
        ( hAPP(hAPP(c_Product__Type_OSigma(U_14645,U_14642),U_14646),hAPP(c_COMBK(tc_fun(U_14642,tc_HOL_Obool),U_14645),U_14644)) = hAPP(hAPP(c_Product__Type_OSigma(U_14645,U_14642),U_14647),hAPP(c_COMBK(tc_fun(U_14642,tc_HOL_Obool),U_14645),U_14644))
        | U_14646 != U_14647
        | ~ sP995(U_14642,U_14644,U_14645,U_14646,U_14647) )
    & ! [U_14642,U_14644,U_14645,U_14646,U_14647] :
        ( U_14646 = U_14647
        | hAPP(hAPP(c_Product__Type_OSigma(U_14645,U_14642),U_14646),hAPP(c_COMBK(tc_fun(U_14642,tc_HOL_Obool),U_14645),U_14644)) != hAPP(hAPP(c_Product__Type_OSigma(U_14645,U_14642),U_14647),hAPP(c_COMBK(tc_fun(U_14642,tc_HOL_Obool),U_14645),U_14644))
        | ~ sP995(U_14642,U_14644,U_14645,U_14646,U_14647) )
    & ! [U_14642,U_14643,U_14644,U_14645,U_14646,U_14647] :
        ( sP995(U_14642,U_14644,U_14645,U_14646,U_14647)
        | ~ hBOOL(hAPP(hAPP(c_member(U_14642),U_14643),U_14644)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP995])],[f_3748_2]) ).

cnf(f_3748_4,plain,
    ( sP995(U_14642,U_14644,U_14645,U_14646,U_14647)
    | ~ hBOOL(hAPP(hAPP(c_member(U_14642),U_14643),U_14644)) ),
    inference(clausify,[status(thm)],[f_3748_3]) ).

cnf(f_3748_5,plain,
    ( U_14646 = U_14647
    | hAPP(hAPP(c_Product__Type_OSigma(U_14645,U_14642),U_14646),hAPP(c_COMBK(tc_fun(U_14642,tc_HOL_Obool),U_14645),U_14644)) != hAPP(hAPP(c_Product__Type_OSigma(U_14645,U_14642),U_14647),hAPP(c_COMBK(tc_fun(U_14642,tc_HOL_Obool),U_14645),U_14644))
    | ~ sP995(U_14642,U_14644,U_14645,U_14646,U_14647) ),
    inference(clausify,[status(thm)],[f_3748_3]) ).

cnf(f_3748_6,plain,
    ( hAPP(hAPP(c_Product__Type_OSigma(U_14645,U_14642),U_14646),hAPP(c_COMBK(tc_fun(U_14642,tc_HOL_Obool),U_14645),U_14644)) = hAPP(hAPP(c_Product__Type_OSigma(U_14645,U_14642),U_14647),hAPP(c_COMBK(tc_fun(U_14642,tc_HOL_Obool),U_14645),U_14644))
    | U_14646 != U_14647
    | ~ sP995(U_14642,U_14644,U_14645,U_14646,U_14647) ),
    inference(clausify,[status(thm)],[f_3748_3]) ).

fof(f_3749_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_3749_2,plain,
    ! [U_14650,U_14649,U_14648] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14648,U_14648),tc_HOL_Obool)),U_14650),hAPP(hAPP(c_Product__Type_OSigma(U_14648,U_14648),U_14649),hAPP(c_COMBK(tc_fun(U_14648,tc_HOL_Obool),U_14648),U_14649))))
      | ~ c_Equiv__Relations_Oequiv(U_14648,U_14649,U_14650) ),
    inference(variable_rename,[status(thm)],[f_3749_1]) ).

fof(f_3749_3,plain,
    ! [U_14649,U_14650,U_14648] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14648,U_14648),tc_HOL_Obool)),U_14650),hAPP(hAPP(c_Product__Type_OSigma(U_14648,U_14648),U_14649),hAPP(c_COMBK(tc_fun(U_14648,tc_HOL_Obool),U_14648),U_14649))))
      | ~ c_Equiv__Relations_Oequiv(U_14648,U_14649,U_14650) ),
    inference(definitional_conversion,[status(esa)],[f_3749_2]) ).

cnf(f_3749_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14648,U_14648),tc_HOL_Obool)),U_14650),hAPP(hAPP(c_Product__Type_OSigma(U_14648,U_14648),U_14649),hAPP(c_COMBK(tc_fun(U_14648,tc_HOL_Obool),U_14648),U_14649))))
    | ~ c_Equiv__Relations_Oequiv(U_14648,U_14649,U_14650) ),
    inference(clausify,[status(thm)],[f_3749_3]) ).

fof(f_3750_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_3750_2,plain,
    ! [U_14655,U_14654,U_14653,U_14652,U_14651] : hAPP(hAPP(c_Product__Type_OSigma(U_14651,U_14652),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14651,tc_HOL_Obool)),U_14653),U_14654)),U_14655) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14651,U_14652),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14651,U_14652),U_14653),U_14655)),hAPP(hAPP(c_Product__Type_OSigma(U_14651,U_14652),U_14654),U_14655)),
    inference(variable_rename,[status(thm)],[f_3750_1]) ).

fof(f_3750_3,plain,
    ! [U_14651,U_14652,U_14653,U_14654,U_14655] : hAPP(hAPP(c_Product__Type_OSigma(U_14651,U_14652),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14651,tc_HOL_Obool)),U_14653),U_14654)),U_14655) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14651,U_14652),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14651,U_14652),U_14653),U_14655)),hAPP(hAPP(c_Product__Type_OSigma(U_14651,U_14652),U_14654),U_14655)),
    inference(definitional_conversion,[status(esa)],[f_3750_2]) ).

cnf(f_3750_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14651,U_14652),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14651,tc_HOL_Obool)),U_14653),U_14654)),U_14655) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14651,U_14652),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14651,U_14652),U_14653),U_14655)),hAPP(hAPP(c_Product__Type_OSigma(U_14651,U_14652),U_14654),U_14655)),
    inference(clausify,[status(thm)],[f_3750_3]) ).

fof(f_3751_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_3751_2,plain,
    ! [U_14660,U_14659,U_14658,U_14657,U_14656] : hAPP(hAPP(c_Product__Type_OSigma(U_14656,U_14657),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14656,tc_HOL_Obool)),U_14658),U_14659)),hAPP(c_COMBK(tc_fun(U_14657,tc_HOL_Obool),U_14656),U_14660)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14656,U_14657),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14656,U_14657),U_14658),hAPP(c_COMBK(tc_fun(U_14657,tc_HOL_Obool),U_14656),U_14660))),hAPP(hAPP(c_Product__Type_OSigma(U_14656,U_14657),U_14659),hAPP(c_COMBK(tc_fun(U_14657,tc_HOL_Obool),U_14656),U_14660))),
    inference(variable_rename,[status(thm)],[f_3751_1]) ).

fof(f_3751_3,plain,
    ! [U_14656,U_14657,U_14658,U_14659,U_14660] : hAPP(hAPP(c_Product__Type_OSigma(U_14656,U_14657),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14656,tc_HOL_Obool)),U_14658),U_14659)),hAPP(c_COMBK(tc_fun(U_14657,tc_HOL_Obool),U_14656),U_14660)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14656,U_14657),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14656,U_14657),U_14658),hAPP(c_COMBK(tc_fun(U_14657,tc_HOL_Obool),U_14656),U_14660))),hAPP(hAPP(c_Product__Type_OSigma(U_14656,U_14657),U_14659),hAPP(c_COMBK(tc_fun(U_14657,tc_HOL_Obool),U_14656),U_14660))),
    inference(definitional_conversion,[status(esa)],[f_3751_2]) ).

cnf(f_3751_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14656,U_14657),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14656,tc_HOL_Obool)),U_14658),U_14659)),hAPP(c_COMBK(tc_fun(U_14657,tc_HOL_Obool),U_14656),U_14660)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14656,U_14657),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14656,U_14657),U_14658),hAPP(c_COMBK(tc_fun(U_14657,tc_HOL_Obool),U_14656),U_14660))),hAPP(hAPP(c_Product__Type_OSigma(U_14656,U_14657),U_14659),hAPP(c_COMBK(tc_fun(U_14657,tc_HOL_Obool),U_14656),U_14660))),
    inference(clausify,[status(thm)],[f_3751_3]) ).

fof(f_3752_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_3752_2,plain,
    ! [U_14665,U_14664,U_14663,U_14662,U_14661] : hAPP(hAPP(c_Product__Type_OSigma(U_14661,U_14662),U_14663),hAPP(hAPP(c_COMBS(U_14661,tc_fun(U_14662,tc_HOL_Obool),tc_fun(U_14662,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14662,tc_HOL_Obool),tc_fun(tc_fun(U_14662,tc_HOL_Obool),tc_fun(U_14662,tc_HOL_Obool)),U_14661),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14662,tc_HOL_Obool))),U_14664)),U_14665)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14661,U_14662),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14661,U_14662),U_14663),U_14664)),hAPP(hAPP(c_Product__Type_OSigma(U_14661,U_14662),U_14663),U_14665)),
    inference(variable_rename,[status(thm)],[f_3752_1]) ).

fof(f_3752_3,plain,
    ! [U_14661,U_14662,U_14663,U_14664,U_14665] : hAPP(hAPP(c_Product__Type_OSigma(U_14661,U_14662),U_14663),hAPP(hAPP(c_COMBS(U_14661,tc_fun(U_14662,tc_HOL_Obool),tc_fun(U_14662,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14662,tc_HOL_Obool),tc_fun(tc_fun(U_14662,tc_HOL_Obool),tc_fun(U_14662,tc_HOL_Obool)),U_14661),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14662,tc_HOL_Obool))),U_14664)),U_14665)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14661,U_14662),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14661,U_14662),U_14663),U_14664)),hAPP(hAPP(c_Product__Type_OSigma(U_14661,U_14662),U_14663),U_14665)),
    inference(definitional_conversion,[status(esa)],[f_3752_2]) ).

cnf(f_3752_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14661,U_14662),U_14663),hAPP(hAPP(c_COMBS(U_14661,tc_fun(U_14662,tc_HOL_Obool),tc_fun(U_14662,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14662,tc_HOL_Obool),tc_fun(tc_fun(U_14662,tc_HOL_Obool),tc_fun(U_14662,tc_HOL_Obool)),U_14661),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_14662,tc_HOL_Obool))),U_14664)),U_14665)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_14661,U_14662),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14661,U_14662),U_14663),U_14664)),hAPP(hAPP(c_Product__Type_OSigma(U_14661,U_14662),U_14663),U_14665)),
    inference(clausify,[status(thm)],[f_3752_3]) ).

fof(f_3753_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_3753_2,plain,
    ! [U_14667,U_14666] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14666,U_14666),tc_HOL_Obool)),c_Relation_OId__on(U_14666,U_14667)),hAPP(hAPP(c_Product__Type_OSigma(U_14666,U_14666),U_14667),hAPP(c_COMBK(tc_fun(U_14666,tc_HOL_Obool),U_14666),U_14667)))),
    inference(variable_rename,[status(thm)],[f_3753_1]) ).

fof(f_3753_3,plain,
    ! [U_14666,U_14667] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14666,U_14666),tc_HOL_Obool)),c_Relation_OId__on(U_14666,U_14667)),hAPP(hAPP(c_Product__Type_OSigma(U_14666,U_14666),U_14667),hAPP(c_COMBK(tc_fun(U_14666,tc_HOL_Obool),U_14666),U_14667)))),
    inference(definitional_conversion,[status(esa)],[f_3753_2]) ).

cnf(f_3753_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14666,U_14666),tc_HOL_Obool)),c_Relation_OId__on(U_14666,U_14667)),hAPP(hAPP(c_Product__Type_OSigma(U_14666,U_14666),U_14667),hAPP(c_COMBK(tc_fun(U_14666,tc_HOL_Obool),U_14666),U_14667)))),
    inference(clausify,[status(thm)],[f_3753_3]) ).

fof(f_3754_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_3754_2,plain,
    ! [U_14672,U_14671,U_14670,U_14669,U_14668] : hAPP(hAPP(c_Product__Type_OSigma(U_14668,U_14669),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14668,tc_HOL_Obool)),U_14670),U_14671)),U_14672) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14668,U_14669),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14668,U_14669),U_14670),U_14672)),hAPP(hAPP(c_Product__Type_OSigma(U_14668,U_14669),U_14671),U_14672)),
    inference(variable_rename,[status(thm)],[f_3754_1]) ).

fof(f_3754_3,plain,
    ! [U_14668,U_14669,U_14670,U_14671,U_14672] : hAPP(hAPP(c_Product__Type_OSigma(U_14668,U_14669),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14668,tc_HOL_Obool)),U_14670),U_14671)),U_14672) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14668,U_14669),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14668,U_14669),U_14670),U_14672)),hAPP(hAPP(c_Product__Type_OSigma(U_14668,U_14669),U_14671),U_14672)),
    inference(definitional_conversion,[status(esa)],[f_3754_2]) ).

cnf(f_3754_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14668,U_14669),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14668,tc_HOL_Obool)),U_14670),U_14671)),U_14672) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14668,U_14669),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14668,U_14669),U_14670),U_14672)),hAPP(hAPP(c_Product__Type_OSigma(U_14668,U_14669),U_14671),U_14672)),
    inference(clausify,[status(thm)],[f_3754_3]) ).

fof(f_3755_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_3755_2,plain,
    ! [U_14677,U_14676,U_14675,U_14674,U_14673] : hAPP(hAPP(c_Product__Type_OSigma(U_14673,U_14674),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14673,tc_HOL_Obool)),U_14675),U_14676)),hAPP(c_COMBK(tc_fun(U_14674,tc_HOL_Obool),U_14673),U_14677)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14673,U_14674),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14673,U_14674),U_14675),hAPP(c_COMBK(tc_fun(U_14674,tc_HOL_Obool),U_14673),U_14677))),hAPP(hAPP(c_Product__Type_OSigma(U_14673,U_14674),U_14676),hAPP(c_COMBK(tc_fun(U_14674,tc_HOL_Obool),U_14673),U_14677))),
    inference(variable_rename,[status(thm)],[f_3755_1]) ).

fof(f_3755_3,plain,
    ! [U_14673,U_14674,U_14675,U_14676,U_14677] : hAPP(hAPP(c_Product__Type_OSigma(U_14673,U_14674),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14673,tc_HOL_Obool)),U_14675),U_14676)),hAPP(c_COMBK(tc_fun(U_14674,tc_HOL_Obool),U_14673),U_14677)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14673,U_14674),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14673,U_14674),U_14675),hAPP(c_COMBK(tc_fun(U_14674,tc_HOL_Obool),U_14673),U_14677))),hAPP(hAPP(c_Product__Type_OSigma(U_14673,U_14674),U_14676),hAPP(c_COMBK(tc_fun(U_14674,tc_HOL_Obool),U_14673),U_14677))),
    inference(definitional_conversion,[status(esa)],[f_3755_2]) ).

cnf(f_3755_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14673,U_14674),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_14673,tc_HOL_Obool)),U_14675),U_14676)),hAPP(c_COMBK(tc_fun(U_14674,tc_HOL_Obool),U_14673),U_14677)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14673,U_14674),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14673,U_14674),U_14675),hAPP(c_COMBK(tc_fun(U_14674,tc_HOL_Obool),U_14673),U_14677))),hAPP(hAPP(c_Product__Type_OSigma(U_14673,U_14674),U_14676),hAPP(c_COMBK(tc_fun(U_14674,tc_HOL_Obool),U_14673),U_14677))),
    inference(clausify,[status(thm)],[f_3755_3]) ).

fof(f_3756_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_3756_2,plain,
    ! [U_14682,U_14681,U_14680,U_14679,U_14678] : hAPP(hAPP(c_Product__Type_OSigma(U_14678,U_14679),U_14680),hAPP(hAPP(c_COMBS(U_14678,tc_fun(U_14679,tc_HOL_Obool),tc_fun(U_14679,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14679,tc_HOL_Obool),tc_fun(tc_fun(U_14679,tc_HOL_Obool),tc_fun(U_14679,tc_HOL_Obool)),U_14678),c_Groups_Ominus__class_Ominus(tc_fun(U_14679,tc_HOL_Obool))),U_14681)),U_14682)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14678,U_14679),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14678,U_14679),U_14680),U_14681)),hAPP(hAPP(c_Product__Type_OSigma(U_14678,U_14679),U_14680),U_14682)),
    inference(variable_rename,[status(thm)],[f_3756_1]) ).

fof(f_3756_3,plain,
    ! [U_14678,U_14679,U_14680,U_14681,U_14682] : hAPP(hAPP(c_Product__Type_OSigma(U_14678,U_14679),U_14680),hAPP(hAPP(c_COMBS(U_14678,tc_fun(U_14679,tc_HOL_Obool),tc_fun(U_14679,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14679,tc_HOL_Obool),tc_fun(tc_fun(U_14679,tc_HOL_Obool),tc_fun(U_14679,tc_HOL_Obool)),U_14678),c_Groups_Ominus__class_Ominus(tc_fun(U_14679,tc_HOL_Obool))),U_14681)),U_14682)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14678,U_14679),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14678,U_14679),U_14680),U_14681)),hAPP(hAPP(c_Product__Type_OSigma(U_14678,U_14679),U_14680),U_14682)),
    inference(definitional_conversion,[status(esa)],[f_3756_2]) ).

cnf(f_3756_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14678,U_14679),U_14680),hAPP(hAPP(c_COMBS(U_14678,tc_fun(U_14679,tc_HOL_Obool),tc_fun(U_14679,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14679,tc_HOL_Obool),tc_fun(tc_fun(U_14679,tc_HOL_Obool),tc_fun(U_14679,tc_HOL_Obool)),U_14678),c_Groups_Ominus__class_Ominus(tc_fun(U_14679,tc_HOL_Obool))),U_14681)),U_14682)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(tc_prod(U_14678,U_14679),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14678,U_14679),U_14680),U_14681)),hAPP(hAPP(c_Product__Type_OSigma(U_14678,U_14679),U_14680),U_14682)),
    inference(clausify,[status(thm)],[f_3756_3]) ).

fof(f_3757_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_3757_2,plain,
    ! [U_14684,U_14683] : hAPP(hAPP(c_Product__Type_OSigma(U_14683,U_14684),c_Orderings_Otop__class_Otop(tc_fun(U_14683,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_14684,tc_HOL_Obool),U_14683),c_Orderings_Otop__class_Otop(tc_fun(U_14684,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14683,U_14684),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3757_1]) ).

fof(f_3757_3,plain,
    ! [U_14683,U_14684] : hAPP(hAPP(c_Product__Type_OSigma(U_14683,U_14684),c_Orderings_Otop__class_Otop(tc_fun(U_14683,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_14684,tc_HOL_Obool),U_14683),c_Orderings_Otop__class_Otop(tc_fun(U_14684,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14683,U_14684),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3757_2]) ).

cnf(f_3757_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14683,U_14684),c_Orderings_Otop__class_Otop(tc_fun(U_14683,tc_HOL_Obool))),hAPP(c_COMBK(tc_fun(U_14684,tc_HOL_Obool),U_14683),c_Orderings_Otop__class_Otop(tc_fun(U_14684,tc_HOL_Obool)))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14683,U_14684),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3757_3]) ).

fof(f_3758_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_3758_2,plain,
    ! [U_14690,U_14689,U_14688,U_14687,U_14686,U_14685] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_14686),U_14688),hAPP(U_14690,U_14687)))
        & hBOOL(hAPP(hAPP(c_member(U_14685),U_14687),U_14689)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14685,U_14686)),hAPP(hAPP(c_Product__Type_OPair(U_14685,U_14686),U_14687),U_14688)),hAPP(hAPP(c_Product__Type_OSigma(U_14685,U_14686),U_14689),U_14690))) ),
    inference(variable_rename,[status(thm)],[f_3758_1]) ).

fof(f_3758_3,plain,
    ( ! [U_14685,U_14686,U_14687,U_14688,U_14689,U_14690] :
        ( hBOOL(hAPP(hAPP(c_member(U_14686),U_14688),hAPP(U_14690,U_14687)))
        | ~ sP996(U_14685,U_14686,U_14687,U_14688,U_14689,U_14690) )
    & ! [U_14685,U_14686,U_14687,U_14688,U_14689,U_14690] :
        ( hBOOL(hAPP(hAPP(c_member(U_14685),U_14687),U_14689))
        | ~ sP996(U_14685,U_14686,U_14687,U_14688,U_14689,U_14690) )
    & ! [U_14685,U_14686,U_14687,U_14688,U_14689,U_14690] :
        ( sP996(U_14685,U_14686,U_14687,U_14688,U_14689,U_14690)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14685,U_14686)),hAPP(hAPP(c_Product__Type_OPair(U_14685,U_14686),U_14687),U_14688)),hAPP(hAPP(c_Product__Type_OSigma(U_14685,U_14686),U_14689),U_14690))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP996])],[f_3758_2]) ).

cnf(f_3758_4,plain,
    ( sP996(U_14685,U_14686,U_14687,U_14688,U_14689,U_14690)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14685,U_14686)),hAPP(hAPP(c_Product__Type_OPair(U_14685,U_14686),U_14687),U_14688)),hAPP(hAPP(c_Product__Type_OSigma(U_14685,U_14686),U_14689),U_14690))) ),
    inference(clausify,[status(thm)],[f_3758_3]) ).

cnf(f_3758_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14685),U_14687),U_14689))
    | ~ sP996(U_14685,U_14686,U_14687,U_14688,U_14689,U_14690) ),
    inference(clausify,[status(thm)],[f_3758_3]) ).

cnf(f_3758_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14686),U_14688),hAPP(U_14690,U_14687)))
    | ~ sP996(U_14685,U_14686,U_14687,U_14688,U_14689,U_14690) ),
    inference(clausify,[status(thm)],[f_3758_3]) ).

fof(f_3759_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_3759_2,plain,
    ! [U_14696,U_14695,U_14694,U_14693,U_14692,U_14691] :
      ( hBOOL(hAPP(hAPP(c_member(U_14692),U_14694),hAPP(U_14696,U_14693)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14691,U_14692)),hAPP(hAPP(c_Product__Type_OPair(U_14691,U_14692),U_14693),U_14694)),hAPP(hAPP(c_Product__Type_OSigma(U_14691,U_14692),U_14695),U_14696))) ),
    inference(variable_rename,[status(thm)],[f_3759_1]) ).

fof(f_3759_3,plain,
    ! [U_14696,U_14695,U_14694,U_14693,U_14692] :
      ( ! [U_14691] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14691,U_14692)),hAPP(hAPP(c_Product__Type_OPair(U_14691,U_14692),U_14693),U_14694)),hAPP(hAPP(c_Product__Type_OSigma(U_14691,U_14692),U_14695),U_14696)))
      | hBOOL(hAPP(hAPP(c_member(U_14692),U_14694),hAPP(U_14696,U_14693))) ),
    inference(miniscope,[status(thm)],[f_3759_2]) ).

fof(f_3759_4,plain,
    ! [U_14691,U_14692,U_14693,U_14694,U_14695,U_14696] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14691,U_14692)),hAPP(hAPP(c_Product__Type_OPair(U_14691,U_14692),U_14693),U_14694)),hAPP(hAPP(c_Product__Type_OSigma(U_14691,U_14692),U_14695),U_14696)))
      | hBOOL(hAPP(hAPP(c_member(U_14692),U_14694),hAPP(U_14696,U_14693))) ),
    inference(definitional_conversion,[status(esa)],[f_3759_3]) ).

cnf(f_3759_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14691,U_14692)),hAPP(hAPP(c_Product__Type_OPair(U_14691,U_14692),U_14693),U_14694)),hAPP(hAPP(c_Product__Type_OSigma(U_14691,U_14692),U_14695),U_14696)))
    | hBOOL(hAPP(hAPP(c_member(U_14692),U_14694),hAPP(U_14696,U_14693))) ),
    inference(clausify,[status(thm)],[f_3759_4]) ).

fof(f_3760_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_3760_2,plain,
    ! [U_14702,U_14701,U_14700,U_14699,U_14698,U_14697] :
      ( hBOOL(hAPP(hAPP(c_member(U_14697),U_14699),U_14701))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14697,U_14698)),hAPP(hAPP(c_Product__Type_OPair(U_14697,U_14698),U_14699),U_14700)),hAPP(hAPP(c_Product__Type_OSigma(U_14697,U_14698),U_14701),U_14702))) ),
    inference(variable_rename,[status(thm)],[f_3760_1]) ).

fof(f_3760_3,plain,
    ! [U_14697,U_14698,U_14699,U_14700,U_14701,U_14702] :
      ( hBOOL(hAPP(hAPP(c_member(U_14697),U_14699),U_14701))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14697,U_14698)),hAPP(hAPP(c_Product__Type_OPair(U_14697,U_14698),U_14699),U_14700)),hAPP(hAPP(c_Product__Type_OSigma(U_14697,U_14698),U_14701),U_14702))) ),
    inference(definitional_conversion,[status(esa)],[f_3760_2]) ).

cnf(f_3760_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14697),U_14699),U_14701))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14697,U_14698)),hAPP(hAPP(c_Product__Type_OPair(U_14697,U_14698),U_14699),U_14700)),hAPP(hAPP(c_Product__Type_OSigma(U_14697,U_14698),U_14701),U_14702))) ),
    inference(clausify,[status(thm)],[f_3760_3]) ).

fof(f_3761_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_3761_2,plain,
    ! [U_14708,U_14707,U_14706,U_14705,U_14704,U_14703] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14703,U_14704)),hAPP(hAPP(c_Product__Type_OPair(U_14703,U_14704),U_14705),U_14706)),hAPP(hAPP(c_Product__Type_OSigma(U_14703,U_14704),U_14707),U_14708)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14704),U_14706),hAPP(U_14708,U_14705)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14703),U_14705),U_14707)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(U_14704),U_14706),hAPP(U_14708,U_14705)))
          & hBOOL(hAPP(hAPP(c_member(U_14703),U_14705),U_14707)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14703,U_14704)),hAPP(hAPP(c_Product__Type_OPair(U_14703,U_14704),U_14705),U_14706)),hAPP(hAPP(c_Product__Type_OSigma(U_14703,U_14704),U_14707),U_14708))) ) ),
    inference(variable_rename,[status(thm)],[f_3761_1]) ).

fof(f_3761_3,plain,
    ( ! [U_14720,U_14718,U_14716,U_14714,U_14712,U_14710] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14710,U_14712)),hAPP(hAPP(c_Product__Type_OPair(U_14710,U_14712),U_14714),U_14716)),hAPP(hAPP(c_Product__Type_OSigma(U_14710,U_14712),U_14718),U_14720)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14712),U_14716),hAPP(U_14720,U_14714)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14710),U_14714),U_14718)) )
    & ! [U_14719,U_14717,U_14715,U_14713,U_14711,U_14709] :
        ( ( hBOOL(hAPP(hAPP(c_member(U_14711),U_14715),hAPP(U_14719,U_14713)))
          & hBOOL(hAPP(hAPP(c_member(U_14709),U_14713),U_14717)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14709,U_14711)),hAPP(hAPP(c_Product__Type_OPair(U_14709,U_14711),U_14713),U_14715)),hAPP(hAPP(c_Product__Type_OSigma(U_14709,U_14711),U_14717),U_14719))) ) ),
    inference(miniscope,[status(thm)],[f_3761_2]) ).

fof(f_3761_4,plain,
    ( ! [U_14711,U_14709,U_14717,U_14713,U_14715,U_14719] :
        ( hBOOL(hAPP(hAPP(c_member(U_14711),U_14715),hAPP(U_14719,U_14713)))
        | ~ sP997(U_14711,U_14709,U_14717,U_14713,U_14715,U_14719) )
    & ! [U_14711,U_14709,U_14717,U_14713,U_14715,U_14719] :
        ( hBOOL(hAPP(hAPP(c_member(U_14709),U_14713),U_14717))
        | ~ sP997(U_14711,U_14709,U_14717,U_14713,U_14715,U_14719) )
    & ! [U_14710,U_14716,U_14712,U_14718,U_14714,U_14720] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14710,U_14712)),hAPP(hAPP(c_Product__Type_OPair(U_14710,U_14712),U_14714),U_14716)),hAPP(hAPP(c_Product__Type_OSigma(U_14710,U_14712),U_14718),U_14720)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14712),U_14716),hAPP(U_14720,U_14714)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14710),U_14714),U_14718)) )
    & ! [U_14711,U_14709,U_14717,U_14713,U_14715,U_14719] :
        ( sP997(U_14711,U_14709,U_14717,U_14713,U_14715,U_14719)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14709,U_14711)),hAPP(hAPP(c_Product__Type_OPair(U_14709,U_14711),U_14713),U_14715)),hAPP(hAPP(c_Product__Type_OSigma(U_14709,U_14711),U_14717),U_14719))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP997])],[f_3761_3]) ).

cnf(f_3761_5,plain,
    ( sP997(U_14711,U_14709,U_14717,U_14713,U_14715,U_14719)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14709,U_14711)),hAPP(hAPP(c_Product__Type_OPair(U_14709,U_14711),U_14713),U_14715)),hAPP(hAPP(c_Product__Type_OSigma(U_14709,U_14711),U_14717),U_14719))) ),
    inference(clausify,[status(thm)],[f_3761_4]) ).

cnf(f_3761_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14710,U_14712)),hAPP(hAPP(c_Product__Type_OPair(U_14710,U_14712),U_14714),U_14716)),hAPP(hAPP(c_Product__Type_OSigma(U_14710,U_14712),U_14718),U_14720)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14712),U_14716),hAPP(U_14720,U_14714)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14710),U_14714),U_14718)) ),
    inference(clausify,[status(thm)],[f_3761_4]) ).

cnf(f_3761_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14709),U_14713),U_14717))
    | ~ sP997(U_14711,U_14709,U_14717,U_14713,U_14715,U_14719) ),
    inference(clausify,[status(thm)],[f_3761_4]) ).

cnf(f_3761_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14711),U_14715),hAPP(U_14719,U_14713)))
    | ~ sP997(U_14711,U_14709,U_14717,U_14713,U_14715,U_14719) ),
    inference(clausify,[status(thm)],[f_3761_4]) ).

fof(f_3762_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_3762_2,plain,
    ! [U_14724,U_14723,U_14722,U_14721] :
      ( hAPP(U_14723,U_14724) = hAPP(c_Finite__Set_Ofold1(U_14721,U_14722),U_14724)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14721),U_14724))
      | ~ c_Finite__Set_Ofolding__one(U_14721,U_14722,U_14723) ),
    inference(variable_rename,[status(thm)],[f_3762_1]) ).

fof(f_3762_3,plain,
    ! [U_14724,U_14723,U_14722,U_14721] :
      ( hAPP(U_14723,U_14724) = hAPP(c_Finite__Set_Ofold1(U_14721,U_14722),U_14724)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14721),U_14724))
      | ~ c_Finite__Set_Ofolding__one(U_14721,U_14722,U_14723) ),
    inference(definitional_conversion,[status(esa)],[f_3762_2]) ).

cnf(f_3762_4,plain,
    ( hAPP(U_14723,U_14724) = hAPP(c_Finite__Set_Ofold1(U_14721,U_14722),U_14724)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14721),U_14724))
    | ~ c_Finite__Set_Ofolding__one(U_14721,U_14722,U_14723) ),
    inference(clausify,[status(thm)],[f_3762_3]) ).

fof(f_3763_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_3763_2,plain,
    ! [U_14728,U_14727,U_14726,U_14725] : hAPP(c_Finite__Set_Ocard(tc_prod(U_14725,U_14726)),hAPP(hAPP(c_Product__Type_OSigma(U_14725,U_14726),hAPP(hAPP(c_Set_Oinsert(U_14725),U_14727),c_Orderings_Obot__class_Obot(tc_fun(U_14725,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(U_14726,tc_HOL_Obool),U_14725),U_14728))) = hAPP(c_Finite__Set_Ocard(U_14726),U_14728),
    inference(variable_rename,[status(thm)],[f_3763_1]) ).

fof(f_3763_3,plain,
    ! [U_14725,U_14726,U_14727,U_14728] : hAPP(c_Finite__Set_Ocard(tc_prod(U_14725,U_14726)),hAPP(hAPP(c_Product__Type_OSigma(U_14725,U_14726),hAPP(hAPP(c_Set_Oinsert(U_14725),U_14727),c_Orderings_Obot__class_Obot(tc_fun(U_14725,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(U_14726,tc_HOL_Obool),U_14725),U_14728))) = hAPP(c_Finite__Set_Ocard(U_14726),U_14728),
    inference(definitional_conversion,[status(esa)],[f_3763_2]) ).

cnf(f_3763_4,plain,
    hAPP(c_Finite__Set_Ocard(tc_prod(U_14725,U_14726)),hAPP(hAPP(c_Product__Type_OSigma(U_14725,U_14726),hAPP(hAPP(c_Set_Oinsert(U_14725),U_14727),c_Orderings_Obot__class_Obot(tc_fun(U_14725,tc_HOL_Obool)))),hAPP(c_COMBK(tc_fun(U_14726,tc_HOL_Obool),U_14725),U_14728))) = hAPP(c_Finite__Set_Ocard(U_14726),U_14728),
    inference(clausify,[status(thm)],[f_3763_3]) ).

fof(f_3764_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_3764_2,plain,
    ! [U_14734,U_14733,U_14732,U_14731,U_14730,U_14729] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14732,U_14729),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14732,U_14729),U_14733),hAPP(c_COMBK(tc_fun(U_14729,tc_HOL_Obool),U_14732),U_14731))),hAPP(hAPP(c_Product__Type_OSigma(U_14732,U_14729),U_14734),hAPP(c_COMBK(tc_fun(U_14729,tc_HOL_Obool),U_14732),U_14731))))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14732,tc_HOL_Obool)),U_14733),U_14734)) )
        & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14732,tc_HOL_Obool)),U_14733),U_14734))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14732,U_14729),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14732,U_14729),U_14733),hAPP(c_COMBK(tc_fun(U_14729,tc_HOL_Obool),U_14732),U_14731))),hAPP(hAPP(c_Product__Type_OSigma(U_14732,U_14729),U_14734),hAPP(c_COMBK(tc_fun(U_14729,tc_HOL_Obool),U_14732),U_14731)))) ) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_14729),U_14730),U_14731)) ),
    inference(variable_rename,[status(thm)],[f_3764_1]) ).

fof(f_3764_3,plain,
    ( ! [U_14729,U_14731,U_14732,U_14733,U_14734] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14732,U_14729),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14732,U_14729),U_14733),hAPP(c_COMBK(tc_fun(U_14729,tc_HOL_Obool),U_14732),U_14731))),hAPP(hAPP(c_Product__Type_OSigma(U_14732,U_14729),U_14734),hAPP(c_COMBK(tc_fun(U_14729,tc_HOL_Obool),U_14732),U_14731))))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14732,tc_HOL_Obool)),U_14733),U_14734))
        | ~ sP998(U_14729,U_14731,U_14732,U_14733,U_14734) )
    & ! [U_14729,U_14731,U_14732,U_14733,U_14734] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14732,tc_HOL_Obool)),U_14733),U_14734))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14732,U_14729),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14732,U_14729),U_14733),hAPP(c_COMBK(tc_fun(U_14729,tc_HOL_Obool),U_14732),U_14731))),hAPP(hAPP(c_Product__Type_OSigma(U_14732,U_14729),U_14734),hAPP(c_COMBK(tc_fun(U_14729,tc_HOL_Obool),U_14732),U_14731))))
        | ~ sP998(U_14729,U_14731,U_14732,U_14733,U_14734) )
    & ! [U_14729,U_14730,U_14731,U_14732,U_14733,U_14734] :
        ( sP998(U_14729,U_14731,U_14732,U_14733,U_14734)
        | ~ hBOOL(hAPP(hAPP(c_member(U_14729),U_14730),U_14731)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP998])],[f_3764_2]) ).

cnf(f_3764_4,plain,
    ( sP998(U_14729,U_14731,U_14732,U_14733,U_14734)
    | ~ hBOOL(hAPP(hAPP(c_member(U_14729),U_14730),U_14731)) ),
    inference(clausify,[status(thm)],[f_3764_3]) ).

cnf(f_3764_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14732,tc_HOL_Obool)),U_14733),U_14734))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14732,U_14729),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14732,U_14729),U_14733),hAPP(c_COMBK(tc_fun(U_14729,tc_HOL_Obool),U_14732),U_14731))),hAPP(hAPP(c_Product__Type_OSigma(U_14732,U_14729),U_14734),hAPP(c_COMBK(tc_fun(U_14729,tc_HOL_Obool),U_14732),U_14731))))
    | ~ sP998(U_14729,U_14731,U_14732,U_14733,U_14734) ),
    inference(clausify,[status(thm)],[f_3764_3]) ).

cnf(f_3764_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14732,U_14729),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14732,U_14729),U_14733),hAPP(c_COMBK(tc_fun(U_14729,tc_HOL_Obool),U_14732),U_14731))),hAPP(hAPP(c_Product__Type_OSigma(U_14732,U_14729),U_14734),hAPP(c_COMBK(tc_fun(U_14729,tc_HOL_Obool),U_14732),U_14731))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14732,tc_HOL_Obool)),U_14733),U_14734))
    | ~ sP998(U_14729,U_14731,U_14732,U_14733,U_14734) ),
    inference(clausify,[status(thm)],[f_3764_3]) ).

fof(f_3765_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_3765_2,plain,
    ! [U_14740,U_14739,U_14738,U_14737,U_14736,U_14735] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14736,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14735,U_14736,U_14737),U_14740)),U_14739))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14735,U_14736),tc_HOL_Obool)),U_14737),hAPP(hAPP(c_Product__Type_OSigma(U_14735,U_14736),U_14738),hAPP(c_COMBK(tc_fun(U_14736,tc_HOL_Obool),U_14735),U_14739)))) ),
    inference(variable_rename,[status(thm)],[f_3765_1]) ).

fof(f_3765_3,plain,
    ! [U_14735,U_14736,U_14737,U_14738,U_14739,U_14740] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14736,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14735,U_14736,U_14737),U_14740)),U_14739))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14735,U_14736),tc_HOL_Obool)),U_14737),hAPP(hAPP(c_Product__Type_OSigma(U_14735,U_14736),U_14738),hAPP(c_COMBK(tc_fun(U_14736,tc_HOL_Obool),U_14735),U_14739)))) ),
    inference(definitional_conversion,[status(esa)],[f_3765_2]) ).

cnf(f_3765_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14736,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_14735,U_14736,U_14737),U_14740)),U_14739))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14735,U_14736),tc_HOL_Obool)),U_14737),hAPP(hAPP(c_Product__Type_OSigma(U_14735,U_14736),U_14738),hAPP(c_COMBK(tc_fun(U_14736,tc_HOL_Obool),U_14735),U_14739)))) ),
    inference(clausify,[status(thm)],[f_3765_3]) ).

fof(f_3766_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_3766_2,plain,
    ! [U_14744,U_14743,U_14742,U_14741] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14742),U_14744))
      | U_14743 = c_Orderings_Obot__class_Obot(tc_fun(U_14741,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14741,U_14742)),hAPP(hAPP(c_Product__Type_OSigma(U_14741,U_14742),U_14743),hAPP(c_COMBK(tc_fun(U_14742,tc_HOL_Obool),U_14741),U_14744)))) ),
    inference(variable_rename,[status(thm)],[f_3766_1]) ).

fof(f_3766_3,plain,
    ! [U_14741,U_14742,U_14743,U_14744] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14742),U_14744))
      | U_14743 = c_Orderings_Obot__class_Obot(tc_fun(U_14741,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14741,U_14742)),hAPP(hAPP(c_Product__Type_OSigma(U_14741,U_14742),U_14743),hAPP(c_COMBK(tc_fun(U_14742,tc_HOL_Obool),U_14741),U_14744)))) ),
    inference(definitional_conversion,[status(esa)],[f_3766_2]) ).

cnf(f_3766_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14742),U_14744))
    | U_14743 = c_Orderings_Obot__class_Obot(tc_fun(U_14741,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14741,U_14742)),hAPP(hAPP(c_Product__Type_OSigma(U_14741,U_14742),U_14743),hAPP(c_COMBK(tc_fun(U_14742,tc_HOL_Obool),U_14741),U_14744)))) ),
    inference(clausify,[status(thm)],[f_3766_3]) ).

fof(f_3767_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_3767_2,plain,
    ! [U_14748,U_14747,U_14746,U_14745] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14745),U_14747))
      | U_14748 = c_Orderings_Obot__class_Obot(tc_fun(U_14746,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14745,U_14746)),hAPP(hAPP(c_Product__Type_OSigma(U_14745,U_14746),U_14747),hAPP(c_COMBK(tc_fun(U_14746,tc_HOL_Obool),U_14745),U_14748)))) ),
    inference(variable_rename,[status(thm)],[f_3767_1]) ).

fof(f_3767_3,plain,
    ! [U_14745,U_14746,U_14747,U_14748] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14745),U_14747))
      | U_14748 = c_Orderings_Obot__class_Obot(tc_fun(U_14746,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14745,U_14746)),hAPP(hAPP(c_Product__Type_OSigma(U_14745,U_14746),U_14747),hAPP(c_COMBK(tc_fun(U_14746,tc_HOL_Obool),U_14745),U_14748)))) ),
    inference(definitional_conversion,[status(esa)],[f_3767_2]) ).

cnf(f_3767_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14745),U_14747))
    | U_14748 = c_Orderings_Obot__class_Obot(tc_fun(U_14746,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14745,U_14746)),hAPP(hAPP(c_Product__Type_OSigma(U_14745,U_14746),U_14747),hAPP(c_COMBK(tc_fun(U_14746,tc_HOL_Obool),U_14745),U_14748)))) ),
    inference(clausify,[status(thm)],[f_3767_3]) ).

fof(f_3768_1,plain,
    ! [V_Qa_2,V_Pa_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_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_2)),hAPP(c_COMBK(tc_fun(T_c,tc_HOL_Obool),T_b),hAPP(c_Set_OCollect(T_c),V_Qa_2))),
    inference(fof_nnf,[status(thm)],[fact_Collect__split]) ).

fof(f_3768_2,plain,
    ! [U_14752,U_14751,U_14750,U_14749] : hAPP(c_Set_OCollect(tc_prod(U_14749,U_14750)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14749,U_14750,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14749,tc_fun(U_14750,tc_HOL_Obool),tc_fun(U_14750,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14750,tc_HOL_Obool),tc_fun(U_14750,tc_HOL_Obool)),U_14749),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14750)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14749),c_fconj),U_14751))),U_14752))) = hAPP(hAPP(c_Product__Type_OSigma(U_14749,U_14750),hAPP(c_Set_OCollect(U_14749),U_14751)),hAPP(c_COMBK(tc_fun(U_14750,tc_HOL_Obool),U_14749),hAPP(c_Set_OCollect(U_14750),U_14752))),
    inference(variable_rename,[status(thm)],[f_3768_1]) ).

fof(f_3768_3,plain,
    ! [U_14749,U_14750,U_14751,U_14752] : hAPP(c_Set_OCollect(tc_prod(U_14749,U_14750)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14749,U_14750,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14749,tc_fun(U_14750,tc_HOL_Obool),tc_fun(U_14750,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14750,tc_HOL_Obool),tc_fun(U_14750,tc_HOL_Obool)),U_14749),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14750)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14749),c_fconj),U_14751))),U_14752))) = hAPP(hAPP(c_Product__Type_OSigma(U_14749,U_14750),hAPP(c_Set_OCollect(U_14749),U_14751)),hAPP(c_COMBK(tc_fun(U_14750,tc_HOL_Obool),U_14749),hAPP(c_Set_OCollect(U_14750),U_14752))),
    inference(definitional_conversion,[status(esa)],[f_3768_2]) ).

cnf(f_3768_4,plain,
    hAPP(c_Set_OCollect(tc_prod(U_14749,U_14750)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14749,U_14750,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_14749,tc_fun(U_14750,tc_HOL_Obool),tc_fun(U_14750,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14750,tc_HOL_Obool),tc_fun(U_14750,tc_HOL_Obool)),U_14749),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14750)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14749),c_fconj),U_14751))),U_14752))) = hAPP(hAPP(c_Product__Type_OSigma(U_14749,U_14750),hAPP(c_Set_OCollect(U_14749),U_14751)),hAPP(c_COMBK(tc_fun(U_14750,tc_HOL_Obool),U_14749),hAPP(c_Set_OCollect(U_14750),U_14752))),
    inference(clausify,[status(thm)],[f_3768_3]) ).

fof(f_3769_1,plain,
    ! [V_Qa_2,V_Pa_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_Pa_2))),V_Qa_2))) = hAPP(hAPP(c_Product__Type_OSigma(T_b,T_c),hAPP(c_Set_OCollect(T_b),V_Pa_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_Qa_2)),
    inference(fof_nnf,[status(thm)],[fact_SetCompr__Sigma__eq]) ).

fof(f_3769_2,plain,
    ! [U_14756,U_14755,U_14754,U_14753] : hAPP(c_Set_OCollect(tc_prod(U_14753,U_14754)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14753,U_14754,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_14753,tc_fun(U_14754,tc_HOL_Obool),tc_fun(U_14754,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14754,tc_HOL_Obool),tc_fun(U_14754,tc_HOL_Obool)),U_14753),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14754)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14753),c_fconj),U_14755))),U_14756))) = hAPP(hAPP(c_Product__Type_OSigma(U_14753,U_14754),hAPP(c_Set_OCollect(U_14753),U_14755)),hAPP(hAPP(c_COMBB(tc_fun(U_14754,tc_HOL_Obool),tc_fun(U_14754,tc_HOL_Obool),U_14753),c_Set_OCollect(U_14754)),U_14756)),
    inference(variable_rename,[status(thm)],[f_3769_1]) ).

fof(f_3769_3,plain,
    ! [U_14753,U_14754,U_14755,U_14756] : hAPP(c_Set_OCollect(tc_prod(U_14753,U_14754)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14753,U_14754,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_14753,tc_fun(U_14754,tc_HOL_Obool),tc_fun(U_14754,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14754,tc_HOL_Obool),tc_fun(U_14754,tc_HOL_Obool)),U_14753),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14754)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14753),c_fconj),U_14755))),U_14756))) = hAPP(hAPP(c_Product__Type_OSigma(U_14753,U_14754),hAPP(c_Set_OCollect(U_14753),U_14755)),hAPP(hAPP(c_COMBB(tc_fun(U_14754,tc_HOL_Obool),tc_fun(U_14754,tc_HOL_Obool),U_14753),c_Set_OCollect(U_14754)),U_14756)),
    inference(definitional_conversion,[status(esa)],[f_3769_2]) ).

cnf(f_3769_4,plain,
    hAPP(c_Set_OCollect(tc_prod(U_14753,U_14754)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14753,U_14754,tc_HOL_Obool),hAPP(hAPP(c_COMBS(U_14753,tc_fun(U_14754,tc_HOL_Obool),tc_fun(U_14754,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14754,tc_HOL_Obool),tc_fun(U_14754,tc_HOL_Obool)),U_14753),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14754)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_14753),c_fconj),U_14755))),U_14756))) = hAPP(hAPP(c_Product__Type_OSigma(U_14753,U_14754),hAPP(c_Set_OCollect(U_14753),U_14755)),hAPP(hAPP(c_COMBB(tc_fun(U_14754,tc_HOL_Obool),tc_fun(U_14754,tc_HOL_Obool),U_14753),c_Set_OCollect(U_14754)),U_14756)),
    inference(clausify,[status(thm)],[f_3769_3]) ).

fof(f_3770_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_3770_2,plain,
    ! [U_14760,U_14759,U_14758,U_14757] :
      ( ( hAPP(c_Set_Oimage(tc_prod(U_14759,U_14758),U_14759,c_Product__Type_Ofst(U_14759,U_14758)),hAPP(hAPP(c_Product__Type_OSigma(U_14759,U_14758),U_14760),hAPP(c_COMBK(tc_fun(U_14758,tc_HOL_Obool),U_14759),U_14757))) = U_14760
        | U_14757 = c_Orderings_Obot__class_Obot(tc_fun(U_14758,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(tc_prod(U_14759,U_14758),U_14759,c_Product__Type_Ofst(U_14759,U_14758)),hAPP(hAPP(c_Product__Type_OSigma(U_14759,U_14758),U_14760),hAPP(c_COMBK(tc_fun(U_14758,tc_HOL_Obool),U_14759),U_14757))) = c_Orderings_Obot__class_Obot(tc_fun(U_14759,tc_HOL_Obool))
        | U_14757 != c_Orderings_Obot__class_Obot(tc_fun(U_14758,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3770_1]) ).

fof(f_3770_3,plain,
    ( ! [U_14768,U_14766,U_14764,U_14762] :
        ( hAPP(c_Set_Oimage(tc_prod(U_14766,U_14764),U_14766,c_Product__Type_Ofst(U_14766,U_14764)),hAPP(hAPP(c_Product__Type_OSigma(U_14766,U_14764),U_14768),hAPP(c_COMBK(tc_fun(U_14764,tc_HOL_Obool),U_14766),U_14762))) = U_14768
        | U_14762 = c_Orderings_Obot__class_Obot(tc_fun(U_14764,tc_HOL_Obool)) )
    & ! [U_14767,U_14765,U_14763,U_14761] :
        ( hAPP(c_Set_Oimage(tc_prod(U_14765,U_14763),U_14765,c_Product__Type_Ofst(U_14765,U_14763)),hAPP(hAPP(c_Product__Type_OSigma(U_14765,U_14763),U_14767),hAPP(c_COMBK(tc_fun(U_14763,tc_HOL_Obool),U_14765),U_14761))) = c_Orderings_Obot__class_Obot(tc_fun(U_14765,tc_HOL_Obool))
        | U_14761 != c_Orderings_Obot__class_Obot(tc_fun(U_14763,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3770_2]) ).

fof(f_3770_4,plain,
    ( ! [U_14762,U_14764,U_14766,U_14768] :
        ( hAPP(c_Set_Oimage(tc_prod(U_14766,U_14764),U_14766,c_Product__Type_Ofst(U_14766,U_14764)),hAPP(hAPP(c_Product__Type_OSigma(U_14766,U_14764),U_14768),hAPP(c_COMBK(tc_fun(U_14764,tc_HOL_Obool),U_14766),U_14762))) = U_14768
        | U_14762 = c_Orderings_Obot__class_Obot(tc_fun(U_14764,tc_HOL_Obool)) )
    & ! [U_14767,U_14763,U_14761,U_14765] :
        ( hAPP(c_Set_Oimage(tc_prod(U_14765,U_14763),U_14765,c_Product__Type_Ofst(U_14765,U_14763)),hAPP(hAPP(c_Product__Type_OSigma(U_14765,U_14763),U_14767),hAPP(c_COMBK(tc_fun(U_14763,tc_HOL_Obool),U_14765),U_14761))) = c_Orderings_Obot__class_Obot(tc_fun(U_14765,tc_HOL_Obool))
        | U_14761 != c_Orderings_Obot__class_Obot(tc_fun(U_14763,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3770_3]) ).

cnf(f_3770_5,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_14765,U_14763),U_14765,c_Product__Type_Ofst(U_14765,U_14763)),hAPP(hAPP(c_Product__Type_OSigma(U_14765,U_14763),U_14767),hAPP(c_COMBK(tc_fun(U_14763,tc_HOL_Obool),U_14765),U_14761))) = c_Orderings_Obot__class_Obot(tc_fun(U_14765,tc_HOL_Obool))
    | U_14761 != c_Orderings_Obot__class_Obot(tc_fun(U_14763,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3770_4]) ).

cnf(f_3770_6,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_14766,U_14764),U_14766,c_Product__Type_Ofst(U_14766,U_14764)),hAPP(hAPP(c_Product__Type_OSigma(U_14766,U_14764),U_14768),hAPP(c_COMBK(tc_fun(U_14764,tc_HOL_Obool),U_14766),U_14762))) = U_14768
    | U_14762 = c_Orderings_Obot__class_Obot(tc_fun(U_14764,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3770_4]) ).

fof(f_3771_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_3771_2,plain,
    ! [U_14772,U_14771,U_14770,U_14769] :
      ( ( hAPP(c_Set_Oimage(tc_prod(U_14770,U_14771),U_14771,c_Product__Type_Osnd(U_14770,U_14771)),hAPP(hAPP(c_Product__Type_OSigma(U_14770,U_14771),U_14769),hAPP(c_COMBK(tc_fun(U_14771,tc_HOL_Obool),U_14770),U_14772))) = U_14772
        | U_14769 = c_Orderings_Obot__class_Obot(tc_fun(U_14770,tc_HOL_Obool)) )
      & ( hAPP(c_Set_Oimage(tc_prod(U_14770,U_14771),U_14771,c_Product__Type_Osnd(U_14770,U_14771)),hAPP(hAPP(c_Product__Type_OSigma(U_14770,U_14771),U_14769),hAPP(c_COMBK(tc_fun(U_14771,tc_HOL_Obool),U_14770),U_14772))) = c_Orderings_Obot__class_Obot(tc_fun(U_14771,tc_HOL_Obool))
        | U_14769 != c_Orderings_Obot__class_Obot(tc_fun(U_14770,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_3771_1]) ).

fof(f_3771_3,plain,
    ( ! [U_14780,U_14778,U_14776,U_14774] :
        ( hAPP(c_Set_Oimage(tc_prod(U_14776,U_14778),U_14778,c_Product__Type_Osnd(U_14776,U_14778)),hAPP(hAPP(c_Product__Type_OSigma(U_14776,U_14778),U_14774),hAPP(c_COMBK(tc_fun(U_14778,tc_HOL_Obool),U_14776),U_14780))) = U_14780
        | U_14774 = c_Orderings_Obot__class_Obot(tc_fun(U_14776,tc_HOL_Obool)) )
    & ! [U_14779,U_14777,U_14775,U_14773] :
        ( hAPP(c_Set_Oimage(tc_prod(U_14775,U_14777),U_14777,c_Product__Type_Osnd(U_14775,U_14777)),hAPP(hAPP(c_Product__Type_OSigma(U_14775,U_14777),U_14773),hAPP(c_COMBK(tc_fun(U_14777,tc_HOL_Obool),U_14775),U_14779))) = c_Orderings_Obot__class_Obot(tc_fun(U_14777,tc_HOL_Obool))
        | U_14773 != c_Orderings_Obot__class_Obot(tc_fun(U_14775,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_3771_2]) ).

fof(f_3771_4,plain,
    ( ! [U_14778,U_14774,U_14776,U_14780] :
        ( hAPP(c_Set_Oimage(tc_prod(U_14776,U_14778),U_14778,c_Product__Type_Osnd(U_14776,U_14778)),hAPP(hAPP(c_Product__Type_OSigma(U_14776,U_14778),U_14774),hAPP(c_COMBK(tc_fun(U_14778,tc_HOL_Obool),U_14776),U_14780))) = U_14780
        | U_14774 = c_Orderings_Obot__class_Obot(tc_fun(U_14776,tc_HOL_Obool)) )
    & ! [U_14777,U_14779,U_14775,U_14773] :
        ( hAPP(c_Set_Oimage(tc_prod(U_14775,U_14777),U_14777,c_Product__Type_Osnd(U_14775,U_14777)),hAPP(hAPP(c_Product__Type_OSigma(U_14775,U_14777),U_14773),hAPP(c_COMBK(tc_fun(U_14777,tc_HOL_Obool),U_14775),U_14779))) = c_Orderings_Obot__class_Obot(tc_fun(U_14777,tc_HOL_Obool))
        | U_14773 != c_Orderings_Obot__class_Obot(tc_fun(U_14775,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3771_3]) ).

cnf(f_3771_5,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_14775,U_14777),U_14777,c_Product__Type_Osnd(U_14775,U_14777)),hAPP(hAPP(c_Product__Type_OSigma(U_14775,U_14777),U_14773),hAPP(c_COMBK(tc_fun(U_14777,tc_HOL_Obool),U_14775),U_14779))) = c_Orderings_Obot__class_Obot(tc_fun(U_14777,tc_HOL_Obool))
    | U_14773 != c_Orderings_Obot__class_Obot(tc_fun(U_14775,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3771_4]) ).

cnf(f_3771_6,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_14776,U_14778),U_14778,c_Product__Type_Osnd(U_14776,U_14778)),hAPP(hAPP(c_Product__Type_OSigma(U_14776,U_14778),U_14774),hAPP(c_COMBK(tc_fun(U_14778,tc_HOL_Obool),U_14776),U_14780))) = U_14780
    | U_14774 = c_Orderings_Obot__class_Obot(tc_fun(U_14776,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3771_4]) ).

fof(f_3772_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_3772_2,plain,
    ! [U_14782,U_14781] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14781,U_14781),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14781,U_14782)),hAPP(hAPP(c_Product__Type_OSigma(U_14781,U_14781),hAPP(c_Relation_OField(U_14781),U_14782)),hAPP(c_COMBK(tc_fun(U_14781,tc_HOL_Obool),U_14781),hAPP(c_Relation_OField(U_14781),U_14782))))),
    inference(variable_rename,[status(thm)],[f_3772_1]) ).

fof(f_3772_3,plain,
    ! [U_14781,U_14782] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14781,U_14781),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14781,U_14782)),hAPP(hAPP(c_Product__Type_OSigma(U_14781,U_14781),hAPP(c_Relation_OField(U_14781),U_14782)),hAPP(c_COMBK(tc_fun(U_14781,tc_HOL_Obool),U_14781),hAPP(c_Relation_OField(U_14781),U_14782))))),
    inference(definitional_conversion,[status(esa)],[f_3772_2]) ).

cnf(f_3772_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14781,U_14781),tc_HOL_Obool)),c_Transitive__Closure_Otrancl(U_14781,U_14782)),hAPP(hAPP(c_Product__Type_OSigma(U_14781,U_14781),hAPP(c_Relation_OField(U_14781),U_14782)),hAPP(c_COMBK(tc_fun(U_14781,tc_HOL_Obool),U_14781),hAPP(c_Relation_OField(U_14781),U_14782))))),
    inference(clausify,[status(thm)],[f_3772_3]) ).

fof(f_3773_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_3773_2,plain,
    ! [U_14785,U_14784,U_14783] : hAPP(c_Finite__Set_Ofold1(U_14783,U_14784),U_14785) = c_HOL_OThe(U_14783,c_Finite__Set_Ofold1Set(U_14783,U_14784,U_14785)),
    inference(variable_rename,[status(thm)],[f_3773_1]) ).

fof(f_3773_3,plain,
    ! [U_14783,U_14784,U_14785] : hAPP(c_Finite__Set_Ofold1(U_14783,U_14784),U_14785) = c_HOL_OThe(U_14783,c_Finite__Set_Ofold1Set(U_14783,U_14784,U_14785)),
    inference(definitional_conversion,[status(esa)],[f_3773_2]) ).

cnf(f_3773_4,plain,
    hAPP(c_Finite__Set_Ofold1(U_14783,U_14784),U_14785) = c_HOL_OThe(U_14783,c_Finite__Set_Ofold1Set(U_14783,U_14784,U_14785)),
    inference(clausify,[status(thm)],[f_3773_3]) ).

fof(f_3774_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_3774_2,plain,
    ! [U_14787,U_14786] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_14786,U_14787) = hAPP(c_Finite__Set_Ofold1(U_14786,c_Lattices_Osemilattice__sup__class_Osup(U_14786)),U_14787)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14786),U_14787))
      | ~ class_Lattices_Olattice(U_14786) ),
    inference(variable_rename,[status(thm)],[f_3774_1]) ).

fof(f_3774_3,plain,
    ! [U_14786,U_14787] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_14786,U_14787) = hAPP(c_Finite__Set_Ofold1(U_14786,c_Lattices_Osemilattice__sup__class_Osup(U_14786)),U_14787)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14786),U_14787))
      | ~ class_Lattices_Olattice(U_14786) ),
    inference(definitional_conversion,[status(esa)],[f_3774_2]) ).

cnf(f_3774_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_14786,U_14787) = hAPP(c_Finite__Set_Ofold1(U_14786,c_Lattices_Osemilattice__sup__class_Osup(U_14786)),U_14787)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14786),U_14787))
    | ~ class_Lattices_Olattice(U_14786) ),
    inference(clausify,[status(thm)],[f_3774_3]) ).

fof(f_3775_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_3775_2,plain,
    ! [U_14789,U_14788] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_14788,U_14789) = hAPP(c_Finite__Set_Ofold1(U_14788,c_Lattices_Osemilattice__inf__class_Oinf(U_14788)),U_14789)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14788),U_14789))
      | ~ class_Lattices_Olattice(U_14788) ),
    inference(variable_rename,[status(thm)],[f_3775_1]) ).

fof(f_3775_3,plain,
    ! [U_14788,U_14789] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_14788,U_14789) = hAPP(c_Finite__Set_Ofold1(U_14788,c_Lattices_Osemilattice__inf__class_Oinf(U_14788)),U_14789)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14788),U_14789))
      | ~ class_Lattices_Olattice(U_14788) ),
    inference(definitional_conversion,[status(esa)],[f_3775_2]) ).

cnf(f_3775_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_14788,U_14789) = hAPP(c_Finite__Set_Ofold1(U_14788,c_Lattices_Osemilattice__inf__class_Oinf(U_14788)),U_14789)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14788),U_14789))
    | ~ class_Lattices_Olattice(U_14788) ),
    inference(clausify,[status(thm)],[f_3775_3]) ).

fof(f_3776_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_3776_2,plain,
    ! [U_14791,U_14790] :
      ( c_Big__Operators_Olinorder__class_OMin(U_14790,U_14791) = hAPP(c_Finite__Set_Ofold1(U_14790,c_Orderings_Oord__class_Omin(U_14790)),U_14791)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14790),U_14791))
      | ~ class_Orderings_Olinorder(U_14790) ),
    inference(variable_rename,[status(thm)],[f_3776_1]) ).

fof(f_3776_3,plain,
    ! [U_14790,U_14791] :
      ( c_Big__Operators_Olinorder__class_OMin(U_14790,U_14791) = hAPP(c_Finite__Set_Ofold1(U_14790,c_Orderings_Oord__class_Omin(U_14790)),U_14791)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14790),U_14791))
      | ~ class_Orderings_Olinorder(U_14790) ),
    inference(definitional_conversion,[status(esa)],[f_3776_2]) ).

cnf(f_3776_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_14790,U_14791) = hAPP(c_Finite__Set_Ofold1(U_14790,c_Orderings_Oord__class_Omin(U_14790)),U_14791)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14790),U_14791))
    | ~ class_Orderings_Olinorder(U_14790) ),
    inference(clausify,[status(thm)],[f_3776_3]) ).

fof(f_3777_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_3777_2,plain,
    ! [U_14793,U_14792] :
      ( c_Big__Operators_Olinorder__class_OMax(U_14792,U_14793) = hAPP(c_Finite__Set_Ofold1(U_14792,c_Orderings_Oord__class_Omax(U_14792)),U_14793)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14792),U_14793))
      | ~ class_Orderings_Olinorder(U_14792) ),
    inference(variable_rename,[status(thm)],[f_3777_1]) ).

fof(f_3777_3,plain,
    ! [U_14792,U_14793] :
      ( c_Big__Operators_Olinorder__class_OMax(U_14792,U_14793) = hAPP(c_Finite__Set_Ofold1(U_14792,c_Orderings_Oord__class_Omax(U_14792)),U_14793)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14792),U_14793))
      | ~ class_Orderings_Olinorder(U_14792) ),
    inference(definitional_conversion,[status(esa)],[f_3777_2]) ).

cnf(f_3777_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_14792,U_14793) = hAPP(c_Finite__Set_Ofold1(U_14792,c_Orderings_Oord__class_Omax(U_14792)),U_14793)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14792),U_14793))
    | ~ class_Orderings_Olinorder(U_14792) ),
    inference(clausify,[status(thm)],[f_3777_3]) ).

fof(f_3778_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_3778_2,plain,
    ! [U_14795,U_14794] :
      ( c_Big__Operators_Olattice_OInf__fin(U_14794,c_Orderings_Oord__class_Omin(U_14794),U_14795) = hAPP(c_Finite__Set_Ofold1(U_14794,c_Orderings_Oord__class_Omin(U_14794)),U_14795)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14794),U_14795))
      | ~ class_Orderings_Olinorder(U_14794) ),
    inference(variable_rename,[status(thm)],[f_3778_1]) ).

fof(f_3778_3,plain,
    ! [U_14794,U_14795] :
      ( c_Big__Operators_Olattice_OInf__fin(U_14794,c_Orderings_Oord__class_Omin(U_14794),U_14795) = hAPP(c_Finite__Set_Ofold1(U_14794,c_Orderings_Oord__class_Omin(U_14794)),U_14795)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14794),U_14795))
      | ~ class_Orderings_Olinorder(U_14794) ),
    inference(definitional_conversion,[status(esa)],[f_3778_2]) ).

cnf(f_3778_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_14794,c_Orderings_Oord__class_Omin(U_14794),U_14795) = hAPP(c_Finite__Set_Ofold1(U_14794,c_Orderings_Oord__class_Omin(U_14794)),U_14795)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14794),U_14795))
    | ~ class_Orderings_Olinorder(U_14794) ),
    inference(clausify,[status(thm)],[f_3778_3]) ).

fof(f_3779_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_3779_2,plain,
    ! [U_14797,U_14796] :
      ( c_Big__Operators_Olattice_OSup__fin(U_14796,c_Orderings_Oord__class_Omax(U_14796),U_14797) = hAPP(c_Finite__Set_Ofold1(U_14796,c_Orderings_Oord__class_Omax(U_14796)),U_14797)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14796),U_14797))
      | ~ class_Orderings_Olinorder(U_14796) ),
    inference(variable_rename,[status(thm)],[f_3779_1]) ).

fof(f_3779_3,plain,
    ! [U_14796,U_14797] :
      ( c_Big__Operators_Olattice_OSup__fin(U_14796,c_Orderings_Oord__class_Omax(U_14796),U_14797) = hAPP(c_Finite__Set_Ofold1(U_14796,c_Orderings_Oord__class_Omax(U_14796)),U_14797)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14796),U_14797))
      | ~ class_Orderings_Olinorder(U_14796) ),
    inference(definitional_conversion,[status(esa)],[f_3779_2]) ).

cnf(f_3779_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_14796,c_Orderings_Oord__class_Omax(U_14796),U_14797) = hAPP(c_Finite__Set_Ofold1(U_14796,c_Orderings_Oord__class_Omax(U_14796)),U_14797)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14796),U_14797))
    | ~ class_Orderings_Olinorder(U_14796) ),
    inference(clausify,[status(thm)],[f_3779_3]) ).

fof(f_3780_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_3780_2,plain,
    ! [U_14803,U_14802,U_14801,U_14800,U_14799,U_14798] : hAPP(hAPP(c_Product__Type_OSigma(U_14798,U_14799),hAPP(hAPP(c_Set_Oinsert(U_14798),U_14800),U_14801)),hAPP(c_COMBK(tc_fun(U_14799,tc_HOL_Obool),U_14798),hAPP(hAPP(c_Set_Oinsert(U_14799),U_14802),U_14803))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14798,U_14799)),hAPP(hAPP(c_Product__Type_OPair(U_14798,U_14799),U_14800),U_14802)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14798,U_14799),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14798,U_14799),U_14801),hAPP(c_COMBK(tc_fun(U_14799,tc_HOL_Obool),U_14798),hAPP(hAPP(c_Set_Oinsert(U_14799),U_14802),U_14803)))),hAPP(hAPP(c_Product__Type_OSigma(U_14798,U_14799),hAPP(hAPP(c_Set_Oinsert(U_14798),U_14800),U_14801)),hAPP(c_COMBK(tc_fun(U_14799,tc_HOL_Obool),U_14798),U_14803)))),
    inference(variable_rename,[status(thm)],[f_3780_1]) ).

fof(f_3780_3,plain,
    ! [U_14798,U_14799,U_14800,U_14801,U_14802,U_14803] : hAPP(hAPP(c_Product__Type_OSigma(U_14798,U_14799),hAPP(hAPP(c_Set_Oinsert(U_14798),U_14800),U_14801)),hAPP(c_COMBK(tc_fun(U_14799,tc_HOL_Obool),U_14798),hAPP(hAPP(c_Set_Oinsert(U_14799),U_14802),U_14803))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14798,U_14799)),hAPP(hAPP(c_Product__Type_OPair(U_14798,U_14799),U_14800),U_14802)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14798,U_14799),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14798,U_14799),U_14801),hAPP(c_COMBK(tc_fun(U_14799,tc_HOL_Obool),U_14798),hAPP(hAPP(c_Set_Oinsert(U_14799),U_14802),U_14803)))),hAPP(hAPP(c_Product__Type_OSigma(U_14798,U_14799),hAPP(hAPP(c_Set_Oinsert(U_14798),U_14800),U_14801)),hAPP(c_COMBK(tc_fun(U_14799,tc_HOL_Obool),U_14798),U_14803)))),
    inference(definitional_conversion,[status(esa)],[f_3780_2]) ).

cnf(f_3780_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14798,U_14799),hAPP(hAPP(c_Set_Oinsert(U_14798),U_14800),U_14801)),hAPP(c_COMBK(tc_fun(U_14799,tc_HOL_Obool),U_14798),hAPP(hAPP(c_Set_Oinsert(U_14799),U_14802),U_14803))) = hAPP(hAPP(c_Set_Oinsert(tc_prod(U_14798,U_14799)),hAPP(hAPP(c_Product__Type_OPair(U_14798,U_14799),U_14800),U_14802)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_14798,U_14799),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14798,U_14799),U_14801),hAPP(c_COMBK(tc_fun(U_14799,tc_HOL_Obool),U_14798),hAPP(hAPP(c_Set_Oinsert(U_14799),U_14802),U_14803)))),hAPP(hAPP(c_Product__Type_OSigma(U_14798,U_14799),hAPP(hAPP(c_Set_Oinsert(U_14798),U_14800),U_14801)),hAPP(c_COMBK(tc_fun(U_14799,tc_HOL_Obool),U_14798),U_14803)))),
    inference(clausify,[status(thm)],[f_3780_3]) ).

fof(f_3781_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_3781_2,plain,
    ! [U_14807,U_14806,U_14805,U_14804] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14804),U_14807))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_14804,tc_HOL_Obool)),U_14807),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_14804),U_14805),U_14806)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14804,U_14804),tc_HOL_Obool)),U_14806),hAPP(hAPP(c_Product__Type_OSigma(U_14804,U_14804),U_14805),hAPP(c_COMBK(tc_fun(U_14804,tc_HOL_Obool),U_14804),U_14805))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14804),U_14805)) ),
    inference(variable_rename,[status(thm)],[f_3781_1]) ).

fof(f_3781_3,plain,
    ! [U_14804,U_14805,U_14806,U_14807] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14804),U_14807))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_14804,tc_HOL_Obool)),U_14807),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_14804),U_14805),U_14806)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14804,U_14804),tc_HOL_Obool)),U_14806),hAPP(hAPP(c_Product__Type_OSigma(U_14804,U_14804),U_14805),hAPP(c_COMBK(tc_fun(U_14804,tc_HOL_Obool),U_14804),U_14805))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14804),U_14805)) ),
    inference(definitional_conversion,[status(esa)],[f_3781_2]) ).

cnf(f_3781_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_14804),U_14807))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_14804,tc_HOL_Obool)),U_14807),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_14804),U_14805),U_14806)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14804,U_14804),tc_HOL_Obool)),U_14806),hAPP(hAPP(c_Product__Type_OSigma(U_14804,U_14804),U_14805),hAPP(c_COMBK(tc_fun(U_14804,tc_HOL_Obool),U_14804),U_14805))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14804),U_14805)) ),
    inference(clausify,[status(thm)],[f_3781_3]) ).

fof(f_3782_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_3782_2,plain,
    ! [U_14815,U_14814,U_14813,U_14812,U_14811,U_14810,U_14809,U_14808] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(U_14808,U_14809),tc_fun(tc_prod(U_14810,U_14811),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14808,U_14809),U_14812),hAPP(c_COMBK(tc_fun(U_14809,tc_HOL_Obool),U_14808),U_14813))),hAPP(c_Product__Type_Oprod_Oprod__case(U_14808,U_14809,tc_fun(tc_prod(U_14810,U_14811),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_14808,tc_fun(U_14809,tc_fun(U_14810,tc_fun(U_14811,tc_HOL_Obool))),tc_fun(U_14809,tc_fun(tc_prod(U_14810,U_14811),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14810,tc_fun(U_14811,tc_HOL_Obool)),tc_fun(tc_prod(U_14810,U_14811),tc_HOL_Obool)),tc_fun(tc_fun(U_14809,tc_fun(U_14810,tc_fun(U_14811,tc_HOL_Obool))),tc_fun(U_14809,tc_fun(tc_prod(U_14810,U_14811),tc_HOL_Obool))),U_14808),c_COMBB(tc_fun(U_14810,tc_fun(U_14811,tc_HOL_Obool)),tc_fun(tc_prod(U_14810,U_14811),tc_HOL_Obool),U_14809)),hAPP(hAPP(c_COMBB(tc_fun(U_14810,tc_HOL_Obool),tc_fun(tc_fun(U_14810,tc_fun(U_14811,tc_HOL_Obool)),tc_fun(tc_prod(U_14810,U_14811),tc_HOL_Obool)),U_14808),c_Product__Type_OSigma(U_14810,U_14811)),U_14814))),hAPP(hAPP(c_COMBB(tc_fun(U_14811,tc_HOL_Obool),tc_fun(U_14810,tc_fun(U_14811,tc_HOL_Obool)),U_14809),c_COMBK(tc_fun(U_14811,tc_HOL_Obool),U_14810)),U_14815)))) = hAPP(hAPP(c_Product__Type_OSigma(U_14810,U_14811),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14808,tc_fun(U_14810,tc_HOL_Obool)),U_14812),U_14814)),hAPP(c_COMBK(tc_fun(U_14811,tc_HOL_Obool),U_14810),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14809,tc_fun(U_14811,tc_HOL_Obool)),U_14813),U_14815))),
    inference(variable_rename,[status(thm)],[f_3782_1]) ).

fof(f_3782_3,plain,
    ! [U_14808,U_14809,U_14810,U_14811,U_14812,U_14813,U_14814,U_14815] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(U_14808,U_14809),tc_fun(tc_prod(U_14810,U_14811),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14808,U_14809),U_14812),hAPP(c_COMBK(tc_fun(U_14809,tc_HOL_Obool),U_14808),U_14813))),hAPP(c_Product__Type_Oprod_Oprod__case(U_14808,U_14809,tc_fun(tc_prod(U_14810,U_14811),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_14808,tc_fun(U_14809,tc_fun(U_14810,tc_fun(U_14811,tc_HOL_Obool))),tc_fun(U_14809,tc_fun(tc_prod(U_14810,U_14811),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14810,tc_fun(U_14811,tc_HOL_Obool)),tc_fun(tc_prod(U_14810,U_14811),tc_HOL_Obool)),tc_fun(tc_fun(U_14809,tc_fun(U_14810,tc_fun(U_14811,tc_HOL_Obool))),tc_fun(U_14809,tc_fun(tc_prod(U_14810,U_14811),tc_HOL_Obool))),U_14808),c_COMBB(tc_fun(U_14810,tc_fun(U_14811,tc_HOL_Obool)),tc_fun(tc_prod(U_14810,U_14811),tc_HOL_Obool),U_14809)),hAPP(hAPP(c_COMBB(tc_fun(U_14810,tc_HOL_Obool),tc_fun(tc_fun(U_14810,tc_fun(U_14811,tc_HOL_Obool)),tc_fun(tc_prod(U_14810,U_14811),tc_HOL_Obool)),U_14808),c_Product__Type_OSigma(U_14810,U_14811)),U_14814))),hAPP(hAPP(c_COMBB(tc_fun(U_14811,tc_HOL_Obool),tc_fun(U_14810,tc_fun(U_14811,tc_HOL_Obool)),U_14809),c_COMBK(tc_fun(U_14811,tc_HOL_Obool),U_14810)),U_14815)))) = hAPP(hAPP(c_Product__Type_OSigma(U_14810,U_14811),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14808,tc_fun(U_14810,tc_HOL_Obool)),U_14812),U_14814)),hAPP(c_COMBK(tc_fun(U_14811,tc_HOL_Obool),U_14810),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14809,tc_fun(U_14811,tc_HOL_Obool)),U_14813),U_14815))),
    inference(definitional_conversion,[status(esa)],[f_3782_2]) ).

cnf(f_3782_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_prod(U_14808,U_14809),tc_fun(tc_prod(U_14810,U_14811),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_14808,U_14809),U_14812),hAPP(c_COMBK(tc_fun(U_14809,tc_HOL_Obool),U_14808),U_14813))),hAPP(c_Product__Type_Oprod_Oprod__case(U_14808,U_14809,tc_fun(tc_prod(U_14810,U_14811),tc_HOL_Obool)),hAPP(hAPP(c_COMBC(U_14808,tc_fun(U_14809,tc_fun(U_14810,tc_fun(U_14811,tc_HOL_Obool))),tc_fun(U_14809,tc_fun(tc_prod(U_14810,U_14811),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14810,tc_fun(U_14811,tc_HOL_Obool)),tc_fun(tc_prod(U_14810,U_14811),tc_HOL_Obool)),tc_fun(tc_fun(U_14809,tc_fun(U_14810,tc_fun(U_14811,tc_HOL_Obool))),tc_fun(U_14809,tc_fun(tc_prod(U_14810,U_14811),tc_HOL_Obool))),U_14808),c_COMBB(tc_fun(U_14810,tc_fun(U_14811,tc_HOL_Obool)),tc_fun(tc_prod(U_14810,U_14811),tc_HOL_Obool),U_14809)),hAPP(hAPP(c_COMBB(tc_fun(U_14810,tc_HOL_Obool),tc_fun(tc_fun(U_14810,tc_fun(U_14811,tc_HOL_Obool)),tc_fun(tc_prod(U_14810,U_14811),tc_HOL_Obool)),U_14808),c_Product__Type_OSigma(U_14810,U_14811)),U_14814))),hAPP(hAPP(c_COMBB(tc_fun(U_14811,tc_HOL_Obool),tc_fun(U_14810,tc_fun(U_14811,tc_HOL_Obool)),U_14809),c_COMBK(tc_fun(U_14811,tc_HOL_Obool),U_14810)),U_14815)))) = hAPP(hAPP(c_Product__Type_OSigma(U_14810,U_14811),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14808,tc_fun(U_14810,tc_HOL_Obool)),U_14812),U_14814)),hAPP(c_COMBK(tc_fun(U_14811,tc_HOL_Obool),U_14810),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14809,tc_fun(U_14811,tc_HOL_Obool)),U_14813),U_14815))),
    inference(clausify,[status(thm)],[f_3782_3]) ).

fof(f_3783_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_3783_2,plain,
    ! [U_14819,U_14818,U_14817,U_14816] : hAPP(hAPP(c_Product__Type_OSigma(U_14816,U_14817),U_14818),U_14819) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14816,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool)),U_14818),hAPP(hAPP(c_COMBS(U_14816,tc_fun(U_14817,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool)),tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14817,tc_HOL_Obool),tc_fun(tc_fun(U_14817,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool)),tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool)),U_14816),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14817,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool))),U_14819)),hAPP(hAPP(c_COMBC(U_14816,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool),tc_fun(U_14817,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14817,tc_fun(tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool),tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool),tc_fun(U_14817,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool))),U_14816),c_COMBC(U_14817,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool),tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14817,tc_prod(U_14816,U_14817)),tc_fun(U_14817,tc_fun(tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool),tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool))),U_14816),hAPP(c_COMBB(tc_prod(U_14816,U_14817),tc_fun(tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool),tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool)),U_14817),c_Set_Oinsert(tc_prod(U_14816,U_14817)))),c_Product__Type_OPair(U_14816,U_14817)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3783_1]) ).

fof(f_3783_3,plain,
    ! [U_14816,U_14817,U_14818,U_14819] : hAPP(hAPP(c_Product__Type_OSigma(U_14816,U_14817),U_14818),U_14819) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14816,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool)),U_14818),hAPP(hAPP(c_COMBS(U_14816,tc_fun(U_14817,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool)),tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14817,tc_HOL_Obool),tc_fun(tc_fun(U_14817,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool)),tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool)),U_14816),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14817,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool))),U_14819)),hAPP(hAPP(c_COMBC(U_14816,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool),tc_fun(U_14817,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14817,tc_fun(tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool),tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool),tc_fun(U_14817,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool))),U_14816),c_COMBC(U_14817,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool),tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14817,tc_prod(U_14816,U_14817)),tc_fun(U_14817,tc_fun(tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool),tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool))),U_14816),hAPP(c_COMBB(tc_prod(U_14816,U_14817),tc_fun(tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool),tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool)),U_14817),c_Set_Oinsert(tc_prod(U_14816,U_14817)))),c_Product__Type_OPair(U_14816,U_14817)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_3783_2]) ).

cnf(f_3783_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_14816,U_14817),U_14818),U_14819) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14816,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool)),U_14818),hAPP(hAPP(c_COMBS(U_14816,tc_fun(U_14817,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool)),tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_14817,tc_HOL_Obool),tc_fun(tc_fun(U_14817,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool)),tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool)),U_14816),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14817,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool))),U_14819)),hAPP(hAPP(c_COMBC(U_14816,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool),tc_fun(U_14817,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14817,tc_fun(tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool),tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool))),tc_fun(tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool),tc_fun(U_14817,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool))),U_14816),c_COMBC(U_14817,tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool),tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14817,tc_prod(U_14816,U_14817)),tc_fun(U_14817,tc_fun(tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool),tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool))),U_14816),hAPP(c_COMBB(tc_prod(U_14816,U_14817),tc_fun(tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool),tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool)),U_14817),c_Set_Oinsert(tc_prod(U_14816,U_14817)))),c_Product__Type_OPair(U_14816,U_14817)))),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_14816,U_14817),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3783_3]) ).

fof(f_3784_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_3784_2,plain,
    ! [U_14822,U_14821,U_14820] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14820),hAPP(c_Finite__Set_Ofold1(U_14820,c_Lattices_Osemilattice__inf__class_Oinf(U_14820)),U_14821)),U_14822))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14820),U_14822),U_14821))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14820),U_14821))
      | ~ class_Lattices_Osemilattice__inf(U_14820) ),
    inference(variable_rename,[status(thm)],[f_3784_1]) ).

fof(f_3784_3,plain,
    ! [U_14820,U_14821,U_14822] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14820),hAPP(c_Finite__Set_Ofold1(U_14820,c_Lattices_Osemilattice__inf__class_Oinf(U_14820)),U_14821)),U_14822))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14820),U_14822),U_14821))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14820),U_14821))
      | ~ class_Lattices_Osemilattice__inf(U_14820) ),
    inference(definitional_conversion,[status(esa)],[f_3784_2]) ).

cnf(f_3784_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14820),hAPP(c_Finite__Set_Ofold1(U_14820,c_Lattices_Osemilattice__inf__class_Oinf(U_14820)),U_14821)),U_14822))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14820),U_14822),U_14821))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14820),U_14821))
    | ~ class_Lattices_Osemilattice__inf(U_14820) ),
    inference(clausify,[status(thm)],[f_3784_3]) ).

fof(f_3785_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_3785_2,plain,
    ! [U_14825,U_14824,U_14823] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_14823,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_14823),U_14824),U_14825)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14823,U_14823),tc_HOL_Obool)),U_14825),hAPP(hAPP(c_Product__Type_OSigma(U_14823,U_14823),U_14824),hAPP(c_COMBK(tc_fun(U_14823,tc_HOL_Obool),U_14823),U_14824))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14823),U_14824)) ),
    inference(variable_rename,[status(thm)],[f_3785_1]) ).

fof(f_3785_3,plain,
    ! [U_14823,U_14824,U_14825] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_14823,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_14823),U_14824),U_14825)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14823,U_14823),tc_HOL_Obool)),U_14825),hAPP(hAPP(c_Product__Type_OSigma(U_14823,U_14823),U_14824),hAPP(c_COMBK(tc_fun(U_14823,tc_HOL_Obool),U_14823),U_14824))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14823),U_14824)) ),
    inference(definitional_conversion,[status(esa)],[f_3785_2]) ).

cnf(f_3785_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_14823,tc_HOL_Obool)),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_14823),U_14824),U_14825)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14823,U_14823),tc_HOL_Obool)),U_14825),hAPP(hAPP(c_Product__Type_OSigma(U_14823,U_14823),U_14824),hAPP(c_COMBK(tc_fun(U_14823,tc_HOL_Obool),U_14823),U_14824))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14823),U_14824)) ),
    inference(clausify,[status(thm)],[f_3785_3]) ).

fof(f_3786_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_3786_2,plain,
    ! [U_14830,U_14829,U_14828] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14828),U_14830),hAPP(c_Finite__Set_Ofold1(U_14828,c_Lattices_Osemilattice__inf__class_Oinf(U_14828)),U_14829)))
          | ? [U_14827] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14828),U_14830),U_14827))
              & hBOOL(hAPP(hAPP(c_member(U_14828),U_14827),U_14829)) ) )
        & ( ! [U_14826] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14828),U_14830),U_14826))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14828),U_14826),U_14829)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14828),U_14830),hAPP(c_Finite__Set_Ofold1(U_14828,c_Lattices_Osemilattice__inf__class_Oinf(U_14828)),U_14829))) ) )
      | U_14829 = c_Orderings_Obot__class_Obot(tc_fun(U_14828,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14828),U_14829))
      | ~ class_Lattices_Osemilattice__inf(U_14828) ),
    inference(variable_rename,[status(thm)],[f_3786_1]) ).

fof(f_3786_3,plain,
    ! [U_14830,U_14829,U_14828] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14828),U_14830),hAPP(c_Finite__Set_Ofold1(U_14828,c_Lattices_Osemilattice__inf__class_Oinf(U_14828)),U_14829)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14828),U_14830),sK333(U_14830,U_14829,U_14828)))
            & hBOOL(hAPP(hAPP(c_member(U_14828),sK333(U_14830,U_14829,U_14828)),U_14829)) ) )
        & ( ! [U_14826] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14828),U_14830),U_14826))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14828),U_14826),U_14829)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14828),U_14830),hAPP(c_Finite__Set_Ofold1(U_14828,c_Lattices_Osemilattice__inf__class_Oinf(U_14828)),U_14829))) ) )
      | U_14829 = c_Orderings_Obot__class_Obot(tc_fun(U_14828,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14828),U_14829))
      | ~ class_Lattices_Osemilattice__inf(U_14828) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK333]),skolemize(U_14827,sK333(U_14830,U_14829,U_14828))],[f_3786_2]) ).

fof(f_3786_4,plain,
    ( ! [U_14828,U_14829,U_14830] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14828),U_14830),sK333(U_14830,U_14829,U_14828)))
        | ~ sP999(U_14828,U_14829,U_14830) )
    & ! [U_14828,U_14829,U_14830] :
        ( hBOOL(hAPP(hAPP(c_member(U_14828),sK333(U_14830,U_14829,U_14828)),U_14829))
        | ~ sP999(U_14828,U_14829,U_14830) )
    & ! [U_14826,U_14828,U_14829,U_14830] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14828),U_14830),hAPP(c_Finite__Set_Ofold1(U_14828,c_Lattices_Osemilattice__inf__class_Oinf(U_14828)),U_14829)))
        | sP999(U_14828,U_14829,U_14830)
        | ~ sP1000(U_14826,U_14828,U_14829,U_14830) )
    & ! [U_14826,U_14828,U_14829,U_14830] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14828),U_14830),U_14826))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14828),U_14826),U_14829))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14828),U_14830),hAPP(c_Finite__Set_Ofold1(U_14828,c_Lattices_Osemilattice__inf__class_Oinf(U_14828)),U_14829)))
        | ~ sP1000(U_14826,U_14828,U_14829,U_14830) )
    & ! [U_14826,U_14828,U_14829,U_14830] :
        ( sP1000(U_14826,U_14828,U_14829,U_14830)
        | U_14829 = c_Orderings_Obot__class_Obot(tc_fun(U_14828,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14828),U_14829))
        | ~ class_Lattices_Osemilattice__inf(U_14828) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP999,sP1000])],[f_3786_3]) ).

cnf(f_3786_5,plain,
    ( sP1000(U_14826,U_14828,U_14829,U_14830)
    | U_14829 = c_Orderings_Obot__class_Obot(tc_fun(U_14828,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14828),U_14829))
    | ~ class_Lattices_Osemilattice__inf(U_14828) ),
    inference(clausify,[status(thm)],[f_3786_4]) ).

cnf(f_3786_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14828),U_14830),U_14826))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14828),U_14826),U_14829))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14828),U_14830),hAPP(c_Finite__Set_Ofold1(U_14828,c_Lattices_Osemilattice__inf__class_Oinf(U_14828)),U_14829)))
    | ~ sP1000(U_14826,U_14828,U_14829,U_14830) ),
    inference(clausify,[status(thm)],[f_3786_4]) ).

cnf(f_3786_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14828),U_14830),hAPP(c_Finite__Set_Ofold1(U_14828,c_Lattices_Osemilattice__inf__class_Oinf(U_14828)),U_14829)))
    | sP999(U_14828,U_14829,U_14830)
    | ~ sP1000(U_14826,U_14828,U_14829,U_14830) ),
    inference(clausify,[status(thm)],[f_3786_4]) ).

cnf(f_3786_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14828),sK333(U_14830,U_14829,U_14828)),U_14829))
    | ~ sP999(U_14828,U_14829,U_14830) ),
    inference(clausify,[status(thm)],[f_3786_4]) ).

cnf(f_3786_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14828),U_14830),sK333(U_14830,U_14829,U_14828)))
    | ~ sP999(U_14828,U_14829,U_14830) ),
    inference(clausify,[status(thm)],[f_3786_4]) ).

fof(f_3787_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_3787_2,plain,
    ! [U_14833,U_14832,U_14831] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14831),hAPP(c_Finite__Set_Ofold1(U_14831,c_Orderings_Oord__class_Omin(U_14831)),U_14832)),U_14833))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14831),U_14833),U_14832))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14831),U_14832))
      | ~ class_Orderings_Olinorder(U_14831) ),
    inference(variable_rename,[status(thm)],[f_3787_1]) ).

fof(f_3787_3,plain,
    ! [U_14831,U_14832,U_14833] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14831),hAPP(c_Finite__Set_Ofold1(U_14831,c_Orderings_Oord__class_Omin(U_14831)),U_14832)),U_14833))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14831),U_14833),U_14832))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14831),U_14832))
      | ~ class_Orderings_Olinorder(U_14831) ),
    inference(definitional_conversion,[status(esa)],[f_3787_2]) ).

cnf(f_3787_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14831),hAPP(c_Finite__Set_Ofold1(U_14831,c_Orderings_Oord__class_Omin(U_14831)),U_14832)),U_14833))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14831),U_14833),U_14832))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14831),U_14832))
    | ~ class_Orderings_Olinorder(U_14831) ),
    inference(clausify,[status(thm)],[f_3787_3]) ).

fof(f_3788_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_3788_2,plain,
    ! [U_14836,U_14835,U_14834] :
      ( hAPP(c_Finite__Set_Ofold1(U_14834,c_Groups_Otimes__class_Otimes(U_14834)),hAPP(hAPP(c_Set_Oinsert(U_14834),U_14836),U_14835)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14834),U_14836),hAPP(c_Finite__Set_Ofold1(U_14834,c_Groups_Otimes__class_Otimes(U_14834)),U_14835))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14834),U_14835))
      | U_14835 = c_Orderings_Obot__class_Obot(tc_fun(U_14834,tc_HOL_Obool))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_14834) ),
    inference(variable_rename,[status(thm)],[f_3788_1]) ).

fof(f_3788_3,plain,
    ! [U_14834,U_14836,U_14835] :
      ( hAPP(c_Finite__Set_Ofold1(U_14834,c_Groups_Otimes__class_Otimes(U_14834)),hAPP(hAPP(c_Set_Oinsert(U_14834),U_14836),U_14835)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14834),U_14836),hAPP(c_Finite__Set_Ofold1(U_14834,c_Groups_Otimes__class_Otimes(U_14834)),U_14835))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14834),U_14835))
      | U_14835 = c_Orderings_Obot__class_Obot(tc_fun(U_14834,tc_HOL_Obool))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_14834) ),
    inference(definitional_conversion,[status(esa)],[f_3788_2]) ).

cnf(f_3788_4,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_14834,c_Groups_Otimes__class_Otimes(U_14834)),hAPP(hAPP(c_Set_Oinsert(U_14834),U_14836),U_14835)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14834),U_14836),hAPP(c_Finite__Set_Ofold1(U_14834,c_Groups_Otimes__class_Otimes(U_14834)),U_14835))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14834),U_14835))
    | U_14835 = c_Orderings_Obot__class_Obot(tc_fun(U_14834,tc_HOL_Obool))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_14834) ),
    inference(clausify,[status(thm)],[f_3788_3]) ).

fof(f_3789_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_3789_2,plain,
    ! [U_14841,U_14840,U_14839] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14839),hAPP(c_Finite__Set_Ofold1(U_14839,c_Orderings_Oord__class_Omin(U_14839)),U_14840)),U_14841))
          | ! [U_14838] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14839),U_14838),U_14841))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14839),U_14838),U_14840)) ) )
        & ( ? [U_14837] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14839),U_14837),U_14841))
              & hBOOL(hAPP(hAPP(c_member(U_14839),U_14837),U_14840)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14839),hAPP(c_Finite__Set_Ofold1(U_14839,c_Orderings_Oord__class_Omin(U_14839)),U_14840)),U_14841)) ) )
      | U_14840 = c_Orderings_Obot__class_Obot(tc_fun(U_14839,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14839),U_14840))
      | ~ class_Orderings_Olinorder(U_14839) ),
    inference(variable_rename,[status(thm)],[f_3789_1]) ).

fof(f_3789_3,plain,
    ! [U_14841,U_14840,U_14839] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14839),hAPP(c_Finite__Set_Ofold1(U_14839,c_Orderings_Oord__class_Omin(U_14839)),U_14840)),U_14841))
          | ! [U_14838] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14839),U_14838),U_14841))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14839),U_14838),U_14840)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14839),sK334(U_14841,U_14840,U_14839)),U_14841))
            & hBOOL(hAPP(hAPP(c_member(U_14839),sK334(U_14841,U_14840,U_14839)),U_14840)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14839),hAPP(c_Finite__Set_Ofold1(U_14839,c_Orderings_Oord__class_Omin(U_14839)),U_14840)),U_14841)) ) )
      | U_14840 = c_Orderings_Obot__class_Obot(tc_fun(U_14839,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14839),U_14840))
      | ~ class_Orderings_Olinorder(U_14839) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK334]),skolemize(U_14837,sK334(U_14841,U_14840,U_14839))],[f_3789_2]) ).

fof(f_3789_4,plain,
    ( ! [U_14839,U_14840,U_14841] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14839),sK334(U_14841,U_14840,U_14839)),U_14841))
        | ~ sP1001(U_14839,U_14840,U_14841) )
    & ! [U_14839,U_14840,U_14841] :
        ( hBOOL(hAPP(hAPP(c_member(U_14839),sK334(U_14841,U_14840,U_14839)),U_14840))
        | ~ sP1001(U_14839,U_14840,U_14841) )
    & ! [U_14838,U_14839,U_14840,U_14841] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14839),hAPP(c_Finite__Set_Ofold1(U_14839,c_Orderings_Oord__class_Omin(U_14839)),U_14840)),U_14841))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14839),U_14838),U_14841))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14839),U_14838),U_14840))
        | ~ sP1002(U_14838,U_14839,U_14840,U_14841) )
    & ! [U_14838,U_14839,U_14840,U_14841] :
        ( sP1001(U_14839,U_14840,U_14841)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14839),hAPP(c_Finite__Set_Ofold1(U_14839,c_Orderings_Oord__class_Omin(U_14839)),U_14840)),U_14841))
        | ~ sP1002(U_14838,U_14839,U_14840,U_14841) )
    & ! [U_14838,U_14839,U_14840,U_14841] :
        ( sP1002(U_14838,U_14839,U_14840,U_14841)
        | U_14840 = c_Orderings_Obot__class_Obot(tc_fun(U_14839,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14839),U_14840))
        | ~ class_Orderings_Olinorder(U_14839) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1001,sP1002])],[f_3789_3]) ).

cnf(f_3789_5,plain,
    ( sP1002(U_14838,U_14839,U_14840,U_14841)
    | U_14840 = c_Orderings_Obot__class_Obot(tc_fun(U_14839,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14839),U_14840))
    | ~ class_Orderings_Olinorder(U_14839) ),
    inference(clausify,[status(thm)],[f_3789_4]) ).

cnf(f_3789_6,plain,
    ( sP1001(U_14839,U_14840,U_14841)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14839),hAPP(c_Finite__Set_Ofold1(U_14839,c_Orderings_Oord__class_Omin(U_14839)),U_14840)),U_14841))
    | ~ sP1002(U_14838,U_14839,U_14840,U_14841) ),
    inference(clausify,[status(thm)],[f_3789_4]) ).

cnf(f_3789_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14839),hAPP(c_Finite__Set_Ofold1(U_14839,c_Orderings_Oord__class_Omin(U_14839)),U_14840)),U_14841))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14839),U_14838),U_14841))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14839),U_14838),U_14840))
    | ~ sP1002(U_14838,U_14839,U_14840,U_14841) ),
    inference(clausify,[status(thm)],[f_3789_4]) ).

cnf(f_3789_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14839),sK334(U_14841,U_14840,U_14839)),U_14840))
    | ~ sP1001(U_14839,U_14840,U_14841) ),
    inference(clausify,[status(thm)],[f_3789_4]) ).

cnf(f_3789_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14839),sK334(U_14841,U_14840,U_14839)),U_14841))
    | ~ sP1001(U_14839,U_14840,U_14841) ),
    inference(clausify,[status(thm)],[f_3789_4]) ).

fof(f_3790_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_3790_2,plain,
    ! [U_14846,U_14845,U_14844] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14844),U_14846),hAPP(c_Finite__Set_Ofold1(U_14844,c_Orderings_Oord__class_Omin(U_14844)),U_14845)))
          | ? [U_14843] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14844),U_14846),U_14843))
              & hBOOL(hAPP(hAPP(c_member(U_14844),U_14843),U_14845)) ) )
        & ( ! [U_14842] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14844),U_14846),U_14842))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14844),U_14842),U_14845)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14844),U_14846),hAPP(c_Finite__Set_Ofold1(U_14844,c_Orderings_Oord__class_Omin(U_14844)),U_14845))) ) )
      | U_14845 = c_Orderings_Obot__class_Obot(tc_fun(U_14844,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14844),U_14845))
      | ~ class_Orderings_Olinorder(U_14844) ),
    inference(variable_rename,[status(thm)],[f_3790_1]) ).

fof(f_3790_3,plain,
    ! [U_14846,U_14845,U_14844] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14844),U_14846),hAPP(c_Finite__Set_Ofold1(U_14844,c_Orderings_Oord__class_Omin(U_14844)),U_14845)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14844),U_14846),sK335(U_14846,U_14845,U_14844)))
            & hBOOL(hAPP(hAPP(c_member(U_14844),sK335(U_14846,U_14845,U_14844)),U_14845)) ) )
        & ( ! [U_14842] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14844),U_14846),U_14842))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14844),U_14842),U_14845)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14844),U_14846),hAPP(c_Finite__Set_Ofold1(U_14844,c_Orderings_Oord__class_Omin(U_14844)),U_14845))) ) )
      | U_14845 = c_Orderings_Obot__class_Obot(tc_fun(U_14844,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14844),U_14845))
      | ~ class_Orderings_Olinorder(U_14844) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK335]),skolemize(U_14843,sK335(U_14846,U_14845,U_14844))],[f_3790_2]) ).

fof(f_3790_4,plain,
    ( ! [U_14845,U_14846,U_14844] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14844),U_14846),sK335(U_14846,U_14845,U_14844)))
        | ~ sP1003(U_14845,U_14846,U_14844) )
    & ! [U_14845,U_14846,U_14844] :
        ( hBOOL(hAPP(hAPP(c_member(U_14844),sK335(U_14846,U_14845,U_14844)),U_14845))
        | ~ sP1003(U_14845,U_14846,U_14844) )
    & ! [U_14845,U_14846,U_14842,U_14844] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14844),U_14846),hAPP(c_Finite__Set_Ofold1(U_14844,c_Orderings_Oord__class_Omin(U_14844)),U_14845)))
        | sP1003(U_14845,U_14846,U_14844)
        | ~ sP1004(U_14845,U_14846,U_14842,U_14844) )
    & ! [U_14845,U_14846,U_14842,U_14844] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14844),U_14846),U_14842))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14844),U_14842),U_14845))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14844),U_14846),hAPP(c_Finite__Set_Ofold1(U_14844,c_Orderings_Oord__class_Omin(U_14844)),U_14845)))
        | ~ sP1004(U_14845,U_14846,U_14842,U_14844) )
    & ! [U_14845,U_14846,U_14842,U_14844] :
        ( sP1004(U_14845,U_14846,U_14842,U_14844)
        | U_14845 = c_Orderings_Obot__class_Obot(tc_fun(U_14844,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14844),U_14845))
        | ~ class_Orderings_Olinorder(U_14844) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1003,sP1004])],[f_3790_3]) ).

cnf(f_3790_5,plain,
    ( sP1004(U_14845,U_14846,U_14842,U_14844)
    | U_14845 = c_Orderings_Obot__class_Obot(tc_fun(U_14844,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14844),U_14845))
    | ~ class_Orderings_Olinorder(U_14844) ),
    inference(clausify,[status(thm)],[f_3790_4]) ).

cnf(f_3790_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14844),U_14846),U_14842))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14844),U_14842),U_14845))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14844),U_14846),hAPP(c_Finite__Set_Ofold1(U_14844,c_Orderings_Oord__class_Omin(U_14844)),U_14845)))
    | ~ sP1004(U_14845,U_14846,U_14842,U_14844) ),
    inference(clausify,[status(thm)],[f_3790_4]) ).

cnf(f_3790_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14844),U_14846),hAPP(c_Finite__Set_Ofold1(U_14844,c_Orderings_Oord__class_Omin(U_14844)),U_14845)))
    | sP1003(U_14845,U_14846,U_14844)
    | ~ sP1004(U_14845,U_14846,U_14842,U_14844) ),
    inference(clausify,[status(thm)],[f_3790_4]) ).

cnf(f_3790_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14844),sK335(U_14846,U_14845,U_14844)),U_14845))
    | ~ sP1003(U_14845,U_14846,U_14844) ),
    inference(clausify,[status(thm)],[f_3790_4]) ).

cnf(f_3790_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14844),U_14846),sK335(U_14846,U_14845,U_14844)))
    | ~ sP1003(U_14845,U_14846,U_14844) ),
    inference(clausify,[status(thm)],[f_3790_4]) ).

fof(f_3791_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_3791_2,plain,
    ! [U_14849,U_14848,U_14847] :
      ( hAPP(c_Finite__Set_Ofold1(U_14847,c_Groups_Otimes__class_Otimes(U_14847)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14847,tc_HOL_Obool)),U_14848),U_14849)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14847),hAPP(c_Finite__Set_Ofold1(U_14847,c_Groups_Otimes__class_Otimes(U_14847)),U_14848)),hAPP(c_Finite__Set_Ofold1(U_14847,c_Groups_Otimes__class_Otimes(U_14847)),U_14849))
      | U_14849 = c_Orderings_Obot__class_Obot(tc_fun(U_14847,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14847),U_14849))
      | U_14848 = c_Orderings_Obot__class_Obot(tc_fun(U_14847,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14847),U_14848))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_14847) ),
    inference(variable_rename,[status(thm)],[f_3791_1]) ).

fof(f_3791_3,plain,
    ! [U_14849,U_14848,U_14847] :
      ( hAPP(c_Finite__Set_Ofold1(U_14847,c_Groups_Otimes__class_Otimes(U_14847)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14847,tc_HOL_Obool)),U_14848),U_14849)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14847),hAPP(c_Finite__Set_Ofold1(U_14847,c_Groups_Otimes__class_Otimes(U_14847)),U_14848)),hAPP(c_Finite__Set_Ofold1(U_14847,c_Groups_Otimes__class_Otimes(U_14847)),U_14849))
      | U_14849 = c_Orderings_Obot__class_Obot(tc_fun(U_14847,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14847),U_14849))
      | U_14848 = c_Orderings_Obot__class_Obot(tc_fun(U_14847,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14847),U_14848))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_14847) ),
    inference(definitional_conversion,[status(esa)],[f_3791_2]) ).

cnf(f_3791_4,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_14847,c_Groups_Otimes__class_Otimes(U_14847)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_14847,tc_HOL_Obool)),U_14848),U_14849)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14847),hAPP(c_Finite__Set_Ofold1(U_14847,c_Groups_Otimes__class_Otimes(U_14847)),U_14848)),hAPP(c_Finite__Set_Ofold1(U_14847,c_Groups_Otimes__class_Otimes(U_14847)),U_14849))
    | U_14849 = c_Orderings_Obot__class_Obot(tc_fun(U_14847,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14847),U_14849))
    | U_14848 = c_Orderings_Obot__class_Obot(tc_fun(U_14847,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14847),U_14848))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_14847) ),
    inference(clausify,[status(thm)],[f_3791_3]) ).

fof(f_3792_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_3792_2,plain,
    ! [U_14854,U_14853,U_14852] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14852),hAPP(c_Finite__Set_Ofold1(U_14852,c_Orderings_Oord__class_Omin(U_14852)),U_14853)),U_14854))
          | ! [U_14851] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14852),U_14851),U_14854))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14852),U_14851),U_14853)) ) )
        & ( ? [U_14850] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14852),U_14850),U_14854))
              & hBOOL(hAPP(hAPP(c_member(U_14852),U_14850),U_14853)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14852),hAPP(c_Finite__Set_Ofold1(U_14852,c_Orderings_Oord__class_Omin(U_14852)),U_14853)),U_14854)) ) )
      | U_14853 = c_Orderings_Obot__class_Obot(tc_fun(U_14852,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14852),U_14853))
      | ~ class_Orderings_Olinorder(U_14852) ),
    inference(variable_rename,[status(thm)],[f_3792_1]) ).

fof(f_3792_3,plain,
    ! [U_14854,U_14853,U_14852] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14852),hAPP(c_Finite__Set_Ofold1(U_14852,c_Orderings_Oord__class_Omin(U_14852)),U_14853)),U_14854))
          | ! [U_14851] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14852),U_14851),U_14854))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14852),U_14851),U_14853)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14852),sK336(U_14854,U_14853,U_14852)),U_14854))
            & hBOOL(hAPP(hAPP(c_member(U_14852),sK336(U_14854,U_14853,U_14852)),U_14853)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14852),hAPP(c_Finite__Set_Ofold1(U_14852,c_Orderings_Oord__class_Omin(U_14852)),U_14853)),U_14854)) ) )
      | U_14853 = c_Orderings_Obot__class_Obot(tc_fun(U_14852,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14852),U_14853))
      | ~ class_Orderings_Olinorder(U_14852) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK336]),skolemize(U_14850,sK336(U_14854,U_14853,U_14852))],[f_3792_2]) ).

fof(f_3792_4,plain,
    ( ! [U_14852,U_14853,U_14854] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14852),sK336(U_14854,U_14853,U_14852)),U_14854))
        | ~ sP1005(U_14852,U_14853,U_14854) )
    & ! [U_14852,U_14853,U_14854] :
        ( hBOOL(hAPP(hAPP(c_member(U_14852),sK336(U_14854,U_14853,U_14852)),U_14853))
        | ~ sP1005(U_14852,U_14853,U_14854) )
    & ! [U_14852,U_14851,U_14853,U_14854] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14852),hAPP(c_Finite__Set_Ofold1(U_14852,c_Orderings_Oord__class_Omin(U_14852)),U_14853)),U_14854))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14852),U_14851),U_14854))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14852),U_14851),U_14853))
        | ~ sP1006(U_14852,U_14851,U_14853,U_14854) )
    & ! [U_14852,U_14851,U_14853,U_14854] :
        ( sP1005(U_14852,U_14853,U_14854)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14852),hAPP(c_Finite__Set_Ofold1(U_14852,c_Orderings_Oord__class_Omin(U_14852)),U_14853)),U_14854))
        | ~ sP1006(U_14852,U_14851,U_14853,U_14854) )
    & ! [U_14852,U_14851,U_14853,U_14854] :
        ( sP1006(U_14852,U_14851,U_14853,U_14854)
        | U_14853 = c_Orderings_Obot__class_Obot(tc_fun(U_14852,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14852),U_14853))
        | ~ class_Orderings_Olinorder(U_14852) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1005,sP1006])],[f_3792_3]) ).

cnf(f_3792_5,plain,
    ( sP1006(U_14852,U_14851,U_14853,U_14854)
    | U_14853 = c_Orderings_Obot__class_Obot(tc_fun(U_14852,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14852),U_14853))
    | ~ class_Orderings_Olinorder(U_14852) ),
    inference(clausify,[status(thm)],[f_3792_4]) ).

cnf(f_3792_6,plain,
    ( sP1005(U_14852,U_14853,U_14854)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14852),hAPP(c_Finite__Set_Ofold1(U_14852,c_Orderings_Oord__class_Omin(U_14852)),U_14853)),U_14854))
    | ~ sP1006(U_14852,U_14851,U_14853,U_14854) ),
    inference(clausify,[status(thm)],[f_3792_4]) ).

cnf(f_3792_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14852),hAPP(c_Finite__Set_Ofold1(U_14852,c_Orderings_Oord__class_Omin(U_14852)),U_14853)),U_14854))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14852),U_14851),U_14854))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14852),U_14851),U_14853))
    | ~ sP1006(U_14852,U_14851,U_14853,U_14854) ),
    inference(clausify,[status(thm)],[f_3792_4]) ).

cnf(f_3792_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14852),sK336(U_14854,U_14853,U_14852)),U_14853))
    | ~ sP1005(U_14852,U_14853,U_14854) ),
    inference(clausify,[status(thm)],[f_3792_4]) ).

cnf(f_3792_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14852),sK336(U_14854,U_14853,U_14852)),U_14854))
    | ~ sP1005(U_14852,U_14853,U_14854) ),
    inference(clausify,[status(thm)],[f_3792_4]) ).

fof(f_3793_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_3793_2,plain,
    ! [U_14859,U_14858,U_14857] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14857),U_14859),hAPP(c_Finite__Set_Ofold1(U_14857,c_Orderings_Oord__class_Omin(U_14857)),U_14858)))
          | ? [U_14856] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14857),U_14859),U_14856))
              & hBOOL(hAPP(hAPP(c_member(U_14857),U_14856),U_14858)) ) )
        & ( ! [U_14855] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14857),U_14859),U_14855))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14857),U_14855),U_14858)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14857),U_14859),hAPP(c_Finite__Set_Ofold1(U_14857,c_Orderings_Oord__class_Omin(U_14857)),U_14858))) ) )
      | U_14858 = c_Orderings_Obot__class_Obot(tc_fun(U_14857,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14857),U_14858))
      | ~ class_Orderings_Olinorder(U_14857) ),
    inference(variable_rename,[status(thm)],[f_3793_1]) ).

fof(f_3793_3,plain,
    ! [U_14859,U_14858,U_14857] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14857),U_14859),hAPP(c_Finite__Set_Ofold1(U_14857,c_Orderings_Oord__class_Omin(U_14857)),U_14858)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14857),U_14859),sK337(U_14859,U_14858,U_14857)))
            & hBOOL(hAPP(hAPP(c_member(U_14857),sK337(U_14859,U_14858,U_14857)),U_14858)) ) )
        & ( ! [U_14855] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14857),U_14859),U_14855))
              | ~ hBOOL(hAPP(hAPP(c_member(U_14857),U_14855),U_14858)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14857),U_14859),hAPP(c_Finite__Set_Ofold1(U_14857,c_Orderings_Oord__class_Omin(U_14857)),U_14858))) ) )
      | U_14858 = c_Orderings_Obot__class_Obot(tc_fun(U_14857,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14857),U_14858))
      | ~ class_Orderings_Olinorder(U_14857) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK337]),skolemize(U_14856,sK337(U_14859,U_14858,U_14857))],[f_3793_2]) ).

fof(f_3793_4,plain,
    ( ! [U_14859,U_14857,U_14858] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14857),U_14859),sK337(U_14859,U_14858,U_14857)))
        | ~ sP1007(U_14859,U_14857,U_14858) )
    & ! [U_14859,U_14857,U_14858] :
        ( hBOOL(hAPP(hAPP(c_member(U_14857),sK337(U_14859,U_14858,U_14857)),U_14858))
        | ~ sP1007(U_14859,U_14857,U_14858) )
    & ! [U_14859,U_14857,U_14855,U_14858] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14857),U_14859),hAPP(c_Finite__Set_Ofold1(U_14857,c_Orderings_Oord__class_Omin(U_14857)),U_14858)))
        | sP1007(U_14859,U_14857,U_14858)
        | ~ sP1008(U_14859,U_14857,U_14855,U_14858) )
    & ! [U_14859,U_14857,U_14855,U_14858] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14857),U_14859),U_14855))
        | ~ hBOOL(hAPP(hAPP(c_member(U_14857),U_14855),U_14858))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14857),U_14859),hAPP(c_Finite__Set_Ofold1(U_14857,c_Orderings_Oord__class_Omin(U_14857)),U_14858)))
        | ~ sP1008(U_14859,U_14857,U_14855,U_14858) )
    & ! [U_14859,U_14857,U_14855,U_14858] :
        ( sP1008(U_14859,U_14857,U_14855,U_14858)
        | U_14858 = c_Orderings_Obot__class_Obot(tc_fun(U_14857,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14857),U_14858))
        | ~ class_Orderings_Olinorder(U_14857) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1007,sP1008])],[f_3793_3]) ).

cnf(f_3793_5,plain,
    ( sP1008(U_14859,U_14857,U_14855,U_14858)
    | U_14858 = c_Orderings_Obot__class_Obot(tc_fun(U_14857,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14857),U_14858))
    | ~ class_Orderings_Olinorder(U_14857) ),
    inference(clausify,[status(thm)],[f_3793_4]) ).

cnf(f_3793_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14857),U_14859),U_14855))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14857),U_14855),U_14858))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14857),U_14859),hAPP(c_Finite__Set_Ofold1(U_14857,c_Orderings_Oord__class_Omin(U_14857)),U_14858)))
    | ~ sP1008(U_14859,U_14857,U_14855,U_14858) ),
    inference(clausify,[status(thm)],[f_3793_4]) ).

cnf(f_3793_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14857),U_14859),hAPP(c_Finite__Set_Ofold1(U_14857,c_Orderings_Oord__class_Omin(U_14857)),U_14858)))
    | sP1007(U_14859,U_14857,U_14858)
    | ~ sP1008(U_14859,U_14857,U_14855,U_14858) ),
    inference(clausify,[status(thm)],[f_3793_4]) ).

cnf(f_3793_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14857),sK337(U_14859,U_14858,U_14857)),U_14858))
    | ~ sP1007(U_14859,U_14857,U_14858) ),
    inference(clausify,[status(thm)],[f_3793_4]) ).

cnf(f_3793_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_14857),U_14859),sK337(U_14859,U_14858,U_14857)))
    | ~ sP1007(U_14859,U_14857,U_14858) ),
    inference(clausify,[status(thm)],[f_3793_4]) ).

fof(f_3794_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_3794_2,plain,
    ! [U_14864,U_14863,U_14862,U_14861,U_14860] :
      ( hBOOL(hAPP(hAPP(c_member(U_14860),U_14861),U_14864))
      | U_14861 = U_14862
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14860,U_14860),tc_HOL_Obool)),U_14863),hAPP(hAPP(c_Product__Type_OSigma(U_14860,U_14860),U_14864),hAPP(c_COMBK(tc_fun(U_14860,tc_HOL_Obool),U_14860),U_14864))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14860,U_14860)),hAPP(hAPP(c_Product__Type_OPair(U_14860,U_14860),U_14861),U_14862)),c_Transitive__Closure_Ortrancl(U_14860,U_14863))) ),
    inference(variable_rename,[status(thm)],[f_3794_1]) ).

fof(f_3794_3,plain,
    ! [U_14861,U_14862,U_14864,U_14863,U_14860] :
      ( hBOOL(hAPP(hAPP(c_member(U_14860),U_14861),U_14864))
      | U_14861 = U_14862
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14860,U_14860),tc_HOL_Obool)),U_14863),hAPP(hAPP(c_Product__Type_OSigma(U_14860,U_14860),U_14864),hAPP(c_COMBK(tc_fun(U_14860,tc_HOL_Obool),U_14860),U_14864))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14860,U_14860)),hAPP(hAPP(c_Product__Type_OPair(U_14860,U_14860),U_14861),U_14862)),c_Transitive__Closure_Ortrancl(U_14860,U_14863))) ),
    inference(definitional_conversion,[status(esa)],[f_3794_2]) ).

cnf(f_3794_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14860),U_14861),U_14864))
    | U_14861 = U_14862
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14860,U_14860),tc_HOL_Obool)),U_14863),hAPP(hAPP(c_Product__Type_OSigma(U_14860,U_14860),U_14864),hAPP(c_COMBK(tc_fun(U_14860,tc_HOL_Obool),U_14860),U_14864))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14860,U_14860)),hAPP(hAPP(c_Product__Type_OPair(U_14860,U_14860),U_14861),U_14862)),c_Transitive__Closure_Ortrancl(U_14860,U_14863))) ),
    inference(clausify,[status(thm)],[f_3794_3]) ).

fof(f_3795_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_3795_2,plain,
    ! [U_14867,U_14866,U_14865] :
      ( hAPP(c_Finite__Set_Ofold1(U_14865,c_Groups_Otimes__class_Otimes(U_14865)),hAPP(hAPP(c_Set_Oinsert(U_14865),U_14867),U_14866)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14865),U_14867),hAPP(c_Finite__Set_Ofold1(U_14865,c_Groups_Otimes__class_Otimes(U_14865)),U_14866))
      | hBOOL(hAPP(hAPP(c_member(U_14865),U_14867),U_14866))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14865),U_14866))
      | U_14866 = c_Orderings_Obot__class_Obot(tc_fun(U_14865,tc_HOL_Obool))
      | ~ class_Groups_Oab__semigroup__mult(U_14865) ),
    inference(variable_rename,[status(thm)],[f_3795_1]) ).

fof(f_3795_3,plain,
    ! [U_14865,U_14866,U_14867] :
      ( hAPP(c_Finite__Set_Ofold1(U_14865,c_Groups_Otimes__class_Otimes(U_14865)),hAPP(hAPP(c_Set_Oinsert(U_14865),U_14867),U_14866)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14865),U_14867),hAPP(c_Finite__Set_Ofold1(U_14865,c_Groups_Otimes__class_Otimes(U_14865)),U_14866))
      | hBOOL(hAPP(hAPP(c_member(U_14865),U_14867),U_14866))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14865),U_14866))
      | U_14866 = c_Orderings_Obot__class_Obot(tc_fun(U_14865,tc_HOL_Obool))
      | ~ class_Groups_Oab__semigroup__mult(U_14865) ),
    inference(definitional_conversion,[status(esa)],[f_3795_2]) ).

cnf(f_3795_4,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_14865,c_Groups_Otimes__class_Otimes(U_14865)),hAPP(hAPP(c_Set_Oinsert(U_14865),U_14867),U_14866)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14865),U_14867),hAPP(c_Finite__Set_Ofold1(U_14865,c_Groups_Otimes__class_Otimes(U_14865)),U_14866))
    | hBOOL(hAPP(hAPP(c_member(U_14865),U_14867),U_14866))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14865),U_14866))
    | U_14866 = c_Orderings_Obot__class_Obot(tc_fun(U_14865,tc_HOL_Obool))
    | ~ class_Groups_Oab__semigroup__mult(U_14865) ),
    inference(clausify,[status(thm)],[f_3795_3]) ).

fof(f_3796_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_3796_2,plain,
    ! [U_14870,U_14869,U_14868] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14868),hAPP(c_Finite__Set_Ofold1(U_14868,c_Orderings_Oord__class_Omin(U_14868)),U_14870)),hAPP(c_Finite__Set_Ofold1(U_14868,c_Orderings_Oord__class_Omin(U_14868)),U_14869)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14868),U_14870))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14868,tc_HOL_Obool)),U_14869),U_14870))
      | U_14869 = c_Orderings_Obot__class_Obot(tc_fun(U_14868,tc_HOL_Obool))
      | ~ class_Orderings_Olinorder(U_14868) ),
    inference(variable_rename,[status(thm)],[f_3796_1]) ).

fof(f_3796_3,plain,
    ! [U_14869,U_14868,U_14870] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14868),hAPP(c_Finite__Set_Ofold1(U_14868,c_Orderings_Oord__class_Omin(U_14868)),U_14870)),hAPP(c_Finite__Set_Ofold1(U_14868,c_Orderings_Oord__class_Omin(U_14868)),U_14869)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14868),U_14870))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14868,tc_HOL_Obool)),U_14869),U_14870))
      | U_14869 = c_Orderings_Obot__class_Obot(tc_fun(U_14868,tc_HOL_Obool))
      | ~ class_Orderings_Olinorder(U_14868) ),
    inference(definitional_conversion,[status(esa)],[f_3796_2]) ).

cnf(f_3796_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_14868),hAPP(c_Finite__Set_Ofold1(U_14868,c_Orderings_Oord__class_Omin(U_14868)),U_14870)),hAPP(c_Finite__Set_Ofold1(U_14868,c_Orderings_Oord__class_Omin(U_14868)),U_14869)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14868),U_14870))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_14868,tc_HOL_Obool)),U_14869),U_14870))
    | U_14869 = c_Orderings_Obot__class_Obot(tc_fun(U_14868,tc_HOL_Obool))
    | ~ class_Orderings_Olinorder(U_14868) ),
    inference(clausify,[status(thm)],[f_3796_3]) ).

fof(f_3797_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_3797_2,plain,
    ! [U_14874,U_14873,U_14872,U_14871] :
      ( hAPP(U_14873,U_14874) = hAPP(c_Finite__Set_Ofold1(U_14871,U_14872),U_14874)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14871),U_14874))
      | ~ c_Big__Operators_Osemilattice__big(U_14871,U_14872,U_14873) ),
    inference(variable_rename,[status(thm)],[f_3797_1]) ).

fof(f_3797_3,plain,
    ! [U_14874,U_14871,U_14872,U_14873] :
      ( hAPP(U_14873,U_14874) = hAPP(c_Finite__Set_Ofold1(U_14871,U_14872),U_14874)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14871),U_14874))
      | ~ c_Big__Operators_Osemilattice__big(U_14871,U_14872,U_14873) ),
    inference(definitional_conversion,[status(esa)],[f_3797_2]) ).

cnf(f_3797_4,plain,
    ( hAPP(U_14873,U_14874) = hAPP(c_Finite__Set_Ofold1(U_14871,U_14872),U_14874)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14871),U_14874))
    | ~ c_Big__Operators_Osemilattice__big(U_14871,U_14872,U_14873) ),
    inference(clausify,[status(thm)],[f_3797_3]) ).

fof(f_3798_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_3798_2,plain,
    ! [U_14881,U_14880,U_14879,U_14878,U_14877,U_14876,U_14875] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14875),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14876,U_14875),U_14878),U_14880)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14877,U_14875),U_14879),U_14881)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14875,U_14875),c_Fun_Oid(U_14875)),hAPP(c_Set_OCollect(U_14875),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_HOL_Obool),tc_HOL_Obool,U_14875),c_HOL_OEx(U_14876)),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool)),tc_fun(U_14876,tc_HOL_Obool),U_14875),hAPP(c_COMBB(tc_fun(U_14877,tc_HOL_Obool),tc_HOL_Obool,U_14876),c_HOL_OEx(U_14877))),hAPP(hAPP(c_COMBC(U_14875,tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool)),tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_fun(tc_fun(U_14877,tc_HOL_Obool),tc_fun(U_14877,tc_HOL_Obool))),tc_fun(tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool)),tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool))),U_14875),c_COMBS(U_14876,tc_fun(U_14877,tc_HOL_Obool),tc_fun(U_14877,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_fun(U_14877,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14876,tc_fun(tc_fun(U_14877,tc_HOL_Obool),tc_fun(U_14877,tc_HOL_Obool))),U_14875),hAPP(c_COMBB(tc_fun(U_14877,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14877,tc_HOL_Obool),tc_fun(U_14877,tc_HOL_Obool)),U_14876),c_COMBS(U_14877,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool)),tc_fun(U_14876,tc_fun(U_14877,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14875),hAPP(c_COMBB(tc_fun(U_14877,tc_HOL_Obool),tc_fun(U_14877,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_14877),c_fconj))),hAPP(hAPP(c_COMBC(U_14875,tc_fun(U_14876,tc_fun(U_14877,U_14875)),tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14877,U_14875),tc_fun(U_14877,tc_HOL_Obool)),tc_fun(tc_fun(U_14876,tc_fun(U_14877,U_14875)),tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool))),U_14875),c_COMBB(tc_fun(U_14877,U_14875),tc_fun(U_14877,tc_HOL_Obool),U_14876)),hAPP(hAPP(c_COMBB(tc_fun(U_14875,tc_HOL_Obool),tc_fun(tc_fun(U_14877,U_14875),tc_fun(U_14877,tc_HOL_Obool)),U_14875),c_COMBB(U_14875,tc_HOL_Obool,U_14877)),c_fequal))),hAPP(hAPP(c_COMBC(U_14876,tc_fun(U_14877,U_14875),tc_fun(U_14877,U_14875)),hAPP(hAPP(c_COMBB(tc_fun(U_14875,U_14875),tc_fun(tc_fun(U_14877,U_14875),tc_fun(U_14877,U_14875)),U_14876),c_COMBB(U_14875,U_14875,U_14877)),hAPP(hAPP(c_COMBB(U_14875,tc_fun(U_14875,U_14875),U_14876),c_Groups_Otimes__class_Otimes(U_14875)),U_14878))),U_14879)))))),hAPP(hAPP(c_COMBC(U_14876,tc_fun(U_14877,tc_HOL_Obool),tc_fun(U_14877,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14877,tc_HOL_Obool),tc_fun(U_14877,tc_HOL_Obool)),U_14876),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14877)),hAPP(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,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14876)),U_14880)))),hAPP(hAPP(c_COMBC(U_14877,tc_fun(U_14877,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14877)),U_14881)))))))
      | ~ c_Fun_Oinj__on(tc_prod(U_14876,U_14877),U_14875,hAPP(c_Product__Type_Oprod_Oprod__case(U_14876,U_14877,U_14875),hAPP(hAPP(c_COMBC(U_14876,tc_fun(U_14877,U_14875),tc_fun(U_14877,U_14875)),hAPP(hAPP(c_COMBB(tc_fun(U_14875,U_14875),tc_fun(tc_fun(U_14877,U_14875),tc_fun(U_14877,U_14875)),U_14876),c_COMBB(U_14875,U_14875,U_14877)),hAPP(hAPP(c_COMBB(U_14875,tc_fun(U_14875,U_14875),U_14876),c_Groups_Otimes__class_Otimes(U_14875)),U_14878))),U_14879)),hAPP(hAPP(c_Product__Type_OSigma(U_14876,U_14877),U_14880),hAPP(c_COMBK(tc_fun(U_14877,tc_HOL_Obool),U_14876),U_14881)))
      | ~ class_Rings_Osemiring__0(U_14875) ),
    inference(variable_rename,[status(thm)],[f_3798_1]) ).

fof(f_3798_3,plain,
    ! [U_14875,U_14876,U_14877,U_14878,U_14879,U_14880,U_14881] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14875),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14876,U_14875),U_14878),U_14880)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14877,U_14875),U_14879),U_14881)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14875,U_14875),c_Fun_Oid(U_14875)),hAPP(c_Set_OCollect(U_14875),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_HOL_Obool),tc_HOL_Obool,U_14875),c_HOL_OEx(U_14876)),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool)),tc_fun(U_14876,tc_HOL_Obool),U_14875),hAPP(c_COMBB(tc_fun(U_14877,tc_HOL_Obool),tc_HOL_Obool,U_14876),c_HOL_OEx(U_14877))),hAPP(hAPP(c_COMBC(U_14875,tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool)),tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_fun(tc_fun(U_14877,tc_HOL_Obool),tc_fun(U_14877,tc_HOL_Obool))),tc_fun(tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool)),tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool))),U_14875),c_COMBS(U_14876,tc_fun(U_14877,tc_HOL_Obool),tc_fun(U_14877,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_fun(U_14877,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14876,tc_fun(tc_fun(U_14877,tc_HOL_Obool),tc_fun(U_14877,tc_HOL_Obool))),U_14875),hAPP(c_COMBB(tc_fun(U_14877,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14877,tc_HOL_Obool),tc_fun(U_14877,tc_HOL_Obool)),U_14876),c_COMBS(U_14877,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool)),tc_fun(U_14876,tc_fun(U_14877,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14875),hAPP(c_COMBB(tc_fun(U_14877,tc_HOL_Obool),tc_fun(U_14877,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_14877),c_fconj))),hAPP(hAPP(c_COMBC(U_14875,tc_fun(U_14876,tc_fun(U_14877,U_14875)),tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14877,U_14875),tc_fun(U_14877,tc_HOL_Obool)),tc_fun(tc_fun(U_14876,tc_fun(U_14877,U_14875)),tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool))),U_14875),c_COMBB(tc_fun(U_14877,U_14875),tc_fun(U_14877,tc_HOL_Obool),U_14876)),hAPP(hAPP(c_COMBB(tc_fun(U_14875,tc_HOL_Obool),tc_fun(tc_fun(U_14877,U_14875),tc_fun(U_14877,tc_HOL_Obool)),U_14875),c_COMBB(U_14875,tc_HOL_Obool,U_14877)),c_fequal))),hAPP(hAPP(c_COMBC(U_14876,tc_fun(U_14877,U_14875),tc_fun(U_14877,U_14875)),hAPP(hAPP(c_COMBB(tc_fun(U_14875,U_14875),tc_fun(tc_fun(U_14877,U_14875),tc_fun(U_14877,U_14875)),U_14876),c_COMBB(U_14875,U_14875,U_14877)),hAPP(hAPP(c_COMBB(U_14875,tc_fun(U_14875,U_14875),U_14876),c_Groups_Otimes__class_Otimes(U_14875)),U_14878))),U_14879)))))),hAPP(hAPP(c_COMBC(U_14876,tc_fun(U_14877,tc_HOL_Obool),tc_fun(U_14877,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14877,tc_HOL_Obool),tc_fun(U_14877,tc_HOL_Obool)),U_14876),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14877)),hAPP(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,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14876)),U_14880)))),hAPP(hAPP(c_COMBC(U_14877,tc_fun(U_14877,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14877)),U_14881)))))))
      | ~ c_Fun_Oinj__on(tc_prod(U_14876,U_14877),U_14875,hAPP(c_Product__Type_Oprod_Oprod__case(U_14876,U_14877,U_14875),hAPP(hAPP(c_COMBC(U_14876,tc_fun(U_14877,U_14875),tc_fun(U_14877,U_14875)),hAPP(hAPP(c_COMBB(tc_fun(U_14875,U_14875),tc_fun(tc_fun(U_14877,U_14875),tc_fun(U_14877,U_14875)),U_14876),c_COMBB(U_14875,U_14875,U_14877)),hAPP(hAPP(c_COMBB(U_14875,tc_fun(U_14875,U_14875),U_14876),c_Groups_Otimes__class_Otimes(U_14875)),U_14878))),U_14879)),hAPP(hAPP(c_Product__Type_OSigma(U_14876,U_14877),U_14880),hAPP(c_COMBK(tc_fun(U_14877,tc_HOL_Obool),U_14876),U_14881)))
      | ~ class_Rings_Osemiring__0(U_14875) ),
    inference(definitional_conversion,[status(esa)],[f_3798_2]) ).

cnf(f_3798_4,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14875),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14876,U_14875),U_14878),U_14880)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14877,U_14875),U_14879),U_14881)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14875,U_14875),c_Fun_Oid(U_14875)),hAPP(c_Set_OCollect(U_14875),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_HOL_Obool),tc_HOL_Obool,U_14875),c_HOL_OEx(U_14876)),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool)),tc_fun(U_14876,tc_HOL_Obool),U_14875),hAPP(c_COMBB(tc_fun(U_14877,tc_HOL_Obool),tc_HOL_Obool,U_14876),c_HOL_OEx(U_14877))),hAPP(hAPP(c_COMBC(U_14875,tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool)),tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_fun(tc_fun(U_14877,tc_HOL_Obool),tc_fun(U_14877,tc_HOL_Obool))),tc_fun(tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool)),tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool))),U_14875),c_COMBS(U_14876,tc_fun(U_14877,tc_HOL_Obool),tc_fun(U_14877,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_fun(U_14877,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_14876,tc_fun(tc_fun(U_14877,tc_HOL_Obool),tc_fun(U_14877,tc_HOL_Obool))),U_14875),hAPP(c_COMBB(tc_fun(U_14877,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(U_14877,tc_HOL_Obool),tc_fun(U_14877,tc_HOL_Obool)),U_14876),c_COMBS(U_14877,tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool)),tc_fun(U_14876,tc_fun(U_14877,tc_fun(tc_HOL_Obool,tc_HOL_Obool))),U_14875),hAPP(c_COMBB(tc_fun(U_14877,tc_HOL_Obool),tc_fun(U_14877,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_14877),c_fconj))),hAPP(hAPP(c_COMBC(U_14875,tc_fun(U_14876,tc_fun(U_14877,U_14875)),tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_14877,U_14875),tc_fun(U_14877,tc_HOL_Obool)),tc_fun(tc_fun(U_14876,tc_fun(U_14877,U_14875)),tc_fun(U_14876,tc_fun(U_14877,tc_HOL_Obool))),U_14875),c_COMBB(tc_fun(U_14877,U_14875),tc_fun(U_14877,tc_HOL_Obool),U_14876)),hAPP(hAPP(c_COMBB(tc_fun(U_14875,tc_HOL_Obool),tc_fun(tc_fun(U_14877,U_14875),tc_fun(U_14877,tc_HOL_Obool)),U_14875),c_COMBB(U_14875,tc_HOL_Obool,U_14877)),c_fequal))),hAPP(hAPP(c_COMBC(U_14876,tc_fun(U_14877,U_14875),tc_fun(U_14877,U_14875)),hAPP(hAPP(c_COMBB(tc_fun(U_14875,U_14875),tc_fun(tc_fun(U_14877,U_14875),tc_fun(U_14877,U_14875)),U_14876),c_COMBB(U_14875,U_14875,U_14877)),hAPP(hAPP(c_COMBB(U_14875,tc_fun(U_14875,U_14875),U_14876),c_Groups_Otimes__class_Otimes(U_14875)),U_14878))),U_14879)))))),hAPP(hAPP(c_COMBC(U_14876,tc_fun(U_14877,tc_HOL_Obool),tc_fun(U_14877,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_14877,tc_HOL_Obool),tc_fun(U_14877,tc_HOL_Obool)),U_14876),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_14877)),hAPP(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,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14876)),U_14880)))),hAPP(hAPP(c_COMBC(U_14877,tc_fun(U_14877,tc_HOL_Obool),tc_HOL_Obool),c_member(U_14877)),U_14881)))))))
    | ~ c_Fun_Oinj__on(tc_prod(U_14876,U_14877),U_14875,hAPP(c_Product__Type_Oprod_Oprod__case(U_14876,U_14877,U_14875),hAPP(hAPP(c_COMBC(U_14876,tc_fun(U_14877,U_14875),tc_fun(U_14877,U_14875)),hAPP(hAPP(c_COMBB(tc_fun(U_14875,U_14875),tc_fun(tc_fun(U_14877,U_14875),tc_fun(U_14877,U_14875)),U_14876),c_COMBB(U_14875,U_14875,U_14877)),hAPP(hAPP(c_COMBB(U_14875,tc_fun(U_14875,U_14875),U_14876),c_Groups_Otimes__class_Otimes(U_14875)),U_14878))),U_14879)),hAPP(hAPP(c_Product__Type_OSigma(U_14876,U_14877),U_14880),hAPP(c_COMBK(tc_fun(U_14877,tc_HOL_Obool),U_14876),U_14881)))
    | ~ class_Rings_Osemiring__0(U_14875) ),
    inference(clausify,[status(thm)],[f_3798_3]) ).

fof(f_3799_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_3799_2,plain,
    ! [U_14883,U_14882] : hAPP(c_Set_Oimage(U_14882,U_14882,c_Fun_Oid(U_14882)),U_14883) = U_14883,
    inference(variable_rename,[status(thm)],[f_3799_1]) ).

fof(f_3799_3,plain,
    ! [U_14883,U_14882] : hAPP(c_Set_Oimage(U_14882,U_14882,c_Fun_Oid(U_14882)),U_14883) = U_14883,
    inference(definitional_conversion,[status(esa)],[f_3799_2]) ).

cnf(f_3799_4,plain,
    hAPP(c_Set_Oimage(U_14882,U_14882,c_Fun_Oid(U_14882)),U_14883) = U_14883,
    inference(clausify,[status(thm)],[f_3799_3]) ).

fof(f_3800_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_3800_2,plain,
    ! [U_14884] : hAPP(c_Set_Oimage(U_14884,U_14884,c_Fun_Oid(U_14884)),c_Orderings_Otop__class_Otop(tc_fun(U_14884,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_14884,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_3800_1]) ).

fof(f_3800_3,plain,
    ! [U_14884] : hAPP(c_Set_Oimage(U_14884,U_14884,c_Fun_Oid(U_14884)),c_Orderings_Otop__class_Otop(tc_fun(U_14884,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_14884,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_3800_2]) ).

cnf(f_3800_4,plain,
    hAPP(c_Set_Oimage(U_14884,U_14884,c_Fun_Oid(U_14884)),c_Orderings_Otop__class_Otop(tc_fun(U_14884,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_14884,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_3800_3]) ).

fof(f_3801_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_3801_2,plain,
    ! [U_14886,U_14885] : hAPP(c_Set_Ovimage(U_14885,U_14885,c_Fun_Oid(U_14885)),U_14886) = U_14886,
    inference(variable_rename,[status(thm)],[f_3801_1]) ).

fof(f_3801_3,plain,
    ! [U_14885,U_14886] : hAPP(c_Set_Ovimage(U_14885,U_14885,c_Fun_Oid(U_14885)),U_14886) = U_14886,
    inference(definitional_conversion,[status(esa)],[f_3801_2]) ).

cnf(f_3801_4,plain,
    hAPP(c_Set_Ovimage(U_14885,U_14885,c_Fun_Oid(U_14885)),U_14886) = U_14886,
    inference(clausify,[status(thm)],[f_3801_3]) ).

fof(f_3802_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_3802_2,plain,
    ! [U_14888,U_14887] : c_Fun_Oinj__on(U_14887,U_14887,c_Fun_Oid(U_14887),U_14888),
    inference(variable_rename,[status(thm)],[f_3802_1]) ).

fof(f_3802_3,plain,
    ! [U_14887,U_14888] : c_Fun_Oinj__on(U_14887,U_14887,c_Fun_Oid(U_14887),U_14888),
    inference(definitional_conversion,[status(esa)],[f_3802_2]) ).

cnf(f_3802_4,plain,
    c_Fun_Oinj__on(U_14887,U_14887,c_Fun_Oid(U_14887),U_14888),
    inference(clausify,[status(thm)],[f_3802_3]) ).

fof(f_3803_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_3803_2,plain,
    ! [U_14890,U_14889] : hAPP(c_Fun_Oid(U_14889),U_14890) = U_14890,
    inference(variable_rename,[status(thm)],[f_3803_1]) ).

fof(f_3803_3,plain,
    ! [U_14889,U_14890] : hAPP(c_Fun_Oid(U_14889),U_14890) = U_14890,
    inference(definitional_conversion,[status(esa)],[f_3803_2]) ).

cnf(f_3803_4,plain,
    hAPP(c_Fun_Oid(U_14889),U_14890) = U_14890,
    inference(clausify,[status(thm)],[f_3803_3]) ).

fof(f_3804_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_3804_2,plain,
    ! [U_14892,U_14891] : hAPP(c_Fun_Oid(U_14891),U_14892) = U_14892,
    inference(variable_rename,[status(thm)],[f_3804_1]) ).

fof(f_3804_3,plain,
    ! [U_14891,U_14892] : hAPP(c_Fun_Oid(U_14891),U_14892) = U_14892,
    inference(definitional_conversion,[status(esa)],[f_3804_2]) ).

cnf(f_3804_4,plain,
    hAPP(c_Fun_Oid(U_14891),U_14892) = U_14892,
    inference(clausify,[status(thm)],[f_3804_3]) ).

fof(f_3805_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_3805_2,plain,
    ! [U_14894,U_14893] : c_Product__Type_Oapfst(U_14893,U_14893,U_14894,c_Fun_Oid(U_14893)) = c_Fun_Oid(tc_prod(U_14893,U_14894)),
    inference(variable_rename,[status(thm)],[f_3805_1]) ).

fof(f_3805_3,plain,
    ! [U_14893,U_14894] : c_Product__Type_Oapfst(U_14893,U_14893,U_14894,c_Fun_Oid(U_14893)) = c_Fun_Oid(tc_prod(U_14893,U_14894)),
    inference(definitional_conversion,[status(esa)],[f_3805_2]) ).

cnf(f_3805_4,plain,
    c_Product__Type_Oapfst(U_14893,U_14893,U_14894,c_Fun_Oid(U_14893)) = c_Fun_Oid(tc_prod(U_14893,U_14894)),
    inference(clausify,[status(thm)],[f_3805_3]) ).

fof(f_3806_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_3806_2,plain,
    ! [U_14896,U_14895] : c_Product__Type_Oapsnd(U_14895,U_14895,U_14896,c_Fun_Oid(U_14895)) = c_Fun_Oid(tc_prod(U_14896,U_14895)),
    inference(variable_rename,[status(thm)],[f_3806_1]) ).

fof(f_3806_3,plain,
    ! [U_14895,U_14896] : c_Product__Type_Oapsnd(U_14895,U_14895,U_14896,c_Fun_Oid(U_14895)) = c_Fun_Oid(tc_prod(U_14896,U_14895)),
    inference(definitional_conversion,[status(esa)],[f_3806_2]) ).

cnf(f_3806_4,plain,
    c_Product__Type_Oapsnd(U_14895,U_14895,U_14896,c_Fun_Oid(U_14895)) = c_Fun_Oid(tc_prod(U_14896,U_14895)),
    inference(clausify,[status(thm)],[f_3806_3]) ).

fof(f_3807_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_3807_2,plain,
    c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
    inference(definitional_conversion,[status(esa)],[f_3807_1]) ).

cnf(f_3807_3,plain,
    c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint),
    inference(clausify,[status(thm)],[f_3807_2]) ).

fof(f_3808_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_3808_2,plain,
    ! [U_14898,U_14897] : hAPP(hAPP(c_Nat_Ocompow(U_14897,U_14897),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14898) = c_Fun_Oid(U_14897),
    inference(variable_rename,[status(thm)],[f_3808_1]) ).

fof(f_3808_3,plain,
    ! [U_14897,U_14898] : hAPP(hAPP(c_Nat_Ocompow(U_14897,U_14897),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14898) = c_Fun_Oid(U_14897),
    inference(definitional_conversion,[status(esa)],[f_3808_2]) ).

cnf(f_3808_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_14897,U_14897),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_14898) = c_Fun_Oid(U_14897),
    inference(clausify,[status(thm)],[f_3808_3]) ).

fof(f_3809_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_3809_2,plain,
    ! [U_14900,U_14899] : hAPP(c_Product__Type_Oprod_Oprod__case(U_14899,U_14900,tc_prod(U_14899,U_14900)),c_Product__Type_OPair(U_14899,U_14900)) = c_Fun_Oid(tc_prod(U_14899,U_14900)),
    inference(variable_rename,[status(thm)],[f_3809_1]) ).

fof(f_3809_3,plain,
    ! [U_14899,U_14900] : hAPP(c_Product__Type_Oprod_Oprod__case(U_14899,U_14900,tc_prod(U_14899,U_14900)),c_Product__Type_OPair(U_14899,U_14900)) = c_Fun_Oid(tc_prod(U_14899,U_14900)),
    inference(definitional_conversion,[status(esa)],[f_3809_2]) ).

cnf(f_3809_4,plain,
    hAPP(c_Product__Type_Oprod_Oprod__case(U_14899,U_14900,tc_prod(U_14899,U_14900)),c_Product__Type_OPair(U_14899,U_14900)) = c_Fun_Oid(tc_prod(U_14899,U_14900)),
    inference(clausify,[status(thm)],[f_3809_3]) ).

fof(f_3810_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_3810_2,plain,
    ! [U_14904,U_14903,U_14902,U_14901] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14902,U_14901),U_14903),U_14904) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14901,U_14901),c_Fun_Oid(U_14901)),hAPP(c_Set_Oimage(U_14902,U_14901,U_14903),U_14904))
      | ~ c_Fun_Oinj__on(U_14902,U_14901,U_14903,U_14904)
      | ~ class_Groups_Ocomm__monoid__add(U_14901) ),
    inference(variable_rename,[status(thm)],[f_3810_1]) ).

fof(f_3810_3,plain,
    ! [U_14901,U_14902,U_14903,U_14904] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14902,U_14901),U_14903),U_14904) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14901,U_14901),c_Fun_Oid(U_14901)),hAPP(c_Set_Oimage(U_14902,U_14901,U_14903),U_14904))
      | ~ c_Fun_Oinj__on(U_14902,U_14901,U_14903,U_14904)
      | ~ class_Groups_Ocomm__monoid__add(U_14901) ),
    inference(definitional_conversion,[status(esa)],[f_3810_2]) ).

cnf(f_3810_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14902,U_14901),U_14903),U_14904) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14901,U_14901),c_Fun_Oid(U_14901)),hAPP(c_Set_Oimage(U_14902,U_14901,U_14903),U_14904))
    | ~ c_Fun_Oinj__on(U_14902,U_14901,U_14903,U_14904)
    | ~ class_Groups_Ocomm__monoid__add(U_14901) ),
    inference(clausify,[status(thm)],[f_3810_3]) ).

fof(f_3811_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_3811_2,plain,
    ! [U_14908,U_14907,U_14906,U_14905] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14906,U_14905),U_14907),U_14908) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14905,U_14905),c_Fun_Oid(U_14905)),hAPP(c_Set_Oimage(U_14906,U_14905,U_14907),U_14908))
      | ~ c_Fun_Oinj__on(U_14906,U_14905,U_14907,U_14908)
      | ~ class_Groups_Ocomm__monoid__mult(U_14905) ),
    inference(variable_rename,[status(thm)],[f_3811_1]) ).

fof(f_3811_3,plain,
    ! [U_14905,U_14906,U_14907,U_14908] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14906,U_14905),U_14907),U_14908) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14905,U_14905),c_Fun_Oid(U_14905)),hAPP(c_Set_Oimage(U_14906,U_14905,U_14907),U_14908))
      | ~ c_Fun_Oinj__on(U_14906,U_14905,U_14907,U_14908)
      | ~ class_Groups_Ocomm__monoid__mult(U_14905) ),
    inference(definitional_conversion,[status(esa)],[f_3811_2]) ).

cnf(f_3811_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14906,U_14905),U_14907),U_14908) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14905,U_14905),c_Fun_Oid(U_14905)),hAPP(c_Set_Oimage(U_14906,U_14905,U_14907),U_14908))
    | ~ c_Fun_Oinj__on(U_14906,U_14905,U_14907,U_14908)
    | ~ class_Groups_Ocomm__monoid__mult(U_14905) ),
    inference(clausify,[status(thm)],[f_3811_3]) ).

fof(f_3812_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_3812_2,plain,
    ! [U_14913,U_14912,U_14911,U_14910] :
    ? [U_14909] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14911,U_14910),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14910,tc_prod(U_14911,U_14910),U_14909),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14911,tc_fun(U_14910,tc_HOL_Obool)),U_14912),U_14913))),hAPP(hAPP(c_Product__Type_OSigma(U_14911,U_14910),U_14912),U_14913)))
      & c_Fun_Oinj__on(U_14910,tc_prod(U_14911,U_14910),U_14909,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14911,tc_fun(U_14910,tc_HOL_Obool)),U_14912),U_14913)) ),
    inference(variable_rename,[status(thm)],[f_3812_1]) ).

fof(f_3812_3,plain,
    ! [U_14913,U_14912,U_14911,U_14910] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14911,U_14910),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14910,tc_prod(U_14911,U_14910),sK338(U_14913,U_14912,U_14911,U_14910)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14911,tc_fun(U_14910,tc_HOL_Obool)),U_14912),U_14913))),hAPP(hAPP(c_Product__Type_OSigma(U_14911,U_14910),U_14912),U_14913)))
      & c_Fun_Oinj__on(U_14910,tc_prod(U_14911,U_14910),sK338(U_14913,U_14912,U_14911,U_14910),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14911,tc_fun(U_14910,tc_HOL_Obool)),U_14912),U_14913)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK338]),skolemize(U_14909,sK338(U_14913,U_14912,U_14911,U_14910))],[f_3812_2]) ).

fof(f_3812_4,plain,
    ( ! [U_14910,U_14911,U_14912,U_14913] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14911,U_14910),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14910,tc_prod(U_14911,U_14910),sK338(U_14913,U_14912,U_14911,U_14910)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14911,tc_fun(U_14910,tc_HOL_Obool)),U_14912),U_14913))),hAPP(hAPP(c_Product__Type_OSigma(U_14911,U_14910),U_14912),U_14913)))
    & ! [U_14910,U_14911,U_14912,U_14913] : c_Fun_Oinj__on(U_14910,tc_prod(U_14911,U_14910),sK338(U_14913,U_14912,U_14911,U_14910),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14911,tc_fun(U_14910,tc_HOL_Obool)),U_14912),U_14913)) ),
    inference(definitional_conversion,[status(esa)],[f_3812_3]) ).

cnf(f_3812_5,plain,
    c_Fun_Oinj__on(U_14910,tc_prod(U_14911,U_14910),sK338(U_14913,U_14912,U_14911,U_14910),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14911,tc_fun(U_14910,tc_HOL_Obool)),U_14912),U_14913)),
    inference(clausify,[status(thm)],[f_3812_4]) ).

cnf(f_3812_6,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_14911,U_14910),tc_HOL_Obool)),hAPP(c_Set_Oimage(U_14910,tc_prod(U_14911,U_14910),sK338(U_14913,U_14912,U_14911,U_14910)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_14911,tc_fun(U_14910,tc_HOL_Obool)),U_14912),U_14913))),hAPP(hAPP(c_Product__Type_OSigma(U_14911,U_14910),U_14912),U_14913))),
    inference(clausify,[status(thm)],[f_3812_4]) ).

fof(f_3813_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_3813_2,plain,
    ! [U_14920,U_14919,U_14918,U_14917,U_14916,U_14915] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14916,U_14915),hAPP(hAPP(c_COMBS(U_14916,tc_fun(U_14918,tc_HOL_Obool),U_14915),hAPP(hAPP(c_COMBB(tc_fun(U_14918,U_14915),tc_fun(tc_fun(U_14918,tc_HOL_Obool),U_14915),U_14916),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14918,U_14915)),U_14920)),U_14919)),U_14917) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_14916,U_14918),U_14915),hAPP(c_Product__Type_Oprod_Oprod__case(U_14916,U_14918,U_14915),U_14920)),hAPP(hAPP(c_Product__Type_OSigma(U_14916,U_14918),U_14917),U_14919))
      | ? [U_14914] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14918),hAPP(U_14919,U_14914)))
          & hBOOL(hAPP(hAPP(c_member(U_14916),U_14914),U_14917)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14916),U_14917))
      | ~ class_Groups_Ocomm__monoid__mult(U_14915) ),
    inference(variable_rename,[status(thm)],[f_3813_1]) ).

fof(f_3813_3,plain,
    ! [U_14920,U_14919,U_14918,U_14917,U_14916,U_14915] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14916,U_14915),hAPP(hAPP(c_COMBS(U_14916,tc_fun(U_14918,tc_HOL_Obool),U_14915),hAPP(hAPP(c_COMBB(tc_fun(U_14918,U_14915),tc_fun(tc_fun(U_14918,tc_HOL_Obool),U_14915),U_14916),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14918,U_14915)),U_14920)),U_14919)),U_14917) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_14916,U_14918),U_14915),hAPP(c_Product__Type_Oprod_Oprod__case(U_14916,U_14918,U_14915),U_14920)),hAPP(hAPP(c_Product__Type_OSigma(U_14916,U_14918),U_14917),U_14919))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14918),hAPP(U_14919,sK339(U_14920,U_14919,U_14918,U_14917,U_14916,U_14915))))
        & hBOOL(hAPP(hAPP(c_member(U_14916),sK339(U_14920,U_14919,U_14918,U_14917,U_14916,U_14915)),U_14917)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14916),U_14917))
      | ~ class_Groups_Ocomm__monoid__mult(U_14915) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK339]),skolemize(U_14914,sK339(U_14920,U_14919,U_14918,U_14917,U_14916,U_14915))],[f_3813_2]) ).

fof(f_3813_4,plain,
    ( ! [U_14915,U_14916,U_14917,U_14918,U_14919,U_14920] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14918),hAPP(U_14919,sK339(U_14920,U_14919,U_14918,U_14917,U_14916,U_14915))))
        | ~ sP1009(U_14915,U_14916,U_14917,U_14918,U_14919,U_14920) )
    & ! [U_14915,U_14916,U_14917,U_14918,U_14919,U_14920] :
        ( hBOOL(hAPP(hAPP(c_member(U_14916),sK339(U_14920,U_14919,U_14918,U_14917,U_14916,U_14915)),U_14917))
        | ~ sP1009(U_14915,U_14916,U_14917,U_14918,U_14919,U_14920) )
    & ! [U_14915,U_14916,U_14917,U_14918,U_14919,U_14920] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14916,U_14915),hAPP(hAPP(c_COMBS(U_14916,tc_fun(U_14918,tc_HOL_Obool),U_14915),hAPP(hAPP(c_COMBB(tc_fun(U_14918,U_14915),tc_fun(tc_fun(U_14918,tc_HOL_Obool),U_14915),U_14916),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14918,U_14915)),U_14920)),U_14919)),U_14917) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_14916,U_14918),U_14915),hAPP(c_Product__Type_Oprod_Oprod__case(U_14916,U_14918,U_14915),U_14920)),hAPP(hAPP(c_Product__Type_OSigma(U_14916,U_14918),U_14917),U_14919))
        | sP1009(U_14915,U_14916,U_14917,U_14918,U_14919,U_14920)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14916),U_14917))
        | ~ class_Groups_Ocomm__monoid__mult(U_14915) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1009])],[f_3813_3]) ).

cnf(f_3813_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14916,U_14915),hAPP(hAPP(c_COMBS(U_14916,tc_fun(U_14918,tc_HOL_Obool),U_14915),hAPP(hAPP(c_COMBB(tc_fun(U_14918,U_14915),tc_fun(tc_fun(U_14918,tc_HOL_Obool),U_14915),U_14916),c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_14918,U_14915)),U_14920)),U_14919)),U_14917) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(tc_prod(U_14916,U_14918),U_14915),hAPP(c_Product__Type_Oprod_Oprod__case(U_14916,U_14918,U_14915),U_14920)),hAPP(hAPP(c_Product__Type_OSigma(U_14916,U_14918),U_14917),U_14919))
    | sP1009(U_14915,U_14916,U_14917,U_14918,U_14919,U_14920)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14916),U_14917))
    | ~ class_Groups_Ocomm__monoid__mult(U_14915) ),
    inference(clausify,[status(thm)],[f_3813_4]) ).

cnf(f_3813_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14916),sK339(U_14920,U_14919,U_14918,U_14917,U_14916,U_14915)),U_14917))
    | ~ sP1009(U_14915,U_14916,U_14917,U_14918,U_14919,U_14920) ),
    inference(clausify,[status(thm)],[f_3813_4]) ).

cnf(f_3813_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14918),hAPP(U_14919,sK339(U_14920,U_14919,U_14918,U_14917,U_14916,U_14915))))
    | ~ sP1009(U_14915,U_14916,U_14917,U_14918,U_14919,U_14920) ),
    inference(clausify,[status(thm)],[f_3813_4]) ).

fof(f_3814_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_3814_2,plain,
    ! [U_14927,U_14926,U_14925,U_14924,U_14923,U_14922] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14923,U_14922),hAPP(hAPP(c_COMBS(U_14923,tc_fun(U_14925,tc_HOL_Obool),U_14922),hAPP(hAPP(c_COMBB(tc_fun(U_14925,U_14922),tc_fun(tc_fun(U_14925,tc_HOL_Obool),U_14922),U_14923),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14925,U_14922)),U_14927)),U_14926)),U_14924) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_14923,U_14925),U_14922),hAPP(c_Product__Type_Oprod_Oprod__case(U_14923,U_14925,U_14922),U_14927)),hAPP(hAPP(c_Product__Type_OSigma(U_14923,U_14925),U_14924),U_14926))
      | ? [U_14921] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14925),hAPP(U_14926,U_14921)))
          & hBOOL(hAPP(hAPP(c_member(U_14923),U_14921),U_14924)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14923),U_14924))
      | ~ class_Groups_Ocomm__monoid__add(U_14922) ),
    inference(variable_rename,[status(thm)],[f_3814_1]) ).

fof(f_3814_3,plain,
    ! [U_14927,U_14926,U_14925,U_14924,U_14923,U_14922] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14923,U_14922),hAPP(hAPP(c_COMBS(U_14923,tc_fun(U_14925,tc_HOL_Obool),U_14922),hAPP(hAPP(c_COMBB(tc_fun(U_14925,U_14922),tc_fun(tc_fun(U_14925,tc_HOL_Obool),U_14922),U_14923),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14925,U_14922)),U_14927)),U_14926)),U_14924) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_14923,U_14925),U_14922),hAPP(c_Product__Type_Oprod_Oprod__case(U_14923,U_14925,U_14922),U_14927)),hAPP(hAPP(c_Product__Type_OSigma(U_14923,U_14925),U_14924),U_14926))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14925),hAPP(U_14926,sK340(U_14927,U_14926,U_14925,U_14924,U_14923,U_14922))))
        & hBOOL(hAPP(hAPP(c_member(U_14923),sK340(U_14927,U_14926,U_14925,U_14924,U_14923,U_14922)),U_14924)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14923),U_14924))
      | ~ class_Groups_Ocomm__monoid__add(U_14922) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK340]),skolemize(U_14921,sK340(U_14927,U_14926,U_14925,U_14924,U_14923,U_14922))],[f_3814_2]) ).

fof(f_3814_4,plain,
    ( ! [U_14922,U_14923,U_14924,U_14925,U_14926,U_14927] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14925),hAPP(U_14926,sK340(U_14927,U_14926,U_14925,U_14924,U_14923,U_14922))))
        | ~ sP1010(U_14922,U_14923,U_14924,U_14925,U_14926,U_14927) )
    & ! [U_14922,U_14923,U_14924,U_14925,U_14926,U_14927] :
        ( hBOOL(hAPP(hAPP(c_member(U_14923),sK340(U_14927,U_14926,U_14925,U_14924,U_14923,U_14922)),U_14924))
        | ~ sP1010(U_14922,U_14923,U_14924,U_14925,U_14926,U_14927) )
    & ! [U_14922,U_14923,U_14924,U_14925,U_14926,U_14927] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14923,U_14922),hAPP(hAPP(c_COMBS(U_14923,tc_fun(U_14925,tc_HOL_Obool),U_14922),hAPP(hAPP(c_COMBB(tc_fun(U_14925,U_14922),tc_fun(tc_fun(U_14925,tc_HOL_Obool),U_14922),U_14923),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14925,U_14922)),U_14927)),U_14926)),U_14924) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_14923,U_14925),U_14922),hAPP(c_Product__Type_Oprod_Oprod__case(U_14923,U_14925,U_14922),U_14927)),hAPP(hAPP(c_Product__Type_OSigma(U_14923,U_14925),U_14924),U_14926))
        | sP1010(U_14922,U_14923,U_14924,U_14925,U_14926,U_14927)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14923),U_14924))
        | ~ class_Groups_Ocomm__monoid__add(U_14922) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1010])],[f_3814_3]) ).

cnf(f_3814_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14923,U_14922),hAPP(hAPP(c_COMBS(U_14923,tc_fun(U_14925,tc_HOL_Obool),U_14922),hAPP(hAPP(c_COMBB(tc_fun(U_14925,U_14922),tc_fun(tc_fun(U_14925,tc_HOL_Obool),U_14922),U_14923),c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14925,U_14922)),U_14927)),U_14926)),U_14924) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_prod(U_14923,U_14925),U_14922),hAPP(c_Product__Type_Oprod_Oprod__case(U_14923,U_14925,U_14922),U_14927)),hAPP(hAPP(c_Product__Type_OSigma(U_14923,U_14925),U_14924),U_14926))
    | sP1010(U_14922,U_14923,U_14924,U_14925,U_14926,U_14927)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14923),U_14924))
    | ~ class_Groups_Ocomm__monoid__add(U_14922) ),
    inference(clausify,[status(thm)],[f_3814_4]) ).

cnf(f_3814_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14923),sK340(U_14927,U_14926,U_14925,U_14924,U_14923,U_14922)),U_14924))
    | ~ sP1010(U_14922,U_14923,U_14924,U_14925,U_14926,U_14927) ),
    inference(clausify,[status(thm)],[f_3814_4]) ).

cnf(f_3814_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14925),hAPP(U_14926,sK340(U_14927,U_14926,U_14925,U_14924,U_14923,U_14922))))
    | ~ sP1010(U_14922,U_14923,U_14924,U_14925,U_14926,U_14927) ),
    inference(clausify,[status(thm)],[f_3814_4]) ).

fof(f_3815_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_3815_2,plain,
    ! [U_14934,U_14933,U_14932,U_14931,U_14930,U_14929] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14929,U_14930,c_Groups_Otimes__class_Otimes(U_14929)),hAPP(hAPP(c_COMBS(U_14930,tc_fun(U_14932,tc_HOL_Obool),U_14929),hAPP(hAPP(c_COMBC(U_14930,U_14929,tc_fun(tc_fun(U_14932,tc_HOL_Obool),U_14929)),hAPP(hAPP(c_COMBB(tc_fun(U_14932,U_14929),tc_fun(U_14929,tc_fun(tc_fun(U_14932,tc_HOL_Obool),U_14929)),U_14930),c_Finite__Set_Ofold__image(U_14929,U_14932,c_Groups_Otimes__class_Otimes(U_14929))),U_14934)),c_Groups_Oone__class_Oone(U_14929))),U_14933)),c_Groups_Oone__class_Oone(U_14929)),U_14931) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14929,tc_prod(U_14930,U_14932),c_Groups_Otimes__class_Otimes(U_14929)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14930,U_14932,U_14929),U_14934)),c_Groups_Oone__class_Oone(U_14929)),hAPP(hAPP(c_Product__Type_OSigma(U_14930,U_14932),U_14931),U_14933))
      | ? [U_14928] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14932),hAPP(U_14933,U_14928)))
          & hBOOL(hAPP(hAPP(c_member(U_14930),U_14928),U_14931)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14930),U_14931))
      | ~ class_Groups_Ocomm__monoid__mult(U_14929) ),
    inference(variable_rename,[status(thm)],[f_3815_1]) ).

fof(f_3815_3,plain,
    ! [U_14934,U_14933,U_14932,U_14931,U_14930,U_14929] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14929,U_14930,c_Groups_Otimes__class_Otimes(U_14929)),hAPP(hAPP(c_COMBS(U_14930,tc_fun(U_14932,tc_HOL_Obool),U_14929),hAPP(hAPP(c_COMBC(U_14930,U_14929,tc_fun(tc_fun(U_14932,tc_HOL_Obool),U_14929)),hAPP(hAPP(c_COMBB(tc_fun(U_14932,U_14929),tc_fun(U_14929,tc_fun(tc_fun(U_14932,tc_HOL_Obool),U_14929)),U_14930),c_Finite__Set_Ofold__image(U_14929,U_14932,c_Groups_Otimes__class_Otimes(U_14929))),U_14934)),c_Groups_Oone__class_Oone(U_14929))),U_14933)),c_Groups_Oone__class_Oone(U_14929)),U_14931) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14929,tc_prod(U_14930,U_14932),c_Groups_Otimes__class_Otimes(U_14929)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14930,U_14932,U_14929),U_14934)),c_Groups_Oone__class_Oone(U_14929)),hAPP(hAPP(c_Product__Type_OSigma(U_14930,U_14932),U_14931),U_14933))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14932),hAPP(U_14933,sK341(U_14934,U_14933,U_14932,U_14931,U_14930,U_14929))))
        & hBOOL(hAPP(hAPP(c_member(U_14930),sK341(U_14934,U_14933,U_14932,U_14931,U_14930,U_14929)),U_14931)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14930),U_14931))
      | ~ class_Groups_Ocomm__monoid__mult(U_14929) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK341]),skolemize(U_14928,sK341(U_14934,U_14933,U_14932,U_14931,U_14930,U_14929))],[f_3815_2]) ).

fof(f_3815_4,plain,
    ( ! [U_14929,U_14930,U_14931,U_14932,U_14933,U_14934] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14932),hAPP(U_14933,sK341(U_14934,U_14933,U_14932,U_14931,U_14930,U_14929))))
        | ~ sP1011(U_14929,U_14930,U_14931,U_14932,U_14933,U_14934) )
    & ! [U_14929,U_14930,U_14931,U_14932,U_14933,U_14934] :
        ( hBOOL(hAPP(hAPP(c_member(U_14930),sK341(U_14934,U_14933,U_14932,U_14931,U_14930,U_14929)),U_14931))
        | ~ sP1011(U_14929,U_14930,U_14931,U_14932,U_14933,U_14934) )
    & ! [U_14929,U_14930,U_14931,U_14932,U_14933,U_14934] :
        ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14929,U_14930,c_Groups_Otimes__class_Otimes(U_14929)),hAPP(hAPP(c_COMBS(U_14930,tc_fun(U_14932,tc_HOL_Obool),U_14929),hAPP(hAPP(c_COMBC(U_14930,U_14929,tc_fun(tc_fun(U_14932,tc_HOL_Obool),U_14929)),hAPP(hAPP(c_COMBB(tc_fun(U_14932,U_14929),tc_fun(U_14929,tc_fun(tc_fun(U_14932,tc_HOL_Obool),U_14929)),U_14930),c_Finite__Set_Ofold__image(U_14929,U_14932,c_Groups_Otimes__class_Otimes(U_14929))),U_14934)),c_Groups_Oone__class_Oone(U_14929))),U_14933)),c_Groups_Oone__class_Oone(U_14929)),U_14931) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14929,tc_prod(U_14930,U_14932),c_Groups_Otimes__class_Otimes(U_14929)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14930,U_14932,U_14929),U_14934)),c_Groups_Oone__class_Oone(U_14929)),hAPP(hAPP(c_Product__Type_OSigma(U_14930,U_14932),U_14931),U_14933))
        | sP1011(U_14929,U_14930,U_14931,U_14932,U_14933,U_14934)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14930),U_14931))
        | ~ class_Groups_Ocomm__monoid__mult(U_14929) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1011])],[f_3815_3]) ).

cnf(f_3815_5,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14929,U_14930,c_Groups_Otimes__class_Otimes(U_14929)),hAPP(hAPP(c_COMBS(U_14930,tc_fun(U_14932,tc_HOL_Obool),U_14929),hAPP(hAPP(c_COMBC(U_14930,U_14929,tc_fun(tc_fun(U_14932,tc_HOL_Obool),U_14929)),hAPP(hAPP(c_COMBB(tc_fun(U_14932,U_14929),tc_fun(U_14929,tc_fun(tc_fun(U_14932,tc_HOL_Obool),U_14929)),U_14930),c_Finite__Set_Ofold__image(U_14929,U_14932,c_Groups_Otimes__class_Otimes(U_14929))),U_14934)),c_Groups_Oone__class_Oone(U_14929))),U_14933)),c_Groups_Oone__class_Oone(U_14929)),U_14931) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_14929,tc_prod(U_14930,U_14932),c_Groups_Otimes__class_Otimes(U_14929)),hAPP(c_Product__Type_Oprod_Oprod__case(U_14930,U_14932,U_14929),U_14934)),c_Groups_Oone__class_Oone(U_14929)),hAPP(hAPP(c_Product__Type_OSigma(U_14930,U_14932),U_14931),U_14933))
    | sP1011(U_14929,U_14930,U_14931,U_14932,U_14933,U_14934)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14930),U_14931))
    | ~ class_Groups_Ocomm__monoid__mult(U_14929) ),
    inference(clausify,[status(thm)],[f_3815_4]) ).

cnf(f_3815_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14930),sK341(U_14934,U_14933,U_14932,U_14931,U_14930,U_14929)),U_14931))
    | ~ sP1011(U_14929,U_14930,U_14931,U_14932,U_14933,U_14934) ),
    inference(clausify,[status(thm)],[f_3815_4]) ).

cnf(f_3815_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14932),hAPP(U_14933,sK341(U_14934,U_14933,U_14932,U_14931,U_14930,U_14929))))
    | ~ sP1011(U_14929,U_14930,U_14931,U_14932,U_14933,U_14934) ),
    inference(clausify,[status(thm)],[f_3815_4]) ).

fof(f_3816_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_3816_2,plain,
    ! [U_14939,U_14938,U_14937,U_14936] :
      ( hAPP(c_Finite__Set_Ocard(tc_prod(U_14936,U_14938)),hAPP(hAPP(c_Product__Type_OSigma(U_14936,U_14938),U_14937),U_14939)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14936,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_14938,tc_HOL_Obool),tc_Nat_Onat,U_14936),c_Finite__Set_Ocard(U_14938)),U_14939)),U_14937)
      | ? [U_14935] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14938),hAPP(U_14939,U_14935)))
          & hBOOL(hAPP(hAPP(c_member(U_14936),U_14935),U_14937)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14936),U_14937)) ),
    inference(variable_rename,[status(thm)],[f_3816_1]) ).

fof(f_3816_3,plain,
    ! [U_14939,U_14938,U_14937,U_14936] :
      ( hAPP(c_Finite__Set_Ocard(tc_prod(U_14936,U_14938)),hAPP(hAPP(c_Product__Type_OSigma(U_14936,U_14938),U_14937),U_14939)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14936,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_14938,tc_HOL_Obool),tc_Nat_Onat,U_14936),c_Finite__Set_Ocard(U_14938)),U_14939)),U_14937)
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14938),hAPP(U_14939,sK342(U_14939,U_14938,U_14937,U_14936))))
        & hBOOL(hAPP(hAPP(c_member(U_14936),sK342(U_14939,U_14938,U_14937,U_14936)),U_14937)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14936),U_14937)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK342]),skolemize(U_14935,sK342(U_14939,U_14938,U_14937,U_14936))],[f_3816_2]) ).

fof(f_3816_4,plain,
    ( ! [U_14937,U_14936,U_14938,U_14939] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14938),hAPP(U_14939,sK342(U_14939,U_14938,U_14937,U_14936))))
        | ~ sP1012(U_14937,U_14936,U_14938,U_14939) )
    & ! [U_14937,U_14936,U_14938,U_14939] :
        ( hBOOL(hAPP(hAPP(c_member(U_14936),sK342(U_14939,U_14938,U_14937,U_14936)),U_14937))
        | ~ sP1012(U_14937,U_14936,U_14938,U_14939) )
    & ! [U_14937,U_14936,U_14938,U_14939] :
        ( hAPP(c_Finite__Set_Ocard(tc_prod(U_14936,U_14938)),hAPP(hAPP(c_Product__Type_OSigma(U_14936,U_14938),U_14937),U_14939)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14936,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_14938,tc_HOL_Obool),tc_Nat_Onat,U_14936),c_Finite__Set_Ocard(U_14938)),U_14939)),U_14937)
        | sP1012(U_14937,U_14936,U_14938,U_14939)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14936),U_14937)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1012])],[f_3816_3]) ).

cnf(f_3816_5,plain,
    ( hAPP(c_Finite__Set_Ocard(tc_prod(U_14936,U_14938)),hAPP(hAPP(c_Product__Type_OSigma(U_14936,U_14938),U_14937),U_14939)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_14936,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_fun(U_14938,tc_HOL_Obool),tc_Nat_Onat,U_14936),c_Finite__Set_Ocard(U_14938)),U_14939)),U_14937)
    | sP1012(U_14937,U_14936,U_14938,U_14939)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14936),U_14937)) ),
    inference(clausify,[status(thm)],[f_3816_4]) ).

cnf(f_3816_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14936),sK342(U_14939,U_14938,U_14937,U_14936)),U_14937))
    | ~ sP1012(U_14937,U_14936,U_14938,U_14939) ),
    inference(clausify,[status(thm)],[f_3816_4]) ).

cnf(f_3816_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14938),hAPP(U_14939,sK342(U_14939,U_14938,U_14937,U_14936))))
    | ~ sP1012(U_14937,U_14936,U_14938,U_14939) ),
    inference(clausify,[status(thm)],[f_3816_4]) ).

fof(f_3817_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_3817_2,plain,
    ! [U_14943,U_14942] :
      ( hBOOL(hAPP(hAPP(c_member(U_14942),hAPP(c_Finite__Set_Ofold1(U_14942,c_Groups_Otimes__class_Otimes(U_14942)),U_14943)),U_14943))
      | ? [U_14941,U_14940] : ~ hBOOL(hAPP(hAPP(c_member(U_14942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14942),U_14941),U_14940)),hAPP(hAPP(c_Set_Oinsert(U_14942),U_14941),hAPP(hAPP(c_Set_Oinsert(U_14942),U_14940),c_Orderings_Obot__class_Obot(tc_fun(U_14942,tc_HOL_Obool))))))
      | U_14943 = c_Orderings_Obot__class_Obot(tc_fun(U_14942,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14942),U_14943))
      | ~ class_Groups_Oab__semigroup__mult(U_14942) ),
    inference(variable_rename,[status(thm)],[f_3817_1]) ).

fof(f_3817_3,plain,
    ! [U_14943,U_14942] :
      ( hBOOL(hAPP(hAPP(c_member(U_14942),hAPP(c_Finite__Set_Ofold1(U_14942,c_Groups_Otimes__class_Otimes(U_14942)),U_14943)),U_14943))
      | ? [U_14940] : ~ hBOOL(hAPP(hAPP(c_member(U_14942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14942),sK343(U_14943,U_14942)),U_14940)),hAPP(hAPP(c_Set_Oinsert(U_14942),sK343(U_14943,U_14942)),hAPP(hAPP(c_Set_Oinsert(U_14942),U_14940),c_Orderings_Obot__class_Obot(tc_fun(U_14942,tc_HOL_Obool))))))
      | U_14943 = c_Orderings_Obot__class_Obot(tc_fun(U_14942,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14942),U_14943))
      | ~ class_Groups_Oab__semigroup__mult(U_14942) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK343]),skolemize(U_14941,sK343(U_14943,U_14942))],[f_3817_2]) ).

fof(f_3817_4,plain,
    ! [U_14943,U_14942] :
      ( hBOOL(hAPP(hAPP(c_member(U_14942),hAPP(c_Finite__Set_Ofold1(U_14942,c_Groups_Otimes__class_Otimes(U_14942)),U_14943)),U_14943))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14942),sK343(U_14943,U_14942)),sK344(U_14943,U_14942))),hAPP(hAPP(c_Set_Oinsert(U_14942),sK343(U_14943,U_14942)),hAPP(hAPP(c_Set_Oinsert(U_14942),sK344(U_14943,U_14942)),c_Orderings_Obot__class_Obot(tc_fun(U_14942,tc_HOL_Obool))))))
      | U_14943 = c_Orderings_Obot__class_Obot(tc_fun(U_14942,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14942),U_14943))
      | ~ class_Groups_Oab__semigroup__mult(U_14942) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK344]),skolemize(U_14940,sK344(U_14943,U_14942))],[f_3817_3]) ).

fof(f_3817_5,plain,
    ! [U_14942,U_14943] :
      ( hBOOL(hAPP(hAPP(c_member(U_14942),hAPP(c_Finite__Set_Ofold1(U_14942,c_Groups_Otimes__class_Otimes(U_14942)),U_14943)),U_14943))
      | ~ hBOOL(hAPP(hAPP(c_member(U_14942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14942),sK343(U_14943,U_14942)),sK344(U_14943,U_14942))),hAPP(hAPP(c_Set_Oinsert(U_14942),sK343(U_14943,U_14942)),hAPP(hAPP(c_Set_Oinsert(U_14942),sK344(U_14943,U_14942)),c_Orderings_Obot__class_Obot(tc_fun(U_14942,tc_HOL_Obool))))))
      | U_14943 = c_Orderings_Obot__class_Obot(tc_fun(U_14942,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14942),U_14943))
      | ~ class_Groups_Oab__semigroup__mult(U_14942) ),
    inference(definitional_conversion,[status(esa)],[f_3817_4]) ).

cnf(f_3817_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14942),hAPP(c_Finite__Set_Ofold1(U_14942,c_Groups_Otimes__class_Otimes(U_14942)),U_14943)),U_14943))
    | ~ hBOOL(hAPP(hAPP(c_member(U_14942),hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14942),sK343(U_14943,U_14942)),sK344(U_14943,U_14942))),hAPP(hAPP(c_Set_Oinsert(U_14942),sK343(U_14943,U_14942)),hAPP(hAPP(c_Set_Oinsert(U_14942),sK344(U_14943,U_14942)),c_Orderings_Obot__class_Obot(tc_fun(U_14942,tc_HOL_Obool))))))
    | U_14943 = c_Orderings_Obot__class_Obot(tc_fun(U_14942,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14942),U_14943))
    | ~ class_Groups_Oab__semigroup__mult(U_14942) ),
    inference(clausify,[status(thm)],[f_3817_5]) ).

fof(f_3818_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_3818_2,plain,
    ! [U_14948,U_14947,U_14946,U_14945] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14945,U_14947)),hAPP(hAPP(c_Product__Type_OSigma(U_14945,U_14947),U_14946),U_14948)))
      | ? [U_14944] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14947),hAPP(U_14948,U_14944)))
          & hBOOL(hAPP(hAPP(c_member(U_14945),U_14944),U_14946)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14945),U_14946)) ),
    inference(variable_rename,[status(thm)],[f_3818_1]) ).

fof(f_3818_3,plain,
    ! [U_14948,U_14947,U_14946,U_14945] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14945,U_14947)),hAPP(hAPP(c_Product__Type_OSigma(U_14945,U_14947),U_14946),U_14948)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14947),hAPP(U_14948,sK345(U_14948,U_14947,U_14946,U_14945))))
        & hBOOL(hAPP(hAPP(c_member(U_14945),sK345(U_14948,U_14947,U_14946,U_14945)),U_14946)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14945),U_14946)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK345]),skolemize(U_14944,sK345(U_14948,U_14947,U_14946,U_14945))],[f_3818_2]) ).

fof(f_3818_4,plain,
    ( ! [U_14946,U_14945,U_14947,U_14948] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14947),hAPP(U_14948,sK345(U_14948,U_14947,U_14946,U_14945))))
        | ~ sP1013(U_14946,U_14945,U_14947,U_14948) )
    & ! [U_14946,U_14945,U_14947,U_14948] :
        ( hBOOL(hAPP(hAPP(c_member(U_14945),sK345(U_14948,U_14947,U_14946,U_14945)),U_14946))
        | ~ sP1013(U_14946,U_14945,U_14947,U_14948) )
    & ! [U_14946,U_14945,U_14947,U_14948] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14945,U_14947)),hAPP(hAPP(c_Product__Type_OSigma(U_14945,U_14947),U_14946),U_14948)))
        | sP1013(U_14946,U_14945,U_14947,U_14948)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14945),U_14946)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1013])],[f_3818_3]) ).

cnf(f_3818_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(U_14945,U_14947)),hAPP(hAPP(c_Product__Type_OSigma(U_14945,U_14947),U_14946),U_14948)))
    | sP1013(U_14946,U_14945,U_14947,U_14948)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14945),U_14946)) ),
    inference(clausify,[status(thm)],[f_3818_4]) ).

cnf(f_3818_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14945),sK345(U_14948,U_14947,U_14946,U_14945)),U_14946))
    | ~ sP1013(U_14946,U_14945,U_14947,U_14948) ),
    inference(clausify,[status(thm)],[f_3818_4]) ).

cnf(f_3818_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14947),hAPP(U_14948,sK345(U_14948,U_14947,U_14946,U_14945))))
    | ~ sP1013(U_14946,U_14945,U_14947,U_14948) ),
    inference(clausify,[status(thm)],[f_3818_4]) ).

fof(f_3819_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_3819_2,plain,
    ! [U_14953,U_14952,U_14951] :
      ( hAPP(U_14952,hAPP(c_Finite__Set_Ofold1(U_14951,c_Groups_Otimes__class_Otimes(U_14951)),U_14953)) = hAPP(c_Finite__Set_Ofold1(U_14951,c_Groups_Otimes__class_Otimes(U_14951)),hAPP(c_Set_Oimage(U_14951,U_14951,U_14952),U_14953))
      | U_14953 = c_Orderings_Obot__class_Obot(tc_fun(U_14951,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14951),U_14953))
      | ? [U_14950,U_14949] : hAPP(U_14952,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14951),U_14950),U_14949)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14951),hAPP(U_14952,U_14950)),hAPP(U_14952,U_14949))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_14951) ),
    inference(variable_rename,[status(thm)],[f_3819_1]) ).

fof(f_3819_3,plain,
    ! [U_14953,U_14952,U_14951] :
      ( hAPP(U_14952,hAPP(c_Finite__Set_Ofold1(U_14951,c_Groups_Otimes__class_Otimes(U_14951)),U_14953)) = hAPP(c_Finite__Set_Ofold1(U_14951,c_Groups_Otimes__class_Otimes(U_14951)),hAPP(c_Set_Oimage(U_14951,U_14951,U_14952),U_14953))
      | U_14953 = c_Orderings_Obot__class_Obot(tc_fun(U_14951,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14951),U_14953))
      | ? [U_14949] : hAPP(U_14952,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14951),sK346(U_14953,U_14952,U_14951)),U_14949)) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14951),hAPP(U_14952,sK346(U_14953,U_14952,U_14951))),hAPP(U_14952,U_14949))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_14951) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK346]),skolemize(U_14950,sK346(U_14953,U_14952,U_14951))],[f_3819_2]) ).

fof(f_3819_4,plain,
    ! [U_14953,U_14952,U_14951] :
      ( hAPP(U_14952,hAPP(c_Finite__Set_Ofold1(U_14951,c_Groups_Otimes__class_Otimes(U_14951)),U_14953)) = hAPP(c_Finite__Set_Ofold1(U_14951,c_Groups_Otimes__class_Otimes(U_14951)),hAPP(c_Set_Oimage(U_14951,U_14951,U_14952),U_14953))
      | U_14953 = c_Orderings_Obot__class_Obot(tc_fun(U_14951,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14951),U_14953))
      | hAPP(U_14952,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14951),sK346(U_14953,U_14952,U_14951)),sK347(U_14953,U_14952,U_14951))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14951),hAPP(U_14952,sK346(U_14953,U_14952,U_14951))),hAPP(U_14952,sK347(U_14953,U_14952,U_14951)))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_14951) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK347]),skolemize(U_14949,sK347(U_14953,U_14952,U_14951))],[f_3819_3]) ).

fof(f_3819_5,plain,
    ! [U_14951,U_14952,U_14953] :
      ( hAPP(U_14952,hAPP(c_Finite__Set_Ofold1(U_14951,c_Groups_Otimes__class_Otimes(U_14951)),U_14953)) = hAPP(c_Finite__Set_Ofold1(U_14951,c_Groups_Otimes__class_Otimes(U_14951)),hAPP(c_Set_Oimage(U_14951,U_14951,U_14952),U_14953))
      | U_14953 = c_Orderings_Obot__class_Obot(tc_fun(U_14951,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14951),U_14953))
      | hAPP(U_14952,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14951),sK346(U_14953,U_14952,U_14951)),sK347(U_14953,U_14952,U_14951))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14951),hAPP(U_14952,sK346(U_14953,U_14952,U_14951))),hAPP(U_14952,sK347(U_14953,U_14952,U_14951)))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_14951) ),
    inference(definitional_conversion,[status(esa)],[f_3819_4]) ).

cnf(f_3819_6,plain,
    ( hAPP(U_14952,hAPP(c_Finite__Set_Ofold1(U_14951,c_Groups_Otimes__class_Otimes(U_14951)),U_14953)) = hAPP(c_Finite__Set_Ofold1(U_14951,c_Groups_Otimes__class_Otimes(U_14951)),hAPP(c_Set_Oimage(U_14951,U_14951,U_14952),U_14953))
    | U_14953 = c_Orderings_Obot__class_Obot(tc_fun(U_14951,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_14951),U_14953))
    | hAPP(U_14952,hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14951),sK346(U_14953,U_14952,U_14951)),sK347(U_14953,U_14952,U_14951))) != hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_14951),hAPP(U_14952,sK346(U_14953,U_14952,U_14951))),hAPP(U_14952,sK347(U_14953,U_14952,U_14951)))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_14951) ),
    inference(clausify,[status(thm)],[f_3819_5]) ).

fof(f_3820_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_3820_2,plain,
    ! [U_14960,U_14959,U_14958,U_14957,U_14956] :
      ( ? [U_14955] :
          ( ? [U_14954] :
              ( U_14958 = hAPP(hAPP(c_Product__Type_OPair(U_14956,U_14957),U_14955),U_14954)
              & hBOOL(hAPP(hAPP(c_member(U_14957),U_14954),hAPP(U_14960,U_14955))) )
          & hBOOL(hAPP(hAPP(c_member(U_14956),U_14955),U_14959)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14956,U_14957)),U_14958),hAPP(hAPP(c_Product__Type_OSigma(U_14956,U_14957),U_14959),U_14960))) ),
    inference(variable_rename,[status(thm)],[f_3820_1]) ).

fof(f_3820_3,plain,
    ! [U_14960,U_14959,U_14958,U_14957,U_14956] :
      ( ( ? [U_14954] :
            ( U_14958 = hAPP(hAPP(c_Product__Type_OPair(U_14956,U_14957),sK348(U_14960,U_14959,U_14958,U_14957,U_14956)),U_14954)
            & hBOOL(hAPP(hAPP(c_member(U_14957),U_14954),hAPP(U_14960,sK348(U_14960,U_14959,U_14958,U_14957,U_14956)))) )
        & hBOOL(hAPP(hAPP(c_member(U_14956),sK348(U_14960,U_14959,U_14958,U_14957,U_14956)),U_14959)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14956,U_14957)),U_14958),hAPP(hAPP(c_Product__Type_OSigma(U_14956,U_14957),U_14959),U_14960))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK348]),skolemize(U_14955,sK348(U_14960,U_14959,U_14958,U_14957,U_14956))],[f_3820_2]) ).

fof(f_3820_4,plain,
    ! [U_14960,U_14959,U_14958,U_14957,U_14956] :
      ( ( U_14958 = hAPP(hAPP(c_Product__Type_OPair(U_14956,U_14957),sK348(U_14960,U_14959,U_14958,U_14957,U_14956)),sK349(U_14960,U_14959,U_14958,U_14957,U_14956))
        & hBOOL(hAPP(hAPP(c_member(U_14957),sK349(U_14960,U_14959,U_14958,U_14957,U_14956)),hAPP(U_14960,sK348(U_14960,U_14959,U_14958,U_14957,U_14956))))
        & hBOOL(hAPP(hAPP(c_member(U_14956),sK348(U_14960,U_14959,U_14958,U_14957,U_14956)),U_14959)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14956,U_14957)),U_14958),hAPP(hAPP(c_Product__Type_OSigma(U_14956,U_14957),U_14959),U_14960))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK349]),skolemize(U_14954,sK349(U_14960,U_14959,U_14958,U_14957,U_14956))],[f_3820_3]) ).

fof(f_3820_5,plain,
    ( ! [U_14956,U_14957,U_14958,U_14959,U_14960] :
        ( U_14958 = hAPP(hAPP(c_Product__Type_OPair(U_14956,U_14957),sK348(U_14960,U_14959,U_14958,U_14957,U_14956)),sK349(U_14960,U_14959,U_14958,U_14957,U_14956))
        | ~ sP1014(U_14956,U_14957,U_14958,U_14959,U_14960) )
    & ! [U_14956,U_14957,U_14958,U_14959,U_14960] :
        ( hBOOL(hAPP(hAPP(c_member(U_14957),sK349(U_14960,U_14959,U_14958,U_14957,U_14956)),hAPP(U_14960,sK348(U_14960,U_14959,U_14958,U_14957,U_14956))))
        | ~ sP1014(U_14956,U_14957,U_14958,U_14959,U_14960) )
    & ! [U_14956,U_14957,U_14958,U_14959,U_14960] :
        ( hBOOL(hAPP(hAPP(c_member(U_14956),sK348(U_14960,U_14959,U_14958,U_14957,U_14956)),U_14959))
        | ~ sP1014(U_14956,U_14957,U_14958,U_14959,U_14960) )
    & ! [U_14956,U_14957,U_14958,U_14959,U_14960] :
        ( sP1014(U_14956,U_14957,U_14958,U_14959,U_14960)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14956,U_14957)),U_14958),hAPP(hAPP(c_Product__Type_OSigma(U_14956,U_14957),U_14959),U_14960))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1014])],[f_3820_4]) ).

cnf(f_3820_6,plain,
    ( sP1014(U_14956,U_14957,U_14958,U_14959,U_14960)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14956,U_14957)),U_14958),hAPP(hAPP(c_Product__Type_OSigma(U_14956,U_14957),U_14959),U_14960))) ),
    inference(clausify,[status(thm)],[f_3820_5]) ).

cnf(f_3820_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14956),sK348(U_14960,U_14959,U_14958,U_14957,U_14956)),U_14959))
    | ~ sP1014(U_14956,U_14957,U_14958,U_14959,U_14960) ),
    inference(clausify,[status(thm)],[f_3820_5]) ).

cnf(f_3820_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_14957),sK349(U_14960,U_14959,U_14958,U_14957,U_14956)),hAPP(U_14960,sK348(U_14960,U_14959,U_14958,U_14957,U_14956))))
    | ~ sP1014(U_14956,U_14957,U_14958,U_14959,U_14960) ),
    inference(clausify,[status(thm)],[f_3820_5]) ).

cnf(f_3820_9,plain,
    ( U_14958 = hAPP(hAPP(c_Product__Type_OPair(U_14956,U_14957),sK348(U_14960,U_14959,U_14958,U_14957,U_14956)),sK349(U_14960,U_14959,U_14958,U_14957,U_14956))
    | ~ sP1014(U_14956,U_14957,U_14958,U_14959,U_14960) ),
    inference(clausify,[status(thm)],[f_3820_5]) ).

fof(f_3821_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_3821_2,plain,
    ! [U_14966,U_14965,U_14964,U_14963,U_14962,U_14961] :
      ( hAPP(c_Set_Oimage(tc_prod(U_14961,U_14964),tc_prod(U_14962,U_14965),c_Product__Type_Omap__pair(U_14961,U_14962,U_14964,U_14965,U_14963,U_14966)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14961,U_14964),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14962,U_14965),tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_14964,U_14965,U_14966),c_Orderings_Otop__class_Otop(tc_fun(U_14964,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14965,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_14961,U_14962,U_14963),c_Orderings_Otop__class_Otop(tc_fun(U_14961,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14962,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3821_1]) ).

fof(f_3821_3,plain,
    ! [U_14963,U_14961,U_14962,U_14964,U_14965,U_14966] :
      ( hAPP(c_Set_Oimage(tc_prod(U_14961,U_14964),tc_prod(U_14962,U_14965),c_Product__Type_Omap__pair(U_14961,U_14962,U_14964,U_14965,U_14963,U_14966)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14961,U_14964),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14962,U_14965),tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_14964,U_14965,U_14966),c_Orderings_Otop__class_Otop(tc_fun(U_14964,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14965,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_14961,U_14962,U_14963),c_Orderings_Otop__class_Otop(tc_fun(U_14961,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14962,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3821_2]) ).

cnf(f_3821_4,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_14961,U_14964),tc_prod(U_14962,U_14965),c_Product__Type_Omap__pair(U_14961,U_14962,U_14964,U_14965,U_14963,U_14966)),c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14961,U_14964),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_prod(U_14962,U_14965),tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_14964,U_14965,U_14966),c_Orderings_Otop__class_Otop(tc_fun(U_14964,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14965,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_14961,U_14962,U_14963),c_Orderings_Otop__class_Otop(tc_fun(U_14961,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_14962,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3821_3]) ).

fof(f_3822_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_3822_2,plain,
    ! [U_14975,U_14974,U_14973,U_14972,U_14971,U_14970,U_14969,U_14968,U_14967] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14972,U_14973)),hAPP(hAPP(c_Product__Type_OPair(U_14972,U_14973),hAPP(U_14974,U_14969)),hAPP(U_14975,U_14970))),hAPP(c_Set_Oimage(tc_prod(U_14967,U_14968),tc_prod(U_14972,U_14973),c_Product__Type_Omap__pair(U_14967,U_14972,U_14968,U_14973,U_14974,U_14975)),U_14971)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14967,U_14968)),hAPP(hAPP(c_Product__Type_OPair(U_14967,U_14968),U_14969),U_14970)),U_14971)) ),
    inference(variable_rename,[status(thm)],[f_3822_1]) ).

fof(f_3822_3,plain,
    ! [U_14967,U_14968,U_14969,U_14970,U_14971,U_14972,U_14973,U_14974,U_14975] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14972,U_14973)),hAPP(hAPP(c_Product__Type_OPair(U_14972,U_14973),hAPP(U_14974,U_14969)),hAPP(U_14975,U_14970))),hAPP(c_Set_Oimage(tc_prod(U_14967,U_14968),tc_prod(U_14972,U_14973),c_Product__Type_Omap__pair(U_14967,U_14972,U_14968,U_14973,U_14974,U_14975)),U_14971)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14967,U_14968)),hAPP(hAPP(c_Product__Type_OPair(U_14967,U_14968),U_14969),U_14970)),U_14971)) ),
    inference(definitional_conversion,[status(esa)],[f_3822_2]) ).

cnf(f_3822_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_14972,U_14973)),hAPP(hAPP(c_Product__Type_OPair(U_14972,U_14973),hAPP(U_14974,U_14969)),hAPP(U_14975,U_14970))),hAPP(c_Set_Oimage(tc_prod(U_14967,U_14968),tc_prod(U_14972,U_14973),c_Product__Type_Omap__pair(U_14967,U_14972,U_14968,U_14973,U_14974,U_14975)),U_14971)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_14967,U_14968)),hAPP(hAPP(c_Product__Type_OPair(U_14967,U_14968),U_14969),U_14970)),U_14971)) ),
    inference(clausify,[status(thm)],[f_3822_3]) ).

fof(f_3823_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_3823_2,plain,
    ! [U_14983,U_14982,U_14981,U_14980,U_14979,U_14978,U_14977,U_14976] : hAPP(c_Product__Type_Omap__pair(U_14976,U_14977,U_14978,U_14979,U_14980,U_14981),hAPP(hAPP(c_Product__Type_OPair(U_14976,U_14978),U_14982),U_14983)) = hAPP(hAPP(c_Product__Type_OPair(U_14977,U_14979),hAPP(U_14980,U_14982)),hAPP(U_14981,U_14983)),
    inference(variable_rename,[status(thm)],[f_3823_1]) ).

fof(f_3823_3,plain,
    ! [U_14976,U_14977,U_14978,U_14979,U_14980,U_14981,U_14982,U_14983] : hAPP(c_Product__Type_Omap__pair(U_14976,U_14977,U_14978,U_14979,U_14980,U_14981),hAPP(hAPP(c_Product__Type_OPair(U_14976,U_14978),U_14982),U_14983)) = hAPP(hAPP(c_Product__Type_OPair(U_14977,U_14979),hAPP(U_14980,U_14982)),hAPP(U_14981,U_14983)),
    inference(definitional_conversion,[status(esa)],[f_3823_2]) ).

cnf(f_3823_4,plain,
    hAPP(c_Product__Type_Omap__pair(U_14976,U_14977,U_14978,U_14979,U_14980,U_14981),hAPP(hAPP(c_Product__Type_OPair(U_14976,U_14978),U_14982),U_14983)) = hAPP(hAPP(c_Product__Type_OPair(U_14977,U_14979),hAPP(U_14980,U_14982)),hAPP(U_14981,U_14983)),
    inference(clausify,[status(thm)],[f_3823_3]) ).

fof(f_3824_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_3824_2,plain,
    ! [U_14986,U_14985,U_14984] : hAPP(c_Product__Type_Omap__pair(U_14984,U_14984,U_14985,U_14985,c_COMBI(U_14984),c_COMBI(U_14985)),U_14986) = U_14986,
    inference(variable_rename,[status(thm)],[f_3824_1]) ).

fof(f_3824_3,plain,
    ! [U_14984,U_14986,U_14985] : hAPP(c_Product__Type_Omap__pair(U_14984,U_14984,U_14985,U_14985,c_COMBI(U_14984),c_COMBI(U_14985)),U_14986) = U_14986,
    inference(definitional_conversion,[status(esa)],[f_3824_2]) ).

cnf(f_3824_4,plain,
    hAPP(c_Product__Type_Omap__pair(U_14984,U_14984,U_14985,U_14985,c_COMBI(U_14984),c_COMBI(U_14985)),U_14986) = U_14986,
    inference(clausify,[status(thm)],[f_3824_3]) ).

fof(f_3825_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_3825_2,plain,
    ! [U_14993,U_14992,U_14991,U_14990,U_14989,U_14988,U_14987] : hAPP(c_Product__Type_Ofst(U_14987,U_14988),hAPP(c_Product__Type_Omap__pair(U_14989,U_14987,U_14990,U_14988,U_14991,U_14992),U_14993)) = hAPP(U_14991,hAPP(c_Product__Type_Ofst(U_14989,U_14990),U_14993)),
    inference(variable_rename,[status(thm)],[f_3825_1]) ).

fof(f_3825_3,plain,
    ! [U_14987,U_14988,U_14989,U_14990,U_14991,U_14992,U_14993] : hAPP(c_Product__Type_Ofst(U_14987,U_14988),hAPP(c_Product__Type_Omap__pair(U_14989,U_14987,U_14990,U_14988,U_14991,U_14992),U_14993)) = hAPP(U_14991,hAPP(c_Product__Type_Ofst(U_14989,U_14990),U_14993)),
    inference(definitional_conversion,[status(esa)],[f_3825_2]) ).

cnf(f_3825_4,plain,
    hAPP(c_Product__Type_Ofst(U_14987,U_14988),hAPP(c_Product__Type_Omap__pair(U_14989,U_14987,U_14990,U_14988,U_14991,U_14992),U_14993)) = hAPP(U_14991,hAPP(c_Product__Type_Ofst(U_14989,U_14990),U_14993)),
    inference(clausify,[status(thm)],[f_3825_3]) ).

fof(f_3826_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_3826_2,plain,
    ! [U_15000,U_14999,U_14998,U_14997,U_14996,U_14995,U_14994] : hAPP(c_Product__Type_Osnd(U_14994,U_14995),hAPP(c_Product__Type_Omap__pair(U_14996,U_14994,U_14997,U_14995,U_14998,U_14999),U_15000)) = hAPP(U_14999,hAPP(c_Product__Type_Osnd(U_14996,U_14997),U_15000)),
    inference(variable_rename,[status(thm)],[f_3826_1]) ).

fof(f_3826_3,plain,
    ! [U_14994,U_14995,U_14996,U_14997,U_14998,U_14999,U_15000] : hAPP(c_Product__Type_Osnd(U_14994,U_14995),hAPP(c_Product__Type_Omap__pair(U_14996,U_14994,U_14997,U_14995,U_14998,U_14999),U_15000)) = hAPP(U_14999,hAPP(c_Product__Type_Osnd(U_14996,U_14997),U_15000)),
    inference(definitional_conversion,[status(esa)],[f_3826_2]) ).

cnf(f_3826_4,plain,
    hAPP(c_Product__Type_Osnd(U_14994,U_14995),hAPP(c_Product__Type_Omap__pair(U_14996,U_14994,U_14997,U_14995,U_14998,U_14999),U_15000)) = hAPP(U_14999,hAPP(c_Product__Type_Osnd(U_14996,U_14997),U_15000)),
    inference(clausify,[status(thm)],[f_3826_3]) ).

fof(f_3827_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_3827_2,plain,
    ! [U_15002,U_15001] : c_Product__Type_Omap__pair(U_15001,U_15001,U_15002,U_15002,c_COMBI(U_15001),c_COMBI(U_15002)) = c_Fun_Oid(tc_prod(U_15001,U_15002)),
    inference(variable_rename,[status(thm)],[f_3827_1]) ).

fof(f_3827_3,plain,
    ! [U_15001,U_15002] : c_Product__Type_Omap__pair(U_15001,U_15001,U_15002,U_15002,c_COMBI(U_15001),c_COMBI(U_15002)) = c_Fun_Oid(tc_prod(U_15001,U_15002)),
    inference(definitional_conversion,[status(esa)],[f_3827_2]) ).

cnf(f_3827_4,plain,
    c_Product__Type_Omap__pair(U_15001,U_15001,U_15002,U_15002,c_COMBI(U_15001),c_COMBI(U_15002)) = c_Fun_Oid(tc_prod(U_15001,U_15002)),
    inference(clausify,[status(thm)],[f_3827_3]) ).

fof(f_3828_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_3828_2,plain,
    ! [U_15006,U_15005,U_15004,U_15003] : c_Product__Type_Oapsnd(U_15003,U_15004,U_15005,U_15006) = c_Product__Type_Omap__pair(U_15005,U_15005,U_15003,U_15004,c_Fun_Oid(U_15005),U_15006),
    inference(variable_rename,[status(thm)],[f_3828_1]) ).

fof(f_3828_3,plain,
    ! [U_15003,U_15004,U_15005,U_15006] : c_Product__Type_Oapsnd(U_15003,U_15004,U_15005,U_15006) = c_Product__Type_Omap__pair(U_15005,U_15005,U_15003,U_15004,c_Fun_Oid(U_15005),U_15006),
    inference(definitional_conversion,[status(esa)],[f_3828_2]) ).

cnf(f_3828_4,plain,
    c_Product__Type_Oapsnd(U_15003,U_15004,U_15005,U_15006) = c_Product__Type_Omap__pair(U_15005,U_15005,U_15003,U_15004,c_Fun_Oid(U_15005),U_15006),
    inference(clausify,[status(thm)],[f_3828_3]) ).

fof(f_3829_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_3829_2,plain,
    ! [U_15010,U_15009,U_15008,U_15007] : c_Product__Type_Oapfst(U_15007,U_15008,U_15009,U_15010) = c_Product__Type_Omap__pair(U_15007,U_15008,U_15009,U_15009,U_15010,c_Fun_Oid(U_15009)),
    inference(variable_rename,[status(thm)],[f_3829_1]) ).

fof(f_3829_3,plain,
    ! [U_15008,U_15007,U_15009,U_15010] : c_Product__Type_Oapfst(U_15007,U_15008,U_15009,U_15010) = c_Product__Type_Omap__pair(U_15007,U_15008,U_15009,U_15009,U_15010,c_Fun_Oid(U_15009)),
    inference(definitional_conversion,[status(esa)],[f_3829_2]) ).

cnf(f_3829_4,plain,
    c_Product__Type_Oapfst(U_15007,U_15008,U_15009,U_15010) = c_Product__Type_Omap__pair(U_15007,U_15008,U_15009,U_15009,U_15010,c_Fun_Oid(U_15009)),
    inference(clausify,[status(thm)],[f_3829_3]) ).

fof(f_3830_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_3830_2,plain,
    ! [U_15012,U_15011] : c_Product__Type_Omap__pair(U_15011,U_15011,U_15012,U_15012,c_Fun_Oid(U_15011),c_Fun_Oid(U_15012)) = c_Fun_Oid(tc_prod(U_15011,U_15012)),
    inference(variable_rename,[status(thm)],[f_3830_1]) ).

fof(f_3830_3,plain,
    ! [U_15011,U_15012] : c_Product__Type_Omap__pair(U_15011,U_15011,U_15012,U_15012,c_Fun_Oid(U_15011),c_Fun_Oid(U_15012)) = c_Fun_Oid(tc_prod(U_15011,U_15012)),
    inference(definitional_conversion,[status(esa)],[f_3830_2]) ).

cnf(f_3830_4,plain,
    c_Product__Type_Omap__pair(U_15011,U_15011,U_15012,U_15012,c_Fun_Oid(U_15011),c_Fun_Oid(U_15012)) = c_Fun_Oid(tc_prod(U_15011,U_15012)),
    inference(clausify,[status(thm)],[f_3830_3]) ).

fof(f_3831_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_3831_2,plain,
    ! [U_15018,U_15017,U_15016,U_15015,U_15014,U_15013] : c_Product__Type_Omap__pair(U_15013,U_15014,U_15015,U_15016,U_15017,U_15018) = hAPP(c_Product__Type_Oprod_Oprod__case(U_15013,U_15015,tc_prod(U_15014,U_15016)),hAPP(hAPP(c_COMBC(U_15013,tc_fun(U_15015,U_15016),tc_fun(U_15015,tc_prod(U_15014,U_15016))),hAPP(hAPP(c_COMBB(tc_fun(U_15016,tc_prod(U_15014,U_15016)),tc_fun(tc_fun(U_15015,U_15016),tc_fun(U_15015,tc_prod(U_15014,U_15016))),U_15013),c_COMBB(U_15016,tc_prod(U_15014,U_15016),U_15015)),hAPP(hAPP(c_COMBB(U_15014,tc_fun(U_15016,tc_prod(U_15014,U_15016)),U_15013),c_Product__Type_OPair(U_15014,U_15016)),U_15017))),U_15018)),
    inference(variable_rename,[status(thm)],[f_3831_1]) ).

fof(f_3831_3,plain,
    ! [U_15013,U_15014,U_15015,U_15016,U_15017,U_15018] : c_Product__Type_Omap__pair(U_15013,U_15014,U_15015,U_15016,U_15017,U_15018) = hAPP(c_Product__Type_Oprod_Oprod__case(U_15013,U_15015,tc_prod(U_15014,U_15016)),hAPP(hAPP(c_COMBC(U_15013,tc_fun(U_15015,U_15016),tc_fun(U_15015,tc_prod(U_15014,U_15016))),hAPP(hAPP(c_COMBB(tc_fun(U_15016,tc_prod(U_15014,U_15016)),tc_fun(tc_fun(U_15015,U_15016),tc_fun(U_15015,tc_prod(U_15014,U_15016))),U_15013),c_COMBB(U_15016,tc_prod(U_15014,U_15016),U_15015)),hAPP(hAPP(c_COMBB(U_15014,tc_fun(U_15016,tc_prod(U_15014,U_15016)),U_15013),c_Product__Type_OPair(U_15014,U_15016)),U_15017))),U_15018)),
    inference(definitional_conversion,[status(esa)],[f_3831_2]) ).

cnf(f_3831_4,plain,
    c_Product__Type_Omap__pair(U_15013,U_15014,U_15015,U_15016,U_15017,U_15018) = hAPP(c_Product__Type_Oprod_Oprod__case(U_15013,U_15015,tc_prod(U_15014,U_15016)),hAPP(hAPP(c_COMBC(U_15013,tc_fun(U_15015,U_15016),tc_fun(U_15015,tc_prod(U_15014,U_15016))),hAPP(hAPP(c_COMBB(tc_fun(U_15016,tc_prod(U_15014,U_15016)),tc_fun(tc_fun(U_15015,U_15016),tc_fun(U_15015,tc_prod(U_15014,U_15016))),U_15013),c_COMBB(U_15016,tc_prod(U_15014,U_15016),U_15015)),hAPP(hAPP(c_COMBB(U_15014,tc_fun(U_15016,tc_prod(U_15014,U_15016)),U_15013),c_Product__Type_OPair(U_15014,U_15016)),U_15017))),U_15018)),
    inference(clausify,[status(thm)],[f_3831_3]) ).

fof(f_3832_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_3832_2,plain,
    ! [U_15028,U_15027,U_15026,U_15025,U_15024,U_15023,U_15022,U_15021,U_15020,U_15019] :
      ( hAPP(c_Set_Oimage(tc_prod(U_15019,U_15024),tc_prod(U_15020,U_15025),c_Product__Type_Omap__pair(U_15019,U_15020,U_15024,U_15025,U_15021,U_15026)),hAPP(hAPP(c_Product__Type_OSigma(U_15019,U_15024),U_15022),hAPP(c_COMBK(tc_fun(U_15024,tc_HOL_Obool),U_15019),U_15027))) = hAPP(hAPP(c_Product__Type_OSigma(U_15020,U_15025),U_15023),hAPP(c_COMBK(tc_fun(U_15025,tc_HOL_Obool),U_15020),U_15028))
      | hAPP(c_Set_Oimage(U_15024,U_15025,U_15026),U_15027) != U_15028
      | hAPP(c_Set_Oimage(U_15019,U_15020,U_15021),U_15022) != U_15023 ),
    inference(variable_rename,[status(thm)],[f_3832_1]) ).

fof(f_3832_3,plain,
    ! [U_15019,U_15020,U_15021,U_15022,U_15023,U_15024,U_15025,U_15026,U_15027,U_15028] :
      ( hAPP(c_Set_Oimage(tc_prod(U_15019,U_15024),tc_prod(U_15020,U_15025),c_Product__Type_Omap__pair(U_15019,U_15020,U_15024,U_15025,U_15021,U_15026)),hAPP(hAPP(c_Product__Type_OSigma(U_15019,U_15024),U_15022),hAPP(c_COMBK(tc_fun(U_15024,tc_HOL_Obool),U_15019),U_15027))) = hAPP(hAPP(c_Product__Type_OSigma(U_15020,U_15025),U_15023),hAPP(c_COMBK(tc_fun(U_15025,tc_HOL_Obool),U_15020),U_15028))
      | hAPP(c_Set_Oimage(U_15024,U_15025,U_15026),U_15027) != U_15028
      | hAPP(c_Set_Oimage(U_15019,U_15020,U_15021),U_15022) != U_15023 ),
    inference(definitional_conversion,[status(esa)],[f_3832_2]) ).

cnf(f_3832_4,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_15019,U_15024),tc_prod(U_15020,U_15025),c_Product__Type_Omap__pair(U_15019,U_15020,U_15024,U_15025,U_15021,U_15026)),hAPP(hAPP(c_Product__Type_OSigma(U_15019,U_15024),U_15022),hAPP(c_COMBK(tc_fun(U_15024,tc_HOL_Obool),U_15019),U_15027))) = hAPP(hAPP(c_Product__Type_OSigma(U_15020,U_15025),U_15023),hAPP(c_COMBK(tc_fun(U_15025,tc_HOL_Obool),U_15020),U_15028))
    | hAPP(c_Set_Oimage(U_15024,U_15025,U_15026),U_15027) != U_15028
    | hAPP(c_Set_Oimage(U_15019,U_15020,U_15021),U_15022) != U_15023 ),
    inference(clausify,[status(thm)],[f_3832_3]) ).

fof(f_3833_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_3833_2,plain,
    ! [U_15032,U_15031,U_15030,U_15029] :
      ( c_Wellfounded_Owf(U_15031,hAPP(c_Set_Oimage(tc_prod(U_15029,U_15029),tc_prod(U_15031,U_15031),c_Product__Type_Omap__pair(U_15029,U_15031,U_15029,U_15031,U_15032,U_15032)),U_15030))
      | ~ c_Fun_Oinj__on(U_15029,U_15031,U_15032,c_Orderings_Otop__class_Otop(tc_fun(U_15029,tc_HOL_Obool)))
      | ~ c_Wellfounded_Owf(U_15029,U_15030) ),
    inference(variable_rename,[status(thm)],[f_3833_1]) ).

fof(f_3833_3,plain,
    ! [U_15030,U_15029,U_15031,U_15032] :
      ( c_Wellfounded_Owf(U_15031,hAPP(c_Set_Oimage(tc_prod(U_15029,U_15029),tc_prod(U_15031,U_15031),c_Product__Type_Omap__pair(U_15029,U_15031,U_15029,U_15031,U_15032,U_15032)),U_15030))
      | ~ c_Fun_Oinj__on(U_15029,U_15031,U_15032,c_Orderings_Otop__class_Otop(tc_fun(U_15029,tc_HOL_Obool)))
      | ~ c_Wellfounded_Owf(U_15029,U_15030) ),
    inference(definitional_conversion,[status(esa)],[f_3833_2]) ).

cnf(f_3833_4,plain,
    ( c_Wellfounded_Owf(U_15031,hAPP(c_Set_Oimage(tc_prod(U_15029,U_15029),tc_prod(U_15031,U_15031),c_Product__Type_Omap__pair(U_15029,U_15031,U_15029,U_15031,U_15032,U_15032)),U_15030))
    | ~ c_Fun_Oinj__on(U_15029,U_15031,U_15032,c_Orderings_Otop__class_Otop(tc_fun(U_15029,tc_HOL_Obool)))
    | ~ c_Wellfounded_Owf(U_15029,U_15030) ),
    inference(clausify,[status(thm)],[f_3833_3]) ).

fof(f_3834_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_3834_2,plain,
    ! [U_15040,U_15039,U_15038,U_15037,U_15036,U_15035,U_15034,U_15033] :
      ( c_Fun_Oinj__on(tc_prod(U_15033,U_15037),tc_prod(U_15034,U_15038),c_Product__Type_Omap__pair(U_15033,U_15034,U_15037,U_15038,U_15035,U_15039),hAPP(hAPP(c_Product__Type_OSigma(U_15033,U_15037),U_15036),hAPP(c_COMBK(tc_fun(U_15037,tc_HOL_Obool),U_15033),U_15040)))
      | ~ c_Fun_Oinj__on(U_15037,U_15038,U_15039,U_15040)
      | ~ c_Fun_Oinj__on(U_15033,U_15034,U_15035,U_15036) ),
    inference(variable_rename,[status(thm)],[f_3834_1]) ).

fof(f_3834_3,plain,
    ! [U_15033,U_15034,U_15035,U_15036,U_15037,U_15038,U_15039,U_15040] :
      ( c_Fun_Oinj__on(tc_prod(U_15033,U_15037),tc_prod(U_15034,U_15038),c_Product__Type_Omap__pair(U_15033,U_15034,U_15037,U_15038,U_15035,U_15039),hAPP(hAPP(c_Product__Type_OSigma(U_15033,U_15037),U_15036),hAPP(c_COMBK(tc_fun(U_15037,tc_HOL_Obool),U_15033),U_15040)))
      | ~ c_Fun_Oinj__on(U_15037,U_15038,U_15039,U_15040)
      | ~ c_Fun_Oinj__on(U_15033,U_15034,U_15035,U_15036) ),
    inference(definitional_conversion,[status(esa)],[f_3834_2]) ).

cnf(f_3834_4,plain,
    ( c_Fun_Oinj__on(tc_prod(U_15033,U_15037),tc_prod(U_15034,U_15038),c_Product__Type_Omap__pair(U_15033,U_15034,U_15037,U_15038,U_15035,U_15039),hAPP(hAPP(c_Product__Type_OSigma(U_15033,U_15037),U_15036),hAPP(c_COMBK(tc_fun(U_15037,tc_HOL_Obool),U_15033),U_15040)))
    | ~ c_Fun_Oinj__on(U_15037,U_15038,U_15039,U_15040)
    | ~ c_Fun_Oinj__on(U_15033,U_15034,U_15035,U_15036) ),
    inference(clausify,[status(thm)],[f_3834_3]) ).

fof(f_3835_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_3835_2,plain,
    ! [U_15050,U_15049,U_15048,U_15047,U_15046,U_15045,U_15044,U_15043] :
      ( ? [U_15042,U_15041] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15046,U_15047)),hAPP(hAPP(c_Product__Type_OPair(U_15046,U_15047),U_15042),U_15041)),U_15050))
          & U_15045 = hAPP(hAPP(c_Product__Type_OPair(U_15043,U_15044),hAPP(U_15048,U_15042)),hAPP(U_15049,U_15041)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15043,U_15044)),U_15045),hAPP(c_Set_Oimage(tc_prod(U_15046,U_15047),tc_prod(U_15043,U_15044),c_Product__Type_Omap__pair(U_15046,U_15043,U_15047,U_15044,U_15048,U_15049)),U_15050))) ),
    inference(variable_rename,[status(thm)],[f_3835_1]) ).

fof(f_3835_3,plain,
    ! [U_15050,U_15049,U_15048,U_15047,U_15046,U_15045,U_15044,U_15043] :
      ( ? [U_15041] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15046,U_15047)),hAPP(hAPP(c_Product__Type_OPair(U_15046,U_15047),sK350(U_15050,U_15049,U_15048,U_15047,U_15046,U_15045,U_15044,U_15043)),U_15041)),U_15050))
          & U_15045 = hAPP(hAPP(c_Product__Type_OPair(U_15043,U_15044),hAPP(U_15048,sK350(U_15050,U_15049,U_15048,U_15047,U_15046,U_15045,U_15044,U_15043))),hAPP(U_15049,U_15041)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15043,U_15044)),U_15045),hAPP(c_Set_Oimage(tc_prod(U_15046,U_15047),tc_prod(U_15043,U_15044),c_Product__Type_Omap__pair(U_15046,U_15043,U_15047,U_15044,U_15048,U_15049)),U_15050))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK350]),skolemize(U_15042,sK350(U_15050,U_15049,U_15048,U_15047,U_15046,U_15045,U_15044,U_15043))],[f_3835_2]) ).

fof(f_3835_4,plain,
    ! [U_15050,U_15049,U_15048,U_15047,U_15046,U_15045,U_15044,U_15043] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15046,U_15047)),hAPP(hAPP(c_Product__Type_OPair(U_15046,U_15047),sK350(U_15050,U_15049,U_15048,U_15047,U_15046,U_15045,U_15044,U_15043)),sK351(U_15050,U_15049,U_15048,U_15047,U_15046,U_15045,U_15044,U_15043))),U_15050))
        & U_15045 = hAPP(hAPP(c_Product__Type_OPair(U_15043,U_15044),hAPP(U_15048,sK350(U_15050,U_15049,U_15048,U_15047,U_15046,U_15045,U_15044,U_15043))),hAPP(U_15049,sK351(U_15050,U_15049,U_15048,U_15047,U_15046,U_15045,U_15044,U_15043))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15043,U_15044)),U_15045),hAPP(c_Set_Oimage(tc_prod(U_15046,U_15047),tc_prod(U_15043,U_15044),c_Product__Type_Omap__pair(U_15046,U_15043,U_15047,U_15044,U_15048,U_15049)),U_15050))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK351]),skolemize(U_15041,sK351(U_15050,U_15049,U_15048,U_15047,U_15046,U_15045,U_15044,U_15043))],[f_3835_3]) ).

fof(f_3835_5,plain,
    ( ! [U_15043,U_15044,U_15045,U_15046,U_15047,U_15048,U_15049,U_15050] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15046,U_15047)),hAPP(hAPP(c_Product__Type_OPair(U_15046,U_15047),sK350(U_15050,U_15049,U_15048,U_15047,U_15046,U_15045,U_15044,U_15043)),sK351(U_15050,U_15049,U_15048,U_15047,U_15046,U_15045,U_15044,U_15043))),U_15050))
        | ~ sP1015(U_15043,U_15044,U_15045,U_15046,U_15047,U_15048,U_15049,U_15050) )
    & ! [U_15043,U_15044,U_15045,U_15046,U_15047,U_15048,U_15049,U_15050] :
        ( U_15045 = hAPP(hAPP(c_Product__Type_OPair(U_15043,U_15044),hAPP(U_15048,sK350(U_15050,U_15049,U_15048,U_15047,U_15046,U_15045,U_15044,U_15043))),hAPP(U_15049,sK351(U_15050,U_15049,U_15048,U_15047,U_15046,U_15045,U_15044,U_15043)))
        | ~ sP1015(U_15043,U_15044,U_15045,U_15046,U_15047,U_15048,U_15049,U_15050) )
    & ! [U_15043,U_15044,U_15045,U_15046,U_15047,U_15048,U_15049,U_15050] :
        ( sP1015(U_15043,U_15044,U_15045,U_15046,U_15047,U_15048,U_15049,U_15050)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15043,U_15044)),U_15045),hAPP(c_Set_Oimage(tc_prod(U_15046,U_15047),tc_prod(U_15043,U_15044),c_Product__Type_Omap__pair(U_15046,U_15043,U_15047,U_15044,U_15048,U_15049)),U_15050))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1015])],[f_3835_4]) ).

cnf(f_3835_6,plain,
    ( sP1015(U_15043,U_15044,U_15045,U_15046,U_15047,U_15048,U_15049,U_15050)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15043,U_15044)),U_15045),hAPP(c_Set_Oimage(tc_prod(U_15046,U_15047),tc_prod(U_15043,U_15044),c_Product__Type_Omap__pair(U_15046,U_15043,U_15047,U_15044,U_15048,U_15049)),U_15050))) ),
    inference(clausify,[status(thm)],[f_3835_5]) ).

cnf(f_3835_7,plain,
    ( U_15045 = hAPP(hAPP(c_Product__Type_OPair(U_15043,U_15044),hAPP(U_15048,sK350(U_15050,U_15049,U_15048,U_15047,U_15046,U_15045,U_15044,U_15043))),hAPP(U_15049,sK351(U_15050,U_15049,U_15048,U_15047,U_15046,U_15045,U_15044,U_15043)))
    | ~ sP1015(U_15043,U_15044,U_15045,U_15046,U_15047,U_15048,U_15049,U_15050) ),
    inference(clausify,[status(thm)],[f_3835_5]) ).

cnf(f_3835_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15046,U_15047)),hAPP(hAPP(c_Product__Type_OPair(U_15046,U_15047),sK350(U_15050,U_15049,U_15048,U_15047,U_15046,U_15045,U_15044,U_15043)),sK351(U_15050,U_15049,U_15048,U_15047,U_15046,U_15045,U_15044,U_15043))),U_15050))
    | ~ sP1015(U_15043,U_15044,U_15045,U_15046,U_15047,U_15048,U_15049,U_15050) ),
    inference(clausify,[status(thm)],[f_3835_5]) ).

fof(f_3836_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_3836_2,plain,
    ! [U_15055,U_15054,U_15053] :
      ( ( c_Relation_Orefl__on(U_15053,U_15054,U_15055)
        | ? [U_15052] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15053,U_15053)),hAPP(hAPP(c_Product__Type_OPair(U_15053,U_15053),U_15052),U_15052)),U_15055))
            & hBOOL(hAPP(hAPP(c_member(U_15053),U_15052),U_15054)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15053,U_15053),tc_HOL_Obool)),U_15055),hAPP(hAPP(c_Product__Type_OSigma(U_15053,U_15053),U_15054),hAPP(c_COMBK(tc_fun(U_15053,tc_HOL_Obool),U_15053),U_15054)))) )
      & ( ( ! [U_15051] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15053,U_15053)),hAPP(hAPP(c_Product__Type_OPair(U_15053,U_15053),U_15051),U_15051)),U_15055))
              | ~ hBOOL(hAPP(hAPP(c_member(U_15053),U_15051),U_15054)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15053,U_15053),tc_HOL_Obool)),U_15055),hAPP(hAPP(c_Product__Type_OSigma(U_15053,U_15053),U_15054),hAPP(c_COMBK(tc_fun(U_15053,tc_HOL_Obool),U_15053),U_15054)))) )
        | ~ c_Relation_Orefl__on(U_15053,U_15054,U_15055) ) ),
    inference(variable_rename,[status(thm)],[f_3836_1]) ).

fof(f_3836_3,plain,
    ( ! [U_15061,U_15059,U_15057] :
        ( c_Relation_Orefl__on(U_15057,U_15059,U_15061)
        | ? [U_15052] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15057,U_15057)),hAPP(hAPP(c_Product__Type_OPair(U_15057,U_15057),U_15052),U_15052)),U_15061))
            & hBOOL(hAPP(hAPP(c_member(U_15057),U_15052),U_15059)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15057,U_15057),tc_HOL_Obool)),U_15061),hAPP(hAPP(c_Product__Type_OSigma(U_15057,U_15057),U_15059),hAPP(c_COMBK(tc_fun(U_15057,tc_HOL_Obool),U_15057),U_15059)))) )
    & ! [U_15060,U_15058,U_15056] :
        ( ( ! [U_15051] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15056,U_15056)),hAPP(hAPP(c_Product__Type_OPair(U_15056,U_15056),U_15051),U_15051)),U_15060))
              | ~ hBOOL(hAPP(hAPP(c_member(U_15056),U_15051),U_15058)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15056,U_15056),tc_HOL_Obool)),U_15060),hAPP(hAPP(c_Product__Type_OSigma(U_15056,U_15056),U_15058),hAPP(c_COMBK(tc_fun(U_15056,tc_HOL_Obool),U_15056),U_15058)))) )
        | ~ c_Relation_Orefl__on(U_15056,U_15058,U_15060) ) ),
    inference(miniscope,[status(thm)],[f_3836_2]) ).

fof(f_3836_4,plain,
    ( ! [U_15061,U_15059,U_15057] :
        ( c_Relation_Orefl__on(U_15057,U_15059,U_15061)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15057,U_15057)),hAPP(hAPP(c_Product__Type_OPair(U_15057,U_15057),sK352(U_15061,U_15059,U_15057)),sK352(U_15061,U_15059,U_15057))),U_15061))
          & hBOOL(hAPP(hAPP(c_member(U_15057),sK352(U_15061,U_15059,U_15057)),U_15059)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15057,U_15057),tc_HOL_Obool)),U_15061),hAPP(hAPP(c_Product__Type_OSigma(U_15057,U_15057),U_15059),hAPP(c_COMBK(tc_fun(U_15057,tc_HOL_Obool),U_15057),U_15059)))) )
    & ! [U_15060,U_15058,U_15056] :
        ( ( ! [U_15051] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15056,U_15056)),hAPP(hAPP(c_Product__Type_OPair(U_15056,U_15056),U_15051),U_15051)),U_15060))
              | ~ hBOOL(hAPP(hAPP(c_member(U_15056),U_15051),U_15058)) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15056,U_15056),tc_HOL_Obool)),U_15060),hAPP(hAPP(c_Product__Type_OSigma(U_15056,U_15056),U_15058),hAPP(c_COMBK(tc_fun(U_15056,tc_HOL_Obool),U_15056),U_15058)))) )
        | ~ c_Relation_Orefl__on(U_15056,U_15058,U_15060) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK352]),skolemize(U_15052,sK352(U_15061,U_15059,U_15057))],[f_3836_3]) ).

fof(f_3836_5,plain,
    ( ! [U_15059,U_15057,U_15061] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15057,U_15057)),hAPP(hAPP(c_Product__Type_OPair(U_15057,U_15057),sK352(U_15061,U_15059,U_15057)),sK352(U_15061,U_15059,U_15057))),U_15061))
        | ~ sP1017(U_15059,U_15057,U_15061) )
    & ! [U_15059,U_15057,U_15061] :
        ( hBOOL(hAPP(hAPP(c_member(U_15057),sK352(U_15061,U_15059,U_15057)),U_15059))
        | ~ sP1017(U_15059,U_15057,U_15061) )
    & ! [U_15051,U_15060,U_15056,U_15058] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15056,U_15056)),hAPP(hAPP(c_Product__Type_OPair(U_15056,U_15056),U_15051),U_15051)),U_15060))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15056),U_15051),U_15058))
        | ~ sP1016(U_15051,U_15060,U_15056,U_15058) )
    & ! [U_15051,U_15060,U_15056,U_15058] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15056,U_15056),tc_HOL_Obool)),U_15060),hAPP(hAPP(c_Product__Type_OSigma(U_15056,U_15056),U_15058),hAPP(c_COMBK(tc_fun(U_15056,tc_HOL_Obool),U_15056),U_15058))))
        | ~ sP1016(U_15051,U_15060,U_15056,U_15058) )
    & ! [U_15059,U_15057,U_15061] :
        ( c_Relation_Orefl__on(U_15057,U_15059,U_15061)
        | sP1017(U_15059,U_15057,U_15061)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15057,U_15057),tc_HOL_Obool)),U_15061),hAPP(hAPP(c_Product__Type_OSigma(U_15057,U_15057),U_15059),hAPP(c_COMBK(tc_fun(U_15057,tc_HOL_Obool),U_15057),U_15059)))) )
    & ! [U_15051,U_15060,U_15056,U_15058] :
        ( sP1016(U_15051,U_15060,U_15056,U_15058)
        | ~ c_Relation_Orefl__on(U_15056,U_15058,U_15060) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1016,sP1017])],[f_3836_4]) ).

cnf(f_3836_6,plain,
    ( sP1016(U_15051,U_15060,U_15056,U_15058)
    | ~ c_Relation_Orefl__on(U_15056,U_15058,U_15060) ),
    inference(clausify,[status(thm)],[f_3836_5]) ).

cnf(f_3836_7,plain,
    ( c_Relation_Orefl__on(U_15057,U_15059,U_15061)
    | sP1017(U_15059,U_15057,U_15061)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15057,U_15057),tc_HOL_Obool)),U_15061),hAPP(hAPP(c_Product__Type_OSigma(U_15057,U_15057),U_15059),hAPP(c_COMBK(tc_fun(U_15057,tc_HOL_Obool),U_15057),U_15059)))) ),
    inference(clausify,[status(thm)],[f_3836_5]) ).

cnf(f_3836_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15056,U_15056),tc_HOL_Obool)),U_15060),hAPP(hAPP(c_Product__Type_OSigma(U_15056,U_15056),U_15058),hAPP(c_COMBK(tc_fun(U_15056,tc_HOL_Obool),U_15056),U_15058))))
    | ~ sP1016(U_15051,U_15060,U_15056,U_15058) ),
    inference(clausify,[status(thm)],[f_3836_5]) ).

cnf(f_3836_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15056,U_15056)),hAPP(hAPP(c_Product__Type_OPair(U_15056,U_15056),U_15051),U_15051)),U_15060))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15056),U_15051),U_15058))
    | ~ sP1016(U_15051,U_15060,U_15056,U_15058) ),
    inference(clausify,[status(thm)],[f_3836_5]) ).

cnf(f_3836_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15057),sK352(U_15061,U_15059,U_15057)),U_15059))
    | ~ sP1017(U_15059,U_15057,U_15061) ),
    inference(clausify,[status(thm)],[f_3836_5]) ).

cnf(f_3836_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15057,U_15057)),hAPP(hAPP(c_Product__Type_OPair(U_15057,U_15057),sK352(U_15061,U_15059,U_15057)),sK352(U_15061,U_15059,U_15057))),U_15061))
    | ~ sP1017(U_15059,U_15057,U_15061) ),
    inference(clausify,[status(thm)],[f_3836_5]) ).

fof(f_3837_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_3837_2,plain,
    ! [U_15063,U_15062] : c_Relation_Orefl__on(U_15062,U_15063,c_Relation_OId__on(U_15062,U_15063)),
    inference(variable_rename,[status(thm)],[f_3837_1]) ).

fof(f_3837_3,plain,
    ! [U_15063,U_15062] : c_Relation_Orefl__on(U_15062,U_15063,c_Relation_OId__on(U_15062,U_15063)),
    inference(definitional_conversion,[status(esa)],[f_3837_2]) ).

cnf(f_3837_4,plain,
    c_Relation_Orefl__on(U_15062,U_15063,c_Relation_OId__on(U_15062,U_15063)),
    inference(clausify,[status(thm)],[f_3837_3]) ).

fof(f_3838_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_3838_2,plain,
    ! [U_15066,U_15065,U_15064] :
      ( ( c_Relation_Orefl__on(U_15064,U_15065,hAPP(c_Relation_Oconverse(U_15064,U_15064),U_15066))
        | ~ c_Relation_Orefl__on(U_15064,U_15065,U_15066) )
      & ( c_Relation_Orefl__on(U_15064,U_15065,U_15066)
        | ~ c_Relation_Orefl__on(U_15064,U_15065,hAPP(c_Relation_Oconverse(U_15064,U_15064),U_15066)) ) ),
    inference(variable_rename,[status(thm)],[f_3838_1]) ).

fof(f_3838_3,plain,
    ( ! [U_15072,U_15070,U_15068] :
        ( c_Relation_Orefl__on(U_15068,U_15070,hAPP(c_Relation_Oconverse(U_15068,U_15068),U_15072))
        | ~ c_Relation_Orefl__on(U_15068,U_15070,U_15072) )
    & ! [U_15071,U_15069,U_15067] :
        ( c_Relation_Orefl__on(U_15067,U_15069,U_15071)
        | ~ c_Relation_Orefl__on(U_15067,U_15069,hAPP(c_Relation_Oconverse(U_15067,U_15067),U_15071)) ) ),
    inference(miniscope,[status(thm)],[f_3838_2]) ).

fof(f_3838_4,plain,
    ( ! [U_15070,U_15072,U_15068] :
        ( c_Relation_Orefl__on(U_15068,U_15070,hAPP(c_Relation_Oconverse(U_15068,U_15068),U_15072))
        | ~ c_Relation_Orefl__on(U_15068,U_15070,U_15072) )
    & ! [U_15067,U_15069,U_15071] :
        ( c_Relation_Orefl__on(U_15067,U_15069,U_15071)
        | ~ c_Relation_Orefl__on(U_15067,U_15069,hAPP(c_Relation_Oconverse(U_15067,U_15067),U_15071)) ) ),
    inference(definitional_conversion,[status(esa)],[f_3838_3]) ).

cnf(f_3838_5,plain,
    ( c_Relation_Orefl__on(U_15067,U_15069,U_15071)
    | ~ c_Relation_Orefl__on(U_15067,U_15069,hAPP(c_Relation_Oconverse(U_15067,U_15067),U_15071)) ),
    inference(clausify,[status(thm)],[f_3838_4]) ).

cnf(f_3838_6,plain,
    ( c_Relation_Orefl__on(U_15068,U_15070,hAPP(c_Relation_Oconverse(U_15068,U_15068),U_15072))
    | ~ c_Relation_Orefl__on(U_15068,U_15070,U_15072) ),
    inference(clausify,[status(thm)],[f_3838_4]) ).

fof(f_3839_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_3839_2,plain,
    ! [U_15074,U_15073] : c_Relation_Orefl__on(U_15073,c_Orderings_Otop__class_Otop(tc_fun(U_15073,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15073,U_15074)),
    inference(variable_rename,[status(thm)],[f_3839_1]) ).

fof(f_3839_3,plain,
    ! [U_15074,U_15073] : c_Relation_Orefl__on(U_15073,c_Orderings_Otop__class_Otop(tc_fun(U_15073,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15073,U_15074)),
    inference(definitional_conversion,[status(esa)],[f_3839_2]) ).

cnf(f_3839_4,plain,
    c_Relation_Orefl__on(U_15073,c_Orderings_Otop__class_Otop(tc_fun(U_15073,tc_HOL_Obool)),c_Transitive__Closure_Ortrancl(U_15073,U_15074)),
    inference(clausify,[status(thm)],[f_3839_3]) ).

fof(f_3840_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_3840_2,plain,
    ! [U_15075] : c_Relation_Orefl__on(U_15075,c_Orderings_Obot__class_Obot(tc_fun(U_15075,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15075,U_15075),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_3840_1]) ).

fof(f_3840_3,plain,
    ! [U_15075] : c_Relation_Orefl__on(U_15075,c_Orderings_Obot__class_Obot(tc_fun(U_15075,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15075,U_15075),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_3840_2]) ).

cnf(f_3840_4,plain,
    c_Relation_Orefl__on(U_15075,c_Orderings_Obot__class_Obot(tc_fun(U_15075,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(U_15075,U_15075),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_3840_3]) ).

fof(f_3841_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_3841_2,plain,
    ! [U_15080,U_15079,U_15078,U_15077,U_15076] :
      ( c_Relation_Orefl__on(U_15076,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15076,tc_HOL_Obool)),U_15077),U_15079),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15076,U_15076),tc_HOL_Obool)),U_15078),U_15080))
      | ~ c_Relation_Orefl__on(U_15076,U_15079,U_15080)
      | ~ c_Relation_Orefl__on(U_15076,U_15077,U_15078) ),
    inference(variable_rename,[status(thm)],[f_3841_1]) ).

fof(f_3841_3,plain,
    ! [U_15076,U_15077,U_15078,U_15079,U_15080] :
      ( c_Relation_Orefl__on(U_15076,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15076,tc_HOL_Obool)),U_15077),U_15079),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15076,U_15076),tc_HOL_Obool)),U_15078),U_15080))
      | ~ c_Relation_Orefl__on(U_15076,U_15079,U_15080)
      | ~ c_Relation_Orefl__on(U_15076,U_15077,U_15078) ),
    inference(definitional_conversion,[status(esa)],[f_3841_2]) ).

cnf(f_3841_4,plain,
    ( c_Relation_Orefl__on(U_15076,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15076,tc_HOL_Obool)),U_15077),U_15079),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15076,U_15076),tc_HOL_Obool)),U_15078),U_15080))
    | ~ c_Relation_Orefl__on(U_15076,U_15079,U_15080)
    | ~ c_Relation_Orefl__on(U_15076,U_15077,U_15078) ),
    inference(clausify,[status(thm)],[f_3841_3]) ).

fof(f_3842_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_3842_2,plain,
    ! [U_15081] : c_Relation_Orefl__on(U_15081,c_Orderings_Otop__class_Otop(tc_fun(U_15081,tc_HOL_Obool)),c_Relation_OId(U_15081)),
    inference(variable_rename,[status(thm)],[f_3842_1]) ).

fof(f_3842_3,plain,
    ! [U_15081] : c_Relation_Orefl__on(U_15081,c_Orderings_Otop__class_Otop(tc_fun(U_15081,tc_HOL_Obool)),c_Relation_OId(U_15081)),
    inference(definitional_conversion,[status(esa)],[f_3842_2]) ).

cnf(f_3842_4,plain,
    c_Relation_Orefl__on(U_15081,c_Orderings_Otop__class_Otop(tc_fun(U_15081,tc_HOL_Obool)),c_Relation_OId(U_15081)),
    inference(clausify,[status(thm)],[f_3842_3]) ).

fof(f_3843_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_3843_2,plain,
    ! [U_15086,U_15085,U_15084,U_15083,U_15082] :
      ( c_Relation_Orefl__on(U_15082,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15082,tc_HOL_Obool)),U_15083),U_15085),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15082,U_15082),tc_HOL_Obool)),U_15084),U_15086))
      | ~ c_Relation_Orefl__on(U_15082,U_15085,U_15086)
      | ~ c_Relation_Orefl__on(U_15082,U_15083,U_15084) ),
    inference(variable_rename,[status(thm)],[f_3843_1]) ).

fof(f_3843_3,plain,
    ! [U_15082,U_15083,U_15084,U_15085,U_15086] :
      ( c_Relation_Orefl__on(U_15082,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15082,tc_HOL_Obool)),U_15083),U_15085),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15082,U_15082),tc_HOL_Obool)),U_15084),U_15086))
      | ~ c_Relation_Orefl__on(U_15082,U_15085,U_15086)
      | ~ c_Relation_Orefl__on(U_15082,U_15083,U_15084) ),
    inference(definitional_conversion,[status(esa)],[f_3843_2]) ).

cnf(f_3843_4,plain,
    ( c_Relation_Orefl__on(U_15082,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15082,tc_HOL_Obool)),U_15083),U_15085),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(U_15082,U_15082),tc_HOL_Obool)),U_15084),U_15086))
    | ~ c_Relation_Orefl__on(U_15082,U_15085,U_15086)
    | ~ c_Relation_Orefl__on(U_15082,U_15083,U_15084) ),
    inference(clausify,[status(thm)],[f_3843_3]) ).

fof(f_3844_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_3844_2,plain,
    ! [U_15090,U_15089,U_15088,U_15087] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15087,U_15087)),hAPP(hAPP(c_Product__Type_OPair(U_15087,U_15087),U_15090),U_15090)),U_15089))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15087),U_15090),U_15088))
      | ~ c_Relation_Orefl__on(U_15087,U_15088,U_15089) ),
    inference(variable_rename,[status(thm)],[f_3844_1]) ).

fof(f_3844_3,plain,
    ! [U_15087,U_15088,U_15089,U_15090] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15087,U_15087)),hAPP(hAPP(c_Product__Type_OPair(U_15087,U_15087),U_15090),U_15090)),U_15089))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15087),U_15090),U_15088))
      | ~ c_Relation_Orefl__on(U_15087,U_15088,U_15089) ),
    inference(definitional_conversion,[status(esa)],[f_3844_2]) ).

cnf(f_3844_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15087,U_15087)),hAPP(hAPP(c_Product__Type_OPair(U_15087,U_15087),U_15090),U_15090)),U_15089))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15087),U_15090),U_15088))
    | ~ c_Relation_Orefl__on(U_15087,U_15088,U_15089) ),
    inference(clausify,[status(thm)],[f_3844_3]) ).

fof(f_3845_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_3845_2,plain,
    ! [U_15095,U_15094,U_15093,U_15092,U_15091] :
      ( hBOOL(hAPP(hAPP(c_member(U_15091),U_15094),U_15092))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15091,U_15091)),hAPP(hAPP(c_Product__Type_OPair(U_15091,U_15091),U_15094),U_15095)),U_15093))
      | ~ c_Relation_Orefl__on(U_15091,U_15092,U_15093) ),
    inference(variable_rename,[status(thm)],[f_3845_1]) ).

fof(f_3845_3,plain,
    ! [U_15091,U_15092,U_15093,U_15094,U_15095] :
      ( hBOOL(hAPP(hAPP(c_member(U_15091),U_15094),U_15092))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15091,U_15091)),hAPP(hAPP(c_Product__Type_OPair(U_15091,U_15091),U_15094),U_15095)),U_15093))
      | ~ c_Relation_Orefl__on(U_15091,U_15092,U_15093) ),
    inference(definitional_conversion,[status(esa)],[f_3845_2]) ).

cnf(f_3845_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15091),U_15094),U_15092))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15091,U_15091)),hAPP(hAPP(c_Product__Type_OPair(U_15091,U_15091),U_15094),U_15095)),U_15093))
    | ~ c_Relation_Orefl__on(U_15091,U_15092,U_15093) ),
    inference(clausify,[status(thm)],[f_3845_3]) ).

fof(f_3846_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_3846_2,plain,
    ! [U_15100,U_15099,U_15098,U_15097,U_15096] :
      ( hBOOL(hAPP(hAPP(c_member(U_15096),U_15100),U_15097))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15096,U_15096)),hAPP(hAPP(c_Product__Type_OPair(U_15096,U_15096),U_15099),U_15100)),U_15098))
      | ~ c_Relation_Orefl__on(U_15096,U_15097,U_15098) ),
    inference(variable_rename,[status(thm)],[f_3846_1]) ).

fof(f_3846_3,plain,
    ! [U_15096,U_15097,U_15098,U_15099,U_15100] :
      ( hBOOL(hAPP(hAPP(c_member(U_15096),U_15100),U_15097))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15096,U_15096)),hAPP(hAPP(c_Product__Type_OPair(U_15096,U_15096),U_15099),U_15100)),U_15098))
      | ~ c_Relation_Orefl__on(U_15096,U_15097,U_15098) ),
    inference(definitional_conversion,[status(esa)],[f_3846_2]) ).

cnf(f_3846_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15096),U_15100),U_15097))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15096,U_15096)),hAPP(hAPP(c_Product__Type_OPair(U_15096,U_15096),U_15099),U_15100)),U_15098))
    | ~ c_Relation_Orefl__on(U_15096,U_15097,U_15098) ),
    inference(clausify,[status(thm)],[f_3846_3]) ).

fof(f_3847_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_3847_2,plain,
    ! [U_15103,U_15102,U_15101] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15101,U_15101),tc_HOL_Obool)),U_15103),hAPP(hAPP(c_Relation_Orel__comp(U_15101,U_15101,U_15101),hAPP(c_Relation_Oconverse(U_15101,U_15101),U_15103)),U_15103)))
      | ~ c_Relation_Orefl__on(U_15101,U_15102,U_15103) ),
    inference(variable_rename,[status(thm)],[f_3847_1]) ).

fof(f_3847_3,plain,
    ! [U_15101,U_15102,U_15103] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15101,U_15101),tc_HOL_Obool)),U_15103),hAPP(hAPP(c_Relation_Orel__comp(U_15101,U_15101,U_15101),hAPP(c_Relation_Oconverse(U_15101,U_15101),U_15103)),U_15103)))
      | ~ c_Relation_Orefl__on(U_15101,U_15102,U_15103) ),
    inference(definitional_conversion,[status(esa)],[f_3847_2]) ).

cnf(f_3847_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15101,U_15101),tc_HOL_Obool)),U_15103),hAPP(hAPP(c_Relation_Orel__comp(U_15101,U_15101,U_15101),hAPP(c_Relation_Oconverse(U_15101,U_15101),U_15103)),U_15103)))
    | ~ c_Relation_Orefl__on(U_15101,U_15102,U_15103) ),
    inference(clausify,[status(thm)],[f_3847_3]) ).

fof(f_3848_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_3848_2,plain,
    ! [U_15105,U_15104] : c_Relation_Orefl__on(U_15104,c_Orderings_Otop__class_Otop(tc_fun(U_15104,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15104,U_15104),tc_HOL_Obool)),U_15105),c_Relation_OId(U_15104))),
    inference(variable_rename,[status(thm)],[f_3848_1]) ).

fof(f_3848_3,plain,
    ! [U_15104,U_15105] : c_Relation_Orefl__on(U_15104,c_Orderings_Otop__class_Otop(tc_fun(U_15104,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15104,U_15104),tc_HOL_Obool)),U_15105),c_Relation_OId(U_15104))),
    inference(definitional_conversion,[status(esa)],[f_3848_2]) ).

cnf(f_3848_4,plain,
    c_Relation_Orefl__on(U_15104,c_Orderings_Otop__class_Otop(tc_fun(U_15104,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15104,U_15104),tc_HOL_Obool)),U_15105),c_Relation_OId(U_15104))),
    inference(clausify,[status(thm)],[f_3848_3]) ).

fof(f_3849_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_3849_2,plain,
    ! [U_15107,U_15106] :
      ( ( c_Predicate_Oreflp(U_15106,U_15107)
        | ~ c_Relation_Orefl__on(U_15106,c_Orderings_Otop__class_Otop(tc_fun(U_15106,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_15106,U_15106)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15106,U_15106,tc_HOL_Obool),U_15107))) )
      & ( c_Relation_Orefl__on(U_15106,c_Orderings_Otop__class_Otop(tc_fun(U_15106,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_15106,U_15106)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15106,U_15106,tc_HOL_Obool),U_15107)))
        | ~ c_Predicate_Oreflp(U_15106,U_15107) ) ),
    inference(variable_rename,[status(thm)],[f_3849_1]) ).

fof(f_3849_3,plain,
    ( ! [U_15111,U_15109] :
        ( c_Predicate_Oreflp(U_15109,U_15111)
        | ~ c_Relation_Orefl__on(U_15109,c_Orderings_Otop__class_Otop(tc_fun(U_15109,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_15109,U_15109)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15109,U_15109,tc_HOL_Obool),U_15111))) )
    & ! [U_15110,U_15108] :
        ( c_Relation_Orefl__on(U_15108,c_Orderings_Otop__class_Otop(tc_fun(U_15108,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_15108,U_15108)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15108,U_15108,tc_HOL_Obool),U_15110)))
        | ~ c_Predicate_Oreflp(U_15108,U_15110) ) ),
    inference(miniscope,[status(thm)],[f_3849_2]) ).

fof(f_3849_4,plain,
    ( ! [U_15109,U_15111] :
        ( c_Predicate_Oreflp(U_15109,U_15111)
        | ~ c_Relation_Orefl__on(U_15109,c_Orderings_Otop__class_Otop(tc_fun(U_15109,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_15109,U_15109)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15109,U_15109,tc_HOL_Obool),U_15111))) )
    & ! [U_15110,U_15108] :
        ( c_Relation_Orefl__on(U_15108,c_Orderings_Otop__class_Otop(tc_fun(U_15108,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_15108,U_15108)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15108,U_15108,tc_HOL_Obool),U_15110)))
        | ~ c_Predicate_Oreflp(U_15108,U_15110) ) ),
    inference(definitional_conversion,[status(esa)],[f_3849_3]) ).

cnf(f_3849_5,plain,
    ( c_Relation_Orefl__on(U_15108,c_Orderings_Otop__class_Otop(tc_fun(U_15108,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_15108,U_15108)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15108,U_15108,tc_HOL_Obool),U_15110)))
    | ~ c_Predicate_Oreflp(U_15108,U_15110) ),
    inference(clausify,[status(thm)],[f_3849_4]) ).

cnf(f_3849_6,plain,
    ( c_Predicate_Oreflp(U_15109,U_15111)
    | ~ c_Relation_Orefl__on(U_15109,c_Orderings_Otop__class_Otop(tc_fun(U_15109,tc_HOL_Obool)),hAPP(c_Set_OCollect(tc_prod(U_15109,U_15109)),hAPP(c_Product__Type_Oprod_Oprod__case(U_15109,U_15109,tc_HOL_Obool),U_15111))) ),
    inference(clausify,[status(thm)],[f_3849_4]) ).

fof(f_3850_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_3850_2,plain,
    ! [U_15115,U_15114,U_15113] :
      ( c_Relation_Orefl__on(U_15113,U_15115,U_15114)
      | ? [U_15112] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15113,U_15113)),hAPP(hAPP(c_Product__Type_OPair(U_15113,U_15113),U_15112),U_15112)),U_15114))
          & hBOOL(hAPP(hAPP(c_member(U_15113),U_15112),U_15115)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15113,U_15113),tc_HOL_Obool)),U_15114),hAPP(hAPP(c_Product__Type_OSigma(U_15113,U_15113),U_15115),hAPP(c_COMBK(tc_fun(U_15113,tc_HOL_Obool),U_15113),U_15115)))) ),
    inference(variable_rename,[status(thm)],[f_3850_1]) ).

fof(f_3850_3,plain,
    ! [U_15115,U_15114,U_15113] :
      ( c_Relation_Orefl__on(U_15113,U_15115,U_15114)
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15113,U_15113)),hAPP(hAPP(c_Product__Type_OPair(U_15113,U_15113),sK353(U_15115,U_15114,U_15113)),sK353(U_15115,U_15114,U_15113))),U_15114))
        & hBOOL(hAPP(hAPP(c_member(U_15113),sK353(U_15115,U_15114,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_15114),hAPP(hAPP(c_Product__Type_OSigma(U_15113,U_15113),U_15115),hAPP(c_COMBK(tc_fun(U_15113,tc_HOL_Obool),U_15113),U_15115)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK353]),skolemize(U_15112,sK353(U_15115,U_15114,U_15113))],[f_3850_2]) ).

fof(f_3850_4,plain,
    ( ! [U_15113,U_15114,U_15115] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15113,U_15113)),hAPP(hAPP(c_Product__Type_OPair(U_15113,U_15113),sK353(U_15115,U_15114,U_15113)),sK353(U_15115,U_15114,U_15113))),U_15114))
        | ~ sP1018(U_15113,U_15114,U_15115) )
    & ! [U_15113,U_15114,U_15115] :
        ( hBOOL(hAPP(hAPP(c_member(U_15113),sK353(U_15115,U_15114,U_15113)),U_15115))
        | ~ sP1018(U_15113,U_15114,U_15115) )
    & ! [U_15113,U_15114,U_15115] :
        ( c_Relation_Orefl__on(U_15113,U_15115,U_15114)
        | sP1018(U_15113,U_15114,U_15115)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15113,U_15113),tc_HOL_Obool)),U_15114),hAPP(hAPP(c_Product__Type_OSigma(U_15113,U_15113),U_15115),hAPP(c_COMBK(tc_fun(U_15113,tc_HOL_Obool),U_15113),U_15115)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1018])],[f_3850_3]) ).

cnf(f_3850_5,plain,
    ( c_Relation_Orefl__on(U_15113,U_15115,U_15114)
    | sP1018(U_15113,U_15114,U_15115)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15113,U_15113),tc_HOL_Obool)),U_15114),hAPP(hAPP(c_Product__Type_OSigma(U_15113,U_15113),U_15115),hAPP(c_COMBK(tc_fun(U_15113,tc_HOL_Obool),U_15113),U_15115)))) ),
    inference(clausify,[status(thm)],[f_3850_4]) ).

cnf(f_3850_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15113),sK353(U_15115,U_15114,U_15113)),U_15115))
    | ~ sP1018(U_15113,U_15114,U_15115) ),
    inference(clausify,[status(thm)],[f_3850_4]) ).

cnf(f_3850_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15113,U_15113)),hAPP(hAPP(c_Product__Type_OPair(U_15113,U_15113),sK353(U_15115,U_15114,U_15113)),sK353(U_15115,U_15114,U_15113))),U_15114))
    | ~ sP1018(U_15113,U_15114,U_15115) ),
    inference(clausify,[status(thm)],[f_3850_4]) ).

fof(f_3851_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_3851_2,plain,
    ! [U_15118,U_15117,U_15116] :
      ( hBOOL(hAPP(hAPP(U_15117,U_15118),U_15118))
      | ~ c_Predicate_Oreflp(U_15116,U_15117) ),
    inference(variable_rename,[status(thm)],[f_3851_1]) ).

fof(f_3851_3,plain,
    ! [U_15118,U_15117] :
      ( ! [U_15116] : ~ c_Predicate_Oreflp(U_15116,U_15117)
      | hBOOL(hAPP(hAPP(U_15117,U_15118),U_15118)) ),
    inference(miniscope,[status(thm)],[f_3851_2]) ).

fof(f_3851_4,plain,
    ! [U_15118,U_15117,U_15116] :
      ( ~ c_Predicate_Oreflp(U_15116,U_15117)
      | hBOOL(hAPP(hAPP(U_15117,U_15118),U_15118)) ),
    inference(definitional_conversion,[status(esa)],[f_3851_3]) ).

cnf(f_3851_5,plain,
    ( ~ c_Predicate_Oreflp(U_15116,U_15117)
    | hBOOL(hAPP(hAPP(U_15117,U_15118),U_15118)) ),
    inference(clausify,[status(thm)],[f_3851_4]) ).

fof(f_3852_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_3852_2,plain,
    ! [U_15122,U_15121,U_15120] :
      ( 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_15120,tc_Nat_Onat),U_15122),U_15121)))
      | ? [U_15119] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_15122,U_15119)))
          & hBOOL(hAPP(hAPP(c_member(U_15120),U_15119),U_15121)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15120),U_15121)) ),
    inference(variable_rename,[status(thm)],[f_3852_1]) ).

fof(f_3852_3,plain,
    ! [U_15122,U_15121,U_15120] :
      ( 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_15120,tc_Nat_Onat),U_15122),U_15121)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_15122,sK354(U_15122,U_15121,U_15120))))
        & hBOOL(hAPP(hAPP(c_member(U_15120),sK354(U_15122,U_15121,U_15120)),U_15121)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15120),U_15121)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK354]),skolemize(U_15119,sK354(U_15122,U_15121,U_15120))],[f_3852_2]) ).

fof(f_3852_4,plain,
    ( ! [U_15120,U_15121,U_15122] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_15122,sK354(U_15122,U_15121,U_15120))))
        | ~ sP1019(U_15120,U_15121,U_15122) )
    & ! [U_15120,U_15121,U_15122] :
        ( hBOOL(hAPP(hAPP(c_member(U_15120),sK354(U_15122,U_15121,U_15120)),U_15121))
        | ~ sP1019(U_15120,U_15121,U_15122) )
    & ! [U_15120,U_15121,U_15122] :
        ( 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_15120,tc_Nat_Onat),U_15122),U_15121)))
        | sP1019(U_15120,U_15121,U_15122)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15120),U_15121)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1019])],[f_3852_3]) ).

cnf(f_3852_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_15120,tc_Nat_Onat),U_15122),U_15121)))
    | sP1019(U_15120,U_15121,U_15122)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15120),U_15121)) ),
    inference(clausify,[status(thm)],[f_3852_4]) ).

cnf(f_3852_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15120),sK354(U_15122,U_15121,U_15120)),U_15121))
    | ~ sP1019(U_15120,U_15121,U_15122) ),
    inference(clausify,[status(thm)],[f_3852_4]) ).

cnf(f_3852_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_15122,sK354(U_15122,U_15121,U_15120))))
    | ~ sP1019(U_15120,U_15121,U_15122) ),
    inference(clausify,[status(thm)],[f_3852_4]) ).

fof(f_3853_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_3853_2,plain,
    ! [U_15129,U_15128,U_15127,U_15126,U_15125] :
      ( hAPP(U_15128,hAPP(U_15127,U_15129)) = hAPP(U_15127,hAPP(c_Set_Oimage(U_15125,U_15125,U_15128),U_15129))
      | U_15129 = c_Orderings_Obot__class_Obot(tc_fun(U_15125,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15125),U_15129))
      | ? [U_15124,U_15123] : hAPP(U_15128,hAPP(hAPP(U_15126,U_15124),U_15123)) != hAPP(hAPP(U_15126,hAPP(U_15128,U_15124)),hAPP(U_15128,U_15123))
      | ~ c_Finite__Set_Ofolding__one__idem(U_15125,U_15126,U_15127) ),
    inference(variable_rename,[status(thm)],[f_3853_1]) ).

fof(f_3853_3,plain,
    ! [U_15129,U_15128,U_15127,U_15126,U_15125] :
      ( hAPP(U_15128,hAPP(U_15127,U_15129)) = hAPP(U_15127,hAPP(c_Set_Oimage(U_15125,U_15125,U_15128),U_15129))
      | U_15129 = c_Orderings_Obot__class_Obot(tc_fun(U_15125,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15125),U_15129))
      | ? [U_15123] : hAPP(U_15128,hAPP(hAPP(U_15126,sK355(U_15129,U_15128,U_15127,U_15126,U_15125)),U_15123)) != hAPP(hAPP(U_15126,hAPP(U_15128,sK355(U_15129,U_15128,U_15127,U_15126,U_15125))),hAPP(U_15128,U_15123))
      | ~ c_Finite__Set_Ofolding__one__idem(U_15125,U_15126,U_15127) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK355]),skolemize(U_15124,sK355(U_15129,U_15128,U_15127,U_15126,U_15125))],[f_3853_2]) ).

fof(f_3853_4,plain,
    ! [U_15129,U_15128,U_15127,U_15126,U_15125] :
      ( hAPP(U_15128,hAPP(U_15127,U_15129)) = hAPP(U_15127,hAPP(c_Set_Oimage(U_15125,U_15125,U_15128),U_15129))
      | U_15129 = c_Orderings_Obot__class_Obot(tc_fun(U_15125,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15125),U_15129))
      | hAPP(U_15128,hAPP(hAPP(U_15126,sK355(U_15129,U_15128,U_15127,U_15126,U_15125)),sK356(U_15129,U_15128,U_15127,U_15126,U_15125))) != hAPP(hAPP(U_15126,hAPP(U_15128,sK355(U_15129,U_15128,U_15127,U_15126,U_15125))),hAPP(U_15128,sK356(U_15129,U_15128,U_15127,U_15126,U_15125)))
      | ~ c_Finite__Set_Ofolding__one__idem(U_15125,U_15126,U_15127) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK356]),skolemize(U_15123,sK356(U_15129,U_15128,U_15127,U_15126,U_15125))],[f_3853_3]) ).

fof(f_3853_5,plain,
    ! [U_15125,U_15126,U_15127,U_15128,U_15129] :
      ( hAPP(U_15128,hAPP(U_15127,U_15129)) = hAPP(U_15127,hAPP(c_Set_Oimage(U_15125,U_15125,U_15128),U_15129))
      | U_15129 = c_Orderings_Obot__class_Obot(tc_fun(U_15125,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15125),U_15129))
      | hAPP(U_15128,hAPP(hAPP(U_15126,sK355(U_15129,U_15128,U_15127,U_15126,U_15125)),sK356(U_15129,U_15128,U_15127,U_15126,U_15125))) != hAPP(hAPP(U_15126,hAPP(U_15128,sK355(U_15129,U_15128,U_15127,U_15126,U_15125))),hAPP(U_15128,sK356(U_15129,U_15128,U_15127,U_15126,U_15125)))
      | ~ c_Finite__Set_Ofolding__one__idem(U_15125,U_15126,U_15127) ),
    inference(definitional_conversion,[status(esa)],[f_3853_4]) ).

cnf(f_3853_6,plain,
    ( hAPP(U_15128,hAPP(U_15127,U_15129)) = hAPP(U_15127,hAPP(c_Set_Oimage(U_15125,U_15125,U_15128),U_15129))
    | U_15129 = c_Orderings_Obot__class_Obot(tc_fun(U_15125,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15125),U_15129))
    | hAPP(U_15128,hAPP(hAPP(U_15126,sK355(U_15129,U_15128,U_15127,U_15126,U_15125)),sK356(U_15129,U_15128,U_15127,U_15126,U_15125))) != hAPP(hAPP(U_15126,hAPP(U_15128,sK355(U_15129,U_15128,U_15127,U_15126,U_15125))),hAPP(U_15128,sK356(U_15129,U_15128,U_15127,U_15126,U_15125)))
    | ~ c_Finite__Set_Ofolding__one__idem(U_15125,U_15126,U_15127) ),
    inference(clausify,[status(thm)],[f_3853_5]) ).

fof(f_3854_1,plain,
    ! [V_Pa_2,V_y_2] :
      ( hBOOL(hAPP(V_Pa_2,V_y_2))
      | ? [B_x] : ~ hBOOL(hAPP(V_Pa_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_3854_2,plain,
    ! [U_15132,U_15131] :
      ( hBOOL(hAPP(U_15132,U_15131))
      | ? [U_15130] : ~ hBOOL(hAPP(U_15132,hAPP(c_Int_ORep__Integ,U_15130)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_15131),c_Int_OInteg)) ),
    inference(variable_rename,[status(thm)],[f_3854_1]) ).

fof(f_3854_3,plain,
    ! [U_15132,U_15131] :
      ( hBOOL(hAPP(U_15132,U_15131))
      | ~ hBOOL(hAPP(U_15132,hAPP(c_Int_ORep__Integ,sK357(U_15132,U_15131))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_15131),c_Int_OInteg)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK357]),skolemize(U_15130,sK357(U_15132,U_15131))],[f_3854_2]) ).

fof(f_3854_4,plain,
    ! [U_15132,U_15131] :
      ( hBOOL(hAPP(U_15132,U_15131))
      | ~ hBOOL(hAPP(U_15132,hAPP(c_Int_ORep__Integ,sK357(U_15132,U_15131))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_15131),c_Int_OInteg)) ),
    inference(definitional_conversion,[status(esa)],[f_3854_3]) ).

cnf(f_3854_5,plain,
    ( hBOOL(hAPP(U_15132,U_15131))
    | ~ hBOOL(hAPP(U_15132,hAPP(c_Int_ORep__Integ,sK357(U_15132,U_15131))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_15131),c_Int_OInteg)) ),
    inference(clausify,[status(thm)],[f_3854_4]) ).

fof(f_3855_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_3855_2,plain,
    ! [U_15134] :
      ( ? [U_15133] : U_15134 = hAPP(c_Int_ORep__Integ,U_15133)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_15134),c_Int_OInteg)) ),
    inference(variable_rename,[status(thm)],[f_3855_1]) ).

fof(f_3855_3,plain,
    ! [U_15134] :
      ( U_15134 = hAPP(c_Int_ORep__Integ,sK358(U_15134))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_15134),c_Int_OInteg)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK358]),skolemize(U_15133,sK358(U_15134))],[f_3855_2]) ).

fof(f_3855_4,plain,
    ! [U_15134] :
      ( U_15134 = hAPP(c_Int_ORep__Integ,sK358(U_15134))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_15134),c_Int_OInteg)) ),
    inference(definitional_conversion,[status(esa)],[f_3855_3]) ).

cnf(f_3855_5,plain,
    ( U_15134 = hAPP(c_Int_ORep__Integ,sK358(U_15134))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_15134),c_Int_OInteg)) ),
    inference(clausify,[status(thm)],[f_3855_4]) ).

fof(f_3856_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_3856_2,plain,
    ! [U_15143,U_15142,U_15141,U_15140,U_15139,U_15138,U_15137,U_15136] :
      ( hAPP(U_15141,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15137,tc_HOL_Obool)),U_15142),U_15143)) = hAPP(hAPP(U_15138,hAPP(U_15141,U_15142)),hAPP(U_15141,U_15143))
      | ? [U_15135] :
          ( hAPP(U_15140,U_15135) != U_15139
          & hBOOL(hAPP(hAPP(c_member(U_15137),U_15135),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15137,tc_HOL_Obool)),U_15142),U_15143))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15137),U_15143))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15137),U_15142))
      | ~ c_Finite__Set_Ofolding__image__simple(U_15136,U_15137,U_15138,U_15139,U_15140,U_15141) ),
    inference(variable_rename,[status(thm)],[f_3856_1]) ).

fof(f_3856_3,plain,
    ! [U_15143,U_15142,U_15141,U_15140,U_15139,U_15138,U_15137] :
      ( ! [U_15136] : ~ c_Finite__Set_Ofolding__image__simple(U_15136,U_15137,U_15138,U_15139,U_15140,U_15141)
      | hAPP(U_15141,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15137,tc_HOL_Obool)),U_15142),U_15143)) = hAPP(hAPP(U_15138,hAPP(U_15141,U_15142)),hAPP(U_15141,U_15143))
      | ? [U_15135] :
          ( hAPP(U_15140,U_15135) != U_15139
          & hBOOL(hAPP(hAPP(c_member(U_15137),U_15135),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15137,tc_HOL_Obool)),U_15142),U_15143))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15137),U_15143))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15137),U_15142)) ),
    inference(miniscope,[status(thm)],[f_3856_2]) ).

fof(f_3856_4,plain,
    ! [U_15143,U_15142,U_15141,U_15140,U_15139,U_15138,U_15137] :
      ( ! [U_15136] : ~ c_Finite__Set_Ofolding__image__simple(U_15136,U_15137,U_15138,U_15139,U_15140,U_15141)
      | hAPP(U_15141,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15137,tc_HOL_Obool)),U_15142),U_15143)) = hAPP(hAPP(U_15138,hAPP(U_15141,U_15142)),hAPP(U_15141,U_15143))
      | ( hAPP(U_15140,sK359(U_15143,U_15142,U_15141,U_15140,U_15139,U_15138,U_15137)) != U_15139
        & hBOOL(hAPP(hAPP(c_member(U_15137),sK359(U_15143,U_15142,U_15141,U_15140,U_15139,U_15138,U_15137)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15137,tc_HOL_Obool)),U_15142),U_15143))) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15137),U_15143))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15137),U_15142)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK359]),skolemize(U_15135,sK359(U_15143,U_15142,U_15141,U_15140,U_15139,U_15138,U_15137))],[f_3856_3]) ).

fof(f_3856_5,plain,
    ( ! [U_15137,U_15138,U_15139,U_15140,U_15141,U_15142,U_15143] :
        ( hAPP(U_15140,sK359(U_15143,U_15142,U_15141,U_15140,U_15139,U_15138,U_15137)) != U_15139
        | ~ sP1020(U_15137,U_15138,U_15139,U_15140,U_15141,U_15142,U_15143) )
    & ! [U_15137,U_15138,U_15139,U_15140,U_15141,U_15142,U_15143] :
        ( hBOOL(hAPP(hAPP(c_member(U_15137),sK359(U_15143,U_15142,U_15141,U_15140,U_15139,U_15138,U_15137)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15137,tc_HOL_Obool)),U_15142),U_15143)))
        | ~ sP1020(U_15137,U_15138,U_15139,U_15140,U_15141,U_15142,U_15143) )
    & ! [U_15136,U_15137,U_15138,U_15139,U_15140,U_15141,U_15142,U_15143] :
        ( ~ c_Finite__Set_Ofolding__image__simple(U_15136,U_15137,U_15138,U_15139,U_15140,U_15141)
        | hAPP(U_15141,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15137,tc_HOL_Obool)),U_15142),U_15143)) = hAPP(hAPP(U_15138,hAPP(U_15141,U_15142)),hAPP(U_15141,U_15143))
        | sP1020(U_15137,U_15138,U_15139,U_15140,U_15141,U_15142,U_15143)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15137),U_15143))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15137),U_15142)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1020])],[f_3856_4]) ).

cnf(f_3856_6,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple(U_15136,U_15137,U_15138,U_15139,U_15140,U_15141)
    | hAPP(U_15141,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15137,tc_HOL_Obool)),U_15142),U_15143)) = hAPP(hAPP(U_15138,hAPP(U_15141,U_15142)),hAPP(U_15141,U_15143))
    | sP1020(U_15137,U_15138,U_15139,U_15140,U_15141,U_15142,U_15143)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15137),U_15143))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15137),U_15142)) ),
    inference(clausify,[status(thm)],[f_3856_5]) ).

cnf(f_3856_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15137),sK359(U_15143,U_15142,U_15141,U_15140,U_15139,U_15138,U_15137)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15137,tc_HOL_Obool)),U_15142),U_15143)))
    | ~ sP1020(U_15137,U_15138,U_15139,U_15140,U_15141,U_15142,U_15143) ),
    inference(clausify,[status(thm)],[f_3856_5]) ).

cnf(f_3856_8,plain,
    ( hAPP(U_15140,sK359(U_15143,U_15142,U_15141,U_15140,U_15139,U_15138,U_15137)) != U_15139
    | ~ sP1020(U_15137,U_15138,U_15139,U_15140,U_15141,U_15142,U_15143) ),
    inference(clausify,[status(thm)],[f_3856_5]) ).

fof(f_3857_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_3857_2,plain,
    ! [U_15144] : c_Finite__Set_Ofun__left__comm__idem(U_15144,tc_fun(U_15144,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15144,tc_HOL_Obool),tc_fun(tc_fun(U_15144,tc_HOL_Obool),tc_fun(U_15144,tc_HOL_Obool)),U_15144),hAPP(c_COMBC(tc_fun(U_15144,tc_HOL_Obool),tc_fun(U_15144,tc_HOL_Obool),tc_fun(U_15144,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_15144,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_15144,tc_fun(U_15144,tc_HOL_Obool),tc_fun(U_15144,tc_HOL_Obool)),c_Set_Oinsert(U_15144)),c_Orderings_Obot__class_Obot(tc_fun(U_15144,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_3857_1]) ).

fof(f_3857_3,plain,
    ! [U_15144] : c_Finite__Set_Ofun__left__comm__idem(U_15144,tc_fun(U_15144,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15144,tc_HOL_Obool),tc_fun(tc_fun(U_15144,tc_HOL_Obool),tc_fun(U_15144,tc_HOL_Obool)),U_15144),hAPP(c_COMBC(tc_fun(U_15144,tc_HOL_Obool),tc_fun(U_15144,tc_HOL_Obool),tc_fun(U_15144,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_15144,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_15144,tc_fun(U_15144,tc_HOL_Obool),tc_fun(U_15144,tc_HOL_Obool)),c_Set_Oinsert(U_15144)),c_Orderings_Obot__class_Obot(tc_fun(U_15144,tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_3857_2]) ).

cnf(f_3857_4,plain,
    c_Finite__Set_Ofun__left__comm__idem(U_15144,tc_fun(U_15144,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_15144,tc_HOL_Obool),tc_fun(tc_fun(U_15144,tc_HOL_Obool),tc_fun(U_15144,tc_HOL_Obool)),U_15144),hAPP(c_COMBC(tc_fun(U_15144,tc_HOL_Obool),tc_fun(U_15144,tc_HOL_Obool),tc_fun(U_15144,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_15144,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_15144,tc_fun(U_15144,tc_HOL_Obool),tc_fun(U_15144,tc_HOL_Obool)),c_Set_Oinsert(U_15144)),c_Orderings_Obot__class_Obot(tc_fun(U_15144,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_3857_3]) ).

fof(f_3858_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_3858_2,plain,
    ! [U_15145] : c_Finite__Set_Ofun__left__comm__idem(U_15145,tc_fun(U_15145,tc_HOL_Obool),c_Set_Oinsert(U_15145)),
    inference(variable_rename,[status(thm)],[f_3858_1]) ).

fof(f_3858_3,plain,
    ! [U_15145] : c_Finite__Set_Ofun__left__comm__idem(U_15145,tc_fun(U_15145,tc_HOL_Obool),c_Set_Oinsert(U_15145)),
    inference(definitional_conversion,[status(esa)],[f_3858_2]) ).

cnf(f_3858_4,plain,
    c_Finite__Set_Ofun__left__comm__idem(U_15145,tc_fun(U_15145,tc_HOL_Obool),c_Set_Oinsert(U_15145)),
    inference(clausify,[status(thm)],[f_3858_3]) ).

fof(f_3859_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_3859_2,plain,
    ! [U_15150,U_15149,U_15148,U_15147,U_15146] :
      ( hAPP(hAPP(U_15148,U_15149),hAPP(hAPP(U_15148,U_15149),U_15150)) = hAPP(hAPP(U_15148,U_15149),U_15150)
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_15146,U_15147,U_15148) ),
    inference(variable_rename,[status(thm)],[f_3859_1]) ).

fof(f_3859_3,plain,
    ! [U_15150,U_15149,U_15148] :
      ( ! [U_15147,U_15146] : ~ c_Finite__Set_Ofun__left__comm__idem(U_15146,U_15147,U_15148)
      | hAPP(hAPP(U_15148,U_15149),hAPP(hAPP(U_15148,U_15149),U_15150)) = hAPP(hAPP(U_15148,U_15149),U_15150) ),
    inference(miniscope,[status(thm)],[f_3859_2]) ).

fof(f_3859_4,plain,
    ! [U_15146,U_15149,U_15147,U_15150,U_15148] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(U_15146,U_15147,U_15148)
      | hAPP(hAPP(U_15148,U_15149),hAPP(hAPP(U_15148,U_15149),U_15150)) = hAPP(hAPP(U_15148,U_15149),U_15150) ),
    inference(definitional_conversion,[status(esa)],[f_3859_3]) ).

cnf(f_3859_5,plain,
    ( ~ c_Finite__Set_Ofun__left__comm__idem(U_15146,U_15147,U_15148)
    | hAPP(hAPP(U_15148,U_15149),hAPP(hAPP(U_15148,U_15149),U_15150)) = hAPP(hAPP(U_15148,U_15149),U_15150) ),
    inference(clausify,[status(thm)],[f_3859_4]) ).

fof(f_3860_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_3860_2,plain,
    ! [U_15155,U_15154,U_15153,U_15152,U_15151] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_15154,U_15152,hAPP(hAPP(c_COMBB(U_15151,tc_fun(U_15152,U_15152),U_15154),U_15153),U_15155))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_15151,U_15152,U_15153) ),
    inference(variable_rename,[status(thm)],[f_3860_1]) ).

fof(f_3860_3,plain,
    ! [U_15151,U_15152,U_15153,U_15154,U_15155] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_15154,U_15152,hAPP(hAPP(c_COMBB(U_15151,tc_fun(U_15152,U_15152),U_15154),U_15153),U_15155))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_15151,U_15152,U_15153) ),
    inference(definitional_conversion,[status(esa)],[f_3860_2]) ).

cnf(f_3860_4,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_15154,U_15152,hAPP(hAPP(c_COMBB(U_15151,tc_fun(U_15152,U_15152),U_15154),U_15153),U_15155))
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_15151,U_15152,U_15153) ),
    inference(clausify,[status(thm)],[f_3860_3]) ).

fof(f_3861_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_3861_2,plain,
    ! [U_15156] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_15156,U_15156,c_Groups_Otimes__class_Otimes(U_15156))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_15156) ),
    inference(variable_rename,[status(thm)],[f_3861_1]) ).

fof(f_3861_3,plain,
    ! [U_15156] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_15156,U_15156,c_Groups_Otimes__class_Otimes(U_15156))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_15156) ),
    inference(definitional_conversion,[status(esa)],[f_3861_2]) ).

cnf(f_3861_4,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_15156,U_15156,c_Groups_Otimes__class_Otimes(U_15156))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_15156) ),
    inference(clausify,[status(thm)],[f_3861_3]) ).

fof(f_3862_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_3862_2,plain,
    ! [U_15157] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_15157,U_15157,c_Lattices_Osemilattice__inf__class_Oinf(U_15157))
      | ~ class_Lattices_Osemilattice__inf(U_15157) ),
    inference(variable_rename,[status(thm)],[f_3862_1]) ).

fof(f_3862_3,plain,
    ! [U_15157] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_15157,U_15157,c_Lattices_Osemilattice__inf__class_Oinf(U_15157))
      | ~ class_Lattices_Osemilattice__inf(U_15157) ),
    inference(definitional_conversion,[status(esa)],[f_3862_2]) ).

cnf(f_3862_4,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_15157,U_15157,c_Lattices_Osemilattice__inf__class_Oinf(U_15157))
    | ~ class_Lattices_Osemilattice__inf(U_15157) ),
    inference(clausify,[status(thm)],[f_3862_3]) ).

fof(f_3863_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_3863_2,plain,
    ! [U_15158] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_15158,U_15158,c_Lattices_Osemilattice__sup__class_Osup(U_15158))
      | ~ class_Lattices_Osemilattice__sup(U_15158) ),
    inference(variable_rename,[status(thm)],[f_3863_1]) ).

fof(f_3863_3,plain,
    ! [U_15158] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_15158,U_15158,c_Lattices_Osemilattice__sup__class_Osup(U_15158))
      | ~ class_Lattices_Osemilattice__sup(U_15158) ),
    inference(definitional_conversion,[status(esa)],[f_3863_2]) ).

cnf(f_3863_4,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_15158,U_15158,c_Lattices_Osemilattice__sup__class_Osup(U_15158))
    | ~ class_Lattices_Osemilattice__sup(U_15158) ),
    inference(clausify,[status(thm)],[f_3863_3]) ).

fof(f_3864_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_3864_2,plain,
    ! [U_15159] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_15159,U_15159,c_Orderings_Oord__class_Omax(U_15159))
      | ~ class_Orderings_Olinorder(U_15159) ),
    inference(variable_rename,[status(thm)],[f_3864_1]) ).

fof(f_3864_3,plain,
    ! [U_15159] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_15159,U_15159,c_Orderings_Oord__class_Omax(U_15159))
      | ~ class_Orderings_Olinorder(U_15159) ),
    inference(definitional_conversion,[status(esa)],[f_3864_2]) ).

cnf(f_3864_4,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_15159,U_15159,c_Orderings_Oord__class_Omax(U_15159))
    | ~ class_Orderings_Olinorder(U_15159) ),
    inference(clausify,[status(thm)],[f_3864_3]) ).

fof(f_3865_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_3865_2,plain,
    ! [U_15160] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_15160,U_15160,c_Orderings_Oord__class_Omin(U_15160))
      | ~ class_Orderings_Olinorder(U_15160) ),
    inference(variable_rename,[status(thm)],[f_3865_1]) ).

fof(f_3865_3,plain,
    ! [U_15160] :
      ( c_Finite__Set_Ofun__left__comm__idem(U_15160,U_15160,c_Orderings_Oord__class_Omin(U_15160))
      | ~ class_Orderings_Olinorder(U_15160) ),
    inference(definitional_conversion,[status(esa)],[f_3865_2]) ).

cnf(f_3865_4,plain,
    ( c_Finite__Set_Ofun__left__comm__idem(U_15160,U_15160,c_Orderings_Oord__class_Omin(U_15160))
    | ~ class_Orderings_Olinorder(U_15160) ),
    inference(clausify,[status(thm)],[f_3865_3]) ).

fof(f_3866_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_3866_2,plain,
    ! [U_15165,U_15164,U_15163,U_15162,U_15161] :
      ( hAPP(c_Relation_OImage(U_15162,U_15161,U_15163),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15162,tc_HOL_Obool)),U_15164),U_15165)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15161,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15162,U_15161,U_15163),U_15164)),hAPP(c_Relation_OImage(U_15162,U_15161,U_15163),U_15165))
      | ~ c_Relation_Osingle__valued(U_15161,U_15162,hAPP(c_Relation_Oconverse(U_15162,U_15161),U_15163)) ),
    inference(variable_rename,[status(thm)],[f_3866_1]) ).

fof(f_3866_3,plain,
    ! [U_15161,U_15162,U_15163,U_15164,U_15165] :
      ( hAPP(c_Relation_OImage(U_15162,U_15161,U_15163),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15162,tc_HOL_Obool)),U_15164),U_15165)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15161,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15162,U_15161,U_15163),U_15164)),hAPP(c_Relation_OImage(U_15162,U_15161,U_15163),U_15165))
      | ~ c_Relation_Osingle__valued(U_15161,U_15162,hAPP(c_Relation_Oconverse(U_15162,U_15161),U_15163)) ),
    inference(definitional_conversion,[status(esa)],[f_3866_2]) ).

cnf(f_3866_4,plain,
    ( hAPP(c_Relation_OImage(U_15162,U_15161,U_15163),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15162,tc_HOL_Obool)),U_15164),U_15165)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15161,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_15162,U_15161,U_15163),U_15164)),hAPP(c_Relation_OImage(U_15162,U_15161,U_15163),U_15165))
    | ~ c_Relation_Osingle__valued(U_15161,U_15162,hAPP(c_Relation_Oconverse(U_15162,U_15161),U_15163)) ),
    inference(clausify,[status(thm)],[f_3866_3]) ).

fof(f_3867_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_3867_2,plain,
    ! [U_15170,U_15169,U_15168,U_15167] :
      ( ? [U_15166] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15167),hAPP(c_Set_OCollect(U_15167),hAPP(hAPP(c_COMBS(U_15167,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15167),c_fconj),hAPP(hAPP(c_COMBC(U_15167,tc_fun(U_15167,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15167)),U_15168))),hAPP(hAPP(c_COMBC(U_15167,U_15169,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_15169,tc_fun(U_15169,tc_HOL_Obool),U_15167),c_fequal),U_15170)),hAPP(U_15170,U_15166))))))
          & hBOOL(hAPP(hAPP(c_member(U_15167),U_15166),U_15168)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15169),hAPP(c_Set_Oimage(U_15167,U_15169,U_15170),U_15168)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15167),U_15168)) ),
    inference(variable_rename,[status(thm)],[f_3867_1]) ).

fof(f_3867_3,plain,
    ! [U_15170,U_15169,U_15168,U_15167] :
      ( ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15167),hAPP(c_Set_OCollect(U_15167),hAPP(hAPP(c_COMBS(U_15167,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15167),c_fconj),hAPP(hAPP(c_COMBC(U_15167,tc_fun(U_15167,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15167)),U_15168))),hAPP(hAPP(c_COMBC(U_15167,U_15169,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_15169,tc_fun(U_15169,tc_HOL_Obool),U_15167),c_fequal),U_15170)),hAPP(U_15170,sK360(U_15170,U_15169,U_15168,U_15167)))))))
        & hBOOL(hAPP(hAPP(c_member(U_15167),sK360(U_15170,U_15169,U_15168,U_15167)),U_15168)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15169),hAPP(c_Set_Oimage(U_15167,U_15169,U_15170),U_15168)))
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15167),U_15168)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK360]),skolemize(U_15166,sK360(U_15170,U_15169,U_15168,U_15167))],[f_3867_2]) ).

fof(f_3867_4,plain,
    ( ! [U_15167,U_15168,U_15169,U_15170] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15167),hAPP(c_Set_OCollect(U_15167),hAPP(hAPP(c_COMBS(U_15167,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15167),c_fconj),hAPP(hAPP(c_COMBC(U_15167,tc_fun(U_15167,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15167)),U_15168))),hAPP(hAPP(c_COMBC(U_15167,U_15169,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_15169,tc_fun(U_15169,tc_HOL_Obool),U_15167),c_fequal),U_15170)),hAPP(U_15170,sK360(U_15170,U_15169,U_15168,U_15167)))))))
        | ~ sP1021(U_15167,U_15168,U_15169,U_15170) )
    & ! [U_15167,U_15168,U_15169,U_15170] :
        ( hBOOL(hAPP(hAPP(c_member(U_15167),sK360(U_15170,U_15169,U_15168,U_15167)),U_15168))
        | ~ sP1021(U_15167,U_15168,U_15169,U_15170) )
    & ! [U_15167,U_15168,U_15169,U_15170] :
        ( sP1021(U_15167,U_15168,U_15169,U_15170)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15169),hAPP(c_Set_Oimage(U_15167,U_15169,U_15170),U_15168)))
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15167),U_15168)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1021])],[f_3867_3]) ).

cnf(f_3867_5,plain,
    ( sP1021(U_15167,U_15168,U_15169,U_15170)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15169),hAPP(c_Set_Oimage(U_15167,U_15169,U_15170),U_15168)))
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15167),U_15168)) ),
    inference(clausify,[status(thm)],[f_3867_4]) ).

cnf(f_3867_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15167),sK360(U_15170,U_15169,U_15168,U_15167)),U_15168))
    | ~ sP1021(U_15167,U_15168,U_15169,U_15170) ),
    inference(clausify,[status(thm)],[f_3867_4]) ).

cnf(f_3867_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15167),hAPP(c_Set_OCollect(U_15167),hAPP(hAPP(c_COMBS(U_15167,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15167),c_fconj),hAPP(hAPP(c_COMBC(U_15167,tc_fun(U_15167,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15167)),U_15168))),hAPP(hAPP(c_COMBC(U_15167,U_15169,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_15169,tc_fun(U_15169,tc_HOL_Obool),U_15167),c_fequal),U_15170)),hAPP(U_15170,sK360(U_15170,U_15169,U_15168,U_15167)))))))
    | ~ sP1021(U_15167,U_15168,U_15169,U_15170) ),
    inference(clausify,[status(thm)],[f_3867_4]) ).

fof(f_3868_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_3868_2,plain,
    ! [U_15172,U_15171] : c_Relation_Osingle__valued(U_15171,U_15171,c_Relation_OId__on(U_15171,U_15172)),
    inference(variable_rename,[status(thm)],[f_3868_1]) ).

fof(f_3868_3,plain,
    ! [U_15172,U_15171] : c_Relation_Osingle__valued(U_15171,U_15171,c_Relation_OId__on(U_15171,U_15172)),
    inference(definitional_conversion,[status(esa)],[f_3868_2]) ).

cnf(f_3868_4,plain,
    c_Relation_Osingle__valued(U_15171,U_15171,c_Relation_OId__on(U_15171,U_15172)),
    inference(clausify,[status(thm)],[f_3868_3]) ).

fof(f_3869_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_3869_2,plain,
    ! [U_15175,U_15174,U_15173] :
      ( c_Relation_Osingle__valued(U_15173,U_15173,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15173,U_15173),tc_HOL_Obool),U_15175),U_15174))
      | ~ c_Relation_Osingle__valued(U_15173,U_15173,U_15174) ),
    inference(variable_rename,[status(thm)],[f_3869_1]) ).

fof(f_3869_3,plain,
    ! [U_15175,U_15173,U_15174] :
      ( c_Relation_Osingle__valued(U_15173,U_15173,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15173,U_15173),tc_HOL_Obool),U_15175),U_15174))
      | ~ c_Relation_Osingle__valued(U_15173,U_15173,U_15174) ),
    inference(definitional_conversion,[status(esa)],[f_3869_2]) ).

cnf(f_3869_4,plain,
    ( c_Relation_Osingle__valued(U_15173,U_15173,hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15173,U_15173),tc_HOL_Obool),U_15175),U_15174))
    | ~ c_Relation_Osingle__valued(U_15173,U_15173,U_15174) ),
    inference(clausify,[status(thm)],[f_3869_3]) ).

fof(f_3870_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_3870_2,plain,
    ! [U_15179,U_15178,U_15177,U_15176] :
      ( c_Relation_Osingle__valued(U_15176,U_15177,U_15178)
      | ~ c_Relation_Osingle__valued(U_15176,U_15177,U_15179)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15176,U_15177),tc_HOL_Obool)),U_15178),U_15179)) ),
    inference(variable_rename,[status(thm)],[f_3870_1]) ).

fof(f_3870_3,plain,
    ! [U_15176,U_15177,U_15178,U_15179] :
      ( c_Relation_Osingle__valued(U_15176,U_15177,U_15178)
      | ~ c_Relation_Osingle__valued(U_15176,U_15177,U_15179)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15176,U_15177),tc_HOL_Obool)),U_15178),U_15179)) ),
    inference(definitional_conversion,[status(esa)],[f_3870_2]) ).

cnf(f_3870_4,plain,
    ( c_Relation_Osingle__valued(U_15176,U_15177,U_15178)
    | ~ c_Relation_Osingle__valued(U_15176,U_15177,U_15179)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15176,U_15177),tc_HOL_Obool)),U_15178),U_15179)) ),
    inference(clausify,[status(thm)],[f_3870_3]) ).

fof(f_3871_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_3871_2,plain,
    ! [U_15184,U_15183,U_15182,U_15181,U_15180] :
      ( c_Relation_Osingle__valued(U_15180,U_15183,hAPP(hAPP(c_Relation_Orel__comp(U_15180,U_15181,U_15183),U_15182),U_15184))
      | ~ c_Relation_Osingle__valued(U_15181,U_15183,U_15184)
      | ~ c_Relation_Osingle__valued(U_15180,U_15181,U_15182) ),
    inference(variable_rename,[status(thm)],[f_3871_1]) ).

fof(f_3871_3,plain,
    ! [U_15181,U_15180,U_15182,U_15183,U_15184] :
      ( c_Relation_Osingle__valued(U_15180,U_15183,hAPP(hAPP(c_Relation_Orel__comp(U_15180,U_15181,U_15183),U_15182),U_15184))
      | ~ c_Relation_Osingle__valued(U_15181,U_15183,U_15184)
      | ~ c_Relation_Osingle__valued(U_15180,U_15181,U_15182) ),
    inference(definitional_conversion,[status(esa)],[f_3871_2]) ).

cnf(f_3871_4,plain,
    ( c_Relation_Osingle__valued(U_15180,U_15183,hAPP(hAPP(c_Relation_Orel__comp(U_15180,U_15181,U_15183),U_15182),U_15184))
    | ~ c_Relation_Osingle__valued(U_15181,U_15183,U_15184)
    | ~ c_Relation_Osingle__valued(U_15180,U_15181,U_15182) ),
    inference(clausify,[status(thm)],[f_3871_3]) ).

fof(f_3872_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_3872_2,plain,
    ! [U_15185] : c_Relation_Osingle__valued(U_15185,U_15185,c_Relation_OId(U_15185)),
    inference(variable_rename,[status(thm)],[f_3872_1]) ).

fof(f_3872_3,plain,
    ! [U_15185] : c_Relation_Osingle__valued(U_15185,U_15185,c_Relation_OId(U_15185)),
    inference(definitional_conversion,[status(esa)],[f_3872_2]) ).

cnf(f_3872_4,plain,
    c_Relation_Osingle__valued(U_15185,U_15185,c_Relation_OId(U_15185)),
    inference(clausify,[status(thm)],[f_3872_3]) ).

fof(f_3873_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_3873_2,plain,
    ! [U_15191,U_15190,U_15189,U_15188,U_15187,U_15186] :
      ( U_15190 = U_15191
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15186,U_15187)),hAPP(hAPP(c_Product__Type_OPair(U_15186,U_15187),U_15189),U_15191)),U_15188))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15186,U_15187)),hAPP(hAPP(c_Product__Type_OPair(U_15186,U_15187),U_15189),U_15190)),U_15188))
      | ~ c_Relation_Osingle__valued(U_15186,U_15187,U_15188) ),
    inference(variable_rename,[status(thm)],[f_3873_1]) ).

fof(f_3873_3,plain,
    ! [U_15186,U_15187,U_15188,U_15189,U_15190,U_15191] :
      ( U_15190 = U_15191
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15186,U_15187)),hAPP(hAPP(c_Product__Type_OPair(U_15186,U_15187),U_15189),U_15191)),U_15188))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15186,U_15187)),hAPP(hAPP(c_Product__Type_OPair(U_15186,U_15187),U_15189),U_15190)),U_15188))
      | ~ c_Relation_Osingle__valued(U_15186,U_15187,U_15188) ),
    inference(definitional_conversion,[status(esa)],[f_3873_2]) ).

cnf(f_3873_4,plain,
    ( U_15190 = U_15191
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15186,U_15187)),hAPP(hAPP(c_Product__Type_OPair(U_15186,U_15187),U_15189),U_15191)),U_15188))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15186,U_15187)),hAPP(hAPP(c_Product__Type_OPair(U_15186,U_15187),U_15189),U_15190)),U_15188))
    | ~ c_Relation_Osingle__valued(U_15186,U_15187,U_15188) ),
    inference(clausify,[status(thm)],[f_3873_3]) ).

fof(f_3874_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_3874_2,plain,
    ! [U_15200,U_15199,U_15198] :
      ( ( c_Relation_Osingle__valued(U_15198,U_15199,U_15200)
        | ? [U_15197,U_15196] :
            ( ? [U_15195] :
                ( U_15196 != U_15195
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15198,U_15199)),hAPP(hAPP(c_Product__Type_OPair(U_15198,U_15199),U_15197),U_15195)),U_15200)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15198,U_15199)),hAPP(hAPP(c_Product__Type_OPair(U_15198,U_15199),U_15197),U_15196)),U_15200)) ) )
      & ( ! [U_15194,U_15193] :
            ( ! [U_15192] :
                ( U_15193 = U_15192
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15198,U_15199)),hAPP(hAPP(c_Product__Type_OPair(U_15198,U_15199),U_15194),U_15192)),U_15200)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15198,U_15199)),hAPP(hAPP(c_Product__Type_OPair(U_15198,U_15199),U_15194),U_15193)),U_15200)) )
        | ~ c_Relation_Osingle__valued(U_15198,U_15199,U_15200) ) ),
    inference(variable_rename,[status(thm)],[f_3874_1]) ).

fof(f_3874_3,plain,
    ( ! [U_15206,U_15204,U_15202] :
        ( c_Relation_Osingle__valued(U_15202,U_15204,U_15206)
        | ? [U_15197,U_15196] :
            ( ? [U_15195] :
                ( U_15196 != U_15195
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15202,U_15204)),hAPP(hAPP(c_Product__Type_OPair(U_15202,U_15204),U_15197),U_15195)),U_15206)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15202,U_15204)),hAPP(hAPP(c_Product__Type_OPair(U_15202,U_15204),U_15197),U_15196)),U_15206)) ) )
    & ! [U_15205,U_15203,U_15201] :
        ( ! [U_15194,U_15193] :
            ( ! [U_15192] :
                ( U_15193 = U_15192
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15201,U_15203)),hAPP(hAPP(c_Product__Type_OPair(U_15201,U_15203),U_15194),U_15192)),U_15205)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15201,U_15203)),hAPP(hAPP(c_Product__Type_OPair(U_15201,U_15203),U_15194),U_15193)),U_15205)) )
        | ~ c_Relation_Osingle__valued(U_15201,U_15203,U_15205) ) ),
    inference(miniscope,[status(thm)],[f_3874_2]) ).

fof(f_3874_4,plain,
    ( ! [U_15206,U_15204,U_15202] :
        ( c_Relation_Osingle__valued(U_15202,U_15204,U_15206)
        | ? [U_15196] :
            ( ? [U_15195] :
                ( U_15196 != U_15195
                & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15202,U_15204)),hAPP(hAPP(c_Product__Type_OPair(U_15202,U_15204),sK361(U_15206,U_15204,U_15202)),U_15195)),U_15206)) )
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15202,U_15204)),hAPP(hAPP(c_Product__Type_OPair(U_15202,U_15204),sK361(U_15206,U_15204,U_15202)),U_15196)),U_15206)) ) )
    & ! [U_15205,U_15203,U_15201] :
        ( ! [U_15194,U_15193] :
            ( ! [U_15192] :
                ( U_15193 = U_15192
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15201,U_15203)),hAPP(hAPP(c_Product__Type_OPair(U_15201,U_15203),U_15194),U_15192)),U_15205)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15201,U_15203)),hAPP(hAPP(c_Product__Type_OPair(U_15201,U_15203),U_15194),U_15193)),U_15205)) )
        | ~ c_Relation_Osingle__valued(U_15201,U_15203,U_15205) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK361]),skolemize(U_15197,sK361(U_15206,U_15204,U_15202))],[f_3874_3]) ).

fof(f_3874_5,plain,
    ( ! [U_15206,U_15204,U_15202] :
        ( c_Relation_Osingle__valued(U_15202,U_15204,U_15206)
        | ( ? [U_15195] :
              ( sK362(U_15206,U_15204,U_15202) != U_15195
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15202,U_15204)),hAPP(hAPP(c_Product__Type_OPair(U_15202,U_15204),sK361(U_15206,U_15204,U_15202)),U_15195)),U_15206)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15202,U_15204)),hAPP(hAPP(c_Product__Type_OPair(U_15202,U_15204),sK361(U_15206,U_15204,U_15202)),sK362(U_15206,U_15204,U_15202))),U_15206)) ) )
    & ! [U_15205,U_15203,U_15201] :
        ( ! [U_15194,U_15193] :
            ( ! [U_15192] :
                ( U_15193 = U_15192
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15201,U_15203)),hAPP(hAPP(c_Product__Type_OPair(U_15201,U_15203),U_15194),U_15192)),U_15205)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15201,U_15203)),hAPP(hAPP(c_Product__Type_OPair(U_15201,U_15203),U_15194),U_15193)),U_15205)) )
        | ~ c_Relation_Osingle__valued(U_15201,U_15203,U_15205) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK362]),skolemize(U_15196,sK362(U_15206,U_15204,U_15202))],[f_3874_4]) ).

fof(f_3874_6,plain,
    ( ! [U_15206,U_15204,U_15202] :
        ( c_Relation_Osingle__valued(U_15202,U_15204,U_15206)
        | ( sK362(U_15206,U_15204,U_15202) != sK363(U_15206,U_15204,U_15202)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15202,U_15204)),hAPP(hAPP(c_Product__Type_OPair(U_15202,U_15204),sK361(U_15206,U_15204,U_15202)),sK363(U_15206,U_15204,U_15202))),U_15206))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15202,U_15204)),hAPP(hAPP(c_Product__Type_OPair(U_15202,U_15204),sK361(U_15206,U_15204,U_15202)),sK362(U_15206,U_15204,U_15202))),U_15206)) ) )
    & ! [U_15205,U_15203,U_15201] :
        ( ! [U_15194,U_15193] :
            ( ! [U_15192] :
                ( U_15193 = U_15192
                | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15201,U_15203)),hAPP(hAPP(c_Product__Type_OPair(U_15201,U_15203),U_15194),U_15192)),U_15205)) )
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15201,U_15203)),hAPP(hAPP(c_Product__Type_OPair(U_15201,U_15203),U_15194),U_15193)),U_15205)) )
        | ~ c_Relation_Osingle__valued(U_15201,U_15203,U_15205) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK363]),skolemize(U_15195,sK363(U_15206,U_15204,U_15202))],[f_3874_5]) ).

fof(f_3874_7,plain,
    ( ! [U_15204,U_15202,U_15206] :
        ( sK362(U_15206,U_15204,U_15202) != sK363(U_15206,U_15204,U_15202)
        | ~ sP1022(U_15204,U_15202,U_15206) )
    & ! [U_15204,U_15202,U_15206] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15202,U_15204)),hAPP(hAPP(c_Product__Type_OPair(U_15202,U_15204),sK361(U_15206,U_15204,U_15202)),sK363(U_15206,U_15204,U_15202))),U_15206))
        | ~ sP1022(U_15204,U_15202,U_15206) )
    & ! [U_15204,U_15202,U_15206] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15202,U_15204)),hAPP(hAPP(c_Product__Type_OPair(U_15202,U_15204),sK361(U_15206,U_15204,U_15202)),sK362(U_15206,U_15204,U_15202))),U_15206))
        | ~ sP1022(U_15204,U_15202,U_15206) )
    & ! [U_15204,U_15202,U_15206] :
        ( c_Relation_Osingle__valued(U_15202,U_15204,U_15206)
        | sP1022(U_15204,U_15202,U_15206) )
    & ! [U_15205,U_15192,U_15193,U_15203,U_15194,U_15201] :
        ( U_15193 = U_15192
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15201,U_15203)),hAPP(hAPP(c_Product__Type_OPair(U_15201,U_15203),U_15194),U_15192)),U_15205))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15201,U_15203)),hAPP(hAPP(c_Product__Type_OPair(U_15201,U_15203),U_15194),U_15193)),U_15205))
        | ~ c_Relation_Osingle__valued(U_15201,U_15203,U_15205) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1022])],[f_3874_6]) ).

cnf(f_3874_8,plain,
    ( U_15193 = U_15192
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15201,U_15203)),hAPP(hAPP(c_Product__Type_OPair(U_15201,U_15203),U_15194),U_15192)),U_15205))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15201,U_15203)),hAPP(hAPP(c_Product__Type_OPair(U_15201,U_15203),U_15194),U_15193)),U_15205))
    | ~ c_Relation_Osingle__valued(U_15201,U_15203,U_15205) ),
    inference(clausify,[status(thm)],[f_3874_7]) ).

cnf(f_3874_9,plain,
    ( c_Relation_Osingle__valued(U_15202,U_15204,U_15206)
    | sP1022(U_15204,U_15202,U_15206) ),
    inference(clausify,[status(thm)],[f_3874_7]) ).

cnf(f_3874_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15202,U_15204)),hAPP(hAPP(c_Product__Type_OPair(U_15202,U_15204),sK361(U_15206,U_15204,U_15202)),sK362(U_15206,U_15204,U_15202))),U_15206))
    | ~ sP1022(U_15204,U_15202,U_15206) ),
    inference(clausify,[status(thm)],[f_3874_7]) ).

cnf(f_3874_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15202,U_15204)),hAPP(hAPP(c_Product__Type_OPair(U_15202,U_15204),sK361(U_15206,U_15204,U_15202)),sK363(U_15206,U_15204,U_15202))),U_15206))
    | ~ sP1022(U_15204,U_15202,U_15206) ),
    inference(clausify,[status(thm)],[f_3874_7]) ).

cnf(f_3874_12,plain,
    ( sK362(U_15206,U_15204,U_15202) != sK363(U_15206,U_15204,U_15202)
    | ~ sP1022(U_15204,U_15202,U_15206) ),
    inference(clausify,[status(thm)],[f_3874_7]) ).

fof(f_3875_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_3875_2,plain,
    ! [U_15211,U_15210,U_15209,U_15208,U_15207] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15207,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15207,U_15207),U_15211),U_15210)),c_Transitive__Closure_Ortrancl(U_15207,U_15208)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15207,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15207,U_15207),U_15210),U_15211)),c_Transitive__Closure_Ortrancl(U_15207,U_15208)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15207,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15207,U_15207),U_15209),U_15211)),c_Transitive__Closure_Ortrancl(U_15207,U_15208)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15207,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15207,U_15207),U_15209),U_15210)),c_Transitive__Closure_Ortrancl(U_15207,U_15208)))
      | ~ c_Relation_Osingle__valued(U_15207,U_15207,U_15208) ),
    inference(variable_rename,[status(thm)],[f_3875_1]) ).

fof(f_3875_3,plain,
    ! [U_15208,U_15210,U_15207,U_15209,U_15211] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15207,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15207,U_15207),U_15211),U_15210)),c_Transitive__Closure_Ortrancl(U_15207,U_15208)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15207,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15207,U_15207),U_15210),U_15211)),c_Transitive__Closure_Ortrancl(U_15207,U_15208)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15207,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15207,U_15207),U_15209),U_15211)),c_Transitive__Closure_Ortrancl(U_15207,U_15208)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15207,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15207,U_15207),U_15209),U_15210)),c_Transitive__Closure_Ortrancl(U_15207,U_15208)))
      | ~ c_Relation_Osingle__valued(U_15207,U_15207,U_15208) ),
    inference(definitional_conversion,[status(esa)],[f_3875_2]) ).

cnf(f_3875_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15207,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15207,U_15207),U_15211),U_15210)),c_Transitive__Closure_Ortrancl(U_15207,U_15208)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_15207,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15207,U_15207),U_15210),U_15211)),c_Transitive__Closure_Ortrancl(U_15207,U_15208)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15207,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15207,U_15207),U_15209),U_15211)),c_Transitive__Closure_Ortrancl(U_15207,U_15208)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15207,U_15207)),hAPP(hAPP(c_Product__Type_OPair(U_15207,U_15207),U_15209),U_15210)),c_Transitive__Closure_Ortrancl(U_15207,U_15208)))
    | ~ c_Relation_Osingle__valued(U_15207,U_15207,U_15208) ),
    inference(clausify,[status(thm)],[f_3875_3]) ).

fof(f_3876_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_3876_2,plain,
    ! [U_15218,U_15217,U_15216] :
      ( ( c_Relation_Orefl__on(U_15216,U_15217,U_15218)
        | ? [U_15215] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15216,U_15216)),hAPP(hAPP(c_Product__Type_OPair(U_15216,U_15216),U_15215),U_15215)),U_15218))
            & hBOOL(hAPP(hAPP(c_member(U_15216),U_15215),U_15217)) )
        | ? [U_15214] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15216,U_15216,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15216,tc_fun(U_15216,tc_HOL_Obool),tc_fun(U_15216,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15216,tc_HOL_Obool),tc_fun(U_15216,tc_HOL_Obool)),U_15216),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15216)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15216),c_fconj),hAPP(hAPP(c_COMBC(U_15216,tc_fun(U_15216,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15216)),U_15217)))),hAPP(hAPP(c_COMBC(U_15216,tc_fun(U_15216,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15216)),U_15217))),U_15214))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15216,U_15216)),U_15214),U_15218)) ) )
      & ( ( ! [U_15213] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15216,U_15216)),hAPP(hAPP(c_Product__Type_OPair(U_15216,U_15216),U_15213),U_15213)),U_15218))
              | ~ hBOOL(hAPP(hAPP(c_member(U_15216),U_15213),U_15217)) )
          & ! [U_15212] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15216,U_15216,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15216,tc_fun(U_15216,tc_HOL_Obool),tc_fun(U_15216,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15216,tc_HOL_Obool),tc_fun(U_15216,tc_HOL_Obool)),U_15216),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15216)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15216),c_fconj),hAPP(hAPP(c_COMBC(U_15216,tc_fun(U_15216,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15216)),U_15217)))),hAPP(hAPP(c_COMBC(U_15216,tc_fun(U_15216,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15216)),U_15217))),U_15212))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15216,U_15216)),U_15212),U_15218)) ) )
        | ~ c_Relation_Orefl__on(U_15216,U_15217,U_15218) ) ),
    inference(variable_rename,[status(thm)],[f_3876_1]) ).

fof(f_3876_3,plain,
    ( ! [U_15224,U_15222,U_15220] :
        ( c_Relation_Orefl__on(U_15220,U_15222,U_15224)
        | ? [U_15215] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15220,U_15220)),hAPP(hAPP(c_Product__Type_OPair(U_15220,U_15220),U_15215),U_15215)),U_15224))
            & hBOOL(hAPP(hAPP(c_member(U_15220),U_15215),U_15222)) )
        | ? [U_15214] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15220,U_15220,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15220,tc_fun(U_15220,tc_HOL_Obool),tc_fun(U_15220,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15220,tc_HOL_Obool),tc_fun(U_15220,tc_HOL_Obool)),U_15220),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15220)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15220),c_fconj),hAPP(hAPP(c_COMBC(U_15220,tc_fun(U_15220,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15220)),U_15222)))),hAPP(hAPP(c_COMBC(U_15220,tc_fun(U_15220,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15220)),U_15222))),U_15214))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15220,U_15220)),U_15214),U_15224)) ) )
    & ! [U_15223,U_15221,U_15219] :
        ( ( ! [U_15213] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15219,U_15219)),hAPP(hAPP(c_Product__Type_OPair(U_15219,U_15219),U_15213),U_15213)),U_15223))
              | ~ hBOOL(hAPP(hAPP(c_member(U_15219),U_15213),U_15221)) )
          & ! [U_15212] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15219,U_15219,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15219,tc_fun(U_15219,tc_HOL_Obool),tc_fun(U_15219,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15219,tc_HOL_Obool),tc_fun(U_15219,tc_HOL_Obool)),U_15219),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15219)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15219),c_fconj),hAPP(hAPP(c_COMBC(U_15219,tc_fun(U_15219,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15219)),U_15221)))),hAPP(hAPP(c_COMBC(U_15219,tc_fun(U_15219,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15219)),U_15221))),U_15212))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15219,U_15219)),U_15212),U_15223)) ) )
        | ~ c_Relation_Orefl__on(U_15219,U_15221,U_15223) ) ),
    inference(miniscope,[status(thm)],[f_3876_2]) ).

fof(f_3876_4,plain,
    ( ! [U_15224,U_15222,U_15220] :
        ( c_Relation_Orefl__on(U_15220,U_15222,U_15224)
        | ? [U_15215] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15220,U_15220)),hAPP(hAPP(c_Product__Type_OPair(U_15220,U_15220),U_15215),U_15215)),U_15224))
            & hBOOL(hAPP(hAPP(c_member(U_15220),U_15215),U_15222)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15220,U_15220,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15220,tc_fun(U_15220,tc_HOL_Obool),tc_fun(U_15220,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15220,tc_HOL_Obool),tc_fun(U_15220,tc_HOL_Obool)),U_15220),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15220)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15220),c_fconj),hAPP(hAPP(c_COMBC(U_15220,tc_fun(U_15220,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15220)),U_15222)))),hAPP(hAPP(c_COMBC(U_15220,tc_fun(U_15220,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15220)),U_15222))),sK364(U_15224,U_15222,U_15220)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15220,U_15220)),sK364(U_15224,U_15222,U_15220)),U_15224)) ) )
    & ! [U_15223,U_15221,U_15219] :
        ( ( ! [U_15213] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15219,U_15219)),hAPP(hAPP(c_Product__Type_OPair(U_15219,U_15219),U_15213),U_15213)),U_15223))
              | ~ hBOOL(hAPP(hAPP(c_member(U_15219),U_15213),U_15221)) )
          & ! [U_15212] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15219,U_15219,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15219,tc_fun(U_15219,tc_HOL_Obool),tc_fun(U_15219,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15219,tc_HOL_Obool),tc_fun(U_15219,tc_HOL_Obool)),U_15219),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15219)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15219),c_fconj),hAPP(hAPP(c_COMBC(U_15219,tc_fun(U_15219,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15219)),U_15221)))),hAPP(hAPP(c_COMBC(U_15219,tc_fun(U_15219,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15219)),U_15221))),U_15212))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15219,U_15219)),U_15212),U_15223)) ) )
        | ~ c_Relation_Orefl__on(U_15219,U_15221,U_15223) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK364]),skolemize(U_15214,sK364(U_15224,U_15222,U_15220))],[f_3876_3]) ).

fof(f_3876_5,plain,
    ( ! [U_15224,U_15222,U_15220] :
        ( c_Relation_Orefl__on(U_15220,U_15222,U_15224)
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15220,U_15220)),hAPP(hAPP(c_Product__Type_OPair(U_15220,U_15220),sK365(U_15224,U_15222,U_15220)),sK365(U_15224,U_15222,U_15220))),U_15224))
          & hBOOL(hAPP(hAPP(c_member(U_15220),sK365(U_15224,U_15222,U_15220)),U_15222)) )
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15220,U_15220,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15220,tc_fun(U_15220,tc_HOL_Obool),tc_fun(U_15220,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15220,tc_HOL_Obool),tc_fun(U_15220,tc_HOL_Obool)),U_15220),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15220)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15220),c_fconj),hAPP(hAPP(c_COMBC(U_15220,tc_fun(U_15220,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15220)),U_15222)))),hAPP(hAPP(c_COMBC(U_15220,tc_fun(U_15220,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15220)),U_15222))),sK364(U_15224,U_15222,U_15220)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15220,U_15220)),sK364(U_15224,U_15222,U_15220)),U_15224)) ) )
    & ! [U_15223,U_15221,U_15219] :
        ( ( ! [U_15213] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15219,U_15219)),hAPP(hAPP(c_Product__Type_OPair(U_15219,U_15219),U_15213),U_15213)),U_15223))
              | ~ hBOOL(hAPP(hAPP(c_member(U_15219),U_15213),U_15221)) )
          & ! [U_15212] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15219,U_15219,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15219,tc_fun(U_15219,tc_HOL_Obool),tc_fun(U_15219,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15219,tc_HOL_Obool),tc_fun(U_15219,tc_HOL_Obool)),U_15219),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15219)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15219),c_fconj),hAPP(hAPP(c_COMBC(U_15219,tc_fun(U_15219,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15219)),U_15221)))),hAPP(hAPP(c_COMBC(U_15219,tc_fun(U_15219,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15219)),U_15221))),U_15212))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15219,U_15219)),U_15212),U_15223)) ) )
        | ~ c_Relation_Orefl__on(U_15219,U_15221,U_15223) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK365]),skolemize(U_15215,sK365(U_15224,U_15222,U_15220))],[f_3876_4]) ).

fof(f_3876_6,plain,
    ( ! [U_15220,U_15222,U_15224] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15220,U_15220)),hAPP(hAPP(c_Product__Type_OPair(U_15220,U_15220),sK365(U_15224,U_15222,U_15220)),sK365(U_15224,U_15222,U_15220))),U_15224))
        | ~ sP1025(U_15220,U_15222,U_15224) )
    & ! [U_15220,U_15222,U_15224] :
        ( hBOOL(hAPP(hAPP(c_member(U_15220),sK365(U_15224,U_15222,U_15220)),U_15222))
        | ~ sP1025(U_15220,U_15222,U_15224) )
    & ! [U_15220,U_15222,U_15224] :
        ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15220,U_15220,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15220,tc_fun(U_15220,tc_HOL_Obool),tc_fun(U_15220,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15220,tc_HOL_Obool),tc_fun(U_15220,tc_HOL_Obool)),U_15220),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15220)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15220),c_fconj),hAPP(hAPP(c_COMBC(U_15220,tc_fun(U_15220,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15220)),U_15222)))),hAPP(hAPP(c_COMBC(U_15220,tc_fun(U_15220,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15220)),U_15222))),sK364(U_15224,U_15222,U_15220)))
        | ~ sP1024(U_15220,U_15222,U_15224) )
    & ! [U_15220,U_15222,U_15224] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15220,U_15220)),sK364(U_15224,U_15222,U_15220)),U_15224))
        | ~ sP1024(U_15220,U_15222,U_15224) )
    & ! [U_15213,U_15212,U_15223,U_15219,U_15221] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15219,U_15219)),hAPP(hAPP(c_Product__Type_OPair(U_15219,U_15219),U_15213),U_15213)),U_15223))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15219),U_15213),U_15221))
        | ~ sP1023(U_15213,U_15212,U_15223,U_15219,U_15221) )
    & ! [U_15213,U_15212,U_15223,U_15219,U_15221] :
        ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15219,U_15219,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15219,tc_fun(U_15219,tc_HOL_Obool),tc_fun(U_15219,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15219,tc_HOL_Obool),tc_fun(U_15219,tc_HOL_Obool)),U_15219),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15219)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15219),c_fconj),hAPP(hAPP(c_COMBC(U_15219,tc_fun(U_15219,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15219)),U_15221)))),hAPP(hAPP(c_COMBC(U_15219,tc_fun(U_15219,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15219)),U_15221))),U_15212))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15219,U_15219)),U_15212),U_15223))
        | ~ sP1023(U_15213,U_15212,U_15223,U_15219,U_15221) )
    & ! [U_15220,U_15222,U_15224] :
        ( c_Relation_Orefl__on(U_15220,U_15222,U_15224)
        | sP1025(U_15220,U_15222,U_15224)
        | sP1024(U_15220,U_15222,U_15224) )
    & ! [U_15213,U_15212,U_15223,U_15219,U_15221] :
        ( sP1023(U_15213,U_15212,U_15223,U_15219,U_15221)
        | ~ c_Relation_Orefl__on(U_15219,U_15221,U_15223) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1023,sP1024,sP1025])],[f_3876_5]) ).

cnf(f_3876_7,plain,
    ( sP1023(U_15213,U_15212,U_15223,U_15219,U_15221)
    | ~ c_Relation_Orefl__on(U_15219,U_15221,U_15223) ),
    inference(clausify,[status(thm)],[f_3876_6]) ).

cnf(f_3876_8,plain,
    ( c_Relation_Orefl__on(U_15220,U_15222,U_15224)
    | sP1025(U_15220,U_15222,U_15224)
    | sP1024(U_15220,U_15222,U_15224) ),
    inference(clausify,[status(thm)],[f_3876_6]) ).

cnf(f_3876_9,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15219,U_15219,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15219,tc_fun(U_15219,tc_HOL_Obool),tc_fun(U_15219,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15219,tc_HOL_Obool),tc_fun(U_15219,tc_HOL_Obool)),U_15219),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15219)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15219),c_fconj),hAPP(hAPP(c_COMBC(U_15219,tc_fun(U_15219,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15219)),U_15221)))),hAPP(hAPP(c_COMBC(U_15219,tc_fun(U_15219,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15219)),U_15221))),U_15212))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15219,U_15219)),U_15212),U_15223))
    | ~ sP1023(U_15213,U_15212,U_15223,U_15219,U_15221) ),
    inference(clausify,[status(thm)],[f_3876_6]) ).

cnf(f_3876_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15219,U_15219)),hAPP(hAPP(c_Product__Type_OPair(U_15219,U_15219),U_15213),U_15213)),U_15223))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15219),U_15213),U_15221))
    | ~ sP1023(U_15213,U_15212,U_15223,U_15219,U_15221) ),
    inference(clausify,[status(thm)],[f_3876_6]) ).

cnf(f_3876_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15220,U_15220)),sK364(U_15224,U_15222,U_15220)),U_15224))
    | ~ sP1024(U_15220,U_15222,U_15224) ),
    inference(clausify,[status(thm)],[f_3876_6]) ).

cnf(f_3876_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15220,U_15220,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15220,tc_fun(U_15220,tc_HOL_Obool),tc_fun(U_15220,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(U_15220,tc_HOL_Obool),tc_fun(U_15220,tc_HOL_Obool)),U_15220),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_15220)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_15220),c_fconj),hAPP(hAPP(c_COMBC(U_15220,tc_fun(U_15220,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15220)),U_15222)))),hAPP(hAPP(c_COMBC(U_15220,tc_fun(U_15220,tc_HOL_Obool),tc_HOL_Obool),c_member(U_15220)),U_15222))),sK364(U_15224,U_15222,U_15220)))
    | ~ sP1024(U_15220,U_15222,U_15224) ),
    inference(clausify,[status(thm)],[f_3876_6]) ).

cnf(f_3876_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15220),sK365(U_15224,U_15222,U_15220)),U_15222))
    | ~ sP1025(U_15220,U_15222,U_15224) ),
    inference(clausify,[status(thm)],[f_3876_6]) ).

cnf(f_3876_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15220,U_15220)),hAPP(hAPP(c_Product__Type_OPair(U_15220,U_15220),sK365(U_15224,U_15222,U_15220)),sK365(U_15224,U_15222,U_15220))),U_15224))
    | ~ sP1025(U_15220,U_15222,U_15224) ),
    inference(clausify,[status(thm)],[f_3876_6]) ).

fof(f_3877_1,plain,
    ! [V_x_2,V_Pa_2] :
      ( hBOOL(hAPP(V_Pa_2,V_x_2))
      | ? [B_y] :
          ( ~ hBOOL(hAPP(V_Pa_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_3877_2,plain,
    ! [U_15227,U_15226] :
      ( hBOOL(hAPP(U_15226,U_15227))
      | ? [U_15225] :
          ( ~ hBOOL(hAPP(U_15226,hAPP(c_Int_OAbs__Integ,U_15225)))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_15225),c_Int_OInteg)) ) ),
    inference(variable_rename,[status(thm)],[f_3877_1]) ).

fof(f_3877_3,plain,
    ! [U_15227,U_15226] :
      ( hBOOL(hAPP(U_15226,U_15227))
      | ( ~ hBOOL(hAPP(U_15226,hAPP(c_Int_OAbs__Integ,sK366(U_15227,U_15226))))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK366(U_15227,U_15226)),c_Int_OInteg)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK366]),skolemize(U_15225,sK366(U_15227,U_15226))],[f_3877_2]) ).

fof(f_3877_4,plain,
    ( ! [U_15227,U_15226] :
        ( ~ hBOOL(hAPP(U_15226,hAPP(c_Int_OAbs__Integ,sK366(U_15227,U_15226))))
        | ~ sP1026(U_15227,U_15226) )
    & ! [U_15227,U_15226] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK366(U_15227,U_15226)),c_Int_OInteg))
        | ~ sP1026(U_15227,U_15226) )
    & ! [U_15227,U_15226] :
        ( hBOOL(hAPP(U_15226,U_15227))
        | sP1026(U_15227,U_15226) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1026])],[f_3877_3]) ).

cnf(f_3877_5,plain,
    ( hBOOL(hAPP(U_15226,U_15227))
    | sP1026(U_15227,U_15226) ),
    inference(clausify,[status(thm)],[f_3877_4]) ).

cnf(f_3877_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK366(U_15227,U_15226)),c_Int_OInteg))
    | ~ sP1026(U_15227,U_15226) ),
    inference(clausify,[status(thm)],[f_3877_4]) ).

cnf(f_3877_7,plain,
    ( ~ hBOOL(hAPP(U_15226,hAPP(c_Int_OAbs__Integ,sK366(U_15227,U_15226))))
    | ~ sP1026(U_15227,U_15226) ),
    inference(clausify,[status(thm)],[f_3877_4]) ).

fof(f_3878_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_3878_2,plain,
    ! [U_15232,U_15231,U_15230] :
      ( ( hBOOL(hAPP(c_Predicate_OPowp(U_15230,U_15231),U_15232))
        | ? [U_15229] :
            ( ~ hBOOL(hAPP(U_15231,U_15229))
            & hBOOL(hAPP(hAPP(c_member(U_15230),U_15229),U_15232)) ) )
      & ( ! [U_15228] :
            ( hBOOL(hAPP(U_15231,U_15228))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15230),U_15228),U_15232)) )
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_15230,U_15231),U_15232)) ) ),
    inference(variable_rename,[status(thm)],[f_3878_1]) ).

fof(f_3878_3,plain,
    ( ! [U_15238,U_15236,U_15234] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_15234,U_15236),U_15238))
        | ? [U_15229] :
            ( ~ hBOOL(hAPP(U_15236,U_15229))
            & hBOOL(hAPP(hAPP(c_member(U_15234),U_15229),U_15238)) ) )
    & ! [U_15237,U_15235,U_15233] :
        ( ! [U_15228] :
            ( hBOOL(hAPP(U_15235,U_15228))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15233),U_15228),U_15237)) )
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_15233,U_15235),U_15237)) ) ),
    inference(miniscope,[status(thm)],[f_3878_2]) ).

fof(f_3878_4,plain,
    ( ! [U_15238,U_15236,U_15234] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_15234,U_15236),U_15238))
        | ( ~ hBOOL(hAPP(U_15236,sK367(U_15238,U_15236,U_15234)))
          & hBOOL(hAPP(hAPP(c_member(U_15234),sK367(U_15238,U_15236,U_15234)),U_15238)) ) )
    & ! [U_15237,U_15235,U_15233] :
        ( ! [U_15228] :
            ( hBOOL(hAPP(U_15235,U_15228))
            | ~ hBOOL(hAPP(hAPP(c_member(U_15233),U_15228),U_15237)) )
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_15233,U_15235),U_15237)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK367]),skolemize(U_15229,sK367(U_15238,U_15236,U_15234))],[f_3878_3]) ).

fof(f_3878_5,plain,
    ( ! [U_15238,U_15234,U_15236] :
        ( ~ hBOOL(hAPP(U_15236,sK367(U_15238,U_15236,U_15234)))
        | ~ sP1027(U_15238,U_15234,U_15236) )
    & ! [U_15238,U_15234,U_15236] :
        ( hBOOL(hAPP(hAPP(c_member(U_15234),sK367(U_15238,U_15236,U_15234)),U_15238))
        | ~ sP1027(U_15238,U_15234,U_15236) )
    & ! [U_15238,U_15234,U_15236] :
        ( hBOOL(hAPP(c_Predicate_OPowp(U_15234,U_15236),U_15238))
        | sP1027(U_15238,U_15234,U_15236) )
    & ! [U_15237,U_15228,U_15235,U_15233] :
        ( hBOOL(hAPP(U_15235,U_15228))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15233),U_15228),U_15237))
        | ~ hBOOL(hAPP(c_Predicate_OPowp(U_15233,U_15235),U_15237)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1027])],[f_3878_4]) ).

cnf(f_3878_6,plain,
    ( hBOOL(hAPP(U_15235,U_15228))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15233),U_15228),U_15237))
    | ~ hBOOL(hAPP(c_Predicate_OPowp(U_15233,U_15235),U_15237)) ),
    inference(clausify,[status(thm)],[f_3878_5]) ).

cnf(f_3878_7,plain,
    ( hBOOL(hAPP(c_Predicate_OPowp(U_15234,U_15236),U_15238))
    | sP1027(U_15238,U_15234,U_15236) ),
    inference(clausify,[status(thm)],[f_3878_5]) ).

cnf(f_3878_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15234),sK367(U_15238,U_15236,U_15234)),U_15238))
    | ~ sP1027(U_15238,U_15234,U_15236) ),
    inference(clausify,[status(thm)],[f_3878_5]) ).

cnf(f_3878_9,plain,
    ( ~ hBOOL(hAPP(U_15236,sK367(U_15238,U_15236,U_15234)))
    | ~ sP1027(U_15238,U_15234,U_15236) ),
    inference(clausify,[status(thm)],[f_3878_5]) ).

fof(f_3879_1,plain,
    ! [V_Pa_2,T_b,B_x] :
      ( hBOOL(hAPP(V_Pa_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_3879_2,plain,
    ! [U_15241,U_15240,U_15239] :
      ( hBOOL(hAPP(U_15241,U_15239))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15240),U_15239),c_Orderings_Obot__class_Obot(tc_fun(U_15240,tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3879_1]) ).

fof(f_3879_3,plain,
    ! [U_15241,U_15239,U_15240] :
      ( hBOOL(hAPP(U_15241,U_15239))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15240),U_15239),c_Orderings_Obot__class_Obot(tc_fun(U_15240,tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3879_2]) ).

cnf(f_3879_4,plain,
    ( hBOOL(hAPP(U_15241,U_15239))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15240),U_15239),c_Orderings_Obot__class_Obot(tc_fun(U_15240,tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3879_3]) ).

fof(f_3880_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_3880_2,plain,
    ! [U_15247,U_15246,U_15245,U_15244] :
      ( ( c_Equiv__Relations_Ocongruent(U_15244,U_15245,U_15246,U_15247)
        | ? [U_15243] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15244,U_15244,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15244,tc_fun(U_15244,U_15245),tc_fun(U_15244,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15245,tc_HOL_Obool),tc_fun(tc_fun(U_15244,U_15245),tc_fun(U_15244,tc_HOL_Obool)),U_15244),c_COMBB(U_15245,tc_HOL_Obool,U_15244)),hAPP(hAPP(c_COMBB(U_15245,tc_fun(U_15245,tc_HOL_Obool),U_15244),c_fequal),U_15247))),U_15247)),U_15243))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15244,U_15244)),U_15243),U_15246)) ) )
      & ( ! [U_15242] :
            ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15244,U_15244,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15244,tc_fun(U_15244,U_15245),tc_fun(U_15244,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15245,tc_HOL_Obool),tc_fun(tc_fun(U_15244,U_15245),tc_fun(U_15244,tc_HOL_Obool)),U_15244),c_COMBB(U_15245,tc_HOL_Obool,U_15244)),hAPP(hAPP(c_COMBB(U_15245,tc_fun(U_15245,tc_HOL_Obool),U_15244),c_fequal),U_15247))),U_15247)),U_15242))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15244,U_15244)),U_15242),U_15246)) )
        | ~ c_Equiv__Relations_Ocongruent(U_15244,U_15245,U_15246,U_15247) ) ),
    inference(variable_rename,[status(thm)],[f_3880_1]) ).

fof(f_3880_3,plain,
    ( ! [U_15255,U_15253,U_15251,U_15249] :
        ( c_Equiv__Relations_Ocongruent(U_15249,U_15251,U_15253,U_15255)
        | ? [U_15243] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15249,U_15249,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15249,tc_fun(U_15249,U_15251),tc_fun(U_15249,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15251,tc_HOL_Obool),tc_fun(tc_fun(U_15249,U_15251),tc_fun(U_15249,tc_HOL_Obool)),U_15249),c_COMBB(U_15251,tc_HOL_Obool,U_15249)),hAPP(hAPP(c_COMBB(U_15251,tc_fun(U_15251,tc_HOL_Obool),U_15249),c_fequal),U_15255))),U_15255)),U_15243))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15249,U_15249)),U_15243),U_15253)) ) )
    & ! [U_15254,U_15252,U_15250,U_15248] :
        ( ! [U_15242] :
            ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15248,U_15248,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15248,tc_fun(U_15248,U_15250),tc_fun(U_15248,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15250,tc_HOL_Obool),tc_fun(tc_fun(U_15248,U_15250),tc_fun(U_15248,tc_HOL_Obool)),U_15248),c_COMBB(U_15250,tc_HOL_Obool,U_15248)),hAPP(hAPP(c_COMBB(U_15250,tc_fun(U_15250,tc_HOL_Obool),U_15248),c_fequal),U_15254))),U_15254)),U_15242))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15248,U_15248)),U_15242),U_15252)) )
        | ~ c_Equiv__Relations_Ocongruent(U_15248,U_15250,U_15252,U_15254) ) ),
    inference(miniscope,[status(thm)],[f_3880_2]) ).

fof(f_3880_4,plain,
    ( ! [U_15255,U_15253,U_15251,U_15249] :
        ( c_Equiv__Relations_Ocongruent(U_15249,U_15251,U_15253,U_15255)
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15249,U_15249,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15249,tc_fun(U_15249,U_15251),tc_fun(U_15249,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15251,tc_HOL_Obool),tc_fun(tc_fun(U_15249,U_15251),tc_fun(U_15249,tc_HOL_Obool)),U_15249),c_COMBB(U_15251,tc_HOL_Obool,U_15249)),hAPP(hAPP(c_COMBB(U_15251,tc_fun(U_15251,tc_HOL_Obool),U_15249),c_fequal),U_15255))),U_15255)),sK368(U_15255,U_15253,U_15251,U_15249)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15249,U_15249)),sK368(U_15255,U_15253,U_15251,U_15249)),U_15253)) ) )
    & ! [U_15254,U_15252,U_15250,U_15248] :
        ( ! [U_15242] :
            ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15248,U_15248,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15248,tc_fun(U_15248,U_15250),tc_fun(U_15248,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15250,tc_HOL_Obool),tc_fun(tc_fun(U_15248,U_15250),tc_fun(U_15248,tc_HOL_Obool)),U_15248),c_COMBB(U_15250,tc_HOL_Obool,U_15248)),hAPP(hAPP(c_COMBB(U_15250,tc_fun(U_15250,tc_HOL_Obool),U_15248),c_fequal),U_15254))),U_15254)),U_15242))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15248,U_15248)),U_15242),U_15252)) )
        | ~ c_Equiv__Relations_Ocongruent(U_15248,U_15250,U_15252,U_15254) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK368]),skolemize(U_15243,sK368(U_15255,U_15253,U_15251,U_15249))],[f_3880_3]) ).

fof(f_3880_5,plain,
    ( ! [U_15249,U_15253,U_15255,U_15251] :
        ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15249,U_15249,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15249,tc_fun(U_15249,U_15251),tc_fun(U_15249,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15251,tc_HOL_Obool),tc_fun(tc_fun(U_15249,U_15251),tc_fun(U_15249,tc_HOL_Obool)),U_15249),c_COMBB(U_15251,tc_HOL_Obool,U_15249)),hAPP(hAPP(c_COMBB(U_15251,tc_fun(U_15251,tc_HOL_Obool),U_15249),c_fequal),U_15255))),U_15255)),sK368(U_15255,U_15253,U_15251,U_15249)))
        | ~ sP1028(U_15249,U_15253,U_15255,U_15251) )
    & ! [U_15249,U_15253,U_15255,U_15251] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15249,U_15249)),sK368(U_15255,U_15253,U_15251,U_15249)),U_15253))
        | ~ sP1028(U_15249,U_15253,U_15255,U_15251) )
    & ! [U_15249,U_15253,U_15255,U_15251] :
        ( c_Equiv__Relations_Ocongruent(U_15249,U_15251,U_15253,U_15255)
        | sP1028(U_15249,U_15253,U_15255,U_15251) )
    & ! [U_15242,U_15250,U_15248,U_15254,U_15252] :
        ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15248,U_15248,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15248,tc_fun(U_15248,U_15250),tc_fun(U_15248,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15250,tc_HOL_Obool),tc_fun(tc_fun(U_15248,U_15250),tc_fun(U_15248,tc_HOL_Obool)),U_15248),c_COMBB(U_15250,tc_HOL_Obool,U_15248)),hAPP(hAPP(c_COMBB(U_15250,tc_fun(U_15250,tc_HOL_Obool),U_15248),c_fequal),U_15254))),U_15254)),U_15242))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15248,U_15248)),U_15242),U_15252))
        | ~ c_Equiv__Relations_Ocongruent(U_15248,U_15250,U_15252,U_15254) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1028])],[f_3880_4]) ).

cnf(f_3880_6,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15248,U_15248,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15248,tc_fun(U_15248,U_15250),tc_fun(U_15248,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15250,tc_HOL_Obool),tc_fun(tc_fun(U_15248,U_15250),tc_fun(U_15248,tc_HOL_Obool)),U_15248),c_COMBB(U_15250,tc_HOL_Obool,U_15248)),hAPP(hAPP(c_COMBB(U_15250,tc_fun(U_15250,tc_HOL_Obool),U_15248),c_fequal),U_15254))),U_15254)),U_15242))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15248,U_15248)),U_15242),U_15252))
    | ~ c_Equiv__Relations_Ocongruent(U_15248,U_15250,U_15252,U_15254) ),
    inference(clausify,[status(thm)],[f_3880_5]) ).

cnf(f_3880_7,plain,
    ( c_Equiv__Relations_Ocongruent(U_15249,U_15251,U_15253,U_15255)
    | sP1028(U_15249,U_15253,U_15255,U_15251) ),
    inference(clausify,[status(thm)],[f_3880_5]) ).

cnf(f_3880_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15249,U_15249)),sK368(U_15255,U_15253,U_15251,U_15249)),U_15253))
    | ~ sP1028(U_15249,U_15253,U_15255,U_15251) ),
    inference(clausify,[status(thm)],[f_3880_5]) ).

cnf(f_3880_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15249,U_15249,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_15249,tc_fun(U_15249,U_15251),tc_fun(U_15249,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_15251,tc_HOL_Obool),tc_fun(tc_fun(U_15249,U_15251),tc_fun(U_15249,tc_HOL_Obool)),U_15249),c_COMBB(U_15251,tc_HOL_Obool,U_15249)),hAPP(hAPP(c_COMBB(U_15251,tc_fun(U_15251,tc_HOL_Obool),U_15249),c_fequal),U_15255))),U_15255)),sK368(U_15255,U_15253,U_15251,U_15249)))
    | ~ sP1028(U_15249,U_15253,U_15255,U_15251) ),
    inference(clausify,[status(thm)],[f_3880_5]) ).

fof(f_3881_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_3881_2,plain,
    ! [U_15257] :
    ? [U_15256] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),U_15256),c_Int_OInteg))
      & U_15257 = hAPP(c_Int_OAbs__Integ,U_15256) ),
    inference(variable_rename,[status(thm)],[f_3881_1]) ).

fof(f_3881_3,plain,
    ! [U_15257] :
      ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK369(U_15257)),c_Int_OInteg))
      & U_15257 = hAPP(c_Int_OAbs__Integ,sK369(U_15257)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK369]),skolemize(U_15256,sK369(U_15257))],[f_3881_2]) ).

fof(f_3881_4,plain,
    ( ! [U_15257] : hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK369(U_15257)),c_Int_OInteg))
    & ! [U_15257] : U_15257 = hAPP(c_Int_OAbs__Integ,sK369(U_15257)) ),
    inference(definitional_conversion,[status(esa)],[f_3881_3]) ).

cnf(f_3881_5,plain,
    U_15257 = hAPP(c_Int_OAbs__Integ,sK369(U_15257)),
    inference(clausify,[status(thm)],[f_3881_4]) ).

cnf(f_3881_6,plain,
    hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),sK369(U_15257)),c_Int_OInteg)),
    inference(clausify,[status(thm)],[f_3881_4]) ).

fof(f_3882_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_3882_2,plain,
    ! [U_15262,U_15261,U_15260,U_15259] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15261),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15259,tc_fun(U_15261,tc_HOL_Obool)),U_15260),U_15262)))
      | ? [U_15258] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15261),hAPP(U_15262,U_15258)))
          & hBOOL(hAPP(hAPP(c_member(U_15259),U_15258),U_15260)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15259),U_15260)) ),
    inference(variable_rename,[status(thm)],[f_3882_1]) ).

fof(f_3882_3,plain,
    ! [U_15262,U_15261,U_15260,U_15259] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15261),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15259,tc_fun(U_15261,tc_HOL_Obool)),U_15260),U_15262)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15261),hAPP(U_15262,sK370(U_15262,U_15261,U_15260,U_15259))))
        & hBOOL(hAPP(hAPP(c_member(U_15259),sK370(U_15262,U_15261,U_15260,U_15259)),U_15260)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15259),U_15260)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK370]),skolemize(U_15258,sK370(U_15262,U_15261,U_15260,U_15259))],[f_3882_2]) ).

fof(f_3882_4,plain,
    ( ! [U_15260,U_15259,U_15261,U_15262] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15261),hAPP(U_15262,sK370(U_15262,U_15261,U_15260,U_15259))))
        | ~ sP1029(U_15260,U_15259,U_15261,U_15262) )
    & ! [U_15260,U_15259,U_15261,U_15262] :
        ( hBOOL(hAPP(hAPP(c_member(U_15259),sK370(U_15262,U_15261,U_15260,U_15259)),U_15260))
        | ~ sP1029(U_15260,U_15259,U_15261,U_15262) )
    & ! [U_15260,U_15259,U_15261,U_15262] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15261),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15259,tc_fun(U_15261,tc_HOL_Obool)),U_15260),U_15262)))
        | sP1029(U_15260,U_15259,U_15261,U_15262)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15259),U_15260)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1029])],[f_3882_3]) ).

cnf(f_3882_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15261),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15259,tc_fun(U_15261,tc_HOL_Obool)),U_15260),U_15262)))
    | sP1029(U_15260,U_15259,U_15261,U_15262)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15259),U_15260)) ),
    inference(clausify,[status(thm)],[f_3882_4]) ).

cnf(f_3882_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15259),sK370(U_15262,U_15261,U_15260,U_15259)),U_15260))
    | ~ sP1029(U_15260,U_15259,U_15261,U_15262) ),
    inference(clausify,[status(thm)],[f_3882_4]) ).

cnf(f_3882_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15261),hAPP(U_15262,sK370(U_15262,U_15261,U_15260,U_15259))))
    | ~ sP1029(U_15260,U_15259,U_15261,U_15262) ),
    inference(clausify,[status(thm)],[f_3882_4]) ).

fof(f_3883_1,plain,
    ! [V_n_2,V_ts_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_ts_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_ts_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_triples__valid__Suc]) ).

fof(f_3883_2,plain,
    ! [U_15267,U_15266,U_15265] :
      ( ! [U_15264] :
          ( c_Hoare__Mirabelle_Otriple__valid(U_15265,U_15267,U_15264)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15265)),U_15264),U_15266)) )
      | ? [U_15263] :
          ( ~ c_Hoare__Mirabelle_Otriple__valid(U_15265,hAPP(c_Nat_OSuc,U_15267),U_15263)
          & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15265)),U_15263),U_15266)) ) ),
    inference(variable_rename,[status(thm)],[f_3883_1]) ).

fof(f_3883_3,plain,
    ! [U_15267,U_15266,U_15265] :
      ( ! [U_15264] :
          ( c_Hoare__Mirabelle_Otriple__valid(U_15265,U_15267,U_15264)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15265)),U_15264),U_15266)) )
      | ( ~ c_Hoare__Mirabelle_Otriple__valid(U_15265,hAPP(c_Nat_OSuc,U_15267),sK371(U_15267,U_15266,U_15265))
        & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15265)),sK371(U_15267,U_15266,U_15265)),U_15266)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK371]),skolemize(U_15263,sK371(U_15267,U_15266,U_15265))],[f_3883_2]) ).

fof(f_3883_4,plain,
    ( ! [U_15265,U_15267,U_15266] :
        ( ~ c_Hoare__Mirabelle_Otriple__valid(U_15265,hAPP(c_Nat_OSuc,U_15267),sK371(U_15267,U_15266,U_15265))
        | ~ sP1030(U_15265,U_15267,U_15266) )
    & ! [U_15265,U_15267,U_15266] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15265)),sK371(U_15267,U_15266,U_15265)),U_15266))
        | ~ sP1030(U_15265,U_15267,U_15266) )
    & ! [U_15265,U_15264,U_15267,U_15266] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_15265,U_15267,U_15264)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15265)),U_15264),U_15266))
        | sP1030(U_15265,U_15267,U_15266) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1030])],[f_3883_3]) ).

cnf(f_3883_5,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_15265,U_15267,U_15264)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15265)),U_15264),U_15266))
    | sP1030(U_15265,U_15267,U_15266) ),
    inference(clausify,[status(thm)],[f_3883_4]) ).

cnf(f_3883_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15265)),sK371(U_15267,U_15266,U_15265)),U_15266))
    | ~ sP1030(U_15265,U_15267,U_15266) ),
    inference(clausify,[status(thm)],[f_3883_4]) ).

cnf(f_3883_7,plain,
    ( ~ c_Hoare__Mirabelle_Otriple__valid(U_15265,hAPP(c_Nat_OSuc,U_15267),sK371(U_15267,U_15266,U_15265))
    | ~ sP1030(U_15265,U_15267,U_15266) ),
    inference(clausify,[status(thm)],[f_3883_4]) ).

fof(f_3884_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_3884_2,plain,
    ! [U_15270,U_15269] :
      ( 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_15270),U_15269)
      | ? [U_15268] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15270),U_15268))
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_15268),U_15269)) ) ),
    inference(variable_rename,[status(thm)],[f_3884_1]) ).

fof(f_3884_3,plain,
    ! [U_15270,U_15269] :
      ( 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_15270),U_15269)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15270),sK372(U_15270,U_15269)))
        & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK372(U_15270,U_15269)),U_15269)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK372]),skolemize(U_15268,sK372(U_15270,U_15269))],[f_3884_2]) ).

fof(f_3884_4,plain,
    ( ! [U_15270,U_15269] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15270),sK372(U_15270,U_15269)))
        | ~ sP1031(U_15270,U_15269) )
    & ! [U_15270,U_15269] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK372(U_15270,U_15269)),U_15269))
        | ~ sP1031(U_15270,U_15269) )
    & ! [U_15270,U_15269] :
        ( 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_15270),U_15269)
        | sP1031(U_15270,U_15269) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1031])],[f_3884_3]) ).

cnf(f_3884_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_15270),U_15269)
    | sP1031(U_15270,U_15269) ),
    inference(clausify,[status(thm)],[f_3884_4]) ).

cnf(f_3884_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK372(U_15270,U_15269)),U_15269))
    | ~ sP1031(U_15270,U_15269) ),
    inference(clausify,[status(thm)],[f_3884_4]) ).

cnf(f_3884_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_15270),sK372(U_15270,U_15269)))
    | ~ sP1031(U_15270,U_15269) ),
    inference(clausify,[status(thm)],[f_3884_4]) ).

fof(f_3885_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_3885_2,plain,
    ! [U_15276,U_15275,U_15274] :
      ( c_Wellfounded_OwfP(U_15274,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15276,tc_fun(U_15274,tc_fun(U_15274,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_15276,tc_HOL_Obool))),U_15275))
      | ? [U_15273,U_15272] :
          ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15274,tc_HOL_Obool)),c_Predicate_ODomainP(U_15274,U_15274,hAPP(U_15275,U_15273))),c_Predicate_ORangeP(U_15274,U_15274,hAPP(U_15275,U_15272))) != c_Orderings_Obot__class_Obot(tc_fun(U_15274,tc_HOL_Obool))
          & hAPP(U_15275,U_15273) != hAPP(U_15275,U_15272) )
      | ? [U_15271] : ~ c_Wellfounded_OwfP(U_15274,hAPP(U_15275,U_15271)) ),
    inference(variable_rename,[status(thm)],[f_3885_1]) ).

fof(f_3885_3,plain,
    ! [U_15276,U_15275,U_15274] :
      ( c_Wellfounded_OwfP(U_15274,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15276,tc_fun(U_15274,tc_fun(U_15274,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_15276,tc_HOL_Obool))),U_15275))
      | ? [U_15273,U_15272] :
          ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15274,tc_HOL_Obool)),c_Predicate_ODomainP(U_15274,U_15274,hAPP(U_15275,U_15273))),c_Predicate_ORangeP(U_15274,U_15274,hAPP(U_15275,U_15272))) != c_Orderings_Obot__class_Obot(tc_fun(U_15274,tc_HOL_Obool))
          & hAPP(U_15275,U_15273) != hAPP(U_15275,U_15272) )
      | ~ c_Wellfounded_OwfP(U_15274,hAPP(U_15275,sK373(U_15276,U_15275,U_15274))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK373]),skolemize(U_15271,sK373(U_15276,U_15275,U_15274))],[f_3885_2]) ).

fof(f_3885_4,plain,
    ! [U_15276,U_15275,U_15274] :
      ( c_Wellfounded_OwfP(U_15274,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15276,tc_fun(U_15274,tc_fun(U_15274,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_15276,tc_HOL_Obool))),U_15275))
      | ? [U_15272] :
          ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15274,tc_HOL_Obool)),c_Predicate_ODomainP(U_15274,U_15274,hAPP(U_15275,sK374(U_15276,U_15275,U_15274)))),c_Predicate_ORangeP(U_15274,U_15274,hAPP(U_15275,U_15272))) != c_Orderings_Obot__class_Obot(tc_fun(U_15274,tc_HOL_Obool))
          & hAPP(U_15275,sK374(U_15276,U_15275,U_15274)) != hAPP(U_15275,U_15272) )
      | ~ c_Wellfounded_OwfP(U_15274,hAPP(U_15275,sK373(U_15276,U_15275,U_15274))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK374]),skolemize(U_15273,sK374(U_15276,U_15275,U_15274))],[f_3885_3]) ).

fof(f_3885_5,plain,
    ! [U_15276,U_15275,U_15274] :
      ( c_Wellfounded_OwfP(U_15274,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15276,tc_fun(U_15274,tc_fun(U_15274,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_15276,tc_HOL_Obool))),U_15275))
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15274,tc_HOL_Obool)),c_Predicate_ODomainP(U_15274,U_15274,hAPP(U_15275,sK374(U_15276,U_15275,U_15274)))),c_Predicate_ORangeP(U_15274,U_15274,hAPP(U_15275,sK375(U_15276,U_15275,U_15274)))) != c_Orderings_Obot__class_Obot(tc_fun(U_15274,tc_HOL_Obool))
        & hAPP(U_15275,sK374(U_15276,U_15275,U_15274)) != hAPP(U_15275,sK375(U_15276,U_15275,U_15274)) )
      | ~ c_Wellfounded_OwfP(U_15274,hAPP(U_15275,sK373(U_15276,U_15275,U_15274))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK375]),skolemize(U_15272,sK375(U_15276,U_15275,U_15274))],[f_3885_4]) ).

fof(f_3885_6,plain,
    ( ! [U_15274,U_15275,U_15276] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15274,tc_HOL_Obool)),c_Predicate_ODomainP(U_15274,U_15274,hAPP(U_15275,sK374(U_15276,U_15275,U_15274)))),c_Predicate_ORangeP(U_15274,U_15274,hAPP(U_15275,sK375(U_15276,U_15275,U_15274)))) != c_Orderings_Obot__class_Obot(tc_fun(U_15274,tc_HOL_Obool))
        | ~ sP1032(U_15274,U_15275,U_15276) )
    & ! [U_15274,U_15275,U_15276] :
        ( hAPP(U_15275,sK374(U_15276,U_15275,U_15274)) != hAPP(U_15275,sK375(U_15276,U_15275,U_15274))
        | ~ sP1032(U_15274,U_15275,U_15276) )
    & ! [U_15274,U_15275,U_15276] :
        ( c_Wellfounded_OwfP(U_15274,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15276,tc_fun(U_15274,tc_fun(U_15274,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_15276,tc_HOL_Obool))),U_15275))
        | sP1032(U_15274,U_15275,U_15276)
        | ~ c_Wellfounded_OwfP(U_15274,hAPP(U_15275,sK373(U_15276,U_15275,U_15274))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1032])],[f_3885_5]) ).

cnf(f_3885_7,plain,
    ( c_Wellfounded_OwfP(U_15274,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15276,tc_fun(U_15274,tc_fun(U_15274,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_15276,tc_HOL_Obool))),U_15275))
    | sP1032(U_15274,U_15275,U_15276)
    | ~ c_Wellfounded_OwfP(U_15274,hAPP(U_15275,sK373(U_15276,U_15275,U_15274))) ),
    inference(clausify,[status(thm)],[f_3885_6]) ).

cnf(f_3885_8,plain,
    ( hAPP(U_15275,sK374(U_15276,U_15275,U_15274)) != hAPP(U_15275,sK375(U_15276,U_15275,U_15274))
    | ~ sP1032(U_15274,U_15275,U_15276) ),
    inference(clausify,[status(thm)],[f_3885_6]) ).

cnf(f_3885_9,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15274,tc_HOL_Obool)),c_Predicate_ODomainP(U_15274,U_15274,hAPP(U_15275,sK374(U_15276,U_15275,U_15274)))),c_Predicate_ORangeP(U_15274,U_15274,hAPP(U_15275,sK375(U_15276,U_15275,U_15274)))) != c_Orderings_Obot__class_Obot(tc_fun(U_15274,tc_HOL_Obool))
    | ~ sP1032(U_15274,U_15275,U_15276) ),
    inference(clausify,[status(thm)],[f_3885_6]) ).

fof(f_3886_1,plain,
    ! [V_ts_2,V_Ga_2,T_b] :
      ( ( c_Hoare__Mirabelle_Ohoare__valids(T_b,V_Ga_2,V_ts_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_ts_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_ts_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_ts_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_hoare__valids__def]) ).

fof(f_3886_2,plain,
    ! [U_15285,U_15284,U_15283] :
      ( ( c_Hoare__Mirabelle_Ohoare__valids(U_15283,U_15284,U_15285)
        | ? [U_15282] :
            ( ? [U_15281] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(U_15283,U_15282,U_15281)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15283)),U_15281),U_15285)) )
            & ! [U_15280] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_15283,U_15282,U_15280)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15283)),U_15280),U_15284)) ) ) )
      & ( ! [U_15279] :
            ( ! [U_15278] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_15283,U_15279,U_15278)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15283)),U_15278),U_15285)) )
            | ? [U_15277] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(U_15283,U_15279,U_15277)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15283)),U_15277),U_15284)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_15283,U_15284,U_15285) ) ),
    inference(variable_rename,[status(thm)],[f_3886_1]) ).

fof(f_3886_3,plain,
    ( ! [U_15291,U_15289,U_15287] :
        ( c_Hoare__Mirabelle_Ohoare__valids(U_15287,U_15289,U_15291)
        | ? [U_15282] :
            ( ? [U_15281] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(U_15287,U_15282,U_15281)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15287)),U_15281),U_15291)) )
            & ! [U_15280] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_15287,U_15282,U_15280)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15287)),U_15280),U_15289)) ) ) )
    & ! [U_15290,U_15288,U_15286] :
        ( ! [U_15279] :
            ( ! [U_15278] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_15286,U_15279,U_15278)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15286)),U_15278),U_15290)) )
            | ? [U_15277] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(U_15286,U_15279,U_15277)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15286)),U_15277),U_15288)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_15286,U_15288,U_15290) ) ),
    inference(miniscope,[status(thm)],[f_3886_2]) ).

fof(f_3886_4,plain,
    ( ! [U_15291,U_15289,U_15287] :
        ( c_Hoare__Mirabelle_Ohoare__valids(U_15287,U_15289,U_15291)
        | ? [U_15282] :
            ( ? [U_15281] :
                ( ~ c_Hoare__Mirabelle_Otriple__valid(U_15287,U_15282,U_15281)
                & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15287)),U_15281),U_15291)) )
            & ! [U_15280] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_15287,U_15282,U_15280)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15287)),U_15280),U_15289)) ) ) )
    & ! [U_15290,U_15288,U_15286] :
        ( ! [U_15279] :
            ( ! [U_15278] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_15286,U_15279,U_15278)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15286)),U_15278),U_15290)) )
            | ( ~ c_Hoare__Mirabelle_Otriple__valid(U_15286,U_15279,sK376(U_15290,U_15288,U_15286,U_15279))
              & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15286)),sK376(U_15290,U_15288,U_15286,U_15279)),U_15288)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_15286,U_15288,U_15290) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK376]),skolemize(U_15277,sK376(U_15290,U_15288,U_15286,U_15279))],[f_3886_3]) ).

fof(f_3886_5,plain,
    ( ! [U_15291,U_15289,U_15287] :
        ( c_Hoare__Mirabelle_Ohoare__valids(U_15287,U_15289,U_15291)
        | ( ? [U_15281] :
              ( ~ c_Hoare__Mirabelle_Otriple__valid(U_15287,sK377(U_15291,U_15289,U_15287),U_15281)
              & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15287)),U_15281),U_15291)) )
          & ! [U_15280] :
              ( c_Hoare__Mirabelle_Otriple__valid(U_15287,sK377(U_15291,U_15289,U_15287),U_15280)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15287)),U_15280),U_15289)) ) ) )
    & ! [U_15290,U_15288,U_15286] :
        ( ! [U_15279] :
            ( ! [U_15278] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_15286,U_15279,U_15278)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15286)),U_15278),U_15290)) )
            | ( ~ c_Hoare__Mirabelle_Otriple__valid(U_15286,U_15279,sK376(U_15290,U_15288,U_15286,U_15279))
              & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15286)),sK376(U_15290,U_15288,U_15286,U_15279)),U_15288)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_15286,U_15288,U_15290) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK377]),skolemize(U_15282,sK377(U_15291,U_15289,U_15287))],[f_3886_4]) ).

fof(f_3886_6,plain,
    ( ! [U_15291,U_15289,U_15287] :
        ( c_Hoare__Mirabelle_Ohoare__valids(U_15287,U_15289,U_15291)
        | ( ~ c_Hoare__Mirabelle_Otriple__valid(U_15287,sK377(U_15291,U_15289,U_15287),sK378(U_15291,U_15289,U_15287))
          & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15287)),sK378(U_15291,U_15289,U_15287)),U_15291))
          & ! [U_15280] :
              ( c_Hoare__Mirabelle_Otriple__valid(U_15287,sK377(U_15291,U_15289,U_15287),U_15280)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15287)),U_15280),U_15289)) ) ) )
    & ! [U_15290,U_15288,U_15286] :
        ( ! [U_15279] :
            ( ! [U_15278] :
                ( c_Hoare__Mirabelle_Otriple__valid(U_15286,U_15279,U_15278)
                | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15286)),U_15278),U_15290)) )
            | ( ~ c_Hoare__Mirabelle_Otriple__valid(U_15286,U_15279,sK376(U_15290,U_15288,U_15286,U_15279))
              & hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15286)),sK376(U_15290,U_15288,U_15286,U_15279)),U_15288)) ) )
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_15286,U_15288,U_15290) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK378]),skolemize(U_15281,sK378(U_15291,U_15289,U_15287))],[f_3886_5]) ).

fof(f_3886_7,plain,
    ( ! [U_15291,U_15287,U_15280,U_15289] :
        ( ~ c_Hoare__Mirabelle_Otriple__valid(U_15287,sK377(U_15291,U_15289,U_15287),sK378(U_15291,U_15289,U_15287))
        | ~ sP1034(U_15291,U_15287,U_15280,U_15289) )
    & ! [U_15291,U_15287,U_15280,U_15289] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15287)),sK378(U_15291,U_15289,U_15287)),U_15291))
        | ~ sP1034(U_15291,U_15287,U_15280,U_15289) )
    & ! [U_15291,U_15287,U_15280,U_15289] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_15287,sK377(U_15291,U_15289,U_15287),U_15280)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15287)),U_15280),U_15289))
        | ~ sP1034(U_15291,U_15287,U_15280,U_15289) )
    & ! [U_15279,U_15286,U_15290,U_15288] :
        ( ~ c_Hoare__Mirabelle_Otriple__valid(U_15286,U_15279,sK376(U_15290,U_15288,U_15286,U_15279))
        | ~ sP1033(U_15279,U_15286,U_15290,U_15288) )
    & ! [U_15279,U_15286,U_15290,U_15288] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15286)),sK376(U_15290,U_15288,U_15286,U_15279)),U_15288))
        | ~ sP1033(U_15279,U_15286,U_15290,U_15288) )
    & ! [U_15291,U_15287,U_15280,U_15289] :
        ( c_Hoare__Mirabelle_Ohoare__valids(U_15287,U_15289,U_15291)
        | sP1034(U_15291,U_15287,U_15280,U_15289) )
    & ! [U_15278,U_15279,U_15286,U_15290,U_15288] :
        ( c_Hoare__Mirabelle_Otriple__valid(U_15286,U_15279,U_15278)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15286)),U_15278),U_15290))
        | sP1033(U_15279,U_15286,U_15290,U_15288)
        | ~ c_Hoare__Mirabelle_Ohoare__valids(U_15286,U_15288,U_15290) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1033,sP1034])],[f_3886_6]) ).

cnf(f_3886_8,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_15286,U_15279,U_15278)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15286)),U_15278),U_15290))
    | sP1033(U_15279,U_15286,U_15290,U_15288)
    | ~ c_Hoare__Mirabelle_Ohoare__valids(U_15286,U_15288,U_15290) ),
    inference(clausify,[status(thm)],[f_3886_7]) ).

cnf(f_3886_9,plain,
    ( c_Hoare__Mirabelle_Ohoare__valids(U_15287,U_15289,U_15291)
    | sP1034(U_15291,U_15287,U_15280,U_15289) ),
    inference(clausify,[status(thm)],[f_3886_7]) ).

cnf(f_3886_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15286)),sK376(U_15290,U_15288,U_15286,U_15279)),U_15288))
    | ~ sP1033(U_15279,U_15286,U_15290,U_15288) ),
    inference(clausify,[status(thm)],[f_3886_7]) ).

cnf(f_3886_11,plain,
    ( ~ c_Hoare__Mirabelle_Otriple__valid(U_15286,U_15279,sK376(U_15290,U_15288,U_15286,U_15279))
    | ~ sP1033(U_15279,U_15286,U_15290,U_15288) ),
    inference(clausify,[status(thm)],[f_3886_7]) ).

cnf(f_3886_12,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(U_15287,sK377(U_15291,U_15289,U_15287),U_15280)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15287)),U_15280),U_15289))
    | ~ sP1034(U_15291,U_15287,U_15280,U_15289) ),
    inference(clausify,[status(thm)],[f_3886_7]) ).

cnf(f_3886_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(U_15287)),sK378(U_15291,U_15289,U_15287)),U_15291))
    | ~ sP1034(U_15291,U_15287,U_15280,U_15289) ),
    inference(clausify,[status(thm)],[f_3886_7]) ).

cnf(f_3886_14,plain,
    ( ~ c_Hoare__Mirabelle_Otriple__valid(U_15287,sK377(U_15291,U_15289,U_15287),sK378(U_15291,U_15289,U_15287))
    | ~ sP1034(U_15291,U_15287,U_15280,U_15289) ),
    inference(clausify,[status(thm)],[f_3886_7]) ).

fof(f_3887_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_3887_2,plain,
    ! [U_15295,U_15294,U_15293] :
      ( ? [U_15292] : hAPP(U_15295,U_15292) = c_Option_Ooption_ONone(U_15294)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15293),c_Orderings_Otop__class_Otop(tc_fun(U_15293,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15293),c_Map_Odom(U_15293,U_15294,U_15295))) ),
    inference(variable_rename,[status(thm)],[f_3887_1]) ).

fof(f_3887_3,plain,
    ! [U_15295,U_15294,U_15293] :
      ( hAPP(U_15295,sK379(U_15295,U_15294,U_15293)) = c_Option_Ooption_ONone(U_15294)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15293),c_Orderings_Otop__class_Otop(tc_fun(U_15293,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15293),c_Map_Odom(U_15293,U_15294,U_15295))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK379]),skolemize(U_15292,sK379(U_15295,U_15294,U_15293))],[f_3887_2]) ).

fof(f_3887_4,plain,
    ! [U_15294,U_15295,U_15293] :
      ( hAPP(U_15295,sK379(U_15295,U_15294,U_15293)) = c_Option_Ooption_ONone(U_15294)
      | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15293),c_Orderings_Otop__class_Otop(tc_fun(U_15293,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15293),c_Map_Odom(U_15293,U_15294,U_15295))) ),
    inference(definitional_conversion,[status(esa)],[f_3887_3]) ).

cnf(f_3887_5,plain,
    ( hAPP(U_15295,sK379(U_15295,U_15294,U_15293)) = c_Option_Ooption_ONone(U_15294)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_15293),c_Orderings_Otop__class_Otop(tc_fun(U_15293,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15293),c_Map_Odom(U_15293,U_15294,U_15295))) ),
    inference(clausify,[status(thm)],[f_3887_4]) ).

fof(f_3888_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_3888_2,plain,
    ! [U_15301,U_15300,U_15299,U_15298,U_15297,U_15296] : hAPP(c_Set_Ovimage(U_15296,tc_prod(U_15297,U_15298),U_15299),hAPP(hAPP(c_Product__Type_OSigma(U_15297,U_15298),U_15300),hAPP(c_COMBK(tc_fun(U_15298,tc_HOL_Obool),U_15297),U_15301))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15296,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_15296,U_15297,hAPP(c_Fun_Ocomp(tc_prod(U_15297,U_15298),U_15297,U_15296,c_Product__Type_Ofst(U_15297,U_15298)),U_15299)),U_15300)),hAPP(c_Set_Ovimage(U_15296,U_15298,hAPP(c_Fun_Ocomp(tc_prod(U_15297,U_15298),U_15298,U_15296,c_Product__Type_Osnd(U_15297,U_15298)),U_15299)),U_15301)),
    inference(variable_rename,[status(thm)],[f_3888_1]) ).

fof(f_3888_3,plain,
    ! [U_15296,U_15297,U_15298,U_15299,U_15300,U_15301] : hAPP(c_Set_Ovimage(U_15296,tc_prod(U_15297,U_15298),U_15299),hAPP(hAPP(c_Product__Type_OSigma(U_15297,U_15298),U_15300),hAPP(c_COMBK(tc_fun(U_15298,tc_HOL_Obool),U_15297),U_15301))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15296,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_15296,U_15297,hAPP(c_Fun_Ocomp(tc_prod(U_15297,U_15298),U_15297,U_15296,c_Product__Type_Ofst(U_15297,U_15298)),U_15299)),U_15300)),hAPP(c_Set_Ovimage(U_15296,U_15298,hAPP(c_Fun_Ocomp(tc_prod(U_15297,U_15298),U_15298,U_15296,c_Product__Type_Osnd(U_15297,U_15298)),U_15299)),U_15301)),
    inference(definitional_conversion,[status(esa)],[f_3888_2]) ).

cnf(f_3888_4,plain,
    hAPP(c_Set_Ovimage(U_15296,tc_prod(U_15297,U_15298),U_15299),hAPP(hAPP(c_Product__Type_OSigma(U_15297,U_15298),U_15300),hAPP(c_COMBK(tc_fun(U_15298,tc_HOL_Obool),U_15297),U_15301))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15296,tc_HOL_Obool)),hAPP(c_Set_Ovimage(U_15296,U_15297,hAPP(c_Fun_Ocomp(tc_prod(U_15297,U_15298),U_15297,U_15296,c_Product__Type_Ofst(U_15297,U_15298)),U_15299)),U_15300)),hAPP(c_Set_Ovimage(U_15296,U_15298,hAPP(c_Fun_Ocomp(tc_prod(U_15297,U_15298),U_15298,U_15296,c_Product__Type_Osnd(U_15297,U_15298)),U_15299)),U_15301)),
    inference(clausify,[status(thm)],[f_3888_3]) ).

fof(f_3889_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_3889_2,plain,
    ! [U_15306,U_15305,U_15304,U_15303] :
      ( ? [U_15302] :
          ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_15304,U_15302)))
          & hBOOL(hAPP(hAPP(c_member(U_15303),U_15302),U_15305)) )
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15303,tc_Nat_Onat),U_15304),U_15305) != hAPP(c_Nat_OSuc,U_15306) ),
    inference(variable_rename,[status(thm)],[f_3889_1]) ).

fof(f_3889_3,plain,
    ! [U_15306,U_15305,U_15304,U_15303] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_15304,sK380(U_15306,U_15305,U_15304,U_15303))))
        & hBOOL(hAPP(hAPP(c_member(U_15303),sK380(U_15306,U_15305,U_15304,U_15303)),U_15305)) )
      | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15303,tc_Nat_Onat),U_15304),U_15305) != hAPP(c_Nat_OSuc,U_15306) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK380]),skolemize(U_15302,sK380(U_15306,U_15305,U_15304,U_15303))],[f_3889_2]) ).

fof(f_3889_4,plain,
    ( ! [U_15303,U_15304,U_15305,U_15306] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_15304,sK380(U_15306,U_15305,U_15304,U_15303))))
        | ~ sP1035(U_15303,U_15304,U_15305,U_15306) )
    & ! [U_15303,U_15304,U_15305,U_15306] :
        ( hBOOL(hAPP(hAPP(c_member(U_15303),sK380(U_15306,U_15305,U_15304,U_15303)),U_15305))
        | ~ sP1035(U_15303,U_15304,U_15305,U_15306) )
    & ! [U_15303,U_15304,U_15305,U_15306] :
        ( sP1035(U_15303,U_15304,U_15305,U_15306)
        | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15303,tc_Nat_Onat),U_15304),U_15305) != hAPP(c_Nat_OSuc,U_15306) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1035])],[f_3889_3]) ).

cnf(f_3889_5,plain,
    ( sP1035(U_15303,U_15304,U_15305,U_15306)
    | hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15303,tc_Nat_Onat),U_15304),U_15305) != hAPP(c_Nat_OSuc,U_15306) ),
    inference(clausify,[status(thm)],[f_3889_4]) ).

cnf(f_3889_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15303),sK380(U_15306,U_15305,U_15304,U_15303)),U_15305))
    | ~ sP1035(U_15303,U_15304,U_15305,U_15306) ),
    inference(clausify,[status(thm)],[f_3889_4]) ).

cnf(f_3889_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(U_15304,sK380(U_15306,U_15305,U_15304,U_15303))))
    | ~ sP1035(U_15303,U_15304,U_15305,U_15306) ),
    inference(clausify,[status(thm)],[f_3889_4]) ).

fof(f_3890_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_3890_2,plain,
    ! [U_15310,U_15309,U_15308,U_15307] :
      ( hAPP(c_Fun_Ocomp(U_15308,U_15308,U_15308,hAPP(U_15309,U_15310)),hAPP(U_15309,U_15310)) = hAPP(U_15309,U_15310)
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_15307,U_15308,U_15309) ),
    inference(variable_rename,[status(thm)],[f_3890_1]) ).

fof(f_3890_3,plain,
    ! [U_15310,U_15309,U_15308] :
      ( ! [U_15307] : ~ c_Finite__Set_Ofun__left__comm__idem(U_15307,U_15308,U_15309)
      | hAPP(c_Fun_Ocomp(U_15308,U_15308,U_15308,hAPP(U_15309,U_15310)),hAPP(U_15309,U_15310)) = hAPP(U_15309,U_15310) ),
    inference(miniscope,[status(thm)],[f_3890_2]) ).

fof(f_3890_4,plain,
    ! [U_15310,U_15307,U_15308,U_15309] :
      ( ~ c_Finite__Set_Ofun__left__comm__idem(U_15307,U_15308,U_15309)
      | hAPP(c_Fun_Ocomp(U_15308,U_15308,U_15308,hAPP(U_15309,U_15310)),hAPP(U_15309,U_15310)) = hAPP(U_15309,U_15310) ),
    inference(definitional_conversion,[status(esa)],[f_3890_3]) ).

cnf(f_3890_5,plain,
    ( ~ c_Finite__Set_Ofun__left__comm__idem(U_15307,U_15308,U_15309)
    | hAPP(c_Fun_Ocomp(U_15308,U_15308,U_15308,hAPP(U_15309,U_15310)),hAPP(U_15309,U_15310)) = hAPP(U_15309,U_15310) ),
    inference(clausify,[status(thm)],[f_3890_4]) ).

fof(f_3891_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_3891_2,plain,
    ! [U_15321,U_15320,U_15319,U_15318,U_15317,U_15316,U_15315,U_15314,U_15313,U_15312,U_15311] : hAPP(c_Product__Type_Omap__pair(U_15311,U_15312,U_15313,U_15314,U_15315,U_15316),hAPP(c_Product__Type_Omap__pair(U_15317,U_15311,U_15318,U_15313,U_15319,U_15320),U_15321)) = hAPP(c_Product__Type_Omap__pair(U_15317,U_15312,U_15318,U_15314,hAPP(c_Fun_Ocomp(U_15311,U_15312,U_15317,U_15315),U_15319),hAPP(c_Fun_Ocomp(U_15313,U_15314,U_15318,U_15316),U_15320)),U_15321),
    inference(variable_rename,[status(thm)],[f_3891_1]) ).

fof(f_3891_3,plain,
    ! [U_15311,U_15312,U_15313,U_15314,U_15315,U_15316,U_15317,U_15318,U_15319,U_15320,U_15321] : hAPP(c_Product__Type_Omap__pair(U_15311,U_15312,U_15313,U_15314,U_15315,U_15316),hAPP(c_Product__Type_Omap__pair(U_15317,U_15311,U_15318,U_15313,U_15319,U_15320),U_15321)) = hAPP(c_Product__Type_Omap__pair(U_15317,U_15312,U_15318,U_15314,hAPP(c_Fun_Ocomp(U_15311,U_15312,U_15317,U_15315),U_15319),hAPP(c_Fun_Ocomp(U_15313,U_15314,U_15318,U_15316),U_15320)),U_15321),
    inference(definitional_conversion,[status(esa)],[f_3891_2]) ).

cnf(f_3891_4,plain,
    hAPP(c_Product__Type_Omap__pair(U_15311,U_15312,U_15313,U_15314,U_15315,U_15316),hAPP(c_Product__Type_Omap__pair(U_15317,U_15311,U_15318,U_15313,U_15319,U_15320),U_15321)) = hAPP(c_Product__Type_Omap__pair(U_15317,U_15312,U_15318,U_15314,hAPP(c_Fun_Ocomp(U_15311,U_15312,U_15317,U_15315),U_15319),hAPP(c_Fun_Ocomp(U_15313,U_15314,U_15318,U_15316),U_15320)),U_15321),
    inference(clausify,[status(thm)],[f_3891_3]) ).

fof(f_3892_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_3892_2,plain,
    ! [U_15331,U_15330,U_15329,U_15328,U_15327,U_15326,U_15325,U_15324,U_15323,U_15322] : c_Product__Type_Omap__pair(U_15322,U_15323,U_15324,U_15325,hAPP(c_Fun_Ocomp(U_15326,U_15323,U_15322,U_15327),U_15328),hAPP(c_Fun_Ocomp(U_15329,U_15325,U_15324,U_15330),U_15331)) = hAPP(c_Fun_Ocomp(tc_prod(U_15326,U_15329),tc_prod(U_15323,U_15325),tc_prod(U_15322,U_15324),c_Product__Type_Omap__pair(U_15326,U_15323,U_15329,U_15325,U_15327,U_15330)),c_Product__Type_Omap__pair(U_15322,U_15326,U_15324,U_15329,U_15328,U_15331)),
    inference(variable_rename,[status(thm)],[f_3892_1]) ).

fof(f_3892_3,plain,
    ! [U_15322,U_15323,U_15324,U_15325,U_15326,U_15327,U_15328,U_15329,U_15330,U_15331] : c_Product__Type_Omap__pair(U_15322,U_15323,U_15324,U_15325,hAPP(c_Fun_Ocomp(U_15326,U_15323,U_15322,U_15327),U_15328),hAPP(c_Fun_Ocomp(U_15329,U_15325,U_15324,U_15330),U_15331)) = hAPP(c_Fun_Ocomp(tc_prod(U_15326,U_15329),tc_prod(U_15323,U_15325),tc_prod(U_15322,U_15324),c_Product__Type_Omap__pair(U_15326,U_15323,U_15329,U_15325,U_15327,U_15330)),c_Product__Type_Omap__pair(U_15322,U_15326,U_15324,U_15329,U_15328,U_15331)),
    inference(definitional_conversion,[status(esa)],[f_3892_2]) ).

cnf(f_3892_4,plain,
    c_Product__Type_Omap__pair(U_15322,U_15323,U_15324,U_15325,hAPP(c_Fun_Ocomp(U_15326,U_15323,U_15322,U_15327),U_15328),hAPP(c_Fun_Ocomp(U_15329,U_15325,U_15324,U_15330),U_15331)) = hAPP(c_Fun_Ocomp(tc_prod(U_15326,U_15329),tc_prod(U_15323,U_15325),tc_prod(U_15322,U_15324),c_Product__Type_Omap__pair(U_15326,U_15323,U_15329,U_15325,U_15327,U_15330)),c_Product__Type_Omap__pair(U_15322,U_15326,U_15324,U_15329,U_15328,U_15331)),
    inference(clausify,[status(thm)],[f_3892_3]) ).

fof(f_3893_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_3893_2,plain,
    ! [U_15341,U_15340,U_15339,U_15338,U_15337,U_15336,U_15335,U_15334,U_15333,U_15332] : hAPP(c_Fun_Ocomp(tc_prod(U_15332,U_15333),tc_prod(U_15334,U_15335),tc_prod(U_15336,U_15337),c_Product__Type_Omap__pair(U_15332,U_15334,U_15333,U_15335,U_15338,U_15339)),c_Product__Type_Omap__pair(U_15336,U_15332,U_15337,U_15333,U_15340,U_15341)) = c_Product__Type_Omap__pair(U_15336,U_15334,U_15337,U_15335,hAPP(c_Fun_Ocomp(U_15332,U_15334,U_15336,U_15338),U_15340),hAPP(c_Fun_Ocomp(U_15333,U_15335,U_15337,U_15339),U_15341)),
    inference(variable_rename,[status(thm)],[f_3893_1]) ).

fof(f_3893_3,plain,
    ! [U_15332,U_15333,U_15334,U_15335,U_15336,U_15337,U_15338,U_15339,U_15340,U_15341] : hAPP(c_Fun_Ocomp(tc_prod(U_15332,U_15333),tc_prod(U_15334,U_15335),tc_prod(U_15336,U_15337),c_Product__Type_Omap__pair(U_15332,U_15334,U_15333,U_15335,U_15338,U_15339)),c_Product__Type_Omap__pair(U_15336,U_15332,U_15337,U_15333,U_15340,U_15341)) = c_Product__Type_Omap__pair(U_15336,U_15334,U_15337,U_15335,hAPP(c_Fun_Ocomp(U_15332,U_15334,U_15336,U_15338),U_15340),hAPP(c_Fun_Ocomp(U_15333,U_15335,U_15337,U_15339),U_15341)),
    inference(definitional_conversion,[status(esa)],[f_3893_2]) ).

cnf(f_3893_4,plain,
    hAPP(c_Fun_Ocomp(tc_prod(U_15332,U_15333),tc_prod(U_15334,U_15335),tc_prod(U_15336,U_15337),c_Product__Type_Omap__pair(U_15332,U_15334,U_15333,U_15335,U_15338,U_15339)),c_Product__Type_Omap__pair(U_15336,U_15332,U_15337,U_15333,U_15340,U_15341)) = c_Product__Type_Omap__pair(U_15336,U_15334,U_15337,U_15335,hAPP(c_Fun_Ocomp(U_15332,U_15334,U_15336,U_15338),U_15340),hAPP(c_Fun_Ocomp(U_15333,U_15335,U_15337,U_15339),U_15341)),
    inference(clausify,[status(thm)],[f_3893_3]) ).

fof(f_3894_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_3894_2,plain,
    ! [U_15347,U_15346,U_15345,U_15344,U_15343,U_15342] :
      ( c_Fun_Oinj__on(U_15344,U_15343,U_15345,hAPP(c_Set_Oimage(U_15342,U_15344,U_15346),U_15347))
      | ~ c_Fun_Oinj__on(U_15342,U_15343,hAPP(c_Fun_Ocomp(U_15344,U_15343,U_15342,U_15345),U_15346),U_15347) ),
    inference(variable_rename,[status(thm)],[f_3894_1]) ).

fof(f_3894_3,plain,
    ! [U_15343,U_15342,U_15344,U_15345,U_15346,U_15347] :
      ( c_Fun_Oinj__on(U_15344,U_15343,U_15345,hAPP(c_Set_Oimage(U_15342,U_15344,U_15346),U_15347))
      | ~ c_Fun_Oinj__on(U_15342,U_15343,hAPP(c_Fun_Ocomp(U_15344,U_15343,U_15342,U_15345),U_15346),U_15347) ),
    inference(definitional_conversion,[status(esa)],[f_3894_2]) ).

cnf(f_3894_4,plain,
    ( c_Fun_Oinj__on(U_15344,U_15343,U_15345,hAPP(c_Set_Oimage(U_15342,U_15344,U_15346),U_15347))
    | ~ c_Fun_Oinj__on(U_15342,U_15343,hAPP(c_Fun_Ocomp(U_15344,U_15343,U_15342,U_15345),U_15346),U_15347) ),
    inference(clausify,[status(thm)],[f_3894_3]) ).

fof(f_3895_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_3895_2,plain,
    ! [U_15353,U_15352,U_15351,U_15350,U_15349,U_15348] :
      ( c_Fun_Oinj__on(U_15348,U_15352,hAPP(c_Fun_Ocomp(U_15349,U_15352,U_15348,U_15353),U_15350),U_15351)
      | ~ c_Fun_Oinj__on(U_15349,U_15352,U_15353,hAPP(c_Set_Oimage(U_15348,U_15349,U_15350),U_15351))
      | ~ c_Fun_Oinj__on(U_15348,U_15349,U_15350,U_15351) ),
    inference(variable_rename,[status(thm)],[f_3895_1]) ).

fof(f_3895_3,plain,
    ! [U_15348,U_15349,U_15350,U_15351,U_15352,U_15353] :
      ( c_Fun_Oinj__on(U_15348,U_15352,hAPP(c_Fun_Ocomp(U_15349,U_15352,U_15348,U_15353),U_15350),U_15351)
      | ~ c_Fun_Oinj__on(U_15349,U_15352,U_15353,hAPP(c_Set_Oimage(U_15348,U_15349,U_15350),U_15351))
      | ~ c_Fun_Oinj__on(U_15348,U_15349,U_15350,U_15351) ),
    inference(definitional_conversion,[status(esa)],[f_3895_2]) ).

cnf(f_3895_4,plain,
    ( c_Fun_Oinj__on(U_15348,U_15352,hAPP(c_Fun_Ocomp(U_15349,U_15352,U_15348,U_15353),U_15350),U_15351)
    | ~ c_Fun_Oinj__on(U_15349,U_15352,U_15353,hAPP(c_Set_Oimage(U_15348,U_15349,U_15350),U_15351))
    | ~ c_Fun_Oinj__on(U_15348,U_15349,U_15350,U_15351) ),
    inference(clausify,[status(thm)],[f_3895_3]) ).

fof(f_3896_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_3896_2,plain,
    ! [U_15359,U_15358,U_15357,U_15356,U_15355,U_15354] :
      ( ( ( c_Fun_Oinj__on(U_15355,U_15358,U_15359,hAPP(c_Set_Oimage(U_15354,U_15355,U_15356),U_15357))
          | ~ c_Fun_Oinj__on(U_15354,U_15358,hAPP(c_Fun_Ocomp(U_15355,U_15358,U_15354,U_15359),U_15356),U_15357) )
        & ( c_Fun_Oinj__on(U_15354,U_15358,hAPP(c_Fun_Ocomp(U_15355,U_15358,U_15354,U_15359),U_15356),U_15357)
          | ~ c_Fun_Oinj__on(U_15355,U_15358,U_15359,hAPP(c_Set_Oimage(U_15354,U_15355,U_15356),U_15357)) ) )
      | ~ c_Fun_Oinj__on(U_15354,U_15355,U_15356,U_15357) ),
    inference(variable_rename,[status(thm)],[f_3896_1]) ).

fof(f_3896_3,plain,
    ( ! [U_15354,U_15355,U_15356,U_15357,U_15358,U_15359] :
        ( c_Fun_Oinj__on(U_15355,U_15358,U_15359,hAPP(c_Set_Oimage(U_15354,U_15355,U_15356),U_15357))
        | ~ c_Fun_Oinj__on(U_15354,U_15358,hAPP(c_Fun_Ocomp(U_15355,U_15358,U_15354,U_15359),U_15356),U_15357)
        | ~ sP1036(U_15354,U_15355,U_15356,U_15357,U_15358,U_15359) )
    & ! [U_15354,U_15355,U_15356,U_15357,U_15358,U_15359] :
        ( c_Fun_Oinj__on(U_15354,U_15358,hAPP(c_Fun_Ocomp(U_15355,U_15358,U_15354,U_15359),U_15356),U_15357)
        | ~ c_Fun_Oinj__on(U_15355,U_15358,U_15359,hAPP(c_Set_Oimage(U_15354,U_15355,U_15356),U_15357))
        | ~ sP1036(U_15354,U_15355,U_15356,U_15357,U_15358,U_15359) )
    & ! [U_15354,U_15355,U_15356,U_15357,U_15358,U_15359] :
        ( sP1036(U_15354,U_15355,U_15356,U_15357,U_15358,U_15359)
        | ~ c_Fun_Oinj__on(U_15354,U_15355,U_15356,U_15357) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1036])],[f_3896_2]) ).

cnf(f_3896_4,plain,
    ( sP1036(U_15354,U_15355,U_15356,U_15357,U_15358,U_15359)
    | ~ c_Fun_Oinj__on(U_15354,U_15355,U_15356,U_15357) ),
    inference(clausify,[status(thm)],[f_3896_3]) ).

cnf(f_3896_5,plain,
    ( c_Fun_Oinj__on(U_15354,U_15358,hAPP(c_Fun_Ocomp(U_15355,U_15358,U_15354,U_15359),U_15356),U_15357)
    | ~ c_Fun_Oinj__on(U_15355,U_15358,U_15359,hAPP(c_Set_Oimage(U_15354,U_15355,U_15356),U_15357))
    | ~ sP1036(U_15354,U_15355,U_15356,U_15357,U_15358,U_15359) ),
    inference(clausify,[status(thm)],[f_3896_3]) ).

cnf(f_3896_6,plain,
    ( c_Fun_Oinj__on(U_15355,U_15358,U_15359,hAPP(c_Set_Oimage(U_15354,U_15355,U_15356),U_15357))
    | ~ c_Fun_Oinj__on(U_15354,U_15358,hAPP(c_Fun_Ocomp(U_15355,U_15358,U_15354,U_15359),U_15356),U_15357)
    | ~ sP1036(U_15354,U_15355,U_15356,U_15357,U_15358,U_15359) ),
    inference(clausify,[status(thm)],[f_3896_3]) ).

fof(f_3897_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_3897_2,plain,
    ! [U_15364,U_15363,U_15362,U_15361,U_15360] :
      ( c_Fun_Oinj__on(U_15363,U_15361,hAPP(c_Fun_Ocomp(U_15360,U_15361,U_15363,U_15362),U_15364),c_Orderings_Otop__class_Otop(tc_fun(U_15363,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_15363,U_15360,U_15364,c_Orderings_Otop__class_Otop(tc_fun(U_15363,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_15360,U_15361,U_15362,c_Orderings_Otop__class_Otop(tc_fun(U_15360,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_3897_1]) ).

fof(f_3897_3,plain,
    ! [U_15363,U_15364,U_15360,U_15362,U_15361] :
      ( c_Fun_Oinj__on(U_15363,U_15361,hAPP(c_Fun_Ocomp(U_15360,U_15361,U_15363,U_15362),U_15364),c_Orderings_Otop__class_Otop(tc_fun(U_15363,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_15363,U_15360,U_15364,c_Orderings_Otop__class_Otop(tc_fun(U_15363,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_15360,U_15361,U_15362,c_Orderings_Otop__class_Otop(tc_fun(U_15360,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_3897_2]) ).

cnf(f_3897_4,plain,
    ( c_Fun_Oinj__on(U_15363,U_15361,hAPP(c_Fun_Ocomp(U_15360,U_15361,U_15363,U_15362),U_15364),c_Orderings_Otop__class_Otop(tc_fun(U_15363,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_15363,U_15360,U_15364,c_Orderings_Otop__class_Otop(tc_fun(U_15363,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_15360,U_15361,U_15362,c_Orderings_Otop__class_Otop(tc_fun(U_15360,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_3897_3]) ).

fof(f_3898_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_3898_2,plain,
    ! [U_15370,U_15369,U_15368,U_15367,U_15366,U_15365] :
      ( c_Fun_Oinj__on(U_15365,U_15367,U_15369,U_15370)
      | ~ c_Fun_Oinj__on(U_15365,U_15366,hAPP(c_Fun_Ocomp(U_15367,U_15366,U_15365,U_15368),U_15369),U_15370) ),
    inference(variable_rename,[status(thm)],[f_3898_1]) ).

fof(f_3898_3,plain,
    ! [U_15367,U_15365,U_15366,U_15368,U_15369,U_15370] :
      ( c_Fun_Oinj__on(U_15365,U_15367,U_15369,U_15370)
      | ~ c_Fun_Oinj__on(U_15365,U_15366,hAPP(c_Fun_Ocomp(U_15367,U_15366,U_15365,U_15368),U_15369),U_15370) ),
    inference(definitional_conversion,[status(esa)],[f_3898_2]) ).

cnf(f_3898_4,plain,
    ( c_Fun_Oinj__on(U_15365,U_15367,U_15369,U_15370)
    | ~ c_Fun_Oinj__on(U_15365,U_15366,hAPP(c_Fun_Ocomp(U_15367,U_15366,U_15365,U_15368),U_15369),U_15370) ),
    inference(clausify,[status(thm)],[f_3898_3]) ).

fof(f_3899_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_3899_2,plain,
    ! [U_15373,U_15372,U_15371] : hAPP(c_Fun_Ocomp(U_15371,U_15371,U_15372,c_Fun_Oid(U_15371)),U_15373) = U_15373,
    inference(variable_rename,[status(thm)],[f_3899_1]) ).

fof(f_3899_3,plain,
    ! [U_15373,U_15372,U_15371] : hAPP(c_Fun_Ocomp(U_15371,U_15371,U_15372,c_Fun_Oid(U_15371)),U_15373) = U_15373,
    inference(definitional_conversion,[status(esa)],[f_3899_2]) ).

cnf(f_3899_4,plain,
    hAPP(c_Fun_Ocomp(U_15371,U_15371,U_15372,c_Fun_Oid(U_15371)),U_15373) = U_15373,
    inference(clausify,[status(thm)],[f_3899_3]) ).

fof(f_3900_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_3900_2,plain,
    ! [U_15376,U_15375,U_15374] : hAPP(c_Fun_Ocomp(U_15374,U_15375,U_15374,U_15376),c_Fun_Oid(U_15374)) = U_15376,
    inference(variable_rename,[status(thm)],[f_3900_1]) ).

fof(f_3900_3,plain,
    ! [U_15374,U_15375,U_15376] : hAPP(c_Fun_Ocomp(U_15374,U_15375,U_15374,U_15376),c_Fun_Oid(U_15374)) = U_15376,
    inference(definitional_conversion,[status(esa)],[f_3900_2]) ).

cnf(f_3900_4,plain,
    hAPP(c_Fun_Ocomp(U_15374,U_15375,U_15374,U_15376),c_Fun_Oid(U_15374)) = U_15376,
    inference(clausify,[status(thm)],[f_3900_3]) ).

fof(f_3901_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_3901_2,plain,
    ! [U_15383,U_15382,U_15381,U_15380,U_15379,U_15378,U_15377] :
      ( hAPP(U_15380,hAPP(U_15381,U_15383)) = hAPP(U_15382,U_15383)
      | hAPP(c_Fun_Ocomp(U_15377,U_15378,U_15379,U_15380),U_15381) != hAPP(c_Fun_Ocomp(U_15378,U_15378,U_15379,c_Fun_Oid(U_15378)),U_15382) ),
    inference(variable_rename,[status(thm)],[f_3901_1]) ).

fof(f_3901_3,plain,
    ! [U_15383,U_15382,U_15381,U_15380] :
      ( ! [U_15379,U_15378,U_15377] : hAPP(c_Fun_Ocomp(U_15377,U_15378,U_15379,U_15380),U_15381) != hAPP(c_Fun_Ocomp(U_15378,U_15378,U_15379,c_Fun_Oid(U_15378)),U_15382)
      | hAPP(U_15380,hAPP(U_15381,U_15383)) = hAPP(U_15382,U_15383) ),
    inference(miniscope,[status(thm)],[f_3901_2]) ).

fof(f_3901_4,plain,
    ! [U_15377,U_15378,U_15379,U_15380,U_15381,U_15382,U_15383] :
      ( hAPP(c_Fun_Ocomp(U_15377,U_15378,U_15379,U_15380),U_15381) != hAPP(c_Fun_Ocomp(U_15378,U_15378,U_15379,c_Fun_Oid(U_15378)),U_15382)
      | hAPP(U_15380,hAPP(U_15381,U_15383)) = hAPP(U_15382,U_15383) ),
    inference(definitional_conversion,[status(esa)],[f_3901_3]) ).

cnf(f_3901_5,plain,
    ( hAPP(c_Fun_Ocomp(U_15377,U_15378,U_15379,U_15380),U_15381) != hAPP(c_Fun_Ocomp(U_15378,U_15378,U_15379,c_Fun_Oid(U_15378)),U_15382)
    | hAPP(U_15380,hAPP(U_15381,U_15383)) = hAPP(U_15382,U_15383) ),
    inference(clausify,[status(thm)],[f_3901_4]) ).

fof(f_3902_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_3902_2,plain,
    ! [U_15389,U_15388,U_15387,U_15386,U_15385,U_15384] : hAPP(c_Set_Ovimage(U_15384,U_15385,hAPP(c_Fun_Ocomp(U_15386,U_15385,U_15384,U_15387),U_15388)),U_15389) = hAPP(c_Set_Ovimage(U_15384,U_15386,U_15388),hAPP(c_Set_Ovimage(U_15386,U_15385,U_15387),U_15389)),
    inference(variable_rename,[status(thm)],[f_3902_1]) ).

fof(f_3902_3,plain,
    ! [U_15384,U_15385,U_15386,U_15387,U_15388,U_15389] : hAPP(c_Set_Ovimage(U_15384,U_15385,hAPP(c_Fun_Ocomp(U_15386,U_15385,U_15384,U_15387),U_15388)),U_15389) = hAPP(c_Set_Ovimage(U_15384,U_15386,U_15388),hAPP(c_Set_Ovimage(U_15386,U_15385,U_15387),U_15389)),
    inference(definitional_conversion,[status(esa)],[f_3902_2]) ).

cnf(f_3902_4,plain,
    hAPP(c_Set_Ovimage(U_15384,U_15385,hAPP(c_Fun_Ocomp(U_15386,U_15385,U_15384,U_15387),U_15388)),U_15389) = hAPP(c_Set_Ovimage(U_15384,U_15386,U_15388),hAPP(c_Set_Ovimage(U_15386,U_15385,U_15387),U_15389)),
    inference(clausify,[status(thm)],[f_3902_3]) ).

fof(f_3903_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_3903_2,plain,
    ! [U_15396,U_15395,U_15394,U_15393,U_15392,U_15391,U_15390] : hAPP(c_Product__Type_Oapfst(U_15390,U_15391,U_15392,U_15393),hAPP(c_Product__Type_Oapfst(U_15394,U_15390,U_15392,U_15395),U_15396)) = hAPP(c_Product__Type_Oapfst(U_15394,U_15391,U_15392,hAPP(c_Fun_Ocomp(U_15390,U_15391,U_15394,U_15393),U_15395)),U_15396),
    inference(variable_rename,[status(thm)],[f_3903_1]) ).

fof(f_3903_3,plain,
    ! [U_15390,U_15391,U_15392,U_15393,U_15394,U_15395,U_15396] : hAPP(c_Product__Type_Oapfst(U_15390,U_15391,U_15392,U_15393),hAPP(c_Product__Type_Oapfst(U_15394,U_15390,U_15392,U_15395),U_15396)) = hAPP(c_Product__Type_Oapfst(U_15394,U_15391,U_15392,hAPP(c_Fun_Ocomp(U_15390,U_15391,U_15394,U_15393),U_15395)),U_15396),
    inference(definitional_conversion,[status(esa)],[f_3903_2]) ).

cnf(f_3903_4,plain,
    hAPP(c_Product__Type_Oapfst(U_15390,U_15391,U_15392,U_15393),hAPP(c_Product__Type_Oapfst(U_15394,U_15390,U_15392,U_15395),U_15396)) = hAPP(c_Product__Type_Oapfst(U_15394,U_15391,U_15392,hAPP(c_Fun_Ocomp(U_15390,U_15391,U_15394,U_15393),U_15395)),U_15396),
    inference(clausify,[status(thm)],[f_3903_3]) ).

fof(f_3904_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_3904_2,plain,
    ! [U_15403,U_15402,U_15401,U_15400,U_15399,U_15398,U_15397] : hAPP(c_Product__Type_Oapsnd(U_15397,U_15398,U_15399,U_15400),hAPP(c_Product__Type_Oapsnd(U_15401,U_15397,U_15399,U_15402),U_15403)) = hAPP(c_Product__Type_Oapsnd(U_15401,U_15398,U_15399,hAPP(c_Fun_Ocomp(U_15397,U_15398,U_15401,U_15400),U_15402)),U_15403),
    inference(variable_rename,[status(thm)],[f_3904_1]) ).

fof(f_3904_3,plain,
    ! [U_15398,U_15397,U_15399,U_15400,U_15401,U_15402,U_15403] : hAPP(c_Product__Type_Oapsnd(U_15397,U_15398,U_15399,U_15400),hAPP(c_Product__Type_Oapsnd(U_15401,U_15397,U_15399,U_15402),U_15403)) = hAPP(c_Product__Type_Oapsnd(U_15401,U_15398,U_15399,hAPP(c_Fun_Ocomp(U_15397,U_15398,U_15401,U_15400),U_15402)),U_15403),
    inference(definitional_conversion,[status(esa)],[f_3904_2]) ).

cnf(f_3904_4,plain,
    hAPP(c_Product__Type_Oapsnd(U_15397,U_15398,U_15399,U_15400),hAPP(c_Product__Type_Oapsnd(U_15401,U_15397,U_15399,U_15402),U_15403)) = hAPP(c_Product__Type_Oapsnd(U_15401,U_15398,U_15399,hAPP(c_Fun_Ocomp(U_15397,U_15398,U_15401,U_15400),U_15402)),U_15403),
    inference(clausify,[status(thm)],[f_3904_3]) ).

fof(f_3905_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_3905_2,plain,
    ! [U_15410,U_15409,U_15408,U_15407,U_15406,U_15405,U_15404] : hAPP(c_Fun_Ocomp(U_15404,U_15405,U_15406,U_15407),hAPP(c_Fun_Ocomp(U_15408,U_15404,U_15406,U_15409),U_15410)) = hAPP(c_Fun_Ocomp(U_15408,U_15405,U_15406,hAPP(c_Fun_Ocomp(U_15404,U_15405,U_15408,U_15407),U_15409)),U_15410),
    inference(variable_rename,[status(thm)],[f_3905_1]) ).

fof(f_3905_3,plain,
    ! [U_15404,U_15405,U_15406,U_15407,U_15408,U_15409,U_15410] : hAPP(c_Fun_Ocomp(U_15404,U_15405,U_15406,U_15407),hAPP(c_Fun_Ocomp(U_15408,U_15404,U_15406,U_15409),U_15410)) = hAPP(c_Fun_Ocomp(U_15408,U_15405,U_15406,hAPP(c_Fun_Ocomp(U_15404,U_15405,U_15408,U_15407),U_15409)),U_15410),
    inference(definitional_conversion,[status(esa)],[f_3905_2]) ).

cnf(f_3905_4,plain,
    hAPP(c_Fun_Ocomp(U_15404,U_15405,U_15406,U_15407),hAPP(c_Fun_Ocomp(U_15408,U_15404,U_15406,U_15409),U_15410)) = hAPP(c_Fun_Ocomp(U_15408,U_15405,U_15406,hAPP(c_Fun_Ocomp(U_15404,U_15405,U_15408,U_15407),U_15409)),U_15410),
    inference(clausify,[status(thm)],[f_3905_3]) ).

fof(f_3906_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_3906_2,plain,
    ! [U_15416,U_15415,U_15414,U_15413,U_15412,U_15411] : hAPP(hAPP(c_Fun_Ocomp(U_15411,U_15412,U_15413,U_15414),U_15415),U_15416) = hAPP(U_15414,hAPP(U_15415,U_15416)),
    inference(variable_rename,[status(thm)],[f_3906_1]) ).

fof(f_3906_3,plain,
    ! [U_15411,U_15412,U_15413,U_15414,U_15415,U_15416] : hAPP(hAPP(c_Fun_Ocomp(U_15411,U_15412,U_15413,U_15414),U_15415),U_15416) = hAPP(U_15414,hAPP(U_15415,U_15416)),
    inference(definitional_conversion,[status(esa)],[f_3906_2]) ).

cnf(f_3906_4,plain,
    hAPP(hAPP(c_Fun_Ocomp(U_15411,U_15412,U_15413,U_15414),U_15415),U_15416) = hAPP(U_15414,hAPP(U_15415,U_15416)),
    inference(clausify,[status(thm)],[f_3906_3]) ).

fof(f_3907_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_3907_2,plain,
    ! [U_15425,U_15424,U_15423,U_15422,U_15421,U_15420,U_15419,U_15418,U_15417] :
      ( hAPP(U_15420,hAPP(U_15421,U_15425)) = hAPP(U_15423,hAPP(U_15424,U_15425))
      | hAPP(c_Fun_Ocomp(U_15417,U_15418,U_15419,U_15420),U_15421) != hAPP(c_Fun_Ocomp(U_15422,U_15418,U_15419,U_15423),U_15424) ),
    inference(variable_rename,[status(thm)],[f_3907_1]) ).

fof(f_3907_3,plain,
    ! [U_15425,U_15424,U_15423,U_15422,U_15421,U_15420] :
      ( ! [U_15419,U_15418,U_15417] : hAPP(c_Fun_Ocomp(U_15417,U_15418,U_15419,U_15420),U_15421) != hAPP(c_Fun_Ocomp(U_15422,U_15418,U_15419,U_15423),U_15424)
      | hAPP(U_15420,hAPP(U_15421,U_15425)) = hAPP(U_15423,hAPP(U_15424,U_15425)) ),
    inference(miniscope,[status(thm)],[f_3907_2]) ).

fof(f_3907_4,plain,
    ! [U_15418,U_15417,U_15419,U_15420,U_15421,U_15422,U_15423,U_15424,U_15425] :
      ( hAPP(c_Fun_Ocomp(U_15417,U_15418,U_15419,U_15420),U_15421) != hAPP(c_Fun_Ocomp(U_15422,U_15418,U_15419,U_15423),U_15424)
      | hAPP(U_15420,hAPP(U_15421,U_15425)) = hAPP(U_15423,hAPP(U_15424,U_15425)) ),
    inference(definitional_conversion,[status(esa)],[f_3907_3]) ).

cnf(f_3907_5,plain,
    ( hAPP(c_Fun_Ocomp(U_15417,U_15418,U_15419,U_15420),U_15421) != hAPP(c_Fun_Ocomp(U_15422,U_15418,U_15419,U_15423),U_15424)
    | hAPP(U_15420,hAPP(U_15421,U_15425)) = hAPP(U_15423,hAPP(U_15424,U_15425)) ),
    inference(clausify,[status(thm)],[f_3907_4]) ).

fof(f_3908_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_3908_2,plain,
    ! [U_15434,U_15433,U_15432,U_15431,U_15430,U_15429,U_15428,U_15427] :
      ( ! [U_15426] : hAPP(U_15430,hAPP(U_15431,U_15426)) = hAPP(U_15433,hAPP(U_15434,U_15426))
      | hAPP(c_Fun_Ocomp(U_15427,U_15428,U_15429,U_15430),U_15431) != hAPP(c_Fun_Ocomp(U_15432,U_15428,U_15429,U_15433),U_15434) ),
    inference(variable_rename,[status(thm)],[f_3908_1]) ).

fof(f_3908_3,plain,
    ! [U_15434,U_15433,U_15432,U_15431,U_15430] :
      ( ! [U_15429,U_15428,U_15427] : hAPP(c_Fun_Ocomp(U_15427,U_15428,U_15429,U_15430),U_15431) != hAPP(c_Fun_Ocomp(U_15432,U_15428,U_15429,U_15433),U_15434)
      | ! [U_15426] : hAPP(U_15430,hAPP(U_15431,U_15426)) = hAPP(U_15433,hAPP(U_15434,U_15426)) ),
    inference(miniscope,[status(thm)],[f_3908_2]) ).

fof(f_3908_4,plain,
    ! [U_15427,U_15426,U_15428,U_15429,U_15430,U_15431,U_15432,U_15433,U_15434] :
      ( hAPP(c_Fun_Ocomp(U_15427,U_15428,U_15429,U_15430),U_15431) != hAPP(c_Fun_Ocomp(U_15432,U_15428,U_15429,U_15433),U_15434)
      | hAPP(U_15430,hAPP(U_15431,U_15426)) = hAPP(U_15433,hAPP(U_15434,U_15426)) ),
    inference(definitional_conversion,[status(esa)],[f_3908_3]) ).

cnf(f_3908_5,plain,
    ( hAPP(c_Fun_Ocomp(U_15427,U_15428,U_15429,U_15430),U_15431) != hAPP(c_Fun_Ocomp(U_15432,U_15428,U_15429,U_15433),U_15434)
    | hAPP(U_15430,hAPP(U_15431,U_15426)) = hAPP(U_15433,hAPP(U_15434,U_15426)) ),
    inference(clausify,[status(thm)],[f_3908_4]) ).

fof(f_3909_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_3909_2,plain,
    ! [U_15440,U_15439,U_15438,U_15437,U_15436,U_15435] : hAPP(hAPP(c_Fun_Ocomp(U_15435,U_15436,U_15437,U_15438),U_15439),U_15440) = hAPP(U_15438,hAPP(U_15439,U_15440)),
    inference(variable_rename,[status(thm)],[f_3909_1]) ).

fof(f_3909_3,plain,
    ! [U_15436,U_15435,U_15437,U_15438,U_15439,U_15440] : hAPP(hAPP(c_Fun_Ocomp(U_15435,U_15436,U_15437,U_15438),U_15439),U_15440) = hAPP(U_15438,hAPP(U_15439,U_15440)),
    inference(definitional_conversion,[status(esa)],[f_3909_2]) ).

cnf(f_3909_4,plain,
    hAPP(hAPP(c_Fun_Ocomp(U_15435,U_15436,U_15437,U_15438),U_15439),U_15440) = hAPP(U_15438,hAPP(U_15439,U_15440)),
    inference(clausify,[status(thm)],[f_3909_3]) ).

fof(f_3910_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_3910_2,plain,
    ! [U_15451,U_15450,U_15449,U_15448,U_15447,U_15446,U_15445,U_15444,U_15443,U_15442,U_15441] :
      ( hAPP(hAPP(c_Fun_Ocomp(U_15447,U_15448,U_15449,U_15441),U_15442),U_15443) = hAPP(hAPP(c_Fun_Ocomp(U_15450,U_15448,U_15451,U_15444),U_15445),U_15446)
      | hAPP(U_15441,hAPP(U_15442,U_15443)) != hAPP(U_15444,hAPP(U_15445,U_15446)) ),
    inference(variable_rename,[status(thm)],[f_3910_1]) ).

fof(f_3910_3,plain,
    ! [U_15441,U_15442,U_15443,U_15444,U_15445,U_15446,U_15447,U_15448,U_15449,U_15450,U_15451] :
      ( hAPP(hAPP(c_Fun_Ocomp(U_15447,U_15448,U_15449,U_15441),U_15442),U_15443) = hAPP(hAPP(c_Fun_Ocomp(U_15450,U_15448,U_15451,U_15444),U_15445),U_15446)
      | hAPP(U_15441,hAPP(U_15442,U_15443)) != hAPP(U_15444,hAPP(U_15445,U_15446)) ),
    inference(definitional_conversion,[status(esa)],[f_3910_2]) ).

cnf(f_3910_4,plain,
    ( hAPP(hAPP(c_Fun_Ocomp(U_15447,U_15448,U_15449,U_15441),U_15442),U_15443) = hAPP(hAPP(c_Fun_Ocomp(U_15450,U_15448,U_15451,U_15444),U_15445),U_15446)
    | hAPP(U_15441,hAPP(U_15442,U_15443)) != hAPP(U_15444,hAPP(U_15445,U_15446)) ),
    inference(clausify,[status(thm)],[f_3910_3]) ).

fof(f_3911_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_3911_2,plain,
    ! [U_15458,U_15457,U_15456,U_15455,U_15454,U_15453,U_15452] : hAPP(c_Fun_Ocomp(U_15452,U_15453,U_15454,U_15455),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_15454,U_15452),U_15456),U_15457),U_15458)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_15454,U_15453),hAPP(c_Fun_Ocomp(U_15452,U_15453,U_15454,U_15455),U_15456)),U_15457),hAPP(U_15455,U_15458)),
    inference(variable_rename,[status(thm)],[f_3911_1]) ).

fof(f_3911_3,plain,
    ! [U_15453,U_15452,U_15454,U_15455,U_15456,U_15457,U_15458] : hAPP(c_Fun_Ocomp(U_15452,U_15453,U_15454,U_15455),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_15454,U_15452),U_15456),U_15457),U_15458)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_15454,U_15453),hAPP(c_Fun_Ocomp(U_15452,U_15453,U_15454,U_15455),U_15456)),U_15457),hAPP(U_15455,U_15458)),
    inference(definitional_conversion,[status(esa)],[f_3911_2]) ).

cnf(f_3911_4,plain,
    hAPP(c_Fun_Ocomp(U_15452,U_15453,U_15454,U_15455),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_15454,U_15452),U_15456),U_15457),U_15458)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_15454,U_15453),hAPP(c_Fun_Ocomp(U_15452,U_15453,U_15454,U_15455),U_15456)),U_15457),hAPP(U_15455,U_15458)),
    inference(clausify,[status(thm)],[f_3911_3]) ).

fof(f_3912_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_3912_2,plain,
    ! [U_15465,U_15464,U_15463,U_15462,U_15461,U_15460,U_15459] :
      ( hAPP(U_15462,hAPP(U_15463,U_15465)) = hAPP(U_15464,U_15465)
      | hAPP(c_Fun_Ocomp(U_15459,U_15460,U_15461,U_15462),U_15463) != U_15464 ),
    inference(variable_rename,[status(thm)],[f_3912_1]) ).

fof(f_3912_3,plain,
    ! [U_15465,U_15464,U_15463,U_15462] :
      ( ! [U_15461,U_15460,U_15459] : hAPP(c_Fun_Ocomp(U_15459,U_15460,U_15461,U_15462),U_15463) != U_15464
      | hAPP(U_15462,hAPP(U_15463,U_15465)) = hAPP(U_15464,U_15465) ),
    inference(miniscope,[status(thm)],[f_3912_2]) ).

fof(f_3912_4,plain,
    ! [U_15459,U_15460,U_15461,U_15462,U_15463,U_15464,U_15465] :
      ( hAPP(c_Fun_Ocomp(U_15459,U_15460,U_15461,U_15462),U_15463) != U_15464
      | hAPP(U_15462,hAPP(U_15463,U_15465)) = hAPP(U_15464,U_15465) ),
    inference(definitional_conversion,[status(esa)],[f_3912_3]) ).

cnf(f_3912_5,plain,
    ( hAPP(c_Fun_Ocomp(U_15459,U_15460,U_15461,U_15462),U_15463) != U_15464
    | hAPP(U_15462,hAPP(U_15463,U_15465)) = hAPP(U_15464,U_15465) ),
    inference(clausify,[status(thm)],[f_3912_4]) ).

fof(f_3913_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_3913_2,plain,
    ! [U_15471,U_15470,U_15469,U_15468,U_15467,U_15466] : hAPP(hAPP(c_Fun_Ocomp(U_15466,U_15467,U_15468,hAPP(c_COMBK(U_15467,U_15466),U_15469)),U_15470),U_15471) = U_15469,
    inference(variable_rename,[status(thm)],[f_3913_1]) ).

fof(f_3913_3,plain,
    ! [U_15466,U_15467,U_15468,U_15469,U_15470,U_15471] : hAPP(hAPP(c_Fun_Ocomp(U_15466,U_15467,U_15468,hAPP(c_COMBK(U_15467,U_15466),U_15469)),U_15470),U_15471) = U_15469,
    inference(definitional_conversion,[status(esa)],[f_3913_2]) ).

cnf(f_3913_4,plain,
    hAPP(hAPP(c_Fun_Ocomp(U_15466,U_15467,U_15468,hAPP(c_COMBK(U_15467,U_15466),U_15469)),U_15470),U_15471) = U_15469,
    inference(clausify,[status(thm)],[f_3913_3]) ).

fof(f_3914_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_3914_2,plain,
    ! [U_15475,U_15474,U_15473,U_15472] : hAPP(hAPP(c_Nat_Ocompow(U_15472,U_15472),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_15473),U_15474)),U_15475) = hAPP(c_Fun_Ocomp(U_15472,U_15472,U_15472,hAPP(hAPP(c_Nat_Ocompow(U_15472,U_15472),U_15473),U_15475)),hAPP(hAPP(c_Nat_Ocompow(U_15472,U_15472),U_15474),U_15475)),
    inference(variable_rename,[status(thm)],[f_3914_1]) ).

fof(f_3914_3,plain,
    ! [U_15472,U_15473,U_15474,U_15475] : hAPP(hAPP(c_Nat_Ocompow(U_15472,U_15472),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_15473),U_15474)),U_15475) = hAPP(c_Fun_Ocomp(U_15472,U_15472,U_15472,hAPP(hAPP(c_Nat_Ocompow(U_15472,U_15472),U_15473),U_15475)),hAPP(hAPP(c_Nat_Ocompow(U_15472,U_15472),U_15474),U_15475)),
    inference(definitional_conversion,[status(esa)],[f_3914_2]) ).

cnf(f_3914_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_15472,U_15472),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_15473),U_15474)),U_15475) = hAPP(c_Fun_Ocomp(U_15472,U_15472,U_15472,hAPP(hAPP(c_Nat_Ocompow(U_15472,U_15472),U_15473),U_15475)),hAPP(hAPP(c_Nat_Ocompow(U_15472,U_15472),U_15474),U_15475)),
    inference(clausify,[status(thm)],[f_3914_3]) ).

fof(f_3915_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_3915_2,plain,
    ! [U_15479,U_15478,U_15477,U_15476] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(U_15476,U_15477),tc_fun(U_15476,U_15477)),U_15478),c_Fun_Ocomp(U_15477,U_15477,U_15476,U_15479)) = c_Fun_Ocomp(U_15477,U_15477,U_15476,hAPP(hAPP(c_Nat_Ocompow(U_15477,U_15477),U_15478),U_15479)),
    inference(variable_rename,[status(thm)],[f_3915_1]) ).

fof(f_3915_3,plain,
    ! [U_15477,U_15476,U_15478,U_15479] : hAPP(hAPP(c_Nat_Ocompow(tc_fun(U_15476,U_15477),tc_fun(U_15476,U_15477)),U_15478),c_Fun_Ocomp(U_15477,U_15477,U_15476,U_15479)) = c_Fun_Ocomp(U_15477,U_15477,U_15476,hAPP(hAPP(c_Nat_Ocompow(U_15477,U_15477),U_15478),U_15479)),
    inference(definitional_conversion,[status(esa)],[f_3915_2]) ).

cnf(f_3915_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(tc_fun(U_15476,U_15477),tc_fun(U_15476,U_15477)),U_15478),c_Fun_Ocomp(U_15477,U_15477,U_15476,U_15479)) = c_Fun_Ocomp(U_15477,U_15477,U_15476,hAPP(hAPP(c_Nat_Ocompow(U_15477,U_15477),U_15478),U_15479)),
    inference(clausify,[status(thm)],[f_3915_3]) ).

fof(f_3916_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_3916_2,plain,
    ! [U_15482,U_15481,U_15480] : hAPP(hAPP(c_Nat_Ocompow(U_15480,U_15480),hAPP(c_Nat_OSuc,U_15481)),U_15482) = hAPP(c_Fun_Ocomp(U_15480,U_15480,U_15480,U_15482),hAPP(hAPP(c_Nat_Ocompow(U_15480,U_15480),U_15481),U_15482)),
    inference(variable_rename,[status(thm)],[f_3916_1]) ).

fof(f_3916_3,plain,
    ! [U_15480,U_15481,U_15482] : hAPP(hAPP(c_Nat_Ocompow(U_15480,U_15480),hAPP(c_Nat_OSuc,U_15481)),U_15482) = hAPP(c_Fun_Ocomp(U_15480,U_15480,U_15480,U_15482),hAPP(hAPP(c_Nat_Ocompow(U_15480,U_15480),U_15481),U_15482)),
    inference(definitional_conversion,[status(esa)],[f_3916_2]) ).

cnf(f_3916_4,plain,
    hAPP(hAPP(c_Nat_Ocompow(U_15480,U_15480),hAPP(c_Nat_OSuc,U_15481)),U_15482) = hAPP(c_Fun_Ocomp(U_15480,U_15480,U_15480,U_15482),hAPP(hAPP(c_Nat_Ocompow(U_15480,U_15480),U_15481),U_15482)),
    inference(clausify,[status(thm)],[f_3916_3]) ).

fof(f_3917_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_3917_2,plain,
    ! [U_15487,U_15486,U_15485,U_15484,U_15483] :
      ( hAPP(c_Set_Oimage(U_15483,U_15486,hAPP(c_Fun_Ocomp(U_15484,U_15486,U_15483,U_15487),U_15485)),c_Orderings_Otop__class_Otop(tc_fun(U_15483,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_15486,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_15484,U_15486,U_15487),c_Orderings_Otop__class_Otop(tc_fun(U_15484,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_15486,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_15483,U_15484,U_15485),c_Orderings_Otop__class_Otop(tc_fun(U_15483,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_15484,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_3917_1]) ).

fof(f_3917_3,plain,
    ! [U_15483,U_15484,U_15485,U_15486,U_15487] :
      ( hAPP(c_Set_Oimage(U_15483,U_15486,hAPP(c_Fun_Ocomp(U_15484,U_15486,U_15483,U_15487),U_15485)),c_Orderings_Otop__class_Otop(tc_fun(U_15483,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_15486,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_15484,U_15486,U_15487),c_Orderings_Otop__class_Otop(tc_fun(U_15484,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_15486,tc_HOL_Obool))
      | hAPP(c_Set_Oimage(U_15483,U_15484,U_15485),c_Orderings_Otop__class_Otop(tc_fun(U_15483,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_15484,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_3917_2]) ).

cnf(f_3917_4,plain,
    ( hAPP(c_Set_Oimage(U_15483,U_15486,hAPP(c_Fun_Ocomp(U_15484,U_15486,U_15483,U_15487),U_15485)),c_Orderings_Otop__class_Otop(tc_fun(U_15483,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_15486,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_15484,U_15486,U_15487),c_Orderings_Otop__class_Otop(tc_fun(U_15484,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_15486,tc_HOL_Obool))
    | hAPP(c_Set_Oimage(U_15483,U_15484,U_15485),c_Orderings_Otop__class_Otop(tc_fun(U_15483,tc_HOL_Obool))) != c_Orderings_Otop__class_Otop(tc_fun(U_15484,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_3917_3]) ).

fof(f_3918_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_3918_2,plain,
    ! [U_15493,U_15492,U_15491,U_15490,U_15489,U_15488] : hAPP(c_Set_Oimage(U_15488,U_15489,hAPP(c_Fun_Ocomp(U_15490,U_15489,U_15488,U_15491),U_15492)),U_15493) = hAPP(c_Set_Oimage(U_15490,U_15489,U_15491),hAPP(c_Set_Oimage(U_15488,U_15490,U_15492),U_15493)),
    inference(variable_rename,[status(thm)],[f_3918_1]) ).

fof(f_3918_3,plain,
    ! [U_15490,U_15488,U_15489,U_15491,U_15492,U_15493] : hAPP(c_Set_Oimage(U_15488,U_15489,hAPP(c_Fun_Ocomp(U_15490,U_15489,U_15488,U_15491),U_15492)),U_15493) = hAPP(c_Set_Oimage(U_15490,U_15489,U_15491),hAPP(c_Set_Oimage(U_15488,U_15490,U_15492),U_15493)),
    inference(definitional_conversion,[status(esa)],[f_3918_2]) ).

cnf(f_3918_4,plain,
    hAPP(c_Set_Oimage(U_15488,U_15489,hAPP(c_Fun_Ocomp(U_15490,U_15489,U_15488,U_15491),U_15492)),U_15493) = hAPP(c_Set_Oimage(U_15490,U_15489,U_15491),hAPP(c_Set_Oimage(U_15488,U_15490,U_15492),U_15493)),
    inference(clausify,[status(thm)],[f_3918_3]) ).

fof(f_3919_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_3919_2,plain,
    ! [U_15499,U_15498,U_15497,U_15496,U_15495,U_15494] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15496,U_15494),U_15499),hAPP(c_Set_Oimage(U_15495,U_15496,U_15497),U_15498)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15495,U_15494),hAPP(c_Fun_Ocomp(U_15496,U_15494,U_15495,U_15499),U_15497)),U_15498)
      | ~ c_Fun_Oinj__on(U_15495,U_15496,U_15497,U_15498)
      | ~ class_Groups_Ocomm__monoid__add(U_15494) ),
    inference(variable_rename,[status(thm)],[f_3919_1]) ).

fof(f_3919_3,plain,
    ! [U_15494,U_15495,U_15496,U_15497,U_15498,U_15499] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15496,U_15494),U_15499),hAPP(c_Set_Oimage(U_15495,U_15496,U_15497),U_15498)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15495,U_15494),hAPP(c_Fun_Ocomp(U_15496,U_15494,U_15495,U_15499),U_15497)),U_15498)
      | ~ c_Fun_Oinj__on(U_15495,U_15496,U_15497,U_15498)
      | ~ class_Groups_Ocomm__monoid__add(U_15494) ),
    inference(definitional_conversion,[status(esa)],[f_3919_2]) ).

cnf(f_3919_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15496,U_15494),U_15499),hAPP(c_Set_Oimage(U_15495,U_15496,U_15497),U_15498)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15495,U_15494),hAPP(c_Fun_Ocomp(U_15496,U_15494,U_15495,U_15499),U_15497)),U_15498)
    | ~ c_Fun_Oinj__on(U_15495,U_15496,U_15497,U_15498)
    | ~ class_Groups_Ocomm__monoid__add(U_15494) ),
    inference(clausify,[status(thm)],[f_3919_3]) ).

fof(f_3920_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_3920_2,plain,
    ! [U_15505,U_15504,U_15503,U_15502,U_15501,U_15500] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15502,U_15500),U_15505),hAPP(c_Set_Oimage(U_15501,U_15502,U_15503),U_15504)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15501,U_15500),hAPP(c_Fun_Ocomp(U_15502,U_15500,U_15501,U_15505),U_15503)),U_15504)
      | ~ c_Fun_Oinj__on(U_15501,U_15502,U_15503,U_15504)
      | ~ class_Groups_Ocomm__monoid__mult(U_15500) ),
    inference(variable_rename,[status(thm)],[f_3920_1]) ).

fof(f_3920_3,plain,
    ! [U_15500,U_15501,U_15502,U_15503,U_15504,U_15505] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15502,U_15500),U_15505),hAPP(c_Set_Oimage(U_15501,U_15502,U_15503),U_15504)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15501,U_15500),hAPP(c_Fun_Ocomp(U_15502,U_15500,U_15501,U_15505),U_15503)),U_15504)
      | ~ c_Fun_Oinj__on(U_15501,U_15502,U_15503,U_15504)
      | ~ class_Groups_Ocomm__monoid__mult(U_15500) ),
    inference(definitional_conversion,[status(esa)],[f_3920_2]) ).

cnf(f_3920_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15502,U_15500),U_15505),hAPP(c_Set_Oimage(U_15501,U_15502,U_15503),U_15504)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15501,U_15500),hAPP(c_Fun_Ocomp(U_15502,U_15500,U_15501,U_15505),U_15503)),U_15504)
    | ~ c_Fun_Oinj__on(U_15501,U_15502,U_15503,U_15504)
    | ~ class_Groups_Ocomm__monoid__mult(U_15500) ),
    inference(clausify,[status(thm)],[f_3920_3]) ).

fof(f_3921_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_3921_2,plain,
    ! [U_15513,U_15512,U_15511,U_15510,U_15509,U_15508,U_15507,U_15506] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15508,U_15506),U_15513),U_15511) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15507,U_15506),U_15512),U_15510)
      | U_15512 != hAPP(c_Fun_Ocomp(U_15508,U_15506,U_15507,U_15513),U_15509)
      | U_15511 != hAPP(c_Set_Oimage(U_15507,U_15508,U_15509),U_15510)
      | ~ c_Fun_Oinj__on(U_15507,U_15508,U_15509,U_15510)
      | ~ class_Groups_Ocomm__monoid__mult(U_15506) ),
    inference(variable_rename,[status(thm)],[f_3921_1]) ).

fof(f_3921_3,plain,
    ! [U_15506,U_15507,U_15508,U_15509,U_15510,U_15511,U_15512,U_15513] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15508,U_15506),U_15513),U_15511) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15507,U_15506),U_15512),U_15510)
      | U_15512 != hAPP(c_Fun_Ocomp(U_15508,U_15506,U_15507,U_15513),U_15509)
      | U_15511 != hAPP(c_Set_Oimage(U_15507,U_15508,U_15509),U_15510)
      | ~ c_Fun_Oinj__on(U_15507,U_15508,U_15509,U_15510)
      | ~ class_Groups_Ocomm__monoid__mult(U_15506) ),
    inference(definitional_conversion,[status(esa)],[f_3921_2]) ).

cnf(f_3921_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15508,U_15506),U_15513),U_15511) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15507,U_15506),U_15512),U_15510)
    | U_15512 != hAPP(c_Fun_Ocomp(U_15508,U_15506,U_15507,U_15513),U_15509)
    | U_15511 != hAPP(c_Set_Oimage(U_15507,U_15508,U_15509),U_15510)
    | ~ c_Fun_Oinj__on(U_15507,U_15508,U_15509,U_15510)
    | ~ class_Groups_Ocomm__monoid__mult(U_15506) ),
    inference(clausify,[status(thm)],[f_3921_3]) ).

fof(f_3922_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_3922_2,plain,
    ! [U_15518,U_15517,U_15516,U_15515,U_15514] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15515,U_15514),U_15518),hAPP(c_Set_Oimage(U_15515,U_15515,U_15517),U_15516)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15515,U_15514),hAPP(c_Fun_Ocomp(U_15515,U_15514,U_15515,U_15518),U_15517)),U_15516)
      | ~ c_Fun_Oinj__on(U_15515,U_15515,U_15517,U_15516)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15515),U_15516))
      | ~ class_Groups_Ocomm__monoid__add(U_15514) ),
    inference(variable_rename,[status(thm)],[f_3922_1]) ).

fof(f_3922_3,plain,
    ! [U_15515,U_15517,U_15514,U_15516,U_15518] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15515,U_15514),U_15518),hAPP(c_Set_Oimage(U_15515,U_15515,U_15517),U_15516)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15515,U_15514),hAPP(c_Fun_Ocomp(U_15515,U_15514,U_15515,U_15518),U_15517)),U_15516)
      | ~ c_Fun_Oinj__on(U_15515,U_15515,U_15517,U_15516)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15515),U_15516))
      | ~ class_Groups_Ocomm__monoid__add(U_15514) ),
    inference(definitional_conversion,[status(esa)],[f_3922_2]) ).

cnf(f_3922_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15515,U_15514),U_15518),hAPP(c_Set_Oimage(U_15515,U_15515,U_15517),U_15516)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15515,U_15514),hAPP(c_Fun_Ocomp(U_15515,U_15514,U_15515,U_15518),U_15517)),U_15516)
    | ~ c_Fun_Oinj__on(U_15515,U_15515,U_15517,U_15516)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15515),U_15516))
    | ~ class_Groups_Ocomm__monoid__add(U_15514) ),
    inference(clausify,[status(thm)],[f_3922_3]) ).

fof(f_3923_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_3923_2,plain,
    ! [U_15523,U_15522,U_15521,U_15520,U_15519] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15520,U_15519),U_15523),hAPP(c_Set_Oimage(U_15520,U_15520,U_15522),U_15521)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15520,U_15519),hAPP(c_Fun_Ocomp(U_15520,U_15519,U_15520,U_15523),U_15522)),U_15521)
      | ~ c_Fun_Oinj__on(U_15520,U_15520,U_15522,U_15521)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15520),U_15521))
      | ~ class_Groups_Ocomm__monoid__mult(U_15519) ),
    inference(variable_rename,[status(thm)],[f_3923_1]) ).

fof(f_3923_3,plain,
    ! [U_15520,U_15519,U_15521,U_15522,U_15523] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15520,U_15519),U_15523),hAPP(c_Set_Oimage(U_15520,U_15520,U_15522),U_15521)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15520,U_15519),hAPP(c_Fun_Ocomp(U_15520,U_15519,U_15520,U_15523),U_15522)),U_15521)
      | ~ c_Fun_Oinj__on(U_15520,U_15520,U_15522,U_15521)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15520),U_15521))
      | ~ class_Groups_Ocomm__monoid__mult(U_15519) ),
    inference(definitional_conversion,[status(esa)],[f_3923_2]) ).

cnf(f_3923_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15520,U_15519),U_15523),hAPP(c_Set_Oimage(U_15520,U_15520,U_15522),U_15521)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15520,U_15519),hAPP(c_Fun_Ocomp(U_15520,U_15519,U_15520,U_15523),U_15522)),U_15521)
    | ~ c_Fun_Oinj__on(U_15520,U_15520,U_15522,U_15521)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15520),U_15521))
    | ~ class_Groups_Ocomm__monoid__mult(U_15519) ),
    inference(clausify,[status(thm)],[f_3923_3]) ).

fof(f_3924_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_3924_2,plain,
    ! [U_15530,U_15529,U_15528,U_15527,U_15526,U_15525,U_15524] :
      ( hAPP(c_Fun_Othe__inv__into(U_15527,U_15525,U_15529,hAPP(c_Fun_Ocomp(U_15524,U_15525,U_15527,U_15526),U_15528)),U_15530) = hAPP(hAPP(c_Fun_Ocomp(U_15524,U_15527,U_15525,c_Fun_Othe__inv__into(U_15527,U_15524,U_15529,U_15528)),c_Fun_Othe__inv__into(U_15524,U_15525,hAPP(c_Set_Oimage(U_15527,U_15524,U_15528),U_15529),U_15526)),U_15530)
      | ~ hBOOL(hAPP(hAPP(c_member(U_15525),U_15530),hAPP(c_Set_Oimage(U_15524,U_15525,U_15526),hAPP(c_Set_Oimage(U_15527,U_15524,U_15528),U_15529))))
      | ~ c_Fun_Oinj__on(U_15527,U_15524,U_15528,U_15529)
      | ~ c_Fun_Oinj__on(U_15524,U_15525,U_15526,hAPP(c_Set_Oimage(U_15527,U_15524,U_15528),U_15529)) ),
    inference(variable_rename,[status(thm)],[f_3924_1]) ).

fof(f_3924_3,plain,
    ! [U_15524,U_15525,U_15526,U_15527,U_15528,U_15529,U_15530] :
      ( hAPP(c_Fun_Othe__inv__into(U_15527,U_15525,U_15529,hAPP(c_Fun_Ocomp(U_15524,U_15525,U_15527,U_15526),U_15528)),U_15530) = hAPP(hAPP(c_Fun_Ocomp(U_15524,U_15527,U_15525,c_Fun_Othe__inv__into(U_15527,U_15524,U_15529,U_15528)),c_Fun_Othe__inv__into(U_15524,U_15525,hAPP(c_Set_Oimage(U_15527,U_15524,U_15528),U_15529),U_15526)),U_15530)
      | ~ hBOOL(hAPP(hAPP(c_member(U_15525),U_15530),hAPP(c_Set_Oimage(U_15524,U_15525,U_15526),hAPP(c_Set_Oimage(U_15527,U_15524,U_15528),U_15529))))
      | ~ c_Fun_Oinj__on(U_15527,U_15524,U_15528,U_15529)
      | ~ c_Fun_Oinj__on(U_15524,U_15525,U_15526,hAPP(c_Set_Oimage(U_15527,U_15524,U_15528),U_15529)) ),
    inference(definitional_conversion,[status(esa)],[f_3924_2]) ).

cnf(f_3924_4,plain,
    ( hAPP(c_Fun_Othe__inv__into(U_15527,U_15525,U_15529,hAPP(c_Fun_Ocomp(U_15524,U_15525,U_15527,U_15526),U_15528)),U_15530) = hAPP(hAPP(c_Fun_Ocomp(U_15524,U_15527,U_15525,c_Fun_Othe__inv__into(U_15527,U_15524,U_15529,U_15528)),c_Fun_Othe__inv__into(U_15524,U_15525,hAPP(c_Set_Oimage(U_15527,U_15524,U_15528),U_15529),U_15526)),U_15530)
    | ~ hBOOL(hAPP(hAPP(c_member(U_15525),U_15530),hAPP(c_Set_Oimage(U_15524,U_15525,U_15526),hAPP(c_Set_Oimage(U_15527,U_15524,U_15528),U_15529))))
    | ~ c_Fun_Oinj__on(U_15527,U_15524,U_15528,U_15529)
    | ~ c_Fun_Oinj__on(U_15524,U_15525,U_15526,hAPP(c_Set_Oimage(U_15527,U_15524,U_15528),U_15529)) ),
    inference(clausify,[status(thm)],[f_3924_3]) ).

fof(f_3925_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_3925_2,plain,
    ! [U_15537,U_15536,U_15535,U_15534,U_15533,U_15532,U_15531] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15531,U_15534,c_Groups_Otimes__class_Otimes(U_15531)),U_15536),U_15537),hAPP(c_Set_Oimage(U_15532,U_15534,U_15535),U_15533)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15531,U_15532,c_Groups_Otimes__class_Otimes(U_15531)),hAPP(c_Fun_Ocomp(U_15534,U_15531,U_15532,U_15536),U_15535)),U_15537),U_15533)
      | ~ c_Fun_Oinj__on(U_15532,U_15534,U_15535,U_15533)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15532),U_15533))
      | ~ class_Groups_Oab__semigroup__mult(U_15531) ),
    inference(variable_rename,[status(thm)],[f_3925_1]) ).

fof(f_3925_3,plain,
    ! [U_15531,U_15532,U_15533,U_15534,U_15535,U_15536,U_15537] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15531,U_15534,c_Groups_Otimes__class_Otimes(U_15531)),U_15536),U_15537),hAPP(c_Set_Oimage(U_15532,U_15534,U_15535),U_15533)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15531,U_15532,c_Groups_Otimes__class_Otimes(U_15531)),hAPP(c_Fun_Ocomp(U_15534,U_15531,U_15532,U_15536),U_15535)),U_15537),U_15533)
      | ~ c_Fun_Oinj__on(U_15532,U_15534,U_15535,U_15533)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15532),U_15533))
      | ~ class_Groups_Oab__semigroup__mult(U_15531) ),
    inference(definitional_conversion,[status(esa)],[f_3925_2]) ).

cnf(f_3925_4,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15531,U_15534,c_Groups_Otimes__class_Otimes(U_15531)),U_15536),U_15537),hAPP(c_Set_Oimage(U_15532,U_15534,U_15535),U_15533)) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15531,U_15532,c_Groups_Otimes__class_Otimes(U_15531)),hAPP(c_Fun_Ocomp(U_15534,U_15531,U_15532,U_15536),U_15535)),U_15537),U_15533)
    | ~ c_Fun_Oinj__on(U_15532,U_15534,U_15535,U_15533)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15532),U_15533))
    | ~ class_Groups_Oab__semigroup__mult(U_15531) ),
    inference(clausify,[status(thm)],[f_3925_3]) ).

fof(f_3926_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_3926_2,plain,
    ! [U_15538] : c_Nitpick_Onum(U_15538) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_15538,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_15538)),
    inference(variable_rename,[status(thm)],[f_3926_1]) ).

fof(f_3926_3,plain,
    ! [U_15538] : c_Nitpick_Onum(U_15538) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_15538,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_15538)),
    inference(definitional_conversion,[status(esa)],[f_3926_2]) ).

cnf(f_3926_4,plain,
    c_Nitpick_Onum(U_15538) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_15538,c_Product__Type_Ofst(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_15538)),
    inference(clausify,[status(thm)],[f_3926_3]) ).

fof(f_3927_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_3927_2,plain,
    ! [U_15539] : c_Nitpick_Odenom(U_15539) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_15539,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_15539)),
    inference(variable_rename,[status(thm)],[f_3927_1]) ).

fof(f_3927_3,plain,
    ! [U_15539] : c_Nitpick_Odenom(U_15539) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_15539,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_15539)),
    inference(definitional_conversion,[status(esa)],[f_3927_2]) ).

cnf(f_3927_4,plain,
    c_Nitpick_Odenom(U_15539) = hAPP(c_Fun_Ocomp(tc_prod(tc_Int_Oint,tc_Int_Oint),tc_Int_Oint,U_15539,c_Product__Type_Osnd(tc_Int_Oint,tc_Int_Oint)),c_Nitpick_ORep__Frac(U_15539)),
    inference(clausify,[status(thm)],[f_3927_3]) ).

fof(f_3928_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_3928_2,plain,
    ! [U_15545,U_15544,U_15543,U_15542,U_15541,U_15540] : hAPP(c_Fun_Ocomp(tc_prod(U_15540,U_15541),U_15540,tc_prod(U_15542,U_15543),c_Product__Type_Ofst(U_15540,U_15541)),c_Product__Type_Omap__pair(U_15542,U_15540,U_15543,U_15541,U_15544,U_15545)) = hAPP(c_Fun_Ocomp(U_15542,U_15540,tc_prod(U_15542,U_15543),U_15544),c_Product__Type_Ofst(U_15542,U_15543)),
    inference(variable_rename,[status(thm)],[f_3928_1]) ).

fof(f_3928_3,plain,
    ! [U_15540,U_15541,U_15542,U_15543,U_15544,U_15545] : hAPP(c_Fun_Ocomp(tc_prod(U_15540,U_15541),U_15540,tc_prod(U_15542,U_15543),c_Product__Type_Ofst(U_15540,U_15541)),c_Product__Type_Omap__pair(U_15542,U_15540,U_15543,U_15541,U_15544,U_15545)) = hAPP(c_Fun_Ocomp(U_15542,U_15540,tc_prod(U_15542,U_15543),U_15544),c_Product__Type_Ofst(U_15542,U_15543)),
    inference(definitional_conversion,[status(esa)],[f_3928_2]) ).

cnf(f_3928_4,plain,
    hAPP(c_Fun_Ocomp(tc_prod(U_15540,U_15541),U_15540,tc_prod(U_15542,U_15543),c_Product__Type_Ofst(U_15540,U_15541)),c_Product__Type_Omap__pair(U_15542,U_15540,U_15543,U_15541,U_15544,U_15545)) = hAPP(c_Fun_Ocomp(U_15542,U_15540,tc_prod(U_15542,U_15543),U_15544),c_Product__Type_Ofst(U_15542,U_15543)),
    inference(clausify,[status(thm)],[f_3928_3]) ).

fof(f_3929_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_3929_2,plain,
    ! [U_15551,U_15550,U_15549,U_15548,U_15547,U_15546] : hAPP(c_Fun_Ocomp(tc_prod(U_15546,U_15547),U_15547,tc_prod(U_15548,U_15549),c_Product__Type_Osnd(U_15546,U_15547)),c_Product__Type_Omap__pair(U_15548,U_15546,U_15549,U_15547,U_15550,U_15551)) = hAPP(c_Fun_Ocomp(U_15549,U_15547,tc_prod(U_15548,U_15549),U_15551),c_Product__Type_Osnd(U_15548,U_15549)),
    inference(variable_rename,[status(thm)],[f_3929_1]) ).

fof(f_3929_3,plain,
    ! [U_15546,U_15547,U_15548,U_15549,U_15550,U_15551] : hAPP(c_Fun_Ocomp(tc_prod(U_15546,U_15547),U_15547,tc_prod(U_15548,U_15549),c_Product__Type_Osnd(U_15546,U_15547)),c_Product__Type_Omap__pair(U_15548,U_15546,U_15549,U_15547,U_15550,U_15551)) = hAPP(c_Fun_Ocomp(U_15549,U_15547,tc_prod(U_15548,U_15549),U_15551),c_Product__Type_Osnd(U_15548,U_15549)),
    inference(definitional_conversion,[status(esa)],[f_3929_2]) ).

cnf(f_3929_4,plain,
    hAPP(c_Fun_Ocomp(tc_prod(U_15546,U_15547),U_15547,tc_prod(U_15548,U_15549),c_Product__Type_Osnd(U_15546,U_15547)),c_Product__Type_Omap__pair(U_15548,U_15546,U_15549,U_15547,U_15550,U_15551)) = hAPP(c_Fun_Ocomp(U_15549,U_15547,tc_prod(U_15548,U_15549),U_15551),c_Product__Type_Osnd(U_15548,U_15549)),
    inference(clausify,[status(thm)],[f_3929_3]) ).

fof(f_3930_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_3930_2,plain,
    ! [U_15557,U_15556,U_15555,U_15554,U_15553,U_15552] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15552,tc_fun(U_15553,tc_HOL_Obool)),U_15554),hAPP(c_Fun_Ocomp(U_15555,tc_fun(U_15553,tc_HOL_Obool),U_15552,U_15556),U_15557)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15555,tc_fun(U_15553,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_15552,U_15555,U_15557),U_15554)),U_15556),
    inference(variable_rename,[status(thm)],[f_3930_1]) ).

fof(f_3930_3,plain,
    ! [U_15552,U_15553,U_15554,U_15555,U_15556,U_15557] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15552,tc_fun(U_15553,tc_HOL_Obool)),U_15554),hAPP(c_Fun_Ocomp(U_15555,tc_fun(U_15553,tc_HOL_Obool),U_15552,U_15556),U_15557)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15555,tc_fun(U_15553,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_15552,U_15555,U_15557),U_15554)),U_15556),
    inference(definitional_conversion,[status(esa)],[f_3930_2]) ).

cnf(f_3930_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15552,tc_fun(U_15553,tc_HOL_Obool)),U_15554),hAPP(c_Fun_Ocomp(U_15555,tc_fun(U_15553,tc_HOL_Obool),U_15552,U_15556),U_15557)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15555,tc_fun(U_15553,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_15552,U_15555,U_15557),U_15554)),U_15556),
    inference(clausify,[status(thm)],[f_3930_3]) ).

fof(f_3931_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_3931_2,plain,
    ! [U_15564,U_15563,U_15562,U_15561,U_15560,U_15559,U_15558] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15558,U_15559,U_15560),hAPP(c_Fun_Ocomp(U_15561,tc_fun(U_15559,U_15560),U_15558,U_15562),U_15563)),U_15564) = hAPP(hAPP(U_15562,hAPP(U_15563,hAPP(c_Product__Type_Ofst(U_15558,U_15559),U_15564))),hAPP(c_Product__Type_Osnd(U_15558,U_15559),U_15564)),
    inference(variable_rename,[status(thm)],[f_3931_1]) ).

fof(f_3931_3,plain,
    ! [U_15558,U_15559,U_15560,U_15561,U_15562,U_15563,U_15564] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15558,U_15559,U_15560),hAPP(c_Fun_Ocomp(U_15561,tc_fun(U_15559,U_15560),U_15558,U_15562),U_15563)),U_15564) = hAPP(hAPP(U_15562,hAPP(U_15563,hAPP(c_Product__Type_Ofst(U_15558,U_15559),U_15564))),hAPP(c_Product__Type_Osnd(U_15558,U_15559),U_15564)),
    inference(definitional_conversion,[status(esa)],[f_3931_2]) ).

cnf(f_3931_4,plain,
    hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_15558,U_15559,U_15560),hAPP(c_Fun_Ocomp(U_15561,tc_fun(U_15559,U_15560),U_15558,U_15562),U_15563)),U_15564) = hAPP(hAPP(U_15562,hAPP(U_15563,hAPP(c_Product__Type_Ofst(U_15558,U_15559),U_15564))),hAPP(c_Product__Type_Osnd(U_15558,U_15559),U_15564)),
    inference(clausify,[status(thm)],[f_3931_3]) ).

fof(f_3932_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_3932_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_3932_1]) ).

cnf(f_3932_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_3932_2]) ).

fof(f_3933_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_3933_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_3933_1]) ).

cnf(f_3933_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_3933_2]) ).

fof(f_3934_1,plain,
    ! [V_c_2,V_b_2,V_Pa_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_Pa_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_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_Pa_2,V_b_2)),V_c_2),V_Pa_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_3934_2,plain,
    ! [U_15569,U_15568,U_15567,U_15566,U_15565] :
      ( c_Hoare__Mirabelle_Ohoare__valids(U_15565,U_15566,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_15565)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15565),U_15567),c_Com_Ocom_OWhile(U_15568,U_15569)),c_Hoare__Mirabelle_Opeek__and(U_15565,U_15567,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_15568)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_15565),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__valids(U_15565,U_15566,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_15565)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15565),c_Hoare__Mirabelle_Opeek__and(U_15565,U_15567,U_15568)),U_15569),U_15567)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_15565),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3934_1]) ).

fof(f_3934_3,plain,
    ! [U_15565,U_15566,U_15567,U_15568,U_15569] :
      ( c_Hoare__Mirabelle_Ohoare__valids(U_15565,U_15566,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_15565)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15565),U_15567),c_Com_Ocom_OWhile(U_15568,U_15569)),c_Hoare__Mirabelle_Opeek__and(U_15565,U_15567,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_15568)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_15565),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__valids(U_15565,U_15566,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_15565)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15565),c_Hoare__Mirabelle_Opeek__and(U_15565,U_15567,U_15568)),U_15569),U_15567)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_15565),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3934_2]) ).

cnf(f_3934_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__valids(U_15565,U_15566,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_15565)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15565),U_15567),c_Com_Ocom_OWhile(U_15568,U_15569)),c_Hoare__Mirabelle_Opeek__and(U_15565,U_15567,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_15568)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_15565),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__valids(U_15565,U_15566,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_15565)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15565),c_Hoare__Mirabelle_Opeek__and(U_15565,U_15567,U_15568)),U_15569),U_15567)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_15565),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3934_3]) ).

fof(f_3935_1,plain,
    ! [V_d_2,V_Qa_2,V_c_2,V_b_2,V_Pa_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_Pa_2),c_Com_Ocom_OCond(V_b_2,V_c_2,V_d_2)),V_Qa_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_Pa_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2))),V_d_2),V_Qa_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_Pa_2,V_b_2)),V_c_2),V_Qa_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_3935_2,plain,
    ! [U_15576,U_15575,U_15574,U_15573,U_15572,U_15571,U_15570] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_15570,U_15571,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_15570)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15570),U_15572),c_Com_Ocom_OCond(U_15573,U_15574,U_15576)),U_15575)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_15570),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_15570,U_15571,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_15570)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15570),c_Hoare__Mirabelle_Opeek__and(U_15570,U_15572,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_15573))),U_15576),U_15575)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_15570),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_15570,U_15571,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_15570)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15570),c_Hoare__Mirabelle_Opeek__and(U_15570,U_15572,U_15573)),U_15574),U_15575)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_15570),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3935_1]) ).

fof(f_3935_3,plain,
    ! [U_15570,U_15571,U_15572,U_15573,U_15574,U_15575,U_15576] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_15570,U_15571,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_15570)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15570),U_15572),c_Com_Ocom_OCond(U_15573,U_15574,U_15576)),U_15575)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_15570),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_15570,U_15571,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_15570)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15570),c_Hoare__Mirabelle_Opeek__and(U_15570,U_15572,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_15573))),U_15576),U_15575)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_15570),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_15570,U_15571,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_15570)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15570),c_Hoare__Mirabelle_Opeek__and(U_15570,U_15572,U_15573)),U_15574),U_15575)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_15570),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3935_2]) ).

cnf(f_3935_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_15570,U_15571,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_15570)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15570),U_15572),c_Com_Ocom_OCond(U_15573,U_15574,U_15576)),U_15575)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_15570),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_15570,U_15571,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_15570)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15570),c_Hoare__Mirabelle_Opeek__and(U_15570,U_15572,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_15573))),U_15576),U_15575)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_15570),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_15570,U_15571,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_15570)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15570),c_Hoare__Mirabelle_Opeek__and(U_15570,U_15572,U_15573)),U_15574),U_15575)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_15570),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3935_3]) ).

fof(f_3936_1,plain,
    ! [V_s_2,V_Z_2,V_p_2,V_Pa_2,T_b] :
      ( ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_p_2),V_Z_2),V_s_2))
        | ~ hBOOL(hAPP(V_p_2,V_s_2))
        | ~ hBOOL(hAPP(hAPP(V_Pa_2,V_Z_2),V_s_2)) )
      & ( ( hBOOL(hAPP(V_p_2,V_s_2))
          & hBOOL(hAPP(hAPP(V_Pa_2,V_Z_2),V_s_2)) )
        | ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_2,V_p_2),V_Z_2),V_s_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_peek__and__def]) ).

fof(f_3936_2,plain,
    ! [U_15581,U_15580,U_15579,U_15578,U_15577] :
      ( ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_15577,U_15578,U_15579),U_15580),U_15581))
        | ~ hBOOL(hAPP(U_15579,U_15581))
        | ~ hBOOL(hAPP(hAPP(U_15578,U_15580),U_15581)) )
      & ( ( hBOOL(hAPP(U_15579,U_15581))
          & hBOOL(hAPP(hAPP(U_15578,U_15580),U_15581)) )
        | ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_15577,U_15578,U_15579),U_15580),U_15581)) ) ),
    inference(variable_rename,[status(thm)],[f_3936_1]) ).

fof(f_3936_3,plain,
    ( ! [U_15591,U_15589,U_15587,U_15585] :
        ( ! [U_15583] : hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_15583,U_15585,U_15587),U_15589),U_15591))
        | ~ hBOOL(hAPP(U_15587,U_15591))
        | ~ hBOOL(hAPP(hAPP(U_15585,U_15589),U_15591)) )
    & ! [U_15590,U_15588,U_15586,U_15584] :
        ( ! [U_15582] : ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_15582,U_15584,U_15586),U_15588),U_15590))
        | ( hBOOL(hAPP(U_15586,U_15590))
          & hBOOL(hAPP(hAPP(U_15584,U_15588),U_15590)) ) ) ),
    inference(miniscope,[status(thm)],[f_3936_2]) ).

fof(f_3936_4,plain,
    ( ! [U_15586,U_15588,U_15584,U_15590] :
        ( hBOOL(hAPP(U_15586,U_15590))
        | ~ sP1037(U_15586,U_15588,U_15584,U_15590) )
    & ! [U_15586,U_15588,U_15584,U_15590] :
        ( hBOOL(hAPP(hAPP(U_15584,U_15588),U_15590))
        | ~ sP1037(U_15586,U_15588,U_15584,U_15590) )
    & ! [U_15587,U_15583,U_15589,U_15585,U_15591] :
        ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_15583,U_15585,U_15587),U_15589),U_15591))
        | ~ hBOOL(hAPP(U_15587,U_15591))
        | ~ hBOOL(hAPP(hAPP(U_15585,U_15589),U_15591)) )
    & ! [U_15586,U_15588,U_15582,U_15584,U_15590] :
        ( ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_15582,U_15584,U_15586),U_15588),U_15590))
        | sP1037(U_15586,U_15588,U_15584,U_15590) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1037])],[f_3936_3]) ).

cnf(f_3936_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_15582,U_15584,U_15586),U_15588),U_15590))
    | sP1037(U_15586,U_15588,U_15584,U_15590) ),
    inference(clausify,[status(thm)],[f_3936_4]) ).

cnf(f_3936_6,plain,
    ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(U_15583,U_15585,U_15587),U_15589),U_15591))
    | ~ hBOOL(hAPP(U_15587,U_15591))
    | ~ hBOOL(hAPP(hAPP(U_15585,U_15589),U_15591)) ),
    inference(clausify,[status(thm)],[f_3936_4]) ).

cnf(f_3936_7,plain,
    ( hBOOL(hAPP(hAPP(U_15584,U_15588),U_15590))
    | ~ sP1037(U_15586,U_15588,U_15584,U_15590) ),
    inference(clausify,[status(thm)],[f_3936_4]) ).

cnf(f_3936_8,plain,
    ( hBOOL(hAPP(U_15586,U_15590))
    | ~ sP1037(U_15586,U_15588,U_15584,U_15590) ),
    inference(clausify,[status(thm)],[f_3936_4]) ).

fof(f_3937_1,plain,
    ! [V_c_2,V_b_2,V_Pa_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_Pa_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_b,V_Pa_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_Pa_2,V_b_2)),V_c_2),V_Pa_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_3937_2,plain,
    ! [U_15596,U_15595,U_15594,U_15593,U_15592] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_15592,U_15593,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_15592)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15592),U_15594),c_Com_Ocom_OWhile(U_15595,U_15596)),c_Hoare__Mirabelle_Opeek__and(U_15592,U_15594,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_15595)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_15592),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_15592,U_15593,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_15592)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15592),c_Hoare__Mirabelle_Opeek__and(U_15592,U_15594,U_15595)),U_15596),U_15594)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_15592),tc_HOL_Obool)))) ),
    inference(variable_rename,[status(thm)],[f_3937_1]) ).

fof(f_3937_3,plain,
    ! [U_15593,U_15594,U_15592,U_15595,U_15596] :
      ( c_Hoare__Mirabelle_Ohoare__derivs(U_15592,U_15593,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_15592)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15592),U_15594),c_Com_Ocom_OWhile(U_15595,U_15596)),c_Hoare__Mirabelle_Opeek__and(U_15592,U_15594,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_15595)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_15592),tc_HOL_Obool))))
      | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_15592,U_15593,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_15592)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15592),c_Hoare__Mirabelle_Opeek__and(U_15592,U_15594,U_15595)),U_15596),U_15594)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_15592),tc_HOL_Obool)))) ),
    inference(definitional_conversion,[status(esa)],[f_3937_2]) ).

cnf(f_3937_4,plain,
    ( c_Hoare__Mirabelle_Ohoare__derivs(U_15592,U_15593,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_15592)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15592),U_15594),c_Com_Ocom_OWhile(U_15595,U_15596)),c_Hoare__Mirabelle_Opeek__and(U_15592,U_15594,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),U_15595)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_15592),tc_HOL_Obool))))
    | ~ c_Hoare__Mirabelle_Ohoare__derivs(U_15592,U_15593,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(U_15592)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(U_15592),c_Hoare__Mirabelle_Opeek__and(U_15592,U_15594,U_15595)),U_15596),U_15594)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(U_15592),tc_HOL_Obool)))) ),
    inference(clausify,[status(thm)],[f_3937_3]) ).

fof(f_3938_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_3938_2,plain,
    ! [U_15602,U_15601,U_15600,U_15599,U_15598,U_15597] :
      ( hAPP(U_15600,U_15601) = hAPP(c_Fun_Ocomp(U_15598,U_15598,U_15598,hAPP(U_15600,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15597,tc_HOL_Obool)),U_15601),hAPP(hAPP(c_Set_Oinsert(U_15597),U_15602),c_Orderings_Obot__class_Obot(tc_fun(U_15597,tc_HOL_Obool)))))),hAPP(U_15599,U_15602))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15597),U_15602),U_15601))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15597),U_15601))
      | ~ c_Finite__Set_Ofolding(U_15597,U_15598,U_15599,U_15600) ),
    inference(variable_rename,[status(thm)],[f_3938_1]) ).

fof(f_3938_3,plain,
    ! [U_15597,U_15598,U_15599,U_15600,U_15601,U_15602] :
      ( hAPP(U_15600,U_15601) = hAPP(c_Fun_Ocomp(U_15598,U_15598,U_15598,hAPP(U_15600,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15597,tc_HOL_Obool)),U_15601),hAPP(hAPP(c_Set_Oinsert(U_15597),U_15602),c_Orderings_Obot__class_Obot(tc_fun(U_15597,tc_HOL_Obool)))))),hAPP(U_15599,U_15602))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15597),U_15602),U_15601))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15597),U_15601))
      | ~ c_Finite__Set_Ofolding(U_15597,U_15598,U_15599,U_15600) ),
    inference(definitional_conversion,[status(esa)],[f_3938_2]) ).

cnf(f_3938_4,plain,
    ( hAPP(U_15600,U_15601) = hAPP(c_Fun_Ocomp(U_15598,U_15598,U_15598,hAPP(U_15600,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15597,tc_HOL_Obool)),U_15601),hAPP(hAPP(c_Set_Oinsert(U_15597),U_15602),c_Orderings_Obot__class_Obot(tc_fun(U_15597,tc_HOL_Obool)))))),hAPP(U_15599,U_15602))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15597),U_15602),U_15601))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15597),U_15601))
    | ~ c_Finite__Set_Ofolding(U_15597,U_15598,U_15599,U_15600) ),
    inference(clausify,[status(thm)],[f_3938_3]) ).

fof(f_3939_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_3939_2,plain,
    ! [U_15610,U_15609,U_15608,U_15607,U_15606,U_15605,U_15604,U_15603] :
      ( hAPP(hAPP(U_15607,U_15610),hAPP(c_Set_Oimage(U_15604,U_15604,U_15609),U_15608)) = hAPP(hAPP(U_15607,hAPP(c_Fun_Ocomp(U_15604,U_15603,U_15604,U_15610),U_15609)),U_15608)
      | ~ c_Fun_Oinj__on(U_15604,U_15604,U_15609,U_15608)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15604),U_15608))
      | ~ c_Finite__Set_Ofolding__image(U_15603,U_15604,U_15605,U_15606,U_15607) ),
    inference(variable_rename,[status(thm)],[f_3939_1]) ).

fof(f_3939_3,plain,
    ! [U_15604,U_15605,U_15606,U_15603,U_15607,U_15608,U_15609,U_15610] :
      ( hAPP(hAPP(U_15607,U_15610),hAPP(c_Set_Oimage(U_15604,U_15604,U_15609),U_15608)) = hAPP(hAPP(U_15607,hAPP(c_Fun_Ocomp(U_15604,U_15603,U_15604,U_15610),U_15609)),U_15608)
      | ~ c_Fun_Oinj__on(U_15604,U_15604,U_15609,U_15608)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15604),U_15608))
      | ~ c_Finite__Set_Ofolding__image(U_15603,U_15604,U_15605,U_15606,U_15607) ),
    inference(definitional_conversion,[status(esa)],[f_3939_2]) ).

cnf(f_3939_4,plain,
    ( hAPP(hAPP(U_15607,U_15610),hAPP(c_Set_Oimage(U_15604,U_15604,U_15609),U_15608)) = hAPP(hAPP(U_15607,hAPP(c_Fun_Ocomp(U_15604,U_15603,U_15604,U_15610),U_15609)),U_15608)
    | ~ c_Fun_Oinj__on(U_15604,U_15604,U_15609,U_15608)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15604),U_15608))
    | ~ c_Finite__Set_Ofolding__image(U_15603,U_15604,U_15605,U_15606,U_15607) ),
    inference(clausify,[status(thm)],[f_3939_3]) ).

fof(f_3940_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_3940_2,plain,
    ! [U_15621,U_15620,U_15619,U_15618,U_15617,U_15616,U_15615,U_15614,U_15613,U_15612,U_15611] :
      ( hAPP(c_Fun_Ocomp(U_15615,U_15616,U_15617,U_15618),hAPP(c_Fun_Ocomp(U_15619,U_15615,U_15617,U_15620),U_15621)) = hAPP(c_Fun_Ocomp(U_15619,U_15616,U_15617,hAPP(c_Fun_Ocomp(U_15615,U_15616,U_15619,U_15618),U_15620)),U_15621)
      | ~ c_Finite__Set_Ofolding(U_15611,U_15612,U_15613,U_15614) ),
    inference(variable_rename,[status(thm)],[f_3940_1]) ).

fof(f_3940_3,plain,
    ( ! [U_15621,U_15620,U_15619,U_15618,U_15617,U_15616,U_15615] : hAPP(c_Fun_Ocomp(U_15615,U_15616,U_15617,U_15618),hAPP(c_Fun_Ocomp(U_15619,U_15615,U_15617,U_15620),U_15621)) = hAPP(c_Fun_Ocomp(U_15619,U_15616,U_15617,hAPP(c_Fun_Ocomp(U_15615,U_15616,U_15619,U_15618),U_15620)),U_15621)
    | ! [U_15614,U_15613,U_15612,U_15611] : ~ c_Finite__Set_Ofolding(U_15611,U_15612,U_15613,U_15614) ),
    inference(miniscope,[status(thm)],[f_3940_2]) ).

fof(f_3940_4,plain,
    ! [U_15611,U_15612,U_15613,U_15615,U_15614,U_15616,U_15617,U_15618,U_15619,U_15620,U_15621] :
      ( hAPP(c_Fun_Ocomp(U_15615,U_15616,U_15617,U_15618),hAPP(c_Fun_Ocomp(U_15619,U_15615,U_15617,U_15620),U_15621)) = hAPP(c_Fun_Ocomp(U_15619,U_15616,U_15617,hAPP(c_Fun_Ocomp(U_15615,U_15616,U_15619,U_15618),U_15620)),U_15621)
      | ~ c_Finite__Set_Ofolding(U_15611,U_15612,U_15613,U_15614) ),
    inference(definitional_conversion,[status(esa)],[f_3940_3]) ).

cnf(f_3940_5,plain,
    ( hAPP(c_Fun_Ocomp(U_15615,U_15616,U_15617,U_15618),hAPP(c_Fun_Ocomp(U_15619,U_15615,U_15617,U_15620),U_15621)) = hAPP(c_Fun_Ocomp(U_15619,U_15616,U_15617,hAPP(c_Fun_Ocomp(U_15615,U_15616,U_15619,U_15618),U_15620)),U_15621)
    | ~ c_Finite__Set_Ofolding(U_15611,U_15612,U_15613,U_15614) ),
    inference(clausify,[status(thm)],[f_3940_4]) ).

fof(f_3941_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_3941_2,plain,
    ! [U_15627,U_15626,U_15625,U_15624,U_15623,U_15622] :
      ( hAPP(c_Fun_Ocomp(U_15623,U_15623,U_15623,hAPP(U_15624,U_15626)),hAPP(U_15624,U_15627)) = hAPP(c_Fun_Ocomp(U_15623,U_15623,U_15623,hAPP(U_15624,U_15627)),hAPP(U_15624,U_15626))
      | ~ c_Finite__Set_Ofolding(U_15622,U_15623,U_15624,U_15625) ),
    inference(variable_rename,[status(thm)],[f_3941_1]) ).

fof(f_3941_3,plain,
    ! [U_15627,U_15626,U_15625,U_15624,U_15623] :
      ( ! [U_15622] : ~ c_Finite__Set_Ofolding(U_15622,U_15623,U_15624,U_15625)
      | hAPP(c_Fun_Ocomp(U_15623,U_15623,U_15623,hAPP(U_15624,U_15626)),hAPP(U_15624,U_15627)) = hAPP(c_Fun_Ocomp(U_15623,U_15623,U_15623,hAPP(U_15624,U_15627)),hAPP(U_15624,U_15626)) ),
    inference(miniscope,[status(thm)],[f_3941_2]) ).

fof(f_3941_4,plain,
    ! [U_15623,U_15622,U_15624,U_15625,U_15626,U_15627] :
      ( ~ c_Finite__Set_Ofolding(U_15622,U_15623,U_15624,U_15625)
      | hAPP(c_Fun_Ocomp(U_15623,U_15623,U_15623,hAPP(U_15624,U_15626)),hAPP(U_15624,U_15627)) = hAPP(c_Fun_Ocomp(U_15623,U_15623,U_15623,hAPP(U_15624,U_15627)),hAPP(U_15624,U_15626)) ),
    inference(definitional_conversion,[status(esa)],[f_3941_3]) ).

cnf(f_3941_5,plain,
    ( ~ c_Finite__Set_Ofolding(U_15622,U_15623,U_15624,U_15625)
    | hAPP(c_Fun_Ocomp(U_15623,U_15623,U_15623,hAPP(U_15624,U_15626)),hAPP(U_15624,U_15627)) = hAPP(c_Fun_Ocomp(U_15623,U_15623,U_15623,hAPP(U_15624,U_15627)),hAPP(U_15624,U_15626)) ),
    inference(clausify,[status(thm)],[f_3941_4]) ).

fof(f_3942_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_3942_2,plain,
    ! [U_15635,U_15634,U_15633,U_15632,U_15631,U_15630,U_15629,U_15628] :
      ( hAPP(c_Fun_Ocomp(U_15629,U_15629,U_15632,hAPP(U_15630,U_15633)),hAPP(c_Fun_Ocomp(U_15629,U_15629,U_15632,hAPP(U_15630,U_15634)),U_15635)) = hAPP(c_Fun_Ocomp(U_15629,U_15629,U_15632,hAPP(U_15630,U_15634)),hAPP(c_Fun_Ocomp(U_15629,U_15629,U_15632,hAPP(U_15630,U_15633)),U_15635))
      | ~ c_Finite__Set_Ofolding(U_15628,U_15629,U_15630,U_15631) ),
    inference(variable_rename,[status(thm)],[f_3942_1]) ).

fof(f_3942_3,plain,
    ! [U_15635,U_15634,U_15633,U_15632,U_15631,U_15630,U_15629] :
      ( ! [U_15628] : ~ c_Finite__Set_Ofolding(U_15628,U_15629,U_15630,U_15631)
      | hAPP(c_Fun_Ocomp(U_15629,U_15629,U_15632,hAPP(U_15630,U_15633)),hAPP(c_Fun_Ocomp(U_15629,U_15629,U_15632,hAPP(U_15630,U_15634)),U_15635)) = hAPP(c_Fun_Ocomp(U_15629,U_15629,U_15632,hAPP(U_15630,U_15634)),hAPP(c_Fun_Ocomp(U_15629,U_15629,U_15632,hAPP(U_15630,U_15633)),U_15635)) ),
    inference(miniscope,[status(thm)],[f_3942_2]) ).

fof(f_3942_4,plain,
    ! [U_15629,U_15628,U_15630,U_15631,U_15632,U_15633,U_15634,U_15635] :
      ( ~ c_Finite__Set_Ofolding(U_15628,U_15629,U_15630,U_15631)
      | hAPP(c_Fun_Ocomp(U_15629,U_15629,U_15632,hAPP(U_15630,U_15633)),hAPP(c_Fun_Ocomp(U_15629,U_15629,U_15632,hAPP(U_15630,U_15634)),U_15635)) = hAPP(c_Fun_Ocomp(U_15629,U_15629,U_15632,hAPP(U_15630,U_15634)),hAPP(c_Fun_Ocomp(U_15629,U_15629,U_15632,hAPP(U_15630,U_15633)),U_15635)) ),
    inference(definitional_conversion,[status(esa)],[f_3942_3]) ).

cnf(f_3942_5,plain,
    ( ~ c_Finite__Set_Ofolding(U_15628,U_15629,U_15630,U_15631)
    | hAPP(c_Fun_Ocomp(U_15629,U_15629,U_15632,hAPP(U_15630,U_15633)),hAPP(c_Fun_Ocomp(U_15629,U_15629,U_15632,hAPP(U_15630,U_15634)),U_15635)) = hAPP(c_Fun_Ocomp(U_15629,U_15629,U_15632,hAPP(U_15630,U_15634)),hAPP(c_Fun_Ocomp(U_15629,U_15629,U_15632,hAPP(U_15630,U_15633)),U_15635)) ),
    inference(clausify,[status(thm)],[f_3942_4]) ).

fof(f_3943_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_3943_2,plain,
    ! [U_15643,U_15642,U_15641,U_15640,U_15639,U_15638,U_15637,U_15636] :
      ( hAPP(hAPP(U_15640,hAPP(hAPP(c_COMBS(U_15637,U_15636,U_15636),hAPP(hAPP(c_COMBB(U_15636,tc_fun(U_15636,U_15636),U_15637),U_15638),U_15642)),U_15643)),U_15641) = hAPP(hAPP(U_15638,hAPP(hAPP(U_15640,U_15642),U_15641)),hAPP(hAPP(U_15640,U_15643),U_15641))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15637),U_15641))
      | ~ c_Finite__Set_Ofolding__image(U_15636,U_15637,U_15638,U_15639,U_15640) ),
    inference(variable_rename,[status(thm)],[f_3943_1]) ).

fof(f_3943_3,plain,
    ! [U_15636,U_15637,U_15638,U_15639,U_15640,U_15641,U_15642,U_15643] :
      ( hAPP(hAPP(U_15640,hAPP(hAPP(c_COMBS(U_15637,U_15636,U_15636),hAPP(hAPP(c_COMBB(U_15636,tc_fun(U_15636,U_15636),U_15637),U_15638),U_15642)),U_15643)),U_15641) = hAPP(hAPP(U_15638,hAPP(hAPP(U_15640,U_15642),U_15641)),hAPP(hAPP(U_15640,U_15643),U_15641))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15637),U_15641))
      | ~ c_Finite__Set_Ofolding__image(U_15636,U_15637,U_15638,U_15639,U_15640) ),
    inference(definitional_conversion,[status(esa)],[f_3943_2]) ).

cnf(f_3943_4,plain,
    ( hAPP(hAPP(U_15640,hAPP(hAPP(c_COMBS(U_15637,U_15636,U_15636),hAPP(hAPP(c_COMBB(U_15636,tc_fun(U_15636,U_15636),U_15637),U_15638),U_15642)),U_15643)),U_15641) = hAPP(hAPP(U_15638,hAPP(hAPP(U_15640,U_15642),U_15641)),hAPP(hAPP(U_15640,U_15643),U_15641))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15637),U_15641))
    | ~ c_Finite__Set_Ofolding__image(U_15636,U_15637,U_15638,U_15639,U_15640) ),
    inference(clausify,[status(thm)],[f_3943_3]) ).

fof(f_3944_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_3944_2,plain,
    ! [U_15649,U_15648,U_15647,U_15646,U_15645,U_15644] :
      ( hAPP(c_Fun_Ocomp(U_15645,U_15645,U_15645,hAPP(U_15646,U_15649)),hAPP(U_15647,U_15648)) = hAPP(c_Fun_Ocomp(U_15645,U_15645,U_15645,hAPP(U_15647,U_15648)),hAPP(U_15646,U_15649))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15644),U_15648))
      | ~ c_Finite__Set_Ofolding(U_15644,U_15645,U_15646,U_15647) ),
    inference(variable_rename,[status(thm)],[f_3944_1]) ).

fof(f_3944_3,plain,
    ! [U_15645,U_15644,U_15646,U_15647,U_15648,U_15649] :
      ( hAPP(c_Fun_Ocomp(U_15645,U_15645,U_15645,hAPP(U_15646,U_15649)),hAPP(U_15647,U_15648)) = hAPP(c_Fun_Ocomp(U_15645,U_15645,U_15645,hAPP(U_15647,U_15648)),hAPP(U_15646,U_15649))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15644),U_15648))
      | ~ c_Finite__Set_Ofolding(U_15644,U_15645,U_15646,U_15647) ),
    inference(definitional_conversion,[status(esa)],[f_3944_2]) ).

cnf(f_3944_4,plain,
    ( hAPP(c_Fun_Ocomp(U_15645,U_15645,U_15645,hAPP(U_15646,U_15649)),hAPP(U_15647,U_15648)) = hAPP(c_Fun_Ocomp(U_15645,U_15645,U_15645,hAPP(U_15647,U_15648)),hAPP(U_15646,U_15649))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15644),U_15648))
    | ~ c_Finite__Set_Ofolding(U_15644,U_15645,U_15646,U_15647) ),
    inference(clausify,[status(thm)],[f_3944_3]) ).

fof(f_3945_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_3945_2,plain,
    ! [U_15657,U_15656,U_15655,U_15654,U_15653,U_15652,U_15651,U_15650] :
      ( hAPP(c_Fun_Ocomp(U_15651,U_15651,U_15655,hAPP(U_15652,U_15656)),hAPP(c_Fun_Ocomp(U_15651,U_15651,U_15655,hAPP(U_15653,U_15654)),U_15657)) = hAPP(c_Fun_Ocomp(U_15651,U_15651,U_15655,hAPP(U_15653,U_15654)),hAPP(c_Fun_Ocomp(U_15651,U_15651,U_15655,hAPP(U_15652,U_15656)),U_15657))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15650),U_15654))
      | ~ c_Finite__Set_Ofolding(U_15650,U_15651,U_15652,U_15653) ),
    inference(variable_rename,[status(thm)],[f_3945_1]) ).

fof(f_3945_3,plain,
    ! [U_15655,U_15651,U_15650,U_15652,U_15653,U_15654,U_15656,U_15657] :
      ( hAPP(c_Fun_Ocomp(U_15651,U_15651,U_15655,hAPP(U_15652,U_15656)),hAPP(c_Fun_Ocomp(U_15651,U_15651,U_15655,hAPP(U_15653,U_15654)),U_15657)) = hAPP(c_Fun_Ocomp(U_15651,U_15651,U_15655,hAPP(U_15653,U_15654)),hAPP(c_Fun_Ocomp(U_15651,U_15651,U_15655,hAPP(U_15652,U_15656)),U_15657))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15650),U_15654))
      | ~ c_Finite__Set_Ofolding(U_15650,U_15651,U_15652,U_15653) ),
    inference(definitional_conversion,[status(esa)],[f_3945_2]) ).

cnf(f_3945_4,plain,
    ( hAPP(c_Fun_Ocomp(U_15651,U_15651,U_15655,hAPP(U_15652,U_15656)),hAPP(c_Fun_Ocomp(U_15651,U_15651,U_15655,hAPP(U_15653,U_15654)),U_15657)) = hAPP(c_Fun_Ocomp(U_15651,U_15651,U_15655,hAPP(U_15653,U_15654)),hAPP(c_Fun_Ocomp(U_15651,U_15651,U_15655,hAPP(U_15652,U_15656)),U_15657))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15650),U_15654))
    | ~ c_Finite__Set_Ofolding(U_15650,U_15651,U_15652,U_15653) ),
    inference(clausify,[status(thm)],[f_3945_3]) ).

fof(f_3946_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_3946_2,plain,
    ! [U_15663,U_15662,U_15661,U_15660,U_15659,U_15658] :
      ( hAPP(c_Fun_Ocomp(U_15659,U_15659,U_15659,hAPP(U_15661,U_15663)),hAPP(U_15661,U_15662)) = hAPP(c_Fun_Ocomp(U_15659,U_15659,U_15659,hAPP(U_15661,U_15662)),hAPP(U_15661,U_15663))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15658),U_15663))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15658),U_15662))
      | ~ c_Finite__Set_Ofolding(U_15658,U_15659,U_15660,U_15661) ),
    inference(variable_rename,[status(thm)],[f_3946_1]) ).

fof(f_3946_3,plain,
    ! [U_15659,U_15660,U_15658,U_15661,U_15662,U_15663] :
      ( hAPP(c_Fun_Ocomp(U_15659,U_15659,U_15659,hAPP(U_15661,U_15663)),hAPP(U_15661,U_15662)) = hAPP(c_Fun_Ocomp(U_15659,U_15659,U_15659,hAPP(U_15661,U_15662)),hAPP(U_15661,U_15663))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15658),U_15663))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15658),U_15662))
      | ~ c_Finite__Set_Ofolding(U_15658,U_15659,U_15660,U_15661) ),
    inference(definitional_conversion,[status(esa)],[f_3946_2]) ).

cnf(f_3946_4,plain,
    ( hAPP(c_Fun_Ocomp(U_15659,U_15659,U_15659,hAPP(U_15661,U_15663)),hAPP(U_15661,U_15662)) = hAPP(c_Fun_Ocomp(U_15659,U_15659,U_15659,hAPP(U_15661,U_15662)),hAPP(U_15661,U_15663))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15658),U_15663))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15658),U_15662))
    | ~ c_Finite__Set_Ofolding(U_15658,U_15659,U_15660,U_15661) ),
    inference(clausify,[status(thm)],[f_3946_3]) ).

fof(f_3947_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_3947_2,plain,
    ! [U_15671,U_15670,U_15669,U_15668,U_15667,U_15666,U_15665,U_15664] :
      ( hAPP(c_Fun_Ocomp(U_15665,U_15665,U_15670,hAPP(U_15667,U_15669)),hAPP(c_Fun_Ocomp(U_15665,U_15665,U_15670,hAPP(U_15667,U_15668)),U_15671)) = hAPP(c_Fun_Ocomp(U_15665,U_15665,U_15670,hAPP(U_15667,U_15668)),hAPP(c_Fun_Ocomp(U_15665,U_15665,U_15670,hAPP(U_15667,U_15669)),U_15671))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15664),U_15669))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15664),U_15668))
      | ~ c_Finite__Set_Ofolding(U_15664,U_15665,U_15666,U_15667) ),
    inference(variable_rename,[status(thm)],[f_3947_1]) ).

fof(f_3947_3,plain,
    ! [U_15664,U_15666,U_15665,U_15667,U_15668,U_15669,U_15670,U_15671] :
      ( hAPP(c_Fun_Ocomp(U_15665,U_15665,U_15670,hAPP(U_15667,U_15669)),hAPP(c_Fun_Ocomp(U_15665,U_15665,U_15670,hAPP(U_15667,U_15668)),U_15671)) = hAPP(c_Fun_Ocomp(U_15665,U_15665,U_15670,hAPP(U_15667,U_15668)),hAPP(c_Fun_Ocomp(U_15665,U_15665,U_15670,hAPP(U_15667,U_15669)),U_15671))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15664),U_15669))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15664),U_15668))
      | ~ c_Finite__Set_Ofolding(U_15664,U_15665,U_15666,U_15667) ),
    inference(definitional_conversion,[status(esa)],[f_3947_2]) ).

cnf(f_3947_4,plain,
    ( hAPP(c_Fun_Ocomp(U_15665,U_15665,U_15670,hAPP(U_15667,U_15669)),hAPP(c_Fun_Ocomp(U_15665,U_15665,U_15670,hAPP(U_15667,U_15668)),U_15671)) = hAPP(c_Fun_Ocomp(U_15665,U_15665,U_15670,hAPP(U_15667,U_15668)),hAPP(c_Fun_Ocomp(U_15665,U_15665,U_15670,hAPP(U_15667,U_15669)),U_15671))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15664),U_15669))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15664),U_15668))
    | ~ c_Finite__Set_Ofolding(U_15664,U_15665,U_15666,U_15667) ),
    inference(clausify,[status(thm)],[f_3947_3]) ).

fof(f_3948_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_3948_2,plain,
    ! [U_15675,U_15674,U_15673,U_15672] :
      ( hAPP(U_15675,c_Orderings_Obot__class_Obot(tc_fun(U_15672,tc_HOL_Obool))) = c_Fun_Oid(U_15673)
      | ~ c_Finite__Set_Ofolding(U_15672,U_15673,U_15674,U_15675) ),
    inference(variable_rename,[status(thm)],[f_3948_1]) ).

fof(f_3948_3,plain,
    ! [U_15674,U_15675,U_15673,U_15672] :
      ( hAPP(U_15675,c_Orderings_Obot__class_Obot(tc_fun(U_15672,tc_HOL_Obool))) = c_Fun_Oid(U_15673)
      | ~ c_Finite__Set_Ofolding(U_15672,U_15673,U_15674,U_15675) ),
    inference(definitional_conversion,[status(esa)],[f_3948_2]) ).

cnf(f_3948_4,plain,
    ( hAPP(U_15675,c_Orderings_Obot__class_Obot(tc_fun(U_15672,tc_HOL_Obool))) = c_Fun_Oid(U_15673)
    | ~ c_Finite__Set_Ofolding(U_15672,U_15673,U_15674,U_15675) ),
    inference(clausify,[status(thm)],[f_3948_3]) ).

fof(f_3949_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_3949_2,plain,
    ! [U_15682,U_15681,U_15680,U_15679,U_15678,U_15677,U_15676] :
      ( hAPP(hAPP(U_15680,U_15682),U_15681) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15676,U_15677,U_15678),U_15682),U_15679),U_15681)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15677),U_15681))
      | ~ c_Finite__Set_Ofolding__image(U_15676,U_15677,U_15678,U_15679,U_15680) ),
    inference(variable_rename,[status(thm)],[f_3949_1]) ).

fof(f_3949_3,plain,
    ! [U_15676,U_15677,U_15678,U_15679,U_15680,U_15681,U_15682] :
      ( hAPP(hAPP(U_15680,U_15682),U_15681) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15676,U_15677,U_15678),U_15682),U_15679),U_15681)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15677),U_15681))
      | ~ c_Finite__Set_Ofolding__image(U_15676,U_15677,U_15678,U_15679,U_15680) ),
    inference(definitional_conversion,[status(esa)],[f_3949_2]) ).

cnf(f_3949_4,plain,
    ( hAPP(hAPP(U_15680,U_15682),U_15681) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15676,U_15677,U_15678),U_15682),U_15679),U_15681)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15677),U_15681))
    | ~ c_Finite__Set_Ofolding__image(U_15676,U_15677,U_15678,U_15679,U_15680) ),
    inference(clausify,[status(thm)],[f_3949_3]) ).

fof(f_3950_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_3950_2,plain,
    ! [U_15688,U_15687,U_15686,U_15685,U_15684,U_15683] :
      ( hAPP(U_15686,hAPP(hAPP(c_Set_Oinsert(U_15683),U_15688),U_15687)) = hAPP(c_Fun_Ocomp(U_15684,U_15684,U_15684,hAPP(U_15686,U_15687)),hAPP(U_15685,U_15688))
      | hBOOL(hAPP(hAPP(c_member(U_15683),U_15688),U_15687))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15683),U_15687))
      | ~ c_Finite__Set_Ofolding(U_15683,U_15684,U_15685,U_15686) ),
    inference(variable_rename,[status(thm)],[f_3950_1]) ).

fof(f_3950_3,plain,
    ! [U_15684,U_15685,U_15683,U_15686,U_15687,U_15688] :
      ( hAPP(U_15686,hAPP(hAPP(c_Set_Oinsert(U_15683),U_15688),U_15687)) = hAPP(c_Fun_Ocomp(U_15684,U_15684,U_15684,hAPP(U_15686,U_15687)),hAPP(U_15685,U_15688))
      | hBOOL(hAPP(hAPP(c_member(U_15683),U_15688),U_15687))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15683),U_15687))
      | ~ c_Finite__Set_Ofolding(U_15683,U_15684,U_15685,U_15686) ),
    inference(definitional_conversion,[status(esa)],[f_3950_2]) ).

cnf(f_3950_4,plain,
    ( hAPP(U_15686,hAPP(hAPP(c_Set_Oinsert(U_15683),U_15688),U_15687)) = hAPP(c_Fun_Ocomp(U_15684,U_15684,U_15684,hAPP(U_15686,U_15687)),hAPP(U_15685,U_15688))
    | hBOOL(hAPP(hAPP(c_member(U_15683),U_15688),U_15687))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15683),U_15687))
    | ~ c_Finite__Set_Ofolding(U_15683,U_15684,U_15685,U_15686) ),
    inference(clausify,[status(thm)],[f_3950_3]) ).

fof(f_3951_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_3951_2,plain,
    ! [U_15694,U_15693,U_15692,U_15691,U_15690,U_15689] :
      ( hAPP(c_Fun_Ocomp(U_15690,U_15690,U_15690,hAPP(U_15692,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15689,tc_HOL_Obool)),U_15693),U_15694))),hAPP(U_15692,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15689,tc_HOL_Obool)),U_15693),U_15694))) = hAPP(c_Fun_Ocomp(U_15690,U_15690,U_15690,hAPP(U_15692,U_15693)),hAPP(U_15692,U_15694))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15689),U_15694))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15689),U_15693))
      | ~ c_Finite__Set_Ofolding(U_15689,U_15690,U_15691,U_15692) ),
    inference(variable_rename,[status(thm)],[f_3951_1]) ).

fof(f_3951_3,plain,
    ! [U_15689,U_15690,U_15691,U_15692,U_15693,U_15694] :
      ( hAPP(c_Fun_Ocomp(U_15690,U_15690,U_15690,hAPP(U_15692,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15689,tc_HOL_Obool)),U_15693),U_15694))),hAPP(U_15692,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15689,tc_HOL_Obool)),U_15693),U_15694))) = hAPP(c_Fun_Ocomp(U_15690,U_15690,U_15690,hAPP(U_15692,U_15693)),hAPP(U_15692,U_15694))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15689),U_15694))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15689),U_15693))
      | ~ c_Finite__Set_Ofolding(U_15689,U_15690,U_15691,U_15692) ),
    inference(definitional_conversion,[status(esa)],[f_3951_2]) ).

cnf(f_3951_4,plain,
    ( hAPP(c_Fun_Ocomp(U_15690,U_15690,U_15690,hAPP(U_15692,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15689,tc_HOL_Obool)),U_15693),U_15694))),hAPP(U_15692,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15689,tc_HOL_Obool)),U_15693),U_15694))) = hAPP(c_Fun_Ocomp(U_15690,U_15690,U_15690,hAPP(U_15692,U_15693)),hAPP(U_15692,U_15694))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15689),U_15694))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15689),U_15693))
    | ~ c_Finite__Set_Ofolding(U_15689,U_15690,U_15691,U_15692) ),
    inference(clausify,[status(thm)],[f_3951_3]) ).

fof(f_3952_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_3952_2,plain,
    ! [U_15700,U_15699,U_15698,U_15697,U_15696,U_15695] :
      ( hAPP(U_15698,hAPP(hAPP(c_Set_Oinsert(U_15695),U_15700),U_15699)) = hAPP(c_Fun_Ocomp(U_15696,U_15696,U_15696,hAPP(U_15698,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15695,tc_HOL_Obool)),U_15699),hAPP(hAPP(c_Set_Oinsert(U_15695),U_15700),c_Orderings_Obot__class_Obot(tc_fun(U_15695,tc_HOL_Obool)))))),hAPP(U_15697,U_15700))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15695),U_15699))
      | ~ c_Finite__Set_Ofolding(U_15695,U_15696,U_15697,U_15698) ),
    inference(variable_rename,[status(thm)],[f_3952_1]) ).

fof(f_3952_3,plain,
    ! [U_15695,U_15697,U_15698,U_15696,U_15699,U_15700] :
      ( hAPP(U_15698,hAPP(hAPP(c_Set_Oinsert(U_15695),U_15700),U_15699)) = hAPP(c_Fun_Ocomp(U_15696,U_15696,U_15696,hAPP(U_15698,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15695,tc_HOL_Obool)),U_15699),hAPP(hAPP(c_Set_Oinsert(U_15695),U_15700),c_Orderings_Obot__class_Obot(tc_fun(U_15695,tc_HOL_Obool)))))),hAPP(U_15697,U_15700))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15695),U_15699))
      | ~ c_Finite__Set_Ofolding(U_15695,U_15696,U_15697,U_15698) ),
    inference(definitional_conversion,[status(esa)],[f_3952_2]) ).

cnf(f_3952_4,plain,
    ( hAPP(U_15698,hAPP(hAPP(c_Set_Oinsert(U_15695),U_15700),U_15699)) = hAPP(c_Fun_Ocomp(U_15696,U_15696,U_15696,hAPP(U_15698,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_15695,tc_HOL_Obool)),U_15699),hAPP(hAPP(c_Set_Oinsert(U_15695),U_15700),c_Orderings_Obot__class_Obot(tc_fun(U_15695,tc_HOL_Obool)))))),hAPP(U_15697,U_15700))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15695),U_15699))
    | ~ c_Finite__Set_Ofolding(U_15695,U_15696,U_15697,U_15698) ),
    inference(clausify,[status(thm)],[f_3952_3]) ).

fof(f_3953_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_3953_2,plain,
    ! [U_15706,U_15705,U_15704,U_15703,U_15702,U_15701] :
      ( hAPP(U_15704,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15701,tc_HOL_Obool)),U_15705),U_15706)) = hAPP(c_Fun_Ocomp(U_15702,U_15702,U_15702,hAPP(U_15704,U_15705)),hAPP(U_15704,U_15706))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15701,tc_HOL_Obool)),U_15705),U_15706) != c_Orderings_Obot__class_Obot(tc_fun(U_15701,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15701),U_15706))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15701),U_15705))
      | ~ c_Finite__Set_Ofolding(U_15701,U_15702,U_15703,U_15704) ),
    inference(variable_rename,[status(thm)],[f_3953_1]) ).

fof(f_3953_3,plain,
    ! [U_15701,U_15702,U_15703,U_15704,U_15705,U_15706] :
      ( hAPP(U_15704,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15701,tc_HOL_Obool)),U_15705),U_15706)) = hAPP(c_Fun_Ocomp(U_15702,U_15702,U_15702,hAPP(U_15704,U_15705)),hAPP(U_15704,U_15706))
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15701,tc_HOL_Obool)),U_15705),U_15706) != c_Orderings_Obot__class_Obot(tc_fun(U_15701,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15701),U_15706))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15701),U_15705))
      | ~ c_Finite__Set_Ofolding(U_15701,U_15702,U_15703,U_15704) ),
    inference(definitional_conversion,[status(esa)],[f_3953_2]) ).

cnf(f_3953_4,plain,
    ( hAPP(U_15704,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15701,tc_HOL_Obool)),U_15705),U_15706)) = hAPP(c_Fun_Ocomp(U_15702,U_15702,U_15702,hAPP(U_15704,U_15705)),hAPP(U_15704,U_15706))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_15701,tc_HOL_Obool)),U_15705),U_15706) != c_Orderings_Obot__class_Obot(tc_fun(U_15701,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15701),U_15706))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15701),U_15705))
    | ~ c_Finite__Set_Ofolding(U_15701,U_15702,U_15703,U_15704) ),
    inference(clausify,[status(thm)],[f_3953_3]) ).

fof(f_3954_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_3954_2,plain,
    ! [U_15714,U_15713,U_15712,U_15711,U_15710,U_15709] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15714,U_15709),U_15713),hAPP(c_Set_Oimage(U_15710,U_15714,U_15712),U_15711)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15710,U_15709),hAPP(c_Fun_Ocomp(U_15714,U_15709,U_15710,U_15713),U_15712)),U_15711)
      | ? [U_15708] :
          ( ? [U_15707] :
              ( hAPP(U_15713,hAPP(U_15712,U_15708)) != c_Groups_Ozero__class_Ozero(U_15709)
              & hAPP(U_15712,U_15708) = hAPP(U_15712,U_15707)
              & U_15708 != U_15707
              & hBOOL(hAPP(hAPP(c_member(U_15710),U_15707),U_15711)) )
          & hBOOL(hAPP(hAPP(c_member(U_15710),U_15708),U_15711)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15710),U_15711))
      | ~ class_Groups_Ocomm__monoid__add(U_15709) ),
    inference(variable_rename,[status(thm)],[f_3954_1]) ).

fof(f_3954_3,plain,
    ! [U_15714,U_15713,U_15712,U_15711,U_15710,U_15709] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15714,U_15709),U_15713),hAPP(c_Set_Oimage(U_15710,U_15714,U_15712),U_15711)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15710,U_15709),hAPP(c_Fun_Ocomp(U_15714,U_15709,U_15710,U_15713),U_15712)),U_15711)
      | ( ? [U_15707] :
            ( hAPP(U_15713,hAPP(U_15712,sK381(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709))) != c_Groups_Ozero__class_Ozero(U_15709)
            & hAPP(U_15712,sK381(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709)) = hAPP(U_15712,U_15707)
            & sK381(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709) != U_15707
            & hBOOL(hAPP(hAPP(c_member(U_15710),U_15707),U_15711)) )
        & hBOOL(hAPP(hAPP(c_member(U_15710),sK381(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709)),U_15711)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15710),U_15711))
      | ~ class_Groups_Ocomm__monoid__add(U_15709) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK381]),skolemize(U_15708,sK381(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709))],[f_3954_2]) ).

fof(f_3954_4,plain,
    ! [U_15714,U_15713,U_15712,U_15711,U_15710,U_15709] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15714,U_15709),U_15713),hAPP(c_Set_Oimage(U_15710,U_15714,U_15712),U_15711)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15710,U_15709),hAPP(c_Fun_Ocomp(U_15714,U_15709,U_15710,U_15713),U_15712)),U_15711)
      | ( hAPP(U_15713,hAPP(U_15712,sK381(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709))) != c_Groups_Ozero__class_Ozero(U_15709)
        & hAPP(U_15712,sK381(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709)) = hAPP(U_15712,sK382(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709))
        & sK381(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709) != sK382(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709)
        & hBOOL(hAPP(hAPP(c_member(U_15710),sK382(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709)),U_15711))
        & hBOOL(hAPP(hAPP(c_member(U_15710),sK381(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709)),U_15711)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15710),U_15711))
      | ~ class_Groups_Ocomm__monoid__add(U_15709) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK382]),skolemize(U_15707,sK382(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709))],[f_3954_3]) ).

fof(f_3954_5,plain,
    ( ! [U_15709,U_15710,U_15711,U_15712,U_15713,U_15714] :
        ( hAPP(U_15713,hAPP(U_15712,sK381(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709))) != c_Groups_Ozero__class_Ozero(U_15709)
        | ~ sP1038(U_15709,U_15710,U_15711,U_15712,U_15713,U_15714) )
    & ! [U_15709,U_15710,U_15711,U_15712,U_15713,U_15714] :
        ( hAPP(U_15712,sK381(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709)) = hAPP(U_15712,sK382(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709))
        | ~ sP1038(U_15709,U_15710,U_15711,U_15712,U_15713,U_15714) )
    & ! [U_15709,U_15710,U_15711,U_15712,U_15713,U_15714] :
        ( sK381(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709) != sK382(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709)
        | ~ sP1038(U_15709,U_15710,U_15711,U_15712,U_15713,U_15714) )
    & ! [U_15709,U_15710,U_15711,U_15712,U_15713,U_15714] :
        ( hBOOL(hAPP(hAPP(c_member(U_15710),sK382(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709)),U_15711))
        | ~ sP1038(U_15709,U_15710,U_15711,U_15712,U_15713,U_15714) )
    & ! [U_15709,U_15710,U_15711,U_15712,U_15713,U_15714] :
        ( hBOOL(hAPP(hAPP(c_member(U_15710),sK381(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709)),U_15711))
        | ~ sP1038(U_15709,U_15710,U_15711,U_15712,U_15713,U_15714) )
    & ! [U_15709,U_15710,U_15711,U_15712,U_15713,U_15714] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15714,U_15709),U_15713),hAPP(c_Set_Oimage(U_15710,U_15714,U_15712),U_15711)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15710,U_15709),hAPP(c_Fun_Ocomp(U_15714,U_15709,U_15710,U_15713),U_15712)),U_15711)
        | sP1038(U_15709,U_15710,U_15711,U_15712,U_15713,U_15714)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15710),U_15711))
        | ~ class_Groups_Ocomm__monoid__add(U_15709) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1038])],[f_3954_4]) ).

cnf(f_3954_6,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15714,U_15709),U_15713),hAPP(c_Set_Oimage(U_15710,U_15714,U_15712),U_15711)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15710,U_15709),hAPP(c_Fun_Ocomp(U_15714,U_15709,U_15710,U_15713),U_15712)),U_15711)
    | sP1038(U_15709,U_15710,U_15711,U_15712,U_15713,U_15714)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15710),U_15711))
    | ~ class_Groups_Ocomm__monoid__add(U_15709) ),
    inference(clausify,[status(thm)],[f_3954_5]) ).

cnf(f_3954_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15710),sK381(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709)),U_15711))
    | ~ sP1038(U_15709,U_15710,U_15711,U_15712,U_15713,U_15714) ),
    inference(clausify,[status(thm)],[f_3954_5]) ).

cnf(f_3954_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15710),sK382(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709)),U_15711))
    | ~ sP1038(U_15709,U_15710,U_15711,U_15712,U_15713,U_15714) ),
    inference(clausify,[status(thm)],[f_3954_5]) ).

cnf(f_3954_9,plain,
    ( sK381(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709) != sK382(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709)
    | ~ sP1038(U_15709,U_15710,U_15711,U_15712,U_15713,U_15714) ),
    inference(clausify,[status(thm)],[f_3954_5]) ).

cnf(f_3954_10,plain,
    ( hAPP(U_15712,sK381(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709)) = hAPP(U_15712,sK382(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709))
    | ~ sP1038(U_15709,U_15710,U_15711,U_15712,U_15713,U_15714) ),
    inference(clausify,[status(thm)],[f_3954_5]) ).

cnf(f_3954_11,plain,
    ( hAPP(U_15713,hAPP(U_15712,sK381(U_15714,U_15713,U_15712,U_15711,U_15710,U_15709))) != c_Groups_Ozero__class_Ozero(U_15709)
    | ~ sP1038(U_15709,U_15710,U_15711,U_15712,U_15713,U_15714) ),
    inference(clausify,[status(thm)],[f_3954_5]) ).

fof(f_3955_1,plain,
    ! [V_Pa_2,V_f_2,T_b,T_c] : c_Random__Sequence_Omap(T_c,T_b,V_f_2,V_Pa_2) = c_Random__Sequence_Obind(T_c,T_b,V_Pa_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_3955_2,plain,
    ! [U_15718,U_15717,U_15716,U_15715] : c_Random__Sequence_Omap(U_15715,U_15716,U_15717,U_15718) = c_Random__Sequence_Obind(U_15715,U_15716,U_15718,hAPP(c_Fun_Ocomp(U_15716,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_15716)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),U_15715,c_Random__Sequence_Osingle(U_15716)),U_15717)),
    inference(variable_rename,[status(thm)],[f_3955_1]) ).

fof(f_3955_3,plain,
    ! [U_15716,U_15717,U_15715,U_15718] : c_Random__Sequence_Omap(U_15715,U_15716,U_15717,U_15718) = c_Random__Sequence_Obind(U_15715,U_15716,U_15718,hAPP(c_Fun_Ocomp(U_15716,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_15716)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),U_15715,c_Random__Sequence_Osingle(U_15716)),U_15717)),
    inference(definitional_conversion,[status(esa)],[f_3955_2]) ).

cnf(f_3955_4,plain,
    c_Random__Sequence_Omap(U_15715,U_15716,U_15717,U_15718) = c_Random__Sequence_Obind(U_15715,U_15716,U_15718,hAPP(c_Fun_Ocomp(U_15716,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_15716)))),tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))))),U_15715,c_Random__Sequence_Osingle(U_15716)),U_15717)),
    inference(clausify,[status(thm)],[f_3955_3]) ).

fof(f_3956_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_3956_2,plain,
    ! [U_15724,U_15723,U_15722,U_15721,U_15720,U_15719] :
      ( hAPP(U_15722,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15719,tc_HOL_Obool)),U_15723),U_15724)) = hAPP(c_Fun_Ocomp(U_15720,U_15720,U_15720,hAPP(U_15722,U_15723)),hAPP(U_15722,U_15724))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15719),U_15724))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15719),U_15723))
      | ~ c_Finite__Set_Ofolding__idem(U_15719,U_15720,U_15721,U_15722) ),
    inference(variable_rename,[status(thm)],[f_3956_1]) ).

fof(f_3956_3,plain,
    ! [U_15719,U_15722,U_15720,U_15721,U_15723,U_15724] :
      ( hAPP(U_15722,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15719,tc_HOL_Obool)),U_15723),U_15724)) = hAPP(c_Fun_Ocomp(U_15720,U_15720,U_15720,hAPP(U_15722,U_15723)),hAPP(U_15722,U_15724))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15719),U_15724))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15719),U_15723))
      | ~ c_Finite__Set_Ofolding__idem(U_15719,U_15720,U_15721,U_15722) ),
    inference(definitional_conversion,[status(esa)],[f_3956_2]) ).

cnf(f_3956_4,plain,
    ( hAPP(U_15722,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15719,tc_HOL_Obool)),U_15723),U_15724)) = hAPP(c_Fun_Ocomp(U_15720,U_15720,U_15720,hAPP(U_15722,U_15723)),hAPP(U_15722,U_15724))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15719),U_15724))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15719),U_15723))
    | ~ c_Finite__Set_Ofolding__idem(U_15719,U_15720,U_15721,U_15722) ),
    inference(clausify,[status(thm)],[f_3956_3]) ).

fof(f_3957_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_3957_2,plain,
    ! [U_15730,U_15729,U_15728,U_15727,U_15726,U_15725] :
      ( hAPP(c_Fun_Ocomp(U_15726,U_15726,U_15726,hAPP(U_15728,U_15729)),hAPP(U_15728,U_15730)) = hAPP(U_15728,U_15729)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15725,tc_HOL_Obool)),U_15730),U_15729))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15725),U_15729))
      | ~ c_Finite__Set_Ofolding__idem(U_15725,U_15726,U_15727,U_15728) ),
    inference(variable_rename,[status(thm)],[f_3957_1]) ).

fof(f_3957_3,plain,
    ! [U_15728,U_15726,U_15727,U_15725,U_15729,U_15730] :
      ( hAPP(c_Fun_Ocomp(U_15726,U_15726,U_15726,hAPP(U_15728,U_15729)),hAPP(U_15728,U_15730)) = hAPP(U_15728,U_15729)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15725,tc_HOL_Obool)),U_15730),U_15729))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15725),U_15729))
      | ~ c_Finite__Set_Ofolding__idem(U_15725,U_15726,U_15727,U_15728) ),
    inference(definitional_conversion,[status(esa)],[f_3957_2]) ).

cnf(f_3957_4,plain,
    ( hAPP(c_Fun_Ocomp(U_15726,U_15726,U_15726,hAPP(U_15728,U_15729)),hAPP(U_15728,U_15730)) = hAPP(U_15728,U_15729)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15725,tc_HOL_Obool)),U_15730),U_15729))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15725),U_15729))
    | ~ c_Finite__Set_Ofolding__idem(U_15725,U_15726,U_15727,U_15728) ),
    inference(clausify,[status(thm)],[f_3957_3]) ).

fof(f_3958_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_3958_2,plain,
    ! [U_15737,U_15736,U_15735,U_15734,U_15733,U_15732,U_15731] :
      ( hAPP(c_Fun_Ocomp(U_15732,U_15732,U_15735,hAPP(U_15733,U_15736)),hAPP(c_Fun_Ocomp(U_15732,U_15732,U_15735,hAPP(U_15733,U_15736)),U_15737)) = hAPP(c_Fun_Ocomp(U_15732,U_15732,U_15735,hAPP(U_15733,U_15736)),U_15737)
      | ~ c_Finite__Set_Ofolding__idem(U_15731,U_15732,U_15733,U_15734) ),
    inference(variable_rename,[status(thm)],[f_3958_1]) ).

fof(f_3958_3,plain,
    ! [U_15737,U_15736,U_15735,U_15734,U_15733,U_15732] :
      ( ! [U_15731] : ~ c_Finite__Set_Ofolding__idem(U_15731,U_15732,U_15733,U_15734)
      | hAPP(c_Fun_Ocomp(U_15732,U_15732,U_15735,hAPP(U_15733,U_15736)),hAPP(c_Fun_Ocomp(U_15732,U_15732,U_15735,hAPP(U_15733,U_15736)),U_15737)) = hAPP(c_Fun_Ocomp(U_15732,U_15732,U_15735,hAPP(U_15733,U_15736)),U_15737) ),
    inference(miniscope,[status(thm)],[f_3958_2]) ).

fof(f_3958_4,plain,
    ! [U_15731,U_15734,U_15732,U_15735,U_15733,U_15736,U_15737] :
      ( ~ c_Finite__Set_Ofolding__idem(U_15731,U_15732,U_15733,U_15734)
      | hAPP(c_Fun_Ocomp(U_15732,U_15732,U_15735,hAPP(U_15733,U_15736)),hAPP(c_Fun_Ocomp(U_15732,U_15732,U_15735,hAPP(U_15733,U_15736)),U_15737)) = hAPP(c_Fun_Ocomp(U_15732,U_15732,U_15735,hAPP(U_15733,U_15736)),U_15737) ),
    inference(definitional_conversion,[status(esa)],[f_3958_3]) ).

cnf(f_3958_5,plain,
    ( ~ c_Finite__Set_Ofolding__idem(U_15731,U_15732,U_15733,U_15734)
    | hAPP(c_Fun_Ocomp(U_15732,U_15732,U_15735,hAPP(U_15733,U_15736)),hAPP(c_Fun_Ocomp(U_15732,U_15732,U_15735,hAPP(U_15733,U_15736)),U_15737)) = hAPP(c_Fun_Ocomp(U_15732,U_15732,U_15735,hAPP(U_15733,U_15736)),U_15737) ),
    inference(clausify,[status(thm)],[f_3958_4]) ).

fof(f_3959_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_3959_2,plain,
    ! [U_15742,U_15741,U_15740,U_15739,U_15738] :
      ( hAPP(c_Fun_Ocomp(U_15739,U_15739,U_15739,hAPP(U_15740,U_15742)),hAPP(U_15740,U_15742)) = hAPP(U_15740,U_15742)
      | ~ c_Finite__Set_Ofolding__idem(U_15738,U_15739,U_15740,U_15741) ),
    inference(variable_rename,[status(thm)],[f_3959_1]) ).

fof(f_3959_3,plain,
    ! [U_15742,U_15741,U_15740,U_15739] :
      ( ! [U_15738] : ~ c_Finite__Set_Ofolding__idem(U_15738,U_15739,U_15740,U_15741)
      | hAPP(c_Fun_Ocomp(U_15739,U_15739,U_15739,hAPP(U_15740,U_15742)),hAPP(U_15740,U_15742)) = hAPP(U_15740,U_15742) ),
    inference(miniscope,[status(thm)],[f_3959_2]) ).

fof(f_3959_4,plain,
    ! [U_15738,U_15740,U_15739,U_15741,U_15742] :
      ( ~ c_Finite__Set_Ofolding__idem(U_15738,U_15739,U_15740,U_15741)
      | hAPP(c_Fun_Ocomp(U_15739,U_15739,U_15739,hAPP(U_15740,U_15742)),hAPP(U_15740,U_15742)) = hAPP(U_15740,U_15742) ),
    inference(definitional_conversion,[status(esa)],[f_3959_3]) ).

cnf(f_3959_5,plain,
    ( ~ c_Finite__Set_Ofolding__idem(U_15738,U_15739,U_15740,U_15741)
    | hAPP(c_Fun_Ocomp(U_15739,U_15739,U_15739,hAPP(U_15740,U_15742)),hAPP(U_15740,U_15742)) = hAPP(U_15740,U_15742) ),
    inference(clausify,[status(thm)],[f_3959_4]) ).

fof(f_3960_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_3960_2,plain,
    ! [U_15748,U_15747,U_15746,U_15745,U_15744,U_15743] :
      ( hAPP(c_Fun_Ocomp(U_15744,U_15744,U_15744,hAPP(U_15746,U_15747)),hAPP(U_15745,U_15748)) = hAPP(U_15746,U_15747)
      | ~ hBOOL(hAPP(hAPP(c_member(U_15743),U_15748),U_15747))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15743),U_15747))
      | ~ c_Finite__Set_Ofolding__idem(U_15743,U_15744,U_15745,U_15746) ),
    inference(variable_rename,[status(thm)],[f_3960_1]) ).

fof(f_3960_3,plain,
    ! [U_15743,U_15744,U_15745,U_15746,U_15747,U_15748] :
      ( hAPP(c_Fun_Ocomp(U_15744,U_15744,U_15744,hAPP(U_15746,U_15747)),hAPP(U_15745,U_15748)) = hAPP(U_15746,U_15747)
      | ~ hBOOL(hAPP(hAPP(c_member(U_15743),U_15748),U_15747))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15743),U_15747))
      | ~ c_Finite__Set_Ofolding__idem(U_15743,U_15744,U_15745,U_15746) ),
    inference(definitional_conversion,[status(esa)],[f_3960_2]) ).

cnf(f_3960_4,plain,
    ( hAPP(c_Fun_Ocomp(U_15744,U_15744,U_15744,hAPP(U_15746,U_15747)),hAPP(U_15745,U_15748)) = hAPP(U_15746,U_15747)
    | ~ hBOOL(hAPP(hAPP(c_member(U_15743),U_15748),U_15747))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15743),U_15747))
    | ~ c_Finite__Set_Ofolding__idem(U_15743,U_15744,U_15745,U_15746) ),
    inference(clausify,[status(thm)],[f_3960_3]) ).

fof(f_3961_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_3961_2,plain,
    ! [U_15754,U_15753,U_15752,U_15751,U_15750,U_15749] :
      ( hAPP(U_15752,hAPP(hAPP(c_Set_Oinsert(U_15749),U_15754),U_15753)) = hAPP(c_Fun_Ocomp(U_15750,U_15750,U_15750,hAPP(U_15752,U_15753)),hAPP(U_15751,U_15754))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15749),U_15753))
      | ~ c_Finite__Set_Ofolding__idem(U_15749,U_15750,U_15751,U_15752) ),
    inference(variable_rename,[status(thm)],[f_3961_1]) ).

fof(f_3961_3,plain,
    ! [U_15751,U_15749,U_15750,U_15752,U_15753,U_15754] :
      ( hAPP(U_15752,hAPP(hAPP(c_Set_Oinsert(U_15749),U_15754),U_15753)) = hAPP(c_Fun_Ocomp(U_15750,U_15750,U_15750,hAPP(U_15752,U_15753)),hAPP(U_15751,U_15754))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15749),U_15753))
      | ~ c_Finite__Set_Ofolding__idem(U_15749,U_15750,U_15751,U_15752) ),
    inference(definitional_conversion,[status(esa)],[f_3961_2]) ).

cnf(f_3961_4,plain,
    ( hAPP(U_15752,hAPP(hAPP(c_Set_Oinsert(U_15749),U_15754),U_15753)) = hAPP(c_Fun_Ocomp(U_15750,U_15750,U_15750,hAPP(U_15752,U_15753)),hAPP(U_15751,U_15754))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15749),U_15753))
    | ~ c_Finite__Set_Ofolding__idem(U_15749,U_15750,U_15751,U_15752) ),
    inference(clausify,[status(thm)],[f_3961_3]) ).

fof(f_3962_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_3962_2,plain,
    ! [U_15763,U_15762,U_15761,U_15760,U_15759,U_15758,U_15757,U_15756] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15758,U_15756),U_15763),U_15761) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15757,U_15756),U_15762),U_15760)
      | ? [U_15755] :
          ( hAPP(U_15762,U_15755) != hAPP(hAPP(c_Fun_Ocomp(U_15758,U_15756,U_15757,U_15763),U_15759),U_15755)
          & hBOOL(hAPP(hAPP(c_member(U_15757),U_15755),U_15760)) )
      | U_15761 != hAPP(c_Set_Oimage(U_15757,U_15758,U_15759),U_15760)
      | ~ c_Fun_Oinj__on(U_15757,U_15758,U_15759,U_15760)
      | ~ class_Groups_Ocomm__monoid__mult(U_15756) ),
    inference(variable_rename,[status(thm)],[f_3962_1]) ).

fof(f_3962_3,plain,
    ! [U_15763,U_15762,U_15761,U_15760,U_15759,U_15758,U_15757,U_15756] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15758,U_15756),U_15763),U_15761) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15757,U_15756),U_15762),U_15760)
      | ( hAPP(U_15762,sK383(U_15763,U_15762,U_15761,U_15760,U_15759,U_15758,U_15757,U_15756)) != hAPP(hAPP(c_Fun_Ocomp(U_15758,U_15756,U_15757,U_15763),U_15759),sK383(U_15763,U_15762,U_15761,U_15760,U_15759,U_15758,U_15757,U_15756))
        & hBOOL(hAPP(hAPP(c_member(U_15757),sK383(U_15763,U_15762,U_15761,U_15760,U_15759,U_15758,U_15757,U_15756)),U_15760)) )
      | U_15761 != hAPP(c_Set_Oimage(U_15757,U_15758,U_15759),U_15760)
      | ~ c_Fun_Oinj__on(U_15757,U_15758,U_15759,U_15760)
      | ~ class_Groups_Ocomm__monoid__mult(U_15756) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK383]),skolemize(U_15755,sK383(U_15763,U_15762,U_15761,U_15760,U_15759,U_15758,U_15757,U_15756))],[f_3962_2]) ).

fof(f_3962_4,plain,
    ( ! [U_15756,U_15757,U_15758,U_15759,U_15760,U_15761,U_15762,U_15763] :
        ( hAPP(U_15762,sK383(U_15763,U_15762,U_15761,U_15760,U_15759,U_15758,U_15757,U_15756)) != hAPP(hAPP(c_Fun_Ocomp(U_15758,U_15756,U_15757,U_15763),U_15759),sK383(U_15763,U_15762,U_15761,U_15760,U_15759,U_15758,U_15757,U_15756))
        | ~ sP1039(U_15756,U_15757,U_15758,U_15759,U_15760,U_15761,U_15762,U_15763) )
    & ! [U_15756,U_15757,U_15758,U_15759,U_15760,U_15761,U_15762,U_15763] :
        ( hBOOL(hAPP(hAPP(c_member(U_15757),sK383(U_15763,U_15762,U_15761,U_15760,U_15759,U_15758,U_15757,U_15756)),U_15760))
        | ~ sP1039(U_15756,U_15757,U_15758,U_15759,U_15760,U_15761,U_15762,U_15763) )
    & ! [U_15756,U_15757,U_15758,U_15759,U_15760,U_15761,U_15762,U_15763] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15758,U_15756),U_15763),U_15761) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15757,U_15756),U_15762),U_15760)
        | sP1039(U_15756,U_15757,U_15758,U_15759,U_15760,U_15761,U_15762,U_15763)
        | U_15761 != hAPP(c_Set_Oimage(U_15757,U_15758,U_15759),U_15760)
        | ~ c_Fun_Oinj__on(U_15757,U_15758,U_15759,U_15760)
        | ~ class_Groups_Ocomm__monoid__mult(U_15756) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1039])],[f_3962_3]) ).

cnf(f_3962_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15758,U_15756),U_15763),U_15761) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15757,U_15756),U_15762),U_15760)
    | sP1039(U_15756,U_15757,U_15758,U_15759,U_15760,U_15761,U_15762,U_15763)
    | U_15761 != hAPP(c_Set_Oimage(U_15757,U_15758,U_15759),U_15760)
    | ~ c_Fun_Oinj__on(U_15757,U_15758,U_15759,U_15760)
    | ~ class_Groups_Ocomm__monoid__mult(U_15756) ),
    inference(clausify,[status(thm)],[f_3962_4]) ).

cnf(f_3962_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15757),sK383(U_15763,U_15762,U_15761,U_15760,U_15759,U_15758,U_15757,U_15756)),U_15760))
    | ~ sP1039(U_15756,U_15757,U_15758,U_15759,U_15760,U_15761,U_15762,U_15763) ),
    inference(clausify,[status(thm)],[f_3962_4]) ).

cnf(f_3962_7,plain,
    ( hAPP(U_15762,sK383(U_15763,U_15762,U_15761,U_15760,U_15759,U_15758,U_15757,U_15756)) != hAPP(hAPP(c_Fun_Ocomp(U_15758,U_15756,U_15757,U_15763),U_15759),sK383(U_15763,U_15762,U_15761,U_15760,U_15759,U_15758,U_15757,U_15756))
    | ~ sP1039(U_15756,U_15757,U_15758,U_15759,U_15760,U_15761,U_15762,U_15763) ),
    inference(clausify,[status(thm)],[f_3962_4]) ).

fof(f_3963_1,plain,
    ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Opos__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Opos__bind(T_c,T_b,V_Pa_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_3963_2,plain,
    ! [U_15767,U_15766,U_15765,U_15764] : c_New__Random__Sequence_Opos__map(U_15764,U_15765,U_15766,U_15767) = c_New__Random__Sequence_Opos__bind(U_15764,U_15765,U_15767,hAPP(c_Fun_Ocomp(U_15765,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_15765))))),U_15764,c_New__Random__Sequence_Opos__single(U_15765)),U_15766)),
    inference(variable_rename,[status(thm)],[f_3963_1]) ).

fof(f_3963_3,plain,
    ! [U_15764,U_15767,U_15766,U_15765] : c_New__Random__Sequence_Opos__map(U_15764,U_15765,U_15766,U_15767) = c_New__Random__Sequence_Opos__bind(U_15764,U_15765,U_15767,hAPP(c_Fun_Ocomp(U_15765,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_15765))))),U_15764,c_New__Random__Sequence_Opos__single(U_15765)),U_15766)),
    inference(definitional_conversion,[status(esa)],[f_3963_2]) ).

cnf(f_3963_4,plain,
    c_New__Random__Sequence_Opos__map(U_15764,U_15765,U_15766,U_15767) = c_New__Random__Sequence_Opos__bind(U_15764,U_15765,U_15767,hAPP(c_Fun_Ocomp(U_15765,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_15765))))),U_15764,c_New__Random__Sequence_Opos__single(U_15765)),U_15766)),
    inference(clausify,[status(thm)],[f_3963_3]) ).

fof(f_3964_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_3964_2,plain,
    ! [U_15772,U_15771,U_15770,U_15769,U_15768] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(U_15768),U_15769),U_15770),U_15771),U_15772) = c_New__DSequence_Opos__single(U_15768,U_15769),
    inference(variable_rename,[status(thm)],[f_3964_1]) ).

fof(f_3964_3,plain,
    ! [U_15770,U_15768,U_15769,U_15771,U_15772] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(U_15768),U_15769),U_15770),U_15771),U_15772) = c_New__DSequence_Opos__single(U_15768,U_15769),
    inference(definitional_conversion,[status(esa)],[f_3964_2]) ).

cnf(f_3964_4,plain,
    hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(U_15768),U_15769),U_15770),U_15771),U_15772) = c_New__DSequence_Opos__single(U_15768,U_15769),
    inference(clausify,[status(thm)],[f_3964_3]) ).

fof(f_3965_1,plain,
    ! [V_Pa_2,V_f_2,T_b,T_c] : c_New__Random__Sequence_Oneg__map(T_c,T_b,V_f_2,V_Pa_2) = c_New__Random__Sequence_Oneg__bind(T_c,T_b,V_Pa_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_3965_2,plain,
    ! [U_15776,U_15775,U_15774,U_15773] : c_New__Random__Sequence_Oneg__map(U_15773,U_15774,U_15775,U_15776) = c_New__Random__Sequence_Oneg__bind(U_15773,U_15774,U_15776,hAPP(c_Fun_Ocomp(U_15774,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_15774)))))),U_15773,c_New__Random__Sequence_Oneg__single(U_15774)),U_15775)),
    inference(variable_rename,[status(thm)],[f_3965_1]) ).

fof(f_3965_3,plain,
    ! [U_15773,U_15774,U_15775,U_15776] : c_New__Random__Sequence_Oneg__map(U_15773,U_15774,U_15775,U_15776) = c_New__Random__Sequence_Oneg__bind(U_15773,U_15774,U_15776,hAPP(c_Fun_Ocomp(U_15774,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_15774)))))),U_15773,c_New__Random__Sequence_Oneg__single(U_15774)),U_15775)),
    inference(definitional_conversion,[status(esa)],[f_3965_2]) ).

cnf(f_3965_4,plain,
    c_New__Random__Sequence_Oneg__map(U_15773,U_15774,U_15775,U_15776) = c_New__Random__Sequence_Oneg__bind(U_15773,U_15774,U_15776,hAPP(c_Fun_Ocomp(U_15774,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_15774)))))),U_15773,c_New__Random__Sequence_Oneg__single(U_15774)),U_15775)),
    inference(clausify,[status(thm)],[f_3965_3]) ).

fof(f_3966_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_3966_2,plain,
    ! [U_15779,U_15778,U_15777] : hAPP(c_New__DSequence_Opos__single(U_15777,U_15778),U_15779) = c_Lazy__Sequence_Osingle(U_15777,U_15778),
    inference(variable_rename,[status(thm)],[f_3966_1]) ).

fof(f_3966_3,plain,
    ! [U_15777,U_15778,U_15779] : hAPP(c_New__DSequence_Opos__single(U_15777,U_15778),U_15779) = c_Lazy__Sequence_Osingle(U_15777,U_15778),
    inference(definitional_conversion,[status(esa)],[f_3966_2]) ).

cnf(f_3966_4,plain,
    hAPP(c_New__DSequence_Opos__single(U_15777,U_15778),U_15779) = c_Lazy__Sequence_Osingle(U_15777,U_15778),
    inference(clausify,[status(thm)],[f_3966_3]) ).

fof(f_3967_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_3967_2,plain,
    ! [U_15784,U_15783,U_15782,U_15781,U_15780] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(U_15780),U_15781),U_15782),U_15783),U_15784) = c_New__DSequence_Oneg__single(U_15780,U_15781),
    inference(variable_rename,[status(thm)],[f_3967_1]) ).

fof(f_3967_3,plain,
    ! [U_15780,U_15781,U_15782,U_15783,U_15784] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(U_15780),U_15781),U_15782),U_15783),U_15784) = c_New__DSequence_Oneg__single(U_15780,U_15781),
    inference(definitional_conversion,[status(esa)],[f_3967_2]) ).

cnf(f_3967_4,plain,
    hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(U_15780),U_15781),U_15782),U_15783),U_15784) = c_New__DSequence_Oneg__single(U_15780,U_15781),
    inference(clausify,[status(thm)],[f_3967_3]) ).

fof(f_3968_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_3968_2,plain,
    ! [U_15787,U_15786,U_15785] : hAPP(c_New__DSequence_Oneg__single(U_15785,U_15786),U_15787) = c_Lazy__Sequence_Ohb__single(U_15785,U_15786),
    inference(variable_rename,[status(thm)],[f_3968_1]) ).

fof(f_3968_3,plain,
    ! [U_15785,U_15786,U_15787] : hAPP(c_New__DSequence_Oneg__single(U_15785,U_15786),U_15787) = c_Lazy__Sequence_Ohb__single(U_15785,U_15786),
    inference(definitional_conversion,[status(esa)],[f_3968_2]) ).

cnf(f_3968_4,plain,
    hAPP(c_New__DSequence_Oneg__single(U_15785,U_15786),U_15787) = c_Lazy__Sequence_Ohb__single(U_15785,U_15786),
    inference(clausify,[status(thm)],[f_3968_3]) ).

fof(f_3969_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_3969_2,plain,
    ! [U_15790,U_15789] :
      ( c_Wellfounded_Owf(U_15789,U_15790)
      | ? [U_15788] :
          ( U_15788 != c_Orderings_Obot__class_Obot(tc_fun(U_15789,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15789,tc_HOL_Obool)),U_15788),hAPP(c_Relation_OImage(U_15789,U_15789,U_15790),U_15788))) ) ),
    inference(variable_rename,[status(thm)],[f_3969_1]) ).

fof(f_3969_3,plain,
    ! [U_15790,U_15789] :
      ( c_Wellfounded_Owf(U_15789,U_15790)
      | ( sK384(U_15790,U_15789) != c_Orderings_Obot__class_Obot(tc_fun(U_15789,tc_HOL_Obool))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15789,tc_HOL_Obool)),sK384(U_15790,U_15789)),hAPP(c_Relation_OImage(U_15789,U_15789,U_15790),sK384(U_15790,U_15789)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK384]),skolemize(U_15788,sK384(U_15790,U_15789))],[f_3969_2]) ).

fof(f_3969_4,plain,
    ( ! [U_15789,U_15790] :
        ( sK384(U_15790,U_15789) != c_Orderings_Obot__class_Obot(tc_fun(U_15789,tc_HOL_Obool))
        | ~ sP1040(U_15789,U_15790) )
    & ! [U_15789,U_15790] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15789,tc_HOL_Obool)),sK384(U_15790,U_15789)),hAPP(c_Relation_OImage(U_15789,U_15789,U_15790),sK384(U_15790,U_15789))))
        | ~ sP1040(U_15789,U_15790) )
    & ! [U_15789,U_15790] :
        ( c_Wellfounded_Owf(U_15789,U_15790)
        | sP1040(U_15789,U_15790) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1040])],[f_3969_3]) ).

cnf(f_3969_5,plain,
    ( c_Wellfounded_Owf(U_15789,U_15790)
    | sP1040(U_15789,U_15790) ),
    inference(clausify,[status(thm)],[f_3969_4]) ).

cnf(f_3969_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15789,tc_HOL_Obool)),sK384(U_15790,U_15789)),hAPP(c_Relation_OImage(U_15789,U_15789,U_15790),sK384(U_15790,U_15789))))
    | ~ sP1040(U_15789,U_15790) ),
    inference(clausify,[status(thm)],[f_3969_4]) ).

cnf(f_3969_7,plain,
    ( sK384(U_15790,U_15789) != c_Orderings_Obot__class_Obot(tc_fun(U_15789,tc_HOL_Obool))
    | ~ sP1040(U_15789,U_15790) ),
    inference(clausify,[status(thm)],[f_3969_4]) ).

fof(f_3970_1,plain,
    ! [V_Qa_2,V_Pa_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_Pa_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_Qa_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_Pa_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_Pa_2),V_Qa_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__separatorE]) ).

fof(f_3970_2,plain,
    ! [U_15797,U_15796,U_15795,U_15794,U_15793] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15793,U_15793)),hAPP(hAPP(c_Product__Type_OPair(U_15793,U_15793),U_15794),U_15795)),c_Transitive__Closure_Ortrancl(U_15793,U_15796)))
      | ? [U_15792] :
          ( ? [U_15791] :
              ( U_15792 != U_15791
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15793,U_15793)),hAPP(hAPP(c_Product__Type_OPair(U_15793,U_15793),U_15792),U_15791)),U_15797)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15793,U_15793)),hAPP(hAPP(c_Product__Type_OPair(U_15793,U_15793),U_15794),U_15792)),c_Transitive__Closure_Ortrancl(U_15793,U_15796))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15793,U_15793)),hAPP(hAPP(c_Product__Type_OPair(U_15793,U_15793),U_15794),U_15795)),c_Transitive__Closure_Ortrancl(U_15793,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15793,U_15793),tc_HOL_Obool)),U_15796),U_15797)))) ),
    inference(variable_rename,[status(thm)],[f_3970_1]) ).

fof(f_3970_3,plain,
    ! [U_15797,U_15796,U_15795,U_15794,U_15793] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15793,U_15793)),hAPP(hAPP(c_Product__Type_OPair(U_15793,U_15793),U_15794),U_15795)),c_Transitive__Closure_Ortrancl(U_15793,U_15796)))
      | ( ? [U_15791] :
            ( sK385(U_15797,U_15796,U_15795,U_15794,U_15793) != U_15791
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15793,U_15793)),hAPP(hAPP(c_Product__Type_OPair(U_15793,U_15793),sK385(U_15797,U_15796,U_15795,U_15794,U_15793)),U_15791)),U_15797)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15793,U_15793)),hAPP(hAPP(c_Product__Type_OPair(U_15793,U_15793),U_15794),sK385(U_15797,U_15796,U_15795,U_15794,U_15793))),c_Transitive__Closure_Ortrancl(U_15793,U_15796))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15793,U_15793)),hAPP(hAPP(c_Product__Type_OPair(U_15793,U_15793),U_15794),U_15795)),c_Transitive__Closure_Ortrancl(U_15793,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15793,U_15793),tc_HOL_Obool)),U_15796),U_15797)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK385]),skolemize(U_15792,sK385(U_15797,U_15796,U_15795,U_15794,U_15793))],[f_3970_2]) ).

fof(f_3970_4,plain,
    ! [U_15797,U_15796,U_15795,U_15794,U_15793] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15793,U_15793)),hAPP(hAPP(c_Product__Type_OPair(U_15793,U_15793),U_15794),U_15795)),c_Transitive__Closure_Ortrancl(U_15793,U_15796)))
      | ( sK385(U_15797,U_15796,U_15795,U_15794,U_15793) != sK386(U_15797,U_15796,U_15795,U_15794,U_15793)
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15793,U_15793)),hAPP(hAPP(c_Product__Type_OPair(U_15793,U_15793),sK385(U_15797,U_15796,U_15795,U_15794,U_15793)),sK386(U_15797,U_15796,U_15795,U_15794,U_15793))),U_15797))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15793,U_15793)),hAPP(hAPP(c_Product__Type_OPair(U_15793,U_15793),U_15794),sK385(U_15797,U_15796,U_15795,U_15794,U_15793))),c_Transitive__Closure_Ortrancl(U_15793,U_15796))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15793,U_15793)),hAPP(hAPP(c_Product__Type_OPair(U_15793,U_15793),U_15794),U_15795)),c_Transitive__Closure_Ortrancl(U_15793,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15793,U_15793),tc_HOL_Obool)),U_15796),U_15797)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK386]),skolemize(U_15791,sK386(U_15797,U_15796,U_15795,U_15794,U_15793))],[f_3970_3]) ).

fof(f_3970_5,plain,
    ( ! [U_15793,U_15794,U_15795,U_15796,U_15797] :
        ( sK385(U_15797,U_15796,U_15795,U_15794,U_15793) != sK386(U_15797,U_15796,U_15795,U_15794,U_15793)
        | ~ sP1041(U_15793,U_15794,U_15795,U_15796,U_15797) )
    & ! [U_15793,U_15794,U_15795,U_15796,U_15797] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15793,U_15793)),hAPP(hAPP(c_Product__Type_OPair(U_15793,U_15793),sK385(U_15797,U_15796,U_15795,U_15794,U_15793)),sK386(U_15797,U_15796,U_15795,U_15794,U_15793))),U_15797))
        | ~ sP1041(U_15793,U_15794,U_15795,U_15796,U_15797) )
    & ! [U_15793,U_15794,U_15795,U_15796,U_15797] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15793,U_15793)),hAPP(hAPP(c_Product__Type_OPair(U_15793,U_15793),U_15794),sK385(U_15797,U_15796,U_15795,U_15794,U_15793))),c_Transitive__Closure_Ortrancl(U_15793,U_15796)))
        | ~ sP1041(U_15793,U_15794,U_15795,U_15796,U_15797) )
    & ! [U_15793,U_15794,U_15795,U_15796,U_15797] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15793,U_15793)),hAPP(hAPP(c_Product__Type_OPair(U_15793,U_15793),U_15794),U_15795)),c_Transitive__Closure_Ortrancl(U_15793,U_15796)))
        | sP1041(U_15793,U_15794,U_15795,U_15796,U_15797)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15793,U_15793)),hAPP(hAPP(c_Product__Type_OPair(U_15793,U_15793),U_15794),U_15795)),c_Transitive__Closure_Ortrancl(U_15793,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15793,U_15793),tc_HOL_Obool)),U_15796),U_15797)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1041])],[f_3970_4]) ).

cnf(f_3970_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15793,U_15793)),hAPP(hAPP(c_Product__Type_OPair(U_15793,U_15793),U_15794),U_15795)),c_Transitive__Closure_Ortrancl(U_15793,U_15796)))
    | sP1041(U_15793,U_15794,U_15795,U_15796,U_15797)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15793,U_15793)),hAPP(hAPP(c_Product__Type_OPair(U_15793,U_15793),U_15794),U_15795)),c_Transitive__Closure_Ortrancl(U_15793,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15793,U_15793),tc_HOL_Obool)),U_15796),U_15797)))) ),
    inference(clausify,[status(thm)],[f_3970_5]) ).

cnf(f_3970_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15793,U_15793)),hAPP(hAPP(c_Product__Type_OPair(U_15793,U_15793),U_15794),sK385(U_15797,U_15796,U_15795,U_15794,U_15793))),c_Transitive__Closure_Ortrancl(U_15793,U_15796)))
    | ~ sP1041(U_15793,U_15794,U_15795,U_15796,U_15797) ),
    inference(clausify,[status(thm)],[f_3970_5]) ).

cnf(f_3970_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15793,U_15793)),hAPP(hAPP(c_Product__Type_OPair(U_15793,U_15793),sK385(U_15797,U_15796,U_15795,U_15794,U_15793)),sK386(U_15797,U_15796,U_15795,U_15794,U_15793))),U_15797))
    | ~ sP1041(U_15793,U_15794,U_15795,U_15796,U_15797) ),
    inference(clausify,[status(thm)],[f_3970_5]) ).

cnf(f_3970_9,plain,
    ( sK385(U_15797,U_15796,U_15795,U_15794,U_15793) != sK386(U_15797,U_15796,U_15795,U_15794,U_15793)
    | ~ sP1041(U_15793,U_15794,U_15795,U_15796,U_15797) ),
    inference(clausify,[status(thm)],[f_3970_5]) ).

fof(f_3971_1,plain,
    ! [V_Qa_2,V_Pa_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_Pa_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_Qa_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_Pa_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_Pa_2),V_Qa_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_rtrancl__Un__separator__converseE]) ).

fof(f_3971_2,plain,
    ! [U_15804,U_15803,U_15802,U_15801,U_15800] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15800,U_15800)),hAPP(hAPP(c_Product__Type_OPair(U_15800,U_15800),U_15801),U_15802)),c_Transitive__Closure_Ortrancl(U_15800,U_15803)))
      | ? [U_15799] :
          ( ? [U_15798] :
              ( U_15798 != U_15799
              & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15800,U_15800)),hAPP(hAPP(c_Product__Type_OPair(U_15800,U_15800),U_15798),U_15799)),U_15804)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15800,U_15800)),hAPP(hAPP(c_Product__Type_OPair(U_15800,U_15800),U_15799),U_15802)),c_Transitive__Closure_Ortrancl(U_15800,U_15803))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15800,U_15800)),hAPP(hAPP(c_Product__Type_OPair(U_15800,U_15800),U_15801),U_15802)),c_Transitive__Closure_Ortrancl(U_15800,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15800,U_15800),tc_HOL_Obool)),U_15803),U_15804)))) ),
    inference(variable_rename,[status(thm)],[f_3971_1]) ).

fof(f_3971_3,plain,
    ! [U_15804,U_15803,U_15802,U_15801,U_15800] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15800,U_15800)),hAPP(hAPP(c_Product__Type_OPair(U_15800,U_15800),U_15801),U_15802)),c_Transitive__Closure_Ortrancl(U_15800,U_15803)))
      | ( ? [U_15798] :
            ( U_15798 != sK387(U_15804,U_15803,U_15802,U_15801,U_15800)
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15800,U_15800)),hAPP(hAPP(c_Product__Type_OPair(U_15800,U_15800),U_15798),sK387(U_15804,U_15803,U_15802,U_15801,U_15800))),U_15804)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15800,U_15800)),hAPP(hAPP(c_Product__Type_OPair(U_15800,U_15800),sK387(U_15804,U_15803,U_15802,U_15801,U_15800)),U_15802)),c_Transitive__Closure_Ortrancl(U_15800,U_15803))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15800,U_15800)),hAPP(hAPP(c_Product__Type_OPair(U_15800,U_15800),U_15801),U_15802)),c_Transitive__Closure_Ortrancl(U_15800,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15800,U_15800),tc_HOL_Obool)),U_15803),U_15804)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK387]),skolemize(U_15799,sK387(U_15804,U_15803,U_15802,U_15801,U_15800))],[f_3971_2]) ).

fof(f_3971_4,plain,
    ! [U_15804,U_15803,U_15802,U_15801,U_15800] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15800,U_15800)),hAPP(hAPP(c_Product__Type_OPair(U_15800,U_15800),U_15801),U_15802)),c_Transitive__Closure_Ortrancl(U_15800,U_15803)))
      | ( sK388(U_15804,U_15803,U_15802,U_15801,U_15800) != sK387(U_15804,U_15803,U_15802,U_15801,U_15800)
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15800,U_15800)),hAPP(hAPP(c_Product__Type_OPair(U_15800,U_15800),sK388(U_15804,U_15803,U_15802,U_15801,U_15800)),sK387(U_15804,U_15803,U_15802,U_15801,U_15800))),U_15804))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15800,U_15800)),hAPP(hAPP(c_Product__Type_OPair(U_15800,U_15800),sK387(U_15804,U_15803,U_15802,U_15801,U_15800)),U_15802)),c_Transitive__Closure_Ortrancl(U_15800,U_15803))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15800,U_15800)),hAPP(hAPP(c_Product__Type_OPair(U_15800,U_15800),U_15801),U_15802)),c_Transitive__Closure_Ortrancl(U_15800,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15800,U_15800),tc_HOL_Obool)),U_15803),U_15804)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK388]),skolemize(U_15798,sK388(U_15804,U_15803,U_15802,U_15801,U_15800))],[f_3971_3]) ).

fof(f_3971_5,plain,
    ( ! [U_15801,U_15802,U_15800,U_15803,U_15804] :
        ( sK388(U_15804,U_15803,U_15802,U_15801,U_15800) != sK387(U_15804,U_15803,U_15802,U_15801,U_15800)
        | ~ sP1042(U_15801,U_15802,U_15800,U_15803,U_15804) )
    & ! [U_15801,U_15802,U_15800,U_15803,U_15804] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15800,U_15800)),hAPP(hAPP(c_Product__Type_OPair(U_15800,U_15800),sK388(U_15804,U_15803,U_15802,U_15801,U_15800)),sK387(U_15804,U_15803,U_15802,U_15801,U_15800))),U_15804))
        | ~ sP1042(U_15801,U_15802,U_15800,U_15803,U_15804) )
    & ! [U_15801,U_15802,U_15800,U_15803,U_15804] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15800,U_15800)),hAPP(hAPP(c_Product__Type_OPair(U_15800,U_15800),sK387(U_15804,U_15803,U_15802,U_15801,U_15800)),U_15802)),c_Transitive__Closure_Ortrancl(U_15800,U_15803)))
        | ~ sP1042(U_15801,U_15802,U_15800,U_15803,U_15804) )
    & ! [U_15801,U_15802,U_15800,U_15803,U_15804] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15800,U_15800)),hAPP(hAPP(c_Product__Type_OPair(U_15800,U_15800),U_15801),U_15802)),c_Transitive__Closure_Ortrancl(U_15800,U_15803)))
        | sP1042(U_15801,U_15802,U_15800,U_15803,U_15804)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15800,U_15800)),hAPP(hAPP(c_Product__Type_OPair(U_15800,U_15800),U_15801),U_15802)),c_Transitive__Closure_Ortrancl(U_15800,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15800,U_15800),tc_HOL_Obool)),U_15803),U_15804)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1042])],[f_3971_4]) ).

cnf(f_3971_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15800,U_15800)),hAPP(hAPP(c_Product__Type_OPair(U_15800,U_15800),U_15801),U_15802)),c_Transitive__Closure_Ortrancl(U_15800,U_15803)))
    | sP1042(U_15801,U_15802,U_15800,U_15803,U_15804)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15800,U_15800)),hAPP(hAPP(c_Product__Type_OPair(U_15800,U_15800),U_15801),U_15802)),c_Transitive__Closure_Ortrancl(U_15800,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_prod(U_15800,U_15800),tc_HOL_Obool)),U_15803),U_15804)))) ),
    inference(clausify,[status(thm)],[f_3971_5]) ).

cnf(f_3971_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15800,U_15800)),hAPP(hAPP(c_Product__Type_OPair(U_15800,U_15800),sK387(U_15804,U_15803,U_15802,U_15801,U_15800)),U_15802)),c_Transitive__Closure_Ortrancl(U_15800,U_15803)))
    | ~ sP1042(U_15801,U_15802,U_15800,U_15803,U_15804) ),
    inference(clausify,[status(thm)],[f_3971_5]) ).

cnf(f_3971_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15800,U_15800)),hAPP(hAPP(c_Product__Type_OPair(U_15800,U_15800),sK388(U_15804,U_15803,U_15802,U_15801,U_15800)),sK387(U_15804,U_15803,U_15802,U_15801,U_15800))),U_15804))
    | ~ sP1042(U_15801,U_15802,U_15800,U_15803,U_15804) ),
    inference(clausify,[status(thm)],[f_3971_5]) ).

cnf(f_3971_9,plain,
    ( sK388(U_15804,U_15803,U_15802,U_15801,U_15800) != sK387(U_15804,U_15803,U_15802,U_15801,U_15800)
    | ~ sP1042(U_15801,U_15802,U_15800,U_15803,U_15804) ),
    inference(clausify,[status(thm)],[f_3971_5]) ).

fof(f_3972_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_3972_2,plain,
    ! [U_15810,U_15809,U_15808,U_15807,U_15806] :
      ( ? [U_15805] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15806,U_15806)),hAPP(hAPP(c_Product__Type_OPair(U_15806,U_15806),U_15805),U_15808)),U_15810))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15806,U_15806)),hAPP(hAPP(c_Product__Type_OPair(U_15806,U_15806),U_15807),U_15805)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15806,U_15806),tc_HOL_Obool),U_15809),U_15810))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15806,U_15806)),hAPP(hAPP(c_Product__Type_OPair(U_15806,U_15806),U_15807),U_15808)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15806,U_15806),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15809)),U_15810))) ),
    inference(variable_rename,[status(thm)],[f_3972_1]) ).

fof(f_3972_3,plain,
    ! [U_15810,U_15809,U_15808,U_15807,U_15806] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15806,U_15806)),hAPP(hAPP(c_Product__Type_OPair(U_15806,U_15806),sK389(U_15810,U_15809,U_15808,U_15807,U_15806)),U_15808)),U_15810))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15806,U_15806)),hAPP(hAPP(c_Product__Type_OPair(U_15806,U_15806),U_15807),sK389(U_15810,U_15809,U_15808,U_15807,U_15806))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15806,U_15806),tc_HOL_Obool),U_15809),U_15810))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15806,U_15806)),hAPP(hAPP(c_Product__Type_OPair(U_15806,U_15806),U_15807),U_15808)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15806,U_15806),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15809)),U_15810))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK389]),skolemize(U_15805,sK389(U_15810,U_15809,U_15808,U_15807,U_15806))],[f_3972_2]) ).

fof(f_3972_4,plain,
    ( ! [U_15806,U_15807,U_15808,U_15809,U_15810] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15806,U_15806)),hAPP(hAPP(c_Product__Type_OPair(U_15806,U_15806),sK389(U_15810,U_15809,U_15808,U_15807,U_15806)),U_15808)),U_15810))
        | ~ sP1043(U_15806,U_15807,U_15808,U_15809,U_15810) )
    & ! [U_15806,U_15807,U_15808,U_15809,U_15810] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15806,U_15806)),hAPP(hAPP(c_Product__Type_OPair(U_15806,U_15806),U_15807),sK389(U_15810,U_15809,U_15808,U_15807,U_15806))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15806,U_15806),tc_HOL_Obool),U_15809),U_15810)))
        | ~ sP1043(U_15806,U_15807,U_15808,U_15809,U_15810) )
    & ! [U_15806,U_15807,U_15808,U_15809,U_15810] :
        ( sP1043(U_15806,U_15807,U_15808,U_15809,U_15810)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15806,U_15806)),hAPP(hAPP(c_Product__Type_OPair(U_15806,U_15806),U_15807),U_15808)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15806,U_15806),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15809)),U_15810))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1043])],[f_3972_3]) ).

cnf(f_3972_5,plain,
    ( sP1043(U_15806,U_15807,U_15808,U_15809,U_15810)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15806,U_15806)),hAPP(hAPP(c_Product__Type_OPair(U_15806,U_15806),U_15807),U_15808)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15806,U_15806),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15809)),U_15810))) ),
    inference(clausify,[status(thm)],[f_3972_4]) ).

cnf(f_3972_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15806,U_15806)),hAPP(hAPP(c_Product__Type_OPair(U_15806,U_15806),U_15807),sK389(U_15810,U_15809,U_15808,U_15807,U_15806))),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15806,U_15806),tc_HOL_Obool),U_15809),U_15810)))
    | ~ sP1043(U_15806,U_15807,U_15808,U_15809,U_15810) ),
    inference(clausify,[status(thm)],[f_3972_4]) ).

cnf(f_3972_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15806,U_15806)),hAPP(hAPP(c_Product__Type_OPair(U_15806,U_15806),sK389(U_15810,U_15809,U_15808,U_15807,U_15806)),U_15808)),U_15810))
    | ~ sP1043(U_15806,U_15807,U_15808,U_15809,U_15810) ),
    inference(clausify,[status(thm)],[f_3972_4]) ).

fof(f_3973_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_3973_2,plain,
    ! [U_15816,U_15815,U_15814,U_15813,U_15812] :
      ( ? [U_15811] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15812,U_15812)),hAPP(hAPP(c_Product__Type_OPair(U_15812,U_15812),U_15811),U_15814)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15812,U_15812),tc_HOL_Obool),U_15815),U_15816)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15812,U_15812)),hAPP(hAPP(c_Product__Type_OPair(U_15812,U_15812),U_15813),U_15811)),U_15816)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15812,U_15812)),hAPP(hAPP(c_Product__Type_OPair(U_15812,U_15812),U_15813),U_15814)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15812,U_15812),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15815)),U_15816))) ),
    inference(variable_rename,[status(thm)],[f_3973_1]) ).

fof(f_3973_3,plain,
    ! [U_15816,U_15815,U_15814,U_15813,U_15812] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15812,U_15812)),hAPP(hAPP(c_Product__Type_OPair(U_15812,U_15812),sK390(U_15816,U_15815,U_15814,U_15813,U_15812)),U_15814)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15812,U_15812),tc_HOL_Obool),U_15815),U_15816)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15812,U_15812)),hAPP(hAPP(c_Product__Type_OPair(U_15812,U_15812),U_15813),sK390(U_15816,U_15815,U_15814,U_15813,U_15812))),U_15816)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15812,U_15812)),hAPP(hAPP(c_Product__Type_OPair(U_15812,U_15812),U_15813),U_15814)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15812,U_15812),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15815)),U_15816))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK390]),skolemize(U_15811,sK390(U_15816,U_15815,U_15814,U_15813,U_15812))],[f_3973_2]) ).

fof(f_3973_4,plain,
    ( ! [U_15812,U_15813,U_15814,U_15815,U_15816] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15812,U_15812)),hAPP(hAPP(c_Product__Type_OPair(U_15812,U_15812),sK390(U_15816,U_15815,U_15814,U_15813,U_15812)),U_15814)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15812,U_15812),tc_HOL_Obool),U_15815),U_15816)))
        | ~ sP1044(U_15812,U_15813,U_15814,U_15815,U_15816) )
    & ! [U_15812,U_15813,U_15814,U_15815,U_15816] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15812,U_15812)),hAPP(hAPP(c_Product__Type_OPair(U_15812,U_15812),U_15813),sK390(U_15816,U_15815,U_15814,U_15813,U_15812))),U_15816))
        | ~ sP1044(U_15812,U_15813,U_15814,U_15815,U_15816) )
    & ! [U_15812,U_15813,U_15814,U_15815,U_15816] :
        ( sP1044(U_15812,U_15813,U_15814,U_15815,U_15816)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15812,U_15812)),hAPP(hAPP(c_Product__Type_OPair(U_15812,U_15812),U_15813),U_15814)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15812,U_15812),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15815)),U_15816))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1044])],[f_3973_3]) ).

cnf(f_3973_5,plain,
    ( sP1044(U_15812,U_15813,U_15814,U_15815,U_15816)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15812,U_15812)),hAPP(hAPP(c_Product__Type_OPair(U_15812,U_15812),U_15813),U_15814)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15812,U_15812),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15815)),U_15816))) ),
    inference(clausify,[status(thm)],[f_3973_4]) ).

cnf(f_3973_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15812,U_15812)),hAPP(hAPP(c_Product__Type_OPair(U_15812,U_15812),U_15813),sK390(U_15816,U_15815,U_15814,U_15813,U_15812))),U_15816))
    | ~ sP1044(U_15812,U_15813,U_15814,U_15815,U_15816) ),
    inference(clausify,[status(thm)],[f_3973_4]) ).

cnf(f_3973_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15812,U_15812)),hAPP(hAPP(c_Product__Type_OPair(U_15812,U_15812),sK390(U_15816,U_15815,U_15814,U_15813,U_15812)),U_15814)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15812,U_15812),tc_HOL_Obool),U_15815),U_15816)))
    | ~ sP1044(U_15812,U_15813,U_15814,U_15815,U_15816) ),
    inference(clausify,[status(thm)],[f_3973_4]) ).

fof(f_3974_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_3974_2,plain,
    ! [U_15822,U_15821,U_15820,U_15819,U_15818] :
      ( ? [U_15817] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15818,U_15818)),hAPP(hAPP(c_Product__Type_OPair(U_15818,U_15818),U_15817),U_15820)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15818,U_15818),tc_HOL_Obool),U_15821),U_15822)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15818,U_15818)),hAPP(hAPP(c_Product__Type_OPair(U_15818,U_15818),U_15819),U_15817)),U_15822)) )
      | ~ 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)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15818,U_15818),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15821)),U_15822))) ),
    inference(variable_rename,[status(thm)],[f_3974_1]) ).

fof(f_3974_3,plain,
    ! [U_15822,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),sK391(U_15822,U_15821,U_15820,U_15819,U_15818)),U_15820)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15818,U_15818),tc_HOL_Obool),U_15821),U_15822)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15818,U_15818)),hAPP(hAPP(c_Product__Type_OPair(U_15818,U_15818),U_15819),sK391(U_15822,U_15821,U_15820,U_15819,U_15818))),U_15822)) )
      | ~ 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)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15818,U_15818),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15821)),U_15822))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK391]),skolemize(U_15817,sK391(U_15822,U_15821,U_15820,U_15819,U_15818))],[f_3974_2]) ).

fof(f_3974_4,plain,
    ( ! [U_15818,U_15819,U_15820,U_15821,U_15822] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15818,U_15818)),hAPP(hAPP(c_Product__Type_OPair(U_15818,U_15818),sK391(U_15822,U_15821,U_15820,U_15819,U_15818)),U_15820)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15818,U_15818),tc_HOL_Obool),U_15821),U_15822)))
        | ~ sP1045(U_15818,U_15819,U_15820,U_15821,U_15822) )
    & ! [U_15818,U_15819,U_15820,U_15821,U_15822] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15818,U_15818)),hAPP(hAPP(c_Product__Type_OPair(U_15818,U_15818),U_15819),sK391(U_15822,U_15821,U_15820,U_15819,U_15818))),U_15822))
        | ~ sP1045(U_15818,U_15819,U_15820,U_15821,U_15822) )
    & ! [U_15818,U_15819,U_15820,U_15821,U_15822] :
        ( sP1045(U_15818,U_15819,U_15820,U_15821,U_15822)
        | ~ 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)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15818,U_15818),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15821)),U_15822))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1045])],[f_3974_3]) ).

cnf(f_3974_5,plain,
    ( sP1045(U_15818,U_15819,U_15820,U_15821,U_15822)
    | ~ 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)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15818,U_15818),tc_HOL_Obool),hAPP(c_Nat_OSuc,U_15821)),U_15822))) ),
    inference(clausify,[status(thm)],[f_3974_4]) ).

cnf(f_3974_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15818,U_15818)),hAPP(hAPP(c_Product__Type_OPair(U_15818,U_15818),U_15819),sK391(U_15822,U_15821,U_15820,U_15819,U_15818))),U_15822))
    | ~ sP1045(U_15818,U_15819,U_15820,U_15821,U_15822) ),
    inference(clausify,[status(thm)],[f_3974_4]) ).

cnf(f_3974_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15818,U_15818)),hAPP(hAPP(c_Product__Type_OPair(U_15818,U_15818),sK391(U_15822,U_15821,U_15820,U_15819,U_15818)),U_15820)),hAPP(hAPP(c_Nat_Ocompow(tc_prod(U_15818,U_15818),tc_HOL_Obool),U_15821),U_15822)))
    | ~ sP1045(U_15818,U_15819,U_15820,U_15821,U_15822) ),
    inference(clausify,[status(thm)],[f_3974_4]) ).

fof(f_3975_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_3975_2,plain,
    ! [U_15829,U_15828,U_15827,U_15826,U_15825,U_15824] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15824,U_15827),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_15824,U_15827),U_15825),U_15828)),hAPP(hAPP(c_Product__Type_OSigma(U_15824,U_15827),U_15826),U_15829)))
      | ? [U_15823] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15827,tc_HOL_Obool)),hAPP(U_15828,U_15823)),hAPP(U_15829,U_15823)))
          & hBOOL(hAPP(hAPP(c_member(U_15824),U_15823),U_15825)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15824,tc_HOL_Obool)),U_15825),U_15826)) ),
    inference(variable_rename,[status(thm)],[f_3975_1]) ).

fof(f_3975_3,plain,
    ! [U_15829,U_15828,U_15827,U_15826,U_15825,U_15824] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15824,U_15827),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_15824,U_15827),U_15825),U_15828)),hAPP(hAPP(c_Product__Type_OSigma(U_15824,U_15827),U_15826),U_15829)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15827,tc_HOL_Obool)),hAPP(U_15828,sK392(U_15829,U_15828,U_15827,U_15826,U_15825,U_15824))),hAPP(U_15829,sK392(U_15829,U_15828,U_15827,U_15826,U_15825,U_15824))))
        & hBOOL(hAPP(hAPP(c_member(U_15824),sK392(U_15829,U_15828,U_15827,U_15826,U_15825,U_15824)),U_15825)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15824,tc_HOL_Obool)),U_15825),U_15826)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK392]),skolemize(U_15823,sK392(U_15829,U_15828,U_15827,U_15826,U_15825,U_15824))],[f_3975_2]) ).

fof(f_3975_4,plain,
    ( ! [U_15824,U_15825,U_15826,U_15827,U_15828,U_15829] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15827,tc_HOL_Obool)),hAPP(U_15828,sK392(U_15829,U_15828,U_15827,U_15826,U_15825,U_15824))),hAPP(U_15829,sK392(U_15829,U_15828,U_15827,U_15826,U_15825,U_15824))))
        | ~ sP1046(U_15824,U_15825,U_15826,U_15827,U_15828,U_15829) )
    & ! [U_15824,U_15825,U_15826,U_15827,U_15828,U_15829] :
        ( hBOOL(hAPP(hAPP(c_member(U_15824),sK392(U_15829,U_15828,U_15827,U_15826,U_15825,U_15824)),U_15825))
        | ~ sP1046(U_15824,U_15825,U_15826,U_15827,U_15828,U_15829) )
    & ! [U_15824,U_15825,U_15826,U_15827,U_15828,U_15829] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15824,U_15827),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_15824,U_15827),U_15825),U_15828)),hAPP(hAPP(c_Product__Type_OSigma(U_15824,U_15827),U_15826),U_15829)))
        | sP1046(U_15824,U_15825,U_15826,U_15827,U_15828,U_15829)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15824,tc_HOL_Obool)),U_15825),U_15826)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1046])],[f_3975_3]) ).

cnf(f_3975_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_15824,U_15827),tc_HOL_Obool)),hAPP(hAPP(c_Product__Type_OSigma(U_15824,U_15827),U_15825),U_15828)),hAPP(hAPP(c_Product__Type_OSigma(U_15824,U_15827),U_15826),U_15829)))
    | sP1046(U_15824,U_15825,U_15826,U_15827,U_15828,U_15829)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15824,tc_HOL_Obool)),U_15825),U_15826)) ),
    inference(clausify,[status(thm)],[f_3975_4]) ).

cnf(f_3975_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15824),sK392(U_15829,U_15828,U_15827,U_15826,U_15825,U_15824)),U_15825))
    | ~ sP1046(U_15824,U_15825,U_15826,U_15827,U_15828,U_15829) ),
    inference(clausify,[status(thm)],[f_3975_4]) ).

cnf(f_3975_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15827,tc_HOL_Obool)),hAPP(U_15828,sK392(U_15829,U_15828,U_15827,U_15826,U_15825,U_15824))),hAPP(U_15829,sK392(U_15829,U_15828,U_15827,U_15826,U_15825,U_15824))))
    | ~ sP1046(U_15824,U_15825,U_15826,U_15827,U_15828,U_15829) ),
    inference(clausify,[status(thm)],[f_3975_4]) ).

fof(f_3976_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_3976_2,plain,
    ! [U_15834,U_15833,U_15832,U_15831] :
      ( ? [U_15830] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15831,U_15831)),hAPP(hAPP(c_Product__Type_OPair(U_15831,U_15831),U_15830),U_15833)),U_15834))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15831,U_15831)),hAPP(hAPP(c_Product__Type_OPair(U_15831,U_15831),U_15832),U_15830)),c_Transitive__Closure_Ortrancl(U_15831,U_15834))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15831,U_15831)),hAPP(hAPP(c_Product__Type_OPair(U_15831,U_15831),U_15832),U_15833)),c_Transitive__Closure_Otrancl(U_15831,U_15834))) ),
    inference(variable_rename,[status(thm)],[f_3976_1]) ).

fof(f_3976_3,plain,
    ! [U_15834,U_15833,U_15832,U_15831] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15831,U_15831)),hAPP(hAPP(c_Product__Type_OPair(U_15831,U_15831),sK393(U_15834,U_15833,U_15832,U_15831)),U_15833)),U_15834))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15831,U_15831)),hAPP(hAPP(c_Product__Type_OPair(U_15831,U_15831),U_15832),sK393(U_15834,U_15833,U_15832,U_15831))),c_Transitive__Closure_Ortrancl(U_15831,U_15834))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15831,U_15831)),hAPP(hAPP(c_Product__Type_OPair(U_15831,U_15831),U_15832),U_15833)),c_Transitive__Closure_Otrancl(U_15831,U_15834))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK393]),skolemize(U_15830,sK393(U_15834,U_15833,U_15832,U_15831))],[f_3976_2]) ).

fof(f_3976_4,plain,
    ( ! [U_15831,U_15832,U_15833,U_15834] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15831,U_15831)),hAPP(hAPP(c_Product__Type_OPair(U_15831,U_15831),sK393(U_15834,U_15833,U_15832,U_15831)),U_15833)),U_15834))
        | ~ sP1047(U_15831,U_15832,U_15833,U_15834) )
    & ! [U_15831,U_15832,U_15833,U_15834] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15831,U_15831)),hAPP(hAPP(c_Product__Type_OPair(U_15831,U_15831),U_15832),sK393(U_15834,U_15833,U_15832,U_15831))),c_Transitive__Closure_Ortrancl(U_15831,U_15834)))
        | ~ sP1047(U_15831,U_15832,U_15833,U_15834) )
    & ! [U_15831,U_15832,U_15833,U_15834] :
        ( sP1047(U_15831,U_15832,U_15833,U_15834)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15831,U_15831)),hAPP(hAPP(c_Product__Type_OPair(U_15831,U_15831),U_15832),U_15833)),c_Transitive__Closure_Otrancl(U_15831,U_15834))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1047])],[f_3976_3]) ).

cnf(f_3976_5,plain,
    ( sP1047(U_15831,U_15832,U_15833,U_15834)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15831,U_15831)),hAPP(hAPP(c_Product__Type_OPair(U_15831,U_15831),U_15832),U_15833)),c_Transitive__Closure_Otrancl(U_15831,U_15834))) ),
    inference(clausify,[status(thm)],[f_3976_4]) ).

cnf(f_3976_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15831,U_15831)),hAPP(hAPP(c_Product__Type_OPair(U_15831,U_15831),U_15832),sK393(U_15834,U_15833,U_15832,U_15831))),c_Transitive__Closure_Ortrancl(U_15831,U_15834)))
    | ~ sP1047(U_15831,U_15832,U_15833,U_15834) ),
    inference(clausify,[status(thm)],[f_3976_4]) ).

cnf(f_3976_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15831,U_15831)),hAPP(hAPP(c_Product__Type_OPair(U_15831,U_15831),sK393(U_15834,U_15833,U_15832,U_15831)),U_15833)),U_15834))
    | ~ sP1047(U_15831,U_15832,U_15833,U_15834) ),
    inference(clausify,[status(thm)],[f_3976_4]) ).

fof(f_3977_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_3977_2,plain,
    ! [U_15839,U_15838,U_15837,U_15836] :
      ( ? [U_15835] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15836,U_15836)),hAPP(hAPP(c_Product__Type_OPair(U_15836,U_15836),U_15835),U_15838)),c_Transitive__Closure_Ortrancl(U_15836,U_15839)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15836,U_15836)),hAPP(hAPP(c_Product__Type_OPair(U_15836,U_15836),U_15837),U_15835)),U_15839)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15836,U_15836)),hAPP(hAPP(c_Product__Type_OPair(U_15836,U_15836),U_15837),U_15838)),c_Transitive__Closure_Otrancl(U_15836,U_15839))) ),
    inference(variable_rename,[status(thm)],[f_3977_1]) ).

fof(f_3977_3,plain,
    ! [U_15839,U_15838,U_15837,U_15836] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15836,U_15836)),hAPP(hAPP(c_Product__Type_OPair(U_15836,U_15836),sK394(U_15839,U_15838,U_15837,U_15836)),U_15838)),c_Transitive__Closure_Ortrancl(U_15836,U_15839)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_15836,U_15836)),hAPP(hAPP(c_Product__Type_OPair(U_15836,U_15836),U_15837),sK394(U_15839,U_15838,U_15837,U_15836))),U_15839)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15836,U_15836)),hAPP(hAPP(c_Product__Type_OPair(U_15836,U_15836),U_15837),U_15838)),c_Transitive__Closure_Otrancl(U_15836,U_15839))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK394]),skolemize(U_15835,sK394(U_15839,U_15838,U_15837,U_15836))],[f_3977_2]) ).

fof(f_3977_4,plain,
    ( ! [U_15836,U_15837,U_15838,U_15839] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15836,U_15836)),hAPP(hAPP(c_Product__Type_OPair(U_15836,U_15836),sK394(U_15839,U_15838,U_15837,U_15836)),U_15838)),c_Transitive__Closure_Ortrancl(U_15836,U_15839)))
        | ~ sP1048(U_15836,U_15837,U_15838,U_15839) )
    & ! [U_15836,U_15837,U_15838,U_15839] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15836,U_15836)),hAPP(hAPP(c_Product__Type_OPair(U_15836,U_15836),U_15837),sK394(U_15839,U_15838,U_15837,U_15836))),U_15839))
        | ~ sP1048(U_15836,U_15837,U_15838,U_15839) )
    & ! [U_15836,U_15837,U_15838,U_15839] :
        ( sP1048(U_15836,U_15837,U_15838,U_15839)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15836,U_15836)),hAPP(hAPP(c_Product__Type_OPair(U_15836,U_15836),U_15837),U_15838)),c_Transitive__Closure_Otrancl(U_15836,U_15839))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1048])],[f_3977_3]) ).

cnf(f_3977_5,plain,
    ( sP1048(U_15836,U_15837,U_15838,U_15839)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15836,U_15836)),hAPP(hAPP(c_Product__Type_OPair(U_15836,U_15836),U_15837),U_15838)),c_Transitive__Closure_Otrancl(U_15836,U_15839))) ),
    inference(clausify,[status(thm)],[f_3977_4]) ).

cnf(f_3977_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15836,U_15836)),hAPP(hAPP(c_Product__Type_OPair(U_15836,U_15836),U_15837),sK394(U_15839,U_15838,U_15837,U_15836))),U_15839))
    | ~ sP1048(U_15836,U_15837,U_15838,U_15839) ),
    inference(clausify,[status(thm)],[f_3977_4]) ).

cnf(f_3977_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15836,U_15836)),hAPP(hAPP(c_Product__Type_OPair(U_15836,U_15836),sK394(U_15839,U_15838,U_15837,U_15836)),U_15838)),c_Transitive__Closure_Ortrancl(U_15836,U_15839)))
    | ~ sP1048(U_15836,U_15837,U_15838,U_15839) ),
    inference(clausify,[status(thm)],[f_3977_4]) ).

fof(f_3978_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_3978_2,plain,
    ! [U_15844,U_15843,U_15842,U_15841] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15841,U_15842,c_Groups_Otimes__class_Otimes(U_15841)),U_15844),c_Groups_Oone__class_Oone(U_15841)),U_15843) = c_Groups_Oone__class_Oone(U_15841)
      | ? [U_15840] :
          ( hAPP(U_15844,U_15840) != c_Groups_Oone__class_Oone(U_15841)
          & hBOOL(hAPP(hAPP(c_member(U_15842),U_15840),U_15843)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15842),U_15843))
      | ~ class_Groups_Ocomm__monoid__mult(U_15841) ),
    inference(variable_rename,[status(thm)],[f_3978_1]) ).

fof(f_3978_3,plain,
    ! [U_15844,U_15843,U_15842,U_15841] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15841,U_15842,c_Groups_Otimes__class_Otimes(U_15841)),U_15844),c_Groups_Oone__class_Oone(U_15841)),U_15843) = c_Groups_Oone__class_Oone(U_15841)
      | ( hAPP(U_15844,sK395(U_15844,U_15843,U_15842,U_15841)) != c_Groups_Oone__class_Oone(U_15841)
        & hBOOL(hAPP(hAPP(c_member(U_15842),sK395(U_15844,U_15843,U_15842,U_15841)),U_15843)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15842),U_15843))
      | ~ class_Groups_Ocomm__monoid__mult(U_15841) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK395]),skolemize(U_15840,sK395(U_15844,U_15843,U_15842,U_15841))],[f_3978_2]) ).

fof(f_3978_4,plain,
    ( ! [U_15841,U_15842,U_15843,U_15844] :
        ( hAPP(U_15844,sK395(U_15844,U_15843,U_15842,U_15841)) != c_Groups_Oone__class_Oone(U_15841)
        | ~ sP1049(U_15841,U_15842,U_15843,U_15844) )
    & ! [U_15841,U_15842,U_15843,U_15844] :
        ( hBOOL(hAPP(hAPP(c_member(U_15842),sK395(U_15844,U_15843,U_15842,U_15841)),U_15843))
        | ~ sP1049(U_15841,U_15842,U_15843,U_15844) )
    & ! [U_15841,U_15842,U_15843,U_15844] :
        ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15841,U_15842,c_Groups_Otimes__class_Otimes(U_15841)),U_15844),c_Groups_Oone__class_Oone(U_15841)),U_15843) = c_Groups_Oone__class_Oone(U_15841)
        | sP1049(U_15841,U_15842,U_15843,U_15844)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15842),U_15843))
        | ~ class_Groups_Ocomm__monoid__mult(U_15841) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1049])],[f_3978_3]) ).

cnf(f_3978_5,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15841,U_15842,c_Groups_Otimes__class_Otimes(U_15841)),U_15844),c_Groups_Oone__class_Oone(U_15841)),U_15843) = c_Groups_Oone__class_Oone(U_15841)
    | sP1049(U_15841,U_15842,U_15843,U_15844)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15842),U_15843))
    | ~ class_Groups_Ocomm__monoid__mult(U_15841) ),
    inference(clausify,[status(thm)],[f_3978_4]) ).

cnf(f_3978_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15842),sK395(U_15844,U_15843,U_15842,U_15841)),U_15843))
    | ~ sP1049(U_15841,U_15842,U_15843,U_15844) ),
    inference(clausify,[status(thm)],[f_3978_4]) ).

cnf(f_3978_7,plain,
    ( hAPP(U_15844,sK395(U_15844,U_15843,U_15842,U_15841)) != c_Groups_Oone__class_Oone(U_15841)
    | ~ sP1049(U_15841,U_15842,U_15843,U_15844) ),
    inference(clausify,[status(thm)],[f_3978_4]) ).

fof(f_3979_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_3979_2,plain,
    ! [U_15847,U_15846] :
      ( hAPP(c_Finite__Set_Ocard(U_15846),U_15847) = 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_15845] : hBOOL(hAPP(hAPP(c_member(U_15846),U_15845),U_15847)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15846),U_15847)) ),
    inference(variable_rename,[status(thm)],[f_3979_1]) ).

fof(f_3979_3,plain,
    ! [U_15847,U_15846] :
      ( hAPP(c_Finite__Set_Ocard(U_15846),U_15847) = 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_15846),sK396(U_15847,U_15846)),U_15847)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15846),U_15847)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK396]),skolemize(U_15845,sK396(U_15847,U_15846))],[f_3979_2]) ).

fof(f_3979_4,plain,
    ( ! [U_15847,U_15846] :
        ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1050(U_15847,U_15846) )
    & ! [U_15847,U_15846] :
        ( hBOOL(hAPP(hAPP(c_member(U_15846),sK396(U_15847,U_15846)),U_15847))
        | ~ sP1050(U_15847,U_15846) )
    & ! [U_15847,U_15846] :
        ( hAPP(c_Finite__Set_Ocard(U_15846),U_15847) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP1050(U_15847,U_15846)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15846),U_15847)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1050])],[f_3979_3]) ).

cnf(f_3979_5,plain,
    ( hAPP(c_Finite__Set_Ocard(U_15846),U_15847) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP1050(U_15847,U_15846)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15846),U_15847)) ),
    inference(clausify,[status(thm)],[f_3979_4]) ).

cnf(f_3979_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15846),sK396(U_15847,U_15846)),U_15847))
    | ~ sP1050(U_15847,U_15846) ),
    inference(clausify,[status(thm)],[f_3979_4]) ).

cnf(f_3979_7,plain,
    ( c_Groups_Oone__class_Oone(tc_Nat_Onat) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1050(U_15847,U_15846) ),
    inference(clausify,[status(thm)],[f_3979_4]) ).

fof(f_3980_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_3980_2,plain,
    ! [U_15855,U_15854,U_15853,U_15852] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15852,tc_HOL_Obool),tc_fun(U_15852,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15852,tc_HOL_Obool),tc_fun(U_15852,tc_HOL_Obool)),U_15853),U_15854)),c_Wellfounded_Omax__ext(U_15852,U_15855)))
        | ? [U_15851] :
            ( ! [U_15850] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15852,U_15852)),hAPP(hAPP(c_Product__Type_OPair(U_15852,U_15852),U_15851),U_15850)),U_15855))
                | ~ hBOOL(hAPP(hAPP(c_member(U_15852),U_15850),U_15854)) )
            & hBOOL(hAPP(hAPP(c_member(U_15852),U_15851),U_15853)) )
        | U_15854 = c_Orderings_Obot__class_Obot(tc_fun(U_15852,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15852),U_15854))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15852),U_15853)) )
      & ( ( ! [U_15849] :
              ( ? [U_15848] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15852,U_15852)),hAPP(hAPP(c_Product__Type_OPair(U_15852,U_15852),U_15849),U_15848)),U_15855))
                  & hBOOL(hAPP(hAPP(c_member(U_15852),U_15848),U_15854)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_15852),U_15849),U_15853)) )
          & U_15854 != c_Orderings_Obot__class_Obot(tc_fun(U_15852,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15852),U_15854))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15852),U_15853)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15852,tc_HOL_Obool),tc_fun(U_15852,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15852,tc_HOL_Obool),tc_fun(U_15852,tc_HOL_Obool)),U_15853),U_15854)),c_Wellfounded_Omax__ext(U_15852,U_15855))) ) ),
    inference(variable_rename,[status(thm)],[f_3980_1]) ).

fof(f_3980_3,plain,
    ( ! [U_15863,U_15861,U_15859,U_15857] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15857,tc_HOL_Obool),tc_fun(U_15857,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15857,tc_HOL_Obool),tc_fun(U_15857,tc_HOL_Obool)),U_15859),U_15861)),c_Wellfounded_Omax__ext(U_15857,U_15863)))
        | ? [U_15851] :
            ( ! [U_15850] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15857,U_15857)),hAPP(hAPP(c_Product__Type_OPair(U_15857,U_15857),U_15851),U_15850)),U_15863))
                | ~ hBOOL(hAPP(hAPP(c_member(U_15857),U_15850),U_15861)) )
            & hBOOL(hAPP(hAPP(c_member(U_15857),U_15851),U_15859)) )
        | U_15861 = c_Orderings_Obot__class_Obot(tc_fun(U_15857,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15857),U_15861))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15857),U_15859)) )
    & ! [U_15862,U_15860,U_15858,U_15856] :
        ( ( ! [U_15849] :
              ( ? [U_15848] :
                  ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15856,U_15856)),hAPP(hAPP(c_Product__Type_OPair(U_15856,U_15856),U_15849),U_15848)),U_15862))
                  & hBOOL(hAPP(hAPP(c_member(U_15856),U_15848),U_15860)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_15856),U_15849),U_15858)) )
          & U_15860 != c_Orderings_Obot__class_Obot(tc_fun(U_15856,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15856),U_15860))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15856),U_15858)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15856,tc_HOL_Obool),tc_fun(U_15856,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15856,tc_HOL_Obool),tc_fun(U_15856,tc_HOL_Obool)),U_15858),U_15860)),c_Wellfounded_Omax__ext(U_15856,U_15862))) ) ),
    inference(miniscope,[status(thm)],[f_3980_2]) ).

fof(f_3980_4,plain,
    ( ! [U_15863,U_15861,U_15859,U_15857] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15857,tc_HOL_Obool),tc_fun(U_15857,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15857,tc_HOL_Obool),tc_fun(U_15857,tc_HOL_Obool)),U_15859),U_15861)),c_Wellfounded_Omax__ext(U_15857,U_15863)))
        | ? [U_15851] :
            ( ! [U_15850] :
                ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15857,U_15857)),hAPP(hAPP(c_Product__Type_OPair(U_15857,U_15857),U_15851),U_15850)),U_15863))
                | ~ hBOOL(hAPP(hAPP(c_member(U_15857),U_15850),U_15861)) )
            & hBOOL(hAPP(hAPP(c_member(U_15857),U_15851),U_15859)) )
        | U_15861 = c_Orderings_Obot__class_Obot(tc_fun(U_15857,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15857),U_15861))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15857),U_15859)) )
    & ! [U_15862,U_15860,U_15858,U_15856] :
        ( ( ! [U_15849] :
              ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15856,U_15856)),hAPP(hAPP(c_Product__Type_OPair(U_15856,U_15856),U_15849),sK397(U_15862,U_15860,U_15858,U_15856,U_15849))),U_15862))
                & hBOOL(hAPP(hAPP(c_member(U_15856),sK397(U_15862,U_15860,U_15858,U_15856,U_15849)),U_15860)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_15856),U_15849),U_15858)) )
          & U_15860 != c_Orderings_Obot__class_Obot(tc_fun(U_15856,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15856),U_15860))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15856),U_15858)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15856,tc_HOL_Obool),tc_fun(U_15856,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15856,tc_HOL_Obool),tc_fun(U_15856,tc_HOL_Obool)),U_15858),U_15860)),c_Wellfounded_Omax__ext(U_15856,U_15862))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK397]),skolemize(U_15848,sK397(U_15862,U_15860,U_15858,U_15856,U_15849))],[f_3980_3]) ).

fof(f_3980_5,plain,
    ( ! [U_15863,U_15861,U_15859,U_15857] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15857,tc_HOL_Obool),tc_fun(U_15857,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15857,tc_HOL_Obool),tc_fun(U_15857,tc_HOL_Obool)),U_15859),U_15861)),c_Wellfounded_Omax__ext(U_15857,U_15863)))
        | ( ! [U_15850] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15857,U_15857)),hAPP(hAPP(c_Product__Type_OPair(U_15857,U_15857),sK398(U_15863,U_15861,U_15859,U_15857)),U_15850)),U_15863))
              | ~ hBOOL(hAPP(hAPP(c_member(U_15857),U_15850),U_15861)) )
          & hBOOL(hAPP(hAPP(c_member(U_15857),sK398(U_15863,U_15861,U_15859,U_15857)),U_15859)) )
        | U_15861 = c_Orderings_Obot__class_Obot(tc_fun(U_15857,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15857),U_15861))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15857),U_15859)) )
    & ! [U_15862,U_15860,U_15858,U_15856] :
        ( ( ! [U_15849] :
              ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15856,U_15856)),hAPP(hAPP(c_Product__Type_OPair(U_15856,U_15856),U_15849),sK397(U_15862,U_15860,U_15858,U_15856,U_15849))),U_15862))
                & hBOOL(hAPP(hAPP(c_member(U_15856),sK397(U_15862,U_15860,U_15858,U_15856,U_15849)),U_15860)) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_15856),U_15849),U_15858)) )
          & U_15860 != c_Orderings_Obot__class_Obot(tc_fun(U_15856,tc_HOL_Obool))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15856),U_15860))
          & hBOOL(hAPP(c_Finite__Set_Ofinite(U_15856),U_15858)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15856,tc_HOL_Obool),tc_fun(U_15856,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15856,tc_HOL_Obool),tc_fun(U_15856,tc_HOL_Obool)),U_15858),U_15860)),c_Wellfounded_Omax__ext(U_15856,U_15862))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK398]),skolemize(U_15851,sK398(U_15863,U_15861,U_15859,U_15857))],[f_3980_4]) ).

fof(f_3980_6,plain,
    ( ! [U_15859,U_15850,U_15861,U_15863,U_15857] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15857,U_15857)),hAPP(hAPP(c_Product__Type_OPair(U_15857,U_15857),sK398(U_15863,U_15861,U_15859,U_15857)),U_15850)),U_15863))
        | ~ hBOOL(hAPP(hAPP(c_member(U_15857),U_15850),U_15861))
        | ~ sP1053(U_15859,U_15850,U_15861,U_15863,U_15857) )
    & ! [U_15859,U_15850,U_15861,U_15863,U_15857] :
        ( hBOOL(hAPP(hAPP(c_member(U_15857),sK398(U_15863,U_15861,U_15859,U_15857)),U_15859))
        | ~ sP1053(U_15859,U_15850,U_15861,U_15863,U_15857) )
    & ! [U_15849,U_15856,U_15858,U_15860,U_15862] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15856,U_15856)),hAPP(hAPP(c_Product__Type_OPair(U_15856,U_15856),U_15849),sK397(U_15862,U_15860,U_15858,U_15856,U_15849))),U_15862))
        | ~ sP1051(U_15849,U_15856,U_15858,U_15860,U_15862) )
    & ! [U_15849,U_15856,U_15858,U_15860,U_15862] :
        ( hBOOL(hAPP(hAPP(c_member(U_15856),sK397(U_15862,U_15860,U_15858,U_15856,U_15849)),U_15860))
        | ~ sP1051(U_15849,U_15856,U_15858,U_15860,U_15862) )
    & ! [U_15849,U_15856,U_15858,U_15860,U_15862] :
        ( sP1051(U_15849,U_15856,U_15858,U_15860,U_15862)
        | ~ hBOOL(hAPP(hAPP(c_member(U_15856),U_15849),U_15858))
        | ~ sP1052(U_15849,U_15856,U_15858,U_15860,U_15862) )
    & ! [U_15849,U_15856,U_15858,U_15860,U_15862] :
        ( U_15860 != c_Orderings_Obot__class_Obot(tc_fun(U_15856,tc_HOL_Obool))
        | ~ sP1052(U_15849,U_15856,U_15858,U_15860,U_15862) )
    & ! [U_15849,U_15856,U_15858,U_15860,U_15862] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15856),U_15860))
        | ~ sP1052(U_15849,U_15856,U_15858,U_15860,U_15862) )
    & ! [U_15849,U_15856,U_15858,U_15860,U_15862] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15856),U_15858))
        | ~ sP1052(U_15849,U_15856,U_15858,U_15860,U_15862) )
    & ! [U_15859,U_15850,U_15861,U_15863,U_15857] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15857,tc_HOL_Obool),tc_fun(U_15857,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15857,tc_HOL_Obool),tc_fun(U_15857,tc_HOL_Obool)),U_15859),U_15861)),c_Wellfounded_Omax__ext(U_15857,U_15863)))
        | sP1053(U_15859,U_15850,U_15861,U_15863,U_15857)
        | U_15861 = c_Orderings_Obot__class_Obot(tc_fun(U_15857,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15857),U_15861))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15857),U_15859)) )
    & ! [U_15849,U_15856,U_15858,U_15860,U_15862] :
        ( sP1052(U_15849,U_15856,U_15858,U_15860,U_15862)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15856,tc_HOL_Obool),tc_fun(U_15856,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15856,tc_HOL_Obool),tc_fun(U_15856,tc_HOL_Obool)),U_15858),U_15860)),c_Wellfounded_Omax__ext(U_15856,U_15862))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1051,sP1052,sP1053])],[f_3980_5]) ).

cnf(f_3980_7,plain,
    ( sP1052(U_15849,U_15856,U_15858,U_15860,U_15862)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15856,tc_HOL_Obool),tc_fun(U_15856,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15856,tc_HOL_Obool),tc_fun(U_15856,tc_HOL_Obool)),U_15858),U_15860)),c_Wellfounded_Omax__ext(U_15856,U_15862))) ),
    inference(clausify,[status(thm)],[f_3980_6]) ).

cnf(f_3980_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(U_15857,tc_HOL_Obool),tc_fun(U_15857,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(U_15857,tc_HOL_Obool),tc_fun(U_15857,tc_HOL_Obool)),U_15859),U_15861)),c_Wellfounded_Omax__ext(U_15857,U_15863)))
    | sP1053(U_15859,U_15850,U_15861,U_15863,U_15857)
    | U_15861 = c_Orderings_Obot__class_Obot(tc_fun(U_15857,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15857),U_15861))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15857),U_15859)) ),
    inference(clausify,[status(thm)],[f_3980_6]) ).

cnf(f_3980_9,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15856),U_15858))
    | ~ sP1052(U_15849,U_15856,U_15858,U_15860,U_15862) ),
    inference(clausify,[status(thm)],[f_3980_6]) ).

cnf(f_3980_10,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_15856),U_15860))
    | ~ sP1052(U_15849,U_15856,U_15858,U_15860,U_15862) ),
    inference(clausify,[status(thm)],[f_3980_6]) ).

cnf(f_3980_11,plain,
    ( U_15860 != c_Orderings_Obot__class_Obot(tc_fun(U_15856,tc_HOL_Obool))
    | ~ sP1052(U_15849,U_15856,U_15858,U_15860,U_15862) ),
    inference(clausify,[status(thm)],[f_3980_6]) ).

cnf(f_3980_12,plain,
    ( sP1051(U_15849,U_15856,U_15858,U_15860,U_15862)
    | ~ hBOOL(hAPP(hAPP(c_member(U_15856),U_15849),U_15858))
    | ~ sP1052(U_15849,U_15856,U_15858,U_15860,U_15862) ),
    inference(clausify,[status(thm)],[f_3980_6]) ).

cnf(f_3980_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15856),sK397(U_15862,U_15860,U_15858,U_15856,U_15849)),U_15860))
    | ~ sP1051(U_15849,U_15856,U_15858,U_15860,U_15862) ),
    inference(clausify,[status(thm)],[f_3980_6]) ).

cnf(f_3980_14,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_15856,U_15856)),hAPP(hAPP(c_Product__Type_OPair(U_15856,U_15856),U_15849),sK397(U_15862,U_15860,U_15858,U_15856,U_15849))),U_15862))
    | ~ sP1051(U_15849,U_15856,U_15858,U_15860,U_15862) ),
    inference(clausify,[status(thm)],[f_3980_6]) ).

cnf(f_3980_15,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15857),sK398(U_15863,U_15861,U_15859,U_15857)),U_15859))
    | ~ sP1053(U_15859,U_15850,U_15861,U_15863,U_15857) ),
    inference(clausify,[status(thm)],[f_3980_6]) ).

cnf(f_3980_16,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_15857,U_15857)),hAPP(hAPP(c_Product__Type_OPair(U_15857,U_15857),sK398(U_15863,U_15861,U_15859,U_15857)),U_15850)),U_15863))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15857),U_15850),U_15861))
    | ~ sP1053(U_15859,U_15850,U_15861,U_15863,U_15857) ),
    inference(clausify,[status(thm)],[f_3980_6]) ).

fof(f_3981_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_3981_2,plain,
    ! [U_15870,U_15869,U_15868,U_15867,U_15866,U_15865] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15865,U_15866,c_Groups_Otimes__class_Otimes(U_15865)),U_15868),U_15870),U_15867) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15865,U_15866,c_Groups_Otimes__class_Otimes(U_15865)),U_15869),U_15870),U_15867)
      | ? [U_15864] :
          ( hAPP(U_15868,U_15864) != hAPP(U_15869,U_15864)
          & hBOOL(hAPP(hAPP(c_member(U_15866),U_15864),U_15867)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15866),U_15867))
      | ~ class_Groups_Oab__semigroup__mult(U_15865) ),
    inference(variable_rename,[status(thm)],[f_3981_1]) ).

fof(f_3981_3,plain,
    ! [U_15870,U_15869,U_15868,U_15867,U_15866,U_15865] :
      ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15865,U_15866,c_Groups_Otimes__class_Otimes(U_15865)),U_15868),U_15870),U_15867) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15865,U_15866,c_Groups_Otimes__class_Otimes(U_15865)),U_15869),U_15870),U_15867)
      | ( hAPP(U_15868,sK399(U_15870,U_15869,U_15868,U_15867,U_15866,U_15865)) != hAPP(U_15869,sK399(U_15870,U_15869,U_15868,U_15867,U_15866,U_15865))
        & hBOOL(hAPP(hAPP(c_member(U_15866),sK399(U_15870,U_15869,U_15868,U_15867,U_15866,U_15865)),U_15867)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15866),U_15867))
      | ~ class_Groups_Oab__semigroup__mult(U_15865) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK399]),skolemize(U_15864,sK399(U_15870,U_15869,U_15868,U_15867,U_15866,U_15865))],[f_3981_2]) ).

fof(f_3981_4,plain,
    ( ! [U_15867,U_15869,U_15865,U_15866,U_15870,U_15868] :
        ( hAPP(U_15868,sK399(U_15870,U_15869,U_15868,U_15867,U_15866,U_15865)) != hAPP(U_15869,sK399(U_15870,U_15869,U_15868,U_15867,U_15866,U_15865))
        | ~ sP1054(U_15867,U_15869,U_15865,U_15866,U_15870,U_15868) )
    & ! [U_15867,U_15869,U_15865,U_15866,U_15870,U_15868] :
        ( hBOOL(hAPP(hAPP(c_member(U_15866),sK399(U_15870,U_15869,U_15868,U_15867,U_15866,U_15865)),U_15867))
        | ~ sP1054(U_15867,U_15869,U_15865,U_15866,U_15870,U_15868) )
    & ! [U_15867,U_15869,U_15865,U_15866,U_15870,U_15868] :
        ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15865,U_15866,c_Groups_Otimes__class_Otimes(U_15865)),U_15868),U_15870),U_15867) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15865,U_15866,c_Groups_Otimes__class_Otimes(U_15865)),U_15869),U_15870),U_15867)
        | sP1054(U_15867,U_15869,U_15865,U_15866,U_15870,U_15868)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15866),U_15867))
        | ~ class_Groups_Oab__semigroup__mult(U_15865) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1054])],[f_3981_3]) ).

cnf(f_3981_5,plain,
    ( hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15865,U_15866,c_Groups_Otimes__class_Otimes(U_15865)),U_15868),U_15870),U_15867) = hAPP(hAPP(hAPP(c_Finite__Set_Ofold__image(U_15865,U_15866,c_Groups_Otimes__class_Otimes(U_15865)),U_15869),U_15870),U_15867)
    | sP1054(U_15867,U_15869,U_15865,U_15866,U_15870,U_15868)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15866),U_15867))
    | ~ class_Groups_Oab__semigroup__mult(U_15865) ),
    inference(clausify,[status(thm)],[f_3981_4]) ).

cnf(f_3981_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15866),sK399(U_15870,U_15869,U_15868,U_15867,U_15866,U_15865)),U_15867))
    | ~ sP1054(U_15867,U_15869,U_15865,U_15866,U_15870,U_15868) ),
    inference(clausify,[status(thm)],[f_3981_4]) ).

cnf(f_3981_7,plain,
    ( hAPP(U_15868,sK399(U_15870,U_15869,U_15868,U_15867,U_15866,U_15865)) != hAPP(U_15869,sK399(U_15870,U_15869,U_15868,U_15867,U_15866,U_15865))
    | ~ sP1054(U_15867,U_15869,U_15865,U_15866,U_15870,U_15868) ),
    inference(clausify,[status(thm)],[f_3981_4]) ).

fof(f_3982_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_3982_2,plain,
    ! [U_15877,U_15876,U_15875,U_15874,U_15873,U_15872] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15872),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15873,U_15872),U_15876),U_15875)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15873,U_15872),U_15877),U_15874)))
      | ? [U_15871] :
          ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15872),hAPP(U_15876,U_15871)),hAPP(U_15877,U_15871)))
          & hBOOL(hAPP(hAPP(c_member(U_15873),U_15871),U_15875)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15873,tc_HOL_Obool)),U_15875),U_15874))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15873),U_15874))
      | ~ class_Rings_Ocomm__semiring__1(U_15872) ),
    inference(variable_rename,[status(thm)],[f_3982_1]) ).

fof(f_3982_3,plain,
    ! [U_15877,U_15876,U_15875,U_15874,U_15873,U_15872] :
      ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15872),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15873,U_15872),U_15876),U_15875)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15873,U_15872),U_15877),U_15874)))
      | ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15872),hAPP(U_15876,sK400(U_15877,U_15876,U_15875,U_15874,U_15873,U_15872))),hAPP(U_15877,sK400(U_15877,U_15876,U_15875,U_15874,U_15873,U_15872))))
        & hBOOL(hAPP(hAPP(c_member(U_15873),sK400(U_15877,U_15876,U_15875,U_15874,U_15873,U_15872)),U_15875)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15873,tc_HOL_Obool)),U_15875),U_15874))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15873),U_15874))
      | ~ class_Rings_Ocomm__semiring__1(U_15872) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK400]),skolemize(U_15871,sK400(U_15877,U_15876,U_15875,U_15874,U_15873,U_15872))],[f_3982_2]) ).

fof(f_3982_4,plain,
    ( ! [U_15872,U_15873,U_15874,U_15875,U_15876,U_15877] :
        ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15872),hAPP(U_15876,sK400(U_15877,U_15876,U_15875,U_15874,U_15873,U_15872))),hAPP(U_15877,sK400(U_15877,U_15876,U_15875,U_15874,U_15873,U_15872))))
        | ~ sP1055(U_15872,U_15873,U_15874,U_15875,U_15876,U_15877) )
    & ! [U_15872,U_15873,U_15874,U_15875,U_15876,U_15877] :
        ( hBOOL(hAPP(hAPP(c_member(U_15873),sK400(U_15877,U_15876,U_15875,U_15874,U_15873,U_15872)),U_15875))
        | ~ sP1055(U_15872,U_15873,U_15874,U_15875,U_15876,U_15877) )
    & ! [U_15872,U_15873,U_15874,U_15875,U_15876,U_15877] :
        ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15872),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15873,U_15872),U_15876),U_15875)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15873,U_15872),U_15877),U_15874)))
        | sP1055(U_15872,U_15873,U_15874,U_15875,U_15876,U_15877)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15873,tc_HOL_Obool)),U_15875),U_15874))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15873),U_15874))
        | ~ class_Rings_Ocomm__semiring__1(U_15872) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1055])],[f_3982_3]) ).

cnf(f_3982_5,plain,
    ( hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15872),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15873,U_15872),U_15876),U_15875)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_15873,U_15872),U_15877),U_15874)))
    | sP1055(U_15872,U_15873,U_15874,U_15875,U_15876,U_15877)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_15873,tc_HOL_Obool)),U_15875),U_15874))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15873),U_15874))
    | ~ class_Rings_Ocomm__semiring__1(U_15872) ),
    inference(clausify,[status(thm)],[f_3982_4]) ).

cnf(f_3982_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15873),sK400(U_15877,U_15876,U_15875,U_15874,U_15873,U_15872)),U_15875))
    | ~ sP1055(U_15872,U_15873,U_15874,U_15875,U_15876,U_15877) ),
    inference(clausify,[status(thm)],[f_3982_4]) ).

cnf(f_3982_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Rings_Odvd__class_Odvd(U_15872),hAPP(U_15876,sK400(U_15877,U_15876,U_15875,U_15874,U_15873,U_15872))),hAPP(U_15877,sK400(U_15877,U_15876,U_15875,U_15874,U_15873,U_15872))))
    | ~ sP1055(U_15872,U_15873,U_15874,U_15875,U_15876,U_15877) ),
    inference(clausify,[status(thm)],[f_3982_4]) ).

fof(f_3983_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_3983_2,plain,
    ! [U_15881,U_15880,U_15879] :
      ( c_Big__Operators_Olinorder__class_OMax(U_15879,U_15880) = U_15881
      | ~ hBOOL(hAPP(hAPP(c_member(U_15879),U_15881),U_15880))
      | ? [U_15878] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15879),U_15878),U_15881))
          & hBOOL(hAPP(hAPP(c_member(U_15879),U_15878),U_15880)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15879),U_15880))
      | ~ class_Orderings_Olinorder(U_15879) ),
    inference(variable_rename,[status(thm)],[f_3983_1]) ).

fof(f_3983_3,plain,
    ! [U_15881,U_15880,U_15879] :
      ( c_Big__Operators_Olinorder__class_OMax(U_15879,U_15880) = U_15881
      | ~ hBOOL(hAPP(hAPP(c_member(U_15879),U_15881),U_15880))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15879),sK401(U_15881,U_15880,U_15879)),U_15881))
        & hBOOL(hAPP(hAPP(c_member(U_15879),sK401(U_15881,U_15880,U_15879)),U_15880)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15879),U_15880))
      | ~ class_Orderings_Olinorder(U_15879) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK401]),skolemize(U_15878,sK401(U_15881,U_15880,U_15879))],[f_3983_2]) ).

fof(f_3983_4,plain,
    ( ! [U_15879,U_15881,U_15880] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15879),sK401(U_15881,U_15880,U_15879)),U_15881))
        | ~ sP1056(U_15879,U_15881,U_15880) )
    & ! [U_15879,U_15881,U_15880] :
        ( hBOOL(hAPP(hAPP(c_member(U_15879),sK401(U_15881,U_15880,U_15879)),U_15880))
        | ~ sP1056(U_15879,U_15881,U_15880) )
    & ! [U_15879,U_15881,U_15880] :
        ( c_Big__Operators_Olinorder__class_OMax(U_15879,U_15880) = U_15881
        | ~ hBOOL(hAPP(hAPP(c_member(U_15879),U_15881),U_15880))
        | sP1056(U_15879,U_15881,U_15880)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15879),U_15880))
        | ~ class_Orderings_Olinorder(U_15879) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1056])],[f_3983_3]) ).

cnf(f_3983_5,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_15879,U_15880) = U_15881
    | ~ hBOOL(hAPP(hAPP(c_member(U_15879),U_15881),U_15880))
    | sP1056(U_15879,U_15881,U_15880)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15879),U_15880))
    | ~ class_Orderings_Olinorder(U_15879) ),
    inference(clausify,[status(thm)],[f_3983_4]) ).

cnf(f_3983_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15879),sK401(U_15881,U_15880,U_15879)),U_15880))
    | ~ sP1056(U_15879,U_15881,U_15880) ),
    inference(clausify,[status(thm)],[f_3983_4]) ).

cnf(f_3983_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15879),sK401(U_15881,U_15880,U_15879)),U_15881))
    | ~ sP1056(U_15879,U_15881,U_15880) ),
    inference(clausify,[status(thm)],[f_3983_4]) ).

fof(f_3984_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_3984_2,plain,
    ! [U_15885,U_15884,U_15883] :
      ( c_Big__Operators_Olinorder__class_OMin(U_15883,U_15884) = U_15885
      | ~ hBOOL(hAPP(hAPP(c_member(U_15883),U_15885),U_15884))
      | ? [U_15882] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15883),U_15885),U_15882))
          & hBOOL(hAPP(hAPP(c_member(U_15883),U_15882),U_15884)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15883),U_15884))
      | ~ class_Orderings_Olinorder(U_15883) ),
    inference(variable_rename,[status(thm)],[f_3984_1]) ).

fof(f_3984_3,plain,
    ! [U_15885,U_15884,U_15883] :
      ( c_Big__Operators_Olinorder__class_OMin(U_15883,U_15884) = U_15885
      | ~ hBOOL(hAPP(hAPP(c_member(U_15883),U_15885),U_15884))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15883),U_15885),sK402(U_15885,U_15884,U_15883)))
        & hBOOL(hAPP(hAPP(c_member(U_15883),sK402(U_15885,U_15884,U_15883)),U_15884)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15883),U_15884))
      | ~ class_Orderings_Olinorder(U_15883) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK402]),skolemize(U_15882,sK402(U_15885,U_15884,U_15883))],[f_3984_2]) ).

fof(f_3984_4,plain,
    ( ! [U_15884,U_15883,U_15885] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15883),U_15885),sK402(U_15885,U_15884,U_15883)))
        | ~ sP1057(U_15884,U_15883,U_15885) )
    & ! [U_15884,U_15883,U_15885] :
        ( hBOOL(hAPP(hAPP(c_member(U_15883),sK402(U_15885,U_15884,U_15883)),U_15884))
        | ~ sP1057(U_15884,U_15883,U_15885) )
    & ! [U_15884,U_15883,U_15885] :
        ( c_Big__Operators_Olinorder__class_OMin(U_15883,U_15884) = U_15885
        | ~ hBOOL(hAPP(hAPP(c_member(U_15883),U_15885),U_15884))
        | sP1057(U_15884,U_15883,U_15885)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15883),U_15884))
        | ~ class_Orderings_Olinorder(U_15883) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1057])],[f_3984_3]) ).

cnf(f_3984_5,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_15883,U_15884) = U_15885
    | ~ hBOOL(hAPP(hAPP(c_member(U_15883),U_15885),U_15884))
    | sP1057(U_15884,U_15883,U_15885)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15883),U_15884))
    | ~ class_Orderings_Olinorder(U_15883) ),
    inference(clausify,[status(thm)],[f_3984_4]) ).

cnf(f_3984_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15883),sK402(U_15885,U_15884,U_15883)),U_15884))
    | ~ sP1057(U_15884,U_15883,U_15885) ),
    inference(clausify,[status(thm)],[f_3984_4]) ).

cnf(f_3984_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15883),U_15885),sK402(U_15885,U_15884,U_15883)))
    | ~ sP1057(U_15884,U_15883,U_15885) ),
    inference(clausify,[status(thm)],[f_3984_4]) ).

fof(f_3985_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_3985_2,plain,
    ! [U_15894,U_15893,U_15892,U_15891,U_15890,U_15889,U_15888,U_15887] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15889,U_15887),U_15894),U_15892) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15888,U_15887),U_15893),U_15891)
      | ? [U_15886] :
          ( hAPP(U_15893,U_15886) != hAPP(U_15894,hAPP(U_15890,U_15886))
          & hBOOL(hAPP(hAPP(c_member(U_15888),U_15886),U_15891)) )
      | U_15892 != hAPP(c_Set_Oimage(U_15888,U_15889,U_15890),U_15891)
      | ~ c_Fun_Oinj__on(U_15888,U_15889,U_15890,U_15891)
      | ~ class_Groups_Ocomm__monoid__add(U_15887) ),
    inference(variable_rename,[status(thm)],[f_3985_1]) ).

fof(f_3985_3,plain,
    ! [U_15894,U_15893,U_15892,U_15891,U_15890,U_15889,U_15888,U_15887] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15889,U_15887),U_15894),U_15892) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15888,U_15887),U_15893),U_15891)
      | ( hAPP(U_15893,sK403(U_15894,U_15893,U_15892,U_15891,U_15890,U_15889,U_15888,U_15887)) != hAPP(U_15894,hAPP(U_15890,sK403(U_15894,U_15893,U_15892,U_15891,U_15890,U_15889,U_15888,U_15887)))
        & hBOOL(hAPP(hAPP(c_member(U_15888),sK403(U_15894,U_15893,U_15892,U_15891,U_15890,U_15889,U_15888,U_15887)),U_15891)) )
      | U_15892 != hAPP(c_Set_Oimage(U_15888,U_15889,U_15890),U_15891)
      | ~ c_Fun_Oinj__on(U_15888,U_15889,U_15890,U_15891)
      | ~ class_Groups_Ocomm__monoid__add(U_15887) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK403]),skolemize(U_15886,sK403(U_15894,U_15893,U_15892,U_15891,U_15890,U_15889,U_15888,U_15887))],[f_3985_2]) ).

fof(f_3985_4,plain,
    ( ! [U_15888,U_15889,U_15887,U_15890,U_15891,U_15892,U_15893,U_15894] :
        ( hAPP(U_15893,sK403(U_15894,U_15893,U_15892,U_15891,U_15890,U_15889,U_15888,U_15887)) != hAPP(U_15894,hAPP(U_15890,sK403(U_15894,U_15893,U_15892,U_15891,U_15890,U_15889,U_15888,U_15887)))
        | ~ sP1058(U_15888,U_15889,U_15887,U_15890,U_15891,U_15892,U_15893,U_15894) )
    & ! [U_15888,U_15889,U_15887,U_15890,U_15891,U_15892,U_15893,U_15894] :
        ( hBOOL(hAPP(hAPP(c_member(U_15888),sK403(U_15894,U_15893,U_15892,U_15891,U_15890,U_15889,U_15888,U_15887)),U_15891))
        | ~ sP1058(U_15888,U_15889,U_15887,U_15890,U_15891,U_15892,U_15893,U_15894) )
    & ! [U_15888,U_15889,U_15887,U_15890,U_15891,U_15892,U_15893,U_15894] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15889,U_15887),U_15894),U_15892) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15888,U_15887),U_15893),U_15891)
        | sP1058(U_15888,U_15889,U_15887,U_15890,U_15891,U_15892,U_15893,U_15894)
        | U_15892 != hAPP(c_Set_Oimage(U_15888,U_15889,U_15890),U_15891)
        | ~ c_Fun_Oinj__on(U_15888,U_15889,U_15890,U_15891)
        | ~ class_Groups_Ocomm__monoid__add(U_15887) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1058])],[f_3985_3]) ).

cnf(f_3985_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15889,U_15887),U_15894),U_15892) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15888,U_15887),U_15893),U_15891)
    | sP1058(U_15888,U_15889,U_15887,U_15890,U_15891,U_15892,U_15893,U_15894)
    | U_15892 != hAPP(c_Set_Oimage(U_15888,U_15889,U_15890),U_15891)
    | ~ c_Fun_Oinj__on(U_15888,U_15889,U_15890,U_15891)
    | ~ class_Groups_Ocomm__monoid__add(U_15887) ),
    inference(clausify,[status(thm)],[f_3985_4]) ).

cnf(f_3985_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_15888),sK403(U_15894,U_15893,U_15892,U_15891,U_15890,U_15889,U_15888,U_15887)),U_15891))
    | ~ sP1058(U_15888,U_15889,U_15887,U_15890,U_15891,U_15892,U_15893,U_15894) ),
    inference(clausify,[status(thm)],[f_3985_4]) ).

cnf(f_3985_7,plain,
    ( hAPP(U_15893,sK403(U_15894,U_15893,U_15892,U_15891,U_15890,U_15889,U_15888,U_15887)) != hAPP(U_15894,hAPP(U_15890,sK403(U_15894,U_15893,U_15892,U_15891,U_15890,U_15889,U_15888,U_15887)))
    | ~ sP1058(U_15888,U_15889,U_15887,U_15890,U_15891,U_15892,U_15893,U_15894) ),
    inference(clausify,[status(thm)],[f_3985_4]) ).

fof(f_3986_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_3986_2,plain,
    ! [U_15903,U_15902,U_15901,U_15900,U_15899,U_15898,U_15897,U_15896] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15897,U_15896),U_15902),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15897,U_15898),U_15900)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15897,U_15896),U_15903),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15897,U_15899),U_15901))
      | ? [U_15895] :
          ( hAPP(U_15902,U_15895) != hAPP(U_15903,U_15895)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15897),U_15895),U_15901))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15897),U_15899),U_15895)) )
      | U_15900 != U_15901
      | U_15898 != U_15899
      | ~ class_Orderings_Oord(U_15897)
      | ~ class_Groups_Ocomm__monoid__add(U_15896) ),
    inference(variable_rename,[status(thm)],[f_3986_1]) ).

fof(f_3986_3,plain,
    ! [U_15903,U_15902,U_15901,U_15900,U_15899,U_15898,U_15897,U_15896] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15897,U_15896),U_15902),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15897,U_15898),U_15900)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15897,U_15896),U_15903),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15897,U_15899),U_15901))
      | ( hAPP(U_15902,sK404(U_15903,U_15902,U_15901,U_15900,U_15899,U_15898,U_15897,U_15896)) != hAPP(U_15903,sK404(U_15903,U_15902,U_15901,U_15900,U_15899,U_15898,U_15897,U_15896))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15897),sK404(U_15903,U_15902,U_15901,U_15900,U_15899,U_15898,U_15897,U_15896)),U_15901))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15897),U_15899),sK404(U_15903,U_15902,U_15901,U_15900,U_15899,U_15898,U_15897,U_15896))) )
      | U_15900 != U_15901
      | U_15898 != U_15899
      | ~ class_Orderings_Oord(U_15897)
      | ~ class_Groups_Ocomm__monoid__add(U_15896) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK404]),skolemize(U_15895,sK404(U_15903,U_15902,U_15901,U_15900,U_15899,U_15898,U_15897,U_15896))],[f_3986_2]) ).

fof(f_3986_4,plain,
    ( ! [U_15897,U_15896,U_15898,U_15899,U_15900,U_15901,U_15902,U_15903] :
        ( hAPP(U_15902,sK404(U_15903,U_15902,U_15901,U_15900,U_15899,U_15898,U_15897,U_15896)) != hAPP(U_15903,sK404(U_15903,U_15902,U_15901,U_15900,U_15899,U_15898,U_15897,U_15896))
        | ~ sP1059(U_15897,U_15896,U_15898,U_15899,U_15900,U_15901,U_15902,U_15903) )
    & ! [U_15897,U_15896,U_15898,U_15899,U_15900,U_15901,U_15902,U_15903] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15897),sK404(U_15903,U_15902,U_15901,U_15900,U_15899,U_15898,U_15897,U_15896)),U_15901))
        | ~ sP1059(U_15897,U_15896,U_15898,U_15899,U_15900,U_15901,U_15902,U_15903) )
    & ! [U_15897,U_15896,U_15898,U_15899,U_15900,U_15901,U_15902,U_15903] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15897),U_15899),sK404(U_15903,U_15902,U_15901,U_15900,U_15899,U_15898,U_15897,U_15896)))
        | ~ sP1059(U_15897,U_15896,U_15898,U_15899,U_15900,U_15901,U_15902,U_15903) )
    & ! [U_15897,U_15896,U_15898,U_15899,U_15900,U_15901,U_15902,U_15903] :
        ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15897,U_15896),U_15902),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15897,U_15898),U_15900)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15897,U_15896),U_15903),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15897,U_15899),U_15901))
        | sP1059(U_15897,U_15896,U_15898,U_15899,U_15900,U_15901,U_15902,U_15903)
        | U_15900 != U_15901
        | U_15898 != U_15899
        | ~ class_Orderings_Oord(U_15897)
        | ~ class_Groups_Ocomm__monoid__add(U_15896) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1059])],[f_3986_3]) ).

cnf(f_3986_5,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15897,U_15896),U_15902),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15897,U_15898),U_15900)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_15897,U_15896),U_15903),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(U_15897,U_15899),U_15901))
    | sP1059(U_15897,U_15896,U_15898,U_15899,U_15900,U_15901,U_15902,U_15903)
    | U_15900 != U_15901
    | U_15898 != U_15899
    | ~ class_Orderings_Oord(U_15897)
    | ~ class_Groups_Ocomm__monoid__add(U_15896) ),
    inference(clausify,[status(thm)],[f_3986_4]) ).

cnf(f_3986_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15897),U_15899),sK404(U_15903,U_15902,U_15901,U_15900,U_15899,U_15898,U_15897,U_15896)))
    | ~ sP1059(U_15897,U_15896,U_15898,U_15899,U_15900,U_15901,U_15902,U_15903) ),
    inference(clausify,[status(thm)],[f_3986_4]) ).

cnf(f_3986_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_15897),sK404(U_15903,U_15902,U_15901,U_15900,U_15899,U_15898,U_15897,U_15896)),U_15901))
    | ~ sP1059(U_15897,U_15896,U_15898,U_15899,U_15900,U_15901,U_15902,U_15903) ),
    inference(clausify,[status(thm)],[f_3986_4]) ).

cnf(f_3986_8,plain,
    ( hAPP(U_15902,sK404(U_15903,U_15902,U_15901,U_15900,U_15899,U_15898,U_15897,U_15896)) != hAPP(U_15903,sK404(U_15903,U_15902,U_15901,U_15900,U_15899,U_15898,U_15897,U_15896))
    | ~ sP1059(U_15897,U_15896,U_15898,U_15899,U_15900,U_15901,U_15902,U_15903) ),
    inference(clausify,[status(thm)],[f_3986_4]) ).

fof(f_3987_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_3987_2,plain,
    ! [U_15906,U_15905,U_15904] :
      ( c_Big__Operators_Olattice_OSup__fin(U_15904,c_Orderings_Oord__class_Omax(U_15904),hAPP(hAPP(c_Set_Oinsert(U_15904),U_15906),U_15905)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15904,U_15904,c_Orderings_Oord__class_Omax(U_15904)),U_15906),U_15905)
      | hBOOL(hAPP(hAPP(c_member(U_15904),U_15906),U_15905))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15904),U_15905))
      | ~ class_Orderings_Olinorder(U_15904) ),
    inference(variable_rename,[status(thm)],[f_3987_1]) ).

fof(f_3987_3,plain,
    ! [U_15905,U_15906,U_15904] :
      ( c_Big__Operators_Olattice_OSup__fin(U_15904,c_Orderings_Oord__class_Omax(U_15904),hAPP(hAPP(c_Set_Oinsert(U_15904),U_15906),U_15905)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15904,U_15904,c_Orderings_Oord__class_Omax(U_15904)),U_15906),U_15905)
      | hBOOL(hAPP(hAPP(c_member(U_15904),U_15906),U_15905))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15904),U_15905))
      | ~ class_Orderings_Olinorder(U_15904) ),
    inference(definitional_conversion,[status(esa)],[f_3987_2]) ).

cnf(f_3987_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_15904,c_Orderings_Oord__class_Omax(U_15904),hAPP(hAPP(c_Set_Oinsert(U_15904),U_15906),U_15905)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15904,U_15904,c_Orderings_Oord__class_Omax(U_15904)),U_15906),U_15905)
    | hBOOL(hAPP(hAPP(c_member(U_15904),U_15906),U_15905))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15904),U_15905))
    | ~ class_Orderings_Olinorder(U_15904) ),
    inference(clausify,[status(thm)],[f_3987_3]) ).

fof(f_3988_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_3988_2,plain,
    ! [U_15912,U_15911,U_15910,U_15909,U_15908,U_15907] :
      ( hAPP(hAPP(U_15910,U_15911),U_15912) = hAPP(hAPP(c_Finite__Set_Ofold(U_15907,U_15908,U_15909),U_15912),U_15911)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15907),U_15911))
      | ~ c_Finite__Set_Ofolding(U_15907,U_15908,U_15909,U_15910) ),
    inference(variable_rename,[status(thm)],[f_3988_1]) ).

fof(f_3988_3,plain,
    ! [U_15910,U_15907,U_15911,U_15912,U_15908,U_15909] :
      ( hAPP(hAPP(U_15910,U_15911),U_15912) = hAPP(hAPP(c_Finite__Set_Ofold(U_15907,U_15908,U_15909),U_15912),U_15911)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15907),U_15911))
      | ~ c_Finite__Set_Ofolding(U_15907,U_15908,U_15909,U_15910) ),
    inference(definitional_conversion,[status(esa)],[f_3988_2]) ).

cnf(f_3988_4,plain,
    ( hAPP(hAPP(U_15910,U_15911),U_15912) = hAPP(hAPP(c_Finite__Set_Ofold(U_15907,U_15908,U_15909),U_15912),U_15911)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15907),U_15911))
    | ~ c_Finite__Set_Ofolding(U_15907,U_15908,U_15909,U_15910) ),
    inference(clausify,[status(thm)],[f_3988_3]) ).

fof(f_3989_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_3989_2,plain,
    ! [U_15916,U_15915,U_15914,U_15913] : hAPP(hAPP(c_Finite__Set_Ofold(U_15913,U_15914,U_15915),U_15916),c_Orderings_Obot__class_Obot(tc_fun(U_15913,tc_HOL_Obool))) = U_15916,
    inference(variable_rename,[status(thm)],[f_3989_1]) ).

fof(f_3989_3,plain,
    ! [U_15913,U_15915,U_15914,U_15916] : hAPP(hAPP(c_Finite__Set_Ofold(U_15913,U_15914,U_15915),U_15916),c_Orderings_Obot__class_Obot(tc_fun(U_15913,tc_HOL_Obool))) = U_15916,
    inference(definitional_conversion,[status(esa)],[f_3989_2]) ).

cnf(f_3989_4,plain,
    hAPP(hAPP(c_Finite__Set_Ofold(U_15913,U_15914,U_15915),U_15916),c_Orderings_Obot__class_Obot(tc_fun(U_15913,tc_HOL_Obool))) = U_15916,
    inference(clausify,[status(thm)],[f_3989_3]) ).

fof(f_3990_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_3990_2,plain,
    ! [U_15920,U_15919,U_15918,U_15917] : hAPP(c_Finite__Set_Ofold__image(U_15917,U_15918,U_15919),U_15920) = c_Finite__Set_Ofold(U_15918,U_15917,hAPP(hAPP(c_COMBB(U_15917,tc_fun(U_15917,U_15917),U_15918),U_15919),U_15920)),
    inference(variable_rename,[status(thm)],[f_3990_1]) ).

fof(f_3990_3,plain,
    ! [U_15917,U_15918,U_15919,U_15920] : hAPP(c_Finite__Set_Ofold__image(U_15917,U_15918,U_15919),U_15920) = c_Finite__Set_Ofold(U_15918,U_15917,hAPP(hAPP(c_COMBB(U_15917,tc_fun(U_15917,U_15917),U_15918),U_15919),U_15920)),
    inference(definitional_conversion,[status(esa)],[f_3990_2]) ).

cnf(f_3990_4,plain,
    hAPP(c_Finite__Set_Ofold__image(U_15917,U_15918,U_15919),U_15920) = c_Finite__Set_Ofold(U_15918,U_15917,hAPP(hAPP(c_COMBB(U_15917,tc_fun(U_15917,U_15917),U_15918),U_15919),U_15920)),
    inference(clausify,[status(thm)],[f_3990_3]) ).

fof(f_3991_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_3991_2,plain,
    ! [U_15925,U_15924,U_15923,U_15922,U_15921] : hAPP(hAPP(c_Finite__Set_Ofold(U_15921,U_15922,U_15923),U_15924),U_15925) = c_HOL_OThe(U_15922,c_Finite__Set_Ofold__graph(U_15921,U_15922,U_15923,U_15924,U_15925)),
    inference(variable_rename,[status(thm)],[f_3991_1]) ).

fof(f_3991_3,plain,
    ! [U_15921,U_15922,U_15923,U_15924,U_15925] : hAPP(hAPP(c_Finite__Set_Ofold(U_15921,U_15922,U_15923),U_15924),U_15925) = c_HOL_OThe(U_15922,c_Finite__Set_Ofold__graph(U_15921,U_15922,U_15923,U_15924,U_15925)),
    inference(definitional_conversion,[status(esa)],[f_3991_2]) ).

cnf(f_3991_4,plain,
    hAPP(hAPP(c_Finite__Set_Ofold(U_15921,U_15922,U_15923),U_15924),U_15925) = c_HOL_OThe(U_15922,c_Finite__Set_Ofold__graph(U_15921,U_15922,U_15923,U_15924,U_15925)),
    inference(clausify,[status(thm)],[f_3991_3]) ).

fof(f_3992_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_3992_2,plain,
    ! [U_15928,U_15927,U_15926] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15926,tc_HOL_Obool)),U_15927),U_15928) = hAPP(hAPP(c_Finite__Set_Ofold(U_15926,tc_fun(U_15926,tc_HOL_Obool),c_Set_Oinsert(U_15926)),U_15928),U_15927)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15926),U_15927)) ),
    inference(variable_rename,[status(thm)],[f_3992_1]) ).

fof(f_3992_3,plain,
    ! [U_15926,U_15927,U_15928] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15926,tc_HOL_Obool)),U_15927),U_15928) = hAPP(hAPP(c_Finite__Set_Ofold(U_15926,tc_fun(U_15926,tc_HOL_Obool),c_Set_Oinsert(U_15926)),U_15928),U_15927)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15926),U_15927)) ),
    inference(definitional_conversion,[status(esa)],[f_3992_2]) ).

cnf(f_3992_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_15926,tc_HOL_Obool)),U_15927),U_15928) = hAPP(hAPP(c_Finite__Set_Ofold(U_15926,tc_fun(U_15926,tc_HOL_Obool),c_Set_Oinsert(U_15926)),U_15928),U_15927)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15926),U_15927)) ),
    inference(clausify,[status(thm)],[f_3992_3]) ).

fof(f_3993_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_3993_2,plain,
    ! [U_15932,U_15931,U_15930,U_15929] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15929,U_15929,c_Lattices_Osemilattice__sup__class_Osup(U_15929)),U_15931),hAPP(hAPP(c_Set_Oinsert(U_15929),U_15932),U_15930)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15929),U_15932),hAPP(hAPP(c_Finite__Set_Ofold(U_15929,U_15929,c_Lattices_Osemilattice__sup__class_Osup(U_15929)),U_15931),U_15930))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15929),U_15930))
      | ~ class_Lattices_Osemilattice__sup(U_15929) ),
    inference(variable_rename,[status(thm)],[f_3993_1]) ).

fof(f_3993_3,plain,
    ! [U_15929,U_15930,U_15931,U_15932] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15929,U_15929,c_Lattices_Osemilattice__sup__class_Osup(U_15929)),U_15931),hAPP(hAPP(c_Set_Oinsert(U_15929),U_15932),U_15930)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15929),U_15932),hAPP(hAPP(c_Finite__Set_Ofold(U_15929,U_15929,c_Lattices_Osemilattice__sup__class_Osup(U_15929)),U_15931),U_15930))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15929),U_15930))
      | ~ class_Lattices_Osemilattice__sup(U_15929) ),
    inference(definitional_conversion,[status(esa)],[f_3993_2]) ).

cnf(f_3993_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15929,U_15929,c_Lattices_Osemilattice__sup__class_Osup(U_15929)),U_15931),hAPP(hAPP(c_Set_Oinsert(U_15929),U_15932),U_15930)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15929),U_15932),hAPP(hAPP(c_Finite__Set_Ofold(U_15929,U_15929,c_Lattices_Osemilattice__sup__class_Osup(U_15929)),U_15931),U_15930))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15929),U_15930))
    | ~ class_Lattices_Osemilattice__sup(U_15929) ),
    inference(clausify,[status(thm)],[f_3993_3]) ).

fof(f_3994_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_3994_2,plain,
    ! [U_15936,U_15935,U_15934,U_15933] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15933,U_15933,c_Lattices_Osemilattice__inf__class_Oinf(U_15933)),U_15935),hAPP(hAPP(c_Set_Oinsert(U_15933),U_15936),U_15934)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15933),U_15936),hAPP(hAPP(c_Finite__Set_Ofold(U_15933,U_15933,c_Lattices_Osemilattice__inf__class_Oinf(U_15933)),U_15935),U_15934))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15933),U_15934))
      | ~ class_Lattices_Osemilattice__inf(U_15933) ),
    inference(variable_rename,[status(thm)],[f_3994_1]) ).

fof(f_3994_3,plain,
    ! [U_15933,U_15934,U_15935,U_15936] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15933,U_15933,c_Lattices_Osemilattice__inf__class_Oinf(U_15933)),U_15935),hAPP(hAPP(c_Set_Oinsert(U_15933),U_15936),U_15934)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15933),U_15936),hAPP(hAPP(c_Finite__Set_Ofold(U_15933,U_15933,c_Lattices_Osemilattice__inf__class_Oinf(U_15933)),U_15935),U_15934))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15933),U_15934))
      | ~ class_Lattices_Osemilattice__inf(U_15933) ),
    inference(definitional_conversion,[status(esa)],[f_3994_2]) ).

cnf(f_3994_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15933,U_15933,c_Lattices_Osemilattice__inf__class_Oinf(U_15933)),U_15935),hAPP(hAPP(c_Set_Oinsert(U_15933),U_15936),U_15934)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15933),U_15936),hAPP(hAPP(c_Finite__Set_Ofold(U_15933,U_15933,c_Lattices_Osemilattice__inf__class_Oinf(U_15933)),U_15935),U_15934))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15933),U_15934))
    | ~ class_Lattices_Osemilattice__inf(U_15933) ),
    inference(clausify,[status(thm)],[f_3994_3]) ).

fof(f_3995_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_3995_2,plain,
    ! [U_15940,U_15939,U_15938,U_15937] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15937,U_15937,c_Orderings_Oord__class_Omin(U_15937)),U_15939),hAPP(hAPP(c_Set_Oinsert(U_15937),U_15940),U_15938)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15937),U_15940),hAPP(hAPP(c_Finite__Set_Ofold(U_15937,U_15937,c_Orderings_Oord__class_Omin(U_15937)),U_15939),U_15938))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15937),U_15938))
      | ~ class_Orderings_Olinorder(U_15937) ),
    inference(variable_rename,[status(thm)],[f_3995_1]) ).

fof(f_3995_3,plain,
    ! [U_15937,U_15938,U_15939,U_15940] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15937,U_15937,c_Orderings_Oord__class_Omin(U_15937)),U_15939),hAPP(hAPP(c_Set_Oinsert(U_15937),U_15940),U_15938)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15937),U_15940),hAPP(hAPP(c_Finite__Set_Ofold(U_15937,U_15937,c_Orderings_Oord__class_Omin(U_15937)),U_15939),U_15938))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15937),U_15938))
      | ~ class_Orderings_Olinorder(U_15937) ),
    inference(definitional_conversion,[status(esa)],[f_3995_2]) ).

cnf(f_3995_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15937,U_15937,c_Orderings_Oord__class_Omin(U_15937)),U_15939),hAPP(hAPP(c_Set_Oinsert(U_15937),U_15940),U_15938)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15937),U_15940),hAPP(hAPP(c_Finite__Set_Ofold(U_15937,U_15937,c_Orderings_Oord__class_Omin(U_15937)),U_15939),U_15938))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15937),U_15938))
    | ~ class_Orderings_Olinorder(U_15937) ),
    inference(clausify,[status(thm)],[f_3995_3]) ).

fof(f_3996_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_3996_2,plain,
    ! [U_15944,U_15943,U_15942,U_15941] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15941,U_15941,c_Orderings_Oord__class_Omax(U_15941)),U_15943),hAPP(hAPP(c_Set_Oinsert(U_15941),U_15944),U_15942)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15941),U_15944),hAPP(hAPP(c_Finite__Set_Ofold(U_15941,U_15941,c_Orderings_Oord__class_Omax(U_15941)),U_15943),U_15942))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15941),U_15942))
      | ~ class_Orderings_Olinorder(U_15941) ),
    inference(variable_rename,[status(thm)],[f_3996_1]) ).

fof(f_3996_3,plain,
    ! [U_15941,U_15942,U_15943,U_15944] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15941,U_15941,c_Orderings_Oord__class_Omax(U_15941)),U_15943),hAPP(hAPP(c_Set_Oinsert(U_15941),U_15944),U_15942)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15941),U_15944),hAPP(hAPP(c_Finite__Set_Ofold(U_15941,U_15941,c_Orderings_Oord__class_Omax(U_15941)),U_15943),U_15942))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15941),U_15942))
      | ~ class_Orderings_Olinorder(U_15941) ),
    inference(definitional_conversion,[status(esa)],[f_3996_2]) ).

cnf(f_3996_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15941,U_15941,c_Orderings_Oord__class_Omax(U_15941)),U_15943),hAPP(hAPP(c_Set_Oinsert(U_15941),U_15944),U_15942)) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15941),U_15944),hAPP(hAPP(c_Finite__Set_Ofold(U_15941,U_15941,c_Orderings_Oord__class_Omax(U_15941)),U_15943),U_15942))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15941),U_15942))
    | ~ class_Orderings_Olinorder(U_15941) ),
    inference(clausify,[status(thm)],[f_3996_3]) ).

fof(f_3997_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_3997_2,plain,
    ! [U_15950,U_15949,U_15948,U_15947,U_15946,U_15945] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15945,U_15946,U_15947),U_15949),hAPP(hAPP(c_Set_Oinsert(U_15945),U_15950),U_15948)) = hAPP(hAPP(U_15947,U_15950),hAPP(hAPP(c_Finite__Set_Ofold(U_15945,U_15946,U_15947),U_15949),U_15948))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15945),U_15948))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_15945,U_15946,U_15947) ),
    inference(variable_rename,[status(thm)],[f_3997_1]) ).

fof(f_3997_3,plain,
    ! [U_15945,U_15946,U_15947,U_15948,U_15949,U_15950] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15945,U_15946,U_15947),U_15949),hAPP(hAPP(c_Set_Oinsert(U_15945),U_15950),U_15948)) = hAPP(hAPP(U_15947,U_15950),hAPP(hAPP(c_Finite__Set_Ofold(U_15945,U_15946,U_15947),U_15949),U_15948))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15945),U_15948))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_15945,U_15946,U_15947) ),
    inference(definitional_conversion,[status(esa)],[f_3997_2]) ).

cnf(f_3997_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15945,U_15946,U_15947),U_15949),hAPP(hAPP(c_Set_Oinsert(U_15945),U_15950),U_15948)) = hAPP(hAPP(U_15947,U_15950),hAPP(hAPP(c_Finite__Set_Ofold(U_15945,U_15946,U_15947),U_15949),U_15948))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15945),U_15948))
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_15945,U_15946,U_15947) ),
    inference(clausify,[status(thm)],[f_3997_3]) ).

fof(f_3998_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_3998_2,plain,
    ! [U_15956,U_15955,U_15954,U_15953,U_15952,U_15951] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15951,U_15952,U_15953),U_15955),hAPP(hAPP(c_Set_Oinsert(U_15951),U_15956),U_15954)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15951,U_15952,U_15953),hAPP(hAPP(U_15953,U_15956),U_15955)),U_15954)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15951),U_15954))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_15951,U_15952,U_15953) ),
    inference(variable_rename,[status(thm)],[f_3998_1]) ).

fof(f_3998_3,plain,
    ! [U_15951,U_15952,U_15953,U_15954,U_15955,U_15956] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_15951,U_15952,U_15953),U_15955),hAPP(hAPP(c_Set_Oinsert(U_15951),U_15956),U_15954)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15951,U_15952,U_15953),hAPP(hAPP(U_15953,U_15956),U_15955)),U_15954)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15951),U_15954))
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_15951,U_15952,U_15953) ),
    inference(definitional_conversion,[status(esa)],[f_3998_2]) ).

cnf(f_3998_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_15951,U_15952,U_15953),U_15955),hAPP(hAPP(c_Set_Oinsert(U_15951),U_15956),U_15954)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15951,U_15952,U_15953),hAPP(hAPP(U_15953,U_15956),U_15955)),U_15954)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15951),U_15954))
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_15951,U_15952,U_15953) ),
    inference(clausify,[status(thm)],[f_3998_3]) ).

fof(f_3999_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_3999_2,plain,
    ! [U_15961,U_15960,U_15959,U_15958,U_15957] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15957),U_15960),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15958,U_15957),U_15959),U_15961)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15958,U_15957,hAPP(hAPP(c_COMBB(U_15957,tc_fun(U_15957,U_15957),U_15958),c_Lattices_Osemilattice__sup__class_Osup(U_15957)),U_15961)),U_15960),U_15959)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15958),U_15959))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_15957) ),
    inference(variable_rename,[status(thm)],[f_3999_1]) ).

fof(f_3999_3,plain,
    ! [U_15957,U_15958,U_15959,U_15960,U_15961] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15957),U_15960),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15958,U_15957),U_15959),U_15961)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15958,U_15957,hAPP(hAPP(c_COMBB(U_15957,tc_fun(U_15957,U_15957),U_15958),c_Lattices_Osemilattice__sup__class_Osup(U_15957)),U_15961)),U_15960),U_15959)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15958),U_15959))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_15957) ),
    inference(definitional_conversion,[status(esa)],[f_3999_2]) ).

cnf(f_3999_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15957),U_15960),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_15958,U_15957),U_15959),U_15961)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15958,U_15957,hAPP(hAPP(c_COMBB(U_15957,tc_fun(U_15957,U_15957),U_15958),c_Lattices_Osemilattice__sup__class_Osup(U_15957)),U_15961)),U_15960),U_15959)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15958),U_15959))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_15957) ),
    inference(clausify,[status(thm)],[f_3999_3]) ).

fof(f_4000_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_4000_2,plain,
    ! [U_15966,U_15965,U_15964,U_15963,U_15962] :
      ( hAPP(U_15964,hAPP(hAPP(c_Set_Oinsert(U_15962),U_15966),U_15965)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15962,U_15962,U_15963),U_15966),U_15965)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15962),U_15965))
      | ~ c_Finite__Set_Ofolding__one__idem(U_15962,U_15963,U_15964) ),
    inference(variable_rename,[status(thm)],[f_4000_1]) ).

fof(f_4000_3,plain,
    ! [U_15963,U_15962,U_15964,U_15965,U_15966] :
      ( hAPP(U_15964,hAPP(hAPP(c_Set_Oinsert(U_15962),U_15966),U_15965)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15962,U_15962,U_15963),U_15966),U_15965)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15962),U_15965))
      | ~ c_Finite__Set_Ofolding__one__idem(U_15962,U_15963,U_15964) ),
    inference(definitional_conversion,[status(esa)],[f_4000_2]) ).

cnf(f_4000_4,plain,
    ( hAPP(U_15964,hAPP(hAPP(c_Set_Oinsert(U_15962),U_15966),U_15965)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15962,U_15962,U_15963),U_15966),U_15965)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15962),U_15965))
    | ~ c_Finite__Set_Ofolding__one__idem(U_15962,U_15963,U_15964) ),
    inference(clausify,[status(thm)],[f_4000_3]) ).

fof(f_4001_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_4001_2,plain,
    ! [U_15970,U_15969,U_15968,U_15967] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15967),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15967),U_15969),U_15970)),hAPP(hAPP(c_Finite__Set_Ofold(U_15967,U_15967,c_Lattices_Osemilattice__sup__class_Osup(U_15967)),U_15970),U_15968)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15967),U_15969),U_15968))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15967),U_15968))
      | ~ class_Lattices_Osemilattice__sup(U_15967) ),
    inference(variable_rename,[status(thm)],[f_4001_1]) ).

fof(f_4001_3,plain,
    ! [U_15967,U_15968,U_15969,U_15970] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15967),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15967),U_15969),U_15970)),hAPP(hAPP(c_Finite__Set_Ofold(U_15967,U_15967,c_Lattices_Osemilattice__sup__class_Osup(U_15967)),U_15970),U_15968)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15967),U_15969),U_15968))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15967),U_15968))
      | ~ class_Lattices_Osemilattice__sup(U_15967) ),
    inference(definitional_conversion,[status(esa)],[f_4001_2]) ).

cnf(f_4001_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15967),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_15967),U_15969),U_15970)),hAPP(hAPP(c_Finite__Set_Ofold(U_15967,U_15967,c_Lattices_Osemilattice__sup__class_Osup(U_15967)),U_15970),U_15968)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15967),U_15969),U_15968))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15967),U_15968))
    | ~ class_Lattices_Osemilattice__sup(U_15967) ),
    inference(clausify,[status(thm)],[f_4001_3]) ).

fof(f_4002_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_4002_2,plain,
    ! [U_15974,U_15973,U_15972,U_15971] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15971),hAPP(hAPP(c_Finite__Set_Ofold(U_15971,U_15971,c_Lattices_Osemilattice__inf__class_Oinf(U_15971)),U_15974),U_15972)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15971),U_15973),U_15974)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15971),U_15973),U_15972))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15971),U_15972))
      | ~ class_Lattices_Osemilattice__inf(U_15971) ),
    inference(variable_rename,[status(thm)],[f_4002_1]) ).

fof(f_4002_3,plain,
    ! [U_15971,U_15972,U_15973,U_15974] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15971),hAPP(hAPP(c_Finite__Set_Ofold(U_15971,U_15971,c_Lattices_Osemilattice__inf__class_Oinf(U_15971)),U_15974),U_15972)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15971),U_15973),U_15974)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15971),U_15973),U_15972))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15971),U_15972))
      | ~ class_Lattices_Osemilattice__inf(U_15971) ),
    inference(definitional_conversion,[status(esa)],[f_4002_2]) ).

cnf(f_4002_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15971),hAPP(hAPP(c_Finite__Set_Ofold(U_15971,U_15971,c_Lattices_Osemilattice__inf__class_Oinf(U_15971)),U_15974),U_15972)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_15971),U_15973),U_15974)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15971),U_15973),U_15972))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15971),U_15972))
    | ~ class_Lattices_Osemilattice__inf(U_15971) ),
    inference(clausify,[status(thm)],[f_4002_3]) ).

fof(f_4003_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_4003_2,plain,
    ! [U_15978,U_15977,U_15976,U_15975] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15975),hAPP(hAPP(c_Finite__Set_Ofold(U_15975,U_15975,c_Orderings_Oord__class_Omin(U_15975)),U_15978),U_15976)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15975),U_15977),U_15978)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15975),U_15977),U_15976))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15975),U_15976))
      | ~ class_Orderings_Olinorder(U_15975) ),
    inference(variable_rename,[status(thm)],[f_4003_1]) ).

fof(f_4003_3,plain,
    ! [U_15975,U_15976,U_15977,U_15978] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15975),hAPP(hAPP(c_Finite__Set_Ofold(U_15975,U_15975,c_Orderings_Oord__class_Omin(U_15975)),U_15978),U_15976)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15975),U_15977),U_15978)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15975),U_15977),U_15976))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15975),U_15976))
      | ~ class_Orderings_Olinorder(U_15975) ),
    inference(definitional_conversion,[status(esa)],[f_4003_2]) ).

cnf(f_4003_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15975),hAPP(hAPP(c_Finite__Set_Ofold(U_15975,U_15975,c_Orderings_Oord__class_Omin(U_15975)),U_15978),U_15976)),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_15975),U_15977),U_15978)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15975),U_15977),U_15976))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15975),U_15976))
    | ~ class_Orderings_Olinorder(U_15975) ),
    inference(clausify,[status(thm)],[f_4003_3]) ).

fof(f_4004_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_4004_2,plain,
    ! [U_15982,U_15981,U_15980,U_15979] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15979),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15979),U_15981),U_15982)),hAPP(hAPP(c_Finite__Set_Ofold(U_15979,U_15979,c_Orderings_Oord__class_Omax(U_15979)),U_15982),U_15980)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15979),U_15981),U_15980))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15979),U_15980))
      | ~ class_Orderings_Olinorder(U_15979) ),
    inference(variable_rename,[status(thm)],[f_4004_1]) ).

fof(f_4004_3,plain,
    ! [U_15979,U_15980,U_15981,U_15982] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15979),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15979),U_15981),U_15982)),hAPP(hAPP(c_Finite__Set_Ofold(U_15979,U_15979,c_Orderings_Oord__class_Omax(U_15979)),U_15982),U_15980)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_15979),U_15981),U_15980))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15979),U_15980))
      | ~ class_Orderings_Olinorder(U_15979) ),
    inference(definitional_conversion,[status(esa)],[f_4004_2]) ).

cnf(f_4004_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_15979),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_15979),U_15981),U_15982)),hAPP(hAPP(c_Finite__Set_Ofold(U_15979,U_15979,c_Orderings_Oord__class_Omax(U_15979)),U_15982),U_15980)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_15979),U_15981),U_15980))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15979),U_15980))
    | ~ class_Orderings_Olinorder(U_15979) ),
    inference(clausify,[status(thm)],[f_4004_3]) ).

fof(f_4005_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_4005_2,plain,
    ! [U_15985,U_15984,U_15983] :
      ( hAPP(c_Finite__Set_Ofold1(U_15983,c_Groups_Otimes__class_Otimes(U_15983)),hAPP(hAPP(c_Set_Oinsert(U_15983),U_15985),U_15984)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15983,U_15983,c_Groups_Otimes__class_Otimes(U_15983)),U_15985),U_15984)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15983),U_15984))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_15983) ),
    inference(variable_rename,[status(thm)],[f_4005_1]) ).

fof(f_4005_3,plain,
    ! [U_15983,U_15984,U_15985] :
      ( hAPP(c_Finite__Set_Ofold1(U_15983,c_Groups_Otimes__class_Otimes(U_15983)),hAPP(hAPP(c_Set_Oinsert(U_15983),U_15985),U_15984)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15983,U_15983,c_Groups_Otimes__class_Otimes(U_15983)),U_15985),U_15984)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15983),U_15984))
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_15983) ),
    inference(definitional_conversion,[status(esa)],[f_4005_2]) ).

cnf(f_4005_4,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_15983,c_Groups_Otimes__class_Otimes(U_15983)),hAPP(hAPP(c_Set_Oinsert(U_15983),U_15985),U_15984)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15983,U_15983,c_Groups_Otimes__class_Otimes(U_15983)),U_15985),U_15984)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15983),U_15984))
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_15983) ),
    inference(clausify,[status(thm)],[f_4005_3]) ).

fof(f_4006_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_4006_2,plain,
    ! [U_15988,U_15987,U_15986] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_15986,hAPP(hAPP(c_Set_Oinsert(U_15986),U_15988),U_15987)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15986,U_15986,c_Lattices_Osemilattice__sup__class_Osup(U_15986)),U_15988),U_15987)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15986),U_15987))
      | ~ class_Lattices_Olattice(U_15986) ),
    inference(variable_rename,[status(thm)],[f_4006_1]) ).

fof(f_4006_3,plain,
    ! [U_15986,U_15987,U_15988] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_15986,hAPP(hAPP(c_Set_Oinsert(U_15986),U_15988),U_15987)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15986,U_15986,c_Lattices_Osemilattice__sup__class_Osup(U_15986)),U_15988),U_15987)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15986),U_15987))
      | ~ class_Lattices_Olattice(U_15986) ),
    inference(definitional_conversion,[status(esa)],[f_4006_2]) ).

cnf(f_4006_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_15986,hAPP(hAPP(c_Set_Oinsert(U_15986),U_15988),U_15987)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15986,U_15986,c_Lattices_Osemilattice__sup__class_Osup(U_15986)),U_15988),U_15987)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15986),U_15987))
    | ~ class_Lattices_Olattice(U_15986) ),
    inference(clausify,[status(thm)],[f_4006_3]) ).

fof(f_4007_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_4007_2,plain,
    ! [U_15991,U_15990,U_15989] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_15989,hAPP(hAPP(c_Set_Oinsert(U_15989),U_15991),U_15990)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15989,U_15989,c_Lattices_Osemilattice__inf__class_Oinf(U_15989)),U_15991),U_15990)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15989),U_15990))
      | ~ class_Lattices_Olattice(U_15989) ),
    inference(variable_rename,[status(thm)],[f_4007_1]) ).

fof(f_4007_3,plain,
    ! [U_15989,U_15990,U_15991] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_15989,hAPP(hAPP(c_Set_Oinsert(U_15989),U_15991),U_15990)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15989,U_15989,c_Lattices_Osemilattice__inf__class_Oinf(U_15989)),U_15991),U_15990)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15989),U_15990))
      | ~ class_Lattices_Olattice(U_15989) ),
    inference(definitional_conversion,[status(esa)],[f_4007_2]) ).

cnf(f_4007_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_15989,hAPP(hAPP(c_Set_Oinsert(U_15989),U_15991),U_15990)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15989,U_15989,c_Lattices_Osemilattice__inf__class_Oinf(U_15989)),U_15991),U_15990)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15989),U_15990))
    | ~ class_Lattices_Olattice(U_15989) ),
    inference(clausify,[status(thm)],[f_4007_3]) ).

fof(f_4008_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_4008_2,plain,
    ! [U_15994,U_15993,U_15992] :
      ( c_Big__Operators_Olinorder__class_OMin(U_15992,hAPP(hAPP(c_Set_Oinsert(U_15992),U_15994),U_15993)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15992,U_15992,c_Orderings_Oord__class_Omin(U_15992)),U_15994),U_15993)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15992),U_15993))
      | ~ class_Orderings_Olinorder(U_15992) ),
    inference(variable_rename,[status(thm)],[f_4008_1]) ).

fof(f_4008_3,plain,
    ! [U_15992,U_15993,U_15994] :
      ( c_Big__Operators_Olinorder__class_OMin(U_15992,hAPP(hAPP(c_Set_Oinsert(U_15992),U_15994),U_15993)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15992,U_15992,c_Orderings_Oord__class_Omin(U_15992)),U_15994),U_15993)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15992),U_15993))
      | ~ class_Orderings_Olinorder(U_15992) ),
    inference(definitional_conversion,[status(esa)],[f_4008_2]) ).

cnf(f_4008_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_15992,hAPP(hAPP(c_Set_Oinsert(U_15992),U_15994),U_15993)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15992,U_15992,c_Orderings_Oord__class_Omin(U_15992)),U_15994),U_15993)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15992),U_15993))
    | ~ class_Orderings_Olinorder(U_15992) ),
    inference(clausify,[status(thm)],[f_4008_3]) ).

fof(f_4009_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_4009_2,plain,
    ! [U_15997,U_15996,U_15995] :
      ( c_Big__Operators_Olinorder__class_OMax(U_15995,hAPP(hAPP(c_Set_Oinsert(U_15995),U_15997),U_15996)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15995,U_15995,c_Orderings_Oord__class_Omax(U_15995)),U_15997),U_15996)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15995),U_15996))
      | ~ class_Orderings_Olinorder(U_15995) ),
    inference(variable_rename,[status(thm)],[f_4009_1]) ).

fof(f_4009_3,plain,
    ! [U_15995,U_15996,U_15997] :
      ( c_Big__Operators_Olinorder__class_OMax(U_15995,hAPP(hAPP(c_Set_Oinsert(U_15995),U_15997),U_15996)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15995,U_15995,c_Orderings_Oord__class_Omax(U_15995)),U_15997),U_15996)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15995),U_15996))
      | ~ class_Orderings_Olinorder(U_15995) ),
    inference(definitional_conversion,[status(esa)],[f_4009_2]) ).

cnf(f_4009_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_15995,hAPP(hAPP(c_Set_Oinsert(U_15995),U_15997),U_15996)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15995,U_15995,c_Orderings_Oord__class_Omax(U_15995)),U_15997),U_15996)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15995),U_15996))
    | ~ class_Orderings_Olinorder(U_15995) ),
    inference(clausify,[status(thm)],[f_4009_3]) ).

fof(f_4010_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_4010_2,plain,
    ! [U_16000,U_15999,U_15998] :
      ( c_Big__Operators_Olattice_OInf__fin(U_15998,c_Orderings_Oord__class_Omin(U_15998),hAPP(hAPP(c_Set_Oinsert(U_15998),U_16000),U_15999)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15998,U_15998,c_Orderings_Oord__class_Omin(U_15998)),U_16000),U_15999)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15998),U_15999))
      | ~ class_Orderings_Olinorder(U_15998) ),
    inference(variable_rename,[status(thm)],[f_4010_1]) ).

fof(f_4010_3,plain,
    ! [U_15998,U_15999,U_16000] :
      ( c_Big__Operators_Olattice_OInf__fin(U_15998,c_Orderings_Oord__class_Omin(U_15998),hAPP(hAPP(c_Set_Oinsert(U_15998),U_16000),U_15999)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15998,U_15998,c_Orderings_Oord__class_Omin(U_15998)),U_16000),U_15999)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15998),U_15999))
      | ~ class_Orderings_Olinorder(U_15998) ),
    inference(definitional_conversion,[status(esa)],[f_4010_2]) ).

cnf(f_4010_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_15998,c_Orderings_Oord__class_Omin(U_15998),hAPP(hAPP(c_Set_Oinsert(U_15998),U_16000),U_15999)) = hAPP(hAPP(c_Finite__Set_Ofold(U_15998,U_15998,c_Orderings_Oord__class_Omin(U_15998)),U_16000),U_15999)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_15998),U_15999))
    | ~ class_Orderings_Olinorder(U_15998) ),
    inference(clausify,[status(thm)],[f_4010_3]) ).

fof(f_4011_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_4011_2,plain,
    ! [U_16003,U_16002,U_16001] :
      ( c_Big__Operators_Olattice_OSup__fin(U_16001,c_Orderings_Oord__class_Omax(U_16001),hAPP(hAPP(c_Set_Oinsert(U_16001),U_16003),U_16002)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16001,U_16001,c_Orderings_Oord__class_Omax(U_16001)),U_16003),U_16002)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16001),U_16002))
      | ~ class_Orderings_Olinorder(U_16001) ),
    inference(variable_rename,[status(thm)],[f_4011_1]) ).

fof(f_4011_3,plain,
    ! [U_16001,U_16002,U_16003] :
      ( c_Big__Operators_Olattice_OSup__fin(U_16001,c_Orderings_Oord__class_Omax(U_16001),hAPP(hAPP(c_Set_Oinsert(U_16001),U_16003),U_16002)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16001,U_16001,c_Orderings_Oord__class_Omax(U_16001)),U_16003),U_16002)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16001),U_16002))
      | ~ class_Orderings_Olinorder(U_16001) ),
    inference(definitional_conversion,[status(esa)],[f_4011_2]) ).

cnf(f_4011_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_16001,c_Orderings_Oord__class_Omax(U_16001),hAPP(hAPP(c_Set_Oinsert(U_16001),U_16003),U_16002)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16001,U_16001,c_Orderings_Oord__class_Omax(U_16001)),U_16003),U_16002)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16001),U_16002))
    | ~ class_Orderings_Olinorder(U_16001) ),
    inference(clausify,[status(thm)],[f_4011_3]) ).

fof(f_4012_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_4012_2,plain,
    ! [U_16006,U_16005,U_16004] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16004,tc_HOL_Obool)),U_16006),U_16005) = hAPP(hAPP(c_Finite__Set_Ofold(U_16004,tc_fun(U_16004,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_16004,tc_HOL_Obool),tc_fun(tc_fun(U_16004,tc_HOL_Obool),tc_fun(U_16004,tc_HOL_Obool)),U_16004),hAPP(c_COMBC(tc_fun(U_16004,tc_HOL_Obool),tc_fun(U_16004,tc_HOL_Obool),tc_fun(U_16004,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_16004,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_16004,tc_fun(U_16004,tc_HOL_Obool),tc_fun(U_16004,tc_HOL_Obool)),c_Set_Oinsert(U_16004)),c_Orderings_Obot__class_Obot(tc_fun(U_16004,tc_HOL_Obool))))),U_16006),U_16005)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16004),U_16005)) ),
    inference(variable_rename,[status(thm)],[f_4012_1]) ).

fof(f_4012_3,plain,
    ! [U_16004,U_16005,U_16006] :
      ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16004,tc_HOL_Obool)),U_16006),U_16005) = hAPP(hAPP(c_Finite__Set_Ofold(U_16004,tc_fun(U_16004,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_16004,tc_HOL_Obool),tc_fun(tc_fun(U_16004,tc_HOL_Obool),tc_fun(U_16004,tc_HOL_Obool)),U_16004),hAPP(c_COMBC(tc_fun(U_16004,tc_HOL_Obool),tc_fun(U_16004,tc_HOL_Obool),tc_fun(U_16004,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_16004,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_16004,tc_fun(U_16004,tc_HOL_Obool),tc_fun(U_16004,tc_HOL_Obool)),c_Set_Oinsert(U_16004)),c_Orderings_Obot__class_Obot(tc_fun(U_16004,tc_HOL_Obool))))),U_16006),U_16005)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16004),U_16005)) ),
    inference(definitional_conversion,[status(esa)],[f_4012_2]) ).

cnf(f_4012_4,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16004,tc_HOL_Obool)),U_16006),U_16005) = hAPP(hAPP(c_Finite__Set_Ofold(U_16004,tc_fun(U_16004,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_16004,tc_HOL_Obool),tc_fun(tc_fun(U_16004,tc_HOL_Obool),tc_fun(U_16004,tc_HOL_Obool)),U_16004),hAPP(c_COMBC(tc_fun(U_16004,tc_HOL_Obool),tc_fun(U_16004,tc_HOL_Obool),tc_fun(U_16004,tc_HOL_Obool)),c_Groups_Ominus__class_Ominus(tc_fun(U_16004,tc_HOL_Obool)))),hAPP(hAPP(c_COMBC(U_16004,tc_fun(U_16004,tc_HOL_Obool),tc_fun(U_16004,tc_HOL_Obool)),c_Set_Oinsert(U_16004)),c_Orderings_Obot__class_Obot(tc_fun(U_16004,tc_HOL_Obool))))),U_16006),U_16005)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16004),U_16005)) ),
    inference(clausify,[status(thm)],[f_4012_3]) ).

fof(f_4013_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_4013_2,plain,
    ! [U_16011,U_16010,U_16009,U_16008,U_16007] :
      ( hAPP(U_16009,hAPP(hAPP(c_Set_Oinsert(U_16007),U_16011),U_16010)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16007,U_16007,U_16008),U_16011),U_16010)
      | hBOOL(hAPP(hAPP(c_member(U_16007),U_16011),U_16010))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16007),U_16010))
      | ~ c_Finite__Set_Ofolding__one(U_16007,U_16008,U_16009) ),
    inference(variable_rename,[status(thm)],[f_4013_1]) ).

fof(f_4013_3,plain,
    ! [U_16007,U_16008,U_16009,U_16010,U_16011] :
      ( hAPP(U_16009,hAPP(hAPP(c_Set_Oinsert(U_16007),U_16011),U_16010)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16007,U_16007,U_16008),U_16011),U_16010)
      | hBOOL(hAPP(hAPP(c_member(U_16007),U_16011),U_16010))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16007),U_16010))
      | ~ c_Finite__Set_Ofolding__one(U_16007,U_16008,U_16009) ),
    inference(definitional_conversion,[status(esa)],[f_4013_2]) ).

cnf(f_4013_4,plain,
    ( hAPP(U_16009,hAPP(hAPP(c_Set_Oinsert(U_16007),U_16011),U_16010)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16007,U_16007,U_16008),U_16011),U_16010)
    | hBOOL(hAPP(hAPP(c_member(U_16007),U_16011),U_16010))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16007),U_16010))
    | ~ c_Finite__Set_Ofolding__one(U_16007,U_16008,U_16009) ),
    inference(clausify,[status(thm)],[f_4013_3]) ).

fof(f_4014_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_4014_2,plain,
    ! [U_16015,U_16014,U_16013,U_16012] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16013,U_16012),U_16014),U_16015) = hAPP(hAPP(c_Finite__Set_Ofold(U_16013,U_16012,hAPP(hAPP(c_COMBB(U_16012,tc_fun(U_16012,U_16012),U_16013),c_Lattices_Osemilattice__sup__class_Osup(U_16012)),U_16015)),c_Orderings_Obot__class_Obot(U_16012)),U_16014)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16013),U_16014))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16012) ),
    inference(variable_rename,[status(thm)],[f_4014_1]) ).

fof(f_4014_3,plain,
    ! [U_16012,U_16013,U_16014,U_16015] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16013,U_16012),U_16014),U_16015) = hAPP(hAPP(c_Finite__Set_Ofold(U_16013,U_16012,hAPP(hAPP(c_COMBB(U_16012,tc_fun(U_16012,U_16012),U_16013),c_Lattices_Osemilattice__sup__class_Osup(U_16012)),U_16015)),c_Orderings_Obot__class_Obot(U_16012)),U_16014)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16013),U_16014))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16012) ),
    inference(definitional_conversion,[status(esa)],[f_4014_2]) ).

cnf(f_4014_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16013,U_16012),U_16014),U_16015) = hAPP(hAPP(c_Finite__Set_Ofold(U_16013,U_16012,hAPP(hAPP(c_COMBB(U_16012,tc_fun(U_16012,U_16012),U_16013),c_Lattices_Osemilattice__sup__class_Osup(U_16012)),U_16015)),c_Orderings_Obot__class_Obot(U_16012)),U_16014)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16013),U_16014))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16012) ),
    inference(clausify,[status(thm)],[f_4014_3]) ).

fof(f_4015_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_4015_2,plain,
    ! [U_16018,U_16017,U_16016] :
      ( hAPP(c_Finite__Set_Ofold1(U_16016,c_Groups_Otimes__class_Otimes(U_16016)),hAPP(hAPP(c_Set_Oinsert(U_16016),U_16018),U_16017)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16016,U_16016,c_Groups_Otimes__class_Otimes(U_16016)),U_16018),U_16017)
      | hBOOL(hAPP(hAPP(c_member(U_16016),U_16018),U_16017))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16016),U_16017))
      | ~ class_Groups_Oab__semigroup__mult(U_16016) ),
    inference(variable_rename,[status(thm)],[f_4015_1]) ).

fof(f_4015_3,plain,
    ! [U_16016,U_16017,U_16018] :
      ( hAPP(c_Finite__Set_Ofold1(U_16016,c_Groups_Otimes__class_Otimes(U_16016)),hAPP(hAPP(c_Set_Oinsert(U_16016),U_16018),U_16017)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16016,U_16016,c_Groups_Otimes__class_Otimes(U_16016)),U_16018),U_16017)
      | hBOOL(hAPP(hAPP(c_member(U_16016),U_16018),U_16017))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16016),U_16017))
      | ~ class_Groups_Oab__semigroup__mult(U_16016) ),
    inference(definitional_conversion,[status(esa)],[f_4015_2]) ).

cnf(f_4015_4,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_16016,c_Groups_Otimes__class_Otimes(U_16016)),hAPP(hAPP(c_Set_Oinsert(U_16016),U_16018),U_16017)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16016,U_16016,c_Groups_Otimes__class_Otimes(U_16016)),U_16018),U_16017)
    | hBOOL(hAPP(hAPP(c_member(U_16016),U_16018),U_16017))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16016),U_16017))
    | ~ class_Groups_Oab__semigroup__mult(U_16016) ),
    inference(clausify,[status(thm)],[f_4015_3]) ).

fof(f_4016_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_4016_2,plain,
    ! [U_16021,U_16020,U_16019] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_16019,hAPP(hAPP(c_Set_Oinsert(U_16019),U_16021),U_16020)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16019,U_16019,c_Lattices_Osemilattice__sup__class_Osup(U_16019)),U_16021),U_16020)
      | hBOOL(hAPP(hAPP(c_member(U_16019),U_16021),U_16020))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16019),U_16020))
      | ~ class_Lattices_Olattice(U_16019) ),
    inference(variable_rename,[status(thm)],[f_4016_1]) ).

fof(f_4016_3,plain,
    ! [U_16019,U_16020,U_16021] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_16019,hAPP(hAPP(c_Set_Oinsert(U_16019),U_16021),U_16020)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16019,U_16019,c_Lattices_Osemilattice__sup__class_Osup(U_16019)),U_16021),U_16020)
      | hBOOL(hAPP(hAPP(c_member(U_16019),U_16021),U_16020))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16019),U_16020))
      | ~ class_Lattices_Olattice(U_16019) ),
    inference(definitional_conversion,[status(esa)],[f_4016_2]) ).

cnf(f_4016_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_16019,hAPP(hAPP(c_Set_Oinsert(U_16019),U_16021),U_16020)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16019,U_16019,c_Lattices_Osemilattice__sup__class_Osup(U_16019)),U_16021),U_16020)
    | hBOOL(hAPP(hAPP(c_member(U_16019),U_16021),U_16020))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16019),U_16020))
    | ~ class_Lattices_Olattice(U_16019) ),
    inference(clausify,[status(thm)],[f_4016_3]) ).

fof(f_4017_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_4017_2,plain,
    ! [U_16024,U_16023,U_16022] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_16022,hAPP(hAPP(c_Set_Oinsert(U_16022),U_16024),U_16023)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16022,U_16022,c_Lattices_Osemilattice__inf__class_Oinf(U_16022)),U_16024),U_16023)
      | hBOOL(hAPP(hAPP(c_member(U_16022),U_16024),U_16023))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16022),U_16023))
      | ~ class_Lattices_Olattice(U_16022) ),
    inference(variable_rename,[status(thm)],[f_4017_1]) ).

fof(f_4017_3,plain,
    ! [U_16022,U_16023,U_16024] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_16022,hAPP(hAPP(c_Set_Oinsert(U_16022),U_16024),U_16023)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16022,U_16022,c_Lattices_Osemilattice__inf__class_Oinf(U_16022)),U_16024),U_16023)
      | hBOOL(hAPP(hAPP(c_member(U_16022),U_16024),U_16023))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16022),U_16023))
      | ~ class_Lattices_Olattice(U_16022) ),
    inference(definitional_conversion,[status(esa)],[f_4017_2]) ).

cnf(f_4017_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_16022,hAPP(hAPP(c_Set_Oinsert(U_16022),U_16024),U_16023)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16022,U_16022,c_Lattices_Osemilattice__inf__class_Oinf(U_16022)),U_16024),U_16023)
    | hBOOL(hAPP(hAPP(c_member(U_16022),U_16024),U_16023))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16022),U_16023))
    | ~ class_Lattices_Olattice(U_16022) ),
    inference(clausify,[status(thm)],[f_4017_3]) ).

fof(f_4018_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_4018_2,plain,
    ! [U_16027,U_16026,U_16025] :
      ( c_Big__Operators_Olinorder__class_OMin(U_16025,hAPP(hAPP(c_Set_Oinsert(U_16025),U_16027),U_16026)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16025,U_16025,c_Orderings_Oord__class_Omin(U_16025)),U_16027),U_16026)
      | hBOOL(hAPP(hAPP(c_member(U_16025),U_16027),U_16026))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16025),U_16026))
      | ~ class_Orderings_Olinorder(U_16025) ),
    inference(variable_rename,[status(thm)],[f_4018_1]) ).

fof(f_4018_3,plain,
    ! [U_16025,U_16026,U_16027] :
      ( c_Big__Operators_Olinorder__class_OMin(U_16025,hAPP(hAPP(c_Set_Oinsert(U_16025),U_16027),U_16026)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16025,U_16025,c_Orderings_Oord__class_Omin(U_16025)),U_16027),U_16026)
      | hBOOL(hAPP(hAPP(c_member(U_16025),U_16027),U_16026))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16025),U_16026))
      | ~ class_Orderings_Olinorder(U_16025) ),
    inference(definitional_conversion,[status(esa)],[f_4018_2]) ).

cnf(f_4018_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_16025,hAPP(hAPP(c_Set_Oinsert(U_16025),U_16027),U_16026)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16025,U_16025,c_Orderings_Oord__class_Omin(U_16025)),U_16027),U_16026)
    | hBOOL(hAPP(hAPP(c_member(U_16025),U_16027),U_16026))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16025),U_16026))
    | ~ class_Orderings_Olinorder(U_16025) ),
    inference(clausify,[status(thm)],[f_4018_3]) ).

fof(f_4019_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_4019_2,plain,
    ! [U_16030,U_16029,U_16028] :
      ( c_Big__Operators_Olinorder__class_OMax(U_16028,hAPP(hAPP(c_Set_Oinsert(U_16028),U_16030),U_16029)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16028,U_16028,c_Orderings_Oord__class_Omax(U_16028)),U_16030),U_16029)
      | hBOOL(hAPP(hAPP(c_member(U_16028),U_16030),U_16029))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16028),U_16029))
      | ~ class_Orderings_Olinorder(U_16028) ),
    inference(variable_rename,[status(thm)],[f_4019_1]) ).

fof(f_4019_3,plain,
    ! [U_16028,U_16029,U_16030] :
      ( c_Big__Operators_Olinorder__class_OMax(U_16028,hAPP(hAPP(c_Set_Oinsert(U_16028),U_16030),U_16029)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16028,U_16028,c_Orderings_Oord__class_Omax(U_16028)),U_16030),U_16029)
      | hBOOL(hAPP(hAPP(c_member(U_16028),U_16030),U_16029))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16028),U_16029))
      | ~ class_Orderings_Olinorder(U_16028) ),
    inference(definitional_conversion,[status(esa)],[f_4019_2]) ).

cnf(f_4019_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_16028,hAPP(hAPP(c_Set_Oinsert(U_16028),U_16030),U_16029)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16028,U_16028,c_Orderings_Oord__class_Omax(U_16028)),U_16030),U_16029)
    | hBOOL(hAPP(hAPP(c_member(U_16028),U_16030),U_16029))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16028),U_16029))
    | ~ class_Orderings_Olinorder(U_16028) ),
    inference(clausify,[status(thm)],[f_4019_3]) ).

fof(f_4020_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_4020_2,plain,
    ! [U_16033,U_16032,U_16031] :
      ( c_Big__Operators_Olattice_OInf__fin(U_16031,c_Orderings_Oord__class_Omin(U_16031),hAPP(hAPP(c_Set_Oinsert(U_16031),U_16033),U_16032)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16031,U_16031,c_Orderings_Oord__class_Omin(U_16031)),U_16033),U_16032)
      | hBOOL(hAPP(hAPP(c_member(U_16031),U_16033),U_16032))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16031),U_16032))
      | ~ class_Orderings_Olinorder(U_16031) ),
    inference(variable_rename,[status(thm)],[f_4020_1]) ).

fof(f_4020_3,plain,
    ! [U_16031,U_16032,U_16033] :
      ( c_Big__Operators_Olattice_OInf__fin(U_16031,c_Orderings_Oord__class_Omin(U_16031),hAPP(hAPP(c_Set_Oinsert(U_16031),U_16033),U_16032)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16031,U_16031,c_Orderings_Oord__class_Omin(U_16031)),U_16033),U_16032)
      | hBOOL(hAPP(hAPP(c_member(U_16031),U_16033),U_16032))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16031),U_16032))
      | ~ class_Orderings_Olinorder(U_16031) ),
    inference(definitional_conversion,[status(esa)],[f_4020_2]) ).

cnf(f_4020_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_16031,c_Orderings_Oord__class_Omin(U_16031),hAPP(hAPP(c_Set_Oinsert(U_16031),U_16033),U_16032)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16031,U_16031,c_Orderings_Oord__class_Omin(U_16031)),U_16033),U_16032)
    | hBOOL(hAPP(hAPP(c_member(U_16031),U_16033),U_16032))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16031),U_16032))
    | ~ class_Orderings_Olinorder(U_16031) ),
    inference(clausify,[status(thm)],[f_4020_3]) ).

fof(f_4021_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_4021_2,plain,
    ! [U_16039,U_16038,U_16037,U_16036,U_16035,U_16034] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_16034,U_16035,U_16036),U_16039),U_16037) = hAPP(hAPP(U_16036,U_16038),hAPP(hAPP(c_Finite__Set_Ofold(U_16034,U_16035,U_16036),U_16039),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16034,tc_HOL_Obool)),U_16037),hAPP(hAPP(c_Set_Oinsert(U_16034),U_16038),c_Orderings_Obot__class_Obot(tc_fun(U_16034,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16034),U_16038),U_16037))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16034),U_16037))
      | ~ c_Finite__Set_Ofun__left__comm(U_16034,U_16035,U_16036) ),
    inference(variable_rename,[status(thm)],[f_4021_1]) ).

fof(f_4021_3,plain,
    ! [U_16034,U_16035,U_16036,U_16037,U_16038,U_16039] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_16034,U_16035,U_16036),U_16039),U_16037) = hAPP(hAPP(U_16036,U_16038),hAPP(hAPP(c_Finite__Set_Ofold(U_16034,U_16035,U_16036),U_16039),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16034,tc_HOL_Obool)),U_16037),hAPP(hAPP(c_Set_Oinsert(U_16034),U_16038),c_Orderings_Obot__class_Obot(tc_fun(U_16034,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16034),U_16038),U_16037))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16034),U_16037))
      | ~ c_Finite__Set_Ofun__left__comm(U_16034,U_16035,U_16036) ),
    inference(definitional_conversion,[status(esa)],[f_4021_2]) ).

cnf(f_4021_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_16034,U_16035,U_16036),U_16039),U_16037) = hAPP(hAPP(U_16036,U_16038),hAPP(hAPP(c_Finite__Set_Ofold(U_16034,U_16035,U_16036),U_16039),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16034,tc_HOL_Obool)),U_16037),hAPP(hAPP(c_Set_Oinsert(U_16034),U_16038),c_Orderings_Obot__class_Obot(tc_fun(U_16034,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16034),U_16038),U_16037))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16034),U_16037))
    | ~ c_Finite__Set_Ofun__left__comm(U_16034,U_16035,U_16036) ),
    inference(clausify,[status(thm)],[f_4021_3]) ).

fof(f_4022_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_4022_2,plain,
    ! [U_16045,U_16044,U_16043,U_16042,U_16041,U_16040] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_16040,U_16041,U_16042),U_16044),hAPP(hAPP(c_Set_Oinsert(U_16040),U_16045),U_16043)) = hAPP(hAPP(U_16042,U_16045),hAPP(hAPP(c_Finite__Set_Ofold(U_16040,U_16041,U_16042),U_16044),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16040,tc_HOL_Obool)),U_16043),hAPP(hAPP(c_Set_Oinsert(U_16040),U_16045),c_Orderings_Obot__class_Obot(tc_fun(U_16040,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16040),U_16043))
      | ~ c_Finite__Set_Ofun__left__comm(U_16040,U_16041,U_16042) ),
    inference(variable_rename,[status(thm)],[f_4022_1]) ).

fof(f_4022_3,plain,
    ! [U_16040,U_16041,U_16042,U_16043,U_16044,U_16045] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_16040,U_16041,U_16042),U_16044),hAPP(hAPP(c_Set_Oinsert(U_16040),U_16045),U_16043)) = hAPP(hAPP(U_16042,U_16045),hAPP(hAPP(c_Finite__Set_Ofold(U_16040,U_16041,U_16042),U_16044),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16040,tc_HOL_Obool)),U_16043),hAPP(hAPP(c_Set_Oinsert(U_16040),U_16045),c_Orderings_Obot__class_Obot(tc_fun(U_16040,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16040),U_16043))
      | ~ c_Finite__Set_Ofun__left__comm(U_16040,U_16041,U_16042) ),
    inference(definitional_conversion,[status(esa)],[f_4022_2]) ).

cnf(f_4022_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_16040,U_16041,U_16042),U_16044),hAPP(hAPP(c_Set_Oinsert(U_16040),U_16045),U_16043)) = hAPP(hAPP(U_16042,U_16045),hAPP(hAPP(c_Finite__Set_Ofold(U_16040,U_16041,U_16042),U_16044),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16040,tc_HOL_Obool)),U_16043),hAPP(hAPP(c_Set_Oinsert(U_16040),U_16045),c_Orderings_Obot__class_Obot(tc_fun(U_16040,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16040),U_16043))
    | ~ c_Finite__Set_Ofun__left__comm(U_16040,U_16041,U_16042) ),
    inference(clausify,[status(thm)],[f_4022_3]) ).

fof(f_4023_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_4023_2,plain,
    ! [U_16052,U_16051,U_16050,U_16049,U_16048,U_16047,U_16046] :
      ( U_16052 = U_16051
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16046,U_16047,U_16048,U_16049,U_16050),U_16052))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16046,U_16047,U_16048,U_16049,U_16050),U_16051))
      | ~ c_Finite__Set_Ofun__left__comm(U_16046,U_16047,U_16048) ),
    inference(variable_rename,[status(thm)],[f_4023_1]) ).

fof(f_4023_3,plain,
    ! [U_16047,U_16048,U_16046,U_16049,U_16050,U_16051,U_16052] :
      ( U_16052 = U_16051
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16046,U_16047,U_16048,U_16049,U_16050),U_16052))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16046,U_16047,U_16048,U_16049,U_16050),U_16051))
      | ~ c_Finite__Set_Ofun__left__comm(U_16046,U_16047,U_16048) ),
    inference(definitional_conversion,[status(esa)],[f_4023_2]) ).

cnf(f_4023_4,plain,
    ( U_16052 = U_16051
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16046,U_16047,U_16048,U_16049,U_16050),U_16052))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16046,U_16047,U_16048,U_16049,U_16050),U_16051))
    | ~ c_Finite__Set_Ofun__left__comm(U_16046,U_16047,U_16048) ),
    inference(clausify,[status(thm)],[f_4023_3]) ).

fof(f_4024_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_4024_2,plain,
    ! [U_16057,U_16056,U_16055,U_16054,U_16053] :
      ( c_Finite__Set_Ofun__left__comm(U_16056,U_16054,hAPP(hAPP(c_COMBB(U_16053,tc_fun(U_16054,U_16054),U_16056),U_16055),U_16057))
      | ~ c_Finite__Set_Ofun__left__comm(U_16053,U_16054,U_16055) ),
    inference(variable_rename,[status(thm)],[f_4024_1]) ).

fof(f_4024_3,plain,
    ! [U_16056,U_16055,U_16053,U_16054,U_16057] :
      ( c_Finite__Set_Ofun__left__comm(U_16056,U_16054,hAPP(hAPP(c_COMBB(U_16053,tc_fun(U_16054,U_16054),U_16056),U_16055),U_16057))
      | ~ c_Finite__Set_Ofun__left__comm(U_16053,U_16054,U_16055) ),
    inference(definitional_conversion,[status(esa)],[f_4024_2]) ).

cnf(f_4024_4,plain,
    ( c_Finite__Set_Ofun__left__comm(U_16056,U_16054,hAPP(hAPP(c_COMBB(U_16053,tc_fun(U_16054,U_16054),U_16056),U_16055),U_16057))
    | ~ c_Finite__Set_Ofun__left__comm(U_16053,U_16054,U_16055) ),
    inference(clausify,[status(thm)],[f_4024_3]) ).

fof(f_4025_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_4025_2,plain,
    ! [U_16063,U_16062,U_16061,U_16060,U_16059,U_16058] :
      ( hAPP(hAPP(U_16060,U_16061),hAPP(hAPP(U_16060,U_16062),U_16063)) = hAPP(hAPP(U_16060,U_16062),hAPP(hAPP(U_16060,U_16061),U_16063))
      | ~ c_Finite__Set_Ofun__left__comm(U_16058,U_16059,U_16060) ),
    inference(variable_rename,[status(thm)],[f_4025_1]) ).

fof(f_4025_3,plain,
    ! [U_16063,U_16062,U_16061,U_16060] :
      ( ! [U_16059,U_16058] : ~ c_Finite__Set_Ofun__left__comm(U_16058,U_16059,U_16060)
      | hAPP(hAPP(U_16060,U_16061),hAPP(hAPP(U_16060,U_16062),U_16063)) = hAPP(hAPP(U_16060,U_16062),hAPP(hAPP(U_16060,U_16061),U_16063)) ),
    inference(miniscope,[status(thm)],[f_4025_2]) ).

fof(f_4025_4,plain,
    ! [U_16063,U_16058,U_16059,U_16060,U_16061,U_16062] :
      ( ~ c_Finite__Set_Ofun__left__comm(U_16058,U_16059,U_16060)
      | hAPP(hAPP(U_16060,U_16061),hAPP(hAPP(U_16060,U_16062),U_16063)) = hAPP(hAPP(U_16060,U_16062),hAPP(hAPP(U_16060,U_16061),U_16063)) ),
    inference(definitional_conversion,[status(esa)],[f_4025_3]) ).

cnf(f_4025_5,plain,
    ( ~ c_Finite__Set_Ofun__left__comm(U_16058,U_16059,U_16060)
    | hAPP(hAPP(U_16060,U_16061),hAPP(hAPP(U_16060,U_16062),U_16063)) = hAPP(hAPP(U_16060,U_16062),hAPP(hAPP(U_16060,U_16061),U_16063)) ),
    inference(clausify,[status(thm)],[f_4025_4]) ).

fof(f_4026_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_4026_2,plain,
    ! [U_16064] :
      ( c_Finite__Set_Ofun__left__comm(U_16064,U_16064,c_Groups_Otimes__class_Otimes(U_16064))
      | ~ class_Groups_Oab__semigroup__mult(U_16064) ),
    inference(variable_rename,[status(thm)],[f_4026_1]) ).

fof(f_4026_3,plain,
    ! [U_16064] :
      ( c_Finite__Set_Ofun__left__comm(U_16064,U_16064,c_Groups_Otimes__class_Otimes(U_16064))
      | ~ class_Groups_Oab__semigroup__mult(U_16064) ),
    inference(definitional_conversion,[status(esa)],[f_4026_2]) ).

cnf(f_4026_4,plain,
    ( c_Finite__Set_Ofun__left__comm(U_16064,U_16064,c_Groups_Otimes__class_Otimes(U_16064))
    | ~ class_Groups_Oab__semigroup__mult(U_16064) ),
    inference(clausify,[status(thm)],[f_4026_3]) ).

fof(f_4027_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_4027_2,plain,
    ! [U_16069,U_16068,U_16067,U_16066,U_16065] :
      ( hAPP(c_Fun_Ocomp(U_16066,U_16066,U_16066,hAPP(U_16067,U_16068)),hAPP(U_16067,U_16069)) = hAPP(c_Fun_Ocomp(U_16066,U_16066,U_16066,hAPP(U_16067,U_16069)),hAPP(U_16067,U_16068))
      | ~ c_Finite__Set_Ofun__left__comm(U_16065,U_16066,U_16067) ),
    inference(variable_rename,[status(thm)],[f_4027_1]) ).

fof(f_4027_3,plain,
    ! [U_16069,U_16068,U_16067,U_16066] :
      ( ! [U_16065] : ~ c_Finite__Set_Ofun__left__comm(U_16065,U_16066,U_16067)
      | hAPP(c_Fun_Ocomp(U_16066,U_16066,U_16066,hAPP(U_16067,U_16068)),hAPP(U_16067,U_16069)) = hAPP(c_Fun_Ocomp(U_16066,U_16066,U_16066,hAPP(U_16067,U_16069)),hAPP(U_16067,U_16068)) ),
    inference(miniscope,[status(thm)],[f_4027_2]) ).

fof(f_4027_4,plain,
    ! [U_16065,U_16066,U_16067,U_16068,U_16069] :
      ( ~ c_Finite__Set_Ofun__left__comm(U_16065,U_16066,U_16067)
      | hAPP(c_Fun_Ocomp(U_16066,U_16066,U_16066,hAPP(U_16067,U_16068)),hAPP(U_16067,U_16069)) = hAPP(c_Fun_Ocomp(U_16066,U_16066,U_16066,hAPP(U_16067,U_16069)),hAPP(U_16067,U_16068)) ),
    inference(definitional_conversion,[status(esa)],[f_4027_3]) ).

cnf(f_4027_5,plain,
    ( ~ c_Finite__Set_Ofun__left__comm(U_16065,U_16066,U_16067)
    | hAPP(c_Fun_Ocomp(U_16066,U_16066,U_16066,hAPP(U_16067,U_16068)),hAPP(U_16067,U_16069)) = hAPP(c_Fun_Ocomp(U_16066,U_16066,U_16066,hAPP(U_16067,U_16069)),hAPP(U_16067,U_16068)) ),
    inference(clausify,[status(thm)],[f_4027_4]) ).

fof(f_4028_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_4028_2,plain,
    ! [U_16075,U_16074,U_16073,U_16072,U_16071,U_16070] :
      ( hAPP(hAPP(U_16072,U_16074),hAPP(hAPP(c_Finite__Set_Ofold(U_16070,U_16071,U_16072),U_16075),U_16073)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16070,U_16071,U_16072),hAPP(hAPP(U_16072,U_16074),U_16075)),U_16073)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16070),U_16073))
      | ~ c_Finite__Set_Ofun__left__comm(U_16070,U_16071,U_16072) ),
    inference(variable_rename,[status(thm)],[f_4028_1]) ).

fof(f_4028_3,plain,
    ! [U_16070,U_16071,U_16072,U_16073,U_16074,U_16075] :
      ( hAPP(hAPP(U_16072,U_16074),hAPP(hAPP(c_Finite__Set_Ofold(U_16070,U_16071,U_16072),U_16075),U_16073)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16070,U_16071,U_16072),hAPP(hAPP(U_16072,U_16074),U_16075)),U_16073)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16070),U_16073))
      | ~ c_Finite__Set_Ofun__left__comm(U_16070,U_16071,U_16072) ),
    inference(definitional_conversion,[status(esa)],[f_4028_2]) ).

cnf(f_4028_4,plain,
    ( hAPP(hAPP(U_16072,U_16074),hAPP(hAPP(c_Finite__Set_Ofold(U_16070,U_16071,U_16072),U_16075),U_16073)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16070,U_16071,U_16072),hAPP(hAPP(U_16072,U_16074),U_16075)),U_16073)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16070),U_16073))
    | ~ c_Finite__Set_Ofun__left__comm(U_16070,U_16071,U_16072) ),
    inference(clausify,[status(thm)],[f_4028_3]) ).

fof(f_4029_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_4029_2,plain,
    ! [U_16081,U_16080,U_16079,U_16078,U_16077,U_16076] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_16076,U_16077,U_16078),U_16079),U_16080) = U_16081
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16076,U_16077,U_16078,U_16079,U_16080),U_16081))
      | ~ c_Finite__Set_Ofun__left__comm(U_16076,U_16077,U_16078) ),
    inference(variable_rename,[status(thm)],[f_4029_1]) ).

fof(f_4029_3,plain,
    ! [U_16076,U_16077,U_16078,U_16079,U_16080,U_16081] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_16076,U_16077,U_16078),U_16079),U_16080) = U_16081
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16076,U_16077,U_16078,U_16079,U_16080),U_16081))
      | ~ c_Finite__Set_Ofun__left__comm(U_16076,U_16077,U_16078) ),
    inference(definitional_conversion,[status(esa)],[f_4029_2]) ).

cnf(f_4029_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_16076,U_16077,U_16078),U_16079),U_16080) = U_16081
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16076,U_16077,U_16078,U_16079,U_16080),U_16081))
    | ~ c_Finite__Set_Ofun__left__comm(U_16076,U_16077,U_16078) ),
    inference(clausify,[status(thm)],[f_4029_3]) ).

fof(f_4030_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_4030_2,plain,
    ! [U_16086,U_16085,U_16084,U_16083,U_16082] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16082,U_16083,U_16084,U_16086,U_16085),hAPP(hAPP(c_Finite__Set_Ofold(U_16082,U_16083,U_16084),U_16086),U_16085)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16082),U_16085))
      | ~ c_Finite__Set_Ofun__left__comm(U_16082,U_16083,U_16084) ),
    inference(variable_rename,[status(thm)],[f_4030_1]) ).

fof(f_4030_3,plain,
    ! [U_16082,U_16083,U_16084,U_16085,U_16086] :
      ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16082,U_16083,U_16084,U_16086,U_16085),hAPP(hAPP(c_Finite__Set_Ofold(U_16082,U_16083,U_16084),U_16086),U_16085)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16082),U_16085))
      | ~ c_Finite__Set_Ofun__left__comm(U_16082,U_16083,U_16084) ),
    inference(definitional_conversion,[status(esa)],[f_4030_2]) ).

cnf(f_4030_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16082,U_16083,U_16084,U_16086,U_16085),hAPP(hAPP(c_Finite__Set_Ofold(U_16082,U_16083,U_16084),U_16086),U_16085)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16082),U_16085))
    | ~ c_Finite__Set_Ofun__left__comm(U_16082,U_16083,U_16084) ),
    inference(clausify,[status(thm)],[f_4030_3]) ).

fof(f_4031_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_4031_2,plain,
    ! [U_16092,U_16091,U_16090,U_16089,U_16088,U_16087] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_16087,U_16088,U_16089),U_16092),hAPP(hAPP(c_Set_Oinsert(U_16087),U_16091),U_16090)) = hAPP(hAPP(U_16089,U_16091),hAPP(hAPP(c_Finite__Set_Ofold(U_16087,U_16088,U_16089),U_16092),U_16090))
      | hBOOL(hAPP(hAPP(c_member(U_16087),U_16091),U_16090))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16087),U_16090))
      | ~ c_Finite__Set_Ofun__left__comm(U_16087,U_16088,U_16089) ),
    inference(variable_rename,[status(thm)],[f_4031_1]) ).

fof(f_4031_3,plain,
    ! [U_16087,U_16088,U_16089,U_16090,U_16091,U_16092] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_16087,U_16088,U_16089),U_16092),hAPP(hAPP(c_Set_Oinsert(U_16087),U_16091),U_16090)) = hAPP(hAPP(U_16089,U_16091),hAPP(hAPP(c_Finite__Set_Ofold(U_16087,U_16088,U_16089),U_16092),U_16090))
      | hBOOL(hAPP(hAPP(c_member(U_16087),U_16091),U_16090))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16087),U_16090))
      | ~ c_Finite__Set_Ofun__left__comm(U_16087,U_16088,U_16089) ),
    inference(definitional_conversion,[status(esa)],[f_4031_2]) ).

cnf(f_4031_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_16087,U_16088,U_16089),U_16092),hAPP(hAPP(c_Set_Oinsert(U_16087),U_16091),U_16090)) = hAPP(hAPP(U_16089,U_16091),hAPP(hAPP(c_Finite__Set_Ofold(U_16087,U_16088,U_16089),U_16092),U_16090))
    | hBOOL(hAPP(hAPP(c_member(U_16087),U_16091),U_16090))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16087),U_16090))
    | ~ c_Finite__Set_Ofun__left__comm(U_16087,U_16088,U_16089) ),
    inference(clausify,[status(thm)],[f_4031_3]) ).

fof(f_4032_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_4032_2,plain,
    ! [U_16098,U_16097,U_16096,U_16095,U_16094,U_16093] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_16093,U_16094,U_16095),U_16098),hAPP(hAPP(c_Set_Oinsert(U_16093),U_16097),U_16096)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16093,U_16094,U_16095),hAPP(hAPP(U_16095,U_16097),U_16098)),U_16096)
      | hBOOL(hAPP(hAPP(c_member(U_16093),U_16097),U_16096))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16093),U_16096))
      | ~ c_Finite__Set_Ofun__left__comm(U_16093,U_16094,U_16095) ),
    inference(variable_rename,[status(thm)],[f_4032_1]) ).

fof(f_4032_3,plain,
    ! [U_16094,U_16095,U_16096,U_16097,U_16098,U_16093] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_16093,U_16094,U_16095),U_16098),hAPP(hAPP(c_Set_Oinsert(U_16093),U_16097),U_16096)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16093,U_16094,U_16095),hAPP(hAPP(U_16095,U_16097),U_16098)),U_16096)
      | hBOOL(hAPP(hAPP(c_member(U_16093),U_16097),U_16096))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16093),U_16096))
      | ~ c_Finite__Set_Ofun__left__comm(U_16093,U_16094,U_16095) ),
    inference(definitional_conversion,[status(esa)],[f_4032_2]) ).

cnf(f_4032_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_16093,U_16094,U_16095),U_16098),hAPP(hAPP(c_Set_Oinsert(U_16093),U_16097),U_16096)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16093,U_16094,U_16095),hAPP(hAPP(U_16095,U_16097),U_16098)),U_16096)
    | hBOOL(hAPP(hAPP(c_member(U_16093),U_16097),U_16096))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16093),U_16096))
    | ~ c_Finite__Set_Ofun__left__comm(U_16093,U_16094,U_16095) ),
    inference(clausify,[status(thm)],[f_4032_3]) ).

fof(f_4033_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_4033_2,plain,
    ! [U_16106,U_16105,U_16104,U_16103,U_16102,U_16101,U_16100] :
      ( ? [U_16099] :
          ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16100,U_16101,U_16102,U_16103,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16100,tc_HOL_Obool)),U_16104),hAPP(hAPP(c_Set_Oinsert(U_16100),U_16106),c_Orderings_Obot__class_Obot(tc_fun(U_16100,tc_HOL_Obool))))),U_16099))
          & U_16105 = hAPP(hAPP(U_16102,U_16106),U_16099) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_16100),U_16106),U_16104))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16100,U_16101,U_16102,U_16103,U_16104),U_16105))
      | ~ c_Finite__Set_Ofun__left__comm(U_16100,U_16101,U_16102) ),
    inference(variable_rename,[status(thm)],[f_4033_1]) ).

fof(f_4033_3,plain,
    ! [U_16106,U_16105,U_16104,U_16103,U_16102,U_16101,U_16100] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16100,U_16101,U_16102,U_16103,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16100,tc_HOL_Obool)),U_16104),hAPP(hAPP(c_Set_Oinsert(U_16100),U_16106),c_Orderings_Obot__class_Obot(tc_fun(U_16100,tc_HOL_Obool))))),sK405(U_16106,U_16105,U_16104,U_16103,U_16102,U_16101,U_16100)))
        & U_16105 = hAPP(hAPP(U_16102,U_16106),sK405(U_16106,U_16105,U_16104,U_16103,U_16102,U_16101,U_16100)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_16100),U_16106),U_16104))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16100,U_16101,U_16102,U_16103,U_16104),U_16105))
      | ~ c_Finite__Set_Ofun__left__comm(U_16100,U_16101,U_16102) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK405]),skolemize(U_16099,sK405(U_16106,U_16105,U_16104,U_16103,U_16102,U_16101,U_16100))],[f_4033_2]) ).

fof(f_4033_4,plain,
    ( ! [U_16100,U_16101,U_16102,U_16103,U_16104,U_16105,U_16106] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16100,U_16101,U_16102,U_16103,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16100,tc_HOL_Obool)),U_16104),hAPP(hAPP(c_Set_Oinsert(U_16100),U_16106),c_Orderings_Obot__class_Obot(tc_fun(U_16100,tc_HOL_Obool))))),sK405(U_16106,U_16105,U_16104,U_16103,U_16102,U_16101,U_16100)))
        | ~ sP1060(U_16100,U_16101,U_16102,U_16103,U_16104,U_16105,U_16106) )
    & ! [U_16100,U_16101,U_16102,U_16103,U_16104,U_16105,U_16106] :
        ( U_16105 = hAPP(hAPP(U_16102,U_16106),sK405(U_16106,U_16105,U_16104,U_16103,U_16102,U_16101,U_16100))
        | ~ sP1060(U_16100,U_16101,U_16102,U_16103,U_16104,U_16105,U_16106) )
    & ! [U_16100,U_16101,U_16102,U_16103,U_16104,U_16105,U_16106] :
        ( sP1060(U_16100,U_16101,U_16102,U_16103,U_16104,U_16105,U_16106)
        | ~ hBOOL(hAPP(hAPP(c_member(U_16100),U_16106),U_16104))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16100,U_16101,U_16102,U_16103,U_16104),U_16105))
        | ~ c_Finite__Set_Ofun__left__comm(U_16100,U_16101,U_16102) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1060])],[f_4033_3]) ).

cnf(f_4033_5,plain,
    ( sP1060(U_16100,U_16101,U_16102,U_16103,U_16104,U_16105,U_16106)
    | ~ hBOOL(hAPP(hAPP(c_member(U_16100),U_16106),U_16104))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16100,U_16101,U_16102,U_16103,U_16104),U_16105))
    | ~ c_Finite__Set_Ofun__left__comm(U_16100,U_16101,U_16102) ),
    inference(clausify,[status(thm)],[f_4033_4]) ).

cnf(f_4033_6,plain,
    ( U_16105 = hAPP(hAPP(U_16102,U_16106),sK405(U_16106,U_16105,U_16104,U_16103,U_16102,U_16101,U_16100))
    | ~ sP1060(U_16100,U_16101,U_16102,U_16103,U_16104,U_16105,U_16106) ),
    inference(clausify,[status(thm)],[f_4033_4]) ).

cnf(f_4033_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16100,U_16101,U_16102,U_16103,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16100,tc_HOL_Obool)),U_16104),hAPP(hAPP(c_Set_Oinsert(U_16100),U_16106),c_Orderings_Obot__class_Obot(tc_fun(U_16100,tc_HOL_Obool))))),sK405(U_16106,U_16105,U_16104,U_16103,U_16102,U_16101,U_16100)))
    | ~ sP1060(U_16100,U_16101,U_16102,U_16103,U_16104,U_16105,U_16106) ),
    inference(clausify,[status(thm)],[f_4033_4]) ).

fof(f_4034_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_4034_2,plain,
    ! [U_16110,U_16109,U_16108,U_16107] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16108,U_16107),U_16109),U_16110) = hAPP(hAPP(c_Finite__Set_Ofold(U_16108,U_16107,hAPP(hAPP(c_COMBB(U_16107,tc_fun(U_16107,U_16107),U_16108),c_Lattices_Osemilattice__inf__class_Oinf(U_16107)),U_16110)),c_Orderings_Otop__class_Otop(U_16107)),U_16109)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16108),U_16109))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16107) ),
    inference(variable_rename,[status(thm)],[f_4034_1]) ).

fof(f_4034_3,plain,
    ! [U_16107,U_16109,U_16110,U_16108] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16108,U_16107),U_16109),U_16110) = hAPP(hAPP(c_Finite__Set_Ofold(U_16108,U_16107,hAPP(hAPP(c_COMBB(U_16107,tc_fun(U_16107,U_16107),U_16108),c_Lattices_Osemilattice__inf__class_Oinf(U_16107)),U_16110)),c_Orderings_Otop__class_Otop(U_16107)),U_16109)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16108),U_16109))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16107) ),
    inference(definitional_conversion,[status(esa)],[f_4034_2]) ).

cnf(f_4034_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16108,U_16107),U_16109),U_16110) = hAPP(hAPP(c_Finite__Set_Ofold(U_16108,U_16107,hAPP(hAPP(c_COMBB(U_16107,tc_fun(U_16107,U_16107),U_16108),c_Lattices_Osemilattice__inf__class_Oinf(U_16107)),U_16110)),c_Orderings_Otop__class_Otop(U_16107)),U_16109)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16108),U_16109))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16107) ),
    inference(clausify,[status(thm)],[f_4034_3]) ).

fof(f_4035_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_4035_2,plain,
    ! [U_16116,U_16115,U_16114,U_16113,U_16112,U_16111] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_16111),U_16116),U_16113))
      | hBOOL(hAPP(hAPP(U_16114,U_16116),U_16115))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16111,tc_fun(U_16112,tc_HOL_Obool)),U_16113),U_16114),U_16115)) ),
    inference(variable_rename,[status(thm)],[f_4035_1]) ).

fof(f_4035_3,plain,
    ! [U_16111,U_16112,U_16113,U_16114,U_16115,U_16116] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_16111),U_16116),U_16113))
      | hBOOL(hAPP(hAPP(U_16114,U_16116),U_16115))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16111,tc_fun(U_16112,tc_HOL_Obool)),U_16113),U_16114),U_16115)) ),
    inference(definitional_conversion,[status(esa)],[f_4035_2]) ).

cnf(f_4035_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16111),U_16116),U_16113))
    | hBOOL(hAPP(hAPP(U_16114,U_16116),U_16115))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16111,tc_fun(U_16112,tc_HOL_Obool)),U_16113),U_16114),U_16115)) ),
    inference(clausify,[status(thm)],[f_4035_3]) ).

fof(f_4036_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_4036_2,plain,
    ! [U_16122,U_16121,U_16120,U_16119,U_16118,U_16117] :
      ( hBOOL(hAPP(hAPP(U_16120,U_16122),U_16121))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16117),U_16122),U_16119))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16117,tc_fun(U_16118,tc_HOL_Obool)),U_16119),U_16120),U_16121)) ),
    inference(variable_rename,[status(thm)],[f_4036_1]) ).

fof(f_4036_3,plain,
    ! [U_16117,U_16118,U_16119,U_16120,U_16121,U_16122] :
      ( hBOOL(hAPP(hAPP(U_16120,U_16122),U_16121))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16117),U_16122),U_16119))
      | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16117,tc_fun(U_16118,tc_HOL_Obool)),U_16119),U_16120),U_16121)) ),
    inference(definitional_conversion,[status(esa)],[f_4036_2]) ).

cnf(f_4036_4,plain,
    ( hBOOL(hAPP(hAPP(U_16120,U_16122),U_16121))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16117),U_16122),U_16119))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16117,tc_fun(U_16118,tc_HOL_Obool)),U_16119),U_16120),U_16121)) ),
    inference(clausify,[status(thm)],[f_4036_3]) ).

fof(f_4037_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_4037_2,plain,
    ! [U_16128,U_16127,U_16126,U_16125,U_16124,U_16123] :
      ( hBOOL(hAPP(hAPP(c_member(U_16123),U_16124),hAPP(U_16127,U_16128)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16125),U_16128),U_16126))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16123),U_16124),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16125,tc_fun(U_16123,tc_HOL_Obool)),U_16126),U_16127))) ),
    inference(variable_rename,[status(thm)],[f_4037_1]) ).

fof(f_4037_3,plain,
    ! [U_16123,U_16124,U_16125,U_16126,U_16127,U_16128] :
      ( hBOOL(hAPP(hAPP(c_member(U_16123),U_16124),hAPP(U_16127,U_16128)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16125),U_16128),U_16126))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16123),U_16124),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16125,tc_fun(U_16123,tc_HOL_Obool)),U_16126),U_16127))) ),
    inference(definitional_conversion,[status(esa)],[f_4037_2]) ).

cnf(f_4037_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16123),U_16124),hAPP(U_16127,U_16128)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16125),U_16128),U_16126))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16123),U_16124),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16125,tc_fun(U_16123,tc_HOL_Obool)),U_16126),U_16127))) ),
    inference(clausify,[status(thm)],[f_4037_3]) ).

fof(f_4038_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_4038_2,plain,
    ! [U_16134,U_16133,U_16132,U_16131,U_16130,U_16129] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_16131),U_16134),U_16132))
      | hBOOL(hAPP(hAPP(c_member(U_16129),U_16130),hAPP(U_16133,U_16134)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16129),U_16130),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16131,tc_fun(U_16129,tc_HOL_Obool)),U_16132),U_16133))) ),
    inference(variable_rename,[status(thm)],[f_4038_1]) ).

fof(f_4038_3,plain,
    ! [U_16129,U_16130,U_16131,U_16132,U_16133,U_16134] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_16131),U_16134),U_16132))
      | hBOOL(hAPP(hAPP(c_member(U_16129),U_16130),hAPP(U_16133,U_16134)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16129),U_16130),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16131,tc_fun(U_16129,tc_HOL_Obool)),U_16132),U_16133))) ),
    inference(definitional_conversion,[status(esa)],[f_4038_2]) ).

cnf(f_4038_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16131),U_16134),U_16132))
    | hBOOL(hAPP(hAPP(c_member(U_16129),U_16130),hAPP(U_16133,U_16134)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16129),U_16130),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16131,tc_fun(U_16129,tc_HOL_Obool)),U_16132),U_16133))) ),
    inference(clausify,[status(thm)],[f_4038_3]) ).

fof(f_4039_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_4039_2,plain,
    ! [U_16142,U_16141,U_16140,U_16139,U_16138,U_16137,U_16136,U_16135] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_16135),U_16142),U_16138))
      | hBOOL(hAPP(hAPP(hAPP(U_16139,U_16142),U_16140),U_16141))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16135,tc_fun(U_16136,tc_fun(U_16137,tc_HOL_Obool))),U_16138),U_16139),U_16140),U_16141)) ),
    inference(variable_rename,[status(thm)],[f_4039_1]) ).

fof(f_4039_3,plain,
    ! [U_16135,U_16136,U_16137,U_16138,U_16139,U_16140,U_16141,U_16142] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_16135),U_16142),U_16138))
      | hBOOL(hAPP(hAPP(hAPP(U_16139,U_16142),U_16140),U_16141))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16135,tc_fun(U_16136,tc_fun(U_16137,tc_HOL_Obool))),U_16138),U_16139),U_16140),U_16141)) ),
    inference(definitional_conversion,[status(esa)],[f_4039_2]) ).

cnf(f_4039_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16135),U_16142),U_16138))
    | hBOOL(hAPP(hAPP(hAPP(U_16139,U_16142),U_16140),U_16141))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16135,tc_fun(U_16136,tc_fun(U_16137,tc_HOL_Obool))),U_16138),U_16139),U_16140),U_16141)) ),
    inference(clausify,[status(thm)],[f_4039_3]) ).

fof(f_4040_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_4040_2,plain,
    ! [U_16150,U_16149,U_16148,U_16147,U_16146,U_16145,U_16144,U_16143] :
      ( hBOOL(hAPP(hAPP(hAPP(U_16147,U_16150),U_16148),U_16149))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16143),U_16150),U_16146))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16143,tc_fun(U_16144,tc_fun(U_16145,tc_HOL_Obool))),U_16146),U_16147),U_16148),U_16149)) ),
    inference(variable_rename,[status(thm)],[f_4040_1]) ).

fof(f_4040_3,plain,
    ! [U_16143,U_16144,U_16145,U_16146,U_16147,U_16148,U_16149,U_16150] :
      ( hBOOL(hAPP(hAPP(hAPP(U_16147,U_16150),U_16148),U_16149))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16143),U_16150),U_16146))
      | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16143,tc_fun(U_16144,tc_fun(U_16145,tc_HOL_Obool))),U_16146),U_16147),U_16148),U_16149)) ),
    inference(definitional_conversion,[status(esa)],[f_4040_2]) ).

cnf(f_4040_4,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_16147,U_16150),U_16148),U_16149))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16143),U_16150),U_16146))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16143,tc_fun(U_16144,tc_fun(U_16145,tc_HOL_Obool))),U_16146),U_16147),U_16148),U_16149)) ),
    inference(clausify,[status(thm)],[f_4040_3]) ).

fof(f_4041_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_4041_2,plain,
    ! [U_16155,U_16154,U_16153,U_16152] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_16154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16152,tc_fun(U_16154,tc_HOL_Obool)),U_16153),U_16155)))
      | ! [U_16151] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16154),hAPP(U_16155,U_16151)))
          | ~ hBOOL(hAPP(hAPP(c_member(U_16152),U_16151),U_16153)) ) ),
    inference(variable_rename,[status(thm)],[f_4041_1]) ).

fof(f_4041_3,plain,
    ! [U_16152,U_16151,U_16153,U_16154,U_16155] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_16154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16152,tc_fun(U_16154,tc_HOL_Obool)),U_16153),U_16155)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16154),hAPP(U_16155,U_16151)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16152),U_16151),U_16153)) ),
    inference(definitional_conversion,[status(esa)],[f_4041_2]) ).

cnf(f_4041_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_16154),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16152,tc_fun(U_16154,tc_HOL_Obool)),U_16153),U_16155)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16154),hAPP(U_16155,U_16151)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16152),U_16151),U_16153)) ),
    inference(clausify,[status(thm)],[f_4041_3]) ).

fof(f_4042_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_4042_2,plain,
    ! [U_16160,U_16159,U_16158,U_16157,U_16156] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16159,tc_HOL_Obool)),hAPP(U_16160,U_16157)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16156,tc_fun(U_16159,tc_HOL_Obool)),U_16158),U_16160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16156,tc_fun(U_16159,tc_HOL_Obool)),U_16158),U_16160)
      | ~ hBOOL(hAPP(hAPP(c_member(U_16156),U_16157),U_16158)) ),
    inference(variable_rename,[status(thm)],[f_4042_1]) ).

fof(f_4042_3,plain,
    ! [U_16156,U_16157,U_16158,U_16159,U_16160] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16159,tc_HOL_Obool)),hAPP(U_16160,U_16157)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16156,tc_fun(U_16159,tc_HOL_Obool)),U_16158),U_16160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16156,tc_fun(U_16159,tc_HOL_Obool)),U_16158),U_16160)
      | ~ hBOOL(hAPP(hAPP(c_member(U_16156),U_16157),U_16158)) ),
    inference(definitional_conversion,[status(esa)],[f_4042_2]) ).

cnf(f_4042_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16159,tc_HOL_Obool)),hAPP(U_16160,U_16157)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16156,tc_fun(U_16159,tc_HOL_Obool)),U_16158),U_16160)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16156,tc_fun(U_16159,tc_HOL_Obool)),U_16158),U_16160)
    | ~ hBOOL(hAPP(hAPP(c_member(U_16156),U_16157),U_16158)) ),
    inference(clausify,[status(thm)],[f_4042_3]) ).

fof(f_4043_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_4043_2,plain,
    ! [U_16167,U_16166,U_16165,U_16164,U_16163] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_16163),U_16164),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16165,tc_fun(U_16163,tc_HOL_Obool)),U_16166),U_16167)))
        | ? [U_16162] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_16163),U_16164),hAPP(U_16167,U_16162)))
            & hBOOL(hAPP(hAPP(c_member(U_16165),U_16162),U_16166)) ) )
      & ( ! [U_16161] :
            ( hBOOL(hAPP(hAPP(c_member(U_16163),U_16164),hAPP(U_16167,U_16161)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16165),U_16161),U_16166)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_16163),U_16164),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16165,tc_fun(U_16163,tc_HOL_Obool)),U_16166),U_16167))) ) ),
    inference(variable_rename,[status(thm)],[f_4043_1]) ).

fof(f_4043_3,plain,
    ( ! [U_16177,U_16175,U_16173,U_16171,U_16169] :
        ( hBOOL(hAPP(hAPP(c_member(U_16169),U_16171),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16173,tc_fun(U_16169,tc_HOL_Obool)),U_16175),U_16177)))
        | ? [U_16162] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_16169),U_16171),hAPP(U_16177,U_16162)))
            & hBOOL(hAPP(hAPP(c_member(U_16173),U_16162),U_16175)) ) )
    & ! [U_16176,U_16174,U_16172,U_16170,U_16168] :
        ( ! [U_16161] :
            ( hBOOL(hAPP(hAPP(c_member(U_16168),U_16170),hAPP(U_16176,U_16161)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16172),U_16161),U_16174)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_16168),U_16170),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16172,tc_fun(U_16168,tc_HOL_Obool)),U_16174),U_16176))) ) ),
    inference(miniscope,[status(thm)],[f_4043_2]) ).

fof(f_4043_4,plain,
    ( ! [U_16177,U_16175,U_16173,U_16171,U_16169] :
        ( hBOOL(hAPP(hAPP(c_member(U_16169),U_16171),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16173,tc_fun(U_16169,tc_HOL_Obool)),U_16175),U_16177)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_16169),U_16171),hAPP(U_16177,sK406(U_16177,U_16175,U_16173,U_16171,U_16169))))
          & hBOOL(hAPP(hAPP(c_member(U_16173),sK406(U_16177,U_16175,U_16173,U_16171,U_16169)),U_16175)) ) )
    & ! [U_16176,U_16174,U_16172,U_16170,U_16168] :
        ( ! [U_16161] :
            ( hBOOL(hAPP(hAPP(c_member(U_16168),U_16170),hAPP(U_16176,U_16161)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16172),U_16161),U_16174)) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_16168),U_16170),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16172,tc_fun(U_16168,tc_HOL_Obool)),U_16174),U_16176))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK406]),skolemize(U_16162,sK406(U_16177,U_16175,U_16173,U_16171,U_16169))],[f_4043_3]) ).

fof(f_4043_5,plain,
    ( ! [U_16169,U_16171,U_16175,U_16177,U_16173] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_16169),U_16171),hAPP(U_16177,sK406(U_16177,U_16175,U_16173,U_16171,U_16169))))
        | ~ sP1061(U_16169,U_16171,U_16175,U_16177,U_16173) )
    & ! [U_16169,U_16171,U_16175,U_16177,U_16173] :
        ( hBOOL(hAPP(hAPP(c_member(U_16173),sK406(U_16177,U_16175,U_16173,U_16171,U_16169)),U_16175))
        | ~ sP1061(U_16169,U_16171,U_16175,U_16177,U_16173) )
    & ! [U_16169,U_16171,U_16175,U_16177,U_16173] :
        ( hBOOL(hAPP(hAPP(c_member(U_16169),U_16171),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16173,tc_fun(U_16169,tc_HOL_Obool)),U_16175),U_16177)))
        | sP1061(U_16169,U_16171,U_16175,U_16177,U_16173) )
    & ! [U_16170,U_16172,U_16161,U_16168,U_16176,U_16174] :
        ( hBOOL(hAPP(hAPP(c_member(U_16168),U_16170),hAPP(U_16176,U_16161)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16172),U_16161),U_16174))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16168),U_16170),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16172,tc_fun(U_16168,tc_HOL_Obool)),U_16174),U_16176))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1061])],[f_4043_4]) ).

cnf(f_4043_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16168),U_16170),hAPP(U_16176,U_16161)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16172),U_16161),U_16174))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16168),U_16170),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16172,tc_fun(U_16168,tc_HOL_Obool)),U_16174),U_16176))) ),
    inference(clausify,[status(thm)],[f_4043_5]) ).

cnf(f_4043_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16169),U_16171),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16173,tc_fun(U_16169,tc_HOL_Obool)),U_16175),U_16177)))
    | sP1061(U_16169,U_16171,U_16175,U_16177,U_16173) ),
    inference(clausify,[status(thm)],[f_4043_5]) ).

cnf(f_4043_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16173),sK406(U_16177,U_16175,U_16173,U_16171,U_16169)),U_16175))
    | ~ sP1061(U_16169,U_16171,U_16175,U_16177,U_16173) ),
    inference(clausify,[status(thm)],[f_4043_5]) ).

cnf(f_4043_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16169),U_16171),hAPP(U_16177,sK406(U_16177,U_16175,U_16173,U_16171,U_16169))))
    | ~ sP1061(U_16169,U_16171,U_16175,U_16177,U_16173) ),
    inference(clausify,[status(thm)],[f_4043_5]) ).

fof(f_4044_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_4044_2,plain,
    ! [U_16182,U_16181,U_16180,U_16179,U_16178] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16181,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16178,tc_fun(U_16181,tc_HOL_Obool)),U_16180),U_16182)),hAPP(U_16182,U_16179)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16178),U_16179),U_16180)) ),
    inference(variable_rename,[status(thm)],[f_4044_1]) ).

fof(f_4044_3,plain,
    ! [U_16178,U_16179,U_16180,U_16181,U_16182] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16181,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16178,tc_fun(U_16181,tc_HOL_Obool)),U_16180),U_16182)),hAPP(U_16182,U_16179)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16178),U_16179),U_16180)) ),
    inference(definitional_conversion,[status(esa)],[f_4044_2]) ).

cnf(f_4044_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16181,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16178,tc_fun(U_16181,tc_HOL_Obool)),U_16180),U_16182)),hAPP(U_16182,U_16179)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16178),U_16179),U_16180)) ),
    inference(clausify,[status(thm)],[f_4044_3]) ).

fof(f_4045_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_4045_2,plain,
    ! [U_16188,U_16187,U_16186,U_16185,U_16184,U_16183] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16183,tc_fun(U_16186,tc_HOL_Obool)),U_16185),hAPP(hAPP(c_COMBB(tc_fun(U_16186,tc_HOL_Obool),tc_fun(U_16186,tc_HOL_Obool),U_16183),hAPP(c_Set_Oinsert(U_16186),U_16187)),U_16188)) = hAPP(hAPP(c_Set_Oinsert(U_16186),U_16187),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16183,tc_fun(U_16186,tc_HOL_Obool)),U_16185),U_16188))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16183),U_16184),U_16185)) ),
    inference(variable_rename,[status(thm)],[f_4045_1]) ).

fof(f_4045_3,plain,
    ! [U_16183,U_16184,U_16185,U_16186,U_16187,U_16188] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16183,tc_fun(U_16186,tc_HOL_Obool)),U_16185),hAPP(hAPP(c_COMBB(tc_fun(U_16186,tc_HOL_Obool),tc_fun(U_16186,tc_HOL_Obool),U_16183),hAPP(c_Set_Oinsert(U_16186),U_16187)),U_16188)) = hAPP(hAPP(c_Set_Oinsert(U_16186),U_16187),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16183,tc_fun(U_16186,tc_HOL_Obool)),U_16185),U_16188))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16183),U_16184),U_16185)) ),
    inference(definitional_conversion,[status(esa)],[f_4045_2]) ).

cnf(f_4045_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16183,tc_fun(U_16186,tc_HOL_Obool)),U_16185),hAPP(hAPP(c_COMBB(tc_fun(U_16186,tc_HOL_Obool),tc_fun(U_16186,tc_HOL_Obool),U_16183),hAPP(c_Set_Oinsert(U_16186),U_16187)),U_16188)) = hAPP(hAPP(c_Set_Oinsert(U_16186),U_16187),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16183,tc_fun(U_16186,tc_HOL_Obool)),U_16185),U_16188))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16183),U_16184),U_16185)) ),
    inference(clausify,[status(thm)],[f_4045_3]) ).

fof(f_4046_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_4046_2,plain,
    ! [U_16194,U_16193,U_16192,U_16191,U_16190,U_16189] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16189,tc_fun(U_16190,tc_fun(U_16191,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16189,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16190,U_16191),tc_HOL_Obool),tc_fun(U_16190,tc_fun(U_16191,tc_HOL_Obool)),U_16189),hAPP(c_COMBC(U_16190,tc_fun(tc_prod(U_16190,U_16191),tc_HOL_Obool),tc_fun(U_16191,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16191,tc_fun(tc_fun(tc_prod(U_16190,U_16191),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16190,U_16191),tc_HOL_Obool),tc_fun(U_16191,tc_HOL_Obool)),U_16190),c_COMBC(U_16191,tc_fun(tc_prod(U_16190,U_16191),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16191,tc_prod(U_16190,U_16191)),tc_fun(U_16191,tc_fun(tc_fun(tc_prod(U_16190,U_16191),tc_HOL_Obool),tc_HOL_Obool)),U_16190),hAPP(c_COMBB(tc_prod(U_16190,U_16191),tc_fun(tc_fun(tc_prod(U_16190,U_16191),tc_HOL_Obool),tc_HOL_Obool),U_16191),c_member(tc_prod(U_16190,U_16191)))),c_Product__Type_OPair(U_16190,U_16191))))),U_16192)),U_16193),U_16194))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16190,U_16191)),hAPP(hAPP(c_Product__Type_OPair(U_16190,U_16191),U_16193),U_16194)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16189,tc_fun(tc_prod(U_16190,U_16191),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16189,tc_HOL_Obool))),U_16192))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16190,U_16191)),hAPP(hAPP(c_Product__Type_OPair(U_16190,U_16191),U_16193),U_16194)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16189,tc_fun(tc_prod(U_16190,U_16191),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16189,tc_HOL_Obool))),U_16192)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16189,tc_fun(U_16190,tc_fun(U_16191,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16189,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16190,U_16191),tc_HOL_Obool),tc_fun(U_16190,tc_fun(U_16191,tc_HOL_Obool)),U_16189),hAPP(c_COMBC(U_16190,tc_fun(tc_prod(U_16190,U_16191),tc_HOL_Obool),tc_fun(U_16191,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16191,tc_fun(tc_fun(tc_prod(U_16190,U_16191),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16190,U_16191),tc_HOL_Obool),tc_fun(U_16191,tc_HOL_Obool)),U_16190),c_COMBC(U_16191,tc_fun(tc_prod(U_16190,U_16191),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16191,tc_prod(U_16190,U_16191)),tc_fun(U_16191,tc_fun(tc_fun(tc_prod(U_16190,U_16191),tc_HOL_Obool),tc_HOL_Obool)),U_16190),hAPP(c_COMBB(tc_prod(U_16190,U_16191),tc_fun(tc_fun(tc_prod(U_16190,U_16191),tc_HOL_Obool),tc_HOL_Obool),U_16191),c_member(tc_prod(U_16190,U_16191)))),c_Product__Type_OPair(U_16190,U_16191))))),U_16192)),U_16193),U_16194)) ) ),
    inference(variable_rename,[status(thm)],[f_4046_1]) ).

fof(f_4046_3,plain,
    ( ! [U_16206,U_16204,U_16202,U_16200,U_16198,U_16196] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16196,tc_fun(U_16198,tc_fun(U_16200,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16196,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool),tc_fun(U_16198,tc_fun(U_16200,tc_HOL_Obool)),U_16196),hAPP(c_COMBC(U_16198,tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool),tc_fun(U_16200,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16200,tc_fun(tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool),tc_fun(U_16200,tc_HOL_Obool)),U_16198),c_COMBC(U_16200,tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16200,tc_prod(U_16198,U_16200)),tc_fun(U_16200,tc_fun(tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool),tc_HOL_Obool)),U_16198),hAPP(c_COMBB(tc_prod(U_16198,U_16200),tc_fun(tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool),tc_HOL_Obool),U_16200),c_member(tc_prod(U_16198,U_16200)))),c_Product__Type_OPair(U_16198,U_16200))))),U_16202)),U_16204),U_16206))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16198,U_16200)),hAPP(hAPP(c_Product__Type_OPair(U_16198,U_16200),U_16204),U_16206)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16196,tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16196,tc_HOL_Obool))),U_16202))) )
    & ! [U_16205,U_16203,U_16201,U_16199,U_16197,U_16195] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16197,U_16199)),hAPP(hAPP(c_Product__Type_OPair(U_16197,U_16199),U_16203),U_16205)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16195,tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16195,tc_HOL_Obool))),U_16201)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16195,tc_fun(U_16197,tc_fun(U_16199,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16195,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool),tc_fun(U_16197,tc_fun(U_16199,tc_HOL_Obool)),U_16195),hAPP(c_COMBC(U_16197,tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool),tc_fun(U_16199,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16199,tc_fun(tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool),tc_fun(U_16199,tc_HOL_Obool)),U_16197),c_COMBC(U_16199,tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16199,tc_prod(U_16197,U_16199)),tc_fun(U_16199,tc_fun(tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool),tc_HOL_Obool)),U_16197),hAPP(c_COMBB(tc_prod(U_16197,U_16199),tc_fun(tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool),tc_HOL_Obool),U_16199),c_member(tc_prod(U_16197,U_16199)))),c_Product__Type_OPair(U_16197,U_16199))))),U_16201)),U_16203),U_16205)) ) ),
    inference(miniscope,[status(thm)],[f_4046_2]) ).

fof(f_4046_4,plain,
    ( ! [U_16196,U_16198,U_16200,U_16202,U_16204,U_16206] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16196,tc_fun(U_16198,tc_fun(U_16200,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16196,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool),tc_fun(U_16198,tc_fun(U_16200,tc_HOL_Obool)),U_16196),hAPP(c_COMBC(U_16198,tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool),tc_fun(U_16200,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16200,tc_fun(tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool),tc_fun(U_16200,tc_HOL_Obool)),U_16198),c_COMBC(U_16200,tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16200,tc_prod(U_16198,U_16200)),tc_fun(U_16200,tc_fun(tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool),tc_HOL_Obool)),U_16198),hAPP(c_COMBB(tc_prod(U_16198,U_16200),tc_fun(tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool),tc_HOL_Obool),U_16200),c_member(tc_prod(U_16198,U_16200)))),c_Product__Type_OPair(U_16198,U_16200))))),U_16202)),U_16204),U_16206))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16198,U_16200)),hAPP(hAPP(c_Product__Type_OPair(U_16198,U_16200),U_16204),U_16206)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16196,tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16196,tc_HOL_Obool))),U_16202))) )
    & ! [U_16197,U_16201,U_16199,U_16195,U_16203,U_16205] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16197,U_16199)),hAPP(hAPP(c_Product__Type_OPair(U_16197,U_16199),U_16203),U_16205)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16195,tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16195,tc_HOL_Obool))),U_16201)))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16195,tc_fun(U_16197,tc_fun(U_16199,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16195,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool),tc_fun(U_16197,tc_fun(U_16199,tc_HOL_Obool)),U_16195),hAPP(c_COMBC(U_16197,tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool),tc_fun(U_16199,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16199,tc_fun(tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool),tc_fun(U_16199,tc_HOL_Obool)),U_16197),c_COMBC(U_16199,tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16199,tc_prod(U_16197,U_16199)),tc_fun(U_16199,tc_fun(tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool),tc_HOL_Obool)),U_16197),hAPP(c_COMBB(tc_prod(U_16197,U_16199),tc_fun(tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool),tc_HOL_Obool),U_16199),c_member(tc_prod(U_16197,U_16199)))),c_Product__Type_OPair(U_16197,U_16199))))),U_16201)),U_16203),U_16205)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4046_3]) ).

cnf(f_4046_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_16197,U_16199)),hAPP(hAPP(c_Product__Type_OPair(U_16197,U_16199),U_16203),U_16205)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16195,tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16195,tc_HOL_Obool))),U_16201)))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16195,tc_fun(U_16197,tc_fun(U_16199,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16195,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool),tc_fun(U_16197,tc_fun(U_16199,tc_HOL_Obool)),U_16195),hAPP(c_COMBC(U_16197,tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool),tc_fun(U_16199,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16199,tc_fun(tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool),tc_fun(U_16199,tc_HOL_Obool)),U_16197),c_COMBC(U_16199,tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16199,tc_prod(U_16197,U_16199)),tc_fun(U_16199,tc_fun(tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool),tc_HOL_Obool)),U_16197),hAPP(c_COMBB(tc_prod(U_16197,U_16199),tc_fun(tc_fun(tc_prod(U_16197,U_16199),tc_HOL_Obool),tc_HOL_Obool),U_16199),c_member(tc_prod(U_16197,U_16199)))),c_Product__Type_OPair(U_16197,U_16199))))),U_16201)),U_16203),U_16205)) ),
    inference(clausify,[status(thm)],[f_4046_4]) ).

cnf(f_4046_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16196,tc_fun(U_16198,tc_fun(U_16200,tc_HOL_Obool))),c_Orderings_Otop__class_Otop(tc_fun(U_16196,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool),tc_fun(U_16198,tc_fun(U_16200,tc_HOL_Obool)),U_16196),hAPP(c_COMBC(U_16198,tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool),tc_fun(U_16200,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16200,tc_fun(tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool),tc_fun(U_16200,tc_HOL_Obool)),U_16198),c_COMBC(U_16200,tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16200,tc_prod(U_16198,U_16200)),tc_fun(U_16200,tc_fun(tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool),tc_HOL_Obool)),U_16198),hAPP(c_COMBB(tc_prod(U_16198,U_16200),tc_fun(tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool),tc_HOL_Obool),U_16200),c_member(tc_prod(U_16198,U_16200)))),c_Product__Type_OPair(U_16198,U_16200))))),U_16202)),U_16204),U_16206))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_16198,U_16200)),hAPP(hAPP(c_Product__Type_OPair(U_16198,U_16200),U_16204),U_16206)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16196,tc_fun(tc_prod(U_16198,U_16200),tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16196,tc_HOL_Obool))),U_16202))) ),
    inference(clausify,[status(thm)],[f_4046_4]) ).

fof(f_4047_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_4047_2,plain,
    ! [U_16210,U_16209,U_16208,U_16207] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16207,tc_fun(U_16208,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16207,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16208,tc_HOL_Obool),tc_fun(U_16208,tc_HOL_Obool),U_16207),hAPP(c_COMBC(U_16208,tc_fun(U_16208,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16208))),U_16209)),U_16210))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16208),U_16210),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16207,tc_fun(U_16208,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16207,tc_HOL_Obool))),U_16209))) )
      & ( hBOOL(hAPP(hAPP(c_member(U_16208),U_16210),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16207,tc_fun(U_16208,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16207,tc_HOL_Obool))),U_16209)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16207,tc_fun(U_16208,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16207,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16208,tc_HOL_Obool),tc_fun(U_16208,tc_HOL_Obool),U_16207),hAPP(c_COMBC(U_16208,tc_fun(U_16208,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16208))),U_16209)),U_16210)) ) ),
    inference(variable_rename,[status(thm)],[f_4047_1]) ).

fof(f_4047_3,plain,
    ( ! [U_16218,U_16216,U_16214,U_16212] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16212,tc_fun(U_16214,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16212,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16214,tc_HOL_Obool),tc_fun(U_16214,tc_HOL_Obool),U_16212),hAPP(c_COMBC(U_16214,tc_fun(U_16214,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16214))),U_16216)),U_16218))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16214),U_16218),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16212,tc_fun(U_16214,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16212,tc_HOL_Obool))),U_16216))) )
    & ! [U_16217,U_16215,U_16213,U_16211] :
        ( hBOOL(hAPP(hAPP(c_member(U_16213),U_16217),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16211,tc_fun(U_16213,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16211,tc_HOL_Obool))),U_16215)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16211,tc_fun(U_16213,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16211,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16213,tc_HOL_Obool),tc_fun(U_16213,tc_HOL_Obool),U_16211),hAPP(c_COMBC(U_16213,tc_fun(U_16213,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16213))),U_16215)),U_16217)) ) ),
    inference(miniscope,[status(thm)],[f_4047_2]) ).

fof(f_4047_4,plain,
    ( ! [U_16212,U_16214,U_16216,U_16218] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16212,tc_fun(U_16214,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16212,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16214,tc_HOL_Obool),tc_fun(U_16214,tc_HOL_Obool),U_16212),hAPP(c_COMBC(U_16214,tc_fun(U_16214,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16214))),U_16216)),U_16218))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16214),U_16218),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16212,tc_fun(U_16214,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16212,tc_HOL_Obool))),U_16216))) )
    & ! [U_16217,U_16213,U_16211,U_16215] :
        ( hBOOL(hAPP(hAPP(c_member(U_16213),U_16217),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16211,tc_fun(U_16213,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16211,tc_HOL_Obool))),U_16215)))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16211,tc_fun(U_16213,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16211,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16213,tc_HOL_Obool),tc_fun(U_16213,tc_HOL_Obool),U_16211),hAPP(c_COMBC(U_16213,tc_fun(U_16213,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16213))),U_16215)),U_16217)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4047_3]) ).

cnf(f_4047_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16213),U_16217),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16211,tc_fun(U_16213,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16211,tc_HOL_Obool))),U_16215)))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16211,tc_fun(U_16213,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16211,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16213,tc_HOL_Obool),tc_fun(U_16213,tc_HOL_Obool),U_16211),hAPP(c_COMBC(U_16213,tc_fun(U_16213,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16213))),U_16215)),U_16217)) ),
    inference(clausify,[status(thm)],[f_4047_4]) ).

cnf(f_4047_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16212,tc_fun(U_16214,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16212,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_16214,tc_HOL_Obool),tc_fun(U_16214,tc_HOL_Obool),U_16212),hAPP(c_COMBC(U_16214,tc_fun(U_16214,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16214))),U_16216)),U_16218))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16214),U_16218),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16212,tc_fun(U_16214,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16212,tc_HOL_Obool))),U_16216))) ),
    inference(clausify,[status(thm)],[f_4047_4]) ).

fof(f_4048_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_4048_2,plain,
    ! [U_16224,U_16223,U_16222,U_16221] :
      ( ( c_Orderings_Otop__class_Otop(tc_fun(U_16221,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16222,tc_fun(U_16221,tc_HOL_Obool)),U_16223),U_16224)
        | ? [U_16220] :
            ( hAPP(U_16224,U_16220) != c_Orderings_Otop__class_Otop(tc_fun(U_16221,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_16222),U_16220),U_16223)) ) )
      & ( ! [U_16219] :
            ( hAPP(U_16224,U_16219) = c_Orderings_Otop__class_Otop(tc_fun(U_16221,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16222),U_16219),U_16223)) )
        | c_Orderings_Otop__class_Otop(tc_fun(U_16221,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16222,tc_fun(U_16221,tc_HOL_Obool)),U_16223),U_16224) ) ),
    inference(variable_rename,[status(thm)],[f_4048_1]) ).

fof(f_4048_3,plain,
    ( ! [U_16232,U_16230,U_16228,U_16226] :
        ( c_Orderings_Otop__class_Otop(tc_fun(U_16226,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16228,tc_fun(U_16226,tc_HOL_Obool)),U_16230),U_16232)
        | ? [U_16220] :
            ( hAPP(U_16232,U_16220) != c_Orderings_Otop__class_Otop(tc_fun(U_16226,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_16228),U_16220),U_16230)) ) )
    & ! [U_16231,U_16229,U_16227,U_16225] :
        ( ! [U_16219] :
            ( hAPP(U_16231,U_16219) = c_Orderings_Otop__class_Otop(tc_fun(U_16225,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16227),U_16219),U_16229)) )
        | c_Orderings_Otop__class_Otop(tc_fun(U_16225,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16227,tc_fun(U_16225,tc_HOL_Obool)),U_16229),U_16231) ) ),
    inference(miniscope,[status(thm)],[f_4048_2]) ).

fof(f_4048_4,plain,
    ( ! [U_16232,U_16230,U_16228,U_16226] :
        ( c_Orderings_Otop__class_Otop(tc_fun(U_16226,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16228,tc_fun(U_16226,tc_HOL_Obool)),U_16230),U_16232)
        | ( hAPP(U_16232,sK407(U_16232,U_16230,U_16228,U_16226)) != c_Orderings_Otop__class_Otop(tc_fun(U_16226,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_16228),sK407(U_16232,U_16230,U_16228,U_16226)),U_16230)) ) )
    & ! [U_16231,U_16229,U_16227,U_16225] :
        ( ! [U_16219] :
            ( hAPP(U_16231,U_16219) = c_Orderings_Otop__class_Otop(tc_fun(U_16225,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16227),U_16219),U_16229)) )
        | c_Orderings_Otop__class_Otop(tc_fun(U_16225,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16227,tc_fun(U_16225,tc_HOL_Obool)),U_16229),U_16231) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK407]),skolemize(U_16220,sK407(U_16232,U_16230,U_16228,U_16226))],[f_4048_3]) ).

fof(f_4048_5,plain,
    ( ! [U_16228,U_16226,U_16232,U_16230] :
        ( hAPP(U_16232,sK407(U_16232,U_16230,U_16228,U_16226)) != c_Orderings_Otop__class_Otop(tc_fun(U_16226,tc_HOL_Obool))
        | ~ sP1062(U_16228,U_16226,U_16232,U_16230) )
    & ! [U_16228,U_16226,U_16232,U_16230] :
        ( hBOOL(hAPP(hAPP(c_member(U_16228),sK407(U_16232,U_16230,U_16228,U_16226)),U_16230))
        | ~ sP1062(U_16228,U_16226,U_16232,U_16230) )
    & ! [U_16228,U_16226,U_16232,U_16230] :
        ( c_Orderings_Otop__class_Otop(tc_fun(U_16226,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16228,tc_fun(U_16226,tc_HOL_Obool)),U_16230),U_16232)
        | sP1062(U_16228,U_16226,U_16232,U_16230) )
    & ! [U_16219,U_16231,U_16225,U_16229,U_16227] :
        ( hAPP(U_16231,U_16219) = c_Orderings_Otop__class_Otop(tc_fun(U_16225,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16227),U_16219),U_16229))
        | c_Orderings_Otop__class_Otop(tc_fun(U_16225,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16227,tc_fun(U_16225,tc_HOL_Obool)),U_16229),U_16231) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1062])],[f_4048_4]) ).

cnf(f_4048_6,plain,
    ( hAPP(U_16231,U_16219) = c_Orderings_Otop__class_Otop(tc_fun(U_16225,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16227),U_16219),U_16229))
    | c_Orderings_Otop__class_Otop(tc_fun(U_16225,tc_HOL_Obool)) != hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16227,tc_fun(U_16225,tc_HOL_Obool)),U_16229),U_16231) ),
    inference(clausify,[status(thm)],[f_4048_5]) ).

cnf(f_4048_7,plain,
    ( c_Orderings_Otop__class_Otop(tc_fun(U_16226,tc_HOL_Obool)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16228,tc_fun(U_16226,tc_HOL_Obool)),U_16230),U_16232)
    | sP1062(U_16228,U_16226,U_16232,U_16230) ),
    inference(clausify,[status(thm)],[f_4048_5]) ).

cnf(f_4048_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16228),sK407(U_16232,U_16230,U_16228,U_16226)),U_16230))
    | ~ sP1062(U_16228,U_16226,U_16232,U_16230) ),
    inference(clausify,[status(thm)],[f_4048_5]) ).

cnf(f_4048_9,plain,
    ( hAPP(U_16232,sK407(U_16232,U_16230,U_16228,U_16226)) != c_Orderings_Otop__class_Otop(tc_fun(U_16226,tc_HOL_Obool))
    | ~ sP1062(U_16228,U_16226,U_16232,U_16230) ),
    inference(clausify,[status(thm)],[f_4048_5]) ).

fof(f_4049_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_4049_2,plain,
    ! [U_16238,U_16237,U_16236,U_16235] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16235,tc_fun(U_16236,tc_HOL_Obool)),U_16237),U_16238) = c_Orderings_Otop__class_Otop(tc_fun(U_16236,tc_HOL_Obool))
        | ? [U_16234] :
            ( hAPP(U_16238,U_16234) != c_Orderings_Otop__class_Otop(tc_fun(U_16236,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_16235),U_16234),U_16237)) ) )
      & ( ! [U_16233] :
            ( hAPP(U_16238,U_16233) = c_Orderings_Otop__class_Otop(tc_fun(U_16236,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16235),U_16233),U_16237)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16235,tc_fun(U_16236,tc_HOL_Obool)),U_16237),U_16238) != c_Orderings_Otop__class_Otop(tc_fun(U_16236,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4049_1]) ).

fof(f_4049_3,plain,
    ( ! [U_16246,U_16244,U_16242,U_16240] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16240,tc_fun(U_16242,tc_HOL_Obool)),U_16244),U_16246) = c_Orderings_Otop__class_Otop(tc_fun(U_16242,tc_HOL_Obool))
        | ? [U_16234] :
            ( hAPP(U_16246,U_16234) != c_Orderings_Otop__class_Otop(tc_fun(U_16242,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(U_16240),U_16234),U_16244)) ) )
    & ! [U_16245,U_16243,U_16241,U_16239] :
        ( ! [U_16233] :
            ( hAPP(U_16245,U_16233) = c_Orderings_Otop__class_Otop(tc_fun(U_16241,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16239),U_16233),U_16243)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16239,tc_fun(U_16241,tc_HOL_Obool)),U_16243),U_16245) != c_Orderings_Otop__class_Otop(tc_fun(U_16241,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4049_2]) ).

fof(f_4049_4,plain,
    ( ! [U_16246,U_16244,U_16242,U_16240] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16240,tc_fun(U_16242,tc_HOL_Obool)),U_16244),U_16246) = c_Orderings_Otop__class_Otop(tc_fun(U_16242,tc_HOL_Obool))
        | ( hAPP(U_16246,sK408(U_16246,U_16244,U_16242,U_16240)) != c_Orderings_Otop__class_Otop(tc_fun(U_16242,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(U_16240),sK408(U_16246,U_16244,U_16242,U_16240)),U_16244)) ) )
    & ! [U_16245,U_16243,U_16241,U_16239] :
        ( ! [U_16233] :
            ( hAPP(U_16245,U_16233) = c_Orderings_Otop__class_Otop(tc_fun(U_16241,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16239),U_16233),U_16243)) )
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16239,tc_fun(U_16241,tc_HOL_Obool)),U_16243),U_16245) != c_Orderings_Otop__class_Otop(tc_fun(U_16241,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK408]),skolemize(U_16234,sK408(U_16246,U_16244,U_16242,U_16240))],[f_4049_3]) ).

fof(f_4049_5,plain,
    ( ! [U_16244,U_16242,U_16246,U_16240] :
        ( hAPP(U_16246,sK408(U_16246,U_16244,U_16242,U_16240)) != c_Orderings_Otop__class_Otop(tc_fun(U_16242,tc_HOL_Obool))
        | ~ sP1063(U_16244,U_16242,U_16246,U_16240) )
    & ! [U_16244,U_16242,U_16246,U_16240] :
        ( hBOOL(hAPP(hAPP(c_member(U_16240),sK408(U_16246,U_16244,U_16242,U_16240)),U_16244))
        | ~ sP1063(U_16244,U_16242,U_16246,U_16240) )
    & ! [U_16244,U_16242,U_16246,U_16240] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16240,tc_fun(U_16242,tc_HOL_Obool)),U_16244),U_16246) = c_Orderings_Otop__class_Otop(tc_fun(U_16242,tc_HOL_Obool))
        | sP1063(U_16244,U_16242,U_16246,U_16240) )
    & ! [U_16233,U_16245,U_16239,U_16241,U_16243] :
        ( hAPP(U_16245,U_16233) = c_Orderings_Otop__class_Otop(tc_fun(U_16241,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16239),U_16233),U_16243))
        | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16239,tc_fun(U_16241,tc_HOL_Obool)),U_16243),U_16245) != c_Orderings_Otop__class_Otop(tc_fun(U_16241,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1063])],[f_4049_4]) ).

cnf(f_4049_6,plain,
    ( hAPP(U_16245,U_16233) = c_Orderings_Otop__class_Otop(tc_fun(U_16241,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16239),U_16233),U_16243))
    | hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16239,tc_fun(U_16241,tc_HOL_Obool)),U_16243),U_16245) != c_Orderings_Otop__class_Otop(tc_fun(U_16241,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4049_5]) ).

cnf(f_4049_7,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16240,tc_fun(U_16242,tc_HOL_Obool)),U_16244),U_16246) = c_Orderings_Otop__class_Otop(tc_fun(U_16242,tc_HOL_Obool))
    | sP1063(U_16244,U_16242,U_16246,U_16240) ),
    inference(clausify,[status(thm)],[f_4049_5]) ).

cnf(f_4049_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16240),sK408(U_16246,U_16244,U_16242,U_16240)),U_16244))
    | ~ sP1063(U_16244,U_16242,U_16246,U_16240) ),
    inference(clausify,[status(thm)],[f_4049_5]) ).

cnf(f_4049_9,plain,
    ( hAPP(U_16246,sK408(U_16246,U_16244,U_16242,U_16240)) != c_Orderings_Otop__class_Otop(tc_fun(U_16242,tc_HOL_Obool))
    | ~ sP1063(U_16244,U_16242,U_16246,U_16240) ),
    inference(clausify,[status(thm)],[f_4049_5]) ).

fof(f_4050_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_4050_2,plain,
    ! [U_16250,U_16249,U_16248,U_16247] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16248,tc_fun(U_16249,tc_HOL_Obool)),U_16247),hAPP(c_COMBK(tc_fun(U_16249,tc_HOL_Obool),U_16248),U_16250)) = U_16250
        | U_16247 = c_Orderings_Obot__class_Obot(tc_fun(U_16248,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16248,tc_fun(U_16249,tc_HOL_Obool)),U_16247),hAPP(c_COMBK(tc_fun(U_16249,tc_HOL_Obool),U_16248),U_16250)) = c_Orderings_Otop__class_Otop(tc_fun(U_16249,tc_HOL_Obool))
        | U_16247 != c_Orderings_Obot__class_Obot(tc_fun(U_16248,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4050_1]) ).

fof(f_4050_3,plain,
    ( ! [U_16258,U_16256,U_16254,U_16252] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16254,tc_fun(U_16256,tc_HOL_Obool)),U_16252),hAPP(c_COMBK(tc_fun(U_16256,tc_HOL_Obool),U_16254),U_16258)) = U_16258
        | U_16252 = c_Orderings_Obot__class_Obot(tc_fun(U_16254,tc_HOL_Obool)) )
    & ! [U_16257,U_16255,U_16253,U_16251] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16253,tc_fun(U_16255,tc_HOL_Obool)),U_16251),hAPP(c_COMBK(tc_fun(U_16255,tc_HOL_Obool),U_16253),U_16257)) = c_Orderings_Otop__class_Otop(tc_fun(U_16255,tc_HOL_Obool))
        | U_16251 != c_Orderings_Obot__class_Obot(tc_fun(U_16253,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4050_2]) ).

fof(f_4050_4,plain,
    ( ! [U_16252,U_16254,U_16256,U_16258] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16254,tc_fun(U_16256,tc_HOL_Obool)),U_16252),hAPP(c_COMBK(tc_fun(U_16256,tc_HOL_Obool),U_16254),U_16258)) = U_16258
        | U_16252 = c_Orderings_Obot__class_Obot(tc_fun(U_16254,tc_HOL_Obool)) )
    & ! [U_16255,U_16253,U_16257,U_16251] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16253,tc_fun(U_16255,tc_HOL_Obool)),U_16251),hAPP(c_COMBK(tc_fun(U_16255,tc_HOL_Obool),U_16253),U_16257)) = c_Orderings_Otop__class_Otop(tc_fun(U_16255,tc_HOL_Obool))
        | U_16251 != c_Orderings_Obot__class_Obot(tc_fun(U_16253,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4050_3]) ).

cnf(f_4050_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16253,tc_fun(U_16255,tc_HOL_Obool)),U_16251),hAPP(c_COMBK(tc_fun(U_16255,tc_HOL_Obool),U_16253),U_16257)) = c_Orderings_Otop__class_Otop(tc_fun(U_16255,tc_HOL_Obool))
    | U_16251 != c_Orderings_Obot__class_Obot(tc_fun(U_16253,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4050_4]) ).

cnf(f_4050_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16254,tc_fun(U_16256,tc_HOL_Obool)),U_16252),hAPP(c_COMBK(tc_fun(U_16256,tc_HOL_Obool),U_16254),U_16258)) = U_16258
    | U_16252 = c_Orderings_Obot__class_Obot(tc_fun(U_16254,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4050_4]) ).

fof(f_4051_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_4051_2,plain,
    ! [U_16261,U_16260,U_16259] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16259,tc_fun(U_16260,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_16259,tc_HOL_Obool))),U_16261) = c_Orderings_Otop__class_Otop(tc_fun(U_16260,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4051_1]) ).

fof(f_4051_3,plain,
    ! [U_16259,U_16260,U_16261] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16259,tc_fun(U_16260,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_16259,tc_HOL_Obool))),U_16261) = c_Orderings_Otop__class_Otop(tc_fun(U_16260,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4051_2]) ).

cnf(f_4051_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16259,tc_fun(U_16260,tc_HOL_Obool)),c_Orderings_Obot__class_Obot(tc_fun(U_16259,tc_HOL_Obool))),U_16261) = c_Orderings_Otop__class_Otop(tc_fun(U_16260,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4051_3]) ).

fof(f_4052_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_4052_2,plain,
    ! [U_16266,U_16265,U_16264,U_16263,U_16262] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16262,tc_fun(U_16263,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_16262),U_16264),U_16265)),U_16266) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16263,tc_HOL_Obool)),hAPP(U_16266,U_16264)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16262,tc_fun(U_16263,tc_HOL_Obool)),U_16265),U_16266)),
    inference(variable_rename,[status(thm)],[f_4052_1]) ).

fof(f_4052_3,plain,
    ! [U_16262,U_16263,U_16264,U_16265,U_16266] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16262,tc_fun(U_16263,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_16262),U_16264),U_16265)),U_16266) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16263,tc_HOL_Obool)),hAPP(U_16266,U_16264)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16262,tc_fun(U_16263,tc_HOL_Obool)),U_16265),U_16266)),
    inference(definitional_conversion,[status(esa)],[f_4052_2]) ).

cnf(f_4052_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16262,tc_fun(U_16263,tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(U_16262),U_16264),U_16265)),U_16266) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16263,tc_HOL_Obool)),hAPP(U_16266,U_16264)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16262,tc_fun(U_16263,tc_HOL_Obool)),U_16265),U_16266)),
    inference(clausify,[status(thm)],[f_4052_3]) ).

fof(f_4053_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_4053_2,plain,
    ! [U_16271,U_16270,U_16269,U_16268,U_16267] : hAPP(hAPP(c_Set_Oinsert(U_16267),U_16268),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16269,tc_fun(U_16267,tc_HOL_Obool)),U_16270),U_16271)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16269,tc_fun(U_16267,tc_HOL_Obool)),U_16270),hAPP(hAPP(c_COMBB(tc_fun(U_16267,tc_HOL_Obool),tc_fun(U_16267,tc_HOL_Obool),U_16269),hAPP(c_Set_Oinsert(U_16267),U_16268)),U_16271)),
    inference(variable_rename,[status(thm)],[f_4053_1]) ).

fof(f_4053_3,plain,
    ! [U_16267,U_16268,U_16269,U_16270,U_16271] : hAPP(hAPP(c_Set_Oinsert(U_16267),U_16268),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16269,tc_fun(U_16267,tc_HOL_Obool)),U_16270),U_16271)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16269,tc_fun(U_16267,tc_HOL_Obool)),U_16270),hAPP(hAPP(c_COMBB(tc_fun(U_16267,tc_HOL_Obool),tc_fun(U_16267,tc_HOL_Obool),U_16269),hAPP(c_Set_Oinsert(U_16267),U_16268)),U_16271)),
    inference(definitional_conversion,[status(esa)],[f_4053_2]) ).

cnf(f_4053_4,plain,
    hAPP(hAPP(c_Set_Oinsert(U_16267),U_16268),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16269,tc_fun(U_16267,tc_HOL_Obool)),U_16270),U_16271)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16269,tc_fun(U_16267,tc_HOL_Obool)),U_16270),hAPP(hAPP(c_COMBB(tc_fun(U_16267,tc_HOL_Obool),tc_fun(U_16267,tc_HOL_Obool),U_16269),hAPP(c_Set_Oinsert(U_16267),U_16268)),U_16271)),
    inference(clausify,[status(thm)],[f_4053_3]) ).

fof(f_4054_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_4054_2,plain,
    ! [U_16276,U_16275,U_16274,U_16273,U_16272] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16272,tc_fun(U_16273,tc_HOL_Obool)),U_16274),hAPP(hAPP(c_COMBB(tc_fun(U_16273,tc_HOL_Obool),tc_fun(U_16273,tc_HOL_Obool),U_16272),hAPP(c_Set_Oinsert(U_16273),U_16275)),U_16276)) = hAPP(hAPP(c_Set_Oinsert(U_16273),U_16275),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16272,tc_fun(U_16273,tc_HOL_Obool)),U_16274),U_16276)),
    inference(variable_rename,[status(thm)],[f_4054_1]) ).

fof(f_4054_3,plain,
    ! [U_16272,U_16273,U_16274,U_16275,U_16276] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16272,tc_fun(U_16273,tc_HOL_Obool)),U_16274),hAPP(hAPP(c_COMBB(tc_fun(U_16273,tc_HOL_Obool),tc_fun(U_16273,tc_HOL_Obool),U_16272),hAPP(c_Set_Oinsert(U_16273),U_16275)),U_16276)) = hAPP(hAPP(c_Set_Oinsert(U_16273),U_16275),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16272,tc_fun(U_16273,tc_HOL_Obool)),U_16274),U_16276)),
    inference(definitional_conversion,[status(esa)],[f_4054_2]) ).

cnf(f_4054_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16272,tc_fun(U_16273,tc_HOL_Obool)),U_16274),hAPP(hAPP(c_COMBB(tc_fun(U_16273,tc_HOL_Obool),tc_fun(U_16273,tc_HOL_Obool),U_16272),hAPP(c_Set_Oinsert(U_16273),U_16275)),U_16276)) = hAPP(hAPP(c_Set_Oinsert(U_16273),U_16275),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16272,tc_fun(U_16273,tc_HOL_Obool)),U_16274),U_16276)),
    inference(clausify,[status(thm)],[f_4054_3]) ).

fof(f_4055_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_4055_2,plain,
    ! [U_16282,U_16281,U_16280,U_16279,U_16278,U_16277] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16277,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16278,U_16277,U_16279),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16280,tc_fun(U_16278,tc_HOL_Obool)),U_16281),U_16282))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16280,tc_fun(U_16277,tc_HOL_Obool)),U_16281),hAPP(hAPP(c_COMBB(tc_fun(U_16278,tc_HOL_Obool),tc_fun(U_16277,tc_HOL_Obool),U_16280),c_Relation_OImage(U_16278,U_16277,U_16279)),U_16282)))),
    inference(variable_rename,[status(thm)],[f_4055_1]) ).

fof(f_4055_3,plain,
    ! [U_16277,U_16278,U_16279,U_16280,U_16281,U_16282] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16277,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16278,U_16277,U_16279),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16280,tc_fun(U_16278,tc_HOL_Obool)),U_16281),U_16282))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16280,tc_fun(U_16277,tc_HOL_Obool)),U_16281),hAPP(hAPP(c_COMBB(tc_fun(U_16278,tc_HOL_Obool),tc_fun(U_16277,tc_HOL_Obool),U_16280),c_Relation_OImage(U_16278,U_16277,U_16279)),U_16282)))),
    inference(definitional_conversion,[status(esa)],[f_4055_2]) ).

cnf(f_4055_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16277,tc_HOL_Obool)),hAPP(c_Relation_OImage(U_16278,U_16277,U_16279),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16280,tc_fun(U_16278,tc_HOL_Obool)),U_16281),U_16282))),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16280,tc_fun(U_16277,tc_HOL_Obool)),U_16281),hAPP(hAPP(c_COMBB(tc_fun(U_16278,tc_HOL_Obool),tc_fun(U_16277,tc_HOL_Obool),U_16280),c_Relation_OImage(U_16278,U_16277,U_16279)),U_16282)))),
    inference(clausify,[status(thm)],[f_4055_3]) ).

fof(f_4056_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_4056_2,plain,
    ! [U_16286,U_16285,U_16284,U_16283] : hAPP(c_Set_OPow(U_16283),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16284,tc_fun(U_16283,tc_HOL_Obool)),U_16285),U_16286)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16284,tc_fun(tc_fun(U_16283,tc_HOL_Obool),tc_HOL_Obool)),U_16285),hAPP(hAPP(c_COMBB(tc_fun(U_16283,tc_HOL_Obool),tc_fun(tc_fun(U_16283,tc_HOL_Obool),tc_HOL_Obool),U_16284),c_Set_OPow(U_16283)),U_16286)),
    inference(variable_rename,[status(thm)],[f_4056_1]) ).

fof(f_4056_3,plain,
    ! [U_16283,U_16284,U_16285,U_16286] : hAPP(c_Set_OPow(U_16283),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16284,tc_fun(U_16283,tc_HOL_Obool)),U_16285),U_16286)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16284,tc_fun(tc_fun(U_16283,tc_HOL_Obool),tc_HOL_Obool)),U_16285),hAPP(hAPP(c_COMBB(tc_fun(U_16283,tc_HOL_Obool),tc_fun(tc_fun(U_16283,tc_HOL_Obool),tc_HOL_Obool),U_16284),c_Set_OPow(U_16283)),U_16286)),
    inference(definitional_conversion,[status(esa)],[f_4056_2]) ).

cnf(f_4056_4,plain,
    hAPP(c_Set_OPow(U_16283),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16284,tc_fun(U_16283,tc_HOL_Obool)),U_16285),U_16286)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16284,tc_fun(tc_fun(U_16283,tc_HOL_Obool),tc_HOL_Obool)),U_16285),hAPP(hAPP(c_COMBB(tc_fun(U_16283,tc_HOL_Obool),tc_fun(tc_fun(U_16283,tc_HOL_Obool),tc_HOL_Obool),U_16284),c_Set_OPow(U_16283)),U_16286)),
    inference(clausify,[status(thm)],[f_4056_3]) ).

fof(f_4057_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_4057_2,plain,
    ! [U_16293,U_16292,U_16291,U_16290,U_16289] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16289),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16290,U_16289),U_16291),U_16292)),U_16293))
          | ! [U_16288] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16289),hAPP(U_16292,U_16288)),U_16293))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16290),U_16288),U_16291)) ) )
        & ( ? [U_16287] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16289),hAPP(U_16292,U_16287)),U_16293))
              & hBOOL(hAPP(hAPP(c_member(U_16290),U_16287),U_16291)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16289),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16290,U_16289),U_16291),U_16292)),U_16293)) ) )
      | ~ class_Orderings_Olinorder(U_16289)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16289) ),
    inference(variable_rename,[status(thm)],[f_4057_1]) ).

fof(f_4057_3,plain,
    ! [U_16293,U_16292,U_16291,U_16290,U_16289] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16289),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16290,U_16289),U_16291),U_16292)),U_16293))
          | ! [U_16288] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16289),hAPP(U_16292,U_16288)),U_16293))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16290),U_16288),U_16291)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16289),hAPP(U_16292,sK409(U_16293,U_16292,U_16291,U_16290,U_16289))),U_16293))
            & hBOOL(hAPP(hAPP(c_member(U_16290),sK409(U_16293,U_16292,U_16291,U_16290,U_16289)),U_16291)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16289),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16290,U_16289),U_16291),U_16292)),U_16293)) ) )
      | ~ class_Orderings_Olinorder(U_16289)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16289) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK409]),skolemize(U_16287,sK409(U_16293,U_16292,U_16291,U_16290,U_16289))],[f_4057_2]) ).

fof(f_4057_4,plain,
    ( ! [U_16289,U_16290,U_16291,U_16292,U_16293] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16289),hAPP(U_16292,sK409(U_16293,U_16292,U_16291,U_16290,U_16289))),U_16293))
        | ~ sP1064(U_16289,U_16290,U_16291,U_16292,U_16293) )
    & ! [U_16289,U_16290,U_16291,U_16292,U_16293] :
        ( hBOOL(hAPP(hAPP(c_member(U_16290),sK409(U_16293,U_16292,U_16291,U_16290,U_16289)),U_16291))
        | ~ sP1064(U_16289,U_16290,U_16291,U_16292,U_16293) )
    & ! [U_16288,U_16289,U_16290,U_16291,U_16292,U_16293] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16289),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16290,U_16289),U_16291),U_16292)),U_16293))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16289),hAPP(U_16292,U_16288)),U_16293))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16290),U_16288),U_16291))
        | ~ sP1065(U_16288,U_16289,U_16290,U_16291,U_16292,U_16293) )
    & ! [U_16288,U_16289,U_16290,U_16291,U_16292,U_16293] :
        ( sP1064(U_16289,U_16290,U_16291,U_16292,U_16293)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16289),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16290,U_16289),U_16291),U_16292)),U_16293))
        | ~ sP1065(U_16288,U_16289,U_16290,U_16291,U_16292,U_16293) )
    & ! [U_16288,U_16289,U_16290,U_16291,U_16292,U_16293] :
        ( sP1065(U_16288,U_16289,U_16290,U_16291,U_16292,U_16293)
        | ~ class_Orderings_Olinorder(U_16289)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_16289) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1064,sP1065])],[f_4057_3]) ).

cnf(f_4057_5,plain,
    ( sP1065(U_16288,U_16289,U_16290,U_16291,U_16292,U_16293)
    | ~ class_Orderings_Olinorder(U_16289)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16289) ),
    inference(clausify,[status(thm)],[f_4057_4]) ).

cnf(f_4057_6,plain,
    ( sP1064(U_16289,U_16290,U_16291,U_16292,U_16293)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16289),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16290,U_16289),U_16291),U_16292)),U_16293))
    | ~ sP1065(U_16288,U_16289,U_16290,U_16291,U_16292,U_16293) ),
    inference(clausify,[status(thm)],[f_4057_4]) ).

cnf(f_4057_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16289),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16290,U_16289),U_16291),U_16292)),U_16293))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16289),hAPP(U_16292,U_16288)),U_16293))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16290),U_16288),U_16291))
    | ~ sP1065(U_16288,U_16289,U_16290,U_16291,U_16292,U_16293) ),
    inference(clausify,[status(thm)],[f_4057_4]) ).

cnf(f_4057_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16290),sK409(U_16293,U_16292,U_16291,U_16290,U_16289)),U_16291))
    | ~ sP1064(U_16289,U_16290,U_16291,U_16292,U_16293) ),
    inference(clausify,[status(thm)],[f_4057_4]) ).

cnf(f_4057_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16289),hAPP(U_16292,sK409(U_16293,U_16292,U_16291,U_16290,U_16289))),U_16293))
    | ~ sP1064(U_16289,U_16290,U_16291,U_16292,U_16293) ),
    inference(clausify,[status(thm)],[f_4057_4]) ).

fof(f_4058_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_4058_2,plain,
    ! [U_16299,U_16298,U_16297,U_16296,U_16295,U_16294] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16295,U_16294),U_16296),hAPP(hAPP(c_COMBB(tc_fun(U_16297,U_16294),U_16294,U_16295),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16297,U_16294),U_16298)),U_16299)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16297,U_16294),U_16298),hAPP(hAPP(c_COMBB(tc_fun(U_16295,U_16294),U_16294,U_16297),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16295,U_16294),U_16296)),hAPP(c_COMBC(U_16295,U_16297,U_16294),U_16299)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16294) ),
    inference(variable_rename,[status(thm)],[f_4058_1]) ).

fof(f_4058_3,plain,
    ! [U_16296,U_16294,U_16295,U_16297,U_16298,U_16299] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16295,U_16294),U_16296),hAPP(hAPP(c_COMBB(tc_fun(U_16297,U_16294),U_16294,U_16295),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16297,U_16294),U_16298)),U_16299)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16297,U_16294),U_16298),hAPP(hAPP(c_COMBB(tc_fun(U_16295,U_16294),U_16294,U_16297),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16295,U_16294),U_16296)),hAPP(c_COMBC(U_16295,U_16297,U_16294),U_16299)))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16294) ),
    inference(definitional_conversion,[status(esa)],[f_4058_2]) ).

cnf(f_4058_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16295,U_16294),U_16296),hAPP(hAPP(c_COMBB(tc_fun(U_16297,U_16294),U_16294,U_16295),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16297,U_16294),U_16298)),U_16299)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16297,U_16294),U_16298),hAPP(hAPP(c_COMBB(tc_fun(U_16295,U_16294),U_16294,U_16297),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16295,U_16294),U_16296)),hAPP(c_COMBC(U_16295,U_16297,U_16294),U_16299)))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16294) ),
    inference(clausify,[status(thm)],[f_4058_3]) ).

fof(f_4059_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_4059_2,plain,
    ! [U_16305,U_16304,U_16303,U_16302,U_16301,U_16300] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16301,tc_fun(U_16302,U_16300)),U_16303),U_16304),U_16305) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16301,U_16300),U_16303),hAPP(hAPP(c_COMBC(U_16301,U_16302,U_16300),U_16304),U_16305))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16300) ),
    inference(variable_rename,[status(thm)],[f_4059_1]) ).

fof(f_4059_3,plain,
    ! [U_16300,U_16301,U_16302,U_16303,U_16304,U_16305] :
      ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16301,tc_fun(U_16302,U_16300)),U_16303),U_16304),U_16305) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16301,U_16300),U_16303),hAPP(hAPP(c_COMBC(U_16301,U_16302,U_16300),U_16304),U_16305))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16300) ),
    inference(definitional_conversion,[status(esa)],[f_4059_2]) ).

cnf(f_4059_4,plain,
    ( hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16301,tc_fun(U_16302,U_16300)),U_16303),U_16304),U_16305) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16301,U_16300),U_16303),hAPP(hAPP(c_COMBC(U_16301,U_16302,U_16300),U_16304),U_16305))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16300) ),
    inference(clausify,[status(thm)],[f_4059_3]) ).

fof(f_4060_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_4060_2,plain,
    ! [U_16312,U_16311,U_16310,U_16309,U_16308,U_16307,U_16306] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16306,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16307,tc_fun(U_16306,tc_HOL_Obool)),U_16308),U_16309)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16310,tc_fun(U_16306,tc_HOL_Obool)),U_16311),U_16312)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16307,tc_fun(U_16306,tc_HOL_Obool)),U_16308),hAPP(hAPP(c_COMBB(tc_fun(U_16310,tc_fun(U_16306,tc_HOL_Obool)),tc_fun(U_16306,tc_HOL_Obool),U_16307),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16310,tc_fun(U_16306,tc_HOL_Obool)),U_16311)),hAPP(hAPP(c_COMBC(U_16307,tc_fun(U_16310,tc_fun(U_16306,tc_HOL_Obool)),tc_fun(U_16310,tc_fun(U_16306,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16306,tc_HOL_Obool),tc_fun(U_16306,tc_HOL_Obool)),tc_fun(tc_fun(U_16310,tc_fun(U_16306,tc_HOL_Obool)),tc_fun(U_16310,tc_fun(U_16306,tc_HOL_Obool))),U_16307),c_COMBB(tc_fun(U_16306,tc_HOL_Obool),tc_fun(U_16306,tc_HOL_Obool),U_16310)),hAPP(hAPP(c_COMBB(tc_fun(U_16306,tc_HOL_Obool),tc_fun(tc_fun(U_16306,tc_HOL_Obool),tc_fun(U_16306,tc_HOL_Obool)),U_16307),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16306,tc_HOL_Obool))),U_16309))),U_16312))),
    inference(variable_rename,[status(thm)],[f_4060_1]) ).

fof(f_4060_3,plain,
    ! [U_16306,U_16307,U_16308,U_16309,U_16310,U_16311,U_16312] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16306,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16307,tc_fun(U_16306,tc_HOL_Obool)),U_16308),U_16309)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16310,tc_fun(U_16306,tc_HOL_Obool)),U_16311),U_16312)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16307,tc_fun(U_16306,tc_HOL_Obool)),U_16308),hAPP(hAPP(c_COMBB(tc_fun(U_16310,tc_fun(U_16306,tc_HOL_Obool)),tc_fun(U_16306,tc_HOL_Obool),U_16307),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16310,tc_fun(U_16306,tc_HOL_Obool)),U_16311)),hAPP(hAPP(c_COMBC(U_16307,tc_fun(U_16310,tc_fun(U_16306,tc_HOL_Obool)),tc_fun(U_16310,tc_fun(U_16306,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16306,tc_HOL_Obool),tc_fun(U_16306,tc_HOL_Obool)),tc_fun(tc_fun(U_16310,tc_fun(U_16306,tc_HOL_Obool)),tc_fun(U_16310,tc_fun(U_16306,tc_HOL_Obool))),U_16307),c_COMBB(tc_fun(U_16306,tc_HOL_Obool),tc_fun(U_16306,tc_HOL_Obool),U_16310)),hAPP(hAPP(c_COMBB(tc_fun(U_16306,tc_HOL_Obool),tc_fun(tc_fun(U_16306,tc_HOL_Obool),tc_fun(U_16306,tc_HOL_Obool)),U_16307),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16306,tc_HOL_Obool))),U_16309))),U_16312))),
    inference(definitional_conversion,[status(esa)],[f_4060_2]) ).

cnf(f_4060_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16306,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16307,tc_fun(U_16306,tc_HOL_Obool)),U_16308),U_16309)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16310,tc_fun(U_16306,tc_HOL_Obool)),U_16311),U_16312)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16307,tc_fun(U_16306,tc_HOL_Obool)),U_16308),hAPP(hAPP(c_COMBB(tc_fun(U_16310,tc_fun(U_16306,tc_HOL_Obool)),tc_fun(U_16306,tc_HOL_Obool),U_16307),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16310,tc_fun(U_16306,tc_HOL_Obool)),U_16311)),hAPP(hAPP(c_COMBC(U_16307,tc_fun(U_16310,tc_fun(U_16306,tc_HOL_Obool)),tc_fun(U_16310,tc_fun(U_16306,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16306,tc_HOL_Obool),tc_fun(U_16306,tc_HOL_Obool)),tc_fun(tc_fun(U_16310,tc_fun(U_16306,tc_HOL_Obool)),tc_fun(U_16310,tc_fun(U_16306,tc_HOL_Obool))),U_16307),c_COMBB(tc_fun(U_16306,tc_HOL_Obool),tc_fun(U_16306,tc_HOL_Obool),U_16310)),hAPP(hAPP(c_COMBB(tc_fun(U_16306,tc_HOL_Obool),tc_fun(tc_fun(U_16306,tc_HOL_Obool),tc_fun(U_16306,tc_HOL_Obool)),U_16307),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16306,tc_HOL_Obool))),U_16309))),U_16312))),
    inference(clausify,[status(thm)],[f_4060_3]) ).

fof(f_4061_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_4061_2,plain,
    ! [U_16317,U_16316,U_16315,U_16314,U_16313] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16313,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16314,tc_fun(U_16313,tc_HOL_Obool)),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_16315),hAPP(hAPP(c_COMBC(U_16314,tc_fun(U_16313,tc_HOL_Obool),tc_fun(U_16313,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16313,tc_HOL_Obool),tc_fun(tc_fun(U_16313,tc_HOL_Obool),tc_fun(U_16313,tc_HOL_Obool)),U_16314),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16313,tc_HOL_Obool))),U_16316)),U_16317)),
    inference(variable_rename,[status(thm)],[f_4061_1]) ).

fof(f_4061_3,plain,
    ! [U_16313,U_16314,U_16315,U_16316,U_16317] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16313,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16314,tc_fun(U_16313,tc_HOL_Obool)),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_16315),hAPP(hAPP(c_COMBC(U_16314,tc_fun(U_16313,tc_HOL_Obool),tc_fun(U_16313,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16313,tc_HOL_Obool),tc_fun(tc_fun(U_16313,tc_HOL_Obool),tc_fun(U_16313,tc_HOL_Obool)),U_16314),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16313,tc_HOL_Obool))),U_16316)),U_16317)),
    inference(definitional_conversion,[status(esa)],[f_4061_2]) ).

cnf(f_4061_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16313,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16314,tc_fun(U_16313,tc_HOL_Obool)),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_16315),hAPP(hAPP(c_COMBC(U_16314,tc_fun(U_16313,tc_HOL_Obool),tc_fun(U_16313,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16313,tc_HOL_Obool),tc_fun(tc_fun(U_16313,tc_HOL_Obool),tc_fun(U_16313,tc_HOL_Obool)),U_16314),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16313,tc_HOL_Obool))),U_16316)),U_16317)),
    inference(clausify,[status(thm)],[f_4061_3]) ).

fof(f_4062_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_4062_2,plain,
    ! [U_16322,U_16321,U_16320,U_16319,U_16318] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16318,tc_HOL_Obool)),U_16319),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16320,tc_fun(U_16318,tc_HOL_Obool)),U_16321),U_16322)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16320,tc_fun(U_16318,tc_HOL_Obool)),U_16321),hAPP(hAPP(c_COMBB(tc_fun(U_16318,tc_HOL_Obool),tc_fun(U_16318,tc_HOL_Obool),U_16320),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16318,tc_HOL_Obool)),U_16319)),U_16322)),
    inference(variable_rename,[status(thm)],[f_4062_1]) ).

fof(f_4062_3,plain,
    ! [U_16318,U_16319,U_16320,U_16321,U_16322] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16318,tc_HOL_Obool)),U_16319),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16320,tc_fun(U_16318,tc_HOL_Obool)),U_16321),U_16322)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16320,tc_fun(U_16318,tc_HOL_Obool)),U_16321),hAPP(hAPP(c_COMBB(tc_fun(U_16318,tc_HOL_Obool),tc_fun(U_16318,tc_HOL_Obool),U_16320),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16318,tc_HOL_Obool)),U_16319)),U_16322)),
    inference(definitional_conversion,[status(esa)],[f_4062_2]) ).

cnf(f_4062_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16318,tc_HOL_Obool)),U_16319),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16320,tc_fun(U_16318,tc_HOL_Obool)),U_16321),U_16322)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16320,tc_fun(U_16318,tc_HOL_Obool)),U_16321),hAPP(hAPP(c_COMBB(tc_fun(U_16318,tc_HOL_Obool),tc_fun(U_16318,tc_HOL_Obool),U_16320),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16318,tc_HOL_Obool)),U_16319)),U_16322)),
    inference(clausify,[status(thm)],[f_4062_3]) ).

fof(f_4063_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_4063_2,plain,
    ! [U_16327,U_16326,U_16325,U_16324,U_16323] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16323,tc_HOL_Obool)),U_16324),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16325,tc_fun(U_16323,tc_HOL_Obool)),U_16326),U_16327)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16325,tc_fun(U_16323,tc_HOL_Obool)),U_16326),hAPP(hAPP(c_COMBB(tc_fun(U_16323,tc_HOL_Obool),tc_fun(U_16323,tc_HOL_Obool),U_16325),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16323,tc_HOL_Obool)),U_16324)),U_16327)),
    inference(variable_rename,[status(thm)],[f_4063_1]) ).

fof(f_4063_3,plain,
    ! [U_16323,U_16324,U_16325,U_16326,U_16327] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16323,tc_HOL_Obool)),U_16324),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16325,tc_fun(U_16323,tc_HOL_Obool)),U_16326),U_16327)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16325,tc_fun(U_16323,tc_HOL_Obool)),U_16326),hAPP(hAPP(c_COMBB(tc_fun(U_16323,tc_HOL_Obool),tc_fun(U_16323,tc_HOL_Obool),U_16325),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16323,tc_HOL_Obool)),U_16324)),U_16327)),
    inference(definitional_conversion,[status(esa)],[f_4063_2]) ).

cnf(f_4063_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16323,tc_HOL_Obool)),U_16324),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16325,tc_fun(U_16323,tc_HOL_Obool)),U_16326),U_16327)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16325,tc_fun(U_16323,tc_HOL_Obool)),U_16326),hAPP(hAPP(c_COMBB(tc_fun(U_16323,tc_HOL_Obool),tc_fun(U_16323,tc_HOL_Obool),U_16325),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16323,tc_HOL_Obool)),U_16324)),U_16327)),
    inference(clausify,[status(thm)],[f_4063_3]) ).

fof(f_4064_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_4064_2,plain,
    ! [U_16332,U_16331,U_16330,U_16329,U_16328] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16328,tc_fun(U_16329,tc_HOL_Obool)),U_16330),hAPP(hAPP(c_COMBC(U_16328,tc_fun(U_16329,tc_HOL_Obool),tc_fun(U_16329,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16329,tc_HOL_Obool),tc_fun(tc_fun(U_16329,tc_HOL_Obool),tc_fun(U_16329,tc_HOL_Obool)),U_16328),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16329,tc_HOL_Obool))),U_16331)),U_16332)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16329,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16328,tc_fun(U_16329,tc_HOL_Obool)),U_16330),U_16331)),U_16332),
    inference(variable_rename,[status(thm)],[f_4064_1]) ).

fof(f_4064_3,plain,
    ! [U_16328,U_16329,U_16330,U_16331,U_16332] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16328,tc_fun(U_16329,tc_HOL_Obool)),U_16330),hAPP(hAPP(c_COMBC(U_16328,tc_fun(U_16329,tc_HOL_Obool),tc_fun(U_16329,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16329,tc_HOL_Obool),tc_fun(tc_fun(U_16329,tc_HOL_Obool),tc_fun(U_16329,tc_HOL_Obool)),U_16328),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16329,tc_HOL_Obool))),U_16331)),U_16332)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16329,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16328,tc_fun(U_16329,tc_HOL_Obool)),U_16330),U_16331)),U_16332),
    inference(definitional_conversion,[status(esa)],[f_4064_2]) ).

cnf(f_4064_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16328,tc_fun(U_16329,tc_HOL_Obool)),U_16330),hAPP(hAPP(c_COMBC(U_16328,tc_fun(U_16329,tc_HOL_Obool),tc_fun(U_16329,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16329,tc_HOL_Obool),tc_fun(tc_fun(U_16329,tc_HOL_Obool),tc_fun(U_16329,tc_HOL_Obool)),U_16328),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16329,tc_HOL_Obool))),U_16331)),U_16332)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16329,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16328,tc_fun(U_16329,tc_HOL_Obool)),U_16330),U_16331)),U_16332),
    inference(clausify,[status(thm)],[f_4064_3]) ).

fof(f_4065_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_4065_2,plain,
    ! [U_16337,U_16336,U_16335,U_16334,U_16333] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16333,tc_fun(U_16334,tc_HOL_Obool)),U_16335),hAPP(hAPP(c_COMBB(tc_fun(U_16334,tc_HOL_Obool),tc_fun(U_16334,tc_HOL_Obool),U_16333),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16334,tc_HOL_Obool)),U_16336)),U_16337)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16334,tc_HOL_Obool)),U_16336),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16333,tc_fun(U_16334,tc_HOL_Obool)),U_16335),U_16337)),
    inference(variable_rename,[status(thm)],[f_4065_1]) ).

fof(f_4065_3,plain,
    ! [U_16333,U_16334,U_16335,U_16336,U_16337] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16333,tc_fun(U_16334,tc_HOL_Obool)),U_16335),hAPP(hAPP(c_COMBB(tc_fun(U_16334,tc_HOL_Obool),tc_fun(U_16334,tc_HOL_Obool),U_16333),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16334,tc_HOL_Obool)),U_16336)),U_16337)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16334,tc_HOL_Obool)),U_16336),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16333,tc_fun(U_16334,tc_HOL_Obool)),U_16335),U_16337)),
    inference(definitional_conversion,[status(esa)],[f_4065_2]) ).

cnf(f_4065_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16333,tc_fun(U_16334,tc_HOL_Obool)),U_16335),hAPP(hAPP(c_COMBB(tc_fun(U_16334,tc_HOL_Obool),tc_fun(U_16334,tc_HOL_Obool),U_16333),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16334,tc_HOL_Obool)),U_16336)),U_16337)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16334,tc_HOL_Obool)),U_16336),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16333,tc_fun(U_16334,tc_HOL_Obool)),U_16335),U_16337)),
    inference(clausify,[status(thm)],[f_4065_3]) ).

fof(f_4066_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_4066_2,plain,
    ! [U_16344,U_16343,U_16342,U_16341,U_16340] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16340),U_16341),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16342,U_16340),U_16343),U_16344)))
          | ? [U_16339] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16340),U_16341),hAPP(U_16344,U_16339)))
              & hBOOL(hAPP(hAPP(c_member(U_16342),U_16339),U_16343)) ) )
        & ( ! [U_16338] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16340),U_16341),hAPP(U_16344,U_16338)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16342),U_16338),U_16343)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16340),U_16341),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16342,U_16340),U_16343),U_16344))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16340) ),
    inference(variable_rename,[status(thm)],[f_4066_1]) ).

fof(f_4066_3,plain,
    ! [U_16344,U_16343,U_16342,U_16341,U_16340] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16340),U_16341),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16342,U_16340),U_16343),U_16344)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16340),U_16341),hAPP(U_16344,sK410(U_16344,U_16343,U_16342,U_16341,U_16340))))
            & hBOOL(hAPP(hAPP(c_member(U_16342),sK410(U_16344,U_16343,U_16342,U_16341,U_16340)),U_16343)) ) )
        & ( ! [U_16338] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16340),U_16341),hAPP(U_16344,U_16338)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16342),U_16338),U_16343)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16340),U_16341),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16342,U_16340),U_16343),U_16344))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16340) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK410]),skolemize(U_16339,sK410(U_16344,U_16343,U_16342,U_16341,U_16340))],[f_4066_2]) ).

fof(f_4066_4,plain,
    ( ! [U_16340,U_16341,U_16342,U_16343,U_16344] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16340),U_16341),hAPP(U_16344,sK410(U_16344,U_16343,U_16342,U_16341,U_16340))))
        | ~ sP1066(U_16340,U_16341,U_16342,U_16343,U_16344) )
    & ! [U_16340,U_16341,U_16342,U_16343,U_16344] :
        ( hBOOL(hAPP(hAPP(c_member(U_16342),sK410(U_16344,U_16343,U_16342,U_16341,U_16340)),U_16343))
        | ~ sP1066(U_16340,U_16341,U_16342,U_16343,U_16344) )
    & ! [U_16338,U_16340,U_16341,U_16342,U_16343,U_16344] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16340),U_16341),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16342,U_16340),U_16343),U_16344)))
        | sP1066(U_16340,U_16341,U_16342,U_16343,U_16344)
        | ~ sP1067(U_16338,U_16340,U_16341,U_16342,U_16343,U_16344) )
    & ! [U_16338,U_16340,U_16341,U_16342,U_16343,U_16344] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16340),U_16341),hAPP(U_16344,U_16338)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16342),U_16338),U_16343))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16340),U_16341),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16342,U_16340),U_16343),U_16344)))
        | ~ sP1067(U_16338,U_16340,U_16341,U_16342,U_16343,U_16344) )
    & ! [U_16338,U_16340,U_16341,U_16342,U_16343,U_16344] :
        ( sP1067(U_16338,U_16340,U_16341,U_16342,U_16343,U_16344)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_16340) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1066,sP1067])],[f_4066_3]) ).

cnf(f_4066_5,plain,
    ( sP1067(U_16338,U_16340,U_16341,U_16342,U_16343,U_16344)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16340) ),
    inference(clausify,[status(thm)],[f_4066_4]) ).

cnf(f_4066_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16340),U_16341),hAPP(U_16344,U_16338)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16342),U_16338),U_16343))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16340),U_16341),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16342,U_16340),U_16343),U_16344)))
    | ~ sP1067(U_16338,U_16340,U_16341,U_16342,U_16343,U_16344) ),
    inference(clausify,[status(thm)],[f_4066_4]) ).

cnf(f_4066_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16340),U_16341),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16342,U_16340),U_16343),U_16344)))
    | sP1066(U_16340,U_16341,U_16342,U_16343,U_16344)
    | ~ sP1067(U_16338,U_16340,U_16341,U_16342,U_16343,U_16344) ),
    inference(clausify,[status(thm)],[f_4066_4]) ).

cnf(f_4066_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16342),sK410(U_16344,U_16343,U_16342,U_16341,U_16340)),U_16343))
    | ~ sP1066(U_16340,U_16341,U_16342,U_16343,U_16344) ),
    inference(clausify,[status(thm)],[f_4066_4]) ).

cnf(f_4066_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16340),U_16341),hAPP(U_16344,sK410(U_16344,U_16343,U_16342,U_16341,U_16340))))
    | ~ sP1066(U_16340,U_16341,U_16342,U_16343,U_16344) ),
    inference(clausify,[status(thm)],[f_4066_4]) ).

fof(f_4067_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_4067_2,plain,
    ! [U_16351,U_16350,U_16349,U_16348,U_16347] :
      ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16347,tc_HOL_Obool)),U_16348),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16349,tc_fun(U_16347,tc_HOL_Obool)),U_16350),U_16351)))
        | ? [U_16346] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16347,tc_HOL_Obool)),U_16348),hAPP(U_16351,U_16346)))
            & hBOOL(hAPP(hAPP(c_member(U_16349),U_16346),U_16350)) ) )
      & ( ! [U_16345] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16347,tc_HOL_Obool)),U_16348),hAPP(U_16351,U_16345)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16349),U_16345),U_16350)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16347,tc_HOL_Obool)),U_16348),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16349,tc_fun(U_16347,tc_HOL_Obool)),U_16350),U_16351))) ) ),
    inference(variable_rename,[status(thm)],[f_4067_1]) ).

fof(f_4067_3,plain,
    ( ! [U_16361,U_16359,U_16357,U_16355,U_16353] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16353,tc_HOL_Obool)),U_16355),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16357,tc_fun(U_16353,tc_HOL_Obool)),U_16359),U_16361)))
        | ? [U_16346] :
            ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16353,tc_HOL_Obool)),U_16355),hAPP(U_16361,U_16346)))
            & hBOOL(hAPP(hAPP(c_member(U_16357),U_16346),U_16359)) ) )
    & ! [U_16360,U_16358,U_16356,U_16354,U_16352] :
        ( ! [U_16345] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16352,tc_HOL_Obool)),U_16354),hAPP(U_16360,U_16345)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16356),U_16345),U_16358)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16352,tc_HOL_Obool)),U_16354),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16356,tc_fun(U_16352,tc_HOL_Obool)),U_16358),U_16360))) ) ),
    inference(miniscope,[status(thm)],[f_4067_2]) ).

fof(f_4067_4,plain,
    ( ! [U_16361,U_16359,U_16357,U_16355,U_16353] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16353,tc_HOL_Obool)),U_16355),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16357,tc_fun(U_16353,tc_HOL_Obool)),U_16359),U_16361)))
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16353,tc_HOL_Obool)),U_16355),hAPP(U_16361,sK411(U_16361,U_16359,U_16357,U_16355,U_16353))))
          & hBOOL(hAPP(hAPP(c_member(U_16357),sK411(U_16361,U_16359,U_16357,U_16355,U_16353)),U_16359)) ) )
    & ! [U_16360,U_16358,U_16356,U_16354,U_16352] :
        ( ! [U_16345] :
            ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16352,tc_HOL_Obool)),U_16354),hAPP(U_16360,U_16345)))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16356),U_16345),U_16358)) )
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16352,tc_HOL_Obool)),U_16354),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16356,tc_fun(U_16352,tc_HOL_Obool)),U_16358),U_16360))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK411]),skolemize(U_16346,sK411(U_16361,U_16359,U_16357,U_16355,U_16353))],[f_4067_3]) ).

fof(f_4067_5,plain,
    ( ! [U_16355,U_16353,U_16359,U_16357,U_16361] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16353,tc_HOL_Obool)),U_16355),hAPP(U_16361,sK411(U_16361,U_16359,U_16357,U_16355,U_16353))))
        | ~ sP1068(U_16355,U_16353,U_16359,U_16357,U_16361) )
    & ! [U_16355,U_16353,U_16359,U_16357,U_16361] :
        ( hBOOL(hAPP(hAPP(c_member(U_16357),sK411(U_16361,U_16359,U_16357,U_16355,U_16353)),U_16359))
        | ~ sP1068(U_16355,U_16353,U_16359,U_16357,U_16361) )
    & ! [U_16355,U_16353,U_16359,U_16357,U_16361] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16353,tc_HOL_Obool)),U_16355),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16357,tc_fun(U_16353,tc_HOL_Obool)),U_16359),U_16361)))
        | sP1068(U_16355,U_16353,U_16359,U_16357,U_16361) )
    & ! [U_16356,U_16352,U_16345,U_16354,U_16360,U_16358] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16352,tc_HOL_Obool)),U_16354),hAPP(U_16360,U_16345)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16356),U_16345),U_16358))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16352,tc_HOL_Obool)),U_16354),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16356,tc_fun(U_16352,tc_HOL_Obool)),U_16358),U_16360))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1068])],[f_4067_4]) ).

cnf(f_4067_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16352,tc_HOL_Obool)),U_16354),hAPP(U_16360,U_16345)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16356),U_16345),U_16358))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16352,tc_HOL_Obool)),U_16354),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16356,tc_fun(U_16352,tc_HOL_Obool)),U_16358),U_16360))) ),
    inference(clausify,[status(thm)],[f_4067_5]) ).

cnf(f_4067_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16353,tc_HOL_Obool)),U_16355),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16357,tc_fun(U_16353,tc_HOL_Obool)),U_16359),U_16361)))
    | sP1068(U_16355,U_16353,U_16359,U_16357,U_16361) ),
    inference(clausify,[status(thm)],[f_4067_5]) ).

cnf(f_4067_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16357),sK411(U_16361,U_16359,U_16357,U_16355,U_16353)),U_16359))
    | ~ sP1068(U_16355,U_16353,U_16359,U_16357,U_16361) ),
    inference(clausify,[status(thm)],[f_4067_5]) ).

cnf(f_4067_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16353,tc_HOL_Obool)),U_16355),hAPP(U_16361,sK411(U_16361,U_16359,U_16357,U_16355,U_16353))))
    | ~ sP1068(U_16355,U_16353,U_16359,U_16357,U_16361) ),
    inference(clausify,[status(thm)],[f_4067_5]) ).

fof(f_4068_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_4068_2,plain,
    ! [U_16366,U_16365,U_16364,U_16363,U_16362] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16362,tc_fun(U_16363,tc_HOL_Obool)),U_16364),hAPP(hAPP(c_COMBS(U_16362,tc_fun(U_16363,tc_HOL_Obool),tc_fun(U_16363,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16363,tc_HOL_Obool),tc_fun(tc_fun(U_16363,tc_HOL_Obool),tc_fun(U_16363,tc_HOL_Obool)),U_16362),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16363,tc_HOL_Obool))),U_16365)),U_16366)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16363,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16362,tc_fun(U_16363,tc_HOL_Obool)),U_16364),U_16365)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16362,tc_fun(U_16363,tc_HOL_Obool)),U_16364),U_16366)),
    inference(variable_rename,[status(thm)],[f_4068_1]) ).

fof(f_4068_3,plain,
    ! [U_16362,U_16363,U_16364,U_16365,U_16366] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16362,tc_fun(U_16363,tc_HOL_Obool)),U_16364),hAPP(hAPP(c_COMBS(U_16362,tc_fun(U_16363,tc_HOL_Obool),tc_fun(U_16363,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16363,tc_HOL_Obool),tc_fun(tc_fun(U_16363,tc_HOL_Obool),tc_fun(U_16363,tc_HOL_Obool)),U_16362),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16363,tc_HOL_Obool))),U_16365)),U_16366)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16363,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16362,tc_fun(U_16363,tc_HOL_Obool)),U_16364),U_16365)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16362,tc_fun(U_16363,tc_HOL_Obool)),U_16364),U_16366)),
    inference(definitional_conversion,[status(esa)],[f_4068_2]) ).

cnf(f_4068_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16362,tc_fun(U_16363,tc_HOL_Obool)),U_16364),hAPP(hAPP(c_COMBS(U_16362,tc_fun(U_16363,tc_HOL_Obool),tc_fun(U_16363,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16363,tc_HOL_Obool),tc_fun(tc_fun(U_16363,tc_HOL_Obool),tc_fun(U_16363,tc_HOL_Obool)),U_16362),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16363,tc_HOL_Obool))),U_16365)),U_16366)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16363,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16362,tc_fun(U_16363,tc_HOL_Obool)),U_16364),U_16365)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16362,tc_fun(U_16363,tc_HOL_Obool)),U_16364),U_16366)),
    inference(clausify,[status(thm)],[f_4068_3]) ).

fof(f_4069_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_4069_2,plain,
    ! [U_16371,U_16370,U_16369,U_16368,U_16367] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16369,tc_HOL_Obool)),U_16370),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16368,tc_fun(U_16369,tc_HOL_Obool)),U_16367),U_16371)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16368,tc_fun(U_16369,tc_HOL_Obool)),U_16367),hAPP(hAPP(c_COMBB(tc_fun(U_16369,tc_HOL_Obool),tc_fun(U_16369,tc_HOL_Obool),U_16368),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16369,tc_HOL_Obool)),U_16370)),U_16371))
        | U_16367 = c_Orderings_Obot__class_Obot(tc_fun(U_16368,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16369,tc_HOL_Obool)),U_16370),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16368,tc_fun(U_16369,tc_HOL_Obool)),U_16367),U_16371)) = U_16370
        | U_16367 != c_Orderings_Obot__class_Obot(tc_fun(U_16368,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4069_1]) ).

fof(f_4069_3,plain,
    ( ! [U_16381,U_16379,U_16377,U_16375,U_16373] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16377,tc_HOL_Obool)),U_16379),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16375,tc_fun(U_16377,tc_HOL_Obool)),U_16373),U_16381)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16375,tc_fun(U_16377,tc_HOL_Obool)),U_16373),hAPP(hAPP(c_COMBB(tc_fun(U_16377,tc_HOL_Obool),tc_fun(U_16377,tc_HOL_Obool),U_16375),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16377,tc_HOL_Obool)),U_16379)),U_16381))
        | U_16373 = c_Orderings_Obot__class_Obot(tc_fun(U_16375,tc_HOL_Obool)) )
    & ! [U_16380,U_16378,U_16376,U_16374,U_16372] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16376,tc_HOL_Obool)),U_16378),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16374,tc_fun(U_16376,tc_HOL_Obool)),U_16372),U_16380)) = U_16378
        | U_16372 != c_Orderings_Obot__class_Obot(tc_fun(U_16374,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4069_2]) ).

fof(f_4069_4,plain,
    ( ! [U_16373,U_16375,U_16377,U_16379,U_16381] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16377,tc_HOL_Obool)),U_16379),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16375,tc_fun(U_16377,tc_HOL_Obool)),U_16373),U_16381)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16375,tc_fun(U_16377,tc_HOL_Obool)),U_16373),hAPP(hAPP(c_COMBB(tc_fun(U_16377,tc_HOL_Obool),tc_fun(U_16377,tc_HOL_Obool),U_16375),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16377,tc_HOL_Obool)),U_16379)),U_16381))
        | U_16373 = c_Orderings_Obot__class_Obot(tc_fun(U_16375,tc_HOL_Obool)) )
    & ! [U_16376,U_16378,U_16374,U_16372,U_16380] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16376,tc_HOL_Obool)),U_16378),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16374,tc_fun(U_16376,tc_HOL_Obool)),U_16372),U_16380)) = U_16378
        | U_16372 != c_Orderings_Obot__class_Obot(tc_fun(U_16374,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4069_3]) ).

cnf(f_4069_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16376,tc_HOL_Obool)),U_16378),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16374,tc_fun(U_16376,tc_HOL_Obool)),U_16372),U_16380)) = U_16378
    | U_16372 != c_Orderings_Obot__class_Obot(tc_fun(U_16374,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4069_4]) ).

cnf(f_4069_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16377,tc_HOL_Obool)),U_16379),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16375,tc_fun(U_16377,tc_HOL_Obool)),U_16373),U_16381)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16375,tc_fun(U_16377,tc_HOL_Obool)),U_16373),hAPP(hAPP(c_COMBB(tc_fun(U_16377,tc_HOL_Obool),tc_fun(U_16377,tc_HOL_Obool),U_16375),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16377,tc_HOL_Obool)),U_16379)),U_16381))
    | U_16373 = c_Orderings_Obot__class_Obot(tc_fun(U_16375,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4069_4]) ).

fof(f_4070_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_4070_2,plain,
    ! [U_16386,U_16385,U_16384,U_16383,U_16382] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16384,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16383,tc_fun(U_16384,tc_HOL_Obool)),U_16382),U_16385)),U_16386) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16383,tc_fun(U_16384,tc_HOL_Obool)),U_16382),hAPP(hAPP(c_COMBC(U_16383,tc_fun(U_16384,tc_HOL_Obool),tc_fun(U_16384,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16384,tc_HOL_Obool),tc_fun(tc_fun(U_16384,tc_HOL_Obool),tc_fun(U_16384,tc_HOL_Obool)),U_16383),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16384,tc_HOL_Obool))),U_16385)),U_16386))
        | U_16382 = c_Orderings_Obot__class_Obot(tc_fun(U_16383,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16384,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16383,tc_fun(U_16384,tc_HOL_Obool)),U_16382),U_16385)),U_16386) = U_16386
        | U_16382 != c_Orderings_Obot__class_Obot(tc_fun(U_16383,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4070_1]) ).

fof(f_4070_3,plain,
    ( ! [U_16396,U_16394,U_16392,U_16390,U_16388] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16392,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16390,tc_fun(U_16392,tc_HOL_Obool)),U_16388),U_16394)),U_16396) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16390,tc_fun(U_16392,tc_HOL_Obool)),U_16388),hAPP(hAPP(c_COMBC(U_16390,tc_fun(U_16392,tc_HOL_Obool),tc_fun(U_16392,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16392,tc_HOL_Obool),tc_fun(tc_fun(U_16392,tc_HOL_Obool),tc_fun(U_16392,tc_HOL_Obool)),U_16390),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16392,tc_HOL_Obool))),U_16394)),U_16396))
        | U_16388 = c_Orderings_Obot__class_Obot(tc_fun(U_16390,tc_HOL_Obool)) )
    & ! [U_16395,U_16393,U_16391,U_16389,U_16387] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16391,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16389,tc_fun(U_16391,tc_HOL_Obool)),U_16387),U_16393)),U_16395) = U_16395
        | U_16387 != c_Orderings_Obot__class_Obot(tc_fun(U_16389,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4070_2]) ).

fof(f_4070_4,plain,
    ( ! [U_16396,U_16388,U_16390,U_16392,U_16394] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16392,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16390,tc_fun(U_16392,tc_HOL_Obool)),U_16388),U_16394)),U_16396) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16390,tc_fun(U_16392,tc_HOL_Obool)),U_16388),hAPP(hAPP(c_COMBC(U_16390,tc_fun(U_16392,tc_HOL_Obool),tc_fun(U_16392,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16392,tc_HOL_Obool),tc_fun(tc_fun(U_16392,tc_HOL_Obool),tc_fun(U_16392,tc_HOL_Obool)),U_16390),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16392,tc_HOL_Obool))),U_16394)),U_16396))
        | U_16388 = c_Orderings_Obot__class_Obot(tc_fun(U_16390,tc_HOL_Obool)) )
    & ! [U_16389,U_16393,U_16387,U_16395,U_16391] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16391,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16389,tc_fun(U_16391,tc_HOL_Obool)),U_16387),U_16393)),U_16395) = U_16395
        | U_16387 != c_Orderings_Obot__class_Obot(tc_fun(U_16389,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4070_3]) ).

cnf(f_4070_5,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16391,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16389,tc_fun(U_16391,tc_HOL_Obool)),U_16387),U_16393)),U_16395) = U_16395
    | U_16387 != c_Orderings_Obot__class_Obot(tc_fun(U_16389,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4070_4]) ).

cnf(f_4070_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16392,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16390,tc_fun(U_16392,tc_HOL_Obool)),U_16388),U_16394)),U_16396) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16390,tc_fun(U_16392,tc_HOL_Obool)),U_16388),hAPP(hAPP(c_COMBC(U_16390,tc_fun(U_16392,tc_HOL_Obool),tc_fun(U_16392,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16392,tc_HOL_Obool),tc_fun(tc_fun(U_16392,tc_HOL_Obool),tc_fun(U_16392,tc_HOL_Obool)),U_16390),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16392,tc_HOL_Obool))),U_16394)),U_16396))
    | U_16388 = c_Orderings_Obot__class_Obot(tc_fun(U_16390,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4070_4]) ).

fof(f_4071_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_4071_2,plain,
    ! [U_16400,U_16399,U_16398,U_16397] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16399,U_16397),U_16398),hAPP(c_COMBK(U_16397,U_16399),U_16400)) = U_16400
      | U_16398 = c_Orderings_Obot__class_Obot(tc_fun(U_16399,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16397) ),
    inference(variable_rename,[status(thm)],[f_4071_1]) ).

fof(f_4071_3,plain,
    ! [U_16397,U_16399,U_16398,U_16400] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16399,U_16397),U_16398),hAPP(c_COMBK(U_16397,U_16399),U_16400)) = U_16400
      | U_16398 = c_Orderings_Obot__class_Obot(tc_fun(U_16399,tc_HOL_Obool))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16397) ),
    inference(definitional_conversion,[status(esa)],[f_4071_2]) ).

cnf(f_4071_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16399,U_16397),U_16398),hAPP(c_COMBK(U_16397,U_16399),U_16400)) = U_16400
    | U_16398 = c_Orderings_Obot__class_Obot(tc_fun(U_16399,tc_HOL_Obool))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16397) ),
    inference(clausify,[status(thm)],[f_4071_3]) ).

fof(f_4072_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_4072_2,plain,
    ! [U_16405,U_16404,U_16403,U_16402,U_16401] : hAPP(c_Relation_Oconverse(U_16401,U_16402),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16403,tc_fun(tc_prod(U_16401,U_16402),tc_HOL_Obool)),U_16404),U_16405)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16403,tc_fun(tc_prod(U_16402,U_16401),tc_HOL_Obool)),U_16404),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16401,U_16402),tc_HOL_Obool),tc_fun(tc_prod(U_16402,U_16401),tc_HOL_Obool),U_16403),c_Relation_Oconverse(U_16401,U_16402)),U_16405)),
    inference(variable_rename,[status(thm)],[f_4072_1]) ).

fof(f_4072_3,plain,
    ! [U_16401,U_16402,U_16403,U_16404,U_16405] : hAPP(c_Relation_Oconverse(U_16401,U_16402),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16403,tc_fun(tc_prod(U_16401,U_16402),tc_HOL_Obool)),U_16404),U_16405)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16403,tc_fun(tc_prod(U_16402,U_16401),tc_HOL_Obool)),U_16404),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16401,U_16402),tc_HOL_Obool),tc_fun(tc_prod(U_16402,U_16401),tc_HOL_Obool),U_16403),c_Relation_Oconverse(U_16401,U_16402)),U_16405)),
    inference(definitional_conversion,[status(esa)],[f_4072_2]) ).

cnf(f_4072_4,plain,
    hAPP(c_Relation_Oconverse(U_16401,U_16402),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16403,tc_fun(tc_prod(U_16401,U_16402),tc_HOL_Obool)),U_16404),U_16405)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16403,tc_fun(tc_prod(U_16402,U_16401),tc_HOL_Obool)),U_16404),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_16401,U_16402),tc_HOL_Obool),tc_fun(tc_prod(U_16402,U_16401),tc_HOL_Obool),U_16403),c_Relation_Oconverse(U_16401,U_16402)),U_16405)),
    inference(clausify,[status(thm)],[f_4072_3]) ).

fof(f_4073_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_4073_2,plain,
    ! [U_16410,U_16409,U_16408,U_16407,U_16406] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16406,tc_fun(U_16407,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16406,tc_HOL_Obool)),U_16408),U_16409)),U_16410) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16407,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16406,tc_fun(U_16407,tc_HOL_Obool)),U_16408),U_16410)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16406,tc_fun(U_16407,tc_HOL_Obool)),U_16409),U_16410)),
    inference(variable_rename,[status(thm)],[f_4073_1]) ).

fof(f_4073_3,plain,
    ! [U_16406,U_16407,U_16408,U_16409,U_16410] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16406,tc_fun(U_16407,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16406,tc_HOL_Obool)),U_16408),U_16409)),U_16410) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16407,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16406,tc_fun(U_16407,tc_HOL_Obool)),U_16408),U_16410)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16406,tc_fun(U_16407,tc_HOL_Obool)),U_16409),U_16410)),
    inference(definitional_conversion,[status(esa)],[f_4073_2]) ).

cnf(f_4073_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16406,tc_fun(U_16407,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16406,tc_HOL_Obool)),U_16408),U_16409)),U_16410) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16407,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16406,tc_fun(U_16407,tc_HOL_Obool)),U_16408),U_16410)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16406,tc_fun(U_16407,tc_HOL_Obool)),U_16409),U_16410)),
    inference(clausify,[status(thm)],[f_4073_3]) ).

fof(f_4074_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_4074_2,plain,
    ! [U_16416,U_16415,U_16414,U_16413,U_16412,U_16411] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16411,tc_fun(U_16412,tc_HOL_Obool)),U_16413),hAPP(hAPP(c_COMBC(U_16411,tc_fun(U_16414,tc_fun(U_16412,tc_HOL_Obool)),tc_fun(U_16412,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16414,tc_HOL_Obool),tc_fun(tc_fun(U_16414,tc_fun(U_16412,tc_HOL_Obool)),tc_fun(U_16412,tc_HOL_Obool)),U_16411),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16414,tc_fun(U_16412,tc_HOL_Obool))),U_16415)),U_16416)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16414,tc_fun(U_16412,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16411,tc_fun(U_16414,tc_HOL_Obool)),U_16413),U_16415)),U_16416),
    inference(variable_rename,[status(thm)],[f_4074_1]) ).

fof(f_4074_3,plain,
    ! [U_16411,U_16412,U_16413,U_16414,U_16415,U_16416] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16411,tc_fun(U_16412,tc_HOL_Obool)),U_16413),hAPP(hAPP(c_COMBC(U_16411,tc_fun(U_16414,tc_fun(U_16412,tc_HOL_Obool)),tc_fun(U_16412,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16414,tc_HOL_Obool),tc_fun(tc_fun(U_16414,tc_fun(U_16412,tc_HOL_Obool)),tc_fun(U_16412,tc_HOL_Obool)),U_16411),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16414,tc_fun(U_16412,tc_HOL_Obool))),U_16415)),U_16416)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16414,tc_fun(U_16412,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16411,tc_fun(U_16414,tc_HOL_Obool)),U_16413),U_16415)),U_16416),
    inference(definitional_conversion,[status(esa)],[f_4074_2]) ).

cnf(f_4074_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16411,tc_fun(U_16412,tc_HOL_Obool)),U_16413),hAPP(hAPP(c_COMBC(U_16411,tc_fun(U_16414,tc_fun(U_16412,tc_HOL_Obool)),tc_fun(U_16412,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16414,tc_HOL_Obool),tc_fun(tc_fun(U_16414,tc_fun(U_16412,tc_HOL_Obool)),tc_fun(U_16412,tc_HOL_Obool)),U_16411),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16414,tc_fun(U_16412,tc_HOL_Obool))),U_16415)),U_16416)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16414,tc_fun(U_16412,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16411,tc_fun(U_16414,tc_HOL_Obool)),U_16413),U_16415)),U_16416),
    inference(clausify,[status(thm)],[f_4074_3]) ).

fof(f_4075_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_4075_2,plain,
    ! [U_16422,U_16421,U_16420,U_16419,U_16418,U_16417] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16417,tc_fun(U_16418,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16419,tc_fun(U_16417,tc_HOL_Obool)),U_16420),U_16421)),U_16422) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16419,tc_fun(U_16418,tc_HOL_Obool)),U_16420),hAPP(hAPP(c_COMBC(U_16419,tc_fun(U_16417,tc_fun(U_16418,tc_HOL_Obool)),tc_fun(U_16418,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16417,tc_HOL_Obool),tc_fun(tc_fun(U_16417,tc_fun(U_16418,tc_HOL_Obool)),tc_fun(U_16418,tc_HOL_Obool)),U_16419),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16417,tc_fun(U_16418,tc_HOL_Obool))),U_16421)),U_16422)),
    inference(variable_rename,[status(thm)],[f_4075_1]) ).

fof(f_4075_3,plain,
    ! [U_16417,U_16418,U_16419,U_16420,U_16421,U_16422] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16417,tc_fun(U_16418,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16419,tc_fun(U_16417,tc_HOL_Obool)),U_16420),U_16421)),U_16422) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16419,tc_fun(U_16418,tc_HOL_Obool)),U_16420),hAPP(hAPP(c_COMBC(U_16419,tc_fun(U_16417,tc_fun(U_16418,tc_HOL_Obool)),tc_fun(U_16418,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16417,tc_HOL_Obool),tc_fun(tc_fun(U_16417,tc_fun(U_16418,tc_HOL_Obool)),tc_fun(U_16418,tc_HOL_Obool)),U_16419),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16417,tc_fun(U_16418,tc_HOL_Obool))),U_16421)),U_16422)),
    inference(definitional_conversion,[status(esa)],[f_4075_2]) ).

cnf(f_4075_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16417,tc_fun(U_16418,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16419,tc_fun(U_16417,tc_HOL_Obool)),U_16420),U_16421)),U_16422) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16419,tc_fun(U_16418,tc_HOL_Obool)),U_16420),hAPP(hAPP(c_COMBC(U_16419,tc_fun(U_16417,tc_fun(U_16418,tc_HOL_Obool)),tc_fun(U_16418,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16417,tc_HOL_Obool),tc_fun(tc_fun(U_16417,tc_fun(U_16418,tc_HOL_Obool)),tc_fun(U_16418,tc_HOL_Obool)),U_16419),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16417,tc_fun(U_16418,tc_HOL_Obool))),U_16421)),U_16422)),
    inference(clausify,[status(thm)],[f_4075_3]) ).

fof(f_4076_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_4076_2,plain,
    ! [U_16427,U_16426,U_16425,U_16424,U_16423] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16423,tc_HOL_Obool)),U_16424),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16425,tc_fun(U_16423,tc_HOL_Obool)),U_16426),U_16427)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16425,tc_fun(U_16423,tc_HOL_Obool)),U_16426),hAPP(hAPP(c_COMBB(tc_fun(U_16423,tc_HOL_Obool),tc_fun(U_16423,tc_HOL_Obool),U_16425),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16423,tc_HOL_Obool)),U_16424)),U_16427)),
    inference(variable_rename,[status(thm)],[f_4076_1]) ).

fof(f_4076_3,plain,
    ! [U_16423,U_16424,U_16425,U_16426,U_16427] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16423,tc_HOL_Obool)),U_16424),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16425,tc_fun(U_16423,tc_HOL_Obool)),U_16426),U_16427)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16425,tc_fun(U_16423,tc_HOL_Obool)),U_16426),hAPP(hAPP(c_COMBB(tc_fun(U_16423,tc_HOL_Obool),tc_fun(U_16423,tc_HOL_Obool),U_16425),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16423,tc_HOL_Obool)),U_16424)),U_16427)),
    inference(definitional_conversion,[status(esa)],[f_4076_2]) ).

cnf(f_4076_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16423,tc_HOL_Obool)),U_16424),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16425,tc_fun(U_16423,tc_HOL_Obool)),U_16426),U_16427)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16425,tc_fun(U_16423,tc_HOL_Obool)),U_16426),hAPP(hAPP(c_COMBB(tc_fun(U_16423,tc_HOL_Obool),tc_fun(U_16423,tc_HOL_Obool),U_16425),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16423,tc_HOL_Obool)),U_16424)),U_16427)),
    inference(clausify,[status(thm)],[f_4076_3]) ).

fof(f_4077_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_4077_2,plain,
    ! [U_16432,U_16431,U_16430,U_16429,U_16428] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16428,tc_fun(U_16429,tc_HOL_Obool)),U_16430),hAPP(hAPP(c_COMBB(tc_fun(U_16429,tc_HOL_Obool),tc_fun(U_16429,tc_HOL_Obool),U_16428),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16429,tc_HOL_Obool)),U_16431)),U_16432)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16429,tc_HOL_Obool)),U_16431),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16428,tc_fun(U_16429,tc_HOL_Obool)),U_16430),U_16432)),
    inference(variable_rename,[status(thm)],[f_4077_1]) ).

fof(f_4077_3,plain,
    ! [U_16428,U_16429,U_16430,U_16431,U_16432] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16428,tc_fun(U_16429,tc_HOL_Obool)),U_16430),hAPP(hAPP(c_COMBB(tc_fun(U_16429,tc_HOL_Obool),tc_fun(U_16429,tc_HOL_Obool),U_16428),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16429,tc_HOL_Obool)),U_16431)),U_16432)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16429,tc_HOL_Obool)),U_16431),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16428,tc_fun(U_16429,tc_HOL_Obool)),U_16430),U_16432)),
    inference(definitional_conversion,[status(esa)],[f_4077_2]) ).

cnf(f_4077_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16428,tc_fun(U_16429,tc_HOL_Obool)),U_16430),hAPP(hAPP(c_COMBB(tc_fun(U_16429,tc_HOL_Obool),tc_fun(U_16429,tc_HOL_Obool),U_16428),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16429,tc_HOL_Obool)),U_16431)),U_16432)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16429,tc_HOL_Obool)),U_16431),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16428,tc_fun(U_16429,tc_HOL_Obool)),U_16430),U_16432)),
    inference(clausify,[status(thm)],[f_4077_3]) ).

fof(f_4078_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_4078_2,plain,
    ! [U_16436,U_16435,U_16434,U_16433] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16433,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16434,tc_fun(U_16433,tc_HOL_Obool)),U_16435),U_16436)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16434,tc_fun(U_16433,tc_HOL_Obool)),U_16435),hAPP(hAPP(c_COMBB(tc_fun(U_16433,tc_HOL_Obool),tc_fun(U_16433,tc_HOL_Obool),U_16434),c_Groups_Ouminus__class_Ouminus(tc_fun(U_16433,tc_HOL_Obool))),U_16436)),
    inference(variable_rename,[status(thm)],[f_4078_1]) ).

fof(f_4078_3,plain,
    ! [U_16433,U_16434,U_16435,U_16436] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16433,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16434,tc_fun(U_16433,tc_HOL_Obool)),U_16435),U_16436)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16434,tc_fun(U_16433,tc_HOL_Obool)),U_16435),hAPP(hAPP(c_COMBB(tc_fun(U_16433,tc_HOL_Obool),tc_fun(U_16433,tc_HOL_Obool),U_16434),c_Groups_Ouminus__class_Ouminus(tc_fun(U_16433,tc_HOL_Obool))),U_16436)),
    inference(definitional_conversion,[status(esa)],[f_4078_2]) ).

cnf(f_4078_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16433,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16434,tc_fun(U_16433,tc_HOL_Obool)),U_16435),U_16436)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16434,tc_fun(U_16433,tc_HOL_Obool)),U_16435),hAPP(hAPP(c_COMBB(tc_fun(U_16433,tc_HOL_Obool),tc_fun(U_16433,tc_HOL_Obool),U_16434),c_Groups_Ouminus__class_Ouminus(tc_fun(U_16433,tc_HOL_Obool))),U_16436)),
    inference(clausify,[status(thm)],[f_4078_3]) ).

fof(f_4079_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_4079_2,plain,
    ! [U_16440,U_16439,U_16438,U_16437] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16437,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16438,tc_fun(U_16437,tc_HOL_Obool)),U_16439),U_16440)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16438,tc_fun(U_16437,tc_HOL_Obool)),U_16439),hAPP(hAPP(c_COMBB(tc_fun(U_16437,tc_HOL_Obool),tc_fun(U_16437,tc_HOL_Obool),U_16438),c_Groups_Ouminus__class_Ouminus(tc_fun(U_16437,tc_HOL_Obool))),U_16440)),
    inference(variable_rename,[status(thm)],[f_4079_1]) ).

fof(f_4079_3,plain,
    ! [U_16437,U_16438,U_16439,U_16440] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16437,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16438,tc_fun(U_16437,tc_HOL_Obool)),U_16439),U_16440)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16438,tc_fun(U_16437,tc_HOL_Obool)),U_16439),hAPP(hAPP(c_COMBB(tc_fun(U_16437,tc_HOL_Obool),tc_fun(U_16437,tc_HOL_Obool),U_16438),c_Groups_Ouminus__class_Ouminus(tc_fun(U_16437,tc_HOL_Obool))),U_16440)),
    inference(definitional_conversion,[status(esa)],[f_4079_2]) ).

cnf(f_4079_4,plain,
    hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(U_16437,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16438,tc_fun(U_16437,tc_HOL_Obool)),U_16439),U_16440)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16438,tc_fun(U_16437,tc_HOL_Obool)),U_16439),hAPP(hAPP(c_COMBB(tc_fun(U_16437,tc_HOL_Obool),tc_fun(U_16437,tc_HOL_Obool),U_16438),c_Groups_Ouminus__class_Ouminus(tc_fun(U_16437,tc_HOL_Obool))),U_16440)),
    inference(clausify,[status(thm)],[f_4079_3]) ).

fof(f_4080_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_4080_2,plain,
    ! [U_16446,U_16445,U_16444,U_16443,U_16442,U_16441] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16441,tc_fun(U_16442,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_16443,U_16441,U_16444),U_16445)),U_16446) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16443,tc_fun(U_16442,tc_HOL_Obool)),U_16445),hAPP(hAPP(c_COMBB(U_16441,tc_fun(U_16442,tc_HOL_Obool),U_16443),U_16446),U_16444)),
    inference(variable_rename,[status(thm)],[f_4080_1]) ).

fof(f_4080_3,plain,
    ! [U_16441,U_16442,U_16443,U_16444,U_16445,U_16446] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16441,tc_fun(U_16442,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_16443,U_16441,U_16444),U_16445)),U_16446) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16443,tc_fun(U_16442,tc_HOL_Obool)),U_16445),hAPP(hAPP(c_COMBB(U_16441,tc_fun(U_16442,tc_HOL_Obool),U_16443),U_16446),U_16444)),
    inference(definitional_conversion,[status(esa)],[f_4080_2]) ).

cnf(f_4080_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16441,tc_fun(U_16442,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_16443,U_16441,U_16444),U_16445)),U_16446) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16443,tc_fun(U_16442,tc_HOL_Obool)),U_16445),hAPP(hAPP(c_COMBB(U_16441,tc_fun(U_16442,tc_HOL_Obool),U_16443),U_16446),U_16444)),
    inference(clausify,[status(thm)],[f_4080_3]) ).

fof(f_4081_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_4081_2,plain,
    ! [U_16452,U_16451,U_16450,U_16449,U_16448,U_16447] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16447,tc_fun(U_16448,tc_HOL_Obool)),U_16449),hAPP(hAPP(c_COMBB(U_16450,tc_fun(U_16448,tc_HOL_Obool),U_16447),U_16451),U_16452)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16450,tc_fun(U_16448,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_16447,U_16450,U_16452),U_16449)),U_16451),
    inference(variable_rename,[status(thm)],[f_4081_1]) ).

fof(f_4081_3,plain,
    ! [U_16447,U_16448,U_16449,U_16450,U_16451,U_16452] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16447,tc_fun(U_16448,tc_HOL_Obool)),U_16449),hAPP(hAPP(c_COMBB(U_16450,tc_fun(U_16448,tc_HOL_Obool),U_16447),U_16451),U_16452)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16450,tc_fun(U_16448,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_16447,U_16450,U_16452),U_16449)),U_16451),
    inference(definitional_conversion,[status(esa)],[f_4081_2]) ).

cnf(f_4081_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16447,tc_fun(U_16448,tc_HOL_Obool)),U_16449),hAPP(hAPP(c_COMBB(U_16450,tc_fun(U_16448,tc_HOL_Obool),U_16447),U_16451),U_16452)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16450,tc_fun(U_16448,tc_HOL_Obool)),hAPP(c_Set_Oimage(U_16447,U_16450,U_16452),U_16449)),U_16451),
    inference(clausify,[status(thm)],[f_4081_3]) ).

fof(f_4082_1,plain,
    ! [V_Pa_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_Pa_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_Pa_2))),
    inference(fof_nnf,[status(thm)],[fact_Collect__ball__eq]) ).

fof(f_4082_2,plain,
    ! [U_16456,U_16455,U_16454,U_16453] : hAPP(c_Set_OCollect(U_16453),hAPP(hAPP(c_COMBB(tc_fun(U_16454,tc_HOL_Obool),tc_HOL_Obool,U_16453),c_HOL_OAll(U_16454)),hAPP(hAPP(c_COMBB(tc_fun(U_16454,tc_HOL_Obool),tc_fun(U_16454,tc_HOL_Obool),U_16453),hAPP(c_COMBS(U_16454,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16454),c_fimplies),hAPP(hAPP(c_COMBC(U_16454,tc_fun(U_16454,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16454)),U_16455)))),U_16456))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16454,tc_fun(U_16453,tc_HOL_Obool)),U_16455),hAPP(hAPP(c_COMBB(tc_fun(U_16453,tc_HOL_Obool),tc_fun(U_16453,tc_HOL_Obool),U_16454),c_Set_OCollect(U_16453)),hAPP(c_COMBC(U_16453,U_16454,tc_HOL_Obool),U_16456))),
    inference(variable_rename,[status(thm)],[f_4082_1]) ).

fof(f_4082_3,plain,
    ! [U_16453,U_16454,U_16455,U_16456] : hAPP(c_Set_OCollect(U_16453),hAPP(hAPP(c_COMBB(tc_fun(U_16454,tc_HOL_Obool),tc_HOL_Obool,U_16453),c_HOL_OAll(U_16454)),hAPP(hAPP(c_COMBB(tc_fun(U_16454,tc_HOL_Obool),tc_fun(U_16454,tc_HOL_Obool),U_16453),hAPP(c_COMBS(U_16454,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16454),c_fimplies),hAPP(hAPP(c_COMBC(U_16454,tc_fun(U_16454,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16454)),U_16455)))),U_16456))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16454,tc_fun(U_16453,tc_HOL_Obool)),U_16455),hAPP(hAPP(c_COMBB(tc_fun(U_16453,tc_HOL_Obool),tc_fun(U_16453,tc_HOL_Obool),U_16454),c_Set_OCollect(U_16453)),hAPP(c_COMBC(U_16453,U_16454,tc_HOL_Obool),U_16456))),
    inference(definitional_conversion,[status(esa)],[f_4082_2]) ).

cnf(f_4082_4,plain,
    hAPP(c_Set_OCollect(U_16453),hAPP(hAPP(c_COMBB(tc_fun(U_16454,tc_HOL_Obool),tc_HOL_Obool,U_16453),c_HOL_OAll(U_16454)),hAPP(hAPP(c_COMBB(tc_fun(U_16454,tc_HOL_Obool),tc_fun(U_16454,tc_HOL_Obool),U_16453),hAPP(c_COMBS(U_16454,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16454),c_fimplies),hAPP(hAPP(c_COMBC(U_16454,tc_fun(U_16454,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16454)),U_16455)))),U_16456))) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16454,tc_fun(U_16453,tc_HOL_Obool)),U_16455),hAPP(hAPP(c_COMBB(tc_fun(U_16453,tc_HOL_Obool),tc_fun(U_16453,tc_HOL_Obool),U_16454),c_Set_OCollect(U_16453)),hAPP(c_COMBC(U_16453,U_16454,tc_HOL_Obool),U_16456))),
    inference(clausify,[status(thm)],[f_4082_3]) ).

fof(f_4083_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_4083_2,plain,
    ! [U_16457] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16457,tc_HOL_Obool) = c_Set_OBall(U_16457),
    inference(variable_rename,[status(thm)],[f_4083_1]) ).

fof(f_4083_3,plain,
    ! [U_16457] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16457,tc_HOL_Obool) = c_Set_OBall(U_16457),
    inference(definitional_conversion,[status(esa)],[f_4083_2]) ).

cnf(f_4083_4,plain,
    c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16457,tc_HOL_Obool) = c_Set_OBall(U_16457),
    inference(clausify,[status(thm)],[f_4083_3]) ).

fof(f_4084_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_4084_2,plain,
    ! [U_16463,U_16462,U_16461,U_16460,U_16459,U_16458] : hAPP(c_Set_Ovimage(U_16458,U_16459,U_16460),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16461,tc_fun(U_16459,tc_HOL_Obool)),U_16462),U_16463)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16461,tc_fun(U_16458,tc_HOL_Obool)),U_16462),hAPP(hAPP(c_COMBB(tc_fun(U_16459,tc_HOL_Obool),tc_fun(U_16458,tc_HOL_Obool),U_16461),c_Set_Ovimage(U_16458,U_16459,U_16460)),U_16463)),
    inference(variable_rename,[status(thm)],[f_4084_1]) ).

fof(f_4084_3,plain,
    ! [U_16458,U_16459,U_16460,U_16461,U_16462,U_16463] : hAPP(c_Set_Ovimage(U_16458,U_16459,U_16460),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16461,tc_fun(U_16459,tc_HOL_Obool)),U_16462),U_16463)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16461,tc_fun(U_16458,tc_HOL_Obool)),U_16462),hAPP(hAPP(c_COMBB(tc_fun(U_16459,tc_HOL_Obool),tc_fun(U_16458,tc_HOL_Obool),U_16461),c_Set_Ovimage(U_16458,U_16459,U_16460)),U_16463)),
    inference(definitional_conversion,[status(esa)],[f_4084_2]) ).

cnf(f_4084_4,plain,
    hAPP(c_Set_Ovimage(U_16458,U_16459,U_16460),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16461,tc_fun(U_16459,tc_HOL_Obool)),U_16462),U_16463)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16461,tc_fun(U_16458,tc_HOL_Obool)),U_16462),hAPP(hAPP(c_COMBB(tc_fun(U_16459,tc_HOL_Obool),tc_fun(U_16458,tc_HOL_Obool),U_16461),c_Set_Ovimage(U_16458,U_16459,U_16460)),U_16463)),
    inference(clausify,[status(thm)],[f_4084_3]) ).

fof(f_4085_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_4085_2,plain,
    ! [U_16468,U_16467,U_16466,U_16465,U_16464] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16464),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16465,U_16464),U_16467),U_16468)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16465,U_16464),U_16466),U_16468)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16465,tc_HOL_Obool)),U_16466),U_16467))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16464) ),
    inference(variable_rename,[status(thm)],[f_4085_1]) ).

fof(f_4085_3,plain,
    ! [U_16465,U_16464,U_16466,U_16467,U_16468] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16464),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16465,U_16464),U_16467),U_16468)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16465,U_16464),U_16466),U_16468)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16465,tc_HOL_Obool)),U_16466),U_16467))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16464) ),
    inference(definitional_conversion,[status(esa)],[f_4085_2]) ).

cnf(f_4085_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16464),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16465,U_16464),U_16467),U_16468)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16465,U_16464),U_16466),U_16468)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16465,tc_HOL_Obool)),U_16466),U_16467))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16464) ),
    inference(clausify,[status(thm)],[f_4085_3]) ).

fof(f_4086_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_4086_2,plain,
    ! [U_16472,U_16471,U_16470,U_16469] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16469,tc_fun(U_16470,tc_HOL_Obool)),U_16471),U_16472) = hAPP(c_Set_OCollect(U_16470),hAPP(hAPP(c_COMBB(tc_fun(U_16469,tc_HOL_Obool),tc_HOL_Obool,U_16470),c_HOL_OAll(U_16469)),hAPP(hAPP(c_COMBB(tc_fun(U_16469,tc_HOL_Obool),tc_fun(U_16469,tc_HOL_Obool),U_16470),hAPP(c_COMBS(U_16469,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16469),c_fimplies),hAPP(hAPP(c_COMBC(U_16469,tc_fun(U_16469,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16469)),U_16471)))),hAPP(hAPP(c_COMBC(U_16470,tc_fun(U_16469,tc_fun(U_16470,tc_HOL_Obool)),tc_fun(U_16469,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16470,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_16469,tc_fun(U_16470,tc_HOL_Obool)),tc_fun(U_16469,tc_HOL_Obool)),U_16470),c_COMBB(tc_fun(U_16470,tc_HOL_Obool),tc_HOL_Obool,U_16469)),c_member(U_16470))),U_16472)))),
    inference(variable_rename,[status(thm)],[f_4086_1]) ).

fof(f_4086_3,plain,
    ! [U_16469,U_16470,U_16471,U_16472] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16469,tc_fun(U_16470,tc_HOL_Obool)),U_16471),U_16472) = hAPP(c_Set_OCollect(U_16470),hAPP(hAPP(c_COMBB(tc_fun(U_16469,tc_HOL_Obool),tc_HOL_Obool,U_16470),c_HOL_OAll(U_16469)),hAPP(hAPP(c_COMBB(tc_fun(U_16469,tc_HOL_Obool),tc_fun(U_16469,tc_HOL_Obool),U_16470),hAPP(c_COMBS(U_16469,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16469),c_fimplies),hAPP(hAPP(c_COMBC(U_16469,tc_fun(U_16469,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16469)),U_16471)))),hAPP(hAPP(c_COMBC(U_16470,tc_fun(U_16469,tc_fun(U_16470,tc_HOL_Obool)),tc_fun(U_16469,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16470,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_16469,tc_fun(U_16470,tc_HOL_Obool)),tc_fun(U_16469,tc_HOL_Obool)),U_16470),c_COMBB(tc_fun(U_16470,tc_HOL_Obool),tc_HOL_Obool,U_16469)),c_member(U_16470))),U_16472)))),
    inference(definitional_conversion,[status(esa)],[f_4086_2]) ).

cnf(f_4086_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16469,tc_fun(U_16470,tc_HOL_Obool)),U_16471),U_16472) = hAPP(c_Set_OCollect(U_16470),hAPP(hAPP(c_COMBB(tc_fun(U_16469,tc_HOL_Obool),tc_HOL_Obool,U_16470),c_HOL_OAll(U_16469)),hAPP(hAPP(c_COMBB(tc_fun(U_16469,tc_HOL_Obool),tc_fun(U_16469,tc_HOL_Obool),U_16470),hAPP(c_COMBS(U_16469,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16469),c_fimplies),hAPP(hAPP(c_COMBC(U_16469,tc_fun(U_16469,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16469)),U_16471)))),hAPP(hAPP(c_COMBC(U_16470,tc_fun(U_16469,tc_fun(U_16470,tc_HOL_Obool)),tc_fun(U_16469,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16470,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_16469,tc_fun(U_16470,tc_HOL_Obool)),tc_fun(U_16469,tc_HOL_Obool)),U_16470),c_COMBB(tc_fun(U_16470,tc_HOL_Obool),tc_HOL_Obool,U_16469)),c_member(U_16470))),U_16472)))),
    inference(clausify,[status(thm)],[f_4086_3]) ).

fof(f_4087_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_4087_2,plain,
    ! [U_16477,U_16476,U_16475,U_16474,U_16473] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16474,tc_fun(U_16475,tc_HOL_Obool)),U_16473),hAPP(hAPP(c_COMBC(U_16474,tc_fun(U_16475,tc_HOL_Obool),tc_fun(U_16475,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16475,tc_HOL_Obool),tc_fun(tc_fun(U_16475,tc_HOL_Obool),tc_fun(U_16475,tc_HOL_Obool)),U_16474),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16475,tc_HOL_Obool))),U_16476)),U_16477)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16475,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16474,tc_fun(U_16475,tc_HOL_Obool)),U_16473),U_16476)),U_16477)
        | U_16473 = c_Orderings_Obot__class_Obot(tc_fun(U_16474,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16474,tc_fun(U_16475,tc_HOL_Obool)),U_16473),hAPP(hAPP(c_COMBC(U_16474,tc_fun(U_16475,tc_HOL_Obool),tc_fun(U_16475,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16475,tc_HOL_Obool),tc_fun(tc_fun(U_16475,tc_HOL_Obool),tc_fun(U_16475,tc_HOL_Obool)),U_16474),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16475,tc_HOL_Obool))),U_16476)),U_16477)) = c_Orderings_Otop__class_Otop(tc_fun(U_16475,tc_HOL_Obool))
        | U_16473 != c_Orderings_Obot__class_Obot(tc_fun(U_16474,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4087_1]) ).

fof(f_4087_3,plain,
    ( ! [U_16487,U_16485,U_16483,U_16481,U_16479] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16481,tc_fun(U_16483,tc_HOL_Obool)),U_16479),hAPP(hAPP(c_COMBC(U_16481,tc_fun(U_16483,tc_HOL_Obool),tc_fun(U_16483,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16483,tc_HOL_Obool),tc_fun(tc_fun(U_16483,tc_HOL_Obool),tc_fun(U_16483,tc_HOL_Obool)),U_16481),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16483,tc_HOL_Obool))),U_16485)),U_16487)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16483,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16481,tc_fun(U_16483,tc_HOL_Obool)),U_16479),U_16485)),U_16487)
        | U_16479 = c_Orderings_Obot__class_Obot(tc_fun(U_16481,tc_HOL_Obool)) )
    & ! [U_16486,U_16484,U_16482,U_16480,U_16478] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16480,tc_fun(U_16482,tc_HOL_Obool)),U_16478),hAPP(hAPP(c_COMBC(U_16480,tc_fun(U_16482,tc_HOL_Obool),tc_fun(U_16482,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16482,tc_HOL_Obool),tc_fun(tc_fun(U_16482,tc_HOL_Obool),tc_fun(U_16482,tc_HOL_Obool)),U_16480),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16482,tc_HOL_Obool))),U_16484)),U_16486)) = c_Orderings_Otop__class_Otop(tc_fun(U_16482,tc_HOL_Obool))
        | U_16478 != c_Orderings_Obot__class_Obot(tc_fun(U_16480,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4087_2]) ).

fof(f_4087_4,plain,
    ( ! [U_16479,U_16481,U_16483,U_16485,U_16487] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16481,tc_fun(U_16483,tc_HOL_Obool)),U_16479),hAPP(hAPP(c_COMBC(U_16481,tc_fun(U_16483,tc_HOL_Obool),tc_fun(U_16483,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16483,tc_HOL_Obool),tc_fun(tc_fun(U_16483,tc_HOL_Obool),tc_fun(U_16483,tc_HOL_Obool)),U_16481),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16483,tc_HOL_Obool))),U_16485)),U_16487)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16483,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16481,tc_fun(U_16483,tc_HOL_Obool)),U_16479),U_16485)),U_16487)
        | U_16479 = c_Orderings_Obot__class_Obot(tc_fun(U_16481,tc_HOL_Obool)) )
    & ! [U_16484,U_16480,U_16478,U_16482,U_16486] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16480,tc_fun(U_16482,tc_HOL_Obool)),U_16478),hAPP(hAPP(c_COMBC(U_16480,tc_fun(U_16482,tc_HOL_Obool),tc_fun(U_16482,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16482,tc_HOL_Obool),tc_fun(tc_fun(U_16482,tc_HOL_Obool),tc_fun(U_16482,tc_HOL_Obool)),U_16480),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16482,tc_HOL_Obool))),U_16484)),U_16486)) = c_Orderings_Otop__class_Otop(tc_fun(U_16482,tc_HOL_Obool))
        | U_16478 != c_Orderings_Obot__class_Obot(tc_fun(U_16480,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4087_3]) ).

cnf(f_4087_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16480,tc_fun(U_16482,tc_HOL_Obool)),U_16478),hAPP(hAPP(c_COMBC(U_16480,tc_fun(U_16482,tc_HOL_Obool),tc_fun(U_16482,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16482,tc_HOL_Obool),tc_fun(tc_fun(U_16482,tc_HOL_Obool),tc_fun(U_16482,tc_HOL_Obool)),U_16480),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16482,tc_HOL_Obool))),U_16484)),U_16486)) = c_Orderings_Otop__class_Otop(tc_fun(U_16482,tc_HOL_Obool))
    | U_16478 != c_Orderings_Obot__class_Obot(tc_fun(U_16480,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4087_4]) ).

cnf(f_4087_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16481,tc_fun(U_16483,tc_HOL_Obool)),U_16479),hAPP(hAPP(c_COMBC(U_16481,tc_fun(U_16483,tc_HOL_Obool),tc_fun(U_16483,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16483,tc_HOL_Obool),tc_fun(tc_fun(U_16483,tc_HOL_Obool),tc_fun(U_16483,tc_HOL_Obool)),U_16481),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16483,tc_HOL_Obool))),U_16485)),U_16487)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16483,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16481,tc_fun(U_16483,tc_HOL_Obool)),U_16479),U_16485)),U_16487)
    | U_16479 = c_Orderings_Obot__class_Obot(tc_fun(U_16481,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4087_4]) ).

fof(f_4088_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_4088_2,plain,
    ! [U_16492,U_16491,U_16490,U_16489,U_16488] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16489,tc_fun(U_16490,tc_HOL_Obool)),U_16488),hAPP(hAPP(c_COMBB(tc_fun(U_16490,tc_HOL_Obool),tc_fun(U_16490,tc_HOL_Obool),U_16489),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16490,tc_HOL_Obool)),U_16491)),U_16492)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16490,tc_HOL_Obool)),U_16491),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16489,tc_fun(U_16490,tc_HOL_Obool)),U_16488),U_16492))
        | U_16488 = c_Orderings_Obot__class_Obot(tc_fun(U_16489,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16489,tc_fun(U_16490,tc_HOL_Obool)),U_16488),hAPP(hAPP(c_COMBB(tc_fun(U_16490,tc_HOL_Obool),tc_fun(U_16490,tc_HOL_Obool),U_16489),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16490,tc_HOL_Obool)),U_16491)),U_16492)) = c_Orderings_Otop__class_Otop(tc_fun(U_16490,tc_HOL_Obool))
        | U_16488 != c_Orderings_Obot__class_Obot(tc_fun(U_16489,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4088_1]) ).

fof(f_4088_3,plain,
    ( ! [U_16502,U_16500,U_16498,U_16496,U_16494] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16496,tc_fun(U_16498,tc_HOL_Obool)),U_16494),hAPP(hAPP(c_COMBB(tc_fun(U_16498,tc_HOL_Obool),tc_fun(U_16498,tc_HOL_Obool),U_16496),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16498,tc_HOL_Obool)),U_16500)),U_16502)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16498,tc_HOL_Obool)),U_16500),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16496,tc_fun(U_16498,tc_HOL_Obool)),U_16494),U_16502))
        | U_16494 = c_Orderings_Obot__class_Obot(tc_fun(U_16496,tc_HOL_Obool)) )
    & ! [U_16501,U_16499,U_16497,U_16495,U_16493] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16495,tc_fun(U_16497,tc_HOL_Obool)),U_16493),hAPP(hAPP(c_COMBB(tc_fun(U_16497,tc_HOL_Obool),tc_fun(U_16497,tc_HOL_Obool),U_16495),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16497,tc_HOL_Obool)),U_16499)),U_16501)) = c_Orderings_Otop__class_Otop(tc_fun(U_16497,tc_HOL_Obool))
        | U_16493 != c_Orderings_Obot__class_Obot(tc_fun(U_16495,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4088_2]) ).

fof(f_4088_4,plain,
    ( ! [U_16494,U_16496,U_16498,U_16500,U_16502] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16496,tc_fun(U_16498,tc_HOL_Obool)),U_16494),hAPP(hAPP(c_COMBB(tc_fun(U_16498,tc_HOL_Obool),tc_fun(U_16498,tc_HOL_Obool),U_16496),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16498,tc_HOL_Obool)),U_16500)),U_16502)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16498,tc_HOL_Obool)),U_16500),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16496,tc_fun(U_16498,tc_HOL_Obool)),U_16494),U_16502))
        | U_16494 = c_Orderings_Obot__class_Obot(tc_fun(U_16496,tc_HOL_Obool)) )
    & ! [U_16499,U_16495,U_16493,U_16497,U_16501] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16495,tc_fun(U_16497,tc_HOL_Obool)),U_16493),hAPP(hAPP(c_COMBB(tc_fun(U_16497,tc_HOL_Obool),tc_fun(U_16497,tc_HOL_Obool),U_16495),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16497,tc_HOL_Obool)),U_16499)),U_16501)) = c_Orderings_Otop__class_Otop(tc_fun(U_16497,tc_HOL_Obool))
        | U_16493 != c_Orderings_Obot__class_Obot(tc_fun(U_16495,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4088_3]) ).

cnf(f_4088_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16495,tc_fun(U_16497,tc_HOL_Obool)),U_16493),hAPP(hAPP(c_COMBB(tc_fun(U_16497,tc_HOL_Obool),tc_fun(U_16497,tc_HOL_Obool),U_16495),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16497,tc_HOL_Obool)),U_16499)),U_16501)) = c_Orderings_Otop__class_Otop(tc_fun(U_16497,tc_HOL_Obool))
    | U_16493 != c_Orderings_Obot__class_Obot(tc_fun(U_16495,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4088_4]) ).

cnf(f_4088_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16496,tc_fun(U_16498,tc_HOL_Obool)),U_16494),hAPP(hAPP(c_COMBB(tc_fun(U_16498,tc_HOL_Obool),tc_fun(U_16498,tc_HOL_Obool),U_16496),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16498,tc_HOL_Obool)),U_16500)),U_16502)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16498,tc_HOL_Obool)),U_16500),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16496,tc_fun(U_16498,tc_HOL_Obool)),U_16494),U_16502))
    | U_16494 = c_Orderings_Obot__class_Obot(tc_fun(U_16496,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4088_4]) ).

fof(f_4089_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_4089_2,plain,
    ! [U_16507,U_16506,U_16505,U_16504,U_16503] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16505,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16504,tc_fun(U_16505,tc_HOL_Obool)),U_16503),U_16506)),U_16507) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16504,tc_fun(U_16505,tc_HOL_Obool)),U_16503),hAPP(hAPP(c_COMBC(U_16504,tc_fun(U_16505,tc_HOL_Obool),tc_fun(U_16505,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16505,tc_HOL_Obool),tc_fun(tc_fun(U_16505,tc_HOL_Obool),tc_fun(U_16505,tc_HOL_Obool)),U_16504),c_Groups_Ominus__class_Ominus(tc_fun(U_16505,tc_HOL_Obool))),U_16506)),U_16507))
        | U_16503 = c_Orderings_Obot__class_Obot(tc_fun(U_16504,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16505,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16504,tc_fun(U_16505,tc_HOL_Obool)),U_16503),U_16506)),U_16507) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16505,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16505,tc_HOL_Obool))),U_16507)
        | U_16503 != c_Orderings_Obot__class_Obot(tc_fun(U_16504,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4089_1]) ).

fof(f_4089_3,plain,
    ( ! [U_16517,U_16515,U_16513,U_16511,U_16509] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16513,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16511,tc_fun(U_16513,tc_HOL_Obool)),U_16509),U_16515)),U_16517) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16511,tc_fun(U_16513,tc_HOL_Obool)),U_16509),hAPP(hAPP(c_COMBC(U_16511,tc_fun(U_16513,tc_HOL_Obool),tc_fun(U_16513,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16513,tc_HOL_Obool),tc_fun(tc_fun(U_16513,tc_HOL_Obool),tc_fun(U_16513,tc_HOL_Obool)),U_16511),c_Groups_Ominus__class_Ominus(tc_fun(U_16513,tc_HOL_Obool))),U_16515)),U_16517))
        | U_16509 = c_Orderings_Obot__class_Obot(tc_fun(U_16511,tc_HOL_Obool)) )
    & ! [U_16516,U_16514,U_16512,U_16510,U_16508] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16512,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16510,tc_fun(U_16512,tc_HOL_Obool)),U_16508),U_16514)),U_16516) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16512,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16512,tc_HOL_Obool))),U_16516)
        | U_16508 != c_Orderings_Obot__class_Obot(tc_fun(U_16510,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4089_2]) ).

fof(f_4089_4,plain,
    ( ! [U_16509,U_16511,U_16513,U_16515,U_16517] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16513,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16511,tc_fun(U_16513,tc_HOL_Obool)),U_16509),U_16515)),U_16517) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16511,tc_fun(U_16513,tc_HOL_Obool)),U_16509),hAPP(hAPP(c_COMBC(U_16511,tc_fun(U_16513,tc_HOL_Obool),tc_fun(U_16513,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16513,tc_HOL_Obool),tc_fun(tc_fun(U_16513,tc_HOL_Obool),tc_fun(U_16513,tc_HOL_Obool)),U_16511),c_Groups_Ominus__class_Ominus(tc_fun(U_16513,tc_HOL_Obool))),U_16515)),U_16517))
        | U_16509 = c_Orderings_Obot__class_Obot(tc_fun(U_16511,tc_HOL_Obool)) )
    & ! [U_16514,U_16510,U_16508,U_16516,U_16512] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16512,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16510,tc_fun(U_16512,tc_HOL_Obool)),U_16508),U_16514)),U_16516) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16512,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16512,tc_HOL_Obool))),U_16516)
        | U_16508 != c_Orderings_Obot__class_Obot(tc_fun(U_16510,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4089_3]) ).

cnf(f_4089_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16512,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16510,tc_fun(U_16512,tc_HOL_Obool)),U_16508),U_16514)),U_16516) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16512,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(U_16512,tc_HOL_Obool))),U_16516)
    | U_16508 != c_Orderings_Obot__class_Obot(tc_fun(U_16510,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4089_4]) ).

cnf(f_4089_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16513,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16511,tc_fun(U_16513,tc_HOL_Obool)),U_16509),U_16515)),U_16517) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16511,tc_fun(U_16513,tc_HOL_Obool)),U_16509),hAPP(hAPP(c_COMBC(U_16511,tc_fun(U_16513,tc_HOL_Obool),tc_fun(U_16513,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16513,tc_HOL_Obool),tc_fun(tc_fun(U_16513,tc_HOL_Obool),tc_fun(U_16513,tc_HOL_Obool)),U_16511),c_Groups_Ominus__class_Ominus(tc_fun(U_16513,tc_HOL_Obool))),U_16515)),U_16517))
    | U_16509 = c_Orderings_Obot__class_Obot(tc_fun(U_16511,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4089_4]) ).

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_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_4090_2,plain,
    ! [U_16522,U_16521,U_16520,U_16519,U_16518] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16519,tc_fun(U_16520,tc_HOL_Obool)),U_16518),hAPP(hAPP(c_COMBC(U_16519,tc_fun(U_16520,tc_HOL_Obool),tc_fun(U_16520,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16520,tc_HOL_Obool),tc_fun(tc_fun(U_16520,tc_HOL_Obool),tc_fun(U_16520,tc_HOL_Obool)),U_16519),c_Groups_Ominus__class_Ominus(tc_fun(U_16520,tc_HOL_Obool))),U_16521)),U_16522)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16520,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16519,tc_fun(U_16520,tc_HOL_Obool)),U_16518),U_16521)),U_16522)
        | U_16518 = c_Orderings_Obot__class_Obot(tc_fun(U_16519,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16519,tc_fun(U_16520,tc_HOL_Obool)),U_16518),hAPP(hAPP(c_COMBC(U_16519,tc_fun(U_16520,tc_HOL_Obool),tc_fun(U_16520,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16520,tc_HOL_Obool),tc_fun(tc_fun(U_16520,tc_HOL_Obool),tc_fun(U_16520,tc_HOL_Obool)),U_16519),c_Groups_Ominus__class_Ominus(tc_fun(U_16520,tc_HOL_Obool))),U_16521)),U_16522)) = c_Orderings_Otop__class_Otop(tc_fun(U_16520,tc_HOL_Obool))
        | U_16518 != c_Orderings_Obot__class_Obot(tc_fun(U_16519,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4090_1]) ).

fof(f_4090_3,plain,
    ( ! [U_16532,U_16530,U_16528,U_16526,U_16524] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16526,tc_fun(U_16528,tc_HOL_Obool)),U_16524),hAPP(hAPP(c_COMBC(U_16526,tc_fun(U_16528,tc_HOL_Obool),tc_fun(U_16528,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16528,tc_HOL_Obool),tc_fun(tc_fun(U_16528,tc_HOL_Obool),tc_fun(U_16528,tc_HOL_Obool)),U_16526),c_Groups_Ominus__class_Ominus(tc_fun(U_16528,tc_HOL_Obool))),U_16530)),U_16532)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16528,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16526,tc_fun(U_16528,tc_HOL_Obool)),U_16524),U_16530)),U_16532)
        | U_16524 = c_Orderings_Obot__class_Obot(tc_fun(U_16526,tc_HOL_Obool)) )
    & ! [U_16531,U_16529,U_16527,U_16525,U_16523] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16525,tc_fun(U_16527,tc_HOL_Obool)),U_16523),hAPP(hAPP(c_COMBC(U_16525,tc_fun(U_16527,tc_HOL_Obool),tc_fun(U_16527,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16527,tc_HOL_Obool),tc_fun(tc_fun(U_16527,tc_HOL_Obool),tc_fun(U_16527,tc_HOL_Obool)),U_16525),c_Groups_Ominus__class_Ominus(tc_fun(U_16527,tc_HOL_Obool))),U_16529)),U_16531)) = c_Orderings_Otop__class_Otop(tc_fun(U_16527,tc_HOL_Obool))
        | U_16523 != c_Orderings_Obot__class_Obot(tc_fun(U_16525,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4090_2]) ).

fof(f_4090_4,plain,
    ( ! [U_16524,U_16526,U_16528,U_16530,U_16532] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16526,tc_fun(U_16528,tc_HOL_Obool)),U_16524),hAPP(hAPP(c_COMBC(U_16526,tc_fun(U_16528,tc_HOL_Obool),tc_fun(U_16528,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16528,tc_HOL_Obool),tc_fun(tc_fun(U_16528,tc_HOL_Obool),tc_fun(U_16528,tc_HOL_Obool)),U_16526),c_Groups_Ominus__class_Ominus(tc_fun(U_16528,tc_HOL_Obool))),U_16530)),U_16532)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16528,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16526,tc_fun(U_16528,tc_HOL_Obool)),U_16524),U_16530)),U_16532)
        | U_16524 = c_Orderings_Obot__class_Obot(tc_fun(U_16526,tc_HOL_Obool)) )
    & ! [U_16527,U_16529,U_16525,U_16523,U_16531] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16525,tc_fun(U_16527,tc_HOL_Obool)),U_16523),hAPP(hAPP(c_COMBC(U_16525,tc_fun(U_16527,tc_HOL_Obool),tc_fun(U_16527,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16527,tc_HOL_Obool),tc_fun(tc_fun(U_16527,tc_HOL_Obool),tc_fun(U_16527,tc_HOL_Obool)),U_16525),c_Groups_Ominus__class_Ominus(tc_fun(U_16527,tc_HOL_Obool))),U_16529)),U_16531)) = c_Orderings_Otop__class_Otop(tc_fun(U_16527,tc_HOL_Obool))
        | U_16523 != c_Orderings_Obot__class_Obot(tc_fun(U_16525,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_16525,tc_fun(U_16527,tc_HOL_Obool)),U_16523),hAPP(hAPP(c_COMBC(U_16525,tc_fun(U_16527,tc_HOL_Obool),tc_fun(U_16527,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16527,tc_HOL_Obool),tc_fun(tc_fun(U_16527,tc_HOL_Obool),tc_fun(U_16527,tc_HOL_Obool)),U_16525),c_Groups_Ominus__class_Ominus(tc_fun(U_16527,tc_HOL_Obool))),U_16529)),U_16531)) = c_Orderings_Otop__class_Otop(tc_fun(U_16527,tc_HOL_Obool))
    | U_16523 != c_Orderings_Obot__class_Obot(tc_fun(U_16525,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_16526,tc_fun(U_16528,tc_HOL_Obool)),U_16524),hAPP(hAPP(c_COMBC(U_16526,tc_fun(U_16528,tc_HOL_Obool),tc_fun(U_16528,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16528,tc_HOL_Obool),tc_fun(tc_fun(U_16528,tc_HOL_Obool),tc_fun(U_16528,tc_HOL_Obool)),U_16526),c_Groups_Ominus__class_Ominus(tc_fun(U_16528,tc_HOL_Obool))),U_16530)),U_16532)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16528,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16526,tc_fun(U_16528,tc_HOL_Obool)),U_16524),U_16530)),U_16532)
    | U_16524 = c_Orderings_Obot__class_Obot(tc_fun(U_16526,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4090_4]) ).

fof(f_4091_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_4091_2,plain,
    ! [U_16537,U_16536,U_16535,U_16534,U_16533] :
      ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16535,tc_HOL_Obool)),U_16536),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16534,tc_fun(U_16535,tc_HOL_Obool)),U_16533),U_16537)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16534,tc_fun(U_16535,tc_HOL_Obool)),U_16533),hAPP(hAPP(c_COMBB(tc_fun(U_16535,tc_HOL_Obool),tc_fun(U_16535,tc_HOL_Obool),U_16534),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16535,tc_HOL_Obool)),U_16536)),U_16537))
        | U_16533 = c_Orderings_Obot__class_Obot(tc_fun(U_16534,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16535,tc_HOL_Obool)),U_16536),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16534,tc_fun(U_16535,tc_HOL_Obool)),U_16533),U_16537)) = U_16536
        | U_16533 != c_Orderings_Obot__class_Obot(tc_fun(U_16534,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4091_1]) ).

fof(f_4091_3,plain,
    ( ! [U_16547,U_16545,U_16543,U_16541,U_16539] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16543,tc_HOL_Obool)),U_16545),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16541,tc_fun(U_16543,tc_HOL_Obool)),U_16539),U_16547)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16541,tc_fun(U_16543,tc_HOL_Obool)),U_16539),hAPP(hAPP(c_COMBB(tc_fun(U_16543,tc_HOL_Obool),tc_fun(U_16543,tc_HOL_Obool),U_16541),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16543,tc_HOL_Obool)),U_16545)),U_16547))
        | U_16539 = c_Orderings_Obot__class_Obot(tc_fun(U_16541,tc_HOL_Obool)) )
    & ! [U_16546,U_16544,U_16542,U_16540,U_16538] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16542,tc_HOL_Obool)),U_16544),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16540,tc_fun(U_16542,tc_HOL_Obool)),U_16538),U_16546)) = U_16544
        | U_16538 != c_Orderings_Obot__class_Obot(tc_fun(U_16540,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4091_2]) ).

fof(f_4091_4,plain,
    ( ! [U_16539,U_16541,U_16543,U_16545,U_16547] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16543,tc_HOL_Obool)),U_16545),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16541,tc_fun(U_16543,tc_HOL_Obool)),U_16539),U_16547)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16541,tc_fun(U_16543,tc_HOL_Obool)),U_16539),hAPP(hAPP(c_COMBB(tc_fun(U_16543,tc_HOL_Obool),tc_fun(U_16543,tc_HOL_Obool),U_16541),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16543,tc_HOL_Obool)),U_16545)),U_16547))
        | U_16539 = c_Orderings_Obot__class_Obot(tc_fun(U_16541,tc_HOL_Obool)) )
    & ! [U_16540,U_16544,U_16542,U_16538,U_16546] :
        ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16542,tc_HOL_Obool)),U_16544),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16540,tc_fun(U_16542,tc_HOL_Obool)),U_16538),U_16546)) = U_16544
        | U_16538 != c_Orderings_Obot__class_Obot(tc_fun(U_16540,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4091_3]) ).

cnf(f_4091_5,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16542,tc_HOL_Obool)),U_16544),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16540,tc_fun(U_16542,tc_HOL_Obool)),U_16538),U_16546)) = U_16544
    | U_16538 != c_Orderings_Obot__class_Obot(tc_fun(U_16540,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4091_4]) ).

cnf(f_4091_6,plain,
    ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16543,tc_HOL_Obool)),U_16545),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16541,tc_fun(U_16543,tc_HOL_Obool)),U_16539),U_16547)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16541,tc_fun(U_16543,tc_HOL_Obool)),U_16539),hAPP(hAPP(c_COMBB(tc_fun(U_16543,tc_HOL_Obool),tc_fun(U_16543,tc_HOL_Obool),U_16541),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16543,tc_HOL_Obool)),U_16545)),U_16547))
    | U_16539 = c_Orderings_Obot__class_Obot(tc_fun(U_16541,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4091_4]) ).

fof(f_4092_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_4092_2,plain,
    ! [U_16552,U_16551,U_16550,U_16549,U_16548] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16548),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16549,U_16548),U_16551),U_16552)),hAPP(U_16552,U_16550)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16549),U_16550),U_16551))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16548) ),
    inference(variable_rename,[status(thm)],[f_4092_1]) ).

fof(f_4092_3,plain,
    ! [U_16548,U_16549,U_16550,U_16551,U_16552] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16548),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16549,U_16548),U_16551),U_16552)),hAPP(U_16552,U_16550)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16549),U_16550),U_16551))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16548) ),
    inference(definitional_conversion,[status(esa)],[f_4092_2]) ).

cnf(f_4092_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16548),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16549,U_16548),U_16551),U_16552)),hAPP(U_16552,U_16550)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16549),U_16550),U_16551))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16548) ),
    inference(clausify,[status(thm)],[f_4092_3]) ).

fof(f_4093_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_4093_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_4093_1]) ).

cnf(f_4093_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_4093_2]) ).

fof(f_4094_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_4094_2,plain,
    ! [U_16557,U_16556,U_16555,U_16554,U_16553] :
      ( ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16554,tc_fun(U_16555,tc_HOL_Obool)),U_16553),hAPP(hAPP(c_COMBB(tc_fun(U_16555,tc_HOL_Obool),tc_fun(U_16555,tc_HOL_Obool),U_16554),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16555,tc_HOL_Obool)),U_16556)),U_16557)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16555,tc_HOL_Obool)),U_16556),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16554,tc_fun(U_16555,tc_HOL_Obool)),U_16553),U_16557))
        | U_16553 = c_Orderings_Obot__class_Obot(tc_fun(U_16554,tc_HOL_Obool)) )
      & ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16554,tc_fun(U_16555,tc_HOL_Obool)),U_16553),hAPP(hAPP(c_COMBB(tc_fun(U_16555,tc_HOL_Obool),tc_fun(U_16555,tc_HOL_Obool),U_16554),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16555,tc_HOL_Obool)),U_16556)),U_16557)) = c_Orderings_Otop__class_Otop(tc_fun(U_16555,tc_HOL_Obool))
        | U_16553 != c_Orderings_Obot__class_Obot(tc_fun(U_16554,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4094_1]) ).

fof(f_4094_3,plain,
    ( ! [U_16567,U_16565,U_16563,U_16561,U_16559] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16561,tc_fun(U_16563,tc_HOL_Obool)),U_16559),hAPP(hAPP(c_COMBB(tc_fun(U_16563,tc_HOL_Obool),tc_fun(U_16563,tc_HOL_Obool),U_16561),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16563,tc_HOL_Obool)),U_16565)),U_16567)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16563,tc_HOL_Obool)),U_16565),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16561,tc_fun(U_16563,tc_HOL_Obool)),U_16559),U_16567))
        | U_16559 = c_Orderings_Obot__class_Obot(tc_fun(U_16561,tc_HOL_Obool)) )
    & ! [U_16566,U_16564,U_16562,U_16560,U_16558] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16560,tc_fun(U_16562,tc_HOL_Obool)),U_16558),hAPP(hAPP(c_COMBB(tc_fun(U_16562,tc_HOL_Obool),tc_fun(U_16562,tc_HOL_Obool),U_16560),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16562,tc_HOL_Obool)),U_16564)),U_16566)) = c_Orderings_Otop__class_Otop(tc_fun(U_16562,tc_HOL_Obool))
        | U_16558 != c_Orderings_Obot__class_Obot(tc_fun(U_16560,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4094_2]) ).

fof(f_4094_4,plain,
    ( ! [U_16559,U_16561,U_16563,U_16565,U_16567] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16561,tc_fun(U_16563,tc_HOL_Obool)),U_16559),hAPP(hAPP(c_COMBB(tc_fun(U_16563,tc_HOL_Obool),tc_fun(U_16563,tc_HOL_Obool),U_16561),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16563,tc_HOL_Obool)),U_16565)),U_16567)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16563,tc_HOL_Obool)),U_16565),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16561,tc_fun(U_16563,tc_HOL_Obool)),U_16559),U_16567))
        | U_16559 = c_Orderings_Obot__class_Obot(tc_fun(U_16561,tc_HOL_Obool)) )
    & ! [U_16560,U_16564,U_16558,U_16562,U_16566] :
        ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16560,tc_fun(U_16562,tc_HOL_Obool)),U_16558),hAPP(hAPP(c_COMBB(tc_fun(U_16562,tc_HOL_Obool),tc_fun(U_16562,tc_HOL_Obool),U_16560),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16562,tc_HOL_Obool)),U_16564)),U_16566)) = c_Orderings_Otop__class_Otop(tc_fun(U_16562,tc_HOL_Obool))
        | U_16558 != c_Orderings_Obot__class_Obot(tc_fun(U_16560,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4094_3]) ).

cnf(f_4094_5,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16560,tc_fun(U_16562,tc_HOL_Obool)),U_16558),hAPP(hAPP(c_COMBB(tc_fun(U_16562,tc_HOL_Obool),tc_fun(U_16562,tc_HOL_Obool),U_16560),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16562,tc_HOL_Obool)),U_16564)),U_16566)) = c_Orderings_Otop__class_Otop(tc_fun(U_16562,tc_HOL_Obool))
    | U_16558 != c_Orderings_Obot__class_Obot(tc_fun(U_16560,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4094_4]) ).

cnf(f_4094_6,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16561,tc_fun(U_16563,tc_HOL_Obool)),U_16559),hAPP(hAPP(c_COMBB(tc_fun(U_16563,tc_HOL_Obool),tc_fun(U_16563,tc_HOL_Obool),U_16561),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16563,tc_HOL_Obool)),U_16565)),U_16567)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_16563,tc_HOL_Obool)),U_16565),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16561,tc_fun(U_16563,tc_HOL_Obool)),U_16559),U_16567))
    | U_16559 = c_Orderings_Obot__class_Obot(tc_fun(U_16561,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4094_4]) ).

fof(f_4095_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_4095_2,plain,
    ! [U_16573,U_16572,U_16571,U_16570,U_16569,U_16568] :
      ( hAPP(c_Relation_OImage(U_16569,U_16568,U_16570),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16572,tc_fun(U_16569,tc_HOL_Obool)),U_16571),U_16573)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16572,tc_fun(U_16568,tc_HOL_Obool)),U_16571),hAPP(hAPP(c_COMBB(tc_fun(U_16569,tc_HOL_Obool),tc_fun(U_16568,tc_HOL_Obool),U_16572),c_Relation_OImage(U_16569,U_16568,U_16570)),U_16573))
      | U_16571 = c_Orderings_Obot__class_Obot(tc_fun(U_16572,tc_HOL_Obool))
      | ~ c_Relation_Osingle__valued(U_16568,U_16569,hAPP(c_Relation_Oconverse(U_16569,U_16568),U_16570)) ),
    inference(variable_rename,[status(thm)],[f_4095_1]) ).

fof(f_4095_3,plain,
    ! [U_16568,U_16569,U_16570,U_16571,U_16572,U_16573] :
      ( hAPP(c_Relation_OImage(U_16569,U_16568,U_16570),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16572,tc_fun(U_16569,tc_HOL_Obool)),U_16571),U_16573)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16572,tc_fun(U_16568,tc_HOL_Obool)),U_16571),hAPP(hAPP(c_COMBB(tc_fun(U_16569,tc_HOL_Obool),tc_fun(U_16568,tc_HOL_Obool),U_16572),c_Relation_OImage(U_16569,U_16568,U_16570)),U_16573))
      | U_16571 = c_Orderings_Obot__class_Obot(tc_fun(U_16572,tc_HOL_Obool))
      | ~ c_Relation_Osingle__valued(U_16568,U_16569,hAPP(c_Relation_Oconverse(U_16569,U_16568),U_16570)) ),
    inference(definitional_conversion,[status(esa)],[f_4095_2]) ).

cnf(f_4095_4,plain,
    ( hAPP(c_Relation_OImage(U_16569,U_16568,U_16570),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16572,tc_fun(U_16569,tc_HOL_Obool)),U_16571),U_16573)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16572,tc_fun(U_16568,tc_HOL_Obool)),U_16571),hAPP(hAPP(c_COMBB(tc_fun(U_16569,tc_HOL_Obool),tc_fun(U_16568,tc_HOL_Obool),U_16572),c_Relation_OImage(U_16569,U_16568,U_16570)),U_16573))
    | U_16571 = c_Orderings_Obot__class_Obot(tc_fun(U_16572,tc_HOL_Obool))
    | ~ c_Relation_Osingle__valued(U_16568,U_16569,hAPP(c_Relation_Oconverse(U_16569,U_16568),U_16570)) ),
    inference(clausify,[status(thm)],[f_4095_3]) ).

fof(f_4096_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_4096_2,plain,
    ! [U_16578,U_16577,U_16576,U_16575,U_16574] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16574),U_16577),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16575,U_16574),U_16576),U_16578)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16575,U_16574,hAPP(hAPP(c_COMBB(U_16574,tc_fun(U_16574,U_16574),U_16575),c_Lattices_Osemilattice__inf__class_Oinf(U_16574)),U_16578)),U_16577),U_16576)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16575),U_16576))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16574) ),
    inference(variable_rename,[status(thm)],[f_4096_1]) ).

fof(f_4096_3,plain,
    ! [U_16574,U_16575,U_16576,U_16577,U_16578] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16574),U_16577),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16575,U_16574),U_16576),U_16578)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16575,U_16574,hAPP(hAPP(c_COMBB(U_16574,tc_fun(U_16574,U_16574),U_16575),c_Lattices_Osemilattice__inf__class_Oinf(U_16574)),U_16578)),U_16577),U_16576)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16575),U_16576))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16574) ),
    inference(definitional_conversion,[status(esa)],[f_4096_2]) ).

cnf(f_4096_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16574),U_16577),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16575,U_16574),U_16576),U_16578)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16575,U_16574,hAPP(hAPP(c_COMBB(U_16574,tc_fun(U_16574,U_16574),U_16575),c_Lattices_Osemilattice__inf__class_Oinf(U_16574)),U_16578)),U_16577),U_16576)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16575),U_16576))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16574) ),
    inference(clausify,[status(thm)],[f_4096_3]) ).

fof(f_4097_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_4097_2,plain,
    ! [U_16580,U_16579] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16579,U_16580) = hAPP(hAPP(c_Finite__Set_Ofold(U_16579,U_16579,c_Lattices_Osemilattice__inf__class_Oinf(U_16579)),c_Orderings_Otop__class_Otop(U_16579)),U_16580)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16579),U_16580))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16579) ),
    inference(variable_rename,[status(thm)],[f_4097_1]) ).

fof(f_4097_3,plain,
    ! [U_16579,U_16580] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16579,U_16580) = hAPP(hAPP(c_Finite__Set_Ofold(U_16579,U_16579,c_Lattices_Osemilattice__inf__class_Oinf(U_16579)),c_Orderings_Otop__class_Otop(U_16579)),U_16580)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16579),U_16580))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16579) ),
    inference(definitional_conversion,[status(esa)],[f_4097_2]) ).

cnf(f_4097_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_16579,U_16580) = hAPP(hAPP(c_Finite__Set_Ofold(U_16579,U_16579,c_Lattices_Osemilattice__inf__class_Oinf(U_16579)),c_Orderings_Otop__class_Otop(U_16579)),U_16580)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16579),U_16580))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16579) ),
    inference(clausify,[status(thm)],[f_4097_3]) ).

fof(f_4098_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_4098_2,plain,
    ! [U_16582,U_16581] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16581,U_16582) = hAPP(hAPP(c_Finite__Set_Ofold(U_16581,U_16581,c_Lattices_Osemilattice__sup__class_Osup(U_16581)),c_Orderings_Obot__class_Obot(U_16581)),U_16582)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16581),U_16582))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16581) ),
    inference(variable_rename,[status(thm)],[f_4098_1]) ).

fof(f_4098_3,plain,
    ! [U_16582,U_16581] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16581,U_16582) = hAPP(hAPP(c_Finite__Set_Ofold(U_16581,U_16581,c_Lattices_Osemilattice__sup__class_Osup(U_16581)),c_Orderings_Obot__class_Obot(U_16581)),U_16582)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16581),U_16582))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16581) ),
    inference(definitional_conversion,[status(esa)],[f_4098_2]) ).

cnf(f_4098_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_16581,U_16582) = hAPP(hAPP(c_Finite__Set_Ofold(U_16581,U_16581,c_Lattices_Osemilattice__sup__class_Osup(U_16581)),c_Orderings_Obot__class_Obot(U_16581)),U_16582)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16581),U_16582))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16581) ),
    inference(clausify,[status(thm)],[f_4098_3]) ).

fof(f_4099_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_4099_2,plain,
    ! [U_16585,U_16584] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_16584),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16584,tc_HOL_Obool),U_16585)))
      | ! [U_16583] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16584),U_16583))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16584,tc_HOL_Obool)),U_16583),U_16585)) ) ),
    inference(variable_rename,[status(thm)],[f_4099_1]) ).

fof(f_4099_3,plain,
    ! [U_16584,U_16585,U_16583] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_16584),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16584,tc_HOL_Obool),U_16585)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16584),U_16583))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16584,tc_HOL_Obool)),U_16583),U_16585)) ),
    inference(definitional_conversion,[status(esa)],[f_4099_2]) ).

cnf(f_4099_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_16584),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16584,tc_HOL_Obool),U_16585)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16584),U_16583))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16584,tc_HOL_Obool)),U_16583),U_16585)) ),
    inference(clausify,[status(thm)],[f_4099_3]) ).

fof(f_4100_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_4100_2,plain,
    ! [U_16589,U_16588,U_16587,U_16586] :
      ( hBOOL(hAPP(hAPP(c_member(U_16586),U_16589),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16586,tc_HOL_Obool),U_16588)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16586),U_16589),U_16587))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16586,tc_HOL_Obool)),U_16587),U_16588)) ),
    inference(variable_rename,[status(thm)],[f_4100_1]) ).

fof(f_4100_3,plain,
    ! [U_16586,U_16587,U_16588,U_16589] :
      ( hBOOL(hAPP(hAPP(c_member(U_16586),U_16589),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16586,tc_HOL_Obool),U_16588)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16586),U_16589),U_16587))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16586,tc_HOL_Obool)),U_16587),U_16588)) ),
    inference(definitional_conversion,[status(esa)],[f_4100_2]) ).

cnf(f_4100_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16586),U_16589),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16586,tc_HOL_Obool),U_16588)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16586),U_16589),U_16587))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16586,tc_HOL_Obool)),U_16587),U_16588)) ),
    inference(clausify,[status(thm)],[f_4100_3]) ).

fof(f_4101_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_4101_2,plain,
    ! [U_16593,U_16592,U_16591,U_16590] :
      ( hBOOL(hAPP(hAPP(c_member(U_16590),U_16591),U_16593))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16590,tc_HOL_Obool)),U_16593),U_16592))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16590),U_16591),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16590,tc_HOL_Obool),U_16592))) ),
    inference(variable_rename,[status(thm)],[f_4101_1]) ).

fof(f_4101_3,plain,
    ! [U_16590,U_16591,U_16592,U_16593] :
      ( hBOOL(hAPP(hAPP(c_member(U_16590),U_16591),U_16593))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16590,tc_HOL_Obool)),U_16593),U_16592))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16590),U_16591),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16590,tc_HOL_Obool),U_16592))) ),
    inference(definitional_conversion,[status(esa)],[f_4101_2]) ).

cnf(f_4101_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16590),U_16591),U_16593))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16590,tc_HOL_Obool)),U_16593),U_16592))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16590),U_16591),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16590,tc_HOL_Obool),U_16592))) ),
    inference(clausify,[status(thm)],[f_4101_3]) ).

fof(f_4102_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_4102_2,plain,
    ! [U_16597,U_16596,U_16595,U_16594] :
      ( hBOOL(hAPP(hAPP(c_member(U_16594),U_16595),U_16597))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16594,tc_HOL_Obool)),U_16597),U_16596))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16594),U_16595),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16594,tc_HOL_Obool),U_16596))) ),
    inference(variable_rename,[status(thm)],[f_4102_1]) ).

fof(f_4102_3,plain,
    ! [U_16594,U_16595,U_16596,U_16597] :
      ( hBOOL(hAPP(hAPP(c_member(U_16594),U_16595),U_16597))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16594,tc_HOL_Obool)),U_16597),U_16596))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16594),U_16595),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16594,tc_HOL_Obool),U_16596))) ),
    inference(definitional_conversion,[status(esa)],[f_4102_2]) ).

cnf(f_4102_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16594),U_16595),U_16597))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16594,tc_HOL_Obool)),U_16597),U_16596))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16594),U_16595),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16594,tc_HOL_Obool),U_16596))) ),
    inference(clausify,[status(thm)],[f_4102_3]) ).

fof(f_4103_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_4103_2,plain,
    ! [U_16601,U_16600,U_16599,U_16598] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16598,tc_HOL_Obool),tc_fun(U_16599,tc_HOL_Obool)),U_16600),hAPP(hAPP(c_COMBC(tc_fun(U_16598,tc_HOL_Obool),tc_fun(U_16598,tc_fun(U_16599,tc_HOL_Obool)),tc_fun(U_16599,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16598,tc_fun(U_16599,tc_HOL_Obool))),U_16601)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16598,tc_fun(U_16599,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16598,tc_HOL_Obool),U_16600)),U_16601),
    inference(variable_rename,[status(thm)],[f_4103_1]) ).

fof(f_4103_3,plain,
    ! [U_16598,U_16599,U_16600,U_16601] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16598,tc_HOL_Obool),tc_fun(U_16599,tc_HOL_Obool)),U_16600),hAPP(hAPP(c_COMBC(tc_fun(U_16598,tc_HOL_Obool),tc_fun(U_16598,tc_fun(U_16599,tc_HOL_Obool)),tc_fun(U_16599,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16598,tc_fun(U_16599,tc_HOL_Obool))),U_16601)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16598,tc_fun(U_16599,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16598,tc_HOL_Obool),U_16600)),U_16601),
    inference(definitional_conversion,[status(esa)],[f_4103_2]) ).

cnf(f_4103_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16598,tc_HOL_Obool),tc_fun(U_16599,tc_HOL_Obool)),U_16600),hAPP(hAPP(c_COMBC(tc_fun(U_16598,tc_HOL_Obool),tc_fun(U_16598,tc_fun(U_16599,tc_HOL_Obool)),tc_fun(U_16599,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16598,tc_fun(U_16599,tc_HOL_Obool))),U_16601)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16598,tc_fun(U_16599,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16598,tc_HOL_Obool),U_16600)),U_16601),
    inference(clausify,[status(thm)],[f_4103_3]) ).

fof(f_4104_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_4104_2,plain,
    ! [U_16605,U_16604,U_16603,U_16602] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16602,tc_fun(U_16603,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16602,tc_HOL_Obool),U_16604)),U_16605) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16602,tc_HOL_Obool),tc_fun(U_16603,tc_HOL_Obool)),U_16604),hAPP(hAPP(c_COMBC(tc_fun(U_16602,tc_HOL_Obool),tc_fun(U_16602,tc_fun(U_16603,tc_HOL_Obool)),tc_fun(U_16603,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16602,tc_fun(U_16603,tc_HOL_Obool))),U_16605)),
    inference(variable_rename,[status(thm)],[f_4104_1]) ).

fof(f_4104_3,plain,
    ! [U_16602,U_16603,U_16604,U_16605] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16602,tc_fun(U_16603,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16602,tc_HOL_Obool),U_16604)),U_16605) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16602,tc_HOL_Obool),tc_fun(U_16603,tc_HOL_Obool)),U_16604),hAPP(hAPP(c_COMBC(tc_fun(U_16602,tc_HOL_Obool),tc_fun(U_16602,tc_fun(U_16603,tc_HOL_Obool)),tc_fun(U_16603,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16602,tc_fun(U_16603,tc_HOL_Obool))),U_16605)),
    inference(definitional_conversion,[status(esa)],[f_4104_2]) ).

cnf(f_4104_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16602,tc_fun(U_16603,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16602,tc_HOL_Obool),U_16604)),U_16605) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16602,tc_HOL_Obool),tc_fun(U_16603,tc_HOL_Obool)),U_16604),hAPP(hAPP(c_COMBC(tc_fun(U_16602,tc_HOL_Obool),tc_fun(U_16602,tc_fun(U_16603,tc_HOL_Obool)),tc_fun(U_16603,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16602,tc_fun(U_16603,tc_HOL_Obool))),U_16605)),
    inference(clausify,[status(thm)],[f_4104_3]) ).

fof(f_4105_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_4105_2,plain,
    ! [U_16608,U_16607,U_16606] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16606,tc_HOL_Obool)),U_16607),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16606,tc_HOL_Obool),U_16608)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16606,tc_HOL_Obool),tc_fun(U_16606,tc_HOL_Obool)),U_16608),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16606,tc_HOL_Obool)),U_16607)),
    inference(variable_rename,[status(thm)],[f_4105_1]) ).

fof(f_4105_3,plain,
    ! [U_16606,U_16608,U_16607] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16606,tc_HOL_Obool)),U_16607),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16606,tc_HOL_Obool),U_16608)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16606,tc_HOL_Obool),tc_fun(U_16606,tc_HOL_Obool)),U_16608),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16606,tc_HOL_Obool)),U_16607)),
    inference(definitional_conversion,[status(esa)],[f_4105_2]) ).

cnf(f_4105_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16606,tc_HOL_Obool)),U_16607),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16606,tc_HOL_Obool),U_16608)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16606,tc_HOL_Obool),tc_fun(U_16606,tc_HOL_Obool)),U_16608),hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16606,tc_HOL_Obool)),U_16607)),
    inference(clausify,[status(thm)],[f_4105_3]) ).

fof(f_4106_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_4106_2,plain,
    ! [U_16615,U_16614,U_16613,U_16612,U_16611] :
      ( ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16611,tc_fun(U_16612,tc_HOL_Obool)),U_16613),U_16614),U_16615))
        | ? [U_16610] :
            ( ~ hBOOL(hAPP(hAPP(U_16614,U_16610),U_16615))
            & hBOOL(hAPP(hAPP(c_member(U_16611),U_16610),U_16613)) ) )
      & ( ! [U_16609] :
            ( hBOOL(hAPP(hAPP(U_16614,U_16609),U_16615))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16611),U_16609),U_16613)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16611,tc_fun(U_16612,tc_HOL_Obool)),U_16613),U_16614),U_16615)) ) ),
    inference(variable_rename,[status(thm)],[f_4106_1]) ).

fof(f_4106_3,plain,
    ( ! [U_16625,U_16623,U_16621,U_16619,U_16617] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16617,tc_fun(U_16619,tc_HOL_Obool)),U_16621),U_16623),U_16625))
        | ? [U_16610] :
            ( ~ hBOOL(hAPP(hAPP(U_16623,U_16610),U_16625))
            & hBOOL(hAPP(hAPP(c_member(U_16617),U_16610),U_16621)) ) )
    & ! [U_16624,U_16622,U_16620,U_16618,U_16616] :
        ( ! [U_16609] :
            ( hBOOL(hAPP(hAPP(U_16622,U_16609),U_16624))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16616),U_16609),U_16620)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16616,tc_fun(U_16618,tc_HOL_Obool)),U_16620),U_16622),U_16624)) ) ),
    inference(miniscope,[status(thm)],[f_4106_2]) ).

fof(f_4106_4,plain,
    ( ! [U_16625,U_16623,U_16621,U_16619,U_16617] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16617,tc_fun(U_16619,tc_HOL_Obool)),U_16621),U_16623),U_16625))
        | ( ~ hBOOL(hAPP(hAPP(U_16623,sK412(U_16625,U_16623,U_16621,U_16619,U_16617)),U_16625))
          & hBOOL(hAPP(hAPP(c_member(U_16617),sK412(U_16625,U_16623,U_16621,U_16619,U_16617)),U_16621)) ) )
    & ! [U_16624,U_16622,U_16620,U_16618,U_16616] :
        ( ! [U_16609] :
            ( hBOOL(hAPP(hAPP(U_16622,U_16609),U_16624))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16616),U_16609),U_16620)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16616,tc_fun(U_16618,tc_HOL_Obool)),U_16620),U_16622),U_16624)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK412]),skolemize(U_16610,sK412(U_16625,U_16623,U_16621,U_16619,U_16617))],[f_4106_3]) ).

fof(f_4106_5,plain,
    ( ! [U_16617,U_16619,U_16623,U_16621,U_16625] :
        ( ~ hBOOL(hAPP(hAPP(U_16623,sK412(U_16625,U_16623,U_16621,U_16619,U_16617)),U_16625))
        | ~ sP1069(U_16617,U_16619,U_16623,U_16621,U_16625) )
    & ! [U_16617,U_16619,U_16623,U_16621,U_16625] :
        ( hBOOL(hAPP(hAPP(c_member(U_16617),sK412(U_16625,U_16623,U_16621,U_16619,U_16617)),U_16621))
        | ~ sP1069(U_16617,U_16619,U_16623,U_16621,U_16625) )
    & ! [U_16617,U_16619,U_16623,U_16621,U_16625] :
        ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16617,tc_fun(U_16619,tc_HOL_Obool)),U_16621),U_16623),U_16625))
        | sP1069(U_16617,U_16619,U_16623,U_16621,U_16625) )
    & ! [U_16609,U_16616,U_16620,U_16624,U_16622,U_16618] :
        ( hBOOL(hAPP(hAPP(U_16622,U_16609),U_16624))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16616),U_16609),U_16620))
        | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16616,tc_fun(U_16618,tc_HOL_Obool)),U_16620),U_16622),U_16624)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1069])],[f_4106_4]) ).

cnf(f_4106_6,plain,
    ( hBOOL(hAPP(hAPP(U_16622,U_16609),U_16624))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16616),U_16609),U_16620))
    | ~ hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16616,tc_fun(U_16618,tc_HOL_Obool)),U_16620),U_16622),U_16624)) ),
    inference(clausify,[status(thm)],[f_4106_5]) ).

cnf(f_4106_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16617,tc_fun(U_16619,tc_HOL_Obool)),U_16621),U_16623),U_16625))
    | sP1069(U_16617,U_16619,U_16623,U_16621,U_16625) ),
    inference(clausify,[status(thm)],[f_4106_5]) ).

cnf(f_4106_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16617),sK412(U_16625,U_16623,U_16621,U_16619,U_16617)),U_16621))
    | ~ sP1069(U_16617,U_16619,U_16623,U_16621,U_16625) ),
    inference(clausify,[status(thm)],[f_4106_5]) ).

cnf(f_4106_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_16623,sK412(U_16625,U_16623,U_16621,U_16619,U_16617)),U_16625))
    | ~ sP1069(U_16617,U_16619,U_16623,U_16621,U_16625) ),
    inference(clausify,[status(thm)],[f_4106_5]) ).

fof(f_4107_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_4107_2,plain,
    ! [U_16634,U_16633,U_16632,U_16631,U_16630,U_16629,U_16628] :
      ( ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16628,tc_fun(U_16629,tc_fun(U_16630,tc_HOL_Obool))),U_16631),U_16632),U_16633),U_16634))
        | ? [U_16627] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_16632,U_16627),U_16633),U_16634))
            & hBOOL(hAPP(hAPP(c_member(U_16628),U_16627),U_16631)) ) )
      & ( ! [U_16626] :
            ( hBOOL(hAPP(hAPP(hAPP(U_16632,U_16626),U_16633),U_16634))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16628),U_16626),U_16631)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16628,tc_fun(U_16629,tc_fun(U_16630,tc_HOL_Obool))),U_16631),U_16632),U_16633),U_16634)) ) ),
    inference(variable_rename,[status(thm)],[f_4107_1]) ).

fof(f_4107_3,plain,
    ( ! [U_16648,U_16646,U_16644,U_16642,U_16640,U_16638,U_16636] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16636,tc_fun(U_16638,tc_fun(U_16640,tc_HOL_Obool))),U_16642),U_16644),U_16646),U_16648))
        | ? [U_16627] :
            ( ~ hBOOL(hAPP(hAPP(hAPP(U_16644,U_16627),U_16646),U_16648))
            & hBOOL(hAPP(hAPP(c_member(U_16636),U_16627),U_16642)) ) )
    & ! [U_16647,U_16645,U_16643,U_16641,U_16639,U_16637,U_16635] :
        ( ! [U_16626] :
            ( hBOOL(hAPP(hAPP(hAPP(U_16643,U_16626),U_16645),U_16647))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16635),U_16626),U_16641)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16635,tc_fun(U_16637,tc_fun(U_16639,tc_HOL_Obool))),U_16641),U_16643),U_16645),U_16647)) ) ),
    inference(miniscope,[status(thm)],[f_4107_2]) ).

fof(f_4107_4,plain,
    ( ! [U_16648,U_16646,U_16644,U_16642,U_16640,U_16638,U_16636] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16636,tc_fun(U_16638,tc_fun(U_16640,tc_HOL_Obool))),U_16642),U_16644),U_16646),U_16648))
        | ( ~ hBOOL(hAPP(hAPP(hAPP(U_16644,sK413(U_16648,U_16646,U_16644,U_16642,U_16640,U_16638,U_16636)),U_16646),U_16648))
          & hBOOL(hAPP(hAPP(c_member(U_16636),sK413(U_16648,U_16646,U_16644,U_16642,U_16640,U_16638,U_16636)),U_16642)) ) )
    & ! [U_16647,U_16645,U_16643,U_16641,U_16639,U_16637,U_16635] :
        ( ! [U_16626] :
            ( hBOOL(hAPP(hAPP(hAPP(U_16643,U_16626),U_16645),U_16647))
            | ~ hBOOL(hAPP(hAPP(c_member(U_16635),U_16626),U_16641)) )
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16635,tc_fun(U_16637,tc_fun(U_16639,tc_HOL_Obool))),U_16641),U_16643),U_16645),U_16647)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK413]),skolemize(U_16627,sK413(U_16648,U_16646,U_16644,U_16642,U_16640,U_16638,U_16636))],[f_4107_3]) ).

fof(f_4107_5,plain,
    ( ! [U_16636,U_16638,U_16640,U_16642,U_16646,U_16644,U_16648] :
        ( ~ hBOOL(hAPP(hAPP(hAPP(U_16644,sK413(U_16648,U_16646,U_16644,U_16642,U_16640,U_16638,U_16636)),U_16646),U_16648))
        | ~ sP1070(U_16636,U_16638,U_16640,U_16642,U_16646,U_16644,U_16648) )
    & ! [U_16636,U_16638,U_16640,U_16642,U_16646,U_16644,U_16648] :
        ( hBOOL(hAPP(hAPP(c_member(U_16636),sK413(U_16648,U_16646,U_16644,U_16642,U_16640,U_16638,U_16636)),U_16642))
        | ~ sP1070(U_16636,U_16638,U_16640,U_16642,U_16646,U_16644,U_16648) )
    & ! [U_16636,U_16638,U_16640,U_16642,U_16646,U_16644,U_16648] :
        ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16636,tc_fun(U_16638,tc_fun(U_16640,tc_HOL_Obool))),U_16642),U_16644),U_16646),U_16648))
        | sP1070(U_16636,U_16638,U_16640,U_16642,U_16646,U_16644,U_16648) )
    & ! [U_16639,U_16637,U_16626,U_16635,U_16643,U_16647,U_16641,U_16645] :
        ( hBOOL(hAPP(hAPP(hAPP(U_16643,U_16626),U_16645),U_16647))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16635),U_16626),U_16641))
        | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16635,tc_fun(U_16637,tc_fun(U_16639,tc_HOL_Obool))),U_16641),U_16643),U_16645),U_16647)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1070])],[f_4107_4]) ).

cnf(f_4107_6,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_16643,U_16626),U_16645),U_16647))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16635),U_16626),U_16641))
    | ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16635,tc_fun(U_16637,tc_fun(U_16639,tc_HOL_Obool))),U_16641),U_16643),U_16645),U_16647)) ),
    inference(clausify,[status(thm)],[f_4107_5]) ).

cnf(f_4107_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16636,tc_fun(U_16638,tc_fun(U_16640,tc_HOL_Obool))),U_16642),U_16644),U_16646),U_16648))
    | sP1070(U_16636,U_16638,U_16640,U_16642,U_16646,U_16644,U_16648) ),
    inference(clausify,[status(thm)],[f_4107_5]) ).

cnf(f_4107_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16636),sK413(U_16648,U_16646,U_16644,U_16642,U_16640,U_16638,U_16636)),U_16642))
    | ~ sP1070(U_16636,U_16638,U_16640,U_16642,U_16646,U_16644,U_16648) ),
    inference(clausify,[status(thm)],[f_4107_5]) ).

cnf(f_4107_9,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(U_16644,sK413(U_16648,U_16646,U_16644,U_16642,U_16640,U_16638,U_16636)),U_16646),U_16648))
    | ~ sP1070(U_16636,U_16638,U_16640,U_16642,U_16646,U_16644,U_16648) ),
    inference(clausify,[status(thm)],[f_4107_5]) ).

fof(f_4108_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_4108_2,plain,
    ! [U_16652,U_16651,U_16650,U_16649] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16649,tc_fun(U_16650,tc_HOL_Obool)),U_16651),U_16652) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16650,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16649,tc_fun(U_16650,tc_HOL_Obool),U_16652),U_16651)),
    inference(variable_rename,[status(thm)],[f_4108_1]) ).

fof(f_4108_3,plain,
    ! [U_16650,U_16651,U_16649,U_16652] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16649,tc_fun(U_16650,tc_HOL_Obool)),U_16651),U_16652) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16650,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16649,tc_fun(U_16650,tc_HOL_Obool),U_16652),U_16651)),
    inference(definitional_conversion,[status(esa)],[f_4108_2]) ).

cnf(f_4108_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16649,tc_fun(U_16650,tc_HOL_Obool)),U_16651),U_16652) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16650,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16649,tc_fun(U_16650,tc_HOL_Obool),U_16652),U_16651)),
    inference(clausify,[status(thm)],[f_4108_3]) ).

fof(f_4109_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_4109_2,plain,
    ! [U_16656,U_16655,U_16654,U_16653] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16653,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16654,tc_fun(U_16653,tc_HOL_Obool),U_16655),U_16656)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16654,tc_fun(U_16653,tc_HOL_Obool)),U_16656),U_16655),
    inference(variable_rename,[status(thm)],[f_4109_1]) ).

fof(f_4109_3,plain,
    ! [U_16653,U_16654,U_16655,U_16656] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16653,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16654,tc_fun(U_16653,tc_HOL_Obool),U_16655),U_16656)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16654,tc_fun(U_16653,tc_HOL_Obool)),U_16656),U_16655),
    inference(definitional_conversion,[status(esa)],[f_4109_2]) ).

cnf(f_4109_4,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16653,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16654,tc_fun(U_16653,tc_HOL_Obool),U_16655),U_16656)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16654,tc_fun(U_16653,tc_HOL_Obool)),U_16656),U_16655),
    inference(clausify,[status(thm)],[f_4109_3]) ).

fof(f_4110_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_4110_2,plain,
    ! [U_16658,U_16657] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16657,tc_HOL_Obool),U_16658) = hAPP(c_Set_OCollect(U_16657),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16657,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_16657),c_HOL_OAll(tc_fun(U_16657,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16657,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_16657,tc_HOL_Obool),tc_HOL_Obool),U_16657),hAPP(c_COMBS(tc_fun(U_16657,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_16657,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(U_16657,tc_HOL_Obool),tc_fun(tc_fun(U_16657,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_16657,tc_HOL_Obool))),U_16658)))),c_member(U_16657)))),
    inference(variable_rename,[status(thm)],[f_4110_1]) ).

fof(f_4110_3,plain,
    ! [U_16657,U_16658] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16657,tc_HOL_Obool),U_16658) = hAPP(c_Set_OCollect(U_16657),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16657,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_16657),c_HOL_OAll(tc_fun(U_16657,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16657,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_16657,tc_HOL_Obool),tc_HOL_Obool),U_16657),hAPP(c_COMBS(tc_fun(U_16657,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_16657,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(U_16657,tc_HOL_Obool),tc_fun(tc_fun(U_16657,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_16657,tc_HOL_Obool))),U_16658)))),c_member(U_16657)))),
    inference(definitional_conversion,[status(esa)],[f_4110_2]) ).

cnf(f_4110_4,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16657,tc_HOL_Obool),U_16658) = hAPP(c_Set_OCollect(U_16657),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16657,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool,U_16657),c_HOL_OAll(tc_fun(U_16657,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_16657,tc_HOL_Obool),tc_HOL_Obool),tc_fun(tc_fun(U_16657,tc_HOL_Obool),tc_HOL_Obool),U_16657),hAPP(c_COMBS(tc_fun(U_16657,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_16657,tc_HOL_Obool)),c_fimplies),hAPP(hAPP(c_COMBC(tc_fun(U_16657,tc_HOL_Obool),tc_fun(tc_fun(U_16657,tc_HOL_Obool),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_fun(U_16657,tc_HOL_Obool))),U_16658)))),c_member(U_16657)))),
    inference(clausify,[status(thm)],[f_4110_3]) ).

fof(f_4111_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_4111_2,plain,
    ! [U_16662,U_16661,U_16660,U_16659] : hAPP(c_Set_Ovimage(U_16659,U_16660,U_16661),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16660,tc_HOL_Obool),U_16662)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16660,tc_HOL_Obool),tc_fun(U_16659,tc_HOL_Obool)),U_16662),c_Set_Ovimage(U_16659,U_16660,U_16661)),
    inference(variable_rename,[status(thm)],[f_4111_1]) ).

fof(f_4111_3,plain,
    ! [U_16659,U_16660,U_16661,U_16662] : hAPP(c_Set_Ovimage(U_16659,U_16660,U_16661),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16660,tc_HOL_Obool),U_16662)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16660,tc_HOL_Obool),tc_fun(U_16659,tc_HOL_Obool)),U_16662),c_Set_Ovimage(U_16659,U_16660,U_16661)),
    inference(definitional_conversion,[status(esa)],[f_4111_2]) ).

cnf(f_4111_4,plain,
    hAPP(c_Set_Ovimage(U_16659,U_16660,U_16661),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16660,tc_HOL_Obool),U_16662)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16660,tc_HOL_Obool),tc_fun(U_16659,tc_HOL_Obool)),U_16662),c_Set_Ovimage(U_16659,U_16660,U_16661)),
    inference(clausify,[status(thm)],[f_4111_3]) ).

fof(f_4112_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_4112_2,plain,
    ! [U_16664,U_16663] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16663,U_16664) = c_Complete__Lattice_OInf__class_OInf(U_16663,hAPP(c_Set_OCollect(U_16663),hAPP(hAPP(c_COMBB(tc_fun(U_16663,tc_HOL_Obool),tc_HOL_Obool,U_16663),c_HOL_OAll(U_16663)),hAPP(hAPP(c_COMBB(tc_fun(U_16663,tc_HOL_Obool),tc_fun(U_16663,tc_HOL_Obool),U_16663),hAPP(c_COMBS(U_16663,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16663),c_fimplies),hAPP(hAPP(c_COMBC(U_16663,tc_fun(U_16663,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16663)),U_16664)))),hAPP(c_COMBC(U_16663,U_16663,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_16663))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16663) ),
    inference(variable_rename,[status(thm)],[f_4112_1]) ).

fof(f_4112_3,plain,
    ! [U_16663,U_16664] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16663,U_16664) = c_Complete__Lattice_OInf__class_OInf(U_16663,hAPP(c_Set_OCollect(U_16663),hAPP(hAPP(c_COMBB(tc_fun(U_16663,tc_HOL_Obool),tc_HOL_Obool,U_16663),c_HOL_OAll(U_16663)),hAPP(hAPP(c_COMBB(tc_fun(U_16663,tc_HOL_Obool),tc_fun(U_16663,tc_HOL_Obool),U_16663),hAPP(c_COMBS(U_16663,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16663),c_fimplies),hAPP(hAPP(c_COMBC(U_16663,tc_fun(U_16663,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16663)),U_16664)))),hAPP(c_COMBC(U_16663,U_16663,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_16663))))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16663) ),
    inference(definitional_conversion,[status(esa)],[f_4112_2]) ).

cnf(f_4112_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_16663,U_16664) = c_Complete__Lattice_OInf__class_OInf(U_16663,hAPP(c_Set_OCollect(U_16663),hAPP(hAPP(c_COMBB(tc_fun(U_16663,tc_HOL_Obool),tc_HOL_Obool,U_16663),c_HOL_OAll(U_16663)),hAPP(hAPP(c_COMBB(tc_fun(U_16663,tc_HOL_Obool),tc_fun(U_16663,tc_HOL_Obool),U_16663),hAPP(c_COMBS(U_16663,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16663),c_fimplies),hAPP(hAPP(c_COMBC(U_16663,tc_fun(U_16663,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16663)),U_16664)))),hAPP(c_COMBC(U_16663,U_16663,tc_HOL_Obool),c_Orderings_Oord__class_Oless__eq(U_16663))))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16663) ),
    inference(clausify,[status(thm)],[f_4112_3]) ).

fof(f_4113_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_4113_2,plain,
    ! [U_16666,U_16665] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16665,U_16666) = c_Complete__Lattice_OSup__class_OSup(U_16665,hAPP(c_Set_OCollect(U_16665),hAPP(hAPP(c_COMBB(tc_fun(U_16665,tc_HOL_Obool),tc_HOL_Obool,U_16665),c_HOL_OAll(U_16665)),hAPP(hAPP(c_COMBB(tc_fun(U_16665,tc_HOL_Obool),tc_fun(U_16665,tc_HOL_Obool),U_16665),hAPP(c_COMBS(U_16665,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16665),c_fimplies),hAPP(hAPP(c_COMBC(U_16665,tc_fun(U_16665,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16665)),U_16666)))),c_Orderings_Oord__class_Oless__eq(U_16665)))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16665) ),
    inference(variable_rename,[status(thm)],[f_4113_1]) ).

fof(f_4113_3,plain,
    ! [U_16665,U_16666] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16665,U_16666) = c_Complete__Lattice_OSup__class_OSup(U_16665,hAPP(c_Set_OCollect(U_16665),hAPP(hAPP(c_COMBB(tc_fun(U_16665,tc_HOL_Obool),tc_HOL_Obool,U_16665),c_HOL_OAll(U_16665)),hAPP(hAPP(c_COMBB(tc_fun(U_16665,tc_HOL_Obool),tc_fun(U_16665,tc_HOL_Obool),U_16665),hAPP(c_COMBS(U_16665,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16665),c_fimplies),hAPP(hAPP(c_COMBC(U_16665,tc_fun(U_16665,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16665)),U_16666)))),c_Orderings_Oord__class_Oless__eq(U_16665)))))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16665) ),
    inference(definitional_conversion,[status(esa)],[f_4113_2]) ).

cnf(f_4113_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_16665,U_16666) = c_Complete__Lattice_OSup__class_OSup(U_16665,hAPP(c_Set_OCollect(U_16665),hAPP(hAPP(c_COMBB(tc_fun(U_16665,tc_HOL_Obool),tc_HOL_Obool,U_16665),c_HOL_OAll(U_16665)),hAPP(hAPP(c_COMBB(tc_fun(U_16665,tc_HOL_Obool),tc_fun(U_16665,tc_HOL_Obool),U_16665),hAPP(c_COMBS(U_16665,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_16665),c_fimplies),hAPP(hAPP(c_COMBC(U_16665,tc_fun(U_16665,tc_HOL_Obool),tc_HOL_Obool),c_member(U_16665)),U_16666)))),c_Orderings_Oord__class_Oless__eq(U_16665)))))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16665) ),
    inference(clausify,[status(thm)],[f_4113_3]) ).

fof(f_4114_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_4114_2,plain,
    ! [U_16668,U_16667] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16667,tc_HOL_Obool)),U_16668))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16667),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16667,tc_HOL_Obool),U_16668))) ),
    inference(variable_rename,[status(thm)],[f_4114_1]) ).

fof(f_4114_3,plain,
    ! [U_16667,U_16668] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16667,tc_HOL_Obool)),U_16668))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16667),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16667,tc_HOL_Obool),U_16668))) ),
    inference(definitional_conversion,[status(esa)],[f_4114_2]) ).

cnf(f_4114_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16667,tc_HOL_Obool)),U_16668))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16667),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16667,tc_HOL_Obool),U_16668))) ),
    inference(clausify,[status(thm)],[f_4114_3]) ).

fof(f_4115_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_4115_2,plain,
    ! [U_16670,U_16669] : hAPP(c_Relation_OField(U_16669),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_16669,U_16669),tc_HOL_Obool),U_16670)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16669,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(U_16669,U_16669),tc_HOL_Obool),tc_fun(U_16669,tc_HOL_Obool),c_Relation_OField(U_16669)),U_16670)),
    inference(variable_rename,[status(thm)],[f_4115_1]) ).

fof(f_4115_3,plain,
    ! [U_16669,U_16670] : hAPP(c_Relation_OField(U_16669),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_16669,U_16669),tc_HOL_Obool),U_16670)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16669,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(U_16669,U_16669),tc_HOL_Obool),tc_fun(U_16669,tc_HOL_Obool),c_Relation_OField(U_16669)),U_16670)),
    inference(definitional_conversion,[status(esa)],[f_4115_2]) ).

cnf(f_4115_4,plain,
    hAPP(c_Relation_OField(U_16669),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_16669,U_16669),tc_HOL_Obool),U_16670)) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16669,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_fun(tc_prod(U_16669,U_16669),tc_HOL_Obool),tc_fun(U_16669,tc_HOL_Obool),c_Relation_OField(U_16669)),U_16670)),
    inference(clausify,[status(thm)],[f_4115_3]) ).

fof(f_4116_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_4116_2,plain,
    ! [U_16674,U_16673,U_16672,U_16671] : hAPP(hAPP(c_Product__Type_OSigma(U_16671,U_16672),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16671,tc_HOL_Obool),U_16673)),U_16674) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16671,tc_HOL_Obool),tc_fun(tc_prod(U_16671,U_16672),tc_HOL_Obool)),U_16673),hAPP(hAPP(c_COMBC(tc_fun(U_16671,tc_HOL_Obool),tc_fun(U_16671,tc_fun(U_16672,tc_HOL_Obool)),tc_fun(tc_prod(U_16671,U_16672),tc_HOL_Obool)),c_Product__Type_OSigma(U_16671,U_16672)),U_16674)),
    inference(variable_rename,[status(thm)],[f_4116_1]) ).

fof(f_4116_3,plain,
    ! [U_16671,U_16672,U_16673,U_16674] : hAPP(hAPP(c_Product__Type_OSigma(U_16671,U_16672),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16671,tc_HOL_Obool),U_16673)),U_16674) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16671,tc_HOL_Obool),tc_fun(tc_prod(U_16671,U_16672),tc_HOL_Obool)),U_16673),hAPP(hAPP(c_COMBC(tc_fun(U_16671,tc_HOL_Obool),tc_fun(U_16671,tc_fun(U_16672,tc_HOL_Obool)),tc_fun(tc_prod(U_16671,U_16672),tc_HOL_Obool)),c_Product__Type_OSigma(U_16671,U_16672)),U_16674)),
    inference(definitional_conversion,[status(esa)],[f_4116_2]) ).

cnf(f_4116_4,plain,
    hAPP(hAPP(c_Product__Type_OSigma(U_16671,U_16672),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16671,tc_HOL_Obool),U_16673)),U_16674) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16671,tc_HOL_Obool),tc_fun(tc_prod(U_16671,U_16672),tc_HOL_Obool)),U_16673),hAPP(hAPP(c_COMBC(tc_fun(U_16671,tc_HOL_Obool),tc_fun(U_16671,tc_fun(U_16672,tc_HOL_Obool)),tc_fun(tc_prod(U_16671,U_16672),tc_HOL_Obool)),c_Product__Type_OSigma(U_16671,U_16672)),U_16674)),
    inference(clausify,[status(thm)],[f_4116_3]) ).

fof(f_4117_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_4117_2,plain,
    ! [U_16678,U_16677,U_16676,U_16675] : hAPP(c_Set_Oimage(U_16675,U_16676,U_16677),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16675,tc_HOL_Obool),U_16678)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16675,tc_HOL_Obool),tc_fun(U_16676,tc_HOL_Obool)),U_16678),c_Set_Oimage(U_16675,U_16676,U_16677)),
    inference(variable_rename,[status(thm)],[f_4117_1]) ).

fof(f_4117_3,plain,
    ! [U_16675,U_16676,U_16677,U_16678] : hAPP(c_Set_Oimage(U_16675,U_16676,U_16677),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16675,tc_HOL_Obool),U_16678)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16675,tc_HOL_Obool),tc_fun(U_16676,tc_HOL_Obool)),U_16678),c_Set_Oimage(U_16675,U_16676,U_16677)),
    inference(definitional_conversion,[status(esa)],[f_4117_2]) ).

cnf(f_4117_4,plain,
    hAPP(c_Set_Oimage(U_16675,U_16676,U_16677),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16675,tc_HOL_Obool),U_16678)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16675,tc_HOL_Obool),tc_fun(U_16676,tc_HOL_Obool)),U_16678),c_Set_Oimage(U_16675,U_16676,U_16677)),
    inference(clausify,[status(thm)],[f_4117_3]) ).

fof(f_4118_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_4118_2,plain,
    ! [U_16681,U_16680,U_16679] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16679,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16679,tc_HOL_Obool),U_16680)),U_16681) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16679,tc_HOL_Obool),tc_fun(U_16679,tc_HOL_Obool)),U_16680),hAPP(hAPP(c_COMBC(tc_fun(U_16679,tc_HOL_Obool),tc_fun(U_16679,tc_HOL_Obool),tc_fun(U_16679,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16679,tc_HOL_Obool))),U_16681)),
    inference(variable_rename,[status(thm)],[f_4118_1]) ).

fof(f_4118_3,plain,
    ! [U_16679,U_16680,U_16681] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16679,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16679,tc_HOL_Obool),U_16680)),U_16681) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16679,tc_HOL_Obool),tc_fun(U_16679,tc_HOL_Obool)),U_16680),hAPP(hAPP(c_COMBC(tc_fun(U_16679,tc_HOL_Obool),tc_fun(U_16679,tc_HOL_Obool),tc_fun(U_16679,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16679,tc_HOL_Obool))),U_16681)),
    inference(definitional_conversion,[status(esa)],[f_4118_2]) ).

cnf(f_4118_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16679,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16679,tc_HOL_Obool),U_16680)),U_16681) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16679,tc_HOL_Obool),tc_fun(U_16679,tc_HOL_Obool)),U_16680),hAPP(hAPP(c_COMBC(tc_fun(U_16679,tc_HOL_Obool),tc_fun(U_16679,tc_HOL_Obool),tc_fun(U_16679,tc_HOL_Obool)),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16679,tc_HOL_Obool))),U_16681)),
    inference(clausify,[status(thm)],[f_4118_3]) ).

fof(f_4119_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_4119_2,plain,
    ! [U_16684,U_16683,U_16682] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16682,tc_HOL_Obool)),U_16683),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16682,tc_HOL_Obool),U_16684)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16682,tc_HOL_Obool),tc_fun(U_16682,tc_HOL_Obool)),U_16684),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16682,tc_HOL_Obool)),U_16683)),
    inference(variable_rename,[status(thm)],[f_4119_1]) ).

fof(f_4119_3,plain,
    ! [U_16682,U_16683,U_16684] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16682,tc_HOL_Obool)),U_16683),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16682,tc_HOL_Obool),U_16684)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16682,tc_HOL_Obool),tc_fun(U_16682,tc_HOL_Obool)),U_16684),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16682,tc_HOL_Obool)),U_16683)),
    inference(definitional_conversion,[status(esa)],[f_4119_2]) ).

cnf(f_4119_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16682,tc_HOL_Obool)),U_16683),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16682,tc_HOL_Obool),U_16684)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16682,tc_HOL_Obool),tc_fun(U_16682,tc_HOL_Obool)),U_16684),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16682,tc_HOL_Obool)),U_16683)),
    inference(clausify,[status(thm)],[f_4119_3]) ).

fof(f_4120_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_4120_2,plain,
    ! [U_16687,U_16686,U_16685] : hAPP(c_Relation_ODomain(U_16685,U_16686),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_16685,U_16686),tc_HOL_Obool),U_16687)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_16685,U_16686),tc_HOL_Obool),tc_fun(U_16685,tc_HOL_Obool)),U_16687),c_Relation_ODomain(U_16685,U_16686)),
    inference(variable_rename,[status(thm)],[f_4120_1]) ).

fof(f_4120_3,plain,
    ! [U_16685,U_16686,U_16687] : hAPP(c_Relation_ODomain(U_16685,U_16686),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_16685,U_16686),tc_HOL_Obool),U_16687)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_16685,U_16686),tc_HOL_Obool),tc_fun(U_16685,tc_HOL_Obool)),U_16687),c_Relation_ODomain(U_16685,U_16686)),
    inference(definitional_conversion,[status(esa)],[f_4120_2]) ).

cnf(f_4120_4,plain,
    hAPP(c_Relation_ODomain(U_16685,U_16686),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_16685,U_16686),tc_HOL_Obool),U_16687)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_16685,U_16686),tc_HOL_Obool),tc_fun(U_16685,tc_HOL_Obool)),U_16687),c_Relation_ODomain(U_16685,U_16686)),
    inference(clausify,[status(thm)],[f_4120_3]) ).

fof(f_4121_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_4121_2,plain,
    ! [U_16691,U_16690,U_16689,U_16688] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16688,tc_fun(U_16689,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16688,tc_HOL_Obool),U_16690)),U_16691) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16688,tc_HOL_Obool),tc_fun(U_16689,tc_HOL_Obool)),U_16690),hAPP(hAPP(c_COMBC(tc_fun(U_16688,tc_HOL_Obool),tc_fun(U_16688,tc_fun(U_16689,tc_HOL_Obool)),tc_fun(U_16689,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16688,tc_fun(U_16689,tc_HOL_Obool))),U_16691)),
    inference(variable_rename,[status(thm)],[f_4121_1]) ).

fof(f_4121_3,plain,
    ! [U_16688,U_16689,U_16690,U_16691] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16688,tc_fun(U_16689,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16688,tc_HOL_Obool),U_16690)),U_16691) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16688,tc_HOL_Obool),tc_fun(U_16689,tc_HOL_Obool)),U_16690),hAPP(hAPP(c_COMBC(tc_fun(U_16688,tc_HOL_Obool),tc_fun(U_16688,tc_fun(U_16689,tc_HOL_Obool)),tc_fun(U_16689,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16688,tc_fun(U_16689,tc_HOL_Obool))),U_16691)),
    inference(definitional_conversion,[status(esa)],[f_4121_2]) ).

cnf(f_4121_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16688,tc_fun(U_16689,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16688,tc_HOL_Obool),U_16690)),U_16691) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16688,tc_HOL_Obool),tc_fun(U_16689,tc_HOL_Obool)),U_16690),hAPP(hAPP(c_COMBC(tc_fun(U_16688,tc_HOL_Obool),tc_fun(U_16688,tc_fun(U_16689,tc_HOL_Obool)),tc_fun(U_16689,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16688,tc_fun(U_16689,tc_HOL_Obool))),U_16691)),
    inference(clausify,[status(thm)],[f_4121_3]) ).

fof(f_4122_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_4122_2,plain,
    ! [U_16695,U_16694,U_16693,U_16692] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16692,tc_HOL_Obool),tc_fun(U_16693,tc_HOL_Obool)),U_16694),hAPP(hAPP(c_COMBC(tc_fun(U_16692,tc_HOL_Obool),tc_fun(U_16692,tc_fun(U_16693,tc_HOL_Obool)),tc_fun(U_16693,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16692,tc_fun(U_16693,tc_HOL_Obool))),U_16695)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16692,tc_fun(U_16693,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16692,tc_HOL_Obool),U_16694)),U_16695),
    inference(variable_rename,[status(thm)],[f_4122_1]) ).

fof(f_4122_3,plain,
    ! [U_16692,U_16693,U_16694,U_16695] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16692,tc_HOL_Obool),tc_fun(U_16693,tc_HOL_Obool)),U_16694),hAPP(hAPP(c_COMBC(tc_fun(U_16692,tc_HOL_Obool),tc_fun(U_16692,tc_fun(U_16693,tc_HOL_Obool)),tc_fun(U_16693,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16692,tc_fun(U_16693,tc_HOL_Obool))),U_16695)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16692,tc_fun(U_16693,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16692,tc_HOL_Obool),U_16694)),U_16695),
    inference(definitional_conversion,[status(esa)],[f_4122_2]) ).

cnf(f_4122_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16692,tc_HOL_Obool),tc_fun(U_16693,tc_HOL_Obool)),U_16694),hAPP(hAPP(c_COMBC(tc_fun(U_16692,tc_HOL_Obool),tc_fun(U_16692,tc_fun(U_16693,tc_HOL_Obool)),tc_fun(U_16693,tc_HOL_Obool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16692,tc_fun(U_16693,tc_HOL_Obool))),U_16695)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16692,tc_fun(U_16693,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16692,tc_HOL_Obool),U_16694)),U_16695),
    inference(clausify,[status(thm)],[f_4122_3]) ).

fof(f_4123_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_4123_2,plain,
    ! [U_16698,U_16697,U_16696] : hAPP(c_Relation_ORange(U_16696,U_16697),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),U_16698)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),tc_fun(U_16697,tc_HOL_Obool)),U_16698),c_Relation_ORange(U_16696,U_16697)),
    inference(variable_rename,[status(thm)],[f_4123_1]) ).

fof(f_4123_3,plain,
    ! [U_16696,U_16697,U_16698] : hAPP(c_Relation_ORange(U_16696,U_16697),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),U_16698)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),tc_fun(U_16697,tc_HOL_Obool)),U_16698),c_Relation_ORange(U_16696,U_16697)),
    inference(definitional_conversion,[status(esa)],[f_4123_2]) ).

cnf(f_4123_4,plain,
    hAPP(c_Relation_ORange(U_16696,U_16697),c_Complete__Lattice_OSup__class_OSup(tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),U_16698)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(tc_prod(U_16696,U_16697),tc_HOL_Obool),tc_fun(U_16697,tc_HOL_Obool)),U_16698),c_Relation_ORange(U_16696,U_16697)),
    inference(clausify,[status(thm)],[f_4123_3]) ).

fof(f_4124_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_4124_2,plain,
    ! [U_16701,U_16700,U_16699] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16699,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16699,tc_HOL_Obool),U_16700)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16699,tc_HOL_Obool),U_16701)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_16699,tc_HOL_Obool),tc_HOL_Obool)),U_16700),U_16701)) ),
    inference(variable_rename,[status(thm)],[f_4124_1]) ).

fof(f_4124_3,plain,
    ! [U_16699,U_16700,U_16701] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16699,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16699,tc_HOL_Obool),U_16700)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16699,tc_HOL_Obool),U_16701)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_16699,tc_HOL_Obool),tc_HOL_Obool)),U_16700),U_16701)) ),
    inference(definitional_conversion,[status(esa)],[f_4124_2]) ).

cnf(f_4124_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16699,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16699,tc_HOL_Obool),U_16700)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16699,tc_HOL_Obool),U_16701)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_16699,tc_HOL_Obool),tc_HOL_Obool)),U_16700),U_16701)) ),
    inference(clausify,[status(thm)],[f_4124_3]) ).

fof(f_4125_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_4125_2,plain,
    ! [U_16704,U_16703,U_16702] :
      ( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16702,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_16702),U_16703),U_16704)) = U_16703
      | ~ c_Equiv__Relations_Oequiv(U_16702,U_16703,U_16704) ),
    inference(variable_rename,[status(thm)],[f_4125_1]) ).

fof(f_4125_3,plain,
    ! [U_16702,U_16703,U_16704] :
      ( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16702,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_16702),U_16703),U_16704)) = U_16703
      | ~ c_Equiv__Relations_Oequiv(U_16702,U_16703,U_16704) ),
    inference(definitional_conversion,[status(esa)],[f_4125_2]) ).

cnf(f_4125_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16702,tc_HOL_Obool),hAPP(hAPP(c_Equiv__Relations_Oquotient(U_16702),U_16703),U_16704)) = U_16703
    | ~ c_Equiv__Relations_Oequiv(U_16702,U_16703,U_16704) ),
    inference(clausify,[status(thm)],[f_4125_3]) ).

fof(f_4126_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_4126_2,plain,
    ! [U_16707,U_16706,U_16705] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16705,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16705,tc_HOL_Obool)),U_16706),U_16707)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16705,tc_HOL_Obool)),U_16706),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16705,tc_HOL_Obool),U_16707)),
    inference(variable_rename,[status(thm)],[f_4126_1]) ).

fof(f_4126_3,plain,
    ! [U_16705,U_16706,U_16707] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16705,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16705,tc_HOL_Obool)),U_16706),U_16707)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16705,tc_HOL_Obool)),U_16706),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16705,tc_HOL_Obool),U_16707)),
    inference(definitional_conversion,[status(esa)],[f_4126_2]) ).

cnf(f_4126_4,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16705,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16705,tc_HOL_Obool)),U_16706),U_16707)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16705,tc_HOL_Obool)),U_16706),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16705,tc_HOL_Obool),U_16707)),
    inference(clausify,[status(thm)],[f_4126_3]) ).

fof(f_4127_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_4127_2,plain,
    ! [U_16708] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16708,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16708,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_16708,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4127_1]) ).

fof(f_4127_3,plain,
    ! [U_16708] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16708,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16708,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_16708,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4127_2]) ).

cnf(f_4127_4,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16708,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16708,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_16708,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4127_3]) ).

fof(f_4128_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_4128_2,plain,
    ! [U_16711,U_16710,U_16709] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16709,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16709,tc_HOL_Obool),U_16711)),U_16710))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16709,tc_HOL_Obool)),U_16710),U_16711)) ),
    inference(variable_rename,[status(thm)],[f_4128_1]) ).

fof(f_4128_3,plain,
    ! [U_16709,U_16710,U_16711] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16709,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16709,tc_HOL_Obool),U_16711)),U_16710))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16709,tc_HOL_Obool)),U_16710),U_16711)) ),
    inference(definitional_conversion,[status(esa)],[f_4128_2]) ).

cnf(f_4128_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16709,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16709,tc_HOL_Obool),U_16711)),U_16710))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16709,tc_HOL_Obool)),U_16710),U_16711)) ),
    inference(clausify,[status(thm)],[f_4128_3]) ).

fof(f_4129_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_4129_2,plain,
    ! [U_16716,U_16715,U_16714] :
      ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16714,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16714,tc_HOL_Obool),U_16715)),U_16716) = c_Orderings_Obot__class_Obot(tc_fun(U_16714,tc_HOL_Obool))
        | ? [U_16713] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16714,tc_HOL_Obool)),U_16713),U_16716) != c_Orderings_Obot__class_Obot(tc_fun(U_16714,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16714,tc_HOL_Obool)),U_16713),U_16715)) ) )
      & ( ! [U_16712] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16714,tc_HOL_Obool)),U_16712),U_16716) = c_Orderings_Obot__class_Obot(tc_fun(U_16714,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16714,tc_HOL_Obool)),U_16712),U_16715)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16714,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16714,tc_HOL_Obool),U_16715)),U_16716) != c_Orderings_Obot__class_Obot(tc_fun(U_16714,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4129_1]) ).

fof(f_4129_3,plain,
    ( ! [U_16722,U_16720,U_16718] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16718,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16718,tc_HOL_Obool),U_16720)),U_16722) = c_Orderings_Obot__class_Obot(tc_fun(U_16718,tc_HOL_Obool))
        | ? [U_16713] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16718,tc_HOL_Obool)),U_16713),U_16722) != c_Orderings_Obot__class_Obot(tc_fun(U_16718,tc_HOL_Obool))
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16718,tc_HOL_Obool)),U_16713),U_16720)) ) )
    & ! [U_16721,U_16719,U_16717] :
        ( ! [U_16712] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16717,tc_HOL_Obool)),U_16712),U_16721) = c_Orderings_Obot__class_Obot(tc_fun(U_16717,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16717,tc_HOL_Obool)),U_16712),U_16719)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16717,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16717,tc_HOL_Obool),U_16719)),U_16721) != c_Orderings_Obot__class_Obot(tc_fun(U_16717,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4129_2]) ).

fof(f_4129_4,plain,
    ( ! [U_16722,U_16720,U_16718] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16718,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16718,tc_HOL_Obool),U_16720)),U_16722) = c_Orderings_Obot__class_Obot(tc_fun(U_16718,tc_HOL_Obool))
        | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16718,tc_HOL_Obool)),sK414(U_16722,U_16720,U_16718)),U_16722) != c_Orderings_Obot__class_Obot(tc_fun(U_16718,tc_HOL_Obool))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16718,tc_HOL_Obool)),sK414(U_16722,U_16720,U_16718)),U_16720)) ) )
    & ! [U_16721,U_16719,U_16717] :
        ( ! [U_16712] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16717,tc_HOL_Obool)),U_16712),U_16721) = c_Orderings_Obot__class_Obot(tc_fun(U_16717,tc_HOL_Obool))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16717,tc_HOL_Obool)),U_16712),U_16719)) )
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16717,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16717,tc_HOL_Obool),U_16719)),U_16721) != c_Orderings_Obot__class_Obot(tc_fun(U_16717,tc_HOL_Obool)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK414]),skolemize(U_16713,sK414(U_16722,U_16720,U_16718))],[f_4129_3]) ).

fof(f_4129_5,plain,
    ( ! [U_16722,U_16720,U_16718] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16718,tc_HOL_Obool)),sK414(U_16722,U_16720,U_16718)),U_16722) != c_Orderings_Obot__class_Obot(tc_fun(U_16718,tc_HOL_Obool))
        | ~ sP1071(U_16722,U_16720,U_16718) )
    & ! [U_16722,U_16720,U_16718] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16718,tc_HOL_Obool)),sK414(U_16722,U_16720,U_16718)),U_16720))
        | ~ sP1071(U_16722,U_16720,U_16718) )
    & ! [U_16722,U_16720,U_16718] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16718,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16718,tc_HOL_Obool),U_16720)),U_16722) = c_Orderings_Obot__class_Obot(tc_fun(U_16718,tc_HOL_Obool))
        | sP1071(U_16722,U_16720,U_16718) )
    & ! [U_16719,U_16721,U_16712,U_16717] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16717,tc_HOL_Obool)),U_16712),U_16721) = c_Orderings_Obot__class_Obot(tc_fun(U_16717,tc_HOL_Obool))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16717,tc_HOL_Obool)),U_16712),U_16719))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16717,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16717,tc_HOL_Obool),U_16719)),U_16721) != c_Orderings_Obot__class_Obot(tc_fun(U_16717,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1071])],[f_4129_4]) ).

cnf(f_4129_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16717,tc_HOL_Obool)),U_16712),U_16721) = c_Orderings_Obot__class_Obot(tc_fun(U_16717,tc_HOL_Obool))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16717,tc_HOL_Obool)),U_16712),U_16719))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16717,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16717,tc_HOL_Obool),U_16719)),U_16721) != c_Orderings_Obot__class_Obot(tc_fun(U_16717,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4129_5]) ).

cnf(f_4129_7,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16718,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16718,tc_HOL_Obool),U_16720)),U_16722) = c_Orderings_Obot__class_Obot(tc_fun(U_16718,tc_HOL_Obool))
    | sP1071(U_16722,U_16720,U_16718) ),
    inference(clausify,[status(thm)],[f_4129_5]) ).

cnf(f_4129_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16718,tc_HOL_Obool)),sK414(U_16722,U_16720,U_16718)),U_16720))
    | ~ sP1071(U_16722,U_16720,U_16718) ),
    inference(clausify,[status(thm)],[f_4129_5]) ).

cnf(f_4129_9,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16718,tc_HOL_Obool)),sK414(U_16722,U_16720,U_16718)),U_16722) != c_Orderings_Obot__class_Obot(tc_fun(U_16718,tc_HOL_Obool))
    | ~ sP1071(U_16722,U_16720,U_16718) ),
    inference(clausify,[status(thm)],[f_4129_5]) ).

fof(f_4130_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_4130_2,plain,
    ! [U_16727,U_16726,U_16725] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16725),c_Complete__Lattice_OSup__class_OSup(U_16725,U_16726)),U_16727))
          | ? [U_16724] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16725),U_16724),U_16727))
              & hBOOL(hAPP(hAPP(c_member(U_16725),U_16724),U_16726)) ) )
        & ( ! [U_16723] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16725),U_16723),U_16727))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16725),U_16723),U_16726)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16725),c_Complete__Lattice_OSup__class_OSup(U_16725,U_16726)),U_16727)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16725) ),
    inference(variable_rename,[status(thm)],[f_4130_1]) ).

fof(f_4130_3,plain,
    ! [U_16727,U_16726,U_16725] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16725),c_Complete__Lattice_OSup__class_OSup(U_16725,U_16726)),U_16727))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16725),sK415(U_16727,U_16726,U_16725)),U_16727))
            & hBOOL(hAPP(hAPP(c_member(U_16725),sK415(U_16727,U_16726,U_16725)),U_16726)) ) )
        & ( ! [U_16723] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16725),U_16723),U_16727))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16725),U_16723),U_16726)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16725),c_Complete__Lattice_OSup__class_OSup(U_16725,U_16726)),U_16727)) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16725) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK415]),skolemize(U_16724,sK415(U_16727,U_16726,U_16725))],[f_4130_2]) ).

fof(f_4130_4,plain,
    ( ! [U_16725,U_16726,U_16727] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16725),sK415(U_16727,U_16726,U_16725)),U_16727))
        | ~ sP1072(U_16725,U_16726,U_16727) )
    & ! [U_16725,U_16726,U_16727] :
        ( hBOOL(hAPP(hAPP(c_member(U_16725),sK415(U_16727,U_16726,U_16725)),U_16726))
        | ~ sP1072(U_16725,U_16726,U_16727) )
    & ! [U_16725,U_16723,U_16726,U_16727] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16725),c_Complete__Lattice_OSup__class_OSup(U_16725,U_16726)),U_16727))
        | sP1072(U_16725,U_16726,U_16727)
        | ~ sP1073(U_16725,U_16723,U_16726,U_16727) )
    & ! [U_16725,U_16723,U_16726,U_16727] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16725),U_16723),U_16727))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16725),U_16723),U_16726))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16725),c_Complete__Lattice_OSup__class_OSup(U_16725,U_16726)),U_16727))
        | ~ sP1073(U_16725,U_16723,U_16726,U_16727) )
    & ! [U_16725,U_16723,U_16726,U_16727] :
        ( sP1073(U_16725,U_16723,U_16726,U_16727)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_16725) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1072,sP1073])],[f_4130_3]) ).

cnf(f_4130_5,plain,
    ( sP1073(U_16725,U_16723,U_16726,U_16727)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16725) ),
    inference(clausify,[status(thm)],[f_4130_4]) ).

cnf(f_4130_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16725),U_16723),U_16727))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16725),U_16723),U_16726))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16725),c_Complete__Lattice_OSup__class_OSup(U_16725,U_16726)),U_16727))
    | ~ sP1073(U_16725,U_16723,U_16726,U_16727) ),
    inference(clausify,[status(thm)],[f_4130_4]) ).

cnf(f_4130_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16725),c_Complete__Lattice_OSup__class_OSup(U_16725,U_16726)),U_16727))
    | sP1072(U_16725,U_16726,U_16727)
    | ~ sP1073(U_16725,U_16723,U_16726,U_16727) ),
    inference(clausify,[status(thm)],[f_4130_4]) ).

cnf(f_4130_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16725),sK415(U_16727,U_16726,U_16725)),U_16726))
    | ~ sP1072(U_16725,U_16726,U_16727) ),
    inference(clausify,[status(thm)],[f_4130_4]) ).

cnf(f_4130_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16725),sK415(U_16727,U_16726,U_16725)),U_16727))
    | ~ sP1072(U_16725,U_16726,U_16727) ),
    inference(clausify,[status(thm)],[f_4130_4]) ).

fof(f_4131_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_4131_2,plain,
    ! [U_16732,U_16731,U_16730] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16730),U_16731),c_Complete__Lattice_OInf__class_OInf(U_16730,U_16732)))
          | ? [U_16729] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16730),U_16731),U_16729))
              & hBOOL(hAPP(hAPP(c_member(U_16730),U_16729),U_16732)) ) )
        & ( ! [U_16728] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16730),U_16731),U_16728))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16730),U_16728),U_16732)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16730),U_16731),c_Complete__Lattice_OInf__class_OInf(U_16730,U_16732))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16730) ),
    inference(variable_rename,[status(thm)],[f_4131_1]) ).

fof(f_4131_3,plain,
    ! [U_16732,U_16731,U_16730] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16730),U_16731),c_Complete__Lattice_OInf__class_OInf(U_16730,U_16732)))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16730),U_16731),sK416(U_16732,U_16731,U_16730)))
            & hBOOL(hAPP(hAPP(c_member(U_16730),sK416(U_16732,U_16731,U_16730)),U_16732)) ) )
        & ( ! [U_16728] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16730),U_16731),U_16728))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16730),U_16728),U_16732)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16730),U_16731),c_Complete__Lattice_OInf__class_OInf(U_16730,U_16732))) ) )
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16730) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK416]),skolemize(U_16729,sK416(U_16732,U_16731,U_16730))],[f_4131_2]) ).

fof(f_4131_4,plain,
    ( ! [U_16730,U_16731,U_16732] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16730),U_16731),sK416(U_16732,U_16731,U_16730)))
        | ~ sP1074(U_16730,U_16731,U_16732) )
    & ! [U_16730,U_16731,U_16732] :
        ( hBOOL(hAPP(hAPP(c_member(U_16730),sK416(U_16732,U_16731,U_16730)),U_16732))
        | ~ sP1074(U_16730,U_16731,U_16732) )
    & ! [U_16728,U_16730,U_16731,U_16732] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16730),U_16731),c_Complete__Lattice_OInf__class_OInf(U_16730,U_16732)))
        | sP1074(U_16730,U_16731,U_16732)
        | ~ sP1075(U_16728,U_16730,U_16731,U_16732) )
    & ! [U_16728,U_16730,U_16731,U_16732] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16730),U_16731),U_16728))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16730),U_16728),U_16732))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16730),U_16731),c_Complete__Lattice_OInf__class_OInf(U_16730,U_16732)))
        | ~ sP1075(U_16728,U_16730,U_16731,U_16732) )
    & ! [U_16728,U_16730,U_16731,U_16732] :
        ( sP1075(U_16728,U_16730,U_16731,U_16732)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_16730) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1074,sP1075])],[f_4131_3]) ).

cnf(f_4131_5,plain,
    ( sP1075(U_16728,U_16730,U_16731,U_16732)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16730) ),
    inference(clausify,[status(thm)],[f_4131_4]) ).

cnf(f_4131_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16730),U_16731),U_16728))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16730),U_16728),U_16732))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16730),U_16731),c_Complete__Lattice_OInf__class_OInf(U_16730,U_16732)))
    | ~ sP1075(U_16728,U_16730,U_16731,U_16732) ),
    inference(clausify,[status(thm)],[f_4131_4]) ).

cnf(f_4131_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16730),U_16731),c_Complete__Lattice_OInf__class_OInf(U_16730,U_16732)))
    | sP1074(U_16730,U_16731,U_16732)
    | ~ sP1075(U_16728,U_16730,U_16731,U_16732) ),
    inference(clausify,[status(thm)],[f_4131_4]) ).

cnf(f_4131_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16730),sK416(U_16732,U_16731,U_16730)),U_16732))
    | ~ sP1074(U_16730,U_16731,U_16732) ),
    inference(clausify,[status(thm)],[f_4131_4]) ).

cnf(f_4131_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16730),U_16731),sK416(U_16732,U_16731,U_16730)))
    | ~ sP1074(U_16730,U_16731,U_16732) ),
    inference(clausify,[status(thm)],[f_4131_4]) ).

fof(f_4132_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_4132_2,plain,
    ! [U_16737,U_16736,U_16735] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16735),U_16736),c_Complete__Lattice_OSup__class_OSup(U_16735,U_16737)))
          | ! [U_16734] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16735),U_16736),U_16734))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16735),U_16734),U_16737)) ) )
        & ( ? [U_16733] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16735),U_16736),U_16733))
              & hBOOL(hAPP(hAPP(c_member(U_16735),U_16733),U_16737)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16735),U_16736),c_Complete__Lattice_OSup__class_OSup(U_16735,U_16737))) ) )
      | ~ class_Orderings_Olinorder(U_16735)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16735) ),
    inference(variable_rename,[status(thm)],[f_4132_1]) ).

fof(f_4132_3,plain,
    ! [U_16737,U_16736,U_16735] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16735),U_16736),c_Complete__Lattice_OSup__class_OSup(U_16735,U_16737)))
          | ! [U_16734] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16735),U_16736),U_16734))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16735),U_16734),U_16737)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16735),U_16736),sK417(U_16737,U_16736,U_16735)))
            & hBOOL(hAPP(hAPP(c_member(U_16735),sK417(U_16737,U_16736,U_16735)),U_16737)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16735),U_16736),c_Complete__Lattice_OSup__class_OSup(U_16735,U_16737))) ) )
      | ~ class_Orderings_Olinorder(U_16735)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16735) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK417]),skolemize(U_16733,sK417(U_16737,U_16736,U_16735))],[f_4132_2]) ).

fof(f_4132_4,plain,
    ( ! [U_16735,U_16737,U_16736] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16735),U_16736),sK417(U_16737,U_16736,U_16735)))
        | ~ sP1076(U_16735,U_16737,U_16736) )
    & ! [U_16735,U_16737,U_16736] :
        ( hBOOL(hAPP(hAPP(c_member(U_16735),sK417(U_16737,U_16736,U_16735)),U_16737))
        | ~ sP1076(U_16735,U_16737,U_16736) )
    & ! [U_16735,U_16734,U_16737,U_16736] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16735),U_16736),c_Complete__Lattice_OSup__class_OSup(U_16735,U_16737)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16735),U_16736),U_16734))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16735),U_16734),U_16737))
        | ~ sP1077(U_16735,U_16734,U_16737,U_16736) )
    & ! [U_16735,U_16734,U_16737,U_16736] :
        ( sP1076(U_16735,U_16737,U_16736)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16735),U_16736),c_Complete__Lattice_OSup__class_OSup(U_16735,U_16737)))
        | ~ sP1077(U_16735,U_16734,U_16737,U_16736) )
    & ! [U_16735,U_16734,U_16737,U_16736] :
        ( sP1077(U_16735,U_16734,U_16737,U_16736)
        | ~ class_Orderings_Olinorder(U_16735)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_16735) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1076,sP1077])],[f_4132_3]) ).

cnf(f_4132_5,plain,
    ( sP1077(U_16735,U_16734,U_16737,U_16736)
    | ~ class_Orderings_Olinorder(U_16735)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16735) ),
    inference(clausify,[status(thm)],[f_4132_4]) ).

cnf(f_4132_6,plain,
    ( sP1076(U_16735,U_16737,U_16736)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16735),U_16736),c_Complete__Lattice_OSup__class_OSup(U_16735,U_16737)))
    | ~ sP1077(U_16735,U_16734,U_16737,U_16736) ),
    inference(clausify,[status(thm)],[f_4132_4]) ).

cnf(f_4132_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16735),U_16736),c_Complete__Lattice_OSup__class_OSup(U_16735,U_16737)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16735),U_16736),U_16734))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16735),U_16734),U_16737))
    | ~ sP1077(U_16735,U_16734,U_16737,U_16736) ),
    inference(clausify,[status(thm)],[f_4132_4]) ).

cnf(f_4132_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16735),sK417(U_16737,U_16736,U_16735)),U_16737))
    | ~ sP1076(U_16735,U_16737,U_16736) ),
    inference(clausify,[status(thm)],[f_4132_4]) ).

cnf(f_4132_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16735),U_16736),sK417(U_16737,U_16736,U_16735)))
    | ~ sP1076(U_16735,U_16737,U_16736) ),
    inference(clausify,[status(thm)],[f_4132_4]) ).

fof(f_4133_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_4133_2,plain,
    ! [U_16742,U_16741,U_16740] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16740),c_Complete__Lattice_OInf__class_OInf(U_16740,U_16741)),U_16742))
          | ! [U_16739] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16740),U_16739),U_16742))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16740),U_16739),U_16741)) ) )
        & ( ? [U_16738] :
              ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16740),U_16738),U_16742))
              & hBOOL(hAPP(hAPP(c_member(U_16740),U_16738),U_16741)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16740),c_Complete__Lattice_OInf__class_OInf(U_16740,U_16741)),U_16742)) ) )
      | ~ class_Orderings_Olinorder(U_16740)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16740) ),
    inference(variable_rename,[status(thm)],[f_4133_1]) ).

fof(f_4133_3,plain,
    ! [U_16742,U_16741,U_16740] :
      ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16740),c_Complete__Lattice_OInf__class_OInf(U_16740,U_16741)),U_16742))
          | ! [U_16739] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16740),U_16739),U_16742))
              | ~ hBOOL(hAPP(hAPP(c_member(U_16740),U_16739),U_16741)) ) )
        & ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16740),sK418(U_16742,U_16741,U_16740)),U_16742))
            & hBOOL(hAPP(hAPP(c_member(U_16740),sK418(U_16742,U_16741,U_16740)),U_16741)) )
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16740),c_Complete__Lattice_OInf__class_OInf(U_16740,U_16741)),U_16742)) ) )
      | ~ class_Orderings_Olinorder(U_16740)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16740) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK418]),skolemize(U_16738,sK418(U_16742,U_16741,U_16740))],[f_4133_2]) ).

fof(f_4133_4,plain,
    ( ! [U_16740,U_16741,U_16742] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16740),sK418(U_16742,U_16741,U_16740)),U_16742))
        | ~ sP1078(U_16740,U_16741,U_16742) )
    & ! [U_16740,U_16741,U_16742] :
        ( hBOOL(hAPP(hAPP(c_member(U_16740),sK418(U_16742,U_16741,U_16740)),U_16741))
        | ~ sP1078(U_16740,U_16741,U_16742) )
    & ! [U_16740,U_16739,U_16741,U_16742] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16740),c_Complete__Lattice_OInf__class_OInf(U_16740,U_16741)),U_16742))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16740),U_16739),U_16742))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16740),U_16739),U_16741))
        | ~ sP1079(U_16740,U_16739,U_16741,U_16742) )
    & ! [U_16740,U_16739,U_16741,U_16742] :
        ( sP1078(U_16740,U_16741,U_16742)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16740),c_Complete__Lattice_OInf__class_OInf(U_16740,U_16741)),U_16742))
        | ~ sP1079(U_16740,U_16739,U_16741,U_16742) )
    & ! [U_16740,U_16739,U_16741,U_16742] :
        ( sP1079(U_16740,U_16739,U_16741,U_16742)
        | ~ class_Orderings_Olinorder(U_16740)
        | ~ class_Complete__Lattice_Ocomplete__lattice(U_16740) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1078,sP1079])],[f_4133_3]) ).

cnf(f_4133_5,plain,
    ( sP1079(U_16740,U_16739,U_16741,U_16742)
    | ~ class_Orderings_Olinorder(U_16740)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16740) ),
    inference(clausify,[status(thm)],[f_4133_4]) ).

cnf(f_4133_6,plain,
    ( sP1078(U_16740,U_16741,U_16742)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16740),c_Complete__Lattice_OInf__class_OInf(U_16740,U_16741)),U_16742))
    | ~ sP1079(U_16740,U_16739,U_16741,U_16742) ),
    inference(clausify,[status(thm)],[f_4133_4]) ).

cnf(f_4133_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16740),c_Complete__Lattice_OInf__class_OInf(U_16740,U_16741)),U_16742))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16740),U_16739),U_16742))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16740),U_16739),U_16741))
    | ~ sP1079(U_16740,U_16739,U_16741,U_16742) ),
    inference(clausify,[status(thm)],[f_4133_4]) ).

cnf(f_4133_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16740),sK418(U_16742,U_16741,U_16740)),U_16741))
    | ~ sP1078(U_16740,U_16741,U_16742) ),
    inference(clausify,[status(thm)],[f_4133_4]) ).

cnf(f_4133_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16740),sK418(U_16742,U_16741,U_16740)),U_16742))
    | ~ sP1078(U_16740,U_16741,U_16742) ),
    inference(clausify,[status(thm)],[f_4133_4]) ).

fof(f_4134_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_4134_2,plain,
    ! [U_16744,U_16743] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16743,tc_HOL_Obool),hAPP(c_Set_OPow(U_16743),U_16744)) = U_16744,
    inference(variable_rename,[status(thm)],[f_4134_1]) ).

fof(f_4134_3,plain,
    ! [U_16743,U_16744] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16743,tc_HOL_Obool),hAPP(c_Set_OPow(U_16743),U_16744)) = U_16744,
    inference(definitional_conversion,[status(esa)],[f_4134_2]) ).

cnf(f_4134_4,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16743,tc_HOL_Obool),hAPP(c_Set_OPow(U_16743),U_16744)) = U_16744,
    inference(clausify,[status(thm)],[f_4134_3]) ).

fof(f_4135_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_4135_2,plain,
    ! [U_16747,U_16746,U_16745] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16745,tc_HOL_Obool)),U_16746),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16745,tc_HOL_Obool),U_16747)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16745,tc_HOL_Obool)),U_16746),U_16747)) ),
    inference(variable_rename,[status(thm)],[f_4135_1]) ).

fof(f_4135_3,plain,
    ! [U_16745,U_16746,U_16747] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16745,tc_HOL_Obool)),U_16746),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16745,tc_HOL_Obool),U_16747)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16745,tc_HOL_Obool)),U_16746),U_16747)) ),
    inference(definitional_conversion,[status(esa)],[f_4135_2]) ).

cnf(f_4135_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16745,tc_HOL_Obool)),U_16746),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16745,tc_HOL_Obool),U_16747)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_fun(U_16745,tc_HOL_Obool)),U_16746),U_16747)) ),
    inference(clausify,[status(thm)],[f_4135_3]) ).

fof(f_4136_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_4136_2,plain,
    ! [U_16749,U_16748] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_16748,tc_HOL_Obool),tc_HOL_Obool)),U_16749),hAPP(c_Set_OPow(U_16748),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16748,tc_HOL_Obool),U_16749)))),
    inference(variable_rename,[status(thm)],[f_4136_1]) ).

fof(f_4136_3,plain,
    ! [U_16748,U_16749] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_16748,tc_HOL_Obool),tc_HOL_Obool)),U_16749),hAPP(c_Set_OPow(U_16748),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16748,tc_HOL_Obool),U_16749)))),
    inference(definitional_conversion,[status(esa)],[f_4136_2]) ).

cnf(f_4136_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_16748,tc_HOL_Obool),tc_HOL_Obool)),U_16749),hAPP(c_Set_OPow(U_16748),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16748,tc_HOL_Obool),U_16749)))),
    inference(clausify,[status(thm)],[f_4136_3]) ).

fof(f_4137_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_4137_2,plain,
    ! [U_16750] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16750,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16750,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_16750,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4137_1]) ).

fof(f_4137_3,plain,
    ! [U_16750] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16750,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16750,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_16750,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4137_2]) ).

cnf(f_4137_4,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16750,tc_HOL_Obool),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16750,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_16750,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4137_3]) ).

fof(f_4138_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_4138_2,plain,
    ! [U_16753,U_16752,U_16751] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16751,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16751,tc_HOL_Obool),U_16753)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16751,tc_HOL_Obool),U_16752)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_16751,tc_HOL_Obool),tc_HOL_Obool)),U_16752),U_16753)) ),
    inference(variable_rename,[status(thm)],[f_4138_1]) ).

fof(f_4138_3,plain,
    ! [U_16751,U_16752,U_16753] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16751,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16751,tc_HOL_Obool),U_16753)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16751,tc_HOL_Obool),U_16752)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_16751,tc_HOL_Obool),tc_HOL_Obool)),U_16752),U_16753)) ),
    inference(definitional_conversion,[status(esa)],[f_4138_2]) ).

cnf(f_4138_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16751,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16751,tc_HOL_Obool),U_16753)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16751,tc_HOL_Obool),U_16752)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_fun(U_16751,tc_HOL_Obool),tc_HOL_Obool)),U_16752),U_16753)) ),
    inference(clausify,[status(thm)],[f_4138_3]) ).

fof(f_4139_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_4139_2,plain,
    ! [U_16754] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16754,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_16754,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_16754,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4139_1]) ).

fof(f_4139_3,plain,
    ! [U_16754] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16754,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_16754,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_16754,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4139_2]) ).

cnf(f_4139_4,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16754,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_16754,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(U_16754,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4139_3]) ).

fof(f_4140_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_4140_2,plain,
    ! [U_16757,U_16756,U_16755] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16755,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_16755,tc_HOL_Obool),tc_HOL_Obool)),U_16756),U_16757)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16755,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16755,tc_HOL_Obool),U_16756)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16755,tc_HOL_Obool),U_16757)),
    inference(variable_rename,[status(thm)],[f_4140_1]) ).

fof(f_4140_3,plain,
    ! [U_16755,U_16756,U_16757] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16755,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_16755,tc_HOL_Obool),tc_HOL_Obool)),U_16756),U_16757)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16755,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16755,tc_HOL_Obool),U_16756)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16755,tc_HOL_Obool),U_16757)),
    inference(definitional_conversion,[status(esa)],[f_4140_2]) ).

cnf(f_4140_4,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16755,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_16755,tc_HOL_Obool),tc_HOL_Obool)),U_16756),U_16757)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16755,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16755,tc_HOL_Obool),U_16756)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16755,tc_HOL_Obool),U_16757)),
    inference(clausify,[status(thm)],[f_4140_3]) ).

fof(f_4141_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_4141_2,plain,
    ! [U_16760,U_16759,U_16758] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16758,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16758,tc_HOL_Obool)),U_16759),U_16760)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16758,tc_HOL_Obool)),U_16759),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16758,tc_HOL_Obool),U_16760)),
    inference(variable_rename,[status(thm)],[f_4141_1]) ).

fof(f_4141_3,plain,
    ! [U_16758,U_16759,U_16760] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16758,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16758,tc_HOL_Obool)),U_16759),U_16760)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16758,tc_HOL_Obool)),U_16759),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16758,tc_HOL_Obool),U_16760)),
    inference(definitional_conversion,[status(esa)],[f_4141_2]) ).

cnf(f_4141_4,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16758,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16758,tc_HOL_Obool)),U_16759),U_16760)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16758,tc_HOL_Obool)),U_16759),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16758,tc_HOL_Obool),U_16760)),
    inference(clausify,[status(thm)],[f_4141_3]) ).

fof(f_4142_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_4142_2,plain,
    ! [U_16764,U_16763,U_16762,U_16761] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16761,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16762,tc_fun(U_16761,tc_HOL_Obool),U_16763),U_16764)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16762,tc_fun(U_16761,tc_HOL_Obool)),U_16764),U_16763),
    inference(variable_rename,[status(thm)],[f_4142_1]) ).

fof(f_4142_3,plain,
    ! [U_16761,U_16762,U_16763,U_16764] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16761,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16762,tc_fun(U_16761,tc_HOL_Obool),U_16763),U_16764)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16762,tc_fun(U_16761,tc_HOL_Obool)),U_16764),U_16763),
    inference(definitional_conversion,[status(esa)],[f_4142_2]) ).

cnf(f_4142_4,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16761,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16762,tc_fun(U_16761,tc_HOL_Obool),U_16763),U_16764)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16762,tc_fun(U_16761,tc_HOL_Obool)),U_16764),U_16763),
    inference(clausify,[status(thm)],[f_4142_3]) ).

fof(f_4143_1,plain,
    ! [V_B_2,V_A_2,T_b,T_c] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_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_4143_2,plain,
    ! [U_16768,U_16767,U_16766,U_16765] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16765,tc_fun(U_16766,tc_HOL_Obool)),U_16767),U_16768) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16766,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16765,tc_fun(U_16766,tc_HOL_Obool),U_16768),U_16767)),
    inference(variable_rename,[status(thm)],[f_4143_1]) ).

fof(f_4143_3,plain,
    ! [U_16765,U_16766,U_16767,U_16768] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16765,tc_fun(U_16766,tc_HOL_Obool)),U_16767),U_16768) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16766,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16765,tc_fun(U_16766,tc_HOL_Obool),U_16768),U_16767)),
    inference(definitional_conversion,[status(esa)],[f_4143_2]) ).

cnf(f_4143_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16765,tc_fun(U_16766,tc_HOL_Obool)),U_16767),U_16768) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16766,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16765,tc_fun(U_16766,tc_HOL_Obool),U_16768),U_16767)),
    inference(clausify,[status(thm)],[f_4143_3]) ).

fof(f_4144_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_4144_2,plain,
    ! [U_16771,U_16770,U_16769] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16769),U_16770),c_Complete__Lattice_OSup__class_OSup(U_16769,U_16771)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16769),U_16770),U_16771))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16769) ),
    inference(variable_rename,[status(thm)],[f_4144_1]) ).

fof(f_4144_3,plain,
    ! [U_16769,U_16770,U_16771] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16769),U_16770),c_Complete__Lattice_OSup__class_OSup(U_16769,U_16771)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16769),U_16770),U_16771))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16769) ),
    inference(definitional_conversion,[status(esa)],[f_4144_2]) ).

cnf(f_4144_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16769),U_16770),c_Complete__Lattice_OSup__class_OSup(U_16769,U_16771)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16769),U_16770),U_16771))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16769) ),
    inference(clausify,[status(thm)],[f_4144_3]) ).

fof(f_4145_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_4145_2,plain,
    ! [U_16772] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16772,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_16772,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_16772,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4145_1]) ).

fof(f_4145_3,plain,
    ! [U_16772] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16772,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_16772,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_16772,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4145_2]) ).

cnf(f_4145_4,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16772,tc_HOL_Obool),c_Orderings_Otop__class_Otop(tc_fun(tc_fun(U_16772,tc_HOL_Obool),tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(tc_fun(U_16772,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4145_3]) ).

fof(f_4146_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_4146_2,plain,
    ! [U_16775,U_16774,U_16773] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16773),c_Complete__Lattice_OInf__class_OInf(U_16773,U_16775)),U_16774))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16773),U_16774),U_16775))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16773) ),
    inference(variable_rename,[status(thm)],[f_4146_1]) ).

fof(f_4146_3,plain,
    ! [U_16773,U_16774,U_16775] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16773),c_Complete__Lattice_OInf__class_OInf(U_16773,U_16775)),U_16774))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16773),U_16774),U_16775))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16773) ),
    inference(definitional_conversion,[status(esa)],[f_4146_2]) ).

cnf(f_4146_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16773),c_Complete__Lattice_OInf__class_OInf(U_16773,U_16775)),U_16774))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16773),U_16774),U_16775))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16773) ),
    inference(clausify,[status(thm)],[f_4146_3]) ).

fof(f_4147_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_4147_2,plain,
    ! [U_16778,U_16777,U_16776] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16776,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_16776,tc_HOL_Obool),tc_HOL_Obool)),U_16777),U_16778)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16776,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16776,tc_HOL_Obool),U_16777)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16776,tc_HOL_Obool),U_16778)),
    inference(variable_rename,[status(thm)],[f_4147_1]) ).

fof(f_4147_3,plain,
    ! [U_16776,U_16777,U_16778] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16776,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_16776,tc_HOL_Obool),tc_HOL_Obool)),U_16777),U_16778)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16776,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16776,tc_HOL_Obool),U_16777)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16776,tc_HOL_Obool),U_16778)),
    inference(definitional_conversion,[status(esa)],[f_4147_2]) ).

cnf(f_4147_4,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16776,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(U_16776,tc_HOL_Obool),tc_HOL_Obool)),U_16777),U_16778)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16776,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16776,tc_HOL_Obool),U_16777)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16776,tc_HOL_Obool),U_16778)),
    inference(clausify,[status(thm)],[f_4147_3]) ).

fof(f_4148_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_4148_2,plain,
    ! [U_16779] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16779,c_Orderings_Obot__class_Obot(tc_fun(U_16779,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_16779)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16779) ),
    inference(variable_rename,[status(thm)],[f_4148_1]) ).

fof(f_4148_3,plain,
    ! [U_16779] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16779,c_Orderings_Obot__class_Obot(tc_fun(U_16779,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_16779)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16779) ),
    inference(definitional_conversion,[status(esa)],[f_4148_2]) ).

cnf(f_4148_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_16779,c_Orderings_Obot__class_Obot(tc_fun(U_16779,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_16779)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16779) ),
    inference(clausify,[status(thm)],[f_4148_3]) ).

fof(f_4149_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_4149_2,plain,
    ! [U_16781,U_16780] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16780,hAPP(hAPP(c_Set_Oinsert(U_16780),U_16781),c_Orderings_Obot__class_Obot(tc_fun(U_16780,tc_HOL_Obool)))) = U_16781
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16780) ),
    inference(variable_rename,[status(thm)],[f_4149_1]) ).

fof(f_4149_3,plain,
    ! [U_16780,U_16781] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16780,hAPP(hAPP(c_Set_Oinsert(U_16780),U_16781),c_Orderings_Obot__class_Obot(tc_fun(U_16780,tc_HOL_Obool)))) = U_16781
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16780) ),
    inference(definitional_conversion,[status(esa)],[f_4149_2]) ).

cnf(f_4149_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_16780,hAPP(hAPP(c_Set_Oinsert(U_16780),U_16781),c_Orderings_Obot__class_Obot(tc_fun(U_16780,tc_HOL_Obool)))) = U_16781
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16780) ),
    inference(clausify,[status(thm)],[f_4149_3]) ).

fof(f_4150_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_4150_2,plain,
    ! [U_16784,U_16783,U_16782] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16782,hAPP(hAPP(c_Set_Oinsert(U_16782),U_16783),U_16784)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16782),U_16783),c_Complete__Lattice_OSup__class_OSup(U_16782,U_16784))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16782) ),
    inference(variable_rename,[status(thm)],[f_4150_1]) ).

fof(f_4150_3,plain,
    ! [U_16782,U_16783,U_16784] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16782,hAPP(hAPP(c_Set_Oinsert(U_16782),U_16783),U_16784)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16782),U_16783),c_Complete__Lattice_OSup__class_OSup(U_16782,U_16784))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16782) ),
    inference(definitional_conversion,[status(esa)],[f_4150_2]) ).

cnf(f_4150_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_16782,hAPP(hAPP(c_Set_Oinsert(U_16782),U_16783),U_16784)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16782),U_16783),c_Complete__Lattice_OSup__class_OSup(U_16782,U_16784))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16782) ),
    inference(clausify,[status(thm)],[f_4150_3]) ).

fof(f_4151_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_4151_2,plain,
    ! [U_16789,U_16788,U_16787,U_16786,U_16785] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16785,tc_fun(U_16786,tc_HOL_Obool)),U_16787),hAPP(hAPP(c_COMBS(U_16785,tc_fun(U_16786,tc_HOL_Obool),tc_fun(U_16786,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16786,tc_HOL_Obool),tc_fun(tc_fun(U_16786,tc_HOL_Obool),tc_fun(U_16786,tc_HOL_Obool)),U_16785),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16786,tc_HOL_Obool))),U_16788)),U_16789)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16786,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16786,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16785,tc_fun(U_16786,tc_HOL_Obool),U_16788),U_16787))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16786,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16785,tc_fun(U_16786,tc_HOL_Obool),U_16789),U_16787))),
    inference(variable_rename,[status(thm)],[f_4151_1]) ).

fof(f_4151_3,plain,
    ! [U_16785,U_16786,U_16787,U_16788,U_16789] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16785,tc_fun(U_16786,tc_HOL_Obool)),U_16787),hAPP(hAPP(c_COMBS(U_16785,tc_fun(U_16786,tc_HOL_Obool),tc_fun(U_16786,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16786,tc_HOL_Obool),tc_fun(tc_fun(U_16786,tc_HOL_Obool),tc_fun(U_16786,tc_HOL_Obool)),U_16785),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16786,tc_HOL_Obool))),U_16788)),U_16789)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16786,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16786,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16785,tc_fun(U_16786,tc_HOL_Obool),U_16788),U_16787))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16786,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16785,tc_fun(U_16786,tc_HOL_Obool),U_16789),U_16787))),
    inference(definitional_conversion,[status(esa)],[f_4151_2]) ).

cnf(f_4151_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16785,tc_fun(U_16786,tc_HOL_Obool)),U_16787),hAPP(hAPP(c_COMBS(U_16785,tc_fun(U_16786,tc_HOL_Obool),tc_fun(U_16786,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16786,tc_HOL_Obool),tc_fun(tc_fun(U_16786,tc_HOL_Obool),tc_fun(U_16786,tc_HOL_Obool)),U_16785),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16786,tc_HOL_Obool))),U_16788)),U_16789)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16786,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16786,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16785,tc_fun(U_16786,tc_HOL_Obool),U_16788),U_16787))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16786,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16785,tc_fun(U_16786,tc_HOL_Obool),U_16789),U_16787))),
    inference(clausify,[status(thm)],[f_4151_3]) ).

fof(f_4152_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_4152_2,plain,
    ! [U_16791,U_16790] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16790,hAPP(hAPP(c_Set_Oinsert(U_16790),U_16791),c_Orderings_Obot__class_Obot(tc_fun(U_16790,tc_HOL_Obool)))) = U_16791
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16790) ),
    inference(variable_rename,[status(thm)],[f_4152_1]) ).

fof(f_4152_3,plain,
    ! [U_16790,U_16791] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16790,hAPP(hAPP(c_Set_Oinsert(U_16790),U_16791),c_Orderings_Obot__class_Obot(tc_fun(U_16790,tc_HOL_Obool)))) = U_16791
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16790) ),
    inference(definitional_conversion,[status(esa)],[f_4152_2]) ).

cnf(f_4152_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_16790,hAPP(hAPP(c_Set_Oinsert(U_16790),U_16791),c_Orderings_Obot__class_Obot(tc_fun(U_16790,tc_HOL_Obool)))) = U_16791
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16790) ),
    inference(clausify,[status(thm)],[f_4152_3]) ).

fof(f_4153_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_4153_2,plain,
    ! [U_16792] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16792,c_Orderings_Otop__class_Otop(tc_fun(U_16792,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_16792)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16792) ),
    inference(variable_rename,[status(thm)],[f_4153_1]) ).

fof(f_4153_3,plain,
    ! [U_16792] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16792,c_Orderings_Otop__class_Otop(tc_fun(U_16792,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_16792)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16792) ),
    inference(definitional_conversion,[status(esa)],[f_4153_2]) ).

cnf(f_4153_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_16792,c_Orderings_Otop__class_Otop(tc_fun(U_16792,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_16792)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16792) ),
    inference(clausify,[status(thm)],[f_4153_3]) ).

fof(f_4154_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_4154_2,plain,
    ! [U_16793] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16793,c_Orderings_Obot__class_Obot(tc_fun(U_16793,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_16793)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16793) ),
    inference(variable_rename,[status(thm)],[f_4154_1]) ).

fof(f_4154_3,plain,
    ! [U_16793] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16793,c_Orderings_Obot__class_Obot(tc_fun(U_16793,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_16793)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16793) ),
    inference(definitional_conversion,[status(esa)],[f_4154_2]) ).

cnf(f_4154_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_16793,c_Orderings_Obot__class_Obot(tc_fun(U_16793,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(U_16793)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16793) ),
    inference(clausify,[status(thm)],[f_4154_3]) ).

fof(f_4155_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_4155_2,plain,
    ! [U_16794] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16794,c_Orderings_Otop__class_Otop(tc_fun(U_16794,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_16794)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16794) ),
    inference(variable_rename,[status(thm)],[f_4155_1]) ).

fof(f_4155_3,plain,
    ! [U_16794] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16794,c_Orderings_Otop__class_Otop(tc_fun(U_16794,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_16794)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16794) ),
    inference(definitional_conversion,[status(esa)],[f_4155_2]) ).

cnf(f_4155_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_16794,c_Orderings_Otop__class_Otop(tc_fun(U_16794,tc_HOL_Obool))) = c_Orderings_Obot__class_Obot(U_16794)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16794) ),
    inference(clausify,[status(thm)],[f_4155_3]) ).

fof(f_4156_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_4156_2,plain,
    ! [U_16797,U_16796,U_16795] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16795,hAPP(hAPP(c_Set_Oinsert(U_16795),U_16796),U_16797)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16795),U_16796),c_Complete__Lattice_OInf__class_OInf(U_16795,U_16797))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16795) ),
    inference(variable_rename,[status(thm)],[f_4156_1]) ).

fof(f_4156_3,plain,
    ! [U_16795,U_16796,U_16797] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16795,hAPP(hAPP(c_Set_Oinsert(U_16795),U_16796),U_16797)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16795),U_16796),c_Complete__Lattice_OInf__class_OInf(U_16795,U_16797))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16795) ),
    inference(definitional_conversion,[status(esa)],[f_4156_2]) ).

cnf(f_4156_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_16795,hAPP(hAPP(c_Set_Oinsert(U_16795),U_16796),U_16797)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16795),U_16796),c_Complete__Lattice_OInf__class_OInf(U_16795,U_16797))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16795) ),
    inference(clausify,[status(thm)],[f_4156_3]) ).

fof(f_4157_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_4157_2,plain,
    ! [U_16800,U_16799,U_16798] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16798,tc_HOL_Obool)),U_16799),U_16800) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16798,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16798,tc_HOL_Obool)),U_16799),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16798,tc_HOL_Obool)),U_16800),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16798,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_4157_1]) ).

fof(f_4157_3,plain,
    ! [U_16798,U_16799,U_16800] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16798,tc_HOL_Obool)),U_16799),U_16800) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16798,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16798,tc_HOL_Obool)),U_16799),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16798,tc_HOL_Obool)),U_16800),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16798,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_4157_2]) ).

cnf(f_4157_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16798,tc_HOL_Obool)),U_16799),U_16800) = c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16798,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16798,tc_HOL_Obool)),U_16799),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16798,tc_HOL_Obool)),U_16800),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16798,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_4157_3]) ).

fof(f_4158_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_4158_2,plain,
    ! [U_16805,U_16804,U_16803,U_16802,U_16801] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16801,tc_fun(U_16802,tc_HOL_Obool)),U_16803),hAPP(hAPP(c_COMBS(U_16801,tc_fun(U_16802,tc_HOL_Obool),tc_fun(U_16802,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16802,tc_HOL_Obool),tc_fun(tc_fun(U_16802,tc_HOL_Obool),tc_fun(U_16802,tc_HOL_Obool)),U_16801),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16802,tc_HOL_Obool))),U_16804)),U_16805)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16802,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16802,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16801,tc_fun(U_16802,tc_HOL_Obool),U_16804),U_16803))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16802,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16801,tc_fun(U_16802,tc_HOL_Obool),U_16805),U_16803))),
    inference(variable_rename,[status(thm)],[f_4158_1]) ).

fof(f_4158_3,plain,
    ! [U_16801,U_16802,U_16803,U_16804,U_16805] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16801,tc_fun(U_16802,tc_HOL_Obool)),U_16803),hAPP(hAPP(c_COMBS(U_16801,tc_fun(U_16802,tc_HOL_Obool),tc_fun(U_16802,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16802,tc_HOL_Obool),tc_fun(tc_fun(U_16802,tc_HOL_Obool),tc_fun(U_16802,tc_HOL_Obool)),U_16801),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16802,tc_HOL_Obool))),U_16804)),U_16805)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16802,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16802,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16801,tc_fun(U_16802,tc_HOL_Obool),U_16804),U_16803))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16802,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16801,tc_fun(U_16802,tc_HOL_Obool),U_16805),U_16803))),
    inference(definitional_conversion,[status(esa)],[f_4158_2]) ).

cnf(f_4158_4,plain,
    hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_16801,tc_fun(U_16802,tc_HOL_Obool)),U_16803),hAPP(hAPP(c_COMBS(U_16801,tc_fun(U_16802,tc_HOL_Obool),tc_fun(U_16802,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_16802,tc_HOL_Obool),tc_fun(tc_fun(U_16802,tc_HOL_Obool),tc_fun(U_16802,tc_HOL_Obool)),U_16801),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16802,tc_HOL_Obool))),U_16804)),U_16805)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16802,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16802,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16801,tc_fun(U_16802,tc_HOL_Obool),U_16804),U_16803))),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16802,tc_HOL_Obool),hAPP(c_Set_Oimage(U_16801,tc_fun(U_16802,tc_HOL_Obool),U_16805),U_16803))),
    inference(clausify,[status(thm)],[f_4158_3]) ).

fof(f_4159_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_4159_2,plain,
    ! [U_16808,U_16807,U_16806] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16806,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16806,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_16806,tc_HOL_Obool),tc_HOL_Obool)),U_16807),U_16808))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16806,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16806,tc_HOL_Obool),U_16807)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16806,tc_HOL_Obool),U_16808)))),
    inference(variable_rename,[status(thm)],[f_4159_1]) ).

fof(f_4159_3,plain,
    ! [U_16806,U_16807,U_16808] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16806,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16806,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_16806,tc_HOL_Obool),tc_HOL_Obool)),U_16807),U_16808))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16806,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16806,tc_HOL_Obool),U_16807)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16806,tc_HOL_Obool),U_16808)))),
    inference(definitional_conversion,[status(esa)],[f_4159_2]) ).

cnf(f_4159_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16806,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16806,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_16806,tc_HOL_Obool),tc_HOL_Obool)),U_16807),U_16808))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16806,tc_HOL_Obool)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16806,tc_HOL_Obool),U_16807)),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16806,tc_HOL_Obool),U_16808)))),
    inference(clausify,[status(thm)],[f_4159_3]) ).

fof(f_4160_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_4160_2,plain,
    ! [U_16811,U_16810,U_16809] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16809,tc_HOL_Obool)),U_16810),U_16811) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16809,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16809,tc_HOL_Obool)),U_16810),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16809,tc_HOL_Obool)),U_16811),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16809,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_4160_1]) ).

fof(f_4160_3,plain,
    ! [U_16809,U_16810,U_16811] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16809,tc_HOL_Obool)),U_16810),U_16811) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16809,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16809,tc_HOL_Obool)),U_16810),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16809,tc_HOL_Obool)),U_16811),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16809,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_4160_2]) ).

cnf(f_4160_4,plain,
    hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16809,tc_HOL_Obool)),U_16810),U_16811) = c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16809,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16809,tc_HOL_Obool)),U_16810),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16809,tc_HOL_Obool)),U_16811),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16809,tc_HOL_Obool),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_4160_3]) ).

fof(f_4161_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_4161_2,plain,
    ! [U_16814,U_16813,U_16812] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16812,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16812,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16812,tc_HOL_Obool),U_16813)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16812,tc_HOL_Obool),U_16814))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16812,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_16812,tc_HOL_Obool),tc_HOL_Obool)),U_16813),U_16814)))),
    inference(variable_rename,[status(thm)],[f_4161_1]) ).

fof(f_4161_3,plain,
    ! [U_16812,U_16813,U_16814] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16812,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16812,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16812,tc_HOL_Obool),U_16813)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16812,tc_HOL_Obool),U_16814))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16812,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_16812,tc_HOL_Obool),tc_HOL_Obool)),U_16813),U_16814)))),
    inference(definitional_conversion,[status(esa)],[f_4161_2]) ).

cnf(f_4161_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16812,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16812,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16812,tc_HOL_Obool),U_16813)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16812,tc_HOL_Obool),U_16814))),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16812,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_fun(U_16812,tc_HOL_Obool),tc_HOL_Obool)),U_16813),U_16814)))),
    inference(clausify,[status(thm)],[f_4161_3]) ).

fof(f_4162_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_4162_2,plain,
    ! [U_16817,U_16816,U_16815] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16815,hAPP(hAPP(c_Set_Oinsert(U_16815),U_16816),hAPP(hAPP(c_Set_Oinsert(U_16815),U_16817),c_Orderings_Obot__class_Obot(tc_fun(U_16815,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16815),U_16816),U_16817)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16815) ),
    inference(variable_rename,[status(thm)],[f_4162_1]) ).

fof(f_4162_3,plain,
    ! [U_16815,U_16816,U_16817] :
      ( c_Complete__Lattice_OSup__class_OSup(U_16815,hAPP(hAPP(c_Set_Oinsert(U_16815),U_16816),hAPP(hAPP(c_Set_Oinsert(U_16815),U_16817),c_Orderings_Obot__class_Obot(tc_fun(U_16815,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16815),U_16816),U_16817)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16815) ),
    inference(definitional_conversion,[status(esa)],[f_4162_2]) ).

cnf(f_4162_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_16815,hAPP(hAPP(c_Set_Oinsert(U_16815),U_16816),hAPP(hAPP(c_Set_Oinsert(U_16815),U_16817),c_Orderings_Obot__class_Obot(tc_fun(U_16815,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16815),U_16816),U_16817)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16815) ),
    inference(clausify,[status(thm)],[f_4162_3]) ).

fof(f_4163_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_4163_2,plain,
    ! [U_16820,U_16819,U_16818] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16818,hAPP(hAPP(c_Set_Oinsert(U_16818),U_16819),hAPP(hAPP(c_Set_Oinsert(U_16818),U_16820),c_Orderings_Obot__class_Obot(tc_fun(U_16818,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16818),U_16819),U_16820)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16818) ),
    inference(variable_rename,[status(thm)],[f_4163_1]) ).

fof(f_4163_3,plain,
    ! [U_16818,U_16819,U_16820] :
      ( c_Complete__Lattice_OInf__class_OInf(U_16818,hAPP(hAPP(c_Set_Oinsert(U_16818),U_16819),hAPP(hAPP(c_Set_Oinsert(U_16818),U_16820),c_Orderings_Obot__class_Obot(tc_fun(U_16818,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16818),U_16819),U_16820)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16818) ),
    inference(definitional_conversion,[status(esa)],[f_4163_2]) ).

cnf(f_4163_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_16818,hAPP(hAPP(c_Set_Oinsert(U_16818),U_16819),hAPP(hAPP(c_Set_Oinsert(U_16818),U_16820),c_Orderings_Obot__class_Obot(tc_fun(U_16818,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16818),U_16819),U_16820)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16818) ),
    inference(clausify,[status(thm)],[f_4163_3]) ).

fof(f_4164_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_4164_2,plain,
    ! [U_16823,U_16822,U_16821] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16821),U_16823),c_Complete__Lattice_OSup__class_OSup(U_16821,U_16822)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16821,U_16821,c_Lattices_Osemilattice__sup__class_Osup(U_16821)),U_16823),U_16822)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16821),U_16822))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16821) ),
    inference(variable_rename,[status(thm)],[f_4164_1]) ).

fof(f_4164_3,plain,
    ! [U_16821,U_16822,U_16823] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16821),U_16823),c_Complete__Lattice_OSup__class_OSup(U_16821,U_16822)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16821,U_16821,c_Lattices_Osemilattice__sup__class_Osup(U_16821)),U_16823),U_16822)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16821),U_16822))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16821) ),
    inference(definitional_conversion,[status(esa)],[f_4164_2]) ).

cnf(f_4164_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16821),U_16823),c_Complete__Lattice_OSup__class_OSup(U_16821,U_16822)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16821,U_16821,c_Lattices_Osemilattice__sup__class_Osup(U_16821)),U_16823),U_16822)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16821),U_16822))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16821) ),
    inference(clausify,[status(thm)],[f_4164_3]) ).

fof(f_4165_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_4165_2,plain,
    ! [U_16825,U_16824] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_16824,U_16825) = c_Complete__Lattice_OSup__class_OSup(U_16824,U_16825)
      | U_16825 = c_Orderings_Obot__class_Obot(tc_fun(U_16824,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16824),U_16825))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16824) ),
    inference(variable_rename,[status(thm)],[f_4165_1]) ).

fof(f_4165_3,plain,
    ! [U_16824,U_16825] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_16824,U_16825) = c_Complete__Lattice_OSup__class_OSup(U_16824,U_16825)
      | U_16825 = c_Orderings_Obot__class_Obot(tc_fun(U_16824,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16824),U_16825))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16824) ),
    inference(definitional_conversion,[status(esa)],[f_4165_2]) ).

cnf(f_4165_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_16824,U_16825) = c_Complete__Lattice_OSup__class_OSup(U_16824,U_16825)
    | U_16825 = c_Orderings_Obot__class_Obot(tc_fun(U_16824,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16824),U_16825))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16824) ),
    inference(clausify,[status(thm)],[f_4165_3]) ).

fof(f_4166_1,plain,
    ! [V_B_2,V_A_2,T_b] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__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_4166_2,plain,
    ! [U_16828,U_16827,U_16826] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16826),U_16828),c_Complete__Lattice_OInf__class_OInf(U_16826,U_16827)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16826,U_16826,c_Lattices_Osemilattice__inf__class_Oinf(U_16826)),U_16828),U_16827)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16826),U_16827))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16826) ),
    inference(variable_rename,[status(thm)],[f_4166_1]) ).

fof(f_4166_3,plain,
    ! [U_16827,U_16826,U_16828] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16826),U_16828),c_Complete__Lattice_OInf__class_OInf(U_16826,U_16827)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16826,U_16826,c_Lattices_Osemilattice__inf__class_Oinf(U_16826)),U_16828),U_16827)
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16826),U_16827))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16826) ),
    inference(definitional_conversion,[status(esa)],[f_4166_2]) ).

cnf(f_4166_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16826),U_16828),c_Complete__Lattice_OInf__class_OInf(U_16826,U_16827)) = hAPP(hAPP(c_Finite__Set_Ofold(U_16826,U_16826,c_Lattices_Osemilattice__inf__class_Oinf(U_16826)),U_16828),U_16827)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16826),U_16827))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16826) ),
    inference(clausify,[status(thm)],[f_4166_3]) ).

fof(f_4167_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_4167_2,plain,
    ! [U_16830,U_16829] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_16829,U_16830) = c_Complete__Lattice_OInf__class_OInf(U_16829,U_16830)
      | U_16830 = c_Orderings_Obot__class_Obot(tc_fun(U_16829,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16829),U_16830))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16829) ),
    inference(variable_rename,[status(thm)],[f_4167_1]) ).

fof(f_4167_3,plain,
    ! [U_16829,U_16830] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_16829,U_16830) = c_Complete__Lattice_OInf__class_OInf(U_16829,U_16830)
      | U_16830 = c_Orderings_Obot__class_Obot(tc_fun(U_16829,tc_HOL_Obool))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16829),U_16830))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_16829) ),
    inference(definitional_conversion,[status(esa)],[f_4167_2]) ).

cnf(f_4167_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_16829,U_16830) = c_Complete__Lattice_OInf__class_OInf(U_16829,U_16830)
    | U_16830 = c_Orderings_Obot__class_Obot(tc_fun(U_16829,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16829),U_16830))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_16829) ),
    inference(clausify,[status(thm)],[f_4167_3]) ).

fof(f_4168_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_4168_2,plain,
    ! [U_16839,U_16838,U_16837,U_16836,U_16835,U_16834,U_16833,U_16832] :
      ( hAPP(c_Set_Oimage(U_16832,U_16833,U_16834),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16836,tc_fun(U_16832,tc_HOL_Obool)),U_16837),U_16838)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16836,tc_fun(U_16833,tc_HOL_Obool)),U_16837),hAPP(hAPP(c_COMBB(tc_fun(U_16832,tc_HOL_Obool),tc_fun(U_16833,tc_HOL_Obool),U_16836),c_Set_Oimage(U_16832,U_16833,U_16834)),U_16838))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16836),U_16839),U_16837))
      | ? [U_16831] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16832,tc_HOL_Obool)),hAPP(U_16838,U_16831)),U_16835))
          & hBOOL(hAPP(hAPP(c_member(U_16836),U_16831),U_16837)) )
      | ~ c_Fun_Oinj__on(U_16832,U_16833,U_16834,U_16835) ),
    inference(variable_rename,[status(thm)],[f_4168_1]) ).

fof(f_4168_3,plain,
    ! [U_16839,U_16838,U_16837,U_16836,U_16835,U_16834,U_16833,U_16832] :
      ( hAPP(c_Set_Oimage(U_16832,U_16833,U_16834),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16836,tc_fun(U_16832,tc_HOL_Obool)),U_16837),U_16838)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16836,tc_fun(U_16833,tc_HOL_Obool)),U_16837),hAPP(hAPP(c_COMBB(tc_fun(U_16832,tc_HOL_Obool),tc_fun(U_16833,tc_HOL_Obool),U_16836),c_Set_Oimage(U_16832,U_16833,U_16834)),U_16838))
      | ~ hBOOL(hAPP(hAPP(c_member(U_16836),U_16839),U_16837))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16832,tc_HOL_Obool)),hAPP(U_16838,sK419(U_16839,U_16838,U_16837,U_16836,U_16835,U_16834,U_16833,U_16832))),U_16835))
        & hBOOL(hAPP(hAPP(c_member(U_16836),sK419(U_16839,U_16838,U_16837,U_16836,U_16835,U_16834,U_16833,U_16832)),U_16837)) )
      | ~ c_Fun_Oinj__on(U_16832,U_16833,U_16834,U_16835) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK419]),skolemize(U_16831,sK419(U_16839,U_16838,U_16837,U_16836,U_16835,U_16834,U_16833,U_16832))],[f_4168_2]) ).

fof(f_4168_4,plain,
    ( ! [U_16832,U_16833,U_16834,U_16835,U_16836,U_16837,U_16838,U_16839] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16832,tc_HOL_Obool)),hAPP(U_16838,sK419(U_16839,U_16838,U_16837,U_16836,U_16835,U_16834,U_16833,U_16832))),U_16835))
        | ~ sP1080(U_16832,U_16833,U_16834,U_16835,U_16836,U_16837,U_16838,U_16839) )
    & ! [U_16832,U_16833,U_16834,U_16835,U_16836,U_16837,U_16838,U_16839] :
        ( hBOOL(hAPP(hAPP(c_member(U_16836),sK419(U_16839,U_16838,U_16837,U_16836,U_16835,U_16834,U_16833,U_16832)),U_16837))
        | ~ sP1080(U_16832,U_16833,U_16834,U_16835,U_16836,U_16837,U_16838,U_16839) )
    & ! [U_16832,U_16833,U_16834,U_16835,U_16836,U_16837,U_16838,U_16839] :
        ( hAPP(c_Set_Oimage(U_16832,U_16833,U_16834),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16836,tc_fun(U_16832,tc_HOL_Obool)),U_16837),U_16838)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16836,tc_fun(U_16833,tc_HOL_Obool)),U_16837),hAPP(hAPP(c_COMBB(tc_fun(U_16832,tc_HOL_Obool),tc_fun(U_16833,tc_HOL_Obool),U_16836),c_Set_Oimage(U_16832,U_16833,U_16834)),U_16838))
        | ~ hBOOL(hAPP(hAPP(c_member(U_16836),U_16839),U_16837))
        | sP1080(U_16832,U_16833,U_16834,U_16835,U_16836,U_16837,U_16838,U_16839)
        | ~ c_Fun_Oinj__on(U_16832,U_16833,U_16834,U_16835) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1080])],[f_4168_3]) ).

cnf(f_4168_5,plain,
    ( hAPP(c_Set_Oimage(U_16832,U_16833,U_16834),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16836,tc_fun(U_16832,tc_HOL_Obool)),U_16837),U_16838)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16836,tc_fun(U_16833,tc_HOL_Obool)),U_16837),hAPP(hAPP(c_COMBB(tc_fun(U_16832,tc_HOL_Obool),tc_fun(U_16833,tc_HOL_Obool),U_16836),c_Set_Oimage(U_16832,U_16833,U_16834)),U_16838))
    | ~ hBOOL(hAPP(hAPP(c_member(U_16836),U_16839),U_16837))
    | sP1080(U_16832,U_16833,U_16834,U_16835,U_16836,U_16837,U_16838,U_16839)
    | ~ c_Fun_Oinj__on(U_16832,U_16833,U_16834,U_16835) ),
    inference(clausify,[status(thm)],[f_4168_4]) ).

cnf(f_4168_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16836),sK419(U_16839,U_16838,U_16837,U_16836,U_16835,U_16834,U_16833,U_16832)),U_16837))
    | ~ sP1080(U_16832,U_16833,U_16834,U_16835,U_16836,U_16837,U_16838,U_16839) ),
    inference(clausify,[status(thm)],[f_4168_4]) ).

cnf(f_4168_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16832,tc_HOL_Obool)),hAPP(U_16838,sK419(U_16839,U_16838,U_16837,U_16836,U_16835,U_16834,U_16833,U_16832))),U_16835))
    | ~ sP1080(U_16832,U_16833,U_16834,U_16835,U_16836,U_16837,U_16838,U_16839) ),
    inference(clausify,[status(thm)],[f_4168_4]) ).

fof(f_4169_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_4169_2,plain,
    ! [U_16845,U_16844,U_16843] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_16845),hAPP(c_Finite__Set_Ocard(tc_fun(U_16843,tc_HOL_Obool)),U_16844)) = hAPP(c_Finite__Set_Ocard(U_16843),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16843,tc_HOL_Obool),U_16844))
      | ? [U_16842] :
          ( ? [U_16841] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16843,tc_HOL_Obool)),U_16842),U_16841) != c_Orderings_Obot__class_Obot(tc_fun(U_16843,tc_HOL_Obool))
              & U_16842 != U_16841
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16843,tc_HOL_Obool)),U_16841),U_16844)) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16843,tc_HOL_Obool)),U_16842),U_16844)) )
      | ? [U_16840] :
          ( hAPP(c_Finite__Set_Ocard(U_16843),U_16840) != U_16845
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16843,tc_HOL_Obool)),U_16840),U_16844)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16843),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16843,tc_HOL_Obool),U_16844)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16843,tc_HOL_Obool)),U_16844)) ),
    inference(variable_rename,[status(thm)],[f_4169_1]) ).

fof(f_4169_3,plain,
    ! [U_16845,U_16844,U_16843] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_16845),hAPP(c_Finite__Set_Ocard(tc_fun(U_16843,tc_HOL_Obool)),U_16844)) = hAPP(c_Finite__Set_Ocard(U_16843),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16843,tc_HOL_Obool),U_16844))
      | ? [U_16842] :
          ( ? [U_16841] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16843,tc_HOL_Obool)),U_16842),U_16841) != c_Orderings_Obot__class_Obot(tc_fun(U_16843,tc_HOL_Obool))
              & U_16842 != U_16841
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16843,tc_HOL_Obool)),U_16841),U_16844)) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16843,tc_HOL_Obool)),U_16842),U_16844)) )
      | ( hAPP(c_Finite__Set_Ocard(U_16843),sK420(U_16845,U_16844,U_16843)) != U_16845
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16843,tc_HOL_Obool)),sK420(U_16845,U_16844,U_16843)),U_16844)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16843),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16843,tc_HOL_Obool),U_16844)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16843,tc_HOL_Obool)),U_16844)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK420]),skolemize(U_16840,sK420(U_16845,U_16844,U_16843))],[f_4169_2]) ).

fof(f_4169_4,plain,
    ! [U_16845,U_16844,U_16843] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_16845),hAPP(c_Finite__Set_Ocard(tc_fun(U_16843,tc_HOL_Obool)),U_16844)) = hAPP(c_Finite__Set_Ocard(U_16843),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16843,tc_HOL_Obool),U_16844))
      | ( ? [U_16841] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16843,tc_HOL_Obool)),sK421(U_16845,U_16844,U_16843)),U_16841) != c_Orderings_Obot__class_Obot(tc_fun(U_16843,tc_HOL_Obool))
            & sK421(U_16845,U_16844,U_16843) != U_16841
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16843,tc_HOL_Obool)),U_16841),U_16844)) )
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16843,tc_HOL_Obool)),sK421(U_16845,U_16844,U_16843)),U_16844)) )
      | ( hAPP(c_Finite__Set_Ocard(U_16843),sK420(U_16845,U_16844,U_16843)) != U_16845
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16843,tc_HOL_Obool)),sK420(U_16845,U_16844,U_16843)),U_16844)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16843),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16843,tc_HOL_Obool),U_16844)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16843,tc_HOL_Obool)),U_16844)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK421]),skolemize(U_16842,sK421(U_16845,U_16844,U_16843))],[f_4169_3]) ).

fof(f_4169_5,plain,
    ! [U_16845,U_16844,U_16843] :
      ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_16845),hAPP(c_Finite__Set_Ocard(tc_fun(U_16843,tc_HOL_Obool)),U_16844)) = hAPP(c_Finite__Set_Ocard(U_16843),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16843,tc_HOL_Obool),U_16844))
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16843,tc_HOL_Obool)),sK421(U_16845,U_16844,U_16843)),sK422(U_16845,U_16844,U_16843)) != c_Orderings_Obot__class_Obot(tc_fun(U_16843,tc_HOL_Obool))
        & sK421(U_16845,U_16844,U_16843) != sK422(U_16845,U_16844,U_16843)
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16843,tc_HOL_Obool)),sK422(U_16845,U_16844,U_16843)),U_16844))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16843,tc_HOL_Obool)),sK421(U_16845,U_16844,U_16843)),U_16844)) )
      | ( hAPP(c_Finite__Set_Ocard(U_16843),sK420(U_16845,U_16844,U_16843)) != U_16845
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16843,tc_HOL_Obool)),sK420(U_16845,U_16844,U_16843)),U_16844)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16843),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16843,tc_HOL_Obool),U_16844)))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16843,tc_HOL_Obool)),U_16844)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK422]),skolemize(U_16841,sK422(U_16845,U_16844,U_16843))],[f_4169_4]) ).

fof(f_4169_6,plain,
    ( ! [U_16843,U_16844,U_16845] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16843,tc_HOL_Obool)),sK421(U_16845,U_16844,U_16843)),sK422(U_16845,U_16844,U_16843)) != c_Orderings_Obot__class_Obot(tc_fun(U_16843,tc_HOL_Obool))
        | ~ sP1082(U_16843,U_16844,U_16845) )
    & ! [U_16843,U_16844,U_16845] :
        ( sK421(U_16845,U_16844,U_16843) != sK422(U_16845,U_16844,U_16843)
        | ~ sP1082(U_16843,U_16844,U_16845) )
    & ! [U_16843,U_16844,U_16845] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16843,tc_HOL_Obool)),sK422(U_16845,U_16844,U_16843)),U_16844))
        | ~ sP1082(U_16843,U_16844,U_16845) )
    & ! [U_16843,U_16844,U_16845] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16843,tc_HOL_Obool)),sK421(U_16845,U_16844,U_16843)),U_16844))
        | ~ sP1082(U_16843,U_16844,U_16845) )
    & ! [U_16843,U_16844,U_16845] :
        ( hAPP(c_Finite__Set_Ocard(U_16843),sK420(U_16845,U_16844,U_16843)) != U_16845
        | ~ sP1081(U_16843,U_16844,U_16845) )
    & ! [U_16843,U_16844,U_16845] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16843,tc_HOL_Obool)),sK420(U_16845,U_16844,U_16843)),U_16844))
        | ~ sP1081(U_16843,U_16844,U_16845) )
    & ! [U_16843,U_16844,U_16845] :
        ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_16845),hAPP(c_Finite__Set_Ocard(tc_fun(U_16843,tc_HOL_Obool)),U_16844)) = hAPP(c_Finite__Set_Ocard(U_16843),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16843,tc_HOL_Obool),U_16844))
        | sP1082(U_16843,U_16844,U_16845)
        | sP1081(U_16843,U_16844,U_16845)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16843),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16843,tc_HOL_Obool),U_16844)))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16843,tc_HOL_Obool)),U_16844)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1081,sP1082])],[f_4169_5]) ).

cnf(f_4169_7,plain,
    ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),U_16845),hAPP(c_Finite__Set_Ocard(tc_fun(U_16843,tc_HOL_Obool)),U_16844)) = hAPP(c_Finite__Set_Ocard(U_16843),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16843,tc_HOL_Obool),U_16844))
    | sP1082(U_16843,U_16844,U_16845)
    | sP1081(U_16843,U_16844,U_16845)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16843),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16843,tc_HOL_Obool),U_16844)))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16843,tc_HOL_Obool)),U_16844)) ),
    inference(clausify,[status(thm)],[f_4169_6]) ).

cnf(f_4169_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16843,tc_HOL_Obool)),sK420(U_16845,U_16844,U_16843)),U_16844))
    | ~ sP1081(U_16843,U_16844,U_16845) ),
    inference(clausify,[status(thm)],[f_4169_6]) ).

cnf(f_4169_9,plain,
    ( hAPP(c_Finite__Set_Ocard(U_16843),sK420(U_16845,U_16844,U_16843)) != U_16845
    | ~ sP1081(U_16843,U_16844,U_16845) ),
    inference(clausify,[status(thm)],[f_4169_6]) ).

cnf(f_4169_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16843,tc_HOL_Obool)),sK421(U_16845,U_16844,U_16843)),U_16844))
    | ~ sP1082(U_16843,U_16844,U_16845) ),
    inference(clausify,[status(thm)],[f_4169_6]) ).

cnf(f_4169_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16843,tc_HOL_Obool)),sK422(U_16845,U_16844,U_16843)),U_16844))
    | ~ sP1082(U_16843,U_16844,U_16845) ),
    inference(clausify,[status(thm)],[f_4169_6]) ).

cnf(f_4169_12,plain,
    ( sK421(U_16845,U_16844,U_16843) != sK422(U_16845,U_16844,U_16843)
    | ~ sP1082(U_16843,U_16844,U_16845) ),
    inference(clausify,[status(thm)],[f_4169_6]) ).

cnf(f_4169_13,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16843,tc_HOL_Obool)),sK421(U_16845,U_16844,U_16843)),sK422(U_16845,U_16844,U_16843)) != c_Orderings_Obot__class_Obot(tc_fun(U_16843,tc_HOL_Obool))
    | ~ sP1082(U_16843,U_16844,U_16845) ),
    inference(clausify,[status(thm)],[f_4169_6]) ).

fof(f_4170_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_4170_2,plain,
    ! [U_16847,U_16846] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16846,tc_HOL_Obool),U_16847) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16846,tc_HOL_Obool),tc_fun(U_16846,tc_HOL_Obool)),U_16847),c_COMBI(tc_fun(U_16846,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4170_1]) ).

fof(f_4170_3,plain,
    ! [U_16846,U_16847] : c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16846,tc_HOL_Obool),U_16847) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16846,tc_HOL_Obool),tc_fun(U_16846,tc_HOL_Obool)),U_16847),c_COMBI(tc_fun(U_16846,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_4170_2]) ).

cnf(f_4170_4,plain,
    c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16846,tc_HOL_Obool),U_16847) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(tc_fun(U_16846,tc_HOL_Obool),tc_fun(U_16846,tc_HOL_Obool)),U_16847),c_COMBI(tc_fun(U_16846,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4170_3]) ).

fof(f_4171_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_4171_2,plain,
    ! [U_16849,U_16848] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16848,tc_HOL_Obool),U_16849) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16848,tc_HOL_Obool),tc_fun(U_16848,tc_HOL_Obool)),U_16849),c_COMBI(tc_fun(U_16848,tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4171_1]) ).

fof(f_4171_3,plain,
    ! [U_16848,U_16849] : c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16848,tc_HOL_Obool),U_16849) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16848,tc_HOL_Obool),tc_fun(U_16848,tc_HOL_Obool)),U_16849),c_COMBI(tc_fun(U_16848,tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_4171_2]) ).

cnf(f_4171_4,plain,
    c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16848,tc_HOL_Obool),U_16849) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_fun(U_16848,tc_HOL_Obool),tc_fun(U_16848,tc_HOL_Obool)),U_16849),c_COMBI(tc_fun(U_16848,tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4171_3]) ).

fof(f_4172_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_4172_2,plain,
    ! [U_16852,U_16851] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_16851),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16851,tc_HOL_Obool),U_16852)))
      | ? [U_16850] :
          ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16851),U_16850))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16851,tc_HOL_Obool)),U_16850),U_16852)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16851,tc_HOL_Obool)),U_16852)) ),
    inference(variable_rename,[status(thm)],[f_4172_1]) ).

fof(f_4172_3,plain,
    ! [U_16852,U_16851] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_16851),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16851,tc_HOL_Obool),U_16852)))
      | ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16851),sK423(U_16852,U_16851)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16851,tc_HOL_Obool)),sK423(U_16852,U_16851)),U_16852)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16851,tc_HOL_Obool)),U_16852)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK423]),skolemize(U_16850,sK423(U_16852,U_16851))],[f_4172_2]) ).

fof(f_4172_4,plain,
    ( ! [U_16851,U_16852] :
        ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16851),sK423(U_16852,U_16851)))
        | ~ sP1083(U_16851,U_16852) )
    & ! [U_16851,U_16852] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16851,tc_HOL_Obool)),sK423(U_16852,U_16851)),U_16852))
        | ~ sP1083(U_16851,U_16852) )
    & ! [U_16851,U_16852] :
        ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_16851),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16851,tc_HOL_Obool),U_16852)))
        | sP1083(U_16851,U_16852)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16851,tc_HOL_Obool)),U_16852)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1083])],[f_4172_3]) ).

cnf(f_4172_5,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(U_16851),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16851,tc_HOL_Obool),U_16852)))
    | sP1083(U_16851,U_16852)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(U_16851,tc_HOL_Obool)),U_16852)) ),
    inference(clausify,[status(thm)],[f_4172_4]) ).

cnf(f_4172_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16851,tc_HOL_Obool)),sK423(U_16852,U_16851)),U_16852))
    | ~ sP1083(U_16851,U_16852) ),
    inference(clausify,[status(thm)],[f_4172_4]) ).

cnf(f_4172_7,plain,
    ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16851),sK423(U_16852,U_16851)))
    | ~ sP1083(U_16851,U_16852) ),
    inference(clausify,[status(thm)],[f_4172_4]) ).

fof(f_4173_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_4173_2,plain,
    ! [U_16857,U_16856,U_16855] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16855,tc_HOL_Obool)),U_16856),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16855,tc_HOL_Obool),U_16857)) = c_Orderings_Obot__class_Obot(tc_fun(U_16855,tc_HOL_Obool))
      | ? [U_16854] :
          ( ? [U_16853] :
              ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16855,tc_HOL_Obool)),U_16854),U_16853) != c_Orderings_Obot__class_Obot(tc_fun(U_16855,tc_HOL_Obool))
              & U_16854 != U_16853
              & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16855,tc_HOL_Obool)),U_16853),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16855,tc_HOL_Obool)),U_16856),U_16857))) )
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16855,tc_HOL_Obool)),U_16854),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16855,tc_HOL_Obool)),U_16856),U_16857))) )
      | hBOOL(hAPP(hAPP(c_member(tc_fun(U_16855,tc_HOL_Obool)),U_16856),U_16857)) ),
    inference(variable_rename,[status(thm)],[f_4173_1]) ).

fof(f_4173_3,plain,
    ! [U_16857,U_16856,U_16855] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16855,tc_HOL_Obool)),U_16856),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16855,tc_HOL_Obool),U_16857)) = c_Orderings_Obot__class_Obot(tc_fun(U_16855,tc_HOL_Obool))
      | ( ? [U_16853] :
            ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16855,tc_HOL_Obool)),sK424(U_16857,U_16856,U_16855)),U_16853) != c_Orderings_Obot__class_Obot(tc_fun(U_16855,tc_HOL_Obool))
            & sK424(U_16857,U_16856,U_16855) != U_16853
            & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16855,tc_HOL_Obool)),U_16853),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16855,tc_HOL_Obool)),U_16856),U_16857))) )
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16855,tc_HOL_Obool)),sK424(U_16857,U_16856,U_16855)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16855,tc_HOL_Obool)),U_16856),U_16857))) )
      | hBOOL(hAPP(hAPP(c_member(tc_fun(U_16855,tc_HOL_Obool)),U_16856),U_16857)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK424]),skolemize(U_16854,sK424(U_16857,U_16856,U_16855))],[f_4173_2]) ).

fof(f_4173_4,plain,
    ! [U_16857,U_16856,U_16855] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16855,tc_HOL_Obool)),U_16856),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16855,tc_HOL_Obool),U_16857)) = c_Orderings_Obot__class_Obot(tc_fun(U_16855,tc_HOL_Obool))
      | ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16855,tc_HOL_Obool)),sK424(U_16857,U_16856,U_16855)),sK425(U_16857,U_16856,U_16855)) != c_Orderings_Obot__class_Obot(tc_fun(U_16855,tc_HOL_Obool))
        & sK424(U_16857,U_16856,U_16855) != sK425(U_16857,U_16856,U_16855)
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16855,tc_HOL_Obool)),sK425(U_16857,U_16856,U_16855)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16855,tc_HOL_Obool)),U_16856),U_16857)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16855,tc_HOL_Obool)),sK424(U_16857,U_16856,U_16855)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16855,tc_HOL_Obool)),U_16856),U_16857))) )
      | hBOOL(hAPP(hAPP(c_member(tc_fun(U_16855,tc_HOL_Obool)),U_16856),U_16857)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK425]),skolemize(U_16853,sK425(U_16857,U_16856,U_16855))],[f_4173_3]) ).

fof(f_4173_5,plain,
    ( ! [U_16856,U_16857,U_16855] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16855,tc_HOL_Obool)),sK424(U_16857,U_16856,U_16855)),sK425(U_16857,U_16856,U_16855)) != c_Orderings_Obot__class_Obot(tc_fun(U_16855,tc_HOL_Obool))
        | ~ sP1084(U_16856,U_16857,U_16855) )
    & ! [U_16856,U_16857,U_16855] :
        ( sK424(U_16857,U_16856,U_16855) != sK425(U_16857,U_16856,U_16855)
        | ~ sP1084(U_16856,U_16857,U_16855) )
    & ! [U_16856,U_16857,U_16855] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16855,tc_HOL_Obool)),sK425(U_16857,U_16856,U_16855)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16855,tc_HOL_Obool)),U_16856),U_16857)))
        | ~ sP1084(U_16856,U_16857,U_16855) )
    & ! [U_16856,U_16857,U_16855] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16855,tc_HOL_Obool)),sK424(U_16857,U_16856,U_16855)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16855,tc_HOL_Obool)),U_16856),U_16857)))
        | ~ sP1084(U_16856,U_16857,U_16855) )
    & ! [U_16856,U_16857,U_16855] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16855,tc_HOL_Obool)),U_16856),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16855,tc_HOL_Obool),U_16857)) = c_Orderings_Obot__class_Obot(tc_fun(U_16855,tc_HOL_Obool))
        | sP1084(U_16856,U_16857,U_16855)
        | hBOOL(hAPP(hAPP(c_member(tc_fun(U_16855,tc_HOL_Obool)),U_16856),U_16857)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1084])],[f_4173_4]) ).

cnf(f_4173_6,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16855,tc_HOL_Obool)),U_16856),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16855,tc_HOL_Obool),U_16857)) = c_Orderings_Obot__class_Obot(tc_fun(U_16855,tc_HOL_Obool))
    | sP1084(U_16856,U_16857,U_16855)
    | hBOOL(hAPP(hAPP(c_member(tc_fun(U_16855,tc_HOL_Obool)),U_16856),U_16857)) ),
    inference(clausify,[status(thm)],[f_4173_5]) ).

cnf(f_4173_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16855,tc_HOL_Obool)),sK424(U_16857,U_16856,U_16855)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16855,tc_HOL_Obool)),U_16856),U_16857)))
    | ~ sP1084(U_16856,U_16857,U_16855) ),
    inference(clausify,[status(thm)],[f_4173_5]) ).

cnf(f_4173_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16855,tc_HOL_Obool)),sK425(U_16857,U_16856,U_16855)),hAPP(hAPP(c_Set_Oinsert(tc_fun(U_16855,tc_HOL_Obool)),U_16856),U_16857)))
    | ~ sP1084(U_16856,U_16857,U_16855) ),
    inference(clausify,[status(thm)],[f_4173_5]) ).

cnf(f_4173_9,plain,
    ( sK424(U_16857,U_16856,U_16855) != sK425(U_16857,U_16856,U_16855)
    | ~ sP1084(U_16856,U_16857,U_16855) ),
    inference(clausify,[status(thm)],[f_4173_5]) ).

cnf(f_4173_10,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16855,tc_HOL_Obool)),sK424(U_16857,U_16856,U_16855)),sK425(U_16857,U_16856,U_16855)) != c_Orderings_Obot__class_Obot(tc_fun(U_16855,tc_HOL_Obool))
    | ~ sP1084(U_16856,U_16857,U_16855) ),
    inference(clausify,[status(thm)],[f_4173_5]) ).

fof(f_4174_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_4174_2,plain,
    ! [U_16862,U_16861,U_16860,U_16859] :
      ( c_Fun_Oinj__on(U_16860,U_16861,U_16862,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16860,tc_HOL_Obool),U_16859))
      | ? [U_16858] :
          ( ~ c_Fun_Oinj__on(U_16860,U_16861,U_16862,U_16858)
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16860,tc_HOL_Obool)),U_16858),U_16859)) )
      | U_16859 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16860,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_4174_1]) ).

fof(f_4174_3,plain,
    ! [U_16862,U_16861,U_16860,U_16859] :
      ( c_Fun_Oinj__on(U_16860,U_16861,U_16862,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16860,tc_HOL_Obool),U_16859))
      | ( ~ c_Fun_Oinj__on(U_16860,U_16861,U_16862,sK426(U_16862,U_16861,U_16860,U_16859))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16860,tc_HOL_Obool)),sK426(U_16862,U_16861,U_16860,U_16859)),U_16859)) )
      | U_16859 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16860,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK426]),skolemize(U_16858,sK426(U_16862,U_16861,U_16860,U_16859))],[f_4174_2]) ).

fof(f_4174_4,plain,
    ( ! [U_16860,U_16862,U_16861,U_16859] :
        ( ~ c_Fun_Oinj__on(U_16860,U_16861,U_16862,sK426(U_16862,U_16861,U_16860,U_16859))
        | ~ sP1085(U_16860,U_16862,U_16861,U_16859) )
    & ! [U_16860,U_16862,U_16861,U_16859] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16860,tc_HOL_Obool)),sK426(U_16862,U_16861,U_16860,U_16859)),U_16859))
        | ~ sP1085(U_16860,U_16862,U_16861,U_16859) )
    & ! [U_16860,U_16862,U_16861,U_16859] :
        ( c_Fun_Oinj__on(U_16860,U_16861,U_16862,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16860,tc_HOL_Obool),U_16859))
        | sP1085(U_16860,U_16862,U_16861,U_16859)
        | U_16859 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16860,tc_HOL_Obool),tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1085])],[f_4174_3]) ).

cnf(f_4174_5,plain,
    ( c_Fun_Oinj__on(U_16860,U_16861,U_16862,c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16860,tc_HOL_Obool),U_16859))
    | sP1085(U_16860,U_16862,U_16861,U_16859)
    | U_16859 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16860,tc_HOL_Obool),tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4174_4]) ).

cnf(f_4174_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16860,tc_HOL_Obool)),sK426(U_16862,U_16861,U_16860,U_16859)),U_16859))
    | ~ sP1085(U_16860,U_16862,U_16861,U_16859) ),
    inference(clausify,[status(thm)],[f_4174_4]) ).

cnf(f_4174_7,plain,
    ( ~ c_Fun_Oinj__on(U_16860,U_16861,U_16862,sK426(U_16862,U_16861,U_16860,U_16859))
    | ~ sP1085(U_16860,U_16862,U_16861,U_16859) ),
    inference(clausify,[status(thm)],[f_4174_4]) ).

fof(f_4175_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_4175_2,plain,
    ! [U_16866,U_16865,U_16864] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16864,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16864,tc_HOL_Obool),U_16865)),U_16866))
      | U_16865 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16864,tc_HOL_Obool),tc_HOL_Obool))
      | ? [U_16863] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16864,tc_HOL_Obool)),U_16863),U_16866))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16864,tc_HOL_Obool)),U_16863),U_16865)) ) ),
    inference(variable_rename,[status(thm)],[f_4175_1]) ).

fof(f_4175_3,plain,
    ! [U_16866,U_16865,U_16864] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16864,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16864,tc_HOL_Obool),U_16865)),U_16866))
      | U_16865 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16864,tc_HOL_Obool),tc_HOL_Obool))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16864,tc_HOL_Obool)),sK427(U_16866,U_16865,U_16864)),U_16866))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16864,tc_HOL_Obool)),sK427(U_16866,U_16865,U_16864)),U_16865)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK427]),skolemize(U_16863,sK427(U_16866,U_16865,U_16864))],[f_4175_2]) ).

fof(f_4175_4,plain,
    ( ! [U_16864,U_16865,U_16866] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16864,tc_HOL_Obool)),sK427(U_16866,U_16865,U_16864)),U_16866))
        | ~ sP1086(U_16864,U_16865,U_16866) )
    & ! [U_16864,U_16865,U_16866] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16864,tc_HOL_Obool)),sK427(U_16866,U_16865,U_16864)),U_16865))
        | ~ sP1086(U_16864,U_16865,U_16866) )
    & ! [U_16864,U_16865,U_16866] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16864,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16864,tc_HOL_Obool),U_16865)),U_16866))
        | U_16865 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16864,tc_HOL_Obool),tc_HOL_Obool))
        | sP1086(U_16864,U_16865,U_16866) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1086])],[f_4175_3]) ).

cnf(f_4175_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16864,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16864,tc_HOL_Obool),U_16865)),U_16866))
    | U_16865 = c_Orderings_Obot__class_Obot(tc_fun(tc_fun(U_16864,tc_HOL_Obool),tc_HOL_Obool))
    | sP1086(U_16864,U_16865,U_16866) ),
    inference(clausify,[status(thm)],[f_4175_4]) ).

cnf(f_4175_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16864,tc_HOL_Obool)),sK427(U_16866,U_16865,U_16864)),U_16865))
    | ~ sP1086(U_16864,U_16865,U_16866) ),
    inference(clausify,[status(thm)],[f_4175_4]) ).

cnf(f_4175_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16864,tc_HOL_Obool)),sK427(U_16866,U_16865,U_16864)),U_16866))
    | ~ sP1086(U_16864,U_16865,U_16866) ),
    inference(clausify,[status(thm)],[f_4175_4]) ).

fof(f_4176_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_4176_2,plain,
    ! [U_16873,U_16872,U_16871,U_16870,U_16869,U_16868] :
      ( c_Fun_Oinj__on(U_16870,U_16871,U_16872,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16869,tc_fun(U_16870,tc_HOL_Obool)),U_16868),U_16873))
      | ? [U_16867] :
          ( ~ c_Fun_Oinj__on(U_16870,U_16871,U_16872,hAPP(U_16873,U_16867))
          & hBOOL(hAPP(hAPP(c_member(U_16869),U_16867),U_16868)) )
      | U_16868 = c_Orderings_Obot__class_Obot(tc_fun(U_16869,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_4176_1]) ).

fof(f_4176_3,plain,
    ! [U_16873,U_16872,U_16871,U_16870,U_16869,U_16868] :
      ( c_Fun_Oinj__on(U_16870,U_16871,U_16872,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16869,tc_fun(U_16870,tc_HOL_Obool)),U_16868),U_16873))
      | ( ~ c_Fun_Oinj__on(U_16870,U_16871,U_16872,hAPP(U_16873,sK428(U_16873,U_16872,U_16871,U_16870,U_16869,U_16868)))
        & hBOOL(hAPP(hAPP(c_member(U_16869),sK428(U_16873,U_16872,U_16871,U_16870,U_16869,U_16868)),U_16868)) )
      | U_16868 = c_Orderings_Obot__class_Obot(tc_fun(U_16869,tc_HOL_Obool)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK428]),skolemize(U_16867,sK428(U_16873,U_16872,U_16871,U_16870,U_16869,U_16868))],[f_4176_2]) ).

fof(f_4176_4,plain,
    ( ! [U_16869,U_16868,U_16870,U_16871,U_16872,U_16873] :
        ( ~ c_Fun_Oinj__on(U_16870,U_16871,U_16872,hAPP(U_16873,sK428(U_16873,U_16872,U_16871,U_16870,U_16869,U_16868)))
        | ~ sP1087(U_16869,U_16868,U_16870,U_16871,U_16872,U_16873) )
    & ! [U_16869,U_16868,U_16870,U_16871,U_16872,U_16873] :
        ( hBOOL(hAPP(hAPP(c_member(U_16869),sK428(U_16873,U_16872,U_16871,U_16870,U_16869,U_16868)),U_16868))
        | ~ sP1087(U_16869,U_16868,U_16870,U_16871,U_16872,U_16873) )
    & ! [U_16869,U_16868,U_16870,U_16871,U_16872,U_16873] :
        ( c_Fun_Oinj__on(U_16870,U_16871,U_16872,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16869,tc_fun(U_16870,tc_HOL_Obool)),U_16868),U_16873))
        | sP1087(U_16869,U_16868,U_16870,U_16871,U_16872,U_16873)
        | U_16868 = c_Orderings_Obot__class_Obot(tc_fun(U_16869,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1087])],[f_4176_3]) ).

cnf(f_4176_5,plain,
    ( c_Fun_Oinj__on(U_16870,U_16871,U_16872,hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_16869,tc_fun(U_16870,tc_HOL_Obool)),U_16868),U_16873))
    | sP1087(U_16869,U_16868,U_16870,U_16871,U_16872,U_16873)
    | U_16868 = c_Orderings_Obot__class_Obot(tc_fun(U_16869,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4176_4]) ).

cnf(f_4176_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16869),sK428(U_16873,U_16872,U_16871,U_16870,U_16869,U_16868)),U_16868))
    | ~ sP1087(U_16869,U_16868,U_16870,U_16871,U_16872,U_16873) ),
    inference(clausify,[status(thm)],[f_4176_4]) ).

cnf(f_4176_7,plain,
    ( ~ c_Fun_Oinj__on(U_16870,U_16871,U_16872,hAPP(U_16873,sK428(U_16873,U_16872,U_16871,U_16870,U_16869,U_16868)))
    | ~ sP1087(U_16869,U_16868,U_16870,U_16871,U_16872,U_16873) ),
    inference(clausify,[status(thm)],[f_4176_4]) ).

fof(f_4177_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_4177_2,plain,
    ! [U_16881,U_16880,U_16879,U_16878,U_16877,U_16876,U_16875] :
      ( ? [U_16874] :
          ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16875,U_16876,U_16877,U_16878,U_16880),U_16874))
          & U_16881 = hAPP(hAPP(U_16877,U_16879),U_16874) )
      | hBOOL(hAPP(hAPP(c_member(U_16875),U_16879),U_16880))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16875,U_16876,U_16877,U_16878,hAPP(hAPP(c_Set_Oinsert(U_16875),U_16879),U_16880)),U_16881))
      | ~ c_Finite__Set_Ofun__left__comm(U_16875,U_16876,U_16877) ),
    inference(variable_rename,[status(thm)],[f_4177_1]) ).

fof(f_4177_3,plain,
    ! [U_16881,U_16880,U_16879,U_16878,U_16877,U_16876,U_16875] :
      ( ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16875,U_16876,U_16877,U_16878,U_16880),sK429(U_16881,U_16880,U_16879,U_16878,U_16877,U_16876,U_16875)))
        & U_16881 = hAPP(hAPP(U_16877,U_16879),sK429(U_16881,U_16880,U_16879,U_16878,U_16877,U_16876,U_16875)) )
      | hBOOL(hAPP(hAPP(c_member(U_16875),U_16879),U_16880))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16875,U_16876,U_16877,U_16878,hAPP(hAPP(c_Set_Oinsert(U_16875),U_16879),U_16880)),U_16881))
      | ~ c_Finite__Set_Ofun__left__comm(U_16875,U_16876,U_16877) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK429]),skolemize(U_16874,sK429(U_16881,U_16880,U_16879,U_16878,U_16877,U_16876,U_16875))],[f_4177_2]) ).

fof(f_4177_4,plain,
    ( ! [U_16876,U_16877,U_16875,U_16878,U_16879,U_16880,U_16881] :
        ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16875,U_16876,U_16877,U_16878,U_16880),sK429(U_16881,U_16880,U_16879,U_16878,U_16877,U_16876,U_16875)))
        | ~ sP1088(U_16876,U_16877,U_16875,U_16878,U_16879,U_16880,U_16881) )
    & ! [U_16876,U_16877,U_16875,U_16878,U_16879,U_16880,U_16881] :
        ( U_16881 = hAPP(hAPP(U_16877,U_16879),sK429(U_16881,U_16880,U_16879,U_16878,U_16877,U_16876,U_16875))
        | ~ sP1088(U_16876,U_16877,U_16875,U_16878,U_16879,U_16880,U_16881) )
    & ! [U_16876,U_16877,U_16875,U_16878,U_16879,U_16880,U_16881] :
        ( sP1088(U_16876,U_16877,U_16875,U_16878,U_16879,U_16880,U_16881)
        | hBOOL(hAPP(hAPP(c_member(U_16875),U_16879),U_16880))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16875,U_16876,U_16877,U_16878,hAPP(hAPP(c_Set_Oinsert(U_16875),U_16879),U_16880)),U_16881))
        | ~ c_Finite__Set_Ofun__left__comm(U_16875,U_16876,U_16877) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1088])],[f_4177_3]) ).

cnf(f_4177_5,plain,
    ( sP1088(U_16876,U_16877,U_16875,U_16878,U_16879,U_16880,U_16881)
    | hBOOL(hAPP(hAPP(c_member(U_16875),U_16879),U_16880))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16875,U_16876,U_16877,U_16878,hAPP(hAPP(c_Set_Oinsert(U_16875),U_16879),U_16880)),U_16881))
    | ~ c_Finite__Set_Ofun__left__comm(U_16875,U_16876,U_16877) ),
    inference(clausify,[status(thm)],[f_4177_4]) ).

cnf(f_4177_6,plain,
    ( U_16881 = hAPP(hAPP(U_16877,U_16879),sK429(U_16881,U_16880,U_16879,U_16878,U_16877,U_16876,U_16875))
    | ~ sP1088(U_16876,U_16877,U_16875,U_16878,U_16879,U_16880,U_16881) ),
    inference(clausify,[status(thm)],[f_4177_4]) ).

cnf(f_4177_7,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(U_16875,U_16876,U_16877,U_16878,U_16880),sK429(U_16881,U_16880,U_16879,U_16878,U_16877,U_16876,U_16875)))
    | ~ sP1088(U_16876,U_16877,U_16875,U_16878,U_16879,U_16880,U_16881) ),
    inference(clausify,[status(thm)],[f_4177_4]) ).

fof(f_4178_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_4178_2,plain,
    ! [U_16886,U_16885,U_16884,U_16883] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16883),hAPP(hAPP(c_Finite__Set_Ofold(U_16883,U_16883,c_Orderings_Oord__class_Omax(U_16883)),U_16886),U_16884)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_16883),U_16885),U_16886)))
      | ? [U_16882] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16883),U_16882),U_16885))
          & hBOOL(hAPP(hAPP(c_member(U_16883),U_16882),U_16884)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16883),U_16884))
      | ~ class_Orderings_Olinorder(U_16883) ),
    inference(variable_rename,[status(thm)],[f_4178_1]) ).

fof(f_4178_3,plain,
    ! [U_16886,U_16885,U_16884,U_16883] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16883),hAPP(hAPP(c_Finite__Set_Ofold(U_16883,U_16883,c_Orderings_Oord__class_Omax(U_16883)),U_16886),U_16884)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_16883),U_16885),U_16886)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16883),sK430(U_16886,U_16885,U_16884,U_16883)),U_16885))
        & hBOOL(hAPP(hAPP(c_member(U_16883),sK430(U_16886,U_16885,U_16884,U_16883)),U_16884)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16883),U_16884))
      | ~ class_Orderings_Olinorder(U_16883) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK430]),skolemize(U_16882,sK430(U_16886,U_16885,U_16884,U_16883))],[f_4178_2]) ).

fof(f_4178_4,plain,
    ( ! [U_16883,U_16884,U_16885,U_16886] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16883),sK430(U_16886,U_16885,U_16884,U_16883)),U_16885))
        | ~ sP1089(U_16883,U_16884,U_16885,U_16886) )
    & ! [U_16883,U_16884,U_16885,U_16886] :
        ( hBOOL(hAPP(hAPP(c_member(U_16883),sK430(U_16886,U_16885,U_16884,U_16883)),U_16884))
        | ~ sP1089(U_16883,U_16884,U_16885,U_16886) )
    & ! [U_16883,U_16884,U_16885,U_16886] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16883),hAPP(hAPP(c_Finite__Set_Ofold(U_16883,U_16883,c_Orderings_Oord__class_Omax(U_16883)),U_16886),U_16884)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_16883),U_16885),U_16886)))
        | sP1089(U_16883,U_16884,U_16885,U_16886)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16883),U_16884))
        | ~ class_Orderings_Olinorder(U_16883) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1089])],[f_4178_3]) ).

cnf(f_4178_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16883),hAPP(hAPP(c_Finite__Set_Ofold(U_16883,U_16883,c_Orderings_Oord__class_Omax(U_16883)),U_16886),U_16884)),hAPP(hAPP(c_Orderings_Oord__class_Omax(U_16883),U_16885),U_16886)))
    | sP1089(U_16883,U_16884,U_16885,U_16886)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16883),U_16884))
    | ~ class_Orderings_Olinorder(U_16883) ),
    inference(clausify,[status(thm)],[f_4178_4]) ).

cnf(f_4178_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16883),sK430(U_16886,U_16885,U_16884,U_16883)),U_16884))
    | ~ sP1089(U_16883,U_16884,U_16885,U_16886) ),
    inference(clausify,[status(thm)],[f_4178_4]) ).

cnf(f_4178_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16883),sK430(U_16886,U_16885,U_16884,U_16883)),U_16885))
    | ~ sP1089(U_16883,U_16884,U_16885,U_16886) ),
    inference(clausify,[status(thm)],[f_4178_4]) ).

fof(f_4179_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_4179_2,plain,
    ! [U_16891,U_16890,U_16889,U_16888] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16888),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_16888),U_16890),U_16891)),hAPP(hAPP(c_Finite__Set_Ofold(U_16888,U_16888,c_Orderings_Oord__class_Omin(U_16888)),U_16891),U_16889)))
      | ? [U_16887] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16888),U_16890),U_16887))
          & hBOOL(hAPP(hAPP(c_member(U_16888),U_16887),U_16889)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16888),U_16889))
      | ~ class_Orderings_Olinorder(U_16888) ),
    inference(variable_rename,[status(thm)],[f_4179_1]) ).

fof(f_4179_3,plain,
    ! [U_16891,U_16890,U_16889,U_16888] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16888),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_16888),U_16890),U_16891)),hAPP(hAPP(c_Finite__Set_Ofold(U_16888,U_16888,c_Orderings_Oord__class_Omin(U_16888)),U_16891),U_16889)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16888),U_16890),sK431(U_16891,U_16890,U_16889,U_16888)))
        & hBOOL(hAPP(hAPP(c_member(U_16888),sK431(U_16891,U_16890,U_16889,U_16888)),U_16889)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16888),U_16889))
      | ~ class_Orderings_Olinorder(U_16888) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK431]),skolemize(U_16887,sK431(U_16891,U_16890,U_16889,U_16888))],[f_4179_2]) ).

fof(f_4179_4,plain,
    ( ! [U_16888,U_16889,U_16890,U_16891] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16888),U_16890),sK431(U_16891,U_16890,U_16889,U_16888)))
        | ~ sP1090(U_16888,U_16889,U_16890,U_16891) )
    & ! [U_16888,U_16889,U_16890,U_16891] :
        ( hBOOL(hAPP(hAPP(c_member(U_16888),sK431(U_16891,U_16890,U_16889,U_16888)),U_16889))
        | ~ sP1090(U_16888,U_16889,U_16890,U_16891) )
    & ! [U_16888,U_16889,U_16890,U_16891] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16888),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_16888),U_16890),U_16891)),hAPP(hAPP(c_Finite__Set_Ofold(U_16888,U_16888,c_Orderings_Oord__class_Omin(U_16888)),U_16891),U_16889)))
        | sP1090(U_16888,U_16889,U_16890,U_16891)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16888),U_16889))
        | ~ class_Orderings_Olinorder(U_16888) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1090])],[f_4179_3]) ).

cnf(f_4179_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16888),hAPP(hAPP(c_Orderings_Oord__class_Omin(U_16888),U_16890),U_16891)),hAPP(hAPP(c_Finite__Set_Ofold(U_16888,U_16888,c_Orderings_Oord__class_Omin(U_16888)),U_16891),U_16889)))
    | sP1090(U_16888,U_16889,U_16890,U_16891)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16888),U_16889))
    | ~ class_Orderings_Olinorder(U_16888) ),
    inference(clausify,[status(thm)],[f_4179_4]) ).

cnf(f_4179_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16888),sK431(U_16891,U_16890,U_16889,U_16888)),U_16889))
    | ~ sP1090(U_16888,U_16889,U_16890,U_16891) ),
    inference(clausify,[status(thm)],[f_4179_4]) ).

cnf(f_4179_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16888),U_16890),sK431(U_16891,U_16890,U_16889,U_16888)))
    | ~ sP1090(U_16888,U_16889,U_16890,U_16891) ),
    inference(clausify,[status(thm)],[f_4179_4]) ).

fof(f_4180_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_4180_2,plain,
    ! [U_16895,U_16894,U_16893] :
      ( hBOOL(hAPP(hAPP(c_member(U_16893),U_16895),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16893,tc_HOL_Obool),U_16894)))
      | ? [U_16892] :
          ( ~ hBOOL(hAPP(hAPP(c_member(U_16893),U_16895),U_16892))
          & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16893,tc_HOL_Obool)),U_16892),U_16894)) ) ),
    inference(variable_rename,[status(thm)],[f_4180_1]) ).

fof(f_4180_3,plain,
    ! [U_16895,U_16894,U_16893] :
      ( hBOOL(hAPP(hAPP(c_member(U_16893),U_16895),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16893,tc_HOL_Obool),U_16894)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_16893),U_16895),sK432(U_16895,U_16894,U_16893)))
        & hBOOL(hAPP(hAPP(c_member(tc_fun(U_16893,tc_HOL_Obool)),sK432(U_16895,U_16894,U_16893)),U_16894)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK432]),skolemize(U_16892,sK432(U_16895,U_16894,U_16893))],[f_4180_2]) ).

fof(f_4180_4,plain,
    ( ! [U_16895,U_16894,U_16893] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_16893),U_16895),sK432(U_16895,U_16894,U_16893)))
        | ~ sP1091(U_16895,U_16894,U_16893) )
    & ! [U_16895,U_16894,U_16893] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16893,tc_HOL_Obool)),sK432(U_16895,U_16894,U_16893)),U_16894))
        | ~ sP1091(U_16895,U_16894,U_16893) )
    & ! [U_16895,U_16894,U_16893] :
        ( hBOOL(hAPP(hAPP(c_member(U_16893),U_16895),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16893,tc_HOL_Obool),U_16894)))
        | sP1091(U_16895,U_16894,U_16893) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1091])],[f_4180_3]) ).

cnf(f_4180_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16893),U_16895),c_Complete__Lattice_OInf__class_OInf(tc_fun(U_16893,tc_HOL_Obool),U_16894)))
    | sP1091(U_16895,U_16894,U_16893) ),
    inference(clausify,[status(thm)],[f_4180_4]) ).

cnf(f_4180_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16893,tc_HOL_Obool)),sK432(U_16895,U_16894,U_16893)),U_16894))
    | ~ sP1091(U_16895,U_16894,U_16893) ),
    inference(clausify,[status(thm)],[f_4180_4]) ).

cnf(f_4180_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_16893),U_16895),sK432(U_16895,U_16894,U_16893)))
    | ~ sP1091(U_16895,U_16894,U_16893) ),
    inference(clausify,[status(thm)],[f_4180_4]) ).

fof(f_4181_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_4181_2,plain,
    ! [U_16900,U_16899,U_16898,U_16897] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16897),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16897),U_16899),U_16900)),hAPP(hAPP(c_Finite__Set_Ofold(U_16897,U_16897,c_Lattices_Osemilattice__inf__class_Oinf(U_16897)),U_16900),U_16898)))
      | ? [U_16896] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16897),U_16899),U_16896))
          & hBOOL(hAPP(hAPP(c_member(U_16897),U_16896),U_16898)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16897),U_16898))
      | ~ class_Lattices_Osemilattice__inf(U_16897) ),
    inference(variable_rename,[status(thm)],[f_4181_1]) ).

fof(f_4181_3,plain,
    ! [U_16900,U_16899,U_16898,U_16897] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16897),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16897),U_16899),U_16900)),hAPP(hAPP(c_Finite__Set_Ofold(U_16897,U_16897,c_Lattices_Osemilattice__inf__class_Oinf(U_16897)),U_16900),U_16898)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16897),U_16899),sK433(U_16900,U_16899,U_16898,U_16897)))
        & hBOOL(hAPP(hAPP(c_member(U_16897),sK433(U_16900,U_16899,U_16898,U_16897)),U_16898)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16897),U_16898))
      | ~ class_Lattices_Osemilattice__inf(U_16897) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK433]),skolemize(U_16896,sK433(U_16900,U_16899,U_16898,U_16897))],[f_4181_2]) ).

fof(f_4181_4,plain,
    ( ! [U_16897,U_16898,U_16899,U_16900] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16897),U_16899),sK433(U_16900,U_16899,U_16898,U_16897)))
        | ~ sP1092(U_16897,U_16898,U_16899,U_16900) )
    & ! [U_16897,U_16898,U_16899,U_16900] :
        ( hBOOL(hAPP(hAPP(c_member(U_16897),sK433(U_16900,U_16899,U_16898,U_16897)),U_16898))
        | ~ sP1092(U_16897,U_16898,U_16899,U_16900) )
    & ! [U_16897,U_16898,U_16899,U_16900] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16897),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16897),U_16899),U_16900)),hAPP(hAPP(c_Finite__Set_Ofold(U_16897,U_16897,c_Lattices_Osemilattice__inf__class_Oinf(U_16897)),U_16900),U_16898)))
        | sP1092(U_16897,U_16898,U_16899,U_16900)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16897),U_16898))
        | ~ class_Lattices_Osemilattice__inf(U_16897) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1092])],[f_4181_3]) ).

cnf(f_4181_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16897),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(U_16897),U_16899),U_16900)),hAPP(hAPP(c_Finite__Set_Ofold(U_16897,U_16897,c_Lattices_Osemilattice__inf__class_Oinf(U_16897)),U_16900),U_16898)))
    | sP1092(U_16897,U_16898,U_16899,U_16900)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16897),U_16898))
    | ~ class_Lattices_Osemilattice__inf(U_16897) ),
    inference(clausify,[status(thm)],[f_4181_4]) ).

cnf(f_4181_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16897),sK433(U_16900,U_16899,U_16898,U_16897)),U_16898))
    | ~ sP1092(U_16897,U_16898,U_16899,U_16900) ),
    inference(clausify,[status(thm)],[f_4181_4]) ).

cnf(f_4181_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16897),U_16899),sK433(U_16900,U_16899,U_16898,U_16897)))
    | ~ sP1092(U_16897,U_16898,U_16899,U_16900) ),
    inference(clausify,[status(thm)],[f_4181_4]) ).

fof(f_4182_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_4182_2,plain,
    ! [U_16905,U_16904,U_16903,U_16902] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16902),hAPP(hAPP(c_Finite__Set_Ofold(U_16902,U_16902,c_Lattices_Osemilattice__sup__class_Osup(U_16902)),U_16905),U_16903)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16902),U_16904),U_16905)))
      | ? [U_16901] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16902),U_16901),U_16904))
          & hBOOL(hAPP(hAPP(c_member(U_16902),U_16901),U_16903)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16902),U_16903))
      | ~ class_Lattices_Osemilattice__sup(U_16902) ),
    inference(variable_rename,[status(thm)],[f_4182_1]) ).

fof(f_4182_3,plain,
    ! [U_16905,U_16904,U_16903,U_16902] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16902),hAPP(hAPP(c_Finite__Set_Ofold(U_16902,U_16902,c_Lattices_Osemilattice__sup__class_Osup(U_16902)),U_16905),U_16903)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16902),U_16904),U_16905)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16902),sK434(U_16905,U_16904,U_16903,U_16902)),U_16904))
        & hBOOL(hAPP(hAPP(c_member(U_16902),sK434(U_16905,U_16904,U_16903,U_16902)),U_16903)) )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16902),U_16903))
      | ~ class_Lattices_Osemilattice__sup(U_16902) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK434]),skolemize(U_16901,sK434(U_16905,U_16904,U_16903,U_16902))],[f_4182_2]) ).

fof(f_4182_4,plain,
    ( ! [U_16902,U_16903,U_16904,U_16905] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16902),sK434(U_16905,U_16904,U_16903,U_16902)),U_16904))
        | ~ sP1093(U_16902,U_16903,U_16904,U_16905) )
    & ! [U_16902,U_16903,U_16904,U_16905] :
        ( hBOOL(hAPP(hAPP(c_member(U_16902),sK434(U_16905,U_16904,U_16903,U_16902)),U_16903))
        | ~ sP1093(U_16902,U_16903,U_16904,U_16905) )
    & ! [U_16902,U_16903,U_16904,U_16905] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16902),hAPP(hAPP(c_Finite__Set_Ofold(U_16902,U_16902,c_Lattices_Osemilattice__sup__class_Osup(U_16902)),U_16905),U_16903)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16902),U_16904),U_16905)))
        | sP1093(U_16902,U_16903,U_16904,U_16905)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16902),U_16903))
        | ~ class_Lattices_Osemilattice__sup(U_16902) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1093])],[f_4182_3]) ).

cnf(f_4182_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16902),hAPP(hAPP(c_Finite__Set_Ofold(U_16902,U_16902,c_Lattices_Osemilattice__sup__class_Osup(U_16902)),U_16905),U_16903)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(U_16902),U_16904),U_16905)))
    | sP1093(U_16902,U_16903,U_16904,U_16905)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16902),U_16903))
    | ~ class_Lattices_Osemilattice__sup(U_16902) ),
    inference(clausify,[status(thm)],[f_4182_4]) ).

cnf(f_4182_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16902),sK434(U_16905,U_16904,U_16903,U_16902)),U_16903))
    | ~ sP1093(U_16902,U_16903,U_16904,U_16905) ),
    inference(clausify,[status(thm)],[f_4182_4]) ).

cnf(f_4182_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_16902),sK434(U_16905,U_16904,U_16903,U_16902)),U_16904))
    | ~ sP1093(U_16902,U_16903,U_16904,U_16905) ),
    inference(clausify,[status(thm)],[f_4182_4]) ).

fof(f_4183_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_4183_2,plain,
    ! [U_16913,U_16912,U_16911,U_16910,U_16909,U_16908,U_16907,U_16906] :
      ( hAPP(U_16911,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16907,tc_HOL_Obool)),U_16912),U_16913)) = hAPP(hAPP(U_16908,hAPP(U_16911,U_16912)),hAPP(U_16911,U_16913))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16907),U_16913))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16907),U_16912))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_16906,U_16907,U_16908,U_16909,U_16910,U_16911) ),
    inference(variable_rename,[status(thm)],[f_4183_1]) ).

fof(f_4183_3,plain,
    ! [U_16913,U_16912,U_16911,U_16910,U_16909,U_16908,U_16907] :
      ( ! [U_16906] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_16906,U_16907,U_16908,U_16909,U_16910,U_16911)
      | hAPP(U_16911,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16907,tc_HOL_Obool)),U_16912),U_16913)) = hAPP(hAPP(U_16908,hAPP(U_16911,U_16912)),hAPP(U_16911,U_16913))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16907),U_16913))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16907),U_16912)) ),
    inference(miniscope,[status(thm)],[f_4183_2]) ).

fof(f_4183_4,plain,
    ! [U_16909,U_16906,U_16910,U_16907,U_16911,U_16908,U_16912,U_16913] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_16906,U_16907,U_16908,U_16909,U_16910,U_16911)
      | hAPP(U_16911,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16907,tc_HOL_Obool)),U_16912),U_16913)) = hAPP(hAPP(U_16908,hAPP(U_16911,U_16912)),hAPP(U_16911,U_16913))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16907),U_16913))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16907),U_16912)) ),
    inference(definitional_conversion,[status(esa)],[f_4183_3]) ).

cnf(f_4183_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_16906,U_16907,U_16908,U_16909,U_16910,U_16911)
    | hAPP(U_16911,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16907,tc_HOL_Obool)),U_16912),U_16913)) = hAPP(hAPP(U_16908,hAPP(U_16911,U_16912)),hAPP(U_16911,U_16913))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16907),U_16913))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16907),U_16912)) ),
    inference(clausify,[status(thm)],[f_4183_4]) ).

fof(f_4184_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_4184_2,plain,
    ! [U_16920,U_16919,U_16918,U_16917,U_16916,U_16915,U_16914] :
      ( hAPP(hAPP(U_16916,U_16920),U_16920) = U_16920
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_16914,U_16915,U_16916,U_16917,U_16918,U_16919) ),
    inference(variable_rename,[status(thm)],[f_4184_1]) ).

fof(f_4184_3,plain,
    ! [U_16920,U_16919,U_16918,U_16917,U_16916] :
      ( ! [U_16915,U_16914] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_16914,U_16915,U_16916,U_16917,U_16918,U_16919)
      | hAPP(hAPP(U_16916,U_16920),U_16920) = U_16920 ),
    inference(miniscope,[status(thm)],[f_4184_2]) ).

fof(f_4184_4,plain,
    ! [U_16916,U_16918,U_16915,U_16917,U_16914,U_16919,U_16920] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_16914,U_16915,U_16916,U_16917,U_16918,U_16919)
      | hAPP(hAPP(U_16916,U_16920),U_16920) = U_16920 ),
    inference(definitional_conversion,[status(esa)],[f_4184_3]) ).

cnf(f_4184_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_16914,U_16915,U_16916,U_16917,U_16918,U_16919)
    | hAPP(hAPP(U_16916,U_16920),U_16920) = U_16920 ),
    inference(clausify,[status(thm)],[f_4184_4]) ).

fof(f_4185_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_4185_2,plain,
    ! [U_16928,U_16927,U_16926,U_16925,U_16924,U_16923,U_16922,U_16921] :
      ( hAPP(hAPP(U_16923,hAPP(U_16925,U_16928)),hAPP(U_16926,U_16927)) = hAPP(U_16926,U_16927)
      | ~ hBOOL(hAPP(hAPP(c_member(U_16922),U_16928),U_16927))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16922),U_16927))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_16921,U_16922,U_16923,U_16924,U_16925,U_16926) ),
    inference(variable_rename,[status(thm)],[f_4185_1]) ).

fof(f_4185_3,plain,
    ! [U_16928,U_16927,U_16926,U_16925,U_16924,U_16923,U_16922] :
      ( ! [U_16921] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_16921,U_16922,U_16923,U_16924,U_16925,U_16926)
      | hAPP(hAPP(U_16923,hAPP(U_16925,U_16928)),hAPP(U_16926,U_16927)) = hAPP(U_16926,U_16927)
      | ~ hBOOL(hAPP(hAPP(c_member(U_16922),U_16928),U_16927))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16922),U_16927)) ),
    inference(miniscope,[status(thm)],[f_4185_2]) ).

fof(f_4185_4,plain,
    ! [U_16922,U_16921,U_16923,U_16924,U_16925,U_16926,U_16927,U_16928] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_16921,U_16922,U_16923,U_16924,U_16925,U_16926)
      | hAPP(hAPP(U_16923,hAPP(U_16925,U_16928)),hAPP(U_16926,U_16927)) = hAPP(U_16926,U_16927)
      | ~ hBOOL(hAPP(hAPP(c_member(U_16922),U_16928),U_16927))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16922),U_16927)) ),
    inference(definitional_conversion,[status(esa)],[f_4185_3]) ).

cnf(f_4185_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_16921,U_16922,U_16923,U_16924,U_16925,U_16926)
    | hAPP(hAPP(U_16923,hAPP(U_16925,U_16928)),hAPP(U_16926,U_16927)) = hAPP(U_16926,U_16927)
    | ~ hBOOL(hAPP(hAPP(c_member(U_16922),U_16928),U_16927))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16922),U_16927)) ),
    inference(clausify,[status(thm)],[f_4185_4]) ).

fof(f_4186_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_4186_2,plain,
    ! [U_16936,U_16935,U_16934,U_16933,U_16932,U_16931,U_16930,U_16929] :
      ( hAPP(U_16934,hAPP(hAPP(c_Set_Oinsert(U_16930),U_16936),U_16935)) = hAPP(hAPP(U_16931,hAPP(U_16933,U_16936)),hAPP(U_16934,U_16935))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16930),U_16935))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_16929,U_16930,U_16931,U_16932,U_16933,U_16934) ),
    inference(variable_rename,[status(thm)],[f_4186_1]) ).

fof(f_4186_3,plain,
    ! [U_16936,U_16935,U_16934,U_16933,U_16932,U_16931,U_16930] :
      ( ! [U_16929] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_16929,U_16930,U_16931,U_16932,U_16933,U_16934)
      | hAPP(U_16934,hAPP(hAPP(c_Set_Oinsert(U_16930),U_16936),U_16935)) = hAPP(hAPP(U_16931,hAPP(U_16933,U_16936)),hAPP(U_16934,U_16935))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16930),U_16935)) ),
    inference(miniscope,[status(thm)],[f_4186_2]) ).

fof(f_4186_4,plain,
    ! [U_16930,U_16929,U_16931,U_16932,U_16933,U_16934,U_16935,U_16936] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_16929,U_16930,U_16931,U_16932,U_16933,U_16934)
      | hAPP(U_16934,hAPP(hAPP(c_Set_Oinsert(U_16930),U_16936),U_16935)) = hAPP(hAPP(U_16931,hAPP(U_16933,U_16936)),hAPP(U_16934,U_16935))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16930),U_16935)) ),
    inference(definitional_conversion,[status(esa)],[f_4186_3]) ).

cnf(f_4186_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_16929,U_16930,U_16931,U_16932,U_16933,U_16934)
    | hAPP(U_16934,hAPP(hAPP(c_Set_Oinsert(U_16930),U_16936),U_16935)) = hAPP(hAPP(U_16931,hAPP(U_16933,U_16936)),hAPP(U_16934,U_16935))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16930),U_16935)) ),
    inference(clausify,[status(thm)],[f_4186_4]) ).

fof(f_4187_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_4187_2,plain,
    ! [U_16944,U_16943,U_16942,U_16941,U_16940,U_16939,U_16938,U_16937] :
      ( hAPP(hAPP(U_16939,hAPP(U_16942,U_16944)),hAPP(U_16942,U_16943)) = hAPP(U_16942,U_16943)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16938,tc_HOL_Obool)),U_16944),U_16943))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16938),U_16943))
      | ~ c_Finite__Set_Ofolding__image__simple__idem(U_16937,U_16938,U_16939,U_16940,U_16941,U_16942) ),
    inference(variable_rename,[status(thm)],[f_4187_1]) ).

fof(f_4187_3,plain,
    ! [U_16944,U_16943,U_16942,U_16941,U_16940,U_16939,U_16938] :
      ( ! [U_16937] : ~ c_Finite__Set_Ofolding__image__simple__idem(U_16937,U_16938,U_16939,U_16940,U_16941,U_16942)
      | hAPP(hAPP(U_16939,hAPP(U_16942,U_16944)),hAPP(U_16942,U_16943)) = hAPP(U_16942,U_16943)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16938,tc_HOL_Obool)),U_16944),U_16943))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16938),U_16943)) ),
    inference(miniscope,[status(thm)],[f_4187_2]) ).

fof(f_4187_4,plain,
    ! [U_16937,U_16938,U_16939,U_16940,U_16941,U_16942,U_16943,U_16944] :
      ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_16937,U_16938,U_16939,U_16940,U_16941,U_16942)
      | hAPP(hAPP(U_16939,hAPP(U_16942,U_16944)),hAPP(U_16942,U_16943)) = hAPP(U_16942,U_16943)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16938,tc_HOL_Obool)),U_16944),U_16943))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16938),U_16943)) ),
    inference(definitional_conversion,[status(esa)],[f_4187_3]) ).

cnf(f_4187_5,plain,
    ( ~ c_Finite__Set_Ofolding__image__simple__idem(U_16937,U_16938,U_16939,U_16940,U_16941,U_16942)
    | hAPP(hAPP(U_16939,hAPP(U_16942,U_16944)),hAPP(U_16942,U_16943)) = hAPP(U_16942,U_16943)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16938,tc_HOL_Obool)),U_16944),U_16943))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_16938),U_16943)) ),
    inference(clausify,[status(thm)],[f_4187_4]) ).

fof(f_4188_1,plain,
    ! [V_Qa_2,V_Pa_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_Pa_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_Qa_2))))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(V_Qa_2,B_x))
          & hBOOL(hAPP(V_Pa_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_4188_2,plain,
    ! [U_16950,U_16949,U_16948,U_16947,U_16946] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16946,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16946,tc_HOL_Obool)),U_16947),hAPP(c_Set_OCollect(U_16946),U_16949))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16946,tc_HOL_Obool)),U_16948),hAPP(c_Set_OCollect(U_16946),U_16950))))
      | ? [U_16945] :
          ( ~ hBOOL(hAPP(U_16950,U_16945))
          & hBOOL(hAPP(U_16949,U_16945))
          & hBOOL(hAPP(hAPP(c_member(U_16946),U_16945),U_16947)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16946,tc_HOL_Obool)),U_16947),U_16948)) ),
    inference(variable_rename,[status(thm)],[f_4188_1]) ).

fof(f_4188_3,plain,
    ! [U_16950,U_16949,U_16948,U_16947,U_16946] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16946,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16946,tc_HOL_Obool)),U_16947),hAPP(c_Set_OCollect(U_16946),U_16949))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16946,tc_HOL_Obool)),U_16948),hAPP(c_Set_OCollect(U_16946),U_16950))))
      | ( ~ hBOOL(hAPP(U_16950,sK435(U_16950,U_16949,U_16948,U_16947,U_16946)))
        & hBOOL(hAPP(U_16949,sK435(U_16950,U_16949,U_16948,U_16947,U_16946)))
        & hBOOL(hAPP(hAPP(c_member(U_16946),sK435(U_16950,U_16949,U_16948,U_16947,U_16946)),U_16947)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16946,tc_HOL_Obool)),U_16947),U_16948)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK435]),skolemize(U_16945,sK435(U_16950,U_16949,U_16948,U_16947,U_16946))],[f_4188_2]) ).

fof(f_4188_4,plain,
    ( ! [U_16946,U_16947,U_16948,U_16949,U_16950] :
        ( ~ hBOOL(hAPP(U_16950,sK435(U_16950,U_16949,U_16948,U_16947,U_16946)))
        | ~ sP1094(U_16946,U_16947,U_16948,U_16949,U_16950) )
    & ! [U_16946,U_16947,U_16948,U_16949,U_16950] :
        ( hBOOL(hAPP(U_16949,sK435(U_16950,U_16949,U_16948,U_16947,U_16946)))
        | ~ sP1094(U_16946,U_16947,U_16948,U_16949,U_16950) )
    & ! [U_16946,U_16947,U_16948,U_16949,U_16950] :
        ( hBOOL(hAPP(hAPP(c_member(U_16946),sK435(U_16950,U_16949,U_16948,U_16947,U_16946)),U_16947))
        | ~ sP1094(U_16946,U_16947,U_16948,U_16949,U_16950) )
    & ! [U_16946,U_16947,U_16948,U_16949,U_16950] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16946,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16946,tc_HOL_Obool)),U_16947),hAPP(c_Set_OCollect(U_16946),U_16949))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16946,tc_HOL_Obool)),U_16948),hAPP(c_Set_OCollect(U_16946),U_16950))))
        | sP1094(U_16946,U_16947,U_16948,U_16949,U_16950)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16946,tc_HOL_Obool)),U_16947),U_16948)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1094])],[f_4188_3]) ).

cnf(f_4188_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16946,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16946,tc_HOL_Obool)),U_16947),hAPP(c_Set_OCollect(U_16946),U_16949))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_16946,tc_HOL_Obool)),U_16948),hAPP(c_Set_OCollect(U_16946),U_16950))))
    | sP1094(U_16946,U_16947,U_16948,U_16949,U_16950)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_16946,tc_HOL_Obool)),U_16947),U_16948)) ),
    inference(clausify,[status(thm)],[f_4188_4]) ).

cnf(f_4188_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16946),sK435(U_16950,U_16949,U_16948,U_16947,U_16946)),U_16947))
    | ~ sP1094(U_16946,U_16947,U_16948,U_16949,U_16950) ),
    inference(clausify,[status(thm)],[f_4188_4]) ).

cnf(f_4188_7,plain,
    ( hBOOL(hAPP(U_16949,sK435(U_16950,U_16949,U_16948,U_16947,U_16946)))
    | ~ sP1094(U_16946,U_16947,U_16948,U_16949,U_16950) ),
    inference(clausify,[status(thm)],[f_4188_4]) ).

cnf(f_4188_8,plain,
    ( ~ hBOOL(hAPP(U_16950,sK435(U_16950,U_16949,U_16948,U_16947,U_16946)))
    | ~ sP1094(U_16946,U_16947,U_16948,U_16949,U_16950) ),
    inference(clausify,[status(thm)],[f_4188_4]) ).

fof(f_4189_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_4189_2,plain,
    ! [U_16954,U_16953,U_16952] :
      ( ? [U_16951] :
          ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16952,tc_HOL_Obool)),U_16951),U_16954))
          & hBOOL(hAPP(hAPP(c_member(U_16952),U_16953),U_16951)) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_16952),U_16953),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16952,tc_HOL_Obool),U_16954))) ),
    inference(variable_rename,[status(thm)],[f_4189_1]) ).

fof(f_4189_3,plain,
    ! [U_16954,U_16953,U_16952] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16952,tc_HOL_Obool)),sK436(U_16954,U_16953,U_16952)),U_16954))
        & hBOOL(hAPP(hAPP(c_member(U_16952),U_16953),sK436(U_16954,U_16953,U_16952))) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_16952),U_16953),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16952,tc_HOL_Obool),U_16954))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK436]),skolemize(U_16951,sK436(U_16954,U_16953,U_16952))],[f_4189_2]) ).

fof(f_4189_4,plain,
    ( ! [U_16953,U_16954,U_16952] :
        ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16952,tc_HOL_Obool)),sK436(U_16954,U_16953,U_16952)),U_16954))
        | ~ sP1095(U_16953,U_16954,U_16952) )
    & ! [U_16953,U_16954,U_16952] :
        ( hBOOL(hAPP(hAPP(c_member(U_16952),U_16953),sK436(U_16954,U_16953,U_16952)))
        | ~ sP1095(U_16953,U_16954,U_16952) )
    & ! [U_16953,U_16954,U_16952] :
        ( sP1095(U_16953,U_16954,U_16952)
        | ~ hBOOL(hAPP(hAPP(c_member(U_16952),U_16953),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16952,tc_HOL_Obool),U_16954))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1095])],[f_4189_3]) ).

cnf(f_4189_5,plain,
    ( sP1095(U_16953,U_16954,U_16952)
    | ~ hBOOL(hAPP(hAPP(c_member(U_16952),U_16953),c_Complete__Lattice_OSup__class_OSup(tc_fun(U_16952,tc_HOL_Obool),U_16954))) ),
    inference(clausify,[status(thm)],[f_4189_4]) ).

cnf(f_4189_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16952),U_16953),sK436(U_16954,U_16953,U_16952)))
    | ~ sP1095(U_16953,U_16954,U_16952) ),
    inference(clausify,[status(thm)],[f_4189_4]) ).

cnf(f_4189_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_fun(U_16952,tc_HOL_Obool)),sK436(U_16954,U_16953,U_16952)),U_16954))
    | ~ sP1095(U_16953,U_16954,U_16952) ),
    inference(clausify,[status(thm)],[f_4189_4]) ).

fof(f_4190_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_4190_2,plain,
    ! [U_16960,U_16959,U_16958,U_16957,U_16956,U_16955] :
      ( c_Map_Omap__add(U_16955,U_16957,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16955,tc_Option_Ooption(U_16957)),U_16959),U_16956),hAPP(c_Option_Ooption_OSome(U_16957),U_16960)),U_16958) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16955,tc_Option_Ooption(U_16957)),c_Map_Omap__add(U_16955,U_16957,U_16959,U_16958)),U_16956),hAPP(c_Option_Ooption_OSome(U_16957),U_16960))
      | hBOOL(hAPP(hAPP(c_member(U_16955),U_16956),c_Map_Odom(U_16955,U_16957,U_16958))) ),
    inference(variable_rename,[status(thm)],[f_4190_1]) ).

fof(f_4190_3,plain,
    ! [U_16955,U_16956,U_16957,U_16958,U_16959,U_16960] :
      ( c_Map_Omap__add(U_16955,U_16957,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16955,tc_Option_Ooption(U_16957)),U_16959),U_16956),hAPP(c_Option_Ooption_OSome(U_16957),U_16960)),U_16958) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16955,tc_Option_Ooption(U_16957)),c_Map_Omap__add(U_16955,U_16957,U_16959,U_16958)),U_16956),hAPP(c_Option_Ooption_OSome(U_16957),U_16960))
      | hBOOL(hAPP(hAPP(c_member(U_16955),U_16956),c_Map_Odom(U_16955,U_16957,U_16958))) ),
    inference(definitional_conversion,[status(esa)],[f_4190_2]) ).

cnf(f_4190_4,plain,
    ( c_Map_Omap__add(U_16955,U_16957,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16955,tc_Option_Ooption(U_16957)),U_16959),U_16956),hAPP(c_Option_Ooption_OSome(U_16957),U_16960)),U_16958) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16955,tc_Option_Ooption(U_16957)),c_Map_Omap__add(U_16955,U_16957,U_16959,U_16958)),U_16956),hAPP(c_Option_Ooption_OSome(U_16957),U_16960))
    | hBOOL(hAPP(hAPP(c_member(U_16955),U_16956),c_Map_Odom(U_16955,U_16957,U_16958))) ),
    inference(clausify,[status(thm)],[f_4190_3]) ).

fof(f_4191_1,plain,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_2)))
      | ? [B_x] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(V_f_2,B_x)))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) )
      | ~ class_Rings_Olinordered__semidom(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__pos]) ).

fof(f_4191_2,plain,
    ! [U_16965,U_16964,U_16963,U_16962] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16962),c_Groups_Ozero__class_Ozero(U_16962)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_16963,U_16962),U_16965),U_16964)))
      | ? [U_16961] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16962),c_Groups_Ozero__class_Ozero(U_16962)),hAPP(U_16965,U_16961)))
          & hBOOL(hAPP(hAPP(c_member(U_16963),U_16961),U_16964)) )
      | ~ class_Rings_Olinordered__semidom(U_16962) ),
    inference(variable_rename,[status(thm)],[f_4191_1]) ).

fof(f_4191_3,plain,
    ! [U_16965,U_16964,U_16963,U_16962] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16962),c_Groups_Ozero__class_Ozero(U_16962)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_16963,U_16962),U_16965),U_16964)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16962),c_Groups_Ozero__class_Ozero(U_16962)),hAPP(U_16965,sK437(U_16965,U_16964,U_16963,U_16962))))
        & hBOOL(hAPP(hAPP(c_member(U_16963),sK437(U_16965,U_16964,U_16963,U_16962)),U_16964)) )
      | ~ class_Rings_Olinordered__semidom(U_16962) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK437]),skolemize(U_16961,sK437(U_16965,U_16964,U_16963,U_16962))],[f_4191_2]) ).

fof(f_4191_4,plain,
    ( ! [U_16962,U_16963,U_16964,U_16965] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16962),c_Groups_Ozero__class_Ozero(U_16962)),hAPP(U_16965,sK437(U_16965,U_16964,U_16963,U_16962))))
        | ~ sP1096(U_16962,U_16963,U_16964,U_16965) )
    & ! [U_16962,U_16963,U_16964,U_16965] :
        ( hBOOL(hAPP(hAPP(c_member(U_16963),sK437(U_16965,U_16964,U_16963,U_16962)),U_16964))
        | ~ sP1096(U_16962,U_16963,U_16964,U_16965) )
    & ! [U_16962,U_16963,U_16964,U_16965] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16962),c_Groups_Ozero__class_Ozero(U_16962)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_16963,U_16962),U_16965),U_16964)))
        | sP1096(U_16962,U_16963,U_16964,U_16965)
        | ~ class_Rings_Olinordered__semidom(U_16962) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1096])],[f_4191_3]) ).

cnf(f_4191_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16962),c_Groups_Ozero__class_Ozero(U_16962)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_16963,U_16962),U_16965),U_16964)))
    | sP1096(U_16962,U_16963,U_16964,U_16965)
    | ~ class_Rings_Olinordered__semidom(U_16962) ),
    inference(clausify,[status(thm)],[f_4191_4]) ).

cnf(f_4191_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_16963),sK437(U_16965,U_16964,U_16963,U_16962)),U_16964))
    | ~ sP1096(U_16962,U_16963,U_16964,U_16965) ),
    inference(clausify,[status(thm)],[f_4191_4]) ).

cnf(f_4191_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(U_16962),c_Groups_Ozero__class_Ozero(U_16962)),hAPP(U_16965,sK437(U_16965,U_16964,U_16963,U_16962))))
    | ~ sP1096(U_16962,U_16963,U_16964,U_16965) ),
    inference(clausify,[status(thm)],[f_4191_4]) ).

fof(f_4192_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_4192_2,plain,
    ! [U_16971,U_16970,U_16969,U_16968,U_16967,U_16966] : c_Map_Omap__add(U_16966,U_16967,U_16968,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16966,tc_Option_Ooption(U_16967)),U_16969),U_16970),hAPP(c_Option_Ooption_OSome(U_16967),U_16971))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16966,tc_Option_Ooption(U_16967)),c_Map_Omap__add(U_16966,U_16967,U_16968,U_16969)),U_16970),hAPP(c_Option_Ooption_OSome(U_16967),U_16971)),
    inference(variable_rename,[status(thm)],[f_4192_1]) ).

fof(f_4192_3,plain,
    ! [U_16967,U_16966,U_16968,U_16969,U_16970,U_16971] : c_Map_Omap__add(U_16966,U_16967,U_16968,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16966,tc_Option_Ooption(U_16967)),U_16969),U_16970),hAPP(c_Option_Ooption_OSome(U_16967),U_16971))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16966,tc_Option_Ooption(U_16967)),c_Map_Omap__add(U_16966,U_16967,U_16968,U_16969)),U_16970),hAPP(c_Option_Ooption_OSome(U_16967),U_16971)),
    inference(definitional_conversion,[status(esa)],[f_4192_2]) ).

cnf(f_4192_4,plain,
    c_Map_Omap__add(U_16966,U_16967,U_16968,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16966,tc_Option_Ooption(U_16967)),U_16969),U_16970),hAPP(c_Option_Ooption_OSome(U_16967),U_16971))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_16966,tc_Option_Ooption(U_16967)),c_Map_Omap__add(U_16966,U_16967,U_16968,U_16969)),U_16970),hAPP(c_Option_Ooption_OSome(U_16967),U_16971)),
    inference(clausify,[status(thm)],[f_4192_3]) ).

fof(f_4193_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_4193_2,plain,
    ! [U_16975,U_16974,U_16973,U_16972] : c_Map_Odom(U_16972,U_16973,c_Map_Omap__add(U_16972,U_16973,U_16974,U_16975)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16972,tc_HOL_Obool)),c_Map_Odom(U_16972,U_16973,U_16975)),c_Map_Odom(U_16972,U_16973,U_16974)),
    inference(variable_rename,[status(thm)],[f_4193_1]) ).

fof(f_4193_3,plain,
    ! [U_16972,U_16973,U_16974,U_16975] : c_Map_Odom(U_16972,U_16973,c_Map_Omap__add(U_16972,U_16973,U_16974,U_16975)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16972,tc_HOL_Obool)),c_Map_Odom(U_16972,U_16973,U_16975)),c_Map_Odom(U_16972,U_16973,U_16974)),
    inference(definitional_conversion,[status(esa)],[f_4193_2]) ).

cnf(f_4193_4,plain,
    c_Map_Odom(U_16972,U_16973,c_Map_Omap__add(U_16972,U_16973,U_16974,U_16975)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_16972,tc_HOL_Obool)),c_Map_Odom(U_16972,U_16973,U_16975)),c_Map_Odom(U_16972,U_16973,U_16974)),
    inference(clausify,[status(thm)],[f_4193_3]) ).

fof(f_4194_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_4194_2,plain,
    ! [U_16981,U_16980,U_16979,U_16978,U_16977,U_16976] :
      ( ( hAPP(U_16978,U_16980) = hAPP(c_Option_Ooption_OSome(U_16977),U_16981)
        & hAPP(U_16979,U_16980) = c_Option_Ooption_ONone(U_16977) )
      | hAPP(U_16979,U_16980) = hAPP(c_Option_Ooption_OSome(U_16977),U_16981)
      | hAPP(c_Map_Omap__add(U_16976,U_16977,U_16978,U_16979),U_16980) != hAPP(c_Option_Ooption_OSome(U_16977),U_16981) ),
    inference(variable_rename,[status(thm)],[f_4194_1]) ).

fof(f_4194_3,plain,
    ! [U_16981,U_16980,U_16979,U_16978,U_16977] :
      ( ! [U_16976] : hAPP(c_Map_Omap__add(U_16976,U_16977,U_16978,U_16979),U_16980) != hAPP(c_Option_Ooption_OSome(U_16977),U_16981)
      | ( hAPP(U_16978,U_16980) = hAPP(c_Option_Ooption_OSome(U_16977),U_16981)
        & hAPP(U_16979,U_16980) = c_Option_Ooption_ONone(U_16977) )
      | hAPP(U_16979,U_16980) = hAPP(c_Option_Ooption_OSome(U_16977),U_16981) ),
    inference(miniscope,[status(thm)],[f_4194_2]) ).

fof(f_4194_4,plain,
    ( ! [U_16977,U_16978,U_16979,U_16980,U_16981] :
        ( hAPP(U_16978,U_16980) = hAPP(c_Option_Ooption_OSome(U_16977),U_16981)
        | ~ sP1097(U_16977,U_16978,U_16979,U_16980,U_16981) )
    & ! [U_16977,U_16978,U_16979,U_16980,U_16981] :
        ( hAPP(U_16979,U_16980) = c_Option_Ooption_ONone(U_16977)
        | ~ sP1097(U_16977,U_16978,U_16979,U_16980,U_16981) )
    & ! [U_16977,U_16976,U_16978,U_16979,U_16980,U_16981] :
        ( hAPP(c_Map_Omap__add(U_16976,U_16977,U_16978,U_16979),U_16980) != hAPP(c_Option_Ooption_OSome(U_16977),U_16981)
        | sP1097(U_16977,U_16978,U_16979,U_16980,U_16981)
        | hAPP(U_16979,U_16980) = hAPP(c_Option_Ooption_OSome(U_16977),U_16981) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1097])],[f_4194_3]) ).

cnf(f_4194_5,plain,
    ( hAPP(c_Map_Omap__add(U_16976,U_16977,U_16978,U_16979),U_16980) != hAPP(c_Option_Ooption_OSome(U_16977),U_16981)
    | sP1097(U_16977,U_16978,U_16979,U_16980,U_16981)
    | hAPP(U_16979,U_16980) = hAPP(c_Option_Ooption_OSome(U_16977),U_16981) ),
    inference(clausify,[status(thm)],[f_4194_4]) ).

cnf(f_4194_6,plain,
    ( hAPP(U_16979,U_16980) = c_Option_Ooption_ONone(U_16977)
    | ~ sP1097(U_16977,U_16978,U_16979,U_16980,U_16981) ),
    inference(clausify,[status(thm)],[f_4194_4]) ).

cnf(f_4194_7,plain,
    ( hAPP(U_16978,U_16980) = hAPP(c_Option_Ooption_OSome(U_16977),U_16981)
    | ~ sP1097(U_16977,U_16978,U_16979,U_16980,U_16981) ),
    inference(clausify,[status(thm)],[f_4194_4]) ).

fof(f_4195_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_4195_2,plain,
    ! [U_16987,U_16986,U_16985,U_16984,U_16983,U_16982] :
      ( ( hAPP(c_Map_Omap__add(U_16982,U_16983,U_16984,U_16985),U_16986) = hAPP(c_Option_Ooption_OSome(U_16983),U_16987)
        | ( ( hAPP(U_16984,U_16986) != hAPP(c_Option_Ooption_OSome(U_16983),U_16987)
            | hAPP(U_16985,U_16986) != c_Option_Ooption_ONone(U_16983) )
          & hAPP(U_16985,U_16986) != hAPP(c_Option_Ooption_OSome(U_16983),U_16987) ) )
      & ( ( hAPP(U_16984,U_16986) = hAPP(c_Option_Ooption_OSome(U_16983),U_16987)
          & hAPP(U_16985,U_16986) = c_Option_Ooption_ONone(U_16983) )
        | hAPP(U_16985,U_16986) = hAPP(c_Option_Ooption_OSome(U_16983),U_16987)
        | hAPP(c_Map_Omap__add(U_16982,U_16983,U_16984,U_16985),U_16986) != hAPP(c_Option_Ooption_OSome(U_16983),U_16987) ) ),
    inference(variable_rename,[status(thm)],[f_4195_1]) ).

fof(f_4195_3,plain,
    ( ! [U_16999,U_16997,U_16995,U_16993,U_16991] :
        ( ! [U_16989] : hAPP(c_Map_Omap__add(U_16989,U_16991,U_16993,U_16995),U_16997) = hAPP(c_Option_Ooption_OSome(U_16991),U_16999)
        | ( ( hAPP(U_16993,U_16997) != hAPP(c_Option_Ooption_OSome(U_16991),U_16999)
            | hAPP(U_16995,U_16997) != c_Option_Ooption_ONone(U_16991) )
          & hAPP(U_16995,U_16997) != hAPP(c_Option_Ooption_OSome(U_16991),U_16999) ) )
    & ! [U_16998,U_16996,U_16994,U_16992,U_16990] :
        ( ! [U_16988] : hAPP(c_Map_Omap__add(U_16988,U_16990,U_16992,U_16994),U_16996) != hAPP(c_Option_Ooption_OSome(U_16990),U_16998)
        | ( hAPP(U_16992,U_16996) = hAPP(c_Option_Ooption_OSome(U_16990),U_16998)
          & hAPP(U_16994,U_16996) = c_Option_Ooption_ONone(U_16990) )
        | hAPP(U_16994,U_16996) = hAPP(c_Option_Ooption_OSome(U_16990),U_16998) ) ),
    inference(miniscope,[status(thm)],[f_4195_2]) ).

fof(f_4195_4,plain,
    ( ! [U_16995,U_16999,U_16993,U_16991,U_16997] :
        ( hAPP(U_16993,U_16997) != hAPP(c_Option_Ooption_OSome(U_16991),U_16999)
        | hAPP(U_16995,U_16997) != c_Option_Ooption_ONone(U_16991)
        | ~ sP1099(U_16995,U_16999,U_16993,U_16991,U_16997) )
    & ! [U_16995,U_16999,U_16993,U_16991,U_16997] :
        ( hAPP(U_16995,U_16997) != hAPP(c_Option_Ooption_OSome(U_16991),U_16999)
        | ~ sP1099(U_16995,U_16999,U_16993,U_16991,U_16997) )
    & ! [U_16994,U_16990,U_16996,U_16992,U_16998] :
        ( hAPP(U_16992,U_16996) = hAPP(c_Option_Ooption_OSome(U_16990),U_16998)
        | ~ sP1098(U_16994,U_16990,U_16996,U_16992,U_16998) )
    & ! [U_16994,U_16990,U_16996,U_16992,U_16998] :
        ( hAPP(U_16994,U_16996) = c_Option_Ooption_ONone(U_16990)
        | ~ sP1098(U_16994,U_16990,U_16996,U_16992,U_16998) )
    & ! [U_16995,U_16999,U_16993,U_16989,U_16991,U_16997] :
        ( hAPP(c_Map_Omap__add(U_16989,U_16991,U_16993,U_16995),U_16997) = hAPP(c_Option_Ooption_OSome(U_16991),U_16999)
        | sP1099(U_16995,U_16999,U_16993,U_16991,U_16997) )
    & ! [U_16994,U_16988,U_16990,U_16996,U_16992,U_16998] :
        ( hAPP(c_Map_Omap__add(U_16988,U_16990,U_16992,U_16994),U_16996) != hAPP(c_Option_Ooption_OSome(U_16990),U_16998)
        | sP1098(U_16994,U_16990,U_16996,U_16992,U_16998)
        | hAPP(U_16994,U_16996) = hAPP(c_Option_Ooption_OSome(U_16990),U_16998) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1098,sP1099])],[f_4195_3]) ).

cnf(f_4195_5,plain,
    ( hAPP(c_Map_Omap__add(U_16988,U_16990,U_16992,U_16994),U_16996) != hAPP(c_Option_Ooption_OSome(U_16990),U_16998)
    | sP1098(U_16994,U_16990,U_16996,U_16992,U_16998)
    | hAPP(U_16994,U_16996) = hAPP(c_Option_Ooption_OSome(U_16990),U_16998) ),
    inference(clausify,[status(thm)],[f_4195_4]) ).

cnf(f_4195_6,plain,
    ( hAPP(c_Map_Omap__add(U_16989,U_16991,U_16993,U_16995),U_16997) = hAPP(c_Option_Ooption_OSome(U_16991),U_16999)
    | sP1099(U_16995,U_16999,U_16993,U_16991,U_16997) ),
    inference(clausify,[status(thm)],[f_4195_4]) ).

cnf(f_4195_7,plain,
    ( hAPP(U_16994,U_16996) = c_Option_Ooption_ONone(U_16990)
    | ~ sP1098(U_16994,U_16990,U_16996,U_16992,U_16998) ),
    inference(clausify,[status(thm)],[f_4195_4]) ).

cnf(f_4195_8,plain,
    ( hAPP(U_16992,U_16996) = hAPP(c_Option_Ooption_OSome(U_16990),U_16998)
    | ~ sP1098(U_16994,U_16990,U_16996,U_16992,U_16998) ),
    inference(clausify,[status(thm)],[f_4195_4]) ).

cnf(f_4195_9,plain,
    ( hAPP(U_16995,U_16997) != hAPP(c_Option_Ooption_OSome(U_16991),U_16999)
    | ~ sP1099(U_16995,U_16999,U_16993,U_16991,U_16997) ),
    inference(clausify,[status(thm)],[f_4195_4]) ).

cnf(f_4195_10,plain,
    ( hAPP(U_16993,U_16997) != hAPP(c_Option_Ooption_OSome(U_16991),U_16999)
    | hAPP(U_16995,U_16997) != c_Option_Ooption_ONone(U_16991)
    | ~ sP1099(U_16995,U_16999,U_16993,U_16991,U_16997) ),
    inference(clausify,[status(thm)],[f_4195_4]) ).

fof(f_4196_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_4196_2,plain,
    ! [U_17002,U_17001,U_17000] : c_Map_Omap__add(U_17000,U_17001,U_17002,hAPP(c_COMBK(tc_Option_Ooption(U_17001),U_17000),c_Option_Ooption_ONone(U_17001))) = U_17002,
    inference(variable_rename,[status(thm)],[f_4196_1]) ).

fof(f_4196_3,plain,
    ! [U_17002,U_17001,U_17000] : c_Map_Omap__add(U_17000,U_17001,U_17002,hAPP(c_COMBK(tc_Option_Ooption(U_17001),U_17000),c_Option_Ooption_ONone(U_17001))) = U_17002,
    inference(definitional_conversion,[status(esa)],[f_4196_2]) ).

cnf(f_4196_4,plain,
    c_Map_Omap__add(U_17000,U_17001,U_17002,hAPP(c_COMBK(tc_Option_Ooption(U_17001),U_17000),c_Option_Ooption_ONone(U_17001))) = U_17002,
    inference(clausify,[status(thm)],[f_4196_3]) ).

fof(f_4197_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_4197_2,plain,
    ! [U_17005,U_17004,U_17003] : c_Map_Omap__add(U_17003,U_17004,hAPP(c_COMBK(tc_Option_Ooption(U_17004),U_17003),c_Option_Ooption_ONone(U_17004)),U_17005) = U_17005,
    inference(variable_rename,[status(thm)],[f_4197_1]) ).

fof(f_4197_3,plain,
    ! [U_17003,U_17004,U_17005] : c_Map_Omap__add(U_17003,U_17004,hAPP(c_COMBK(tc_Option_Ooption(U_17004),U_17003),c_Option_Ooption_ONone(U_17004)),U_17005) = U_17005,
    inference(definitional_conversion,[status(esa)],[f_4197_2]) ).

cnf(f_4197_4,plain,
    c_Map_Omap__add(U_17003,U_17004,hAPP(c_COMBK(tc_Option_Ooption(U_17004),U_17003),c_Option_Ooption_ONone(U_17004)),U_17005) = U_17005,
    inference(clausify,[status(thm)],[f_4197_3]) ).

fof(f_4198_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_4198_2,plain,
    ! [U_17010,U_17009,U_17008,U_17007,U_17006] : hAPP(c_Map_Omap__add(U_17006,U_17007,U_17008,U_17009),U_17010) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17007),U_17007,hAPP(U_17008,U_17010),c_Option_Ooption_OSome(U_17007)),hAPP(U_17009,U_17010)),
    inference(variable_rename,[status(thm)],[f_4198_1]) ).

fof(f_4198_3,plain,
    ! [U_17007,U_17006,U_17008,U_17009,U_17010] : hAPP(c_Map_Omap__add(U_17006,U_17007,U_17008,U_17009),U_17010) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17007),U_17007,hAPP(U_17008,U_17010),c_Option_Ooption_OSome(U_17007)),hAPP(U_17009,U_17010)),
    inference(definitional_conversion,[status(esa)],[f_4198_2]) ).

cnf(f_4198_4,plain,
    hAPP(c_Map_Omap__add(U_17006,U_17007,U_17008,U_17009),U_17010) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17007),U_17007,hAPP(U_17008,U_17010),c_Option_Ooption_OSome(U_17007)),hAPP(U_17009,U_17010)),
    inference(clausify,[status(thm)],[f_4198_3]) ).

fof(f_4199_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_4199_2,plain,
    ! [U_17015,U_17014,U_17013,U_17012,U_17011] :
      ( ( hAPP(c_Map_Omap__add(U_17011,U_17012,U_17013,U_17014),U_17015) = c_Option_Ooption_ONone(U_17012)
        | hAPP(U_17013,U_17015) != c_Option_Ooption_ONone(U_17012)
        | hAPP(U_17014,U_17015) != c_Option_Ooption_ONone(U_17012) )
      & ( ( hAPP(U_17013,U_17015) = c_Option_Ooption_ONone(U_17012)
          & hAPP(U_17014,U_17015) = c_Option_Ooption_ONone(U_17012) )
        | hAPP(c_Map_Omap__add(U_17011,U_17012,U_17013,U_17014),U_17015) != c_Option_Ooption_ONone(U_17012) ) ),
    inference(variable_rename,[status(thm)],[f_4199_1]) ).

fof(f_4199_3,plain,
    ( ! [U_17025,U_17023,U_17021,U_17019] :
        ( ! [U_17017] : hAPP(c_Map_Omap__add(U_17017,U_17019,U_17021,U_17023),U_17025) = c_Option_Ooption_ONone(U_17019)
        | hAPP(U_17021,U_17025) != c_Option_Ooption_ONone(U_17019)
        | hAPP(U_17023,U_17025) != c_Option_Ooption_ONone(U_17019) )
    & ! [U_17024,U_17022,U_17020,U_17018] :
        ( ! [U_17016] : hAPP(c_Map_Omap__add(U_17016,U_17018,U_17020,U_17022),U_17024) != c_Option_Ooption_ONone(U_17018)
        | ( hAPP(U_17020,U_17024) = c_Option_Ooption_ONone(U_17018)
          & hAPP(U_17022,U_17024) = c_Option_Ooption_ONone(U_17018) ) ) ),
    inference(miniscope,[status(thm)],[f_4199_2]) ).

fof(f_4199_4,plain,
    ( ! [U_17018,U_17020,U_17022,U_17024] :
        ( hAPP(U_17020,U_17024) = c_Option_Ooption_ONone(U_17018)
        | ~ sP1100(U_17018,U_17020,U_17022,U_17024) )
    & ! [U_17018,U_17020,U_17022,U_17024] :
        ( hAPP(U_17022,U_17024) = c_Option_Ooption_ONone(U_17018)
        | ~ sP1100(U_17018,U_17020,U_17022,U_17024) )
    & ! [U_17019,U_17023,U_17017,U_17021,U_17025] :
        ( hAPP(c_Map_Omap__add(U_17017,U_17019,U_17021,U_17023),U_17025) = c_Option_Ooption_ONone(U_17019)
        | hAPP(U_17021,U_17025) != c_Option_Ooption_ONone(U_17019)
        | hAPP(U_17023,U_17025) != c_Option_Ooption_ONone(U_17019) )
    & ! [U_17016,U_17018,U_17020,U_17022,U_17024] :
        ( hAPP(c_Map_Omap__add(U_17016,U_17018,U_17020,U_17022),U_17024) != c_Option_Ooption_ONone(U_17018)
        | sP1100(U_17018,U_17020,U_17022,U_17024) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1100])],[f_4199_3]) ).

cnf(f_4199_5,plain,
    ( hAPP(c_Map_Omap__add(U_17016,U_17018,U_17020,U_17022),U_17024) != c_Option_Ooption_ONone(U_17018)
    | sP1100(U_17018,U_17020,U_17022,U_17024) ),
    inference(clausify,[status(thm)],[f_4199_4]) ).

cnf(f_4199_6,plain,
    ( hAPP(c_Map_Omap__add(U_17017,U_17019,U_17021,U_17023),U_17025) = c_Option_Ooption_ONone(U_17019)
    | hAPP(U_17021,U_17025) != c_Option_Ooption_ONone(U_17019)
    | hAPP(U_17023,U_17025) != c_Option_Ooption_ONone(U_17019) ),
    inference(clausify,[status(thm)],[f_4199_4]) ).

cnf(f_4199_7,plain,
    ( hAPP(U_17022,U_17024) = c_Option_Ooption_ONone(U_17018)
    | ~ sP1100(U_17018,U_17020,U_17022,U_17024) ),
    inference(clausify,[status(thm)],[f_4199_4]) ).

cnf(f_4199_8,plain,
    ( hAPP(U_17020,U_17024) = c_Option_Ooption_ONone(U_17018)
    | ~ sP1100(U_17018,U_17020,U_17022,U_17024) ),
    inference(clausify,[status(thm)],[f_4199_4]) ).

fof(f_4200_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_4200_2,plain,
    ! [U_17031,U_17030,U_17029,U_17028,U_17027,U_17026] :
      ( hAPP(c_Map_Omap__add(U_17030,U_17028,U_17031,U_17026),U_17027) = hAPP(c_Option_Ooption_OSome(U_17028),U_17029)
      | hAPP(U_17026,U_17027) != hAPP(c_Option_Ooption_OSome(U_17028),U_17029) ),
    inference(variable_rename,[status(thm)],[f_4200_1]) ).

fof(f_4200_3,plain,
    ! [U_17027,U_17030,U_17031,U_17029,U_17026,U_17028] :
      ( hAPP(c_Map_Omap__add(U_17030,U_17028,U_17031,U_17026),U_17027) = hAPP(c_Option_Ooption_OSome(U_17028),U_17029)
      | hAPP(U_17026,U_17027) != hAPP(c_Option_Ooption_OSome(U_17028),U_17029) ),
    inference(definitional_conversion,[status(esa)],[f_4200_2]) ).

cnf(f_4200_4,plain,
    ( hAPP(c_Map_Omap__add(U_17030,U_17028,U_17031,U_17026),U_17027) = hAPP(c_Option_Ooption_OSome(U_17028),U_17029)
    | hAPP(U_17026,U_17027) != hAPP(c_Option_Ooption_OSome(U_17028),U_17029) ),
    inference(clausify,[status(thm)],[f_4200_3]) ).

fof(f_4201_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_4201_2,plain,
    ! [U_17036,U_17035,U_17034,U_17033,U_17032] : c_Map_Omap__add(U_17032,U_17033,U_17034,c_Map_Omap__add(U_17032,U_17033,U_17035,U_17036)) = c_Map_Omap__add(U_17032,U_17033,c_Map_Omap__add(U_17032,U_17033,U_17034,U_17035),U_17036),
    inference(variable_rename,[status(thm)],[f_4201_1]) ).

fof(f_4201_3,plain,
    ! [U_17034,U_17033,U_17032,U_17035,U_17036] : c_Map_Omap__add(U_17032,U_17033,U_17034,c_Map_Omap__add(U_17032,U_17033,U_17035,U_17036)) = c_Map_Omap__add(U_17032,U_17033,c_Map_Omap__add(U_17032,U_17033,U_17034,U_17035),U_17036),
    inference(definitional_conversion,[status(esa)],[f_4201_2]) ).

cnf(f_4201_4,plain,
    c_Map_Omap__add(U_17032,U_17033,U_17034,c_Map_Omap__add(U_17032,U_17033,U_17035,U_17036)) = c_Map_Omap__add(U_17032,U_17033,c_Map_Omap__add(U_17032,U_17033,U_17034,U_17035),U_17036),
    inference(clausify,[status(thm)],[f_4201_3]) ).

fof(f_4202_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_4202_2,plain,
    ! [U_17041,U_17040,U_17039,U_17038,U_17037] :
      ( hAPP(c_Map_Omap__add(U_17037,U_17039,U_17040,U_17041),U_17038) = hAPP(U_17041,U_17038)
      | hBOOL(hAPP(hAPP(c_member(U_17037),U_17038),c_Map_Odom(U_17037,U_17039,U_17040))) ),
    inference(variable_rename,[status(thm)],[f_4202_1]) ).

fof(f_4202_3,plain,
    ! [U_17037,U_17038,U_17039,U_17040,U_17041] :
      ( hAPP(c_Map_Omap__add(U_17037,U_17039,U_17040,U_17041),U_17038) = hAPP(U_17041,U_17038)
      | hBOOL(hAPP(hAPP(c_member(U_17037),U_17038),c_Map_Odom(U_17037,U_17039,U_17040))) ),
    inference(definitional_conversion,[status(esa)],[f_4202_2]) ).

cnf(f_4202_4,plain,
    ( hAPP(c_Map_Omap__add(U_17037,U_17039,U_17040,U_17041),U_17038) = hAPP(U_17041,U_17038)
    | hBOOL(hAPP(hAPP(c_member(U_17037),U_17038),c_Map_Odom(U_17037,U_17039,U_17040))) ),
    inference(clausify,[status(thm)],[f_4202_3]) ).

fof(f_4203_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_4203_2,plain,
    ! [U_17046,U_17045,U_17044,U_17043,U_17042] :
      ( hAPP(c_Map_Omap__add(U_17042,U_17044,U_17046,U_17045),U_17043) = hAPP(U_17046,U_17043)
      | hBOOL(hAPP(hAPP(c_member(U_17042),U_17043),c_Map_Odom(U_17042,U_17044,U_17045))) ),
    inference(variable_rename,[status(thm)],[f_4203_1]) ).

fof(f_4203_3,plain,
    ! [U_17042,U_17043,U_17044,U_17045,U_17046] :
      ( hAPP(c_Map_Omap__add(U_17042,U_17044,U_17046,U_17045),U_17043) = hAPP(U_17046,U_17043)
      | hBOOL(hAPP(hAPP(c_member(U_17042),U_17043),c_Map_Odom(U_17042,U_17044,U_17045))) ),
    inference(definitional_conversion,[status(esa)],[f_4203_2]) ).

cnf(f_4203_4,plain,
    ( hAPP(c_Map_Omap__add(U_17042,U_17044,U_17046,U_17045),U_17043) = hAPP(U_17046,U_17043)
    | hBOOL(hAPP(hAPP(c_member(U_17042),U_17043),c_Map_Odom(U_17042,U_17044,U_17045))) ),
    inference(clausify,[status(thm)],[f_4203_3]) ).

fof(f_4204_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_4204_2,plain,
    ! [U_17051,U_17050,U_17049,U_17048,U_17047] :
      ( hAPP(c_Map_Omap__add(U_17047,U_17049,U_17051,U_17050),U_17048) = hAPP(U_17050,U_17048)
      | ~ hBOOL(hAPP(hAPP(c_member(U_17047),U_17048),c_Map_Odom(U_17047,U_17049,U_17050))) ),
    inference(variable_rename,[status(thm)],[f_4204_1]) ).

fof(f_4204_3,plain,
    ! [U_17047,U_17048,U_17049,U_17050,U_17051] :
      ( hAPP(c_Map_Omap__add(U_17047,U_17049,U_17051,U_17050),U_17048) = hAPP(U_17050,U_17048)
      | ~ hBOOL(hAPP(hAPP(c_member(U_17047),U_17048),c_Map_Odom(U_17047,U_17049,U_17050))) ),
    inference(definitional_conversion,[status(esa)],[f_4204_2]) ).

cnf(f_4204_4,plain,
    ( hAPP(c_Map_Omap__add(U_17047,U_17049,U_17051,U_17050),U_17048) = hAPP(U_17050,U_17048)
    | ~ hBOOL(hAPP(hAPP(c_member(U_17047),U_17048),c_Map_Odom(U_17047,U_17049,U_17050))) ),
    inference(clausify,[status(thm)],[f_4204_3]) ).

fof(f_4205_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_4205_2,plain,
    ! [U_17055,U_17054,U_17053,U_17052] :
      ( ( c_Fun_Oinj__on(U_17052,tc_Option_Ooption(U_17053),c_Map_Omap__add(U_17052,U_17053,U_17054,U_17055),c_Map_Odom(U_17052,U_17053,U_17055))
        | ~ c_Fun_Oinj__on(U_17052,tc_Option_Ooption(U_17053),U_17055,c_Map_Odom(U_17052,U_17053,U_17055)) )
      & ( c_Fun_Oinj__on(U_17052,tc_Option_Ooption(U_17053),U_17055,c_Map_Odom(U_17052,U_17053,U_17055))
        | ~ c_Fun_Oinj__on(U_17052,tc_Option_Ooption(U_17053),c_Map_Omap__add(U_17052,U_17053,U_17054,U_17055),c_Map_Odom(U_17052,U_17053,U_17055)) ) ),
    inference(variable_rename,[status(thm)],[f_4205_1]) ).

fof(f_4205_3,plain,
    ( ! [U_17063,U_17061,U_17059,U_17057] :
        ( c_Fun_Oinj__on(U_17057,tc_Option_Ooption(U_17059),c_Map_Omap__add(U_17057,U_17059,U_17061,U_17063),c_Map_Odom(U_17057,U_17059,U_17063))
        | ~ c_Fun_Oinj__on(U_17057,tc_Option_Ooption(U_17059),U_17063,c_Map_Odom(U_17057,U_17059,U_17063)) )
    & ! [U_17062,U_17060,U_17058,U_17056] :
        ( c_Fun_Oinj__on(U_17056,tc_Option_Ooption(U_17058),U_17062,c_Map_Odom(U_17056,U_17058,U_17062))
        | ~ c_Fun_Oinj__on(U_17056,tc_Option_Ooption(U_17058),c_Map_Omap__add(U_17056,U_17058,U_17060,U_17062),c_Map_Odom(U_17056,U_17058,U_17062)) ) ),
    inference(miniscope,[status(thm)],[f_4205_2]) ).

fof(f_4205_4,plain,
    ( ! [U_17061,U_17059,U_17057,U_17063] :
        ( c_Fun_Oinj__on(U_17057,tc_Option_Ooption(U_17059),c_Map_Omap__add(U_17057,U_17059,U_17061,U_17063),c_Map_Odom(U_17057,U_17059,U_17063))
        | ~ c_Fun_Oinj__on(U_17057,tc_Option_Ooption(U_17059),U_17063,c_Map_Odom(U_17057,U_17059,U_17063)) )
    & ! [U_17058,U_17056,U_17062,U_17060] :
        ( c_Fun_Oinj__on(U_17056,tc_Option_Ooption(U_17058),U_17062,c_Map_Odom(U_17056,U_17058,U_17062))
        | ~ c_Fun_Oinj__on(U_17056,tc_Option_Ooption(U_17058),c_Map_Omap__add(U_17056,U_17058,U_17060,U_17062),c_Map_Odom(U_17056,U_17058,U_17062)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4205_3]) ).

cnf(f_4205_5,plain,
    ( c_Fun_Oinj__on(U_17056,tc_Option_Ooption(U_17058),U_17062,c_Map_Odom(U_17056,U_17058,U_17062))
    | ~ c_Fun_Oinj__on(U_17056,tc_Option_Ooption(U_17058),c_Map_Omap__add(U_17056,U_17058,U_17060,U_17062),c_Map_Odom(U_17056,U_17058,U_17062)) ),
    inference(clausify,[status(thm)],[f_4205_4]) ).

cnf(f_4205_6,plain,
    ( c_Fun_Oinj__on(U_17057,tc_Option_Ooption(U_17059),c_Map_Omap__add(U_17057,U_17059,U_17061,U_17063),c_Map_Odom(U_17057,U_17059,U_17063))
    | ~ c_Fun_Oinj__on(U_17057,tc_Option_Ooption(U_17059),U_17063,c_Map_Odom(U_17057,U_17059,U_17063)) ),
    inference(clausify,[status(thm)],[f_4205_4]) ).

fof(f_4206_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_4206_2,plain,
    ! [U_17067,U_17066,U_17065,U_17064] :
      ( c_Map_Omap__add(U_17064,U_17065,U_17066,U_17067) = c_Map_Omap__add(U_17064,U_17065,U_17067,U_17066)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17064,tc_HOL_Obool)),c_Map_Odom(U_17064,U_17065,U_17066)),c_Map_Odom(U_17064,U_17065,U_17067)) != c_Orderings_Obot__class_Obot(tc_fun(U_17064,tc_HOL_Obool)) ),
    inference(variable_rename,[status(thm)],[f_4206_1]) ).

fof(f_4206_3,plain,
    ! [U_17065,U_17064,U_17066,U_17067] :
      ( c_Map_Omap__add(U_17064,U_17065,U_17066,U_17067) = c_Map_Omap__add(U_17064,U_17065,U_17067,U_17066)
      | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17064,tc_HOL_Obool)),c_Map_Odom(U_17064,U_17065,U_17066)),c_Map_Odom(U_17064,U_17065,U_17067)) != c_Orderings_Obot__class_Obot(tc_fun(U_17064,tc_HOL_Obool)) ),
    inference(definitional_conversion,[status(esa)],[f_4206_2]) ).

cnf(f_4206_4,plain,
    ( c_Map_Omap__add(U_17064,U_17065,U_17066,U_17067) = c_Map_Omap__add(U_17064,U_17065,U_17067,U_17066)
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_17064,tc_HOL_Obool)),c_Map_Odom(U_17064,U_17065,U_17066)),c_Map_Odom(U_17064,U_17065,U_17067)) != c_Orderings_Obot__class_Obot(tc_fun(U_17064,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4206_3]) ).

fof(f_4207_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_4207_2,plain,
    ! [U_17071,U_17070,U_17069,U_17068] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17068)),hAPP(c_Set_Oimage(U_17069,tc_Option_Ooption(U_17068),c_Map_Omap__add(U_17069,U_17068,U_17070,c_Map_Omap__of(U_17069,U_17068,U_17071))),c_Orderings_Otop__class_Otop(tc_fun(U_17069,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17068)),hAPP(c_Set_Oimage(U_17069,tc_Option_Ooption(U_17068),U_17070),c_Orderings_Otop__class_Otop(tc_fun(U_17069,tc_HOL_Obool))))) ),
    inference(variable_rename,[status(thm)],[f_4207_1]) ).

fof(f_4207_3,plain,
    ! [U_17068,U_17069,U_17070,U_17071] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17068)),hAPP(c_Set_Oimage(U_17069,tc_Option_Ooption(U_17068),c_Map_Omap__add(U_17069,U_17068,U_17070,c_Map_Omap__of(U_17069,U_17068,U_17071))),c_Orderings_Otop__class_Otop(tc_fun(U_17069,tc_HOL_Obool)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17068)),hAPP(c_Set_Oimage(U_17069,tc_Option_Ooption(U_17068),U_17070),c_Orderings_Otop__class_Otop(tc_fun(U_17069,tc_HOL_Obool))))) ),
    inference(definitional_conversion,[status(esa)],[f_4207_2]) ).

cnf(f_4207_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17068)),hAPP(c_Set_Oimage(U_17069,tc_Option_Ooption(U_17068),c_Map_Omap__add(U_17069,U_17068,U_17070,c_Map_Omap__of(U_17069,U_17068,U_17071))),c_Orderings_Otop__class_Otop(tc_fun(U_17069,tc_HOL_Obool)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17068)),hAPP(c_Set_Oimage(U_17069,tc_Option_Ooption(U_17068),U_17070),c_Orderings_Otop__class_Otop(tc_fun(U_17069,tc_HOL_Obool))))) ),
    inference(clausify,[status(thm)],[f_4207_3]) ).

fof(f_4208_1,plain,
    ! [V_f_2,V_A_2,T_b,T_c] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_c),c_Groups_Ozero__class_Ozero(T_c)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_b,T_c),V_f_2),V_A_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),V_A_2)) )
      | ~ class_Rings_Olinordered__semidom(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_setprod__nonneg]) ).

fof(f_4208_2,plain,
    ! [U_17076,U_17075,U_17074,U_17073] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17073),c_Groups_Ozero__class_Ozero(U_17073)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_17074,U_17073),U_17076),U_17075)))
      | ? [U_17072] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17073),c_Groups_Ozero__class_Ozero(U_17073)),hAPP(U_17076,U_17072)))
          & hBOOL(hAPP(hAPP(c_member(U_17074),U_17072),U_17075)) )
      | ~ class_Rings_Olinordered__semidom(U_17073) ),
    inference(variable_rename,[status(thm)],[f_4208_1]) ).

fof(f_4208_3,plain,
    ! [U_17076,U_17075,U_17074,U_17073] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17073),c_Groups_Ozero__class_Ozero(U_17073)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_17074,U_17073),U_17076),U_17075)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17073),c_Groups_Ozero__class_Ozero(U_17073)),hAPP(U_17076,sK438(U_17076,U_17075,U_17074,U_17073))))
        & hBOOL(hAPP(hAPP(c_member(U_17074),sK438(U_17076,U_17075,U_17074,U_17073)),U_17075)) )
      | ~ class_Rings_Olinordered__semidom(U_17073) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK438]),skolemize(U_17072,sK438(U_17076,U_17075,U_17074,U_17073))],[f_4208_2]) ).

fof(f_4208_4,plain,
    ( ! [U_17073,U_17074,U_17075,U_17076] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17073),c_Groups_Ozero__class_Ozero(U_17073)),hAPP(U_17076,sK438(U_17076,U_17075,U_17074,U_17073))))
        | ~ sP1101(U_17073,U_17074,U_17075,U_17076) )
    & ! [U_17073,U_17074,U_17075,U_17076] :
        ( hBOOL(hAPP(hAPP(c_member(U_17074),sK438(U_17076,U_17075,U_17074,U_17073)),U_17075))
        | ~ sP1101(U_17073,U_17074,U_17075,U_17076) )
    & ! [U_17073,U_17074,U_17075,U_17076] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17073),c_Groups_Ozero__class_Ozero(U_17073)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_17074,U_17073),U_17076),U_17075)))
        | sP1101(U_17073,U_17074,U_17075,U_17076)
        | ~ class_Rings_Olinordered__semidom(U_17073) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1101])],[f_4208_3]) ).

cnf(f_4208_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17073),c_Groups_Ozero__class_Ozero(U_17073)),hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(U_17074,U_17073),U_17076),U_17075)))
    | sP1101(U_17073,U_17074,U_17075,U_17076)
    | ~ class_Rings_Olinordered__semidom(U_17073) ),
    inference(clausify,[status(thm)],[f_4208_4]) ).

cnf(f_4208_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17074),sK438(U_17076,U_17075,U_17074,U_17073)),U_17075))
    | ~ sP1101(U_17073,U_17074,U_17075,U_17076) ),
    inference(clausify,[status(thm)],[f_4208_4]) ).

cnf(f_4208_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17073),c_Groups_Ozero__class_Ozero(U_17073)),hAPP(U_17076,sK438(U_17076,U_17075,U_17074,U_17073))))
    | ~ sP1101(U_17073,U_17074,U_17075,U_17076) ),
    inference(clausify,[status(thm)],[f_4208_4]) ).

fof(f_4209_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_4209_2,plain,
    ! [U_17079,U_17078,U_17077] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_17077),c_Map_Odom(U_17077,U_17078,c_Map_Omap__of(U_17077,U_17078,U_17079)))),
    inference(variable_rename,[status(thm)],[f_4209_1]) ).

fof(f_4209_3,plain,
    ! [U_17077,U_17079,U_17078] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_17077),c_Map_Odom(U_17077,U_17078,c_Map_Omap__of(U_17077,U_17078,U_17079)))),
    inference(definitional_conversion,[status(esa)],[f_4209_2]) ).

cnf(f_4209_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_17077),c_Map_Odom(U_17077,U_17078,c_Map_Omap__of(U_17077,U_17078,U_17079)))),
    inference(clausify,[status(thm)],[f_4209_3]) ).

fof(f_4210_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_4210_2,plain,
    ! [U_17082,U_17081,U_17080] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17080)),hAPP(c_Set_Oimage(U_17081,tc_Option_Ooption(U_17080),c_Map_Omap__of(U_17081,U_17080,U_17082)),c_Orderings_Otop__class_Otop(tc_fun(U_17081,tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_4210_1]) ).

fof(f_4210_3,plain,
    ! [U_17080,U_17081,U_17082] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17080)),hAPP(c_Set_Oimage(U_17081,tc_Option_Ooption(U_17080),c_Map_Omap__of(U_17081,U_17080,U_17082)),c_Orderings_Otop__class_Otop(tc_fun(U_17081,tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_4210_2]) ).

cnf(f_4210_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Option_Ooption(U_17080)),hAPP(c_Set_Oimage(U_17081,tc_Option_Ooption(U_17080),c_Map_Omap__of(U_17081,U_17080,U_17082)),c_Orderings_Otop__class_Otop(tc_fun(U_17081,tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_4210_3]) ).

fof(f_4211_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_4211_2,plain,
    ! [U_17086,U_17085,U_17084,U_17083] : c_Map_Omap__add(U_17083,U_17084,U_17085,c_Map_Omap__of(U_17083,U_17084,U_17086)) = c_List_Ofoldr(tc_prod(U_17083,U_17084),tc_fun(U_17083,tc_Option_Ooption(U_17084)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17083,U_17084,tc_fun(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_fun(U_17083,tc_Option_Ooption(U_17084)))),hAPP(hAPP(c_COMBC(U_17083,tc_fun(U_17084,tc_Option_Ooption(U_17084)),tc_fun(U_17084,tc_fun(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_fun(U_17083,tc_Option_Ooption(U_17084))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17084),tc_fun(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_fun(U_17083,tc_Option_Ooption(U_17084)))),tc_fun(tc_fun(U_17084,tc_Option_Ooption(U_17084)),tc_fun(U_17084,tc_fun(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_fun(U_17083,tc_Option_Ooption(U_17084))))),U_17083),c_COMBB(tc_Option_Ooption(U_17084),tc_fun(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_fun(U_17083,tc_Option_Ooption(U_17084))),U_17084)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_fun(tc_Option_Ooption(U_17084),tc_fun(U_17083,tc_Option_Ooption(U_17084)))),tc_fun(tc_Option_Ooption(U_17084),tc_fun(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_fun(U_17083,tc_Option_Ooption(U_17084)))),U_17083),c_COMBC(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_Option_Ooption(U_17084),tc_fun(U_17083,tc_Option_Ooption(U_17084)))),hAPP(c_COMBC(tc_fun(U_17083,tc_Option_Ooption(U_17084)),U_17083,tc_fun(tc_Option_Ooption(U_17084),tc_fun(U_17083,tc_Option_Ooption(U_17084)))),c_Fun_Ofun__upd(U_17083,tc_Option_Ooption(U_17084)))))),c_Option_Ooption_OSome(U_17084))),U_17086,U_17085),
    inference(variable_rename,[status(thm)],[f_4211_1]) ).

fof(f_4211_3,plain,
    ! [U_17083,U_17084,U_17085,U_17086] : c_Map_Omap__add(U_17083,U_17084,U_17085,c_Map_Omap__of(U_17083,U_17084,U_17086)) = c_List_Ofoldr(tc_prod(U_17083,U_17084),tc_fun(U_17083,tc_Option_Ooption(U_17084)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17083,U_17084,tc_fun(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_fun(U_17083,tc_Option_Ooption(U_17084)))),hAPP(hAPP(c_COMBC(U_17083,tc_fun(U_17084,tc_Option_Ooption(U_17084)),tc_fun(U_17084,tc_fun(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_fun(U_17083,tc_Option_Ooption(U_17084))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17084),tc_fun(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_fun(U_17083,tc_Option_Ooption(U_17084)))),tc_fun(tc_fun(U_17084,tc_Option_Ooption(U_17084)),tc_fun(U_17084,tc_fun(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_fun(U_17083,tc_Option_Ooption(U_17084))))),U_17083),c_COMBB(tc_Option_Ooption(U_17084),tc_fun(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_fun(U_17083,tc_Option_Ooption(U_17084))),U_17084)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_fun(tc_Option_Ooption(U_17084),tc_fun(U_17083,tc_Option_Ooption(U_17084)))),tc_fun(tc_Option_Ooption(U_17084),tc_fun(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_fun(U_17083,tc_Option_Ooption(U_17084)))),U_17083),c_COMBC(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_Option_Ooption(U_17084),tc_fun(U_17083,tc_Option_Ooption(U_17084)))),hAPP(c_COMBC(tc_fun(U_17083,tc_Option_Ooption(U_17084)),U_17083,tc_fun(tc_Option_Ooption(U_17084),tc_fun(U_17083,tc_Option_Ooption(U_17084)))),c_Fun_Ofun__upd(U_17083,tc_Option_Ooption(U_17084)))))),c_Option_Ooption_OSome(U_17084))),U_17086,U_17085),
    inference(definitional_conversion,[status(esa)],[f_4211_2]) ).

cnf(f_4211_4,plain,
    c_Map_Omap__add(U_17083,U_17084,U_17085,c_Map_Omap__of(U_17083,U_17084,U_17086)) = c_List_Ofoldr(tc_prod(U_17083,U_17084),tc_fun(U_17083,tc_Option_Ooption(U_17084)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17083,U_17084,tc_fun(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_fun(U_17083,tc_Option_Ooption(U_17084)))),hAPP(hAPP(c_COMBC(U_17083,tc_fun(U_17084,tc_Option_Ooption(U_17084)),tc_fun(U_17084,tc_fun(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_fun(U_17083,tc_Option_Ooption(U_17084))))),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17084),tc_fun(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_fun(U_17083,tc_Option_Ooption(U_17084)))),tc_fun(tc_fun(U_17084,tc_Option_Ooption(U_17084)),tc_fun(U_17084,tc_fun(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_fun(U_17083,tc_Option_Ooption(U_17084))))),U_17083),c_COMBB(tc_Option_Ooption(U_17084),tc_fun(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_fun(U_17083,tc_Option_Ooption(U_17084))),U_17084)),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_fun(tc_Option_Ooption(U_17084),tc_fun(U_17083,tc_Option_Ooption(U_17084)))),tc_fun(tc_Option_Ooption(U_17084),tc_fun(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_fun(U_17083,tc_Option_Ooption(U_17084)))),U_17083),c_COMBC(tc_fun(U_17083,tc_Option_Ooption(U_17084)),tc_Option_Ooption(U_17084),tc_fun(U_17083,tc_Option_Ooption(U_17084)))),hAPP(c_COMBC(tc_fun(U_17083,tc_Option_Ooption(U_17084)),U_17083,tc_fun(tc_Option_Ooption(U_17084),tc_fun(U_17083,tc_Option_Ooption(U_17084)))),c_Fun_Ofun__upd(U_17083,tc_Option_Ooption(U_17084)))))),c_Option_Ooption_OSome(U_17084))),U_17086,U_17085),
    inference(clausify,[status(thm)],[f_4211_3]) ).

fof(f_4212_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_4212_2,plain,
    ! [U_17089,U_17088,U_17087] : c_Smallcheck_Oorelse(U_17087,U_17088,U_17089) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17087),U_17087,U_17089,c_Option_Ooption_OSome(U_17087)),U_17088),
    inference(variable_rename,[status(thm)],[f_4212_1]) ).

fof(f_4212_3,plain,
    ! [U_17088,U_17087,U_17089] : c_Smallcheck_Oorelse(U_17087,U_17088,U_17089) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17087),U_17087,U_17089,c_Option_Ooption_OSome(U_17087)),U_17088),
    inference(definitional_conversion,[status(esa)],[f_4212_2]) ).

cnf(f_4212_4,plain,
    c_Smallcheck_Oorelse(U_17087,U_17088,U_17089) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17087),U_17087,U_17089,c_Option_Ooption_OSome(U_17087)),U_17088),
    inference(clausify,[status(thm)],[f_4212_3]) ).

fof(f_4213_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_4213_2,plain,
    ! [U_17091,U_17090] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,U_17090,U_17091) = c_Smallcheck_Ofull__small_H(U_17090,hAPP(c_Code__Numeral_Oint__of,U_17091),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_17091))),
    inference(variable_rename,[status(thm)],[f_4213_1]) ).

fof(f_4213_3,plain,
    ! [U_17090,U_17091] : c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,U_17090,U_17091) = c_Smallcheck_Ofull__small_H(U_17090,hAPP(c_Code__Numeral_Oint__of,U_17091),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_17091))),
    inference(definitional_conversion,[status(esa)],[f_4213_2]) ).

cnf(f_4213_4,plain,
    c_Smallcheck_Ofull__small__class_Ofull__small(tc_Int_Oint,U_17090,U_17091) = c_Smallcheck_Ofull__small_H(U_17090,hAPP(c_Code__Numeral_Oint__of,U_17091),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_17091))),
    inference(clausify,[status(thm)],[f_4213_3]) ).

fof(f_4214_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_4214_2,plain,
    ! [U_17094,U_17093,U_17092] :
      ( ( c_Smallcheck_Osmall_H(U_17094,U_17092,U_17093) = 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_17094,U_17092,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17093),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_17094,U_17093))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17092),U_17093)) )
      & ( c_Smallcheck_Osmall_H(U_17094,U_17092,U_17093) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17092),U_17093)) ) ),
    inference(variable_rename,[status(thm)],[f_4214_1]) ).

fof(f_4214_3,plain,
    ( ! [U_17100,U_17098,U_17096] :
        ( c_Smallcheck_Osmall_H(U_17100,U_17096,U_17098) = 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_17100,U_17096,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17098),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_17100,U_17098))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17096),U_17098)) )
    & ! [U_17099,U_17097,U_17095] :
        ( c_Smallcheck_Osmall_H(U_17099,U_17095,U_17097) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17095),U_17097)) ) ),
    inference(miniscope,[status(thm)],[f_4214_2]) ).

fof(f_4214_4,plain,
    ( ! [U_17100,U_17098,U_17096] :
        ( c_Smallcheck_Osmall_H(U_17100,U_17096,U_17098) = 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_17100,U_17096,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17098),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_17100,U_17098))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17096),U_17098)) )
    & ! [U_17095,U_17099,U_17097] :
        ( c_Smallcheck_Osmall_H(U_17099,U_17095,U_17097) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17095),U_17097)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4214_3]) ).

cnf(f_4214_5,plain,
    ( c_Smallcheck_Osmall_H(U_17099,U_17095,U_17097) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17095),U_17097)) ),
    inference(clausify,[status(thm)],[f_4214_4]) ).

cnf(f_4214_6,plain,
    ( c_Smallcheck_Osmall_H(U_17100,U_17096,U_17098) = 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_17100,U_17096,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17098),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_17100,U_17098))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17096),U_17098)) ),
    inference(clausify,[status(thm)],[f_4214_4]) ).

fof(f_4215_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_4215_2,plain,
    ! [U_17103,U_17102,U_17101] :
      ( ( ( c_Smallcheck_Osmall_H(U_17101,U_17102,U_17103) = 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_17101,U_17102,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17103),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_17101,U_17103))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17102),U_17103)) )
        & ( c_Smallcheck_Osmall_H(U_17101,U_17102,U_17103) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17102),U_17103)) ) )
      | ~ 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_17101),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17102),U_17103)))) ),
    inference(variable_rename,[status(thm)],[f_4215_1]) ).

fof(f_4215_3,plain,
    ( ! [U_17101,U_17102,U_17103] :
        ( c_Smallcheck_Osmall_H(U_17101,U_17102,U_17103) = 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_17101,U_17102,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17103),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_17101,U_17103))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17102),U_17103))
        | ~ sP1102(U_17101,U_17102,U_17103) )
    & ! [U_17101,U_17102,U_17103] :
        ( c_Smallcheck_Osmall_H(U_17101,U_17102,U_17103) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17102),U_17103))
        | ~ sP1102(U_17101,U_17102,U_17103) )
    & ! [U_17101,U_17102,U_17103] :
        ( sP1102(U_17101,U_17102,U_17103)
        | ~ 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_17101),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17102),U_17103)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1102])],[f_4215_2]) ).

cnf(f_4215_4,plain,
    ( sP1102(U_17101,U_17102,U_17103)
    | ~ 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_17101),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17102),U_17103)))) ),
    inference(clausify,[status(thm)],[f_4215_3]) ).

cnf(f_4215_5,plain,
    ( c_Smallcheck_Osmall_H(U_17101,U_17102,U_17103) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17102),U_17103))
    | ~ sP1102(U_17101,U_17102,U_17103) ),
    inference(clausify,[status(thm)],[f_4215_3]) ).

cnf(f_4215_6,plain,
    ( c_Smallcheck_Osmall_H(U_17101,U_17102,U_17103) = 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_17101,U_17102,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17103),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Option_Ooption_OSome(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(U_17101,U_17103))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17102),U_17103))
    | ~ sP1102(U_17101,U_17102,U_17103) ),
    inference(clausify,[status(thm)],[f_4215_3]) ).

fof(f_4216_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_4216_2,plain,
    ! [U_17105,U_17104] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),U_17104),U_17105) = c_Smallcheck_Osmall_H(U_17104,hAPP(c_Code__Numeral_Oint__of,U_17105),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_17105))),
    inference(variable_rename,[status(thm)],[f_4216_1]) ).

fof(f_4216_3,plain,
    ! [U_17105,U_17104] : hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),U_17104),U_17105) = c_Smallcheck_Osmall_H(U_17104,hAPP(c_Code__Numeral_Oint__of,U_17105),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_17105))),
    inference(definitional_conversion,[status(esa)],[f_4216_2]) ).

cnf(f_4216_4,plain,
    hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_Int_Oint),U_17104),U_17105) = c_Smallcheck_Osmall_H(U_17104,hAPP(c_Code__Numeral_Oint__of,U_17105),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Code__Numeral_Oint__of,U_17105))),
    inference(clausify,[status(thm)],[f_4216_3]) ).

fof(f_4217_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_4217_2,plain,
    ! [U_17109,U_17108,U_17107,U_17106] :
      ( hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(U_17107,U_17106)),U_17108),U_17109) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(U_17107),hAPP(hAPP(c_COMBC(U_17107,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(U_17106,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_17107),c_Smallcheck_Osmall__class_Osmall(U_17106)),hAPP(hAPP(c_COMBB(tc_fun(U_17106,tc_prod(U_17107,U_17106)),tc_fun(U_17106,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),U_17107),hAPP(c_COMBB(tc_prod(U_17107,U_17106),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),U_17106),U_17108)),c_Product__Type_OPair(U_17107,U_17106)))),U_17109)),U_17109)
      | ~ class_Smallcheck_Osmall(U_17107)
      | ~ class_Smallcheck_Osmall(U_17106) ),
    inference(variable_rename,[status(thm)],[f_4217_1]) ).

fof(f_4217_3,plain,
    ! [U_17107,U_17106,U_17108,U_17109] :
      ( hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(U_17107,U_17106)),U_17108),U_17109) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(U_17107),hAPP(hAPP(c_COMBC(U_17107,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(U_17106,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_17107),c_Smallcheck_Osmall__class_Osmall(U_17106)),hAPP(hAPP(c_COMBB(tc_fun(U_17106,tc_prod(U_17107,U_17106)),tc_fun(U_17106,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),U_17107),hAPP(c_COMBB(tc_prod(U_17107,U_17106),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),U_17106),U_17108)),c_Product__Type_OPair(U_17107,U_17106)))),U_17109)),U_17109)
      | ~ class_Smallcheck_Osmall(U_17107)
      | ~ class_Smallcheck_Osmall(U_17106) ),
    inference(definitional_conversion,[status(esa)],[f_4217_2]) ).

cnf(f_4217_4,plain,
    ( hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(tc_prod(U_17107,U_17106)),U_17108),U_17109) = hAPP(hAPP(c_Smallcheck_Osmall__class_Osmall(U_17107),hAPP(hAPP(c_COMBC(U_17107,tc_Code__Numeral_Ocode__numeral,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),hAPP(hAPP(c_COMBB(tc_fun(U_17106,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_17107),c_Smallcheck_Osmall__class_Osmall(U_17106)),hAPP(hAPP(c_COMBB(tc_fun(U_17106,tc_prod(U_17107,U_17106)),tc_fun(U_17106,tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm))),U_17107),hAPP(c_COMBB(tc_prod(U_17107,U_17106),tc_Option_Ooption(tc_List_Olist(tc_Code__Evaluation_Oterm)),U_17106),U_17108)),c_Product__Type_OPair(U_17107,U_17106)))),U_17109)),U_17109)
    | ~ class_Smallcheck_Osmall(U_17107)
    | ~ class_Smallcheck_Osmall(U_17106) ),
    inference(clausify,[status(thm)],[f_4217_3]) ).

fof(f_4218_1,plain,
    ! [V_Pa_2,V_a2_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2),V_a2_2))
      | ? [B_f,B_d,B_i] :
          ( ~ hBOOL(hAPP(hAPP(hAPP(V_Pa_2,B_f),B_d),B_i))
          & ( hBOOL(hAPP(hAPP(hAPP(V_Pa_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_4218_2,plain,
    ! [U_17116,U_17115,U_17114,U_17113] :
      ( hBOOL(hAPP(hAPP(hAPP(U_17116,U_17113),U_17114),U_17115))
      | ? [U_17112,U_17111,U_17110] :
          ( ~ hBOOL(hAPP(hAPP(hAPP(U_17116,U_17112),U_17111),U_17110))
          & ( hBOOL(hAPP(hAPP(hAPP(U_17116,U_17112),U_17111),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17110),c_Groups_Oone__class_Oone(tc_Int_Oint))))
            | hAPP(U_17112,U_17110) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17111),U_17110)) )
          & 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_17112),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17111),U_17110)))) )
      | ~ 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_17113),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17114),U_17115)))) ),
    inference(variable_rename,[status(thm)],[f_4218_1]) ).

fof(f_4218_3,plain,
    ! [U_17116,U_17115,U_17114,U_17113] :
      ( hBOOL(hAPP(hAPP(hAPP(U_17116,U_17113),U_17114),U_17115))
      | ? [U_17111,U_17110] :
          ( ~ hBOOL(hAPP(hAPP(hAPP(U_17116,sK439(U_17116,U_17115,U_17114,U_17113)),U_17111),U_17110))
          & ( hBOOL(hAPP(hAPP(hAPP(U_17116,sK439(U_17116,U_17115,U_17114,U_17113)),U_17111),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17110),c_Groups_Oone__class_Oone(tc_Int_Oint))))
            | hAPP(sK439(U_17116,U_17115,U_17114,U_17113),U_17110) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_17111),U_17110)) )
          & 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)),sK439(U_17116,U_17115,U_17114,U_17113)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17111),U_17110)))) )
      | ~ 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_17113),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17114),U_17115)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK439]),skolemize(U_17112,sK439(U_17116,U_17115,U_17114,U_17113))],[f_4218_2]) ).

fof(f_4218_4,plain,
    ! [U_17116,U_17115,U_17114,U_17113] :
      ( hBOOL(hAPP(hAPP(hAPP(U_17116,U_17113),U_17114),U_17115))
      | ? [U_17110] :
          ( ~ hBOOL(hAPP(hAPP(hAPP(U_17116,sK439(U_17116,U_17115,U_17114,U_17113)),sK440(U_17116,U_17115,U_17114,U_17113)),U_17110))
          & ( hBOOL(hAPP(hAPP(hAPP(U_17116,sK439(U_17116,U_17115,U_17114,U_17113)),sK440(U_17116,U_17115,U_17114,U_17113)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17110),c_Groups_Oone__class_Oone(tc_Int_Oint))))
            | hAPP(sK439(U_17116,U_17115,U_17114,U_17113),U_17110) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK440(U_17116,U_17115,U_17114,U_17113)),U_17110)) )
          & 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)),sK439(U_17116,U_17115,U_17114,U_17113)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK440(U_17116,U_17115,U_17114,U_17113)),U_17110)))) )
      | ~ 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_17113),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17114),U_17115)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK440]),skolemize(U_17111,sK440(U_17116,U_17115,U_17114,U_17113))],[f_4218_3]) ).

fof(f_4218_5,plain,
    ! [U_17116,U_17115,U_17114,U_17113] :
      ( hBOOL(hAPP(hAPP(hAPP(U_17116,U_17113),U_17114),U_17115))
      | ( ~ hBOOL(hAPP(hAPP(hAPP(U_17116,sK439(U_17116,U_17115,U_17114,U_17113)),sK440(U_17116,U_17115,U_17114,U_17113)),sK441(U_17116,U_17115,U_17114,U_17113)))
        & ( hBOOL(hAPP(hAPP(hAPP(U_17116,sK439(U_17116,U_17115,U_17114,U_17113)),sK440(U_17116,U_17115,U_17114,U_17113)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK441(U_17116,U_17115,U_17114,U_17113)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
          | hAPP(sK439(U_17116,U_17115,U_17114,U_17113),sK441(U_17116,U_17115,U_17114,U_17113)) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK440(U_17116,U_17115,U_17114,U_17113)),sK441(U_17116,U_17115,U_17114,U_17113))) )
        & 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)),sK439(U_17116,U_17115,U_17114,U_17113)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK440(U_17116,U_17115,U_17114,U_17113)),sK441(U_17116,U_17115,U_17114,U_17113))))) )
      | ~ 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_17113),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17114),U_17115)))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK441]),skolemize(U_17110,sK441(U_17116,U_17115,U_17114,U_17113))],[f_4218_4]) ).

fof(f_4218_6,plain,
    ( ! [U_17113,U_17114,U_17115,U_17116] :
        ( ~ hBOOL(hAPP(hAPP(hAPP(U_17116,sK439(U_17116,U_17115,U_17114,U_17113)),sK440(U_17116,U_17115,U_17114,U_17113)),sK441(U_17116,U_17115,U_17114,U_17113)))
        | ~ sP1103(U_17113,U_17114,U_17115,U_17116) )
    & ! [U_17113,U_17114,U_17115,U_17116] :
        ( hBOOL(hAPP(hAPP(hAPP(U_17116,sK439(U_17116,U_17115,U_17114,U_17113)),sK440(U_17116,U_17115,U_17114,U_17113)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK441(U_17116,U_17115,U_17114,U_17113)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
        | hAPP(sK439(U_17116,U_17115,U_17114,U_17113),sK441(U_17116,U_17115,U_17114,U_17113)) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK440(U_17116,U_17115,U_17114,U_17113)),sK441(U_17116,U_17115,U_17114,U_17113)))
        | ~ sP1103(U_17113,U_17114,U_17115,U_17116) )
    & ! [U_17113,U_17114,U_17115,U_17116] :
        ( 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)),sK439(U_17116,U_17115,U_17114,U_17113)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK440(U_17116,U_17115,U_17114,U_17113)),sK441(U_17116,U_17115,U_17114,U_17113)))))
        | ~ sP1103(U_17113,U_17114,U_17115,U_17116) )
    & ! [U_17113,U_17114,U_17115,U_17116] :
        ( hBOOL(hAPP(hAPP(hAPP(U_17116,U_17113),U_17114),U_17115))
        | sP1103(U_17113,U_17114,U_17115,U_17116)
        | ~ 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_17113),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17114),U_17115)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1103])],[f_4218_5]) ).

cnf(f_4218_7,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_17116,U_17113),U_17114),U_17115))
    | sP1103(U_17113,U_17114,U_17115,U_17116)
    | ~ 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_17113),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),U_17114),U_17115)))) ),
    inference(clausify,[status(thm)],[f_4218_6]) ).

cnf(f_4218_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)),sK439(U_17116,U_17115,U_17114,U_17113)),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),sK440(U_17116,U_17115,U_17114,U_17113)),sK441(U_17116,U_17115,U_17114,U_17113)))))
    | ~ sP1103(U_17113,U_17114,U_17115,U_17116) ),
    inference(clausify,[status(thm)],[f_4218_6]) ).

cnf(f_4218_9,plain,
    ( hBOOL(hAPP(hAPP(hAPP(U_17116,sK439(U_17116,U_17115,U_17114,U_17113)),sK440(U_17116,U_17115,U_17114,U_17113)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK441(U_17116,U_17115,U_17114,U_17113)),c_Groups_Oone__class_Oone(tc_Int_Oint))))
    | hAPP(sK439(U_17116,U_17115,U_17114,U_17113),sK441(U_17116,U_17115,U_17114,U_17113)) != c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),sK440(U_17116,U_17115,U_17114,U_17113)),sK441(U_17116,U_17115,U_17114,U_17113)))
    | ~ sP1103(U_17113,U_17114,U_17115,U_17116) ),
    inference(clausify,[status(thm)],[f_4218_6]) ).

cnf(f_4218_10,plain,
    ( ~ hBOOL(hAPP(hAPP(hAPP(U_17116,sK439(U_17116,U_17115,U_17114,U_17113)),sK440(U_17116,U_17115,U_17114,U_17113)),sK441(U_17116,U_17115,U_17114,U_17113)))
    | ~ sP1103(U_17113,U_17114,U_17115,U_17116) ),
    inference(clausify,[status(thm)],[f_4218_6]) ).

fof(f_4219_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_4219_2,plain,
    c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies),
    inference(definitional_conversion,[status(esa)],[f_4219_1]) ).

cnf(f_4219_3,plain,
    c_Com_Obody = c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom,c_Com_Obodies),
    inference(clausify,[status(thm)],[f_4219_2]) ).

fof(f_4220_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_4220_2,plain,
    ! [U_17123,U_17122,U_17121,U_17120,U_17119,U_17118,U_17117] :
      ( hAPP(c_Map_Omap__of(U_17118,U_17120,hAPP(hAPP(c_List_Omap(tc_prod(U_17117,U_17120),tc_prod(U_17118,U_17120)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17117,U_17120,tc_prod(U_17118,U_17120)),hAPP(hAPP(c_COMBB(U_17118,tc_fun(U_17120,tc_prod(U_17118,U_17120)),U_17117),c_Product__Type_OPair(U_17118,U_17120)),U_17119))),U_17121)),hAPP(U_17119,U_17122)) = hAPP(c_Option_Ooption_OSome(U_17120),U_17123)
      | hAPP(c_Map_Omap__of(U_17117,U_17120,U_17121),U_17122) != hAPP(c_Option_Ooption_OSome(U_17120),U_17123)
      | ~ c_Fun_Oinj__on(U_17117,U_17118,U_17119,c_Orderings_Otop__class_Otop(tc_fun(U_17117,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4220_1]) ).

fof(f_4220_3,plain,
    ! [U_17120,U_17119,U_17117,U_17118,U_17121,U_17122,U_17123] :
      ( hAPP(c_Map_Omap__of(U_17118,U_17120,hAPP(hAPP(c_List_Omap(tc_prod(U_17117,U_17120),tc_prod(U_17118,U_17120)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17117,U_17120,tc_prod(U_17118,U_17120)),hAPP(hAPP(c_COMBB(U_17118,tc_fun(U_17120,tc_prod(U_17118,U_17120)),U_17117),c_Product__Type_OPair(U_17118,U_17120)),U_17119))),U_17121)),hAPP(U_17119,U_17122)) = hAPP(c_Option_Ooption_OSome(U_17120),U_17123)
      | hAPP(c_Map_Omap__of(U_17117,U_17120,U_17121),U_17122) != hAPP(c_Option_Ooption_OSome(U_17120),U_17123)
      | ~ c_Fun_Oinj__on(U_17117,U_17118,U_17119,c_Orderings_Otop__class_Otop(tc_fun(U_17117,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_4220_2]) ).

cnf(f_4220_4,plain,
    ( hAPP(c_Map_Omap__of(U_17118,U_17120,hAPP(hAPP(c_List_Omap(tc_prod(U_17117,U_17120),tc_prod(U_17118,U_17120)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17117,U_17120,tc_prod(U_17118,U_17120)),hAPP(hAPP(c_COMBB(U_17118,tc_fun(U_17120,tc_prod(U_17118,U_17120)),U_17117),c_Product__Type_OPair(U_17118,U_17120)),U_17119))),U_17121)),hAPP(U_17119,U_17122)) = hAPP(c_Option_Ooption_OSome(U_17120),U_17123)
    | hAPP(c_Map_Omap__of(U_17117,U_17120,U_17121),U_17122) != hAPP(c_Option_Ooption_OSome(U_17120),U_17123)
    | ~ c_Fun_Oinj__on(U_17117,U_17118,U_17119,c_Orderings_Otop__class_Otop(tc_fun(U_17117,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4220_3]) ).

fof(f_4221_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_4221_2,plain,
    ! [U_17129,U_17128,U_17127,U_17126,U_17125,U_17124] : c_Map_Omap__comp(U_17124,U_17125,U_17126,U_17127,U_17128,U_17129) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17125),U_17124,c_Option_Ooption_ONone(U_17125),U_17127),hAPP(U_17128,U_17129)),
    inference(variable_rename,[status(thm)],[f_4221_1]) ).

fof(f_4221_3,plain,
    ! [U_17124,U_17125,U_17126,U_17127,U_17128,U_17129] : c_Map_Omap__comp(U_17124,U_17125,U_17126,U_17127,U_17128,U_17129) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17125),U_17124,c_Option_Ooption_ONone(U_17125),U_17127),hAPP(U_17128,U_17129)),
    inference(definitional_conversion,[status(esa)],[f_4221_2]) ).

cnf(f_4221_4,plain,
    c_Map_Omap__comp(U_17124,U_17125,U_17126,U_17127,U_17128,U_17129) = hAPP(c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17125),U_17124,c_Option_Ooption_ONone(U_17125),U_17127),hAPP(U_17128,U_17129)),
    inference(clausify,[status(thm)],[f_4221_3]) ).

fof(f_4222_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_4222_2,plain,
    ! [U_17132,U_17131,U_17130] :
      ( c_Fun_Oinj__on(tc_List_Olist(U_17130),tc_List_Olist(U_17131),hAPP(c_List_Omap(U_17130,U_17131),U_17132),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17130),tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_17130,U_17131,U_17132,c_Orderings_Otop__class_Otop(tc_fun(U_17130,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4222_1]) ).

fof(f_4222_3,plain,
    ! [U_17130,U_17131,U_17132] :
      ( c_Fun_Oinj__on(tc_List_Olist(U_17130),tc_List_Olist(U_17131),hAPP(c_List_Omap(U_17130,U_17131),U_17132),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17130),tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(U_17130,U_17131,U_17132,c_Orderings_Otop__class_Otop(tc_fun(U_17130,tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_4222_2]) ).

cnf(f_4222_4,plain,
    ( c_Fun_Oinj__on(tc_List_Olist(U_17130),tc_List_Olist(U_17131),hAPP(c_List_Omap(U_17130,U_17131),U_17132),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17130),tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_17130,U_17131,U_17132,c_Orderings_Otop__class_Otop(tc_fun(U_17130,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4222_3]) ).

fof(f_4223_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_4223_2,plain,
    ! [U_17141,U_17140,U_17139,U_17138,U_17137,U_17136,U_17135] :
      ( ( c_Map_Omap__comp(U_17135,U_17136,U_17137,U_17138,U_17139,U_17140) = hAPP(c_Option_Ooption_OSome(U_17136),U_17141)
        | ! [U_17134] :
            ( hAPP(U_17138,U_17134) != hAPP(c_Option_Ooption_OSome(U_17136),U_17141)
            | hAPP(U_17139,U_17140) != hAPP(c_Option_Ooption_OSome(U_17135),U_17134) ) )
      & ( ? [U_17133] :
            ( hAPP(U_17138,U_17133) = hAPP(c_Option_Ooption_OSome(U_17136),U_17141)
            & hAPP(U_17139,U_17140) = hAPP(c_Option_Ooption_OSome(U_17135),U_17133) )
        | c_Map_Omap__comp(U_17135,U_17136,U_17137,U_17138,U_17139,U_17140) != hAPP(c_Option_Ooption_OSome(U_17136),U_17141) ) ),
    inference(variable_rename,[status(thm)],[f_4223_1]) ).

fof(f_4223_3,plain,
    ( ! [U_17155,U_17153,U_17151,U_17149,U_17147,U_17145,U_17143] :
        ( c_Map_Omap__comp(U_17143,U_17145,U_17147,U_17149,U_17151,U_17153) = hAPP(c_Option_Ooption_OSome(U_17145),U_17155)
        | ! [U_17134] :
            ( hAPP(U_17149,U_17134) != hAPP(c_Option_Ooption_OSome(U_17145),U_17155)
            | hAPP(U_17151,U_17153) != hAPP(c_Option_Ooption_OSome(U_17143),U_17134) ) )
    & ! [U_17154,U_17152,U_17150,U_17148,U_17146,U_17144,U_17142] :
        ( ? [U_17133] :
            ( hAPP(U_17148,U_17133) = hAPP(c_Option_Ooption_OSome(U_17144),U_17154)
            & hAPP(U_17150,U_17152) = hAPP(c_Option_Ooption_OSome(U_17142),U_17133) )
        | c_Map_Omap__comp(U_17142,U_17144,U_17146,U_17148,U_17150,U_17152) != hAPP(c_Option_Ooption_OSome(U_17144),U_17154) ) ),
    inference(miniscope,[status(thm)],[f_4223_2]) ).

fof(f_4223_4,plain,
    ( ! [U_17155,U_17153,U_17151,U_17149,U_17147,U_17145,U_17143] :
        ( c_Map_Omap__comp(U_17143,U_17145,U_17147,U_17149,U_17151,U_17153) = hAPP(c_Option_Ooption_OSome(U_17145),U_17155)
        | ! [U_17134] :
            ( hAPP(U_17149,U_17134) != hAPP(c_Option_Ooption_OSome(U_17145),U_17155)
            | hAPP(U_17151,U_17153) != hAPP(c_Option_Ooption_OSome(U_17143),U_17134) ) )
    & ! [U_17154,U_17152,U_17150,U_17148,U_17146,U_17144,U_17142] :
        ( ( hAPP(U_17148,sK442(U_17154,U_17152,U_17150,U_17148,U_17146,U_17144,U_17142)) = hAPP(c_Option_Ooption_OSome(U_17144),U_17154)
          & hAPP(U_17150,U_17152) = hAPP(c_Option_Ooption_OSome(U_17142),sK442(U_17154,U_17152,U_17150,U_17148,U_17146,U_17144,U_17142)) )
        | c_Map_Omap__comp(U_17142,U_17144,U_17146,U_17148,U_17150,U_17152) != hAPP(c_Option_Ooption_OSome(U_17144),U_17154) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK442]),skolemize(U_17133,sK442(U_17154,U_17152,U_17150,U_17148,U_17146,U_17144,U_17142))],[f_4223_3]) ).

fof(f_4223_5,plain,
    ( ! [U_17148,U_17144,U_17142,U_17146,U_17150,U_17152,U_17154] :
        ( hAPP(U_17148,sK442(U_17154,U_17152,U_17150,U_17148,U_17146,U_17144,U_17142)) = hAPP(c_Option_Ooption_OSome(U_17144),U_17154)
        | ~ sP1104(U_17148,U_17144,U_17142,U_17146,U_17150,U_17152,U_17154) )
    & ! [U_17148,U_17144,U_17142,U_17146,U_17150,U_17152,U_17154] :
        ( hAPP(U_17150,U_17152) = hAPP(c_Option_Ooption_OSome(U_17142),sK442(U_17154,U_17152,U_17150,U_17148,U_17146,U_17144,U_17142))
        | ~ sP1104(U_17148,U_17144,U_17142,U_17146,U_17150,U_17152,U_17154) )
    & ! [U_17147,U_17155,U_17145,U_17134,U_17143,U_17149,U_17153,U_17151] :
        ( c_Map_Omap__comp(U_17143,U_17145,U_17147,U_17149,U_17151,U_17153) = hAPP(c_Option_Ooption_OSome(U_17145),U_17155)
        | hAPP(U_17149,U_17134) != hAPP(c_Option_Ooption_OSome(U_17145),U_17155)
        | hAPP(U_17151,U_17153) != hAPP(c_Option_Ooption_OSome(U_17143),U_17134) )
    & ! [U_17148,U_17144,U_17142,U_17146,U_17150,U_17152,U_17154] :
        ( sP1104(U_17148,U_17144,U_17142,U_17146,U_17150,U_17152,U_17154)
        | c_Map_Omap__comp(U_17142,U_17144,U_17146,U_17148,U_17150,U_17152) != hAPP(c_Option_Ooption_OSome(U_17144),U_17154) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1104])],[f_4223_4]) ).

cnf(f_4223_6,plain,
    ( sP1104(U_17148,U_17144,U_17142,U_17146,U_17150,U_17152,U_17154)
    | c_Map_Omap__comp(U_17142,U_17144,U_17146,U_17148,U_17150,U_17152) != hAPP(c_Option_Ooption_OSome(U_17144),U_17154) ),
    inference(clausify,[status(thm)],[f_4223_5]) ).

cnf(f_4223_7,plain,
    ( c_Map_Omap__comp(U_17143,U_17145,U_17147,U_17149,U_17151,U_17153) = hAPP(c_Option_Ooption_OSome(U_17145),U_17155)
    | hAPP(U_17149,U_17134) != hAPP(c_Option_Ooption_OSome(U_17145),U_17155)
    | hAPP(U_17151,U_17153) != hAPP(c_Option_Ooption_OSome(U_17143),U_17134) ),
    inference(clausify,[status(thm)],[f_4223_5]) ).

cnf(f_4223_8,plain,
    ( hAPP(U_17150,U_17152) = hAPP(c_Option_Ooption_OSome(U_17142),sK442(U_17154,U_17152,U_17150,U_17148,U_17146,U_17144,U_17142))
    | ~ sP1104(U_17148,U_17144,U_17142,U_17146,U_17150,U_17152,U_17154) ),
    inference(clausify,[status(thm)],[f_4223_5]) ).

cnf(f_4223_9,plain,
    ( hAPP(U_17148,sK442(U_17154,U_17152,U_17150,U_17148,U_17146,U_17144,U_17142)) = hAPP(c_Option_Ooption_OSome(U_17144),U_17154)
    | ~ sP1104(U_17148,U_17144,U_17142,U_17146,U_17150,U_17152,U_17154) ),
    inference(clausify,[status(thm)],[f_4223_5]) ).

fof(f_4224_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_4224_2,plain,
    ! [U_17162,U_17161,U_17160,U_17159,U_17158,U_17157,U_17156] :
      ( c_Map_Omap__comp(U_17158,U_17160,U_17161,U_17162,U_17156,U_17157) = hAPP(U_17162,U_17159)
      | hAPP(U_17156,U_17157) != hAPP(c_Option_Ooption_OSome(U_17158),U_17159) ),
    inference(variable_rename,[status(thm)],[f_4224_1]) ).

fof(f_4224_3,plain,
    ! [U_17161,U_17158,U_17162,U_17156,U_17157,U_17160,U_17159] :
      ( c_Map_Omap__comp(U_17158,U_17160,U_17161,U_17162,U_17156,U_17157) = hAPP(U_17162,U_17159)
      | hAPP(U_17156,U_17157) != hAPP(c_Option_Ooption_OSome(U_17158),U_17159) ),
    inference(definitional_conversion,[status(esa)],[f_4224_2]) ).

cnf(f_4224_4,plain,
    ( c_Map_Omap__comp(U_17158,U_17160,U_17161,U_17162,U_17156,U_17157) = hAPP(U_17162,U_17159)
    | hAPP(U_17156,U_17157) != hAPP(c_Option_Ooption_OSome(U_17158),U_17159) ),
    inference(clausify,[status(thm)],[f_4224_3]) ).

fof(f_4225_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_4225_2,plain,
    ! [U_17168,U_17167,U_17166,U_17165,U_17164,U_17163] :
      ( c_Map_Omap__comp(U_17165,U_17166,U_17167,U_17168,U_17163,U_17164) = c_Option_Ooption_ONone(U_17166)
      | hAPP(U_17163,U_17164) != c_Option_Ooption_ONone(U_17165) ),
    inference(variable_rename,[status(thm)],[f_4225_1]) ).

fof(f_4225_3,plain,
    ! [U_17165,U_17164,U_17163,U_17166,U_17167,U_17168] :
      ( c_Map_Omap__comp(U_17165,U_17166,U_17167,U_17168,U_17163,U_17164) = c_Option_Ooption_ONone(U_17166)
      | hAPP(U_17163,U_17164) != c_Option_Ooption_ONone(U_17165) ),
    inference(definitional_conversion,[status(esa)],[f_4225_2]) ).

cnf(f_4225_4,plain,
    ( c_Map_Omap__comp(U_17165,U_17166,U_17167,U_17168,U_17163,U_17164) = c_Option_Ooption_ONone(U_17166)
    | hAPP(U_17163,U_17164) != c_Option_Ooption_ONone(U_17165) ),
    inference(clausify,[status(thm)],[f_4225_3]) ).

fof(f_4226_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_4226_2,plain,
    ! [U_17174,U_17173,U_17172,U_17171,U_17170,U_17169] : hAPP(hAPP(c_List_Omap(U_17169,U_17170),U_17171),hAPP(hAPP(c_List_Omap(U_17172,U_17169),U_17173),U_17174)) = hAPP(hAPP(c_List_Omap(U_17172,U_17170),hAPP(c_Fun_Ocomp(U_17169,U_17170,U_17172,U_17171),U_17173)),U_17174),
    inference(variable_rename,[status(thm)],[f_4226_1]) ).

fof(f_4226_3,plain,
    ! [U_17169,U_17170,U_17171,U_17172,U_17173,U_17174] : hAPP(hAPP(c_List_Omap(U_17169,U_17170),U_17171),hAPP(hAPP(c_List_Omap(U_17172,U_17169),U_17173),U_17174)) = hAPP(hAPP(c_List_Omap(U_17172,U_17170),hAPP(c_Fun_Ocomp(U_17169,U_17170,U_17172,U_17171),U_17173)),U_17174),
    inference(definitional_conversion,[status(esa)],[f_4226_2]) ).

cnf(f_4226_4,plain,
    hAPP(hAPP(c_List_Omap(U_17169,U_17170),U_17171),hAPP(hAPP(c_List_Omap(U_17172,U_17169),U_17173),U_17174)) = hAPP(hAPP(c_List_Omap(U_17172,U_17170),hAPP(c_Fun_Ocomp(U_17169,U_17170,U_17172,U_17171),U_17173)),U_17174),
    inference(clausify,[status(thm)],[f_4226_3]) ).

fof(f_4227_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_4227_2,plain,
    ! [U_17180,U_17179,U_17178,U_17177,U_17176,U_17175] : hAPP(hAPP(c_List_Omap(U_17175,U_17176),U_17177),hAPP(hAPP(c_List_Omap(U_17178,U_17175),U_17179),U_17180)) = hAPP(hAPP(c_List_Omap(U_17178,U_17176),hAPP(c_Fun_Ocomp(U_17175,U_17176,U_17178,U_17177),U_17179)),U_17180),
    inference(variable_rename,[status(thm)],[f_4227_1]) ).

fof(f_4227_3,plain,
    ! [U_17175,U_17176,U_17177,U_17178,U_17179,U_17180] : hAPP(hAPP(c_List_Omap(U_17175,U_17176),U_17177),hAPP(hAPP(c_List_Omap(U_17178,U_17175),U_17179),U_17180)) = hAPP(hAPP(c_List_Omap(U_17178,U_17176),hAPP(c_Fun_Ocomp(U_17175,U_17176,U_17178,U_17177),U_17179)),U_17180),
    inference(definitional_conversion,[status(esa)],[f_4227_2]) ).

cnf(f_4227_4,plain,
    hAPP(hAPP(c_List_Omap(U_17175,U_17176),U_17177),hAPP(hAPP(c_List_Omap(U_17178,U_17175),U_17179),U_17180)) = hAPP(hAPP(c_List_Omap(U_17178,U_17176),hAPP(c_Fun_Ocomp(U_17175,U_17176,U_17178,U_17177),U_17179)),U_17180),
    inference(clausify,[status(thm)],[f_4227_3]) ).

fof(f_4228_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_4228_2,plain,
    ! [U_17185,U_17184,U_17183,U_17182,U_17181] : hAPP(c_Fun_Ocomp(tc_List_Olist(U_17181),tc_List_Olist(U_17182),tc_List_Olist(U_17183),hAPP(c_List_Omap(U_17181,U_17182),U_17184)),hAPP(c_List_Omap(U_17183,U_17181),U_17185)) = hAPP(c_List_Omap(U_17183,U_17182),hAPP(c_Fun_Ocomp(U_17181,U_17182,U_17183,U_17184),U_17185)),
    inference(variable_rename,[status(thm)],[f_4228_1]) ).

fof(f_4228_3,plain,
    ! [U_17181,U_17182,U_17183,U_17184,U_17185] : hAPP(c_Fun_Ocomp(tc_List_Olist(U_17181),tc_List_Olist(U_17182),tc_List_Olist(U_17183),hAPP(c_List_Omap(U_17181,U_17182),U_17184)),hAPP(c_List_Omap(U_17183,U_17181),U_17185)) = hAPP(c_List_Omap(U_17183,U_17182),hAPP(c_Fun_Ocomp(U_17181,U_17182,U_17183,U_17184),U_17185)),
    inference(definitional_conversion,[status(esa)],[f_4228_2]) ).

cnf(f_4228_4,plain,
    hAPP(c_Fun_Ocomp(tc_List_Olist(U_17181),tc_List_Olist(U_17182),tc_List_Olist(U_17183),hAPP(c_List_Omap(U_17181,U_17182),U_17184)),hAPP(c_List_Omap(U_17183,U_17181),U_17185)) = hAPP(c_List_Omap(U_17183,U_17182),hAPP(c_Fun_Ocomp(U_17181,U_17182,U_17183,U_17184),U_17185)),
    inference(clausify,[status(thm)],[f_4228_3]) ).

fof(f_4229_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_4229_2,plain,
    ! [U_17190,U_17189,U_17188,U_17187,U_17186] : hAPP(c_Fun_Ocomp(tc_List_Olist(U_17186),tc_List_Olist(U_17187),tc_List_Olist(U_17188),hAPP(c_List_Omap(U_17186,U_17187),U_17189)),hAPP(c_List_Omap(U_17188,U_17186),U_17190)) = hAPP(c_List_Omap(U_17188,U_17187),hAPP(c_Fun_Ocomp(U_17186,U_17187,U_17188,U_17189),U_17190)),
    inference(variable_rename,[status(thm)],[f_4229_1]) ).

fof(f_4229_3,plain,
    ! [U_17186,U_17187,U_17188,U_17189,U_17190] : hAPP(c_Fun_Ocomp(tc_List_Olist(U_17186),tc_List_Olist(U_17187),tc_List_Olist(U_17188),hAPP(c_List_Omap(U_17186,U_17187),U_17189)),hAPP(c_List_Omap(U_17188,U_17186),U_17190)) = hAPP(c_List_Omap(U_17188,U_17187),hAPP(c_Fun_Ocomp(U_17186,U_17187,U_17188,U_17189),U_17190)),
    inference(definitional_conversion,[status(esa)],[f_4229_2]) ).

cnf(f_4229_4,plain,
    hAPP(c_Fun_Ocomp(tc_List_Olist(U_17186),tc_List_Olist(U_17187),tc_List_Olist(U_17188),hAPP(c_List_Omap(U_17186,U_17187),U_17189)),hAPP(c_List_Omap(U_17188,U_17186),U_17190)) = hAPP(c_List_Omap(U_17188,U_17187),hAPP(c_Fun_Ocomp(U_17186,U_17187,U_17188,U_17189),U_17190)),
    inference(clausify,[status(thm)],[f_4229_3]) ).

fof(f_4230_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_4230_2,plain,
    ! [U_17195,U_17194,U_17193,U_17192,U_17191] :
      ( U_17194 = U_17195
      | ~ c_Fun_Oinj__on(U_17191,U_17192,U_17193,c_Orderings_Otop__class_Otop(tc_fun(U_17191,tc_HOL_Obool)))
      | hAPP(hAPP(c_List_Omap(U_17191,U_17192),U_17193),U_17194) != hAPP(hAPP(c_List_Omap(U_17191,U_17192),U_17193),U_17195) ),
    inference(variable_rename,[status(thm)],[f_4230_1]) ).

fof(f_4230_3,plain,
    ! [U_17191,U_17192,U_17193,U_17194,U_17195] :
      ( U_17194 = U_17195
      | ~ c_Fun_Oinj__on(U_17191,U_17192,U_17193,c_Orderings_Otop__class_Otop(tc_fun(U_17191,tc_HOL_Obool)))
      | hAPP(hAPP(c_List_Omap(U_17191,U_17192),U_17193),U_17194) != hAPP(hAPP(c_List_Omap(U_17191,U_17192),U_17193),U_17195) ),
    inference(definitional_conversion,[status(esa)],[f_4230_2]) ).

cnf(f_4230_4,plain,
    ( U_17194 = U_17195
    | ~ c_Fun_Oinj__on(U_17191,U_17192,U_17193,c_Orderings_Otop__class_Otop(tc_fun(U_17191,tc_HOL_Obool)))
    | hAPP(hAPP(c_List_Omap(U_17191,U_17192),U_17193),U_17194) != hAPP(hAPP(c_List_Omap(U_17191,U_17192),U_17193),U_17195) ),
    inference(clausify,[status(thm)],[f_4230_3]) ).

fof(f_4231_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_4231_2,plain,
    ! [U_17198,U_17197,U_17196] :
      ( c_Fun_Oinj__on(U_17196,U_17197,U_17198,c_Orderings_Otop__class_Otop(tc_fun(U_17196,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(tc_List_Olist(U_17196),tc_List_Olist(U_17197),hAPP(c_List_Omap(U_17196,U_17197),U_17198),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17196),tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4231_1]) ).

fof(f_4231_3,plain,
    ! [U_17196,U_17197,U_17198] :
      ( c_Fun_Oinj__on(U_17196,U_17197,U_17198,c_Orderings_Otop__class_Otop(tc_fun(U_17196,tc_HOL_Obool)))
      | ~ c_Fun_Oinj__on(tc_List_Olist(U_17196),tc_List_Olist(U_17197),hAPP(c_List_Omap(U_17196,U_17197),U_17198),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17196),tc_HOL_Obool))) ),
    inference(definitional_conversion,[status(esa)],[f_4231_2]) ).

cnf(f_4231_4,plain,
    ( c_Fun_Oinj__on(U_17196,U_17197,U_17198,c_Orderings_Otop__class_Otop(tc_fun(U_17196,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(tc_List_Olist(U_17196),tc_List_Olist(U_17197),hAPP(c_List_Omap(U_17196,U_17197),U_17198),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17196),tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4231_3]) ).

fof(f_4232_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_4232_2,plain,
    ! [U_17203,U_17202,U_17201,U_17200,U_17199] :
      ( ( ( hAPP(hAPP(c_List_Omap(U_17199,U_17200),U_17201),U_17202) = hAPP(hAPP(c_List_Omap(U_17199,U_17200),U_17201),U_17203)
          | U_17202 != U_17203 )
        & ( U_17202 = U_17203
          | hAPP(hAPP(c_List_Omap(U_17199,U_17200),U_17201),U_17202) != hAPP(hAPP(c_List_Omap(U_17199,U_17200),U_17201),U_17203) ) )
      | ~ c_Fun_Oinj__on(U_17199,U_17200,U_17201,c_Orderings_Otop__class_Otop(tc_fun(U_17199,tc_HOL_Obool))) ),
    inference(variable_rename,[status(thm)],[f_4232_1]) ).

fof(f_4232_3,plain,
    ( ! [U_17199,U_17200,U_17201,U_17202,U_17203] :
        ( hAPP(hAPP(c_List_Omap(U_17199,U_17200),U_17201),U_17202) = hAPP(hAPP(c_List_Omap(U_17199,U_17200),U_17201),U_17203)
        | U_17202 != U_17203
        | ~ sP1105(U_17199,U_17200,U_17201,U_17202,U_17203) )
    & ! [U_17199,U_17200,U_17201,U_17202,U_17203] :
        ( U_17202 = U_17203
        | hAPP(hAPP(c_List_Omap(U_17199,U_17200),U_17201),U_17202) != hAPP(hAPP(c_List_Omap(U_17199,U_17200),U_17201),U_17203)
        | ~ sP1105(U_17199,U_17200,U_17201,U_17202,U_17203) )
    & ! [U_17199,U_17200,U_17201,U_17202,U_17203] :
        ( sP1105(U_17199,U_17200,U_17201,U_17202,U_17203)
        | ~ c_Fun_Oinj__on(U_17199,U_17200,U_17201,c_Orderings_Otop__class_Otop(tc_fun(U_17199,tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1105])],[f_4232_2]) ).

cnf(f_4232_4,plain,
    ( sP1105(U_17199,U_17200,U_17201,U_17202,U_17203)
    | ~ c_Fun_Oinj__on(U_17199,U_17200,U_17201,c_Orderings_Otop__class_Otop(tc_fun(U_17199,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4232_3]) ).

cnf(f_4232_5,plain,
    ( U_17202 = U_17203
    | hAPP(hAPP(c_List_Omap(U_17199,U_17200),U_17201),U_17202) != hAPP(hAPP(c_List_Omap(U_17199,U_17200),U_17201),U_17203)
    | ~ sP1105(U_17199,U_17200,U_17201,U_17202,U_17203) ),
    inference(clausify,[status(thm)],[f_4232_3]) ).

cnf(f_4232_6,plain,
    ( hAPP(hAPP(c_List_Omap(U_17199,U_17200),U_17201),U_17202) = hAPP(hAPP(c_List_Omap(U_17199,U_17200),U_17201),U_17203)
    | U_17202 != U_17203
    | ~ sP1105(U_17199,U_17200,U_17201,U_17202,U_17203) ),
    inference(clausify,[status(thm)],[f_4232_3]) ).

fof(f_4233_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_4233_2,plain,
    ! [U_17206,U_17205,U_17204] :
      ( ( c_Fun_Oinj__on(tc_List_Olist(U_17204),tc_List_Olist(U_17205),hAPP(c_List_Omap(U_17204,U_17205),U_17206),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17204),tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(U_17204,U_17205,U_17206,c_Orderings_Otop__class_Otop(tc_fun(U_17204,tc_HOL_Obool))) )
      & ( c_Fun_Oinj__on(U_17204,U_17205,U_17206,c_Orderings_Otop__class_Otop(tc_fun(U_17204,tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(tc_List_Olist(U_17204),tc_List_Olist(U_17205),hAPP(c_List_Omap(U_17204,U_17205),U_17206),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17204),tc_HOL_Obool))) ) ),
    inference(variable_rename,[status(thm)],[f_4233_1]) ).

fof(f_4233_3,plain,
    ( ! [U_17212,U_17210,U_17208] :
        ( c_Fun_Oinj__on(tc_List_Olist(U_17208),tc_List_Olist(U_17210),hAPP(c_List_Omap(U_17208,U_17210),U_17212),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17208),tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(U_17208,U_17210,U_17212,c_Orderings_Otop__class_Otop(tc_fun(U_17208,tc_HOL_Obool))) )
    & ! [U_17211,U_17209,U_17207] :
        ( c_Fun_Oinj__on(U_17207,U_17209,U_17211,c_Orderings_Otop__class_Otop(tc_fun(U_17207,tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(tc_List_Olist(U_17207),tc_List_Olist(U_17209),hAPP(c_List_Omap(U_17207,U_17209),U_17211),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17207),tc_HOL_Obool))) ) ),
    inference(miniscope,[status(thm)],[f_4233_2]) ).

fof(f_4233_4,plain,
    ( ! [U_17212,U_17210,U_17208] :
        ( c_Fun_Oinj__on(tc_List_Olist(U_17208),tc_List_Olist(U_17210),hAPP(c_List_Omap(U_17208,U_17210),U_17212),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17208),tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(U_17208,U_17210,U_17212,c_Orderings_Otop__class_Otop(tc_fun(U_17208,tc_HOL_Obool))) )
    & ! [U_17209,U_17207,U_17211] :
        ( c_Fun_Oinj__on(U_17207,U_17209,U_17211,c_Orderings_Otop__class_Otop(tc_fun(U_17207,tc_HOL_Obool)))
        | ~ c_Fun_Oinj__on(tc_List_Olist(U_17207),tc_List_Olist(U_17209),hAPP(c_List_Omap(U_17207,U_17209),U_17211),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17207),tc_HOL_Obool))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4233_3]) ).

cnf(f_4233_5,plain,
    ( c_Fun_Oinj__on(U_17207,U_17209,U_17211,c_Orderings_Otop__class_Otop(tc_fun(U_17207,tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(tc_List_Olist(U_17207),tc_List_Olist(U_17209),hAPP(c_List_Omap(U_17207,U_17209),U_17211),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17207),tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4233_4]) ).

cnf(f_4233_6,plain,
    ( c_Fun_Oinj__on(tc_List_Olist(U_17208),tc_List_Olist(U_17210),hAPP(c_List_Omap(U_17208,U_17210),U_17212),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17208),tc_HOL_Obool)))
    | ~ c_Fun_Oinj__on(U_17208,U_17210,U_17212,c_Orderings_Otop__class_Otop(tc_fun(U_17208,tc_HOL_Obool))) ),
    inference(clausify,[status(thm)],[f_4233_4]) ).

fof(f_4234_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_4234_2,plain,
    ! [U_17213] : hAPP(c_List_Omap(U_17213,U_17213),c_Fun_Oid(U_17213)) = c_Fun_Oid(tc_List_Olist(U_17213)),
    inference(variable_rename,[status(thm)],[f_4234_1]) ).

fof(f_4234_3,plain,
    ! [U_17213] : hAPP(c_List_Omap(U_17213,U_17213),c_Fun_Oid(U_17213)) = c_Fun_Oid(tc_List_Olist(U_17213)),
    inference(definitional_conversion,[status(esa)],[f_4234_2]) ).

cnf(f_4234_4,plain,
    hAPP(c_List_Omap(U_17213,U_17213),c_Fun_Oid(U_17213)) = c_Fun_Oid(tc_List_Olist(U_17213)),
    inference(clausify,[status(thm)],[f_4234_3]) ).

fof(f_4235_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_4235_2,plain,
    ! [U_17214] : hAPP(c_List_Omap(U_17214,U_17214),c_COMBI(U_17214)) = c_Fun_Oid(tc_List_Olist(U_17214)),
    inference(variable_rename,[status(thm)],[f_4235_1]) ).

fof(f_4235_3,plain,
    ! [U_17214] : hAPP(c_List_Omap(U_17214,U_17214),c_COMBI(U_17214)) = c_Fun_Oid(tc_List_Olist(U_17214)),
    inference(definitional_conversion,[status(esa)],[f_4235_2]) ).

cnf(f_4235_4,plain,
    hAPP(c_List_Omap(U_17214,U_17214),c_COMBI(U_17214)) = c_Fun_Oid(tc_List_Olist(U_17214)),
    inference(clausify,[status(thm)],[f_4235_3]) ).

fof(f_4236_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_4236_2,plain,
    ! [U_17216,U_17215] : hAPP(hAPP(c_List_Omap(U_17215,U_17215),c_COMBI(U_17215)),U_17216) = U_17216,
    inference(variable_rename,[status(thm)],[f_4236_1]) ).

fof(f_4236_3,plain,
    ! [U_17215,U_17216] : hAPP(hAPP(c_List_Omap(U_17215,U_17215),c_COMBI(U_17215)),U_17216) = U_17216,
    inference(definitional_conversion,[status(esa)],[f_4236_2]) ).

cnf(f_4236_4,plain,
    hAPP(hAPP(c_List_Omap(U_17215,U_17215),c_COMBI(U_17215)),U_17216) = U_17216,
    inference(clausify,[status(thm)],[f_4236_3]) ).

fof(f_4237_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_4237_2,plain,
    ! [U_17223,U_17222,U_17221,U_17220,U_17219,U_17218,U_17217] : c_List_Ofoldr(U_17217,U_17218,U_17219,hAPP(hAPP(c_List_Omap(U_17220,U_17217),U_17221),U_17222),U_17223) = c_List_Ofoldr(U_17220,U_17218,hAPP(c_Fun_Ocomp(U_17217,tc_fun(U_17218,U_17218),U_17220,U_17219),U_17221),U_17222,U_17223),
    inference(variable_rename,[status(thm)],[f_4237_1]) ).

fof(f_4237_3,plain,
    ! [U_17217,U_17218,U_17219,U_17220,U_17221,U_17222,U_17223] : c_List_Ofoldr(U_17217,U_17218,U_17219,hAPP(hAPP(c_List_Omap(U_17220,U_17217),U_17221),U_17222),U_17223) = c_List_Ofoldr(U_17220,U_17218,hAPP(c_Fun_Ocomp(U_17217,tc_fun(U_17218,U_17218),U_17220,U_17219),U_17221),U_17222,U_17223),
    inference(definitional_conversion,[status(esa)],[f_4237_2]) ).

cnf(f_4237_4,plain,
    c_List_Ofoldr(U_17217,U_17218,U_17219,hAPP(hAPP(c_List_Omap(U_17220,U_17217),U_17221),U_17222),U_17223) = c_List_Ofoldr(U_17220,U_17218,hAPP(c_Fun_Ocomp(U_17217,tc_fun(U_17218,U_17218),U_17220,U_17219),U_17221),U_17222,U_17223),
    inference(clausify,[status(thm)],[f_4237_3]) ).

fof(f_4238_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_4238_2,plain,
    ! [U_17228,U_17227,U_17226,U_17225,U_17224] : c_Map_Omap__comp(U_17224,U_17225,U_17226,U_17227,hAPP(c_COMBK(tc_Option_Ooption(U_17224),U_17226),c_Option_Ooption_ONone(U_17224)),U_17228) = c_Option_Ooption_ONone(U_17225),
    inference(variable_rename,[status(thm)],[f_4238_1]) ).

fof(f_4238_3,plain,
    ! [U_17226,U_17225,U_17224,U_17227,U_17228] : c_Map_Omap__comp(U_17224,U_17225,U_17226,U_17227,hAPP(c_COMBK(tc_Option_Ooption(U_17224),U_17226),c_Option_Ooption_ONone(U_17224)),U_17228) = c_Option_Ooption_ONone(U_17225),
    inference(definitional_conversion,[status(esa)],[f_4238_2]) ).

cnf(f_4238_4,plain,
    c_Map_Omap__comp(U_17224,U_17225,U_17226,U_17227,hAPP(c_COMBK(tc_Option_Ooption(U_17224),U_17226),c_Option_Ooption_ONone(U_17224)),U_17228) = c_Option_Ooption_ONone(U_17225),
    inference(clausify,[status(thm)],[f_4238_3]) ).

fof(f_4239_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_4239_2,plain,
    ! [U_17233,U_17232,U_17231,U_17230,U_17229] : c_Map_Omap__comp(U_17229,U_17230,U_17231,hAPP(c_COMBK(tc_Option_Ooption(U_17230),U_17229),c_Option_Ooption_ONone(U_17230)),U_17232,U_17233) = c_Option_Ooption_ONone(U_17230),
    inference(variable_rename,[status(thm)],[f_4239_1]) ).

fof(f_4239_3,plain,
    ! [U_17229,U_17230,U_17231,U_17232,U_17233] : c_Map_Omap__comp(U_17229,U_17230,U_17231,hAPP(c_COMBK(tc_Option_Ooption(U_17230),U_17229),c_Option_Ooption_ONone(U_17230)),U_17232,U_17233) = c_Option_Ooption_ONone(U_17230),
    inference(definitional_conversion,[status(esa)],[f_4239_2]) ).

cnf(f_4239_4,plain,
    c_Map_Omap__comp(U_17229,U_17230,U_17231,hAPP(c_COMBK(tc_Option_Ooption(U_17230),U_17229),c_Option_Ooption_ONone(U_17230)),U_17232,U_17233) = c_Option_Ooption_ONone(U_17230),
    inference(clausify,[status(thm)],[f_4239_3]) ).

fof(f_4240_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_4240_2,plain,
    ! [U_17241,U_17240,U_17239,U_17238,U_17237,U_17236] :
      ( ( c_Map_Omap__comp(U_17236,U_17237,U_17238,U_17239,U_17240,U_17241) = c_Option_Ooption_ONone(U_17237)
        | ( ! [U_17235] :
              ( hAPP(U_17239,U_17235) != c_Option_Ooption_ONone(U_17237)
              | hAPP(U_17240,U_17241) != hAPP(c_Option_Ooption_OSome(U_17236),U_17235) )
          & hAPP(U_17240,U_17241) != c_Option_Ooption_ONone(U_17236) ) )
      & ( ? [U_17234] :
            ( hAPP(U_17239,U_17234) = c_Option_Ooption_ONone(U_17237)
            & hAPP(U_17240,U_17241) = hAPP(c_Option_Ooption_OSome(U_17236),U_17234) )
        | hAPP(U_17240,U_17241) = c_Option_Ooption_ONone(U_17236)
        | c_Map_Omap__comp(U_17236,U_17237,U_17238,U_17239,U_17240,U_17241) != c_Option_Ooption_ONone(U_17237) ) ),
    inference(variable_rename,[status(thm)],[f_4240_1]) ).

fof(f_4240_3,plain,
    ( ! [U_17253,U_17251,U_17249,U_17247,U_17245,U_17243] :
        ( c_Map_Omap__comp(U_17243,U_17245,U_17247,U_17249,U_17251,U_17253) = c_Option_Ooption_ONone(U_17245)
        | ( ! [U_17235] :
              ( hAPP(U_17249,U_17235) != c_Option_Ooption_ONone(U_17245)
              | hAPP(U_17251,U_17253) != hAPP(c_Option_Ooption_OSome(U_17243),U_17235) )
          & hAPP(U_17251,U_17253) != c_Option_Ooption_ONone(U_17243) ) )
    & ! [U_17252,U_17250,U_17248,U_17246,U_17244,U_17242] :
        ( ? [U_17234] :
            ( hAPP(U_17248,U_17234) = c_Option_Ooption_ONone(U_17244)
            & hAPP(U_17250,U_17252) = hAPP(c_Option_Ooption_OSome(U_17242),U_17234) )
        | hAPP(U_17250,U_17252) = c_Option_Ooption_ONone(U_17242)
        | c_Map_Omap__comp(U_17242,U_17244,U_17246,U_17248,U_17250,U_17252) != c_Option_Ooption_ONone(U_17244) ) ),
    inference(miniscope,[status(thm)],[f_4240_2]) ).

fof(f_4240_4,plain,
    ( ! [U_17253,U_17251,U_17249,U_17247,U_17245,U_17243] :
        ( c_Map_Omap__comp(U_17243,U_17245,U_17247,U_17249,U_17251,U_17253) = c_Option_Ooption_ONone(U_17245)
        | ( ! [U_17235] :
              ( hAPP(U_17249,U_17235) != c_Option_Ooption_ONone(U_17245)
              | hAPP(U_17251,U_17253) != hAPP(c_Option_Ooption_OSome(U_17243),U_17235) )
          & hAPP(U_17251,U_17253) != c_Option_Ooption_ONone(U_17243) ) )
    & ! [U_17252,U_17250,U_17248,U_17246,U_17244,U_17242] :
        ( ( hAPP(U_17248,sK443(U_17252,U_17250,U_17248,U_17246,U_17244,U_17242)) = c_Option_Ooption_ONone(U_17244)
          & hAPP(U_17250,U_17252) = hAPP(c_Option_Ooption_OSome(U_17242),sK443(U_17252,U_17250,U_17248,U_17246,U_17244,U_17242)) )
        | hAPP(U_17250,U_17252) = c_Option_Ooption_ONone(U_17242)
        | c_Map_Omap__comp(U_17242,U_17244,U_17246,U_17248,U_17250,U_17252) != c_Option_Ooption_ONone(U_17244) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK443]),skolemize(U_17234,sK443(U_17252,U_17250,U_17248,U_17246,U_17244,U_17242))],[f_4240_3]) ).

fof(f_4240_5,plain,
    ( ! [U_17245,U_17249,U_17235,U_17243,U_17251,U_17253] :
        ( hAPP(U_17249,U_17235) != c_Option_Ooption_ONone(U_17245)
        | hAPP(U_17251,U_17253) != hAPP(c_Option_Ooption_OSome(U_17243),U_17235)
        | ~ sP1107(U_17245,U_17249,U_17235,U_17243,U_17251,U_17253) )
    & ! [U_17245,U_17249,U_17235,U_17243,U_17251,U_17253] :
        ( hAPP(U_17251,U_17253) != c_Option_Ooption_ONone(U_17243)
        | ~ sP1107(U_17245,U_17249,U_17235,U_17243,U_17251,U_17253) )
    & ! [U_17246,U_17244,U_17250,U_17242,U_17248,U_17252] :
        ( hAPP(U_17248,sK443(U_17252,U_17250,U_17248,U_17246,U_17244,U_17242)) = c_Option_Ooption_ONone(U_17244)
        | ~ sP1106(U_17246,U_17244,U_17250,U_17242,U_17248,U_17252) )
    & ! [U_17246,U_17244,U_17250,U_17242,U_17248,U_17252] :
        ( hAPP(U_17250,U_17252) = hAPP(c_Option_Ooption_OSome(U_17242),sK443(U_17252,U_17250,U_17248,U_17246,U_17244,U_17242))
        | ~ sP1106(U_17246,U_17244,U_17250,U_17242,U_17248,U_17252) )
    & ! [U_17245,U_17247,U_17249,U_17235,U_17243,U_17251,U_17253] :
        ( c_Map_Omap__comp(U_17243,U_17245,U_17247,U_17249,U_17251,U_17253) = c_Option_Ooption_ONone(U_17245)
        | sP1107(U_17245,U_17249,U_17235,U_17243,U_17251,U_17253) )
    & ! [U_17246,U_17244,U_17250,U_17242,U_17248,U_17252] :
        ( sP1106(U_17246,U_17244,U_17250,U_17242,U_17248,U_17252)
        | hAPP(U_17250,U_17252) = c_Option_Ooption_ONone(U_17242)
        | c_Map_Omap__comp(U_17242,U_17244,U_17246,U_17248,U_17250,U_17252) != c_Option_Ooption_ONone(U_17244) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1106,sP1107])],[f_4240_4]) ).

cnf(f_4240_6,plain,
    ( sP1106(U_17246,U_17244,U_17250,U_17242,U_17248,U_17252)
    | hAPP(U_17250,U_17252) = c_Option_Ooption_ONone(U_17242)
    | c_Map_Omap__comp(U_17242,U_17244,U_17246,U_17248,U_17250,U_17252) != c_Option_Ooption_ONone(U_17244) ),
    inference(clausify,[status(thm)],[f_4240_5]) ).

cnf(f_4240_7,plain,
    ( c_Map_Omap__comp(U_17243,U_17245,U_17247,U_17249,U_17251,U_17253) = c_Option_Ooption_ONone(U_17245)
    | sP1107(U_17245,U_17249,U_17235,U_17243,U_17251,U_17253) ),
    inference(clausify,[status(thm)],[f_4240_5]) ).

cnf(f_4240_8,plain,
    ( hAPP(U_17250,U_17252) = hAPP(c_Option_Ooption_OSome(U_17242),sK443(U_17252,U_17250,U_17248,U_17246,U_17244,U_17242))
    | ~ sP1106(U_17246,U_17244,U_17250,U_17242,U_17248,U_17252) ),
    inference(clausify,[status(thm)],[f_4240_5]) ).

cnf(f_4240_9,plain,
    ( hAPP(U_17248,sK443(U_17252,U_17250,U_17248,U_17246,U_17244,U_17242)) = c_Option_Ooption_ONone(U_17244)
    | ~ sP1106(U_17246,U_17244,U_17250,U_17242,U_17248,U_17252) ),
    inference(clausify,[status(thm)],[f_4240_5]) ).

cnf(f_4240_10,plain,
    ( hAPP(U_17251,U_17253) != c_Option_Ooption_ONone(U_17243)
    | ~ sP1107(U_17245,U_17249,U_17235,U_17243,U_17251,U_17253) ),
    inference(clausify,[status(thm)],[f_4240_5]) ).

cnf(f_4240_11,plain,
    ( hAPP(U_17249,U_17235) != c_Option_Ooption_ONone(U_17245)
    | hAPP(U_17251,U_17253) != hAPP(c_Option_Ooption_OSome(U_17243),U_17235)
    | ~ sP1107(U_17245,U_17249,U_17235,U_17243,U_17251,U_17253) ),
    inference(clausify,[status(thm)],[f_4240_5]) ).

fof(f_4241_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_4241_2,plain,
    ! [U_17258,U_17257,U_17256,U_17255,U_17254] : c_Map_Omap__of(U_17254,U_17255,hAPP(hAPP(c_List_Omap(tc_prod(U_17254,U_17256),tc_prod(U_17254,U_17255)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17254,U_17256,tc_prod(U_17254,U_17255)),hAPP(hAPP(c_COMBC(U_17254,tc_fun(U_17256,U_17255),tc_fun(U_17256,tc_prod(U_17254,U_17255))),hAPP(hAPP(c_COMBB(tc_fun(U_17255,tc_prod(U_17254,U_17255)),tc_fun(tc_fun(U_17256,U_17255),tc_fun(U_17256,tc_prod(U_17254,U_17255))),U_17254),c_COMBB(U_17255,tc_prod(U_17254,U_17255),U_17256)),c_Product__Type_OPair(U_17254,U_17255))),U_17257))),U_17258)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17256),tc_Option_Ooption(U_17255),U_17254,hAPP(c_Option_Omap(U_17256,U_17255),U_17257)),c_Map_Omap__of(U_17254,U_17256,U_17258)),
    inference(variable_rename,[status(thm)],[f_4241_1]) ).

fof(f_4241_3,plain,
    ! [U_17255,U_17254,U_17256,U_17257,U_17258] : c_Map_Omap__of(U_17254,U_17255,hAPP(hAPP(c_List_Omap(tc_prod(U_17254,U_17256),tc_prod(U_17254,U_17255)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17254,U_17256,tc_prod(U_17254,U_17255)),hAPP(hAPP(c_COMBC(U_17254,tc_fun(U_17256,U_17255),tc_fun(U_17256,tc_prod(U_17254,U_17255))),hAPP(hAPP(c_COMBB(tc_fun(U_17255,tc_prod(U_17254,U_17255)),tc_fun(tc_fun(U_17256,U_17255),tc_fun(U_17256,tc_prod(U_17254,U_17255))),U_17254),c_COMBB(U_17255,tc_prod(U_17254,U_17255),U_17256)),c_Product__Type_OPair(U_17254,U_17255))),U_17257))),U_17258)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17256),tc_Option_Ooption(U_17255),U_17254,hAPP(c_Option_Omap(U_17256,U_17255),U_17257)),c_Map_Omap__of(U_17254,U_17256,U_17258)),
    inference(definitional_conversion,[status(esa)],[f_4241_2]) ).

cnf(f_4241_4,plain,
    c_Map_Omap__of(U_17254,U_17255,hAPP(hAPP(c_List_Omap(tc_prod(U_17254,U_17256),tc_prod(U_17254,U_17255)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17254,U_17256,tc_prod(U_17254,U_17255)),hAPP(hAPP(c_COMBC(U_17254,tc_fun(U_17256,U_17255),tc_fun(U_17256,tc_prod(U_17254,U_17255))),hAPP(hAPP(c_COMBB(tc_fun(U_17255,tc_prod(U_17254,U_17255)),tc_fun(tc_fun(U_17256,U_17255),tc_fun(U_17256,tc_prod(U_17254,U_17255))),U_17254),c_COMBB(U_17255,tc_prod(U_17254,U_17255),U_17256)),c_Product__Type_OPair(U_17254,U_17255))),U_17257))),U_17258)) = hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17256),tc_Option_Ooption(U_17255),U_17254,hAPP(c_Option_Omap(U_17256,U_17255),U_17257)),c_Map_Omap__of(U_17254,U_17256,U_17258)),
    inference(clausify,[status(thm)],[f_4241_3]) ).

fof(f_4242_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_4242_2,plain,
    ! [U_17262,U_17261,U_17260,U_17259] :
      ( c_Map_Omap__of(U_17259,U_17261,hAPP(hAPP(c_List_Omap(U_17259,tc_prod(U_17259,U_17261)),hAPP(hAPP(c_COMBS(U_17259,U_17261,tc_prod(U_17259,U_17261)),c_Product__Type_OPair(U_17259,U_17261)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17261),U_17261,U_17259),c_Option_Othe(U_17261)),U_17262))),U_17260)) = U_17262
      | hAPP(c_List_Oset(U_17259),U_17260) != c_Map_Odom(U_17259,U_17261,U_17262) ),
    inference(variable_rename,[status(thm)],[f_4242_1]) ).

fof(f_4242_3,plain,
    ! [U_17259,U_17260,U_17261,U_17262] :
      ( c_Map_Omap__of(U_17259,U_17261,hAPP(hAPP(c_List_Omap(U_17259,tc_prod(U_17259,U_17261)),hAPP(hAPP(c_COMBS(U_17259,U_17261,tc_prod(U_17259,U_17261)),c_Product__Type_OPair(U_17259,U_17261)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17261),U_17261,U_17259),c_Option_Othe(U_17261)),U_17262))),U_17260)) = U_17262
      | hAPP(c_List_Oset(U_17259),U_17260) != c_Map_Odom(U_17259,U_17261,U_17262) ),
    inference(definitional_conversion,[status(esa)],[f_4242_2]) ).

cnf(f_4242_4,plain,
    ( c_Map_Omap__of(U_17259,U_17261,hAPP(hAPP(c_List_Omap(U_17259,tc_prod(U_17259,U_17261)),hAPP(hAPP(c_COMBS(U_17259,U_17261,tc_prod(U_17259,U_17261)),c_Product__Type_OPair(U_17259,U_17261)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17261),U_17261,U_17259),c_Option_Othe(U_17261)),U_17262))),U_17260)) = U_17262
    | hAPP(c_List_Oset(U_17259),U_17260) != c_Map_Odom(U_17259,U_17261,U_17262) ),
    inference(clausify,[status(thm)],[f_4242_3]) ).

fof(f_4243_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_4243_2,plain,
    ! [U_17264,U_17263] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_17263),hAPP(c_List_Oset(U_17263),U_17264))),
    inference(variable_rename,[status(thm)],[f_4243_1]) ).

fof(f_4243_3,plain,
    ! [U_17263,U_17264] : hBOOL(hAPP(c_Finite__Set_Ofinite(U_17263),hAPP(c_List_Oset(U_17263),U_17264))),
    inference(definitional_conversion,[status(esa)],[f_4243_2]) ).

cnf(f_4243_4,plain,
    hBOOL(hAPP(c_Finite__Set_Ofinite(U_17263),hAPP(c_List_Oset(U_17263),U_17264))),
    inference(clausify,[status(thm)],[f_4243_3]) ).

fof(f_4244_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_4244_2,plain,
    ! [U_17271,U_17270,U_17269,U_17268,U_17267] :
      ( ( hAPP(hAPP(c_List_Omap(U_17267,U_17268),U_17269),U_17270) = hAPP(hAPP(c_List_Omap(U_17267,U_17268),U_17271),U_17270)
        | ? [U_17266] :
            ( hAPP(U_17269,U_17266) != hAPP(U_17271,U_17266)
            & hBOOL(hAPP(hAPP(c_member(U_17267),U_17266),hAPP(c_List_Oset(U_17267),U_17270))) ) )
      & ( ! [U_17265] :
            ( hAPP(U_17269,U_17265) = hAPP(U_17271,U_17265)
            | ~ hBOOL(hAPP(hAPP(c_member(U_17267),U_17265),hAPP(c_List_Oset(U_17267),U_17270))) )
        | hAPP(hAPP(c_List_Omap(U_17267,U_17268),U_17269),U_17270) != hAPP(hAPP(c_List_Omap(U_17267,U_17268),U_17271),U_17270) ) ),
    inference(variable_rename,[status(thm)],[f_4244_1]) ).

fof(f_4244_3,plain,
    ( ! [U_17281,U_17279,U_17277,U_17275,U_17273] :
        ( hAPP(hAPP(c_List_Omap(U_17273,U_17275),U_17277),U_17279) = hAPP(hAPP(c_List_Omap(U_17273,U_17275),U_17281),U_17279)
        | ? [U_17266] :
            ( hAPP(U_17277,U_17266) != hAPP(U_17281,U_17266)
            & hBOOL(hAPP(hAPP(c_member(U_17273),U_17266),hAPP(c_List_Oset(U_17273),U_17279))) ) )
    & ! [U_17280,U_17278,U_17276,U_17274,U_17272] :
        ( ! [U_17265] :
            ( hAPP(U_17276,U_17265) = hAPP(U_17280,U_17265)
            | ~ hBOOL(hAPP(hAPP(c_member(U_17272),U_17265),hAPP(c_List_Oset(U_17272),U_17278))) )
        | hAPP(hAPP(c_List_Omap(U_17272,U_17274),U_17276),U_17278) != hAPP(hAPP(c_List_Omap(U_17272,U_17274),U_17280),U_17278) ) ),
    inference(miniscope,[status(thm)],[f_4244_2]) ).

fof(f_4244_4,plain,
    ( ! [U_17281,U_17279,U_17277,U_17275,U_17273] :
        ( hAPP(hAPP(c_List_Omap(U_17273,U_17275),U_17277),U_17279) = hAPP(hAPP(c_List_Omap(U_17273,U_17275),U_17281),U_17279)
        | ( hAPP(U_17277,sK444(U_17281,U_17279,U_17277,U_17275,U_17273)) != hAPP(U_17281,sK444(U_17281,U_17279,U_17277,U_17275,U_17273))
          & hBOOL(hAPP(hAPP(c_member(U_17273),sK444(U_17281,U_17279,U_17277,U_17275,U_17273)),hAPP(c_List_Oset(U_17273),U_17279))) ) )
    & ! [U_17280,U_17278,U_17276,U_17274,U_17272] :
        ( ! [U_17265] :
            ( hAPP(U_17276,U_17265) = hAPP(U_17280,U_17265)
            | ~ hBOOL(hAPP(hAPP(c_member(U_17272),U_17265),hAPP(c_List_Oset(U_17272),U_17278))) )
        | hAPP(hAPP(c_List_Omap(U_17272,U_17274),U_17276),U_17278) != hAPP(hAPP(c_List_Omap(U_17272,U_17274),U_17280),U_17278) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK444]),skolemize(U_17266,sK444(U_17281,U_17279,U_17277,U_17275,U_17273))],[f_4244_3]) ).

fof(f_4244_5,plain,
    ( ! [U_17273,U_17275,U_17277,U_17281,U_17279] :
        ( hAPP(U_17277,sK444(U_17281,U_17279,U_17277,U_17275,U_17273)) != hAPP(U_17281,sK444(U_17281,U_17279,U_17277,U_17275,U_17273))
        | ~ sP1108(U_17273,U_17275,U_17277,U_17281,U_17279) )
    & ! [U_17273,U_17275,U_17277,U_17281,U_17279] :
        ( hBOOL(hAPP(hAPP(c_member(U_17273),sK444(U_17281,U_17279,U_17277,U_17275,U_17273)),hAPP(c_List_Oset(U_17273),U_17279)))
        | ~ sP1108(U_17273,U_17275,U_17277,U_17281,U_17279) )
    & ! [U_17273,U_17275,U_17277,U_17281,U_17279] :
        ( hAPP(hAPP(c_List_Omap(U_17273,U_17275),U_17277),U_17279) = hAPP(hAPP(c_List_Omap(U_17273,U_17275),U_17281),U_17279)
        | sP1108(U_17273,U_17275,U_17277,U_17281,U_17279) )
    & ! [U_17274,U_17276,U_17265,U_17278,U_17272,U_17280] :
        ( hAPP(U_17276,U_17265) = hAPP(U_17280,U_17265)
        | ~ hBOOL(hAPP(hAPP(c_member(U_17272),U_17265),hAPP(c_List_Oset(U_17272),U_17278)))
        | hAPP(hAPP(c_List_Omap(U_17272,U_17274),U_17276),U_17278) != hAPP(hAPP(c_List_Omap(U_17272,U_17274),U_17280),U_17278) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1108])],[f_4244_4]) ).

cnf(f_4244_6,plain,
    ( hAPP(U_17276,U_17265) = hAPP(U_17280,U_17265)
    | ~ hBOOL(hAPP(hAPP(c_member(U_17272),U_17265),hAPP(c_List_Oset(U_17272),U_17278)))
    | hAPP(hAPP(c_List_Omap(U_17272,U_17274),U_17276),U_17278) != hAPP(hAPP(c_List_Omap(U_17272,U_17274),U_17280),U_17278) ),
    inference(clausify,[status(thm)],[f_4244_5]) ).

cnf(f_4244_7,plain,
    ( hAPP(hAPP(c_List_Omap(U_17273,U_17275),U_17277),U_17279) = hAPP(hAPP(c_List_Omap(U_17273,U_17275),U_17281),U_17279)
    | sP1108(U_17273,U_17275,U_17277,U_17281,U_17279) ),
    inference(clausify,[status(thm)],[f_4244_5]) ).

cnf(f_4244_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17273),sK444(U_17281,U_17279,U_17277,U_17275,U_17273)),hAPP(c_List_Oset(U_17273),U_17279)))
    | ~ sP1108(U_17273,U_17275,U_17277,U_17281,U_17279) ),
    inference(clausify,[status(thm)],[f_4244_5]) ).

cnf(f_4244_9,plain,
    ( hAPP(U_17277,sK444(U_17281,U_17279,U_17277,U_17275,U_17273)) != hAPP(U_17281,sK444(U_17281,U_17279,U_17277,U_17275,U_17273))
    | ~ sP1108(U_17273,U_17275,U_17277,U_17281,U_17279) ),
    inference(clausify,[status(thm)],[f_4244_5]) ).

fof(f_4245_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_4245_2,plain,
    ! [U_17285,U_17284,U_17283,U_17282] : hAPP(c_List_Oset(U_17282),hAPP(hAPP(c_List_Omap(U_17283,U_17282),U_17284),U_17285)) = hAPP(c_Set_Oimage(U_17283,U_17282,U_17284),hAPP(c_List_Oset(U_17283),U_17285)),
    inference(variable_rename,[status(thm)],[f_4245_1]) ).

fof(f_4245_3,plain,
    ! [U_17283,U_17284,U_17285,U_17282] : hAPP(c_List_Oset(U_17282),hAPP(hAPP(c_List_Omap(U_17283,U_17282),U_17284),U_17285)) = hAPP(c_Set_Oimage(U_17283,U_17282,U_17284),hAPP(c_List_Oset(U_17283),U_17285)),
    inference(definitional_conversion,[status(esa)],[f_4245_2]) ).

cnf(f_4245_4,plain,
    hAPP(c_List_Oset(U_17282),hAPP(hAPP(c_List_Omap(U_17283,U_17282),U_17284),U_17285)) = hAPP(c_Set_Oimage(U_17283,U_17282,U_17284),hAPP(c_List_Oset(U_17283),U_17285)),
    inference(clausify,[status(thm)],[f_4245_3]) ).

fof(f_4246_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_4246_2,plain,
    ! [U_17290,U_17289,U_17288,U_17287,U_17286] : c_Map_Odom(U_17286,U_17287,hAPP(hAPP(c_COMBS(U_17286,tc_Option_Ooption(U_17288),tc_Option_Ooption(U_17287)),hAPP(hAPP(c_COMBB(tc_fun(U_17288,U_17287),tc_fun(tc_Option_Ooption(U_17288),tc_Option_Ooption(U_17287)),U_17286),c_Option_Omap(U_17288,U_17287)),U_17289)),U_17290)) = c_Map_Odom(U_17286,U_17288,U_17290),
    inference(variable_rename,[status(thm)],[f_4246_1]) ).

fof(f_4246_3,plain,
    ! [U_17286,U_17287,U_17288,U_17289,U_17290] : c_Map_Odom(U_17286,U_17287,hAPP(hAPP(c_COMBS(U_17286,tc_Option_Ooption(U_17288),tc_Option_Ooption(U_17287)),hAPP(hAPP(c_COMBB(tc_fun(U_17288,U_17287),tc_fun(tc_Option_Ooption(U_17288),tc_Option_Ooption(U_17287)),U_17286),c_Option_Omap(U_17288,U_17287)),U_17289)),U_17290)) = c_Map_Odom(U_17286,U_17288,U_17290),
    inference(definitional_conversion,[status(esa)],[f_4246_2]) ).

cnf(f_4246_4,plain,
    c_Map_Odom(U_17286,U_17287,hAPP(hAPP(c_COMBS(U_17286,tc_Option_Ooption(U_17288),tc_Option_Ooption(U_17287)),hAPP(hAPP(c_COMBB(tc_fun(U_17288,U_17287),tc_fun(tc_Option_Ooption(U_17288),tc_Option_Ooption(U_17287)),U_17286),c_Option_Omap(U_17288,U_17287)),U_17289)),U_17290)) = c_Map_Odom(U_17286,U_17288,U_17290),
    inference(clausify,[status(thm)],[f_4246_3]) ).

fof(f_4247_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_4247_2,plain,
    ! [U_17291] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_17291)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17291),tc_HOL_Obool)))),
    inference(variable_rename,[status(thm)],[f_4247_1]) ).

fof(f_4247_3,plain,
    ! [U_17291] : ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_17291)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17291),tc_HOL_Obool)))),
    inference(definitional_conversion,[status(esa)],[f_4247_2]) ).

cnf(f_4247_4,plain,
    ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_17291)),c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_17291),tc_HOL_Obool)))),
    inference(clausify,[status(thm)],[f_4247_3]) ).

fof(f_4248_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_4248_2,plain,
    ! [U_17292] : hAPP(c_Option_Omap(U_17292,U_17292),c_Fun_Oid(U_17292)) = c_Fun_Oid(tc_Option_Ooption(U_17292)),
    inference(variable_rename,[status(thm)],[f_4248_1]) ).

fof(f_4248_3,plain,
    ! [U_17292] : hAPP(c_Option_Omap(U_17292,U_17292),c_Fun_Oid(U_17292)) = c_Fun_Oid(tc_Option_Ooption(U_17292)),
    inference(definitional_conversion,[status(esa)],[f_4248_2]) ).

cnf(f_4248_4,plain,
    hAPP(c_Option_Omap(U_17292,U_17292),c_Fun_Oid(U_17292)) = c_Fun_Oid(tc_Option_Ooption(U_17292)),
    inference(clausify,[status(thm)],[f_4248_3]) ).

fof(f_4249_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_4249_2,plain,
    ! [U_17293] : hAPP(c_Option_Omap(U_17293,U_17293),c_COMBI(U_17293)) = c_Fun_Oid(tc_Option_Ooption(U_17293)),
    inference(variable_rename,[status(thm)],[f_4249_1]) ).

fof(f_4249_3,plain,
    ! [U_17293] : hAPP(c_Option_Omap(U_17293,U_17293),c_COMBI(U_17293)) = c_Fun_Oid(tc_Option_Ooption(U_17293)),
    inference(definitional_conversion,[status(esa)],[f_4249_2]) ).

cnf(f_4249_4,plain,
    hAPP(c_Option_Omap(U_17293,U_17293),c_COMBI(U_17293)) = c_Fun_Oid(tc_Option_Ooption(U_17293)),
    inference(clausify,[status(thm)],[f_4249_3]) ).

fof(f_4250_1,plain,
    ! [V_g_2,V_f_2,T_b,T_c,T_d] : hAPP(c_Fun_Ocomp(tc_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_4250_2,plain,
    ! [U_17298,U_17297,U_17296,U_17295,U_17294] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17294),tc_Option_Ooption(U_17295),tc_Option_Ooption(U_17296),hAPP(c_Option_Omap(U_17294,U_17295),U_17297)),hAPP(c_Option_Omap(U_17296,U_17294),U_17298)) = hAPP(c_Option_Omap(U_17296,U_17295),hAPP(c_Fun_Ocomp(U_17294,U_17295,U_17296,U_17297),U_17298)),
    inference(variable_rename,[status(thm)],[f_4250_1]) ).

fof(f_4250_3,plain,
    ! [U_17294,U_17295,U_17296,U_17297,U_17298] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17294),tc_Option_Ooption(U_17295),tc_Option_Ooption(U_17296),hAPP(c_Option_Omap(U_17294,U_17295),U_17297)),hAPP(c_Option_Omap(U_17296,U_17294),U_17298)) = hAPP(c_Option_Omap(U_17296,U_17295),hAPP(c_Fun_Ocomp(U_17294,U_17295,U_17296,U_17297),U_17298)),
    inference(definitional_conversion,[status(esa)],[f_4250_2]) ).

cnf(f_4250_4,plain,
    hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17294),tc_Option_Ooption(U_17295),tc_Option_Ooption(U_17296),hAPP(c_Option_Omap(U_17294,U_17295),U_17297)),hAPP(c_Option_Omap(U_17296,U_17294),U_17298)) = hAPP(c_Option_Omap(U_17296,U_17295),hAPP(c_Fun_Ocomp(U_17294,U_17295,U_17296,U_17297),U_17298)),
    inference(clausify,[status(thm)],[f_4250_3]) ).

fof(f_4251_1,plain,
    ! [V_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_4251_2,plain,
    ! [U_17304,U_17303,U_17302,U_17301,U_17300,U_17299] : hAPP(hAPP(c_Option_Omap(U_17299,U_17300),U_17301),hAPP(hAPP(c_Option_Omap(U_17302,U_17299),U_17303),U_17304)) = hAPP(hAPP(c_Option_Omap(U_17302,U_17300),hAPP(c_Fun_Ocomp(U_17299,U_17300,U_17302,U_17301),U_17303)),U_17304),
    inference(variable_rename,[status(thm)],[f_4251_1]) ).

fof(f_4251_3,plain,
    ! [U_17299,U_17300,U_17301,U_17302,U_17303,U_17304] : hAPP(hAPP(c_Option_Omap(U_17299,U_17300),U_17301),hAPP(hAPP(c_Option_Omap(U_17302,U_17299),U_17303),U_17304)) = hAPP(hAPP(c_Option_Omap(U_17302,U_17300),hAPP(c_Fun_Ocomp(U_17299,U_17300,U_17302,U_17301),U_17303)),U_17304),
    inference(definitional_conversion,[status(esa)],[f_4251_2]) ).

cnf(f_4251_4,plain,
    hAPP(hAPP(c_Option_Omap(U_17299,U_17300),U_17301),hAPP(hAPP(c_Option_Omap(U_17302,U_17299),U_17303),U_17304)) = hAPP(hAPP(c_Option_Omap(U_17302,U_17300),hAPP(c_Fun_Ocomp(U_17299,U_17300,U_17302,U_17301),U_17303)),U_17304),
    inference(clausify,[status(thm)],[f_4251_3]) ).

fof(f_4252_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_4252_2,plain,
    ! [U_17310,U_17309,U_17308,U_17307,U_17306,U_17305] : hAPP(hAPP(c_Option_Omap(U_17305,U_17306),U_17307),hAPP(hAPP(c_Option_Omap(U_17308,U_17305),U_17309),U_17310)) = hAPP(hAPP(c_Option_Omap(U_17308,U_17306),hAPP(c_Fun_Ocomp(U_17305,U_17306,U_17308,U_17307),U_17309)),U_17310),
    inference(variable_rename,[status(thm)],[f_4252_1]) ).

fof(f_4252_3,plain,
    ! [U_17305,U_17306,U_17307,U_17308,U_17309,U_17310] : hAPP(hAPP(c_Option_Omap(U_17305,U_17306),U_17307),hAPP(hAPP(c_Option_Omap(U_17308,U_17305),U_17309),U_17310)) = hAPP(hAPP(c_Option_Omap(U_17308,U_17306),hAPP(c_Fun_Ocomp(U_17305,U_17306,U_17308,U_17307),U_17309)),U_17310),
    inference(definitional_conversion,[status(esa)],[f_4252_2]) ).

cnf(f_4252_4,plain,
    hAPP(hAPP(c_Option_Omap(U_17305,U_17306),U_17307),hAPP(hAPP(c_Option_Omap(U_17308,U_17305),U_17309),U_17310)) = hAPP(hAPP(c_Option_Omap(U_17308,U_17306),hAPP(c_Fun_Ocomp(U_17305,U_17306,U_17308,U_17307),U_17309)),U_17310),
    inference(clausify,[status(thm)],[f_4252_3]) ).

fof(f_4253_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_4253_2,plain,
    ! [U_17315,U_17314,U_17313,U_17312,U_17311] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17311),tc_Option_Ooption(U_17312),U_17313,hAPP(c_Option_Omap(U_17311,U_17312),U_17314)),hAPP(c_COMBK(tc_Option_Ooption(U_17311),U_17313),c_Option_Ooption_ONone(U_17311))),U_17315) = c_Option_Ooption_ONone(U_17312),
    inference(variable_rename,[status(thm)],[f_4253_1]) ).

fof(f_4253_3,plain,
    ! [U_17311,U_17312,U_17313,U_17314,U_17315] : hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17311),tc_Option_Ooption(U_17312),U_17313,hAPP(c_Option_Omap(U_17311,U_17312),U_17314)),hAPP(c_COMBK(tc_Option_Ooption(U_17311),U_17313),c_Option_Ooption_ONone(U_17311))),U_17315) = c_Option_Ooption_ONone(U_17312),
    inference(definitional_conversion,[status(esa)],[f_4253_2]) ).

cnf(f_4253_4,plain,
    hAPP(hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17311),tc_Option_Ooption(U_17312),U_17313,hAPP(c_Option_Omap(U_17311,U_17312),U_17314)),hAPP(c_COMBK(tc_Option_Ooption(U_17311),U_17313),c_Option_Ooption_ONone(U_17311))),U_17315) = c_Option_Ooption_ONone(U_17312),
    inference(clausify,[status(thm)],[f_4253_3]) ).

fof(f_4254_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_4254_2,plain,
    ! [U_17318,U_17317,U_17316] : hAPP(hAPP(c_Option_Omap(U_17316,U_17317),U_17318),c_Option_Ooption_ONone(U_17316)) = c_Option_Ooption_ONone(U_17317),
    inference(variable_rename,[status(thm)],[f_4254_1]) ).

fof(f_4254_3,plain,
    ! [U_17316,U_17317,U_17318] : hAPP(hAPP(c_Option_Omap(U_17316,U_17317),U_17318),c_Option_Ooption_ONone(U_17316)) = c_Option_Ooption_ONone(U_17317),
    inference(definitional_conversion,[status(esa)],[f_4254_2]) ).

cnf(f_4254_4,plain,
    hAPP(hAPP(c_Option_Omap(U_17316,U_17317),U_17318),c_Option_Ooption_ONone(U_17316)) = c_Option_Ooption_ONone(U_17317),
    inference(clausify,[status(thm)],[f_4254_3]) ).

fof(f_4255_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_4255_2,plain,
    ! [U_17322,U_17321,U_17320,U_17319] :
      ( ( hAPP(hAPP(c_Option_Omap(U_17319,U_17320),U_17321),U_17322) = c_Option_Ooption_ONone(U_17320)
        | U_17322 != c_Option_Ooption_ONone(U_17319) )
      & ( U_17322 = c_Option_Ooption_ONone(U_17319)
        | hAPP(hAPP(c_Option_Omap(U_17319,U_17320),U_17321),U_17322) != c_Option_Ooption_ONone(U_17320) ) ),
    inference(variable_rename,[status(thm)],[f_4255_1]) ).

fof(f_4255_3,plain,
    ( ! [U_17330,U_17328,U_17326,U_17324] :
        ( hAPP(hAPP(c_Option_Omap(U_17324,U_17326),U_17328),U_17330) = c_Option_Ooption_ONone(U_17326)
        | U_17330 != c_Option_Ooption_ONone(U_17324) )
    & ! [U_17329,U_17327,U_17325,U_17323] :
        ( U_17329 = c_Option_Ooption_ONone(U_17323)
        | hAPP(hAPP(c_Option_Omap(U_17323,U_17325),U_17327),U_17329) != c_Option_Ooption_ONone(U_17325) ) ),
    inference(miniscope,[status(thm)],[f_4255_2]) ).

fof(f_4255_4,plain,
    ( ! [U_17324,U_17330,U_17326,U_17328] :
        ( hAPP(hAPP(c_Option_Omap(U_17324,U_17326),U_17328),U_17330) = c_Option_Ooption_ONone(U_17326)
        | U_17330 != c_Option_Ooption_ONone(U_17324) )
    & ! [U_17329,U_17325,U_17327,U_17323] :
        ( U_17329 = c_Option_Ooption_ONone(U_17323)
        | hAPP(hAPP(c_Option_Omap(U_17323,U_17325),U_17327),U_17329) != c_Option_Ooption_ONone(U_17325) ) ),
    inference(definitional_conversion,[status(esa)],[f_4255_3]) ).

cnf(f_4255_5,plain,
    ( U_17329 = c_Option_Ooption_ONone(U_17323)
    | hAPP(hAPP(c_Option_Omap(U_17323,U_17325),U_17327),U_17329) != c_Option_Ooption_ONone(U_17325) ),
    inference(clausify,[status(thm)],[f_4255_4]) ).

cnf(f_4255_6,plain,
    ( hAPP(hAPP(c_Option_Omap(U_17324,U_17326),U_17328),U_17330) = c_Option_Ooption_ONone(U_17326)
    | U_17330 != c_Option_Ooption_ONone(U_17324) ),
    inference(clausify,[status(thm)],[f_4255_4]) ).

fof(f_4256_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_4256_2,plain,
    ! [U_17334,U_17333,U_17332,U_17331] : hAPP(hAPP(c_Option_Omap(U_17331,U_17332),U_17333),hAPP(c_Option_Ooption_OSome(U_17331),U_17334)) = hAPP(c_Option_Ooption_OSome(U_17332),hAPP(U_17333,U_17334)),
    inference(variable_rename,[status(thm)],[f_4256_1]) ).

fof(f_4256_3,plain,
    ! [U_17331,U_17332,U_17333,U_17334] : hAPP(hAPP(c_Option_Omap(U_17331,U_17332),U_17333),hAPP(c_Option_Ooption_OSome(U_17331),U_17334)) = hAPP(c_Option_Ooption_OSome(U_17332),hAPP(U_17333,U_17334)),
    inference(definitional_conversion,[status(esa)],[f_4256_2]) ).

cnf(f_4256_4,plain,
    hAPP(hAPP(c_Option_Omap(U_17331,U_17332),U_17333),hAPP(c_Option_Ooption_OSome(U_17331),U_17334)) = hAPP(c_Option_Ooption_OSome(U_17332),hAPP(U_17333,U_17334)),
    inference(clausify,[status(thm)],[f_4256_3]) ).

fof(f_4257_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_4257_2,plain,
    ! [U_17341,U_17340,U_17339,U_17338,U_17337] :
      ( ( hAPP(hAPP(c_Option_Omap(U_17337,U_17338),U_17339),U_17340) = hAPP(c_Option_Ooption_OSome(U_17338),U_17341)
        | ! [U_17336] :
            ( hAPP(U_17339,U_17336) != U_17341
            | U_17340 != hAPP(c_Option_Ooption_OSome(U_17337),U_17336) ) )
      & ( ? [U_17335] :
            ( hAPP(U_17339,U_17335) = U_17341
            & U_17340 = hAPP(c_Option_Ooption_OSome(U_17337),U_17335) )
        | hAPP(hAPP(c_Option_Omap(U_17337,U_17338),U_17339),U_17340) != hAPP(c_Option_Ooption_OSome(U_17338),U_17341) ) ),
    inference(variable_rename,[status(thm)],[f_4257_1]) ).

fof(f_4257_3,plain,
    ( ! [U_17351,U_17349,U_17347,U_17345,U_17343] :
        ( hAPP(hAPP(c_Option_Omap(U_17343,U_17345),U_17347),U_17349) = hAPP(c_Option_Ooption_OSome(U_17345),U_17351)
        | ! [U_17336] :
            ( hAPP(U_17347,U_17336) != U_17351
            | U_17349 != hAPP(c_Option_Ooption_OSome(U_17343),U_17336) ) )
    & ! [U_17350,U_17348,U_17346,U_17344,U_17342] :
        ( ? [U_17335] :
            ( hAPP(U_17346,U_17335) = U_17350
            & U_17348 = hAPP(c_Option_Ooption_OSome(U_17342),U_17335) )
        | hAPP(hAPP(c_Option_Omap(U_17342,U_17344),U_17346),U_17348) != hAPP(c_Option_Ooption_OSome(U_17344),U_17350) ) ),
    inference(miniscope,[status(thm)],[f_4257_2]) ).

fof(f_4257_4,plain,
    ( ! [U_17351,U_17349,U_17347,U_17345,U_17343] :
        ( hAPP(hAPP(c_Option_Omap(U_17343,U_17345),U_17347),U_17349) = hAPP(c_Option_Ooption_OSome(U_17345),U_17351)
        | ! [U_17336] :
            ( hAPP(U_17347,U_17336) != U_17351
            | U_17349 != hAPP(c_Option_Ooption_OSome(U_17343),U_17336) ) )
    & ! [U_17350,U_17348,U_17346,U_17344,U_17342] :
        ( ( hAPP(U_17346,sK445(U_17350,U_17348,U_17346,U_17344,U_17342)) = U_17350
          & U_17348 = hAPP(c_Option_Ooption_OSome(U_17342),sK445(U_17350,U_17348,U_17346,U_17344,U_17342)) )
        | hAPP(hAPP(c_Option_Omap(U_17342,U_17344),U_17346),U_17348) != hAPP(c_Option_Ooption_OSome(U_17344),U_17350) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK445]),skolemize(U_17335,sK445(U_17350,U_17348,U_17346,U_17344,U_17342))],[f_4257_3]) ).

fof(f_4257_5,plain,
    ( ! [U_17344,U_17348,U_17342,U_17346,U_17350] :
        ( hAPP(U_17346,sK445(U_17350,U_17348,U_17346,U_17344,U_17342)) = U_17350
        | ~ sP1109(U_17344,U_17348,U_17342,U_17346,U_17350) )
    & ! [U_17344,U_17348,U_17342,U_17346,U_17350] :
        ( U_17348 = hAPP(c_Option_Ooption_OSome(U_17342),sK445(U_17350,U_17348,U_17346,U_17344,U_17342))
        | ~ sP1109(U_17344,U_17348,U_17342,U_17346,U_17350) )
    & ! [U_17347,U_17349,U_17336,U_17351,U_17343,U_17345] :
        ( hAPP(hAPP(c_Option_Omap(U_17343,U_17345),U_17347),U_17349) = hAPP(c_Option_Ooption_OSome(U_17345),U_17351)
        | hAPP(U_17347,U_17336) != U_17351
        | U_17349 != hAPP(c_Option_Ooption_OSome(U_17343),U_17336) )
    & ! [U_17344,U_17348,U_17342,U_17346,U_17350] :
        ( sP1109(U_17344,U_17348,U_17342,U_17346,U_17350)
        | hAPP(hAPP(c_Option_Omap(U_17342,U_17344),U_17346),U_17348) != hAPP(c_Option_Ooption_OSome(U_17344),U_17350) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1109])],[f_4257_4]) ).

cnf(f_4257_6,plain,
    ( sP1109(U_17344,U_17348,U_17342,U_17346,U_17350)
    | hAPP(hAPP(c_Option_Omap(U_17342,U_17344),U_17346),U_17348) != hAPP(c_Option_Ooption_OSome(U_17344),U_17350) ),
    inference(clausify,[status(thm)],[f_4257_5]) ).

cnf(f_4257_7,plain,
    ( hAPP(hAPP(c_Option_Omap(U_17343,U_17345),U_17347),U_17349) = hAPP(c_Option_Ooption_OSome(U_17345),U_17351)
    | hAPP(U_17347,U_17336) != U_17351
    | U_17349 != hAPP(c_Option_Ooption_OSome(U_17343),U_17336) ),
    inference(clausify,[status(thm)],[f_4257_5]) ).

cnf(f_4257_8,plain,
    ( U_17348 = hAPP(c_Option_Ooption_OSome(U_17342),sK445(U_17350,U_17348,U_17346,U_17344,U_17342))
    | ~ sP1109(U_17344,U_17348,U_17342,U_17346,U_17350) ),
    inference(clausify,[status(thm)],[f_4257_5]) ).

cnf(f_4257_9,plain,
    ( hAPP(U_17346,sK445(U_17350,U_17348,U_17346,U_17344,U_17342)) = U_17350
    | ~ sP1109(U_17344,U_17348,U_17342,U_17346,U_17350) ),
    inference(clausify,[status(thm)],[f_4257_5]) ).

fof(f_4258_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_4258_2,plain,
    ! [U_17358,U_17357,U_17356,U_17355,U_17354,U_17353,U_17352] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17352),tc_Option_Ooption(U_17353),U_17354,hAPP(c_Option_Omap(U_17352,U_17353),U_17355)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17354,tc_Option_Ooption(U_17352)),U_17356),U_17357),hAPP(c_Option_Ooption_OSome(U_17352),U_17358))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17354,tc_Option_Ooption(U_17353)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17352),tc_Option_Ooption(U_17353),U_17354,hAPP(c_Option_Omap(U_17352,U_17353),U_17355)),U_17356)),U_17357),hAPP(c_Option_Ooption_OSome(U_17353),hAPP(U_17355,U_17358))),
    inference(variable_rename,[status(thm)],[f_4258_1]) ).

fof(f_4258_3,plain,
    ! [U_17353,U_17352,U_17354,U_17355,U_17356,U_17357,U_17358] : hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17352),tc_Option_Ooption(U_17353),U_17354,hAPP(c_Option_Omap(U_17352,U_17353),U_17355)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17354,tc_Option_Ooption(U_17352)),U_17356),U_17357),hAPP(c_Option_Ooption_OSome(U_17352),U_17358))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17354,tc_Option_Ooption(U_17353)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17352),tc_Option_Ooption(U_17353),U_17354,hAPP(c_Option_Omap(U_17352,U_17353),U_17355)),U_17356)),U_17357),hAPP(c_Option_Ooption_OSome(U_17353),hAPP(U_17355,U_17358))),
    inference(definitional_conversion,[status(esa)],[f_4258_2]) ).

cnf(f_4258_4,plain,
    hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17352),tc_Option_Ooption(U_17353),U_17354,hAPP(c_Option_Omap(U_17352,U_17353),U_17355)),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17354,tc_Option_Ooption(U_17352)),U_17356),U_17357),hAPP(c_Option_Ooption_OSome(U_17352),U_17358))) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17354,tc_Option_Ooption(U_17353)),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_17352),tc_Option_Ooption(U_17353),U_17354,hAPP(c_Option_Omap(U_17352,U_17353),U_17355)),U_17356)),U_17357),hAPP(c_Option_Ooption_OSome(U_17353),hAPP(U_17355,U_17358))),
    inference(clausify,[status(thm)],[f_4258_3]) ).

fof(f_4259_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_4259_2,plain,
    ! [U_17363,U_17362,U_17361,U_17360,U_17359] :
      ( ( ( hAPP(hAPP(c_List_Omap(U_17359,U_17360),U_17361),U_17362) = hAPP(hAPP(c_List_Omap(U_17359,U_17360),U_17361),U_17363)
          | U_17362 != U_17363 )
        & ( U_17362 = U_17363
          | hAPP(hAPP(c_List_Omap(U_17359,U_17360),U_17361),U_17362) != hAPP(hAPP(c_List_Omap(U_17359,U_17360),U_17361),U_17363) ) )
      | ~ c_Fun_Oinj__on(U_17359,U_17360,U_17361,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17359,tc_HOL_Obool)),hAPP(c_List_Oset(U_17359),U_17362)),hAPP(c_List_Oset(U_17359),U_17363))) ),
    inference(variable_rename,[status(thm)],[f_4259_1]) ).

fof(f_4259_3,plain,
    ( ! [U_17359,U_17360,U_17361,U_17362,U_17363] :
        ( hAPP(hAPP(c_List_Omap(U_17359,U_17360),U_17361),U_17362) = hAPP(hAPP(c_List_Omap(U_17359,U_17360),U_17361),U_17363)
        | U_17362 != U_17363
        | ~ sP1110(U_17359,U_17360,U_17361,U_17362,U_17363) )
    & ! [U_17359,U_17360,U_17361,U_17362,U_17363] :
        ( U_17362 = U_17363
        | hAPP(hAPP(c_List_Omap(U_17359,U_17360),U_17361),U_17362) != hAPP(hAPP(c_List_Omap(U_17359,U_17360),U_17361),U_17363)
        | ~ sP1110(U_17359,U_17360,U_17361,U_17362,U_17363) )
    & ! [U_17359,U_17360,U_17361,U_17362,U_17363] :
        ( sP1110(U_17359,U_17360,U_17361,U_17362,U_17363)
        | ~ c_Fun_Oinj__on(U_17359,U_17360,U_17361,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17359,tc_HOL_Obool)),hAPP(c_List_Oset(U_17359),U_17362)),hAPP(c_List_Oset(U_17359),U_17363))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1110])],[f_4259_2]) ).

cnf(f_4259_4,plain,
    ( sP1110(U_17359,U_17360,U_17361,U_17362,U_17363)
    | ~ c_Fun_Oinj__on(U_17359,U_17360,U_17361,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17359,tc_HOL_Obool)),hAPP(c_List_Oset(U_17359),U_17362)),hAPP(c_List_Oset(U_17359),U_17363))) ),
    inference(clausify,[status(thm)],[f_4259_3]) ).

cnf(f_4259_5,plain,
    ( U_17362 = U_17363
    | hAPP(hAPP(c_List_Omap(U_17359,U_17360),U_17361),U_17362) != hAPP(hAPP(c_List_Omap(U_17359,U_17360),U_17361),U_17363)
    | ~ sP1110(U_17359,U_17360,U_17361,U_17362,U_17363) ),
    inference(clausify,[status(thm)],[f_4259_3]) ).

cnf(f_4259_6,plain,
    ( hAPP(hAPP(c_List_Omap(U_17359,U_17360),U_17361),U_17362) = hAPP(hAPP(c_List_Omap(U_17359,U_17360),U_17361),U_17363)
    | U_17362 != U_17363
    | ~ sP1110(U_17359,U_17360,U_17361,U_17362,U_17363) ),
    inference(clausify,[status(thm)],[f_4259_3]) ).

fof(f_4260_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_4260_2,plain,
    ! [U_17368,U_17367,U_17366,U_17365,U_17364] :
      ( U_17367 = U_17368
      | ~ c_Fun_Oinj__on(U_17364,U_17365,U_17366,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17364,tc_HOL_Obool)),hAPP(c_List_Oset(U_17364),U_17367)),hAPP(c_List_Oset(U_17364),U_17368)))
      | hAPP(hAPP(c_List_Omap(U_17364,U_17365),U_17366),U_17367) != hAPP(hAPP(c_List_Omap(U_17364,U_17365),U_17366),U_17368) ),
    inference(variable_rename,[status(thm)],[f_4260_1]) ).

fof(f_4260_3,plain,
    ! [U_17365,U_17366,U_17367,U_17368,U_17364] :
      ( U_17367 = U_17368
      | ~ c_Fun_Oinj__on(U_17364,U_17365,U_17366,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17364,tc_HOL_Obool)),hAPP(c_List_Oset(U_17364),U_17367)),hAPP(c_List_Oset(U_17364),U_17368)))
      | hAPP(hAPP(c_List_Omap(U_17364,U_17365),U_17366),U_17367) != hAPP(hAPP(c_List_Omap(U_17364,U_17365),U_17366),U_17368) ),
    inference(definitional_conversion,[status(esa)],[f_4260_2]) ).

cnf(f_4260_4,plain,
    ( U_17367 = U_17368
    | ~ c_Fun_Oinj__on(U_17364,U_17365,U_17366,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_17364,tc_HOL_Obool)),hAPP(c_List_Oset(U_17364),U_17367)),hAPP(c_List_Oset(U_17364),U_17368)))
    | hAPP(hAPP(c_List_Omap(U_17364,U_17365),U_17366),U_17367) != hAPP(hAPP(c_List_Omap(U_17364,U_17365),U_17366),U_17368) ),
    inference(clausify,[status(thm)],[f_4260_3]) ).

fof(f_4261_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_4261_2,plain,
    ! [U_17374,U_17373,U_17372,U_17371,U_17370,U_17369] :
      ( hAPP(hAPP(c_List_Omap(U_17369,U_17372),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17369,U_17372),U_17373),U_17370),U_17374)),U_17371) = hAPP(hAPP(c_List_Omap(U_17369,U_17372),U_17373),U_17371)
      | hBOOL(hAPP(hAPP(c_member(U_17369),U_17370),hAPP(c_List_Oset(U_17369),U_17371))) ),
    inference(variable_rename,[status(thm)],[f_4261_1]) ).

fof(f_4261_3,plain,
    ! [U_17369,U_17370,U_17371,U_17372,U_17373,U_17374] :
      ( hAPP(hAPP(c_List_Omap(U_17369,U_17372),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17369,U_17372),U_17373),U_17370),U_17374)),U_17371) = hAPP(hAPP(c_List_Omap(U_17369,U_17372),U_17373),U_17371)
      | hBOOL(hAPP(hAPP(c_member(U_17369),U_17370),hAPP(c_List_Oset(U_17369),U_17371))) ),
    inference(definitional_conversion,[status(esa)],[f_4261_2]) ).

cnf(f_4261_4,plain,
    ( hAPP(hAPP(c_List_Omap(U_17369,U_17372),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17369,U_17372),U_17373),U_17370),U_17374)),U_17371) = hAPP(hAPP(c_List_Omap(U_17369,U_17372),U_17373),U_17371)
    | hBOOL(hAPP(hAPP(c_member(U_17369),U_17370),hAPP(c_List_Oset(U_17369),U_17371))) ),
    inference(clausify,[status(thm)],[f_4261_3]) ).

fof(f_4262_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_4262_2,plain,
    ! [U_17378,U_17377,U_17376,U_17375] :
      ( c_Fun_Oinj__on(tc_List_Olist(U_17375),tc_List_Olist(U_17376),hAPP(c_List_Omap(U_17375,U_17376),U_17377),U_17378)
      | ~ c_Fun_Oinj__on(U_17375,U_17376,U_17377,c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17375,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(U_17375),tc_fun(U_17375,tc_HOL_Obool),c_List_Oset(U_17375)),U_17378))) ),
    inference(variable_rename,[status(thm)],[f_4262_1]) ).

fof(f_4262_3,plain,
    ! [U_17375,U_17376,U_17377,U_17378] :
      ( c_Fun_Oinj__on(tc_List_Olist(U_17375),tc_List_Olist(U_17376),hAPP(c_List_Omap(U_17375,U_17376),U_17377),U_17378)
      | ~ c_Fun_Oinj__on(U_17375,U_17376,U_17377,c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17375,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(U_17375),tc_fun(U_17375,tc_HOL_Obool),c_List_Oset(U_17375)),U_17378))) ),
    inference(definitional_conversion,[status(esa)],[f_4262_2]) ).

cnf(f_4262_4,plain,
    ( c_Fun_Oinj__on(tc_List_Olist(U_17375),tc_List_Olist(U_17376),hAPP(c_List_Omap(U_17375,U_17376),U_17377),U_17378)
    | ~ c_Fun_Oinj__on(U_17375,U_17376,U_17377,c_Complete__Lattice_OSup__class_OSup(tc_fun(U_17375,tc_HOL_Obool),hAPP(c_Set_Oimage(tc_List_Olist(U_17375),tc_fun(U_17375,tc_HOL_Obool),c_List_Oset(U_17375)),U_17378))) ),
    inference(clausify,[status(thm)],[f_4262_3]) ).

fof(f_4263_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_4263_2,plain,
    ! [U_17382,U_17381,U_17380,U_17379] :
      ( hAPP(c_Set_Oimage(tc_prod(U_17379,U_17380),U_17379,c_Product__Type_Ofst(U_17379,U_17380)),hAPP(c_List_Oset(tc_prod(U_17379,U_17380)),U_17381)) = hAPP(c_Set_Oimage(tc_prod(U_17379,U_17380),U_17379,c_Product__Type_Ofst(U_17379,U_17380)),hAPP(c_List_Oset(tc_prod(U_17379,U_17380)),U_17382))
      | c_Map_Omap__of(U_17379,U_17380,U_17381) != c_Map_Omap__of(U_17379,U_17380,U_17382) ),
    inference(variable_rename,[status(thm)],[f_4263_1]) ).

fof(f_4263_3,plain,
    ! [U_17379,U_17380,U_17381,U_17382] :
      ( hAPP(c_Set_Oimage(tc_prod(U_17379,U_17380),U_17379,c_Product__Type_Ofst(U_17379,U_17380)),hAPP(c_List_Oset(tc_prod(U_17379,U_17380)),U_17381)) = hAPP(c_Set_Oimage(tc_prod(U_17379,U_17380),U_17379,c_Product__Type_Ofst(U_17379,U_17380)),hAPP(c_List_Oset(tc_prod(U_17379,U_17380)),U_17382))
      | c_Map_Omap__of(U_17379,U_17380,U_17381) != c_Map_Omap__of(U_17379,U_17380,U_17382) ),
    inference(definitional_conversion,[status(esa)],[f_4263_2]) ).

cnf(f_4263_4,plain,
    ( hAPP(c_Set_Oimage(tc_prod(U_17379,U_17380),U_17379,c_Product__Type_Ofst(U_17379,U_17380)),hAPP(c_List_Oset(tc_prod(U_17379,U_17380)),U_17381)) = hAPP(c_Set_Oimage(tc_prod(U_17379,U_17380),U_17379,c_Product__Type_Ofst(U_17379,U_17380)),hAPP(c_List_Oset(tc_prod(U_17379,U_17380)),U_17382))
    | c_Map_Omap__of(U_17379,U_17380,U_17381) != c_Map_Omap__of(U_17379,U_17380,U_17382) ),
    inference(clausify,[status(thm)],[f_4263_3]) ).

fof(f_4264_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_4264_2,plain,
    ! [U_17387,U_17386,U_17385,U_17384,U_17383] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17383,U_17384)),hAPP(hAPP(c_Product__Type_OPair(U_17383,U_17384),U_17386),U_17387)),hAPP(c_List_Oset(tc_prod(U_17383,U_17384)),U_17385)))
      | hAPP(c_Map_Omap__of(U_17383,U_17384,U_17385),U_17386) != hAPP(c_Option_Ooption_OSome(U_17384),U_17387) ),
    inference(variable_rename,[status(thm)],[f_4264_1]) ).

fof(f_4264_3,plain,
    ! [U_17383,U_17384,U_17385,U_17386,U_17387] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17383,U_17384)),hAPP(hAPP(c_Product__Type_OPair(U_17383,U_17384),U_17386),U_17387)),hAPP(c_List_Oset(tc_prod(U_17383,U_17384)),U_17385)))
      | hAPP(c_Map_Omap__of(U_17383,U_17384,U_17385),U_17386) != hAPP(c_Option_Ooption_OSome(U_17384),U_17387) ),
    inference(definitional_conversion,[status(esa)],[f_4264_2]) ).

cnf(f_4264_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17383,U_17384)),hAPP(hAPP(c_Product__Type_OPair(U_17383,U_17384),U_17386),U_17387)),hAPP(c_List_Oset(tc_prod(U_17383,U_17384)),U_17385)))
    | hAPP(c_Map_Omap__of(U_17383,U_17384,U_17385),U_17386) != hAPP(c_Option_Ooption_OSome(U_17384),U_17387) ),
    inference(clausify,[status(thm)],[f_4264_3]) ).

fof(f_4265_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_4265_2,plain,
    ! [U_17392,U_17391,U_17390,U_17389,U_17388] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17388,U_17389)),hAPP(hAPP(c_Product__Type_OPair(U_17388,U_17389),U_17391),U_17392)),hAPP(c_List_Oset(tc_prod(U_17388,U_17389)),U_17390)))
      | hAPP(c_Map_Omap__of(U_17388,U_17389,U_17390),U_17391) != hAPP(c_Option_Ooption_OSome(U_17389),U_17392) ),
    inference(variable_rename,[status(thm)],[f_4265_1]) ).

fof(f_4265_3,plain,
    ! [U_17388,U_17389,U_17390,U_17391,U_17392] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17388,U_17389)),hAPP(hAPP(c_Product__Type_OPair(U_17388,U_17389),U_17391),U_17392)),hAPP(c_List_Oset(tc_prod(U_17388,U_17389)),U_17390)))
      | hAPP(c_Map_Omap__of(U_17388,U_17389,U_17390),U_17391) != hAPP(c_Option_Ooption_OSome(U_17389),U_17392) ),
    inference(definitional_conversion,[status(esa)],[f_4265_2]) ).

cnf(f_4265_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17388,U_17389)),hAPP(hAPP(c_Product__Type_OPair(U_17388,U_17389),U_17391),U_17392)),hAPP(c_List_Oset(tc_prod(U_17388,U_17389)),U_17390)))
    | hAPP(c_Map_Omap__of(U_17388,U_17389,U_17390),U_17391) != hAPP(c_Option_Ooption_OSome(U_17389),U_17392) ),
    inference(clausify,[status(thm)],[f_4265_3]) ).

fof(f_4266_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_4266_2,plain,
    ! [U_17395,U_17394,U_17393] : c_Map_Odom(U_17393,U_17394,c_Map_Omap__of(U_17393,U_17394,U_17395)) = hAPP(c_Set_Oimage(tc_prod(U_17393,U_17394),U_17393,c_Product__Type_Ofst(U_17393,U_17394)),hAPP(c_List_Oset(tc_prod(U_17393,U_17394)),U_17395)),
    inference(variable_rename,[status(thm)],[f_4266_1]) ).

fof(f_4266_3,plain,
    ! [U_17393,U_17394,U_17395] : c_Map_Odom(U_17393,U_17394,c_Map_Omap__of(U_17393,U_17394,U_17395)) = hAPP(c_Set_Oimage(tc_prod(U_17393,U_17394),U_17393,c_Product__Type_Ofst(U_17393,U_17394)),hAPP(c_List_Oset(tc_prod(U_17393,U_17394)),U_17395)),
    inference(definitional_conversion,[status(esa)],[f_4266_2]) ).

cnf(f_4266_4,plain,
    c_Map_Odom(U_17393,U_17394,c_Map_Omap__of(U_17393,U_17394,U_17395)) = hAPP(c_Set_Oimage(tc_prod(U_17393,U_17394),U_17393,c_Product__Type_Ofst(U_17393,U_17394)),hAPP(c_List_Oset(tc_prod(U_17393,U_17394)),U_17395)),
    inference(clausify,[status(thm)],[f_4266_3]) ).

fof(f_4267_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_4267_2,plain,
    ! [U_17399,U_17398,U_17397,U_17396] :
      ( ( hAPP(c_Map_Omap__of(U_17396,U_17397,U_17398),U_17399) = c_Option_Ooption_ONone(U_17397)
        | hBOOL(hAPP(hAPP(c_member(U_17396),U_17399),hAPP(c_Set_Oimage(tc_prod(U_17396,U_17397),U_17396,c_Product__Type_Ofst(U_17396,U_17397)),hAPP(c_List_Oset(tc_prod(U_17396,U_17397)),U_17398)))) )
      & ( ~ hBOOL(hAPP(hAPP(c_member(U_17396),U_17399),hAPP(c_Set_Oimage(tc_prod(U_17396,U_17397),U_17396,c_Product__Type_Ofst(U_17396,U_17397)),hAPP(c_List_Oset(tc_prod(U_17396,U_17397)),U_17398))))
        | hAPP(c_Map_Omap__of(U_17396,U_17397,U_17398),U_17399) != c_Option_Ooption_ONone(U_17397) ) ),
    inference(variable_rename,[status(thm)],[f_4267_1]) ).

fof(f_4267_3,plain,
    ( ! [U_17407,U_17405,U_17403,U_17401] :
        ( hAPP(c_Map_Omap__of(U_17401,U_17403,U_17405),U_17407) = c_Option_Ooption_ONone(U_17403)
        | hBOOL(hAPP(hAPP(c_member(U_17401),U_17407),hAPP(c_Set_Oimage(tc_prod(U_17401,U_17403),U_17401,c_Product__Type_Ofst(U_17401,U_17403)),hAPP(c_List_Oset(tc_prod(U_17401,U_17403)),U_17405)))) )
    & ! [U_17406,U_17404,U_17402,U_17400] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_17400),U_17406),hAPP(c_Set_Oimage(tc_prod(U_17400,U_17402),U_17400,c_Product__Type_Ofst(U_17400,U_17402)),hAPP(c_List_Oset(tc_prod(U_17400,U_17402)),U_17404))))
        | hAPP(c_Map_Omap__of(U_17400,U_17402,U_17404),U_17406) != c_Option_Ooption_ONone(U_17402) ) ),
    inference(miniscope,[status(thm)],[f_4267_2]) ).

fof(f_4267_4,plain,
    ( ! [U_17401,U_17403,U_17405,U_17407] :
        ( hAPP(c_Map_Omap__of(U_17401,U_17403,U_17405),U_17407) = c_Option_Ooption_ONone(U_17403)
        | hBOOL(hAPP(hAPP(c_member(U_17401),U_17407),hAPP(c_Set_Oimage(tc_prod(U_17401,U_17403),U_17401,c_Product__Type_Ofst(U_17401,U_17403)),hAPP(c_List_Oset(tc_prod(U_17401,U_17403)),U_17405)))) )
    & ! [U_17402,U_17404,U_17406,U_17400] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_17400),U_17406),hAPP(c_Set_Oimage(tc_prod(U_17400,U_17402),U_17400,c_Product__Type_Ofst(U_17400,U_17402)),hAPP(c_List_Oset(tc_prod(U_17400,U_17402)),U_17404))))
        | hAPP(c_Map_Omap__of(U_17400,U_17402,U_17404),U_17406) != c_Option_Ooption_ONone(U_17402) ) ),
    inference(definitional_conversion,[status(esa)],[f_4267_3]) ).

cnf(f_4267_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_17400),U_17406),hAPP(c_Set_Oimage(tc_prod(U_17400,U_17402),U_17400,c_Product__Type_Ofst(U_17400,U_17402)),hAPP(c_List_Oset(tc_prod(U_17400,U_17402)),U_17404))))
    | hAPP(c_Map_Omap__of(U_17400,U_17402,U_17404),U_17406) != c_Option_Ooption_ONone(U_17402) ),
    inference(clausify,[status(thm)],[f_4267_4]) ).

cnf(f_4267_6,plain,
    ( hAPP(c_Map_Omap__of(U_17401,U_17403,U_17405),U_17407) = c_Option_Ooption_ONone(U_17403)
    | hBOOL(hAPP(hAPP(c_member(U_17401),U_17407),hAPP(c_Set_Oimage(tc_prod(U_17401,U_17403),U_17401,c_Product__Type_Ofst(U_17401,U_17403)),hAPP(c_List_Oset(tc_prod(U_17401,U_17403)),U_17405)))) ),
    inference(clausify,[status(thm)],[f_4267_4]) ).

fof(f_4268_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_4268_2,plain,
    ! [U_17410,U_17409,U_17408] : hAPP(c_Option_Omap(U_17408,U_17409),U_17410) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17409),U_17408,c_Option_Ooption_ONone(U_17409),hAPP(hAPP(c_COMBB(U_17409,tc_Option_Ooption(U_17409),U_17408),c_Option_Ooption_OSome(U_17409)),U_17410)),
    inference(variable_rename,[status(thm)],[f_4268_1]) ).

fof(f_4268_3,plain,
    ! [U_17408,U_17409,U_17410] : hAPP(c_Option_Omap(U_17408,U_17409),U_17410) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17409),U_17408,c_Option_Ooption_ONone(U_17409),hAPP(hAPP(c_COMBB(U_17409,tc_Option_Ooption(U_17409),U_17408),c_Option_Ooption_OSome(U_17409)),U_17410)),
    inference(definitional_conversion,[status(esa)],[f_4268_2]) ).

cnf(f_4268_4,plain,
    hAPP(c_Option_Omap(U_17408,U_17409),U_17410) = c_Option_Ooption_Ooption__case(tc_Option_Ooption(U_17409),U_17408,c_Option_Ooption_ONone(U_17409),hAPP(hAPP(c_COMBB(U_17409,tc_Option_Ooption(U_17409),U_17408),c_Option_Ooption_OSome(U_17409)),U_17410)),
    inference(clausify,[status(thm)],[f_4268_3]) ).

fof(f_4269_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_4269_2,plain,
    ( ( c_Com_OWT__bodies
      | ? [U_17412] :
          ( ~ 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_17412))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),U_17412),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))) ) )
    & ( ! [U_17411] :
          ( 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_17411))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),U_17411),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_4269_1]) ).

fof(f_4269_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)),sK446))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),sK446),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))) ) )
    & ( ! [U_17411] :
          ( 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_17411))
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),U_17411),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,[sK446]),skolemize(U_17412,sK446)],[f_4269_2]) ).

fof(f_4269_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)),sK446))
      | ~ sP1111 )
    & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),sK446),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))
      | ~ sP1111 )
    & ( c_Com_OWT__bodies
      | sP1111 )
    & ! [U_17411] :
        ( 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_17411))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),U_17411),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,[sP1111])],[f_4269_3]) ).

cnf(f_4269_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_17411))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),U_17411),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))
    | ~ c_Com_OWT__bodies ),
    inference(clausify,[status(thm)],[f_4269_4]) ).

cnf(f_4269_6,plain,
    ( c_Com_OWT__bodies
    | sP1111 ),
    inference(clausify,[status(thm)],[f_4269_4]) ).

cnf(f_4269_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),sK446),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies)))
    | ~ sP1111 ),
    inference(clausify,[status(thm)],[f_4269_4]) ).

cnf(f_4269_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)),sK446))
    | ~ sP1111 ),
    inference(clausify,[status(thm)],[f_4269_4]) ).

fof(f_4270_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_4270_2,plain,
    ! [U_17416,U_17415,U_17414,U_17413] : c_Map_Omap__of(U_17413,U_17414,hAPP(hAPP(c_List_Omap(U_17413,tc_prod(U_17413,U_17414)),hAPP(hAPP(c_COMBS(U_17413,U_17414,tc_prod(U_17413,U_17414)),c_Product__Type_OPair(U_17413,U_17414)),U_17415)),U_17416)) = c_Map_Orestrict__map(U_17413,U_17414,hAPP(c_Fun_Ocomp(U_17414,tc_Option_Ooption(U_17414),U_17413,c_Option_Ooption_OSome(U_17414)),U_17415),hAPP(c_List_Oset(U_17413),U_17416)),
    inference(variable_rename,[status(thm)],[f_4270_1]) ).

fof(f_4270_3,plain,
    ! [U_17413,U_17414,U_17415,U_17416] : c_Map_Omap__of(U_17413,U_17414,hAPP(hAPP(c_List_Omap(U_17413,tc_prod(U_17413,U_17414)),hAPP(hAPP(c_COMBS(U_17413,U_17414,tc_prod(U_17413,U_17414)),c_Product__Type_OPair(U_17413,U_17414)),U_17415)),U_17416)) = c_Map_Orestrict__map(U_17413,U_17414,hAPP(c_Fun_Ocomp(U_17414,tc_Option_Ooption(U_17414),U_17413,c_Option_Ooption_OSome(U_17414)),U_17415),hAPP(c_List_Oset(U_17413),U_17416)),
    inference(definitional_conversion,[status(esa)],[f_4270_2]) ).

cnf(f_4270_4,plain,
    c_Map_Omap__of(U_17413,U_17414,hAPP(hAPP(c_List_Omap(U_17413,tc_prod(U_17413,U_17414)),hAPP(hAPP(c_COMBS(U_17413,U_17414,tc_prod(U_17413,U_17414)),c_Product__Type_OPair(U_17413,U_17414)),U_17415)),U_17416)) = c_Map_Orestrict__map(U_17413,U_17414,hAPP(c_Fun_Ocomp(U_17414,tc_Option_Ooption(U_17414),U_17413,c_Option_Ooption_OSome(U_17414)),U_17415),hAPP(c_List_Oset(U_17413),U_17416)),
    inference(clausify,[status(thm)],[f_4270_3]) ).

fof(f_4271_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_4271_2,plain,
    ! [U_17419,U_17418,U_17417] :
      ( c_Map_Oran(U_17417,U_17418,c_Map_Omap__of(U_17417,U_17418,U_17419)) = hAPP(c_Set_Oimage(tc_prod(U_17417,U_17418),U_17418,c_Product__Type_Osnd(U_17417,U_17418)),hAPP(c_List_Oset(tc_prod(U_17417,U_17418)),U_17419))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17417),hAPP(hAPP(c_List_Omap(tc_prod(U_17417,U_17418),U_17417),c_Product__Type_Ofst(U_17417,U_17418)),U_17419))) ),
    inference(variable_rename,[status(thm)],[f_4271_1]) ).

fof(f_4271_3,plain,
    ! [U_17417,U_17418,U_17419] :
      ( c_Map_Oran(U_17417,U_17418,c_Map_Omap__of(U_17417,U_17418,U_17419)) = hAPP(c_Set_Oimage(tc_prod(U_17417,U_17418),U_17418,c_Product__Type_Osnd(U_17417,U_17418)),hAPP(c_List_Oset(tc_prod(U_17417,U_17418)),U_17419))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17417),hAPP(hAPP(c_List_Omap(tc_prod(U_17417,U_17418),U_17417),c_Product__Type_Ofst(U_17417,U_17418)),U_17419))) ),
    inference(definitional_conversion,[status(esa)],[f_4271_2]) ).

cnf(f_4271_4,plain,
    ( c_Map_Oran(U_17417,U_17418,c_Map_Omap__of(U_17417,U_17418,U_17419)) = hAPP(c_Set_Oimage(tc_prod(U_17417,U_17418),U_17418,c_Product__Type_Osnd(U_17417,U_17418)),hAPP(c_List_Oset(tc_prod(U_17417,U_17418)),U_17419))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17417),hAPP(hAPP(c_List_Omap(tc_prod(U_17417,U_17418),U_17417),c_Product__Type_Ofst(U_17417,U_17418)),U_17419))) ),
    inference(clausify,[status(thm)],[f_4271_3]) ).

fof(f_4272_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_4272_2,plain,
    ! [U_17422,U_17421,U_17420] :
      ( hAPP(c_List_Oset(tc_prod(U_17420,U_17421)),U_17422) = hAPP(c_Set_OCollect(tc_prod(U_17420,U_17421)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17420,U_17421,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17420,tc_fun(U_17421,tc_Option_Ooption(U_17421)),tc_fun(U_17421,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17421),tc_HOL_Obool),tc_fun(tc_fun(U_17421,tc_Option_Ooption(U_17421)),tc_fun(U_17421,tc_HOL_Obool)),U_17420),c_COMBB(tc_Option_Ooption(U_17421),tc_HOL_Obool,U_17421)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17421),tc_fun(tc_Option_Ooption(U_17421),tc_HOL_Obool),U_17420),c_fequal),c_Map_Omap__of(U_17420,U_17421,U_17422)))),c_Option_Ooption_OSome(U_17421))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17420),hAPP(hAPP(c_List_Omap(tc_prod(U_17420,U_17421),U_17420),c_Product__Type_Ofst(U_17420,U_17421)),U_17422))) ),
    inference(variable_rename,[status(thm)],[f_4272_1]) ).

fof(f_4272_3,plain,
    ! [U_17420,U_17421,U_17422] :
      ( hAPP(c_List_Oset(tc_prod(U_17420,U_17421)),U_17422) = hAPP(c_Set_OCollect(tc_prod(U_17420,U_17421)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17420,U_17421,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17420,tc_fun(U_17421,tc_Option_Ooption(U_17421)),tc_fun(U_17421,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17421),tc_HOL_Obool),tc_fun(tc_fun(U_17421,tc_Option_Ooption(U_17421)),tc_fun(U_17421,tc_HOL_Obool)),U_17420),c_COMBB(tc_Option_Ooption(U_17421),tc_HOL_Obool,U_17421)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17421),tc_fun(tc_Option_Ooption(U_17421),tc_HOL_Obool),U_17420),c_fequal),c_Map_Omap__of(U_17420,U_17421,U_17422)))),c_Option_Ooption_OSome(U_17421))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17420),hAPP(hAPP(c_List_Omap(tc_prod(U_17420,U_17421),U_17420),c_Product__Type_Ofst(U_17420,U_17421)),U_17422))) ),
    inference(definitional_conversion,[status(esa)],[f_4272_2]) ).

cnf(f_4272_4,plain,
    ( hAPP(c_List_Oset(tc_prod(U_17420,U_17421)),U_17422) = hAPP(c_Set_OCollect(tc_prod(U_17420,U_17421)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17420,U_17421,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17420,tc_fun(U_17421,tc_Option_Ooption(U_17421)),tc_fun(U_17421,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_17421),tc_HOL_Obool),tc_fun(tc_fun(U_17421,tc_Option_Ooption(U_17421)),tc_fun(U_17421,tc_HOL_Obool)),U_17420),c_COMBB(tc_Option_Ooption(U_17421),tc_HOL_Obool,U_17421)),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_17421),tc_fun(tc_Option_Ooption(U_17421),tc_HOL_Obool),U_17420),c_fequal),c_Map_Omap__of(U_17420,U_17421,U_17422)))),c_Option_Ooption_OSome(U_17421))))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17420),hAPP(hAPP(c_List_Omap(tc_prod(U_17420,U_17421),U_17420),c_Product__Type_Ofst(U_17420,U_17421)),U_17422))) ),
    inference(clausify,[status(thm)],[f_4272_3]) ).

fof(f_4273_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_4273_2,plain,
    ! [U_17426,U_17425,U_17424,U_17423] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_17423),hAPP(hAPP(c_List_Omap(U_17424,U_17423),U_17425),U_17426)))
        | ~ c_Fun_Oinj__on(U_17424,U_17423,U_17425,hAPP(c_List_Oset(U_17424),U_17426))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17424),U_17426)) )
      & ( ( c_Fun_Oinj__on(U_17424,U_17423,U_17425,hAPP(c_List_Oset(U_17424),U_17426))
          & hBOOL(hAPP(c_List_Odistinct(U_17424),U_17426)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17423),hAPP(hAPP(c_List_Omap(U_17424,U_17423),U_17425),U_17426))) ) ),
    inference(variable_rename,[status(thm)],[f_4273_1]) ).

fof(f_4273_3,plain,
    ( ! [U_17434,U_17432,U_17430,U_17428] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17428),hAPP(hAPP(c_List_Omap(U_17430,U_17428),U_17432),U_17434)))
        | ~ c_Fun_Oinj__on(U_17430,U_17428,U_17432,hAPP(c_List_Oset(U_17430),U_17434))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17430),U_17434)) )
    & ! [U_17433,U_17431,U_17429,U_17427] :
        ( ( c_Fun_Oinj__on(U_17429,U_17427,U_17431,hAPP(c_List_Oset(U_17429),U_17433))
          & hBOOL(hAPP(c_List_Odistinct(U_17429),U_17433)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17427),hAPP(hAPP(c_List_Omap(U_17429,U_17427),U_17431),U_17433))) ) ),
    inference(miniscope,[status(thm)],[f_4273_2]) ).

fof(f_4273_4,plain,
    ( ! [U_17429,U_17427,U_17431,U_17433] :
        ( c_Fun_Oinj__on(U_17429,U_17427,U_17431,hAPP(c_List_Oset(U_17429),U_17433))
        | ~ sP1112(U_17429,U_17427,U_17431,U_17433) )
    & ! [U_17429,U_17427,U_17431,U_17433] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17429),U_17433))
        | ~ sP1112(U_17429,U_17427,U_17431,U_17433) )
    & ! [U_17428,U_17432,U_17430,U_17434] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17428),hAPP(hAPP(c_List_Omap(U_17430,U_17428),U_17432),U_17434)))
        | ~ c_Fun_Oinj__on(U_17430,U_17428,U_17432,hAPP(c_List_Oset(U_17430),U_17434))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17430),U_17434)) )
    & ! [U_17429,U_17427,U_17431,U_17433] :
        ( sP1112(U_17429,U_17427,U_17431,U_17433)
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17427),hAPP(hAPP(c_List_Omap(U_17429,U_17427),U_17431),U_17433))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1112])],[f_4273_3]) ).

cnf(f_4273_5,plain,
    ( sP1112(U_17429,U_17427,U_17431,U_17433)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17427),hAPP(hAPP(c_List_Omap(U_17429,U_17427),U_17431),U_17433))) ),
    inference(clausify,[status(thm)],[f_4273_4]) ).

cnf(f_4273_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17428),hAPP(hAPP(c_List_Omap(U_17430,U_17428),U_17432),U_17434)))
    | ~ c_Fun_Oinj__on(U_17430,U_17428,U_17432,hAPP(c_List_Oset(U_17430),U_17434))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17430),U_17434)) ),
    inference(clausify,[status(thm)],[f_4273_4]) ).

cnf(f_4273_7,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17429),U_17433))
    | ~ sP1112(U_17429,U_17427,U_17431,U_17433) ),
    inference(clausify,[status(thm)],[f_4273_4]) ).

cnf(f_4273_8,plain,
    ( c_Fun_Oinj__on(U_17429,U_17427,U_17431,hAPP(c_List_Oset(U_17429),U_17433))
    | ~ sP1112(U_17429,U_17427,U_17431,U_17433) ),
    inference(clausify,[status(thm)],[f_4273_4]) ).

fof(f_4274_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_4274_2,plain,
    ! [U_17438,U_17437,U_17436,U_17435] :
      ( ( ( c_Map_Omap__of(U_17435,U_17436,U_17437) = c_Map_Omap__of(U_17435,U_17436,U_17438)
          | hAPP(c_List_Oset(tc_prod(U_17435,U_17436)),U_17437) != hAPP(c_List_Oset(tc_prod(U_17435,U_17436)),U_17438) )
        & ( hAPP(c_List_Oset(tc_prod(U_17435,U_17436)),U_17437) = hAPP(c_List_Oset(tc_prod(U_17435,U_17436)),U_17438)
          | c_Map_Omap__of(U_17435,U_17436,U_17437) != c_Map_Omap__of(U_17435,U_17436,U_17438) ) )
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17435),hAPP(hAPP(c_List_Omap(tc_prod(U_17435,U_17436),U_17435),c_Product__Type_Ofst(U_17435,U_17436)),U_17438)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17435),hAPP(hAPP(c_List_Omap(tc_prod(U_17435,U_17436),U_17435),c_Product__Type_Ofst(U_17435,U_17436)),U_17437))) ),
    inference(variable_rename,[status(thm)],[f_4274_1]) ).

fof(f_4274_3,plain,
    ( ! [U_17435,U_17436,U_17437,U_17438] :
        ( c_Map_Omap__of(U_17435,U_17436,U_17437) = c_Map_Omap__of(U_17435,U_17436,U_17438)
        | hAPP(c_List_Oset(tc_prod(U_17435,U_17436)),U_17437) != hAPP(c_List_Oset(tc_prod(U_17435,U_17436)),U_17438)
        | ~ sP1113(U_17435,U_17436,U_17437,U_17438) )
    & ! [U_17435,U_17436,U_17437,U_17438] :
        ( hAPP(c_List_Oset(tc_prod(U_17435,U_17436)),U_17437) = hAPP(c_List_Oset(tc_prod(U_17435,U_17436)),U_17438)
        | c_Map_Omap__of(U_17435,U_17436,U_17437) != c_Map_Omap__of(U_17435,U_17436,U_17438)
        | ~ sP1113(U_17435,U_17436,U_17437,U_17438) )
    & ! [U_17435,U_17436,U_17437,U_17438] :
        ( sP1113(U_17435,U_17436,U_17437,U_17438)
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17435),hAPP(hAPP(c_List_Omap(tc_prod(U_17435,U_17436),U_17435),c_Product__Type_Ofst(U_17435,U_17436)),U_17438)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17435),hAPP(hAPP(c_List_Omap(tc_prod(U_17435,U_17436),U_17435),c_Product__Type_Ofst(U_17435,U_17436)),U_17437))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1113])],[f_4274_2]) ).

cnf(f_4274_4,plain,
    ( sP1113(U_17435,U_17436,U_17437,U_17438)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17435),hAPP(hAPP(c_List_Omap(tc_prod(U_17435,U_17436),U_17435),c_Product__Type_Ofst(U_17435,U_17436)),U_17438)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17435),hAPP(hAPP(c_List_Omap(tc_prod(U_17435,U_17436),U_17435),c_Product__Type_Ofst(U_17435,U_17436)),U_17437))) ),
    inference(clausify,[status(thm)],[f_4274_3]) ).

cnf(f_4274_5,plain,
    ( hAPP(c_List_Oset(tc_prod(U_17435,U_17436)),U_17437) = hAPP(c_List_Oset(tc_prod(U_17435,U_17436)),U_17438)
    | c_Map_Omap__of(U_17435,U_17436,U_17437) != c_Map_Omap__of(U_17435,U_17436,U_17438)
    | ~ sP1113(U_17435,U_17436,U_17437,U_17438) ),
    inference(clausify,[status(thm)],[f_4274_3]) ).

cnf(f_4274_6,plain,
    ( c_Map_Omap__of(U_17435,U_17436,U_17437) = c_Map_Omap__of(U_17435,U_17436,U_17438)
    | hAPP(c_List_Oset(tc_prod(U_17435,U_17436)),U_17437) != hAPP(c_List_Oset(tc_prod(U_17435,U_17436)),U_17438)
    | ~ sP1113(U_17435,U_17436,U_17437,U_17438) ),
    inference(clausify,[status(thm)],[f_4274_3]) ).

fof(f_4275_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_4275_2,plain,
    ! [U_17443,U_17442,U_17441,U_17440,U_17439] :
      ( hAPP(c_Map_Omap__of(U_17439,U_17440,U_17441),U_17442) = hAPP(c_Option_Ooption_OSome(U_17440),U_17443)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17439,U_17440)),hAPP(hAPP(c_Product__Type_OPair(U_17439,U_17440),U_17442),U_17443)),hAPP(c_List_Oset(tc_prod(U_17439,U_17440)),U_17441)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17439),hAPP(hAPP(c_List_Omap(tc_prod(U_17439,U_17440),U_17439),c_Product__Type_Ofst(U_17439,U_17440)),U_17441))) ),
    inference(variable_rename,[status(thm)],[f_4275_1]) ).

fof(f_4275_3,plain,
    ! [U_17440,U_17439,U_17441,U_17442,U_17443] :
      ( hAPP(c_Map_Omap__of(U_17439,U_17440,U_17441),U_17442) = hAPP(c_Option_Ooption_OSome(U_17440),U_17443)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17439,U_17440)),hAPP(hAPP(c_Product__Type_OPair(U_17439,U_17440),U_17442),U_17443)),hAPP(c_List_Oset(tc_prod(U_17439,U_17440)),U_17441)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17439),hAPP(hAPP(c_List_Omap(tc_prod(U_17439,U_17440),U_17439),c_Product__Type_Ofst(U_17439,U_17440)),U_17441))) ),
    inference(definitional_conversion,[status(esa)],[f_4275_2]) ).

cnf(f_4275_4,plain,
    ( hAPP(c_Map_Omap__of(U_17439,U_17440,U_17441),U_17442) = hAPP(c_Option_Ooption_OSome(U_17440),U_17443)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17439,U_17440)),hAPP(hAPP(c_Product__Type_OPair(U_17439,U_17440),U_17442),U_17443)),hAPP(c_List_Oset(tc_prod(U_17439,U_17440)),U_17441)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17439),hAPP(hAPP(c_List_Omap(tc_prod(U_17439,U_17440),U_17439),c_Product__Type_Ofst(U_17439,U_17440)),U_17441))) ),
    inference(clausify,[status(thm)],[f_4275_3]) ).

fof(f_4276_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_4276_2,plain,
    ! [U_17448,U_17447,U_17446,U_17445,U_17444] :
      ( ( ( hAPP(c_Map_Omap__of(U_17444,U_17445,U_17446),U_17447) = hAPP(c_Option_Ooption_OSome(U_17445),U_17448)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17444,U_17445)),hAPP(hAPP(c_Product__Type_OPair(U_17444,U_17445),U_17447),U_17448)),hAPP(c_List_Oset(tc_prod(U_17444,U_17445)),U_17446))) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17444,U_17445)),hAPP(hAPP(c_Product__Type_OPair(U_17444,U_17445),U_17447),U_17448)),hAPP(c_List_Oset(tc_prod(U_17444,U_17445)),U_17446)))
          | hAPP(c_Map_Omap__of(U_17444,U_17445,U_17446),U_17447) != hAPP(c_Option_Ooption_OSome(U_17445),U_17448) ) )
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17444),hAPP(hAPP(c_List_Omap(tc_prod(U_17444,U_17445),U_17444),c_Product__Type_Ofst(U_17444,U_17445)),U_17446))) ),
    inference(variable_rename,[status(thm)],[f_4276_1]) ).

fof(f_4276_3,plain,
    ( ! [U_17444,U_17445,U_17446,U_17447,U_17448] :
        ( hAPP(c_Map_Omap__of(U_17444,U_17445,U_17446),U_17447) = hAPP(c_Option_Ooption_OSome(U_17445),U_17448)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17444,U_17445)),hAPP(hAPP(c_Product__Type_OPair(U_17444,U_17445),U_17447),U_17448)),hAPP(c_List_Oset(tc_prod(U_17444,U_17445)),U_17446)))
        | ~ sP1114(U_17444,U_17445,U_17446,U_17447,U_17448) )
    & ! [U_17444,U_17445,U_17446,U_17447,U_17448] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17444,U_17445)),hAPP(hAPP(c_Product__Type_OPair(U_17444,U_17445),U_17447),U_17448)),hAPP(c_List_Oset(tc_prod(U_17444,U_17445)),U_17446)))
        | hAPP(c_Map_Omap__of(U_17444,U_17445,U_17446),U_17447) != hAPP(c_Option_Ooption_OSome(U_17445),U_17448)
        | ~ sP1114(U_17444,U_17445,U_17446,U_17447,U_17448) )
    & ! [U_17444,U_17445,U_17446,U_17447,U_17448] :
        ( sP1114(U_17444,U_17445,U_17446,U_17447,U_17448)
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17444),hAPP(hAPP(c_List_Omap(tc_prod(U_17444,U_17445),U_17444),c_Product__Type_Ofst(U_17444,U_17445)),U_17446))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1114])],[f_4276_2]) ).

cnf(f_4276_4,plain,
    ( sP1114(U_17444,U_17445,U_17446,U_17447,U_17448)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17444),hAPP(hAPP(c_List_Omap(tc_prod(U_17444,U_17445),U_17444),c_Product__Type_Ofst(U_17444,U_17445)),U_17446))) ),
    inference(clausify,[status(thm)],[f_4276_3]) ).

cnf(f_4276_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17444,U_17445)),hAPP(hAPP(c_Product__Type_OPair(U_17444,U_17445),U_17447),U_17448)),hAPP(c_List_Oset(tc_prod(U_17444,U_17445)),U_17446)))
    | hAPP(c_Map_Omap__of(U_17444,U_17445,U_17446),U_17447) != hAPP(c_Option_Ooption_OSome(U_17445),U_17448)
    | ~ sP1114(U_17444,U_17445,U_17446,U_17447,U_17448) ),
    inference(clausify,[status(thm)],[f_4276_3]) ).

cnf(f_4276_6,plain,
    ( hAPP(c_Map_Omap__of(U_17444,U_17445,U_17446),U_17447) = hAPP(c_Option_Ooption_OSome(U_17445),U_17448)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17444,U_17445)),hAPP(hAPP(c_Product__Type_OPair(U_17444,U_17445),U_17447),U_17448)),hAPP(c_List_Oset(tc_prod(U_17444,U_17445)),U_17446)))
    | ~ sP1114(U_17444,U_17445,U_17446,U_17447,U_17448) ),
    inference(clausify,[status(thm)],[f_4276_3]) ).

fof(f_4277_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_4277_2,plain,
    ! [U_17453,U_17452,U_17451,U_17450,U_17449] :
      ( ( ( hAPP(c_Option_Ooption_OSome(U_17450),U_17452) = hAPP(c_Map_Omap__of(U_17449,U_17450,U_17451),U_17453)
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17449,U_17450)),hAPP(hAPP(c_Product__Type_OPair(U_17449,U_17450),U_17453),U_17452)),hAPP(c_List_Oset(tc_prod(U_17449,U_17450)),U_17451))) )
        & ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17449,U_17450)),hAPP(hAPP(c_Product__Type_OPair(U_17449,U_17450),U_17453),U_17452)),hAPP(c_List_Oset(tc_prod(U_17449,U_17450)),U_17451)))
          | hAPP(c_Option_Ooption_OSome(U_17450),U_17452) != hAPP(c_Map_Omap__of(U_17449,U_17450,U_17451),U_17453) ) )
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17449),hAPP(hAPP(c_List_Omap(tc_prod(U_17449,U_17450),U_17449),c_Product__Type_Ofst(U_17449,U_17450)),U_17451))) ),
    inference(variable_rename,[status(thm)],[f_4277_1]) ).

fof(f_4277_3,plain,
    ( ! [U_17449,U_17451,U_17450,U_17452,U_17453] :
        ( hAPP(c_Option_Ooption_OSome(U_17450),U_17452) = hAPP(c_Map_Omap__of(U_17449,U_17450,U_17451),U_17453)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17449,U_17450)),hAPP(hAPP(c_Product__Type_OPair(U_17449,U_17450),U_17453),U_17452)),hAPP(c_List_Oset(tc_prod(U_17449,U_17450)),U_17451)))
        | ~ sP1115(U_17449,U_17451,U_17450,U_17452,U_17453) )
    & ! [U_17449,U_17451,U_17450,U_17452,U_17453] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17449,U_17450)),hAPP(hAPP(c_Product__Type_OPair(U_17449,U_17450),U_17453),U_17452)),hAPP(c_List_Oset(tc_prod(U_17449,U_17450)),U_17451)))
        | hAPP(c_Option_Ooption_OSome(U_17450),U_17452) != hAPP(c_Map_Omap__of(U_17449,U_17450,U_17451),U_17453)
        | ~ sP1115(U_17449,U_17451,U_17450,U_17452,U_17453) )
    & ! [U_17449,U_17451,U_17450,U_17452,U_17453] :
        ( sP1115(U_17449,U_17451,U_17450,U_17452,U_17453)
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17449),hAPP(hAPP(c_List_Omap(tc_prod(U_17449,U_17450),U_17449),c_Product__Type_Ofst(U_17449,U_17450)),U_17451))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1115])],[f_4277_2]) ).

cnf(f_4277_4,plain,
    ( sP1115(U_17449,U_17451,U_17450,U_17452,U_17453)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17449),hAPP(hAPP(c_List_Omap(tc_prod(U_17449,U_17450),U_17449),c_Product__Type_Ofst(U_17449,U_17450)),U_17451))) ),
    inference(clausify,[status(thm)],[f_4277_3]) ).

cnf(f_4277_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17449,U_17450)),hAPP(hAPP(c_Product__Type_OPair(U_17449,U_17450),U_17453),U_17452)),hAPP(c_List_Oset(tc_prod(U_17449,U_17450)),U_17451)))
    | hAPP(c_Option_Ooption_OSome(U_17450),U_17452) != hAPP(c_Map_Omap__of(U_17449,U_17450,U_17451),U_17453)
    | ~ sP1115(U_17449,U_17451,U_17450,U_17452,U_17453) ),
    inference(clausify,[status(thm)],[f_4277_3]) ).

cnf(f_4277_6,plain,
    ( hAPP(c_Option_Ooption_OSome(U_17450),U_17452) = hAPP(c_Map_Omap__of(U_17449,U_17450,U_17451),U_17453)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17449,U_17450)),hAPP(hAPP(c_Product__Type_OPair(U_17449,U_17450),U_17453),U_17452)),hAPP(c_List_Oset(tc_prod(U_17449,U_17450)),U_17451)))
    | ~ sP1115(U_17449,U_17451,U_17450,U_17452,U_17453) ),
    inference(clausify,[status(thm)],[f_4277_3]) ).

fof(f_4278_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_4278_2,plain,
    ! [U_17455,U_17454] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_17454,U_17455) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17454),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_17455),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_4278_1]) ).

fof(f_4278_3,plain,
    ! [U_17454,U_17455] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_17454,U_17455) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17454),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_17455),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(definitional_conversion,[status(esa)],[f_4278_2]) ).

cnf(f_4278_4,plain,
    c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Int_Oint,U_17454,U_17455) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17454),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_17455),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_4278_3]) ).

fof(f_4279_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_4279_2,plain,
    ! [U_17461,U_17460,U_17459,U_17458,U_17457] :
      ( ? [U_17456] : hAPP(c_Map_Omap__of(U_17457,U_17458,U_17461),U_17459) = hAPP(c_Option_Ooption_OSome(U_17458),U_17456)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17457,U_17458)),hAPP(hAPP(c_Product__Type_OPair(U_17457,U_17458),U_17459),U_17460)),hAPP(c_List_Oset(tc_prod(U_17457,U_17458)),U_17461))) ),
    inference(variable_rename,[status(thm)],[f_4279_1]) ).

fof(f_4279_3,plain,
    ! [U_17461,U_17460,U_17459,U_17458,U_17457] :
      ( hAPP(c_Map_Omap__of(U_17457,U_17458,U_17461),U_17459) = hAPP(c_Option_Ooption_OSome(U_17458),sK447(U_17461,U_17460,U_17459,U_17458,U_17457))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17457,U_17458)),hAPP(hAPP(c_Product__Type_OPair(U_17457,U_17458),U_17459),U_17460)),hAPP(c_List_Oset(tc_prod(U_17457,U_17458)),U_17461))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK447]),skolemize(U_17456,sK447(U_17461,U_17460,U_17459,U_17458,U_17457))],[f_4279_2]) ).

fof(f_4279_4,plain,
    ! [U_17458,U_17457,U_17459,U_17460,U_17461] :
      ( hAPP(c_Map_Omap__of(U_17457,U_17458,U_17461),U_17459) = hAPP(c_Option_Ooption_OSome(U_17458),sK447(U_17461,U_17460,U_17459,U_17458,U_17457))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17457,U_17458)),hAPP(hAPP(c_Product__Type_OPair(U_17457,U_17458),U_17459),U_17460)),hAPP(c_List_Oset(tc_prod(U_17457,U_17458)),U_17461))) ),
    inference(definitional_conversion,[status(esa)],[f_4279_3]) ).

cnf(f_4279_5,plain,
    ( hAPP(c_Map_Omap__of(U_17457,U_17458,U_17461),U_17459) = hAPP(c_Option_Ooption_OSome(U_17458),sK447(U_17461,U_17460,U_17459,U_17458,U_17457))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17457,U_17458)),hAPP(hAPP(c_Product__Type_OPair(U_17457,U_17458),U_17459),U_17460)),hAPP(c_List_Oset(tc_prod(U_17457,U_17458)),U_17461))) ),
    inference(clausify,[status(thm)],[f_4279_4]) ).

fof(f_4280_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_4280_2,plain,
    ! [U_17463,U_17462] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_17462,U_17463) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17462,U_17463)),
    inference(variable_rename,[status(thm)],[f_4280_1]) ).

fof(f_4280_3,plain,
    ! [U_17463,U_17462] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_17462,U_17463) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17462,U_17463)),
    inference(definitional_conversion,[status(esa)],[f_4280_2]) ).

cnf(f_4280_4,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_17462,U_17463) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17462,U_17463)),
    inference(clausify,[status(thm)],[f_4280_3]) ).

fof(f_4281_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_4281_2,plain,
    ! [U_17465,U_17464] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17464,U_17465)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_17464,U_17465),
    inference(variable_rename,[status(thm)],[f_4281_1]) ).

fof(f_4281_3,plain,
    ! [U_17464,U_17465] : hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17464,U_17465)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_17464,U_17465),
    inference(definitional_conversion,[status(esa)],[f_4281_2]) ).

cnf(f_4281_4,plain,
    hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17464,U_17465)) = c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,U_17464,U_17465),
    inference(clausify,[status(thm)],[f_4281_3]) ).

fof(f_4282_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_4282_2,plain,
    ! [U_17467,U_17466] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(U_17466,U_17467))),
    inference(variable_rename,[status(thm)],[f_4282_1]) ).

fof(f_4282_3,plain,
    ! [U_17466,U_17467] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(U_17466,U_17467))),
    inference(definitional_conversion,[status(esa)],[f_4282_2]) ).

cnf(f_4282_4,plain,
    hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(U_17466,U_17467))),
    inference(clausify,[status(thm)],[f_4282_3]) ).

fof(f_4283_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_4283_2,plain,
    ! [U_17469,U_17468] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_17468),U_17469) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17468,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_17469),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(variable_rename,[status(thm)],[f_4283_1]) ).

fof(f_4283_3,plain,
    ! [U_17468,U_17469] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_17468),U_17469) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17468,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_17469),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(definitional_conversion,[status(esa)],[f_4283_2]) ).

cnf(f_4283_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Int_Oint,U_17468),U_17469) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_17468,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),U_17469),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
    inference(clausify,[status(thm)],[f_4283_3]) ).

fof(f_4284_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_4284_2,plain,
    ! [U_17471,U_17470] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_17470,U_17471) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17470),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_17471)),
    inference(variable_rename,[status(thm)],[f_4284_1]) ).

fof(f_4284_3,plain,
    ! [U_17470,U_17471] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_17470,U_17471) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17470),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_17471)),
    inference(definitional_conversion,[status(esa)],[f_4284_2]) ).

cnf(f_4284_4,plain,
    c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Int_Oint,U_17470,U_17471) = hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_17470),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_17471)),
    inference(clausify,[status(thm)],[f_4284_3]) ).

fof(f_4285_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_4285_2,plain,
    ! [U_17472] :
      ( ( c_List_Onat__list(U_17472)
        | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17472)) )
      & ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17472))
        | ~ c_List_Onat__list(U_17472) ) ),
    inference(variable_rename,[status(thm)],[f_4285_1]) ).

fof(f_4285_3,plain,
    ( ! [U_17474] :
        ( c_List_Onat__list(U_17474)
        | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17474)) )
    & ! [U_17473] :
        ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17473))
        | ~ c_List_Onat__list(U_17473) ) ),
    inference(miniscope,[status(thm)],[f_4285_2]) ).

fof(f_4285_4,plain,
    ( ! [U_17474] :
        ( c_List_Onat__list(U_17474)
        | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17474)) )
    & ! [U_17473] :
        ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17473))
        | ~ c_List_Onat__list(U_17473) ) ),
    inference(definitional_conversion,[status(esa)],[f_4285_3]) ).

cnf(f_4285_5,plain,
    ( c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17473))
    | ~ c_List_Onat__list(U_17473) ),
    inference(clausify,[status(thm)],[f_4285_4]) ).

cnf(f_4285_6,plain,
    ( c_List_Onat__list(U_17474)
    | ~ c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),U_17474)) ),
    inference(clausify,[status(thm)],[f_4285_4]) ).

fof(f_4286_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_4286_2,plain,
    ! [U_17477,U_17476,U_17475] :
      ( hAPP(c_List_Oset(U_17475),c_List_Oremove1(U_17475,U_17477,U_17476)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17475,tc_HOL_Obool)),hAPP(c_List_Oset(U_17475),U_17476)),hAPP(hAPP(c_Set_Oinsert(U_17475),U_17477),c_Orderings_Obot__class_Obot(tc_fun(U_17475,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17475),U_17476)) ),
    inference(variable_rename,[status(thm)],[f_4286_1]) ).

fof(f_4286_3,plain,
    ! [U_17475,U_17476,U_17477] :
      ( hAPP(c_List_Oset(U_17475),c_List_Oremove1(U_17475,U_17477,U_17476)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17475,tc_HOL_Obool)),hAPP(c_List_Oset(U_17475),U_17476)),hAPP(hAPP(c_Set_Oinsert(U_17475),U_17477),c_Orderings_Obot__class_Obot(tc_fun(U_17475,tc_HOL_Obool))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17475),U_17476)) ),
    inference(definitional_conversion,[status(esa)],[f_4286_2]) ).

cnf(f_4286_4,plain,
    ( hAPP(c_List_Oset(U_17475),c_List_Oremove1(U_17475,U_17477,U_17476)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17475,tc_HOL_Obool)),hAPP(c_List_Oset(U_17475),U_17476)),hAPP(hAPP(c_Set_Oinsert(U_17475),U_17477),c_Orderings_Obot__class_Obot(tc_fun(U_17475,tc_HOL_Obool))))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17475),U_17476)) ),
    inference(clausify,[status(thm)],[f_4286_3]) ).

fof(f_4287_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_4287_2,plain,
    ! [U_17480,U_17479,U_17478] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17478,tc_HOL_Obool)),hAPP(c_List_Oset(U_17478),c_List_Oremove1(U_17478,U_17479,U_17480))),hAPP(c_List_Oset(U_17478),U_17480))),
    inference(variable_rename,[status(thm)],[f_4287_1]) ).

fof(f_4287_3,plain,
    ! [U_17478,U_17479,U_17480] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17478,tc_HOL_Obool)),hAPP(c_List_Oset(U_17478),c_List_Oremove1(U_17478,U_17479,U_17480))),hAPP(c_List_Oset(U_17478),U_17480))),
    inference(definitional_conversion,[status(esa)],[f_4287_2]) ).

cnf(f_4287_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17478,tc_HOL_Obool)),hAPP(c_List_Oset(U_17478),c_List_Oremove1(U_17478,U_17479,U_17480))),hAPP(c_List_Oset(U_17478),U_17480))),
    inference(clausify,[status(thm)],[f_4287_3]) ).

fof(f_4288_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_4288_2,plain,
    ! [U_17483,U_17482,U_17481] :
      ( c_List_Oremove1(U_17481,U_17482,U_17483) = U_17483
      | hBOOL(hAPP(hAPP(c_member(U_17481),U_17482),hAPP(c_List_Oset(U_17481),U_17483))) ),
    inference(variable_rename,[status(thm)],[f_4288_1]) ).

fof(f_4288_3,plain,
    ! [U_17481,U_17482,U_17483] :
      ( c_List_Oremove1(U_17481,U_17482,U_17483) = U_17483
      | hBOOL(hAPP(hAPP(c_member(U_17481),U_17482),hAPP(c_List_Oset(U_17481),U_17483))) ),
    inference(definitional_conversion,[status(esa)],[f_4288_2]) ).

cnf(f_4288_4,plain,
    ( c_List_Oremove1(U_17481,U_17482,U_17483) = U_17483
    | hBOOL(hAPP(hAPP(c_member(U_17481),U_17482),hAPP(c_List_Oset(U_17481),U_17483))) ),
    inference(clausify,[status(thm)],[f_4288_3]) ).

fof(f_4289_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_4289_2,plain,
    ! [U_17487,U_17486,U_17485,U_17484] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_17484),U_17485),hAPP(c_List_Oset(U_17484),c_List_Oremove1(U_17484,U_17487,U_17486))))
      | hBOOL(hAPP(hAPP(c_member(U_17484),U_17485),hAPP(c_List_Oset(U_17484),U_17486))) ),
    inference(variable_rename,[status(thm)],[f_4289_1]) ).

fof(f_4289_3,plain,
    ! [U_17484,U_17485,U_17486,U_17487] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_17484),U_17485),hAPP(c_List_Oset(U_17484),c_List_Oremove1(U_17484,U_17487,U_17486))))
      | hBOOL(hAPP(hAPP(c_member(U_17484),U_17485),hAPP(c_List_Oset(U_17484),U_17486))) ),
    inference(definitional_conversion,[status(esa)],[f_4289_2]) ).

cnf(f_4289_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_17484),U_17485),hAPP(c_List_Oset(U_17484),c_List_Oremove1(U_17484,U_17487,U_17486))))
    | hBOOL(hAPP(hAPP(c_member(U_17484),U_17485),hAPP(c_List_Oset(U_17484),U_17486))) ),
    inference(clausify,[status(thm)],[f_4289_3]) ).

fof(f_4290_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_4290_2,plain,
    ! [U_17491,U_17490,U_17489,U_17488] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_17490),U_17488),hAPP(c_List_Oset(U_17490),c_List_Oremove1(U_17490,U_17489,U_17491))))
          | ~ hBOOL(hAPP(hAPP(c_member(U_17490),U_17488),hAPP(c_List_Oset(U_17490),U_17491))) )
        & ( hBOOL(hAPP(hAPP(c_member(U_17490),U_17488),hAPP(c_List_Oset(U_17490),U_17491)))
          | ~ hBOOL(hAPP(hAPP(c_member(U_17490),U_17488),hAPP(c_List_Oset(U_17490),c_List_Oremove1(U_17490,U_17489,U_17491)))) ) )
      | U_17488 = U_17489 ),
    inference(variable_rename,[status(thm)],[f_4290_1]) ).

fof(f_4290_3,plain,
    ( ! [U_17489,U_17488,U_17490,U_17491] :
        ( hBOOL(hAPP(hAPP(c_member(U_17490),U_17488),hAPP(c_List_Oset(U_17490),c_List_Oremove1(U_17490,U_17489,U_17491))))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17490),U_17488),hAPP(c_List_Oset(U_17490),U_17491)))
        | ~ sP1116(U_17489,U_17488,U_17490,U_17491) )
    & ! [U_17489,U_17488,U_17490,U_17491] :
        ( hBOOL(hAPP(hAPP(c_member(U_17490),U_17488),hAPP(c_List_Oset(U_17490),U_17491)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17490),U_17488),hAPP(c_List_Oset(U_17490),c_List_Oremove1(U_17490,U_17489,U_17491))))
        | ~ sP1116(U_17489,U_17488,U_17490,U_17491) )
    & ! [U_17489,U_17488,U_17490,U_17491] :
        ( sP1116(U_17489,U_17488,U_17490,U_17491)
        | U_17488 = U_17489 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1116])],[f_4290_2]) ).

cnf(f_4290_4,plain,
    ( sP1116(U_17489,U_17488,U_17490,U_17491)
    | U_17488 = U_17489 ),
    inference(clausify,[status(thm)],[f_4290_3]) ).

cnf(f_4290_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17490),U_17488),hAPP(c_List_Oset(U_17490),U_17491)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17490),U_17488),hAPP(c_List_Oset(U_17490),c_List_Oremove1(U_17490,U_17489,U_17491))))
    | ~ sP1116(U_17489,U_17488,U_17490,U_17491) ),
    inference(clausify,[status(thm)],[f_4290_3]) ).

cnf(f_4290_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17490),U_17488),hAPP(c_List_Oset(U_17490),c_List_Oremove1(U_17490,U_17489,U_17491))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17490),U_17488),hAPP(c_List_Oset(U_17490),U_17491)))
    | ~ sP1116(U_17489,U_17488,U_17490,U_17491) ),
    inference(clausify,[status(thm)],[f_4290_3]) ).

fof(f_4291_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_4291_2,plain,
    ! [U_17495,U_17494,U_17493,U_17492] : c_List_Oremove1(U_17492,U_17493,c_List_Oremove1(U_17492,U_17494,U_17495)) = c_List_Oremove1(U_17492,U_17494,c_List_Oremove1(U_17492,U_17493,U_17495)),
    inference(variable_rename,[status(thm)],[f_4291_1]) ).

fof(f_4291_3,plain,
    ! [U_17494,U_17495,U_17493,U_17492] : c_List_Oremove1(U_17492,U_17493,c_List_Oremove1(U_17492,U_17494,U_17495)) = c_List_Oremove1(U_17492,U_17494,c_List_Oremove1(U_17492,U_17493,U_17495)),
    inference(definitional_conversion,[status(esa)],[f_4291_2]) ).

cnf(f_4291_4,plain,
    c_List_Oremove1(U_17492,U_17493,c_List_Oremove1(U_17492,U_17494,U_17495)) = c_List_Oremove1(U_17492,U_17494,c_List_Oremove1(U_17492,U_17493,U_17495)),
    inference(clausify,[status(thm)],[f_4291_3]) ).

fof(f_4292_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_4292_2,plain,
    ! [U_17498,U_17497,U_17496] :
      ( hBOOL(hAPP(c_List_Odistinct(U_17496),c_List_Oremove1(U_17496,U_17498,U_17497)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17496),U_17497)) ),
    inference(variable_rename,[status(thm)],[f_4292_1]) ).

fof(f_4292_3,plain,
    ! [U_17497,U_17496,U_17498] :
      ( hBOOL(hAPP(c_List_Odistinct(U_17496),c_List_Oremove1(U_17496,U_17498,U_17497)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17496),U_17497)) ),
    inference(definitional_conversion,[status(esa)],[f_4292_2]) ).

cnf(f_4292_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17496),c_List_Oremove1(U_17496,U_17498,U_17497)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17496),U_17497)) ),
    inference(clausify,[status(thm)],[f_4292_3]) ).

fof(f_4293_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_4293_2,plain,
    ! [U_17501,U_17500,U_17499] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_17499,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17499,tc_HOL_Obool)),U_17500),hAPP(hAPP(c_Set_Oinsert(U_17499),U_17501),c_Orderings_Obot__class_Obot(tc_fun(U_17499,tc_HOL_Obool))))) = c_List_Oremove1(U_17499,U_17501,c_List_Olinorder__class_Osorted__list__of__set(U_17499,U_17500))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17499),U_17500))
      | ~ class_Orderings_Olinorder(U_17499) ),
    inference(variable_rename,[status(thm)],[f_4293_1]) ).

fof(f_4293_3,plain,
    ! [U_17499,U_17500,U_17501] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_17499,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17499,tc_HOL_Obool)),U_17500),hAPP(hAPP(c_Set_Oinsert(U_17499),U_17501),c_Orderings_Obot__class_Obot(tc_fun(U_17499,tc_HOL_Obool))))) = c_List_Oremove1(U_17499,U_17501,c_List_Olinorder__class_Osorted__list__of__set(U_17499,U_17500))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17499),U_17500))
      | ~ class_Orderings_Olinorder(U_17499) ),
    inference(definitional_conversion,[status(esa)],[f_4293_2]) ).

cnf(f_4293_4,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(U_17499,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17499,tc_HOL_Obool)),U_17500),hAPP(hAPP(c_Set_Oinsert(U_17499),U_17501),c_Orderings_Obot__class_Obot(tc_fun(U_17499,tc_HOL_Obool))))) = c_List_Oremove1(U_17499,U_17501,c_List_Olinorder__class_Osorted__list__of__set(U_17499,U_17500))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17499),U_17500))
    | ~ class_Orderings_Olinorder(U_17499) ),
    inference(clausify,[status(thm)],[f_4293_3]) ).

fof(f_4294_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_4294_2,plain,
    ! [U_17506,U_17505,U_17504,U_17503,U_17502] :
      ( ( hAPP(c_Map_Omap__of(U_17502,U_17505,hAPP(hAPP(c_List_Ozip(U_17502,U_17505),U_17504),hAPP(hAPP(c_List_Omap(U_17502,U_17505),U_17506),U_17504))),U_17503) = c_Option_Ooption_ONone(U_17505)
        | hBOOL(hAPP(hAPP(c_member(U_17502),U_17503),hAPP(c_List_Oset(U_17502),U_17504))) )
      & ( hAPP(c_Map_Omap__of(U_17502,U_17505,hAPP(hAPP(c_List_Ozip(U_17502,U_17505),U_17504),hAPP(hAPP(c_List_Omap(U_17502,U_17505),U_17506),U_17504))),U_17503) = hAPP(c_Option_Ooption_OSome(U_17505),hAPP(U_17506,U_17503))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17502),U_17503),hAPP(c_List_Oset(U_17502),U_17504))) ) ),
    inference(variable_rename,[status(thm)],[f_4294_1]) ).

fof(f_4294_3,plain,
    ( ! [U_17516,U_17514,U_17512,U_17510,U_17508] :
        ( hAPP(c_Map_Omap__of(U_17508,U_17514,hAPP(hAPP(c_List_Ozip(U_17508,U_17514),U_17512),hAPP(hAPP(c_List_Omap(U_17508,U_17514),U_17516),U_17512))),U_17510) = c_Option_Ooption_ONone(U_17514)
        | hBOOL(hAPP(hAPP(c_member(U_17508),U_17510),hAPP(c_List_Oset(U_17508),U_17512))) )
    & ! [U_17515,U_17513,U_17511,U_17509,U_17507] :
        ( hAPP(c_Map_Omap__of(U_17507,U_17513,hAPP(hAPP(c_List_Ozip(U_17507,U_17513),U_17511),hAPP(hAPP(c_List_Omap(U_17507,U_17513),U_17515),U_17511))),U_17509) = hAPP(c_Option_Ooption_OSome(U_17513),hAPP(U_17515,U_17509))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17507),U_17509),hAPP(c_List_Oset(U_17507),U_17511))) ) ),
    inference(miniscope,[status(thm)],[f_4294_2]) ).

fof(f_4294_4,plain,
    ( ! [U_17508,U_17510,U_17512,U_17514,U_17516] :
        ( hAPP(c_Map_Omap__of(U_17508,U_17514,hAPP(hAPP(c_List_Ozip(U_17508,U_17514),U_17512),hAPP(hAPP(c_List_Omap(U_17508,U_17514),U_17516),U_17512))),U_17510) = c_Option_Ooption_ONone(U_17514)
        | hBOOL(hAPP(hAPP(c_member(U_17508),U_17510),hAPP(c_List_Oset(U_17508),U_17512))) )
    & ! [U_17511,U_17509,U_17513,U_17507,U_17515] :
        ( hAPP(c_Map_Omap__of(U_17507,U_17513,hAPP(hAPP(c_List_Ozip(U_17507,U_17513),U_17511),hAPP(hAPP(c_List_Omap(U_17507,U_17513),U_17515),U_17511))),U_17509) = hAPP(c_Option_Ooption_OSome(U_17513),hAPP(U_17515,U_17509))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17507),U_17509),hAPP(c_List_Oset(U_17507),U_17511))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4294_3]) ).

cnf(f_4294_5,plain,
    ( hAPP(c_Map_Omap__of(U_17507,U_17513,hAPP(hAPP(c_List_Ozip(U_17507,U_17513),U_17511),hAPP(hAPP(c_List_Omap(U_17507,U_17513),U_17515),U_17511))),U_17509) = hAPP(c_Option_Ooption_OSome(U_17513),hAPP(U_17515,U_17509))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17507),U_17509),hAPP(c_List_Oset(U_17507),U_17511))) ),
    inference(clausify,[status(thm)],[f_4294_4]) ).

cnf(f_4294_6,plain,
    ( hAPP(c_Map_Omap__of(U_17508,U_17514,hAPP(hAPP(c_List_Ozip(U_17508,U_17514),U_17512),hAPP(hAPP(c_List_Omap(U_17508,U_17514),U_17516),U_17512))),U_17510) = c_Option_Ooption_ONone(U_17514)
    | hBOOL(hAPP(hAPP(c_member(U_17508),U_17510),hAPP(c_List_Oset(U_17508),U_17512))) ),
    inference(clausify,[status(thm)],[f_4294_4]) ).

fof(f_4295_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_4295_2,plain,
    ! [U_17520,U_17519,U_17518,U_17517] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17519,U_17517)),hAPP(hAPP(c_List_Ozip(U_17519,U_17517),U_17520),U_17518)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17517),U_17518)) ),
    inference(variable_rename,[status(thm)],[f_4295_1]) ).

fof(f_4295_3,plain,
    ! [U_17517,U_17518,U_17519,U_17520] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17519,U_17517)),hAPP(hAPP(c_List_Ozip(U_17519,U_17517),U_17520),U_17518)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17517),U_17518)) ),
    inference(definitional_conversion,[status(esa)],[f_4295_2]) ).

cnf(f_4295_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17519,U_17517)),hAPP(hAPP(c_List_Ozip(U_17519,U_17517),U_17520),U_17518)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17517),U_17518)) ),
    inference(clausify,[status(thm)],[f_4295_3]) ).

fof(f_4296_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_4296_2,plain,
    ! [U_17524,U_17523,U_17522,U_17521] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17521,U_17523)),hAPP(hAPP(c_List_Ozip(U_17521,U_17523),U_17522),U_17524)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17521),U_17522)) ),
    inference(variable_rename,[status(thm)],[f_4296_1]) ).

fof(f_4296_3,plain,
    ! [U_17521,U_17522,U_17523,U_17524] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17521,U_17523)),hAPP(hAPP(c_List_Ozip(U_17521,U_17523),U_17522),U_17524)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17521),U_17522)) ),
    inference(definitional_conversion,[status(esa)],[f_4296_2]) ).

cnf(f_4296_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_prod(U_17521,U_17523)),hAPP(hAPP(c_List_Ozip(U_17521,U_17523),U_17522),U_17524)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17521),U_17522)) ),
    inference(clausify,[status(thm)],[f_4296_3]) ).

fof(f_4297_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_4297_2,plain,
    ! [U_17526,U_17525] : hAPP(hAPP(c_List_Ozip(U_17525,U_17525),U_17526),U_17526) = hAPP(hAPP(c_List_Omap(U_17525,tc_prod(U_17525,U_17525)),hAPP(hAPP(c_COMBS(U_17525,U_17525,tc_prod(U_17525,U_17525)),c_Product__Type_OPair(U_17525,U_17525)),c_COMBI(U_17525))),U_17526),
    inference(variable_rename,[status(thm)],[f_4297_1]) ).

fof(f_4297_3,plain,
    ! [U_17525,U_17526] : hAPP(hAPP(c_List_Ozip(U_17525,U_17525),U_17526),U_17526) = hAPP(hAPP(c_List_Omap(U_17525,tc_prod(U_17525,U_17525)),hAPP(hAPP(c_COMBS(U_17525,U_17525,tc_prod(U_17525,U_17525)),c_Product__Type_OPair(U_17525,U_17525)),c_COMBI(U_17525))),U_17526),
    inference(definitional_conversion,[status(esa)],[f_4297_2]) ).

cnf(f_4297_4,plain,
    hAPP(hAPP(c_List_Ozip(U_17525,U_17525),U_17526),U_17526) = hAPP(hAPP(c_List_Omap(U_17525,tc_prod(U_17525,U_17525)),hAPP(hAPP(c_COMBS(U_17525,U_17525,tc_prod(U_17525,U_17525)),c_Product__Type_OPair(U_17525,U_17525)),c_COMBI(U_17525))),U_17526),
    inference(clausify,[status(thm)],[f_4297_3]) ).

fof(f_4298_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_4298_2,plain,
    ! [U_17529,U_17528,U_17527] : hAPP(hAPP(c_List_Ozip(U_17527,U_17528),hAPP(hAPP(c_List_Omap(tc_prod(U_17527,U_17528),U_17527),c_Product__Type_Ofst(U_17527,U_17528)),U_17529)),hAPP(hAPP(c_List_Omap(tc_prod(U_17527,U_17528),U_17528),c_Product__Type_Osnd(U_17527,U_17528)),U_17529)) = U_17529,
    inference(variable_rename,[status(thm)],[f_4298_1]) ).

fof(f_4298_3,plain,
    ! [U_17527,U_17528,U_17529] : hAPP(hAPP(c_List_Ozip(U_17527,U_17528),hAPP(hAPP(c_List_Omap(tc_prod(U_17527,U_17528),U_17527),c_Product__Type_Ofst(U_17527,U_17528)),U_17529)),hAPP(hAPP(c_List_Omap(tc_prod(U_17527,U_17528),U_17528),c_Product__Type_Osnd(U_17527,U_17528)),U_17529)) = U_17529,
    inference(definitional_conversion,[status(esa)],[f_4298_2]) ).

cnf(f_4298_4,plain,
    hAPP(hAPP(c_List_Ozip(U_17527,U_17528),hAPP(hAPP(c_List_Omap(tc_prod(U_17527,U_17528),U_17527),c_Product__Type_Ofst(U_17527,U_17528)),U_17529)),hAPP(hAPP(c_List_Omap(tc_prod(U_17527,U_17528),U_17528),c_Product__Type_Osnd(U_17527,U_17528)),U_17529)) = U_17529,
    inference(clausify,[status(thm)],[f_4298_3]) ).

fof(f_4299_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_4299_2,plain,
    ! [U_17537,U_17536,U_17535,U_17534,U_17533,U_17532,U_17531,U_17530] : hAPP(hAPP(c_List_Omap(tc_prod(U_17530,U_17531),U_17532),U_17533),hAPP(hAPP(c_List_Ozip(U_17530,U_17531),U_17534),hAPP(hAPP(c_List_Omap(U_17535,U_17531),U_17536),U_17537))) = hAPP(hAPP(c_List_Omap(tc_prod(U_17530,U_17535),U_17532),hAPP(c_Product__Type_Oprod_Oprod__case(U_17530,U_17535,U_17532),hAPP(hAPP(c_COMBB(tc_fun(U_17535,tc_prod(U_17530,U_17531)),tc_fun(U_17535,U_17532),U_17530),hAPP(c_COMBB(tc_prod(U_17530,U_17531),U_17532,U_17535),U_17533)),hAPP(hAPP(c_COMBC(U_17530,tc_fun(U_17535,U_17531),tc_fun(U_17535,tc_prod(U_17530,U_17531))),hAPP(hAPP(c_COMBB(tc_fun(U_17531,tc_prod(U_17530,U_17531)),tc_fun(tc_fun(U_17535,U_17531),tc_fun(U_17535,tc_prod(U_17530,U_17531))),U_17530),c_COMBB(U_17531,tc_prod(U_17530,U_17531),U_17535)),c_Product__Type_OPair(U_17530,U_17531))),U_17536)))),hAPP(hAPP(c_List_Ozip(U_17530,U_17535),U_17534),U_17537)),
    inference(variable_rename,[status(thm)],[f_4299_1]) ).

fof(f_4299_3,plain,
    ! [U_17530,U_17531,U_17532,U_17533,U_17534,U_17535,U_17536,U_17537] : hAPP(hAPP(c_List_Omap(tc_prod(U_17530,U_17531),U_17532),U_17533),hAPP(hAPP(c_List_Ozip(U_17530,U_17531),U_17534),hAPP(hAPP(c_List_Omap(U_17535,U_17531),U_17536),U_17537))) = hAPP(hAPP(c_List_Omap(tc_prod(U_17530,U_17535),U_17532),hAPP(c_Product__Type_Oprod_Oprod__case(U_17530,U_17535,U_17532),hAPP(hAPP(c_COMBB(tc_fun(U_17535,tc_prod(U_17530,U_17531)),tc_fun(U_17535,U_17532),U_17530),hAPP(c_COMBB(tc_prod(U_17530,U_17531),U_17532,U_17535),U_17533)),hAPP(hAPP(c_COMBC(U_17530,tc_fun(U_17535,U_17531),tc_fun(U_17535,tc_prod(U_17530,U_17531))),hAPP(hAPP(c_COMBB(tc_fun(U_17531,tc_prod(U_17530,U_17531)),tc_fun(tc_fun(U_17535,U_17531),tc_fun(U_17535,tc_prod(U_17530,U_17531))),U_17530),c_COMBB(U_17531,tc_prod(U_17530,U_17531),U_17535)),c_Product__Type_OPair(U_17530,U_17531))),U_17536)))),hAPP(hAPP(c_List_Ozip(U_17530,U_17535),U_17534),U_17537)),
    inference(definitional_conversion,[status(esa)],[f_4299_2]) ).

cnf(f_4299_4,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_17530,U_17531),U_17532),U_17533),hAPP(hAPP(c_List_Ozip(U_17530,U_17531),U_17534),hAPP(hAPP(c_List_Omap(U_17535,U_17531),U_17536),U_17537))) = hAPP(hAPP(c_List_Omap(tc_prod(U_17530,U_17535),U_17532),hAPP(c_Product__Type_Oprod_Oprod__case(U_17530,U_17535,U_17532),hAPP(hAPP(c_COMBB(tc_fun(U_17535,tc_prod(U_17530,U_17531)),tc_fun(U_17535,U_17532),U_17530),hAPP(c_COMBB(tc_prod(U_17530,U_17531),U_17532,U_17535),U_17533)),hAPP(hAPP(c_COMBC(U_17530,tc_fun(U_17535,U_17531),tc_fun(U_17535,tc_prod(U_17530,U_17531))),hAPP(hAPP(c_COMBB(tc_fun(U_17531,tc_prod(U_17530,U_17531)),tc_fun(tc_fun(U_17535,U_17531),tc_fun(U_17535,tc_prod(U_17530,U_17531))),U_17530),c_COMBB(U_17531,tc_prod(U_17530,U_17531),U_17535)),c_Product__Type_OPair(U_17530,U_17531))),U_17536)))),hAPP(hAPP(c_List_Ozip(U_17530,U_17535),U_17534),U_17537)),
    inference(clausify,[status(thm)],[f_4299_3]) ).

fof(f_4300_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_4300_2,plain,
    ! [U_17545,U_17544,U_17543,U_17542,U_17541,U_17540,U_17539,U_17538] : hAPP(hAPP(c_List_Omap(tc_prod(U_17538,U_17539),U_17540),U_17541),hAPP(hAPP(c_List_Ozip(U_17538,U_17539),hAPP(hAPP(c_List_Omap(U_17542,U_17538),U_17543),U_17544)),U_17545)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17542,U_17539),U_17540),hAPP(c_Product__Type_Oprod_Oprod__case(U_17542,U_17539,U_17540),hAPP(hAPP(c_COMBB(tc_fun(U_17539,tc_prod(U_17538,U_17539)),tc_fun(U_17539,U_17540),U_17542),hAPP(c_COMBB(tc_prod(U_17538,U_17539),U_17540,U_17539),U_17541)),hAPP(hAPP(c_COMBB(U_17538,tc_fun(U_17539,tc_prod(U_17538,U_17539)),U_17542),c_Product__Type_OPair(U_17538,U_17539)),U_17543)))),hAPP(hAPP(c_List_Ozip(U_17542,U_17539),U_17544),U_17545)),
    inference(variable_rename,[status(thm)],[f_4300_1]) ).

fof(f_4300_3,plain,
    ! [U_17538,U_17539,U_17540,U_17541,U_17542,U_17543,U_17544,U_17545] : hAPP(hAPP(c_List_Omap(tc_prod(U_17538,U_17539),U_17540),U_17541),hAPP(hAPP(c_List_Ozip(U_17538,U_17539),hAPP(hAPP(c_List_Omap(U_17542,U_17538),U_17543),U_17544)),U_17545)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17542,U_17539),U_17540),hAPP(c_Product__Type_Oprod_Oprod__case(U_17542,U_17539,U_17540),hAPP(hAPP(c_COMBB(tc_fun(U_17539,tc_prod(U_17538,U_17539)),tc_fun(U_17539,U_17540),U_17542),hAPP(c_COMBB(tc_prod(U_17538,U_17539),U_17540,U_17539),U_17541)),hAPP(hAPP(c_COMBB(U_17538,tc_fun(U_17539,tc_prod(U_17538,U_17539)),U_17542),c_Product__Type_OPair(U_17538,U_17539)),U_17543)))),hAPP(hAPP(c_List_Ozip(U_17542,U_17539),U_17544),U_17545)),
    inference(definitional_conversion,[status(esa)],[f_4300_2]) ).

cnf(f_4300_4,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_17538,U_17539),U_17540),U_17541),hAPP(hAPP(c_List_Ozip(U_17538,U_17539),hAPP(hAPP(c_List_Omap(U_17542,U_17538),U_17543),U_17544)),U_17545)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17542,U_17539),U_17540),hAPP(c_Product__Type_Oprod_Oprod__case(U_17542,U_17539,U_17540),hAPP(hAPP(c_COMBB(tc_fun(U_17539,tc_prod(U_17538,U_17539)),tc_fun(U_17539,U_17540),U_17542),hAPP(c_COMBB(tc_prod(U_17538,U_17539),U_17540,U_17539),U_17541)),hAPP(hAPP(c_COMBB(U_17538,tc_fun(U_17539,tc_prod(U_17538,U_17539)),U_17542),c_Product__Type_OPair(U_17538,U_17539)),U_17543)))),hAPP(hAPP(c_List_Ozip(U_17542,U_17539),U_17544),U_17545)),
    inference(clausify,[status(thm)],[f_4300_3]) ).

fof(f_4301_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_4301_2,plain,
    ! [U_17549,U_17548,U_17547,U_17546] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17546,U_17546)),hAPP(hAPP(c_Product__Type_OPair(U_17546,U_17546),U_17547),U_17548)),hAPP(c_List_Oset(tc_prod(U_17546,U_17546)),hAPP(hAPP(c_List_Ozip(U_17546,U_17546),U_17549),U_17549))))
        | U_17547 != U_17548
        | ~ hBOOL(hAPP(hAPP(c_member(U_17546),U_17547),hAPP(c_List_Oset(U_17546),U_17549))) )
      & ( ( U_17547 = U_17548
          & hBOOL(hAPP(hAPP(c_member(U_17546),U_17547),hAPP(c_List_Oset(U_17546),U_17549))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17546,U_17546)),hAPP(hAPP(c_Product__Type_OPair(U_17546,U_17546),U_17547),U_17548)),hAPP(c_List_Oset(tc_prod(U_17546,U_17546)),hAPP(hAPP(c_List_Ozip(U_17546,U_17546),U_17549),U_17549)))) ) ),
    inference(variable_rename,[status(thm)],[f_4301_1]) ).

fof(f_4301_3,plain,
    ( ! [U_17557,U_17555,U_17553,U_17551] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17551,U_17551)),hAPP(hAPP(c_Product__Type_OPair(U_17551,U_17551),U_17553),U_17555)),hAPP(c_List_Oset(tc_prod(U_17551,U_17551)),hAPP(hAPP(c_List_Ozip(U_17551,U_17551),U_17557),U_17557))))
        | U_17553 != U_17555
        | ~ hBOOL(hAPP(hAPP(c_member(U_17551),U_17553),hAPP(c_List_Oset(U_17551),U_17557))) )
    & ! [U_17556,U_17554,U_17552,U_17550] :
        ( ( U_17552 = U_17554
          & hBOOL(hAPP(hAPP(c_member(U_17550),U_17552),hAPP(c_List_Oset(U_17550),U_17556))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17550,U_17550)),hAPP(hAPP(c_Product__Type_OPair(U_17550,U_17550),U_17552),U_17554)),hAPP(c_List_Oset(tc_prod(U_17550,U_17550)),hAPP(hAPP(c_List_Ozip(U_17550,U_17550),U_17556),U_17556)))) ) ),
    inference(miniscope,[status(thm)],[f_4301_2]) ).

fof(f_4301_4,plain,
    ( ! [U_17552,U_17550,U_17556,U_17554] :
        ( U_17552 = U_17554
        | ~ sP1117(U_17552,U_17550,U_17556,U_17554) )
    & ! [U_17552,U_17550,U_17556,U_17554] :
        ( hBOOL(hAPP(hAPP(c_member(U_17550),U_17552),hAPP(c_List_Oset(U_17550),U_17556)))
        | ~ sP1117(U_17552,U_17550,U_17556,U_17554) )
    & ! [U_17555,U_17551,U_17553,U_17557] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17551,U_17551)),hAPP(hAPP(c_Product__Type_OPair(U_17551,U_17551),U_17553),U_17555)),hAPP(c_List_Oset(tc_prod(U_17551,U_17551)),hAPP(hAPP(c_List_Ozip(U_17551,U_17551),U_17557),U_17557))))
        | U_17553 != U_17555
        | ~ hBOOL(hAPP(hAPP(c_member(U_17551),U_17553),hAPP(c_List_Oset(U_17551),U_17557))) )
    & ! [U_17552,U_17550,U_17556,U_17554] :
        ( sP1117(U_17552,U_17550,U_17556,U_17554)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17550,U_17550)),hAPP(hAPP(c_Product__Type_OPair(U_17550,U_17550),U_17552),U_17554)),hAPP(c_List_Oset(tc_prod(U_17550,U_17550)),hAPP(hAPP(c_List_Ozip(U_17550,U_17550),U_17556),U_17556)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1117])],[f_4301_3]) ).

cnf(f_4301_5,plain,
    ( sP1117(U_17552,U_17550,U_17556,U_17554)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17550,U_17550)),hAPP(hAPP(c_Product__Type_OPair(U_17550,U_17550),U_17552),U_17554)),hAPP(c_List_Oset(tc_prod(U_17550,U_17550)),hAPP(hAPP(c_List_Ozip(U_17550,U_17550),U_17556),U_17556)))) ),
    inference(clausify,[status(thm)],[f_4301_4]) ).

cnf(f_4301_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17551,U_17551)),hAPP(hAPP(c_Product__Type_OPair(U_17551,U_17551),U_17553),U_17555)),hAPP(c_List_Oset(tc_prod(U_17551,U_17551)),hAPP(hAPP(c_List_Ozip(U_17551,U_17551),U_17557),U_17557))))
    | U_17553 != U_17555
    | ~ hBOOL(hAPP(hAPP(c_member(U_17551),U_17553),hAPP(c_List_Oset(U_17551),U_17557))) ),
    inference(clausify,[status(thm)],[f_4301_4]) ).

cnf(f_4301_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17550),U_17552),hAPP(c_List_Oset(U_17550),U_17556)))
    | ~ sP1117(U_17552,U_17550,U_17556,U_17554) ),
    inference(clausify,[status(thm)],[f_4301_4]) ).

cnf(f_4301_8,plain,
    ( U_17552 = U_17554
    | ~ sP1117(U_17552,U_17550,U_17556,U_17554) ),
    inference(clausify,[status(thm)],[f_4301_4]) ).

fof(f_4302_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_4302_2,plain,
    ! [U_17563,U_17562,U_17561,U_17560,U_17559,U_17558] :
      ( hBOOL(hAPP(hAPP(c_member(U_17558),U_17560),hAPP(c_List_Oset(U_17558),U_17562)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17558,U_17559)),hAPP(hAPP(c_Product__Type_OPair(U_17558,U_17559),U_17560),U_17561)),hAPP(c_List_Oset(tc_prod(U_17558,U_17559)),hAPP(hAPP(c_List_Ozip(U_17558,U_17559),U_17562),U_17563)))) ),
    inference(variable_rename,[status(thm)],[f_4302_1]) ).

fof(f_4302_3,plain,
    ! [U_17558,U_17559,U_17560,U_17561,U_17562,U_17563] :
      ( hBOOL(hAPP(hAPP(c_member(U_17558),U_17560),hAPP(c_List_Oset(U_17558),U_17562)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17558,U_17559)),hAPP(hAPP(c_Product__Type_OPair(U_17558,U_17559),U_17560),U_17561)),hAPP(c_List_Oset(tc_prod(U_17558,U_17559)),hAPP(hAPP(c_List_Ozip(U_17558,U_17559),U_17562),U_17563)))) ),
    inference(definitional_conversion,[status(esa)],[f_4302_2]) ).

cnf(f_4302_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17558),U_17560),hAPP(c_List_Oset(U_17558),U_17562)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17558,U_17559)),hAPP(hAPP(c_Product__Type_OPair(U_17558,U_17559),U_17560),U_17561)),hAPP(c_List_Oset(tc_prod(U_17558,U_17559)),hAPP(hAPP(c_List_Ozip(U_17558,U_17559),U_17562),U_17563)))) ),
    inference(clausify,[status(thm)],[f_4302_3]) ).

fof(f_4303_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_4303_2,plain,
    ! [U_17569,U_17568,U_17567,U_17566,U_17565,U_17564] :
      ( hBOOL(hAPP(hAPP(c_member(U_17565),U_17567),hAPP(c_List_Oset(U_17565),U_17569)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17564,U_17565)),hAPP(hAPP(c_Product__Type_OPair(U_17564,U_17565),U_17566),U_17567)),hAPP(c_List_Oset(tc_prod(U_17564,U_17565)),hAPP(hAPP(c_List_Ozip(U_17564,U_17565),U_17568),U_17569)))) ),
    inference(variable_rename,[status(thm)],[f_4303_1]) ).

fof(f_4303_3,plain,
    ! [U_17569,U_17568,U_17567,U_17566,U_17565] :
      ( ! [U_17564] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17564,U_17565)),hAPP(hAPP(c_Product__Type_OPair(U_17564,U_17565),U_17566),U_17567)),hAPP(c_List_Oset(tc_prod(U_17564,U_17565)),hAPP(hAPP(c_List_Ozip(U_17564,U_17565),U_17568),U_17569))))
      | hBOOL(hAPP(hAPP(c_member(U_17565),U_17567),hAPP(c_List_Oset(U_17565),U_17569))) ),
    inference(miniscope,[status(thm)],[f_4303_2]) ).

fof(f_4303_4,plain,
    ! [U_17564,U_17565,U_17566,U_17567,U_17568,U_17569] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17564,U_17565)),hAPP(hAPP(c_Product__Type_OPair(U_17564,U_17565),U_17566),U_17567)),hAPP(c_List_Oset(tc_prod(U_17564,U_17565)),hAPP(hAPP(c_List_Ozip(U_17564,U_17565),U_17568),U_17569))))
      | hBOOL(hAPP(hAPP(c_member(U_17565),U_17567),hAPP(c_List_Oset(U_17565),U_17569))) ),
    inference(definitional_conversion,[status(esa)],[f_4303_3]) ).

cnf(f_4303_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17564,U_17565)),hAPP(hAPP(c_Product__Type_OPair(U_17564,U_17565),U_17566),U_17567)),hAPP(c_List_Oset(tc_prod(U_17564,U_17565)),hAPP(hAPP(c_List_Ozip(U_17564,U_17565),U_17568),U_17569))))
    | hBOOL(hAPP(hAPP(c_member(U_17565),U_17567),hAPP(c_List_Oset(U_17565),U_17569))) ),
    inference(clausify,[status(thm)],[f_4303_4]) ).

fof(f_4304_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_4304_2,plain,
    ! [U_17575,U_17574,U_17573,U_17572,U_17571,U_17570] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_17571),U_17573),hAPP(c_List_Oset(U_17571),U_17575)))
        & hBOOL(hAPP(hAPP(c_member(U_17570),U_17572),hAPP(c_List_Oset(U_17570),U_17574))) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17570,U_17571)),hAPP(hAPP(c_Product__Type_OPair(U_17570,U_17571),U_17572),U_17573)),hAPP(c_List_Oset(tc_prod(U_17570,U_17571)),hAPP(hAPP(c_List_Ozip(U_17570,U_17571),U_17574),U_17575)))) ),
    inference(variable_rename,[status(thm)],[f_4304_1]) ).

fof(f_4304_3,plain,
    ( ! [U_17570,U_17571,U_17572,U_17573,U_17574,U_17575] :
        ( hBOOL(hAPP(hAPP(c_member(U_17571),U_17573),hAPP(c_List_Oset(U_17571),U_17575)))
        | ~ sP1118(U_17570,U_17571,U_17572,U_17573,U_17574,U_17575) )
    & ! [U_17570,U_17571,U_17572,U_17573,U_17574,U_17575] :
        ( hBOOL(hAPP(hAPP(c_member(U_17570),U_17572),hAPP(c_List_Oset(U_17570),U_17574)))
        | ~ sP1118(U_17570,U_17571,U_17572,U_17573,U_17574,U_17575) )
    & ! [U_17570,U_17571,U_17572,U_17573,U_17574,U_17575] :
        ( sP1118(U_17570,U_17571,U_17572,U_17573,U_17574,U_17575)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17570,U_17571)),hAPP(hAPP(c_Product__Type_OPair(U_17570,U_17571),U_17572),U_17573)),hAPP(c_List_Oset(tc_prod(U_17570,U_17571)),hAPP(hAPP(c_List_Ozip(U_17570,U_17571),U_17574),U_17575)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1118])],[f_4304_2]) ).

cnf(f_4304_4,plain,
    ( sP1118(U_17570,U_17571,U_17572,U_17573,U_17574,U_17575)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17570,U_17571)),hAPP(hAPP(c_Product__Type_OPair(U_17570,U_17571),U_17572),U_17573)),hAPP(c_List_Oset(tc_prod(U_17570,U_17571)),hAPP(hAPP(c_List_Ozip(U_17570,U_17571),U_17574),U_17575)))) ),
    inference(clausify,[status(thm)],[f_4304_3]) ).

cnf(f_4304_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17570),U_17572),hAPP(c_List_Oset(U_17570),U_17574)))
    | ~ sP1118(U_17570,U_17571,U_17572,U_17573,U_17574,U_17575) ),
    inference(clausify,[status(thm)],[f_4304_3]) ).

cnf(f_4304_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17571),U_17573),hAPP(c_List_Oset(U_17571),U_17575)))
    | ~ sP1118(U_17570,U_17571,U_17572,U_17573,U_17574,U_17575) ),
    inference(clausify,[status(thm)],[f_4304_3]) ).

fof(f_4305_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_4305_2,plain,
    ! [U_17581,U_17580,U_17579,U_17578,U_17577,U_17576] : hAPP(hAPP(c_List_Ozip(U_17576,U_17577),U_17578),hAPP(hAPP(c_List_Omap(U_17579,U_17577),U_17580),U_17581)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17576,U_17579),tc_prod(U_17576,U_17577)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17576,U_17579,tc_prod(U_17576,U_17577)),hAPP(hAPP(c_COMBC(U_17576,tc_fun(U_17579,U_17577),tc_fun(U_17579,tc_prod(U_17576,U_17577))),hAPP(hAPP(c_COMBB(tc_fun(U_17577,tc_prod(U_17576,U_17577)),tc_fun(tc_fun(U_17579,U_17577),tc_fun(U_17579,tc_prod(U_17576,U_17577))),U_17576),c_COMBB(U_17577,tc_prod(U_17576,U_17577),U_17579)),c_Product__Type_OPair(U_17576,U_17577))),U_17580))),hAPP(hAPP(c_List_Ozip(U_17576,U_17579),U_17578),U_17581)),
    inference(variable_rename,[status(thm)],[f_4305_1]) ).

fof(f_4305_3,plain,
    ! [U_17576,U_17577,U_17578,U_17579,U_17580,U_17581] : hAPP(hAPP(c_List_Ozip(U_17576,U_17577),U_17578),hAPP(hAPP(c_List_Omap(U_17579,U_17577),U_17580),U_17581)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17576,U_17579),tc_prod(U_17576,U_17577)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17576,U_17579,tc_prod(U_17576,U_17577)),hAPP(hAPP(c_COMBC(U_17576,tc_fun(U_17579,U_17577),tc_fun(U_17579,tc_prod(U_17576,U_17577))),hAPP(hAPP(c_COMBB(tc_fun(U_17577,tc_prod(U_17576,U_17577)),tc_fun(tc_fun(U_17579,U_17577),tc_fun(U_17579,tc_prod(U_17576,U_17577))),U_17576),c_COMBB(U_17577,tc_prod(U_17576,U_17577),U_17579)),c_Product__Type_OPair(U_17576,U_17577))),U_17580))),hAPP(hAPP(c_List_Ozip(U_17576,U_17579),U_17578),U_17581)),
    inference(definitional_conversion,[status(esa)],[f_4305_2]) ).

cnf(f_4305_4,plain,
    hAPP(hAPP(c_List_Ozip(U_17576,U_17577),U_17578),hAPP(hAPP(c_List_Omap(U_17579,U_17577),U_17580),U_17581)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17576,U_17579),tc_prod(U_17576,U_17577)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17576,U_17579,tc_prod(U_17576,U_17577)),hAPP(hAPP(c_COMBC(U_17576,tc_fun(U_17579,U_17577),tc_fun(U_17579,tc_prod(U_17576,U_17577))),hAPP(hAPP(c_COMBB(tc_fun(U_17577,tc_prod(U_17576,U_17577)),tc_fun(tc_fun(U_17579,U_17577),tc_fun(U_17579,tc_prod(U_17576,U_17577))),U_17576),c_COMBB(U_17577,tc_prod(U_17576,U_17577),U_17579)),c_Product__Type_OPair(U_17576,U_17577))),U_17580))),hAPP(hAPP(c_List_Ozip(U_17576,U_17579),U_17578),U_17581)),
    inference(clausify,[status(thm)],[f_4305_3]) ).

fof(f_4306_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_4306_2,plain,
    ! [U_17587,U_17586,U_17585,U_17584,U_17583,U_17582] : hAPP(hAPP(c_List_Ozip(U_17582,U_17583),hAPP(hAPP(c_List_Omap(U_17584,U_17582),U_17585),U_17586)),U_17587) = hAPP(hAPP(c_List_Omap(tc_prod(U_17584,U_17583),tc_prod(U_17582,U_17583)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17584,U_17583,tc_prod(U_17582,U_17583)),hAPP(hAPP(c_COMBB(U_17582,tc_fun(U_17583,tc_prod(U_17582,U_17583)),U_17584),c_Product__Type_OPair(U_17582,U_17583)),U_17585))),hAPP(hAPP(c_List_Ozip(U_17584,U_17583),U_17586),U_17587)),
    inference(variable_rename,[status(thm)],[f_4306_1]) ).

fof(f_4306_3,plain,
    ! [U_17582,U_17583,U_17584,U_17585,U_17586,U_17587] : hAPP(hAPP(c_List_Ozip(U_17582,U_17583),hAPP(hAPP(c_List_Omap(U_17584,U_17582),U_17585),U_17586)),U_17587) = hAPP(hAPP(c_List_Omap(tc_prod(U_17584,U_17583),tc_prod(U_17582,U_17583)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17584,U_17583,tc_prod(U_17582,U_17583)),hAPP(hAPP(c_COMBB(U_17582,tc_fun(U_17583,tc_prod(U_17582,U_17583)),U_17584),c_Product__Type_OPair(U_17582,U_17583)),U_17585))),hAPP(hAPP(c_List_Ozip(U_17584,U_17583),U_17586),U_17587)),
    inference(definitional_conversion,[status(esa)],[f_4306_2]) ).

cnf(f_4306_4,plain,
    hAPP(hAPP(c_List_Ozip(U_17582,U_17583),hAPP(hAPP(c_List_Omap(U_17584,U_17582),U_17585),U_17586)),U_17587) = hAPP(hAPP(c_List_Omap(tc_prod(U_17584,U_17583),tc_prod(U_17582,U_17583)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17584,U_17583,tc_prod(U_17582,U_17583)),hAPP(hAPP(c_COMBB(U_17582,tc_fun(U_17583,tc_prod(U_17582,U_17583)),U_17584),c_Product__Type_OPair(U_17582,U_17583)),U_17585))),hAPP(hAPP(c_List_Ozip(U_17584,U_17583),U_17586),U_17587)),
    inference(clausify,[status(thm)],[f_4306_3]) ).

fof(f_4307_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_4307_2,plain,
    ! [U_17595,U_17594,U_17593,U_17592,U_17591,U_17590,U_17589,U_17588] : hAPP(hAPP(c_List_Ozip(U_17588,U_17589),hAPP(hAPP(c_List_Omap(U_17590,U_17588),U_17591),U_17592)),hAPP(hAPP(c_List_Omap(U_17593,U_17589),U_17594),U_17595)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17590,U_17593),tc_prod(U_17588,U_17589)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17590,U_17593,tc_prod(U_17588,U_17589)),hAPP(hAPP(c_COMBC(U_17590,tc_fun(U_17593,U_17589),tc_fun(U_17593,tc_prod(U_17588,U_17589))),hAPP(hAPP(c_COMBB(tc_fun(U_17589,tc_prod(U_17588,U_17589)),tc_fun(tc_fun(U_17593,U_17589),tc_fun(U_17593,tc_prod(U_17588,U_17589))),U_17590),c_COMBB(U_17589,tc_prod(U_17588,U_17589),U_17593)),hAPP(hAPP(c_COMBB(U_17588,tc_fun(U_17589,tc_prod(U_17588,U_17589)),U_17590),c_Product__Type_OPair(U_17588,U_17589)),U_17591))),U_17594))),hAPP(hAPP(c_List_Ozip(U_17590,U_17593),U_17592),U_17595)),
    inference(variable_rename,[status(thm)],[f_4307_1]) ).

fof(f_4307_3,plain,
    ! [U_17588,U_17589,U_17590,U_17591,U_17592,U_17593,U_17594,U_17595] : hAPP(hAPP(c_List_Ozip(U_17588,U_17589),hAPP(hAPP(c_List_Omap(U_17590,U_17588),U_17591),U_17592)),hAPP(hAPP(c_List_Omap(U_17593,U_17589),U_17594),U_17595)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17590,U_17593),tc_prod(U_17588,U_17589)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17590,U_17593,tc_prod(U_17588,U_17589)),hAPP(hAPP(c_COMBC(U_17590,tc_fun(U_17593,U_17589),tc_fun(U_17593,tc_prod(U_17588,U_17589))),hAPP(hAPP(c_COMBB(tc_fun(U_17589,tc_prod(U_17588,U_17589)),tc_fun(tc_fun(U_17593,U_17589),tc_fun(U_17593,tc_prod(U_17588,U_17589))),U_17590),c_COMBB(U_17589,tc_prod(U_17588,U_17589),U_17593)),hAPP(hAPP(c_COMBB(U_17588,tc_fun(U_17589,tc_prod(U_17588,U_17589)),U_17590),c_Product__Type_OPair(U_17588,U_17589)),U_17591))),U_17594))),hAPP(hAPP(c_List_Ozip(U_17590,U_17593),U_17592),U_17595)),
    inference(definitional_conversion,[status(esa)],[f_4307_2]) ).

cnf(f_4307_4,plain,
    hAPP(hAPP(c_List_Ozip(U_17588,U_17589),hAPP(hAPP(c_List_Omap(U_17590,U_17588),U_17591),U_17592)),hAPP(hAPP(c_List_Omap(U_17593,U_17589),U_17594),U_17595)) = hAPP(hAPP(c_List_Omap(tc_prod(U_17590,U_17593),tc_prod(U_17588,U_17589)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17590,U_17593,tc_prod(U_17588,U_17589)),hAPP(hAPP(c_COMBC(U_17590,tc_fun(U_17593,U_17589),tc_fun(U_17593,tc_prod(U_17588,U_17589))),hAPP(hAPP(c_COMBB(tc_fun(U_17589,tc_prod(U_17588,U_17589)),tc_fun(tc_fun(U_17593,U_17589),tc_fun(U_17593,tc_prod(U_17588,U_17589))),U_17590),c_COMBB(U_17589,tc_prod(U_17588,U_17589),U_17593)),hAPP(hAPP(c_COMBB(U_17588,tc_fun(U_17589,tc_prod(U_17588,U_17589)),U_17590),c_Product__Type_OPair(U_17588,U_17589)),U_17591))),U_17594))),hAPP(hAPP(c_List_Ozip(U_17590,U_17593),U_17592),U_17595)),
    inference(clausify,[status(thm)],[f_4307_3]) ).

fof(f_4308_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_4308_2,plain,
    ! [U_17598,U_17597,U_17596] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_17596,hAPP(hAPP(c_Set_Oinsert(U_17596),U_17598),U_17597)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17596,U_17596,c_COMBI(U_17596)),U_17598),c_List_Olinorder__class_Osorted__list__of__set(U_17596,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17596,tc_HOL_Obool)),U_17597),hAPP(hAPP(c_Set_Oinsert(U_17596),U_17598),c_Orderings_Obot__class_Obot(tc_fun(U_17596,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17596),U_17597))
      | ~ class_Orderings_Olinorder(U_17596) ),
    inference(variable_rename,[status(thm)],[f_4308_1]) ).

fof(f_4308_3,plain,
    ! [U_17596,U_17597,U_17598] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_17596,hAPP(hAPP(c_Set_Oinsert(U_17596),U_17598),U_17597)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17596,U_17596,c_COMBI(U_17596)),U_17598),c_List_Olinorder__class_Osorted__list__of__set(U_17596,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17596,tc_HOL_Obool)),U_17597),hAPP(hAPP(c_Set_Oinsert(U_17596),U_17598),c_Orderings_Obot__class_Obot(tc_fun(U_17596,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17596),U_17597))
      | ~ class_Orderings_Olinorder(U_17596) ),
    inference(definitional_conversion,[status(esa)],[f_4308_2]) ).

cnf(f_4308_4,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(U_17596,hAPP(hAPP(c_Set_Oinsert(U_17596),U_17598),U_17597)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17596,U_17596,c_COMBI(U_17596)),U_17598),c_List_Olinorder__class_Osorted__list__of__set(U_17596,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_17596,tc_HOL_Obool)),U_17597),hAPP(hAPP(c_Set_Oinsert(U_17596),U_17598),c_Orderings_Obot__class_Obot(tc_fun(U_17596,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17596),U_17597))
    | ~ class_Orderings_Olinorder(U_17596) ),
    inference(clausify,[status(thm)],[f_4308_3]) ).

fof(f_4309_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_4309_2,plain,
    ! [U_17606,U_17605,U_17604,U_17603,U_17602,U_17601,U_17600,U_17599] :
      ( c_Map_Omap__of(U_17601,U_17599,hAPP(hAPP(c_List_Ozip(U_17601,U_17599),U_17602),U_17600)) = c_Map_Omap__of(U_17601,U_17599,hAPP(hAPP(c_List_Ozip(U_17601,U_17599),U_17602),U_17603))
      | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17601,tc_Option_Ooption(U_17599)),c_Map_Omap__of(U_17601,U_17599,hAPP(hAPP(c_List_Ozip(U_17601,U_17599),U_17602),U_17600))),U_17604),hAPP(c_Option_Ooption_OSome(U_17599),U_17605)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17601,tc_Option_Ooption(U_17599)),c_Map_Omap__of(U_17601,U_17599,hAPP(hAPP(c_List_Ozip(U_17601,U_17599),U_17602),U_17603))),U_17604),hAPP(c_Option_Ooption_OSome(U_17599),U_17606))
      | hBOOL(hAPP(hAPP(c_member(U_17601),U_17604),hAPP(c_List_Oset(U_17601),U_17602)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17599)),U_17603) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17601)),U_17602)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17599)),U_17600) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17601)),U_17602) ),
    inference(variable_rename,[status(thm)],[f_4309_1]) ).

fof(f_4309_3,plain,
    ! [U_17599,U_17600,U_17601,U_17602,U_17603,U_17604,U_17605,U_17606] :
      ( c_Map_Omap__of(U_17601,U_17599,hAPP(hAPP(c_List_Ozip(U_17601,U_17599),U_17602),U_17600)) = c_Map_Omap__of(U_17601,U_17599,hAPP(hAPP(c_List_Ozip(U_17601,U_17599),U_17602),U_17603))
      | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17601,tc_Option_Ooption(U_17599)),c_Map_Omap__of(U_17601,U_17599,hAPP(hAPP(c_List_Ozip(U_17601,U_17599),U_17602),U_17600))),U_17604),hAPP(c_Option_Ooption_OSome(U_17599),U_17605)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17601,tc_Option_Ooption(U_17599)),c_Map_Omap__of(U_17601,U_17599,hAPP(hAPP(c_List_Ozip(U_17601,U_17599),U_17602),U_17603))),U_17604),hAPP(c_Option_Ooption_OSome(U_17599),U_17606))
      | hBOOL(hAPP(hAPP(c_member(U_17601),U_17604),hAPP(c_List_Oset(U_17601),U_17602)))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17599)),U_17603) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17601)),U_17602)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17599)),U_17600) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17601)),U_17602) ),
    inference(definitional_conversion,[status(esa)],[f_4309_2]) ).

cnf(f_4309_4,plain,
    ( c_Map_Omap__of(U_17601,U_17599,hAPP(hAPP(c_List_Ozip(U_17601,U_17599),U_17602),U_17600)) = c_Map_Omap__of(U_17601,U_17599,hAPP(hAPP(c_List_Ozip(U_17601,U_17599),U_17602),U_17603))
    | hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17601,tc_Option_Ooption(U_17599)),c_Map_Omap__of(U_17601,U_17599,hAPP(hAPP(c_List_Ozip(U_17601,U_17599),U_17602),U_17600))),U_17604),hAPP(c_Option_Ooption_OSome(U_17599),U_17605)) != hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17601,tc_Option_Ooption(U_17599)),c_Map_Omap__of(U_17601,U_17599,hAPP(hAPP(c_List_Ozip(U_17601,U_17599),U_17602),U_17603))),U_17604),hAPP(c_Option_Ooption_OSome(U_17599),U_17606))
    | hBOOL(hAPP(hAPP(c_member(U_17601),U_17604),hAPP(c_List_Oset(U_17601),U_17602)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17599)),U_17603) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17601)),U_17602)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17599)),U_17600) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17601)),U_17602) ),
    inference(clausify,[status(thm)],[f_4309_3]) ).

fof(f_4310_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_4310_2,plain,
    ! [U_17610,U_17609,U_17608,U_17607] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(U_17607,U_17608))),hAPP(hAPP(c_List_Ozip(U_17607,U_17608),U_17609),U_17610)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17607)),U_17609)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17608)),U_17610)),
    inference(variable_rename,[status(thm)],[f_4310_1]) ).

fof(f_4310_3,plain,
    ! [U_17608,U_17607,U_17609,U_17610] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(U_17607,U_17608))),hAPP(hAPP(c_List_Ozip(U_17607,U_17608),U_17609),U_17610)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17607)),U_17609)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17608)),U_17610)),
    inference(definitional_conversion,[status(esa)],[f_4310_2]) ).

cnf(f_4310_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_prod(U_17607,U_17608))),hAPP(hAPP(c_List_Ozip(U_17607,U_17608),U_17609),U_17610)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17607)),U_17609)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17608)),U_17610)),
    inference(clausify,[status(thm)],[f_4310_3]) ).

fof(f_4311_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_4311_2,plain,
    ! [U_17615,U_17614,U_17613,U_17612,U_17611] :
      ( hAPP(c_List_Oset(U_17612),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17612,U_17611,U_17613),U_17614),U_17615)) = hAPP(hAPP(c_Set_Oinsert(U_17612),U_17614),hAPP(c_List_Oset(U_17612),U_17615))
      | ~ class_Orderings_Olinorder(U_17611) ),
    inference(variable_rename,[status(thm)],[f_4311_1]) ).

fof(f_4311_3,plain,
    ! [U_17611,U_17612,U_17613,U_17614,U_17615] :
      ( hAPP(c_List_Oset(U_17612),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17612,U_17611,U_17613),U_17614),U_17615)) = hAPP(hAPP(c_Set_Oinsert(U_17612),U_17614),hAPP(c_List_Oset(U_17612),U_17615))
      | ~ class_Orderings_Olinorder(U_17611) ),
    inference(definitional_conversion,[status(esa)],[f_4311_2]) ).

cnf(f_4311_4,plain,
    ( hAPP(c_List_Oset(U_17612),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17612,U_17611,U_17613),U_17614),U_17615)) = hAPP(hAPP(c_Set_Oinsert(U_17612),U_17614),hAPP(c_List_Oset(U_17612),U_17615))
    | ~ class_Orderings_Olinorder(U_17611) ),
    inference(clausify,[status(thm)],[f_4311_3]) ).

fof(f_4312_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_4312_2,plain,
    ! [U_17616] :
      ( c_Finite__Set_Ofun__left__comm(U_17616,tc_List_Olist(U_17616),c_List_Olinorder__class_Oinsort__key(U_17616,U_17616,c_COMBI(U_17616)))
      | ~ class_Orderings_Olinorder(U_17616) ),
    inference(variable_rename,[status(thm)],[f_4312_1]) ).

fof(f_4312_3,plain,
    ! [U_17616] :
      ( c_Finite__Set_Ofun__left__comm(U_17616,tc_List_Olist(U_17616),c_List_Olinorder__class_Oinsort__key(U_17616,U_17616,c_COMBI(U_17616)))
      | ~ class_Orderings_Olinorder(U_17616) ),
    inference(definitional_conversion,[status(esa)],[f_4312_2]) ).

cnf(f_4312_4,plain,
    ( c_Finite__Set_Ofun__left__comm(U_17616,tc_List_Olist(U_17616),c_List_Olinorder__class_Oinsort__key(U_17616,U_17616,c_COMBI(U_17616)))
    | ~ class_Orderings_Olinorder(U_17616) ),
    inference(clausify,[status(thm)],[f_4312_3]) ).

fof(f_4313_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_4313_2,plain,
    ! [U_17619,U_17618,U_17617] :
      ( U_17618 != U_17619
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17617)),U_17618) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17617)),U_17619) ),
    inference(variable_rename,[status(thm)],[f_4313_1]) ).

fof(f_4313_3,plain,
    ! [U_17619,U_17618] :
      ( ! [U_17617] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17617)),U_17618) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17617)),U_17619)
      | U_17618 != U_17619 ),
    inference(miniscope,[status(thm)],[f_4313_2]) ).

fof(f_4313_4,plain,
    ! [U_17617,U_17618,U_17619] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17617)),U_17618) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17617)),U_17619)
      | U_17618 != U_17619 ),
    inference(definitional_conversion,[status(esa)],[f_4313_3]) ).

cnf(f_4313_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17617)),U_17618) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17617)),U_17619)
    | U_17618 != U_17619 ),
    inference(clausify,[status(thm)],[f_4313_4]) ).

fof(f_4314_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_4314_2,plain,
    ! [U_17624,U_17623,U_17622,U_17621,U_17620] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17621)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17621,U_17620,U_17622),U_17623),U_17624)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17621)),U_17624))
      | ~ class_Orderings_Olinorder(U_17620) ),
    inference(variable_rename,[status(thm)],[f_4314_1]) ).

fof(f_4314_3,plain,
    ! [U_17620,U_17621,U_17622,U_17623,U_17624] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17621)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17621,U_17620,U_17622),U_17623),U_17624)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17621)),U_17624))
      | ~ class_Orderings_Olinorder(U_17620) ),
    inference(definitional_conversion,[status(esa)],[f_4314_2]) ).

cnf(f_4314_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17621)),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17621,U_17620,U_17622),U_17623),U_17624)) = hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17621)),U_17624))
    | ~ class_Orderings_Olinorder(U_17620) ),
    inference(clausify,[status(thm)],[f_4314_3]) ).

fof(f_4315_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_4315_2,plain,
    ! [U_17630,U_17629,U_17628,U_17627,U_17626,U_17625] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17629,U_17625,U_17626),U_17628),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17629,U_17625,U_17626),U_17627),U_17630)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17629,U_17625,U_17626),U_17627),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17629,U_17625,U_17626),U_17628),U_17630))
      | hAPP(U_17626,U_17627) = hAPP(U_17626,U_17628)
      | ~ class_Orderings_Olinorder(U_17625) ),
    inference(variable_rename,[status(thm)],[f_4315_1]) ).

fof(f_4315_3,plain,
    ! [U_17625,U_17626,U_17627,U_17628,U_17629,U_17630] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17629,U_17625,U_17626),U_17628),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17629,U_17625,U_17626),U_17627),U_17630)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17629,U_17625,U_17626),U_17627),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17629,U_17625,U_17626),U_17628),U_17630))
      | hAPP(U_17626,U_17627) = hAPP(U_17626,U_17628)
      | ~ class_Orderings_Olinorder(U_17625) ),
    inference(definitional_conversion,[status(esa)],[f_4315_2]) ).

cnf(f_4315_4,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17629,U_17625,U_17626),U_17628),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17629,U_17625,U_17626),U_17627),U_17630)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17629,U_17625,U_17626),U_17627),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17629,U_17625,U_17626),U_17628),U_17630))
    | hAPP(U_17626,U_17627) = hAPP(U_17626,U_17628)
    | ~ class_Orderings_Olinorder(U_17625) ),
    inference(clausify,[status(thm)],[f_4315_3]) ).

fof(f_4316_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_4316_2,plain,
    ! [U_17634,U_17633,U_17632,U_17631] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17631,U_17631,c_COMBI(U_17631)),U_17632),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17631,U_17631,c_COMBI(U_17631)),U_17633),U_17634)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17631,U_17631,c_COMBI(U_17631)),U_17633),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17631,U_17631,c_COMBI(U_17631)),U_17632),U_17634))
      | ~ class_Orderings_Olinorder(U_17631) ),
    inference(variable_rename,[status(thm)],[f_4316_1]) ).

fof(f_4316_3,plain,
    ! [U_17631,U_17632,U_17633,U_17634] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17631,U_17631,c_COMBI(U_17631)),U_17632),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17631,U_17631,c_COMBI(U_17631)),U_17633),U_17634)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17631,U_17631,c_COMBI(U_17631)),U_17633),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17631,U_17631,c_COMBI(U_17631)),U_17632),U_17634))
      | ~ class_Orderings_Olinorder(U_17631) ),
    inference(definitional_conversion,[status(esa)],[f_4316_2]) ).

cnf(f_4316_4,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17631,U_17631,c_COMBI(U_17631)),U_17632),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17631,U_17631,c_COMBI(U_17631)),U_17633),U_17634)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17631,U_17631,c_COMBI(U_17631)),U_17633),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17631,U_17631,c_COMBI(U_17631)),U_17632),U_17634))
    | ~ class_Orderings_Olinorder(U_17631) ),
    inference(clausify,[status(thm)],[f_4316_3]) ).

fof(f_4317_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_4317_2,plain,
    ! [U_17639,U_17638,U_17637,U_17636,U_17635] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17635)),U_17637) = U_17639
        & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17635)),U_17636) = U_17639 )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17635),tc_List_Olist(U_17635))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17635),tc_List_Olist(U_17635)),U_17636),U_17637)),hAPP(c_List_Olexn(U_17635,U_17638),U_17639))) ),
    inference(variable_rename,[status(thm)],[f_4317_1]) ).

fof(f_4317_3,plain,
    ( ! [U_17635,U_17636,U_17637,U_17639] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17635)),U_17637) = U_17639
        | ~ sP1119(U_17635,U_17636,U_17637,U_17639) )
    & ! [U_17635,U_17636,U_17637,U_17639] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17635)),U_17636) = U_17639
        | ~ sP1119(U_17635,U_17636,U_17637,U_17639) )
    & ! [U_17635,U_17636,U_17637,U_17638,U_17639] :
        ( sP1119(U_17635,U_17636,U_17637,U_17639)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17635),tc_List_Olist(U_17635))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17635),tc_List_Olist(U_17635)),U_17636),U_17637)),hAPP(c_List_Olexn(U_17635,U_17638),U_17639))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1119])],[f_4317_2]) ).

cnf(f_4317_4,plain,
    ( sP1119(U_17635,U_17636,U_17637,U_17639)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17635),tc_List_Olist(U_17635))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17635),tc_List_Olist(U_17635)),U_17636),U_17637)),hAPP(c_List_Olexn(U_17635,U_17638),U_17639))) ),
    inference(clausify,[status(thm)],[f_4317_3]) ).

cnf(f_4317_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17635)),U_17636) = U_17639
    | ~ sP1119(U_17635,U_17636,U_17637,U_17639) ),
    inference(clausify,[status(thm)],[f_4317_3]) ).

cnf(f_4317_6,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17635)),U_17637) = U_17639
    | ~ sP1119(U_17635,U_17636,U_17637,U_17639) ),
    inference(clausify,[status(thm)],[f_4317_3]) ).

fof(f_4318_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_4318_2,plain,
    ! [U_17643,U_17642,U_17641,U_17640] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17640)),hAPP(hAPP(c_List_Omap(U_17641,U_17640),U_17642),U_17643)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17641)),U_17643),
    inference(variable_rename,[status(thm)],[f_4318_1]) ).

fof(f_4318_3,plain,
    ! [U_17641,U_17640,U_17642,U_17643] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17640)),hAPP(hAPP(c_List_Omap(U_17641,U_17640),U_17642),U_17643)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17641)),U_17643),
    inference(definitional_conversion,[status(esa)],[f_4318_2]) ).

cnf(f_4318_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17640)),hAPP(hAPP(c_List_Omap(U_17641,U_17640),U_17642),U_17643)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17641)),U_17643),
    inference(clausify,[status(thm)],[f_4318_3]) ).

fof(f_4319_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_4319_2,plain,
    ! [U_17650,U_17649,U_17648,U_17647,U_17646,U_17645,U_17644] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17644)),U_17647) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17648)),U_17650)
      | hAPP(hAPP(c_List_Omap(U_17644,U_17645),U_17646),U_17647) != hAPP(hAPP(c_List_Omap(U_17648,U_17645),U_17649),U_17650) ),
    inference(variable_rename,[status(thm)],[f_4319_1]) ).

fof(f_4319_3,plain,
    ! [U_17644,U_17645,U_17646,U_17647,U_17648,U_17649,U_17650] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17644)),U_17647) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17648)),U_17650)
      | hAPP(hAPP(c_List_Omap(U_17644,U_17645),U_17646),U_17647) != hAPP(hAPP(c_List_Omap(U_17648,U_17645),U_17649),U_17650) ),
    inference(definitional_conversion,[status(esa)],[f_4319_2]) ).

cnf(f_4319_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17644)),U_17647) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17648)),U_17650)
    | hAPP(hAPP(c_List_Omap(U_17644,U_17645),U_17646),U_17647) != hAPP(hAPP(c_List_Omap(U_17648,U_17645),U_17649),U_17650) ),
    inference(clausify,[status(thm)],[f_4319_3]) ).

fof(f_4320_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_4320_2,plain,
    ! [U_17653,U_17652,U_17651] :
      ( c_List_Oremove1(U_17651,U_17652,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17651,U_17651,c_COMBI(U_17651)),U_17652),U_17653)) = U_17653
      | ~ class_Orderings_Olinorder(U_17651) ),
    inference(variable_rename,[status(thm)],[f_4320_1]) ).

fof(f_4320_3,plain,
    ! [U_17652,U_17651,U_17653] :
      ( c_List_Oremove1(U_17651,U_17652,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17651,U_17651,c_COMBI(U_17651)),U_17652),U_17653)) = U_17653
      | ~ class_Orderings_Olinorder(U_17651) ),
    inference(definitional_conversion,[status(esa)],[f_4320_2]) ).

cnf(f_4320_4,plain,
    ( c_List_Oremove1(U_17651,U_17652,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17651,U_17651,c_COMBI(U_17651)),U_17652),U_17653)) = U_17653
    | ~ class_Orderings_Olinorder(U_17651) ),
    inference(clausify,[status(thm)],[f_4320_3]) ).

fof(f_4321_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_4321_2,plain,
    ! [U_17655,U_17654] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_17654),hAPP(c_List_Oset(U_17654),U_17655))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17654)),U_17655))),
    inference(variable_rename,[status(thm)],[f_4321_1]) ).

fof(f_4321_3,plain,
    ! [U_17654,U_17655] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_17654),hAPP(c_List_Oset(U_17654),U_17655))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17654)),U_17655))),
    inference(definitional_conversion,[status(esa)],[f_4321_2]) ).

cnf(f_4321_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(U_17654),hAPP(c_List_Oset(U_17654),U_17655))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17654)),U_17655))),
    inference(clausify,[status(thm)],[f_4321_3]) ).

fof(f_4322_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_4322_2,plain,
    ! [U_17657,U_17656] :
      ( hBOOL(hAPP(c_List_Odistinct(U_17656),U_17657))
      | hAPP(c_Finite__Set_Ocard(U_17656),hAPP(c_List_Oset(U_17656),U_17657)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17656)),U_17657) ),
    inference(variable_rename,[status(thm)],[f_4322_1]) ).

fof(f_4322_3,plain,
    ! [U_17656,U_17657] :
      ( hBOOL(hAPP(c_List_Odistinct(U_17656),U_17657))
      | hAPP(c_Finite__Set_Ocard(U_17656),hAPP(c_List_Oset(U_17656),U_17657)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17656)),U_17657) ),
    inference(definitional_conversion,[status(esa)],[f_4322_2]) ).

cnf(f_4322_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17656),U_17657))
    | hAPP(c_Finite__Set_Ocard(U_17656),hAPP(c_List_Oset(U_17656),U_17657)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17656)),U_17657) ),
    inference(clausify,[status(thm)],[f_4322_3]) ).

fof(f_4323_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_4323_2,plain,
    ! [U_17659,U_17658] :
      ( hAPP(c_Finite__Set_Ocard(U_17658),hAPP(c_List_Oset(U_17658),U_17659)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17658)),U_17659)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17658),U_17659)) ),
    inference(variable_rename,[status(thm)],[f_4323_1]) ).

fof(f_4323_3,plain,
    ! [U_17658,U_17659] :
      ( hAPP(c_Finite__Set_Ocard(U_17658),hAPP(c_List_Oset(U_17658),U_17659)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17658)),U_17659)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17658),U_17659)) ),
    inference(definitional_conversion,[status(esa)],[f_4323_2]) ).

cnf(f_4323_4,plain,
    ( hAPP(c_Finite__Set_Ocard(U_17658),hAPP(c_List_Oset(U_17658),U_17659)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17658)),U_17659)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17658),U_17659)) ),
    inference(clausify,[status(thm)],[f_4323_3]) ).

fof(f_4324_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_4324_2,plain,
    ! [U_17664,U_17663,U_17662,U_17661,U_17660] :
      ( U_17661 = U_17664
      | c_Map_Omap__of(U_17662,U_17660,hAPP(hAPP(c_List_Ozip(U_17662,U_17660),U_17663),U_17661)) != c_Map_Omap__of(U_17662,U_17660,hAPP(hAPP(c_List_Ozip(U_17662,U_17660),U_17663),U_17664))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17662),U_17663))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17660)),U_17664) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17662)),U_17663)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17660)),U_17661) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17662)),U_17663) ),
    inference(variable_rename,[status(thm)],[f_4324_1]) ).

fof(f_4324_3,plain,
    ! [U_17660,U_17661,U_17662,U_17663,U_17664] :
      ( U_17661 = U_17664
      | c_Map_Omap__of(U_17662,U_17660,hAPP(hAPP(c_List_Ozip(U_17662,U_17660),U_17663),U_17661)) != c_Map_Omap__of(U_17662,U_17660,hAPP(hAPP(c_List_Ozip(U_17662,U_17660),U_17663),U_17664))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17662),U_17663))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17660)),U_17664) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17662)),U_17663)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17660)),U_17661) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17662)),U_17663) ),
    inference(definitional_conversion,[status(esa)],[f_4324_2]) ).

cnf(f_4324_4,plain,
    ( U_17661 = U_17664
    | c_Map_Omap__of(U_17662,U_17660,hAPP(hAPP(c_List_Ozip(U_17662,U_17660),U_17663),U_17661)) != c_Map_Omap__of(U_17662,U_17660,hAPP(hAPP(c_List_Ozip(U_17662,U_17660),U_17663),U_17664))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17662),U_17663))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17660)),U_17664) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17662)),U_17663)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17660)),U_17661) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17662)),U_17663) ),
    inference(clausify,[status(thm)],[f_4324_3]) ).

fof(f_4325_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_4325_2,plain,
    ! [U_17668,U_17667,U_17666,U_17665] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(U_17665,U_17667),U_17665),c_Product__Type_Ofst(U_17665,U_17667)),hAPP(hAPP(c_List_Ozip(U_17665,U_17667),U_17666),U_17668)) = U_17666
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17665)),U_17666) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17667)),U_17668) ),
    inference(variable_rename,[status(thm)],[f_4325_1]) ).

fof(f_4325_3,plain,
    ! [U_17665,U_17666,U_17667,U_17668] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(U_17665,U_17667),U_17665),c_Product__Type_Ofst(U_17665,U_17667)),hAPP(hAPP(c_List_Ozip(U_17665,U_17667),U_17666),U_17668)) = U_17666
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17665)),U_17666) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17667)),U_17668) ),
    inference(definitional_conversion,[status(esa)],[f_4325_2]) ).

cnf(f_4325_4,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_17665,U_17667),U_17665),c_Product__Type_Ofst(U_17665,U_17667)),hAPP(hAPP(c_List_Ozip(U_17665,U_17667),U_17666),U_17668)) = U_17666
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17665)),U_17666) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17667)),U_17668) ),
    inference(clausify,[status(thm)],[f_4325_3]) ).

fof(f_4326_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_4326_2,plain,
    ! [U_17672,U_17671,U_17670,U_17669] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(U_17669,U_17671),U_17671),c_Product__Type_Osnd(U_17669,U_17671)),hAPP(hAPP(c_List_Ozip(U_17669,U_17671),U_17670),U_17672)) = U_17672
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17669)),U_17670) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17671)),U_17672) ),
    inference(variable_rename,[status(thm)],[f_4326_1]) ).

fof(f_4326_3,plain,
    ! [U_17669,U_17670,U_17671,U_17672] :
      ( hAPP(hAPP(c_List_Omap(tc_prod(U_17669,U_17671),U_17671),c_Product__Type_Osnd(U_17669,U_17671)),hAPP(hAPP(c_List_Ozip(U_17669,U_17671),U_17670),U_17672)) = U_17672
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17669)),U_17670) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17671)),U_17672) ),
    inference(definitional_conversion,[status(esa)],[f_4326_2]) ).

cnf(f_4326_4,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_17669,U_17671),U_17671),c_Product__Type_Osnd(U_17669,U_17671)),hAPP(hAPP(c_List_Ozip(U_17669,U_17671),U_17670),U_17672)) = U_17672
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17669)),U_17670) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17671)),U_17672) ),
    inference(clausify,[status(thm)],[f_4326_3]) ).

fof(f_4327_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_4327_2,plain,
    ! [U_17677,U_17676,U_17675,U_17674,U_17673] :
      ( ( ( hBOOL(hAPP(c_List_Odistinct(U_17674),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17674,U_17673,U_17675),U_17676),U_17677)))
          | ~ hBOOL(hAPP(c_List_Odistinct(U_17674),U_17677))
          | hBOOL(hAPP(hAPP(c_member(U_17674),U_17676),hAPP(c_List_Oset(U_17674),U_17677))) )
        & ( ( hBOOL(hAPP(c_List_Odistinct(U_17674),U_17677))
            & ~ hBOOL(hAPP(hAPP(c_member(U_17674),U_17676),hAPP(c_List_Oset(U_17674),U_17677))) )
          | ~ hBOOL(hAPP(c_List_Odistinct(U_17674),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17674,U_17673,U_17675),U_17676),U_17677))) ) )
      | ~ class_Orderings_Olinorder(U_17673) ),
    inference(variable_rename,[status(thm)],[f_4327_1]) ).

fof(f_4327_3,plain,
    ( ! [U_17674,U_17676,U_17677] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17674),U_17677))
        | ~ sP1120(U_17674,U_17676,U_17677) )
    & ! [U_17674,U_17676,U_17677] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_17674),U_17676),hAPP(c_List_Oset(U_17674),U_17677)))
        | ~ sP1120(U_17674,U_17676,U_17677) )
    & ! [U_17674,U_17673,U_17675,U_17676,U_17677] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17674),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17674,U_17673,U_17675),U_17676),U_17677)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17674),U_17677))
        | hBOOL(hAPP(hAPP(c_member(U_17674),U_17676),hAPP(c_List_Oset(U_17674),U_17677)))
        | ~ sP1121(U_17674,U_17673,U_17675,U_17676,U_17677) )
    & ! [U_17674,U_17673,U_17675,U_17676,U_17677] :
        ( sP1120(U_17674,U_17676,U_17677)
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17674),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17674,U_17673,U_17675),U_17676),U_17677)))
        | ~ sP1121(U_17674,U_17673,U_17675,U_17676,U_17677) )
    & ! [U_17674,U_17673,U_17675,U_17676,U_17677] :
        ( sP1121(U_17674,U_17673,U_17675,U_17676,U_17677)
        | ~ class_Orderings_Olinorder(U_17673) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1120,sP1121])],[f_4327_2]) ).

cnf(f_4327_4,plain,
    ( sP1121(U_17674,U_17673,U_17675,U_17676,U_17677)
    | ~ class_Orderings_Olinorder(U_17673) ),
    inference(clausify,[status(thm)],[f_4327_3]) ).

cnf(f_4327_5,plain,
    ( sP1120(U_17674,U_17676,U_17677)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17674),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17674,U_17673,U_17675),U_17676),U_17677)))
    | ~ sP1121(U_17674,U_17673,U_17675,U_17676,U_17677) ),
    inference(clausify,[status(thm)],[f_4327_3]) ).

cnf(f_4327_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17674),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17674,U_17673,U_17675),U_17676),U_17677)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17674),U_17677))
    | hBOOL(hAPP(hAPP(c_member(U_17674),U_17676),hAPP(c_List_Oset(U_17674),U_17677)))
    | ~ sP1121(U_17674,U_17673,U_17675,U_17676,U_17677) ),
    inference(clausify,[status(thm)],[f_4327_3]) ).

cnf(f_4327_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_17674),U_17676),hAPP(c_List_Oset(U_17674),U_17677)))
    | ~ sP1120(U_17674,U_17676,U_17677) ),
    inference(clausify,[status(thm)],[f_4327_3]) ).

cnf(f_4327_8,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17674),U_17677))
    | ~ sP1120(U_17674,U_17676,U_17677) ),
    inference(clausify,[status(thm)],[f_4327_3]) ).

fof(f_4328_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_4328_2,plain,
    ! [U_17680,U_17679,U_17678] :
      ( 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_17678)),U_17680)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17678),U_17679),hAPP(c_List_Oset(U_17678),U_17680))) ),
    inference(variable_rename,[status(thm)],[f_4328_1]) ).

fof(f_4328_3,plain,
    ! [U_17679,U_17680,U_17678] :
      ( 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_17678)),U_17680)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17678),U_17679),hAPP(c_List_Oset(U_17678),U_17680))) ),
    inference(definitional_conversion,[status(esa)],[f_4328_2]) ).

cnf(f_4328_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_17678)),U_17680)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17678),U_17679),hAPP(c_List_Oset(U_17678),U_17680))) ),
    inference(clausify,[status(thm)],[f_4328_3]) ).

fof(f_4329_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_4329_2,plain,
    ! [U_17685,U_17684,U_17683,U_17682,U_17681] :
      ( ( ( hAPP(hAPP(c_List_Ozip(U_17681,U_17683),U_17682),U_17684) = U_17685
          | hAPP(hAPP(c_List_Omap(tc_prod(U_17681,U_17683),U_17683),c_Product__Type_Osnd(U_17681,U_17683)),U_17685) != U_17684
          | hAPP(hAPP(c_List_Omap(tc_prod(U_17681,U_17683),U_17681),c_Product__Type_Ofst(U_17681,U_17683)),U_17685) != U_17682 )
        & ( ( hAPP(hAPP(c_List_Omap(tc_prod(U_17681,U_17683),U_17683),c_Product__Type_Osnd(U_17681,U_17683)),U_17685) = U_17684
            & hAPP(hAPP(c_List_Omap(tc_prod(U_17681,U_17683),U_17681),c_Product__Type_Ofst(U_17681,U_17683)),U_17685) = U_17682 )
          | hAPP(hAPP(c_List_Ozip(U_17681,U_17683),U_17682),U_17684) != U_17685 ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17681)),U_17682) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17683)),U_17684) ),
    inference(variable_rename,[status(thm)],[f_4329_1]) ).

fof(f_4329_3,plain,
    ( ! [U_17681,U_17682,U_17683,U_17684,U_17685] :
        ( hAPP(hAPP(c_List_Omap(tc_prod(U_17681,U_17683),U_17683),c_Product__Type_Osnd(U_17681,U_17683)),U_17685) = U_17684
        | ~ sP1122(U_17681,U_17682,U_17683,U_17684,U_17685) )
    & ! [U_17681,U_17682,U_17683,U_17684,U_17685] :
        ( hAPP(hAPP(c_List_Omap(tc_prod(U_17681,U_17683),U_17681),c_Product__Type_Ofst(U_17681,U_17683)),U_17685) = U_17682
        | ~ sP1122(U_17681,U_17682,U_17683,U_17684,U_17685) )
    & ! [U_17681,U_17682,U_17683,U_17684,U_17685] :
        ( hAPP(hAPP(c_List_Ozip(U_17681,U_17683),U_17682),U_17684) = U_17685
        | hAPP(hAPP(c_List_Omap(tc_prod(U_17681,U_17683),U_17683),c_Product__Type_Osnd(U_17681,U_17683)),U_17685) != U_17684
        | hAPP(hAPP(c_List_Omap(tc_prod(U_17681,U_17683),U_17681),c_Product__Type_Ofst(U_17681,U_17683)),U_17685) != U_17682
        | ~ sP1123(U_17681,U_17682,U_17683,U_17684,U_17685) )
    & ! [U_17681,U_17682,U_17683,U_17684,U_17685] :
        ( sP1122(U_17681,U_17682,U_17683,U_17684,U_17685)
        | hAPP(hAPP(c_List_Ozip(U_17681,U_17683),U_17682),U_17684) != U_17685
        | ~ sP1123(U_17681,U_17682,U_17683,U_17684,U_17685) )
    & ! [U_17681,U_17682,U_17683,U_17684,U_17685] :
        ( sP1123(U_17681,U_17682,U_17683,U_17684,U_17685)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17681)),U_17682) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17683)),U_17684) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1122,sP1123])],[f_4329_2]) ).

cnf(f_4329_4,plain,
    ( sP1123(U_17681,U_17682,U_17683,U_17684,U_17685)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17681)),U_17682) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17683)),U_17684) ),
    inference(clausify,[status(thm)],[f_4329_3]) ).

cnf(f_4329_5,plain,
    ( sP1122(U_17681,U_17682,U_17683,U_17684,U_17685)
    | hAPP(hAPP(c_List_Ozip(U_17681,U_17683),U_17682),U_17684) != U_17685
    | ~ sP1123(U_17681,U_17682,U_17683,U_17684,U_17685) ),
    inference(clausify,[status(thm)],[f_4329_3]) ).

cnf(f_4329_6,plain,
    ( hAPP(hAPP(c_List_Ozip(U_17681,U_17683),U_17682),U_17684) = U_17685
    | hAPP(hAPP(c_List_Omap(tc_prod(U_17681,U_17683),U_17683),c_Product__Type_Osnd(U_17681,U_17683)),U_17685) != U_17684
    | hAPP(hAPP(c_List_Omap(tc_prod(U_17681,U_17683),U_17681),c_Product__Type_Ofst(U_17681,U_17683)),U_17685) != U_17682
    | ~ sP1123(U_17681,U_17682,U_17683,U_17684,U_17685) ),
    inference(clausify,[status(thm)],[f_4329_3]) ).

cnf(f_4329_7,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_17681,U_17683),U_17681),c_Product__Type_Ofst(U_17681,U_17683)),U_17685) = U_17682
    | ~ sP1122(U_17681,U_17682,U_17683,U_17684,U_17685) ),
    inference(clausify,[status(thm)],[f_4329_3]) ).

cnf(f_4329_8,plain,
    ( hAPP(hAPP(c_List_Omap(tc_prod(U_17681,U_17683),U_17683),c_Product__Type_Osnd(U_17681,U_17683)),U_17685) = U_17684
    | ~ sP1122(U_17681,U_17682,U_17683,U_17684,U_17685) ),
    inference(clausify,[status(thm)],[f_4329_3]) ).

fof(f_4330_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_4330_2,plain,
    ! [U_17687,U_17686] : c_List_Olenlex(U_17686,U_17687) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17686),tc_List_Olist(U_17686),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17686),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17686),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),tc_List_Olist(U_17686)),c_COMBS(tc_List_Olist(U_17686),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_17686)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17686)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17686),tc_fun(tc_List_Olist(U_17686),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17686),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),tc_List_Olist(U_17686)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17686))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17686)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17686))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17686)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17686),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17686),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),tc_List_Olist(U_17686)),c_COMBS(tc_List_Olist(U_17686),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_17686)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17686)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17686),tc_fun(tc_List_Olist(U_17686),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17686),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),tc_List_Olist(U_17686)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17686))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17686)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17686))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17686)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17686),tc_fun(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17686),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),tc_List_Olist(U_17686)),c_COMBC(tc_List_Olist(U_17686),tc_fun(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17686),tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686))),tc_fun(tc_List_Olist(U_17686),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(U_17686)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17686)),c_member(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686))))),c_Product__Type_OPair(tc_List_Olist(U_17686),tc_List_Olist(U_17686))))),c_List_Olex(U_17686,U_17687)))))),
    inference(variable_rename,[status(thm)],[f_4330_1]) ).

fof(f_4330_3,plain,
    ! [U_17686,U_17687] : c_List_Olenlex(U_17686,U_17687) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17686),tc_List_Olist(U_17686),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17686),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17686),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),tc_List_Olist(U_17686)),c_COMBS(tc_List_Olist(U_17686),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_17686)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17686)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17686),tc_fun(tc_List_Olist(U_17686),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17686),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),tc_List_Olist(U_17686)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17686))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17686)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17686))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17686)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17686),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17686),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),tc_List_Olist(U_17686)),c_COMBS(tc_List_Olist(U_17686),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_17686)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17686)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17686),tc_fun(tc_List_Olist(U_17686),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17686),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),tc_List_Olist(U_17686)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17686))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17686)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17686))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17686)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17686),tc_fun(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17686),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),tc_List_Olist(U_17686)),c_COMBC(tc_List_Olist(U_17686),tc_fun(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17686),tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686))),tc_fun(tc_List_Olist(U_17686),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(U_17686)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17686)),c_member(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686))))),c_Product__Type_OPair(tc_List_Olist(U_17686),tc_List_Olist(U_17686))))),c_List_Olex(U_17686,U_17687)))))),
    inference(definitional_conversion,[status(esa)],[f_4330_2]) ).

cnf(f_4330_4,plain,
    c_List_Olenlex(U_17686,U_17687) = hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17686),tc_List_Olist(U_17686),tc_HOL_Obool),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17686),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17686),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),tc_List_Olist(U_17686)),c_COMBS(tc_List_Olist(U_17686),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_17686)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17686)),c_fdisj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17686),tc_fun(tc_List_Olist(U_17686),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17686),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),tc_List_Olist(U_17686)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17686))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17686)),c_Orderings_Oord__class_Oless(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17686))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17686)))))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17686),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17686),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),tc_List_Olist(U_17686)),c_COMBS(tc_List_Olist(U_17686),tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_List_Olist(U_17686)),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17686)),c_fconj)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17686),tc_fun(tc_List_Olist(U_17686),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17686),tc_Nat_Onat),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),tc_List_Olist(U_17686)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_17686))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_17686)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17686))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17686)))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17686),tc_fun(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17686),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686)),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686)),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17686),tc_HOL_Obool)),tc_List_Olist(U_17686)),c_COMBC(tc_List_Olist(U_17686),tc_fun(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686)),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17686),tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686))),tc_fun(tc_List_Olist(U_17686),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686)),tc_HOL_Obool),tc_HOL_Obool)),tc_List_Olist(U_17686)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686)),tc_fun(tc_fun(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686)),tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17686)),c_member(tc_prod(tc_List_Olist(U_17686),tc_List_Olist(U_17686))))),c_Product__Type_OPair(tc_List_Olist(U_17686),tc_List_Olist(U_17686))))),c_List_Olex(U_17686,U_17687)))))),
    inference(clausify,[status(thm)],[f_4330_3]) ).

fof(f_4331_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_4331_2,plain,
    ! [U_17689,U_17688] : c_List_Olenlex(U_17688,U_17689) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(U_17688)),tc_List_Olist(U_17688)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(U_17688),c_Wellfounded_Oless__than,c_List_Olex(U_17688,U_17689))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17688),tc_List_Olist(U_17688),tc_prod(tc_Nat_Onat,tc_List_Olist(U_17688))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(U_17688),tc_prod(tc_Nat_Onat,tc_List_Olist(U_17688))),tc_List_Olist(U_17688)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(U_17688))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17688)))),c_COMBI(tc_List_Olist(U_17688)))),
    inference(variable_rename,[status(thm)],[f_4331_1]) ).

fof(f_4331_3,plain,
    ! [U_17688,U_17689] : c_List_Olenlex(U_17688,U_17689) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(U_17688)),tc_List_Olist(U_17688)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(U_17688),c_Wellfounded_Oless__than,c_List_Olex(U_17688,U_17689))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17688),tc_List_Olist(U_17688),tc_prod(tc_Nat_Onat,tc_List_Olist(U_17688))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(U_17688),tc_prod(tc_Nat_Onat,tc_List_Olist(U_17688))),tc_List_Olist(U_17688)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(U_17688))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17688)))),c_COMBI(tc_List_Olist(U_17688)))),
    inference(definitional_conversion,[status(esa)],[f_4331_2]) ).

cnf(f_4331_4,plain,
    c_List_Olenlex(U_17688,U_17689) = hAPP(hAPP(c_Relation_Oinv__image(tc_prod(tc_Nat_Onat,tc_List_Olist(U_17688)),tc_List_Olist(U_17688)),c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_List_Olist(U_17688),c_Wellfounded_Oless__than,c_List_Olex(U_17688,U_17689))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17688),tc_List_Olist(U_17688),tc_prod(tc_Nat_Onat,tc_List_Olist(U_17688))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_List_Olist(U_17688),tc_prod(tc_Nat_Onat,tc_List_Olist(U_17688))),tc_List_Olist(U_17688)),c_Product__Type_OPair(tc_Nat_Onat,tc_List_Olist(U_17688))),c_Nat_Osize__class_Osize(tc_List_Olist(U_17688)))),c_COMBI(tc_List_Olist(U_17688)))),
    inference(clausify,[status(thm)],[f_4331_3]) ).

fof(f_4332_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_4332_2,plain,
    ! [U_17692,U_17691,U_17690] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_17690)),hAPP(c_Set_OCollect(tc_List_Olist(U_17690)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17690),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_17690)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17690),tc_fun(U_17690,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17690,tc_HOL_Obool),tc_fun(tc_fun(U_17690,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17690)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_17690,tc_HOL_Obool))),c_List_Oset(U_17690))),U_17691))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17690),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_17690)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17690)))),U_17692)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17690),U_17691)) ),
    inference(variable_rename,[status(thm)],[f_4332_1]) ).

fof(f_4332_3,plain,
    ! [U_17690,U_17691,U_17692] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_17690)),hAPP(c_Set_OCollect(tc_List_Olist(U_17690)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17690),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_17690)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17690),tc_fun(U_17690,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17690,tc_HOL_Obool),tc_fun(tc_fun(U_17690,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17690)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_17690,tc_HOL_Obool))),c_List_Oset(U_17690))),U_17691))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17690),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_17690)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17690)))),U_17692)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17690),U_17691)) ),
    inference(definitional_conversion,[status(esa)],[f_4332_2]) ).

cnf(f_4332_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_17690)),hAPP(c_Set_OCollect(tc_List_Olist(U_17690)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17690),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_17690)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17690),tc_fun(U_17690,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17690,tc_HOL_Obool),tc_fun(tc_fun(U_17690,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17690)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_17690,tc_HOL_Obool))),c_List_Oset(U_17690))),U_17691))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17690),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_17690)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17690)))),U_17692)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17690),U_17691)) ),
    inference(clausify,[status(thm)],[f_4332_3]) ).

fof(f_4333_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_4333_2,plain,
    ! [U_17697,U_17696,U_17695] :
      ( ( U_17695 = U_17696
        | ? [U_17694] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17697,U_17697,tc_HOL_Obool),c_fequal),U_17694))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17697,U_17697)),U_17694),hAPP(c_List_Oset(tc_prod(U_17697,U_17697)),hAPP(hAPP(c_List_Ozip(U_17697,U_17697),U_17695),U_17696)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17697)),U_17695) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17697)),U_17696) )
      & ( ( ! [U_17693] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17697,U_17697,tc_HOL_Obool),c_fequal),U_17693))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17697,U_17697)),U_17693),hAPP(c_List_Oset(tc_prod(U_17697,U_17697)),hAPP(hAPP(c_List_Ozip(U_17697,U_17697),U_17695),U_17696)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17697)),U_17695) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17697)),U_17696) )
        | U_17695 != U_17696 ) ),
    inference(variable_rename,[status(thm)],[f_4333_1]) ).

fof(f_4333_3,plain,
    ( ! [U_17703,U_17701,U_17699] :
        ( U_17699 = U_17701
        | ? [U_17694] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17703,U_17703,tc_HOL_Obool),c_fequal),U_17694))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17703,U_17703)),U_17694),hAPP(c_List_Oset(tc_prod(U_17703,U_17703)),hAPP(hAPP(c_List_Ozip(U_17703,U_17703),U_17699),U_17701)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17703)),U_17699) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17703)),U_17701) )
    & ! [U_17702,U_17700,U_17698] :
        ( ( ! [U_17693] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17702,U_17702,tc_HOL_Obool),c_fequal),U_17693))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17702,U_17702)),U_17693),hAPP(c_List_Oset(tc_prod(U_17702,U_17702)),hAPP(hAPP(c_List_Ozip(U_17702,U_17702),U_17698),U_17700)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17702)),U_17698) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17702)),U_17700) )
        | U_17698 != U_17700 ) ),
    inference(miniscope,[status(thm)],[f_4333_2]) ).

fof(f_4333_4,plain,
    ( ! [U_17703,U_17701,U_17699] :
        ( U_17699 = U_17701
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17703,U_17703,tc_HOL_Obool),c_fequal),sK448(U_17703,U_17701,U_17699)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17703,U_17703)),sK448(U_17703,U_17701,U_17699)),hAPP(c_List_Oset(tc_prod(U_17703,U_17703)),hAPP(hAPP(c_List_Ozip(U_17703,U_17703),U_17699),U_17701)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17703)),U_17699) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17703)),U_17701) )
    & ! [U_17702,U_17700,U_17698] :
        ( ( ! [U_17693] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17702,U_17702,tc_HOL_Obool),c_fequal),U_17693))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17702,U_17702)),U_17693),hAPP(c_List_Oset(tc_prod(U_17702,U_17702)),hAPP(hAPP(c_List_Ozip(U_17702,U_17702),U_17698),U_17700)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17702)),U_17698) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17702)),U_17700) )
        | U_17698 != U_17700 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK448]),skolemize(U_17694,sK448(U_17703,U_17701,U_17699))],[f_4333_3]) ).

fof(f_4333_5,plain,
    ( ! [U_17701,U_17699,U_17703] :
        ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17703,U_17703,tc_HOL_Obool),c_fequal),sK448(U_17703,U_17701,U_17699)))
        | ~ sP1125(U_17701,U_17699,U_17703) )
    & ! [U_17701,U_17699,U_17703] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17703,U_17703)),sK448(U_17703,U_17701,U_17699)),hAPP(c_List_Oset(tc_prod(U_17703,U_17703)),hAPP(hAPP(c_List_Ozip(U_17703,U_17703),U_17699),U_17701))))
        | ~ sP1125(U_17701,U_17699,U_17703) )
    & ! [U_17693,U_17702,U_17698,U_17700] :
        ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17702,U_17702,tc_HOL_Obool),c_fequal),U_17693))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17702,U_17702)),U_17693),hAPP(c_List_Oset(tc_prod(U_17702,U_17702)),hAPP(hAPP(c_List_Ozip(U_17702,U_17702),U_17698),U_17700))))
        | ~ sP1124(U_17693,U_17702,U_17698,U_17700) )
    & ! [U_17693,U_17702,U_17698,U_17700] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17702)),U_17698) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17702)),U_17700)
        | ~ sP1124(U_17693,U_17702,U_17698,U_17700) )
    & ! [U_17701,U_17699,U_17703] :
        ( U_17699 = U_17701
        | sP1125(U_17701,U_17699,U_17703)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17703)),U_17699) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17703)),U_17701) )
    & ! [U_17693,U_17702,U_17698,U_17700] :
        ( sP1124(U_17693,U_17702,U_17698,U_17700)
        | U_17698 != U_17700 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1124,sP1125])],[f_4333_4]) ).

cnf(f_4333_6,plain,
    ( sP1124(U_17693,U_17702,U_17698,U_17700)
    | U_17698 != U_17700 ),
    inference(clausify,[status(thm)],[f_4333_5]) ).

cnf(f_4333_7,plain,
    ( U_17699 = U_17701
    | sP1125(U_17701,U_17699,U_17703)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17703)),U_17699) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17703)),U_17701) ),
    inference(clausify,[status(thm)],[f_4333_5]) ).

cnf(f_4333_8,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17702)),U_17698) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17702)),U_17700)
    | ~ sP1124(U_17693,U_17702,U_17698,U_17700) ),
    inference(clausify,[status(thm)],[f_4333_5]) ).

cnf(f_4333_9,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17702,U_17702,tc_HOL_Obool),c_fequal),U_17693))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17702,U_17702)),U_17693),hAPP(c_List_Oset(tc_prod(U_17702,U_17702)),hAPP(hAPP(c_List_Ozip(U_17702,U_17702),U_17698),U_17700))))
    | ~ sP1124(U_17693,U_17702,U_17698,U_17700) ),
    inference(clausify,[status(thm)],[f_4333_5]) ).

cnf(f_4333_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17703,U_17703)),sK448(U_17703,U_17701,U_17699)),hAPP(c_List_Oset(tc_prod(U_17703,U_17703)),hAPP(hAPP(c_List_Ozip(U_17703,U_17703),U_17699),U_17701))))
    | ~ sP1125(U_17701,U_17699,U_17703) ),
    inference(clausify,[status(thm)],[f_4333_5]) ).

cnf(f_4333_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17703,U_17703,tc_HOL_Obool),c_fequal),sK448(U_17703,U_17701,U_17699)))
    | ~ sP1125(U_17701,U_17699,U_17703) ),
    inference(clausify,[status(thm)],[f_4333_5]) ).

fof(f_4334_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_4334_2,plain,
    ! [U_17708,U_17707,U_17706,U_17705,U_17704] :
      ( ( ( hAPP(c_Map_Omap__of(U_17704,U_17706,hAPP(hAPP(c_List_Ozip(U_17704,U_17706),U_17705),U_17707)),U_17708) = c_Option_Ooption_ONone(U_17706)
          | hBOOL(hAPP(hAPP(c_member(U_17704),U_17708),hAPP(c_List_Oset(U_17704),U_17705))) )
        & ( ~ hBOOL(hAPP(hAPP(c_member(U_17704),U_17708),hAPP(c_List_Oset(U_17704),U_17705)))
          | hAPP(c_Map_Omap__of(U_17704,U_17706,hAPP(hAPP(c_List_Ozip(U_17704,U_17706),U_17705),U_17707)),U_17708) != c_Option_Ooption_ONone(U_17706) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17704)),U_17705) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17706)),U_17707) ),
    inference(variable_rename,[status(thm)],[f_4334_1]) ).

fof(f_4334_3,plain,
    ( ! [U_17704,U_17705,U_17707,U_17706,U_17708] :
        ( hAPP(c_Map_Omap__of(U_17704,U_17706,hAPP(hAPP(c_List_Ozip(U_17704,U_17706),U_17705),U_17707)),U_17708) = c_Option_Ooption_ONone(U_17706)
        | hBOOL(hAPP(hAPP(c_member(U_17704),U_17708),hAPP(c_List_Oset(U_17704),U_17705)))
        | ~ sP1126(U_17704,U_17705,U_17707,U_17706,U_17708) )
    & ! [U_17704,U_17705,U_17707,U_17706,U_17708] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_17704),U_17708),hAPP(c_List_Oset(U_17704),U_17705)))
        | hAPP(c_Map_Omap__of(U_17704,U_17706,hAPP(hAPP(c_List_Ozip(U_17704,U_17706),U_17705),U_17707)),U_17708) != c_Option_Ooption_ONone(U_17706)
        | ~ sP1126(U_17704,U_17705,U_17707,U_17706,U_17708) )
    & ! [U_17704,U_17705,U_17707,U_17706,U_17708] :
        ( sP1126(U_17704,U_17705,U_17707,U_17706,U_17708)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17704)),U_17705) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17706)),U_17707) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1126])],[f_4334_2]) ).

cnf(f_4334_4,plain,
    ( sP1126(U_17704,U_17705,U_17707,U_17706,U_17708)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17704)),U_17705) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17706)),U_17707) ),
    inference(clausify,[status(thm)],[f_4334_3]) ).

cnf(f_4334_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_17704),U_17708),hAPP(c_List_Oset(U_17704),U_17705)))
    | hAPP(c_Map_Omap__of(U_17704,U_17706,hAPP(hAPP(c_List_Ozip(U_17704,U_17706),U_17705),U_17707)),U_17708) != c_Option_Ooption_ONone(U_17706)
    | ~ sP1126(U_17704,U_17705,U_17707,U_17706,U_17708) ),
    inference(clausify,[status(thm)],[f_4334_3]) ).

cnf(f_4334_6,plain,
    ( hAPP(c_Map_Omap__of(U_17704,U_17706,hAPP(hAPP(c_List_Ozip(U_17704,U_17706),U_17705),U_17707)),U_17708) = c_Option_Ooption_ONone(U_17706)
    | hBOOL(hAPP(hAPP(c_member(U_17704),U_17708),hAPP(c_List_Oset(U_17704),U_17705)))
    | ~ sP1126(U_17704,U_17705,U_17707,U_17706,U_17708) ),
    inference(clausify,[status(thm)],[f_4334_3]) ).

fof(f_4335_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_4335_2,plain,
    ! [U_17715,U_17714,U_17713,U_17712,U_17711] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_17711),U_17715),hAPP(c_List_Oset(U_17711),U_17712)))
          | ! [U_17710] : hAPP(c_Map_Omap__of(U_17711,U_17713,hAPP(hAPP(c_List_Ozip(U_17711,U_17713),U_17712),U_17714)),U_17715) != hAPP(c_Option_Ooption_OSome(U_17713),U_17710) )
        & ( ? [U_17709] : hAPP(c_Map_Omap__of(U_17711,U_17713,hAPP(hAPP(c_List_Ozip(U_17711,U_17713),U_17712),U_17714)),U_17715) = hAPP(c_Option_Ooption_OSome(U_17713),U_17709)
          | ~ hBOOL(hAPP(hAPP(c_member(U_17711),U_17715),hAPP(c_List_Oset(U_17711),U_17712))) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17711)),U_17712) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17713)),U_17714) ),
    inference(variable_rename,[status(thm)],[f_4335_1]) ).

fof(f_4335_3,plain,
    ! [U_17715,U_17714,U_17713,U_17712,U_17711] :
      ( ( ( hBOOL(hAPP(hAPP(c_member(U_17711),U_17715),hAPP(c_List_Oset(U_17711),U_17712)))
          | ! [U_17710] : hAPP(c_Map_Omap__of(U_17711,U_17713,hAPP(hAPP(c_List_Ozip(U_17711,U_17713),U_17712),U_17714)),U_17715) != hAPP(c_Option_Ooption_OSome(U_17713),U_17710) )
        & ( hAPP(c_Map_Omap__of(U_17711,U_17713,hAPP(hAPP(c_List_Ozip(U_17711,U_17713),U_17712),U_17714)),U_17715) = hAPP(c_Option_Ooption_OSome(U_17713),sK449(U_17715,U_17714,U_17713,U_17712,U_17711))
          | ~ hBOOL(hAPP(hAPP(c_member(U_17711),U_17715),hAPP(c_List_Oset(U_17711),U_17712))) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17711)),U_17712) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17713)),U_17714) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK449]),skolemize(U_17709,sK449(U_17715,U_17714,U_17713,U_17712,U_17711))],[f_4335_2]) ).

fof(f_4335_4,plain,
    ( ! [U_17712,U_17711,U_17710,U_17713,U_17714,U_17715] :
        ( hBOOL(hAPP(hAPP(c_member(U_17711),U_17715),hAPP(c_List_Oset(U_17711),U_17712)))
        | hAPP(c_Map_Omap__of(U_17711,U_17713,hAPP(hAPP(c_List_Ozip(U_17711,U_17713),U_17712),U_17714)),U_17715) != hAPP(c_Option_Ooption_OSome(U_17713),U_17710)
        | ~ sP1127(U_17712,U_17711,U_17710,U_17713,U_17714,U_17715) )
    & ! [U_17712,U_17711,U_17710,U_17713,U_17714,U_17715] :
        ( hAPP(c_Map_Omap__of(U_17711,U_17713,hAPP(hAPP(c_List_Ozip(U_17711,U_17713),U_17712),U_17714)),U_17715) = hAPP(c_Option_Ooption_OSome(U_17713),sK449(U_17715,U_17714,U_17713,U_17712,U_17711))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17711),U_17715),hAPP(c_List_Oset(U_17711),U_17712)))
        | ~ sP1127(U_17712,U_17711,U_17710,U_17713,U_17714,U_17715) )
    & ! [U_17712,U_17711,U_17710,U_17713,U_17714,U_17715] :
        ( sP1127(U_17712,U_17711,U_17710,U_17713,U_17714,U_17715)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17711)),U_17712) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17713)),U_17714) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1127])],[f_4335_3]) ).

cnf(f_4335_5,plain,
    ( sP1127(U_17712,U_17711,U_17710,U_17713,U_17714,U_17715)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17711)),U_17712) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17713)),U_17714) ),
    inference(clausify,[status(thm)],[f_4335_4]) ).

cnf(f_4335_6,plain,
    ( hAPP(c_Map_Omap__of(U_17711,U_17713,hAPP(hAPP(c_List_Ozip(U_17711,U_17713),U_17712),U_17714)),U_17715) = hAPP(c_Option_Ooption_OSome(U_17713),sK449(U_17715,U_17714,U_17713,U_17712,U_17711))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17711),U_17715),hAPP(c_List_Oset(U_17711),U_17712)))
    | ~ sP1127(U_17712,U_17711,U_17710,U_17713,U_17714,U_17715) ),
    inference(clausify,[status(thm)],[f_4335_4]) ).

cnf(f_4335_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17711),U_17715),hAPP(c_List_Oset(U_17711),U_17712)))
    | hAPP(c_Map_Omap__of(U_17711,U_17713,hAPP(hAPP(c_List_Ozip(U_17711,U_17713),U_17712),U_17714)),U_17715) != hAPP(c_Option_Ooption_OSome(U_17713),U_17710)
    | ~ sP1127(U_17712,U_17711,U_17710,U_17713,U_17714,U_17715) ),
    inference(clausify,[status(thm)],[f_4335_4]) ).

fof(f_4336_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_4336_2,plain,
    ! [U_17718,U_17717,U_17716] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17716)),c_List_Oremove1(U_17716,U_17717,U_17718)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17716)),U_17718)
        | hBOOL(hAPP(hAPP(c_member(U_17716),U_17717),hAPP(c_List_Oset(U_17716),U_17718))) )
      & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17716)),c_List_Oremove1(U_17716,U_17717,U_17718)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17716)),U_17718)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17716),U_17717),hAPP(c_List_Oset(U_17716),U_17718))) ) ),
    inference(variable_rename,[status(thm)],[f_4336_1]) ).

fof(f_4336_3,plain,
    ( ! [U_17724,U_17722,U_17720] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17720)),c_List_Oremove1(U_17720,U_17722,U_17724)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17720)),U_17724)
        | hBOOL(hAPP(hAPP(c_member(U_17720),U_17722),hAPP(c_List_Oset(U_17720),U_17724))) )
    & ! [U_17723,U_17721,U_17719] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17719)),c_List_Oremove1(U_17719,U_17721,U_17723)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17719)),U_17723)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17719),U_17721),hAPP(c_List_Oset(U_17719),U_17723))) ) ),
    inference(miniscope,[status(thm)],[f_4336_2]) ).

fof(f_4336_4,plain,
    ( ! [U_17720,U_17722,U_17724] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17720)),c_List_Oremove1(U_17720,U_17722,U_17724)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17720)),U_17724)
        | hBOOL(hAPP(hAPP(c_member(U_17720),U_17722),hAPP(c_List_Oset(U_17720),U_17724))) )
    & ! [U_17719,U_17723,U_17721] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17719)),c_List_Oremove1(U_17719,U_17721,U_17723)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17719)),U_17723)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ hBOOL(hAPP(hAPP(c_member(U_17719),U_17721),hAPP(c_List_Oset(U_17719),U_17723))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4336_3]) ).

cnf(f_4336_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17719)),c_List_Oremove1(U_17719,U_17721,U_17723)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17719)),U_17723)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17719),U_17721),hAPP(c_List_Oset(U_17719),U_17723))) ),
    inference(clausify,[status(thm)],[f_4336_4]) ).

cnf(f_4336_6,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17720)),c_List_Oremove1(U_17720,U_17722,U_17724)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17720)),U_17724)
    | hBOOL(hAPP(hAPP(c_member(U_17720),U_17722),hAPP(c_List_Oset(U_17720),U_17724))) ),
    inference(clausify,[status(thm)],[f_4336_4]) ).

fof(f_4337_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_4337_2,plain,
    ! [U_17728,U_17727,U_17726,U_17725] :
      ( c_Map_Odom(U_17725,U_17727,c_Map_Omap__of(U_17725,U_17727,hAPP(hAPP(c_List_Ozip(U_17725,U_17727),U_17726),U_17728))) = hAPP(c_List_Oset(U_17725),U_17726)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17725),U_17726))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17725)),U_17726) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17727)),U_17728) ),
    inference(variable_rename,[status(thm)],[f_4337_1]) ).

fof(f_4337_3,plain,
    ! [U_17725,U_17726,U_17727,U_17728] :
      ( c_Map_Odom(U_17725,U_17727,c_Map_Omap__of(U_17725,U_17727,hAPP(hAPP(c_List_Ozip(U_17725,U_17727),U_17726),U_17728))) = hAPP(c_List_Oset(U_17725),U_17726)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17725),U_17726))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17725)),U_17726) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17727)),U_17728) ),
    inference(definitional_conversion,[status(esa)],[f_4337_2]) ).

cnf(f_4337_4,plain,
    ( c_Map_Odom(U_17725,U_17727,c_Map_Omap__of(U_17725,U_17727,hAPP(hAPP(c_List_Ozip(U_17725,U_17727),U_17726),U_17728))) = hAPP(c_List_Oset(U_17725),U_17726)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17725),U_17726))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17725)),U_17726) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17727)),U_17728) ),
    inference(clausify,[status(thm)],[f_4337_3]) ).

fof(f_4338_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_4338_2,plain,
    ! [U_17731,U_17730,U_17729] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_17729)),hAPP(c_Set_OCollect(tc_List_Olist(U_17729)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17729),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_17729)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17729),tc_fun(U_17729,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17729,tc_HOL_Obool),tc_fun(tc_fun(U_17729,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17729)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_17729,tc_HOL_Obool))),c_List_Oset(U_17729))),U_17730))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17729),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_17729)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17729)))),U_17731)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17729),U_17730)) ),
    inference(variable_rename,[status(thm)],[f_4338_1]) ).

fof(f_4338_3,plain,
    ! [U_17729,U_17730,U_17731] :
      ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_17729)),hAPP(c_Set_OCollect(tc_List_Olist(U_17729)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17729),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_17729)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17729),tc_fun(U_17729,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17729,tc_HOL_Obool),tc_fun(tc_fun(U_17729,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17729)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_17729,tc_HOL_Obool))),c_List_Oset(U_17729))),U_17730))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17729),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_17729)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17729)))),U_17731)))))
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17729),U_17730)) ),
    inference(definitional_conversion,[status(esa)],[f_4338_2]) ).

cnf(f_4338_4,plain,
    ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_List_Olist(U_17729)),hAPP(c_Set_OCollect(tc_List_Olist(U_17729)),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17729),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_17729)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17729),tc_fun(U_17729,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17729,tc_HOL_Obool),tc_fun(tc_fun(U_17729,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17729)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_17729,tc_HOL_Obool))),c_List_Oset(U_17729))),U_17730))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17729),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_17729)),c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_17729)))),U_17731)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17729),U_17730)) ),
    inference(clausify,[status(thm)],[f_4338_3]) ).

fof(f_4339_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_4339_2,plain,
    ! [U_17733,U_17732] :
      ( ( c_Nitpick_Ocard_H(U_17732,U_17733) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_17732),U_17733)) )
      & ( c_Nitpick_Ocard_H(U_17732,U_17733) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17732)),c_Hilbert__Choice_OEps(tc_List_Olist(U_17732),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17732),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_17732)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17732),tc_fun(U_17732,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17732,tc_HOL_Obool),tc_fun(tc_fun(U_17732,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17732)),c_fequal),c_List_Oset(U_17732))),U_17733))),c_List_Odistinct(U_17732))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17732),U_17733)) ) ),
    inference(variable_rename,[status(thm)],[f_4339_1]) ).

fof(f_4339_3,plain,
    ( ! [U_17737,U_17735] :
        ( c_Nitpick_Ocard_H(U_17735,U_17737) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_17735),U_17737)) )
    & ! [U_17736,U_17734] :
        ( c_Nitpick_Ocard_H(U_17734,U_17736) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17734)),c_Hilbert__Choice_OEps(tc_List_Olist(U_17734),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17734),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_17734)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17734),tc_fun(U_17734,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17734,tc_HOL_Obool),tc_fun(tc_fun(U_17734,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17734)),c_fequal),c_List_Oset(U_17734))),U_17736))),c_List_Odistinct(U_17734))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17734),U_17736)) ) ),
    inference(miniscope,[status(thm)],[f_4339_2]) ).

fof(f_4339_4,plain,
    ( ! [U_17735,U_17737] :
        ( c_Nitpick_Ocard_H(U_17735,U_17737) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_17735),U_17737)) )
    & ! [U_17736,U_17734] :
        ( c_Nitpick_Ocard_H(U_17734,U_17736) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17734)),c_Hilbert__Choice_OEps(tc_List_Olist(U_17734),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17734),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_17734)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17734),tc_fun(U_17734,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17734,tc_HOL_Obool),tc_fun(tc_fun(U_17734,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17734)),c_fequal),c_List_Oset(U_17734))),U_17736))),c_List_Odistinct(U_17734))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17734),U_17736)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4339_3]) ).

cnf(f_4339_5,plain,
    ( c_Nitpick_Ocard_H(U_17734,U_17736) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17734)),c_Hilbert__Choice_OEps(tc_List_Olist(U_17734),hAPP(hAPP(c_COMBS(tc_List_Olist(U_17734),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_17734)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17734),tc_fun(U_17734,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_17734,tc_HOL_Obool),tc_fun(tc_fun(U_17734,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_17734)),c_fequal),c_List_Oset(U_17734))),U_17736))),c_List_Odistinct(U_17734))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_17734),U_17736)) ),
    inference(clausify,[status(thm)],[f_4339_4]) ).

cnf(f_4339_6,plain,
    ( c_Nitpick_Ocard_H(U_17735,U_17737) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_17735),U_17737)) ),
    inference(clausify,[status(thm)],[f_4339_4]) ).

fof(f_4340_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_4340_2,plain,
    ! [U_17743,U_17742,U_17741,U_17740] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17740),tc_List_Olist(U_17740))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17740),tc_List_Olist(U_17740)),U_17741),U_17742)),c_List_Olistrel(U_17740,U_17743)))
        | ? [U_17739] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17740,U_17740,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17740,tc_fun(tc_prod(U_17740,U_17740),tc_HOL_Obool),tc_fun(U_17740,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17740,tc_fun(tc_fun(tc_prod(U_17740,U_17740),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17740,U_17740),tc_HOL_Obool),tc_fun(U_17740,tc_HOL_Obool)),U_17740),c_COMBC(U_17740,tc_fun(tc_prod(U_17740,U_17740),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17740,tc_prod(U_17740,U_17740)),tc_fun(U_17740,tc_fun(tc_fun(tc_prod(U_17740,U_17740),tc_HOL_Obool),tc_HOL_Obool)),U_17740),hAPP(c_COMBB(tc_prod(U_17740,U_17740),tc_fun(tc_fun(tc_prod(U_17740,U_17740),tc_HOL_Obool),tc_HOL_Obool),U_17740),c_member(tc_prod(U_17740,U_17740)))),c_Product__Type_OPair(U_17740,U_17740)))),U_17743)),U_17739))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17740,U_17740)),U_17739),hAPP(c_List_Oset(tc_prod(U_17740,U_17740)),hAPP(hAPP(c_List_Ozip(U_17740,U_17740),U_17741),U_17742)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17740)),U_17741) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17740)),U_17742) )
      & ( ( ! [U_17738] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17740,U_17740,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17740,tc_fun(tc_prod(U_17740,U_17740),tc_HOL_Obool),tc_fun(U_17740,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17740,tc_fun(tc_fun(tc_prod(U_17740,U_17740),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17740,U_17740),tc_HOL_Obool),tc_fun(U_17740,tc_HOL_Obool)),U_17740),c_COMBC(U_17740,tc_fun(tc_prod(U_17740,U_17740),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17740,tc_prod(U_17740,U_17740)),tc_fun(U_17740,tc_fun(tc_fun(tc_prod(U_17740,U_17740),tc_HOL_Obool),tc_HOL_Obool)),U_17740),hAPP(c_COMBB(tc_prod(U_17740,U_17740),tc_fun(tc_fun(tc_prod(U_17740,U_17740),tc_HOL_Obool),tc_HOL_Obool),U_17740),c_member(tc_prod(U_17740,U_17740)))),c_Product__Type_OPair(U_17740,U_17740)))),U_17743)),U_17738))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17740,U_17740)),U_17738),hAPP(c_List_Oset(tc_prod(U_17740,U_17740)),hAPP(hAPP(c_List_Ozip(U_17740,U_17740),U_17741),U_17742)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17740)),U_17741) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17740)),U_17742) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17740),tc_List_Olist(U_17740))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17740),tc_List_Olist(U_17740)),U_17741),U_17742)),c_List_Olistrel(U_17740,U_17743))) ) ),
    inference(variable_rename,[status(thm)],[f_4340_1]) ).

fof(f_4340_3,plain,
    ( ! [U_17751,U_17749,U_17747,U_17745] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17745),tc_List_Olist(U_17745))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17745),tc_List_Olist(U_17745)),U_17747),U_17749)),c_List_Olistrel(U_17745,U_17751)))
        | ? [U_17739] :
            ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17745,U_17745,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17745,tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_fun(U_17745,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17745,tc_fun(tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_fun(U_17745,tc_HOL_Obool)),U_17745),c_COMBC(U_17745,tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17745,tc_prod(U_17745,U_17745)),tc_fun(U_17745,tc_fun(tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_HOL_Obool)),U_17745),hAPP(c_COMBB(tc_prod(U_17745,U_17745),tc_fun(tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_HOL_Obool),U_17745),c_member(tc_prod(U_17745,U_17745)))),c_Product__Type_OPair(U_17745,U_17745)))),U_17751)),U_17739))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17745,U_17745)),U_17739),hAPP(c_List_Oset(tc_prod(U_17745,U_17745)),hAPP(hAPP(c_List_Ozip(U_17745,U_17745),U_17747),U_17749)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17745)),U_17747) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17745)),U_17749) )
    & ! [U_17750,U_17748,U_17746,U_17744] :
        ( ( ! [U_17738] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17744,U_17744,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17744,tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_fun(U_17744,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17744,tc_fun(tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_fun(U_17744,tc_HOL_Obool)),U_17744),c_COMBC(U_17744,tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17744,tc_prod(U_17744,U_17744)),tc_fun(U_17744,tc_fun(tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_HOL_Obool)),U_17744),hAPP(c_COMBB(tc_prod(U_17744,U_17744),tc_fun(tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_HOL_Obool),U_17744),c_member(tc_prod(U_17744,U_17744)))),c_Product__Type_OPair(U_17744,U_17744)))),U_17750)),U_17738))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17744,U_17744)),U_17738),hAPP(c_List_Oset(tc_prod(U_17744,U_17744)),hAPP(hAPP(c_List_Ozip(U_17744,U_17744),U_17746),U_17748)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17744)),U_17746) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17744)),U_17748) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17744),tc_List_Olist(U_17744))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17744),tc_List_Olist(U_17744)),U_17746),U_17748)),c_List_Olistrel(U_17744,U_17750))) ) ),
    inference(miniscope,[status(thm)],[f_4340_2]) ).

fof(f_4340_4,plain,
    ( ! [U_17751,U_17749,U_17747,U_17745] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17745),tc_List_Olist(U_17745))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17745),tc_List_Olist(U_17745)),U_17747),U_17749)),c_List_Olistrel(U_17745,U_17751)))
        | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17745,U_17745,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17745,tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_fun(U_17745,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17745,tc_fun(tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_fun(U_17745,tc_HOL_Obool)),U_17745),c_COMBC(U_17745,tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17745,tc_prod(U_17745,U_17745)),tc_fun(U_17745,tc_fun(tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_HOL_Obool)),U_17745),hAPP(c_COMBB(tc_prod(U_17745,U_17745),tc_fun(tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_HOL_Obool),U_17745),c_member(tc_prod(U_17745,U_17745)))),c_Product__Type_OPair(U_17745,U_17745)))),U_17751)),sK450(U_17751,U_17749,U_17747,U_17745)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17745,U_17745)),sK450(U_17751,U_17749,U_17747,U_17745)),hAPP(c_List_Oset(tc_prod(U_17745,U_17745)),hAPP(hAPP(c_List_Ozip(U_17745,U_17745),U_17747),U_17749)))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17745)),U_17747) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17745)),U_17749) )
    & ! [U_17750,U_17748,U_17746,U_17744] :
        ( ( ! [U_17738] :
              ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17744,U_17744,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17744,tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_fun(U_17744,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17744,tc_fun(tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_fun(U_17744,tc_HOL_Obool)),U_17744),c_COMBC(U_17744,tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17744,tc_prod(U_17744,U_17744)),tc_fun(U_17744,tc_fun(tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_HOL_Obool)),U_17744),hAPP(c_COMBB(tc_prod(U_17744,U_17744),tc_fun(tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_HOL_Obool),U_17744),c_member(tc_prod(U_17744,U_17744)))),c_Product__Type_OPair(U_17744,U_17744)))),U_17750)),U_17738))
              | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17744,U_17744)),U_17738),hAPP(c_List_Oset(tc_prod(U_17744,U_17744)),hAPP(hAPP(c_List_Ozip(U_17744,U_17744),U_17746),U_17748)))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17744)),U_17746) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17744)),U_17748) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17744),tc_List_Olist(U_17744))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17744),tc_List_Olist(U_17744)),U_17746),U_17748)),c_List_Olistrel(U_17744,U_17750))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK450]),skolemize(U_17739,sK450(U_17751,U_17749,U_17747,U_17745))],[f_4340_3]) ).

fof(f_4340_5,plain,
    ( ! [U_17749,U_17747,U_17745,U_17751] :
        ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17745,U_17745,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17745,tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_fun(U_17745,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17745,tc_fun(tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_fun(U_17745,tc_HOL_Obool)),U_17745),c_COMBC(U_17745,tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17745,tc_prod(U_17745,U_17745)),tc_fun(U_17745,tc_fun(tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_HOL_Obool)),U_17745),hAPP(c_COMBB(tc_prod(U_17745,U_17745),tc_fun(tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_HOL_Obool),U_17745),c_member(tc_prod(U_17745,U_17745)))),c_Product__Type_OPair(U_17745,U_17745)))),U_17751)),sK450(U_17751,U_17749,U_17747,U_17745)))
        | ~ sP1129(U_17749,U_17747,U_17745,U_17751) )
    & ! [U_17749,U_17747,U_17745,U_17751] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17745,U_17745)),sK450(U_17751,U_17749,U_17747,U_17745)),hAPP(c_List_Oset(tc_prod(U_17745,U_17745)),hAPP(hAPP(c_List_Ozip(U_17745,U_17745),U_17747),U_17749))))
        | ~ sP1129(U_17749,U_17747,U_17745,U_17751) )
    & ! [U_17738,U_17746,U_17744,U_17748,U_17750] :
        ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17744,U_17744,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17744,tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_fun(U_17744,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17744,tc_fun(tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_fun(U_17744,tc_HOL_Obool)),U_17744),c_COMBC(U_17744,tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17744,tc_prod(U_17744,U_17744)),tc_fun(U_17744,tc_fun(tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_HOL_Obool)),U_17744),hAPP(c_COMBB(tc_prod(U_17744,U_17744),tc_fun(tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_HOL_Obool),U_17744),c_member(tc_prod(U_17744,U_17744)))),c_Product__Type_OPair(U_17744,U_17744)))),U_17750)),U_17738))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17744,U_17744)),U_17738),hAPP(c_List_Oset(tc_prod(U_17744,U_17744)),hAPP(hAPP(c_List_Ozip(U_17744,U_17744),U_17746),U_17748))))
        | ~ sP1128(U_17738,U_17746,U_17744,U_17748,U_17750) )
    & ! [U_17738,U_17746,U_17744,U_17748,U_17750] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17744)),U_17746) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17744)),U_17748)
        | ~ sP1128(U_17738,U_17746,U_17744,U_17748,U_17750) )
    & ! [U_17749,U_17747,U_17745,U_17751] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17745),tc_List_Olist(U_17745))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17745),tc_List_Olist(U_17745)),U_17747),U_17749)),c_List_Olistrel(U_17745,U_17751)))
        | sP1129(U_17749,U_17747,U_17745,U_17751)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17745)),U_17747) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17745)),U_17749) )
    & ! [U_17738,U_17746,U_17744,U_17748,U_17750] :
        ( sP1128(U_17738,U_17746,U_17744,U_17748,U_17750)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17744),tc_List_Olist(U_17744))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17744),tc_List_Olist(U_17744)),U_17746),U_17748)),c_List_Olistrel(U_17744,U_17750))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1128,sP1129])],[f_4340_4]) ).

cnf(f_4340_6,plain,
    ( sP1128(U_17738,U_17746,U_17744,U_17748,U_17750)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17744),tc_List_Olist(U_17744))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17744),tc_List_Olist(U_17744)),U_17746),U_17748)),c_List_Olistrel(U_17744,U_17750))) ),
    inference(clausify,[status(thm)],[f_4340_5]) ).

cnf(f_4340_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17745),tc_List_Olist(U_17745))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17745),tc_List_Olist(U_17745)),U_17747),U_17749)),c_List_Olistrel(U_17745,U_17751)))
    | sP1129(U_17749,U_17747,U_17745,U_17751)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17745)),U_17747) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17745)),U_17749) ),
    inference(clausify,[status(thm)],[f_4340_5]) ).

cnf(f_4340_8,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17744)),U_17746) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17744)),U_17748)
    | ~ sP1128(U_17738,U_17746,U_17744,U_17748,U_17750) ),
    inference(clausify,[status(thm)],[f_4340_5]) ).

cnf(f_4340_9,plain,
    ( hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17744,U_17744,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17744,tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_fun(U_17744,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17744,tc_fun(tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_fun(U_17744,tc_HOL_Obool)),U_17744),c_COMBC(U_17744,tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17744,tc_prod(U_17744,U_17744)),tc_fun(U_17744,tc_fun(tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_HOL_Obool)),U_17744),hAPP(c_COMBB(tc_prod(U_17744,U_17744),tc_fun(tc_fun(tc_prod(U_17744,U_17744),tc_HOL_Obool),tc_HOL_Obool),U_17744),c_member(tc_prod(U_17744,U_17744)))),c_Product__Type_OPair(U_17744,U_17744)))),U_17750)),U_17738))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17744,U_17744)),U_17738),hAPP(c_List_Oset(tc_prod(U_17744,U_17744)),hAPP(hAPP(c_List_Ozip(U_17744,U_17744),U_17746),U_17748))))
    | ~ sP1128(U_17738,U_17746,U_17744,U_17748,U_17750) ),
    inference(clausify,[status(thm)],[f_4340_5]) ).

cnf(f_4340_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17745,U_17745)),sK450(U_17751,U_17749,U_17747,U_17745)),hAPP(c_List_Oset(tc_prod(U_17745,U_17745)),hAPP(hAPP(c_List_Ozip(U_17745,U_17745),U_17747),U_17749))))
    | ~ sP1129(U_17749,U_17747,U_17745,U_17751) ),
    inference(clausify,[status(thm)],[f_4340_5]) ).

cnf(f_4340_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(U_17745,U_17745,tc_HOL_Obool),hAPP(hAPP(c_COMBC(U_17745,tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_fun(U_17745,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17745,tc_fun(tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_fun(U_17745,tc_HOL_Obool)),U_17745),c_COMBC(U_17745,tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17745,tc_prod(U_17745,U_17745)),tc_fun(U_17745,tc_fun(tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_HOL_Obool)),U_17745),hAPP(c_COMBB(tc_prod(U_17745,U_17745),tc_fun(tc_fun(tc_prod(U_17745,U_17745),tc_HOL_Obool),tc_HOL_Obool),U_17745),c_member(tc_prod(U_17745,U_17745)))),c_Product__Type_OPair(U_17745,U_17745)))),U_17751)),sK450(U_17751,U_17749,U_17747,U_17745)))
    | ~ sP1129(U_17749,U_17747,U_17745,U_17751) ),
    inference(clausify,[status(thm)],[f_4340_5]) ).

fof(f_4341_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_4341_2,plain,
    ! [U_17754,U_17753,U_17752] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17752),tc_List_Olist(U_17752))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17752),tc_List_Olist(U_17752)),U_17753),U_17753)),c_List_Olistrel(U_17752,c_Transitive__Closure_Ortrancl(U_17752,U_17754)))),
    inference(variable_rename,[status(thm)],[f_4341_1]) ).

fof(f_4341_3,plain,
    ! [U_17752,U_17753,U_17754] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17752),tc_List_Olist(U_17752))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17752),tc_List_Olist(U_17752)),U_17753),U_17753)),c_List_Olistrel(U_17752,c_Transitive__Closure_Ortrancl(U_17752,U_17754)))),
    inference(definitional_conversion,[status(esa)],[f_4341_2]) ).

cnf(f_4341_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17752),tc_List_Olist(U_17752))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17752),tc_List_Olist(U_17752)),U_17753),U_17753)),c_List_Olistrel(U_17752,c_Transitive__Closure_Ortrancl(U_17752,U_17754)))),
    inference(clausify,[status(thm)],[f_4341_3]) ).

fof(f_4342_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_4342_2,plain,
    ! [U_17758,U_17757,U_17756,U_17755] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17755)),U_17756) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17755)),U_17757)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17755),tc_List_Olist(U_17755))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17755),tc_List_Olist(U_17755)),U_17756),U_17757)),c_List_Olistrel(U_17755,U_17758))) ),
    inference(variable_rename,[status(thm)],[f_4342_1]) ).

fof(f_4342_3,plain,
    ! [U_17755,U_17756,U_17757,U_17758] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17755)),U_17756) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17755)),U_17757)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17755),tc_List_Olist(U_17755))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17755),tc_List_Olist(U_17755)),U_17756),U_17757)),c_List_Olistrel(U_17755,U_17758))) ),
    inference(definitional_conversion,[status(esa)],[f_4342_2]) ).

cnf(f_4342_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17755)),U_17756) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17755)),U_17757)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17755),tc_List_Olist(U_17755))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17755),tc_List_Olist(U_17755)),U_17756),U_17757)),c_List_Olistrel(U_17755,U_17758))) ),
    inference(clausify,[status(thm)],[f_4342_3]) ).

fof(f_4343_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_4343_2,plain,
    ! [U_17763,U_17762,U_17761,U_17760,U_17759] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17759),tc_List_Olist(U_17759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17759),tc_List_Olist(U_17759)),U_17760),U_17763)),c_List_Olistrel(U_17759,c_Transitive__Closure_Ortrancl(U_17759,U_17762))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17759),tc_List_Olist(U_17759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17759),tc_List_Olist(U_17759)),U_17761),U_17763)),c_List_Olistrel(U_17759,c_Transitive__Closure_Ortrancl(U_17759,U_17762))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17759),tc_List_Olist(U_17759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17759),tc_List_Olist(U_17759)),U_17760),U_17761)),c_List_Olistrel(U_17759,c_Transitive__Closure_Ortrancl(U_17759,U_17762)))) ),
    inference(variable_rename,[status(thm)],[f_4343_1]) ).

fof(f_4343_3,plain,
    ! [U_17759,U_17760,U_17761,U_17762,U_17763] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17759),tc_List_Olist(U_17759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17759),tc_List_Olist(U_17759)),U_17760),U_17763)),c_List_Olistrel(U_17759,c_Transitive__Closure_Ortrancl(U_17759,U_17762))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17759),tc_List_Olist(U_17759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17759),tc_List_Olist(U_17759)),U_17761),U_17763)),c_List_Olistrel(U_17759,c_Transitive__Closure_Ortrancl(U_17759,U_17762))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17759),tc_List_Olist(U_17759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17759),tc_List_Olist(U_17759)),U_17760),U_17761)),c_List_Olistrel(U_17759,c_Transitive__Closure_Ortrancl(U_17759,U_17762)))) ),
    inference(definitional_conversion,[status(esa)],[f_4343_2]) ).

cnf(f_4343_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17759),tc_List_Olist(U_17759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17759),tc_List_Olist(U_17759)),U_17760),U_17763)),c_List_Olistrel(U_17759,c_Transitive__Closure_Ortrancl(U_17759,U_17762))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17759),tc_List_Olist(U_17759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17759),tc_List_Olist(U_17759)),U_17761),U_17763)),c_List_Olistrel(U_17759,c_Transitive__Closure_Ortrancl(U_17759,U_17762))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17759),tc_List_Olist(U_17759))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17759),tc_List_Olist(U_17759)),U_17760),U_17761)),c_List_Olistrel(U_17759,c_Transitive__Closure_Ortrancl(U_17759,U_17762)))) ),
    inference(clausify,[status(thm)],[f_4343_3]) ).

fof(f_4344_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_4344_2,plain,
    ! [U_17766,U_17765,U_17764] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_17764),tc_List_Olist(U_17764)),tc_HOL_Obool)),c_List_Olistrel(U_17764,U_17765)),c_List_Olistrel(U_17764,U_17766)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_17764,U_17764),tc_HOL_Obool)),U_17765),U_17766)) ),
    inference(variable_rename,[status(thm)],[f_4344_1]) ).

fof(f_4344_3,plain,
    ! [U_17764,U_17765,U_17766] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_17764),tc_List_Olist(U_17764)),tc_HOL_Obool)),c_List_Olistrel(U_17764,U_17765)),c_List_Olistrel(U_17764,U_17766)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_17764,U_17764),tc_HOL_Obool)),U_17765),U_17766)) ),
    inference(definitional_conversion,[status(esa)],[f_4344_2]) ).

cnf(f_4344_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_17764),tc_List_Olist(U_17764)),tc_HOL_Obool)),c_List_Olistrel(U_17764,U_17765)),c_List_Olistrel(U_17764,U_17766)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_17764,U_17764),tc_HOL_Obool)),U_17765),U_17766)) ),
    inference(clausify,[status(thm)],[f_4344_3]) ).

fof(f_4345_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_4345_2,plain,
    ! [U_17770,U_17769,U_17768,U_17767] :
      ( ( c_List_Olistrelp(U_17767,hAPP(hAPP(c_COMBC(U_17767,tc_fun(tc_prod(U_17767,U_17767),tc_HOL_Obool),tc_fun(U_17767,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17767,tc_fun(tc_fun(tc_prod(U_17767,U_17767),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17767,U_17767),tc_HOL_Obool),tc_fun(U_17767,tc_HOL_Obool)),U_17767),c_COMBC(U_17767,tc_fun(tc_prod(U_17767,U_17767),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17767,tc_prod(U_17767,U_17767)),tc_fun(U_17767,tc_fun(tc_fun(tc_prod(U_17767,U_17767),tc_HOL_Obool),tc_HOL_Obool)),U_17767),hAPP(c_COMBB(tc_prod(U_17767,U_17767),tc_fun(tc_fun(tc_prod(U_17767,U_17767),tc_HOL_Obool),tc_HOL_Obool),U_17767),c_member(tc_prod(U_17767,U_17767)))),c_Product__Type_OPair(U_17767,U_17767)))),U_17768),U_17769,U_17770)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17767),tc_List_Olist(U_17767))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17767),tc_List_Olist(U_17767)),U_17769),U_17770)),c_List_Olistrel(U_17767,U_17768))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17767),tc_List_Olist(U_17767))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17767),tc_List_Olist(U_17767)),U_17769),U_17770)),c_List_Olistrel(U_17767,U_17768)))
        | ~ c_List_Olistrelp(U_17767,hAPP(hAPP(c_COMBC(U_17767,tc_fun(tc_prod(U_17767,U_17767),tc_HOL_Obool),tc_fun(U_17767,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17767,tc_fun(tc_fun(tc_prod(U_17767,U_17767),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17767,U_17767),tc_HOL_Obool),tc_fun(U_17767,tc_HOL_Obool)),U_17767),c_COMBC(U_17767,tc_fun(tc_prod(U_17767,U_17767),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17767,tc_prod(U_17767,U_17767)),tc_fun(U_17767,tc_fun(tc_fun(tc_prod(U_17767,U_17767),tc_HOL_Obool),tc_HOL_Obool)),U_17767),hAPP(c_COMBB(tc_prod(U_17767,U_17767),tc_fun(tc_fun(tc_prod(U_17767,U_17767),tc_HOL_Obool),tc_HOL_Obool),U_17767),c_member(tc_prod(U_17767,U_17767)))),c_Product__Type_OPair(U_17767,U_17767)))),U_17768),U_17769,U_17770) ) ),
    inference(variable_rename,[status(thm)],[f_4345_1]) ).

fof(f_4345_3,plain,
    ( ! [U_17778,U_17776,U_17774,U_17772] :
        ( c_List_Olistrelp(U_17772,hAPP(hAPP(c_COMBC(U_17772,tc_fun(tc_prod(U_17772,U_17772),tc_HOL_Obool),tc_fun(U_17772,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17772,tc_fun(tc_fun(tc_prod(U_17772,U_17772),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17772,U_17772),tc_HOL_Obool),tc_fun(U_17772,tc_HOL_Obool)),U_17772),c_COMBC(U_17772,tc_fun(tc_prod(U_17772,U_17772),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17772,tc_prod(U_17772,U_17772)),tc_fun(U_17772,tc_fun(tc_fun(tc_prod(U_17772,U_17772),tc_HOL_Obool),tc_HOL_Obool)),U_17772),hAPP(c_COMBB(tc_prod(U_17772,U_17772),tc_fun(tc_fun(tc_prod(U_17772,U_17772),tc_HOL_Obool),tc_HOL_Obool),U_17772),c_member(tc_prod(U_17772,U_17772)))),c_Product__Type_OPair(U_17772,U_17772)))),U_17774),U_17776,U_17778)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17772),tc_List_Olist(U_17772))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17772),tc_List_Olist(U_17772)),U_17776),U_17778)),c_List_Olistrel(U_17772,U_17774))) )
    & ! [U_17777,U_17775,U_17773,U_17771] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17771),tc_List_Olist(U_17771))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17771),tc_List_Olist(U_17771)),U_17775),U_17777)),c_List_Olistrel(U_17771,U_17773)))
        | ~ c_List_Olistrelp(U_17771,hAPP(hAPP(c_COMBC(U_17771,tc_fun(tc_prod(U_17771,U_17771),tc_HOL_Obool),tc_fun(U_17771,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17771,tc_fun(tc_fun(tc_prod(U_17771,U_17771),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17771,U_17771),tc_HOL_Obool),tc_fun(U_17771,tc_HOL_Obool)),U_17771),c_COMBC(U_17771,tc_fun(tc_prod(U_17771,U_17771),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17771,tc_prod(U_17771,U_17771)),tc_fun(U_17771,tc_fun(tc_fun(tc_prod(U_17771,U_17771),tc_HOL_Obool),tc_HOL_Obool)),U_17771),hAPP(c_COMBB(tc_prod(U_17771,U_17771),tc_fun(tc_fun(tc_prod(U_17771,U_17771),tc_HOL_Obool),tc_HOL_Obool),U_17771),c_member(tc_prod(U_17771,U_17771)))),c_Product__Type_OPair(U_17771,U_17771)))),U_17773),U_17775,U_17777) ) ),
    inference(miniscope,[status(thm)],[f_4345_2]) ).

fof(f_4345_4,plain,
    ( ! [U_17774,U_17772,U_17776,U_17778] :
        ( c_List_Olistrelp(U_17772,hAPP(hAPP(c_COMBC(U_17772,tc_fun(tc_prod(U_17772,U_17772),tc_HOL_Obool),tc_fun(U_17772,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17772,tc_fun(tc_fun(tc_prod(U_17772,U_17772),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17772,U_17772),tc_HOL_Obool),tc_fun(U_17772,tc_HOL_Obool)),U_17772),c_COMBC(U_17772,tc_fun(tc_prod(U_17772,U_17772),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17772,tc_prod(U_17772,U_17772)),tc_fun(U_17772,tc_fun(tc_fun(tc_prod(U_17772,U_17772),tc_HOL_Obool),tc_HOL_Obool)),U_17772),hAPP(c_COMBB(tc_prod(U_17772,U_17772),tc_fun(tc_fun(tc_prod(U_17772,U_17772),tc_HOL_Obool),tc_HOL_Obool),U_17772),c_member(tc_prod(U_17772,U_17772)))),c_Product__Type_OPair(U_17772,U_17772)))),U_17774),U_17776,U_17778)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17772),tc_List_Olist(U_17772))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17772),tc_List_Olist(U_17772)),U_17776),U_17778)),c_List_Olistrel(U_17772,U_17774))) )
    & ! [U_17773,U_17771,U_17775,U_17777] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17771),tc_List_Olist(U_17771))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17771),tc_List_Olist(U_17771)),U_17775),U_17777)),c_List_Olistrel(U_17771,U_17773)))
        | ~ c_List_Olistrelp(U_17771,hAPP(hAPP(c_COMBC(U_17771,tc_fun(tc_prod(U_17771,U_17771),tc_HOL_Obool),tc_fun(U_17771,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17771,tc_fun(tc_fun(tc_prod(U_17771,U_17771),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17771,U_17771),tc_HOL_Obool),tc_fun(U_17771,tc_HOL_Obool)),U_17771),c_COMBC(U_17771,tc_fun(tc_prod(U_17771,U_17771),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17771,tc_prod(U_17771,U_17771)),tc_fun(U_17771,tc_fun(tc_fun(tc_prod(U_17771,U_17771),tc_HOL_Obool),tc_HOL_Obool)),U_17771),hAPP(c_COMBB(tc_prod(U_17771,U_17771),tc_fun(tc_fun(tc_prod(U_17771,U_17771),tc_HOL_Obool),tc_HOL_Obool),U_17771),c_member(tc_prod(U_17771,U_17771)))),c_Product__Type_OPair(U_17771,U_17771)))),U_17773),U_17775,U_17777) ) ),
    inference(definitional_conversion,[status(esa)],[f_4345_3]) ).

cnf(f_4345_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17771),tc_List_Olist(U_17771))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17771),tc_List_Olist(U_17771)),U_17775),U_17777)),c_List_Olistrel(U_17771,U_17773)))
    | ~ c_List_Olistrelp(U_17771,hAPP(hAPP(c_COMBC(U_17771,tc_fun(tc_prod(U_17771,U_17771),tc_HOL_Obool),tc_fun(U_17771,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17771,tc_fun(tc_fun(tc_prod(U_17771,U_17771),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17771,U_17771),tc_HOL_Obool),tc_fun(U_17771,tc_HOL_Obool)),U_17771),c_COMBC(U_17771,tc_fun(tc_prod(U_17771,U_17771),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17771,tc_prod(U_17771,U_17771)),tc_fun(U_17771,tc_fun(tc_fun(tc_prod(U_17771,U_17771),tc_HOL_Obool),tc_HOL_Obool)),U_17771),hAPP(c_COMBB(tc_prod(U_17771,U_17771),tc_fun(tc_fun(tc_prod(U_17771,U_17771),tc_HOL_Obool),tc_HOL_Obool),U_17771),c_member(tc_prod(U_17771,U_17771)))),c_Product__Type_OPair(U_17771,U_17771)))),U_17773),U_17775,U_17777) ),
    inference(clausify,[status(thm)],[f_4345_4]) ).

cnf(f_4345_6,plain,
    ( c_List_Olistrelp(U_17772,hAPP(hAPP(c_COMBC(U_17772,tc_fun(tc_prod(U_17772,U_17772),tc_HOL_Obool),tc_fun(U_17772,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17772,tc_fun(tc_fun(tc_prod(U_17772,U_17772),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(U_17772,U_17772),tc_HOL_Obool),tc_fun(U_17772,tc_HOL_Obool)),U_17772),c_COMBC(U_17772,tc_fun(tc_prod(U_17772,U_17772),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_17772,tc_prod(U_17772,U_17772)),tc_fun(U_17772,tc_fun(tc_fun(tc_prod(U_17772,U_17772),tc_HOL_Obool),tc_HOL_Obool)),U_17772),hAPP(c_COMBB(tc_prod(U_17772,U_17772),tc_fun(tc_fun(tc_prod(U_17772,U_17772),tc_HOL_Obool),tc_HOL_Obool),U_17772),c_member(tc_prod(U_17772,U_17772)))),c_Product__Type_OPair(U_17772,U_17772)))),U_17774),U_17776,U_17778)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17772),tc_List_Olist(U_17772))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17772),tc_List_Olist(U_17772)),U_17776),U_17778)),c_List_Olistrel(U_17772,U_17774))) ),
    inference(clausify,[status(thm)],[f_4345_4]) ).

fof(f_4346_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_4346_2,plain,
    ! [U_17781,U_17780,U_17779] : hAPP(c_List_Olexn(U_17779,U_17780),hAPP(c_Nat_OSuc,U_17781)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(U_17779),tc_List_Olist(U_17779)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(U_17779,tc_List_Olist(U_17779)),tc_prod(U_17779,tc_List_Olist(U_17779))),tc_prod(tc_List_Olist(U_17779),tc_List_Olist(U_17779)),c_Product__Type_Omap__pair(tc_prod(U_17779,tc_List_Olist(U_17779)),tc_List_Olist(U_17779),tc_prod(U_17779,tc_List_Olist(U_17779)),tc_List_Olist(U_17779),hAPP(c_Product__Type_Oprod_Oprod__case(U_17779,tc_List_Olist(U_17779),tc_List_Olist(U_17779)),c_List_Olist_OCons(U_17779)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17779,tc_List_Olist(U_17779),tc_List_Olist(U_17779)),c_List_Olist_OCons(U_17779)))),c_Wellfounded_Olex__prod(U_17779,tc_List_Olist(U_17779),U_17780,hAPP(c_List_Olexn(U_17779,U_17780),U_17781)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_17779),tc_List_Olist(U_17779))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17779),tc_List_Olist(U_17779),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17779),tc_fun(tc_List_Olist(U_17779),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17779),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17779),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17779),tc_HOL_Obool)),tc_List_Olist(U_17779)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17779))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17779)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17779),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_17779)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17779)))),hAPP(c_Nat_OSuc,U_17781))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17779),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_17779)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17779)))),hAPP(c_Nat_OSuc,U_17781)))))),
    inference(variable_rename,[status(thm)],[f_4346_1]) ).

fof(f_4346_3,plain,
    ! [U_17779,U_17780,U_17781] : hAPP(c_List_Olexn(U_17779,U_17780),hAPP(c_Nat_OSuc,U_17781)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(U_17779),tc_List_Olist(U_17779)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(U_17779,tc_List_Olist(U_17779)),tc_prod(U_17779,tc_List_Olist(U_17779))),tc_prod(tc_List_Olist(U_17779),tc_List_Olist(U_17779)),c_Product__Type_Omap__pair(tc_prod(U_17779,tc_List_Olist(U_17779)),tc_List_Olist(U_17779),tc_prod(U_17779,tc_List_Olist(U_17779)),tc_List_Olist(U_17779),hAPP(c_Product__Type_Oprod_Oprod__case(U_17779,tc_List_Olist(U_17779),tc_List_Olist(U_17779)),c_List_Olist_OCons(U_17779)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17779,tc_List_Olist(U_17779),tc_List_Olist(U_17779)),c_List_Olist_OCons(U_17779)))),c_Wellfounded_Olex__prod(U_17779,tc_List_Olist(U_17779),U_17780,hAPP(c_List_Olexn(U_17779,U_17780),U_17781)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_17779),tc_List_Olist(U_17779))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17779),tc_List_Olist(U_17779),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17779),tc_fun(tc_List_Olist(U_17779),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17779),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17779),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17779),tc_HOL_Obool)),tc_List_Olist(U_17779)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17779))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17779)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17779),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_17779)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17779)))),hAPP(c_Nat_OSuc,U_17781))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17779),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_17779)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17779)))),hAPP(c_Nat_OSuc,U_17781)))))),
    inference(definitional_conversion,[status(esa)],[f_4346_2]) ).

cnf(f_4346_4,plain,
    hAPP(c_List_Olexn(U_17779,U_17780),hAPP(c_Nat_OSuc,U_17781)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(tc_List_Olist(U_17779),tc_List_Olist(U_17779)),tc_HOL_Obool)),hAPP(c_Set_Oimage(tc_prod(tc_prod(U_17779,tc_List_Olist(U_17779)),tc_prod(U_17779,tc_List_Olist(U_17779))),tc_prod(tc_List_Olist(U_17779),tc_List_Olist(U_17779)),c_Product__Type_Omap__pair(tc_prod(U_17779,tc_List_Olist(U_17779)),tc_List_Olist(U_17779),tc_prod(U_17779,tc_List_Olist(U_17779)),tc_List_Olist(U_17779),hAPP(c_Product__Type_Oprod_Oprod__case(U_17779,tc_List_Olist(U_17779),tc_List_Olist(U_17779)),c_List_Olist_OCons(U_17779)),hAPP(c_Product__Type_Oprod_Oprod__case(U_17779,tc_List_Olist(U_17779),tc_List_Olist(U_17779)),c_List_Olist_OCons(U_17779)))),c_Wellfounded_Olex__prod(U_17779,tc_List_Olist(U_17779),U_17780,hAPP(c_List_Olexn(U_17779,U_17780),U_17781)))),hAPP(c_Set_OCollect(tc_prod(tc_List_Olist(U_17779),tc_List_Olist(U_17779))),hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_17779),tc_List_Olist(U_17779),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17779),tc_fun(tc_List_Olist(U_17779),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17779),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17779),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17779),tc_HOL_Obool)),tc_List_Olist(U_17779)),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17779))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17779)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17779),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_17779)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17779)))),hAPP(c_Nat_OSuc,U_17781))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17779),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_17779)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_17779)))),hAPP(c_Nat_OSuc,U_17781)))))),
    inference(clausify,[status(thm)],[f_4346_3]) ).

fof(f_4347_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_4347_2,plain,
    ! [U_17785,U_17784,U_17783,U_17782] :
      ( U_17783 != hAPP(hAPP(c_List_Olist_OCons(U_17782),U_17785),U_17784)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17782)),U_17783)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17782)),U_17784))) ),
    inference(variable_rename,[status(thm)],[f_4347_1]) ).

fof(f_4347_3,plain,
    ! [U_17782,U_17783,U_17784,U_17785] :
      ( U_17783 != hAPP(hAPP(c_List_Olist_OCons(U_17782),U_17785),U_17784)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17782)),U_17783)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17782)),U_17784))) ),
    inference(definitional_conversion,[status(esa)],[f_4347_2]) ).

cnf(f_4347_4,plain,
    ( U_17783 != hAPP(hAPP(c_List_Olist_OCons(U_17782),U_17785),U_17784)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17782)),U_17783)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17782)),U_17784))) ),
    inference(clausify,[status(thm)],[f_4347_3]) ).

fof(f_4348_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_4348_2,plain,
    ! [U_17789,U_17788,U_17787,U_17786] :
      ( hBOOL(hAPP(hAPP(c_member(U_17786),U_17787),hAPP(c_List_Oset(U_17786),U_17789)))
      | U_17787 = U_17788
      | ~ hBOOL(hAPP(hAPP(c_member(U_17786),U_17787),hAPP(c_List_Oset(U_17786),hAPP(hAPP(c_List_Olist_OCons(U_17786),U_17788),U_17789)))) ),
    inference(variable_rename,[status(thm)],[f_4348_1]) ).

fof(f_4348_3,plain,
    ! [U_17786,U_17787,U_17788,U_17789] :
      ( hBOOL(hAPP(hAPP(c_member(U_17786),U_17787),hAPP(c_List_Oset(U_17786),U_17789)))
      | U_17787 = U_17788
      | ~ hBOOL(hAPP(hAPP(c_member(U_17786),U_17787),hAPP(c_List_Oset(U_17786),hAPP(hAPP(c_List_Olist_OCons(U_17786),U_17788),U_17789)))) ),
    inference(definitional_conversion,[status(esa)],[f_4348_2]) ).

cnf(f_4348_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17786),U_17787),hAPP(c_List_Oset(U_17786),U_17789)))
    | U_17787 = U_17788
    | ~ hBOOL(hAPP(hAPP(c_member(U_17786),U_17787),hAPP(c_List_Oset(U_17786),hAPP(hAPP(c_List_Olist_OCons(U_17786),U_17788),U_17789)))) ),
    inference(clausify,[status(thm)],[f_4348_3]) ).

fof(f_4349_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_4349_2,plain,
    ! [U_17795,U_17794,U_17793,U_17792,U_17791,U_17790] : hAPP(hAPP(c_List_Ozip(U_17790,U_17791),hAPP(hAPP(c_List_Olist_OCons(U_17790),U_17792),U_17793)),hAPP(hAPP(c_List_Olist_OCons(U_17791),U_17794),U_17795)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17790,U_17791)),hAPP(hAPP(c_Product__Type_OPair(U_17790,U_17791),U_17792),U_17794)),hAPP(hAPP(c_List_Ozip(U_17790,U_17791),U_17793),U_17795)),
    inference(variable_rename,[status(thm)],[f_4349_1]) ).

fof(f_4349_3,plain,
    ! [U_17794,U_17790,U_17791,U_17792,U_17793,U_17795] : hAPP(hAPP(c_List_Ozip(U_17790,U_17791),hAPP(hAPP(c_List_Olist_OCons(U_17790),U_17792),U_17793)),hAPP(hAPP(c_List_Olist_OCons(U_17791),U_17794),U_17795)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17790,U_17791)),hAPP(hAPP(c_Product__Type_OPair(U_17790,U_17791),U_17792),U_17794)),hAPP(hAPP(c_List_Ozip(U_17790,U_17791),U_17793),U_17795)),
    inference(definitional_conversion,[status(esa)],[f_4349_2]) ).

cnf(f_4349_4,plain,
    hAPP(hAPP(c_List_Ozip(U_17790,U_17791),hAPP(hAPP(c_List_Olist_OCons(U_17790),U_17792),U_17793)),hAPP(hAPP(c_List_Olist_OCons(U_17791),U_17794),U_17795)) = hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17790,U_17791)),hAPP(hAPP(c_Product__Type_OPair(U_17790,U_17791),U_17792),U_17794)),hAPP(hAPP(c_List_Ozip(U_17790,U_17791),U_17793),U_17795)),
    inference(clausify,[status(thm)],[f_4349_3]) ).

fof(f_4350_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_4350_2,plain,
    ! [U_17798,U_17797,U_17796] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17796,tc_HOL_Obool)),hAPP(c_List_Oset(U_17796),U_17797)),hAPP(c_List_Oset(U_17796),hAPP(hAPP(c_List_Olist_OCons(U_17796),U_17798),U_17797)))),
    inference(variable_rename,[status(thm)],[f_4350_1]) ).

fof(f_4350_3,plain,
    ! [U_17796,U_17797,U_17798] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17796,tc_HOL_Obool)),hAPP(c_List_Oset(U_17796),U_17797)),hAPP(c_List_Oset(U_17796),hAPP(hAPP(c_List_Olist_OCons(U_17796),U_17798),U_17797)))),
    inference(definitional_conversion,[status(esa)],[f_4350_2]) ).

cnf(f_4350_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17796,tc_HOL_Obool)),hAPP(c_List_Oset(U_17796),U_17797)),hAPP(c_List_Oset(U_17796),hAPP(hAPP(c_List_Olist_OCons(U_17796),U_17798),U_17797)))),
    inference(clausify,[status(thm)],[f_4350_3]) ).

fof(f_4351_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_4351_2,plain,
    ! [U_17801,U_17800,U_17799] : hAPP(c_List_Oset(U_17799),hAPP(hAPP(c_List_Olist_OCons(U_17799),U_17800),U_17801)) = hAPP(hAPP(c_Set_Oinsert(U_17799),U_17800),hAPP(c_List_Oset(U_17799),U_17801)),
    inference(variable_rename,[status(thm)],[f_4351_1]) ).

fof(f_4351_3,plain,
    ! [U_17799,U_17800,U_17801] : hAPP(c_List_Oset(U_17799),hAPP(hAPP(c_List_Olist_OCons(U_17799),U_17800),U_17801)) = hAPP(hAPP(c_Set_Oinsert(U_17799),U_17800),hAPP(c_List_Oset(U_17799),U_17801)),
    inference(definitional_conversion,[status(esa)],[f_4351_2]) ).

cnf(f_4351_4,plain,
    hAPP(c_List_Oset(U_17799),hAPP(hAPP(c_List_Olist_OCons(U_17799),U_17800),U_17801)) = hAPP(hAPP(c_Set_Oinsert(U_17799),U_17800),hAPP(c_List_Oset(U_17799),U_17801)),
    inference(clausify,[status(thm)],[f_4351_3]) ).

fof(f_4352_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_4352_2,plain,
    ! [U_17807,U_17806,U_17805,U_17804,U_17803,U_17802] : c_List_Ofoldr(U_17802,U_17803,U_17804,hAPP(hAPP(c_List_Olist_OCons(U_17802),U_17805),U_17806),U_17807) = hAPP(hAPP(U_17804,U_17805),c_List_Ofoldr(U_17802,U_17803,U_17804,U_17806,U_17807)),
    inference(variable_rename,[status(thm)],[f_4352_1]) ).

fof(f_4352_3,plain,
    ! [U_17802,U_17803,U_17804,U_17805,U_17806,U_17807] : c_List_Ofoldr(U_17802,U_17803,U_17804,hAPP(hAPP(c_List_Olist_OCons(U_17802),U_17805),U_17806),U_17807) = hAPP(hAPP(U_17804,U_17805),c_List_Ofoldr(U_17802,U_17803,U_17804,U_17806,U_17807)),
    inference(definitional_conversion,[status(esa)],[f_4352_2]) ).

cnf(f_4352_4,plain,
    c_List_Ofoldr(U_17802,U_17803,U_17804,hAPP(hAPP(c_List_Olist_OCons(U_17802),U_17805),U_17806),U_17807) = hAPP(hAPP(U_17804,U_17805),c_List_Ofoldr(U_17802,U_17803,U_17804,U_17806,U_17807)),
    inference(clausify,[status(thm)],[f_4352_3]) ).

fof(f_4353_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_4353_2,plain,
    ! [U_17810,U_17809,U_17808] : U_17808 != hAPP(hAPP(c_List_Olist_OCons(U_17809),U_17810),U_17808),
    inference(variable_rename,[status(thm)],[f_4353_1]) ).

fof(f_4353_3,plain,
    ! [U_17808,U_17809,U_17810] : U_17808 != hAPP(hAPP(c_List_Olist_OCons(U_17809),U_17810),U_17808),
    inference(definitional_conversion,[status(esa)],[f_4353_2]) ).

cnf(f_4353_4,plain,
    U_17808 != hAPP(hAPP(c_List_Olist_OCons(U_17809),U_17810),U_17808),
    inference(clausify,[status(thm)],[f_4353_3]) ).

fof(f_4354_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_4354_2,plain,
    ! [U_17813,U_17812,U_17811] : hAPP(hAPP(c_List_Olist_OCons(U_17811),U_17812),U_17813) != U_17813,
    inference(variable_rename,[status(thm)],[f_4354_1]) ).

fof(f_4354_3,plain,
    ! [U_17811,U_17812,U_17813] : hAPP(hAPP(c_List_Olist_OCons(U_17811),U_17812),U_17813) != U_17813,
    inference(definitional_conversion,[status(esa)],[f_4354_2]) ).

cnf(f_4354_4,plain,
    hAPP(hAPP(c_List_Olist_OCons(U_17811),U_17812),U_17813) != U_17813,
    inference(clausify,[status(thm)],[f_4354_3]) ).

fof(f_4355_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_4355_2,plain,
    ! [U_17818,U_17817,U_17816,U_17815,U_17814] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(U_17814),U_17815),U_17816) = hAPP(hAPP(c_List_Olist_OCons(U_17814),U_17817),U_17818)
        | U_17816 != U_17818
        | U_17815 != U_17817 )
      & ( ( U_17816 = U_17818
          & U_17815 = U_17817 )
        | hAPP(hAPP(c_List_Olist_OCons(U_17814),U_17815),U_17816) != hAPP(hAPP(c_List_Olist_OCons(U_17814),U_17817),U_17818) ) ),
    inference(variable_rename,[status(thm)],[f_4355_1]) ).

fof(f_4355_3,plain,
    ( ! [U_17828,U_17826,U_17824,U_17822] :
        ( ! [U_17820] : hAPP(hAPP(c_List_Olist_OCons(U_17820),U_17822),U_17824) = hAPP(hAPP(c_List_Olist_OCons(U_17820),U_17826),U_17828)
        | U_17824 != U_17828
        | U_17822 != U_17826 )
    & ! [U_17827,U_17825,U_17823,U_17821] :
        ( ! [U_17819] : hAPP(hAPP(c_List_Olist_OCons(U_17819),U_17821),U_17823) != hAPP(hAPP(c_List_Olist_OCons(U_17819),U_17825),U_17827)
        | ( U_17823 = U_17827
          & U_17821 = U_17825 ) ) ),
    inference(miniscope,[status(thm)],[f_4355_2]) ).

fof(f_4355_4,plain,
    ( ! [U_17823,U_17825,U_17821,U_17827] :
        ( U_17823 = U_17827
        | ~ sP1130(U_17823,U_17825,U_17821,U_17827) )
    & ! [U_17823,U_17825,U_17821,U_17827] :
        ( U_17821 = U_17825
        | ~ sP1130(U_17823,U_17825,U_17821,U_17827) )
    & ! [U_17828,U_17822,U_17824,U_17820,U_17826] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_17820),U_17822),U_17824) = hAPP(hAPP(c_List_Olist_OCons(U_17820),U_17826),U_17828)
        | U_17824 != U_17828
        | U_17822 != U_17826 )
    & ! [U_17823,U_17825,U_17821,U_17819,U_17827] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_17819),U_17821),U_17823) != hAPP(hAPP(c_List_Olist_OCons(U_17819),U_17825),U_17827)
        | sP1130(U_17823,U_17825,U_17821,U_17827) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1130])],[f_4355_3]) ).

cnf(f_4355_5,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_17819),U_17821),U_17823) != hAPP(hAPP(c_List_Olist_OCons(U_17819),U_17825),U_17827)
    | sP1130(U_17823,U_17825,U_17821,U_17827) ),
    inference(clausify,[status(thm)],[f_4355_4]) ).

cnf(f_4355_6,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_17820),U_17822),U_17824) = hAPP(hAPP(c_List_Olist_OCons(U_17820),U_17826),U_17828)
    | U_17824 != U_17828
    | U_17822 != U_17826 ),
    inference(clausify,[status(thm)],[f_4355_4]) ).

cnf(f_4355_7,plain,
    ( U_17821 = U_17825
    | ~ sP1130(U_17823,U_17825,U_17821,U_17827) ),
    inference(clausify,[status(thm)],[f_4355_4]) ).

cnf(f_4355_8,plain,
    ( U_17823 = U_17827
    | ~ sP1130(U_17823,U_17825,U_17821,U_17827) ),
    inference(clausify,[status(thm)],[f_4355_4]) ).

fof(f_4356_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_4356_2,plain,
    ! [U_17834,U_17833,U_17832,U_17831,U_17830,U_17829] :
      ( ( c_List_Olistrelp(U_17829,U_17830,hAPP(hAPP(c_List_Olist_OCons(U_17829),U_17831),U_17832),hAPP(hAPP(c_List_Olist_OCons(U_17829),U_17833),U_17834))
        | ~ c_List_Olistrelp(U_17829,U_17830,U_17832,U_17834)
        | ~ hBOOL(hAPP(hAPP(U_17830,U_17831),U_17833)) )
      & ( ( c_List_Olistrelp(U_17829,U_17830,U_17832,U_17834)
          & hBOOL(hAPP(hAPP(U_17830,U_17831),U_17833)) )
        | ~ c_List_Olistrelp(U_17829,U_17830,hAPP(hAPP(c_List_Olist_OCons(U_17829),U_17831),U_17832),hAPP(hAPP(c_List_Olist_OCons(U_17829),U_17833),U_17834)) ) ),
    inference(variable_rename,[status(thm)],[f_4356_1]) ).

fof(f_4356_3,plain,
    ( ! [U_17846,U_17844,U_17842,U_17840,U_17838,U_17836] :
        ( c_List_Olistrelp(U_17836,U_17838,hAPP(hAPP(c_List_Olist_OCons(U_17836),U_17840),U_17842),hAPP(hAPP(c_List_Olist_OCons(U_17836),U_17844),U_17846))
        | ~ c_List_Olistrelp(U_17836,U_17838,U_17842,U_17846)
        | ~ hBOOL(hAPP(hAPP(U_17838,U_17840),U_17844)) )
    & ! [U_17845,U_17843,U_17841,U_17839,U_17837,U_17835] :
        ( ( c_List_Olistrelp(U_17835,U_17837,U_17841,U_17845)
          & hBOOL(hAPP(hAPP(U_17837,U_17839),U_17843)) )
        | ~ c_List_Olistrelp(U_17835,U_17837,hAPP(hAPP(c_List_Olist_OCons(U_17835),U_17839),U_17841),hAPP(hAPP(c_List_Olist_OCons(U_17835),U_17843),U_17845)) ) ),
    inference(miniscope,[status(thm)],[f_4356_2]) ).

fof(f_4356_4,plain,
    ( ! [U_17841,U_17837,U_17835,U_17839,U_17845,U_17843] :
        ( c_List_Olistrelp(U_17835,U_17837,U_17841,U_17845)
        | ~ sP1131(U_17841,U_17837,U_17835,U_17839,U_17845,U_17843) )
    & ! [U_17841,U_17837,U_17835,U_17839,U_17845,U_17843] :
        ( hBOOL(hAPP(hAPP(U_17837,U_17839),U_17843))
        | ~ sP1131(U_17841,U_17837,U_17835,U_17839,U_17845,U_17843) )
    & ! [U_17836,U_17846,U_17842,U_17840,U_17838,U_17844] :
        ( c_List_Olistrelp(U_17836,U_17838,hAPP(hAPP(c_List_Olist_OCons(U_17836),U_17840),U_17842),hAPP(hAPP(c_List_Olist_OCons(U_17836),U_17844),U_17846))
        | ~ c_List_Olistrelp(U_17836,U_17838,U_17842,U_17846)
        | ~ hBOOL(hAPP(hAPP(U_17838,U_17840),U_17844)) )
    & ! [U_17841,U_17837,U_17835,U_17839,U_17845,U_17843] :
        ( sP1131(U_17841,U_17837,U_17835,U_17839,U_17845,U_17843)
        | ~ c_List_Olistrelp(U_17835,U_17837,hAPP(hAPP(c_List_Olist_OCons(U_17835),U_17839),U_17841),hAPP(hAPP(c_List_Olist_OCons(U_17835),U_17843),U_17845)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1131])],[f_4356_3]) ).

cnf(f_4356_5,plain,
    ( sP1131(U_17841,U_17837,U_17835,U_17839,U_17845,U_17843)
    | ~ c_List_Olistrelp(U_17835,U_17837,hAPP(hAPP(c_List_Olist_OCons(U_17835),U_17839),U_17841),hAPP(hAPP(c_List_Olist_OCons(U_17835),U_17843),U_17845)) ),
    inference(clausify,[status(thm)],[f_4356_4]) ).

cnf(f_4356_6,plain,
    ( c_List_Olistrelp(U_17836,U_17838,hAPP(hAPP(c_List_Olist_OCons(U_17836),U_17840),U_17842),hAPP(hAPP(c_List_Olist_OCons(U_17836),U_17844),U_17846))
    | ~ c_List_Olistrelp(U_17836,U_17838,U_17842,U_17846)
    | ~ hBOOL(hAPP(hAPP(U_17838,U_17840),U_17844)) ),
    inference(clausify,[status(thm)],[f_4356_4]) ).

cnf(f_4356_7,plain,
    ( hBOOL(hAPP(hAPP(U_17837,U_17839),U_17843))
    | ~ sP1131(U_17841,U_17837,U_17835,U_17839,U_17845,U_17843) ),
    inference(clausify,[status(thm)],[f_4356_4]) ).

cnf(f_4356_8,plain,
    ( c_List_Olistrelp(U_17835,U_17837,U_17841,U_17845)
    | ~ sP1131(U_17841,U_17837,U_17835,U_17839,U_17845,U_17843) ),
    inference(clausify,[status(thm)],[f_4356_4]) ).

fof(f_4357_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_4357_2,plain,
    ! [U_17852,U_17851,U_17850,U_17849,U_17848,U_17847] :
      ( c_List_Olistrelp(U_17850,U_17847,hAPP(hAPP(c_List_Olist_OCons(U_17850),U_17848),U_17851),hAPP(hAPP(c_List_Olist_OCons(U_17850),U_17849),U_17852))
      | ~ c_List_Olistrelp(U_17850,U_17847,U_17851,U_17852)
      | ~ hBOOL(hAPP(hAPP(U_17847,U_17848),U_17849)) ),
    inference(variable_rename,[status(thm)],[f_4357_1]) ).

fof(f_4357_3,plain,
    ! [U_17850,U_17847,U_17849,U_17851,U_17852,U_17848] :
      ( c_List_Olistrelp(U_17850,U_17847,hAPP(hAPP(c_List_Olist_OCons(U_17850),U_17848),U_17851),hAPP(hAPP(c_List_Olist_OCons(U_17850),U_17849),U_17852))
      | ~ c_List_Olistrelp(U_17850,U_17847,U_17851,U_17852)
      | ~ hBOOL(hAPP(hAPP(U_17847,U_17848),U_17849)) ),
    inference(definitional_conversion,[status(esa)],[f_4357_2]) ).

cnf(f_4357_4,plain,
    ( c_List_Olistrelp(U_17850,U_17847,hAPP(hAPP(c_List_Olist_OCons(U_17850),U_17848),U_17851),hAPP(hAPP(c_List_Olist_OCons(U_17850),U_17849),U_17852))
    | ~ c_List_Olistrelp(U_17850,U_17847,U_17851,U_17852)
    | ~ hBOOL(hAPP(hAPP(U_17847,U_17848),U_17849)) ),
    inference(clausify,[status(thm)],[f_4357_3]) ).

fof(f_4358_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_4358_2,plain,
    ! [U_17857,U_17856,U_17855,U_17854,U_17853] : hAPP(hAPP(c_List_Omap(U_17853,U_17854),U_17855),hAPP(hAPP(c_List_Olist_OCons(U_17853),U_17856),U_17857)) = hAPP(hAPP(c_List_Olist_OCons(U_17854),hAPP(U_17855,U_17856)),hAPP(hAPP(c_List_Omap(U_17853,U_17854),U_17855),U_17857)),
    inference(variable_rename,[status(thm)],[f_4358_1]) ).

fof(f_4358_3,plain,
    ! [U_17854,U_17853,U_17855,U_17856,U_17857] : hAPP(hAPP(c_List_Omap(U_17853,U_17854),U_17855),hAPP(hAPP(c_List_Olist_OCons(U_17853),U_17856),U_17857)) = hAPP(hAPP(c_List_Olist_OCons(U_17854),hAPP(U_17855,U_17856)),hAPP(hAPP(c_List_Omap(U_17853,U_17854),U_17855),U_17857)),
    inference(definitional_conversion,[status(esa)],[f_4358_2]) ).

cnf(f_4358_4,plain,
    hAPP(hAPP(c_List_Omap(U_17853,U_17854),U_17855),hAPP(hAPP(c_List_Olist_OCons(U_17853),U_17856),U_17857)) = hAPP(hAPP(c_List_Olist_OCons(U_17854),hAPP(U_17855,U_17856)),hAPP(hAPP(c_List_Omap(U_17853,U_17854),U_17855),U_17857)),
    inference(clausify,[status(thm)],[f_4358_3]) ).

fof(f_4359_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_4359_2,plain,
    ! [U_17861,U_17860,U_17859,U_17858] :
      ( ( c_List_Oremove1(U_17860,U_17858,hAPP(hAPP(c_List_Olist_OCons(U_17860),U_17859),U_17861)) = hAPP(hAPP(c_List_Olist_OCons(U_17860),U_17859),c_List_Oremove1(U_17860,U_17858,U_17861))
        | U_17858 = U_17859 )
      & ( c_List_Oremove1(U_17860,U_17858,hAPP(hAPP(c_List_Olist_OCons(U_17860),U_17859),U_17861)) = U_17861
        | U_17858 != U_17859 ) ),
    inference(variable_rename,[status(thm)],[f_4359_1]) ).

fof(f_4359_3,plain,
    ( ! [U_17869,U_17867,U_17865,U_17863] :
        ( c_List_Oremove1(U_17867,U_17863,hAPP(hAPP(c_List_Olist_OCons(U_17867),U_17865),U_17869)) = hAPP(hAPP(c_List_Olist_OCons(U_17867),U_17865),c_List_Oremove1(U_17867,U_17863,U_17869))
        | U_17863 = U_17865 )
    & ! [U_17868,U_17866,U_17864,U_17862] :
        ( c_List_Oremove1(U_17866,U_17862,hAPP(hAPP(c_List_Olist_OCons(U_17866),U_17864),U_17868)) = U_17868
        | U_17862 != U_17864 ) ),
    inference(miniscope,[status(thm)],[f_4359_2]) ).

fof(f_4359_4,plain,
    ( ! [U_17869,U_17863,U_17865,U_17867] :
        ( c_List_Oremove1(U_17867,U_17863,hAPP(hAPP(c_List_Olist_OCons(U_17867),U_17865),U_17869)) = hAPP(hAPP(c_List_Olist_OCons(U_17867),U_17865),c_List_Oremove1(U_17867,U_17863,U_17869))
        | U_17863 = U_17865 )
    & ! [U_17864,U_17868,U_17862,U_17866] :
        ( c_List_Oremove1(U_17866,U_17862,hAPP(hAPP(c_List_Olist_OCons(U_17866),U_17864),U_17868)) = U_17868
        | U_17862 != U_17864 ) ),
    inference(definitional_conversion,[status(esa)],[f_4359_3]) ).

cnf(f_4359_5,plain,
    ( c_List_Oremove1(U_17866,U_17862,hAPP(hAPP(c_List_Olist_OCons(U_17866),U_17864),U_17868)) = U_17868
    | U_17862 != U_17864 ),
    inference(clausify,[status(thm)],[f_4359_4]) ).

cnf(f_4359_6,plain,
    ( c_List_Oremove1(U_17867,U_17863,hAPP(hAPP(c_List_Olist_OCons(U_17867),U_17865),U_17869)) = hAPP(hAPP(c_List_Olist_OCons(U_17867),U_17865),c_List_Oremove1(U_17867,U_17863,U_17869))
    | U_17863 = U_17865 ),
    inference(clausify,[status(thm)],[f_4359_4]) ).

fof(f_4360_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_4360_2,plain,
    ! [U_17875,U_17874,U_17873,U_17872,U_17871,U_17870] :
      ( ( ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17874,U_17870,U_17871),U_17872),hAPP(hAPP(c_List_Olist_OCons(U_17874),U_17873),U_17875)) = hAPP(hAPP(c_List_Olist_OCons(U_17874),U_17873),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17874,U_17870,U_17871),U_17872),U_17875))
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17870),hAPP(U_17871,U_17872)),hAPP(U_17871,U_17873))) )
        & ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17874,U_17870,U_17871),U_17872),hAPP(hAPP(c_List_Olist_OCons(U_17874),U_17873),U_17875)) = hAPP(hAPP(c_List_Olist_OCons(U_17874),U_17872),hAPP(hAPP(c_List_Olist_OCons(U_17874),U_17873),U_17875))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17870),hAPP(U_17871,U_17872)),hAPP(U_17871,U_17873))) ) )
      | ~ class_Orderings_Olinorder(U_17870) ),
    inference(variable_rename,[status(thm)],[f_4360_1]) ).

fof(f_4360_3,plain,
    ( ! [U_17871,U_17870,U_17872,U_17873,U_17874,U_17875] :
        ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17874,U_17870,U_17871),U_17872),hAPP(hAPP(c_List_Olist_OCons(U_17874),U_17873),U_17875)) = hAPP(hAPP(c_List_Olist_OCons(U_17874),U_17873),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17874,U_17870,U_17871),U_17872),U_17875))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17870),hAPP(U_17871,U_17872)),hAPP(U_17871,U_17873)))
        | ~ sP1132(U_17871,U_17870,U_17872,U_17873,U_17874,U_17875) )
    & ! [U_17871,U_17870,U_17872,U_17873,U_17874,U_17875] :
        ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17874,U_17870,U_17871),U_17872),hAPP(hAPP(c_List_Olist_OCons(U_17874),U_17873),U_17875)) = hAPP(hAPP(c_List_Olist_OCons(U_17874),U_17872),hAPP(hAPP(c_List_Olist_OCons(U_17874),U_17873),U_17875))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17870),hAPP(U_17871,U_17872)),hAPP(U_17871,U_17873)))
        | ~ sP1132(U_17871,U_17870,U_17872,U_17873,U_17874,U_17875) )
    & ! [U_17871,U_17870,U_17872,U_17873,U_17874,U_17875] :
        ( sP1132(U_17871,U_17870,U_17872,U_17873,U_17874,U_17875)
        | ~ class_Orderings_Olinorder(U_17870) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1132])],[f_4360_2]) ).

cnf(f_4360_4,plain,
    ( sP1132(U_17871,U_17870,U_17872,U_17873,U_17874,U_17875)
    | ~ class_Orderings_Olinorder(U_17870) ),
    inference(clausify,[status(thm)],[f_4360_3]) ).

cnf(f_4360_5,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17874,U_17870,U_17871),U_17872),hAPP(hAPP(c_List_Olist_OCons(U_17874),U_17873),U_17875)) = hAPP(hAPP(c_List_Olist_OCons(U_17874),U_17872),hAPP(hAPP(c_List_Olist_OCons(U_17874),U_17873),U_17875))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17870),hAPP(U_17871,U_17872)),hAPP(U_17871,U_17873)))
    | ~ sP1132(U_17871,U_17870,U_17872,U_17873,U_17874,U_17875) ),
    inference(clausify,[status(thm)],[f_4360_3]) ).

cnf(f_4360_6,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17874,U_17870,U_17871),U_17872),hAPP(hAPP(c_List_Olist_OCons(U_17874),U_17873),U_17875)) = hAPP(hAPP(c_List_Olist_OCons(U_17874),U_17873),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_17874,U_17870,U_17871),U_17872),U_17875))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_17870),hAPP(U_17871,U_17872)),hAPP(U_17871,U_17873)))
    | ~ sP1132(U_17871,U_17870,U_17872,U_17873,U_17874,U_17875) ),
    inference(clausify,[status(thm)],[f_4360_3]) ).

fof(f_4361_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_4361_2,plain,
    ! [U_17878,U_17877,U_17876] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_17876),hAPP(hAPP(c_List_Olist_OCons(U_17876),U_17877),U_17878)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17876),U_17878))
        | hBOOL(hAPP(hAPP(c_member(U_17876),U_17877),hAPP(c_List_Oset(U_17876),U_17878))) )
      & ( ( hBOOL(hAPP(c_List_Odistinct(U_17876),U_17878))
          & ~ hBOOL(hAPP(hAPP(c_member(U_17876),U_17877),hAPP(c_List_Oset(U_17876),U_17878))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17876),hAPP(hAPP(c_List_Olist_OCons(U_17876),U_17877),U_17878))) ) ),
    inference(variable_rename,[status(thm)],[f_4361_1]) ).

fof(f_4361_3,plain,
    ( ! [U_17884,U_17882,U_17880] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17880),hAPP(hAPP(c_List_Olist_OCons(U_17880),U_17882),U_17884)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17880),U_17884))
        | hBOOL(hAPP(hAPP(c_member(U_17880),U_17882),hAPP(c_List_Oset(U_17880),U_17884))) )
    & ! [U_17883,U_17881,U_17879] :
        ( ( hBOOL(hAPP(c_List_Odistinct(U_17879),U_17883))
          & ~ hBOOL(hAPP(hAPP(c_member(U_17879),U_17881),hAPP(c_List_Oset(U_17879),U_17883))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17879),hAPP(hAPP(c_List_Olist_OCons(U_17879),U_17881),U_17883))) ) ),
    inference(miniscope,[status(thm)],[f_4361_2]) ).

fof(f_4361_4,plain,
    ( ! [U_17881,U_17879,U_17883] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17879),U_17883))
        | ~ sP1133(U_17881,U_17879,U_17883) )
    & ! [U_17881,U_17879,U_17883] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_17879),U_17881),hAPP(c_List_Oset(U_17879),U_17883)))
        | ~ sP1133(U_17881,U_17879,U_17883) )
    & ! [U_17884,U_17880,U_17882] :
        ( hBOOL(hAPP(c_List_Odistinct(U_17880),hAPP(hAPP(c_List_Olist_OCons(U_17880),U_17882),U_17884)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17880),U_17884))
        | hBOOL(hAPP(hAPP(c_member(U_17880),U_17882),hAPP(c_List_Oset(U_17880),U_17884))) )
    & ! [U_17881,U_17879,U_17883] :
        ( sP1133(U_17881,U_17879,U_17883)
        | ~ hBOOL(hAPP(c_List_Odistinct(U_17879),hAPP(hAPP(c_List_Olist_OCons(U_17879),U_17881),U_17883))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1133])],[f_4361_3]) ).

cnf(f_4361_5,plain,
    ( sP1133(U_17881,U_17879,U_17883)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17879),hAPP(hAPP(c_List_Olist_OCons(U_17879),U_17881),U_17883))) ),
    inference(clausify,[status(thm)],[f_4361_4]) ).

cnf(f_4361_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17880),hAPP(hAPP(c_List_Olist_OCons(U_17880),U_17882),U_17884)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17880),U_17884))
    | hBOOL(hAPP(hAPP(c_member(U_17880),U_17882),hAPP(c_List_Oset(U_17880),U_17884))) ),
    inference(clausify,[status(thm)],[f_4361_4]) ).

cnf(f_4361_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_17879),U_17881),hAPP(c_List_Oset(U_17879),U_17883)))
    | ~ sP1133(U_17881,U_17879,U_17883) ),
    inference(clausify,[status(thm)],[f_4361_4]) ).

cnf(f_4361_8,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17879),U_17883))
    | ~ sP1133(U_17881,U_17879,U_17883) ),
    inference(clausify,[status(thm)],[f_4361_4]) ).

fof(f_4362_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_4362_2,plain,
    ! [U_17890,U_17889,U_17888,U_17887,U_17886,U_17885] :
      ( ( hAPP(c_Map_Omap__of(U_17887,U_17888,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17887,U_17888)),hAPP(hAPP(c_Product__Type_OPair(U_17887,U_17888),U_17885),U_17889)),U_17890)),U_17886) = hAPP(c_Map_Omap__of(U_17887,U_17888,U_17890),U_17886)
        | U_17885 = U_17886 )
      & ( hAPP(c_Map_Omap__of(U_17887,U_17888,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17887,U_17888)),hAPP(hAPP(c_Product__Type_OPair(U_17887,U_17888),U_17885),U_17889)),U_17890)),U_17886) = hAPP(c_Option_Ooption_OSome(U_17888),U_17889)
        | U_17885 != U_17886 ) ),
    inference(variable_rename,[status(thm)],[f_4362_1]) ).

fof(f_4362_3,plain,
    ( ! [U_17902,U_17900,U_17898,U_17896,U_17894,U_17892] :
        ( hAPP(c_Map_Omap__of(U_17896,U_17898,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17896,U_17898)),hAPP(hAPP(c_Product__Type_OPair(U_17896,U_17898),U_17892),U_17900)),U_17902)),U_17894) = hAPP(c_Map_Omap__of(U_17896,U_17898,U_17902),U_17894)
        | U_17892 = U_17894 )
    & ! [U_17901,U_17899,U_17897,U_17895,U_17893,U_17891] :
        ( hAPP(c_Map_Omap__of(U_17895,U_17897,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17895,U_17897)),hAPP(hAPP(c_Product__Type_OPair(U_17895,U_17897),U_17891),U_17899)),U_17901)),U_17893) = hAPP(c_Option_Ooption_OSome(U_17897),U_17899)
        | U_17891 != U_17893 ) ),
    inference(miniscope,[status(thm)],[f_4362_2]) ).

fof(f_4362_4,plain,
    ( ! [U_17892,U_17894,U_17896,U_17898,U_17900,U_17902] :
        ( hAPP(c_Map_Omap__of(U_17896,U_17898,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17896,U_17898)),hAPP(hAPP(c_Product__Type_OPair(U_17896,U_17898),U_17892),U_17900)),U_17902)),U_17894) = hAPP(c_Map_Omap__of(U_17896,U_17898,U_17902),U_17894)
        | U_17892 = U_17894 )
    & ! [U_17897,U_17891,U_17895,U_17893,U_17899,U_17901] :
        ( hAPP(c_Map_Omap__of(U_17895,U_17897,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17895,U_17897)),hAPP(hAPP(c_Product__Type_OPair(U_17895,U_17897),U_17891),U_17899)),U_17901)),U_17893) = hAPP(c_Option_Ooption_OSome(U_17897),U_17899)
        | U_17891 != U_17893 ) ),
    inference(definitional_conversion,[status(esa)],[f_4362_3]) ).

cnf(f_4362_5,plain,
    ( hAPP(c_Map_Omap__of(U_17895,U_17897,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17895,U_17897)),hAPP(hAPP(c_Product__Type_OPair(U_17895,U_17897),U_17891),U_17899)),U_17901)),U_17893) = hAPP(c_Option_Ooption_OSome(U_17897),U_17899)
    | U_17891 != U_17893 ),
    inference(clausify,[status(thm)],[f_4362_4]) ).

cnf(f_4362_6,plain,
    ( hAPP(c_Map_Omap__of(U_17896,U_17898,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17896,U_17898)),hAPP(hAPP(c_Product__Type_OPair(U_17896,U_17898),U_17892),U_17900)),U_17902)),U_17894) = hAPP(c_Map_Omap__of(U_17896,U_17898,U_17902),U_17894)
    | U_17892 = U_17894 ),
    inference(clausify,[status(thm)],[f_4362_4]) ).

fof(f_4363_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_4363_2,plain,
    ! [U_17905,U_17904,U_17903] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17903)),hAPP(hAPP(c_List_Olist_OCons(U_17903),U_17904),U_17905)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17903)),U_17905)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_4363_1]) ).

fof(f_4363_3,plain,
    ! [U_17903,U_17904,U_17905] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17903)),hAPP(hAPP(c_List_Olist_OCons(U_17903),U_17904),U_17905)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17903)),U_17905)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_4363_2]) ).

cnf(f_4363_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17903)),hAPP(hAPP(c_List_Olist_OCons(U_17903),U_17904),U_17905)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17903)),U_17905)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_4363_3]) ).

fof(f_4364_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_4364_2,plain,
    ! [U_17911,U_17910,U_17909,U_17908,U_17907,U_17906] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17906),tc_List_Olist(U_17906))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17906),tc_List_Olist(U_17906)),hAPP(hAPP(c_List_Olist_OCons(U_17906),U_17907),U_17910)),hAPP(hAPP(c_List_Olist_OCons(U_17906),U_17908),U_17911))),c_List_Olistrel(U_17906,U_17909)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17906),tc_List_Olist(U_17906))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17906),tc_List_Olist(U_17906)),U_17910),U_17911)),c_List_Olistrel(U_17906,U_17909)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17906,U_17906)),hAPP(hAPP(c_Product__Type_OPair(U_17906,U_17906),U_17907),U_17908)),U_17909)) ),
    inference(variable_rename,[status(thm)],[f_4364_1]) ).

fof(f_4364_3,plain,
    ! [U_17906,U_17907,U_17908,U_17909,U_17910,U_17911] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17906),tc_List_Olist(U_17906))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17906),tc_List_Olist(U_17906)),hAPP(hAPP(c_List_Olist_OCons(U_17906),U_17907),U_17910)),hAPP(hAPP(c_List_Olist_OCons(U_17906),U_17908),U_17911))),c_List_Olistrel(U_17906,U_17909)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17906),tc_List_Olist(U_17906))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17906),tc_List_Olist(U_17906)),U_17910),U_17911)),c_List_Olistrel(U_17906,U_17909)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17906,U_17906)),hAPP(hAPP(c_Product__Type_OPair(U_17906,U_17906),U_17907),U_17908)),U_17909)) ),
    inference(definitional_conversion,[status(esa)],[f_4364_2]) ).

cnf(f_4364_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17906),tc_List_Olist(U_17906))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17906),tc_List_Olist(U_17906)),hAPP(hAPP(c_List_Olist_OCons(U_17906),U_17907),U_17910)),hAPP(hAPP(c_List_Olist_OCons(U_17906),U_17908),U_17911))),c_List_Olistrel(U_17906,U_17909)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17906),tc_List_Olist(U_17906))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17906),tc_List_Olist(U_17906)),U_17910),U_17911)),c_List_Olistrel(U_17906,U_17909)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17906,U_17906)),hAPP(hAPP(c_Product__Type_OPair(U_17906,U_17906),U_17907),U_17908)),U_17909)) ),
    inference(clausify,[status(thm)],[f_4364_3]) ).

fof(f_4365_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_4365_2,plain,
    ! [U_17915,U_17914,U_17913,U_17912] : c_Map_Omap__of(U_17912,U_17913,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17912,U_17913)),U_17914),U_17915)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17912,tc_Option_Ooption(U_17913)),c_Map_Omap__of(U_17912,U_17913,U_17915)),hAPP(c_Product__Type_Ofst(U_17912,U_17913),U_17914)),hAPP(c_Option_Ooption_OSome(U_17913),hAPP(c_Product__Type_Osnd(U_17912,U_17913),U_17914))),
    inference(variable_rename,[status(thm)],[f_4365_1]) ).

fof(f_4365_3,plain,
    ! [U_17912,U_17913,U_17914,U_17915] : c_Map_Omap__of(U_17912,U_17913,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17912,U_17913)),U_17914),U_17915)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17912,tc_Option_Ooption(U_17913)),c_Map_Omap__of(U_17912,U_17913,U_17915)),hAPP(c_Product__Type_Ofst(U_17912,U_17913),U_17914)),hAPP(c_Option_Ooption_OSome(U_17913),hAPP(c_Product__Type_Osnd(U_17912,U_17913),U_17914))),
    inference(definitional_conversion,[status(esa)],[f_4365_2]) ).

cnf(f_4365_4,plain,
    c_Map_Omap__of(U_17912,U_17913,hAPP(hAPP(c_List_Olist_OCons(tc_prod(U_17912,U_17913)),U_17914),U_17915)) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_17912,tc_Option_Ooption(U_17913)),c_Map_Omap__of(U_17912,U_17913,U_17915)),hAPP(c_Product__Type_Ofst(U_17912,U_17913),U_17914)),hAPP(c_Option_Ooption_OSome(U_17913),hAPP(c_Product__Type_Osnd(U_17912,U_17913),U_17914))),
    inference(clausify,[status(thm)],[f_4365_3]) ).

fof(f_4366_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_4366_2,plain,
    ! [U_17921,U_17920,U_17919,U_17918,U_17917,U_17916] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17916),tc_List_Olist(U_17916))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17916),tc_List_Olist(U_17916)),hAPP(hAPP(c_List_Olist_OCons(U_17916),U_17917),U_17918)),hAPP(hAPP(c_List_Olist_OCons(U_17916),U_17919),U_17920))),c_List_Olex(U_17916,U_17921)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17916),tc_List_Olist(U_17916))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17916),tc_List_Olist(U_17916)),U_17918),U_17920)),c_List_Olex(U_17916,U_17921)))
            | U_17917 != U_17919 )
          & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17916)),U_17918) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17916)),U_17920)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17916,U_17916)),hAPP(hAPP(c_Product__Type_OPair(U_17916,U_17916),U_17917),U_17919)),U_17921)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17916),tc_List_Olist(U_17916))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17916),tc_List_Olist(U_17916)),U_17918),U_17920)),c_List_Olex(U_17916,U_17921)))
          & U_17917 = U_17919 )
        | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17916)),U_17918) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17916)),U_17920)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17916,U_17916)),hAPP(hAPP(c_Product__Type_OPair(U_17916,U_17916),U_17917),U_17919)),U_17921)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17916),tc_List_Olist(U_17916))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17916),tc_List_Olist(U_17916)),hAPP(hAPP(c_List_Olist_OCons(U_17916),U_17917),U_17918)),hAPP(hAPP(c_List_Olist_OCons(U_17916),U_17919),U_17920))),c_List_Olex(U_17916,U_17921))) ) ),
    inference(variable_rename,[status(thm)],[f_4366_1]) ).

fof(f_4366_3,plain,
    ( ! [U_17933,U_17931,U_17929,U_17927,U_17925,U_17923] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17923),tc_List_Olist(U_17923))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17923),tc_List_Olist(U_17923)),hAPP(hAPP(c_List_Olist_OCons(U_17923),U_17925),U_17927)),hAPP(hAPP(c_List_Olist_OCons(U_17923),U_17929),U_17931))),c_List_Olex(U_17923,U_17933)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17923),tc_List_Olist(U_17923))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17923),tc_List_Olist(U_17923)),U_17927),U_17931)),c_List_Olex(U_17923,U_17933)))
            | U_17925 != U_17929 )
          & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17923)),U_17927) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17923)),U_17931)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17923,U_17923)),hAPP(hAPP(c_Product__Type_OPair(U_17923,U_17923),U_17925),U_17929)),U_17933)) ) ) )
    & ! [U_17932,U_17930,U_17928,U_17926,U_17924,U_17922] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17922),tc_List_Olist(U_17922))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17922),tc_List_Olist(U_17922)),U_17926),U_17930)),c_List_Olex(U_17922,U_17932)))
          & U_17924 = U_17928 )
        | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17922)),U_17926) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17922)),U_17930)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17922,U_17922)),hAPP(hAPP(c_Product__Type_OPair(U_17922,U_17922),U_17924),U_17928)),U_17932)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17922),tc_List_Olist(U_17922))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17922),tc_List_Olist(U_17922)),hAPP(hAPP(c_List_Olist_OCons(U_17922),U_17924),U_17926)),hAPP(hAPP(c_List_Olist_OCons(U_17922),U_17928),U_17930))),c_List_Olex(U_17922,U_17932))) ) ),
    inference(miniscope,[status(thm)],[f_4366_2]) ).

fof(f_4366_4,plain,
    ( ! [U_17923,U_17925,U_17927,U_17931,U_17929,U_17933] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17923),tc_List_Olist(U_17923))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17923),tc_List_Olist(U_17923)),U_17927),U_17931)),c_List_Olex(U_17923,U_17933)))
        | U_17925 != U_17929
        | ~ sP1136(U_17923,U_17925,U_17927,U_17931,U_17929,U_17933) )
    & ! [U_17923,U_17925,U_17927,U_17931,U_17929,U_17933] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17923)),U_17927) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17923)),U_17931)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17923,U_17923)),hAPP(hAPP(c_Product__Type_OPair(U_17923,U_17923),U_17925),U_17929)),U_17933))
        | ~ sP1136(U_17923,U_17925,U_17927,U_17931,U_17929,U_17933) )
    & ! [U_17922,U_17924,U_17926,U_17930,U_17928,U_17932] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17922),tc_List_Olist(U_17922))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17922),tc_List_Olist(U_17922)),U_17926),U_17930)),c_List_Olex(U_17922,U_17932)))
        | ~ sP1135(U_17922,U_17924,U_17926,U_17930,U_17928,U_17932) )
    & ! [U_17922,U_17924,U_17926,U_17930,U_17928,U_17932] :
        ( U_17924 = U_17928
        | ~ sP1135(U_17922,U_17924,U_17926,U_17930,U_17928,U_17932) )
    & ! [U_17922,U_17924,U_17926,U_17930,U_17928,U_17932] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17922)),U_17926) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17922)),U_17930)
        | ~ sP1134(U_17922,U_17924,U_17926,U_17930,U_17928,U_17932) )
    & ! [U_17922,U_17924,U_17926,U_17930,U_17928,U_17932] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17922,U_17922)),hAPP(hAPP(c_Product__Type_OPair(U_17922,U_17922),U_17924),U_17928)),U_17932))
        | ~ sP1134(U_17922,U_17924,U_17926,U_17930,U_17928,U_17932) )
    & ! [U_17923,U_17925,U_17927,U_17931,U_17929,U_17933] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17923),tc_List_Olist(U_17923))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17923),tc_List_Olist(U_17923)),hAPP(hAPP(c_List_Olist_OCons(U_17923),U_17925),U_17927)),hAPP(hAPP(c_List_Olist_OCons(U_17923),U_17929),U_17931))),c_List_Olex(U_17923,U_17933)))
        | sP1136(U_17923,U_17925,U_17927,U_17931,U_17929,U_17933) )
    & ! [U_17922,U_17924,U_17926,U_17930,U_17928,U_17932] :
        ( sP1135(U_17922,U_17924,U_17926,U_17930,U_17928,U_17932)
        | sP1134(U_17922,U_17924,U_17926,U_17930,U_17928,U_17932)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17922),tc_List_Olist(U_17922))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17922),tc_List_Olist(U_17922)),hAPP(hAPP(c_List_Olist_OCons(U_17922),U_17924),U_17926)),hAPP(hAPP(c_List_Olist_OCons(U_17922),U_17928),U_17930))),c_List_Olex(U_17922,U_17932))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1134,sP1135,sP1136])],[f_4366_3]) ).

cnf(f_4366_5,plain,
    ( sP1135(U_17922,U_17924,U_17926,U_17930,U_17928,U_17932)
    | sP1134(U_17922,U_17924,U_17926,U_17930,U_17928,U_17932)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17922),tc_List_Olist(U_17922))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17922),tc_List_Olist(U_17922)),hAPP(hAPP(c_List_Olist_OCons(U_17922),U_17924),U_17926)),hAPP(hAPP(c_List_Olist_OCons(U_17922),U_17928),U_17930))),c_List_Olex(U_17922,U_17932))) ),
    inference(clausify,[status(thm)],[f_4366_4]) ).

cnf(f_4366_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17923),tc_List_Olist(U_17923))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17923),tc_List_Olist(U_17923)),hAPP(hAPP(c_List_Olist_OCons(U_17923),U_17925),U_17927)),hAPP(hAPP(c_List_Olist_OCons(U_17923),U_17929),U_17931))),c_List_Olex(U_17923,U_17933)))
    | sP1136(U_17923,U_17925,U_17927,U_17931,U_17929,U_17933) ),
    inference(clausify,[status(thm)],[f_4366_4]) ).

cnf(f_4366_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17922,U_17922)),hAPP(hAPP(c_Product__Type_OPair(U_17922,U_17922),U_17924),U_17928)),U_17932))
    | ~ sP1134(U_17922,U_17924,U_17926,U_17930,U_17928,U_17932) ),
    inference(clausify,[status(thm)],[f_4366_4]) ).

cnf(f_4366_8,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17922)),U_17926) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17922)),U_17930)
    | ~ sP1134(U_17922,U_17924,U_17926,U_17930,U_17928,U_17932) ),
    inference(clausify,[status(thm)],[f_4366_4]) ).

cnf(f_4366_9,plain,
    ( U_17924 = U_17928
    | ~ sP1135(U_17922,U_17924,U_17926,U_17930,U_17928,U_17932) ),
    inference(clausify,[status(thm)],[f_4366_4]) ).

cnf(f_4366_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17922),tc_List_Olist(U_17922))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17922),tc_List_Olist(U_17922)),U_17926),U_17930)),c_List_Olex(U_17922,U_17932)))
    | ~ sP1135(U_17922,U_17924,U_17926,U_17930,U_17928,U_17932) ),
    inference(clausify,[status(thm)],[f_4366_4]) ).

cnf(f_4366_11,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17923)),U_17927) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17923)),U_17931)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_17923,U_17923)),hAPP(hAPP(c_Product__Type_OPair(U_17923,U_17923),U_17925),U_17929)),U_17933))
    | ~ sP1136(U_17923,U_17925,U_17927,U_17931,U_17929,U_17933) ),
    inference(clausify,[status(thm)],[f_4366_4]) ).

cnf(f_4366_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17923),tc_List_Olist(U_17923))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17923),tc_List_Olist(U_17923)),U_17927),U_17931)),c_List_Olex(U_17923,U_17933)))
    | U_17925 != U_17929
    | ~ sP1136(U_17923,U_17925,U_17927,U_17931,U_17929,U_17933) ),
    inference(clausify,[status(thm)],[f_4366_4]) ).

fof(f_4367_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_4367_2,plain,
    ! [U_17937,U_17936,U_17935,U_17934] : hAPP(c_Relation_OImage(tc_List_Olist(U_17934),tc_List_Olist(U_17934),c_List_Olistrel(U_17934,U_17935)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_17934)),hAPP(hAPP(c_List_Olist_OCons(U_17934),U_17936),U_17937)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_17934),tc_HOL_Obool)))) = c_List_Oset__Cons(U_17934,hAPP(c_Relation_OImage(U_17934,U_17934,U_17935),hAPP(hAPP(c_Set_Oinsert(U_17934),U_17936),c_Orderings_Obot__class_Obot(tc_fun(U_17934,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(U_17934),tc_List_Olist(U_17934),c_List_Olistrel(U_17934,U_17935)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_17934)),U_17937),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_17934),tc_HOL_Obool))))),
    inference(variable_rename,[status(thm)],[f_4367_1]) ).

fof(f_4367_3,plain,
    ! [U_17934,U_17936,U_17935,U_17937] : hAPP(c_Relation_OImage(tc_List_Olist(U_17934),tc_List_Olist(U_17934),c_List_Olistrel(U_17934,U_17935)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_17934)),hAPP(hAPP(c_List_Olist_OCons(U_17934),U_17936),U_17937)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_17934),tc_HOL_Obool)))) = c_List_Oset__Cons(U_17934,hAPP(c_Relation_OImage(U_17934,U_17934,U_17935),hAPP(hAPP(c_Set_Oinsert(U_17934),U_17936),c_Orderings_Obot__class_Obot(tc_fun(U_17934,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(U_17934),tc_List_Olist(U_17934),c_List_Olistrel(U_17934,U_17935)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_17934)),U_17937),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_17934),tc_HOL_Obool))))),
    inference(definitional_conversion,[status(esa)],[f_4367_2]) ).

cnf(f_4367_4,plain,
    hAPP(c_Relation_OImage(tc_List_Olist(U_17934),tc_List_Olist(U_17934),c_List_Olistrel(U_17934,U_17935)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_17934)),hAPP(hAPP(c_List_Olist_OCons(U_17934),U_17936),U_17937)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_17934),tc_HOL_Obool)))) = c_List_Oset__Cons(U_17934,hAPP(c_Relation_OImage(U_17934,U_17934,U_17935),hAPP(hAPP(c_Set_Oinsert(U_17934),U_17936),c_Orderings_Obot__class_Obot(tc_fun(U_17934,tc_HOL_Obool)))),hAPP(c_Relation_OImage(tc_List_Olist(U_17934),tc_List_Olist(U_17934),c_List_Olistrel(U_17934,U_17935)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_17934)),U_17937),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_17934),tc_HOL_Obool))))),
    inference(clausify,[status(thm)],[f_4367_3]) ).

fof(f_4368_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_4368_2,plain,
    ! [U_17940,U_17939,U_17938] : c_List_Oset__Cons(U_17938,U_17939,U_17940) = hAPP(c_Set_OCollect(tc_List_Olist(U_17938)),hAPP(hAPP(c_COMBB(tc_fun(U_17938,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(U_17938)),c_HOL_OEx(U_17938)),hAPP(hAPP(c_COMBB(tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),tc_fun(U_17938,tc_HOL_Obool),tc_List_Olist(U_17938)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_HOL_Obool,U_17938),c_HOL_OEx(tc_List_Olist(U_17938)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17938),tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_17938,tc_fun(tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool))),tc_fun(tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool))),tc_List_Olist(U_17938)),c_COMBS(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_17938,tc_fun(tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool))),tc_List_Olist(U_17938)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17938),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),U_17938),c_COMBS(tc_List_Olist(U_17938),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(U_17938)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17938),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_17938),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17938)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17938),tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_List_Olist(U_17938))),tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(U_17938),tc_List_Olist(U_17938)),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),tc_fun(tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_List_Olist(U_17938))),tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool))),tc_List_Olist(U_17938)),c_COMBB(tc_fun(tc_List_Olist(U_17938),tc_List_Olist(U_17938)),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),U_17938)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17938),tc_List_Olist(U_17938)),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),tc_List_Olist(U_17938)),c_COMBB(tc_List_Olist(U_17938),tc_HOL_Obool,tc_List_Olist(U_17938))),c_fequal))),c_List_Olist_OCons(U_17938)))))),hAPP(hAPP(c_COMBC(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),U_17938),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17938))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17938),c_fconj),hAPP(hAPP(c_COMBC(U_17938,tc_fun(U_17938,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17938)),U_17939)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17938),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_17938))),U_17940)))))),
    inference(variable_rename,[status(thm)],[f_4368_1]) ).

fof(f_4368_3,plain,
    ! [U_17938,U_17939,U_17940] : c_List_Oset__Cons(U_17938,U_17939,U_17940) = hAPP(c_Set_OCollect(tc_List_Olist(U_17938)),hAPP(hAPP(c_COMBB(tc_fun(U_17938,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(U_17938)),c_HOL_OEx(U_17938)),hAPP(hAPP(c_COMBB(tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),tc_fun(U_17938,tc_HOL_Obool),tc_List_Olist(U_17938)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_HOL_Obool,U_17938),c_HOL_OEx(tc_List_Olist(U_17938)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17938),tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_17938,tc_fun(tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool))),tc_fun(tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool))),tc_List_Olist(U_17938)),c_COMBS(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_17938,tc_fun(tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool))),tc_List_Olist(U_17938)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17938),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),U_17938),c_COMBS(tc_List_Olist(U_17938),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(U_17938)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17938),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_17938),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17938)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17938),tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_List_Olist(U_17938))),tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(U_17938),tc_List_Olist(U_17938)),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),tc_fun(tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_List_Olist(U_17938))),tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool))),tc_List_Olist(U_17938)),c_COMBB(tc_fun(tc_List_Olist(U_17938),tc_List_Olist(U_17938)),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),U_17938)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17938),tc_List_Olist(U_17938)),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),tc_List_Olist(U_17938)),c_COMBB(tc_List_Olist(U_17938),tc_HOL_Obool,tc_List_Olist(U_17938))),c_fequal))),c_List_Olist_OCons(U_17938)))))),hAPP(hAPP(c_COMBC(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),U_17938),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17938))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17938),c_fconj),hAPP(hAPP(c_COMBC(U_17938,tc_fun(U_17938,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17938)),U_17939)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17938),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_17938))),U_17940)))))),
    inference(definitional_conversion,[status(esa)],[f_4368_2]) ).

cnf(f_4368_4,plain,
    c_List_Oset__Cons(U_17938,U_17939,U_17940) = hAPP(c_Set_OCollect(tc_List_Olist(U_17938)),hAPP(hAPP(c_COMBB(tc_fun(U_17938,tc_HOL_Obool),tc_HOL_Obool,tc_List_Olist(U_17938)),c_HOL_OEx(U_17938)),hAPP(hAPP(c_COMBB(tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),tc_fun(U_17938,tc_HOL_Obool),tc_List_Olist(U_17938)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_HOL_Obool,U_17938),c_HOL_OEx(tc_List_Olist(U_17938)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17938),tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_17938,tc_fun(tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool))),tc_fun(tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool))),tc_List_Olist(U_17938)),c_COMBS(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_fun(U_17938,tc_fun(tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool))),tc_List_Olist(U_17938)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17938),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),U_17938),c_COMBS(tc_List_Olist(U_17938),tc_HOL_Obool,tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_fun(tc_HOL_Obool,tc_HOL_Obool))),tc_List_Olist(U_17938)),hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17938),tc_fun(tc_HOL_Obool,tc_HOL_Obool)),U_17938),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_List_Olist(U_17938)),c_fconj))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17938),tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_List_Olist(U_17938))),tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool))),hAPP(hAPP(c_COMBB(tc_fun(tc_fun(tc_List_Olist(U_17938),tc_List_Olist(U_17938)),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),tc_fun(tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_List_Olist(U_17938))),tc_fun(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool))),tc_List_Olist(U_17938)),c_COMBB(tc_fun(tc_List_Olist(U_17938),tc_List_Olist(U_17938)),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),U_17938)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17938),tc_List_Olist(U_17938)),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),tc_List_Olist(U_17938)),c_COMBB(tc_List_Olist(U_17938),tc_HOL_Obool,tc_List_Olist(U_17938))),c_fequal))),c_List_Olist_OCons(U_17938)))))),hAPP(hAPP(c_COMBC(U_17938,tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool)),U_17938),c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_17938))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_17938),c_fconj),hAPP(hAPP(c_COMBC(U_17938,tc_fun(U_17938,tc_HOL_Obool),tc_HOL_Obool),c_member(U_17938)),U_17939)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_17938),tc_fun(tc_List_Olist(U_17938),tc_HOL_Obool),tc_HOL_Obool),c_member(tc_List_Olist(U_17938))),U_17940)))))),
    inference(clausify,[status(thm)],[f_4368_3]) ).

fof(f_4369_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_4369_2,plain,
    ! [U_17947,U_17946,U_17945,U_17944,U_17943] :
      ( ? [U_17942,U_17941] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17943),tc_List_Olist(U_17943))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17943),tc_List_Olist(U_17943)),U_17941),U_17946)),c_List_Olistrel(U_17943,U_17947)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17943,U_17943)),hAPP(hAPP(c_Product__Type_OPair(U_17943,U_17943),U_17942),U_17945)),U_17947))
          & U_17944 = hAPP(hAPP(c_List_Olist_OCons(U_17943),U_17942),U_17941) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17943),tc_List_Olist(U_17943))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17943),tc_List_Olist(U_17943)),U_17944),hAPP(hAPP(c_List_Olist_OCons(U_17943),U_17945),U_17946))),c_List_Olistrel(U_17943,U_17947))) ),
    inference(variable_rename,[status(thm)],[f_4369_1]) ).

fof(f_4369_3,plain,
    ! [U_17947,U_17946,U_17945,U_17944,U_17943] :
      ( ? [U_17941] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17943),tc_List_Olist(U_17943))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17943),tc_List_Olist(U_17943)),U_17941),U_17946)),c_List_Olistrel(U_17943,U_17947)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17943,U_17943)),hAPP(hAPP(c_Product__Type_OPair(U_17943,U_17943),sK451(U_17947,U_17946,U_17945,U_17944,U_17943)),U_17945)),U_17947))
          & U_17944 = hAPP(hAPP(c_List_Olist_OCons(U_17943),sK451(U_17947,U_17946,U_17945,U_17944,U_17943)),U_17941) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17943),tc_List_Olist(U_17943))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17943),tc_List_Olist(U_17943)),U_17944),hAPP(hAPP(c_List_Olist_OCons(U_17943),U_17945),U_17946))),c_List_Olistrel(U_17943,U_17947))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK451]),skolemize(U_17942,sK451(U_17947,U_17946,U_17945,U_17944,U_17943))],[f_4369_2]) ).

fof(f_4369_4,plain,
    ! [U_17947,U_17946,U_17945,U_17944,U_17943] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17943),tc_List_Olist(U_17943))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17943),tc_List_Olist(U_17943)),sK452(U_17947,U_17946,U_17945,U_17944,U_17943)),U_17946)),c_List_Olistrel(U_17943,U_17947)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17943,U_17943)),hAPP(hAPP(c_Product__Type_OPair(U_17943,U_17943),sK451(U_17947,U_17946,U_17945,U_17944,U_17943)),U_17945)),U_17947))
        & U_17944 = hAPP(hAPP(c_List_Olist_OCons(U_17943),sK451(U_17947,U_17946,U_17945,U_17944,U_17943)),sK452(U_17947,U_17946,U_17945,U_17944,U_17943)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17943),tc_List_Olist(U_17943))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17943),tc_List_Olist(U_17943)),U_17944),hAPP(hAPP(c_List_Olist_OCons(U_17943),U_17945),U_17946))),c_List_Olistrel(U_17943,U_17947))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK452]),skolemize(U_17941,sK452(U_17947,U_17946,U_17945,U_17944,U_17943))],[f_4369_3]) ).

fof(f_4369_5,plain,
    ( ! [U_17943,U_17944,U_17945,U_17946,U_17947] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17943),tc_List_Olist(U_17943))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17943),tc_List_Olist(U_17943)),sK452(U_17947,U_17946,U_17945,U_17944,U_17943)),U_17946)),c_List_Olistrel(U_17943,U_17947)))
        | ~ sP1137(U_17943,U_17944,U_17945,U_17946,U_17947) )
    & ! [U_17943,U_17944,U_17945,U_17946,U_17947] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17943,U_17943)),hAPP(hAPP(c_Product__Type_OPair(U_17943,U_17943),sK451(U_17947,U_17946,U_17945,U_17944,U_17943)),U_17945)),U_17947))
        | ~ sP1137(U_17943,U_17944,U_17945,U_17946,U_17947) )
    & ! [U_17943,U_17944,U_17945,U_17946,U_17947] :
        ( U_17944 = hAPP(hAPP(c_List_Olist_OCons(U_17943),sK451(U_17947,U_17946,U_17945,U_17944,U_17943)),sK452(U_17947,U_17946,U_17945,U_17944,U_17943))
        | ~ sP1137(U_17943,U_17944,U_17945,U_17946,U_17947) )
    & ! [U_17943,U_17944,U_17945,U_17946,U_17947] :
        ( sP1137(U_17943,U_17944,U_17945,U_17946,U_17947)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17943),tc_List_Olist(U_17943))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17943),tc_List_Olist(U_17943)),U_17944),hAPP(hAPP(c_List_Olist_OCons(U_17943),U_17945),U_17946))),c_List_Olistrel(U_17943,U_17947))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1137])],[f_4369_4]) ).

cnf(f_4369_6,plain,
    ( sP1137(U_17943,U_17944,U_17945,U_17946,U_17947)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17943),tc_List_Olist(U_17943))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17943),tc_List_Olist(U_17943)),U_17944),hAPP(hAPP(c_List_Olist_OCons(U_17943),U_17945),U_17946))),c_List_Olistrel(U_17943,U_17947))) ),
    inference(clausify,[status(thm)],[f_4369_5]) ).

cnf(f_4369_7,plain,
    ( U_17944 = hAPP(hAPP(c_List_Olist_OCons(U_17943),sK451(U_17947,U_17946,U_17945,U_17944,U_17943)),sK452(U_17947,U_17946,U_17945,U_17944,U_17943))
    | ~ sP1137(U_17943,U_17944,U_17945,U_17946,U_17947) ),
    inference(clausify,[status(thm)],[f_4369_5]) ).

cnf(f_4369_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17943,U_17943)),hAPP(hAPP(c_Product__Type_OPair(U_17943,U_17943),sK451(U_17947,U_17946,U_17945,U_17944,U_17943)),U_17945)),U_17947))
    | ~ sP1137(U_17943,U_17944,U_17945,U_17946,U_17947) ),
    inference(clausify,[status(thm)],[f_4369_5]) ).

cnf(f_4369_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17943),tc_List_Olist(U_17943))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17943),tc_List_Olist(U_17943)),sK452(U_17947,U_17946,U_17945,U_17944,U_17943)),U_17946)),c_List_Olistrel(U_17943,U_17947)))
    | ~ sP1137(U_17943,U_17944,U_17945,U_17946,U_17947) ),
    inference(clausify,[status(thm)],[f_4369_5]) ).

fof(f_4370_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_4370_2,plain,
    ! [U_17954,U_17953,U_17952,U_17951,U_17950] :
      ( ? [U_17949,U_17948] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17950),tc_List_Olist(U_17950))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17950),tc_List_Olist(U_17950)),U_17952),U_17948)),c_List_Olistrel(U_17950,U_17954)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17950,U_17950)),hAPP(hAPP(c_Product__Type_OPair(U_17950,U_17950),U_17951),U_17949)),U_17954))
          & U_17953 = hAPP(hAPP(c_List_Olist_OCons(U_17950),U_17949),U_17948) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17950),tc_List_Olist(U_17950))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17950),tc_List_Olist(U_17950)),hAPP(hAPP(c_List_Olist_OCons(U_17950),U_17951),U_17952)),U_17953)),c_List_Olistrel(U_17950,U_17954))) ),
    inference(variable_rename,[status(thm)],[f_4370_1]) ).

fof(f_4370_3,plain,
    ! [U_17954,U_17953,U_17952,U_17951,U_17950] :
      ( ? [U_17948] :
          ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17950),tc_List_Olist(U_17950))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17950),tc_List_Olist(U_17950)),U_17952),U_17948)),c_List_Olistrel(U_17950,U_17954)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17950,U_17950)),hAPP(hAPP(c_Product__Type_OPair(U_17950,U_17950),U_17951),sK453(U_17954,U_17953,U_17952,U_17951,U_17950))),U_17954))
          & U_17953 = hAPP(hAPP(c_List_Olist_OCons(U_17950),sK453(U_17954,U_17953,U_17952,U_17951,U_17950)),U_17948) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17950),tc_List_Olist(U_17950))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17950),tc_List_Olist(U_17950)),hAPP(hAPP(c_List_Olist_OCons(U_17950),U_17951),U_17952)),U_17953)),c_List_Olistrel(U_17950,U_17954))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK453]),skolemize(U_17949,sK453(U_17954,U_17953,U_17952,U_17951,U_17950))],[f_4370_2]) ).

fof(f_4370_4,plain,
    ! [U_17954,U_17953,U_17952,U_17951,U_17950] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17950),tc_List_Olist(U_17950))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17950),tc_List_Olist(U_17950)),U_17952),sK454(U_17954,U_17953,U_17952,U_17951,U_17950))),c_List_Olistrel(U_17950,U_17954)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_17950,U_17950)),hAPP(hAPP(c_Product__Type_OPair(U_17950,U_17950),U_17951),sK453(U_17954,U_17953,U_17952,U_17951,U_17950))),U_17954))
        & U_17953 = hAPP(hAPP(c_List_Olist_OCons(U_17950),sK453(U_17954,U_17953,U_17952,U_17951,U_17950)),sK454(U_17954,U_17953,U_17952,U_17951,U_17950)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17950),tc_List_Olist(U_17950))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17950),tc_List_Olist(U_17950)),hAPP(hAPP(c_List_Olist_OCons(U_17950),U_17951),U_17952)),U_17953)),c_List_Olistrel(U_17950,U_17954))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK454]),skolemize(U_17948,sK454(U_17954,U_17953,U_17952,U_17951,U_17950))],[f_4370_3]) ).

fof(f_4370_5,plain,
    ( ! [U_17950,U_17951,U_17952,U_17953,U_17954] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17950),tc_List_Olist(U_17950))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17950),tc_List_Olist(U_17950)),U_17952),sK454(U_17954,U_17953,U_17952,U_17951,U_17950))),c_List_Olistrel(U_17950,U_17954)))
        | ~ sP1138(U_17950,U_17951,U_17952,U_17953,U_17954) )
    & ! [U_17950,U_17951,U_17952,U_17953,U_17954] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17950,U_17950)),hAPP(hAPP(c_Product__Type_OPair(U_17950,U_17950),U_17951),sK453(U_17954,U_17953,U_17952,U_17951,U_17950))),U_17954))
        | ~ sP1138(U_17950,U_17951,U_17952,U_17953,U_17954) )
    & ! [U_17950,U_17951,U_17952,U_17953,U_17954] :
        ( U_17953 = hAPP(hAPP(c_List_Olist_OCons(U_17950),sK453(U_17954,U_17953,U_17952,U_17951,U_17950)),sK454(U_17954,U_17953,U_17952,U_17951,U_17950))
        | ~ sP1138(U_17950,U_17951,U_17952,U_17953,U_17954) )
    & ! [U_17950,U_17951,U_17952,U_17953,U_17954] :
        ( sP1138(U_17950,U_17951,U_17952,U_17953,U_17954)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17950),tc_List_Olist(U_17950))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17950),tc_List_Olist(U_17950)),hAPP(hAPP(c_List_Olist_OCons(U_17950),U_17951),U_17952)),U_17953)),c_List_Olistrel(U_17950,U_17954))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1138])],[f_4370_4]) ).

cnf(f_4370_6,plain,
    ( sP1138(U_17950,U_17951,U_17952,U_17953,U_17954)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17950),tc_List_Olist(U_17950))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17950),tc_List_Olist(U_17950)),hAPP(hAPP(c_List_Olist_OCons(U_17950),U_17951),U_17952)),U_17953)),c_List_Olistrel(U_17950,U_17954))) ),
    inference(clausify,[status(thm)],[f_4370_5]) ).

cnf(f_4370_7,plain,
    ( U_17953 = hAPP(hAPP(c_List_Olist_OCons(U_17950),sK453(U_17954,U_17953,U_17952,U_17951,U_17950)),sK454(U_17954,U_17953,U_17952,U_17951,U_17950))
    | ~ sP1138(U_17950,U_17951,U_17952,U_17953,U_17954) ),
    inference(clausify,[status(thm)],[f_4370_5]) ).

cnf(f_4370_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_17950,U_17950)),hAPP(hAPP(c_Product__Type_OPair(U_17950,U_17950),U_17951),sK453(U_17954,U_17953,U_17952,U_17951,U_17950))),U_17954))
    | ~ sP1138(U_17950,U_17951,U_17952,U_17953,U_17954) ),
    inference(clausify,[status(thm)],[f_4370_5]) ).

cnf(f_4370_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_17950),tc_List_Olist(U_17950))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_17950),tc_List_Olist(U_17950)),U_17952),sK454(U_17954,U_17953,U_17952,U_17951,U_17950))),c_List_Olistrel(U_17950,U_17954)))
    | ~ sP1138(U_17950,U_17951,U_17952,U_17953,U_17954) ),
    inference(clausify,[status(thm)],[f_4370_5]) ).

fof(f_4371_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_4371_2,plain,
    ! [U_17957,U_17956,U_17955] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17955)),c_List_Osublist(U_17955,U_17956,U_17957)) = 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_17955)),U_17956)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_17957)))),
    inference(variable_rename,[status(thm)],[f_4371_1]) ).

fof(f_4371_3,plain,
    ! [U_17955,U_17956,U_17957] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17955)),c_List_Osublist(U_17955,U_17956,U_17957)) = 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_17955)),U_17956)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_17957)))),
    inference(definitional_conversion,[status(esa)],[f_4371_2]) ).

cnf(f_4371_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_17955)),c_List_Osublist(U_17955,U_17956,U_17957)) = 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_17955)),U_17956)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_17957)))),
    inference(clausify,[status(thm)],[f_4371_3]) ).

fof(f_4372_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_4372_2,plain,
    ! [U_17961,U_17960,U_17959,U_17958] :
      ( ( hAPP(c_Random_Opick(U_17959,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17959)),U_17960),U_17961)),U_17958) = hAPP(c_Random_Opick(U_17959,U_17961),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_17958),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17959),U_17960)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17958),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17959),U_17960))) )
      & ( hAPP(c_Random_Opick(U_17959,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17959)),U_17960),U_17961)),U_17958) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_17959),U_17960)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17958),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17959),U_17960))) ) ),
    inference(variable_rename,[status(thm)],[f_4372_1]) ).

fof(f_4372_3,plain,
    ( ! [U_17969,U_17967,U_17965,U_17963] :
        ( hAPP(c_Random_Opick(U_17965,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17965)),U_17967),U_17969)),U_17963) = hAPP(c_Random_Opick(U_17965,U_17969),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_17963),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17965),U_17967)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17963),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17965),U_17967))) )
    & ! [U_17968,U_17966,U_17964,U_17962] :
        ( hAPP(c_Random_Opick(U_17964,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17964)),U_17966),U_17968)),U_17962) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_17964),U_17966)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17962),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17964),U_17966))) ) ),
    inference(miniscope,[status(thm)],[f_4372_2]) ).

fof(f_4372_4,plain,
    ( ! [U_17963,U_17965,U_17967,U_17969] :
        ( hAPP(c_Random_Opick(U_17965,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17965)),U_17967),U_17969)),U_17963) = hAPP(c_Random_Opick(U_17965,U_17969),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_17963),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17965),U_17967)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17963),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17965),U_17967))) )
    & ! [U_17964,U_17968,U_17962,U_17966] :
        ( hAPP(c_Random_Opick(U_17964,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17964)),U_17966),U_17968)),U_17962) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_17964),U_17966)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17962),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17964),U_17966))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4372_3]) ).

cnf(f_4372_5,plain,
    ( hAPP(c_Random_Opick(U_17964,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17964)),U_17966),U_17968)),U_17962) = hAPP(c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_17964),U_17966)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17962),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17964),U_17966))) ),
    inference(clausify,[status(thm)],[f_4372_4]) ).

cnf(f_4372_6,plain,
    ( hAPP(c_Random_Opick(U_17965,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17965)),U_17967),U_17969)),U_17963) = hAPP(c_Random_Opick(U_17965,U_17969),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_17963),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17965),U_17967)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17963),hAPP(c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17965),U_17967))) ),
    inference(clausify,[status(thm)],[f_4372_4]) ).

fof(f_4373_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_4373_2,plain,
    ! [U_17972,U_17971,U_17970] :
      ( hBOOL(hAPP(c_List_Odistinct(U_17970),c_List_Osublist(U_17970,U_17971,U_17972)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17970),U_17971)) ),
    inference(variable_rename,[status(thm)],[f_4373_1]) ).

fof(f_4373_3,plain,
    ! [U_17970,U_17972,U_17971] :
      ( hBOOL(hAPP(c_List_Odistinct(U_17970),c_List_Osublist(U_17970,U_17971,U_17972)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_17970),U_17971)) ),
    inference(definitional_conversion,[status(esa)],[f_4373_2]) ).

cnf(f_4373_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_17970),c_List_Osublist(U_17970,U_17971,U_17972)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_17970),U_17971)) ),
    inference(clausify,[status(thm)],[f_4373_3]) ).

fof(f_4374_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_4374_2,plain,
    ! [U_17976,U_17975,U_17974,U_17973] :
      ( hBOOL(hAPP(hAPP(c_member(U_17973),U_17974),hAPP(c_List_Oset(U_17973),U_17975)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17973),U_17974),hAPP(c_List_Oset(U_17973),c_List_Osublist(U_17973,U_17975,U_17976)))) ),
    inference(variable_rename,[status(thm)],[f_4374_1]) ).

fof(f_4374_3,plain,
    ! [U_17973,U_17974,U_17975,U_17976] :
      ( hBOOL(hAPP(hAPP(c_member(U_17973),U_17974),hAPP(c_List_Oset(U_17973),U_17975)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_17973),U_17974),hAPP(c_List_Oset(U_17973),c_List_Osublist(U_17973,U_17975,U_17976)))) ),
    inference(definitional_conversion,[status(esa)],[f_4374_2]) ).

cnf(f_4374_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17973),U_17974),hAPP(c_List_Oset(U_17973),U_17975)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_17973),U_17974),hAPP(c_List_Oset(U_17973),c_List_Osublist(U_17973,U_17975,U_17976)))) ),
    inference(clausify,[status(thm)],[f_4374_3]) ).

fof(f_4375_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_4375_2,plain,
    ! [U_17980,U_17979,U_17978,U_17977] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_17977),U_17978),hAPP(c_List_Oset(U_17977),c_List_Osublist(U_17977,U_17979,U_17980))))
      | hBOOL(hAPP(hAPP(c_member(U_17977),U_17978),hAPP(c_List_Oset(U_17977),U_17979))) ),
    inference(variable_rename,[status(thm)],[f_4375_1]) ).

fof(f_4375_3,plain,
    ! [U_17977,U_17978,U_17979,U_17980] :
      ( ~ hBOOL(hAPP(hAPP(c_member(U_17977),U_17978),hAPP(c_List_Oset(U_17977),c_List_Osublist(U_17977,U_17979,U_17980))))
      | hBOOL(hAPP(hAPP(c_member(U_17977),U_17978),hAPP(c_List_Oset(U_17977),U_17979))) ),
    inference(definitional_conversion,[status(esa)],[f_4375_2]) ).

cnf(f_4375_4,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_17977),U_17978),hAPP(c_List_Oset(U_17977),c_List_Osublist(U_17977,U_17979,U_17980))))
    | hBOOL(hAPP(hAPP(c_member(U_17977),U_17978),hAPP(c_List_Oset(U_17977),U_17979))) ),
    inference(clausify,[status(thm)],[f_4375_3]) ).

fof(f_4376_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_4376_2,plain,
    ! [U_17983,U_17982,U_17981] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17981,tc_HOL_Obool)),hAPP(c_List_Oset(U_17981),c_List_Osublist(U_17981,U_17982,U_17983))),hAPP(c_List_Oset(U_17981),U_17982))),
    inference(variable_rename,[status(thm)],[f_4376_1]) ).

fof(f_4376_3,plain,
    ! [U_17981,U_17982,U_17983] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17981,tc_HOL_Obool)),hAPP(c_List_Oset(U_17981),c_List_Osublist(U_17981,U_17982,U_17983))),hAPP(c_List_Oset(U_17981),U_17982))),
    inference(definitional_conversion,[status(esa)],[f_4376_2]) ).

cnf(f_4376_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_17981,tc_HOL_Obool)),hAPP(c_List_Oset(U_17981),c_List_Osublist(U_17981,U_17982,U_17983))),hAPP(c_List_Oset(U_17981),U_17982))),
    inference(clausify,[status(thm)],[f_4376_3]) ).

fof(f_4377_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_4377_2,plain,
    ! [U_17986,U_17985,U_17984] : c_Random_Oselect__weight(U_17984,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17984)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_17984),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_17985)),U_17986)) = c_Random_Oselect__weight(U_17984,U_17986),
    inference(variable_rename,[status(thm)],[f_4377_1]) ).

fof(f_4377_3,plain,
    ! [U_17984,U_17985,U_17986] : c_Random_Oselect__weight(U_17984,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17984)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_17984),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_17985)),U_17986)) = c_Random_Oselect__weight(U_17984,U_17986),
    inference(definitional_conversion,[status(esa)],[f_4377_2]) ).

cnf(f_4377_4,plain,
    c_Random_Oselect__weight(U_17984,hAPP(hAPP(c_List_Olist_OCons(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17984)),hAPP(hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_17984),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral)),U_17985)),U_17986)) = c_Random_Oselect__weight(U_17984,U_17986),
    inference(clausify,[status(thm)],[f_4377_3]) ).

fof(f_4378_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_4378_2,plain,
    ! [U_17989,U_17988,U_17987] :
      ( hBOOL(hAPP(hAPP(c_member(U_17988),hAPP(c_Random_Opick(U_17988,U_17989),U_17987)),hAPP(c_List_Oset(U_17988),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17988),U_17988),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_17988)),U_17989))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17987),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_17988),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17988)),U_17989)))) ),
    inference(variable_rename,[status(thm)],[f_4378_1]) ).

fof(f_4378_3,plain,
    ! [U_17987,U_17988,U_17989] :
      ( hBOOL(hAPP(hAPP(c_member(U_17988),hAPP(c_Random_Opick(U_17988,U_17989),U_17987)),hAPP(c_List_Oset(U_17988),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17988),U_17988),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_17988)),U_17989))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17987),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_17988),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17988)),U_17989)))) ),
    inference(definitional_conversion,[status(esa)],[f_4378_2]) ).

cnf(f_4378_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_17988),hAPP(c_Random_Opick(U_17988,U_17989),U_17987)),hAPP(c_List_Oset(U_17988),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_17988),U_17988),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_17988)),U_17989))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),U_17987),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_17988),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_17988)),U_17989)))) ),
    inference(clausify,[status(thm)],[f_4378_3]) ).

fof(f_4379_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_4379_2,plain,
    ! [U_17992,U_17991,U_17990] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17990),hAPP(hAPP(c_List_Olist_OCons(U_17990),U_17991),U_17992)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17990),U_17991),hAPP(c_List_Omonoid__add__class_Olistsum(U_17990),U_17992))
      | ~ class_Groups_Omonoid__add(U_17990) ),
    inference(variable_rename,[status(thm)],[f_4379_1]) ).

fof(f_4379_3,plain,
    ! [U_17990,U_17991,U_17992] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17990),hAPP(hAPP(c_List_Olist_OCons(U_17990),U_17991),U_17992)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17990),U_17991),hAPP(c_List_Omonoid__add__class_Olistsum(U_17990),U_17992))
      | ~ class_Groups_Omonoid__add(U_17990) ),
    inference(definitional_conversion,[status(esa)],[f_4379_2]) ).

cnf(f_4379_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17990),hAPP(hAPP(c_List_Olist_OCons(U_17990),U_17991),U_17992)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17990),U_17991),hAPP(c_List_Omonoid__add__class_Olistsum(U_17990),U_17992))
    | ~ class_Groups_Omonoid__add(U_17990) ),
    inference(clausify,[status(thm)],[f_4379_3]) ).

fof(f_4380_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_4380_2,plain,
    ! [U_17997,U_17996,U_17995,U_17994,U_17993] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17993),hAPP(hAPP(c_List_Omap(U_17994,U_17993),hAPP(hAPP(c_COMBS(U_17994,U_17993,U_17993),hAPP(hAPP(c_COMBB(U_17993,tc_fun(U_17993,U_17993),U_17994),c_Groups_Oplus__class_Oplus(U_17993)),U_17995)),U_17996)),U_17997)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17993),hAPP(c_List_Omonoid__add__class_Olistsum(U_17993),hAPP(hAPP(c_List_Omap(U_17994,U_17993),U_17995),U_17997))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17993),hAPP(hAPP(c_List_Omap(U_17994,U_17993),U_17996),U_17997)))
      | ~ class_Groups_Ocomm__monoid__add(U_17993) ),
    inference(variable_rename,[status(thm)],[f_4380_1]) ).

fof(f_4380_3,plain,
    ! [U_17993,U_17994,U_17995,U_17996,U_17997] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17993),hAPP(hAPP(c_List_Omap(U_17994,U_17993),hAPP(hAPP(c_COMBS(U_17994,U_17993,U_17993),hAPP(hAPP(c_COMBB(U_17993,tc_fun(U_17993,U_17993),U_17994),c_Groups_Oplus__class_Oplus(U_17993)),U_17995)),U_17996)),U_17997)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17993),hAPP(c_List_Omonoid__add__class_Olistsum(U_17993),hAPP(hAPP(c_List_Omap(U_17994,U_17993),U_17995),U_17997))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17993),hAPP(hAPP(c_List_Omap(U_17994,U_17993),U_17996),U_17997)))
      | ~ class_Groups_Ocomm__monoid__add(U_17993) ),
    inference(definitional_conversion,[status(esa)],[f_4380_2]) ).

cnf(f_4380_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17993),hAPP(hAPP(c_List_Omap(U_17994,U_17993),hAPP(hAPP(c_COMBS(U_17994,U_17993,U_17993),hAPP(hAPP(c_COMBB(U_17993,tc_fun(U_17993,U_17993),U_17994),c_Groups_Oplus__class_Oplus(U_17993)),U_17995)),U_17996)),U_17997)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_17993),hAPP(c_List_Omonoid__add__class_Olistsum(U_17993),hAPP(hAPP(c_List_Omap(U_17994,U_17993),U_17995),U_17997))),hAPP(c_List_Omonoid__add__class_Olistsum(U_17993),hAPP(hAPP(c_List_Omap(U_17994,U_17993),U_17996),U_17997)))
    | ~ class_Groups_Ocomm__monoid__add(U_17993) ),
    inference(clausify,[status(thm)],[f_4380_3]) ).

fof(f_4381_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_4381_2,plain,
    ! [U_18002,U_18001,U_18000,U_17999,U_17998] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17998),hAPP(hAPP(c_List_Omap(U_17999,U_17998),hAPP(hAPP(c_COMBB(U_17998,U_17998,U_17999),hAPP(c_Groups_Otimes__class_Otimes(U_17998),U_18000)),U_18001)),U_18002)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_17998),U_18000),hAPP(c_List_Omonoid__add__class_Olistsum(U_17998),hAPP(hAPP(c_List_Omap(U_17999,U_17998),U_18001),U_18002)))
      | ~ class_Rings_Osemiring__0(U_17998) ),
    inference(variable_rename,[status(thm)],[f_4381_1]) ).

fof(f_4381_3,plain,
    ! [U_17998,U_17999,U_18000,U_18001,U_18002] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17998),hAPP(hAPP(c_List_Omap(U_17999,U_17998),hAPP(hAPP(c_COMBB(U_17998,U_17998,U_17999),hAPP(c_Groups_Otimes__class_Otimes(U_17998),U_18000)),U_18001)),U_18002)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_17998),U_18000),hAPP(c_List_Omonoid__add__class_Olistsum(U_17998),hAPP(hAPP(c_List_Omap(U_17999,U_17998),U_18001),U_18002)))
      | ~ class_Rings_Osemiring__0(U_17998) ),
    inference(definitional_conversion,[status(esa)],[f_4381_2]) ).

cnf(f_4381_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_17998),hAPP(hAPP(c_List_Omap(U_17999,U_17998),hAPP(hAPP(c_COMBB(U_17998,U_17998,U_17999),hAPP(c_Groups_Otimes__class_Otimes(U_17998),U_18000)),U_18001)),U_18002)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_17998),U_18000),hAPP(c_List_Omonoid__add__class_Olistsum(U_17998),hAPP(hAPP(c_List_Omap(U_17999,U_17998),U_18001),U_18002)))
    | ~ class_Rings_Osemiring__0(U_17998) ),
    inference(clausify,[status(thm)],[f_4381_3]) ).

fof(f_4382_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_4382_2,plain,
    ! [U_18007,U_18006,U_18005,U_18004,U_18003] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18003),hAPP(hAPP(c_List_Omap(U_18004,U_18003),hAPP(hAPP(c_COMBC(U_18004,U_18003,U_18003),hAPP(hAPP(c_COMBB(U_18003,tc_fun(U_18003,U_18003),U_18004),c_Groups_Otimes__class_Otimes(U_18003)),U_18005)),U_18006)),U_18007)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18003),hAPP(c_List_Omonoid__add__class_Olistsum(U_18003),hAPP(hAPP(c_List_Omap(U_18004,U_18003),U_18005),U_18007))),U_18006)
      | ~ class_Rings_Osemiring__0(U_18003) ),
    inference(variable_rename,[status(thm)],[f_4382_1]) ).

fof(f_4382_3,plain,
    ! [U_18003,U_18004,U_18005,U_18006,U_18007] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18003),hAPP(hAPP(c_List_Omap(U_18004,U_18003),hAPP(hAPP(c_COMBC(U_18004,U_18003,U_18003),hAPP(hAPP(c_COMBB(U_18003,tc_fun(U_18003,U_18003),U_18004),c_Groups_Otimes__class_Otimes(U_18003)),U_18005)),U_18006)),U_18007)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18003),hAPP(c_List_Omonoid__add__class_Olistsum(U_18003),hAPP(hAPP(c_List_Omap(U_18004,U_18003),U_18005),U_18007))),U_18006)
      | ~ class_Rings_Osemiring__0(U_18003) ),
    inference(definitional_conversion,[status(esa)],[f_4382_2]) ).

cnf(f_4382_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18003),hAPP(hAPP(c_List_Omap(U_18004,U_18003),hAPP(hAPP(c_COMBC(U_18004,U_18003,U_18003),hAPP(hAPP(c_COMBB(U_18003,tc_fun(U_18003,U_18003),U_18004),c_Groups_Otimes__class_Otimes(U_18003)),U_18005)),U_18006)),U_18007)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18003),hAPP(c_List_Omonoid__add__class_Olistsum(U_18003),hAPP(hAPP(c_List_Omap(U_18004,U_18003),U_18005),U_18007))),U_18006)
    | ~ class_Rings_Osemiring__0(U_18003) ),
    inference(clausify,[status(thm)],[f_4382_3]) ).

fof(f_4383_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_4383_2,plain,
    ! [U_18010,U_18009,U_18008] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18008),hAPP(hAPP(c_List_Omap(U_18009,U_18008),hAPP(c_COMBK(U_18008,U_18009),c_Groups_Ozero__class_Ozero(U_18008))),U_18010)) = c_Groups_Ozero__class_Ozero(U_18008)
      | ~ class_Groups_Omonoid__add(U_18008) ),
    inference(variable_rename,[status(thm)],[f_4383_1]) ).

fof(f_4383_3,plain,
    ! [U_18008,U_18009,U_18010] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18008),hAPP(hAPP(c_List_Omap(U_18009,U_18008),hAPP(c_COMBK(U_18008,U_18009),c_Groups_Ozero__class_Ozero(U_18008))),U_18010)) = c_Groups_Ozero__class_Ozero(U_18008)
      | ~ class_Groups_Omonoid__add(U_18008) ),
    inference(definitional_conversion,[status(esa)],[f_4383_2]) ).

cnf(f_4383_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18008),hAPP(hAPP(c_List_Omap(U_18009,U_18008),hAPP(c_COMBK(U_18008,U_18009),c_Groups_Ozero__class_Ozero(U_18008))),U_18010)) = c_Groups_Ozero__class_Ozero(U_18008)
    | ~ class_Groups_Omonoid__add(U_18008) ),
    inference(clausify,[status(thm)],[f_4383_3]) ).

fof(f_4384_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_4384_2,plain,
    ! [U_18015,U_18014,U_18013,U_18012,U_18011] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18011),hAPP(hAPP(c_List_Omap(U_18012,U_18011),hAPP(hAPP(c_COMBS(U_18012,U_18011,U_18011),hAPP(hAPP(c_COMBB(U_18011,tc_fun(U_18011,U_18011),U_18012),c_Groups_Ominus__class_Ominus(U_18011)),U_18013)),U_18014)),U_18015)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_18011),hAPP(c_List_Omonoid__add__class_Olistsum(U_18011),hAPP(hAPP(c_List_Omap(U_18012,U_18011),U_18013),U_18015))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18011),hAPP(hAPP(c_List_Omap(U_18012,U_18011),U_18014),U_18015)))
      | ~ class_Groups_Oab__group__add(U_18011) ),
    inference(variable_rename,[status(thm)],[f_4384_1]) ).

fof(f_4384_3,plain,
    ! [U_18011,U_18012,U_18013,U_18014,U_18015] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18011),hAPP(hAPP(c_List_Omap(U_18012,U_18011),hAPP(hAPP(c_COMBS(U_18012,U_18011,U_18011),hAPP(hAPP(c_COMBB(U_18011,tc_fun(U_18011,U_18011),U_18012),c_Groups_Ominus__class_Ominus(U_18011)),U_18013)),U_18014)),U_18015)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_18011),hAPP(c_List_Omonoid__add__class_Olistsum(U_18011),hAPP(hAPP(c_List_Omap(U_18012,U_18011),U_18013),U_18015))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18011),hAPP(hAPP(c_List_Omap(U_18012,U_18011),U_18014),U_18015)))
      | ~ class_Groups_Oab__group__add(U_18011) ),
    inference(definitional_conversion,[status(esa)],[f_4384_2]) ).

cnf(f_4384_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18011),hAPP(hAPP(c_List_Omap(U_18012,U_18011),hAPP(hAPP(c_COMBS(U_18012,U_18011,U_18011),hAPP(hAPP(c_COMBB(U_18011,tc_fun(U_18011,U_18011),U_18012),c_Groups_Ominus__class_Ominus(U_18011)),U_18013)),U_18014)),U_18015)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(U_18011),hAPP(c_List_Omonoid__add__class_Olistsum(U_18011),hAPP(hAPP(c_List_Omap(U_18012,U_18011),U_18013),U_18015))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18011),hAPP(hAPP(c_List_Omap(U_18012,U_18011),U_18014),U_18015)))
    | ~ class_Groups_Oab__group__add(U_18011) ),
    inference(clausify,[status(thm)],[f_4384_3]) ).

fof(f_4385_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_4385_2,plain,
    ! [U_18017,U_18016] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18016),hAPP(c_Groups_Oabs__class_Oabs(U_18016),hAPP(c_List_Omonoid__add__class_Olistsum(U_18016),U_18017))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18016),hAPP(hAPP(c_List_Omap(U_18016,U_18016),c_Groups_Oabs__class_Oabs(U_18016)),U_18017))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_18016) ),
    inference(variable_rename,[status(thm)],[f_4385_1]) ).

fof(f_4385_3,plain,
    ! [U_18016,U_18017] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18016),hAPP(c_Groups_Oabs__class_Oabs(U_18016),hAPP(c_List_Omonoid__add__class_Olistsum(U_18016),U_18017))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18016),hAPP(hAPP(c_List_Omap(U_18016,U_18016),c_Groups_Oabs__class_Oabs(U_18016)),U_18017))))
      | ~ class_Groups_Oordered__ab__group__add__abs(U_18016) ),
    inference(definitional_conversion,[status(esa)],[f_4385_2]) ).

cnf(f_4385_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_18016),hAPP(c_Groups_Oabs__class_Oabs(U_18016),hAPP(c_List_Omonoid__add__class_Olistsum(U_18016),U_18017))),hAPP(c_List_Omonoid__add__class_Olistsum(U_18016),hAPP(hAPP(c_List_Omap(U_18016,U_18016),c_Groups_Oabs__class_Oabs(U_18016)),U_18017))))
    | ~ class_Groups_Oordered__ab__group__add__abs(U_18016) ),
    inference(clausify,[status(thm)],[f_4385_3]) ).

fof(f_4386_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_4386_2,plain,
    ! [U_18021,U_18020,U_18019,U_18018] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_18018),hAPP(c_List_Omonoid__add__class_Olistsum(U_18018),hAPP(hAPP(c_List_Omap(U_18019,U_18018),U_18020),U_18021))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18018),hAPP(hAPP(c_List_Omap(U_18019,U_18018),hAPP(c_Fun_Ocomp(U_18018,U_18018,U_18019,c_Groups_Ouminus__class_Ouminus(U_18018)),U_18020)),U_18021))
      | ~ class_Groups_Oab__group__add(U_18018) ),
    inference(variable_rename,[status(thm)],[f_4386_1]) ).

fof(f_4386_3,plain,
    ! [U_18018,U_18019,U_18020,U_18021] :
      ( hAPP(c_Groups_Ouminus__class_Ouminus(U_18018),hAPP(c_List_Omonoid__add__class_Olistsum(U_18018),hAPP(hAPP(c_List_Omap(U_18019,U_18018),U_18020),U_18021))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18018),hAPP(hAPP(c_List_Omap(U_18019,U_18018),hAPP(c_Fun_Ocomp(U_18018,U_18018,U_18019,c_Groups_Ouminus__class_Ouminus(U_18018)),U_18020)),U_18021))
      | ~ class_Groups_Oab__group__add(U_18018) ),
    inference(definitional_conversion,[status(esa)],[f_4386_2]) ).

cnf(f_4386_4,plain,
    ( hAPP(c_Groups_Ouminus__class_Ouminus(U_18018),hAPP(c_List_Omonoid__add__class_Olistsum(U_18018),hAPP(hAPP(c_List_Omap(U_18019,U_18018),U_18020),U_18021))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18018),hAPP(hAPP(c_List_Omap(U_18019,U_18018),hAPP(c_Fun_Ocomp(U_18018,U_18018,U_18019,c_Groups_Ouminus__class_Ouminus(U_18018)),U_18020)),U_18021))
    | ~ class_Groups_Oab__group__add(U_18018) ),
    inference(clausify,[status(thm)],[f_4386_3]) ).

fof(f_4387_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_4387_2,plain,
    ! [U_18023,U_18022] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18022),U_18023) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_18022,U_18022),c_COMBI(U_18022)),hAPP(c_List_Oset(U_18022),U_18023))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18022),U_18023))
      | ~ class_Groups_Ocomm__monoid__add(U_18022) ),
    inference(variable_rename,[status(thm)],[f_4387_1]) ).

fof(f_4387_3,plain,
    ! [U_18022,U_18023] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18022),U_18023) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_18022,U_18022),c_COMBI(U_18022)),hAPP(c_List_Oset(U_18022),U_18023))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18022),U_18023))
      | ~ class_Groups_Ocomm__monoid__add(U_18022) ),
    inference(definitional_conversion,[status(esa)],[f_4387_2]) ).

cnf(f_4387_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18022),U_18023) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_18022,U_18022),c_COMBI(U_18022)),hAPP(c_List_Oset(U_18022),U_18023))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18022),U_18023))
    | ~ class_Groups_Ocomm__monoid__add(U_18022) ),
    inference(clausify,[status(thm)],[f_4387_3]) ).

fof(f_4388_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_4388_2,plain,
    ! [U_18025,U_18024] : c_Random_Oselect__weight(U_18024,U_18025) = 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_18024,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_18024),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18024)),U_18025)))),hAPP(hAPP(c_COMBB(U_18024,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18024,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18024,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(U_18024,U_18025))),
    inference(variable_rename,[status(thm)],[f_4388_1]) ).

fof(f_4388_3,plain,
    ! [U_18024,U_18025] : c_Random_Oselect__weight(U_18024,U_18025) = 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_18024,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_18024),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18024)),U_18025)))),hAPP(hAPP(c_COMBB(U_18024,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18024,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18024,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(U_18024,U_18025))),
    inference(definitional_conversion,[status(esa)],[f_4388_2]) ).

cnf(f_4388_4,plain,
    c_Random_Oselect__weight(U_18024,U_18025) = 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_18024,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_18024),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18024)),U_18025)))),hAPP(hAPP(c_COMBB(U_18024,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18024,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18024,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),c_Random_Opick(U_18024,U_18025))),
    inference(clausify,[status(thm)],[f_4388_3]) ).

fof(f_4389_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_4389_2,plain,
    ! [U_18029,U_18028,U_18027,U_18026] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18026),hAPP(hAPP(c_List_Omap(U_18027,U_18026),U_18029),U_18028)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_18027,U_18026),U_18029),hAPP(c_List_Oset(U_18027),U_18028))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18027),U_18028))
      | ~ class_Groups_Ocomm__monoid__add(U_18026) ),
    inference(variable_rename,[status(thm)],[f_4389_1]) ).

fof(f_4389_3,plain,
    ! [U_18026,U_18027,U_18028,U_18029] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18026),hAPP(hAPP(c_List_Omap(U_18027,U_18026),U_18029),U_18028)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_18027,U_18026),U_18029),hAPP(c_List_Oset(U_18027),U_18028))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18027),U_18028))
      | ~ class_Groups_Ocomm__monoid__add(U_18026) ),
    inference(definitional_conversion,[status(esa)],[f_4389_2]) ).

cnf(f_4389_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18026),hAPP(hAPP(c_List_Omap(U_18027,U_18026),U_18029),U_18028)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(U_18027,U_18026),U_18029),hAPP(c_List_Oset(U_18027),U_18028))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18027),U_18028))
    | ~ class_Groups_Ocomm__monoid__add(U_18026) ),
    inference(clausify,[status(thm)],[f_4389_3]) ).

fof(f_4390_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_4390_2,plain,
    ! [U_18033,U_18032,U_18031,U_18030] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18030),U_18031),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18032,U_18033))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18030),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18030),U_18031),c_List_Oupto(U_18032,U_18033)))
      | ~ class_Groups_Ocomm__monoid__add(U_18030) ),
    inference(variable_rename,[status(thm)],[f_4390_1]) ).

fof(f_4390_3,plain,
    ! [U_18030,U_18031,U_18032,U_18033] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18030),U_18031),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18032,U_18033))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18030),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18030),U_18031),c_List_Oupto(U_18032,U_18033)))
      | ~ class_Groups_Ocomm__monoid__add(U_18030) ),
    inference(definitional_conversion,[status(esa)],[f_4390_2]) ).

cnf(f_4390_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18030),U_18031),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18032,U_18033))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18030),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18030),U_18031),c_List_Oupto(U_18032,U_18033)))
    | ~ class_Groups_Ocomm__monoid__add(U_18030) ),
    inference(clausify,[status(thm)],[f_4390_3]) ).

fof(f_4391_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_4391_2,plain,
    ! [U_18037,U_18036,U_18035,U_18034] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18034),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18034),U_18035),c_List_Oupto(U_18036,U_18037))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18034),U_18035),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18036,U_18037)))
      | ~ class_Groups_Ocomm__monoid__add(U_18034) ),
    inference(variable_rename,[status(thm)],[f_4391_1]) ).

fof(f_4391_3,plain,
    ! [U_18034,U_18035,U_18036,U_18037] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18034),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18034),U_18035),c_List_Oupto(U_18036,U_18037))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18034),U_18035),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18036,U_18037)))
      | ~ class_Groups_Ocomm__monoid__add(U_18034) ),
    inference(definitional_conversion,[status(esa)],[f_4391_2]) ).

cnf(f_4391_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18034),hAPP(hAPP(c_List_Omap(tc_Int_Oint,U_18034),U_18035),c_List_Oupto(U_18036,U_18037))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Int_Oint,U_18034),U_18035),hAPP(c_List_Oset(tc_Int_Oint),c_List_Oupto(U_18036,U_18037)))
    | ~ class_Groups_Ocomm__monoid__add(U_18034) ),
    inference(clausify,[status(thm)],[f_4391_3]) ).

fof(f_4392_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_4392_2,plain,
    ! [U_18041,U_18040,U_18039,U_18038] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18038),hAPP(hAPP(c_List_Omap(U_18039,U_18038),hAPP(c_COMBK(U_18038,U_18039),U_18040)),U_18041)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18038),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_18038),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18039)),U_18041))),U_18040)
      | ~ class_Rings_Osemiring__1(U_18038) ),
    inference(variable_rename,[status(thm)],[f_4392_1]) ).

fof(f_4392_3,plain,
    ! [U_18038,U_18039,U_18040,U_18041] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18038),hAPP(hAPP(c_List_Omap(U_18039,U_18038),hAPP(c_COMBK(U_18038,U_18039),U_18040)),U_18041)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18038),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_18038),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18039)),U_18041))),U_18040)
      | ~ class_Rings_Osemiring__1(U_18038) ),
    inference(definitional_conversion,[status(esa)],[f_4392_2]) ).

cnf(f_4392_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18038),hAPP(hAPP(c_List_Omap(U_18039,U_18038),hAPP(c_COMBK(U_18038,U_18039),U_18040)),U_18041)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(U_18038),hAPP(c_Nat_Osemiring__1__class_Oof__nat(U_18038),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18039)),U_18041))),U_18040)
    | ~ class_Rings_Osemiring__1(U_18038) ),
    inference(clausify,[status(thm)],[f_4392_3]) ).

fof(f_4393_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_4393_2,plain,
    ! [U_18046,U_18045,U_18044,U_18043,U_18042] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18042),hAPP(hAPP(c_List_Omap(U_18043,U_18042),U_18046),U_18045)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18042),hAPP(U_18046,U_18044)),hAPP(c_List_Omonoid__add__class_Olistsum(U_18042),hAPP(hAPP(c_List_Omap(U_18043,U_18042),U_18046),c_List_Oremove1(U_18043,U_18044,U_18045))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18043),U_18044),hAPP(c_List_Oset(U_18043),U_18045)))
      | ~ class_Groups_Ocomm__monoid__add(U_18042) ),
    inference(variable_rename,[status(thm)],[f_4393_1]) ).

fof(f_4393_3,plain,
    ! [U_18042,U_18043,U_18044,U_18045,U_18046] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18042),hAPP(hAPP(c_List_Omap(U_18043,U_18042),U_18046),U_18045)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18042),hAPP(U_18046,U_18044)),hAPP(c_List_Omonoid__add__class_Olistsum(U_18042),hAPP(hAPP(c_List_Omap(U_18043,U_18042),U_18046),c_List_Oremove1(U_18043,U_18044,U_18045))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18043),U_18044),hAPP(c_List_Oset(U_18043),U_18045)))
      | ~ class_Groups_Ocomm__monoid__add(U_18042) ),
    inference(definitional_conversion,[status(esa)],[f_4393_2]) ).

cnf(f_4393_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18042),hAPP(hAPP(c_List_Omap(U_18043,U_18042),U_18046),U_18045)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18042),hAPP(U_18046,U_18044)),hAPP(c_List_Omonoid__add__class_Olistsum(U_18042),hAPP(hAPP(c_List_Omap(U_18043,U_18042),U_18046),c_List_Oremove1(U_18043,U_18044,U_18045))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18043),U_18044),hAPP(c_List_Oset(U_18043),U_18045)))
    | ~ class_Groups_Ocomm__monoid__add(U_18042) ),
    inference(clausify,[status(thm)],[f_4393_3]) ).

fof(f_4394_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_4394_2,plain,
    ! [U_18049,U_18048,U_18047] :
      ( hBOOL(hAPP(hAPP(c_member(U_18047),hAPP(c_Product__Type_Ofst(U_18047,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(U_18047,U_18048),U_18049))),hAPP(c_List_Oset(U_18047),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18047),U_18047),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18047)),U_18048))))
      | ~ 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_18047),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18047)),U_18048)))) ),
    inference(variable_rename,[status(thm)],[f_4394_1]) ).

fof(f_4394_3,plain,
    ! [U_18047,U_18048,U_18049] :
      ( hBOOL(hAPP(hAPP(c_member(U_18047),hAPP(c_Product__Type_Ofst(U_18047,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(U_18047,U_18048),U_18049))),hAPP(c_List_Oset(U_18047),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18047),U_18047),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18047)),U_18048))))
      | ~ 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_18047),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18047)),U_18048)))) ),
    inference(definitional_conversion,[status(esa)],[f_4394_2]) ).

cnf(f_4394_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18047),hAPP(c_Product__Type_Ofst(U_18047,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect__weight(U_18047,U_18048),U_18049))),hAPP(c_List_Oset(U_18047),hAPP(hAPP(c_List_Omap(tc_prod(tc_Code__Numeral_Ocode__numeral,U_18047),U_18047),c_Product__Type_Osnd(tc_Code__Numeral_Ocode__numeral,U_18047)),U_18048))))
    | ~ 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_18047),tc_Code__Numeral_Ocode__numeral),c_Product__Type_Ofst(tc_Code__Numeral_Ocode__numeral,U_18047)),U_18048)))) ),
    inference(clausify,[status(thm)],[f_4394_3]) ).

fof(f_4395_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_4395_2,plain,
    ! [U_18053,U_18052,U_18051,U_18050] :
      ( ( ( c_Nitpick_Osetsum_H(U_18051,U_18050,U_18053,U_18052) = c_Groups_Ozero__class_Ozero(U_18050)
          | hBOOL(hAPP(c_Finite__Set_Ofinite(U_18051),U_18052)) )
        & ( c_Nitpick_Osetsum_H(U_18051,U_18050,U_18053,U_18052) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18050),hAPP(hAPP(c_List_Omap(U_18051,U_18050),U_18053),c_Hilbert__Choice_OEps(tc_List_Olist(U_18051),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18051),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_18051)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18051),tc_fun(U_18051,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18051,tc_HOL_Obool),tc_fun(tc_fun(U_18051,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18051)),c_fequal),c_List_Oset(U_18051))),U_18052))),c_List_Odistinct(U_18051)))))
          | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18051),U_18052)) ) )
      | ~ class_Groups_Ocomm__monoid__add(U_18050) ),
    inference(variable_rename,[status(thm)],[f_4395_1]) ).

fof(f_4395_3,plain,
    ( ! [U_18050,U_18051,U_18052,U_18053] :
        ( c_Nitpick_Osetsum_H(U_18051,U_18050,U_18053,U_18052) = c_Groups_Ozero__class_Ozero(U_18050)
        | hBOOL(hAPP(c_Finite__Set_Ofinite(U_18051),U_18052))
        | ~ sP1139(U_18050,U_18051,U_18052,U_18053) )
    & ! [U_18050,U_18051,U_18052,U_18053] :
        ( c_Nitpick_Osetsum_H(U_18051,U_18050,U_18053,U_18052) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18050),hAPP(hAPP(c_List_Omap(U_18051,U_18050),U_18053),c_Hilbert__Choice_OEps(tc_List_Olist(U_18051),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18051),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_18051)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18051),tc_fun(U_18051,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18051,tc_HOL_Obool),tc_fun(tc_fun(U_18051,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18051)),c_fequal),c_List_Oset(U_18051))),U_18052))),c_List_Odistinct(U_18051)))))
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18051),U_18052))
        | ~ sP1139(U_18050,U_18051,U_18052,U_18053) )
    & ! [U_18050,U_18051,U_18052,U_18053] :
        ( sP1139(U_18050,U_18051,U_18052,U_18053)
        | ~ class_Groups_Ocomm__monoid__add(U_18050) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1139])],[f_4395_2]) ).

cnf(f_4395_4,plain,
    ( sP1139(U_18050,U_18051,U_18052,U_18053)
    | ~ class_Groups_Ocomm__monoid__add(U_18050) ),
    inference(clausify,[status(thm)],[f_4395_3]) ).

cnf(f_4395_5,plain,
    ( c_Nitpick_Osetsum_H(U_18051,U_18050,U_18053,U_18052) = hAPP(c_List_Omonoid__add__class_Olistsum(U_18050),hAPP(hAPP(c_List_Omap(U_18051,U_18050),U_18053),c_Hilbert__Choice_OEps(tc_List_Olist(U_18051),hAPP(hAPP(c_COMBS(tc_List_Olist(U_18051),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_18051)),c_fconj),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18051),tc_fun(U_18051,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_18051,tc_HOL_Obool),tc_fun(tc_fun(U_18051,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_18051)),c_fequal),c_List_Oset(U_18051))),U_18052))),c_List_Odistinct(U_18051)))))
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_18051),U_18052))
    | ~ sP1139(U_18050,U_18051,U_18052,U_18053) ),
    inference(clausify,[status(thm)],[f_4395_3]) ).

cnf(f_4395_6,plain,
    ( c_Nitpick_Osetsum_H(U_18051,U_18050,U_18053,U_18052) = c_Groups_Ozero__class_Ozero(U_18050)
    | hBOOL(hAPP(c_Finite__Set_Ofinite(U_18051),U_18052))
    | ~ sP1139(U_18050,U_18051,U_18052,U_18053) ),
    inference(clausify,[status(thm)],[f_4395_3]) ).

fof(f_4396_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_4396_2,plain,
    ! [U_18058,U_18057,U_18056,U_18055,U_18054] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18057,U_18054,U_18055,U_18056,U_18058) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18057,U_18054,U_18055),U_18056),U_18058)
      | hBOOL(hAPP(hAPP(c_member(U_18054),hAPP(U_18055,U_18056)),hAPP(c_Set_Oimage(U_18057,U_18054,U_18055),hAPP(c_List_Oset(U_18057),U_18058))))
      | ~ class_Orderings_Olinorder(U_18054) ),
    inference(variable_rename,[status(thm)],[f_4396_1]) ).

fof(f_4396_3,plain,
    ! [U_18056,U_18055,U_18054,U_18057,U_18058] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18057,U_18054,U_18055,U_18056,U_18058) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18057,U_18054,U_18055),U_18056),U_18058)
      | hBOOL(hAPP(hAPP(c_member(U_18054),hAPP(U_18055,U_18056)),hAPP(c_Set_Oimage(U_18057,U_18054,U_18055),hAPP(c_List_Oset(U_18057),U_18058))))
      | ~ class_Orderings_Olinorder(U_18054) ),
    inference(definitional_conversion,[status(esa)],[f_4396_2]) ).

cnf(f_4396_4,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_18057,U_18054,U_18055,U_18056,U_18058) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18057,U_18054,U_18055),U_18056),U_18058)
    | hBOOL(hAPP(hAPP(c_member(U_18054),hAPP(U_18055,U_18056)),hAPP(c_Set_Oimage(U_18057,U_18054,U_18055),hAPP(c_List_Oset(U_18057),U_18058))))
    | ~ class_Orderings_Olinorder(U_18054) ),
    inference(clausify,[status(thm)],[f_4396_3]) ).

fof(f_4397_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_4397_2,plain,
    ! [U_18061] :
      ( ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18061) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_18060] :
            ( U_18060 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18060),hAPP(c_List_Oset(tc_Nat_Onat),U_18061))) ) )
      & ( ! [U_18059] :
            ( U_18059 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18059),hAPP(c_List_Oset(tc_Nat_Onat),U_18061))) )
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18061) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4397_1]) ).

fof(f_4397_3,plain,
    ( ! [U_18063] :
        ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18063) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_18060] :
            ( U_18060 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18060),hAPP(c_List_Oset(tc_Nat_Onat),U_18063))) ) )
    & ! [U_18062] :
        ( ! [U_18059] :
            ( U_18059 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18059),hAPP(c_List_Oset(tc_Nat_Onat),U_18062))) )
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18062) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4397_2]) ).

fof(f_4397_4,plain,
    ( ! [U_18063] :
        ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18063) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( sK455(U_18063) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK455(U_18063)),hAPP(c_List_Oset(tc_Nat_Onat),U_18063))) ) )
    & ! [U_18062] :
        ( ! [U_18059] :
            ( U_18059 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18059),hAPP(c_List_Oset(tc_Nat_Onat),U_18062))) )
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18062) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK455]),skolemize(U_18060,sK455(U_18063))],[f_4397_3]) ).

fof(f_4397_5,plain,
    ( ! [U_18063] :
        ( sK455(U_18063) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1140(U_18063) )
    & ! [U_18063] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK455(U_18063)),hAPP(c_List_Oset(tc_Nat_Onat),U_18063)))
        | ~ sP1140(U_18063) )
    & ! [U_18063] :
        ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18063) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP1140(U_18063) )
    & ! [U_18059,U_18062] :
        ( U_18059 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18059),hAPP(c_List_Oset(tc_Nat_Onat),U_18062)))
        | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18062) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1140])],[f_4397_4]) ).

cnf(f_4397_6,plain,
    ( U_18059 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_18059),hAPP(c_List_Oset(tc_Nat_Onat),U_18062)))
    | hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18062) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4397_5]) ).

cnf(f_4397_7,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18063) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP1140(U_18063) ),
    inference(clausify,[status(thm)],[f_4397_5]) ).

cnf(f_4397_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK455(U_18063)),hAPP(c_List_Oset(tc_Nat_Onat),U_18063)))
    | ~ sP1140(U_18063) ),
    inference(clausify,[status(thm)],[f_4397_5]) ).

cnf(f_4397_9,plain,
    ( sK455(U_18063) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1140(U_18063) ),
    inference(clausify,[status(thm)],[f_4397_5]) ).

fof(f_4398_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_4398_2,plain,
    ! [U_18068,U_18067,U_18066,U_18065,U_18064] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18065),c_List_Olinorder__class_Oinsort__insert__key(U_18065,U_18064,U_18067,U_18068,U_18066)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18065),U_18066))
      | ~ class_Orderings_Olinorder(U_18064) ),
    inference(variable_rename,[status(thm)],[f_4398_1]) ).

fof(f_4398_3,plain,
    ! [U_18064,U_18066,U_18067,U_18065,U_18068] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18065),c_List_Olinorder__class_Oinsort__insert__key(U_18065,U_18064,U_18067,U_18068,U_18066)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18065),U_18066))
      | ~ class_Orderings_Olinorder(U_18064) ),
    inference(definitional_conversion,[status(esa)],[f_4398_2]) ).

cnf(f_4398_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18065),c_List_Olinorder__class_Oinsort__insert__key(U_18065,U_18064,U_18067,U_18068,U_18066)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18065),U_18066))
    | ~ class_Orderings_Olinorder(U_18064) ),
    inference(clausify,[status(thm)],[f_4398_3]) ).

fof(f_4399_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_4399_2,plain,
    ! [U_18071,U_18070,U_18069] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18069,U_18069,c_COMBI(U_18069),U_18070,U_18071) = U_18071
      | ~ hBOOL(hAPP(hAPP(c_member(U_18069),U_18070),hAPP(c_List_Oset(U_18069),U_18071)))
      | ~ class_Orderings_Olinorder(U_18069) ),
    inference(variable_rename,[status(thm)],[f_4399_1]) ).

fof(f_4399_3,plain,
    ! [U_18069,U_18070,U_18071] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18069,U_18069,c_COMBI(U_18069),U_18070,U_18071) = U_18071
      | ~ hBOOL(hAPP(hAPP(c_member(U_18069),U_18070),hAPP(c_List_Oset(U_18069),U_18071)))
      | ~ class_Orderings_Olinorder(U_18069) ),
    inference(definitional_conversion,[status(esa)],[f_4399_2]) ).

cnf(f_4399_4,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_18069,U_18069,c_COMBI(U_18069),U_18070,U_18071) = U_18071
    | ~ hBOOL(hAPP(hAPP(c_member(U_18069),U_18070),hAPP(c_List_Oset(U_18069),U_18071)))
    | ~ class_Orderings_Olinorder(U_18069) ),
    inference(clausify,[status(thm)],[f_4399_3]) ).

fof(f_4400_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_4400_2,plain,
    ! [U_18074,U_18073,U_18072] :
      ( hAPP(c_List_Oset(U_18072),c_List_Olinorder__class_Oinsort__insert__key(U_18072,U_18072,c_COMBI(U_18072),U_18073,U_18074)) = hAPP(hAPP(c_Set_Oinsert(U_18072),U_18073),hAPP(c_List_Oset(U_18072),U_18074))
      | ~ class_Orderings_Olinorder(U_18072) ),
    inference(variable_rename,[status(thm)],[f_4400_1]) ).

fof(f_4400_3,plain,
    ! [U_18072,U_18073,U_18074] :
      ( hAPP(c_List_Oset(U_18072),c_List_Olinorder__class_Oinsort__insert__key(U_18072,U_18072,c_COMBI(U_18072),U_18073,U_18074)) = hAPP(hAPP(c_Set_Oinsert(U_18072),U_18073),hAPP(c_List_Oset(U_18072),U_18074))
      | ~ class_Orderings_Olinorder(U_18072) ),
    inference(definitional_conversion,[status(esa)],[f_4400_2]) ).

cnf(f_4400_4,plain,
    ( hAPP(c_List_Oset(U_18072),c_List_Olinorder__class_Oinsort__insert__key(U_18072,U_18072,c_COMBI(U_18072),U_18073,U_18074)) = hAPP(hAPP(c_Set_Oinsert(U_18072),U_18073),hAPP(c_List_Oset(U_18072),U_18074))
    | ~ class_Orderings_Olinorder(U_18072) ),
    inference(clausify,[status(thm)],[f_4400_3]) ).

fof(f_4401_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_4401_2,plain,
    ! [U_18079,U_18078,U_18077,U_18076,U_18075] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18078,U_18075,U_18076,U_18077,U_18079) = U_18079
      | ~ hBOOL(hAPP(hAPP(c_member(U_18075),hAPP(U_18076,U_18077)),hAPP(c_Set_Oimage(U_18078,U_18075,U_18076),hAPP(c_List_Oset(U_18078),U_18079))))
      | ~ class_Orderings_Olinorder(U_18075) ),
    inference(variable_rename,[status(thm)],[f_4401_1]) ).

fof(f_4401_3,plain,
    ! [U_18075,U_18076,U_18077,U_18078,U_18079] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18078,U_18075,U_18076,U_18077,U_18079) = U_18079
      | ~ hBOOL(hAPP(hAPP(c_member(U_18075),hAPP(U_18076,U_18077)),hAPP(c_Set_Oimage(U_18078,U_18075,U_18076),hAPP(c_List_Oset(U_18078),U_18079))))
      | ~ class_Orderings_Olinorder(U_18075) ),
    inference(definitional_conversion,[status(esa)],[f_4401_2]) ).

cnf(f_4401_4,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_18078,U_18075,U_18076,U_18077,U_18079) = U_18079
    | ~ hBOOL(hAPP(hAPP(c_member(U_18075),hAPP(U_18076,U_18077)),hAPP(c_Set_Oimage(U_18078,U_18075,U_18076),hAPP(c_List_Oset(U_18078),U_18079))))
    | ~ class_Orderings_Olinorder(U_18075) ),
    inference(clausify,[status(thm)],[f_4401_3]) ).

fof(f_4402_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_4402_2,plain,
    ! [U_18082,U_18081,U_18080] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18080,U_18080,c_COMBI(U_18080),U_18081,U_18082) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18080,U_18080,c_COMBI(U_18080)),U_18081),U_18082)
      | hBOOL(hAPP(hAPP(c_member(U_18080),U_18081),hAPP(c_List_Oset(U_18080),U_18082)))
      | ~ class_Orderings_Olinorder(U_18080) ),
    inference(variable_rename,[status(thm)],[f_4402_1]) ).

fof(f_4402_3,plain,
    ! [U_18080,U_18081,U_18082] :
      ( c_List_Olinorder__class_Oinsort__insert__key(U_18080,U_18080,c_COMBI(U_18080),U_18081,U_18082) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18080,U_18080,c_COMBI(U_18080)),U_18081),U_18082)
      | hBOOL(hAPP(hAPP(c_member(U_18080),U_18081),hAPP(c_List_Oset(U_18080),U_18082)))
      | ~ class_Orderings_Olinorder(U_18080) ),
    inference(definitional_conversion,[status(esa)],[f_4402_2]) ).

cnf(f_4402_4,plain,
    ( c_List_Olinorder__class_Oinsort__insert__key(U_18080,U_18080,c_COMBI(U_18080),U_18081,U_18082) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18080,U_18080,c_COMBI(U_18080)),U_18081),U_18082)
    | hBOOL(hAPP(hAPP(c_member(U_18080),U_18081),hAPP(c_List_Oset(U_18080),U_18082)))
    | ~ class_Orderings_Olinorder(U_18080) ),
    inference(clausify,[status(thm)],[f_4402_3]) ).

fof(f_4403_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_4403_2,plain,
    ! [U_18088,U_18087,U_18086,U_18085,U_18084,U_18083] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18083),tc_List_Olist(U_18083))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18083),tc_List_Olist(U_18083)),hAPP(hAPP(c_List_Olist_OCons(U_18083),U_18084),U_18085)),hAPP(hAPP(c_List_Olist_OCons(U_18083),U_18086),U_18087))),c_List_Olexord(U_18083,U_18088)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18083),tc_List_Olist(U_18083))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18083),tc_List_Olist(U_18083)),U_18085),U_18087)),c_List_Olexord(U_18083,U_18088)))
            | U_18084 != U_18086 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18083,U_18083)),hAPP(hAPP(c_Product__Type_OPair(U_18083,U_18083),U_18084),U_18086)),U_18088)) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18083),tc_List_Olist(U_18083))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18083),tc_List_Olist(U_18083)),U_18085),U_18087)),c_List_Olexord(U_18083,U_18088)))
          & U_18084 = U_18086 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_18083,U_18083)),hAPP(hAPP(c_Product__Type_OPair(U_18083,U_18083),U_18084),U_18086)),U_18088))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18083),tc_List_Olist(U_18083))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18083),tc_List_Olist(U_18083)),hAPP(hAPP(c_List_Olist_OCons(U_18083),U_18084),U_18085)),hAPP(hAPP(c_List_Olist_OCons(U_18083),U_18086),U_18087))),c_List_Olexord(U_18083,U_18088))) ) ),
    inference(variable_rename,[status(thm)],[f_4403_1]) ).

fof(f_4403_3,plain,
    ( ! [U_18100,U_18098,U_18096,U_18094,U_18092,U_18090] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18090),tc_List_Olist(U_18090))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18090),tc_List_Olist(U_18090)),hAPP(hAPP(c_List_Olist_OCons(U_18090),U_18092),U_18094)),hAPP(hAPP(c_List_Olist_OCons(U_18090),U_18096),U_18098))),c_List_Olexord(U_18090,U_18100)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18090),tc_List_Olist(U_18090))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18090),tc_List_Olist(U_18090)),U_18094),U_18098)),c_List_Olexord(U_18090,U_18100)))
            | U_18092 != U_18096 )
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18090,U_18090)),hAPP(hAPP(c_Product__Type_OPair(U_18090,U_18090),U_18092),U_18096)),U_18100)) ) )
    & ! [U_18099,U_18097,U_18095,U_18093,U_18091,U_18089] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18089),tc_List_Olist(U_18089))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18089),tc_List_Olist(U_18089)),U_18093),U_18097)),c_List_Olexord(U_18089,U_18099)))
          & U_18091 = U_18095 )
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_18089,U_18089)),hAPP(hAPP(c_Product__Type_OPair(U_18089,U_18089),U_18091),U_18095)),U_18099))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18089),tc_List_Olist(U_18089))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18089),tc_List_Olist(U_18089)),hAPP(hAPP(c_List_Olist_OCons(U_18089),U_18091),U_18093)),hAPP(hAPP(c_List_Olist_OCons(U_18089),U_18095),U_18097))),c_List_Olexord(U_18089,U_18099))) ) ),
    inference(miniscope,[status(thm)],[f_4403_2]) ).

fof(f_4403_4,plain,
    ( ! [U_18092,U_18090,U_18096,U_18098,U_18094,U_18100] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18090),tc_List_Olist(U_18090))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18090),tc_List_Olist(U_18090)),U_18094),U_18098)),c_List_Olexord(U_18090,U_18100)))
        | U_18092 != U_18096
        | ~ sP1142(U_18092,U_18090,U_18096,U_18098,U_18094,U_18100) )
    & ! [U_18092,U_18090,U_18096,U_18098,U_18094,U_18100] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18090,U_18090)),hAPP(hAPP(c_Product__Type_OPair(U_18090,U_18090),U_18092),U_18096)),U_18100))
        | ~ sP1142(U_18092,U_18090,U_18096,U_18098,U_18094,U_18100) )
    & ! [U_18089,U_18093,U_18097,U_18091,U_18095,U_18099] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18089),tc_List_Olist(U_18089))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18089),tc_List_Olist(U_18089)),U_18093),U_18097)),c_List_Olexord(U_18089,U_18099)))
        | ~ sP1141(U_18089,U_18093,U_18097,U_18091,U_18095,U_18099) )
    & ! [U_18089,U_18093,U_18097,U_18091,U_18095,U_18099] :
        ( U_18091 = U_18095
        | ~ sP1141(U_18089,U_18093,U_18097,U_18091,U_18095,U_18099) )
    & ! [U_18092,U_18090,U_18096,U_18098,U_18094,U_18100] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18090),tc_List_Olist(U_18090))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18090),tc_List_Olist(U_18090)),hAPP(hAPP(c_List_Olist_OCons(U_18090),U_18092),U_18094)),hAPP(hAPP(c_List_Olist_OCons(U_18090),U_18096),U_18098))),c_List_Olexord(U_18090,U_18100)))
        | sP1142(U_18092,U_18090,U_18096,U_18098,U_18094,U_18100) )
    & ! [U_18089,U_18093,U_18097,U_18091,U_18095,U_18099] :
        ( sP1141(U_18089,U_18093,U_18097,U_18091,U_18095,U_18099)
        | hBOOL(hAPP(hAPP(c_member(tc_prod(U_18089,U_18089)),hAPP(hAPP(c_Product__Type_OPair(U_18089,U_18089),U_18091),U_18095)),U_18099))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18089),tc_List_Olist(U_18089))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18089),tc_List_Olist(U_18089)),hAPP(hAPP(c_List_Olist_OCons(U_18089),U_18091),U_18093)),hAPP(hAPP(c_List_Olist_OCons(U_18089),U_18095),U_18097))),c_List_Olexord(U_18089,U_18099))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1141,sP1142])],[f_4403_3]) ).

cnf(f_4403_5,plain,
    ( sP1141(U_18089,U_18093,U_18097,U_18091,U_18095,U_18099)
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_18089,U_18089)),hAPP(hAPP(c_Product__Type_OPair(U_18089,U_18089),U_18091),U_18095)),U_18099))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18089),tc_List_Olist(U_18089))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18089),tc_List_Olist(U_18089)),hAPP(hAPP(c_List_Olist_OCons(U_18089),U_18091),U_18093)),hAPP(hAPP(c_List_Olist_OCons(U_18089),U_18095),U_18097))),c_List_Olexord(U_18089,U_18099))) ),
    inference(clausify,[status(thm)],[f_4403_4]) ).

cnf(f_4403_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18090),tc_List_Olist(U_18090))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18090),tc_List_Olist(U_18090)),hAPP(hAPP(c_List_Olist_OCons(U_18090),U_18092),U_18094)),hAPP(hAPP(c_List_Olist_OCons(U_18090),U_18096),U_18098))),c_List_Olexord(U_18090,U_18100)))
    | sP1142(U_18092,U_18090,U_18096,U_18098,U_18094,U_18100) ),
    inference(clausify,[status(thm)],[f_4403_4]) ).

cnf(f_4403_7,plain,
    ( U_18091 = U_18095
    | ~ sP1141(U_18089,U_18093,U_18097,U_18091,U_18095,U_18099) ),
    inference(clausify,[status(thm)],[f_4403_4]) ).

cnf(f_4403_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18089),tc_List_Olist(U_18089))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18089),tc_List_Olist(U_18089)),U_18093),U_18097)),c_List_Olexord(U_18089,U_18099)))
    | ~ sP1141(U_18089,U_18093,U_18097,U_18091,U_18095,U_18099) ),
    inference(clausify,[status(thm)],[f_4403_4]) ).

cnf(f_4403_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18090,U_18090)),hAPP(hAPP(c_Product__Type_OPair(U_18090,U_18090),U_18092),U_18096)),U_18100))
    | ~ sP1142(U_18092,U_18090,U_18096,U_18098,U_18094,U_18100) ),
    inference(clausify,[status(thm)],[f_4403_4]) ).

cnf(f_4403_10,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18090),tc_List_Olist(U_18090))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18090),tc_List_Olist(U_18090)),U_18094),U_18098)),c_List_Olexord(U_18090,U_18100)))
    | U_18092 != U_18096
    | ~ sP1142(U_18092,U_18090,U_18096,U_18098,U_18094,U_18100) ),
    inference(clausify,[status(thm)],[f_4403_4]) ).

fof(f_4404_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_4404_2,plain,
    ! [U_18104,U_18103,U_18102,U_18101] : hAPP(c_List_Oset(tc_prod(U_18101,U_18102)),hAPP(hAPP(c_List_Ozip(U_18101,U_18102),U_18103),U_18104)) = hAPP(c_Set_OCollect(tc_prod(U_18101,U_18102)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_18101,U_18102)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_18101,U_18102),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_18101,U_18102)),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_18101,U_18102)),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_18101,U_18102),tc_fun(tc_Nat_Onat,tc_prod(U_18101,U_18102)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_18101,U_18102),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(U_18101,U_18102)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(U_18101,U_18102)),c_COMBB(tc_prod(U_18101,U_18102),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_18102,tc_prod(U_18101,U_18102)),hAPP(hAPP(c_COMBB(U_18101,tc_fun(U_18102,tc_prod(U_18101,U_18102)),tc_Nat_Onat),c_Product__Type_OPair(U_18101,U_18102)),hAPP(c_List_Onth(U_18101),U_18103))),hAPP(c_List_Onth(U_18102),U_18104)))))),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_18101)),U_18103)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18102)),U_18104)))))),
    inference(variable_rename,[status(thm)],[f_4404_1]) ).

fof(f_4404_3,plain,
    ! [U_18101,U_18102,U_18103,U_18104] : hAPP(c_List_Oset(tc_prod(U_18101,U_18102)),hAPP(hAPP(c_List_Ozip(U_18101,U_18102),U_18103),U_18104)) = hAPP(c_Set_OCollect(tc_prod(U_18101,U_18102)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_18101,U_18102)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_18101,U_18102),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_18101,U_18102)),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_18101,U_18102)),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_18101,U_18102),tc_fun(tc_Nat_Onat,tc_prod(U_18101,U_18102)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_18101,U_18102),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(U_18101,U_18102)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(U_18101,U_18102)),c_COMBB(tc_prod(U_18101,U_18102),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_18102,tc_prod(U_18101,U_18102)),hAPP(hAPP(c_COMBB(U_18101,tc_fun(U_18102,tc_prod(U_18101,U_18102)),tc_Nat_Onat),c_Product__Type_OPair(U_18101,U_18102)),hAPP(c_List_Onth(U_18101),U_18103))),hAPP(c_List_Onth(U_18102),U_18104)))))),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_18101)),U_18103)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18102)),U_18104)))))),
    inference(definitional_conversion,[status(esa)],[f_4404_2]) ).

cnf(f_4404_4,plain,
    hAPP(c_List_Oset(tc_prod(U_18101,U_18102)),hAPP(hAPP(c_List_Ozip(U_18101,U_18102),U_18103),U_18104)) = hAPP(c_Set_OCollect(tc_prod(U_18101,U_18102)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,tc_prod(U_18101,U_18102)),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_18101,U_18102),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_18101,U_18102)),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_18101,U_18102)),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_18101,U_18102),tc_fun(tc_Nat_Onat,tc_prod(U_18101,U_18102)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(U_18101,U_18102),tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,tc_prod(U_18101,U_18102)),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),tc_prod(U_18101,U_18102)),c_COMBB(tc_prod(U_18101,U_18102),tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(hAPP(c_COMBS(tc_Nat_Onat,U_18102,tc_prod(U_18101,U_18102)),hAPP(hAPP(c_COMBB(U_18101,tc_fun(U_18102,tc_prod(U_18101,U_18102)),tc_Nat_Onat),c_Product__Type_OPair(U_18101,U_18102)),hAPP(c_List_Onth(U_18101),U_18103))),hAPP(c_List_Onth(U_18102),U_18104)))))),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_18101)),U_18103)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18102)),U_18104)))))),
    inference(clausify,[status(thm)],[f_4404_3]) ).

fof(f_4405_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_4405_2,plain,
    ! [U_18109,U_18108,U_18107,U_18106,U_18105] :
      ( hAPP(hAPP(c_List_Onth(tc_prod(U_18106,U_18108)),hAPP(hAPP(c_List_Ozip(U_18106,U_18108),U_18107),U_18109)),U_18105) = hAPP(hAPP(c_Product__Type_OPair(U_18106,U_18108),hAPP(hAPP(c_List_Onth(U_18106),U_18107),U_18105)),hAPP(hAPP(c_List_Onth(U_18108),U_18109),U_18105))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18105),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18108)),U_18109)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18105),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18106)),U_18107))) ),
    inference(variable_rename,[status(thm)],[f_4405_1]) ).

fof(f_4405_3,plain,
    ! [U_18105,U_18106,U_18107,U_18108,U_18109] :
      ( hAPP(hAPP(c_List_Onth(tc_prod(U_18106,U_18108)),hAPP(hAPP(c_List_Ozip(U_18106,U_18108),U_18107),U_18109)),U_18105) = hAPP(hAPP(c_Product__Type_OPair(U_18106,U_18108),hAPP(hAPP(c_List_Onth(U_18106),U_18107),U_18105)),hAPP(hAPP(c_List_Onth(U_18108),U_18109),U_18105))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18105),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18108)),U_18109)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18105),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18106)),U_18107))) ),
    inference(definitional_conversion,[status(esa)],[f_4405_2]) ).

cnf(f_4405_4,plain,
    ( hAPP(hAPP(c_List_Onth(tc_prod(U_18106,U_18108)),hAPP(hAPP(c_List_Ozip(U_18106,U_18108),U_18107),U_18109)),U_18105) = hAPP(hAPP(c_Product__Type_OPair(U_18106,U_18108),hAPP(hAPP(c_List_Onth(U_18106),U_18107),U_18105)),hAPP(hAPP(c_List_Onth(U_18108),U_18109),U_18105))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18105),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18108)),U_18109)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18105),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18106)),U_18107))) ),
    inference(clausify,[status(thm)],[f_4405_3]) ).

fof(f_4406_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_4406_2,plain,
    ! [U_18114,U_18113,U_18112,U_18111,U_18110] :
      ( hAPP(hAPP(c_List_Onth(U_18113),hAPP(hAPP(c_List_Omap(U_18111,U_18113),U_18114),U_18112)),U_18110) = hAPP(U_18114,hAPP(hAPP(c_List_Onth(U_18111),U_18112),U_18110))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18110),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18111)),U_18112))) ),
    inference(variable_rename,[status(thm)],[f_4406_1]) ).

fof(f_4406_3,plain,
    ! [U_18111,U_18110,U_18112,U_18113,U_18114] :
      ( hAPP(hAPP(c_List_Onth(U_18113),hAPP(hAPP(c_List_Omap(U_18111,U_18113),U_18114),U_18112)),U_18110) = hAPP(U_18114,hAPP(hAPP(c_List_Onth(U_18111),U_18112),U_18110))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18110),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18111)),U_18112))) ),
    inference(definitional_conversion,[status(esa)],[f_4406_2]) ).

cnf(f_4406_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_18113),hAPP(hAPP(c_List_Omap(U_18111,U_18113),U_18114),U_18112)),U_18110) = hAPP(U_18114,hAPP(hAPP(c_List_Onth(U_18111),U_18112),U_18110))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18110),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18111)),U_18112))) ),
    inference(clausify,[status(thm)],[f_4406_3]) ).

fof(f_4407_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_4407_2,plain,
    ! [U_18116,U_18115] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_18116),U_18115)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18116)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18115),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_18116))) ),
    inference(variable_rename,[status(thm)],[f_4407_1]) ).

fof(f_4407_3,plain,
    ! [U_18115,U_18116] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_18116),U_18115)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18116)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18115),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_18116))) ),
    inference(definitional_conversion,[status(esa)],[f_4407_2]) ).

cnf(f_4407_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_18116),U_18115)),hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),U_18116)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18115),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_18116))) ),
    inference(clausify,[status(thm)],[f_4407_3]) ).

fof(f_4408_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_4408_2,plain,
    ! [U_18120,U_18119,U_18118,U_18117] : hAPP(hAPP(c_List_Onth(U_18117),hAPP(hAPP(c_List_Olist_OCons(U_18117),U_18118),U_18119)),U_18120) = c_Nat_Onat_Onat__case(U_18117,U_18118,hAPP(c_List_Onth(U_18117),U_18119),U_18120),
    inference(variable_rename,[status(thm)],[f_4408_1]) ).

fof(f_4408_3,plain,
    ! [U_18117,U_18118,U_18119,U_18120] : hAPP(hAPP(c_List_Onth(U_18117),hAPP(hAPP(c_List_Olist_OCons(U_18117),U_18118),U_18119)),U_18120) = c_Nat_Onat_Onat__case(U_18117,U_18118,hAPP(c_List_Onth(U_18117),U_18119),U_18120),
    inference(definitional_conversion,[status(esa)],[f_4408_2]) ).

cnf(f_4408_4,plain,
    hAPP(hAPP(c_List_Onth(U_18117),hAPP(hAPP(c_List_Olist_OCons(U_18117),U_18118),U_18119)),U_18120) = c_Nat_Onat_Onat__case(U_18117,U_18118,hAPP(c_List_Onth(U_18117),U_18119),U_18120),
    inference(clausify,[status(thm)],[f_4408_3]) ).

fof(f_4409_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_4409_2,plain,
    ! [U_18124,U_18123,U_18122,U_18121] : hAPP(hAPP(c_List_Onth(U_18121),hAPP(hAPP(c_List_Olist_OCons(U_18121),U_18122),U_18123)),hAPP(c_Nat_OSuc,U_18124)) = hAPP(hAPP(c_List_Onth(U_18121),U_18123),U_18124),
    inference(variable_rename,[status(thm)],[f_4409_1]) ).

fof(f_4409_3,plain,
    ! [U_18121,U_18122,U_18123,U_18124] : hAPP(hAPP(c_List_Onth(U_18121),hAPP(hAPP(c_List_Olist_OCons(U_18121),U_18122),U_18123)),hAPP(c_Nat_OSuc,U_18124)) = hAPP(hAPP(c_List_Onth(U_18121),U_18123),U_18124),
    inference(definitional_conversion,[status(esa)],[f_4409_2]) ).

cnf(f_4409_4,plain,
    hAPP(hAPP(c_List_Onth(U_18121),hAPP(hAPP(c_List_Olist_OCons(U_18121),U_18122),U_18123)),hAPP(c_Nat_OSuc,U_18124)) = hAPP(hAPP(c_List_Onth(U_18121),U_18123),U_18124),
    inference(clausify,[status(thm)],[f_4409_3]) ).

fof(f_4410_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_4410_2,plain,
    ! [U_18127,U_18126,U_18125] : hAPP(hAPP(c_List_Onth(U_18125),hAPP(hAPP(c_List_Olist_OCons(U_18125),U_18126),U_18127)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_18126,
    inference(variable_rename,[status(thm)],[f_4410_1]) ).

fof(f_4410_3,plain,
    ! [U_18125,U_18126,U_18127] : hAPP(hAPP(c_List_Onth(U_18125),hAPP(hAPP(c_List_Olist_OCons(U_18125),U_18126),U_18127)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_18126,
    inference(definitional_conversion,[status(esa)],[f_4410_2]) ).

cnf(f_4410_4,plain,
    hAPP(hAPP(c_List_Onth(U_18125),hAPP(hAPP(c_List_Olist_OCons(U_18125),U_18126),U_18127)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = U_18126,
    inference(clausify,[status(thm)],[f_4410_3]) ).

fof(f_4411_1,plain,
    ! [V_Pa_2,V_xs_2,T_b] :
      ( ( ! [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_Pa_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_4411_2,plain,
    ! [U_18134,U_18133,U_18132] :
      ( ( ! [U_18131] :
            ( hBOOL(hAPP(U_18134,U_18131))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18132),U_18131),hAPP(c_List_Oset(U_18132),U_18133))) )
        | ? [U_18130] :
            ( ~ hBOOL(hAPP(U_18134,hAPP(hAPP(c_List_Onth(U_18132),U_18133),U_18130)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18130),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18132)),U_18133))) ) )
      & ( ! [U_18129] :
            ( hBOOL(hAPP(U_18134,hAPP(hAPP(c_List_Onth(U_18132),U_18133),U_18129)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18129),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18132)),U_18133))) )
        | ? [U_18128] :
            ( ~ hBOOL(hAPP(U_18134,U_18128))
            & hBOOL(hAPP(hAPP(c_member(U_18132),U_18128),hAPP(c_List_Oset(U_18132),U_18133))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4411_1]) ).

fof(f_4411_3,plain,
    ( ! [U_18140,U_18138,U_18136] :
        ( ! [U_18131] :
            ( hBOOL(hAPP(U_18140,U_18131))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18136),U_18131),hAPP(c_List_Oset(U_18136),U_18138))) )
        | ? [U_18130] :
            ( ~ hBOOL(hAPP(U_18140,hAPP(hAPP(c_List_Onth(U_18136),U_18138),U_18130)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18130),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18136)),U_18138))) ) )
    & ! [U_18139,U_18137,U_18135] :
        ( ! [U_18129] :
            ( hBOOL(hAPP(U_18139,hAPP(hAPP(c_List_Onth(U_18135),U_18137),U_18129)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18129),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18135)),U_18137))) )
        | ? [U_18128] :
            ( ~ hBOOL(hAPP(U_18139,U_18128))
            & hBOOL(hAPP(hAPP(c_member(U_18135),U_18128),hAPP(c_List_Oset(U_18135),U_18137))) ) ) ),
    inference(miniscope,[status(thm)],[f_4411_2]) ).

fof(f_4411_4,plain,
    ( ! [U_18140,U_18138,U_18136] :
        ( ! [U_18131] :
            ( hBOOL(hAPP(U_18140,U_18131))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18136),U_18131),hAPP(c_List_Oset(U_18136),U_18138))) )
        | ? [U_18130] :
            ( ~ hBOOL(hAPP(U_18140,hAPP(hAPP(c_List_Onth(U_18136),U_18138),U_18130)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18130),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18136)),U_18138))) ) )
    & ! [U_18139,U_18137,U_18135] :
        ( ! [U_18129] :
            ( hBOOL(hAPP(U_18139,hAPP(hAPP(c_List_Onth(U_18135),U_18137),U_18129)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18129),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18135)),U_18137))) )
        | ( ~ hBOOL(hAPP(U_18139,sK456(U_18139,U_18137,U_18135)))
          & hBOOL(hAPP(hAPP(c_member(U_18135),sK456(U_18139,U_18137,U_18135)),hAPP(c_List_Oset(U_18135),U_18137))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK456]),skolemize(U_18128,sK456(U_18139,U_18137,U_18135))],[f_4411_3]) ).

fof(f_4411_5,plain,
    ( ! [U_18140,U_18138,U_18136] :
        ( ! [U_18131] :
            ( hBOOL(hAPP(U_18140,U_18131))
            | ~ hBOOL(hAPP(hAPP(c_member(U_18136),U_18131),hAPP(c_List_Oset(U_18136),U_18138))) )
        | ( ~ hBOOL(hAPP(U_18140,hAPP(hAPP(c_List_Onth(U_18136),U_18138),sK457(U_18140,U_18138,U_18136))))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK457(U_18140,U_18138,U_18136)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18136)),U_18138))) ) )
    & ! [U_18139,U_18137,U_18135] :
        ( ! [U_18129] :
            ( hBOOL(hAPP(U_18139,hAPP(hAPP(c_List_Onth(U_18135),U_18137),U_18129)))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18129),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18135)),U_18137))) )
        | ( ~ hBOOL(hAPP(U_18139,sK456(U_18139,U_18137,U_18135)))
          & hBOOL(hAPP(hAPP(c_member(U_18135),sK456(U_18139,U_18137,U_18135)),hAPP(c_List_Oset(U_18135),U_18137))) ) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK457]),skolemize(U_18130,sK457(U_18140,U_18138,U_18136))],[f_4411_4]) ).

fof(f_4411_6,plain,
    ( ! [U_18138,U_18136,U_18140] :
        ( ~ hBOOL(hAPP(U_18140,hAPP(hAPP(c_List_Onth(U_18136),U_18138),sK457(U_18140,U_18138,U_18136))))
        | ~ sP1144(U_18138,U_18136,U_18140) )
    & ! [U_18138,U_18136,U_18140] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK457(U_18140,U_18138,U_18136)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18136)),U_18138)))
        | ~ sP1144(U_18138,U_18136,U_18140) )
    & ! [U_18139,U_18135,U_18137] :
        ( ~ hBOOL(hAPP(U_18139,sK456(U_18139,U_18137,U_18135)))
        | ~ sP1143(U_18139,U_18135,U_18137) )
    & ! [U_18139,U_18135,U_18137] :
        ( hBOOL(hAPP(hAPP(c_member(U_18135),sK456(U_18139,U_18137,U_18135)),hAPP(c_List_Oset(U_18135),U_18137)))
        | ~ sP1143(U_18139,U_18135,U_18137) )
    & ! [U_18131,U_18138,U_18136,U_18140] :
        ( hBOOL(hAPP(U_18140,U_18131))
        | ~ hBOOL(hAPP(hAPP(c_member(U_18136),U_18131),hAPP(c_List_Oset(U_18136),U_18138)))
        | sP1144(U_18138,U_18136,U_18140) )
    & ! [U_18139,U_18129,U_18135,U_18137] :
        ( hBOOL(hAPP(U_18139,hAPP(hAPP(c_List_Onth(U_18135),U_18137),U_18129)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18129),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18135)),U_18137)))
        | sP1143(U_18139,U_18135,U_18137) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1143,sP1144])],[f_4411_5]) ).

cnf(f_4411_7,plain,
    ( hBOOL(hAPP(U_18139,hAPP(hAPP(c_List_Onth(U_18135),U_18137),U_18129)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18129),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18135)),U_18137)))
    | sP1143(U_18139,U_18135,U_18137) ),
    inference(clausify,[status(thm)],[f_4411_6]) ).

cnf(f_4411_8,plain,
    ( hBOOL(hAPP(U_18140,U_18131))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18136),U_18131),hAPP(c_List_Oset(U_18136),U_18138)))
    | sP1144(U_18138,U_18136,U_18140) ),
    inference(clausify,[status(thm)],[f_4411_6]) ).

cnf(f_4411_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18135),sK456(U_18139,U_18137,U_18135)),hAPP(c_List_Oset(U_18135),U_18137)))
    | ~ sP1143(U_18139,U_18135,U_18137) ),
    inference(clausify,[status(thm)],[f_4411_6]) ).

cnf(f_4411_10,plain,
    ( ~ hBOOL(hAPP(U_18139,sK456(U_18139,U_18137,U_18135)))
    | ~ sP1143(U_18139,U_18135,U_18137) ),
    inference(clausify,[status(thm)],[f_4411_6]) ).

cnf(f_4411_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK457(U_18140,U_18138,U_18136)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18136)),U_18138)))
    | ~ sP1144(U_18138,U_18136,U_18140) ),
    inference(clausify,[status(thm)],[f_4411_6]) ).

cnf(f_4411_12,plain,
    ( ~ hBOOL(hAPP(U_18140,hAPP(hAPP(c_List_Onth(U_18136),U_18138),sK457(U_18140,U_18138,U_18136))))
    | ~ sP1144(U_18138,U_18136,U_18140) ),
    inference(clausify,[status(thm)],[f_4411_6]) ).

fof(f_4412_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_4412_2,plain,
    ! [U_18145,U_18144,U_18143] :
      ( ( U_18143 = U_18144
        | ? [U_18142] :
            ( hAPP(hAPP(c_List_Onth(U_18145),U_18143),U_18142) != hAPP(hAPP(c_List_Onth(U_18145),U_18144),U_18142)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18142),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18145)),U_18143))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18145)),U_18143) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18145)),U_18144) )
      & ( ( ! [U_18141] :
              ( hAPP(hAPP(c_List_Onth(U_18145),U_18143),U_18141) = hAPP(hAPP(c_List_Onth(U_18145),U_18144),U_18141)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18141),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18145)),U_18143))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18145)),U_18143) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18145)),U_18144) )
        | U_18143 != U_18144 ) ),
    inference(variable_rename,[status(thm)],[f_4412_1]) ).

fof(f_4412_3,plain,
    ( ! [U_18151,U_18149,U_18147] :
        ( U_18147 = U_18149
        | ? [U_18142] :
            ( hAPP(hAPP(c_List_Onth(U_18151),U_18147),U_18142) != hAPP(hAPP(c_List_Onth(U_18151),U_18149),U_18142)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18142),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18151)),U_18147))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18151)),U_18147) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18151)),U_18149) )
    & ! [U_18150,U_18148,U_18146] :
        ( ( ! [U_18141] :
              ( hAPP(hAPP(c_List_Onth(U_18150),U_18146),U_18141) = hAPP(hAPP(c_List_Onth(U_18150),U_18148),U_18141)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18141),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18150)),U_18146))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18150)),U_18146) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18150)),U_18148) )
        | U_18146 != U_18148 ) ),
    inference(miniscope,[status(thm)],[f_4412_2]) ).

fof(f_4412_4,plain,
    ( ! [U_18151,U_18149,U_18147] :
        ( U_18147 = U_18149
        | ( hAPP(hAPP(c_List_Onth(U_18151),U_18147),sK458(U_18151,U_18149,U_18147)) != hAPP(hAPP(c_List_Onth(U_18151),U_18149),sK458(U_18151,U_18149,U_18147))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK458(U_18151,U_18149,U_18147)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18151)),U_18147))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18151)),U_18147) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18151)),U_18149) )
    & ! [U_18150,U_18148,U_18146] :
        ( ( ! [U_18141] :
              ( hAPP(hAPP(c_List_Onth(U_18150),U_18146),U_18141) = hAPP(hAPP(c_List_Onth(U_18150),U_18148),U_18141)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18141),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18150)),U_18146))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18150)),U_18146) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18150)),U_18148) )
        | U_18146 != U_18148 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK458]),skolemize(U_18142,sK458(U_18151,U_18149,U_18147))],[f_4412_3]) ).

fof(f_4412_5,plain,
    ( ! [U_18147,U_18149,U_18151] :
        ( hAPP(hAPP(c_List_Onth(U_18151),U_18147),sK458(U_18151,U_18149,U_18147)) != hAPP(hAPP(c_List_Onth(U_18151),U_18149),sK458(U_18151,U_18149,U_18147))
        | ~ sP1146(U_18147,U_18149,U_18151) )
    & ! [U_18147,U_18149,U_18151] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK458(U_18151,U_18149,U_18147)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18151)),U_18147)))
        | ~ sP1146(U_18147,U_18149,U_18151) )
    & ! [U_18141,U_18146,U_18148,U_18150] :
        ( hAPP(hAPP(c_List_Onth(U_18150),U_18146),U_18141) = hAPP(hAPP(c_List_Onth(U_18150),U_18148),U_18141)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18141),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18150)),U_18146)))
        | ~ sP1145(U_18141,U_18146,U_18148,U_18150) )
    & ! [U_18141,U_18146,U_18148,U_18150] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18150)),U_18146) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18150)),U_18148)
        | ~ sP1145(U_18141,U_18146,U_18148,U_18150) )
    & ! [U_18147,U_18149,U_18151] :
        ( U_18147 = U_18149
        | sP1146(U_18147,U_18149,U_18151)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18151)),U_18147) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18151)),U_18149) )
    & ! [U_18141,U_18146,U_18148,U_18150] :
        ( sP1145(U_18141,U_18146,U_18148,U_18150)
        | U_18146 != U_18148 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1145,sP1146])],[f_4412_4]) ).

cnf(f_4412_6,plain,
    ( sP1145(U_18141,U_18146,U_18148,U_18150)
    | U_18146 != U_18148 ),
    inference(clausify,[status(thm)],[f_4412_5]) ).

cnf(f_4412_7,plain,
    ( U_18147 = U_18149
    | sP1146(U_18147,U_18149,U_18151)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18151)),U_18147) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18151)),U_18149) ),
    inference(clausify,[status(thm)],[f_4412_5]) ).

cnf(f_4412_8,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18150)),U_18146) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18150)),U_18148)
    | ~ sP1145(U_18141,U_18146,U_18148,U_18150) ),
    inference(clausify,[status(thm)],[f_4412_5]) ).

cnf(f_4412_9,plain,
    ( hAPP(hAPP(c_List_Onth(U_18150),U_18146),U_18141) = hAPP(hAPP(c_List_Onth(U_18150),U_18148),U_18141)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18141),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18150)),U_18146)))
    | ~ sP1145(U_18141,U_18146,U_18148,U_18150) ),
    inference(clausify,[status(thm)],[f_4412_5]) ).

cnf(f_4412_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK458(U_18151,U_18149,U_18147)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18151)),U_18147)))
    | ~ sP1146(U_18147,U_18149,U_18151) ),
    inference(clausify,[status(thm)],[f_4412_5]) ).

cnf(f_4412_11,plain,
    ( hAPP(hAPP(c_List_Onth(U_18151),U_18147),sK458(U_18151,U_18149,U_18147)) != hAPP(hAPP(c_List_Onth(U_18151),U_18149),sK458(U_18151,U_18149,U_18147))
    | ~ sP1146(U_18147,U_18149,U_18151) ),
    inference(clausify,[status(thm)],[f_4412_5]) ).

fof(f_4413_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_4413_2,plain,
    ! [U_18157,U_18156] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_18156),U_18157))
        | ? [U_18155] :
            ( ? [U_18154] :
                ( hAPP(hAPP(c_List_Onth(U_18156),U_18157),U_18155) = hAPP(hAPP(c_List_Onth(U_18156),U_18157),U_18154)
                & U_18155 != U_18154
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18154),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18156)),U_18157))) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18155),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18156)),U_18157))) ) )
      & ( ! [U_18153] :
            ( ! [U_18152] :
                ( hAPP(hAPP(c_List_Onth(U_18156),U_18157),U_18153) != hAPP(hAPP(c_List_Onth(U_18156),U_18157),U_18152)
                | U_18153 = U_18152
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18152),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18156)),U_18157))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18153),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18156)),U_18157))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18156),U_18157)) ) ),
    inference(variable_rename,[status(thm)],[f_4413_1]) ).

fof(f_4413_3,plain,
    ( ! [U_18161,U_18159] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18159),U_18161))
        | ? [U_18155] :
            ( ? [U_18154] :
                ( hAPP(hAPP(c_List_Onth(U_18159),U_18161),U_18155) = hAPP(hAPP(c_List_Onth(U_18159),U_18161),U_18154)
                & U_18155 != U_18154
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18154),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18159)),U_18161))) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18155),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18159)),U_18161))) ) )
    & ! [U_18160,U_18158] :
        ( ! [U_18153] :
            ( ! [U_18152] :
                ( hAPP(hAPP(c_List_Onth(U_18158),U_18160),U_18153) != hAPP(hAPP(c_List_Onth(U_18158),U_18160),U_18152)
                | U_18153 = U_18152
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18152),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18158)),U_18160))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18153),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18158)),U_18160))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18158),U_18160)) ) ),
    inference(miniscope,[status(thm)],[f_4413_2]) ).

fof(f_4413_4,plain,
    ( ! [U_18161,U_18159] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18159),U_18161))
        | ( ? [U_18154] :
              ( hAPP(hAPP(c_List_Onth(U_18159),U_18161),sK459(U_18161,U_18159)) = hAPP(hAPP(c_List_Onth(U_18159),U_18161),U_18154)
              & sK459(U_18161,U_18159) != U_18154
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18154),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18159)),U_18161))) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK459(U_18161,U_18159)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18159)),U_18161))) ) )
    & ! [U_18160,U_18158] :
        ( ! [U_18153] :
            ( ! [U_18152] :
                ( hAPP(hAPP(c_List_Onth(U_18158),U_18160),U_18153) != hAPP(hAPP(c_List_Onth(U_18158),U_18160),U_18152)
                | U_18153 = U_18152
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18152),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18158)),U_18160))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18153),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18158)),U_18160))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18158),U_18160)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK459]),skolemize(U_18155,sK459(U_18161,U_18159))],[f_4413_3]) ).

fof(f_4413_5,plain,
    ( ! [U_18161,U_18159] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18159),U_18161))
        | ( hAPP(hAPP(c_List_Onth(U_18159),U_18161),sK459(U_18161,U_18159)) = hAPP(hAPP(c_List_Onth(U_18159),U_18161),sK460(U_18161,U_18159))
          & sK459(U_18161,U_18159) != sK460(U_18161,U_18159)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK460(U_18161,U_18159)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18159)),U_18161)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK459(U_18161,U_18159)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18159)),U_18161))) ) )
    & ! [U_18160,U_18158] :
        ( ! [U_18153] :
            ( ! [U_18152] :
                ( hAPP(hAPP(c_List_Onth(U_18158),U_18160),U_18153) != hAPP(hAPP(c_List_Onth(U_18158),U_18160),U_18152)
                | U_18153 = U_18152
                | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18152),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18158)),U_18160))) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18153),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18158)),U_18160))) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18158),U_18160)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK460]),skolemize(U_18154,sK460(U_18161,U_18159))],[f_4413_4]) ).

fof(f_4413_6,plain,
    ( ! [U_18159,U_18161] :
        ( hAPP(hAPP(c_List_Onth(U_18159),U_18161),sK459(U_18161,U_18159)) = hAPP(hAPP(c_List_Onth(U_18159),U_18161),sK460(U_18161,U_18159))
        | ~ sP1147(U_18159,U_18161) )
    & ! [U_18159,U_18161] :
        ( sK459(U_18161,U_18159) != sK460(U_18161,U_18159)
        | ~ sP1147(U_18159,U_18161) )
    & ! [U_18159,U_18161] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK460(U_18161,U_18159)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18159)),U_18161)))
        | ~ sP1147(U_18159,U_18161) )
    & ! [U_18159,U_18161] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK459(U_18161,U_18159)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18159)),U_18161)))
        | ~ sP1147(U_18159,U_18161) )
    & ! [U_18159,U_18161] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18159),U_18161))
        | sP1147(U_18159,U_18161) )
    & ! [U_18153,U_18152,U_18158,U_18160] :
        ( hAPP(hAPP(c_List_Onth(U_18158),U_18160),U_18153) != hAPP(hAPP(c_List_Onth(U_18158),U_18160),U_18152)
        | U_18153 = U_18152
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18152),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18158)),U_18160)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18153),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18158)),U_18160)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18158),U_18160)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1147])],[f_4413_5]) ).

cnf(f_4413_7,plain,
    ( hAPP(hAPP(c_List_Onth(U_18158),U_18160),U_18153) != hAPP(hAPP(c_List_Onth(U_18158),U_18160),U_18152)
    | U_18153 = U_18152
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18152),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18158)),U_18160)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18153),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18158)),U_18160)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18158),U_18160)) ),
    inference(clausify,[status(thm)],[f_4413_6]) ).

cnf(f_4413_8,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18159),U_18161))
    | sP1147(U_18159,U_18161) ),
    inference(clausify,[status(thm)],[f_4413_6]) ).

cnf(f_4413_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK459(U_18161,U_18159)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18159)),U_18161)))
    | ~ sP1147(U_18159,U_18161) ),
    inference(clausify,[status(thm)],[f_4413_6]) ).

cnf(f_4413_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK460(U_18161,U_18159)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18159)),U_18161)))
    | ~ sP1147(U_18159,U_18161) ),
    inference(clausify,[status(thm)],[f_4413_6]) ).

cnf(f_4413_11,plain,
    ( sK459(U_18161,U_18159) != sK460(U_18161,U_18159)
    | ~ sP1147(U_18159,U_18161) ),
    inference(clausify,[status(thm)],[f_4413_6]) ).

cnf(f_4413_12,plain,
    ( hAPP(hAPP(c_List_Onth(U_18159),U_18161),sK459(U_18161,U_18159)) = hAPP(hAPP(c_List_Onth(U_18159),U_18161),sK460(U_18161,U_18159))
    | ~ sP1147(U_18159,U_18161) ),
    inference(clausify,[status(thm)],[f_4413_6]) ).

fof(f_4414_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_4414_2,plain,
    ! [U_18165,U_18164,U_18163,U_18162] :
      ( ( ( hAPP(hAPP(c_List_Onth(U_18162),U_18163),U_18164) = hAPP(hAPP(c_List_Onth(U_18162),U_18163),U_18165)
          | U_18164 != U_18165 )
        & ( U_18164 = U_18165
          | hAPP(hAPP(c_List_Onth(U_18162),U_18163),U_18164) != hAPP(hAPP(c_List_Onth(U_18162),U_18163),U_18165) ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18165),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18162)),U_18163)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18164),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18162)),U_18163)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18162),U_18163)) ),
    inference(variable_rename,[status(thm)],[f_4414_1]) ).

fof(f_4414_3,plain,
    ( ! [U_18163,U_18162,U_18164,U_18165] :
        ( hAPP(hAPP(c_List_Onth(U_18162),U_18163),U_18164) = hAPP(hAPP(c_List_Onth(U_18162),U_18163),U_18165)
        | U_18164 != U_18165
        | ~ sP1148(U_18163,U_18162,U_18164,U_18165) )
    & ! [U_18163,U_18162,U_18164,U_18165] :
        ( U_18164 = U_18165
        | hAPP(hAPP(c_List_Onth(U_18162),U_18163),U_18164) != hAPP(hAPP(c_List_Onth(U_18162),U_18163),U_18165)
        | ~ sP1148(U_18163,U_18162,U_18164,U_18165) )
    & ! [U_18163,U_18162,U_18164,U_18165] :
        ( sP1148(U_18163,U_18162,U_18164,U_18165)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18165),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18162)),U_18163)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18164),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18162)),U_18163)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18162),U_18163)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1148])],[f_4414_2]) ).

cnf(f_4414_4,plain,
    ( sP1148(U_18163,U_18162,U_18164,U_18165)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18165),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18162)),U_18163)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18164),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18162)),U_18163)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18162),U_18163)) ),
    inference(clausify,[status(thm)],[f_4414_3]) ).

cnf(f_4414_5,plain,
    ( U_18164 = U_18165
    | hAPP(hAPP(c_List_Onth(U_18162),U_18163),U_18164) != hAPP(hAPP(c_List_Onth(U_18162),U_18163),U_18165)
    | ~ sP1148(U_18163,U_18162,U_18164,U_18165) ),
    inference(clausify,[status(thm)],[f_4414_3]) ).

cnf(f_4414_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_18162),U_18163),U_18164) = hAPP(hAPP(c_List_Onth(U_18162),U_18163),U_18165)
    | U_18164 != U_18165
    | ~ sP1148(U_18163,U_18162,U_18164,U_18165) ),
    inference(clausify,[status(thm)],[f_4414_3]) ).

fof(f_4415_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_4415_2,plain,
    ! [U_18168,U_18167,U_18166] :
      ( hBOOL(hAPP(hAPP(c_member(U_18167),hAPP(hAPP(c_List_Onth(U_18167),U_18168),U_18166)),hAPP(c_List_Oset(U_18167),U_18168)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18166),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18167)),U_18168))) ),
    inference(variable_rename,[status(thm)],[f_4415_1]) ).

fof(f_4415_3,plain,
    ! [U_18168,U_18167,U_18166] :
      ( hBOOL(hAPP(hAPP(c_member(U_18167),hAPP(hAPP(c_List_Onth(U_18167),U_18168),U_18166)),hAPP(c_List_Oset(U_18167),U_18168)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18166),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18167)),U_18168))) ),
    inference(definitional_conversion,[status(esa)],[f_4415_2]) ).

cnf(f_4415_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18167),hAPP(hAPP(c_List_Onth(U_18167),U_18168),U_18166)),hAPP(c_List_Oset(U_18167),U_18168)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18166),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18167)),U_18168))) ),
    inference(clausify,[status(thm)],[f_4415_3]) ).

fof(f_4416_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_4416_2,plain,
    ! [U_18173,U_18172,U_18171] :
      ( ( hBOOL(hAPP(hAPP(c_member(U_18171),U_18172),hAPP(c_List_Oset(U_18171),U_18173)))
        | ! [U_18170] :
            ( hAPP(hAPP(c_List_Onth(U_18171),U_18173),U_18170) != U_18172
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18170),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18171)),U_18173))) ) )
      & ( ? [U_18169] :
            ( hAPP(hAPP(c_List_Onth(U_18171),U_18173),U_18169) = U_18172
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18169),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18171)),U_18173))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18171),U_18172),hAPP(c_List_Oset(U_18171),U_18173))) ) ),
    inference(variable_rename,[status(thm)],[f_4416_1]) ).

fof(f_4416_3,plain,
    ( ! [U_18179,U_18177,U_18175] :
        ( hBOOL(hAPP(hAPP(c_member(U_18175),U_18177),hAPP(c_List_Oset(U_18175),U_18179)))
        | ! [U_18170] :
            ( hAPP(hAPP(c_List_Onth(U_18175),U_18179),U_18170) != U_18177
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18170),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18175)),U_18179))) ) )
    & ! [U_18178,U_18176,U_18174] :
        ( ? [U_18169] :
            ( hAPP(hAPP(c_List_Onth(U_18174),U_18178),U_18169) = U_18176
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18169),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18174)),U_18178))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18174),U_18176),hAPP(c_List_Oset(U_18174),U_18178))) ) ),
    inference(miniscope,[status(thm)],[f_4416_2]) ).

fof(f_4416_4,plain,
    ( ! [U_18179,U_18177,U_18175] :
        ( hBOOL(hAPP(hAPP(c_member(U_18175),U_18177),hAPP(c_List_Oset(U_18175),U_18179)))
        | ! [U_18170] :
            ( hAPP(hAPP(c_List_Onth(U_18175),U_18179),U_18170) != U_18177
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18170),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18175)),U_18179))) ) )
    & ! [U_18178,U_18176,U_18174] :
        ( ( hAPP(hAPP(c_List_Onth(U_18174),U_18178),sK461(U_18178,U_18176,U_18174)) = U_18176
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK461(U_18178,U_18176,U_18174)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18174)),U_18178))) )
        | ~ hBOOL(hAPP(hAPP(c_member(U_18174),U_18176),hAPP(c_List_Oset(U_18174),U_18178))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK461]),skolemize(U_18169,sK461(U_18178,U_18176,U_18174))],[f_4416_3]) ).

fof(f_4416_5,plain,
    ( ! [U_18176,U_18174,U_18178] :
        ( hAPP(hAPP(c_List_Onth(U_18174),U_18178),sK461(U_18178,U_18176,U_18174)) = U_18176
        | ~ sP1149(U_18176,U_18174,U_18178) )
    & ! [U_18176,U_18174,U_18178] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK461(U_18178,U_18176,U_18174)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18174)),U_18178)))
        | ~ sP1149(U_18176,U_18174,U_18178) )
    & ! [U_18170,U_18177,U_18175,U_18179] :
        ( hBOOL(hAPP(hAPP(c_member(U_18175),U_18177),hAPP(c_List_Oset(U_18175),U_18179)))
        | hAPP(hAPP(c_List_Onth(U_18175),U_18179),U_18170) != U_18177
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18170),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18175)),U_18179))) )
    & ! [U_18176,U_18174,U_18178] :
        ( sP1149(U_18176,U_18174,U_18178)
        | ~ hBOOL(hAPP(hAPP(c_member(U_18174),U_18176),hAPP(c_List_Oset(U_18174),U_18178))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1149])],[f_4416_4]) ).

cnf(f_4416_6,plain,
    ( sP1149(U_18176,U_18174,U_18178)
    | ~ hBOOL(hAPP(hAPP(c_member(U_18174),U_18176),hAPP(c_List_Oset(U_18174),U_18178))) ),
    inference(clausify,[status(thm)],[f_4416_5]) ).

cnf(f_4416_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18175),U_18177),hAPP(c_List_Oset(U_18175),U_18179)))
    | hAPP(hAPP(c_List_Onth(U_18175),U_18179),U_18170) != U_18177
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18170),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18175)),U_18179))) ),
    inference(clausify,[status(thm)],[f_4416_5]) ).

cnf(f_4416_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK461(U_18178,U_18176,U_18174)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18174)),U_18178)))
    | ~ sP1149(U_18176,U_18174,U_18178) ),
    inference(clausify,[status(thm)],[f_4416_5]) ).

cnf(f_4416_9,plain,
    ( hAPP(hAPP(c_List_Onth(U_18174),U_18178),sK461(U_18178,U_18176,U_18174)) = U_18176
    | ~ sP1149(U_18176,U_18174,U_18178) ),
    inference(clausify,[status(thm)],[f_4416_5]) ).

fof(f_4417_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_4417_2,plain,
    ! [U_18183,U_18182,U_18181,U_18180] :
      ( ( hAPP(hAPP(c_List_Onth(U_18181),hAPP(hAPP(c_List_Olist_OCons(U_18181),U_18182),U_18183)),U_18180) = hAPP(hAPP(c_List_Onth(U_18181),U_18183),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18180),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_18180 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Onth(U_18181),hAPP(hAPP(c_List_Olist_OCons(U_18181),U_18182),U_18183)),U_18180) = U_18182
        | U_18180 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4417_1]) ).

fof(f_4417_3,plain,
    ( ! [U_18191,U_18189,U_18187,U_18185] :
        ( hAPP(hAPP(c_List_Onth(U_18187),hAPP(hAPP(c_List_Olist_OCons(U_18187),U_18189),U_18191)),U_18185) = hAPP(hAPP(c_List_Onth(U_18187),U_18191),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18185),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_18185 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_18190,U_18188,U_18186,U_18184] :
        ( hAPP(hAPP(c_List_Onth(U_18186),hAPP(hAPP(c_List_Olist_OCons(U_18186),U_18188),U_18190)),U_18184) = U_18188
        | U_18184 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4417_2]) ).

fof(f_4417_4,plain,
    ( ! [U_18185,U_18187,U_18189,U_18191] :
        ( hAPP(hAPP(c_List_Onth(U_18187),hAPP(hAPP(c_List_Olist_OCons(U_18187),U_18189),U_18191)),U_18185) = hAPP(hAPP(c_List_Onth(U_18187),U_18191),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18185),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | U_18185 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_18190,U_18188,U_18184,U_18186] :
        ( hAPP(hAPP(c_List_Onth(U_18186),hAPP(hAPP(c_List_Olist_OCons(U_18186),U_18188),U_18190)),U_18184) = U_18188
        | U_18184 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_4417_3]) ).

cnf(f_4417_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_18186),hAPP(hAPP(c_List_Olist_OCons(U_18186),U_18188),U_18190)),U_18184) = U_18188
    | U_18184 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4417_4]) ).

cnf(f_4417_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_18187),hAPP(hAPP(c_List_Olist_OCons(U_18187),U_18189),U_18191)),U_18185) = hAPP(hAPP(c_List_Onth(U_18187),U_18191),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18185),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | U_18185 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4417_4]) ).

fof(f_4418_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_4418_2,plain,
    ! [U_18193,U_18192] : hAPP(c_List_Oset(U_18192),U_18193) = hAPP(c_Set_OCollect(U_18192),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_18192),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_18192,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_18192),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_18192),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_18192,tc_fun(tc_Nat_Onat,U_18192),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18192,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_18192),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18192),c_COMBB(U_18192,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_18192),U_18193))))),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_18192)),U_18193))))),
    inference(variable_rename,[status(thm)],[f_4418_1]) ).

fof(f_4418_3,plain,
    ! [U_18192,U_18193] : hAPP(c_List_Oset(U_18192),U_18193) = hAPP(c_Set_OCollect(U_18192),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_18192),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_18192,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_18192),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_18192),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_18192,tc_fun(tc_Nat_Onat,U_18192),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18192,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_18192),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18192),c_COMBB(U_18192,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_18192),U_18193))))),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_18192)),U_18193))))),
    inference(definitional_conversion,[status(esa)],[f_4418_2]) ).

cnf(f_4418_4,plain,
    hAPP(c_List_Oset(U_18192),U_18193) = hAPP(c_Set_OCollect(U_18192),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_18192),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_18192,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_18192),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_18192),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_18192,tc_fun(tc_Nat_Onat,U_18192),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18192,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_18192),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18192),c_COMBB(U_18192,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_18192),U_18193))))),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_18192)),U_18193))))),
    inference(clausify,[status(thm)],[f_4418_3]) ).

fof(f_4419_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_4419_2,plain,
    ! [U_18197,U_18196,U_18195,U_18194] :
      ( ( hAPP(hAPP(c_List_Onth(U_18195),hAPP(hAPP(c_List_Olist_OCons(U_18195),U_18196),U_18197)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18194)) = hAPP(hAPP(c_List_Onth(U_18195),U_18197),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18194)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18194) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Onth(U_18195),hAPP(hAPP(c_List_Olist_OCons(U_18195),U_18196),U_18197)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18194)) = U_18196
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18194) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4419_1]) ).

fof(f_4419_3,plain,
    ( ! [U_18205,U_18203,U_18201,U_18199] :
        ( hAPP(hAPP(c_List_Onth(U_18201),hAPP(hAPP(c_List_Olist_OCons(U_18201),U_18203),U_18205)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18199)) = hAPP(hAPP(c_List_Onth(U_18201),U_18205),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18199)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18199) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_18204,U_18202,U_18200,U_18198] :
        ( hAPP(hAPP(c_List_Onth(U_18200),hAPP(hAPP(c_List_Olist_OCons(U_18200),U_18202),U_18204)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18198)) = U_18202
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18198) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4419_2]) ).

fof(f_4419_4,plain,
    ( ! [U_18199,U_18201,U_18203,U_18205] :
        ( hAPP(hAPP(c_List_Onth(U_18201),hAPP(hAPP(c_List_Olist_OCons(U_18201),U_18203),U_18205)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18199)) = hAPP(hAPP(c_List_Onth(U_18201),U_18205),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18199)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18199) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_18204,U_18200,U_18198,U_18202] :
        ( hAPP(hAPP(c_List_Onth(U_18200),hAPP(hAPP(c_List_Olist_OCons(U_18200),U_18202),U_18204)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18198)) = U_18202
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18198) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_4419_3]) ).

cnf(f_4419_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_18200),hAPP(hAPP(c_List_Olist_OCons(U_18200),U_18202),U_18204)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18198)) = U_18202
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18198) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4419_4]) ).

cnf(f_4419_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_18201),hAPP(hAPP(c_List_Olist_OCons(U_18201),U_18203),U_18205)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18199)) = hAPP(hAPP(c_List_Onth(U_18201),U_18205),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18199)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18199) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4419_4]) ).

fof(f_4420_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_4420_2,plain,
    ! [U_18207,U_18206] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18206),U_18207) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_18206),hAPP(c_List_Onth(U_18206),U_18207)),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_18206)),U_18207)))
      | ~ class_Groups_Ocomm__monoid__add(U_18206) ),
    inference(variable_rename,[status(thm)],[f_4420_1]) ).

fof(f_4420_3,plain,
    ! [U_18206,U_18207] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18206),U_18207) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_18206),hAPP(c_List_Onth(U_18206),U_18207)),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_18206)),U_18207)))
      | ~ class_Groups_Ocomm__monoid__add(U_18206) ),
    inference(definitional_conversion,[status(esa)],[f_4420_2]) ).

cnf(f_4420_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18206),U_18207) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_18206),hAPP(c_List_Onth(U_18206),U_18207)),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_18206)),U_18207)))
    | ~ class_Groups_Ocomm__monoid__add(U_18206) ),
    inference(clausify,[status(thm)],[f_4420_3]) ).

fof(f_4421_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_4421_2,plain,
    ! [U_18210,U_18209,U_18208] : hAPP(c_List_Oset(U_18208),c_List_Osublist(U_18208,U_18209,U_18210)) = hAPP(c_Set_OCollect(U_18208),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_18208),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_18208,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_18208),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_18208),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_18208,tc_fun(tc_Nat_Onat,U_18208),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18208,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_18208),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18208),c_COMBB(U_18208,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_18208),U_18209))))),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_18208)),U_18209)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_18210))))),
    inference(variable_rename,[status(thm)],[f_4421_1]) ).

fof(f_4421_3,plain,
    ! [U_18208,U_18209,U_18210] : hAPP(c_List_Oset(U_18208),c_List_Osublist(U_18208,U_18209,U_18210)) = hAPP(c_Set_OCollect(U_18208),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_18208),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_18208,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_18208),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_18208),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_18208,tc_fun(tc_Nat_Onat,U_18208),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18208,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_18208),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18208),c_COMBB(U_18208,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_18208),U_18209))))),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_18208)),U_18209)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_18210))))),
    inference(definitional_conversion,[status(esa)],[f_4421_2]) ).

cnf(f_4421_4,plain,
    hAPP(c_List_Oset(U_18208),c_List_Osublist(U_18208,U_18209,U_18210)) = hAPP(c_Set_OCollect(U_18208),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool,U_18208),c_HOL_OEx(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(U_18208,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_18208),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_18208),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Nat_Onat),c_fconj)),hAPP(hAPP(c_COMBC(U_18208,tc_fun(tc_Nat_Onat,U_18208),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(U_18208,tc_HOL_Obool),tc_fun(tc_fun(tc_Nat_Onat,U_18208),tc_fun(tc_Nat_Onat,tc_HOL_Obool)),U_18208),c_COMBB(U_18208,tc_HOL_Obool,tc_Nat_Onat)),c_fequal)),hAPP(c_List_Onth(U_18208),U_18209))))),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_18208)),U_18209)))),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_HOL_Obool),c_member(tc_Nat_Onat)),U_18210))))),
    inference(clausify,[status(thm)],[f_4421_3]) ).

fof(f_4422_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_4422_2,plain,
    ! [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_18213)),c_List_Olex(U_18211,U_18214)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18211)),U_18212) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18211)),U_18213)
        | ~ 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_Olexord(U_18211,U_18214))) )
      & ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18211)),U_18212) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18211)),U_18213)
          & 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_Olexord(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_Olex(U_18211,U_18214))) ) ),
    inference(variable_rename,[status(thm)],[f_4422_1]) ).

fof(f_4422_3,plain,
    ( ! [U_18222,U_18220,U_18218,U_18216] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18216),tc_List_Olist(U_18216))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18216),tc_List_Olist(U_18216)),U_18218),U_18220)),c_List_Olex(U_18216,U_18222)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18216)),U_18218) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18216)),U_18220)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18216),tc_List_Olist(U_18216))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18216),tc_List_Olist(U_18216)),U_18218),U_18220)),c_List_Olexord(U_18216,U_18222))) )
    & ! [U_18221,U_18219,U_18217,U_18215] :
        ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18215)),U_18217) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18215)),U_18219)
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18215),tc_List_Olist(U_18215))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18215),tc_List_Olist(U_18215)),U_18217),U_18219)),c_List_Olexord(U_18215,U_18221))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18215),tc_List_Olist(U_18215))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18215),tc_List_Olist(U_18215)),U_18217),U_18219)),c_List_Olex(U_18215,U_18221))) ) ),
    inference(miniscope,[status(thm)],[f_4422_2]) ).

fof(f_4422_4,plain,
    ( ! [U_18221,U_18217,U_18215,U_18219] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18215)),U_18217) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18215)),U_18219)
        | ~ sP1150(U_18221,U_18217,U_18215,U_18219) )
    & ! [U_18221,U_18217,U_18215,U_18219] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18215),tc_List_Olist(U_18215))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18215),tc_List_Olist(U_18215)),U_18217),U_18219)),c_List_Olexord(U_18215,U_18221)))
        | ~ sP1150(U_18221,U_18217,U_18215,U_18219) )
    & ! [U_18216,U_18220,U_18222,U_18218] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18216),tc_List_Olist(U_18216))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18216),tc_List_Olist(U_18216)),U_18218),U_18220)),c_List_Olex(U_18216,U_18222)))
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18216)),U_18218) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18216)),U_18220)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18216),tc_List_Olist(U_18216))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18216),tc_List_Olist(U_18216)),U_18218),U_18220)),c_List_Olexord(U_18216,U_18222))) )
    & ! [U_18221,U_18217,U_18215,U_18219] :
        ( sP1150(U_18221,U_18217,U_18215,U_18219)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18215),tc_List_Olist(U_18215))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18215),tc_List_Olist(U_18215)),U_18217),U_18219)),c_List_Olex(U_18215,U_18221))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1150])],[f_4422_3]) ).

cnf(f_4422_5,plain,
    ( sP1150(U_18221,U_18217,U_18215,U_18219)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18215),tc_List_Olist(U_18215))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18215),tc_List_Olist(U_18215)),U_18217),U_18219)),c_List_Olex(U_18215,U_18221))) ),
    inference(clausify,[status(thm)],[f_4422_4]) ).

cnf(f_4422_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18216),tc_List_Olist(U_18216))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18216),tc_List_Olist(U_18216)),U_18218),U_18220)),c_List_Olex(U_18216,U_18222)))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18216)),U_18218) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18216)),U_18220)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18216),tc_List_Olist(U_18216))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18216),tc_List_Olist(U_18216)),U_18218),U_18220)),c_List_Olexord(U_18216,U_18222))) ),
    inference(clausify,[status(thm)],[f_4422_4]) ).

cnf(f_4422_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18215),tc_List_Olist(U_18215))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18215),tc_List_Olist(U_18215)),U_18217),U_18219)),c_List_Olexord(U_18215,U_18221)))
    | ~ sP1150(U_18221,U_18217,U_18215,U_18219) ),
    inference(clausify,[status(thm)],[f_4422_4]) ).

cnf(f_4422_8,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18215)),U_18217) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18215)),U_18219)
    | ~ sP1150(U_18221,U_18217,U_18215,U_18219) ),
    inference(clausify,[status(thm)],[f_4422_4]) ).

fof(f_4423_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_4423_2,plain,
    ! [U_18228,U_18227,U_18226,U_18225] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18225),tc_List_Olist(U_18225))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18225),tc_List_Olist(U_18225)),U_18226),U_18227)),c_List_Olistrel(U_18225,U_18228)))
        | ? [U_18224] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18225,U_18225)),hAPP(hAPP(c_Product__Type_OPair(U_18225,U_18225),hAPP(hAPP(c_List_Onth(U_18225),U_18226),U_18224)),hAPP(hAPP(c_List_Onth(U_18225),U_18227),U_18224))),U_18228))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18224),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18225)),U_18226))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18225)),U_18226) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18225)),U_18227) )
      & ( ( ! [U_18223] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18225,U_18225)),hAPP(hAPP(c_Product__Type_OPair(U_18225,U_18225),hAPP(hAPP(c_List_Onth(U_18225),U_18226),U_18223)),hAPP(hAPP(c_List_Onth(U_18225),U_18227),U_18223))),U_18228))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18223),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18225)),U_18226))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18225)),U_18226) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18225)),U_18227) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18225),tc_List_Olist(U_18225))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18225),tc_List_Olist(U_18225)),U_18226),U_18227)),c_List_Olistrel(U_18225,U_18228))) ) ),
    inference(variable_rename,[status(thm)],[f_4423_1]) ).

fof(f_4423_3,plain,
    ( ! [U_18236,U_18234,U_18232,U_18230] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18230),tc_List_Olist(U_18230))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18230),tc_List_Olist(U_18230)),U_18232),U_18234)),c_List_Olistrel(U_18230,U_18236)))
        | ? [U_18224] :
            ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18230,U_18230)),hAPP(hAPP(c_Product__Type_OPair(U_18230,U_18230),hAPP(hAPP(c_List_Onth(U_18230),U_18232),U_18224)),hAPP(hAPP(c_List_Onth(U_18230),U_18234),U_18224))),U_18236))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18224),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18230)),U_18232))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18230)),U_18232) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18230)),U_18234) )
    & ! [U_18235,U_18233,U_18231,U_18229] :
        ( ( ! [U_18223] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18229,U_18229)),hAPP(hAPP(c_Product__Type_OPair(U_18229,U_18229),hAPP(hAPP(c_List_Onth(U_18229),U_18231),U_18223)),hAPP(hAPP(c_List_Onth(U_18229),U_18233),U_18223))),U_18235))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18223),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18229)),U_18231))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18229)),U_18231) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18229)),U_18233) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18229),tc_List_Olist(U_18229))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18229),tc_List_Olist(U_18229)),U_18231),U_18233)),c_List_Olistrel(U_18229,U_18235))) ) ),
    inference(miniscope,[status(thm)],[f_4423_2]) ).

fof(f_4423_4,plain,
    ( ! [U_18236,U_18234,U_18232,U_18230] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18230),tc_List_Olist(U_18230))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18230),tc_List_Olist(U_18230)),U_18232),U_18234)),c_List_Olistrel(U_18230,U_18236)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18230,U_18230)),hAPP(hAPP(c_Product__Type_OPair(U_18230,U_18230),hAPP(hAPP(c_List_Onth(U_18230),U_18232),sK462(U_18236,U_18234,U_18232,U_18230))),hAPP(hAPP(c_List_Onth(U_18230),U_18234),sK462(U_18236,U_18234,U_18232,U_18230)))),U_18236))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK462(U_18236,U_18234,U_18232,U_18230)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18230)),U_18232))) )
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18230)),U_18232) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18230)),U_18234) )
    & ! [U_18235,U_18233,U_18231,U_18229] :
        ( ( ! [U_18223] :
              ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18229,U_18229)),hAPP(hAPP(c_Product__Type_OPair(U_18229,U_18229),hAPP(hAPP(c_List_Onth(U_18229),U_18231),U_18223)),hAPP(hAPP(c_List_Onth(U_18229),U_18233),U_18223))),U_18235))
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18223),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18229)),U_18231))) )
          & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18229)),U_18231) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18229)),U_18233) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18229),tc_List_Olist(U_18229))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18229),tc_List_Olist(U_18229)),U_18231),U_18233)),c_List_Olistrel(U_18229,U_18235))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK462]),skolemize(U_18224,sK462(U_18236,U_18234,U_18232,U_18230))],[f_4423_3]) ).

fof(f_4423_5,plain,
    ( ! [U_18230,U_18232,U_18236,U_18234] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18230,U_18230)),hAPP(hAPP(c_Product__Type_OPair(U_18230,U_18230),hAPP(hAPP(c_List_Onth(U_18230),U_18232),sK462(U_18236,U_18234,U_18232,U_18230))),hAPP(hAPP(c_List_Onth(U_18230),U_18234),sK462(U_18236,U_18234,U_18232,U_18230)))),U_18236))
        | ~ sP1152(U_18230,U_18232,U_18236,U_18234) )
    & ! [U_18230,U_18232,U_18236,U_18234] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK462(U_18236,U_18234,U_18232,U_18230)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18230)),U_18232)))
        | ~ sP1152(U_18230,U_18232,U_18236,U_18234) )
    & ! [U_18223,U_18233,U_18229,U_18231,U_18235] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18229,U_18229)),hAPP(hAPP(c_Product__Type_OPair(U_18229,U_18229),hAPP(hAPP(c_List_Onth(U_18229),U_18231),U_18223)),hAPP(hAPP(c_List_Onth(U_18229),U_18233),U_18223))),U_18235))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18223),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18229)),U_18231)))
        | ~ sP1151(U_18223,U_18233,U_18229,U_18231,U_18235) )
    & ! [U_18223,U_18233,U_18229,U_18231,U_18235] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18229)),U_18231) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18229)),U_18233)
        | ~ sP1151(U_18223,U_18233,U_18229,U_18231,U_18235) )
    & ! [U_18230,U_18232,U_18236,U_18234] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18230),tc_List_Olist(U_18230))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18230),tc_List_Olist(U_18230)),U_18232),U_18234)),c_List_Olistrel(U_18230,U_18236)))
        | sP1152(U_18230,U_18232,U_18236,U_18234)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18230)),U_18232) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18230)),U_18234) )
    & ! [U_18223,U_18233,U_18229,U_18231,U_18235] :
        ( sP1151(U_18223,U_18233,U_18229,U_18231,U_18235)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18229),tc_List_Olist(U_18229))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18229),tc_List_Olist(U_18229)),U_18231),U_18233)),c_List_Olistrel(U_18229,U_18235))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1151,sP1152])],[f_4423_4]) ).

cnf(f_4423_6,plain,
    ( sP1151(U_18223,U_18233,U_18229,U_18231,U_18235)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18229),tc_List_Olist(U_18229))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18229),tc_List_Olist(U_18229)),U_18231),U_18233)),c_List_Olistrel(U_18229,U_18235))) ),
    inference(clausify,[status(thm)],[f_4423_5]) ).

cnf(f_4423_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18230),tc_List_Olist(U_18230))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18230),tc_List_Olist(U_18230)),U_18232),U_18234)),c_List_Olistrel(U_18230,U_18236)))
    | sP1152(U_18230,U_18232,U_18236,U_18234)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18230)),U_18232) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18230)),U_18234) ),
    inference(clausify,[status(thm)],[f_4423_5]) ).

cnf(f_4423_8,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18229)),U_18231) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18229)),U_18233)
    | ~ sP1151(U_18223,U_18233,U_18229,U_18231,U_18235) ),
    inference(clausify,[status(thm)],[f_4423_5]) ).

cnf(f_4423_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18229,U_18229)),hAPP(hAPP(c_Product__Type_OPair(U_18229,U_18229),hAPP(hAPP(c_List_Onth(U_18229),U_18231),U_18223)),hAPP(hAPP(c_List_Onth(U_18229),U_18233),U_18223))),U_18235))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18223),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18229)),U_18231)))
    | ~ sP1151(U_18223,U_18233,U_18229,U_18231,U_18235) ),
    inference(clausify,[status(thm)],[f_4423_5]) ).

cnf(f_4423_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK462(U_18236,U_18234,U_18232,U_18230)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18230)),U_18232)))
    | ~ sP1152(U_18230,U_18232,U_18236,U_18234) ),
    inference(clausify,[status(thm)],[f_4423_5]) ).

cnf(f_4423_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18230,U_18230)),hAPP(hAPP(c_Product__Type_OPair(U_18230,U_18230),hAPP(hAPP(c_List_Onth(U_18230),U_18232),sK462(U_18236,U_18234,U_18232,U_18230))),hAPP(hAPP(c_List_Onth(U_18230),U_18234),sK462(U_18236,U_18234,U_18232,U_18230)))),U_18236))
    | ~ sP1152(U_18230,U_18232,U_18236,U_18234) ),
    inference(clausify,[status(thm)],[f_4423_5]) ).

fof(f_4424_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_4424_2,plain,
    ! [U_18239,U_18238,U_18237] :
      ( hAPP(c_Random_Opick(U_18238,hAPP(hAPP(c_List_Omap(U_18238,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18238)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18238),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18239)),hAPP(c_Code__Numeral_Oof__nat,U_18237)) = hAPP(hAPP(c_List_Onth(U_18238),U_18239),U_18237)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18237),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18238)),U_18239))) ),
    inference(variable_rename,[status(thm)],[f_4424_1]) ).

fof(f_4424_3,plain,
    ! [U_18238,U_18239,U_18237] :
      ( hAPP(c_Random_Opick(U_18238,hAPP(hAPP(c_List_Omap(U_18238,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18238)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18238),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18239)),hAPP(c_Code__Numeral_Oof__nat,U_18237)) = hAPP(hAPP(c_List_Onth(U_18238),U_18239),U_18237)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18237),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18238)),U_18239))) ),
    inference(definitional_conversion,[status(esa)],[f_4424_2]) ).

cnf(f_4424_4,plain,
    ( hAPP(c_Random_Opick(U_18238,hAPP(hAPP(c_List_Omap(U_18238,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18238)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18238),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18239)),hAPP(c_Code__Numeral_Oof__nat,U_18237)) = hAPP(hAPP(c_List_Onth(U_18238),U_18239),U_18237)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18237),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18238)),U_18239))) ),
    inference(clausify,[status(thm)],[f_4424_3]) ).

fof(f_4425_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_4425_2,plain,
    ! [U_18241,U_18240] : c_Random_Oselect(U_18240,U_18241) = 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_18240,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_18240)),U_18241)))),hAPP(hAPP(c_COMBB(U_18240,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18240,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18240,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_18240,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(U_18240),U_18241)),c_Code__Numeral_Onat__of))),
    inference(variable_rename,[status(thm)],[f_4425_1]) ).

fof(f_4425_3,plain,
    ! [U_18240,U_18241] : c_Random_Oselect(U_18240,U_18241) = 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_18240,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_18240)),U_18241)))),hAPP(hAPP(c_COMBB(U_18240,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18240,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18240,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_18240,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(U_18240),U_18241)),c_Code__Numeral_Onat__of))),
    inference(definitional_conversion,[status(esa)],[f_4425_2]) ).

cnf(f_4425_4,plain,
    c_Random_Oselect(U_18240,U_18241) = 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_18240,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_18240)),U_18241)))),hAPP(hAPP(c_COMBB(U_18240,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_prod(U_18240,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),tc_Code__Numeral_Ocode__numeral),c_Product__Type_OPair(U_18240,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,U_18240,tc_Code__Numeral_Ocode__numeral),hAPP(c_List_Onth(U_18240),U_18241)),c_Code__Numeral_Onat__of))),
    inference(clausify,[status(thm)],[f_4425_3]) ).

fof(f_4426_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_4426_2,plain,
    ! [U_18247,U_18246,U_18245,U_18244] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18244),tc_List_Olist(U_18244))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18244),tc_List_Olist(U_18244)),U_18245),U_18246)),c_List_Olexord(U_18244,U_18247)))
        | ( ! [U_18243] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18244,U_18244)),hAPP(hAPP(c_Product__Type_OPair(U_18244,U_18244),hAPP(hAPP(c_List_Onth(U_18244),U_18245),U_18243)),hAPP(hAPP(c_List_Onth(U_18244),U_18246),U_18243))),U_18247))
              | hAPP(hAPP(c_List_Otake(U_18244),U_18243),U_18245) != hAPP(hAPP(c_List_Otake(U_18244),U_18243),U_18246)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18243),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18244)),U_18245)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18244)),U_18246)))) )
          & ( hAPP(hAPP(c_List_Otake(U_18244),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18244)),U_18245)),U_18246) != U_18245
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18244)),U_18245)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18244)),U_18246))) ) ) )
      & ( ? [U_18242] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18244,U_18244)),hAPP(hAPP(c_Product__Type_OPair(U_18244,U_18244),hAPP(hAPP(c_List_Onth(U_18244),U_18245),U_18242)),hAPP(hAPP(c_List_Onth(U_18244),U_18246),U_18242))),U_18247))
            & hAPP(hAPP(c_List_Otake(U_18244),U_18242),U_18245) = hAPP(hAPP(c_List_Otake(U_18244),U_18242),U_18246)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18242),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18244)),U_18245)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18244)),U_18246)))) )
        | ( hAPP(hAPP(c_List_Otake(U_18244),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18244)),U_18245)),U_18246) = U_18245
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18244)),U_18245)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18244)),U_18246))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18244),tc_List_Olist(U_18244))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18244),tc_List_Olist(U_18244)),U_18245),U_18246)),c_List_Olexord(U_18244,U_18247))) ) ),
    inference(variable_rename,[status(thm)],[f_4426_1]) ).

fof(f_4426_3,plain,
    ( ! [U_18255,U_18253,U_18251,U_18249] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18249),tc_List_Olist(U_18249))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18249),tc_List_Olist(U_18249)),U_18251),U_18253)),c_List_Olexord(U_18249,U_18255)))
        | ( ! [U_18243] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18249,U_18249)),hAPP(hAPP(c_Product__Type_OPair(U_18249,U_18249),hAPP(hAPP(c_List_Onth(U_18249),U_18251),U_18243)),hAPP(hAPP(c_List_Onth(U_18249),U_18253),U_18243))),U_18255))
              | hAPP(hAPP(c_List_Otake(U_18249),U_18243),U_18251) != hAPP(hAPP(c_List_Otake(U_18249),U_18243),U_18253)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18243),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18251)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18253)))) )
          & ( hAPP(hAPP(c_List_Otake(U_18249),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18251)),U_18253) != U_18251
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18251)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18253))) ) ) )
    & ! [U_18254,U_18252,U_18250,U_18248] :
        ( ? [U_18242] :
            ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18248,U_18248)),hAPP(hAPP(c_Product__Type_OPair(U_18248,U_18248),hAPP(hAPP(c_List_Onth(U_18248),U_18250),U_18242)),hAPP(hAPP(c_List_Onth(U_18248),U_18252),U_18242))),U_18254))
            & hAPP(hAPP(c_List_Otake(U_18248),U_18242),U_18250) = hAPP(hAPP(c_List_Otake(U_18248),U_18242),U_18252)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18242),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18248)),U_18250)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18248)),U_18252)))) )
        | ( hAPP(hAPP(c_List_Otake(U_18248),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18248)),U_18250)),U_18252) = U_18250
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18248)),U_18250)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18248)),U_18252))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18248),tc_List_Olist(U_18248))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18248),tc_List_Olist(U_18248)),U_18250),U_18252)),c_List_Olexord(U_18248,U_18254))) ) ),
    inference(miniscope,[status(thm)],[f_4426_2]) ).

fof(f_4426_4,plain,
    ( ! [U_18255,U_18253,U_18251,U_18249] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18249),tc_List_Olist(U_18249))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18249),tc_List_Olist(U_18249)),U_18251),U_18253)),c_List_Olexord(U_18249,U_18255)))
        | ( ! [U_18243] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18249,U_18249)),hAPP(hAPP(c_Product__Type_OPair(U_18249,U_18249),hAPP(hAPP(c_List_Onth(U_18249),U_18251),U_18243)),hAPP(hAPP(c_List_Onth(U_18249),U_18253),U_18243))),U_18255))
              | hAPP(hAPP(c_List_Otake(U_18249),U_18243),U_18251) != hAPP(hAPP(c_List_Otake(U_18249),U_18243),U_18253)
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18243),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18251)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18253)))) )
          & ( hAPP(hAPP(c_List_Otake(U_18249),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18251)),U_18253) != U_18251
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18251)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18253))) ) ) )
    & ! [U_18254,U_18252,U_18250,U_18248] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18248,U_18248)),hAPP(hAPP(c_Product__Type_OPair(U_18248,U_18248),hAPP(hAPP(c_List_Onth(U_18248),U_18250),sK463(U_18254,U_18252,U_18250,U_18248))),hAPP(hAPP(c_List_Onth(U_18248),U_18252),sK463(U_18254,U_18252,U_18250,U_18248)))),U_18254))
          & hAPP(hAPP(c_List_Otake(U_18248),sK463(U_18254,U_18252,U_18250,U_18248)),U_18250) = hAPP(hAPP(c_List_Otake(U_18248),sK463(U_18254,U_18252,U_18250,U_18248)),U_18252)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK463(U_18254,U_18252,U_18250,U_18248)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18248)),U_18250)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18248)),U_18252)))) )
        | ( hAPP(hAPP(c_List_Otake(U_18248),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18248)),U_18250)),U_18252) = U_18250
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18248)),U_18250)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18248)),U_18252))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18248),tc_List_Olist(U_18248))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18248),tc_List_Olist(U_18248)),U_18250),U_18252)),c_List_Olexord(U_18248,U_18254))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK463]),skolemize(U_18242,sK463(U_18254,U_18252,U_18250,U_18248))],[f_4426_3]) ).

fof(f_4426_5,plain,
    ( ! [U_18243,U_18249,U_18255,U_18251,U_18253] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18249,U_18249)),hAPP(hAPP(c_Product__Type_OPair(U_18249,U_18249),hAPP(hAPP(c_List_Onth(U_18249),U_18251),U_18243)),hAPP(hAPP(c_List_Onth(U_18249),U_18253),U_18243))),U_18255))
        | hAPP(hAPP(c_List_Otake(U_18249),U_18243),U_18251) != hAPP(hAPP(c_List_Otake(U_18249),U_18243),U_18253)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18243),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18251)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18253))))
        | ~ sP1155(U_18243,U_18249,U_18255,U_18251,U_18253) )
    & ! [U_18243,U_18249,U_18255,U_18251,U_18253] :
        ( hAPP(hAPP(c_List_Otake(U_18249),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18251)),U_18253) != U_18251
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18251)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18253)))
        | ~ sP1155(U_18243,U_18249,U_18255,U_18251,U_18253) )
    & ! [U_18252,U_18248,U_18250,U_18254] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18248,U_18248)),hAPP(hAPP(c_Product__Type_OPair(U_18248,U_18248),hAPP(hAPP(c_List_Onth(U_18248),U_18250),sK463(U_18254,U_18252,U_18250,U_18248))),hAPP(hAPP(c_List_Onth(U_18248),U_18252),sK463(U_18254,U_18252,U_18250,U_18248)))),U_18254))
        | ~ sP1154(U_18252,U_18248,U_18250,U_18254) )
    & ! [U_18252,U_18248,U_18250,U_18254] :
        ( hAPP(hAPP(c_List_Otake(U_18248),sK463(U_18254,U_18252,U_18250,U_18248)),U_18250) = hAPP(hAPP(c_List_Otake(U_18248),sK463(U_18254,U_18252,U_18250,U_18248)),U_18252)
        | ~ sP1154(U_18252,U_18248,U_18250,U_18254) )
    & ! [U_18252,U_18248,U_18250,U_18254] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK463(U_18254,U_18252,U_18250,U_18248)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18248)),U_18250)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18248)),U_18252))))
        | ~ sP1154(U_18252,U_18248,U_18250,U_18254) )
    & ! [U_18252,U_18248,U_18250] :
        ( hAPP(hAPP(c_List_Otake(U_18248),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18248)),U_18250)),U_18252) = U_18250
        | ~ sP1153(U_18252,U_18248,U_18250) )
    & ! [U_18252,U_18248,U_18250] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18248)),U_18250)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18248)),U_18252)))
        | ~ sP1153(U_18252,U_18248,U_18250) )
    & ! [U_18243,U_18249,U_18255,U_18251,U_18253] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18249),tc_List_Olist(U_18249))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18249),tc_List_Olist(U_18249)),U_18251),U_18253)),c_List_Olexord(U_18249,U_18255)))
        | sP1155(U_18243,U_18249,U_18255,U_18251,U_18253) )
    & ! [U_18252,U_18248,U_18250,U_18254] :
        ( sP1154(U_18252,U_18248,U_18250,U_18254)
        | sP1153(U_18252,U_18248,U_18250)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18248),tc_List_Olist(U_18248))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18248),tc_List_Olist(U_18248)),U_18250),U_18252)),c_List_Olexord(U_18248,U_18254))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1153,sP1154,sP1155])],[f_4426_4]) ).

cnf(f_4426_6,plain,
    ( sP1154(U_18252,U_18248,U_18250,U_18254)
    | sP1153(U_18252,U_18248,U_18250)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18248),tc_List_Olist(U_18248))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18248),tc_List_Olist(U_18248)),U_18250),U_18252)),c_List_Olexord(U_18248,U_18254))) ),
    inference(clausify,[status(thm)],[f_4426_5]) ).

cnf(f_4426_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18249),tc_List_Olist(U_18249))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18249),tc_List_Olist(U_18249)),U_18251),U_18253)),c_List_Olexord(U_18249,U_18255)))
    | sP1155(U_18243,U_18249,U_18255,U_18251,U_18253) ),
    inference(clausify,[status(thm)],[f_4426_5]) ).

cnf(f_4426_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18248)),U_18250)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18248)),U_18252)))
    | ~ sP1153(U_18252,U_18248,U_18250) ),
    inference(clausify,[status(thm)],[f_4426_5]) ).

cnf(f_4426_9,plain,
    ( hAPP(hAPP(c_List_Otake(U_18248),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18248)),U_18250)),U_18252) = U_18250
    | ~ sP1153(U_18252,U_18248,U_18250) ),
    inference(clausify,[status(thm)],[f_4426_5]) ).

cnf(f_4426_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK463(U_18254,U_18252,U_18250,U_18248)),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18248)),U_18250)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18248)),U_18252))))
    | ~ sP1154(U_18252,U_18248,U_18250,U_18254) ),
    inference(clausify,[status(thm)],[f_4426_5]) ).

cnf(f_4426_11,plain,
    ( hAPP(hAPP(c_List_Otake(U_18248),sK463(U_18254,U_18252,U_18250,U_18248)),U_18250) = hAPP(hAPP(c_List_Otake(U_18248),sK463(U_18254,U_18252,U_18250,U_18248)),U_18252)
    | ~ sP1154(U_18252,U_18248,U_18250,U_18254) ),
    inference(clausify,[status(thm)],[f_4426_5]) ).

cnf(f_4426_12,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_18248,U_18248)),hAPP(hAPP(c_Product__Type_OPair(U_18248,U_18248),hAPP(hAPP(c_List_Onth(U_18248),U_18250),sK463(U_18254,U_18252,U_18250,U_18248))),hAPP(hAPP(c_List_Onth(U_18248),U_18252),sK463(U_18254,U_18252,U_18250,U_18248)))),U_18254))
    | ~ sP1154(U_18252,U_18248,U_18250,U_18254) ),
    inference(clausify,[status(thm)],[f_4426_5]) ).

cnf(f_4426_13,plain,
    ( hAPP(hAPP(c_List_Otake(U_18249),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18251)),U_18253) != U_18251
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18251)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18253)))
    | ~ sP1155(U_18243,U_18249,U_18255,U_18251,U_18253) ),
    inference(clausify,[status(thm)],[f_4426_5]) ).

cnf(f_4426_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_18249,U_18249)),hAPP(hAPP(c_Product__Type_OPair(U_18249,U_18249),hAPP(hAPP(c_List_Onth(U_18249),U_18251),U_18243)),hAPP(hAPP(c_List_Onth(U_18249),U_18253),U_18243))),U_18255))
    | hAPP(hAPP(c_List_Otake(U_18249),U_18243),U_18251) != hAPP(hAPP(c_List_Otake(U_18249),U_18243),U_18253)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18243),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18251)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18249)),U_18253))))
    | ~ sP1155(U_18243,U_18249,U_18255,U_18251,U_18253) ),
    inference(clausify,[status(thm)],[f_4426_5]) ).

fof(f_4427_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_4427_2,plain,
    ! [U_18259,U_18258,U_18257,U_18256] :
      ( hBOOL(hAPP(hAPP(c_member(U_18256),U_18257),hAPP(c_List_Oset(U_18256),U_18259)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18256),U_18257),hAPP(c_List_Oset(U_18256),hAPP(hAPP(c_List_Otake(U_18256),U_18258),U_18259)))) ),
    inference(variable_rename,[status(thm)],[f_4427_1]) ).

fof(f_4427_3,plain,
    ! [U_18259,U_18256,U_18258,U_18257] :
      ( hBOOL(hAPP(hAPP(c_member(U_18256),U_18257),hAPP(c_List_Oset(U_18256),U_18259)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18256),U_18257),hAPP(c_List_Oset(U_18256),hAPP(hAPP(c_List_Otake(U_18256),U_18258),U_18259)))) ),
    inference(definitional_conversion,[status(esa)],[f_4427_2]) ).

cnf(f_4427_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18256),U_18257),hAPP(c_List_Oset(U_18256),U_18259)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18256),U_18257),hAPP(c_List_Oset(U_18256),hAPP(hAPP(c_List_Otake(U_18256),U_18258),U_18259)))) ),
    inference(clausify,[status(thm)],[f_4427_3]) ).

fof(f_4428_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_4428_2,plain,
    ! [U_18263,U_18262,U_18261,U_18260] :
      ( hAPP(hAPP(c_List_Onth(U_18262),hAPP(hAPP(c_List_Otake(U_18262),U_18261),U_18263)),U_18260) = hAPP(hAPP(c_List_Onth(U_18262),U_18263),U_18260)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18260),U_18261)) ),
    inference(variable_rename,[status(thm)],[f_4428_1]) ).

fof(f_4428_3,plain,
    ! [U_18262,U_18260,U_18261,U_18263] :
      ( hAPP(hAPP(c_List_Onth(U_18262),hAPP(hAPP(c_List_Otake(U_18262),U_18261),U_18263)),U_18260) = hAPP(hAPP(c_List_Onth(U_18262),U_18263),U_18260)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18260),U_18261)) ),
    inference(definitional_conversion,[status(esa)],[f_4428_2]) ).

cnf(f_4428_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_18262),hAPP(hAPP(c_List_Otake(U_18262),U_18261),U_18263)),U_18260) = hAPP(hAPP(c_List_Onth(U_18262),U_18263),U_18260)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18260),U_18261)) ),
    inference(clausify,[status(thm)],[f_4428_3]) ).

fof(f_4429_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_4429_2,plain,
    ! [U_18266,U_18265,U_18264] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18264,tc_HOL_Obool)),hAPP(c_List_Oset(U_18264),hAPP(hAPP(c_List_Otake(U_18264),U_18265),U_18266))),hAPP(c_List_Oset(U_18264),U_18266))),
    inference(variable_rename,[status(thm)],[f_4429_1]) ).

fof(f_4429_3,plain,
    ! [U_18264,U_18265,U_18266] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18264,tc_HOL_Obool)),hAPP(c_List_Oset(U_18264),hAPP(hAPP(c_List_Otake(U_18264),U_18265),U_18266))),hAPP(c_List_Oset(U_18264),U_18266))),
    inference(definitional_conversion,[status(esa)],[f_4429_2]) ).

cnf(f_4429_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18264,tc_HOL_Obool)),hAPP(c_List_Oset(U_18264),hAPP(hAPP(c_List_Otake(U_18264),U_18265),U_18266))),hAPP(c_List_Oset(U_18264),U_18266))),
    inference(clausify,[status(thm)],[f_4429_3]) ).

fof(f_4430_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_4430_2,plain,
    ! [U_18269,U_18268,U_18267] :
      ( hAPP(hAPP(c_List_Otake(U_18267),U_18269),U_18268) = U_18268
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18267)),U_18268)),U_18269)) ),
    inference(variable_rename,[status(thm)],[f_4430_1]) ).

fof(f_4430_3,plain,
    ! [U_18267,U_18268,U_18269] :
      ( hAPP(hAPP(c_List_Otake(U_18267),U_18269),U_18268) = U_18268
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18267)),U_18268)),U_18269)) ),
    inference(definitional_conversion,[status(esa)],[f_4430_2]) ).

cnf(f_4430_4,plain,
    ( hAPP(hAPP(c_List_Otake(U_18267),U_18269),U_18268) = U_18268
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18267)),U_18268)),U_18269)) ),
    inference(clausify,[status(thm)],[f_4430_3]) ).

fof(f_4431_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_4431_2,plain,
    ! [U_18272,U_18271,U_18270] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18270),hAPP(hAPP(c_List_Otake(U_18270),U_18272),U_18271)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18270),U_18271)) ),
    inference(variable_rename,[status(thm)],[f_4431_1]) ).

fof(f_4431_3,plain,
    ! [U_18270,U_18271,U_18272] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18270),hAPP(hAPP(c_List_Otake(U_18270),U_18272),U_18271)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18270),U_18271)) ),
    inference(definitional_conversion,[status(esa)],[f_4431_2]) ).

cnf(f_4431_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18270),hAPP(hAPP(c_List_Otake(U_18270),U_18272),U_18271)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18270),U_18271)) ),
    inference(clausify,[status(thm)],[f_4431_3]) ).

fof(f_4432_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_4432_2,plain,
    ! [U_18276,U_18275,U_18274,U_18273] : hAPP(hAPP(c_List_Otake(U_18273),U_18274),hAPP(hAPP(c_List_Otake(U_18273),U_18275),U_18276)) = hAPP(hAPP(c_List_Otake(U_18273),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_18274),U_18275)),U_18276),
    inference(variable_rename,[status(thm)],[f_4432_1]) ).

fof(f_4432_3,plain,
    ! [U_18273,U_18274,U_18275,U_18276] : hAPP(hAPP(c_List_Otake(U_18273),U_18274),hAPP(hAPP(c_List_Otake(U_18273),U_18275),U_18276)) = hAPP(hAPP(c_List_Otake(U_18273),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_18274),U_18275)),U_18276),
    inference(definitional_conversion,[status(esa)],[f_4432_2]) ).

cnf(f_4432_4,plain,
    hAPP(hAPP(c_List_Otake(U_18273),U_18274),hAPP(hAPP(c_List_Otake(U_18273),U_18275),U_18276)) = hAPP(hAPP(c_List_Otake(U_18273),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),U_18274),U_18275)),U_18276),
    inference(clausify,[status(thm)],[f_4432_3]) ).

fof(f_4433_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_4433_2,plain,
    ! [U_18281,U_18280,U_18279,U_18278,U_18277] : hAPP(hAPP(c_List_Otake(tc_prod(U_18277,U_18278)),U_18279),hAPP(hAPP(c_List_Ozip(U_18277,U_18278),U_18280),U_18281)) = hAPP(hAPP(c_List_Ozip(U_18277,U_18278),hAPP(hAPP(c_List_Otake(U_18277),U_18279),U_18280)),hAPP(hAPP(c_List_Otake(U_18278),U_18279),U_18281)),
    inference(variable_rename,[status(thm)],[f_4433_1]) ).

fof(f_4433_3,plain,
    ! [U_18277,U_18278,U_18279,U_18280,U_18281] : hAPP(hAPP(c_List_Otake(tc_prod(U_18277,U_18278)),U_18279),hAPP(hAPP(c_List_Ozip(U_18277,U_18278),U_18280),U_18281)) = hAPP(hAPP(c_List_Ozip(U_18277,U_18278),hAPP(hAPP(c_List_Otake(U_18277),U_18279),U_18280)),hAPP(hAPP(c_List_Otake(U_18278),U_18279),U_18281)),
    inference(definitional_conversion,[status(esa)],[f_4433_2]) ).

cnf(f_4433_4,plain,
    hAPP(hAPP(c_List_Otake(tc_prod(U_18277,U_18278)),U_18279),hAPP(hAPP(c_List_Ozip(U_18277,U_18278),U_18280),U_18281)) = hAPP(hAPP(c_List_Ozip(U_18277,U_18278),hAPP(hAPP(c_List_Otake(U_18277),U_18279),U_18280)),hAPP(hAPP(c_List_Otake(U_18278),U_18279),U_18281)),
    inference(clausify,[status(thm)],[f_4433_3]) ).

fof(f_4434_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_4434_2,plain,
    ! [U_18284,U_18283,U_18282] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18282)),hAPP(hAPP(c_List_Otake(U_18282),U_18283),U_18284)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18282)),U_18284)),U_18283),
    inference(variable_rename,[status(thm)],[f_4434_1]) ).

fof(f_4434_3,plain,
    ! [U_18282,U_18283,U_18284] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18282)),hAPP(hAPP(c_List_Otake(U_18282),U_18283),U_18284)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18282)),U_18284)),U_18283),
    inference(definitional_conversion,[status(esa)],[f_4434_2]) ).

cnf(f_4434_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18282)),hAPP(hAPP(c_List_Otake(U_18282),U_18283),U_18284)) = hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18282)),U_18284)),U_18283),
    inference(clausify,[status(thm)],[f_4434_3]) ).

fof(f_4435_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_4435_2,plain,
    ! [U_18288,U_18287,U_18286,U_18285] : hAPP(hAPP(c_List_Otake(U_18285),hAPP(c_Nat_OSuc,U_18286)),hAPP(hAPP(c_List_Olist_OCons(U_18285),U_18287),U_18288)) = hAPP(hAPP(c_List_Olist_OCons(U_18285),U_18287),hAPP(hAPP(c_List_Otake(U_18285),U_18286),U_18288)),
    inference(variable_rename,[status(thm)],[f_4435_1]) ).

fof(f_4435_3,plain,
    ! [U_18285,U_18286,U_18287,U_18288] : hAPP(hAPP(c_List_Otake(U_18285),hAPP(c_Nat_OSuc,U_18286)),hAPP(hAPP(c_List_Olist_OCons(U_18285),U_18287),U_18288)) = hAPP(hAPP(c_List_Olist_OCons(U_18285),U_18287),hAPP(hAPP(c_List_Otake(U_18285),U_18286),U_18288)),
    inference(definitional_conversion,[status(esa)],[f_4435_2]) ).

cnf(f_4435_4,plain,
    hAPP(hAPP(c_List_Otake(U_18285),hAPP(c_Nat_OSuc,U_18286)),hAPP(hAPP(c_List_Olist_OCons(U_18285),U_18287),U_18288)) = hAPP(hAPP(c_List_Olist_OCons(U_18285),U_18287),hAPP(hAPP(c_List_Otake(U_18285),U_18286),U_18288)),
    inference(clausify,[status(thm)],[f_4435_3]) ).

fof(f_4436_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_4436_2,plain,
    ! [U_18291,U_18290,U_18289] : c_List_Osublist(U_18289,U_18290,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_18291)) = hAPP(hAPP(c_List_Otake(U_18289),U_18291),U_18290),
    inference(variable_rename,[status(thm)],[f_4436_1]) ).

fof(f_4436_3,plain,
    ! [U_18289,U_18290,U_18291] : c_List_Osublist(U_18289,U_18290,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_18291)) = hAPP(hAPP(c_List_Otake(U_18289),U_18291),U_18290),
    inference(definitional_conversion,[status(esa)],[f_4436_2]) ).

cnf(f_4436_4,plain,
    c_List_Osublist(U_18289,U_18290,hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_18291)) = hAPP(hAPP(c_List_Otake(U_18289),U_18291),U_18290),
    inference(clausify,[status(thm)],[f_4436_3]) ).

fof(f_4437_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_4437_2,plain,
    ! [U_18296,U_18295,U_18294,U_18293,U_18292] : hAPP(hAPP(c_List_Otake(U_18292),U_18293),hAPP(hAPP(c_List_Omap(U_18294,U_18292),U_18295),U_18296)) = hAPP(hAPP(c_List_Omap(U_18294,U_18292),U_18295),hAPP(hAPP(c_List_Otake(U_18294),U_18293),U_18296)),
    inference(variable_rename,[status(thm)],[f_4437_1]) ).

fof(f_4437_3,plain,
    ! [U_18292,U_18293,U_18294,U_18295,U_18296] : hAPP(hAPP(c_List_Otake(U_18292),U_18293),hAPP(hAPP(c_List_Omap(U_18294,U_18292),U_18295),U_18296)) = hAPP(hAPP(c_List_Omap(U_18294,U_18292),U_18295),hAPP(hAPP(c_List_Otake(U_18294),U_18293),U_18296)),
    inference(definitional_conversion,[status(esa)],[f_4437_2]) ).

cnf(f_4437_4,plain,
    hAPP(hAPP(c_List_Otake(U_18292),U_18293),hAPP(hAPP(c_List_Omap(U_18294,U_18292),U_18295),U_18296)) = hAPP(hAPP(c_List_Omap(U_18294,U_18292),U_18295),hAPP(hAPP(c_List_Otake(U_18294),U_18293),U_18296)),
    inference(clausify,[status(thm)],[f_4437_3]) ).

fof(f_4438_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_4438_2,plain,
    ! [U_18300,U_18299,U_18298,U_18297] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18299,tc_HOL_Obool)),hAPP(c_List_Oset(U_18299),hAPP(hAPP(c_List_Otake(U_18299),U_18297),U_18300))),hAPP(c_List_Oset(U_18299),hAPP(hAPP(c_List_Otake(U_18299),U_18298),U_18300))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18297),U_18298)) ),
    inference(variable_rename,[status(thm)],[f_4438_1]) ).

fof(f_4438_3,plain,
    ! [U_18297,U_18298,U_18299,U_18300] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18299,tc_HOL_Obool)),hAPP(c_List_Oset(U_18299),hAPP(hAPP(c_List_Otake(U_18299),U_18297),U_18300))),hAPP(c_List_Oset(U_18299),hAPP(hAPP(c_List_Otake(U_18299),U_18298),U_18300))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18297),U_18298)) ),
    inference(definitional_conversion,[status(esa)],[f_4438_2]) ).

cnf(f_4438_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18299,tc_HOL_Obool)),hAPP(c_List_Oset(U_18299),hAPP(hAPP(c_List_Otake(U_18299),U_18297),U_18300))),hAPP(c_List_Oset(U_18299),hAPP(hAPP(c_List_Otake(U_18299),U_18298),U_18300))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_18297),U_18298)) ),
    inference(clausify,[status(thm)],[f_4438_3]) ).

fof(f_4439_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_4439_2,plain,
    ! [U_18303,U_18302,U_18301] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,U_18302),U_18301),U_18303)) = 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_18302)),U_18303)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_18302),U_18301))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18301),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_18302))) ),
    inference(variable_rename,[status(thm)],[f_4439_1]) ).

fof(f_4439_3,plain,
    ! [U_18301,U_18302,U_18303] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,U_18302),U_18301),U_18303)) = 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_18302)),U_18303)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_18302),U_18301))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18301),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_18302))) ),
    inference(definitional_conversion,[status(esa)],[f_4439_2]) ).

cnf(f_4439_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Olist__update(tc_Nat_Onat,U_18302),U_18301),U_18303)) = 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_18302)),U_18303)),hAPP(hAPP(c_List_Onth(tc_Nat_Onat),U_18302),U_18301))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18301),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),U_18302))) ),
    inference(clausify,[status(thm)],[f_4439_3]) ).

fof(f_4440_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_4440_2,plain,
    ! [U_18305,U_18304] :
      ( c_Random_Oselect__weight(U_18305,hAPP(hAPP(c_List_Omap(U_18305,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18305)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18305),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18304)) = c_Random_Oselect(U_18305,U_18304)
      | U_18304 = c_List_Olist_ONil(U_18305) ),
    inference(variable_rename,[status(thm)],[f_4440_1]) ).

fof(f_4440_3,plain,
    ! [U_18304,U_18305] :
      ( c_Random_Oselect__weight(U_18305,hAPP(hAPP(c_List_Omap(U_18305,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18305)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18305),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18304)) = c_Random_Oselect(U_18305,U_18304)
      | U_18304 = c_List_Olist_ONil(U_18305) ),
    inference(definitional_conversion,[status(esa)],[f_4440_2]) ).

cnf(f_4440_4,plain,
    ( c_Random_Oselect__weight(U_18305,hAPP(hAPP(c_List_Omap(U_18305,tc_prod(tc_Code__Numeral_Ocode__numeral,U_18305)),hAPP(c_Product__Type_OPair(tc_Code__Numeral_Ocode__numeral,U_18305),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),U_18304)) = c_Random_Oselect(U_18305,U_18304)
    | U_18304 = c_List_Olist_ONil(U_18305) ),
    inference(clausify,[status(thm)],[f_4440_3]) ).

fof(f_4441_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_4441_2,plain,
    ! [U_18308,U_18307,U_18306] :
      ( U_18307 = c_List_Olist_ONil(U_18306)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18306),tc_List_Olist(U_18306))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18306),tc_List_Olist(U_18306)),U_18307),c_List_Olist_ONil(U_18306))),c_List_Olistrel(U_18306,U_18308))) ),
    inference(variable_rename,[status(thm)],[f_4441_1]) ).

fof(f_4441_3,plain,
    ! [U_18306,U_18307,U_18308] :
      ( U_18307 = c_List_Olist_ONil(U_18306)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18306),tc_List_Olist(U_18306))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18306),tc_List_Olist(U_18306)),U_18307),c_List_Olist_ONil(U_18306))),c_List_Olistrel(U_18306,U_18308))) ),
    inference(definitional_conversion,[status(esa)],[f_4441_2]) ).

cnf(f_4441_4,plain,
    ( U_18307 = c_List_Olist_ONil(U_18306)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18306),tc_List_Olist(U_18306))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18306),tc_List_Olist(U_18306)),U_18307),c_List_Olist_ONil(U_18306))),c_List_Olistrel(U_18306,U_18308))) ),
    inference(clausify,[status(thm)],[f_4441_3]) ).

fof(f_4442_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_4442_2,plain,
    ! [U_18311,U_18310,U_18309] :
      ( U_18310 = c_List_Olist_ONil(U_18309)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18309),tc_List_Olist(U_18309))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18309),tc_List_Olist(U_18309)),c_List_Olist_ONil(U_18309)),U_18310)),c_List_Olistrel(U_18309,U_18311))) ),
    inference(variable_rename,[status(thm)],[f_4442_1]) ).

fof(f_4442_3,plain,
    ! [U_18309,U_18310,U_18311] :
      ( U_18310 = c_List_Olist_ONil(U_18309)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18309),tc_List_Olist(U_18309))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18309),tc_List_Olist(U_18309)),c_List_Olist_ONil(U_18309)),U_18310)),c_List_Olistrel(U_18309,U_18311))) ),
    inference(definitional_conversion,[status(esa)],[f_4442_2]) ).

cnf(f_4442_4,plain,
    ( U_18310 = c_List_Olist_ONil(U_18309)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18309),tc_List_Olist(U_18309))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18309),tc_List_Olist(U_18309)),c_List_Olist_ONil(U_18309)),U_18310)),c_List_Olistrel(U_18309,U_18311))) ),
    inference(clausify,[status(thm)],[f_4442_3]) ).

fof(f_4443_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_4443_2,plain,
    ! [U_18314,U_18313,U_18312] : hAPP(hAPP(c_List_Olist__update(U_18312,U_18313),U_18314),hAPP(hAPP(c_List_Onth(U_18312),U_18313),U_18314)) = U_18313,
    inference(variable_rename,[status(thm)],[f_4443_1]) ).

fof(f_4443_3,plain,
    ! [U_18312,U_18313,U_18314] : hAPP(hAPP(c_List_Olist__update(U_18312,U_18313),U_18314),hAPP(hAPP(c_List_Onth(U_18312),U_18313),U_18314)) = U_18313,
    inference(definitional_conversion,[status(esa)],[f_4443_2]) ).

cnf(f_4443_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18312,U_18313),U_18314),hAPP(hAPP(c_List_Onth(U_18312),U_18313),U_18314)) = U_18313,
    inference(clausify,[status(thm)],[f_4443_3]) ).

fof(f_4444_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_4444_2,plain,
    ! [U_18319,U_18318,U_18317,U_18316,U_18315] :
      ( hAPP(hAPP(c_List_Onth(U_18317),hAPP(hAPP(c_List_Olist__update(U_18317,U_18318),U_18315),U_18319)),U_18316) = hAPP(hAPP(c_List_Onth(U_18317),U_18318),U_18316)
      | U_18315 = U_18316 ),
    inference(variable_rename,[status(thm)],[f_4444_1]) ).

fof(f_4444_3,plain,
    ! [U_18315,U_18316,U_18317,U_18318,U_18319] :
      ( hAPP(hAPP(c_List_Onth(U_18317),hAPP(hAPP(c_List_Olist__update(U_18317,U_18318),U_18315),U_18319)),U_18316) = hAPP(hAPP(c_List_Onth(U_18317),U_18318),U_18316)
      | U_18315 = U_18316 ),
    inference(definitional_conversion,[status(esa)],[f_4444_2]) ).

cnf(f_4444_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_18317),hAPP(hAPP(c_List_Olist__update(U_18317,U_18318),U_18315),U_18319)),U_18316) = hAPP(hAPP(c_List_Onth(U_18317),U_18318),U_18316)
    | U_18315 = U_18316 ),
    inference(clausify,[status(thm)],[f_4444_3]) ).

fof(f_4445_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_4445_2,plain,
    ! [U_18323,U_18322,U_18321,U_18320] :
      ( hAPP(hAPP(c_List_Olist__update(U_18320,U_18321),U_18322),U_18323) = U_18321
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18320)),U_18321)),U_18322)) ),
    inference(variable_rename,[status(thm)],[f_4445_1]) ).

fof(f_4445_3,plain,
    ! [U_18320,U_18321,U_18322,U_18323] :
      ( hAPP(hAPP(c_List_Olist__update(U_18320,U_18321),U_18322),U_18323) = U_18321
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18320)),U_18321)),U_18322)) ),
    inference(definitional_conversion,[status(esa)],[f_4445_2]) ).

cnf(f_4445_4,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_18320,U_18321),U_18322),U_18323) = U_18321
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18320)),U_18321)),U_18322)) ),
    inference(clausify,[status(thm)],[f_4445_3]) ).

fof(f_4446_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_4446_2,plain,
    ! [U_18325,U_18324] : hAPP(hAPP(c_List_Otake(U_18324),U_18325),c_List_Olist_ONil(U_18324)) = c_List_Olist_ONil(U_18324),
    inference(variable_rename,[status(thm)],[f_4446_1]) ).

fof(f_4446_3,plain,
    ! [U_18324,U_18325] : hAPP(hAPP(c_List_Otake(U_18324),U_18325),c_List_Olist_ONil(U_18324)) = c_List_Olist_ONil(U_18324),
    inference(definitional_conversion,[status(esa)],[f_4446_2]) ).

cnf(f_4446_4,plain,
    hAPP(hAPP(c_List_Otake(U_18324),U_18325),c_List_Olist_ONil(U_18324)) = c_List_Olist_ONil(U_18324),
    inference(clausify,[status(thm)],[f_4446_3]) ).

fof(f_4447_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_4447_2,plain,
    ! [U_18328,U_18327,U_18326] :
      ( ( hAPP(hAPP(c_List_Otake(U_18326),U_18327),U_18328) = c_List_Olist_ONil(U_18326)
        | ( U_18328 != c_List_Olist_ONil(U_18326)
          & U_18327 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( U_18328 = c_List_Olist_ONil(U_18326)
        | U_18327 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(U_18326),U_18327),U_18328) != c_List_Olist_ONil(U_18326) ) ),
    inference(variable_rename,[status(thm)],[f_4447_1]) ).

fof(f_4447_3,plain,
    ( ! [U_18334,U_18332,U_18330] :
        ( hAPP(hAPP(c_List_Otake(U_18330),U_18332),U_18334) = c_List_Olist_ONil(U_18330)
        | ( U_18334 != c_List_Olist_ONil(U_18330)
          & U_18332 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_18333,U_18331,U_18329] :
        ( U_18333 = c_List_Olist_ONil(U_18329)
        | U_18331 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(U_18329),U_18331),U_18333) != c_List_Olist_ONil(U_18329) ) ),
    inference(miniscope,[status(thm)],[f_4447_2]) ).

fof(f_4447_4,plain,
    ( ! [U_18334,U_18330,U_18332] :
        ( U_18334 != c_List_Olist_ONil(U_18330)
        | ~ sP1156(U_18334,U_18330,U_18332) )
    & ! [U_18334,U_18330,U_18332] :
        ( U_18332 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1156(U_18334,U_18330,U_18332) )
    & ! [U_18334,U_18330,U_18332] :
        ( hAPP(hAPP(c_List_Otake(U_18330),U_18332),U_18334) = c_List_Olist_ONil(U_18330)
        | sP1156(U_18334,U_18330,U_18332) )
    & ! [U_18331,U_18329,U_18333] :
        ( U_18333 = c_List_Olist_ONil(U_18329)
        | U_18331 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | hAPP(hAPP(c_List_Otake(U_18329),U_18331),U_18333) != c_List_Olist_ONil(U_18329) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1156])],[f_4447_3]) ).

cnf(f_4447_5,plain,
    ( U_18333 = c_List_Olist_ONil(U_18329)
    | U_18331 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | hAPP(hAPP(c_List_Otake(U_18329),U_18331),U_18333) != c_List_Olist_ONil(U_18329) ),
    inference(clausify,[status(thm)],[f_4447_4]) ).

cnf(f_4447_6,plain,
    ( hAPP(hAPP(c_List_Otake(U_18330),U_18332),U_18334) = c_List_Olist_ONil(U_18330)
    | sP1156(U_18334,U_18330,U_18332) ),
    inference(clausify,[status(thm)],[f_4447_4]) ).

cnf(f_4447_7,plain,
    ( U_18332 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1156(U_18334,U_18330,U_18332) ),
    inference(clausify,[status(thm)],[f_4447_4]) ).

cnf(f_4447_8,plain,
    ( U_18334 != c_List_Olist_ONil(U_18330)
    | ~ sP1156(U_18334,U_18330,U_18332) ),
    inference(clausify,[status(thm)],[f_4447_4]) ).

fof(f_4448_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_4448_2,plain,
    ! [U_18336,U_18335] : hAPP(hAPP(c_List_Otake(U_18335),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18336) = c_List_Olist_ONil(U_18335),
    inference(variable_rename,[status(thm)],[f_4448_1]) ).

fof(f_4448_3,plain,
    ! [U_18335,U_18336] : hAPP(hAPP(c_List_Otake(U_18335),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18336) = c_List_Olist_ONil(U_18335),
    inference(definitional_conversion,[status(esa)],[f_4448_2]) ).

cnf(f_4448_4,plain,
    hAPP(hAPP(c_List_Otake(U_18335),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18336) = c_List_Olist_ONil(U_18335),
    inference(clausify,[status(thm)],[f_4448_3]) ).

fof(f_4449_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_4449_2,plain,
    ! [U_18340,U_18339,U_18338,U_18337] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18337)),hAPP(hAPP(c_List_Olist__update(U_18337,U_18338),U_18339),U_18340)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18337)),U_18338),
    inference(variable_rename,[status(thm)],[f_4449_1]) ).

fof(f_4449_3,plain,
    ! [U_18337,U_18338,U_18339,U_18340] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18337)),hAPP(hAPP(c_List_Olist__update(U_18337,U_18338),U_18339),U_18340)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18337)),U_18338),
    inference(definitional_conversion,[status(esa)],[f_4449_2]) ).

cnf(f_4449_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18337)),hAPP(hAPP(c_List_Olist__update(U_18337,U_18338),U_18339),U_18340)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18337)),U_18338),
    inference(clausify,[status(thm)],[f_4449_3]) ).

fof(f_4450_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_4450_2,plain,
    ! [U_18342,U_18341] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18341)),U_18342) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_18342 != c_List_Olist_ONil(U_18341) )
      & ( U_18342 = c_List_Olist_ONil(U_18341)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18341)),U_18342) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4450_1]) ).

fof(f_4450_3,plain,
    ( ! [U_18346,U_18344] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18344)),U_18346) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_18346 != c_List_Olist_ONil(U_18344) )
    & ! [U_18345,U_18343] :
        ( U_18345 = c_List_Olist_ONil(U_18343)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18343)),U_18345) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4450_2]) ).

fof(f_4450_4,plain,
    ( ! [U_18346,U_18344] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18344)),U_18346) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_18346 != c_List_Olist_ONil(U_18344) )
    & ! [U_18345,U_18343] :
        ( U_18345 = c_List_Olist_ONil(U_18343)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18343)),U_18345) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_4450_3]) ).

cnf(f_4450_5,plain,
    ( U_18345 = c_List_Olist_ONil(U_18343)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18343)),U_18345) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4450_4]) ).

cnf(f_4450_6,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18344)),U_18346) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_18346 != c_List_Olist_ONil(U_18344) ),
    inference(clausify,[status(thm)],[f_4450_4]) ).

fof(f_4451_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_4451_2,plain,
    ! [U_18347] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18347)),c_List_Olist_ONil(U_18347)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_4451_1]) ).

fof(f_4451_3,plain,
    ! [U_18347] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18347)),c_List_Olist_ONil(U_18347)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_4451_2]) ).

cnf(f_4451_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18347)),c_List_Olist_ONil(U_18347)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4451_3]) ).

fof(f_4452_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_4452_2,plain,
    ! [U_18351,U_18350,U_18349,U_18348] : hAPP(hAPP(c_List_Otake(U_18348),U_18349),hAPP(hAPP(c_List_Olist_OCons(U_18348),U_18350),U_18351)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_18348),c_List_Olist_ONil(U_18348),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18348),tc_List_Olist(U_18348),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_18348),U_18350)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_18348),tc_List_Olist(U_18348)),c_List_Otake(U_18348)),U_18351)),U_18349),
    inference(variable_rename,[status(thm)],[f_4452_1]) ).

fof(f_4452_3,plain,
    ! [U_18348,U_18349,U_18350,U_18351] : hAPP(hAPP(c_List_Otake(U_18348),U_18349),hAPP(hAPP(c_List_Olist_OCons(U_18348),U_18350),U_18351)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_18348),c_List_Olist_ONil(U_18348),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18348),tc_List_Olist(U_18348),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_18348),U_18350)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_18348),tc_List_Olist(U_18348)),c_List_Otake(U_18348)),U_18351)),U_18349),
    inference(definitional_conversion,[status(esa)],[f_4452_2]) ).

cnf(f_4452_4,plain,
    hAPP(hAPP(c_List_Otake(U_18348),U_18349),hAPP(hAPP(c_List_Olist_OCons(U_18348),U_18350),U_18351)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_18348),c_List_Olist_ONil(U_18348),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18348),tc_List_Olist(U_18348),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_18348),U_18350)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_18348),tc_List_Olist(U_18348)),c_List_Otake(U_18348)),U_18351)),U_18349),
    inference(clausify,[status(thm)],[f_4452_3]) ).

fof(f_4453_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_4453_2,plain,
    ! [U_18355,U_18354,U_18353,U_18352] :
      ( ( c_List_Olist_ONil(U_18352) = hAPP(hAPP(c_List_Omap(U_18353,U_18352),U_18354),U_18355)
        | U_18355 != c_List_Olist_ONil(U_18353) )
      & ( U_18355 = c_List_Olist_ONil(U_18353)
        | c_List_Olist_ONil(U_18352) != hAPP(hAPP(c_List_Omap(U_18353,U_18352),U_18354),U_18355) ) ),
    inference(variable_rename,[status(thm)],[f_4453_1]) ).

fof(f_4453_3,plain,
    ( ! [U_18363,U_18361,U_18359] :
        ( ! [U_18357] : c_List_Olist_ONil(U_18357) = hAPP(hAPP(c_List_Omap(U_18359,U_18357),U_18361),U_18363)
        | U_18363 != c_List_Olist_ONil(U_18359) )
    & ! [U_18362,U_18360,U_18358] :
        ( ! [U_18356] : c_List_Olist_ONil(U_18356) != hAPP(hAPP(c_List_Omap(U_18358,U_18356),U_18360),U_18362)
        | U_18362 = c_List_Olist_ONil(U_18358) ) ),
    inference(miniscope,[status(thm)],[f_4453_2]) ).

fof(f_4453_4,plain,
    ( ! [U_18361,U_18357,U_18359,U_18363] :
        ( c_List_Olist_ONil(U_18357) = hAPP(hAPP(c_List_Omap(U_18359,U_18357),U_18361),U_18363)
        | U_18363 != c_List_Olist_ONil(U_18359) )
    & ! [U_18360,U_18358,U_18356,U_18362] :
        ( c_List_Olist_ONil(U_18356) != hAPP(hAPP(c_List_Omap(U_18358,U_18356),U_18360),U_18362)
        | U_18362 = c_List_Olist_ONil(U_18358) ) ),
    inference(definitional_conversion,[status(esa)],[f_4453_3]) ).

cnf(f_4453_5,plain,
    ( c_List_Olist_ONil(U_18356) != hAPP(hAPP(c_List_Omap(U_18358,U_18356),U_18360),U_18362)
    | U_18362 = c_List_Olist_ONil(U_18358) ),
    inference(clausify,[status(thm)],[f_4453_4]) ).

cnf(f_4453_6,plain,
    ( c_List_Olist_ONil(U_18357) = hAPP(hAPP(c_List_Omap(U_18359,U_18357),U_18361),U_18363)
    | U_18363 != c_List_Olist_ONil(U_18359) ),
    inference(clausify,[status(thm)],[f_4453_4]) ).

fof(f_4454_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_4454_2,plain,
    ! [U_18366,U_18365,U_18364] : hAPP(hAPP(c_List_Omap(U_18364,U_18365),U_18366),c_List_Olist_ONil(U_18364)) = c_List_Olist_ONil(U_18365),
    inference(variable_rename,[status(thm)],[f_4454_1]) ).

fof(f_4454_3,plain,
    ! [U_18366,U_18365,U_18364] : hAPP(hAPP(c_List_Omap(U_18364,U_18365),U_18366),c_List_Olist_ONil(U_18364)) = c_List_Olist_ONil(U_18365),
    inference(definitional_conversion,[status(esa)],[f_4454_2]) ).

cnf(f_4454_4,plain,
    hAPP(hAPP(c_List_Omap(U_18364,U_18365),U_18366),c_List_Olist_ONil(U_18364)) = c_List_Olist_ONil(U_18365),
    inference(clausify,[status(thm)],[f_4454_3]) ).

fof(f_4455_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_4455_2,plain,
    ! [U_18372,U_18371,U_18370,U_18369,U_18368,U_18367] : hAPP(hAPP(c_List_Omap(U_18367,U_18368),U_18369),hAPP(hAPP(c_List_Olist__update(U_18367,U_18370),U_18371),U_18372)) = hAPP(hAPP(c_List_Olist__update(U_18368,hAPP(hAPP(c_List_Omap(U_18367,U_18368),U_18369),U_18370)),U_18371),hAPP(U_18369,U_18372)),
    inference(variable_rename,[status(thm)],[f_4455_1]) ).

fof(f_4455_3,plain,
    ! [U_18367,U_18368,U_18369,U_18370,U_18371,U_18372] : hAPP(hAPP(c_List_Omap(U_18367,U_18368),U_18369),hAPP(hAPP(c_List_Olist__update(U_18367,U_18370),U_18371),U_18372)) = hAPP(hAPP(c_List_Olist__update(U_18368,hAPP(hAPP(c_List_Omap(U_18367,U_18368),U_18369),U_18370)),U_18371),hAPP(U_18369,U_18372)),
    inference(definitional_conversion,[status(esa)],[f_4455_2]) ).

cnf(f_4455_4,plain,
    hAPP(hAPP(c_List_Omap(U_18367,U_18368),U_18369),hAPP(hAPP(c_List_Olist__update(U_18367,U_18370),U_18371),U_18372)) = hAPP(hAPP(c_List_Olist__update(U_18368,hAPP(hAPP(c_List_Omap(U_18367,U_18368),U_18369),U_18370)),U_18371),hAPP(U_18369,U_18372)),
    inference(clausify,[status(thm)],[f_4455_3]) ).

fof(f_4456_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_4456_2,plain,
    ! [U_18376,U_18375,U_18374,U_18373] :
      ( ( hAPP(hAPP(c_List_Omap(U_18373,U_18374),U_18375),U_18376) = c_List_Olist_ONil(U_18374)
        | U_18376 != c_List_Olist_ONil(U_18373) )
      & ( U_18376 = c_List_Olist_ONil(U_18373)
        | hAPP(hAPP(c_List_Omap(U_18373,U_18374),U_18375),U_18376) != c_List_Olist_ONil(U_18374) ) ),
    inference(variable_rename,[status(thm)],[f_4456_1]) ).

fof(f_4456_3,plain,
    ( ! [U_18384,U_18382,U_18380,U_18378] :
        ( hAPP(hAPP(c_List_Omap(U_18378,U_18380),U_18382),U_18384) = c_List_Olist_ONil(U_18380)
        | U_18384 != c_List_Olist_ONil(U_18378) )
    & ! [U_18383,U_18381,U_18379,U_18377] :
        ( U_18383 = c_List_Olist_ONil(U_18377)
        | hAPP(hAPP(c_List_Omap(U_18377,U_18379),U_18381),U_18383) != c_List_Olist_ONil(U_18379) ) ),
    inference(miniscope,[status(thm)],[f_4456_2]) ).

fof(f_4456_4,plain,
    ( ! [U_18378,U_18384,U_18380,U_18382] :
        ( hAPP(hAPP(c_List_Omap(U_18378,U_18380),U_18382),U_18384) = c_List_Olist_ONil(U_18380)
        | U_18384 != c_List_Olist_ONil(U_18378) )
    & ! [U_18383,U_18379,U_18381,U_18377] :
        ( U_18383 = c_List_Olist_ONil(U_18377)
        | hAPP(hAPP(c_List_Omap(U_18377,U_18379),U_18381),U_18383) != c_List_Olist_ONil(U_18379) ) ),
    inference(definitional_conversion,[status(esa)],[f_4456_3]) ).

cnf(f_4456_5,plain,
    ( U_18383 = c_List_Olist_ONil(U_18377)
    | hAPP(hAPP(c_List_Omap(U_18377,U_18379),U_18381),U_18383) != c_List_Olist_ONil(U_18379) ),
    inference(clausify,[status(thm)],[f_4456_4]) ).

cnf(f_4456_6,plain,
    ( hAPP(hAPP(c_List_Omap(U_18378,U_18380),U_18382),U_18384) = c_List_Olist_ONil(U_18380)
    | U_18384 != c_List_Olist_ONil(U_18378) ),
    inference(clausify,[status(thm)],[f_4456_4]) ).

fof(f_4457_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_4457_2,plain,
    ! [U_18391,U_18390,U_18389,U_18388,U_18387,U_18386,U_18385] : hAPP(hAPP(c_List_Ozip(U_18385,U_18386),hAPP(hAPP(c_List_Olist__update(U_18385,U_18387),U_18388),U_18389)),hAPP(hAPP(c_List_Olist__update(U_18386,U_18390),U_18388),U_18391)) = hAPP(hAPP(c_List_Olist__update(tc_prod(U_18385,U_18386),hAPP(hAPP(c_List_Ozip(U_18385,U_18386),U_18387),U_18390)),U_18388),hAPP(hAPP(c_Product__Type_OPair(U_18385,U_18386),U_18389),U_18391)),
    inference(variable_rename,[status(thm)],[f_4457_1]) ).

fof(f_4457_3,plain,
    ! [U_18385,U_18386,U_18387,U_18388,U_18389,U_18390,U_18391] : hAPP(hAPP(c_List_Ozip(U_18385,U_18386),hAPP(hAPP(c_List_Olist__update(U_18385,U_18387),U_18388),U_18389)),hAPP(hAPP(c_List_Olist__update(U_18386,U_18390),U_18388),U_18391)) = hAPP(hAPP(c_List_Olist__update(tc_prod(U_18385,U_18386),hAPP(hAPP(c_List_Ozip(U_18385,U_18386),U_18387),U_18390)),U_18388),hAPP(hAPP(c_Product__Type_OPair(U_18385,U_18386),U_18389),U_18391)),
    inference(definitional_conversion,[status(esa)],[f_4457_2]) ).

cnf(f_4457_4,plain,
    hAPP(hAPP(c_List_Ozip(U_18385,U_18386),hAPP(hAPP(c_List_Olist__update(U_18385,U_18387),U_18388),U_18389)),hAPP(hAPP(c_List_Olist__update(U_18386,U_18390),U_18388),U_18391)) = hAPP(hAPP(c_List_Olist__update(tc_prod(U_18385,U_18386),hAPP(hAPP(c_List_Ozip(U_18385,U_18386),U_18387),U_18390)),U_18388),hAPP(hAPP(c_Product__Type_OPair(U_18385,U_18386),U_18389),U_18391)),
    inference(clausify,[status(thm)],[f_4457_3]) ).

fof(f_4458_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_4458_2,plain,
    ! [U_18397,U_18396,U_18395,U_18394,U_18393,U_18392] : hAPP(hAPP(c_List_Olist__update(tc_prod(U_18392,U_18393),hAPP(hAPP(c_List_Ozip(U_18392,U_18393),U_18394),U_18395)),U_18396),U_18397) = hAPP(hAPP(c_List_Ozip(U_18392,U_18393),hAPP(hAPP(c_List_Olist__update(U_18392,U_18394),U_18396),hAPP(c_Product__Type_Ofst(U_18392,U_18393),U_18397))),hAPP(hAPP(c_List_Olist__update(U_18393,U_18395),U_18396),hAPP(c_Product__Type_Osnd(U_18392,U_18393),U_18397))),
    inference(variable_rename,[status(thm)],[f_4458_1]) ).

fof(f_4458_3,plain,
    ! [U_18392,U_18393,U_18394,U_18395,U_18396,U_18397] : hAPP(hAPP(c_List_Olist__update(tc_prod(U_18392,U_18393),hAPP(hAPP(c_List_Ozip(U_18392,U_18393),U_18394),U_18395)),U_18396),U_18397) = hAPP(hAPP(c_List_Ozip(U_18392,U_18393),hAPP(hAPP(c_List_Olist__update(U_18392,U_18394),U_18396),hAPP(c_Product__Type_Ofst(U_18392,U_18393),U_18397))),hAPP(hAPP(c_List_Olist__update(U_18393,U_18395),U_18396),hAPP(c_Product__Type_Osnd(U_18392,U_18393),U_18397))),
    inference(definitional_conversion,[status(esa)],[f_4458_2]) ).

cnf(f_4458_4,plain,
    hAPP(hAPP(c_List_Olist__update(tc_prod(U_18392,U_18393),hAPP(hAPP(c_List_Ozip(U_18392,U_18393),U_18394),U_18395)),U_18396),U_18397) = hAPP(hAPP(c_List_Ozip(U_18392,U_18393),hAPP(hAPP(c_List_Olist__update(U_18392,U_18394),U_18396),hAPP(c_Product__Type_Ofst(U_18392,U_18393),U_18397))),hAPP(hAPP(c_List_Olist__update(U_18393,U_18395),U_18396),hAPP(c_Product__Type_Osnd(U_18392,U_18393),U_18397))),
    inference(clausify,[status(thm)],[f_4458_3]) ).

fof(f_4459_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_4459_2,plain,
    ! [U_18399,U_18398] : c_List_Osublist(U_18398,c_List_Olist_ONil(U_18398),U_18399) = c_List_Olist_ONil(U_18398),
    inference(variable_rename,[status(thm)],[f_4459_1]) ).

fof(f_4459_3,plain,
    ! [U_18398,U_18399] : c_List_Osublist(U_18398,c_List_Olist_ONil(U_18398),U_18399) = c_List_Olist_ONil(U_18398),
    inference(definitional_conversion,[status(esa)],[f_4459_2]) ).

cnf(f_4459_4,plain,
    c_List_Osublist(U_18398,c_List_Olist_ONil(U_18398),U_18399) = c_List_Olist_ONil(U_18398),
    inference(clausify,[status(thm)],[f_4459_3]) ).

fof(f_4460_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_4460_2,plain,
    ! [U_18401,U_18400] : c_List_Osublist(U_18400,U_18401,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(U_18400),
    inference(variable_rename,[status(thm)],[f_4460_1]) ).

fof(f_4460_3,plain,
    ! [U_18400,U_18401] : c_List_Osublist(U_18400,U_18401,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(U_18400),
    inference(definitional_conversion,[status(esa)],[f_4460_2]) ).

cnf(f_4460_4,plain,
    c_List_Osublist(U_18400,U_18401,c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) = c_List_Olist_ONil(U_18400),
    inference(clausify,[status(thm)],[f_4460_3]) ).

fof(f_4461_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_4461_2,plain,
    ! [U_18405,U_18404,U_18403,U_18402] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18403,U_18402,U_18404),U_18405),c_List_Olist_ONil(U_18403)) = hAPP(hAPP(c_List_Olist_OCons(U_18403),U_18405),c_List_Olist_ONil(U_18403))
      | ~ class_Orderings_Olinorder(U_18402) ),
    inference(variable_rename,[status(thm)],[f_4461_1]) ).

fof(f_4461_3,plain,
    ! [U_18402,U_18403,U_18404,U_18405] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18403,U_18402,U_18404),U_18405),c_List_Olist_ONil(U_18403)) = hAPP(hAPP(c_List_Olist_OCons(U_18403),U_18405),c_List_Olist_ONil(U_18403))
      | ~ class_Orderings_Olinorder(U_18402) ),
    inference(definitional_conversion,[status(esa)],[f_4461_2]) ).

cnf(f_4461_4,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18403,U_18402,U_18404),U_18405),c_List_Olist_ONil(U_18403)) = hAPP(hAPP(c_List_Olist_OCons(U_18403),U_18405),c_List_Olist_ONil(U_18403))
    | ~ class_Orderings_Olinorder(U_18402) ),
    inference(clausify,[status(thm)],[f_4461_3]) ).

fof(f_4462_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_4462_2,plain,
    ! [U_18410,U_18409,U_18408,U_18407,U_18406] : hAPP(hAPP(c_List_Olist__update(U_18406,hAPP(hAPP(c_List_Olist_OCons(U_18406),U_18407),U_18408)),U_18409),U_18410) = c_Nat_Onat_Onat__case(tc_List_Olist(U_18406),hAPP(hAPP(c_List_Olist_OCons(U_18406),U_18410),U_18408),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18406),tc_List_Olist(U_18406),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_18406),U_18407)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_18406,tc_List_Olist(U_18406)),c_List_Olist__update(U_18406,U_18408)),U_18410)),U_18409),
    inference(variable_rename,[status(thm)],[f_4462_1]) ).

fof(f_4462_3,plain,
    ! [U_18406,U_18407,U_18408,U_18409,U_18410] : hAPP(hAPP(c_List_Olist__update(U_18406,hAPP(hAPP(c_List_Olist_OCons(U_18406),U_18407),U_18408)),U_18409),U_18410) = c_Nat_Onat_Onat__case(tc_List_Olist(U_18406),hAPP(hAPP(c_List_Olist_OCons(U_18406),U_18410),U_18408),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18406),tc_List_Olist(U_18406),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_18406),U_18407)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_18406,tc_List_Olist(U_18406)),c_List_Olist__update(U_18406,U_18408)),U_18410)),U_18409),
    inference(definitional_conversion,[status(esa)],[f_4462_2]) ).

cnf(f_4462_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18406,hAPP(hAPP(c_List_Olist_OCons(U_18406),U_18407),U_18408)),U_18409),U_18410) = c_Nat_Onat_Onat__case(tc_List_Olist(U_18406),hAPP(hAPP(c_List_Olist_OCons(U_18406),U_18410),U_18408),hAPP(hAPP(c_COMBB(tc_List_Olist(U_18406),tc_List_Olist(U_18406),tc_Nat_Onat),hAPP(c_List_Olist_OCons(U_18406),U_18407)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,U_18406,tc_List_Olist(U_18406)),c_List_Olist__update(U_18406,U_18408)),U_18410)),U_18409),
    inference(clausify,[status(thm)],[f_4462_3]) ).

fof(f_4463_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_4463_2,plain,
    ! [U_18415,U_18414,U_18413,U_18412,U_18411] : hAPP(hAPP(c_List_Olist__update(U_18411,hAPP(hAPP(c_List_Olist_OCons(U_18411),U_18412),U_18413)),hAPP(c_Nat_OSuc,U_18414)),U_18415) = hAPP(hAPP(c_List_Olist_OCons(U_18411),U_18412),hAPP(hAPP(c_List_Olist__update(U_18411,U_18413),U_18414),U_18415)),
    inference(variable_rename,[status(thm)],[f_4463_1]) ).

fof(f_4463_3,plain,
    ! [U_18412,U_18411,U_18413,U_18414,U_18415] : hAPP(hAPP(c_List_Olist__update(U_18411,hAPP(hAPP(c_List_Olist_OCons(U_18411),U_18412),U_18413)),hAPP(c_Nat_OSuc,U_18414)),U_18415) = hAPP(hAPP(c_List_Olist_OCons(U_18411),U_18412),hAPP(hAPP(c_List_Olist__update(U_18411,U_18413),U_18414),U_18415)),
    inference(definitional_conversion,[status(esa)],[f_4463_2]) ).

cnf(f_4463_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18411,hAPP(hAPP(c_List_Olist_OCons(U_18411),U_18412),U_18413)),hAPP(c_Nat_OSuc,U_18414)),U_18415) = hAPP(hAPP(c_List_Olist_OCons(U_18411),U_18412),hAPP(hAPP(c_List_Olist__update(U_18411,U_18413),U_18414),U_18415)),
    inference(clausify,[status(thm)],[f_4463_3]) ).

fof(f_4464_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_4464_2,plain,
    ! [U_18418,U_18417,U_18416] : hAPP(hAPP(c_List_Olist_OCons(U_18416),U_18417),U_18418) != c_List_Olist_ONil(U_18416),
    inference(variable_rename,[status(thm)],[f_4464_1]) ).

fof(f_4464_3,plain,
    ! [U_18416,U_18418,U_18417] : hAPP(hAPP(c_List_Olist_OCons(U_18416),U_18417),U_18418) != c_List_Olist_ONil(U_18416),
    inference(definitional_conversion,[status(esa)],[f_4464_2]) ).

cnf(f_4464_4,plain,
    hAPP(hAPP(c_List_Olist_OCons(U_18416),U_18417),U_18418) != c_List_Olist_ONil(U_18416),
    inference(clausify,[status(thm)],[f_4464_3]) ).

fof(f_4465_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_4465_2,plain,
    ! [U_18421,U_18420,U_18419] : c_List_Olist_ONil(U_18419) != hAPP(hAPP(c_List_Olist_OCons(U_18419),U_18420),U_18421),
    inference(variable_rename,[status(thm)],[f_4465_1]) ).

fof(f_4465_3,plain,
    ! [U_18419,U_18420,U_18421] : c_List_Olist_ONil(U_18419) != hAPP(hAPP(c_List_Olist_OCons(U_18419),U_18420),U_18421),
    inference(definitional_conversion,[status(esa)],[f_4465_2]) ).

cnf(f_4465_4,plain,
    c_List_Olist_ONil(U_18419) != hAPP(hAPP(c_List_Olist_OCons(U_18419),U_18420),U_18421),
    inference(clausify,[status(thm)],[f_4465_3]) ).

fof(f_4466_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_4466_2,plain,
    ! [U_18425,U_18424,U_18423,U_18422] : hAPP(hAPP(c_List_Olist__update(U_18422,hAPP(hAPP(c_List_Olist_OCons(U_18422),U_18423),U_18424)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18425) = hAPP(hAPP(c_List_Olist_OCons(U_18422),U_18425),U_18424),
    inference(variable_rename,[status(thm)],[f_4466_1]) ).

fof(f_4466_3,plain,
    ! [U_18422,U_18423,U_18424,U_18425] : hAPP(hAPP(c_List_Olist__update(U_18422,hAPP(hAPP(c_List_Olist_OCons(U_18422),U_18423),U_18424)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18425) = hAPP(hAPP(c_List_Olist_OCons(U_18422),U_18425),U_18424),
    inference(definitional_conversion,[status(esa)],[f_4466_2]) ).

cnf(f_4466_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18422,hAPP(hAPP(c_List_Olist_OCons(U_18422),U_18423),U_18424)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18425) = hAPP(hAPP(c_List_Olist_OCons(U_18422),U_18425),U_18424),
    inference(clausify,[status(thm)],[f_4466_3]) ).

fof(f_4467_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_4467_2,plain,
    ! [U_18426] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_18426,c_Orderings_Obot__class_Obot(tc_fun(U_18426,tc_HOL_Obool))) = c_List_Olist_ONil(U_18426)
      | ~ class_Orderings_Olinorder(U_18426) ),
    inference(variable_rename,[status(thm)],[f_4467_1]) ).

fof(f_4467_3,plain,
    ! [U_18426] :
      ( c_List_Olinorder__class_Osorted__list__of__set(U_18426,c_Orderings_Obot__class_Obot(tc_fun(U_18426,tc_HOL_Obool))) = c_List_Olist_ONil(U_18426)
      | ~ class_Orderings_Olinorder(U_18426) ),
    inference(definitional_conversion,[status(esa)],[f_4467_2]) ).

cnf(f_4467_4,plain,
    ( c_List_Olinorder__class_Osorted__list__of__set(U_18426,c_Orderings_Obot__class_Obot(tc_fun(U_18426,tc_HOL_Obool))) = c_List_Olist_ONil(U_18426)
    | ~ class_Orderings_Olinorder(U_18426) ),
    inference(clausify,[status(thm)],[f_4467_3]) ).

fof(f_4468_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_4468_2,plain,
    ! [U_18429,U_18428,U_18427] : hAPP(hAPP(c_List_Ozip(U_18427,U_18428),U_18429),c_List_Olist_ONil(U_18428)) = c_List_Olist_ONil(tc_prod(U_18427,U_18428)),
    inference(variable_rename,[status(thm)],[f_4468_1]) ).

fof(f_4468_3,plain,
    ! [U_18427,U_18428,U_18429] : hAPP(hAPP(c_List_Ozip(U_18427,U_18428),U_18429),c_List_Olist_ONil(U_18428)) = c_List_Olist_ONil(tc_prod(U_18427,U_18428)),
    inference(definitional_conversion,[status(esa)],[f_4468_2]) ).

cnf(f_4468_4,plain,
    hAPP(hAPP(c_List_Ozip(U_18427,U_18428),U_18429),c_List_Olist_ONil(U_18428)) = c_List_Olist_ONil(tc_prod(U_18427,U_18428)),
    inference(clausify,[status(thm)],[f_4468_3]) ).

fof(f_4469_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_4469_2,plain,
    ! [U_18432,U_18431,U_18430] : hAPP(hAPP(c_List_Ozip(U_18430,U_18431),c_List_Olist_ONil(U_18430)),U_18432) = c_List_Olist_ONil(tc_prod(U_18430,U_18431)),
    inference(variable_rename,[status(thm)],[f_4469_1]) ).

fof(f_4469_3,plain,
    ! [U_18430,U_18431,U_18432] : hAPP(hAPP(c_List_Ozip(U_18430,U_18431),c_List_Olist_ONil(U_18430)),U_18432) = c_List_Olist_ONil(tc_prod(U_18430,U_18431)),
    inference(definitional_conversion,[status(esa)],[f_4469_2]) ).

cnf(f_4469_4,plain,
    hAPP(hAPP(c_List_Ozip(U_18430,U_18431),c_List_Olist_ONil(U_18430)),U_18432) = c_List_Olist_ONil(tc_prod(U_18430,U_18431)),
    inference(clausify,[status(thm)],[f_4469_3]) ).

fof(f_4470_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_4470_2,plain,
    ! [U_18434,U_18433] :
      ( c_List_Oupto(U_18434,U_18433) = c_List_Olist_ONil(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_18433),U_18434)) ),
    inference(variable_rename,[status(thm)],[f_4470_1]) ).

fof(f_4470_3,plain,
    ! [U_18433,U_18434] :
      ( c_List_Oupto(U_18434,U_18433) = c_List_Olist_ONil(tc_Int_Oint)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_18433),U_18434)) ),
    inference(definitional_conversion,[status(esa)],[f_4470_2]) ).

cnf(f_4470_4,plain,
    ( c_List_Oupto(U_18434,U_18433) = c_List_Olist_ONil(tc_Int_Oint)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),U_18433),U_18434)) ),
    inference(clausify,[status(thm)],[f_4470_3]) ).

fof(f_4471_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_4471_2,plain,
    ! [U_18438,U_18437,U_18436,U_18435] : c_List_Ofoldr(U_18435,U_18436,U_18437,c_List_Olist_ONil(U_18435),U_18438) = U_18438,
    inference(variable_rename,[status(thm)],[f_4471_1]) ).

fof(f_4471_3,plain,
    ! [U_18436,U_18435,U_18437,U_18438] : c_List_Ofoldr(U_18435,U_18436,U_18437,c_List_Olist_ONil(U_18435),U_18438) = U_18438,
    inference(definitional_conversion,[status(esa)],[f_4471_2]) ).

cnf(f_4471_4,plain,
    c_List_Ofoldr(U_18435,U_18436,U_18437,c_List_Olist_ONil(U_18435),U_18438) = U_18438,
    inference(clausify,[status(thm)],[f_4471_3]) ).

fof(f_4472_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_4472_2,plain,
    ! [U_18441,U_18440,U_18439] : hAPP(c_Map_Omap__of(U_18439,U_18440,c_List_Olist_ONil(tc_prod(U_18439,U_18440))),U_18441) = c_Option_Ooption_ONone(U_18440),
    inference(variable_rename,[status(thm)],[f_4472_1]) ).

fof(f_4472_3,plain,
    ! [U_18439,U_18440,U_18441] : hAPP(c_Map_Omap__of(U_18439,U_18440,c_List_Olist_ONil(tc_prod(U_18439,U_18440))),U_18441) = c_Option_Ooption_ONone(U_18440),
    inference(definitional_conversion,[status(esa)],[f_4472_2]) ).

cnf(f_4472_4,plain,
    hAPP(c_Map_Omap__of(U_18439,U_18440,c_List_Olist_ONil(tc_prod(U_18439,U_18440))),U_18441) = c_Option_Ooption_ONone(U_18440),
    inference(clausify,[status(thm)],[f_4472_3]) ).

fof(f_4473_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_4473_2,plain,
    ! [U_18444,U_18443,U_18442] : hAPP(c_Map_Omap__of(U_18442,U_18443,c_List_Olist_ONil(tc_prod(U_18442,U_18443))),U_18444) = c_Option_Ooption_ONone(U_18443),
    inference(variable_rename,[status(thm)],[f_4473_1]) ).

fof(f_4473_3,plain,
    ! [U_18442,U_18443,U_18444] : hAPP(c_Map_Omap__of(U_18442,U_18443,c_List_Olist_ONil(tc_prod(U_18442,U_18443))),U_18444) = c_Option_Ooption_ONone(U_18443),
    inference(definitional_conversion,[status(esa)],[f_4473_2]) ).

cnf(f_4473_4,plain,
    hAPP(c_Map_Omap__of(U_18442,U_18443,c_List_Olist_ONil(tc_prod(U_18442,U_18443))),U_18444) = c_Option_Ooption_ONone(U_18443),
    inference(clausify,[status(thm)],[f_4473_3]) ).

fof(f_4474_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_4474_2,plain,
    ! [U_18448,U_18447,U_18446,U_18445] :
      ( ( hAPP(hAPP(c_List_Olist__update(U_18445,U_18446),U_18447),U_18448) = c_List_Olist_ONil(U_18445)
        | U_18446 != c_List_Olist_ONil(U_18445) )
      & ( U_18446 = c_List_Olist_ONil(U_18445)
        | hAPP(hAPP(c_List_Olist__update(U_18445,U_18446),U_18447),U_18448) != c_List_Olist_ONil(U_18445) ) ),
    inference(variable_rename,[status(thm)],[f_4474_1]) ).

fof(f_4474_3,plain,
    ( ! [U_18456,U_18454,U_18452,U_18450] :
        ( hAPP(hAPP(c_List_Olist__update(U_18450,U_18452),U_18454),U_18456) = c_List_Olist_ONil(U_18450)
        | U_18452 != c_List_Olist_ONil(U_18450) )
    & ! [U_18455,U_18453,U_18451,U_18449] :
        ( U_18451 = c_List_Olist_ONil(U_18449)
        | hAPP(hAPP(c_List_Olist__update(U_18449,U_18451),U_18453),U_18455) != c_List_Olist_ONil(U_18449) ) ),
    inference(miniscope,[status(thm)],[f_4474_2]) ).

fof(f_4474_4,plain,
    ( ! [U_18450,U_18456,U_18452,U_18454] :
        ( hAPP(hAPP(c_List_Olist__update(U_18450,U_18452),U_18454),U_18456) = c_List_Olist_ONil(U_18450)
        | U_18452 != c_List_Olist_ONil(U_18450) )
    & ! [U_18455,U_18451,U_18449,U_18453] :
        ( U_18451 = c_List_Olist_ONil(U_18449)
        | hAPP(hAPP(c_List_Olist__update(U_18449,U_18451),U_18453),U_18455) != c_List_Olist_ONil(U_18449) ) ),
    inference(definitional_conversion,[status(esa)],[f_4474_3]) ).

cnf(f_4474_5,plain,
    ( U_18451 = c_List_Olist_ONil(U_18449)
    | hAPP(hAPP(c_List_Olist__update(U_18449,U_18451),U_18453),U_18455) != c_List_Olist_ONil(U_18449) ),
    inference(clausify,[status(thm)],[f_4474_4]) ).

cnf(f_4474_6,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_18450,U_18452),U_18454),U_18456) = c_List_Olist_ONil(U_18450)
    | U_18452 != c_List_Olist_ONil(U_18450) ),
    inference(clausify,[status(thm)],[f_4474_4]) ).

fof(f_4475_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_4475_2,plain,
    ! [U_18459,U_18458,U_18457] : hAPP(hAPP(c_List_Olist__update(U_18457,c_List_Olist_ONil(U_18457)),U_18458),U_18459) = c_List_Olist_ONil(U_18457),
    inference(variable_rename,[status(thm)],[f_4475_1]) ).

fof(f_4475_3,plain,
    ! [U_18457,U_18458,U_18459] : hAPP(hAPP(c_List_Olist__update(U_18457,c_List_Olist_ONil(U_18457)),U_18458),U_18459) = c_List_Olist_ONil(U_18457),
    inference(definitional_conversion,[status(esa)],[f_4475_2]) ).

cnf(f_4475_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18457,c_List_Olist_ONil(U_18457)),U_18458),U_18459) = c_List_Olist_ONil(U_18457),
    inference(clausify,[status(thm)],[f_4475_3]) ).

fof(f_4476_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_4476_2,plain,
    ! [U_18462,U_18461,U_18460] : hAPP(hAPP(c_List_Olist__update(U_18460,c_List_Olist_ONil(U_18460)),U_18461),U_18462) = c_List_Olist_ONil(U_18460),
    inference(variable_rename,[status(thm)],[f_4476_1]) ).

fof(f_4476_3,plain,
    ! [U_18460,U_18461,U_18462] : hAPP(hAPP(c_List_Olist__update(U_18460,c_List_Olist_ONil(U_18460)),U_18461),U_18462) = c_List_Olist_ONil(U_18460),
    inference(definitional_conversion,[status(esa)],[f_4476_2]) ).

cnf(f_4476_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18460,c_List_Olist_ONil(U_18460)),U_18461),U_18462) = c_List_Olist_ONil(U_18460),
    inference(clausify,[status(thm)],[f_4476_3]) ).

fof(f_4477_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_4477_2,plain,
    ! [U_18467,U_18466,U_18465,U_18464,U_18463] : hAPP(hAPP(c_List_Olist__update(U_18463,hAPP(hAPP(c_List_Olist__update(U_18463,U_18464),U_18465),U_18466)),U_18465),U_18467) = hAPP(hAPP(c_List_Olist__update(U_18463,U_18464),U_18465),U_18467),
    inference(variable_rename,[status(thm)],[f_4477_1]) ).

fof(f_4477_3,plain,
    ! [U_18463,U_18464,U_18465,U_18466,U_18467] : hAPP(hAPP(c_List_Olist__update(U_18463,hAPP(hAPP(c_List_Olist__update(U_18463,U_18464),U_18465),U_18466)),U_18465),U_18467) = hAPP(hAPP(c_List_Olist__update(U_18463,U_18464),U_18465),U_18467),
    inference(definitional_conversion,[status(esa)],[f_4477_2]) ).

cnf(f_4477_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18463,hAPP(hAPP(c_List_Olist__update(U_18463,U_18464),U_18465),U_18466)),U_18465),U_18467) = hAPP(hAPP(c_List_Olist__update(U_18463,U_18464),U_18465),U_18467),
    inference(clausify,[status(thm)],[f_4477_3]) ).

fof(f_4478_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_4478_2,plain,
    ! [U_18473,U_18472,U_18471,U_18470,U_18469,U_18468] :
      ( hAPP(hAPP(c_List_Olist__update(U_18470,hAPP(hAPP(c_List_Olist__update(U_18470,U_18471),U_18468),U_18472)),U_18469),U_18473) = hAPP(hAPP(c_List_Olist__update(U_18470,hAPP(hAPP(c_List_Olist__update(U_18470,U_18471),U_18469),U_18473)),U_18468),U_18472)
      | U_18468 = U_18469 ),
    inference(variable_rename,[status(thm)],[f_4478_1]) ).

fof(f_4478_3,plain,
    ! [U_18468,U_18469,U_18470,U_18471,U_18472,U_18473] :
      ( hAPP(hAPP(c_List_Olist__update(U_18470,hAPP(hAPP(c_List_Olist__update(U_18470,U_18471),U_18468),U_18472)),U_18469),U_18473) = hAPP(hAPP(c_List_Olist__update(U_18470,hAPP(hAPP(c_List_Olist__update(U_18470,U_18471),U_18469),U_18473)),U_18468),U_18472)
      | U_18468 = U_18469 ),
    inference(definitional_conversion,[status(esa)],[f_4478_2]) ).

cnf(f_4478_4,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_18470,hAPP(hAPP(c_List_Olist__update(U_18470,U_18471),U_18468),U_18472)),U_18469),U_18473) = hAPP(hAPP(c_List_Olist__update(U_18470,hAPP(hAPP(c_List_Olist__update(U_18470,U_18471),U_18469),U_18473)),U_18468),U_18472)
    | U_18468 = U_18469 ),
    inference(clausify,[status(thm)],[f_4478_3]) ).

fof(f_4479_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_4479_2,plain,
    ! [U_18475,U_18474] : c_List_Oremove1(U_18474,U_18475,c_List_Olist_ONil(U_18474)) = c_List_Olist_ONil(U_18474),
    inference(variable_rename,[status(thm)],[f_4479_1]) ).

fof(f_4479_3,plain,
    ! [U_18475,U_18474] : c_List_Oremove1(U_18474,U_18475,c_List_Olist_ONil(U_18474)) = c_List_Olist_ONil(U_18474),
    inference(definitional_conversion,[status(esa)],[f_4479_2]) ).

cnf(f_4479_4,plain,
    c_List_Oremove1(U_18474,U_18475,c_List_Olist_ONil(U_18474)) = c_List_Olist_ONil(U_18474),
    inference(clausify,[status(thm)],[f_4479_3]) ).

fof(f_4480_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_4480_2,plain,
    ! [U_18476] : hBOOL(hAPP(c_List_Odistinct(U_18476),c_List_Olist_ONil(U_18476))),
    inference(variable_rename,[status(thm)],[f_4480_1]) ).

fof(f_4480_3,plain,
    ! [U_18476] : hBOOL(hAPP(c_List_Odistinct(U_18476),c_List_Olist_ONil(U_18476))),
    inference(definitional_conversion,[status(esa)],[f_4480_2]) ).

cnf(f_4480_4,plain,
    hBOOL(hAPP(c_List_Odistinct(U_18476),c_List_Olist_ONil(U_18476))),
    inference(clausify,[status(thm)],[f_4480_3]) ).

fof(f_4481_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_4481_2,plain,
    ! [U_18481,U_18480,U_18479,U_18478,U_18477] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18478,U_18477,U_18479),U_18480),U_18481) != c_List_Olist_ONil(U_18478)
      | ~ class_Orderings_Olinorder(U_18477) ),
    inference(variable_rename,[status(thm)],[f_4481_1]) ).

fof(f_4481_3,plain,
    ! [U_18477,U_18478,U_18479,U_18480,U_18481] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18478,U_18477,U_18479),U_18480),U_18481) != c_List_Olist_ONil(U_18478)
      | ~ class_Orderings_Olinorder(U_18477) ),
    inference(definitional_conversion,[status(esa)],[f_4481_2]) ).

cnf(f_4481_4,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_18478,U_18477,U_18479),U_18480),U_18481) != c_List_Olist_ONil(U_18478)
    | ~ class_Orderings_Olinorder(U_18477) ),
    inference(clausify,[status(thm)],[f_4481_3]) ).

fof(f_4482_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_4482_2,plain,
    ! [U_18483,U_18482] : c_List_Olistrelp(U_18482,U_18483,c_List_Olist_ONil(U_18482),c_List_Olist_ONil(U_18482)),
    inference(variable_rename,[status(thm)],[f_4482_1]) ).

fof(f_4482_3,plain,
    ! [U_18483,U_18482] : c_List_Olistrelp(U_18482,U_18483,c_List_Olist_ONil(U_18482),c_List_Olist_ONil(U_18482)),
    inference(definitional_conversion,[status(esa)],[f_4482_2]) ).

cnf(f_4482_4,plain,
    c_List_Olistrelp(U_18482,U_18483,c_List_Olist_ONil(U_18482),c_List_Olist_ONil(U_18482)),
    inference(clausify,[status(thm)],[f_4482_3]) ).

fof(f_4483_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_4483_2,plain,
    ! [U_18485,U_18484] : c_List_Olistrelp(U_18484,U_18485,c_List_Olist_ONil(U_18484),c_List_Olist_ONil(U_18484)),
    inference(variable_rename,[status(thm)],[f_4483_1]) ).

fof(f_4483_3,plain,
    ! [U_18484,U_18485] : c_List_Olistrelp(U_18484,U_18485,c_List_Olist_ONil(U_18484),c_List_Olist_ONil(U_18484)),
    inference(definitional_conversion,[status(esa)],[f_4483_2]) ).

cnf(f_4483_4,plain,
    c_List_Olistrelp(U_18484,U_18485,c_List_Olist_ONil(U_18484),c_List_Olist_ONil(U_18484)),
    inference(clausify,[status(thm)],[f_4483_3]) ).

fof(f_4484_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_4484_2,plain,
    ! [U_18486] : hAPP(c_List_Oset(U_18486),c_List_Olist_ONil(U_18486)) = c_Orderings_Obot__class_Obot(tc_fun(U_18486,tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4484_1]) ).

fof(f_4484_3,plain,
    ! [U_18486] : hAPP(c_List_Oset(U_18486),c_List_Olist_ONil(U_18486)) = c_Orderings_Obot__class_Obot(tc_fun(U_18486,tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4484_2]) ).

cnf(f_4484_4,plain,
    hAPP(c_List_Oset(U_18486),c_List_Olist_ONil(U_18486)) = c_Orderings_Obot__class_Obot(tc_fun(U_18486,tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4484_3]) ).

fof(f_4485_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_4485_2,plain,
    ! [U_18488,U_18487] :
      ( ( c_Orderings_Obot__class_Obot(tc_fun(U_18487,tc_HOL_Obool)) = hAPP(c_List_Oset(U_18487),U_18488)
        | U_18488 != c_List_Olist_ONil(U_18487) )
      & ( U_18488 = c_List_Olist_ONil(U_18487)
        | c_Orderings_Obot__class_Obot(tc_fun(U_18487,tc_HOL_Obool)) != hAPP(c_List_Oset(U_18487),U_18488) ) ),
    inference(variable_rename,[status(thm)],[f_4485_1]) ).

fof(f_4485_3,plain,
    ( ! [U_18492,U_18490] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_18490,tc_HOL_Obool)) = hAPP(c_List_Oset(U_18490),U_18492)
        | U_18492 != c_List_Olist_ONil(U_18490) )
    & ! [U_18491,U_18489] :
        ( U_18491 = c_List_Olist_ONil(U_18489)
        | c_Orderings_Obot__class_Obot(tc_fun(U_18489,tc_HOL_Obool)) != hAPP(c_List_Oset(U_18489),U_18491) ) ),
    inference(miniscope,[status(thm)],[f_4485_2]) ).

fof(f_4485_4,plain,
    ( ! [U_18490,U_18492] :
        ( c_Orderings_Obot__class_Obot(tc_fun(U_18490,tc_HOL_Obool)) = hAPP(c_List_Oset(U_18490),U_18492)
        | U_18492 != c_List_Olist_ONil(U_18490) )
    & ! [U_18491,U_18489] :
        ( U_18491 = c_List_Olist_ONil(U_18489)
        | c_Orderings_Obot__class_Obot(tc_fun(U_18489,tc_HOL_Obool)) != hAPP(c_List_Oset(U_18489),U_18491) ) ),
    inference(definitional_conversion,[status(esa)],[f_4485_3]) ).

cnf(f_4485_5,plain,
    ( U_18491 = c_List_Olist_ONil(U_18489)
    | c_Orderings_Obot__class_Obot(tc_fun(U_18489,tc_HOL_Obool)) != hAPP(c_List_Oset(U_18489),U_18491) ),
    inference(clausify,[status(thm)],[f_4485_4]) ).

cnf(f_4485_6,plain,
    ( c_Orderings_Obot__class_Obot(tc_fun(U_18490,tc_HOL_Obool)) = hAPP(c_List_Oset(U_18490),U_18492)
    | U_18492 != c_List_Olist_ONil(U_18490) ),
    inference(clausify,[status(thm)],[f_4485_4]) ).

fof(f_4486_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_4486_2,plain,
    ! [U_18494,U_18493] :
      ( ( hAPP(c_List_Oset(U_18493),U_18494) = c_Orderings_Obot__class_Obot(tc_fun(U_18493,tc_HOL_Obool))
        | U_18494 != c_List_Olist_ONil(U_18493) )
      & ( U_18494 = c_List_Olist_ONil(U_18493)
        | hAPP(c_List_Oset(U_18493),U_18494) != c_Orderings_Obot__class_Obot(tc_fun(U_18493,tc_HOL_Obool)) ) ),
    inference(variable_rename,[status(thm)],[f_4486_1]) ).

fof(f_4486_3,plain,
    ( ! [U_18498,U_18496] :
        ( hAPP(c_List_Oset(U_18496),U_18498) = c_Orderings_Obot__class_Obot(tc_fun(U_18496,tc_HOL_Obool))
        | U_18498 != c_List_Olist_ONil(U_18496) )
    & ! [U_18497,U_18495] :
        ( U_18497 = c_List_Olist_ONil(U_18495)
        | hAPP(c_List_Oset(U_18495),U_18497) != c_Orderings_Obot__class_Obot(tc_fun(U_18495,tc_HOL_Obool)) ) ),
    inference(miniscope,[status(thm)],[f_4486_2]) ).

fof(f_4486_4,plain,
    ( ! [U_18496,U_18498] :
        ( hAPP(c_List_Oset(U_18496),U_18498) = c_Orderings_Obot__class_Obot(tc_fun(U_18496,tc_HOL_Obool))
        | U_18498 != c_List_Olist_ONil(U_18496) )
    & ! [U_18497,U_18495] :
        ( U_18497 = c_List_Olist_ONil(U_18495)
        | hAPP(c_List_Oset(U_18495),U_18497) != c_Orderings_Obot__class_Obot(tc_fun(U_18495,tc_HOL_Obool)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4486_3]) ).

cnf(f_4486_5,plain,
    ( U_18497 = c_List_Olist_ONil(U_18495)
    | hAPP(c_List_Oset(U_18495),U_18497) != c_Orderings_Obot__class_Obot(tc_fun(U_18495,tc_HOL_Obool)) ),
    inference(clausify,[status(thm)],[f_4486_4]) ).

cnf(f_4486_6,plain,
    ( hAPP(c_List_Oset(U_18496),U_18498) = c_Orderings_Obot__class_Obot(tc_fun(U_18496,tc_HOL_Obool))
    | U_18498 != c_List_Olist_ONil(U_18496) ),
    inference(clausify,[status(thm)],[f_4486_4]) ).

fof(f_4487_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_4487_2,plain,
    ! [U_18499] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18499),c_List_Olist_ONil(U_18499)) = c_Groups_Ozero__class_Ozero(U_18499)
      | ~ class_Groups_Omonoid__add(U_18499) ),
    inference(variable_rename,[status(thm)],[f_4487_1]) ).

fof(f_4487_3,plain,
    ! [U_18499] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18499),c_List_Olist_ONil(U_18499)) = c_Groups_Ozero__class_Ozero(U_18499)
      | ~ class_Groups_Omonoid__add(U_18499) ),
    inference(definitional_conversion,[status(esa)],[f_4487_2]) ).

cnf(f_4487_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18499),c_List_Olist_ONil(U_18499)) = c_Groups_Ozero__class_Ozero(U_18499)
    | ~ class_Groups_Omonoid__add(U_18499) ),
    inference(clausify,[status(thm)],[f_4487_3]) ).

fof(f_4488_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_4488_2,plain,
    ! [U_18501,U_18500] :
      ( ( 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_18500)),U_18501)))
        | U_18501 = c_List_Olist_ONil(U_18500) )
      & ( U_18501 != c_List_Olist_ONil(U_18500)
        | ~ 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_18500)),U_18501))) ) ),
    inference(variable_rename,[status(thm)],[f_4488_1]) ).

fof(f_4488_3,plain,
    ( ! [U_18505,U_18503] :
        ( 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_18503)),U_18505)))
        | U_18505 = c_List_Olist_ONil(U_18503) )
    & ! [U_18504,U_18502] :
        ( U_18504 != c_List_Olist_ONil(U_18502)
        | ~ 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_18502)),U_18504))) ) ),
    inference(miniscope,[status(thm)],[f_4488_2]) ).

fof(f_4488_4,plain,
    ( ! [U_18503,U_18505] :
        ( 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_18503)),U_18505)))
        | U_18505 = c_List_Olist_ONil(U_18503) )
    & ! [U_18504,U_18502] :
        ( U_18504 != c_List_Olist_ONil(U_18502)
        | ~ 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_18502)),U_18504))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4488_3]) ).

cnf(f_4488_5,plain,
    ( U_18504 != c_List_Olist_ONil(U_18502)
    | ~ 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_18502)),U_18504))) ),
    inference(clausify,[status(thm)],[f_4488_4]) ).

cnf(f_4488_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_18503)),U_18505)))
    | U_18505 = c_List_Olist_ONil(U_18503) ),
    inference(clausify,[status(thm)],[f_4488_4]) ).

fof(f_4489_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_4489_2,plain,
    ! [U_18510,U_18509,U_18508,U_18507,U_18506] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18506,tc_HOL_Obool)),hAPP(c_List_Oset(U_18506),hAPP(hAPP(c_List_Olist__update(U_18506,U_18507),U_18510),U_18509))),U_18508))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18506),U_18509),U_18508))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18506,tc_HOL_Obool)),hAPP(c_List_Oset(U_18506),U_18507)),U_18508)) ),
    inference(variable_rename,[status(thm)],[f_4489_1]) ).

fof(f_4489_3,plain,
    ! [U_18506,U_18507,U_18508,U_18509,U_18510] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18506,tc_HOL_Obool)),hAPP(c_List_Oset(U_18506),hAPP(hAPP(c_List_Olist__update(U_18506,U_18507),U_18510),U_18509))),U_18508))
      | ~ hBOOL(hAPP(hAPP(c_member(U_18506),U_18509),U_18508))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18506,tc_HOL_Obool)),hAPP(c_List_Oset(U_18506),U_18507)),U_18508)) ),
    inference(definitional_conversion,[status(esa)],[f_4489_2]) ).

cnf(f_4489_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18506,tc_HOL_Obool)),hAPP(c_List_Oset(U_18506),hAPP(hAPP(c_List_Olist__update(U_18506,U_18507),U_18510),U_18509))),U_18508))
    | ~ hBOOL(hAPP(hAPP(c_member(U_18506),U_18509),U_18508))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18506,tc_HOL_Obool)),hAPP(c_List_Oset(U_18506),U_18507)),U_18508)) ),
    inference(clausify,[status(thm)],[f_4489_3]) ).

fof(f_4490_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_4490_2,plain,
    ! [U_18513,U_18512,U_18511] : hAPP(hAPP(c_List_Otake(U_18511),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_18511),U_18512),U_18513)) = hAPP(hAPP(c_List_Olist_OCons(U_18511),U_18512),c_List_Olist_ONil(U_18511)),
    inference(variable_rename,[status(thm)],[f_4490_1]) ).

fof(f_4490_3,plain,
    ! [U_18511,U_18512,U_18513] : hAPP(hAPP(c_List_Otake(U_18511),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_18511),U_18512),U_18513)) = hAPP(hAPP(c_List_Olist_OCons(U_18511),U_18512),c_List_Olist_ONil(U_18511)),
    inference(definitional_conversion,[status(esa)],[f_4490_2]) ).

cnf(f_4490_4,plain,
    hAPP(hAPP(c_List_Otake(U_18511),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_18511),U_18512),U_18513)) = hAPP(hAPP(c_List_Olist_OCons(U_18511),U_18512),c_List_Olist_ONil(U_18511)),
    inference(clausify,[status(thm)],[f_4490_3]) ).

fof(f_4491_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_4491_2,plain,
    ! [U_18517,U_18516,U_18515,U_18514] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18514,tc_HOL_Obool)),hAPP(c_List_Oset(U_18514),hAPP(hAPP(c_List_Olist__update(U_18514,U_18515),U_18516),U_18517))),hAPP(hAPP(c_Set_Oinsert(U_18514),U_18517),hAPP(c_List_Oset(U_18514),U_18515)))),
    inference(variable_rename,[status(thm)],[f_4491_1]) ).

fof(f_4491_3,plain,
    ! [U_18514,U_18515,U_18516,U_18517] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18514,tc_HOL_Obool)),hAPP(c_List_Oset(U_18514),hAPP(hAPP(c_List_Olist__update(U_18514,U_18515),U_18516),U_18517))),hAPP(hAPP(c_Set_Oinsert(U_18514),U_18517),hAPP(c_List_Oset(U_18514),U_18515)))),
    inference(definitional_conversion,[status(esa)],[f_4491_2]) ).

cnf(f_4491_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18514,tc_HOL_Obool)),hAPP(c_List_Oset(U_18514),hAPP(hAPP(c_List_Olist__update(U_18514,U_18515),U_18516),U_18517))),hAPP(hAPP(c_Set_Oinsert(U_18514),U_18517),hAPP(c_List_Oset(U_18514),U_18515)))),
    inference(clausify,[status(thm)],[f_4491_3]) ).

fof(f_4492_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_4492_2,plain,
    ! [U_18522,U_18521,U_18520,U_18519,U_18518] :
      ( ( ( hAPP(hAPP(c_List_Onth(U_18519),hAPP(hAPP(c_List_Olist__update(U_18519,U_18520),U_18518),U_18522)),U_18521) = hAPP(hAPP(c_List_Onth(U_18519),U_18520),U_18521)
          | U_18518 = U_18521 )
        & ( hAPP(hAPP(c_List_Onth(U_18519),hAPP(hAPP(c_List_Olist__update(U_18519,U_18520),U_18518),U_18522)),U_18521) = U_18522
          | U_18518 != U_18521 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18518),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18519)),U_18520))) ),
    inference(variable_rename,[status(thm)],[f_4492_1]) ).

fof(f_4492_3,plain,
    ( ! [U_18518,U_18519,U_18520,U_18521,U_18522] :
        ( hAPP(hAPP(c_List_Onth(U_18519),hAPP(hAPP(c_List_Olist__update(U_18519,U_18520),U_18518),U_18522)),U_18521) = hAPP(hAPP(c_List_Onth(U_18519),U_18520),U_18521)
        | U_18518 = U_18521
        | ~ sP1157(U_18518,U_18519,U_18520,U_18521,U_18522) )
    & ! [U_18518,U_18519,U_18520,U_18521,U_18522] :
        ( hAPP(hAPP(c_List_Onth(U_18519),hAPP(hAPP(c_List_Olist__update(U_18519,U_18520),U_18518),U_18522)),U_18521) = U_18522
        | U_18518 != U_18521
        | ~ sP1157(U_18518,U_18519,U_18520,U_18521,U_18522) )
    & ! [U_18518,U_18519,U_18520,U_18521,U_18522] :
        ( sP1157(U_18518,U_18519,U_18520,U_18521,U_18522)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18518),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18519)),U_18520))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1157])],[f_4492_2]) ).

cnf(f_4492_4,plain,
    ( sP1157(U_18518,U_18519,U_18520,U_18521,U_18522)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18518),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18519)),U_18520))) ),
    inference(clausify,[status(thm)],[f_4492_3]) ).

cnf(f_4492_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_18519),hAPP(hAPP(c_List_Olist__update(U_18519,U_18520),U_18518),U_18522)),U_18521) = U_18522
    | U_18518 != U_18521
    | ~ sP1157(U_18518,U_18519,U_18520,U_18521,U_18522) ),
    inference(clausify,[status(thm)],[f_4492_3]) ).

cnf(f_4492_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_18519),hAPP(hAPP(c_List_Olist__update(U_18519,U_18520),U_18518),U_18522)),U_18521) = hAPP(hAPP(c_List_Onth(U_18519),U_18520),U_18521)
    | U_18518 = U_18521
    | ~ sP1157(U_18518,U_18519,U_18520,U_18521,U_18522) ),
    inference(clausify,[status(thm)],[f_4492_3]) ).

fof(f_4493_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_4493_2,plain,
    ! [U_18526,U_18525,U_18524,U_18523] :
      ( ( ( hAPP(hAPP(c_List_Olist__update(U_18524,U_18525),U_18523),U_18526) = U_18525
          | hAPP(hAPP(c_List_Onth(U_18524),U_18525),U_18523) != U_18526 )
        & ( hAPP(hAPP(c_List_Onth(U_18524),U_18525),U_18523) = U_18526
          | hAPP(hAPP(c_List_Olist__update(U_18524,U_18525),U_18523),U_18526) != U_18525 ) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18523),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18524)),U_18525))) ),
    inference(variable_rename,[status(thm)],[f_4493_1]) ).

fof(f_4493_3,plain,
    ( ! [U_18525,U_18524,U_18523,U_18526] :
        ( hAPP(hAPP(c_List_Olist__update(U_18524,U_18525),U_18523),U_18526) = U_18525
        | hAPP(hAPP(c_List_Onth(U_18524),U_18525),U_18523) != U_18526
        | ~ sP1158(U_18525,U_18524,U_18523,U_18526) )
    & ! [U_18525,U_18524,U_18523,U_18526] :
        ( hAPP(hAPP(c_List_Onth(U_18524),U_18525),U_18523) = U_18526
        | hAPP(hAPP(c_List_Olist__update(U_18524,U_18525),U_18523),U_18526) != U_18525
        | ~ sP1158(U_18525,U_18524,U_18523,U_18526) )
    & ! [U_18525,U_18524,U_18523,U_18526] :
        ( sP1158(U_18525,U_18524,U_18523,U_18526)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18523),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18524)),U_18525))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1158])],[f_4493_2]) ).

cnf(f_4493_4,plain,
    ( sP1158(U_18525,U_18524,U_18523,U_18526)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18523),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18524)),U_18525))) ),
    inference(clausify,[status(thm)],[f_4493_3]) ).

cnf(f_4493_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_18524),U_18525),U_18523) = U_18526
    | hAPP(hAPP(c_List_Olist__update(U_18524,U_18525),U_18523),U_18526) != U_18525
    | ~ sP1158(U_18525,U_18524,U_18523,U_18526) ),
    inference(clausify,[status(thm)],[f_4493_3]) ).

cnf(f_4493_6,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_18524,U_18525),U_18523),U_18526) = U_18525
    | hAPP(hAPP(c_List_Onth(U_18524),U_18525),U_18523) != U_18526
    | ~ sP1158(U_18525,U_18524,U_18523,U_18526) ),
    inference(clausify,[status(thm)],[f_4493_3]) ).

fof(f_4494_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_4494_2,plain,
    ! [U_18530,U_18529,U_18528,U_18527] :
      ( hAPP(hAPP(c_List_Onth(U_18528),hAPP(hAPP(c_List_Olist__update(U_18528,U_18529),U_18527),U_18530)),U_18527) = U_18530
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18527),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18528)),U_18529))) ),
    inference(variable_rename,[status(thm)],[f_4494_1]) ).

fof(f_4494_3,plain,
    ! [U_18527,U_18528,U_18529,U_18530] :
      ( hAPP(hAPP(c_List_Onth(U_18528),hAPP(hAPP(c_List_Olist__update(U_18528,U_18529),U_18527),U_18530)),U_18527) = U_18530
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18527),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18528)),U_18529))) ),
    inference(definitional_conversion,[status(esa)],[f_4494_2]) ).

cnf(f_4494_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_18528),hAPP(hAPP(c_List_Olist__update(U_18528,U_18529),U_18527),U_18530)),U_18527) = U_18530
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18527),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18528)),U_18529))) ),
    inference(clausify,[status(thm)],[f_4494_3]) ).

fof(f_4495_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_4495_2,plain,
    ! [U_18532,U_18531] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18531),tc_List_Olist(U_18531))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18531),tc_List_Olist(U_18531)),c_List_Olist_ONil(U_18531)),c_List_Olist_ONil(U_18531))),c_List_Olistrel(U_18531,U_18532))),
    inference(variable_rename,[status(thm)],[f_4495_1]) ).

fof(f_4495_3,plain,
    ! [U_18531,U_18532] : hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18531),tc_List_Olist(U_18531))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18531),tc_List_Olist(U_18531)),c_List_Olist_ONil(U_18531)),c_List_Olist_ONil(U_18531))),c_List_Olistrel(U_18531,U_18532))),
    inference(definitional_conversion,[status(esa)],[f_4495_2]) ).

cnf(f_4495_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18531),tc_List_Olist(U_18531))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18531),tc_List_Olist(U_18531)),c_List_Olist_ONil(U_18531)),c_List_Olist_ONil(U_18531))),c_List_Olistrel(U_18531,U_18532))),
    inference(clausify,[status(thm)],[f_4495_3]) ).

fof(f_4496_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_4496_2,plain,
    ! [U_18535,U_18534,U_18533] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18533),tc_List_Olist(U_18533))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18533),tc_List_Olist(U_18533)),U_18534),c_List_Olist_ONil(U_18533))),c_List_Olexord(U_18533,U_18535))),
    inference(variable_rename,[status(thm)],[f_4496_1]) ).

fof(f_4496_3,plain,
    ! [U_18533,U_18534,U_18535] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18533),tc_List_Olist(U_18533))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18533),tc_List_Olist(U_18533)),U_18534),c_List_Olist_ONil(U_18533))),c_List_Olexord(U_18533,U_18535))),
    inference(definitional_conversion,[status(esa)],[f_4496_2]) ).

cnf(f_4496_4,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18533),tc_List_Olist(U_18533))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18533),tc_List_Olist(U_18533)),U_18534),c_List_Olist_ONil(U_18533))),c_List_Olexord(U_18533,U_18535))),
    inference(clausify,[status(thm)],[f_4496_3]) ).

fof(f_4497_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_4497_2,plain,
    ! [U_18538,U_18537,U_18536] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18536),tc_List_Olist(U_18536))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18536),tc_List_Olist(U_18536)),c_List_Olist_ONil(U_18536)),U_18537)),c_List_Olex(U_18536,U_18538))),
    inference(variable_rename,[status(thm)],[f_4497_1]) ).

fof(f_4497_3,plain,
    ! [U_18536,U_18537,U_18538] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18536),tc_List_Olist(U_18536))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18536),tc_List_Olist(U_18536)),c_List_Olist_ONil(U_18536)),U_18537)),c_List_Olex(U_18536,U_18538))),
    inference(definitional_conversion,[status(esa)],[f_4497_2]) ).

cnf(f_4497_4,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18536),tc_List_Olist(U_18536))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18536),tc_List_Olist(U_18536)),c_List_Olist_ONil(U_18536)),U_18537)),c_List_Olex(U_18536,U_18538))),
    inference(clausify,[status(thm)],[f_4497_3]) ).

fof(f_4498_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_4498_2,plain,
    ! [U_18541,U_18540,U_18539] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18539),tc_List_Olist(U_18539))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18539),tc_List_Olist(U_18539)),U_18540),c_List_Olist_ONil(U_18539))),c_List_Olex(U_18539,U_18541))),
    inference(variable_rename,[status(thm)],[f_4498_1]) ).

fof(f_4498_3,plain,
    ! [U_18539,U_18540,U_18541] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18539),tc_List_Olist(U_18539))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18539),tc_List_Olist(U_18539)),U_18540),c_List_Olist_ONil(U_18539))),c_List_Olex(U_18539,U_18541))),
    inference(definitional_conversion,[status(esa)],[f_4498_2]) ).

cnf(f_4498_4,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18539),tc_List_Olist(U_18539))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18539),tc_List_Olist(U_18539)),U_18540),c_List_Olist_ONil(U_18539))),c_List_Olex(U_18539,U_18541))),
    inference(clausify,[status(thm)],[f_4498_3]) ).

fof(f_4499_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_4499_2,plain,
    ! [U_18545,U_18544,U_18543,U_18542] :
      ( hBOOL(hAPP(hAPP(c_member(U_18543),U_18545),hAPP(c_List_Oset(U_18543),hAPP(hAPP(c_List_Olist__update(U_18543,U_18544),U_18542),U_18545))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18542),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18543)),U_18544))) ),
    inference(variable_rename,[status(thm)],[f_4499_1]) ).

fof(f_4499_3,plain,
    ! [U_18542,U_18543,U_18544,U_18545] :
      ( hBOOL(hAPP(hAPP(c_member(U_18543),U_18545),hAPP(c_List_Oset(U_18543),hAPP(hAPP(c_List_Olist__update(U_18543,U_18544),U_18542),U_18545))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18542),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18543)),U_18544))) ),
    inference(definitional_conversion,[status(esa)],[f_4499_2]) ).

cnf(f_4499_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18543),U_18545),hAPP(c_List_Oset(U_18543),hAPP(hAPP(c_List_Olist__update(U_18543,U_18544),U_18542),U_18545))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18542),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18543)),U_18544))) ),
    inference(clausify,[status(thm)],[f_4499_3]) ).

fof(f_4500_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_4500_2,plain,
    ! [U_18547,U_18546] :
      ( ( c_List_Oupto(U_18546,U_18547) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18546),U_18547)) )
      & ( c_List_Oupto(U_18546,U_18547) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_18546),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18546),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_18547))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18546),U_18547)) ) ),
    inference(variable_rename,[status(thm)],[f_4500_1]) ).

fof(f_4500_3,plain,
    ( ! [U_18551,U_18549] :
        ( c_List_Oupto(U_18549,U_18551) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18549),U_18551)) )
    & ! [U_18550,U_18548] :
        ( c_List_Oupto(U_18548,U_18550) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_18548),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18548),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_18550))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18548),U_18550)) ) ),
    inference(miniscope,[status(thm)],[f_4500_2]) ).

fof(f_4500_4,plain,
    ( ! [U_18549,U_18551] :
        ( c_List_Oupto(U_18549,U_18551) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18549),U_18551)) )
    & ! [U_18550,U_18548] :
        ( c_List_Oupto(U_18548,U_18550) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_18548),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18548),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_18550))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18548),U_18550)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4500_3]) ).

cnf(f_4500_5,plain,
    ( c_List_Oupto(U_18548,U_18550) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_18548),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18548),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_18550))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18548),U_18550)) ),
    inference(clausify,[status(thm)],[f_4500_4]) ).

cnf(f_4500_6,plain,
    ( c_List_Oupto(U_18549,U_18551) = c_List_Olist_ONil(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18549),U_18551)) ),
    inference(clausify,[status(thm)],[f_4500_4]) ).

fof(f_4501_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_4501_2,plain,
    ! [U_18554,U_18553,U_18552] :
      ( ( c_List_Osublist(U_18553,hAPP(hAPP(c_List_Olist_OCons(U_18553),U_18554),c_List_Olist_ONil(U_18553)),U_18552) = c_List_Olist_ONil(U_18553)
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18552)) )
      & ( c_List_Osublist(U_18553,hAPP(hAPP(c_List_Olist_OCons(U_18553),U_18554),c_List_Olist_ONil(U_18553)),U_18552) = hAPP(hAPP(c_List_Olist_OCons(U_18553),U_18554),c_List_Olist_ONil(U_18553))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18552)) ) ),
    inference(variable_rename,[status(thm)],[f_4501_1]) ).

fof(f_4501_3,plain,
    ( ! [U_18560,U_18558,U_18556] :
        ( c_List_Osublist(U_18558,hAPP(hAPP(c_List_Olist_OCons(U_18558),U_18560),c_List_Olist_ONil(U_18558)),U_18556) = c_List_Olist_ONil(U_18558)
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18556)) )
    & ! [U_18559,U_18557,U_18555] :
        ( c_List_Osublist(U_18557,hAPP(hAPP(c_List_Olist_OCons(U_18557),U_18559),c_List_Olist_ONil(U_18557)),U_18555) = hAPP(hAPP(c_List_Olist_OCons(U_18557),U_18559),c_List_Olist_ONil(U_18557))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18555)) ) ),
    inference(miniscope,[status(thm)],[f_4501_2]) ).

fof(f_4501_4,plain,
    ( ! [U_18556,U_18558,U_18560] :
        ( c_List_Osublist(U_18558,hAPP(hAPP(c_List_Olist_OCons(U_18558),U_18560),c_List_Olist_ONil(U_18558)),U_18556) = c_List_Olist_ONil(U_18558)
        | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18556)) )
    & ! [U_18555,U_18557,U_18559] :
        ( c_List_Osublist(U_18557,hAPP(hAPP(c_List_Olist_OCons(U_18557),U_18559),c_List_Olist_ONil(U_18557)),U_18555) = hAPP(hAPP(c_List_Olist_OCons(U_18557),U_18559),c_List_Olist_ONil(U_18557))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18555)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4501_3]) ).

cnf(f_4501_5,plain,
    ( c_List_Osublist(U_18557,hAPP(hAPP(c_List_Olist_OCons(U_18557),U_18559),c_List_Olist_ONil(U_18557)),U_18555) = hAPP(hAPP(c_List_Olist_OCons(U_18557),U_18559),c_List_Olist_ONil(U_18557))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18555)) ),
    inference(clausify,[status(thm)],[f_4501_4]) ).

cnf(f_4501_6,plain,
    ( c_List_Osublist(U_18558,hAPP(hAPP(c_List_Olist_OCons(U_18558),U_18560),c_List_Olist_ONil(U_18558)),U_18556) = c_List_Olist_ONil(U_18558)
    | hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18556)) ),
    inference(clausify,[status(thm)],[f_4501_4]) ).

fof(f_4502_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_4502_2,plain,
    ! [U_18564,U_18563,U_18562,U_18561] :
      ( ( hAPP(hAPP(c_List_Otake(U_18562),U_18561),hAPP(hAPP(c_List_Olist_OCons(U_18562),U_18563),U_18564)) = hAPP(hAPP(c_List_Olist_OCons(U_18562),U_18563),hAPP(hAPP(c_List_Otake(U_18562),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18561),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_18564))
        | U_18561 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Otake(U_18562),U_18561),hAPP(hAPP(c_List_Olist_OCons(U_18562),U_18563),U_18564)) = c_List_Olist_ONil(U_18562)
        | U_18561 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4502_1]) ).

fof(f_4502_3,plain,
    ( ! [U_18572,U_18570,U_18568,U_18566] :
        ( hAPP(hAPP(c_List_Otake(U_18568),U_18566),hAPP(hAPP(c_List_Olist_OCons(U_18568),U_18570),U_18572)) = hAPP(hAPP(c_List_Olist_OCons(U_18568),U_18570),hAPP(hAPP(c_List_Otake(U_18568),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18566),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_18572))
        | U_18566 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_18571,U_18569,U_18567,U_18565] :
        ( hAPP(hAPP(c_List_Otake(U_18567),U_18565),hAPP(hAPP(c_List_Olist_OCons(U_18567),U_18569),U_18571)) = c_List_Olist_ONil(U_18567)
        | U_18565 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4502_2]) ).

fof(f_4502_4,plain,
    ( ! [U_18566,U_18568,U_18570,U_18572] :
        ( hAPP(hAPP(c_List_Otake(U_18568),U_18566),hAPP(hAPP(c_List_Olist_OCons(U_18568),U_18570),U_18572)) = hAPP(hAPP(c_List_Olist_OCons(U_18568),U_18570),hAPP(hAPP(c_List_Otake(U_18568),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18566),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_18572))
        | U_18566 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_18569,U_18571,U_18567,U_18565] :
        ( hAPP(hAPP(c_List_Otake(U_18567),U_18565),hAPP(hAPP(c_List_Olist_OCons(U_18567),U_18569),U_18571)) = c_List_Olist_ONil(U_18567)
        | U_18565 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_4502_3]) ).

cnf(f_4502_5,plain,
    ( hAPP(hAPP(c_List_Otake(U_18567),U_18565),hAPP(hAPP(c_List_Olist_OCons(U_18567),U_18569),U_18571)) = c_List_Olist_ONil(U_18567)
    | U_18565 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4502_4]) ).

cnf(f_4502_6,plain,
    ( hAPP(hAPP(c_List_Otake(U_18568),U_18566),hAPP(hAPP(c_List_Olist_OCons(U_18568),U_18570),U_18572)) = hAPP(hAPP(c_List_Olist_OCons(U_18568),U_18570),hAPP(hAPP(c_List_Otake(U_18568),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18566),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_18572))
    | U_18566 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4502_4]) ).

fof(f_4503_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_4503_2,plain,
    ! [U_18574,U_18573] :
      ( ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18573),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18574)) = 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_18573)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18574))) )
      & ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18573),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18574)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18573)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18573)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18574)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18573)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18574))) ) ),
    inference(variable_rename,[status(thm)],[f_4503_1]) ).

fof(f_4503_3,plain,
    ( ! [U_18578,U_18576] :
        ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18576),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18578)) = 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_18576)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18578))) )
    & ! [U_18577,U_18575] :
        ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18575),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18577)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18575)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18575)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18577)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18575)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18577))) ) ),
    inference(miniscope,[status(thm)],[f_4503_2]) ).

fof(f_4503_4,plain,
    ( ! [U_18576,U_18578] :
        ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18576),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18578)) = 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_18576)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18578))) )
    & ! [U_18575,U_18577] :
        ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18575),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18577)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18575)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18575)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18577)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18575)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18577))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4503_3]) ).

cnf(f_4503_5,plain,
    ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18575),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18577)) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18575)),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18575)),c_Groups_Oone__class_Oone(tc_Int_Oint)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18577)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18575)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18577))) ),
    inference(clausify,[status(thm)],[f_4503_4]) ).

cnf(f_4503_6,plain,
    ( c_List_Oupto(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18576),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18578)) = 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_18576)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),U_18578))) ),
    inference(clausify,[status(thm)],[f_4503_4]) ).

fof(f_4504_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_4504_2,plain,
    ! [U_18581,U_18580,U_18579] :
      ( hBOOL(hAPP(hAPP(c_member(U_18580),hAPP(c_Product__Type_Ofst(U_18580,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(U_18580,U_18579),U_18581))),hAPP(c_List_Oset(U_18580),U_18579)))
      | U_18579 = c_List_Olist_ONil(U_18580) ),
    inference(variable_rename,[status(thm)],[f_4504_1]) ).

fof(f_4504_3,plain,
    ! [U_18580,U_18579,U_18581] :
      ( hBOOL(hAPP(hAPP(c_member(U_18580),hAPP(c_Product__Type_Ofst(U_18580,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(U_18580,U_18579),U_18581))),hAPP(c_List_Oset(U_18580),U_18579)))
      | U_18579 = c_List_Olist_ONil(U_18580) ),
    inference(definitional_conversion,[status(esa)],[f_4504_2]) ).

cnf(f_4504_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_18580),hAPP(c_Product__Type_Ofst(U_18580,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral)),hAPP(c_Random_Oselect(U_18580,U_18579),U_18581))),hAPP(c_List_Oset(U_18580),U_18579)))
    | U_18579 = c_List_Olist_ONil(U_18580) ),
    inference(clausify,[status(thm)],[f_4504_3]) ).

fof(f_4505_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_4505_2,plain,
    ! [U_18583,U_18582] : hAPP(c_Relation_OImage(tc_List_Olist(U_18582),tc_List_Olist(U_18582),c_List_Olistrel(U_18582,U_18583)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18582)),c_List_Olist_ONil(U_18582)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18582),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18582)),c_List_Olist_ONil(U_18582)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18582),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4505_1]) ).

fof(f_4505_3,plain,
    ! [U_18582,U_18583] : hAPP(c_Relation_OImage(tc_List_Olist(U_18582),tc_List_Olist(U_18582),c_List_Olistrel(U_18582,U_18583)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18582)),c_List_Olist_ONil(U_18582)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18582),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18582)),c_List_Olist_ONil(U_18582)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18582),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_4505_2]) ).

cnf(f_4505_4,plain,
    hAPP(c_Relation_OImage(tc_List_Olist(U_18582),tc_List_Olist(U_18582),c_List_Olistrel(U_18582,U_18583)),hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18582)),c_List_Olist_ONil(U_18582)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18582),tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18582)),c_List_Olist_ONil(U_18582)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18582),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4505_3]) ).

fof(f_4506_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_4506_2,plain,
    ! [U_18585,U_18584] : c_List_Oset__Cons(U_18584,U_18585,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18584)),c_List_Olist_ONil(U_18584)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18584),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(U_18584,tc_List_Olist(U_18584),hAPP(hAPP(c_COMBC(U_18584,tc_List_Olist(U_18584),tc_List_Olist(U_18584)),c_List_Olist_OCons(U_18584)),c_List_Olist_ONil(U_18584))),U_18585),
    inference(variable_rename,[status(thm)],[f_4506_1]) ).

fof(f_4506_3,plain,
    ! [U_18584,U_18585] : c_List_Oset__Cons(U_18584,U_18585,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18584)),c_List_Olist_ONil(U_18584)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18584),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(U_18584,tc_List_Olist(U_18584),hAPP(hAPP(c_COMBC(U_18584,tc_List_Olist(U_18584),tc_List_Olist(U_18584)),c_List_Olist_OCons(U_18584)),c_List_Olist_ONil(U_18584))),U_18585),
    inference(definitional_conversion,[status(esa)],[f_4506_2]) ).

cnf(f_4506_4,plain,
    c_List_Oset__Cons(U_18584,U_18585,hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18584)),c_List_Olist_ONil(U_18584)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18584),tc_HOL_Obool)))) = hAPP(c_Set_Oimage(U_18584,tc_List_Olist(U_18584),hAPP(hAPP(c_COMBC(U_18584,tc_List_Olist(U_18584),tc_List_Olist(U_18584)),c_List_Olist_OCons(U_18584)),c_List_Olist_ONil(U_18584))),U_18585),
    inference(clausify,[status(thm)],[f_4506_3]) ).

fof(f_4507_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_4507_2,plain,
    ! [U_18589,U_18588,U_18587,U_18586] :
      ( ( hAPP(hAPP(c_List_Otake(U_18587),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18586)),hAPP(hAPP(c_List_Olist_OCons(U_18587),U_18588),U_18589)) = hAPP(hAPP(c_List_Olist_OCons(U_18587),U_18588),hAPP(hAPP(c_List_Otake(U_18587),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18586)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_18589))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18586) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Otake(U_18587),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18586)),hAPP(hAPP(c_List_Olist_OCons(U_18587),U_18588),U_18589)) = c_List_Olist_ONil(U_18587)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18586) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4507_1]) ).

fof(f_4507_3,plain,
    ( ! [U_18597,U_18595,U_18593,U_18591] :
        ( hAPP(hAPP(c_List_Otake(U_18593),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18591)),hAPP(hAPP(c_List_Olist_OCons(U_18593),U_18595),U_18597)) = hAPP(hAPP(c_List_Olist_OCons(U_18593),U_18595),hAPP(hAPP(c_List_Otake(U_18593),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18591)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_18597))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18591) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_18596,U_18594,U_18592,U_18590] :
        ( hAPP(hAPP(c_List_Otake(U_18592),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18590)),hAPP(hAPP(c_List_Olist_OCons(U_18592),U_18594),U_18596)) = c_List_Olist_ONil(U_18592)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18590) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4507_2]) ).

fof(f_4507_4,plain,
    ( ! [U_18591,U_18593,U_18595,U_18597] :
        ( hAPP(hAPP(c_List_Otake(U_18593),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18591)),hAPP(hAPP(c_List_Olist_OCons(U_18593),U_18595),U_18597)) = hAPP(hAPP(c_List_Olist_OCons(U_18593),U_18595),hAPP(hAPP(c_List_Otake(U_18593),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18591)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_18597))
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18591) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_18596,U_18592,U_18590,U_18594] :
        ( hAPP(hAPP(c_List_Otake(U_18592),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18590)),hAPP(hAPP(c_List_Olist_OCons(U_18592),U_18594),U_18596)) = c_List_Olist_ONil(U_18592)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18590) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_4507_3]) ).

cnf(f_4507_5,plain,
    ( hAPP(hAPP(c_List_Otake(U_18592),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18590)),hAPP(hAPP(c_List_Olist_OCons(U_18592),U_18594),U_18596)) = c_List_Olist_ONil(U_18592)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18590) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4507_4]) ).

cnf(f_4507_6,plain,
    ( hAPP(hAPP(c_List_Otake(U_18593),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18591)),hAPP(hAPP(c_List_Olist_OCons(U_18593),U_18595),U_18597)) = hAPP(hAPP(c_List_Olist_OCons(U_18593),U_18595),hAPP(hAPP(c_List_Otake(U_18593),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18591)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_18597))
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_18591) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4507_4]) ).

fof(f_4508_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_4508_2,plain,
    ! [U_18601,U_18600,U_18599,U_18598] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18598),hAPP(hAPP(c_List_Olist__update(U_18598,U_18599),U_18601),U_18600)))
      | hBOOL(hAPP(hAPP(c_member(U_18598),U_18600),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18598,tc_HOL_Obool)),hAPP(c_List_Oset(U_18598),U_18599)),hAPP(hAPP(c_Set_Oinsert(U_18598),hAPP(hAPP(c_List_Onth(U_18598),U_18599),U_18601)),c_Orderings_Obot__class_Obot(tc_fun(U_18598,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18598),U_18599)) ),
    inference(variable_rename,[status(thm)],[f_4508_1]) ).

fof(f_4508_3,plain,
    ! [U_18598,U_18599,U_18600,U_18601] :
      ( hBOOL(hAPP(c_List_Odistinct(U_18598),hAPP(hAPP(c_List_Olist__update(U_18598,U_18599),U_18601),U_18600)))
      | hBOOL(hAPP(hAPP(c_member(U_18598),U_18600),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18598,tc_HOL_Obool)),hAPP(c_List_Oset(U_18598),U_18599)),hAPP(hAPP(c_Set_Oinsert(U_18598),hAPP(hAPP(c_List_Onth(U_18598),U_18599),U_18601)),c_Orderings_Obot__class_Obot(tc_fun(U_18598,tc_HOL_Obool))))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_18598),U_18599)) ),
    inference(definitional_conversion,[status(esa)],[f_4508_2]) ).

cnf(f_4508_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18598),hAPP(hAPP(c_List_Olist__update(U_18598,U_18599),U_18601),U_18600)))
    | hBOOL(hAPP(hAPP(c_member(U_18598),U_18600),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18598,tc_HOL_Obool)),hAPP(c_List_Oset(U_18598),U_18599)),hAPP(hAPP(c_Set_Oinsert(U_18598),hAPP(hAPP(c_List_Onth(U_18598),U_18599),U_18601)),c_Orderings_Obot__class_Obot(tc_fun(U_18598,tc_HOL_Obool))))))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18598),U_18599)) ),
    inference(clausify,[status(thm)],[f_4508_3]) ).

fof(f_4509_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_4509_2,plain,
    ! [U_18603,U_18602] :
      ( ( ( c_List_Oupto(U_18602,U_18603) = c_List_Olist_ONil(tc_Int_Oint)
          | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18602),U_18603)) )
        & ( c_List_Oupto(U_18602,U_18603) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_18602),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18602),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_18603))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18602),U_18603)) ) )
      | ~ 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_18602),U_18603))) ),
    inference(variable_rename,[status(thm)],[f_4509_1]) ).

fof(f_4509_3,plain,
    ( ! [U_18602,U_18603] :
        ( c_List_Oupto(U_18602,U_18603) = c_List_Olist_ONil(tc_Int_Oint)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18602),U_18603))
        | ~ sP1159(U_18602,U_18603) )
    & ! [U_18602,U_18603] :
        ( c_List_Oupto(U_18602,U_18603) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_18602),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18602),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_18603))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18602),U_18603))
        | ~ sP1159(U_18602,U_18603) )
    & ! [U_18602,U_18603] :
        ( sP1159(U_18602,U_18603)
        | ~ 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_18602),U_18603))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1159])],[f_4509_2]) ).

cnf(f_4509_4,plain,
    ( sP1159(U_18602,U_18603)
    | ~ 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_18602),U_18603))) ),
    inference(clausify,[status(thm)],[f_4509_3]) ).

cnf(f_4509_5,plain,
    ( c_List_Oupto(U_18602,U_18603) = hAPP(hAPP(c_List_Olist_OCons(tc_Int_Oint),U_18602),c_List_Oupto(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18602),c_Groups_Oone__class_Oone(tc_Int_Oint)),U_18603))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18602),U_18603))
    | ~ sP1159(U_18602,U_18603) ),
    inference(clausify,[status(thm)],[f_4509_3]) ).

cnf(f_4509_6,plain,
    ( c_List_Oupto(U_18602,U_18603) = c_List_Olist_ONil(tc_Int_Oint)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18602),U_18603))
    | ~ sP1159(U_18602,U_18603) ),
    inference(clausify,[status(thm)],[f_4509_3]) ).

fof(f_4510_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_4510_2,plain,
    ! [U_18608,U_18607,U_18606,U_18605,U_18604] :
      ( ( hAPP(c_Lazy__Sequence_Oanamorph(U_18605,U_18606,U_18607,U_18604),U_18608) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(U_18606),U_18605),tc_prod(U_18606,U_18605),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18606),U_18605),c_List_Olist_ONil(U_18606)),U_18608),hAPP(c_Product__Type_Oprod_Oprod__case(U_18606,U_18605,tc_prod(tc_List_Olist(U_18606),U_18605)),hAPP(hAPP(c_COMBC(U_18606,tc_fun(U_18605,tc_prod(tc_List_Olist(U_18606),U_18605)),tc_fun(U_18605,tc_prod(tc_List_Olist(U_18606),U_18605))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(U_18606),U_18605),tc_prod(tc_List_Olist(U_18606),U_18605)),tc_fun(tc_fun(U_18605,tc_prod(tc_List_Olist(U_18606),U_18605)),tc_fun(U_18605,tc_prod(tc_List_Olist(U_18606),U_18605))),U_18606),c_COMBB(tc_prod(tc_List_Olist(U_18606),U_18605),tc_prod(tc_List_Olist(U_18606),U_18605),U_18605)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18606),tc_fun(U_18605,tc_prod(tc_List_Olist(U_18606),U_18605))),tc_fun(tc_prod(tc_List_Olist(U_18606),U_18605),tc_prod(tc_List_Olist(U_18606),U_18605)),U_18606),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_18606),U_18605,tc_prod(tc_List_Olist(U_18606),U_18605))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18606),tc_List_Olist(U_18606)),tc_fun(tc_List_Olist(U_18606),tc_fun(U_18605,tc_prod(tc_List_Olist(U_18606),U_18605))),U_18606),hAPP(c_COMBB(tc_List_Olist(U_18606),tc_fun(U_18605,tc_prod(tc_List_Olist(U_18606),U_18605)),tc_List_Olist(U_18606)),c_Product__Type_OPair(tc_List_Olist(U_18606),U_18605))),c_List_Olist_OCons(U_18606))))),c_Lazy__Sequence_Oanamorph(U_18605,U_18606,U_18607,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_18604),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(U_18607,U_18608))
        | U_18604 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
      & ( hAPP(c_Lazy__Sequence_Oanamorph(U_18605,U_18606,U_18607,U_18604),U_18608) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18606),U_18605),c_List_Olist_ONil(U_18606)),U_18608)
        | U_18604 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(variable_rename,[status(thm)],[f_4510_1]) ).

fof(f_4510_3,plain,
    ( ! [U_18618,U_18616,U_18614,U_18612,U_18610] :
        ( hAPP(c_Lazy__Sequence_Oanamorph(U_18612,U_18614,U_18616,U_18610),U_18618) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(U_18614),U_18612),tc_prod(U_18614,U_18612),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18614),U_18612),c_List_Olist_ONil(U_18614)),U_18618),hAPP(c_Product__Type_Oprod_Oprod__case(U_18614,U_18612,tc_prod(tc_List_Olist(U_18614),U_18612)),hAPP(hAPP(c_COMBC(U_18614,tc_fun(U_18612,tc_prod(tc_List_Olist(U_18614),U_18612)),tc_fun(U_18612,tc_prod(tc_List_Olist(U_18614),U_18612))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(U_18614),U_18612),tc_prod(tc_List_Olist(U_18614),U_18612)),tc_fun(tc_fun(U_18612,tc_prod(tc_List_Olist(U_18614),U_18612)),tc_fun(U_18612,tc_prod(tc_List_Olist(U_18614),U_18612))),U_18614),c_COMBB(tc_prod(tc_List_Olist(U_18614),U_18612),tc_prod(tc_List_Olist(U_18614),U_18612),U_18612)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18614),tc_fun(U_18612,tc_prod(tc_List_Olist(U_18614),U_18612))),tc_fun(tc_prod(tc_List_Olist(U_18614),U_18612),tc_prod(tc_List_Olist(U_18614),U_18612)),U_18614),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_18614),U_18612,tc_prod(tc_List_Olist(U_18614),U_18612))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18614),tc_List_Olist(U_18614)),tc_fun(tc_List_Olist(U_18614),tc_fun(U_18612,tc_prod(tc_List_Olist(U_18614),U_18612))),U_18614),hAPP(c_COMBB(tc_List_Olist(U_18614),tc_fun(U_18612,tc_prod(tc_List_Olist(U_18614),U_18612)),tc_List_Olist(U_18614)),c_Product__Type_OPair(tc_List_Olist(U_18614),U_18612))),c_List_Olist_OCons(U_18614))))),c_Lazy__Sequence_Oanamorph(U_18612,U_18614,U_18616,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_18610),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(U_18616,U_18618))
        | U_18610 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_18617,U_18615,U_18613,U_18611,U_18609] :
        ( hAPP(c_Lazy__Sequence_Oanamorph(U_18611,U_18613,U_18615,U_18609),U_18617) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18613),U_18611),c_List_Olist_ONil(U_18613)),U_18617)
        | U_18609 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(miniscope,[status(thm)],[f_4510_2]) ).

fof(f_4510_4,plain,
    ( ! [U_18610,U_18616,U_18612,U_18614,U_18618] :
        ( hAPP(c_Lazy__Sequence_Oanamorph(U_18612,U_18614,U_18616,U_18610),U_18618) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(U_18614),U_18612),tc_prod(U_18614,U_18612),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18614),U_18612),c_List_Olist_ONil(U_18614)),U_18618),hAPP(c_Product__Type_Oprod_Oprod__case(U_18614,U_18612,tc_prod(tc_List_Olist(U_18614),U_18612)),hAPP(hAPP(c_COMBC(U_18614,tc_fun(U_18612,tc_prod(tc_List_Olist(U_18614),U_18612)),tc_fun(U_18612,tc_prod(tc_List_Olist(U_18614),U_18612))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(U_18614),U_18612),tc_prod(tc_List_Olist(U_18614),U_18612)),tc_fun(tc_fun(U_18612,tc_prod(tc_List_Olist(U_18614),U_18612)),tc_fun(U_18612,tc_prod(tc_List_Olist(U_18614),U_18612))),U_18614),c_COMBB(tc_prod(tc_List_Olist(U_18614),U_18612),tc_prod(tc_List_Olist(U_18614),U_18612),U_18612)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18614),tc_fun(U_18612,tc_prod(tc_List_Olist(U_18614),U_18612))),tc_fun(tc_prod(tc_List_Olist(U_18614),U_18612),tc_prod(tc_List_Olist(U_18614),U_18612)),U_18614),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_18614),U_18612,tc_prod(tc_List_Olist(U_18614),U_18612))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18614),tc_List_Olist(U_18614)),tc_fun(tc_List_Olist(U_18614),tc_fun(U_18612,tc_prod(tc_List_Olist(U_18614),U_18612))),U_18614),hAPP(c_COMBB(tc_List_Olist(U_18614),tc_fun(U_18612,tc_prod(tc_List_Olist(U_18614),U_18612)),tc_List_Olist(U_18614)),c_Product__Type_OPair(tc_List_Olist(U_18614),U_18612))),c_List_Olist_OCons(U_18614))))),c_Lazy__Sequence_Oanamorph(U_18612,U_18614,U_18616,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_18610),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(U_18616,U_18618))
        | U_18610 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) )
    & ! [U_18609,U_18611,U_18617,U_18613,U_18615] :
        ( hAPP(c_Lazy__Sequence_Oanamorph(U_18611,U_18613,U_18615,U_18609),U_18617) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18613),U_18611),c_List_Olist_ONil(U_18613)),U_18617)
        | U_18609 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ) ),
    inference(definitional_conversion,[status(esa)],[f_4510_3]) ).

cnf(f_4510_5,plain,
    ( hAPP(c_Lazy__Sequence_Oanamorph(U_18611,U_18613,U_18615,U_18609),U_18617) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18613),U_18611),c_List_Olist_ONil(U_18613)),U_18617)
    | U_18609 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_4510_4]) ).

cnf(f_4510_6,plain,
    ( hAPP(c_Lazy__Sequence_Oanamorph(U_18612,U_18614,U_18616,U_18610),U_18618) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(U_18614),U_18612),tc_prod(U_18614,U_18612),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18614),U_18612),c_List_Olist_ONil(U_18614)),U_18618),hAPP(c_Product__Type_Oprod_Oprod__case(U_18614,U_18612,tc_prod(tc_List_Olist(U_18614),U_18612)),hAPP(hAPP(c_COMBC(U_18614,tc_fun(U_18612,tc_prod(tc_List_Olist(U_18614),U_18612)),tc_fun(U_18612,tc_prod(tc_List_Olist(U_18614),U_18612))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(U_18614),U_18612),tc_prod(tc_List_Olist(U_18614),U_18612)),tc_fun(tc_fun(U_18612,tc_prod(tc_List_Olist(U_18614),U_18612)),tc_fun(U_18612,tc_prod(tc_List_Olist(U_18614),U_18612))),U_18614),c_COMBB(tc_prod(tc_List_Olist(U_18614),U_18612),tc_prod(tc_List_Olist(U_18614),U_18612),U_18612)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18614),tc_fun(U_18612,tc_prod(tc_List_Olist(U_18614),U_18612))),tc_fun(tc_prod(tc_List_Olist(U_18614),U_18612),tc_prod(tc_List_Olist(U_18614),U_18612)),U_18614),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_18614),U_18612,tc_prod(tc_List_Olist(U_18614),U_18612))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_18614),tc_List_Olist(U_18614)),tc_fun(tc_List_Olist(U_18614),tc_fun(U_18612,tc_prod(tc_List_Olist(U_18614),U_18612))),U_18614),hAPP(c_COMBB(tc_List_Olist(U_18614),tc_fun(U_18612,tc_prod(tc_List_Olist(U_18614),U_18612)),tc_List_Olist(U_18614)),c_Product__Type_OPair(tc_List_Olist(U_18614),U_18612))),c_List_Olist_OCons(U_18614))))),c_Lazy__Sequence_Oanamorph(U_18612,U_18614,U_18616,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),U_18610),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(U_18616,U_18618))
    | U_18610 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) ),
    inference(clausify,[status(thm)],[f_4510_4]) ).

fof(f_4511_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_4511_2,plain,
    ! [U_18619] : c_List_Olistset(U_18619,c_List_Olist_ONil(tc_fun(U_18619,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18619)),c_List_Olist_ONil(U_18619)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18619),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4511_1]) ).

fof(f_4511_3,plain,
    ! [U_18619] : c_List_Olistset(U_18619,c_List_Olist_ONil(tc_fun(U_18619,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18619)),c_List_Olist_ONil(U_18619)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18619),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_4511_2]) ).

cnf(f_4511_4,plain,
    c_List_Olistset(U_18619,c_List_Olist_ONil(tc_fun(U_18619,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_18619)),c_List_Olist_ONil(U_18619)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_18619),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4511_3]) ).

fof(f_4512_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_4512_2,plain,
    ! [U_18624,U_18623,U_18622,U_18621,U_18620] : hAPP(hAPP(c_List_Ozip(U_18620,U_18621),hAPP(hAPP(c_List_Olist_OCons(U_18620),U_18622),U_18623)),U_18624) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_18620,U_18621)),U_18621,c_List_Olist_ONil(tc_prod(U_18620,U_18621)),hAPP(hAPP(c_COMBC(U_18621,tc_fun(tc_List_Olist(U_18621),tc_List_Olist(tc_prod(U_18620,U_18621))),tc_fun(tc_List_Olist(U_18621),tc_List_Olist(tc_prod(U_18620,U_18621)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_18620,U_18621)),tc_List_Olist(tc_prod(U_18620,U_18621))),tc_fun(tc_fun(tc_List_Olist(U_18621),tc_List_Olist(tc_prod(U_18620,U_18621))),tc_fun(tc_List_Olist(U_18621),tc_List_Olist(tc_prod(U_18620,U_18621)))),U_18621),c_COMBB(tc_List_Olist(tc_prod(U_18620,U_18621)),tc_List_Olist(tc_prod(U_18620,U_18621)),tc_List_Olist(U_18621))),hAPP(hAPP(c_COMBB(tc_prod(U_18620,U_18621),tc_fun(tc_List_Olist(tc_prod(U_18620,U_18621)),tc_List_Olist(tc_prod(U_18620,U_18621))),U_18621),c_List_Olist_OCons(tc_prod(U_18620,U_18621))),hAPP(c_Product__Type_OPair(U_18620,U_18621),U_18622)))),hAPP(c_List_Ozip(U_18620,U_18621),U_18623))),U_18624),
    inference(variable_rename,[status(thm)],[f_4512_1]) ).

fof(f_4512_3,plain,
    ! [U_18620,U_18621,U_18622,U_18623,U_18624] : hAPP(hAPP(c_List_Ozip(U_18620,U_18621),hAPP(hAPP(c_List_Olist_OCons(U_18620),U_18622),U_18623)),U_18624) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_18620,U_18621)),U_18621,c_List_Olist_ONil(tc_prod(U_18620,U_18621)),hAPP(hAPP(c_COMBC(U_18621,tc_fun(tc_List_Olist(U_18621),tc_List_Olist(tc_prod(U_18620,U_18621))),tc_fun(tc_List_Olist(U_18621),tc_List_Olist(tc_prod(U_18620,U_18621)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_18620,U_18621)),tc_List_Olist(tc_prod(U_18620,U_18621))),tc_fun(tc_fun(tc_List_Olist(U_18621),tc_List_Olist(tc_prod(U_18620,U_18621))),tc_fun(tc_List_Olist(U_18621),tc_List_Olist(tc_prod(U_18620,U_18621)))),U_18621),c_COMBB(tc_List_Olist(tc_prod(U_18620,U_18621)),tc_List_Olist(tc_prod(U_18620,U_18621)),tc_List_Olist(U_18621))),hAPP(hAPP(c_COMBB(tc_prod(U_18620,U_18621),tc_fun(tc_List_Olist(tc_prod(U_18620,U_18621)),tc_List_Olist(tc_prod(U_18620,U_18621))),U_18621),c_List_Olist_OCons(tc_prod(U_18620,U_18621))),hAPP(c_Product__Type_OPair(U_18620,U_18621),U_18622)))),hAPP(c_List_Ozip(U_18620,U_18621),U_18623))),U_18624),
    inference(definitional_conversion,[status(esa)],[f_4512_2]) ).

cnf(f_4512_4,plain,
    hAPP(hAPP(c_List_Ozip(U_18620,U_18621),hAPP(hAPP(c_List_Olist_OCons(U_18620),U_18622),U_18623)),U_18624) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_18620,U_18621)),U_18621,c_List_Olist_ONil(tc_prod(U_18620,U_18621)),hAPP(hAPP(c_COMBC(U_18621,tc_fun(tc_List_Olist(U_18621),tc_List_Olist(tc_prod(U_18620,U_18621))),tc_fun(tc_List_Olist(U_18621),tc_List_Olist(tc_prod(U_18620,U_18621)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_18620,U_18621)),tc_List_Olist(tc_prod(U_18620,U_18621))),tc_fun(tc_fun(tc_List_Olist(U_18621),tc_List_Olist(tc_prod(U_18620,U_18621))),tc_fun(tc_List_Olist(U_18621),tc_List_Olist(tc_prod(U_18620,U_18621)))),U_18621),c_COMBB(tc_List_Olist(tc_prod(U_18620,U_18621)),tc_List_Olist(tc_prod(U_18620,U_18621)),tc_List_Olist(U_18621))),hAPP(hAPP(c_COMBB(tc_prod(U_18620,U_18621),tc_fun(tc_List_Olist(tc_prod(U_18620,U_18621)),tc_List_Olist(tc_prod(U_18620,U_18621))),U_18621),c_List_Olist_OCons(tc_prod(U_18620,U_18621))),hAPP(c_Product__Type_OPair(U_18620,U_18621),U_18622)))),hAPP(c_List_Ozip(U_18620,U_18621),U_18623))),U_18624),
    inference(clausify,[status(thm)],[f_4512_3]) ).

fof(f_4513_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_4513_2,plain,
    ! [U_18630,U_18629,U_18628,U_18627,U_18626,U_18625] : hAPP(c_List_Olist_Olist__case(U_18625,U_18626,U_18627,U_18628),hAPP(hAPP(c_List_Olist_OCons(U_18626),U_18629),U_18630)) = hAPP(hAPP(U_18628,U_18629),U_18630),
    inference(variable_rename,[status(thm)],[f_4513_1]) ).

fof(f_4513_3,plain,
    ! [U_18625,U_18626,U_18627,U_18628,U_18629,U_18630] : hAPP(c_List_Olist_Olist__case(U_18625,U_18626,U_18627,U_18628),hAPP(hAPP(c_List_Olist_OCons(U_18626),U_18629),U_18630)) = hAPP(hAPP(U_18628,U_18629),U_18630),
    inference(definitional_conversion,[status(esa)],[f_4513_2]) ).

cnf(f_4513_4,plain,
    hAPP(c_List_Olist_Olist__case(U_18625,U_18626,U_18627,U_18628),hAPP(hAPP(c_List_Olist_OCons(U_18626),U_18629),U_18630)) = hAPP(hAPP(U_18628,U_18629),U_18630),
    inference(clausify,[status(thm)],[f_4513_3]) ).

fof(f_4514_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_4514_2,plain,
    ! [U_18634,U_18633,U_18632,U_18631] : hAPP(c_List_Olist_Olist__case(U_18631,U_18632,U_18633,U_18634),c_List_Olist_ONil(U_18632)) = U_18633,
    inference(variable_rename,[status(thm)],[f_4514_1]) ).

fof(f_4514_3,plain,
    ! [U_18631,U_18632,U_18633,U_18634] : hAPP(c_List_Olist_Olist__case(U_18631,U_18632,U_18633,U_18634),c_List_Olist_ONil(U_18632)) = U_18633,
    inference(definitional_conversion,[status(esa)],[f_4514_2]) ).

cnf(f_4514_4,plain,
    hAPP(c_List_Olist_Olist__case(U_18631,U_18632,U_18633,U_18634),c_List_Olist_ONil(U_18632)) = U_18633,
    inference(clausify,[status(thm)],[f_4514_3]) ).

fof(f_4515_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_4515_2,plain,
    ! [U_18637,U_18636,U_18635] : c_List_Olistset(U_18635,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18635,tc_HOL_Obool)),U_18636),U_18637)) = c_List_Oset__Cons(U_18635,U_18636,c_List_Olistset(U_18635,U_18637)),
    inference(variable_rename,[status(thm)],[f_4515_1]) ).

fof(f_4515_3,plain,
    ! [U_18635,U_18636,U_18637] : c_List_Olistset(U_18635,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18635,tc_HOL_Obool)),U_18636),U_18637)) = c_List_Oset__Cons(U_18635,U_18636,c_List_Olistset(U_18635,U_18637)),
    inference(definitional_conversion,[status(esa)],[f_4515_2]) ).

cnf(f_4515_4,plain,
    c_List_Olistset(U_18635,hAPP(hAPP(c_List_Olist_OCons(tc_fun(U_18635,tc_HOL_Obool)),U_18636),U_18637)) = c_List_Oset__Cons(U_18635,U_18636,c_List_Olistset(U_18635,U_18637)),
    inference(clausify,[status(thm)],[f_4515_3]) ).

fof(f_4516_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_4516_2,plain,
    ! [U_18642,U_18641,U_18640,U_18639,U_18638] : hAPP(hAPP(c_List_Ozip(U_18638,U_18639),U_18640),hAPP(hAPP(c_List_Olist_OCons(U_18639),U_18641),U_18642)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_18638,U_18639)),U_18638,c_List_Olist_ONil(tc_prod(U_18638,U_18639)),hAPP(hAPP(c_COMBC(U_18638,tc_fun(tc_List_Olist(U_18638),tc_List_Olist(tc_prod(U_18638,U_18639))),tc_fun(tc_List_Olist(U_18638),tc_List_Olist(tc_prod(U_18638,U_18639)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_18638,U_18639)),tc_List_Olist(tc_prod(U_18638,U_18639))),tc_fun(tc_fun(tc_List_Olist(U_18638),tc_List_Olist(tc_prod(U_18638,U_18639))),tc_fun(tc_List_Olist(U_18638),tc_List_Olist(tc_prod(U_18638,U_18639)))),U_18638),c_COMBB(tc_List_Olist(tc_prod(U_18638,U_18639)),tc_List_Olist(tc_prod(U_18638,U_18639)),tc_List_Olist(U_18638))),hAPP(hAPP(c_COMBB(tc_prod(U_18638,U_18639),tc_fun(tc_List_Olist(tc_prod(U_18638,U_18639)),tc_List_Olist(tc_prod(U_18638,U_18639))),U_18638),c_List_Olist_OCons(tc_prod(U_18638,U_18639))),hAPP(hAPP(c_COMBC(U_18638,U_18639,tc_prod(U_18638,U_18639)),c_Product__Type_OPair(U_18638,U_18639)),U_18641)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18638),tc_List_Olist(U_18639),tc_List_Olist(tc_prod(U_18638,U_18639))),c_List_Ozip(U_18638,U_18639)),U_18642))),U_18640),
    inference(variable_rename,[status(thm)],[f_4516_1]) ).

fof(f_4516_3,plain,
    ! [U_18638,U_18639,U_18640,U_18641,U_18642] : hAPP(hAPP(c_List_Ozip(U_18638,U_18639),U_18640),hAPP(hAPP(c_List_Olist_OCons(U_18639),U_18641),U_18642)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_18638,U_18639)),U_18638,c_List_Olist_ONil(tc_prod(U_18638,U_18639)),hAPP(hAPP(c_COMBC(U_18638,tc_fun(tc_List_Olist(U_18638),tc_List_Olist(tc_prod(U_18638,U_18639))),tc_fun(tc_List_Olist(U_18638),tc_List_Olist(tc_prod(U_18638,U_18639)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_18638,U_18639)),tc_List_Olist(tc_prod(U_18638,U_18639))),tc_fun(tc_fun(tc_List_Olist(U_18638),tc_List_Olist(tc_prod(U_18638,U_18639))),tc_fun(tc_List_Olist(U_18638),tc_List_Olist(tc_prod(U_18638,U_18639)))),U_18638),c_COMBB(tc_List_Olist(tc_prod(U_18638,U_18639)),tc_List_Olist(tc_prod(U_18638,U_18639)),tc_List_Olist(U_18638))),hAPP(hAPP(c_COMBB(tc_prod(U_18638,U_18639),tc_fun(tc_List_Olist(tc_prod(U_18638,U_18639)),tc_List_Olist(tc_prod(U_18638,U_18639))),U_18638),c_List_Olist_OCons(tc_prod(U_18638,U_18639))),hAPP(hAPP(c_COMBC(U_18638,U_18639,tc_prod(U_18638,U_18639)),c_Product__Type_OPair(U_18638,U_18639)),U_18641)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18638),tc_List_Olist(U_18639),tc_List_Olist(tc_prod(U_18638,U_18639))),c_List_Ozip(U_18638,U_18639)),U_18642))),U_18640),
    inference(definitional_conversion,[status(esa)],[f_4516_2]) ).

cnf(f_4516_4,plain,
    hAPP(hAPP(c_List_Ozip(U_18638,U_18639),U_18640),hAPP(hAPP(c_List_Olist_OCons(U_18639),U_18641),U_18642)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(tc_prod(U_18638,U_18639)),U_18638,c_List_Olist_ONil(tc_prod(U_18638,U_18639)),hAPP(hAPP(c_COMBC(U_18638,tc_fun(tc_List_Olist(U_18638),tc_List_Olist(tc_prod(U_18638,U_18639))),tc_fun(tc_List_Olist(U_18638),tc_List_Olist(tc_prod(U_18638,U_18639)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(tc_prod(U_18638,U_18639)),tc_List_Olist(tc_prod(U_18638,U_18639))),tc_fun(tc_fun(tc_List_Olist(U_18638),tc_List_Olist(tc_prod(U_18638,U_18639))),tc_fun(tc_List_Olist(U_18638),tc_List_Olist(tc_prod(U_18638,U_18639)))),U_18638),c_COMBB(tc_List_Olist(tc_prod(U_18638,U_18639)),tc_List_Olist(tc_prod(U_18638,U_18639)),tc_List_Olist(U_18638))),hAPP(hAPP(c_COMBB(tc_prod(U_18638,U_18639),tc_fun(tc_List_Olist(tc_prod(U_18638,U_18639)),tc_List_Olist(tc_prod(U_18638,U_18639))),U_18638),c_List_Olist_OCons(tc_prod(U_18638,U_18639))),hAPP(hAPP(c_COMBC(U_18638,U_18639,tc_prod(U_18638,U_18639)),c_Product__Type_OPair(U_18638,U_18639)),U_18641)))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_18638),tc_List_Olist(U_18639),tc_List_Olist(tc_prod(U_18638,U_18639))),c_List_Ozip(U_18638,U_18639)),U_18642))),U_18640),
    inference(clausify,[status(thm)],[f_4516_3]) ).

fof(f_4517_1,plain,
    ! [V_Pa_2,V_a1_2,V_a0_2] :
      ( hBOOL(hAPP(hAPP(V_Pa_2,V_a0_2),V_a1_2))
      | ? [B_i,B_j] :
          ( ~ hBOOL(hAPP(hAPP(V_Pa_2,B_i),B_j))
          & ( hBOOL(hAPP(hAPP(V_Pa_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_4517_2,plain,
    ! [U_18647,U_18646,U_18645] :
      ( hBOOL(hAPP(hAPP(U_18647,U_18645),U_18646))
      | ? [U_18644,U_18643] :
          ( ~ hBOOL(hAPP(hAPP(U_18647,U_18644),U_18643))
          & ( hBOOL(hAPP(hAPP(U_18647,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),U_18644),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_18643))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),U_18644),U_18643)) )
          & 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_18644),U_18643))) )
      | ~ 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_18645),U_18646))) ),
    inference(variable_rename,[status(thm)],[f_4517_1]) ).

fof(f_4517_3,plain,
    ! [U_18647,U_18646,U_18645] :
      ( hBOOL(hAPP(hAPP(U_18647,U_18645),U_18646))
      | ? [U_18643] :
          ( ~ hBOOL(hAPP(hAPP(U_18647,sK464(U_18647,U_18646,U_18645)),U_18643))
          & ( hBOOL(hAPP(hAPP(U_18647,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK464(U_18647,U_18646,U_18645)),c_Groups_Oone__class_Oone(tc_Int_Oint))),U_18643))
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK464(U_18647,U_18646,U_18645)),U_18643)) )
          & 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),sK464(U_18647,U_18646,U_18645)),U_18643))) )
      | ~ 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_18645),U_18646))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK464]),skolemize(U_18644,sK464(U_18647,U_18646,U_18645))],[f_4517_2]) ).

fof(f_4517_4,plain,
    ! [U_18647,U_18646,U_18645] :
      ( hBOOL(hAPP(hAPP(U_18647,U_18645),U_18646))
      | ( ~ hBOOL(hAPP(hAPP(U_18647,sK464(U_18647,U_18646,U_18645)),sK465(U_18647,U_18646,U_18645)))
        & ( hBOOL(hAPP(hAPP(U_18647,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK464(U_18647,U_18646,U_18645)),c_Groups_Oone__class_Oone(tc_Int_Oint))),sK465(U_18647,U_18646,U_18645)))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK464(U_18647,U_18646,U_18645)),sK465(U_18647,U_18646,U_18645))) )
        & 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),sK464(U_18647,U_18646,U_18645)),sK465(U_18647,U_18646,U_18645)))) )
      | ~ 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_18645),U_18646))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK465]),skolemize(U_18643,sK465(U_18647,U_18646,U_18645))],[f_4517_3]) ).

fof(f_4517_5,plain,
    ( ! [U_18645,U_18646,U_18647] :
        ( ~ hBOOL(hAPP(hAPP(U_18647,sK464(U_18647,U_18646,U_18645)),sK465(U_18647,U_18646,U_18645)))
        | ~ sP1160(U_18645,U_18646,U_18647) )
    & ! [U_18645,U_18646,U_18647] :
        ( hBOOL(hAPP(hAPP(U_18647,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK464(U_18647,U_18646,U_18645)),c_Groups_Oone__class_Oone(tc_Int_Oint))),sK465(U_18647,U_18646,U_18645)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK464(U_18647,U_18646,U_18645)),sK465(U_18647,U_18646,U_18645)))
        | ~ sP1160(U_18645,U_18646,U_18647) )
    & ! [U_18645,U_18646,U_18647] :
        ( 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),sK464(U_18647,U_18646,U_18645)),sK465(U_18647,U_18646,U_18645))))
        | ~ sP1160(U_18645,U_18646,U_18647) )
    & ! [U_18645,U_18646,U_18647] :
        ( hBOOL(hAPP(hAPP(U_18647,U_18645),U_18646))
        | sP1160(U_18645,U_18646,U_18647)
        | ~ 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_18645),U_18646))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1160])],[f_4517_4]) ).

cnf(f_4517_6,plain,
    ( hBOOL(hAPP(hAPP(U_18647,U_18645),U_18646))
    | sP1160(U_18645,U_18646,U_18647)
    | ~ 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_18645),U_18646))) ),
    inference(clausify,[status(thm)],[f_4517_5]) ).

cnf(f_4517_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),sK464(U_18647,U_18646,U_18645)),sK465(U_18647,U_18646,U_18645))))
    | ~ sP1160(U_18645,U_18646,U_18647) ),
    inference(clausify,[status(thm)],[f_4517_5]) ).

cnf(f_4517_8,plain,
    ( hBOOL(hAPP(hAPP(U_18647,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),sK464(U_18647,U_18646,U_18645)),c_Groups_Oone__class_Oone(tc_Int_Oint))),sK465(U_18647,U_18646,U_18645)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),sK464(U_18647,U_18646,U_18645)),sK465(U_18647,U_18646,U_18645)))
    | ~ sP1160(U_18645,U_18646,U_18647) ),
    inference(clausify,[status(thm)],[f_4517_5]) ).

cnf(f_4517_9,plain,
    ( ~ hBOOL(hAPP(hAPP(U_18647,sK464(U_18647,U_18646,U_18645)),sK465(U_18647,U_18646,U_18645)))
    | ~ sP1160(U_18645,U_18646,U_18647) ),
    inference(clausify,[status(thm)],[f_4517_5]) ).

fof(f_4518_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_4518_2,plain,
    ! [U_18654,U_18653,U_18652,U_18651,U_18650,U_18649,U_18648] :
      ( ( c_Map_Omap__upds(U_18648,U_18650,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18648,tc_Option_Ooption(U_18650)),U_18653),U_18649),hAPP(c_Option_Ooption_OSome(U_18650),U_18654)),U_18652,U_18651) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18648,tc_Option_Ooption(U_18650)),c_Map_Omap__upds(U_18648,U_18650,U_18653,U_18652,U_18651)),U_18649),hAPP(c_Option_Ooption_OSome(U_18650),U_18654))
        | hBOOL(hAPP(hAPP(c_member(U_18648),U_18649),hAPP(c_List_Oset(U_18648),hAPP(hAPP(c_List_Otake(U_18648),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18650)),U_18651)),U_18652)))) )
      & ( c_Map_Omap__upds(U_18648,U_18650,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18648,tc_Option_Ooption(U_18650)),U_18653),U_18649),hAPP(c_Option_Ooption_OSome(U_18650),U_18654)),U_18652,U_18651) = c_Map_Omap__upds(U_18648,U_18650,U_18653,U_18652,U_18651)
        | ~ hBOOL(hAPP(hAPP(c_member(U_18648),U_18649),hAPP(c_List_Oset(U_18648),hAPP(hAPP(c_List_Otake(U_18648),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18650)),U_18651)),U_18652)))) ) ),
    inference(variable_rename,[status(thm)],[f_4518_1]) ).

fof(f_4518_3,plain,
    ( ! [U_18668,U_18666,U_18664,U_18662,U_18660,U_18658,U_18656] :
        ( c_Map_Omap__upds(U_18656,U_18660,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18656,tc_Option_Ooption(U_18660)),U_18666),U_18658),hAPP(c_Option_Ooption_OSome(U_18660),U_18668)),U_18664,U_18662) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18656,tc_Option_Ooption(U_18660)),c_Map_Omap__upds(U_18656,U_18660,U_18666,U_18664,U_18662)),U_18658),hAPP(c_Option_Ooption_OSome(U_18660),U_18668))
        | hBOOL(hAPP(hAPP(c_member(U_18656),U_18658),hAPP(c_List_Oset(U_18656),hAPP(hAPP(c_List_Otake(U_18656),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18660)),U_18662)),U_18664)))) )
    & ! [U_18667,U_18665,U_18663,U_18661,U_18659,U_18657,U_18655] :
        ( c_Map_Omap__upds(U_18655,U_18659,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18655,tc_Option_Ooption(U_18659)),U_18665),U_18657),hAPP(c_Option_Ooption_OSome(U_18659),U_18667)),U_18663,U_18661) = c_Map_Omap__upds(U_18655,U_18659,U_18665,U_18663,U_18661)
        | ~ hBOOL(hAPP(hAPP(c_member(U_18655),U_18657),hAPP(c_List_Oset(U_18655),hAPP(hAPP(c_List_Otake(U_18655),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18659)),U_18661)),U_18663)))) ) ),
    inference(miniscope,[status(thm)],[f_4518_2]) ).

fof(f_4518_4,plain,
    ( ! [U_18656,U_18658,U_18660,U_18662,U_18664,U_18666,U_18668] :
        ( c_Map_Omap__upds(U_18656,U_18660,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18656,tc_Option_Ooption(U_18660)),U_18666),U_18658),hAPP(c_Option_Ooption_OSome(U_18660),U_18668)),U_18664,U_18662) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18656,tc_Option_Ooption(U_18660)),c_Map_Omap__upds(U_18656,U_18660,U_18666,U_18664,U_18662)),U_18658),hAPP(c_Option_Ooption_OSome(U_18660),U_18668))
        | hBOOL(hAPP(hAPP(c_member(U_18656),U_18658),hAPP(c_List_Oset(U_18656),hAPP(hAPP(c_List_Otake(U_18656),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18660)),U_18662)),U_18664)))) )
    & ! [U_18659,U_18661,U_18657,U_18655,U_18663,U_18665,U_18667] :
        ( c_Map_Omap__upds(U_18655,U_18659,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18655,tc_Option_Ooption(U_18659)),U_18665),U_18657),hAPP(c_Option_Ooption_OSome(U_18659),U_18667)),U_18663,U_18661) = c_Map_Omap__upds(U_18655,U_18659,U_18665,U_18663,U_18661)
        | ~ hBOOL(hAPP(hAPP(c_member(U_18655),U_18657),hAPP(c_List_Oset(U_18655),hAPP(hAPP(c_List_Otake(U_18655),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18659)),U_18661)),U_18663)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4518_3]) ).

cnf(f_4518_5,plain,
    ( c_Map_Omap__upds(U_18655,U_18659,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18655,tc_Option_Ooption(U_18659)),U_18665),U_18657),hAPP(c_Option_Ooption_OSome(U_18659),U_18667)),U_18663,U_18661) = c_Map_Omap__upds(U_18655,U_18659,U_18665,U_18663,U_18661)
    | ~ hBOOL(hAPP(hAPP(c_member(U_18655),U_18657),hAPP(c_List_Oset(U_18655),hAPP(hAPP(c_List_Otake(U_18655),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18659)),U_18661)),U_18663)))) ),
    inference(clausify,[status(thm)],[f_4518_4]) ).

cnf(f_4518_6,plain,
    ( c_Map_Omap__upds(U_18656,U_18660,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18656,tc_Option_Ooption(U_18660)),U_18666),U_18658),hAPP(c_Option_Ooption_OSome(U_18660),U_18668)),U_18664,U_18662) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18656,tc_Option_Ooption(U_18660)),c_Map_Omap__upds(U_18656,U_18660,U_18666,U_18664,U_18662)),U_18658),hAPP(c_Option_Ooption_OSome(U_18660),U_18668))
    | hBOOL(hAPP(hAPP(c_member(U_18656),U_18658),hAPP(c_List_Oset(U_18656),hAPP(hAPP(c_List_Otake(U_18656),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18660)),U_18662)),U_18664)))) ),
    inference(clausify,[status(thm)],[f_4518_4]) ).

fof(f_4519_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_4519_2,plain,
    ! [U_18672,U_18671,U_18670,U_18669] : c_Map_Omap__upds(U_18669,U_18670,U_18671,c_List_Olist_ONil(U_18669),U_18672) = U_18671,
    inference(variable_rename,[status(thm)],[f_4519_1]) ).

fof(f_4519_3,plain,
    ! [U_18670,U_18671,U_18669,U_18672] : c_Map_Omap__upds(U_18669,U_18670,U_18671,c_List_Olist_ONil(U_18669),U_18672) = U_18671,
    inference(definitional_conversion,[status(esa)],[f_4519_2]) ).

cnf(f_4519_4,plain,
    c_Map_Omap__upds(U_18669,U_18670,U_18671,c_List_Olist_ONil(U_18669),U_18672) = U_18671,
    inference(clausify,[status(thm)],[f_4519_3]) ).

fof(f_4520_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_4520_2,plain,
    ! [U_18676,U_18675,U_18674,U_18673] : c_Map_Omap__upds(U_18673,U_18674,U_18675,U_18676,c_List_Olist_ONil(U_18674)) = U_18675,
    inference(variable_rename,[status(thm)],[f_4520_1]) ).

fof(f_4520_3,plain,
    ! [U_18674,U_18675,U_18673,U_18676] : c_Map_Omap__upds(U_18673,U_18674,U_18675,U_18676,c_List_Olist_ONil(U_18674)) = U_18675,
    inference(definitional_conversion,[status(esa)],[f_4520_2]) ).

cnf(f_4520_4,plain,
    c_Map_Omap__upds(U_18673,U_18674,U_18675,U_18676,c_List_Olist_ONil(U_18674)) = U_18675,
    inference(clausify,[status(thm)],[f_4520_3]) ).

fof(f_4521_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_4521_2,plain,
    ! [U_18682,U_18681,U_18680,U_18679,U_18678,U_18677] :
      ( hAPP(c_Map_Omap__upds(U_18677,U_18680,U_18681,U_18679,U_18682),U_18678) = hAPP(U_18681,U_18678)
      | hBOOL(hAPP(hAPP(c_member(U_18677),U_18678),hAPP(c_List_Oset(U_18677),U_18679))) ),
    inference(variable_rename,[status(thm)],[f_4521_1]) ).

fof(f_4521_3,plain,
    ! [U_18677,U_18678,U_18679,U_18680,U_18681,U_18682] :
      ( hAPP(c_Map_Omap__upds(U_18677,U_18680,U_18681,U_18679,U_18682),U_18678) = hAPP(U_18681,U_18678)
      | hBOOL(hAPP(hAPP(c_member(U_18677),U_18678),hAPP(c_List_Oset(U_18677),U_18679))) ),
    inference(definitional_conversion,[status(esa)],[f_4521_2]) ).

cnf(f_4521_4,plain,
    ( hAPP(c_Map_Omap__upds(U_18677,U_18680,U_18681,U_18679,U_18682),U_18678) = hAPP(U_18681,U_18678)
    | hBOOL(hAPP(hAPP(c_member(U_18677),U_18678),hAPP(c_List_Oset(U_18677),U_18679))) ),
    inference(clausify,[status(thm)],[f_4521_3]) ).

fof(f_4522_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_4522_2,plain,
    ! [U_18688,U_18687,U_18686,U_18685,U_18684,U_18683] : c_Map_Omap__add(U_18683,U_18684,U_18685,c_Map_Omap__upds(U_18683,U_18684,U_18686,U_18687,U_18688)) = c_Map_Omap__upds(U_18683,U_18684,c_Map_Omap__add(U_18683,U_18684,U_18685,U_18686),U_18687,U_18688),
    inference(variable_rename,[status(thm)],[f_4522_1]) ).

fof(f_4522_3,plain,
    ! [U_18684,U_18683,U_18685,U_18686,U_18687,U_18688] : c_Map_Omap__add(U_18683,U_18684,U_18685,c_Map_Omap__upds(U_18683,U_18684,U_18686,U_18687,U_18688)) = c_Map_Omap__upds(U_18683,U_18684,c_Map_Omap__add(U_18683,U_18684,U_18685,U_18686),U_18687,U_18688),
    inference(definitional_conversion,[status(esa)],[f_4522_2]) ).

cnf(f_4522_4,plain,
    c_Map_Omap__add(U_18683,U_18684,U_18685,c_Map_Omap__upds(U_18683,U_18684,U_18686,U_18687,U_18688)) = c_Map_Omap__upds(U_18683,U_18684,c_Map_Omap__add(U_18683,U_18684,U_18685,U_18686),U_18687,U_18688),
    inference(clausify,[status(thm)],[f_4522_3]) ).

fof(f_4523_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_4523_2,plain,
    ! [U_18695,U_18694,U_18693,U_18692,U_18691,U_18690,U_18689] : c_Map_Omap__upds(U_18689,U_18690,U_18691,hAPP(hAPP(c_List_Olist_OCons(U_18689),U_18692),U_18693),hAPP(hAPP(c_List_Olist_OCons(U_18690),U_18694),U_18695)) = c_Map_Omap__upds(U_18689,U_18690,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18689,tc_Option_Ooption(U_18690)),U_18691),U_18692),hAPP(c_Option_Ooption_OSome(U_18690),U_18694)),U_18693,U_18695),
    inference(variable_rename,[status(thm)],[f_4523_1]) ).

fof(f_4523_3,plain,
    ! [U_18689,U_18690,U_18691,U_18692,U_18693,U_18694,U_18695] : c_Map_Omap__upds(U_18689,U_18690,U_18691,hAPP(hAPP(c_List_Olist_OCons(U_18689),U_18692),U_18693),hAPP(hAPP(c_List_Olist_OCons(U_18690),U_18694),U_18695)) = c_Map_Omap__upds(U_18689,U_18690,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18689,tc_Option_Ooption(U_18690)),U_18691),U_18692),hAPP(c_Option_Ooption_OSome(U_18690),U_18694)),U_18693,U_18695),
    inference(definitional_conversion,[status(esa)],[f_4523_2]) ).

cnf(f_4523_4,plain,
    c_Map_Omap__upds(U_18689,U_18690,U_18691,hAPP(hAPP(c_List_Olist_OCons(U_18689),U_18692),U_18693),hAPP(hAPP(c_List_Olist_OCons(U_18690),U_18694),U_18695)) = c_Map_Omap__upds(U_18689,U_18690,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18689,tc_Option_Ooption(U_18690)),U_18691),U_18692),hAPP(c_Option_Ooption_OSome(U_18690),U_18694)),U_18693,U_18695),
    inference(clausify,[status(thm)],[f_4523_3]) ).

fof(f_4524_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_4524_2,plain,
    ! [U_18702,U_18701,U_18700,U_18699,U_18698,U_18697,U_18696] :
      ( c_Map_Omap__upds(U_18696,U_18699,U_18701,U_18697,hAPP(hAPP(c_List_Olist__update(U_18699,U_18700),U_18698),U_18702)) = c_Map_Omap__upds(U_18696,U_18699,U_18701,U_18697,U_18700)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18698),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18699)),U_18700)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18696)),U_18697)),U_18698)) ),
    inference(variable_rename,[status(thm)],[f_4524_1]) ).

fof(f_4524_3,plain,
    ! [U_18696,U_18697,U_18698,U_18699,U_18700,U_18701,U_18702] :
      ( c_Map_Omap__upds(U_18696,U_18699,U_18701,U_18697,hAPP(hAPP(c_List_Olist__update(U_18699,U_18700),U_18698),U_18702)) = c_Map_Omap__upds(U_18696,U_18699,U_18701,U_18697,U_18700)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18698),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18699)),U_18700)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18696)),U_18697)),U_18698)) ),
    inference(definitional_conversion,[status(esa)],[f_4524_2]) ).

cnf(f_4524_4,plain,
    ( c_Map_Omap__upds(U_18696,U_18699,U_18701,U_18697,hAPP(hAPP(c_List_Olist__update(U_18699,U_18700),U_18698),U_18702)) = c_Map_Omap__upds(U_18696,U_18699,U_18701,U_18697,U_18700)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18698),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18699)),U_18700)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18696)),U_18697)),U_18698)) ),
    inference(clausify,[status(thm)],[f_4524_3]) ).

fof(f_4525_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_4525_2,plain,
    ! [U_18709,U_18708,U_18707,U_18706,U_18705,U_18704,U_18703] :
      ( c_Map_Omap__upds(U_18703,U_18706,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18703,tc_Option_Ooption(U_18706)),U_18707),U_18704),hAPP(c_Option_Ooption_OSome(U_18706),U_18708)),U_18705,U_18709) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18703,tc_Option_Ooption(U_18706)),c_Map_Omap__upds(U_18703,U_18706,U_18707,U_18705,U_18709)),U_18704),hAPP(c_Option_Ooption_OSome(U_18706),U_18708))
      | hBOOL(hAPP(hAPP(c_member(U_18703),U_18704),hAPP(c_List_Oset(U_18703),U_18705))) ),
    inference(variable_rename,[status(thm)],[f_4525_1]) ).

fof(f_4525_3,plain,
    ! [U_18703,U_18704,U_18705,U_18706,U_18707,U_18708,U_18709] :
      ( c_Map_Omap__upds(U_18703,U_18706,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18703,tc_Option_Ooption(U_18706)),U_18707),U_18704),hAPP(c_Option_Ooption_OSome(U_18706),U_18708)),U_18705,U_18709) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18703,tc_Option_Ooption(U_18706)),c_Map_Omap__upds(U_18703,U_18706,U_18707,U_18705,U_18709)),U_18704),hAPP(c_Option_Ooption_OSome(U_18706),U_18708))
      | hBOOL(hAPP(hAPP(c_member(U_18703),U_18704),hAPP(c_List_Oset(U_18703),U_18705))) ),
    inference(definitional_conversion,[status(esa)],[f_4525_2]) ).

cnf(f_4525_4,plain,
    ( c_Map_Omap__upds(U_18703,U_18706,hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18703,tc_Option_Ooption(U_18706)),U_18707),U_18704),hAPP(c_Option_Ooption_OSome(U_18706),U_18708)),U_18705,U_18709) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18703,tc_Option_Ooption(U_18706)),c_Map_Omap__upds(U_18703,U_18706,U_18707,U_18705,U_18709)),U_18704),hAPP(c_Option_Ooption_OSome(U_18706),U_18708))
    | hBOOL(hAPP(hAPP(c_member(U_18703),U_18704),hAPP(c_List_Oset(U_18703),U_18705))) ),
    inference(clausify,[status(thm)],[f_4525_3]) ).

fof(f_4526_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_4526_2,plain,
    ! [U_18715,U_18714,U_18713,U_18712,U_18711,U_18710] :
      ( c_Map_Orestrict__map(U_18710,U_18712,c_Map_Omap__upds(U_18710,U_18712,U_18715,U_18711,U_18713),U_18714) = c_Map_Omap__upds(U_18710,U_18712,c_Map_Orestrict__map(U_18710,U_18712,U_18715,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18710,tc_HOL_Obool)),U_18714),hAPP(c_List_Oset(U_18710),U_18711))),U_18711,U_18713)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18710,tc_HOL_Obool)),hAPP(c_List_Oset(U_18710),U_18711)),U_18714))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18710)),U_18711) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18712)),U_18713) ),
    inference(variable_rename,[status(thm)],[f_4526_1]) ).

fof(f_4526_3,plain,
    ! [U_18710,U_18711,U_18712,U_18713,U_18714,U_18715] :
      ( c_Map_Orestrict__map(U_18710,U_18712,c_Map_Omap__upds(U_18710,U_18712,U_18715,U_18711,U_18713),U_18714) = c_Map_Omap__upds(U_18710,U_18712,c_Map_Orestrict__map(U_18710,U_18712,U_18715,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18710,tc_HOL_Obool)),U_18714),hAPP(c_List_Oset(U_18710),U_18711))),U_18711,U_18713)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18710,tc_HOL_Obool)),hAPP(c_List_Oset(U_18710),U_18711)),U_18714))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18710)),U_18711) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18712)),U_18713) ),
    inference(definitional_conversion,[status(esa)],[f_4526_2]) ).

cnf(f_4526_4,plain,
    ( c_Map_Orestrict__map(U_18710,U_18712,c_Map_Omap__upds(U_18710,U_18712,U_18715,U_18711,U_18713),U_18714) = c_Map_Omap__upds(U_18710,U_18712,c_Map_Orestrict__map(U_18710,U_18712,U_18715,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_18710,tc_HOL_Obool)),U_18714),hAPP(c_List_Oset(U_18710),U_18711))),U_18711,U_18713)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_18710,tc_HOL_Obool)),hAPP(c_List_Oset(U_18710),U_18711)),U_18714))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18710)),U_18711) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18712)),U_18713) ),
    inference(clausify,[status(thm)],[f_4526_3]) ).

fof(f_4527_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_4527_2,plain,
    ! [U_18720,U_18719,U_18718,U_18717,U_18716] : c_Map_Odom(U_18716,U_18717,c_Map_Omap__upds(U_18716,U_18717,U_18718,U_18719,U_18720)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18716,tc_HOL_Obool)),hAPP(c_List_Oset(U_18716),hAPP(hAPP(c_List_Otake(U_18716),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18717)),U_18720)),U_18719))),c_Map_Odom(U_18716,U_18717,U_18718)),
    inference(variable_rename,[status(thm)],[f_4527_1]) ).

fof(f_4527_3,plain,
    ! [U_18716,U_18717,U_18718,U_18719,U_18720] : c_Map_Odom(U_18716,U_18717,c_Map_Omap__upds(U_18716,U_18717,U_18718,U_18719,U_18720)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18716,tc_HOL_Obool)),hAPP(c_List_Oset(U_18716),hAPP(hAPP(c_List_Otake(U_18716),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18717)),U_18720)),U_18719))),c_Map_Odom(U_18716,U_18717,U_18718)),
    inference(definitional_conversion,[status(esa)],[f_4527_2]) ).

cnf(f_4527_4,plain,
    c_Map_Odom(U_18716,U_18717,c_Map_Omap__upds(U_18716,U_18717,U_18718,U_18719,U_18720)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18716,tc_HOL_Obool)),hAPP(c_List_Oset(U_18716),hAPP(hAPP(c_List_Otake(U_18716),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18717)),U_18720)),U_18719))),c_Map_Odom(U_18716,U_18717,U_18718)),
    inference(clausify,[status(thm)],[f_4527_3]) ).

fof(f_4528_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_4528_2,plain,
    ! [U_18726,U_18725,U_18724,U_18723,U_18722,U_18721] :
      ( c_Map_Omap__upds(U_18721,U_18723,U_18725,hAPP(hAPP(c_List_Oappend(U_18721),U_18722),hAPP(hAPP(c_List_Olist_OCons(U_18721),U_18726),c_List_Olist_ONil(U_18721))),U_18724) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18721,tc_Option_Ooption(U_18723)),c_Map_Omap__upds(U_18721,U_18723,U_18725,U_18722,U_18724)),U_18726),hAPP(c_Option_Ooption_OSome(U_18723),hAPP(hAPP(c_List_Onth(U_18723),U_18724),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18721)),U_18722))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18721)),U_18722)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18723)),U_18724))) ),
    inference(variable_rename,[status(thm)],[f_4528_1]) ).

fof(f_4528_3,plain,
    ! [U_18721,U_18722,U_18723,U_18724,U_18725,U_18726] :
      ( c_Map_Omap__upds(U_18721,U_18723,U_18725,hAPP(hAPP(c_List_Oappend(U_18721),U_18722),hAPP(hAPP(c_List_Olist_OCons(U_18721),U_18726),c_List_Olist_ONil(U_18721))),U_18724) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18721,tc_Option_Ooption(U_18723)),c_Map_Omap__upds(U_18721,U_18723,U_18725,U_18722,U_18724)),U_18726),hAPP(c_Option_Ooption_OSome(U_18723),hAPP(hAPP(c_List_Onth(U_18723),U_18724),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18721)),U_18722))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18721)),U_18722)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18723)),U_18724))) ),
    inference(definitional_conversion,[status(esa)],[f_4528_2]) ).

cnf(f_4528_4,plain,
    ( c_Map_Omap__upds(U_18721,U_18723,U_18725,hAPP(hAPP(c_List_Oappend(U_18721),U_18722),hAPP(hAPP(c_List_Olist_OCons(U_18721),U_18726),c_List_Olist_ONil(U_18721))),U_18724) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(U_18721,tc_Option_Ooption(U_18723)),c_Map_Omap__upds(U_18721,U_18723,U_18725,U_18722,U_18724)),U_18726),hAPP(c_Option_Ooption_OSome(U_18723),hAPP(hAPP(c_List_Onth(U_18723),U_18724),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18721)),U_18722))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18721)),U_18722)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18723)),U_18724))) ),
    inference(clausify,[status(thm)],[f_4528_3]) ).

fof(f_4529_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_4529_2,plain,
    ! [U_18730,U_18729,U_18728,U_18727] : c_List_Osublist(U_18727,hAPP(hAPP(c_List_Olist_OCons(U_18727),U_18728),U_18729),U_18730) = hAPP(hAPP(c_List_Oappend(U_18727),hAPP(hAPP(hAPP(c_If(tc_List_Olist(U_18727)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18730)),hAPP(hAPP(c_List_Olist_OCons(U_18727),U_18728),c_List_Olist_ONil(U_18727))),c_List_Olist_ONil(U_18727))),c_List_Osublist(U_18727,U_18729,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_18730)))),
    inference(variable_rename,[status(thm)],[f_4529_1]) ).

fof(f_4529_3,plain,
    ! [U_18727,U_18728,U_18729,U_18730] : c_List_Osublist(U_18727,hAPP(hAPP(c_List_Olist_OCons(U_18727),U_18728),U_18729),U_18730) = hAPP(hAPP(c_List_Oappend(U_18727),hAPP(hAPP(hAPP(c_If(tc_List_Olist(U_18727)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18730)),hAPP(hAPP(c_List_Olist_OCons(U_18727),U_18728),c_List_Olist_ONil(U_18727))),c_List_Olist_ONil(U_18727))),c_List_Osublist(U_18727,U_18729,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_18730)))),
    inference(definitional_conversion,[status(esa)],[f_4529_2]) ).

cnf(f_4529_4,plain,
    c_List_Osublist(U_18727,hAPP(hAPP(c_List_Olist_OCons(U_18727),U_18728),U_18729),U_18730) = hAPP(hAPP(c_List_Oappend(U_18727),hAPP(hAPP(hAPP(c_If(tc_List_Olist(U_18727)),hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_18730)),hAPP(hAPP(c_List_Olist_OCons(U_18727),U_18728),c_List_Olist_ONil(U_18727))),c_List_Olist_ONil(U_18727))),c_List_Osublist(U_18727,U_18729,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_18730)))),
    inference(clausify,[status(thm)],[f_4529_3]) ).

fof(f_4530_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_4530_2,plain,
    ! [U_18735,U_18734,U_18733,U_18732,U_18731] :
      ( ( hAPP(hAPP(c_List_Oappend(U_18731),U_18732),hAPP(hAPP(c_List_Olist_OCons(U_18731),U_18733),c_List_Olist_ONil(U_18731))) = hAPP(hAPP(c_List_Oappend(U_18731),U_18734),hAPP(hAPP(c_List_Olist_OCons(U_18731),U_18735),c_List_Olist_ONil(U_18731)))
        | U_18733 != U_18735
        | U_18732 != U_18734 )
      & ( ( U_18733 = U_18735
          & U_18732 = U_18734 )
        | hAPP(hAPP(c_List_Oappend(U_18731),U_18732),hAPP(hAPP(c_List_Olist_OCons(U_18731),U_18733),c_List_Olist_ONil(U_18731))) != hAPP(hAPP(c_List_Oappend(U_18731),U_18734),hAPP(hAPP(c_List_Olist_OCons(U_18731),U_18735),c_List_Olist_ONil(U_18731))) ) ),
    inference(variable_rename,[status(thm)],[f_4530_1]) ).

fof(f_4530_3,plain,
    ( ! [U_18745,U_18743,U_18741,U_18739] :
        ( ! [U_18737] : hAPP(hAPP(c_List_Oappend(U_18737),U_18739),hAPP(hAPP(c_List_Olist_OCons(U_18737),U_18741),c_List_Olist_ONil(U_18737))) = hAPP(hAPP(c_List_Oappend(U_18737),U_18743),hAPP(hAPP(c_List_Olist_OCons(U_18737),U_18745),c_List_Olist_ONil(U_18737)))
        | U_18741 != U_18745
        | U_18739 != U_18743 )
    & ! [U_18744,U_18742,U_18740,U_18738] :
        ( ! [U_18736] : hAPP(hAPP(c_List_Oappend(U_18736),U_18738),hAPP(hAPP(c_List_Olist_OCons(U_18736),U_18740),c_List_Olist_ONil(U_18736))) != hAPP(hAPP(c_List_Oappend(U_18736),U_18742),hAPP(hAPP(c_List_Olist_OCons(U_18736),U_18744),c_List_Olist_ONil(U_18736)))
        | ( U_18740 = U_18744
          & U_18738 = U_18742 ) ) ),
    inference(miniscope,[status(thm)],[f_4530_2]) ).

fof(f_4530_4,plain,
    ( ! [U_18740,U_18744,U_18738,U_18742] :
        ( U_18740 = U_18744
        | ~ sP1161(U_18740,U_18744,U_18738,U_18742) )
    & ! [U_18740,U_18744,U_18738,U_18742] :
        ( U_18738 = U_18742
        | ~ sP1161(U_18740,U_18744,U_18738,U_18742) )
    & ! [U_18743,U_18739,U_18741,U_18737,U_18745] :
        ( hAPP(hAPP(c_List_Oappend(U_18737),U_18739),hAPP(hAPP(c_List_Olist_OCons(U_18737),U_18741),c_List_Olist_ONil(U_18737))) = hAPP(hAPP(c_List_Oappend(U_18737),U_18743),hAPP(hAPP(c_List_Olist_OCons(U_18737),U_18745),c_List_Olist_ONil(U_18737)))
        | U_18741 != U_18745
        | U_18739 != U_18743 )
    & ! [U_18740,U_18744,U_18738,U_18736,U_18742] :
        ( hAPP(hAPP(c_List_Oappend(U_18736),U_18738),hAPP(hAPP(c_List_Olist_OCons(U_18736),U_18740),c_List_Olist_ONil(U_18736))) != hAPP(hAPP(c_List_Oappend(U_18736),U_18742),hAPP(hAPP(c_List_Olist_OCons(U_18736),U_18744),c_List_Olist_ONil(U_18736)))
        | sP1161(U_18740,U_18744,U_18738,U_18742) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1161])],[f_4530_3]) ).

cnf(f_4530_5,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18736),U_18738),hAPP(hAPP(c_List_Olist_OCons(U_18736),U_18740),c_List_Olist_ONil(U_18736))) != hAPP(hAPP(c_List_Oappend(U_18736),U_18742),hAPP(hAPP(c_List_Olist_OCons(U_18736),U_18744),c_List_Olist_ONil(U_18736)))
    | sP1161(U_18740,U_18744,U_18738,U_18742) ),
    inference(clausify,[status(thm)],[f_4530_4]) ).

cnf(f_4530_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18737),U_18739),hAPP(hAPP(c_List_Olist_OCons(U_18737),U_18741),c_List_Olist_ONil(U_18737))) = hAPP(hAPP(c_List_Oappend(U_18737),U_18743),hAPP(hAPP(c_List_Olist_OCons(U_18737),U_18745),c_List_Olist_ONil(U_18737)))
    | U_18741 != U_18745
    | U_18739 != U_18743 ),
    inference(clausify,[status(thm)],[f_4530_4]) ).

cnf(f_4530_7,plain,
    ( U_18738 = U_18742
    | ~ sP1161(U_18740,U_18744,U_18738,U_18742) ),
    inference(clausify,[status(thm)],[f_4530_4]) ).

cnf(f_4530_8,plain,
    ( U_18740 = U_18744
    | ~ sP1161(U_18740,U_18744,U_18738,U_18742) ),
    inference(clausify,[status(thm)],[f_4530_4]) ).

fof(f_4531_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_4531_2,plain,
    ! [U_18752,U_18751,U_18750,U_18749,U_18748] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(U_18748),U_18749),U_18750) = hAPP(hAPP(c_List_Oappend(U_18748),U_18751),U_18752)
        | ( ! [U_18747] :
              ( U_18750 != hAPP(hAPP(c_List_Oappend(U_18748),U_18747),U_18752)
              | hAPP(hAPP(c_List_Olist_OCons(U_18748),U_18749),U_18747) != U_18751 )
          & ( hAPP(hAPP(c_List_Olist_OCons(U_18748),U_18749),U_18750) != U_18752
            | U_18751 != c_List_Olist_ONil(U_18748) ) ) )
      & ( ? [U_18746] :
            ( U_18750 = hAPP(hAPP(c_List_Oappend(U_18748),U_18746),U_18752)
            & hAPP(hAPP(c_List_Olist_OCons(U_18748),U_18749),U_18746) = U_18751 )
        | ( hAPP(hAPP(c_List_Olist_OCons(U_18748),U_18749),U_18750) = U_18752
          & U_18751 = c_List_Olist_ONil(U_18748) )
        | hAPP(hAPP(c_List_Olist_OCons(U_18748),U_18749),U_18750) != hAPP(hAPP(c_List_Oappend(U_18748),U_18751),U_18752) ) ),
    inference(variable_rename,[status(thm)],[f_4531_1]) ).

fof(f_4531_3,plain,
    ( ! [U_18762,U_18760,U_18758,U_18756,U_18754] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18754),U_18756),U_18758) = hAPP(hAPP(c_List_Oappend(U_18754),U_18760),U_18762)
        | ( ! [U_18747] :
              ( U_18758 != hAPP(hAPP(c_List_Oappend(U_18754),U_18747),U_18762)
              | hAPP(hAPP(c_List_Olist_OCons(U_18754),U_18756),U_18747) != U_18760 )
          & ( hAPP(hAPP(c_List_Olist_OCons(U_18754),U_18756),U_18758) != U_18762
            | U_18760 != c_List_Olist_ONil(U_18754) ) ) )
    & ! [U_18761,U_18759,U_18757,U_18755,U_18753] :
        ( ? [U_18746] :
            ( U_18757 = hAPP(hAPP(c_List_Oappend(U_18753),U_18746),U_18761)
            & hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18755),U_18746) = U_18759 )
        | ( hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18755),U_18757) = U_18761
          & U_18759 = c_List_Olist_ONil(U_18753) )
        | hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18755),U_18757) != hAPP(hAPP(c_List_Oappend(U_18753),U_18759),U_18761) ) ),
    inference(miniscope,[status(thm)],[f_4531_2]) ).

fof(f_4531_4,plain,
    ( ! [U_18762,U_18760,U_18758,U_18756,U_18754] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18754),U_18756),U_18758) = hAPP(hAPP(c_List_Oappend(U_18754),U_18760),U_18762)
        | ( ! [U_18747] :
              ( U_18758 != hAPP(hAPP(c_List_Oappend(U_18754),U_18747),U_18762)
              | hAPP(hAPP(c_List_Olist_OCons(U_18754),U_18756),U_18747) != U_18760 )
          & ( hAPP(hAPP(c_List_Olist_OCons(U_18754),U_18756),U_18758) != U_18762
            | U_18760 != c_List_Olist_ONil(U_18754) ) ) )
    & ! [U_18761,U_18759,U_18757,U_18755,U_18753] :
        ( ( U_18757 = hAPP(hAPP(c_List_Oappend(U_18753),sK466(U_18761,U_18759,U_18757,U_18755,U_18753)),U_18761)
          & hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18755),sK466(U_18761,U_18759,U_18757,U_18755,U_18753)) = U_18759 )
        | ( hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18755),U_18757) = U_18761
          & U_18759 = c_List_Olist_ONil(U_18753) )
        | hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18755),U_18757) != hAPP(hAPP(c_List_Oappend(U_18753),U_18759),U_18761) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK466]),skolemize(U_18746,sK466(U_18761,U_18759,U_18757,U_18755,U_18753))],[f_4531_3]) ).

fof(f_4531_5,plain,
    ( ! [U_18747,U_18754,U_18762,U_18760,U_18756,U_18758] :
        ( U_18758 != hAPP(hAPP(c_List_Oappend(U_18754),U_18747),U_18762)
        | hAPP(hAPP(c_List_Olist_OCons(U_18754),U_18756),U_18747) != U_18760
        | ~ sP1164(U_18747,U_18754,U_18762,U_18760,U_18756,U_18758) )
    & ! [U_18747,U_18754,U_18762,U_18760,U_18756,U_18758] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18754),U_18756),U_18758) != U_18762
        | U_18760 != c_List_Olist_ONil(U_18754)
        | ~ sP1164(U_18747,U_18754,U_18762,U_18760,U_18756,U_18758) )
    & ! [U_18753,U_18755,U_18759,U_18757,U_18761] :
        ( U_18757 = hAPP(hAPP(c_List_Oappend(U_18753),sK466(U_18761,U_18759,U_18757,U_18755,U_18753)),U_18761)
        | ~ sP1163(U_18753,U_18755,U_18759,U_18757,U_18761) )
    & ! [U_18753,U_18755,U_18759,U_18757,U_18761] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18755),sK466(U_18761,U_18759,U_18757,U_18755,U_18753)) = U_18759
        | ~ sP1163(U_18753,U_18755,U_18759,U_18757,U_18761) )
    & ! [U_18753,U_18755,U_18759,U_18757,U_18761] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18755),U_18757) = U_18761
        | ~ sP1162(U_18753,U_18755,U_18759,U_18757,U_18761) )
    & ! [U_18753,U_18755,U_18759,U_18757,U_18761] :
        ( U_18759 = c_List_Olist_ONil(U_18753)
        | ~ sP1162(U_18753,U_18755,U_18759,U_18757,U_18761) )
    & ! [U_18747,U_18754,U_18762,U_18760,U_18756,U_18758] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_18754),U_18756),U_18758) = hAPP(hAPP(c_List_Oappend(U_18754),U_18760),U_18762)
        | sP1164(U_18747,U_18754,U_18762,U_18760,U_18756,U_18758) )
    & ! [U_18753,U_18755,U_18759,U_18757,U_18761] :
        ( sP1163(U_18753,U_18755,U_18759,U_18757,U_18761)
        | sP1162(U_18753,U_18755,U_18759,U_18757,U_18761)
        | hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18755),U_18757) != hAPP(hAPP(c_List_Oappend(U_18753),U_18759),U_18761) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1162,sP1163,sP1164])],[f_4531_4]) ).

cnf(f_4531_6,plain,
    ( sP1163(U_18753,U_18755,U_18759,U_18757,U_18761)
    | sP1162(U_18753,U_18755,U_18759,U_18757,U_18761)
    | hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18755),U_18757) != hAPP(hAPP(c_List_Oappend(U_18753),U_18759),U_18761) ),
    inference(clausify,[status(thm)],[f_4531_5]) ).

cnf(f_4531_7,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_18754),U_18756),U_18758) = hAPP(hAPP(c_List_Oappend(U_18754),U_18760),U_18762)
    | sP1164(U_18747,U_18754,U_18762,U_18760,U_18756,U_18758) ),
    inference(clausify,[status(thm)],[f_4531_5]) ).

cnf(f_4531_8,plain,
    ( U_18759 = c_List_Olist_ONil(U_18753)
    | ~ sP1162(U_18753,U_18755,U_18759,U_18757,U_18761) ),
    inference(clausify,[status(thm)],[f_4531_5]) ).

cnf(f_4531_9,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18755),U_18757) = U_18761
    | ~ sP1162(U_18753,U_18755,U_18759,U_18757,U_18761) ),
    inference(clausify,[status(thm)],[f_4531_5]) ).

cnf(f_4531_10,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_18753),U_18755),sK466(U_18761,U_18759,U_18757,U_18755,U_18753)) = U_18759
    | ~ sP1163(U_18753,U_18755,U_18759,U_18757,U_18761) ),
    inference(clausify,[status(thm)],[f_4531_5]) ).

cnf(f_4531_11,plain,
    ( U_18757 = hAPP(hAPP(c_List_Oappend(U_18753),sK466(U_18761,U_18759,U_18757,U_18755,U_18753)),U_18761)
    | ~ sP1163(U_18753,U_18755,U_18759,U_18757,U_18761) ),
    inference(clausify,[status(thm)],[f_4531_5]) ).

cnf(f_4531_12,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_18754),U_18756),U_18758) != U_18762
    | U_18760 != c_List_Olist_ONil(U_18754)
    | ~ sP1164(U_18747,U_18754,U_18762,U_18760,U_18756,U_18758) ),
    inference(clausify,[status(thm)],[f_4531_5]) ).

cnf(f_4531_13,plain,
    ( U_18758 != hAPP(hAPP(c_List_Oappend(U_18754),U_18747),U_18762)
    | hAPP(hAPP(c_List_Olist_OCons(U_18754),U_18756),U_18747) != U_18760
    | ~ sP1164(U_18747,U_18754,U_18762,U_18760,U_18756,U_18758) ),
    inference(clausify,[status(thm)],[f_4531_5]) ).

fof(f_4532_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_4532_2,plain,
    ! [U_18769,U_18768,U_18767,U_18766,U_18765] :
      ( ( hAPP(hAPP(c_List_Oappend(U_18765),U_18766),U_18767) = hAPP(hAPP(c_List_Olist_OCons(U_18765),U_18768),U_18769)
        | ( ! [U_18764] :
              ( hAPP(hAPP(c_List_Oappend(U_18765),U_18764),U_18767) != U_18769
              | U_18766 != hAPP(hAPP(c_List_Olist_OCons(U_18765),U_18768),U_18764) )
          & ( U_18767 != hAPP(hAPP(c_List_Olist_OCons(U_18765),U_18768),U_18769)
            | U_18766 != c_List_Olist_ONil(U_18765) ) ) )
      & ( ? [U_18763] :
            ( hAPP(hAPP(c_List_Oappend(U_18765),U_18763),U_18767) = U_18769
            & U_18766 = hAPP(hAPP(c_List_Olist_OCons(U_18765),U_18768),U_18763) )
        | ( U_18767 = hAPP(hAPP(c_List_Olist_OCons(U_18765),U_18768),U_18769)
          & U_18766 = c_List_Olist_ONil(U_18765) )
        | hAPP(hAPP(c_List_Oappend(U_18765),U_18766),U_18767) != hAPP(hAPP(c_List_Olist_OCons(U_18765),U_18768),U_18769) ) ),
    inference(variable_rename,[status(thm)],[f_4532_1]) ).

fof(f_4532_3,plain,
    ( ! [U_18779,U_18777,U_18775,U_18773,U_18771] :
        ( hAPP(hAPP(c_List_Oappend(U_18771),U_18773),U_18775) = hAPP(hAPP(c_List_Olist_OCons(U_18771),U_18777),U_18779)
        | ( ! [U_18764] :
              ( hAPP(hAPP(c_List_Oappend(U_18771),U_18764),U_18775) != U_18779
              | U_18773 != hAPP(hAPP(c_List_Olist_OCons(U_18771),U_18777),U_18764) )
          & ( U_18775 != hAPP(hAPP(c_List_Olist_OCons(U_18771),U_18777),U_18779)
            | U_18773 != c_List_Olist_ONil(U_18771) ) ) )
    & ! [U_18778,U_18776,U_18774,U_18772,U_18770] :
        ( ? [U_18763] :
            ( hAPP(hAPP(c_List_Oappend(U_18770),U_18763),U_18774) = U_18778
            & U_18772 = hAPP(hAPP(c_List_Olist_OCons(U_18770),U_18776),U_18763) )
        | ( U_18774 = hAPP(hAPP(c_List_Olist_OCons(U_18770),U_18776),U_18778)
          & U_18772 = c_List_Olist_ONil(U_18770) )
        | hAPP(hAPP(c_List_Oappend(U_18770),U_18772),U_18774) != hAPP(hAPP(c_List_Olist_OCons(U_18770),U_18776),U_18778) ) ),
    inference(miniscope,[status(thm)],[f_4532_2]) ).

fof(f_4532_4,plain,
    ( ! [U_18779,U_18777,U_18775,U_18773,U_18771] :
        ( hAPP(hAPP(c_List_Oappend(U_18771),U_18773),U_18775) = hAPP(hAPP(c_List_Olist_OCons(U_18771),U_18777),U_18779)
        | ( ! [U_18764] :
              ( hAPP(hAPP(c_List_Oappend(U_18771),U_18764),U_18775) != U_18779
              | U_18773 != hAPP(hAPP(c_List_Olist_OCons(U_18771),U_18777),U_18764) )
          & ( U_18775 != hAPP(hAPP(c_List_Olist_OCons(U_18771),U_18777),U_18779)
            | U_18773 != c_List_Olist_ONil(U_18771) ) ) )
    & ! [U_18778,U_18776,U_18774,U_18772,U_18770] :
        ( ( hAPP(hAPP(c_List_Oappend(U_18770),sK467(U_18778,U_18776,U_18774,U_18772,U_18770)),U_18774) = U_18778
          & U_18772 = hAPP(hAPP(c_List_Olist_OCons(U_18770),U_18776),sK467(U_18778,U_18776,U_18774,U_18772,U_18770)) )
        | ( U_18774 = hAPP(hAPP(c_List_Olist_OCons(U_18770),U_18776),U_18778)
          & U_18772 = c_List_Olist_ONil(U_18770) )
        | hAPP(hAPP(c_List_Oappend(U_18770),U_18772),U_18774) != hAPP(hAPP(c_List_Olist_OCons(U_18770),U_18776),U_18778) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK467]),skolemize(U_18763,sK467(U_18778,U_18776,U_18774,U_18772,U_18770))],[f_4532_3]) ).

fof(f_4532_5,plain,
    ( ! [U_18771,U_18764,U_18777,U_18773,U_18775,U_18779] :
        ( hAPP(hAPP(c_List_Oappend(U_18771),U_18764),U_18775) != U_18779
        | U_18773 != hAPP(hAPP(c_List_Olist_OCons(U_18771),U_18777),U_18764)
        | ~ sP1167(U_18771,U_18764,U_18777,U_18773,U_18775,U_18779) )
    & ! [U_18771,U_18764,U_18777,U_18773,U_18775,U_18779] :
        ( U_18775 != hAPP(hAPP(c_List_Olist_OCons(U_18771),U_18777),U_18779)
        | U_18773 != c_List_Olist_ONil(U_18771)
        | ~ sP1167(U_18771,U_18764,U_18777,U_18773,U_18775,U_18779) )
    & ! [U_18778,U_18772,U_18770,U_18774,U_18776] :
        ( hAPP(hAPP(c_List_Oappend(U_18770),sK467(U_18778,U_18776,U_18774,U_18772,U_18770)),U_18774) = U_18778
        | ~ sP1166(U_18778,U_18772,U_18770,U_18774,U_18776) )
    & ! [U_18778,U_18772,U_18770,U_18774,U_18776] :
        ( U_18772 = hAPP(hAPP(c_List_Olist_OCons(U_18770),U_18776),sK467(U_18778,U_18776,U_18774,U_18772,U_18770))
        | ~ sP1166(U_18778,U_18772,U_18770,U_18774,U_18776) )
    & ! [U_18778,U_18772,U_18770,U_18774,U_18776] :
        ( U_18774 = hAPP(hAPP(c_List_Olist_OCons(U_18770),U_18776),U_18778)
        | ~ sP1165(U_18778,U_18772,U_18770,U_18774,U_18776) )
    & ! [U_18778,U_18772,U_18770,U_18774,U_18776] :
        ( U_18772 = c_List_Olist_ONil(U_18770)
        | ~ sP1165(U_18778,U_18772,U_18770,U_18774,U_18776) )
    & ! [U_18771,U_18764,U_18777,U_18773,U_18775,U_18779] :
        ( hAPP(hAPP(c_List_Oappend(U_18771),U_18773),U_18775) = hAPP(hAPP(c_List_Olist_OCons(U_18771),U_18777),U_18779)
        | sP1167(U_18771,U_18764,U_18777,U_18773,U_18775,U_18779) )
    & ! [U_18778,U_18772,U_18770,U_18774,U_18776] :
        ( sP1166(U_18778,U_18772,U_18770,U_18774,U_18776)
        | sP1165(U_18778,U_18772,U_18770,U_18774,U_18776)
        | hAPP(hAPP(c_List_Oappend(U_18770),U_18772),U_18774) != hAPP(hAPP(c_List_Olist_OCons(U_18770),U_18776),U_18778) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1165,sP1166,sP1167])],[f_4532_4]) ).

cnf(f_4532_6,plain,
    ( sP1166(U_18778,U_18772,U_18770,U_18774,U_18776)
    | sP1165(U_18778,U_18772,U_18770,U_18774,U_18776)
    | hAPP(hAPP(c_List_Oappend(U_18770),U_18772),U_18774) != hAPP(hAPP(c_List_Olist_OCons(U_18770),U_18776),U_18778) ),
    inference(clausify,[status(thm)],[f_4532_5]) ).

cnf(f_4532_7,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18771),U_18773),U_18775) = hAPP(hAPP(c_List_Olist_OCons(U_18771),U_18777),U_18779)
    | sP1167(U_18771,U_18764,U_18777,U_18773,U_18775,U_18779) ),
    inference(clausify,[status(thm)],[f_4532_5]) ).

cnf(f_4532_8,plain,
    ( U_18772 = c_List_Olist_ONil(U_18770)
    | ~ sP1165(U_18778,U_18772,U_18770,U_18774,U_18776) ),
    inference(clausify,[status(thm)],[f_4532_5]) ).

cnf(f_4532_9,plain,
    ( U_18774 = hAPP(hAPP(c_List_Olist_OCons(U_18770),U_18776),U_18778)
    | ~ sP1165(U_18778,U_18772,U_18770,U_18774,U_18776) ),
    inference(clausify,[status(thm)],[f_4532_5]) ).

cnf(f_4532_10,plain,
    ( U_18772 = hAPP(hAPP(c_List_Olist_OCons(U_18770),U_18776),sK467(U_18778,U_18776,U_18774,U_18772,U_18770))
    | ~ sP1166(U_18778,U_18772,U_18770,U_18774,U_18776) ),
    inference(clausify,[status(thm)],[f_4532_5]) ).

cnf(f_4532_11,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18770),sK467(U_18778,U_18776,U_18774,U_18772,U_18770)),U_18774) = U_18778
    | ~ sP1166(U_18778,U_18772,U_18770,U_18774,U_18776) ),
    inference(clausify,[status(thm)],[f_4532_5]) ).

cnf(f_4532_12,plain,
    ( U_18775 != hAPP(hAPP(c_List_Olist_OCons(U_18771),U_18777),U_18779)
    | U_18773 != c_List_Olist_ONil(U_18771)
    | ~ sP1167(U_18771,U_18764,U_18777,U_18773,U_18775,U_18779) ),
    inference(clausify,[status(thm)],[f_4532_5]) ).

cnf(f_4532_13,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18771),U_18764),U_18775) != U_18779
    | U_18773 != hAPP(hAPP(c_List_Olist_OCons(U_18771),U_18777),U_18764)
    | ~ sP1167(U_18771,U_18764,U_18777,U_18773,U_18775,U_18779) ),
    inference(clausify,[status(thm)],[f_4532_5]) ).

fof(f_4533_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_4533_2,plain,
    ! [U_18785,U_18784,U_18783,U_18782,U_18781,U_18780] :
      ( c_Map_Omap__upds(U_18780,U_18782,U_18784,hAPP(hAPP(c_List_Oappend(U_18780),U_18781),U_18785),U_18783) = c_Map_Omap__upds(U_18780,U_18782,U_18784,U_18781,U_18783)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18780)),U_18781) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18782)),U_18783) ),
    inference(variable_rename,[status(thm)],[f_4533_1]) ).

fof(f_4533_3,plain,
    ! [U_18783,U_18785,U_18782,U_18784,U_18781,U_18780] :
      ( c_Map_Omap__upds(U_18780,U_18782,U_18784,hAPP(hAPP(c_List_Oappend(U_18780),U_18781),U_18785),U_18783) = c_Map_Omap__upds(U_18780,U_18782,U_18784,U_18781,U_18783)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18780)),U_18781) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18782)),U_18783) ),
    inference(definitional_conversion,[status(esa)],[f_4533_2]) ).

cnf(f_4533_4,plain,
    ( c_Map_Omap__upds(U_18780,U_18782,U_18784,hAPP(hAPP(c_List_Oappend(U_18780),U_18781),U_18785),U_18783) = c_Map_Omap__upds(U_18780,U_18782,U_18784,U_18781,U_18783)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18780)),U_18781) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18782)),U_18783) ),
    inference(clausify,[status(thm)],[f_4533_3]) ).

fof(f_4534_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_4534_2,plain,
    ! [U_18791,U_18790,U_18789,U_18788,U_18787,U_18786] :
      ( c_Map_Omap__upds(U_18786,U_18788,U_18790,U_18787,hAPP(hAPP(c_List_Oappend(U_18788),U_18789),U_18791)) = c_Map_Omap__upds(U_18786,U_18788,U_18790,U_18787,U_18789)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18786)),U_18787) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18788)),U_18789) ),
    inference(variable_rename,[status(thm)],[f_4534_1]) ).

fof(f_4534_3,plain,
    ! [U_18787,U_18786,U_18788,U_18789,U_18790,U_18791] :
      ( c_Map_Omap__upds(U_18786,U_18788,U_18790,U_18787,hAPP(hAPP(c_List_Oappend(U_18788),U_18789),U_18791)) = c_Map_Omap__upds(U_18786,U_18788,U_18790,U_18787,U_18789)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18786)),U_18787) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18788)),U_18789) ),
    inference(definitional_conversion,[status(esa)],[f_4534_2]) ).

cnf(f_4534_4,plain,
    ( c_Map_Omap__upds(U_18786,U_18788,U_18790,U_18787,hAPP(hAPP(c_List_Oappend(U_18788),U_18789),U_18791)) = c_Map_Omap__upds(U_18786,U_18788,U_18790,U_18787,U_18789)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18786)),U_18787) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18788)),U_18789) ),
    inference(clausify,[status(thm)],[f_4534_3]) ).

fof(f_4535_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_4535_2,plain,
    ! [U_18796,U_18795,U_18794,U_18793,U_18792] : hAPP(hAPP(c_List_Olist__update(U_18792,hAPP(hAPP(c_List_Oappend(U_18792),U_18793),hAPP(hAPP(c_List_Olist_OCons(U_18792),U_18794),U_18795))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18792)),U_18793)),U_18796) = hAPP(hAPP(c_List_Oappend(U_18792),U_18793),hAPP(hAPP(c_List_Olist_OCons(U_18792),U_18796),U_18795)),
    inference(variable_rename,[status(thm)],[f_4535_1]) ).

fof(f_4535_3,plain,
    ! [U_18792,U_18793,U_18794,U_18795,U_18796] : hAPP(hAPP(c_List_Olist__update(U_18792,hAPP(hAPP(c_List_Oappend(U_18792),U_18793),hAPP(hAPP(c_List_Olist_OCons(U_18792),U_18794),U_18795))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18792)),U_18793)),U_18796) = hAPP(hAPP(c_List_Oappend(U_18792),U_18793),hAPP(hAPP(c_List_Olist_OCons(U_18792),U_18796),U_18795)),
    inference(definitional_conversion,[status(esa)],[f_4535_2]) ).

cnf(f_4535_4,plain,
    hAPP(hAPP(c_List_Olist__update(U_18792,hAPP(hAPP(c_List_Oappend(U_18792),U_18793),hAPP(hAPP(c_List_Olist_OCons(U_18792),U_18794),U_18795))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18792)),U_18793)),U_18796) = hAPP(hAPP(c_List_Oappend(U_18792),U_18793),hAPP(hAPP(c_List_Olist_OCons(U_18792),U_18796),U_18795)),
    inference(clausify,[status(thm)],[f_4535_3]) ).

fof(f_4536_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_4536_2,plain,
    ! [U_18800,U_18799,U_18798,U_18797] : hAPP(hAPP(c_List_Onth(U_18797),hAPP(hAPP(c_List_Oappend(U_18797),U_18798),hAPP(hAPP(c_List_Olist_OCons(U_18797),U_18799),U_18800))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18797)),U_18798)) = U_18799,
    inference(variable_rename,[status(thm)],[f_4536_1]) ).

fof(f_4536_3,plain,
    ! [U_18797,U_18798,U_18799,U_18800] : hAPP(hAPP(c_List_Onth(U_18797),hAPP(hAPP(c_List_Oappend(U_18797),U_18798),hAPP(hAPP(c_List_Olist_OCons(U_18797),U_18799),U_18800))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18797)),U_18798)) = U_18799,
    inference(definitional_conversion,[status(esa)],[f_4536_2]) ).

cnf(f_4536_4,plain,
    hAPP(hAPP(c_List_Onth(U_18797),hAPP(hAPP(c_List_Oappend(U_18797),U_18798),hAPP(hAPP(c_List_Olist_OCons(U_18797),U_18799),U_18800))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18797)),U_18798)) = U_18799,
    inference(clausify,[status(thm)],[f_4536_3]) ).

fof(f_4537_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_4537_2,plain,
    ! [U_18806,U_18805,U_18804,U_18803,U_18802,U_18801] :
      ( hAPP(hAPP(c_List_Olist_OCons(U_18801),U_18802),U_18805) = hAPP(hAPP(c_List_Oappend(U_18801),U_18804),U_18806)
      | U_18805 != hAPP(hAPP(c_List_Oappend(U_18801),U_18803),U_18806)
      | hAPP(hAPP(c_List_Olist_OCons(U_18801),U_18802),U_18803) != U_18804 ),
    inference(variable_rename,[status(thm)],[f_4537_1]) ).

fof(f_4537_3,plain,
    ! [U_18801,U_18802,U_18803,U_18804,U_18805,U_18806] :
      ( hAPP(hAPP(c_List_Olist_OCons(U_18801),U_18802),U_18805) = hAPP(hAPP(c_List_Oappend(U_18801),U_18804),U_18806)
      | U_18805 != hAPP(hAPP(c_List_Oappend(U_18801),U_18803),U_18806)
      | hAPP(hAPP(c_List_Olist_OCons(U_18801),U_18802),U_18803) != U_18804 ),
    inference(definitional_conversion,[status(esa)],[f_4537_2]) ).

cnf(f_4537_4,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_18801),U_18802),U_18805) = hAPP(hAPP(c_List_Oappend(U_18801),U_18804),U_18806)
    | U_18805 != hAPP(hAPP(c_List_Oappend(U_18801),U_18803),U_18806)
    | hAPP(hAPP(c_List_Olist_OCons(U_18801),U_18802),U_18803) != U_18804 ),
    inference(clausify,[status(thm)],[f_4537_3]) ).

fof(f_4538_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_4538_2,plain,
    ! [U_18810,U_18809,U_18808,U_18807] : hAPP(hAPP(c_List_Oappend(U_18807),hAPP(hAPP(c_List_Olist_OCons(U_18807),U_18808),U_18809)),U_18810) = hAPP(hAPP(c_List_Olist_OCons(U_18807),U_18808),hAPP(hAPP(c_List_Oappend(U_18807),U_18809),U_18810)),
    inference(variable_rename,[status(thm)],[f_4538_1]) ).

fof(f_4538_3,plain,
    ! [U_18807,U_18808,U_18809,U_18810] : hAPP(hAPP(c_List_Oappend(U_18807),hAPP(hAPP(c_List_Olist_OCons(U_18807),U_18808),U_18809)),U_18810) = hAPP(hAPP(c_List_Olist_OCons(U_18807),U_18808),hAPP(hAPP(c_List_Oappend(U_18807),U_18809),U_18810)),
    inference(definitional_conversion,[status(esa)],[f_4538_2]) ).

cnf(f_4538_4,plain,
    hAPP(hAPP(c_List_Oappend(U_18807),hAPP(hAPP(c_List_Olist_OCons(U_18807),U_18808),U_18809)),U_18810) = hAPP(hAPP(c_List_Olist_OCons(U_18807),U_18808),hAPP(hAPP(c_List_Oappend(U_18807),U_18809),U_18810)),
    inference(clausify,[status(thm)],[f_4538_3]) ).

fof(f_4539_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_4539_2,plain,
    ! [U_18814,U_18813,U_18812,U_18811] : hAPP(hAPP(c_List_Otake(U_18811),U_18812),hAPP(hAPP(c_List_Oappend(U_18811),U_18813),U_18814)) = hAPP(hAPP(c_List_Oappend(U_18811),hAPP(hAPP(c_List_Otake(U_18811),U_18812),U_18813)),hAPP(hAPP(c_List_Otake(U_18811),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18812),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18811)),U_18813))),U_18814)),
    inference(variable_rename,[status(thm)],[f_4539_1]) ).

fof(f_4539_3,plain,
    ! [U_18811,U_18812,U_18813,U_18814] : hAPP(hAPP(c_List_Otake(U_18811),U_18812),hAPP(hAPP(c_List_Oappend(U_18811),U_18813),U_18814)) = hAPP(hAPP(c_List_Oappend(U_18811),hAPP(hAPP(c_List_Otake(U_18811),U_18812),U_18813)),hAPP(hAPP(c_List_Otake(U_18811),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18812),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18811)),U_18813))),U_18814)),
    inference(definitional_conversion,[status(esa)],[f_4539_2]) ).

cnf(f_4539_4,plain,
    hAPP(hAPP(c_List_Otake(U_18811),U_18812),hAPP(hAPP(c_List_Oappend(U_18811),U_18813),U_18814)) = hAPP(hAPP(c_List_Oappend(U_18811),hAPP(hAPP(c_List_Otake(U_18811),U_18812),U_18813)),hAPP(hAPP(c_List_Otake(U_18811),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18812),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18811)),U_18813))),U_18814)),
    inference(clausify,[status(thm)],[f_4539_3]) ).

fof(f_4540_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_4540_2,plain,
    ! [U_18819,U_18818,U_18817,U_18816,U_18815] :
      ( hAPP(hAPP(c_List_Olist__update(U_18816,hAPP(hAPP(c_List_Oappend(U_18816),U_18817),U_18818)),U_18815),U_18819) = hAPP(hAPP(c_List_Oappend(U_18816),hAPP(hAPP(c_List_Olist__update(U_18816,U_18817),U_18815),U_18819)),U_18818)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18815),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18816)),U_18817))) ),
    inference(variable_rename,[status(thm)],[f_4540_1]) ).

fof(f_4540_3,plain,
    ! [U_18815,U_18816,U_18817,U_18818,U_18819] :
      ( hAPP(hAPP(c_List_Olist__update(U_18816,hAPP(hAPP(c_List_Oappend(U_18816),U_18817),U_18818)),U_18815),U_18819) = hAPP(hAPP(c_List_Oappend(U_18816),hAPP(hAPP(c_List_Olist__update(U_18816,U_18817),U_18815),U_18819)),U_18818)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18815),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18816)),U_18817))) ),
    inference(definitional_conversion,[status(esa)],[f_4540_2]) ).

cnf(f_4540_4,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_18816,hAPP(hAPP(c_List_Oappend(U_18816),U_18817),U_18818)),U_18815),U_18819) = hAPP(hAPP(c_List_Oappend(U_18816),hAPP(hAPP(c_List_Olist__update(U_18816,U_18817),U_18815),U_18819)),U_18818)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18815),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18816)),U_18817))) ),
    inference(clausify,[status(thm)],[f_4540_3]) ).

fof(f_4541_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_4541_2,plain,
    ! [U_18823,U_18822,U_18821,U_18820] :
      ( ( c_List_Oremove1(U_18820,U_18821,hAPP(hAPP(c_List_Oappend(U_18820),U_18822),U_18823)) = hAPP(hAPP(c_List_Oappend(U_18820),U_18822),c_List_Oremove1(U_18820,U_18821,U_18823))
        | hBOOL(hAPP(hAPP(c_member(U_18820),U_18821),hAPP(c_List_Oset(U_18820),U_18822))) )
      & ( c_List_Oremove1(U_18820,U_18821,hAPP(hAPP(c_List_Oappend(U_18820),U_18822),U_18823)) = hAPP(hAPP(c_List_Oappend(U_18820),c_List_Oremove1(U_18820,U_18821,U_18822)),U_18823)
        | ~ hBOOL(hAPP(hAPP(c_member(U_18820),U_18821),hAPP(c_List_Oset(U_18820),U_18822))) ) ),
    inference(variable_rename,[status(thm)],[f_4541_1]) ).

fof(f_4541_3,plain,
    ( ! [U_18831,U_18829,U_18827,U_18825] :
        ( c_List_Oremove1(U_18825,U_18827,hAPP(hAPP(c_List_Oappend(U_18825),U_18829),U_18831)) = hAPP(hAPP(c_List_Oappend(U_18825),U_18829),c_List_Oremove1(U_18825,U_18827,U_18831))
        | hBOOL(hAPP(hAPP(c_member(U_18825),U_18827),hAPP(c_List_Oset(U_18825),U_18829))) )
    & ! [U_18830,U_18828,U_18826,U_18824] :
        ( c_List_Oremove1(U_18824,U_18826,hAPP(hAPP(c_List_Oappend(U_18824),U_18828),U_18830)) = hAPP(hAPP(c_List_Oappend(U_18824),c_List_Oremove1(U_18824,U_18826,U_18828)),U_18830)
        | ~ hBOOL(hAPP(hAPP(c_member(U_18824),U_18826),hAPP(c_List_Oset(U_18824),U_18828))) ) ),
    inference(miniscope,[status(thm)],[f_4541_2]) ).

fof(f_4541_4,plain,
    ( ! [U_18831,U_18825,U_18827,U_18829] :
        ( c_List_Oremove1(U_18825,U_18827,hAPP(hAPP(c_List_Oappend(U_18825),U_18829),U_18831)) = hAPP(hAPP(c_List_Oappend(U_18825),U_18829),c_List_Oremove1(U_18825,U_18827,U_18831))
        | hBOOL(hAPP(hAPP(c_member(U_18825),U_18827),hAPP(c_List_Oset(U_18825),U_18829))) )
    & ! [U_18826,U_18830,U_18828,U_18824] :
        ( c_List_Oremove1(U_18824,U_18826,hAPP(hAPP(c_List_Oappend(U_18824),U_18828),U_18830)) = hAPP(hAPP(c_List_Oappend(U_18824),c_List_Oremove1(U_18824,U_18826,U_18828)),U_18830)
        | ~ hBOOL(hAPP(hAPP(c_member(U_18824),U_18826),hAPP(c_List_Oset(U_18824),U_18828))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4541_3]) ).

cnf(f_4541_5,plain,
    ( c_List_Oremove1(U_18824,U_18826,hAPP(hAPP(c_List_Oappend(U_18824),U_18828),U_18830)) = hAPP(hAPP(c_List_Oappend(U_18824),c_List_Oremove1(U_18824,U_18826,U_18828)),U_18830)
    | ~ hBOOL(hAPP(hAPP(c_member(U_18824),U_18826),hAPP(c_List_Oset(U_18824),U_18828))) ),
    inference(clausify,[status(thm)],[f_4541_4]) ).

cnf(f_4541_6,plain,
    ( c_List_Oremove1(U_18825,U_18827,hAPP(hAPP(c_List_Oappend(U_18825),U_18829),U_18831)) = hAPP(hAPP(c_List_Oappend(U_18825),U_18829),c_List_Oremove1(U_18825,U_18827,U_18831))
    | hBOOL(hAPP(hAPP(c_member(U_18825),U_18827),hAPP(c_List_Oset(U_18825),U_18829))) ),
    inference(clausify,[status(thm)],[f_4541_4]) ).

fof(f_4542_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_4542_2,plain,
    ! [U_18834,U_18833,U_18832] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18832)),hAPP(hAPP(c_List_Oappend(U_18832),U_18833),U_18834)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18832)),U_18833)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18832)),U_18834)),
    inference(variable_rename,[status(thm)],[f_4542_1]) ).

fof(f_4542_3,plain,
    ! [U_18833,U_18832,U_18834] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18832)),hAPP(hAPP(c_List_Oappend(U_18832),U_18833),U_18834)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18832)),U_18833)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18832)),U_18834)),
    inference(definitional_conversion,[status(esa)],[f_4542_2]) ).

cnf(f_4542_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18832)),hAPP(hAPP(c_List_Oappend(U_18832),U_18833),U_18834)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18832)),U_18833)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18832)),U_18834)),
    inference(clausify,[status(thm)],[f_4542_3]) ).

fof(f_4543_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_4543_2,plain,
    ! [U_18840,U_18839,U_18838,U_18837,U_18836,U_18835] :
      ( hAPP(hAPP(c_List_Ozip(U_18835,U_18837),hAPP(hAPP(c_List_Oappend(U_18835),U_18836),U_18839)),hAPP(hAPP(c_List_Oappend(U_18837),U_18838),U_18840)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_18835,U_18837)),hAPP(hAPP(c_List_Ozip(U_18835,U_18837),U_18836),U_18838)),hAPP(hAPP(c_List_Ozip(U_18835,U_18837),U_18839),U_18840))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18835)),U_18839) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18837)),U_18840)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18835)),U_18836) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18837)),U_18838) ),
    inference(variable_rename,[status(thm)],[f_4543_1]) ).

fof(f_4543_3,plain,
    ! [U_18835,U_18836,U_18837,U_18838,U_18839,U_18840] :
      ( hAPP(hAPP(c_List_Ozip(U_18835,U_18837),hAPP(hAPP(c_List_Oappend(U_18835),U_18836),U_18839)),hAPP(hAPP(c_List_Oappend(U_18837),U_18838),U_18840)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_18835,U_18837)),hAPP(hAPP(c_List_Ozip(U_18835,U_18837),U_18836),U_18838)),hAPP(hAPP(c_List_Ozip(U_18835,U_18837),U_18839),U_18840))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18835)),U_18839) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18837)),U_18840)
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18835)),U_18836) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18837)),U_18838) ),
    inference(definitional_conversion,[status(esa)],[f_4543_2]) ).

cnf(f_4543_4,plain,
    ( hAPP(hAPP(c_List_Ozip(U_18835,U_18837),hAPP(hAPP(c_List_Oappend(U_18835),U_18836),U_18839)),hAPP(hAPP(c_List_Oappend(U_18837),U_18838),U_18840)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_18835,U_18837)),hAPP(hAPP(c_List_Ozip(U_18835,U_18837),U_18836),U_18838)),hAPP(hAPP(c_List_Ozip(U_18835,U_18837),U_18839),U_18840))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18835)),U_18839) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18837)),U_18840)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18835)),U_18836) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18837)),U_18838) ),
    inference(clausify,[status(thm)],[f_4543_3]) ).

fof(f_4544_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_4544_2,plain,
    ! [U_18845,U_18844,U_18843,U_18842,U_18841] : hAPP(hAPP(c_List_Omap(U_18841,U_18842),U_18843),hAPP(hAPP(c_List_Oappend(U_18841),U_18844),U_18845)) = hAPP(hAPP(c_List_Oappend(U_18842),hAPP(hAPP(c_List_Omap(U_18841,U_18842),U_18843),U_18844)),hAPP(hAPP(c_List_Omap(U_18841,U_18842),U_18843),U_18845)),
    inference(variable_rename,[status(thm)],[f_4544_1]) ).

fof(f_4544_3,plain,
    ! [U_18842,U_18841,U_18843,U_18844,U_18845] : hAPP(hAPP(c_List_Omap(U_18841,U_18842),U_18843),hAPP(hAPP(c_List_Oappend(U_18841),U_18844),U_18845)) = hAPP(hAPP(c_List_Oappend(U_18842),hAPP(hAPP(c_List_Omap(U_18841,U_18842),U_18843),U_18844)),hAPP(hAPP(c_List_Omap(U_18841,U_18842),U_18843),U_18845)),
    inference(definitional_conversion,[status(esa)],[f_4544_2]) ).

cnf(f_4544_4,plain,
    hAPP(hAPP(c_List_Omap(U_18841,U_18842),U_18843),hAPP(hAPP(c_List_Oappend(U_18841),U_18844),U_18845)) = hAPP(hAPP(c_List_Oappend(U_18842),hAPP(hAPP(c_List_Omap(U_18841,U_18842),U_18843),U_18844)),hAPP(hAPP(c_List_Omap(U_18841,U_18842),U_18843),U_18845)),
    inference(clausify,[status(thm)],[f_4544_3]) ).

fof(f_4545_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_4545_2,plain,
    ! [U_18851,U_18850,U_18849,U_18848,U_18847,U_18846] : c_List_Ofoldr(U_18846,U_18847,U_18848,hAPP(hAPP(c_List_Oappend(U_18846),U_18849),U_18850),U_18851) = c_List_Ofoldr(U_18846,U_18847,U_18848,U_18849,c_List_Ofoldr(U_18846,U_18847,U_18848,U_18850,U_18851)),
    inference(variable_rename,[status(thm)],[f_4545_1]) ).

fof(f_4545_3,plain,
    ! [U_18846,U_18847,U_18848,U_18849,U_18850,U_18851] : c_List_Ofoldr(U_18846,U_18847,U_18848,hAPP(hAPP(c_List_Oappend(U_18846),U_18849),U_18850),U_18851) = c_List_Ofoldr(U_18846,U_18847,U_18848,U_18849,c_List_Ofoldr(U_18846,U_18847,U_18848,U_18850,U_18851)),
    inference(definitional_conversion,[status(esa)],[f_4545_2]) ).

cnf(f_4545_4,plain,
    c_List_Ofoldr(U_18846,U_18847,U_18848,hAPP(hAPP(c_List_Oappend(U_18846),U_18849),U_18850),U_18851) = c_List_Ofoldr(U_18846,U_18847,U_18848,U_18849,c_List_Ofoldr(U_18846,U_18847,U_18848,U_18850,U_18851)),
    inference(clausify,[status(thm)],[f_4545_3]) ).

fof(f_4546_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_4546_2,plain,
    ! [U_18855,U_18854,U_18853,U_18852] : c_Map_Omap__of(U_18852,U_18853,hAPP(hAPP(c_List_Oappend(tc_prod(U_18852,U_18853)),U_18854),U_18855)) = c_Map_Omap__add(U_18852,U_18853,c_Map_Omap__of(U_18852,U_18853,U_18855),c_Map_Omap__of(U_18852,U_18853,U_18854)),
    inference(variable_rename,[status(thm)],[f_4546_1]) ).

fof(f_4546_3,plain,
    ! [U_18853,U_18852,U_18854,U_18855] : c_Map_Omap__of(U_18852,U_18853,hAPP(hAPP(c_List_Oappend(tc_prod(U_18852,U_18853)),U_18854),U_18855)) = c_Map_Omap__add(U_18852,U_18853,c_Map_Omap__of(U_18852,U_18853,U_18855),c_Map_Omap__of(U_18852,U_18853,U_18854)),
    inference(definitional_conversion,[status(esa)],[f_4546_2]) ).

cnf(f_4546_4,plain,
    c_Map_Omap__of(U_18852,U_18853,hAPP(hAPP(c_List_Oappend(tc_prod(U_18852,U_18853)),U_18854),U_18855)) = c_Map_Omap__add(U_18852,U_18853,c_Map_Omap__of(U_18852,U_18853,U_18855),c_Map_Omap__of(U_18852,U_18853,U_18854)),
    inference(clausify,[status(thm)],[f_4546_3]) ).

fof(f_4547_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_4547_2,plain,
    ! [U_18859,U_18858,U_18857,U_18856] : hAPP(hAPP(c_List_Oappend(U_18856),hAPP(hAPP(c_List_Oappend(U_18856),U_18857),U_18858)),U_18859) = hAPP(hAPP(c_List_Oappend(U_18856),U_18857),hAPP(hAPP(c_List_Oappend(U_18856),U_18858),U_18859)),
    inference(variable_rename,[status(thm)],[f_4547_1]) ).

fof(f_4547_3,plain,
    ! [U_18856,U_18857,U_18858,U_18859] : hAPP(hAPP(c_List_Oappend(U_18856),hAPP(hAPP(c_List_Oappend(U_18856),U_18857),U_18858)),U_18859) = hAPP(hAPP(c_List_Oappend(U_18856),U_18857),hAPP(hAPP(c_List_Oappend(U_18856),U_18858),U_18859)),
    inference(definitional_conversion,[status(esa)],[f_4547_2]) ).

cnf(f_4547_4,plain,
    hAPP(hAPP(c_List_Oappend(U_18856),hAPP(hAPP(c_List_Oappend(U_18856),U_18857),U_18858)),U_18859) = hAPP(hAPP(c_List_Oappend(U_18856),U_18857),hAPP(hAPP(c_List_Oappend(U_18856),U_18858),U_18859)),
    inference(clausify,[status(thm)],[f_4547_3]) ).

fof(f_4548_1,plain,
    ! [V_ts_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_ts_2)
        | ! [B_us] :
            ( ( V_ys_2 != hAPP(hAPP(c_List_Oappend(T_b),B_us),V_ts_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_ts_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_ts_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_ts_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_ts_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_append__eq__append__conv2]) ).

fof(f_4548_2,plain,
    ! [U_18866,U_18865,U_18864,U_18863,U_18862] :
      ( ( hAPP(hAPP(c_List_Oappend(U_18862),U_18863),U_18864) = hAPP(hAPP(c_List_Oappend(U_18862),U_18865),U_18866)
        | ! [U_18861] :
            ( ( U_18864 != hAPP(hAPP(c_List_Oappend(U_18862),U_18861),U_18866)
              | hAPP(hAPP(c_List_Oappend(U_18862),U_18863),U_18861) != U_18865 )
            & ( hAPP(hAPP(c_List_Oappend(U_18862),U_18861),U_18864) != U_18866
              | U_18863 != hAPP(hAPP(c_List_Oappend(U_18862),U_18865),U_18861) ) ) )
      & ( ? [U_18860] :
            ( ( U_18864 = hAPP(hAPP(c_List_Oappend(U_18862),U_18860),U_18866)
              & hAPP(hAPP(c_List_Oappend(U_18862),U_18863),U_18860) = U_18865 )
            | ( hAPP(hAPP(c_List_Oappend(U_18862),U_18860),U_18864) = U_18866
              & U_18863 = hAPP(hAPP(c_List_Oappend(U_18862),U_18865),U_18860) ) )
        | hAPP(hAPP(c_List_Oappend(U_18862),U_18863),U_18864) != hAPP(hAPP(c_List_Oappend(U_18862),U_18865),U_18866) ) ),
    inference(variable_rename,[status(thm)],[f_4548_1]) ).

fof(f_4548_3,plain,
    ( ! [U_18880,U_18878,U_18876,U_18874,U_18872] :
        ( hAPP(hAPP(c_List_Oappend(U_18872),U_18874),U_18876) = hAPP(hAPP(c_List_Oappend(U_18872),U_18878),U_18880)
        | ( ! [U_18870] :
              ( U_18876 != hAPP(hAPP(c_List_Oappend(U_18872),U_18870),U_18880)
              | hAPP(hAPP(c_List_Oappend(U_18872),U_18874),U_18870) != U_18878 )
          & ! [U_18869] :
              ( hAPP(hAPP(c_List_Oappend(U_18872),U_18869),U_18876) != U_18880
              | U_18874 != hAPP(hAPP(c_List_Oappend(U_18872),U_18878),U_18869) ) ) )
    & ! [U_18879,U_18877,U_18875,U_18873,U_18871] :
        ( ? [U_18868] :
            ( U_18875 = hAPP(hAPP(c_List_Oappend(U_18871),U_18868),U_18879)
            & hAPP(hAPP(c_List_Oappend(U_18871),U_18873),U_18868) = U_18877 )
        | ? [U_18867] :
            ( hAPP(hAPP(c_List_Oappend(U_18871),U_18867),U_18875) = U_18879
            & U_18873 = hAPP(hAPP(c_List_Oappend(U_18871),U_18877),U_18867) )
        | hAPP(hAPP(c_List_Oappend(U_18871),U_18873),U_18875) != hAPP(hAPP(c_List_Oappend(U_18871),U_18877),U_18879) ) ),
    inference(miniscope,[status(thm)],[f_4548_2]) ).

fof(f_4548_4,plain,
    ( ! [U_18880,U_18878,U_18876,U_18874,U_18872] :
        ( hAPP(hAPP(c_List_Oappend(U_18872),U_18874),U_18876) = hAPP(hAPP(c_List_Oappend(U_18872),U_18878),U_18880)
        | ( ! [U_18870] :
              ( U_18876 != hAPP(hAPP(c_List_Oappend(U_18872),U_18870),U_18880)
              | hAPP(hAPP(c_List_Oappend(U_18872),U_18874),U_18870) != U_18878 )
          & ! [U_18869] :
              ( hAPP(hAPP(c_List_Oappend(U_18872),U_18869),U_18876) != U_18880
              | U_18874 != hAPP(hAPP(c_List_Oappend(U_18872),U_18878),U_18869) ) ) )
    & ! [U_18879,U_18877,U_18875,U_18873,U_18871] :
        ( ? [U_18868] :
            ( U_18875 = hAPP(hAPP(c_List_Oappend(U_18871),U_18868),U_18879)
            & hAPP(hAPP(c_List_Oappend(U_18871),U_18873),U_18868) = U_18877 )
        | ( hAPP(hAPP(c_List_Oappend(U_18871),sK468(U_18879,U_18877,U_18875,U_18873,U_18871)),U_18875) = U_18879
          & U_18873 = hAPP(hAPP(c_List_Oappend(U_18871),U_18877),sK468(U_18879,U_18877,U_18875,U_18873,U_18871)) )
        | hAPP(hAPP(c_List_Oappend(U_18871),U_18873),U_18875) != hAPP(hAPP(c_List_Oappend(U_18871),U_18877),U_18879) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK468]),skolemize(U_18867,sK468(U_18879,U_18877,U_18875,U_18873,U_18871))],[f_4548_3]) ).

fof(f_4548_5,plain,
    ( ! [U_18880,U_18878,U_18876,U_18874,U_18872] :
        ( hAPP(hAPP(c_List_Oappend(U_18872),U_18874),U_18876) = hAPP(hAPP(c_List_Oappend(U_18872),U_18878),U_18880)
        | ( ! [U_18870] :
              ( U_18876 != hAPP(hAPP(c_List_Oappend(U_18872),U_18870),U_18880)
              | hAPP(hAPP(c_List_Oappend(U_18872),U_18874),U_18870) != U_18878 )
          & ! [U_18869] :
              ( hAPP(hAPP(c_List_Oappend(U_18872),U_18869),U_18876) != U_18880
              | U_18874 != hAPP(hAPP(c_List_Oappend(U_18872),U_18878),U_18869) ) ) )
    & ! [U_18879,U_18877,U_18875,U_18873,U_18871] :
        ( ( U_18875 = hAPP(hAPP(c_List_Oappend(U_18871),sK469(U_18879,U_18877,U_18875,U_18873,U_18871)),U_18879)
          & hAPP(hAPP(c_List_Oappend(U_18871),U_18873),sK469(U_18879,U_18877,U_18875,U_18873,U_18871)) = U_18877 )
        | ( hAPP(hAPP(c_List_Oappend(U_18871),sK468(U_18879,U_18877,U_18875,U_18873,U_18871)),U_18875) = U_18879
          & U_18873 = hAPP(hAPP(c_List_Oappend(U_18871),U_18877),sK468(U_18879,U_18877,U_18875,U_18873,U_18871)) )
        | hAPP(hAPP(c_List_Oappend(U_18871),U_18873),U_18875) != hAPP(hAPP(c_List_Oappend(U_18871),U_18877),U_18879) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK469]),skolemize(U_18868,sK469(U_18879,U_18877,U_18875,U_18873,U_18871))],[f_4548_4]) ).

fof(f_4548_6,plain,
    ( ! [U_18869,U_18874,U_18872,U_18870,U_18880,U_18876,U_18878] :
        ( U_18876 != hAPP(hAPP(c_List_Oappend(U_18872),U_18870),U_18880)
        | hAPP(hAPP(c_List_Oappend(U_18872),U_18874),U_18870) != U_18878
        | ~ sP1170(U_18869,U_18874,U_18872,U_18870,U_18880,U_18876,U_18878) )
    & ! [U_18869,U_18874,U_18872,U_18870,U_18880,U_18876,U_18878] :
        ( hAPP(hAPP(c_List_Oappend(U_18872),U_18869),U_18876) != U_18880
        | U_18874 != hAPP(hAPP(c_List_Oappend(U_18872),U_18878),U_18869)
        | ~ sP1170(U_18869,U_18874,U_18872,U_18870,U_18880,U_18876,U_18878) )
    & ! [U_18877,U_18879,U_18873,U_18871,U_18875] :
        ( U_18875 = hAPP(hAPP(c_List_Oappend(U_18871),sK469(U_18879,U_18877,U_18875,U_18873,U_18871)),U_18879)
        | ~ sP1169(U_18877,U_18879,U_18873,U_18871,U_18875) )
    & ! [U_18877,U_18879,U_18873,U_18871,U_18875] :
        ( hAPP(hAPP(c_List_Oappend(U_18871),U_18873),sK469(U_18879,U_18877,U_18875,U_18873,U_18871)) = U_18877
        | ~ sP1169(U_18877,U_18879,U_18873,U_18871,U_18875) )
    & ! [U_18877,U_18879,U_18873,U_18871,U_18875] :
        ( hAPP(hAPP(c_List_Oappend(U_18871),sK468(U_18879,U_18877,U_18875,U_18873,U_18871)),U_18875) = U_18879
        | ~ sP1168(U_18877,U_18879,U_18873,U_18871,U_18875) )
    & ! [U_18877,U_18879,U_18873,U_18871,U_18875] :
        ( U_18873 = hAPP(hAPP(c_List_Oappend(U_18871),U_18877),sK468(U_18879,U_18877,U_18875,U_18873,U_18871))
        | ~ sP1168(U_18877,U_18879,U_18873,U_18871,U_18875) )
    & ! [U_18869,U_18874,U_18872,U_18870,U_18880,U_18876,U_18878] :
        ( hAPP(hAPP(c_List_Oappend(U_18872),U_18874),U_18876) = hAPP(hAPP(c_List_Oappend(U_18872),U_18878),U_18880)
        | sP1170(U_18869,U_18874,U_18872,U_18870,U_18880,U_18876,U_18878) )
    & ! [U_18877,U_18879,U_18873,U_18871,U_18875] :
        ( sP1169(U_18877,U_18879,U_18873,U_18871,U_18875)
        | sP1168(U_18877,U_18879,U_18873,U_18871,U_18875)
        | hAPP(hAPP(c_List_Oappend(U_18871),U_18873),U_18875) != hAPP(hAPP(c_List_Oappend(U_18871),U_18877),U_18879) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1168,sP1169,sP1170])],[f_4548_5]) ).

cnf(f_4548_7,plain,
    ( sP1169(U_18877,U_18879,U_18873,U_18871,U_18875)
    | sP1168(U_18877,U_18879,U_18873,U_18871,U_18875)
    | hAPP(hAPP(c_List_Oappend(U_18871),U_18873),U_18875) != hAPP(hAPP(c_List_Oappend(U_18871),U_18877),U_18879) ),
    inference(clausify,[status(thm)],[f_4548_6]) ).

cnf(f_4548_8,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18872),U_18874),U_18876) = hAPP(hAPP(c_List_Oappend(U_18872),U_18878),U_18880)
    | sP1170(U_18869,U_18874,U_18872,U_18870,U_18880,U_18876,U_18878) ),
    inference(clausify,[status(thm)],[f_4548_6]) ).

cnf(f_4548_9,plain,
    ( U_18873 = hAPP(hAPP(c_List_Oappend(U_18871),U_18877),sK468(U_18879,U_18877,U_18875,U_18873,U_18871))
    | ~ sP1168(U_18877,U_18879,U_18873,U_18871,U_18875) ),
    inference(clausify,[status(thm)],[f_4548_6]) ).

cnf(f_4548_10,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18871),sK468(U_18879,U_18877,U_18875,U_18873,U_18871)),U_18875) = U_18879
    | ~ sP1168(U_18877,U_18879,U_18873,U_18871,U_18875) ),
    inference(clausify,[status(thm)],[f_4548_6]) ).

cnf(f_4548_11,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18871),U_18873),sK469(U_18879,U_18877,U_18875,U_18873,U_18871)) = U_18877
    | ~ sP1169(U_18877,U_18879,U_18873,U_18871,U_18875) ),
    inference(clausify,[status(thm)],[f_4548_6]) ).

cnf(f_4548_12,plain,
    ( U_18875 = hAPP(hAPP(c_List_Oappend(U_18871),sK469(U_18879,U_18877,U_18875,U_18873,U_18871)),U_18879)
    | ~ sP1169(U_18877,U_18879,U_18873,U_18871,U_18875) ),
    inference(clausify,[status(thm)],[f_4548_6]) ).

cnf(f_4548_13,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18872),U_18869),U_18876) != U_18880
    | U_18874 != hAPP(hAPP(c_List_Oappend(U_18872),U_18878),U_18869)
    | ~ sP1170(U_18869,U_18874,U_18872,U_18870,U_18880,U_18876,U_18878) ),
    inference(clausify,[status(thm)],[f_4548_6]) ).

cnf(f_4548_14,plain,
    ( U_18876 != hAPP(hAPP(c_List_Oappend(U_18872),U_18870),U_18880)
    | hAPP(hAPP(c_List_Oappend(U_18872),U_18874),U_18870) != U_18878
    | ~ sP1170(U_18869,U_18874,U_18872,U_18870,U_18880,U_18876,U_18878) ),
    inference(clausify,[status(thm)],[f_4548_6]) ).

fof(f_4549_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_4549_2,plain,
    ! [U_18884,U_18883,U_18882,U_18881] :
      ( ( hAPP(hAPP(c_List_Oappend(U_18881),U_18882),U_18883) = hAPP(hAPP(c_List_Oappend(U_18881),U_18882),U_18884)
        | U_18883 != U_18884 )
      & ( U_18883 = U_18884
        | hAPP(hAPP(c_List_Oappend(U_18881),U_18882),U_18883) != hAPP(hAPP(c_List_Oappend(U_18881),U_18882),U_18884) ) ),
    inference(variable_rename,[status(thm)],[f_4549_1]) ).

fof(f_4549_3,plain,
    ( ! [U_18892,U_18890] :
        ( ! [U_18888,U_18886] : hAPP(hAPP(c_List_Oappend(U_18886),U_18888),U_18890) = hAPP(hAPP(c_List_Oappend(U_18886),U_18888),U_18892)
        | U_18890 != U_18892 )
    & ! [U_18891,U_18889] :
        ( ! [U_18887,U_18885] : hAPP(hAPP(c_List_Oappend(U_18885),U_18887),U_18889) != hAPP(hAPP(c_List_Oappend(U_18885),U_18887),U_18891)
        | U_18889 = U_18891 ) ),
    inference(miniscope,[status(thm)],[f_4549_2]) ).

fof(f_4549_4,plain,
    ( ! [U_18892,U_18886,U_18888,U_18890] :
        ( hAPP(hAPP(c_List_Oappend(U_18886),U_18888),U_18890) = hAPP(hAPP(c_List_Oappend(U_18886),U_18888),U_18892)
        | U_18890 != U_18892 )
    & ! [U_18885,U_18889,U_18891,U_18887] :
        ( hAPP(hAPP(c_List_Oappend(U_18885),U_18887),U_18889) != hAPP(hAPP(c_List_Oappend(U_18885),U_18887),U_18891)
        | U_18889 = U_18891 ) ),
    inference(definitional_conversion,[status(esa)],[f_4549_3]) ).

cnf(f_4549_5,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18885),U_18887),U_18889) != hAPP(hAPP(c_List_Oappend(U_18885),U_18887),U_18891)
    | U_18889 = U_18891 ),
    inference(clausify,[status(thm)],[f_4549_4]) ).

cnf(f_4549_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18886),U_18888),U_18890) = hAPP(hAPP(c_List_Oappend(U_18886),U_18888),U_18892)
    | U_18890 != U_18892 ),
    inference(clausify,[status(thm)],[f_4549_4]) ).

fof(f_4550_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_4550_2,plain,
    ! [U_18896,U_18895,U_18894,U_18893] :
      ( ( hAPP(hAPP(c_List_Oappend(U_18893),U_18894),U_18895) = hAPP(hAPP(c_List_Oappend(U_18893),U_18896),U_18895)
        | U_18894 != U_18896 )
      & ( U_18894 = U_18896
        | hAPP(hAPP(c_List_Oappend(U_18893),U_18894),U_18895) != hAPP(hAPP(c_List_Oappend(U_18893),U_18896),U_18895) ) ),
    inference(variable_rename,[status(thm)],[f_4550_1]) ).

fof(f_4550_3,plain,
    ( ! [U_18904,U_18902,U_18900] :
        ( ! [U_18898] : hAPP(hAPP(c_List_Oappend(U_18898),U_18900),U_18902) = hAPP(hAPP(c_List_Oappend(U_18898),U_18904),U_18902)
        | U_18900 != U_18904 )
    & ! [U_18903,U_18901,U_18899] :
        ( ! [U_18897] : hAPP(hAPP(c_List_Oappend(U_18897),U_18899),U_18901) != hAPP(hAPP(c_List_Oappend(U_18897),U_18903),U_18901)
        | U_18899 = U_18903 ) ),
    inference(miniscope,[status(thm)],[f_4550_2]) ).

fof(f_4550_4,plain,
    ( ! [U_18902,U_18898,U_18900,U_18904] :
        ( hAPP(hAPP(c_List_Oappend(U_18898),U_18900),U_18902) = hAPP(hAPP(c_List_Oappend(U_18898),U_18904),U_18902)
        | U_18900 != U_18904 )
    & ! [U_18901,U_18899,U_18897,U_18903] :
        ( hAPP(hAPP(c_List_Oappend(U_18897),U_18899),U_18901) != hAPP(hAPP(c_List_Oappend(U_18897),U_18903),U_18901)
        | U_18899 = U_18903 ) ),
    inference(definitional_conversion,[status(esa)],[f_4550_3]) ).

cnf(f_4550_5,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18897),U_18899),U_18901) != hAPP(hAPP(c_List_Oappend(U_18897),U_18903),U_18901)
    | U_18899 = U_18903 ),
    inference(clausify,[status(thm)],[f_4550_4]) ).

cnf(f_4550_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18898),U_18900),U_18902) = hAPP(hAPP(c_List_Oappend(U_18898),U_18904),U_18902)
    | U_18900 != U_18904 ),
    inference(clausify,[status(thm)],[f_4550_4]) ).

fof(f_4551_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_4551_2,plain,
    ! [U_18910,U_18909,U_18908,U_18907,U_18906,U_18905] :
      ( hAPP(hAPP(c_List_Oappend(U_18905),U_18906),U_18909) = hAPP(hAPP(c_List_Oappend(U_18905),U_18908),U_18910)
      | U_18909 != hAPP(hAPP(c_List_Oappend(U_18905),U_18907),U_18910)
      | hAPP(hAPP(c_List_Oappend(U_18905),U_18906),U_18907) != U_18908 ),
    inference(variable_rename,[status(thm)],[f_4551_1]) ).

fof(f_4551_3,plain,
    ! [U_18905,U_18906,U_18907,U_18908,U_18909,U_18910] :
      ( hAPP(hAPP(c_List_Oappend(U_18905),U_18906),U_18909) = hAPP(hAPP(c_List_Oappend(U_18905),U_18908),U_18910)
      | U_18909 != hAPP(hAPP(c_List_Oappend(U_18905),U_18907),U_18910)
      | hAPP(hAPP(c_List_Oappend(U_18905),U_18906),U_18907) != U_18908 ),
    inference(definitional_conversion,[status(esa)],[f_4551_2]) ).

cnf(f_4551_4,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18905),U_18906),U_18909) = hAPP(hAPP(c_List_Oappend(U_18905),U_18908),U_18910)
    | U_18909 != hAPP(hAPP(c_List_Oappend(U_18905),U_18907),U_18910)
    | hAPP(hAPP(c_List_Oappend(U_18905),U_18906),U_18907) != U_18908 ),
    inference(clausify,[status(thm)],[f_4551_3]) ).

fof(f_4552_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_4552_2,plain,
    ! [U_18913,U_18912,U_18911] : hAPP(c_List_Oset(U_18911),hAPP(hAPP(c_List_Oappend(U_18911),U_18912),U_18913)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18911,tc_HOL_Obool)),hAPP(c_List_Oset(U_18911),U_18912)),hAPP(c_List_Oset(U_18911),U_18913)),
    inference(variable_rename,[status(thm)],[f_4552_1]) ).

fof(f_4552_3,plain,
    ! [U_18911,U_18912,U_18913] : hAPP(c_List_Oset(U_18911),hAPP(hAPP(c_List_Oappend(U_18911),U_18912),U_18913)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18911,tc_HOL_Obool)),hAPP(c_List_Oset(U_18911),U_18912)),hAPP(c_List_Oset(U_18911),U_18913)),
    inference(definitional_conversion,[status(esa)],[f_4552_2]) ).

cnf(f_4552_4,plain,
    hAPP(c_List_Oset(U_18911),hAPP(hAPP(c_List_Oappend(U_18911),U_18912),U_18913)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_18911,tc_HOL_Obool)),hAPP(c_List_Oset(U_18911),U_18912)),hAPP(c_List_Oset(U_18911),U_18913)),
    inference(clausify,[status(thm)],[f_4552_3]) ).

fof(f_4553_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_4553_2,plain,
    ! [U_18916,U_18915,U_18914] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18914),hAPP(hAPP(c_List_Oappend(U_18914),U_18915),U_18916)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18914),hAPP(c_List_Omonoid__add__class_Olistsum(U_18914),U_18915)),hAPP(c_List_Omonoid__add__class_Olistsum(U_18914),U_18916))
      | ~ class_Groups_Omonoid__add(U_18914) ),
    inference(variable_rename,[status(thm)],[f_4553_1]) ).

fof(f_4553_3,plain,
    ! [U_18914,U_18915,U_18916] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18914),hAPP(hAPP(c_List_Oappend(U_18914),U_18915),U_18916)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18914),hAPP(c_List_Omonoid__add__class_Olistsum(U_18914),U_18915)),hAPP(c_List_Omonoid__add__class_Olistsum(U_18914),U_18916))
      | ~ class_Groups_Omonoid__add(U_18914) ),
    inference(definitional_conversion,[status(esa)],[f_4553_2]) ).

cnf(f_4553_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_18914),hAPP(hAPP(c_List_Oappend(U_18914),U_18915),U_18916)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_18914),hAPP(c_List_Omonoid__add__class_Olistsum(U_18914),U_18915)),hAPP(c_List_Omonoid__add__class_Olistsum(U_18914),U_18916))
    | ~ class_Groups_Omonoid__add(U_18914) ),
    inference(clausify,[status(thm)],[f_4553_3]) ).

fof(f_4554_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_4554_2,plain,
    ! [U_18920,U_18919,U_18918,U_18917] : hAPP(hAPP(c_List_Onth(U_18917),hAPP(hAPP(c_List_Oappend(U_18917),U_18918),U_18919)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18917)),U_18918)),U_18920)) = hAPP(hAPP(c_List_Onth(U_18917),U_18919),U_18920),
    inference(variable_rename,[status(thm)],[f_4554_1]) ).

fof(f_4554_3,plain,
    ! [U_18917,U_18918,U_18919,U_18920] : hAPP(hAPP(c_List_Onth(U_18917),hAPP(hAPP(c_List_Oappend(U_18917),U_18918),U_18919)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18917)),U_18918)),U_18920)) = hAPP(hAPP(c_List_Onth(U_18917),U_18919),U_18920),
    inference(definitional_conversion,[status(esa)],[f_4554_2]) ).

cnf(f_4554_4,plain,
    hAPP(hAPP(c_List_Onth(U_18917),hAPP(hAPP(c_List_Oappend(U_18917),U_18918),U_18919)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18917)),U_18918)),U_18920)) = hAPP(hAPP(c_List_Onth(U_18917),U_18919),U_18920),
    inference(clausify,[status(thm)],[f_4554_3]) ).

fof(f_4555_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_4555_2,plain,
    ! [U_18923,U_18922,U_18921] :
      ( U_18921 = hAPP(hAPP(c_List_Oappend(U_18923),c_List_Olist_ONil(U_18923)),U_18922)
      | U_18921 != U_18922 ),
    inference(variable_rename,[status(thm)],[f_4555_1]) ).

fof(f_4555_3,plain,
    ! [U_18921,U_18922,U_18923] :
      ( U_18921 = hAPP(hAPP(c_List_Oappend(U_18923),c_List_Olist_ONil(U_18923)),U_18922)
      | U_18921 != U_18922 ),
    inference(definitional_conversion,[status(esa)],[f_4555_2]) ).

cnf(f_4555_4,plain,
    ( U_18921 = hAPP(hAPP(c_List_Oappend(U_18923),c_List_Olist_ONil(U_18923)),U_18922)
    | U_18921 != U_18922 ),
    inference(clausify,[status(thm)],[f_4555_3]) ).

fof(f_4556_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_4556_2,plain,
    ! [U_18926,U_18925,U_18924] :
      ( ( hAPP(hAPP(c_List_Oappend(U_18924),U_18925),U_18926) = U_18926
        | U_18925 != c_List_Olist_ONil(U_18924) )
      & ( U_18925 = c_List_Olist_ONil(U_18924)
        | hAPP(hAPP(c_List_Oappend(U_18924),U_18925),U_18926) != U_18926 ) ),
    inference(variable_rename,[status(thm)],[f_4556_1]) ).

fof(f_4556_3,plain,
    ( ! [U_18932,U_18930,U_18928] :
        ( hAPP(hAPP(c_List_Oappend(U_18928),U_18930),U_18932) = U_18932
        | U_18930 != c_List_Olist_ONil(U_18928) )
    & ! [U_18931,U_18929,U_18927] :
        ( U_18929 = c_List_Olist_ONil(U_18927)
        | hAPP(hAPP(c_List_Oappend(U_18927),U_18929),U_18931) != U_18931 ) ),
    inference(miniscope,[status(thm)],[f_4556_2]) ).

fof(f_4556_4,plain,
    ( ! [U_18928,U_18930,U_18932] :
        ( hAPP(hAPP(c_List_Oappend(U_18928),U_18930),U_18932) = U_18932
        | U_18930 != c_List_Olist_ONil(U_18928) )
    & ! [U_18929,U_18931,U_18927] :
        ( U_18929 = c_List_Olist_ONil(U_18927)
        | hAPP(hAPP(c_List_Oappend(U_18927),U_18929),U_18931) != U_18931 ) ),
    inference(definitional_conversion,[status(esa)],[f_4556_3]) ).

cnf(f_4556_5,plain,
    ( U_18929 = c_List_Olist_ONil(U_18927)
    | hAPP(hAPP(c_List_Oappend(U_18927),U_18929),U_18931) != U_18931 ),
    inference(clausify,[status(thm)],[f_4556_4]) ).

cnf(f_4556_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18928),U_18930),U_18932) = U_18932
    | U_18930 != c_List_Olist_ONil(U_18928) ),
    inference(clausify,[status(thm)],[f_4556_4]) ).

fof(f_4557_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_4557_2,plain,
    ! [U_18935,U_18934,U_18933] :
      ( ( hAPP(hAPP(c_List_Oappend(U_18933),U_18934),U_18935) = U_18934
        | U_18935 != c_List_Olist_ONil(U_18933) )
      & ( U_18935 = c_List_Olist_ONil(U_18933)
        | hAPP(hAPP(c_List_Oappend(U_18933),U_18934),U_18935) != U_18934 ) ),
    inference(variable_rename,[status(thm)],[f_4557_1]) ).

fof(f_4557_3,plain,
    ( ! [U_18941,U_18939,U_18937] :
        ( hAPP(hAPP(c_List_Oappend(U_18937),U_18939),U_18941) = U_18939
        | U_18941 != c_List_Olist_ONil(U_18937) )
    & ! [U_18940,U_18938,U_18936] :
        ( U_18940 = c_List_Olist_ONil(U_18936)
        | hAPP(hAPP(c_List_Oappend(U_18936),U_18938),U_18940) != U_18938 ) ),
    inference(miniscope,[status(thm)],[f_4557_2]) ).

fof(f_4557_4,plain,
    ( ! [U_18937,U_18939,U_18941] :
        ( hAPP(hAPP(c_List_Oappend(U_18937),U_18939),U_18941) = U_18939
        | U_18941 != c_List_Olist_ONil(U_18937) )
    & ! [U_18938,U_18940,U_18936] :
        ( U_18940 = c_List_Olist_ONil(U_18936)
        | hAPP(hAPP(c_List_Oappend(U_18936),U_18938),U_18940) != U_18938 ) ),
    inference(definitional_conversion,[status(esa)],[f_4557_3]) ).

cnf(f_4557_5,plain,
    ( U_18940 = c_List_Olist_ONil(U_18936)
    | hAPP(hAPP(c_List_Oappend(U_18936),U_18938),U_18940) != U_18938 ),
    inference(clausify,[status(thm)],[f_4557_4]) ).

cnf(f_4557_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18937),U_18939),U_18941) = U_18939
    | U_18941 != c_List_Olist_ONil(U_18937) ),
    inference(clausify,[status(thm)],[f_4557_4]) ).

fof(f_4558_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_4558_2,plain,
    ! [U_18944,U_18943,U_18942] :
      ( ( hAPP(hAPP(c_List_Oappend(U_18942),U_18943),U_18944) = c_List_Olist_ONil(U_18942)
        | U_18944 != c_List_Olist_ONil(U_18942)
        | U_18943 != c_List_Olist_ONil(U_18942) )
      & ( ( U_18944 = c_List_Olist_ONil(U_18942)
          & U_18943 = c_List_Olist_ONil(U_18942) )
        | hAPP(hAPP(c_List_Oappend(U_18942),U_18943),U_18944) != c_List_Olist_ONil(U_18942) ) ),
    inference(variable_rename,[status(thm)],[f_4558_1]) ).

fof(f_4558_3,plain,
    ( ! [U_18950,U_18948,U_18946] :
        ( hAPP(hAPP(c_List_Oappend(U_18946),U_18948),U_18950) = c_List_Olist_ONil(U_18946)
        | U_18950 != c_List_Olist_ONil(U_18946)
        | U_18948 != c_List_Olist_ONil(U_18946) )
    & ! [U_18949,U_18947,U_18945] :
        ( ( U_18949 = c_List_Olist_ONil(U_18945)
          & U_18947 = c_List_Olist_ONil(U_18945) )
        | hAPP(hAPP(c_List_Oappend(U_18945),U_18947),U_18949) != c_List_Olist_ONil(U_18945) ) ),
    inference(miniscope,[status(thm)],[f_4558_2]) ).

fof(f_4558_4,plain,
    ( ! [U_18945,U_18949,U_18947] :
        ( U_18949 = c_List_Olist_ONil(U_18945)
        | ~ sP1171(U_18945,U_18949,U_18947) )
    & ! [U_18945,U_18949,U_18947] :
        ( U_18947 = c_List_Olist_ONil(U_18945)
        | ~ sP1171(U_18945,U_18949,U_18947) )
    & ! [U_18948,U_18946,U_18950] :
        ( hAPP(hAPP(c_List_Oappend(U_18946),U_18948),U_18950) = c_List_Olist_ONil(U_18946)
        | U_18950 != c_List_Olist_ONil(U_18946)
        | U_18948 != c_List_Olist_ONil(U_18946) )
    & ! [U_18945,U_18949,U_18947] :
        ( sP1171(U_18945,U_18949,U_18947)
        | hAPP(hAPP(c_List_Oappend(U_18945),U_18947),U_18949) != c_List_Olist_ONil(U_18945) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1171])],[f_4558_3]) ).

cnf(f_4558_5,plain,
    ( sP1171(U_18945,U_18949,U_18947)
    | hAPP(hAPP(c_List_Oappend(U_18945),U_18947),U_18949) != c_List_Olist_ONil(U_18945) ),
    inference(clausify,[status(thm)],[f_4558_4]) ).

cnf(f_4558_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_18946),U_18948),U_18950) = c_List_Olist_ONil(U_18946)
    | U_18950 != c_List_Olist_ONil(U_18946)
    | U_18948 != c_List_Olist_ONil(U_18946) ),
    inference(clausify,[status(thm)],[f_4558_4]) ).

cnf(f_4558_7,plain,
    ( U_18947 = c_List_Olist_ONil(U_18945)
    | ~ sP1171(U_18945,U_18949,U_18947) ),
    inference(clausify,[status(thm)],[f_4558_4]) ).

cnf(f_4558_8,plain,
    ( U_18949 = c_List_Olist_ONil(U_18945)
    | ~ sP1171(U_18945,U_18949,U_18947) ),
    inference(clausify,[status(thm)],[f_4558_4]) ).

fof(f_4559_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_4559_2,plain,
    ! [U_18953,U_18952,U_18951] :
      ( ( U_18951 = hAPP(hAPP(c_List_Oappend(U_18952),U_18953),U_18951)
        | U_18953 != c_List_Olist_ONil(U_18952) )
      & ( U_18953 = c_List_Olist_ONil(U_18952)
        | U_18951 != hAPP(hAPP(c_List_Oappend(U_18952),U_18953),U_18951) ) ),
    inference(variable_rename,[status(thm)],[f_4559_1]) ).

fof(f_4559_3,plain,
    ( ! [U_18959,U_18957] :
        ( ! [U_18955] : U_18955 = hAPP(hAPP(c_List_Oappend(U_18957),U_18959),U_18955)
        | U_18959 != c_List_Olist_ONil(U_18957) )
    & ! [U_18958,U_18956] :
        ( ! [U_18954] : U_18954 != hAPP(hAPP(c_List_Oappend(U_18956),U_18958),U_18954)
        | U_18958 = c_List_Olist_ONil(U_18956) ) ),
    inference(miniscope,[status(thm)],[f_4559_2]) ).

fof(f_4559_4,plain,
    ( ! [U_18955,U_18959,U_18957] :
        ( U_18955 = hAPP(hAPP(c_List_Oappend(U_18957),U_18959),U_18955)
        | U_18959 != c_List_Olist_ONil(U_18957) )
    & ! [U_18956,U_18958,U_18954] :
        ( U_18954 != hAPP(hAPP(c_List_Oappend(U_18956),U_18958),U_18954)
        | U_18958 = c_List_Olist_ONil(U_18956) ) ),
    inference(definitional_conversion,[status(esa)],[f_4559_3]) ).

cnf(f_4559_5,plain,
    ( U_18954 != hAPP(hAPP(c_List_Oappend(U_18956),U_18958),U_18954)
    | U_18958 = c_List_Olist_ONil(U_18956) ),
    inference(clausify,[status(thm)],[f_4559_4]) ).

cnf(f_4559_6,plain,
    ( U_18955 = hAPP(hAPP(c_List_Oappend(U_18957),U_18959),U_18955)
    | U_18959 != c_List_Olist_ONil(U_18957) ),
    inference(clausify,[status(thm)],[f_4559_4]) ).

fof(f_4560_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_4560_2,plain,
    ! [U_18962,U_18961,U_18960] :
      ( ( U_18960 = hAPP(hAPP(c_List_Oappend(U_18961),U_18960),U_18962)
        | U_18962 != c_List_Olist_ONil(U_18961) )
      & ( U_18962 = c_List_Olist_ONil(U_18961)
        | U_18960 != hAPP(hAPP(c_List_Oappend(U_18961),U_18960),U_18962) ) ),
    inference(variable_rename,[status(thm)],[f_4560_1]) ).

fof(f_4560_3,plain,
    ( ! [U_18968,U_18966] :
        ( ! [U_18964] : U_18964 = hAPP(hAPP(c_List_Oappend(U_18966),U_18964),U_18968)
        | U_18968 != c_List_Olist_ONil(U_18966) )
    & ! [U_18967,U_18965] :
        ( ! [U_18963] : U_18963 != hAPP(hAPP(c_List_Oappend(U_18965),U_18963),U_18967)
        | U_18967 = c_List_Olist_ONil(U_18965) ) ),
    inference(miniscope,[status(thm)],[f_4560_2]) ).

fof(f_4560_4,plain,
    ( ! [U_18968,U_18964,U_18966] :
        ( U_18964 = hAPP(hAPP(c_List_Oappend(U_18966),U_18964),U_18968)
        | U_18968 != c_List_Olist_ONil(U_18966) )
    & ! [U_18967,U_18965,U_18963] :
        ( U_18963 != hAPP(hAPP(c_List_Oappend(U_18965),U_18963),U_18967)
        | U_18967 = c_List_Olist_ONil(U_18965) ) ),
    inference(definitional_conversion,[status(esa)],[f_4560_3]) ).

cnf(f_4560_5,plain,
    ( U_18963 != hAPP(hAPP(c_List_Oappend(U_18965),U_18963),U_18967)
    | U_18967 = c_List_Olist_ONil(U_18965) ),
    inference(clausify,[status(thm)],[f_4560_4]) ).

cnf(f_4560_6,plain,
    ( U_18964 = hAPP(hAPP(c_List_Oappend(U_18966),U_18964),U_18968)
    | U_18968 != c_List_Olist_ONil(U_18966) ),
    inference(clausify,[status(thm)],[f_4560_4]) ).

fof(f_4561_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_4561_2,plain,
    ! [U_18970,U_18969] : hAPP(hAPP(c_List_Oappend(U_18969),U_18970),c_List_Olist_ONil(U_18969)) = U_18970,
    inference(variable_rename,[status(thm)],[f_4561_1]) ).

fof(f_4561_3,plain,
    ! [U_18969,U_18970] : hAPP(hAPP(c_List_Oappend(U_18969),U_18970),c_List_Olist_ONil(U_18969)) = U_18970,
    inference(definitional_conversion,[status(esa)],[f_4561_2]) ).

cnf(f_4561_4,plain,
    hAPP(hAPP(c_List_Oappend(U_18969),U_18970),c_List_Olist_ONil(U_18969)) = U_18970,
    inference(clausify,[status(thm)],[f_4561_3]) ).

fof(f_4562_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_4562_2,plain,
    ! [U_18973,U_18972,U_18971] :
      ( ( c_List_Olist_ONil(U_18971) = hAPP(hAPP(c_List_Oappend(U_18971),U_18972),U_18973)
        | U_18973 != c_List_Olist_ONil(U_18971)
        | U_18972 != c_List_Olist_ONil(U_18971) )
      & ( ( U_18973 = c_List_Olist_ONil(U_18971)
          & U_18972 = c_List_Olist_ONil(U_18971) )
        | c_List_Olist_ONil(U_18971) != hAPP(hAPP(c_List_Oappend(U_18971),U_18972),U_18973) ) ),
    inference(variable_rename,[status(thm)],[f_4562_1]) ).

fof(f_4562_3,plain,
    ( ! [U_18979,U_18977,U_18975] :
        ( c_List_Olist_ONil(U_18975) = hAPP(hAPP(c_List_Oappend(U_18975),U_18977),U_18979)
        | U_18979 != c_List_Olist_ONil(U_18975)
        | U_18977 != c_List_Olist_ONil(U_18975) )
    & ! [U_18978,U_18976,U_18974] :
        ( ( U_18978 = c_List_Olist_ONil(U_18974)
          & U_18976 = c_List_Olist_ONil(U_18974) )
        | c_List_Olist_ONil(U_18974) != hAPP(hAPP(c_List_Oappend(U_18974),U_18976),U_18978) ) ),
    inference(miniscope,[status(thm)],[f_4562_2]) ).

fof(f_4562_4,plain,
    ( ! [U_18974,U_18978,U_18976] :
        ( U_18978 = c_List_Olist_ONil(U_18974)
        | ~ sP1172(U_18974,U_18978,U_18976) )
    & ! [U_18974,U_18978,U_18976] :
        ( U_18976 = c_List_Olist_ONil(U_18974)
        | ~ sP1172(U_18974,U_18978,U_18976) )
    & ! [U_18977,U_18975,U_18979] :
        ( c_List_Olist_ONil(U_18975) = hAPP(hAPP(c_List_Oappend(U_18975),U_18977),U_18979)
        | U_18979 != c_List_Olist_ONil(U_18975)
        | U_18977 != c_List_Olist_ONil(U_18975) )
    & ! [U_18974,U_18978,U_18976] :
        ( sP1172(U_18974,U_18978,U_18976)
        | c_List_Olist_ONil(U_18974) != hAPP(hAPP(c_List_Oappend(U_18974),U_18976),U_18978) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1172])],[f_4562_3]) ).

cnf(f_4562_5,plain,
    ( sP1172(U_18974,U_18978,U_18976)
    | c_List_Olist_ONil(U_18974) != hAPP(hAPP(c_List_Oappend(U_18974),U_18976),U_18978) ),
    inference(clausify,[status(thm)],[f_4562_4]) ).

cnf(f_4562_6,plain,
    ( c_List_Olist_ONil(U_18975) = hAPP(hAPP(c_List_Oappend(U_18975),U_18977),U_18979)
    | U_18979 != c_List_Olist_ONil(U_18975)
    | U_18977 != c_List_Olist_ONil(U_18975) ),
    inference(clausify,[status(thm)],[f_4562_4]) ).

cnf(f_4562_7,plain,
    ( U_18976 = c_List_Olist_ONil(U_18974)
    | ~ sP1172(U_18974,U_18978,U_18976) ),
    inference(clausify,[status(thm)],[f_4562_4]) ).

cnf(f_4562_8,plain,
    ( U_18978 = c_List_Olist_ONil(U_18974)
    | ~ sP1172(U_18974,U_18978,U_18976) ),
    inference(clausify,[status(thm)],[f_4562_4]) ).

fof(f_4563_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_4563_2,plain,
    ! [U_18981,U_18980] : hAPP(hAPP(c_List_Oappend(U_18980),c_List_Olist_ONil(U_18980)),U_18981) = U_18981,
    inference(variable_rename,[status(thm)],[f_4563_1]) ).

fof(f_4563_3,plain,
    ! [U_18980,U_18981] : hAPP(hAPP(c_List_Oappend(U_18980),c_List_Olist_ONil(U_18980)),U_18981) = U_18981,
    inference(definitional_conversion,[status(esa)],[f_4563_2]) ).

cnf(f_4563_4,plain,
    hAPP(hAPP(c_List_Oappend(U_18980),c_List_Olist_ONil(U_18980)),U_18981) = U_18981,
    inference(clausify,[status(thm)],[f_4563_3]) ).

fof(f_4564_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_4564_2,plain,
    ! [U_18986,U_18985,U_18984,U_18983,U_18982] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18982),tc_List_Olist(U_18982))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18982),tc_List_Olist(U_18982)),hAPP(hAPP(c_List_Oappend(U_18982),U_18986),U_18983)),hAPP(hAPP(c_List_Oappend(U_18982),U_18986),U_18984))),c_List_Olexord(U_18982,U_18985)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18982),tc_List_Olist(U_18982))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18982),tc_List_Olist(U_18982)),U_18983),U_18984)),c_List_Olexord(U_18982,U_18985))) ),
    inference(variable_rename,[status(thm)],[f_4564_1]) ).

fof(f_4564_3,plain,
    ! [U_18982,U_18983,U_18984,U_18985,U_18986] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18982),tc_List_Olist(U_18982))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18982),tc_List_Olist(U_18982)),hAPP(hAPP(c_List_Oappend(U_18982),U_18986),U_18983)),hAPP(hAPP(c_List_Oappend(U_18982),U_18986),U_18984))),c_List_Olexord(U_18982,U_18985)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18982),tc_List_Olist(U_18982))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18982),tc_List_Olist(U_18982)),U_18983),U_18984)),c_List_Olexord(U_18982,U_18985))) ),
    inference(definitional_conversion,[status(esa)],[f_4564_2]) ).

cnf(f_4564_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18982),tc_List_Olist(U_18982))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18982),tc_List_Olist(U_18982)),hAPP(hAPP(c_List_Oappend(U_18982),U_18986),U_18983)),hAPP(hAPP(c_List_Oappend(U_18982),U_18986),U_18984))),c_List_Olexord(U_18982,U_18985)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_18982),tc_List_Olist(U_18982))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_18982),tc_List_Olist(U_18982)),U_18983),U_18984)),c_List_Olexord(U_18982,U_18985))) ),
    inference(clausify,[status(thm)],[f_4564_3]) ).

fof(f_4565_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_4565_2,plain,
    ! [U_18989,U_18988,U_18987] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_18987),hAPP(hAPP(c_List_Oappend(U_18987),U_18988),U_18989)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18987,tc_HOL_Obool)),hAPP(c_List_Oset(U_18987),U_18988)),hAPP(c_List_Oset(U_18987),U_18989)) != c_Orderings_Obot__class_Obot(tc_fun(U_18987,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18987),U_18989))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18987),U_18988)) )
      & ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18987,tc_HOL_Obool)),hAPP(c_List_Oset(U_18987),U_18988)),hAPP(c_List_Oset(U_18987),U_18989)) = c_Orderings_Obot__class_Obot(tc_fun(U_18987,tc_HOL_Obool))
          & hBOOL(hAPP(c_List_Odistinct(U_18987),U_18989))
          & hBOOL(hAPP(c_List_Odistinct(U_18987),U_18988)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18987),hAPP(hAPP(c_List_Oappend(U_18987),U_18988),U_18989))) ) ),
    inference(variable_rename,[status(thm)],[f_4565_1]) ).

fof(f_4565_3,plain,
    ( ! [U_18995,U_18993,U_18991] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18991),hAPP(hAPP(c_List_Oappend(U_18991),U_18993),U_18995)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18991,tc_HOL_Obool)),hAPP(c_List_Oset(U_18991),U_18993)),hAPP(c_List_Oset(U_18991),U_18995)) != c_Orderings_Obot__class_Obot(tc_fun(U_18991,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18991),U_18995))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18991),U_18993)) )
    & ! [U_18994,U_18992,U_18990] :
        ( ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18990,tc_HOL_Obool)),hAPP(c_List_Oset(U_18990),U_18992)),hAPP(c_List_Oset(U_18990),U_18994)) = c_Orderings_Obot__class_Obot(tc_fun(U_18990,tc_HOL_Obool))
          & hBOOL(hAPP(c_List_Odistinct(U_18990),U_18994))
          & hBOOL(hAPP(c_List_Odistinct(U_18990),U_18992)) )
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18990),hAPP(hAPP(c_List_Oappend(U_18990),U_18992),U_18994))) ) ),
    inference(miniscope,[status(thm)],[f_4565_2]) ).

fof(f_4565_4,plain,
    ( ! [U_18992,U_18990,U_18994] :
        ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18990,tc_HOL_Obool)),hAPP(c_List_Oset(U_18990),U_18992)),hAPP(c_List_Oset(U_18990),U_18994)) = c_Orderings_Obot__class_Obot(tc_fun(U_18990,tc_HOL_Obool))
        | ~ sP1173(U_18992,U_18990,U_18994) )
    & ! [U_18992,U_18990,U_18994] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18990),U_18994))
        | ~ sP1173(U_18992,U_18990,U_18994) )
    & ! [U_18992,U_18990,U_18994] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18990),U_18992))
        | ~ sP1173(U_18992,U_18990,U_18994) )
    & ! [U_18991,U_18993,U_18995] :
        ( hBOOL(hAPP(c_List_Odistinct(U_18991),hAPP(hAPP(c_List_Oappend(U_18991),U_18993),U_18995)))
        | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18991,tc_HOL_Obool)),hAPP(c_List_Oset(U_18991),U_18993)),hAPP(c_List_Oset(U_18991),U_18995)) != c_Orderings_Obot__class_Obot(tc_fun(U_18991,tc_HOL_Obool))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18991),U_18995))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18991),U_18993)) )
    & ! [U_18992,U_18990,U_18994] :
        ( sP1173(U_18992,U_18990,U_18994)
        | ~ hBOOL(hAPP(c_List_Odistinct(U_18990),hAPP(hAPP(c_List_Oappend(U_18990),U_18992),U_18994))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1173])],[f_4565_3]) ).

cnf(f_4565_5,plain,
    ( sP1173(U_18992,U_18990,U_18994)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18990),hAPP(hAPP(c_List_Oappend(U_18990),U_18992),U_18994))) ),
    inference(clausify,[status(thm)],[f_4565_4]) ).

cnf(f_4565_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18991),hAPP(hAPP(c_List_Oappend(U_18991),U_18993),U_18995)))
    | hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18991,tc_HOL_Obool)),hAPP(c_List_Oset(U_18991),U_18993)),hAPP(c_List_Oset(U_18991),U_18995)) != c_Orderings_Obot__class_Obot(tc_fun(U_18991,tc_HOL_Obool))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18991),U_18995))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_18991),U_18993)) ),
    inference(clausify,[status(thm)],[f_4565_4]) ).

cnf(f_4565_7,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18990),U_18992))
    | ~ sP1173(U_18992,U_18990,U_18994) ),
    inference(clausify,[status(thm)],[f_4565_4]) ).

cnf(f_4565_8,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_18990),U_18994))
    | ~ sP1173(U_18992,U_18990,U_18994) ),
    inference(clausify,[status(thm)],[f_4565_4]) ).

cnf(f_4565_9,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(U_18990,tc_HOL_Obool)),hAPP(c_List_Oset(U_18990),U_18992)),hAPP(c_List_Oset(U_18990),U_18994)) = c_Orderings_Obot__class_Obot(tc_fun(U_18990,tc_HOL_Obool))
    | ~ sP1173(U_18992,U_18990,U_18994) ),
    inference(clausify,[status(thm)],[f_4565_4]) ).

fof(f_4566_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_4566_2,plain,
    ! [U_18999,U_18998,U_18997,U_18996] :
      ( ( hAPP(hAPP(c_List_Onth(U_18997),hAPP(hAPP(c_List_Oappend(U_18997),U_18998),U_18999)),U_18996) = hAPP(hAPP(c_List_Onth(U_18997),U_18999),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_18996),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18997)),U_18998)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18996),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18997)),U_18998))) )
      & ( hAPP(hAPP(c_List_Onth(U_18997),hAPP(hAPP(c_List_Oappend(U_18997),U_18998),U_18999)),U_18996) = hAPP(hAPP(c_List_Onth(U_18997),U_18998),U_18996)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_18996),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_18997)),U_18998))) ) ),
    inference(variable_rename,[status(thm)],[f_4566_1]) ).

fof(f_4566_3,plain,
    ( ! [U_19007,U_19005,U_19003,U_19001] :
        ( hAPP(hAPP(c_List_Onth(U_19003),hAPP(hAPP(c_List_Oappend(U_19003),U_19005),U_19007)),U_19001) = hAPP(hAPP(c_List_Onth(U_19003),U_19007),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19001),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19003)),U_19005)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19001),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19003)),U_19005))) )
    & ! [U_19006,U_19004,U_19002,U_19000] :
        ( hAPP(hAPP(c_List_Onth(U_19002),hAPP(hAPP(c_List_Oappend(U_19002),U_19004),U_19006)),U_19000) = hAPP(hAPP(c_List_Onth(U_19002),U_19004),U_19000)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19000),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19002)),U_19004))) ) ),
    inference(miniscope,[status(thm)],[f_4566_2]) ).

fof(f_4566_4,plain,
    ( ! [U_19001,U_19003,U_19005,U_19007] :
        ( hAPP(hAPP(c_List_Onth(U_19003),hAPP(hAPP(c_List_Oappend(U_19003),U_19005),U_19007)),U_19001) = hAPP(hAPP(c_List_Onth(U_19003),U_19007),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19001),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19003)),U_19005)))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19001),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19003)),U_19005))) )
    & ! [U_19006,U_19002,U_19000,U_19004] :
        ( hAPP(hAPP(c_List_Onth(U_19002),hAPP(hAPP(c_List_Oappend(U_19002),U_19004),U_19006)),U_19000) = hAPP(hAPP(c_List_Onth(U_19002),U_19004),U_19000)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19000),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19002)),U_19004))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4566_3]) ).

cnf(f_4566_5,plain,
    ( hAPP(hAPP(c_List_Onth(U_19002),hAPP(hAPP(c_List_Oappend(U_19002),U_19004),U_19006)),U_19000) = hAPP(hAPP(c_List_Onth(U_19002),U_19004),U_19000)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19000),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19002)),U_19004))) ),
    inference(clausify,[status(thm)],[f_4566_4]) ).

cnf(f_4566_6,plain,
    ( hAPP(hAPP(c_List_Onth(U_19003),hAPP(hAPP(c_List_Oappend(U_19003),U_19005),U_19007)),U_19001) = hAPP(hAPP(c_List_Onth(U_19003),U_19007),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19001),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19003)),U_19005)))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19001),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19003)),U_19005))) ),
    inference(clausify,[status(thm)],[f_4566_4]) ).

fof(f_4567_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_4567_2,plain,
    ! [U_19012,U_19011,U_19010,U_19009,U_19008] :
      ( ( hAPP(hAPP(c_List_Olist__update(U_19009,hAPP(hAPP(c_List_Oappend(U_19009),U_19010),U_19011)),U_19008),U_19012) = hAPP(hAPP(c_List_Oappend(U_19009),U_19010),hAPP(hAPP(c_List_Olist__update(U_19009,U_19011),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19008),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19009)),U_19010))),U_19012))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19008),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19009)),U_19010))) )
      & ( hAPP(hAPP(c_List_Olist__update(U_19009,hAPP(hAPP(c_List_Oappend(U_19009),U_19010),U_19011)),U_19008),U_19012) = hAPP(hAPP(c_List_Oappend(U_19009),hAPP(hAPP(c_List_Olist__update(U_19009,U_19010),U_19008),U_19012)),U_19011)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19008),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19009)),U_19010))) ) ),
    inference(variable_rename,[status(thm)],[f_4567_1]) ).

fof(f_4567_3,plain,
    ( ! [U_19022,U_19020,U_19018,U_19016,U_19014] :
        ( hAPP(hAPP(c_List_Olist__update(U_19016,hAPP(hAPP(c_List_Oappend(U_19016),U_19018),U_19020)),U_19014),U_19022) = hAPP(hAPP(c_List_Oappend(U_19016),U_19018),hAPP(hAPP(c_List_Olist__update(U_19016,U_19020),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19014),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19016)),U_19018))),U_19022))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19014),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19016)),U_19018))) )
    & ! [U_19021,U_19019,U_19017,U_19015,U_19013] :
        ( hAPP(hAPP(c_List_Olist__update(U_19015,hAPP(hAPP(c_List_Oappend(U_19015),U_19017),U_19019)),U_19013),U_19021) = hAPP(hAPP(c_List_Oappend(U_19015),hAPP(hAPP(c_List_Olist__update(U_19015,U_19017),U_19013),U_19021)),U_19019)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19013),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19015)),U_19017))) ) ),
    inference(miniscope,[status(thm)],[f_4567_2]) ).

fof(f_4567_4,plain,
    ( ! [U_19014,U_19016,U_19018,U_19020,U_19022] :
        ( hAPP(hAPP(c_List_Olist__update(U_19016,hAPP(hAPP(c_List_Oappend(U_19016),U_19018),U_19020)),U_19014),U_19022) = hAPP(hAPP(c_List_Oappend(U_19016),U_19018),hAPP(hAPP(c_List_Olist__update(U_19016,U_19020),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19014),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19016)),U_19018))),U_19022))
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19014),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19016)),U_19018))) )
    & ! [U_19015,U_19017,U_19019,U_19013,U_19021] :
        ( hAPP(hAPP(c_List_Olist__update(U_19015,hAPP(hAPP(c_List_Oappend(U_19015),U_19017),U_19019)),U_19013),U_19021) = hAPP(hAPP(c_List_Oappend(U_19015),hAPP(hAPP(c_List_Olist__update(U_19015,U_19017),U_19013),U_19021)),U_19019)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19013),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19015)),U_19017))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4567_3]) ).

cnf(f_4567_5,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_19015,hAPP(hAPP(c_List_Oappend(U_19015),U_19017),U_19019)),U_19013),U_19021) = hAPP(hAPP(c_List_Oappend(U_19015),hAPP(hAPP(c_List_Olist__update(U_19015,U_19017),U_19013),U_19021)),U_19019)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19013),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19015)),U_19017))) ),
    inference(clausify,[status(thm)],[f_4567_4]) ).

cnf(f_4567_6,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_19016,hAPP(hAPP(c_List_Oappend(U_19016),U_19018),U_19020)),U_19014),U_19022) = hAPP(hAPP(c_List_Oappend(U_19016),U_19018),hAPP(hAPP(c_List_Olist__update(U_19016,U_19020),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19014),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19016)),U_19018))),U_19022))
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19014),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19016)),U_19018))) ),
    inference(clausify,[status(thm)],[f_4567_4]) ).

fof(f_4568_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_4568_2,plain,
    ! [U_19026,U_19025,U_19024,U_19023] : c_List_Osublist(U_19023,hAPP(hAPP(c_List_Oappend(U_19023),U_19024),U_19025),U_19026) = hAPP(hAPP(c_List_Oappend(U_19023),c_List_Osublist(U_19023,U_19024,U_19026)),c_List_Osublist(U_19023,U_19025,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_19023)),U_19024)))),U_19026)))),
    inference(variable_rename,[status(thm)],[f_4568_1]) ).

fof(f_4568_3,plain,
    ! [U_19023,U_19024,U_19025,U_19026] : c_List_Osublist(U_19023,hAPP(hAPP(c_List_Oappend(U_19023),U_19024),U_19025),U_19026) = hAPP(hAPP(c_List_Oappend(U_19023),c_List_Osublist(U_19023,U_19024,U_19026)),c_List_Osublist(U_19023,U_19025,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_19023)),U_19024)))),U_19026)))),
    inference(definitional_conversion,[status(esa)],[f_4568_2]) ).

cnf(f_4568_4,plain,
    c_List_Osublist(U_19023,hAPP(hAPP(c_List_Oappend(U_19023),U_19024),U_19025),U_19026) = hAPP(hAPP(c_List_Oappend(U_19023),c_List_Osublist(U_19023,U_19024,U_19026)),c_List_Osublist(U_19023,U_19025,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_19023)),U_19024)))),U_19026)))),
    inference(clausify,[status(thm)],[f_4568_3]) ).

fof(f_4569_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_4569_2,plain,
    ! [U_19033,U_19032,U_19031,U_19030,U_19029,U_19028,U_19027] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19027),tc_List_Olist(U_19027))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19027),tc_List_Olist(U_19027)),hAPP(hAPP(c_List_Oappend(U_19027),U_19031),hAPP(hAPP(c_List_Olist_OCons(U_19027),U_19028),U_19032))),hAPP(hAPP(c_List_Oappend(U_19027),U_19031),hAPP(hAPP(c_List_Olist_OCons(U_19027),U_19029),U_19033)))),c_List_Olexord(U_19027,U_19030)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19027,U_19027)),hAPP(hAPP(c_Product__Type_OPair(U_19027,U_19027),U_19028),U_19029)),U_19030)) ),
    inference(variable_rename,[status(thm)],[f_4569_1]) ).

fof(f_4569_3,plain,
    ! [U_19027,U_19028,U_19029,U_19030,U_19031,U_19032,U_19033] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19027),tc_List_Olist(U_19027))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19027),tc_List_Olist(U_19027)),hAPP(hAPP(c_List_Oappend(U_19027),U_19031),hAPP(hAPP(c_List_Olist_OCons(U_19027),U_19028),U_19032))),hAPP(hAPP(c_List_Oappend(U_19027),U_19031),hAPP(hAPP(c_List_Olist_OCons(U_19027),U_19029),U_19033)))),c_List_Olexord(U_19027,U_19030)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19027,U_19027)),hAPP(hAPP(c_Product__Type_OPair(U_19027,U_19027),U_19028),U_19029)),U_19030)) ),
    inference(definitional_conversion,[status(esa)],[f_4569_2]) ).

cnf(f_4569_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19027),tc_List_Olist(U_19027))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19027),tc_List_Olist(U_19027)),hAPP(hAPP(c_List_Oappend(U_19027),U_19031),hAPP(hAPP(c_List_Olist_OCons(U_19027),U_19028),U_19032))),hAPP(hAPP(c_List_Oappend(U_19027),U_19031),hAPP(hAPP(c_List_Olist_OCons(U_19027),U_19029),U_19033)))),c_List_Olexord(U_19027,U_19030)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19027,U_19027)),hAPP(hAPP(c_Product__Type_OPair(U_19027,U_19027),U_19028),U_19029)),U_19030)) ),
    inference(clausify,[status(thm)],[f_4569_3]) ).

fof(f_4570_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_4570_2,plain,
    ! [U_19036,U_19035,U_19034] :
      ( hAPP(hAPP(c_List_Otake(U_19035),hAPP(c_Nat_OSuc,U_19034)),U_19036) = hAPP(hAPP(c_List_Oappend(U_19035),hAPP(hAPP(c_List_Otake(U_19035),U_19034),U_19036)),hAPP(hAPP(c_List_Olist_OCons(U_19035),hAPP(hAPP(c_List_Onth(U_19035),U_19036),U_19034)),c_List_Olist_ONil(U_19035)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19034),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19035)),U_19036))) ),
    inference(variable_rename,[status(thm)],[f_4570_1]) ).

fof(f_4570_3,plain,
    ! [U_19034,U_19035,U_19036] :
      ( hAPP(hAPP(c_List_Otake(U_19035),hAPP(c_Nat_OSuc,U_19034)),U_19036) = hAPP(hAPP(c_List_Oappend(U_19035),hAPP(hAPP(c_List_Otake(U_19035),U_19034),U_19036)),hAPP(hAPP(c_List_Olist_OCons(U_19035),hAPP(hAPP(c_List_Onth(U_19035),U_19036),U_19034)),c_List_Olist_ONil(U_19035)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19034),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19035)),U_19036))) ),
    inference(definitional_conversion,[status(esa)],[f_4570_2]) ).

cnf(f_4570_4,plain,
    ( hAPP(hAPP(c_List_Otake(U_19035),hAPP(c_Nat_OSuc,U_19034)),U_19036) = hAPP(hAPP(c_List_Oappend(U_19035),hAPP(hAPP(c_List_Otake(U_19035),U_19034),U_19036)),hAPP(hAPP(c_List_Olist_OCons(U_19035),hAPP(hAPP(c_List_Onth(U_19035),U_19036),U_19034)),c_List_Olist_ONil(U_19035)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19034),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19035)),U_19036))) ),
    inference(clausify,[status(thm)],[f_4570_3]) ).

fof(f_4571_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_4571_2,plain,
    ! [U_19042,U_19041,U_19040,U_19039,U_19038,U_19037] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19037),tc_List_Olist(U_19037))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19037),tc_List_Olist(U_19037)),hAPP(hAPP(c_List_Oappend(U_19037),U_19038),hAPP(hAPP(c_List_Olist_OCons(U_19037),U_19039),c_List_Olist_ONil(U_19037)))),hAPP(hAPP(c_List_Oappend(U_19037),U_19040),hAPP(hAPP(c_List_Olist_OCons(U_19037),U_19041),c_List_Olist_ONil(U_19037))))),c_List_Olistrel1(U_19037,U_19042)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19037,U_19037)),hAPP(hAPP(c_Product__Type_OPair(U_19037,U_19037),U_19039),U_19041)),U_19042))
            | U_19038 != U_19040 )
          & ( U_19039 != U_19041
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19037),tc_List_Olist(U_19037))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19037),tc_List_Olist(U_19037)),U_19038),U_19040)),c_List_Olistrel1(U_19037,U_19042))) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19037,U_19037)),hAPP(hAPP(c_Product__Type_OPair(U_19037,U_19037),U_19039),U_19041)),U_19042))
          & U_19038 = U_19040 )
        | ( U_19039 = U_19041
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19037),tc_List_Olist(U_19037))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19037),tc_List_Olist(U_19037)),U_19038),U_19040)),c_List_Olistrel1(U_19037,U_19042))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19037),tc_List_Olist(U_19037))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19037),tc_List_Olist(U_19037)),hAPP(hAPP(c_List_Oappend(U_19037),U_19038),hAPP(hAPP(c_List_Olist_OCons(U_19037),U_19039),c_List_Olist_ONil(U_19037)))),hAPP(hAPP(c_List_Oappend(U_19037),U_19040),hAPP(hAPP(c_List_Olist_OCons(U_19037),U_19041),c_List_Olist_ONil(U_19037))))),c_List_Olistrel1(U_19037,U_19042))) ) ),
    inference(variable_rename,[status(thm)],[f_4571_1]) ).

fof(f_4571_3,plain,
    ( ! [U_19054,U_19052,U_19050,U_19048,U_19046,U_19044] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19044),tc_List_Olist(U_19044))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19044),tc_List_Olist(U_19044)),hAPP(hAPP(c_List_Oappend(U_19044),U_19046),hAPP(hAPP(c_List_Olist_OCons(U_19044),U_19048),c_List_Olist_ONil(U_19044)))),hAPP(hAPP(c_List_Oappend(U_19044),U_19050),hAPP(hAPP(c_List_Olist_OCons(U_19044),U_19052),c_List_Olist_ONil(U_19044))))),c_List_Olistrel1(U_19044,U_19054)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19044,U_19044)),hAPP(hAPP(c_Product__Type_OPair(U_19044,U_19044),U_19048),U_19052)),U_19054))
            | U_19046 != U_19050 )
          & ( U_19048 != U_19052
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19044),tc_List_Olist(U_19044))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19044),tc_List_Olist(U_19044)),U_19046),U_19050)),c_List_Olistrel1(U_19044,U_19054))) ) ) )
    & ! [U_19053,U_19051,U_19049,U_19047,U_19045,U_19043] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19043,U_19043)),hAPP(hAPP(c_Product__Type_OPair(U_19043,U_19043),U_19047),U_19051)),U_19053))
          & U_19045 = U_19049 )
        | ( U_19047 = U_19051
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19043),tc_List_Olist(U_19043))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19043),tc_List_Olist(U_19043)),U_19045),U_19049)),c_List_Olistrel1(U_19043,U_19053))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19043),tc_List_Olist(U_19043))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19043),tc_List_Olist(U_19043)),hAPP(hAPP(c_List_Oappend(U_19043),U_19045),hAPP(hAPP(c_List_Olist_OCons(U_19043),U_19047),c_List_Olist_ONil(U_19043)))),hAPP(hAPP(c_List_Oappend(U_19043),U_19049),hAPP(hAPP(c_List_Olist_OCons(U_19043),U_19051),c_List_Olist_ONil(U_19043))))),c_List_Olistrel1(U_19043,U_19053))) ) ),
    inference(miniscope,[status(thm)],[f_4571_2]) ).

fof(f_4571_4,plain,
    ( ! [U_19044,U_19052,U_19046,U_19048,U_19050,U_19054] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19044,U_19044)),hAPP(hAPP(c_Product__Type_OPair(U_19044,U_19044),U_19048),U_19052)),U_19054))
        | U_19046 != U_19050
        | ~ sP1176(U_19044,U_19052,U_19046,U_19048,U_19050,U_19054) )
    & ! [U_19044,U_19052,U_19046,U_19048,U_19050,U_19054] :
        ( U_19048 != U_19052
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19044),tc_List_Olist(U_19044))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19044),tc_List_Olist(U_19044)),U_19046),U_19050)),c_List_Olistrel1(U_19044,U_19054)))
        | ~ sP1176(U_19044,U_19052,U_19046,U_19048,U_19050,U_19054) )
    & ! [U_19043,U_19051,U_19053,U_19045,U_19047,U_19049] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19043,U_19043)),hAPP(hAPP(c_Product__Type_OPair(U_19043,U_19043),U_19047),U_19051)),U_19053))
        | ~ sP1175(U_19043,U_19051,U_19053,U_19045,U_19047,U_19049) )
    & ! [U_19043,U_19051,U_19053,U_19045,U_19047,U_19049] :
        ( U_19045 = U_19049
        | ~ sP1175(U_19043,U_19051,U_19053,U_19045,U_19047,U_19049) )
    & ! [U_19043,U_19051,U_19053,U_19045,U_19047,U_19049] :
        ( U_19047 = U_19051
        | ~ sP1174(U_19043,U_19051,U_19053,U_19045,U_19047,U_19049) )
    & ! [U_19043,U_19051,U_19053,U_19045,U_19047,U_19049] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19043),tc_List_Olist(U_19043))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19043),tc_List_Olist(U_19043)),U_19045),U_19049)),c_List_Olistrel1(U_19043,U_19053)))
        | ~ sP1174(U_19043,U_19051,U_19053,U_19045,U_19047,U_19049) )
    & ! [U_19044,U_19052,U_19046,U_19048,U_19050,U_19054] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19044),tc_List_Olist(U_19044))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19044),tc_List_Olist(U_19044)),hAPP(hAPP(c_List_Oappend(U_19044),U_19046),hAPP(hAPP(c_List_Olist_OCons(U_19044),U_19048),c_List_Olist_ONil(U_19044)))),hAPP(hAPP(c_List_Oappend(U_19044),U_19050),hAPP(hAPP(c_List_Olist_OCons(U_19044),U_19052),c_List_Olist_ONil(U_19044))))),c_List_Olistrel1(U_19044,U_19054)))
        | sP1176(U_19044,U_19052,U_19046,U_19048,U_19050,U_19054) )
    & ! [U_19043,U_19051,U_19053,U_19045,U_19047,U_19049] :
        ( sP1175(U_19043,U_19051,U_19053,U_19045,U_19047,U_19049)
        | sP1174(U_19043,U_19051,U_19053,U_19045,U_19047,U_19049)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19043),tc_List_Olist(U_19043))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19043),tc_List_Olist(U_19043)),hAPP(hAPP(c_List_Oappend(U_19043),U_19045),hAPP(hAPP(c_List_Olist_OCons(U_19043),U_19047),c_List_Olist_ONil(U_19043)))),hAPP(hAPP(c_List_Oappend(U_19043),U_19049),hAPP(hAPP(c_List_Olist_OCons(U_19043),U_19051),c_List_Olist_ONil(U_19043))))),c_List_Olistrel1(U_19043,U_19053))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1174,sP1175,sP1176])],[f_4571_3]) ).

cnf(f_4571_5,plain,
    ( sP1175(U_19043,U_19051,U_19053,U_19045,U_19047,U_19049)
    | sP1174(U_19043,U_19051,U_19053,U_19045,U_19047,U_19049)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19043),tc_List_Olist(U_19043))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19043),tc_List_Olist(U_19043)),hAPP(hAPP(c_List_Oappend(U_19043),U_19045),hAPP(hAPP(c_List_Olist_OCons(U_19043),U_19047),c_List_Olist_ONil(U_19043)))),hAPP(hAPP(c_List_Oappend(U_19043),U_19049),hAPP(hAPP(c_List_Olist_OCons(U_19043),U_19051),c_List_Olist_ONil(U_19043))))),c_List_Olistrel1(U_19043,U_19053))) ),
    inference(clausify,[status(thm)],[f_4571_4]) ).

cnf(f_4571_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19044),tc_List_Olist(U_19044))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19044),tc_List_Olist(U_19044)),hAPP(hAPP(c_List_Oappend(U_19044),U_19046),hAPP(hAPP(c_List_Olist_OCons(U_19044),U_19048),c_List_Olist_ONil(U_19044)))),hAPP(hAPP(c_List_Oappend(U_19044),U_19050),hAPP(hAPP(c_List_Olist_OCons(U_19044),U_19052),c_List_Olist_ONil(U_19044))))),c_List_Olistrel1(U_19044,U_19054)))
    | sP1176(U_19044,U_19052,U_19046,U_19048,U_19050,U_19054) ),
    inference(clausify,[status(thm)],[f_4571_4]) ).

cnf(f_4571_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19043),tc_List_Olist(U_19043))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19043),tc_List_Olist(U_19043)),U_19045),U_19049)),c_List_Olistrel1(U_19043,U_19053)))
    | ~ sP1174(U_19043,U_19051,U_19053,U_19045,U_19047,U_19049) ),
    inference(clausify,[status(thm)],[f_4571_4]) ).

cnf(f_4571_8,plain,
    ( U_19047 = U_19051
    | ~ sP1174(U_19043,U_19051,U_19053,U_19045,U_19047,U_19049) ),
    inference(clausify,[status(thm)],[f_4571_4]) ).

cnf(f_4571_9,plain,
    ( U_19045 = U_19049
    | ~ sP1175(U_19043,U_19051,U_19053,U_19045,U_19047,U_19049) ),
    inference(clausify,[status(thm)],[f_4571_4]) ).

cnf(f_4571_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19043,U_19043)),hAPP(hAPP(c_Product__Type_OPair(U_19043,U_19043),U_19047),U_19051)),U_19053))
    | ~ sP1175(U_19043,U_19051,U_19053,U_19045,U_19047,U_19049) ),
    inference(clausify,[status(thm)],[f_4571_4]) ).

cnf(f_4571_11,plain,
    ( U_19048 != U_19052
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19044),tc_List_Olist(U_19044))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19044),tc_List_Olist(U_19044)),U_19046),U_19050)),c_List_Olistrel1(U_19044,U_19054)))
    | ~ sP1176(U_19044,U_19052,U_19046,U_19048,U_19050,U_19054) ),
    inference(clausify,[status(thm)],[f_4571_4]) ).

cnf(f_4571_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19044,U_19044)),hAPP(hAPP(c_Product__Type_OPair(U_19044,U_19044),U_19048),U_19052)),U_19054))
    | U_19046 != U_19050
    | ~ sP1176(U_19044,U_19052,U_19046,U_19048,U_19050,U_19054) ),
    inference(clausify,[status(thm)],[f_4571_4]) ).

fof(f_4572_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_4572_2,plain,
    ! [U_19060,U_19059,U_19058,U_19057,U_19056] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19056),tc_List_Olist(U_19056))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19056),tc_List_Olist(U_19056)),U_19058),U_19059)),c_List_Olexord(U_19056,U_19060)))
      | ? [U_19055] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_19056,U_19056)),hAPP(hAPP(c_Product__Type_OPair(U_19056,U_19056),U_19055),U_19055)),U_19060))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19056),tc_List_Olist(U_19056))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19056),tc_List_Olist(U_19056)),hAPP(hAPP(c_List_Oappend(U_19056),U_19057),U_19058)),hAPP(hAPP(c_List_Oappend(U_19056),U_19057),U_19059))),c_List_Olexord(U_19056,U_19060))) ),
    inference(variable_rename,[status(thm)],[f_4572_1]) ).

fof(f_4572_3,plain,
    ! [U_19060,U_19059,U_19058,U_19057,U_19056] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19056),tc_List_Olist(U_19056))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19056),tc_List_Olist(U_19056)),U_19058),U_19059)),c_List_Olexord(U_19056,U_19060)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_19056,U_19056)),hAPP(hAPP(c_Product__Type_OPair(U_19056,U_19056),sK470(U_19060,U_19059,U_19058,U_19057,U_19056)),sK470(U_19060,U_19059,U_19058,U_19057,U_19056))),U_19060))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19056),tc_List_Olist(U_19056))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19056),tc_List_Olist(U_19056)),hAPP(hAPP(c_List_Oappend(U_19056),U_19057),U_19058)),hAPP(hAPP(c_List_Oappend(U_19056),U_19057),U_19059))),c_List_Olexord(U_19056,U_19060))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK470]),skolemize(U_19055,sK470(U_19060,U_19059,U_19058,U_19057,U_19056))],[f_4572_2]) ).

fof(f_4572_4,plain,
    ! [U_19058,U_19057,U_19056,U_19059,U_19060] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19056),tc_List_Olist(U_19056))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19056),tc_List_Olist(U_19056)),U_19058),U_19059)),c_List_Olexord(U_19056,U_19060)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_19056,U_19056)),hAPP(hAPP(c_Product__Type_OPair(U_19056,U_19056),sK470(U_19060,U_19059,U_19058,U_19057,U_19056)),sK470(U_19060,U_19059,U_19058,U_19057,U_19056))),U_19060))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19056),tc_List_Olist(U_19056))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19056),tc_List_Olist(U_19056)),hAPP(hAPP(c_List_Oappend(U_19056),U_19057),U_19058)),hAPP(hAPP(c_List_Oappend(U_19056),U_19057),U_19059))),c_List_Olexord(U_19056,U_19060))) ),
    inference(definitional_conversion,[status(esa)],[f_4572_3]) ).

cnf(f_4572_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19056),tc_List_Olist(U_19056))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19056),tc_List_Olist(U_19056)),U_19058),U_19059)),c_List_Olexord(U_19056,U_19060)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_19056,U_19056)),hAPP(hAPP(c_Product__Type_OPair(U_19056,U_19056),sK470(U_19060,U_19059,U_19058,U_19057,U_19056)),sK470(U_19060,U_19059,U_19058,U_19057,U_19056))),U_19060))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19056),tc_List_Olist(U_19056))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19056),tc_List_Olist(U_19056)),hAPP(hAPP(c_List_Oappend(U_19056),U_19057),U_19058)),hAPP(hAPP(c_List_Oappend(U_19056),U_19057),U_19059))),c_List_Olexord(U_19056,U_19060))) ),
    inference(clausify,[status(thm)],[f_4572_4]) ).

fof(f_4573_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_4573_2,plain,
    ! [U_19064,U_19063,U_19062,U_19061] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19061)),hAPP(hAPP(c_List_Olist_OCons(U_19061),U_19062),U_19064)),c_Wellfounded_Oacc(tc_List_Olist(U_19061),c_List_Olistrel1(U_19061,U_19063))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19061)),U_19064),c_Wellfounded_Oacc(tc_List_Olist(U_19061),c_List_Olistrel1(U_19061,U_19063))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19061),U_19062),c_Wellfounded_Oacc(U_19061,U_19063))) ),
    inference(variable_rename,[status(thm)],[f_4573_1]) ).

fof(f_4573_3,plain,
    ! [U_19061,U_19062,U_19063,U_19064] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19061)),hAPP(hAPP(c_List_Olist_OCons(U_19061),U_19062),U_19064)),c_Wellfounded_Oacc(tc_List_Olist(U_19061),c_List_Olistrel1(U_19061,U_19063))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19061)),U_19064),c_Wellfounded_Oacc(tc_List_Olist(U_19061),c_List_Olistrel1(U_19061,U_19063))))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19061),U_19062),c_Wellfounded_Oacc(U_19061,U_19063))) ),
    inference(definitional_conversion,[status(esa)],[f_4573_2]) ).

cnf(f_4573_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19061)),hAPP(hAPP(c_List_Olist_OCons(U_19061),U_19062),U_19064)),c_Wellfounded_Oacc(tc_List_Olist(U_19061),c_List_Olistrel1(U_19061,U_19063))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19061)),U_19064),c_Wellfounded_Oacc(tc_List_Olist(U_19061),c_List_Olistrel1(U_19061,U_19063))))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19061),U_19062),c_Wellfounded_Oacc(U_19061,U_19063))) ),
    inference(clausify,[status(thm)],[f_4573_3]) ).

fof(f_4574_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_4574_2,plain,
    ! [U_19066,U_19065] : c_List_Olistrel1(U_19065,hAPP(c_Relation_Oconverse(U_19065,U_19065),U_19066)) = hAPP(c_Relation_Oconverse(tc_List_Olist(U_19065),tc_List_Olist(U_19065)),c_List_Olistrel1(U_19065,U_19066)),
    inference(variable_rename,[status(thm)],[f_4574_1]) ).

fof(f_4574_3,plain,
    ! [U_19065,U_19066] : c_List_Olistrel1(U_19065,hAPP(c_Relation_Oconverse(U_19065,U_19065),U_19066)) = hAPP(c_Relation_Oconverse(tc_List_Olist(U_19065),tc_List_Olist(U_19065)),c_List_Olistrel1(U_19065,U_19066)),
    inference(definitional_conversion,[status(esa)],[f_4574_2]) ).

cnf(f_4574_4,plain,
    c_List_Olistrel1(U_19065,hAPP(c_Relation_Oconverse(U_19065,U_19065),U_19066)) = hAPP(c_Relation_Oconverse(tc_List_Olist(U_19065),tc_List_Olist(U_19065)),c_List_Olistrel1(U_19065,U_19066)),
    inference(clausify,[status(thm)],[f_4574_3]) ).

fof(f_4575_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_4575_2,plain,
    ! [U_19068,U_19067] : c_List_Olistrel(U_19067,c_Transitive__Closure_Ortrancl(U_19067,U_19068)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19067),c_List_Olistrel1(U_19067,U_19068)),
    inference(variable_rename,[status(thm)],[f_4575_1]) ).

fof(f_4575_3,plain,
    ! [U_19067,U_19068] : c_List_Olistrel(U_19067,c_Transitive__Closure_Ortrancl(U_19067,U_19068)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19067),c_List_Olistrel1(U_19067,U_19068)),
    inference(definitional_conversion,[status(esa)],[f_4575_2]) ).

cnf(f_4575_4,plain,
    c_List_Olistrel(U_19067,c_Transitive__Closure_Ortrancl(U_19067,U_19068)) = c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19067),c_List_Olistrel1(U_19067,U_19068)),
    inference(clausify,[status(thm)],[f_4575_3]) ).

fof(f_4576_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_4576_2,plain,
    ! [U_19071,U_19070,U_19069] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19069),tc_List_Olist(U_19069)),tc_HOL_Obool)),c_List_Olistrel1(U_19069,U_19070)),c_List_Olistrel1(U_19069,U_19071)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19069,U_19069),tc_HOL_Obool)),U_19070),U_19071)) ),
    inference(variable_rename,[status(thm)],[f_4576_1]) ).

fof(f_4576_3,plain,
    ! [U_19069,U_19070,U_19071] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19069),tc_List_Olist(U_19069)),tc_HOL_Obool)),c_List_Olistrel1(U_19069,U_19070)),c_List_Olistrel1(U_19069,U_19071)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19069,U_19069),tc_HOL_Obool)),U_19070),U_19071)) ),
    inference(definitional_conversion,[status(esa)],[f_4576_2]) ).

cnf(f_4576_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19069),tc_List_Olist(U_19069)),tc_HOL_Obool)),c_List_Olistrel1(U_19069,U_19070)),c_List_Olistrel1(U_19069,U_19071)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19069,U_19069),tc_HOL_Obool)),U_19070),U_19071)) ),
    inference(clausify,[status(thm)],[f_4576_3]) ).

fof(f_4577_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_4577_2,plain,
    ! [U_19073,U_19072] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19072),tc_List_Olist(U_19072)),tc_HOL_Obool)),c_List_Olistrel1(U_19072,c_Transitive__Closure_Ortrancl(U_19072,U_19073))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19072),c_List_Olistrel1(U_19072,U_19073)))),
    inference(variable_rename,[status(thm)],[f_4577_1]) ).

fof(f_4577_3,plain,
    ! [U_19072,U_19073] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19072),tc_List_Olist(U_19072)),tc_HOL_Obool)),c_List_Olistrel1(U_19072,c_Transitive__Closure_Ortrancl(U_19072,U_19073))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19072),c_List_Olistrel1(U_19072,U_19073)))),
    inference(definitional_conversion,[status(esa)],[f_4577_2]) ).

cnf(f_4577_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19072),tc_List_Olist(U_19072)),tc_HOL_Obool)),c_List_Olistrel1(U_19072,c_Transitive__Closure_Ortrancl(U_19072,U_19073))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19072),c_List_Olistrel1(U_19072,U_19073)))),
    inference(clausify,[status(thm)],[f_4577_3]) ).

fof(f_4578_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_4578_2,plain,
    ! [U_19075,U_19074] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19074),tc_List_Olist(U_19074)),tc_HOL_Obool)),c_List_Olistrel(U_19074,U_19075)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19074),c_List_Olistrel1(U_19074,U_19075)))),
    inference(variable_rename,[status(thm)],[f_4578_1]) ).

fof(f_4578_3,plain,
    ! [U_19074,U_19075] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19074),tc_List_Olist(U_19074)),tc_HOL_Obool)),c_List_Olistrel(U_19074,U_19075)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19074),c_List_Olistrel1(U_19074,U_19075)))),
    inference(definitional_conversion,[status(esa)],[f_4578_2]) ).

cnf(f_4578_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19074),tc_List_Olist(U_19074)),tc_HOL_Obool)),c_List_Olistrel(U_19074,U_19075)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19074),c_List_Olistrel1(U_19074,U_19075)))),
    inference(clausify,[status(thm)],[f_4578_3]) ).

fof(f_4579_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_4579_2,plain,
    ! [U_19080,U_19079,U_19078,U_19077,U_19076] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19076),tc_List_Olist(U_19076))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19076),tc_List_Olist(U_19076)),hAPP(hAPP(c_List_Olist_OCons(U_19076),U_19080),U_19077)),hAPP(hAPP(c_List_Olist_OCons(U_19076),U_19080),U_19078))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19076),c_List_Olistrel1(U_19076,U_19079))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19076),tc_List_Olist(U_19076))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19076),tc_List_Olist(U_19076)),U_19077),U_19078)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19076),c_List_Olistrel1(U_19076,U_19079)))) ),
    inference(variable_rename,[status(thm)],[f_4579_1]) ).

fof(f_4579_3,plain,
    ! [U_19076,U_19077,U_19078,U_19079,U_19080] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19076),tc_List_Olist(U_19076))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19076),tc_List_Olist(U_19076)),hAPP(hAPP(c_List_Olist_OCons(U_19076),U_19080),U_19077)),hAPP(hAPP(c_List_Olist_OCons(U_19076),U_19080),U_19078))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19076),c_List_Olistrel1(U_19076,U_19079))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19076),tc_List_Olist(U_19076))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19076),tc_List_Olist(U_19076)),U_19077),U_19078)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19076),c_List_Olistrel1(U_19076,U_19079)))) ),
    inference(definitional_conversion,[status(esa)],[f_4579_2]) ).

cnf(f_4579_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19076),tc_List_Olist(U_19076))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19076),tc_List_Olist(U_19076)),hAPP(hAPP(c_List_Olist_OCons(U_19076),U_19080),U_19077)),hAPP(hAPP(c_List_Olist_OCons(U_19076),U_19080),U_19078))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19076),c_List_Olistrel1(U_19076,U_19079))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19076),tc_List_Olist(U_19076))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19076),tc_List_Olist(U_19076)),U_19077),U_19078)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19076),c_List_Olistrel1(U_19076,U_19079)))) ),
    inference(clausify,[status(thm)],[f_4579_3]) ).

fof(f_4580_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_4580_2,plain,
    ! [U_19085,U_19084,U_19083,U_19082,U_19081] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19081),tc_List_Olist(U_19081))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19081),tc_List_Olist(U_19081)),hAPP(hAPP(c_List_Olist_OCons(U_19081),U_19085),U_19082)),hAPP(hAPP(c_List_Olist_OCons(U_19081),U_19085),U_19083))),c_List_Olistrel1(U_19081,U_19084)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19081),tc_List_Olist(U_19081))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19081),tc_List_Olist(U_19081)),U_19082),U_19083)),c_List_Olistrel1(U_19081,U_19084))) ),
    inference(variable_rename,[status(thm)],[f_4580_1]) ).

fof(f_4580_3,plain,
    ! [U_19081,U_19082,U_19083,U_19084,U_19085] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19081),tc_List_Olist(U_19081))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19081),tc_List_Olist(U_19081)),hAPP(hAPP(c_List_Olist_OCons(U_19081),U_19085),U_19082)),hAPP(hAPP(c_List_Olist_OCons(U_19081),U_19085),U_19083))),c_List_Olistrel1(U_19081,U_19084)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19081),tc_List_Olist(U_19081))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19081),tc_List_Olist(U_19081)),U_19082),U_19083)),c_List_Olistrel1(U_19081,U_19084))) ),
    inference(definitional_conversion,[status(esa)],[f_4580_2]) ).

cnf(f_4580_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19081),tc_List_Olist(U_19081))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19081),tc_List_Olist(U_19081)),hAPP(hAPP(c_List_Olist_OCons(U_19081),U_19085),U_19082)),hAPP(hAPP(c_List_Olist_OCons(U_19081),U_19085),U_19083))),c_List_Olistrel1(U_19081,U_19084)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19081),tc_List_Olist(U_19081))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19081),tc_List_Olist(U_19081)),U_19082),U_19083)),c_List_Olistrel1(U_19081,U_19084))) ),
    inference(clausify,[status(thm)],[f_4580_3]) ).

fof(f_4581_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_4581_2,plain,
    ! [U_19089,U_19088,U_19087,U_19086] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19086)),U_19087) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19086)),U_19088)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19086),tc_List_Olist(U_19086))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19086),tc_List_Olist(U_19086)),U_19087),U_19088)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19086),c_List_Olistrel1(U_19086,U_19089)))) ),
    inference(variable_rename,[status(thm)],[f_4581_1]) ).

fof(f_4581_3,plain,
    ! [U_19086,U_19087,U_19088,U_19089] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19086)),U_19087) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19086)),U_19088)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19086),tc_List_Olist(U_19086))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19086),tc_List_Olist(U_19086)),U_19087),U_19088)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19086),c_List_Olistrel1(U_19086,U_19089)))) ),
    inference(definitional_conversion,[status(esa)],[f_4581_2]) ).

cnf(f_4581_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19086)),U_19087) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19086)),U_19088)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19086),tc_List_Olist(U_19086))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19086),tc_List_Olist(U_19086)),U_19087),U_19088)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19086),c_List_Olistrel1(U_19086,U_19089)))) ),
    inference(clausify,[status(thm)],[f_4581_3]) ).

fof(f_4582_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_4582_2,plain,
    ! [U_19093,U_19092,U_19091,U_19090] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19090)),U_19091) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19090)),U_19092)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19090),tc_List_Olist(U_19090))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19090),tc_List_Olist(U_19090)),U_19091),U_19092)),c_List_Olistrel1(U_19090,U_19093))) ),
    inference(variable_rename,[status(thm)],[f_4582_1]) ).

fof(f_4582_3,plain,
    ! [U_19090,U_19091,U_19092,U_19093] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19090)),U_19091) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19090)),U_19092)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19090),tc_List_Olist(U_19090))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19090),tc_List_Olist(U_19090)),U_19091),U_19092)),c_List_Olistrel1(U_19090,U_19093))) ),
    inference(definitional_conversion,[status(esa)],[f_4582_2]) ).

cnf(f_4582_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19090)),U_19091) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19090)),U_19092)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19090),tc_List_Olist(U_19090))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19090),tc_List_Olist(U_19090)),U_19091),U_19092)),c_List_Olistrel1(U_19090,U_19093))) ),
    inference(clausify,[status(thm)],[f_4582_3]) ).

fof(f_4583_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_4583_2,plain,
    ! [U_19096,U_19095,U_19094] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19094),tc_List_Olist(U_19094))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19094),tc_List_Olist(U_19094)),c_List_Olist_ONil(U_19094)),U_19095)),c_List_Olistrel1(U_19094,U_19096))),
    inference(variable_rename,[status(thm)],[f_4583_1]) ).

fof(f_4583_3,plain,
    ! [U_19094,U_19095,U_19096] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19094),tc_List_Olist(U_19094))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19094),tc_List_Olist(U_19094)),c_List_Olist_ONil(U_19094)),U_19095)),c_List_Olistrel1(U_19094,U_19096))),
    inference(definitional_conversion,[status(esa)],[f_4583_2]) ).

cnf(f_4583_4,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19094),tc_List_Olist(U_19094))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19094),tc_List_Olist(U_19094)),c_List_Olist_ONil(U_19094)),U_19095)),c_List_Olistrel1(U_19094,U_19096))),
    inference(clausify,[status(thm)],[f_4583_3]) ).

fof(f_4584_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_4584_2,plain,
    ! [U_19099,U_19098,U_19097] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19097),tc_List_Olist(U_19097))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19097),tc_List_Olist(U_19097)),U_19098),c_List_Olist_ONil(U_19097))),c_List_Olistrel1(U_19097,U_19099))),
    inference(variable_rename,[status(thm)],[f_4584_1]) ).

fof(f_4584_3,plain,
    ! [U_19097,U_19098,U_19099] : ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19097),tc_List_Olist(U_19097))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19097),tc_List_Olist(U_19097)),U_19098),c_List_Olist_ONil(U_19097))),c_List_Olistrel1(U_19097,U_19099))),
    inference(definitional_conversion,[status(esa)],[f_4584_2]) ).

cnf(f_4584_4,plain,
    ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19097),tc_List_Olist(U_19097))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19097),tc_List_Olist(U_19097)),U_19098),c_List_Olist_ONil(U_19097))),c_List_Olistrel1(U_19097,U_19099))),
    inference(clausify,[status(thm)],[f_4584_3]) ).

fof(f_4585_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_4585_2,plain,
    ! [U_19105,U_19104,U_19103,U_19102,U_19101,U_19100] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19100),tc_List_Olist(U_19100))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19100),tc_List_Olist(U_19100)),hAPP(hAPP(c_List_Oappend(U_19100),U_19101),U_19104)),hAPP(hAPP(c_List_Oappend(U_19100),U_19102),U_19105))),c_List_Olistrel1(U_19100,U_19103)))
      | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19100),tc_List_Olist(U_19100))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19100),tc_List_Olist(U_19100)),U_19104),U_19105)),c_List_Olistrel1(U_19100,U_19103)))
          | U_19101 != U_19102 )
        & ( U_19104 != U_19105
          | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19100),tc_List_Olist(U_19100))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19100),tc_List_Olist(U_19100)),U_19101),U_19102)),c_List_Olistrel1(U_19100,U_19103))) ) ) ),
    inference(variable_rename,[status(thm)],[f_4585_1]) ).

fof(f_4585_3,plain,
    ( ! [U_19100,U_19101,U_19102,U_19103,U_19104,U_19105] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19100),tc_List_Olist(U_19100))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19100),tc_List_Olist(U_19100)),U_19104),U_19105)),c_List_Olistrel1(U_19100,U_19103)))
        | U_19101 != U_19102
        | ~ sP1177(U_19100,U_19101,U_19102,U_19103,U_19104,U_19105) )
    & ! [U_19100,U_19101,U_19102,U_19103,U_19104,U_19105] :
        ( U_19104 != U_19105
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19100),tc_List_Olist(U_19100))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19100),tc_List_Olist(U_19100)),U_19101),U_19102)),c_List_Olistrel1(U_19100,U_19103)))
        | ~ sP1177(U_19100,U_19101,U_19102,U_19103,U_19104,U_19105) )
    & ! [U_19100,U_19101,U_19102,U_19103,U_19104,U_19105] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19100),tc_List_Olist(U_19100))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19100),tc_List_Olist(U_19100)),hAPP(hAPP(c_List_Oappend(U_19100),U_19101),U_19104)),hAPP(hAPP(c_List_Oappend(U_19100),U_19102),U_19105))),c_List_Olistrel1(U_19100,U_19103)))
        | sP1177(U_19100,U_19101,U_19102,U_19103,U_19104,U_19105) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1177])],[f_4585_2]) ).

cnf(f_4585_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19100),tc_List_Olist(U_19100))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19100),tc_List_Olist(U_19100)),hAPP(hAPP(c_List_Oappend(U_19100),U_19101),U_19104)),hAPP(hAPP(c_List_Oappend(U_19100),U_19102),U_19105))),c_List_Olistrel1(U_19100,U_19103)))
    | sP1177(U_19100,U_19101,U_19102,U_19103,U_19104,U_19105) ),
    inference(clausify,[status(thm)],[f_4585_3]) ).

cnf(f_4585_5,plain,
    ( U_19104 != U_19105
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19100),tc_List_Olist(U_19100))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19100),tc_List_Olist(U_19100)),U_19101),U_19102)),c_List_Olistrel1(U_19100,U_19103)))
    | ~ sP1177(U_19100,U_19101,U_19102,U_19103,U_19104,U_19105) ),
    inference(clausify,[status(thm)],[f_4585_3]) ).

cnf(f_4585_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19100),tc_List_Olist(U_19100))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19100),tc_List_Olist(U_19100)),U_19104),U_19105)),c_List_Olistrel1(U_19100,U_19103)))
    | U_19101 != U_19102
    | ~ sP1177(U_19100,U_19101,U_19102,U_19103,U_19104,U_19105) ),
    inference(clausify,[status(thm)],[f_4585_3]) ).

fof(f_4586_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_4586_2,plain,
    ! [U_19109,U_19108,U_19107,U_19106] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19106),tc_List_Olist(U_19106))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19106),tc_List_Olist(U_19106)),U_19107),U_19108)),c_List_Olistrel1(U_19106,hAPP(c_Relation_Oconverse(U_19106,U_19106),U_19109))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19106),tc_List_Olist(U_19106))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19106),tc_List_Olist(U_19106)),U_19107),U_19108)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19106),tc_List_Olist(U_19106)),c_List_Olistrel1(U_19106,U_19109)))) )
      & ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19106),tc_List_Olist(U_19106))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19106),tc_List_Olist(U_19106)),U_19107),U_19108)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19106),tc_List_Olist(U_19106)),c_List_Olistrel1(U_19106,U_19109))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19106),tc_List_Olist(U_19106))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19106),tc_List_Olist(U_19106)),U_19107),U_19108)),c_List_Olistrel1(U_19106,hAPP(c_Relation_Oconverse(U_19106,U_19106),U_19109)))) ) ),
    inference(variable_rename,[status(thm)],[f_4586_1]) ).

fof(f_4586_3,plain,
    ( ! [U_19117,U_19115,U_19113,U_19111] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19111),tc_List_Olist(U_19111))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19111),tc_List_Olist(U_19111)),U_19113),U_19115)),c_List_Olistrel1(U_19111,hAPP(c_Relation_Oconverse(U_19111,U_19111),U_19117))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19111),tc_List_Olist(U_19111))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19111),tc_List_Olist(U_19111)),U_19113),U_19115)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19111),tc_List_Olist(U_19111)),c_List_Olistrel1(U_19111,U_19117)))) )
    & ! [U_19116,U_19114,U_19112,U_19110] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19110),tc_List_Olist(U_19110))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19110),tc_List_Olist(U_19110)),U_19112),U_19114)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19110),tc_List_Olist(U_19110)),c_List_Olistrel1(U_19110,U_19116))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19110),tc_List_Olist(U_19110))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19110),tc_List_Olist(U_19110)),U_19112),U_19114)),c_List_Olistrel1(U_19110,hAPP(c_Relation_Oconverse(U_19110,U_19110),U_19116)))) ) ),
    inference(miniscope,[status(thm)],[f_4586_2]) ).

fof(f_4586_4,plain,
    ( ! [U_19111,U_19113,U_19115,U_19117] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19111),tc_List_Olist(U_19111))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19111),tc_List_Olist(U_19111)),U_19113),U_19115)),c_List_Olistrel1(U_19111,hAPP(c_Relation_Oconverse(U_19111,U_19111),U_19117))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19111),tc_List_Olist(U_19111))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19111),tc_List_Olist(U_19111)),U_19113),U_19115)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19111),tc_List_Olist(U_19111)),c_List_Olistrel1(U_19111,U_19117)))) )
    & ! [U_19116,U_19110,U_19112,U_19114] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19110),tc_List_Olist(U_19110))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19110),tc_List_Olist(U_19110)),U_19112),U_19114)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19110),tc_List_Olist(U_19110)),c_List_Olistrel1(U_19110,U_19116))))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19110),tc_List_Olist(U_19110))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19110),tc_List_Olist(U_19110)),U_19112),U_19114)),c_List_Olistrel1(U_19110,hAPP(c_Relation_Oconverse(U_19110,U_19110),U_19116)))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4586_3]) ).

cnf(f_4586_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19110),tc_List_Olist(U_19110))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19110),tc_List_Olist(U_19110)),U_19112),U_19114)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19110),tc_List_Olist(U_19110)),c_List_Olistrel1(U_19110,U_19116))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19110),tc_List_Olist(U_19110))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19110),tc_List_Olist(U_19110)),U_19112),U_19114)),c_List_Olistrel1(U_19110,hAPP(c_Relation_Oconverse(U_19110,U_19110),U_19116)))) ),
    inference(clausify,[status(thm)],[f_4586_4]) ).

cnf(f_4586_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19111),tc_List_Olist(U_19111))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19111),tc_List_Olist(U_19111)),U_19113),U_19115)),c_List_Olistrel1(U_19111,hAPP(c_Relation_Oconverse(U_19111,U_19111),U_19117))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19111),tc_List_Olist(U_19111))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19111),tc_List_Olist(U_19111)),U_19113),U_19115)),hAPP(c_Relation_Oconverse(tc_List_Olist(U_19111),tc_List_Olist(U_19111)),c_List_Olistrel1(U_19111,U_19117)))) ),
    inference(clausify,[status(thm)],[f_4586_4]) ).

fof(f_4587_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_4587_2,plain,
    ! [U_19121,U_19120,U_19119,U_19118] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19118),tc_List_Olist(U_19118))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19118),tc_List_Olist(U_19118)),U_19119),U_19120)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19118),c_List_Olistrel1(U_19118,U_19121))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19118),tc_List_Olist(U_19118))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19118),tc_List_Olist(U_19118)),U_19119),U_19120)),c_List_Olistrel(U_19118,U_19121))) ),
    inference(variable_rename,[status(thm)],[f_4587_1]) ).

fof(f_4587_3,plain,
    ! [U_19118,U_19119,U_19120,U_19121] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19118),tc_List_Olist(U_19118))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19118),tc_List_Olist(U_19118)),U_19119),U_19120)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19118),c_List_Olistrel1(U_19118,U_19121))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19118),tc_List_Olist(U_19118))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19118),tc_List_Olist(U_19118)),U_19119),U_19120)),c_List_Olistrel(U_19118,U_19121))) ),
    inference(definitional_conversion,[status(esa)],[f_4587_2]) ).

cnf(f_4587_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19118),tc_List_Olist(U_19118))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19118),tc_List_Olist(U_19118)),U_19119),U_19120)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19118),c_List_Olistrel1(U_19118,U_19121))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19118),tc_List_Olist(U_19118))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19118),tc_List_Olist(U_19118)),U_19119),U_19120)),c_List_Olistrel(U_19118,U_19121))) ),
    inference(clausify,[status(thm)],[f_4587_3]) ).

fof(f_4588_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_4588_2,plain,
    ! [U_19125,U_19124,U_19123,U_19122] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19122),tc_List_Olist(U_19122))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19122),tc_List_Olist(U_19122)),U_19123),U_19124)),c_List_Olistrel(U_19122,c_Transitive__Closure_Ortrancl(U_19122,U_19125))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19122),tc_List_Olist(U_19122))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19122),tc_List_Olist(U_19122)),U_19123),U_19124)),c_List_Olistrel1(U_19122,U_19125))) ),
    inference(variable_rename,[status(thm)],[f_4588_1]) ).

fof(f_4588_3,plain,
    ! [U_19122,U_19123,U_19124,U_19125] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19122),tc_List_Olist(U_19122))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19122),tc_List_Olist(U_19122)),U_19123),U_19124)),c_List_Olistrel(U_19122,c_Transitive__Closure_Ortrancl(U_19122,U_19125))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19122),tc_List_Olist(U_19122))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19122),tc_List_Olist(U_19122)),U_19123),U_19124)),c_List_Olistrel1(U_19122,U_19125))) ),
    inference(definitional_conversion,[status(esa)],[f_4588_2]) ).

cnf(f_4588_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19122),tc_List_Olist(U_19122))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19122),tc_List_Olist(U_19122)),U_19123),U_19124)),c_List_Olistrel(U_19122,c_Transitive__Closure_Ortrancl(U_19122,U_19125))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19122),tc_List_Olist(U_19122))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19122),tc_List_Olist(U_19122)),U_19123),U_19124)),c_List_Olistrel1(U_19122,U_19125))) ),
    inference(clausify,[status(thm)],[f_4588_3]) ).

fof(f_4589_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_4589_2,plain,
    ! [U_19130,U_19129,U_19128,U_19127,U_19126] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19126),tc_List_Olist(U_19126))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19126),tc_List_Olist(U_19126)),hAPP(hAPP(c_List_Olist_OCons(U_19126),U_19127),U_19130)),hAPP(hAPP(c_List_Olist_OCons(U_19126),U_19128),U_19130))),c_List_Olistrel1(U_19126,U_19129)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19126,U_19126)),hAPP(hAPP(c_Product__Type_OPair(U_19126,U_19126),U_19127),U_19128)),U_19129)) ),
    inference(variable_rename,[status(thm)],[f_4589_1]) ).

fof(f_4589_3,plain,
    ! [U_19126,U_19127,U_19128,U_19129,U_19130] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19126),tc_List_Olist(U_19126))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19126),tc_List_Olist(U_19126)),hAPP(hAPP(c_List_Olist_OCons(U_19126),U_19127),U_19130)),hAPP(hAPP(c_List_Olist_OCons(U_19126),U_19128),U_19130))),c_List_Olistrel1(U_19126,U_19129)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19126,U_19126)),hAPP(hAPP(c_Product__Type_OPair(U_19126,U_19126),U_19127),U_19128)),U_19129)) ),
    inference(definitional_conversion,[status(esa)],[f_4589_2]) ).

cnf(f_4589_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19126),tc_List_Olist(U_19126))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19126),tc_List_Olist(U_19126)),hAPP(hAPP(c_List_Olist_OCons(U_19126),U_19127),U_19130)),hAPP(hAPP(c_List_Olist_OCons(U_19126),U_19128),U_19130))),c_List_Olistrel1(U_19126,U_19129)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19126,U_19126)),hAPP(hAPP(c_Product__Type_OPair(U_19126,U_19126),U_19127),U_19128)),U_19129)) ),
    inference(clausify,[status(thm)],[f_4589_3]) ).

fof(f_4590_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_4590_2,plain,
    ! [U_19136,U_19135,U_19134,U_19133,U_19132,U_19131] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19131),tc_List_Olist(U_19131))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19131),tc_List_Olist(U_19131)),hAPP(hAPP(c_List_Olist_OCons(U_19131),U_19132),U_19133)),hAPP(hAPP(c_List_Olist_OCons(U_19131),U_19134),U_19135))),c_List_Olistrel1(U_19131,U_19136)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19131),tc_List_Olist(U_19131))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19131),tc_List_Olist(U_19131)),U_19133),U_19135)),c_List_Olistrel1(U_19131,U_19136)))
            | U_19132 != U_19134 )
          & ( U_19133 != U_19135
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19131,U_19131)),hAPP(hAPP(c_Product__Type_OPair(U_19131,U_19131),U_19132),U_19134)),U_19136)) ) ) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19131),tc_List_Olist(U_19131))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19131),tc_List_Olist(U_19131)),U_19133),U_19135)),c_List_Olistrel1(U_19131,U_19136)))
          & U_19132 = U_19134 )
        | ( U_19133 = U_19135
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19131,U_19131)),hAPP(hAPP(c_Product__Type_OPair(U_19131,U_19131),U_19132),U_19134)),U_19136)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19131),tc_List_Olist(U_19131))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19131),tc_List_Olist(U_19131)),hAPP(hAPP(c_List_Olist_OCons(U_19131),U_19132),U_19133)),hAPP(hAPP(c_List_Olist_OCons(U_19131),U_19134),U_19135))),c_List_Olistrel1(U_19131,U_19136))) ) ),
    inference(variable_rename,[status(thm)],[f_4590_1]) ).

fof(f_4590_3,plain,
    ( ! [U_19148,U_19146,U_19144,U_19142,U_19140,U_19138] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19138),tc_List_Olist(U_19138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19138),tc_List_Olist(U_19138)),hAPP(hAPP(c_List_Olist_OCons(U_19138),U_19140),U_19142)),hAPP(hAPP(c_List_Olist_OCons(U_19138),U_19144),U_19146))),c_List_Olistrel1(U_19138,U_19148)))
        | ( ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19138),tc_List_Olist(U_19138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19138),tc_List_Olist(U_19138)),U_19142),U_19146)),c_List_Olistrel1(U_19138,U_19148)))
            | U_19140 != U_19144 )
          & ( U_19142 != U_19146
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19138,U_19138)),hAPP(hAPP(c_Product__Type_OPair(U_19138,U_19138),U_19140),U_19144)),U_19148)) ) ) )
    & ! [U_19147,U_19145,U_19143,U_19141,U_19139,U_19137] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19137),tc_List_Olist(U_19137))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19137),tc_List_Olist(U_19137)),U_19141),U_19145)),c_List_Olistrel1(U_19137,U_19147)))
          & U_19139 = U_19143 )
        | ( U_19141 = U_19145
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19137,U_19137)),hAPP(hAPP(c_Product__Type_OPair(U_19137,U_19137),U_19139),U_19143)),U_19147)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19137),tc_List_Olist(U_19137))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19137),tc_List_Olist(U_19137)),hAPP(hAPP(c_List_Olist_OCons(U_19137),U_19139),U_19141)),hAPP(hAPP(c_List_Olist_OCons(U_19137),U_19143),U_19145))),c_List_Olistrel1(U_19137,U_19147))) ) ),
    inference(miniscope,[status(thm)],[f_4590_2]) ).

fof(f_4590_4,plain,
    ( ! [U_19138,U_19140,U_19142,U_19146,U_19144,U_19148] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19138),tc_List_Olist(U_19138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19138),tc_List_Olist(U_19138)),U_19142),U_19146)),c_List_Olistrel1(U_19138,U_19148)))
        | U_19140 != U_19144
        | ~ sP1180(U_19138,U_19140,U_19142,U_19146,U_19144,U_19148) )
    & ! [U_19138,U_19140,U_19142,U_19146,U_19144,U_19148] :
        ( U_19142 != U_19146
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19138,U_19138)),hAPP(hAPP(c_Product__Type_OPair(U_19138,U_19138),U_19140),U_19144)),U_19148))
        | ~ sP1180(U_19138,U_19140,U_19142,U_19146,U_19144,U_19148) )
    & ! [U_19137,U_19139,U_19141,U_19143,U_19145,U_19147] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19137),tc_List_Olist(U_19137))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19137),tc_List_Olist(U_19137)),U_19141),U_19145)),c_List_Olistrel1(U_19137,U_19147)))
        | ~ sP1179(U_19137,U_19139,U_19141,U_19143,U_19145,U_19147) )
    & ! [U_19137,U_19139,U_19141,U_19143,U_19145,U_19147] :
        ( U_19139 = U_19143
        | ~ sP1179(U_19137,U_19139,U_19141,U_19143,U_19145,U_19147) )
    & ! [U_19137,U_19139,U_19141,U_19143,U_19145,U_19147] :
        ( U_19141 = U_19145
        | ~ sP1178(U_19137,U_19139,U_19141,U_19143,U_19145,U_19147) )
    & ! [U_19137,U_19139,U_19141,U_19143,U_19145,U_19147] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19137,U_19137)),hAPP(hAPP(c_Product__Type_OPair(U_19137,U_19137),U_19139),U_19143)),U_19147))
        | ~ sP1178(U_19137,U_19139,U_19141,U_19143,U_19145,U_19147) )
    & ! [U_19138,U_19140,U_19142,U_19146,U_19144,U_19148] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19138),tc_List_Olist(U_19138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19138),tc_List_Olist(U_19138)),hAPP(hAPP(c_List_Olist_OCons(U_19138),U_19140),U_19142)),hAPP(hAPP(c_List_Olist_OCons(U_19138),U_19144),U_19146))),c_List_Olistrel1(U_19138,U_19148)))
        | sP1180(U_19138,U_19140,U_19142,U_19146,U_19144,U_19148) )
    & ! [U_19137,U_19139,U_19141,U_19143,U_19145,U_19147] :
        ( sP1179(U_19137,U_19139,U_19141,U_19143,U_19145,U_19147)
        | sP1178(U_19137,U_19139,U_19141,U_19143,U_19145,U_19147)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19137),tc_List_Olist(U_19137))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19137),tc_List_Olist(U_19137)),hAPP(hAPP(c_List_Olist_OCons(U_19137),U_19139),U_19141)),hAPP(hAPP(c_List_Olist_OCons(U_19137),U_19143),U_19145))),c_List_Olistrel1(U_19137,U_19147))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1178,sP1179,sP1180])],[f_4590_3]) ).

cnf(f_4590_5,plain,
    ( sP1179(U_19137,U_19139,U_19141,U_19143,U_19145,U_19147)
    | sP1178(U_19137,U_19139,U_19141,U_19143,U_19145,U_19147)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19137),tc_List_Olist(U_19137))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19137),tc_List_Olist(U_19137)),hAPP(hAPP(c_List_Olist_OCons(U_19137),U_19139),U_19141)),hAPP(hAPP(c_List_Olist_OCons(U_19137),U_19143),U_19145))),c_List_Olistrel1(U_19137,U_19147))) ),
    inference(clausify,[status(thm)],[f_4590_4]) ).

cnf(f_4590_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19138),tc_List_Olist(U_19138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19138),tc_List_Olist(U_19138)),hAPP(hAPP(c_List_Olist_OCons(U_19138),U_19140),U_19142)),hAPP(hAPP(c_List_Olist_OCons(U_19138),U_19144),U_19146))),c_List_Olistrel1(U_19138,U_19148)))
    | sP1180(U_19138,U_19140,U_19142,U_19146,U_19144,U_19148) ),
    inference(clausify,[status(thm)],[f_4590_4]) ).

cnf(f_4590_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19137,U_19137)),hAPP(hAPP(c_Product__Type_OPair(U_19137,U_19137),U_19139),U_19143)),U_19147))
    | ~ sP1178(U_19137,U_19139,U_19141,U_19143,U_19145,U_19147) ),
    inference(clausify,[status(thm)],[f_4590_4]) ).

cnf(f_4590_8,plain,
    ( U_19141 = U_19145
    | ~ sP1178(U_19137,U_19139,U_19141,U_19143,U_19145,U_19147) ),
    inference(clausify,[status(thm)],[f_4590_4]) ).

cnf(f_4590_9,plain,
    ( U_19139 = U_19143
    | ~ sP1179(U_19137,U_19139,U_19141,U_19143,U_19145,U_19147) ),
    inference(clausify,[status(thm)],[f_4590_4]) ).

cnf(f_4590_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19137),tc_List_Olist(U_19137))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19137),tc_List_Olist(U_19137)),U_19141),U_19145)),c_List_Olistrel1(U_19137,U_19147)))
    | ~ sP1179(U_19137,U_19139,U_19141,U_19143,U_19145,U_19147) ),
    inference(clausify,[status(thm)],[f_4590_4]) ).

cnf(f_4590_11,plain,
    ( U_19142 != U_19146
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19138,U_19138)),hAPP(hAPP(c_Product__Type_OPair(U_19138,U_19138),U_19140),U_19144)),U_19148))
    | ~ sP1180(U_19138,U_19140,U_19142,U_19146,U_19144,U_19148) ),
    inference(clausify,[status(thm)],[f_4590_4]) ).

cnf(f_4590_12,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19138),tc_List_Olist(U_19138))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19138),tc_List_Olist(U_19138)),U_19142),U_19146)),c_List_Olistrel1(U_19138,U_19148)))
    | U_19140 != U_19144
    | ~ sP1180(U_19138,U_19140,U_19142,U_19146,U_19144,U_19148) ),
    inference(clausify,[status(thm)],[f_4590_4]) ).

fof(f_4591_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_4591_2,plain,
    ! [U_19151,U_19150,U_19149] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19149),tc_List_Olist(U_19149)),tc_HOL_Obool)),c_List_Olistrel1(U_19149,U_19150)),c_List_Olistrel(U_19149,U_19151)))
      | ~ c_Relation_Orefl__on(U_19149,c_Orderings_Otop__class_Otop(tc_fun(U_19149,tc_HOL_Obool)),U_19151)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19149,U_19149),tc_HOL_Obool)),U_19150),U_19151)) ),
    inference(variable_rename,[status(thm)],[f_4591_1]) ).

fof(f_4591_3,plain,
    ! [U_19150,U_19149,U_19151] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19149),tc_List_Olist(U_19149)),tc_HOL_Obool)),c_List_Olistrel1(U_19149,U_19150)),c_List_Olistrel(U_19149,U_19151)))
      | ~ c_Relation_Orefl__on(U_19149,c_Orderings_Otop__class_Otop(tc_fun(U_19149,tc_HOL_Obool)),U_19151)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19149,U_19149),tc_HOL_Obool)),U_19150),U_19151)) ),
    inference(definitional_conversion,[status(esa)],[f_4591_2]) ).

cnf(f_4591_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19149),tc_List_Olist(U_19149)),tc_HOL_Obool)),c_List_Olistrel1(U_19149,U_19150)),c_List_Olistrel(U_19149,U_19151)))
    | ~ c_Relation_Orefl__on(U_19149,c_Orderings_Otop__class_Otop(tc_fun(U_19149,tc_HOL_Obool)),U_19151)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19149,U_19149),tc_HOL_Obool)),U_19150),U_19151)) ),
    inference(clausify,[status(thm)],[f_4591_3]) ).

fof(f_4592_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_4592_2,plain,
    ! [U_19159,U_19158,U_19157,U_19156,U_19155,U_19154,U_19153,U_19152] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19152),tc_List_Olist(U_19152))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19152),tc_List_Olist(U_19152)),U_19156),U_19159)),c_List_Olistrel1(U_19152,U_19155)))
      | U_19159 != hAPP(hAPP(c_List_Oappend(U_19152),U_19157),hAPP(hAPP(c_List_Olist_OCons(U_19152),U_19154),U_19158))
      | U_19156 != hAPP(hAPP(c_List_Oappend(U_19152),U_19157),hAPP(hAPP(c_List_Olist_OCons(U_19152),U_19153),U_19158))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19152,U_19152)),hAPP(hAPP(c_Product__Type_OPair(U_19152,U_19152),U_19153),U_19154)),U_19155)) ),
    inference(variable_rename,[status(thm)],[f_4592_1]) ).

fof(f_4592_3,plain,
    ! [U_19153,U_19155,U_19157,U_19156,U_19154,U_19152,U_19158,U_19159] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19152),tc_List_Olist(U_19152))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19152),tc_List_Olist(U_19152)),U_19156),U_19159)),c_List_Olistrel1(U_19152,U_19155)))
      | U_19159 != hAPP(hAPP(c_List_Oappend(U_19152),U_19157),hAPP(hAPP(c_List_Olist_OCons(U_19152),U_19154),U_19158))
      | U_19156 != hAPP(hAPP(c_List_Oappend(U_19152),U_19157),hAPP(hAPP(c_List_Olist_OCons(U_19152),U_19153),U_19158))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19152,U_19152)),hAPP(hAPP(c_Product__Type_OPair(U_19152,U_19152),U_19153),U_19154)),U_19155)) ),
    inference(definitional_conversion,[status(esa)],[f_4592_2]) ).

cnf(f_4592_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19152),tc_List_Olist(U_19152))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19152),tc_List_Olist(U_19152)),U_19156),U_19159)),c_List_Olistrel1(U_19152,U_19155)))
    | U_19159 != hAPP(hAPP(c_List_Oappend(U_19152),U_19157),hAPP(hAPP(c_List_Olist_OCons(U_19152),U_19154),U_19158))
    | U_19156 != hAPP(hAPP(c_List_Oappend(U_19152),U_19157),hAPP(hAPP(c_List_Olist_OCons(U_19152),U_19153),U_19158))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19152,U_19152)),hAPP(hAPP(c_Product__Type_OPair(U_19152,U_19152),U_19153),U_19154)),U_19155)) ),
    inference(clausify,[status(thm)],[f_4592_3]) ).

fof(f_4593_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_4593_2,plain,
    ! [U_19165,U_19164,U_19163,U_19162,U_19161,U_19160] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19160),tc_List_Olist(U_19160))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19160),tc_List_Olist(U_19160)),hAPP(hAPP(c_List_Olist_OCons(U_19160),U_19161),U_19164)),hAPP(hAPP(c_List_Olist_OCons(U_19160),U_19162),U_19165))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19160),c_List_Olistrel1(U_19160,U_19163))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19160),tc_List_Olist(U_19160))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19160),tc_List_Olist(U_19160)),U_19164),U_19165)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19160),c_List_Olistrel1(U_19160,U_19163))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19160,U_19160)),hAPP(hAPP(c_Product__Type_OPair(U_19160,U_19160),U_19161),U_19162)),c_Transitive__Closure_Ortrancl(U_19160,U_19163))) ),
    inference(variable_rename,[status(thm)],[f_4593_1]) ).

fof(f_4593_3,plain,
    ! [U_19160,U_19161,U_19162,U_19163,U_19164,U_19165] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19160),tc_List_Olist(U_19160))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19160),tc_List_Olist(U_19160)),hAPP(hAPP(c_List_Olist_OCons(U_19160),U_19161),U_19164)),hAPP(hAPP(c_List_Olist_OCons(U_19160),U_19162),U_19165))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19160),c_List_Olistrel1(U_19160,U_19163))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19160),tc_List_Olist(U_19160))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19160),tc_List_Olist(U_19160)),U_19164),U_19165)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19160),c_List_Olistrel1(U_19160,U_19163))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19160,U_19160)),hAPP(hAPP(c_Product__Type_OPair(U_19160,U_19160),U_19161),U_19162)),c_Transitive__Closure_Ortrancl(U_19160,U_19163))) ),
    inference(definitional_conversion,[status(esa)],[f_4593_2]) ).

cnf(f_4593_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19160),tc_List_Olist(U_19160))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19160),tc_List_Olist(U_19160)),hAPP(hAPP(c_List_Olist_OCons(U_19160),U_19161),U_19164)),hAPP(hAPP(c_List_Olist_OCons(U_19160),U_19162),U_19165))),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19160),c_List_Olistrel1(U_19160,U_19163))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19160),tc_List_Olist(U_19160))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19160),tc_List_Olist(U_19160)),U_19164),U_19165)),c_Transitive__Closure_Ortrancl(tc_List_Olist(U_19160),c_List_Olistrel1(U_19160,U_19163))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19160,U_19160)),hAPP(hAPP(c_Product__Type_OPair(U_19160,U_19160),U_19161),U_19162)),c_Transitive__Closure_Ortrancl(U_19160,U_19163))) ),
    inference(clausify,[status(thm)],[f_4593_3]) ).

fof(f_4594_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_4594_2,plain,
    ! [U_19173,U_19172,U_19171,U_19170] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19170),tc_List_Olist(U_19170))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19170),tc_List_Olist(U_19170)),U_19171),U_19172)),c_List_Olistrel1(U_19170,U_19173)))
        | ! [U_19169,U_19168] :
            ( U_19172 != hAPP(hAPP(c_List_Olist__update(U_19170,U_19171),U_19168),U_19169)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19168),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19170)),U_19171)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19170,U_19170)),hAPP(hAPP(c_Product__Type_OPair(U_19170,U_19170),hAPP(hAPP(c_List_Onth(U_19170),U_19171),U_19168)),U_19169)),U_19173)) ) )
      & ( ? [U_19167,U_19166] :
            ( U_19172 = hAPP(hAPP(c_List_Olist__update(U_19170,U_19171),U_19166),U_19167)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19166),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19170)),U_19171)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19170,U_19170)),hAPP(hAPP(c_Product__Type_OPair(U_19170,U_19170),hAPP(hAPP(c_List_Onth(U_19170),U_19171),U_19166)),U_19167)),U_19173)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19170),tc_List_Olist(U_19170))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19170),tc_List_Olist(U_19170)),U_19171),U_19172)),c_List_Olistrel1(U_19170,U_19173))) ) ),
    inference(variable_rename,[status(thm)],[f_4594_1]) ).

fof(f_4594_3,plain,
    ( ! [U_19181,U_19179,U_19177,U_19175] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19175),tc_List_Olist(U_19175))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19175),tc_List_Olist(U_19175)),U_19177),U_19179)),c_List_Olistrel1(U_19175,U_19181)))
        | ! [U_19169,U_19168] :
            ( U_19179 != hAPP(hAPP(c_List_Olist__update(U_19175,U_19177),U_19168),U_19169)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19168),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19175)),U_19177)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19175,U_19175)),hAPP(hAPP(c_Product__Type_OPair(U_19175,U_19175),hAPP(hAPP(c_List_Onth(U_19175),U_19177),U_19168)),U_19169)),U_19181)) ) )
    & ! [U_19180,U_19178,U_19176,U_19174] :
        ( ? [U_19167,U_19166] :
            ( U_19178 = hAPP(hAPP(c_List_Olist__update(U_19174,U_19176),U_19166),U_19167)
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19166),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19174)),U_19176)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19174,U_19174)),hAPP(hAPP(c_Product__Type_OPair(U_19174,U_19174),hAPP(hAPP(c_List_Onth(U_19174),U_19176),U_19166)),U_19167)),U_19180)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19174),tc_List_Olist(U_19174))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19174),tc_List_Olist(U_19174)),U_19176),U_19178)),c_List_Olistrel1(U_19174,U_19180))) ) ),
    inference(miniscope,[status(thm)],[f_4594_2]) ).

fof(f_4594_4,plain,
    ( ! [U_19181,U_19179,U_19177,U_19175] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19175),tc_List_Olist(U_19175))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19175),tc_List_Olist(U_19175)),U_19177),U_19179)),c_List_Olistrel1(U_19175,U_19181)))
        | ! [U_19169,U_19168] :
            ( U_19179 != hAPP(hAPP(c_List_Olist__update(U_19175,U_19177),U_19168),U_19169)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19168),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19175)),U_19177)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19175,U_19175)),hAPP(hAPP(c_Product__Type_OPair(U_19175,U_19175),hAPP(hAPP(c_List_Onth(U_19175),U_19177),U_19168)),U_19169)),U_19181)) ) )
    & ! [U_19180,U_19178,U_19176,U_19174] :
        ( ? [U_19166] :
            ( U_19178 = hAPP(hAPP(c_List_Olist__update(U_19174,U_19176),U_19166),sK471(U_19180,U_19178,U_19176,U_19174))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19166),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19174)),U_19176)))
            & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19174,U_19174)),hAPP(hAPP(c_Product__Type_OPair(U_19174,U_19174),hAPP(hAPP(c_List_Onth(U_19174),U_19176),U_19166)),sK471(U_19180,U_19178,U_19176,U_19174))),U_19180)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19174),tc_List_Olist(U_19174))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19174),tc_List_Olist(U_19174)),U_19176),U_19178)),c_List_Olistrel1(U_19174,U_19180))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK471]),skolemize(U_19167,sK471(U_19180,U_19178,U_19176,U_19174))],[f_4594_3]) ).

fof(f_4594_5,plain,
    ( ! [U_19181,U_19179,U_19177,U_19175] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19175),tc_List_Olist(U_19175))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19175),tc_List_Olist(U_19175)),U_19177),U_19179)),c_List_Olistrel1(U_19175,U_19181)))
        | ! [U_19169,U_19168] :
            ( U_19179 != hAPP(hAPP(c_List_Olist__update(U_19175,U_19177),U_19168),U_19169)
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19168),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19175)),U_19177)))
            | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19175,U_19175)),hAPP(hAPP(c_Product__Type_OPair(U_19175,U_19175),hAPP(hAPP(c_List_Onth(U_19175),U_19177),U_19168)),U_19169)),U_19181)) ) )
    & ! [U_19180,U_19178,U_19176,U_19174] :
        ( ( U_19178 = hAPP(hAPP(c_List_Olist__update(U_19174,U_19176),sK472(U_19180,U_19178,U_19176,U_19174)),sK471(U_19180,U_19178,U_19176,U_19174))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK472(U_19180,U_19178,U_19176,U_19174)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19174)),U_19176)))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19174,U_19174)),hAPP(hAPP(c_Product__Type_OPair(U_19174,U_19174),hAPP(hAPP(c_List_Onth(U_19174),U_19176),sK472(U_19180,U_19178,U_19176,U_19174))),sK471(U_19180,U_19178,U_19176,U_19174))),U_19180)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19174),tc_List_Olist(U_19174))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19174),tc_List_Olist(U_19174)),U_19176),U_19178)),c_List_Olistrel1(U_19174,U_19180))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK472]),skolemize(U_19166,sK472(U_19180,U_19178,U_19176,U_19174))],[f_4594_4]) ).

fof(f_4594_6,plain,
    ( ! [U_19176,U_19180,U_19174,U_19178] :
        ( U_19178 = hAPP(hAPP(c_List_Olist__update(U_19174,U_19176),sK472(U_19180,U_19178,U_19176,U_19174)),sK471(U_19180,U_19178,U_19176,U_19174))
        | ~ sP1181(U_19176,U_19180,U_19174,U_19178) )
    & ! [U_19176,U_19180,U_19174,U_19178] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK472(U_19180,U_19178,U_19176,U_19174)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19174)),U_19176)))
        | ~ sP1181(U_19176,U_19180,U_19174,U_19178) )
    & ! [U_19176,U_19180,U_19174,U_19178] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19174,U_19174)),hAPP(hAPP(c_Product__Type_OPair(U_19174,U_19174),hAPP(hAPP(c_List_Onth(U_19174),U_19176),sK472(U_19180,U_19178,U_19176,U_19174))),sK471(U_19180,U_19178,U_19176,U_19174))),U_19180))
        | ~ sP1181(U_19176,U_19180,U_19174,U_19178) )
    & ! [U_19168,U_19169,U_19175,U_19177,U_19179,U_19181] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19175),tc_List_Olist(U_19175))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19175),tc_List_Olist(U_19175)),U_19177),U_19179)),c_List_Olistrel1(U_19175,U_19181)))
        | U_19179 != hAPP(hAPP(c_List_Olist__update(U_19175,U_19177),U_19168),U_19169)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19168),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19175)),U_19177)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19175,U_19175)),hAPP(hAPP(c_Product__Type_OPair(U_19175,U_19175),hAPP(hAPP(c_List_Onth(U_19175),U_19177),U_19168)),U_19169)),U_19181)) )
    & ! [U_19176,U_19180,U_19174,U_19178] :
        ( sP1181(U_19176,U_19180,U_19174,U_19178)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19174),tc_List_Olist(U_19174))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19174),tc_List_Olist(U_19174)),U_19176),U_19178)),c_List_Olistrel1(U_19174,U_19180))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1181])],[f_4594_5]) ).

cnf(f_4594_7,plain,
    ( sP1181(U_19176,U_19180,U_19174,U_19178)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19174),tc_List_Olist(U_19174))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19174),tc_List_Olist(U_19174)),U_19176),U_19178)),c_List_Olistrel1(U_19174,U_19180))) ),
    inference(clausify,[status(thm)],[f_4594_6]) ).

cnf(f_4594_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19175),tc_List_Olist(U_19175))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19175),tc_List_Olist(U_19175)),U_19177),U_19179)),c_List_Olistrel1(U_19175,U_19181)))
    | U_19179 != hAPP(hAPP(c_List_Olist__update(U_19175,U_19177),U_19168),U_19169)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19168),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19175)),U_19177)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19175,U_19175)),hAPP(hAPP(c_Product__Type_OPair(U_19175,U_19175),hAPP(hAPP(c_List_Onth(U_19175),U_19177),U_19168)),U_19169)),U_19181)) ),
    inference(clausify,[status(thm)],[f_4594_6]) ).

cnf(f_4594_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19174,U_19174)),hAPP(hAPP(c_Product__Type_OPair(U_19174,U_19174),hAPP(hAPP(c_List_Onth(U_19174),U_19176),sK472(U_19180,U_19178,U_19176,U_19174))),sK471(U_19180,U_19178,U_19176,U_19174))),U_19180))
    | ~ sP1181(U_19176,U_19180,U_19174,U_19178) ),
    inference(clausify,[status(thm)],[f_4594_6]) ).

cnf(f_4594_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK472(U_19180,U_19178,U_19176,U_19174)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19174)),U_19176)))
    | ~ sP1181(U_19176,U_19180,U_19174,U_19178) ),
    inference(clausify,[status(thm)],[f_4594_6]) ).

cnf(f_4594_11,plain,
    ( U_19178 = hAPP(hAPP(c_List_Olist__update(U_19174,U_19176),sK472(U_19180,U_19178,U_19176,U_19174)),sK471(U_19180,U_19178,U_19176,U_19174))
    | ~ sP1181(U_19176,U_19180,U_19174,U_19178) ),
    inference(clausify,[status(thm)],[f_4594_6]) ).

fof(f_4595_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_4595_2,plain,
    ! [U_19189,U_19188,U_19187,U_19186] :
      ( ? [U_19185,U_19184] :
          ( ? [U_19183,U_19182] :
              ( U_19188 = hAPP(hAPP(c_List_Oappend(U_19186),U_19183),hAPP(hAPP(c_List_Olist_OCons(U_19186),U_19184),U_19182))
              & U_19187 = hAPP(hAPP(c_List_Oappend(U_19186),U_19183),hAPP(hAPP(c_List_Olist_OCons(U_19186),U_19185),U_19182)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19186,U_19186)),hAPP(hAPP(c_Product__Type_OPair(U_19186,U_19186),U_19185),U_19184)),U_19189)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19186),tc_List_Olist(U_19186))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19186),tc_List_Olist(U_19186)),U_19187),U_19188)),c_List_Olistrel1(U_19186,U_19189))) ),
    inference(variable_rename,[status(thm)],[f_4595_1]) ).

fof(f_4595_3,plain,
    ! [U_19189,U_19188,U_19187,U_19186] :
      ( ? [U_19184] :
          ( ? [U_19183,U_19182] :
              ( U_19188 = hAPP(hAPP(c_List_Oappend(U_19186),U_19183),hAPP(hAPP(c_List_Olist_OCons(U_19186),U_19184),U_19182))
              & U_19187 = hAPP(hAPP(c_List_Oappend(U_19186),U_19183),hAPP(hAPP(c_List_Olist_OCons(U_19186),sK473(U_19189,U_19188,U_19187,U_19186)),U_19182)) )
          & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19186,U_19186)),hAPP(hAPP(c_Product__Type_OPair(U_19186,U_19186),sK473(U_19189,U_19188,U_19187,U_19186)),U_19184)),U_19189)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19186),tc_List_Olist(U_19186))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19186),tc_List_Olist(U_19186)),U_19187),U_19188)),c_List_Olistrel1(U_19186,U_19189))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK473]),skolemize(U_19185,sK473(U_19189,U_19188,U_19187,U_19186))],[f_4595_2]) ).

fof(f_4595_4,plain,
    ! [U_19189,U_19188,U_19187,U_19186] :
      ( ( ? [U_19183,U_19182] :
            ( U_19188 = hAPP(hAPP(c_List_Oappend(U_19186),U_19183),hAPP(hAPP(c_List_Olist_OCons(U_19186),sK474(U_19189,U_19188,U_19187,U_19186)),U_19182))
            & U_19187 = hAPP(hAPP(c_List_Oappend(U_19186),U_19183),hAPP(hAPP(c_List_Olist_OCons(U_19186),sK473(U_19189,U_19188,U_19187,U_19186)),U_19182)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19186,U_19186)),hAPP(hAPP(c_Product__Type_OPair(U_19186,U_19186),sK473(U_19189,U_19188,U_19187,U_19186)),sK474(U_19189,U_19188,U_19187,U_19186))),U_19189)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19186),tc_List_Olist(U_19186))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19186),tc_List_Olist(U_19186)),U_19187),U_19188)),c_List_Olistrel1(U_19186,U_19189))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK474]),skolemize(U_19184,sK474(U_19189,U_19188,U_19187,U_19186))],[f_4595_3]) ).

fof(f_4595_5,plain,
    ! [U_19189,U_19188,U_19187,U_19186] :
      ( ( ? [U_19182] :
            ( U_19188 = hAPP(hAPP(c_List_Oappend(U_19186),sK475(U_19189,U_19188,U_19187,U_19186)),hAPP(hAPP(c_List_Olist_OCons(U_19186),sK474(U_19189,U_19188,U_19187,U_19186)),U_19182))
            & U_19187 = hAPP(hAPP(c_List_Oappend(U_19186),sK475(U_19189,U_19188,U_19187,U_19186)),hAPP(hAPP(c_List_Olist_OCons(U_19186),sK473(U_19189,U_19188,U_19187,U_19186)),U_19182)) )
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19186,U_19186)),hAPP(hAPP(c_Product__Type_OPair(U_19186,U_19186),sK473(U_19189,U_19188,U_19187,U_19186)),sK474(U_19189,U_19188,U_19187,U_19186))),U_19189)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19186),tc_List_Olist(U_19186))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19186),tc_List_Olist(U_19186)),U_19187),U_19188)),c_List_Olistrel1(U_19186,U_19189))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK475]),skolemize(U_19183,sK475(U_19189,U_19188,U_19187,U_19186))],[f_4595_4]) ).

fof(f_4595_6,plain,
    ! [U_19189,U_19188,U_19187,U_19186] :
      ( ( U_19188 = hAPP(hAPP(c_List_Oappend(U_19186),sK475(U_19189,U_19188,U_19187,U_19186)),hAPP(hAPP(c_List_Olist_OCons(U_19186),sK474(U_19189,U_19188,U_19187,U_19186)),sK476(U_19189,U_19188,U_19187,U_19186)))
        & U_19187 = hAPP(hAPP(c_List_Oappend(U_19186),sK475(U_19189,U_19188,U_19187,U_19186)),hAPP(hAPP(c_List_Olist_OCons(U_19186),sK473(U_19189,U_19188,U_19187,U_19186)),sK476(U_19189,U_19188,U_19187,U_19186)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(U_19186,U_19186)),hAPP(hAPP(c_Product__Type_OPair(U_19186,U_19186),sK473(U_19189,U_19188,U_19187,U_19186)),sK474(U_19189,U_19188,U_19187,U_19186))),U_19189)) )
      | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19186),tc_List_Olist(U_19186))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19186),tc_List_Olist(U_19186)),U_19187),U_19188)),c_List_Olistrel1(U_19186,U_19189))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK476]),skolemize(U_19182,sK476(U_19189,U_19188,U_19187,U_19186))],[f_4595_5]) ).

fof(f_4595_7,plain,
    ( ! [U_19186,U_19187,U_19188,U_19189] :
        ( U_19188 = hAPP(hAPP(c_List_Oappend(U_19186),sK475(U_19189,U_19188,U_19187,U_19186)),hAPP(hAPP(c_List_Olist_OCons(U_19186),sK474(U_19189,U_19188,U_19187,U_19186)),sK476(U_19189,U_19188,U_19187,U_19186)))
        | ~ sP1182(U_19186,U_19187,U_19188,U_19189) )
    & ! [U_19186,U_19187,U_19188,U_19189] :
        ( U_19187 = hAPP(hAPP(c_List_Oappend(U_19186),sK475(U_19189,U_19188,U_19187,U_19186)),hAPP(hAPP(c_List_Olist_OCons(U_19186),sK473(U_19189,U_19188,U_19187,U_19186)),sK476(U_19189,U_19188,U_19187,U_19186)))
        | ~ sP1182(U_19186,U_19187,U_19188,U_19189) )
    & ! [U_19186,U_19187,U_19188,U_19189] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19186,U_19186)),hAPP(hAPP(c_Product__Type_OPair(U_19186,U_19186),sK473(U_19189,U_19188,U_19187,U_19186)),sK474(U_19189,U_19188,U_19187,U_19186))),U_19189))
        | ~ sP1182(U_19186,U_19187,U_19188,U_19189) )
    & ! [U_19186,U_19187,U_19188,U_19189] :
        ( sP1182(U_19186,U_19187,U_19188,U_19189)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19186),tc_List_Olist(U_19186))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19186),tc_List_Olist(U_19186)),U_19187),U_19188)),c_List_Olistrel1(U_19186,U_19189))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1182])],[f_4595_6]) ).

cnf(f_4595_8,plain,
    ( sP1182(U_19186,U_19187,U_19188,U_19189)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19186),tc_List_Olist(U_19186))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19186),tc_List_Olist(U_19186)),U_19187),U_19188)),c_List_Olistrel1(U_19186,U_19189))) ),
    inference(clausify,[status(thm)],[f_4595_7]) ).

cnf(f_4595_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(U_19186,U_19186)),hAPP(hAPP(c_Product__Type_OPair(U_19186,U_19186),sK473(U_19189,U_19188,U_19187,U_19186)),sK474(U_19189,U_19188,U_19187,U_19186))),U_19189))
    | ~ sP1182(U_19186,U_19187,U_19188,U_19189) ),
    inference(clausify,[status(thm)],[f_4595_7]) ).

cnf(f_4595_10,plain,
    ( U_19187 = hAPP(hAPP(c_List_Oappend(U_19186),sK475(U_19189,U_19188,U_19187,U_19186)),hAPP(hAPP(c_List_Olist_OCons(U_19186),sK473(U_19189,U_19188,U_19187,U_19186)),sK476(U_19189,U_19188,U_19187,U_19186)))
    | ~ sP1182(U_19186,U_19187,U_19188,U_19189) ),
    inference(clausify,[status(thm)],[f_4595_7]) ).

cnf(f_4595_11,plain,
    ( U_19188 = hAPP(hAPP(c_List_Oappend(U_19186),sK475(U_19189,U_19188,U_19187,U_19186)),hAPP(hAPP(c_List_Olist_OCons(U_19186),sK474(U_19189,U_19188,U_19187,U_19186)),sK476(U_19189,U_19188,U_19187,U_19186)))
    | ~ sP1182(U_19186,U_19187,U_19188,U_19189) ),
    inference(clausify,[status(thm)],[f_4595_7]) ).

fof(f_4596_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_4596_2,plain,
    ! [U_19191,U_19190] : hAPP(c_List_Orotate1(U_19190),U_19191) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_19190),U_19190,c_List_Olist_ONil(U_19190),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19190),tc_fun(tc_List_Olist(U_19190),tc_List_Olist(U_19190)),U_19190),hAPP(c_COMBC(tc_List_Olist(U_19190),tc_List_Olist(U_19190),tc_List_Olist(U_19190)),c_List_Oappend(U_19190))),hAPP(hAPP(c_COMBC(U_19190,tc_List_Olist(U_19190),tc_List_Olist(U_19190)),c_List_Olist_OCons(U_19190)),c_List_Olist_ONil(U_19190)))),U_19191),
    inference(variable_rename,[status(thm)],[f_4596_1]) ).

fof(f_4596_3,plain,
    ! [U_19191,U_19190] : hAPP(c_List_Orotate1(U_19190),U_19191) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_19190),U_19190,c_List_Olist_ONil(U_19190),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19190),tc_fun(tc_List_Olist(U_19190),tc_List_Olist(U_19190)),U_19190),hAPP(c_COMBC(tc_List_Olist(U_19190),tc_List_Olist(U_19190),tc_List_Olist(U_19190)),c_List_Oappend(U_19190))),hAPP(hAPP(c_COMBC(U_19190,tc_List_Olist(U_19190),tc_List_Olist(U_19190)),c_List_Olist_OCons(U_19190)),c_List_Olist_ONil(U_19190)))),U_19191),
    inference(definitional_conversion,[status(esa)],[f_4596_2]) ).

cnf(f_4596_4,plain,
    hAPP(c_List_Orotate1(U_19190),U_19191) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_19190),U_19190,c_List_Olist_ONil(U_19190),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19190),tc_fun(tc_List_Olist(U_19190),tc_List_Olist(U_19190)),U_19190),hAPP(c_COMBC(tc_List_Olist(U_19190),tc_List_Olist(U_19190),tc_List_Olist(U_19190)),c_List_Oappend(U_19190))),hAPP(hAPP(c_COMBC(U_19190,tc_List_Olist(U_19190),tc_List_Olist(U_19190)),c_List_Olist_OCons(U_19190)),c_List_Olist_ONil(U_19190)))),U_19191),
    inference(clausify,[status(thm)],[f_4596_3]) ).

fof(f_4597_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_4597_2,plain,
    ! [U_19195,U_19194,U_19193,U_19192] :
      ( hAPP(hAPP(c_List_Olist__update(U_19193,U_19194),U_19192),U_19195) = hAPP(hAPP(c_List_Oappend(U_19193),hAPP(hAPP(c_List_Otake(U_19193),U_19192),U_19194)),hAPP(hAPP(c_List_Olist_OCons(U_19193),U_19195),hAPP(hAPP(c_List_Odrop(U_19193),hAPP(c_Nat_OSuc,U_19192)),U_19194)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19192),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19193)),U_19194))) ),
    inference(variable_rename,[status(thm)],[f_4597_1]) ).

fof(f_4597_3,plain,
    ! [U_19192,U_19193,U_19194,U_19195] :
      ( hAPP(hAPP(c_List_Olist__update(U_19193,U_19194),U_19192),U_19195) = hAPP(hAPP(c_List_Oappend(U_19193),hAPP(hAPP(c_List_Otake(U_19193),U_19192),U_19194)),hAPP(hAPP(c_List_Olist_OCons(U_19193),U_19195),hAPP(hAPP(c_List_Odrop(U_19193),hAPP(c_Nat_OSuc,U_19192)),U_19194)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19192),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19193)),U_19194))) ),
    inference(definitional_conversion,[status(esa)],[f_4597_2]) ).

cnf(f_4597_4,plain,
    ( hAPP(hAPP(c_List_Olist__update(U_19193,U_19194),U_19192),U_19195) = hAPP(hAPP(c_List_Oappend(U_19193),hAPP(hAPP(c_List_Otake(U_19193),U_19192),U_19194)),hAPP(hAPP(c_List_Olist_OCons(U_19193),U_19195),hAPP(hAPP(c_List_Odrop(U_19193),hAPP(c_Nat_OSuc,U_19192)),U_19194)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19192),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19193)),U_19194))) ),
    inference(clausify,[status(thm)],[f_4597_3]) ).

fof(f_4598_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_4598_2,plain,
    ! [U_19199,U_19198,U_19197,U_19196] : hAPP(hAPP(c_List_Odrop(U_19196),U_19197),hAPP(hAPP(c_List_Oappend(U_19196),U_19198),U_19199)) = hAPP(hAPP(c_List_Oappend(U_19196),hAPP(hAPP(c_List_Odrop(U_19196),U_19197),U_19198)),hAPP(hAPP(c_List_Odrop(U_19196),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19197),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19196)),U_19198))),U_19199)),
    inference(variable_rename,[status(thm)],[f_4598_1]) ).

fof(f_4598_3,plain,
    ! [U_19196,U_19197,U_19198,U_19199] : hAPP(hAPP(c_List_Odrop(U_19196),U_19197),hAPP(hAPP(c_List_Oappend(U_19196),U_19198),U_19199)) = hAPP(hAPP(c_List_Oappend(U_19196),hAPP(hAPP(c_List_Odrop(U_19196),U_19197),U_19198)),hAPP(hAPP(c_List_Odrop(U_19196),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19197),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19196)),U_19198))),U_19199)),
    inference(definitional_conversion,[status(esa)],[f_4598_2]) ).

cnf(f_4598_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19196),U_19197),hAPP(hAPP(c_List_Oappend(U_19196),U_19198),U_19199)) = hAPP(hAPP(c_List_Oappend(U_19196),hAPP(hAPP(c_List_Odrop(U_19196),U_19197),U_19198)),hAPP(hAPP(c_List_Odrop(U_19196),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19197),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19196)),U_19198))),U_19199)),
    inference(clausify,[status(thm)],[f_4598_3]) ).

fof(f_4599_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_4599_2,plain,
    ! [U_19201,U_19200] : hAPP(hAPP(c_List_Odrop(U_19200),U_19201),c_List_Olist_ONil(U_19200)) = c_List_Olist_ONil(U_19200),
    inference(variable_rename,[status(thm)],[f_4599_1]) ).

fof(f_4599_3,plain,
    ! [U_19201,U_19200] : hAPP(hAPP(c_List_Odrop(U_19200),U_19201),c_List_Olist_ONil(U_19200)) = c_List_Olist_ONil(U_19200),
    inference(definitional_conversion,[status(esa)],[f_4599_2]) ).

cnf(f_4599_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19200),U_19201),c_List_Olist_ONil(U_19200)) = c_List_Olist_ONil(U_19200),
    inference(clausify,[status(thm)],[f_4599_3]) ).

fof(f_4600_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_4600_2,plain,
    ! [U_19203,U_19202] :
      ( ( hAPP(c_List_Orotate1(U_19202),U_19203) = c_List_Olist_ONil(U_19202)
        | U_19203 != c_List_Olist_ONil(U_19202) )
      & ( U_19203 = c_List_Olist_ONil(U_19202)
        | hAPP(c_List_Orotate1(U_19202),U_19203) != c_List_Olist_ONil(U_19202) ) ),
    inference(variable_rename,[status(thm)],[f_4600_1]) ).

fof(f_4600_3,plain,
    ( ! [U_19207,U_19205] :
        ( hAPP(c_List_Orotate1(U_19205),U_19207) = c_List_Olist_ONil(U_19205)
        | U_19207 != c_List_Olist_ONil(U_19205) )
    & ! [U_19206,U_19204] :
        ( U_19206 = c_List_Olist_ONil(U_19204)
        | hAPP(c_List_Orotate1(U_19204),U_19206) != c_List_Olist_ONil(U_19204) ) ),
    inference(miniscope,[status(thm)],[f_4600_2]) ).

fof(f_4600_4,plain,
    ( ! [U_19207,U_19205] :
        ( hAPP(c_List_Orotate1(U_19205),U_19207) = c_List_Olist_ONil(U_19205)
        | U_19207 != c_List_Olist_ONil(U_19205) )
    & ! [U_19206,U_19204] :
        ( U_19206 = c_List_Olist_ONil(U_19204)
        | hAPP(c_List_Orotate1(U_19204),U_19206) != c_List_Olist_ONil(U_19204) ) ),
    inference(definitional_conversion,[status(esa)],[f_4600_3]) ).

cnf(f_4600_5,plain,
    ( U_19206 = c_List_Olist_ONil(U_19204)
    | hAPP(c_List_Orotate1(U_19204),U_19206) != c_List_Olist_ONil(U_19204) ),
    inference(clausify,[status(thm)],[f_4600_4]) ).

cnf(f_4600_6,plain,
    ( hAPP(c_List_Orotate1(U_19205),U_19207) = c_List_Olist_ONil(U_19205)
    | U_19207 != c_List_Olist_ONil(U_19205) ),
    inference(clausify,[status(thm)],[f_4600_4]) ).

fof(f_4601_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_4601_2,plain,
    ! [U_19211,U_19210,U_19209,U_19208] : hAPP(hAPP(c_List_Odrop(U_19208),U_19209),hAPP(hAPP(c_List_Otake(U_19208),U_19210),U_19211)) = hAPP(hAPP(c_List_Otake(U_19208),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19210),U_19209)),hAPP(hAPP(c_List_Odrop(U_19208),U_19209),U_19211)),
    inference(variable_rename,[status(thm)],[f_4601_1]) ).

fof(f_4601_3,plain,
    ! [U_19208,U_19209,U_19210,U_19211] : hAPP(hAPP(c_List_Odrop(U_19208),U_19209),hAPP(hAPP(c_List_Otake(U_19208),U_19210),U_19211)) = hAPP(hAPP(c_List_Otake(U_19208),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19210),U_19209)),hAPP(hAPP(c_List_Odrop(U_19208),U_19209),U_19211)),
    inference(definitional_conversion,[status(esa)],[f_4601_2]) ).

cnf(f_4601_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19208),U_19209),hAPP(hAPP(c_List_Otake(U_19208),U_19210),U_19211)) = hAPP(hAPP(c_List_Otake(U_19208),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19210),U_19209)),hAPP(hAPP(c_List_Odrop(U_19208),U_19209),U_19211)),
    inference(clausify,[status(thm)],[f_4601_3]) ).

fof(f_4602_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_4602_2,plain,
    ! [U_19215,U_19214,U_19213,U_19212] : hAPP(hAPP(c_List_Otake(U_19212),U_19213),hAPP(hAPP(c_List_Odrop(U_19212),U_19214),U_19215)) = hAPP(hAPP(c_List_Odrop(U_19212),U_19214),hAPP(hAPP(c_List_Otake(U_19212),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19213),U_19214)),U_19215)),
    inference(variable_rename,[status(thm)],[f_4602_1]) ).

fof(f_4602_3,plain,
    ! [U_19212,U_19213,U_19214,U_19215] : hAPP(hAPP(c_List_Otake(U_19212),U_19213),hAPP(hAPP(c_List_Odrop(U_19212),U_19214),U_19215)) = hAPP(hAPP(c_List_Odrop(U_19212),U_19214),hAPP(hAPP(c_List_Otake(U_19212),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19213),U_19214)),U_19215)),
    inference(definitional_conversion,[status(esa)],[f_4602_2]) ).

cnf(f_4602_4,plain,
    hAPP(hAPP(c_List_Otake(U_19212),U_19213),hAPP(hAPP(c_List_Odrop(U_19212),U_19214),U_19215)) = hAPP(hAPP(c_List_Odrop(U_19212),U_19214),hAPP(hAPP(c_List_Otake(U_19212),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19213),U_19214)),U_19215)),
    inference(clausify,[status(thm)],[f_4602_3]) ).

fof(f_4603_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_4603_2,plain,
    ! [U_19219,U_19218,U_19217,U_19216] :
      ( hBOOL(hAPP(hAPP(c_member(U_19216),U_19217),hAPP(c_List_Oset(U_19216),U_19219)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19216),U_19217),hAPP(c_List_Oset(U_19216),hAPP(hAPP(c_List_Odrop(U_19216),U_19218),U_19219)))) ),
    inference(variable_rename,[status(thm)],[f_4603_1]) ).

fof(f_4603_3,plain,
    ! [U_19216,U_19217,U_19218,U_19219] :
      ( hBOOL(hAPP(hAPP(c_member(U_19216),U_19217),hAPP(c_List_Oset(U_19216),U_19219)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19216),U_19217),hAPP(c_List_Oset(U_19216),hAPP(hAPP(c_List_Odrop(U_19216),U_19218),U_19219)))) ),
    inference(definitional_conversion,[status(esa)],[f_4603_2]) ).

cnf(f_4603_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19216),U_19217),hAPP(c_List_Oset(U_19216),U_19219)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19216),U_19217),hAPP(c_List_Oset(U_19216),hAPP(hAPP(c_List_Odrop(U_19216),U_19218),U_19219)))) ),
    inference(clausify,[status(thm)],[f_4603_3]) ).

fof(f_4604_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_4604_2,plain,
    ! [U_19221,U_19220] : hAPP(c_List_Oset(U_19220),hAPP(c_List_Orotate1(U_19220),U_19221)) = hAPP(c_List_Oset(U_19220),U_19221),
    inference(variable_rename,[status(thm)],[f_4604_1]) ).

fof(f_4604_3,plain,
    ! [U_19220,U_19221] : hAPP(c_List_Oset(U_19220),hAPP(c_List_Orotate1(U_19220),U_19221)) = hAPP(c_List_Oset(U_19220),U_19221),
    inference(definitional_conversion,[status(esa)],[f_4604_2]) ).

cnf(f_4604_4,plain,
    hAPP(c_List_Oset(U_19220),hAPP(c_List_Orotate1(U_19220),U_19221)) = hAPP(c_List_Oset(U_19220),U_19221),
    inference(clausify,[status(thm)],[f_4604_3]) ).

fof(f_4605_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_4605_2,plain,
    ! [U_19224,U_19223,U_19222] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19222,tc_HOL_Obool)),hAPP(c_List_Oset(U_19222),hAPP(hAPP(c_List_Odrop(U_19222),U_19223),U_19224))),hAPP(c_List_Oset(U_19222),U_19224))),
    inference(variable_rename,[status(thm)],[f_4605_1]) ).

fof(f_4605_3,plain,
    ! [U_19222,U_19223,U_19224] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19222,tc_HOL_Obool)),hAPP(c_List_Oset(U_19222),hAPP(hAPP(c_List_Odrop(U_19222),U_19223),U_19224))),hAPP(c_List_Oset(U_19222),U_19224))),
    inference(definitional_conversion,[status(esa)],[f_4605_2]) ).

cnf(f_4605_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19222,tc_HOL_Obool)),hAPP(c_List_Oset(U_19222),hAPP(hAPP(c_List_Odrop(U_19222),U_19223),U_19224))),hAPP(c_List_Oset(U_19222),U_19224))),
    inference(clausify,[status(thm)],[f_4605_3]) ).

fof(f_4606_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_4606_2,plain,
    ! [U_19226,U_19225] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_19225),hAPP(c_List_Orotate1(U_19225),U_19226)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19225),U_19226)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_19225),U_19226))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19225),hAPP(c_List_Orotate1(U_19225),U_19226))) ) ),
    inference(variable_rename,[status(thm)],[f_4606_1]) ).

fof(f_4606_3,plain,
    ( ! [U_19230,U_19228] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19228),hAPP(c_List_Orotate1(U_19228),U_19230)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19228),U_19230)) )
    & ! [U_19229,U_19227] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19227),U_19229))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19227),hAPP(c_List_Orotate1(U_19227),U_19229))) ) ),
    inference(miniscope,[status(thm)],[f_4606_2]) ).

fof(f_4606_4,plain,
    ( ! [U_19228,U_19230] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19228),hAPP(c_List_Orotate1(U_19228),U_19230)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19228),U_19230)) )
    & ! [U_19229,U_19227] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19227),U_19229))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19227),hAPP(c_List_Orotate1(U_19227),U_19229))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4606_3]) ).

cnf(f_4606_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19227),U_19229))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19227),hAPP(c_List_Orotate1(U_19227),U_19229))) ),
    inference(clausify,[status(thm)],[f_4606_4]) ).

cnf(f_4606_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19228),hAPP(c_List_Orotate1(U_19228),U_19230)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19228),U_19230)) ),
    inference(clausify,[status(thm)],[f_4606_4]) ).

fof(f_4607_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_4607_2,plain,
    ! [U_19233,U_19232,U_19231] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19231),hAPP(hAPP(c_List_Odrop(U_19231),U_19233),U_19232)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19231),U_19232)) ),
    inference(variable_rename,[status(thm)],[f_4607_1]) ).

fof(f_4607_3,plain,
    ! [U_19231,U_19232,U_19233] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19231),hAPP(hAPP(c_List_Odrop(U_19231),U_19233),U_19232)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19231),U_19232)) ),
    inference(definitional_conversion,[status(esa)],[f_4607_2]) ).

cnf(f_4607_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19231),hAPP(hAPP(c_List_Odrop(U_19231),U_19233),U_19232)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19231),U_19232)) ),
    inference(clausify,[status(thm)],[f_4607_3]) ).

fof(f_4608_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_4608_2,plain,
    ! [U_19237,U_19236,U_19235,U_19234] : hAPP(hAPP(c_List_Odrop(U_19234),U_19235),hAPP(hAPP(c_List_Odrop(U_19234),U_19236),U_19237)) = hAPP(hAPP(c_List_Odrop(U_19234),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19235),U_19236)),U_19237),
    inference(variable_rename,[status(thm)],[f_4608_1]) ).

fof(f_4608_3,plain,
    ! [U_19234,U_19235,U_19236,U_19237] : hAPP(hAPP(c_List_Odrop(U_19234),U_19235),hAPP(hAPP(c_List_Odrop(U_19234),U_19236),U_19237)) = hAPP(hAPP(c_List_Odrop(U_19234),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19235),U_19236)),U_19237),
    inference(definitional_conversion,[status(esa)],[f_4608_2]) ).

cnf(f_4608_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19234),U_19235),hAPP(hAPP(c_List_Odrop(U_19234),U_19236),U_19237)) = hAPP(hAPP(c_List_Odrop(U_19234),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19235),U_19236)),U_19237),
    inference(clausify,[status(thm)],[f_4608_3]) ).

fof(f_4609_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_4609_2,plain,
    ! [U_19239,U_19238] : hAPP(hAPP(c_List_Odrop(U_19238),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19239) = U_19239,
    inference(variable_rename,[status(thm)],[f_4609_1]) ).

fof(f_4609_3,plain,
    ! [U_19239,U_19238] : hAPP(hAPP(c_List_Odrop(U_19238),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19239) = U_19239,
    inference(definitional_conversion,[status(esa)],[f_4609_2]) ).

cnf(f_4609_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19238),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),U_19239) = U_19239,
    inference(clausify,[status(thm)],[f_4609_3]) ).

fof(f_4610_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_4610_2,plain,
    ! [U_19244,U_19243,U_19242,U_19241,U_19240] : hAPP(hAPP(c_List_Odrop(tc_prod(U_19240,U_19241)),U_19242),hAPP(hAPP(c_List_Ozip(U_19240,U_19241),U_19243),U_19244)) = hAPP(hAPP(c_List_Ozip(U_19240,U_19241),hAPP(hAPP(c_List_Odrop(U_19240),U_19242),U_19243)),hAPP(hAPP(c_List_Odrop(U_19241),U_19242),U_19244)),
    inference(variable_rename,[status(thm)],[f_4610_1]) ).

fof(f_4610_3,plain,
    ! [U_19240,U_19241,U_19242,U_19243,U_19244] : hAPP(hAPP(c_List_Odrop(tc_prod(U_19240,U_19241)),U_19242),hAPP(hAPP(c_List_Ozip(U_19240,U_19241),U_19243),U_19244)) = hAPP(hAPP(c_List_Ozip(U_19240,U_19241),hAPP(hAPP(c_List_Odrop(U_19240),U_19242),U_19243)),hAPP(hAPP(c_List_Odrop(U_19241),U_19242),U_19244)),
    inference(definitional_conversion,[status(esa)],[f_4610_2]) ).

cnf(f_4610_4,plain,
    hAPP(hAPP(c_List_Odrop(tc_prod(U_19240,U_19241)),U_19242),hAPP(hAPP(c_List_Ozip(U_19240,U_19241),U_19243),U_19244)) = hAPP(hAPP(c_List_Ozip(U_19240,U_19241),hAPP(hAPP(c_List_Odrop(U_19240),U_19242),U_19243)),hAPP(hAPP(c_List_Odrop(U_19241),U_19242),U_19244)),
    inference(clausify,[status(thm)],[f_4610_3]) ).

fof(f_4611_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_4611_2,plain,
    ! [U_19249,U_19248,U_19247,U_19246,U_19245] : hAPP(hAPP(c_List_Odrop(U_19245),U_19246),hAPP(hAPP(c_List_Omap(U_19247,U_19245),U_19248),U_19249)) = hAPP(hAPP(c_List_Omap(U_19247,U_19245),U_19248),hAPP(hAPP(c_List_Odrop(U_19247),U_19246),U_19249)),
    inference(variable_rename,[status(thm)],[f_4611_1]) ).

fof(f_4611_3,plain,
    ! [U_19245,U_19246,U_19247,U_19248,U_19249] : hAPP(hAPP(c_List_Odrop(U_19245),U_19246),hAPP(hAPP(c_List_Omap(U_19247,U_19245),U_19248),U_19249)) = hAPP(hAPP(c_List_Omap(U_19247,U_19245),U_19248),hAPP(hAPP(c_List_Odrop(U_19247),U_19246),U_19249)),
    inference(definitional_conversion,[status(esa)],[f_4611_2]) ).

cnf(f_4611_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19245),U_19246),hAPP(hAPP(c_List_Omap(U_19247,U_19245),U_19248),U_19249)) = hAPP(hAPP(c_List_Omap(U_19247,U_19245),U_19248),hAPP(hAPP(c_List_Odrop(U_19247),U_19246),U_19249)),
    inference(clausify,[status(thm)],[f_4611_3]) ).

fof(f_4612_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_4612_2,plain,
    ! [U_19251,U_19250] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19250)),hAPP(c_List_Orotate1(U_19250),U_19251)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19250)),U_19251),
    inference(variable_rename,[status(thm)],[f_4612_1]) ).

fof(f_4612_3,plain,
    ! [U_19250,U_19251] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19250)),hAPP(c_List_Orotate1(U_19250),U_19251)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19250)),U_19251),
    inference(definitional_conversion,[status(esa)],[f_4612_2]) ).

cnf(f_4612_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19250)),hAPP(c_List_Orotate1(U_19250),U_19251)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19250)),U_19251),
    inference(clausify,[status(thm)],[f_4612_3]) ).

fof(f_4613_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_4613_2,plain,
    ! [U_19254,U_19253,U_19252] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19252)),hAPP(hAPP(c_List_Odrop(U_19252),U_19253),U_19254)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19252)),U_19254)),U_19253),
    inference(variable_rename,[status(thm)],[f_4613_1]) ).

fof(f_4613_3,plain,
    ! [U_19252,U_19253,U_19254] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19252)),hAPP(hAPP(c_List_Odrop(U_19252),U_19253),U_19254)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19252)),U_19254)),U_19253),
    inference(definitional_conversion,[status(esa)],[f_4613_2]) ).

cnf(f_4613_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19252)),hAPP(hAPP(c_List_Odrop(U_19252),U_19253),U_19254)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19252)),U_19254)),U_19253),
    inference(clausify,[status(thm)],[f_4613_3]) ).

fof(f_4614_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_4614_2,plain,
    ! [U_19257,U_19256,U_19255] : hAPP(hAPP(c_List_Odrop(U_19255),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_19255),U_19256),U_19257)) = U_19257,
    inference(variable_rename,[status(thm)],[f_4614_1]) ).

fof(f_4614_3,plain,
    ! [U_19255,U_19256,U_19257] : hAPP(hAPP(c_List_Odrop(U_19255),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_19255),U_19256),U_19257)) = U_19257,
    inference(definitional_conversion,[status(esa)],[f_4614_2]) ).

cnf(f_4614_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19255),c_Groups_Oone__class_Oone(tc_Nat_Onat)),hAPP(hAPP(c_List_Olist_OCons(U_19255),U_19256),U_19257)) = U_19257,
    inference(clausify,[status(thm)],[f_4614_3]) ).

fof(f_4615_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_4615_2,plain,
    ! [U_19261,U_19260,U_19259,U_19258] : hAPP(hAPP(c_List_Odrop(U_19258),hAPP(c_Nat_OSuc,U_19259)),hAPP(hAPP(c_List_Olist_OCons(U_19258),U_19260),U_19261)) = hAPP(hAPP(c_List_Odrop(U_19258),U_19259),U_19261),
    inference(variable_rename,[status(thm)],[f_4615_1]) ).

fof(f_4615_3,plain,
    ! [U_19258,U_19259,U_19260,U_19261] : hAPP(hAPP(c_List_Odrop(U_19258),hAPP(c_Nat_OSuc,U_19259)),hAPP(hAPP(c_List_Olist_OCons(U_19258),U_19260),U_19261)) = hAPP(hAPP(c_List_Odrop(U_19258),U_19259),U_19261),
    inference(definitional_conversion,[status(esa)],[f_4615_2]) ).

cnf(f_4615_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19258),hAPP(c_Nat_OSuc,U_19259)),hAPP(hAPP(c_List_Olist_OCons(U_19258),U_19260),U_19261)) = hAPP(hAPP(c_List_Odrop(U_19258),U_19259),U_19261),
    inference(clausify,[status(thm)],[f_4615_3]) ).

fof(f_4616_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_4616_2,plain,
    ! [U_19266,U_19265,U_19264,U_19263,U_19262] :
      ( hAPP(hAPP(c_List_Onth(U_19262),U_19264),U_19263) = U_19265
      | hAPP(hAPP(c_List_Odrop(U_19262),U_19263),U_19264) != hAPP(hAPP(c_List_Olist_OCons(U_19262),U_19265),U_19266) ),
    inference(variable_rename,[status(thm)],[f_4616_1]) ).

fof(f_4616_3,plain,
    ! [U_19262,U_19263,U_19264,U_19265,U_19266] :
      ( hAPP(hAPP(c_List_Onth(U_19262),U_19264),U_19263) = U_19265
      | hAPP(hAPP(c_List_Odrop(U_19262),U_19263),U_19264) != hAPP(hAPP(c_List_Olist_OCons(U_19262),U_19265),U_19266) ),
    inference(definitional_conversion,[status(esa)],[f_4616_2]) ).

cnf(f_4616_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_19262),U_19264),U_19263) = U_19265
    | hAPP(hAPP(c_List_Odrop(U_19262),U_19263),U_19264) != hAPP(hAPP(c_List_Olist_OCons(U_19262),U_19265),U_19266) ),
    inference(clausify,[status(thm)],[f_4616_3]) ).

fof(f_4617_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_4617_2,plain,
    ! [U_19269,U_19268,U_19267] :
      ( hAPP(hAPP(c_List_Odrop(U_19267),U_19269),U_19268) = c_List_Olist_ONil(U_19267)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19267)),U_19268)),U_19269)) ),
    inference(variable_rename,[status(thm)],[f_4617_1]) ).

fof(f_4617_3,plain,
    ! [U_19267,U_19268,U_19269] :
      ( hAPP(hAPP(c_List_Odrop(U_19267),U_19269),U_19268) = c_List_Olist_ONil(U_19267)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19267)),U_19268)),U_19269)) ),
    inference(definitional_conversion,[status(esa)],[f_4617_2]) ).

cnf(f_4617_4,plain,
    ( hAPP(hAPP(c_List_Odrop(U_19267),U_19269),U_19268) = c_List_Olist_ONil(U_19267)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19267)),U_19268)),U_19269)) ),
    inference(clausify,[status(thm)],[f_4617_3]) ).

fof(f_4618_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_4618_2,plain,
    ! [U_19272,U_19271,U_19270] :
      ( ( hAPP(hAPP(c_List_Odrop(U_19270),U_19271),U_19272) = c_List_Olist_ONil(U_19270)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19270)),U_19272)),U_19271)) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19270)),U_19272)),U_19271))
        | hAPP(hAPP(c_List_Odrop(U_19270),U_19271),U_19272) != c_List_Olist_ONil(U_19270) ) ),
    inference(variable_rename,[status(thm)],[f_4618_1]) ).

fof(f_4618_3,plain,
    ( ! [U_19278,U_19276,U_19274] :
        ( hAPP(hAPP(c_List_Odrop(U_19274),U_19276),U_19278) = c_List_Olist_ONil(U_19274)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19274)),U_19278)),U_19276)) )
    & ! [U_19277,U_19275,U_19273] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19273)),U_19277)),U_19275))
        | hAPP(hAPP(c_List_Odrop(U_19273),U_19275),U_19277) != c_List_Olist_ONil(U_19273) ) ),
    inference(miniscope,[status(thm)],[f_4618_2]) ).

fof(f_4618_4,plain,
    ( ! [U_19274,U_19276,U_19278] :
        ( hAPP(hAPP(c_List_Odrop(U_19274),U_19276),U_19278) = c_List_Olist_ONil(U_19274)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19274)),U_19278)),U_19276)) )
    & ! [U_19277,U_19275,U_19273] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19273)),U_19277)),U_19275))
        | hAPP(hAPP(c_List_Odrop(U_19273),U_19275),U_19277) != c_List_Olist_ONil(U_19273) ) ),
    inference(definitional_conversion,[status(esa)],[f_4618_3]) ).

cnf(f_4618_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19273)),U_19277)),U_19275))
    | hAPP(hAPP(c_List_Odrop(U_19273),U_19275),U_19277) != c_List_Olist_ONil(U_19273) ),
    inference(clausify,[status(thm)],[f_4618_4]) ).

cnf(f_4618_6,plain,
    ( hAPP(hAPP(c_List_Odrop(U_19274),U_19276),U_19278) = c_List_Olist_ONil(U_19274)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19274)),U_19278)),U_19276)) ),
    inference(clausify,[status(thm)],[f_4618_4]) ).

fof(f_4619_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_4619_2,plain,
    ! [U_19282,U_19281,U_19280,U_19279] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19281,tc_HOL_Obool)),hAPP(c_List_Oset(U_19281),hAPP(hAPP(c_List_Odrop(U_19281),U_19280),U_19282))),hAPP(c_List_Oset(U_19281),hAPP(hAPP(c_List_Odrop(U_19281),U_19279),U_19282))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19279),U_19280)) ),
    inference(variable_rename,[status(thm)],[f_4619_1]) ).

fof(f_4619_3,plain,
    ! [U_19280,U_19279,U_19281,U_19282] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19281,tc_HOL_Obool)),hAPP(c_List_Oset(U_19281),hAPP(hAPP(c_List_Odrop(U_19281),U_19280),U_19282))),hAPP(c_List_Oset(U_19281),hAPP(hAPP(c_List_Odrop(U_19281),U_19279),U_19282))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19279),U_19280)) ),
    inference(definitional_conversion,[status(esa)],[f_4619_2]) ).

cnf(f_4619_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19281,tc_HOL_Obool)),hAPP(c_List_Oset(U_19281),hAPP(hAPP(c_List_Odrop(U_19281),U_19280),U_19282))),hAPP(c_List_Oset(U_19281),hAPP(hAPP(c_List_Odrop(U_19281),U_19279),U_19282))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19279),U_19280)) ),
    inference(clausify,[status(thm)],[f_4619_3]) ).

fof(f_4620_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_4620_2,plain,
    ! [U_19285,U_19284,U_19283] : hAPP(hAPP(c_List_Oappend(U_19283),hAPP(hAPP(c_List_Otake(U_19283),U_19284),U_19285)),hAPP(hAPP(c_List_Odrop(U_19283),U_19284),U_19285)) = U_19285,
    inference(variable_rename,[status(thm)],[f_4620_1]) ).

fof(f_4620_3,plain,
    ! [U_19283,U_19284,U_19285] : hAPP(hAPP(c_List_Oappend(U_19283),hAPP(hAPP(c_List_Otake(U_19283),U_19284),U_19285)),hAPP(hAPP(c_List_Odrop(U_19283),U_19284),U_19285)) = U_19285,
    inference(definitional_conversion,[status(esa)],[f_4620_2]) ).

cnf(f_4620_4,plain,
    hAPP(hAPP(c_List_Oappend(U_19283),hAPP(hAPP(c_List_Otake(U_19283),U_19284),U_19285)),hAPP(hAPP(c_List_Odrop(U_19283),U_19284),U_19285)) = U_19285,
    inference(clausify,[status(thm)],[f_4620_3]) ).

fof(f_4621_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_4621_2,plain,
    ! [U_19289,U_19288,U_19287,U_19286] :
      ( ( hAPP(hAPP(c_List_Oappend(U_19286),U_19287),U_19288) = U_19289
        | U_19288 != hAPP(hAPP(c_List_Odrop(U_19286),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19286)),U_19287)),U_19289)
        | U_19287 != hAPP(hAPP(c_List_Otake(U_19286),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19286)),U_19287)),U_19289) )
      & ( ( U_19288 = hAPP(hAPP(c_List_Odrop(U_19286),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19286)),U_19287)),U_19289)
          & U_19287 = hAPP(hAPP(c_List_Otake(U_19286),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19286)),U_19287)),U_19289) )
        | hAPP(hAPP(c_List_Oappend(U_19286),U_19287),U_19288) != U_19289 ) ),
    inference(variable_rename,[status(thm)],[f_4621_1]) ).

fof(f_4621_3,plain,
    ( ! [U_19297,U_19295,U_19293,U_19291] :
        ( hAPP(hAPP(c_List_Oappend(U_19291),U_19293),U_19295) = U_19297
        | U_19295 != hAPP(hAPP(c_List_Odrop(U_19291),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19291)),U_19293)),U_19297)
        | U_19293 != hAPP(hAPP(c_List_Otake(U_19291),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19291)),U_19293)),U_19297) )
    & ! [U_19296,U_19294,U_19292,U_19290] :
        ( ( U_19294 = hAPP(hAPP(c_List_Odrop(U_19290),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19290)),U_19292)),U_19296)
          & U_19292 = hAPP(hAPP(c_List_Otake(U_19290),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19290)),U_19292)),U_19296) )
        | hAPP(hAPP(c_List_Oappend(U_19290),U_19292),U_19294) != U_19296 ) ),
    inference(miniscope,[status(thm)],[f_4621_2]) ).

fof(f_4621_4,plain,
    ( ! [U_19296,U_19292,U_19290,U_19294] :
        ( U_19294 = hAPP(hAPP(c_List_Odrop(U_19290),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19290)),U_19292)),U_19296)
        | ~ sP1183(U_19296,U_19292,U_19290,U_19294) )
    & ! [U_19296,U_19292,U_19290,U_19294] :
        ( U_19292 = hAPP(hAPP(c_List_Otake(U_19290),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19290)),U_19292)),U_19296)
        | ~ sP1183(U_19296,U_19292,U_19290,U_19294) )
    & ! [U_19295,U_19291,U_19297,U_19293] :
        ( hAPP(hAPP(c_List_Oappend(U_19291),U_19293),U_19295) = U_19297
        | U_19295 != hAPP(hAPP(c_List_Odrop(U_19291),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19291)),U_19293)),U_19297)
        | U_19293 != hAPP(hAPP(c_List_Otake(U_19291),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19291)),U_19293)),U_19297) )
    & ! [U_19296,U_19292,U_19290,U_19294] :
        ( sP1183(U_19296,U_19292,U_19290,U_19294)
        | hAPP(hAPP(c_List_Oappend(U_19290),U_19292),U_19294) != U_19296 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1183])],[f_4621_3]) ).

cnf(f_4621_5,plain,
    ( sP1183(U_19296,U_19292,U_19290,U_19294)
    | hAPP(hAPP(c_List_Oappend(U_19290),U_19292),U_19294) != U_19296 ),
    inference(clausify,[status(thm)],[f_4621_4]) ).

cnf(f_4621_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19291),U_19293),U_19295) = U_19297
    | U_19295 != hAPP(hAPP(c_List_Odrop(U_19291),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19291)),U_19293)),U_19297)
    | U_19293 != hAPP(hAPP(c_List_Otake(U_19291),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19291)),U_19293)),U_19297) ),
    inference(clausify,[status(thm)],[f_4621_4]) ).

cnf(f_4621_7,plain,
    ( U_19292 = hAPP(hAPP(c_List_Otake(U_19290),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19290)),U_19292)),U_19296)
    | ~ sP1183(U_19296,U_19292,U_19290,U_19294) ),
    inference(clausify,[status(thm)],[f_4621_4]) ).

cnf(f_4621_8,plain,
    ( U_19294 = hAPP(hAPP(c_List_Odrop(U_19290),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19290)),U_19292)),U_19296)
    | ~ sP1183(U_19296,U_19292,U_19290,U_19294) ),
    inference(clausify,[status(thm)],[f_4621_4]) ).

fof(f_4622_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_4622_2,plain,
    ! [U_19301,U_19300,U_19299,U_19298] : hAPP(hAPP(c_List_Odrop(U_19298),U_19299),hAPP(hAPP(c_List_Olist_OCons(U_19298),U_19300),U_19301)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_19298),hAPP(hAPP(c_List_Olist_OCons(U_19298),U_19300),U_19301),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_19298),tc_List_Olist(U_19298)),c_List_Odrop(U_19298)),U_19301),U_19299),
    inference(variable_rename,[status(thm)],[f_4622_1]) ).

fof(f_4622_3,plain,
    ! [U_19298,U_19299,U_19301,U_19300] : hAPP(hAPP(c_List_Odrop(U_19298),U_19299),hAPP(hAPP(c_List_Olist_OCons(U_19298),U_19300),U_19301)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_19298),hAPP(hAPP(c_List_Olist_OCons(U_19298),U_19300),U_19301),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_19298),tc_List_Olist(U_19298)),c_List_Odrop(U_19298)),U_19301),U_19299),
    inference(definitional_conversion,[status(esa)],[f_4622_2]) ).

cnf(f_4622_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19298),U_19299),hAPP(hAPP(c_List_Olist_OCons(U_19298),U_19300),U_19301)) = c_Nat_Onat_Onat__case(tc_List_Olist(U_19298),hAPP(hAPP(c_List_Olist_OCons(U_19298),U_19300),U_19301),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(U_19298),tc_List_Olist(U_19298)),c_List_Odrop(U_19298)),U_19301),U_19299),
    inference(clausify,[status(thm)],[f_4622_3]) ).

fof(f_4623_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_4623_2,plain,
    ! [U_19305,U_19304,U_19303,U_19302] :
      ( ( hAPP(hAPP(c_List_Odrop(U_19303),U_19302),hAPP(hAPP(c_List_Olist_OCons(U_19303),U_19304),U_19305)) = hAPP(hAPP(c_List_Odrop(U_19303),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19302),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19305)
        | U_19302 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Odrop(U_19303),U_19302),hAPP(hAPP(c_List_Olist_OCons(U_19303),U_19304),U_19305)) = hAPP(hAPP(c_List_Olist_OCons(U_19303),U_19304),U_19305)
        | U_19302 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4623_1]) ).

fof(f_4623_3,plain,
    ( ! [U_19313,U_19311,U_19309,U_19307] :
        ( hAPP(hAPP(c_List_Odrop(U_19309),U_19307),hAPP(hAPP(c_List_Olist_OCons(U_19309),U_19311),U_19313)) = hAPP(hAPP(c_List_Odrop(U_19309),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19307),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19313)
        | U_19307 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19312,U_19310,U_19308,U_19306] :
        ( hAPP(hAPP(c_List_Odrop(U_19308),U_19306),hAPP(hAPP(c_List_Olist_OCons(U_19308),U_19310),U_19312)) = hAPP(hAPP(c_List_Olist_OCons(U_19308),U_19310),U_19312)
        | U_19306 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4623_2]) ).

fof(f_4623_4,plain,
    ( ! [U_19307,U_19309,U_19311,U_19313] :
        ( hAPP(hAPP(c_List_Odrop(U_19309),U_19307),hAPP(hAPP(c_List_Olist_OCons(U_19309),U_19311),U_19313)) = hAPP(hAPP(c_List_Odrop(U_19309),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19307),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19313)
        | U_19307 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19308,U_19310,U_19312,U_19306] :
        ( hAPP(hAPP(c_List_Odrop(U_19308),U_19306),hAPP(hAPP(c_List_Olist_OCons(U_19308),U_19310),U_19312)) = hAPP(hAPP(c_List_Olist_OCons(U_19308),U_19310),U_19312)
        | U_19306 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_4623_3]) ).

cnf(f_4623_5,plain,
    ( hAPP(hAPP(c_List_Odrop(U_19308),U_19306),hAPP(hAPP(c_List_Olist_OCons(U_19308),U_19310),U_19312)) = hAPP(hAPP(c_List_Olist_OCons(U_19308),U_19310),U_19312)
    | U_19306 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4623_4]) ).

cnf(f_4623_6,plain,
    ( hAPP(hAPP(c_List_Odrop(U_19309),U_19307),hAPP(hAPP(c_List_Olist_OCons(U_19309),U_19311),U_19313)) = hAPP(hAPP(c_List_Odrop(U_19309),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19307),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19313)
    | U_19307 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4623_4]) ).

fof(f_4624_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_4624_2,plain,
    ! [U_19317,U_19316,U_19315,U_19314] :
      ( hAPP(hAPP(c_List_Onth(U_19316),hAPP(hAPP(c_List_Odrop(U_19316),U_19314),U_19317)),U_19315) = hAPP(hAPP(c_List_Onth(U_19316),U_19317),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19314),U_19315))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19314),U_19315)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19316)),U_19317))) ),
    inference(variable_rename,[status(thm)],[f_4624_1]) ).

fof(f_4624_3,plain,
    ! [U_19314,U_19315,U_19316,U_19317] :
      ( hAPP(hAPP(c_List_Onth(U_19316),hAPP(hAPP(c_List_Odrop(U_19316),U_19314),U_19317)),U_19315) = hAPP(hAPP(c_List_Onth(U_19316),U_19317),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19314),U_19315))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19314),U_19315)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19316)),U_19317))) ),
    inference(definitional_conversion,[status(esa)],[f_4624_2]) ).

cnf(f_4624_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_19316),hAPP(hAPP(c_List_Odrop(U_19316),U_19314),U_19317)),U_19315) = hAPP(hAPP(c_List_Onth(U_19316),U_19317),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19314),U_19315))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19314),U_19315)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19316)),U_19317))) ),
    inference(clausify,[status(thm)],[f_4624_3]) ).

fof(f_4625_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_4625_2,plain,
    ! [U_19322,U_19321,U_19320,U_19319,U_19318] :
      ( ( hAPP(hAPP(c_List_Oappend(U_19318),U_19319),U_19320) = hAPP(hAPP(c_List_Oappend(U_19318),U_19321),U_19322)
        | ( ( hAPP(hAPP(c_List_Oappend(U_19318),hAPP(hAPP(c_List_Odrop(U_19318),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19318)),U_19321)),U_19319)),U_19320) != U_19322
            | hAPP(hAPP(c_List_Otake(U_19318),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19318)),U_19321)),U_19319) != U_19321 )
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19318)),U_19319)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19318)),U_19321))) )
        | ( ( U_19320 != hAPP(hAPP(c_List_Oappend(U_19318),hAPP(hAPP(c_List_Odrop(U_19318),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19318)),U_19319)),U_19321)),U_19322)
            | U_19319 != hAPP(hAPP(c_List_Otake(U_19318),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19318)),U_19319)),U_19321) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19318)),U_19319)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19318)),U_19321))) ) )
      & ( ( ( ( hAPP(hAPP(c_List_Oappend(U_19318),hAPP(hAPP(c_List_Odrop(U_19318),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19318)),U_19321)),U_19319)),U_19320) = U_19322
              & hAPP(hAPP(c_List_Otake(U_19318),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19318)),U_19321)),U_19319) = U_19321 )
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19318)),U_19319)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19318)),U_19321))) )
          & ( ( U_19320 = hAPP(hAPP(c_List_Oappend(U_19318),hAPP(hAPP(c_List_Odrop(U_19318),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19318)),U_19319)),U_19321)),U_19322)
              & U_19319 = hAPP(hAPP(c_List_Otake(U_19318),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19318)),U_19319)),U_19321) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19318)),U_19319)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19318)),U_19321))) ) )
        | hAPP(hAPP(c_List_Oappend(U_19318),U_19319),U_19320) != hAPP(hAPP(c_List_Oappend(U_19318),U_19321),U_19322) ) ),
    inference(variable_rename,[status(thm)],[f_4625_1]) ).

fof(f_4625_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)
        | ( ( hAPP(hAPP(c_List_Oappend(U_19324),hAPP(hAPP(c_List_Odrop(U_19324),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19330)),U_19326)),U_19328) != U_19332
            | hAPP(hAPP(c_List_Otake(U_19324),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19330)),U_19326) != U_19330 )
          & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19326)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19330))) )
        | ( ( U_19328 != hAPP(hAPP(c_List_Oappend(U_19324),hAPP(hAPP(c_List_Odrop(U_19324),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19326)),U_19330)),U_19332)
            | U_19326 != hAPP(hAPP(c_List_Otake(U_19324),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19326)),U_19330) )
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19326)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19330))) ) )
    & ! [U_19331,U_19329,U_19327,U_19325,U_19323] :
        ( ( ( ( hAPP(hAPP(c_List_Oappend(U_19323),hAPP(hAPP(c_List_Odrop(U_19323),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19329)),U_19325)),U_19327) = U_19331
              & hAPP(hAPP(c_List_Otake(U_19323),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19329)),U_19325) = U_19329 )
            | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19325)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19329))) )
          & ( ( U_19327 = hAPP(hAPP(c_List_Oappend(U_19323),hAPP(hAPP(c_List_Odrop(U_19323),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19325)),U_19329)),U_19331)
              & U_19325 = hAPP(hAPP(c_List_Otake(U_19323),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19325)),U_19329) )
            | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19325)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(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(miniscope,[status(thm)],[f_4625_2]) ).

fof(f_4625_4,plain,
    ( ! [U_19324,U_19330,U_19328,U_19326,U_19332] :
        ( hAPP(hAPP(c_List_Oappend(U_19324),hAPP(hAPP(c_List_Odrop(U_19324),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19330)),U_19326)),U_19328) != U_19332
        | hAPP(hAPP(c_List_Otake(U_19324),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19330)),U_19326) != U_19330
        | ~ sP1188(U_19324,U_19330,U_19328,U_19326,U_19332) )
    & ! [U_19324,U_19330,U_19328,U_19326,U_19332] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19326)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19330)))
        | ~ sP1188(U_19324,U_19330,U_19328,U_19326,U_19332) )
    & ! [U_19324,U_19330,U_19328,U_19326,U_19332] :
        ( U_19328 != hAPP(hAPP(c_List_Oappend(U_19324),hAPP(hAPP(c_List_Odrop(U_19324),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19326)),U_19330)),U_19332)
        | U_19326 != hAPP(hAPP(c_List_Otake(U_19324),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19326)),U_19330)
        | ~ sP1187(U_19324,U_19330,U_19328,U_19326,U_19332) )
    & ! [U_19324,U_19330,U_19328,U_19326,U_19332] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19326)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19330)))
        | ~ sP1187(U_19324,U_19330,U_19328,U_19326,U_19332) )
    & ! [U_19325,U_19323,U_19329,U_19327,U_19331] :
        ( hAPP(hAPP(c_List_Oappend(U_19323),hAPP(hAPP(c_List_Odrop(U_19323),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19329)),U_19325)),U_19327) = U_19331
        | ~ sP1185(U_19325,U_19323,U_19329,U_19327,U_19331) )
    & ! [U_19325,U_19323,U_19329,U_19327,U_19331] :
        ( hAPP(hAPP(c_List_Otake(U_19323),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19329)),U_19325) = U_19329
        | ~ sP1185(U_19325,U_19323,U_19329,U_19327,U_19331) )
    & ! [U_19325,U_19323,U_19329,U_19327,U_19331] :
        ( U_19327 = hAPP(hAPP(c_List_Oappend(U_19323),hAPP(hAPP(c_List_Odrop(U_19323),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19325)),U_19329)),U_19331)
        | ~ sP1184(U_19325,U_19323,U_19329,U_19327,U_19331) )
    & ! [U_19325,U_19323,U_19329,U_19327,U_19331] :
        ( U_19325 = hAPP(hAPP(c_List_Otake(U_19323),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19325)),U_19329)
        | ~ sP1184(U_19325,U_19323,U_19329,U_19327,U_19331) )
    & ! [U_19325,U_19323,U_19329,U_19327,U_19331] :
        ( sP1185(U_19325,U_19323,U_19329,U_19327,U_19331)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19325)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19329)))
        | ~ sP1186(U_19325,U_19323,U_19329,U_19327,U_19331) )
    & ! [U_19325,U_19323,U_19329,U_19327,U_19331] :
        ( sP1184(U_19325,U_19323,U_19329,U_19327,U_19331)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19325)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19329)))
        | ~ sP1186(U_19325,U_19323,U_19329,U_19327,U_19331) )
    & ! [U_19324,U_19330,U_19328,U_19326,U_19332] :
        ( hAPP(hAPP(c_List_Oappend(U_19324),U_19326),U_19328) = hAPP(hAPP(c_List_Oappend(U_19324),U_19330),U_19332)
        | sP1188(U_19324,U_19330,U_19328,U_19326,U_19332)
        | sP1187(U_19324,U_19330,U_19328,U_19326,U_19332) )
    & ! [U_19325,U_19323,U_19329,U_19327,U_19331] :
        ( sP1186(U_19325,U_19323,U_19329,U_19327,U_19331)
        | 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,[sP1184,sP1185,sP1186,sP1187,sP1188])],[f_4625_3]) ).

cnf(f_4625_5,plain,
    ( sP1186(U_19325,U_19323,U_19329,U_19327,U_19331)
    | 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_4625_4]) ).

cnf(f_4625_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19324),U_19326),U_19328) = hAPP(hAPP(c_List_Oappend(U_19324),U_19330),U_19332)
    | sP1188(U_19324,U_19330,U_19328,U_19326,U_19332)
    | sP1187(U_19324,U_19330,U_19328,U_19326,U_19332) ),
    inference(clausify,[status(thm)],[f_4625_4]) ).

cnf(f_4625_7,plain,
    ( sP1184(U_19325,U_19323,U_19329,U_19327,U_19331)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19325)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19329)))
    | ~ sP1186(U_19325,U_19323,U_19329,U_19327,U_19331) ),
    inference(clausify,[status(thm)],[f_4625_4]) ).

cnf(f_4625_8,plain,
    ( sP1185(U_19325,U_19323,U_19329,U_19327,U_19331)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19325)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19329)))
    | ~ sP1186(U_19325,U_19323,U_19329,U_19327,U_19331) ),
    inference(clausify,[status(thm)],[f_4625_4]) ).

cnf(f_4625_9,plain,
    ( U_19325 = hAPP(hAPP(c_List_Otake(U_19323),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19325)),U_19329)
    | ~ sP1184(U_19325,U_19323,U_19329,U_19327,U_19331) ),
    inference(clausify,[status(thm)],[f_4625_4]) ).

cnf(f_4625_10,plain,
    ( U_19327 = hAPP(hAPP(c_List_Oappend(U_19323),hAPP(hAPP(c_List_Odrop(U_19323),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19325)),U_19329)),U_19331)
    | ~ sP1184(U_19325,U_19323,U_19329,U_19327,U_19331) ),
    inference(clausify,[status(thm)],[f_4625_4]) ).

cnf(f_4625_11,plain,
    ( hAPP(hAPP(c_List_Otake(U_19323),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19329)),U_19325) = U_19329
    | ~ sP1185(U_19325,U_19323,U_19329,U_19327,U_19331) ),
    inference(clausify,[status(thm)],[f_4625_4]) ).

cnf(f_4625_12,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19323),hAPP(hAPP(c_List_Odrop(U_19323),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19323)),U_19329)),U_19325)),U_19327) = U_19331
    | ~ sP1185(U_19325,U_19323,U_19329,U_19327,U_19331) ),
    inference(clausify,[status(thm)],[f_4625_4]) ).

cnf(f_4625_13,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19326)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19330)))
    | ~ sP1187(U_19324,U_19330,U_19328,U_19326,U_19332) ),
    inference(clausify,[status(thm)],[f_4625_4]) ).

cnf(f_4625_14,plain,
    ( U_19328 != hAPP(hAPP(c_List_Oappend(U_19324),hAPP(hAPP(c_List_Odrop(U_19324),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19326)),U_19330)),U_19332)
    | U_19326 != hAPP(hAPP(c_List_Otake(U_19324),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19326)),U_19330)
    | ~ sP1187(U_19324,U_19330,U_19328,U_19326,U_19332) ),
    inference(clausify,[status(thm)],[f_4625_4]) ).

cnf(f_4625_15,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19326)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19330)))
    | ~ sP1188(U_19324,U_19330,U_19328,U_19326,U_19332) ),
    inference(clausify,[status(thm)],[f_4625_4]) ).

cnf(f_4625_16,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19324),hAPP(hAPP(c_List_Odrop(U_19324),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19330)),U_19326)),U_19328) != U_19332
    | hAPP(hAPP(c_List_Otake(U_19324),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19324)),U_19330)),U_19326) != U_19330
    | ~ sP1188(U_19324,U_19330,U_19328,U_19326,U_19332) ),
    inference(clausify,[status(thm)],[f_4625_4]) ).

fof(f_4626_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_4626_2,plain,
    ! [U_19335,U_19334,U_19333] :
      ( hAPP(hAPP(c_List_Olist_OCons(U_19334),hAPP(hAPP(c_List_Onth(U_19334),U_19335),U_19333)),hAPP(hAPP(c_List_Odrop(U_19334),hAPP(c_Nat_OSuc,U_19333)),U_19335)) = hAPP(hAPP(c_List_Odrop(U_19334),U_19333),U_19335)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19333),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19334)),U_19335))) ),
    inference(variable_rename,[status(thm)],[f_4626_1]) ).

fof(f_4626_3,plain,
    ! [U_19333,U_19334,U_19335] :
      ( hAPP(hAPP(c_List_Olist_OCons(U_19334),hAPP(hAPP(c_List_Onth(U_19334),U_19335),U_19333)),hAPP(hAPP(c_List_Odrop(U_19334),hAPP(c_Nat_OSuc,U_19333)),U_19335)) = hAPP(hAPP(c_List_Odrop(U_19334),U_19333),U_19335)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19333),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19334)),U_19335))) ),
    inference(definitional_conversion,[status(esa)],[f_4626_2]) ).

cnf(f_4626_4,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_19334),hAPP(hAPP(c_List_Onth(U_19334),U_19335),U_19333)),hAPP(hAPP(c_List_Odrop(U_19334),hAPP(c_Nat_OSuc,U_19333)),U_19335)) = hAPP(hAPP(c_List_Odrop(U_19334),U_19333),U_19335)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19333),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19334)),U_19335))) ),
    inference(clausify,[status(thm)],[f_4626_3]) ).

fof(f_4627_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_4627_2,plain,
    ! [U_19339,U_19338,U_19337,U_19336] :
      ( hAPP(c_List_Orotate1(U_19337),hAPP(hAPP(c_List_Olist_OCons(U_19337),U_19338),U_19339)) = hAPP(hAPP(c_List_Oappend(U_19337),U_19339),hAPP(hAPP(c_List_Olist_OCons(U_19337),U_19338),c_List_Olist_ONil(U_19337)))
      & hAPP(c_List_Orotate1(U_19336),c_List_Olist_ONil(U_19336)) = c_List_Olist_ONil(U_19336) ),
    inference(variable_rename,[status(thm)],[f_4627_1]) ).

fof(f_4627_3,plain,
    ( ! [U_19339,U_19338,U_19337] : hAPP(c_List_Orotate1(U_19337),hAPP(hAPP(c_List_Olist_OCons(U_19337),U_19338),U_19339)) = hAPP(hAPP(c_List_Oappend(U_19337),U_19339),hAPP(hAPP(c_List_Olist_OCons(U_19337),U_19338),c_List_Olist_ONil(U_19337)))
    & ! [U_19336] : hAPP(c_List_Orotate1(U_19336),c_List_Olist_ONil(U_19336)) = c_List_Olist_ONil(U_19336) ),
    inference(miniscope,[status(thm)],[f_4627_2]) ).

fof(f_4627_4,plain,
    ( ! [U_19337,U_19338,U_19339] : hAPP(c_List_Orotate1(U_19337),hAPP(hAPP(c_List_Olist_OCons(U_19337),U_19338),U_19339)) = hAPP(hAPP(c_List_Oappend(U_19337),U_19339),hAPP(hAPP(c_List_Olist_OCons(U_19337),U_19338),c_List_Olist_ONil(U_19337)))
    & ! [U_19336] : hAPP(c_List_Orotate1(U_19336),c_List_Olist_ONil(U_19336)) = c_List_Olist_ONil(U_19336) ),
    inference(definitional_conversion,[status(esa)],[f_4627_3]) ).

cnf(f_4627_5,plain,
    hAPP(c_List_Orotate1(U_19336),c_List_Olist_ONil(U_19336)) = c_List_Olist_ONil(U_19336),
    inference(clausify,[status(thm)],[f_4627_4]) ).

cnf(f_4627_6,plain,
    hAPP(c_List_Orotate1(U_19337),hAPP(hAPP(c_List_Olist_OCons(U_19337),U_19338),U_19339)) = hAPP(hAPP(c_List_Oappend(U_19337),U_19339),hAPP(hAPP(c_List_Olist_OCons(U_19337),U_19338),c_List_Olist_ONil(U_19337))),
    inference(clausify,[status(thm)],[f_4627_4]) ).

fof(f_4628_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_4628_2,plain,
    ! [U_19343,U_19342,U_19341,U_19340] :
      ( ( hAPP(hAPP(c_List_Odrop(U_19341),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19340)),hAPP(hAPP(c_List_Olist_OCons(U_19341),U_19342),U_19343)) = hAPP(hAPP(c_List_Odrop(U_19341),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19340)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19343)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19340) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( hAPP(hAPP(c_List_Odrop(U_19341),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19340)),hAPP(hAPP(c_List_Olist_OCons(U_19341),U_19342),U_19343)) = hAPP(hAPP(c_List_Olist_OCons(U_19341),U_19342),U_19343)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19340) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4628_1]) ).

fof(f_4628_3,plain,
    ( ! [U_19351,U_19349,U_19347,U_19345] :
        ( hAPP(hAPP(c_List_Odrop(U_19347),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19345)),hAPP(hAPP(c_List_Olist_OCons(U_19347),U_19349),U_19351)) = hAPP(hAPP(c_List_Odrop(U_19347),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19345)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19351)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19345) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19350,U_19348,U_19346,U_19344] :
        ( hAPP(hAPP(c_List_Odrop(U_19346),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19344)),hAPP(hAPP(c_List_Olist_OCons(U_19346),U_19348),U_19350)) = hAPP(hAPP(c_List_Olist_OCons(U_19346),U_19348),U_19350)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19344) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4628_2]) ).

fof(f_4628_4,plain,
    ( ! [U_19347,U_19345,U_19349,U_19351] :
        ( hAPP(hAPP(c_List_Odrop(U_19347),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19345)),hAPP(hAPP(c_List_Olist_OCons(U_19347),U_19349),U_19351)) = hAPP(hAPP(c_List_Odrop(U_19347),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19345)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19351)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19345) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19346,U_19350,U_19344,U_19348] :
        ( hAPP(hAPP(c_List_Odrop(U_19346),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19344)),hAPP(hAPP(c_List_Olist_OCons(U_19346),U_19348),U_19350)) = hAPP(hAPP(c_List_Olist_OCons(U_19346),U_19348),U_19350)
        | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19344) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa)],[f_4628_3]) ).

cnf(f_4628_5,plain,
    ( hAPP(hAPP(c_List_Odrop(U_19346),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19344)),hAPP(hAPP(c_List_Olist_OCons(U_19346),U_19348),U_19350)) = hAPP(hAPP(c_List_Olist_OCons(U_19346),U_19348),U_19350)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19344) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4628_4]) ).

cnf(f_4628_6,plain,
    ( hAPP(hAPP(c_List_Odrop(U_19347),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19345)),hAPP(hAPP(c_List_Olist_OCons(U_19347),U_19349),U_19351)) = hAPP(hAPP(c_List_Odrop(U_19347),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19345)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19351)
    | hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_19345) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4628_4]) ).

fof(f_4629_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_4629_2,plain,
    ! [U_19355,U_19354,U_19353,U_19352] :
      ( hAPP(hAPP(c_List_Otake(U_19354),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19352),U_19353)),U_19355) = hAPP(hAPP(c_List_Oappend(U_19354),hAPP(hAPP(c_List_Otake(U_19354),U_19352),U_19355)),hAPP(hAPP(c_List_Otake(U_19354),U_19353),hAPP(hAPP(c_List_Odrop(U_19354),U_19352),U_19355)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19352),U_19353)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19354)),U_19355))) ),
    inference(variable_rename,[status(thm)],[f_4629_1]) ).

fof(f_4629_3,plain,
    ! [U_19352,U_19353,U_19354,U_19355] :
      ( hAPP(hAPP(c_List_Otake(U_19354),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19352),U_19353)),U_19355) = hAPP(hAPP(c_List_Oappend(U_19354),hAPP(hAPP(c_List_Otake(U_19354),U_19352),U_19355)),hAPP(hAPP(c_List_Otake(U_19354),U_19353),hAPP(hAPP(c_List_Odrop(U_19354),U_19352),U_19355)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19352),U_19353)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19354)),U_19355))) ),
    inference(definitional_conversion,[status(esa)],[f_4629_2]) ).

cnf(f_4629_4,plain,
    ( hAPP(hAPP(c_List_Otake(U_19354),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19352),U_19353)),U_19355) = hAPP(hAPP(c_List_Oappend(U_19354),hAPP(hAPP(c_List_Otake(U_19354),U_19352),U_19355)),hAPP(hAPP(c_List_Otake(U_19354),U_19353),hAPP(hAPP(c_List_Odrop(U_19354),U_19352),U_19355)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19352),U_19353)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19354)),U_19355))) ),
    inference(clausify,[status(thm)],[f_4629_3]) ).

fof(f_4630_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_4630_2,plain,
    ! [U_19357,U_19356] :
      ( hAPP(c_List_Orotate1(U_19356),U_19357) = U_19357
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19356)),U_19357)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[f_4630_1]) ).

fof(f_4630_3,plain,
    ! [U_19356,U_19357] :
      ( hAPP(c_List_Orotate1(U_19356),U_19357) = U_19357
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19356)),U_19357)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(definitional_conversion,[status(esa)],[f_4630_2]) ).

cnf(f_4630_4,plain,
    ( hAPP(c_List_Orotate1(U_19356),U_19357) = U_19357
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19356)),U_19357)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_4630_3]) ).

fof(f_4631_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_4631_2,plain,
    ! [U_19362,U_19361,U_19360,U_19359,U_19358] : hAPP(hAPP(c_List_Ozip(U_19358,U_19359),hAPP(hAPP(c_List_Oappend(U_19358),U_19360),U_19361)),U_19362) = hAPP(hAPP(c_List_Oappend(tc_prod(U_19358,U_19359)),hAPP(hAPP(c_List_Ozip(U_19358,U_19359),U_19360),hAPP(hAPP(c_List_Otake(U_19359),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19358)),U_19360)),U_19362))),hAPP(hAPP(c_List_Ozip(U_19358,U_19359),U_19361),hAPP(hAPP(c_List_Odrop(U_19359),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19358)),U_19360)),U_19362))),
    inference(variable_rename,[status(thm)],[f_4631_1]) ).

fof(f_4631_3,plain,
    ! [U_19358,U_19359,U_19360,U_19361,U_19362] : hAPP(hAPP(c_List_Ozip(U_19358,U_19359),hAPP(hAPP(c_List_Oappend(U_19358),U_19360),U_19361)),U_19362) = hAPP(hAPP(c_List_Oappend(tc_prod(U_19358,U_19359)),hAPP(hAPP(c_List_Ozip(U_19358,U_19359),U_19360),hAPP(hAPP(c_List_Otake(U_19359),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19358)),U_19360)),U_19362))),hAPP(hAPP(c_List_Ozip(U_19358,U_19359),U_19361),hAPP(hAPP(c_List_Odrop(U_19359),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19358)),U_19360)),U_19362))),
    inference(definitional_conversion,[status(esa)],[f_4631_2]) ).

cnf(f_4631_4,plain,
    hAPP(hAPP(c_List_Ozip(U_19358,U_19359),hAPP(hAPP(c_List_Oappend(U_19358),U_19360),U_19361)),U_19362) = hAPP(hAPP(c_List_Oappend(tc_prod(U_19358,U_19359)),hAPP(hAPP(c_List_Ozip(U_19358,U_19359),U_19360),hAPP(hAPP(c_List_Otake(U_19359),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19358)),U_19360)),U_19362))),hAPP(hAPP(c_List_Ozip(U_19358,U_19359),U_19361),hAPP(hAPP(c_List_Odrop(U_19359),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19358)),U_19360)),U_19362))),
    inference(clausify,[status(thm)],[f_4631_3]) ).

fof(f_4632_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_4632_2,plain,
    ! [U_19367,U_19366,U_19365,U_19364,U_19363] : hAPP(hAPP(c_List_Ozip(U_19363,U_19364),U_19365),hAPP(hAPP(c_List_Oappend(U_19364),U_19366),U_19367)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_19363,U_19364)),hAPP(hAPP(c_List_Ozip(U_19363,U_19364),hAPP(hAPP(c_List_Otake(U_19363),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19364)),U_19366)),U_19365)),U_19366)),hAPP(hAPP(c_List_Ozip(U_19363,U_19364),hAPP(hAPP(c_List_Odrop(U_19363),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19364)),U_19366)),U_19365)),U_19367)),
    inference(variable_rename,[status(thm)],[f_4632_1]) ).

fof(f_4632_3,plain,
    ! [U_19363,U_19364,U_19365,U_19366,U_19367] : hAPP(hAPP(c_List_Ozip(U_19363,U_19364),U_19365),hAPP(hAPP(c_List_Oappend(U_19364),U_19366),U_19367)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_19363,U_19364)),hAPP(hAPP(c_List_Ozip(U_19363,U_19364),hAPP(hAPP(c_List_Otake(U_19363),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19364)),U_19366)),U_19365)),U_19366)),hAPP(hAPP(c_List_Ozip(U_19363,U_19364),hAPP(hAPP(c_List_Odrop(U_19363),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19364)),U_19366)),U_19365)),U_19367)),
    inference(definitional_conversion,[status(esa)],[f_4632_2]) ).

cnf(f_4632_4,plain,
    hAPP(hAPP(c_List_Ozip(U_19363,U_19364),U_19365),hAPP(hAPP(c_List_Oappend(U_19364),U_19366),U_19367)) = hAPP(hAPP(c_List_Oappend(tc_prod(U_19363,U_19364)),hAPP(hAPP(c_List_Ozip(U_19363,U_19364),hAPP(hAPP(c_List_Otake(U_19363),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19364)),U_19366)),U_19365)),U_19366)),hAPP(hAPP(c_List_Ozip(U_19363,U_19364),hAPP(hAPP(c_List_Odrop(U_19363),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19364)),U_19366)),U_19365)),U_19367)),
    inference(clausify,[status(thm)],[f_4632_3]) ).

fof(f_4633_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_4633_2,plain,
    ! [U_19370,U_19369,U_19368] :
      ( U_19370 = hAPP(hAPP(c_List_Oappend(U_19369),hAPP(hAPP(c_List_Otake(U_19369),U_19368),U_19370)),hAPP(hAPP(c_List_Olist_OCons(U_19369),hAPP(hAPP(c_List_Onth(U_19369),U_19370),U_19368)),hAPP(hAPP(c_List_Odrop(U_19369),hAPP(c_Nat_OSuc,U_19368)),U_19370)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19368),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19369)),U_19370))) ),
    inference(variable_rename,[status(thm)],[f_4633_1]) ).

fof(f_4633_3,plain,
    ! [U_19368,U_19369,U_19370] :
      ( U_19370 = hAPP(hAPP(c_List_Oappend(U_19369),hAPP(hAPP(c_List_Otake(U_19369),U_19368),U_19370)),hAPP(hAPP(c_List_Olist_OCons(U_19369),hAPP(hAPP(c_List_Onth(U_19369),U_19370),U_19368)),hAPP(hAPP(c_List_Odrop(U_19369),hAPP(c_Nat_OSuc,U_19368)),U_19370)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19368),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19369)),U_19370))) ),
    inference(definitional_conversion,[status(esa)],[f_4633_2]) ).

cnf(f_4633_4,plain,
    ( U_19370 = hAPP(hAPP(c_List_Oappend(U_19369),hAPP(hAPP(c_List_Otake(U_19369),U_19368),U_19370)),hAPP(hAPP(c_List_Olist_OCons(U_19369),hAPP(hAPP(c_List_Onth(U_19369),U_19370),U_19368)),hAPP(hAPP(c_List_Odrop(U_19369),hAPP(c_Nat_OSuc,U_19368)),U_19370)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19368),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19369)),U_19370))) ),
    inference(clausify,[status(thm)],[f_4633_3]) ).

fof(f_4634_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_4634_2,plain,
    ! [U_19373,U_19372,U_19371] :
      ( hAPP(hAPP(c_List_Oappend(U_19372),hAPP(hAPP(c_List_Otake(U_19372),U_19371),U_19373)),hAPP(hAPP(c_List_Olist_OCons(U_19372),hAPP(c_List_Ohd(U_19372),hAPP(hAPP(c_List_Odrop(U_19372),U_19371),U_19373))),c_List_Olist_ONil(U_19372))) = hAPP(hAPP(c_List_Otake(U_19372),hAPP(c_Nat_OSuc,U_19371)),U_19373)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19371),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19372)),U_19373))) ),
    inference(variable_rename,[status(thm)],[f_4634_1]) ).

fof(f_4634_3,plain,
    ! [U_19371,U_19372,U_19373] :
      ( hAPP(hAPP(c_List_Oappend(U_19372),hAPP(hAPP(c_List_Otake(U_19372),U_19371),U_19373)),hAPP(hAPP(c_List_Olist_OCons(U_19372),hAPP(c_List_Ohd(U_19372),hAPP(hAPP(c_List_Odrop(U_19372),U_19371),U_19373))),c_List_Olist_ONil(U_19372))) = hAPP(hAPP(c_List_Otake(U_19372),hAPP(c_Nat_OSuc,U_19371)),U_19373)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19371),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19372)),U_19373))) ),
    inference(definitional_conversion,[status(esa)],[f_4634_2]) ).

cnf(f_4634_4,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19372),hAPP(hAPP(c_List_Otake(U_19372),U_19371),U_19373)),hAPP(hAPP(c_List_Olist_OCons(U_19372),hAPP(c_List_Ohd(U_19372),hAPP(hAPP(c_List_Odrop(U_19372),U_19371),U_19373))),c_List_Olist_ONil(U_19372))) = hAPP(hAPP(c_List_Otake(U_19372),hAPP(c_Nat_OSuc,U_19371)),U_19373)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19371),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19372)),U_19373))) ),
    inference(clausify,[status(thm)],[f_4634_3]) ).

fof(f_4635_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_4635_2,plain,
    ! [U_19376,U_19375,U_19374] :
      ( hAPP(c_List_Ohd(U_19375),hAPP(hAPP(c_List_Odrop(U_19375),U_19376),U_19374)) = hAPP(hAPP(c_List_Onth(U_19375),U_19374),U_19376)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19376),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19375)),U_19374)))
      | U_19374 = c_List_Olist_ONil(U_19375) ),
    inference(variable_rename,[status(thm)],[f_4635_1]) ).

fof(f_4635_3,plain,
    ! [U_19374,U_19375,U_19376] :
      ( hAPP(c_List_Ohd(U_19375),hAPP(hAPP(c_List_Odrop(U_19375),U_19376),U_19374)) = hAPP(hAPP(c_List_Onth(U_19375),U_19374),U_19376)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19376),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19375)),U_19374)))
      | U_19374 = c_List_Olist_ONil(U_19375) ),
    inference(definitional_conversion,[status(esa)],[f_4635_2]) ).

cnf(f_4635_4,plain,
    ( hAPP(c_List_Ohd(U_19375),hAPP(hAPP(c_List_Odrop(U_19375),U_19376),U_19374)) = hAPP(hAPP(c_List_Onth(U_19375),U_19374),U_19376)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19376),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19375)),U_19374)))
    | U_19374 = c_List_Olist_ONil(U_19375) ),
    inference(clausify,[status(thm)],[f_4635_3]) ).

fof(f_4636_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_4636_2,plain,
    ! [U_19379,U_19378,U_19377] :
      ( hAPP(c_List_Ohd(U_19378),hAPP(hAPP(c_List_Oappend(U_19378),U_19377),U_19379)) = hAPP(c_List_Ohd(U_19378),U_19377)
      | U_19377 = c_List_Olist_ONil(U_19378) ),
    inference(variable_rename,[status(thm)],[f_4636_1]) ).

fof(f_4636_3,plain,
    ! [U_19378,U_19377,U_19379] :
      ( hAPP(c_List_Ohd(U_19378),hAPP(hAPP(c_List_Oappend(U_19378),U_19377),U_19379)) = hAPP(c_List_Ohd(U_19378),U_19377)
      | U_19377 = c_List_Olist_ONil(U_19378) ),
    inference(definitional_conversion,[status(esa)],[f_4636_2]) ).

cnf(f_4636_4,plain,
    ( hAPP(c_List_Ohd(U_19378),hAPP(hAPP(c_List_Oappend(U_19378),U_19377),U_19379)) = hAPP(c_List_Ohd(U_19378),U_19377)
    | U_19377 = c_List_Olist_ONil(U_19378) ),
    inference(clausify,[status(thm)],[f_4636_3]) ).

fof(f_4637_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_4637_2,plain,
    ! [U_19382,U_19381,U_19380] :
      ( ( hAPP(c_List_Ohd(U_19381),hAPP(hAPP(c_List_Oappend(U_19381),U_19380),U_19382)) = hAPP(c_List_Ohd(U_19381),U_19380)
        | U_19380 = c_List_Olist_ONil(U_19381) )
      & ( hAPP(c_List_Ohd(U_19381),hAPP(hAPP(c_List_Oappend(U_19381),U_19380),U_19382)) = hAPP(c_List_Ohd(U_19381),U_19382)
        | U_19380 != c_List_Olist_ONil(U_19381) ) ),
    inference(variable_rename,[status(thm)],[f_4637_1]) ).

fof(f_4637_3,plain,
    ( ! [U_19388,U_19386,U_19384] :
        ( hAPP(c_List_Ohd(U_19386),hAPP(hAPP(c_List_Oappend(U_19386),U_19384),U_19388)) = hAPP(c_List_Ohd(U_19386),U_19384)
        | U_19384 = c_List_Olist_ONil(U_19386) )
    & ! [U_19387,U_19385,U_19383] :
        ( hAPP(c_List_Ohd(U_19385),hAPP(hAPP(c_List_Oappend(U_19385),U_19383),U_19387)) = hAPP(c_List_Ohd(U_19385),U_19387)
        | U_19383 != c_List_Olist_ONil(U_19385) ) ),
    inference(miniscope,[status(thm)],[f_4637_2]) ).

fof(f_4637_4,plain,
    ( ! [U_19384,U_19386,U_19388] :
        ( hAPP(c_List_Ohd(U_19386),hAPP(hAPP(c_List_Oappend(U_19386),U_19384),U_19388)) = hAPP(c_List_Ohd(U_19386),U_19384)
        | U_19384 = c_List_Olist_ONil(U_19386) )
    & ! [U_19387,U_19385,U_19383] :
        ( hAPP(c_List_Ohd(U_19385),hAPP(hAPP(c_List_Oappend(U_19385),U_19383),U_19387)) = hAPP(c_List_Ohd(U_19385),U_19387)
        | U_19383 != c_List_Olist_ONil(U_19385) ) ),
    inference(definitional_conversion,[status(esa)],[f_4637_3]) ).

cnf(f_4637_5,plain,
    ( hAPP(c_List_Ohd(U_19385),hAPP(hAPP(c_List_Oappend(U_19385),U_19383),U_19387)) = hAPP(c_List_Ohd(U_19385),U_19387)
    | U_19383 != c_List_Olist_ONil(U_19385) ),
    inference(clausify,[status(thm)],[f_4637_4]) ).

cnf(f_4637_6,plain,
    ( hAPP(c_List_Ohd(U_19386),hAPP(hAPP(c_List_Oappend(U_19386),U_19384),U_19388)) = hAPP(c_List_Ohd(U_19386),U_19384)
    | U_19384 = c_List_Olist_ONil(U_19386) ),
    inference(clausify,[status(thm)],[f_4637_4]) ).

fof(f_4638_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_4638_2,plain,
    ! [U_19391,U_19390,U_19389] : hAPP(c_List_Ohd(U_19389),hAPP(hAPP(c_List_Olist_OCons(U_19389),U_19390),U_19391)) = U_19390,
    inference(variable_rename,[status(thm)],[f_4638_1]) ).

fof(f_4638_3,plain,
    ! [U_19389,U_19390,U_19391] : hAPP(c_List_Ohd(U_19389),hAPP(hAPP(c_List_Olist_OCons(U_19389),U_19390),U_19391)) = U_19390,
    inference(definitional_conversion,[status(esa)],[f_4638_2]) ).

cnf(f_4638_4,plain,
    hAPP(c_List_Ohd(U_19389),hAPP(hAPP(c_List_Olist_OCons(U_19389),U_19390),U_19391)) = U_19390,
    inference(clausify,[status(thm)],[f_4638_3]) ).

fof(f_4639_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_4639_2,plain,
    ! [U_19395,U_19394,U_19393,U_19392] :
      ( hAPP(c_List_Ohd(U_19394),hAPP(hAPP(c_List_Omap(U_19393,U_19394),U_19395),U_19392)) = hAPP(U_19395,hAPP(c_List_Ohd(U_19393),U_19392))
      | U_19392 = c_List_Olist_ONil(U_19393) ),
    inference(variable_rename,[status(thm)],[f_4639_1]) ).

fof(f_4639_3,plain,
    ! [U_19392,U_19393,U_19394,U_19395] :
      ( hAPP(c_List_Ohd(U_19394),hAPP(hAPP(c_List_Omap(U_19393,U_19394),U_19395),U_19392)) = hAPP(U_19395,hAPP(c_List_Ohd(U_19393),U_19392))
      | U_19392 = c_List_Olist_ONil(U_19393) ),
    inference(definitional_conversion,[status(esa)],[f_4639_2]) ).

cnf(f_4639_4,plain,
    ( hAPP(c_List_Ohd(U_19394),hAPP(hAPP(c_List_Omap(U_19393,U_19394),U_19395),U_19392)) = hAPP(U_19395,hAPP(c_List_Ohd(U_19393),U_19392))
    | U_19392 = c_List_Olist_ONil(U_19393) ),
    inference(clausify,[status(thm)],[f_4639_3]) ).

fof(f_4640_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_4640_2,plain,
    ! [U_19397,U_19396] :
      ( hBOOL(hAPP(hAPP(c_member(U_19397),hAPP(c_List_Ohd(U_19397),U_19396)),hAPP(c_List_Oset(U_19397),U_19396)))
      | U_19396 = c_List_Olist_ONil(U_19397) ),
    inference(variable_rename,[status(thm)],[f_4640_1]) ).

fof(f_4640_3,plain,
    ! [U_19396,U_19397] :
      ( hBOOL(hAPP(hAPP(c_member(U_19397),hAPP(c_List_Ohd(U_19397),U_19396)),hAPP(c_List_Oset(U_19397),U_19396)))
      | U_19396 = c_List_Olist_ONil(U_19397) ),
    inference(definitional_conversion,[status(esa)],[f_4640_2]) ).

cnf(f_4640_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19397),hAPP(c_List_Ohd(U_19397),U_19396)),hAPP(c_List_Oset(U_19397),U_19396)))
    | U_19396 = c_List_Olist_ONil(U_19397) ),
    inference(clausify,[status(thm)],[f_4640_3]) ).

fof(f_4641_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_4641_2,plain,
    ! [U_19399,U_19398] :
      ( hAPP(c_List_Ohd(U_19399),U_19398) = hAPP(hAPP(c_List_Onth(U_19399),U_19398),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_19398 = c_List_Olist_ONil(U_19399) ),
    inference(variable_rename,[status(thm)],[f_4641_1]) ).

fof(f_4641_3,plain,
    ! [U_19398,U_19399] :
      ( hAPP(c_List_Ohd(U_19399),U_19398) = hAPP(hAPP(c_List_Onth(U_19399),U_19398),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
      | U_19398 = c_List_Olist_ONil(U_19399) ),
    inference(definitional_conversion,[status(esa)],[f_4641_2]) ).

cnf(f_4641_4,plain,
    ( hAPP(c_List_Ohd(U_19399),U_19398) = hAPP(hAPP(c_List_Onth(U_19399),U_19398),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))
    | U_19398 = c_List_Olist_ONil(U_19399) ),
    inference(clausify,[status(thm)],[f_4641_3]) ).

fof(f_4642_1,plain,
    ! [T_a,V_xs] :
      ( hAPP(c_List_Orotate1(T_a),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),c_List_Olist_ONil(T_a)))
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_rotate1__hd__tl]) ).

fof(f_4642_2,plain,
    ! [U_19401,U_19400] :
      ( hAPP(c_List_Orotate1(U_19401),U_19400) = hAPP(hAPP(c_List_Oappend(U_19401),hAPP(c_List_Otl(U_19401),U_19400)),hAPP(hAPP(c_List_Olist_OCons(U_19401),hAPP(c_List_Ohd(U_19401),U_19400)),c_List_Olist_ONil(U_19401)))
      | U_19400 = c_List_Olist_ONil(U_19401) ),
    inference(variable_rename,[status(thm)],[f_4642_1]) ).

fof(f_4642_3,plain,
    ! [U_19400,U_19401] :
      ( hAPP(c_List_Orotate1(U_19401),U_19400) = hAPP(hAPP(c_List_Oappend(U_19401),hAPP(c_List_Otl(U_19401),U_19400)),hAPP(hAPP(c_List_Olist_OCons(U_19401),hAPP(c_List_Ohd(U_19401),U_19400)),c_List_Olist_ONil(U_19401)))
      | U_19400 = c_List_Olist_ONil(U_19401) ),
    inference(definitional_conversion,[status(esa)],[f_4642_2]) ).

cnf(f_4642_4,plain,
    ( hAPP(c_List_Orotate1(U_19401),U_19400) = hAPP(hAPP(c_List_Oappend(U_19401),hAPP(c_List_Otl(U_19401),U_19400)),hAPP(hAPP(c_List_Olist_OCons(U_19401),hAPP(c_List_Ohd(U_19401),U_19400)),c_List_Olist_ONil(U_19401)))
    | U_19400 = c_List_Olist_ONil(U_19401) ),
    inference(clausify,[status(thm)],[f_4642_3]) ).

fof(f_4643_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_4643_2,plain,
    ! [U_19404,U_19403,U_19402] :
      ( hAPP(c_List_Ohd(U_19403),hAPP(c_List_Orotate(U_19403,U_19404),U_19402)) = hAPP(hAPP(c_List_Onth(U_19403),U_19402),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19404,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19403)),U_19402)))
      | U_19402 = c_List_Olist_ONil(U_19403) ),
    inference(variable_rename,[status(thm)],[f_4643_1]) ).

fof(f_4643_3,plain,
    ! [U_19402,U_19403,U_19404] :
      ( hAPP(c_List_Ohd(U_19403),hAPP(c_List_Orotate(U_19403,U_19404),U_19402)) = hAPP(hAPP(c_List_Onth(U_19403),U_19402),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19404,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19403)),U_19402)))
      | U_19402 = c_List_Olist_ONil(U_19403) ),
    inference(definitional_conversion,[status(esa)],[f_4643_2]) ).

cnf(f_4643_4,plain,
    ( hAPP(c_List_Ohd(U_19403),hAPP(c_List_Orotate(U_19403,U_19404),U_19402)) = hAPP(hAPP(c_List_Onth(U_19403),U_19402),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19404,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19403)),U_19402)))
    | U_19402 = c_List_Olist_ONil(U_19403) ),
    inference(clausify,[status(thm)],[f_4643_3]) ).

fof(f_4644_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_drop__Suc]) ).

fof(f_4644_2,plain,
    ! [U_19407,U_19406,U_19405] : hAPP(hAPP(c_List_Odrop(U_19405),hAPP(c_Nat_OSuc,U_19406)),U_19407) = hAPP(hAPP(c_List_Odrop(U_19405),U_19406),hAPP(c_List_Otl(U_19405),U_19407)),
    inference(variable_rename,[status(thm)],[f_4644_1]) ).

fof(f_4644_3,plain,
    ! [U_19405,U_19406,U_19407] : hAPP(hAPP(c_List_Odrop(U_19405),hAPP(c_Nat_OSuc,U_19406)),U_19407) = hAPP(hAPP(c_List_Odrop(U_19405),U_19406),hAPP(c_List_Otl(U_19405),U_19407)),
    inference(definitional_conversion,[status(esa)],[f_4644_2]) ).

cnf(f_4644_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19405),hAPP(c_Nat_OSuc,U_19406)),U_19407) = hAPP(hAPP(c_List_Odrop(U_19405),U_19406),hAPP(c_List_Otl(U_19405),U_19407)),
    inference(clausify,[status(thm)],[f_4644_3]) ).

fof(f_4645_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_drop__tl]) ).

fof(f_4645_2,plain,
    ! [U_19410,U_19409,U_19408] : hAPP(hAPP(c_List_Odrop(U_19408),U_19409),hAPP(c_List_Otl(U_19408),U_19410)) = hAPP(c_List_Otl(U_19408),hAPP(hAPP(c_List_Odrop(U_19408),U_19409),U_19410)),
    inference(variable_rename,[status(thm)],[f_4645_1]) ).

fof(f_4645_3,plain,
    ! [U_19408,U_19409,U_19410] : hAPP(hAPP(c_List_Odrop(U_19408),U_19409),hAPP(c_List_Otl(U_19408),U_19410)) = hAPP(c_List_Otl(U_19408),hAPP(hAPP(c_List_Odrop(U_19408),U_19409),U_19410)),
    inference(definitional_conversion,[status(esa)],[f_4645_2]) ).

cnf(f_4645_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19408),U_19409),hAPP(c_List_Otl(U_19408),U_19410)) = hAPP(c_List_Otl(U_19408),hAPP(hAPP(c_List_Odrop(U_19408),U_19409),U_19410)),
    inference(clausify,[status(thm)],[f_4645_3]) ).

fof(f_4646_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Odrop(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_tl__drop]) ).

fof(f_4646_2,plain,
    ! [U_19413,U_19412,U_19411] : hAPP(c_List_Otl(U_19411),hAPP(hAPP(c_List_Odrop(U_19411),U_19412),U_19413)) = hAPP(hAPP(c_List_Odrop(U_19411),U_19412),hAPP(c_List_Otl(U_19411),U_19413)),
    inference(variable_rename,[status(thm)],[f_4646_1]) ).

fof(f_4646_3,plain,
    ! [U_19411,U_19412,U_19413] : hAPP(c_List_Otl(U_19411),hAPP(hAPP(c_List_Odrop(U_19411),U_19412),U_19413)) = hAPP(hAPP(c_List_Odrop(U_19411),U_19412),hAPP(c_List_Otl(U_19411),U_19413)),
    inference(definitional_conversion,[status(esa)],[f_4646_2]) ).

cnf(f_4646_4,plain,
    hAPP(c_List_Otl(U_19411),hAPP(hAPP(c_List_Odrop(U_19411),U_19412),U_19413)) = hAPP(hAPP(c_List_Odrop(U_19411),U_19412),hAPP(c_List_Otl(U_19411),U_19413)),
    inference(clausify,[status(thm)],[f_4646_3]) ).

fof(f_4647_1,plain,
    ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_tl_Osimps_I1_J]) ).

fof(f_4647_2,plain,
    ! [U_19414] : hAPP(c_List_Otl(U_19414),c_List_Olist_ONil(U_19414)) = c_List_Olist_ONil(U_19414),
    inference(variable_rename,[status(thm)],[f_4647_1]) ).

fof(f_4647_3,plain,
    ! [U_19414] : hAPP(c_List_Otl(U_19414),c_List_Olist_ONil(U_19414)) = c_List_Olist_ONil(U_19414),
    inference(definitional_conversion,[status(esa)],[f_4647_2]) ).

cnf(f_4647_4,plain,
    hAPP(c_List_Otl(U_19414),c_List_Olist_ONil(U_19414)) = c_List_Olist_ONil(U_19414),
    inference(clausify,[status(thm)],[f_4647_3]) ).

fof(f_4648_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_4648_2,plain,
    ! [U_19417,U_19416,U_19415] :
      ( ( hAPP(c_List_Orotate(U_19415,U_19416),U_19417) = c_List_Olist_ONil(U_19415)
        | U_19417 != c_List_Olist_ONil(U_19415) )
      & ( U_19417 = c_List_Olist_ONil(U_19415)
        | hAPP(c_List_Orotate(U_19415,U_19416),U_19417) != c_List_Olist_ONil(U_19415) ) ),
    inference(variable_rename,[status(thm)],[f_4648_1]) ).

fof(f_4648_3,plain,
    ( ! [U_19423,U_19421,U_19419] :
        ( hAPP(c_List_Orotate(U_19419,U_19421),U_19423) = c_List_Olist_ONil(U_19419)
        | U_19423 != c_List_Olist_ONil(U_19419) )
    & ! [U_19422,U_19420,U_19418] :
        ( U_19422 = c_List_Olist_ONil(U_19418)
        | hAPP(c_List_Orotate(U_19418,U_19420),U_19422) != c_List_Olist_ONil(U_19418) ) ),
    inference(miniscope,[status(thm)],[f_4648_2]) ).

fof(f_4648_4,plain,
    ( ! [U_19419,U_19421,U_19423] :
        ( hAPP(c_List_Orotate(U_19419,U_19421),U_19423) = c_List_Olist_ONil(U_19419)
        | U_19423 != c_List_Olist_ONil(U_19419) )
    & ! [U_19422,U_19420,U_19418] :
        ( U_19422 = c_List_Olist_ONil(U_19418)
        | hAPP(c_List_Orotate(U_19418,U_19420),U_19422) != c_List_Olist_ONil(U_19418) ) ),
    inference(definitional_conversion,[status(esa)],[f_4648_3]) ).

cnf(f_4648_5,plain,
    ( U_19422 = c_List_Olist_ONil(U_19418)
    | hAPP(c_List_Orotate(U_19418,U_19420),U_19422) != c_List_Olist_ONil(U_19418) ),
    inference(clausify,[status(thm)],[f_4648_4]) ).

cnf(f_4648_6,plain,
    ( hAPP(c_List_Orotate(U_19419,U_19421),U_19423) = c_List_Olist_ONil(U_19419)
    | U_19423 != c_List_Olist_ONil(U_19419) ),
    inference(clausify,[status(thm)],[f_4648_4]) ).

fof(f_4649_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_take__tl]) ).

fof(f_4649_2,plain,
    ! [U_19426,U_19425,U_19424] : hAPP(hAPP(c_List_Otake(U_19424),U_19425),hAPP(c_List_Otl(U_19424),U_19426)) = hAPP(c_List_Otl(U_19424),hAPP(hAPP(c_List_Otake(U_19424),hAPP(c_Nat_OSuc,U_19425)),U_19426)),
    inference(variable_rename,[status(thm)],[f_4649_1]) ).

fof(f_4649_3,plain,
    ! [U_19424,U_19425,U_19426] : hAPP(hAPP(c_List_Otake(U_19424),U_19425),hAPP(c_List_Otl(U_19424),U_19426)) = hAPP(c_List_Otl(U_19424),hAPP(hAPP(c_List_Otake(U_19424),hAPP(c_Nat_OSuc,U_19425)),U_19426)),
    inference(definitional_conversion,[status(esa)],[f_4649_2]) ).

cnf(f_4649_4,plain,
    hAPP(hAPP(c_List_Otake(U_19424),U_19425),hAPP(c_List_Otl(U_19424),U_19426)) = hAPP(c_List_Otl(U_19424),hAPP(hAPP(c_List_Otake(U_19424),hAPP(c_Nat_OSuc,U_19425)),U_19426)),
    inference(clausify,[status(thm)],[f_4649_3]) ).

fof(f_4650_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_4650_2,plain,
    ! [U_19429,U_19428,U_19427] : hAPP(c_List_Oset(U_19427),hAPP(c_List_Orotate(U_19427,U_19428),U_19429)) = hAPP(c_List_Oset(U_19427),U_19429),
    inference(variable_rename,[status(thm)],[f_4650_1]) ).

fof(f_4650_3,plain,
    ! [U_19427,U_19428,U_19429] : hAPP(c_List_Oset(U_19427),hAPP(c_List_Orotate(U_19427,U_19428),U_19429)) = hAPP(c_List_Oset(U_19427),U_19429),
    inference(definitional_conversion,[status(esa)],[f_4650_2]) ).

cnf(f_4650_4,plain,
    hAPP(c_List_Oset(U_19427),hAPP(c_List_Orotate(U_19427,U_19428),U_19429)) = hAPP(c_List_Oset(U_19427),U_19429),
    inference(clausify,[status(thm)],[f_4650_3]) ).

fof(f_4651_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_4651_2,plain,
    ! [U_19432,U_19431,U_19430] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_19430),hAPP(c_List_Orotate(U_19430,U_19431),U_19432)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19430),U_19432)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_19430),U_19432))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19430),hAPP(c_List_Orotate(U_19430,U_19431),U_19432))) ) ),
    inference(variable_rename,[status(thm)],[f_4651_1]) ).

fof(f_4651_3,plain,
    ( ! [U_19438,U_19436,U_19434] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19434),hAPP(c_List_Orotate(U_19434,U_19436),U_19438)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19434),U_19438)) )
    & ! [U_19437,U_19435,U_19433] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19433),U_19437))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19433),hAPP(c_List_Orotate(U_19433,U_19435),U_19437))) ) ),
    inference(miniscope,[status(thm)],[f_4651_2]) ).

fof(f_4651_4,plain,
    ( ! [U_19434,U_19436,U_19438] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19434),hAPP(c_List_Orotate(U_19434,U_19436),U_19438)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19434),U_19438)) )
    & ! [U_19435,U_19433,U_19437] :
        ( hBOOL(hAPP(c_List_Odistinct(U_19433),U_19437))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_19433),hAPP(c_List_Orotate(U_19433,U_19435),U_19437))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4651_3]) ).

cnf(f_4651_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19433),U_19437))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19433),hAPP(c_List_Orotate(U_19433,U_19435),U_19437))) ),
    inference(clausify,[status(thm)],[f_4651_4]) ).

cnf(f_4651_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19434),hAPP(c_List_Orotate(U_19434,U_19436),U_19438)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19434),U_19438)) ),
    inference(clausify,[status(thm)],[f_4651_4]) ).

fof(f_4652_1,plain,
    ! [V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__tl]) ).

fof(f_4652_2,plain,
    ! [U_19440,U_19439] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19439),hAPP(c_List_Otl(U_19439),U_19440)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19439),U_19440)) ),
    inference(variable_rename,[status(thm)],[f_4652_1]) ).

fof(f_4652_3,plain,
    ! [U_19439,U_19440] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19439),hAPP(c_List_Otl(U_19439),U_19440)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19439),U_19440)) ),
    inference(definitional_conversion,[status(esa)],[f_4652_2]) ).

cnf(f_4652_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19439),hAPP(c_List_Otl(U_19439),U_19440)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19439),U_19440)) ),
    inference(clausify,[status(thm)],[f_4652_3]) ).

fof(f_4653_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_4653_2,plain,
    ! [U_19444,U_19443,U_19442,U_19441] : hAPP(c_List_Orotate(U_19441,U_19442),hAPP(c_List_Orotate(U_19441,U_19443),U_19444)) = hAPP(c_List_Orotate(U_19441,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19442),U_19443)),U_19444),
    inference(variable_rename,[status(thm)],[f_4653_1]) ).

fof(f_4653_3,plain,
    ! [U_19441,U_19442,U_19443,U_19444] : hAPP(c_List_Orotate(U_19441,U_19442),hAPP(c_List_Orotate(U_19441,U_19443),U_19444)) = hAPP(c_List_Orotate(U_19441,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19442),U_19443)),U_19444),
    inference(definitional_conversion,[status(esa)],[f_4653_2]) ).

cnf(f_4653_4,plain,
    hAPP(c_List_Orotate(U_19441,U_19442),hAPP(c_List_Orotate(U_19441,U_19443),U_19444)) = hAPP(c_List_Orotate(U_19441,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19442),U_19443)),U_19444),
    inference(clausify,[status(thm)],[f_4653_3]) ).

fof(f_4654_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_4654_2,plain,
    ! [U_19449,U_19448,U_19447,U_19446,U_19445] : hAPP(c_List_Orotate(U_19445,U_19446),hAPP(hAPP(c_List_Omap(U_19447,U_19445),U_19448),U_19449)) = hAPP(hAPP(c_List_Omap(U_19447,U_19445),U_19448),hAPP(c_List_Orotate(U_19447,U_19446),U_19449)),
    inference(variable_rename,[status(thm)],[f_4654_1]) ).

fof(f_4654_3,plain,
    ! [U_19445,U_19446,U_19447,U_19448,U_19449] : hAPP(c_List_Orotate(U_19445,U_19446),hAPP(hAPP(c_List_Omap(U_19447,U_19445),U_19448),U_19449)) = hAPP(hAPP(c_List_Omap(U_19447,U_19445),U_19448),hAPP(c_List_Orotate(U_19447,U_19446),U_19449)),
    inference(definitional_conversion,[status(esa)],[f_4654_2]) ).

cnf(f_4654_4,plain,
    hAPP(c_List_Orotate(U_19445,U_19446),hAPP(hAPP(c_List_Omap(U_19447,U_19445),U_19448),U_19449)) = hAPP(hAPP(c_List_Omap(U_19447,U_19445),U_19448),hAPP(c_List_Orotate(U_19447,U_19446),U_19449)),
    inference(clausify,[status(thm)],[f_4654_3]) ).

fof(f_4655_1,plain,
    ! [V_xs_2,V_f_2,T_b,T_c] : hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),hAPP(c_List_Otl(T_c),V_xs_2)) = hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_map__tl]) ).

fof(f_4655_2,plain,
    ! [U_19453,U_19452,U_19451,U_19450] : hAPP(hAPP(c_List_Omap(U_19450,U_19451),U_19452),hAPP(c_List_Otl(U_19450),U_19453)) = hAPP(c_List_Otl(U_19451),hAPP(hAPP(c_List_Omap(U_19450,U_19451),U_19452),U_19453)),
    inference(variable_rename,[status(thm)],[f_4655_1]) ).

fof(f_4655_3,plain,
    ! [U_19450,U_19451,U_19452,U_19453] : hAPP(hAPP(c_List_Omap(U_19450,U_19451),U_19452),hAPP(c_List_Otl(U_19450),U_19453)) = hAPP(c_List_Otl(U_19451),hAPP(hAPP(c_List_Omap(U_19450,U_19451),U_19452),U_19453)),
    inference(definitional_conversion,[status(esa)],[f_4655_2]) ).

cnf(f_4655_4,plain,
    hAPP(hAPP(c_List_Omap(U_19450,U_19451),U_19452),hAPP(c_List_Otl(U_19450),U_19453)) = hAPP(c_List_Otl(U_19451),hAPP(hAPP(c_List_Omap(U_19450,U_19451),U_19452),U_19453)),
    inference(clausify,[status(thm)],[f_4655_3]) ).

fof(f_4656_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_4656_2,plain,
    ! [U_19456,U_19455,U_19454] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19454)),hAPP(c_List_Orotate(U_19454,U_19455),U_19456)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19454)),U_19456),
    inference(variable_rename,[status(thm)],[f_4656_1]) ).

fof(f_4656_3,plain,
    ! [U_19454,U_19455,U_19456] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19454)),hAPP(c_List_Orotate(U_19454,U_19455),U_19456)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19454)),U_19456),
    inference(definitional_conversion,[status(esa)],[f_4656_2]) ).

cnf(f_4656_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19454)),hAPP(c_List_Orotate(U_19454,U_19455),U_19456)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19454)),U_19456),
    inference(clausify,[status(thm)],[f_4656_3]) ).

fof(f_4657_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_4657_2,plain,
    ! [U_19459,U_19458,U_19457] : hAPP(c_List_Orotate(U_19457,U_19458),U_19459) = hAPP(c_List_Orotate(U_19457,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19458,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19457)),U_19459))),U_19459),
    inference(variable_rename,[status(thm)],[f_4657_1]) ).

fof(f_4657_3,plain,
    ! [U_19457,U_19458,U_19459] : hAPP(c_List_Orotate(U_19457,U_19458),U_19459) = hAPP(c_List_Orotate(U_19457,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19458,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19457)),U_19459))),U_19459),
    inference(definitional_conversion,[status(esa)],[f_4657_2]) ).

cnf(f_4657_4,plain,
    hAPP(c_List_Orotate(U_19457,U_19458),U_19459) = hAPP(c_List_Orotate(U_19457,c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19458,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19457)),U_19459))),U_19459),
    inference(clausify,[status(thm)],[f_4657_3]) ).

fof(f_4658_1,plain,
    ! [V_xs,V_x,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_xs,
    inference(fof_nnf,[status(thm)],[fact_tl_Osimps_I2_J]) ).

fof(f_4658_2,plain,
    ! [U_19462,U_19461,U_19460] : hAPP(c_List_Otl(U_19460),hAPP(hAPP(c_List_Olist_OCons(U_19460),U_19461),U_19462)) = U_19462,
    inference(variable_rename,[status(thm)],[f_4658_1]) ).

fof(f_4658_3,plain,
    ! [U_19460,U_19461,U_19462] : hAPP(c_List_Otl(U_19460),hAPP(hAPP(c_List_Olist_OCons(U_19460),U_19461),U_19462)) = U_19462,
    inference(definitional_conversion,[status(esa)],[f_4658_2]) ).

cnf(f_4658_4,plain,
    hAPP(c_List_Otl(U_19460),hAPP(hAPP(c_List_Olist_OCons(U_19460),U_19461),U_19462)) = U_19462,
    inference(clausify,[status(thm)],[f_4658_3]) ).

fof(f_4659_1,plain,
    ! [V_ys,T_a,V_xs] :
      ( hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = hAPP(hAPP(c_List_Oappend(T_a),hAPP(c_List_Otl(T_a),V_xs)),V_ys)
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_tl__append2]) ).

fof(f_4659_2,plain,
    ! [U_19465,U_19464,U_19463] :
      ( hAPP(c_List_Otl(U_19464),hAPP(hAPP(c_List_Oappend(U_19464),U_19463),U_19465)) = hAPP(hAPP(c_List_Oappend(U_19464),hAPP(c_List_Otl(U_19464),U_19463)),U_19465)
      | U_19463 = c_List_Olist_ONil(U_19464) ),
    inference(variable_rename,[status(thm)],[f_4659_1]) ).

fof(f_4659_3,plain,
    ! [U_19463,U_19464,U_19465] :
      ( hAPP(c_List_Otl(U_19464),hAPP(hAPP(c_List_Oappend(U_19464),U_19463),U_19465)) = hAPP(hAPP(c_List_Oappend(U_19464),hAPP(c_List_Otl(U_19464),U_19463)),U_19465)
      | U_19463 = c_List_Olist_ONil(U_19464) ),
    inference(definitional_conversion,[status(esa)],[f_4659_2]) ).

cnf(f_4659_4,plain,
    ( hAPP(c_List_Otl(U_19464),hAPP(hAPP(c_List_Oappend(U_19464),U_19463),U_19465)) = hAPP(hAPP(c_List_Oappend(U_19464),hAPP(c_List_Otl(U_19464),U_19463)),U_19465)
    | U_19463 = c_List_Olist_ONil(U_19464) ),
    inference(clausify,[status(thm)],[f_4659_3]) ).

fof(f_4660_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_4660_2,plain,
    ! [U_19467,U_19466] : c_List_Orotate(U_19466,U_19467) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(U_19466),tc_List_Olist(U_19466)),U_19467),c_List_Orotate1(U_19466)),
    inference(variable_rename,[status(thm)],[f_4660_1]) ).

fof(f_4660_3,plain,
    ! [U_19466,U_19467] : c_List_Orotate(U_19466,U_19467) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(U_19466),tc_List_Olist(U_19466)),U_19467),c_List_Orotate1(U_19466)),
    inference(definitional_conversion,[status(esa)],[f_4660_2]) ).

cnf(f_4660_4,plain,
    c_List_Orotate(U_19466,U_19467) = hAPP(hAPP(c_Nat_Ocompow(tc_List_Olist(U_19466),tc_List_Olist(U_19466)),U_19467),c_List_Orotate1(U_19466)),
    inference(clausify,[status(thm)],[f_4660_3]) ).

fof(f_4661_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_4661_2,plain,
    ! [U_19470,U_19469,U_19468] : hAPP(c_List_Orotate(U_19468,hAPP(c_Nat_OSuc,U_19469)),U_19470) = hAPP(c_List_Orotate1(U_19468),hAPP(c_List_Orotate(U_19468,U_19469),U_19470)),
    inference(variable_rename,[status(thm)],[f_4661_1]) ).

fof(f_4661_3,plain,
    ! [U_19468,U_19469,U_19470] : hAPP(c_List_Orotate(U_19468,hAPP(c_Nat_OSuc,U_19469)),U_19470) = hAPP(c_List_Orotate1(U_19468),hAPP(c_List_Orotate(U_19468,U_19469),U_19470)),
    inference(definitional_conversion,[status(esa)],[f_4661_2]) ).

cnf(f_4661_4,plain,
    hAPP(c_List_Orotate(U_19468,hAPP(c_Nat_OSuc,U_19469)),U_19470) = hAPP(c_List_Orotate1(U_19468),hAPP(c_List_Orotate(U_19468,U_19469),U_19470)),
    inference(clausify,[status(thm)],[f_4661_3]) ).

fof(f_4662_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_4662_2,plain,
    ! [U_19473,U_19472,U_19471] : hAPP(c_List_Orotate1(U_19471),hAPP(c_List_Orotate(U_19471,U_19472),U_19473)) = hAPP(c_List_Orotate(U_19471,U_19472),hAPP(c_List_Orotate1(U_19471),U_19473)),
    inference(variable_rename,[status(thm)],[f_4662_1]) ).

fof(f_4662_3,plain,
    ! [U_19471,U_19472,U_19473] : hAPP(c_List_Orotate1(U_19471),hAPP(c_List_Orotate(U_19471,U_19472),U_19473)) = hAPP(c_List_Orotate(U_19471,U_19472),hAPP(c_List_Orotate1(U_19471),U_19473)),
    inference(definitional_conversion,[status(esa)],[f_4662_2]) ).

cnf(f_4662_4,plain,
    hAPP(c_List_Orotate1(U_19471),hAPP(c_List_Orotate(U_19471,U_19472),U_19473)) = hAPP(c_List_Orotate(U_19471,U_19472),hAPP(c_List_Orotate1(U_19471),U_19473)),
    inference(clausify,[status(thm)],[f_4662_3]) ).

fof(f_4663_1,plain,
    ! [V_ys_2,V_xs_2,T_b] : hAPP(c_List_Otl(T_b),hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(T_b),T_b,hAPP(c_List_Otl(T_b),V_ys_2),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(T_b)),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Oappend(T_b)),V_ys_2))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_tl__append]) ).

fof(f_4663_2,plain,
    ! [U_19476,U_19475,U_19474] : hAPP(c_List_Otl(U_19474),hAPP(hAPP(c_List_Oappend(U_19474),U_19475),U_19476)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_19474),U_19474,hAPP(c_List_Otl(U_19474),U_19476),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_19474),tc_List_Olist(U_19474)),U_19474),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19474),tc_List_Olist(U_19474),tc_List_Olist(U_19474)),c_List_Oappend(U_19474)),U_19476))),U_19475),
    inference(variable_rename,[status(thm)],[f_4663_1]) ).

fof(f_4663_3,plain,
    ! [U_19474,U_19475,U_19476] : hAPP(c_List_Otl(U_19474),hAPP(hAPP(c_List_Oappend(U_19474),U_19475),U_19476)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_19474),U_19474,hAPP(c_List_Otl(U_19474),U_19476),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_19474),tc_List_Olist(U_19474)),U_19474),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19474),tc_List_Olist(U_19474),tc_List_Olist(U_19474)),c_List_Oappend(U_19474)),U_19476))),U_19475),
    inference(definitional_conversion,[status(esa)],[f_4663_2]) ).

cnf(f_4663_4,plain,
    hAPP(c_List_Otl(U_19474),hAPP(hAPP(c_List_Oappend(U_19474),U_19475),U_19476)) = hAPP(c_List_Olist_Olist__case(tc_List_Olist(U_19474),U_19474,hAPP(c_List_Otl(U_19474),U_19476),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_19474),tc_List_Olist(U_19474)),U_19474),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19474),tc_List_Olist(U_19474),tc_List_Olist(U_19474)),c_List_Oappend(U_19474)),U_19476))),U_19475),
    inference(clausify,[status(thm)],[f_4663_3]) ).

fof(f_4664_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_4664_2,plain,
    ! [U_19477] : c_List_Orotate(U_19477,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(U_19477)),
    inference(variable_rename,[status(thm)],[f_4664_1]) ).

fof(f_4664_3,plain,
    ! [U_19477] : c_List_Orotate(U_19477,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(U_19477)),
    inference(definitional_conversion,[status(esa)],[f_4664_2]) ).

cnf(f_4664_4,plain,
    c_List_Orotate(U_19477,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(U_19477)),
    inference(clausify,[status(thm)],[f_4664_3]) ).

fof(f_4665_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_4665_2,plain,
    ! [U_19480,U_19479,U_19478] : c_List_Orotate(U_19478,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19479),U_19480)) = hAPP(c_Fun_Ocomp(tc_List_Olist(U_19478),tc_List_Olist(U_19478),tc_List_Olist(U_19478),c_List_Orotate(U_19478,U_19479)),c_List_Orotate(U_19478,U_19480)),
    inference(variable_rename,[status(thm)],[f_4665_1]) ).

fof(f_4665_3,plain,
    ! [U_19478,U_19479,U_19480] : c_List_Orotate(U_19478,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19479),U_19480)) = hAPP(c_Fun_Ocomp(tc_List_Olist(U_19478),tc_List_Olist(U_19478),tc_List_Olist(U_19478),c_List_Orotate(U_19478,U_19479)),c_List_Orotate(U_19478,U_19480)),
    inference(definitional_conversion,[status(esa)],[f_4665_2]) ).

cnf(f_4665_4,plain,
    c_List_Orotate(U_19478,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19479),U_19480)) = hAPP(c_Fun_Ocomp(tc_List_Olist(U_19478),tc_List_Olist(U_19478),tc_List_Olist(U_19478),c_List_Orotate(U_19478,U_19479)),c_List_Orotate(U_19478,U_19480)),
    inference(clausify,[status(thm)],[f_4665_3]) ).

fof(f_4666_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_4666_2,plain,
    ! [U_19483,U_19482,U_19481] :
      ( hAPP(c_List_Orotate(U_19482,U_19481),U_19483) = U_19483
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19481,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19482)),U_19483)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(variable_rename,[status(thm)],[f_4666_1]) ).

fof(f_4666_3,plain,
    ! [U_19481,U_19482,U_19483] :
      ( hAPP(c_List_Orotate(U_19482,U_19481),U_19483) = U_19483
      | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19481,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19482)),U_19483)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(definitional_conversion,[status(esa)],[f_4666_2]) ).

cnf(f_4666_4,plain,
    ( hAPP(c_List_Orotate(U_19482,U_19481),U_19483) = U_19483
    | c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19481,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19482)),U_19483)) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4666_3]) ).

fof(f_4667_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_4667_2,plain,
    ! [U_19486,U_19485,U_19484] :
      ( hAPP(c_List_Orotate(U_19484,U_19486),U_19485) = U_19485
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19484)),U_19485)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(variable_rename,[status(thm)],[f_4667_1]) ).

fof(f_4667_3,plain,
    ! [U_19484,U_19485,U_19486] :
      ( hAPP(c_List_Orotate(U_19484,U_19486),U_19485) = U_19485
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19484)),U_19485)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(definitional_conversion,[status(esa)],[f_4667_2]) ).

cnf(f_4667_4,plain,
    ( hAPP(c_List_Orotate(U_19484,U_19486),U_19485) = U_19485
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19484)),U_19485)),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
    inference(clausify,[status(thm)],[f_4667_3]) ).

fof(f_4668_1,plain,
    ! [V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Otl(T_a),V_xs)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(fof_nnf,[status(thm)],[fact_length__tl]) ).

fof(f_4668_2,plain,
    ! [U_19488,U_19487] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19487)),hAPP(c_List_Otl(U_19487),U_19488)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19487)),U_19488)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_4668_1]) ).

fof(f_4668_3,plain,
    ! [U_19487,U_19488] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19487)),hAPP(c_List_Otl(U_19487),U_19488)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19487)),U_19488)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_4668_2]) ).

cnf(f_4668_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19487)),hAPP(c_List_Otl(U_19487),U_19488)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19487)),U_19488)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_4668_3]) ).

fof(f_4669_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Otl(T_a),hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) = hAPP(hAPP(c_List_Otake(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(T_a),V_xs)),
    inference(fof_nnf,[status(thm)],[fact_tl__take]) ).

fof(f_4669_2,plain,
    ! [U_19491,U_19490,U_19489] : hAPP(c_List_Otl(U_19489),hAPP(hAPP(c_List_Otake(U_19489),U_19490),U_19491)) = hAPP(hAPP(c_List_Otake(U_19489),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19490),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(U_19489),U_19491)),
    inference(variable_rename,[status(thm)],[f_4669_1]) ).

fof(f_4669_3,plain,
    ! [U_19489,U_19490,U_19491] : hAPP(c_List_Otl(U_19489),hAPP(hAPP(c_List_Otake(U_19489),U_19490),U_19491)) = hAPP(hAPP(c_List_Otake(U_19489),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19490),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(U_19489),U_19491)),
    inference(definitional_conversion,[status(esa)],[f_4669_2]) ).

cnf(f_4669_4,plain,
    hAPP(c_List_Otl(U_19489),hAPP(hAPP(c_List_Otake(U_19489),U_19490),U_19491)) = hAPP(hAPP(c_List_Otake(U_19489),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19490),c_Groups_Oone__class_Oone(tc_Nat_Onat))),hAPP(c_List_Otl(U_19489),U_19491)),
    inference(clausify,[status(thm)],[f_4669_3]) ).

fof(f_4670_1,plain,
    ! [V_n,T_a,V_xs] :
      ( hAPP(hAPP(c_List_Otake(T_a),hAPP(c_Nat_OSuc,V_n)),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),hAPP(c_List_Ohd(T_a),V_xs)),hAPP(hAPP(c_List_Otake(T_a),V_n),hAPP(c_List_Otl(T_a),V_xs)))
      | V_xs = c_List_Olist_ONil(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_take__Suc]) ).

fof(f_4670_2,plain,
    ! [U_19494,U_19493,U_19492] :
      ( hAPP(hAPP(c_List_Otake(U_19493),hAPP(c_Nat_OSuc,U_19494)),U_19492) = hAPP(hAPP(c_List_Olist_OCons(U_19493),hAPP(c_List_Ohd(U_19493),U_19492)),hAPP(hAPP(c_List_Otake(U_19493),U_19494),hAPP(c_List_Otl(U_19493),U_19492)))
      | U_19492 = c_List_Olist_ONil(U_19493) ),
    inference(variable_rename,[status(thm)],[f_4670_1]) ).

fof(f_4670_3,plain,
    ! [U_19492,U_19493,U_19494] :
      ( hAPP(hAPP(c_List_Otake(U_19493),hAPP(c_Nat_OSuc,U_19494)),U_19492) = hAPP(hAPP(c_List_Olist_OCons(U_19493),hAPP(c_List_Ohd(U_19493),U_19492)),hAPP(hAPP(c_List_Otake(U_19493),U_19494),hAPP(c_List_Otl(U_19493),U_19492)))
      | U_19492 = c_List_Olist_ONil(U_19493) ),
    inference(definitional_conversion,[status(esa)],[f_4670_2]) ).

cnf(f_4670_4,plain,
    ( hAPP(hAPP(c_List_Otake(U_19493),hAPP(c_Nat_OSuc,U_19494)),U_19492) = hAPP(hAPP(c_List_Olist_OCons(U_19493),hAPP(c_List_Ohd(U_19493),U_19492)),hAPP(hAPP(c_List_Otake(U_19493),U_19494),hAPP(c_List_Otl(U_19493),U_19492)))
    | U_19492 = c_List_Olist_ONil(U_19493) ),
    inference(clausify,[status(thm)],[f_4670_3]) ).

fof(f_4671_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_List_Orotate(T_a,V_n),V_xs) = hAPP(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_4671_2,plain,
    ! [U_19497,U_19496,U_19495] : hAPP(c_List_Orotate(U_19495,U_19496),U_19497) = hAPP(hAPP(c_List_Oappend(U_19495),hAPP(hAPP(c_List_Odrop(U_19495),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19496,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19495)),U_19497))),U_19497)),hAPP(hAPP(c_List_Otake(U_19495),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19496,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19495)),U_19497))),U_19497)),
    inference(variable_rename,[status(thm)],[f_4671_1]) ).

fof(f_4671_3,plain,
    ! [U_19495,U_19496,U_19497] : hAPP(c_List_Orotate(U_19495,U_19496),U_19497) = hAPP(hAPP(c_List_Oappend(U_19495),hAPP(hAPP(c_List_Odrop(U_19495),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19496,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19495)),U_19497))),U_19497)),hAPP(hAPP(c_List_Otake(U_19495),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19496,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19495)),U_19497))),U_19497)),
    inference(definitional_conversion,[status(esa)],[f_4671_2]) ).

cnf(f_4671_4,plain,
    hAPP(c_List_Orotate(U_19495,U_19496),U_19497) = hAPP(hAPP(c_List_Oappend(U_19495),hAPP(hAPP(c_List_Odrop(U_19495),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19496,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19495)),U_19497))),U_19497)),hAPP(hAPP(c_List_Otake(U_19495),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_19496,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19495)),U_19497))),U_19497)),
    inference(clausify,[status(thm)],[f_4671_3]) ).

fof(f_4672_1,plain,
    ! [V_xs_2,T_b] :
      ( hAPP(c_Finite__Set_Ofold1(T_b,c_Groups_Otimes__class_Otimes(T_b)),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_b,T_b,c_Groups_Otimes__class_Otimes(T_b),hAPP(c_List_Ohd(T_b),V_xs_2)),hAPP(c_List_Otl(T_b),V_xs_2))
      | V_xs_2 = c_List_Olist_ONil(T_b)
      | ~ class_Lattices_Oab__semigroup__idem__mult(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_fold1__set]) ).

fof(f_4672_2,plain,
    ! [U_19499,U_19498] :
      ( hAPP(c_Finite__Set_Ofold1(U_19498,c_Groups_Otimes__class_Otimes(U_19498)),hAPP(c_List_Oset(U_19498),U_19499)) = hAPP(c_List_Ofoldl(U_19498,U_19498,c_Groups_Otimes__class_Otimes(U_19498),hAPP(c_List_Ohd(U_19498),U_19499)),hAPP(c_List_Otl(U_19498),U_19499))
      | U_19499 = c_List_Olist_ONil(U_19498)
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_19498) ),
    inference(variable_rename,[status(thm)],[f_4672_1]) ).

fof(f_4672_3,plain,
    ! [U_19498,U_19499] :
      ( hAPP(c_Finite__Set_Ofold1(U_19498,c_Groups_Otimes__class_Otimes(U_19498)),hAPP(c_List_Oset(U_19498),U_19499)) = hAPP(c_List_Ofoldl(U_19498,U_19498,c_Groups_Otimes__class_Otimes(U_19498),hAPP(c_List_Ohd(U_19498),U_19499)),hAPP(c_List_Otl(U_19498),U_19499))
      | U_19499 = c_List_Olist_ONil(U_19498)
      | ~ class_Lattices_Oab__semigroup__idem__mult(U_19498) ),
    inference(definitional_conversion,[status(esa)],[f_4672_2]) ).

cnf(f_4672_4,plain,
    ( hAPP(c_Finite__Set_Ofold1(U_19498,c_Groups_Otimes__class_Otimes(U_19498)),hAPP(c_List_Oset(U_19498),U_19499)) = hAPP(c_List_Ofoldl(U_19498,U_19498,c_Groups_Otimes__class_Otimes(U_19498),hAPP(c_List_Ohd(U_19498),U_19499)),hAPP(c_List_Otl(U_19498),U_19499))
    | U_19499 = c_List_Olist_ONil(U_19498)
    | ~ class_Lattices_Oab__semigroup__idem__mult(U_19498) ),
    inference(clausify,[status(thm)],[f_4672_3]) ).

fof(f_4673_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_4673_2,plain,
    ! [U_19503,U_19502,U_19501,U_19500] : c_List_Olist_Olist__size(U_19500,U_19501,hAPP(hAPP(c_List_Olist_OCons(U_19500),U_19502),U_19503)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_19501,U_19502)),c_List_Olist_Olist__size(U_19500,U_19501,U_19503))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(variable_rename,[status(thm)],[f_4673_1]) ).

fof(f_4673_3,plain,
    ! [U_19500,U_19501,U_19502,U_19503] : c_List_Olist_Olist__size(U_19500,U_19501,hAPP(hAPP(c_List_Olist_OCons(U_19500),U_19502),U_19503)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_19501,U_19502)),c_List_Olist_Olist__size(U_19500,U_19501,U_19503))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(definitional_conversion,[status(esa)],[f_4673_2]) ).

cnf(f_4673_4,plain,
    c_List_Olist_Olist__size(U_19500,U_19501,hAPP(hAPP(c_List_Olist_OCons(U_19500),U_19502),U_19503)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(U_19501,U_19502)),c_List_Olist_Olist__size(U_19500,U_19501,U_19503))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),
    inference(clausify,[status(thm)],[f_4673_3]) ).

fof(f_4674_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_4674_2,plain,
    ! [U_19509,U_19508,U_19507,U_19506,U_19505,U_19504] : hAPP(c_List_Ofoldl(U_19504,U_19505,U_19506,U_19507),hAPP(hAPP(c_List_Oappend(U_19505),U_19508),U_19509)) = hAPP(c_List_Ofoldl(U_19504,U_19505,U_19506,hAPP(c_List_Ofoldl(U_19504,U_19505,U_19506,U_19507),U_19508)),U_19509),
    inference(variable_rename,[status(thm)],[f_4674_1]) ).

fof(f_4674_3,plain,
    ! [U_19505,U_19504,U_19506,U_19507,U_19508,U_19509] : hAPP(c_List_Ofoldl(U_19504,U_19505,U_19506,U_19507),hAPP(hAPP(c_List_Oappend(U_19505),U_19508),U_19509)) = hAPP(c_List_Ofoldl(U_19504,U_19505,U_19506,hAPP(c_List_Ofoldl(U_19504,U_19505,U_19506,U_19507),U_19508)),U_19509),
    inference(definitional_conversion,[status(esa)],[f_4674_2]) ).

cnf(f_4674_4,plain,
    hAPP(c_List_Ofoldl(U_19504,U_19505,U_19506,U_19507),hAPP(hAPP(c_List_Oappend(U_19505),U_19508),U_19509)) = hAPP(c_List_Ofoldl(U_19504,U_19505,U_19506,hAPP(c_List_Ofoldl(U_19504,U_19505,U_19506,U_19507),U_19508)),U_19509),
    inference(clausify,[status(thm)],[f_4674_3]) ).

fof(f_4675_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_4675_2,plain,
    ! [U_19515,U_19514,U_19513,U_19512,U_19511,U_19510] : hAPP(c_List_Ofoldl(U_19510,U_19511,U_19512,U_19513),hAPP(hAPP(c_List_Olist_OCons(U_19511),U_19514),U_19515)) = hAPP(c_List_Ofoldl(U_19510,U_19511,U_19512,hAPP(hAPP(U_19512,U_19513),U_19514)),U_19515),
    inference(variable_rename,[status(thm)],[f_4675_1]) ).

fof(f_4675_3,plain,
    ! [U_19510,U_19511,U_19512,U_19513,U_19514,U_19515] : hAPP(c_List_Ofoldl(U_19510,U_19511,U_19512,U_19513),hAPP(hAPP(c_List_Olist_OCons(U_19511),U_19514),U_19515)) = hAPP(c_List_Ofoldl(U_19510,U_19511,U_19512,hAPP(hAPP(U_19512,U_19513),U_19514)),U_19515),
    inference(definitional_conversion,[status(esa)],[f_4675_2]) ).

cnf(f_4675_4,plain,
    hAPP(c_List_Ofoldl(U_19510,U_19511,U_19512,U_19513),hAPP(hAPP(c_List_Olist_OCons(U_19511),U_19514),U_19515)) = hAPP(c_List_Ofoldl(U_19510,U_19511,U_19512,hAPP(hAPP(U_19512,U_19513),U_19514)),U_19515),
    inference(clausify,[status(thm)],[f_4675_3]) ).

fof(f_4676_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_4676_2,plain,
    ! [U_19520,U_19519,U_19518,U_19517,U_19516] : c_List_Olist_Olist__size(U_19516,U_19517,hAPP(hAPP(c_List_Omap(U_19518,U_19516),U_19519),U_19520)) = c_List_Olist_Olist__size(U_19518,hAPP(c_Fun_Ocomp(U_19516,tc_Nat_Onat,U_19518,U_19517),U_19519),U_19520),
    inference(variable_rename,[status(thm)],[f_4676_1]) ).

fof(f_4676_3,plain,
    ! [U_19516,U_19517,U_19518,U_19519,U_19520] : c_List_Olist_Olist__size(U_19516,U_19517,hAPP(hAPP(c_List_Omap(U_19518,U_19516),U_19519),U_19520)) = c_List_Olist_Olist__size(U_19518,hAPP(c_Fun_Ocomp(U_19516,tc_Nat_Onat,U_19518,U_19517),U_19519),U_19520),
    inference(definitional_conversion,[status(esa)],[f_4676_2]) ).

cnf(f_4676_4,plain,
    c_List_Olist_Olist__size(U_19516,U_19517,hAPP(hAPP(c_List_Omap(U_19518,U_19516),U_19519),U_19520)) = c_List_Olist_Olist__size(U_19518,hAPP(c_Fun_Ocomp(U_19516,tc_Nat_Onat,U_19518,U_19517),U_19519),U_19520),
    inference(clausify,[status(thm)],[f_4676_3]) ).

fof(f_4677_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_4677_2,plain,
    ! [U_19527,U_19526,U_19525,U_19524,U_19523,U_19522,U_19521] : hAPP(c_List_Ofoldl(U_19521,U_19522,U_19523,U_19524),hAPP(hAPP(c_List_Omap(U_19525,U_19522),U_19526),U_19527)) = hAPP(c_List_Ofoldl(U_19521,U_19525,hAPP(hAPP(c_COMBC(U_19521,tc_fun(U_19525,U_19522),tc_fun(U_19525,U_19521)),hAPP(hAPP(c_COMBB(tc_fun(U_19522,U_19521),tc_fun(tc_fun(U_19525,U_19522),tc_fun(U_19525,U_19521)),U_19521),c_COMBB(U_19522,U_19521,U_19525)),U_19523)),U_19526),U_19524),U_19527),
    inference(variable_rename,[status(thm)],[f_4677_1]) ).

fof(f_4677_3,plain,
    ! [U_19521,U_19522,U_19523,U_19524,U_19525,U_19526,U_19527] : hAPP(c_List_Ofoldl(U_19521,U_19522,U_19523,U_19524),hAPP(hAPP(c_List_Omap(U_19525,U_19522),U_19526),U_19527)) = hAPP(c_List_Ofoldl(U_19521,U_19525,hAPP(hAPP(c_COMBC(U_19521,tc_fun(U_19525,U_19522),tc_fun(U_19525,U_19521)),hAPP(hAPP(c_COMBB(tc_fun(U_19522,U_19521),tc_fun(tc_fun(U_19525,U_19522),tc_fun(U_19525,U_19521)),U_19521),c_COMBB(U_19522,U_19521,U_19525)),U_19523)),U_19526),U_19524),U_19527),
    inference(definitional_conversion,[status(esa)],[f_4677_2]) ).

cnf(f_4677_4,plain,
    hAPP(c_List_Ofoldl(U_19521,U_19522,U_19523,U_19524),hAPP(hAPP(c_List_Omap(U_19525,U_19522),U_19526),U_19527)) = hAPP(c_List_Ofoldl(U_19521,U_19525,hAPP(hAPP(c_COMBC(U_19521,tc_fun(U_19525,U_19522),tc_fun(U_19525,U_19521)),hAPP(hAPP(c_COMBB(tc_fun(U_19522,U_19521),tc_fun(tc_fun(U_19525,U_19522),tc_fun(U_19525,U_19521)),U_19521),c_COMBB(U_19522,U_19521,U_19525)),U_19523)),U_19526),U_19524),U_19527),
    inference(clausify,[status(thm)],[f_4677_3]) ).

fof(f_4678_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_4678_2,plain,
    ! [U_19530,U_19529,U_19528] :
      ( c_List_Ofoldr(U_19528,U_19528,c_Groups_Oplus__class_Oplus(U_19528),U_19529,U_19530) = hAPP(c_List_Ofoldl(U_19528,U_19528,c_Groups_Oplus__class_Oplus(U_19528),U_19530),U_19529)
      | ~ class_Groups_Oab__semigroup__add(U_19528) ),
    inference(variable_rename,[status(thm)],[f_4678_1]) ).

fof(f_4678_3,plain,
    ! [U_19528,U_19529,U_19530] :
      ( c_List_Ofoldr(U_19528,U_19528,c_Groups_Oplus__class_Oplus(U_19528),U_19529,U_19530) = hAPP(c_List_Ofoldl(U_19528,U_19528,c_Groups_Oplus__class_Oplus(U_19528),U_19530),U_19529)
      | ~ class_Groups_Oab__semigroup__add(U_19528) ),
    inference(definitional_conversion,[status(esa)],[f_4678_2]) ).

cnf(f_4678_4,plain,
    ( c_List_Ofoldr(U_19528,U_19528,c_Groups_Oplus__class_Oplus(U_19528),U_19529,U_19530) = hAPP(c_List_Ofoldl(U_19528,U_19528,c_Groups_Oplus__class_Oplus(U_19528),U_19530),U_19529)
    | ~ class_Groups_Oab__semigroup__add(U_19528) ),
    inference(clausify,[status(thm)],[f_4678_3]) ).

fof(f_4679_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_4679_2,plain,
    ! [U_19533,U_19532,U_19531] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19531),U_19532),hAPP(c_List_Ofoldl(U_19531,U_19531,c_Groups_Oplus__class_Oplus(U_19531),c_Groups_Ozero__class_Ozero(U_19531)),U_19533)) = hAPP(c_List_Ofoldl(U_19531,U_19531,c_Groups_Oplus__class_Oplus(U_19531),U_19532),U_19533)
      | ~ class_Groups_Omonoid__add(U_19531) ),
    inference(variable_rename,[status(thm)],[f_4679_1]) ).

fof(f_4679_3,plain,
    ! [U_19531,U_19532,U_19533] :
      ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19531),U_19532),hAPP(c_List_Ofoldl(U_19531,U_19531,c_Groups_Oplus__class_Oplus(U_19531),c_Groups_Ozero__class_Ozero(U_19531)),U_19533)) = hAPP(c_List_Ofoldl(U_19531,U_19531,c_Groups_Oplus__class_Oplus(U_19531),U_19532),U_19533)
      | ~ class_Groups_Omonoid__add(U_19531) ),
    inference(definitional_conversion,[status(esa)],[f_4679_2]) ).

cnf(f_4679_4,plain,
    ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19531),U_19532),hAPP(c_List_Ofoldl(U_19531,U_19531,c_Groups_Oplus__class_Oplus(U_19531),c_Groups_Ozero__class_Ozero(U_19531)),U_19533)) = hAPP(c_List_Ofoldl(U_19531,U_19531,c_Groups_Oplus__class_Oplus(U_19531),U_19532),U_19533)
    | ~ class_Groups_Omonoid__add(U_19531) ),
    inference(clausify,[status(thm)],[f_4679_3]) ).

fof(f_4680_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_4680_2,plain,
    ! [U_19537,U_19536,U_19535,U_19534] :
      ( hAPP(c_List_Ofoldl(U_19534,U_19534,c_Groups_Oplus__class_Oplus(U_19534),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19534),U_19535),U_19536)),U_19537) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19534),U_19535),hAPP(c_List_Ofoldl(U_19534,U_19534,c_Groups_Oplus__class_Oplus(U_19534),U_19536),U_19537))
      | ~ class_Groups_Osemigroup__add(U_19534) ),
    inference(variable_rename,[status(thm)],[f_4680_1]) ).

fof(f_4680_3,plain,
    ! [U_19534,U_19535,U_19536,U_19537] :
      ( hAPP(c_List_Ofoldl(U_19534,U_19534,c_Groups_Oplus__class_Oplus(U_19534),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19534),U_19535),U_19536)),U_19537) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19534),U_19535),hAPP(c_List_Ofoldl(U_19534,U_19534,c_Groups_Oplus__class_Oplus(U_19534),U_19536),U_19537))
      | ~ class_Groups_Osemigroup__add(U_19534) ),
    inference(definitional_conversion,[status(esa)],[f_4680_2]) ).

cnf(f_4680_4,plain,
    ( hAPP(c_List_Ofoldl(U_19534,U_19534,c_Groups_Oplus__class_Oplus(U_19534),hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19534),U_19535),U_19536)),U_19537) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19534),U_19535),hAPP(c_List_Ofoldl(U_19534,U_19534,c_Groups_Oplus__class_Oplus(U_19534),U_19536),U_19537))
    | ~ class_Groups_Osemigroup__add(U_19534) ),
    inference(clausify,[status(thm)],[f_4680_3]) ).

fof(f_4681_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_4681_2,plain,
    ! [U_19540,U_19539,U_19538] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19538),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19539),U_19540)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19538),U_19539)) ),
    inference(variable_rename,[status(thm)],[f_4681_1]) ).

fof(f_4681_3,plain,
    ! [U_19538,U_19539,U_19540] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19538),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19539),U_19540)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19538),U_19539)) ),
    inference(definitional_conversion,[status(esa)],[f_4681_2]) ).

cnf(f_4681_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19538),hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19539),U_19540)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19538),U_19539)) ),
    inference(clausify,[status(thm)],[f_4681_3]) ).

fof(f_4682_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_4682_2,plain,
    ! [U_19544,U_19543,U_19542,U_19541] : hAPP(c_List_Ofoldl(U_19541,U_19542,U_19543,U_19544),c_List_Olist_ONil(U_19542)) = U_19544,
    inference(variable_rename,[status(thm)],[f_4682_1]) ).

fof(f_4682_3,plain,
    ! [U_19541,U_19542,U_19543,U_19544] : hAPP(c_List_Ofoldl(U_19541,U_19542,U_19543,U_19544),c_List_Olist_ONil(U_19542)) = U_19544,
    inference(definitional_conversion,[status(esa)],[f_4682_2]) ).

cnf(f_4682_4,plain,
    hAPP(c_List_Ofoldl(U_19541,U_19542,U_19543,U_19544),c_List_Olist_ONil(U_19542)) = U_19544,
    inference(clausify,[status(thm)],[f_4682_3]) ).

fof(f_4683_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_4683_2,plain,
    ! [U_19545] :
      ( c_List_Omonoid__add__class_Olistsum(U_19545) = c_List_Ofoldl(U_19545,U_19545,c_Groups_Oplus__class_Oplus(U_19545),c_Groups_Ozero__class_Ozero(U_19545))
      | ~ class_Groups_Omonoid__add(U_19545) ),
    inference(variable_rename,[status(thm)],[f_4683_1]) ).

fof(f_4683_3,plain,
    ! [U_19545] :
      ( c_List_Omonoid__add__class_Olistsum(U_19545) = c_List_Ofoldl(U_19545,U_19545,c_Groups_Oplus__class_Oplus(U_19545),c_Groups_Ozero__class_Ozero(U_19545))
      | ~ class_Groups_Omonoid__add(U_19545) ),
    inference(definitional_conversion,[status(esa)],[f_4683_2]) ).

cnf(f_4683_4,plain,
    ( c_List_Omonoid__add__class_Olistsum(U_19545) = c_List_Ofoldl(U_19545,U_19545,c_Groups_Oplus__class_Oplus(U_19545),c_Groups_Ozero__class_Ozero(U_19545))
    | ~ class_Groups_Omonoid__add(U_19545) ),
    inference(clausify,[status(thm)],[f_4683_3]) ).

fof(f_4684_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_4684_2,plain,
    ! [U_19547,U_19546] :
      ( hAPP(c_List_Ofoldl(U_19546,U_19546,c_Groups_Oplus__class_Oplus(U_19546),c_Groups_Ozero__class_Ozero(U_19546)),U_19547) = c_List_Ofoldr(U_19546,U_19546,c_Groups_Oplus__class_Oplus(U_19546),U_19547,c_Groups_Ozero__class_Ozero(U_19546))
      | ~ class_Groups_Omonoid__add(U_19546) ),
    inference(variable_rename,[status(thm)],[f_4684_1]) ).

fof(f_4684_3,plain,
    ! [U_19546,U_19547] :
      ( hAPP(c_List_Ofoldl(U_19546,U_19546,c_Groups_Oplus__class_Oplus(U_19546),c_Groups_Ozero__class_Ozero(U_19546)),U_19547) = c_List_Ofoldr(U_19546,U_19546,c_Groups_Oplus__class_Oplus(U_19546),U_19547,c_Groups_Ozero__class_Ozero(U_19546))
      | ~ class_Groups_Omonoid__add(U_19546) ),
    inference(definitional_conversion,[status(esa)],[f_4684_2]) ).

cnf(f_4684_4,plain,
    ( hAPP(c_List_Ofoldl(U_19546,U_19546,c_Groups_Oplus__class_Oplus(U_19546),c_Groups_Ozero__class_Ozero(U_19546)),U_19547) = c_List_Ofoldr(U_19546,U_19546,c_Groups_Oplus__class_Oplus(U_19546),U_19547,c_Groups_Ozero__class_Ozero(U_19546))
    | ~ class_Groups_Omonoid__add(U_19546) ),
    inference(clausify,[status(thm)],[f_4684_3]) ).

fof(f_4685_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_4685_2,plain,
    ! [U_19550,U_19549,U_19548] :
      ( hAPP(c_List_Ofoldl(U_19548,U_19548,c_Groups_Oplus__class_Oplus(U_19548),U_19549),U_19550) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19548),U_19549),c_List_Ofoldr(U_19548,U_19548,c_Groups_Oplus__class_Oplus(U_19548),U_19550,c_Groups_Ozero__class_Ozero(U_19548)))
      | ~ class_Groups_Omonoid__add(U_19548) ),
    inference(variable_rename,[status(thm)],[f_4685_1]) ).

fof(f_4685_3,plain,
    ! [U_19548,U_19549,U_19550] :
      ( hAPP(c_List_Ofoldl(U_19548,U_19548,c_Groups_Oplus__class_Oplus(U_19548),U_19549),U_19550) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19548),U_19549),c_List_Ofoldr(U_19548,U_19548,c_Groups_Oplus__class_Oplus(U_19548),U_19550,c_Groups_Ozero__class_Ozero(U_19548)))
      | ~ class_Groups_Omonoid__add(U_19548) ),
    inference(definitional_conversion,[status(esa)],[f_4685_2]) ).

cnf(f_4685_4,plain,
    ( hAPP(c_List_Ofoldl(U_19548,U_19548,c_Groups_Oplus__class_Oplus(U_19548),U_19549),U_19550) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(U_19548),U_19549),c_List_Ofoldr(U_19548,U_19548,c_Groups_Oplus__class_Oplus(U_19548),U_19550,c_Groups_Ozero__class_Ozero(U_19548)))
    | ~ class_Groups_Omonoid__add(U_19548) ),
    inference(clausify,[status(thm)],[f_4685_3]) ).

fof(f_4686_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_4686_2,plain,
    ! [U_19554,U_19553] :
      ( ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19553),U_19554) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_19552] :
            ( U_19552 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_19552),hAPP(c_List_Oset(tc_Nat_Onat),U_19554))) )
        | U_19553 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
      & ( ( ! [U_19551] :
              ( U_19551 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_19551),hAPP(c_List_Oset(tc_Nat_Onat),U_19554))) )
          & U_19553 = 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_19553),U_19554) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4686_1]) ).

fof(f_4686_3,plain,
    ( ! [U_19558,U_19556] :
        ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19556),U_19558) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ? [U_19552] :
            ( U_19552 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
            & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_19552),hAPP(c_List_Oset(tc_Nat_Onat),U_19558))) )
        | U_19556 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19557,U_19555] :
        ( ( ! [U_19551] :
              ( U_19551 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_19551),hAPP(c_List_Oset(tc_Nat_Onat),U_19557))) )
          & U_19555 = 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_19555),U_19557) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4686_2]) ).

fof(f_4686_4,plain,
    ( ! [U_19558,U_19556] :
        ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19556),U_19558) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ( sK477(U_19558,U_19556) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          & hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK477(U_19558,U_19556)),hAPP(c_List_Oset(tc_Nat_Onat),U_19558))) )
        | U_19556 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19557,U_19555] :
        ( ( ! [U_19551] :
              ( U_19551 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
              | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_19551),hAPP(c_List_Oset(tc_Nat_Onat),U_19557))) )
          & U_19555 = 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_19555),U_19557) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK477]),skolemize(U_19552,sK477(U_19558,U_19556))],[f_4686_3]) ).

fof(f_4686_5,plain,
    ( ! [U_19558,U_19556] :
        ( sK477(U_19558,U_19556) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1190(U_19558,U_19556) )
    & ! [U_19558,U_19556] :
        ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK477(U_19558,U_19556)),hAPP(c_List_Oset(tc_Nat_Onat),U_19558)))
        | ~ sP1190(U_19558,U_19556) )
    & ! [U_19551,U_19555,U_19557] :
        ( U_19551 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_19551),hAPP(c_List_Oset(tc_Nat_Onat),U_19557)))
        | ~ sP1189(U_19551,U_19555,U_19557) )
    & ! [U_19551,U_19555,U_19557] :
        ( U_19555 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1189(U_19551,U_19555,U_19557) )
    & ! [U_19558,U_19556] :
        ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19556),U_19558) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | sP1190(U_19558,U_19556)
        | U_19556 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) )
    & ! [U_19551,U_19555,U_19557] :
        ( sP1189(U_19551,U_19555,U_19557)
        | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19555),U_19557) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1189,sP1190])],[f_4686_4]) ).

cnf(f_4686_6,plain,
    ( sP1189(U_19551,U_19555,U_19557)
    | hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19555),U_19557) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4686_5]) ).

cnf(f_4686_7,plain,
    ( hAPP(c_List_Ofoldl(tc_Nat_Onat,tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_19556),U_19558) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | sP1190(U_19558,U_19556)
    | U_19556 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4686_5]) ).

cnf(f_4686_8,plain,
    ( U_19555 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1189(U_19551,U_19555,U_19557) ),
    inference(clausify,[status(thm)],[f_4686_5]) ).

cnf(f_4686_9,plain,
    ( U_19551 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_19551),hAPP(c_List_Oset(tc_Nat_Onat),U_19557)))
    | ~ sP1189(U_19551,U_19555,U_19557) ),
    inference(clausify,[status(thm)],[f_4686_5]) ).

cnf(f_4686_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),sK477(U_19558,U_19556)),hAPP(c_List_Oset(tc_Nat_Onat),U_19558)))
    | ~ sP1190(U_19558,U_19556) ),
    inference(clausify,[status(thm)],[f_4686_5]) ).

cnf(f_4686_11,plain,
    ( sK477(U_19558,U_19556) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1190(U_19558,U_19556) ),
    inference(clausify,[status(thm)],[f_4686_5]) ).

fof(f_4687_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_4687_2,plain,
    ! [U_19560,U_19559] : c_List_Olist_Olist__size(U_19559,U_19560,c_List_Olist_ONil(U_19559)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_4687_1]) ).

fof(f_4687_3,plain,
    ! [U_19560,U_19559] : c_List_Olist_Olist__size(U_19559,U_19560,c_List_Olist_ONil(U_19559)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_4687_2]) ).

cnf(f_4687_4,plain,
    c_List_Olist_Olist__size(U_19559,U_19560,c_List_Olist_ONil(U_19559)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4687_3]) ).

fof(f_4688_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_4688_2,plain,
    ! [U_19565,U_19564,U_19563,U_19562,U_19561] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_19561,U_19562,U_19563),U_19564),hAPP(c_List_Oset(U_19561),U_19565)) = hAPP(c_List_Ofoldl(U_19562,U_19561,hAPP(c_COMBC(U_19561,U_19562,U_19562),U_19563),U_19564),U_19565)
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_19561,U_19562,U_19563) ),
    inference(variable_rename,[status(thm)],[f_4688_1]) ).

fof(f_4688_3,plain,
    ! [U_19562,U_19561,U_19563,U_19564,U_19565] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_19561,U_19562,U_19563),U_19564),hAPP(c_List_Oset(U_19561),U_19565)) = hAPP(c_List_Ofoldl(U_19562,U_19561,hAPP(c_COMBC(U_19561,U_19562,U_19562),U_19563),U_19564),U_19565)
      | ~ c_Finite__Set_Ofun__left__comm__idem(U_19561,U_19562,U_19563) ),
    inference(definitional_conversion,[status(esa)],[f_4688_2]) ).

cnf(f_4688_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_19561,U_19562,U_19563),U_19564),hAPP(c_List_Oset(U_19561),U_19565)) = hAPP(c_List_Ofoldl(U_19562,U_19561,hAPP(c_COMBC(U_19561,U_19562,U_19562),U_19563),U_19564),U_19565)
    | ~ c_Finite__Set_Ofun__left__comm__idem(U_19561,U_19562,U_19563) ),
    inference(clausify,[status(thm)],[f_4688_3]) ).

fof(f_4689_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_4689_2,plain,
    ! [U_19567,U_19566] :
      ( c_Complete__Lattice_OSup__class_OSup(U_19566,hAPP(c_List_Oset(U_19566),U_19567)) = hAPP(c_List_Ofoldl(U_19566,U_19566,c_Lattices_Osemilattice__sup__class_Osup(U_19566),c_Orderings_Obot__class_Obot(U_19566)),U_19567)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19566) ),
    inference(variable_rename,[status(thm)],[f_4689_1]) ).

fof(f_4689_3,plain,
    ! [U_19567,U_19566] :
      ( c_Complete__Lattice_OSup__class_OSup(U_19566,hAPP(c_List_Oset(U_19566),U_19567)) = hAPP(c_List_Ofoldl(U_19566,U_19566,c_Lattices_Osemilattice__sup__class_Osup(U_19566),c_Orderings_Obot__class_Obot(U_19566)),U_19567)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19566) ),
    inference(definitional_conversion,[status(esa)],[f_4689_2]) ).

cnf(f_4689_4,plain,
    ( c_Complete__Lattice_OSup__class_OSup(U_19566,hAPP(c_List_Oset(U_19566),U_19567)) = hAPP(c_List_Ofoldl(U_19566,U_19566,c_Lattices_Osemilattice__sup__class_Osup(U_19566),c_Orderings_Obot__class_Obot(U_19566)),U_19567)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_19566) ),
    inference(clausify,[status(thm)],[f_4689_3]) ).

fof(f_4690_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_4690_2,plain,
    ! [U_19569,U_19568] :
      ( c_Complete__Lattice_OInf__class_OInf(U_19568,hAPP(c_List_Oset(U_19568),U_19569)) = hAPP(c_List_Ofoldl(U_19568,U_19568,c_Lattices_Osemilattice__inf__class_Oinf(U_19568),c_Orderings_Otop__class_Otop(U_19568)),U_19569)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19568) ),
    inference(variable_rename,[status(thm)],[f_4690_1]) ).

fof(f_4690_3,plain,
    ! [U_19568,U_19569] :
      ( c_Complete__Lattice_OInf__class_OInf(U_19568,hAPP(c_List_Oset(U_19568),U_19569)) = hAPP(c_List_Ofoldl(U_19568,U_19568,c_Lattices_Osemilattice__inf__class_Oinf(U_19568),c_Orderings_Otop__class_Otop(U_19568)),U_19569)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19568) ),
    inference(definitional_conversion,[status(esa)],[f_4690_2]) ).

cnf(f_4690_4,plain,
    ( c_Complete__Lattice_OInf__class_OInf(U_19568,hAPP(c_List_Oset(U_19568),U_19569)) = hAPP(c_List_Ofoldl(U_19568,U_19568,c_Lattices_Osemilattice__inf__class_Oinf(U_19568),c_Orderings_Otop__class_Otop(U_19568)),U_19569)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_19568) ),
    inference(clausify,[status(thm)],[f_4690_3]) ).

fof(f_4691_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_4691_2,plain,
    ! [U_19572,U_19571,U_19570] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_19570,hAPP(c_List_Oset(U_19570),hAPP(hAPP(c_List_Olist_OCons(U_19570),U_19571),U_19572))) = hAPP(c_List_Ofoldl(U_19570,U_19570,c_Lattices_Osemilattice__sup__class_Osup(U_19570),U_19571),U_19572)
      | ~ class_Lattices_Olattice(U_19570) ),
    inference(variable_rename,[status(thm)],[f_4691_1]) ).

fof(f_4691_3,plain,
    ! [U_19570,U_19571,U_19572] :
      ( c_Big__Operators_Olattice__class_OSup__fin(U_19570,hAPP(c_List_Oset(U_19570),hAPP(hAPP(c_List_Olist_OCons(U_19570),U_19571),U_19572))) = hAPP(c_List_Ofoldl(U_19570,U_19570,c_Lattices_Osemilattice__sup__class_Osup(U_19570),U_19571),U_19572)
      | ~ class_Lattices_Olattice(U_19570) ),
    inference(definitional_conversion,[status(esa)],[f_4691_2]) ).

cnf(f_4691_4,plain,
    ( c_Big__Operators_Olattice__class_OSup__fin(U_19570,hAPP(c_List_Oset(U_19570),hAPP(hAPP(c_List_Olist_OCons(U_19570),U_19571),U_19572))) = hAPP(c_List_Ofoldl(U_19570,U_19570,c_Lattices_Osemilattice__sup__class_Osup(U_19570),U_19571),U_19572)
    | ~ class_Lattices_Olattice(U_19570) ),
    inference(clausify,[status(thm)],[f_4691_3]) ).

fof(f_4692_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_4692_2,plain,
    ! [U_19575,U_19574,U_19573] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_19573,hAPP(c_List_Oset(U_19573),hAPP(hAPP(c_List_Olist_OCons(U_19573),U_19574),U_19575))) = hAPP(c_List_Ofoldl(U_19573,U_19573,c_Lattices_Osemilattice__inf__class_Oinf(U_19573),U_19574),U_19575)
      | ~ class_Lattices_Olattice(U_19573) ),
    inference(variable_rename,[status(thm)],[f_4692_1]) ).

fof(f_4692_3,plain,
    ! [U_19573,U_19574,U_19575] :
      ( c_Big__Operators_Olattice__class_OInf__fin(U_19573,hAPP(c_List_Oset(U_19573),hAPP(hAPP(c_List_Olist_OCons(U_19573),U_19574),U_19575))) = hAPP(c_List_Ofoldl(U_19573,U_19573,c_Lattices_Osemilattice__inf__class_Oinf(U_19573),U_19574),U_19575)
      | ~ class_Lattices_Olattice(U_19573) ),
    inference(definitional_conversion,[status(esa)],[f_4692_2]) ).

cnf(f_4692_4,plain,
    ( c_Big__Operators_Olattice__class_OInf__fin(U_19573,hAPP(c_List_Oset(U_19573),hAPP(hAPP(c_List_Olist_OCons(U_19573),U_19574),U_19575))) = hAPP(c_List_Ofoldl(U_19573,U_19573,c_Lattices_Osemilattice__inf__class_Oinf(U_19573),U_19574),U_19575)
    | ~ class_Lattices_Olattice(U_19573) ),
    inference(clausify,[status(thm)],[f_4692_3]) ).

fof(f_4693_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_4693_2,plain,
    ! [U_19578,U_19577,U_19576] :
      ( c_Big__Operators_Olinorder__class_OMin(U_19576,hAPP(c_List_Oset(U_19576),hAPP(hAPP(c_List_Olist_OCons(U_19576),U_19577),U_19578))) = hAPP(c_List_Ofoldl(U_19576,U_19576,c_Orderings_Oord__class_Omin(U_19576),U_19577),U_19578)
      | ~ class_Orderings_Olinorder(U_19576) ),
    inference(variable_rename,[status(thm)],[f_4693_1]) ).

fof(f_4693_3,plain,
    ! [U_19576,U_19577,U_19578] :
      ( c_Big__Operators_Olinorder__class_OMin(U_19576,hAPP(c_List_Oset(U_19576),hAPP(hAPP(c_List_Olist_OCons(U_19576),U_19577),U_19578))) = hAPP(c_List_Ofoldl(U_19576,U_19576,c_Orderings_Oord__class_Omin(U_19576),U_19577),U_19578)
      | ~ class_Orderings_Olinorder(U_19576) ),
    inference(definitional_conversion,[status(esa)],[f_4693_2]) ).

cnf(f_4693_4,plain,
    ( c_Big__Operators_Olinorder__class_OMin(U_19576,hAPP(c_List_Oset(U_19576),hAPP(hAPP(c_List_Olist_OCons(U_19576),U_19577),U_19578))) = hAPP(c_List_Ofoldl(U_19576,U_19576,c_Orderings_Oord__class_Omin(U_19576),U_19577),U_19578)
    | ~ class_Orderings_Olinorder(U_19576) ),
    inference(clausify,[status(thm)],[f_4693_3]) ).

fof(f_4694_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_4694_2,plain,
    ! [U_19581,U_19580,U_19579] :
      ( c_Big__Operators_Olinorder__class_OMax(U_19579,hAPP(c_List_Oset(U_19579),hAPP(hAPP(c_List_Olist_OCons(U_19579),U_19580),U_19581))) = hAPP(c_List_Ofoldl(U_19579,U_19579,c_Orderings_Oord__class_Omax(U_19579),U_19580),U_19581)
      | ~ class_Orderings_Olinorder(U_19579) ),
    inference(variable_rename,[status(thm)],[f_4694_1]) ).

fof(f_4694_3,plain,
    ! [U_19579,U_19580,U_19581] :
      ( c_Big__Operators_Olinorder__class_OMax(U_19579,hAPP(c_List_Oset(U_19579),hAPP(hAPP(c_List_Olist_OCons(U_19579),U_19580),U_19581))) = hAPP(c_List_Ofoldl(U_19579,U_19579,c_Orderings_Oord__class_Omax(U_19579),U_19580),U_19581)
      | ~ class_Orderings_Olinorder(U_19579) ),
    inference(definitional_conversion,[status(esa)],[f_4694_2]) ).

cnf(f_4694_4,plain,
    ( c_Big__Operators_Olinorder__class_OMax(U_19579,hAPP(c_List_Oset(U_19579),hAPP(hAPP(c_List_Olist_OCons(U_19579),U_19580),U_19581))) = hAPP(c_List_Ofoldl(U_19579,U_19579,c_Orderings_Oord__class_Omax(U_19579),U_19580),U_19581)
    | ~ class_Orderings_Olinorder(U_19579) ),
    inference(clausify,[status(thm)],[f_4694_3]) ).

fof(f_4695_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_4695_2,plain,
    ! [U_19584,U_19583,U_19582] :
      ( c_Big__Operators_Olattice_OInf__fin(U_19582,c_Orderings_Oord__class_Omin(U_19582),hAPP(c_List_Oset(U_19582),hAPP(hAPP(c_List_Olist_OCons(U_19582),U_19583),U_19584))) = hAPP(c_List_Ofoldl(U_19582,U_19582,c_Orderings_Oord__class_Omin(U_19582),U_19583),U_19584)
      | ~ class_Orderings_Olinorder(U_19582) ),
    inference(variable_rename,[status(thm)],[f_4695_1]) ).

fof(f_4695_3,plain,
    ! [U_19582,U_19583,U_19584] :
      ( c_Big__Operators_Olattice_OInf__fin(U_19582,c_Orderings_Oord__class_Omin(U_19582),hAPP(c_List_Oset(U_19582),hAPP(hAPP(c_List_Olist_OCons(U_19582),U_19583),U_19584))) = hAPP(c_List_Ofoldl(U_19582,U_19582,c_Orderings_Oord__class_Omin(U_19582),U_19583),U_19584)
      | ~ class_Orderings_Olinorder(U_19582) ),
    inference(definitional_conversion,[status(esa)],[f_4695_2]) ).

cnf(f_4695_4,plain,
    ( c_Big__Operators_Olattice_OInf__fin(U_19582,c_Orderings_Oord__class_Omin(U_19582),hAPP(c_List_Oset(U_19582),hAPP(hAPP(c_List_Olist_OCons(U_19582),U_19583),U_19584))) = hAPP(c_List_Ofoldl(U_19582,U_19582,c_Orderings_Oord__class_Omin(U_19582),U_19583),U_19584)
    | ~ class_Orderings_Olinorder(U_19582) ),
    inference(clausify,[status(thm)],[f_4695_3]) ).

fof(f_4696_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_4696_2,plain,
    ! [U_19587,U_19586,U_19585] :
      ( c_Big__Operators_Olattice_OSup__fin(U_19585,c_Orderings_Oord__class_Omax(U_19585),hAPP(c_List_Oset(U_19585),hAPP(hAPP(c_List_Olist_OCons(U_19585),U_19586),U_19587))) = hAPP(c_List_Ofoldl(U_19585,U_19585,c_Orderings_Oord__class_Omax(U_19585),U_19586),U_19587)
      | ~ class_Orderings_Olinorder(U_19585) ),
    inference(variable_rename,[status(thm)],[f_4696_1]) ).

fof(f_4696_3,plain,
    ! [U_19585,U_19586,U_19587] :
      ( c_Big__Operators_Olattice_OSup__fin(U_19585,c_Orderings_Oord__class_Omax(U_19585),hAPP(c_List_Oset(U_19585),hAPP(hAPP(c_List_Olist_OCons(U_19585),U_19586),U_19587))) = hAPP(c_List_Ofoldl(U_19585,U_19585,c_Orderings_Oord__class_Omax(U_19585),U_19586),U_19587)
      | ~ class_Orderings_Olinorder(U_19585) ),
    inference(definitional_conversion,[status(esa)],[f_4696_2]) ).

cnf(f_4696_4,plain,
    ( c_Big__Operators_Olattice_OSup__fin(U_19585,c_Orderings_Oord__class_Omax(U_19585),hAPP(c_List_Oset(U_19585),hAPP(hAPP(c_List_Olist_OCons(U_19585),U_19586),U_19587))) = hAPP(c_List_Ofoldl(U_19585,U_19585,c_Orderings_Oord__class_Omax(U_19585),U_19586),U_19587)
    | ~ class_Orderings_Olinorder(U_19585) ),
    inference(clausify,[status(thm)],[f_4696_3]) ).

fof(f_4697_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_4697_2,plain,
    ! [U_19591,U_19590,U_19589,U_19588] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19589,U_19588),hAPP(c_List_Oset(U_19589),U_19590)),U_19591) = hAPP(c_List_Ofoldl(U_19588,U_19589,hAPP(c_COMBC(U_19589,U_19588,U_19588),hAPP(hAPP(c_COMBB(U_19588,tc_fun(U_19588,U_19588),U_19589),c_Lattices_Osemilattice__sup__class_Osup(U_19588)),U_19591)),c_Orderings_Obot__class_Obot(U_19588)),U_19590)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19588) ),
    inference(variable_rename,[status(thm)],[f_4697_1]) ).

fof(f_4697_3,plain,
    ! [U_19588,U_19589,U_19590,U_19591] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19589,U_19588),hAPP(c_List_Oset(U_19589),U_19590)),U_19591) = hAPP(c_List_Ofoldl(U_19588,U_19589,hAPP(c_COMBC(U_19589,U_19588,U_19588),hAPP(hAPP(c_COMBB(U_19588,tc_fun(U_19588,U_19588),U_19589),c_Lattices_Osemilattice__sup__class_Osup(U_19588)),U_19591)),c_Orderings_Obot__class_Obot(U_19588)),U_19590)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19588) ),
    inference(definitional_conversion,[status(esa)],[f_4697_2]) ).

cnf(f_4697_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(U_19589,U_19588),hAPP(c_List_Oset(U_19589),U_19590)),U_19591) = hAPP(c_List_Ofoldl(U_19588,U_19589,hAPP(c_COMBC(U_19589,U_19588,U_19588),hAPP(hAPP(c_COMBB(U_19588,tc_fun(U_19588,U_19588),U_19589),c_Lattices_Osemilattice__sup__class_Osup(U_19588)),U_19591)),c_Orderings_Obot__class_Obot(U_19588)),U_19590)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_19588) ),
    inference(clausify,[status(thm)],[f_4697_3]) ).

fof(f_4698_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_4698_2,plain,
    ! [U_19595,U_19594,U_19593,U_19592] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19593,U_19592),hAPP(c_List_Oset(U_19593),U_19594)),U_19595) = hAPP(c_List_Ofoldl(U_19592,U_19593,hAPP(c_COMBC(U_19593,U_19592,U_19592),hAPP(hAPP(c_COMBB(U_19592,tc_fun(U_19592,U_19592),U_19593),c_Lattices_Osemilattice__inf__class_Oinf(U_19592)),U_19595)),c_Orderings_Otop__class_Otop(U_19592)),U_19594)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19592) ),
    inference(variable_rename,[status(thm)],[f_4698_1]) ).

fof(f_4698_3,plain,
    ! [U_19592,U_19593,U_19594,U_19595] :
      ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19593,U_19592),hAPP(c_List_Oset(U_19593),U_19594)),U_19595) = hAPP(c_List_Ofoldl(U_19592,U_19593,hAPP(c_COMBC(U_19593,U_19592,U_19592),hAPP(hAPP(c_COMBB(U_19592,tc_fun(U_19592,U_19592),U_19593),c_Lattices_Osemilattice__inf__class_Oinf(U_19592)),U_19595)),c_Orderings_Otop__class_Otop(U_19592)),U_19594)
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_19592) ),
    inference(definitional_conversion,[status(esa)],[f_4698_2]) ).

cnf(f_4698_4,plain,
    ( hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(U_19593,U_19592),hAPP(c_List_Oset(U_19593),U_19594)),U_19595) = hAPP(c_List_Ofoldl(U_19592,U_19593,hAPP(c_COMBC(U_19593,U_19592,U_19592),hAPP(hAPP(c_COMBB(U_19592,tc_fun(U_19592,U_19592),U_19593),c_Lattices_Osemilattice__inf__class_Oinf(U_19592)),U_19595)),c_Orderings_Otop__class_Otop(U_19592)),U_19594)
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_19592) ),
    inference(clausify,[status(thm)],[f_4698_3]) ).

fof(f_4699_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_4699_2,plain,
    ! [U_19600,U_19599,U_19598,U_19597,U_19596] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19599),c_List_Olist_Olist__size(U_19596,U_19600,U_19598)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19599),hAPP(U_19600,U_19597)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19596),U_19597),hAPP(c_List_Oset(U_19596),U_19598))) ),
    inference(variable_rename,[status(thm)],[f_4699_1]) ).

fof(f_4699_3,plain,
    ! [U_19596,U_19597,U_19598,U_19599,U_19600] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19599),c_List_Olist_Olist__size(U_19596,U_19600,U_19598)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19599),hAPP(U_19600,U_19597)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19596),U_19597),hAPP(c_List_Oset(U_19596),U_19598))) ),
    inference(definitional_conversion,[status(esa)],[f_4699_2]) ).

cnf(f_4699_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19599),c_List_Olist_Olist__size(U_19596,U_19600,U_19598)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19599),hAPP(U_19600,U_19597)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19596),U_19597),hAPP(c_List_Oset(U_19596),U_19598))) ),
    inference(clausify,[status(thm)],[f_4699_3]) ).

fof(f_4700_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_4700_2,plain,
    ! [U_19605,U_19604,U_19603,U_19602,U_19601] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19604),c_List_Olist_Olist__size(U_19601,U_19605,U_19603)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19604),hAPP(U_19605,U_19602)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19601),U_19602),hAPP(c_List_Oset(U_19601),U_19603))) ),
    inference(variable_rename,[status(thm)],[f_4700_1]) ).

fof(f_4700_3,plain,
    ! [U_19601,U_19602,U_19603,U_19604,U_19605] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19604),c_List_Olist_Olist__size(U_19601,U_19605,U_19603)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19604),hAPP(U_19605,U_19602)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19601),U_19602),hAPP(c_List_Oset(U_19601),U_19603))) ),
    inference(definitional_conversion,[status(esa)],[f_4700_2]) ).

cnf(f_4700_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19604),c_List_Olist_Olist__size(U_19601,U_19605,U_19603)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19604),hAPP(U_19605,U_19602)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19601),U_19602),hAPP(c_List_Oset(U_19601),U_19603))) ),
    inference(clausify,[status(thm)],[f_4700_3]) ).

fof(f_4701_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_4701_2,plain,
    ! [U_19610,U_19609,U_19608,U_19607,U_19606] : c_Map_Omap__upds(U_19606,U_19607,U_19608,U_19609,U_19610) = hAPP(c_List_Ofoldl(tc_fun(U_19606,tc_Option_Ooption(U_19607)),tc_prod(U_19606,U_19607),hAPP(hAPP(c_COMBB(tc_fun(U_19606,tc_fun(U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607)))),tc_fun(tc_prod(U_19606,U_19607),tc_fun(U_19606,tc_Option_Ooption(U_19607))),tc_fun(U_19606,tc_Option_Ooption(U_19607))),c_Product__Type_Oprod_Oprod__case(U_19606,U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607)))),hAPP(hAPP(c_COMBC(tc_fun(U_19606,tc_Option_Ooption(U_19607)),tc_fun(U_19607,tc_Option_Ooption(U_19607)),tc_fun(U_19606,tc_fun(U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607))))),hAPP(hAPP(c_COMBB(tc_fun(U_19606,tc_fun(tc_fun(U_19607,tc_Option_Ooption(U_19607)),tc_fun(U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607))))),tc_fun(tc_fun(U_19607,tc_Option_Ooption(U_19607)),tc_fun(U_19606,tc_fun(U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607))))),tc_fun(U_19606,tc_Option_Ooption(U_19607))),c_COMBC(U_19606,tc_fun(U_19607,tc_Option_Ooption(U_19607)),tc_fun(U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607))))),hAPP(hAPP(c_COMBB(tc_fun(U_19606,tc_fun(tc_Option_Ooption(U_19607),tc_fun(U_19606,tc_Option_Ooption(U_19607)))),tc_fun(U_19606,tc_fun(tc_fun(U_19607,tc_Option_Ooption(U_19607)),tc_fun(U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607))))),tc_fun(U_19606,tc_Option_Ooption(U_19607))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_19607),tc_fun(U_19606,tc_Option_Ooption(U_19607))),tc_fun(tc_fun(U_19607,tc_Option_Ooption(U_19607)),tc_fun(U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607)))),U_19606),c_COMBB(tc_Option_Ooption(U_19607),tc_fun(U_19606,tc_Option_Ooption(U_19607)),U_19607))),c_Fun_Ofun__upd(U_19606,tc_Option_Ooption(U_19607))))),c_Option_Ooption_OSome(U_19607))),U_19608),hAPP(hAPP(c_List_Ozip(U_19606,U_19607),U_19609),U_19610)),
    inference(variable_rename,[status(thm)],[f_4701_1]) ).

fof(f_4701_3,plain,
    ! [U_19606,U_19607,U_19608,U_19609,U_19610] : c_Map_Omap__upds(U_19606,U_19607,U_19608,U_19609,U_19610) = hAPP(c_List_Ofoldl(tc_fun(U_19606,tc_Option_Ooption(U_19607)),tc_prod(U_19606,U_19607),hAPP(hAPP(c_COMBB(tc_fun(U_19606,tc_fun(U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607)))),tc_fun(tc_prod(U_19606,U_19607),tc_fun(U_19606,tc_Option_Ooption(U_19607))),tc_fun(U_19606,tc_Option_Ooption(U_19607))),c_Product__Type_Oprod_Oprod__case(U_19606,U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607)))),hAPP(hAPP(c_COMBC(tc_fun(U_19606,tc_Option_Ooption(U_19607)),tc_fun(U_19607,tc_Option_Ooption(U_19607)),tc_fun(U_19606,tc_fun(U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607))))),hAPP(hAPP(c_COMBB(tc_fun(U_19606,tc_fun(tc_fun(U_19607,tc_Option_Ooption(U_19607)),tc_fun(U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607))))),tc_fun(tc_fun(U_19607,tc_Option_Ooption(U_19607)),tc_fun(U_19606,tc_fun(U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607))))),tc_fun(U_19606,tc_Option_Ooption(U_19607))),c_COMBC(U_19606,tc_fun(U_19607,tc_Option_Ooption(U_19607)),tc_fun(U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607))))),hAPP(hAPP(c_COMBB(tc_fun(U_19606,tc_fun(tc_Option_Ooption(U_19607),tc_fun(U_19606,tc_Option_Ooption(U_19607)))),tc_fun(U_19606,tc_fun(tc_fun(U_19607,tc_Option_Ooption(U_19607)),tc_fun(U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607))))),tc_fun(U_19606,tc_Option_Ooption(U_19607))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_19607),tc_fun(U_19606,tc_Option_Ooption(U_19607))),tc_fun(tc_fun(U_19607,tc_Option_Ooption(U_19607)),tc_fun(U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607)))),U_19606),c_COMBB(tc_Option_Ooption(U_19607),tc_fun(U_19606,tc_Option_Ooption(U_19607)),U_19607))),c_Fun_Ofun__upd(U_19606,tc_Option_Ooption(U_19607))))),c_Option_Ooption_OSome(U_19607))),U_19608),hAPP(hAPP(c_List_Ozip(U_19606,U_19607),U_19609),U_19610)),
    inference(definitional_conversion,[status(esa)],[f_4701_2]) ).

cnf(f_4701_4,plain,
    c_Map_Omap__upds(U_19606,U_19607,U_19608,U_19609,U_19610) = hAPP(c_List_Ofoldl(tc_fun(U_19606,tc_Option_Ooption(U_19607)),tc_prod(U_19606,U_19607),hAPP(hAPP(c_COMBB(tc_fun(U_19606,tc_fun(U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607)))),tc_fun(tc_prod(U_19606,U_19607),tc_fun(U_19606,tc_Option_Ooption(U_19607))),tc_fun(U_19606,tc_Option_Ooption(U_19607))),c_Product__Type_Oprod_Oprod__case(U_19606,U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607)))),hAPP(hAPP(c_COMBC(tc_fun(U_19606,tc_Option_Ooption(U_19607)),tc_fun(U_19607,tc_Option_Ooption(U_19607)),tc_fun(U_19606,tc_fun(U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607))))),hAPP(hAPP(c_COMBB(tc_fun(U_19606,tc_fun(tc_fun(U_19607,tc_Option_Ooption(U_19607)),tc_fun(U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607))))),tc_fun(tc_fun(U_19607,tc_Option_Ooption(U_19607)),tc_fun(U_19606,tc_fun(U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607))))),tc_fun(U_19606,tc_Option_Ooption(U_19607))),c_COMBC(U_19606,tc_fun(U_19607,tc_Option_Ooption(U_19607)),tc_fun(U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607))))),hAPP(hAPP(c_COMBB(tc_fun(U_19606,tc_fun(tc_Option_Ooption(U_19607),tc_fun(U_19606,tc_Option_Ooption(U_19607)))),tc_fun(U_19606,tc_fun(tc_fun(U_19607,tc_Option_Ooption(U_19607)),tc_fun(U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607))))),tc_fun(U_19606,tc_Option_Ooption(U_19607))),hAPP(c_COMBB(tc_fun(tc_Option_Ooption(U_19607),tc_fun(U_19606,tc_Option_Ooption(U_19607))),tc_fun(tc_fun(U_19607,tc_Option_Ooption(U_19607)),tc_fun(U_19607,tc_fun(U_19606,tc_Option_Ooption(U_19607)))),U_19606),c_COMBB(tc_Option_Ooption(U_19607),tc_fun(U_19606,tc_Option_Ooption(U_19607)),U_19607))),c_Fun_Ofun__upd(U_19606,tc_Option_Ooption(U_19607))))),c_Option_Ooption_OSome(U_19607))),U_19608),hAPP(hAPP(c_List_Ozip(U_19606,U_19607),U_19609),U_19610)),
    inference(clausify,[status(thm)],[f_4701_3]) ).

fof(f_4702_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_4702_2,plain,
    ! [U_19612,U_19611] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19611),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_19612)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_19611),hAPP(c_List_Oset(tc_Nat_Onat),U_19612))) ),
    inference(variable_rename,[status(thm)],[f_4702_1]) ).

fof(f_4702_3,plain,
    ! [U_19611,U_19612] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19611),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_19612)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_19611),hAPP(c_List_Oset(tc_Nat_Onat),U_19612))) ),
    inference(definitional_conversion,[status(esa)],[f_4702_2]) ).

cnf(f_4702_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19611),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_19612)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),U_19611),hAPP(c_List_Oset(tc_Nat_Onat),U_19612))) ),
    inference(clausify,[status(thm)],[f_4702_3]) ).

fof(f_4703_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_4703_2,plain,
    ! [U_19615,U_19614,U_19613] : c_List_Olist_Olist__size(U_19613,U_19614,U_19615) = 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_19613,tc_Nat_Onat),U_19614),U_19615))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19613)),U_19615)),
    inference(variable_rename,[status(thm)],[f_4703_1]) ).

fof(f_4703_3,plain,
    ! [U_19613,U_19614,U_19615] : c_List_Olist_Olist__size(U_19613,U_19614,U_19615) = 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_19613,tc_Nat_Onat),U_19614),U_19615))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19613)),U_19615)),
    inference(definitional_conversion,[status(esa)],[f_4703_2]) ).

cnf(f_4703_4,plain,
    c_List_Olist_Olist__size(U_19613,U_19614,U_19615) = 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_19613,tc_Nat_Onat),U_19614),U_19615))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19613)),U_19615)),
    inference(clausify,[status(thm)],[f_4703_3]) ).

fof(f_4704_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_4704_2,plain,
    ! [U_19618,U_19617,U_19616] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19616),tc_List_Olist(U_19616)),tc_HOL_Obool)),c_List_Olistrel(U_19616,U_19617)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(U_19616),tc_List_Olist(U_19616)),c_List_Olists(U_19616,U_19618)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_19616),tc_HOL_Obool),tc_List_Olist(U_19616)),c_List_Olists(U_19616,U_19618)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19616,U_19616),tc_HOL_Obool)),U_19617),hAPP(hAPP(c_Product__Type_OSigma(U_19616,U_19616),U_19618),hAPP(c_COMBK(tc_fun(U_19616,tc_HOL_Obool),U_19616),U_19618)))) ),
    inference(variable_rename,[status(thm)],[f_4704_1]) ).

fof(f_4704_3,plain,
    ! [U_19616,U_19617,U_19618] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19616),tc_List_Olist(U_19616)),tc_HOL_Obool)),c_List_Olistrel(U_19616,U_19617)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(U_19616),tc_List_Olist(U_19616)),c_List_Olists(U_19616,U_19618)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_19616),tc_HOL_Obool),tc_List_Olist(U_19616)),c_List_Olists(U_19616,U_19618)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19616,U_19616),tc_HOL_Obool)),U_19617),hAPP(hAPP(c_Product__Type_OSigma(U_19616,U_19616),U_19618),hAPP(c_COMBK(tc_fun(U_19616,tc_HOL_Obool),U_19616),U_19618)))) ),
    inference(definitional_conversion,[status(esa)],[f_4704_2]) ).

cnf(f_4704_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(tc_List_Olist(U_19616),tc_List_Olist(U_19616)),tc_HOL_Obool)),c_List_Olistrel(U_19616,U_19617)),hAPP(hAPP(c_Product__Type_OSigma(tc_List_Olist(U_19616),tc_List_Olist(U_19616)),c_List_Olists(U_19616,U_19618)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_19616),tc_HOL_Obool),tc_List_Olist(U_19616)),c_List_Olists(U_19616,U_19618)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_prod(U_19616,U_19616),tc_HOL_Obool)),U_19617),hAPP(hAPP(c_Product__Type_OSigma(U_19616,U_19616),U_19618),hAPP(c_COMBK(tc_fun(U_19616,tc_HOL_Obool),U_19616),U_19618)))) ),
    inference(clausify,[status(thm)],[f_4704_3]) ).

fof(f_4705_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_4705_2,plain,
    ! [U_19621,U_19620,U_19619] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19619)),U_19620),c_List_Olists(U_19619,c_Wellfounded_Oacc(U_19619,U_19621))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19619)),U_19620),c_Wellfounded_Oacc(tc_List_Olist(U_19619),c_List_Olistrel1(U_19619,U_19621)))) ),
    inference(variable_rename,[status(thm)],[f_4705_1]) ).

fof(f_4705_3,plain,
    ! [U_19619,U_19620,U_19621] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19619)),U_19620),c_List_Olists(U_19619,c_Wellfounded_Oacc(U_19619,U_19621))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19619)),U_19620),c_Wellfounded_Oacc(tc_List_Olist(U_19619),c_List_Olistrel1(U_19619,U_19621)))) ),
    inference(definitional_conversion,[status(esa)],[f_4705_2]) ).

cnf(f_4705_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19619)),U_19620),c_List_Olists(U_19619,c_Wellfounded_Oacc(U_19619,U_19621))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19619)),U_19620),c_Wellfounded_Oacc(tc_List_Olist(U_19619),c_List_Olistrel1(U_19619,U_19621)))) ),
    inference(clausify,[status(thm)],[f_4705_3]) ).

fof(f_4706_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_4706_2,plain,
    ! [U_19623,U_19622] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19622)),c_List_Olist_ONil(U_19622)),c_List_Olists(U_19622,U_19623))),
    inference(variable_rename,[status(thm)],[f_4706_1]) ).

fof(f_4706_3,plain,
    ! [U_19622,U_19623] : hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19622)),c_List_Olist_ONil(U_19622)),c_List_Olists(U_19622,U_19623))),
    inference(definitional_conversion,[status(esa)],[f_4706_2]) ).

cnf(f_4706_4,plain,
    hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19622)),c_List_Olist_ONil(U_19622)),c_List_Olists(U_19622,U_19623))),
    inference(clausify,[status(thm)],[f_4706_3]) ).

fof(f_4707_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_4707_2,plain,
    ! [U_19626,U_19625,U_19624] :
      ( c_Equiv__Relations_Oequiv(tc_List_Olist(U_19624),c_List_Olists(U_19624,U_19625),c_List_Olistrel(U_19624,U_19626))
      | ~ c_Equiv__Relations_Oequiv(U_19624,U_19625,U_19626) ),
    inference(variable_rename,[status(thm)],[f_4707_1]) ).

fof(f_4707_3,plain,
    ! [U_19624,U_19625,U_19626] :
      ( c_Equiv__Relations_Oequiv(tc_List_Olist(U_19624),c_List_Olists(U_19624,U_19625),c_List_Olistrel(U_19624,U_19626))
      | ~ c_Equiv__Relations_Oequiv(U_19624,U_19625,U_19626) ),
    inference(definitional_conversion,[status(esa)],[f_4707_2]) ).

cnf(f_4707_4,plain,
    ( c_Equiv__Relations_Oequiv(tc_List_Olist(U_19624),c_List_Olists(U_19624,U_19625),c_List_Olistrel(U_19624,U_19626))
    | ~ c_Equiv__Relations_Oequiv(U_19624,U_19625,U_19626) ),
    inference(clausify,[status(thm)],[f_4707_3]) ).

fof(f_4708_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_4708_2,plain,
    ! [U_19629,U_19628,U_19627] :
      ( c_Relation_Orefl__on(tc_List_Olist(U_19627),c_List_Olists(U_19627,U_19628),c_List_Olistrel(U_19627,U_19629))
      | ~ c_Relation_Orefl__on(U_19627,U_19628,U_19629) ),
    inference(variable_rename,[status(thm)],[f_4708_1]) ).

fof(f_4708_3,plain,
    ! [U_19627,U_19628,U_19629] :
      ( c_Relation_Orefl__on(tc_List_Olist(U_19627),c_List_Olists(U_19627,U_19628),c_List_Olistrel(U_19627,U_19629))
      | ~ c_Relation_Orefl__on(U_19627,U_19628,U_19629) ),
    inference(definitional_conversion,[status(esa)],[f_4708_2]) ).

cnf(f_4708_4,plain,
    ( c_Relation_Orefl__on(tc_List_Olist(U_19627),c_List_Olists(U_19627,U_19628),c_List_Olistrel(U_19627,U_19629))
    | ~ c_Relation_Orefl__on(U_19627,U_19628,U_19629) ),
    inference(clausify,[status(thm)],[f_4708_3]) ).

fof(f_4709_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_4709_2,plain,
    ! [U_19630] : c_List_Olists(U_19630,c_Orderings_Otop__class_Otop(tc_fun(U_19630,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_19630),tc_HOL_Obool)),
    inference(variable_rename,[status(thm)],[f_4709_1]) ).

fof(f_4709_3,plain,
    ! [U_19630] : c_List_Olists(U_19630,c_Orderings_Otop__class_Otop(tc_fun(U_19630,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_19630),tc_HOL_Obool)),
    inference(definitional_conversion,[status(esa)],[f_4709_2]) ).

cnf(f_4709_4,plain,
    c_List_Olists(U_19630,c_Orderings_Otop__class_Otop(tc_fun(U_19630,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(tc_List_Olist(U_19630),tc_HOL_Obool)),
    inference(clausify,[status(thm)],[f_4709_3]) ).

fof(f_4710_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_4710_2,plain,
    ! [U_19633,U_19632,U_19631] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_19631),tc_HOL_Obool)),c_List_Olists(U_19631,U_19632)),c_List_Olists(U_19631,U_19633)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19631,tc_HOL_Obool)),U_19632),U_19633)) ),
    inference(variable_rename,[status(thm)],[f_4710_1]) ).

fof(f_4710_3,plain,
    ! [U_19631,U_19632,U_19633] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_19631),tc_HOL_Obool)),c_List_Olists(U_19631,U_19632)),c_List_Olists(U_19631,U_19633)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19631,tc_HOL_Obool)),U_19632),U_19633)) ),
    inference(definitional_conversion,[status(esa)],[f_4710_2]) ).

cnf(f_4710_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_List_Olist(U_19631),tc_HOL_Obool)),c_List_Olists(U_19631,U_19632)),c_List_Olists(U_19631,U_19633)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19631,tc_HOL_Obool)),U_19632),U_19633)) ),
    inference(clausify,[status(thm)],[f_4710_3]) ).

fof(f_4711_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_4711_2,plain,
    ! [U_19637,U_19636,U_19635,U_19634] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19634)),hAPP(hAPP(c_List_Oappend(U_19634),U_19635),U_19636)),c_List_Olists(U_19634,U_19637)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19634)),U_19636),c_List_Olists(U_19634,U_19637)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19634)),U_19635),c_List_Olists(U_19634,U_19637))) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19634)),U_19636),c_List_Olists(U_19634,U_19637)))
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19634)),U_19635),c_List_Olists(U_19634,U_19637))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19634)),hAPP(hAPP(c_List_Oappend(U_19634),U_19635),U_19636)),c_List_Olists(U_19634,U_19637))) ) ),
    inference(variable_rename,[status(thm)],[f_4711_1]) ).

fof(f_4711_3,plain,
    ( ! [U_19645,U_19643,U_19641,U_19639] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19639)),hAPP(hAPP(c_List_Oappend(U_19639),U_19641),U_19643)),c_List_Olists(U_19639,U_19645)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19639)),U_19643),c_List_Olists(U_19639,U_19645)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19639)),U_19641),c_List_Olists(U_19639,U_19645))) )
    & ! [U_19644,U_19642,U_19640,U_19638] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19638)),U_19642),c_List_Olists(U_19638,U_19644)))
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19638)),U_19640),c_List_Olists(U_19638,U_19644))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19638)),hAPP(hAPP(c_List_Oappend(U_19638),U_19640),U_19642)),c_List_Olists(U_19638,U_19644))) ) ),
    inference(miniscope,[status(thm)],[f_4711_2]) ).

fof(f_4711_4,plain,
    ( ! [U_19640,U_19644,U_19638,U_19642] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19638)),U_19642),c_List_Olists(U_19638,U_19644)))
        | ~ sP1191(U_19640,U_19644,U_19638,U_19642) )
    & ! [U_19640,U_19644,U_19638,U_19642] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19638)),U_19640),c_List_Olists(U_19638,U_19644)))
        | ~ sP1191(U_19640,U_19644,U_19638,U_19642) )
    & ! [U_19643,U_19639,U_19645,U_19641] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19639)),hAPP(hAPP(c_List_Oappend(U_19639),U_19641),U_19643)),c_List_Olists(U_19639,U_19645)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19639)),U_19643),c_List_Olists(U_19639,U_19645)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19639)),U_19641),c_List_Olists(U_19639,U_19645))) )
    & ! [U_19640,U_19644,U_19638,U_19642] :
        ( sP1191(U_19640,U_19644,U_19638,U_19642)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19638)),hAPP(hAPP(c_List_Oappend(U_19638),U_19640),U_19642)),c_List_Olists(U_19638,U_19644))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1191])],[f_4711_3]) ).

cnf(f_4711_5,plain,
    ( sP1191(U_19640,U_19644,U_19638,U_19642)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19638)),hAPP(hAPP(c_List_Oappend(U_19638),U_19640),U_19642)),c_List_Olists(U_19638,U_19644))) ),
    inference(clausify,[status(thm)],[f_4711_4]) ).

cnf(f_4711_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19639)),hAPP(hAPP(c_List_Oappend(U_19639),U_19641),U_19643)),c_List_Olists(U_19639,U_19645)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19639)),U_19643),c_List_Olists(U_19639,U_19645)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19639)),U_19641),c_List_Olists(U_19639,U_19645))) ),
    inference(clausify,[status(thm)],[f_4711_4]) ).

cnf(f_4711_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19638)),U_19640),c_List_Olists(U_19638,U_19644)))
    | ~ sP1191(U_19640,U_19644,U_19638,U_19642) ),
    inference(clausify,[status(thm)],[f_4711_4]) ).

cnf(f_4711_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19638)),U_19642),c_List_Olists(U_19638,U_19644)))
    | ~ sP1191(U_19640,U_19644,U_19638,U_19642) ),
    inference(clausify,[status(thm)],[f_4711_4]) ).

fof(f_4712_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_4712_2,plain,
    ! [U_19649,U_19648,U_19647,U_19646] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19646)),hAPP(hAPP(c_List_Olist_OCons(U_19646),U_19647),U_19648)),c_List_Olists(U_19646,U_19649)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19646)),U_19648),c_List_Olists(U_19646,U_19649)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19646),U_19647),U_19649)) )
      & ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19646)),U_19648),c_List_Olists(U_19646,U_19649)))
          & hBOOL(hAPP(hAPP(c_member(U_19646),U_19647),U_19649)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19646)),hAPP(hAPP(c_List_Olist_OCons(U_19646),U_19647),U_19648)),c_List_Olists(U_19646,U_19649))) ) ),
    inference(variable_rename,[status(thm)],[f_4712_1]) ).

fof(f_4712_3,plain,
    ( ! [U_19657,U_19655,U_19653,U_19651] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19651)),hAPP(hAPP(c_List_Olist_OCons(U_19651),U_19653),U_19655)),c_List_Olists(U_19651,U_19657)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19651)),U_19655),c_List_Olists(U_19651,U_19657)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19651),U_19653),U_19657)) )
    & ! [U_19656,U_19654,U_19652,U_19650] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19650)),U_19654),c_List_Olists(U_19650,U_19656)))
          & hBOOL(hAPP(hAPP(c_member(U_19650),U_19652),U_19656)) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19650)),hAPP(hAPP(c_List_Olist_OCons(U_19650),U_19652),U_19654)),c_List_Olists(U_19650,U_19656))) ) ),
    inference(miniscope,[status(thm)],[f_4712_2]) ).

fof(f_4712_4,plain,
    ( ! [U_19652,U_19656,U_19650,U_19654] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19650)),U_19654),c_List_Olists(U_19650,U_19656)))
        | ~ sP1192(U_19652,U_19656,U_19650,U_19654) )
    & ! [U_19652,U_19656,U_19650,U_19654] :
        ( hBOOL(hAPP(hAPP(c_member(U_19650),U_19652),U_19656))
        | ~ sP1192(U_19652,U_19656,U_19650,U_19654) )
    & ! [U_19651,U_19657,U_19653,U_19655] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19651)),hAPP(hAPP(c_List_Olist_OCons(U_19651),U_19653),U_19655)),c_List_Olists(U_19651,U_19657)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19651)),U_19655),c_List_Olists(U_19651,U_19657)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19651),U_19653),U_19657)) )
    & ! [U_19652,U_19656,U_19650,U_19654] :
        ( sP1192(U_19652,U_19656,U_19650,U_19654)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19650)),hAPP(hAPP(c_List_Olist_OCons(U_19650),U_19652),U_19654)),c_List_Olists(U_19650,U_19656))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1192])],[f_4712_3]) ).

cnf(f_4712_5,plain,
    ( sP1192(U_19652,U_19656,U_19650,U_19654)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19650)),hAPP(hAPP(c_List_Olist_OCons(U_19650),U_19652),U_19654)),c_List_Olists(U_19650,U_19656))) ),
    inference(clausify,[status(thm)],[f_4712_4]) ).

cnf(f_4712_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19651)),hAPP(hAPP(c_List_Olist_OCons(U_19651),U_19653),U_19655)),c_List_Olists(U_19651,U_19657)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19651)),U_19655),c_List_Olists(U_19651,U_19657)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19651),U_19653),U_19657)) ),
    inference(clausify,[status(thm)],[f_4712_4]) ).

cnf(f_4712_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19650),U_19652),U_19656))
    | ~ sP1192(U_19652,U_19656,U_19650,U_19654) ),
    inference(clausify,[status(thm)],[f_4712_4]) ).

cnf(f_4712_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19650)),U_19654),c_List_Olists(U_19650,U_19656)))
    | ~ sP1192(U_19652,U_19656,U_19650,U_19654) ),
    inference(clausify,[status(thm)],[f_4712_4]) ).

fof(f_4713_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_4713_2,plain,
    ! [U_19662,U_19661,U_19660] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19660)),U_19661),c_List_Olists(U_19660,U_19662)))
        | ? [U_19659] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_19660),U_19659),U_19662))
            & hBOOL(hAPP(hAPP(c_member(U_19660),U_19659),hAPP(c_List_Oset(U_19660),U_19661))) ) )
      & ( ! [U_19658] :
            ( hBOOL(hAPP(hAPP(c_member(U_19660),U_19658),U_19662))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19660),U_19658),hAPP(c_List_Oset(U_19660),U_19661))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19660)),U_19661),c_List_Olists(U_19660,U_19662))) ) ),
    inference(variable_rename,[status(thm)],[f_4713_1]) ).

fof(f_4713_3,plain,
    ( ! [U_19668,U_19666,U_19664] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19664)),U_19666),c_List_Olists(U_19664,U_19668)))
        | ? [U_19659] :
            ( ~ hBOOL(hAPP(hAPP(c_member(U_19664),U_19659),U_19668))
            & hBOOL(hAPP(hAPP(c_member(U_19664),U_19659),hAPP(c_List_Oset(U_19664),U_19666))) ) )
    & ! [U_19667,U_19665,U_19663] :
        ( ! [U_19658] :
            ( hBOOL(hAPP(hAPP(c_member(U_19663),U_19658),U_19667))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19663),U_19658),hAPP(c_List_Oset(U_19663),U_19665))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19663)),U_19665),c_List_Olists(U_19663,U_19667))) ) ),
    inference(miniscope,[status(thm)],[f_4713_2]) ).

fof(f_4713_4,plain,
    ( ! [U_19668,U_19666,U_19664] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19664)),U_19666),c_List_Olists(U_19664,U_19668)))
        | ( ~ hBOOL(hAPP(hAPP(c_member(U_19664),sK478(U_19668,U_19666,U_19664)),U_19668))
          & hBOOL(hAPP(hAPP(c_member(U_19664),sK478(U_19668,U_19666,U_19664)),hAPP(c_List_Oset(U_19664),U_19666))) ) )
    & ! [U_19667,U_19665,U_19663] :
        ( ! [U_19658] :
            ( hBOOL(hAPP(hAPP(c_member(U_19663),U_19658),U_19667))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19663),U_19658),hAPP(c_List_Oset(U_19663),U_19665))) )
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19663)),U_19665),c_List_Olists(U_19663,U_19667))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK478]),skolemize(U_19659,sK478(U_19668,U_19666,U_19664))],[f_4713_3]) ).

fof(f_4713_5,plain,
    ( ! [U_19666,U_19664,U_19668] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_19664),sK478(U_19668,U_19666,U_19664)),U_19668))
        | ~ sP1193(U_19666,U_19664,U_19668) )
    & ! [U_19666,U_19664,U_19668] :
        ( hBOOL(hAPP(hAPP(c_member(U_19664),sK478(U_19668,U_19666,U_19664)),hAPP(c_List_Oset(U_19664),U_19666)))
        | ~ sP1193(U_19666,U_19664,U_19668) )
    & ! [U_19666,U_19664,U_19668] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19664)),U_19666),c_List_Olists(U_19664,U_19668)))
        | sP1193(U_19666,U_19664,U_19668) )
    & ! [U_19658,U_19665,U_19663,U_19667] :
        ( hBOOL(hAPP(hAPP(c_member(U_19663),U_19658),U_19667))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19663),U_19658),hAPP(c_List_Oset(U_19663),U_19665)))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19663)),U_19665),c_List_Olists(U_19663,U_19667))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1193])],[f_4713_4]) ).

cnf(f_4713_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19663),U_19658),U_19667))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19663),U_19658),hAPP(c_List_Oset(U_19663),U_19665)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19663)),U_19665),c_List_Olists(U_19663,U_19667))) ),
    inference(clausify,[status(thm)],[f_4713_5]) ).

cnf(f_4713_7,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19664)),U_19666),c_List_Olists(U_19664,U_19668)))
    | sP1193(U_19666,U_19664,U_19668) ),
    inference(clausify,[status(thm)],[f_4713_5]) ).

cnf(f_4713_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19664),sK478(U_19668,U_19666,U_19664)),hAPP(c_List_Oset(U_19664),U_19666)))
    | ~ sP1193(U_19666,U_19664,U_19668) ),
    inference(clausify,[status(thm)],[f_4713_5]) ).

cnf(f_4713_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_19664),sK478(U_19668,U_19666,U_19664)),U_19668))
    | ~ sP1193(U_19666,U_19664,U_19668) ),
    inference(clausify,[status(thm)],[f_4713_5]) ).

fof(f_4714_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_4714_2,plain,
    ! [U_19670,U_19669] : c_List_Olists(U_19669,U_19670) = hAPP(c_Set_OCollect(tc_List_Olist(U_19669)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19669),tc_fun(U_19669,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_19669,tc_HOL_Obool),tc_fun(tc_fun(U_19669,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_19669)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_19669,tc_HOL_Obool))),c_List_Oset(U_19669))),U_19670)),
    inference(variable_rename,[status(thm)],[f_4714_1]) ).

fof(f_4714_3,plain,
    ! [U_19669,U_19670] : c_List_Olists(U_19669,U_19670) = hAPP(c_Set_OCollect(tc_List_Olist(U_19669)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19669),tc_fun(U_19669,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_19669,tc_HOL_Obool),tc_fun(tc_fun(U_19669,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_19669)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_19669,tc_HOL_Obool))),c_List_Oset(U_19669))),U_19670)),
    inference(definitional_conversion,[status(esa)],[f_4714_2]) ).

cnf(f_4714_4,plain,
    c_List_Olists(U_19669,U_19670) = hAPP(c_Set_OCollect(tc_List_Olist(U_19669)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19669),tc_fun(U_19669,tc_HOL_Obool),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_fun(U_19669,tc_HOL_Obool),tc_fun(tc_fun(U_19669,tc_HOL_Obool),tc_HOL_Obool),tc_List_Olist(U_19669)),c_Orderings_Oord__class_Oless__eq(tc_fun(U_19669,tc_HOL_Obool))),c_List_Oset(U_19669))),U_19670)),
    inference(clausify,[status(thm)],[f_4714_3]) ).

fof(f_4715_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_4715_2,plain,
    ! [U_19671] : c_List_Olists(U_19671,c_Orderings_Obot__class_Obot(tc_fun(U_19671,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_19671)),c_List_Olist_ONil(U_19671)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_19671),tc_HOL_Obool))),
    inference(variable_rename,[status(thm)],[f_4715_1]) ).

fof(f_4715_3,plain,
    ! [U_19671] : c_List_Olists(U_19671,c_Orderings_Obot__class_Obot(tc_fun(U_19671,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_19671)),c_List_Olist_ONil(U_19671)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_19671),tc_HOL_Obool))),
    inference(definitional_conversion,[status(esa)],[f_4715_2]) ).

cnf(f_4715_4,plain,
    c_List_Olists(U_19671,c_Orderings_Obot__class_Obot(tc_fun(U_19671,tc_HOL_Obool))) = hAPP(hAPP(c_Set_Oinsert(tc_List_Olist(U_19671)),c_List_Olist_ONil(U_19671)),c_Orderings_Obot__class_Obot(tc_fun(tc_List_Olist(U_19671),tc_HOL_Obool))),
    inference(clausify,[status(thm)],[f_4715_3]) ).

fof(f_4716_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_4716_2,plain,
    ! [U_19674,U_19673,U_19672] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19672)),U_19673),c_Wellfounded_Oacc(tc_List_Olist(U_19672),c_List_Olistrel1(U_19672,U_19674))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19672)),U_19673),c_List_Olists(U_19672,c_Wellfounded_Oacc(U_19672,U_19674)))) ),
    inference(variable_rename,[status(thm)],[f_4716_1]) ).

fof(f_4716_3,plain,
    ! [U_19672,U_19673,U_19674] :
      ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19672)),U_19673),c_Wellfounded_Oacc(tc_List_Olist(U_19672),c_List_Olistrel1(U_19672,U_19674))))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19672)),U_19673),c_List_Olists(U_19672,c_Wellfounded_Oacc(U_19672,U_19674)))) ),
    inference(definitional_conversion,[status(esa)],[f_4716_2]) ).

cnf(f_4716_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19672)),U_19673),c_Wellfounded_Oacc(tc_List_Olist(U_19672),c_List_Olistrel1(U_19672,U_19674))))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19672)),U_19673),c_List_Olists(U_19672,c_Wellfounded_Oacc(U_19672,U_19674)))) ),
    inference(clausify,[status(thm)],[f_4716_3]) ).

fof(f_4717_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_4717_2,plain,
    ! [U_19680,U_19679,U_19678,U_19677] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19678),tc_List_Olist(U_19678))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19678),tc_List_Olist(U_19678)),U_19679),hAPP(hAPP(c_List_Oappend(U_19678),U_19679),U_19677))),c_List_Olexord(U_19678,U_19680)))
      | ! [U_19676,U_19675] : U_19677 != hAPP(hAPP(c_List_Olist_OCons(U_19678),U_19676),U_19675) ),
    inference(variable_rename,[status(thm)],[f_4717_1]) ).

fof(f_4717_3,plain,
    ! [U_19676,U_19675,U_19677,U_19678,U_19679,U_19680] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19678),tc_List_Olist(U_19678))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19678),tc_List_Olist(U_19678)),U_19679),hAPP(hAPP(c_List_Oappend(U_19678),U_19679),U_19677))),c_List_Olexord(U_19678,U_19680)))
      | U_19677 != hAPP(hAPP(c_List_Olist_OCons(U_19678),U_19676),U_19675) ),
    inference(definitional_conversion,[status(esa)],[f_4717_2]) ).

cnf(f_4717_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19678),tc_List_Olist(U_19678))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19678),tc_List_Olist(U_19678)),U_19679),hAPP(hAPP(c_List_Oappend(U_19678),U_19679),U_19677))),c_List_Olexord(U_19678,U_19680)))
    | U_19677 != hAPP(hAPP(c_List_Olist_OCons(U_19678),U_19676),U_19675) ),
    inference(clausify,[status(thm)],[f_4717_3]) ).

fof(f_4718_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_4718_2,plain,
    ! [U_19687,U_19686,U_19685] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19685),tc_List_Olist(U_19685))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19685),tc_List_Olist(U_19685)),c_List_Olist_ONil(U_19685)),U_19686)),c_List_Olexord(U_19685,U_19687)))
        | ! [U_19684,U_19683] : U_19686 != hAPP(hAPP(c_List_Olist_OCons(U_19685),U_19684),U_19683) )
      & ( ? [U_19682,U_19681] : U_19686 = hAPP(hAPP(c_List_Olist_OCons(U_19685),U_19682),U_19681)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19685),tc_List_Olist(U_19685))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19685),tc_List_Olist(U_19685)),c_List_Olist_ONil(U_19685)),U_19686)),c_List_Olexord(U_19685,U_19687))) ) ),
    inference(variable_rename,[status(thm)],[f_4718_1]) ).

fof(f_4718_3,plain,
    ( ! [U_19693,U_19691,U_19689] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19689),tc_List_Olist(U_19689))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19689),tc_List_Olist(U_19689)),c_List_Olist_ONil(U_19689)),U_19691)),c_List_Olexord(U_19689,U_19693)))
        | ! [U_19684,U_19683] : U_19691 != hAPP(hAPP(c_List_Olist_OCons(U_19689),U_19684),U_19683) )
    & ! [U_19692,U_19690,U_19688] :
        ( ? [U_19682,U_19681] : U_19690 = hAPP(hAPP(c_List_Olist_OCons(U_19688),U_19682),U_19681)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19688),tc_List_Olist(U_19688))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19688),tc_List_Olist(U_19688)),c_List_Olist_ONil(U_19688)),U_19690)),c_List_Olexord(U_19688,U_19692))) ) ),
    inference(miniscope,[status(thm)],[f_4718_2]) ).

fof(f_4718_4,plain,
    ( ! [U_19693,U_19691,U_19689] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19689),tc_List_Olist(U_19689))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19689),tc_List_Olist(U_19689)),c_List_Olist_ONil(U_19689)),U_19691)),c_List_Olexord(U_19689,U_19693)))
        | ! [U_19684,U_19683] : U_19691 != hAPP(hAPP(c_List_Olist_OCons(U_19689),U_19684),U_19683) )
    & ! [U_19692,U_19690,U_19688] :
        ( ? [U_19681] : U_19690 = hAPP(hAPP(c_List_Olist_OCons(U_19688),sK479(U_19692,U_19690,U_19688)),U_19681)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19688),tc_List_Olist(U_19688))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19688),tc_List_Olist(U_19688)),c_List_Olist_ONil(U_19688)),U_19690)),c_List_Olexord(U_19688,U_19692))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK479]),skolemize(U_19682,sK479(U_19692,U_19690,U_19688))],[f_4718_3]) ).

fof(f_4718_5,plain,
    ( ! [U_19693,U_19691,U_19689] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19689),tc_List_Olist(U_19689))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19689),tc_List_Olist(U_19689)),c_List_Olist_ONil(U_19689)),U_19691)),c_List_Olexord(U_19689,U_19693)))
        | ! [U_19684,U_19683] : U_19691 != hAPP(hAPP(c_List_Olist_OCons(U_19689),U_19684),U_19683) )
    & ! [U_19692,U_19690,U_19688] :
        ( U_19690 = hAPP(hAPP(c_List_Olist_OCons(U_19688),sK479(U_19692,U_19690,U_19688)),sK480(U_19692,U_19690,U_19688))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19688),tc_List_Olist(U_19688))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19688),tc_List_Olist(U_19688)),c_List_Olist_ONil(U_19688)),U_19690)),c_List_Olexord(U_19688,U_19692))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK480]),skolemize(U_19681,sK480(U_19692,U_19690,U_19688))],[f_4718_4]) ).

fof(f_4718_6,plain,
    ( ! [U_19683,U_19684,U_19689,U_19691,U_19693] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19689),tc_List_Olist(U_19689))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19689),tc_List_Olist(U_19689)),c_List_Olist_ONil(U_19689)),U_19691)),c_List_Olexord(U_19689,U_19693)))
        | U_19691 != hAPP(hAPP(c_List_Olist_OCons(U_19689),U_19684),U_19683) )
    & ! [U_19690,U_19688,U_19692] :
        ( U_19690 = hAPP(hAPP(c_List_Olist_OCons(U_19688),sK479(U_19692,U_19690,U_19688)),sK480(U_19692,U_19690,U_19688))
        | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19688),tc_List_Olist(U_19688))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19688),tc_List_Olist(U_19688)),c_List_Olist_ONil(U_19688)),U_19690)),c_List_Olexord(U_19688,U_19692))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4718_5]) ).

cnf(f_4718_7,plain,
    ( U_19690 = hAPP(hAPP(c_List_Olist_OCons(U_19688),sK479(U_19692,U_19690,U_19688)),sK480(U_19692,U_19690,U_19688))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19688),tc_List_Olist(U_19688))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19688),tc_List_Olist(U_19688)),c_List_Olist_ONil(U_19688)),U_19690)),c_List_Olexord(U_19688,U_19692))) ),
    inference(clausify,[status(thm)],[f_4718_6]) ).

cnf(f_4718_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19689),tc_List_Olist(U_19689))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19689),tc_List_Olist(U_19689)),c_List_Olist_ONil(U_19689)),U_19691)),c_List_Olexord(U_19689,U_19693)))
    | U_19691 != hAPP(hAPP(c_List_Olist_OCons(U_19689),U_19684),U_19683) ),
    inference(clausify,[status(thm)],[f_4718_6]) ).

fof(f_4719_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_4719_2,plain,
    ! [U_19697,U_19696,U_19695,U_19694] :
      ( ( ( c_List_Olast(U_19695,hAPP(hAPP(c_List_Olist__update(U_19695,U_19694),U_19696),U_19697)) = c_List_Olast(U_19695,U_19694)
          | U_19696 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19695)),U_19694)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
        & ( c_List_Olast(U_19695,hAPP(hAPP(c_List_Olist__update(U_19695,U_19694),U_19696),U_19697)) = U_19697
          | U_19696 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19695)),U_19694)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) )
      | U_19694 = c_List_Olist_ONil(U_19695) ),
    inference(variable_rename,[status(thm)],[f_4719_1]) ).

fof(f_4719_3,plain,
    ( ! [U_19695,U_19694,U_19696,U_19697] :
        ( c_List_Olast(U_19695,hAPP(hAPP(c_List_Olist__update(U_19695,U_19694),U_19696),U_19697)) = c_List_Olast(U_19695,U_19694)
        | U_19696 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19695)),U_19694)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ sP1194(U_19695,U_19694,U_19696,U_19697) )
    & ! [U_19695,U_19694,U_19696,U_19697] :
        ( c_List_Olast(U_19695,hAPP(hAPP(c_List_Olist__update(U_19695,U_19694),U_19696),U_19697)) = U_19697
        | U_19696 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19695)),U_19694)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
        | ~ sP1194(U_19695,U_19694,U_19696,U_19697) )
    & ! [U_19695,U_19694,U_19696,U_19697] :
        ( sP1194(U_19695,U_19694,U_19696,U_19697)
        | U_19694 = c_List_Olist_ONil(U_19695) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1194])],[f_4719_2]) ).

cnf(f_4719_4,plain,
    ( sP1194(U_19695,U_19694,U_19696,U_19697)
    | U_19694 = c_List_Olist_ONil(U_19695) ),
    inference(clausify,[status(thm)],[f_4719_3]) ).

cnf(f_4719_5,plain,
    ( c_List_Olast(U_19695,hAPP(hAPP(c_List_Olist__update(U_19695,U_19694),U_19696),U_19697)) = U_19697
    | U_19696 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19695)),U_19694)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ sP1194(U_19695,U_19694,U_19696,U_19697) ),
    inference(clausify,[status(thm)],[f_4719_3]) ).

cnf(f_4719_6,plain,
    ( c_List_Olast(U_19695,hAPP(hAPP(c_List_Olist__update(U_19695,U_19694),U_19696),U_19697)) = c_List_Olast(U_19695,U_19694)
    | U_19696 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19695)),U_19694)),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ sP1194(U_19695,U_19694,U_19696,U_19697) ),
    inference(clausify,[status(thm)],[f_4719_3]) ).

fof(f_4720_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_4720_2,plain,
    ! [U_19703,U_19702,U_19701,U_19700,U_19699] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19699),hAPP(c_List_Omonoid__add__class_Olistsum(U_19699),hAPP(hAPP(c_List_Omap(U_19700,U_19699),U_19702),U_19701))),hAPP(c_List_Omonoid__add__class_Olistsum(U_19699),hAPP(hAPP(c_List_Omap(U_19700,U_19699),U_19703),U_19701))))
      | ? [U_19698] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19699),hAPP(U_19702,U_19698)),hAPP(U_19703,U_19698)))
          & hBOOL(hAPP(hAPP(c_member(U_19700),U_19698),hAPP(c_List_Oset(U_19700),U_19701))) )
      | ~ class_Groups_Oordered__ab__semigroup__add(U_19699)
      | ~ class_Groups_Omonoid__add(U_19699) ),
    inference(variable_rename,[status(thm)],[f_4720_1]) ).

fof(f_4720_3,plain,
    ! [U_19703,U_19702,U_19701,U_19700,U_19699] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19699),hAPP(c_List_Omonoid__add__class_Olistsum(U_19699),hAPP(hAPP(c_List_Omap(U_19700,U_19699),U_19702),U_19701))),hAPP(c_List_Omonoid__add__class_Olistsum(U_19699),hAPP(hAPP(c_List_Omap(U_19700,U_19699),U_19703),U_19701))))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19699),hAPP(U_19702,sK481(U_19703,U_19702,U_19701,U_19700,U_19699))),hAPP(U_19703,sK481(U_19703,U_19702,U_19701,U_19700,U_19699))))
        & hBOOL(hAPP(hAPP(c_member(U_19700),sK481(U_19703,U_19702,U_19701,U_19700,U_19699)),hAPP(c_List_Oset(U_19700),U_19701))) )
      | ~ class_Groups_Oordered__ab__semigroup__add(U_19699)
      | ~ class_Groups_Omonoid__add(U_19699) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK481]),skolemize(U_19698,sK481(U_19703,U_19702,U_19701,U_19700,U_19699))],[f_4720_2]) ).

fof(f_4720_4,plain,
    ( ! [U_19699,U_19700,U_19701,U_19702,U_19703] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19699),hAPP(U_19702,sK481(U_19703,U_19702,U_19701,U_19700,U_19699))),hAPP(U_19703,sK481(U_19703,U_19702,U_19701,U_19700,U_19699))))
        | ~ sP1195(U_19699,U_19700,U_19701,U_19702,U_19703) )
    & ! [U_19699,U_19700,U_19701,U_19702,U_19703] :
        ( hBOOL(hAPP(hAPP(c_member(U_19700),sK481(U_19703,U_19702,U_19701,U_19700,U_19699)),hAPP(c_List_Oset(U_19700),U_19701)))
        | ~ sP1195(U_19699,U_19700,U_19701,U_19702,U_19703) )
    & ! [U_19699,U_19700,U_19701,U_19702,U_19703] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19699),hAPP(c_List_Omonoid__add__class_Olistsum(U_19699),hAPP(hAPP(c_List_Omap(U_19700,U_19699),U_19702),U_19701))),hAPP(c_List_Omonoid__add__class_Olistsum(U_19699),hAPP(hAPP(c_List_Omap(U_19700,U_19699),U_19703),U_19701))))
        | sP1195(U_19699,U_19700,U_19701,U_19702,U_19703)
        | ~ class_Groups_Oordered__ab__semigroup__add(U_19699)
        | ~ class_Groups_Omonoid__add(U_19699) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1195])],[f_4720_3]) ).

cnf(f_4720_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19699),hAPP(c_List_Omonoid__add__class_Olistsum(U_19699),hAPP(hAPP(c_List_Omap(U_19700,U_19699),U_19702),U_19701))),hAPP(c_List_Omonoid__add__class_Olistsum(U_19699),hAPP(hAPP(c_List_Omap(U_19700,U_19699),U_19703),U_19701))))
    | sP1195(U_19699,U_19700,U_19701,U_19702,U_19703)
    | ~ class_Groups_Oordered__ab__semigroup__add(U_19699)
    | ~ class_Groups_Omonoid__add(U_19699) ),
    inference(clausify,[status(thm)],[f_4720_4]) ).

cnf(f_4720_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19700),sK481(U_19703,U_19702,U_19701,U_19700,U_19699)),hAPP(c_List_Oset(U_19700),U_19701)))
    | ~ sP1195(U_19699,U_19700,U_19701,U_19702,U_19703) ),
    inference(clausify,[status(thm)],[f_4720_4]) ).

cnf(f_4720_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_19699),hAPP(U_19702,sK481(U_19703,U_19702,U_19701,U_19700,U_19699))),hAPP(U_19703,sK481(U_19703,U_19702,U_19701,U_19700,U_19699))))
    | ~ sP1195(U_19699,U_19700,U_19701,U_19702,U_19703) ),
    inference(clausify,[status(thm)],[f_4720_4]) ).

fof(f_4721_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_4721_2,plain,
    ! [U_19706,U_19705,U_19704] :
      ( ( c_List_Olast(U_19705,hAPP(hAPP(c_List_Olist_OCons(U_19705),U_19706),U_19704)) = c_List_Olast(U_19705,U_19704)
        | U_19704 = c_List_Olist_ONil(U_19705) )
      & ( c_List_Olast(U_19705,hAPP(hAPP(c_List_Olist_OCons(U_19705),U_19706),U_19704)) = U_19706
        | U_19704 != c_List_Olist_ONil(U_19705) ) ),
    inference(variable_rename,[status(thm)],[f_4721_1]) ).

fof(f_4721_3,plain,
    ( ! [U_19712,U_19710,U_19708] :
        ( c_List_Olast(U_19710,hAPP(hAPP(c_List_Olist_OCons(U_19710),U_19712),U_19708)) = c_List_Olast(U_19710,U_19708)
        | U_19708 = c_List_Olist_ONil(U_19710) )
    & ! [U_19711,U_19709,U_19707] :
        ( c_List_Olast(U_19709,hAPP(hAPP(c_List_Olist_OCons(U_19709),U_19711),U_19707)) = U_19711
        | U_19707 != c_List_Olist_ONil(U_19709) ) ),
    inference(miniscope,[status(thm)],[f_4721_2]) ).

fof(f_4721_4,plain,
    ( ! [U_19708,U_19710,U_19712] :
        ( c_List_Olast(U_19710,hAPP(hAPP(c_List_Olist_OCons(U_19710),U_19712),U_19708)) = c_List_Olast(U_19710,U_19708)
        | U_19708 = c_List_Olist_ONil(U_19710) )
    & ! [U_19707,U_19709,U_19711] :
        ( c_List_Olast(U_19709,hAPP(hAPP(c_List_Olist_OCons(U_19709),U_19711),U_19707)) = U_19711
        | U_19707 != c_List_Olist_ONil(U_19709) ) ),
    inference(definitional_conversion,[status(esa)],[f_4721_3]) ).

cnf(f_4721_5,plain,
    ( c_List_Olast(U_19709,hAPP(hAPP(c_List_Olist_OCons(U_19709),U_19711),U_19707)) = U_19711
    | U_19707 != c_List_Olist_ONil(U_19709) ),
    inference(clausify,[status(thm)],[f_4721_4]) ).

cnf(f_4721_6,plain,
    ( c_List_Olast(U_19710,hAPP(hAPP(c_List_Olist_OCons(U_19710),U_19712),U_19708)) = c_List_Olast(U_19710,U_19708)
    | U_19708 = c_List_Olist_ONil(U_19710) ),
    inference(clausify,[status(thm)],[f_4721_4]) ).

fof(f_4722_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_4722_2,plain,
    ! [U_19715,U_19714,U_19713] :
      ( c_List_Olast(U_19714,hAPP(hAPP(c_List_Olist_OCons(U_19714),U_19715),U_19713)) = c_List_Olast(U_19714,U_19713)
      | U_19713 = c_List_Olist_ONil(U_19714) ),
    inference(variable_rename,[status(thm)],[f_4722_1]) ).

fof(f_4722_3,plain,
    ! [U_19713,U_19714,U_19715] :
      ( c_List_Olast(U_19714,hAPP(hAPP(c_List_Olist_OCons(U_19714),U_19715),U_19713)) = c_List_Olast(U_19714,U_19713)
      | U_19713 = c_List_Olist_ONil(U_19714) ),
    inference(definitional_conversion,[status(esa)],[f_4722_2]) ).

cnf(f_4722_4,plain,
    ( c_List_Olast(U_19714,hAPP(hAPP(c_List_Olist_OCons(U_19714),U_19715),U_19713)) = c_List_Olast(U_19714,U_19713)
    | U_19713 = c_List_Olist_ONil(U_19714) ),
    inference(clausify,[status(thm)],[f_4722_3]) ).

fof(f_4723_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_4723_2,plain,
    ! [U_19718,U_19717,U_19716] :
      ( c_List_Olast(U_19717,hAPP(hAPP(c_List_Olist_OCons(U_19717),U_19718),U_19716)) = U_19718
      | U_19716 != c_List_Olist_ONil(U_19717) ),
    inference(variable_rename,[status(thm)],[f_4723_1]) ).

fof(f_4723_3,plain,
    ! [U_19716,U_19717,U_19718] :
      ( c_List_Olast(U_19717,hAPP(hAPP(c_List_Olist_OCons(U_19717),U_19718),U_19716)) = U_19718
      | U_19716 != c_List_Olist_ONil(U_19717) ),
    inference(definitional_conversion,[status(esa)],[f_4723_2]) ).

cnf(f_4723_4,plain,
    ( c_List_Olast(U_19717,hAPP(hAPP(c_List_Olist_OCons(U_19717),U_19718),U_19716)) = U_19718
    | U_19716 != c_List_Olist_ONil(U_19717) ),
    inference(clausify,[status(thm)],[f_4723_3]) ).

fof(f_4724_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_4724_2,plain,
    ! [U_19721,U_19720,U_19719] :
      ( ( c_List_Olast(U_19720,hAPP(hAPP(c_List_Oappend(U_19720),U_19721),U_19719)) = c_List_Olast(U_19720,U_19719)
        | U_19719 = c_List_Olist_ONil(U_19720) )
      & ( c_List_Olast(U_19720,hAPP(hAPP(c_List_Oappend(U_19720),U_19721),U_19719)) = c_List_Olast(U_19720,U_19721)
        | U_19719 != c_List_Olist_ONil(U_19720) ) ),
    inference(variable_rename,[status(thm)],[f_4724_1]) ).

fof(f_4724_3,plain,
    ( ! [U_19727,U_19725,U_19723] :
        ( c_List_Olast(U_19725,hAPP(hAPP(c_List_Oappend(U_19725),U_19727),U_19723)) = c_List_Olast(U_19725,U_19723)
        | U_19723 = c_List_Olist_ONil(U_19725) )
    & ! [U_19726,U_19724,U_19722] :
        ( c_List_Olast(U_19724,hAPP(hAPP(c_List_Oappend(U_19724),U_19726),U_19722)) = c_List_Olast(U_19724,U_19726)
        | U_19722 != c_List_Olist_ONil(U_19724) ) ),
    inference(miniscope,[status(thm)],[f_4724_2]) ).

fof(f_4724_4,plain,
    ( ! [U_19723,U_19725,U_19727] :
        ( c_List_Olast(U_19725,hAPP(hAPP(c_List_Oappend(U_19725),U_19727),U_19723)) = c_List_Olast(U_19725,U_19723)
        | U_19723 = c_List_Olist_ONil(U_19725) )
    & ! [U_19724,U_19726,U_19722] :
        ( c_List_Olast(U_19724,hAPP(hAPP(c_List_Oappend(U_19724),U_19726),U_19722)) = c_List_Olast(U_19724,U_19726)
        | U_19722 != c_List_Olist_ONil(U_19724) ) ),
    inference(definitional_conversion,[status(esa)],[f_4724_3]) ).

cnf(f_4724_5,plain,
    ( c_List_Olast(U_19724,hAPP(hAPP(c_List_Oappend(U_19724),U_19726),U_19722)) = c_List_Olast(U_19724,U_19726)
    | U_19722 != c_List_Olist_ONil(U_19724) ),
    inference(clausify,[status(thm)],[f_4724_4]) ).

cnf(f_4724_6,plain,
    ( c_List_Olast(U_19725,hAPP(hAPP(c_List_Oappend(U_19725),U_19727),U_19723)) = c_List_Olast(U_19725,U_19723)
    | U_19723 = c_List_Olist_ONil(U_19725) ),
    inference(clausify,[status(thm)],[f_4724_4]) ).

fof(f_4725_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_4725_2,plain,
    ! [U_19730,U_19729,U_19728] :
      ( c_List_Olast(U_19729,hAPP(hAPP(c_List_Oappend(U_19729),U_19730),U_19728)) = c_List_Olast(U_19729,U_19728)
      | U_19728 = c_List_Olist_ONil(U_19729) ),
    inference(variable_rename,[status(thm)],[f_4725_1]) ).

fof(f_4725_3,plain,
    ! [U_19728,U_19729,U_19730] :
      ( c_List_Olast(U_19729,hAPP(hAPP(c_List_Oappend(U_19729),U_19730),U_19728)) = c_List_Olast(U_19729,U_19728)
      | U_19728 = c_List_Olist_ONil(U_19729) ),
    inference(definitional_conversion,[status(esa)],[f_4725_2]) ).

cnf(f_4725_4,plain,
    ( c_List_Olast(U_19729,hAPP(hAPP(c_List_Oappend(U_19729),U_19730),U_19728)) = c_List_Olast(U_19729,U_19728)
    | U_19728 = c_List_Olist_ONil(U_19729) ),
    inference(clausify,[status(thm)],[f_4725_3]) ).

fof(f_4726_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_4726_2,plain,
    ! [U_19733,U_19732,U_19731] :
      ( c_List_Olast(U_19732,hAPP(hAPP(c_List_Oappend(U_19732),U_19733),U_19731)) = c_List_Olast(U_19732,U_19733)
      | U_19731 != c_List_Olist_ONil(U_19732) ),
    inference(variable_rename,[status(thm)],[f_4726_1]) ).

fof(f_4726_3,plain,
    ! [U_19731,U_19732,U_19733] :
      ( c_List_Olast(U_19732,hAPP(hAPP(c_List_Oappend(U_19732),U_19733),U_19731)) = c_List_Olast(U_19732,U_19733)
      | U_19731 != c_List_Olist_ONil(U_19732) ),
    inference(definitional_conversion,[status(esa)],[f_4726_2]) ).

cnf(f_4726_4,plain,
    ( c_List_Olast(U_19732,hAPP(hAPP(c_List_Oappend(U_19732),U_19733),U_19731)) = c_List_Olast(U_19732,U_19733)
    | U_19731 != c_List_Olist_ONil(U_19732) ),
    inference(clausify,[status(thm)],[f_4726_3]) ).

fof(f_4727_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_4727_2,plain,
    ! [U_19737,U_19736,U_19735,U_19734] :
      ( c_List_Olast(U_19736,hAPP(hAPP(c_List_Omap(U_19735,U_19736),U_19737),U_19734)) = hAPP(U_19737,c_List_Olast(U_19735,U_19734))
      | U_19734 = c_List_Olist_ONil(U_19735) ),
    inference(variable_rename,[status(thm)],[f_4727_1]) ).

fof(f_4727_3,plain,
    ! [U_19734,U_19735,U_19736,U_19737] :
      ( c_List_Olast(U_19736,hAPP(hAPP(c_List_Omap(U_19735,U_19736),U_19737),U_19734)) = hAPP(U_19737,c_List_Olast(U_19735,U_19734))
      | U_19734 = c_List_Olist_ONil(U_19735) ),
    inference(definitional_conversion,[status(esa)],[f_4727_2]) ).

cnf(f_4727_4,plain,
    ( c_List_Olast(U_19736,hAPP(hAPP(c_List_Omap(U_19735,U_19736),U_19737),U_19734)) = hAPP(U_19737,c_List_Olast(U_19735,U_19734))
    | U_19734 = c_List_Olist_ONil(U_19735) ),
    inference(clausify,[status(thm)],[f_4727_3]) ).

fof(f_4728_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_4728_2,plain,
    ! [U_19739,U_19738] :
      ( hBOOL(hAPP(hAPP(c_member(U_19739),c_List_Olast(U_19739,U_19738)),hAPP(c_List_Oset(U_19739),U_19738)))
      | U_19738 = c_List_Olist_ONil(U_19739) ),
    inference(variable_rename,[status(thm)],[f_4728_1]) ).

fof(f_4728_3,plain,
    ! [U_19738,U_19739] :
      ( hBOOL(hAPP(hAPP(c_member(U_19739),c_List_Olast(U_19739,U_19738)),hAPP(c_List_Oset(U_19739),U_19738)))
      | U_19738 = c_List_Olist_ONil(U_19739) ),
    inference(definitional_conversion,[status(esa)],[f_4728_2]) ).

cnf(f_4728_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19739),c_List_Olast(U_19739,U_19738)),hAPP(c_List_Oset(U_19739),U_19738)))
    | U_19738 = c_List_Olist_ONil(U_19739) ),
    inference(clausify,[status(thm)],[f_4728_3]) ).

fof(f_4729_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_4729_2,plain,
    ! [U_19742,U_19741,U_19740] : c_List_Olast(U_19740,hAPP(hAPP(c_List_Oappend(U_19740),U_19741),hAPP(hAPP(c_List_Olist_OCons(U_19740),U_19742),c_List_Olist_ONil(U_19740)))) = U_19742,
    inference(variable_rename,[status(thm)],[f_4729_1]) ).

fof(f_4729_3,plain,
    ! [U_19740,U_19741,U_19742] : c_List_Olast(U_19740,hAPP(hAPP(c_List_Oappend(U_19740),U_19741),hAPP(hAPP(c_List_Olist_OCons(U_19740),U_19742),c_List_Olist_ONil(U_19740)))) = U_19742,
    inference(definitional_conversion,[status(esa)],[f_4729_2]) ).

cnf(f_4729_4,plain,
    c_List_Olast(U_19740,hAPP(hAPP(c_List_Oappend(U_19740),U_19741),hAPP(hAPP(c_List_Olist_OCons(U_19740),U_19742),c_List_Olist_ONil(U_19740)))) = U_19742,
    inference(clausify,[status(thm)],[f_4729_3]) ).

fof(f_4730_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_4730_2,plain,
    ! [U_19745,U_19744,U_19743] :
      ( c_List_Olast(U_19744,hAPP(hAPP(c_List_Odrop(U_19744),U_19743),U_19745)) = c_List_Olast(U_19744,U_19745)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19743),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19744)),U_19745))) ),
    inference(variable_rename,[status(thm)],[f_4730_1]) ).

fof(f_4730_3,plain,
    ! [U_19743,U_19744,U_19745] :
      ( c_List_Olast(U_19744,hAPP(hAPP(c_List_Odrop(U_19744),U_19743),U_19745)) = c_List_Olast(U_19744,U_19745)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19743),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19744)),U_19745))) ),
    inference(definitional_conversion,[status(esa)],[f_4730_2]) ).

cnf(f_4730_4,plain,
    ( c_List_Olast(U_19744,hAPP(hAPP(c_List_Odrop(U_19744),U_19743),U_19745)) = c_List_Olast(U_19744,U_19745)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19743),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19744)),U_19745))) ),
    inference(clausify,[status(thm)],[f_4730_3]) ).

fof(f_4731_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_4731_2,plain,
    ! [U_19747,U_19746] :
      ( c_List_Olast(U_19747,U_19746) = hAPP(hAPP(c_List_Onth(U_19747),U_19746),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19747)),U_19746)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | U_19746 = c_List_Olist_ONil(U_19747) ),
    inference(variable_rename,[status(thm)],[f_4731_1]) ).

fof(f_4731_3,plain,
    ! [U_19746,U_19747] :
      ( c_List_Olast(U_19747,U_19746) = hAPP(hAPP(c_List_Onth(U_19747),U_19746),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19747)),U_19746)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
      | U_19746 = c_List_Olist_ONil(U_19747) ),
    inference(definitional_conversion,[status(esa)],[f_4731_2]) ).

cnf(f_4731_4,plain,
    ( c_List_Olast(U_19747,U_19746) = hAPP(hAPP(c_List_Onth(U_19747),U_19746),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19747)),U_19746)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))
    | U_19746 = c_List_Olist_ONil(U_19747) ),
    inference(clausify,[status(thm)],[f_4731_3]) ).

fof(f_4732_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_4732_2,plain,
    ! [U_19753,U_19752,U_19751,U_19750] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19750),tc_List_Olist(U_19750))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19750),tc_List_Olist(U_19750)),U_19753),U_19752)),c_List_Olexord(U_19750,U_19751)))
      | U_19752 = U_19753
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19750),tc_List_Olist(U_19750))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19750),tc_List_Olist(U_19750)),U_19752),U_19753)),c_List_Olexord(U_19750,U_19751)))
      | ? [U_19749,U_19748] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19750,U_19750)),hAPP(hAPP(c_Product__Type_OPair(U_19750,U_19750),U_19748),U_19749)),U_19751))
          & U_19749 != U_19748
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19750,U_19750)),hAPP(hAPP(c_Product__Type_OPair(U_19750,U_19750),U_19749),U_19748)),U_19751)) ) ),
    inference(variable_rename,[status(thm)],[f_4732_1]) ).

fof(f_4732_3,plain,
    ! [U_19753,U_19752,U_19751,U_19750] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19750),tc_List_Olist(U_19750))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19750),tc_List_Olist(U_19750)),U_19753),U_19752)),c_List_Olexord(U_19750,U_19751)))
      | U_19752 = U_19753
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19750),tc_List_Olist(U_19750))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19750),tc_List_Olist(U_19750)),U_19752),U_19753)),c_List_Olexord(U_19750,U_19751)))
      | ? [U_19748] :
          ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19750,U_19750)),hAPP(hAPP(c_Product__Type_OPair(U_19750,U_19750),U_19748),sK482(U_19753,U_19752,U_19751,U_19750))),U_19751))
          & sK482(U_19753,U_19752,U_19751,U_19750) != U_19748
          & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19750,U_19750)),hAPP(hAPP(c_Product__Type_OPair(U_19750,U_19750),sK482(U_19753,U_19752,U_19751,U_19750)),U_19748)),U_19751)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK482]),skolemize(U_19749,sK482(U_19753,U_19752,U_19751,U_19750))],[f_4732_2]) ).

fof(f_4732_4,plain,
    ! [U_19753,U_19752,U_19751,U_19750] :
      ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19750),tc_List_Olist(U_19750))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19750),tc_List_Olist(U_19750)),U_19753),U_19752)),c_List_Olexord(U_19750,U_19751)))
      | U_19752 = U_19753
      | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19750),tc_List_Olist(U_19750))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19750),tc_List_Olist(U_19750)),U_19752),U_19753)),c_List_Olexord(U_19750,U_19751)))
      | ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19750,U_19750)),hAPP(hAPP(c_Product__Type_OPair(U_19750,U_19750),sK483(U_19753,U_19752,U_19751,U_19750)),sK482(U_19753,U_19752,U_19751,U_19750))),U_19751))
        & sK482(U_19753,U_19752,U_19751,U_19750) != sK483(U_19753,U_19752,U_19751,U_19750)
        & ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19750,U_19750)),hAPP(hAPP(c_Product__Type_OPair(U_19750,U_19750),sK482(U_19753,U_19752,U_19751,U_19750)),sK483(U_19753,U_19752,U_19751,U_19750))),U_19751)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK483]),skolemize(U_19748,sK483(U_19753,U_19752,U_19751,U_19750))],[f_4732_3]) ).

fof(f_4732_5,plain,
    ( ! [U_19750,U_19751,U_19752,U_19753] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19750,U_19750)),hAPP(hAPP(c_Product__Type_OPair(U_19750,U_19750),sK483(U_19753,U_19752,U_19751,U_19750)),sK482(U_19753,U_19752,U_19751,U_19750))),U_19751))
        | ~ sP1196(U_19750,U_19751,U_19752,U_19753) )
    & ! [U_19750,U_19751,U_19752,U_19753] :
        ( sK482(U_19753,U_19752,U_19751,U_19750) != sK483(U_19753,U_19752,U_19751,U_19750)
        | ~ sP1196(U_19750,U_19751,U_19752,U_19753) )
    & ! [U_19750,U_19751,U_19752,U_19753] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19750,U_19750)),hAPP(hAPP(c_Product__Type_OPair(U_19750,U_19750),sK482(U_19753,U_19752,U_19751,U_19750)),sK483(U_19753,U_19752,U_19751,U_19750))),U_19751))
        | ~ sP1196(U_19750,U_19751,U_19752,U_19753) )
    & ! [U_19750,U_19751,U_19752,U_19753] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19750),tc_List_Olist(U_19750))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19750),tc_List_Olist(U_19750)),U_19753),U_19752)),c_List_Olexord(U_19750,U_19751)))
        | U_19752 = U_19753
        | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19750),tc_List_Olist(U_19750))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19750),tc_List_Olist(U_19750)),U_19752),U_19753)),c_List_Olexord(U_19750,U_19751)))
        | sP1196(U_19750,U_19751,U_19752,U_19753) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1196])],[f_4732_4]) ).

cnf(f_4732_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19750),tc_List_Olist(U_19750))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19750),tc_List_Olist(U_19750)),U_19753),U_19752)),c_List_Olexord(U_19750,U_19751)))
    | U_19752 = U_19753
    | hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19750),tc_List_Olist(U_19750))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19750),tc_List_Olist(U_19750)),U_19752),U_19753)),c_List_Olexord(U_19750,U_19751)))
    | sP1196(U_19750,U_19751,U_19752,U_19753) ),
    inference(clausify,[status(thm)],[f_4732_5]) ).

cnf(f_4732_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19750,U_19750)),hAPP(hAPP(c_Product__Type_OPair(U_19750,U_19750),sK482(U_19753,U_19752,U_19751,U_19750)),sK483(U_19753,U_19752,U_19751,U_19750))),U_19751))
    | ~ sP1196(U_19750,U_19751,U_19752,U_19753) ),
    inference(clausify,[status(thm)],[f_4732_5]) ).

cnf(f_4732_8,plain,
    ( sK482(U_19753,U_19752,U_19751,U_19750) != sK483(U_19753,U_19752,U_19751,U_19750)
    | ~ sP1196(U_19750,U_19751,U_19752,U_19753) ),
    inference(clausify,[status(thm)],[f_4732_5]) ).

cnf(f_4732_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(U_19750,U_19750)),hAPP(hAPP(c_Product__Type_OPair(U_19750,U_19750),sK483(U_19753,U_19752,U_19751,U_19750)),sK482(U_19753,U_19752,U_19751,U_19750))),U_19751))
    | ~ sP1196(U_19750,U_19751,U_19752,U_19753) ),
    inference(clausify,[status(thm)],[f_4732_5]) ).

fof(f_4733_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_4733_2,plain,
    ! [U_19757,U_19756,U_19755] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19755),tc_List_Olist(U_19755))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19755),tc_List_Olist(U_19755)),U_19757),U_19757)),c_List_Olexord(U_19755,U_19756)))
      | ? [U_19754] : hBOOL(hAPP(hAPP(c_member(tc_prod(U_19755,U_19755)),hAPP(hAPP(c_Product__Type_OPair(U_19755,U_19755),U_19754),U_19754)),U_19756)) ),
    inference(variable_rename,[status(thm)],[f_4733_1]) ).

fof(f_4733_3,plain,
    ! [U_19757,U_19756,U_19755] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19755),tc_List_Olist(U_19755))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19755),tc_List_Olist(U_19755)),U_19757),U_19757)),c_List_Olexord(U_19755,U_19756)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_19755,U_19755)),hAPP(hAPP(c_Product__Type_OPair(U_19755,U_19755),sK484(U_19757,U_19756,U_19755)),sK484(U_19757,U_19756,U_19755))),U_19756)) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK484]),skolemize(U_19754,sK484(U_19757,U_19756,U_19755))],[f_4733_2]) ).

fof(f_4733_4,plain,
    ! [U_19755,U_19756,U_19757] :
      ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19755),tc_List_Olist(U_19755))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19755),tc_List_Olist(U_19755)),U_19757),U_19757)),c_List_Olexord(U_19755,U_19756)))
      | hBOOL(hAPP(hAPP(c_member(tc_prod(U_19755,U_19755)),hAPP(hAPP(c_Product__Type_OPair(U_19755,U_19755),sK484(U_19757,U_19756,U_19755)),sK484(U_19757,U_19756,U_19755))),U_19756)) ),
    inference(definitional_conversion,[status(esa)],[f_4733_3]) ).

cnf(f_4733_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_19755),tc_List_Olist(U_19755))),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19755),tc_List_Olist(U_19755)),U_19757),U_19757)),c_List_Olexord(U_19755,U_19756)))
    | hBOOL(hAPP(hAPP(c_member(tc_prod(U_19755,U_19755)),hAPP(hAPP(c_Product__Type_OPair(U_19755,U_19755),sK484(U_19757,U_19756,U_19755)),sK484(U_19757,U_19756,U_19755))),U_19756)) ),
    inference(clausify,[status(thm)],[f_4733_4]) ).

fof(f_4734_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_4734_2,plain,
    ! [U_19764,U_19763,U_19762] :
      ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19762)),U_19763),c_List_Olists(U_19762,U_19764)))
        | ( ! [U_19761,U_19760] :
              ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19762)),U_19760),c_List_Olists(U_19762,U_19764)))
              | ~ hBOOL(hAPP(hAPP(c_member(U_19762),U_19761),U_19764))
              | U_19763 != hAPP(hAPP(c_List_Olist_OCons(U_19762),U_19761),U_19760) )
          & U_19763 != c_List_Olist_ONil(U_19762) ) )
      & ( ? [U_19759,U_19758] :
            ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19762)),U_19758),c_List_Olists(U_19762,U_19764)))
            & hBOOL(hAPP(hAPP(c_member(U_19762),U_19759),U_19764))
            & U_19763 = hAPP(hAPP(c_List_Olist_OCons(U_19762),U_19759),U_19758) )
        | U_19763 = c_List_Olist_ONil(U_19762)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19762)),U_19763),c_List_Olists(U_19762,U_19764))) ) ),
    inference(variable_rename,[status(thm)],[f_4734_1]) ).

fof(f_4734_3,plain,
    ( ! [U_19770,U_19768,U_19766] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19766)),U_19768),c_List_Olists(U_19766,U_19770)))
        | ( ! [U_19761] :
              ( ! [U_19760] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19766)),U_19760),c_List_Olists(U_19766,U_19770)))
                  | U_19768 != hAPP(hAPP(c_List_Olist_OCons(U_19766),U_19761),U_19760) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_19766),U_19761),U_19770)) )
          & U_19768 != c_List_Olist_ONil(U_19766) ) )
    & ! [U_19769,U_19767,U_19765] :
        ( ? [U_19759] :
            ( ? [U_19758] :
                ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19765)),U_19758),c_List_Olists(U_19765,U_19769)))
                & U_19767 = hAPP(hAPP(c_List_Olist_OCons(U_19765),U_19759),U_19758) )
            & hBOOL(hAPP(hAPP(c_member(U_19765),U_19759),U_19769)) )
        | U_19767 = c_List_Olist_ONil(U_19765)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19765)),U_19767),c_List_Olists(U_19765,U_19769))) ) ),
    inference(miniscope,[status(thm)],[f_4734_2]) ).

fof(f_4734_4,plain,
    ( ! [U_19770,U_19768,U_19766] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19766)),U_19768),c_List_Olists(U_19766,U_19770)))
        | ( ! [U_19761] :
              ( ! [U_19760] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19766)),U_19760),c_List_Olists(U_19766,U_19770)))
                  | U_19768 != hAPP(hAPP(c_List_Olist_OCons(U_19766),U_19761),U_19760) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_19766),U_19761),U_19770)) )
          & U_19768 != c_List_Olist_ONil(U_19766) ) )
    & ! [U_19769,U_19767,U_19765] :
        ( ( ? [U_19758] :
              ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19765)),U_19758),c_List_Olists(U_19765,U_19769)))
              & U_19767 = hAPP(hAPP(c_List_Olist_OCons(U_19765),sK485(U_19769,U_19767,U_19765)),U_19758) )
          & hBOOL(hAPP(hAPP(c_member(U_19765),sK485(U_19769,U_19767,U_19765)),U_19769)) )
        | U_19767 = c_List_Olist_ONil(U_19765)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19765)),U_19767),c_List_Olists(U_19765,U_19769))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK485]),skolemize(U_19759,sK485(U_19769,U_19767,U_19765))],[f_4734_3]) ).

fof(f_4734_5,plain,
    ( ! [U_19770,U_19768,U_19766] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19766)),U_19768),c_List_Olists(U_19766,U_19770)))
        | ( ! [U_19761] :
              ( ! [U_19760] :
                  ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19766)),U_19760),c_List_Olists(U_19766,U_19770)))
                  | U_19768 != hAPP(hAPP(c_List_Olist_OCons(U_19766),U_19761),U_19760) )
              | ~ hBOOL(hAPP(hAPP(c_member(U_19766),U_19761),U_19770)) )
          & U_19768 != c_List_Olist_ONil(U_19766) ) )
    & ! [U_19769,U_19767,U_19765] :
        ( ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19765)),sK486(U_19769,U_19767,U_19765)),c_List_Olists(U_19765,U_19769)))
          & U_19767 = hAPP(hAPP(c_List_Olist_OCons(U_19765),sK485(U_19769,U_19767,U_19765)),sK486(U_19769,U_19767,U_19765))
          & hBOOL(hAPP(hAPP(c_member(U_19765),sK485(U_19769,U_19767,U_19765)),U_19769)) )
        | U_19767 = c_List_Olist_ONil(U_19765)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19765)),U_19767),c_List_Olists(U_19765,U_19769))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK486]),skolemize(U_19758,sK486(U_19769,U_19767,U_19765))],[f_4734_4]) ).

fof(f_4734_6,plain,
    ( ! [U_19770,U_19760,U_19761,U_19766,U_19768] :
        ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19766)),U_19760),c_List_Olists(U_19766,U_19770)))
        | U_19768 != hAPP(hAPP(c_List_Olist_OCons(U_19766),U_19761),U_19760)
        | ~ hBOOL(hAPP(hAPP(c_member(U_19766),U_19761),U_19770))
        | ~ sP1198(U_19770,U_19760,U_19761,U_19766,U_19768) )
    & ! [U_19770,U_19760,U_19761,U_19766,U_19768] :
        ( U_19768 != c_List_Olist_ONil(U_19766)
        | ~ sP1198(U_19770,U_19760,U_19761,U_19766,U_19768) )
    & ! [U_19765,U_19769,U_19767] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19765)),sK486(U_19769,U_19767,U_19765)),c_List_Olists(U_19765,U_19769)))
        | ~ sP1197(U_19765,U_19769,U_19767) )
    & ! [U_19765,U_19769,U_19767] :
        ( U_19767 = hAPP(hAPP(c_List_Olist_OCons(U_19765),sK485(U_19769,U_19767,U_19765)),sK486(U_19769,U_19767,U_19765))
        | ~ sP1197(U_19765,U_19769,U_19767) )
    & ! [U_19765,U_19769,U_19767] :
        ( hBOOL(hAPP(hAPP(c_member(U_19765),sK485(U_19769,U_19767,U_19765)),U_19769))
        | ~ sP1197(U_19765,U_19769,U_19767) )
    & ! [U_19770,U_19760,U_19761,U_19766,U_19768] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19766)),U_19768),c_List_Olists(U_19766,U_19770)))
        | sP1198(U_19770,U_19760,U_19761,U_19766,U_19768) )
    & ! [U_19765,U_19769,U_19767] :
        ( sP1197(U_19765,U_19769,U_19767)
        | U_19767 = c_List_Olist_ONil(U_19765)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19765)),U_19767),c_List_Olists(U_19765,U_19769))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1197,sP1198])],[f_4734_5]) ).

cnf(f_4734_7,plain,
    ( sP1197(U_19765,U_19769,U_19767)
    | U_19767 = c_List_Olist_ONil(U_19765)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19765)),U_19767),c_List_Olists(U_19765,U_19769))) ),
    inference(clausify,[status(thm)],[f_4734_6]) ).

cnf(f_4734_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19766)),U_19768),c_List_Olists(U_19766,U_19770)))
    | sP1198(U_19770,U_19760,U_19761,U_19766,U_19768) ),
    inference(clausify,[status(thm)],[f_4734_6]) ).

cnf(f_4734_9,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19765),sK485(U_19769,U_19767,U_19765)),U_19769))
    | ~ sP1197(U_19765,U_19769,U_19767) ),
    inference(clausify,[status(thm)],[f_4734_6]) ).

cnf(f_4734_10,plain,
    ( U_19767 = hAPP(hAPP(c_List_Olist_OCons(U_19765),sK485(U_19769,U_19767,U_19765)),sK486(U_19769,U_19767,U_19765))
    | ~ sP1197(U_19765,U_19769,U_19767) ),
    inference(clausify,[status(thm)],[f_4734_6]) ).

cnf(f_4734_11,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19765)),sK486(U_19769,U_19767,U_19765)),c_List_Olists(U_19765,U_19769)))
    | ~ sP1197(U_19765,U_19769,U_19767) ),
    inference(clausify,[status(thm)],[f_4734_6]) ).

cnf(f_4734_12,plain,
    ( U_19768 != c_List_Olist_ONil(U_19766)
    | ~ sP1198(U_19770,U_19760,U_19761,U_19766,U_19768) ),
    inference(clausify,[status(thm)],[f_4734_6]) ).

cnf(f_4734_13,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_19766)),U_19760),c_List_Olists(U_19766,U_19770)))
    | U_19768 != hAPP(hAPP(c_List_Olist_OCons(U_19766),U_19761),U_19760)
    | ~ hBOOL(hAPP(hAPP(c_member(U_19766),U_19761),U_19770))
    | ~ sP1198(U_19770,U_19760,U_19761,U_19766,U_19768) ),
    inference(clausify,[status(thm)],[f_4734_6]) ).

fof(f_4735_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_4735_2,plain,
    ! [U_19775,U_19774,U_19773,U_19772] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_19772,U_19774,U_19773)),c_List_Olist_Olist__size(U_19772,U_19775,U_19773)))
      | ? [U_19771] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_19774,U_19771)),hAPP(U_19775,U_19771)))
          & hBOOL(hAPP(hAPP(c_member(U_19772),U_19771),hAPP(c_List_Oset(U_19772),U_19773))) ) ),
    inference(variable_rename,[status(thm)],[f_4735_1]) ).

fof(f_4735_3,plain,
    ! [U_19775,U_19774,U_19773,U_19772] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_19772,U_19774,U_19773)),c_List_Olist_Olist__size(U_19772,U_19775,U_19773)))
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_19774,sK487(U_19775,U_19774,U_19773,U_19772))),hAPP(U_19775,sK487(U_19775,U_19774,U_19773,U_19772))))
        & hBOOL(hAPP(hAPP(c_member(U_19772),sK487(U_19775,U_19774,U_19773,U_19772)),hAPP(c_List_Oset(U_19772),U_19773))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK487]),skolemize(U_19771,sK487(U_19775,U_19774,U_19773,U_19772))],[f_4735_2]) ).

fof(f_4735_4,plain,
    ( ! [U_19774,U_19772,U_19775,U_19773] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_19774,sK487(U_19775,U_19774,U_19773,U_19772))),hAPP(U_19775,sK487(U_19775,U_19774,U_19773,U_19772))))
        | ~ sP1199(U_19774,U_19772,U_19775,U_19773) )
    & ! [U_19774,U_19772,U_19775,U_19773] :
        ( hBOOL(hAPP(hAPP(c_member(U_19772),sK487(U_19775,U_19774,U_19773,U_19772)),hAPP(c_List_Oset(U_19772),U_19773)))
        | ~ sP1199(U_19774,U_19772,U_19775,U_19773) )
    & ! [U_19774,U_19772,U_19775,U_19773] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_19772,U_19774,U_19773)),c_List_Olist_Olist__size(U_19772,U_19775,U_19773)))
        | sP1199(U_19774,U_19772,U_19775,U_19773) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1199])],[f_4735_3]) ).

cnf(f_4735_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_List_Olist_Olist__size(U_19772,U_19774,U_19773)),c_List_Olist_Olist__size(U_19772,U_19775,U_19773)))
    | sP1199(U_19774,U_19772,U_19775,U_19773) ),
    inference(clausify,[status(thm)],[f_4735_4]) ).

cnf(f_4735_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19772),sK487(U_19775,U_19774,U_19773,U_19772)),hAPP(c_List_Oset(U_19772),U_19773)))
    | ~ sP1199(U_19774,U_19772,U_19775,U_19773) ),
    inference(clausify,[status(thm)],[f_4735_4]) ).

cnf(f_4735_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(U_19774,sK487(U_19775,U_19774,U_19773,U_19772))),hAPP(U_19775,sK487(U_19775,U_19774,U_19773,U_19772))))
    | ~ sP1199(U_19774,U_19772,U_19775,U_19773) ),
    inference(clausify,[status(thm)],[f_4735_4]) ).

fof(f_4736_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_4736_2,plain,
    ! [U_19778,U_19777,U_19776] :
      ( c_List_Obutlast(U_19777,hAPP(hAPP(c_List_Otake(U_19777),U_19776),U_19778)) = hAPP(hAPP(c_List_Otake(U_19777),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19776),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19778)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19776),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19777)),U_19778))) ),
    inference(variable_rename,[status(thm)],[f_4736_1]) ).

fof(f_4736_3,plain,
    ! [U_19776,U_19777,U_19778] :
      ( c_List_Obutlast(U_19777,hAPP(hAPP(c_List_Otake(U_19777),U_19776),U_19778)) = hAPP(hAPP(c_List_Otake(U_19777),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19776),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19778)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19776),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19777)),U_19778))) ),
    inference(definitional_conversion,[status(esa)],[f_4736_2]) ).

cnf(f_4736_4,plain,
    ( c_List_Obutlast(U_19777,hAPP(hAPP(c_List_Otake(U_19777),U_19776),U_19778)) = hAPP(hAPP(c_List_Otake(U_19777),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_19776),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19778)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19776),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19777)),U_19778))) ),
    inference(clausify,[status(thm)],[f_4736_3]) ).

fof(f_4737_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_4737_2,plain,
    ! [U_19783,U_19782,U_19781,U_19780] :
      ( hAPP(hAPP(c_List_Otake(U_19781),U_19780),U_19782) = hAPP(hAPP(c_List_Otake(U_19781),U_19780),U_19783)
      | ? [U_19779] :
          ( hAPP(hAPP(c_List_Onth(U_19781),U_19782),U_19779) != hAPP(hAPP(c_List_Onth(U_19781),U_19783),U_19779)
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19779),U_19780)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19780),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19781)),U_19783)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19780),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19781)),U_19782))) ),
    inference(variable_rename,[status(thm)],[f_4737_1]) ).

fof(f_4737_3,plain,
    ! [U_19783,U_19782,U_19781,U_19780] :
      ( hAPP(hAPP(c_List_Otake(U_19781),U_19780),U_19782) = hAPP(hAPP(c_List_Otake(U_19781),U_19780),U_19783)
      | ( hAPP(hAPP(c_List_Onth(U_19781),U_19782),sK488(U_19783,U_19782,U_19781,U_19780)) != hAPP(hAPP(c_List_Onth(U_19781),U_19783),sK488(U_19783,U_19782,U_19781,U_19780))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK488(U_19783,U_19782,U_19781,U_19780)),U_19780)) )
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19780),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19781)),U_19783)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19780),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19781)),U_19782))) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK488]),skolemize(U_19779,sK488(U_19783,U_19782,U_19781,U_19780))],[f_4737_2]) ).

fof(f_4737_4,plain,
    ( ! [U_19780,U_19781,U_19782,U_19783] :
        ( hAPP(hAPP(c_List_Onth(U_19781),U_19782),sK488(U_19783,U_19782,U_19781,U_19780)) != hAPP(hAPP(c_List_Onth(U_19781),U_19783),sK488(U_19783,U_19782,U_19781,U_19780))
        | ~ sP1200(U_19780,U_19781,U_19782,U_19783) )
    & ! [U_19780,U_19781,U_19782,U_19783] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK488(U_19783,U_19782,U_19781,U_19780)),U_19780))
        | ~ sP1200(U_19780,U_19781,U_19782,U_19783) )
    & ! [U_19780,U_19781,U_19782,U_19783] :
        ( hAPP(hAPP(c_List_Otake(U_19781),U_19780),U_19782) = hAPP(hAPP(c_List_Otake(U_19781),U_19780),U_19783)
        | sP1200(U_19780,U_19781,U_19782,U_19783)
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19780),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19781)),U_19783)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19780),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19781)),U_19782))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1200])],[f_4737_3]) ).

cnf(f_4737_5,plain,
    ( hAPP(hAPP(c_List_Otake(U_19781),U_19780),U_19782) = hAPP(hAPP(c_List_Otake(U_19781),U_19780),U_19783)
    | sP1200(U_19780,U_19781,U_19782,U_19783)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19780),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19781)),U_19783)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_19780),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19781)),U_19782))) ),
    inference(clausify,[status(thm)],[f_4737_4]) ).

cnf(f_4737_6,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK488(U_19783,U_19782,U_19781,U_19780)),U_19780))
    | ~ sP1200(U_19780,U_19781,U_19782,U_19783) ),
    inference(clausify,[status(thm)],[f_4737_4]) ).

cnf(f_4737_7,plain,
    ( hAPP(hAPP(c_List_Onth(U_19781),U_19782),sK488(U_19783,U_19782,U_19781,U_19780)) != hAPP(hAPP(c_List_Onth(U_19781),U_19783),sK488(U_19783,U_19782,U_19781,U_19780))
    | ~ sP1200(U_19780,U_19781,U_19782,U_19783) ),
    inference(clausify,[status(thm)],[f_4737_4]) ).

fof(f_4738_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_4738_2,plain,
    ! [U_19787,U_19786,U_19785,U_19784] : hAPP(hAPP(c_List_Omap(U_19784,U_19785),U_19786),c_List_Obutlast(U_19784,U_19787)) = c_List_Obutlast(U_19785,hAPP(hAPP(c_List_Omap(U_19784,U_19785),U_19786),U_19787)),
    inference(variable_rename,[status(thm)],[f_4738_1]) ).

fof(f_4738_3,plain,
    ! [U_19787,U_19784,U_19785,U_19786] : hAPP(hAPP(c_List_Omap(U_19784,U_19785),U_19786),c_List_Obutlast(U_19784,U_19787)) = c_List_Obutlast(U_19785,hAPP(hAPP(c_List_Omap(U_19784,U_19785),U_19786),U_19787)),
    inference(definitional_conversion,[status(esa)],[f_4738_2]) ).

cnf(f_4738_4,plain,
    hAPP(hAPP(c_List_Omap(U_19784,U_19785),U_19786),c_List_Obutlast(U_19784,U_19787)) = c_List_Obutlast(U_19785,hAPP(hAPP(c_List_Omap(U_19784,U_19785),U_19786),U_19787)),
    inference(clausify,[status(thm)],[f_4738_3]) ).

fof(f_4739_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_4739_2,plain,
    ! [U_19790,U_19789,U_19788] :
      ( ( c_List_Obutlast(U_19789,hAPP(hAPP(c_List_Oappend(U_19789),U_19790),U_19788)) = hAPP(hAPP(c_List_Oappend(U_19789),U_19790),c_List_Obutlast(U_19789,U_19788))
        | U_19788 = c_List_Olist_ONil(U_19789) )
      & ( c_List_Obutlast(U_19789,hAPP(hAPP(c_List_Oappend(U_19789),U_19790),U_19788)) = c_List_Obutlast(U_19789,U_19790)
        | U_19788 != c_List_Olist_ONil(U_19789) ) ),
    inference(variable_rename,[status(thm)],[f_4739_1]) ).

fof(f_4739_3,plain,
    ( ! [U_19796,U_19794,U_19792] :
        ( c_List_Obutlast(U_19794,hAPP(hAPP(c_List_Oappend(U_19794),U_19796),U_19792)) = hAPP(hAPP(c_List_Oappend(U_19794),U_19796),c_List_Obutlast(U_19794,U_19792))
        | U_19792 = c_List_Olist_ONil(U_19794) )
    & ! [U_19795,U_19793,U_19791] :
        ( c_List_Obutlast(U_19793,hAPP(hAPP(c_List_Oappend(U_19793),U_19795),U_19791)) = c_List_Obutlast(U_19793,U_19795)
        | U_19791 != c_List_Olist_ONil(U_19793) ) ),
    inference(miniscope,[status(thm)],[f_4739_2]) ).

fof(f_4739_4,plain,
    ( ! [U_19792,U_19794,U_19796] :
        ( c_List_Obutlast(U_19794,hAPP(hAPP(c_List_Oappend(U_19794),U_19796),U_19792)) = hAPP(hAPP(c_List_Oappend(U_19794),U_19796),c_List_Obutlast(U_19794,U_19792))
        | U_19792 = c_List_Olist_ONil(U_19794) )
    & ! [U_19793,U_19795,U_19791] :
        ( c_List_Obutlast(U_19793,hAPP(hAPP(c_List_Oappend(U_19793),U_19795),U_19791)) = c_List_Obutlast(U_19793,U_19795)
        | U_19791 != c_List_Olist_ONil(U_19793) ) ),
    inference(definitional_conversion,[status(esa)],[f_4739_3]) ).

cnf(f_4739_5,plain,
    ( c_List_Obutlast(U_19793,hAPP(hAPP(c_List_Oappend(U_19793),U_19795),U_19791)) = c_List_Obutlast(U_19793,U_19795)
    | U_19791 != c_List_Olist_ONil(U_19793) ),
    inference(clausify,[status(thm)],[f_4739_4]) ).

cnf(f_4739_6,plain,
    ( c_List_Obutlast(U_19794,hAPP(hAPP(c_List_Oappend(U_19794),U_19796),U_19792)) = hAPP(hAPP(c_List_Oappend(U_19794),U_19796),c_List_Obutlast(U_19794,U_19792))
    | U_19792 = c_List_Olist_ONil(U_19794) ),
    inference(clausify,[status(thm)],[f_4739_4]) ).

fof(f_4740_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_4740_2,plain,
    ! [U_19799,U_19798,U_19797] :
      ( ( c_List_Obutlast(U_19798,hAPP(hAPP(c_List_Olist_OCons(U_19798),U_19799),U_19797)) = hAPP(hAPP(c_List_Olist_OCons(U_19798),U_19799),c_List_Obutlast(U_19798,U_19797))
        | U_19797 = c_List_Olist_ONil(U_19798) )
      & ( c_List_Obutlast(U_19798,hAPP(hAPP(c_List_Olist_OCons(U_19798),U_19799),U_19797)) = c_List_Olist_ONil(U_19798)
        | U_19797 != c_List_Olist_ONil(U_19798) ) ),
    inference(variable_rename,[status(thm)],[f_4740_1]) ).

fof(f_4740_3,plain,
    ( ! [U_19805,U_19803,U_19801] :
        ( c_List_Obutlast(U_19803,hAPP(hAPP(c_List_Olist_OCons(U_19803),U_19805),U_19801)) = hAPP(hAPP(c_List_Olist_OCons(U_19803),U_19805),c_List_Obutlast(U_19803,U_19801))
        | U_19801 = c_List_Olist_ONil(U_19803) )
    & ! [U_19804,U_19802,U_19800] :
        ( c_List_Obutlast(U_19802,hAPP(hAPP(c_List_Olist_OCons(U_19802),U_19804),U_19800)) = c_List_Olist_ONil(U_19802)
        | U_19800 != c_List_Olist_ONil(U_19802) ) ),
    inference(miniscope,[status(thm)],[f_4740_2]) ).

fof(f_4740_4,plain,
    ( ! [U_19801,U_19803,U_19805] :
        ( c_List_Obutlast(U_19803,hAPP(hAPP(c_List_Olist_OCons(U_19803),U_19805),U_19801)) = hAPP(hAPP(c_List_Olist_OCons(U_19803),U_19805),c_List_Obutlast(U_19803,U_19801))
        | U_19801 = c_List_Olist_ONil(U_19803) )
    & ! [U_19802,U_19804,U_19800] :
        ( c_List_Obutlast(U_19802,hAPP(hAPP(c_List_Olist_OCons(U_19802),U_19804),U_19800)) = c_List_Olist_ONil(U_19802)
        | U_19800 != c_List_Olist_ONil(U_19802) ) ),
    inference(definitional_conversion,[status(esa)],[f_4740_3]) ).

cnf(f_4740_5,plain,
    ( c_List_Obutlast(U_19802,hAPP(hAPP(c_List_Olist_OCons(U_19802),U_19804),U_19800)) = c_List_Olist_ONil(U_19802)
    | U_19800 != c_List_Olist_ONil(U_19802) ),
    inference(clausify,[status(thm)],[f_4740_4]) ).

cnf(f_4740_6,plain,
    ( c_List_Obutlast(U_19803,hAPP(hAPP(c_List_Olist_OCons(U_19803),U_19805),U_19801)) = hAPP(hAPP(c_List_Olist_OCons(U_19803),U_19805),c_List_Obutlast(U_19803,U_19801))
    | U_19801 = c_List_Olist_ONil(U_19803) ),
    inference(clausify,[status(thm)],[f_4740_4]) ).

fof(f_4741_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_4741_2,plain,
    ! [U_19808,U_19807,U_19806] :
      ( hBOOL(hAPP(hAPP(c_member(U_19806),U_19807),hAPP(c_List_Oset(U_19806),U_19808)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19806),U_19807),hAPP(c_List_Oset(U_19806),c_List_Obutlast(U_19806,U_19808)))) ),
    inference(variable_rename,[status(thm)],[f_4741_1]) ).

fof(f_4741_3,plain,
    ! [U_19806,U_19807,U_19808] :
      ( hBOOL(hAPP(hAPP(c_member(U_19806),U_19807),hAPP(c_List_Oset(U_19806),U_19808)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19806),U_19807),hAPP(c_List_Oset(U_19806),c_List_Obutlast(U_19806,U_19808)))) ),
    inference(definitional_conversion,[status(esa)],[f_4741_2]) ).

cnf(f_4741_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19806),U_19807),hAPP(c_List_Oset(U_19806),U_19808)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19806),U_19807),hAPP(c_List_Oset(U_19806),c_List_Obutlast(U_19806,U_19808)))) ),
    inference(clausify,[status(thm)],[f_4741_3]) ).

fof(f_4742_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_4742_2,plain,
    ! [U_19810,U_19809] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19810),c_List_Obutlast(U_19810,U_19809)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19810),U_19809))
      | U_19809 = c_List_Olist_ONil(U_19810) ),
    inference(variable_rename,[status(thm)],[f_4742_1]) ).

fof(f_4742_3,plain,
    ! [U_19809,U_19810] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19810),c_List_Obutlast(U_19810,U_19809)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19810),U_19809))
      | U_19809 = c_List_Olist_ONil(U_19810) ),
    inference(definitional_conversion,[status(esa)],[f_4742_2]) ).

cnf(f_4742_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19810),c_List_Obutlast(U_19810,U_19809)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19810),U_19809))
    | U_19809 = c_List_Olist_ONil(U_19810) ),
    inference(clausify,[status(thm)],[f_4742_3]) ).

fof(f_4743_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_4743_2,plain,
    ! [U_19811] : c_List_Obutlast(U_19811,c_List_Olist_ONil(U_19811)) = c_List_Olist_ONil(U_19811),
    inference(variable_rename,[status(thm)],[f_4743_1]) ).

fof(f_4743_3,plain,
    ! [U_19811] : c_List_Obutlast(U_19811,c_List_Olist_ONil(U_19811)) = c_List_Olist_ONil(U_19811),
    inference(definitional_conversion,[status(esa)],[f_4743_2]) ).

cnf(f_4743_4,plain,
    c_List_Obutlast(U_19811,c_List_Olist_ONil(U_19811)) = c_List_Olist_ONil(U_19811),
    inference(clausify,[status(thm)],[f_4743_3]) ).

fof(f_4744_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_4744_2,plain,
    ! [U_19814,U_19813,U_19812] : c_List_Obutlast(U_19812,hAPP(hAPP(c_List_Odrop(U_19812),U_19813),U_19814)) = hAPP(hAPP(c_List_Odrop(U_19812),U_19813),c_List_Obutlast(U_19812,U_19814)),
    inference(variable_rename,[status(thm)],[f_4744_1]) ).

fof(f_4744_3,plain,
    ! [U_19812,U_19813,U_19814] : c_List_Obutlast(U_19812,hAPP(hAPP(c_List_Odrop(U_19812),U_19813),U_19814)) = hAPP(hAPP(c_List_Odrop(U_19812),U_19813),c_List_Obutlast(U_19812,U_19814)),
    inference(definitional_conversion,[status(esa)],[f_4744_2]) ).

cnf(f_4744_4,plain,
    c_List_Obutlast(U_19812,hAPP(hAPP(c_List_Odrop(U_19812),U_19813),U_19814)) = hAPP(hAPP(c_List_Odrop(U_19812),U_19813),c_List_Obutlast(U_19812,U_19814)),
    inference(clausify,[status(thm)],[f_4744_3]) ).

fof(f_4745_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_4745_2,plain,
    ! [U_19817,U_19816,U_19815] : hAPP(hAPP(c_List_Odrop(U_19815),U_19816),c_List_Obutlast(U_19815,U_19817)) = c_List_Obutlast(U_19815,hAPP(hAPP(c_List_Odrop(U_19815),U_19816),U_19817)),
    inference(variable_rename,[status(thm)],[f_4745_1]) ).

fof(f_4745_3,plain,
    ! [U_19815,U_19816,U_19817] : hAPP(hAPP(c_List_Odrop(U_19815),U_19816),c_List_Obutlast(U_19815,U_19817)) = c_List_Obutlast(U_19815,hAPP(hAPP(c_List_Odrop(U_19815),U_19816),U_19817)),
    inference(definitional_conversion,[status(esa)],[f_4745_2]) ).

cnf(f_4745_4,plain,
    hAPP(hAPP(c_List_Odrop(U_19815),U_19816),c_List_Obutlast(U_19815,U_19817)) = c_List_Obutlast(U_19815,hAPP(hAPP(c_List_Odrop(U_19815),U_19816),U_19817)),
    inference(clausify,[status(thm)],[f_4745_3]) ).

fof(f_4746_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_4746_2,plain,
    ! [U_19821,U_19820,U_19819,U_19818] :
      ( hBOOL(hAPP(hAPP(c_member(U_19818),U_19819),hAPP(c_List_Oset(U_19818),c_List_Obutlast(U_19818,hAPP(hAPP(c_List_Oappend(U_19818),U_19820),U_19821)))))
      | ( ~ hBOOL(hAPP(hAPP(c_member(U_19818),U_19819),hAPP(c_List_Oset(U_19818),c_List_Obutlast(U_19818,U_19821))))
        & ~ hBOOL(hAPP(hAPP(c_member(U_19818),U_19819),hAPP(c_List_Oset(U_19818),c_List_Obutlast(U_19818,U_19820)))) ) ),
    inference(variable_rename,[status(thm)],[f_4746_1]) ).

fof(f_4746_3,plain,
    ( ! [U_19818,U_19819,U_19820,U_19821] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_19818),U_19819),hAPP(c_List_Oset(U_19818),c_List_Obutlast(U_19818,U_19821))))
        | ~ sP1201(U_19818,U_19819,U_19820,U_19821) )
    & ! [U_19818,U_19819,U_19820,U_19821] :
        ( ~ hBOOL(hAPP(hAPP(c_member(U_19818),U_19819),hAPP(c_List_Oset(U_19818),c_List_Obutlast(U_19818,U_19820))))
        | ~ sP1201(U_19818,U_19819,U_19820,U_19821) )
    & ! [U_19818,U_19819,U_19820,U_19821] :
        ( hBOOL(hAPP(hAPP(c_member(U_19818),U_19819),hAPP(c_List_Oset(U_19818),c_List_Obutlast(U_19818,hAPP(hAPP(c_List_Oappend(U_19818),U_19820),U_19821)))))
        | sP1201(U_19818,U_19819,U_19820,U_19821) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1201])],[f_4746_2]) ).

cnf(f_4746_4,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19818),U_19819),hAPP(c_List_Oset(U_19818),c_List_Obutlast(U_19818,hAPP(hAPP(c_List_Oappend(U_19818),U_19820),U_19821)))))
    | sP1201(U_19818,U_19819,U_19820,U_19821) ),
    inference(clausify,[status(thm)],[f_4746_3]) ).

cnf(f_4746_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_19818),U_19819),hAPP(c_List_Oset(U_19818),c_List_Obutlast(U_19818,U_19820))))
    | ~ sP1201(U_19818,U_19819,U_19820,U_19821) ),
    inference(clausify,[status(thm)],[f_4746_3]) ).

cnf(f_4746_6,plain,
    ( ~ hBOOL(hAPP(hAPP(c_member(U_19818),U_19819),hAPP(c_List_Oset(U_19818),c_List_Obutlast(U_19818,U_19821))))
    | ~ sP1201(U_19818,U_19819,U_19820,U_19821) ),
    inference(clausify,[status(thm)],[f_4746_3]) ).

fof(f_4747_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_4747_2,plain,
    ! [U_19824,U_19823,U_19822] : c_List_Obutlast(U_19822,hAPP(hAPP(c_List_Oappend(U_19822),U_19823),hAPP(hAPP(c_List_Olist_OCons(U_19822),U_19824),c_List_Olist_ONil(U_19822)))) = U_19823,
    inference(variable_rename,[status(thm)],[f_4747_1]) ).

fof(f_4747_3,plain,
    ! [U_19822,U_19823,U_19824] : c_List_Obutlast(U_19822,hAPP(hAPP(c_List_Oappend(U_19822),U_19823),hAPP(hAPP(c_List_Olist_OCons(U_19822),U_19824),c_List_Olist_ONil(U_19822)))) = U_19823,
    inference(definitional_conversion,[status(esa)],[f_4747_2]) ).

cnf(f_4747_4,plain,
    c_List_Obutlast(U_19822,hAPP(hAPP(c_List_Oappend(U_19822),U_19823),hAPP(hAPP(c_List_Olist_OCons(U_19822),U_19824),c_List_Olist_ONil(U_19822)))) = U_19823,
    inference(clausify,[status(thm)],[f_4747_3]) ).

fof(f_4748_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_4748_2,plain,
    ! [U_19827,U_19826,U_19825] :
      ( hAPP(hAPP(c_List_Otake(U_19826),U_19825),c_List_Obutlast(U_19826,U_19827)) = hAPP(hAPP(c_List_Otake(U_19826),U_19825),U_19827)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19825),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19826)),U_19827))) ),
    inference(variable_rename,[status(thm)],[f_4748_1]) ).

fof(f_4748_3,plain,
    ! [U_19825,U_19826,U_19827] :
      ( hAPP(hAPP(c_List_Otake(U_19826),U_19825),c_List_Obutlast(U_19826,U_19827)) = hAPP(hAPP(c_List_Otake(U_19826),U_19825),U_19827)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19825),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19826)),U_19827))) ),
    inference(definitional_conversion,[status(esa)],[f_4748_2]) ).

cnf(f_4748_4,plain,
    ( hAPP(hAPP(c_List_Otake(U_19826),U_19825),c_List_Obutlast(U_19826,U_19827)) = hAPP(hAPP(c_List_Otake(U_19826),U_19825),U_19827)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_19825),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19826)),U_19827))) ),
    inference(clausify,[status(thm)],[f_4748_3]) ).

fof(f_4749_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_4749_2,plain,
    ! [U_19829,U_19828] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19828)),c_List_Obutlast(U_19828,U_19829)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19828)),U_19829)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_4749_1]) ).

fof(f_4749_3,plain,
    ! [U_19828,U_19829] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19828)),c_List_Obutlast(U_19828,U_19829)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19828)),U_19829)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_4749_2]) ).

cnf(f_4749_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19828)),c_List_Obutlast(U_19828,U_19829)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19828)),U_19829)),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_4749_3]) ).

fof(f_4750_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_4750_2,plain,
    ! [U_19831,U_19830] : c_List_Obutlast(U_19830,U_19831) = hAPP(hAPP(c_List_Otake(U_19830),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19830)),U_19831)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19831),
    inference(variable_rename,[status(thm)],[f_4750_1]) ).

fof(f_4750_3,plain,
    ! [U_19830,U_19831] : c_List_Obutlast(U_19830,U_19831) = hAPP(hAPP(c_List_Otake(U_19830),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19830)),U_19831)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19831),
    inference(definitional_conversion,[status(esa)],[f_4750_2]) ).

cnf(f_4750_4,plain,
    c_List_Obutlast(U_19830,U_19831) = hAPP(hAPP(c_List_Otake(U_19830),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19830)),U_19831)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_19831),
    inference(clausify,[status(thm)],[f_4750_3]) ).

fof(f_4751_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_4751_2,plain,
    ! [U_19835,U_19834,U_19833,U_19832] :
      ( ( c_List_Obutlast(U_19833,hAPP(hAPP(c_List_Olist__update(U_19833,U_19834),U_19832),U_19835)) = hAPP(hAPP(c_List_Olist__update(U_19833,c_List_Obutlast(U_19833,U_19834)),U_19832),U_19835)
        | U_19832 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19833)),U_19834)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
      & ( c_List_Obutlast(U_19833,hAPP(hAPP(c_List_Olist__update(U_19833,U_19834),U_19832),U_19835)) = c_List_Obutlast(U_19833,U_19834)
        | U_19832 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19833)),U_19834)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(variable_rename,[status(thm)],[f_4751_1]) ).

fof(f_4751_3,plain,
    ( ! [U_19843,U_19841,U_19839,U_19837] :
        ( c_List_Obutlast(U_19839,hAPP(hAPP(c_List_Olist__update(U_19839,U_19841),U_19837),U_19843)) = hAPP(hAPP(c_List_Olist__update(U_19839,c_List_Obutlast(U_19839,U_19841)),U_19837),U_19843)
        | U_19837 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19839)),U_19841)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    & ! [U_19842,U_19840,U_19838,U_19836] :
        ( c_List_Obutlast(U_19838,hAPP(hAPP(c_List_Olist__update(U_19838,U_19840),U_19836),U_19842)) = c_List_Obutlast(U_19838,U_19840)
        | U_19836 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19838)),U_19840)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(miniscope,[status(thm)],[f_4751_2]) ).

fof(f_4751_4,plain,
    ( ! [U_19837,U_19839,U_19841,U_19843] :
        ( c_List_Obutlast(U_19839,hAPP(hAPP(c_List_Olist__update(U_19839,U_19841),U_19837),U_19843)) = hAPP(hAPP(c_List_Olist__update(U_19839,c_List_Obutlast(U_19839,U_19841)),U_19837),U_19843)
        | U_19837 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19839)),U_19841)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) )
    & ! [U_19838,U_19842,U_19836,U_19840] :
        ( c_List_Obutlast(U_19838,hAPP(hAPP(c_List_Olist__update(U_19838,U_19840),U_19836),U_19842)) = c_List_Obutlast(U_19838,U_19840)
        | U_19836 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19838)),U_19840)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4751_3]) ).

cnf(f_4751_5,plain,
    ( c_List_Obutlast(U_19838,hAPP(hAPP(c_List_Olist__update(U_19838,U_19840),U_19836),U_19842)) = c_List_Obutlast(U_19838,U_19840)
    | U_19836 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19838)),U_19840)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_4751_4]) ).

cnf(f_4751_6,plain,
    ( c_List_Obutlast(U_19839,hAPP(hAPP(c_List_Olist__update(U_19839,U_19841),U_19837),U_19843)) = hAPP(hAPP(c_List_Olist__update(U_19839,c_List_Obutlast(U_19839,U_19841)),U_19837),U_19843)
    | U_19837 = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19839)),U_19841)),c_Groups_Oone__class_Oone(tc_Nat_Onat)) ),
    inference(clausify,[status(thm)],[f_4751_4]) ).

fof(f_4752_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_4752_2,plain,
    ! [U_19845,U_19844] :
      ( hAPP(hAPP(c_List_Oappend(U_19845),c_List_Obutlast(U_19845,U_19844)),hAPP(hAPP(c_List_Olist_OCons(U_19845),c_List_Olast(U_19845,U_19844)),c_List_Olist_ONil(U_19845))) = U_19844
      | U_19844 = c_List_Olist_ONil(U_19845) ),
    inference(variable_rename,[status(thm)],[f_4752_1]) ).

fof(f_4752_3,plain,
    ! [U_19844,U_19845] :
      ( hAPP(hAPP(c_List_Oappend(U_19845),c_List_Obutlast(U_19845,U_19844)),hAPP(hAPP(c_List_Olist_OCons(U_19845),c_List_Olast(U_19845,U_19844)),c_List_Olist_ONil(U_19845))) = U_19844
      | U_19844 = c_List_Olist_ONil(U_19845) ),
    inference(definitional_conversion,[status(esa)],[f_4752_2]) ).

cnf(f_4752_4,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19845),c_List_Obutlast(U_19845,U_19844)),hAPP(hAPP(c_List_Olist_OCons(U_19845),c_List_Olast(U_19845,U_19844)),c_List_Olist_ONil(U_19845))) = U_19844
    | U_19844 = c_List_Olist_ONil(U_19845) ),
    inference(clausify,[status(thm)],[f_4752_3]) ).

fof(f_4753_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_4753_2,plain,
    ! [U_19849,U_19848,U_19847,U_19846] :
      ( ( hAPP(hAPP(c_List_Oappend(U_19846),U_19847),hAPP(hAPP(c_List_Olist_OCons(U_19846),U_19848),c_List_Olist_ONil(U_19846))) = U_19849
        | c_List_Olast(U_19846,U_19849) != U_19848
        | c_List_Obutlast(U_19846,U_19849) != U_19847
        | U_19849 = c_List_Olist_ONil(U_19846) )
      & ( ( c_List_Olast(U_19846,U_19849) = U_19848
          & c_List_Obutlast(U_19846,U_19849) = U_19847
          & U_19849 != c_List_Olist_ONil(U_19846) )
        | hAPP(hAPP(c_List_Oappend(U_19846),U_19847),hAPP(hAPP(c_List_Olist_OCons(U_19846),U_19848),c_List_Olist_ONil(U_19846))) != U_19849 ) ),
    inference(variable_rename,[status(thm)],[f_4753_1]) ).

fof(f_4753_3,plain,
    ( ! [U_19857,U_19855,U_19853,U_19851] :
        ( hAPP(hAPP(c_List_Oappend(U_19851),U_19853),hAPP(hAPP(c_List_Olist_OCons(U_19851),U_19855),c_List_Olist_ONil(U_19851))) = U_19857
        | c_List_Olast(U_19851,U_19857) != U_19855
        | c_List_Obutlast(U_19851,U_19857) != U_19853
        | U_19857 = c_List_Olist_ONil(U_19851) )
    & ! [U_19856,U_19854,U_19852,U_19850] :
        ( ( c_List_Olast(U_19850,U_19856) = U_19854
          & c_List_Obutlast(U_19850,U_19856) = U_19852
          & U_19856 != c_List_Olist_ONil(U_19850) )
        | hAPP(hAPP(c_List_Oappend(U_19850),U_19852),hAPP(hAPP(c_List_Olist_OCons(U_19850),U_19854),c_List_Olist_ONil(U_19850))) != U_19856 ) ),
    inference(miniscope,[status(thm)],[f_4753_2]) ).

fof(f_4753_4,plain,
    ( ! [U_19852,U_19856,U_19850,U_19854] :
        ( c_List_Olast(U_19850,U_19856) = U_19854
        | ~ sP1202(U_19852,U_19856,U_19850,U_19854) )
    & ! [U_19852,U_19856,U_19850,U_19854] :
        ( c_List_Obutlast(U_19850,U_19856) = U_19852
        | ~ sP1202(U_19852,U_19856,U_19850,U_19854) )
    & ! [U_19852,U_19856,U_19850,U_19854] :
        ( U_19856 != c_List_Olist_ONil(U_19850)
        | ~ sP1202(U_19852,U_19856,U_19850,U_19854) )
    & ! [U_19853,U_19851,U_19855,U_19857] :
        ( hAPP(hAPP(c_List_Oappend(U_19851),U_19853),hAPP(hAPP(c_List_Olist_OCons(U_19851),U_19855),c_List_Olist_ONil(U_19851))) = U_19857
        | c_List_Olast(U_19851,U_19857) != U_19855
        | c_List_Obutlast(U_19851,U_19857) != U_19853
        | U_19857 = c_List_Olist_ONil(U_19851) )
    & ! [U_19852,U_19856,U_19850,U_19854] :
        ( sP1202(U_19852,U_19856,U_19850,U_19854)
        | hAPP(hAPP(c_List_Oappend(U_19850),U_19852),hAPP(hAPP(c_List_Olist_OCons(U_19850),U_19854),c_List_Olist_ONil(U_19850))) != U_19856 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1202])],[f_4753_3]) ).

cnf(f_4753_5,plain,
    ( sP1202(U_19852,U_19856,U_19850,U_19854)
    | hAPP(hAPP(c_List_Oappend(U_19850),U_19852),hAPP(hAPP(c_List_Olist_OCons(U_19850),U_19854),c_List_Olist_ONil(U_19850))) != U_19856 ),
    inference(clausify,[status(thm)],[f_4753_4]) ).

cnf(f_4753_6,plain,
    ( hAPP(hAPP(c_List_Oappend(U_19851),U_19853),hAPP(hAPP(c_List_Olist_OCons(U_19851),U_19855),c_List_Olist_ONil(U_19851))) = U_19857
    | c_List_Olast(U_19851,U_19857) != U_19855
    | c_List_Obutlast(U_19851,U_19857) != U_19853
    | U_19857 = c_List_Olist_ONil(U_19851) ),
    inference(clausify,[status(thm)],[f_4753_4]) ).

cnf(f_4753_7,plain,
    ( U_19856 != c_List_Olist_ONil(U_19850)
    | ~ sP1202(U_19852,U_19856,U_19850,U_19854) ),
    inference(clausify,[status(thm)],[f_4753_4]) ).

cnf(f_4753_8,plain,
    ( c_List_Obutlast(U_19850,U_19856) = U_19852
    | ~ sP1202(U_19852,U_19856,U_19850,U_19854) ),
    inference(clausify,[status(thm)],[f_4753_4]) ).

cnf(f_4753_9,plain,
    ( c_List_Olast(U_19850,U_19856) = U_19854
    | ~ sP1202(U_19852,U_19856,U_19850,U_19854) ),
    inference(clausify,[status(thm)],[f_4753_4]) ).

fof(f_4754_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_4754_2,plain,
    ! [U_19861,U_19860,U_19859,U_19858] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19858)),U_19859))),c_List_Ofoldr(tc_List_Olist(U_19860),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19860)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19860))),U_19861,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_19858)),U_19859)),c_List_Ofoldr(tc_List_Olist(U_19860),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19860)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19860),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_19860)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19860)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(U_19860),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_19860)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19860),tc_List_Olist(U_19860),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_19860)))),U_19861),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(variable_rename,[status(thm)],[f_4754_1]) ).

fof(f_4754_3,plain,
    ! [U_19859,U_19858,U_19860,U_19861] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),hAPP(c_Nat_OSuc,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19858)),U_19859))),c_List_Ofoldr(tc_List_Olist(U_19860),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19860)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19860))),U_19861,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_19858)),U_19859)),c_List_Ofoldr(tc_List_Olist(U_19860),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19860)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19860),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_19860)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19860)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(U_19860),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_19860)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19860),tc_List_Olist(U_19860),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_19860)))),U_19861),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(definitional_conversion,[status(esa)],[f_4754_2]) ).

cnf(f_4754_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_19858)),U_19859))),c_List_Ofoldr(tc_List_Olist(U_19860),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19860)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19860))),U_19861,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_19858)),U_19859)),c_List_Ofoldr(tc_List_Olist(U_19860),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19860)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19860),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_19860)),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19860)))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),hAPP(c_List_Ofilter(tc_List_Olist(U_19860),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_19860)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19860),tc_List_Olist(U_19860),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_19860)))),U_19861),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))),
    inference(clausify,[status(thm)],[f_4754_3]) ).

fof(f_4755_1,plain,
    ! [V_no_2,V_yes_2,V_xs_2,V_Pa_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_Pa_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_4755_2,plain,
    ! [U_19866,U_19865,U_19864,U_19863,U_19862] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19862,tc_HOL_Obool)),hAPP(c_List_Oset(U_19862),U_19865)),hAPP(c_List_Oset(U_19862),U_19866)) = hAPP(c_List_Oset(U_19862),U_19864)
      | c_List_Opartition(U_19862,U_19863,U_19864) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19862),tc_List_Olist(U_19862)),U_19865),U_19866) ),
    inference(variable_rename,[status(thm)],[f_4755_1]) ).

fof(f_4755_3,plain,
    ! [U_19862,U_19863,U_19864,U_19865,U_19866] :
      ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19862,tc_HOL_Obool)),hAPP(c_List_Oset(U_19862),U_19865)),hAPP(c_List_Oset(U_19862),U_19866)) = hAPP(c_List_Oset(U_19862),U_19864)
      | c_List_Opartition(U_19862,U_19863,U_19864) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19862),tc_List_Olist(U_19862)),U_19865),U_19866) ),
    inference(definitional_conversion,[status(esa)],[f_4755_2]) ).

cnf(f_4755_4,plain,
    ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_19862,tc_HOL_Obool)),hAPP(c_List_Oset(U_19862),U_19865)),hAPP(c_List_Oset(U_19862),U_19866)) = hAPP(c_List_Oset(U_19862),U_19864)
    | c_List_Opartition(U_19862,U_19863,U_19864) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19862),tc_List_Olist(U_19862)),U_19865),U_19866) ),
    inference(clausify,[status(thm)],[f_4755_3]) ).

fof(f_4756_1,plain,
    ! [V_xs_2,V_Pa_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_Pa_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_4756_2,plain,
    ! [U_19869,U_19868,U_19867] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19867)),hAPP(c_List_Ofilter(U_19867,U_19868),U_19869))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19867)),U_19869))),
    inference(variable_rename,[status(thm)],[f_4756_1]) ).

fof(f_4756_3,plain,
    ! [U_19867,U_19868,U_19869] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19867)),hAPP(c_List_Ofilter(U_19867,U_19868),U_19869))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19867)),U_19869))),
    inference(definitional_conversion,[status(esa)],[f_4756_2]) ).

cnf(f_4756_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19867)),hAPP(c_List_Ofilter(U_19867,U_19868),U_19869))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19867)),U_19869))),
    inference(clausify,[status(thm)],[f_4756_3]) ).

fof(f_4757_1,plain,
    ! [V_xs_2,V_Pa_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_Pa_2),V_xs_2))),hAPP(c_List_Oset(T_b),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_filter__is__subset]) ).

fof(f_4757_2,plain,
    ! [U_19872,U_19871,U_19870] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19870,tc_HOL_Obool)),hAPP(c_List_Oset(U_19870),hAPP(c_List_Ofilter(U_19870,U_19871),U_19872))),hAPP(c_List_Oset(U_19870),U_19872))),
    inference(variable_rename,[status(thm)],[f_4757_1]) ).

fof(f_4757_3,plain,
    ! [U_19870,U_19871,U_19872] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19870,tc_HOL_Obool)),hAPP(c_List_Oset(U_19870),hAPP(c_List_Ofilter(U_19870,U_19871),U_19872))),hAPP(c_List_Oset(U_19870),U_19872))),
    inference(definitional_conversion,[status(esa)],[f_4757_2]) ).

cnf(f_4757_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(U_19870,tc_HOL_Obool)),hAPP(c_List_Oset(U_19870),hAPP(c_List_Ofilter(U_19870,U_19871),U_19872))),hAPP(c_List_Oset(U_19870),U_19872))),
    inference(clausify,[status(thm)],[f_4757_3]) ).

fof(f_4758_1,plain,
    ! [V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_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_4758_2,plain,
    ! [U_19874,U_19873] : hAPP(c_List_Ofilter(U_19873,U_19874),c_List_Olist_ONil(U_19873)) = c_List_Olist_ONil(U_19873),
    inference(variable_rename,[status(thm)],[f_4758_1]) ).

fof(f_4758_3,plain,
    ! [U_19873,U_19874] : hAPP(c_List_Ofilter(U_19873,U_19874),c_List_Olist_ONil(U_19873)) = c_List_Olist_ONil(U_19873),
    inference(definitional_conversion,[status(esa)],[f_4758_2]) ).

cnf(f_4758_4,plain,
    hAPP(c_List_Ofilter(U_19873,U_19874),c_List_Olist_ONil(U_19873)) = c_List_Olist_ONil(U_19873),
    inference(clausify,[status(thm)],[f_4758_3]) ).

fof(f_4759_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = c_List_Olist_ONil(T_b)
        | ? [B_x] :
            ( hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2),V_xs_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_filter__empty__conv]) ).

fof(f_4759_2,plain,
    ! [U_19879,U_19878,U_19877] :
      ( ( hAPP(c_List_Ofilter(U_19877,U_19878),U_19879) = c_List_Olist_ONil(U_19877)
        | ? [U_19876] :
            ( hBOOL(hAPP(U_19878,U_19876))
            & hBOOL(hAPP(hAPP(c_member(U_19877),U_19876),hAPP(c_List_Oset(U_19877),U_19879))) ) )
      & ( ! [U_19875] :
            ( ~ hBOOL(hAPP(U_19878,U_19875))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19877),U_19875),hAPP(c_List_Oset(U_19877),U_19879))) )
        | hAPP(c_List_Ofilter(U_19877,U_19878),U_19879) != c_List_Olist_ONil(U_19877) ) ),
    inference(variable_rename,[status(thm)],[f_4759_1]) ).

fof(f_4759_3,plain,
    ( ! [U_19885,U_19883,U_19881] :
        ( hAPP(c_List_Ofilter(U_19881,U_19883),U_19885) = c_List_Olist_ONil(U_19881)
        | ? [U_19876] :
            ( hBOOL(hAPP(U_19883,U_19876))
            & hBOOL(hAPP(hAPP(c_member(U_19881),U_19876),hAPP(c_List_Oset(U_19881),U_19885))) ) )
    & ! [U_19884,U_19882,U_19880] :
        ( ! [U_19875] :
            ( ~ hBOOL(hAPP(U_19882,U_19875))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19880),U_19875),hAPP(c_List_Oset(U_19880),U_19884))) )
        | hAPP(c_List_Ofilter(U_19880,U_19882),U_19884) != c_List_Olist_ONil(U_19880) ) ),
    inference(miniscope,[status(thm)],[f_4759_2]) ).

fof(f_4759_4,plain,
    ( ! [U_19885,U_19883,U_19881] :
        ( hAPP(c_List_Ofilter(U_19881,U_19883),U_19885) = c_List_Olist_ONil(U_19881)
        | ( hBOOL(hAPP(U_19883,sK489(U_19885,U_19883,U_19881)))
          & hBOOL(hAPP(hAPP(c_member(U_19881),sK489(U_19885,U_19883,U_19881)),hAPP(c_List_Oset(U_19881),U_19885))) ) )
    & ! [U_19884,U_19882,U_19880] :
        ( ! [U_19875] :
            ( ~ hBOOL(hAPP(U_19882,U_19875))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19880),U_19875),hAPP(c_List_Oset(U_19880),U_19884))) )
        | hAPP(c_List_Ofilter(U_19880,U_19882),U_19884) != c_List_Olist_ONil(U_19880) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK489]),skolemize(U_19876,sK489(U_19885,U_19883,U_19881))],[f_4759_3]) ).

fof(f_4759_5,plain,
    ( ! [U_19885,U_19883,U_19881] :
        ( hBOOL(hAPP(U_19883,sK489(U_19885,U_19883,U_19881)))
        | ~ sP1203(U_19885,U_19883,U_19881) )
    & ! [U_19885,U_19883,U_19881] :
        ( hBOOL(hAPP(hAPP(c_member(U_19881),sK489(U_19885,U_19883,U_19881)),hAPP(c_List_Oset(U_19881),U_19885)))
        | ~ sP1203(U_19885,U_19883,U_19881) )
    & ! [U_19885,U_19883,U_19881] :
        ( hAPP(c_List_Ofilter(U_19881,U_19883),U_19885) = c_List_Olist_ONil(U_19881)
        | sP1203(U_19885,U_19883,U_19881) )
    & ! [U_19882,U_19875,U_19880,U_19884] :
        ( ~ hBOOL(hAPP(U_19882,U_19875))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19880),U_19875),hAPP(c_List_Oset(U_19880),U_19884)))
        | hAPP(c_List_Ofilter(U_19880,U_19882),U_19884) != c_List_Olist_ONil(U_19880) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1203])],[f_4759_4]) ).

cnf(f_4759_6,plain,
    ( ~ hBOOL(hAPP(U_19882,U_19875))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19880),U_19875),hAPP(c_List_Oset(U_19880),U_19884)))
    | hAPP(c_List_Ofilter(U_19880,U_19882),U_19884) != c_List_Olist_ONil(U_19880) ),
    inference(clausify,[status(thm)],[f_4759_5]) ).

cnf(f_4759_7,plain,
    ( hAPP(c_List_Ofilter(U_19881,U_19883),U_19885) = c_List_Olist_ONil(U_19881)
    | sP1203(U_19885,U_19883,U_19881) ),
    inference(clausify,[status(thm)],[f_4759_5]) ).

cnf(f_4759_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19881),sK489(U_19885,U_19883,U_19881)),hAPP(c_List_Oset(U_19881),U_19885)))
    | ~ sP1203(U_19885,U_19883,U_19881) ),
    inference(clausify,[status(thm)],[f_4759_5]) ).

cnf(f_4759_9,plain,
    ( hBOOL(hAPP(U_19883,sK489(U_19885,U_19883,U_19881)))
    | ~ sP1203(U_19885,U_19883,U_19881) ),
    inference(clausify,[status(thm)],[f_4759_5]) ).

fof(f_4760_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ( hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2) = V_xs_2
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_2),V_xs_2) != V_xs_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_filter__id__conv]) ).

fof(f_4760_2,plain,
    ! [U_19890,U_19889,U_19888] :
      ( ( hAPP(c_List_Ofilter(U_19888,U_19889),U_19890) = U_19890
        | ? [U_19887] :
            ( ~ hBOOL(hAPP(U_19889,U_19887))
            & hBOOL(hAPP(hAPP(c_member(U_19888),U_19887),hAPP(c_List_Oset(U_19888),U_19890))) ) )
      & ( ! [U_19886] :
            ( hBOOL(hAPP(U_19889,U_19886))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19888),U_19886),hAPP(c_List_Oset(U_19888),U_19890))) )
        | hAPP(c_List_Ofilter(U_19888,U_19889),U_19890) != U_19890 ) ),
    inference(variable_rename,[status(thm)],[f_4760_1]) ).

fof(f_4760_3,plain,
    ( ! [U_19896,U_19894,U_19892] :
        ( hAPP(c_List_Ofilter(U_19892,U_19894),U_19896) = U_19896
        | ? [U_19887] :
            ( ~ hBOOL(hAPP(U_19894,U_19887))
            & hBOOL(hAPP(hAPP(c_member(U_19892),U_19887),hAPP(c_List_Oset(U_19892),U_19896))) ) )
    & ! [U_19895,U_19893,U_19891] :
        ( ! [U_19886] :
            ( hBOOL(hAPP(U_19893,U_19886))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19891),U_19886),hAPP(c_List_Oset(U_19891),U_19895))) )
        | hAPP(c_List_Ofilter(U_19891,U_19893),U_19895) != U_19895 ) ),
    inference(miniscope,[status(thm)],[f_4760_2]) ).

fof(f_4760_4,plain,
    ( ! [U_19896,U_19894,U_19892] :
        ( hAPP(c_List_Ofilter(U_19892,U_19894),U_19896) = U_19896
        | ( ~ hBOOL(hAPP(U_19894,sK490(U_19896,U_19894,U_19892)))
          & hBOOL(hAPP(hAPP(c_member(U_19892),sK490(U_19896,U_19894,U_19892)),hAPP(c_List_Oset(U_19892),U_19896))) ) )
    & ! [U_19895,U_19893,U_19891] :
        ( ! [U_19886] :
            ( hBOOL(hAPP(U_19893,U_19886))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19891),U_19886),hAPP(c_List_Oset(U_19891),U_19895))) )
        | hAPP(c_List_Ofilter(U_19891,U_19893),U_19895) != U_19895 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK490]),skolemize(U_19887,sK490(U_19896,U_19894,U_19892))],[f_4760_3]) ).

fof(f_4760_5,plain,
    ( ! [U_19896,U_19894,U_19892] :
        ( ~ hBOOL(hAPP(U_19894,sK490(U_19896,U_19894,U_19892)))
        | ~ sP1204(U_19896,U_19894,U_19892) )
    & ! [U_19896,U_19894,U_19892] :
        ( hBOOL(hAPP(hAPP(c_member(U_19892),sK490(U_19896,U_19894,U_19892)),hAPP(c_List_Oset(U_19892),U_19896)))
        | ~ sP1204(U_19896,U_19894,U_19892) )
    & ! [U_19896,U_19894,U_19892] :
        ( hAPP(c_List_Ofilter(U_19892,U_19894),U_19896) = U_19896
        | sP1204(U_19896,U_19894,U_19892) )
    & ! [U_19886,U_19895,U_19891,U_19893] :
        ( hBOOL(hAPP(U_19893,U_19886))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19891),U_19886),hAPP(c_List_Oset(U_19891),U_19895)))
        | hAPP(c_List_Ofilter(U_19891,U_19893),U_19895) != U_19895 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1204])],[f_4760_4]) ).

cnf(f_4760_6,plain,
    ( hBOOL(hAPP(U_19893,U_19886))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19891),U_19886),hAPP(c_List_Oset(U_19891),U_19895)))
    | hAPP(c_List_Ofilter(U_19891,U_19893),U_19895) != U_19895 ),
    inference(clausify,[status(thm)],[f_4760_5]) ).

cnf(f_4760_7,plain,
    ( hAPP(c_List_Ofilter(U_19892,U_19894),U_19896) = U_19896
    | sP1204(U_19896,U_19894,U_19892) ),
    inference(clausify,[status(thm)],[f_4760_5]) ).

cnf(f_4760_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_19892),sK490(U_19896,U_19894,U_19892)),hAPP(c_List_Oset(U_19892),U_19896)))
    | ~ sP1204(U_19896,U_19894,U_19892) ),
    inference(clausify,[status(thm)],[f_4760_5]) ).

cnf(f_4760_9,plain,
    ( ~ hBOOL(hAPP(U_19894,sK490(U_19896,U_19894,U_19892)))
    | ~ sP1204(U_19896,U_19894,U_19892) ),
    inference(clausify,[status(thm)],[f_4760_5]) ).

fof(f_4761_1,plain,
    ! [V_xs_2,V_f_2,T_b,V_x_2,V_Pa_2,T_c] :
      ( hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_xs_2)
      | hBOOL(hAPP(V_Pa_2,V_x_2))
      | ~ class_Orderings_Olinorder(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_filter__insort__triv]) ).

fof(f_4761_2,plain,
    ! [U_19902,U_19901,U_19900,U_19899,U_19898,U_19897] :
      ( hAPP(c_List_Ofilter(U_19900,U_19898),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19900,U_19897,U_19901),U_19899),U_19902)) = hAPP(c_List_Ofilter(U_19900,U_19898),U_19902)
      | hBOOL(hAPP(U_19898,U_19899))
      | ~ class_Orderings_Olinorder(U_19897) ),
    inference(variable_rename,[status(thm)],[f_4761_1]) ).

fof(f_4761_3,plain,
    ! [U_19899,U_19898,U_19897,U_19900,U_19901,U_19902] :
      ( hAPP(c_List_Ofilter(U_19900,U_19898),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19900,U_19897,U_19901),U_19899),U_19902)) = hAPP(c_List_Ofilter(U_19900,U_19898),U_19902)
      | hBOOL(hAPP(U_19898,U_19899))
      | ~ class_Orderings_Olinorder(U_19897) ),
    inference(definitional_conversion,[status(esa)],[f_4761_2]) ).

cnf(f_4761_4,plain,
    ( hAPP(c_List_Ofilter(U_19900,U_19898),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_19900,U_19897,U_19901),U_19899),U_19902)) = hAPP(c_List_Ofilter(U_19900,U_19898),U_19902)
    | hBOOL(hAPP(U_19898,U_19899))
    | ~ class_Orderings_Olinorder(U_19897) ),
    inference(clausify,[status(thm)],[f_4761_3]) ).

fof(f_4762_1,plain,
    ! [V_Pa_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__filter]) ).

fof(f_4762_2,plain,
    ! [U_19905,U_19904,U_19903] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19903),hAPP(c_List_Ofilter(U_19903,U_19905),U_19904)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19903),U_19904)) ),
    inference(variable_rename,[status(thm)],[f_4762_1]) ).

fof(f_4762_3,plain,
    ! [U_19905,U_19904,U_19903] :
      ( hBOOL(hAPP(c_List_Odistinct(U_19903),hAPP(c_List_Ofilter(U_19903,U_19905),U_19904)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19903),U_19904)) ),
    inference(definitional_conversion,[status(esa)],[f_4762_2]) ).

cnf(f_4762_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_19903),hAPP(c_List_Ofilter(U_19903,U_19905),U_19904)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19903),U_19904)) ),
    inference(clausify,[status(thm)],[f_4762_3]) ).

fof(f_4763_1,plain,
    ! [V_xs_2,V_x_2,V_Qa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Qa_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_Qa_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_filter__remove1]) ).

fof(f_4763_2,plain,
    ! [U_19909,U_19908,U_19907,U_19906] : hAPP(c_List_Ofilter(U_19906,U_19907),c_List_Oremove1(U_19906,U_19908,U_19909)) = c_List_Oremove1(U_19906,U_19908,hAPP(c_List_Ofilter(U_19906,U_19907),U_19909)),
    inference(variable_rename,[status(thm)],[f_4763_1]) ).

fof(f_4763_3,plain,
    ! [U_19906,U_19907,U_19908,U_19909] : hAPP(c_List_Ofilter(U_19906,U_19907),c_List_Oremove1(U_19906,U_19908,U_19909)) = c_List_Oremove1(U_19906,U_19908,hAPP(c_List_Ofilter(U_19906,U_19907),U_19909)),
    inference(definitional_conversion,[status(esa)],[f_4763_2]) ).

cnf(f_4763_4,plain,
    hAPP(c_List_Ofilter(U_19906,U_19907),c_List_Oremove1(U_19906,U_19908,U_19909)) = c_List_Oremove1(U_19906,U_19908,hAPP(c_List_Ofilter(U_19906,U_19907),U_19909)),
    inference(clausify,[status(thm)],[f_4763_3]) ).

fof(f_4764_1,plain,
    ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
      ( c_List_Oremove1(T_b,V_x_2,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)
      | hBOOL(hAPP(V_Pa_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_remove1__filter__not]) ).

fof(f_4764_2,plain,
    ! [U_19913,U_19912,U_19911,U_19910] :
      ( c_List_Oremove1(U_19912,U_19911,hAPP(c_List_Ofilter(U_19912,U_19910),U_19913)) = hAPP(c_List_Ofilter(U_19912,U_19910),U_19913)
      | hBOOL(hAPP(U_19910,U_19911)) ),
    inference(variable_rename,[status(thm)],[f_4764_1]) ).

fof(f_4764_3,plain,
    ! [U_19910,U_19911,U_19912,U_19913] :
      ( c_List_Oremove1(U_19912,U_19911,hAPP(c_List_Ofilter(U_19912,U_19910),U_19913)) = hAPP(c_List_Ofilter(U_19912,U_19910),U_19913)
      | hBOOL(hAPP(U_19910,U_19911)) ),
    inference(definitional_conversion,[status(esa)],[f_4764_2]) ).

cnf(f_4764_4,plain,
    ( c_List_Oremove1(U_19912,U_19911,hAPP(c_List_Ofilter(U_19912,U_19910),U_19913)) = hAPP(c_List_Ofilter(U_19912,U_19910),U_19913)
    | hBOOL(hAPP(U_19910,U_19911)) ),
    inference(clausify,[status(thm)],[f_4764_3]) ).

fof(f_4765_1,plain,
    ! [V_xs_2,V_Qa_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Ofilter(T_b,V_Qa_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_Qa_2)),V_Pa_2)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_filter__filter]) ).

fof(f_4765_2,plain,
    ! [U_19917,U_19916,U_19915,U_19914] : hAPP(c_List_Ofilter(U_19914,U_19915),hAPP(c_List_Ofilter(U_19914,U_19916),U_19917)) = hAPP(c_List_Ofilter(U_19914,hAPP(hAPP(c_COMBS(U_19914,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19914),c_fconj),U_19916)),U_19915)),U_19917),
    inference(variable_rename,[status(thm)],[f_4765_1]) ).

fof(f_4765_3,plain,
    ! [U_19914,U_19915,U_19916,U_19917] : hAPP(c_List_Ofilter(U_19914,U_19915),hAPP(c_List_Ofilter(U_19914,U_19916),U_19917)) = hAPP(c_List_Ofilter(U_19914,hAPP(hAPP(c_COMBS(U_19914,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19914),c_fconj),U_19916)),U_19915)),U_19917),
    inference(definitional_conversion,[status(esa)],[f_4765_2]) ).

cnf(f_4765_4,plain,
    hAPP(c_List_Ofilter(U_19914,U_19915),hAPP(c_List_Ofilter(U_19914,U_19916),U_19917)) = hAPP(c_List_Ofilter(U_19914,hAPP(hAPP(c_COMBS(U_19914,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19914),c_fconj),U_19916)),U_19915)),U_19917),
    inference(clausify,[status(thm)],[f_4765_3]) ).

fof(f_4766_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Ofst(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_2,V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_partition__filter1]) ).

fof(f_4766_2,plain,
    ! [U_19920,U_19919,U_19918] : hAPP(c_Product__Type_Ofst(tc_List_Olist(U_19918),tc_List_Olist(U_19918)),c_List_Opartition(U_19918,U_19919,U_19920)) = hAPP(c_List_Ofilter(U_19918,U_19919),U_19920),
    inference(variable_rename,[status(thm)],[f_4766_1]) ).

fof(f_4766_3,plain,
    ! [U_19918,U_19919,U_19920] : hAPP(c_Product__Type_Ofst(tc_List_Olist(U_19918),tc_List_Olist(U_19918)),c_List_Opartition(U_19918,U_19919,U_19920)) = hAPP(c_List_Ofilter(U_19918,U_19919),U_19920),
    inference(definitional_conversion,[status(esa)],[f_4766_2]) ).

cnf(f_4766_4,plain,
    hAPP(c_Product__Type_Ofst(tc_List_Olist(U_19918),tc_List_Olist(U_19918)),c_List_Opartition(U_19918,U_19919,U_19920)) = hAPP(c_List_Ofilter(U_19918,U_19919),U_19920),
    inference(clausify,[status(thm)],[f_4766_3]) ).

fof(f_4767_1,plain,
    ! [V_xs_2,V_Pa_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_Pa_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_Pa_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_4767_2,plain,
    ! [U_19923,U_19922,U_19921] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19921)),hAPP(c_List_Ofilter(U_19921,U_19922),U_19923))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19921)),hAPP(c_List_Ofilter(U_19921,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19921),c_fNot),U_19922)),U_19923))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19921)),U_19923),
    inference(variable_rename,[status(thm)],[f_4767_1]) ).

fof(f_4767_3,plain,
    ! [U_19921,U_19922,U_19923] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19921)),hAPP(c_List_Ofilter(U_19921,U_19922),U_19923))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19921)),hAPP(c_List_Ofilter(U_19921,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19921),c_fNot),U_19922)),U_19923))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19921)),U_19923),
    inference(definitional_conversion,[status(esa)],[f_4767_2]) ).

cnf(f_4767_4,plain,
    hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19921)),hAPP(c_List_Ofilter(U_19921,U_19922),U_19923))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19921)),hAPP(c_List_Ofilter(U_19921,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19921),c_fNot),U_19922)),U_19923))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19921)),U_19923),
    inference(clausify,[status(thm)],[f_4767_3]) ).

fof(f_4768_1,plain,
    ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
      ( ( hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)
        | hBOOL(hAPP(V_Pa_2,V_x_2)) )
      & ( hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_xs_2))
        | ~ hBOOL(hAPP(V_Pa_2,V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_filter_Osimps_I2_J]) ).

fof(f_4768_2,plain,
    ! [U_19927,U_19926,U_19925,U_19924] :
      ( ( hAPP(c_List_Ofilter(U_19926,U_19924),hAPP(hAPP(c_List_Olist_OCons(U_19926),U_19925),U_19927)) = hAPP(c_List_Ofilter(U_19926,U_19924),U_19927)
        | hBOOL(hAPP(U_19924,U_19925)) )
      & ( hAPP(c_List_Ofilter(U_19926,U_19924),hAPP(hAPP(c_List_Olist_OCons(U_19926),U_19925),U_19927)) = hAPP(hAPP(c_List_Olist_OCons(U_19926),U_19925),hAPP(c_List_Ofilter(U_19926,U_19924),U_19927))
        | ~ hBOOL(hAPP(U_19924,U_19925)) ) ),
    inference(variable_rename,[status(thm)],[f_4768_1]) ).

fof(f_4768_3,plain,
    ( ! [U_19935,U_19933,U_19931,U_19929] :
        ( hAPP(c_List_Ofilter(U_19933,U_19929),hAPP(hAPP(c_List_Olist_OCons(U_19933),U_19931),U_19935)) = hAPP(c_List_Ofilter(U_19933,U_19929),U_19935)
        | hBOOL(hAPP(U_19929,U_19931)) )
    & ! [U_19934,U_19932,U_19930,U_19928] :
        ( hAPP(c_List_Ofilter(U_19932,U_19928),hAPP(hAPP(c_List_Olist_OCons(U_19932),U_19930),U_19934)) = hAPP(hAPP(c_List_Olist_OCons(U_19932),U_19930),hAPP(c_List_Ofilter(U_19932,U_19928),U_19934))
        | ~ hBOOL(hAPP(U_19928,U_19930)) ) ),
    inference(miniscope,[status(thm)],[f_4768_2]) ).

fof(f_4768_4,plain,
    ( ! [U_19929,U_19931,U_19933,U_19935] :
        ( hAPP(c_List_Ofilter(U_19933,U_19929),hAPP(hAPP(c_List_Olist_OCons(U_19933),U_19931),U_19935)) = hAPP(c_List_Ofilter(U_19933,U_19929),U_19935)
        | hBOOL(hAPP(U_19929,U_19931)) )
    & ! [U_19930,U_19934,U_19928,U_19932] :
        ( hAPP(c_List_Ofilter(U_19932,U_19928),hAPP(hAPP(c_List_Olist_OCons(U_19932),U_19930),U_19934)) = hAPP(hAPP(c_List_Olist_OCons(U_19932),U_19930),hAPP(c_List_Ofilter(U_19932,U_19928),U_19934))
        | ~ hBOOL(hAPP(U_19928,U_19930)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4768_3]) ).

cnf(f_4768_5,plain,
    ( hAPP(c_List_Ofilter(U_19932,U_19928),hAPP(hAPP(c_List_Olist_OCons(U_19932),U_19930),U_19934)) = hAPP(hAPP(c_List_Olist_OCons(U_19932),U_19930),hAPP(c_List_Ofilter(U_19932,U_19928),U_19934))
    | ~ hBOOL(hAPP(U_19928,U_19930)) ),
    inference(clausify,[status(thm)],[f_4768_4]) ).

cnf(f_4768_6,plain,
    ( hAPP(c_List_Ofilter(U_19933,U_19929),hAPP(hAPP(c_List_Olist_OCons(U_19933),U_19931),U_19935)) = hAPP(c_List_Ofilter(U_19933,U_19929),U_19935)
    | hBOOL(hAPP(U_19929,U_19931)) ),
    inference(clausify,[status(thm)],[f_4768_4]) ).

fof(f_4769_1,plain,
    ! [V_ys_2,V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_xs_2)),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_filter__append]) ).

fof(f_4769_2,plain,
    ! [U_19939,U_19938,U_19937,U_19936] : hAPP(c_List_Ofilter(U_19936,U_19937),hAPP(hAPP(c_List_Oappend(U_19936),U_19938),U_19939)) = hAPP(hAPP(c_List_Oappend(U_19936),hAPP(c_List_Ofilter(U_19936,U_19937),U_19938)),hAPP(c_List_Ofilter(U_19936,U_19937),U_19939)),
    inference(variable_rename,[status(thm)],[f_4769_1]) ).

fof(f_4769_3,plain,
    ! [U_19936,U_19937,U_19938,U_19939] : hAPP(c_List_Ofilter(U_19936,U_19937),hAPP(hAPP(c_List_Oappend(U_19936),U_19938),U_19939)) = hAPP(hAPP(c_List_Oappend(U_19936),hAPP(c_List_Ofilter(U_19936,U_19937),U_19938)),hAPP(c_List_Ofilter(U_19936,U_19937),U_19939)),
    inference(definitional_conversion,[status(esa)],[f_4769_2]) ).

cnf(f_4769_4,plain,
    hAPP(c_List_Ofilter(U_19936,U_19937),hAPP(hAPP(c_List_Oappend(U_19936),U_19938),U_19939)) = hAPP(hAPP(c_List_Oappend(U_19936),hAPP(c_List_Ofilter(U_19936,U_19937),U_19938)),hAPP(c_List_Ofilter(U_19936,U_19937),U_19939)),
    inference(clausify,[status(thm)],[f_4769_3]) ).

fof(f_4770_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_4770_2,plain,
    ! [U_19942,U_19941,U_19940] : c_List_Opartition(U_19940,U_19941,U_19942) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19940),tc_List_Olist(U_19940)),hAPP(c_List_Ofilter(U_19940,U_19941),U_19942)),hAPP(c_List_Ofilter(U_19940,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_19940,c_fNot),U_19941)),U_19942)),
    inference(variable_rename,[status(thm)],[f_4770_1]) ).

fof(f_4770_3,plain,
    ! [U_19940,U_19941,U_19942] : c_List_Opartition(U_19940,U_19941,U_19942) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19940),tc_List_Olist(U_19940)),hAPP(c_List_Ofilter(U_19940,U_19941),U_19942)),hAPP(c_List_Ofilter(U_19940,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_19940,c_fNot),U_19941)),U_19942)),
    inference(definitional_conversion,[status(esa)],[f_4770_2]) ).

cnf(f_4770_4,plain,
    c_List_Opartition(U_19940,U_19941,U_19942) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19940),tc_List_Olist(U_19940)),hAPP(c_List_Ofilter(U_19940,U_19941),U_19942)),hAPP(c_List_Ofilter(U_19940,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_19940,c_fNot),U_19941)),U_19942)),
    inference(clausify,[status(thm)],[f_4770_3]) ).

fof(f_4771_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_f_2)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_filter__map]) ).

fof(f_4771_2,plain,
    ! [U_19947,U_19946,U_19945,U_19944,U_19943] : hAPP(c_List_Ofilter(U_19943,U_19944),hAPP(hAPP(c_List_Omap(U_19945,U_19943),U_19946),U_19947)) = hAPP(hAPP(c_List_Omap(U_19945,U_19943),U_19946),hAPP(c_List_Ofilter(U_19945,hAPP(c_Fun_Ocomp(U_19943,tc_HOL_Obool,U_19945,U_19944),U_19946)),U_19947)),
    inference(variable_rename,[status(thm)],[f_4771_1]) ).

fof(f_4771_3,plain,
    ! [U_19943,U_19944,U_19945,U_19946,U_19947] : hAPP(c_List_Ofilter(U_19943,U_19944),hAPP(hAPP(c_List_Omap(U_19945,U_19943),U_19946),U_19947)) = hAPP(hAPP(c_List_Omap(U_19945,U_19943),U_19946),hAPP(c_List_Ofilter(U_19945,hAPP(c_Fun_Ocomp(U_19943,tc_HOL_Obool,U_19945,U_19944),U_19946)),U_19947)),
    inference(definitional_conversion,[status(esa)],[f_4771_2]) ).

cnf(f_4771_4,plain,
    hAPP(c_List_Ofilter(U_19943,U_19944),hAPP(hAPP(c_List_Omap(U_19945,U_19943),U_19946),U_19947)) = hAPP(hAPP(c_List_Omap(U_19945,U_19943),U_19946),hAPP(c_List_Ofilter(U_19945,hAPP(c_Fun_Ocomp(U_19943,tc_HOL_Obool,U_19945,U_19944),U_19946)),U_19947)),
    inference(clausify,[status(thm)],[f_4771_3]) ).

fof(f_4772_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_Product__Type_Osnd(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Opartition(T_b,V_Pa_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_Pa_2)),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_partition__filter2]) ).

fof(f_4772_2,plain,
    ! [U_19950,U_19949,U_19948] : hAPP(c_Product__Type_Osnd(tc_List_Olist(U_19948),tc_List_Olist(U_19948)),c_List_Opartition(U_19948,U_19949,U_19950)) = hAPP(c_List_Ofilter(U_19948,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_19948,c_fNot),U_19949)),U_19950),
    inference(variable_rename,[status(thm)],[f_4772_1]) ).

fof(f_4772_3,plain,
    ! [U_19948,U_19949,U_19950] : hAPP(c_Product__Type_Osnd(tc_List_Olist(U_19948),tc_List_Olist(U_19948)),c_List_Opartition(U_19948,U_19949,U_19950)) = hAPP(c_List_Ofilter(U_19948,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_19948,c_fNot),U_19949)),U_19950),
    inference(definitional_conversion,[status(esa)],[f_4772_2]) ).

cnf(f_4772_4,plain,
    hAPP(c_Product__Type_Osnd(tc_List_Olist(U_19948),tc_List_Olist(U_19948)),c_List_Opartition(U_19948,U_19949,U_19950)) = hAPP(c_List_Ofilter(U_19948,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,U_19948,c_fNot),U_19949)),U_19950),
    inference(clausify,[status(thm)],[f_4772_3]) ).

fof(f_4773_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Oset(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2)),
    inference(fof_nnf,[status(thm)],[fact_set__filter]) ).

fof(f_4773_2,plain,
    ! [U_19953,U_19952,U_19951] : hAPP(c_List_Oset(U_19951),hAPP(c_List_Ofilter(U_19951,U_19952),U_19953)) = hAPP(c_Set_OCollect(U_19951),hAPP(hAPP(c_COMBS(U_19951,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19951),c_fconj),hAPP(hAPP(c_COMBC(U_19951,tc_fun(U_19951,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19951)),hAPP(c_List_Oset(U_19951),U_19953)))),U_19952)),
    inference(variable_rename,[status(thm)],[f_4773_1]) ).

fof(f_4773_3,plain,
    ! [U_19951,U_19952,U_19953] : hAPP(c_List_Oset(U_19951),hAPP(c_List_Ofilter(U_19951,U_19952),U_19953)) = hAPP(c_Set_OCollect(U_19951),hAPP(hAPP(c_COMBS(U_19951,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19951),c_fconj),hAPP(hAPP(c_COMBC(U_19951,tc_fun(U_19951,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19951)),hAPP(c_List_Oset(U_19951),U_19953)))),U_19952)),
    inference(definitional_conversion,[status(esa)],[f_4773_2]) ).

cnf(f_4773_4,plain,
    hAPP(c_List_Oset(U_19951),hAPP(c_List_Ofilter(U_19951,U_19952),U_19953)) = hAPP(c_Set_OCollect(U_19951),hAPP(hAPP(c_COMBS(U_19951,tc_HOL_Obool,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),U_19951),c_fconj),hAPP(hAPP(c_COMBC(U_19951,tc_fun(U_19951,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19951)),hAPP(c_List_Oset(U_19951),U_19953)))),U_19952)),
    inference(clausify,[status(thm)],[f_4773_3]) ).

fof(f_4774_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(c_List_Ofilter(T_b,V_Pa_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_Pa_2),V_f_2)),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_length__filter__map]) ).

fof(f_4774_2,plain,
    ! [U_19958,U_19957,U_19956,U_19955,U_19954] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19954)),hAPP(c_List_Ofilter(U_19954,U_19955),hAPP(hAPP(c_List_Omap(U_19956,U_19954),U_19957),U_19958))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19956)),hAPP(c_List_Ofilter(U_19956,hAPP(c_Fun_Ocomp(U_19954,tc_HOL_Obool,U_19956,U_19955),U_19957)),U_19958)),
    inference(variable_rename,[status(thm)],[f_4774_1]) ).

fof(f_4774_3,plain,
    ! [U_19954,U_19955,U_19956,U_19957,U_19958] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19954)),hAPP(c_List_Ofilter(U_19954,U_19955),hAPP(hAPP(c_List_Omap(U_19956,U_19954),U_19957),U_19958))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19956)),hAPP(c_List_Ofilter(U_19956,hAPP(c_Fun_Ocomp(U_19954,tc_HOL_Obool,U_19956,U_19955),U_19957)),U_19958)),
    inference(definitional_conversion,[status(esa)],[f_4774_2]) ).

cnf(f_4774_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19954)),hAPP(c_List_Ofilter(U_19954,U_19955),hAPP(hAPP(c_List_Omap(U_19956,U_19954),U_19957),U_19958))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19956)),hAPP(c_List_Ofilter(U_19956,hAPP(c_Fun_Ocomp(U_19954,tc_HOL_Obool,U_19956,U_19955),U_19957)),U_19958)),
    inference(clausify,[status(thm)],[f_4774_3]) ).

fof(f_4775_1,plain,
    ! [V_Pa_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_Pa_2),V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)))
      | hBOOL(hAPP(V_Pa_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_4775_2,plain,
    ! [U_19962,U_19961,U_19960,U_19959] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19959)),hAPP(c_List_Ofilter(U_19959,U_19962),U_19961))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19959)),U_19961)))
      | hBOOL(hAPP(U_19962,U_19960))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19959),U_19960),hAPP(c_List_Oset(U_19959),U_19961))) ),
    inference(variable_rename,[status(thm)],[f_4775_1]) ).

fof(f_4775_3,plain,
    ! [U_19959,U_19960,U_19961,U_19962] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19959)),hAPP(c_List_Ofilter(U_19959,U_19962),U_19961))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19959)),U_19961)))
      | hBOOL(hAPP(U_19962,U_19960))
      | ~ hBOOL(hAPP(hAPP(c_member(U_19959),U_19960),hAPP(c_List_Oset(U_19959),U_19961))) ),
    inference(definitional_conversion,[status(esa)],[f_4775_2]) ).

cnf(f_4775_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19959)),hAPP(c_List_Ofilter(U_19959,U_19962),U_19961))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19959)),U_19961)))
    | hBOOL(hAPP(U_19962,U_19960))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19959),U_19960),hAPP(c_List_Oset(U_19959),U_19961))) ),
    inference(clausify,[status(thm)],[f_4775_3]) ).

fof(f_4776_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_4776_2,plain,
    ! [U_19965,U_19964,U_19963] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_19963,tc_HOL_Obool)),hAPP(c_List_Oset(U_19963),U_19964)),hAPP(hAPP(c_Set_Oinsert(U_19963),U_19965),c_Orderings_Obot__class_Obot(tc_fun(U_19963,tc_HOL_Obool)))) = hAPP(c_List_Oset(U_19963),hAPP(c_List_Ofilter(U_19963,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19963),c_fNot),hAPP(hAPP(c_COMBC(U_19963,U_19963,tc_HOL_Obool),c_fequal),U_19965))),U_19964)),
    inference(variable_rename,[status(thm)],[f_4776_1]) ).

fof(f_4776_3,plain,
    ! [U_19963,U_19964,U_19965] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_19963,tc_HOL_Obool)),hAPP(c_List_Oset(U_19963),U_19964)),hAPP(hAPP(c_Set_Oinsert(U_19963),U_19965),c_Orderings_Obot__class_Obot(tc_fun(U_19963,tc_HOL_Obool)))) = hAPP(c_List_Oset(U_19963),hAPP(c_List_Ofilter(U_19963,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19963),c_fNot),hAPP(hAPP(c_COMBC(U_19963,U_19963,tc_HOL_Obool),c_fequal),U_19965))),U_19964)),
    inference(definitional_conversion,[status(esa)],[f_4776_2]) ).

cnf(f_4776_4,plain,
    hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(U_19963,tc_HOL_Obool)),hAPP(c_List_Oset(U_19963),U_19964)),hAPP(hAPP(c_Set_Oinsert(U_19963),U_19965),c_Orderings_Obot__class_Obot(tc_fun(U_19963,tc_HOL_Obool)))) = hAPP(c_List_Oset(U_19963),hAPP(c_List_Ofilter(U_19963,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19963),c_fNot),hAPP(hAPP(c_COMBC(U_19963,U_19963,tc_HOL_Obool),c_fequal),U_19965))),U_19964)),
    inference(clausify,[status(thm)],[f_4776_3]) ).

fof(f_4777_1,plain,
    ! [V_no_2,V_yes_2,V_xs_2,V_Pa_2,T_b] :
      ( ( ! [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_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_Pa_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_4777_2,plain,
    ! [U_19972,U_19971,U_19970,U_19969,U_19968] :
      ( ( ! [U_19967] :
            ( ~ hBOOL(hAPP(U_19969,U_19967))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19968),U_19967),hAPP(c_List_Oset(U_19968),U_19972))) )
        & ! [U_19966] :
            ( hBOOL(hAPP(U_19969,U_19966))
            | ~ hBOOL(hAPP(hAPP(c_member(U_19968),U_19966),hAPP(c_List_Oset(U_19968),U_19971))) ) )
      | c_List_Opartition(U_19968,U_19969,U_19970) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19968),tc_List_Olist(U_19968)),U_19971),U_19972) ),
    inference(variable_rename,[status(thm)],[f_4777_1]) ).

fof(f_4777_3,plain,
    ( ! [U_19966,U_19967,U_19968,U_19969,U_19971,U_19972] :
        ( ~ hBOOL(hAPP(U_19969,U_19967))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19968),U_19967),hAPP(c_List_Oset(U_19968),U_19972)))
        | ~ sP1205(U_19966,U_19967,U_19968,U_19969,U_19971,U_19972) )
    & ! [U_19966,U_19967,U_19968,U_19969,U_19971,U_19972] :
        ( hBOOL(hAPP(U_19969,U_19966))
        | ~ hBOOL(hAPP(hAPP(c_member(U_19968),U_19966),hAPP(c_List_Oset(U_19968),U_19971)))
        | ~ sP1205(U_19966,U_19967,U_19968,U_19969,U_19971,U_19972) )
    & ! [U_19966,U_19967,U_19968,U_19969,U_19970,U_19971,U_19972] :
        ( sP1205(U_19966,U_19967,U_19968,U_19969,U_19971,U_19972)
        | c_List_Opartition(U_19968,U_19969,U_19970) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19968),tc_List_Olist(U_19968)),U_19971),U_19972) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1205])],[f_4777_2]) ).

cnf(f_4777_4,plain,
    ( sP1205(U_19966,U_19967,U_19968,U_19969,U_19971,U_19972)
    | c_List_Opartition(U_19968,U_19969,U_19970) != hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19968),tc_List_Olist(U_19968)),U_19971),U_19972) ),
    inference(clausify,[status(thm)],[f_4777_3]) ).

cnf(f_4777_5,plain,
    ( hBOOL(hAPP(U_19969,U_19966))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19968),U_19966),hAPP(c_List_Oset(U_19968),U_19971)))
    | ~ sP1205(U_19966,U_19967,U_19968,U_19969,U_19971,U_19972) ),
    inference(clausify,[status(thm)],[f_4777_3]) ).

cnf(f_4777_6,plain,
    ( ~ hBOOL(hAPP(U_19969,U_19967))
    | ~ hBOOL(hAPP(hAPP(c_member(U_19968),U_19967),hAPP(c_List_Oset(U_19968),U_19972)))
    | ~ sP1205(U_19966,U_19967,U_19968,U_19969,U_19971,U_19972) ),
    inference(clausify,[status(thm)],[f_4777_3]) ).

fof(f_4778_1,plain,
    ! [V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_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_4778_2,plain,
    ! [U_19974,U_19973] : c_List_Opartition(U_19973,U_19974,c_List_Olist_ONil(U_19973)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19973),tc_List_Olist(U_19973)),c_List_Olist_ONil(U_19973)),c_List_Olist_ONil(U_19973)),
    inference(variable_rename,[status(thm)],[f_4778_1]) ).

fof(f_4778_3,plain,
    ! [U_19974,U_19973] : c_List_Opartition(U_19973,U_19974,c_List_Olist_ONil(U_19973)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19973),tc_List_Olist(U_19973)),c_List_Olist_ONil(U_19973)),c_List_Olist_ONil(U_19973)),
    inference(definitional_conversion,[status(esa)],[f_4778_2]) ).

cnf(f_4778_4,plain,
    c_List_Opartition(U_19973,U_19974,c_List_Olist_ONil(U_19973)) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(U_19973),tc_List_Olist(U_19973)),c_List_Olist_ONil(U_19973)),c_List_Olist_ONil(U_19973)),
    inference(clausify,[status(thm)],[f_4778_3]) ).

fof(f_4779_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_4779_2,plain,
    ! [U_19977,U_19976,U_19975] :
      ( hAPP(c_List_Ofilter(U_19975,hAPP(hAPP(c_COMBC(U_19975,tc_fun(U_19975,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19975)),hAPP(c_List_Oset(U_19975),c_List_Osublist(U_19975,U_19976,U_19977)))),U_19976) = c_List_Osublist(U_19975,U_19976,U_19977)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19975),U_19976)) ),
    inference(variable_rename,[status(thm)],[f_4779_1]) ).

fof(f_4779_3,plain,
    ! [U_19975,U_19976,U_19977] :
      ( hAPP(c_List_Ofilter(U_19975,hAPP(hAPP(c_COMBC(U_19975,tc_fun(U_19975,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19975)),hAPP(c_List_Oset(U_19975),c_List_Osublist(U_19975,U_19976,U_19977)))),U_19976) = c_List_Osublist(U_19975,U_19976,U_19977)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_19975),U_19976)) ),
    inference(definitional_conversion,[status(esa)],[f_4779_2]) ).

cnf(f_4779_4,plain,
    ( hAPP(c_List_Ofilter(U_19975,hAPP(hAPP(c_COMBC(U_19975,tc_fun(U_19975,tc_HOL_Obool),tc_HOL_Obool),c_member(U_19975)),hAPP(c_List_Oset(U_19975),c_List_Osublist(U_19975,U_19976,U_19977)))),U_19976) = c_List_Osublist(U_19975,U_19976,U_19977)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_19975),U_19976)) ),
    inference(clausify,[status(thm)],[f_4779_3]) ).

fof(f_4780_1,plain,
    ! [V_xs_2,V_x_2,V_Pa_2,T_b] : c_List_Opartition(T_b,V_Pa_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_Pa_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_Pa_2,V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_partition_Osimps_I2_J]) ).

fof(f_4780_2,plain,
    ! [U_19981,U_19980,U_19979,U_19978] : c_List_Opartition(U_19978,U_19979,hAPP(hAPP(c_List_Olist_OCons(U_19978),U_19980),U_19981)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_19978),tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_19978),tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_19978),tc_fun(tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),tc_fun(tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),tc_List_Olist(U_19978)),c_COMBS(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),tc_fun(tc_List_Olist(U_19978),tc_fun(tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),tc_List_Olist(U_19978)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_fun(tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),tc_List_Olist(U_19978)),hAPP(c_If(tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),hAPP(U_19979,U_19980)))),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19978),tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),tc_List_Olist(U_19978)),c_Product__Type_OPair(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),hAPP(c_List_Olist_OCons(U_19978),U_19980))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19978),tc_fun(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),tc_fun(tc_fun(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),tc_List_Olist(U_19978)),c_COMBB(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_List_Olist(U_19978))),c_Product__Type_OPair(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),hAPP(c_List_Olist_OCons(U_19978),U_19980)))),c_List_Opartition(U_19978,U_19979,U_19981)),
    inference(variable_rename,[status(thm)],[f_4780_1]) ).

fof(f_4780_3,plain,
    ! [U_19978,U_19979,U_19980,U_19981] : c_List_Opartition(U_19978,U_19979,hAPP(hAPP(c_List_Olist_OCons(U_19978),U_19980),U_19981)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_19978),tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_19978),tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_19978),tc_fun(tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),tc_fun(tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),tc_List_Olist(U_19978)),c_COMBS(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),tc_fun(tc_List_Olist(U_19978),tc_fun(tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),tc_List_Olist(U_19978)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_fun(tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),tc_List_Olist(U_19978)),hAPP(c_If(tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),hAPP(U_19979,U_19980)))),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19978),tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),tc_List_Olist(U_19978)),c_Product__Type_OPair(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),hAPP(c_List_Olist_OCons(U_19978),U_19980))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19978),tc_fun(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),tc_fun(tc_fun(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),tc_List_Olist(U_19978)),c_COMBB(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_List_Olist(U_19978))),c_Product__Type_OPair(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),hAPP(c_List_Olist_OCons(U_19978),U_19980)))),c_List_Opartition(U_19978,U_19979,U_19981)),
    inference(definitional_conversion,[status(esa)],[f_4780_2]) ).

cnf(f_4780_4,plain,
    c_List_Opartition(U_19978,U_19979,hAPP(hAPP(c_List_Olist_OCons(U_19978),U_19980),U_19981)) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_19978),tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),hAPP(hAPP(c_COMBS(tc_List_Olist(U_19978),tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_19978),tc_fun(tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),tc_fun(tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),tc_List_Olist(U_19978)),c_COMBS(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),tc_fun(tc_List_Olist(U_19978),tc_fun(tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),tc_List_Olist(U_19978)),hAPP(c_COMBB(tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_fun(tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),tc_List_Olist(U_19978)),hAPP(c_If(tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),hAPP(U_19979,U_19980)))),hAPP(hAPP(c_COMBB(tc_List_Olist(U_19978),tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),tc_List_Olist(U_19978)),c_Product__Type_OPair(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),hAPP(c_List_Olist_OCons(U_19978),U_19980))))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19978),tc_fun(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978))),tc_fun(tc_fun(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_fun(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),tc_List_Olist(U_19978)),c_COMBB(tc_List_Olist(U_19978),tc_prod(tc_List_Olist(U_19978),tc_List_Olist(U_19978)),tc_List_Olist(U_19978))),c_Product__Type_OPair(tc_List_Olist(U_19978),tc_List_Olist(U_19978)))),hAPP(c_List_Olist_OCons(U_19978),U_19980)))),c_List_Opartition(U_19978,U_19979,U_19981)),
    inference(clausify,[status(thm)],[f_4780_3]) ).

fof(f_4781_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_4781_2,plain,
    ! [U_19984,U_19983,U_19982] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19982)),hAPP(c_List_Ofilter(U_19982,U_19983),U_19984)) = 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_19982)),U_19984)))),hAPP(hAPP(c_COMBB(U_19982,tc_HOL_Obool,tc_Nat_Onat),U_19983),hAPP(c_List_Onth(U_19982),U_19984))))),
    inference(variable_rename,[status(thm)],[f_4781_1]) ).

fof(f_4781_3,plain,
    ! [U_19982,U_19983,U_19984] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19982)),hAPP(c_List_Ofilter(U_19982,U_19983),U_19984)) = 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_19982)),U_19984)))),hAPP(hAPP(c_COMBB(U_19982,tc_HOL_Obool,tc_Nat_Onat),U_19983),hAPP(c_List_Onth(U_19982),U_19984))))),
    inference(definitional_conversion,[status(esa)],[f_4781_2]) ).

cnf(f_4781_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_19982)),hAPP(c_List_Ofilter(U_19982,U_19983),U_19984)) = 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_19982)),U_19984)))),hAPP(hAPP(c_COMBB(U_19982,tc_HOL_Obool,tc_Nat_Onat),U_19983),hAPP(c_List_Onth(U_19982),U_19984))))),
    inference(clausify,[status(thm)],[f_4781_3]) ).

fof(f_4782_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_4782_2,plain,
    ! [U_19988,U_19987,U_19986,U_19985] : c_List_Omap__filter(U_19985,U_19986,U_19987,U_19988) = hAPP(hAPP(c_List_Omap(U_19985,U_19986),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_19986),U_19986,U_19985,c_Option_Othe(U_19986)),U_19987)),hAPP(c_List_Ofilter(U_19985,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19985),c_fNot),hAPP(hAPP(c_COMBC(U_19985,tc_Option_Ooption(U_19986),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_19986),tc_fun(tc_Option_Ooption(U_19986),tc_HOL_Obool),U_19985),c_fequal),U_19987)),c_Option_Ooption_ONone(U_19986)))),U_19988)),
    inference(variable_rename,[status(thm)],[f_4782_1]) ).

fof(f_4782_3,plain,
    ! [U_19985,U_19986,U_19987,U_19988] : c_List_Omap__filter(U_19985,U_19986,U_19987,U_19988) = hAPP(hAPP(c_List_Omap(U_19985,U_19986),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_19986),U_19986,U_19985,c_Option_Othe(U_19986)),U_19987)),hAPP(c_List_Ofilter(U_19985,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19985),c_fNot),hAPP(hAPP(c_COMBC(U_19985,tc_Option_Ooption(U_19986),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_19986),tc_fun(tc_Option_Ooption(U_19986),tc_HOL_Obool),U_19985),c_fequal),U_19987)),c_Option_Ooption_ONone(U_19986)))),U_19988)),
    inference(definitional_conversion,[status(esa)],[f_4782_2]) ).

cnf(f_4782_4,plain,
    c_List_Omap__filter(U_19985,U_19986,U_19987,U_19988) = hAPP(hAPP(c_List_Omap(U_19985,U_19986),hAPP(c_Fun_Ocomp(tc_Option_Ooption(U_19986),U_19986,U_19985,c_Option_Othe(U_19986)),U_19987)),hAPP(c_List_Ofilter(U_19985,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_19985),c_fNot),hAPP(hAPP(c_COMBC(U_19985,tc_Option_Ooption(U_19986),tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_Option_Ooption(U_19986),tc_fun(tc_Option_Ooption(U_19986),tc_HOL_Obool),U_19985),c_fequal),U_19987)),c_Option_Ooption_ONone(U_19986)))),U_19988)),
    inference(clausify,[status(thm)],[f_4782_3]) ).

fof(f_4783_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_4783_2,plain,
    ! [U_19990,U_19989] : c_List_Ofoldr(tc_List_Olist(U_19989),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19989)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19989))),c_List_Otranspose(U_19989,U_19990),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19989))),hAPP(c_List_Ofilter(tc_List_Olist(U_19989),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_19989)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19989),tc_List_Olist(U_19989),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_19989)))),U_19990)),
    inference(variable_rename,[status(thm)],[f_4783_1]) ).

fof(f_4783_3,plain,
    ! [U_19989,U_19990] : c_List_Ofoldr(tc_List_Olist(U_19989),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19989)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19989))),c_List_Otranspose(U_19989,U_19990),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19989))),hAPP(c_List_Ofilter(tc_List_Olist(U_19989),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_19989)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19989),tc_List_Olist(U_19989),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_19989)))),U_19990)),
    inference(definitional_conversion,[status(esa)],[f_4783_2]) ).

cnf(f_4783_4,plain,
    c_List_Ofoldr(tc_List_Olist(U_19989),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_19989)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_19989))),c_List_Otranspose(U_19989,U_19990),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_19989))),hAPP(c_List_Ofilter(tc_List_Olist(U_19989),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_19989)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_19989),tc_List_Olist(U_19989),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_19989)))),U_19990)),
    inference(clausify,[status(thm)],[f_4783_3]) ).

fof(f_4784_1,plain,
    ! [V_Pa_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_Pa_2)),V_xs_2)),V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),V_z_2)
      | ~ hBOOL(hAPP(hAPP(V_Pa_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_4784_2,plain,
    ! [U_19996,U_19995,U_19994,U_19993,U_19992,U_19991] :
      ( hAPP(c_Map_Omap__of(U_19991,U_19992,hAPP(c_List_Ofilter(tc_prod(U_19991,U_19992),hAPP(c_Product__Type_Oprod_Oprod__case(U_19991,U_19992,tc_HOL_Obool),U_19996)),U_19993)),U_19994) = hAPP(c_Option_Ooption_OSome(U_19992),U_19995)
      | ~ hBOOL(hAPP(hAPP(U_19996,U_19994),U_19995))
      | hAPP(c_Map_Omap__of(U_19991,U_19992,U_19993),U_19994) != hAPP(c_Option_Ooption_OSome(U_19992),U_19995) ),
    inference(variable_rename,[status(thm)],[f_4784_1]) ).

fof(f_4784_3,plain,
    ! [U_19991,U_19992,U_19993,U_19994,U_19995,U_19996] :
      ( hAPP(c_Map_Omap__of(U_19991,U_19992,hAPP(c_List_Ofilter(tc_prod(U_19991,U_19992),hAPP(c_Product__Type_Oprod_Oprod__case(U_19991,U_19992,tc_HOL_Obool),U_19996)),U_19993)),U_19994) = hAPP(c_Option_Ooption_OSome(U_19992),U_19995)
      | ~ hBOOL(hAPP(hAPP(U_19996,U_19994),U_19995))
      | hAPP(c_Map_Omap__of(U_19991,U_19992,U_19993),U_19994) != hAPP(c_Option_Ooption_OSome(U_19992),U_19995) ),
    inference(definitional_conversion,[status(esa)],[f_4784_2]) ).

cnf(f_4784_4,plain,
    ( hAPP(c_Map_Omap__of(U_19991,U_19992,hAPP(c_List_Ofilter(tc_prod(U_19991,U_19992),hAPP(c_Product__Type_Oprod_Oprod__case(U_19991,U_19992,tc_HOL_Obool),U_19996)),U_19993)),U_19994) = hAPP(c_Option_Ooption_OSome(U_19992),U_19995)
    | ~ hBOOL(hAPP(hAPP(U_19996,U_19994),U_19995))
    | hAPP(c_Map_Omap__of(U_19991,U_19992,U_19993),U_19994) != hAPP(c_Option_Ooption_OSome(U_19992),U_19995) ),
    inference(clausify,[status(thm)],[f_4784_3]) ).

fof(f_4785_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_4785_2,plain,
    ! [U_20001,U_20000,U_19999,U_19998,U_19997] : c_List_Omap__filter(U_19997,U_19998,U_19999,hAPP(hAPP(c_List_Olist_OCons(U_19997),U_20000),U_20001)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(U_19998),U_19998,c_List_Omap__filter(U_19997,U_19998,U_19999,U_20001),hAPP(hAPP(c_COMBC(U_19998,tc_List_Olist(U_19998),tc_List_Olist(U_19998)),c_List_Olist_OCons(U_19998)),c_List_Omap__filter(U_19997,U_19998,U_19999,U_20001))),hAPP(U_19999,U_20000)),
    inference(variable_rename,[status(thm)],[f_4785_1]) ).

fof(f_4785_3,plain,
    ! [U_19998,U_19997,U_19999,U_20000,U_20001] : c_List_Omap__filter(U_19997,U_19998,U_19999,hAPP(hAPP(c_List_Olist_OCons(U_19997),U_20000),U_20001)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(U_19998),U_19998,c_List_Omap__filter(U_19997,U_19998,U_19999,U_20001),hAPP(hAPP(c_COMBC(U_19998,tc_List_Olist(U_19998),tc_List_Olist(U_19998)),c_List_Olist_OCons(U_19998)),c_List_Omap__filter(U_19997,U_19998,U_19999,U_20001))),hAPP(U_19999,U_20000)),
    inference(definitional_conversion,[status(esa)],[f_4785_2]) ).

cnf(f_4785_4,plain,
    c_List_Omap__filter(U_19997,U_19998,U_19999,hAPP(hAPP(c_List_Olist_OCons(U_19997),U_20000),U_20001)) = hAPP(c_Option_Ooption_Ooption__case(tc_List_Olist(U_19998),U_19998,c_List_Omap__filter(U_19997,U_19998,U_19999,U_20001),hAPP(hAPP(c_COMBC(U_19998,tc_List_Olist(U_19998),tc_List_Olist(U_19998)),c_List_Olist_OCons(U_19998)),c_List_Omap__filter(U_19997,U_19998,U_19999,U_20001))),hAPP(U_19999,U_20000)),
    inference(clausify,[status(thm)],[f_4785_3]) ).

fof(f_4786_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_4786_2,plain,
    ! [U_20005,U_20004,U_20003,U_20002] : c_List_Otranspose(U_20002,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20003),tc_List_Olist(U_20002)),hAPP(c_List_Omap(U_20003,U_20002),U_20004)),U_20005)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20003),tc_List_Olist(U_20002)),hAPP(c_List_Omap(U_20003,U_20002),U_20004)),c_List_Otranspose(U_20003,U_20005)),
    inference(variable_rename,[status(thm)],[f_4786_1]) ).

fof(f_4786_3,plain,
    ! [U_20002,U_20003,U_20004,U_20005] : c_List_Otranspose(U_20002,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20003),tc_List_Olist(U_20002)),hAPP(c_List_Omap(U_20003,U_20002),U_20004)),U_20005)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20003),tc_List_Olist(U_20002)),hAPP(c_List_Omap(U_20003,U_20002),U_20004)),c_List_Otranspose(U_20003,U_20005)),
    inference(definitional_conversion,[status(esa)],[f_4786_2]) ).

cnf(f_4786_4,plain,
    c_List_Otranspose(U_20002,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20003),tc_List_Olist(U_20002)),hAPP(c_List_Omap(U_20003,U_20002),U_20004)),U_20005)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20003),tc_List_Olist(U_20002)),hAPP(c_List_Omap(U_20003,U_20002),U_20004)),c_List_Otranspose(U_20003,U_20005)),
    inference(clausify,[status(thm)],[f_4786_3]) ).

fof(f_4787_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_4787_2,plain,
    ! [U_20007,U_20006] : c_List_Otranspose(U_20006,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20006)),c_List_Olist_ONil(U_20006)),U_20007)) = c_List_Otranspose(U_20006,U_20007),
    inference(variable_rename,[status(thm)],[f_4787_1]) ).

fof(f_4787_3,plain,
    ! [U_20006,U_20007] : c_List_Otranspose(U_20006,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20006)),c_List_Olist_ONil(U_20006)),U_20007)) = c_List_Otranspose(U_20006,U_20007),
    inference(definitional_conversion,[status(esa)],[f_4787_2]) ).

cnf(f_4787_4,plain,
    c_List_Otranspose(U_20006,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20006)),c_List_Olist_ONil(U_20006)),U_20007)) = c_List_Otranspose(U_20006,U_20007),
    inference(clausify,[status(thm)],[f_4787_3]) ).

fof(f_4788_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_4788_2,plain,
    ! [U_20011,U_20010] :
      ( ( c_List_Otranspose(U_20010,U_20011) = c_List_Olist_ONil(tc_List_Olist(U_20010))
        | ? [U_20009] :
            ( U_20009 != c_List_Olist_ONil(U_20010)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20010)),U_20009),hAPP(c_List_Oset(tc_List_Olist(U_20010)),U_20011))) ) )
      & ( ! [U_20008] :
            ( U_20008 = c_List_Olist_ONil(U_20010)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20010)),U_20008),hAPP(c_List_Oset(tc_List_Olist(U_20010)),U_20011))) )
        | c_List_Otranspose(U_20010,U_20011) != c_List_Olist_ONil(tc_List_Olist(U_20010)) ) ),
    inference(variable_rename,[status(thm)],[f_4788_1]) ).

fof(f_4788_3,plain,
    ( ! [U_20015,U_20013] :
        ( c_List_Otranspose(U_20013,U_20015) = c_List_Olist_ONil(tc_List_Olist(U_20013))
        | ? [U_20009] :
            ( U_20009 != c_List_Olist_ONil(U_20013)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20013)),U_20009),hAPP(c_List_Oset(tc_List_Olist(U_20013)),U_20015))) ) )
    & ! [U_20014,U_20012] :
        ( ! [U_20008] :
            ( U_20008 = c_List_Olist_ONil(U_20012)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20012)),U_20008),hAPP(c_List_Oset(tc_List_Olist(U_20012)),U_20014))) )
        | c_List_Otranspose(U_20012,U_20014) != c_List_Olist_ONil(tc_List_Olist(U_20012)) ) ),
    inference(miniscope,[status(thm)],[f_4788_2]) ).

fof(f_4788_4,plain,
    ( ! [U_20015,U_20013] :
        ( c_List_Otranspose(U_20013,U_20015) = c_List_Olist_ONil(tc_List_Olist(U_20013))
        | ( sK491(U_20015,U_20013) != c_List_Olist_ONil(U_20013)
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20013)),sK491(U_20015,U_20013)),hAPP(c_List_Oset(tc_List_Olist(U_20013)),U_20015))) ) )
    & ! [U_20014,U_20012] :
        ( ! [U_20008] :
            ( U_20008 = c_List_Olist_ONil(U_20012)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20012)),U_20008),hAPP(c_List_Oset(tc_List_Olist(U_20012)),U_20014))) )
        | c_List_Otranspose(U_20012,U_20014) != c_List_Olist_ONil(tc_List_Olist(U_20012)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK491]),skolemize(U_20009,sK491(U_20015,U_20013))],[f_4788_3]) ).

fof(f_4788_5,plain,
    ( ! [U_20015,U_20013] :
        ( sK491(U_20015,U_20013) != c_List_Olist_ONil(U_20013)
        | ~ sP1206(U_20015,U_20013) )
    & ! [U_20015,U_20013] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20013)),sK491(U_20015,U_20013)),hAPP(c_List_Oset(tc_List_Olist(U_20013)),U_20015)))
        | ~ sP1206(U_20015,U_20013) )
    & ! [U_20015,U_20013] :
        ( c_List_Otranspose(U_20013,U_20015) = c_List_Olist_ONil(tc_List_Olist(U_20013))
        | sP1206(U_20015,U_20013) )
    & ! [U_20014,U_20008,U_20012] :
        ( U_20008 = c_List_Olist_ONil(U_20012)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20012)),U_20008),hAPP(c_List_Oset(tc_List_Olist(U_20012)),U_20014)))
        | c_List_Otranspose(U_20012,U_20014) != c_List_Olist_ONil(tc_List_Olist(U_20012)) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1206])],[f_4788_4]) ).

cnf(f_4788_6,plain,
    ( U_20008 = c_List_Olist_ONil(U_20012)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20012)),U_20008),hAPP(c_List_Oset(tc_List_Olist(U_20012)),U_20014)))
    | c_List_Otranspose(U_20012,U_20014) != c_List_Olist_ONil(tc_List_Olist(U_20012)) ),
    inference(clausify,[status(thm)],[f_4788_5]) ).

cnf(f_4788_7,plain,
    ( c_List_Otranspose(U_20013,U_20015) = c_List_Olist_ONil(tc_List_Olist(U_20013))
    | sP1206(U_20015,U_20013) ),
    inference(clausify,[status(thm)],[f_4788_5]) ).

cnf(f_4788_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20013)),sK491(U_20015,U_20013)),hAPP(c_List_Oset(tc_List_Olist(U_20013)),U_20015)))
    | ~ sP1206(U_20015,U_20013) ),
    inference(clausify,[status(thm)],[f_4788_5]) ).

cnf(f_4788_9,plain,
    ( sK491(U_20015,U_20013) != c_List_Olist_ONil(U_20013)
    | ~ sP1206(U_20015,U_20013) ),
    inference(clausify,[status(thm)],[f_4788_5]) ).

fof(f_4789_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_4789_2,plain,
    ! [U_20018,U_20017,U_20016] : c_List_Omap__filter(U_20016,U_20017,U_20018,c_List_Olist_ONil(U_20016)) = c_List_Olist_ONil(U_20017),
    inference(variable_rename,[status(thm)],[f_4789_1]) ).

fof(f_4789_3,plain,
    ! [U_20018,U_20017,U_20016] : c_List_Omap__filter(U_20016,U_20017,U_20018,c_List_Olist_ONil(U_20016)) = c_List_Olist_ONil(U_20017),
    inference(definitional_conversion,[status(esa)],[f_4789_2]) ).

cnf(f_4789_4,plain,
    c_List_Omap__filter(U_20016,U_20017,U_20018,c_List_Olist_ONil(U_20016)) = c_List_Olist_ONil(U_20017),
    inference(clausify,[status(thm)],[f_4789_3]) ).

fof(f_4790_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_4790_2,plain,
    ! [U_20019] : c_List_Otranspose(U_20019,c_List_Olist_ONil(tc_List_Olist(U_20019))) = c_List_Olist_ONil(tc_List_Olist(U_20019)),
    inference(variable_rename,[status(thm)],[f_4790_1]) ).

fof(f_4790_3,plain,
    ! [U_20019] : c_List_Otranspose(U_20019,c_List_Olist_ONil(tc_List_Olist(U_20019))) = c_List_Olist_ONil(tc_List_Olist(U_20019)),
    inference(definitional_conversion,[status(esa)],[f_4790_2]) ).

cnf(f_4790_4,plain,
    c_List_Otranspose(U_20019,c_List_Olist_ONil(tc_List_Olist(U_20019))) = c_List_Olist_ONil(tc_List_Olist(U_20019)),
    inference(clausify,[status(thm)],[f_4790_3]) ).

fof(f_4791_1,plain,
    ! [V_is_2,V_xs_2,V_Pa_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_Pa_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_Pa_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_4791_2,plain,
    ! [U_20023,U_20022,U_20021,U_20020] : hAPP(hAPP(c_List_Omap(tc_prod(U_20020,tc_Nat_Onat),U_20020),c_Product__Type_Ofst(U_20020,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20020,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_20020,tc_Nat_Onat)),U_20021),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(U_20020,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(U_20020,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(U_20020,tc_Nat_Onat),U_20022),U_20023))) = hAPP(hAPP(c_List_Omap(tc_prod(U_20020,tc_Nat_Onat),U_20020),c_Product__Type_Ofst(U_20020,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20020,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_20020,tc_Nat_Onat)),U_20021),c_Product__Type_Osnd(U_20020,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(U_20020,tc_Nat_Onat),U_20022),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),U_20023)))),
    inference(variable_rename,[status(thm)],[f_4791_1]) ).

fof(f_4791_3,plain,
    ! [U_20020,U_20021,U_20022,U_20023] : hAPP(hAPP(c_List_Omap(tc_prod(U_20020,tc_Nat_Onat),U_20020),c_Product__Type_Ofst(U_20020,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20020,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_20020,tc_Nat_Onat)),U_20021),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(U_20020,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(U_20020,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(U_20020,tc_Nat_Onat),U_20022),U_20023))) = hAPP(hAPP(c_List_Omap(tc_prod(U_20020,tc_Nat_Onat),U_20020),c_Product__Type_Ofst(U_20020,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20020,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_20020,tc_Nat_Onat)),U_20021),c_Product__Type_Osnd(U_20020,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(U_20020,tc_Nat_Onat),U_20022),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),U_20023)))),
    inference(definitional_conversion,[status(esa)],[f_4791_2]) ).

cnf(f_4791_4,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_20020,tc_Nat_Onat),U_20020),c_Product__Type_Ofst(U_20020,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20020,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_20020,tc_Nat_Onat)),U_20021),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_prod(U_20020,tc_Nat_Onat)),c_Nat_OSuc),c_Product__Type_Osnd(U_20020,tc_Nat_Onat)))),hAPP(hAPP(c_List_Ozip(U_20020,tc_Nat_Onat),U_20022),U_20023))) = hAPP(hAPP(c_List_Omap(tc_prod(U_20020,tc_Nat_Onat),U_20020),c_Product__Type_Ofst(U_20020,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20020,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_prod(U_20020,tc_Nat_Onat)),U_20021),c_Product__Type_Osnd(U_20020,tc_Nat_Onat))),hAPP(hAPP(c_List_Ozip(U_20020,tc_Nat_Onat),U_20022),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),U_20023)))),
    inference(clausify,[status(thm)],[f_4791_3]) ).

fof(f_4792_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_4792_2,plain,
    ! [U_20025,U_20024] : c_Random_Oselect__weight(U_20024,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_20024),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_20024,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_20024,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_20024)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_20025)) = c_Random_Oselect__weight(U_20024,U_20025),
    inference(variable_rename,[status(thm)],[f_4792_1]) ).

fof(f_4792_3,plain,
    ! [U_20024,U_20025] : c_Random_Oselect__weight(U_20024,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_20024),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_20024,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_20024,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_20024)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_20025)) = c_Random_Oselect__weight(U_20024,U_20025),
    inference(definitional_conversion,[status(esa)],[f_4792_2]) ).

cnf(f_4792_4,plain,
    c_Random_Oselect__weight(U_20024,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_20024),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_20024,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_20024,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_20024)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_20025)) = c_Random_Oselect__weight(U_20024,U_20025),
    inference(clausify,[status(thm)],[f_4792_3]) ).

fof(f_4793_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_4793_2,plain,
    ! [U_20027,U_20026] : c_Random_Opick(U_20026,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_20026),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_20026,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_20026,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_20026)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_20027)) = c_Random_Opick(U_20026,U_20027),
    inference(variable_rename,[status(thm)],[f_4793_1]) ).

fof(f_4793_3,plain,
    ! [U_20026,U_20027] : c_Random_Opick(U_20026,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_20026),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_20026,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_20026,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_20026)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_20027)) = c_Random_Opick(U_20026,U_20027),
    inference(definitional_conversion,[status(esa)],[f_4793_2]) ).

cnf(f_4793_4,plain,
    c_Random_Opick(U_20026,hAPP(c_List_Ofilter(tc_prod(tc_Code__Numeral_Ocode__numeral,U_20026),hAPP(c_Product__Type_Oprod_Oprod__case(tc_Code__Numeral_Ocode__numeral,U_20026,tc_HOL_Obool),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(U_20026,tc_HOL_Obool),tc_Code__Numeral_Ocode__numeral),c_COMBK(tc_HOL_Obool,U_20026)),hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral))))),U_20027)) = c_Random_Opick(U_20026,U_20027),
    inference(clausify,[status(thm)],[f_4793_3]) ).

fof(f_4794_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_4794_2,plain,
    ! [U_20030,U_20029,U_20028] :
      ( hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20029)),c_List_Otranspose(U_20029,U_20030)),U_20028) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20029),U_20029),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20029),tc_Nat_Onat,U_20029),c_List_Onth(U_20029)),U_20028)),hAPP(c_List_Ofilter(tc_List_Olist(U_20029),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20029)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20028)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20029)))),U_20030))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20028),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20029))),c_List_Otranspose(U_20029,U_20030)))) ),
    inference(variable_rename,[status(thm)],[f_4794_1]) ).

fof(f_4794_3,plain,
    ! [U_20028,U_20029,U_20030] :
      ( hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20029)),c_List_Otranspose(U_20029,U_20030)),U_20028) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20029),U_20029),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20029),tc_Nat_Onat,U_20029),c_List_Onth(U_20029)),U_20028)),hAPP(c_List_Ofilter(tc_List_Olist(U_20029),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20029)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20028)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20029)))),U_20030))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20028),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20029))),c_List_Otranspose(U_20029,U_20030)))) ),
    inference(definitional_conversion,[status(esa)],[f_4794_2]) ).

cnf(f_4794_4,plain,
    ( hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20029)),c_List_Otranspose(U_20029,U_20030)),U_20028) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20029),U_20029),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20029),tc_Nat_Onat,U_20029),c_List_Onth(U_20029)),U_20028)),hAPP(c_List_Ofilter(tc_List_Olist(U_20029),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20029)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20028)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20029)))),U_20030))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20028),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20029))),c_List_Otranspose(U_20029,U_20030)))) ),
    inference(clausify,[status(thm)],[f_4794_3]) ).

fof(f_4795_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_4795_2,plain,
    ! [U_20032,U_20031] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20031))),c_List_Otranspose(U_20031,U_20032)) = c_List_Ofoldr(tc_List_Olist(U_20031),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_20031)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20031))),U_20032,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(variable_rename,[status(thm)],[f_4795_1]) ).

fof(f_4795_3,plain,
    ! [U_20031,U_20032] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20031))),c_List_Otranspose(U_20031,U_20032)) = c_List_Ofoldr(tc_List_Olist(U_20031),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_20031)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20031))),U_20032,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(definitional_conversion,[status(esa)],[f_4795_2]) ).

cnf(f_4795_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20031))),c_List_Otranspose(U_20031,U_20032)) = c_List_Ofoldr(tc_List_Olist(U_20031),tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_List_Olist(U_20031)),c_Orderings_Oord__class_Omax(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20031))),U_20032,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),
    inference(clausify,[status(thm)],[f_4795_3]) ).

fof(f_4796_1,plain,
    ! [V_xs_2,V_Pa_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_Pa_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_Pa_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_4796_2,plain,
    ! [U_20037,U_20036,U_20035,U_20034,U_20033] : hAPP(hAPP(c_List_Omap(U_20033,U_20034),U_20035),hAPP(c_List_Ofilter(U_20033,U_20036),U_20037)) = c_List_Omap__filter(U_20033,U_20034,hAPP(hAPP(c_COMBC(U_20033,tc_Option_Ooption(U_20034),tc_Option_Ooption(U_20034)),hAPP(hAPP(c_COMBS(U_20033,tc_Option_Ooption(U_20034),tc_fun(tc_Option_Ooption(U_20034),tc_Option_Ooption(U_20034))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_20034),tc_fun(tc_Option_Ooption(U_20034),tc_Option_Ooption(U_20034))),U_20033),c_If(tc_Option_Ooption(U_20034))),U_20036)),hAPP(hAPP(c_COMBB(U_20034,tc_Option_Ooption(U_20034),U_20033),c_Option_Ooption_OSome(U_20034)),U_20035))),c_Option_Ooption_ONone(U_20034)),U_20037),
    inference(variable_rename,[status(thm)],[f_4796_1]) ).

fof(f_4796_3,plain,
    ! [U_20033,U_20034,U_20035,U_20036,U_20037] : hAPP(hAPP(c_List_Omap(U_20033,U_20034),U_20035),hAPP(c_List_Ofilter(U_20033,U_20036),U_20037)) = c_List_Omap__filter(U_20033,U_20034,hAPP(hAPP(c_COMBC(U_20033,tc_Option_Ooption(U_20034),tc_Option_Ooption(U_20034)),hAPP(hAPP(c_COMBS(U_20033,tc_Option_Ooption(U_20034),tc_fun(tc_Option_Ooption(U_20034),tc_Option_Ooption(U_20034))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_20034),tc_fun(tc_Option_Ooption(U_20034),tc_Option_Ooption(U_20034))),U_20033),c_If(tc_Option_Ooption(U_20034))),U_20036)),hAPP(hAPP(c_COMBB(U_20034,tc_Option_Ooption(U_20034),U_20033),c_Option_Ooption_OSome(U_20034)),U_20035))),c_Option_Ooption_ONone(U_20034)),U_20037),
    inference(definitional_conversion,[status(esa)],[f_4796_2]) ).

cnf(f_4796_4,plain,
    hAPP(hAPP(c_List_Omap(U_20033,U_20034),U_20035),hAPP(c_List_Ofilter(U_20033,U_20036),U_20037)) = c_List_Omap__filter(U_20033,U_20034,hAPP(hAPP(c_COMBC(U_20033,tc_Option_Ooption(U_20034),tc_Option_Ooption(U_20034)),hAPP(hAPP(c_COMBS(U_20033,tc_Option_Ooption(U_20034),tc_fun(tc_Option_Ooption(U_20034),tc_Option_Ooption(U_20034))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_Option_Ooption(U_20034),tc_fun(tc_Option_Ooption(U_20034),tc_Option_Ooption(U_20034))),U_20033),c_If(tc_Option_Ooption(U_20034))),U_20036)),hAPP(hAPP(c_COMBB(U_20034,tc_Option_Ooption(U_20034),U_20033),c_Option_Ooption_OSome(U_20034)),U_20035))),c_Option_Ooption_ONone(U_20034)),U_20037),
    inference(clausify,[status(thm)],[f_4796_3]) ).

fof(f_4797_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_4797_2,plain,
    ! [U_20042,U_20041,U_20040,U_20039,U_20038] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20039,U_20038,U_20042),U_20040),c_List_Oremove1(U_20039,U_20040,U_20041)) = U_20041
      | hAPP(c_List_Ohd(U_20039),hAPP(c_List_Ofilter(U_20039,hAPP(hAPP(c_COMBB(U_20038,tc_HOL_Obool,U_20039),hAPP(c_fequal,hAPP(U_20042,U_20040))),U_20042)),U_20041)) != U_20040
      | ~ c_List_Olinorder__class_Osorted(U_20038,hAPP(hAPP(c_List_Omap(U_20039,U_20038),U_20042),U_20041))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20039),U_20040),hAPP(c_List_Oset(U_20039),U_20041)))
      | ~ class_Orderings_Olinorder(U_20038) ),
    inference(variable_rename,[status(thm)],[f_4797_1]) ).

fof(f_4797_3,plain,
    ! [U_20038,U_20039,U_20040,U_20041,U_20042] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20039,U_20038,U_20042),U_20040),c_List_Oremove1(U_20039,U_20040,U_20041)) = U_20041
      | hAPP(c_List_Ohd(U_20039),hAPP(c_List_Ofilter(U_20039,hAPP(hAPP(c_COMBB(U_20038,tc_HOL_Obool,U_20039),hAPP(c_fequal,hAPP(U_20042,U_20040))),U_20042)),U_20041)) != U_20040
      | ~ c_List_Olinorder__class_Osorted(U_20038,hAPP(hAPP(c_List_Omap(U_20039,U_20038),U_20042),U_20041))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20039),U_20040),hAPP(c_List_Oset(U_20039),U_20041)))
      | ~ class_Orderings_Olinorder(U_20038) ),
    inference(definitional_conversion,[status(esa)],[f_4797_2]) ).

cnf(f_4797_4,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20039,U_20038,U_20042),U_20040),c_List_Oremove1(U_20039,U_20040,U_20041)) = U_20041
    | hAPP(c_List_Ohd(U_20039),hAPP(c_List_Ofilter(U_20039,hAPP(hAPP(c_COMBB(U_20038,tc_HOL_Obool,U_20039),hAPP(c_fequal,hAPP(U_20042,U_20040))),U_20042)),U_20041)) != U_20040
    | ~ c_List_Olinorder__class_Osorted(U_20038,hAPP(hAPP(c_List_Omap(U_20039,U_20038),U_20042),U_20041))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20039),U_20040),hAPP(c_List_Oset(U_20039),U_20041)))
    | ~ class_Orderings_Olinorder(U_20038) ),
    inference(clausify,[status(thm)],[f_4797_3]) ).

fof(f_4798_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_4798_2,plain,
    ! [U_20045,U_20044,U_20043] : c_List_Osublist(U_20043,U_20044,U_20045) = hAPP(hAPP(c_List_Omap(tc_prod(U_20043,tc_Nat_Onat),U_20043),c_Product__Type_Ofst(U_20043,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20043,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20043,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_20043,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_20043,tc_Nat_Onat))),U_20045)),hAPP(hAPP(c_List_Ozip(U_20043,tc_Nat_Onat),U_20044),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20043)),U_20044))))),
    inference(variable_rename,[status(thm)],[f_4798_1]) ).

fof(f_4798_3,plain,
    ! [U_20043,U_20044,U_20045] : c_List_Osublist(U_20043,U_20044,U_20045) = hAPP(hAPP(c_List_Omap(tc_prod(U_20043,tc_Nat_Onat),U_20043),c_Product__Type_Ofst(U_20043,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20043,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20043,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_20043,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_20043,tc_Nat_Onat))),U_20045)),hAPP(hAPP(c_List_Ozip(U_20043,tc_Nat_Onat),U_20044),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20043)),U_20044))))),
    inference(definitional_conversion,[status(esa)],[f_4798_2]) ).

cnf(f_4798_4,plain,
    c_List_Osublist(U_20043,U_20044,U_20045) = hAPP(hAPP(c_List_Omap(tc_prod(U_20043,tc_Nat_Onat),U_20043),c_Product__Type_Ofst(U_20043,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20043,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20043,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_20043,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_20043,tc_Nat_Onat))),U_20045)),hAPP(hAPP(c_List_Ozip(U_20043,tc_Nat_Onat),U_20044),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20043)),U_20044))))),
    inference(clausify,[status(thm)],[f_4798_3]) ).

fof(f_4799_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_4799_2,plain,
    ! [U_20046] :
      ( c_List_Olinorder__class_Osorted(U_20046,c_List_Olist_ONil(U_20046))
      | ~ class_Orderings_Olinorder(U_20046) ),
    inference(variable_rename,[status(thm)],[f_4799_1]) ).

fof(f_4799_3,plain,
    ! [U_20046] :
      ( c_List_Olinorder__class_Osorted(U_20046,c_List_Olist_ONil(U_20046))
      | ~ class_Orderings_Olinorder(U_20046) ),
    inference(definitional_conversion,[status(esa)],[f_4799_2]) ).

cnf(f_4799_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20046,c_List_Olist_ONil(U_20046))
    | ~ class_Orderings_Olinorder(U_20046) ),
    inference(clausify,[status(thm)],[f_4799_3]) ).

fof(f_4800_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_4800_2,plain,
    ! [U_20048,U_20047] :
      ( c_List_Olinorder__class_Osorted(U_20047,hAPP(hAPP(c_List_Olist_OCons(U_20047),U_20048),c_List_Olist_ONil(U_20047)))
      | ~ class_Orderings_Olinorder(U_20047) ),
    inference(variable_rename,[status(thm)],[f_4800_1]) ).

fof(f_4800_3,plain,
    ! [U_20047,U_20048] :
      ( c_List_Olinorder__class_Osorted(U_20047,hAPP(hAPP(c_List_Olist_OCons(U_20047),U_20048),c_List_Olist_ONil(U_20047)))
      | ~ class_Orderings_Olinorder(U_20047) ),
    inference(definitional_conversion,[status(esa)],[f_4800_2]) ).

cnf(f_4800_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20047,hAPP(hAPP(c_List_Olist_OCons(U_20047),U_20048),c_List_Olist_ONil(U_20047)))
    | ~ class_Orderings_Olinorder(U_20047) ),
    inference(clausify,[status(thm)],[f_4800_3]) ).

fof(f_4801_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_4801_2,plain,
    ! [U_20051,U_20050,U_20049] :
      ( c_List_Olinorder__class_Osorted(U_20049,hAPP(c_List_Ofilter(U_20049,hAPP(hAPP(c_COMBC(U_20049,U_20049,tc_HOL_Obool),c_fequal),hAPP(U_20050,U_20051))),U_20051))
      | ~ class_Orderings_Olinorder(U_20049) ),
    inference(variable_rename,[status(thm)],[f_4801_1]) ).

fof(f_4801_3,plain,
    ! [U_20049,U_20050,U_20051] :
      ( c_List_Olinorder__class_Osorted(U_20049,hAPP(c_List_Ofilter(U_20049,hAPP(hAPP(c_COMBC(U_20049,U_20049,tc_HOL_Obool),c_fequal),hAPP(U_20050,U_20051))),U_20051))
      | ~ class_Orderings_Olinorder(U_20049) ),
    inference(definitional_conversion,[status(esa)],[f_4801_2]) ).

cnf(f_4801_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20049,hAPP(c_List_Ofilter(U_20049,hAPP(hAPP(c_COMBC(U_20049,U_20049,tc_HOL_Obool),c_fequal),hAPP(U_20050,U_20051))),U_20051))
    | ~ class_Orderings_Olinorder(U_20049) ),
    inference(clausify,[status(thm)],[f_4801_3]) ).

fof(f_4802_1,plain,
    ! [V_Pa_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_Pa_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_4802_2,plain,
    ! [U_20056,U_20055,U_20054,U_20053,U_20052] :
      ( c_List_Olinorder__class_Osorted(U_20052,hAPP(hAPP(c_List_Omap(U_20053,U_20052),U_20054),hAPP(c_List_Ofilter(U_20053,U_20056),U_20055)))
      | ~ c_List_Olinorder__class_Osorted(U_20052,hAPP(hAPP(c_List_Omap(U_20053,U_20052),U_20054),U_20055))
      | ~ class_Orderings_Olinorder(U_20052) ),
    inference(variable_rename,[status(thm)],[f_4802_1]) ).

fof(f_4802_3,plain,
    ! [U_20052,U_20053,U_20054,U_20055,U_20056] :
      ( c_List_Olinorder__class_Osorted(U_20052,hAPP(hAPP(c_List_Omap(U_20053,U_20052),U_20054),hAPP(c_List_Ofilter(U_20053,U_20056),U_20055)))
      | ~ c_List_Olinorder__class_Osorted(U_20052,hAPP(hAPP(c_List_Omap(U_20053,U_20052),U_20054),U_20055))
      | ~ class_Orderings_Olinorder(U_20052) ),
    inference(definitional_conversion,[status(esa)],[f_4802_2]) ).

cnf(f_4802_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20052,hAPP(hAPP(c_List_Omap(U_20053,U_20052),U_20054),hAPP(c_List_Ofilter(U_20053,U_20056),U_20055)))
    | ~ c_List_Olinorder__class_Osorted(U_20052,hAPP(hAPP(c_List_Omap(U_20053,U_20052),U_20054),U_20055))
    | ~ class_Orderings_Olinorder(U_20052) ),
    inference(clausify,[status(thm)],[f_4802_3]) ).

fof(f_4803_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_4803_2,plain,
    ! [U_20061,U_20060,U_20059,U_20058,U_20057] :
      ( c_List_Olinorder__class_Osorted(U_20057,hAPP(hAPP(c_List_Omap(U_20058,U_20057),U_20059),hAPP(c_List_Ofilter(U_20058,hAPP(hAPP(c_COMBC(U_20058,U_20057,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_20057,tc_fun(U_20057,tc_HOL_Obool),U_20058),c_fequal),U_20059)),hAPP(U_20060,U_20061))),U_20061)))
      | ~ class_Orderings_Olinorder(U_20057) ),
    inference(variable_rename,[status(thm)],[f_4803_1]) ).

fof(f_4803_3,plain,
    ! [U_20057,U_20058,U_20059,U_20060,U_20061] :
      ( c_List_Olinorder__class_Osorted(U_20057,hAPP(hAPP(c_List_Omap(U_20058,U_20057),U_20059),hAPP(c_List_Ofilter(U_20058,hAPP(hAPP(c_COMBC(U_20058,U_20057,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_20057,tc_fun(U_20057,tc_HOL_Obool),U_20058),c_fequal),U_20059)),hAPP(U_20060,U_20061))),U_20061)))
      | ~ class_Orderings_Olinorder(U_20057) ),
    inference(definitional_conversion,[status(esa)],[f_4803_2]) ).

cnf(f_4803_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20057,hAPP(hAPP(c_List_Omap(U_20058,U_20057),U_20059),hAPP(c_List_Ofilter(U_20058,hAPP(hAPP(c_COMBC(U_20058,U_20057,tc_HOL_Obool),hAPP(hAPP(c_COMBB(U_20057,tc_fun(U_20057,tc_HOL_Obool),U_20058),c_fequal),U_20059)),hAPP(U_20060,U_20061))),U_20061)))
    | ~ class_Orderings_Olinorder(U_20057) ),
    inference(clausify,[status(thm)],[f_4803_3]) ).

fof(f_4804_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_4804_2,plain,
    ! [U_20063,U_20062] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(U_20062,U_20063)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20063),U_20062),
    inference(variable_rename,[status(thm)],[f_4804_1]) ).

fof(f_4804_3,plain,
    ! [U_20063,U_20062] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(U_20062,U_20063)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20063),U_20062),
    inference(definitional_conversion,[status(esa)],[f_4804_2]) ).

cnf(f_4804_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_Nat_Onat)),c_List_Oupt(U_20062,U_20063)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20063),U_20062),
    inference(clausify,[status(thm)],[f_4804_3]) ).

fof(f_4805_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_4805_2,plain,
    ! [U_20065,U_20064] :
      ( c_List_Olinorder__class_Osorted(U_20064,c_List_Obutlast(U_20064,U_20065))
      | ~ c_List_Olinorder__class_Osorted(U_20064,U_20065)
      | U_20065 = c_List_Olist_ONil(U_20064)
      | ~ class_Orderings_Olinorder(U_20064) ),
    inference(variable_rename,[status(thm)],[f_4805_1]) ).

fof(f_4805_3,plain,
    ! [U_20064,U_20065] :
      ( c_List_Olinorder__class_Osorted(U_20064,c_List_Obutlast(U_20064,U_20065))
      | ~ c_List_Olinorder__class_Osorted(U_20064,U_20065)
      | U_20065 = c_List_Olist_ONil(U_20064)
      | ~ class_Orderings_Olinorder(U_20064) ),
    inference(definitional_conversion,[status(esa)],[f_4805_2]) ).

cnf(f_4805_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20064,c_List_Obutlast(U_20064,U_20065))
    | ~ c_List_Olinorder__class_Osorted(U_20064,U_20065)
    | U_20065 = c_List_Olist_ONil(U_20064)
    | ~ class_Orderings_Olinorder(U_20064) ),
    inference(clausify,[status(thm)],[f_4805_3]) ).

fof(f_4806_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_4806_2,plain,
    ! [U_20072,U_20071,U_20070] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20070,hAPP(hAPP(c_List_Oappend(U_20070),U_20071),U_20072))
          | ? [U_20069] :
              ( ? [U_20068] :
                  ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20070),U_20069),U_20068))
                  & hBOOL(hAPP(hAPP(c_member(U_20070),U_20068),hAPP(c_List_Oset(U_20070),U_20072))) )
              & hBOOL(hAPP(hAPP(c_member(U_20070),U_20069),hAPP(c_List_Oset(U_20070),U_20071))) )
          | ~ c_List_Olinorder__class_Osorted(U_20070,U_20072)
          | ~ c_List_Olinorder__class_Osorted(U_20070,U_20071) )
        & ( ( ! [U_20067] :
                ( ! [U_20066] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20070),U_20067),U_20066))
                    | ~ hBOOL(hAPP(hAPP(c_member(U_20070),U_20066),hAPP(c_List_Oset(U_20070),U_20072))) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_20070),U_20067),hAPP(c_List_Oset(U_20070),U_20071))) )
            & c_List_Olinorder__class_Osorted(U_20070,U_20072)
            & c_List_Olinorder__class_Osorted(U_20070,U_20071) )
          | ~ c_List_Olinorder__class_Osorted(U_20070,hAPP(hAPP(c_List_Oappend(U_20070),U_20071),U_20072)) ) )
      | ~ class_Orderings_Olinorder(U_20070) ),
    inference(variable_rename,[status(thm)],[f_4806_1]) ).

fof(f_4806_3,plain,
    ! [U_20072,U_20071,U_20070] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20070,hAPP(hAPP(c_List_Oappend(U_20070),U_20071),U_20072))
          | ( ? [U_20068] :
                ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20070),sK492(U_20072,U_20071,U_20070)),U_20068))
                & hBOOL(hAPP(hAPP(c_member(U_20070),U_20068),hAPP(c_List_Oset(U_20070),U_20072))) )
            & hBOOL(hAPP(hAPP(c_member(U_20070),sK492(U_20072,U_20071,U_20070)),hAPP(c_List_Oset(U_20070),U_20071))) )
          | ~ c_List_Olinorder__class_Osorted(U_20070,U_20072)
          | ~ c_List_Olinorder__class_Osorted(U_20070,U_20071) )
        & ( ( ! [U_20067] :
                ( ! [U_20066] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20070),U_20067),U_20066))
                    | ~ hBOOL(hAPP(hAPP(c_member(U_20070),U_20066),hAPP(c_List_Oset(U_20070),U_20072))) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_20070),U_20067),hAPP(c_List_Oset(U_20070),U_20071))) )
            & c_List_Olinorder__class_Osorted(U_20070,U_20072)
            & c_List_Olinorder__class_Osorted(U_20070,U_20071) )
          | ~ c_List_Olinorder__class_Osorted(U_20070,hAPP(hAPP(c_List_Oappend(U_20070),U_20071),U_20072)) ) )
      | ~ class_Orderings_Olinorder(U_20070) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK492]),skolemize(U_20069,sK492(U_20072,U_20071,U_20070))],[f_4806_2]) ).

fof(f_4806_4,plain,
    ! [U_20072,U_20071,U_20070] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20070,hAPP(hAPP(c_List_Oappend(U_20070),U_20071),U_20072))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20070),sK492(U_20072,U_20071,U_20070)),sK493(U_20072,U_20071,U_20070)))
            & hBOOL(hAPP(hAPP(c_member(U_20070),sK493(U_20072,U_20071,U_20070)),hAPP(c_List_Oset(U_20070),U_20072)))
            & hBOOL(hAPP(hAPP(c_member(U_20070),sK492(U_20072,U_20071,U_20070)),hAPP(c_List_Oset(U_20070),U_20071))) )
          | ~ c_List_Olinorder__class_Osorted(U_20070,U_20072)
          | ~ c_List_Olinorder__class_Osorted(U_20070,U_20071) )
        & ( ( ! [U_20067] :
                ( ! [U_20066] :
                    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20070),U_20067),U_20066))
                    | ~ hBOOL(hAPP(hAPP(c_member(U_20070),U_20066),hAPP(c_List_Oset(U_20070),U_20072))) )
                | ~ hBOOL(hAPP(hAPP(c_member(U_20070),U_20067),hAPP(c_List_Oset(U_20070),U_20071))) )
            & c_List_Olinorder__class_Osorted(U_20070,U_20072)
            & c_List_Olinorder__class_Osorted(U_20070,U_20071) )
          | ~ c_List_Olinorder__class_Osorted(U_20070,hAPP(hAPP(c_List_Oappend(U_20070),U_20071),U_20072)) ) )
      | ~ class_Orderings_Olinorder(U_20070) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK493]),skolemize(U_20068,sK493(U_20072,U_20071,U_20070))],[f_4806_3]) ).

fof(f_4806_5,plain,
    ( ! [U_20070,U_20071,U_20072] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20070),sK492(U_20072,U_20071,U_20070)),sK493(U_20072,U_20071,U_20070)))
        | ~ sP1208(U_20070,U_20071,U_20072) )
    & ! [U_20070,U_20071,U_20072] :
        ( hBOOL(hAPP(hAPP(c_member(U_20070),sK493(U_20072,U_20071,U_20070)),hAPP(c_List_Oset(U_20070),U_20072)))
        | ~ sP1208(U_20070,U_20071,U_20072) )
    & ! [U_20070,U_20071,U_20072] :
        ( hBOOL(hAPP(hAPP(c_member(U_20070),sK492(U_20072,U_20071,U_20070)),hAPP(c_List_Oset(U_20070),U_20071)))
        | ~ sP1208(U_20070,U_20071,U_20072) )
    & ! [U_20066,U_20067,U_20070,U_20071,U_20072] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20070),U_20067),U_20066))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20070),U_20066),hAPP(c_List_Oset(U_20070),U_20072)))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20070),U_20067),hAPP(c_List_Oset(U_20070),U_20071)))
        | ~ sP1207(U_20066,U_20067,U_20070,U_20071,U_20072) )
    & ! [U_20066,U_20067,U_20070,U_20071,U_20072] :
        ( c_List_Olinorder__class_Osorted(U_20070,U_20072)
        | ~ sP1207(U_20066,U_20067,U_20070,U_20071,U_20072) )
    & ! [U_20066,U_20067,U_20070,U_20071,U_20072] :
        ( c_List_Olinorder__class_Osorted(U_20070,U_20071)
        | ~ sP1207(U_20066,U_20067,U_20070,U_20071,U_20072) )
    & ! [U_20066,U_20067,U_20070,U_20071,U_20072] :
        ( c_List_Olinorder__class_Osorted(U_20070,hAPP(hAPP(c_List_Oappend(U_20070),U_20071),U_20072))
        | sP1208(U_20070,U_20071,U_20072)
        | ~ c_List_Olinorder__class_Osorted(U_20070,U_20072)
        | ~ c_List_Olinorder__class_Osorted(U_20070,U_20071)
        | ~ sP1209(U_20066,U_20067,U_20070,U_20071,U_20072) )
    & ! [U_20066,U_20067,U_20070,U_20071,U_20072] :
        ( sP1207(U_20066,U_20067,U_20070,U_20071,U_20072)
        | ~ c_List_Olinorder__class_Osorted(U_20070,hAPP(hAPP(c_List_Oappend(U_20070),U_20071),U_20072))
        | ~ sP1209(U_20066,U_20067,U_20070,U_20071,U_20072) )
    & ! [U_20066,U_20067,U_20070,U_20071,U_20072] :
        ( sP1209(U_20066,U_20067,U_20070,U_20071,U_20072)
        | ~ class_Orderings_Olinorder(U_20070) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1207,sP1208,sP1209])],[f_4806_4]) ).

cnf(f_4806_6,plain,
    ( sP1209(U_20066,U_20067,U_20070,U_20071,U_20072)
    | ~ class_Orderings_Olinorder(U_20070) ),
    inference(clausify,[status(thm)],[f_4806_5]) ).

cnf(f_4806_7,plain,
    ( sP1207(U_20066,U_20067,U_20070,U_20071,U_20072)
    | ~ c_List_Olinorder__class_Osorted(U_20070,hAPP(hAPP(c_List_Oappend(U_20070),U_20071),U_20072))
    | ~ sP1209(U_20066,U_20067,U_20070,U_20071,U_20072) ),
    inference(clausify,[status(thm)],[f_4806_5]) ).

cnf(f_4806_8,plain,
    ( c_List_Olinorder__class_Osorted(U_20070,hAPP(hAPP(c_List_Oappend(U_20070),U_20071),U_20072))
    | sP1208(U_20070,U_20071,U_20072)
    | ~ c_List_Olinorder__class_Osorted(U_20070,U_20072)
    | ~ c_List_Olinorder__class_Osorted(U_20070,U_20071)
    | ~ sP1209(U_20066,U_20067,U_20070,U_20071,U_20072) ),
    inference(clausify,[status(thm)],[f_4806_5]) ).

cnf(f_4806_9,plain,
    ( c_List_Olinorder__class_Osorted(U_20070,U_20071)
    | ~ sP1207(U_20066,U_20067,U_20070,U_20071,U_20072) ),
    inference(clausify,[status(thm)],[f_4806_5]) ).

cnf(f_4806_10,plain,
    ( c_List_Olinorder__class_Osorted(U_20070,U_20072)
    | ~ sP1207(U_20066,U_20067,U_20070,U_20071,U_20072) ),
    inference(clausify,[status(thm)],[f_4806_5]) ).

cnf(f_4806_11,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20070),U_20067),U_20066))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20070),U_20066),hAPP(c_List_Oset(U_20070),U_20072)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20070),U_20067),hAPP(c_List_Oset(U_20070),U_20071)))
    | ~ sP1207(U_20066,U_20067,U_20070,U_20071,U_20072) ),
    inference(clausify,[status(thm)],[f_4806_5]) ).

cnf(f_4806_12,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20070),sK492(U_20072,U_20071,U_20070)),hAPP(c_List_Oset(U_20070),U_20071)))
    | ~ sP1208(U_20070,U_20071,U_20072) ),
    inference(clausify,[status(thm)],[f_4806_5]) ).

cnf(f_4806_13,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20070),sK493(U_20072,U_20071,U_20070)),hAPP(c_List_Oset(U_20070),U_20072)))
    | ~ sP1208(U_20070,U_20071,U_20072) ),
    inference(clausify,[status(thm)],[f_4806_5]) ).

cnf(f_4806_14,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20070),sK492(U_20072,U_20071,U_20070)),sK493(U_20072,U_20071,U_20070)))
    | ~ sP1208(U_20070,U_20071,U_20072) ),
    inference(clausify,[status(thm)],[f_4806_5]) ).

fof(f_4807_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_4807_2,plain,
    ! [U_20074,U_20073] :
      ( ( c_List_Oupt(U_20073,hAPP(c_Nat_OSuc,U_20074)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20073),U_20074)) )
      & ( c_List_Oupt(U_20073,hAPP(c_Nat_OSuc,U_20074)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20073,U_20074)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20074),c_List_Olist_ONil(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20073),U_20074)) ) ),
    inference(variable_rename,[status(thm)],[f_4807_1]) ).

fof(f_4807_3,plain,
    ( ! [U_20078,U_20076] :
        ( c_List_Oupt(U_20076,hAPP(c_Nat_OSuc,U_20078)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20076),U_20078)) )
    & ! [U_20077,U_20075] :
        ( c_List_Oupt(U_20075,hAPP(c_Nat_OSuc,U_20077)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20075,U_20077)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20077),c_List_Olist_ONil(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20075),U_20077)) ) ),
    inference(miniscope,[status(thm)],[f_4807_2]) ).

fof(f_4807_4,plain,
    ( ! [U_20076,U_20078] :
        ( c_List_Oupt(U_20076,hAPP(c_Nat_OSuc,U_20078)) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20076),U_20078)) )
    & ! [U_20075,U_20077] :
        ( c_List_Oupt(U_20075,hAPP(c_Nat_OSuc,U_20077)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20075,U_20077)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20077),c_List_Olist_ONil(tc_Nat_Onat)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20075),U_20077)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4807_3]) ).

cnf(f_4807_5,plain,
    ( c_List_Oupt(U_20075,hAPP(c_Nat_OSuc,U_20077)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20075,U_20077)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20077),c_List_Olist_ONil(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20075),U_20077)) ),
    inference(clausify,[status(thm)],[f_4807_4]) ).

cnf(f_4807_6,plain,
    ( c_List_Oupt(U_20076,hAPP(c_Nat_OSuc,U_20078)) = c_List_Olist_ONil(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20076),U_20078)) ),
    inference(clausify,[status(thm)],[f_4807_4]) ).

fof(f_4808_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_4808_2,plain,
    ! [U_20080,U_20079] :
      ( c_List_Oupt(U_20079,hAPP(c_Nat_OSuc,U_20080)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20079,U_20080)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20080),c_List_Olist_ONil(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20079),U_20080)) ),
    inference(variable_rename,[status(thm)],[f_4808_1]) ).

fof(f_4808_3,plain,
    ! [U_20079,U_20080] :
      ( c_List_Oupt(U_20079,hAPP(c_Nat_OSuc,U_20080)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20079,U_20080)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20080),c_List_Olist_ONil(tc_Nat_Onat)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20079),U_20080)) ),
    inference(definitional_conversion,[status(esa)],[f_4808_2]) ).

cnf(f_4808_4,plain,
    ( c_List_Oupt(U_20079,hAPP(c_Nat_OSuc,U_20080)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20079,U_20080)),hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20080),c_List_Olist_ONil(tc_Nat_Onat)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20079),U_20080)) ),
    inference(clausify,[status(thm)],[f_4808_3]) ).

fof(f_4809_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_4809_2,plain,
    ! [U_20083,U_20082,U_20081] :
      ( c_List_Oupt(U_20081,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20082),U_20083)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20081,U_20082)),c_List_Oupt(U_20082,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20082),U_20083)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20081),U_20082)) ),
    inference(variable_rename,[status(thm)],[f_4809_1]) ).

fof(f_4809_3,plain,
    ! [U_20081,U_20082,U_20083] :
      ( c_List_Oupt(U_20081,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20082),U_20083)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20081,U_20082)),c_List_Oupt(U_20082,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20082),U_20083)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20081),U_20082)) ),
    inference(definitional_conversion,[status(esa)],[f_4809_2]) ).

cnf(f_4809_4,plain,
    ( c_List_Oupt(U_20081,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20082),U_20083)) = hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),c_List_Oupt(U_20081,U_20082)),c_List_Oupt(U_20082,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20082),U_20083)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20081),U_20082)) ),
    inference(clausify,[status(thm)],[f_4809_3]) ).

fof(f_4810_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_4810_2,plain,
    ! [U_20087,U_20086,U_20085,U_20084] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20084,hAPP(hAPP(c_List_Olist_OCons(U_20084),U_20085),hAPP(hAPP(c_List_Olist_OCons(U_20084),U_20086),U_20087)))
          | ~ c_List_Olinorder__class_Osorted(U_20084,hAPP(hAPP(c_List_Olist_OCons(U_20084),U_20086),U_20087))
          | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20084),U_20085),U_20086)) )
        & ( ( c_List_Olinorder__class_Osorted(U_20084,hAPP(hAPP(c_List_Olist_OCons(U_20084),U_20086),U_20087))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20084),U_20085),U_20086)) )
          | ~ c_List_Olinorder__class_Osorted(U_20084,hAPP(hAPP(c_List_Olist_OCons(U_20084),U_20085),hAPP(hAPP(c_List_Olist_OCons(U_20084),U_20086),U_20087))) ) )
      | ~ class_Orderings_Olinorder(U_20084) ),
    inference(variable_rename,[status(thm)],[f_4810_1]) ).

fof(f_4810_3,plain,
    ( ! [U_20084,U_20085,U_20086,U_20087] :
        ( c_List_Olinorder__class_Osorted(U_20084,hAPP(hAPP(c_List_Olist_OCons(U_20084),U_20086),U_20087))
        | ~ sP1210(U_20084,U_20085,U_20086,U_20087) )
    & ! [U_20084,U_20085,U_20086,U_20087] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20084),U_20085),U_20086))
        | ~ sP1210(U_20084,U_20085,U_20086,U_20087) )
    & ! [U_20084,U_20085,U_20086,U_20087] :
        ( c_List_Olinorder__class_Osorted(U_20084,hAPP(hAPP(c_List_Olist_OCons(U_20084),U_20085),hAPP(hAPP(c_List_Olist_OCons(U_20084),U_20086),U_20087)))
        | ~ c_List_Olinorder__class_Osorted(U_20084,hAPP(hAPP(c_List_Olist_OCons(U_20084),U_20086),U_20087))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20084),U_20085),U_20086))
        | ~ sP1211(U_20084,U_20085,U_20086,U_20087) )
    & ! [U_20084,U_20085,U_20086,U_20087] :
        ( sP1210(U_20084,U_20085,U_20086,U_20087)
        | ~ c_List_Olinorder__class_Osorted(U_20084,hAPP(hAPP(c_List_Olist_OCons(U_20084),U_20085),hAPP(hAPP(c_List_Olist_OCons(U_20084),U_20086),U_20087)))
        | ~ sP1211(U_20084,U_20085,U_20086,U_20087) )
    & ! [U_20084,U_20085,U_20086,U_20087] :
        ( sP1211(U_20084,U_20085,U_20086,U_20087)
        | ~ class_Orderings_Olinorder(U_20084) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1210,sP1211])],[f_4810_2]) ).

cnf(f_4810_4,plain,
    ( sP1211(U_20084,U_20085,U_20086,U_20087)
    | ~ class_Orderings_Olinorder(U_20084) ),
    inference(clausify,[status(thm)],[f_4810_3]) ).

cnf(f_4810_5,plain,
    ( sP1210(U_20084,U_20085,U_20086,U_20087)
    | ~ c_List_Olinorder__class_Osorted(U_20084,hAPP(hAPP(c_List_Olist_OCons(U_20084),U_20085),hAPP(hAPP(c_List_Olist_OCons(U_20084),U_20086),U_20087)))
    | ~ sP1211(U_20084,U_20085,U_20086,U_20087) ),
    inference(clausify,[status(thm)],[f_4810_3]) ).

cnf(f_4810_6,plain,
    ( c_List_Olinorder__class_Osorted(U_20084,hAPP(hAPP(c_List_Olist_OCons(U_20084),U_20085),hAPP(hAPP(c_List_Olist_OCons(U_20084),U_20086),U_20087)))
    | ~ c_List_Olinorder__class_Osorted(U_20084,hAPP(hAPP(c_List_Olist_OCons(U_20084),U_20086),U_20087))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20084),U_20085),U_20086))
    | ~ sP1211(U_20084,U_20085,U_20086,U_20087) ),
    inference(clausify,[status(thm)],[f_4810_3]) ).

cnf(f_4810_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20084),U_20085),U_20086))
    | ~ sP1210(U_20084,U_20085,U_20086,U_20087) ),
    inference(clausify,[status(thm)],[f_4810_3]) ).

cnf(f_4810_8,plain,
    ( c_List_Olinorder__class_Osorted(U_20084,hAPP(hAPP(c_List_Olist_OCons(U_20084),U_20086),U_20087))
    | ~ sP1210(U_20084,U_20085,U_20086,U_20087) ),
    inference(clausify,[status(thm)],[f_4810_3]) ).

fof(f_4811_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_4811_2,plain,
    ! [U_20091,U_20090,U_20089,U_20088] :
      ( c_List_Olinorder__class_Osorted(U_20088,hAPP(hAPP(c_List_Olist_OCons(U_20088),U_20089),hAPP(hAPP(c_List_Olist_OCons(U_20088),U_20090),U_20091)))
      | ~ c_List_Olinorder__class_Osorted(U_20088,hAPP(hAPP(c_List_Olist_OCons(U_20088),U_20090),U_20091))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20088),U_20089),U_20090))
      | ~ class_Orderings_Olinorder(U_20088) ),
    inference(variable_rename,[status(thm)],[f_4811_1]) ).

fof(f_4811_3,plain,
    ! [U_20088,U_20090,U_20091,U_20089] :
      ( c_List_Olinorder__class_Osorted(U_20088,hAPP(hAPP(c_List_Olist_OCons(U_20088),U_20089),hAPP(hAPP(c_List_Olist_OCons(U_20088),U_20090),U_20091)))
      | ~ c_List_Olinorder__class_Osorted(U_20088,hAPP(hAPP(c_List_Olist_OCons(U_20088),U_20090),U_20091))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20088),U_20089),U_20090))
      | ~ class_Orderings_Olinorder(U_20088) ),
    inference(definitional_conversion,[status(esa)],[f_4811_2]) ).

cnf(f_4811_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20088,hAPP(hAPP(c_List_Olist_OCons(U_20088),U_20089),hAPP(hAPP(c_List_Olist_OCons(U_20088),U_20090),U_20091)))
    | ~ c_List_Olinorder__class_Osorted(U_20088,hAPP(hAPP(c_List_Olist_OCons(U_20088),U_20090),U_20091))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20088),U_20089),U_20090))
    | ~ class_Orderings_Olinorder(U_20088) ),
    inference(clausify,[status(thm)],[f_4811_3]) ).

fof(f_4812_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_4812_2,plain,
    ! [U_20094,U_20093,U_20092] :
      ( hAPP(hAPP(c_List_Otake(tc_Nat_Onat),U_20093),c_List_Oupt(U_20092,U_20094)) = c_List_Oupt(U_20092,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20092),U_20093))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20092),U_20093)),U_20094)) ),
    inference(variable_rename,[status(thm)],[f_4812_1]) ).

fof(f_4812_3,plain,
    ! [U_20092,U_20093,U_20094] :
      ( hAPP(hAPP(c_List_Otake(tc_Nat_Onat),U_20093),c_List_Oupt(U_20092,U_20094)) = c_List_Oupt(U_20092,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20092),U_20093))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20092),U_20093)),U_20094)) ),
    inference(definitional_conversion,[status(esa)],[f_4812_2]) ).

cnf(f_4812_4,plain,
    ( hAPP(hAPP(c_List_Otake(tc_Nat_Onat),U_20093),c_List_Oupt(U_20092,U_20094)) = c_List_Oupt(U_20092,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20092),U_20093))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20092),U_20093)),U_20094)) ),
    inference(clausify,[status(thm)],[f_4812_3]) ).

fof(f_4813_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_4813_2,plain,
    ! [U_20096,U_20095] :
      ( ( c_List_Oupt(U_20095,U_20096) = c_List_Olist_ONil(tc_Nat_Onat)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20096),U_20095))
          & U_20096 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
      & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20096),U_20095))
        | U_20096 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oupt(U_20095,U_20096) != c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(variable_rename,[status(thm)],[f_4813_1]) ).

fof(f_4813_3,plain,
    ( ! [U_20100,U_20098] :
        ( c_List_Oupt(U_20098,U_20100) = c_List_Olist_ONil(tc_Nat_Onat)
        | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20100),U_20098))
          & U_20100 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) )
    & ! [U_20099,U_20097] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20099),U_20097))
        | U_20099 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oupt(U_20097,U_20099) != c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(miniscope,[status(thm)],[f_4813_2]) ).

fof(f_4813_4,plain,
    ( ! [U_20100,U_20098] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20100),U_20098))
        | ~ sP1212(U_20100,U_20098) )
    & ! [U_20100,U_20098] :
        ( U_20100 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1212(U_20100,U_20098) )
    & ! [U_20100,U_20098] :
        ( c_List_Oupt(U_20098,U_20100) = c_List_Olist_ONil(tc_Nat_Onat)
        | sP1212(U_20100,U_20098) )
    & ! [U_20099,U_20097] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20099),U_20097))
        | U_20099 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | c_List_Oupt(U_20097,U_20099) != c_List_Olist_ONil(tc_Nat_Onat) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1212])],[f_4813_3]) ).

cnf(f_4813_5,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20099),U_20097))
    | U_20099 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | c_List_Oupt(U_20097,U_20099) != c_List_Olist_ONil(tc_Nat_Onat) ),
    inference(clausify,[status(thm)],[f_4813_4]) ).

cnf(f_4813_6,plain,
    ( c_List_Oupt(U_20098,U_20100) = c_List_Olist_ONil(tc_Nat_Onat)
    | sP1212(U_20100,U_20098) ),
    inference(clausify,[status(thm)],[f_4813_4]) ).

cnf(f_4813_7,plain,
    ( U_20100 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1212(U_20100,U_20098) ),
    inference(clausify,[status(thm)],[f_4813_4]) ).

cnf(f_4813_8,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20100),U_20098))
    | ~ sP1212(U_20100,U_20098) ),
    inference(clausify,[status(thm)],[f_4813_4]) ).

fof(f_4814_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_4814_2,plain,
    ! [U_20102,U_20101] :
      ( c_List_Oupt(U_20102,U_20101) = c_List_Olist_ONil(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20101),U_20102)) ),
    inference(variable_rename,[status(thm)],[f_4814_1]) ).

fof(f_4814_3,plain,
    ! [U_20101,U_20102] :
      ( c_List_Oupt(U_20102,U_20101) = c_List_Olist_ONil(tc_Nat_Onat)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20101),U_20102)) ),
    inference(definitional_conversion,[status(esa)],[f_4814_2]) ).

cnf(f_4814_4,plain,
    ( c_List_Oupt(U_20102,U_20101) = c_List_Olist_ONil(tc_Nat_Onat)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20101),U_20102)) ),
    inference(clausify,[status(thm)],[f_4814_3]) ).

fof(f_4815_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_4815_2,plain,
    ! [U_20107,U_20106,U_20105] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20105,hAPP(hAPP(c_List_Olist_OCons(U_20105),U_20106),U_20107))
          | ? [U_20104] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20105),U_20106),U_20104))
              & hBOOL(hAPP(hAPP(c_member(U_20105),U_20104),hAPP(c_List_Oset(U_20105),U_20107))) )
          | ~ c_List_Olinorder__class_Osorted(U_20105,U_20107) )
        & ( ( ! [U_20103] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20105),U_20106),U_20103))
                | ~ hBOOL(hAPP(hAPP(c_member(U_20105),U_20103),hAPP(c_List_Oset(U_20105),U_20107))) )
            & c_List_Olinorder__class_Osorted(U_20105,U_20107) )
          | ~ c_List_Olinorder__class_Osorted(U_20105,hAPP(hAPP(c_List_Olist_OCons(U_20105),U_20106),U_20107)) ) )
      | ~ class_Orderings_Olinorder(U_20105) ),
    inference(variable_rename,[status(thm)],[f_4815_1]) ).

fof(f_4815_3,plain,
    ! [U_20107,U_20106,U_20105] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20105,hAPP(hAPP(c_List_Olist_OCons(U_20105),U_20106),U_20107))
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20105),U_20106),sK494(U_20107,U_20106,U_20105)))
            & hBOOL(hAPP(hAPP(c_member(U_20105),sK494(U_20107,U_20106,U_20105)),hAPP(c_List_Oset(U_20105),U_20107))) )
          | ~ c_List_Olinorder__class_Osorted(U_20105,U_20107) )
        & ( ( ! [U_20103] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20105),U_20106),U_20103))
                | ~ hBOOL(hAPP(hAPP(c_member(U_20105),U_20103),hAPP(c_List_Oset(U_20105),U_20107))) )
            & c_List_Olinorder__class_Osorted(U_20105,U_20107) )
          | ~ c_List_Olinorder__class_Osorted(U_20105,hAPP(hAPP(c_List_Olist_OCons(U_20105),U_20106),U_20107)) ) )
      | ~ class_Orderings_Olinorder(U_20105) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK494]),skolemize(U_20104,sK494(U_20107,U_20106,U_20105))],[f_4815_2]) ).

fof(f_4815_4,plain,
    ( ! [U_20105,U_20106,U_20107] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20105),U_20106),sK494(U_20107,U_20106,U_20105)))
        | ~ sP1214(U_20105,U_20106,U_20107) )
    & ! [U_20105,U_20106,U_20107] :
        ( hBOOL(hAPP(hAPP(c_member(U_20105),sK494(U_20107,U_20106,U_20105)),hAPP(c_List_Oset(U_20105),U_20107)))
        | ~ sP1214(U_20105,U_20106,U_20107) )
    & ! [U_20103,U_20105,U_20106,U_20107] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20105),U_20106),U_20103))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20105),U_20103),hAPP(c_List_Oset(U_20105),U_20107)))
        | ~ sP1213(U_20103,U_20105,U_20106,U_20107) )
    & ! [U_20103,U_20105,U_20106,U_20107] :
        ( c_List_Olinorder__class_Osorted(U_20105,U_20107)
        | ~ sP1213(U_20103,U_20105,U_20106,U_20107) )
    & ! [U_20103,U_20105,U_20106,U_20107] :
        ( c_List_Olinorder__class_Osorted(U_20105,hAPP(hAPP(c_List_Olist_OCons(U_20105),U_20106),U_20107))
        | sP1214(U_20105,U_20106,U_20107)
        | ~ c_List_Olinorder__class_Osorted(U_20105,U_20107)
        | ~ sP1215(U_20103,U_20105,U_20106,U_20107) )
    & ! [U_20103,U_20105,U_20106,U_20107] :
        ( sP1213(U_20103,U_20105,U_20106,U_20107)
        | ~ c_List_Olinorder__class_Osorted(U_20105,hAPP(hAPP(c_List_Olist_OCons(U_20105),U_20106),U_20107))
        | ~ sP1215(U_20103,U_20105,U_20106,U_20107) )
    & ! [U_20103,U_20105,U_20106,U_20107] :
        ( sP1215(U_20103,U_20105,U_20106,U_20107)
        | ~ class_Orderings_Olinorder(U_20105) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1213,sP1214,sP1215])],[f_4815_3]) ).

cnf(f_4815_5,plain,
    ( sP1215(U_20103,U_20105,U_20106,U_20107)
    | ~ class_Orderings_Olinorder(U_20105) ),
    inference(clausify,[status(thm)],[f_4815_4]) ).

cnf(f_4815_6,plain,
    ( sP1213(U_20103,U_20105,U_20106,U_20107)
    | ~ c_List_Olinorder__class_Osorted(U_20105,hAPP(hAPP(c_List_Olist_OCons(U_20105),U_20106),U_20107))
    | ~ sP1215(U_20103,U_20105,U_20106,U_20107) ),
    inference(clausify,[status(thm)],[f_4815_4]) ).

cnf(f_4815_7,plain,
    ( c_List_Olinorder__class_Osorted(U_20105,hAPP(hAPP(c_List_Olist_OCons(U_20105),U_20106),U_20107))
    | sP1214(U_20105,U_20106,U_20107)
    | ~ c_List_Olinorder__class_Osorted(U_20105,U_20107)
    | ~ sP1215(U_20103,U_20105,U_20106,U_20107) ),
    inference(clausify,[status(thm)],[f_4815_4]) ).

cnf(f_4815_8,plain,
    ( c_List_Olinorder__class_Osorted(U_20105,U_20107)
    | ~ sP1213(U_20103,U_20105,U_20106,U_20107) ),
    inference(clausify,[status(thm)],[f_4815_4]) ).

cnf(f_4815_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20105),U_20106),U_20103))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20105),U_20103),hAPP(c_List_Oset(U_20105),U_20107)))
    | ~ sP1213(U_20103,U_20105,U_20106,U_20107) ),
    inference(clausify,[status(thm)],[f_4815_4]) ).

cnf(f_4815_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20105),sK494(U_20107,U_20106,U_20105)),hAPP(c_List_Oset(U_20105),U_20107)))
    | ~ sP1214(U_20105,U_20106,U_20107) ),
    inference(clausify,[status(thm)],[f_4815_4]) ).

cnf(f_4815_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20105),U_20106),sK494(U_20107,U_20106,U_20105)))
    | ~ sP1214(U_20105,U_20106,U_20107) ),
    inference(clausify,[status(thm)],[f_4815_4]) ).

fof(f_4816_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_4816_2,plain,
    ! [U_20110,U_20109,U_20108] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),U_20108),c_List_Oupt(U_20109,U_20110)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20109),U_20108),U_20110),
    inference(variable_rename,[status(thm)],[f_4816_1]) ).

fof(f_4816_3,plain,
    ! [U_20110,U_20108,U_20109] : hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),U_20108),c_List_Oupt(U_20109,U_20110)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20109),U_20108),U_20110),
    inference(definitional_conversion,[status(esa)],[f_4816_2]) ).

cnf(f_4816_4,plain,
    hAPP(hAPP(c_List_Odrop(tc_Nat_Onat),U_20108),c_List_Oupt(U_20109,U_20110)) = c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20109),U_20108),U_20110),
    inference(clausify,[status(thm)],[f_4816_3]) ).

fof(f_4817_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_4817_2,plain,
    ! [U_20113,U_20112,U_20111] :
      ( c_List_Olinorder__class_Osorted(U_20111,hAPP(hAPP(c_List_Odrop(U_20111),U_20113),U_20112))
      | ~ c_List_Olinorder__class_Osorted(U_20111,U_20112)
      | ~ class_Orderings_Olinorder(U_20111) ),
    inference(variable_rename,[status(thm)],[f_4817_1]) ).

fof(f_4817_3,plain,
    ! [U_20112,U_20111,U_20113] :
      ( c_List_Olinorder__class_Osorted(U_20111,hAPP(hAPP(c_List_Odrop(U_20111),U_20113),U_20112))
      | ~ c_List_Olinorder__class_Osorted(U_20111,U_20112)
      | ~ class_Orderings_Olinorder(U_20111) ),
    inference(definitional_conversion,[status(esa)],[f_4817_2]) ).

cnf(f_4817_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20111,hAPP(hAPP(c_List_Odrop(U_20111),U_20113),U_20112))
    | ~ c_List_Olinorder__class_Osorted(U_20111,U_20112)
    | ~ class_Orderings_Olinorder(U_20111) ),
    inference(clausify,[status(thm)],[f_4817_3]) ).

fof(f_4818_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_4818_2,plain,
    ! [U_20115,U_20114] :
      ( hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(U_20114,U_20115)) = U_20114
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20114),U_20115)) ),
    inference(variable_rename,[status(thm)],[f_4818_1]) ).

fof(f_4818_3,plain,
    ! [U_20114,U_20115] :
      ( hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(U_20114,U_20115)) = U_20114
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20114),U_20115)) ),
    inference(definitional_conversion,[status(esa)],[f_4818_2]) ).

cnf(f_4818_4,plain,
    ( hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(U_20114,U_20115)) = U_20114
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20114),U_20115)) ),
    inference(clausify,[status(thm)],[f_4818_3]) ).

fof(f_4819_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_4819_2,plain,
    ! [U_20116] : c_List_Oupt(U_20116,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    inference(variable_rename,[status(thm)],[f_4819_1]) ).

fof(f_4819_3,plain,
    ! [U_20116] : c_List_Oupt(U_20116,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    inference(definitional_conversion,[status(esa)],[f_4819_2]) ).

cnf(f_4819_4,plain,
    c_List_Oupt(U_20116,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat),
    inference(clausify,[status(thm)],[f_4819_3]) ).

fof(f_4820_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_4820_2,plain,
    ! [U_20117] :
      ( c_List_Olinorder__class_Osorted(U_20117,c_List_Olist_ONil(U_20117))
      | ~ class_Orderings_Olinorder(U_20117) ),
    inference(variable_rename,[status(thm)],[f_4820_1]) ).

fof(f_4820_3,plain,
    ! [U_20117] :
      ( c_List_Olinorder__class_Osorted(U_20117,c_List_Olist_ONil(U_20117))
      | ~ class_Orderings_Olinorder(U_20117) ),
    inference(definitional_conversion,[status(esa)],[f_4820_2]) ).

cnf(f_4820_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20117,c_List_Olist_ONil(U_20117))
    | ~ class_Orderings_Olinorder(U_20117) ),
    inference(clausify,[status(thm)],[f_4820_3]) ).

fof(f_4821_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_4821_2,plain,
    ! [U_20120,U_20119,U_20118] :
      ( c_List_Olinorder__class_Osorted(U_20118,hAPP(hAPP(c_List_Otake(U_20118),U_20120),U_20119))
      | ~ c_List_Olinorder__class_Osorted(U_20118,U_20119)
      | ~ class_Orderings_Olinorder(U_20118) ),
    inference(variable_rename,[status(thm)],[f_4821_1]) ).

fof(f_4821_3,plain,
    ! [U_20118,U_20119,U_20120] :
      ( c_List_Olinorder__class_Osorted(U_20118,hAPP(hAPP(c_List_Otake(U_20118),U_20120),U_20119))
      | ~ c_List_Olinorder__class_Osorted(U_20118,U_20119)
      | ~ class_Orderings_Olinorder(U_20118) ),
    inference(definitional_conversion,[status(esa)],[f_4821_2]) ).

cnf(f_4821_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20118,hAPP(hAPP(c_List_Otake(U_20118),U_20120),U_20119))
    | ~ c_List_Olinorder__class_Osorted(U_20118,U_20119)
    | ~ class_Orderings_Olinorder(U_20118) ),
    inference(clausify,[status(thm)],[f_4821_3]) ).

fof(f_4822_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_4822_2,plain,
    ! [U_20122,U_20121] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20121,U_20122)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20121),U_20122),
    inference(variable_rename,[status(thm)],[f_4822_1]) ).

fof(f_4822_3,plain,
    ! [U_20121,U_20122] : hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20121,U_20122)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20121),U_20122),
    inference(definitional_conversion,[status(esa)],[f_4822_2]) ).

cnf(f_4822_4,plain,
    hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20121,U_20122)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20121),U_20122),
    inference(clausify,[status(thm)],[f_4822_3]) ).

fof(f_4823_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_4823_2,plain,
    ! [U_20124,U_20123] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20123),U_20124) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20123,U_20124)),
    inference(variable_rename,[status(thm)],[f_4823_1]) ).

fof(f_4823_3,plain,
    ! [U_20123,U_20124] : hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20123),U_20124) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20123,U_20124)),
    inference(definitional_conversion,[status(esa)],[f_4823_2]) ).

cnf(f_4823_4,plain,
    hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20123),U_20124) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20123,U_20124)),
    inference(clausify,[status(thm)],[f_4823_3]) ).

fof(f_4824_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_4824_2,plain,
    ! [U_20127,U_20126,U_20125] :
      ( U_20126 = U_20127
      | hAPP(c_List_Oset(U_20125),U_20126) != hAPP(c_List_Oset(U_20125),U_20127)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20125),U_20127))
      | ~ c_List_Olinorder__class_Osorted(U_20125,U_20127)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20125),U_20126))
      | ~ c_List_Olinorder__class_Osorted(U_20125,U_20126)
      | ~ class_Orderings_Olinorder(U_20125) ),
    inference(variable_rename,[status(thm)],[f_4824_1]) ).

fof(f_4824_3,plain,
    ! [U_20125,U_20126,U_20127] :
      ( U_20126 = U_20127
      | hAPP(c_List_Oset(U_20125),U_20126) != hAPP(c_List_Oset(U_20125),U_20127)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20125),U_20127))
      | ~ c_List_Olinorder__class_Osorted(U_20125,U_20127)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20125),U_20126))
      | ~ c_List_Olinorder__class_Osorted(U_20125,U_20126)
      | ~ class_Orderings_Olinorder(U_20125) ),
    inference(definitional_conversion,[status(esa)],[f_4824_2]) ).

cnf(f_4824_4,plain,
    ( U_20126 = U_20127
    | hAPP(c_List_Oset(U_20125),U_20126) != hAPP(c_List_Oset(U_20125),U_20127)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20125),U_20127))
    | ~ c_List_Olinorder__class_Osorted(U_20125,U_20127)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20125),U_20126))
    | ~ c_List_Olinorder__class_Osorted(U_20125,U_20126)
    | ~ class_Orderings_Olinorder(U_20125) ),
    inference(clausify,[status(thm)],[f_4824_3]) ).

fof(f_4825_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_4825_2,plain,
    ! [U_20130,U_20129,U_20128] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20128,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20128,U_20128,c_COMBI(U_20128)),U_20129),U_20130))
          | ~ c_List_Olinorder__class_Osorted(U_20128,U_20130) )
        & ( c_List_Olinorder__class_Osorted(U_20128,U_20130)
          | ~ c_List_Olinorder__class_Osorted(U_20128,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20128,U_20128,c_COMBI(U_20128)),U_20129),U_20130)) ) )
      | ~ class_Orderings_Olinorder(U_20128) ),
    inference(variable_rename,[status(thm)],[f_4825_1]) ).

fof(f_4825_3,plain,
    ( ! [U_20130,U_20128,U_20129] :
        ( c_List_Olinorder__class_Osorted(U_20128,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20128,U_20128,c_COMBI(U_20128)),U_20129),U_20130))
        | ~ c_List_Olinorder__class_Osorted(U_20128,U_20130)
        | ~ sP1216(U_20130,U_20128,U_20129) )
    & ! [U_20130,U_20128,U_20129] :
        ( c_List_Olinorder__class_Osorted(U_20128,U_20130)
        | ~ c_List_Olinorder__class_Osorted(U_20128,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20128,U_20128,c_COMBI(U_20128)),U_20129),U_20130))
        | ~ sP1216(U_20130,U_20128,U_20129) )
    & ! [U_20130,U_20128,U_20129] :
        ( sP1216(U_20130,U_20128,U_20129)
        | ~ class_Orderings_Olinorder(U_20128) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1216])],[f_4825_2]) ).

cnf(f_4825_4,plain,
    ( sP1216(U_20130,U_20128,U_20129)
    | ~ class_Orderings_Olinorder(U_20128) ),
    inference(clausify,[status(thm)],[f_4825_3]) ).

cnf(f_4825_5,plain,
    ( c_List_Olinorder__class_Osorted(U_20128,U_20130)
    | ~ c_List_Olinorder__class_Osorted(U_20128,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20128,U_20128,c_COMBI(U_20128)),U_20129),U_20130))
    | ~ sP1216(U_20130,U_20128,U_20129) ),
    inference(clausify,[status(thm)],[f_4825_3]) ).

cnf(f_4825_6,plain,
    ( c_List_Olinorder__class_Osorted(U_20128,hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20128,U_20128,c_COMBI(U_20128)),U_20129),U_20130))
    | ~ c_List_Olinorder__class_Osorted(U_20128,U_20130)
    | ~ sP1216(U_20130,U_20128,U_20129) ),
    inference(clausify,[status(thm)],[f_4825_3]) ).

fof(f_4826_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_4826_2,plain,
    ! [U_20132,U_20131] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(U_20131,U_20132))),
    inference(variable_rename,[status(thm)],[f_4826_1]) ).

fof(f_4826_3,plain,
    ! [U_20132,U_20131] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(U_20131,U_20132))),
    inference(definitional_conversion,[status(esa)],[f_4826_2]) ).

cnf(f_4826_4,plain,
    hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(U_20131,U_20132))),
    inference(clausify,[status(thm)],[f_4826_3]) ).

fof(f_4827_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_4827_2,plain,
    ! [U_20135,U_20134,U_20133] :
      ( c_List_Olinorder__class_Osorted(U_20133,c_List_Oremove1(U_20133,U_20135,U_20134))
      | ~ c_List_Olinorder__class_Osorted(U_20133,U_20134)
      | ~ class_Orderings_Olinorder(U_20133) ),
    inference(variable_rename,[status(thm)],[f_4827_1]) ).

fof(f_4827_3,plain,
    ! [U_20134,U_20133,U_20135] :
      ( c_List_Olinorder__class_Osorted(U_20133,c_List_Oremove1(U_20133,U_20135,U_20134))
      | ~ c_List_Olinorder__class_Osorted(U_20133,U_20134)
      | ~ class_Orderings_Olinorder(U_20133) ),
    inference(definitional_conversion,[status(esa)],[f_4827_2]) ).

cnf(f_4827_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20133,c_List_Oremove1(U_20133,U_20135,U_20134))
    | ~ c_List_Olinorder__class_Osorted(U_20133,U_20134)
    | ~ class_Orderings_Olinorder(U_20133) ),
    inference(clausify,[status(thm)],[f_4827_3]) ).

fof(f_4828_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_4828_2,plain,
    ! [U_20137,U_20136] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(U_20136,U_20137)),
    inference(variable_rename,[status(thm)],[f_4828_1]) ).

fof(f_4828_3,plain,
    ! [U_20136,U_20137] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(U_20136,U_20137)),
    inference(definitional_conversion,[status(esa)],[f_4828_2]) ).

cnf(f_4828_4,plain,
    c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(U_20136,U_20137)),
    inference(clausify,[status(thm)],[f_4828_3]) ).

fof(f_4829_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_4829_2,plain,
    ! [U_20139,U_20138] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(U_20138,U_20139)),
    inference(variable_rename,[status(thm)],[f_4829_1]) ).

fof(f_4829_3,plain,
    ! [U_20138,U_20139] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(U_20138,U_20139)),
    inference(definitional_conversion,[status(esa)],[f_4829_2]) ).

cnf(f_4829_4,plain,
    c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(U_20138,U_20139)),
    inference(clausify,[status(thm)],[f_4829_3]) ).

fof(f_4830_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_4830_2,plain,
    ! [U_20141,U_20140] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20140),U_20141)) = c_List_Oupt(U_20140,U_20141),
    inference(variable_rename,[status(thm)],[f_4830_1]) ).

fof(f_4830_3,plain,
    ! [U_20140,U_20141] : c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20140),U_20141)) = c_List_Oupt(U_20140,U_20141),
    inference(definitional_conversion,[status(esa)],[f_4830_2]) ).

cnf(f_4830_4,plain,
    c_List_Olinorder__class_Osorted__list__of__set(tc_Nat_Onat,hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,U_20140),U_20141)) = c_List_Oupt(U_20140,U_20141),
    inference(clausify,[status(thm)],[f_4830_3]) ).

fof(f_4831_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_4831_2,plain,
    ! [U_20144,U_20143,U_20142] :
      ( c_List_Olinorder__class_Osorted(U_20142,c_List_Olinorder__class_Oinsort__insert__key(U_20142,U_20142,c_COMBI(U_20142),U_20144,U_20143))
      | ~ c_List_Olinorder__class_Osorted(U_20142,U_20143)
      | ~ class_Orderings_Olinorder(U_20142) ),
    inference(variable_rename,[status(thm)],[f_4831_1]) ).

fof(f_4831_3,plain,
    ! [U_20143,U_20142,U_20144] :
      ( c_List_Olinorder__class_Osorted(U_20142,c_List_Olinorder__class_Oinsort__insert__key(U_20142,U_20142,c_COMBI(U_20142),U_20144,U_20143))
      | ~ c_List_Olinorder__class_Osorted(U_20142,U_20143)
      | ~ class_Orderings_Olinorder(U_20142) ),
    inference(definitional_conversion,[status(esa)],[f_4831_2]) ).

cnf(f_4831_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20142,c_List_Olinorder__class_Oinsort__insert__key(U_20142,U_20142,c_COMBI(U_20142),U_20144,U_20143))
    | ~ c_List_Olinorder__class_Osorted(U_20142,U_20143)
    | ~ class_Orderings_Olinorder(U_20142) ),
    inference(clausify,[status(thm)],[f_4831_3]) ).

fof(f_4832_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_4832_2,plain,
    ! [U_20146,U_20145] :
      ( c_List_Oupt(U_20145,U_20146) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20145),c_List_Oupt(hAPP(c_Nat_OSuc,U_20145),U_20146))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20145),U_20146)) ),
    inference(variable_rename,[status(thm)],[f_4832_1]) ).

fof(f_4832_3,plain,
    ! [U_20145,U_20146] :
      ( c_List_Oupt(U_20145,U_20146) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20145),c_List_Oupt(hAPP(c_Nat_OSuc,U_20145),U_20146))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20145),U_20146)) ),
    inference(definitional_conversion,[status(esa)],[f_4832_2]) ).

cnf(f_4832_4,plain,
    ( c_List_Oupt(U_20145,U_20146) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20145),c_List_Oupt(hAPP(c_Nat_OSuc,U_20145),U_20146))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20145),U_20146)) ),
    inference(clausify,[status(thm)],[f_4832_3]) ).

fof(f_4833_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_4833_2,plain,
    ! [U_20148,U_20147] :
      ( ( c_List_Oupt(U_20147,U_20148) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20147),U_20148)) )
      & ( c_List_Oupt(U_20147,U_20148) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20147),c_List_Oupt(hAPP(c_Nat_OSuc,U_20147),U_20148))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20147),U_20148)) ) ),
    inference(variable_rename,[status(thm)],[f_4833_1]) ).

fof(f_4833_3,plain,
    ( ! [U_20152,U_20150] :
        ( c_List_Oupt(U_20150,U_20152) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20150),U_20152)) )
    & ! [U_20151,U_20149] :
        ( c_List_Oupt(U_20149,U_20151) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20149),c_List_Oupt(hAPP(c_Nat_OSuc,U_20149),U_20151))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20149),U_20151)) ) ),
    inference(miniscope,[status(thm)],[f_4833_2]) ).

fof(f_4833_4,plain,
    ( ! [U_20150,U_20152] :
        ( c_List_Oupt(U_20150,U_20152) = c_List_Olist_ONil(tc_Nat_Onat)
        | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20150),U_20152)) )
    & ! [U_20151,U_20149] :
        ( c_List_Oupt(U_20149,U_20151) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20149),c_List_Oupt(hAPP(c_Nat_OSuc,U_20149),U_20151))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20149),U_20151)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4833_3]) ).

cnf(f_4833_5,plain,
    ( c_List_Oupt(U_20149,U_20151) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20149),c_List_Oupt(hAPP(c_Nat_OSuc,U_20149),U_20151))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20149),U_20151)) ),
    inference(clausify,[status(thm)],[f_4833_4]) ).

cnf(f_4833_6,plain,
    ( c_List_Oupt(U_20150,U_20152) = c_List_Olist_ONil(tc_Nat_Onat)
    | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20150),U_20152)) ),
    inference(clausify,[status(thm)],[f_4833_4]) ).

fof(f_4834_1,plain,
    ! [V_xs,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_xs)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__tl]) ).

fof(f_4834_2,plain,
    ! [U_20154,U_20153] :
      ( c_List_Olinorder__class_Osorted(U_20153,hAPP(c_List_Otl(U_20153),U_20154))
      | ~ c_List_Olinorder__class_Osorted(U_20153,U_20154)
      | ~ class_Orderings_Olinorder(U_20153) ),
    inference(variable_rename,[status(thm)],[f_4834_1]) ).

fof(f_4834_3,plain,
    ! [U_20153,U_20154] :
      ( c_List_Olinorder__class_Osorted(U_20153,hAPP(c_List_Otl(U_20153),U_20154))
      | ~ c_List_Olinorder__class_Osorted(U_20153,U_20154)
      | ~ class_Orderings_Olinorder(U_20153) ),
    inference(definitional_conversion,[status(esa)],[f_4834_2]) ).

cnf(f_4834_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20153,hAPP(c_List_Otl(U_20153),U_20154))
    | ~ c_List_Olinorder__class_Osorted(U_20153,U_20154)
    | ~ class_Orderings_Olinorder(U_20153) ),
    inference(clausify,[status(thm)],[f_4834_3]) ).

fof(f_4835_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_4835_2,plain,
    ! [U_20159,U_20158,U_20157,U_20156,U_20155] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20155,hAPP(hAPP(c_List_Omap(U_20156,U_20155),U_20157),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20156,U_20155,U_20157),U_20158),U_20159)))
          | ~ c_List_Olinorder__class_Osorted(U_20155,hAPP(hAPP(c_List_Omap(U_20156,U_20155),U_20157),U_20159)) )
        & ( c_List_Olinorder__class_Osorted(U_20155,hAPP(hAPP(c_List_Omap(U_20156,U_20155),U_20157),U_20159))
          | ~ c_List_Olinorder__class_Osorted(U_20155,hAPP(hAPP(c_List_Omap(U_20156,U_20155),U_20157),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20156,U_20155,U_20157),U_20158),U_20159))) ) )
      | ~ class_Orderings_Olinorder(U_20155) ),
    inference(variable_rename,[status(thm)],[f_4835_1]) ).

fof(f_4835_3,plain,
    ( ! [U_20155,U_20156,U_20157,U_20158,U_20159] :
        ( c_List_Olinorder__class_Osorted(U_20155,hAPP(hAPP(c_List_Omap(U_20156,U_20155),U_20157),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20156,U_20155,U_20157),U_20158),U_20159)))
        | ~ c_List_Olinorder__class_Osorted(U_20155,hAPP(hAPP(c_List_Omap(U_20156,U_20155),U_20157),U_20159))
        | ~ sP1217(U_20155,U_20156,U_20157,U_20158,U_20159) )
    & ! [U_20155,U_20156,U_20157,U_20158,U_20159] :
        ( c_List_Olinorder__class_Osorted(U_20155,hAPP(hAPP(c_List_Omap(U_20156,U_20155),U_20157),U_20159))
        | ~ c_List_Olinorder__class_Osorted(U_20155,hAPP(hAPP(c_List_Omap(U_20156,U_20155),U_20157),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20156,U_20155,U_20157),U_20158),U_20159)))
        | ~ sP1217(U_20155,U_20156,U_20157,U_20158,U_20159) )
    & ! [U_20155,U_20156,U_20157,U_20158,U_20159] :
        ( sP1217(U_20155,U_20156,U_20157,U_20158,U_20159)
        | ~ class_Orderings_Olinorder(U_20155) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1217])],[f_4835_2]) ).

cnf(f_4835_4,plain,
    ( sP1217(U_20155,U_20156,U_20157,U_20158,U_20159)
    | ~ class_Orderings_Olinorder(U_20155) ),
    inference(clausify,[status(thm)],[f_4835_3]) ).

cnf(f_4835_5,plain,
    ( c_List_Olinorder__class_Osorted(U_20155,hAPP(hAPP(c_List_Omap(U_20156,U_20155),U_20157),U_20159))
    | ~ c_List_Olinorder__class_Osorted(U_20155,hAPP(hAPP(c_List_Omap(U_20156,U_20155),U_20157),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20156,U_20155,U_20157),U_20158),U_20159)))
    | ~ sP1217(U_20155,U_20156,U_20157,U_20158,U_20159) ),
    inference(clausify,[status(thm)],[f_4835_3]) ).

cnf(f_4835_6,plain,
    ( c_List_Olinorder__class_Osorted(U_20155,hAPP(hAPP(c_List_Omap(U_20156,U_20155),U_20157),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20156,U_20155,U_20157),U_20158),U_20159)))
    | ~ c_List_Olinorder__class_Osorted(U_20155,hAPP(hAPP(c_List_Omap(U_20156,U_20155),U_20157),U_20159))
    | ~ sP1217(U_20155,U_20156,U_20157,U_20158,U_20159) ),
    inference(clausify,[status(thm)],[f_4835_3]) ).

fof(f_4836_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_4836_2,plain,
    ! [U_20164,U_20163,U_20162,U_20161,U_20160] :
      ( c_List_Olinorder__class_Osorted(U_20160,hAPP(hAPP(c_List_Omap(U_20161,U_20160),U_20162),c_List_Oremove1(U_20161,U_20164,U_20163)))
      | ~ c_List_Olinorder__class_Osorted(U_20160,hAPP(hAPP(c_List_Omap(U_20161,U_20160),U_20162),U_20163))
      | ~ class_Orderings_Olinorder(U_20160) ),
    inference(variable_rename,[status(thm)],[f_4836_1]) ).

fof(f_4836_3,plain,
    ! [U_20163,U_20160,U_20162,U_20161,U_20164] :
      ( c_List_Olinorder__class_Osorted(U_20160,hAPP(hAPP(c_List_Omap(U_20161,U_20160),U_20162),c_List_Oremove1(U_20161,U_20164,U_20163)))
      | ~ c_List_Olinorder__class_Osorted(U_20160,hAPP(hAPP(c_List_Omap(U_20161,U_20160),U_20162),U_20163))
      | ~ class_Orderings_Olinorder(U_20160) ),
    inference(definitional_conversion,[status(esa)],[f_4836_2]) ).

cnf(f_4836_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20160,hAPP(hAPP(c_List_Omap(U_20161,U_20160),U_20162),c_List_Oremove1(U_20161,U_20164,U_20163)))
    | ~ c_List_Olinorder__class_Osorted(U_20160,hAPP(hAPP(c_List_Omap(U_20161,U_20160),U_20162),U_20163))
    | ~ class_Orderings_Olinorder(U_20160) ),
    inference(clausify,[status(thm)],[f_4836_3]) ).

fof(f_4837_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_4837_2,plain,
    ! [U_20166,U_20165] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(U_20165,U_20166)) = c_List_Oupt(hAPP(c_Nat_OSuc,U_20165),hAPP(c_Nat_OSuc,U_20166)),
    inference(variable_rename,[status(thm)],[f_4837_1]) ).

fof(f_4837_3,plain,
    ! [U_20166,U_20165] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(U_20165,U_20166)) = c_List_Oupt(hAPP(c_Nat_OSuc,U_20165),hAPP(c_Nat_OSuc,U_20166)),
    inference(definitional_conversion,[status(esa)],[f_4837_2]) ).

cnf(f_4837_4,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Nat_Onat),c_Nat_OSuc),c_List_Oupt(U_20165,U_20166)) = c_List_Oupt(hAPP(c_Nat_OSuc,U_20165),hAPP(c_Nat_OSuc,U_20166)),
    inference(clausify,[status(thm)],[f_4837_3]) ).

fof(f_4838_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_4838_2,plain,
    ! [U_20171,U_20170,U_20169,U_20168,U_20167] :
      ( c_List_Olinorder__class_Osorted(U_20167,hAPP(hAPP(c_List_Omap(U_20168,U_20167),U_20169),c_List_Olinorder__class_Oinsort__insert__key(U_20168,U_20167,U_20169,U_20171,U_20170)))
      | ~ c_List_Olinorder__class_Osorted(U_20167,hAPP(hAPP(c_List_Omap(U_20168,U_20167),U_20169),U_20170))
      | ~ class_Orderings_Olinorder(U_20167) ),
    inference(variable_rename,[status(thm)],[f_4838_1]) ).

fof(f_4838_3,plain,
    ! [U_20167,U_20168,U_20169,U_20170,U_20171] :
      ( c_List_Olinorder__class_Osorted(U_20167,hAPP(hAPP(c_List_Omap(U_20168,U_20167),U_20169),c_List_Olinorder__class_Oinsort__insert__key(U_20168,U_20167,U_20169,U_20171,U_20170)))
      | ~ c_List_Olinorder__class_Osorted(U_20167,hAPP(hAPP(c_List_Omap(U_20168,U_20167),U_20169),U_20170))
      | ~ class_Orderings_Olinorder(U_20167) ),
    inference(definitional_conversion,[status(esa)],[f_4838_2]) ).

cnf(f_4838_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20167,hAPP(hAPP(c_List_Omap(U_20168,U_20167),U_20169),c_List_Olinorder__class_Oinsort__insert__key(U_20168,U_20167,U_20169,U_20171,U_20170)))
    | ~ c_List_Olinorder__class_Osorted(U_20167,hAPP(hAPP(c_List_Omap(U_20168,U_20167),U_20169),U_20170))
    | ~ class_Orderings_Olinorder(U_20167) ),
    inference(clausify,[status(thm)],[f_4838_3]) ).

fof(f_4839_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_4839_2,plain,
    ! [U_20173,U_20172] :
      ( ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20172),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20173)) = 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_20172)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20173))) )
      & ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20172),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20173)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20172)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20172)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20173)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20172)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20173))) ) ),
    inference(variable_rename,[status(thm)],[f_4839_1]) ).

fof(f_4839_3,plain,
    ( ! [U_20177,U_20175] :
        ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20175),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20177)) = 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_20175)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20177))) )
    & ! [U_20176,U_20174] :
        ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20174),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20176)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20174)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20174)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20176)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20174)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20176))) ) ),
    inference(miniscope,[status(thm)],[f_4839_2]) ).

fof(f_4839_4,plain,
    ( ! [U_20175,U_20177] :
        ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20175),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20177)) = 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_20175)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20177))) )
    & ! [U_20176,U_20174] :
        ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20174),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20176)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20174)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20174)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20176)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20174)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20176))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4839_3]) ).

cnf(f_4839_5,plain,
    ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20174),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20176)) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20174)),c_List_Oupt(hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20174)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20176)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20174)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20176))) ),
    inference(clausify,[status(thm)],[f_4839_4]) ).

cnf(f_4839_6,plain,
    ( c_List_Oupt(hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20175),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20177)) = 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_20175)),hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),U_20177))) ),
    inference(clausify,[status(thm)],[f_4839_4]) ).

fof(f_4840_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_4840_2,plain,
    ! [U_20181,U_20180,U_20179,U_20178] :
      ( ( c_List_Oupt(U_20178,U_20179) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20180),U_20181)
        | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20178),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20179) != U_20181
        | U_20178 != U_20180
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20178),U_20179)) )
      & ( ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20178),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20179) = U_20181
          & U_20178 = U_20180
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20178),U_20179)) )
        | c_List_Oupt(U_20178,U_20179) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20180),U_20181) ) ),
    inference(variable_rename,[status(thm)],[f_4840_1]) ).

fof(f_4840_3,plain,
    ( ! [U_20189,U_20187,U_20185,U_20183] :
        ( c_List_Oupt(U_20183,U_20185) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20187),U_20189)
        | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20183),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20185) != U_20189
        | U_20183 != U_20187
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20183),U_20185)) )
    & ! [U_20188,U_20186,U_20184,U_20182] :
        ( ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20182),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20184) = U_20188
          & U_20182 = U_20186
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20182),U_20184)) )
        | c_List_Oupt(U_20182,U_20184) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20186),U_20188) ) ),
    inference(miniscope,[status(thm)],[f_4840_2]) ).

fof(f_4840_4,plain,
    ( ! [U_20188,U_20184,U_20182,U_20186] :
        ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20182),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20184) = U_20188
        | ~ sP1218(U_20188,U_20184,U_20182,U_20186) )
    & ! [U_20188,U_20184,U_20182,U_20186] :
        ( U_20182 = U_20186
        | ~ sP1218(U_20188,U_20184,U_20182,U_20186) )
    & ! [U_20188,U_20184,U_20182,U_20186] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20182),U_20184))
        | ~ sP1218(U_20188,U_20184,U_20182,U_20186) )
    & ! [U_20183,U_20189,U_20185,U_20187] :
        ( c_List_Oupt(U_20183,U_20185) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20187),U_20189)
        | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20183),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20185) != U_20189
        | U_20183 != U_20187
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20183),U_20185)) )
    & ! [U_20188,U_20184,U_20182,U_20186] :
        ( sP1218(U_20188,U_20184,U_20182,U_20186)
        | c_List_Oupt(U_20182,U_20184) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20186),U_20188) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1218])],[f_4840_3]) ).

cnf(f_4840_5,plain,
    ( sP1218(U_20188,U_20184,U_20182,U_20186)
    | c_List_Oupt(U_20182,U_20184) != hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20186),U_20188) ),
    inference(clausify,[status(thm)],[f_4840_4]) ).

cnf(f_4840_6,plain,
    ( c_List_Oupt(U_20183,U_20185) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),U_20187),U_20189)
    | c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20183),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20185) != U_20189
    | U_20183 != U_20187
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20183),U_20185)) ),
    inference(clausify,[status(thm)],[f_4840_4]) ).

cnf(f_4840_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20182),U_20184))
    | ~ sP1218(U_20188,U_20184,U_20182,U_20186) ),
    inference(clausify,[status(thm)],[f_4840_4]) ).

cnf(f_4840_8,plain,
    ( U_20182 = U_20186
    | ~ sP1218(U_20188,U_20184,U_20182,U_20186) ),
    inference(clausify,[status(thm)],[f_4840_4]) ).

cnf(f_4840_9,plain,
    ( c_List_Oupt(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20182),c_Groups_Oone__class_Oone(tc_Nat_Onat)),U_20184) = U_20188
    | ~ sP1218(U_20188,U_20184,U_20182,U_20186) ),
    inference(clausify,[status(thm)],[f_4840_4]) ).

fof(f_4841_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_4841_2,plain,
    ! [U_20191,U_20190] :
      ( c_List_Olast(tc_Nat_Onat,c_List_Oupt(U_20190,U_20191)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20191),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20190),U_20191)) ),
    inference(variable_rename,[status(thm)],[f_4841_1]) ).

fof(f_4841_3,plain,
    ! [U_20191,U_20190] :
      ( c_List_Olast(tc_Nat_Onat,c_List_Oupt(U_20190,U_20191)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20191),c_Groups_Oone__class_Oone(tc_Nat_Onat))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20190),U_20191)) ),
    inference(definitional_conversion,[status(esa)],[f_4841_2]) ).

cnf(f_4841_4,plain,
    ( c_List_Olast(tc_Nat_Onat,c_List_Oupt(U_20190,U_20191)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20191),c_Groups_Oone__class_Oone(tc_Nat_Onat))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20190),U_20191)) ),
    inference(clausify,[status(thm)],[f_4841_3]) ).

fof(f_4842_1,plain,
    ! [V_x_2,V_Pa_2,V_xs_2,V_f_2,T_c,T_b] :
      ( hAPP(c_List_Ofilter(T_c,V_Pa_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_Pa_2),V_xs_2))
      | ~ hBOOL(hAPP(V_Pa_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_4842_2,plain,
    ! [U_20197,U_20196,U_20195,U_20194,U_20193,U_20192] :
      ( hAPP(c_List_Ofilter(U_20193,U_20196),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20193,U_20192,U_20194),U_20197),U_20195)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20193,U_20192,U_20194),U_20197),hAPP(c_List_Ofilter(U_20193,U_20196),U_20195))
      | ~ hBOOL(hAPP(U_20196,U_20197))
      | ~ c_List_Olinorder__class_Osorted(U_20192,hAPP(hAPP(c_List_Omap(U_20193,U_20192),U_20194),U_20195))
      | ~ class_Orderings_Olinorder(U_20192) ),
    inference(variable_rename,[status(thm)],[f_4842_1]) ).

fof(f_4842_3,plain,
    ! [U_20192,U_20193,U_20194,U_20195,U_20196,U_20197] :
      ( hAPP(c_List_Ofilter(U_20193,U_20196),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20193,U_20192,U_20194),U_20197),U_20195)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20193,U_20192,U_20194),U_20197),hAPP(c_List_Ofilter(U_20193,U_20196),U_20195))
      | ~ hBOOL(hAPP(U_20196,U_20197))
      | ~ c_List_Olinorder__class_Osorted(U_20192,hAPP(hAPP(c_List_Omap(U_20193,U_20192),U_20194),U_20195))
      | ~ class_Orderings_Olinorder(U_20192) ),
    inference(definitional_conversion,[status(esa)],[f_4842_2]) ).

cnf(f_4842_4,plain,
    ( hAPP(c_List_Ofilter(U_20193,U_20196),hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20193,U_20192,U_20194),U_20197),U_20195)) = hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20193,U_20192,U_20194),U_20197),hAPP(c_List_Ofilter(U_20193,U_20196),U_20195))
    | ~ hBOOL(hAPP(U_20196,U_20197))
    | ~ c_List_Olinorder__class_Osorted(U_20192,hAPP(hAPP(c_List_Omap(U_20193,U_20192),U_20194),U_20195))
    | ~ class_Orderings_Olinorder(U_20192) ),
    inference(clausify,[status(thm)],[f_4842_3]) ).

fof(f_4843_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_4843_2,plain,
    ! [U_20199,U_20198] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20198),hAPP(c_List_Onth(U_20198),U_20199)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20198)),U_20199))) = U_20199,
    inference(variable_rename,[status(thm)],[f_4843_1]) ).

fof(f_4843_3,plain,
    ! [U_20199,U_20198] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20198),hAPP(c_List_Onth(U_20198),U_20199)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20198)),U_20199))) = U_20199,
    inference(definitional_conversion,[status(esa)],[f_4843_2]) ).

cnf(f_4843_4,plain,
    hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20198),hAPP(c_List_Onth(U_20198),U_20199)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20198)),U_20199))) = U_20199,
    inference(clausify,[status(thm)],[f_4843_3]) ).

fof(f_4844_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_4844_2,plain,
    ! [U_20201,U_20200] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_20200,U_20201) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20200,hAPP(c_Nat_OSuc,U_20201))),
    inference(variable_rename,[status(thm)],[f_4844_1]) ).

fof(f_4844_3,plain,
    ! [U_20200,U_20201] : c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_20200,U_20201) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20200,hAPP(c_Nat_OSuc,U_20201))),
    inference(definitional_conversion,[status(esa)],[f_4844_2]) ).

cnf(f_4844_4,plain,
    c_SetInterval_Oord__class_OatLeastAtMost(tc_Nat_Onat,U_20200,U_20201) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20200,hAPP(c_Nat_OSuc,U_20201))),
    inference(clausify,[status(thm)],[f_4844_3]) ).

fof(f_4845_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_4845_2,plain,
    ! [U_20202] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_20202) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_20202)),
    inference(variable_rename,[status(thm)],[f_4845_1]) ).

fof(f_4845_3,plain,
    ! [U_20202] : hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_20202) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_20202)),
    inference(definitional_conversion,[status(esa)],[f_4845_2]) ).

cnf(f_4845_4,plain,
    hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),U_20202) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_20202)),
    inference(clausify,[status(thm)],[f_4845_3]) ).

fof(f_4846_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_4846_2,plain,
    ! [U_20206,U_20205,U_20204,U_20203] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_20203),U_20204),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20205,U_20206))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20203),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20203),U_20204),c_List_Oupt(U_20205,U_20206)))
      | ~ class_Groups_Ocomm__monoid__add(U_20203) ),
    inference(variable_rename,[status(thm)],[f_4846_1]) ).

fof(f_4846_3,plain,
    ! [U_20203,U_20204,U_20205,U_20206] :
      ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_20203),U_20204),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20205,U_20206))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20203),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20203),U_20204),c_List_Oupt(U_20205,U_20206)))
      | ~ class_Groups_Ocomm__monoid__add(U_20203) ),
    inference(definitional_conversion,[status(esa)],[f_4846_2]) ).

cnf(f_4846_4,plain,
    ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_20203),U_20204),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20205,U_20206))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20203),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20203),U_20204),c_List_Oupt(U_20205,U_20206)))
    | ~ class_Groups_Ocomm__monoid__add(U_20203) ),
    inference(clausify,[status(thm)],[f_4846_3]) ).

fof(f_4847_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_4847_2,plain,
    ! [U_20210,U_20209,U_20208,U_20207] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20207),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20207),U_20208),c_List_Oupt(U_20209,U_20210))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_20207),U_20208),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20209,U_20210)))
      | ~ class_Groups_Ocomm__monoid__add(U_20207) ),
    inference(variable_rename,[status(thm)],[f_4847_1]) ).

fof(f_4847_3,plain,
    ! [U_20207,U_20208,U_20209,U_20210] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20207),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20207),U_20208),c_List_Oupt(U_20209,U_20210))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_20207),U_20208),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20209,U_20210)))
      | ~ class_Groups_Ocomm__monoid__add(U_20207) ),
    inference(definitional_conversion,[status(esa)],[f_4847_2]) ).

cnf(f_4847_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20207),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20207),U_20208),c_List_Oupt(U_20209,U_20210))) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(tc_Nat_Onat,U_20207),U_20208),hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(U_20209,U_20210)))
    | ~ class_Groups_Ocomm__monoid__add(U_20207) ),
    inference(clausify,[status(thm)],[f_4847_3]) ).

fof(f_4848_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_4848_2,plain,
    ! [U_20213,U_20212,U_20211] :
      ( hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(U_20211,U_20213)),U_20212) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20211),U_20212)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20211),U_20212)),U_20213)) ),
    inference(variable_rename,[status(thm)],[f_4848_1]) ).

fof(f_4848_3,plain,
    ! [U_20211,U_20212,U_20213] :
      ( hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(U_20211,U_20213)),U_20212) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20211),U_20212)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20211),U_20212)),U_20213)) ),
    inference(definitional_conversion,[status(esa)],[f_4848_2]) ).

cnf(f_4848_4,plain,
    ( hAPP(hAPP(c_List_Onth(tc_Nat_Onat),c_List_Oupt(U_20211,U_20213)),U_20212) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20211),U_20212)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20211),U_20212)),U_20213)) ),
    inference(clausify,[status(thm)],[f_4848_3]) ).

fof(f_4849_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_4849_2,plain,
    ! [U_20215,U_20214] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_20214,U_20215) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_20214),hAPP(c_Nat_OSuc,U_20215))),
    inference(variable_rename,[status(thm)],[f_4849_1]) ).

fof(f_4849_3,plain,
    ! [U_20214,U_20215] : c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_20214,U_20215) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_20214),hAPP(c_Nat_OSuc,U_20215))),
    inference(definitional_conversion,[status(esa)],[f_4849_2]) ).

cnf(f_4849_4,plain,
    c_SetInterval_Oord__class_OgreaterThanAtMost(tc_Nat_Onat,U_20214,U_20215) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_20214),hAPP(c_Nat_OSuc,U_20215))),
    inference(clausify,[status(thm)],[f_4849_3]) ).

fof(f_4850_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_4850_2,plain,
    ! [U_20220,U_20219,U_20218] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20218,hAPP(hAPP(c_List_Olist_OCons(U_20218),U_20219),U_20220))
          | ~ c_List_Olinorder__class_Osorted(U_20218,U_20220)
          | ? [U_20217] :
              ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20218),U_20219),U_20217))
              & hBOOL(hAPP(hAPP(c_member(U_20218),U_20217),hAPP(c_List_Oset(U_20218),U_20220))) ) )
        & ( ( c_List_Olinorder__class_Osorted(U_20218,U_20220)
            & ! [U_20216] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20218),U_20219),U_20216))
                | ~ hBOOL(hAPP(hAPP(c_member(U_20218),U_20216),hAPP(c_List_Oset(U_20218),U_20220))) ) )
          | ~ c_List_Olinorder__class_Osorted(U_20218,hAPP(hAPP(c_List_Olist_OCons(U_20218),U_20219),U_20220)) ) )
      | ~ class_Orderings_Olinorder(U_20218) ),
    inference(variable_rename,[status(thm)],[f_4850_1]) ).

fof(f_4850_3,plain,
    ! [U_20220,U_20219,U_20218] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20218,hAPP(hAPP(c_List_Olist_OCons(U_20218),U_20219),U_20220))
          | ~ c_List_Olinorder__class_Osorted(U_20218,U_20220)
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20218),U_20219),sK495(U_20220,U_20219,U_20218)))
            & hBOOL(hAPP(hAPP(c_member(U_20218),sK495(U_20220,U_20219,U_20218)),hAPP(c_List_Oset(U_20218),U_20220))) ) )
        & ( ( c_List_Olinorder__class_Osorted(U_20218,U_20220)
            & ! [U_20216] :
                ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20218),U_20219),U_20216))
                | ~ hBOOL(hAPP(hAPP(c_member(U_20218),U_20216),hAPP(c_List_Oset(U_20218),U_20220))) ) )
          | ~ c_List_Olinorder__class_Osorted(U_20218,hAPP(hAPP(c_List_Olist_OCons(U_20218),U_20219),U_20220)) ) )
      | ~ class_Orderings_Olinorder(U_20218) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK495]),skolemize(U_20217,sK495(U_20220,U_20219,U_20218))],[f_4850_2]) ).

fof(f_4850_4,plain,
    ( ! [U_20218,U_20219,U_20220] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20218),U_20219),sK495(U_20220,U_20219,U_20218)))
        | ~ sP1220(U_20218,U_20219,U_20220) )
    & ! [U_20218,U_20219,U_20220] :
        ( hBOOL(hAPP(hAPP(c_member(U_20218),sK495(U_20220,U_20219,U_20218)),hAPP(c_List_Oset(U_20218),U_20220)))
        | ~ sP1220(U_20218,U_20219,U_20220) )
    & ! [U_20216,U_20218,U_20219,U_20220] :
        ( c_List_Olinorder__class_Osorted(U_20218,U_20220)
        | ~ sP1219(U_20216,U_20218,U_20219,U_20220) )
    & ! [U_20216,U_20218,U_20219,U_20220] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20218),U_20219),U_20216))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20218),U_20216),hAPP(c_List_Oset(U_20218),U_20220)))
        | ~ sP1219(U_20216,U_20218,U_20219,U_20220) )
    & ! [U_20216,U_20218,U_20219,U_20220] :
        ( c_List_Olinorder__class_Osorted(U_20218,hAPP(hAPP(c_List_Olist_OCons(U_20218),U_20219),U_20220))
        | ~ c_List_Olinorder__class_Osorted(U_20218,U_20220)
        | sP1220(U_20218,U_20219,U_20220)
        | ~ sP1221(U_20216,U_20218,U_20219,U_20220) )
    & ! [U_20216,U_20218,U_20219,U_20220] :
        ( sP1219(U_20216,U_20218,U_20219,U_20220)
        | ~ c_List_Olinorder__class_Osorted(U_20218,hAPP(hAPP(c_List_Olist_OCons(U_20218),U_20219),U_20220))
        | ~ sP1221(U_20216,U_20218,U_20219,U_20220) )
    & ! [U_20216,U_20218,U_20219,U_20220] :
        ( sP1221(U_20216,U_20218,U_20219,U_20220)
        | ~ class_Orderings_Olinorder(U_20218) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1219,sP1220,sP1221])],[f_4850_3]) ).

cnf(f_4850_5,plain,
    ( sP1221(U_20216,U_20218,U_20219,U_20220)
    | ~ class_Orderings_Olinorder(U_20218) ),
    inference(clausify,[status(thm)],[f_4850_4]) ).

cnf(f_4850_6,plain,
    ( sP1219(U_20216,U_20218,U_20219,U_20220)
    | ~ c_List_Olinorder__class_Osorted(U_20218,hAPP(hAPP(c_List_Olist_OCons(U_20218),U_20219),U_20220))
    | ~ sP1221(U_20216,U_20218,U_20219,U_20220) ),
    inference(clausify,[status(thm)],[f_4850_4]) ).

cnf(f_4850_7,plain,
    ( c_List_Olinorder__class_Osorted(U_20218,hAPP(hAPP(c_List_Olist_OCons(U_20218),U_20219),U_20220))
    | ~ c_List_Olinorder__class_Osorted(U_20218,U_20220)
    | sP1220(U_20218,U_20219,U_20220)
    | ~ sP1221(U_20216,U_20218,U_20219,U_20220) ),
    inference(clausify,[status(thm)],[f_4850_4]) ).

cnf(f_4850_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20218),U_20219),U_20216))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20218),U_20216),hAPP(c_List_Oset(U_20218),U_20220)))
    | ~ sP1219(U_20216,U_20218,U_20219,U_20220) ),
    inference(clausify,[status(thm)],[f_4850_4]) ).

cnf(f_4850_9,plain,
    ( c_List_Olinorder__class_Osorted(U_20218,U_20220)
    | ~ sP1219(U_20216,U_20218,U_20219,U_20220) ),
    inference(clausify,[status(thm)],[f_4850_4]) ).

cnf(f_4850_10,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20218),sK495(U_20220,U_20219,U_20218)),hAPP(c_List_Oset(U_20218),U_20220)))
    | ~ sP1220(U_20218,U_20219,U_20220) ),
    inference(clausify,[status(thm)],[f_4850_4]) ).

cnf(f_4850_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20218),U_20219),sK495(U_20220,U_20219,U_20218)))
    | ~ sP1220(U_20218,U_20219,U_20220) ),
    inference(clausify,[status(thm)],[f_4850_4]) ).

fof(f_4851_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_4851_2,plain,
    ! [U_20222,U_20221] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_20221,U_20222) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_20221),U_20222)),
    inference(variable_rename,[status(thm)],[f_4851_1]) ).

fof(f_4851_3,plain,
    ! [U_20222,U_20221] : c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_20221,U_20222) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_20221),U_20222)),
    inference(definitional_conversion,[status(esa)],[f_4851_2]) ).

cnf(f_4851_4,plain,
    c_SetInterval_Oord__class_OgreaterThanLessThan(tc_Nat_Onat,U_20221,U_20222) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(hAPP(c_Nat_OSuc,U_20221),U_20222)),
    inference(clausify,[status(thm)],[f_4851_3]) ).

fof(f_4852_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_4852_2,plain,
    ! [U_20227,U_20226,U_20225,U_20224,U_20223] :
      ( hAPP(hAPP(c_List_Onth(U_20226),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20226),U_20227),c_List_Oupt(U_20225,U_20224))),U_20223) = hAPP(U_20227,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20225),U_20223))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20223),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20224),U_20225))) ),
    inference(variable_rename,[status(thm)],[f_4852_1]) ).

fof(f_4852_3,plain,
    ! [U_20223,U_20225,U_20227,U_20226,U_20224] :
      ( hAPP(hAPP(c_List_Onth(U_20226),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20226),U_20227),c_List_Oupt(U_20225,U_20224))),U_20223) = hAPP(U_20227,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20225),U_20223))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20223),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20224),U_20225))) ),
    inference(definitional_conversion,[status(esa)],[f_4852_2]) ).

cnf(f_4852_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_20226),hAPP(hAPP(c_List_Omap(tc_Nat_Onat,U_20226),U_20227),c_List_Oupt(U_20225,U_20224))),U_20223) = hAPP(U_20227,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20225),U_20223))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20223),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),U_20224),U_20225))) ),
    inference(clausify,[status(thm)],[f_4852_3]) ).

fof(f_4853_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_4853_2,plain,
    ! [U_20229,U_20228] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_20228),c_List_Olinorder__class_Osorted__list__of__set(U_20228,U_20229)))
        & c_List_Olinorder__class_Osorted(U_20228,c_List_Olinorder__class_Osorted__list__of__set(U_20228,U_20229))
        & hAPP(c_List_Oset(U_20228),c_List_Olinorder__class_Osorted__list__of__set(U_20228,U_20229)) = U_20229 )
      | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20228),U_20229))
      | ~ class_Orderings_Olinorder(U_20228) ),
    inference(variable_rename,[status(thm)],[f_4853_1]) ).

fof(f_4853_3,plain,
    ( ! [U_20228,U_20229] :
        ( hBOOL(hAPP(c_List_Odistinct(U_20228),c_List_Olinorder__class_Osorted__list__of__set(U_20228,U_20229)))
        | ~ sP1222(U_20228,U_20229) )
    & ! [U_20228,U_20229] :
        ( c_List_Olinorder__class_Osorted(U_20228,c_List_Olinorder__class_Osorted__list__of__set(U_20228,U_20229))
        | ~ sP1222(U_20228,U_20229) )
    & ! [U_20228,U_20229] :
        ( hAPP(c_List_Oset(U_20228),c_List_Olinorder__class_Osorted__list__of__set(U_20228,U_20229)) = U_20229
        | ~ sP1222(U_20228,U_20229) )
    & ! [U_20228,U_20229] :
        ( sP1222(U_20228,U_20229)
        | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20228),U_20229))
        | ~ class_Orderings_Olinorder(U_20228) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1222])],[f_4853_2]) ).

cnf(f_4853_4,plain,
    ( sP1222(U_20228,U_20229)
    | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(U_20228),U_20229))
    | ~ class_Orderings_Olinorder(U_20228) ),
    inference(clausify,[status(thm)],[f_4853_3]) ).

cnf(f_4853_5,plain,
    ( hAPP(c_List_Oset(U_20228),c_List_Olinorder__class_Osorted__list__of__set(U_20228,U_20229)) = U_20229
    | ~ sP1222(U_20228,U_20229) ),
    inference(clausify,[status(thm)],[f_4853_3]) ).

cnf(f_4853_6,plain,
    ( c_List_Olinorder__class_Osorted(U_20228,c_List_Olinorder__class_Osorted__list__of__set(U_20228,U_20229))
    | ~ sP1222(U_20228,U_20229) ),
    inference(clausify,[status(thm)],[f_4853_3]) ).

cnf(f_4853_7,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_20228),c_List_Olinorder__class_Osorted__list__of__set(U_20228,U_20229)))
    | ~ sP1222(U_20228,U_20229) ),
    inference(clausify,[status(thm)],[f_4853_3]) ).

fof(f_4854_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_4854_2,plain,
    ! [U_20230] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_20230) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_20230))),
    inference(variable_rename,[status(thm)],[f_4854_1]) ).

fof(f_4854_3,plain,
    ! [U_20230] : hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_20230) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_20230))),
    inference(definitional_conversion,[status(esa)],[f_4854_2]) ).

cnf(f_4854_4,plain,
    hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),U_20230) = hAPP(c_List_Oset(tc_Nat_Onat),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_OSuc,U_20230))),
    inference(clausify,[status(thm)],[f_4854_3]) ).

fof(f_4855_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_4855_2,plain,
    ! [U_20233,U_20232,U_20231] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20231,U_20231,c_COMBI(U_20231)),U_20232),c_List_Oremove1(U_20231,U_20232,U_20233)) = U_20233
      | ~ c_List_Olinorder__class_Osorted(U_20231,U_20233)
      | ~ hBOOL(hAPP(hAPP(c_member(U_20231),U_20232),hAPP(c_List_Oset(U_20231),U_20233)))
      | ~ class_Orderings_Olinorder(U_20231) ),
    inference(variable_rename,[status(thm)],[f_4855_1]) ).

fof(f_4855_3,plain,
    ! [U_20231,U_20232,U_20233] :
      ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20231,U_20231,c_COMBI(U_20231)),U_20232),c_List_Oremove1(U_20231,U_20232,U_20233)) = U_20233
      | ~ c_List_Olinorder__class_Osorted(U_20231,U_20233)
      | ~ hBOOL(hAPP(hAPP(c_member(U_20231),U_20232),hAPP(c_List_Oset(U_20231),U_20233)))
      | ~ class_Orderings_Olinorder(U_20231) ),
    inference(definitional_conversion,[status(esa)],[f_4855_2]) ).

cnf(f_4855_4,plain,
    ( hAPP(hAPP(c_List_Olinorder__class_Oinsort__key(U_20231,U_20231,c_COMBI(U_20231)),U_20232),c_List_Oremove1(U_20231,U_20232,U_20233)) = U_20233
    | ~ c_List_Olinorder__class_Osorted(U_20231,U_20233)
    | ~ hBOOL(hAPP(hAPP(c_member(U_20231),U_20232),hAPP(c_List_Oset(U_20231),U_20233)))
    | ~ class_Orderings_Olinorder(U_20231) ),
    inference(clausify,[status(thm)],[f_4855_3]) ).

fof(f_4856_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_4856_2,plain,
    ! [U_20237,U_20236,U_20235,U_20234] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20234),hAPP(hAPP(c_List_Onth(U_20234),U_20235),U_20236)),hAPP(hAPP(c_List_Onth(U_20234),U_20235),U_20237)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20237),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20234)),U_20235)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20236),U_20237))
      | ~ c_List_Olinorder__class_Osorted(U_20234,U_20235)
      | ~ class_Orderings_Olinorder(U_20234) ),
    inference(variable_rename,[status(thm)],[f_4856_1]) ).

fof(f_4856_3,plain,
    ! [U_20234,U_20235,U_20236,U_20237] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20234),hAPP(hAPP(c_List_Onth(U_20234),U_20235),U_20236)),hAPP(hAPP(c_List_Onth(U_20234),U_20235),U_20237)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20237),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20234)),U_20235)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20236),U_20237))
      | ~ c_List_Olinorder__class_Osorted(U_20234,U_20235)
      | ~ class_Orderings_Olinorder(U_20234) ),
    inference(definitional_conversion,[status(esa)],[f_4856_2]) ).

cnf(f_4856_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20234),hAPP(hAPP(c_List_Onth(U_20234),U_20235),U_20236)),hAPP(hAPP(c_List_Onth(U_20234),U_20235),U_20237)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20237),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20234)),U_20235)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20236),U_20237))
    | ~ c_List_Olinorder__class_Osorted(U_20234,U_20235)
    | ~ class_Orderings_Olinorder(U_20234) ),
    inference(clausify,[status(thm)],[f_4856_3]) ).

fof(f_4857_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_4857_2,plain,
    ! [U_20243,U_20242] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20242,U_20243)
          | ? [U_20241] :
              ( ? [U_20240] :
                  ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20242),hAPP(hAPP(c_List_Onth(U_20242),U_20243),U_20240)),hAPP(hAPP(c_List_Onth(U_20242),U_20243),U_20241)))
                  & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20240),U_20241)) )
              & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20241),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20242)),U_20243))) ) )
        & ( ! [U_20239] :
              ( ! [U_20238] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20242),hAPP(hAPP(c_List_Onth(U_20242),U_20243),U_20238)),hAPP(hAPP(c_List_Onth(U_20242),U_20243),U_20239)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20238),U_20239)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20239),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20242)),U_20243))) )
          | ~ c_List_Olinorder__class_Osorted(U_20242,U_20243) ) )
      | ~ class_Orderings_Olinorder(U_20242) ),
    inference(variable_rename,[status(thm)],[f_4857_1]) ).

fof(f_4857_3,plain,
    ! [U_20243,U_20242] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20242,U_20243)
          | ( ? [U_20240] :
                ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20242),hAPP(hAPP(c_List_Onth(U_20242),U_20243),U_20240)),hAPP(hAPP(c_List_Onth(U_20242),U_20243),sK496(U_20243,U_20242))))
                & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20240),sK496(U_20243,U_20242))) )
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK496(U_20243,U_20242)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20242)),U_20243))) ) )
        & ( ! [U_20239] :
              ( ! [U_20238] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20242),hAPP(hAPP(c_List_Onth(U_20242),U_20243),U_20238)),hAPP(hAPP(c_List_Onth(U_20242),U_20243),U_20239)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20238),U_20239)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20239),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20242)),U_20243))) )
          | ~ c_List_Olinorder__class_Osorted(U_20242,U_20243) ) )
      | ~ class_Orderings_Olinorder(U_20242) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK496]),skolemize(U_20241,sK496(U_20243,U_20242))],[f_4857_2]) ).

fof(f_4857_4,plain,
    ! [U_20243,U_20242] :
      ( ( ( c_List_Olinorder__class_Osorted(U_20242,U_20243)
          | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20242),hAPP(hAPP(c_List_Onth(U_20242),U_20243),sK497(U_20243,U_20242))),hAPP(hAPP(c_List_Onth(U_20242),U_20243),sK496(U_20243,U_20242))))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK497(U_20243,U_20242)),sK496(U_20243,U_20242)))
            & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK496(U_20243,U_20242)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20242)),U_20243))) ) )
        & ( ! [U_20239] :
              ( ! [U_20238] :
                  ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20242),hAPP(hAPP(c_List_Onth(U_20242),U_20243),U_20238)),hAPP(hAPP(c_List_Onth(U_20242),U_20243),U_20239)))
                  | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20238),U_20239)) )
              | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20239),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20242)),U_20243))) )
          | ~ c_List_Olinorder__class_Osorted(U_20242,U_20243) ) )
      | ~ class_Orderings_Olinorder(U_20242) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK497]),skolemize(U_20240,sK497(U_20243,U_20242))],[f_4857_3]) ).

fof(f_4857_5,plain,
    ( ! [U_20242,U_20243] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20242),hAPP(hAPP(c_List_Onth(U_20242),U_20243),sK497(U_20243,U_20242))),hAPP(hAPP(c_List_Onth(U_20242),U_20243),sK496(U_20243,U_20242))))
        | ~ sP1223(U_20242,U_20243) )
    & ! [U_20242,U_20243] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK497(U_20243,U_20242)),sK496(U_20243,U_20242)))
        | ~ sP1223(U_20242,U_20243) )
    & ! [U_20242,U_20243] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK496(U_20243,U_20242)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20242)),U_20243)))
        | ~ sP1223(U_20242,U_20243) )
    & ! [U_20238,U_20239,U_20242,U_20243] :
        ( c_List_Olinorder__class_Osorted(U_20242,U_20243)
        | sP1223(U_20242,U_20243)
        | ~ sP1224(U_20238,U_20239,U_20242,U_20243) )
    & ! [U_20238,U_20239,U_20242,U_20243] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20242),hAPP(hAPP(c_List_Onth(U_20242),U_20243),U_20238)),hAPP(hAPP(c_List_Onth(U_20242),U_20243),U_20239)))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20238),U_20239))
        | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20239),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20242)),U_20243)))
        | ~ c_List_Olinorder__class_Osorted(U_20242,U_20243)
        | ~ sP1224(U_20238,U_20239,U_20242,U_20243) )
    & ! [U_20238,U_20239,U_20242,U_20243] :
        ( sP1224(U_20238,U_20239,U_20242,U_20243)
        | ~ class_Orderings_Olinorder(U_20242) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1223,sP1224])],[f_4857_4]) ).

cnf(f_4857_6,plain,
    ( sP1224(U_20238,U_20239,U_20242,U_20243)
    | ~ class_Orderings_Olinorder(U_20242) ),
    inference(clausify,[status(thm)],[f_4857_5]) ).

cnf(f_4857_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20242),hAPP(hAPP(c_List_Onth(U_20242),U_20243),U_20238)),hAPP(hAPP(c_List_Onth(U_20242),U_20243),U_20239)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20238),U_20239))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20239),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20242)),U_20243)))
    | ~ c_List_Olinorder__class_Osorted(U_20242,U_20243)
    | ~ sP1224(U_20238,U_20239,U_20242,U_20243) ),
    inference(clausify,[status(thm)],[f_4857_5]) ).

cnf(f_4857_8,plain,
    ( c_List_Olinorder__class_Osorted(U_20242,U_20243)
    | sP1223(U_20242,U_20243)
    | ~ sP1224(U_20238,U_20239,U_20242,U_20243) ),
    inference(clausify,[status(thm)],[f_4857_5]) ).

cnf(f_4857_9,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK496(U_20243,U_20242)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20242)),U_20243)))
    | ~ sP1223(U_20242,U_20243) ),
    inference(clausify,[status(thm)],[f_4857_5]) ).

cnf(f_4857_10,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK497(U_20243,U_20242)),sK496(U_20243,U_20242)))
    | ~ sP1223(U_20242,U_20243) ),
    inference(clausify,[status(thm)],[f_4857_5]) ).

cnf(f_4857_11,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20242),hAPP(hAPP(c_List_Onth(U_20242),U_20243),sK497(U_20243,U_20242))),hAPP(hAPP(c_List_Onth(U_20242),U_20243),sK496(U_20243,U_20242))))
    | ~ sP1223(U_20242,U_20243) ),
    inference(clausify,[status(thm)],[f_4857_5]) ).

fof(f_4858_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_4858_2,plain,
    ! [U_20248,U_20247,U_20246,U_20245,U_20244] :
      ( U_20247 = U_20248
      | hAPP(c_List_Oset(U_20245),U_20247) != hAPP(c_List_Oset(U_20245),U_20248)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20244),hAPP(hAPP(c_List_Omap(U_20245,U_20244),U_20246),U_20248)))
      | ~ c_List_Olinorder__class_Osorted(U_20244,hAPP(hAPP(c_List_Omap(U_20245,U_20244),U_20246),U_20248))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20244),hAPP(hAPP(c_List_Omap(U_20245,U_20244),U_20246),U_20247)))
      | ~ c_List_Olinorder__class_Osorted(U_20244,hAPP(hAPP(c_List_Omap(U_20245,U_20244),U_20246),U_20247))
      | ~ c_Fun_Oinj__on(U_20245,U_20244,U_20246,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20245,tc_HOL_Obool)),hAPP(c_List_Oset(U_20245),U_20247)),hAPP(c_List_Oset(U_20245),U_20248)))
      | ~ class_Orderings_Olinorder(U_20244) ),
    inference(variable_rename,[status(thm)],[f_4858_1]) ).

fof(f_4858_3,plain,
    ! [U_20246,U_20248,U_20247,U_20244,U_20245] :
      ( U_20247 = U_20248
      | hAPP(c_List_Oset(U_20245),U_20247) != hAPP(c_List_Oset(U_20245),U_20248)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20244),hAPP(hAPP(c_List_Omap(U_20245,U_20244),U_20246),U_20248)))
      | ~ c_List_Olinorder__class_Osorted(U_20244,hAPP(hAPP(c_List_Omap(U_20245,U_20244),U_20246),U_20248))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20244),hAPP(hAPP(c_List_Omap(U_20245,U_20244),U_20246),U_20247)))
      | ~ c_List_Olinorder__class_Osorted(U_20244,hAPP(hAPP(c_List_Omap(U_20245,U_20244),U_20246),U_20247))
      | ~ c_Fun_Oinj__on(U_20245,U_20244,U_20246,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20245,tc_HOL_Obool)),hAPP(c_List_Oset(U_20245),U_20247)),hAPP(c_List_Oset(U_20245),U_20248)))
      | ~ class_Orderings_Olinorder(U_20244) ),
    inference(definitional_conversion,[status(esa)],[f_4858_2]) ).

cnf(f_4858_4,plain,
    ( U_20247 = U_20248
    | hAPP(c_List_Oset(U_20245),U_20247) != hAPP(c_List_Oset(U_20245),U_20248)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20244),hAPP(hAPP(c_List_Omap(U_20245,U_20244),U_20246),U_20248)))
    | ~ c_List_Olinorder__class_Osorted(U_20244,hAPP(hAPP(c_List_Omap(U_20245,U_20244),U_20246),U_20248))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20244),hAPP(hAPP(c_List_Omap(U_20245,U_20244),U_20246),U_20247)))
    | ~ c_List_Olinorder__class_Osorted(U_20244,hAPP(hAPP(c_List_Omap(U_20245,U_20244),U_20246),U_20247))
    | ~ c_Fun_Oinj__on(U_20245,U_20244,U_20246,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(U_20245,tc_HOL_Obool)),hAPP(c_List_Oset(U_20245),U_20247)),hAPP(c_List_Oset(U_20245),U_20248)))
    | ~ class_Orderings_Olinorder(U_20244) ),
    inference(clausify,[status(thm)],[f_4858_3]) ).

fof(f_4859_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_4859_2,plain,
    ! [U_20252,U_20251,U_20250,U_20249] : hAPP(hAPP(c_List_Omap(tc_prod(U_20249,tc_Nat_Onat),U_20249),c_Product__Type_Ofst(U_20249,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20249,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20249,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_20249,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_20249,tc_Nat_Onat))),U_20250)),hAPP(hAPP(c_List_Ozip(U_20249,tc_Nat_Onat),U_20251),c_List_Oupt(U_20252,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20252),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20249)),U_20251)))))) = hAPP(hAPP(c_List_Omap(tc_prod(U_20249,tc_Nat_Onat),U_20249),c_Product__Type_Ofst(U_20249,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20249,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20249,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_20249,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_20249,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_20249,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(U_20249,tc_Nat_Onat))),U_20252))),U_20250)),hAPP(hAPP(c_List_Ozip(U_20249,tc_Nat_Onat),U_20251),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20249)),U_20251))))),
    inference(variable_rename,[status(thm)],[f_4859_1]) ).

fof(f_4859_3,plain,
    ! [U_20249,U_20250,U_20251,U_20252] : hAPP(hAPP(c_List_Omap(tc_prod(U_20249,tc_Nat_Onat),U_20249),c_Product__Type_Ofst(U_20249,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20249,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20249,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_20249,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_20249,tc_Nat_Onat))),U_20250)),hAPP(hAPP(c_List_Ozip(U_20249,tc_Nat_Onat),U_20251),c_List_Oupt(U_20252,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20252),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20249)),U_20251)))))) = hAPP(hAPP(c_List_Omap(tc_prod(U_20249,tc_Nat_Onat),U_20249),c_Product__Type_Ofst(U_20249,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20249,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20249,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_20249,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_20249,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_20249,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(U_20249,tc_Nat_Onat))),U_20252))),U_20250)),hAPP(hAPP(c_List_Ozip(U_20249,tc_Nat_Onat),U_20251),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20249)),U_20251))))),
    inference(definitional_conversion,[status(esa)],[f_4859_2]) ).

cnf(f_4859_4,plain,
    hAPP(hAPP(c_List_Omap(tc_prod(U_20249,tc_Nat_Onat),U_20249),c_Product__Type_Ofst(U_20249,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20249,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20249,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_20249,tc_Nat_Onat)),c_member(tc_Nat_Onat)),c_Product__Type_Osnd(U_20249,tc_Nat_Onat))),U_20250)),hAPP(hAPP(c_List_Ozip(U_20249,tc_Nat_Onat),U_20251),c_List_Oupt(U_20252,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20252),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20249)),U_20251)))))) = hAPP(hAPP(c_List_Omap(tc_prod(U_20249,tc_Nat_Onat),U_20249),c_Product__Type_Ofst(U_20249,tc_Nat_Onat)),hAPP(c_List_Ofilter(tc_prod(U_20249,tc_Nat_Onat),hAPP(hAPP(c_COMBC(tc_prod(U_20249,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_20249,tc_Nat_Onat)),c_member(tc_Nat_Onat)),hAPP(hAPP(c_COMBC(tc_prod(U_20249,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_20249,tc_Nat_Onat)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Product__Type_Osnd(U_20249,tc_Nat_Onat))),U_20252))),U_20250)),hAPP(hAPP(c_List_Ozip(U_20249,tc_Nat_Onat),U_20251),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20249)),U_20251))))),
    inference(clausify,[status(thm)],[f_4859_3]) ).

fof(f_4860_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_4860_2,plain,
    ! [U_20256,U_20255,U_20254] :
      ( c_List_Otranspose(U_20255,U_20254) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_20255)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20255)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_20255),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20255)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_20255)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_20255),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20255),tc_fun(tc_Nat_Onat,U_20255),tc_Nat_Onat),c_List_Onth(U_20255)),hAPP(c_List_Onth(tc_List_Olist(U_20255)),U_20254))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20255))),U_20254)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_20256))
      | ? [U_20253] :
          ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20255)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20255)),U_20254),U_20253)) != U_20256
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20253),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20255))),U_20254))) )
      | ( U_20256 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & U_20254 = c_List_Olist_ONil(tc_List_Olist(U_20255)) ) ),
    inference(variable_rename,[status(thm)],[f_4860_1]) ).

fof(f_4860_3,plain,
    ! [U_20256,U_20255,U_20254] :
      ( c_List_Otranspose(U_20255,U_20254) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_20255)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20255)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_20255),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20255)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_20255)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_20255),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20255),tc_fun(tc_Nat_Onat,U_20255),tc_Nat_Onat),c_List_Onth(U_20255)),hAPP(c_List_Onth(tc_List_Olist(U_20255)),U_20254))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20255))),U_20254)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_20256))
      | ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20255)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20255)),U_20254),sK498(U_20256,U_20255,U_20254))) != U_20256
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK498(U_20256,U_20255,U_20254)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20255))),U_20254))) )
      | ( U_20256 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        & U_20254 = c_List_Olist_ONil(tc_List_Olist(U_20255)) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK498]),skolemize(U_20253,sK498(U_20256,U_20255,U_20254))],[f_4860_2]) ).

fof(f_4860_4,plain,
    ( ! [U_20254,U_20255,U_20256] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20255)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20255)),U_20254),sK498(U_20256,U_20255,U_20254))) != U_20256
        | ~ sP1226(U_20254,U_20255,U_20256) )
    & ! [U_20254,U_20255,U_20256] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK498(U_20256,U_20255,U_20254)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20255))),U_20254)))
        | ~ sP1226(U_20254,U_20255,U_20256) )
    & ! [U_20254,U_20255,U_20256] :
        ( U_20256 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | ~ sP1225(U_20254,U_20255,U_20256) )
    & ! [U_20254,U_20255,U_20256] :
        ( U_20254 = c_List_Olist_ONil(tc_List_Olist(U_20255))
        | ~ sP1225(U_20254,U_20255,U_20256) )
    & ! [U_20254,U_20255,U_20256] :
        ( c_List_Otranspose(U_20255,U_20254) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_20255)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20255)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_20255),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20255)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_20255)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_20255),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20255),tc_fun(tc_Nat_Onat,U_20255),tc_Nat_Onat),c_List_Onth(U_20255)),hAPP(c_List_Onth(tc_List_Olist(U_20255)),U_20254))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20255))),U_20254)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_20256))
        | sP1226(U_20254,U_20255,U_20256)
        | sP1225(U_20254,U_20255,U_20256) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1225,sP1226])],[f_4860_3]) ).

cnf(f_4860_5,plain,
    ( c_List_Otranspose(U_20255,U_20254) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_List_Olist(U_20255)),hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20255)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,U_20255),tc_fun(tc_List_Olist(tc_Nat_Onat),tc_List_Olist(U_20255)),tc_Nat_Onat),c_List_Omap(tc_Nat_Onat,U_20255)),hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,U_20255),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20255),tc_fun(tc_Nat_Onat,U_20255),tc_Nat_Onat),c_List_Onth(U_20255)),hAPP(c_List_Onth(tc_List_Olist(U_20255)),U_20254))))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20255))),U_20254)))),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),U_20256))
    | sP1226(U_20254,U_20255,U_20256)
    | sP1225(U_20254,U_20255,U_20256) ),
    inference(clausify,[status(thm)],[f_4860_4]) ).

cnf(f_4860_6,plain,
    ( U_20254 = c_List_Olist_ONil(tc_List_Olist(U_20255))
    | ~ sP1225(U_20254,U_20255,U_20256) ),
    inference(clausify,[status(thm)],[f_4860_4]) ).

cnf(f_4860_7,plain,
    ( U_20256 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | ~ sP1225(U_20254,U_20255,U_20256) ),
    inference(clausify,[status(thm)],[f_4860_4]) ).

cnf(f_4860_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK498(U_20256,U_20255,U_20254)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20255))),U_20254)))
    | ~ sP1226(U_20254,U_20255,U_20256) ),
    inference(clausify,[status(thm)],[f_4860_4]) ).

cnf(f_4860_9,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20255)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20255)),U_20254),sK498(U_20256,U_20255,U_20254))) != U_20256
    | ~ sP1226(U_20254,U_20255,U_20256) ),
    inference(clausify,[status(thm)],[f_4860_4]) ).

fof(f_4861_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_4861_2,plain,
    ! [U_20258,U_20257] :
      ( c_List_Otranspose(U_20257,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20257)),c_List_Olist_ONil(U_20257)),U_20258)) = c_List_Otranspose(U_20257,U_20258)
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20257)),c_List_Otranspose__rel(U_20257)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20257)),c_List_Olist_ONil(U_20257)),U_20258))) ),
    inference(variable_rename,[status(thm)],[f_4861_1]) ).

fof(f_4861_3,plain,
    ! [U_20257,U_20258] :
      ( c_List_Otranspose(U_20257,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20257)),c_List_Olist_ONil(U_20257)),U_20258)) = c_List_Otranspose(U_20257,U_20258)
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20257)),c_List_Otranspose__rel(U_20257)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20257)),c_List_Olist_ONil(U_20257)),U_20258))) ),
    inference(definitional_conversion,[status(esa)],[f_4861_2]) ).

cnf(f_4861_4,plain,
    ( c_List_Otranspose(U_20257,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20257)),c_List_Olist_ONil(U_20257)),U_20258)) = c_List_Otranspose(U_20257,U_20258)
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20257)),c_List_Otranspose__rel(U_20257)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20257)),c_List_Olist_ONil(U_20257)),U_20258))) ),
    inference(clausify,[status(thm)],[f_4861_3]) ).

fof(f_4862_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_4862_2,plain,
    ! [U_20259] :
      ( c_List_Otranspose(U_20259,c_List_Olist_ONil(tc_List_Olist(U_20259))) = c_List_Olist_ONil(tc_List_Olist(U_20259))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20259)),c_List_Otranspose__rel(U_20259)),c_List_Olist_ONil(tc_List_Olist(U_20259)))) ),
    inference(variable_rename,[status(thm)],[f_4862_1]) ).

fof(f_4862_3,plain,
    ! [U_20259] :
      ( c_List_Otranspose(U_20259,c_List_Olist_ONil(tc_List_Olist(U_20259))) = c_List_Olist_ONil(tc_List_Olist(U_20259))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20259)),c_List_Otranspose__rel(U_20259)),c_List_Olist_ONil(tc_List_Olist(U_20259)))) ),
    inference(definitional_conversion,[status(esa)],[f_4862_2]) ).

cnf(f_4862_4,plain,
    ( c_List_Otranspose(U_20259,c_List_Olist_ONil(tc_List_Olist(U_20259))) = c_List_Olist_ONil(tc_List_Olist(U_20259))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20259)),c_List_Otranspose__rel(U_20259)),c_List_Olist_ONil(tc_List_Olist(U_20259)))) ),
    inference(clausify,[status(thm)],[f_4862_3]) ).

fof(f_4863_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_4863_2,plain,
    ! [U_20262,U_20261,U_20260] :
      ( hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20260),U_20260),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20260),tc_Nat_Onat,U_20260),c_List_Onth(U_20260)),U_20262)),hAPP(c_List_Ofilter(tc_List_Olist(U_20260),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20260)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20262)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20260)))),c_List_Otranspose(U_20260,U_20261))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20260)),U_20261),U_20262)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20262),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20260))),U_20261)))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20260),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20260))),U_20261))) ),
    inference(variable_rename,[status(thm)],[f_4863_1]) ).

fof(f_4863_3,plain,
    ! [U_20260,U_20261,U_20262] :
      ( hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20260),U_20260),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20260),tc_Nat_Onat,U_20260),c_List_Onth(U_20260)),U_20262)),hAPP(c_List_Ofilter(tc_List_Olist(U_20260),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20260)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20262)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20260)))),c_List_Otranspose(U_20260,U_20261))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20260)),U_20261),U_20262)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20262),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20260))),U_20261)))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20260),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20260))),U_20261))) ),
    inference(definitional_conversion,[status(esa)],[f_4863_2]) ).

cnf(f_4863_4,plain,
    ( hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20260),U_20260),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20260),tc_Nat_Onat,U_20260),c_List_Onth(U_20260)),U_20262)),hAPP(c_List_Ofilter(tc_List_Olist(U_20260),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20260)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20262)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20260)))),c_List_Otranspose(U_20260,U_20261))) = hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20260)),U_20261),U_20262)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20262),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20260))),U_20261)))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20260),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20260))),U_20261))) ),
    inference(clausify,[status(thm)],[f_4863_3]) ).

fof(f_4864_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_4864_2,plain,
    ! [U_20264,U_20263] : c_List_Oconcat(U_20263,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20263),tc_List_Olist(U_20263)),c_List_Olist_Olist__case(tc_List_Olist(U_20263),U_20263,c_List_Olist_ONil(U_20263),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20263),tc_fun(tc_List_Olist(U_20263),tc_List_Olist(U_20263)),U_20263),c_COMBK(tc_List_Olist(U_20263),tc_List_Olist(U_20263))),hAPP(hAPP(c_COMBC(U_20263,tc_List_Olist(U_20263),tc_List_Olist(U_20263)),c_List_Olist_OCons(U_20263)),c_List_Olist_ONil(U_20263))))),U_20264)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20263),U_20263),c_List_Ohd(U_20263)),hAPP(c_List_Ofilter(tc_List_Olist(U_20263),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20263)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20263),tc_List_Olist(U_20263),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20263)))),U_20264)),
    inference(variable_rename,[status(thm)],[f_4864_1]) ).

fof(f_4864_3,plain,
    ! [U_20263,U_20264] : c_List_Oconcat(U_20263,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20263),tc_List_Olist(U_20263)),c_List_Olist_Olist__case(tc_List_Olist(U_20263),U_20263,c_List_Olist_ONil(U_20263),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20263),tc_fun(tc_List_Olist(U_20263),tc_List_Olist(U_20263)),U_20263),c_COMBK(tc_List_Olist(U_20263),tc_List_Olist(U_20263))),hAPP(hAPP(c_COMBC(U_20263,tc_List_Olist(U_20263),tc_List_Olist(U_20263)),c_List_Olist_OCons(U_20263)),c_List_Olist_ONil(U_20263))))),U_20264)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20263),U_20263),c_List_Ohd(U_20263)),hAPP(c_List_Ofilter(tc_List_Olist(U_20263),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20263)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20263),tc_List_Olist(U_20263),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20263)))),U_20264)),
    inference(definitional_conversion,[status(esa)],[f_4864_2]) ).

cnf(f_4864_4,plain,
    c_List_Oconcat(U_20263,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20263),tc_List_Olist(U_20263)),c_List_Olist_Olist__case(tc_List_Olist(U_20263),U_20263,c_List_Olist_ONil(U_20263),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20263),tc_fun(tc_List_Olist(U_20263),tc_List_Olist(U_20263)),U_20263),c_COMBK(tc_List_Olist(U_20263),tc_List_Olist(U_20263))),hAPP(hAPP(c_COMBC(U_20263,tc_List_Olist(U_20263),tc_List_Olist(U_20263)),c_List_Olist_OCons(U_20263)),c_List_Olist_ONil(U_20263))))),U_20264)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20263),U_20263),c_List_Ohd(U_20263)),hAPP(c_List_Ofilter(tc_List_Olist(U_20263),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20263)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20263),tc_List_Olist(U_20263),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20263)))),U_20264)),
    inference(clausify,[status(thm)],[f_4864_3]) ).

fof(f_4865_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_4865_2,plain,
    ! [U_20266,U_20265] : c_Fun_Oinj__on(tc_List_Olist(U_20265),tc_List_Olist(U_20265),c_List_Orev(U_20265),U_20266),
    inference(variable_rename,[status(thm)],[f_4865_1]) ).

fof(f_4865_3,plain,
    ! [U_20265,U_20266] : c_Fun_Oinj__on(tc_List_Olist(U_20265),tc_List_Olist(U_20265),c_List_Orev(U_20265),U_20266),
    inference(definitional_conversion,[status(esa)],[f_4865_2]) ).

cnf(f_4865_4,plain,
    c_Fun_Oinj__on(tc_List_Olist(U_20265),tc_List_Olist(U_20265),c_List_Orev(U_20265),U_20266),
    inference(clausify,[status(thm)],[f_4865_3]) ).

fof(f_4866_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_4866_2,plain,
    ! [U_20269,U_20268,U_20267] : hAPP(c_List_Ofilter(U_20267,U_20268),c_List_Oconcat(U_20267,U_20269)) = c_List_Oconcat(U_20267,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20267),tc_List_Olist(U_20267)),c_List_Ofilter(U_20267,U_20268)),U_20269)),
    inference(variable_rename,[status(thm)],[f_4866_1]) ).

fof(f_4866_3,plain,
    ! [U_20267,U_20268,U_20269] : hAPP(c_List_Ofilter(U_20267,U_20268),c_List_Oconcat(U_20267,U_20269)) = c_List_Oconcat(U_20267,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20267),tc_List_Olist(U_20267)),c_List_Ofilter(U_20267,U_20268)),U_20269)),
    inference(definitional_conversion,[status(esa)],[f_4866_2]) ).

cnf(f_4866_4,plain,
    hAPP(c_List_Ofilter(U_20267,U_20268),c_List_Oconcat(U_20267,U_20269)) = c_List_Oconcat(U_20267,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20267),tc_List_Olist(U_20267)),c_List_Ofilter(U_20267,U_20268)),U_20269)),
    inference(clausify,[status(thm)],[f_4866_3]) ).

fof(f_4867_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_4867_2,plain,
    ! [U_20271,U_20270] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20270)),c_List_Oconcat(U_20270,U_20271)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20270),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20270))),U_20271)),
    inference(variable_rename,[status(thm)],[f_4867_1]) ).

fof(f_4867_3,plain,
    ! [U_20270,U_20271] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20270)),c_List_Oconcat(U_20270,U_20271)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20270),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20270))),U_20271)),
    inference(definitional_conversion,[status(esa)],[f_4867_2]) ).

cnf(f_4867_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20270)),c_List_Oconcat(U_20270,U_20271)) = hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20270),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20270))),U_20271)),
    inference(clausify,[status(thm)],[f_4867_3]) ).

fof(f_4868_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_4868_2,plain,
    ! [U_20272] : hAPP(c_List_Orev(U_20272),c_List_Olist_ONil(U_20272)) = c_List_Olist_ONil(U_20272),
    inference(variable_rename,[status(thm)],[f_4868_1]) ).

fof(f_4868_3,plain,
    ! [U_20272] : hAPP(c_List_Orev(U_20272),c_List_Olist_ONil(U_20272)) = c_List_Olist_ONil(U_20272),
    inference(definitional_conversion,[status(esa)],[f_4868_2]) ).

cnf(f_4868_4,plain,
    hAPP(c_List_Orev(U_20272),c_List_Olist_ONil(U_20272)) = c_List_Olist_ONil(U_20272),
    inference(clausify,[status(thm)],[f_4868_3]) ).

fof(f_4869_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_4869_2,plain,
    ! [U_20273] : c_List_Oconcat(U_20273,c_List_Olist_ONil(tc_List_Olist(U_20273))) = c_List_Olist_ONil(U_20273),
    inference(variable_rename,[status(thm)],[f_4869_1]) ).

fof(f_4869_3,plain,
    ! [U_20273] : c_List_Oconcat(U_20273,c_List_Olist_ONil(tc_List_Olist(U_20273))) = c_List_Olist_ONil(U_20273),
    inference(definitional_conversion,[status(esa)],[f_4869_2]) ).

cnf(f_4869_4,plain,
    c_List_Oconcat(U_20273,c_List_Olist_ONil(tc_List_Olist(U_20273))) = c_List_Olist_ONil(U_20273),
    inference(clausify,[status(thm)],[f_4869_3]) ).

fof(f_4870_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_4870_2,plain,
    ! [U_20275,U_20274] :
      ( ( c_List_Olist_ONil(U_20274) = hAPP(c_List_Orev(U_20274),U_20275)
        | U_20275 != c_List_Olist_ONil(U_20274) )
      & ( U_20275 = c_List_Olist_ONil(U_20274)
        | c_List_Olist_ONil(U_20274) != hAPP(c_List_Orev(U_20274),U_20275) ) ),
    inference(variable_rename,[status(thm)],[f_4870_1]) ).

fof(f_4870_3,plain,
    ( ! [U_20279,U_20277] :
        ( c_List_Olist_ONil(U_20277) = hAPP(c_List_Orev(U_20277),U_20279)
        | U_20279 != c_List_Olist_ONil(U_20277) )
    & ! [U_20278,U_20276] :
        ( U_20278 = c_List_Olist_ONil(U_20276)
        | c_List_Olist_ONil(U_20276) != hAPP(c_List_Orev(U_20276),U_20278) ) ),
    inference(miniscope,[status(thm)],[f_4870_2]) ).

fof(f_4870_4,plain,
    ( ! [U_20279,U_20277] :
        ( c_List_Olist_ONil(U_20277) = hAPP(c_List_Orev(U_20277),U_20279)
        | U_20279 != c_List_Olist_ONil(U_20277) )
    & ! [U_20278,U_20276] :
        ( U_20278 = c_List_Olist_ONil(U_20276)
        | c_List_Olist_ONil(U_20276) != hAPP(c_List_Orev(U_20276),U_20278) ) ),
    inference(definitional_conversion,[status(esa)],[f_4870_3]) ).

cnf(f_4870_5,plain,
    ( U_20278 = c_List_Olist_ONil(U_20276)
    | c_List_Olist_ONil(U_20276) != hAPP(c_List_Orev(U_20276),U_20278) ),
    inference(clausify,[status(thm)],[f_4870_4]) ).

cnf(f_4870_6,plain,
    ( c_List_Olist_ONil(U_20277) = hAPP(c_List_Orev(U_20277),U_20279)
    | U_20279 != c_List_Olist_ONil(U_20277) ),
    inference(clausify,[status(thm)],[f_4870_4]) ).

fof(f_4871_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_4871_2,plain,
    ! [U_20281,U_20280] :
      ( ( hAPP(c_List_Orev(U_20280),U_20281) = c_List_Olist_ONil(U_20280)
        | U_20281 != c_List_Olist_ONil(U_20280) )
      & ( U_20281 = c_List_Olist_ONil(U_20280)
        | hAPP(c_List_Orev(U_20280),U_20281) != c_List_Olist_ONil(U_20280) ) ),
    inference(variable_rename,[status(thm)],[f_4871_1]) ).

fof(f_4871_3,plain,
    ( ! [U_20285,U_20283] :
        ( hAPP(c_List_Orev(U_20283),U_20285) = c_List_Olist_ONil(U_20283)
        | U_20285 != c_List_Olist_ONil(U_20283) )
    & ! [U_20284,U_20282] :
        ( U_20284 = c_List_Olist_ONil(U_20282)
        | hAPP(c_List_Orev(U_20282),U_20284) != c_List_Olist_ONil(U_20282) ) ),
    inference(miniscope,[status(thm)],[f_4871_2]) ).

fof(f_4871_4,plain,
    ( ! [U_20283,U_20285] :
        ( hAPP(c_List_Orev(U_20283),U_20285) = c_List_Olist_ONil(U_20283)
        | U_20285 != c_List_Olist_ONil(U_20283) )
    & ! [U_20284,U_20282] :
        ( U_20284 = c_List_Olist_ONil(U_20282)
        | hAPP(c_List_Orev(U_20282),U_20284) != c_List_Olist_ONil(U_20282) ) ),
    inference(definitional_conversion,[status(esa)],[f_4871_3]) ).

cnf(f_4871_5,plain,
    ( U_20284 = c_List_Olist_ONil(U_20282)
    | hAPP(c_List_Orev(U_20282),U_20284) != c_List_Olist_ONil(U_20282) ),
    inference(clausify,[status(thm)],[f_4871_4]) ).

cnf(f_4871_6,plain,
    ( hAPP(c_List_Orev(U_20283),U_20285) = c_List_Olist_ONil(U_20283)
    | U_20285 != c_List_Olist_ONil(U_20283) ),
    inference(clausify,[status(thm)],[f_4871_4]) ).

fof(f_4872_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_4872_2,plain,
    ! [U_20289,U_20288] :
      ( ( c_List_Olist_ONil(U_20288) = c_List_Oconcat(U_20288,U_20289)
        | ? [U_20287] :
            ( U_20287 != c_List_Olist_ONil(U_20288)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20288)),U_20287),hAPP(c_List_Oset(tc_List_Olist(U_20288)),U_20289))) ) )
      & ( ! [U_20286] :
            ( U_20286 = c_List_Olist_ONil(U_20288)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20288)),U_20286),hAPP(c_List_Oset(tc_List_Olist(U_20288)),U_20289))) )
        | c_List_Olist_ONil(U_20288) != c_List_Oconcat(U_20288,U_20289) ) ),
    inference(variable_rename,[status(thm)],[f_4872_1]) ).

fof(f_4872_3,plain,
    ( ! [U_20293,U_20291] :
        ( c_List_Olist_ONil(U_20291) = c_List_Oconcat(U_20291,U_20293)
        | ? [U_20287] :
            ( U_20287 != c_List_Olist_ONil(U_20291)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20291)),U_20287),hAPP(c_List_Oset(tc_List_Olist(U_20291)),U_20293))) ) )
    & ! [U_20292,U_20290] :
        ( ! [U_20286] :
            ( U_20286 = c_List_Olist_ONil(U_20290)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20290)),U_20286),hAPP(c_List_Oset(tc_List_Olist(U_20290)),U_20292))) )
        | c_List_Olist_ONil(U_20290) != c_List_Oconcat(U_20290,U_20292) ) ),
    inference(miniscope,[status(thm)],[f_4872_2]) ).

fof(f_4872_4,plain,
    ( ! [U_20293,U_20291] :
        ( c_List_Olist_ONil(U_20291) = c_List_Oconcat(U_20291,U_20293)
        | ( sK499(U_20293,U_20291) != c_List_Olist_ONil(U_20291)
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20291)),sK499(U_20293,U_20291)),hAPP(c_List_Oset(tc_List_Olist(U_20291)),U_20293))) ) )
    & ! [U_20292,U_20290] :
        ( ! [U_20286] :
            ( U_20286 = c_List_Olist_ONil(U_20290)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20290)),U_20286),hAPP(c_List_Oset(tc_List_Olist(U_20290)),U_20292))) )
        | c_List_Olist_ONil(U_20290) != c_List_Oconcat(U_20290,U_20292) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK499]),skolemize(U_20287,sK499(U_20293,U_20291))],[f_4872_3]) ).

fof(f_4872_5,plain,
    ( ! [U_20293,U_20291] :
        ( sK499(U_20293,U_20291) != c_List_Olist_ONil(U_20291)
        | ~ sP1227(U_20293,U_20291) )
    & ! [U_20293,U_20291] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20291)),sK499(U_20293,U_20291)),hAPP(c_List_Oset(tc_List_Olist(U_20291)),U_20293)))
        | ~ sP1227(U_20293,U_20291) )
    & ! [U_20293,U_20291] :
        ( c_List_Olist_ONil(U_20291) = c_List_Oconcat(U_20291,U_20293)
        | sP1227(U_20293,U_20291) )
    & ! [U_20286,U_20290,U_20292] :
        ( U_20286 = c_List_Olist_ONil(U_20290)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20290)),U_20286),hAPP(c_List_Oset(tc_List_Olist(U_20290)),U_20292)))
        | c_List_Olist_ONil(U_20290) != c_List_Oconcat(U_20290,U_20292) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1227])],[f_4872_4]) ).

cnf(f_4872_6,plain,
    ( U_20286 = c_List_Olist_ONil(U_20290)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20290)),U_20286),hAPP(c_List_Oset(tc_List_Olist(U_20290)),U_20292)))
    | c_List_Olist_ONil(U_20290) != c_List_Oconcat(U_20290,U_20292) ),
    inference(clausify,[status(thm)],[f_4872_5]) ).

cnf(f_4872_7,plain,
    ( c_List_Olist_ONil(U_20291) = c_List_Oconcat(U_20291,U_20293)
    | sP1227(U_20293,U_20291) ),
    inference(clausify,[status(thm)],[f_4872_5]) ).

cnf(f_4872_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20291)),sK499(U_20293,U_20291)),hAPP(c_List_Oset(tc_List_Olist(U_20291)),U_20293)))
    | ~ sP1227(U_20293,U_20291) ),
    inference(clausify,[status(thm)],[f_4872_5]) ).

cnf(f_4872_9,plain,
    ( sK499(U_20293,U_20291) != c_List_Olist_ONil(U_20291)
    | ~ sP1227(U_20293,U_20291) ),
    inference(clausify,[status(thm)],[f_4872_5]) ).

fof(f_4873_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_4873_2,plain,
    ! [U_20297,U_20296] :
      ( ( c_List_Oconcat(U_20296,U_20297) = c_List_Olist_ONil(U_20296)
        | ? [U_20295] :
            ( U_20295 != c_List_Olist_ONil(U_20296)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20296)),U_20295),hAPP(c_List_Oset(tc_List_Olist(U_20296)),U_20297))) ) )
      & ( ! [U_20294] :
            ( U_20294 = c_List_Olist_ONil(U_20296)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20296)),U_20294),hAPP(c_List_Oset(tc_List_Olist(U_20296)),U_20297))) )
        | c_List_Oconcat(U_20296,U_20297) != c_List_Olist_ONil(U_20296) ) ),
    inference(variable_rename,[status(thm)],[f_4873_1]) ).

fof(f_4873_3,plain,
    ( ! [U_20301,U_20299] :
        ( c_List_Oconcat(U_20299,U_20301) = c_List_Olist_ONil(U_20299)
        | ? [U_20295] :
            ( U_20295 != c_List_Olist_ONil(U_20299)
            & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20299)),U_20295),hAPP(c_List_Oset(tc_List_Olist(U_20299)),U_20301))) ) )
    & ! [U_20300,U_20298] :
        ( ! [U_20294] :
            ( U_20294 = c_List_Olist_ONil(U_20298)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20298)),U_20294),hAPP(c_List_Oset(tc_List_Olist(U_20298)),U_20300))) )
        | c_List_Oconcat(U_20298,U_20300) != c_List_Olist_ONil(U_20298) ) ),
    inference(miniscope,[status(thm)],[f_4873_2]) ).

fof(f_4873_4,plain,
    ( ! [U_20301,U_20299] :
        ( c_List_Oconcat(U_20299,U_20301) = c_List_Olist_ONil(U_20299)
        | ( sK500(U_20301,U_20299) != c_List_Olist_ONil(U_20299)
          & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20299)),sK500(U_20301,U_20299)),hAPP(c_List_Oset(tc_List_Olist(U_20299)),U_20301))) ) )
    & ! [U_20300,U_20298] :
        ( ! [U_20294] :
            ( U_20294 = c_List_Olist_ONil(U_20298)
            | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20298)),U_20294),hAPP(c_List_Oset(tc_List_Olist(U_20298)),U_20300))) )
        | c_List_Oconcat(U_20298,U_20300) != c_List_Olist_ONil(U_20298) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK500]),skolemize(U_20295,sK500(U_20301,U_20299))],[f_4873_3]) ).

fof(f_4873_5,plain,
    ( ! [U_20299,U_20301] :
        ( sK500(U_20301,U_20299) != c_List_Olist_ONil(U_20299)
        | ~ sP1228(U_20299,U_20301) )
    & ! [U_20299,U_20301] :
        ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20299)),sK500(U_20301,U_20299)),hAPP(c_List_Oset(tc_List_Olist(U_20299)),U_20301)))
        | ~ sP1228(U_20299,U_20301) )
    & ! [U_20299,U_20301] :
        ( c_List_Oconcat(U_20299,U_20301) = c_List_Olist_ONil(U_20299)
        | sP1228(U_20299,U_20301) )
    & ! [U_20294,U_20298,U_20300] :
        ( U_20294 = c_List_Olist_ONil(U_20298)
        | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20298)),U_20294),hAPP(c_List_Oset(tc_List_Olist(U_20298)),U_20300)))
        | c_List_Oconcat(U_20298,U_20300) != c_List_Olist_ONil(U_20298) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1228])],[f_4873_4]) ).

cnf(f_4873_6,plain,
    ( U_20294 = c_List_Olist_ONil(U_20298)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20298)),U_20294),hAPP(c_List_Oset(tc_List_Olist(U_20298)),U_20300)))
    | c_List_Oconcat(U_20298,U_20300) != c_List_Olist_ONil(U_20298) ),
    inference(clausify,[status(thm)],[f_4873_5]) ).

cnf(f_4873_7,plain,
    ( c_List_Oconcat(U_20299,U_20301) = c_List_Olist_ONil(U_20299)
    | sP1228(U_20299,U_20301) ),
    inference(clausify,[status(thm)],[f_4873_5]) ).

cnf(f_4873_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20299)),sK500(U_20301,U_20299)),hAPP(c_List_Oset(tc_List_Olist(U_20299)),U_20301)))
    | ~ sP1228(U_20299,U_20301) ),
    inference(clausify,[status(thm)],[f_4873_5]) ).

cnf(f_4873_9,plain,
    ( sK500(U_20301,U_20299) != c_List_Olist_ONil(U_20299)
    | ~ sP1228(U_20299,U_20301) ),
    inference(clausify,[status(thm)],[f_4873_5]) ).

fof(f_4874_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_4874_2,plain,
    ! [U_20304,U_20303,U_20302] :
      ( ( hAPP(c_List_Orev(U_20302),U_20303) = hAPP(hAPP(c_List_Olist_OCons(U_20302),U_20304),c_List_Olist_ONil(U_20302))
        | U_20303 != hAPP(hAPP(c_List_Olist_OCons(U_20302),U_20304),c_List_Olist_ONil(U_20302)) )
      & ( U_20303 = hAPP(hAPP(c_List_Olist_OCons(U_20302),U_20304),c_List_Olist_ONil(U_20302))
        | hAPP(c_List_Orev(U_20302),U_20303) != hAPP(hAPP(c_List_Olist_OCons(U_20302),U_20304),c_List_Olist_ONil(U_20302)) ) ),
    inference(variable_rename,[status(thm)],[f_4874_1]) ).

fof(f_4874_3,plain,
    ( ! [U_20310,U_20308,U_20306] :
        ( hAPP(c_List_Orev(U_20306),U_20308) = hAPP(hAPP(c_List_Olist_OCons(U_20306),U_20310),c_List_Olist_ONil(U_20306))
        | U_20308 != hAPP(hAPP(c_List_Olist_OCons(U_20306),U_20310),c_List_Olist_ONil(U_20306)) )
    & ! [U_20309,U_20307,U_20305] :
        ( U_20307 = hAPP(hAPP(c_List_Olist_OCons(U_20305),U_20309),c_List_Olist_ONil(U_20305))
        | hAPP(c_List_Orev(U_20305),U_20307) != hAPP(hAPP(c_List_Olist_OCons(U_20305),U_20309),c_List_Olist_ONil(U_20305)) ) ),
    inference(miniscope,[status(thm)],[f_4874_2]) ).

fof(f_4874_4,plain,
    ( ! [U_20308,U_20306,U_20310] :
        ( hAPP(c_List_Orev(U_20306),U_20308) = hAPP(hAPP(c_List_Olist_OCons(U_20306),U_20310),c_List_Olist_ONil(U_20306))
        | U_20308 != hAPP(hAPP(c_List_Olist_OCons(U_20306),U_20310),c_List_Olist_ONil(U_20306)) )
    & ! [U_20307,U_20309,U_20305] :
        ( U_20307 = hAPP(hAPP(c_List_Olist_OCons(U_20305),U_20309),c_List_Olist_ONil(U_20305))
        | hAPP(c_List_Orev(U_20305),U_20307) != hAPP(hAPP(c_List_Olist_OCons(U_20305),U_20309),c_List_Olist_ONil(U_20305)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4874_3]) ).

cnf(f_4874_5,plain,
    ( U_20307 = hAPP(hAPP(c_List_Olist_OCons(U_20305),U_20309),c_List_Olist_ONil(U_20305))
    | hAPP(c_List_Orev(U_20305),U_20307) != hAPP(hAPP(c_List_Olist_OCons(U_20305),U_20309),c_List_Olist_ONil(U_20305)) ),
    inference(clausify,[status(thm)],[f_4874_4]) ).

cnf(f_4874_6,plain,
    ( hAPP(c_List_Orev(U_20306),U_20308) = hAPP(hAPP(c_List_Olist_OCons(U_20306),U_20310),c_List_Olist_ONil(U_20306))
    | U_20308 != hAPP(hAPP(c_List_Olist_OCons(U_20306),U_20310),c_List_Olist_ONil(U_20306)) ),
    inference(clausify,[status(thm)],[f_4874_4]) ).

fof(f_4875_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_4875_2,plain,
    ! [U_20313,U_20312,U_20311] :
      ( ( hAPP(hAPP(c_List_Olist_OCons(U_20311),U_20312),c_List_Olist_ONil(U_20311)) = hAPP(c_List_Orev(U_20311),U_20313)
        | U_20313 != hAPP(hAPP(c_List_Olist_OCons(U_20311),U_20312),c_List_Olist_ONil(U_20311)) )
      & ( U_20313 = hAPP(hAPP(c_List_Olist_OCons(U_20311),U_20312),c_List_Olist_ONil(U_20311))
        | hAPP(hAPP(c_List_Olist_OCons(U_20311),U_20312),c_List_Olist_ONil(U_20311)) != hAPP(c_List_Orev(U_20311),U_20313) ) ),
    inference(variable_rename,[status(thm)],[f_4875_1]) ).

fof(f_4875_3,plain,
    ( ! [U_20319,U_20317,U_20315] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_20315),U_20317),c_List_Olist_ONil(U_20315)) = hAPP(c_List_Orev(U_20315),U_20319)
        | U_20319 != hAPP(hAPP(c_List_Olist_OCons(U_20315),U_20317),c_List_Olist_ONil(U_20315)) )
    & ! [U_20318,U_20316,U_20314] :
        ( U_20318 = hAPP(hAPP(c_List_Olist_OCons(U_20314),U_20316),c_List_Olist_ONil(U_20314))
        | hAPP(hAPP(c_List_Olist_OCons(U_20314),U_20316),c_List_Olist_ONil(U_20314)) != hAPP(c_List_Orev(U_20314),U_20318) ) ),
    inference(miniscope,[status(thm)],[f_4875_2]) ).

fof(f_4875_4,plain,
    ( ! [U_20315,U_20317,U_20319] :
        ( hAPP(hAPP(c_List_Olist_OCons(U_20315),U_20317),c_List_Olist_ONil(U_20315)) = hAPP(c_List_Orev(U_20315),U_20319)
        | U_20319 != hAPP(hAPP(c_List_Olist_OCons(U_20315),U_20317),c_List_Olist_ONil(U_20315)) )
    & ! [U_20316,U_20318,U_20314] :
        ( U_20318 = hAPP(hAPP(c_List_Olist_OCons(U_20314),U_20316),c_List_Olist_ONil(U_20314))
        | hAPP(hAPP(c_List_Olist_OCons(U_20314),U_20316),c_List_Olist_ONil(U_20314)) != hAPP(c_List_Orev(U_20314),U_20318) ) ),
    inference(definitional_conversion,[status(esa)],[f_4875_3]) ).

cnf(f_4875_5,plain,
    ( U_20318 = hAPP(hAPP(c_List_Olist_OCons(U_20314),U_20316),c_List_Olist_ONil(U_20314))
    | hAPP(hAPP(c_List_Olist_OCons(U_20314),U_20316),c_List_Olist_ONil(U_20314)) != hAPP(c_List_Orev(U_20314),U_20318) ),
    inference(clausify,[status(thm)],[f_4875_4]) ).

cnf(f_4875_6,plain,
    ( hAPP(hAPP(c_List_Olist_OCons(U_20315),U_20317),c_List_Olist_ONil(U_20315)) = hAPP(c_List_Orev(U_20315),U_20319)
    | U_20319 != hAPP(hAPP(c_List_Olist_OCons(U_20315),U_20317),c_List_Olist_ONil(U_20315)) ),
    inference(clausify,[status(thm)],[f_4875_4]) ).

fof(f_4876_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_4876_2,plain,
    ! [U_20322,U_20321,U_20320] : c_List_Oconcat(U_20320,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20320)),U_20321),U_20322)) = hAPP(hAPP(c_List_Oappend(U_20320),U_20321),c_List_Oconcat(U_20320,U_20322)),
    inference(variable_rename,[status(thm)],[f_4876_1]) ).

fof(f_4876_3,plain,
    ! [U_20320,U_20321,U_20322] : c_List_Oconcat(U_20320,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20320)),U_20321),U_20322)) = hAPP(hAPP(c_List_Oappend(U_20320),U_20321),c_List_Oconcat(U_20320,U_20322)),
    inference(definitional_conversion,[status(esa)],[f_4876_2]) ).

cnf(f_4876_4,plain,
    c_List_Oconcat(U_20320,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20320)),U_20321),U_20322)) = hAPP(hAPP(c_List_Oappend(U_20320),U_20321),c_List_Oconcat(U_20320,U_20322)),
    inference(clausify,[status(thm)],[f_4876_3]) ).

fof(f_4877_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_4877_2,plain,
    ! [U_20326,U_20325,U_20324,U_20323] :
      ( ( hAPP(c_List_Orev(U_20323),U_20324) = hAPP(hAPP(c_List_Olist_OCons(U_20323),U_20325),U_20326)
        | U_20324 != hAPP(hAPP(c_List_Oappend(U_20323),hAPP(c_List_Orev(U_20323),U_20326)),hAPP(hAPP(c_List_Olist_OCons(U_20323),U_20325),c_List_Olist_ONil(U_20323))) )
      & ( U_20324 = hAPP(hAPP(c_List_Oappend(U_20323),hAPP(c_List_Orev(U_20323),U_20326)),hAPP(hAPP(c_List_Olist_OCons(U_20323),U_20325),c_List_Olist_ONil(U_20323)))
        | hAPP(c_List_Orev(U_20323),U_20324) != hAPP(hAPP(c_List_Olist_OCons(U_20323),U_20325),U_20326) ) ),
    inference(variable_rename,[status(thm)],[f_4877_1]) ).

fof(f_4877_3,plain,
    ( ! [U_20334,U_20332,U_20330,U_20328] :
        ( hAPP(c_List_Orev(U_20328),U_20330) = hAPP(hAPP(c_List_Olist_OCons(U_20328),U_20332),U_20334)
        | U_20330 != hAPP(hAPP(c_List_Oappend(U_20328),hAPP(c_List_Orev(U_20328),U_20334)),hAPP(hAPP(c_List_Olist_OCons(U_20328),U_20332),c_List_Olist_ONil(U_20328))) )
    & ! [U_20333,U_20331,U_20329,U_20327] :
        ( U_20329 = hAPP(hAPP(c_List_Oappend(U_20327),hAPP(c_List_Orev(U_20327),U_20333)),hAPP(hAPP(c_List_Olist_OCons(U_20327),U_20331),c_List_Olist_ONil(U_20327)))
        | hAPP(c_List_Orev(U_20327),U_20329) != hAPP(hAPP(c_List_Olist_OCons(U_20327),U_20331),U_20333) ) ),
    inference(miniscope,[status(thm)],[f_4877_2]) ).

fof(f_4877_4,plain,
    ( ! [U_20330,U_20328,U_20332,U_20334] :
        ( hAPP(c_List_Orev(U_20328),U_20330) = hAPP(hAPP(c_List_Olist_OCons(U_20328),U_20332),U_20334)
        | U_20330 != hAPP(hAPP(c_List_Oappend(U_20328),hAPP(c_List_Orev(U_20328),U_20334)),hAPP(hAPP(c_List_Olist_OCons(U_20328),U_20332),c_List_Olist_ONil(U_20328))) )
    & ! [U_20331,U_20333,U_20329,U_20327] :
        ( U_20329 = hAPP(hAPP(c_List_Oappend(U_20327),hAPP(c_List_Orev(U_20327),U_20333)),hAPP(hAPP(c_List_Olist_OCons(U_20327),U_20331),c_List_Olist_ONil(U_20327)))
        | hAPP(c_List_Orev(U_20327),U_20329) != hAPP(hAPP(c_List_Olist_OCons(U_20327),U_20331),U_20333) ) ),
    inference(definitional_conversion,[status(esa)],[f_4877_3]) ).

cnf(f_4877_5,plain,
    ( U_20329 = hAPP(hAPP(c_List_Oappend(U_20327),hAPP(c_List_Orev(U_20327),U_20333)),hAPP(hAPP(c_List_Olist_OCons(U_20327),U_20331),c_List_Olist_ONil(U_20327)))
    | hAPP(c_List_Orev(U_20327),U_20329) != hAPP(hAPP(c_List_Olist_OCons(U_20327),U_20331),U_20333) ),
    inference(clausify,[status(thm)],[f_4877_4]) ).

cnf(f_4877_6,plain,
    ( hAPP(c_List_Orev(U_20328),U_20330) = hAPP(hAPP(c_List_Olist_OCons(U_20328),U_20332),U_20334)
    | U_20330 != hAPP(hAPP(c_List_Oappend(U_20328),hAPP(c_List_Orev(U_20328),U_20334)),hAPP(hAPP(c_List_Olist_OCons(U_20328),U_20332),c_List_Olist_ONil(U_20328))) ),
    inference(clausify,[status(thm)],[f_4877_4]) ).

fof(f_4878_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_4878_2,plain,
    ! [U_20337,U_20336,U_20335] : hAPP(c_List_Orev(U_20335),hAPP(hAPP(c_List_Olist_OCons(U_20335),U_20336),U_20337)) = hAPP(hAPP(c_List_Oappend(U_20335),hAPP(c_List_Orev(U_20335),U_20337)),hAPP(hAPP(c_List_Olist_OCons(U_20335),U_20336),c_List_Olist_ONil(U_20335))),
    inference(variable_rename,[status(thm)],[f_4878_1]) ).

fof(f_4878_3,plain,
    ! [U_20335,U_20336,U_20337] : hAPP(c_List_Orev(U_20335),hAPP(hAPP(c_List_Olist_OCons(U_20335),U_20336),U_20337)) = hAPP(hAPP(c_List_Oappend(U_20335),hAPP(c_List_Orev(U_20335),U_20337)),hAPP(hAPP(c_List_Olist_OCons(U_20335),U_20336),c_List_Olist_ONil(U_20335))),
    inference(definitional_conversion,[status(esa)],[f_4878_2]) ).

cnf(f_4878_4,plain,
    hAPP(c_List_Orev(U_20335),hAPP(hAPP(c_List_Olist_OCons(U_20335),U_20336),U_20337)) = hAPP(hAPP(c_List_Oappend(U_20335),hAPP(c_List_Orev(U_20335),U_20337)),hAPP(hAPP(c_List_Olist_OCons(U_20335),U_20336),c_List_Olist_ONil(U_20335))),
    inference(clausify,[status(thm)],[f_4878_3]) ).

fof(f_4879_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_4879_2,plain,
    ! [U_20339,U_20338] : hAPP(c_List_Orev(U_20338),c_List_Oconcat(U_20338,U_20339)) = c_List_Oconcat(U_20338,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20338),tc_List_Olist(U_20338)),c_List_Orev(U_20338)),hAPP(c_List_Orev(tc_List_Olist(U_20338)),U_20339))),
    inference(variable_rename,[status(thm)],[f_4879_1]) ).

fof(f_4879_3,plain,
    ! [U_20338,U_20339] : hAPP(c_List_Orev(U_20338),c_List_Oconcat(U_20338,U_20339)) = c_List_Oconcat(U_20338,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20338),tc_List_Olist(U_20338)),c_List_Orev(U_20338)),hAPP(c_List_Orev(tc_List_Olist(U_20338)),U_20339))),
    inference(definitional_conversion,[status(esa)],[f_4879_2]) ).

cnf(f_4879_4,plain,
    hAPP(c_List_Orev(U_20338),c_List_Oconcat(U_20338,U_20339)) = c_List_Oconcat(U_20338,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20338),tc_List_Olist(U_20338)),c_List_Orev(U_20338)),hAPP(c_List_Orev(tc_List_Olist(U_20338)),U_20339))),
    inference(clausify,[status(thm)],[f_4879_3]) ).

fof(f_4880_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_4880_2,plain,
    ! [U_20343,U_20342,U_20341,U_20340] : hAPP(c_List_Orev(U_20340),hAPP(hAPP(c_List_Omap(U_20341,U_20340),U_20342),U_20343)) = hAPP(hAPP(c_List_Omap(U_20341,U_20340),U_20342),hAPP(c_List_Orev(U_20341),U_20343)),
    inference(variable_rename,[status(thm)],[f_4880_1]) ).

fof(f_4880_3,plain,
    ! [U_20340,U_20341,U_20342,U_20343] : hAPP(c_List_Orev(U_20340),hAPP(hAPP(c_List_Omap(U_20341,U_20340),U_20342),U_20343)) = hAPP(hAPP(c_List_Omap(U_20341,U_20340),U_20342),hAPP(c_List_Orev(U_20341),U_20343)),
    inference(definitional_conversion,[status(esa)],[f_4880_2]) ).

cnf(f_4880_4,plain,
    hAPP(c_List_Orev(U_20340),hAPP(hAPP(c_List_Omap(U_20341,U_20340),U_20342),U_20343)) = hAPP(hAPP(c_List_Omap(U_20341,U_20340),U_20342),hAPP(c_List_Orev(U_20341),U_20343)),
    inference(clausify,[status(thm)],[f_4880_3]) ).

fof(f_4881_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_4881_2,plain,
    ! [U_20347,U_20346,U_20345,U_20344] : hAPP(hAPP(c_List_Omap(U_20344,U_20345),U_20346),c_List_Oconcat(U_20344,U_20347)) = c_List_Oconcat(U_20345,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20344),tc_List_Olist(U_20345)),hAPP(c_List_Omap(U_20344,U_20345),U_20346)),U_20347)),
    inference(variable_rename,[status(thm)],[f_4881_1]) ).

fof(f_4881_3,plain,
    ! [U_20344,U_20345,U_20346,U_20347] : hAPP(hAPP(c_List_Omap(U_20344,U_20345),U_20346),c_List_Oconcat(U_20344,U_20347)) = c_List_Oconcat(U_20345,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20344),tc_List_Olist(U_20345)),hAPP(c_List_Omap(U_20344,U_20345),U_20346)),U_20347)),
    inference(definitional_conversion,[status(esa)],[f_4881_2]) ).

cnf(f_4881_4,plain,
    hAPP(hAPP(c_List_Omap(U_20344,U_20345),U_20346),c_List_Oconcat(U_20344,U_20347)) = c_List_Oconcat(U_20345,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20344),tc_List_Olist(U_20345)),hAPP(c_List_Omap(U_20344,U_20345),U_20346)),U_20347)),
    inference(clausify,[status(thm)],[f_4881_3]) ).

fof(f_4882_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_4882_2,plain,
    ! [U_20349,U_20348] : hAPP(c_List_Orev(U_20348),U_20349) = hAPP(c_List_Ofoldl(tc_List_Olist(U_20348),U_20348,hAPP(c_COMBC(U_20348,tc_List_Olist(U_20348),tc_List_Olist(U_20348)),c_List_Olist_OCons(U_20348)),c_List_Olist_ONil(U_20348)),U_20349),
    inference(variable_rename,[status(thm)],[f_4882_1]) ).

fof(f_4882_3,plain,
    ! [U_20348,U_20349] : hAPP(c_List_Orev(U_20348),U_20349) = hAPP(c_List_Ofoldl(tc_List_Olist(U_20348),U_20348,hAPP(c_COMBC(U_20348,tc_List_Olist(U_20348),tc_List_Olist(U_20348)),c_List_Olist_OCons(U_20348)),c_List_Olist_ONil(U_20348)),U_20349),
    inference(definitional_conversion,[status(esa)],[f_4882_2]) ).

cnf(f_4882_4,plain,
    hAPP(c_List_Orev(U_20348),U_20349) = hAPP(c_List_Ofoldl(tc_List_Olist(U_20348),U_20348,hAPP(c_COMBC(U_20348,tc_List_Olist(U_20348),tc_List_Olist(U_20348)),c_List_Olist_OCons(U_20348)),c_List_Olist_ONil(U_20348)),U_20349),
    inference(clausify,[status(thm)],[f_4882_3]) ).

fof(f_4883_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_4883_2,plain,
    ! [U_20351,U_20350] : c_List_Oconcat(U_20350,U_20351) = hAPP(c_List_Ofoldl(tc_List_Olist(U_20350),tc_List_Olist(U_20350),c_List_Oappend(U_20350),c_List_Olist_ONil(U_20350)),U_20351),
    inference(variable_rename,[status(thm)],[f_4883_1]) ).

fof(f_4883_3,plain,
    ! [U_20350,U_20351] : c_List_Oconcat(U_20350,U_20351) = hAPP(c_List_Ofoldl(tc_List_Olist(U_20350),tc_List_Olist(U_20350),c_List_Oappend(U_20350),c_List_Olist_ONil(U_20350)),U_20351),
    inference(definitional_conversion,[status(esa)],[f_4883_2]) ).

cnf(f_4883_4,plain,
    c_List_Oconcat(U_20350,U_20351) = hAPP(c_List_Ofoldl(tc_List_Olist(U_20350),tc_List_Olist(U_20350),c_List_Oappend(U_20350),c_List_Olist_ONil(U_20350)),U_20351),
    inference(clausify,[status(thm)],[f_4883_3]) ).

fof(f_4884_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_4884_2,plain,
    ! [U_20354,U_20353,U_20352] : hAPP(c_List_Ofoldl(tc_List_Olist(U_20352),tc_List_Olist(U_20352),c_List_Oappend(U_20352),U_20353),U_20354) = hAPP(hAPP(c_List_Oappend(U_20352),U_20353),c_List_Oconcat(U_20352,U_20354)),
    inference(variable_rename,[status(thm)],[f_4884_1]) ).

fof(f_4884_3,plain,
    ! [U_20352,U_20353,U_20354] : hAPP(c_List_Ofoldl(tc_List_Olist(U_20352),tc_List_Olist(U_20352),c_List_Oappend(U_20352),U_20353),U_20354) = hAPP(hAPP(c_List_Oappend(U_20352),U_20353),c_List_Oconcat(U_20352,U_20354)),
    inference(definitional_conversion,[status(esa)],[f_4884_2]) ).

cnf(f_4884_4,plain,
    hAPP(c_List_Ofoldl(tc_List_Olist(U_20352),tc_List_Olist(U_20352),c_List_Oappend(U_20352),U_20353),U_20354) = hAPP(hAPP(c_List_Oappend(U_20352),U_20353),c_List_Oconcat(U_20352,U_20354)),
    inference(clausify,[status(thm)],[f_4884_3]) ).

fof(f_4885_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_4885_2,plain,
    ! [U_20357,U_20356,U_20355] : hAPP(c_List_Orev(U_20355),hAPP(hAPP(c_List_Oappend(U_20355),U_20356),U_20357)) = hAPP(hAPP(c_List_Oappend(U_20355),hAPP(c_List_Orev(U_20355),U_20357)),hAPP(c_List_Orev(U_20355),U_20356)),
    inference(variable_rename,[status(thm)],[f_4885_1]) ).

fof(f_4885_3,plain,
    ! [U_20355,U_20356,U_20357] : hAPP(c_List_Orev(U_20355),hAPP(hAPP(c_List_Oappend(U_20355),U_20356),U_20357)) = hAPP(hAPP(c_List_Oappend(U_20355),hAPP(c_List_Orev(U_20355),U_20357)),hAPP(c_List_Orev(U_20355),U_20356)),
    inference(definitional_conversion,[status(esa)],[f_4885_2]) ).

cnf(f_4885_4,plain,
    hAPP(c_List_Orev(U_20355),hAPP(hAPP(c_List_Oappend(U_20355),U_20356),U_20357)) = hAPP(hAPP(c_List_Oappend(U_20355),hAPP(c_List_Orev(U_20355),U_20357)),hAPP(c_List_Orev(U_20355),U_20356)),
    inference(clausify,[status(thm)],[f_4885_3]) ).

fof(f_4886_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_4886_2,plain,
    ! [U_20360,U_20359,U_20358] : c_List_Oconcat(U_20358,hAPP(hAPP(c_List_Oappend(tc_List_Olist(U_20358)),U_20359),U_20360)) = hAPP(hAPP(c_List_Oappend(U_20358),c_List_Oconcat(U_20358,U_20359)),c_List_Oconcat(U_20358,U_20360)),
    inference(variable_rename,[status(thm)],[f_4886_1]) ).

fof(f_4886_3,plain,
    ! [U_20358,U_20359,U_20360] : c_List_Oconcat(U_20358,hAPP(hAPP(c_List_Oappend(tc_List_Olist(U_20358)),U_20359),U_20360)) = hAPP(hAPP(c_List_Oappend(U_20358),c_List_Oconcat(U_20358,U_20359)),c_List_Oconcat(U_20358,U_20360)),
    inference(definitional_conversion,[status(esa)],[f_4886_2]) ).

cnf(f_4886_4,plain,
    c_List_Oconcat(U_20358,hAPP(hAPP(c_List_Oappend(tc_List_Olist(U_20358)),U_20359),U_20360)) = hAPP(hAPP(c_List_Oappend(U_20358),c_List_Oconcat(U_20358,U_20359)),c_List_Oconcat(U_20358,U_20360)),
    inference(clausify,[status(thm)],[f_4886_3]) ).

fof(f_4887_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_4887_2,plain,
    ! [U_20362,U_20361] :
      ( ( hBOOL(hAPP(c_List_Odistinct(U_20361),hAPP(c_List_Orev(U_20361),U_20362)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20361),U_20362)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_20361),U_20362))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20361),hAPP(c_List_Orev(U_20361),U_20362))) ) ),
    inference(variable_rename,[status(thm)],[f_4887_1]) ).

fof(f_4887_3,plain,
    ( ! [U_20366,U_20364] :
        ( hBOOL(hAPP(c_List_Odistinct(U_20364),hAPP(c_List_Orev(U_20364),U_20366)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20364),U_20366)) )
    & ! [U_20365,U_20363] :
        ( hBOOL(hAPP(c_List_Odistinct(U_20363),U_20365))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20363),hAPP(c_List_Orev(U_20363),U_20365))) ) ),
    inference(miniscope,[status(thm)],[f_4887_2]) ).

fof(f_4887_4,plain,
    ( ! [U_20364,U_20366] :
        ( hBOOL(hAPP(c_List_Odistinct(U_20364),hAPP(c_List_Orev(U_20364),U_20366)))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20364),U_20366)) )
    & ! [U_20365,U_20363] :
        ( hBOOL(hAPP(c_List_Odistinct(U_20363),U_20365))
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20363),hAPP(c_List_Orev(U_20363),U_20365))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4887_3]) ).

cnf(f_4887_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_20363),U_20365))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20363),hAPP(c_List_Orev(U_20363),U_20365))) ),
    inference(clausify,[status(thm)],[f_4887_4]) ).

cnf(f_4887_6,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_20364),hAPP(c_List_Orev(U_20364),U_20366)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20364),U_20366)) ),
    inference(clausify,[status(thm)],[f_4887_4]) ).

fof(f_4888_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_4888_2,plain,
    ! [U_20368,U_20367] : hAPP(c_List_Oset(U_20367),c_List_Oconcat(U_20367,U_20368)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_20367),tc_fun(U_20367,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_20367)),U_20368)),c_List_Oset(U_20367)),
    inference(variable_rename,[status(thm)],[f_4888_1]) ).

fof(f_4888_3,plain,
    ! [U_20367,U_20368] : hAPP(c_List_Oset(U_20367),c_List_Oconcat(U_20367,U_20368)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_20367),tc_fun(U_20367,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_20367)),U_20368)),c_List_Oset(U_20367)),
    inference(definitional_conversion,[status(esa)],[f_4888_2]) ).

cnf(f_4888_4,plain,
    hAPP(c_List_Oset(U_20367),c_List_Oconcat(U_20367,U_20368)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_20367),tc_fun(U_20367,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_20367)),U_20368)),c_List_Oset(U_20367)),
    inference(clausify,[status(thm)],[f_4888_3]) ).

fof(f_4889_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_4889_2,plain,
    ! [U_20370,U_20369] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20369)),hAPP(c_List_Orev(U_20369),U_20370)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20369)),U_20370),
    inference(variable_rename,[status(thm)],[f_4889_1]) ).

fof(f_4889_3,plain,
    ! [U_20369,U_20370] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20369)),hAPP(c_List_Orev(U_20369),U_20370)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20369)),U_20370),
    inference(definitional_conversion,[status(esa)],[f_4889_2]) ).

cnf(f_4889_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20369)),hAPP(c_List_Orev(U_20369),U_20370)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20369)),U_20370),
    inference(clausify,[status(thm)],[f_4889_3]) ).

fof(f_4890_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_4890_2,plain,
    ! [U_20372,U_20371] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20371),hAPP(c_List_Orev(U_20371),U_20372)) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20371),U_20372)
      | ~ class_Groups_Ocomm__monoid__add(U_20371) ),
    inference(variable_rename,[status(thm)],[f_4890_1]) ).

fof(f_4890_3,plain,
    ! [U_20371,U_20372] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20371),hAPP(c_List_Orev(U_20371),U_20372)) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20371),U_20372)
      | ~ class_Groups_Ocomm__monoid__add(U_20371) ),
    inference(definitional_conversion,[status(esa)],[f_4890_2]) ).

cnf(f_4890_4,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20371),hAPP(c_List_Orev(U_20371),U_20372)) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20371),U_20372)
    | ~ class_Groups_Ocomm__monoid__add(U_20371) ),
    inference(clausify,[status(thm)],[f_4890_3]) ).

fof(f_4891_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_4891_2,plain,
    ! [U_20375,U_20374,U_20373] :
      ( ( hAPP(c_List_Orev(U_20373),U_20374) = hAPP(c_List_Orev(U_20373),U_20375)
        | U_20374 != U_20375 )
      & ( U_20374 = U_20375
        | hAPP(c_List_Orev(U_20373),U_20374) != hAPP(c_List_Orev(U_20373),U_20375) ) ),
    inference(variable_rename,[status(thm)],[f_4891_1]) ).

fof(f_4891_3,plain,
    ( ! [U_20381,U_20379] :
        ( ! [U_20377] : hAPP(c_List_Orev(U_20377),U_20379) = hAPP(c_List_Orev(U_20377),U_20381)
        | U_20379 != U_20381 )
    & ! [U_20380,U_20378] :
        ( ! [U_20376] : hAPP(c_List_Orev(U_20376),U_20378) != hAPP(c_List_Orev(U_20376),U_20380)
        | U_20378 = U_20380 ) ),
    inference(miniscope,[status(thm)],[f_4891_2]) ).

fof(f_4891_4,plain,
    ( ! [U_20381,U_20377,U_20379] :
        ( hAPP(c_List_Orev(U_20377),U_20379) = hAPP(c_List_Orev(U_20377),U_20381)
        | U_20379 != U_20381 )
    & ! [U_20380,U_20376,U_20378] :
        ( hAPP(c_List_Orev(U_20376),U_20378) != hAPP(c_List_Orev(U_20376),U_20380)
        | U_20378 = U_20380 ) ),
    inference(definitional_conversion,[status(esa)],[f_4891_3]) ).

cnf(f_4891_5,plain,
    ( hAPP(c_List_Orev(U_20376),U_20378) != hAPP(c_List_Orev(U_20376),U_20380)
    | U_20378 = U_20380 ),
    inference(clausify,[status(thm)],[f_4891_4]) ).

cnf(f_4891_6,plain,
    ( hAPP(c_List_Orev(U_20377),U_20379) = hAPP(c_List_Orev(U_20377),U_20381)
    | U_20379 != U_20381 ),
    inference(clausify,[status(thm)],[f_4891_4]) ).

fof(f_4892_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_4892_2,plain,
    ! [U_20384,U_20383,U_20382] :
      ( ( hAPP(c_List_Orev(U_20382),U_20383) = U_20384
        | U_20383 != hAPP(c_List_Orev(U_20382),U_20384) )
      & ( U_20383 = hAPP(c_List_Orev(U_20382),U_20384)
        | hAPP(c_List_Orev(U_20382),U_20383) != U_20384 ) ),
    inference(variable_rename,[status(thm)],[f_4892_1]) ).

fof(f_4892_3,plain,
    ( ! [U_20390,U_20388,U_20386] :
        ( hAPP(c_List_Orev(U_20386),U_20388) = U_20390
        | U_20388 != hAPP(c_List_Orev(U_20386),U_20390) )
    & ! [U_20389,U_20387,U_20385] :
        ( U_20387 = hAPP(c_List_Orev(U_20385),U_20389)
        | hAPP(c_List_Orev(U_20385),U_20387) != U_20389 ) ),
    inference(miniscope,[status(thm)],[f_4892_2]) ).

fof(f_4892_4,plain,
    ( ! [U_20386,U_20388,U_20390] :
        ( hAPP(c_List_Orev(U_20386),U_20388) = U_20390
        | U_20388 != hAPP(c_List_Orev(U_20386),U_20390) )
    & ! [U_20387,U_20389,U_20385] :
        ( U_20387 = hAPP(c_List_Orev(U_20385),U_20389)
        | hAPP(c_List_Orev(U_20385),U_20387) != U_20389 ) ),
    inference(definitional_conversion,[status(esa)],[f_4892_3]) ).

cnf(f_4892_5,plain,
    ( U_20387 = hAPP(c_List_Orev(U_20385),U_20389)
    | hAPP(c_List_Orev(U_20385),U_20387) != U_20389 ),
    inference(clausify,[status(thm)],[f_4892_4]) ).

cnf(f_4892_6,plain,
    ( hAPP(c_List_Orev(U_20386),U_20388) = U_20390
    | U_20388 != hAPP(c_List_Orev(U_20386),U_20390) ),
    inference(clausify,[status(thm)],[f_4892_4]) ).

fof(f_4893_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_4893_2,plain,
    ! [U_20392,U_20391] : hAPP(c_List_Orev(U_20391),hAPP(c_List_Orev(U_20391),U_20392)) = U_20392,
    inference(variable_rename,[status(thm)],[f_4893_1]) ).

fof(f_4893_3,plain,
    ! [U_20391,U_20392] : hAPP(c_List_Orev(U_20391),hAPP(c_List_Orev(U_20391),U_20392)) = U_20392,
    inference(definitional_conversion,[status(esa)],[f_4893_2]) ).

cnf(f_4893_4,plain,
    hAPP(c_List_Orev(U_20391),hAPP(c_List_Orev(U_20391),U_20392)) = U_20392,
    inference(clausify,[status(thm)],[f_4893_3]) ).

fof(f_4894_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_4894_2,plain,
    ! [U_20397,U_20396,U_20395,U_20394,U_20393] : c_List_Ofoldr(U_20393,U_20394,U_20395,U_20396,U_20397) = hAPP(c_List_Ofoldl(U_20394,U_20393,hAPP(c_COMBC(U_20393,U_20394,U_20394),U_20395),U_20397),hAPP(c_List_Orev(U_20393),U_20396)),
    inference(variable_rename,[status(thm)],[f_4894_1]) ).

fof(f_4894_3,plain,
    ! [U_20393,U_20394,U_20395,U_20396,U_20397] : c_List_Ofoldr(U_20393,U_20394,U_20395,U_20396,U_20397) = hAPP(c_List_Ofoldl(U_20394,U_20393,hAPP(c_COMBC(U_20393,U_20394,U_20394),U_20395),U_20397),hAPP(c_List_Orev(U_20393),U_20396)),
    inference(definitional_conversion,[status(esa)],[f_4894_2]) ).

cnf(f_4894_4,plain,
    c_List_Ofoldr(U_20393,U_20394,U_20395,U_20396,U_20397) = hAPP(c_List_Ofoldl(U_20394,U_20393,hAPP(c_COMBC(U_20393,U_20394,U_20394),U_20395),U_20397),hAPP(c_List_Orev(U_20393),U_20396)),
    inference(clausify,[status(thm)],[f_4894_3]) ).

fof(f_4895_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_4895_2,plain,
    ! [U_20402,U_20401,U_20400,U_20399,U_20398] : hAPP(c_List_Ofoldl(U_20398,U_20399,U_20400,U_20401),U_20402) = c_List_Ofoldr(U_20399,U_20398,hAPP(c_COMBC(U_20398,U_20399,U_20398),U_20400),hAPP(c_List_Orev(U_20399),U_20402),U_20401),
    inference(variable_rename,[status(thm)],[f_4895_1]) ).

fof(f_4895_3,plain,
    ! [U_20398,U_20399,U_20400,U_20401,U_20402] : hAPP(c_List_Ofoldl(U_20398,U_20399,U_20400,U_20401),U_20402) = c_List_Ofoldr(U_20399,U_20398,hAPP(c_COMBC(U_20398,U_20399,U_20398),U_20400),hAPP(c_List_Orev(U_20399),U_20402),U_20401),
    inference(definitional_conversion,[status(esa)],[f_4895_2]) ).

cnf(f_4895_4,plain,
    hAPP(c_List_Ofoldl(U_20398,U_20399,U_20400,U_20401),U_20402) = c_List_Ofoldr(U_20399,U_20398,hAPP(c_COMBC(U_20398,U_20399,U_20398),U_20400),hAPP(c_List_Orev(U_20399),U_20402),U_20401),
    inference(clausify,[status(thm)],[f_4895_3]) ).

fof(f_4896_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_4896_2,plain,
    ! [U_20404,U_20403] : hAPP(c_List_Oset(U_20403),hAPP(c_List_Orev(U_20403),U_20404)) = hAPP(c_List_Oset(U_20403),U_20404),
    inference(variable_rename,[status(thm)],[f_4896_1]) ).

fof(f_4896_3,plain,
    ! [U_20403,U_20404] : hAPP(c_List_Oset(U_20403),hAPP(c_List_Orev(U_20403),U_20404)) = hAPP(c_List_Oset(U_20403),U_20404),
    inference(definitional_conversion,[status(esa)],[f_4896_2]) ).

cnf(f_4896_4,plain,
    hAPP(c_List_Oset(U_20403),hAPP(c_List_Orev(U_20403),U_20404)) = hAPP(c_List_Oset(U_20403),U_20404),
    inference(clausify,[status(thm)],[f_4896_3]) ).

fof(f_4897_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_4897_2,plain,
    ! [U_20408,U_20407,U_20406,U_20405] :
      ( hAPP(hAPP(c_List_Ozip(U_20405,U_20407),hAPP(c_List_Orev(U_20405),U_20406)),hAPP(c_List_Orev(U_20407),U_20408)) = hAPP(c_List_Orev(tc_prod(U_20405,U_20407)),hAPP(hAPP(c_List_Ozip(U_20405,U_20407),U_20406),U_20408))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20405)),U_20406) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20407)),U_20408) ),
    inference(variable_rename,[status(thm)],[f_4897_1]) ).

fof(f_4897_3,plain,
    ! [U_20405,U_20406,U_20407,U_20408] :
      ( hAPP(hAPP(c_List_Ozip(U_20405,U_20407),hAPP(c_List_Orev(U_20405),U_20406)),hAPP(c_List_Orev(U_20407),U_20408)) = hAPP(c_List_Orev(tc_prod(U_20405,U_20407)),hAPP(hAPP(c_List_Ozip(U_20405,U_20407),U_20406),U_20408))
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20405)),U_20406) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20407)),U_20408) ),
    inference(definitional_conversion,[status(esa)],[f_4897_2]) ).

cnf(f_4897_4,plain,
    ( hAPP(hAPP(c_List_Ozip(U_20405,U_20407),hAPP(c_List_Orev(U_20405),U_20406)),hAPP(c_List_Orev(U_20407),U_20408)) = hAPP(c_List_Orev(tc_prod(U_20405,U_20407)),hAPP(hAPP(c_List_Ozip(U_20405,U_20407),U_20406),U_20408))
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20405)),U_20406) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20407)),U_20408) ),
    inference(clausify,[status(thm)],[f_4897_3]) ).

fof(f_4898_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] : hAPP(c_List_Orev(T_b),hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),hAPP(c_List_Orev(T_b),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_rev__filter]) ).

fof(f_4898_2,plain,
    ! [U_20411,U_20410,U_20409] : hAPP(c_List_Orev(U_20409),hAPP(c_List_Ofilter(U_20409,U_20410),U_20411)) = hAPP(c_List_Ofilter(U_20409,U_20410),hAPP(c_List_Orev(U_20409),U_20411)),
    inference(variable_rename,[status(thm)],[f_4898_1]) ).

fof(f_4898_3,plain,
    ! [U_20409,U_20410,U_20411] : hAPP(c_List_Orev(U_20409),hAPP(c_List_Ofilter(U_20409,U_20410),U_20411)) = hAPP(c_List_Ofilter(U_20409,U_20410),hAPP(c_List_Orev(U_20409),U_20411)),
    inference(definitional_conversion,[status(esa)],[f_4898_2]) ).

cnf(f_4898_4,plain,
    hAPP(c_List_Orev(U_20409),hAPP(c_List_Ofilter(U_20409,U_20410),U_20411)) = hAPP(c_List_Ofilter(U_20409,U_20410),hAPP(c_List_Orev(U_20409),U_20411)),
    inference(clausify,[status(thm)],[f_4898_3]) ).

fof(f_4899_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_4899_2,plain,
    ! [U_20413,U_20412] :
      ( c_List_Olast(U_20413,hAPP(c_List_Orev(U_20413),U_20412)) = hAPP(c_List_Ohd(U_20413),U_20412)
      | U_20412 = c_List_Olist_ONil(U_20413) ),
    inference(variable_rename,[status(thm)],[f_4899_1]) ).

fof(f_4899_3,plain,
    ! [U_20412,U_20413] :
      ( c_List_Olast(U_20413,hAPP(c_List_Orev(U_20413),U_20412)) = hAPP(c_List_Ohd(U_20413),U_20412)
      | U_20412 = c_List_Olist_ONil(U_20413) ),
    inference(definitional_conversion,[status(esa)],[f_4899_2]) ).

cnf(f_4899_4,plain,
    ( c_List_Olast(U_20413,hAPP(c_List_Orev(U_20413),U_20412)) = hAPP(c_List_Ohd(U_20413),U_20412)
    | U_20412 = c_List_Olist_ONil(U_20413) ),
    inference(clausify,[status(thm)],[f_4899_3]) ).

fof(f_4900_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_4900_2,plain,
    ! [U_20415,U_20414] :
      ( hAPP(c_List_Ohd(U_20415),hAPP(c_List_Orev(U_20415),U_20414)) = c_List_Olast(U_20415,U_20414)
      | U_20414 = c_List_Olist_ONil(U_20415) ),
    inference(variable_rename,[status(thm)],[f_4900_1]) ).

fof(f_4900_3,plain,
    ! [U_20414,U_20415] :
      ( hAPP(c_List_Ohd(U_20415),hAPP(c_List_Orev(U_20415),U_20414)) = c_List_Olast(U_20415,U_20414)
      | U_20414 = c_List_Olist_ONil(U_20415) ),
    inference(definitional_conversion,[status(esa)],[f_4900_2]) ).

cnf(f_4900_4,plain,
    ( hAPP(c_List_Ohd(U_20415),hAPP(c_List_Orev(U_20415),U_20414)) = c_List_Olast(U_20415,U_20414)
    | U_20414 = c_List_Olist_ONil(U_20415) ),
    inference(clausify,[status(thm)],[f_4900_3]) ).

fof(f_4901_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_4901_2,plain,
    ! [U_20417,U_20416] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20416),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20416))),c_List_Otranspose(U_20416,U_20417)))),
    inference(variable_rename,[status(thm)],[f_4901_1]) ).

fof(f_4901_3,plain,
    ! [U_20416,U_20417] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20416),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20416))),c_List_Otranspose(U_20416,U_20417)))),
    inference(definitional_conversion,[status(esa)],[f_4901_2]) ).

cnf(f_4901_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_20416),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20416))),c_List_Otranspose(U_20416,U_20417)))),
    inference(clausify,[status(thm)],[f_4901_3]) ).

fof(f_4902_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_4902_2,plain,
    ! [U_20420,U_20419,U_20418] : hAPP(c_List_Orev(U_20418),hAPP(hAPP(c_List_Otake(U_20418),U_20419),U_20420)) = hAPP(hAPP(c_List_Odrop(U_20418),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20418)),U_20420)),U_20419)),hAPP(c_List_Orev(U_20418),U_20420)),
    inference(variable_rename,[status(thm)],[f_4902_1]) ).

fof(f_4902_3,plain,
    ! [U_20418,U_20419,U_20420] : hAPP(c_List_Orev(U_20418),hAPP(hAPP(c_List_Otake(U_20418),U_20419),U_20420)) = hAPP(hAPP(c_List_Odrop(U_20418),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20418)),U_20420)),U_20419)),hAPP(c_List_Orev(U_20418),U_20420)),
    inference(definitional_conversion,[status(esa)],[f_4902_2]) ).

cnf(f_4902_4,plain,
    hAPP(c_List_Orev(U_20418),hAPP(hAPP(c_List_Otake(U_20418),U_20419),U_20420)) = hAPP(hAPP(c_List_Odrop(U_20418),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20418)),U_20420)),U_20419)),hAPP(c_List_Orev(U_20418),U_20420)),
    inference(clausify,[status(thm)],[f_4902_3]) ).

fof(f_4903_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_4903_2,plain,
    ! [U_20423,U_20422,U_20421] : hAPP(c_List_Orev(U_20421),hAPP(hAPP(c_List_Odrop(U_20421),U_20422),U_20423)) = hAPP(hAPP(c_List_Otake(U_20421),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20421)),U_20423)),U_20422)),hAPP(c_List_Orev(U_20421),U_20423)),
    inference(variable_rename,[status(thm)],[f_4903_1]) ).

fof(f_4903_3,plain,
    ! [U_20421,U_20422,U_20423] : hAPP(c_List_Orev(U_20421),hAPP(hAPP(c_List_Odrop(U_20421),U_20422),U_20423)) = hAPP(hAPP(c_List_Otake(U_20421),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20421)),U_20423)),U_20422)),hAPP(c_List_Orev(U_20421),U_20423)),
    inference(definitional_conversion,[status(esa)],[f_4903_2]) ).

cnf(f_4903_4,plain,
    hAPP(c_List_Orev(U_20421),hAPP(hAPP(c_List_Odrop(U_20421),U_20422),U_20423)) = hAPP(hAPP(c_List_Otake(U_20421),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20421)),U_20423)),U_20422)),hAPP(c_List_Orev(U_20421),U_20423)),
    inference(clausify,[status(thm)],[f_4903_3]) ).

fof(f_4904_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_4904_2,plain,
    ! [U_20426,U_20425,U_20424] : hAPP(c_List_Orotate(U_20424,U_20425),hAPP(c_List_Orev(U_20424),U_20426)) = hAPP(c_List_Orev(U_20424),hAPP(c_List_Orotate(U_20424,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20424)),U_20426)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_20425,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20424)),U_20426)))),U_20426)),
    inference(variable_rename,[status(thm)],[f_4904_1]) ).

fof(f_4904_3,plain,
    ! [U_20426,U_20424,U_20425] : hAPP(c_List_Orotate(U_20424,U_20425),hAPP(c_List_Orev(U_20424),U_20426)) = hAPP(c_List_Orev(U_20424),hAPP(c_List_Orotate(U_20424,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20424)),U_20426)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_20425,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20424)),U_20426)))),U_20426)),
    inference(definitional_conversion,[status(esa)],[f_4904_2]) ).

cnf(f_4904_4,plain,
    hAPP(c_List_Orotate(U_20424,U_20425),hAPP(c_List_Orev(U_20424),U_20426)) = hAPP(c_List_Orev(U_20424),hAPP(c_List_Orotate(U_20424,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20424)),U_20426)),c_Divides_Odiv__class_Omod(tc_Nat_Onat,U_20425,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20424)),U_20426)))),U_20426)),
    inference(clausify,[status(thm)],[f_4904_3]) ).

fof(f_4905_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_4905_2,plain,
    ! [U_20430,U_20429,U_20428,U_20427] : c_List_Otranspose(U_20427,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20427)),hAPP(hAPP(c_List_Olist_OCons(U_20427),U_20428),U_20429)),U_20430)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20427)),hAPP(hAPP(c_List_Olist_OCons(U_20427),U_20428),c_List_Oconcat(U_20427,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20427),tc_List_Olist(U_20427)),c_List_Olist_Olist__case(tc_List_Olist(U_20427),U_20427,c_List_Olist_ONil(U_20427),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20427),tc_fun(tc_List_Olist(U_20427),tc_List_Olist(U_20427)),U_20427),c_COMBK(tc_List_Olist(U_20427),tc_List_Olist(U_20427))),hAPP(hAPP(c_COMBC(U_20427,tc_List_Olist(U_20427),tc_List_Olist(U_20427)),c_List_Olist_OCons(U_20427)),c_List_Olist_ONil(U_20427))))),U_20430)))),c_List_Otranspose(U_20427,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20427)),U_20429),c_List_Oconcat(tc_List_Olist(U_20427),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20427),tc_List_Olist(tc_List_Olist(U_20427))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20427)),U_20427,c_List_Olist_ONil(tc_List_Olist(U_20427)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20427),tc_List_Olist(tc_List_Olist(U_20427))),U_20427),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20427),tc_List_Olist(tc_List_Olist(U_20427)),tc_List_Olist(tc_List_Olist(U_20427))),c_List_Olist_OCons(tc_List_Olist(U_20427))),c_List_Olist_ONil(tc_List_Olist(U_20427)))))),U_20430))))),
    inference(variable_rename,[status(thm)],[f_4905_1]) ).

fof(f_4905_3,plain,
    ! [U_20427,U_20428,U_20429,U_20430] : c_List_Otranspose(U_20427,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20427)),hAPP(hAPP(c_List_Olist_OCons(U_20427),U_20428),U_20429)),U_20430)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20427)),hAPP(hAPP(c_List_Olist_OCons(U_20427),U_20428),c_List_Oconcat(U_20427,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20427),tc_List_Olist(U_20427)),c_List_Olist_Olist__case(tc_List_Olist(U_20427),U_20427,c_List_Olist_ONil(U_20427),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20427),tc_fun(tc_List_Olist(U_20427),tc_List_Olist(U_20427)),U_20427),c_COMBK(tc_List_Olist(U_20427),tc_List_Olist(U_20427))),hAPP(hAPP(c_COMBC(U_20427,tc_List_Olist(U_20427),tc_List_Olist(U_20427)),c_List_Olist_OCons(U_20427)),c_List_Olist_ONil(U_20427))))),U_20430)))),c_List_Otranspose(U_20427,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20427)),U_20429),c_List_Oconcat(tc_List_Olist(U_20427),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20427),tc_List_Olist(tc_List_Olist(U_20427))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20427)),U_20427,c_List_Olist_ONil(tc_List_Olist(U_20427)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20427),tc_List_Olist(tc_List_Olist(U_20427))),U_20427),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20427),tc_List_Olist(tc_List_Olist(U_20427)),tc_List_Olist(tc_List_Olist(U_20427))),c_List_Olist_OCons(tc_List_Olist(U_20427))),c_List_Olist_ONil(tc_List_Olist(U_20427)))))),U_20430))))),
    inference(definitional_conversion,[status(esa)],[f_4905_2]) ).

cnf(f_4905_4,plain,
    c_List_Otranspose(U_20427,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20427)),hAPP(hAPP(c_List_Olist_OCons(U_20427),U_20428),U_20429)),U_20430)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20427)),hAPP(hAPP(c_List_Olist_OCons(U_20427),U_20428),c_List_Oconcat(U_20427,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20427),tc_List_Olist(U_20427)),c_List_Olist_Olist__case(tc_List_Olist(U_20427),U_20427,c_List_Olist_ONil(U_20427),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20427),tc_fun(tc_List_Olist(U_20427),tc_List_Olist(U_20427)),U_20427),c_COMBK(tc_List_Olist(U_20427),tc_List_Olist(U_20427))),hAPP(hAPP(c_COMBC(U_20427,tc_List_Olist(U_20427),tc_List_Olist(U_20427)),c_List_Olist_OCons(U_20427)),c_List_Olist_ONil(U_20427))))),U_20430)))),c_List_Otranspose(U_20427,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20427)),U_20429),c_List_Oconcat(tc_List_Olist(U_20427),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20427),tc_List_Olist(tc_List_Olist(U_20427))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20427)),U_20427,c_List_Olist_ONil(tc_List_Olist(U_20427)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20427),tc_List_Olist(tc_List_Olist(U_20427))),U_20427),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20427),tc_List_Olist(tc_List_Olist(U_20427)),tc_List_Olist(tc_List_Olist(U_20427))),c_List_Olist_OCons(tc_List_Olist(U_20427))),c_List_Olist_ONil(tc_List_Olist(U_20427)))))),U_20430))))),
    inference(clausify,[status(thm)],[f_4905_3]) ).

fof(f_4906_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_4906_2,plain,
    ! [U_20433,U_20432,U_20431] :
      ( hAPP(hAPP(c_List_Onth(U_20432),hAPP(c_List_Orev(U_20432),U_20433)),U_20431) = hAPP(hAPP(c_List_Onth(U_20432),U_20433),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20432)),U_20433)),hAPP(c_Nat_OSuc,U_20431)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20431),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20432)),U_20433))) ),
    inference(variable_rename,[status(thm)],[f_4906_1]) ).

fof(f_4906_3,plain,
    ! [U_20432,U_20433,U_20431] :
      ( hAPP(hAPP(c_List_Onth(U_20432),hAPP(c_List_Orev(U_20432),U_20433)),U_20431) = hAPP(hAPP(c_List_Onth(U_20432),U_20433),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20432)),U_20433)),hAPP(c_Nat_OSuc,U_20431)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20431),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20432)),U_20433))) ),
    inference(definitional_conversion,[status(esa)],[f_4906_2]) ).

cnf(f_4906_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_20432),hAPP(c_List_Orev(U_20432),U_20433)),U_20431) = hAPP(hAPP(c_List_Onth(U_20432),U_20433),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20432)),U_20433)),hAPP(c_Nat_OSuc,U_20431)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20431),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20432)),U_20433))) ),
    inference(clausify,[status(thm)],[f_4906_3]) ).

fof(f_4907_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_4907_2,plain,
    ! [U_20437,U_20436,U_20435] :
      ( U_20436 = U_20437
      | ? [U_20434] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20435),tc_List_Olist(U_20435),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20435),tc_fun(tc_List_Olist(U_20435),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20435),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20435),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20435),tc_HOL_Obool)),tc_List_Olist(U_20435)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20435))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20435)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20435))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20435)))),U_20434))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20435),tc_List_Olist(U_20435))),U_20434),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20435),tc_List_Olist(U_20435))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20435),tc_List_Olist(U_20435)),U_20436),U_20437)))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20435))),U_20436) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20435))),U_20437)
      | c_List_Oconcat(U_20435,U_20436) != c_List_Oconcat(U_20435,U_20437) ),
    inference(variable_rename,[status(thm)],[f_4907_1]) ).

fof(f_4907_3,plain,
    ! [U_20437,U_20436,U_20435] :
      ( U_20436 = U_20437
      | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20435),tc_List_Olist(U_20435),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20435),tc_fun(tc_List_Olist(U_20435),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20435),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20435),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20435),tc_HOL_Obool)),tc_List_Olist(U_20435)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20435))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20435)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20435))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20435)))),sK501(U_20437,U_20436,U_20435)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20435),tc_List_Olist(U_20435))),sK501(U_20437,U_20436,U_20435)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20435),tc_List_Olist(U_20435))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20435),tc_List_Olist(U_20435)),U_20436),U_20437)))) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20435))),U_20436) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20435))),U_20437)
      | c_List_Oconcat(U_20435,U_20436) != c_List_Oconcat(U_20435,U_20437) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK501]),skolemize(U_20434,sK501(U_20437,U_20436,U_20435))],[f_4907_2]) ).

fof(f_4907_4,plain,
    ( ! [U_20435,U_20436,U_20437] :
        ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20435),tc_List_Olist(U_20435),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20435),tc_fun(tc_List_Olist(U_20435),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20435),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20435),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20435),tc_HOL_Obool)),tc_List_Olist(U_20435)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20435))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20435)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20435))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20435)))),sK501(U_20437,U_20436,U_20435)))
        | ~ sP1229(U_20435,U_20436,U_20437) )
    & ! [U_20435,U_20436,U_20437] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20435),tc_List_Olist(U_20435))),sK501(U_20437,U_20436,U_20435)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20435),tc_List_Olist(U_20435))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20435),tc_List_Olist(U_20435)),U_20436),U_20437))))
        | ~ sP1229(U_20435,U_20436,U_20437) )
    & ! [U_20435,U_20436,U_20437] :
        ( U_20436 = U_20437
        | sP1229(U_20435,U_20436,U_20437)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20435))),U_20436) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20435))),U_20437)
        | c_List_Oconcat(U_20435,U_20436) != c_List_Oconcat(U_20435,U_20437) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1229])],[f_4907_3]) ).

cnf(f_4907_5,plain,
    ( U_20436 = U_20437
    | sP1229(U_20435,U_20436,U_20437)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20435))),U_20436) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20435))),U_20437)
    | c_List_Oconcat(U_20435,U_20436) != c_List_Oconcat(U_20435,U_20437) ),
    inference(clausify,[status(thm)],[f_4907_4]) ).

cnf(f_4907_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20435),tc_List_Olist(U_20435))),sK501(U_20437,U_20436,U_20435)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20435),tc_List_Olist(U_20435))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20435),tc_List_Olist(U_20435)),U_20436),U_20437))))
    | ~ sP1229(U_20435,U_20436,U_20437) ),
    inference(clausify,[status(thm)],[f_4907_4]) ).

cnf(f_4907_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20435),tc_List_Olist(U_20435),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20435),tc_fun(tc_List_Olist(U_20435),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20435),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20435),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20435),tc_HOL_Obool)),tc_List_Olist(U_20435)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20435))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20435)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20435))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20435)))),sK501(U_20437,U_20436,U_20435)))
    | ~ sP1229(U_20435,U_20436,U_20437) ),
    inference(clausify,[status(thm)],[f_4907_4]) ).

fof(f_4908_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_4908_2,plain,
    ! [U_20441,U_20440,U_20439] :
      ( ( ( c_List_Oconcat(U_20439,U_20440) = c_List_Oconcat(U_20439,U_20441)
          | U_20440 != U_20441 )
        & ( U_20440 = U_20441
          | c_List_Oconcat(U_20439,U_20440) != c_List_Oconcat(U_20439,U_20441) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20439))),U_20440) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20439))),U_20441)
      | ? [U_20438] :
          ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20439),tc_List_Olist(U_20439),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20439),tc_fun(tc_List_Olist(U_20439),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20439),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20439),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20439),tc_HOL_Obool)),tc_List_Olist(U_20439)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20439))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20439)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20439))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20439)))),U_20438))
          & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20439),tc_List_Olist(U_20439))),U_20438),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20439),tc_List_Olist(U_20439))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20439),tc_List_Olist(U_20439)),U_20440),U_20441)))) ) ),
    inference(variable_rename,[status(thm)],[f_4908_1]) ).

fof(f_4908_3,plain,
    ! [U_20441,U_20440,U_20439] :
      ( ( ( c_List_Oconcat(U_20439,U_20440) = c_List_Oconcat(U_20439,U_20441)
          | U_20440 != U_20441 )
        & ( U_20440 = U_20441
          | c_List_Oconcat(U_20439,U_20440) != c_List_Oconcat(U_20439,U_20441) ) )
      | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20439))),U_20440) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20439))),U_20441)
      | ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20439),tc_List_Olist(U_20439),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20439),tc_fun(tc_List_Olist(U_20439),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20439),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20439),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20439),tc_HOL_Obool)),tc_List_Olist(U_20439)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20439))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20439)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20439))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20439)))),sK502(U_20441,U_20440,U_20439)))
        & hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20439),tc_List_Olist(U_20439))),sK502(U_20441,U_20440,U_20439)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20439),tc_List_Olist(U_20439))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20439),tc_List_Olist(U_20439)),U_20440),U_20441)))) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK502]),skolemize(U_20438,sK502(U_20441,U_20440,U_20439))],[f_4908_2]) ).

fof(f_4908_4,plain,
    ( ! [U_20441,U_20439,U_20440] :
        ( c_List_Oconcat(U_20439,U_20440) = c_List_Oconcat(U_20439,U_20441)
        | U_20440 != U_20441
        | ~ sP1231(U_20441,U_20439,U_20440) )
    & ! [U_20441,U_20439,U_20440] :
        ( U_20440 = U_20441
        | c_List_Oconcat(U_20439,U_20440) != c_List_Oconcat(U_20439,U_20441)
        | ~ sP1231(U_20441,U_20439,U_20440) )
    & ! [U_20441,U_20439,U_20440] :
        ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20439),tc_List_Olist(U_20439),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20439),tc_fun(tc_List_Olist(U_20439),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20439),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20439),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20439),tc_HOL_Obool)),tc_List_Olist(U_20439)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20439))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20439)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20439))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20439)))),sK502(U_20441,U_20440,U_20439)))
        | ~ sP1230(U_20441,U_20439,U_20440) )
    & ! [U_20441,U_20439,U_20440] :
        ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20439),tc_List_Olist(U_20439))),sK502(U_20441,U_20440,U_20439)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20439),tc_List_Olist(U_20439))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20439),tc_List_Olist(U_20439)),U_20440),U_20441))))
        | ~ sP1230(U_20441,U_20439,U_20440) )
    & ! [U_20441,U_20439,U_20440] :
        ( sP1231(U_20441,U_20439,U_20440)
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20439))),U_20440) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20439))),U_20441)
        | sP1230(U_20441,U_20439,U_20440) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1230,sP1231])],[f_4908_3]) ).

cnf(f_4908_5,plain,
    ( sP1231(U_20441,U_20439,U_20440)
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20439))),U_20440) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20439))),U_20441)
    | sP1230(U_20441,U_20439,U_20440) ),
    inference(clausify,[status(thm)],[f_4908_4]) ).

cnf(f_4908_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_List_Olist(U_20439),tc_List_Olist(U_20439))),sK502(U_20441,U_20440,U_20439)),hAPP(c_List_Oset(tc_prod(tc_List_Olist(U_20439),tc_List_Olist(U_20439))),hAPP(hAPP(c_List_Ozip(tc_List_Olist(U_20439),tc_List_Olist(U_20439)),U_20440),U_20441))))
    | ~ sP1230(U_20441,U_20439,U_20440) ),
    inference(clausify,[status(thm)],[f_4908_4]) ).

cnf(f_4908_7,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_List_Olist(U_20439),tc_List_Olist(U_20439),tc_HOL_Obool),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20439),tc_fun(tc_List_Olist(U_20439),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20439),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_fun(tc_fun(tc_List_Olist(U_20439),tc_Nat_Onat),tc_fun(tc_List_Olist(U_20439),tc_HOL_Obool)),tc_List_Olist(U_20439)),c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20439))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_HOL_Obool),tc_List_Olist(U_20439)),c_fequal),c_Nat_Osize__class_Osize(tc_List_Olist(U_20439))))),c_Nat_Osize__class_Osize(tc_List_Olist(U_20439)))),sK502(U_20441,U_20440,U_20439)))
    | ~ sP1230(U_20441,U_20439,U_20440) ),
    inference(clausify,[status(thm)],[f_4908_4]) ).

cnf(f_4908_8,plain,
    ( U_20440 = U_20441
    | c_List_Oconcat(U_20439,U_20440) != c_List_Oconcat(U_20439,U_20441)
    | ~ sP1231(U_20441,U_20439,U_20440) ),
    inference(clausify,[status(thm)],[f_4908_4]) ).

cnf(f_4908_9,plain,
    ( c_List_Oconcat(U_20439,U_20440) = c_List_Oconcat(U_20439,U_20441)
    | U_20440 != U_20441
    | ~ sP1231(U_20441,U_20439,U_20440) ),
    inference(clausify,[status(thm)],[f_4908_4]) ).

fof(f_4909_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_4909_2,plain,
    ! [U_20445,U_20444,U_20443,U_20442] :
      ( hAPP(c_List_Orev(U_20443),hAPP(hAPP(c_List_Olist__update(U_20443,U_20444),U_20442),U_20445)) = hAPP(hAPP(c_List_Olist__update(U_20443,hAPP(c_List_Orev(U_20443),U_20444)),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_20443)),U_20444)),U_20442)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_20445)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20442),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20443)),U_20444))) ),
    inference(variable_rename,[status(thm)],[f_4909_1]) ).

fof(f_4909_3,plain,
    ! [U_20442,U_20443,U_20444,U_20445] :
      ( hAPP(c_List_Orev(U_20443),hAPP(hAPP(c_List_Olist__update(U_20443,U_20444),U_20442),U_20445)) = hAPP(hAPP(c_List_Olist__update(U_20443,hAPP(c_List_Orev(U_20443),U_20444)),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_20443)),U_20444)),U_20442)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_20445)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20442),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20443)),U_20444))) ),
    inference(definitional_conversion,[status(esa)],[f_4909_2]) ).

cnf(f_4909_4,plain,
    ( hAPP(c_List_Orev(U_20443),hAPP(hAPP(c_List_Olist__update(U_20443,U_20444),U_20442),U_20445)) = hAPP(hAPP(c_List_Olist__update(U_20443,hAPP(c_List_Orev(U_20443),U_20444)),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_20443)),U_20444)),U_20442)),c_Groups_Oone__class_Oone(tc_Nat_Onat))),U_20445)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20442),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20443)),U_20444))) ),
    inference(clausify,[status(thm)],[f_4909_3]) ).

fof(f_4910_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_4910_2,plain,
    ! [U_20449,U_20448,U_20447,U_20446] : c_List_Oconcat(U_20446,hAPP(hAPP(c_List_Omap(U_20447,tc_List_Olist(U_20446)),hAPP(hAPP(c_COMBC(U_20447,tc_List_Olist(U_20446),tc_List_Olist(U_20446)),hAPP(hAPP(c_COMBB(U_20446,tc_fun(tc_List_Olist(U_20446),tc_List_Olist(U_20446)),U_20447),c_List_Olist_OCons(U_20446)),U_20448)),c_List_Olist_ONil(U_20446))),U_20449)) = hAPP(hAPP(c_List_Omap(U_20447,U_20446),U_20448),U_20449),
    inference(variable_rename,[status(thm)],[f_4910_1]) ).

fof(f_4910_3,plain,
    ! [U_20446,U_20447,U_20448,U_20449] : c_List_Oconcat(U_20446,hAPP(hAPP(c_List_Omap(U_20447,tc_List_Olist(U_20446)),hAPP(hAPP(c_COMBC(U_20447,tc_List_Olist(U_20446),tc_List_Olist(U_20446)),hAPP(hAPP(c_COMBB(U_20446,tc_fun(tc_List_Olist(U_20446),tc_List_Olist(U_20446)),U_20447),c_List_Olist_OCons(U_20446)),U_20448)),c_List_Olist_ONil(U_20446))),U_20449)) = hAPP(hAPP(c_List_Omap(U_20447,U_20446),U_20448),U_20449),
    inference(definitional_conversion,[status(esa)],[f_4910_2]) ).

cnf(f_4910_4,plain,
    c_List_Oconcat(U_20446,hAPP(hAPP(c_List_Omap(U_20447,tc_List_Olist(U_20446)),hAPP(hAPP(c_COMBC(U_20447,tc_List_Olist(U_20446),tc_List_Olist(U_20446)),hAPP(hAPP(c_COMBB(U_20446,tc_fun(tc_List_Olist(U_20446),tc_List_Olist(U_20446)),U_20447),c_List_Olist_OCons(U_20446)),U_20448)),c_List_Olist_ONil(U_20446))),U_20449)) = hAPP(hAPP(c_List_Omap(U_20447,U_20446),U_20448),U_20449),
    inference(clausify,[status(thm)],[f_4910_3]) ).

fof(f_4911_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_4911_2,plain,
    ! [U_20453,U_20452,U_20451,U_20450] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20450),hAPP(hAPP(c_List_Onth(U_20450),U_20451),U_20453)),hAPP(hAPP(c_List_Onth(U_20450),U_20451),U_20452)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20453),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20450)),U_20451)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20452),U_20453))
      | ~ c_List_Olinorder__class_Osorted(U_20450,hAPP(c_List_Orev(U_20450),U_20451))
      | ~ class_Orderings_Olinorder(U_20450) ),
    inference(variable_rename,[status(thm)],[f_4911_1]) ).

fof(f_4911_3,plain,
    ! [U_20450,U_20451,U_20452,U_20453] :
      ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20450),hAPP(hAPP(c_List_Onth(U_20450),U_20451),U_20453)),hAPP(hAPP(c_List_Onth(U_20450),U_20451),U_20452)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20453),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20450)),U_20451)))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20452),U_20453))
      | ~ c_List_Olinorder__class_Osorted(U_20450,hAPP(c_List_Orev(U_20450),U_20451))
      | ~ class_Orderings_Olinorder(U_20450) ),
    inference(definitional_conversion,[status(esa)],[f_4911_2]) ).

cnf(f_4911_4,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20450),hAPP(hAPP(c_List_Onth(U_20450),U_20451),U_20453)),hAPP(hAPP(c_List_Onth(U_20450),U_20451),U_20452)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20453),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20450)),U_20451)))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20452),U_20453))
    | ~ c_List_Olinorder__class_Osorted(U_20450,hAPP(c_List_Orev(U_20450),U_20451))
    | ~ class_Orderings_Olinorder(U_20450) ),
    inference(clausify,[status(thm)],[f_4911_3]) ).

fof(f_4912_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_4912_2,plain,
    ! [U_20456,U_20455,U_20454] :
      ( ( ( c_List_Ofoldr(U_20454,U_20454,c_Orderings_Oord__class_Omax(U_20454),U_20455,U_20456) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_20454),hAPP(hAPP(c_List_Onth(U_20454),U_20455),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_20456)
          | U_20455 = c_List_Olist_ONil(U_20454) )
        & ( c_List_Ofoldr(U_20454,U_20454,c_Orderings_Oord__class_Omax(U_20454),U_20455,U_20456) = U_20456
          | U_20455 != c_List_Olist_ONil(U_20454) ) )
      | ~ c_List_Olinorder__class_Osorted(U_20454,hAPP(c_List_Orev(U_20454),U_20455))
      | ~ class_Orderings_Olinorder(U_20454) ),
    inference(variable_rename,[status(thm)],[f_4912_1]) ).

fof(f_4912_3,plain,
    ( ! [U_20456,U_20454,U_20455] :
        ( c_List_Ofoldr(U_20454,U_20454,c_Orderings_Oord__class_Omax(U_20454),U_20455,U_20456) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_20454),hAPP(hAPP(c_List_Onth(U_20454),U_20455),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_20456)
        | U_20455 = c_List_Olist_ONil(U_20454)
        | ~ sP1232(U_20456,U_20454,U_20455) )
    & ! [U_20456,U_20454,U_20455] :
        ( c_List_Ofoldr(U_20454,U_20454,c_Orderings_Oord__class_Omax(U_20454),U_20455,U_20456) = U_20456
        | U_20455 != c_List_Olist_ONil(U_20454)
        | ~ sP1232(U_20456,U_20454,U_20455) )
    & ! [U_20456,U_20454,U_20455] :
        ( sP1232(U_20456,U_20454,U_20455)
        | ~ c_List_Olinorder__class_Osorted(U_20454,hAPP(c_List_Orev(U_20454),U_20455))
        | ~ class_Orderings_Olinorder(U_20454) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1232])],[f_4912_2]) ).

cnf(f_4912_4,plain,
    ( sP1232(U_20456,U_20454,U_20455)
    | ~ c_List_Olinorder__class_Osorted(U_20454,hAPP(c_List_Orev(U_20454),U_20455))
    | ~ class_Orderings_Olinorder(U_20454) ),
    inference(clausify,[status(thm)],[f_4912_3]) ).

cnf(f_4912_5,plain,
    ( c_List_Ofoldr(U_20454,U_20454,c_Orderings_Oord__class_Omax(U_20454),U_20455,U_20456) = U_20456
    | U_20455 != c_List_Olist_ONil(U_20454)
    | ~ sP1232(U_20456,U_20454,U_20455) ),
    inference(clausify,[status(thm)],[f_4912_3]) ).

cnf(f_4912_6,plain,
    ( c_List_Ofoldr(U_20454,U_20454,c_Orderings_Oord__class_Omax(U_20454),U_20455,U_20456) = hAPP(hAPP(c_Orderings_Oord__class_Omax(U_20454),hAPP(hAPP(c_List_Onth(U_20454),U_20455),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))),U_20456)
    | U_20455 = c_List_Olist_ONil(U_20454)
    | ~ sP1232(U_20456,U_20454,U_20455) ),
    inference(clausify,[status(thm)],[f_4912_3]) ).

fof(f_4913_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_4913_2,plain,
    ! [U_20460,U_20459,U_20458,U_20457] :
      ( c_List_Otranspose(U_20457,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20457)),hAPP(hAPP(c_List_Olist_OCons(U_20457),U_20458),U_20459)),U_20460)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20457)),hAPP(hAPP(c_List_Olist_OCons(U_20457),U_20458),c_List_Oconcat(U_20457,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20457),tc_List_Olist(U_20457)),c_List_Olist_Olist__case(tc_List_Olist(U_20457),U_20457,c_List_Olist_ONil(U_20457),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20457),tc_fun(tc_List_Olist(U_20457),tc_List_Olist(U_20457)),U_20457),c_COMBK(tc_List_Olist(U_20457),tc_List_Olist(U_20457))),hAPP(hAPP(c_COMBC(U_20457,tc_List_Olist(U_20457),tc_List_Olist(U_20457)),c_List_Olist_OCons(U_20457)),c_List_Olist_ONil(U_20457))))),U_20460)))),c_List_Otranspose(U_20457,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20457)),U_20459),c_List_Oconcat(tc_List_Olist(U_20457),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20457),tc_List_Olist(tc_List_Olist(U_20457))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20457)),U_20457,c_List_Olist_ONil(tc_List_Olist(U_20457)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20457),tc_List_Olist(tc_List_Olist(U_20457))),U_20457),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20457),tc_List_Olist(tc_List_Olist(U_20457)),tc_List_Olist(tc_List_Olist(U_20457))),c_List_Olist_OCons(tc_List_Olist(U_20457))),c_List_Olist_ONil(tc_List_Olist(U_20457)))))),U_20460)))))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20457)),c_List_Otranspose__rel(U_20457)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20457)),hAPP(hAPP(c_List_Olist_OCons(U_20457),U_20458),U_20459)),U_20460))) ),
    inference(variable_rename,[status(thm)],[f_4913_1]) ).

fof(f_4913_3,plain,
    ! [U_20457,U_20458,U_20459,U_20460] :
      ( c_List_Otranspose(U_20457,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20457)),hAPP(hAPP(c_List_Olist_OCons(U_20457),U_20458),U_20459)),U_20460)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20457)),hAPP(hAPP(c_List_Olist_OCons(U_20457),U_20458),c_List_Oconcat(U_20457,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20457),tc_List_Olist(U_20457)),c_List_Olist_Olist__case(tc_List_Olist(U_20457),U_20457,c_List_Olist_ONil(U_20457),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20457),tc_fun(tc_List_Olist(U_20457),tc_List_Olist(U_20457)),U_20457),c_COMBK(tc_List_Olist(U_20457),tc_List_Olist(U_20457))),hAPP(hAPP(c_COMBC(U_20457,tc_List_Olist(U_20457),tc_List_Olist(U_20457)),c_List_Olist_OCons(U_20457)),c_List_Olist_ONil(U_20457))))),U_20460)))),c_List_Otranspose(U_20457,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20457)),U_20459),c_List_Oconcat(tc_List_Olist(U_20457),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20457),tc_List_Olist(tc_List_Olist(U_20457))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20457)),U_20457,c_List_Olist_ONil(tc_List_Olist(U_20457)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20457),tc_List_Olist(tc_List_Olist(U_20457))),U_20457),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20457),tc_List_Olist(tc_List_Olist(U_20457)),tc_List_Olist(tc_List_Olist(U_20457))),c_List_Olist_OCons(tc_List_Olist(U_20457))),c_List_Olist_ONil(tc_List_Olist(U_20457)))))),U_20460)))))
      | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20457)),c_List_Otranspose__rel(U_20457)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20457)),hAPP(hAPP(c_List_Olist_OCons(U_20457),U_20458),U_20459)),U_20460))) ),
    inference(definitional_conversion,[status(esa)],[f_4913_2]) ).

cnf(f_4913_4,plain,
    ( c_List_Otranspose(U_20457,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20457)),hAPP(hAPP(c_List_Olist_OCons(U_20457),U_20458),U_20459)),U_20460)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20457)),hAPP(hAPP(c_List_Olist_OCons(U_20457),U_20458),c_List_Oconcat(U_20457,hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20457),tc_List_Olist(U_20457)),c_List_Olist_Olist__case(tc_List_Olist(U_20457),U_20457,c_List_Olist_ONil(U_20457),hAPP(hAPP(c_COMBB(tc_List_Olist(U_20457),tc_fun(tc_List_Olist(U_20457),tc_List_Olist(U_20457)),U_20457),c_COMBK(tc_List_Olist(U_20457),tc_List_Olist(U_20457))),hAPP(hAPP(c_COMBC(U_20457,tc_List_Olist(U_20457),tc_List_Olist(U_20457)),c_List_Olist_OCons(U_20457)),c_List_Olist_ONil(U_20457))))),U_20460)))),c_List_Otranspose(U_20457,hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20457)),U_20459),c_List_Oconcat(tc_List_Olist(U_20457),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20457),tc_List_Olist(tc_List_Olist(U_20457))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20457)),U_20457,c_List_Olist_ONil(tc_List_Olist(U_20457)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20457),tc_List_Olist(tc_List_Olist(U_20457))),U_20457),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20457),tc_List_Olist(tc_List_Olist(U_20457)),tc_List_Olist(tc_List_Olist(U_20457))),c_List_Olist_OCons(tc_List_Olist(U_20457))),c_List_Olist_ONil(tc_List_Olist(U_20457)))))),U_20460)))))
    | ~ hBOOL(hAPP(c_Wellfounded_Oaccp(tc_List_Olist(tc_List_Olist(U_20457)),c_List_Otranspose__rel(U_20457)),hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20457)),hAPP(hAPP(c_List_Olist_OCons(U_20457),U_20458),U_20459)),U_20460))) ),
    inference(clausify,[status(thm)],[f_4913_3]) ).

fof(f_4914_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_4914_2,plain,
    ! [U_20462,U_20461] :
      ( ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20461))),c_List_Otranspose(U_20461,U_20462)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20461)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20461)),U_20462),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
          | U_20462 = c_List_Olist_ONil(tc_List_Olist(U_20461)) )
        & ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20461))),c_List_Otranspose(U_20461,U_20462)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
          | U_20462 != c_List_Olist_ONil(tc_List_Olist(U_20461)) ) )
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20461),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20461))),U_20462))) ),
    inference(variable_rename,[status(thm)],[f_4914_1]) ).

fof(f_4914_3,plain,
    ( ! [U_20461,U_20462] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20461))),c_List_Otranspose(U_20461,U_20462)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20461)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20461)),U_20462),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
        | U_20462 = c_List_Olist_ONil(tc_List_Olist(U_20461))
        | ~ sP1233(U_20461,U_20462) )
    & ! [U_20461,U_20462] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20461))),c_List_Otranspose(U_20461,U_20462)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
        | U_20462 != c_List_Olist_ONil(tc_List_Olist(U_20461))
        | ~ sP1233(U_20461,U_20462) )
    & ! [U_20461,U_20462] :
        ( sP1233(U_20461,U_20462)
        | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20461),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20461))),U_20462))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1233])],[f_4914_2]) ).

cnf(f_4914_4,plain,
    ( sP1233(U_20461,U_20462)
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20461),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20461))),U_20462))) ),
    inference(clausify,[status(thm)],[f_4914_3]) ).

cnf(f_4914_5,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20461))),c_List_Otranspose(U_20461,U_20462)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat)
    | U_20462 != c_List_Olist_ONil(tc_List_Olist(U_20461))
    | ~ sP1233(U_20461,U_20462) ),
    inference(clausify,[status(thm)],[f_4914_3]) ).

cnf(f_4914_6,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20461))),c_List_Otranspose(U_20461,U_20462)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20461)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20461)),U_20462),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)))
    | U_20462 = c_List_Olist_ONil(tc_List_Olist(U_20461))
    | ~ sP1233(U_20461,U_20462) ),
    inference(clausify,[status(thm)],[f_4914_3]) ).

fof(f_4915_1,plain,
    ! [V_i_2,V_xs_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),c_List_Otranspose(T_b,V_xs_2))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_i_2))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),V_xs_2)))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_transpose__column__length]) ).

fof(f_4915_2,plain,
    ! [U_20465,U_20464,U_20463] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20463))),hAPP(c_List_Ofilter(tc_List_Olist(U_20463),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20463)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20465)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20463)))),c_List_Otranspose(U_20463,U_20464))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20463)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20463)),U_20464),U_20465))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20465),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20463))),U_20464)))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20463),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20463))),U_20464))) ),
    inference(variable_rename,[status(thm)],[f_4915_1]) ).

fof(f_4915_3,plain,
    ! [U_20463,U_20464,U_20465] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20463))),hAPP(c_List_Ofilter(tc_List_Olist(U_20463),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20463)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20465)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20463)))),c_List_Otranspose(U_20463,U_20464))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20463)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20463)),U_20464),U_20465))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20465),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20463))),U_20464)))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20463),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20463))),U_20464))) ),
    inference(definitional_conversion,[status(esa)],[f_4915_2]) ).

cnf(f_4915_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20463))),hAPP(c_List_Ofilter(tc_List_Olist(U_20463),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20463)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20465)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20463)))),c_List_Otranspose(U_20463,U_20464))) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20463)),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20463)),U_20464),U_20465))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20465),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20463))),U_20464)))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20463),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20463))),U_20464))) ),
    inference(clausify,[status(thm)],[f_4915_3]) ).

fof(f_4916_1,plain,
    ! [V_xss_2,T_b] : c_List_Oconcat(tc_List_Olist(T_b),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(T_b)),T_b,c_List_Olist_ONil(tc_List_Olist(T_b)),hAPP(c_COMBK(tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),T_b),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b)),tc_List_Olist(tc_List_Olist(T_b))),c_List_Olist_OCons(tc_List_Olist(T_b))),c_List_Olist_ONil(tc_List_Olist(T_b)))))),V_xss_2)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Otl(T_b)),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b)))),V_xss_2)),
    inference(fof_nnf,[status(thm)],[fact_transpose__aux__filter__tail]) ).

fof(f_4916_2,plain,
    ! [U_20467,U_20466] : c_List_Oconcat(tc_List_Olist(U_20466),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20466),tc_List_Olist(tc_List_Olist(U_20466))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20466)),U_20466,c_List_Olist_ONil(tc_List_Olist(U_20466)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20466),tc_List_Olist(tc_List_Olist(U_20466))),U_20466),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20466),tc_List_Olist(tc_List_Olist(U_20466)),tc_List_Olist(tc_List_Olist(U_20466))),c_List_Olist_OCons(tc_List_Olist(U_20466))),c_List_Olist_ONil(tc_List_Olist(U_20466)))))),U_20467)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20466),tc_List_Olist(U_20466)),c_List_Otl(U_20466)),hAPP(c_List_Ofilter(tc_List_Olist(U_20466),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20466)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20466),tc_List_Olist(U_20466),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20466)))),U_20467)),
    inference(variable_rename,[status(thm)],[f_4916_1]) ).

fof(f_4916_3,plain,
    ! [U_20466,U_20467] : c_List_Oconcat(tc_List_Olist(U_20466),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20466),tc_List_Olist(tc_List_Olist(U_20466))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20466)),U_20466,c_List_Olist_ONil(tc_List_Olist(U_20466)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20466),tc_List_Olist(tc_List_Olist(U_20466))),U_20466),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20466),tc_List_Olist(tc_List_Olist(U_20466)),tc_List_Olist(tc_List_Olist(U_20466))),c_List_Olist_OCons(tc_List_Olist(U_20466))),c_List_Olist_ONil(tc_List_Olist(U_20466)))))),U_20467)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20466),tc_List_Olist(U_20466)),c_List_Otl(U_20466)),hAPP(c_List_Ofilter(tc_List_Olist(U_20466),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20466)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20466),tc_List_Olist(U_20466),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20466)))),U_20467)),
    inference(definitional_conversion,[status(esa)],[f_4916_2]) ).

cnf(f_4916_4,plain,
    c_List_Oconcat(tc_List_Olist(U_20466),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20466),tc_List_Olist(tc_List_Olist(U_20466))),c_List_Olist_Olist__case(tc_List_Olist(tc_List_Olist(U_20466)),U_20466,c_List_Olist_ONil(tc_List_Olist(U_20466)),hAPP(c_COMBK(tc_fun(tc_List_Olist(U_20466),tc_List_Olist(tc_List_Olist(U_20466))),U_20466),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20466),tc_List_Olist(tc_List_Olist(U_20466)),tc_List_Olist(tc_List_Olist(U_20466))),c_List_Olist_OCons(tc_List_Olist(U_20466))),c_List_Olist_ONil(tc_List_Olist(U_20466)))))),U_20467)) = hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20466),tc_List_Olist(U_20466)),c_List_Otl(U_20466)),hAPP(c_List_Ofilter(tc_List_Olist(U_20466),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20466)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20466),tc_List_Olist(U_20466),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20466)))),U_20467)),
    inference(clausify,[status(thm)],[f_4916_3]) ).

fof(f_4917_1,plain,
    ! [V_j_2,V_i_2,V_xs_2,T_b] :
      ( hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),c_List_Otranspose(T_b,V_xs_2)),V_i_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),hAPP(hAPP(c_List_Onth(tc_List_Olist(T_b)),V_xs_2),V_j_2)),V_i_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),hAPP(c_List_Ofilter(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(T_b)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2)),c_Nat_Osize__class_Osize(tc_List_Olist(T_b)))),V_xs_2))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_b))),c_List_Otranspose(T_b,V_xs_2))))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__nth__transpose__sorted]) ).

fof(f_4917_2,plain,
    ! [U_20471,U_20470,U_20469,U_20468] :
      ( hAPP(hAPP(c_List_Onth(U_20468),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20468)),c_List_Otranspose(U_20468,U_20469)),U_20470)),U_20471) = hAPP(hAPP(c_List_Onth(U_20468),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20468)),U_20469),U_20471)),U_20470)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20471),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20468))),hAPP(c_List_Ofilter(tc_List_Olist(U_20468),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20468)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20470)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20468)))),U_20469))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20470),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20468))),c_List_Otranspose(U_20468,U_20469))))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20468),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20468))),U_20469))) ),
    inference(variable_rename,[status(thm)],[f_4917_1]) ).

fof(f_4917_3,plain,
    ! [U_20468,U_20469,U_20470,U_20471] :
      ( hAPP(hAPP(c_List_Onth(U_20468),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20468)),c_List_Otranspose(U_20468,U_20469)),U_20470)),U_20471) = hAPP(hAPP(c_List_Onth(U_20468),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20468)),U_20469),U_20471)),U_20470)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20471),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20468))),hAPP(c_List_Ofilter(tc_List_Olist(U_20468),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20468)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20470)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20468)))),U_20469))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20470),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20468))),c_List_Otranspose(U_20468,U_20469))))
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20468),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20468))),U_20469))) ),
    inference(definitional_conversion,[status(esa)],[f_4917_2]) ).

cnf(f_4917_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_20468),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20468)),c_List_Otranspose(U_20468,U_20469)),U_20470)),U_20471) = hAPP(hAPP(c_List_Onth(U_20468),hAPP(hAPP(c_List_Onth(tc_List_Olist(U_20468)),U_20469),U_20471)),U_20470)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20471),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20468))),hAPP(c_List_Ofilter(tc_List_Olist(U_20468),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_List_Olist(U_20468)),hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20470)),c_Nat_Osize__class_Osize(tc_List_Olist(U_20468)))),U_20469))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20470),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20468))),c_List_Otranspose(U_20468,U_20469))))
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20468),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20468))),U_20469))) ),
    inference(clausify,[status(thm)],[f_4917_3]) ).

fof(f_4918_1,plain,
    ! [V_xs_2,T_b] :
      ( c_List_Otranspose(T_b,c_List_Otranspose(T_b,V_xs_2)) = c_List_OtakeWhile(tc_List_Olist(T_b),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(T_b)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(T_b))),V_xs_2)
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(T_b))),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_transpose__transpose]) ).

fof(f_4918_2,plain,
    ! [U_20473,U_20472] :
      ( c_List_Otranspose(U_20472,c_List_Otranspose(U_20472,U_20473)) = c_List_OtakeWhile(tc_List_Olist(U_20472),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20472)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20472),tc_List_Olist(U_20472),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20472))),U_20473)
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20472),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20472))),U_20473))) ),
    inference(variable_rename,[status(thm)],[f_4918_1]) ).

fof(f_4918_3,plain,
    ! [U_20473,U_20472] :
      ( c_List_Otranspose(U_20472,c_List_Otranspose(U_20472,U_20473)) = c_List_OtakeWhile(tc_List_Olist(U_20472),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20472)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20472),tc_List_Olist(U_20472),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20472))),U_20473)
      | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20472),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20472))),U_20473))) ),
    inference(definitional_conversion,[status(esa)],[f_4918_2]) ).

cnf(f_4918_4,plain,
    ( c_List_Otranspose(U_20472,c_List_Otranspose(U_20472,U_20473)) = c_List_OtakeWhile(tc_List_Olist(U_20472),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_List_Olist(U_20472)),c_fNot),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20472),tc_List_Olist(U_20472),tc_HOL_Obool),c_fequal),c_List_Olist_ONil(U_20472))),U_20473)
    | ~ c_List_Olinorder__class_Osorted(tc_Nat_Onat,hAPP(c_List_Orev(tc_Nat_Onat),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20472),tc_Nat_Onat),c_Nat_Osize__class_Osize(tc_List_Olist(U_20472))),U_20473))) ),
    inference(clausify,[status(thm)],[f_4918_3]) ).

fof(f_4919_1,plain,
    c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__list__functions_I2_J]) ).

fof(f_4919_2,plain,
    c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
    inference(definitional_conversion,[status(esa)],[f_4919_1]) ).

cnf(f_4919_3,plain,
    c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)),
    inference(clausify,[status(thm)],[f_4919_2]) ).

fof(f_4920_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OtakeWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__map]) ).

fof(f_4920_2,plain,
    ! [U_20478,U_20477,U_20476,U_20475,U_20474] : c_List_OtakeWhile(U_20474,U_20475,hAPP(hAPP(c_List_Omap(U_20476,U_20474),U_20477),U_20478)) = hAPP(hAPP(c_List_Omap(U_20476,U_20474),U_20477),c_List_OtakeWhile(U_20476,hAPP(c_Fun_Ocomp(U_20474,tc_HOL_Obool,U_20476,U_20475),U_20477),U_20478)),
    inference(variable_rename,[status(thm)],[f_4920_1]) ).

fof(f_4920_3,plain,
    ! [U_20474,U_20475,U_20476,U_20477,U_20478] : c_List_OtakeWhile(U_20474,U_20475,hAPP(hAPP(c_List_Omap(U_20476,U_20474),U_20477),U_20478)) = hAPP(hAPP(c_List_Omap(U_20476,U_20474),U_20477),c_List_OtakeWhile(U_20476,hAPP(c_Fun_Ocomp(U_20474,tc_HOL_Obool,U_20476,U_20475),U_20477),U_20478)),
    inference(definitional_conversion,[status(esa)],[f_4920_2]) ).

cnf(f_4920_4,plain,
    c_List_OtakeWhile(U_20474,U_20475,hAPP(hAPP(c_List_Omap(U_20476,U_20474),U_20477),U_20478)) = hAPP(hAPP(c_List_Omap(U_20476,U_20474),U_20477),c_List_OtakeWhile(U_20476,hAPP(c_Fun_Ocomp(U_20474,tc_HOL_Obool,U_20476,U_20475),U_20477),U_20478)),
    inference(clausify,[status(thm)],[f_4920_3]) ).

fof(f_4921_1,plain,
    ! [V_l_2] : c_List_Oreturn__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),V_l_2),
    inference(fof_nnf,[status(thm)],[fact_return__list__def]) ).

fof(f_4921_2,plain,
    ! [U_20479] : c_List_Oreturn__list(U_20479) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),U_20479),
    inference(variable_rename,[status(thm)],[f_4921_1]) ).

fof(f_4921_3,plain,
    ! [U_20479] : c_List_Oreturn__list(U_20479) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),U_20479),
    inference(definitional_conversion,[status(esa)],[f_4921_2]) ).

cnf(f_4921_4,plain,
    c_List_Oreturn__list(U_20479) = hAPP(hAPP(c_List_Omap(tc_Int_Oint,tc_Nat_Onat),c_Int_Onat),U_20479),
    inference(clausify,[status(thm)],[f_4921_3]) ).

fof(f_4922_1,plain,
    ! [V_ys_2,V_Pa_2,V_xs_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),c_List_OtakeWhile(T_c,V_Pa_2,V_ys_2)) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_c,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Osnd(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_zip__takeWhile__snd]) ).

fof(f_4922_2,plain,
    ! [U_20484,U_20483,U_20482,U_20481,U_20480] : hAPP(hAPP(c_List_Ozip(U_20480,U_20481),U_20482),c_List_OtakeWhile(U_20481,U_20483,U_20484)) = c_List_OtakeWhile(tc_prod(U_20480,U_20481),hAPP(c_Fun_Ocomp(U_20481,tc_HOL_Obool,tc_prod(U_20480,U_20481),U_20483),c_Product__Type_Osnd(U_20480,U_20481)),hAPP(hAPP(c_List_Ozip(U_20480,U_20481),U_20482),U_20484)),
    inference(variable_rename,[status(thm)],[f_4922_1]) ).

fof(f_4922_3,plain,
    ! [U_20480,U_20481,U_20482,U_20483,U_20484] : hAPP(hAPP(c_List_Ozip(U_20480,U_20481),U_20482),c_List_OtakeWhile(U_20481,U_20483,U_20484)) = c_List_OtakeWhile(tc_prod(U_20480,U_20481),hAPP(c_Fun_Ocomp(U_20481,tc_HOL_Obool,tc_prod(U_20480,U_20481),U_20483),c_Product__Type_Osnd(U_20480,U_20481)),hAPP(hAPP(c_List_Ozip(U_20480,U_20481),U_20482),U_20484)),
    inference(definitional_conversion,[status(esa)],[f_4922_2]) ).

cnf(f_4922_4,plain,
    hAPP(hAPP(c_List_Ozip(U_20480,U_20481),U_20482),c_List_OtakeWhile(U_20481,U_20483,U_20484)) = c_List_OtakeWhile(tc_prod(U_20480,U_20481),hAPP(c_Fun_Ocomp(U_20481,tc_HOL_Obool,tc_prod(U_20480,U_20481),U_20483),c_Product__Type_Osnd(U_20480,U_20481)),hAPP(hAPP(c_List_Ozip(U_20480,U_20481),U_20482),U_20484)),
    inference(clausify,[status(thm)],[f_4922_3]) ).

fof(f_4923_1,plain,
    ! [V_ys_2,V_xs_2,V_Pa_2,T_c,T_b] : hAPP(hAPP(c_List_Ozip(T_b,T_c),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2) = c_List_OtakeWhile(tc_prod(T_b,T_c),hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,tc_prod(T_b,T_c),V_Pa_2),c_Product__Type_Ofst(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)),
    inference(fof_nnf,[status(thm)],[fact_zip__takeWhile__fst]) ).

fof(f_4923_2,plain,
    ! [U_20489,U_20488,U_20487,U_20486,U_20485] : hAPP(hAPP(c_List_Ozip(U_20485,U_20486),c_List_OtakeWhile(U_20485,U_20487,U_20488)),U_20489) = c_List_OtakeWhile(tc_prod(U_20485,U_20486),hAPP(c_Fun_Ocomp(U_20485,tc_HOL_Obool,tc_prod(U_20485,U_20486),U_20487),c_Product__Type_Ofst(U_20485,U_20486)),hAPP(hAPP(c_List_Ozip(U_20485,U_20486),U_20488),U_20489)),
    inference(variable_rename,[status(thm)],[f_4923_1]) ).

fof(f_4923_3,plain,
    ! [U_20485,U_20486,U_20487,U_20488,U_20489] : hAPP(hAPP(c_List_Ozip(U_20485,U_20486),c_List_OtakeWhile(U_20485,U_20487,U_20488)),U_20489) = c_List_OtakeWhile(tc_prod(U_20485,U_20486),hAPP(c_Fun_Ocomp(U_20485,tc_HOL_Obool,tc_prod(U_20485,U_20486),U_20487),c_Product__Type_Ofst(U_20485,U_20486)),hAPP(hAPP(c_List_Ozip(U_20485,U_20486),U_20488),U_20489)),
    inference(definitional_conversion,[status(esa)],[f_4923_2]) ).

cnf(f_4923_4,plain,
    hAPP(hAPP(c_List_Ozip(U_20485,U_20486),c_List_OtakeWhile(U_20485,U_20487,U_20488)),U_20489) = c_List_OtakeWhile(tc_prod(U_20485,U_20486),hAPP(c_Fun_Ocomp(U_20485,tc_HOL_Obool,tc_prod(U_20485,U_20486),U_20487),c_Product__Type_Ofst(U_20485,U_20486)),hAPP(hAPP(c_List_Ozip(U_20485,U_20486),U_20488),U_20489)),
    inference(clausify,[status(thm)],[f_4923_3]) ).

fof(f_4924_1,plain,
    ! [V_xs_2,V_Pa_2,V_x_2,T_b] :
      ( ( hBOOL(hAPP(V_Pa_2,V_x_2))
        & hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_set__takeWhileD]) ).

fof(f_4924_2,plain,
    ! [U_20493,U_20492,U_20491,U_20490] :
      ( ( hBOOL(hAPP(U_20492,U_20491))
        & hBOOL(hAPP(hAPP(c_member(U_20490),U_20491),hAPP(c_List_Oset(U_20490),U_20493))) )
      | ~ hBOOL(hAPP(hAPP(c_member(U_20490),U_20491),hAPP(c_List_Oset(U_20490),c_List_OtakeWhile(U_20490,U_20492,U_20493)))) ),
    inference(variable_rename,[status(thm)],[f_4924_1]) ).

fof(f_4924_3,plain,
    ( ! [U_20490,U_20491,U_20492,U_20493] :
        ( hBOOL(hAPP(U_20492,U_20491))
        | ~ sP1234(U_20490,U_20491,U_20492,U_20493) )
    & ! [U_20490,U_20491,U_20492,U_20493] :
        ( hBOOL(hAPP(hAPP(c_member(U_20490),U_20491),hAPP(c_List_Oset(U_20490),U_20493)))
        | ~ sP1234(U_20490,U_20491,U_20492,U_20493) )
    & ! [U_20490,U_20491,U_20492,U_20493] :
        ( sP1234(U_20490,U_20491,U_20492,U_20493)
        | ~ hBOOL(hAPP(hAPP(c_member(U_20490),U_20491),hAPP(c_List_Oset(U_20490),c_List_OtakeWhile(U_20490,U_20492,U_20493)))) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1234])],[f_4924_2]) ).

cnf(f_4924_4,plain,
    ( sP1234(U_20490,U_20491,U_20492,U_20493)
    | ~ hBOOL(hAPP(hAPP(c_member(U_20490),U_20491),hAPP(c_List_Oset(U_20490),c_List_OtakeWhile(U_20490,U_20492,U_20493)))) ),
    inference(clausify,[status(thm)],[f_4924_3]) ).

cnf(f_4924_5,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20490),U_20491),hAPP(c_List_Oset(U_20490),U_20493)))
    | ~ sP1234(U_20490,U_20491,U_20492,U_20493) ),
    inference(clausify,[status(thm)],[f_4924_3]) ).

cnf(f_4924_6,plain,
    ( hBOOL(hAPP(U_20492,U_20491))
    | ~ sP1234(U_20490,U_20491,U_20492,U_20493) ),
    inference(clausify,[status(thm)],[f_4924_3]) ).

fof(f_4925_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ( c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = V_xs_2
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) != V_xs_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__eq__all__conv]) ).

fof(f_4925_2,plain,
    ! [U_20498,U_20497,U_20496] :
      ( ( c_List_OtakeWhile(U_20496,U_20497,U_20498) = U_20498
        | ? [U_20495] :
            ( ~ hBOOL(hAPP(U_20497,U_20495))
            & hBOOL(hAPP(hAPP(c_member(U_20496),U_20495),hAPP(c_List_Oset(U_20496),U_20498))) ) )
      & ( ! [U_20494] :
            ( hBOOL(hAPP(U_20497,U_20494))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20496),U_20494),hAPP(c_List_Oset(U_20496),U_20498))) )
        | c_List_OtakeWhile(U_20496,U_20497,U_20498) != U_20498 ) ),
    inference(variable_rename,[status(thm)],[f_4925_1]) ).

fof(f_4925_3,plain,
    ( ! [U_20504,U_20502,U_20500] :
        ( c_List_OtakeWhile(U_20500,U_20502,U_20504) = U_20504
        | ? [U_20495] :
            ( ~ hBOOL(hAPP(U_20502,U_20495))
            & hBOOL(hAPP(hAPP(c_member(U_20500),U_20495),hAPP(c_List_Oset(U_20500),U_20504))) ) )
    & ! [U_20503,U_20501,U_20499] :
        ( ! [U_20494] :
            ( hBOOL(hAPP(U_20501,U_20494))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20499),U_20494),hAPP(c_List_Oset(U_20499),U_20503))) )
        | c_List_OtakeWhile(U_20499,U_20501,U_20503) != U_20503 ) ),
    inference(miniscope,[status(thm)],[f_4925_2]) ).

fof(f_4925_4,plain,
    ( ! [U_20504,U_20502,U_20500] :
        ( c_List_OtakeWhile(U_20500,U_20502,U_20504) = U_20504
        | ( ~ hBOOL(hAPP(U_20502,sK503(U_20504,U_20502,U_20500)))
          & hBOOL(hAPP(hAPP(c_member(U_20500),sK503(U_20504,U_20502,U_20500)),hAPP(c_List_Oset(U_20500),U_20504))) ) )
    & ! [U_20503,U_20501,U_20499] :
        ( ! [U_20494] :
            ( hBOOL(hAPP(U_20501,U_20494))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20499),U_20494),hAPP(c_List_Oset(U_20499),U_20503))) )
        | c_List_OtakeWhile(U_20499,U_20501,U_20503) != U_20503 ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK503]),skolemize(U_20495,sK503(U_20504,U_20502,U_20500))],[f_4925_3]) ).

fof(f_4925_5,plain,
    ( ! [U_20502,U_20500,U_20504] :
        ( ~ hBOOL(hAPP(U_20502,sK503(U_20504,U_20502,U_20500)))
        | ~ sP1235(U_20502,U_20500,U_20504) )
    & ! [U_20502,U_20500,U_20504] :
        ( hBOOL(hAPP(hAPP(c_member(U_20500),sK503(U_20504,U_20502,U_20500)),hAPP(c_List_Oset(U_20500),U_20504)))
        | ~ sP1235(U_20502,U_20500,U_20504) )
    & ! [U_20502,U_20500,U_20504] :
        ( c_List_OtakeWhile(U_20500,U_20502,U_20504) = U_20504
        | sP1235(U_20502,U_20500,U_20504) )
    & ! [U_20494,U_20499,U_20503,U_20501] :
        ( hBOOL(hAPP(U_20501,U_20494))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20499),U_20494),hAPP(c_List_Oset(U_20499),U_20503)))
        | c_List_OtakeWhile(U_20499,U_20501,U_20503) != U_20503 ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1235])],[f_4925_4]) ).

cnf(f_4925_6,plain,
    ( hBOOL(hAPP(U_20501,U_20494))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20499),U_20494),hAPP(c_List_Oset(U_20499),U_20503)))
    | c_List_OtakeWhile(U_20499,U_20501,U_20503) != U_20503 ),
    inference(clausify,[status(thm)],[f_4925_5]) ).

cnf(f_4925_7,plain,
    ( c_List_OtakeWhile(U_20500,U_20502,U_20504) = U_20504
    | sP1235(U_20502,U_20500,U_20504) ),
    inference(clausify,[status(thm)],[f_4925_5]) ).

cnf(f_4925_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20500),sK503(U_20504,U_20502,U_20500)),hAPP(c_List_Oset(U_20500),U_20504)))
    | ~ sP1235(U_20502,U_20500,U_20504) ),
    inference(clausify,[status(thm)],[f_4925_5]) ).

cnf(f_4925_9,plain,
    ( ~ hBOOL(hAPP(U_20502,sK503(U_20504,U_20502,U_20500)))
    | ~ sP1235(U_20502,U_20500,U_20504) ),
    inference(clausify,[status(thm)],[f_4925_5]) ).

fof(f_4926_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_length__takeWhile__le]) ).

fof(f_4926_2,plain,
    ! [U_20507,U_20506,U_20505] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20505)),c_List_OtakeWhile(U_20505,U_20506,U_20507))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20505)),U_20507))),
    inference(variable_rename,[status(thm)],[f_4926_1]) ).

fof(f_4926_3,plain,
    ! [U_20505,U_20506,U_20507] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20505)),c_List_OtakeWhile(U_20505,U_20506,U_20507))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20505)),U_20507))),
    inference(definitional_conversion,[status(esa)],[f_4926_2]) ).

cnf(f_4926_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20505)),c_List_OtakeWhile(U_20505,U_20506,U_20507))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20505)),U_20507))),
    inference(clausify,[status(thm)],[f_4926_3]) ).

fof(f_4927_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__eq__take]) ).

fof(f_4927_2,plain,
    ! [U_20510,U_20509,U_20508] : c_List_OtakeWhile(U_20508,U_20509,U_20510) = hAPP(hAPP(c_List_Otake(U_20508),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20508)),c_List_OtakeWhile(U_20508,U_20509,U_20510))),U_20510),
    inference(variable_rename,[status(thm)],[f_4927_1]) ).

fof(f_4927_3,plain,
    ! [U_20508,U_20509,U_20510] : c_List_OtakeWhile(U_20508,U_20509,U_20510) = hAPP(hAPP(c_List_Otake(U_20508),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20508)),c_List_OtakeWhile(U_20508,U_20509,U_20510))),U_20510),
    inference(definitional_conversion,[status(esa)],[f_4927_2]) ).

cnf(f_4927_4,plain,
    c_List_OtakeWhile(U_20508,U_20509,U_20510) = hAPP(hAPP(c_List_Otake(U_20508),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20508)),c_List_OtakeWhile(U_20508,U_20509,U_20510))),U_20510),
    inference(clausify,[status(thm)],[f_4927_3]) ).

fof(f_4928_1,plain,
    ! [V_Pa_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__takeWhile]) ).

fof(f_4928_2,plain,
    ! [U_20513,U_20512,U_20511] :
      ( hBOOL(hAPP(c_List_Odistinct(U_20511),c_List_OtakeWhile(U_20511,U_20513,U_20512)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20511),U_20512)) ),
    inference(variable_rename,[status(thm)],[f_4928_1]) ).

fof(f_4928_3,plain,
    ! [U_20511,U_20512,U_20513] :
      ( hBOOL(hAPP(c_List_Odistinct(U_20511),c_List_OtakeWhile(U_20511,U_20513,U_20512)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20511),U_20512)) ),
    inference(definitional_conversion,[status(esa)],[f_4928_2]) ).

cnf(f_4928_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_20511),c_List_OtakeWhile(U_20511,U_20513,U_20512)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20511),U_20512)) ),
    inference(clausify,[status(thm)],[f_4928_3]) ).

fof(f_4929_1,plain,
    ! [V_l_2,V_xs_2,T_b,V_x_2,V_Pa_2] :
      ( c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_l_2))) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)
      | hBOOL(hAPP(V_Pa_2,V_x_2)) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__tail]) ).

fof(f_4929_2,plain,
    ! [U_20518,U_20517,U_20516,U_20515,U_20514] :
      ( c_List_OtakeWhile(U_20516,U_20514,hAPP(hAPP(c_List_Oappend(U_20516),U_20517),hAPP(hAPP(c_List_Olist_OCons(U_20516),U_20515),U_20518))) = c_List_OtakeWhile(U_20516,U_20514,U_20517)
      | hBOOL(hAPP(U_20514,U_20515)) ),
    inference(variable_rename,[status(thm)],[f_4929_1]) ).

fof(f_4929_3,plain,
    ! [U_20515,U_20514,U_20516,U_20517,U_20518] :
      ( c_List_OtakeWhile(U_20516,U_20514,hAPP(hAPP(c_List_Oappend(U_20516),U_20517),hAPP(hAPP(c_List_Olist_OCons(U_20516),U_20515),U_20518))) = c_List_OtakeWhile(U_20516,U_20514,U_20517)
      | hBOOL(hAPP(U_20514,U_20515)) ),
    inference(definitional_conversion,[status(esa)],[f_4929_2]) ).

cnf(f_4929_4,plain,
    ( c_List_OtakeWhile(U_20516,U_20514,hAPP(hAPP(c_List_Oappend(U_20516),U_20517),hAPP(hAPP(c_List_Olist_OCons(U_20516),U_20515),U_20518))) = c_List_OtakeWhile(U_20516,U_20514,U_20517)
    | hBOOL(hAPP(U_20514,U_20515)) ),
    inference(clausify,[status(thm)],[f_4929_3]) ).

fof(f_4930_1,plain,
    ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
      ( ( c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Olist_ONil(T_b)
        | hBOOL(hAPP(V_Pa_2,V_x_2)) )
      & ( c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))
        | ~ hBOOL(hAPP(V_Pa_2,V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile_Osimps_I2_J]) ).

fof(f_4930_2,plain,
    ! [U_20522,U_20521,U_20520,U_20519] :
      ( ( c_List_OtakeWhile(U_20521,U_20519,hAPP(hAPP(c_List_Olist_OCons(U_20521),U_20520),U_20522)) = c_List_Olist_ONil(U_20521)
        | hBOOL(hAPP(U_20519,U_20520)) )
      & ( c_List_OtakeWhile(U_20521,U_20519,hAPP(hAPP(c_List_Olist_OCons(U_20521),U_20520),U_20522)) = hAPP(hAPP(c_List_Olist_OCons(U_20521),U_20520),c_List_OtakeWhile(U_20521,U_20519,U_20522))
        | ~ hBOOL(hAPP(U_20519,U_20520)) ) ),
    inference(variable_rename,[status(thm)],[f_4930_1]) ).

fof(f_4930_3,plain,
    ( ! [U_20530,U_20528,U_20526,U_20524] :
        ( c_List_OtakeWhile(U_20528,U_20524,hAPP(hAPP(c_List_Olist_OCons(U_20528),U_20526),U_20530)) = c_List_Olist_ONil(U_20528)
        | hBOOL(hAPP(U_20524,U_20526)) )
    & ! [U_20529,U_20527,U_20525,U_20523] :
        ( c_List_OtakeWhile(U_20527,U_20523,hAPP(hAPP(c_List_Olist_OCons(U_20527),U_20525),U_20529)) = hAPP(hAPP(c_List_Olist_OCons(U_20527),U_20525),c_List_OtakeWhile(U_20527,U_20523,U_20529))
        | ~ hBOOL(hAPP(U_20523,U_20525)) ) ),
    inference(miniscope,[status(thm)],[f_4930_2]) ).

fof(f_4930_4,plain,
    ( ! [U_20524,U_20526,U_20528,U_20530] :
        ( c_List_OtakeWhile(U_20528,U_20524,hAPP(hAPP(c_List_Olist_OCons(U_20528),U_20526),U_20530)) = c_List_Olist_ONil(U_20528)
        | hBOOL(hAPP(U_20524,U_20526)) )
    & ! [U_20529,U_20523,U_20525,U_20527] :
        ( c_List_OtakeWhile(U_20527,U_20523,hAPP(hAPP(c_List_Olist_OCons(U_20527),U_20525),U_20529)) = hAPP(hAPP(c_List_Olist_OCons(U_20527),U_20525),c_List_OtakeWhile(U_20527,U_20523,U_20529))
        | ~ hBOOL(hAPP(U_20523,U_20525)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4930_3]) ).

cnf(f_4930_5,plain,
    ( c_List_OtakeWhile(U_20527,U_20523,hAPP(hAPP(c_List_Olist_OCons(U_20527),U_20525),U_20529)) = hAPP(hAPP(c_List_Olist_OCons(U_20527),U_20525),c_List_OtakeWhile(U_20527,U_20523,U_20529))
    | ~ hBOOL(hAPP(U_20523,U_20525)) ),
    inference(clausify,[status(thm)],[f_4930_4]) ).

cnf(f_4930_6,plain,
    ( c_List_OtakeWhile(U_20528,U_20524,hAPP(hAPP(c_List_Olist_OCons(U_20528),U_20526),U_20530)) = c_List_Olist_ONil(U_20528)
    | hBOOL(hAPP(U_20524,U_20526)) ),
    inference(clausify,[status(thm)],[f_4930_4]) ).

fof(f_4931_1,plain,
    ! [V_Pa_2,V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))
      | ~ c_List_Olinorder__class_Osorted(T_b,V_xs_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__takeWhile]) ).

fof(f_4931_2,plain,
    ! [U_20533,U_20532,U_20531] :
      ( c_List_Olinorder__class_Osorted(U_20531,c_List_OtakeWhile(U_20531,U_20533,U_20532))
      | ~ c_List_Olinorder__class_Osorted(U_20531,U_20532)
      | ~ class_Orderings_Olinorder(U_20531) ),
    inference(variable_rename,[status(thm)],[f_4931_1]) ).

fof(f_4931_3,plain,
    ! [U_20531,U_20533,U_20532] :
      ( c_List_Olinorder__class_Osorted(U_20531,c_List_OtakeWhile(U_20531,U_20533,U_20532))
      | ~ c_List_Olinorder__class_Osorted(U_20531,U_20532)
      | ~ class_Orderings_Olinorder(U_20531) ),
    inference(definitional_conversion,[status(esa)],[f_4931_2]) ).

cnf(f_4931_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20531,c_List_OtakeWhile(U_20531,U_20533,U_20532))
    | ~ c_List_Olinorder__class_Osorted(U_20531,U_20532)
    | ~ class_Orderings_Olinorder(U_20531) ),
    inference(clausify,[status(thm)],[f_4931_3]) ).

fof(f_4932_1,plain,
    ! [V_Pa_2,T_b] : c_List_OtakeWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
    inference(fof_nnf,[status(thm)],[fact_takeWhile_Osimps_I1_J]) ).

fof(f_4932_2,plain,
    ! [U_20535,U_20534] : c_List_OtakeWhile(U_20534,U_20535,c_List_Olist_ONil(U_20534)) = c_List_Olist_ONil(U_20534),
    inference(variable_rename,[status(thm)],[f_4932_1]) ).

fof(f_4932_3,plain,
    ! [U_20535,U_20534] : c_List_OtakeWhile(U_20534,U_20535,c_List_Olist_ONil(U_20534)) = c_List_Olist_ONil(U_20534),
    inference(definitional_conversion,[status(esa)],[f_4932_2]) ).

cnf(f_4932_4,plain,
    c_List_OtakeWhile(U_20534,U_20535,c_List_Olist_ONil(U_20534)) = c_List_Olist_ONil(U_20534),
    inference(clausify,[status(thm)],[f_4932_3]) ).

fof(f_4933_1,plain,
    ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
      ( c_List_OtakeWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)
      | hBOOL(hAPP(V_Pa_2,V_x_2))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__append1]) ).

fof(f_4933_2,plain,
    ! [U_20540,U_20539,U_20538,U_20537,U_20536] :
      ( c_List_OtakeWhile(U_20536,U_20539,hAPP(hAPP(c_List_Oappend(U_20536),U_20538),U_20540)) = c_List_OtakeWhile(U_20536,U_20539,U_20538)
      | hBOOL(hAPP(U_20539,U_20537))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20536),U_20537),hAPP(c_List_Oset(U_20536),U_20538))) ),
    inference(variable_rename,[status(thm)],[f_4933_1]) ).

fof(f_4933_3,plain,
    ! [U_20536,U_20537,U_20538,U_20539,U_20540] :
      ( c_List_OtakeWhile(U_20536,U_20539,hAPP(hAPP(c_List_Oappend(U_20536),U_20538),U_20540)) = c_List_OtakeWhile(U_20536,U_20539,U_20538)
      | hBOOL(hAPP(U_20539,U_20537))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20536),U_20537),hAPP(c_List_Oset(U_20536),U_20538))) ),
    inference(definitional_conversion,[status(esa)],[f_4933_2]) ).

cnf(f_4933_4,plain,
    ( c_List_OtakeWhile(U_20536,U_20539,hAPP(hAPP(c_List_Oappend(U_20536),U_20538),U_20540)) = c_List_OtakeWhile(U_20536,U_20539,U_20538)
    | hBOOL(hAPP(U_20539,U_20537))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20536),U_20537),hAPP(c_List_Oset(U_20536),U_20538))) ),
    inference(clausify,[status(thm)],[f_4933_3]) ).

fof(f_4934_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ~ hBOOL(hAPP(V_Pa_2,hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))) ),
    inference(fof_nnf,[status(thm)],[fact_nth__length__takeWhile]) ).

fof(f_4934_2,plain,
    ! [U_20543,U_20542,U_20541] :
      ( ~ hBOOL(hAPP(U_20542,hAPP(hAPP(c_List_Onth(U_20541),U_20543),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20541)),c_List_OtakeWhile(U_20541,U_20542,U_20543)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20541)),c_List_OtakeWhile(U_20541,U_20542,U_20543))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20541)),U_20543))) ),
    inference(variable_rename,[status(thm)],[f_4934_1]) ).

fof(f_4934_3,plain,
    ! [U_20541,U_20542,U_20543] :
      ( ~ hBOOL(hAPP(U_20542,hAPP(hAPP(c_List_Onth(U_20541),U_20543),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20541)),c_List_OtakeWhile(U_20541,U_20542,U_20543)))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20541)),c_List_OtakeWhile(U_20541,U_20542,U_20543))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20541)),U_20543))) ),
    inference(definitional_conversion,[status(esa)],[f_4934_2]) ).

cnf(f_4934_4,plain,
    ( ~ hBOOL(hAPP(U_20542,hAPP(hAPP(c_List_Onth(U_20541),U_20543),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20541)),c_List_OtakeWhile(U_20541,U_20542,U_20543)))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20541)),c_List_OtakeWhile(U_20541,U_20542,U_20543))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20541)),U_20543))) ),
    inference(clausify,[status(thm)],[f_4934_3]) ).

fof(f_4935_1,plain,
    ! [V_xs_2,V_Pa_2,T_b,V_j_2] :
      ( hAPP(hAPP(c_List_Onth(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),V_j_2)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__nth]) ).

fof(f_4935_2,plain,
    ! [U_20547,U_20546,U_20545,U_20544] :
      ( hAPP(hAPP(c_List_Onth(U_20545),c_List_OtakeWhile(U_20545,U_20546,U_20547)),U_20544) = hAPP(hAPP(c_List_Onth(U_20545),U_20547),U_20544)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20544),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20545)),c_List_OtakeWhile(U_20545,U_20546,U_20547)))) ),
    inference(variable_rename,[status(thm)],[f_4935_1]) ).

fof(f_4935_3,plain,
    ! [U_20545,U_20544,U_20546,U_20547] :
      ( hAPP(hAPP(c_List_Onth(U_20545),c_List_OtakeWhile(U_20545,U_20546,U_20547)),U_20544) = hAPP(hAPP(c_List_Onth(U_20545),U_20547),U_20544)
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20544),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20545)),c_List_OtakeWhile(U_20545,U_20546,U_20547)))) ),
    inference(definitional_conversion,[status(esa)],[f_4935_2]) ).

cnf(f_4935_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_20545),c_List_OtakeWhile(U_20545,U_20546,U_20547)),U_20544) = hAPP(hAPP(c_List_Onth(U_20545),U_20547),U_20544)
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20544),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20545)),c_List_OtakeWhile(U_20545,U_20546,U_20547)))) ),
    inference(clausify,[status(thm)],[f_4935_3]) ).

fof(f_4936_1,plain,
    ! [V_ys_2,V_xs_2,V_m_2,T_c,T_b] : c_Map_Omap__upds(T_b,T_c,V_m_2,V_xs_2,V_ys_2) = c_Map_Omap__add(T_b,T_c,V_m_2,c_Map_Omap__of(T_b,T_c,hAPP(c_List_Orev(tc_prod(T_b,T_c)),hAPP(hAPP(c_List_Ozip(T_b,T_c),V_xs_2),V_ys_2)))),
    inference(fof_nnf,[status(thm)],[fact_map__upds__def]) ).

fof(f_4936_2,plain,
    ! [U_20552,U_20551,U_20550,U_20549,U_20548] : c_Map_Omap__upds(U_20548,U_20549,U_20550,U_20551,U_20552) = c_Map_Omap__add(U_20548,U_20549,U_20550,c_Map_Omap__of(U_20548,U_20549,hAPP(c_List_Orev(tc_prod(U_20548,U_20549)),hAPP(hAPP(c_List_Ozip(U_20548,U_20549),U_20551),U_20552)))),
    inference(variable_rename,[status(thm)],[f_4936_1]) ).

fof(f_4936_3,plain,
    ! [U_20551,U_20552,U_20549,U_20548,U_20550] : c_Map_Omap__upds(U_20548,U_20549,U_20550,U_20551,U_20552) = c_Map_Omap__add(U_20548,U_20549,U_20550,c_Map_Omap__of(U_20548,U_20549,hAPP(c_List_Orev(tc_prod(U_20548,U_20549)),hAPP(hAPP(c_List_Ozip(U_20548,U_20549),U_20551),U_20552)))),
    inference(definitional_conversion,[status(esa)],[f_4936_2]) ).

cnf(f_4936_4,plain,
    c_Map_Omap__upds(U_20548,U_20549,U_20550,U_20551,U_20552) = c_Map_Omap__add(U_20548,U_20549,U_20550,c_Map_Omap__of(U_20548,U_20549,hAPP(c_List_Orev(tc_prod(U_20548,U_20549)),hAPP(hAPP(c_List_Ozip(U_20548,U_20549),U_20551),U_20552)))),
    inference(clausify,[status(thm)],[f_4936_3]) ).

fof(f_4937_1,plain,
    ! [T_b,V_xs_2] :
      ( c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),c_List_Olast(T_b,V_xs_2))),V_xs_2) = c_List_Obutlast(T_b,V_xs_2)
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
      | V_xs_2 = c_List_Olist_ONil(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__not__last]) ).

fof(f_4937_2,plain,
    ! [U_20554,U_20553] :
      ( c_List_OtakeWhile(U_20554,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20554),c_fNot),hAPP(hAPP(c_COMBC(U_20554,U_20554,tc_HOL_Obool),c_fequal),c_List_Olast(U_20554,U_20553))),U_20553) = c_List_Obutlast(U_20554,U_20553)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20554),U_20553))
      | U_20553 = c_List_Olist_ONil(U_20554) ),
    inference(variable_rename,[status(thm)],[f_4937_1]) ).

fof(f_4937_3,plain,
    ! [U_20554,U_20553] :
      ( c_List_OtakeWhile(U_20554,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20554),c_fNot),hAPP(hAPP(c_COMBC(U_20554,U_20554,tc_HOL_Obool),c_fequal),c_List_Olast(U_20554,U_20553))),U_20553) = c_List_Obutlast(U_20554,U_20553)
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20554),U_20553))
      | U_20553 = c_List_Olist_ONil(U_20554) ),
    inference(definitional_conversion,[status(esa)],[f_4937_2]) ).

cnf(f_4937_4,plain,
    ( c_List_OtakeWhile(U_20554,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20554),c_fNot),hAPP(hAPP(c_COMBC(U_20554,U_20554,tc_HOL_Obool),c_fequal),c_List_Olast(U_20554,U_20553))),U_20553) = c_List_Obutlast(U_20554,U_20553)
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20554),U_20553))
    | U_20553 = c_List_Olist_ONil(U_20554) ),
    inference(clausify,[status(thm)],[f_4937_3]) ).

fof(f_4938_1,plain,
    ! [V_t_2,V_xs_2,V_f_2,T_c,T_b] :
      ( hAPP(c_List_Ofilter(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2)),V_xs_2) = c_List_OtakeWhile(T_c,hAPP(hAPP(c_COMBB(T_b,tc_HOL_Obool,T_c),hAPP(c_Orderings_Oord__class_Oless(T_b),V_t_2)),V_f_2),V_xs_2)
      | ~ c_List_Olinorder__class_Osorted(T_b,hAPP(c_List_Orev(T_b),hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)))
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_filter__equals__takeWhile__sorted__rev]) ).

fof(f_4938_2,plain,
    ! [U_20559,U_20558,U_20557,U_20556,U_20555] :
      ( hAPP(c_List_Ofilter(U_20556,hAPP(hAPP(c_COMBB(U_20555,tc_HOL_Obool,U_20556),hAPP(c_Orderings_Oord__class_Oless(U_20555),U_20559)),U_20557)),U_20558) = c_List_OtakeWhile(U_20556,hAPP(hAPP(c_COMBB(U_20555,tc_HOL_Obool,U_20556),hAPP(c_Orderings_Oord__class_Oless(U_20555),U_20559)),U_20557),U_20558)
      | ~ c_List_Olinorder__class_Osorted(U_20555,hAPP(c_List_Orev(U_20555),hAPP(hAPP(c_List_Omap(U_20556,U_20555),U_20557),U_20558)))
      | ~ class_Orderings_Olinorder(U_20555) ),
    inference(variable_rename,[status(thm)],[f_4938_1]) ).

fof(f_4938_3,plain,
    ! [U_20555,U_20556,U_20557,U_20558,U_20559] :
      ( hAPP(c_List_Ofilter(U_20556,hAPP(hAPP(c_COMBB(U_20555,tc_HOL_Obool,U_20556),hAPP(c_Orderings_Oord__class_Oless(U_20555),U_20559)),U_20557)),U_20558) = c_List_OtakeWhile(U_20556,hAPP(hAPP(c_COMBB(U_20555,tc_HOL_Obool,U_20556),hAPP(c_Orderings_Oord__class_Oless(U_20555),U_20559)),U_20557),U_20558)
      | ~ c_List_Olinorder__class_Osorted(U_20555,hAPP(c_List_Orev(U_20555),hAPP(hAPP(c_List_Omap(U_20556,U_20555),U_20557),U_20558)))
      | ~ class_Orderings_Olinorder(U_20555) ),
    inference(definitional_conversion,[status(esa)],[f_4938_2]) ).

cnf(f_4938_4,plain,
    ( hAPP(c_List_Ofilter(U_20556,hAPP(hAPP(c_COMBB(U_20555,tc_HOL_Obool,U_20556),hAPP(c_Orderings_Oord__class_Oless(U_20555),U_20559)),U_20557)),U_20558) = c_List_OtakeWhile(U_20556,hAPP(hAPP(c_COMBB(U_20555,tc_HOL_Obool,U_20556),hAPP(c_Orderings_Oord__class_Oless(U_20555),U_20559)),U_20557),U_20558)
    | ~ c_List_Olinorder__class_Osorted(U_20555,hAPP(c_List_Orev(U_20555),hAPP(hAPP(c_List_Omap(U_20556,U_20555),U_20557),U_20558)))
    | ~ class_Orderings_Olinorder(U_20555) ),
    inference(clausify,[status(thm)],[f_4938_3]) ).

fof(f_4939_1,plain,
    ! [V_l] :
      ( c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l
      | ~ c_List_Onat__list(V_l) ),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__list__return__embed]) ).

fof(f_4939_2,plain,
    ! [U_20560] :
      ( c_List_Oembed__list(c_List_Oreturn__list(U_20560)) = U_20560
      | ~ c_List_Onat__list(U_20560) ),
    inference(variable_rename,[status(thm)],[f_4939_1]) ).

fof(f_4939_3,plain,
    ! [U_20560] :
      ( c_List_Oembed__list(c_List_Oreturn__list(U_20560)) = U_20560
      | ~ c_List_Onat__list(U_20560) ),
    inference(definitional_conversion,[status(esa)],[f_4939_2]) ).

cnf(f_4939_4,plain,
    ( c_List_Oembed__list(c_List_Oreturn__list(U_20560)) = U_20560
    | ~ c_List_Onat__list(U_20560) ),
    inference(clausify,[status(thm)],[f_4939_3]) ).

fof(f_4940_1,plain,
    ! [V_xss_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,c_List_Oconcat(T_b,V_xss_2))) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(T_b)),V_xss_2)),c_List_Oset(T_b))),
    inference(fof_nnf,[status(thm)],[fact_length__remdups__concat]) ).

fof(f_4940_2,plain,
    ! [U_20562,U_20561] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20561)),c_List_Oremdups(U_20561,c_List_Oconcat(U_20561,U_20562))) = hAPP(c_Finite__Set_Ocard(U_20561),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_20561),tc_fun(U_20561,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_20561)),U_20562)),c_List_Oset(U_20561))),
    inference(variable_rename,[status(thm)],[f_4940_1]) ).

fof(f_4940_3,plain,
    ! [U_20561,U_20562] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20561)),c_List_Oremdups(U_20561,c_List_Oconcat(U_20561,U_20562))) = hAPP(c_Finite__Set_Ocard(U_20561),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_20561),tc_fun(U_20561,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_20561)),U_20562)),c_List_Oset(U_20561))),
    inference(definitional_conversion,[status(esa)],[f_4940_2]) ).

cnf(f_4940_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20561)),c_List_Oremdups(U_20561,c_List_Oconcat(U_20561,U_20562))) = hAPP(c_Finite__Set_Ocard(U_20561),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(tc_List_Olist(U_20561),tc_fun(U_20561,tc_HOL_Obool)),hAPP(c_List_Oset(tc_List_Olist(U_20561)),U_20562)),c_List_Oset(U_20561))),
    inference(clausify,[status(thm)],[f_4940_3]) ).

fof(f_4941_1,plain,
    ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))),
    inference(fof_nnf,[status(thm)],[fact_distinct__remdups]) ).

fof(f_4941_2,plain,
    ! [U_20564,U_20563] : hBOOL(hAPP(c_List_Odistinct(U_20563),c_List_Oremdups(U_20563,U_20564))),
    inference(variable_rename,[status(thm)],[f_4941_1]) ).

fof(f_4941_3,plain,
    ! [U_20563,U_20564] : hBOOL(hAPP(c_List_Odistinct(U_20563),c_List_Oremdups(U_20563,U_20564))),
    inference(definitional_conversion,[status(esa)],[f_4941_2]) ).

cnf(f_4941_4,plain,
    hBOOL(hAPP(c_List_Odistinct(U_20563),c_List_Oremdups(U_20563,U_20564))),
    inference(clausify,[status(thm)],[f_4941_3]) ).

fof(f_4942_1,plain,
    ! [V_xs,T_a] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oremdups(T_a,V_xs))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs))),
    inference(fof_nnf,[status(thm)],[fact_length__remdups__leq]) ).

fof(f_4942_2,plain,
    ! [U_20566,U_20565] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20565)),c_List_Oremdups(U_20565,U_20566))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20565)),U_20566))),
    inference(variable_rename,[status(thm)],[f_4942_1]) ).

fof(f_4942_3,plain,
    ! [U_20565,U_20566] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20565)),c_List_Oremdups(U_20565,U_20566))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20565)),U_20566))),
    inference(definitional_conversion,[status(esa)],[f_4942_2]) ).

cnf(f_4942_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20565)),c_List_Oremdups(U_20565,U_20566))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20565)),U_20566))),
    inference(clausify,[status(thm)],[f_4942_3]) ).

fof(f_4943_1,plain,
    ! [V_xs_2,V_f_2,T_c,T_b] : c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_Oremdups(T_c,V_xs_2))) = c_List_Oremdups(T_b,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_remdups__map__remdups]) ).

fof(f_4943_2,plain,
    ! [U_20570,U_20569,U_20568,U_20567] : c_List_Oremdups(U_20567,hAPP(hAPP(c_List_Omap(U_20568,U_20567),U_20569),c_List_Oremdups(U_20568,U_20570))) = c_List_Oremdups(U_20567,hAPP(hAPP(c_List_Omap(U_20568,U_20567),U_20569),U_20570)),
    inference(variable_rename,[status(thm)],[f_4943_1]) ).

fof(f_4943_3,plain,
    ! [U_20567,U_20568,U_20569,U_20570] : c_List_Oremdups(U_20567,hAPP(hAPP(c_List_Omap(U_20568,U_20567),U_20569),c_List_Oremdups(U_20568,U_20570))) = c_List_Oremdups(U_20567,hAPP(hAPP(c_List_Omap(U_20568,U_20567),U_20569),U_20570)),
    inference(definitional_conversion,[status(esa)],[f_4943_2]) ).

cnf(f_4943_4,plain,
    c_List_Oremdups(U_20567,hAPP(hAPP(c_List_Omap(U_20568,U_20567),U_20569),c_List_Oremdups(U_20568,U_20570))) = c_List_Oremdups(U_20567,hAPP(hAPP(c_List_Omap(U_20568,U_20567),U_20569),U_20570)),
    inference(clausify,[status(thm)],[f_4943_3]) ).

fof(f_4944_1,plain,
    ! [V_l_2] : c_List_Oembed__list(V_l_2) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),V_l_2),
    inference(fof_nnf,[status(thm)],[fact_embed__list__def]) ).

fof(f_4944_2,plain,
    ! [U_20571] : c_List_Oembed__list(U_20571) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_20571),
    inference(variable_rename,[status(thm)],[f_4944_1]) ).

fof(f_4944_3,plain,
    ! [U_20571] : c_List_Oembed__list(U_20571) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_20571),
    inference(definitional_conversion,[status(esa)],[f_4944_2]) ).

cnf(f_4944_4,plain,
    c_List_Oembed__list(U_20571) = hAPP(hAPP(c_List_Omap(tc_Nat_Onat,tc_Int_Oint),c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint)),U_20571),
    inference(clausify,[status(thm)],[f_4944_3]) ).

fof(f_4945_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_List_Oset(T_b),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_List_Oset(T_b),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_set__remdups]) ).

fof(f_4945_2,plain,
    ! [U_20573,U_20572] : hAPP(c_List_Oset(U_20572),c_List_Oremdups(U_20572,U_20573)) = hAPP(c_List_Oset(U_20572),U_20573),
    inference(variable_rename,[status(thm)],[f_4945_1]) ).

fof(f_4945_3,plain,
    ! [U_20572,U_20573] : hAPP(c_List_Oset(U_20572),c_List_Oremdups(U_20572,U_20573)) = hAPP(c_List_Oset(U_20572),U_20573),
    inference(definitional_conversion,[status(esa)],[f_4945_2]) ).

cnf(f_4945_4,plain,
    hAPP(c_List_Oset(U_20572),c_List_Oremdups(U_20572,U_20573)) = hAPP(c_List_Oset(U_20572),U_20573),
    inference(clausify,[status(thm)],[f_4945_3]) ).

fof(f_4946_1,plain,
    ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a),
    inference(fof_nnf,[status(thm)],[fact_remdups_Osimps_I1_J]) ).

fof(f_4946_2,plain,
    ! [U_20574] : c_List_Oremdups(U_20574,c_List_Olist_ONil(U_20574)) = c_List_Olist_ONil(U_20574),
    inference(variable_rename,[status(thm)],[f_4946_1]) ).

fof(f_4946_3,plain,
    ! [U_20574] : c_List_Oremdups(U_20574,c_List_Olist_ONil(U_20574)) = c_List_Olist_ONil(U_20574),
    inference(definitional_conversion,[status(esa)],[f_4946_2]) ).

cnf(f_4946_4,plain,
    c_List_Oremdups(U_20574,c_List_Olist_ONil(U_20574)) = c_List_Olist_ONil(U_20574),
    inference(clausify,[status(thm)],[f_4946_3]) ).

fof(f_4947_1,plain,
    ! [V_x_2,T_b] :
      ( ( c_List_Olist_ONil(T_b) = c_List_Oremdups(T_b,V_x_2)
        | V_x_2 != c_List_Olist_ONil(T_b) )
      & ( V_x_2 = c_List_Olist_ONil(T_b)
        | c_List_Olist_ONil(T_b) != c_List_Oremdups(T_b,V_x_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_remdups__eq__nil__right__iff]) ).

fof(f_4947_2,plain,
    ! [U_20576,U_20575] :
      ( ( c_List_Olist_ONil(U_20575) = c_List_Oremdups(U_20575,U_20576)
        | U_20576 != c_List_Olist_ONil(U_20575) )
      & ( U_20576 = c_List_Olist_ONil(U_20575)
        | c_List_Olist_ONil(U_20575) != c_List_Oremdups(U_20575,U_20576) ) ),
    inference(variable_rename,[status(thm)],[f_4947_1]) ).

fof(f_4947_3,plain,
    ( ! [U_20580,U_20578] :
        ( c_List_Olist_ONil(U_20578) = c_List_Oremdups(U_20578,U_20580)
        | U_20580 != c_List_Olist_ONil(U_20578) )
    & ! [U_20579,U_20577] :
        ( U_20579 = c_List_Olist_ONil(U_20577)
        | c_List_Olist_ONil(U_20577) != c_List_Oremdups(U_20577,U_20579) ) ),
    inference(miniscope,[status(thm)],[f_4947_2]) ).

fof(f_4947_4,plain,
    ( ! [U_20580,U_20578] :
        ( c_List_Olist_ONil(U_20578) = c_List_Oremdups(U_20578,U_20580)
        | U_20580 != c_List_Olist_ONil(U_20578) )
    & ! [U_20579,U_20577] :
        ( U_20579 = c_List_Olist_ONil(U_20577)
        | c_List_Olist_ONil(U_20577) != c_List_Oremdups(U_20577,U_20579) ) ),
    inference(definitional_conversion,[status(esa)],[f_4947_3]) ).

cnf(f_4947_5,plain,
    ( U_20579 = c_List_Olist_ONil(U_20577)
    | c_List_Olist_ONil(U_20577) != c_List_Oremdups(U_20577,U_20579) ),
    inference(clausify,[status(thm)],[f_4947_4]) ).

cnf(f_4947_6,plain,
    ( c_List_Olist_ONil(U_20578) = c_List_Oremdups(U_20578,U_20580)
    | U_20580 != c_List_Olist_ONil(U_20578) ),
    inference(clausify,[status(thm)],[f_4947_4]) ).

fof(f_4948_1,plain,
    ! [V_x_2,T_b] :
      ( ( c_List_Oremdups(T_b,V_x_2) = c_List_Olist_ONil(T_b)
        | V_x_2 != c_List_Olist_ONil(T_b) )
      & ( V_x_2 = c_List_Olist_ONil(T_b)
        | c_List_Oremdups(T_b,V_x_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_remdups__eq__nil__iff]) ).

fof(f_4948_2,plain,
    ! [U_20582,U_20581] :
      ( ( c_List_Oremdups(U_20581,U_20582) = c_List_Olist_ONil(U_20581)
        | U_20582 != c_List_Olist_ONil(U_20581) )
      & ( U_20582 = c_List_Olist_ONil(U_20581)
        | c_List_Oremdups(U_20581,U_20582) != c_List_Olist_ONil(U_20581) ) ),
    inference(variable_rename,[status(thm)],[f_4948_1]) ).

fof(f_4948_3,plain,
    ( ! [U_20586,U_20584] :
        ( c_List_Oremdups(U_20584,U_20586) = c_List_Olist_ONil(U_20584)
        | U_20586 != c_List_Olist_ONil(U_20584) )
    & ! [U_20585,U_20583] :
        ( U_20585 = c_List_Olist_ONil(U_20583)
        | c_List_Oremdups(U_20583,U_20585) != c_List_Olist_ONil(U_20583) ) ),
    inference(miniscope,[status(thm)],[f_4948_2]) ).

fof(f_4948_4,plain,
    ( ! [U_20584,U_20586] :
        ( c_List_Oremdups(U_20584,U_20586) = c_List_Olist_ONil(U_20584)
        | U_20586 != c_List_Olist_ONil(U_20584) )
    & ! [U_20585,U_20583] :
        ( U_20585 = c_List_Olist_ONil(U_20583)
        | c_List_Oremdups(U_20583,U_20585) != c_List_Olist_ONil(U_20583) ) ),
    inference(definitional_conversion,[status(esa)],[f_4948_3]) ).

cnf(f_4948_5,plain,
    ( U_20585 = c_List_Olist_ONil(U_20583)
    | c_List_Oremdups(U_20583,U_20585) != c_List_Olist_ONil(U_20583) ),
    inference(clausify,[status(thm)],[f_4948_4]) ).

cnf(f_4948_6,plain,
    ( c_List_Oremdups(U_20584,U_20586) = c_List_Olist_ONil(U_20584)
    | U_20586 != c_List_Olist_ONil(U_20584) ),
    inference(clausify,[status(thm)],[f_4948_4]) ).

fof(f_4949_1,plain,
    ! [V_l,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l))
      | ~ c_List_Olinorder__class_Osorted(T_a,V_l)
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__remdups]) ).

fof(f_4949_2,plain,
    ! [U_20588,U_20587] :
      ( c_List_Olinorder__class_Osorted(U_20587,c_List_Oremdups(U_20587,U_20588))
      | ~ c_List_Olinorder__class_Osorted(U_20587,U_20588)
      | ~ class_Orderings_Olinorder(U_20587) ),
    inference(variable_rename,[status(thm)],[f_4949_1]) ).

fof(f_4949_3,plain,
    ! [U_20588,U_20587] :
      ( c_List_Olinorder__class_Osorted(U_20587,c_List_Oremdups(U_20587,U_20588))
      | ~ c_List_Olinorder__class_Osorted(U_20587,U_20588)
      | ~ class_Orderings_Olinorder(U_20587) ),
    inference(definitional_conversion,[status(esa)],[f_4949_2]) ).

cnf(f_4949_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20587,c_List_Oremdups(U_20587,U_20588))
    | ~ c_List_Olinorder__class_Osorted(U_20587,U_20588)
    | ~ class_Orderings_Olinorder(U_20587) ),
    inference(clausify,[status(thm)],[f_4949_3]) ).

fof(f_4950_1,plain,
    ! [V_x,V_xs,T_a] :
      ( c_List_Oremove1(T_a,V_x,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,c_List_Oremove1(T_a,V_x,V_xs))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_remove1__remdups]) ).

fof(f_4950_2,plain,
    ! [U_20591,U_20590,U_20589] :
      ( c_List_Oremove1(U_20589,U_20591,c_List_Oremdups(U_20589,U_20590)) = c_List_Oremdups(U_20589,c_List_Oremove1(U_20589,U_20591,U_20590))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20589),U_20590)) ),
    inference(variable_rename,[status(thm)],[f_4950_1]) ).

fof(f_4950_3,plain,
    ! [U_20589,U_20590,U_20591] :
      ( c_List_Oremove1(U_20589,U_20591,c_List_Oremdups(U_20589,U_20590)) = c_List_Oremdups(U_20589,c_List_Oremove1(U_20589,U_20591,U_20590))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20589),U_20590)) ),
    inference(definitional_conversion,[status(esa)],[f_4950_2]) ).

cnf(f_4950_4,plain,
    ( c_List_Oremove1(U_20589,U_20591,c_List_Oremdups(U_20589,U_20590)) = c_List_Oremdups(U_20589,c_List_Oremove1(U_20589,U_20591,U_20590))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20589),U_20590)) ),
    inference(clausify,[status(thm)],[f_4950_3]) ).

fof(f_4951_1,plain,
    ! [V_xs,T_a] :
      ( c_List_Oremdups(T_a,V_xs) = V_xs
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__remdups__id]) ).

fof(f_4951_2,plain,
    ! [U_20593,U_20592] :
      ( c_List_Oremdups(U_20592,U_20593) = U_20593
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20592),U_20593)) ),
    inference(variable_rename,[status(thm)],[f_4951_1]) ).

fof(f_4951_3,plain,
    ! [U_20592,U_20593] :
      ( c_List_Oremdups(U_20592,U_20593) = U_20593
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20592),U_20593)) ),
    inference(definitional_conversion,[status(esa)],[f_4951_2]) ).

cnf(f_4951_4,plain,
    ( c_List_Oremdups(U_20592,U_20593) = U_20593
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20592),U_20593)) ),
    inference(clausify,[status(thm)],[f_4951_3]) ).

fof(f_4952_1,plain,
    ! [V_xs_2,T_b] :
      ( ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
        | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) )
      & ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2))
        | c_List_Oremdups(T_b,V_xs_2) != V_xs_2 ) ),
    inference(fof_nnf,[status(thm)],[fact_remdups__id__iff__distinct]) ).

fof(f_4952_2,plain,
    ! [U_20595,U_20594] :
      ( ( c_List_Oremdups(U_20594,U_20595) = U_20595
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20594),U_20595)) )
      & ( hBOOL(hAPP(c_List_Odistinct(U_20594),U_20595))
        | c_List_Oremdups(U_20594,U_20595) != U_20595 ) ),
    inference(variable_rename,[status(thm)],[f_4952_1]) ).

fof(f_4952_3,plain,
    ( ! [U_20599,U_20597] :
        ( c_List_Oremdups(U_20597,U_20599) = U_20599
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20597),U_20599)) )
    & ! [U_20598,U_20596] :
        ( hBOOL(hAPP(c_List_Odistinct(U_20596),U_20598))
        | c_List_Oremdups(U_20596,U_20598) != U_20598 ) ),
    inference(miniscope,[status(thm)],[f_4952_2]) ).

fof(f_4952_4,plain,
    ( ! [U_20597,U_20599] :
        ( c_List_Oremdups(U_20597,U_20599) = U_20599
        | ~ hBOOL(hAPP(c_List_Odistinct(U_20597),U_20599)) )
    & ! [U_20598,U_20596] :
        ( hBOOL(hAPP(c_List_Odistinct(U_20596),U_20598))
        | c_List_Oremdups(U_20596,U_20598) != U_20598 ) ),
    inference(definitional_conversion,[status(esa)],[f_4952_3]) ).

cnf(f_4952_5,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_20596),U_20598))
    | c_List_Oremdups(U_20596,U_20598) != U_20598 ),
    inference(clausify,[status(thm)],[f_4952_4]) ).

cnf(f_4952_6,plain,
    ( c_List_Oremdups(U_20597,U_20599) = U_20599
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20597),U_20599)) ),
    inference(clausify,[status(thm)],[f_4952_4]) ).

fof(f_4953_1,plain,
    ! [V_xs_2,T_b] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2)
        | c_List_Oremdups(T_b,V_xs_2) != V_xs_2 )
      & ( c_List_Oremdups(T_b,V_xs_2) = V_xs_2
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_length__remdups__eq]) ).

fof(f_4953_2,plain,
    ! [U_20601,U_20600] :
      ( ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20600)),c_List_Oremdups(U_20600,U_20601)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20600)),U_20601)
        | c_List_Oremdups(U_20600,U_20601) != U_20601 )
      & ( c_List_Oremdups(U_20600,U_20601) = U_20601
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20600)),c_List_Oremdups(U_20600,U_20601)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20600)),U_20601) ) ),
    inference(variable_rename,[status(thm)],[f_4953_1]) ).

fof(f_4953_3,plain,
    ( ! [U_20605,U_20603] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20603)),c_List_Oremdups(U_20603,U_20605)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20603)),U_20605)
        | c_List_Oremdups(U_20603,U_20605) != U_20605 )
    & ! [U_20604,U_20602] :
        ( c_List_Oremdups(U_20602,U_20604) = U_20604
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20602)),c_List_Oremdups(U_20602,U_20604)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20602)),U_20604) ) ),
    inference(miniscope,[status(thm)],[f_4953_2]) ).

fof(f_4953_4,plain,
    ( ! [U_20603,U_20605] :
        ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20603)),c_List_Oremdups(U_20603,U_20605)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20603)),U_20605)
        | c_List_Oremdups(U_20603,U_20605) != U_20605 )
    & ! [U_20604,U_20602] :
        ( c_List_Oremdups(U_20602,U_20604) = U_20604
        | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20602)),c_List_Oremdups(U_20602,U_20604)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20602)),U_20604) ) ),
    inference(definitional_conversion,[status(esa)],[f_4953_3]) ).

cnf(f_4953_5,plain,
    ( c_List_Oremdups(U_20602,U_20604) = U_20604
    | hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20602)),c_List_Oremdups(U_20602,U_20604)) != hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20602)),U_20604) ),
    inference(clausify,[status(thm)],[f_4953_4]) ).

cnf(f_4953_6,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20603)),c_List_Oremdups(U_20603,U_20605)) = hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20603)),U_20605)
    | c_List_Oremdups(U_20603,U_20605) != U_20605 ),
    inference(clausify,[status(thm)],[f_4953_4]) ).

fof(f_4954_1,plain,
    ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs),
    inference(fof_nnf,[status(thm)],[fact_remdups__remdups]) ).

fof(f_4954_2,plain,
    ! [U_20607,U_20606] : c_List_Oremdups(U_20606,c_List_Oremdups(U_20606,U_20607)) = c_List_Oremdups(U_20606,U_20607),
    inference(variable_rename,[status(thm)],[f_4954_1]) ).

fof(f_4954_3,plain,
    ! [U_20607,U_20606] : c_List_Oremdups(U_20606,c_List_Oremdups(U_20606,U_20607)) = c_List_Oremdups(U_20606,U_20607),
    inference(definitional_conversion,[status(esa)],[f_4954_2]) ).

cnf(f_4954_4,plain,
    c_List_Oremdups(U_20606,c_List_Oremdups(U_20606,U_20607)) = c_List_Oremdups(U_20606,U_20607),
    inference(clausify,[status(thm)],[f_4954_3]) ).

fof(f_4955_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] : c_List_Oremdups(T_b,hAPP(c_List_Ofilter(T_b,V_Pa_2),V_xs_2)) = hAPP(c_List_Ofilter(T_b,V_Pa_2),c_List_Oremdups(T_b,V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_remdups__filter]) ).

fof(f_4955_2,plain,
    ! [U_20610,U_20609,U_20608] : c_List_Oremdups(U_20608,hAPP(c_List_Ofilter(U_20608,U_20609),U_20610)) = hAPP(c_List_Ofilter(U_20608,U_20609),c_List_Oremdups(U_20608,U_20610)),
    inference(variable_rename,[status(thm)],[f_4955_1]) ).

fof(f_4955_3,plain,
    ! [U_20608,U_20609,U_20610] : c_List_Oremdups(U_20608,hAPP(c_List_Ofilter(U_20608,U_20609),U_20610)) = hAPP(c_List_Ofilter(U_20608,U_20609),c_List_Oremdups(U_20608,U_20610)),
    inference(definitional_conversion,[status(esa)],[f_4955_2]) ).

cnf(f_4955_4,plain,
    c_List_Oremdups(U_20608,hAPP(c_List_Ofilter(U_20608,U_20609),U_20610)) = hAPP(c_List_Ofilter(U_20608,U_20609),c_List_Oremdups(U_20608,U_20610)),
    inference(clausify,[status(thm)],[f_4955_3]) ).

fof(f_4956_1,plain,
    ! [V_xs_2,V_x_2,T_b] :
      ( ( c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),c_List_Oremdups(T_b,V_xs_2))
        | hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) )
      & ( c_List_Oremdups(T_b,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_Oremdups(T_b,V_xs_2)
        | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) ) ),
    inference(fof_nnf,[status(thm)],[fact_remdups_Osimps_I2_J]) ).

fof(f_4956_2,plain,
    ! [U_20613,U_20612,U_20611] :
      ( ( c_List_Oremdups(U_20611,hAPP(hAPP(c_List_Olist_OCons(U_20611),U_20612),U_20613)) = hAPP(hAPP(c_List_Olist_OCons(U_20611),U_20612),c_List_Oremdups(U_20611,U_20613))
        | hBOOL(hAPP(hAPP(c_member(U_20611),U_20612),hAPP(c_List_Oset(U_20611),U_20613))) )
      & ( c_List_Oremdups(U_20611,hAPP(hAPP(c_List_Olist_OCons(U_20611),U_20612),U_20613)) = c_List_Oremdups(U_20611,U_20613)
        | ~ hBOOL(hAPP(hAPP(c_member(U_20611),U_20612),hAPP(c_List_Oset(U_20611),U_20613))) ) ),
    inference(variable_rename,[status(thm)],[f_4956_1]) ).

fof(f_4956_3,plain,
    ( ! [U_20619,U_20617,U_20615] :
        ( c_List_Oremdups(U_20615,hAPP(hAPP(c_List_Olist_OCons(U_20615),U_20617),U_20619)) = hAPP(hAPP(c_List_Olist_OCons(U_20615),U_20617),c_List_Oremdups(U_20615,U_20619))
        | hBOOL(hAPP(hAPP(c_member(U_20615),U_20617),hAPP(c_List_Oset(U_20615),U_20619))) )
    & ! [U_20618,U_20616,U_20614] :
        ( c_List_Oremdups(U_20614,hAPP(hAPP(c_List_Olist_OCons(U_20614),U_20616),U_20618)) = c_List_Oremdups(U_20614,U_20618)
        | ~ hBOOL(hAPP(hAPP(c_member(U_20614),U_20616),hAPP(c_List_Oset(U_20614),U_20618))) ) ),
    inference(miniscope,[status(thm)],[f_4956_2]) ).

fof(f_4956_4,plain,
    ( ! [U_20615,U_20617,U_20619] :
        ( c_List_Oremdups(U_20615,hAPP(hAPP(c_List_Olist_OCons(U_20615),U_20617),U_20619)) = hAPP(hAPP(c_List_Olist_OCons(U_20615),U_20617),c_List_Oremdups(U_20615,U_20619))
        | hBOOL(hAPP(hAPP(c_member(U_20615),U_20617),hAPP(c_List_Oset(U_20615),U_20619))) )
    & ! [U_20616,U_20618,U_20614] :
        ( c_List_Oremdups(U_20614,hAPP(hAPP(c_List_Olist_OCons(U_20614),U_20616),U_20618)) = c_List_Oremdups(U_20614,U_20618)
        | ~ hBOOL(hAPP(hAPP(c_member(U_20614),U_20616),hAPP(c_List_Oset(U_20614),U_20618))) ) ),
    inference(definitional_conversion,[status(esa)],[f_4956_3]) ).

cnf(f_4956_5,plain,
    ( c_List_Oremdups(U_20614,hAPP(hAPP(c_List_Olist_OCons(U_20614),U_20616),U_20618)) = c_List_Oremdups(U_20614,U_20618)
    | ~ hBOOL(hAPP(hAPP(c_member(U_20614),U_20616),hAPP(c_List_Oset(U_20614),U_20618))) ),
    inference(clausify,[status(thm)],[f_4956_4]) ).

cnf(f_4956_6,plain,
    ( c_List_Oremdups(U_20615,hAPP(hAPP(c_List_Olist_OCons(U_20615),U_20617),U_20619)) = hAPP(hAPP(c_List_Olist_OCons(U_20615),U_20617),c_List_Oremdups(U_20615,U_20619))
    | hBOOL(hAPP(hAPP(c_member(U_20615),U_20617),hAPP(c_List_Oset(U_20615),U_20619))) ),
    inference(clausify,[status(thm)],[f_4956_4]) ).

fof(f_4957_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_Oremdups(T_b,V_xs_2)) = hAPP(c_Finite__Set_Ocard(T_b),hAPP(c_List_Oset(T_b),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_length__remdups__card__conv]) ).

fof(f_4957_2,plain,
    ! [U_20621,U_20620] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20620)),c_List_Oremdups(U_20620,U_20621)) = hAPP(c_Finite__Set_Ocard(U_20620),hAPP(c_List_Oset(U_20620),U_20621)),
    inference(variable_rename,[status(thm)],[f_4957_1]) ).

fof(f_4957_3,plain,
    ! [U_20620,U_20621] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20620)),c_List_Oremdups(U_20620,U_20621)) = hAPP(c_Finite__Set_Ocard(U_20620),hAPP(c_List_Oset(U_20620),U_20621)),
    inference(definitional_conversion,[status(esa)],[f_4957_2]) ).

cnf(f_4957_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20620)),c_List_Oremdups(U_20620,U_20621)) = hAPP(c_Finite__Set_Ocard(U_20620),hAPP(c_List_Oset(U_20620),U_20621)),
    inference(clausify,[status(thm)],[f_4957_3]) ).

fof(f_4958_1,plain,
    ! [V_xs_2,V_y_2,V_f_2,T_c,T_b] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_c,V_f_2),V_y_2),hAPP(c_List_Oset(T_b),V_xs_2)) = hAPP(c_List_Ofoldl(T_c,T_b,hAPP(c_COMBC(T_b,T_c,T_c),V_f_2),V_y_2),c_List_Oremdups(T_b,V_xs_2))
      | ~ c_Finite__Set_Ofun__left__comm(T_b,T_c,V_f_2) ),
    inference(fof_nnf,[status(thm)],[fact_fun__left__comm_Ofold__set__remdups]) ).

fof(f_4958_2,plain,
    ! [U_20626,U_20625,U_20624,U_20623,U_20622] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_20622,U_20623,U_20624),U_20625),hAPP(c_List_Oset(U_20622),U_20626)) = hAPP(c_List_Ofoldl(U_20623,U_20622,hAPP(c_COMBC(U_20622,U_20623,U_20623),U_20624),U_20625),c_List_Oremdups(U_20622,U_20626))
      | ~ c_Finite__Set_Ofun__left__comm(U_20622,U_20623,U_20624) ),
    inference(variable_rename,[status(thm)],[f_4958_1]) ).

fof(f_4958_3,plain,
    ! [U_20622,U_20623,U_20624,U_20625,U_20626] :
      ( hAPP(hAPP(c_Finite__Set_Ofold(U_20622,U_20623,U_20624),U_20625),hAPP(c_List_Oset(U_20622),U_20626)) = hAPP(c_List_Ofoldl(U_20623,U_20622,hAPP(c_COMBC(U_20622,U_20623,U_20623),U_20624),U_20625),c_List_Oremdups(U_20622,U_20626))
      | ~ c_Finite__Set_Ofun__left__comm(U_20622,U_20623,U_20624) ),
    inference(definitional_conversion,[status(esa)],[f_4958_2]) ).

cnf(f_4958_4,plain,
    ( hAPP(hAPP(c_Finite__Set_Ofold(U_20622,U_20623,U_20624),U_20625),hAPP(c_List_Oset(U_20622),U_20626)) = hAPP(c_List_Ofoldl(U_20623,U_20622,hAPP(c_COMBC(U_20622,U_20623,U_20623),U_20624),U_20625),c_List_Oremdups(U_20622,U_20626))
    | ~ c_Finite__Set_Ofun__left__comm(U_20622,U_20623,U_20624) ),
    inference(clausify,[status(thm)],[f_4958_3]) ).

fof(f_4959_1,plain,
    ! [V_m,V_l] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),V_l),V_m) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(V_l)),c_List_Oembed__list(V_m))),
    inference(fof_nnf,[status(thm)],[fact_transfer__nat__int__list__functions_I1_J]) ).

fof(f_4959_2,plain,
    ! [U_20628,U_20627] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),U_20627),U_20628) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(U_20627)),c_List_Oembed__list(U_20628))),
    inference(variable_rename,[status(thm)],[f_4959_1]) ).

fof(f_4959_3,plain,
    ! [U_20628,U_20627] : hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),U_20627),U_20628) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(U_20627)),c_List_Oembed__list(U_20628))),
    inference(definitional_conversion,[status(esa)],[f_4959_2]) ).

cnf(f_4959_4,plain,
    hAPP(hAPP(c_List_Oappend(tc_Nat_Onat),U_20627),U_20628) = c_List_Oreturn__list(hAPP(hAPP(c_List_Oappend(tc_Int_Oint),c_List_Oembed__list(U_20627)),c_List_Oembed__list(U_20628))),
    inference(clausify,[status(thm)],[f_4959_3]) ).

fof(f_4960_1,plain,
    ! [V_x_2,V_xs_2,T_b] :
      ( c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(c_List_Orev(T_b),hAPP(c_List_Otl(T_b),c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_takeWhile__neq__rev]) ).

fof(f_4960_2,plain,
    ! [U_20631,U_20630,U_20629] :
      ( c_List_OtakeWhile(U_20629,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20629),c_fNot),hAPP(hAPP(c_COMBC(U_20629,U_20629,tc_HOL_Obool),c_fequal),U_20631)),hAPP(c_List_Orev(U_20629),U_20630)) = hAPP(c_List_Orev(U_20629),hAPP(c_List_Otl(U_20629),c_List_OdropWhile(U_20629,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20629),c_fNot),hAPP(hAPP(c_COMBC(U_20629,U_20629,tc_HOL_Obool),c_fequal),U_20631)),U_20630)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20629),U_20631),hAPP(c_List_Oset(U_20629),U_20630)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20629),U_20630)) ),
    inference(variable_rename,[status(thm)],[f_4960_1]) ).

fof(f_4960_3,plain,
    ! [U_20629,U_20630,U_20631] :
      ( c_List_OtakeWhile(U_20629,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20629),c_fNot),hAPP(hAPP(c_COMBC(U_20629,U_20629,tc_HOL_Obool),c_fequal),U_20631)),hAPP(c_List_Orev(U_20629),U_20630)) = hAPP(c_List_Orev(U_20629),hAPP(c_List_Otl(U_20629),c_List_OdropWhile(U_20629,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20629),c_fNot),hAPP(hAPP(c_COMBC(U_20629,U_20629,tc_HOL_Obool),c_fequal),U_20631)),U_20630)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20629),U_20631),hAPP(c_List_Oset(U_20629),U_20630)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20629),U_20630)) ),
    inference(definitional_conversion,[status(esa)],[f_4960_2]) ).

cnf(f_4960_4,plain,
    ( c_List_OtakeWhile(U_20629,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20629),c_fNot),hAPP(hAPP(c_COMBC(U_20629,U_20629,tc_HOL_Obool),c_fequal),U_20631)),hAPP(c_List_Orev(U_20629),U_20630)) = hAPP(c_List_Orev(U_20629),hAPP(c_List_Otl(U_20629),c_List_OdropWhile(U_20629,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20629),c_fNot),hAPP(hAPP(c_COMBC(U_20629,U_20629,tc_HOL_Obool),c_fequal),U_20631)),U_20630)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20629),U_20631),hAPP(c_List_Oset(U_20629),U_20630)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20629),U_20630)) ),
    inference(clausify,[status(thm)],[f_4960_3]) ).

fof(f_4961_1,plain,
    ! [V_x_2,V_xs_2,T_b] :
      ( c_List_OdropWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),hAPP(c_List_Orev(T_b),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),hAPP(c_List_Orev(T_b),c_List_OtakeWhile(T_b,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_b),c_fNot),hAPP(hAPP(c_COMBC(T_b,T_b,tc_HOL_Obool),c_fequal),V_x_2)),V_xs_2)))
      | ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__neq__rev]) ).

fof(f_4961_2,plain,
    ! [U_20634,U_20633,U_20632] :
      ( c_List_OdropWhile(U_20632,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20632),c_fNot),hAPP(hAPP(c_COMBC(U_20632,U_20632,tc_HOL_Obool),c_fequal),U_20634)),hAPP(c_List_Orev(U_20632),U_20633)) = hAPP(hAPP(c_List_Olist_OCons(U_20632),U_20634),hAPP(c_List_Orev(U_20632),c_List_OtakeWhile(U_20632,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20632),c_fNot),hAPP(hAPP(c_COMBC(U_20632,U_20632,tc_HOL_Obool),c_fequal),U_20634)),U_20633)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20632),U_20634),hAPP(c_List_Oset(U_20632),U_20633)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20632),U_20633)) ),
    inference(variable_rename,[status(thm)],[f_4961_1]) ).

fof(f_4961_3,plain,
    ! [U_20632,U_20633,U_20634] :
      ( c_List_OdropWhile(U_20632,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20632),c_fNot),hAPP(hAPP(c_COMBC(U_20632,U_20632,tc_HOL_Obool),c_fequal),U_20634)),hAPP(c_List_Orev(U_20632),U_20633)) = hAPP(hAPP(c_List_Olist_OCons(U_20632),U_20634),hAPP(c_List_Orev(U_20632),c_List_OtakeWhile(U_20632,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20632),c_fNot),hAPP(hAPP(c_COMBC(U_20632,U_20632,tc_HOL_Obool),c_fequal),U_20634)),U_20633)))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20632),U_20634),hAPP(c_List_Oset(U_20632),U_20633)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20632),U_20633)) ),
    inference(definitional_conversion,[status(esa)],[f_4961_2]) ).

cnf(f_4961_4,plain,
    ( c_List_OdropWhile(U_20632,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20632),c_fNot),hAPP(hAPP(c_COMBC(U_20632,U_20632,tc_HOL_Obool),c_fequal),U_20634)),hAPP(c_List_Orev(U_20632),U_20633)) = hAPP(hAPP(c_List_Olist_OCons(U_20632),U_20634),hAPP(c_List_Orev(U_20632),c_List_OtakeWhile(U_20632,hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,U_20632),c_fNot),hAPP(hAPP(c_COMBC(U_20632,U_20632,tc_HOL_Obool),c_fequal),U_20634)),U_20633)))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20632),U_20634),hAPP(c_List_Oset(U_20632),U_20633)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20632),U_20633)) ),
    inference(clausify,[status(thm)],[f_4961_3]) ).

fof(f_4962_1,plain,
    ! [V_xs_2,V_f_2,T_c,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),V_xs_2)) = hAPP(hAPP(c_List_Omap(T_c,T_b),V_f_2),c_List_OdropWhile(T_c,hAPP(c_Fun_Ocomp(T_b,tc_HOL_Obool,T_c,V_Pa_2),V_f_2),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__map]) ).

fof(f_4962_2,plain,
    ! [U_20639,U_20638,U_20637,U_20636,U_20635] : c_List_OdropWhile(U_20635,U_20636,hAPP(hAPP(c_List_Omap(U_20637,U_20635),U_20638),U_20639)) = hAPP(hAPP(c_List_Omap(U_20637,U_20635),U_20638),c_List_OdropWhile(U_20637,hAPP(c_Fun_Ocomp(U_20635,tc_HOL_Obool,U_20637,U_20636),U_20638),U_20639)),
    inference(variable_rename,[status(thm)],[f_4962_1]) ).

fof(f_4962_3,plain,
    ! [U_20635,U_20636,U_20637,U_20638,U_20639] : c_List_OdropWhile(U_20635,U_20636,hAPP(hAPP(c_List_Omap(U_20637,U_20635),U_20638),U_20639)) = hAPP(hAPP(c_List_Omap(U_20637,U_20635),U_20638),c_List_OdropWhile(U_20637,hAPP(c_Fun_Ocomp(U_20635,tc_HOL_Obool,U_20637,U_20636),U_20638),U_20639)),
    inference(definitional_conversion,[status(esa)],[f_4962_2]) ).

cnf(f_4962_4,plain,
    c_List_OdropWhile(U_20635,U_20636,hAPP(hAPP(c_List_Omap(U_20637,U_20635),U_20638),U_20639)) = hAPP(hAPP(c_List_Omap(U_20637,U_20635),U_20638),c_List_OdropWhile(U_20637,hAPP(c_Fun_Ocomp(U_20635,tc_HOL_Obool,U_20637,U_20636),U_20638),U_20639)),
    inference(clausify,[status(thm)],[f_4962_3]) ).

fof(f_4963_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] : hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)) = V_xs_2,
    inference(fof_nnf,[status(thm)],[fact_takeWhile__dropWhile__id]) ).

fof(f_4963_2,plain,
    ! [U_20642,U_20641,U_20640] : hAPP(hAPP(c_List_Oappend(U_20640),c_List_OtakeWhile(U_20640,U_20641,U_20642)),c_List_OdropWhile(U_20640,U_20641,U_20642)) = U_20642,
    inference(variable_rename,[status(thm)],[f_4963_1]) ).

fof(f_4963_3,plain,
    ! [U_20640,U_20641,U_20642] : hAPP(hAPP(c_List_Oappend(U_20640),c_List_OtakeWhile(U_20640,U_20641,U_20642)),c_List_OdropWhile(U_20640,U_20641,U_20642)) = U_20642,
    inference(definitional_conversion,[status(esa)],[f_4963_2]) ).

cnf(f_4963_4,plain,
    hAPP(hAPP(c_List_Oappend(U_20640),c_List_OtakeWhile(U_20640,U_20641,U_20642)),c_List_OdropWhile(U_20640,U_20641,U_20642)) = U_20642,
    inference(clausify,[status(thm)],[f_4963_3]) ).

fof(f_4964_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_length__dropWhile__le]) ).

fof(f_4964_2,plain,
    ! [U_20645,U_20644,U_20643] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20643)),c_List_OdropWhile(U_20643,U_20644,U_20645))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20643)),U_20645))),
    inference(variable_rename,[status(thm)],[f_4964_1]) ).

fof(f_4964_3,plain,
    ! [U_20643,U_20644,U_20645] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20643)),c_List_OdropWhile(U_20643,U_20644,U_20645))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20643)),U_20645))),
    inference(definitional_conversion,[status(esa)],[f_4964_2]) ).

cnf(f_4964_4,plain,
    hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20643)),c_List_OdropWhile(U_20643,U_20644,U_20645))),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20643)),U_20645))),
    inference(clausify,[status(thm)],[f_4964_3]) ).

fof(f_4965_1,plain,
    ! [V_Pa_2,V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__dropWhile]) ).

fof(f_4965_2,plain,
    ! [U_20648,U_20647,U_20646] :
      ( hBOOL(hAPP(c_List_Odistinct(U_20646),c_List_OdropWhile(U_20646,U_20648,U_20647)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20646),U_20647)) ),
    inference(variable_rename,[status(thm)],[f_4965_1]) ).

fof(f_4965_3,plain,
    ! [U_20646,U_20647,U_20648] :
      ( hBOOL(hAPP(c_List_Odistinct(U_20646),c_List_OdropWhile(U_20646,U_20648,U_20647)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20646),U_20647)) ),
    inference(definitional_conversion,[status(esa)],[f_4965_2]) ).

cnf(f_4965_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(U_20646),c_List_OdropWhile(U_20646,U_20648,U_20647)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20646),U_20647)) ),
    inference(clausify,[status(thm)],[f_4965_3]) ).

fof(f_4966_1,plain,
    ! [V_xs_2,T_b,V_x_2,V_Pa_2] :
      ( ( c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)
        | hBOOL(hAPP(V_Pa_2,V_x_2)) )
      & ( c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Olist_OCons(T_b),V_x_2),V_xs_2)) = c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)
        | ~ hBOOL(hAPP(V_Pa_2,V_x_2)) ) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile_Osimps_I2_J]) ).

fof(f_4966_2,plain,
    ! [U_20652,U_20651,U_20650,U_20649] :
      ( ( c_List_OdropWhile(U_20651,U_20649,hAPP(hAPP(c_List_Olist_OCons(U_20651),U_20650),U_20652)) = hAPP(hAPP(c_List_Olist_OCons(U_20651),U_20650),U_20652)
        | hBOOL(hAPP(U_20649,U_20650)) )
      & ( c_List_OdropWhile(U_20651,U_20649,hAPP(hAPP(c_List_Olist_OCons(U_20651),U_20650),U_20652)) = c_List_OdropWhile(U_20651,U_20649,U_20652)
        | ~ hBOOL(hAPP(U_20649,U_20650)) ) ),
    inference(variable_rename,[status(thm)],[f_4966_1]) ).

fof(f_4966_3,plain,
    ( ! [U_20660,U_20658,U_20656,U_20654] :
        ( c_List_OdropWhile(U_20658,U_20654,hAPP(hAPP(c_List_Olist_OCons(U_20658),U_20656),U_20660)) = hAPP(hAPP(c_List_Olist_OCons(U_20658),U_20656),U_20660)
        | hBOOL(hAPP(U_20654,U_20656)) )
    & ! [U_20659,U_20657,U_20655,U_20653] :
        ( c_List_OdropWhile(U_20657,U_20653,hAPP(hAPP(c_List_Olist_OCons(U_20657),U_20655),U_20659)) = c_List_OdropWhile(U_20657,U_20653,U_20659)
        | ~ hBOOL(hAPP(U_20653,U_20655)) ) ),
    inference(miniscope,[status(thm)],[f_4966_2]) ).

fof(f_4966_4,plain,
    ( ! [U_20660,U_20654,U_20656,U_20658] :
        ( c_List_OdropWhile(U_20658,U_20654,hAPP(hAPP(c_List_Olist_OCons(U_20658),U_20656),U_20660)) = hAPP(hAPP(c_List_Olist_OCons(U_20658),U_20656),U_20660)
        | hBOOL(hAPP(U_20654,U_20656)) )
    & ! [U_20653,U_20655,U_20657,U_20659] :
        ( c_List_OdropWhile(U_20657,U_20653,hAPP(hAPP(c_List_Olist_OCons(U_20657),U_20655),U_20659)) = c_List_OdropWhile(U_20657,U_20653,U_20659)
        | ~ hBOOL(hAPP(U_20653,U_20655)) ) ),
    inference(definitional_conversion,[status(esa)],[f_4966_3]) ).

cnf(f_4966_5,plain,
    ( c_List_OdropWhile(U_20657,U_20653,hAPP(hAPP(c_List_Olist_OCons(U_20657),U_20655),U_20659)) = c_List_OdropWhile(U_20657,U_20653,U_20659)
    | ~ hBOOL(hAPP(U_20653,U_20655)) ),
    inference(clausify,[status(thm)],[f_4966_4]) ).

cnf(f_4966_6,plain,
    ( c_List_OdropWhile(U_20658,U_20654,hAPP(hAPP(c_List_Olist_OCons(U_20658),U_20656),U_20660)) = hAPP(hAPP(c_List_Olist_OCons(U_20658),U_20656),U_20660)
    | hBOOL(hAPP(U_20654,U_20656)) ),
    inference(clausify,[status(thm)],[f_4966_4]) ).

fof(f_4967_1,plain,
    ! [V_Pa_2,V_xs_2,T_b] :
      ( c_List_Olinorder__class_Osorted(T_b,c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))
      | ~ c_List_Olinorder__class_Osorted(T_b,V_xs_2)
      | ~ class_Orderings_Olinorder(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__dropWhile]) ).

fof(f_4967_2,plain,
    ! [U_20663,U_20662,U_20661] :
      ( c_List_Olinorder__class_Osorted(U_20661,c_List_OdropWhile(U_20661,U_20663,U_20662))
      | ~ c_List_Olinorder__class_Osorted(U_20661,U_20662)
      | ~ class_Orderings_Olinorder(U_20661) ),
    inference(variable_rename,[status(thm)],[f_4967_1]) ).

fof(f_4967_3,plain,
    ! [U_20663,U_20661,U_20662] :
      ( c_List_Olinorder__class_Osorted(U_20661,c_List_OdropWhile(U_20661,U_20663,U_20662))
      | ~ c_List_Olinorder__class_Osorted(U_20661,U_20662)
      | ~ class_Orderings_Olinorder(U_20661) ),
    inference(definitional_conversion,[status(esa)],[f_4967_2]) ).

cnf(f_4967_4,plain,
    ( c_List_Olinorder__class_Osorted(U_20661,c_List_OdropWhile(U_20661,U_20663,U_20662))
    | ~ c_List_Olinorder__class_Osorted(U_20661,U_20662)
    | ~ class_Orderings_Olinorder(U_20661) ),
    inference(clausify,[status(thm)],[f_4967_3]) ).

fof(f_4968_1,plain,
    ! [V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,c_List_Olist_ONil(T_b)) = c_List_Olist_ONil(T_b),
    inference(fof_nnf,[status(thm)],[fact_dropWhile_Osimps_I1_J]) ).

fof(f_4968_2,plain,
    ! [U_20665,U_20664] : c_List_OdropWhile(U_20664,U_20665,c_List_Olist_ONil(U_20664)) = c_List_Olist_ONil(U_20664),
    inference(variable_rename,[status(thm)],[f_4968_1]) ).

fof(f_4968_3,plain,
    ! [U_20665,U_20664] : c_List_OdropWhile(U_20664,U_20665,c_List_Olist_ONil(U_20664)) = c_List_Olist_ONil(U_20664),
    inference(definitional_conversion,[status(esa)],[f_4968_2]) ).

cnf(f_4968_4,plain,
    c_List_OdropWhile(U_20664,U_20665,c_List_Olist_ONil(U_20664)) = c_List_Olist_ONil(U_20664),
    inference(clausify,[status(thm)],[f_4968_3]) ).

fof(f_4969_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ~ hBOOL(hAPP(V_Pa_2,hAPP(c_List_Ohd(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2))))
      | c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = c_List_Olist_ONil(T_b) ),
    inference(fof_nnf,[status(thm)],[fact_hd__dropWhile]) ).

fof(f_4969_2,plain,
    ! [U_20668,U_20667,U_20666] :
      ( ~ hBOOL(hAPP(U_20667,hAPP(c_List_Ohd(U_20666),c_List_OdropWhile(U_20666,U_20667,U_20668))))
      | c_List_OdropWhile(U_20666,U_20667,U_20668) = c_List_Olist_ONil(U_20666) ),
    inference(variable_rename,[status(thm)],[f_4969_1]) ).

fof(f_4969_3,plain,
    ! [U_20666,U_20667,U_20668] :
      ( ~ hBOOL(hAPP(U_20667,hAPP(c_List_Ohd(U_20666),c_List_OdropWhile(U_20666,U_20667,U_20668))))
      | c_List_OdropWhile(U_20666,U_20667,U_20668) = c_List_Olist_ONil(U_20666) ),
    inference(definitional_conversion,[status(esa)],[f_4969_2]) ).

cnf(f_4969_4,plain,
    ( ~ hBOOL(hAPP(U_20667,hAPP(c_List_Ohd(U_20666),c_List_OdropWhile(U_20666,U_20667,U_20668))))
    | c_List_OdropWhile(U_20666,U_20667,U_20668) = c_List_Olist_ONil(U_20666) ),
    inference(clausify,[status(thm)],[f_4969_3]) ).

fof(f_4970_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] :
      ( ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = c_List_Olist_ONil(T_b)
        | ? [B_x] :
            ( ~ hBOOL(hAPP(V_Pa_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_Pa_2,B_x))
            | ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
        | c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) != c_List_Olist_ONil(T_b) ) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__eq__Nil__conv]) ).

fof(f_4970_2,plain,
    ! [U_20673,U_20672,U_20671] :
      ( ( c_List_OdropWhile(U_20671,U_20672,U_20673) = c_List_Olist_ONil(U_20671)
        | ? [U_20670] :
            ( ~ hBOOL(hAPP(U_20672,U_20670))
            & hBOOL(hAPP(hAPP(c_member(U_20671),U_20670),hAPP(c_List_Oset(U_20671),U_20673))) ) )
      & ( ! [U_20669] :
            ( hBOOL(hAPP(U_20672,U_20669))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20671),U_20669),hAPP(c_List_Oset(U_20671),U_20673))) )
        | c_List_OdropWhile(U_20671,U_20672,U_20673) != c_List_Olist_ONil(U_20671) ) ),
    inference(variable_rename,[status(thm)],[f_4970_1]) ).

fof(f_4970_3,plain,
    ( ! [U_20679,U_20677,U_20675] :
        ( c_List_OdropWhile(U_20675,U_20677,U_20679) = c_List_Olist_ONil(U_20675)
        | ? [U_20670] :
            ( ~ hBOOL(hAPP(U_20677,U_20670))
            & hBOOL(hAPP(hAPP(c_member(U_20675),U_20670),hAPP(c_List_Oset(U_20675),U_20679))) ) )
    & ! [U_20678,U_20676,U_20674] :
        ( ! [U_20669] :
            ( hBOOL(hAPP(U_20676,U_20669))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20674),U_20669),hAPP(c_List_Oset(U_20674),U_20678))) )
        | c_List_OdropWhile(U_20674,U_20676,U_20678) != c_List_Olist_ONil(U_20674) ) ),
    inference(miniscope,[status(thm)],[f_4970_2]) ).

fof(f_4970_4,plain,
    ( ! [U_20679,U_20677,U_20675] :
        ( c_List_OdropWhile(U_20675,U_20677,U_20679) = c_List_Olist_ONil(U_20675)
        | ( ~ hBOOL(hAPP(U_20677,sK504(U_20679,U_20677,U_20675)))
          & hBOOL(hAPP(hAPP(c_member(U_20675),sK504(U_20679,U_20677,U_20675)),hAPP(c_List_Oset(U_20675),U_20679))) ) )
    & ! [U_20678,U_20676,U_20674] :
        ( ! [U_20669] :
            ( hBOOL(hAPP(U_20676,U_20669))
            | ~ hBOOL(hAPP(hAPP(c_member(U_20674),U_20669),hAPP(c_List_Oset(U_20674),U_20678))) )
        | c_List_OdropWhile(U_20674,U_20676,U_20678) != c_List_Olist_ONil(U_20674) ) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK504]),skolemize(U_20670,sK504(U_20679,U_20677,U_20675))],[f_4970_3]) ).

fof(f_4970_5,plain,
    ( ! [U_20677,U_20679,U_20675] :
        ( ~ hBOOL(hAPP(U_20677,sK504(U_20679,U_20677,U_20675)))
        | ~ sP1236(U_20677,U_20679,U_20675) )
    & ! [U_20677,U_20679,U_20675] :
        ( hBOOL(hAPP(hAPP(c_member(U_20675),sK504(U_20679,U_20677,U_20675)),hAPP(c_List_Oset(U_20675),U_20679)))
        | ~ sP1236(U_20677,U_20679,U_20675) )
    & ! [U_20677,U_20679,U_20675] :
        ( c_List_OdropWhile(U_20675,U_20677,U_20679) = c_List_Olist_ONil(U_20675)
        | sP1236(U_20677,U_20679,U_20675) )
    & ! [U_20676,U_20669,U_20674,U_20678] :
        ( hBOOL(hAPP(U_20676,U_20669))
        | ~ hBOOL(hAPP(hAPP(c_member(U_20674),U_20669),hAPP(c_List_Oset(U_20674),U_20678)))
        | c_List_OdropWhile(U_20674,U_20676,U_20678) != c_List_Olist_ONil(U_20674) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1236])],[f_4970_4]) ).

cnf(f_4970_6,plain,
    ( hBOOL(hAPP(U_20676,U_20669))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20674),U_20669),hAPP(c_List_Oset(U_20674),U_20678)))
    | c_List_OdropWhile(U_20674,U_20676,U_20678) != c_List_Olist_ONil(U_20674) ),
    inference(clausify,[status(thm)],[f_4970_5]) ).

cnf(f_4970_7,plain,
    ( c_List_OdropWhile(U_20675,U_20677,U_20679) = c_List_Olist_ONil(U_20675)
    | sP1236(U_20677,U_20679,U_20675) ),
    inference(clausify,[status(thm)],[f_4970_5]) ).

cnf(f_4970_8,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20675),sK504(U_20679,U_20677,U_20675)),hAPP(c_List_Oset(U_20675),U_20679)))
    | ~ sP1236(U_20677,U_20679,U_20675) ),
    inference(clausify,[status(thm)],[f_4970_5]) ).

cnf(f_4970_9,plain,
    ( ~ hBOOL(hAPP(U_20677,sK504(U_20679,U_20677,U_20675)))
    | ~ sP1236(U_20677,U_20679,U_20675) ),
    inference(clausify,[status(thm)],[f_4970_5]) ).

fof(f_4971_1,plain,
    ! [V_ys_2,V_Pa_2,V_xs_2,V_x_2,T_b] :
      ( c_List_OdropWhile(T_b,V_Pa_2,hAPP(hAPP(c_List_Oappend(T_b),V_xs_2),V_ys_2)) = hAPP(hAPP(c_List_Oappend(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_ys_2)
      | hBOOL(hAPP(V_Pa_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_dropWhile__append1]) ).

fof(f_4971_2,plain,
    ! [U_20684,U_20683,U_20682,U_20681,U_20680] :
      ( c_List_OdropWhile(U_20680,U_20683,hAPP(hAPP(c_List_Oappend(U_20680),U_20682),U_20684)) = hAPP(hAPP(c_List_Oappend(U_20680),c_List_OdropWhile(U_20680,U_20683,U_20682)),U_20684)
      | hBOOL(hAPP(U_20683,U_20681))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20680),U_20681),hAPP(c_List_Oset(U_20680),U_20682))) ),
    inference(variable_rename,[status(thm)],[f_4971_1]) ).

fof(f_4971_3,plain,
    ! [U_20680,U_20681,U_20682,U_20683,U_20684] :
      ( c_List_OdropWhile(U_20680,U_20683,hAPP(hAPP(c_List_Oappend(U_20680),U_20682),U_20684)) = hAPP(hAPP(c_List_Oappend(U_20680),c_List_OdropWhile(U_20680,U_20683,U_20682)),U_20684)
      | hBOOL(hAPP(U_20683,U_20681))
      | ~ hBOOL(hAPP(hAPP(c_member(U_20680),U_20681),hAPP(c_List_Oset(U_20680),U_20682))) ),
    inference(definitional_conversion,[status(esa)],[f_4971_2]) ).

cnf(f_4971_4,plain,
    ( c_List_OdropWhile(U_20680,U_20683,hAPP(hAPP(c_List_Oappend(U_20680),U_20682),U_20684)) = hAPP(hAPP(c_List_Oappend(U_20680),c_List_OdropWhile(U_20680,U_20683,U_20682)),U_20684)
    | hBOOL(hAPP(U_20683,U_20681))
    | ~ hBOOL(hAPP(hAPP(c_member(U_20680),U_20681),hAPP(c_List_Oset(U_20680),U_20682))) ),
    inference(clausify,[status(thm)],[f_4971_3]) ).

fof(f_4972_1,plain,
    ! [V_ys_2,V_y_2,V_xs_2,V_Pa_2,T_b] :
      ( ( c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)
        | hBOOL(hAPP(V_Pa_2,V_y_2))
        | V_xs_2 != hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) )
      & ( ( ~ hBOOL(hAPP(V_Pa_2,V_y_2))
          & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_b),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2)),hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2)) )
        | c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) != hAPP(hAPP(c_List_Olist_OCons(T_b),V_y_2),V_ys_2) ) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__eq__Cons__conv]) ).

fof(f_4972_2,plain,
    ! [U_20689,U_20688,U_20687,U_20686,U_20685] :
      ( ( c_List_OdropWhile(U_20685,U_20686,U_20687) = hAPP(hAPP(c_List_Olist_OCons(U_20685),U_20688),U_20689)
        | hBOOL(hAPP(U_20686,U_20688))
        | U_20687 != hAPP(hAPP(c_List_Oappend(U_20685),c_List_OtakeWhile(U_20685,U_20686,U_20687)),hAPP(hAPP(c_List_Olist_OCons(U_20685),U_20688),U_20689)) )
      & ( ( ~ hBOOL(hAPP(U_20686,U_20688))
          & U_20687 = hAPP(hAPP(c_List_Oappend(U_20685),c_List_OtakeWhile(U_20685,U_20686,U_20687)),hAPP(hAPP(c_List_Olist_OCons(U_20685),U_20688),U_20689)) )
        | c_List_OdropWhile(U_20685,U_20686,U_20687) != hAPP(hAPP(c_List_Olist_OCons(U_20685),U_20688),U_20689) ) ),
    inference(variable_rename,[status(thm)],[f_4972_1]) ).

fof(f_4972_3,plain,
    ( ! [U_20699,U_20697,U_20695,U_20693,U_20691] :
        ( c_List_OdropWhile(U_20691,U_20693,U_20695) = hAPP(hAPP(c_List_Olist_OCons(U_20691),U_20697),U_20699)
        | hBOOL(hAPP(U_20693,U_20697))
        | U_20695 != hAPP(hAPP(c_List_Oappend(U_20691),c_List_OtakeWhile(U_20691,U_20693,U_20695)),hAPP(hAPP(c_List_Olist_OCons(U_20691),U_20697),U_20699)) )
    & ! [U_20698,U_20696,U_20694,U_20692,U_20690] :
        ( ( ~ hBOOL(hAPP(U_20692,U_20696))
          & U_20694 = hAPP(hAPP(c_List_Oappend(U_20690),c_List_OtakeWhile(U_20690,U_20692,U_20694)),hAPP(hAPP(c_List_Olist_OCons(U_20690),U_20696),U_20698)) )
        | c_List_OdropWhile(U_20690,U_20692,U_20694) != hAPP(hAPP(c_List_Olist_OCons(U_20690),U_20696),U_20698) ) ),
    inference(miniscope,[status(thm)],[f_4972_2]) ).

fof(f_4972_4,plain,
    ( ! [U_20690,U_20692,U_20694,U_20696,U_20698] :
        ( ~ hBOOL(hAPP(U_20692,U_20696))
        | ~ sP1237(U_20690,U_20692,U_20694,U_20696,U_20698) )
    & ! [U_20690,U_20692,U_20694,U_20696,U_20698] :
        ( U_20694 = hAPP(hAPP(c_List_Oappend(U_20690),c_List_OtakeWhile(U_20690,U_20692,U_20694)),hAPP(hAPP(c_List_Olist_OCons(U_20690),U_20696),U_20698))
        | ~ sP1237(U_20690,U_20692,U_20694,U_20696,U_20698) )
    & ! [U_20695,U_20693,U_20691,U_20699,U_20697] :
        ( c_List_OdropWhile(U_20691,U_20693,U_20695) = hAPP(hAPP(c_List_Olist_OCons(U_20691),U_20697),U_20699)
        | hBOOL(hAPP(U_20693,U_20697))
        | U_20695 != hAPP(hAPP(c_List_Oappend(U_20691),c_List_OtakeWhile(U_20691,U_20693,U_20695)),hAPP(hAPP(c_List_Olist_OCons(U_20691),U_20697),U_20699)) )
    & ! [U_20690,U_20692,U_20694,U_20696,U_20698] :
        ( sP1237(U_20690,U_20692,U_20694,U_20696,U_20698)
        | c_List_OdropWhile(U_20690,U_20692,U_20694) != hAPP(hAPP(c_List_Olist_OCons(U_20690),U_20696),U_20698) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1237])],[f_4972_3]) ).

cnf(f_4972_5,plain,
    ( sP1237(U_20690,U_20692,U_20694,U_20696,U_20698)
    | c_List_OdropWhile(U_20690,U_20692,U_20694) != hAPP(hAPP(c_List_Olist_OCons(U_20690),U_20696),U_20698) ),
    inference(clausify,[status(thm)],[f_4972_4]) ).

cnf(f_4972_6,plain,
    ( c_List_OdropWhile(U_20691,U_20693,U_20695) = hAPP(hAPP(c_List_Olist_OCons(U_20691),U_20697),U_20699)
    | hBOOL(hAPP(U_20693,U_20697))
    | U_20695 != hAPP(hAPP(c_List_Oappend(U_20691),c_List_OtakeWhile(U_20691,U_20693,U_20695)),hAPP(hAPP(c_List_Olist_OCons(U_20691),U_20697),U_20699)) ),
    inference(clausify,[status(thm)],[f_4972_4]) ).

cnf(f_4972_7,plain,
    ( U_20694 = hAPP(hAPP(c_List_Oappend(U_20690),c_List_OtakeWhile(U_20690,U_20692,U_20694)),hAPP(hAPP(c_List_Olist_OCons(U_20690),U_20696),U_20698))
    | ~ sP1237(U_20690,U_20692,U_20694,U_20696,U_20698) ),
    inference(clausify,[status(thm)],[f_4972_4]) ).

cnf(f_4972_8,plain,
    ( ~ hBOOL(hAPP(U_20692,U_20696))
    | ~ sP1237(U_20690,U_20692,U_20694,U_20696,U_20698) ),
    inference(clausify,[status(thm)],[f_4972_4]) ).

fof(f_4973_1,plain,
    ! [V_xs_2,V_Pa_2,T_b] : c_List_OdropWhile(T_b,V_Pa_2,V_xs_2) = hAPP(hAPP(c_List_Odrop(T_b),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,V_xs_2))),V_xs_2),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__eq__drop]) ).

fof(f_4973_2,plain,
    ! [U_20702,U_20701,U_20700] : c_List_OdropWhile(U_20700,U_20701,U_20702) = hAPP(hAPP(c_List_Odrop(U_20700),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20700)),c_List_OtakeWhile(U_20700,U_20701,U_20702))),U_20702),
    inference(variable_rename,[status(thm)],[f_4973_1]) ).

fof(f_4973_3,plain,
    ! [U_20701,U_20702,U_20700] : c_List_OdropWhile(U_20700,U_20701,U_20702) = hAPP(hAPP(c_List_Odrop(U_20700),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20700)),c_List_OtakeWhile(U_20700,U_20701,U_20702))),U_20702),
    inference(definitional_conversion,[status(esa)],[f_4973_2]) ).

cnf(f_4973_4,plain,
    c_List_OdropWhile(U_20700,U_20701,U_20702) = hAPP(hAPP(c_List_Odrop(U_20700),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20700)),c_List_OtakeWhile(U_20700,U_20701,U_20702))),U_20702),
    inference(clausify,[status(thm)],[f_4973_3]) ).

fof(f_4974_1,plain,
    ! [V_xs_2,V_Pa_2,T_b,V_j_2] :
      ( hAPP(hAPP(c_List_Onth(T_b),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)),V_j_2) = hAPP(hAPP(c_List_Onth(T_b),V_xs_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_j_2),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),c_List_OtakeWhile(T_b,V_Pa_2,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)),c_List_OdropWhile(T_b,V_Pa_2,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_dropWhile__nth]) ).

fof(f_4974_2,plain,
    ! [U_20706,U_20705,U_20704,U_20703] :
      ( hAPP(hAPP(c_List_Onth(U_20704),c_List_OdropWhile(U_20704,U_20705,U_20706)),U_20703) = hAPP(hAPP(c_List_Onth(U_20704),U_20706),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20703),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20704)),c_List_OtakeWhile(U_20704,U_20705,U_20706))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20703),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20704)),c_List_OdropWhile(U_20704,U_20705,U_20706)))) ),
    inference(variable_rename,[status(thm)],[f_4974_1]) ).

fof(f_4974_3,plain,
    ! [U_20703,U_20704,U_20705,U_20706] :
      ( hAPP(hAPP(c_List_Onth(U_20704),c_List_OdropWhile(U_20704,U_20705,U_20706)),U_20703) = hAPP(hAPP(c_List_Onth(U_20704),U_20706),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20703),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20704)),c_List_OtakeWhile(U_20704,U_20705,U_20706))))
      | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20703),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20704)),c_List_OdropWhile(U_20704,U_20705,U_20706)))) ),
    inference(definitional_conversion,[status(esa)],[f_4974_2]) ).

cnf(f_4974_4,plain,
    ( hAPP(hAPP(c_List_Onth(U_20704),c_List_OdropWhile(U_20704,U_20705,U_20706)),U_20703) = hAPP(hAPP(c_List_Onth(U_20704),U_20706),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),U_20703),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20704)),c_List_OtakeWhile(U_20704,U_20705,U_20706))))
    | ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20703),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20704)),c_List_OdropWhile(U_20704,U_20705,U_20706)))) ),
    inference(clausify,[status(thm)],[f_4974_3]) ).

fof(f_4975_1,plain,
    ! [V_f_2,V_Pa_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),hAPP(c_List_Ofilter(T_b,V_Pa_2),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))
      | ? [B_x] :
          ( hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_c)
          & ~ hBOOL(hAPP(V_Pa_2,B_x))
          & hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) )
      | ~ class_Groups_Omonoid__add(T_c) ),
    inference(fof_nnf,[status(thm)],[fact_listsum__map__filter]) ).

fof(f_4975_2,plain,
    ! [U_20712,U_20711,U_20710,U_20709,U_20708] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20708),hAPP(hAPP(c_List_Omap(U_20709,U_20708),U_20712),hAPP(c_List_Ofilter(U_20709,U_20711),U_20710))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20708),hAPP(hAPP(c_List_Omap(U_20709,U_20708),U_20712),U_20710))
      | ? [U_20707] :
          ( hAPP(U_20712,U_20707) != c_Groups_Ozero__class_Ozero(U_20708)
          & ~ hBOOL(hAPP(U_20711,U_20707))
          & hBOOL(hAPP(hAPP(c_member(U_20709),U_20707),hAPP(c_List_Oset(U_20709),U_20710))) )
      | ~ class_Groups_Omonoid__add(U_20708) ),
    inference(variable_rename,[status(thm)],[f_4975_1]) ).

fof(f_4975_3,plain,
    ! [U_20712,U_20711,U_20710,U_20709,U_20708] :
      ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20708),hAPP(hAPP(c_List_Omap(U_20709,U_20708),U_20712),hAPP(c_List_Ofilter(U_20709,U_20711),U_20710))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20708),hAPP(hAPP(c_List_Omap(U_20709,U_20708),U_20712),U_20710))
      | ( hAPP(U_20712,sK505(U_20712,U_20711,U_20710,U_20709,U_20708)) != c_Groups_Ozero__class_Ozero(U_20708)
        & ~ hBOOL(hAPP(U_20711,sK505(U_20712,U_20711,U_20710,U_20709,U_20708)))
        & hBOOL(hAPP(hAPP(c_member(U_20709),sK505(U_20712,U_20711,U_20710,U_20709,U_20708)),hAPP(c_List_Oset(U_20709),U_20710))) )
      | ~ class_Groups_Omonoid__add(U_20708) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK505]),skolemize(U_20707,sK505(U_20712,U_20711,U_20710,U_20709,U_20708))],[f_4975_2]) ).

fof(f_4975_4,plain,
    ( ! [U_20708,U_20709,U_20710,U_20711,U_20712] :
        ( hAPP(U_20712,sK505(U_20712,U_20711,U_20710,U_20709,U_20708)) != c_Groups_Ozero__class_Ozero(U_20708)
        | ~ sP1238(U_20708,U_20709,U_20710,U_20711,U_20712) )
    & ! [U_20708,U_20709,U_20710,U_20711,U_20712] :
        ( ~ hBOOL(hAPP(U_20711,sK505(U_20712,U_20711,U_20710,U_20709,U_20708)))
        | ~ sP1238(U_20708,U_20709,U_20710,U_20711,U_20712) )
    & ! [U_20708,U_20709,U_20710,U_20711,U_20712] :
        ( hBOOL(hAPP(hAPP(c_member(U_20709),sK505(U_20712,U_20711,U_20710,U_20709,U_20708)),hAPP(c_List_Oset(U_20709),U_20710)))
        | ~ sP1238(U_20708,U_20709,U_20710,U_20711,U_20712) )
    & ! [U_20708,U_20709,U_20710,U_20711,U_20712] :
        ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20708),hAPP(hAPP(c_List_Omap(U_20709,U_20708),U_20712),hAPP(c_List_Ofilter(U_20709,U_20711),U_20710))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20708),hAPP(hAPP(c_List_Omap(U_20709,U_20708),U_20712),U_20710))
        | sP1238(U_20708,U_20709,U_20710,U_20711,U_20712)
        | ~ class_Groups_Omonoid__add(U_20708) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1238])],[f_4975_3]) ).

cnf(f_4975_5,plain,
    ( hAPP(c_List_Omonoid__add__class_Olistsum(U_20708),hAPP(hAPP(c_List_Omap(U_20709,U_20708),U_20712),hAPP(c_List_Ofilter(U_20709,U_20711),U_20710))) = hAPP(c_List_Omonoid__add__class_Olistsum(U_20708),hAPP(hAPP(c_List_Omap(U_20709,U_20708),U_20712),U_20710))
    | sP1238(U_20708,U_20709,U_20710,U_20711,U_20712)
    | ~ class_Groups_Omonoid__add(U_20708) ),
    inference(clausify,[status(thm)],[f_4975_4]) ).

cnf(f_4975_6,plain,
    ( hBOOL(hAPP(hAPP(c_member(U_20709),sK505(U_20712,U_20711,U_20710,U_20709,U_20708)),hAPP(c_List_Oset(U_20709),U_20710)))
    | ~ sP1238(U_20708,U_20709,U_20710,U_20711,U_20712) ),
    inference(clausify,[status(thm)],[f_4975_4]) ).

cnf(f_4975_7,plain,
    ( ~ hBOOL(hAPP(U_20711,sK505(U_20712,U_20711,U_20710,U_20709,U_20708)))
    | ~ sP1238(U_20708,U_20709,U_20710,U_20711,U_20712) ),
    inference(clausify,[status(thm)],[f_4975_4]) ).

cnf(f_4975_8,plain,
    ( hAPP(U_20712,sK505(U_20712,U_20711,U_20710,U_20709,U_20708)) != c_Groups_Ozero__class_Ozero(U_20708)
    | ~ sP1238(U_20708,U_20709,U_20710,U_20711,U_20712) ),
    inference(clausify,[status(thm)],[f_4975_4]) ).

fof(f_4976_1,plain,
    ! [V_xs,T_a] :
      ( c_List_Olinorder__class_Osorted(T_a,V_xs)
      | ? [B_i,B_j] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i)),hAPP(hAPP(c_List_Onth(T_a),V_xs),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_a)),V_xs)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) )
      | ~ class_Orderings_Olinorder(T_a) ),
    inference(fof_nnf,[status(thm)],[fact_sorted__nth__monoI]) ).

fof(f_4976_2,plain,
    ! [U_20716,U_20715] :
      ( c_List_Olinorder__class_Osorted(U_20715,U_20716)
      | ? [U_20714,U_20713] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20715),hAPP(hAPP(c_List_Onth(U_20715),U_20716),U_20714)),hAPP(hAPP(c_List_Onth(U_20715),U_20716),U_20713)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20713),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20715)),U_20716)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),U_20714),U_20713)) )
      | ~ class_Orderings_Olinorder(U_20715) ),
    inference(variable_rename,[status(thm)],[f_4976_1]) ).

fof(f_4976_3,plain,
    ! [U_20716,U_20715] :
      ( c_List_Olinorder__class_Osorted(U_20715,U_20716)
      | ? [U_20713] :
          ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20715),hAPP(hAPP(c_List_Onth(U_20715),U_20716),sK506(U_20716,U_20715))),hAPP(hAPP(c_List_Onth(U_20715),U_20716),U_20713)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),U_20713),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20715)),U_20716)))
          & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK506(U_20716,U_20715)),U_20713)) )
      | ~ class_Orderings_Olinorder(U_20715) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK506]),skolemize(U_20714,sK506(U_20716,U_20715))],[f_4976_2]) ).

fof(f_4976_4,plain,
    ! [U_20716,U_20715] :
      ( c_List_Olinorder__class_Osorted(U_20715,U_20716)
      | ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20715),hAPP(hAPP(c_List_Onth(U_20715),U_20716),sK506(U_20716,U_20715))),hAPP(hAPP(c_List_Onth(U_20715),U_20716),sK507(U_20716,U_20715))))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK507(U_20716,U_20715)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20715)),U_20716)))
        & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK506(U_20716,U_20715)),sK507(U_20716,U_20715))) )
      | ~ class_Orderings_Olinorder(U_20715) ),
    inference(skolemize,[status(esa),new_symbols(skolem,[sK507]),skolemize(U_20713,sK507(U_20716,U_20715))],[f_4976_3]) ).

fof(f_4976_5,plain,
    ( ! [U_20716,U_20715] :
        ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20715),hAPP(hAPP(c_List_Onth(U_20715),U_20716),sK506(U_20716,U_20715))),hAPP(hAPP(c_List_Onth(U_20715),U_20716),sK507(U_20716,U_20715))))
        | ~ sP1239(U_20716,U_20715) )
    & ! [U_20716,U_20715] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK507(U_20716,U_20715)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20715)),U_20716)))
        | ~ sP1239(U_20716,U_20715) )
    & ! [U_20716,U_20715] :
        ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK506(U_20716,U_20715)),sK507(U_20716,U_20715)))
        | ~ sP1239(U_20716,U_20715) )
    & ! [U_20716,U_20715] :
        ( c_List_Olinorder__class_Osorted(U_20715,U_20716)
        | sP1239(U_20716,U_20715)
        | ~ class_Orderings_Olinorder(U_20715) ) ),
    inference(definitional_conversion,[status(esa),new_symbols(definitional,[sP1239])],[f_4976_4]) ).

cnf(f_4976_6,plain,
    ( c_List_Olinorder__class_Osorted(U_20715,U_20716)
    | sP1239(U_20716,U_20715)
    | ~ class_Orderings_Olinorder(U_20715) ),
    inference(clausify,[status(thm)],[f_4976_5]) ).

cnf(f_4976_7,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),sK506(U_20716,U_20715)),sK507(U_20716,U_20715)))
    | ~ sP1239(U_20716,U_20715) ),
    inference(clausify,[status(thm)],[f_4976_5]) ).

cnf(f_4976_8,plain,
    ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),sK507(U_20716,U_20715)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20715)),U_20716)))
    | ~ sP1239(U_20716,U_20715) ),
    inference(clausify,[status(thm)],[f_4976_5]) ).

cnf(f_4976_9,plain,
    ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(U_20715),hAPP(hAPP(c_List_Onth(U_20715),U_20716),sK506(U_20716,U_20715))),hAPP(hAPP(c_List_Onth(U_20715),U_20716),sK507(U_20716,U_20715))))
    | ~ sP1239(U_20716,U_20715) ),
    inference(clausify,[status(thm)],[f_4976_5]) ).

fof(f_4977_1,plain,
    ! [V_xs_2,V_n_2,T_b] : c_Enum_On__lists(T_b,hAPP(c_Nat_OSuc,V_n_2),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))),hAPP(hAPP(c_COMBC(tc_List_Olist(T_b),tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_List_Olist(T_b)),tc_fun(tc_List_Olist(T_b),tc_List_Olist(tc_List_Olist(T_b))),tc_List_Olist(T_b)),c_List_Omap(T_b,tc_List_Olist(T_b))),hAPP(c_COMBC(T_b,tc_List_Olist(T_b),tc_List_Olist(T_b)),c_List_Olist_OCons(T_b)))),V_xs_2)),c_Enum_On__lists(T_b,V_n_2,V_xs_2))),
    inference(fof_nnf,[status(thm)],[fact_n__lists_Osimps_I2_J]) ).

fof(f_4977_2,plain,
    ! [U_20719,U_20718,U_20717] : c_Enum_On__lists(U_20717,hAPP(c_Nat_OSuc,U_20718),U_20719) = c_List_Oconcat(tc_List_Olist(U_20717),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20717),tc_List_Olist(tc_List_Olist(U_20717))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20717),tc_List_Olist(U_20717),tc_List_Olist(tc_List_Olist(U_20717))),hAPP(hAPP(c_COMBB(tc_fun(U_20717,tc_List_Olist(U_20717)),tc_fun(tc_List_Olist(U_20717),tc_List_Olist(tc_List_Olist(U_20717))),tc_List_Olist(U_20717)),c_List_Omap(U_20717,tc_List_Olist(U_20717))),hAPP(c_COMBC(U_20717,tc_List_Olist(U_20717),tc_List_Olist(U_20717)),c_List_Olist_OCons(U_20717)))),U_20719)),c_Enum_On__lists(U_20717,U_20718,U_20719))),
    inference(variable_rename,[status(thm)],[f_4977_1]) ).

fof(f_4977_3,plain,
    ! [U_20717,U_20718,U_20719] : c_Enum_On__lists(U_20717,hAPP(c_Nat_OSuc,U_20718),U_20719) = c_List_Oconcat(tc_List_Olist(U_20717),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20717),tc_List_Olist(tc_List_Olist(U_20717))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20717),tc_List_Olist(U_20717),tc_List_Olist(tc_List_Olist(U_20717))),hAPP(hAPP(c_COMBB(tc_fun(U_20717,tc_List_Olist(U_20717)),tc_fun(tc_List_Olist(U_20717),tc_List_Olist(tc_List_Olist(U_20717))),tc_List_Olist(U_20717)),c_List_Omap(U_20717,tc_List_Olist(U_20717))),hAPP(c_COMBC(U_20717,tc_List_Olist(U_20717),tc_List_Olist(U_20717)),c_List_Olist_OCons(U_20717)))),U_20719)),c_Enum_On__lists(U_20717,U_20718,U_20719))),
    inference(definitional_conversion,[status(esa)],[f_4977_2]) ).

cnf(f_4977_4,plain,
    c_Enum_On__lists(U_20717,hAPP(c_Nat_OSuc,U_20718),U_20719) = c_List_Oconcat(tc_List_Olist(U_20717),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20717),tc_List_Olist(tc_List_Olist(U_20717))),hAPP(hAPP(c_COMBC(tc_List_Olist(U_20717),tc_List_Olist(U_20717),tc_List_Olist(tc_List_Olist(U_20717))),hAPP(hAPP(c_COMBB(tc_fun(U_20717,tc_List_Olist(U_20717)),tc_fun(tc_List_Olist(U_20717),tc_List_Olist(tc_List_Olist(U_20717))),tc_List_Olist(U_20717)),c_List_Omap(U_20717,tc_List_Olist(U_20717))),hAPP(c_COMBC(U_20717,tc_List_Olist(U_20717),tc_List_Olist(U_20717)),c_List_Olist_OCons(U_20717)))),U_20719)),c_Enum_On__lists(U_20717,U_20718,U_20719))),
    inference(clausify,[status(thm)],[f_4977_3]) ).

fof(f_4978_1,plain,
    ! [V_xs_2,T_b] : hAPP(c_Set_Oimage(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool),c_List_Oset(T_b)),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_Osublists(T_b,V_xs_2))) = hAPP(c_Set_OPow(T_b),hAPP(c_List_Oset(T_b),V_xs_2)),
    inference(fof_nnf,[status(thm)],[fact_sublists__powset]) ).

fof(f_4978_2,plain,
    ! [U_20721,U_20720] : hAPP(c_Set_Oimage(tc_List_Olist(U_20720),tc_fun(U_20720,tc_HOL_Obool),c_List_Oset(U_20720)),hAPP(c_List_Oset(tc_List_Olist(U_20720)),c_Enum_Osublists(U_20720,U_20721))) = hAPP(c_Set_OPow(U_20720),hAPP(c_List_Oset(U_20720),U_20721)),
    inference(variable_rename,[status(thm)],[f_4978_1]) ).

fof(f_4978_3,plain,
    ! [U_20720,U_20721] : hAPP(c_Set_Oimage(tc_List_Olist(U_20720),tc_fun(U_20720,tc_HOL_Obool),c_List_Oset(U_20720)),hAPP(c_List_Oset(tc_List_Olist(U_20720)),c_Enum_Osublists(U_20720,U_20721))) = hAPP(c_Set_OPow(U_20720),hAPP(c_List_Oset(U_20720),U_20721)),
    inference(definitional_conversion,[status(esa)],[f_4978_2]) ).

cnf(f_4978_4,plain,
    hAPP(c_Set_Oimage(tc_List_Olist(U_20720),tc_fun(U_20720,tc_HOL_Obool),c_List_Oset(U_20720)),hAPP(c_List_Oset(tc_List_Olist(U_20720)),c_Enum_Osublists(U_20720,U_20721))) = hAPP(c_Set_OPow(U_20720),hAPP(c_List_Oset(U_20720),U_20721)),
    inference(clausify,[status(thm)],[f_4978_3]) ).

fof(f_4979_1,plain,
    ! [V_n,V_xs,T_a] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs)))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__n__lists]) ).

fof(f_4979_2,plain,
    ! [U_20724,U_20723,U_20722] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_20722)),c_Enum_On__lists(U_20722,U_20724,U_20723)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20722),U_20723)) ),
    inference(variable_rename,[status(thm)],[f_4979_1]) ).

fof(f_4979_3,plain,
    ! [U_20722,U_20723,U_20724] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_20722)),c_Enum_On__lists(U_20722,U_20724,U_20723)))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20722),U_20723)) ),
    inference(definitional_conversion,[status(esa)],[f_4979_2]) ).

cnf(f_4979_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(U_20722)),c_Enum_On__lists(U_20722,U_20724,U_20723)))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20722),U_20723)) ),
    inference(clausify,[status(thm)],[f_4979_3]) ).

fof(f_4980_1,plain,
    ! [V_xs_2,T_b] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(T_b),tc_fun(T_b,tc_HOL_Obool)),c_List_Oset(T_b)),c_Enum_Osublists(T_b,V_xs_2))))
      | ~ hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) ),
    inference(fof_nnf,[status(thm)],[fact_distinct__set__sublists]) ).

fof(f_4980_2,plain,
    ! [U_20726,U_20725] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_fun(U_20725,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20725),tc_fun(U_20725,tc_HOL_Obool)),c_List_Oset(U_20725)),c_Enum_Osublists(U_20725,U_20726))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20725),U_20726)) ),
    inference(variable_rename,[status(thm)],[f_4980_1]) ).

fof(f_4980_3,plain,
    ! [U_20725,U_20726] :
      ( hBOOL(hAPP(c_List_Odistinct(tc_fun(U_20725,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20725),tc_fun(U_20725,tc_HOL_Obool)),c_List_Oset(U_20725)),c_Enum_Osublists(U_20725,U_20726))))
      | ~ hBOOL(hAPP(c_List_Odistinct(U_20725),U_20726)) ),
    inference(definitional_conversion,[status(esa)],[f_4980_2]) ).

cnf(f_4980_4,plain,
    ( hBOOL(hAPP(c_List_Odistinct(tc_fun(U_20725,tc_HOL_Obool)),hAPP(hAPP(c_List_Omap(tc_List_Olist(U_20725),tc_fun(U_20725,tc_HOL_Obool)),c_List_Oset(U_20725)),c_Enum_Osublists(U_20725,U_20726))))
    | ~ hBOOL(hAPP(c_List_Odistinct(U_20725),U_20726)) ),
    inference(clausify,[status(thm)],[f_4980_3]) ).

fof(f_4981_1,plain,
    ! [V_xs,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(T_a))),c_Enum_On__lists(T_a,V_n,V_xs)) = hAPP(hAPP(c_Power_Opower__class_Opower(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__n__lists]) ).

fof(f_4981_2,plain,
    ! [U_20729,U_20728,U_20727] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20727))),c_Enum_On__lists(U_20727,U_20728,U_20729)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20727)),U_20729)),U_20728),
    inference(variable_rename,[status(thm)],[f_4981_1]) ).

fof(f_4981_3,plain,
    ! [U_20727,U_20728,U_20729] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20727))),c_Enum_On__lists(U_20727,U_20728,U_20729)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20727)),U_20729)),U_20728),
    inference(definitional_conversion,[status(esa)],[f_4981_2]) ).

cnf(f_4981_4,plain,
    hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(tc_List_Olist(U_20727))),c_Enum_On__lists(U_20727,U_20728,U_20729)) = hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20727)),U_20729)),U_20728),
    inference(clausify,[status(thm)],[f_4981_3]) ).

fof(f_4982_1,plain,
    ! [V_xs_2,V_n_2,V_ys_2,T_b] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_ys_2) = V_n_2
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_b)),V_ys_2),hAPP(c_List_Oset(tc_List_Olist(T_b)),c_Enum_On__lists(T_b,V_n_2,V_xs_2)))) ),
    inference(fof_nnf,[status(thm)],[fact_length__n__lists__elem]) ).

fof(f_4982_2,plain,
    ! [U_20733,U_20732,U_20731,U_20730] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20730)),U_20731) = U_20732
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20730)),U_20731),hAPP(c_List_Oset(tc_List_Olist(U_20730)),c_Enum_On__lists(U_20730,U_20732,U_20733)))) ),
    inference(variable_rename,[status(thm)],[f_4982_1]) ).

fof(f_4982_3,plain,
    ! [U_20730,U_20731,U_20732,U_20733] :
      ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20730)),U_20731) = U_20732
      | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20730)),U_20731),hAPP(c_List_Oset(tc_List_Olist(U_20730)),c_Enum_On__lists(U_20730,U_20732,U_20733)))) ),
    inference(definitional_conversion,[status(esa)],[f_4982_2]) ).

cnf(f_4982_4,plain,
    ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(U_20730)),U_20731) = U_20732
    | ~ hBOOL(hAPP(hAPP(c_member(tc_List_Olist(U_20730)),U_20731),hAPP(c_List_Oset(tc_List_Olist(U_20730)),c_Enum_On__lists(U_20730,U_20732,U_20733)))) ),
    inference(clausify,[status(thm)],[f_4982_3]) ).

fof(f_4983_1,plain,
    ! [T_a] : c_Enum_Osublists(T_a,c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),c_List_Olist_ONil(tc_List_Olist(T_a))),
    inference(fof_nnf,[status(thm)],[fact_sublists_Osimps_I1_J]) ).

fof(f_4983_2,plain,
    ! [U_20734] : c_Enum_Osublists(U_20734,c_List_Olist_ONil(U_20734)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20734)),c_List_Olist_ONil(U_20734)),c_List_Olist_ONil(tc_List_Olist(U_20734))),
    inference(variable_rename,[status(thm)],[f_4983_1]) ).

fof(f_4983_3,plain,
    ! [U_20734] : c_Enum_Osublists(U_20734,c_List_Olist_ONil(U_20734)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20734)),c_List_Olist_ONil(U_20734)),c_List_Olist_ONil(tc_List_Olist(U_20734))),
    inference(definitional_conversion,[status(esa)],[f_4983_2]) ).

cnf(f_4983_4,plain,
    c_Enum_Osublists(U_20734,c_List_Olist_ONil(U_20734)) = hAPP(hAPP(c_List_Olist_OCons(tc_List_Olist(U_20734)),c_List_Olist_ONil(U_20734)),c_List_Olist_ONil(tc_List_Olist(U_20734))),
    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_20736,U_20735] :
      ( class_Lattices_Obounded__lattice(tc_fun(U_20736,U_20735))
      | ~ class_Lattices_Obounded__lattice(U_20735) ),
    inference(variable_rename,[status(thm)],[f_4985_1]) ).

fof(f_4985_3,plain,
    ! [U_20735,U_20736] :
      ( class_Lattices_Obounded__lattice(tc_fun(U_20736,U_20735))
      | ~ class_Lattices_Obounded__lattice(U_20735) ),
    inference(definitional_conversion,[status(esa)],[f_4985_2]) ).

cnf(f_4985_4,plain,
    ( class_Lattices_Obounded__lattice(tc_fun(U_20736,U_20735))
    | ~ class_Lattices_Obounded__lattice(U_20735) ),
    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_20738,U_20737] :
      ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(U_20738,U_20737))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_20737) ),
    inference(variable_rename,[status(thm)],[f_4986_1]) ).

fof(f_4986_3,plain,
    ! [U_20737,U_20738] :
      ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(U_20738,U_20737))
      | ~ class_Complete__Lattice_Ocomplete__lattice(U_20737) ),
    inference(definitional_conversion,[status(esa)],[f_4986_2]) ).

cnf(f_4986_4,plain,
    ( class_Complete__Lattice_Ocomplete__lattice(tc_fun(U_20738,U_20737))
    | ~ class_Complete__Lattice_Ocomplete__lattice(U_20737) ),
    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_20740,U_20739] :
      ( class_Lattices_Obounded__lattice__top(tc_fun(U_20740,U_20739))
      | ~ class_Lattices_Obounded__lattice(U_20739) ),
    inference(variable_rename,[status(thm)],[f_4987_1]) ).

fof(f_4987_3,plain,
    ! [U_20739,U_20740] :
      ( class_Lattices_Obounded__lattice__top(tc_fun(U_20740,U_20739))
      | ~ class_Lattices_Obounded__lattice(U_20739) ),
    inference(definitional_conversion,[status(esa)],[f_4987_2]) ).

cnf(f_4987_4,plain,
    ( class_Lattices_Obounded__lattice__top(tc_fun(U_20740,U_20739))
    | ~ class_Lattices_Obounded__lattice(U_20739) ),
    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_20742,U_20741] :
      ( class_Lattices_Obounded__lattice__bot(tc_fun(U_20742,U_20741))
      | ~ class_Lattices_Obounded__lattice(U_20741) ),
    inference(variable_rename,[status(thm)],[f_4988_1]) ).

fof(f_4988_3,plain,
    ! [U_20741,U_20742] :
      ( class_Lattices_Obounded__lattice__bot(tc_fun(U_20742,U_20741))
      | ~ class_Lattices_Obounded__lattice(U_20741) ),
    inference(definitional_conversion,[status(esa)],[f_4988_2]) ).

cnf(f_4988_4,plain,
    ( class_Lattices_Obounded__lattice__bot(tc_fun(U_20742,U_20741))
    | ~ class_Lattices_Obounded__lattice(U_20741) ),
    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_20744,U_20743] :
      ( class_Lattices_Osemilattice__sup(tc_fun(U_20744,U_20743))
      | ~ class_Lattices_Olattice(U_20743) ),
    inference(variable_rename,[status(thm)],[f_4989_1]) ).

fof(f_4989_3,plain,
    ! [U_20743,U_20744] :
      ( class_Lattices_Osemilattice__sup(tc_fun(U_20744,U_20743))
      | ~ class_Lattices_Olattice(U_20743) ),
    inference(definitional_conversion,[status(esa)],[f_4989_2]) ).

cnf(f_4989_4,plain,
    ( class_Lattices_Osemilattice__sup(tc_fun(U_20744,U_20743))
    | ~ class_Lattices_Olattice(U_20743) ),
    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_20746,U_20745] :
      ( class_Lattices_Osemilattice__inf(tc_fun(U_20746,U_20745))
      | ~ class_Lattices_Olattice(U_20745) ),
    inference(variable_rename,[status(thm)],[f_4990_1]) ).

fof(f_4990_3,plain,
    ! [U_20745,U_20746] :
      ( class_Lattices_Osemilattice__inf(tc_fun(U_20746,U_20745))
      | ~ class_Lattices_Olattice(U_20745) ),
    inference(definitional_conversion,[status(esa)],[f_4990_2]) ).

cnf(f_4990_4,plain,
    ( class_Lattices_Osemilattice__inf(tc_fun(U_20746,U_20745))
    | ~ class_Lattices_Olattice(U_20745) ),
    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_20748,U_20747] :
      ( class_Lattices_Odistrib__lattice(tc_fun(U_20748,U_20747))
      | ~ class_Lattices_Odistrib__lattice(U_20747) ),
    inference(variable_rename,[status(thm)],[f_4991_1]) ).

fof(f_4991_3,plain,
    ! [U_20748,U_20747] :
      ( class_Lattices_Odistrib__lattice(tc_fun(U_20748,U_20747))
      | ~ class_Lattices_Odistrib__lattice(U_20747) ),
    inference(definitional_conversion,[status(esa)],[f_4991_2]) ).

cnf(f_4991_4,plain,
    ( class_Lattices_Odistrib__lattice(tc_fun(U_20748,U_20747))
    | ~ class_Lattices_Odistrib__lattice(U_20747) ),
    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_20750,U_20749] :
      ( class_Lattices_Oboolean__algebra(tc_fun(U_20750,U_20749))
      | ~ class_Lattices_Oboolean__algebra(U_20749) ),
    inference(variable_rename,[status(thm)],[f_4992_1]) ).

fof(f_4992_3,plain,
    ! [U_20750,U_20749] :
      ( class_Lattices_Oboolean__algebra(tc_fun(U_20750,U_20749))
      | ~ class_Lattices_Oboolean__algebra(U_20749) ),
    inference(definitional_conversion,[status(esa)],[f_4992_2]) ).

cnf(f_4992_4,plain,
    ( class_Lattices_Oboolean__algebra(tc_fun(U_20750,U_20749))
    | ~ class_Lattices_Oboolean__algebra(U_20749) ),
    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_20752,U_20751] :
      ( class_Orderings_Opreorder(tc_fun(U_20752,U_20751))
      | ~ class_Orderings_Opreorder(U_20751) ),
    inference(variable_rename,[status(thm)],[f_4993_1]) ).

fof(f_4993_3,plain,
    ! [U_20752,U_20751] :
      ( class_Orderings_Opreorder(tc_fun(U_20752,U_20751))
      | ~ class_Orderings_Opreorder(U_20751) ),
    inference(definitional_conversion,[status(esa)],[f_4993_2]) ).

cnf(f_4993_4,plain,
    ( class_Orderings_Opreorder(tc_fun(U_20752,U_20751))
    | ~ class_Orderings_Opreorder(U_20751) ),
    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_20754,U_20753] :
      ( class_Finite__Set_Ofinite(tc_fun(U_20753,U_20754))
      | ~ class_Finite__Set_Ofinite(U_20754)
      | ~ class_Finite__Set_Ofinite(U_20753) ),
    inference(variable_rename,[status(thm)],[f_4994_1]) ).

fof(f_4994_3,plain,
    ! [U_20754,U_20753] :
      ( class_Finite__Set_Ofinite(tc_fun(U_20753,U_20754))
      | ~ class_Finite__Set_Ofinite(U_20754)
      | ~ class_Finite__Set_Ofinite(U_20753) ),
    inference(definitional_conversion,[status(esa)],[f_4994_2]) ).

cnf(f_4994_4,plain,
    ( class_Finite__Set_Ofinite(tc_fun(U_20753,U_20754))
    | ~ class_Finite__Set_Ofinite(U_20754)
    | ~ class_Finite__Set_Ofinite(U_20753) ),
    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_20756,U_20755] :
      ( class_Lattices_Olattice(tc_fun(U_20756,U_20755))
      | ~ class_Lattices_Olattice(U_20755) ),
    inference(variable_rename,[status(thm)],[f_4995_1]) ).

fof(f_4995_3,plain,
    ! [U_20755,U_20756] :
      ( class_Lattices_Olattice(tc_fun(U_20756,U_20755))
      | ~ class_Lattices_Olattice(U_20755) ),
    inference(definitional_conversion,[status(esa)],[f_4995_2]) ).

cnf(f_4995_4,plain,
    ( class_Lattices_Olattice(tc_fun(U_20756,U_20755))
    | ~ class_Lattices_Olattice(U_20755) ),
    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_20758,U_20757] :
      ( class_Orderings_Oorder(tc_fun(U_20758,U_20757))
      | ~ class_Orderings_Oorder(U_20757) ),
    inference(variable_rename,[status(thm)],[f_4996_1]) ).

fof(f_4996_3,plain,
    ! [U_20758,U_20757] :
      ( class_Orderings_Oorder(tc_fun(U_20758,U_20757))
      | ~ class_Orderings_Oorder(U_20757) ),
    inference(definitional_conversion,[status(esa)],[f_4996_2]) ).

cnf(f_4996_4,plain,
    ( class_Orderings_Oorder(tc_fun(U_20758,U_20757))
    | ~ class_Orderings_Oorder(U_20757) ),
    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_20760,U_20759] :
      ( class_Orderings_Otop(tc_fun(U_20760,U_20759))
      | ~ class_Orderings_Otop(U_20759) ),
    inference(variable_rename,[status(thm)],[f_4997_1]) ).

fof(f_4997_3,plain,
    ! [U_20759,U_20760] :
      ( class_Orderings_Otop(tc_fun(U_20760,U_20759))
      | ~ class_Orderings_Otop(U_20759) ),
    inference(definitional_conversion,[status(esa)],[f_4997_2]) ).

cnf(f_4997_4,plain,
    ( class_Orderings_Otop(tc_fun(U_20760,U_20759))
    | ~ class_Orderings_Otop(U_20759) ),
    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_20762,U_20761] :
      ( class_Orderings_Oord(tc_fun(U_20762,U_20761))
      | ~ class_Orderings_Oord(U_20761) ),
    inference(variable_rename,[status(thm)],[f_4998_1]) ).

fof(f_4998_3,plain,
    ! [U_20761,U_20762] :
      ( class_Orderings_Oord(tc_fun(U_20762,U_20761))
      | ~ class_Orderings_Oord(U_20761) ),
    inference(definitional_conversion,[status(esa)],[f_4998_2]) ).

cnf(f_4998_4,plain,
    ( class_Orderings_Oord(tc_fun(U_20762,U_20761))
    | ~ class_Orderings_Oord(U_20761) ),
    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_20764,U_20763] :
      ( class_Orderings_Obot(tc_fun(U_20764,U_20763))
      | ~ class_Orderings_Obot(U_20763) ),
    inference(variable_rename,[status(thm)],[f_4999_1]) ).

fof(f_4999_3,plain,
    ! [U_20763,U_20764] :
      ( class_Orderings_Obot(tc_fun(U_20764,U_20763))
      | ~ class_Orderings_Obot(U_20763) ),
    inference(definitional_conversion,[status(esa)],[f_4999_2]) ).

cnf(f_4999_4,plain,
    ( class_Orderings_Obot(tc_fun(U_20764,U_20763))
    | ~ class_Orderings_Obot(U_20763) ),
    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_20766,U_20765] :
      ( class_Groups_Ouminus(tc_fun(U_20766,U_20765))
      | ~ class_Groups_Ouminus(U_20765) ),
    inference(variable_rename,[status(thm)],[f_5000_1]) ).

fof(f_5000_3,plain,
    ! [U_20765,U_20766] :
      ( class_Groups_Ouminus(tc_fun(U_20766,U_20765))
      | ~ class_Groups_Ouminus(U_20765) ),
    inference(definitional_conversion,[status(esa)],[f_5000_2]) ).

cnf(f_5000_4,plain,
    ( class_Groups_Ouminus(tc_fun(U_20766,U_20765))
    | ~ class_Groups_Ouminus(U_20765) ),
    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_20768,U_20767] :
      ( class_Groups_Ominus(tc_fun(U_20768,U_20767))
      | ~ class_Groups_Ominus(U_20767) ),
    inference(variable_rename,[status(thm)],[f_5001_1]) ).

fof(f_5001_3,plain,
    ! [U_20767,U_20768] :
      ( class_Groups_Ominus(tc_fun(U_20768,U_20767))
      | ~ class_Groups_Ominus(U_20767) ),
    inference(definitional_conversion,[status(esa)],[f_5001_2]) ).

cnf(f_5001_4,plain,
    ( class_Groups_Ominus(tc_fun(U_20768,U_20767))
    | ~ class_Groups_Ominus(U_20767) ),
    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_20770,U_20769] :
      ( class_Finite__Set_Ofinite(tc_sum(U_20769,U_20770))
      | ~ class_Finite__Set_Ofinite(U_20770)
      | ~ class_Finite__Set_Ofinite(U_20769) ),
    inference(variable_rename,[status(thm)],[f_5138_1]) ).

fof(f_5138_3,plain,
    ! [U_20770,U_20769] :
      ( class_Finite__Set_Ofinite(tc_sum(U_20769,U_20770))
      | ~ class_Finite__Set_Ofinite(U_20770)
      | ~ class_Finite__Set_Ofinite(U_20769) ),
    inference(definitional_conversion,[status(esa)],[f_5138_2]) ).

cnf(f_5138_4,plain,
    ( class_Finite__Set_Ofinite(tc_sum(U_20769,U_20770))
    | ~ class_Finite__Set_Ofinite(U_20770)
    | ~ class_Finite__Set_Ofinite(U_20769) ),
    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_20771] :
      ( class_Finite__Set_Ofinite(tc_Option_Ooption(U_20771))
      | ~ class_Finite__Set_Ofinite(U_20771) ),
    inference(variable_rename,[status(thm)],[f_5139_1]) ).

fof(f_5139_3,plain,
    ! [U_20771] :
      ( class_Finite__Set_Ofinite(tc_Option_Ooption(U_20771))
      | ~ class_Finite__Set_Ofinite(U_20771) ),
    inference(definitional_conversion,[status(esa)],[f_5139_2]) ).

cnf(f_5139_4,plain,
    ( class_Finite__Set_Ofinite(tc_Option_Ooption(U_20771))
    | ~ class_Finite__Set_Ofinite(U_20771) ),
    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_20773,U_20772] :
      ( class_Finite__Set_Ofinite(tc_prod(U_20772,U_20773))
      | ~ class_Finite__Set_Ofinite(U_20773)
      | ~ class_Finite__Set_Ofinite(U_20772) ),
    inference(variable_rename,[status(thm)],[f_5140_1]) ).

fof(f_5140_3,plain,
    ! [U_20773,U_20772] :
      ( class_Finite__Set_Ofinite(tc_prod(U_20772,U_20773))
      | ~ class_Finite__Set_Ofinite(U_20773)
      | ~ class_Finite__Set_Ofinite(U_20772) ),
    inference(definitional_conversion,[status(esa)],[f_5140_2]) ).

cnf(f_5140_4,plain,
    ( class_Finite__Set_Ofinite(tc_prod(U_20772,U_20773))
    | ~ class_Finite__Set_Ofinite(U_20773)
    | ~ class_Finite__Set_Ofinite(U_20772) ),
    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_20775,U_20774] :
      ( class_Smallcheck_Osmall(tc_prod(U_20774,U_20775))
      | ~ class_Smallcheck_Osmall(U_20775)
      | ~ class_Smallcheck_Osmall(U_20774) ),
    inference(variable_rename,[status(thm)],[f_5141_1]) ).

fof(f_5141_3,plain,
    ! [U_20775,U_20774] :
      ( class_Smallcheck_Osmall(tc_prod(U_20774,U_20775))
      | ~ class_Smallcheck_Osmall(U_20775)
      | ~ class_Smallcheck_Osmall(U_20774) ),
    inference(definitional_conversion,[status(esa)],[f_5141_2]) ).

cnf(f_5141_4,plain,
    ( class_Smallcheck_Osmall(tc_prod(U_20774,U_20775))
    | ~ class_Smallcheck_Osmall(U_20775)
    | ~ class_Smallcheck_Osmall(U_20774) ),
    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_20777,U_20776] : hAPP(c_COMBI(U_20776),U_20777) = U_20777,
    inference(variable_rename,[status(thm)],[f_5185_1]) ).

fof(f_5185_3,plain,
    ! [U_20776,U_20777] : hAPP(c_COMBI(U_20776),U_20777) = U_20777,
    inference(definitional_conversion,[status(esa)],[f_5185_2]) ).

cnf(f_5185_4,plain,
    hAPP(c_COMBI(U_20776),U_20777) = U_20777,
    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_20781,U_20780,U_20779,U_20778] : hAPP(hAPP(c_COMBK(U_20778,U_20779),U_20780),U_20781) = U_20780,
    inference(variable_rename,[status(thm)],[f_5186_1]) ).

fof(f_5186_3,plain,
    ! [U_20778,U_20779,U_20780,U_20781] : hAPP(hAPP(c_COMBK(U_20778,U_20779),U_20780),U_20781) = U_20780,
    inference(definitional_conversion,[status(esa)],[f_5186_2]) ).

cnf(f_5186_4,plain,
    hAPP(hAPP(c_COMBK(U_20778,U_20779),U_20780),U_20781) = U_20780,
    inference(clausify,[status(thm)],[f_5186_3]) ).

fof(f_5187_1,plain,
    ! [V_R_2,V_Qa_2,V_Pa_2,T_d,T_b,T_c] : hAPP(hAPP(hAPP(c_COMBB(T_c,T_b,T_d),V_Pa_2),V_Qa_2),V_R_2) = hAPP(V_Pa_2,hAPP(V_Qa_2,V_R_2)),
    inference(fof_nnf,[status(thm)],[help_c__COMBB__1]) ).

fof(f_5187_2,plain,
    ! [U_20787,U_20786,U_20785,U_20784,U_20783,U_20782] : hAPP(hAPP(hAPP(c_COMBB(U_20782,U_20783,U_20784),U_20785),U_20786),U_20787) = hAPP(U_20785,hAPP(U_20786,U_20787)),
    inference(variable_rename,[status(thm)],[f_5187_1]) ).

fof(f_5187_3,plain,
    ! [U_20782,U_20783,U_20784,U_20785,U_20786,U_20787] : hAPP(hAPP(hAPP(c_COMBB(U_20782,U_20783,U_20784),U_20785),U_20786),U_20787) = hAPP(U_20785,hAPP(U_20786,U_20787)),
    inference(definitional_conversion,[status(esa)],[f_5187_2]) ).

cnf(f_5187_4,plain,
    hAPP(hAPP(hAPP(c_COMBB(U_20782,U_20783,U_20784),U_20785),U_20786),U_20787) = hAPP(U_20785,hAPP(U_20786,U_20787)),
    inference(clausify,[status(thm)],[f_5187_3]) ).

fof(f_5188_1,plain,
    ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBC(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),V_Qa_2),
    inference(fof_nnf,[status(thm)],[help_c__COMBC__1]) ).

fof(f_5188_2,plain,
    ! [U_20793,U_20792,U_20791,U_20790,U_20789,U_20788] : hAPP(hAPP(hAPP(c_COMBC(U_20788,U_20789,U_20790),U_20791),U_20792),U_20793) = hAPP(hAPP(U_20791,U_20793),U_20792),
    inference(variable_rename,[status(thm)],[f_5188_1]) ).

fof(f_5188_3,plain,
    ! [U_20788,U_20789,U_20790,U_20791,U_20792,U_20793] : hAPP(hAPP(hAPP(c_COMBC(U_20788,U_20789,U_20790),U_20791),U_20792),U_20793) = hAPP(hAPP(U_20791,U_20793),U_20792),
    inference(definitional_conversion,[status(esa)],[f_5188_2]) ).

cnf(f_5188_4,plain,
    hAPP(hAPP(hAPP(c_COMBC(U_20788,U_20789,U_20790),U_20791),U_20792),U_20793) = hAPP(hAPP(U_20791,U_20793),U_20792),
    inference(clausify,[status(thm)],[f_5188_3]) ).

fof(f_5189_1,plain,
    ! [V_R_2,V_Qa_2,V_Pa_2,T_b,T_d,T_c] : hAPP(hAPP(hAPP(c_COMBS(T_c,T_d,T_b),V_Pa_2),V_Qa_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Qa_2,V_R_2)),
    inference(fof_nnf,[status(thm)],[help_c__COMBS__1]) ).

fof(f_5189_2,plain,
    ! [U_20799,U_20798,U_20797,U_20796,U_20795,U_20794] : hAPP(hAPP(hAPP(c_COMBS(U_20794,U_20795,U_20796),U_20797),U_20798),U_20799) = hAPP(hAPP(U_20797,U_20799),hAPP(U_20798,U_20799)),
    inference(variable_rename,[status(thm)],[f_5189_1]) ).

fof(f_5189_3,plain,
    ! [U_20794,U_20795,U_20796,U_20797,U_20798,U_20799] : hAPP(hAPP(hAPP(c_COMBS(U_20794,U_20795,U_20796),U_20797),U_20798),U_20799) = hAPP(hAPP(U_20797,U_20799),hAPP(U_20798,U_20799)),
    inference(definitional_conversion,[status(esa)],[f_5189_2]) ).

cnf(f_5189_4,plain,
    hAPP(hAPP(hAPP(c_COMBS(U_20794,U_20795,U_20796),U_20797),U_20798),U_20799) = hAPP(hAPP(U_20797,U_20799),hAPP(U_20798,U_20799)),
    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_20801,U_20800] :
      ( U_20800 = U_20801
      | ~ hBOOL(hAPP(hAPP(c_fequal,U_20800),U_20801)) ),
    inference(variable_rename,[status(thm)],[f_5190_1]) ).

fof(f_5190_3,plain,
    ! [U_20800,U_20801] :
      ( U_20800 = U_20801
      | ~ hBOOL(hAPP(hAPP(c_fequal,U_20800),U_20801)) ),
    inference(definitional_conversion,[status(esa)],[f_5190_2]) ).

cnf(f_5190_4,plain,
    ( U_20800 = U_20801
    | ~ hBOOL(hAPP(hAPP(c_fequal,U_20800),U_20801)) ),
    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_20803,U_20802] :
      ( hBOOL(hAPP(hAPP(c_fequal,U_20802),U_20803))
      | U_20802 != U_20803 ),
    inference(variable_rename,[status(thm)],[f_5191_1]) ).

fof(f_5191_3,plain,
    ! [U_20802,U_20803] :
      ( hBOOL(hAPP(hAPP(c_fequal,U_20802),U_20803))
      | U_20802 != U_20803 ),
    inference(definitional_conversion,[status(esa)],[f_5191_2]) ).

cnf(f_5191_4,plain,
    ( hBOOL(hAPP(hAPP(c_fequal,U_20802),U_20803))
    | U_20802 != U_20803 ),
    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_Pa_2] :
      ( ~ hBOOL(V_Pa_2)
      | ~ hBOOL(hAPP(c_fNot,V_Pa_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fNot__1]) ).

fof(f_5194_2,plain,
    ! [U_20804] :
      ( ~ hBOOL(U_20804)
      | ~ hBOOL(hAPP(c_fNot,U_20804)) ),
    inference(variable_rename,[status(thm)],[f_5194_1]) ).

fof(f_5194_3,plain,
    ! [U_20804] :
      ( ~ hBOOL(U_20804)
      | ~ hBOOL(hAPP(c_fNot,U_20804)) ),
    inference(definitional_conversion,[status(esa)],[f_5194_2]) ).

cnf(f_5194_4,plain,
    ( ~ hBOOL(U_20804)
    | ~ hBOOL(hAPP(c_fNot,U_20804)) ),
    inference(clausify,[status(thm)],[f_5194_3]) ).

fof(f_5195_1,plain,
    ! [V_Pa_2] :
      ( hBOOL(hAPP(c_fNot,V_Pa_2))
      | hBOOL(V_Pa_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fNot__2]) ).

fof(f_5195_2,plain,
    ! [U_20805] :
      ( hBOOL(hAPP(c_fNot,U_20805))
      | hBOOL(U_20805) ),
    inference(variable_rename,[status(thm)],[f_5195_1]) ).

fof(f_5195_3,plain,
    ! [U_20805] :
      ( hBOOL(hAPP(c_fNot,U_20805))
      | hBOOL(U_20805) ),
    inference(definitional_conversion,[status(esa)],[f_5195_2]) ).

cnf(f_5195_4,plain,
    ( hBOOL(hAPP(c_fNot,U_20805))
    | hBOOL(U_20805) ),
    inference(clausify,[status(thm)],[f_5195_3]) ).

fof(f_5196_1,plain,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2))
      | ~ hBOOL(V_Qa_2)
      | ~ hBOOL(V_Pa_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fconj__1]) ).

fof(f_5196_2,plain,
    ! [U_20807,U_20806] :
      ( hBOOL(hAPP(hAPP(c_fconj,U_20806),U_20807))
      | ~ hBOOL(U_20807)
      | ~ hBOOL(U_20806) ),
    inference(variable_rename,[status(thm)],[f_5196_1]) ).

fof(f_5196_3,plain,
    ! [U_20807] :
      ( ! [U_20806] :
          ( hBOOL(hAPP(hAPP(c_fconj,U_20806),U_20807))
          | ~ hBOOL(U_20806) )
      | ~ hBOOL(U_20807) ),
    inference(miniscope,[status(thm)],[f_5196_2]) ).

fof(f_5196_4,plain,
    ! [U_20806,U_20807] :
      ( hBOOL(hAPP(hAPP(c_fconj,U_20806),U_20807))
      | ~ hBOOL(U_20806)
      | ~ hBOOL(U_20807) ),
    inference(definitional_conversion,[status(esa)],[f_5196_3]) ).

cnf(f_5196_5,plain,
    ( hBOOL(hAPP(hAPP(c_fconj,U_20806),U_20807))
    | ~ hBOOL(U_20806)
    | ~ hBOOL(U_20807) ),
    inference(clausify,[status(thm)],[f_5196_4]) ).

fof(f_5197_1,plain,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(V_Pa_2)
      | ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fconj__2]) ).

fof(f_5197_2,plain,
    ! [U_20809,U_20808] :
      ( hBOOL(U_20808)
      | ~ hBOOL(hAPP(hAPP(c_fconj,U_20808),U_20809)) ),
    inference(variable_rename,[status(thm)],[f_5197_1]) ).

fof(f_5197_3,plain,
    ! [U_20808,U_20809] :
      ( hBOOL(U_20808)
      | ~ hBOOL(hAPP(hAPP(c_fconj,U_20808),U_20809)) ),
    inference(definitional_conversion,[status(esa)],[f_5197_2]) ).

cnf(f_5197_4,plain,
    ( hBOOL(U_20808)
    | ~ hBOOL(hAPP(hAPP(c_fconj,U_20808),U_20809)) ),
    inference(clausify,[status(thm)],[f_5197_3]) ).

fof(f_5198_1,plain,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(V_Qa_2)
      | ~ hBOOL(hAPP(hAPP(c_fconj,V_Pa_2),V_Qa_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fconj__3]) ).

fof(f_5198_2,plain,
    ! [U_20811,U_20810] :
      ( hBOOL(U_20811)
      | ~ hBOOL(hAPP(hAPP(c_fconj,U_20810),U_20811)) ),
    inference(variable_rename,[status(thm)],[f_5198_1]) ).

fof(f_5198_3,plain,
    ! [U_20811] :
      ( ! [U_20810] : ~ hBOOL(hAPP(hAPP(c_fconj,U_20810),U_20811))
      | hBOOL(U_20811) ),
    inference(miniscope,[status(thm)],[f_5198_2]) ).

fof(f_5198_4,plain,
    ! [U_20810,U_20811] :
      ( ~ hBOOL(hAPP(hAPP(c_fconj,U_20810),U_20811))
      | hBOOL(U_20811) ),
    inference(definitional_conversion,[status(esa)],[f_5198_3]) ).

cnf(f_5198_5,plain,
    ( ~ hBOOL(hAPP(hAPP(c_fconj,U_20810),U_20811))
    | hBOOL(U_20811) ),
    inference(clausify,[status(thm)],[f_5198_4]) ).

fof(f_5199_1,plain,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2))
      | ~ hBOOL(V_Pa_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fdisj__1]) ).

fof(f_5199_2,plain,
    ! [U_20813,U_20812] :
      ( hBOOL(hAPP(hAPP(c_fdisj,U_20812),U_20813))
      | ~ hBOOL(U_20812) ),
    inference(variable_rename,[status(thm)],[f_5199_1]) ).

fof(f_5199_3,plain,
    ! [U_20812,U_20813] :
      ( hBOOL(hAPP(hAPP(c_fdisj,U_20812),U_20813))
      | ~ hBOOL(U_20812) ),
    inference(definitional_conversion,[status(esa)],[f_5199_2]) ).

cnf(f_5199_4,plain,
    ( hBOOL(hAPP(hAPP(c_fdisj,U_20812),U_20813))
    | ~ hBOOL(U_20812) ),
    inference(clausify,[status(thm)],[f_5199_3]) ).

fof(f_5200_1,plain,
    ! [V_Pa_2,V_Qa_2] :
      ( hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2))
      | ~ hBOOL(V_Qa_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fdisj__2]) ).

fof(f_5200_2,plain,
    ! [U_20815,U_20814] :
      ( hBOOL(hAPP(hAPP(c_fdisj,U_20815),U_20814))
      | ~ hBOOL(U_20814) ),
    inference(variable_rename,[status(thm)],[f_5200_1]) ).

fof(f_5200_3,plain,
    ! [U_20814,U_20815] :
      ( hBOOL(hAPP(hAPP(c_fdisj,U_20815),U_20814))
      | ~ hBOOL(U_20814) ),
    inference(definitional_conversion,[status(esa)],[f_5200_2]) ).

cnf(f_5200_4,plain,
    ( hBOOL(hAPP(hAPP(c_fdisj,U_20815),U_20814))
    | ~ hBOOL(U_20814) ),
    inference(clausify,[status(thm)],[f_5200_3]) ).

fof(f_5201_1,plain,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(V_Qa_2)
      | hBOOL(V_Pa_2)
      | ~ hBOOL(hAPP(hAPP(c_fdisj,V_Pa_2),V_Qa_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fdisj__3]) ).

fof(f_5201_2,plain,
    ! [U_20817,U_20816] :
      ( hBOOL(U_20817)
      | hBOOL(U_20816)
      | ~ hBOOL(hAPP(hAPP(c_fdisj,U_20816),U_20817)) ),
    inference(variable_rename,[status(thm)],[f_5201_1]) ).

fof(f_5201_3,plain,
    ! [U_20817] :
      ( ! [U_20816] :
          ( hBOOL(U_20816)
          | ~ hBOOL(hAPP(hAPP(c_fdisj,U_20816),U_20817)) )
      | hBOOL(U_20817) ),
    inference(miniscope,[status(thm)],[f_5201_2]) ).

fof(f_5201_4,plain,
    ! [U_20816,U_20817] :
      ( hBOOL(U_20816)
      | ~ hBOOL(hAPP(hAPP(c_fdisj,U_20816),U_20817))
      | hBOOL(U_20817) ),
    inference(definitional_conversion,[status(esa)],[f_5201_3]) ).

cnf(f_5201_5,plain,
    ( hBOOL(U_20816)
    | ~ hBOOL(hAPP(hAPP(c_fdisj,U_20816),U_20817))
    | hBOOL(U_20817) ),
    inference(clausify,[status(thm)],[f_5201_4]) ).

fof(f_5202_1,plain,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2))
      | hBOOL(V_Pa_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fimplies__1]) ).

fof(f_5202_2,plain,
    ! [U_20819,U_20818] :
      ( hBOOL(hAPP(hAPP(c_fimplies,U_20818),U_20819))
      | hBOOL(U_20818) ),
    inference(variable_rename,[status(thm)],[f_5202_1]) ).

fof(f_5202_3,plain,
    ! [U_20819,U_20818] :
      ( hBOOL(hAPP(hAPP(c_fimplies,U_20818),U_20819))
      | hBOOL(U_20818) ),
    inference(definitional_conversion,[status(esa)],[f_5202_2]) ).

cnf(f_5202_4,plain,
    ( hBOOL(hAPP(hAPP(c_fimplies,U_20818),U_20819))
    | hBOOL(U_20818) ),
    inference(clausify,[status(thm)],[f_5202_3]) ).

fof(f_5203_1,plain,
    ! [V_Pa_2,V_Qa_2] :
      ( hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2))
      | ~ hBOOL(V_Qa_2) ),
    inference(fof_nnf,[status(thm)],[help_c__fimplies__2]) ).

fof(f_5203_2,plain,
    ! [U_20821,U_20820] :
      ( hBOOL(hAPP(hAPP(c_fimplies,U_20821),U_20820))
      | ~ hBOOL(U_20820) ),
    inference(variable_rename,[status(thm)],[f_5203_1]) ).

fof(f_5203_3,plain,
    ! [U_20820,U_20821] :
      ( hBOOL(hAPP(hAPP(c_fimplies,U_20821),U_20820))
      | ~ hBOOL(U_20820) ),
    inference(definitional_conversion,[status(esa)],[f_5203_2]) ).

cnf(f_5203_4,plain,
    ( hBOOL(hAPP(hAPP(c_fimplies,U_20821),U_20820))
    | ~ hBOOL(U_20820) ),
    inference(clausify,[status(thm)],[f_5203_3]) ).

fof(f_5204_1,plain,
    ! [V_Qa_2,V_Pa_2] :
      ( hBOOL(V_Qa_2)
      | ~ hBOOL(V_Pa_2)
      | ~ hBOOL(hAPP(hAPP(c_fimplies,V_Pa_2),V_Qa_2)) ),
    inference(fof_nnf,[status(thm)],[help_c__fimplies__3]) ).

fof(f_5204_2,plain,
    ! [U_20823,U_20822] :
      ( hBOOL(U_20823)
      | ~ hBOOL(U_20822)
      | ~ hBOOL(hAPP(hAPP(c_fimplies,U_20822),U_20823)) ),
    inference(variable_rename,[status(thm)],[f_5204_1]) ).

fof(f_5204_3,plain,
    ! [U_20823] :
      ( ! [U_20822] :
          ( ~ hBOOL(U_20822)
          | ~ hBOOL(hAPP(hAPP(c_fimplies,U_20822),U_20823)) )
      | hBOOL(U_20823) ),
    inference(miniscope,[status(thm)],[f_5204_2]) ).

fof(f_5204_4,plain,
    ! [U_20822,U_20823] :
      ( ~ hBOOL(U_20822)
      | ~ hBOOL(hAPP(hAPP(c_fimplies,U_20822),U_20823))
      | hBOOL(U_20823) ),
    inference(definitional_conversion,[status(esa)],[f_5204_3]) ).

cnf(f_5204_5,plain,
    ( ~ hBOOL(U_20822)
    | ~ hBOOL(hAPP(hAPP(c_fimplies,U_20822),U_20823))
    | hBOOL(U_20823) ),
    inference(clausify,[status(thm)],[f_5204_4]) ).

fof(f_5205_1,plain,
    hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs)),
    inference(fof_nnf,[status(thm)],[conj_0]) ).

fof(f_5205_2,plain,
    hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs)),
    inference(definitional_conversion,[status(esa)],[f_5205_1]) ).

cnf(f_5205_3,plain,
    hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),v_x),v_Procs)),
    inference(clausify,[status(thm)],[f_5205_2]) ).

fof(f_5206_1,plain,
    ! [B_x] :
      ( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,B_x)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),B_x),v_G)) ),
    inference(fof_nnf,[status(thm)],[conj_1]) ).

fof(f_5206_2,plain,
    ! [U_20824] :
      ( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,U_20824)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),U_20824),v_G)) ),
    inference(variable_rename,[status(thm)],[f_5206_1]) ).

fof(f_5206_3,plain,
    ! [U_20824] :
      ( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,U_20824)
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),U_20824),v_G)) ),
    inference(definitional_conversion,[status(esa)],[f_5206_2]) ).

cnf(f_5206_4,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,U_20824)
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(t_a)),U_20824),v_G)) ),
    inference(clausify,[status(thm)],[f_5206_3]) ).

fof(f_5207_1,plain,
    ! [B_x] :
      ( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Com_Ocom_OBODY,B_x)),v_Q(B_x)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs)) ),
    inference(fof_nnf,[status(thm)],[conj_2]) ).

fof(f_5207_2,plain,
    ! [U_20825] :
      ( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(U_20825)),hAPP(c_Com_Ocom_OBODY,U_20825)),v_Q(U_20825)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),U_20825),v_Procs)) ),
    inference(variable_rename,[status(thm)],[f_5207_1]) ).

fof(f_5207_3,plain,
    ! [U_20825] :
      ( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(U_20825)),hAPP(c_Com_Ocom_OBODY,U_20825)),v_Q(U_20825)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),U_20825),v_Procs)) ),
    inference(definitional_conversion,[status(esa)],[f_5207_2]) ).

cnf(f_5207_4,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(U_20825)),hAPP(c_Com_Ocom_OBODY,U_20825)),v_Q(U_20825)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),U_20825),v_Procs)) ),
    inference(clausify,[status(thm)],[f_5207_3]) ).

fof(f_5208_1,plain,
    ! [B_x] :
      ( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(B_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,B_x))),v_Q(B_x)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),v_Procs)) ),
    inference(fof_nnf,[status(thm)],[conj_3]) ).

fof(f_5208_2,plain,
    ! [U_20826] :
      ( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(U_20826)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_20826))),v_Q(U_20826)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),U_20826),v_Procs)) ),
    inference(variable_rename,[status(thm)],[f_5208_1]) ).

fof(f_5208_3,plain,
    ! [U_20826] :
      ( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(U_20826)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_20826))),v_Q(U_20826)))
      | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),U_20826),v_Procs)) ),
    inference(definitional_conversion,[status(esa)],[f_5208_2]) ).

cnf(f_5208_4,plain,
    ( c_Hoare__Mirabelle_Otriple__valid(t_a,v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(U_20826)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,U_20826))),v_Q(U_20826)))
    | ~ hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),U_20826),v_Procs)) ),
    inference(clausify,[status(thm)],[f_5208_3]) ).

fof(f_5209_1,negated_conjecture,
    ~ c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))),
    inference(negate,[status(cth)],[conj_4]) ).

fof(f_5209_2,negated_conjecture,
    ~ c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))),
    inference(definitional_conversion,[status(esa)],[f_5209_1]) ).

cnf(f_5209_3,negated_conjecture,
    ~ c_Hoare__Mirabelle_Otriple__valid(t_a,hAPP(c_Nat_OSuc,v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_P(v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_Q(v_x))),
    inference(clausify,[status(thm)],[f_5209_2]) ).

cnf(f_2127_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2127_4]) ).

cnf(f_2128_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2128_4]) ).

cnf(f_2129_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2129_4]) ).

cnf(f_2134_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2134_4]) ).

cnf(f_2136_4_true,plain,
    $true,
    inference(clause_is_true,[status(thm)],[f_2136_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_Option_Othe(Eq_x_0) = c_Option_Othe(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_7,axiom,
    ( c_member(Eq_x_0) = c_member(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_8,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_9,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_10,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_11,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_12,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_13,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_14,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_15,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_16,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_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_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_19,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_20,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_21,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_22,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_23,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_24,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_25,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_26,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_27,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_28,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_29,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_30,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_31,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_32,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_33,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_34,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_35,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_36,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_37,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_38,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_39,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_40,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_41,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_42,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_43,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_44,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_45,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_46,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_47,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_48,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_49,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_50,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_51,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_52,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_53,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_54,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_55,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_56,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_57,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_58,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_59,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_60,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_61,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_62,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_63,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_64,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_65,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_66,axiom,
    ( c_If(Eq_x_0) = c_If(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_67,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_68,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_69,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_70,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_71,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_72,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_73,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_74,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_75,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_76,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_77,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_78,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_79,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_80,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_81,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_82,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_83,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_84,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_85,axiom,
    ( c_COMBI(Eq_x_0) = c_COMBI(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_86,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_87,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_88,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_89,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_90,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_91,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_92,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_93,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_94,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_95,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_96,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_97,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_98,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_99,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_100,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_101,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_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_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_104,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_105,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_106,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_107,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_108,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_109,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_110,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_111,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_112,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_113,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_114,axiom,
    ( c_Nitpick_Oplus__frac(Eq_x_0,Eq_x_1,Eq_x_2) = c_Nitpick_Oplus__frac(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_115,axiom,
    ( c_Nitpick_Odenom(Eq_x_0) = c_Nitpick_Odenom(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_116,axiom,
    ( c_Nitpick_Onum(Eq_x_0) = c_Nitpick_Onum(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_117,axiom,
    ( c_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_118,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_119,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_120,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_121,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_122,axiom,
    ( c_Nitpick_Ouminus__frac(Eq_x_0,Eq_x_1) = c_Nitpick_Ouminus__frac(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_123,axiom,
    ( 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_124,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_125,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_126,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_127,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_128,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_129,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_130,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_131,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_132,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_133,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_134,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_135,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_136,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_137,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_138,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_139,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_140,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_141,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_142,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_143,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_144,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_145,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_146,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_147,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_148,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_149,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_150,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_151,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_152,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_153,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_154,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_155,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_156,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_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_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_159,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_160,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_161,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_162,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_163,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_164,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_165,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_166,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_167,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_168,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_169,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_170,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_171,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_172,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_173,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_174,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_175,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_176,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_177,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_178,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_179,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_180,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_181,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_182,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_183,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_184,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_185,axiom,
    ( c_Predicate_Opred__comp(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = c_Predicate_Opred__comp(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_186,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_187,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_188,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_189,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_190,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_191,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_192,axiom,
    ( c_Predicate_Oconversep(Eq_x_0,Eq_x_1,Eq_x_2) = c_Predicate_Oconversep(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_193,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_194,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_195,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_196,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_197,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_198,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_199,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_200,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_201,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_202,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_203,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_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_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_207,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_208,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_209,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_210,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_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_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_213,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_214,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_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_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_218,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_219,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_220,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_221,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_222,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_223,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_224,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_225,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_226,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_227,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_228,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_229,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_230,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_231,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_232,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_233,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_234,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_235,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_236,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_237,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_238,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_239,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_240,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_241,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_242,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_243,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_244,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_245,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_246,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_247,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_248,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_249,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_250,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_251,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_252,axiom,
    ( c_New__DSequence_Opos__single(Eq_x_0,Eq_x_1) = c_New__DSequence_Opos__single(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_253,axiom,
    ( c_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_254,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_255,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_256,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_257,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_258,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_259,axiom,
    ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI(Eq_x_0,Eq_x_1) = c_Complete__Lattice_Ocomplete__lattice__class_OINFI(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_260,axiom,
    ( c_HOL_OAll(Eq_x_0) = c_HOL_OAll(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_261,axiom,
    ( c_Set_OBall(Eq_x_0) = c_Set_OBall(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_262,axiom,
    ( c_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_263,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_264,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_265,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_266,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_267,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_268,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_269,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_270,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_271,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_272,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_273,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_274,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_275,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_276,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_277,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_278,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_279,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_280,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_281,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_282,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_283,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_284,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_285,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_286,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_287,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_288,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_289,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_290,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_291,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_292,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_293,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_294,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_295,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_296,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_297,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_298,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_299,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_300,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_301,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_302,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_303,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_304,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_305,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_306,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_307,axiom,
    ( c_List_Otl(Eq_x_0) = c_List_Otl(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_308,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_309,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_310,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_311,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_312,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_313,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_314,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_315,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_316,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_317,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_318,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_319,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_320,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_321,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_322,axiom,
    ( c_List_OtakeWhile(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_OtakeWhile(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_323,axiom,
    ( c_List_Oreturn__list(Eq_x_0) = c_List_Oreturn__list(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_324,axiom,
    ( c_List_Oembed__list(Eq_x_0) = c_List_Oembed__list(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_325,axiom,
    ( c_List_Oremdups(Eq_x_0,Eq_x_1) = c_List_Oremdups(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_326,axiom,
    ( c_List_OdropWhile(Eq_x_0,Eq_x_1,Eq_x_2) = c_List_OdropWhile(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_327,axiom,
    ( c_Enum_On__lists(Eq_x_0,Eq_x_1,Eq_x_2) = c_Enum_On__lists(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_328,axiom,
    ( c_Enum_Osublists(Eq_x_0,Eq_x_1) = c_Enum_Osublists(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,
    ( v_P(Eq_x_0) = v_P(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_330,axiom,
    ( v_Q(Eq_x_0) = v_Q(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_331,axiom,
    ( sK1(Eq_x_0,Eq_x_1) = sK1(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_332,axiom,
    ( sK2(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = 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_333,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_334,axiom,
    ( sK4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_335,axiom,
    ( sK5(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = 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_336,axiom,
    ( sK6(Eq_x_0,Eq_x_1,Eq_x_2) = sK6(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_337,axiom,
    ( sK7(Eq_x_0,Eq_x_1,Eq_x_2) = 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_338,axiom,
    ( sK8(Eq_x_0) = sK8(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_339,axiom,
    ( sK9(Eq_x_0,Eq_x_1) = sK9(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_340,axiom,
    ( sK10(Eq_x_0) = sK10(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_341,axiom,
    ( sK11(Eq_x_0,Eq_x_1) = sK11(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_342,axiom,
    ( sK12(Eq_x_0) = sK12(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_343,axiom,
    ( sK13(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK13(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_344,axiom,
    ( sK14(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK14(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_345,axiom,
    ( sK15(Eq_x_0,Eq_x_1,Eq_x_2) = sK15(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK16(Eq_x_0,Eq_x_1) = sK16(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_347,axiom,
    ( sK17(Eq_x_0) = sK17(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_348,axiom,
    ( sK18(Eq_x_0) = sK18(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_349,axiom,
    ( sK19(Eq_x_0,Eq_x_1) = sK19(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_350,axiom,
    ( sK20(Eq_x_0,Eq_x_1) = sK20(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_351,axiom,
    ( sK21(Eq_x_0) = sK21(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_352,axiom,
    ( sK22(Eq_x_0) = sK22(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_353,axiom,
    ( sK23(Eq_x_0,Eq_x_1) = sK23(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_354,axiom,
    ( sK24(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK24(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_355,axiom,
    ( sK25(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK25(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_356,axiom,
    ( sK26(Eq_x_0) = sK26(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_357,axiom,
    ( sK27(Eq_x_0) = sK27(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_358,axiom,
    ( sK28(Eq_x_0) = sK28(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_359,axiom,
    ( sK29(Eq_x_0) = sK29(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_360,axiom,
    ( sK30(Eq_x_0) = sK30(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_361,axiom,
    ( sK31(Eq_x_0) = sK31(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_362,axiom,
    ( sK32(Eq_x_0) = sK32(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_363,axiom,
    ( sK33(Eq_x_0) = sK33(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_364,axiom,
    ( sK34(Eq_x_0,Eq_x_1) = sK34(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_365,axiom,
    ( sK35(Eq_x_0,Eq_x_1) = sK35(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_366,axiom,
    ( sK36(Eq_x_0,Eq_x_1) = sK36(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_367,axiom,
    ( sK37(Eq_x_0,Eq_x_1) = sK37(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,
    ( sK38(Eq_x_0,Eq_x_1) = sK38(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_369,axiom,
    ( sK39(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK39(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_370,axiom,
    ( sK40(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK40(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_371,axiom,
    ( sK41(Eq_x_0,Eq_x_1) = sK41(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_372,axiom,
    ( sK42(Eq_x_0,Eq_x_1,Eq_x_2) = sK42(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_373,axiom,
    ( sK43(Eq_x_0,Eq_x_1,Eq_x_2) = sK43(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_374,axiom,
    ( sK44(Eq_x_0,Eq_x_1,Eq_x_2) = sK44(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_375,axiom,
    ( sK45(Eq_x_0,Eq_x_1,Eq_x_2) = sK45(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_376,axiom,
    ( sK46(Eq_x_0,Eq_x_1,Eq_x_2) = sK46(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_377,axiom,
    ( sK47(Eq_x_0,Eq_x_1,Eq_x_2) = sK47(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_378,axiom,
    ( sK48(Eq_x_0,Eq_x_1,Eq_x_2) = sK48(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_379,axiom,
    ( sK49(Eq_x_0,Eq_x_1,Eq_x_2) = sK49(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_380,axiom,
    ( sK50(Eq_x_0,Eq_x_1,Eq_x_2) = sK50(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_381,axiom,
    ( sK51(Eq_x_0,Eq_x_1,Eq_x_2) = sK51(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_382,axiom,
    ( sK52(Eq_x_0,Eq_x_1,Eq_x_2) = sK52(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK53(Eq_x_0,Eq_x_1,Eq_x_2) = sK53(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_384,axiom,
    ( sK54(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK54(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_385,axiom,
    ( sK55(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK55(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_386,axiom,
    ( sK56(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK56(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_387,axiom,
    ( sK57(Eq_x_0,Eq_x_1,Eq_x_2) = sK57(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_388,axiom,
    ( sK58(Eq_x_0,Eq_x_1) = sK58(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_389,axiom,
    ( sK59(Eq_x_0,Eq_x_1,Eq_x_2) = sK59(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_390,axiom,
    ( sK60(Eq_x_0,Eq_x_1,Eq_x_2) = sK60(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_391,axiom,
    ( sK61(Eq_x_0,Eq_x_1,Eq_x_2) = sK61(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_392,axiom,
    ( sK62(Eq_x_0,Eq_x_1,Eq_x_2) = sK62(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_393,axiom,
    ( sK63(Eq_x_0,Eq_x_1,Eq_x_2) = sK63(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_394,axiom,
    ( sK64(Eq_x_0,Eq_x_1,Eq_x_2) = sK64(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_395,axiom,
    ( sK65(Eq_x_0,Eq_x_1,Eq_x_2) = sK65(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_396,axiom,
    ( sK66(Eq_x_0,Eq_x_1,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_397,axiom,
    ( sK67(Eq_x_0,Eq_x_1,Eq_x_2) = sK67(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_398,axiom,
    ( sK68(Eq_x_0,Eq_x_1,Eq_x_2) = sK68(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_399,axiom,
    ( sK69(Eq_x_0,Eq_x_1,Eq_x_2) = sK69(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_400,axiom,
    ( sK70(Eq_x_0,Eq_x_1,Eq_x_2) = sK70(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_401,axiom,
    ( sK71(Eq_x_0,Eq_x_1,Eq_x_2) = sK71(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_402,axiom,
    ( sK72(Eq_x_0,Eq_x_1,Eq_x_2) = sK72(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_403,axiom,
    ( sK73(Eq_x_0,Eq_x_1,Eq_x_2) = sK73(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_404,axiom,
    ( sK74(Eq_x_0,Eq_x_1,Eq_x_2) = sK74(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_405,axiom,
    ( sK75(Eq_x_0,Eq_x_1,Eq_x_2) = sK75(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_406,axiom,
    ( sK76(Eq_x_0,Eq_x_1,Eq_x_2) = sK76(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_407,axiom,
    ( sK77(Eq_x_0,Eq_x_1,Eq_x_2) = sK77(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_408,axiom,
    ( sK78(Eq_x_0,Eq_x_1,Eq_x_2) = sK78(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_409,axiom,
    ( sK79(Eq_x_0,Eq_x_1,Eq_x_2) = sK79(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_410,axiom,
    ( sK80(Eq_x_0,Eq_x_1,Eq_x_2) = sK80(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_411,axiom,
    ( sK81(Eq_x_0,Eq_x_1,Eq_x_2) = sK81(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_412,axiom,
    ( sK82(Eq_x_0,Eq_x_1,Eq_x_2) = sK82(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_413,axiom,
    ( sK83(Eq_x_0,Eq_x_1,Eq_x_2) = 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_414,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_415,axiom,
    ( sK85(Eq_x_0,Eq_x_1) = sK85(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_416,axiom,
    ( sK86(Eq_x_0,Eq_x_1,Eq_x_2) = sK86(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_417,axiom,
    ( sK87(Eq_x_0,Eq_x_1,Eq_x_2) = sK87(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_418,axiom,
    ( sK88(Eq_x_0,Eq_x_1,Eq_x_2) = sK88(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_419,axiom,
    ( sK89(Eq_x_0,Eq_x_1,Eq_x_2) = sK89(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_420,axiom,
    ( sK90(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK90(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_421,axiom,
    ( sK91(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK91(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_422,axiom,
    ( sK92(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK92(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_423,axiom,
    ( sK93(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK93(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_424,axiom,
    ( sK94(Eq_x_0,Eq_x_1,Eq_x_2) = sK94(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_425,axiom,
    ( sK95(Eq_x_0,Eq_x_1,Eq_x_2) = sK95(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_426,axiom,
    ( sK96(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK96(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_427,axiom,
    ( sK97(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK97(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_428,axiom,
    ( sK98(Eq_x_0,Eq_x_1,Eq_x_2) = 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_429,axiom,
    ( sK99(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK99(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_430,axiom,
    ( sK100(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK100(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_431,axiom,
    ( sK101(Eq_x_0) = sK101(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_432,axiom,
    ( sK102(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK102(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_433,axiom,
    ( sK103(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK103(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_434,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_435,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_436,axiom,
    ( sK106(Eq_x_0,Eq_x_1) = sK106(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_437,axiom,
    ( sK107(Eq_x_0,Eq_x_1) = sK107(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_438,axiom,
    ( sK108(Eq_x_0,Eq_x_1) = sK108(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_439,axiom,
    ( sK109(Eq_x_0,Eq_x_1) = sK109(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_440,axiom,
    ( sK110(Eq_x_0,Eq_x_1) = sK110(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_441,axiom,
    ( sK111(Eq_x_0,Eq_x_1,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_442,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_443,axiom,
    ( sK113(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK113(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK114(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK114(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK115(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK115(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_446,axiom,
    ( sK116(Eq_x_0,Eq_x_1,Eq_x_2) = sK116(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_447,axiom,
    ( sK117(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK117(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_448,axiom,
    ( sK118(Eq_x_0,Eq_x_1) = sK118(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_449,axiom,
    ( sK119(Eq_x_0,Eq_x_1) = sK119(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_450,axiom,
    ( sK120(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK120(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_451,axiom,
    ( sK121(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK121(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_452,axiom,
    ( sK122(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK122(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_453,axiom,
    ( sK123(Eq_x_0,Eq_x_1) = sK123(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_454,axiom,
    ( sK124(Eq_x_0,Eq_x_1) = sK124(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_455,axiom,
    ( sK125(Eq_x_0,Eq_x_1,Eq_x_2) = sK125(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_456,axiom,
    ( sK126(Eq_x_0,Eq_x_1) = sK126(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_457,axiom,
    ( sK127(Eq_x_0,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_458,axiom,
    ( sK128(Eq_x_0,Eq_x_1) = sK128(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_459,axiom,
    ( sK129(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = 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_460,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_461,axiom,
    ( sK131(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK131(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_462,axiom,
    ( sK132(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = 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_463,axiom,
    ( sK133(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK133(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK134(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK134(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK135(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK135(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK136(Eq_x_0,Eq_x_1,Eq_x_2) = sK136(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK137(Eq_x_0,Eq_x_1) = sK137(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_468,axiom,
    ( sK138(Eq_x_0,Eq_x_1) = sK138(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,
    ( sK139(Eq_x_0,Eq_x_1,Eq_x_2) = sK139(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_470,axiom,
    ( sK140(Eq_x_0,Eq_x_1) = sK140(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_471,axiom,
    ( sK141(Eq_x_0,Eq_x_1) = sK141(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_472,axiom,
    ( sK142(Eq_x_0,Eq_x_1,Eq_x_2) = sK142(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_473,axiom,
    ( sK143(Eq_x_0,Eq_x_1) = sK143(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_474,axiom,
    ( sK144(Eq_x_0,Eq_x_1) = sK144(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_475,axiom,
    ( sK145(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK145(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_476,axiom,
    ( sK146(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK146(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_477,axiom,
    ( sK147(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK147(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_478,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_479,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_480,axiom,
    ( sK150(Eq_x_0) = sK150(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_481,axiom,
    ( sK151(Eq_x_0) = sK151(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_482,axiom,
    ( sK152(Eq_x_0) = sK152(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_483,axiom,
    ( sK153(Eq_x_0,Eq_x_1) = sK153(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_484,axiom,
    ( sK154(Eq_x_0) = sK154(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_485,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_486,axiom,
    ( sK156(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK156(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_487,axiom,
    ( sK157(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7,Eq_x_8) = sK157(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_488,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_489,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_490,axiom,
    ( sK160(Eq_x_0,Eq_x_1) = sK160(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,
    ( sK161(Eq_x_0,Eq_x_1) = sK161(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,
    ( 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_493,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_494,axiom,
    ( sK164(Eq_x_0,Eq_x_1) = sK164(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,
    ( sK165(Eq_x_0,Eq_x_1) = sK165(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_496,axiom,
    ( sK166(Eq_x_0,Eq_x_1) = sK166(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_497,axiom,
    ( sK167(Eq_x_0,Eq_x_1) = sK167(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_498,axiom,
    ( sK168(Eq_x_0,Eq_x_1) = sK168(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_499,axiom,
    ( sK169(Eq_x_0,Eq_x_1) = sK169(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_500,axiom,
    ( sK170(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK170(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_501,axiom,
    ( sK171(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK171(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_502,axiom,
    ( sK172(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK172(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_503,axiom,
    ( sK173(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK173(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_504,axiom,
    ( sK174(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK174(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_505,axiom,
    ( sK175(Eq_x_0,Eq_x_1,Eq_x_2) = sK175(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_506,axiom,
    ( sK176(Eq_x_0,Eq_x_1,Eq_x_2) = sK176(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_507,axiom,
    ( sK177(Eq_x_0,Eq_x_1,Eq_x_2) = sK177(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_508,axiom,
    ( sK178(Eq_x_0,Eq_x_1,Eq_x_2) = sK178(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_509,axiom,
    ( sK179(Eq_x_0,Eq_x_1,Eq_x_2) = sK179(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_510,axiom,
    ( sK180(Eq_x_0,Eq_x_1,Eq_x_2) = sK180(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_511,axiom,
    ( sK181(Eq_x_0,Eq_x_1,Eq_x_2) = sK181(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_512,axiom,
    ( sK182(Eq_x_0,Eq_x_1,Eq_x_2) = sK182(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_513,axiom,
    ( sK183(Eq_x_0,Eq_x_1,Eq_x_2) = sK183(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_514,axiom,
    ( sK184(Eq_x_0,Eq_x_1,Eq_x_2) = sK184(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_515,axiom,
    ( sK185(Eq_x_0,Eq_x_1,Eq_x_2) = sK185(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_516,axiom,
    ( sK186(Eq_x_0,Eq_x_1,Eq_x_2) = sK186(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_517,axiom,
    ( sK187(Eq_x_0,Eq_x_1,Eq_x_2) = sK187(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_518,axiom,
    ( sK188(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK188(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_519,axiom,
    ( sK189(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK189(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,
    ( sK190(Eq_x_0,Eq_x_1,Eq_x_2) = sK190(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_521,axiom,
    ( sK191(Eq_x_0,Eq_x_1,Eq_x_2) = sK191(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_522,axiom,
    ( sK192(Eq_x_0,Eq_x_1,Eq_x_2) = sK192(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_523,axiom,
    ( sK193(Eq_x_0,Eq_x_1,Eq_x_2,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_524,axiom,
    ( sK194(Eq_x_0,Eq_x_1) = sK194(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_525,axiom,
    ( sK195(Eq_x_0,Eq_x_1) = sK195(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_526,axiom,
    ( sK196(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK196(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_527,axiom,
    ( sK197(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK197(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_528,axiom,
    ( sK198(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK198(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,
    ( sK199(Eq_x_0,Eq_x_1,Eq_x_2) = sK199(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_530,axiom,
    ( sK200(Eq_x_0,Eq_x_1,Eq_x_2) = 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_531,axiom,
    ( sK201(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK201(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_532,axiom,
    ( sK202(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK202(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_533,axiom,
    ( sK203(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK203(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_534,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_535,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_536,axiom,
    ( sK206(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK206(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK207(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK207(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK208(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK208(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK209(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK209(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_540,axiom,
    ( sK210(Eq_x_0,Eq_x_1,Eq_x_2) = 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_541,axiom,
    ( sK211(Eq_x_0,Eq_x_1,Eq_x_2) = sK211(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_542,axiom,
    ( sK212(Eq_x_0,Eq_x_1) = sK212(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_543,axiom,
    ( sK213(Eq_x_0,Eq_x_1) = sK213(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_544,axiom,
    ( sK214(Eq_x_0,Eq_x_1) = sK214(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_545,axiom,
    ( sK215(Eq_x_0,Eq_x_1) = sK215(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_546,axiom,
    ( sK216(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK216(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_547,axiom,
    ( sK217(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK217(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_548,axiom,
    ( sK218(Eq_x_0,Eq_x_1,Eq_x_2) = sK218(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_549,axiom,
    ( sK219(Eq_x_0,Eq_x_1,Eq_x_2) = sK219(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_550,axiom,
    ( sK220(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK220(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_551,axiom,
    ( sK221(Eq_x_0,Eq_x_1,Eq_x_2,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_552,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_553,axiom,
    ( sK223(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK223(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_554,axiom,
    ( sK224(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK224(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_555,axiom,
    ( sK225(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK225(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_556,axiom,
    ( sK226(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK226(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_557,axiom,
    ( sK227(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK227(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_558,axiom,
    ( sK228(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK228(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_559,axiom,
    ( sK229(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK229(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK230(Eq_x_0,Eq_x_1) = sK230(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_561,axiom,
    ( sK231(Eq_x_0,Eq_x_1) = sK231(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_562,axiom,
    ( sK232(Eq_x_0,Eq_x_1) = sK232(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_563,axiom,
    ( sK233(Eq_x_0,Eq_x_1) = sK233(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_564,axiom,
    ( sK234(Eq_x_0,Eq_x_1) = sK234(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_565,axiom,
    ( sK235(Eq_x_0,Eq_x_1) = sK235(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_566,axiom,
    ( sK236(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK236(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_567,axiom,
    ( sK237(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK237(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_568,axiom,
    ( sK238(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK238(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_569,axiom,
    ( sK239(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = 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_570,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_571,axiom,
    ( sK241(Eq_x_0,Eq_x_1) = sK241(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_572,axiom,
    ( sK242(Eq_x_0,Eq_x_1) = sK242(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_573,axiom,
    ( sK243(Eq_x_0,Eq_x_1) = sK243(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_574,axiom,
    ( sK244(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK244(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_575,axiom,
    ( sK245(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK245(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_576,axiom,
    ( sK246(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK246(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_577,axiom,
    ( sK247(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK247(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_578,axiom,
    ( sK248(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK248(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_579,axiom,
    ( sK249(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK249(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_580,axiom,
    ( sK250(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK250(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_581,axiom,
    ( sK251(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK251(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_582,axiom,
    ( sK252(Eq_x_0,Eq_x_1,Eq_x_2) = sK252(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_583,axiom,
    ( sK253(Eq_x_0,Eq_x_1,Eq_x_2) = sK253(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_584,axiom,
    ( sK254(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK254(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_585,axiom,
    ( sK255(Eq_x_0,Eq_x_1,Eq_x_2) = sK255(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_586,axiom,
    ( sK256(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK256(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_587,axiom,
    ( sK257(Eq_x_0,Eq_x_1,Eq_x_2) = sK257(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_588,axiom,
    ( sK258(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,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_589,axiom,
    ( sK259(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK259(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_590,axiom,
    ( sK260(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK260(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_591,axiom,
    ( sK261(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK261(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_592,axiom,
    ( sK262(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK262(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_593,axiom,
    ( sK263(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = 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_594,axiom,
    ( sK264(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK264(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_595,axiom,
    ( sK265(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK265(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_596,axiom,
    ( sK266(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK266(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_597,axiom,
    ( sK267(Eq_x_0,Eq_x_1,Eq_x_2) = sK267(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_598,axiom,
    ( sK268(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK268(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,
    ( sK269(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK269(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_600,axiom,
    ( sK270(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK270(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_601,axiom,
    ( sK271(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK271(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_602,axiom,
    ( sK272(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK272(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_603,axiom,
    ( sK273(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,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_604,axiom,
    ( sK274(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK274(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_605,axiom,
    ( sK275(Eq_x_0) = sK275(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_606,axiom,
    ( sK276(Eq_x_0) = sK276(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_607,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_608,axiom,
    ( sK278(Eq_x_0,Eq_x_1) = sK278(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_609,axiom,
    ( sK279(Eq_x_0,Eq_x_1) = sK279(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_610,axiom,
    ( sK280(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK280(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK281(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK281(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_613,axiom,
    ( sK283(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK283(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_614,axiom,
    ( sK284(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK284(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_615,axiom,
    ( sK285(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK285(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_616,axiom,
    ( sK286(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK286(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_617,axiom,
    ( sK287(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK287(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_618,axiom,
    ( sK288(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = 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_619,axiom,
    ( sK289(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK289(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_620,axiom,
    ( sK290(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK290(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_621,axiom,
    ( sK291(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK291(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,
    ( sK292(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK292(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,
    ( sK293(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK293(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_624,axiom,
    ( sK294(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK294(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,
    ( sK295(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK295(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_626,axiom,
    ( sK296(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK296(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_627,axiom,
    ( sK297(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK297(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_628,axiom,
    ( sK298(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK298(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_629,axiom,
    ( sK299(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK299(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_630,axiom,
    ( sK300(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK300(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_631,axiom,
    ( sK301(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) = sK301(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_632,axiom,
    ( sK302(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) = sK302(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_633,axiom,
    ( sK303(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK303(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_634,axiom,
    ( sK304(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK304(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_635,axiom,
    ( sK305(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK305(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_636,axiom,
    ( sK306(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK306(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_637,axiom,
    ( sK307(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK307(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,
    ( sK308(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK308(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_639,axiom,
    ( sK309(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK309(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_640,axiom,
    ( sK310(Eq_x_0,Eq_x_1,Eq_x_2) = sK310(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_641,axiom,
    ( sK311(Eq_x_0) = sK311(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_642,axiom,
    ( sK312(Eq_x_0) = sK312(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_643,axiom,
    ( sK313(Eq_x_0) = sK313(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_644,axiom,
    ( sK314(Eq_x_0) = sK314(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_645,axiom,
    ( sK315(Eq_x_0,Eq_x_1,Eq_x_2) = sK315(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK316(Eq_x_0,Eq_x_1,Eq_x_2) = sK316(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_647,axiom,
    ( sK317(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK317(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_648,axiom,
    ( sK318(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK318(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_649,axiom,
    ( sK319(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK319(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_650,axiom,
    ( sK320(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK320(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_651,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_652,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_653,axiom,
    ( sK323(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK323(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK324(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK324(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_655,axiom,
    ( sK325(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK325(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_656,axiom,
    ( sK326(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK326(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_657,axiom,
    ( sK327(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK327(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_658,axiom,
    ( sK328(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK328(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_659,axiom,
    ( sK329(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK329(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_660,axiom,
    ( sK330(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK330(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_661,axiom,
    ( sK331(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK331(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,
    ( sK332(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK332(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,
    ( sK333(Eq_x_0,Eq_x_1,Eq_x_2) = sK333(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_664,axiom,
    ( sK334(Eq_x_0,Eq_x_1,Eq_x_2) = sK334(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_665,axiom,
    ( sK335(Eq_x_0,Eq_x_1,Eq_x_2) = sK335(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_666,axiom,
    ( sK336(Eq_x_0,Eq_x_1,Eq_x_2) = sK336(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_667,axiom,
    ( sK337(Eq_x_0,Eq_x_1,Eq_x_2) = sK337(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_668,axiom,
    ( sK338(Eq_x_0,Eq_x_1,Eq_x_2,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_669,axiom,
    ( sK339(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK339(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_670,axiom,
    ( sK340(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK340(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,
    ( sK341(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK341(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_672,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_673,axiom,
    ( sK343(Eq_x_0,Eq_x_1) = sK343(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_674,axiom,
    ( sK344(Eq_x_0,Eq_x_1) = sK344(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,
    ( sK345(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK345(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_676,axiom,
    ( sK346(Eq_x_0,Eq_x_1,Eq_x_2) = sK346(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_677,axiom,
    ( sK347(Eq_x_0,Eq_x_1,Eq_x_2) = sK347(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_678,axiom,
    ( sK348(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK348(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_679,axiom,
    ( sK349(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK349(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_680,axiom,
    ( sK350(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK350(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_681,axiom,
    ( sK351(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK351(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_682,axiom,
    ( sK352(Eq_x_0,Eq_x_1,Eq_x_2) = sK352(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_683,axiom,
    ( sK353(Eq_x_0,Eq_x_1,Eq_x_2) = sK353(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_684,axiom,
    ( sK354(Eq_x_0,Eq_x_1,Eq_x_2) = sK354(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_685,axiom,
    ( sK355(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK355(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_686,axiom,
    ( sK356(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK356(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_687,axiom,
    ( sK357(Eq_x_0,Eq_x_1) = sK357(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_688,axiom,
    ( sK358(Eq_x_0) = sK358(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_689,axiom,
    ( sK359(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK359(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_690,axiom,
    ( sK360(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK360(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_691,axiom,
    ( sK361(Eq_x_0,Eq_x_1,Eq_x_2) = 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_692,axiom,
    ( sK362(Eq_x_0,Eq_x_1,Eq_x_2) = sK362(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK363(Eq_x_0,Eq_x_1,Eq_x_2) = sK363(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK364(Eq_x_0,Eq_x_1,Eq_x_2) = sK364(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_695,axiom,
    ( sK365(Eq_x_0,Eq_x_1,Eq_x_2) = sK365(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_696,axiom,
    ( sK366(Eq_x_0,Eq_x_1) = sK366(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_697,axiom,
    ( sK367(Eq_x_0,Eq_x_1,Eq_x_2) = sK367(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_698,axiom,
    ( sK368(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK368(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK369(Eq_x_0) = sK369(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_700,axiom,
    ( sK370(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK370(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_701,axiom,
    ( sK371(Eq_x_0,Eq_x_1,Eq_x_2) = 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_702,axiom,
    ( sK372(Eq_x_0,Eq_x_1) = sK372(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,
    ( sK373(Eq_x_0,Eq_x_1,Eq_x_2) = sK373(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_704,axiom,
    ( sK374(Eq_x_0,Eq_x_1,Eq_x_2) = sK374(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_705,axiom,
    ( sK375(Eq_x_0,Eq_x_1,Eq_x_2) = sK375(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_706,axiom,
    ( sK376(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK376(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_707,axiom,
    ( sK377(Eq_x_0,Eq_x_1,Eq_x_2) = sK377(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_708,axiom,
    ( sK378(Eq_x_0,Eq_x_1,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_709,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_710,axiom,
    ( sK380(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK380(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_711,axiom,
    ( sK381(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK381(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,
    ( sK382(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK382(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,
    ( sK383(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK383(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_714,axiom,
    ( sK384(Eq_x_0,Eq_x_1) = sK384(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_715,axiom,
    ( sK385(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK385(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_716,axiom,
    ( sK386(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK386(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_717,axiom,
    ( sK387(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK387(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_718,axiom,
    ( sK388(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK388(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_719,axiom,
    ( sK389(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK389(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_720,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_721,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_722,axiom,
    ( sK392(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK392(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_723,axiom,
    ( sK393(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK393(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_724,axiom,
    ( sK394(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK394(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_725,axiom,
    ( sK395(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK395(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_726,axiom,
    ( sK396(Eq_x_0,Eq_x_1) = sK396(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_727,axiom,
    ( sK397(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK397(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_728,axiom,
    ( sK398(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK398(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_729,axiom,
    ( sK399(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK399(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_730,axiom,
    ( sK400(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK400(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_731,axiom,
    ( sK401(Eq_x_0,Eq_x_1,Eq_x_2) = sK401(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_732,axiom,
    ( sK402(Eq_x_0,Eq_x_1,Eq_x_2) = sK402(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_733,axiom,
    ( sK403(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK403(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_734,axiom,
    ( sK404(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK404(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_735,axiom,
    ( sK405(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK405(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_736,axiom,
    ( sK406(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK406(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_737,axiom,
    ( sK407(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK407(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_738,axiom,
    ( sK408(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK408(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sK409(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK409(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,
    ( sK410(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK410(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,
    ( sK411(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK411(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_742,axiom,
    ( sK412(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK412(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_743,axiom,
    ( sK413(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK413(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_744,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_745,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_746,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_747,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_748,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_749,axiom,
    ( sK419(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7) = sK419(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_750,axiom,
    ( sK420(Eq_x_0,Eq_x_1,Eq_x_2) = sK420(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_751,axiom,
    ( sK421(Eq_x_0,Eq_x_1,Eq_x_2) = sK421(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_752,axiom,
    ( sK422(Eq_x_0,Eq_x_1,Eq_x_2) = sK422(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_753,axiom,
    ( sK423(Eq_x_0,Eq_x_1) = sK423(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_754,axiom,
    ( sK424(Eq_x_0,Eq_x_1,Eq_x_2) = sK424(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_755,axiom,
    ( sK425(Eq_x_0,Eq_x_1,Eq_x_2) = sK425(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_756,axiom,
    ( sK426(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK426(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_757,axiom,
    ( sK427(Eq_x_0,Eq_x_1,Eq_x_2) = sK427(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_758,axiom,
    ( sK428(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK428(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_759,axiom,
    ( sK429(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK429(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_760,axiom,
    ( sK430(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK430(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_761,axiom,
    ( sK431(Eq_x_0,Eq_x_1,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_762,axiom,
    ( sK432(Eq_x_0,Eq_x_1,Eq_x_2) = sK432(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_763,axiom,
    ( sK433(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK433(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_765,axiom,
    ( sK435(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK435(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_766,axiom,
    ( sK436(Eq_x_0,Eq_x_1,Eq_x_2) = sK436(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK437(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK437(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_768,axiom,
    ( sK438(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK438(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_769,axiom,
    ( sK439(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK439(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_770,axiom,
    ( sK440(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK440(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_771,axiom,
    ( sK441(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK441(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_772,axiom,
    ( sK442(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6) = sK442(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_773,axiom,
    ( sK443(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5) = sK443(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_774,axiom,
    ( sK444(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK444(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_775,axiom,
    ( sK445(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK445(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_776,axiom,
    ( sK447(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK447(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_777,axiom,
    ( sK448(Eq_x_0,Eq_x_1,Eq_x_2) = sK448(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK449(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK449(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_779,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_780,axiom,
    ( sK451(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK451(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_781,axiom,
    ( sK452(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK452(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_782,axiom,
    ( sK453(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK453(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_783,axiom,
    ( sK454(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK454(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_784,axiom,
    ( sK455(Eq_x_0) = sK455(Eq_y_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_785,axiom,
    ( sK456(Eq_x_0,Eq_x_1,Eq_x_2) = sK456(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_786,axiom,
    ( sK457(Eq_x_0,Eq_x_1,Eq_x_2) = sK457(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_787,axiom,
    ( sK458(Eq_x_0,Eq_x_1,Eq_x_2) = 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_788,axiom,
    ( sK459(Eq_x_0,Eq_x_1) = sK459(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_789,axiom,
    ( sK460(Eq_x_0,Eq_x_1) = sK460(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_790,axiom,
    ( sK461(Eq_x_0,Eq_x_1,Eq_x_2) = sK461(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_791,axiom,
    ( sK462(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK462(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_792,axiom,
    ( sK463(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK463(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_793,axiom,
    ( sK464(Eq_x_0,Eq_x_1,Eq_x_2) = sK464(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK465(Eq_x_0,Eq_x_1,Eq_x_2) = sK465(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( sK466(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK466(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,
    ( sK467(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK467(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,
    ( sK468(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK468(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,
    ( sK469(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK469(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,
    ( sK470(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK470(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_800,axiom,
    ( sK471(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK471(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_801,axiom,
    ( sK472(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = 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_802,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_803,axiom,
    ( sK474(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK474(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_804,axiom,
    ( sK475(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK475(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_805,axiom,
    ( sK476(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK476(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_806,axiom,
    ( sK477(Eq_x_0,Eq_x_1) = sK477(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_807,axiom,
    ( sK478(Eq_x_0,Eq_x_1,Eq_x_2) = sK478(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_808,axiom,
    ( sK479(Eq_x_0,Eq_x_1,Eq_x_2) = sK479(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_809,axiom,
    ( sK480(Eq_x_0,Eq_x_1,Eq_x_2) = sK480(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_810,axiom,
    ( sK481(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK481(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,
    ( 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_812,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_813,axiom,
    ( sK484(Eq_x_0,Eq_x_1,Eq_x_2) = sK484(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_814,axiom,
    ( sK485(Eq_x_0,Eq_x_1,Eq_x_2) = sK485(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_815,axiom,
    ( sK486(Eq_x_0,Eq_x_1,Eq_x_2) = sK486(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_816,axiom,
    ( sK487(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK487(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_817,axiom,
    ( sK488(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3) = sK488(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_818,axiom,
    ( sK489(Eq_x_0,Eq_x_1,Eq_x_2) = sK489(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_819,axiom,
    ( sK490(Eq_x_0,Eq_x_1,Eq_x_2) = sK490(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_820,axiom,
    ( sK491(Eq_x_0,Eq_x_1) = sK491(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_821,axiom,
    ( sK492(Eq_x_0,Eq_x_1,Eq_x_2) = 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_822,axiom,
    ( sK493(Eq_x_0,Eq_x_1,Eq_x_2) = sK493(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_823,axiom,
    ( sK494(Eq_x_0,Eq_x_1,Eq_x_2) = sK494(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_824,axiom,
    ( sK495(Eq_x_0,Eq_x_1,Eq_x_2) = sK495(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_825,axiom,
    ( sK496(Eq_x_0,Eq_x_1) = sK496(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_826,axiom,
    ( sK497(Eq_x_0,Eq_x_1) = sK497(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_827,axiom,
    ( sK498(Eq_x_0,Eq_x_1,Eq_x_2) = sK498(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_828,axiom,
    ( sK499(Eq_x_0,Eq_x_1) = sK499(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_829,axiom,
    ( sK500(Eq_x_0,Eq_x_1) = sK500(Eq_y_0,Eq_y_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_830,axiom,
    ( sK501(Eq_x_0,Eq_x_1,Eq_x_2) = sK501(Eq_y_0,Eq_y_1,Eq_y_2)
    | 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,
    ( 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_832,axiom,
    ( sK503(Eq_x_0,Eq_x_1,Eq_x_2) = sK503(Eq_y_0,Eq_y_1,Eq_y_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_functions]) ).

cnf(equality_833,axiom,
    ( sK504(Eq_x_0,Eq_x_1,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_834,axiom,
    ( sK505(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4) = sK505(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_835,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_836,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_837,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_838,axiom,
    ( hBOOL(Eq_y_0)
    | ~ hBOOL(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_839,axiom,
    ( c_Natural_Oevaln(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ c_Natural_Oevaln(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_840,axiom,
    ( 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_841,axiom,
    ( class_Groups_Ozero(Eq_y_0)
    | ~ class_Groups_Ozero(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_842,axiom,
    ( class_Rings_Olinordered__semidom(Eq_y_0)
    | ~ class_Rings_Olinordered__semidom(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_843,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_844,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_845,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_846,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_847,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_848,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_849,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_850,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_851,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_852,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_853,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_854,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_855,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_856,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_857,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_858,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_859,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_860,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_861,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_862,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_863,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_864,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_865,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_866,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_867,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_868,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_869,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_870,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_871,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_872,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_873,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_874,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_875,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_876,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_877,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_878,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_879,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_880,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_881,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_882,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_883,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_884,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_885,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_886,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_887,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_888,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_889,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_890,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_891,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_892,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_893,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_894,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_895,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_896,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_897,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_898,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_899,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_900,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_901,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_902,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_903,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_904,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_905,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_906,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_907,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_908,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_909,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_910,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_911,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_912,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_913,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_914,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_915,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_916,axiom,
    ( class_Rings_Oinverse(Eq_y_0)
    | ~ class_Rings_Oinverse(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_917,axiom,
    ( c_Nitpick_Oless__frac(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Nitpick_Oless__frac(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_918,axiom,
    ( c_Nitpick_Oless__eq__frac(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Nitpick_Oless__eq__frac(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_919,axiom,
    ( 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_920,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_921,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_922,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_923,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_924,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_925,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_926,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_927,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_928,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_929,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_930,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_931,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_932,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_933,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_934,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_935,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_936,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_937,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_938,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_939,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_940,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_941,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_942,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_943,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_944,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_945,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_946,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_947,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_948,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_949,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_950,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_951,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_952,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_953,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_954,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_955,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_956,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_957,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_958,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_959,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_960,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_961,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_962,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_963,axiom,
    ( c_Finite__Set_Ofolding(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ c_Finite__Set_Ofolding(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_964,axiom,
    ( c_Finite__Set_Ofolding__image(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ c_Finite__Set_Ofolding__image(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_965,axiom,
    ( c_Finite__Set_Ofolding__idem(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ c_Finite__Set_Ofolding__idem(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_966,axiom,
    ( c_Finite__Set_Ofun__left__comm(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ c_Finite__Set_Ofun__left__comm(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_967,axiom,
    ( c_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_968,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_969,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_970,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_971,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_972,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_973,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_974,axiom,
    ( sP0(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP0(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_975,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_976,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_977,axiom,
    ( sP3(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP3(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP4(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP4(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP5(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP5(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_980,axiom,
    ( sP6(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP6(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_981,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_982,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_983,axiom,
    ( sP9(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP9(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_984,axiom,
    ( sP10(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP10(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_985,axiom,
    ( sP11(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP11(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_986,axiom,
    ( sP12(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP12(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_987,axiom,
    ( sP13(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP13(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_988,axiom,
    ( sP14(Eq_y_0,Eq_y_1)
    | ~ sP14(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_989,axiom,
    ( sP15(Eq_y_0,Eq_y_1)
    | ~ sP15(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_990,axiom,
    ( sP16(Eq_y_0,Eq_y_1)
    | ~ sP16(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_991,axiom,
    ( sP17(Eq_y_0,Eq_y_1)
    | ~ sP17(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,
    ( sP18(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP18(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_993,axiom,
    ( sP19(Eq_y_0,Eq_y_1)
    | ~ sP19(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,
    ( sP20(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP20(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_995,axiom,
    ( sP21(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP21(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_996,axiom,
    ( sP22(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP22(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP23(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP23(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP24(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP24(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1000,axiom,
    ( sP26(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP26(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP27(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP27(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP28(Eq_y_0)
    | ~ sP28(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1003,axiom,
    ( sP29(Eq_y_0,Eq_y_1)
    | ~ sP29(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1004,axiom,
    ( sP30(Eq_y_0,Eq_y_1)
    | ~ sP30(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1005,axiom,
    ( sP31(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP31(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP32(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP32(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP33(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP33(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1009,axiom,
    ( sP35(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP35(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP36(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP36(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1012,axiom,
    ( sP38(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP38(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1014,axiom,
    ( sP40(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP40(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1016,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_1017,axiom,
    ( sP43(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP43(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1018,axiom,
    ( sP44(Eq_y_0,Eq_y_1)
    | ~ sP44(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1019,axiom,
    ( sP45(Eq_y_0,Eq_y_1)
    | ~ sP45(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1020,axiom,
    ( sP46(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP46(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP47(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP47(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP48(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP48(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP49(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP49(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP50(Eq_y_0,Eq_y_1)
    | ~ sP50(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1025,axiom,
    ( sP51(Eq_y_0,Eq_y_1)
    | ~ sP51(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1026,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_1027,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_1028,axiom,
    ( sP54(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP54(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP55(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP55(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP56(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP56(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP57(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP57(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP58(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP58(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1034,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_1035,axiom,
    ( sP61(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP61(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1037,axiom,
    ( sP63(Eq_y_0,Eq_y_1)
    | ~ sP63(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1038,axiom,
    ( sP64(Eq_y_0,Eq_y_1)
    | ~ sP64(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1039,axiom,
    ( sP65(Eq_y_0,Eq_y_1)
    | ~ sP65(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,
    ( sP66(Eq_y_0,Eq_y_1)
    | ~ sP66(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,
    ( sP67(Eq_y_0,Eq_y_1)
    | ~ sP67(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,
    ( sP68(Eq_y_0,Eq_y_1)
    | ~ sP68(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,
    ( 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_1044,axiom,
    ( sP70(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP70(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1045,axiom,
    ( sP71(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP71(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1046,axiom,
    ( sP72(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP72(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP73(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP73(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1048,axiom,
    ( sP74(Eq_y_0,Eq_y_1)
    | ~ sP74(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,
    ( 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_1050,axiom,
    ( sP76(Eq_y_0,Eq_y_1)
    | ~ sP76(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1051,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_1052,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_1053,axiom,
    ( sP79(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP79(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP80(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP80(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP81(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP81(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1056,axiom,
    ( sP82(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP82(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1057,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_1058,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_1059,axiom,
    ( sP85(Eq_y_0)
    | ~ sP85(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1060,axiom,
    ( sP86(Eq_y_0)
    | ~ sP86(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1061,axiom,
    ( sP87(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP87(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1062,axiom,
    ( sP88(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP88(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP89(Eq_y_0,Eq_y_1)
    | ~ sP89(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1064,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_1065,axiom,
    ( sP91(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP91(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1066,axiom,
    ( sP92(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP92(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1067,axiom,
    ( sP93(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP93(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1068,axiom,
    ( sP94(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP94(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1069,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_1070,axiom,
    ( sP96(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP96(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1071,axiom,
    ( sP97(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP97(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1072,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_1073,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_1074,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_1075,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_1076,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_1077,axiom,
    ( sP103(Eq_y_0,Eq_y_1)
    | ~ sP103(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1078,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_1079,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_1080,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_1081,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_1082,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_1083,axiom,
    ( sP109(Eq_y_0,Eq_y_1)
    | ~ sP109(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1084,axiom,
    ( sP110(Eq_y_0,Eq_y_1)
    | ~ sP110(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1085,axiom,
    ( sP111(Eq_y_0,Eq_y_1)
    | ~ sP111(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1086,axiom,
    ( sP112(Eq_y_0,Eq_y_1)
    | ~ sP112(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1087,axiom,
    ( sP113(Eq_y_0,Eq_y_1)
    | ~ sP113(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1088,axiom,
    ( sP114(Eq_y_0,Eq_y_1)
    | ~ sP114(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1089,axiom,
    ( sP115(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP115(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP116(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP116(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1091,axiom,
    ( sP117(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP117(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1092,axiom,
    ( sP118(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP118(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1093,axiom,
    ( sP119(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP119(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1094,axiom,
    ( sP120(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP120(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1095,axiom,
    ( sP121(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP121(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1097,axiom,
    ( sP123(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP123(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1098,axiom,
    ( sP124(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP124(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP125(Eq_y_0,Eq_y_1)
    | ~ sP125(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1100,axiom,
    ( sP126(Eq_y_0,Eq_y_1)
    | ~ sP126(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1101,axiom,
    ( sP127(Eq_y_0,Eq_y_1)
    | ~ sP127(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1102,axiom,
    ( sP128(Eq_y_0,Eq_y_1)
    | ~ sP128(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1103,axiom,
    ( sP129(Eq_y_0)
    | ~ sP129(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1104,axiom,
    ( sP130(Eq_y_0)
    | ~ sP130(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1105,axiom,
    ( sP131(Eq_y_0,Eq_y_1)
    | ~ sP131(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,
    ( sP132(Eq_y_0,Eq_y_1)
    | ~ sP132(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,
    ( sP133(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP133(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1108,axiom,
    ( sP134(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP134(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1110,axiom,
    ( sP136(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP136(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP137(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP137(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP138(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP138(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP139(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP139(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1115,axiom,
    ( sP141(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP141(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP142(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP142(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP143(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP143(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1118,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_1119,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_1120,axiom,
    ( sP146(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP146(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP147(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP147(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1122,axiom,
    ( sP148(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP148(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1123,axiom,
    ( sP149(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP149(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1124,axiom,
    ( sP150(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP150(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP151(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP151(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1126,axiom,
    ( sP152(Eq_y_0,Eq_y_1)
    | ~ sP152(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,
    ( sP153(Eq_y_0,Eq_y_1)
    | ~ sP153(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1128,axiom,
    ( sP154(Eq_y_0,Eq_y_1)
    | ~ sP154(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1129,axiom,
    ( sP155(Eq_y_0,Eq_y_1)
    | ~ sP155(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,
    ( sP156(Eq_y_0,Eq_y_1)
    | ~ sP156(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,
    ( sP157(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP157(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1132,axiom,
    ( sP158(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP158(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1133,axiom,
    ( 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_1134,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_1135,axiom,
    ( sP161(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP161(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1136,axiom,
    ( sP162(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP162(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1137,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_1138,axiom,
    ( sP164(Eq_y_0,Eq_y_1)
    | ~ sP164(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1139,axiom,
    ( sP165(Eq_y_0,Eq_y_1)
    | ~ sP165(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1140,axiom,
    ( 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_1141,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_1142,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_1143,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_1144,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_1145,axiom,
    ( sP171(Eq_y_0,Eq_y_1)
    | ~ sP171(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1146,axiom,
    ( sP172(Eq_y_0,Eq_y_1)
    | ~ sP172(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1147,axiom,
    ( sP173(Eq_y_0,Eq_y_1)
    | ~ sP173(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,
    ( sP174(Eq_y_0,Eq_y_1)
    | ~ sP174(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,
    ( sP175(Eq_y_0,Eq_y_1)
    | ~ sP175(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,
    ( sP176(Eq_y_0,Eq_y_1)
    | ~ sP176(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1151,axiom,
    ( sP177(Eq_y_0,Eq_y_1)
    | ~ sP177(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1152,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_1153,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_1154,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_1155,axiom,
    ( sP181(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP181(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP182(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP182(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP183(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP183(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP184(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP184(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1159,axiom,
    ( sP185(Eq_y_0,Eq_y_1)
    | ~ sP185(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1160,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_1161,axiom,
    ( sP187(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP187(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP188(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP188(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP189(Eq_y_0,Eq_y_1)
    | ~ sP189(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1164,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_1165,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_1166,axiom,
    ( sP192(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP192(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1167,axiom,
    ( sP193(Eq_y_0,Eq_y_1)
    | ~ sP193(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,
    ( 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_1169,axiom,
    ( sP195(Eq_y_0,Eq_y_1)
    | ~ sP195(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,
    ( sP196(Eq_y_0,Eq_y_1)
    | ~ sP196(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,
    ( 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_1172,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_1173,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_1174,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_1175,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_1176,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_1177,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_1178,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_1179,axiom,
    ( sP205(Eq_y_0,Eq_y_1)
    | ~ sP205(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1180,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_1181,axiom,
    ( sP207(Eq_y_0)
    | ~ sP207(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1182,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_1183,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_1184,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_1185,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_1186,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_1187,axiom,
    ( sP213(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP213(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1188,axiom,
    ( sP214(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP214(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1189,axiom,
    ( sP215(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP215(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1190,axiom,
    ( sP216(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP216(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1191,axiom,
    ( sP217(Eq_y_0,Eq_y_1)
    | ~ sP217(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1192,axiom,
    ( 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_1193,axiom,
    ( sP219(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP219(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1194,axiom,
    ( sP220(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP220(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_1195,axiom,
    ( sP221(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP221(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_1196,axiom,
    ( sP222(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP222(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP223(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP223(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1198,axiom,
    ( sP224(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP224(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_1199,axiom,
    ( sP225(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP225(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP226(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP226(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1201,axiom,
    ( sP227(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP227(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_1202,axiom,
    ( sP228(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP228(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP229(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP229(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP230(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP230(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1205,axiom,
    ( sP231(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP231(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1206,axiom,
    ( sP232(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP232(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1207,axiom,
    ( sP233(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP233(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP234(Eq_y_0,Eq_y_1)
    | ~ sP234(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1209,axiom,
    ( sP235(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP235(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP236(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP236(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP237(Eq_y_0,Eq_y_1)
    | ~ sP237(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1212,axiom,
    ( sP238(Eq_y_0,Eq_y_1)
    | ~ sP238(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1213,axiom,
    ( sP239(Eq_y_0,Eq_y_1)
    | ~ sP239(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1214,axiom,
    ( sP240(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP240(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_1215,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_1216,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_1217,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_1218,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_1219,axiom,
    ( sP245(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP245(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP246(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP246(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP247(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP247(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP248(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP248(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_1223,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_1224,axiom,
    ( sP250(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP250(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP251(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP251(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1226,axiom,
    ( sP252(Eq_y_0,Eq_y_1)
    | ~ sP252(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1227,axiom,
    ( 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_1228,axiom,
    ( sP254(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP254(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP255(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP255(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP256(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP256(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP257(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP257(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1232,axiom,
    ( sP258(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP258(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1233,axiom,
    ( sP259(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP259(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_1234,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_1235,axiom,
    ( sP261(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP261(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1236,axiom,
    ( sP262(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP262(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1237,axiom,
    ( 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_1238,axiom,
    ( sP264(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP264(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP265(Eq_y_0,Eq_y_1)
    | ~ sP265(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,
    ( sP266(Eq_y_0,Eq_y_1)
    | ~ sP266(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,
    ( sP267(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP267(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1242,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_1243,axiom,
    ( sP269(Eq_y_0,Eq_y_1)
    | ~ sP269(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,
    ( sP270(Eq_y_0,Eq_y_1)
    | ~ sP270(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1245,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_1246,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_1247,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_1248,axiom,
    ( sP274(Eq_y_0,Eq_y_1)
    | ~ sP274(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1249,axiom,
    ( sP275(Eq_y_0,Eq_y_1)
    | ~ sP275(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1250,axiom,
    ( sP276(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP276(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP277(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP277(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP278(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP278(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1254,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_1255,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_1256,axiom,
    ( sP282(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP282(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1257,axiom,
    ( sP283(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP283(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1258,axiom,
    ( sP284(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP284(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1259,axiom,
    ( sP285(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP285(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1260,axiom,
    ( sP286(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP286(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP287(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP287(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP288(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP288(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1263,axiom,
    ( 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_1264,axiom,
    ( sP290(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP290(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP291(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP291(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1266,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_1267,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_1268,axiom,
    ( sP294(Eq_y_0,Eq_y_1)
    | ~ sP294(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,
    ( sP295(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP295(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1270,axiom,
    ( sP296(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP296(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1271,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_1272,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_1273,axiom,
    ( sP299(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP299(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1274,axiom,
    ( sP300(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP300(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_1275,axiom,
    ( sP301(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP301(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_1276,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_1277,axiom,
    ( sP303(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP303(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1279,axiom,
    ( sP305(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP305(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_1280,axiom,
    ( sP306(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP306(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1281,axiom,
    ( sP307(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP307(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1282,axiom,
    ( sP308(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP308(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1283,axiom,
    ( sP309(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP309(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1285,axiom,
    ( sP311(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP311(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP312(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP312(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1288,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_1289,axiom,
    ( sP315(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP315(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP316(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP316(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP317(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP317(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1292,axiom,
    ( sP318(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP318(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1293,axiom,
    ( sP319(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP319(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1294,axiom,
    ( sP320(Eq_y_0,Eq_y_1)
    | ~ sP320(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1295,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_1296,axiom,
    ( sP322(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP322(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1297,axiom,
    ( sP323(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP323(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1299,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_1300,axiom,
    ( sP326(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP326(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP327(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP327(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1302,axiom,
    ( sP328(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP328(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1303,axiom,
    ( sP329(Eq_y_0,Eq_y_1)
    | ~ sP329(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1304,axiom,
    ( sP330(Eq_y_0,Eq_y_1)
    | ~ sP330(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1305,axiom,
    ( sP331(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP331(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1307,axiom,
    ( sP333(Eq_y_0,Eq_y_1)
    | ~ sP333(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1308,axiom,
    ( sP334(Eq_y_0,Eq_y_1)
    | ~ sP334(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1309,axiom,
    ( sP335(Eq_y_0,Eq_y_1)
    | ~ sP335(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1310,axiom,
    ( sP336(Eq_y_0,Eq_y_1)
    | ~ sP336(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1311,axiom,
    ( sP337(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP337(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1312,axiom,
    ( sP338(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP338(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1313,axiom,
    ( sP339(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP339(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1314,axiom,
    ( sP340(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP340(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1315,axiom,
    ( sP341(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP341(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1316,axiom,
    ( sP342(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP342(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1318,axiom,
    ( sP344(Eq_y_0,Eq_y_1)
    | ~ sP344(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1319,axiom,
    ( sP345(Eq_y_0,Eq_y_1)
    | ~ sP345(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1320,axiom,
    ( sP346(Eq_y_0,Eq_y_1)
    | ~ sP346(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1321,axiom,
    ( sP347(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP347(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP348(Eq_y_0,Eq_y_1)
    | ~ sP348(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1323,axiom,
    ( sP349(Eq_y_0,Eq_y_1)
    | ~ sP349(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,
    ( 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_1325,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_1326,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_1327,axiom,
    ( sP353(Eq_y_0,Eq_y_1)
    | ~ sP353(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,
    ( 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_1329,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_1330,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_1331,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_1332,axiom,
    ( sP358(Eq_y_0,Eq_y_1)
    | ~ sP358(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1333,axiom,
    ( sP359(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP359(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP360(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP360(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1336,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_1337,axiom,
    ( sP363(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP363(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1338,axiom,
    ( sP364(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP364(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_1339,axiom,
    ( sP365(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP365(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_1340,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_1341,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_1342,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_1343,axiom,
    ( sP369(Eq_y_0,Eq_y_1)
    | ~ sP369(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1344,axiom,
    ( 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_1345,axiom,
    ( sP371(Eq_y_0,Eq_y_1)
    | ~ sP371(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1346,axiom,
    ( sP372(Eq_y_0,Eq_y_1)
    | ~ sP372(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1347,axiom,
    ( sP373(Eq_y_0,Eq_y_1)
    | ~ sP373(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1348,axiom,
    ( sP374(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP374(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_1349,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_1350,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_1351,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_1352,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_1353,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_1354,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_1355,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_1356,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_1357,axiom,
    ( sP383(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP383(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP384(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP384(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP385(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP385(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP386(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP386(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP387(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP387(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1362,axiom,
    ( sP388(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP388(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1363,axiom,
    ( sP389(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP389(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1364,axiom,
    ( sP390(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP390(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1366,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_1367,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_1368,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_1369,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_1370,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_1371,axiom,
    ( sP397(Eq_y_0,Eq_y_1)
    | ~ sP397(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,
    ( 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_1373,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_1374,axiom,
    ( sP400(Eq_y_0,Eq_y_1)
    | ~ sP400(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,
    ( sP401(Eq_y_0,Eq_y_1)
    | ~ sP401(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1376,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_1377,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_1378,axiom,
    ( sP404(Eq_y_0,Eq_y_1)
    | ~ sP404(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,
    ( sP405(Eq_y_0,Eq_y_1)
    | ~ sP405(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,
    ( sP406(Eq_y_0,Eq_y_1)
    | ~ sP406(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,
    ( sP407(Eq_y_0,Eq_y_1)
    | ~ sP407(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,
    ( sP408(Eq_y_0,Eq_y_1)
    | ~ sP408(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,
    ( sP409(Eq_y_0)
    | ~ sP409(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1384,axiom,
    ( sP410(Eq_y_0,Eq_y_1)
    | ~ sP410(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,
    ( sP411(Eq_y_0,Eq_y_1)
    | ~ sP411(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,
    ( 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_1387,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_1388,axiom,
    ( sP414(Eq_y_0,Eq_y_1)
    | ~ sP414(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,
    ( sP415(Eq_y_0,Eq_y_1)
    | ~ sP415(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,
    ( 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_1391,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_1392,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_1393,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_1394,axiom,
    ( sP420(Eq_y_0)
    | ~ sP420(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1395,axiom,
    ( sP421(Eq_y_0,Eq_y_1)
    | ~ sP421(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,
    ( sP422(Eq_y_0,Eq_y_1)
    | ~ sP422(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1397,axiom,
    ( sP423(Eq_y_0,Eq_y_1)
    | ~ sP423(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1398,axiom,
    ( sP424(Eq_y_0)
    | ~ sP424(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1399,axiom,
    ( sP425(Eq_y_0,Eq_y_1)
    | ~ sP425(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1400,axiom,
    ( sP426(Eq_y_0,Eq_y_1)
    | ~ sP426(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1401,axiom,
    ( sP427(Eq_y_0,Eq_y_1)
    | ~ sP427(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1402,axiom,
    ( sP428(Eq_y_0,Eq_y_1)
    | ~ sP428(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1403,axiom,
    ( sP429(Eq_y_0,Eq_y_1)
    | ~ sP429(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1404,axiom,
    ( sP430(Eq_y_0)
    | ~ sP430(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1405,axiom,
    ( sP431(Eq_y_0,Eq_y_1)
    | ~ sP431(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1406,axiom,
    ( sP432(Eq_y_0,Eq_y_1)
    | ~ sP432(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1407,axiom,
    ( sP433(Eq_y_0,Eq_y_1)
    | ~ sP433(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1408,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_1409,axiom,
    ( sP435(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP435(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP436(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP436(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1411,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_1412,axiom,
    ( sP438(Eq_y_0,Eq_y_1)
    | ~ sP438(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1413,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_1414,axiom,
    ( sP440(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP440(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1415,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_1416,axiom,
    ( sP442(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP442(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1418,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_1419,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_1420,axiom,
    ( sP446(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP446(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1422,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_1423,axiom,
    ( sP449(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP449(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1424,axiom,
    ( sP450(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP450(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1426,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_1427,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_1428,axiom,
    ( sP454(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP454(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1430,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_1431,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_1432,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_1433,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_1434,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_1435,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_1436,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_1437,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_1438,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_1439,axiom,
    ( sP465(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP465(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1441,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_1442,axiom,
    ( sP468(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP468(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP469(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP469(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1444,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_1445,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_1446,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_1447,axiom,
    ( sP473(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP473(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1448,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_1449,axiom,
    ( sP475(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP475(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1451,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_1452,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_1453,axiom,
    ( sP479(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP479(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1454,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_1455,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_1456,axiom,
    ( sP482(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP482(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1458,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_1459,axiom,
    ( sP485(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP485(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP486(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP486(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1461,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_1462,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_1463,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_1464,axiom,
    ( sP490(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP490(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1466,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_1467,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_1468,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_1469,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_1470,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_1471,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_1472,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_1473,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_1474,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_1475,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_1476,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_1477,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_1478,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_1479,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_1480,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_1481,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_1482,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_1483,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_1484,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_1485,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_1486,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_1487,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_1488,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_1489,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_1490,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_1491,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_1492,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_1493,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_1494,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_1495,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_1496,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_1497,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_1498,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_1499,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_1500,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_1501,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_1502,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_1503,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_1504,axiom,
    ( sP530(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP530(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP531(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP531(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1506,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_1507,axiom,
    ( sP533(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP533(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP534(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP534(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP535(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP535(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP536(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP536(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP537(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP537(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP538(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP538(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1513,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_1514,axiom,
    ( sP540(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP540(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP541(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP541(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP542(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP542(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP543(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP543(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP544(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP544(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP545(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP545(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP546(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP546(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1522,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_1523,axiom,
    ( sP549(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP549(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP550(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP550(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP551(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP551(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP552(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP552(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP553(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP553(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP554(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP554(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP555(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP555(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP556(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP556(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP557(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP557(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP558(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP558(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP559(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP559(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1534,axiom,
    ( sP560(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP560(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP561(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP561(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1536,axiom,
    ( sP562(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP562(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP563(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP563(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1538,axiom,
    ( sP564(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP564(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1539,axiom,
    ( sP565(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP565(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1540,axiom,
    ( sP566(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP566(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1541,axiom,
    ( sP567(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP567(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1542,axiom,
    ( sP568(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP568(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1543,axiom,
    ( sP569(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP569(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1544,axiom,
    ( sP570(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP570(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1545,axiom,
    ( sP571(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP571(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1546,axiom,
    ( sP572(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP572(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1547,axiom,
    ( sP573(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP573(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1548,axiom,
    ( sP574(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP574(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1549,axiom,
    ( 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_1550,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_1551,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_1552,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_1553,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_1554,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_1555,axiom,
    ( sP581(Eq_y_0,Eq_y_1)
    | ~ sP581(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1556,axiom,
    ( sP582(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP582(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1557,axiom,
    ( sP583(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP583(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1558,axiom,
    ( sP584(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP584(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1559,axiom,
    ( sP585(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP585(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1560,axiom,
    ( sP586(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP586(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1561,axiom,
    ( sP587(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP587(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1562,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_1563,axiom,
    ( sP589(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP589(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1564,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_1565,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_1566,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_1567,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_1568,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_1569,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_1570,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_1571,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_1572,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_1573,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_1574,axiom,
    ( sP600(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP600(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1575,axiom,
    ( sP601(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP601(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1576,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_1577,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_1578,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_1579,axiom,
    ( sP605(Eq_y_0,Eq_y_1)
    | ~ sP605(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1580,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_1581,axiom,
    ( sP607(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP607(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1582,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_1583,axiom,
    ( sP609(Eq_y_0,Eq_y_1)
    | ~ sP609(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1584,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_1585,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_1586,axiom,
    ( sP612(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP612(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP613(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP613(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1588,axiom,
    ( sP614(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP614(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_1589,axiom,
    ( sP615(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP615(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_1590,axiom,
    ( sP616(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP616(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP617(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP617(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP618(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP618(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1593,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_1594,axiom,
    ( sP620(Eq_y_0,Eq_y_1)
    | ~ sP620(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1595,axiom,
    ( sP621(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP621(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP622(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP622(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1597,axiom,
    ( 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_1598,axiom,
    ( sP624(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP624(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1599,axiom,
    ( sP625(Eq_y_0,Eq_y_1)
    | ~ sP625(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1600,axiom,
    ( sP626(Eq_y_0,Eq_y_1)
    | ~ sP626(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1601,axiom,
    ( sP627(Eq_y_0,Eq_y_1)
    | ~ sP627(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1602,axiom,
    ( sP628(Eq_y_0)
    | ~ sP628(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1603,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_1604,axiom,
    ( sP630(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP630(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_1605,axiom,
    ( sP631(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP631(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP632(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP632(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1608,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_1609,axiom,
    ( sP635(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP635(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP636(Eq_y_0,Eq_y_1)
    | ~ sP636(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1611,axiom,
    ( 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_1612,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_1613,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_1614,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_1615,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_1616,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_1617,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_1618,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_1619,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_1620,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_1621,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_1622,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_1623,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_1624,axiom,
    ( sP650(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP650(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1625,axiom,
    ( 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_1626,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_1627,axiom,
    ( sP653(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP653(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1628,axiom,
    ( sP654(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP654(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1629,axiom,
    ( sP655(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP655(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1630,axiom,
    ( sP656(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP656(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1631,axiom,
    ( sP657(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP657(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1632,axiom,
    ( sP658(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP658(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1633,axiom,
    ( sP659(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP659(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_1634,axiom,
    ( sP660(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP660(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_1635,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_1636,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_1637,axiom,
    ( sP663(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP663(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP664(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP664(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1640,axiom,
    ( sP666(Eq_y_0,Eq_y_1)
    | ~ sP666(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1641,axiom,
    ( sP667(Eq_y_0,Eq_y_1)
    | ~ sP667(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1642,axiom,
    ( sP668(Eq_y_0,Eq_y_1)
    | ~ sP668(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1643,axiom,
    ( sP669(Eq_y_0,Eq_y_1)
    | ~ sP669(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1644,axiom,
    ( sP670(Eq_y_0,Eq_y_1)
    | ~ sP670(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1645,axiom,
    ( sP671(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP671(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP672(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP672(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1648,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_1649,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_1650,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_1651,axiom,
    ( sP677(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP677(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP678(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP678(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1653,axiom,
    ( sP679(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP679(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1654,axiom,
    ( sP680(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP680(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP681(Eq_y_0,Eq_y_1)
    | ~ sP681(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1656,axiom,
    ( sP682(Eq_y_0,Eq_y_1)
    | ~ sP682(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1657,axiom,
    ( sP683(Eq_y_0,Eq_y_1)
    | ~ sP683(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1658,axiom,
    ( sP684(Eq_y_0,Eq_y_1)
    | ~ sP684(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,
    ( sP685(Eq_y_0,Eq_y_1)
    | ~ sP685(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,
    ( sP686(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP686(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1661,axiom,
    ( sP687(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP687(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1662,axiom,
    ( 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_1663,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_1664,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_1665,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_1666,axiom,
    ( sP692(Eq_y_0,Eq_y_1)
    | ~ sP692(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1667,axiom,
    ( sP693(Eq_y_0,Eq_y_1)
    | ~ sP693(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1668,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_1669,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_1670,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_1671,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_1672,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_1673,axiom,
    ( sP699(Eq_y_0,Eq_y_1)
    | ~ sP699(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1674,axiom,
    ( sP700(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP700(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1675,axiom,
    ( sP701(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP701(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP702(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP702(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1677,axiom,
    ( sP703(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP703(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP704(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP704(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP705(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP705(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1680,axiom,
    ( sP706(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP706(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_1681,axiom,
    ( sP707(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP707(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1682,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_1683,axiom,
    ( sP709(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP709(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_1684,axiom,
    ( sP710(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP710(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP711(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP711(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1686,axiom,
    ( sP712(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP712(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1687,axiom,
    ( 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_1688,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_1689,axiom,
    ( sP715(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP715(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1690,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_1691,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_1692,axiom,
    ( sP718(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP718(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1693,axiom,
    ( sP719(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP719(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1695,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_1696,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_1697,axiom,
    ( sP723(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP723(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1699,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_1700,axiom,
    ( sP726(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP726(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP727(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP727(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1702,axiom,
    ( sP728(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP728(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1703,axiom,
    ( sP729(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP729(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP730(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP730(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP731(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP731(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP732(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP732(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP733(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP733(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP734(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP734(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1709,axiom,
    ( sP735(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP735(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP736(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP736(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP737(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP737(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1713,axiom,
    ( sP739(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP739(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP740(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP740(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1715,axiom,
    ( sP741(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP741(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP742(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP742(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1717,axiom,
    ( sP743(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP743(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1718,axiom,
    ( sP744(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP744(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1719,axiom,
    ( sP745(Eq_y_0,Eq_y_1)
    | ~ sP745(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,
    ( 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_1721,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_1722,axiom,
    ( sP748(Eq_y_0,Eq_y_1)
    | ~ sP748(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1723,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_1724,axiom,
    ( sP750(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP750(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP751(Eq_y_0,Eq_y_1)
    | ~ sP751(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1726,axiom,
    ( sP752(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP752(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP753(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP753(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP754(Eq_y_0,Eq_y_1)
    | ~ sP754(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1729,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_1730,axiom,
    ( sP756(Eq_y_0)
    | ~ sP756(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1731,axiom,
    ( sP757(Eq_y_0,Eq_y_1)
    | ~ sP757(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1732,axiom,
    ( sP758(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP758(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1733,axiom,
    ( sP759(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP759(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1734,axiom,
    ( 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_1735,axiom,
    ( sP761(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP761(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP762(Eq_y_0,Eq_y_1)
    | ~ sP762(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1737,axiom,
    ( sP763(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP763(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1738,axiom,
    ( sP764(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)
    | ~ sP764(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_1739,axiom,
    ( sP765(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP765(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP766(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP766(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1742,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_1743,axiom,
    ( sP769(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP769(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP770(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP770(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1746,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_1747,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_1748,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_1749,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_1750,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_1751,axiom,
    ( sP777(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP777(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP778(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP778(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1753,axiom,
    ( 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_1754,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_1755,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_1756,axiom,
    ( sP782(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP782(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1757,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_1758,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_1759,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_1760,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_1761,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_1762,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_1763,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_1764,axiom,
    ( sP790(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP790(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_1765,axiom,
    ( sP791(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP791(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_1766,axiom,
    ( sP792(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)
    | ~ sP792(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_1767,axiom,
    ( sP793(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP793(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1768,axiom,
    ( sP794(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP794(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1769,axiom,
    ( sP795(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP795(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP796(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP796(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_1771,axiom,
    ( sP797(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP797(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP798(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP798(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP799(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP799(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1775,axiom,
    ( sP801(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP801(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1777,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_1778,axiom,
    ( sP804(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP804(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1779,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_1780,axiom,
    ( sP806(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP806(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1781,axiom,
    ( sP807(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP807(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_1782,axiom,
    ( sP808(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP808(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP809(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP809(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1785,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_1786,axiom,
    ( sP812(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP812(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1787,axiom,
    ( sP813(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP813(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP814(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP814(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP815(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP815(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP816(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP816(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP817(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP817(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP818(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP818(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP819(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP819(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP820(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP820(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP821(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP821(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1796,axiom,
    ( sP822(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP822(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP823(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP823(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP824(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP824(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1800,axiom,
    ( sP826(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP826(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1802,axiom,
    ( sP828(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP828(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1803,axiom,
    ( sP829(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP829(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1804,axiom,
    ( sP830(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP830(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6)
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1805,axiom,
    ( sP831(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP831(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1806,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_1807,axiom,
    ( sP833(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP833(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP834(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP834(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP835(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP835(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1810,axiom,
    ( sP836(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP836(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1812,axiom,
    ( sP838(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP838(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1813,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_1814,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_1815,axiom,
    ( sP841(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP841(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP842(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP842(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1818,axiom,
    ( sP844(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP844(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1819,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_1820,axiom,
    ( sP846(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP846(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP847(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP847(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1823,axiom,
    ( sP849(Eq_y_0,Eq_y_1)
    | ~ sP849(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1824,axiom,
    ( sP850(Eq_y_0,Eq_y_1)
    | ~ sP850(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1825,axiom,
    ( sP851(Eq_y_0,Eq_y_1)
    | ~ sP851(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1826,axiom,
    ( sP852(Eq_y_0,Eq_y_1)
    | ~ sP852(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1827,axiom,
    ( sP853(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP853(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1828,axiom,
    ( sP854(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP854(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1829,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_1830,axiom,
    ( sP856(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP856(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1831,axiom,
    ( sP857(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP857(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP858(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP858(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP859(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP859(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP860(Eq_y_0,Eq_y_1)
    | ~ sP860(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1835,axiom,
    ( sP861(Eq_y_0,Eq_y_1)
    | ~ sP861(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1836,axiom,
    ( sP862(Eq_y_0,Eq_y_1)
    | ~ sP862(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1837,axiom,
    ( sP863(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP863(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1838,axiom,
    ( sP864(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP864(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1840,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_1841,axiom,
    ( sP867(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP867(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1842,axiom,
    ( sP868(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP868(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP869(Eq_y_0,Eq_y_1)
    | ~ sP869(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1844,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_1845,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_1846,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_1847,axiom,
    ( sP873(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP873(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP874(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP874(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP875(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP875(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP876(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP876(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP877(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP877(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP878(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP878(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP879(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP879(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1854,axiom,
    ( sP880(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP880(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP881(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP881(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP882(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP882(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1857,axiom,
    ( sP883(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP883(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1858,axiom,
    ( sP884(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP884(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1859,axiom,
    ( sP885(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP885(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1860,axiom,
    ( sP886(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP886(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1861,axiom,
    ( sP887(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP887(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1862,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_1863,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_1864,axiom,
    ( sP890(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP890(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1866,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_1867,axiom,
    ( sP893(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP893(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP894(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP894(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP895(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP895(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP896(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP896(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1871,axiom,
    ( sP897(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP897(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1872,axiom,
    ( sP898(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP898(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1873,axiom,
    ( sP899(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP899(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1874,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_1875,axiom,
    ( sP901(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP901(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP902(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP902(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1878,axiom,
    ( sP904(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP904(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_1879,axiom,
    ( sP905(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP905(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP906(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP906(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1881,axiom,
    ( sP907(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP907(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1882,axiom,
    ( sP908(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP908(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1883,axiom,
    ( sP909(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP909(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_1884,axiom,
    ( sP910(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP910(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_1885,axiom,
    ( sP911(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP911(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1886,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_1887,axiom,
    ( sP913(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP913(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP914(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP914(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1889,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_1890,axiom,
    ( sP916(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP916(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1891,axiom,
    ( sP917(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP917(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP918(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP918(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP919(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP919(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP920(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP920(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP921(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP921(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP922(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP922(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP923(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP923(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP924(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP924(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1900,axiom,
    ( sP926(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP926(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1901,axiom,
    ( sP927(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP927(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP928(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP928(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP929(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP929(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_1904,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_1905,axiom,
    ( sP931(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP931(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP932(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP932(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP933(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP933(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1908,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_1909,axiom,
    ( sP935(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP935(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1911,axiom,
    ( sP937(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP937(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1913,axiom,
    ( sP939(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP939(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP940(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP940(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP941(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP941(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1916,axiom,
    ( sP942(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP942(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP943(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP943(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP944(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP944(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1919,axiom,
    ( sP945(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP945(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1920,axiom,
    ( sP946(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP946(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1921,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_1922,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_1923,axiom,
    ( sP949(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP949(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1924,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_1925,axiom,
    ( sP951(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP951(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP952(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP952(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP953(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP953(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP954(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP954(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP955(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP955(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_1930,axiom,
    ( sP956(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)
    | ~ sP956(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_1931,axiom,
    ( sP957(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP957(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_1932,axiom,
    ( sP958(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP958(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_1933,axiom,
    ( sP959(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP959(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1934,axiom,
    ( sP960(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP960(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP961(Eq_y_0,Eq_y_1)
    | ~ sP961(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1936,axiom,
    ( sP962(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP962(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP963(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP963(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP964(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP964(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP965(Eq_y_0,Eq_y_1)
    | ~ sP965(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1940,axiom,
    ( sP966(Eq_y_0,Eq_y_1)
    | ~ sP966(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1941,axiom,
    ( sP967(Eq_y_0,Eq_y_1)
    | ~ sP967(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1942,axiom,
    ( sP968(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP968(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP969(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP969(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1944,axiom,
    ( sP970(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP970(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP971(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP971(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_1946,axiom,
    ( sP972(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP972(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1947,axiom,
    ( 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_1948,axiom,
    ( sP974(Eq_y_0)
    | ~ sP974(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1949,axiom,
    ( sP975(Eq_y_0)
    | ~ sP975(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1950,axiom,
    ( sP976(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP976(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1951,axiom,
    ( sP977(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP977(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP978(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP978(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1953,axiom,
    ( sP979(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP979(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1954,axiom,
    ( sP980(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP980(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1955,axiom,
    ( sP981(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP981(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP982(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP982(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP983(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP983(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP984(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP984(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP985(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP985(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP986(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP986(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP987(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP987(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP988(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP988(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP989(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP989(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP990(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP990(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_1965,axiom,
    ( sP991(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP991(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_1966,axiom,
    ( sP992(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP992(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP993(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP993(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP994(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP994(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP995(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP995(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP996(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP996(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_1971,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_1972,axiom,
    ( sP998(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP998(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP999(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP999(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_1975,axiom,
    ( sP1001(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1001(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1002(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1002(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1977,axiom,
    ( sP1003(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1003(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1004(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1004(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1005(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1005(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1006(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1006(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_1982,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_1983,axiom,
    ( sP1009(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1009(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,
    ( 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_1985,axiom,
    ( sP1011(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1011(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,
    ( sP1012(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1012(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1013(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1013(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1988,axiom,
    ( sP1014(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1014(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1015(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP1015(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,
    ( 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_1991,axiom,
    ( sP1017(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1017(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_1992,axiom,
    ( sP1018(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1018(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1019(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1019(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1020(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP1020(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_1995,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_1996,axiom,
    ( sP1022(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1022(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1023(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1023(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1024(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1024(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_2000,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_2001,axiom,
    ( sP1027(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1027(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2002,axiom,
    ( sP1028(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1028(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2004,axiom,
    ( sP1030(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1030(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2005,axiom,
    ( sP1031(Eq_y_0,Eq_y_1)
    | ~ sP1031(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,
    ( 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_2007,axiom,
    ( sP1033(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1033(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2009,axiom,
    ( sP1035(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1035(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1036(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1036(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_2011,axiom,
    ( sP1037(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1037(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1038(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1038(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2013,axiom,
    ( sP1039(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP1039(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2014,axiom,
    ( sP1040(Eq_y_0,Eq_y_1)
    | ~ sP1040(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2015,axiom,
    ( sP1041(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1041(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1042(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1042(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2017,axiom,
    ( sP1043(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1043(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1044(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1044(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1045(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1045(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1046(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1046(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_2021,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_2022,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_2023,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_2024,axiom,
    ( sP1050(Eq_y_0,Eq_y_1)
    | ~ sP1050(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2025,axiom,
    ( sP1051(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1051(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1052(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1052(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2028,axiom,
    ( sP1054(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1054(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_2029,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_2030,axiom,
    ( sP1056(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1056(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1057(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1057(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1058(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP1058(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5,Eq_x_6,Eq_x_7)
    | Eq_x_7 != Eq_y_7
    | Eq_x_6 != Eq_y_6
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2033,axiom,
    ( sP1059(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP1059(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_2034,axiom,
    ( sP1060(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP1060(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_2035,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_2036,axiom,
    ( sP1062(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1062(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1063(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1063(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1064(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1064(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1065(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1065(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_2040,axiom,
    ( sP1066(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1066(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1067(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1067(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,
    ( 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_2043,axiom,
    ( sP1069(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1069(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1070(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP1070(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_2045,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_2046,axiom,
    ( sP1072(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1072(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1073(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1073(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1074(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1074(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1075(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1075(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2050,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_2051,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_2052,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_2053,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_2054,axiom,
    ( sP1080(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6,Eq_y_7)
    | ~ sP1080(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_2055,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_2056,axiom,
    ( sP1082(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1082(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1083(Eq_y_0,Eq_y_1)
    | ~ sP1083(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2058,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_2059,axiom,
    ( sP1085(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1085(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1086(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1086(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1087(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1087(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_2062,axiom,
    ( sP1088(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP1088(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_2063,axiom,
    ( sP1089(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1089(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2064,axiom,
    ( sP1090(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1090(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2065,axiom,
    ( sP1091(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1091(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1092(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1092(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2068,axiom,
    ( sP1094(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1094(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2069,axiom,
    ( sP1095(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1095(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_2071,axiom,
    ( sP1097(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1097(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1098(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1098(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1099(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1099(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2075,axiom,
    ( sP1101(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1101(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2077,axiom,
    ( sP1103(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1103(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1104(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP1104(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_2079,axiom,
    ( sP1105(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1105(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2080,axiom,
    ( sP1106(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1106(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_2081,axiom,
    ( sP1107(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1107(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2082,axiom,
    ( sP1108(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1108(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2084,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_2085,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_2086,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_2087,axiom,
    ( sP1114(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1114(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1115(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1115(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2089,axiom,
    ( sP1116(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1116(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2090,axiom,
    ( sP1117(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1117(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2091,axiom,
    ( 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_2092,axiom,
    ( sP1119(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1119(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2093,axiom,
    ( sP1120(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1120(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_2095,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_2096,axiom,
    ( sP1123(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1123(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2098,axiom,
    ( sP1125(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1125(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_2100,axiom,
    ( sP1127(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1127(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_2101,axiom,
    ( sP1128(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1128(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2102,axiom,
    ( sP1129(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1129(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2104,axiom,
    ( sP1131(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1131(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,
    ( sP1132(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1132(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,
    ( sP1133(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1133(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1134(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1134(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2108,axiom,
    ( sP1135(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1135(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_2109,axiom,
    ( sP1136(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1136(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_2110,axiom,
    ( sP1137(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1137(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2112,axiom,
    ( sP1139(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1139(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1140(Eq_y_0)
    | ~ sP1140(Eq_x_0)
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2114,axiom,
    ( sP1141(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1141(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2115,axiom,
    ( sP1142(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1142(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2116,axiom,
    ( sP1143(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1143(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1144(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1144(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1145(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1145(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1146(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1146(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1147(Eq_y_0,Eq_y_1)
    | ~ sP1147(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2121,axiom,
    ( sP1148(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1148(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1149(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1149(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1150(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1150(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1151(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1151(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1152(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1152(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2126,axiom,
    ( sP1153(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1153(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2127,axiom,
    ( sP1154(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1154(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1155(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1155(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2130,axiom,
    ( sP1157(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1157(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1158(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1158(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2133,axiom,
    ( sP1160(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1160(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2134,axiom,
    ( sP1161(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1161(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2135,axiom,
    ( sP1162(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1162(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2136,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_2137,axiom,
    ( sP1164(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1164(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_2138,axiom,
    ( sP1165(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1165(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1166(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1166(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1167(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1167(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_2141,axiom,
    ( sP1168(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1168(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1169(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1169(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2143,axiom,
    ( sP1170(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5,Eq_y_6)
    | ~ sP1170(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_2144,axiom,
    ( sP1171(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1171(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2145,axiom,
    ( 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_2146,axiom,
    ( sP1173(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1173(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1174(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1174(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2148,axiom,
    ( sP1175(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1175(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2149,axiom,
    ( 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_2150,axiom,
    ( sP1177(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1177(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_2151,axiom,
    ( sP1178(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1178(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4,Eq_x_5)
    | Eq_x_5 != Eq_y_5
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2152,axiom,
    ( 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_2153,axiom,
    ( sP1180(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1180(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_2154,axiom,
    ( sP1181(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1181(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1182(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1182(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1183(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1183(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2157,axiom,
    ( sP1184(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1184(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1185(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1185(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1186(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1186(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1187(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1187(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1188(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1188(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1189(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1189(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1190(Eq_y_0,Eq_y_1)
    | ~ sP1190(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2164,axiom,
    ( sP1191(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1191(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1192(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1192(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1193(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1193(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_2168,axiom,
    ( sP1195(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1195(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2169,axiom,
    ( sP1196(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1196(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1197(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1197(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_2172,axiom,
    ( sP1199(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1199(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2173,axiom,
    ( sP1200(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1200(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1201(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1201(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2175,axiom,
    ( sP1202(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1202(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1203(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1203(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1204(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1204(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2178,axiom,
    ( sP1205(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4,Eq_y_5)
    | ~ sP1205(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_2179,axiom,
    ( sP1206(Eq_y_0,Eq_y_1)
    | ~ sP1206(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2180,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_2181,axiom,
    ( sP1208(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1208(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1209(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1209(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1210(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1210(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2185,axiom,
    ( sP1212(Eq_y_0,Eq_y_1)
    | ~ sP1212(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2186,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_2187,axiom,
    ( sP1214(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1214(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2188,axiom,
    ( sP1215(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1215(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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_2190,axiom,
    ( sP1217(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1217(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2191,axiom,
    ( sP1218(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1218(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2192,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_2193,axiom,
    ( sP1220(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1220(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1221(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1221(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2195,axiom,
    ( sP1222(Eq_y_0,Eq_y_1)
    | ~ sP1222(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2196,axiom,
    ( sP1223(Eq_y_0,Eq_y_1)
    | ~ sP1223(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2197,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_2198,axiom,
    ( sP1225(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1225(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_2200,axiom,
    ( sP1227(Eq_y_0,Eq_y_1)
    | ~ sP1227(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2201,axiom,
    ( sP1228(Eq_y_0,Eq_y_1)
    | ~ sP1228(Eq_x_0,Eq_x_1)
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2202,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_2203,axiom,
    ( sP1230(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1230(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2204,axiom,
    ( sP1231(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1231(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( 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_2206,axiom,
    ( sP1233(Eq_y_0,Eq_y_1)
    | ~ sP1233(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,
    ( sP1234(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3)
    | ~ sP1234(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3)
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1235(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1235(Eq_x_0,Eq_x_1,Eq_x_2)
    | 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,
    ( sP1236(Eq_y_0,Eq_y_1,Eq_y_2)
    | ~ sP1236(Eq_x_0,Eq_x_1,Eq_x_2)
    | Eq_x_2 != Eq_y_2
    | Eq_x_1 != Eq_y_1
    | Eq_x_0 != Eq_y_0 ),
    theory(equality,[substitution_predicates]) ).

cnf(equality_2210,axiom,
    ( sP1237(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1237(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( sP1238(Eq_y_0,Eq_y_1,Eq_y_2,Eq_y_3,Eq_y_4)
    | ~ sP1238(Eq_x_0,Eq_x_1,Eq_x_2,Eq_x_3,Eq_x_4)
    | Eq_x_4 != Eq_y_4
    | Eq_x_3 != Eq_y_3
    | 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,
    ( 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(sat_proved,plain,
    $false,
    inference(cadical,[status(thm)],[]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02  % Problem  : SWW334+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.03  This is a FOF_CAX_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
% 0.10/0.36  % Computer : n007.cluster.edu
% 0.10/0.36  % Model    : x86_64 x86_64
% 0.10/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36  % Memory   : 8046.5625MB
% 0.10/0.36  % OS       : Linux 6.8.0-71-generic
% 0.03/0.36  % CPULimit : 300
% 0.03/0.36  % WCLimit  : 300
% 0.03/0.36  % DateTime : Sun Sep 20 05:20:34 UTC 2026
% 0.03/0.36  % CPUTime  : 
% 59.76/60.12  % SZS status Theorem for theBenchmark
% 59.76/60.12  % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------